LMFDB - Embedded newform 637.2.bl.b.625.18

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			625.18
Character	$\chi$	$=$	637.625
Dual form			637.2.bl.b.53.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.445939 - 0.304036i) q^{2} +(0.759470 - 0.704685i) q^{3} +(-0.624259 + 1.59058i) q^{4} +(-1.39712 - 0.430954i) q^{5} +(0.124428 - 0.545153i) q^{6} +(-2.52342 + 0.795220i) q^{7} +(0.445412 + 1.95148i) q^{8} +(-0.143977 + 1.92124i) q^{9} +O(q^{10})$	\(q+(0.445939 - 0.304036i) q^{2} +(0.759470 - 0.704685i) q^{3} +(-0.624259 + 1.59058i) q^{4} +(-1.39712 - 0.430954i) q^{5} +(0.124428 - 0.545153i) q^{6} +(-2.52342 + 0.795220i) q^{7} +(0.445412 + 1.95148i) q^{8} +(-0.143977 + 1.92124i) q^{9} +(-0.754055 + 0.232595i) q^{10} +(-0.221253 - 2.95241i) q^{11} +(0.646756 + 1.64791i) q^{12} +(-0.900969 - 0.433884i) q^{13} +(-0.883513 + 1.12183i) q^{14} +(-1.36476 + 0.657233i) q^{15} +(-1.71319 - 1.58960i) q^{16} +(-1.60960 - 0.242608i) q^{17} +(0.519920 + 0.900528i) q^{18} +(-3.14438 + 5.44623i) q^{19} +(1.55763 - 1.95321i) q^{20} +(-1.35608 + 2.38216i) q^{21} +(-0.996305 - 1.24933i) q^{22} +(-4.90272 + 0.738966i) q^{23} +(1.71346 + 1.16821i) q^{24} +(-2.36497 - 1.61241i) q^{25} +(-0.533693 + 0.0804413i) q^{26} +(3.18240 + 3.99060i) q^{27} +(0.310399 - 4.51013i) q^{28} +(-2.76636 + 3.46890i) q^{29} +(-0.408776 + 0.708021i) q^{30} +(1.69569 + 2.93702i) q^{31} +(-5.20589 - 0.784662i) q^{32} +(-2.24856 - 2.08636i) q^{33} +(-0.791544 + 0.381187i) q^{34} +(3.86822 - 0.0235405i) q^{35} +(-2.96601 - 1.42836i) q^{36} +(3.65447 + 9.31143i) q^{37} +(0.253647 + 3.38469i) q^{38} +(-0.990011 + 0.305378i) q^{39} +(0.218704 - 2.91840i) q^{40} +(-1.53474 - 6.72415i) q^{41} +(0.119534 + 1.47459i) q^{42} +(-1.07998 + 4.73170i) q^{43} +(4.83418 + 1.49115i) q^{44} +(1.02912 - 2.62215i) q^{45} +(-1.96164 + 1.82013i) q^{46} +(7.45360 - 5.08178i) q^{47} -2.42129 q^{48} +(5.73525 - 4.01334i) q^{49} -1.54486 q^{50} +(-1.39340 + 0.950007i) q^{51} +(1.25257 - 1.16221i) q^{52} +(-1.40641 + 3.58348i) q^{53} +(2.63244 + 0.812001i) q^{54} +(-0.963239 + 4.22022i) q^{55} +(-2.67582 - 4.57019i) q^{56} +(1.44981 + 6.35205i) q^{57} +(-0.178955 + 2.38799i) q^{58} +(14.4429 - 4.45505i) q^{59} +(-0.193423 - 2.58105i) q^{60} +(-0.255188 - 0.650210i) q^{61} +(1.64913 + 0.794180i) q^{62} +(-1.16449 - 4.96257i) q^{63} +(1.65116 - 0.795159i) q^{64} +(1.07178 + 0.994464i) q^{65} +(-1.63705 - 0.246745i) q^{66} +(-6.37686 - 11.0450i) q^{67} +(1.39069 - 2.40875i) q^{68} +(-3.20273 + 4.01609i) q^{69} +(1.71783 - 1.18657i) q^{70} +(-6.47848 - 8.12376i) q^{71} +(-3.81338 + 0.574775i) q^{72} +(6.50680 + 4.43626i) q^{73} +(4.46068 + 3.04124i) q^{74} +(-2.93237 + 0.441983i) q^{75} +(-6.69978 - 8.40126i) q^{76} +(2.90613 + 7.27422i) q^{77} +(-0.348638 + 0.437179i) q^{78} +(-2.81233 + 4.87109i) q^{79} +(1.70848 + 2.95917i) q^{80} +(-0.486256 - 0.0732913i) q^{81} +(-2.72879 - 2.53194i) q^{82} +(10.7997 - 5.20086i) q^{83} +(-2.94248 - 3.64404i) q^{84} +(2.14425 + 1.03262i) q^{85} +(0.957002 + 2.43840i) q^{86} +(0.343519 + 4.58394i) q^{87} +(5.66302 - 1.74681i) q^{88} +(-0.788139 + 10.5170i) q^{89} +(-0.338304 - 1.48221i) q^{90} +(2.61855 + 0.378401i) q^{91} +(1.88517 - 8.25949i) q^{92} +(3.35750 + 1.03565i) q^{93} +(1.77880 - 4.53232i) q^{94} +(6.74016 - 6.25395i) q^{95} +(-4.50666 + 3.07259i) q^{96} -14.6532 q^{97} +(1.33737 - 3.53343i) q^{98} +5.70414 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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

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 $

$2$	0.445939	−	0.304036i	0.315326	−	0.214986i	−0.395306	−	0.918550i	$-0.629361\pi$
$2$	0.445939	−	0.304036i	0.315326	−	0.214986i	0.710632	+	0.703564i	$0.248409\pi$
$3$	0.759470	−	0.704685i	0.438480	−	0.406850i	−0.429800	−	0.902924i	$-0.641416\pi$
$3$	0.759470	−	0.704685i	0.438480	−	0.406850i	0.868280	+	0.496074i	$0.165225\pi$
$4$	−0.624259	+	1.59058i	−0.312129	+	0.795292i
$5$	−1.39712	−	0.430954i	−0.624811	−	0.192729i	−0.0338475	−	0.999427i	$-0.510776\pi$
$5$	−1.39712	−	0.430954i	−0.624811	−	0.192729i	−0.590963	+	0.806698i	$0.701252\pi$
$6$	0.124428	−	0.545153i	0.0507973	−	0.222558i
$7$	−2.52342	+	0.795220i	−0.953761	+	0.300565i
$7$	−2.52342	+	0.795220i	−0.953761	+	0.300565i
$8$	0.445412	+	1.95148i	0.157477	+	0.689952i
$9$	−0.143977	+	1.92124i	−0.0479922	+	0.640412i
$10$	−0.754055	+	0.232595i	−0.238453	+	0.0735531i
$11$	−0.221253	−	2.95241i	−0.0667102	−	0.890186i	−0.925716	−	0.378220i	$-0.876536\pi$
$11$	−0.221253	−	2.95241i	−0.0667102	−	0.890186i	0.859006	−	0.511966i	$-0.171083\pi$
$12$	0.646756	+	1.64791i	0.186702	+	0.475710i
$13$	−0.900969	−	0.433884i	−0.249884	−	0.120338i
$13$	−0.900969	−	0.433884i	−0.249884	−	0.120338i
$14$	−0.883513	+	1.12183i	−0.236129	+	0.299821i
$15$	−1.36476	+	0.657233i	−0.352379	+	0.169697i
$16$	−1.71319	−	1.58960i	−0.428297	−	0.397401i
$17$	−1.60960	−	0.242608i	−0.390385	−	0.0588411i	−0.0490828	−	0.998795i	$-0.515630\pi$
$17$	−1.60960	−	0.242608i	−0.390385	−	0.0588411i	−0.341302	+	0.939954i	$0.610868\pi$
$18$	0.519920	+	0.900528i	0.122546	+	0.212256i
$19$	−3.14438	+	5.44623i	−0.721371	+	1.24945i	0.239080	+	0.971000i	$0.423154\pi$
$19$	−3.14438	+	5.44623i	−0.721371	+	1.24945i	−0.960450	+	0.278451i	$0.910179\pi$
$20$	1.55763	−	1.95321i	0.348297	−	0.436751i
$21$	−1.35608	+	2.38216i	−0.295921	+	0.519830i
$22$	−0.996305	−	1.24933i	−0.212413	−	0.266357i
$23$	−4.90272	+	0.738966i	−1.02229	+	0.154085i	−0.638729	−	0.769432i	$-0.720539\pi$
$23$	−4.90272	+	0.738966i	−1.02229	+	0.154085i	−0.383558	+	0.923517i	$0.625301\pi$
$24$	1.71346	+	1.16821i	0.349758	+	0.238461i
$25$	−2.36497	−	1.61241i	−0.472994	−	0.322482i
$26$	−0.533693	+	0.0804413i	−0.104666	+	0.0157758i
$27$	3.18240	+	3.99060i	0.612453	+	0.767992i
$28$	0.310399	−	4.51013i	0.0586599	−	0.852334i
$29$	−2.76636	+	3.46890i	−0.513700	+	0.644159i	−0.969258	−	0.246047i	$-0.920868\pi$
$29$	−2.76636	+	3.46890i	−0.513700	+	0.644159i	0.455558	+	0.890206i	$0.349440\pi$
$30$	−0.408776	+	0.708021i	−0.0746320	+	0.129266i
$31$	1.69569	+	2.93702i	0.304555	+	0.527504i	0.977162	−	0.212495i	$-0.0681590\pi$
$31$	1.69569	+	2.93702i	0.304555	+	0.527504i	−0.672607	+	0.740000i	$0.734826\pi$
$32$	−5.20589	−	0.784662i	−0.920280	−	0.138710i
$33$	−2.24856	−	2.08636i	−0.391424	−	0.363188i
$34$	−0.791544	+	0.381187i	−0.135749	+	0.0653731i
$35$	3.86822	−	0.0235405i	0.653848	−	0.00397907i
$36$	−2.96601	−	1.42836i	−0.494335	−	0.238059i
$37$	3.65447	+	9.31143i	0.600791	+	1.53079i	0.830204	+	0.557460i	$0.188224\pi$
$37$	3.65447	+	9.31143i	0.600791	+	1.53079i	−0.229413	+	0.973329i	$0.573681\pi$
$38$	0.253647	+	3.38469i	0.0411471	+	0.549069i
$39$	−0.990011	+	0.305378i	−0.158529	+	0.0488996i
$40$	0.218704	−	2.91840i	0.0345801	−	0.461440i
$41$	−1.53474	−	6.72415i	−0.239687	−	1.05014i	−0.941298	−	0.337577i	$-0.890393\pi$
$41$	−1.53474	−	6.72415i	−0.239687	−	1.05014i	0.701611	−	0.712560i	$-0.252464\pi$
$42$	0.119534	+	1.47459i	0.0184445	+	0.227535i
$43$	−1.07998	+	4.73170i	−0.164695	+	0.721578i	0.823365	+	0.567512i	$0.192094\pi$
$43$	−1.07998	+	4.73170i	−0.164695	+	0.721578i	−0.988061	+	0.154066i	$0.950763\pi$
$44$	4.83418	+	1.49115i	0.728780	+	0.224799i
$45$	1.02912	−	2.62215i	0.153412	−	0.390887i
$46$	−1.96164	+	1.82013i	−0.289228	+	0.268364i
$47$	7.45360	−	5.08178i	1.08722	−	0.741253i	0.119386	−	0.992848i	$-0.461907\pi$
$47$	7.45360	−	5.08178i	1.08722	−	0.741253i	0.967833	+	0.251595i	$0.0809550\pi$
$48$	−2.42129			−0.349482
$49$	5.73525	−	4.01334i	0.819322	−	0.573334i
$50$	−1.54486			−0.218477
$51$	−1.39340	+	0.950007i	−0.195116	+	0.133028i
$52$	1.25257	−	1.16221i	0.173700	−	0.161170i
$53$	−1.40641	+	3.58348i	−0.193186	+	0.492229i	−0.994342	−	0.106226i	$-0.966123\pi$
$53$	−1.40641	+	3.58348i	−0.193186	+	0.492229i	0.801156	+	0.598455i	$0.204219\pi$
$54$	2.63244	+	0.812001i	0.358230	+	0.110499i
$55$	−0.963239	+	4.22022i	−0.129883	+	0.569055i
$56$	−2.67582	−	4.57019i	−0.357571	−	0.610718i
$57$	1.44981	+	6.35205i	0.192033	+	0.841350i
$58$	−0.178955	+	2.38799i	−0.0234980	+	0.313559i
$59$	14.4429	−	4.45505i	1.88031	−	0.579998i	0.887417	−	0.460967i	$-0.152497\pi$
$59$	14.4429	−	4.45505i	1.88031	−	0.579998i	0.992891	−	0.119031i	$-0.0379787\pi$
$60$	−0.193423	−	2.58105i	−0.0249708	−	0.333212i
$61$	−0.255188	−	0.650210i	−0.0326735	−	0.0832508i	0.913606	−	0.406601i	$-0.133286\pi$
$61$	−0.255188	−	0.650210i	−0.0326735	−	0.0832508i	−0.946279	+	0.323350i	$0.895191\pi$
$62$	1.64913	+	0.794180i	0.209440	+	0.100861i
$63$	−1.16449	−	4.96257i	−0.146712	−	0.625225i
$64$	1.65116	−	0.795159i	0.206396	−	0.0993948i
$65$	1.07178	+	0.994464i	0.132938	+	0.123348i
$66$	−1.63705	−	0.246745i	−0.201506	−	0.0303722i
$67$	−6.37686	−	11.0450i	−0.779057	−	1.34937i	−0.932486	−	0.361207i	$-0.882365\pi$
$67$	−6.37686	−	11.0450i	−0.779057	−	1.34937i	0.153429	−	0.988160i	$-0.450968\pi$
$68$	1.39069	−	2.40875i	0.168646	−	0.292104i
$69$	−3.20273	+	4.01609i	−0.385563	+	0.483481i
$70$	1.71783	−	1.18657i	0.205320	−	0.141823i
$71$	−6.47848	−	8.12376i	−0.768854	−	0.964113i	0.231107	−	0.972928i	$-0.425765\pi$
$71$	−6.47848	−	8.12376i	−0.768854	−	0.964113i	−0.999961	+	0.00881562i	$0.997194\pi$
$72$	−3.81338	+	0.574775i	−0.449411	+	0.0677379i
$73$	6.50680	+	4.43626i	0.761564	+	0.519225i	0.880713	−	0.473651i	$-0.157064\pi$
$73$	6.50680	+	4.43626i	0.761564	+	0.519225i	−0.119149	+	0.992876i	$0.538017\pi$
$74$	4.46068	+	3.04124i	0.518543	+	0.353537i
$75$	−2.93237	+	0.441983i	−0.338601	+	0.0510358i
$76$	−6.69978	−	8.40126i	−0.768518	−	0.963691i
$77$	2.90613	+	7.27422i	0.331184	+	0.828974i
$78$	−0.348638	+	0.437179i	−0.0394755	+	0.0495007i
$79$	−2.81233	+	4.87109i	−0.316412	+	0.548041i	−0.979737	−	0.200291i	$-0.935811\pi$
$79$	−2.81233	+	4.87109i	−0.316412	+	0.548041i	0.663325	+	0.748331i	$0.269145\pi$
$80$	1.70848	+	2.95917i	0.191014	+	0.330846i
$81$	−0.486256	−	0.0732913i	−0.0540284	−	0.00814347i
$82$	−2.72879	−	2.53194i	−0.301344	−	0.279606i
$83$	10.7997	−	5.20086i	1.18542	−	0.570868i	0.265934	−	0.963991i	$-0.414320\pi$
$83$	10.7997	−	5.20086i	1.18542	−	0.570868i	0.919486	+	0.393123i	$0.128605\pi$
$84$	−2.94248	−	3.64404i	−0.321051	−	0.397598i
$85$	2.14425	+	1.03262i	0.232576	+	0.112003i
$86$	0.957002	+	2.43840i	0.103196	+	0.262940i
$87$	0.343519	+	4.58394i	0.0368291	+	0.491450i
$88$	5.66302	−	1.74681i	0.603680	−	0.186211i
$89$	−0.788139	+	10.5170i	−0.0835426	+	1.11480i	0.785103	+	0.619365i	$0.212610\pi$
$89$	−0.788139	+	10.5170i	−0.0835426	+	1.11480i	−0.868646	+	0.495434i	$0.835009\pi$
$90$	−0.338304	−	1.48221i	−0.0356604	−	0.156238i
$91$	2.61855	+	0.378401i	0.274499	+	0.0396672i
$92$	1.88517	−	8.25949i	0.196543	−	0.861111i
$93$	3.35750	+	1.03565i	0.348157	+	0.107392i
$94$	1.77880	−	4.53232i	0.183470	−	0.467473i
$95$	6.74016	−	6.25395i	0.691525	−	0.641642i
$96$	−4.50666	+	3.07259i	−0.459959	+	0.313595i
$97$	−14.6532			−1.48781			−0.743904	−	0.668286i	$-0.767028\pi$
$97$	−14.6532			−1.48781			−0.743904	+	0.668286i	$0.767028\pi$
$98$	1.33737	−	3.53343i	0.135095	−	0.356930i
$99$	5.70414			0.573287
$100$	4.04103	−	2.75513i	0.404103	−	0.275513i
$101$	−8.79041	+	8.15631i	−0.874679	+	0.811583i	−0.983204	−	0.182510i	$-0.941578\pi$
$101$	−8.79041	+	8.15631i	−0.874679	+	0.811583i	0.108525	+	0.994094i	$0.465387\pi$
$102$	−0.332537	+	0.847290i	−0.0329260	+	0.0838942i
$103$	−0.977769	−	0.301602i	−0.0963424	−	0.0297177i	0.246209	−	0.969217i	$-0.420815\pi$
$103$	−0.977769	−	0.301602i	−0.0963424	−	0.0297177i	−0.342552	+	0.939499i	$0.611291\pi$
$104$	0.445412	−	1.95148i	0.0436763	−	0.191358i
$105$	2.92121	−	2.74375i	0.285081	−	0.267763i
$106$	0.462333	+	2.02561i	0.0449058	+	0.196745i
$107$	−1.24661	+	16.6348i	−0.120514	+	1.60815i	0.529555	+	0.848276i	$0.322359\pi$
$107$	−1.24661	+	16.6348i	−0.120514	+	1.60815i	−0.650069	+	0.759875i	$0.725260\pi$
$108$	−8.33403	+	2.57071i	−0.801943	+	0.247367i
$109$	−1.02079	−	13.6215i	−0.0977738	−	1.30470i	−0.803111	−	0.595829i	$-0.796824\pi$
$109$	−1.02079	−	13.6215i	−0.0977738	−	1.30470i	0.705338	−	0.708872i	$-0.250795\pi$
$110$	0.853554	+	2.17482i	0.0813832	+	0.207361i
$111$	9.33709	+	4.49650i	0.886237	+	0.426789i
$112$	5.58717	+	2.64887i	0.527938	+	0.250295i
$113$	−0.236091	+	0.113695i	−0.0222095	+	0.0106955i	−0.444956	−	0.895553i	$-0.646781\pi$
$113$	−0.236091	+	0.113695i	−0.0222095	+	0.0106955i	0.422746	+	0.906248i	$0.361066\pi$
$114$	2.57778	+	2.39183i	0.241431	+	0.224015i
$115$	7.16814	+	1.08042i	0.668433	+	0.100750i
$116$	−3.79066	−	6.56562i	−0.351954	−	0.609603i
$117$	0.963312	−	1.66850i	0.0890582	−	0.154253i
$118$	5.08616	−	6.37784i	0.468219	−	0.587128i
$119$	4.25461	−	0.667784i	0.390020	−	0.0612157i
$120$	−1.89046	−	2.37056i	−0.172574	−	0.216401i
$121$	2.20935	−	0.333006i	0.200850	−	0.0302733i
$122$	−0.311485	−	0.212367i	−0.0282006	−	0.0192268i
$123$	−5.90401	−	4.02528i	−0.532346	−	0.362948i
$124$	−5.73013	+	0.863678i	−0.514581	+	0.0775605i
$125$	7.16722	+	8.98741i	0.641056	+	0.803858i
$126$	−2.02809	−	1.85895i	−0.180677	−	0.165609i
$127$	−12.7658	+	16.0078i	−1.13278	+	1.42046i	−0.239535	+	0.970888i	$0.576995\pi$
$127$	−12.7658	+	16.0078i	−1.13278	+	1.42046i	−0.893244	+	0.449573i	$0.851576\pi$
$128$	5.75925	−	9.97532i	0.509051	−	0.881702i
$129$	2.51415	+	4.35463i	0.221358	+	0.383404i
$130$	0.780300	+	0.117611i	0.0684368	+	0.0103152i
$131$	−1.84843	−	1.71509i	−0.161498	−	0.149848i	0.595284	−	0.803515i	$-0.297039\pi$
$131$	−1.84843	−	1.71509i	−0.161498	−	0.149848i	−0.756783	+	0.653667i	$0.773230\pi$
$132$	4.72221	−	2.27410i	0.411015	−	0.197935i
$133$	3.60363	−	16.2436i	0.312475	−	1.40850i
$134$	−6.20178	−	2.98662i	−0.535752	−	0.258004i
$135$	−2.72643	−	6.94682i	−0.234653	−	0.597887i
$136$	−0.243491	−	3.24916i	−0.0208792	−	0.278613i
$137$	11.0744	−	3.41600i	0.946149	−	0.291848i	0.216975	−	0.976177i	$-0.430381\pi$
$137$	11.0744	−	3.41600i	0.946149	−	0.291848i	0.729173	+	0.684329i	$0.239905\pi$
$138$	−0.207184	+	2.76468i	−0.0176367	+	0.235345i
$139$	0.413004	+	1.80949i	0.0350306	+	0.153479i	0.989418	−	0.145091i	$-0.0463475\pi$
$139$	0.413004	+	1.80949i	0.0350306	+	0.153479i	−0.954388	+	0.298570i	$0.903490\pi$
$140$	−2.37732	+	6.16742i	−0.200921	+	0.521242i
$141$	2.07973	−	9.11190i	0.175145	−	0.767360i
$142$	−5.35892	−	1.65301i	−0.449711	−	0.138717i
$143$	−1.08166	+	2.75603i	−0.0904531	+	0.230471i
$144$	3.30067	−	3.06257i	0.275055	−	0.255214i
$145$	5.35987	−	3.65430i	0.445113	−	0.303473i
$146$	4.25042			0.351767
$147$	1.52761	−	7.08956i	0.125995	−	0.584737i
$148$	−17.0920			−1.40495
$149$	−8.29319	+	5.65420i	−0.679405	+	0.463210i	−0.853208	−	0.521570i	$-0.825347\pi$
$149$	−8.29319	+	5.65420i	−0.679405	+	0.463210i	0.173804	+	0.984780i	$0.444394\pi$
$150$	−1.17328	+	1.08864i	−0.0957977	+	0.0888873i
$151$	−1.46964	+	3.74457i	−0.119597	+	0.304729i	−0.978118	−	0.208050i	$-0.933288\pi$
$151$	−1.46964	+	3.74457i	−0.119597	+	0.304729i	0.858521	+	0.512778i	$0.171384\pi$
$152$	−12.0288	−	3.71038i	−0.975661	−	0.300951i
$153$	0.697852	−	3.05749i	0.0564180	−	0.247183i
$154$	3.50758	+	2.36029i	0.282649	+	0.190197i
$155$	−1.10336	−	4.83413i	−0.0886239	−	0.388287i
$156$	0.132293	−	1.76533i	0.0105919	−	0.141340i
$157$	4.49820	−	1.38751i	0.358995	−	0.110735i	−0.110011	−	0.993930i	$-0.535089\pi$
$157$	4.49820	−	1.38751i	0.358995	−	0.110735i	0.469006	+	0.883195i	$0.344612\pi$
$158$	0.226862	+	3.02726i	0.0180481	+	0.240836i
$159$	1.45710	+	3.71263i	0.115556	+	0.294431i
$160$	6.93510	+	3.33977i	0.548268	+	0.264032i
$161$	11.7839	−	5.76345i	0.928705	−	0.454224i
$162$	−0.239123	+	0.115156i	−0.0187873	+	0.00904749i
$163$	−10.2536	−	9.51396i	−0.803125	−	0.745191i	0.167479	−	0.985876i	$-0.446437\pi$
$163$	−10.2536	−	9.51396i	−0.803125	−	0.745191i	−0.970603	+	0.240685i	$0.922628\pi$
$164$	11.6534	+	1.75647i	0.909979	+	0.137157i
$165$	2.24238	+	3.88391i	0.174569	+	0.302362i
$166$	3.23475	−	5.60276i	0.251065	−	0.434858i
$167$	0.812983	−	1.01945i	0.0629105	−	0.0788873i	−0.749381	−	0.662139i	$-0.769649\pi$
$167$	0.812983	−	1.01945i	0.0629105	−	0.0788873i	0.812291	+	0.583252i	$0.198220\pi$
$168$	−5.25275	−	1.58532i	−0.405258	−	0.122310i
$169$	0.623490	+	0.781831i	0.0479608	+	0.0601409i
$170$	1.27016	−	0.191445i	0.0974165	−	0.0146832i
$171$	−10.0108	−	6.82523i	−0.765543	−	0.521939i
$172$	−6.85199	−	4.67160i	−0.522459	−	0.356207i
$173$	−2.19845	+	0.331363i	−0.167145	+	0.0251930i	−0.232081	−	0.972696i	$-0.574554\pi$
$173$	−2.19845	+	0.331363i	−0.167145	+	0.0251930i	0.0649366	+	0.997889i	$0.479315\pi$
$174$	1.54687	+	1.93972i	0.117268	+	0.147049i
$175$	7.25003	+	2.18811i	0.548051	+	0.165406i
$176$	−4.31412	+	5.40974i	−0.325189	+	0.407774i
$177$	7.82956	−	13.5612i	0.588506	−	1.01932i
$178$	2.84608	+	4.92956i	0.213323	+	0.369486i
$179$	−17.7476	−	2.67502i	−1.32652	−	0.199940i	−0.552716	−	0.833369i	$-0.686409\pi$
$179$	−17.7476	−	2.67502i	−1.32652	−	0.199940i	−0.773801	+	0.633429i	$0.781647\pi$
$180$	3.52832	+	3.27380i	0.262985	+	0.244015i
$181$	−18.1782	+	8.75416i	−1.35117	+	0.650691i	−0.962650	−	0.270747i	$-0.912729\pi$
$181$	−18.1782	+	8.75416i	−1.35117	+	0.650691i	−0.388524	+	0.921439i	$0.627015\pi$
$182$	1.28276	−	0.627390i	0.0950846	−	0.0465053i
$183$	−0.652001	−	0.313987i	−0.0481973	−	0.0232106i
$184$	−3.62581	−	9.23840i	−0.267298	−	0.681064i
$185$	−1.09293	−	14.5841i	−0.0803536	−	1.07224i
$186$	1.81211	−	0.558963i	0.132871	−	0.0409852i
$187$	−0.360151	+	4.80588i	−0.0263368	+	0.351440i
$188$	3.43002	+	15.0279i	0.250160	+	1.09602i
$189$	−11.2039	−	7.53924i	−0.814966	−	0.548399i
$190$	1.10427	−	4.83813i	0.0801122	−	0.350995i
$191$	19.5770	+	6.03870i	1.41654	+	0.436945i	0.906135	−	0.422988i	$-0.139019\pi$
$191$	19.5770	+	6.03870i	1.41654	+	0.436945i	0.510406	+	0.859933i	$0.329495\pi$
$192$	0.693673	−	1.76745i	0.0500616	−	0.127555i
$193$	−5.96192	+	5.53185i	−0.429148	+	0.398192i	−0.864956	−	0.501849i	$-0.832653\pi$
$193$	−5.96192	+	5.53185i	−0.429148	+	0.398192i	0.435807	+	0.900040i	$0.356463\pi$
$194$	−6.53443	+	4.45510i	−0.469145	+	0.319858i
$195$	1.51477			0.108475
$196$	2.80328	+	11.6278i	0.200234	+	0.830555i
$197$	10.0603			0.716766			0.358383	−	0.933575i	$-0.383328\pi$
$197$	10.0603			0.716766			0.358383	+	0.933575i	$0.383328\pi$
$198$	2.54370	−	1.73426i	0.180773	−	0.123249i
$199$	18.1220	−	16.8147i	1.28463	−	1.19196i	0.314534	−	0.949246i	$-0.398152\pi$
$199$	18.1220	−	16.8147i	1.28463	−	1.19196i	0.970097	−	0.242717i	$-0.0780387\pi$
$200$	2.09320	−	5.33338i	0.148011	−	0.377127i
$201$	−12.6263	−	3.89470i	−0.890591	−	0.274711i
$202$	−1.44017	+	6.30982i	−0.101330	+	0.443957i
$203$	4.22213	−	10.9533i	0.296335	−	0.768774i
$204$	−0.641222	−	2.80938i	−0.0448945	−	0.196696i
$205$	−0.753582	+	10.0559i	−0.0526324	+	0.702331i
$206$	−0.527723	+	0.162781i	−0.0367682	+	0.0113415i
$207$	−0.713850	−	9.52567i	−0.0496160	−	0.662080i
$208$	0.853824	+	2.17551i	0.0592020	+	0.150844i
$209$	16.7752	+	8.07852i	1.16037	+	0.558803i
$210$	0.468480	−	2.11170i	0.0323282	−	0.145721i
$211$	16.0320	−	7.72059i	1.10369	−	0.531508i	0.208871	−	0.977943i	$-0.433021\pi$
$211$	16.0320	−	7.72059i	1.10369	−	0.531508i	0.894816	+	0.446436i	$0.147307\pi$
$212$	−4.82187	−	4.47404i	−0.331167	−	0.307278i
$213$	−10.6449	−	1.60446i	−0.729377	−	0.109936i
$214$	4.50168	+	7.79713i	0.307728	+	0.533001i
$215$	3.54801	−	6.14533i	0.241972	−	0.419108i
$216$	−6.37010	+	7.98785i	−0.433430	+	0.543504i
$217$	−6.61450	−	6.06287i	−0.449022	−	0.411575i
$218$	−4.59663	−	5.76399i	−0.311323	−	0.390386i
$219$	8.06790	−	1.21604i	0.545178	−	0.0821723i
$220$	−6.11131	−	4.16662i	−0.412025	−	0.280914i
$221$	1.34493	+	0.916961i	0.0904701	+	0.0616814i
$222$	5.53087	−	0.833644i	0.371208	−	0.0559505i
$223$	18.0922	+	22.6868i	1.21154	+	1.51922i	0.790839	+	0.612024i	$0.209644\pi$
$223$	18.0922	+	22.6868i	1.21154	+	1.51922i	0.420701	+	0.907199i	$0.361784\pi$
$224$	13.7606	−	2.15980i	0.919419	−	0.144308i
$225$	3.43832	−	4.31152i	0.229222	−	0.287435i
$226$	−0.0707145	+	0.122481i	−0.00470386	+	0.00814732i
$227$	6.11724	+	10.5954i	0.406015	+	0.703239i	0.994439	−	0.105314i	$-0.0335846\pi$
$227$	6.11724	+	10.5954i	0.406015	+	0.703239i	−0.588424	+	0.808553i	$0.700251\pi$
$228$	−11.0085	−	1.65927i	−0.729058	−	0.109888i
$229$	7.17873	+	6.66089i	0.474384	+	0.440164i	0.880775	−	0.473535i	$-0.157022\pi$
$229$	7.17873	+	6.66089i	0.474384	+	0.440164i	−0.406391	+	0.913699i	$0.633213\pi$
$230$	3.52504	−	1.69757i	0.232434	−	0.111934i
$231$	7.33316	+	3.47665i	0.482486	+	0.228747i
$232$	−8.00166	−	3.85340i	−0.525335	−	0.252988i
$233$	9.08190	+	23.1403i	0.594975	+	1.51597i	0.837842	+	0.545912i	$0.183817\pi$
$233$	9.08190	+	23.1403i	0.594975	+	1.51597i	−0.242867	+	0.970060i	$0.578088\pi$
$234$	−0.0777073	−	1.03693i	−0.00507989	−	0.0677864i
$235$	−12.6036	+	3.88769i	−0.822167	+	0.253605i
$236$	−1.92998	+	25.7538i	−0.125631	+	1.67643i
$237$	1.29671	+	5.68126i	0.0842303	+	0.369037i
$238$	1.69427	−	1.59135i	0.109823	−	0.103152i
$239$	−2.27176	+	9.95325i	−0.146948	+	0.643822i	0.846775	+	0.531952i	$0.178541\pi$
$239$	−2.27176	+	9.95325i	−0.146948	+	0.643822i	−0.993723	+	0.111870i	$0.964316\pi$
$240$	3.38283	+	1.04346i	0.218360	+	0.0673553i
$241$	0.817596	−	2.08320i	0.0526660	−	0.134191i	−0.902120	−	0.431486i	$-0.857989\pi$
$241$	0.817596	−	2.08320i	0.0526660	−	0.134191i	0.954786	+	0.297295i	$0.0960846\pi$
$242$	0.883989	−	0.820222i	0.0568250	−	0.0527259i
$243$	−13.0727	+	8.91284i	−0.838617	+	0.571759i
$244$	1.19352			0.0764071
$245$	−9.74240	+	3.13549i	−0.622419	+	0.200319i
$246$	−3.85666			−0.245891
$247$	5.19602	−	3.54259i	0.330615	−	0.225409i
$248$	−4.97625	+	4.61729i	−0.315992	+	0.293198i
$249$	4.53707	−	11.5603i	0.287525	−	0.732603i
$250$	5.92864	+	1.82874i	0.374960	+	0.115660i
$251$	0.289512	−	1.26843i	0.0182738	−	0.0800629i	−0.964969	−	0.262365i	$-0.915498\pi$
$251$	0.289512	−	1.26843i	0.0182738	−	0.0800629i	0.983243	+	0.182302i	$0.0583548\pi$
$252$	8.62033	+	1.24570i	0.543030	+	0.0784719i
$253$	3.26647	+	14.3113i	0.205361	+	0.899746i
$254$	−0.825815	+	11.0197i	−0.0518163	+	0.691440i
$255$	2.35616	−	0.726780i	0.147549	−	0.0455127i
$256$	−0.190672	−	2.54434i	−0.0119170	−	0.159021i
$257$	1.82918	+	4.66066i	0.114101	+	0.290724i	0.976504	−	0.215497i	$-0.0691372\pi$
$257$	1.82918	+	4.66066i	0.114101	+	0.290724i	−0.862404	+	0.506221i	$0.831042\pi$
$258$	2.44512	+	1.17751i	0.152227	+	0.0733085i
$259$	−16.6264	−	20.5905i	−1.03311	−	1.27943i
$260$	−2.25085	+	1.08395i	−0.139591	+	0.0672237i
$261$	−6.26629	−	5.81427i	−0.387874	−	0.359894i
$262$	−1.34574	−	0.202837i	−0.0831399	−	0.0125313i
$263$	10.3246	+	17.8828i	0.636644	+	1.10270i	0.986164	+	0.165771i	$0.0530113\pi$
$263$	10.3246	+	17.8828i	0.636644	+	1.10270i	−0.349520	+	0.936929i	$0.613655\pi$
$264$	3.06995	−	5.31730i	0.188942	−	0.327257i
$265$	3.50925	−	4.40046i	0.215571	−	0.270318i
$266$	−3.33163	−	8.33927i	−0.204275	−	0.511314i
$267$	6.81260	+	8.54273i	0.416924	+	0.522807i
$268$	21.5489	−	3.24797i	1.31631	−	0.198401i
$269$	−6.39175	−	4.35782i	−0.389712	−	0.265701i	0.352575	−	0.935784i	$-0.385306\pi$
$269$	−6.39175	−	4.35782i	−0.389712	−	0.265701i	−0.742286	+	0.670083i	$0.766259\pi$
$270$	−3.32790	−	2.26892i	−0.202530	−	0.138082i
$271$	−20.5414	+	3.09611i	−1.24780	+	0.188076i	−0.739531	−	0.673123i	$-0.764953\pi$
$271$	−20.5414	+	3.09611i	−1.24780	+	0.188076i	−0.508269	+	0.861198i	$0.669714\pi$
$272$	2.37189	+	2.97426i	0.143817	+	0.180341i
$273$	2.25537	−	1.55787i	0.136501	−	0.0942867i
$274$	3.89991	−	4.89033i	0.235602	−	0.295436i
$275$	−4.23725	+	7.33912i	−0.255516	+	0.442566i
$276$	−4.38861	−	7.60129i	−0.264163	−	0.457544i
$277$	−4.86297	−	0.732974i	−0.292187	−	0.0440402i	0.00131292	−	0.999999i	$-0.499582\pi$
$277$	−4.86297	−	0.732974i	−0.292187	−	0.0440402i	−0.293500	+	0.955959i	$0.594820\pi$
$278$	0.734324	+	0.681353i	0.0440418	+	0.0408649i
$279$	−5.88685	+	2.83496i	−0.352436	+	0.169724i
$280$	1.76889	+	7.53826i	0.105711	+	0.450497i
$281$	−19.1366	−	9.21570i	−1.14159	−	0.549763i	−0.235095	−	0.971972i	$-0.575540\pi$
$281$	−19.1366	−	9.21570i	−1.14159	−	0.549763i	−0.906498	+	0.422210i	$0.861255\pi$
$282$	−1.84291	−	4.69566i	−0.109744	−	0.279623i
$283$	−1.39323	−	18.5914i	−0.0828192	−	1.10515i	−0.871517	−	0.490365i	$-0.836864\pi$
$283$	−1.39323	−	18.5914i	−0.0828192	−	1.10515i	0.788698	−	0.614780i	$-0.210755\pi$
$284$	16.9658	−	5.23325i	1.00673	−	0.310536i
$285$	0.711880	−	9.49938i	0.0421681	−	0.562695i
$286$	0.355577	+	1.55788i	0.0210257	+	0.0921196i
$287$	9.21998	+	15.7474i	0.544238	+	0.929538i
$288$	2.25705	−	9.88877i	0.132998	−	0.582701i
$289$	−13.7128	−	4.22984i	−0.806635	−	0.248814i
$290$	1.27914	−	3.25919i	0.0751135	−	0.191386i
$291$	−11.1287	+	10.3259i	−0.652375	+	0.605315i
$292$	−11.1182	+	7.58025i	−0.650642	+	0.443600i
$293$	−17.4352			−1.01858			−0.509289	−	0.860596i	$-0.670091\pi$
$293$	−17.4352			−1.01858			−0.509289	+	0.860596i	$0.670091\pi$
$294$	−1.47426	−	3.62596i	−0.0859806	−	0.211470i
$295$	−22.0984			−1.28662
$296$	−16.5433	+	11.2790i	−0.961561	+	0.655581i
$297$	11.0778	−	10.2787i	0.642799	−	0.596430i
$298$	−1.97917	+	5.04285i	−0.114651	+	0.292125i
$299$	4.73782	+	1.46142i	0.273995	+	0.0845163i
$300$	1.12754	−	4.94009i	0.0650988	−	0.285216i
$301$	−1.03750	−	12.7989i	−0.0598008	−	0.737715i
$302$	0.483116	+	2.11667i	0.0278002	+	0.121801i
$303$	−0.928424	+	12.3890i	−0.0533365	+	0.711727i
$304$	14.0443	−	4.33208i	0.805494	−	0.248462i
$305$	0.0763182	+	1.01840i	0.00436997	+	0.0583131i
$306$	−0.618387	−	1.57562i	−0.0353508	−	0.0900725i
$307$	10.6258	+	5.11710i	0.606445	+	0.292048i	0.711796	−	0.702387i	$-0.247882\pi$
$307$	10.6258	+	5.11710i	0.606445	+	0.292048i	−0.105351	+	0.994435i	$0.533597\pi$
$308$	−13.3844	+	0.0814526i	−0.762649	+	0.00464119i
$309$	−0.955121	+	0.459962i	−0.0543349	+	0.0261663i
$310$	−1.96178	−	1.82027i	−0.111422	−	0.103384i
$311$	−3.49850	−	0.527314i	−0.198382	−	0.0299012i	0.0490996	−	0.998794i	$-0.484365\pi$
$311$	−3.49850	−	0.527314i	−0.198382	−	0.0299012i	−0.247481	+	0.968893i	$0.579603\pi$
$312$	−1.03690	−	1.79597i	−0.0587030	−	0.101677i
$313$	−11.1372	+	19.2901i	−0.629509	+	1.09034i	0.358141	+	0.933668i	$0.383411\pi$
$313$	−11.1372	+	19.2901i	−0.629509	+	1.09034i	−0.987650	+	0.156675i	$0.949923\pi$
$314$	1.58407	−	1.98636i	0.0893941	−	0.112097i
$315$	−0.511706	+	7.43515i	−0.0288314	+	0.418923i
$316$	−5.99227	−	7.51407i	−0.337091	−	0.422699i
$317$	−22.2335	+	3.35116i	−1.24876	+	0.188220i	−0.739952	−	0.672660i	$-0.765152\pi$
$317$	−22.2335	+	3.35116i	−1.24876	+	0.188220i	−0.508808	+	0.860880i	$0.669914\pi$
$318$	1.77855	+	1.21259i	0.0997361	+	0.0679989i
$319$	10.8537	+	7.39993i	0.607691	+	0.414316i
$320$	−2.64955	+	0.399356i	−0.148114	+	0.0223247i
$321$	10.7756	+	13.5121i	0.601433	+	0.754174i
$322$	3.50262	−	6.15289i	0.195194	−	0.342887i
$323$	6.38249	−	8.00339i	0.355131	−	0.445321i
$324$	0.420125	−	0.727678i	0.0233403	−	0.0404266i
$325$	1.43117	+	2.47885i	0.0793869	+	0.137502i
$326$	−7.46507	−	1.12518i	−0.413452	−	0.0623178i
$327$	−10.3741	−	9.62577i	−0.573690	−	0.532306i
$328$	12.4385	−	5.99004i	0.686799	−	0.330745i
$329$	−14.7674	+	18.7507i	−0.814152	+	1.03376i
$330$	2.18081	+	1.05022i	0.120050	+	0.0578129i
$331$	−13.1922	−	33.6132i	−0.725109	−	1.84755i	−0.477307	−	0.878736i	$-0.658387\pi$
$331$	−13.1922	−	33.6132i	−0.725109	−	1.84755i	−0.247802	−	0.968811i	$-0.579708\pi$
$332$	1.53060	+	20.4245i	0.0840028	+	1.12094i
$333$	−18.4156	+	5.68046i	−1.00917	+	0.311288i
$334$	0.0525917	−	0.701787i	0.00287769	−	0.0384001i
$335$	4.14932	+	18.1794i	0.226702	+	0.993245i
$336$	6.10991	−	1.92545i	0.333323	−	0.105042i
$337$	−3.58491	+	15.7065i	−0.195283	+	0.855589i	0.778416	+	0.627749i	$0.216024\pi$
$337$	−3.58491	+	15.7065i	−0.195283	+	0.855589i	−0.973698	+	0.227840i	$0.926834\pi$
$338$	0.515743	+	0.159086i	0.0280527	+	0.00865312i
$339$	−0.0991844	+	0.252718i	−0.00538696	+	0.0137257i
$340$	−2.98103	+	2.76599i	−0.161669	+	0.150007i
$341$	8.29612	−	5.65620i	0.449260	−	0.306300i
$342$	−6.53931			−0.353605
$343$	−11.2809	+	14.6881i	−0.609113	+	0.793083i
$344$	−9.71485			−0.523790
$345$	6.20535	−	4.23073i	0.334085	−	0.227775i
$346$	−0.879627	+	0.816174i	−0.0472890	+	0.0438778i
$347$	2.80690	−	7.15187i	0.150682	−	0.383932i	−0.835524	−	0.549454i	$-0.814836\pi$
$347$	2.80690	−	7.15187i	0.150682	−	0.383932i	0.986206	+	0.165522i	$0.0529309\pi$
$348$	−7.50559	−	2.31517i	−0.402342	−	0.124106i
$349$	1.88492	−	8.25838i	0.100898	−	0.442061i	−0.899093	−	0.437757i	$-0.855773\pi$
$349$	1.88492	−	8.25838i	0.100898	−	0.442061i	0.999991	−	0.00430378i	$-0.00136994\pi$
$350$	3.89833	−	1.22851i	0.208375	−	0.0656664i
$351$	−1.13579	−	4.97620i	−0.0606237	−	0.265610i
$352$	−1.16483	+	15.5435i	−0.0620855	+	0.828474i
$353$	4.08290	−	1.25941i	0.217311	−	0.0670316i	−0.184188	−	0.982891i	$-0.558966\pi$
$353$	4.08290	−	1.25941i	0.217311	−	0.0670316i	0.401499	+	0.915859i	$0.368489\pi$
$354$	−0.631586	−	8.42793i	−0.0335684	−	0.447939i
$355$	5.55024	+	14.1418i	0.294576	+	0.750568i
$356$	−16.2362	−	7.81892i	−0.860515	−	0.414402i
$357$	2.76067	−	3.50532i	0.146110	−	0.185521i
$358$	−8.72764	+	4.20301i	−0.461270	+	0.222136i
$359$	−3.90450	−	3.62285i	−0.206072	−	0.191207i	0.570384	−	0.821378i	$-0.306794\pi$
$359$	−3.90450	−	3.62285i	−0.206072	−	0.191207i	−0.776456	+	0.630171i	$0.782985\pi$
$360$	5.57545	+	0.840364i	0.293852	+	0.0442911i
$361$	−10.2743	−	17.7956i	−0.540752	−	0.936610i
$362$	−5.44478	+	9.43064i	−0.286171	+	0.495663i
$363$	1.44327	−	1.80980i	0.0757521	−	0.0949901i
$364$	−2.23653	+	3.92881i	−0.117226	+	0.205926i
$365$	−7.17896	−	9.00213i	−0.375764	−	0.471193i
$366$	−0.386216	+	0.0582127i	−0.0201878	+	0.00304283i
$367$	5.55252	+	3.78564i	0.289839	+	0.197609i	0.699507	−	0.714626i	$-0.253403\pi$
$367$	5.55252	+	3.78564i	0.289839	+	0.197609i	−0.409668	+	0.912235i	$0.634355\pi$
$368$	9.57393	+	6.52739i	0.499076	+	0.340264i
$369$	13.1397	−	1.98048i	0.684023	−	0.103100i
$370$	−4.92146	−	6.17132i	−0.255855	−	0.320832i
$371$	0.699309	−	10.1610i	0.0363063	−	0.527534i
$372$	−3.74324	+	4.69387i	−0.194078	+	0.243366i
$373$	−13.4142	+	23.2340i	−0.694559	+	1.20301i	0.275770	+	0.961224i	$0.411067\pi$
$373$	−13.4142	+	23.2340i	−0.694559	+	1.20301i	−0.970329	+	0.241788i	$0.922266\pi$
$374$	1.30055	+	2.25262i	0.0672500	+	0.116480i
$375$	11.7766	+	1.77503i	0.608140	+	0.0916624i
$376$	13.2369	+	12.2821i	0.682641	+	0.633398i
$377$	3.99750	−	1.92510i	0.205882	−	0.0991475i
$378$	−7.28846	+	0.0443548i	−0.374878	+	0.00228136i
$379$	21.0063	+	10.1161i	1.07902	+	0.519630i	0.887004	−	0.461761i	$-0.152782\pi$
$379$	21.0063	+	10.1161i	1.07902	+	0.519630i	0.192019	+	0.981391i	$0.438497\pi$
$380$	5.73984	+	14.6249i	0.294448	+	0.750240i
$381$	1.58522	+	21.1533i	0.0812132	+	1.08372i
$382$	10.5661	−	3.25922i	0.540610	−	0.166756i
$383$	−2.57405	+	34.3483i	−0.131528	+	1.75511i	0.407848	+	0.913050i	$0.366279\pi$
$383$	−2.57405	+	34.3483i	−0.131528	+	1.75511i	−0.539376	+	0.842065i	$0.681340\pi$
$384$	−2.65548	−	11.6344i	−0.135512	−	0.593716i
$385$	−0.925355	−	11.4154i	−0.0471604	−	0.581781i
$386$	−0.976769	+	4.27951i	−0.0497162	+	0.217821i
$387$	−8.93522	−	2.75615i	−0.454203	−	0.140103i
$388$	9.14739	−	23.3072i	0.464388	−	1.18324i
$389$	−10.1182	+	9.38831i	−0.513013	+	0.476006i	−0.893679	−	0.448706i	$-0.851885\pi$
$389$	−10.1182	+	9.38831i	−0.513013	+	0.476006i	0.380667	+	0.924712i	$0.375695\pi$
$390$	0.675493	−	0.460544i	0.0342049	−	0.0233205i
$391$	8.07068			0.408152
$392$	10.3865	+	9.40463i	0.524598	+	0.475006i
$393$	−2.61243			−0.131780
$394$	4.48627	−	3.05869i	0.226015	−	0.154095i
$395$	6.02838	−	5.59352i	0.303321	−	0.281440i
$396$	−3.56086	+	9.07291i	−0.178940	+	0.455931i
$397$	−26.4551	−	8.16033i	−1.32774	−	0.409555i	−0.451866	−	0.892086i	$-0.649241\pi$
$397$	−26.4551	−	8.16033i	−1.32774	−	0.409555i	−0.875879	+	0.482531i	$0.839718\pi$
$398$	2.96900	−	13.0081i	0.148823	−	0.652035i
$399$	−8.70976	−	14.8759i	−0.436033	−	0.744729i
$400$	1.48854	+	6.52173i	0.0744271	+	0.326087i
$401$	−1.07019	+	14.2807i	−0.0534427	+	0.713144i	0.904553	+	0.426361i	$0.140205\pi$
$401$	−1.07019	+	14.2807i	−0.0534427	+	0.713144i	−0.957996	+	0.286783i	$0.907414\pi$
$402$	−6.81469	+	2.10205i	−0.339886	+	0.104841i
$403$	−0.253438	−	3.38189i	−0.0126246	−	0.168464i
$404$	−7.48582	−	19.0735i	−0.372433	−	0.948944i
$405$	0.647772	+	0.311951i	0.0321881	+	0.0155010i
$406$	−1.44740	−	6.16820i	−0.0718332	−	0.306123i
$407$	26.6826	−	12.8497i	1.32261	−	0.636935i
$408$	−2.47456	−	2.29605i	−0.122509	−	0.113672i
$409$	−6.14612	−	0.926378i	−0.303906	−	0.0458065i	−0.00468103	−	0.999989i	$-0.501490\pi$
$409$	−6.14612	−	0.926378i	−0.303906	−	0.0458065i	−0.299225	+	0.954183i	$0.596728\pi$
$410$	2.72129	+	4.71341i	0.134395	+	0.232779i
$411$	6.00346	−	10.3983i	0.296129	−	0.512911i
$412$	1.09010	−	1.36695i	0.0537055	−	0.0673446i
$413$	−32.9027	+	22.7272i	−1.61904	+	1.11833i
$414$	−3.21448	−	4.03083i	−0.157983	−	0.198104i
$415$	−17.3298	+	2.61205i	−0.850686	+	0.128220i
$416$	4.34989	+	2.96571i	0.213271	+	0.145406i
$417$	1.58879	+	1.08322i	0.0778031	+	0.0530453i
$418$	9.93688	−	1.49774i	0.486029	−	0.0732571i
$419$	−17.2844	−	21.6739i	−0.844397	−	1.05884i	−0.997503	−	0.0706304i	$-0.977499\pi$
$419$	−17.2844	−	21.6739i	−0.844397	−	1.05884i	0.153106	−	0.988210i	$-0.451073\pi$
$420$	2.54059	+	6.35924i	0.123968	+	0.310299i
$421$	−7.67213	+	9.62055i	−0.373917	+	0.468877i	−0.932813	−	0.360361i	$-0.882654\pi$
$421$	−7.67213	+	9.62055i	−0.373917	+	0.468877i	0.558896	+	0.829238i	$0.311225\pi$
$422$	4.80194	−	8.31721i	0.233755	−	0.404875i
$423$	8.69015	+	15.0518i	0.422529	+	0.731842i
$424$	−7.61953	−	1.14846i	−0.370037	−	0.0557741i
$425$	3.41547	+	3.16909i	0.165675	+	0.153724i
$426$	−5.23479	+	2.52094i	−0.253626	+	0.122140i
$427$	1.16101	+	1.43782i	0.0561850	+	0.0695809i
$428$	−25.6809	−	12.3673i	−1.24133	−	0.597795i
$429$	1.12064	+	2.85535i	0.0541052	+	0.137858i
$430$	−0.286207	−	3.81916i	−0.0138021	−	0.184176i
$431$	30.1931	−	9.31335i	1.45435	−	0.448608i	0.535948	−	0.844251i	$-0.319954\pi$
$431$	30.1931	−	9.31335i	1.45435	−	0.448608i	0.918404	+	0.395643i	$0.129478\pi$
$432$	0.891437	−	11.8954i	0.0428893	−	0.572318i
$433$	1.10233	+	4.82962i	0.0529745	+	0.232097i	0.994484	−	0.104891i	$-0.0334492\pi$
$433$	1.10233	+	4.82962i	0.0529745	+	0.232097i	−0.941509	+	0.336987i	$0.890592\pi$
$434$	−4.79299	−	0.692624i	−0.230071	−	0.0332470i
$435$	1.49553	−	6.55236i	0.0717053	−	0.314161i
$436$	22.3033	+	6.87967i	1.06814	+	0.329476i
$437$	11.3914	−	29.0249i	0.544926	−	1.38845i
$438$	3.22807	−	2.99521i	0.154243	−	0.143117i
$439$	17.0393	−	11.6172i	0.813241	−	0.554458i	−0.0837608	−	0.996486i	$-0.526693\pi$
$439$	17.0393	−	11.6172i	0.813241	−	0.554458i	0.897001	+	0.442028i	$0.145741\pi$
$440$	−8.66472			−0.413074
$441$	6.88483	+	11.5966i	0.327849	+	0.552219i
$442$	0.878547			0.0417882
$443$	12.5433	−	8.55186i	0.595949	−	0.406311i	−0.227437	−	0.973793i	$-0.573035\pi$
$443$	12.5433	−	8.55186i	0.595949	−	0.406311i	0.823386	+	0.567482i	$0.192082\pi$
$444$	−12.9808	+	12.0444i	−0.616043	+	0.571604i
$445$	5.63347	−	14.3538i	0.267052	−	0.680437i
$446$	14.9656	+	4.61628i	0.708642	+	0.218587i
$447$	−2.31400	+	10.1383i	−0.109448	+	0.479525i
$448$	−3.53425	+	3.31955i	−0.166977	+	0.156834i
$449$	−1.90543	−	8.34825i	−0.0899230	−	0.393978i	0.909858	−	0.414920i	$-0.136191\pi$
$449$	−1.90543	−	8.34825i	−0.0899230	−	0.393978i	−0.999781	+	0.0209421i	$0.993333\pi$
$450$	0.222424	−	2.96805i	0.0104852	−	0.139915i
$451$	−19.5129	+	6.01894i	−0.918827	+	0.283421i
$452$	−0.0334603	−	0.446497i	−0.00157384	−	0.0210015i
$453$	1.52260	+	3.87952i	0.0715380	+	0.182276i
$454$	5.94928	+	2.86502i	0.279214	+	0.134462i
$455$	−3.49536	−	1.65715i	−0.163865	−	0.0776883i
$456$	−11.7501	+	5.65856i	−0.550250	+	0.264987i
$457$	4.01602	+	3.72633i	0.187862	+	0.174310i	0.768497	−	0.639854i	$-0.221005\pi$
$457$	4.01602	+	3.72633i	0.187862	+	0.174310i	−0.580635	+	0.814164i	$0.697196\pi$
$458$	5.22642	+	0.787757i	0.244215	+	0.0368095i
$459$	−4.15423	−	7.19534i	−0.193903	−	0.335850i
$460$	−6.19328	+	10.7271i	−0.288763	+	0.500152i
$461$	−0.512179	+	0.642252i	−0.0238546	+	0.0299127i	−0.793616	−	0.608419i	$-0.791804\pi$
$461$	−0.512179	+	0.642252i	−0.0238546	+	0.0299127i	0.769761	+	0.638332i	$0.220375\pi$
$462$	4.32716	−	0.679171i	0.201318	−	0.0315979i
$463$	−10.6615	−	13.3691i	−0.495482	−	0.621315i	0.469722	−	0.882815i	$-0.344354\pi$
$463$	−10.6615	−	13.3691i	−0.495482	−	0.621315i	−0.965203	+	0.261500i	$0.915783\pi$
$464$	10.2535	−	1.54546i	0.476006	−	0.0717463i
$465$	−4.24451	−	2.89386i	−0.196834	−	0.134199i
$466$	11.0855	+	7.55794i	0.513524	+	0.350115i
$467$	26.1558	−	3.94236i	1.21035	−	0.182431i	0.487304	−	0.873233i	$-0.337980\pi$
$467$	26.1558	−	3.94236i	1.21035	−	0.182431i	0.723044	+	0.690802i	$0.242742\pi$
$468$	2.05254	+	2.57381i	0.0948788	+	0.118974i
$469$	24.8747	+	22.8002i	1.14861	+	1.05282i
$470$	−4.43843	+	5.56561i	−0.204729	+	0.256722i
$471$	2.43849	−	4.22359i	0.112360	−	0.194613i
$472$	15.1270	+	26.2007i	0.696276	+	1.20599i
$473$	14.2089	+	2.14164i	0.653325	+	0.0984729i
$474$	2.30556	+	2.13925i	0.105898	+	0.0982588i
$475$	16.2179	−	7.81015i	0.744130	−	0.358354i
$476$	−1.59381	+	7.18419i	−0.0730522	+	0.329287i
$477$	−6.68223	−	3.21799i	−0.305958	−	0.147342i
$478$	2.01308	+	5.12924i	0.0920760	+	0.234606i
$479$	−0.901009	−	12.0231i	−0.0411681	−	0.549351i	−0.979213	−	0.202836i	$-0.934984\pi$
$479$	−0.901009	−	12.0231i	−0.0411681	−	0.549351i	0.938045	−	0.346515i	$-0.112635\pi$
$480$	7.62048	−	2.35061i	0.347826	−	0.107290i
$481$	0.747517	−	9.97492i	0.0340838	−	0.454817i
$482$	−0.268770	−	1.17756i	−0.0122421	−	0.0536363i
$483$	4.88814	−	12.6811i	0.222418	−	0.577012i
$484$	−0.849531	+	3.72204i	−0.0386151	+	0.169184i
$485$	20.4723	+	6.31486i	0.929599	+	0.286743i
$486$	−3.11982	+	7.94917i	−0.141518	+	0.360581i
$487$	−25.7011	+	23.8471i	−1.16463	+	1.08062i	−0.169153	+	0.985590i	$0.554103\pi$
$487$	−25.7011	+	23.8471i	−1.16463	+	1.08062i	−0.995475	+	0.0950265i	$0.969706\pi$
$488$	1.15521	−	0.787606i	0.0522937	−	0.0356533i
$489$	−14.4917			−0.655335
$490$	−3.39121	+	4.36027i	−0.153199	+	0.196977i
$491$	20.9665			0.946203			0.473102	−	0.881008i	$-0.343134\pi$
$491$	20.9665			0.946203			0.473102	+	0.881008i	$0.343134\pi$
$492$	10.0882	−	6.87800i	0.454810	−	0.310084i
$493$	5.29431	−	4.91240i	0.238444	−	0.221243i
$494$	1.24003	−	3.15955i	0.0557918	−	0.142155i
$495$	−7.96936	−	2.45822i	−0.358196	−	0.110489i
$496$	1.76367	−	7.72714i	0.0791911	−	0.346959i
$497$	22.8081	+	15.3478i	1.02308	+	0.688443i
$498$	−1.49148	−	6.53461i	−0.0668349	−	0.292823i
$499$	0.600635	−	8.01492i	0.0268881	−	0.358797i	−0.967490	−	0.252909i	$-0.918613\pi$
$499$	0.600635	−	8.01492i	0.0268881	−	0.358797i	0.994378	−	0.105888i	$-0.0337684\pi$
$500$	−18.7694	+	5.78960i	−0.839395	+	0.258919i
$501$	−0.100954	−	1.34714i	−0.00451029	−	0.0601857i
$502$	−0.256545	−	0.653666i	−0.0114502	−	0.0291745i
$503$	−12.2254	−	5.88743i	−0.545103	−	0.262508i	0.141004	−	0.990009i	$-0.454967\pi$
$503$	−12.2254	−	5.88743i	−0.545103	−	0.262508i	−0.686106	+	0.727502i	$0.740681\pi$
$504$	9.16567	−	4.48287i	0.408272	−	0.199683i
$505$	15.7963	−	7.60708i	0.702924	−	0.338510i
$506$	5.80781	+	5.38886i	0.258189	+	0.239564i
$507$	1.02447	+	0.154414i	0.0454982	+	0.00685775i
$508$	−17.4926	−	30.2980i	−0.776108	−	1.34426i
$509$	5.22294	−	9.04639i	0.231503	−	0.400974i	−0.726748	−	0.686904i	$-0.758969\pi$
$509$	5.22294	−	9.04639i	0.231503	−	0.400974i	0.958251	+	0.285930i	$0.0923025\pi$
$510$	0.829737	−	1.04046i	0.0367414	−	0.0460722i
$511$	−19.9472	−	6.02020i	−0.882411	−	0.266318i
$512$	13.5047	+	16.9344i	0.596831	+	0.748402i
$513$	−31.7404	+	4.78410i	−1.40137	+	0.211223i
$514$	2.23271	+	1.52224i	0.0984806	+	0.0671429i
$515$	1.23608	+	0.842747i	0.0544683	+	0.0371359i
$516$	−8.49589	+	1.28055i	−0.374011	+	0.0563731i
$517$	−16.6526	−	20.8817i	−0.732382	−	0.918378i
$518$	−13.6746	−	4.12709i	−0.600827	−	0.181334i
$519$	−1.43615	+	1.80087i	−0.0630400	+	0.0790496i
$520$	−1.46329	+	2.53450i	−0.0641696	+	0.111145i
$521$	−4.81852	−	8.34592i	−0.211103	−	0.365641i	0.740957	−	0.671553i	$-0.234372\pi$
$521$	−4.81852	−	8.34592i	−0.211103	−	0.365641i	−0.952060	+	0.305911i	$0.901039\pi$
$522$	−4.56213	−	0.687630i	−0.199679	−	0.0300968i
$523$	−9.33496	−	8.66157i	−0.408189	−	0.378744i	0.449184	−	0.893439i	$-0.351715\pi$
$523$	−9.33496	−	8.66157i	−0.408189	−	0.378744i	−0.857373	+	0.514695i	$0.827905\pi$
$524$	3.88190	−	1.86942i	0.169582	−	0.0816662i
$525$	7.04811	−	3.44719i	0.307605	−	0.150448i
$526$	10.0412	+	4.83557i	0.437815	+	0.210841i
$527$	−2.01683	−	5.13881i	−0.0878547	−	0.223850i
$528$	0.535716	+	7.14863i	0.0233140	+	0.311104i
$529$	1.51238	−	0.466507i	0.0657556	−	0.0202829i
$530$	0.227012	−	3.02927i	0.00986079	−	0.131583i
$531$	6.47976	+	28.3897i	0.281198	+	1.23201i
$532$	23.5872	+	15.8721i	1.02263	+	0.688142i
$533$	−1.53474	+	6.72415i	−0.0664772	+	0.291255i
$534$	5.63530	+	1.73826i	0.243863	+	0.0752219i
$535$	8.91052	−	22.7036i	0.385235	−	0.981563i
$536$	18.7138	−	17.3639i	0.808314	−	0.750006i
$537$	−15.3638	+	10.4749i	−0.662997	+	0.452024i
$538$	−4.17526			−0.180008
$539$	−13.1180	−	16.0449i	−0.565031	−	0.691101i
$540$	12.7515			0.548737
$541$	6.71943	−	4.58123i	0.288891	−	0.196963i	−0.410199	−	0.911996i	$-0.634541\pi$
$541$	6.71943	−	4.58123i	0.288891	−	0.196963i	0.699090	+	0.715033i	$0.253588\pi$
$542$	−8.21886	+	7.62599i	−0.353030	+	0.327564i
$543$	−7.63687	+	19.4584i	−0.327729	+	0.835041i
$544$	8.18902	+	2.52598i	0.351102	+	0.108300i
$545$	−4.44407	+	19.4707i	−0.190363	+	0.834035i
$546$	0.532106	−	1.38043i	0.0227720	−	0.0590768i
$547$	−2.74014	−	12.0053i	−0.117160	−	0.513311i	−0.999118	−	0.0419839i	$-0.986632\pi$
$547$	−2.74014	−	12.0053i	−0.117160	−	0.513311i	0.881958	−	0.471327i	$-0.156225\pi$
$548$	−1.47985	+	19.7472i	−0.0632160	+	0.843559i
$549$	1.28595	−	0.396662i	0.0548829	−	0.0169291i
$550$	0.341805	+	4.56107i	0.0145746	+	0.194485i
$551$	−10.1940	−	25.9738i	−0.434277	−	1.10652i
$552$	−9.26386	−	4.46124i	−0.394296	−	0.189883i
$553$	3.22308	−	14.5282i	0.137059	−	0.617802i
$554$	−2.39144	+	1.15165i	−0.101602	+	0.0489291i
$555$	−11.1072	−	10.3060i	−0.471476	−	0.437466i
$556$	−3.13597	−	0.472671i	−0.132995	−	0.0200457i
$557$	20.0550	+	34.7363i	0.849758	+	1.47182i	0.881424	+	0.472326i	$0.156585\pi$
$557$	20.0550	+	34.7363i	0.849758	+	1.47182i	−0.0316659	+	0.999499i	$0.510081\pi$
$558$	−1.76324	+	3.05403i	−0.0746441	+	0.129287i
$559$	3.02604	−	3.79453i	0.127988	−	0.160492i
$560$	−6.66440	−	6.10861i	−0.281622	−	0.258136i
$561$	3.11311	+	3.90371i	0.131435	+	0.164815i
$562$	−11.3357	+	1.70857i	−0.478166	+	0.0720719i
$563$	10.2322	+	6.97622i	0.431237	+	0.294013i	0.759419	−	0.650602i	$-0.225483\pi$
$563$	10.2322	+	6.97622i	0.431237	+	0.294013i	−0.328182	+	0.944615i	$0.606436\pi$
$564$	13.1950	+	8.99617i	0.555608	+	0.378807i
$565$	0.378844	−	0.0571016i	0.0159381	−	0.00240228i
$566$	−6.27375	−	7.86704i	−0.263706	−	0.330676i
$567$	1.28531	−	0.201736i	0.0539779	−	0.00847211i
$568$	12.9677	−	16.2610i	0.544115	−	0.682298i
$569$	−5.18985	+	8.98908i	−0.217570	+	0.376842i	−0.954064	−	0.299601i	$-0.903146\pi$
$569$	−5.18985	+	8.98908i	−0.217570	+	0.376842i	0.736495	+	0.676443i	$0.236480\pi$
$570$	−2.57070	−	4.45258i	−0.107675	−	0.186498i
$571$	−16.4686	−	2.48224i	−0.689189	−	0.103879i	−0.204895	−	0.978784i	$-0.565685\pi$
$571$	−16.4686	−	2.48224i	−0.689189	−	0.103879i	−0.484294	+	0.874905i	$0.660924\pi$
$572$	−3.70846	−	3.44095i	−0.155059	−	0.143873i
$573$	19.1235	−	9.20941i	0.798897	−	0.384728i
$574$	8.89931	+	4.21916i	0.371450	+	0.176104i
$575$	12.7863	+	6.15756i	0.533226	+	0.256788i
$576$	1.28996	+	3.28676i	0.0537483	+	0.136948i
$577$	−2.83246	−	37.7965i	−0.117917	−	1.57349i	−0.671697	−	0.740826i	$-0.734434\pi$
$577$	−2.83246	−	37.7965i	−0.117917	−	1.57349i	0.553780	−	0.832663i	$-0.313185\pi$
$578$	−7.40109	+	2.28293i	−0.307845	+	0.0949575i
$579$	−0.629685	+	8.40256i	−0.0261688	+	0.349198i
$580$	2.46653	+	10.8066i	0.102417	+	0.448718i
$581$	−23.1163	+	21.7120i	−0.959025	+	0.900768i
$582$	−1.82326	+	7.98824i	−0.0755767	+	0.331123i
$583$	10.8911	+	3.35946i	0.451063	+	0.139135i
$584$	−5.75907	+	14.6739i	−0.238312	+	0.607209i
$585$	−2.06491	+	1.91596i	−0.0853736	+	0.0792151i
$586$	−7.77504	+	5.30094i	−0.321184	+	0.218980i
$587$	19.3774			0.799791			0.399896	−	0.916561i	$-0.369046\pi$
$587$	19.3774			0.799791			0.399896	+	0.916561i	$0.369046\pi$
$588$	10.3229	+	6.85551i	0.425710	+	0.282717i
$589$	−21.3276			−0.878788
$590$	−9.85454	+	6.71871i	−0.405705	+	0.276605i
$591$	7.64049	−	7.08934i	0.314288	−	0.291616i
$592$	8.54071	−	21.7614i	0.351021	−	0.894387i
$593$	−18.2397	−	5.62620i	−0.749014	−	0.231040i	−0.103333	−	0.994647i	$-0.532951\pi$
$593$	−18.2397	−	5.62620i	−0.749014	−	0.231040i	−0.645682	+	0.763606i	$0.723427\pi$
$594$	1.81493	−	7.95171i	0.0744673	−	0.326263i
$595$	−6.23199	−	0.900569i	−0.255486	−	0.0369197i
$596$	−3.81639	−	16.7207i	−0.156325	−	0.684907i
$597$	1.91400	−	25.5406i	0.0783348	−	1.04531i
$598$	2.55710	−	0.788762i	0.104568	−	0.0322549i
$599$	1.35319	+	18.0570i	0.0552898	+	0.737791i	0.954107	+	0.299467i	$0.0968087\pi$
$599$	1.35319	+	18.0570i	0.0552898	+	0.737791i	−0.898817	+	0.438324i	$0.855572\pi$
$600$	−2.16863	−	5.52559i	−0.0885341	−	0.225581i
$601$	−33.7644	−	16.2601i	−1.37728	−	0.663263i	−0.408861	−	0.912596i	$-0.634074\pi$
$601$	−33.7644	−	16.2601i	−1.37728	−	0.663263i	−0.968418	+	0.249334i	$0.919788\pi$
$602$	−4.35398	−	5.39207i	−0.177455	−	0.219765i
$603$	22.1382	−	10.6612i	0.901539	−	0.434158i
$604$	−5.03862	−	4.67516i	−0.205019	−	0.190230i
$605$	−3.23024	−	0.486880i	−0.131328	−	0.0197945i
$606$	3.35267	+	5.80699i	0.136193	+	0.235893i
$607$	17.5564	−	30.4087i	0.712594	−	1.23425i	−0.251286	−	0.967913i	$-0.580854\pi$
$607$	17.5564	−	30.4087i	0.712594	−	1.23425i	0.963880	−	0.266336i	$-0.0858132\pi$
$608$	20.6428	−	25.8852i	0.837174	−	1.04978i
$609$	−4.51208	−	11.2940i	−0.182839	−	0.457657i
$610$	0.343662	+	0.430938i	0.0139145	+	0.0174482i
$611$	−8.92036	+	1.34453i	−0.360879	+	0.0543938i
$612$	4.42755	+	3.01866i	0.178973	+	0.122022i
$613$	−12.2350	−	8.34170i	−0.494168	−	0.336918i	0.290458	−	0.956888i	$-0.406192\pi$
$613$	−12.2350	−	8.34170i	−0.494168	−	0.336918i	−0.784626	+	0.619970i	$0.787145\pi$
$614$	6.29422	−	0.948702i	0.254014	−	0.0382865i
$615$	6.51389	+	8.16816i	0.262665	+	0.329372i
$616$	−12.9011	+	8.91128i	−0.519799	+	0.359046i
$617$	8.83477	−	11.0785i	0.355674	−	0.446002i	−0.571517	−	0.820591i	$-0.693645\pi$
$617$	8.83477	−	11.0785i	0.355674	−	0.446002i	0.927191	+	0.374589i	$0.122216\pi$
$618$	−0.286080	+	0.495506i	−0.0115078	+	0.0199322i
$619$	23.4325	+	40.5863i	0.941831	+	1.63130i	0.761975	+	0.647606i	$0.224230\pi$
$619$	23.4325	+	40.5863i	0.941831	+	1.63130i	0.179856	+	0.983693i	$0.442437\pi$
$620$	8.37788	+	1.26276i	0.336464	+	0.0507137i
$621$	−18.5513	−	17.2131i	−0.744439	−	0.690738i
$622$	−1.72044	+	0.828520i	−0.0689833	+	0.0332206i
$623$	−6.37452	−	27.1655i	−0.255390	−	1.08836i
$624$	2.18150	+	1.05056i	0.0873300	+	0.0420559i
$625$	−0.911658	−	2.32287i	−0.0364663	−	0.0929147i
$626$	0.898400	+	11.9883i	0.0359073	+	0.479149i
$627$	18.4331	−	5.68586i	0.736147	−	0.227071i
$628$	−0.601085	+	8.02093i	−0.0239859	+	0.320070i
$629$	−3.62320	−	15.8743i	−0.144466	−	0.632948i
$630$	2.03236	+	3.47120i	0.0809712	+	0.138296i
$631$	0.834988	−	3.65832i	0.0332404	−	0.145636i	−0.955585	−	0.294717i	$-0.904775\pi$
$631$	0.834988	−	3.65832i	0.0332404	−	0.145636i	0.988825	+	0.149082i	$0.0476317\pi$
$632$	−10.7585	−	3.31855i	−0.427949	−	0.132005i
$633$	6.73522	−	17.1611i	0.267701	−	0.682091i
$634$	−8.89591	+	8.25420i	−0.353302	+	0.327816i
$635$	24.7339	−	16.8633i	0.981536	−	0.669200i
$636$	−6.81486			−0.270227
$637$	−6.90861	+	1.12746i	−0.273729	+	0.0446717i
$638$	7.08993			0.280693
$639$	16.5404	−	11.2771i	0.654328	−	0.446114i
$640$	−12.3453	+	11.4547i	−0.487990	+	0.452788i
$641$	10.1919	−	25.9687i	0.402558	−	1.02570i	−0.575581	−	0.817745i	$-0.695224\pi$
$641$	10.1919	−	25.9687i	0.402558	−	1.02570i	0.978138	−	0.207955i	$-0.0666808\pi$
$642$	8.91341	+	2.74942i	0.351784	+	0.108511i
$643$	2.17689	−	9.53760i	0.0858483	−	0.376126i	−0.913693	−	0.406405i	$-0.866782\pi$
$643$	2.17689	−	9.53760i	0.0858483	−	0.376126i	0.999541	+	0.0302786i	$0.00963945\pi$
$644$	1.81103	+	22.3413i	0.0713647	+	0.880369i
$645$	−1.63592	−	7.16743i	−0.0644142	−	0.282217i
$646$	0.412882	−	5.50953i	0.0162446	−	0.216769i
$647$	−16.0029	+	4.93623i	−0.629137	+	0.194063i	−0.592895	−	0.805280i	$-0.702015\pi$
$647$	−16.0029	+	4.93623i	−0.629137	+	0.194063i	−0.0362423	+	0.999343i	$0.511539\pi$
$648$	−0.0735580	−	0.981563i	−0.00288963	−	0.0385594i
$649$	−16.3487	−	41.6558i	−0.641742	−	1.63513i
$650$	1.39187	+	0.670291i	0.0545938	+	0.0262910i
$651$	−9.29594	+	0.0565715i	−0.364337	+	0.00221721i
$652$	21.5337	−	10.3701i	0.843323	−	0.406123i
$653$	−8.46948	−	7.85853i	−0.331436	−	0.307528i	0.496846	−	0.867839i	$-0.334491\pi$
$653$	−8.46948	−	7.85853i	−0.331436	−	0.307528i	−0.828283	+	0.560311i	$0.810682\pi$
$654$	−7.55280	−	1.13840i	−0.295338	−	0.0445150i
$655$	1.84335	+	3.19278i	0.0720257	+	0.124752i
$656$	−8.05944	+	13.9594i	−0.314668	+	0.545022i
$657$	−9.45994	+	11.8624i	−0.369067	+	0.462796i
$658$	−0.884472	+	12.8515i	−0.0344803	+	0.501002i
$659$	13.0750	+	16.3955i	0.509329	+	0.638679i	0.968305	−	0.249770i	$-0.0803550\pi$
$659$	13.0750	+	16.3955i	0.509329	+	0.638679i	−0.458976	+	0.888449i	$0.651784\pi$
$660$	−7.57752	+	1.14213i	−0.294955	+	0.0444572i
$661$	17.7349	+	12.0914i	0.689807	+	0.470302i	0.856795	−	0.515657i	$-0.172452\pi$
$661$	17.7349	+	12.0914i	0.689807	+	0.470302i	−0.166989	+	0.985959i	$0.553404\pi$
$662$	−16.1025	−	10.9785i	−0.625842	−	0.426692i
$663$	1.66761	−	0.251351i	0.0647645	−	0.00976167i
$664$	14.9597	+	18.7588i	0.580548	+	0.727984i
$665$	−12.0349	+	21.1412i	−0.466695	+	0.819821i
$666$	−6.48517	+	8.13215i	−0.251295	+	0.315114i
$667$	10.9993	−	19.0513i	0.425893	−	0.737669i
$668$	1.11401	+	1.92952i	0.0431022	+	0.0746553i
$669$	29.7275	+	4.48071i	1.14933	+	0.173234i
$670$	7.37753	+	6.84534i	0.285019	+	0.264459i
$671$	−1.86323	+	0.897282i	−0.0719290	+	0.0346392i
$672$	8.92879	−	11.3372i	0.344435	−	0.437342i
$673$	−13.7374	−	6.61559i	−0.529538	−	0.255012i	0.149956	−	0.988693i	$-0.452087\pi$
$673$	−13.7374	−	6.61559i	−0.529538	−	0.255012i	−0.679495	+	0.733680i	$0.737801\pi$
$674$	3.17670	+	8.09409i	0.122362	+	0.311773i
$675$	−1.09180	−	14.5690i	−0.0420232	−	0.560761i
$676$	−1.63279	+	0.503648i	−0.0627995	+	0.0193711i
$677$	2.08561	−	27.8305i	0.0801563	−	1.06961i	−0.801586	−	0.597880i	$-0.796010\pi$
$677$	2.08561	−	27.8305i	0.0801563	−	1.06961i	0.881742	−	0.471732i	$-0.156371\pi$
$678$	0.0326051	+	0.142852i	0.00125219	+	0.00548621i
$679$	36.9761	−	11.6525i	1.41901	−	0.447183i
$680$	−1.06005	+	4.64440i	−0.0406512	+	0.178104i
$681$	12.1123	+	3.73614i	0.464143	+	0.143169i
$682$	1.97987	−	5.04463i	0.0758133	−	0.193169i
$683$	12.4642	−	11.5651i	0.476931	−	0.442527i	−0.404712	−	0.914444i	$-0.632628\pi$
$683$	12.4642	−	11.5651i	0.476931	−	0.442527i	0.881643	+	0.471917i	$0.156438\pi$
$684$	17.1054	−	11.6623i	0.654042	−	0.445918i
$685$	−16.9444			−0.647411
$686$	−0.564892	+	9.97980i	−0.0215677	+	0.381031i
$687$	10.1459			0.387089
$688$	9.37174	−	6.38955i	0.357294	−	0.243599i
$689$	2.82195	−	2.61839i	0.107508	−	0.0997526i
$690$	1.48091	−	3.77330i	0.0563773	−	0.143647i
$691$	12.8134	+	3.95240i	0.487443	+	0.150356i	0.528728	−	0.848791i	$-0.322669\pi$
$691$	12.8134	+	3.95240i	0.487443	+	0.150356i	−0.0412851	+	0.999147i	$0.513145\pi$
$692$	0.845339	−	3.70367i	0.0321350	−	0.140793i
$693$	−14.3939	+	4.53604i	−0.546779	+	0.172310i
$694$	−0.922718	−	4.04269i	−0.0350259	−	0.153459i
$695$	0.202791	−	2.70606i	0.00769231	−	0.102647i
$696$	−8.79246	+	2.71211i	−0.333277	+	0.102802i
$697$	0.838989	+	11.1955i	0.0317790	+	0.424061i
$698$	−1.67028	−	4.25582i	−0.0632212	−	0.161085i
$699$	23.2041	+	11.1745i	0.877659	+	0.422658i
$700$	−8.00627	+	10.1658i	−0.302608	+	0.384233i
$701$	8.66771	−	4.17415i	0.327375	−	0.157655i	−0.262976	−	0.964802i	$-0.584704\pi$
$701$	8.66771	−	4.17415i	0.327375	−	0.157655i	0.590350	+	0.807147i	$0.298990\pi$
$702$	−2.01943	−	1.87376i	−0.0762186	−	0.0707206i
$703$	−62.2032	−	9.37563i	−2.34604	−	0.353609i
$704$	−2.71296	−	4.69899i	−0.102249	−	0.177100i
$705$	−6.83244	+	11.8341i	−0.257325	+	0.445700i
$706$	1.43782	−	1.80297i	0.0541130	−	0.0678556i
$707$	15.6958	−	27.5721i	0.590301	−	1.03695i
$708$	16.6826	+	20.9193i	0.626969	+	0.786194i
$709$	−20.1915	+	3.04338i	−0.758309	+	0.114297i	−0.516805	−	0.856103i	$-0.672879\pi$
$709$	−20.1915	+	3.04338i	−0.758309	+	0.114297i	−0.241504	+	0.970400i	$0.577641\pi$
$710$	6.77468	+	4.61890i	0.254249	+	0.173344i
$711$	−8.95361	−	6.10447i	−0.335787	−	0.228935i
$712$	−20.8747	+	3.14636i	−0.782314	+	0.117915i
$713$	−10.4838	−	13.1463i	−0.392623	−	0.492333i
$714$	0.165347	−	2.40250i	0.00618794	−	0.0899114i
$715$	2.69893	−	3.38436i	0.100934	−	0.126568i
$716$	15.3339	−	26.5591i	0.573056	−	0.992562i
$717$	5.28857	+	9.16008i	0.197505	+	0.342089i
$718$	−2.84265	−	0.428460i	−0.106087	−	0.0159900i
$719$	6.48890	+	6.02082i	0.241995	+	0.224539i	0.791841	−	0.610728i	$-0.209123\pi$
$719$	6.48890	+	6.02082i	0.241995	+	0.224539i	−0.549846	+	0.835266i	$0.685313\pi$
$720$	−5.93125	+	2.85634i	−0.221045	+	0.106450i
$721$	2.70716	−	0.0164747i	0.100820	−	0.000613550i
$722$	−9.99220	−	4.81199i	−0.371871	−	0.179084i
$723$	−0.847061	−	2.15828i	−0.0315025	−	0.0802671i
$724$	−2.57634	−	34.3788i	−0.0957488	−	1.27768i
$725$	12.1357	−	3.74336i	0.450707	−	0.139025i
$726$	0.0933649	−	1.24587i	0.00346510	−	0.0462385i
$727$	−0.511582	−	2.24139i	−0.0189735	−	0.0831284i	0.964555	−	0.263883i	$-0.0850032\pi$
$727$	−0.511582	−	2.24139i	−0.0189735	−	0.0831284i	−0.983528	+	0.180754i	$0.942146\pi$
$728$	0.427895	+	5.27859i	0.0158588	+	0.195638i
$729$	−3.31933	+	14.5430i	−0.122938	+	0.538628i
$730$	−5.93834	−	1.83174i	−0.219788	−	0.0677956i
$731$	2.88628	−	7.35413i	0.106753	−	0.272002i
$732$	0.906441	−	0.841054i	0.0335030	−	0.0310863i
$733$	−18.5889	+	12.6737i	−0.686598	+	0.468114i	−0.855692	−	0.517485i	$-0.826868\pi$
$733$	−18.5889	+	12.6737i	−0.686598	+	0.468114i	0.169094	+	0.985600i	$0.445916\pi$
$734$	3.62705			0.133877
$735$	−5.18953	+	9.24663i	−0.191419	+	0.341067i
$736$	26.1028			0.962163
$737$	−31.1986	+	21.2709i	−1.14922	+	0.783522i
$738$	5.25734	−	4.87810i	0.193525	−	0.179565i
$739$	−5.08115	+	12.9466i	−0.186913	+	0.476247i	−0.993358	−	0.115062i	$-0.963293\pi$
$739$	−5.08115	+	12.9466i	−0.186913	+	0.476247i	0.806445	+	0.591309i	$0.201389\pi$
$740$	23.8795	+	7.36585i	0.877828	+	0.270774i
$741$	1.44981	−	6.35205i	0.0532603	−	0.233348i
$742$	−2.77747	−	4.74381i	−0.101964	−	0.174151i
$743$	11.1044	+	48.6514i	0.407380	+	1.78485i	0.596201	+	0.802835i	$0.296676\pi$
$743$	11.1044	+	48.6514i	0.407380	+	1.78485i	−0.188821	+	0.982012i	$0.560467\pi$
$744$	−0.525580	+	7.01338i	−0.0192687	+	0.257123i
$745$	14.0233	−	4.32561i	0.513773	−	0.158478i
$746$	1.08208	+	14.4393i	0.0396177	+	0.528662i
$747$	8.43717	+	21.4976i	0.308700	+	0.786554i
$748$	−7.41933	−	3.57296i	−0.271277	−	0.130640i
$749$	−10.0826	−	42.9679i	−0.368412	−	1.57001i
$750$	5.79131	−	2.78895i	0.211469	−	0.101838i
$751$	28.0850	+	26.0590i	1.02483	+	0.950908i	0.998811	−	0.0487538i	$-0.0155250\pi$
$751$	28.0850	+	26.0590i	1.02483	+	0.950908i	0.0260238	+	0.999661i	$0.491715\pi$
$752$	−20.8474	−	3.14224i	−0.760227	−	0.114586i
$753$	−0.673972	−	1.16735i	−0.0245609	−	0.0425407i
$754$	1.19734	−	2.07386i	0.0436047	−	0.0755255i
$755$	3.66700	−	4.59827i	0.133456	−	0.167348i
$756$	18.9859	−	13.1144i	0.690512	−	0.476964i
$757$	12.2331	+	15.3399i	0.444621	+	0.557537i	0.952754	−	0.303741i	$-0.0982359\pi$
$757$	12.2331	+	15.3399i	0.444621	+	0.557537i	−0.508134	+	0.861278i	$0.669664\pi$
$758$	12.4432	−	1.87551i	0.451957	−	0.0681216i
$759$	12.5658	+	8.56721i	0.456109	+	0.310970i
$760$	15.2066	+	10.3677i	0.551601	+	0.376076i
$761$	49.5346	−	7.46615i	1.79563	−	0.270648i	0.835356	−	0.549709i	$-0.185261\pi$
$761$	49.5346	−	7.46615i	1.79563	−	0.270648i	0.960273	+	0.279062i	$0.0900234\pi$
$762$	7.13827	+	8.95110i	0.258592	+	0.324264i
$763$	13.4079	+	33.5609i	0.485400	+	1.21499i
$764$	−21.8262	+	27.3692i	−0.789643	+	0.990181i
$765$	−2.29262	+	3.97093i	−0.0828899	+	0.143569i
$766$	9.29524	+	16.0998i	0.335851	+	0.581710i
$767$	−14.9456	−	2.25269i	−0.539654	−	0.0813398i
$768$	−1.93777	−	1.79799i	−0.0699232	−	0.0648793i
$769$	24.5061	−	11.8015i	0.883711	−	0.425573i	0.0637324	−	0.997967i	$-0.479700\pi$
$769$	24.5061	−	11.8015i	0.883711	−	0.425573i	0.819979	+	0.572394i	$0.193985\pi$
$770$	−3.88333	−	4.80921i	−0.139946	−	0.173312i
$771$	4.67351	+	2.25064i	0.168312	+	0.0810549i
$772$	−5.07710	−	12.9362i	−0.182729	−	0.465586i
$773$	0.535407	+	7.14451i	0.0192573	+	0.256970i	0.998520	+	0.0543779i	$0.0173176\pi$
$773$	0.535407	+	7.14451i	0.0192573	+	0.256970i	−0.979263	+	0.202592i	$0.935063\pi$
$774$	−4.82253	+	1.48755i	−0.173342	+	0.0534690i
$775$	0.725424	−	9.68012i	0.0260580	−	0.347720i
$776$	−6.52672	−	28.5954i	−0.234296	−	1.02652i
$777$	−27.1371	−	3.92151i	−0.973537	−	0.140683i
$778$	−1.65771	+	7.26291i	−0.0594318	+	0.260388i
$779$	41.4471	+	12.7847i	1.48500	+	0.458061i
$780$	−0.945606	+	2.40937i	−0.0338581	+	0.0862691i
$781$	−22.5513	+	20.9246i	−0.806949	+	0.748739i
$782$	3.59903	−	2.45378i	0.128701	−	0.0877469i
$783$	−22.6467			−0.809326
$784$	−16.2052	−	2.24118i	−0.578756	−	0.0800422i
$785$	−6.88247			−0.245646
$786$	−1.16498	+	0.794272i	−0.0415536	+	0.0283308i
$787$	−10.3703	+	9.62227i	−0.369663	+	0.342997i	−0.843028	−	0.537869i	$-0.819229\pi$
$787$	−10.3703	+	9.62227i	−0.369663	+	0.342997i	0.473366	+	0.880866i	$0.343039\pi$
$788$	−6.28022	+	16.0017i	−0.223724	+	0.570039i
$789$	20.4430	+	6.30583i	0.727790	+	0.224493i
$790$	0.987657	−	4.32721i	0.0351393	−	0.153955i
$791$	0.505342	−	0.474644i	0.0179679	−	0.0168764i
$792$	2.54069	+	11.1315i	0.0902796	+	0.395541i
$793$	−0.0521985	+	0.696541i	−0.00185362	+	0.0247349i
$794$	−14.2784	+	4.40430i	−0.506721	+	0.156303i
$795$	−0.435769	−	5.81493i	−0.0154551	−	0.206234i
$796$	15.4324	+	39.3212i	0.546989	+	1.39370i
$797$	−34.3493	−	16.5418i	−1.21671	−	0.585939i	−0.288320	−	0.957534i	$-0.593097\pi$
$797$	−34.3493	−	16.5418i	−1.21671	−	0.585939i	−0.928395	+	0.371595i	$0.878811\pi$
$798$	−8.40684	−	3.98568i	−0.297599	−	0.141092i
$799$	−13.2302	+	6.37131i	−0.468050	+	0.225401i
$800$	11.0466	+	10.2497i	0.390556	+	0.362383i
$801$	−20.0921	−	3.02840i	−0.709921	−	0.107003i
$802$	3.86460	+	6.69369i	0.136464	+	0.236362i
$803$	11.6580	−	20.1923i	0.411403	−	0.712571i
$804$	14.0769	−	17.6519i	0.496455	−	0.622535i
$805$	−18.9474	+	2.97389i	−0.667807	+	0.104816i
$806$	−1.14124	−	1.43106i	−0.0401983	−	0.0504071i
$807$	−7.92524	+	1.19454i	−0.278982	+	0.0420497i
$808$	−19.8322	−	13.5214i	−0.697696	−	0.475681i
$809$	17.8234	+	12.1518i	0.626637	+	0.427234i	0.834564	−	0.550910i	$-0.185719\pi$
$809$	17.8234	+	12.1518i	0.626637	+	0.427234i	−0.207927	+	0.978144i	$0.566672\pi$
$810$	0.383711	−	0.0578351i	0.0134822	−	0.00203212i
$811$	12.2367	+	15.3443i	0.429687	+	0.538810i	0.948793	−	0.315900i	$-0.102306\pi$
$811$	12.2367	+	15.3443i	0.429687	+	0.538810i	−0.519106	+	0.854710i	$0.673735\pi$
$812$	14.7865	+	13.5534i	0.518905	+	0.475630i
$813$	−13.4188	+	16.8266i	−0.470617	+	0.590135i
$814$	7.99205	−	13.8426i	0.280121	−	0.485184i
$815$	10.2254	+	17.7110i	0.358181	+	0.620388i
$816$	3.89730	+	0.587423i	0.136433	+	0.0205639i
$817$	−22.3741	−	20.7601i	−0.782770	−	0.726304i
$818$	−3.02244	+	1.45553i	−0.105677	+	0.0508915i
$819$	−1.10401	+	4.97638i	−0.0385771	+	0.173889i
$820$	−15.5243	−	7.47609i	−0.542131	−	0.261076i
$821$	−6.64848	−	16.9401i	−0.232034	−	0.591212i	0.766674	−	0.642037i	$-0.221910\pi$
$821$	−6.64848	−	16.9401i	−0.232034	−	0.591212i	−0.998708	+	0.0508246i	$0.983815\pi$
$822$	−0.484281	−	6.46227i	−0.0168912	−	0.225398i
$823$	−20.0121	+	6.17293i	−0.697579	+	0.215175i	−0.623208	−	0.782056i	$-0.714171\pi$
$823$	−20.0121	+	6.17293i	−0.697579	+	0.215175i	−0.0743710	+	0.997231i	$0.523695\pi$
$824$	0.153059	−	2.04243i	0.00533207	−	0.0711515i
$825$	1.95371	+	8.55977i	0.0680195	+	0.298013i
$826$	−7.76271	+	20.1386i	−0.270099	+	0.700710i
$827$	12.0695	−	52.8801i	0.419699	−	1.83882i	−0.114449	−	0.993429i	$-0.536510\pi$
$827$	12.0695	−	52.8801i	0.419699	−	1.83882i	0.534148	−	0.845391i	$-0.320633\pi$
$828$	15.5970	+	4.81104i	0.542034	+	0.167195i
$829$	−0.355026	+	0.904590i	−0.0123305	+	0.0314177i	−0.936906	−	0.349580i	$-0.886324\pi$
$829$	−0.355026	+	0.904590i	−0.0123305	+	0.0314177i	0.924576	+	0.380998i	$0.124419\pi$
$830$	−6.93387	+	6.43369i	−0.240678	+	0.223317i
$831$	−4.20980	+	2.87019i	−0.146036	+	0.0995658i
$832$	−1.83265			−0.0635358
$833$	−10.2051	+	5.06845i	−0.353586	+	0.175611i
$834$	1.03784			0.0359374
$835$	−1.57517	+	1.07393i	−0.0545110	+	0.0371650i
$836$	−23.3217	+	21.6393i	−0.806596	+	0.748412i
$837$	−6.32412	+	16.1136i	−0.218594	+	0.556967i
$838$	−14.2974	−	4.41017i	−0.493896	−	0.152347i
$839$	8.34148	−	36.5464i	0.287980	−	1.26172i	−0.599312	−	0.800515i	$-0.704559\pi$
$839$	8.34148	−	36.5464i	0.287980	−	1.26172i	0.887292	−	0.461207i	$-0.152584\pi$
$840$	6.65552	+	4.47857i	0.229637	+	0.154525i
$841$	2.07255	+	9.08044i	0.0714673	+	0.313119i
$842$	−0.496309	+	6.62278i	−0.0171039	+	0.228236i
$843$	−21.0278	+	6.48623i	−0.724237	+	0.223398i
$844$	2.27216	+	30.3199i	0.0782110	+	1.04365i
$845$	−0.534156	−	1.36101i	−0.0183755	−	0.0468201i
$846$	8.45155	+	4.07005i	0.290570	+	0.139931i
$847$	−5.31029	+	2.59723i	−0.182464	+	0.0892419i
$848$	8.10577	−	3.90353i	0.278353	−	0.134048i
$849$	−14.1592	−	13.1378i	−0.485943	−	0.450889i
$850$	2.48661	+	0.374796i	0.0852900	+	0.0128554i
$851$	−24.7976	−	42.9508i	−0.850052	−	1.47233i
$852$	9.19721	−	15.9300i	0.315091	−	0.545754i
$853$	−18.1394	+	22.7461i	−0.621081	+	0.778810i	−0.988496	−	0.151247i	$-0.951671\pi$
$853$	−18.1394	+	22.7461i	−0.621081	+	0.778810i	0.367416	+	0.930057i	$0.380243\pi$
$854$	0.954886	+	0.288191i	0.0326755	+	0.00986170i
$855$	11.0449	+	13.8499i	0.377727	+	0.473655i
$856$	−33.0178	+	4.97663i	−1.12853	+	0.170098i
$857$	25.9261	+	17.6761i	0.885619	+	0.603805i	0.918398	−	0.395658i	$-0.129483\pi$
$857$	25.9261	+	17.6761i	0.885619	+	0.603805i	−0.0327788	+	0.999463i	$0.510436\pi$
$858$	1.36787	+	0.932597i	0.0466983	+	0.0318383i
$859$	−0.465361	+	0.0701419i	−0.0158779	+	0.00239321i	−0.156976	−	0.987602i	$-0.550175\pi$
$859$	−0.465361	+	0.0701419i	−0.0158779	+	0.00239321i	0.141099	+	0.989996i	$0.454937\pi$
$860$	7.55980	+	9.47968i	0.257787	+	0.323255i
$861$	18.0992	+	5.46248i	0.616821	+	0.186161i
$862$	10.6327	−	13.3330i	0.362151	−	0.454123i
$863$	4.78272	−	8.28392i	0.162806	−	0.281988i	−0.773068	−	0.634323i	$-0.781279\pi$
$863$	4.78272	−	8.28392i	0.162806	−	0.281988i	0.935874	+	0.352335i	$0.114612\pi$
$864$	−13.4359	−	23.2717i	−0.457100	−	0.791721i
$865$	3.21430	+	0.484477i	0.109289	+	0.0164727i
$866$	1.95995	+	1.81857i	0.0666018	+	0.0617974i
$867$	−13.3952	+	6.45077i	−0.454923	+	0.219080i
$868$	13.7727	−	6.73613i	0.467475	−	0.228639i
$869$	15.0037	+	7.22541i	0.508966	+	0.245105i
$870$	−1.32524	−	3.37665i	−0.0449297	−	0.114479i
$871$	0.953086	+	12.7181i	0.0322941	+	0.430935i
$872$	26.1273	−	8.05922i	0.884784	−	0.272920i
$873$	2.10972	−	28.1523i	0.0714033	−	0.952810i
$874$	−3.74473	−	16.4067i	−0.126667	−	0.554966i
$875$	−25.2328	−	16.9795i	−0.853026	−	0.574010i
$876$	−3.10224	+	13.5918i	−0.104815	+	0.459224i
$877$	9.99552	+	3.08321i	0.337525	+	0.104113i	0.458884	−	0.888496i	$-0.348249\pi$
$877$	9.99552	+	3.08321i	0.337525	+	0.104113i	−0.121360	+	0.992609i	$0.538725\pi$
$878$	4.06643	−	10.3611i	0.137236	−	0.349670i
$879$	−13.2415	+	12.2864i	−0.446626	+	0.414408i
$880$	8.35869	−	5.69886i	0.281772	−	0.192109i
$881$	−9.81474			−0.330667			−0.165333	−	0.986238i	$-0.552870\pi$
$881$	−9.81474			−0.330667			−0.165333	+	0.986238i	$0.552870\pi$
$882$	6.59600	+	3.07814i	0.222099	+	0.103646i
$883$	6.57910			0.221404			0.110702	−	0.993854i	$-0.464690\pi$
$883$	6.57910			0.221404			0.110702	+	0.993854i	$0.464690\pi$
$884$	−2.29809	+	1.56681i	−0.0772931	+	0.0526976i
$885$	−16.7831	+	15.5724i	−0.564157	+	0.523461i
$886$	2.99346	−	7.62721i	0.100567	−	0.256241i
$887$	−10.2232	−	3.15345i	−0.343262	−	0.105882i	0.118331	−	0.992974i	$-0.462246\pi$
$887$	−10.2232	−	3.15345i	−0.343262	−	0.105882i	−0.461593	+	0.887092i	$0.652722\pi$
$888$	−4.61598	+	20.2239i	−0.154902	+	0.678671i
$889$	19.4837	−	50.5459i	0.653461	−	1.69525i
$890$	−1.85190	−	8.11371i	−0.0620759	−	0.271972i
$891$	−0.108801	+	1.45184i	−0.00364496	+	0.0486386i
$892$	−47.3795	+	14.6146i	−1.58638	+	0.489335i
$893$	4.23956	+	56.5730i	0.141872	+	1.89314i
$894$	2.05050	+	5.22459i	0.0685790	+	0.174737i
$895$	23.6427	+	11.3857i	0.790288	+	0.380583i
$896$	−6.60042	+	29.7517i	−0.220504	+	0.993936i
$897$	4.62808	−	2.22876i	0.154527	−	0.0744163i
$898$	−3.38787	−	3.14349i	−0.113055	−	0.104900i
$899$	−14.8791	−	2.24267i	−0.496247	−	0.0747971i
$900$	4.71144	+	8.16045i	0.157048	+	0.272015i
$901$	3.13314	−	5.42676i	0.104380	−	0.180792i
$902$	−6.87159	+	8.61670i	−0.228799	+	0.286905i
$903$	−9.80713	−	8.98925i	−0.326361	−	0.299143i
$904$	−0.327032	−	0.410085i	−0.0108769	−	0.0136392i
$905$	29.1697	−	4.39663i	0.969635	−	0.146149i
$906$	1.85850	+	1.26710i	0.0617445	+	0.0420967i
$907$	26.6305	+	18.1564i	0.884252	+	0.602873i	0.918010	−	0.396557i	$-0.129795\pi$
$907$	26.6305	+	18.1564i	0.884252	+	0.602873i	−0.0337577	+	0.999430i	$0.510747\pi$
$908$	−20.6716	+	3.11574i	−0.686010	+	0.103399i
$909$	−14.4046	−	18.0628i	−0.477770	−	0.599105i
$910$	−2.06255	+	0.323728i	−0.0683728	+	0.0107315i
$911$	11.3752	−	14.2640i	0.376877	−	0.472589i	−0.556830	−	0.830626i	$-0.687983\pi$
$911$	11.3752	−	14.2640i	0.376877	−	0.472589i	0.933707	+	0.358038i	$0.116554\pi$
$912$	7.61345	−	13.1869i	0.252106	−	0.436661i
$913$	−17.7445	−	30.7344i	−0.587258	−	1.01716i
$914$	2.92384	+	0.440698i	0.0967119	+	0.0145770i
$915$	0.775610	+	0.719661i	0.0256409	+	0.0237912i
$916$	−15.0761	+	7.26027i	−0.498128	+	0.239886i
$917$	6.02824	+	2.85798i	0.199070	+	0.0943790i
$918$	−4.04018	−	1.94565i	−0.133346	−	0.0642159i
$919$	17.0949	+	43.5570i	0.563908	+	1.43681i	0.873914	+	0.486080i	$0.161574\pi$
$919$	17.0949	+	43.5570i	0.563908	+	1.43681i	−0.310006	+	0.950734i	$0.600331\pi$
$920$	1.08436	+	14.4697i	0.0357501	+	0.477052i
$921$	11.6759	−	3.60154i	0.384734	−	0.118675i
$922$	−0.0331328	+	0.442126i	−0.00109117	+	0.0145606i
$923$	2.31214	+	10.1302i	0.0761051	+	0.333438i
$924$	−10.1077	+	9.49368i	−0.332518	+	0.312319i
$925$	6.37114	−	27.9138i	0.209482	−	0.917799i
$926$	−8.81906	−	2.72032i	−0.289812	−	0.0893952i
$927$	0.720224	−	1.83510i	0.0236553	−	0.0602726i
$928$	17.1233	−	15.8881i	0.562099	−	0.521552i
$929$	18.2693	−	12.4558i	0.599396	−	0.408662i	−0.225257	−	0.974299i	$-0.572322\pi$
$929$	18.2693	−	12.4558i	0.599396	−	0.408662i	0.824654	+	0.565638i	$0.191370\pi$
$930$	−2.77263			−0.0909181
$931$	3.82375	+	43.8550i	0.125318	+	1.43729i
$932$	−42.4761			−1.39135
$933$	−3.02860	+	2.06486i	−0.0991518	+	0.0676006i
$934$	10.4653	−	9.71036i	0.342434	−	0.317733i
$935$	2.57429	−	6.55918i	0.0841882	−	0.214508i
$936$	3.68512	+	1.13671i	0.120452	+	0.0371545i
$937$	−10.4445	+	45.7602i	−0.341206	+	1.49492i	0.455327	+	0.890324i	$0.349522\pi$
$937$	−10.4445	+	45.7602i	−0.341206	+	1.49492i	−0.796533	+	0.604595i	$0.793335\pi$
$938$	18.0247	+	2.60470i	0.588526	+	0.0850465i
$939$	5.13513	+	22.4985i	0.167579	+	0.734210i
$940$	1.68419	−	22.4740i	0.0549323	−	0.733020i
$941$	−1.14019	+	0.351703i	−0.0371692	+	0.0114652i	−0.313284	−	0.949659i	$-0.601429\pi$
$941$	−1.14019	+	0.351703i	−0.0371692	+	0.0114652i	0.276115	+	0.961125i	$0.410953\pi$
$942$	−0.196705	−	2.62485i	−0.00640900	−	0.0855222i
$943$	12.4933	+	31.8325i	0.406839	+	1.03661i
$944$	−31.8252	−	15.3262i	−1.03582	−	0.498825i
$945$	12.4042	+	15.3616i	0.403507	+	0.499713i
$946$	6.98743	−	3.36497i	0.227181	−	0.109405i
$947$	−29.9226	−	27.7641i	−0.972354	−	0.902213i	0.0228788	−	0.999738i	$-0.492717\pi$
$947$	−29.9226	−	27.7641i	−0.972354	−	0.902213i	−0.995233	+	0.0975253i	$0.968907\pi$
$948$	−9.84600	−	1.48405i	−0.319783	−	0.0481996i
$949$	−3.93761	−	6.82013i	−0.127820	−	0.221391i
$950$	4.85764	−	8.41368i	0.157603	−	0.272976i
$951$	−14.5242	+	18.2127i	−0.470979	+	0.590589i
$952$	3.19822	+	8.00535i	0.103655	+	0.259455i
$953$	−12.3184	−	15.4468i	−0.399032	−	0.500371i	0.541205	−	0.840891i	$-0.317968\pi$
$953$	−12.3184	−	15.4468i	−0.399032	−	0.500371i	−0.940237	+	0.340520i	$0.889397\pi$
$954$	−3.95825	+	0.596610i	−0.128153	+	0.0193160i
$955$	−24.7490	−	16.8736i	−0.800859	−	0.546016i
$956$	−14.4133	−	9.82684i	−0.466160	−	0.317823i
$957$	13.4577	−	2.02842i	0.435025	−	0.0655695i
$958$	−4.05726	−	5.08764i	−0.131084	−	0.164374i
$959$	−25.2288	+	17.4265i	−0.814681	+	0.562733i
$960$	−1.73084	+	2.17040i	−0.0558625	+	0.0700493i
$961$	9.74928	−	16.8862i	0.314493	−	0.544718i
$962$	−2.69939	−	4.67548i	−0.0870317	−	0.150743i
$963$	−31.7800	−	4.79006i	−1.02410	−	0.154358i
$964$	2.80311	+	2.60091i	0.0902822	+	0.0837697i
$965$	10.7135	−	5.15935i	0.344880	−	0.166085i
$966$	−1.67571	−	7.14118i	−0.0539152	−	0.229764i
$967$	45.4100	+	21.8683i	1.46029	+	0.703238i	0.984347	−	0.176239i	$-0.0563932\pi$
$967$	45.4100	+	21.8683i	1.46029	+	0.703238i	0.475941	+	0.879477i	$0.342108\pi$
$968$	1.63393	+	4.16318i	0.0525164	+	0.133810i
$969$	−0.792561	−	10.5760i	−0.0254607	−	0.339750i
$970$	11.0493	−	3.40827i	0.354773	−	0.109433i
$971$	2.51808	−	33.6014i	0.0808090	−	1.07832i	−0.798476	−	0.602026i	$-0.794360\pi$
$971$	2.51808	−	33.6014i	0.0808090	−	1.07832i	0.879285	−	0.476295i	$-0.158021\pi$
$972$	−6.01586	−	26.3572i	−0.192959	−	0.845408i
$973$	−2.48112	−	4.23766i	−0.0795412	−	0.135853i
$974$	−4.21073	+	18.4484i	−0.134920	+	0.591125i
$975$	2.83374	+	0.874094i	0.0907524	+	0.0279934i
$976$	−0.596391	+	1.51958i	−0.0190900	+	0.0486405i
$977$	−41.7658	+	38.7530i	−1.33621	+	1.23982i	−0.388197	+	0.921576i	$0.626902\pi$
$977$	−41.7658	+	38.7530i	−1.33621	+	1.23982i	−0.948009	+	0.318243i	$0.896907\pi$
$978$	−6.46239	+	4.40598i	−0.206645	+	0.140888i
$979$	31.2249			0.997951
$980$	1.09452	−	17.4535i	0.0349632	−	0.557530i
$981$	26.3170			0.840238
$982$	9.34976	−	6.37456i	0.298363	−	0.203420i
$983$	−0.660837	+	0.613167i	−0.0210774	+	0.0195570i	−0.690641	−	0.723198i	$-0.742672\pi$
$983$	−0.660837	+	0.613167i	−0.0210774	+	0.0195570i	0.669564	+	0.742755i	$0.266481\pi$
$984$	5.22554	−	13.3145i	0.166584	−	0.424449i
$985$	−14.0554	−	4.33553i	−0.447843	−	0.138141i
$986$	0.867391	−	3.80029i	0.0276234	−	0.121026i
$987$	1.99794	+	24.6469i	0.0635950	+	0.784521i
$988$	2.39113	+	10.4762i	0.0760718	+	0.333292i
$989$	1.79827	−	23.9963i	0.0571817	−	0.763037i
$990$	−4.30124	+	1.32676i	−0.136702	+	0.0421671i
$991$	3.47543	+	46.3764i	0.110401	+	1.47319i	0.727391	+	0.686224i	$0.240733\pi$
$991$	3.47543	+	46.3764i	0.110401	+	1.47319i	−0.616990	+	0.786971i	$0.711648\pi$
$992$	−6.52300	−	16.6203i	−0.207106	−	0.527696i
$993$	−33.7058	−	16.2319i	−1.06962	−	0.515102i
$994$	14.8373	−	0.0902940i	0.470610	−	0.00286395i
$995$	−32.5649	+	15.6824i	−1.03238	+	0.497167i
$996$	15.5553	+	14.4332i	0.492888	+	0.457334i
$997$	28.5681	+	4.30595i	0.904762	+	0.136371i	0.584912	−	0.811097i	$-0.301129\pi$
$997$	28.5681	+	4.30595i	0.904762	+	0.136371i	0.319851	+	0.947468i	$0.396367\pi$
$998$	−2.16898	−	3.75678i	−0.0686577	−	0.118919i
$999$	−25.5282	+	44.2162i	−0.807678	+	1.39894i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.625.18	yes	348
49.4	even	21	inner	637.2.bl.b.53.18	✓	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.53.18	✓	348	49.4	even	21	inner
637.2.bl.b.625.18	yes	348	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.445939 - 0.304036i) q^{2} +(0.759470 - 0.704685i) q^{3} +(-0.624259 + 1.59058i) q^{4} +(-1.39712 - 0.430954i) q^{5} +(0.124428 - 0.545153i) q^{6} +(-2.52342 + 0.795220i) q^{7} +(0.445412 + 1.95148i) q^{8} +(-0.143977 + 1.92124i) q^{9} +O(q^{10})\)	\(q+(0.445939 - 0.304036i) q^{2} +(0.759470 - 0.704685i) q^{3} +(-0.624259 + 1.59058i) q^{4} +(-1.39712 - 0.430954i) q^{5} +(0.124428 - 0.545153i) q^{6} +(-2.52342 + 0.795220i) q^{7} +(0.445412 + 1.95148i) q^{8} +(-0.143977 + 1.92124i) q^{9} +(-0.754055 + 0.232595i) q^{10} +(-0.221253 - 2.95241i) q^{11} +(0.646756 + 1.64791i) q^{12} +(-0.900969 - 0.433884i) q^{13} +(-0.883513 + 1.12183i) q^{14} +(-1.36476 + 0.657233i) q^{15} +(-1.71319 - 1.58960i) q^{16} +(-1.60960 - 0.242608i) q^{17} +(0.519920 + 0.900528i) q^{18} +(-3.14438 + 5.44623i) q^{19} +(1.55763 - 1.95321i) q^{20} +(-1.35608 + 2.38216i) q^{21} +(-0.996305 - 1.24933i) q^{22} +(-4.90272 + 0.738966i) q^{23} +(1.71346 + 1.16821i) q^{24} +(-2.36497 - 1.61241i) q^{25} +(-0.533693 + 0.0804413i) q^{26} +(3.18240 + 3.99060i) q^{27} +(0.310399 - 4.51013i) q^{28} +(-2.76636 + 3.46890i) q^{29} +(-0.408776 + 0.708021i) q^{30} +(1.69569 + 2.93702i) q^{31} +(-5.20589 - 0.784662i) q^{32} +(-2.24856 - 2.08636i) q^{33} +(-0.791544 + 0.381187i) q^{34} +(3.86822 - 0.0235405i) q^{35} +(-2.96601 - 1.42836i) q^{36} +(3.65447 + 9.31143i) q^{37} +(0.253647 + 3.38469i) q^{38} +(-0.990011 + 0.305378i) q^{39} +(0.218704 - 2.91840i) q^{40} +(-1.53474 - 6.72415i) q^{41} +(0.119534 + 1.47459i) q^{42} +(-1.07998 + 4.73170i) q^{43} +(4.83418 + 1.49115i) q^{44} +(1.02912 - 2.62215i) q^{45} +(-1.96164 + 1.82013i) q^{46} +(7.45360 - 5.08178i) q^{47} -2.42129 q^{48} +(5.73525 - 4.01334i) q^{49} -1.54486 q^{50} +(-1.39340 + 0.950007i) q^{51} +(1.25257 - 1.16221i) q^{52} +(-1.40641 + 3.58348i) q^{53} +(2.63244 + 0.812001i) q^{54} +(-0.963239 + 4.22022i) q^{55} +(-2.67582 - 4.57019i) q^{56} +(1.44981 + 6.35205i) q^{57} +(-0.178955 + 2.38799i) q^{58} +(14.4429 - 4.45505i) q^{59} +(-0.193423 - 2.58105i) q^{60} +(-0.255188 - 0.650210i) q^{61} +(1.64913 + 0.794180i) q^{62} +(-1.16449 - 4.96257i) q^{63} +(1.65116 - 0.795159i) q^{64} +(1.07178 + 0.994464i) q^{65} +(-1.63705 - 0.246745i) q^{66} +(-6.37686 - 11.0450i) q^{67} +(1.39069 - 2.40875i) q^{68} +(-3.20273 + 4.01609i) q^{69} +(1.71783 - 1.18657i) q^{70} +(-6.47848 - 8.12376i) q^{71} +(-3.81338 + 0.574775i) q^{72} +(6.50680 + 4.43626i) q^{73} +(4.46068 + 3.04124i) q^{74} +(-2.93237 + 0.441983i) q^{75} +(-6.69978 - 8.40126i) q^{76} +(2.90613 + 7.27422i) q^{77} +(-0.348638 + 0.437179i) q^{78} +(-2.81233 + 4.87109i) q^{79} +(1.70848 + 2.95917i) q^{80} +(-0.486256 - 0.0732913i) q^{81} +(-2.72879 - 2.53194i) q^{82} +(10.7997 - 5.20086i) q^{83} +(-2.94248 - 3.64404i) q^{84} +(2.14425 + 1.03262i) q^{85} +(0.957002 + 2.43840i) q^{86} +(0.343519 + 4.58394i) q^{87} +(5.66302 - 1.74681i) q^{88} +(-0.788139 + 10.5170i) q^{89} +(-0.338304 - 1.48221i) q^{90} +(2.61855 + 0.378401i) q^{91} +(1.88517 - 8.25949i) q^{92} +(3.35750 + 1.03565i) q^{93} +(1.77880 - 4.53232i) q^{94} +(6.74016 - 6.25395i) q^{95} +(-4.50666 + 3.07259i) q^{96} -14.6532 q^{97} +(1.33737 - 3.53343i) q^{98} +5.70414 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more