LMFDB - Embedded newform 418.2.j.c.177.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(23,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("418.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.j (of order $9$, degree $6$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			177.4
Character	$\chi$	$=$	418.177
Dual form			418.2.j.c.111.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(1.46132 + 0.531876i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.712779 - 4.04237i) q^{5} +(-1.46132 + 0.531876i) q^{6} +(-0.291586 + 0.505042i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.445574 - 0.373881i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(1.46132 + 0.531876i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.712779 - 4.04237i) q^{5} +(-1.46132 + 0.531876i) q^{6} +(-0.291586 + 0.505042i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.445574 - 0.373881i) q^{9} +(3.14441 + 2.63847i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(0.777551 - 1.34676i) q^{12} +(-1.18777 + 0.432311i) q^{13} +(-0.101267 - 0.574312i) q^{14} +(1.10844 - 6.28630i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.52251 - 2.11664i) q^{17} +0.581655 q^{18} +(-3.09925 - 3.06507i) q^{19} -4.10473 q^{20} +(-0.694720 + 0.582939i) q^{21} +(0.939693 + 0.342020i) q^{22} +(1.35152 - 7.66484i) q^{23} +(0.270041 + 1.53148i) q^{24} +(-11.1342 + 4.05253i) q^{25} +(0.631997 - 1.09465i) q^{26} +(-2.78492 - 4.82362i) q^{27} +(0.446736 + 0.374856i) q^{28} +(7.36272 + 6.17806i) q^{29} +(3.19164 + 5.52808i) q^{30} +(0.00593469 - 0.0102792i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.270041 - 1.53148i) q^{33} +(-0.571808 + 3.24288i) q^{34} +(2.24940 + 0.818716i) q^{35} +(-0.445574 + 0.373881i) q^{36} +5.09229 q^{37} +(4.34435 + 0.355820i) q^{38} -1.96564 q^{39} +(3.14441 - 2.63847i) q^{40} +(2.24964 + 0.818804i) q^{41} +(0.157480 - 0.893115i) q^{42} +(0.0356939 + 0.202430i) q^{43} +(-0.939693 + 0.342020i) q^{44} +(-1.19377 + 2.06767i) q^{45} +(3.89154 + 6.74035i) q^{46} +(2.30596 + 1.93493i) q^{47} +(-1.19128 - 0.999601i) q^{48} +(3.32996 + 5.76765i) q^{49} +(5.92441 - 10.2614i) q^{50} +(4.81199 - 1.75142i) q^{51} +(0.219490 + 1.24479i) q^{52} +(-2.07932 + 11.7924i) q^{53} +(5.23394 + 1.90500i) q^{54} +(-3.14441 + 2.63847i) q^{55} -0.583172 q^{56} +(-2.89875 - 6.12746i) q^{57} -9.61135 q^{58} +(7.70908 - 6.46868i) q^{59} +(-5.99832 - 2.18321i) q^{60} +(1.31454 - 7.45511i) q^{61} +(0.00206110 + 0.0116891i) q^{62} +(0.318749 - 0.116015i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.59418 + 4.49324i) q^{65} +(1.19128 + 0.999601i) q^{66} +(-10.0372 - 8.42218i) q^{67} +(-1.64645 - 2.85174i) q^{68} +(6.05175 - 10.4819i) q^{69} +(-2.24940 + 0.818716i) q^{70} +(0.249348 + 1.41412i) q^{71} +(0.101003 - 0.572819i) q^{72} +(0.954053 + 0.347247i) q^{73} +(-3.90092 + 3.27326i) q^{74} -18.4261 q^{75} +(-3.55668 + 2.51992i) q^{76} +0.583172 q^{77} +(1.50577 - 1.26349i) q^{78} +(13.4408 + 4.89204i) q^{79} +(-0.712779 + 4.04237i) q^{80} +(-1.20107 - 6.81163i) q^{81} +(-2.24964 + 0.818804i) q^{82} +(-5.71980 + 9.90699i) q^{83} +(0.453446 + 0.785392i) q^{84} +(-10.3542 - 8.68824i) q^{85} +(-0.157463 - 0.132127i) q^{86} +(7.47332 + 12.9442i) q^{87} +(0.500000 - 0.866025i) q^{88} +(0.710740 - 0.258688i) q^{89} +(-0.414592 - 2.35127i) q^{90} +(0.128001 - 0.725927i) q^{91} +(-7.31371 - 2.66197i) q^{92} +(0.0141397 - 0.0118646i) q^{93} -3.01022 q^{94} +(-10.1811 + 14.7130i) q^{95} +1.55510 q^{96} +(-3.59622 + 3.01759i) q^{97} +(-6.25827 - 2.27782i) q^{98} +(-0.101003 + 0.572819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) $ 30 * q - 12 * q^7 + 15 * q^8	$ 30 q - 12 q^{7} + 15 q^{8} - 15 q^{11} + 3 q^{12} - 3 q^{13} + 9 q^{14} + 27 q^{15} - 36 q^{18} - 9 q^{19} + 18 q^{20} - 27 q^{21} - 3 q^{23} - 12 q^{25} + 3 q^{27} + 9 q^{28} + 3 q^{29} + 9 q^{30} + 30 q^{31} - 9 q^{34} + 15 q^{35} + 18 q^{37} + 6 q^{38} - 6 q^{41} - 45 q^{42} + 39 q^{43} - 18 q^{45} + 21 q^{46} + 45 q^{47} - 33 q^{49} + 36 q^{50} - 36 q^{51} + 6 q^{52} - 24 q^{53} + 45 q^{54} - 24 q^{56} - 24 q^{57} - 30 q^{58} + 3 q^{59} - 9 q^{60} - 27 q^{61} + 15 q^{62} - 93 q^{63} - 15 q^{64} + 18 q^{65} - 9 q^{67} - 21 q^{68} + 48 q^{69} - 15 q^{70} + 39 q^{73} + 3 q^{74} - 42 q^{75} - 15 q^{76} + 24 q^{77} + 6 q^{78} + 21 q^{79} + 84 q^{81} + 6 q^{82} - 36 q^{83} - 27 q^{84} + 63 q^{85} + 6 q^{86} - 21 q^{87} + 15 q^{88} + 54 q^{89} + 12 q^{90} + 3 q^{91} - 3 q^{92} + 51 q^{93} - 78 q^{94} + 6 q^{95} + 6 q^{96} - 18 q^{97} + 3 q^{98}+O(q^{100}) $ 30 * q - 12 * q^7 + 15 * q^8 - 15 * q^11 + 3 * q^12 - 3 * q^13 + 9 * q^14 + 27 * q^15 - 36 * q^18 - 9 * q^19 + 18 * q^20 - 27 * q^21 - 3 * q^23 - 12 * q^25 + 3 * q^27 + 9 * q^28 + 3 * q^29 + 9 * q^30 + 30 * q^31 - 9 * q^34 + 15 * q^35 + 18 * q^37 + 6 * q^38 - 6 * q^41 - 45 * q^42 + 39 * q^43 - 18 * q^45 + 21 * q^46 + 45 * q^47 - 33 * q^49 + 36 * q^50 - 36 * q^51 + 6 * q^52 - 24 * q^53 + 45 * q^54 - 24 * q^56 - 24 * q^57 - 30 * q^58 + 3 * q^59 - 9 * q^60 - 27 * q^61 + 15 * q^62 - 93 * q^63 - 15 * q^64 + 18 * q^65 - 9 * q^67 - 21 * q^68 + 48 * q^69 - 15 * q^70 + 39 * q^73 + 3 * q^74 - 42 * q^75 - 15 * q^76 + 24 * q^77 + 6 * q^78 + 21 * q^79 + 84 * q^81 + 6 * q^82 - 36 * q^83 - 27 * q^84 + 63 * q^85 + 6 * q^86 - 21 * q^87 + 15 * q^88 + 54 * q^89 + 12 * q^90 + 3 * q^91 - 3 * q^92 + 51 * q^93 - 78 * q^94 + 6 * q^95 + 6 * q^96 - 18 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	1.46132	+	0.531876i	0.843693	+	0.307079i	0.727466	−	0.686144i	$-0.240698\pi$
$3$	1.46132	+	0.531876i	0.843693	+	0.307079i	0.116227	+	0.993223i	$0.462920\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.712779	−	4.04237i	−0.318764	−	1.80780i	−0.550289	−	0.834974i	$-0.685483\pi$
$5$	−0.712779	−	4.04237i	−0.318764	−	1.80780i	0.231525	−	0.972829i	$-0.425628\pi$
$6$	−1.46132	+	0.531876i	−0.596581	+	0.217138i
$7$	−0.291586	+	0.505042i	−0.110209	+	0.190888i	−0.915855	−	0.401510i	$-0.868485\pi$
$7$	−0.291586	+	0.505042i	−0.110209	+	0.190888i	0.805645	+	0.592398i	$0.201819\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.445574	−	0.373881i	−0.148525	−	0.124627i
$10$	3.14441	+	2.63847i	0.994348	+	0.834357i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	0.777551	−	1.34676i	0.224460	−	0.388776i
$13$	−1.18777	+	0.432311i	−0.329427	+	0.119902i	−0.501438	−	0.865193i	$-0.667196\pi$
$13$	−1.18777	+	0.432311i	−0.329427	+	0.119902i	0.172012	+	0.985095i	$0.444973\pi$
$14$	−0.101267	−	0.574312i	−0.0270647	−	0.153491i
$15$	1.10844	−	6.28630i	0.286199	−	1.62312i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	2.52251	−	2.11664i	0.611800	−	0.513361i	−0.283414	−	0.958998i	$-0.591467\pi$
$17$	2.52251	−	2.11664i	0.611800	−	0.513361i	0.895214	+	0.445637i	$0.147023\pi$
$18$	0.581655			0.137097
$19$	−3.09925	−	3.06507i	−0.711017	−	0.703175i
$19$	−3.09925	−	3.06507i	−0.711017	−	0.703175i
$20$	−4.10473			−0.917846
$21$	−0.694720	+	0.582939i	−0.151600	+	0.127208i
$22$	0.939693	+	0.342020i	0.200343	+	0.0729189i
$23$	1.35152	−	7.66484i	0.281811	−	1.59823i	−0.434647	−	0.900601i	$-0.643127\pi$
$23$	1.35152	−	7.66484i	0.281811	−	1.59823i	0.716458	−	0.697630i	$-0.245762\pi$
$24$	0.270041	+	1.53148i	0.0551218	+	0.312611i
$25$	−11.1342	+	4.05253i	−2.22685	+	0.810506i
$26$	0.631997	−	1.09465i	0.123945	−	0.214679i
$27$	−2.78492	−	4.82362i	−0.535958	−	0.928307i
$28$	0.446736	+	0.374856i	0.0844251	+	0.0708411i
$29$	7.36272	+	6.17806i	1.36722	+	1.14724i	0.973677	+	0.227932i	$0.0731964\pi$
$29$	7.36272	+	6.17806i	1.36722	+	1.14724i	0.393547	+	0.919305i	$0.371248\pi$
$30$	3.19164	+	5.52808i	0.582711	+	1.00928i
$31$	0.00593469	−	0.0102792i	0.00106590	−	0.00184620i	−0.865492	−	0.500923i	$-0.832994\pi$
$31$	0.00593469	−	0.0102792i	0.00106590	−	0.00184620i	0.866558	+	0.499077i	$0.166327\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−0.270041	−	1.53148i	−0.0470081	−	0.266596i
$34$	−0.571808	+	3.24288i	−0.0980642	+	0.556150i
$35$	2.24940	+	0.818716i	0.380218	+	0.138388i
$36$	−0.445574	+	0.373881i	−0.0742623	+	0.0623135i
$37$	5.09229			0.837168			0.418584	−	0.908178i	$-0.362527\pi$
$37$	5.09229			0.837168			0.418584	+	0.908178i	$0.362527\pi$
$38$	4.34435	+	0.355820i	0.704747	+	0.0577216i
$39$	−1.96564			−0.314754
$40$	3.14441	−	2.63847i	0.497174	−	0.417179i
$41$	2.24964	+	0.818804i	0.351335	+	0.127876i	0.511658	−	0.859189i	$-0.329031\pi$
$41$	2.24964	+	0.818804i	0.351335	+	0.127876i	−0.160323	+	0.987065i	$0.551254\pi$
$42$	0.157480	−	0.893115i	0.0242997	−	0.137811i
$43$	0.0356939	+	0.202430i	0.00544328	+	0.0308704i	0.987408	−	0.158192i	$-0.0505664\pi$
$43$	0.0356939	+	0.202430i	0.00544328	+	0.0308704i	−0.981965	+	0.189062i	$0.939455\pi$
$44$	−0.939693	+	0.342020i	−0.141664	+	0.0515615i
$45$	−1.19377	+	2.06767i	−0.177957	+	0.308230i
$46$	3.89154	+	6.74035i	0.573777	+	0.993811i
$47$	2.30596	+	1.93493i	0.336359	+	0.282238i	0.795285	−	0.606236i	$-0.207321\pi$
$47$	2.30596	+	1.93493i	0.336359	+	0.282238i	−0.458926	+	0.888474i	$0.651766\pi$
$48$	−1.19128	−	0.999601i	−0.171946	−	0.144280i
$49$	3.32996	+	5.76765i	0.475708	+	0.823950i
$50$	5.92441	−	10.2614i	0.837837	−	1.45118i
$51$	4.81199	−	1.75142i	0.673813	−	0.245248i
$52$	0.219490	+	1.24479i	0.0304378	+	0.172621i
$53$	−2.07932	+	11.7924i	−0.285617	+	1.61981i	0.417456	+	0.908697i	$0.362922\pi$
$53$	−2.07932	+	11.7924i	−0.285617	+	1.61981i	−0.703073	+	0.711117i	$0.748189\pi$
$54$	5.23394	+	1.90500i	0.712249	+	0.259237i
$55$	−3.14441	+	2.63847i	−0.423992	+	0.355771i
$56$	−0.583172			−0.0779296
$57$	−2.89875	−	6.12746i	−0.383949	−	0.811602i
$58$	−9.61135			−1.26203
$59$	7.70908	−	6.46868i	1.00364	−	0.842151i	0.0161523	−	0.999870i	$-0.494858\pi$
$59$	7.70908	−	6.46868i	1.00364	−	0.842151i	0.987484	+	0.157719i	$0.0504139\pi$
$60$	−5.99832	−	2.18321i	−0.774380	−	0.281851i
$61$	1.31454	−	7.45511i	0.168309	−	0.954529i	−0.777277	−	0.629158i	$-0.783400\pi$
$61$	1.31454	−	7.45511i	0.168309	−	0.954529i	0.945587	−	0.325371i	$-0.105489\pi$
$62$	0.00206110	+	0.0116891i	0.000261759	+	0.00148451i
$63$	0.318749	−	0.116015i	0.0401585	−	0.0146165i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.59418	+	4.49324i	0.321768	+	0.557318i
$66$	1.19128	+	0.999601i	0.146636	+	0.123042i
$67$	−10.0372	−	8.42218i	−1.22623	−	1.02893i	−0.998474	−	0.0552160i	$-0.982415\pi$
$67$	−10.0372	−	8.42218i	−1.22623	−	1.02893i	−0.227760	−	0.973717i	$-0.573140\pi$
$68$	−1.64645	−	2.85174i	−0.199662	−	0.345825i
$69$	6.05175	−	10.4819i	0.728545	−	1.26188i
$70$	−2.24940	+	0.818716i	−0.268855	+	0.0978552i
$71$	0.249348	+	1.41412i	0.0295922	+	0.167826i	0.996022	−	0.0891039i	$-0.0284003\pi$
$71$	0.249348	+	1.41412i	0.0295922	+	0.167826i	−0.966430	+	0.256929i	$0.917289\pi$
$72$	0.101003	−	0.572819i	0.0119034	−	0.0675073i
$73$	0.954053	+	0.347247i	0.111663	+	0.0406422i	0.397248	−	0.917711i	$-0.369965\pi$
$73$	0.954053	+	0.347247i	0.111663	+	0.0406422i	−0.285584	+	0.958354i	$0.592188\pi$
$74$	−3.90092	+	3.27326i	−0.453473	+	0.380509i
$75$	−18.4261			−2.12766
$76$	−3.55668	+	2.51992i	−0.407980	+	0.289055i
$77$	0.583172			0.0664586
$78$	1.50577	−	1.26349i	0.170495	−	0.143062i
$79$	13.4408	+	4.89204i	1.51220	+	0.550397i	0.959187	−	0.282773i	$-0.0912544\pi$
$79$	13.4408	+	4.89204i	1.51220	+	0.550397i	0.553017	+	0.833170i	$0.313477\pi$
$80$	−0.712779	+	4.04237i	−0.0796911	+	0.451951i
$81$	−1.20107	−	6.81163i	−0.133453	−	0.756848i
$82$	−2.24964	+	0.818804i	−0.248432	+	0.0904217i
$83$	−5.71980	+	9.90699i	−0.627830	+	1.08743i	0.360156	+	0.932892i	$0.382723\pi$
$83$	−5.71980	+	9.90699i	−0.627830	+	1.08743i	−0.987986	+	0.154542i	$0.950610\pi$
$84$	0.453446	+	0.785392i	0.0494750	+	0.0856933i
$85$	−10.3542	−	8.68824i	−1.12308	−	0.942372i
$86$	−0.157463	−	0.132127i	−0.0169797	−	0.0142476i
$87$	7.47332	+	12.9442i	0.801224	+	1.38776i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	0.710740	−	0.258688i	0.0753383	−	0.0274209i	−0.304076	−	0.952648i	$-0.598348\pi$
$89$	0.710740	−	0.258688i	0.0753383	−	0.0274209i	0.379414	+	0.925227i	$0.376125\pi$
$90$	−0.414592	−	2.35127i	−0.0437018	−	0.247845i
$91$	0.128001	−	0.725927i	0.0134181	−	0.0760978i
$92$	−7.31371	−	2.66197i	−0.762507	−	0.277530i
$93$	0.0141397	−	0.0118646i	0.00146622	−	0.00123031i
$94$	−3.01022			−0.310480
$95$	−10.1811	+	14.7130i	−1.04456	+	1.50953i
$96$	1.55510			0.158717
$97$	−3.59622	+	3.01759i	−0.365141	+	0.306390i	−0.806836	−	0.590776i	$-0.798822\pi$
$97$	−3.59622	+	3.01759i	−0.365141	+	0.306390i	0.441695	+	0.897165i	$0.354377\pi$
$98$	−6.25827	−	2.27782i	−0.632181	−	0.230095i
$99$	−0.101003	+	0.572819i	−0.0101512	+	0.0575704i
$100$	2.05752	+	11.6688i	0.205752	+	1.16688i
$101$	−7.71962	+	2.80971i	−0.768131	+	0.279577i	−0.696214	−	0.717834i	$-0.745134\pi$
$101$	−7.71962	+	2.80971i	−0.768131	+	0.279577i	−0.0719163	+	0.997411i	$0.522911\pi$
$102$	−2.56041	+	4.43475i	−0.253518	+	0.439106i
$103$	3.85591	+	6.67864i	0.379934	+	0.658066i	0.991052	−	0.133474i	$-0.0426132\pi$
$103$	3.85591	+	6.67864i	0.379934	+	0.658066i	−0.611118	+	0.791540i	$0.709280\pi$
$104$	−0.968275	−	0.812479i	−0.0949472	−	0.0796701i
$105$	2.85164	+	2.39281i	0.278291	+	0.233514i
$106$	−5.98717	−	10.3701i	−0.581526	−	1.00723i
$107$	3.31177	−	5.73616i	0.320161	−	0.554535i	−0.660360	−	0.750949i	$-0.729596\pi$
$107$	3.31177	−	5.73616i	0.320161	−	0.554535i	0.980521	+	0.196414i	$0.0629297\pi$
$108$	−5.23394	+	1.90500i	−0.503636	+	0.183309i
$109$	1.78019	+	10.0960i	0.170512	+	0.967019i	0.943198	+	0.332231i	$0.107801\pi$
$109$	1.78019	+	10.0960i	0.170512	+	0.967019i	−0.772686	+	0.634788i	$0.781087\pi$
$110$	0.712779	−	4.04237i	0.0679608	−	0.385425i
$111$	7.44146	+	2.70847i	0.706312	+	0.257077i
$112$	0.446736	−	0.374856i	0.0422126	−	0.0354205i
$113$	7.22414			0.679590			0.339795	−	0.940499i	$-0.389642\pi$
$113$	7.22414			0.679590			0.339795	+	0.940499i	$0.389642\pi$
$114$	6.15923	+	2.83062i	0.576865	+	0.265112i
$115$	−31.9475			−2.97912
$116$	7.36272	−	6.17806i	0.683612	−	0.573618i
$117$	0.690870	+	0.251456i	0.0638709	+	0.0232471i
$118$	−1.74751	+	9.91060i	−0.160871	+	0.912345i
$119$	0.333462	+	1.89116i	0.0305684	+	0.173362i
$120$	5.99832	−	2.18321i	0.547569	−	0.199299i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	3.78506	+	6.55591i	0.342683	+	0.593544i
$123$	2.85195	+	2.39307i	0.257151	+	0.215775i
$124$	−0.00909247	−	0.00762949i	−0.000816528	−	0.000685148i
$125$	14.0563	+	24.3462i	1.25723	+	2.17759i
$126$	−0.169603	+	0.293760i	−0.0151094	+	0.0261702i
$127$	−3.82487	+	1.39214i	−0.339402	+	0.123532i	−0.506098	−	0.862476i	$-0.668912\pi$
$127$	−3.82487	+	1.39214i	−0.339402	+	0.123532i	0.166696	+	0.986008i	$0.446690\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−0.0555078	+	0.314800i	−0.00488719	+	0.0277166i
$130$	−4.87546	−	1.77452i	−0.427606	−	0.155636i
$131$	14.2671	−	11.9715i	1.24652	−	1.04596i	0.249538	−	0.968365i	$-0.419721\pi$
$131$	14.2671	−	11.9715i	1.24652	−	1.04596i	0.996985	−	0.0775921i	$-0.0247232\pi$
$132$	−1.55510			−0.135354
$133$	2.45169	−	0.671519i	0.212588	−	0.0582281i
$134$	13.1026			1.13189
$135$	−17.5138	+	14.6959i	−1.50735	+	1.26482i
$136$	3.09432	+	1.12624i	0.265336	+	0.0965744i
$137$	2.73963	−	15.5372i	0.234062	−	1.32743i	−0.610518	−	0.792002i	$-0.709039\pi$
$137$	2.73963	−	15.5372i	0.234062	−	1.32743i	0.844580	−	0.535429i	$-0.179850\pi$
$138$	2.10175	+	11.9196i	0.178913	+	1.01467i
$139$	−11.7252	+	4.26764i	−0.994522	+	0.361976i	−0.787470	−	0.616353i	$-0.788609\pi$
$139$	−11.7252	+	4.26764i	−0.994522	+	0.361976i	−0.207053	+	0.978330i	$0.566387\pi$
$140$	1.19688	−	2.07306i	0.101155	−	0.175206i
$141$	2.34060	+	4.05403i	0.197114	+	0.341411i
$142$	−1.09999	−	0.923003i	−0.0923093	−	0.0774567i
$143$	0.968275	+	0.812479i	0.0809712	+	0.0679429i
$144$	0.290828	+	0.503728i	0.0242356	+	0.0419774i
$145$	19.7260	−	34.1664i	1.63816	−	2.83737i
$146$	−0.954053	+	0.347247i	−0.0789580	+	0.0287384i
$147$	1.79845	+	10.1995i	0.148333	+	0.841241i
$148$	0.884267	−	5.01493i	0.0726863	−	0.412225i
$149$	1.30888	+	0.476392i	0.107227	+	0.0390276i	0.395077	−	0.918648i	$-0.370718\pi$
$149$	1.30888	+	0.476392i	0.107227	+	0.0390276i	−0.287849	+	0.957676i	$0.592940\pi$
$150$	14.1152	−	11.8441i	1.15250	−	0.967065i
$151$	−4.54237			−0.369653			−0.184827	−	0.982771i	$-0.559172\pi$
$151$	−4.54237			−0.369653			−0.184827	+	0.982771i	$0.559172\pi$
$152$	1.10480	−	4.21656i	0.0896114	−	0.342008i
$153$	−1.91534			−0.154846
$154$	−0.446736	+	0.374856i	−0.0359990	+	0.0302067i
$155$	−0.0457824	−	0.0166634i	−0.00367733	−	0.00133844i
$156$	−0.341330	+	1.93578i	−0.0273282	+	0.154986i
$157$	0.477067	+	2.70558i	0.0380741	+	0.215929i	0.997909	−	0.0646371i	$-0.0205890\pi$
$157$	0.477067	+	2.70558i	0.0380741	+	0.215929i	−0.959835	+	0.280566i	$0.909478\pi$
$158$	−13.4408	+	4.89204i	−1.06929	+	0.389189i
$159$	−9.31067	+	16.1266i	−0.738384	+	1.27892i
$160$	−2.05237	−	3.55480i	−0.162254	−	0.281032i
$161$	3.47698	+	2.91754i	0.274025	+	0.229934i
$162$	5.29851	+	4.44598i	0.416290	+	0.349309i
$163$	−0.454463	−	0.787153i	−0.0355963	−	0.0616546i	0.847678	−	0.530510i	$-0.178000\pi$
$163$	−0.454463	−	0.787153i	−0.0355963	−	0.0616546i	−0.883275	+	0.468856i	$0.844666\pi$
$164$	1.19701	−	2.07328i	0.0934708	−	0.161896i
$165$	−5.99832	+	2.18321i	−0.466968	+	0.169963i
$166$	−1.98647	−	11.2658i	−0.154180	−	0.874397i
$167$	1.74168	−	9.87757i	0.134775	−	0.764349i	−0.840241	−	0.542214i	$-0.817586\pi$
$167$	1.74168	−	9.87757i	0.134775	−	0.764349i	0.975016	−	0.222135i	$-0.0713026\pi$
$168$	−0.852200	−	0.310176i	−0.0657487	−	0.0239306i
$169$	−8.73468	+	7.32927i	−0.671899	+	0.563790i
$170$	13.5165			1.03667
$171$	0.234974	+	2.52446i	0.0179689	+	0.193051i
$172$	0.205553			0.0156733
$173$	−9.16309	+	7.68875i	−0.696657	+	0.584565i	−0.920820	−	0.389987i	$-0.872480\pi$
$173$	−9.16309	+	7.68875i	−0.696657	+	0.584565i	0.224163	+	0.974552i	$0.428035\pi$
$174$	−14.0453	−	5.11205i	−1.06477	−	0.387544i
$175$	1.19989	−	6.80492i	0.0907032	−	0.514404i
$176$	0.173648	+	0.984808i	0.0130892	+	0.0742327i
$177$	14.7060	−	5.35253i	1.10537	−	0.402321i
$178$	−0.378177	+	0.655022i	−0.0283456	+	0.0490960i
$179$	−4.97171	−	8.61125i	−0.371603	−	0.643635i	0.618210	−	0.786013i	$-0.287858\pi$
$179$	−4.97171	−	8.61125i	−0.371603	−	0.643635i	−0.989812	+	0.142379i	$0.954525\pi$
$180$	1.82896	+	1.53468i	0.136323	+	0.114388i
$181$	−10.4420	−	8.76184i	−0.776144	−	0.651263i	0.166130	−	0.986104i	$-0.446873\pi$
$181$	−10.4420	−	8.76184i	−0.776144	−	0.651263i	−0.942275	+	0.334841i	$0.891317\pi$
$182$	0.368563	+	0.638369i	0.0273197	+	0.0473191i
$183$	5.88615	−	10.1951i	0.435117	−	0.753645i
$184$	7.31371	−	2.66197i	0.539174	−	0.196243i
$185$	−3.62968	−	20.5849i	−0.266859	−	1.51343i
$186$	−0.00320522	+	0.0181777i	−0.000235018	+	0.00133285i
$187$	−3.09432	−	1.12624i	−0.226279	−	0.0823589i
$188$	2.30596	−	1.93493i	0.168179	−	0.141119i
$189$	3.24818			0.236270
$190$	−1.65821	−	17.8151i	−0.120299	−	1.29244i
$191$	24.8623			1.79897			0.899485	−	0.436951i	$-0.143942\pi$
$191$	24.8623			1.79897			0.899485	+	0.436951i	$0.143942\pi$
$192$	−1.19128	+	0.999601i	−0.0859731	+	0.0721400i
$193$	7.55612	+	2.75020i	0.543901	+	0.197964i	0.599335	−	0.800499i	$-0.295432\pi$
$193$	7.55612	+	2.75020i	0.543901	+	0.197964i	−0.0554335	+	0.998462i	$0.517654\pi$
$194$	0.815197	−	4.62321i	0.0585277	−	0.331927i
$195$	1.40107	+	7.94584i	0.100332	+	0.569014i
$196$	6.25827	−	2.27782i	0.447019	−	0.162702i
$197$	12.0867	−	20.9347i	0.861140	−	1.49154i	−0.00968909	−	0.999953i	$-0.503084\pi$
$197$	12.0867	−	20.9347i	0.861140	−	1.49154i	0.870829	−	0.491586i	$-0.163582\pi$
$198$	−0.290828	−	0.503728i	−0.0206682	−	0.0357984i
$199$	−2.78499	−	2.33688i	−0.197423	−	0.165657i	0.538717	−	0.842487i	$-0.318909\pi$
$199$	−2.78499	−	2.33688i	−0.197423	−	0.165657i	−0.736140	+	0.676829i	$0.763354\pi$
$200$	−9.07672	−	7.61627i	−0.641821	−	0.538552i
$201$	−10.1879	−	17.6460i	−0.718602	−	1.24465i
$202$	4.10752	−	7.11444i	0.289004	−	0.500570i
$203$	−5.26705	+	1.91705i	−0.369674	+	0.134550i
$204$	−0.889220	−	5.04302i	−0.0622578	−	0.353082i
$205$	1.70641	−	9.67752i	0.119181	−	0.675907i
$206$	−7.24675	−	2.63760i	−0.504905	−	0.183770i
$207$	−3.46794	+	2.90995i	−0.241038	+	0.202255i
$208$	1.26399			0.0876422
$209$	−1.10480	+	4.21656i	−0.0764208	+	0.291666i
$210$	−3.72255			−0.256880
$211$	1.05341	−	0.883914i	0.0725196	−	0.0608512i	−0.605807	−	0.795611i	$-0.707150\pi$
$211$	1.05341	−	0.883914i	0.0725196	−	0.0608512i	0.678327	+	0.734760i	$0.262705\pi$
$212$	11.2522	+	4.09547i	0.772804	+	0.281278i
$213$	−0.387762	+	2.19911i	−0.0265690	+	0.150680i
$214$	1.15017	+	6.52292i	0.0786237	+	0.445897i
$215$	0.792857	−	0.288576i	0.0540724	−	0.0196807i
$216$	2.78492	−	4.82362i	0.189490	−	0.328206i
$217$	0.00346095	+	0.00599453i	0.000234944	+	0.000406935i
$218$	−7.85328	−	6.58968i	−0.531891	−	0.446310i
$219$	1.20948	+	1.01488i	0.0817293	+	0.0685790i
$220$	2.05237	+	3.55480i	0.138370	+	0.239665i
$221$	−2.08111	+	3.60458i	−0.139990	+	0.242471i
$222$	−7.44146	+	2.70847i	−0.499438	+	0.181781i
$223$	2.69617	+	15.2908i	0.180549	+	1.02395i	0.931542	+	0.363634i	$0.118464\pi$
$223$	2.69617	+	15.2908i	0.180549	+	1.02395i	−0.750993	+	0.660311i	$0.770425\pi$
$224$	−0.101267	+	0.574312i	−0.00676617	+	0.0383729i
$225$	6.47629	+	2.35718i	0.431753	+	0.157145i
$226$	−5.53402	+	4.64359i	−0.368117	+	0.308887i
$227$	−17.9004			−1.18809			−0.594044	−	0.804432i	$-0.702470\pi$
$227$	−17.9004			−1.18809			−0.594044	+	0.804432i	$0.702470\pi$
$228$	−6.53773	+	1.79069i	−0.432972	+	0.118591i
$229$	19.8041			1.30869			0.654345	−	0.756196i	$-0.272945\pi$
$229$	19.8041			1.30869			0.654345	+	0.756196i	$0.272945\pi$
$230$	24.4732	−	20.5354i	1.61371	−	1.35407i
$231$	0.852200	+	0.310176i	0.0560707	+	0.0204081i
$232$	−1.66899	+	9.46534i	−0.109575	+	0.621430i
$233$	4.94642	+	28.0526i	0.324051	+	1.83778i	0.516262	+	0.856431i	$0.327323\pi$
$233$	4.94642	+	28.0526i	0.324051	+	1.83778i	−0.192211	+	0.981354i	$0.561566\pi$
$234$	−0.690870	+	0.251456i	−0.0451636	+	0.0164382i
$235$	6.17806	−	10.7007i	0.403012	−	0.698038i
$236$	−5.03174	−	8.71523i	−0.327539	−	0.567313i
$237$	17.0393	+	14.2976i	1.10682	+	0.928732i
$238$	−1.47106	−	1.23437i	−0.0953547	−	0.0800121i
$239$	−5.02723	−	8.70742i	−0.325185	−	0.563236i	0.656365	−	0.754443i	$-0.272093\pi$
$239$	−5.02723	−	8.70742i	−0.325185	−	0.563236i	−0.981550	+	0.191207i	$0.938760\pi$
$240$	−3.19164	+	5.52808i	−0.206019	+	0.356836i
$241$	20.6981	−	7.53348i	1.33328	−	0.485274i	0.425591	−	0.904916i	$-0.360066\pi$
$241$	20.6981	−	7.53348i	1.33328	−	0.485274i	0.907690	+	0.419641i	$0.137844\pi$
$242$	−0.173648	−	0.984808i	−0.0111625	−	0.0633058i
$243$	−1.03378	+	5.86289i	−0.0663173	+	0.376104i
$244$	−7.11358	−	2.58913i	−0.455400	−	0.165752i
$245$	20.9415	−	17.5720i	1.33790	−	1.12263i
$246$	−3.72295			−0.237367
$247$	5.00624	+	2.30074i	0.318540	+	0.146393i
$248$	0.0118694			0.000753706
$249$	−13.6278	+	11.4350i	−0.863624	+	0.724666i
$250$	−26.4171	−	9.61505i	−1.67077	−	0.608109i
$251$	3.14691	−	17.8470i	0.198631	−	1.12649i	−0.708520	−	0.705691i	$-0.750637\pi$
$251$	3.14691	−	17.8470i	0.198631	−	1.12649i	0.907152	−	0.420804i	$-0.138252\pi$
$252$	−0.0589024	−	0.334052i	−0.00371050	−	0.0210433i
$253$	−7.31371	+	2.66197i	−0.459809	+	0.167357i
$254$	2.03517	−	3.52502i	0.127698	−	0.221179i
$255$	−10.5098	−	18.2035i	−0.658148	−	1.13995i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−13.7952	−	11.5755i	−0.860518	−	0.722061i	0.101561	−	0.994829i	$-0.467616\pi$
$257$	−13.7952	−	11.5755i	−0.860518	−	0.722061i	−0.962080	+	0.272769i	$0.912061\pi$
$258$	−0.159828	−	0.276831i	−0.00995047	−	0.0172347i
$259$	−1.48484	+	2.57182i	−0.0922636	+	0.159805i
$260$	4.87546	−	1.77452i	0.302363	−	0.110051i
$261$	−0.970779	−	5.50556i	−0.0600897	−	0.340786i
$262$	−3.23409	+	18.3414i	−0.199803	+	1.13314i
$263$	26.5118	+	9.64949i	1.63479	+	0.595013i	0.986116	−	0.166057i	$-0.0531036\pi$
$263$	26.5118	+	9.64949i	1.63479	+	0.595013i	0.648669	+	0.761070i	$0.275326\pi$
$264$	1.19128	−	0.999601i	0.0733181	−	0.0615212i
$265$	49.1515			3.01935
$266$	−1.44646	+	2.09033i	−0.0886879	+	0.128166i
$267$	1.17621			0.0719828
$268$	−10.0372	+	8.42218i	−0.613117	+	0.514467i
$269$	15.8905	+	5.78366i	0.968859	+	0.352636i	0.777499	−	0.628884i	$-0.216488\pi$
$269$	15.8905	+	5.78366i	0.968859	+	0.352636i	0.191360	+	0.981520i	$0.438710\pi$
$270$	3.97007	−	22.5154i	0.241611	−	1.37024i
$271$	−0.768944	−	4.36090i	−0.0467100	−	0.264906i	0.952505	−	0.304523i	$-0.0984971\pi$
$271$	−0.768944	−	4.36090i	−0.0467100	−	0.264906i	−0.999215	+	0.0396176i	$0.987386\pi$
$272$	−3.09432	+	1.12624i	−0.187621	+	0.0682884i
$273$	0.573153	−	0.992730i	0.0346888	−	0.0600828i
$274$	7.88844	+	13.6632i	0.476558	+	0.825422i
$275$	9.07672	+	7.61627i	0.547347	+	0.459278i
$276$	−9.27182	−	7.77998i	−0.558098	−	0.468300i
$277$	14.3391	+	24.8360i	0.861552	+	1.49225i	0.870431	+	0.492291i	$0.163840\pi$
$277$	14.3391	+	24.8360i	0.861552	+	1.49225i	−0.00887917	+	0.999961i	$0.502826\pi$
$278$	6.23887	−	10.8060i	0.374183	−	0.648103i
$279$	−0.00648753	+	0.00236127i	−0.000388398	+	0.000141365i
$280$	0.415673	+	2.35740i	0.0248412	+	0.140881i
$281$	−3.57973	+	20.3017i	−0.213549	+	1.21110i	0.669858	+	0.742489i	$0.266355\pi$
$281$	−3.57973	+	20.3017i	−0.213549	+	1.21110i	−0.883407	+	0.468607i	$0.844756\pi$
$282$	−4.39888	−	1.60106i	−0.261950	−	0.0953419i
$283$	−5.15324	+	4.32408i	−0.306328	+	0.257040i	−0.782972	−	0.622056i	$-0.786297\pi$
$283$	−5.15324	+	4.32408i	−0.306328	+	0.257040i	0.476644	+	0.879096i	$0.341853\pi$
$284$	1.43594			0.0852073
$285$	−22.7033	+	16.0854i	−1.34483	+	0.952814i
$286$	−1.26399			−0.0747415
$287$	−1.06950	+	0.897413i	−0.0631303	+	0.0529726i
$288$	−0.546577	−	0.198938i	−0.0322074	−	0.0117225i
$289$	−1.06911	+	6.06321i	−0.0628887	+	0.356660i
$290$	6.85077	+	38.8527i	0.402291	+	2.28151i
$291$	−6.86021	+	2.49691i	−0.402153	+	0.146372i
$292$	0.507641	−	0.879260i	0.0297074	−	0.0514548i
$293$	−11.7070	−	20.2771i	−0.683928	−	1.18460i	−0.973772	−	0.227525i	$-0.926937\pi$
$293$	−11.7070	−	20.2771i	−0.683928	−	1.18460i	0.289844	−	0.957074i	$-0.406397\pi$
$294$	−7.93380	−	6.65725i	−0.462709	−	0.388259i
$295$	−31.6437	−	26.5522i	−1.84237	−	1.54593i
$296$	2.54615	+	4.41005i	0.147992	+	0.256329i
$297$	−2.78492	+	4.82362i	−0.161598	+	0.279895i
$298$	−1.30888	+	0.476392i	−0.0758212	+	0.0275967i
$299$	1.70831	+	9.68831i	0.0987942	+	0.560290i
$300$	−3.19966	+	18.1462i	−0.184733	+	1.04767i
$301$	−0.112644	−	0.0409990i	−0.00649268	−	0.00236314i
$302$	3.47966	−	2.91978i	0.200232	−	0.168014i
$303$	−12.7752			−0.733918
$304$	1.86403	+	3.94023i	0.106909	+	0.225988i
$305$	−31.0733			−1.77925
$306$	1.46723	−	1.23116i	0.0838762	−	0.0703805i
$307$	−11.4192	−	4.15623i	−0.651726	−	0.237209i	−0.00506567	−	0.999987i	$-0.501612\pi$
$307$	−11.4192	−	4.15623i	−0.651726	−	0.237209i	−0.646660	+	0.762778i	$0.723835\pi$
$308$	0.101267	−	0.574312i	0.00577021	−	0.0327245i
$309$	2.08251	+	11.8105i	0.118470	+	0.671875i
$310$	0.0457824	−	0.0166634i	0.00260026	−	0.000946419i
$311$	9.80557	−	16.9838i	0.556023	−	0.963060i	−0.441800	−	0.897114i	$-0.645660\pi$
$311$	9.80557	−	16.9838i	0.556023	−	0.963060i	0.997823	−	0.0659467i	$-0.0210067\pi$
$312$	−0.982820	−	1.70229i	−0.0556412	−	0.0963734i
$313$	10.1259	+	8.49667i	0.572352	+	0.480260i	0.882425	−	0.470452i	$-0.155909\pi$
$313$	10.1259	+	8.49667i	0.572352	+	0.480260i	−0.310074	+	0.950713i	$0.600354\pi$
$314$	−2.10457	−	1.76594i	−0.118768	−	0.0996578i
$315$	−0.696173	−	1.20581i	−0.0392249	−	0.0679395i
$316$	7.15168	−	12.3871i	0.402313	−	0.696827i
$317$	−9.44036	+	3.43601i	−0.530223	+	0.192985i	−0.593238	−	0.805027i	$-0.702151\pi$
$317$	−9.44036	+	3.43601i	−0.530223	+	0.192985i	0.0630148	+	0.998013i	$0.479928\pi$
$318$	−3.23356	−	18.3384i	−0.181329	−	1.02837i
$319$	1.66899	−	9.46534i	0.0934457	−	0.529957i
$320$	3.85718	+	1.40390i	0.215623	+	0.0784804i
$321$	7.89048	−	6.62090i	0.440404	−	0.369542i
$322$	−4.53888			−0.252942
$323$	−14.3056	−	1.17168i	−0.795982	−	0.0651942i
$324$	−6.91671			−0.384262
$325$	11.4729	−	9.62691i	0.636402	−	0.534005i
$326$	0.854111	+	0.310871i	0.0473049	+	0.0172176i
$327$	−2.76838	+	15.7003i	−0.153092	+	0.868228i
$328$	0.415718	+	2.35765i	0.0229542	+	0.130180i
$329$	−1.64961	+	0.600407i	−0.0909457	+	0.0331015i
$330$	3.19164	−	5.52808i	0.175694	−	0.304311i
$331$	−9.69254	−	16.7880i	−0.532750	−	0.922750i	−0.999269	−	0.0382386i	$-0.987825\pi$
$331$	−9.69254	−	16.7880i	−0.532750	−	0.922750i	0.466519	−	0.884511i	$-0.345508\pi$
$332$	8.76325	+	7.35324i	0.480946	+	0.403561i
$333$	−2.26899	−	1.90391i	−0.124340	−	0.104334i
$334$	5.01497	+	8.68619i	0.274407	+	0.475287i
$335$	−26.8913	+	46.5771i	−1.46923	+	2.54478i
$336$	0.852200	−	0.310176i	0.0464913	−	0.0169215i
$337$	4.20884	+	23.8695i	0.229270	+	1.30026i	0.854351	+	0.519696i	$0.173955\pi$
$337$	4.20884	+	23.8695i	0.229270	+	1.30026i	−0.625081	+	0.780560i	$0.714934\pi$
$338$	1.97999	−	11.2291i	0.107697	−	0.610782i
$339$	10.5568	+	3.84235i	0.573365	+	0.208688i
$340$	−10.3542	+	8.68824i	−0.561538	+	0.471186i
$341$	−0.0118694			−0.000642763
$342$	−1.80270	−	1.78281i	−0.0974786	−	0.0964035i
$343$	−7.96608			−0.430128
$344$	−0.157463	+	0.132127i	−0.00848983	+	0.00712382i
$345$	−46.6854	−	16.9921i	−2.51346	−	0.914824i
$346$	2.07710	−	11.7798i	0.111666	−	0.633288i
$347$	−0.0754721	−	0.428023i	−0.00405155	−	0.0229775i	0.982715	−	0.185125i	$-0.0592690\pi$
$347$	−0.0754721	−	0.428023i	−0.00405155	−	0.0229775i	−0.986767	+	0.162148i	$0.948158\pi$
$348$	14.0453	−	5.11205i	0.752904	−	0.274035i
$349$	−1.30098	+	2.25336i	−0.0696397	+	0.120620i	−0.898743	−	0.438476i	$-0.855518\pi$
$349$	−1.30098	+	2.25336i	−0.0696397	+	0.120620i	0.829103	+	0.559096i	$0.188852\pi$
$350$	3.45495	+	5.98415i	0.184675	+	0.319866i
$351$	5.39314	+	4.52538i	0.287864	+	0.241547i
$352$	−0.766044	−	0.642788i	−0.0408303	−	0.0342607i
$353$	−13.1992	−	22.8618i	−0.702525	−	1.21681i	−0.967577	−	0.252575i	$-0.918723\pi$
$353$	−13.1992	−	22.8618i	−0.702525	−	1.21681i	0.265052	−	0.964234i	$-0.414611\pi$
$354$	−7.82488	+	13.5531i	−0.415888	+	0.720338i
$355$	5.53868	−	2.01591i	0.293963	−	0.106994i
$356$	−0.131339	−	0.744863i	−0.00696098	−	0.0394777i
$357$	−0.518568	+	2.94095i	−0.0274455	+	0.155651i
$358$	9.34375	+	3.40085i	0.493833	+	0.179740i
$359$	−9.75407	+	8.18464i	−0.514800	+	0.431969i	−0.862815	−	0.505521i	$-0.831300\pi$
$359$	−9.75407	+	8.18464i	−0.514800	+	0.431969i	0.348014	+	0.937489i	$0.386856\pi$
$360$	−2.38754			−0.125834
$361$	0.210699	+	18.9988i	0.0110894	+	0.999939i
$362$	13.6310			0.716430
$363$	−1.19128	+	0.999601i	−0.0625259	+	0.0524654i
$364$	−0.692671	−	0.252112i	−0.0363059	−	0.0132142i
$365$	0.723671	−	4.10414i	0.0378787	−	0.214821i
$366$	2.04424	+	11.5935i	0.106854	+	0.606000i
$367$	2.22057	−	0.808220i	0.115913	−	0.0421888i	−0.283413	−	0.958998i	$-0.591467\pi$
$367$	2.22057	−	0.808220i	0.115913	−	0.0421888i	0.399325	+	0.916809i	$0.369244\pi$
$368$	−3.89154	+	6.74035i	−0.202861	+	0.351365i
$369$	−0.696248	−	1.20594i	−0.0362452	−	0.0627785i
$370$	16.0122	+	13.4359i	0.832436	+	0.698497i
$371$	−5.34937	−	4.48865i	−0.277725	−	0.233039i
$372$	−0.00922905	−	0.0159852i	−0.000478504	−	0.000828793i
$373$	−10.2574	+	17.7663i	−0.531108	+	0.919907i	0.468233	+	0.883605i	$0.344891\pi$
$373$	−10.2574	+	17.7663i	−0.531108	+	0.919907i	−0.999341	+	0.0363013i	$0.988442\pi$
$374$	3.09432	−	1.12624i	0.160004	−	0.0582365i
$375$	7.59153	+	43.0537i	0.392025	+	2.22328i
$376$	−0.522718	+	2.96448i	−0.0269571	+	0.152882i
$377$	−11.4160	−	4.15510i	−0.587956	−	0.213998i
$378$	−2.48825	+	2.08789i	−0.127982	+	0.107389i
$379$	19.7645			1.01523			0.507616	−	0.861583i	$-0.330527\pi$
$379$	19.7645			1.01523			0.507616	+	0.861583i	$0.330527\pi$
$380$	12.7216	+	12.5813i	0.652604	+	0.645406i
$381$	−6.32980			−0.324285
$382$	−19.0456	+	15.9812i	−0.974458	+	0.817667i
$383$	−9.19605	−	3.34709i	−0.469896	−	0.171028i	0.0962092	−	0.995361i	$-0.469328\pi$
$383$	−9.19605	−	3.34709i	−0.469896	−	0.171028i	−0.566105	+	0.824333i	$0.691550\pi$
$384$	0.270041	−	1.53148i	0.0137805	−	0.0781529i
$385$	−0.415673	−	2.35740i	−0.0211846	−	0.120144i
$386$	−7.55612	+	2.75020i	−0.384596	+	0.139982i
$387$	0.0597806	−	0.103543i	0.00303882	−	0.00526339i
$388$	2.34727	+	4.06559i	0.119164	+	0.206399i
$389$	−7.63471	−	6.40628i	−0.387095	−	0.324811i	0.428385	−	0.903596i	$-0.359083\pi$
$389$	−7.63471	−	6.40628i	−0.387095	−	0.324811i	−0.815480	+	0.578785i	$0.803527\pi$
$390$	−6.18077	−	5.18628i	−0.312975	−	0.262618i
$391$	−12.8145	−	22.1954i	−0.648057	−	1.12247i
$392$	−3.32996	+	5.76765i	−0.168188	+	0.291310i
$393$	27.2162	−	9.90587i	1.37287	−	0.499685i
$394$	4.19766	+	23.8061i	0.211475	+	1.19933i
$395$	10.1951	−	57.8195i	0.512973	−	2.90921i
$396$	0.546577	+	0.198938i	0.0274665	+	0.00999700i
$397$	20.9220	−	17.5557i	1.05005	−	0.881094i	0.0569484	−	0.998377i	$-0.481863\pi$
$397$	20.9220	−	17.5557i	1.05005	−	0.881094i	0.993099	+	0.117283i	$0.0374185\pi$
$398$	3.63554			0.182233
$399$	3.93986	+	0.322690i	0.197240	+	0.0161547i
$400$	11.8488			0.592441
$401$	5.53699	−	4.64609i	0.276504	−	0.232015i	−0.493981	−	0.869473i	$-0.664459\pi$
$401$	5.53699	−	4.64609i	0.276504	−	0.232015i	0.770485	+	0.637458i	$0.220014\pi$
$402$	19.1471	+	6.96896i	0.954968	+	0.347580i
$403$	−0.00260521	+	0.0147749i	−0.000129775	+	0.000735990i
$404$	1.42653	+	8.09024i	0.0709724	+	0.402504i
$405$	−26.6790	+	9.71037i	−1.32569	+	0.482512i
$406$	2.80254	−	4.85414i	0.139088	−	0.240907i
$407$	−2.54615	−	4.41005i	−0.126208	−	0.218598i
$408$	3.92277	+	3.29159i	0.194206	+	0.162958i
$409$	−9.38316	−	7.87340i	−0.463967	−	0.389315i	0.380621	−	0.924731i	$-0.375710\pi$
$409$	−9.38316	−	7.87340i	−0.463967	−	0.389315i	−0.844588	+	0.535416i	$0.820155\pi$
$410$	4.91341	+	8.51027i	0.242656	+	0.420292i
$411$	12.2673	−	21.2476i	0.605103	−	1.04807i
$412$	7.24675	−	2.63760i	0.357022	−	0.129945i
$413$	1.01910	+	5.77958i	0.0501465	+	0.284395i
$414$	0.786118	−	4.45830i	0.0386356	−	0.219113i
$415$	44.1247	+	16.0601i	2.16600	+	0.788358i
$416$	−0.968275	+	0.812479i	−0.0474736	+	0.0398351i
$417$	−19.4042			−0.950227
$418$	−1.86403	−	3.94023i	−0.0911725	−	0.192723i
$419$	8.76540			0.428218			0.214109	−	0.976810i	$-0.431315\pi$
$419$	8.76540			0.428218			0.214109	+	0.976810i	$0.431315\pi$
$420$	2.85164	−	2.39281i	0.139146	−	0.116757i
$421$	12.6915	+	4.61932i	0.618544	+	0.225132i	0.632238	−	0.774775i	$-0.282137\pi$
$421$	12.6915	+	4.61932i	0.618544	+	0.225132i	−0.0136934	+	0.999906i	$0.504359\pi$
$422$	−0.238788	+	1.35424i	−0.0116240	+	0.0659231i
$423$	−0.304042	−	1.72431i	−0.0147830	−	0.0838387i
$424$	−11.2522	+	4.09547i	−0.546455	+	0.198893i
$425$	−19.5085	+	33.7898i	−0.946303	+	1.63904i
$426$	−1.11652	−	1.93386i	−0.0540954	−	0.0936959i
$427$	3.38184	+	2.83770i	0.163659	+	0.137326i
$428$	−5.07393	−	4.25753i	−0.245258	−	0.205796i
$429$	0.982820	+	1.70229i	0.0474510	+	0.0821875i
$430$	−0.421870	+	0.730701i	−0.0203444	+	0.0352375i
$431$	5.06633	−	1.84399i	0.244037	−	0.0888221i	−0.217106	−	0.976148i	$-0.569662\pi$
$431$	5.06633	−	1.84399i	0.244037	−	0.0888221i	0.461143	+	0.887326i	$0.347440\pi$
$432$	0.967193	+	5.48522i	0.0465341	+	0.263908i
$433$	5.88038	−	33.3493i	0.282593	−	1.60266i	−0.431166	−	0.902273i	$-0.641898\pi$
$433$	5.88038	−	33.3493i	0.282593	−	1.60266i	0.713759	−	0.700392i	$-0.246991\pi$
$434$	−0.00650445	−	0.00236743i	−0.000312224	−	0.000113640i
$435$	46.9983	−	39.4363i	2.25340	−	1.89082i
$436$	10.2517			0.490969
$437$	−27.6820	+	19.6128i	−1.32421	+	0.938206i
$438$	−1.57887			−0.0754412
$439$	−25.6786	+	21.5469i	−1.22557	+	1.02838i	−0.227059	+	0.973881i	$0.572911\pi$
$439$	−25.6786	+	21.5469i	−1.22557	+	1.02838i	−0.998514	+	0.0544970i	$0.982644\pi$
$440$	−3.85718	−	1.40390i	−0.183884	−	0.0669283i
$441$	0.672673	−	3.81492i	0.0320321	−	0.181663i
$442$	−0.722761	−	4.09898i	−0.0343782	−	0.194969i
$443$	7.63329	−	2.77829i	0.362668	−	0.132000i	−0.154257	−	0.988031i	$-0.549299\pi$
$443$	7.63329	−	2.77829i	0.362668	−	0.132000i	0.516926	+	0.856030i	$0.327076\pi$
$444$	3.95952	−	6.85809i	0.187910	−	0.325470i
$445$	−1.55231	−	2.68869i	−0.0735868	−	0.127456i
$446$	−11.8941	−	9.98034i	−0.563202	−	0.472583i
$447$	1.65930	+	1.39232i	0.0784824	+	0.0658545i
$448$	−0.291586	−	0.505042i	−0.0137761	−	0.0238610i
$449$	5.93617	−	10.2817i	0.280145	−	0.485226i	−0.691275	−	0.722592i	$-0.742951\pi$
$449$	5.93617	−	10.2817i	0.280145	−	0.485226i	0.971420	+	0.237366i	$0.0762840\pi$
$450$	−6.47629	+	2.35718i	−0.305295	+	0.111118i
$451$	−0.415718	−	2.35765i	−0.0195754	−	0.111017i
$452$	1.25446	−	7.11439i	0.0590048	−	0.334633i
$453$	−6.63785	−	2.41598i	−0.311874	−	0.113513i
$454$	13.7125	−	11.5061i	0.643558	−	0.540009i
$455$	−3.02570			−0.141847
$456$	3.85716	−	5.57412i	0.180628	−	0.261032i
$457$	−28.0102			−1.31026			−0.655131	−	0.755516i	$-0.727386\pi$
$457$	−28.0102			−1.31026			−0.655131	+	0.755516i	$0.727386\pi$
$458$	−15.1708	+	12.7298i	−0.708885	+	0.594825i
$459$	−17.2349	−	6.27299i	−0.804456	−	0.292798i
$460$	−5.54762	+	31.4621i	−0.258659	+	1.46693i
$461$	−0.832604	−	4.72193i	−0.0387782	−	0.219922i	0.959260	−	0.282523i	$-0.0911715\pi$
$461$	−0.832604	−	4.72193i	−0.0387782	−	0.219922i	−0.998039	+	0.0626011i	$0.980060\pi$
$462$	−0.852200	+	0.310176i	−0.0396479	+	0.0144307i
$463$	−9.94650	+	17.2278i	−0.462253	+	0.800645i	−0.999073	−	0.0430514i	$-0.986292\pi$
$463$	−9.94650	+	17.2278i	−0.462253	+	0.800645i	0.536820	+	0.843697i	$0.319625\pi$
$464$	−4.80568	−	8.32368i	−0.223098	−	0.386417i
$465$	−0.0580398	−	0.0487012i	−0.00269153	−	0.00225846i
$466$	−21.8210	−	18.3100i	−1.01084	−	0.848195i
$467$	−10.5621	−	18.2940i	−0.488754	−	0.846546i	0.511162	−	0.859484i	$-0.329215\pi$
$467$	−10.5621	−	18.2940i	−0.488754	−	0.846546i	−0.999916	+	0.0129376i	$0.995882\pi$
$468$	0.367604	−	0.636709i	0.0169925	−	0.0294319i
$469$	7.18025	−	2.61340i	0.331553	−	0.120675i
$470$	2.14562	+	12.1684i	0.0989700	+	0.561287i
$471$	−0.741888	+	4.20745i	−0.0341844	+	0.193869i
$472$	9.45658	+	3.44191i	0.435275	+	0.158427i
$473$	0.157463	−	0.132127i	0.00724015	−	0.00607521i
$474$	−22.2432			−1.02166
$475$	46.9291	+	21.5674i	2.15325	+	0.989581i
$476$	1.92033			0.0880183
$477$	5.33545	−	4.47698i	0.244294	−	0.204987i
$478$	9.44810	+	3.43883i	0.432146	+	0.157288i
$479$	−0.126464	+	0.717214i	−0.00577830	+	0.0327704i	−0.987561	−	0.157239i	$-0.949741\pi$
$479$	−0.126464	+	0.717214i	−0.00577830	+	0.0327704i	0.981782	+	0.190009i	$0.0608518\pi$
$480$	−1.10844	−	6.28630i	−0.0505933	−	0.286929i
$481$	−6.04845	+	2.20145i	−0.275785	+	0.100378i
$482$	−11.0132	+	19.0755i	−0.501638	+	0.868863i
$483$	3.52921	+	6.11277i	0.160585	+	0.278141i
$484$	0.766044	+	0.642788i	0.0348202	+	0.0292176i
$485$	14.7615	+	12.3864i	0.670286	+	0.562437i
$486$	−2.97666	−	5.15573i	−0.135024	−	0.233869i
$487$	−5.11070	+	8.85199i	−0.231588	+	0.401122i	−0.958276	−	0.285846i	$-0.907725\pi$
$487$	−5.11070	+	8.85199i	−0.231588	+	0.401122i	0.726688	+	0.686968i	$0.241059\pi$
$488$	7.11358	−	2.58913i	0.322017	−	0.117204i
$489$	−0.245447	−	1.39200i	−0.0110995	−	0.0629484i
$490$	−4.74704	+	26.9218i	−0.214450	+	1.21620i
$491$	8.38460	+	3.05175i	0.378392	+	0.137723i	0.524212	−	0.851588i	$-0.324360\pi$
$491$	8.38460	+	3.05175i	0.378392	+	0.137723i	−0.145820	+	0.989311i	$0.546582\pi$
$492$	2.85195	−	2.39307i	0.128576	−	0.107888i
$493$	31.6493			1.42541
$494$	−5.31389	+	1.45548i	−0.239083	+	0.0654852i
$495$	2.38754			0.107312
$496$	−0.00909247	+	0.00762949i	−0.000408264	+	0.000342574i
$497$	−0.786898	−	0.286407i	−0.0352972	−	0.0128471i
$498$	3.08916	−	17.5195i	0.138429	−	0.785068i
$499$	−6.46107	−	36.6426i	−0.289237	−	1.64035i	−0.689744	−	0.724053i	$-0.742277\pi$
$499$	−6.46107	−	36.6426i	−0.289237	−	1.64035i	0.400507	−	0.916294i	$-0.368834\pi$
$500$	26.4171	−	9.61505i	1.18141	−	0.429998i
$501$	7.79880	−	13.5079i	0.348425	−	0.603489i
$502$	9.06117	+	15.6944i	0.404420	+	0.700476i
$503$	4.96786	+	4.16853i	0.221506	+	0.185865i	0.746787	−	0.665063i	$-0.231595\pi$
$503$	4.96786	+	4.16853i	0.221506	+	0.185865i	−0.525281	+	0.850929i	$0.676040\pi$
$504$	0.259846	+	0.218037i	0.0115745	+	0.00971213i
$505$	16.8603	+	29.2028i	0.750272	+	1.29951i
$506$	3.89154	−	6.74035i	0.173000	−	0.299645i
$507$	−16.6624	+	6.06463i	−0.740004	+	0.269340i
$508$	0.706807	+	4.00850i	0.0313595	+	0.177848i
$509$	3.40460	−	19.3084i	0.150906	−	0.855831i	−0.811528	−	0.584314i	$-0.801364\pi$
$509$	3.40460	−	19.3084i	0.150906	−	0.855831i	0.962434	−	0.271517i	$-0.0875253\pi$
$510$	19.7519	+	7.18911i	0.874630	+	0.318339i
$511$	−0.453563	+	0.380584i	−0.0200644	+	0.0168361i
$512$	−1.00000			−0.0441942
$513$	−6.15358	+	23.4856i	−0.271687	+	1.03691i
$514$	18.0083			0.794312
$515$	24.2491	−	20.3474i	1.06854	−	0.896615i
$516$	0.300379	+	0.109329i	0.0132234	+	0.00481294i
$517$	0.522718	−	2.96448i	0.0229891	−	0.130378i
$518$	−0.515680	−	2.92457i	−0.0226577	−	0.128498i
$519$	−17.4797	+	6.36208i	−0.767272	+	0.279264i
$520$	−2.59418	+	4.49324i	−0.113762	+	0.197042i
$521$	12.2631	+	21.2404i	0.537257	+	0.930557i	0.999050	+	0.0435692i	$0.0138729\pi$
$521$	12.2631	+	21.2404i	0.537257	+	0.930557i	−0.461793	+	0.886988i	$0.652794\pi$
$522$	4.28257	+	3.59350i	0.187443	+	0.157283i
$523$	5.93624	+	4.98110i	0.259574	+	0.217808i	0.763282	−	0.646066i	$-0.223587\pi$
$523$	5.93624	+	4.98110i	0.259574	+	0.217808i	−0.503708	+	0.863874i	$0.668031\pi$
$524$	−9.31219	−	16.1292i	−0.406805	−	0.704607i
$525$	5.37280	−	9.30596i	0.234488	−	0.406145i
$526$	−26.5118	+	9.64949i	−1.15597	+	0.420738i
$527$	−0.00678700	−	0.0384910i	−0.000295646	−	0.00167669i
$528$	−0.270041	+	1.53148i	−0.0117520	+	0.0666490i
$529$	−35.3103	−	12.8519i	−1.53523	−	0.558778i
$530$	−37.6522	+	31.5939i	−1.63551	+	1.37235i
$531$	−5.85348			−0.254019
$532$	−0.235587	−	2.53105i	−0.0102140	−	0.109735i
$533$	−3.02603			−0.131072
$534$	−0.901028	+	0.756052i	−0.0389913	+	0.0327176i
$535$	−25.5482	−	9.29879i	−1.10455	−	0.402022i
$536$	2.27524	−	12.9035i	0.0982754	−	0.557348i
$537$	−2.68513	−	15.2281i	−0.115872	−	0.657141i
$538$	−15.8905	+	5.78366i	−0.685086	+	0.249351i
$539$	3.32996	−	5.76765i	0.143431	−	0.248430i
$540$	11.4314	+	19.7997i	0.491927	+	0.852043i
$541$	−22.8166	−	19.1454i	−0.980962	−	0.823125i	0.00327227	−	0.999995i	$-0.498958\pi$
$541$	−22.8166	−	19.1454i	−0.980962	−	0.823125i	−0.984234	+	0.176870i	$0.943403\pi$
$542$	3.39218	+	2.84637i	0.145706	+	0.122262i
$543$	−10.5988	−	18.3577i	−0.454838	−	0.787803i
$544$	1.64645	−	2.85174i	0.0705912	−	0.122267i
$545$	39.5428	−	14.3924i	1.69383	−	0.616503i
$546$	0.199054	+	1.12889i	0.00851872	+	0.0483121i
$547$	−3.18216	+	18.0469i	−0.136059	+	0.771631i	0.838057	+	0.545583i	$0.183692\pi$
$547$	−3.18216	+	18.0469i	−0.136059	+	0.771631i	−0.974116	+	0.226048i	$0.927419\pi$
$548$	−14.8254	−	5.39601i	−0.633310	−	0.230506i
$549$	−3.37304	+	2.83032i	−0.143958	+	0.120795i
$550$	−11.8488			−0.505235
$551$	−3.88274	−	41.7146i	−0.165410	−	1.77710i
$552$	12.1035			0.515159
$553$	−6.38982	+	5.36170i	−0.271723	+	0.228002i
$554$	−26.9487	−	9.80851i	−1.14494	−	0.416724i
$555$	5.64452	−	32.0117i	0.239597	−	1.35882i
$556$	2.16674	+	12.2882i	0.0918901	+	0.521135i
$557$	−28.5726	+	10.3996i	−1.21066	+	0.440644i	−0.866933	−	0.498425i	$-0.833912\pi$
$557$	−28.5726	+	10.3996i	−1.21066	+	0.440644i	−0.343727	+	0.939070i	$0.611690\pi$
$558$	0.00345194	−	0.00597894i	0.000146132	−	0.000253109i
$559$	−0.129909	−	0.225009i	−0.00549456	−	0.00951686i
$560$	−1.83373	−	1.53868i	−0.0774892	−	0.0650212i
$561$	−3.92277	−	3.29159i	−0.165619	−	0.138971i
$562$	−10.3074	−	17.8530i	−0.434792	−	0.753083i
$563$	−11.5532	+	20.0107i	−0.486910	+	0.843352i	−0.999887	−	0.0150501i	$-0.995209\pi$
$563$	−11.5532	+	20.0107i	−0.486910	+	0.843352i	0.512977	+	0.858402i	$0.328543\pi$
$564$	4.39888	−	1.60106i	0.185226	−	0.0674169i
$565$	−5.14922	−	29.2027i	−0.216629	−	1.22857i
$566$	1.16814	−	6.62487i	0.0491007	−	0.278464i
$567$	3.79038	+	1.37958i	0.159181	+	0.0579371i
$568$	−1.09999	+	0.923003i	−0.0461547	+	0.0387284i
$569$	−13.6558			−0.572481			−0.286241	−	0.958158i	$-0.592406\pi$
$569$	−13.6558			−0.572481			−0.286241	+	0.958158i	$0.592406\pi$
$570$	7.05226	−	26.9155i	0.295387	−	1.12737i
$571$	29.9803			1.25464			0.627319	−	0.778762i	$-0.284152\pi$
$571$	29.9803			1.25464			0.627319	+	0.778762i	$0.284152\pi$
$572$	0.968275	−	0.812479i	0.0404856	−	0.0339715i
$573$	36.3317	+	13.2237i	1.51778	+	0.552426i
$574$	0.242435	−	1.37492i	0.0101190	−	0.0573879i
$575$	16.0139	+	90.8193i	0.667825	+	3.78743i
$576$	0.546577	−	0.198938i	0.0227741	−	0.00828908i
$577$	−23.6733	+	41.0034i	−0.985533	+	1.70699i	−0.345988	+	0.938239i	$0.612456\pi$
$577$	−23.6733	+	41.0034i	−0.985533	+	1.70699i	−0.639545	+	0.768754i	$0.720877\pi$
$578$	−3.07837	−	5.33190i	−0.128044	−	0.221778i
$579$	9.57913	+	8.03784i	0.398095	+	0.334041i
$580$	−30.2220	−	25.3593i	−1.25490	−	1.05299i
$581$	−3.33563	−	5.77748i	−0.138385	−	0.239690i
$582$	3.65024	−	6.32240i	0.151307	−	0.262072i
$583$	11.2522	−	4.09547i	0.466019	−	0.169617i
$584$	0.176302	+	0.999857i	0.00729542	+	0.0413744i
$585$	0.524041	−	2.97198i	0.0216664	−	0.122876i
$586$	22.0019	+	8.00804i	0.908890	+	0.330809i
$587$	−11.5308	+	9.67551i	−0.475928	+	0.399351i	−0.848951	−	0.528471i	$-0.822766\pi$
$587$	−11.5308	+	9.67551i	−0.475928	+	0.399351i	0.373023	+	0.927822i	$0.378321\pi$
$588$	10.3568			0.427109
$589$	−0.0498995	+	0.0136675i	−0.00205607	+	0.000563160i
$590$	41.3079			1.70062
$591$	28.7972	−	24.1637i	1.18456	−	0.993962i
$592$	−4.78519	−	1.74167i	−0.196670	−	0.0715821i
$593$	−5.02348	+	28.4896i	−0.206289	+	1.16993i	0.689108	+	0.724658i	$0.258002\pi$
$593$	−5.02348	+	28.4896i	−0.206289	+	1.16993i	−0.895398	+	0.445267i	$0.853109\pi$
$594$	−0.967193	−	5.48522i	−0.0396844	−	0.225061i
$595$	7.40708	−	2.69596i	0.303661	−	0.110523i
$596$	0.696439	−	1.20627i	0.0285272	−	0.0494106i
$597$	−2.82682	−	4.89620i	−0.115694	−	0.200388i
$598$	−7.53617	−	6.32360i	−0.308177	−	0.258591i
$599$	4.80135	+	4.02881i	0.196178	+	0.164613i	0.735585	−	0.677432i	$-0.236907\pi$
$599$	4.80135	+	4.02881i	0.196178	+	0.164613i	−0.539407	+	0.842045i	$0.681352\pi$
$600$	−9.21306	−	15.9575i	−0.376122	−	0.651462i
$601$	10.2474	−	17.7490i	0.418000	−	0.723997i	−0.577738	−	0.816222i	$-0.696065\pi$
$601$	10.2474	−	17.7490i	0.418000	−	0.723997i	0.995738	+	0.0922250i	$0.0293979\pi$
$602$	0.112644	−	0.0409990i	0.00459101	−	0.00167099i
$603$	1.32341	+	7.50541i	0.0538932	+	0.305644i
$604$	−0.788775	+	4.47336i	−0.0320948	+	0.182019i
$605$	3.85718	+	1.40390i	0.156817	+	0.0570767i
$606$	9.78640	−	8.21177i	0.397545	−	0.333580i
$607$	18.1497			0.736673			0.368336	−	0.929693i	$-0.379927\pi$
$607$	18.1497			0.736673			0.368336	+	0.929693i	$0.379927\pi$
$608$	−3.96066	−	1.82022i	−0.160626	−	0.0738196i
$609$	−8.71647			−0.353209
$610$	23.8035	−	19.9735i	0.963776	−	0.808704i
$611$	−3.57543	−	1.30135i	−0.144646	−	0.0526470i
$612$	−0.332595	+	1.88624i	−0.0134444	+	0.0762467i
$613$	−3.35878	−	19.0486i	−0.135660	−	0.769365i	−0.974398	−	0.224830i	$-0.927817\pi$
$613$	−3.35878	−	19.0486i	−0.135660	−	0.769365i	0.838738	−	0.544535i	$-0.183294\pi$
$614$	11.4192	−	4.15623i	0.460840	−	0.167732i
$615$	7.64085	−	13.2343i	0.308109	−	0.533660i
$616$	0.291586	+	0.505042i	0.0117483	+	0.0203487i
$617$	16.1238	+	13.5295i	0.649121	+	0.544677i	0.906804	−	0.421552i	$-0.138515\pi$
$617$	16.1238	+	13.5295i	0.649121	+	0.544677i	−0.257683	+	0.966229i	$0.582959\pi$
$618$	−9.18693	−	7.70875i	−0.369553	−	0.310091i
$619$	2.51693	+	4.35946i	0.101164	+	0.175221i	0.912165	−	0.409824i	$-0.134410\pi$
$619$	2.51693	+	4.35946i	0.101164	+	0.175221i	−0.811000	+	0.585046i	$0.801077\pi$
$620$	−0.0243603	+	0.0421933i	−0.000978333	+	0.00169452i
$621$	−40.7362	+	14.8268i	−1.63469	+	0.594978i
$622$	3.40544	+	19.3132i	0.136546	+	0.774389i
$623$	−0.0765935	+	0.434383i	−0.00306865	+	0.0174032i
$624$	1.84710	+	0.672288i	0.0739431	+	0.0269131i
$625$	43.0136	−	36.0927i	1.72054	−	1.44371i
$626$	−13.2185			−0.528316
$627$	−3.85716	+	5.57412i	−0.154040	+	0.222609i
$628$	2.74732			0.109630
$629$	12.8454	−	10.7786i	0.512179	−	0.429769i
$630$	1.30838	+	0.476210i	0.0521270	+	0.0189727i
$631$	−7.00618	+	39.7340i	−0.278912	+	1.58179i	0.447344	+	0.894362i	$0.352370\pi$
$631$	−7.00618	+	39.7340i	−0.278912	+	1.58179i	−0.726256	+	0.687424i	$0.758741\pi$
$632$	2.48375	+	14.0861i	0.0987983	+	0.560313i
$633$	2.00950	−	0.731397i	0.0798704	−	0.0290704i
$634$	5.02311	−	8.70028i	0.199493	−	0.345532i
$635$	8.35382	+	14.4692i	0.331511	+	0.574194i
$636$	14.2648	+	11.9696i	0.565635	+	0.474624i
$637$	−6.44862	−	5.41104i	−0.255504	−	0.214393i
$638$	4.80568	+	8.32368i	0.190259	+	0.329538i
$639$	0.417611	−	0.723323i	0.0165204	−	0.0286142i
$640$	−3.85718	+	1.40390i	−0.152469	+	0.0554940i
$641$	−7.28179	−	41.2971i	−0.287613	−	1.63114i	−0.695799	−	0.718237i	$-0.744949\pi$
$641$	−7.28179	−	41.2971i	−0.287613	−	1.63114i	0.408185	−	0.912899i	$-0.366162\pi$
$642$	−1.78863	+	10.1438i	−0.0705915	+	0.400344i
$643$	13.5919	+	4.94705i	0.536012	+	0.195093i	0.595821	−	0.803117i	$-0.296827\pi$
$643$	13.5919	+	4.94705i	0.536012	+	0.195093i	−0.0598085	+	0.998210i	$0.519049\pi$
$644$	3.47698	−	2.91754i	0.137012	−	0.114967i
$645$	1.31210			0.0516640
$646$	11.7118	−	8.29787i	0.460796	−	0.326475i
$647$	−8.57731			−0.337209			−0.168605	−	0.985684i	$-0.553926\pi$
$647$	−8.57731			−0.337209			−0.168605	+	0.985684i	$0.553926\pi$
$648$	5.29851	−	4.44598i	0.208145	−	0.174654i
$649$	−9.45658	−	3.44191i	−0.371203	−	0.135107i
$650$	−2.60070	+	14.7493i	−0.102008	+	0.578515i
$651$	0.00186919	+	0.0106007i	7.32594e−5	+	0.000415475i
$652$	−0.854111	+	0.310871i	−0.0334496	+	0.0121747i
$653$	−0.356535	+	0.617537i	−0.0139523	+	0.0241661i	−0.872917	−	0.487868i	$-0.837775\pi$
$653$	−0.356535	+	0.617537i	−0.0139523	+	0.0241661i	0.858965	+	0.512034i	$0.171108\pi$
$654$	−7.97124	−	13.8066i	−0.311700	−	0.539881i
$655$	−58.5626	−	49.1399i	−2.28823	−	1.92005i
$656$	−1.83393	−	1.53885i	−0.0716028	−	0.0600819i
$657$	−0.295272	−	0.511426i	−0.0115197	−	0.0199526i
$658$	0.877737	−	1.52028i	0.0342177	−	0.0592669i
$659$	−36.7998	+	13.3940i	−1.43352	+	0.521758i	−0.937938	−	0.346804i	$-0.887267\pi$
$659$	−36.7998	+	13.3940i	−1.43352	+	0.521758i	−0.495581	+	0.868562i	$0.665045\pi$
$660$	1.10844	+	6.28630i	0.0431461	+	0.244694i
$661$	−0.764413	+	4.33520i	−0.0297322	+	0.168620i	−0.996058	−	0.0887007i	$-0.971729\pi$
$661$	−0.764413	+	4.33520i	−0.0297322	+	0.168620i	0.966326	+	0.257321i	$0.0828396\pi$
$662$	18.2160	+	6.63008i	0.707985	+	0.257686i
$663$	−4.95835	+	4.16055i	−0.192567	+	0.161583i
$664$	−11.4396			−0.443943
$665$	−4.46204	−	9.43198i	−0.173031	−	0.365756i
$666$	2.96196			0.114774
$667$	57.3047	−	48.0844i	2.21885	−	1.86183i
$668$	−9.42506	−	3.43044i	−0.364667	−	0.132728i
$669$	−4.19283	+	23.7787i	−0.162104	+	0.919338i
$670$	−9.33925	−	52.9655i	−0.360807	−	2.04624i
$671$	−7.11358	+	2.58913i	−0.274617	+	0.0999523i
$672$	−0.453446	+	0.785392i	−0.0174921	+	0.0302972i
$673$	−12.3869	−	21.4547i	−0.477479	−	0.827017i	0.522188	−	0.852830i	$-0.325116\pi$
$673$	−12.3869	−	21.4547i	−0.477479	−	0.827017i	−0.999667	+	0.0258130i	$0.991783\pi$
$674$	−18.5672	−	15.5797i	−0.715181	−	0.600108i
$675$	50.5559	+	42.4214i	1.94590	+	1.63280i
$676$	5.70116	+	9.87470i	0.219275	+	0.379796i
$677$	−17.9273	+	31.0509i	−0.689001	+	1.19338i	0.283161	+	0.959072i	$0.408617\pi$
$677$	−17.9273	+	31.0509i	−0.689001	+	1.19338i	−0.972162	+	0.234312i	$0.924716\pi$
$678$	−10.5568	+	3.84235i	−0.405431	+	0.147565i
$679$	−0.475400	−	2.69613i	−0.0182442	−	0.103468i
$680$	2.34712	−	13.3112i	0.0900078	−	0.510460i
$681$	−26.1581	−	9.52078i	−1.00238	−	0.364837i
$682$	0.00909247	−	0.00762949i	0.000348169	−	0.000292148i
$683$	2.67888			0.102504			0.0512522	−	0.998686i	$-0.483679\pi$
$683$	2.67888			0.102504			0.0512522	+	0.998686i	$0.483679\pi$
$684$	2.52692	+	0.206965i	0.0966190	+	0.00791349i
$685$	−64.7598			−2.47435
$686$	6.10237	−	5.12050i	0.232990	−	0.195501i
$687$	28.9401	+	10.5333i	1.10413	+	0.401871i
$688$	0.0356939	−	0.202430i	0.00136082	−	0.00771759i
$689$	−2.62825	−	14.9055i	−0.100128	−	0.567856i
$690$	46.6854	−	16.9921i	1.77728	−	0.646879i
$691$	8.19017	−	14.1858i	0.311569	−	0.539653i	−0.667134	−	0.744938i	$-0.732479\pi$
$691$	8.19017	−	14.1858i	0.311569	−	0.539653i	0.978702	+	0.205285i	$0.0658123\pi$
$692$	5.98078	+	10.3590i	0.227355	+	0.393791i
$693$	−0.259846	−	0.218037i	−0.00987074	−	0.00828254i
$694$	0.332943	+	0.279372i	0.0126383	+	0.0106048i
$695$	25.6089	+	44.3559i	0.971400	+	1.68251i
$696$	−7.47332	+	12.9442i	−0.283276	+	0.490648i
$697$	7.40788	−	2.69625i	0.280593	−	0.102128i
$698$	−0.451825	−	2.56242i	−0.0171018	−	0.0969892i
$699$	−7.69220	+	43.6246i	−0.290946	+	1.65003i
$700$	−6.49318	−	2.36332i	−0.245419	−	0.0893252i
$701$	−1.13408	+	0.951603i	−0.0428335	+	0.0359416i	−0.663953	−	0.747774i	$-0.731123\pi$
$701$	−1.13408	+	0.951603i	−0.0428335	+	0.0359416i	0.621120	+	0.783716i	$0.286678\pi$
$702$	−7.04024			−0.265717
$703$	−15.7823	−	15.6082i	−0.595240	−	0.588676i
$704$	1.00000			0.0376889
$705$	14.7196	−	12.3512i	0.554371	−	0.465173i
$706$	24.8065	+	9.02881i	0.933604	+	0.339804i
$707$	0.831911	−	4.71800i	0.0312872	−	0.177439i
$708$	−2.71755	−	15.4120i	−0.102132	−	0.579218i
$709$	12.2966	−	4.47561i	0.461810	−	0.168085i	−0.100629	−	0.994924i	$-0.532085\pi$
$709$	12.2966	−	4.47561i	0.461810	−	0.168085i	0.562439	+	0.826839i	$0.309863\pi$
$710$	−2.94707	+	5.10447i	−0.110602	+	0.191568i
$711$	−4.15981	−	7.20500i	−0.156005	−	0.270209i
$712$	0.579401	+	0.486175i	0.0217140	+	0.0182202i
$713$	−0.0707675	−	0.0593810i	−0.00265026	−	0.00222384i
$714$	−1.49316	−	2.58622i	−0.0558800	−	0.0967870i
$715$	2.59418	−	4.49324i	0.0970167	−	0.168038i
$716$	−9.34375	+	3.40085i	−0.349192	+	0.127096i
$717$	−2.71511	−	15.3982i	−0.101398	−	0.575056i
$718$	2.21107	−	12.5396i	0.0825163	−	0.467973i
$719$	13.1191	+	4.77497i	0.489261	+	0.178076i	0.574858	−	0.818253i	$-0.305057\pi$
$719$	13.1191	+	4.77497i	0.489261	+	0.178076i	−0.0855966	+	0.996330i	$0.527280\pi$
$720$	1.82896	−	1.53468i	0.0681613	−	0.0571941i
$721$	−4.49732			−0.167489
$722$	−12.3736	−	14.4185i	−0.460498	−	0.536602i
$723$	34.2534			1.27390
$724$	−10.4420	+	8.76184i	−0.388072	+	0.325631i
$725$	−107.015	−	38.9503i	−3.97444	−	1.44658i
$726$	0.270041	−	1.53148i	0.0100222	−	0.0568385i
$727$	−5.76641	−	32.7029i	−0.213864	−	1.21288i	−0.882867	−	0.469624i	$-0.844390\pi$
$727$	−5.76641	−	32.7029i	−0.213864	−	1.21288i	0.669002	−	0.743260i	$-0.266722\pi$
$728$	0.692671	−	0.252112i	0.0256721	−	0.00934388i
$729$	−15.0041	+	25.9878i	−0.555707	+	0.962513i
$730$	2.08373	+	3.60912i	0.0771223	+	0.133580i
$731$	0.518511	+	0.435083i	0.0191778	+	0.0160921i
$732$	−9.01811	−	7.56709i	−0.333319	−	0.279688i
$733$	−3.66917	−	6.35520i	−0.135524	−	0.234735i	0.790273	−	0.612754i	$-0.209938\pi$
$733$	−3.66917	−	6.35520i	−0.135524	−	0.234735i	−0.925798	+	0.378020i	$0.876605\pi$
$734$	−1.18154	+	2.04649i	−0.0436114	+	0.0755372i
$735$	39.9483	−	14.5400i	1.47351	−	0.536315i
$736$	−1.35152	−	7.66484i	−0.0498176	−	0.282530i
$737$	−2.27524	+	12.9035i	−0.0838096	+	0.475308i
$738$	1.30852	+	0.476261i	0.0481672	+	0.0175314i
$739$	7.22919	−	6.06601i	0.265930	−	0.223142i	−0.500066	−	0.865987i	$-0.666691\pi$
$739$	7.22919	−	6.06601i	0.265930	−	0.223142i	0.765996	+	0.642846i	$0.222246\pi$
$740$	−20.9025			−0.768391
$741$	6.09201	+	6.02482i	0.223795	+	0.221327i
$742$	6.98310			0.256358
$743$	−13.1378	+	11.0239i	−0.481980	+	0.404429i	−0.851142	−	0.524936i	$-0.824089\pi$
$743$	−13.1378	+	11.0239i	−0.481980	+	0.404429i	0.369162	+	0.929365i	$0.379645\pi$
$744$	0.0173449	+	0.00631304i	0.000635897	+	0.000231447i
$745$	0.992814	−	5.63053i	0.0363739	−	0.206286i
$746$	−3.56236	−	20.2031i	−0.130427	−	0.739690i
$747$	6.25263	−	2.27577i	0.228772	−	0.0832661i
$748$	−1.64645	+	2.85174i	−0.0602003	+	0.104270i
$749$	1.93133	+	3.34517i	0.0705694	+	0.122230i
$750$	−33.4898	−	28.1013i	−1.22288	−	1.02611i
$751$	−16.9175	−	14.1955i	−0.617330	−	0.518001i	0.279633	−	0.960107i	$-0.409787\pi$
$751$	−16.9175	−	14.1955i	−0.617330	−	0.518001i	−0.896963	+	0.442106i	$0.854232\pi$
$752$	−1.50511	−	2.60692i	−0.0548856	−	0.0950647i
$753$	14.0911	−	24.4064i	0.513507	−	0.889420i
$754$	11.4160	−	4.15510i	0.415747	−	0.151320i
$755$	3.23771	+	18.3620i	0.117832	+	0.668260i
$756$	0.564040	−	3.19883i	0.0205139	−	0.116340i
$757$	28.3419	+	10.3156i	1.03010	+	0.374927i	0.801120	−	0.598503i	$-0.204238\pi$
$757$	28.3419	+	10.3156i	1.03010	+	0.374927i	0.228983	+	0.973430i	$0.426460\pi$
$758$	−15.1405	+	12.7044i	−0.549926	+	0.461443i
$759$	−12.1035			−0.439329
$760$	−17.8324	−	1.46055i	−0.646849	−	0.0529795i
$761$	−40.8050			−1.47918			−0.739591	−	0.673057i	$-0.764981\pi$
$761$	−40.8050			−1.47918			−0.739591	+	0.673057i	$0.764981\pi$
$762$	4.84890	−	4.06871i	0.175657	−	0.147394i
$763$	−5.61797	−	2.04477i	−0.203384	−	0.0740258i
$764$	4.31729	−	24.4846i	0.156194	−	0.885820i
$765$	1.36521	+	7.74251i	0.0493594	+	0.279931i
$766$	9.19605	−	3.34709i	0.332267	−	0.120935i
$767$	−6.36009	+	11.0160i	−0.229649	+	0.397765i
$768$	0.777551	+	1.34676i	0.0280575	+	0.0485970i
$769$	37.7778	+	31.6993i	1.36230	+	1.14311i	0.975264	+	0.221042i	$0.0709457\pi$
$769$	37.7778	+	31.6993i	1.36230	+	1.14311i	0.387036	+	0.922064i	$0.373499\pi$
$770$	1.83373	+	1.53868i	0.0660830	+	0.0554502i
$771$	−14.0024	−	24.2528i	−0.504283	−	0.873444i
$772$	4.02053	−	6.96375i	0.144702	−	0.250631i
$773$	−11.9077	+	4.33404i	−0.428289	+	0.155885i	−0.547165	−	0.837024i	$-0.684293\pi$
$773$	−11.9077	+	4.33404i	−0.428289	+	0.155885i	0.118876	+	0.992909i	$0.462071\pi$
$774$	0.0207616	+	0.117745i	0.000746259	+	0.00423225i
$775$	−0.0244215	+	0.138501i	−0.000877248	+	0.00497512i
$776$	−4.41142	−	1.60562i	−0.158361	−	0.0576386i
$777$	−3.53772	+	2.96850i	−0.126915	+	0.106494i
$778$	9.96641			0.357313
$779$	−4.46252	−	9.43299i	−0.159886	−	0.337972i
$780$	8.06842			0.288896
$781$	1.09999	−	0.923003i	0.0393608	−	0.0330277i
$782$	24.0834	+	8.76563i	0.861220	+	0.313458i
$783$	9.29603	−	52.7204i	0.332213	−	1.88407i
$784$	−1.15648	−	6.55873i	−0.0413029	−	0.234240i
$785$	10.5969	−	3.85696i	0.378220	−	0.137661i
$786$	−14.4814	+	25.0826i	−0.516535	+	0.894665i
$787$	−3.55082	−	6.15020i	−0.126573	−	0.219231i	0.795774	−	0.605594i	$-0.207065\pi$
$787$	−3.55082	−	6.15020i	−0.126573	−	0.219231i	−0.922347	+	0.386363i	$0.873731\pi$
$788$	−18.5179	−	15.5383i	−0.659672	−	0.553530i
$789$	33.6098	+	28.2020i	1.19654	+	1.00402i
$790$	29.3557	+	50.8456i	1.04443	+	1.80900i
$791$	−2.10646	+	3.64850i	−0.0748971	+	0.129726i
$792$	−0.546577	+	0.198938i	−0.0194218	+	0.00706895i
$793$	1.66157	+	9.42320i	0.0590039	+	0.334628i
$794$	−4.74264	+	26.8969i	−0.168310	+	0.954534i
$795$	71.8259	+	26.1425i	2.54740	+	0.927179i
$796$	−2.78499	+	2.33688i	−0.0987113	+	0.0828286i
$797$	34.5627			1.22427			0.612137	−	0.790752i	$-0.290310\pi$
$797$	34.5627			1.22427			0.612137	+	0.790752i	$0.290310\pi$
$798$	−3.22553	+	2.28530i	−0.114183	+	0.0808987i
$799$	9.91236			0.350674
$800$	−9.07672	+	7.61627i	−0.320910	+	0.269276i
$801$	−0.413406	−	0.150467i	−0.0146070	−	0.00531650i
$802$	−1.25513	+	7.11822i	−0.0443204	+	0.251353i
$803$	−0.176302	−	0.999857i	−0.00622156	−	0.0352842i
$804$	−19.1471	+	6.96896i	−0.675265	+	0.245776i
$805$	9.31544	−	16.1348i	0.328326	−	0.568677i
$806$	−0.00750141	−	0.0129928i	−0.000264226	−	0.000457653i
$807$	20.1448	+	16.9035i	0.709132	+	0.595032i
$808$	−6.29309	−	5.28053i	−0.221390	−	0.185768i
$809$	12.7167	+	22.0259i	0.447094	+	0.774390i	0.998195	−	0.0600484i	$-0.0191255\pi$
$809$	12.7167	+	22.0259i	0.447094	+	0.774390i	−0.551101	+	0.834438i	$0.685792\pi$
$810$	14.1956	−	24.5875i	0.498783	−	0.863918i
$811$	6.67577	−	2.42978i	0.234418	−	0.0853212i	−0.222140	−	0.975015i	$-0.571304\pi$
$811$	6.67577	−	2.42978i	0.234418	−	0.0853212i	0.456558	+	0.889694i	$0.349082\pi$
$812$	0.973311	+	5.51992i	0.0341565	+	0.193711i
$813$	1.19579	−	6.78164i	0.0419381	−	0.237843i
$814$	4.78519	+	1.74167i	0.167721	+	0.0610454i
$815$	−2.85803	+	2.39817i	−0.100113	+	0.0840044i
$816$	−5.12081			−0.179264
$817$	0.509839	−	0.736787i	0.0178370	−	0.0257769i
$818$	12.2488			0.428271
$819$	−0.328444	+	0.275597i	−0.0114768	+	0.00963014i
$820$	−9.23418	−	3.36097i	−0.322472	−	0.117370i
$821$	4.49135	−	25.4717i	0.156749	−	0.888968i	−0.800420	−	0.599439i	$-0.795390\pi$
$821$	4.49135	−	25.4717i	0.156749	−	0.888968i	0.957169	−	0.289529i	$-0.0934986\pi$
$822$	4.26040	+	24.1619i	0.148598	+	0.842744i
$823$	−47.1396	+	17.1574i	−1.64318	+	0.598070i	−0.987591	−	0.157045i	$-0.949803\pi$
$823$	−47.1396	+	17.1574i	−1.64318	+	0.598070i	−0.655592	+	0.755115i	$0.727581\pi$
$824$	−3.85591	+	6.67864i	−0.134327	+	0.232661i
$825$	9.21306	+	15.9575i	0.320758	+	0.555568i
$826$	−4.49572	−	3.77236i	−0.156426	−	0.131257i
$827$	−8.53510	−	7.16180i	−0.296794	−	0.249040i	0.482214	−	0.876053i	$-0.339833\pi$
$827$	−8.53510	−	7.16180i	−0.296794	−	0.249040i	−0.779009	+	0.627013i	$0.784277\pi$
$828$	2.26354	+	3.92056i	0.0786633	+	0.136249i
$829$	−5.19830	+	9.00372i	−0.180544	+	0.312712i	−0.942066	−	0.335427i	$-0.891119\pi$
$829$	−5.19830	+	9.00372i	−0.180544	+	0.312712i	0.761522	+	0.648139i	$0.224453\pi$
$830$	−44.1247	+	16.0601i	−1.53159	+	0.557453i
$831$	7.74427	+	43.9199i	0.268646	+	1.52357i
$832$	0.219490	−	1.24479i	0.00760945	−	0.0431553i
$833$	20.6079	+	7.50067i	0.714022	+	0.259883i
$834$	14.8645	−	12.4728i	0.514714	−	0.431896i
$835$	−41.1702			−1.42475
$836$	3.96066	+	1.82022i	0.136982	+	0.0629535i
$837$	−0.0661106			−0.00228512
$838$	−6.71468	+	5.63429i	−0.231955	+	0.194633i
$839$	52.7515	+	19.2000i	1.82119	+	0.662857i	0.995049	+	0.0993876i	$0.0316884\pi$
$839$	52.7515	+	19.2000i	1.82119	+	0.662857i	0.826137	+	0.563470i	$0.190534\pi$
$840$	−0.646414	+	3.66600i	−0.0223034	+	0.126489i
$841$	11.0055	+	62.4153i	0.379500	+	2.15225i
$842$	−12.6915	+	4.61932i	−0.437377	+	0.159192i
$843$	−16.0291	+	27.7632i	−0.552072	+	0.956216i
$844$	−0.687563	−	1.19089i	−0.0236669	−	0.0409923i
$845$	35.8535	+	30.0847i	1.23340	+	1.03494i
$846$	1.34127	+	1.12546i	0.0461139	+	0.0386942i
$847$	−0.291586	−	0.505042i	−0.0100190	−	0.0173534i
$848$	5.98717	−	10.3701i	0.205600	−	0.356110i
$849$	−9.83040	+	3.57797i	−0.337378	+	0.122796i
$850$	−6.77524	−	38.4243i	−0.232389	−	1.31794i
$851$	6.88233	−	39.0316i	0.235923	−	1.33799i
$852$	2.09836	+	0.763742i	0.0718887	+	0.0261654i
$853$	16.0203	−	13.4426i	0.548523	−	0.460266i	−0.325917	−	0.945398i	$-0.605673\pi$
$853$	16.0203	−	13.4426i	0.548523	−	0.460266i	0.874441	+	0.485133i	$0.161229\pi$
$854$	−4.41468			−0.151067
$855$	10.0373	−	2.74924i	0.343270	−	0.0940219i
$856$	6.62354			0.226388
$857$	3.46631	−	2.90858i	0.118407	−	0.0993553i	−0.581662	−	0.813431i	$-0.697597\pi$
$857$	3.46631	−	2.90858i	0.118407	−	0.0993553i	0.700069	+	0.714076i	$0.253153\pi$
$858$	−1.84710	−	0.672288i	−0.0630588	−	0.0229515i
$859$	−7.17650	+	40.7000i	−0.244859	+	1.38867i	0.575960	+	0.817478i	$0.304628\pi$
$859$	−7.17650	+	40.7000i	−0.244859	+	1.38867i	−0.820820	+	0.571188i	$0.806483\pi$
$860$	−0.146514	−	0.830922i	−0.00499609	−	0.0283342i
$861$	−2.04019	+	0.742567i	−0.0695293	+	0.0253066i
$862$	−2.69574	+	4.66916i	−0.0918173	+	0.159032i
$863$	−0.877062	−	1.51912i	−0.0298555	−	0.0517113i	0.850712	−	0.525633i	$-0.176171\pi$
$863$	−0.877062	−	1.51912i	−0.0298555	−	0.0517113i	−0.880567	+	0.473921i	$0.842838\pi$
$864$	−4.26675	−	3.58023i	−0.145158	−	0.121802i
$865$	37.6120	+	31.5602i	1.27885	+	1.07308i
$866$	16.9319	+	29.3269i	0.575369	+	0.996568i
$867$	−4.78719	+	8.29165i	−0.162581	+	0.281599i
$868$	0.00650445	−	0.00236743i	0.000220775	−	8.03557e-5i
$869$	−2.48375	−	14.0861i	−0.0842555	−	0.477837i
$870$	−10.6537	+	60.4199i	−0.361193	+	2.04843i
$871$	15.5628	+	5.66439i	0.527325	+	0.191931i
$872$	−7.85328	+	6.58968i	−0.265945	+	0.223155i
$873$	2.73060			0.0924168
$874$	8.59878	−	32.8179i	0.290858	−	1.11008i
$875$	−16.3944			−0.554233
$876$	1.20948	−	1.01488i	0.0408646	−	0.0342895i
$877$	−20.5263	−	7.47098i	−0.693125	−	0.252277i	−0.0286525	−	0.999589i	$-0.509122\pi$
$877$	−20.5263	−	7.47098i	−0.693125	−	0.252277i	−0.664473	+	0.747312i	$0.731344\pi$
$878$	5.82087	−	33.0118i	0.196445	−	1.11409i
$879$	−6.32272	−	35.8579i	−0.213260	−	1.20946i
$880$	3.85718	−	1.40390i	0.130026	−	0.0473255i
$881$	−29.0788	+	50.3660i	−0.979691	+	1.69688i	−0.316197	+	0.948693i	$0.602406\pi$
$881$	−29.0788	+	50.3660i	−0.979691	+	1.69688i	−0.663494	+	0.748182i	$0.730927\pi$
$882$	1.93689	+	3.35479i	0.0652183	+	0.112961i
$883$	−4.06093	−	3.40752i	−0.136661	−	0.114672i	0.571895	−	0.820327i	$-0.306209\pi$
$883$	−4.06093	−	3.40752i	−0.136661	−	0.114672i	−0.708556	+	0.705655i	$0.750653\pi$
$884$	3.18844	+	2.67542i	0.107239	+	0.0899841i
$885$	−32.1190	−	55.6318i	−1.07967	−	1.87004i
$886$	−4.06159	+	7.03487i	−0.136452	+	0.236341i
$887$	−45.7074	+	16.6361i	−1.53470	+	0.558587i	−0.964768	−	0.263102i	$-0.915254\pi$
$887$	−45.7074	+	16.6361i	−1.53470	+	0.558587i	−0.569936	+	0.821689i	$0.693032\pi$
$888$	1.37513	+	7.79873i	0.0461462	+	0.261708i
$889$	0.412190	−	2.33765i	0.0138244	−	0.0784021i
$890$	2.91740	+	1.06185i	0.0977914	+	0.0355931i
$891$	−5.29851	+	4.44598i	−0.177507	+	0.148946i
$892$	15.5266			0.519871
$893$	−1.21605	−	13.0648i	−0.0406936	−	0.437195i
$894$	−2.16607			−0.0724441
$895$	−31.2661	+	26.2354i	−1.04511	+	0.876952i
$896$	0.548003	+	0.199457i	0.0183075	+	0.00666338i
$897$	−2.65660	+	15.0663i	−0.0887012	+	0.503050i
$898$	2.06161	+	11.6920i	0.0687968	+	0.390166i
$899$	0.107201	−	0.0390179i	0.00357535	−	0.00130132i
$900$	3.44596	−	5.96858i	0.114865	−	0.198953i
$901$	19.7152	+	34.1478i	0.656809	+	1.13763i
$902$	1.83393	+	1.53885i	0.0610631	+	0.0512380i
$903$	−0.142802	−	0.119825i	−0.00475215	−	0.00398753i
$904$	3.61207	+	6.25629i	0.120136	+	0.208081i
$905$	−27.9758	+	48.4555i	−0.929947	+	1.61072i
$906$	6.63785	−	2.41598i	0.220528	−	0.0802656i
$907$	6.17260	+	35.0065i	0.204958	+	1.16237i	0.897506	+	0.441002i	$0.145377\pi$
$907$	6.17260	+	35.0065i	0.204958	+	1.16237i	−0.692548	+	0.721371i	$0.743512\pi$
$908$	−3.10836	+	17.6284i	−0.103155	+	0.585019i
$909$	4.49016	+	1.63428i	0.148929	+	0.0542058i
$910$	2.31782	−	1.94488i	0.0768351	−	0.0644723i
$911$	52.4417			1.73747			0.868736	−	0.495275i	$-0.164933\pi$
$911$	52.4417			1.73747			0.868736	+	0.495275i	$0.164933\pi$
$912$	0.628222	+	6.74936i	0.0208025	+	0.223494i
$913$	11.4396			0.378596
$914$	21.4571	−	18.0046i	0.709736	−	0.595539i
$915$	−45.4080	−	16.5271i	−1.50114	−	0.546371i
$916$	3.43894	−	19.5032i	0.113626	−	0.644404i
$917$	1.88603	+	10.6962i	0.0622823	+	0.353220i
$918$	17.2349	−	6.27299i	0.568836	−	0.207039i
$919$	1.16889	−	2.02457i	0.0385580	−	0.0667844i	−0.846102	−	0.533020i	$-0.821057\pi$
$919$	1.16889	−	2.02457i	0.0385580	−	0.0667844i	0.884660	+	0.466236i	$0.154390\pi$
$920$	−15.9737	−	27.6673i	−0.526638	−	0.912165i
$921$	−14.4764	−	12.1472i	−0.477014	−	0.400263i
$922$	3.67301	+	3.08202i	0.120964	+	0.101501i
$923$	−0.907508	−	1.57185i	−0.0298710	−	0.0517381i
$924$	0.453446	−	0.785392i	0.0149173	−	0.0258375i
$925$	−56.6988	+	20.6367i	−1.86425	+	0.678530i
$926$	−3.45438	−	19.5908i	−0.113518	−	0.643793i
$927$	0.778921	−	4.41748i	0.0255831	−	0.145089i
$928$	9.03172	+	3.28728i	0.296481	+	0.107910i
$929$	5.25813	−	4.41209i	0.172514	−	0.144756i	−0.552443	−	0.833551i	$-0.686304\pi$
$929$	5.25813	−	4.41209i	0.172514	−	0.144756i	0.724956	+	0.688795i	$0.241860\pi$
$930$	0.0757655			0.00248445
$931$	7.35789	−	28.0819i	0.241145	−	0.920348i
$932$	28.4853			0.933068
$933$	23.3623	−	19.6033i	0.764848	−	0.641784i
$934$	19.8502	+	7.22487i	0.649518	+	0.236405i
$935$	−2.34712	+	13.3112i	−0.0767589	+	0.435321i
$936$	0.127668	+	0.724039i	0.00417295	+	0.0236660i
$937$	−4.24998	+	1.54686i	−0.138841	+	0.0505339i	−0.410506	−	0.911858i	$-0.634648\pi$
$937$	−4.24998	+	1.54686i	−0.138841	+	0.0505339i	0.271665	+	0.962392i	$0.412426\pi$
$938$	−3.82053	+	6.61736i	−0.124745	+	0.216064i
$939$	10.2780	+	17.8021i	0.335411	+	0.580949i
$940$	−9.46534	−	7.94236i	−0.308725	−	0.259051i
$941$	26.9336	+	22.6000i	0.878011	+	0.736739i	0.965769	−	0.259403i	$-0.0835257\pi$
$941$	26.9336	+	22.6000i	0.878011	+	0.736739i	−0.0877579	+	0.996142i	$0.527970\pi$
$942$	−2.13618	−	3.69997i	−0.0696005	−	0.120552i
$943$	9.31644	−	16.1365i	0.303385	−	0.525478i
$944$	−9.45658	+	3.44191i	−0.307786	+	0.112025i
$945$	−2.31523	−	13.1303i	−0.0753145	−	0.427130i
$946$	−0.0356939	+	0.202430i	−0.00116051	+	0.00658158i
$947$	−41.9866	−	15.2819i	−1.36438	−	0.496595i	−0.446976	−	0.894546i	$-0.647499\pi$
$947$	−41.9866	−	15.2819i	−1.36438	−	0.496595i	−0.917407	+	0.397951i	$0.869721\pi$
$948$	17.0393	−	14.2976i	0.553410	−	0.464366i
$949$	−1.28331			−0.0416580
$950$	−49.8130	+	13.6438i	−1.61615	+	0.442665i
$951$	−15.6229			−0.506607
$952$	−1.47106	+	1.23437i	−0.0476773	+	0.0400060i
$953$	33.2858	+	12.1150i	1.07823	+	0.392444i	0.819249	−	0.573437i	$-0.194390\pi$
$953$	33.2858	+	12.1150i	1.07823	+	0.392444i	0.258983	+	0.965882i	$0.416613\pi$
$954$	−1.20945	+	6.85913i	−0.0391574	+	0.222072i
$955$	−17.7213	−	100.503i	−0.573448	−	3.25218i
$956$	−9.44810	+	3.43883i	−0.305573	+	0.111220i
$957$	7.47332	−	12.9442i	0.241578	−	0.418426i
$958$	−0.364139	−	0.630708i	−0.0117648	−	0.0203772i
$959$	7.04809	+	5.91405i	0.227595	+	0.190975i
$960$	4.88987	+	4.10309i	0.157820	+	0.132427i
$961$	15.4999	+	26.8467i	0.499998	+	0.866021i
$962$	3.21831	−	5.57428i	0.103763	−	0.179722i
$963$	−3.62028	+	1.31767i	−0.116662	+	0.0424614i
$964$	−3.82485	−	21.6918i	−0.123190	−	0.698646i
$965$	5.73149	−	32.5049i	0.184503	−	1.04637i
$966$	−6.63275	−	2.41412i	−0.213405	−	0.0776731i
$967$	−39.1478	+	32.8489i	−1.25891	+	1.05635i	−0.263112	+	0.964765i	$0.584749\pi$
$967$	−39.1478	+	32.8489i	−1.25891	+	1.05635i	−0.995797	+	0.0915846i	$0.970807\pi$
$968$	−1.00000			−0.0321412
$969$	−20.2818	−	9.32099i	−0.651545	−	0.299433i
$970$	−19.2698			−0.618716
$971$	−8.82536	+	7.40536i	−0.283219	+	0.237649i	−0.773319	−	0.634017i	$-0.781405\pi$
$971$	−8.82536	+	7.40536i	−0.283219	+	0.237649i	0.490100	+	0.871666i	$0.336960\pi$
$972$	5.59430	+	2.03616i	0.179437	+	0.0653098i
$973$	1.26358	−	7.16612i	0.0405085	−	0.229735i
$974$	−1.77493	−	10.0661i	−0.0568724	−	0.322539i
$975$	21.8859	−	7.96582i	0.700910	−	0.255110i
$976$	−3.78506	+	6.55591i	−0.121157	+	0.209850i
$977$	25.3338	+	43.8794i	0.810499	+	1.40383i	0.912515	+	0.409043i	$0.134138\pi$
$977$	25.3338	+	43.8794i	0.810499	+	1.40383i	−0.102016	+	0.994783i	$0.532529\pi$
$978$	1.08278	+	0.908564i	0.0346236	+	0.0290527i
$979$	−0.579401	−	0.486175i	−0.0185177	−	0.0155382i
$980$	−13.6686	−	23.6747i	−0.436626	−	0.756259i
$981$	2.98148	−	5.16408i	0.0951915	−	0.164876i
$982$	−8.38460	+	3.05175i	−0.267563	+	0.0973851i
$983$	7.95302	+	45.1038i	0.253662	+	1.43859i	0.799484	+	0.600688i	$0.205106\pi$
$983$	7.95302	+	45.1038i	0.253662	+	1.43859i	−0.545822	+	0.837901i	$0.683782\pi$
$984$	−0.646483	+	3.66639i	−0.0206091	+	0.116880i
$985$	−93.2411	−	33.9370i	−2.97091	−	1.08132i
$986$	−24.2448	+	20.3438i	−0.772111	+	0.647878i
$987$	−2.72994			−0.0868950
$988$	3.13511	−	4.53067i	0.0997413	−	0.144140i
$989$	1.59984			0.0508719
$990$	−1.82896	+	1.53468i	−0.0581282	+	0.0487753i
$991$	−7.98354	−	2.90577i	−0.253606	−	0.0923049i	0.212089	−	0.977250i	$-0.431973\pi$
$991$	−7.98354	−	2.90577i	−0.253606	−	0.0923049i	−0.465695	+	0.884945i	$0.654196\pi$
$992$	0.00206110	−	0.0116891i	6.54399e−5	−	0.000371128i
$993$	−5.23476	−	29.6878i	−0.166120	−	0.942114i
$994$	0.786898	−	0.286407i	0.0249589	−	0.00908429i
$995$	−7.46146	+	12.9236i	−0.236544	+	0.409707i
$996$	8.89488	+	15.4064i	0.281845	+	0.488170i
$997$	−15.0620	−	12.6385i	−0.477018	−	0.400266i	0.372329	−	0.928101i	$-0.378559\pi$
$997$	−15.0620	−	12.6385i	−0.477018	−	0.400266i	−0.849347	+	0.527835i	$0.823004\pi$
$998$	28.5029	+	23.9167i	0.902242	+	0.757071i
$999$	−14.1816	−	24.5633i	−0.448687	−	0.777149i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.j.c.177.4	yes	30
19.4	even	9		7942.2.a.bz.1.6		15
19.15	odd	18		7942.2.a.cb.1.10		15
19.16	even	9	inner	418.2.j.c.111.4	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.c.111.4	✓	30	19.16	even	9	inner
418.2.j.c.177.4	yes	30	1.1	even	1	trivial
7942.2.a.bz.1.6		15	19.4	even	9
7942.2.a.cb.1.10		15	19.15	odd	18

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.j (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(1.46132 + 0.531876i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.712779 - 4.04237i) q^{5} +(-1.46132 + 0.531876i) q^{6} +(-0.291586 + 0.505042i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.445574 - 0.373881i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(1.46132 + 0.531876i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.712779 - 4.04237i) q^{5} +(-1.46132 + 0.531876i) q^{6} +(-0.291586 + 0.505042i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.445574 - 0.373881i) q^{9} +(3.14441 + 2.63847i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(0.777551 - 1.34676i) q^{12} +(-1.18777 + 0.432311i) q^{13} +(-0.101267 - 0.574312i) q^{14} +(1.10844 - 6.28630i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.52251 - 2.11664i) q^{17} +0.581655 q^{18} +(-3.09925 - 3.06507i) q^{19} -4.10473 q^{20} +(-0.694720 + 0.582939i) q^{21} +(0.939693 + 0.342020i) q^{22} +(1.35152 - 7.66484i) q^{23} +(0.270041 + 1.53148i) q^{24} +(-11.1342 + 4.05253i) q^{25} +(0.631997 - 1.09465i) q^{26} +(-2.78492 - 4.82362i) q^{27} +(0.446736 + 0.374856i) q^{28} +(7.36272 + 6.17806i) q^{29} +(3.19164 + 5.52808i) q^{30} +(0.00593469 - 0.0102792i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.270041 - 1.53148i) q^{33} +(-0.571808 + 3.24288i) q^{34} +(2.24940 + 0.818716i) q^{35} +(-0.445574 + 0.373881i) q^{36} +5.09229 q^{37} +(4.34435 + 0.355820i) q^{38} -1.96564 q^{39} +(3.14441 - 2.63847i) q^{40} +(2.24964 + 0.818804i) q^{41} +(0.157480 - 0.893115i) q^{42} +(0.0356939 + 0.202430i) q^{43} +(-0.939693 + 0.342020i) q^{44} +(-1.19377 + 2.06767i) q^{45} +(3.89154 + 6.74035i) q^{46} +(2.30596 + 1.93493i) q^{47} +(-1.19128 - 0.999601i) q^{48} +(3.32996 + 5.76765i) q^{49} +(5.92441 - 10.2614i) q^{50} +(4.81199 - 1.75142i) q^{51} +(0.219490 + 1.24479i) q^{52} +(-2.07932 + 11.7924i) q^{53} +(5.23394 + 1.90500i) q^{54} +(-3.14441 + 2.63847i) q^{55} -0.583172 q^{56} +(-2.89875 - 6.12746i) q^{57} -9.61135 q^{58} +(7.70908 - 6.46868i) q^{59} +(-5.99832 - 2.18321i) q^{60} +(1.31454 - 7.45511i) q^{61} +(0.00206110 + 0.0116891i) q^{62} +(0.318749 - 0.116015i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.59418 + 4.49324i) q^{65} +(1.19128 + 0.999601i) q^{66} +(-10.0372 - 8.42218i) q^{67} +(-1.64645 - 2.85174i) q^{68} +(6.05175 - 10.4819i) q^{69} +(-2.24940 + 0.818716i) q^{70} +(0.249348 + 1.41412i) q^{71} +(0.101003 - 0.572819i) q^{72} +(0.954053 + 0.347247i) q^{73} +(-3.90092 + 3.27326i) q^{74} -18.4261 q^{75} +(-3.55668 + 2.51992i) q^{76} +0.583172 q^{77} +(1.50577 - 1.26349i) q^{78} +(13.4408 + 4.89204i) q^{79} +(-0.712779 + 4.04237i) q^{80} +(-1.20107 - 6.81163i) q^{81} +(-2.24964 + 0.818804i) q^{82} +(-5.71980 + 9.90699i) q^{83} +(0.453446 + 0.785392i) q^{84} +(-10.3542 - 8.68824i) q^{85} +(-0.157463 - 0.132127i) q^{86} +(7.47332 + 12.9442i) q^{87} +(0.500000 - 0.866025i) q^{88} +(0.710740 - 0.258688i) q^{89} +(-0.414592 - 2.35127i) q^{90} +(0.128001 - 0.725927i) q^{91} +(-7.31371 - 2.66197i) q^{92} +(0.0141397 - 0.0118646i) q^{93} -3.01022 q^{94} +(-10.1811 + 14.7130i) q^{95} +1.55510 q^{96} +(-3.59622 + 3.01759i) q^{97} +(-6.25827 - 2.27782i) q^{98} +(-0.101003 + 0.572819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) \) 30 * q - 12 * q^7 + 15 * q^8	\( 30 q - 12 q^{7} + 15 q^{8} - 15 q^{11} + 3 q^{12} - 3 q^{13} + 9 q^{14} + 27 q^{15} - 36 q^{18} - 9 q^{19} + 18 q^{20} - 27 q^{21} - 3 q^{23} - 12 q^{25} + 3 q^{27} + 9 q^{28} + 3 q^{29} + 9 q^{30} + 30 q^{31} - 9 q^{34} + 15 q^{35} + 18 q^{37} + 6 q^{38} - 6 q^{41} - 45 q^{42} + 39 q^{43} - 18 q^{45} + 21 q^{46} + 45 q^{47} - 33 q^{49} + 36 q^{50} - 36 q^{51} + 6 q^{52} - 24 q^{53} + 45 q^{54} - 24 q^{56} - 24 q^{57} - 30 q^{58} + 3 q^{59} - 9 q^{60} - 27 q^{61} + 15 q^{62} - 93 q^{63} - 15 q^{64} + 18 q^{65} - 9 q^{67} - 21 q^{68} + 48 q^{69} - 15 q^{70} + 39 q^{73} + 3 q^{74} - 42 q^{75} - 15 q^{76} + 24 q^{77} + 6 q^{78} + 21 q^{79} + 84 q^{81} + 6 q^{82} - 36 q^{83} - 27 q^{84} + 63 q^{85} + 6 q^{86} - 21 q^{87} + 15 q^{88} + 54 q^{89} + 12 q^{90} + 3 q^{91} - 3 q^{92} + 51 q^{93} - 78 q^{94} + 6 q^{95} + 6 q^{96} - 18 q^{97} + 3 q^{98}+O(q^{100}) \) 30 * q - 12 * q^7 + 15 * q^8 - 15 * q^11 + 3 * q^12 - 3 * q^13 + 9 * q^14 + 27 * q^15 - 36 * q^18 - 9 * q^19 + 18 * q^20 - 27 * q^21 - 3 * q^23 - 12 * q^25 + 3 * q^27 + 9 * q^28 + 3 * q^29 + 9 * q^30 + 30 * q^31 - 9 * q^34 + 15 * q^35 + 18 * q^37 + 6 * q^38 - 6 * q^41 - 45 * q^42 + 39 * q^43 - 18 * q^45 + 21 * q^46 + 45 * q^47 - 33 * q^49 + 36 * q^50 - 36 * q^51 + 6 * q^52 - 24 * q^53 + 45 * q^54 - 24 * q^56 - 24 * q^57 - 30 * q^58 + 3 * q^59 - 9 * q^60 - 27 * q^61 + 15 * q^62 - 93 * q^63 - 15 * q^64 + 18 * q^65 - 9 * q^67 - 21 * q^68 + 48 * q^69 - 15 * q^70 + 39 * q^73 + 3 * q^74 - 42 * q^75 - 15 * q^76 + 24 * q^77 + 6 * q^78 + 21 * q^79 + 84 * q^81 + 6 * q^82 - 36 * q^83 - 27 * q^84 + 63 * q^85 + 6 * q^86 - 21 * q^87 + 15 * q^88 + 54 * q^89 + 12 * q^90 + 3 * q^91 - 3 * q^92 + 51 * q^93 - 78 * q^94 + 6 * q^95 + 6 * q^96 - 18 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

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