LMFDB - Embedded newform 637.2.bl.b.53.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.20
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.b.625.20

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12577 + 0.767535i) q^{2} +(-0.0507932 - 0.0471292i) q^{3} +(-0.0524406 - 0.133616i) q^{4} +(0.822051 - 0.253569i) q^{5} +(-0.0210080 - 0.0920421i) q^{6} +(-2.32385 + 1.26480i) q^{7} +(0.649898 - 2.84739i) q^{8} +(-0.223831 - 2.98682i) q^{9} +O(q^{10})$	\(q+(1.12577 + 0.767535i) q^{2} +(-0.0507932 - 0.0471292i) q^{3} +(-0.0524406 - 0.133616i) q^{4} +(0.822051 - 0.253569i) q^{5} +(-0.0210080 - 0.0920421i) q^{6} +(-2.32385 + 1.26480i) q^{7} +(0.649898 - 2.84739i) q^{8} +(-0.223831 - 2.98682i) q^{9} +(1.12006 + 0.345493i) q^{10} +(0.329926 - 4.40256i) q^{11} +(-0.00363361 + 0.00925829i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(-3.58689 - 0.359769i) q^{14} +(-0.0537052 - 0.0258630i) q^{15} +(2.70666 - 2.51141i) q^{16} +(7.62761 - 1.14968i) q^{17} +(2.04051 - 3.53427i) q^{18} +(-0.00360290 - 0.00624041i) q^{19} +(-0.0769898 - 0.0965422i) q^{20} +(0.177645 + 0.0452781i) q^{21} +(3.75054 - 4.70302i) q^{22} +(3.66154 + 0.551889i) q^{23} +(-0.167206 + 0.113999i) q^{24} +(-3.51972 + 2.39971i) q^{25} +(-1.34730 - 0.203073i) q^{26} +(-0.259003 + 0.324779i) q^{27} +(0.290862 + 0.244178i) q^{28} +(-3.01613 - 3.78211i) q^{29} +(-0.0406087 - 0.0703364i) q^{30} +(-1.38027 + 2.39069i) q^{31} +(-0.801319 + 0.120779i) q^{32} +(-0.224247 + 0.208071i) q^{33} +(9.46933 + 4.56019i) q^{34} +(-1.58961 + 1.62899i) q^{35} +(-0.387351 + 0.186538i) q^{36} +(-2.04066 + 5.19953i) q^{37} +(0.000733704 - 0.00979060i) q^{38} +(0.0662117 + 0.0204236i) q^{39} +(-0.187761 - 2.50549i) q^{40} +(2.13558 - 9.35658i) q^{41} +(0.165234 + 0.187321i) q^{42} +(0.997409 + 4.36993i) q^{43} +(-0.605555 + 0.186789i) q^{44} +(-0.941368 - 2.39857i) q^{45} +(3.69845 + 3.43166i) q^{46} +(7.00132 + 4.77342i) q^{47} -0.255841 q^{48} +(3.80057 - 5.87841i) q^{49} -5.80425 q^{50} +(-0.441615 - 0.301088i) q^{51} +(0.105221 + 0.0976311i) q^{52} +(0.126003 + 0.321051i) q^{53} +(-0.540856 + 0.166832i) q^{54} +(-0.845137 - 3.70279i) q^{55} +(2.09111 + 7.43890i) q^{56} +(-0.000111103 + 0.000486772i) q^{57} +(-0.492560 - 6.57276i) q^{58} +(-2.64773 - 0.816715i) q^{59} +(-0.000639397 + 0.00853216i) q^{60} +(2.59051 - 6.60050i) q^{61} +(-3.38880 + 1.63196i) q^{62} +(4.29788 + 6.65783i) q^{63} +(-7.64813 - 3.68315i) q^{64} +(-0.630623 + 0.585133i) q^{65} +(-0.412152 + 0.0621219i) q^{66} +(-8.07221 + 13.9815i) q^{67} +(-0.553612 - 0.958884i) q^{68} +(-0.159972 - 0.200598i) q^{69} +(-3.03984 + 0.613777i) q^{70} +(7.71283 - 9.67159i) q^{71} +(-8.65012 - 1.30380i) q^{72} +(-5.85753 + 3.99360i) q^{73} +(-6.28813 + 4.28718i) q^{74} +(0.291874 + 0.0439930i) q^{75} +(-0.000644883 + 0.000808657i) q^{76} +(4.80165 + 10.6482i) q^{77} +(0.0588631 + 0.0738120i) q^{78} +(8.47799 + 14.6843i) q^{79} +(1.58820 - 2.75084i) q^{80} +(-8.85677 + 1.33494i) q^{81} +(9.58567 - 8.89420i) q^{82} +(-4.51922 - 2.17634i) q^{83} +(-0.00326590 - 0.0261107i) q^{84} +(5.97877 - 2.87922i) q^{85} +(-2.23123 + 5.68507i) q^{86} +(-0.0250488 + 0.334253i) q^{87} +(-12.3214 - 3.80064i) q^{88} +(-0.0121990 - 0.162784i) q^{89} +(0.781222 - 3.42276i) q^{90} +(1.54494 - 2.14783i) q^{91} +(-0.118272 - 0.518183i) q^{92} +(0.182780 - 0.0563801i) q^{93} +(4.21809 + 10.7475i) q^{94} +(-0.00454415 - 0.00421635i) q^{95} +(0.0463938 + 0.0316308i) q^{96} +12.1250 q^{97} +(8.79044 - 3.70065i) q^{98} -13.2235 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.12577	+	0.767535i	0.796038	+	0.542729i	0.891669	−	0.452688i	$-0.149535\pi$
$2$	1.12577	+	0.767535i	0.796038	+	0.542729i	−0.0956317	+	0.995417i	$0.530487\pi$
$3$	−0.0507932	−	0.0471292i	−0.0293255	−	0.0272101i	0.665374	−	0.746510i	$-0.268272\pi$
$3$	−0.0507932	−	0.0471292i	−0.0293255	−	0.0272101i	−0.694699	+	0.719300i	$0.744463\pi$
$4$	−0.0524406	−	0.133616i	−0.0262203	−	0.0668082i
$5$	0.822051	−	0.253569i	0.367633	−	0.113400i	−0.105434	−	0.994426i	$-0.533623\pi$
$5$	0.822051	−	0.253569i	0.367633	−	0.113400i	0.473067	+	0.881027i	$0.343147\pi$
$6$	−0.0210080	−	0.0920421i	−0.00857649	−	0.0375760i
$7$	−2.32385	+	1.26480i	−0.878333	+	0.478049i
$7$	−2.32385	+	1.26480i	−0.878333	+	0.478049i
$8$	0.649898	−	2.84739i	0.229774	−	1.00670i
$9$	−0.223831	−	2.98682i	−0.0746105	−	0.995608i
$10$	1.12006	+	0.345493i	0.354195	+	0.109255i
$11$	0.329926	−	4.40256i	0.0994764	−	1.32742i	−0.694509	−	0.719484i	$-0.744378\pi$
$11$	0.329926	−	4.40256i	0.0994764	−	1.32742i	0.793985	−	0.607937i	$-0.208003\pi$
$12$	−0.00363361	+	0.00925829i	−0.00104893	+	0.00267264i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$14$	−3.58689	−	0.359769i	−0.958637	−	0.0961522i
$15$	−0.0537052	−	0.0258630i	−0.0138666	−	0.00667781i
$16$	2.70666	−	2.51141i	0.676665	−	0.627854i
$17$	7.62761	−	1.14968i	1.84997	−	0.278838i	0.872297	−	0.488977i	$-0.162630\pi$
$17$	7.62761	−	1.14968i	1.84997	−	0.278838i	0.977672	+	0.210139i	$0.0673917\pi$
$18$	2.04051	−	3.53427i	0.480953	−	0.833035i
$19$	−0.00360290	−	0.00624041i	−0.000826562	−	0.00143165i	0.865612	−	0.500716i	$-0.166930\pi$
$19$	−0.00360290	−	0.00624041i	−0.000826562	−	0.00143165i	−0.866438	+	0.499284i	$0.833596\pi$
$20$	−0.0769898	−	0.0965422i	−0.0172155	−	0.0215875i
$21$	0.177645	+	0.0452781i	0.0387653	+	0.00988050i
$22$	3.75054	−	4.70302i	0.799617	−	1.00269i
$23$	3.66154	+	0.551889i	0.763485	+	0.115077i	0.519230	−	0.854634i	$-0.326219\pi$
$23$	3.66154	+	0.551889i	0.763485	+	0.115077i	0.244254	+	0.969711i	$0.421457\pi$
$24$	−0.167206	+	0.113999i	−0.0341307	+	0.0232699i
$25$	−3.51972	+	2.39971i	−0.703945	+	0.479941i
$26$	−1.34730	−	0.203073i	−0.264228	−	0.0398259i
$27$	−0.259003	+	0.324779i	−0.0498451	+	0.0625037i
$28$	0.290862	+	0.244178i	0.0549677	+	0.0461453i
$29$	−3.01613	−	3.78211i	−0.560081	−	0.702320i	0.418492	−	0.908221i	$-0.362559\pi$
$29$	−3.01613	−	3.78211i	−0.560081	−	0.702320i	−0.978573	+	0.205901i	$0.933988\pi$
$30$	−0.0406087	−	0.0703364i	−0.00741410	−	0.0128416i
$31$	−1.38027	+	2.39069i	−0.247903	+	0.429381i	−0.962944	−	0.269702i	$-0.913075\pi$
$31$	−1.38027	+	2.39069i	−0.247903	+	0.429381i	0.715041	+	0.699083i	$0.246408\pi$
$32$	−0.801319	+	0.120779i	−0.141654	+	0.0213510i
$33$	−0.224247	+	0.208071i	−0.0390364	+	0.0362205i
$34$	9.46933	+	4.56019i	1.62398	+	0.782066i
$35$	−1.58961	+	1.62899i	−0.268693	+	0.275349i
$36$	−0.387351	+	0.186538i	−0.0645585	+	0.0310897i
$37$	−2.04066	+	5.19953i	−0.335483	+	0.854797i	0.659214	+	0.751955i	$0.270889\pi$
$37$	−2.04066	+	5.19953i	−0.335483	+	0.854797i	−0.994698	+	0.102842i	$0.967206\pi$
$38$	0.000733704	−	0.00979060i	0.000119022	−	0.00158824i
$39$	0.0662117	+	0.0204236i	0.0106024	+	0.00327040i
$40$	−0.187761	−	2.50549i	−0.0296876	−	0.396153i
$41$	2.13558	−	9.35658i	0.333521	−	1.46125i	−0.478739	−	0.877957i	$-0.658906\pi$
$41$	2.13558	−	9.35658i	0.333521	−	1.46125i	0.812260	−	0.583295i	$-0.198237\pi$
$42$	0.165234	+	0.187321i	0.0254962	+	0.0289043i
$43$	0.997409	+	4.36993i	0.152103	+	0.666409i	0.992272	+	0.124083i	$0.0395989\pi$
$43$	0.997409	+	4.36993i	0.152103	+	0.666409i	−0.840168	+	0.542326i	$0.817544\pi$
$44$	−0.605555	+	0.186789i	−0.0912909	+	0.0281595i
$45$	−0.941368	−	2.39857i	−0.140331	−	0.357557i
$46$	3.69845	+	3.43166i	0.545307	+	0.505971i
$47$	7.00132	+	4.77342i	1.02125	+	0.696275i	0.953489	−	0.301427i	$-0.0974630\pi$
$47$	7.00132	+	4.77342i	1.02125	+	0.696275i	0.0677580	+	0.997702i	$0.478415\pi$
$48$	−0.255841			−0.0369275
$49$	3.80057	−	5.87841i	0.542938	−	0.839772i
$50$	−5.80425			−0.820844
$51$	−0.441615	−	0.301088i	−0.0618384	−	0.0421607i
$52$	0.105221	+	0.0976311i	0.0145916	+	0.0135390i
$53$	0.126003	+	0.321051i	0.0173079	+	0.0440997i	0.939266	−	0.343189i	$-0.111507\pi$
$53$	0.126003	+	0.321051i	0.0173079	+	0.0440997i	−0.921959	+	0.387288i	$0.873412\pi$
$54$	−0.540856	+	0.166832i	−0.0736011	+	0.0227029i
$55$	−0.845137	−	3.70279i	−0.113958	−	0.499284i
$56$	2.09111	+	7.43890i	0.279436	+	0.994065i
$57$	−0.000111103	0	0.000486772i	−1.47159e−5	0	6.44746e-5i
$58$	−0.492560	−	6.57276i	−0.0646763	−	0.863045i
$59$	−2.64773	−	0.816715i	−0.344705	−	0.106327i	0.117569	−	0.993065i	$-0.462490\pi$
$59$	−2.64773	−	0.816715i	−0.344705	−	0.106327i	−0.462273	+	0.886737i	$0.652966\pi$
$60$	−0.000639397		0.00853216i	−8.25458e−5		0.00110150i
$61$	2.59051	−	6.60050i	0.331680	−	0.845108i	−0.663602	−	0.748086i	$-0.730973\pi$
$61$	2.59051	−	6.60050i	0.331680	−	0.845108i	0.995282	−	0.0970218i	$-0.0309317\pi$
$62$	−3.38880	+	1.63196i	−0.430378	+	0.207259i
$63$	4.29788	+	6.65783i	0.541482	+	0.838808i
$64$	−7.64813	−	3.68315i	−0.956016	−	0.460393i
$65$	−0.630623	+	0.585133i	−0.0782192	+	0.0725768i
$66$	−0.412152	+	0.0621219i	−0.0507324	+	0.00764668i
$67$	−8.07221	+	13.9815i	−0.986178	+	1.70811i	−0.349596	+	0.936900i	$0.613681\pi$
$67$	−8.07221	+	13.9815i	−0.986178	+	1.70811i	−0.636581	+	0.771210i	$0.719652\pi$
$68$	−0.553612	−	0.958884i	−0.0671353	−	0.116282i
$69$	−0.159972	−	0.200598i	−0.0192583	−	0.0241492i
$70$	−3.03984	+	0.613777i	−0.363330	+	0.0733604i
$71$	7.71283	−	9.67159i	0.915345	−	1.14781i	−0.0732659	−	0.997312i	$-0.523342\pi$
$71$	7.71283	−	9.67159i	0.915345	−	1.14781i	0.988611	−	0.150494i	$-0.0480864\pi$
$72$	−8.65012	−	1.30380i	−1.01943	−	0.153654i
$73$	−5.85753	+	3.99360i	−0.685572	+	0.467415i	−0.855339	−	0.518069i	$-0.826651\pi$
$73$	−5.85753	+	3.99360i	−0.685572	+	0.467415i	0.169767	+	0.985484i	$0.445699\pi$
$74$	−6.28813	+	4.28718i	−0.730981	+	0.498374i
$75$	0.291874	+	0.0439930i	0.0337028	+	0.00507987i
$76$	−0.000644883	0	0.000808657i	−7.39731e−5	0	9.27593e-5i
$77$	4.80165	+	10.6482i	0.547199	+	1.21347i
$78$	0.0588631	+	0.0738120i	0.00666494	+	0.00835757i
$79$	8.47799	+	14.6843i	0.953848	+	1.65211i	0.736982	+	0.675912i	$0.236250\pi$
$79$	8.47799	+	14.6843i	0.953848	+	1.65211i	0.216866	+	0.976201i	$0.430417\pi$
$80$	1.58820	−	2.75084i	0.177566	−	0.307553i
$81$	−8.85677	+	1.33494i	−0.984086	+	0.148327i
$82$	9.58567	−	8.89420i	1.05856	−	0.982200i
$83$	−4.51922	−	2.17634i	−0.496049	−	0.238885i	0.169095	−	0.985600i	$-0.445916\pi$
$83$	−4.51922	−	2.17634i	−0.496049	−	0.238885i	−0.665144	+	0.746715i	$0.731630\pi$
$84$	−0.00326590	−	0.0261107i	−0.000356339	−	0.00284891i
$85$	5.97877	−	2.87922i	0.648488	−	0.312296i
$86$	−2.23123	+	5.68507i	−0.240599	+	0.613037i
$87$	−0.0250488	+	0.334253i	−0.00268552	+	0.0358357i
$88$	−12.3214	−	3.80064i	−1.31346	−	0.405150i
$89$	−0.0121990	−	0.162784i	−0.00129309	−	0.0172551i	0.996520	−	0.0833549i	$-0.0265635\pi$
$89$	−0.0121990	−	0.162784i	−0.00129309	−	0.0172551i	−0.997813	+	0.0660997i	$0.978944\pi$
$90$	0.781222	−	3.42276i	0.0823481	−	0.360790i
$91$	1.54494	−	2.14783i	0.161954	−	0.225153i
$92$	−0.118272	−	0.518183i	−0.0123307	−	0.0540244i
$93$	0.182780	−	0.0563801i	0.0189534	−	0.00584634i
$94$	4.21809	+	10.7475i	0.435063	+	1.10852i
$95$	−0.00454415	−	0.00421635i	−0.000466219	−	0.000432588i
$96$	0.0463938	+	0.0316308i	0.00473505	+	0.00322830i
$97$	12.1250			1.23111			0.615555	−	0.788094i	$-0.288932\pi$
$97$	12.1250			1.23111			0.615555	+	0.788094i	$0.288932\pi$
$98$	8.79044	−	3.70065i	0.887968	−	0.373822i
$99$	−13.2235			−1.32901
$100$	0.505216	+	0.344451i	0.0505216	+	0.0344451i
$101$	11.0219	+	10.2268i	1.09672	+	1.01761i	0.999751	+	0.0223188i	$0.00710490\pi$
$101$	11.0219	+	10.2268i	1.09672	+	1.01761i	0.0969679	+	0.995288i	$0.469086\pi$
$102$	−0.266060	−	0.677909i	−0.0263438	−	0.0671230i
$103$	−3.75423	+	1.15803i	−0.369915	+	0.114104i	−0.474139	−	0.880450i	$-0.657240\pi$
$103$	−3.75423	+	1.15803i	−0.369915	+	0.114104i	0.104224	+	0.994554i	$0.466764\pi$
$104$	0.649898	+	2.84739i	0.0637277	+	0.279209i
$105$	0.157514	−	0.00782435i	0.0153718	−	0.000763578i
$106$	−0.104568	+	0.458140i	−0.0101565	+	0.0444985i
$107$	0.371305	+	4.95472i	0.0358954	+	0.478991i	0.985965	+	0.166953i	$0.0533927\pi$
$107$	0.371305	+	4.95472i	0.0358954	+	0.478991i	−0.950069	+	0.312038i	$0.898988\pi$
$108$	0.0569780	+	0.0175754i	0.00548271	+	0.00169119i
$109$	0.528408	−	7.05112i	0.0506123	−	0.675375i	−0.912981	−	0.408002i	$-0.866226\pi$
$109$	0.528408	−	7.05112i	0.0506123	−	0.675375i	0.963593	−	0.267372i	$-0.0861554\pi$
$110$	1.89059	−	4.81715i	0.180261	−	0.459297i
$111$	0.348702	−	0.167926i	0.0330973	−	0.0159388i
$112$	−3.11344	+	9.25954i	−0.294193	+	0.874944i
$113$	5.14252	+	2.47651i	0.483768	+	0.232970i	0.659839	−	0.751407i	$-0.270625\pi$
$113$	5.14252	+	2.47651i	0.483768	+	0.232970i	−0.176071	+	0.984377i	$0.556339\pi$
$114$	−0.000498691	0	0.000462717i	−4.67067e−5	0	4.33374e-5i
$115$	3.14992	−	0.474774i	0.293731	−	0.0442729i
$116$	−0.347184	+	0.601340i	−0.0322352	+	0.0558330i
$117$	1.49760	+	2.59392i	0.138453	+	0.239808i
$118$	−2.35386	−	2.95165i	−0.216691	−	0.271722i
$119$	−16.2713	+	12.3191i	−1.49159	+	1.12929i
$120$	−0.108545	+	0.136111i	−0.00990876	+	0.0124252i
$121$	−8.39652	−	1.26557i	−0.763320	−	0.115052i
$122$	7.98242	−	5.44232i	0.722695	−	0.492725i
$123$	−0.549442	+	0.374603i	−0.0495415	+	0.0337768i
$124$	0.391818	+	0.0590570i	0.0351863	+	0.00530348i
$125$	−4.96675	+	6.22811i	−0.444240	+	0.557059i
$126$	−0.271706	+	10.7939i	−0.0242055	+	0.961601i
$127$	−4.62753	−	5.80274i	−0.410627	−	0.514910i	0.532913	−	0.846170i	$-0.321097\pi$
$127$	−4.62753	−	5.80274i	−0.410627	−	0.514910i	−0.943539	+	0.331261i	$0.892526\pi$
$128$	−4.97270	−	8.61297i	−0.439529	−	0.761286i
$129$	0.155290	−	0.268970i	0.0136725	−	0.0236815i
$130$	−1.15904	+	0.174698i	−0.101655	+	0.0153220i
$131$	−11.0526	+	10.2553i	−0.965667	+	0.896008i	−0.994622	−	0.103573i	$-0.966973\pi$
$131$	−11.0526	+	10.2553i	−0.965667	+	0.896008i	0.0289551	+	0.999581i	$0.490782\pi$
$132$	0.0395613	+	0.0190517i	0.00344337	+	0.00165824i
$133$	0.0162655	+	0.00994484i	0.00141039	+	0.000862327i
$134$	−19.8187	+	9.54419i	−1.71208	+	0.824492i
$135$	−0.130559	+	0.332660i	−0.0112368	+	0.0286308i
$136$	1.68359	−	22.4660i	0.144367	−	1.92644i
$137$	−12.0845	−	3.72757i	−1.03245	−	0.318468i	−0.268181	−	0.963368i	$-0.586423\pi$
$137$	−12.0845	−	3.72757i	−1.03245	−	0.318468i	−0.764267	+	0.644900i	$0.776899\pi$
$138$	−0.0261247	−	0.348610i	−0.00222388	−	0.0296757i
$139$	0.935714	−	4.09963i	0.0793663	−	0.347726i	−0.919617	−	0.392817i	$-0.871501\pi$
$139$	0.935714	−	4.09963i	0.0793663	−	0.347726i	0.998983	+	0.0450908i	$0.0143577\pi$
$140$	0.301019	+	0.126973i	0.0254408	+	0.0107312i
$141$	−0.130652	−	0.572424i	−0.0110029	−	0.0482068i
$142$	16.1061	−	4.96809i	1.35160	−	0.416912i
$143$	1.61294	+	4.10972i	0.134881	+	0.343672i
$144$	−8.10699	−	7.52219i	−0.675582	−	0.626849i
$145$	−3.43844	−	2.34429i	−0.285547	−	0.194683i
$146$	−9.65944			−0.799421
$147$	−0.470088	+	0.119465i	−0.0387722	+	0.00985334i
$148$	0.801756			0.0659039
$149$	−7.58385	−	5.17058i	−0.621293	−	0.423590i	0.211342	−	0.977412i	$-0.432217\pi$
$149$	−7.58385	−	5.17058i	−0.621293	−	0.423590i	−0.832635	+	0.553822i	$0.813169\pi$
$150$	0.294816	+	0.273550i	0.0240717	+	0.0223352i
$151$	1.44629	+	3.68508i	0.117697	+	0.299887i	0.977567	−	0.210627i	$-0.0675504\pi$
$151$	1.44629	+	3.68508i	0.117697	+	0.299887i	−0.859869	+	0.510514i	$0.829455\pi$
$152$	−0.0201104	+	0.00620323i	−0.00163117	+	0.000503149i
$153$	−5.14119	−	22.5250i	−0.415640	−	1.82104i
$154$	−2.76731	+	15.6728i	−0.222996	+	1.26295i
$155$	−0.528444	+	2.31527i	−0.0424457	+	0.185967i
$156$	−0.000743251	−	0.00991800i	−5.95077e−5	−	0.000794075i
$157$	21.7097	+	6.69656i	1.73262	+	0.534444i	0.990703	−	0.136043i	$-0.0434384\pi$
$157$	21.7097	+	6.69656i	1.73262	+	0.534444i	0.741922	+	0.670487i	$0.233915\pi$
$158$	−1.72648	+	23.0383i	−0.137351	+	1.83283i
$159$	0.00873077	−	0.0222456i	0.000692395	−	0.00176419i
$160$	−0.628099	+	0.302477i	−0.0496556	+	0.0239129i
$161$	−9.20691	+	3.34861i	−0.725606	+	0.263907i
$162$	−10.9953	−	5.29505i	−0.863871	−	0.416018i
$163$	−0.397743	+	0.369051i	−0.0311536	+	0.0289063i	−0.695596	−	0.718433i	$-0.744860\pi$
$163$	−0.397743	+	0.369051i	−0.0311536	+	0.0289063i	0.664442	+	0.747340i	$0.268669\pi$
$164$	−1.36218	+	0.205316i	−0.106369	+	0.0160325i
$165$	−0.131582	+	0.227907i	−0.0102437	+	0.0177426i
$166$	−3.41717	−	5.91872i	−0.265224	−	0.459382i
$167$	5.75128	+	7.21188i	0.445047	+	0.558072i	0.952866	−	0.303392i	$-0.0981193\pi$
$167$	5.75128	+	7.21188i	0.445047	+	0.558072i	−0.507818	+	0.861464i	$0.669548\pi$
$168$	0.244375	−	0.476398i	0.0188540	−	0.0367549i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	8.94060	+	1.34758i	0.685713	+	0.103355i
$171$	−0.0178326	+	0.0121580i	−0.00136369	+	0.000929748i
$172$	0.531590	−	0.362432i	0.0405334	−	0.0276352i
$173$	5.16455	+	0.778430i	0.392653	+	0.0591830i	0.342402	−	0.939554i	$-0.388760\pi$
$173$	5.16455	+	0.778430i	0.392653	+	0.0591830i	0.0502515	+	0.998737i	$0.483998\pi$
$174$	−0.284750	+	0.357066i	−0.0215869	+	0.0270691i
$175$	5.14417	−	10.0283i	0.388862	−	0.758068i
$176$	−10.1636	−	12.7448i	−0.766114	−	0.960676i
$177$	0.0959954	+	0.166269i	0.00721546	+	0.0124975i
$178$	0.111210	−	0.192621i	0.00833551	−	0.0144375i
$179$	12.7607	−	1.92337i	0.953780	−	0.143759i	0.346326	−	0.938114i	$-0.387429\pi$
$179$	12.7607	−	1.92337i	0.953780	−	0.143759i	0.607454	+	0.794355i	$0.292191\pi$
$180$	−0.271122	+	0.251564i	−0.0202082	+	0.0187505i
$181$	7.01118	+	3.37641i	0.521137	+	0.250966i	0.675911	−	0.736984i	$-0.263751\pi$
$181$	7.01118	+	3.37641i	0.521137	+	0.250966i	−0.154774	+	0.987950i	$0.549465\pi$
$182$	3.38778	−	1.23215i	0.251119	−	0.0913333i
$183$	−0.442657	+	0.213172i	−0.0327221	+	0.0157581i
$184$	3.95107	−	10.0672i	0.291277	−	0.742161i
$185$	−0.359090	+	4.79173i	−0.0264009	+	0.352295i
$186$	0.249041	+	0.0768190i	0.0182606	+	0.00563264i
$187$	−2.54497	−	33.9603i	−0.186107	−	2.48342i
$188$	0.270654	−	1.18581i	0.0197395	−	0.0864842i
$189$	0.191104	−	1.08232i	0.0139007	−	0.0787275i
$190$	−0.00187945	−	0.00823442i	−0.000136350	−	0.000597388i
$191$	8.87987	−	2.73908i	0.642525	−	0.198193i	0.0436645	−	0.999046i	$-0.486097\pi$
$191$	8.87987	−	2.73908i	0.642525	−	0.198193i	0.598860	+	0.800854i	$0.295621\pi$
$192$	0.214889	+	0.547529i	0.0155083	+	0.0395145i
$193$	−10.7211	−	9.94771i	−0.771721	−	0.716052i	0.192458	−	0.981305i	$-0.438354\pi$
$193$	−10.7211	−	9.94771i	−0.771721	−	0.716052i	−0.964179	+	0.265253i	$0.914545\pi$
$194$	13.6500	+	9.30638i	0.980010	+	0.668159i
$195$	0.0596082			0.00426863
$196$	−0.984755	−	0.199551i	−0.0703397	−	0.0142537i
$197$	25.6698			1.82889			0.914447	−	0.404705i	$-0.132626\pi$
$197$	25.6698			1.82889			0.914447	+	0.404705i	$0.132626\pi$
$198$	−14.8866	−	10.1495i	−1.05794	−	0.721294i
$199$	3.63715	+	3.37478i	0.257831	+	0.239232i	0.798488	−	0.602011i	$-0.205634\pi$
$199$	3.63715	+	3.37478i	0.257831	+	0.239232i	−0.540657	+	0.841243i	$0.681824\pi$
$200$	4.54544	+	11.5816i	0.321411	+	0.818942i
$201$	1.06895	−	0.329727i	0.0753979	−	0.0232572i
$202$	4.55864	+	19.9727i	0.320745	+	1.40527i
$203$	11.7926	+	4.97426i	0.827681	+	0.349124i
$204$	−0.0170717	+	0.0747962i	−0.00119526	+	0.00523678i
$205$	−0.616986	−	8.23311i	−0.0430922	−	0.575025i
$206$	−5.11521	−	1.57783i	−0.356394	−	0.109933i
$207$	0.828826	−	11.0599i	0.0576074	−	0.768717i
$208$	−1.34896	+	3.43708i	−0.0935333	+	0.238319i
$209$	−0.0286624	+	0.0138031i	−0.00198262	+	0.000954781i
$210$	0.183330	+	0.112089i	0.0126510	+	0.00773490i
$211$	−3.24345	−	1.56196i	−0.223288	−	0.107530i	0.318896	−	0.947790i	$-0.396688\pi$
$211$	−3.24345	−	1.56196i	−0.223288	−	0.107530i	−0.542184	+	0.840260i	$0.682402\pi$
$212$	0.0362900	−	0.0336722i	0.00249240	−	0.00231261i
$213$	−0.847574	+	0.127751i	−0.0580748	+	0.00875337i
$214$	−3.38492	+	5.86285i	−0.231388	+	0.400776i
$215$	1.92800	+	3.33940i	0.131489	+	0.227745i
$216$	0.756447	+	0.948554i	0.0514697	+	0.0645409i
$217$	0.183791	−	7.30138i	0.0124765	−	0.495650i
$218$	6.00684	−	7.53234i	0.406835	−	0.510155i
$219$	0.485738	+	0.0732132i	0.0328231	+	0.00494729i
$220$	−0.450434	+	0.307100i	−0.0303682	+	0.0207047i
$221$	−6.37342	+	4.34532i	−0.428722	+	0.292298i
$222$	0.521446	+	0.0785953i	0.0349972	+	0.00527497i
$223$	−1.10564	+	1.38643i	−0.0740393	+	0.0928423i	−0.817472	−	0.575969i	$-0.804625\pi$
$223$	−1.10564	+	1.38643i	−0.0740393	+	0.0928423i	0.743433	+	0.668811i	$0.233196\pi$
$224$	1.70938	−	1.29418i	0.114213	−	0.0864710i
$225$	7.95532	+	9.97566i	0.530355	+	0.665044i
$226$	3.88847	+	6.73504i	0.258657	+	0.448008i
$227$	−11.4383	+	19.8118i	−0.759189	+	1.31495i	0.184076	+	0.982912i	$0.441071\pi$
$227$	−11.4383	+	19.8118i	−0.759189	+	1.31495i	−0.943265	+	0.332041i	$0.892263\pi$
$228$	7.08671e−5	0	1.06815e-5i	4.69329e−6	0	7.07399e-7i
$229$	−14.9599	+	13.8808i	−0.988580	+	0.917268i	−0.996574	−	0.0827000i	$-0.973646\pi$
$229$	−14.9599	+	13.8808i	−0.988580	+	0.917268i	0.00799461	+	0.999968i	$0.497455\pi$
$230$	3.91048	+	1.88319i	0.257849	+	0.124174i
$231$	0.257949	−	0.767153i	0.0169718	−	0.0504750i
$232$	−12.7293	+	6.13011i	−0.835720	+	0.402461i
$233$	3.99363	−	10.1756i	0.261631	−	0.666626i	−0.738338	−	0.674431i	$-0.764389\pi$
$233$	3.99363	−	10.1756i	0.261631	−	0.666626i	0.999970	+	0.00780474i	$0.00248435\pi$
$234$	−0.304975	+	4.06961i	−0.0199368	+	0.266039i
$235$	6.96584	+	2.14868i	0.454401	+	0.140164i
$236$	0.0297217	+	0.396609i	0.00193472	+	0.0258170i
$237$	0.261436	−	1.14542i	0.0169821	−	0.0744033i
$238$	−27.7730	+	1.37959i	−1.80026	+	0.0894258i
$239$	−1.76915	−	7.75115i	−0.114437	−	0.501380i	−0.999364	−	0.0356516i	$-0.988649\pi$
$239$	−1.76915	−	7.75115i	−0.114437	−	0.501380i	0.884927	−	0.465729i	$-0.154208\pi$
$240$	−0.210315	+	0.0648734i	−0.0135757	+	0.00418756i
$241$	5.14127	+	13.0997i	0.331178	+	0.843829i	0.995357	+	0.0962547i	$0.0306863\pi$
$241$	5.14127	+	13.0997i	0.331178	+	0.843829i	−0.664178	+	0.747574i	$0.731218\pi$
$242$	−8.48115	−	7.86936i	−0.545189	−	0.505862i
$243$	1.54246	+	1.05163i	0.0989487	+	0.0674621i
$244$	−1.01778			−0.0651569
$245$	1.63368	−	5.79606i	0.104372	−	0.370297i
$246$	−0.906064			−0.0577685
$247$	0.00595371	+	0.00405917i	0.000378826	+	0.000258279i
$248$	5.91020	+	5.48386i	0.375298	+	0.348226i
$249$	0.126977	+	0.323531i	0.00804681	+	0.0205029i
$250$	−10.3717	+	3.19924i	−0.655964	+	0.202338i
$251$	3.69057	+	16.1694i	0.232946	+	1.02060i	0.947181	+	0.320699i	$0.103918\pi$
$251$	3.69057	+	16.1694i	0.232946	+	1.02060i	−0.714235	+	0.699906i	$0.753225\pi$
$252$	0.664212	−	0.923408i	0.0418414	−	0.0581692i
$253$	3.63776	−	15.9381i	0.228704	−	1.00202i
$254$	−0.755715	−	10.0843i	−0.0474178	−	0.632746i
$255$	−0.439376	−	0.135530i	−0.0275148	−	0.00848720i
$256$	−0.256082	+	3.41718i	−0.0160051	+	0.213574i
$257$	5.07405	−	12.9285i	0.316511	−	0.806456i	−0.680752	−	0.732514i	$-0.738347\pi$
$257$	5.07405	−	12.9285i	0.316511	−	0.806456i	0.997263	−	0.0739420i	$-0.0235580\pi$
$258$	0.381264	−	0.183607i	0.0237365	−	0.0114309i
$259$	−1.83416	−	14.6640i	−0.113969	−	0.911174i
$260$	0.111254	+	0.0535769i	0.00689965	+	0.00332270i
$261$	−10.6214	+	9.85520i	−0.657447	+	0.610022i
$262$	−20.3139	+	3.06183i	−1.25500	+	0.189160i
$263$	4.04388	−	7.00421i	0.249357	−	0.431898i	−0.713991	−	0.700155i	$-0.753114\pi$
$263$	4.04388	−	7.00421i	0.249357	−	0.431898i	0.963347	+	0.268257i	$0.0864476\pi$
$264$	0.446721	+	0.773744i	0.0274938	+	0.0476206i
$265$	0.184990	+	0.231970i	0.0113638	+	0.0142498i
$266$	0.0106781	+	0.0236799i	0.000654717	+	0.00145191i
$267$	−0.00705228	+	0.00884328i	−0.000431592	+	0.000541200i
$268$	2.29147	+	0.345383i	0.139974	+	0.0210976i
$269$	13.1701	−	8.97922i	0.802995	−	0.547473i	−0.0908418	−	0.995865i	$-0.528956\pi$
$269$	13.1701	−	8.97922i	0.802995	−	0.547473i	0.893837	+	0.448393i	$0.148003\pi$
$270$	−0.402308	+	0.274289i	−0.0244837	+	0.0166927i
$271$	15.7551	+	2.37470i	0.957054	+	0.144253i	0.608955	−	0.793205i	$-0.291589\pi$
$271$	15.7551	+	2.37470i	0.957054	+	0.144253i	0.348099	+	0.937458i	$0.386827\pi$
$272$	17.7581	−	22.2679i	1.07674	−	1.35019i
$273$	−0.179698	+	0.0362831i	−0.0108758	+	0.00219595i
$274$	−10.7433	−	13.4717i	−0.649025	−	0.813852i
$275$	9.40360	+	16.2875i	0.567058	+	0.982174i
$276$	−0.0184142	+	0.0318943i	−0.00110840	+	0.00191981i
$277$	−17.4348	+	2.62788i	−1.04756	+	0.157894i	−0.650194	−	0.759768i	$-0.725313\pi$
$277$	−17.4348	+	2.62788i	−1.04756	+	0.157894i	−0.397363	+	0.917662i	$0.630074\pi$
$278$	4.20001	−	3.89704i	0.251900	−	0.233729i
$279$	7.44953	+	3.58750i	0.445991	+	0.214778i
$280$	3.60527	+	5.58492i	0.215456	+	0.333763i
$281$	−14.6493	+	7.05475i	−0.873906	+	0.420851i	−0.816395	−	0.577494i	$-0.804031\pi$
$281$	−14.6493	+	7.05475i	−0.873906	+	0.420851i	−0.0575113	+	0.998345i	$0.518317\pi$
$282$	0.292272	−	0.744696i	0.0174045	−	0.0443460i
$283$	−1.65455	+	22.0785i	−0.0983530	+	1.31243i	0.701688	+	0.712485i	$0.252430\pi$
$283$	−1.65455	+	22.0785i	−0.0983530	+	1.31243i	−0.800041	+	0.599946i	$0.795189\pi$
$284$	−1.69675	−	0.523377i	−0.100683	−	0.0310567i
$285$	3.20985e−5	0	0.000428324i	1.90135e−6	0	2.53717e-5i
$286$	−1.33855	+	5.86458i	−0.0791502	+	0.346780i
$287$	6.87143	+	24.4444i	0.405607	+	1.44291i
$288$	0.540107	+	2.36636i	0.0318261	+	0.139439i
$289$	40.6140	−	12.5278i	2.38906	−	0.736927i
$290$	−2.07156	−	5.27825i	−0.121646	−	0.309949i
$291$	−0.615869	−	0.571443i	−0.0361029	−	0.0334986i
$292$	0.840782	+	0.573236i	0.0492031	+	0.0335461i
$293$	19.4423			1.13583			0.567916	−	0.823087i	$-0.307750\pi$
$293$	19.4423			1.13583			0.567916	+	0.823087i	$0.307750\pi$
$294$	−0.620903	−	0.226319i	−0.0362118	−	0.0131992i
$295$	−2.38366			−0.138782
$296$	13.4789	+	9.18973i	0.783443	+	0.534142i
$297$	1.34441	+	1.24743i	0.0780104	+	0.0723830i
$298$	−4.56905	−	11.6417i	−0.264678	−	0.674388i
$299$	−3.53839	+	1.09145i	−0.204630	+	0.0631201i
$300$	−0.00942787	−	0.0413062i	−0.000544319	−	0.00238482i
$301$	−7.84492	−	8.89355i	−0.452173	−	0.512616i
$302$	−1.20024	+	5.25861i	−0.0690663	+	0.302599i
$303$	−0.0778553	−	1.03891i	−0.00447267	−	0.0596836i
$304$	−0.0254241	−	0.00784229i	−0.00145817	−	0.000449786i
$305$	0.455845	−	6.08282i	0.0261016	−	0.348302i
$306$	11.5010	−	29.3039i	0.657466	−	1.67520i
$307$	16.2183	−	7.81030i	0.925625	−	0.445757i	0.0905486	−	0.995892i	$-0.471138\pi$
$307$	16.2183	−	7.81030i	0.925625	−	0.445757i	0.835076	+	0.550135i	$0.185424\pi$
$308$	1.17097	−	1.19998i	0.0667222	−	0.0683749i
$309$	0.245266	+	0.118114i	0.0139527	+	0.00671927i
$310$	−2.37195	+	2.20085i	−0.134718	+	0.125000i
$311$	−15.3961	+	2.32058i	−0.873031	+	0.131588i	−0.570249	−	0.821472i	$-0.693153\pi$
$311$	−15.3961	+	2.32058i	−0.873031	+	0.131588i	−0.302782	+	0.953060i	$0.597915\pi$
$312$	0.101185	−	0.175257i	0.00572846	−	0.00992199i
$313$	−10.0262	−	17.3658i	−0.566713	−	0.981575i	−0.996888	−	0.0788297i	$-0.974882\pi$
$313$	−10.0262	−	17.3658i	−0.566713	−	0.981575i	0.430176	−	0.902745i	$-0.358452\pi$
$314$	19.3002	+	24.2017i	1.08918	+	1.36578i
$315$	5.22130	+	4.38327i	0.294187	+	0.246969i
$316$	1.51747	−	1.90285i	0.0853645	−	0.107044i
$317$	−20.3059	−	3.06063i	−1.14050	−	0.171902i	−0.448485	−	0.893790i	$-0.648036\pi$
$317$	−20.3059	−	3.06063i	−1.14050	−	0.171902i	−0.692010	+	0.721888i	$0.743275\pi$
$318$	0.0269031	−	0.0183422i	0.00150865	−	0.00102858i
$319$	−17.6460	+	12.0309i	−0.987989	+	0.673599i
$320$	−7.22109	−	1.08840i	−0.403671	−	0.0608436i
$321$	0.214652	−	0.269166i	0.0119807	−	0.0150234i
$322$	−12.9350	−	3.29687i	−0.720840	−	0.183728i
$323$	−0.0346560	−	0.0434573i	−0.00192831	−	0.00241803i
$324$	0.642824	+	1.11340i	0.0357125	+	0.0618558i
$325$	2.12997	−	3.68921i	0.118149	−	0.204641i
$326$	−0.731025	+	0.110184i	−0.0404877	+	0.00610255i
$327$	−0.359153	+	0.333246i	−0.0198612	+	0.0184285i
$328$	−25.2539	−	12.1616i	−1.39441	−	0.671515i
$329$	−22.3074	−	2.23746i	−1.22985	−	0.123355i
$330$	−0.323058	+	0.155576i	−0.0177837	+	0.00856420i
$331$	10.9977	−	28.0218i	0.604490	−	1.54021i	−0.220690	−	0.975344i	$-0.570831\pi$
$331$	10.9977	−	28.0218i	0.604490	−	1.54021i	0.825179	−	0.564871i	$-0.191074\pi$
$332$	−0.0538045	+	0.717971i	−0.00295290	+	0.0394038i
$333$	15.9868	+	4.93129i	0.876073	+	0.270233i
$334$	0.939234	+	12.5332i	0.0513926	+	0.685786i
$335$	−3.09050	+	13.5404i	−0.168852	+	0.739789i
$336$	0.594537	−	0.323588i	0.0324346	−	0.0176531i
$337$	3.86002	+	16.9118i	0.210268	+	0.921246i	0.964384	+	0.264505i	$0.0852086\pi$
$337$	3.86002	+	16.9118i	0.210268	+	0.921246i	−0.754116	+	0.656741i	$0.771934\pi$
$338$	1.30199	−	0.401610i	0.0708188	−	0.0218447i
$339$	−0.144489	−	0.368153i	−0.00784759	−	0.0199953i
$340$	−0.698241	−	0.647873i	−0.0378674	−	0.0351359i
$341$	10.0698	+	6.86546i	0.545309	+	0.371785i
$342$	−0.0294070			−0.00159015
$343$	−1.39696	+	18.4675i	−0.0754286	+	0.997151i
$344$	13.0911			0.705826
$345$	−0.182370	−	0.124338i	−0.00981848	−	0.00669413i
$346$	5.21660	+	4.84030i	0.280446	+	0.260216i
$347$	−0.942439	−	2.40130i	−0.0505928	−	0.128908i	0.903343	−	0.428918i	$-0.141105\pi$
$347$	−0.942439	−	2.40130i	−0.0505928	−	0.128908i	−0.953936	+	0.300010i	$0.903010\pi$
$348$	0.0459753	−	0.0141815i	0.00246453	−	0.000760208i
$349$	−1.65212	−	7.23841i	−0.0884359	−	0.387463i	0.911268	−	0.411815i	$-0.135105\pi$
$349$	−1.65212	−	7.23841i	−0.0884359	−	0.387463i	−0.999703	+	0.0243518i	$0.992248\pi$
$350$	13.4882	−	7.34120i	0.720975	−	0.392404i
$351$	0.0924369	−	0.404993i	0.00493392	−	0.0216169i
$352$	0.267362	+	3.56770i	0.0142504	+	0.190159i
$353$	6.08292	+	1.87633i	0.323761	+	0.0998670i	0.452375	−	0.891828i	$-0.350577\pi$
$353$	6.08292	+	1.87633i	0.323761	+	0.0998670i	−0.128614	+	0.991695i	$0.541053\pi$
$354$	−0.0195487	+	0.260860i	−0.00103900	+	0.0138645i
$355$	3.88793	−	9.90628i	0.206350	−	0.525771i
$356$	−0.0211109	+	0.0101665i	−0.00111888	+	0.000538823i
$357$	1.40706	+	0.141130i	0.0744696	+	0.00746937i
$358$	15.8418	+	7.62902i	0.837267	+	0.403206i
$359$	1.44919	−	1.34465i	0.0764851	−	0.0709678i	−0.641004	−	0.767538i	$-0.721482\pi$
$359$	1.44919	−	1.34465i	0.0764851	−	0.0709678i	0.717489	+	0.696570i	$0.245291\pi$
$360$	−7.44144	+	1.12162i	−0.392198	+	0.0591144i
$361$	9.49997	−	16.4544i	0.499999	−	0.866023i
$362$	5.30145	+	9.18237i	0.278638	+	0.482615i
$363$	0.366841	+	0.460004i	0.0192542	+	0.0241439i
$364$	−0.368002	−	0.0937964i	−0.0192886	−	0.00491627i
$365$	−3.80254	+	4.76823i	−0.199034	+	0.249581i
$366$	−0.661946	−	0.0997722i	−0.0346005	−	0.00521518i
$367$	−24.8685	+	16.9551i	−1.29813	+	0.885047i	−0.997635	−	0.0687374i	$-0.978103\pi$
$367$	−24.8685	+	16.9551i	−1.29813	+	0.885047i	−0.300491	+	0.953785i	$0.597151\pi$
$368$	11.2966	−	7.70188i	0.588875	−	0.401488i
$369$	−28.4245	−	4.28430i	−1.47972	−	0.223032i
$370$	−4.08207	+	5.11876i	−0.212217	+	0.266111i
$371$	−0.698877	−	0.586706i	−0.0362839	−	0.0304602i
$372$	−0.0171184	−	0.0214658i	−0.000887547	−	0.00111295i
$373$	−1.53893	−	2.66550i	−0.0796825	−	0.138014i	0.823430	−	0.567417i	$-0.192057\pi$
$373$	−1.53893	−	2.66550i	−0.0796825	−	0.138014i	−0.903113	+	0.429403i	$0.858724\pi$
$374$	23.2007	−	40.1848i	1.19968	−	2.07790i
$375$	0.545803	−	0.0822666i	0.0281852	−	0.00424823i
$376$	18.1419	−	16.8332i	0.935598	−	0.868108i
$377$	4.35843	+	2.09891i	0.224471	+	0.108099i
$378$	1.04586	−	1.07177i	0.0537932	−	0.0551257i
$379$	−9.36756	+	4.51118i	−0.481179	+	0.231724i	−0.658718	−	0.752390i	$-0.728901\pi$
$379$	−9.36756	+	4.51118i	−0.481179	+	0.231724i	0.177539	+	0.984114i	$0.443187\pi$
$380$	−0.000325076	0	0.000828280i	−1.66760e−5	0	4.24899e-5i
$381$	−0.0384314	+	0.512831i	−0.00196890	+	0.0262732i
$382$	12.0990	+	3.73205i	0.619039	+	0.190948i
$383$	−2.54447	−	33.9535i	−0.130016	−	1.73494i	−0.556849	−	0.830614i	$-0.687990\pi$
$383$	−2.54447	−	33.9535i	−0.130016	−	1.73494i	0.426833	−	0.904330i	$-0.359629\pi$
$384$	−0.153343	+	0.671840i	−0.00782526	+	0.0342847i
$385$	6.64725	+	7.53580i	0.338775	+	0.384060i
$386$	−4.43423	−	19.4276i	−0.225696	−	0.988840i
$387$	12.8290	−	3.95721i	0.652133	−	0.201156i
$388$	−0.635843	−	1.62010i	−0.0322800	−	0.0822482i
$389$	18.1015	+	16.7957i	0.917781	+	0.851576i	0.989305	−	0.145863i	$-0.0465958\pi$
$389$	18.1015	+	16.7957i	0.917781	+	0.851576i	−0.0715241	+	0.997439i	$0.522786\pi$
$390$	0.0671050	+	0.0457514i	0.00339799	+	0.00231671i
$391$	28.5633			1.44451
$392$	−14.2681	−	14.6421i	−0.720649	−	0.739536i
$393$	1.04472			0.0526991
$394$	28.8982	+	19.7024i	1.45587	+	0.992594i
$395$	10.6928	+	9.92150i	0.538015	+	0.499205i
$396$	0.693448	+	1.76688i	0.0348471	+	0.0887889i
$397$	−9.65641	+	2.97861i	−0.484641	+	0.149492i	−0.527441	−	0.849592i	$-0.676848\pi$
$397$	−9.65641	+	2.97861i	−0.484641	+	0.149492i	0.0427997	+	0.999084i	$0.486372\pi$
$398$	1.50432	+	6.59086i	0.0754048	+	0.330370i
$399$	−0.000357483	−	0.00127171i	−1.78965e−5	−	6.36651e-5i
$400$	−3.50004	+	15.3347i	−0.175002	+	0.766734i
$401$	−1.84046	−	24.5593i	−0.0919083	−	1.22643i	−0.832327	−	0.554285i	$-0.812992\pi$
$401$	−1.84046	−	24.5593i	−0.0919083	−	1.22643i	0.740419	−	0.672146i	$-0.234627\pi$
$402$	1.45647	+	0.449260i	0.0726419	+	0.0224071i
$403$	0.206295	−	2.75282i	0.0102763	−	0.137128i
$404$	0.788476	−	2.00900i	0.0392282	−	0.0999517i
$405$	−6.94222	+	3.34320i	−0.344962	+	0.166125i
$406$	9.45785	+	14.6511i	0.469385	+	0.727123i
$407$	22.2180	+	10.6996i	1.10130	+	0.530360i
$408$	−1.14432	+	1.06177i	−0.0566522	+	0.0525656i
$409$	10.2483	−	1.54468i	0.506746	−	0.0763797i	0.109307	−	0.994008i	$-0.465137\pi$
$409$	10.2483	−	1.54468i	0.506746	−	0.0763797i	0.397439	+	0.917628i	$0.369899\pi$
$410$	5.62462	−	9.74212i	0.277780	−	0.481129i
$411$	0.438133	+	0.758868i	0.0216115	+	0.0374322i
$412$	0.351605	+	0.440899i	0.0173223	+	0.0217215i
$413$	7.18590	−	1.45092i	0.353595	−	0.0713949i
$414$	9.42194	−	11.8147i	0.463063	−	0.580662i
$415$	−4.26689	−	0.643130i	−0.209453	−	0.0315700i
$416$	0.669559	−	0.456498i	0.0328278	−	0.0223816i
$417$	−0.240740	+	0.164134i	−0.0117891	+	0.00803768i
$418$	−0.0428616	−	0.00646035i	−0.00209643	−	0.000315986i
$419$	4.14300	−	5.19515i	0.202399	−	0.253800i	−0.670265	−	0.742122i	$-0.733819\pi$
$419$	4.14300	−	5.19515i	0.202399	−	0.253800i	0.872663	+	0.488322i	$0.162391\pi$
$420$	−0.00930560	−	0.0206362i	−0.000454067	−	0.00100694i
$421$	−15.6387	−	19.6103i	−0.762183	−	0.955747i	0.237695	−	0.971340i	$-0.423608\pi$
$421$	−15.6387	−	19.6103i	−0.762183	−	0.955747i	−0.999878	+	0.0155924i	$0.995037\pi$
$422$	−2.45251	−	4.24787i	−0.119386	−	0.206783i
$423$	12.6902	−	21.9801i	0.617021	−	1.06871i
$424$	0.996046	−	0.150130i	0.0483722	−	0.00729094i
$425$	−24.0882	+	22.3506i	−1.16845	+	1.08416i
$426$	−1.05222	−	0.506725i	−0.0509805	−	0.0245509i
$427$	2.32835	+	18.6151i	0.112677	+	0.900846i
$428$	0.642561	−	0.309441i	0.0310593	−	0.0149574i
$429$	0.111761	−	0.284763i	0.00539588	−	0.0137485i
$430$	−0.392623	+	5.23919i	−0.0189340	+	0.252656i
$431$	−2.24799	−	0.693415i	−0.108282	−	0.0334006i	0.240141	−	0.970738i	$-0.422806\pi$
$431$	−2.24799	−	0.693415i	−0.108282	−	0.0334006i	−0.348423	+	0.937338i	$0.613283\pi$
$432$	0.114622	+	1.52953i	0.00551477	+	0.0735895i
$433$	5.63168	−	24.6740i	0.270641	−	1.18576i	−0.638617	−	0.769525i	$-0.720493\pi$
$433$	5.63168	−	24.6740i	0.270641	−	1.18576i	0.909258	−	0.416233i	$-0.136650\pi$
$434$	5.81097	−	8.07858i	0.278935	−	0.387784i
$435$	0.0641649	+	0.281125i	0.00307647	+	0.0134789i
$436$	−0.969855	+	0.299161i	−0.0464476	+	0.0143272i
$437$	−0.00974817	−	0.0248379i	−0.000466318	−	0.00118816i
$438$	0.490634	+	0.455242i	0.0234434	+	0.0217523i
$439$	4.30256	+	2.93344i	0.205350	+	0.140005i	0.661629	−	0.749832i	$-0.269866\pi$
$439$	4.30256	+	2.93344i	0.205350	+	0.140005i	−0.456279	+	0.889837i	$0.650818\pi$
$440$	−11.0925			−0.528816
$441$	−18.4085	−	10.0359i	−0.876593	−	0.477898i
$442$	−10.5102			−0.499918
$443$	−20.7672	−	14.1588i	−0.986678	−	0.672705i	−0.0414580	−	0.999140i	$-0.513200\pi$
$443$	−20.7672	−	14.1588i	−0.986678	−	0.672705i	−0.945220	+	0.326435i	$0.894153\pi$
$444$	−0.0407238	−	0.0377861i	−0.00193266	−	0.00179325i
$445$	−0.0513053	−	0.130724i	−0.00243211	−	0.00619691i
$446$	−2.30883	+	0.712180i	−0.109326	+	0.0337227i
$447$	0.141523	+	0.620051i	0.00669379	+	0.0293274i
$448$	22.4316	−	1.11426i	1.05979	−	0.0526439i
$449$	−4.12002	+	18.0510i	−0.194436	+	0.851878i	0.779743	+	0.626100i	$0.215350\pi$
$449$	−4.12002	+	18.0510i	−0.194436	+	0.851878i	−0.974179	+	0.225778i	$0.927507\pi$
$450$	1.29917	+	17.3363i	0.0612436	+	0.817239i
$451$	−40.4883	−	12.4890i	−1.90652	−	0.588084i
$452$	0.0612253	−	0.816995i	0.00287979	−	0.0384282i
$453$	0.100213	−	0.255339i	0.00470843	−	0.0119969i
$454$	−28.0831	+	13.5241i	−1.31801	+	0.634718i
$455$	0.725399	−	2.15737i	0.0340072	−	0.101139i
$456$	0.00131383		0.000632705i	6.15255e−5		2.96291e-5i
$457$	−21.4649	+	19.9165i	−1.00408	+	0.931654i	−0.997663	−	0.0683258i	$-0.978234\pi$
$457$	−21.4649	+	19.9165i	−1.00408	+	0.931654i	−0.00642072	+	0.999979i	$0.502044\pi$
$458$	−27.4954	+	4.14426i	−1.28477	+	0.193649i
$459$	−1.60218	+	2.77506i	−0.0747834	+	0.129529i
$460$	−0.228621	−	0.395983i	−0.0106595	−	0.0184628i
$461$	−14.0844	−	17.6612i	−0.655974	−	0.822565i	0.336924	−	0.941532i	$-0.390613\pi$
$461$	−14.0844	−	17.6612i	−0.655974	−	0.822565i	−0.992898	+	0.118966i	$0.962042\pi$
$462$	0.879208	−	0.665651i	0.0409044	−	0.0309689i
$463$	−10.5261	+	13.1993i	−0.489190	+	0.613425i	−0.963753	−	0.266797i	$-0.914035\pi$
$463$	−10.5261	+	13.1993i	−0.489190	+	0.613425i	0.474563	+	0.880222i	$0.342606\pi$
$464$	−17.6621	−	2.66213i	−0.819942	−	0.123586i
$465$	0.135958	−	0.0926947i	0.00630491	−	0.00429861i
$466$	12.3060	−	8.39011i	0.570066	−	0.388664i
$467$	−9.60465	−	1.44767i	−0.444450	−	0.0669901i	−0.0769953	−	0.997031i	$-0.524533\pi$
$467$	−9.60465	−	1.44767i	−0.444450	−	0.0669901i	−0.367455	+	0.930041i	$0.619771\pi$
$468$	0.268055	−	0.336130i	0.0123908	−	0.0155376i
$469$	1.07486	−	42.7006i	0.0496326	−	1.97173i
$470$	6.19272	+	7.76543i	0.285649	+	0.358193i
$471$	−0.787103	−	1.36330i	−0.0362678	−	0.0628177i
$472$	−4.04626	+	7.00832i	−0.186244	+	0.322584i
$473$	19.5680	−	2.94939i	0.899735	−	0.135613i
$474$	1.17347	−	1.08882i	0.0538992	−	0.0500112i
$475$	0.0276564	+	0.0133186i	0.00126896	+	0.000611099i
$476$	2.49931	+	1.52810i	0.114556	+	0.0700402i
$477$	0.930719	−	0.448210i	0.0426147	−	0.0205221i
$478$	3.95763	−	10.0839i	0.181018	−	0.461226i
$479$	−1.94530	+	25.9582i	−0.0888828	+	1.18606i	0.757264	+	0.653109i	$0.226536\pi$
$479$	−1.94530	+	25.9582i	−0.0888828	+	1.18606i	−0.846147	+	0.532950i	$0.821083\pi$
$480$	0.0461587	+	0.0142381i	0.00210685	+	0.000649876i
$481$	−0.417416	−	5.57002i	−0.0190325	−	0.253971i
$482$	−4.26664	+	18.6934i	−0.194340	+	0.851460i
$483$	0.625466	+	0.263828i	0.0284597	+	0.0120046i
$484$	0.271217	+	1.18828i	0.0123281	+	0.0540127i
$485$	9.96739	−	3.07453i	0.452596	−	0.139607i
$486$	0.929285	+	2.36778i	0.0421532	+	0.107405i
$487$	−14.0455	−	13.0323i	−0.636464	−	0.590552i	0.294505	−	0.955650i	$-0.404845\pi$
$487$	−14.0455	−	13.0323i	−0.636464	−	0.590552i	−0.930969	+	0.365098i	$0.881036\pi$
$488$	−17.1106	−	11.6658i	−0.774562	−	0.528087i
$489$	0.0375957			0.00170014
$490$	6.28782	−	5.27111i	0.284055	−	0.238124i
$491$	−10.1787			−0.459358			−0.229679	−	0.973266i	$-0.573768\pi$
$491$	−10.1787			−0.459358			−0.229679	+	0.973266i	$0.573768\pi$
$492$	0.0788661	+	0.0537700i	0.00355556	+	0.00242414i
$493$	−27.3541	−	25.3809i	−1.23197	−	1.14310i
$494$	0.00358694	+	0.00913937i	0.000161384	+	0.000411200i
$495$	−10.8704	+	3.35308i	−0.488588	+	0.150710i
$496$	2.26811	+	9.93722i	0.101841	+	0.446194i
$497$	−5.69087	+	32.2305i	−0.255270	+	1.44574i
$498$	−0.105375	+	0.461679i	−0.00472198	+	0.0206884i
$499$	0.478948	+	6.39111i	0.0214406	+	0.286106i	0.997610	+	0.0690956i	$0.0220113\pi$
$499$	0.478948	+	6.39111i	0.0214406	+	0.286106i	−0.976169	+	0.217010i	$0.930370\pi$
$500$	1.09264	+	0.337034i	0.0488642	+	0.0150726i
$501$	0.0477641	−	0.637368i	0.00213394	−	0.0284755i
$502$	−8.25588	+	21.0356i	−0.368478	+	0.938867i
$503$	37.1804	−	17.9051i	1.65779	−	0.798351i	0.658855	−	0.752270i	$-0.271041\pi$
$503$	37.1804	−	17.9051i	1.65779	−	0.798351i	0.998938	−	0.0460812i	$-0.0146733\pi$
$504$	21.7506	−	7.91083i	0.968850	−	0.352376i
$505$	11.6538	+	5.61216i	0.518586	+	0.249738i
$506$	16.3283	−	15.1504i	0.725881	−	0.673519i
$507$	−0.0685162	+	0.0103272i	−0.00304291	+	0.000458645i
$508$	−0.532670	+	0.922612i	−0.0236334	+	0.0409343i
$509$	−2.03336	−	3.52189i	−0.0901272	−	0.156105i	0.817437	−	0.576018i	$-0.195394\pi$
$509$	−2.03336	−	3.52189i	−0.0901272	−	0.156105i	−0.907565	+	0.419913i	$0.862061\pi$
$510$	−0.390612	−	0.489812i	−0.0172966	−	0.0216892i
$511$	8.56094	−	16.6891i	0.378714	−	0.738283i
$512$	−15.3128	+	19.2016i	−0.676737	+	0.848601i
$513$	0.00295991		0.000446135i	0.000130683		1.96974e-5i
$514$	15.6353	−	10.6599i	0.689642	−	0.470190i
$515$	−2.79253	+	1.90391i	−0.123053	+	0.0838964i
$516$	−0.0440823	−	0.00664434i	−0.00194062	−	0.000292501i
$517$	23.3252	−	29.2488i	1.02584	−	1.28636i
$518$	9.19027	−	17.9160i	0.403797	−	0.787183i
$519$	−0.225637	−	0.282940i	−0.00990437	−	0.0124197i
$520$	1.25626	+	2.17591i	0.0550906	+	0.0954198i
$521$	12.2968	−	21.2987i	0.538733	−	0.933113i	−0.460239	−	0.887795i	$-0.652236\pi$
$521$	12.2968	−	21.2987i	0.538733	−	0.933113i	0.998973	−	0.0453184i	$-0.0144302\pi$
$522$	−19.5214	+	2.94238i	−0.854429	+	0.128784i
$523$	3.89725	−	3.61612i	0.170415	−	0.158122i	−0.590355	−	0.807144i	$-0.701012\pi$
$523$	3.89725	−	3.61612i	0.170415	−	0.158122i	0.760770	+	0.649022i	$0.224822\pi$
$524$	1.94988	+	0.939011i	0.0851807	+	0.0410209i
$525$	−0.733915	+	0.266929i	−0.0320307	+	0.0116497i
$526$	9.92845	−	4.78129i	0.432901	−	0.208474i
$527$	−7.77962	+	19.8221i	−0.338886	+	0.863466i
$528$	−0.0844087	+	1.12636i	−0.00367342	+	0.0490183i
$529$	−8.87586	−	2.73784i	−0.385907	−	0.119037i
$530$	0.0302104	+	0.403130i	0.00131226	+	0.0175108i
$531$	−1.84674	+	8.09110i	−0.0801417	+	0.351124i
$532$	0.000475823	−	0.00269485i	2.06295e−5	−	0.000116836i
$533$	2.13558	+	9.35658i	0.0925022	+	0.405279i
$534$	−0.0147267	+	0.00454260i	−0.000637289	+	0.000196578i
$535$	1.56160	+	3.97888i	0.0675137	+	0.172022i
$536$	34.5646	+	32.0713i	1.49296	+	1.38527i
$537$	−0.738804	−	0.503708i	−0.0318817	−	0.0217366i
$538$	21.7183			0.936343
$539$	−24.6261	−	18.6717i	−1.06072	−	0.804245i
$540$	0.0512954			0.00220740
$541$	21.7958	+	14.8601i	0.937076	+	0.638887i	0.932526	−	0.361102i	$-0.117599\pi$
$541$	21.7958	+	14.8601i	0.937076	+	0.638887i	0.00454959	+	0.999990i	$0.498552\pi$
$542$	15.9139	+	14.7659i	0.683560	+	0.634251i
$543$	−0.196993	−	0.501930i	−0.00845378	−	0.0215399i
$544$	−5.97329	+	1.84252i	−0.256103	+	0.0789973i
$545$	−1.35357	−	5.93037i	−0.0579805	−	0.254029i
$546$	−0.230147	−	0.0970782i	−0.00984936	−	0.00415456i
$547$	3.46260	−	15.1706i	0.148050	−	0.648650i	−0.845376	−	0.534172i	$-0.820623\pi$
$547$	3.46260	−	15.1706i	0.148050	−	0.648650i	0.993426	−	0.114478i	$-0.0365194\pi$
$548$	0.135653	+	1.81016i	0.00579481	+	0.0773263i
$549$	−20.2944	−	6.25999i	−0.866143	−	0.267170i
$550$	−1.91497	+	25.5535i	−0.0816547	+	1.08961i
$551$	−0.0127351	+	0.0324484i	−0.000542532	+	0.00138235i
$552$	−0.675145	+	0.325133i	−0.0287361	+	0.0138386i
$553$	−38.2743	−	23.4012i	−1.62759	−	0.995120i
$554$	−21.6445	−	10.4235i	−0.919588	−	0.442850i
$555$	0.244070	−	0.226464i	0.0103602	−	0.00961285i
$556$	−0.596847	+	0.0899603i	−0.0253120	+	0.00381517i
$557$	−19.8294	+	34.3456i	−0.840200	+	1.45527i	0.0495262	+	0.998773i	$0.484229\pi$
$557$	−19.8294	+	34.3456i	−0.840200	+	1.45527i	−0.889726	+	0.456495i	$0.849104\pi$
$558$	5.63290	+	9.75646i	0.238460	+	0.413024i
$559$	−2.79468	−	3.50441i	−0.118202	−	0.148221i
$560$	−0.211478	+	8.40129i	−0.00893657	+	0.355019i
$561$	−1.47126	+	1.84490i	−0.0621165	+	0.0778916i
$562$	−21.9065	−	3.30188i	−0.924070	−	0.139281i
$563$	36.6116	−	24.9613i	1.54299	−	1.05200i	0.569864	−	0.821739i	$-0.306996\pi$
$563$	36.6116	−	24.9613i	1.54299	−	1.05200i	0.973130	−	0.230256i	$-0.0739563\pi$
$564$	−0.0696338	+	0.0474755i	−0.00293211	+	0.00199908i
$565$	4.85538	+	0.731831i	0.204267	+	0.0307884i
$566$	−18.8087	+	23.5853i	−0.790587	+	0.991364i
$567$	18.8934	−	14.3042i	0.793448	−	0.600722i
$568$	−22.5262	−	28.2470i	−0.945179	−	1.18522i
$569$	−10.0903	−	17.4770i	−0.423009	−	0.732673i	0.573223	−	0.819399i	$-0.305693\pi$
$569$	−10.0903	−	17.4770i	−0.423009	−	0.732673i	−0.996232	+	0.0867261i	$0.972360\pi$
$570$	−0.000292618	0	0.000506830i	−1.22564e−5	0	2.12288e-5i
$571$	−41.7536	+	6.29335i	−1.74734	+	0.263368i	−0.943474	−	0.331448i	$-0.892463\pi$
$571$	−41.7536	+	6.29335i	−1.74734	+	0.263368i	−0.803862	+	0.594816i	$0.797225\pi$
$572$	0.464542	−	0.431032i	0.0194235	−	0.0180223i
$573$	−0.580128	−	0.279375i	−0.0242352	−	0.0116710i
$574$	−11.0263	+	32.7927i	−0.460229	+	1.36874i
$575$	−14.2120	+	6.84413i	−0.592681	+	0.285420i
$576$	−9.28901	+	23.6680i	−0.387042	+	0.986167i
$577$	−1.92231	+	25.6514i	−0.0800267	+	1.06788i	0.802199	+	0.597056i	$0.203663\pi$
$577$	−1.92231	+	25.6514i	−0.0800267	+	1.06788i	−0.882226	+	0.470826i	$0.843956\pi$
$578$	55.3374	+	17.0693i	2.30173	+	0.709990i
$579$	0.0757305	+	1.01055i	0.00314725	+	0.0419972i
$580$	−0.132922	+	0.582368i	−0.00551927	+	0.0241815i
$581$	13.2546	−	0.658409i	0.549895	−	0.0273154i
$582$	−0.254723	−	1.11601i	−0.0105586	−	0.0462602i
$583$	1.45502	−	0.448813i	0.0602606	−	0.0185879i
$584$	7.56453	+	19.2741i	0.313022	+	0.797568i
$585$	1.88884	+	1.75259i	0.0780940	+	0.0724606i
$586$	21.8875	+	14.9226i	0.904165	+	0.616449i
$587$	−26.4750			−1.09274			−0.546370	−	0.837544i	$-0.683991\pi$
$587$	−26.4750			−1.09274			−0.546370	+	0.837544i	$0.683991\pi$
$588$	0.0406142	+	0.0565466i	0.00167490	+	0.00233194i
$589$	0.0198919			0.000819630
$590$	−2.68345	−	1.82954i	−0.110476	−	0.0753211i
$591$	−1.30385	−	1.20980i	−0.0536332	−	0.0497644i
$592$	7.53479	+	19.1983i	0.309678	+	0.789046i
$593$	−39.0655	+	12.0501i	−1.60423	+	0.494838i	−0.962314	−	0.271939i	$-0.912335\pi$
$593$	−39.0655	+	12.0501i	−1.60423	+	0.494838i	−0.641912	+	0.766778i	$0.721859\pi$
$594$	0.556045	+	2.43619i	0.0228148	+	0.0999581i
$595$	−10.2521	+	14.2528i	−0.420296	+	0.584309i
$596$	−0.293173	+	1.28447i	−0.0120088	+	0.0526141i
$597$	−0.0256917	−	0.342832i	−0.00105149	−	0.0140312i
$598$	−4.82113	−	1.48712i	−0.197151	−	0.0608129i
$599$	1.34189	−	17.9063i	0.0548282	−	0.731631i	−0.900268	−	0.435336i	$-0.856630\pi$
$599$	1.34189	−	17.9063i	0.0548282	−	0.731631i	0.955096	−	0.296295i	$-0.0957512\pi$
$600$	0.314954	−	0.802489i	0.0128579	−	0.0327615i
$601$	−13.7429	+	6.61823i	−0.560584	+	0.269963i	−0.692645	−	0.721278i	$-0.743555\pi$
$601$	−13.7429	+	6.61823i	−0.560584	+	0.269963i	0.132061	+	0.991242i	$0.457841\pi$
$602$	−2.00543	−	16.0333i	−0.0817354	−	0.653469i
$603$	43.5670	+	20.9808i	1.77419	+	0.854403i
$604$	0.416543	−	0.386495i	0.0169489	−	0.0157263i
$605$	−7.22328	+	1.08873i	−0.293668	+	0.0442633i
$606$	0.709750	−	1.22932i	0.0288316	−	0.0499378i
$607$	4.60911	+	7.98321i	0.187078	+	0.324028i	0.944275	−	0.329158i	$-0.106765\pi$
$607$	4.60911	+	7.98321i	0.187078	+	0.324028i	−0.757197	+	0.653187i	$0.773432\pi$
$608$	0.00364078	+	0.00456540i	0.000147653	+	0.000185151i
$609$	−0.364553	−	0.808437i	−0.0147724	−	0.0327595i
$610$	5.18196	−	6.49797i	0.209811	−	0.263095i
$611$	−8.37908	−	1.26294i	−0.338981	−	0.0510932i
$612$	−2.74010	+	1.86817i	−0.110762	+	0.0755163i
$613$	29.4438	−	20.0744i	1.18922	−	0.810799i	0.203485	−	0.979078i	$-0.434773\pi$
$613$	29.4438	−	20.0744i	1.18922	−	0.810799i	0.985739	+	0.168279i	$0.0538209\pi$
$614$	24.2527	+	3.65550i	0.978757	+	0.147524i
$615$	−0.356681	+	0.447264i	−0.0143828	+	0.0180354i
$616$	33.4401	−	6.75193i	1.34734	−	0.272043i
$617$	4.94382	+	6.19935i	0.199031	+	0.249576i	0.871324	−	0.490709i	$-0.163262\pi$
$617$	4.94382	+	6.19935i	0.199031	+	0.249576i	−0.672293	+	0.740285i	$0.734691\pi$
$618$	0.185456	+	0.321219i	0.00746013	+	0.0129213i
$619$	−18.0458	+	31.2562i	−0.725322	+	1.25629i	0.233519	+	0.972352i	$0.424976\pi$
$619$	−18.0458	+	31.2562i	−0.725322	+	1.25629i	−0.958841	+	0.283942i	$0.908358\pi$
$620$	0.337069	−	0.0508050i	0.0135370	−	0.00204038i
$621$	−1.12759	+	1.04625i	−0.0452487	+	0.0419846i
$622$	−19.1135	−	9.20458i	−0.766382	−	0.369070i
$623$	0.234238	+	0.362858i	0.00938456	+	0.0145376i
$624$	0.230505	−	0.111005i	0.00922758	−	0.00444377i
$625$	5.27798	−	13.4481i	0.211119	−	0.537923i
$626$	2.04175	−	27.2453i	0.0816049	−	1.08894i
$627$	0.00210639		0.000649735i	8.41210e−5		2.59479e-5i
$628$	−0.243700	−	3.25195i	−0.00972468	−	0.129767i
$629$	−9.58762	+	42.0061i	−0.382283	+	1.67489i
$630$	2.51366	+	8.94207i	0.100146	+	0.356261i
$631$	4.05523	+	17.7671i	0.161436	+	0.707298i	0.989243	+	0.146284i	$0.0467314\pi$
$631$	4.05523	+	17.7671i	0.161436	+	0.707298i	−0.827806	+	0.561014i	$0.810411\pi$
$632$	47.3218	−	14.5968i	1.88236	−	0.580631i
$633$	0.0911311	+	0.232198i	0.00362214	+	0.00922905i
$634$	−20.5106	−	19.0311i	−0.814581	−	0.755820i
$635$	−5.27546	−	3.59675i	−0.209350	−	0.142733i
$636$	−0.00343023			−0.000136017
$637$	−0.873649	+	6.94527i	−0.0346152	+	0.275182i
$638$	−29.0994			−1.15206
$639$	−30.6137	−	20.8721i	−1.21106	−	0.825686i
$640$	−6.27180	−	5.81938i	−0.247915	−	0.230031i
$641$	6.16512	+	15.7085i	0.243508	+	0.620447i	0.999414	−	0.0342325i	$-0.0108987\pi$
$641$	6.16512	+	15.7085i	0.243508	+	0.620447i	−0.755906	+	0.654680i	$0.772803\pi$
$642$	0.448243	−	0.138265i	0.0176907	−	0.00545687i
$643$	4.98246	+	21.8296i	0.196489	+	0.860875i	0.973006	+	0.230779i	$0.0741273\pi$
$643$	4.98246	+	21.8296i	0.196489	+	0.860875i	−0.776517	+	0.630096i	$0.783016\pi$
$644$	0.930244	+	1.05459i	0.0366568	+	0.0415567i
$645$	0.0594538	−	0.260484i	0.00234099	−	0.0102565i
$646$	−0.00565962	−	0.0755224i	−0.000222675	−	0.00297139i
$647$	−38.5157	−	11.8805i	−1.51421	−	0.467072i	−0.577267	−	0.816556i	$-0.695881\pi$
$647$	−38.5157	−	11.8805i	−1.51421	−	0.467072i	−0.936942	+	0.349484i	$0.886357\pi$
$648$	−1.95489	+	26.0863i	−0.0767955	+	1.02476i
$649$	−4.46919	+	11.3873i	−0.175431	+	0.446991i
$650$	5.22945	−	2.51837i	0.205116	−	0.0987785i
$651$	−0.353444	+	0.362199i	−0.0138525	+	0.0141957i
$652$	0.0701691	+	0.0337917i	0.00274804	+	0.00132338i
$653$	6.56810	−	6.09430i	0.257030	−	0.238489i	−0.541124	−	0.840943i	$-0.682001\pi$
$653$	6.56810	−	6.09430i	0.257030	−	0.238489i	0.798153	+	0.602454i	$0.205810\pi$
$654$	−0.660101	+	0.0994942i	−0.0258120	+	0.00389053i
$655$	−6.48535	+	11.2330i	−0.253404	+	0.438908i
$656$	−17.7180	−	30.6884i	−0.691771	−	1.19818i
$657$	13.2393	+	16.6015i	0.516513	+	0.647687i
$658$	−23.3956	−	19.6406i	−0.912057	−	0.765670i
$659$	−0.640024	+	0.802565i	−0.0249318	+	0.0312635i	−0.794141	−	0.607733i	$-0.792079\pi$
$659$	−0.640024	+	0.802565i	−0.0249318	+	0.0312635i	0.769209	+	0.638997i	$0.220650\pi$
$660$	0.0373524	+	0.00562997i	0.00145394	+	0.000219146i
$661$	−31.9930	+	21.8125i	−1.24438	+	0.848407i	−0.992841	−	0.119440i	$-0.961890\pi$
$661$	−31.9930	+	21.8125i	−1.24438	+	0.848407i	−0.251543	+	0.967846i	$0.580938\pi$
$662$	33.8886	−	23.1048i	1.31712	−	0.897995i
$663$	0.528518	+	0.0796613i	0.0205259	+	0.00309379i
$664$	−9.13393	+	11.4536i	−0.354465	+	0.444485i
$665$	0.0158928	+	0.00405074i	0.000616295	+	0.000157081i
$666$	14.2125	+	17.8219i	0.550724	+	0.690586i
$667$	−8.95639	−	15.5129i	−0.346793	−	0.600663i
$668$	0.662025	−	1.14666i	0.0256145	−	0.0443656i
$669$	0.121501	−	0.0183133i	0.00469748	−	0.000708032i
$670$	−13.8719	+	12.8712i	−0.535918	+	0.497259i
$671$	−28.2044	−	13.5825i	−1.08882	−	0.524348i
$672$	−0.147819	−	0.0148264i	−0.00570224	−	0.000571939i
$673$	1.99528	−	0.960875i	0.0769123	−	0.0370390i	−0.395032	−	0.918667i	$-0.629267\pi$
$673$	1.99528	−	0.960875i	0.0769123	−	0.0370390i	0.471944	+	0.881628i	$0.343552\pi$
$674$	−8.63495	+	22.0015i	−0.332606	+	0.847466i
$675$	0.132243	−	1.76466i	0.00509004	−	0.0679219i
$676$	−0.137162	−	0.0423088i	−0.00527545	−	0.00162726i
$677$	3.13931	+	41.8912i	0.120654	+	1.61001i	0.648870	+	0.760899i	$0.275242\pi$
$677$	3.13931	+	41.8912i	0.120654	+	1.61001i	−0.528216	+	0.849110i	$0.677139\pi$
$678$	0.119909	−	0.525355i	0.00460507	−	0.0201761i
$679$	−28.1768	+	15.3357i	−1.08132	+	0.588531i
$680$	−4.31268	−	18.8951i	−0.165384	−	0.724593i
$681$	1.51470	−	0.467224i	0.0580435	−	0.0179041i
$682$	6.06674	+	15.4578i	0.232308	+	0.591910i
$683$	−2.04720	−	1.89952i	−0.0783337	−	0.0726831i	0.640034	−	0.768346i	$-0.278920\pi$
$683$	−2.04720	−	1.89952i	−0.0783337	−	0.0726831i	−0.718368	+	0.695663i	$0.755111\pi$
$684$	0.00255966	+	0.00174515i	9.78711e−5	+	6.67274e-5i
$685$	−10.8793			−0.415676
$686$	−15.7471	+	19.7179i	−0.601227	+	0.752832i
$687$	1.41405			0.0539495
$688$	13.6744	+	9.32302i	0.521330	+	0.355437i
$689$	−0.252824	−	0.234586i	−0.00963181	−	0.00893702i
$690$	−0.109873	−	0.279951i	−0.00418278	−	0.0106576i
$691$	5.00965	−	1.54527i	0.190576	−	0.0587849i	−0.197998	−	0.980202i	$-0.563444\pi$
$691$	5.00965	−	1.54527i	0.190576	−	0.0587849i	0.388574	+	0.921417i	$0.372968\pi$
$692$	−0.166821	−	0.730889i	−0.00634157	−	0.0277842i
$693$	30.7295	−	16.7251i	1.16732	−	0.635333i
$694$	0.782111	−	3.42665i	0.0296885	−	0.130074i
$695$	−0.270336	−	3.60738i	−0.0102544	−	0.136836i
$696$	0.935470	+	0.288554i	0.0354589	+	0.0109376i
$697$	5.53232	−	73.8236i	0.209551	−	2.79627i
$698$	3.69583	−	9.41682i	0.139889	−	0.356432i
$699$	−0.682418	+	0.328635i	−0.0258114	+	0.0124301i
$700$	−1.60971	−	0.161455i	−0.0608413	−	0.00610243i
$701$	−16.1341	−	7.76979i	−0.609378	−	0.293461i	0.103631	−	0.994616i	$-0.466954\pi$
$701$	−16.1341	−	7.76979i	−0.609378	−	0.293461i	−0.713009	+	0.701155i	$0.752668\pi$
$702$	0.414909	−	0.384979i	0.0156597	−	0.0145301i
$703$	0.0397995	−	0.00599881i	0.00150107	−	0.000226249i
$704$	−18.7386	+	32.4562i	−0.706237	+	1.22324i
$705$	−0.252552	−	0.437433i	−0.00951165	−	0.0164747i
$706$	5.40780	+	6.78116i	0.203525	+	0.255212i
$707$	−38.5481	−	9.82513i	−1.44975	−	0.369512i
$708$	0.0171822	−	0.0215458i	0.000645746	−	0.000809740i
$709$	−47.4188	−	7.14723i	−1.78085	−	0.268420i	−0.825608	−	0.564244i	$-0.809168\pi$
$709$	−47.4188	−	7.14723i	−1.78085	−	0.268420i	−0.955242	+	0.295824i	$0.904406\pi$
$710$	11.9803	−	8.16804i	0.449613	−	0.306541i
$711$	41.9618	−	28.6091i	1.57369	−	1.07292i
$712$	−0.471439	−	0.0710580i	−0.0176679	−	0.00266301i
$713$	−6.37331	+	7.99187i	−0.238682	+	0.299298i
$714$	1.47570	+	1.23885i	0.0552268	+	0.0463627i
$715$	2.36802	+	2.96940i	0.0885590	+	0.111049i
$716$	−0.926172	−	1.60418i	−0.0346127	−	0.0599509i
$717$	−0.275445	+	0.477085i	−0.0102867	+	0.0178171i
$718$	2.66351	−	0.401460i	0.0994013	−	0.0149823i
$719$	−31.2420	+	28.9883i	−1.16513	+	1.08108i	−0.169708	+	0.985494i	$0.554282\pi$
$719$	−31.2420	+	28.9883i	−1.16513	+	1.08108i	−0.995421	+	0.0955869i	$0.969527\pi$
$720$	−8.57176	−	4.12794i	−0.319451	−	0.153839i
$721$	7.25960	−	7.43942i	0.270361	−	0.277058i
$722$	23.3241	−	11.2323i	0.868034	−	0.418023i
$723$	0.356239	−	0.907683i	0.0132487	−	0.0337571i
$724$	0.0834729	−	1.11387i	0.00310225	−	0.0413966i
$725$	19.6919	+	6.07414i	0.731338	+	0.225588i
$726$	0.0599083	+	0.799421i	0.00222341	+	0.0296693i
$727$	3.98035	−	17.4391i	0.147623	−	0.646779i	−0.845919	−	0.533312i	$-0.820947\pi$
$727$	3.98035	−	17.4391i	0.147623	−	0.646779i	0.993542	−	0.113467i	$-0.0361957\pi$
$728$	−5.11164	−	5.79492i	−0.189450	−	0.214774i
$729$	5.95045	+	26.0706i	0.220387	+	0.965579i
$730$	−7.94056	+	2.44934i	−0.293893	+	0.0906540i
$731$	12.6319	+	32.1855i	0.467206	+	1.19042i
$732$	0.0516965	+	0.0479673i	0.00191076	+	0.00177292i
$733$	1.64555	+	1.12192i	0.0607797	+	0.0414389i	0.593329	−	0.804960i	$-0.297813\pi$
$733$	1.64555	+	1.12192i	0.0607797	+	0.0414389i	−0.532549	+	0.846399i	$0.678766\pi$
$734$	−41.0098			−1.51370
$735$	−0.356144	+	0.217407i	−0.0131366	+	0.00801916i
$736$	−3.00072			−0.110608
$737$	58.8910	+	40.1512i	2.16928	+	1.47899i
$738$	−28.7110	−	26.6399i	−1.05687	−	0.980628i
$739$	8.98595	+	22.8958i	0.330553	+	0.842236i	0.995449	+	0.0952996i	$0.0303809\pi$
$739$	8.98595	+	22.8958i	0.330553	+	0.842236i	−0.664895	+	0.746937i	$0.731524\pi$
$740$	0.659084	−	0.203301i	0.0242284	−	0.00747348i
$741$	−0.000111103	0	0.000486772i	−4.08146e−6	0	1.78820e-5i
$742$	−0.336456	−	1.19691i	−0.0123517	−	0.0439398i
$743$	−11.7359	+	51.4183i	−0.430548	+	1.88635i	0.0315074	+	0.999504i	$0.489969\pi$
$743$	−11.7359	+	51.4183i	−0.430548	+	1.88635i	−0.462056	+	0.886851i	$0.652888\pi$
$744$	−0.0417479	−	0.557086i	−0.00153055	−	0.0204238i
$745$	−7.54541	−	2.32745i	−0.276443	−	0.0852712i
$746$	0.313391	−	4.18191i	0.0114740	−	0.153111i
$747$	−5.48881	+	13.9853i	−0.200825	+	0.511694i
$748$	−4.40419	+	2.12095i	−0.161033	+	0.0775496i
$749$	−7.12958	−	11.0444i	−0.260509	−	0.403554i
$750$	0.677590	+	0.326310i	0.0247421	+	0.0119152i
$751$	−29.7301	+	27.5855i	−1.08487	+	1.00661i	−0.0849183	+	0.996388i	$0.527063\pi$
$751$	−29.7301	+	27.5855i	−1.08487	+	1.00661i	−0.999948	+	0.0102207i	$0.996747\pi$
$752$	30.9382	−	4.66319i	1.12820	−	0.170049i
$753$	0.574597	−	0.995231i	0.0209395	−	0.0362682i
$754$	3.29559	+	5.70814i	0.120018	+	0.207878i
$755$	2.12334	+	2.66259i	0.0772764	+	0.0969015i
$756$	−0.154638	+	0.0312231i	−0.00562412	+	0.00113557i
$757$	19.2049	−	24.0822i	0.698014	−	0.875282i	−0.298860	−	0.954297i	$-0.596606\pi$
$757$	19.2049	−	24.0822i	0.698014	−	0.875282i	0.996873	+	0.0790154i	$0.0251776\pi$
$758$	−14.0082	−	2.11139i	−0.508800	−	0.0766892i
$759$	−0.935923	+	0.638101i	−0.0339718	+	0.0231616i
$760$	−0.0149588	+	0.0101988i	−0.000542613	+	0.000369948i
$761$	−8.16878	−	1.23125i	−0.296118	−	0.0446326i	−0.000697009	−	1.00000i	$-0.500222\pi$
$761$	−8.16878	−	1.23125i	−0.296118	−	0.0446326i	−0.295421	+	0.955367i	$0.595460\pi$
$762$	−0.436881	+	0.547831i	−0.0158265	+	0.0198458i
$763$	7.69030	+	17.0541i	0.278408	+	0.617399i
$764$	−0.831651	−	1.04286i	−0.0300881	−	0.0377292i
$765$	−9.93797	−	17.2131i	−0.359308	−	0.622340i
$766$	23.1960	−	40.1767i	0.838107	−	1.45164i
$767$	2.73988	−	0.412970i	0.0989313	−	0.0149115i
$768$	0.174056	−	0.161501i	0.00628071	−	0.00582765i
$769$	25.5274	+	12.2934i	0.920542	+	0.443310i	0.833265	−	0.552874i	$-0.186469\pi$
$769$	25.5274	+	12.2934i	0.920542	+	0.443310i	0.0872777	+	0.996184i	$0.472183\pi$
$770$	1.69927	+	13.5856i	0.0612374	+	0.489589i
$771$	−0.867037	+	0.417543i	−0.0312256	+	0.0150374i
$772$	−0.766958	+	1.95418i	−0.0276034	+	0.0703323i
$773$	0.161234	−	2.15152i	0.00579919	−	0.0773849i	−0.993553	−	0.113366i	$-0.963837\pi$
$773$	0.161234	−	2.15152i	0.00579919	−	0.0773849i	0.999352	+	0.0359814i	$0.0114557\pi$
$774$	17.4797	+	5.39178i	0.628296	+	0.193804i
$775$	−0.878803	−	11.7268i	−0.0315675	−	0.421240i
$776$	7.88003	−	34.5247i	0.282877	−	1.23936i
$777$	−0.597939	+	0.831272i	−0.0214509	+	0.0298217i
$778$	7.48674	+	32.8016i	0.268413	+	1.17599i
$779$	−0.0660832	+	0.0203840i	−0.00236768	+	0.000730331i
$780$	−0.00312589	−	0.00796464i	−0.000111925	−	0.000285180i
$781$	−40.0351	−	37.1471i	−1.43257	−	1.32923i
$782$	32.1557	+	21.9234i	1.14988	+	0.783978i
$783$	2.00953			0.0718149
$784$	−4.47627	−	25.4557i	−0.159867	−	0.909131i
$785$	19.5446			0.697575
$786$	1.17611	+	0.801858i	0.0419505	+	0.0286013i
$787$	−3.00840	−	2.79139i	−0.107238	−	0.0995022i	0.624732	−	0.780839i	$-0.285208\pi$
$787$	−3.00840	−	2.79139i	−0.107238	−	0.0995022i	−0.731970	+	0.681337i	$0.761399\pi$
$788$	−1.34614	−	3.42990i	−0.0479541	−	0.122185i
$789$	−0.535505	+	0.165181i	−0.0190645	+	0.00588062i
$790$	4.42254	+	19.3764i	0.157347	+	0.689382i
$791$	−15.0827	+	0.749218i	−0.536280	+	0.0266391i
$792$	−8.59393	+	37.6525i	−0.305372	+	1.33792i
$793$	0.529885	+	7.07083i	0.0188168	+	0.251092i
$794$	−13.1571	−	4.05841i	−0.466926	−	0.144028i
$795$	0.00153633	−	0.0205009i	5.44880e−5	−	0.000727092i
$796$	0.260192	−	0.662958i	0.00922226	−	0.0234979i
$797$	−2.76841	+	1.33320i	−0.0980621	+	0.0472242i	−0.482272	−	0.876022i	$-0.660188\pi$
$797$	−2.76841	+	1.33320i	−0.0980621	+	0.0472242i	0.384210	+	0.923246i	$0.374474\pi$
$798$	0.000573639	−	0.00170603i	2.03066e−5	−	6.03928e-5i
$799$	58.8913	+	28.3605i	2.08342	+	1.00332i
$800$	2.53058	−	2.34804i	0.0894697	−	0.0830157i
$801$	−0.483478	+	0.0728726i	−0.0170829	+	0.00257483i
$802$	16.7782	−	29.0606i	0.592457	−	1.02617i
$803$	15.6495	+	27.1057i	0.552258	+	0.956540i
$804$	−0.100113	−	0.125538i	−0.00353073	−	0.00442739i
$805$	−6.71945	+	5.08732i	−0.236829	+	0.179304i
$806$	2.34512	−	2.94069i	0.0826034	−	0.103581i
$807$	−1.09214	−	0.164613i	−0.0384450	−	0.00579465i
$808$	36.2828	−	24.7372i	1.27643	−	0.870252i
$809$	25.6405	−	17.4814i	0.901472	−	0.614613i	−0.0213783	−	0.999771i	$-0.506805\pi$
$809$	25.6405	−	17.4814i	0.901472	−	0.614613i	0.922851	+	0.385158i	$0.125853\pi$
$810$	−10.3813	−	1.56474i	−0.364763	−	0.0549792i
$811$	−21.3707	+	26.7980i	−0.750428	+	0.941007i	−0.999623	−	0.0274467i	$-0.991262\pi$
$811$	−21.3707	+	26.7980i	−0.750428	+	0.941007i	0.249196	+	0.968453i	$0.419834\pi$
$812$	0.0462296	−	1.83654i	0.00162234	−	0.0644500i
$813$	−0.688334	−	0.863144i	−0.0241409	−	0.0302718i
$814$	16.7999	+	29.0983i	0.588837	+	1.01990i
$815$	−0.233385	+	0.404234i	−0.00817511	+	0.0141597i
$816$	−1.95146	+	0.294135i	−0.0683147	+	0.0102968i
$817$	0.0236766	−	0.0219687i	0.000828339	−	0.000768587i
$818$	12.7228	+	6.12698i	0.444842	+	0.214225i
$819$	−6.76098	−	4.13372i	−0.236248	−	0.144444i
$820$	−1.06772	+	0.514188i	−0.0372865	+	0.0179562i
$821$	4.06677	−	10.3620i	0.141931	−	0.361635i	−0.842178	−	0.539200i	$-0.818727\pi$
$821$	4.06677	−	10.3620i	0.141931	−	0.361635i	0.984109	+	0.177565i	$0.0568219\pi$
$822$	−0.0892225	+	1.19059i	−0.00311199	+	0.0415266i
$823$	−26.6525	−	8.22120i	−0.929047	−	0.286573i	−0.206940	−	0.978354i	$-0.566350\pi$
$823$	−26.6525	−	8.22120i	−0.929047	−	0.286573i	−0.722108	+	0.691781i	$0.756827\pi$
$824$	0.857485	+	11.4423i	0.0298719	+	0.398613i
$825$	0.289979	−	1.27048i	0.0100958	−	0.0442324i
$826$	9.20328	+	3.88204i	0.320223	+	0.135073i
$827$	0.787638	+	3.45087i	0.0273889	+	0.119998i	0.986774	−	0.162100i	$-0.0518267\pi$
$827$	0.787638	+	3.45087i	0.0273889	+	0.119998i	−0.959385	+	0.282098i	$0.908970\pi$
$828$	−1.52125	+	0.469243i	−0.0528671	+	0.0163073i
$829$	6.80614	+	17.3418i	0.236387	+	0.602304i	0.999008	−	0.0445421i	$-0.0141829\pi$
$829$	6.80614	+	17.3418i	0.236387	+	0.602304i	−0.762621	+	0.646846i	$0.776088\pi$
$830$	−4.30990	−	3.99900i	−0.149599	−	0.138807i
$831$	1.00942	+	0.688212i	0.0350164	+	0.0238738i
$832$	8.48878			0.294296
$833$	22.2310	−	49.2077i	0.770259	−	1.70494i
$834$	−0.396996			−0.0137469
$835$	6.55656	+	4.47019i	0.226899	+	0.154697i
$836$	0.00334740	+	0.00310593i	0.000115772	+	0.000107421i
$837$	−0.418954	−	1.06748i	−0.0144812	−	0.0368974i
$838$	8.65151	−	2.66864i	0.298861	−	0.0921866i
$839$	−3.13941	−	13.7546i	−0.108384	−	0.474863i	−0.999766	−	0.0216102i	$-0.993121\pi$
$839$	−3.13941	−	13.7546i	−0.108384	−	0.474863i	0.891382	−	0.453253i	$-0.149736\pi$
$840$	0.0800893	−	0.453590i	0.00276334	−	0.0156503i
$841$	1.24581	−	5.45826i	0.0429590	−	0.188216i
$842$	−2.55393	−	34.0799i	−0.0880143	−	1.17447i
$843$	1.07657	+	0.332079i	0.0370791	+	0.0114374i
$844$	−0.0386155	+	0.515288i	−0.00132920	+	0.0177369i
$845$	0.314292	−	0.800803i	0.0108120	−	0.0275485i
$846$	31.1568	−	15.0043i	1.07119	−	0.515859i
$847$	21.1130	−	7.67891i	0.725450	−	0.263850i
$848$	1.14734	+	0.552530i	0.0393998	+	0.0189739i
$849$	1.12458	−	1.04346i	0.0385956	−	0.0358115i
$850$	−44.2726	+	6.67301i	−1.51854	+	0.228882i
$851$	−10.3415	+	17.9121i	−0.354504	+	0.614018i
$852$	0.0615169	+	0.106550i	0.00210754	+	0.00365036i
$853$	−28.7969	−	36.1102i	−0.985987	−	1.23639i	−0.971633	−	0.236492i	$-0.924002\pi$
$853$	−28.7969	−	36.1102i	−0.985987	−	1.23639i	−0.0143537	−	0.999897i	$-0.504569\pi$
$854$	−11.6665	+	22.7433i	−0.399220	+	0.778260i
$855$	−0.0115764	+	0.0145163i	−0.000395904	+	0.000496447i
$856$	14.3493	+	2.16281i	0.490450	+	0.0739235i
$857$	0.903896	−	0.616266i	0.0308765	−	0.0210512i	−0.547783	−	0.836620i	$-0.684528\pi$
$857$	0.903896	−	0.616266i	0.0308765	−	0.0210512i	0.578660	+	0.815569i	$0.303576\pi$
$858$	0.344382	−	0.234796i	0.0117570	−	0.00801580i
$859$	31.1271	+	4.69165i	1.06204	+	0.160077i	0.656749	−	0.754110i	$-0.271931\pi$
$859$	31.1271	+	4.69165i	1.06204	+	0.160077i	0.405293	+	0.914187i	$0.367169\pi$
$860$	0.345093	−	0.432733i	0.0117676	−	0.0147561i
$861$	0.803023	−	1.56545i	0.0273670	−	0.0533505i
$862$	−1.99850	−	2.50604i	−0.0680691	−	0.0853560i
$863$	−12.2997	−	21.3038i	−0.418688	−	0.725189i	0.577119	−	0.816660i	$-0.304177\pi$
$863$	−12.2997	−	21.3038i	−0.418688	−	0.725189i	−0.995808	+	0.0914703i	$0.970843\pi$
$864$	0.168317	−	0.291534i	0.00572626	−	0.00991817i
$865$	4.44291	−	0.669661i	0.151063	−	0.0227692i
$866$	25.2781	−	23.4547i	0.858986	−	0.797023i
$867$	−2.65334	−	1.27778i	−0.0901122	−	0.0433957i
$868$	−0.985221	+	0.358331i	−0.0334406	+	0.0121625i
$869$	67.4456	−	32.4801i	2.28794	−	1.10181i
$870$	−0.143538	+	0.365730i	−0.00486641	+	0.0123994i
$871$	1.20647	−	16.0993i	0.0408798	−	0.545503i
$872$	−19.7339	−	6.08709i	−0.668273	−	0.206135i
$873$	−2.71396	−	36.2153i	−0.0918537	−	1.22570i
$874$	0.00808981	−	0.0354438i	0.000273642	−	0.00119890i
$875$	3.66469	−	20.7551i	0.123889	−	0.701652i
$876$	−0.0156899	−	0.0687419i	−0.000530112	−	0.00232257i
$877$	−12.7752	+	3.94063i	−0.431388	+	0.133066i	−0.502842	−	0.864378i	$-0.667712\pi$
$877$	−12.7752	+	3.94063i	−0.431388	+	0.133066i	0.0714540	+	0.997444i	$0.477236\pi$
$878$	2.59217	+	6.60474i	0.0874814	+	0.222899i
$879$	−0.987538	−	0.916301i	−0.0333088	−	0.0309061i
$880$	−11.5867	−	7.89970i	−0.390589	−	0.266299i
$881$	−17.2871			−0.582417			−0.291208	−	0.956660i	$-0.594057\pi$
$881$	−17.2871			−0.582417			−0.291208	+	0.956660i	$0.594057\pi$
$882$	−13.0208	−	25.4272i	−0.438432	−	0.856177i
$883$	−30.6020			−1.02984			−0.514919	−	0.857239i	$-0.672178\pi$
$883$	−30.6020			−1.02984			−0.514919	+	0.857239i	$0.672178\pi$
$884$	0.914832	+	0.623722i	0.0307691	+	0.0209780i
$885$	0.121074	+	0.112340i	0.00406985	+	0.00377627i
$886$	−12.5116	−	31.8790i	−0.420336	−	1.07100i
$887$	3.03057	−	0.934807i	0.101757	−	0.0313877i	−0.243459	−	0.969911i	$-0.578282\pi$
$887$	3.03057	−	0.934807i	0.101757	−	0.0313877i	0.345215	+	0.938524i	$0.387806\pi$
$888$	−0.251530	−	1.10202i	−0.00844079	−	0.0369815i
$889$	18.0930	+	7.63180i	0.606819	+	0.255963i
$890$	0.0425773	−	0.186543i	0.00142719	−	0.00625295i
$891$	2.95509	+	39.4329i	0.0989991	+	1.32105i
$892$	0.243230	+	0.0750266i	0.00814396	+	0.00251208i
$893$	0.00456302	−	0.0608892i	0.000152696	−	0.00203758i
$894$	−0.316590	+	0.806657i	−0.0105883	+	0.0269786i
$895$	10.0022	−	4.81683i	0.334338	−	0.161009i
$896$	22.4495	+	13.7258i	0.749985	+	0.458547i
$897$	0.231166	+	0.111323i	0.00771839	+	0.00371698i
$898$	−18.4929	+	17.1589i	−0.617117	+	0.572601i
$899$	13.2049	−	1.99032i	0.440409	−	0.0663810i
$900$	0.915730	−	1.58609i	0.0305243	−	0.0528697i
$901$	1.33021	+	2.30399i	0.0443157	+	0.0767570i
$902$	−35.9947	−	45.1359i	−1.19849	−	1.50286i
$903$	−0.0206778	+	0.821457i	−0.000688113	+	0.0273364i
$904$	10.3937	−	13.0333i	0.345689	−	0.433480i
$905$	6.61970	+	0.997760i	0.220046	+	0.0331667i
$906$	0.308799	−	0.210535i	0.0102591	−	0.00699457i
$907$	15.1822	−	10.3511i	0.504118	−	0.343702i	−0.284408	−	0.958703i	$-0.591797\pi$
$907$	15.1822	−	10.3511i	0.504118	−	0.343702i	0.788526	+	0.615001i	$0.210845\pi$
$908$	3.24701	+	0.489408i	0.107756	+	0.0162416i
$909$	28.0787	−	35.2095i	0.931310	−	1.16783i
$910$	2.47249	−	1.87193i	0.0819622	−	0.0620539i
$911$	1.54638	+	1.93909i	0.0512337	+	0.0642450i	0.806788	−	0.590841i	$-0.201204\pi$
$911$	1.54638	+	1.93909i	0.0512337	+	0.0642450i	−0.755554	+	0.655086i	$0.772632\pi$
$912$	0.000921770		0.00159655i	3.05229e−5		5.28672e-5i
$913$	−11.0725	+	19.1781i	−0.366446	+	0.634703i
$914$	−39.4510	+	5.94629i	−1.30492	+	0.196686i
$915$	−0.309833	+	0.287483i	−0.0102428	+	0.00950389i
$916$	2.63921	+	1.27098i	0.0872019	+	0.0419942i
$917$	12.7136	−	37.8110i	0.419842	−	1.24863i
$918$	−3.93364	+	1.89434i	−0.129829	+	0.0625225i
$919$	−1.04972	+	2.67464i	−0.0346270	+	0.0882282i	−0.947141	−	0.320816i	$-0.896043\pi$
$919$	−1.04972	+	2.67464i	−0.0346270	+	0.0882282i	0.912514	+	0.409045i	$0.134138\pi$
$920$	0.695260	−	9.27760i	0.0229220	−	0.305873i
$921$	−1.19187	−	0.367643i	−0.0392735	−	0.0121143i
$922$	−2.30010	−	30.6927i	−0.0757497	−	1.01081i
$923$	−2.75268	+	12.0603i	−0.0906055	+	0.396969i
$924$	−0.116031	+	0.00576372i	−0.00381715	+	0.000189612i
$925$	−5.29477	−	23.1979i	−0.174091	−	0.762742i
$926$	−21.9809	+	6.78021i	−0.722337	+	0.222812i
$927$	4.29913	+	10.9540i	0.141202	+	0.359777i
$928$	2.87368	+	2.66639i	0.0943332	+	0.0875284i
$929$	24.5206	+	16.7179i	0.804495	+	0.548496i	0.894302	−	0.447464i	$-0.147673\pi$
$929$	24.5206	+	16.7179i	0.804495	+	0.548496i	−0.0898069	+	0.995959i	$0.528625\pi$
$930$	0.224204			0.00735192
$931$	−0.0503767	−	0.00253778i	−0.00165103	−	8.31724e-5i
$932$	−1.56906			−0.0513961
$933$	0.891383	+	0.607735i	0.0291826	+	0.0198963i
$934$	−9.70146	−	9.00164i	−0.317441	−	0.294543i
$935$	−10.7034	−	27.2718i	−0.350038	−	0.891883i
$936$	8.35918	−	2.57847i	0.273228	−	0.0842798i
$937$	−2.76806	−	12.1276i	−0.0904285	−	0.396193i	0.909376	−	0.415975i	$-0.136560\pi$
$937$	−2.76806	−	12.1276i	−0.0904285	−	0.396193i	−0.999804	+	0.0197825i	$0.993703\pi$
$938$	33.9843	−	47.2459i	1.10963	−	1.54263i
$939$	−0.309177	+	1.35459i	−0.0100896	+	0.0442055i
$940$	−0.0781941	−	1.04343i	−0.00255041	−	0.0340328i
$941$	−26.7501	−	8.25133i	−0.872030	−	0.268986i	−0.173732	−	0.984793i	$-0.555583\pi$
$941$	−26.7501	−	8.25133i	−0.872030	−	0.268986i	−0.698298	+	0.715807i	$0.746059\pi$
$942$	0.160288	−	2.13889i	0.00522245	−	0.0696888i
$943$	12.9833	−	33.0809i	0.422795	−	1.07726i
$944$	−9.21761	+	4.43897i	−0.300008	+	0.144476i
$945$	−0.117347	−	0.938184i	−0.00381731	−	0.0305191i
$946$	24.2927	+	11.6988i	0.789824	+	0.380359i
$947$	−41.1249	+	38.1584i	−1.33638	+	1.23998i	−0.388463	+	0.921464i	$0.626994\pi$
$947$	−41.1249	+	38.1584i	−1.33638	+	1.23998i	−0.947918	+	0.318516i	$0.896816\pi$
$948$	−0.166757	+	0.0251346i	−0.00541602	+	0.000816334i
$949$	3.54470	−	6.13959i	0.115066	−	0.199300i
$950$	0.0209121	+	0.0362209i	0.000678479	+	0.00117516i
$951$	0.887159	+	1.11246i	0.0287681	+	0.0360741i
$952$	24.5025	+	54.3369i	0.794130	+	1.76107i
$953$	20.9722	−	26.2984i	0.679357	−	0.851887i	−0.315937	−	0.948780i	$-0.602319\pi$
$953$	20.9722	−	26.2984i	0.679357	−	0.851887i	0.995295	+	0.0968928i	$0.0308904\pi$
$954$	1.39179	+	0.209779i	0.0450608	+	0.00679183i
$955$	6.60516	−	4.50332i	0.213738	−	0.145724i
$956$	−0.942906	+	0.642862i	−0.0304958	+	0.0207917i
$957$	1.46331	+	0.220558i	0.0473019	+	0.00712962i
$958$	−22.1138	+	27.7298i	−0.714463	+	0.895908i
$959$	32.7972	−	6.62213i	1.05908	−	0.213840i
$960$	0.315487	+	0.395608i	0.0101823	+	0.0127682i
$961$	11.6897	+	20.2472i	0.377088	+	0.653135i
$962$	3.80528	−	6.59093i	0.122687	−	0.212500i
$963$	14.7158	−	2.21805i	0.474209	−	0.0714755i
$964$	1.48073	−	1.37392i	0.0476911	−	0.0442509i
$965$	−11.3357	−	5.45899i	−0.364910	−	0.175731i
$966$	0.501632	+	0.777076i	0.0161397	+	0.0250020i
$967$	40.1446	−	19.3326i	1.29096	−	0.621695i	0.342779	−	0.939416i	$-0.388632\pi$
$967$	40.1446	−	19.3326i	1.29096	−	0.621695i	0.948184	+	0.317721i	$0.102918\pi$
$968$	−9.06046	+	23.0857i	−0.291214	+	0.742001i
$969$	−0.000287817		0.00384064i	−9.24600e−6		0.000123379i
$970$	13.5808	+	4.18911i	0.436052	+	0.134504i
$971$	2.58082	+	34.4386i	0.0828224	+	1.10519i	0.871505	+	0.490387i	$0.163145\pi$
$971$	2.58082	+	34.4386i	0.0828224	+	1.10519i	−0.788682	+	0.614801i	$0.789236\pi$
$972$	0.0596276	−	0.261246i	0.00191256	−	0.00837946i
$973$	3.01075	+	10.7104i	0.0965202	+	0.343360i
$974$	−5.80921	−	25.4518i	−0.186139	−	0.815529i
$975$	−0.282058	+	0.0870032i	−0.00903307	+	0.00278633i
$976$	−9.56498	−	24.3712i	−0.306167	−	0.780102i
$977$	9.44257	+	8.76142i	0.302095	+	0.280303i	0.816624	−	0.577170i	$-0.195843\pi$
$977$	9.44257	+	8.76142i	0.302095	+	0.280303i	−0.514530	+	0.857473i	$0.672033\pi$
$978$	0.0423240	+	0.0288560i	0.00135337	+	0.000922714i
$979$	−0.720693			−0.0230334
$980$	−0.860120	+	0.0856623i	−0.0274755	+	0.00273638i
$981$	−21.1787			−0.676185
$982$	−11.4588	−	7.81250i	−0.365666	−	0.249307i
$983$	−25.3546	−	23.5256i	−0.808686	−	0.750351i	0.163001	−	0.986626i	$-0.447883\pi$
$983$	−25.3546	−	23.5256i	−0.808686	−	0.750351i	−0.971686	+	0.236275i	$0.924073\pi$
$984$	0.709559	+	1.80793i	0.0226199	+	0.0576346i
$985$	21.1019	−	6.50906i	0.672361	−	0.207396i
$986$	−11.3136	−	49.5682i	−0.360299	−	1.57857i
$987$	1.02762	+	1.16498i	0.0327094	+	0.0370817i
$988$	0.000230156	−	0.00100838i	7.32223e−6	−	3.20808e-5i
$989$	1.24034	+	16.5512i	0.0394405	+	0.526296i
$990$	−14.8111	−	4.56863i	−0.470729	−	0.145201i
$991$	1.80002	−	24.0196i	0.0571794	−	0.763007i	−0.892752	−	0.450548i	$-0.851229\pi$
$991$	1.80002	−	24.0196i	0.0571794	−	0.763007i	0.949931	−	0.312458i	$-0.101152\pi$
$992$	0.817288	−	2.08241i	0.0259489	−	0.0661167i
$993$	−1.87925	+	0.905001i	−0.0596363	+	0.0287193i
$994$	−31.1446	+	31.9161i	−0.987848	+	1.01232i
$995$	3.84567	+	1.85198i	0.121916	+	0.0587116i
$996$	0.0365703	−	0.0339323i	0.00115877	−	0.00107519i
$997$	10.7760	−	1.62422i	0.341280	−	0.0514396i	0.0238335	−	0.999716i	$-0.492413\pi$
$997$	10.7760	−	1.62422i	0.341280	−	0.0514396i	0.317446	+	0.948276i	$0.397175\pi$
$998$	−4.36622	+	7.56251i	−0.138210	+	0.239387i
$999$	−1.16016	−	2.00946i	−0.0367058	−	0.0635764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.53.20	✓	348
49.37	even	21	inner	637.2.bl.b.625.20	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.53.20	✓	348	1.1	even	1	trivial
637.2.bl.b.625.20	yes	348	49.37	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12577 + 0.767535i) q^{2} +(-0.0507932 - 0.0471292i) q^{3} +(-0.0524406 - 0.133616i) q^{4} +(0.822051 - 0.253569i) q^{5} +(-0.0210080 - 0.0920421i) q^{6} +(-2.32385 + 1.26480i) q^{7} +(0.649898 - 2.84739i) q^{8} +(-0.223831 - 2.98682i) q^{9} +O(q^{10})\)	\(q+(1.12577 + 0.767535i) q^{2} +(-0.0507932 - 0.0471292i) q^{3} +(-0.0524406 - 0.133616i) q^{4} +(0.822051 - 0.253569i) q^{5} +(-0.0210080 - 0.0920421i) q^{6} +(-2.32385 + 1.26480i) q^{7} +(0.649898 - 2.84739i) q^{8} +(-0.223831 - 2.98682i) q^{9} +(1.12006 + 0.345493i) q^{10} +(0.329926 - 4.40256i) q^{11} +(-0.00363361 + 0.00925829i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(-3.58689 - 0.359769i) q^{14} +(-0.0537052 - 0.0258630i) q^{15} +(2.70666 - 2.51141i) q^{16} +(7.62761 - 1.14968i) q^{17} +(2.04051 - 3.53427i) q^{18} +(-0.00360290 - 0.00624041i) q^{19} +(-0.0769898 - 0.0965422i) q^{20} +(0.177645 + 0.0452781i) q^{21} +(3.75054 - 4.70302i) q^{22} +(3.66154 + 0.551889i) q^{23} +(-0.167206 + 0.113999i) q^{24} +(-3.51972 + 2.39971i) q^{25} +(-1.34730 - 0.203073i) q^{26} +(-0.259003 + 0.324779i) q^{27} +(0.290862 + 0.244178i) q^{28} +(-3.01613 - 3.78211i) q^{29} +(-0.0406087 - 0.0703364i) q^{30} +(-1.38027 + 2.39069i) q^{31} +(-0.801319 + 0.120779i) q^{32} +(-0.224247 + 0.208071i) q^{33} +(9.46933 + 4.56019i) q^{34} +(-1.58961 + 1.62899i) q^{35} +(-0.387351 + 0.186538i) q^{36} +(-2.04066 + 5.19953i) q^{37} +(0.000733704 - 0.00979060i) q^{38} +(0.0662117 + 0.0204236i) q^{39} +(-0.187761 - 2.50549i) q^{40} +(2.13558 - 9.35658i) q^{41} +(0.165234 + 0.187321i) q^{42} +(0.997409 + 4.36993i) q^{43} +(-0.605555 + 0.186789i) q^{44} +(-0.941368 - 2.39857i) q^{45} +(3.69845 + 3.43166i) q^{46} +(7.00132 + 4.77342i) q^{47} -0.255841 q^{48} +(3.80057 - 5.87841i) q^{49} -5.80425 q^{50} +(-0.441615 - 0.301088i) q^{51} +(0.105221 + 0.0976311i) q^{52} +(0.126003 + 0.321051i) q^{53} +(-0.540856 + 0.166832i) q^{54} +(-0.845137 - 3.70279i) q^{55} +(2.09111 + 7.43890i) q^{56} +(-0.000111103 + 0.000486772i) q^{57} +(-0.492560 - 6.57276i) q^{58} +(-2.64773 - 0.816715i) q^{59} +(-0.000639397 + 0.00853216i) q^{60} +(2.59051 - 6.60050i) q^{61} +(-3.38880 + 1.63196i) q^{62} +(4.29788 + 6.65783i) q^{63} +(-7.64813 - 3.68315i) q^{64} +(-0.630623 + 0.585133i) q^{65} +(-0.412152 + 0.0621219i) q^{66} +(-8.07221 + 13.9815i) q^{67} +(-0.553612 - 0.958884i) q^{68} +(-0.159972 - 0.200598i) q^{69} +(-3.03984 + 0.613777i) q^{70} +(7.71283 - 9.67159i) q^{71} +(-8.65012 - 1.30380i) q^{72} +(-5.85753 + 3.99360i) q^{73} +(-6.28813 + 4.28718i) q^{74} +(0.291874 + 0.0439930i) q^{75} +(-0.000644883 + 0.000808657i) q^{76} +(4.80165 + 10.6482i) q^{77} +(0.0588631 + 0.0738120i) q^{78} +(8.47799 + 14.6843i) q^{79} +(1.58820 - 2.75084i) q^{80} +(-8.85677 + 1.33494i) q^{81} +(9.58567 - 8.89420i) q^{82} +(-4.51922 - 2.17634i) q^{83} +(-0.00326590 - 0.0261107i) q^{84} +(5.97877 - 2.87922i) q^{85} +(-2.23123 + 5.68507i) q^{86} +(-0.0250488 + 0.334253i) q^{87} +(-12.3214 - 3.80064i) q^{88} +(-0.0121990 - 0.162784i) q^{89} +(0.781222 - 3.42276i) q^{90} +(1.54494 - 2.14783i) q^{91} +(-0.118272 - 0.518183i) q^{92} +(0.182780 - 0.0563801i) q^{93} +(4.21809 + 10.7475i) q^{94} +(-0.00454415 - 0.00421635i) q^{95} +(0.0463938 + 0.0316308i) q^{96} +12.1250 q^{97} +(8.79044 - 3.70065i) q^{98} -13.2235 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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