LMFDB - Embedded newform 342.2.x.c.281.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(29,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([3, 17]))

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

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

chi := DirichletCharacter("342.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.x (of order $18$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			281.4
Character	$\chi$	$=$	342.281
Dual form			342.2.x.c.185.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(-0.746969 - 1.56270i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.40944 - 3.87239i) q^{5} +(-1.57670 - 0.716956i) q^{6} +(0.224791 + 0.389350i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.88407 + 2.33458i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(-0.746969 - 1.56270i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.40944 - 3.87239i) q^{5} +(-1.57670 - 0.716956i) q^{6} +(0.224791 + 0.389350i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.88407 + 2.33458i) q^{9} +(-1.40944 - 3.87239i) q^{10} +1.76672i q^{11} +(-1.66867 + 0.464261i) q^{12} +(0.993593 + 2.72987i) q^{13} +(0.422469 + 0.153766i) q^{14} +(-7.10420 + 0.690032i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.996305 - 2.73733i) q^{17} +(0.0573559 + 2.99945i) q^{18} +(1.30611 + 4.15861i) q^{19} +(-3.56882 - 2.06046i) q^{20} +(0.440526 - 0.642114i) q^{21} +(1.13563 + 1.35339i) q^{22} +(1.03209 + 0.181985i) q^{23} +(-0.979855 + 1.42825i) q^{24} +(-9.17870 - 7.70184i) q^{25} +(2.51586 + 1.45254i) q^{26} +(5.05560 + 1.20038i) q^{27} +(0.422469 - 0.153766i) q^{28} +(0.697791 - 3.95737i) q^{29} +(-4.99859 + 5.09509i) q^{30} +1.93871i q^{31} +(-0.939693 + 0.342020i) q^{32} +(2.76086 - 1.31969i) q^{33} +(-0.996305 - 2.73733i) q^{34} +(1.82454 - 0.321716i) q^{35} +(1.97195 + 2.26085i) q^{36} -1.92037i q^{37} +(3.67365 + 2.34613i) q^{38} +(3.52379 - 3.59182i) q^{39} +(-4.05831 + 0.715589i) q^{40} +(1.94166 - 1.62925i) q^{41} +(-0.0752809 - 0.775052i) q^{42} +(-1.05122 - 5.96178i) q^{43} +(1.73988 + 0.306788i) q^{44} +(6.38494 + 10.5863i) q^{45} +(0.907603 - 0.524005i) q^{46} +(-2.67277 - 0.471281i) q^{47} +(0.167446 + 1.72394i) q^{48} +(3.39894 - 5.88713i) q^{49} -11.9819 q^{50} +(-5.02183 + 0.487771i) q^{51} +(2.86094 - 0.504460i) q^{52} +(9.34372 + 7.84031i) q^{53} +(4.64441 - 2.33013i) q^{54} +(6.84144 + 2.49008i) q^{55} +(0.224791 - 0.389350i) q^{56} +(5.52304 - 5.14742i) q^{57} +(-2.00921 - 3.48005i) q^{58} +(2.52025 + 14.2930i) q^{59} +(-0.554083 + 7.11610i) q^{60} +(-14.0885 + 5.12780i) q^{61} +(1.24618 + 1.48514i) q^{62} +(-1.33249 - 0.208770i) q^{63} +(-0.500000 + 0.866025i) q^{64} +11.9715 q^{65} +(1.26666 - 2.78559i) q^{66} +(5.40252 - 6.43847i) q^{67} +(-2.52273 - 1.45650i) q^{68} +(-0.486550 - 1.74878i) q^{69} +(1.19089 - 1.41924i) q^{70} +(6.00202 - 5.03629i) q^{71} +(2.96384 + 0.464365i) q^{72} +(1.97920 + 11.2246i) q^{73} +(-1.23439 - 1.47109i) q^{74} +(-5.17948 + 20.0966i) q^{75} +(4.32224 - 0.564136i) q^{76} +(-0.687873 + 0.397144i) q^{77} +(0.390605 - 5.01655i) q^{78} +(-5.70748 + 15.6812i) q^{79} +(-2.64887 + 3.15680i) q^{80} +(-1.90054 - 8.79704i) q^{81} +(0.440140 - 2.49616i) q^{82} +(1.83095 - 1.05710i) q^{83} +(-0.555863 - 0.545335i) q^{84} +(-9.19578 - 7.71617i) q^{85} +(-4.63745 - 3.89128i) q^{86} +(-6.70542 + 1.86559i) q^{87} +(1.53003 - 0.883361i) q^{88} +(2.34281 - 13.2867i) q^{89} +(11.6959 + 4.00543i) q^{90} +(-0.839525 + 1.00051i) q^{91} +(0.358441 - 0.984807i) q^{92} +(3.02962 - 1.44815i) q^{93} +(-2.35039 + 1.35700i) q^{94} +(17.9447 + 0.803509i) q^{95} +(1.23640 + 1.21298i) q^{96} +(-7.29486 - 8.69367i) q^{97} +(-1.18044 - 6.69460i) q^{98} +(-4.12456 - 3.32863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9}+O(q^{10}) $ 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9	$ 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9} + 3 q^{13} + 3 q^{14} + 27 q^{15} - 27 q^{17} - 18 q^{18} + 3 q^{19} + 18 q^{23} + 3 q^{24} - 6 q^{27} + 3 q^{28} + 57 q^{33} + 27 q^{34} + 9 q^{38} - 30 q^{39} + 9 q^{41} - 3 q^{43} - 9 q^{44} + 27 q^{45} - 30 q^{49} - 132 q^{50} - 66 q^{51} + 6 q^{52} + 27 q^{54} + 102 q^{57} - 54 q^{59} + 6 q^{60} - 24 q^{61} - 3 q^{62} - 30 q^{64} + 36 q^{65} - 63 q^{66} + 51 q^{67} - 18 q^{68} + 3 q^{69} - 18 q^{71} - 3 q^{72} - 66 q^{73} - 6 q^{74} + 3 q^{78} - 51 q^{79} - 30 q^{81} - 36 q^{83} + 60 q^{84} - 3 q^{86} + 54 q^{87} - 27 q^{89} + 36 q^{90} - 69 q^{91} + 69 q^{93} + 18 q^{94} - 27 q^{95} + 81 q^{97} + 60 q^{98} + 51 q^{99}+O(q^{100}) $ 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9 + 3 * q^13 + 3 * q^14 + 27 * q^15 - 27 * q^17 - 18 * q^18 + 3 * q^19 + 18 * q^23 + 3 * q^24 - 6 * q^27 + 3 * q^28 + 57 * q^33 + 27 * q^34 + 9 * q^38 - 30 * q^39 + 9 * q^41 - 3 * q^43 - 9 * q^44 + 27 * q^45 - 30 * q^49 - 132 * q^50 - 66 * q^51 + 6 * q^52 + 27 * q^54 + 102 * q^57 - 54 * q^59 + 6 * q^60 - 24 * q^61 - 3 * q^62 - 30 * q^64 + 36 * q^65 - 63 * q^66 + 51 * q^67 - 18 * q^68 + 3 * q^69 - 18 * q^71 - 3 * q^72 - 66 * q^73 - 6 * q^74 + 3 * q^78 - 51 * q^79 - 30 * q^81 - 36 * q^83 + 60 * q^84 - 3 * q^86 + 54 * q^87 - 27 * q^89 + 36 * q^90 - 69 * q^91 + 69 * q^93 + 18 * q^94 - 27 * q^95 + 81 * q^97 + 60 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	−0.746969	−	1.56270i	−0.431263	−	0.902226i
$3$	−0.746969	−	1.56270i	−0.431263	−	0.902226i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	1.40944	−	3.87239i	0.630319	−	1.73179i	−0.0498756	−	0.998755i	$-0.515882\pi$
$5$	1.40944	−	3.87239i	0.630319	−	1.73179i	0.680195	−	0.733032i	$-0.261895\pi$
$6$	−1.57670	−	0.716956i	−0.643684	−	0.292696i
$7$	0.224791	+	0.389350i	0.0849631	+	0.147160i	0.905375	−	0.424612i	$-0.139589\pi$
$7$	0.224791	+	0.389350i	0.0849631	+	0.147160i	−0.820412	+	0.571772i	$0.806256\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−1.88407	+	2.33458i	−0.628024	+	0.778194i
$10$	−1.40944	−	3.87239i	−0.445703	−	1.22456i
$11$			1.76672i			0.532687i	0.963878	+	0.266343i	$0.0858155\pi$
$11$			1.76672i			0.532687i	−0.963878	+	0.266343i	$0.914184\pi$
$12$	−1.66867	+	0.464261i	−0.481704	+	0.134021i
$13$	0.993593	+	2.72987i	0.275573	+	0.757131i	0.997851	+	0.0655275i	$0.0208730\pi$
$13$	0.993593	+	2.72987i	0.275573	+	0.757131i	−0.722278	+	0.691603i	$0.756905\pi$
$14$	0.422469	+	0.153766i	0.112910	+	0.0410958i
$15$	−7.10420	+	0.690032i	−1.83430	+	0.178165i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.996305	−	2.73733i	0.241640	−	0.663899i	−0.758289	−	0.651919i	$-0.773964\pi$
$17$	0.996305	−	2.73733i	0.241640	−	0.663899i	0.999928	−	0.0119803i	$-0.00381353\pi$
$18$	0.0573559	+	2.99945i	0.0135189	+	0.706978i
$19$	1.30611	+	4.15861i	0.299643	+	0.954051i
$19$	1.30611	+	4.15861i	0.299643	+	0.954051i
$20$	−3.56882	−	2.06046i	−0.798012	−	0.460732i
$21$	0.440526	−	0.642114i	0.0961305	−	0.140121i
$22$	1.13563	+	1.35339i	0.242117	+	0.288543i
$23$	1.03209	+	0.181985i	0.215205	+	0.0379465i	0.280211	−	0.959938i	$-0.409596\pi$
$23$	1.03209	+	0.181985i	0.215205	+	0.0379465i	−0.0650059	+	0.997885i	$0.520707\pi$
$24$	−0.979855	+	1.42825i	−0.200012	+	0.291539i
$25$	−9.17870	−	7.70184i	−1.83574	−	1.54037i
$26$	2.51586	+	1.45254i	0.493402	+	0.284866i
$27$	5.05560	+	1.20038i	0.972950	+	0.231014i
$28$	0.422469	−	0.153766i	0.0798392	−	0.0290591i
$29$	0.697791	−	3.95737i	0.129577	−	0.734865i	−0.848907	−	0.528542i	$-0.822739\pi$
$29$	0.697791	−	3.95737i	0.129577	−	0.734865i	0.978484	−	0.206323i	$-0.0661499\pi$
$30$	−4.99859	+	5.09509i	−0.912614	+	0.930232i
$31$			1.93871i			0.348202i	0.984728	+	0.174101i	$0.0557019\pi$
$31$			1.93871i			0.348202i	−0.984728	+	0.174101i	$0.944298\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	2.76086	−	1.31969i	0.480604	−	0.229728i
$34$	−0.996305	−	2.73733i	−0.170865	−	0.469448i
$35$	1.82454	−	0.321716i	0.308404	−	0.0543800i
$36$	1.97195	+	2.26085i	0.328658	+	0.376808i
$37$		−	1.92037i		−	0.315707i	−0.987463	−	0.157854i	$-0.949543\pi$
$37$		−	1.92037i		−	0.315707i	0.987463	−	0.157854i	$-0.0504574\pi$
$38$	3.67365	+	2.34613i	0.595944	+	0.380592i
$39$	3.52379	−	3.59182i	0.564259	−	0.575152i
$40$	−4.05831	+	0.715589i	−0.641675	+	0.113145i
$41$	1.94166	−	1.62925i	0.303237	−	0.254446i	−0.478453	−	0.878113i	$-0.658802\pi$
$41$	1.94166	−	1.62925i	0.303237	−	0.254446i	0.781690	+	0.623667i	$0.214358\pi$
$42$	−0.0752809	−	0.775052i	−0.0116161	−	0.119593i
$43$	−1.05122	−	5.96178i	−0.160310	−	0.909164i	−0.953769	−	0.300540i	$-0.902833\pi$
$43$	−1.05122	−	5.96178i	−0.160310	−	0.909164i	0.793459	−	0.608624i	$-0.208278\pi$
$44$	1.73988	+	0.306788i	0.262297	+	0.0462500i
$45$	6.38494	+	10.5863i	0.951810	+	1.57811i
$46$	0.907603	−	0.524005i	0.133819	−	0.0772603i
$47$	−2.67277	−	0.471281i	−0.389864	−	0.0687435i	−0.0247193	−	0.999694i	$-0.507869\pi$
$47$	−2.67277	−	0.471281i	−0.389864	−	0.0687435i	−0.365144	+	0.930951i	$0.618980\pi$
$48$	0.167446	+	1.72394i	0.0241688	+	0.248829i
$49$	3.39894	−	5.88713i	0.485563	−	0.841019i
$50$	−11.9819			−1.69450
$51$	−5.02183	+	0.487771i	−0.703197	+	0.0683016i
$52$	2.86094	−	0.504460i	0.396740	−	0.0699560i
$53$	9.34372	+	7.84031i	1.28346	+	1.07695i	0.992758	+	0.120135i	$0.0383328\pi$
$53$	9.34372	+	7.84031i	1.28346	+	1.07695i	0.290701	+	0.956814i	$0.406112\pi$
$54$	4.64441	−	2.33013i	0.632023	−	0.317090i
$55$	6.84144	+	2.49008i	0.922500	+	0.335763i
$56$	0.224791	−	0.389350i	0.0300390	−	0.0520291i
$57$	5.52304	−	5.14742i	0.731545	−	0.681793i
$58$	−2.00921	−	3.48005i	−0.263822	−	0.456953i
$59$	2.52025	+	14.2930i	0.328108	+	1.86079i	0.486865	+	0.873477i	$0.338140\pi$
$59$	2.52025	+	14.2930i	0.328108	+	1.86079i	−0.158757	+	0.987318i	$0.550749\pi$
$60$	−0.554083	+	7.11610i	−0.0715318	+	0.918684i
$61$	−14.0885	+	5.12780i	−1.80385	+	0.656547i	−0.805934	+	0.592005i	$0.798337\pi$
$61$	−14.0885	+	5.12780i	−1.80385	+	0.656547i	−0.997915	+	0.0645424i	$0.979441\pi$
$62$	1.24618	+	1.48514i	0.158265	+	0.188612i
$63$	−1.33249	−	0.208770i	−0.167878	−	0.0263026i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	11.9715			1.48489
$66$	1.26666	−	2.78559i	0.155915	−	0.342882i
$67$	5.40252	−	6.43847i	0.660022	−	0.786584i	−0.327366	−	0.944897i	$-0.606161\pi$
$67$	5.40252	−	6.43847i	0.660022	−	0.786584i	0.987389	+	0.158313i	$0.0506056\pi$
$68$	−2.52273	−	1.45650i	−0.305926	−	0.176627i
$69$	−0.486550	−	1.74878i	−0.0585738	−	0.210529i
$70$	1.19089	−	1.41924i	0.142338	−	0.169632i
$71$	6.00202	−	5.03629i	0.712309	−	0.597698i	−0.212937	−	0.977066i	$-0.568303\pi$
$71$	6.00202	−	5.03629i	0.712309	−	0.597698i	0.925246	+	0.379368i	$0.123859\pi$
$72$	2.96384	+	0.464365i	0.349292	+	0.0547259i
$73$	1.97920	+	11.2246i	0.231648	+	1.31374i	0.849559	+	0.527493i	$0.176868\pi$
$73$	1.97920	+	11.2246i	0.231648	+	1.31374i	−0.617911	+	0.786248i	$0.712021\pi$
$74$	−1.23439	−	1.47109i	−0.143495	−	0.171011i
$75$	−5.17948	+	20.0966i	−0.598074	+	2.32056i
$76$	4.32224	−	0.564136i	0.495795	−	0.0647109i
$77$	−0.687873	+	0.397144i	−0.0783904	+	0.0452587i
$78$	0.390605	−	5.01655i	0.0442273	−	0.568012i
$79$	−5.70748	+	15.6812i	−0.642141	+	1.76427i	0.00275238	+	0.999996i	$0.499124\pi$
$79$	−5.70748	+	15.6812i	−0.642141	+	1.76427i	−0.644894	+	0.764272i	$0.723098\pi$
$80$	−2.64887	+	3.15680i	−0.296153	+	0.352941i
$81$	−1.90054	−	8.79704i	−0.211171	−	0.977449i
$82$	0.440140	−	2.49616i	0.0486053	−	0.275654i
$83$	1.83095	−	1.05710i	0.200972	−	0.116032i	−0.396137	−	0.918192i	$-0.629649\pi$
$83$	1.83095	−	1.05710i	0.200972	−	0.116032i	0.597109	+	0.802160i	$0.296316\pi$
$84$	−0.555863	−	0.545335i	−0.0606496	−	0.0595009i
$85$	−9.19578	−	7.71617i	−0.997422	−	0.836936i
$86$	−4.63745	−	3.89128i	−0.500069	−	0.419607i
$87$	−6.70542	+	1.86559i	−0.718896	+	0.200013i
$88$	1.53003	−	0.883361i	0.163101	−	0.0941666i
$89$	2.34281	−	13.2867i	0.248337	−	1.40839i	−0.564275	−	0.825587i	$-0.690844\pi$
$89$	2.34281	−	13.2867i	0.248337	−	1.40839i	0.812613	−	0.582804i	$-0.198045\pi$
$90$	11.6959	+	4.00543i	1.23286	+	0.422209i
$91$	−0.839525	+	1.00051i	−0.0880061	+	0.104882i
$92$	0.358441	−	0.984807i	0.0373700	−	0.102673i
$93$	3.02962	−	1.44815i	0.314157	−	0.150167i
$94$	−2.35039	+	1.35700i	−0.242425	+	0.139964i
$95$	17.9447	+	0.803509i	1.84108	+	0.0824383i
$96$	1.23640	+	1.21298i	0.126189	+	0.123799i
$97$	−7.29486	−	8.69367i	−0.740681	−	0.882709i	0.255783	−	0.966734i	$-0.417667\pi$
$97$	−7.29486	−	8.69367i	−0.740681	−	0.882709i	−0.996464	+	0.0840254i	$0.973222\pi$
$98$	−1.18044	−	6.69460i	−0.119242	−	0.676257i
$99$	−4.12456	−	3.32863i	−0.414534	−	0.334540i
$100$	−9.17870	+	7.70184i	−0.917870	+	0.770184i
$101$	2.47985	−	2.95537i	0.246755	−	0.294071i	−0.628424	−	0.777871i	$-0.716300\pi$
$101$	2.47985	−	2.95537i	0.246755	−	0.294071i	0.875178	+	0.483801i	$0.160744\pi$
$102$	−3.53341	+	3.60163i	−0.349860	+	0.356614i
$103$	13.9046	+	8.02783i	1.37006	+	0.791006i	0.990935	−	0.134339i	$-0.0428912\pi$
$103$	13.9046	+	8.02783i	1.37006	+	0.791006i	0.379126	+	0.925345i	$0.376225\pi$
$104$	1.86734	−	2.22541i	0.183108	−	0.218220i
$105$	−1.86563	−	2.61091i	−0.182066	−	0.254798i
$106$	12.1974			1.18471
$107$	−2.27949	+	3.94820i	−0.220367	+	0.381687i	−0.954919	−	0.296865i	$-0.904059\pi$
$107$	−2.27949	+	3.94820i	−0.220367	+	0.381687i	0.734552	+	0.678552i	$0.237392\pi$
$108$	2.06004	−	4.77035i	0.198228	−	0.459027i
$109$	−8.34728	−	9.94790i	−0.799524	−	0.952836i	0.200113	−	0.979773i	$-0.435869\pi$
$109$	−8.34728	−	9.94790i	−0.799524	−	0.952836i	−0.999637	+	0.0269369i	$0.991425\pi$
$110$	6.84144	−	2.49008i	0.652306	−	0.237420i
$111$	−3.00097	+	1.43446i	−0.284839	+	0.136153i
$112$	−0.0780692	−	0.442752i	−0.00737684	−	0.0418362i
$113$	−0.940197	−	1.62847i	−0.0884463	−	0.153194i	0.818408	−	0.574637i	$-0.194857\pi$
$113$	−0.940197	−	1.62847i	−0.0884463	−	0.153194i	−0.906855	+	0.421444i	$0.861524\pi$
$114$	0.922197	−	7.49330i	0.0863716	−	0.701812i
$115$	2.15938	−	3.74016i	0.201363	−	0.348771i
$116$	−3.77608	−	1.37438i	−0.350600	−	0.127608i
$117$	−8.24511	−	2.82366i	−0.762261	−	0.261047i
$118$	11.1180	+	9.32912i	1.02350	+	0.858815i
$119$	1.28974	−	0.227416i	0.118230	−	0.0208472i
$120$	4.14969	+	5.80740i	0.378813	+	0.530141i
$121$	7.87869			0.716245
$122$	−7.49634	+	12.9840i	−0.678687	+	1.17552i
$123$	−3.99640	−	1.81724i	−0.360343	−	0.163855i
$124$	1.90925	+	0.336653i	0.171456	+	0.0302323i
$125$	−24.9173	+	14.3860i	−2.22867	+	1.28672i
$126$	−1.15494	+	0.696582i	−0.102891	+	0.0620565i
$127$	−9.22641	−	1.62687i	−0.818712	−	0.144361i	−0.251420	−	0.967878i	$-0.580898\pi$
$127$	−9.22641	−	1.62687i	−0.818712	−	0.144361i	−0.567291	+	0.823517i	$0.692009\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−8.53126	+	6.09602i	−0.751135	+	0.536725i
$130$	9.17074	−	7.69516i	0.804327	−	0.674910i
$131$	−14.0380	+	2.47528i	−1.22651	+	0.216266i	−0.749124	−	0.662430i	$-0.769525\pi$
$131$	−14.0380	+	2.47528i	−1.22651	+	0.216266i	−0.477382	+	0.878696i	$0.658414\pi$
$132$	−0.820220	−	2.94808i	−0.0713910	−	0.256597i
$133$	−1.32555	+	1.44336i	−0.114940	+	0.125155i
$134$		−	8.40482i		−	0.726066i
$135$	11.7739	−	17.8854i	1.01334	−	1.53933i
$136$	−2.86875	+	0.505837i	−0.245993	+	0.0433752i
$137$	1.42905	+	3.92629i	0.122092	+	0.335445i	0.985649	−	0.168805i	$-0.0539909\pi$
$137$	1.42905	+	3.92629i	0.122092	+	0.335445i	−0.863557	+	0.504251i	$0.831769\pi$
$138$	−1.49682	−	1.02690i	−0.127417	−	0.0874153i
$139$	−16.1657	+	5.88384i	−1.37116	+	0.499061i	−0.919486	−	0.393122i	$-0.871395\pi$
$139$	−16.1657	+	5.88384i	−1.37116	+	0.499061i	−0.451673	+	0.892184i	$0.649173\pi$
$140$		−	1.85269i		−	0.156581i
$141$	1.26001	+	4.52877i	0.106112	+	0.381392i
$142$	1.36055	−	7.71605i	0.114175	−	0.647516i
$143$	−4.82293	+	1.75540i	−0.403314	+	0.146794i
$144$	2.56892	−	1.54940i	0.214077	−	0.129116i
$145$	−14.3410	−	8.27978i	−1.19096	−	0.687598i
$146$	8.73120	+	7.32634i	0.722599	+	0.606332i
$147$	−11.7387	−	0.914017i	−0.968195	−	0.0753869i
$148$	−1.89120	−	0.333469i	−0.155455	−	0.0274110i
$149$	5.09357	+	6.07028i	0.417281	+	0.497296i	0.933208	−	0.359336i	$-0.116997\pi$
$149$	5.09357	+	6.07028i	0.417281	+	0.497296i	−0.515927	+	0.856633i	$0.672552\pi$
$150$	8.95014	+	18.7242i	0.730776	+	1.52882i
$151$	5.12150	+	2.95690i	0.416782	+	0.240629i	0.693699	−	0.720265i	$-0.255980\pi$
$151$	5.12150	+	2.95690i	0.416782	+	0.240629i	−0.276918	+	0.960894i	$0.589313\pi$
$152$	2.94841	−	3.21044i	0.239147	−	0.260401i
$153$	4.51340	+	7.48328i	0.364887	+	0.604987i
$154$	−0.271662	+	0.746386i	−0.0218912	+	0.0601455i
$155$	7.50744	+	2.73248i	0.603012	+	0.219478i
$156$	−2.92535	−	4.09397i	−0.234216	−	0.327780i
$157$	10.7619	+	3.91702i	0.858895	+	0.312612i	0.733661	−	0.679515i	$-0.237810\pi$
$157$	10.7619	+	3.91702i	0.858895	+	0.312612i	0.125233	+	0.992127i	$0.460032\pi$
$158$	5.70748	+	15.6812i	0.454062	+	1.24753i
$159$	5.27259	−	20.4579i	0.418144	−	1.62242i
$160$			4.12092i			0.325787i
$161$	0.161149	+	0.442752i	0.0127003	+	0.0348938i
$162$	−7.11053	−	5.51728i	−0.558656	−	0.433479i
$163$	4.85009	+	8.40060i	0.379888	+	0.657986i	0.991046	−	0.133523i	$-0.0426291\pi$
$163$	4.85009	+	8.40060i	0.379888	+	0.657986i	−0.611157	+	0.791509i	$0.709296\pi$
$164$	−1.26733	−	2.19508i	−0.0989619	−	0.171407i
$165$	−1.21909	−	12.5512i	−0.0949064	−	0.977106i
$166$	0.723097	−	1.98669i	0.0561232	−	0.154197i
$167$	1.72275	−	9.77018i	0.133310	−	0.756039i	−0.842711	−	0.538366i	$-0.819042\pi$
$167$	1.72275	−	9.77018i	0.133310	−	0.756039i	0.976022	−	0.217674i	$-0.0698469\pi$
$168$	−0.776350	−	0.0604492i	−0.0598967	−	0.00466376i
$169$	3.49360	−	2.93147i	0.268738	−	0.225498i
$170$	−12.0042			−0.920683
$171$	−12.1694	−	4.78590i	−0.930620	−	0.365987i
$172$	−6.05375			−0.461594
$173$	−9.58724	+	8.04465i	−0.728904	+	0.611623i	−0.929833	−	0.367983i	$-0.880049\pi$
$173$	−9.58724	+	8.04465i	−0.728904	+	0.611623i	0.200928	+	0.979606i	$0.435604\pi$
$174$	−3.93747	+	5.73929i	−0.298498	+	0.435094i
$175$	0.935420	−	5.30503i	0.0707111	−	0.401023i
$176$	0.604255	−	1.66018i	0.0455474	−	0.125140i
$177$	20.4532	−	14.6149i	1.53736	−	1.09852i
$178$	−6.74585	−	11.6842i	−0.505623	−	0.875765i
$179$	4.55859	+	7.89570i	0.340725	+	0.590152i	0.984567	−	0.175005i	$-0.0559943\pi$
$179$	4.55859	+	7.89570i	0.340725	+	0.590152i	−0.643843	+	0.765158i	$0.722661\pi$
$180$	11.5342	−	4.44964i	0.859710	−	0.331657i
$181$	8.40001	+	23.0788i	0.624368	+	1.71544i	0.696035	+	0.718008i	$0.254946\pi$
$181$	8.40001	+	23.0788i	0.624368	+	1.71544i	−0.0716666	+	0.997429i	$0.522832\pi$
$182$			1.30607i			0.0968123i
$183$	18.5369	+	18.1858i	1.37029	+	1.34434i
$184$	−0.358441	−	0.984807i	−0.0264246	−	0.0726010i
$185$	−7.43643	−	2.70664i	−0.546737	−	0.198996i
$186$	1.38997	−	3.05675i	0.101917	−	0.224132i
$187$	4.83610	+	1.76019i	0.353650	+	0.128718i
$188$	−0.928243	+	2.55033i	−0.0676991	+	0.186002i
$189$	0.669085	+	2.23823i	0.0486688	+	0.162807i
$190$	14.2629	−	10.9191i	1.03474	−	0.792154i
$191$	−16.5910	−	9.57880i	−1.20048	−	0.693098i	−0.239819	−	0.970818i	$-0.577088\pi$
$191$	−16.5910	−	9.57880i	−1.20048	−	0.693098i	−0.960662	+	0.277720i	$0.910421\pi$
$192$	1.72682	+	0.134456i	0.124623	+	0.00970355i
$193$	8.15964	+	9.72428i	0.587344	+	0.699969i	0.975093	−	0.221796i	$-0.0711918\pi$
$193$	8.15964	+	9.72428i	0.587344	+	0.699969i	−0.387749	+	0.921765i	$0.626747\pi$
$194$	−11.1764	−	1.97070i	−0.802417	−	0.141488i
$195$	−8.94238	−	18.7080i	−0.640377	−	1.33970i
$196$	−5.20747	−	4.36959i	−0.371962	−	0.312114i
$197$	−13.9798	−	8.07124i	−0.996019	−	0.575052i	−0.0889512	−	0.996036i	$-0.528352\pi$
$197$	−13.9798	−	8.07124i	−0.996019	−	0.575052i	−0.907068	+	0.420984i	$0.861685\pi$
$198$	−5.29920	+	0.101332i	−0.376598	+	0.00720135i
$199$	4.71134	−	1.71479i	0.333978	−	0.121558i	−0.169587	−	0.985515i	$-0.554244\pi$
$199$	4.71134	−	1.71479i	0.333978	−	0.121558i	0.503565	+	0.863957i	$0.332021\pi$
$200$	−2.08064	+	11.7999i	−0.147124	+	0.834380i
$201$	−14.0969	−	3.63318i	−0.994320	−	0.256265i
$202$		−	3.85797i		−	0.271446i
$203$	1.69766	−	0.617897i	0.119152	−	0.0433679i
$204$	−0.391671	+	5.03024i	−0.0274225	+	0.352187i
$205$	−3.57244	−	9.81521i	−0.249510	−	0.685524i
$206$	15.8117	−	2.78804i	1.10166	−	0.194252i
$207$	−2.36939	+	2.06662i	−0.164684	+	0.143640i
$208$		−	2.90507i		−	0.201430i
$209$	−7.34712	+	2.30754i	−0.508211	+	0.159616i
$210$	−3.10741	−	0.800869i	−0.214432	−	0.0552652i
$211$	−20.6707	+	3.64479i	−1.42303	+	0.250918i	−0.831570	−	0.555419i	$-0.812558\pi$
$211$	−20.6707	+	3.64479i	−1.42303	+	0.250918i	−0.591456	+	0.806337i	$0.701447\pi$
$212$	9.34372	−	7.84031i	0.641729	−	0.538475i
$213$	−12.3536	−	5.61741i	−0.846451	−	0.384899i
$214$	0.791660	+	4.48973i	0.0541168	+	0.306911i
$215$	−24.5680	−	4.33200i	−1.67552	−	0.295440i
$216$	−1.48824	−	4.97847i	−0.101262	−	0.338742i
$217$	−0.754835	+	0.435804i	−0.0512416	+	0.0295843i
$218$	−12.7888	−	2.25501i	−0.866165	−	0.152728i
$219$	16.0623	−	11.4773i	1.08539	−	0.775567i
$220$	3.64026	−	6.30511i	0.245426	−	0.425090i
$221$	8.46248			0.569248
$222$	−1.37682	+	3.02784i	−0.0924062	+	0.203216i
$223$	3.62655	−	0.639458i	0.242852	−	0.0428213i	−0.0508974	−	0.998704i	$-0.516208\pi$
$223$	3.62655	−	0.639458i	0.242852	−	0.0428213i	0.293749	+	0.955883i	$0.405097\pi$
$224$	−0.344400	−	0.288986i	−0.0230112	−	0.0193087i
$225$	35.2739	−	6.91758i	2.35159	−	0.461172i
$226$	−1.76699	−	0.643133i	−0.117539	−	0.0427806i
$227$	−1.42666	+	2.47105i	−0.0946909	+	0.164009i	−0.909480	−	0.415749i	$-0.863520\pi$
$227$	−1.42666	+	2.47105i	−0.0946909	+	0.164009i	0.814789	+	0.579758i	$0.196853\pi$
$228$	−4.11016	−	6.33298i	−0.272202	−	0.419412i
$229$	−0.757905	−	1.31273i	−0.0500838	−	0.0867477i	0.839897	−	0.542746i	$-0.182616\pi$
$229$	−0.757905	−	1.31273i	−0.0500838	−	0.0867477i	−0.889980	+	0.455999i	$0.849282\pi$
$230$	−0.749945	−	4.25315i	−0.0494499	−	0.280444i
$231$	1.13444	+	0.778286i	0.0746405	+	0.0512075i
$232$	−3.77608	+	1.37438i	−0.247912	+	0.0902325i
$233$	1.13766	+	1.35581i	0.0745305	+	0.0888220i	0.802021	−	0.597295i	$-0.203758\pi$
$233$	1.13766	+	1.35581i	0.0745305	+	0.0888220i	−0.727491	+	0.686117i	$0.759314\pi$
$234$	−8.13113	+	3.13681i	−0.531549	+	0.205060i
$235$	−5.59208	+	9.68578i	−0.364787	+	0.631830i
$236$	14.5135			0.944750
$237$	28.7683	−	2.79427i	1.86870	−	0.181507i
$238$	0.841817	−	1.00324i	0.0545669	−	0.0650303i
$239$	−20.8076	−	12.0133i	−1.34593	−	0.777073i	−0.358260	−	0.933622i	$-0.616630\pi$
$239$	−20.8076	−	12.0133i	−1.34593	−	0.777073i	−0.987670	+	0.156549i	$0.949963\pi$
$240$	6.91177	+	1.78136i	0.446153	+	0.114986i
$241$	−0.223901	+	0.266835i	−0.0144227	+	0.0171884i	−0.773208	−	0.634153i	$-0.781349\pi$
$241$	−0.223901	+	0.266835i	−0.0144227	+	0.0171884i	0.758785	+	0.651341i	$0.225793\pi$
$242$	6.03543	−	5.06433i	0.387972	−	0.325547i
$243$	−12.3275	+	9.54109i	−0.790810	+	0.612061i
$244$	2.60345	+	14.7649i	0.166669	+	0.945226i
$245$	−18.0067	−	21.4596i	−1.15041	−	1.37100i
$246$	−4.22952	+	1.17675i	−0.269664	+	0.0750265i
$247$	−10.0547	+	7.69750i	−0.639768	+	0.489780i
$248$	1.67897	−	0.969353i	0.106615	−	0.0615540i
$249$	−3.01959	−	2.07160i	−0.191359	−	0.131283i
$250$	−9.84060	+	27.0368i	−0.622374	+	1.70996i
$251$	9.30090	−	11.0844i	0.587068	−	0.699640i	−0.387972	−	0.921671i	$-0.626824\pi$
$251$	9.30090	−	11.0844i	0.587068	−	0.699640i	0.975040	+	0.222031i	$0.0712686\pi$
$252$	−0.436983	+	1.27600i	−0.0275274	+	0.0803802i
$253$	−0.321517	+	1.82341i	−0.0202136	+	0.114637i
$254$	−8.11357	+	4.68437i	−0.509091	+	0.293924i
$255$	−5.18911	+	20.1340i	−0.324955	+	1.26084i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	18.4543	+	15.4850i	1.15115	+	0.965929i	0.999746	−	0.0225434i	$-0.00717639\pi$
$257$	18.4543	+	15.4850i	1.15115	+	0.965929i	0.151403	+	0.988472i	$0.451621\pi$
$258$	−2.61688	+	10.1536i	−0.162920	+	0.632136i
$259$	0.747696	−	0.431683i	0.0464596	−	0.0268235i
$260$	2.07884	−	11.7897i	0.128924	−	0.731165i
$261$	7.92411	+	9.08502i	0.490490	+	0.562349i
$262$	−9.16265	+	10.9196i	−0.566070	+	0.674616i
$263$	−3.84222	+	10.5564i	−0.236921	+	0.650936i	0.763068	+	0.646318i	$0.223692\pi$
$263$	−3.84222	+	10.5564i	−0.236921	+	0.650936i	−0.999989	+	0.00461806i	$0.998530\pi$
$264$	−2.52331	−	1.73113i	−0.155299	−	0.106544i
$265$	43.5301	−	25.1321i	2.67403	−	1.54385i
$266$	−0.0876611	+	1.95772i	−0.00537484	+	0.120036i
$267$	−22.5132	+	6.26367i	−1.37779	+	0.383330i
$268$	−5.40252	−	6.43847i	−0.330011	−	0.393292i
$269$	−2.41265	−	13.6828i	−0.147102	−	0.834257i	−0.965655	−	0.259826i	$-0.916335\pi$
$269$	−2.41265	−	13.6828i	−0.147102	−	0.834257i	0.818553	−	0.574430i	$-0.194776\pi$
$270$	−2.47718	−	21.2691i	−0.150757	−	1.29440i
$271$	−11.7067	+	9.82309i	−0.711131	+	0.596710i	−0.924916	−	0.380171i	$-0.875865\pi$
$271$	−11.7067	+	9.82309i	−0.711131	+	0.596710i	0.213785	+	0.976881i	$0.431421\pi$
$272$	−1.87244	+	2.23149i	−0.113533	+	0.135304i
$273$	2.19059	+	0.564579i	0.132581	+	0.0341699i
$274$	3.61849	+	2.08913i	0.218601	+	0.126209i
$275$	13.6070	−	16.2162i	0.820534	−	0.977875i
$276$	−1.80670	+	0.175485i	−0.108751	+	0.0105630i
$277$	−5.12258			−0.307786			−0.153893	−	0.988088i	$-0.549181\pi$
$277$	−5.12258			−0.307786			−0.153893	+	0.988088i	$0.549181\pi$
$278$	−8.60160	+	14.8984i	−0.515890	+	0.893548i
$279$	−4.52607	−	3.65267i	−0.270969	−	0.218679i
$280$	−1.19089	−	1.41924i	−0.0711691	−	0.0848161i
$281$	−7.67441	+	2.79326i	−0.457817	+	0.166632i	−0.560626	−	0.828069i	$-0.689439\pi$
$281$	−7.67441	+	2.79326i	−0.457817	+	0.166632i	0.102809	+	0.994701i	$0.467217\pi$
$282$	3.87626	+	2.65933i	0.230828	+	0.158361i
$283$	3.52982	+	20.0186i	0.209826	+	1.18998i	0.889662	+	0.456619i	$0.150940\pi$
$283$	3.52982	+	20.0186i	0.209826	+	1.18998i	−0.679836	+	0.733364i	$0.737949\pi$
$284$	−3.91754	−	6.78538i	−0.232463	−	0.402638i
$285$	−12.1485	−	28.6424i	−0.719614	−	1.69663i
$286$	−2.56623	+	4.44483i	−0.151744	+	0.262829i
$287$	1.07082	+	0.389746i	0.0632083	+	0.0230060i
$288$	0.971976	−	2.83818i	0.0572742	−	0.167241i
$289$	6.52242	+	5.47296i	0.383672	+	0.321939i
$290$	−16.3080	+	2.87554i	−0.957638	+	0.168857i
$291$	−8.13658	+	17.8936i	−0.476975	+	1.04894i
$292$	11.3978			0.667004
$293$	0.808522	−	1.40040i	0.0472344	−	0.0818123i	−0.841442	−	0.540348i	$-0.818293\pi$
$293$	0.808522	−	1.40040i	0.0472344	−	0.0818123i	0.888676	+	0.458536i	$0.151626\pi$
$294$	−9.57991	+	6.84534i	−0.558712	+	0.399228i
$295$	58.9004	+	10.3857i	3.42931	+	0.604680i
$296$	−1.66309	+	0.960186i	−0.0966652	+	0.0558097i
$297$	−2.12074	+	8.93184i	−0.123058	+	0.518278i
$298$	7.80380	+	1.37602i	0.452062	+	0.0797107i
$299$	0.528679	+	2.99829i	0.0305743	+	0.173396i
$300$	18.8919	+	8.59053i	1.09072	+	0.495974i
$301$	2.08491	−	1.74945i	0.120172	−	0.100837i
$302$	5.82395	−	1.02692i	0.335131	−	0.0590926i
$303$	−6.47074	−	1.66770i	−0.371734	−	0.0958066i
$304$	0.194983	−	4.35454i	0.0111831	−	0.249750i
$305$			61.7836i			3.53772i
$306$	8.26762	+	2.83137i	0.472628	+	0.161859i
$307$	25.2959	−	4.46035i	1.44371	−	0.254566i	0.603735	−	0.797185i	$-0.293679\pi$
$307$	25.2959	−	4.46035i	1.44371	−	0.254566i	0.839978	+	0.542620i	$0.182568\pi$
$308$	0.271662	+	0.746386i	0.0154794	+	0.0425293i
$309$	2.15878	−	27.7253i	0.122809	−	1.57724i
$310$	7.50744	−	2.73248i	0.426394	−	0.155195i
$311$		−	28.5583i		−	1.61939i	−0.586850	−	0.809695i	$-0.699632\pi$
$311$		−	28.5583i		−	1.61939i	0.586850	−	0.809695i	$-0.300368\pi$
$312$	−4.87251	−	1.25578i	−0.275851	−	0.0710948i
$313$	−4.56787	+	25.9057i	−0.258191	+	1.46428i	0.529555	+	0.848275i	$0.322359\pi$
$313$	−4.56787	+	25.9057i	−0.258191	+	1.46428i	−0.787746	+	0.616000i	$0.788752\pi$
$314$	10.7619	−	3.91702i	0.607330	−	0.221050i
$315$	−2.68650	+	4.86569i	−0.151367	+	0.274150i
$316$	14.4518	+	8.34377i	0.812979	+	0.469374i
$317$	19.5617	+	16.4142i	1.09870	+	0.921915i	0.997337	−	0.0729350i	$-0.0232366\pi$
$317$	19.5617	+	16.4142i	1.09870	+	0.921915i	0.101359	+	0.994850i	$0.467681\pi$
$318$	−9.11105	−	19.0608i	−0.510922	−	1.06888i
$319$	6.99157	+	1.23280i	0.391453	+	0.0690237i
$320$	2.64887	+	3.15680i	0.148077	+	0.176471i
$321$	7.87257	+	0.612985i	0.439404	+	0.0342135i
$322$	0.408043	+	0.235583i	0.0227393	+	0.0131286i
$323$	12.6848	+	0.567987i	0.705800	+	0.0316036i
$324$	−8.99342	+	0.344072i	−0.499634	+	0.0191151i
$325$	11.9052	−	32.7092i	0.660380	−	1.81438i
$326$	9.11518	+	3.31766i	0.504843	+	0.183748i
$327$	−9.31044	+	20.4751i	−0.514868	+	1.13227i
$328$	−2.38180	−	0.866906i	−0.131513	−	0.0478669i
$329$	−0.417322	−	1.14658i	−0.0230077	−	0.0632131i
$330$	−9.00161	−	8.83112i	−0.495522	−	0.486137i
$331$			7.15744i			0.393408i	0.980463	+	0.196704i	$0.0630239\pi$
$331$			7.15744i			0.393408i	−0.980463	+	0.196704i	$0.936976\pi$
$332$	−0.723097	−	1.98669i	−0.0396851	−	0.109034i
$333$	4.48326	+	3.61812i	0.245681	+	0.198272i
$334$	−4.96045	−	8.59175i	−0.271424	−	0.470120i
$335$	−17.3178	−	29.9953i	−0.946172	−	1.63882i
$336$	−0.633575	+	0.452721i	−0.0345643	+	0.0246980i
$337$	1.76597	−	4.85195i	0.0961983	−	0.264303i	−0.882255	−	0.470772i	$-0.843975\pi$
$337$	1.76597	−	4.85195i	0.0961983	−	0.264303i	0.978453	+	0.206470i	$0.0661975\pi$
$338$	0.791934	−	4.49128i	0.0430755	−	0.244293i
$339$	−1.84251	+	2.68567i	−0.100072	+	0.145865i
$340$	−9.19578	+	7.71617i	−0.498711	+	0.418468i
$341$	−3.42516			−0.185483
$342$	−12.3986	+	4.15615i	−0.670442	+	0.224739i
$343$	6.20328			0.334946
$344$	−4.63745	+	3.89128i	−0.250034	+	0.209804i
$345$	−7.45774	−	0.580685i	−0.401511	−	0.0312630i
$346$	−2.17325	+	12.3251i	−0.116835	+	0.662602i
$347$	7.60051	−	20.8822i	0.408017	−	1.12102i	−0.550215	−	0.835023i	$-0.685454\pi$
$347$	7.60051	−	20.8822i	0.408017	−	1.12102i	0.958232	−	0.285993i	$-0.0923235\pi$
$348$	0.672869	+	6.92750i	0.0360696	+	0.371353i
$349$	0.378885	+	0.656248i	0.0202812	+	0.0351281i	0.875988	−	0.482333i	$-0.160211\pi$
$349$	0.378885	+	0.656248i	0.0202812	+	0.0351281i	−0.855707	+	0.517461i	$0.826877\pi$
$350$	−2.69344	−	4.66517i	−0.143970	−	0.249364i
$351$	1.74631	+	14.9938i	0.0932111	+	0.800312i
$352$	−0.604255	−	1.66018i	−0.0322069	−	0.0884877i
$353$			7.69393i			0.409506i	0.978814	+	0.204753i	$0.0656392\pi$
$353$			7.69393i			0.409506i	−0.978814	+	0.204753i	$0.934361\pi$
$354$	6.27381	−	24.3427i	0.333449	−	1.29380i
$355$	−11.0430	−	30.3405i	−0.586104	−	1.61031i
$356$	−12.6781	−	4.61443i	−0.671935	−	0.244565i
$357$	−1.31878	−	1.84560i	−0.0697971	−	0.0976797i
$358$	8.56734	+	3.11826i	0.452798	+	0.164805i
$359$	7.39702	−	20.3231i	0.390400	−	1.07261i	−0.576420	−	0.817154i	$-0.695551\pi$
$359$	7.39702	−	20.3231i	0.390400	−	1.07261i	0.966819	−	0.255461i	$-0.0822271\pi$
$360$	5.97555	−	10.8227i	0.314939	−	0.570405i
$361$	−15.5881	+	10.8633i	−0.820428	+	0.571750i
$362$	21.2696	+	12.2800i	1.11790	+	0.645422i
$363$	−5.88514	−	12.3120i	−0.308890	−	0.646215i
$364$	0.839525	+	1.00051i	0.0440031	+	0.0524408i
$365$	46.2557	+	8.15612i	2.42113	+	0.426911i
$366$	25.8897	+	2.01586i	1.35328	+	0.105371i
$367$	−10.6980	−	8.97669i	−0.558431	−	0.468579i	0.319353	−	0.947636i	$-0.396534\pi$
$367$	−10.6980	−	8.97669i	−0.558431	−	0.468579i	−0.877784	+	0.479056i	$0.840979\pi$
$368$	−0.907603	−	0.524005i	−0.0473121	−	0.0273156i
$369$	0.145378	+	7.60260i	0.00756807	+	0.395775i
$370$	−7.43643	+	2.70664i	−0.386602	+	0.140712i
$371$	−0.952238	+	5.40041i	−0.0494377	+	0.280375i
$372$	−0.900066	−	3.23506i	−0.0466662	−	0.167730i
$373$			17.1877i			0.889947i	0.895544	+	0.444974i	$0.146787\pi$
$373$			17.1877i			0.889947i	−0.895544	+	0.444974i	$0.853213\pi$
$374$	4.83610	−	1.76019i	0.250069	−	0.0910175i
$375$	41.0935	+	28.1924i	2.12206	+	1.45585i
$376$	0.928243	+	2.55033i	0.0478705	+	0.131523i
$377$	11.4964	−	2.02713i	0.592097	−	0.104403i
$378$	1.95126	+	1.28451i	0.100362	+	0.0660679i
$379$			4.13452i			0.212376i	0.994346	+	0.106188i	$0.0338645\pi$
$379$			4.13452i			0.212376i	−0.994346	+	0.106188i	$0.966135\pi$
$380$	3.90736	−	17.5325i	0.200443	−	0.899400i
$381$	4.34954	+	15.6333i	0.222834	+	0.800921i
$382$	−18.8666	+	3.32668i	−0.965297	+	0.170208i
$383$	−22.6649	+	19.0181i	−1.15812	+	0.971781i	−0.999878	−	0.0156182i	$-0.995028\pi$
$383$	−22.6649	+	19.0181i	−1.15812	+	0.971781i	−0.158246	+	0.987400i	$0.550584\pi$
$384$	1.40925	−	1.00698i	0.0719155	−	0.0513873i
$385$	0.568384	+	3.22346i	0.0289675	+	0.164283i
$386$	12.5013	+	2.20432i	0.636299	+	0.112197i
$387$	15.8989	+	8.77827i	0.808184	+	0.446225i
$388$	−9.82834	+	5.67439i	−0.498958	+	0.288074i
$389$	−33.9184	−	5.98073i	−1.71973	−	0.303235i	−0.775215	−	0.631697i	$-0.782359\pi$
$389$	−33.9184	−	5.98073i	−1.71973	−	0.303235i	−0.944517	+	0.328462i	$0.893470\pi$
$390$	−18.8755	−	8.58308i	−0.955798	−	0.434621i
$391$	1.52643	−	2.64385i	0.0771948	−	0.133705i
$392$	−6.79788			−0.343345
$393$	14.3541	+	20.0882i	0.724067	+	1.01332i
$394$	−15.8972	+	2.80311i	−0.800891	+	0.141219i
$395$	52.6793	+	44.2032i	2.65058	+	2.22410i
$396$	−3.99429	+	3.48388i	−0.200720	+	0.175072i
$397$	−25.3495	−	9.22645i	−1.27225	−	0.463062i	−0.384391	−	0.923171i	$-0.625588\pi$
$397$	−25.3495	−	9.22645i	−1.27225	−	0.463062i	−0.887863	+	0.460108i	$0.847811\pi$
$398$	2.50685	−	4.34199i	0.125657	−	0.217644i
$399$	3.24568	+	0.993301i	0.162487	+	0.0497272i
$400$	5.99097	+	10.3767i	0.299549	+	0.518833i
$401$	1.89796	+	10.7639i	0.0947797	+	0.537523i	0.994815	+	0.101705i	$0.0324297\pi$
$401$	1.89796	+	10.7639i	0.0947797	+	0.537523i	−0.900035	+	0.435818i	$0.856459\pi$
$402$	−13.1342	+	6.27815i	−0.655076	+	0.313125i
$403$	−5.29242	+	1.92628i	−0.263634	+	0.0959551i
$404$	−2.47985	−	2.95537i	−0.123377	−	0.147035i
$405$	−36.7443	−	5.03924i	−1.82584	−	0.250402i
$406$	0.903305	−	1.56457i	0.0448303	−	0.0776483i
$407$	3.39276			0.168173
$408$	2.93334	+	4.10515i	0.145222	+	0.203235i
$409$	−4.20117	+	5.00675i	−0.207734	+	0.247568i	−0.859844	−	0.510556i	$-0.829440\pi$
$409$	−4.20117	+	5.00675i	−0.207734	+	0.247568i	0.652110	+	0.758124i	$0.273884\pi$
$410$	−9.04575	−	5.22256i	−0.446738	−	0.257924i
$411$	5.06816	−	5.16600i	0.249994	−	0.254820i
$412$	10.3204	−	12.2993i	0.508449	−	0.605945i
$413$	−4.99846	+	4.19421i	−0.245958	+	0.206383i
$414$	−0.486659	+	3.10614i	−0.0239180	+	0.152658i
$415$	−1.51290	−	8.58006i	−0.0742651	−	0.421178i
$416$	−1.86734	−	2.22541i	−0.0915540	−	0.109110i
$417$	21.2700	+	20.8672i	1.04160	+	1.02187i
$418$	−4.14496	+	6.49031i	−0.202736	+	0.317452i
$419$	−23.1895	+	13.3885i	−1.13288	+	0.654069i	−0.944658	−	0.328058i	$-0.893606\pi$
$419$	−23.1895	+	13.3885i	−1.13288	+	0.654069i	−0.188222	+	0.982126i	$0.560273\pi$
$420$	−2.89520	+	1.38390i	−0.141271	+	0.0675276i
$421$	7.21828	−	19.8321i	0.351798	−	0.966556i	−0.629995	−	0.776599i	$-0.716943\pi$
$421$	7.21828	−	19.8321i	0.351798	−	0.966556i	0.981792	−	0.189957i	$-0.0608347\pi$
$422$	−13.4918	+	16.0789i	−0.656771	+	0.782709i
$423$	6.13594	−	5.35187i	0.298340	−	0.260217i
$424$	2.11805	−	12.0120i	0.102862	−	0.583357i
$425$	−30.2272	+	17.4517i	−1.46624	+	0.846532i
$426$	−13.0742	+	3.63752i	−0.633446	+	0.176239i
$427$	−5.16348	−	4.33268i	−0.249878	−	0.209673i
$428$	3.49239	+	2.93046i	0.168811	+	0.141649i
$429$	6.34575	+	6.22557i	0.306376	+	0.300573i
$430$	−21.6047	+	12.4735i	−1.04187	+	0.601526i
$431$	−2.12205	+	12.0347i	−0.102215	+	0.579692i	0.890081	+	0.455803i	$0.150648\pi$
$431$	−2.12205	+	12.0347i	−0.102215	+	0.579692i	−0.992296	+	0.123889i	$0.960463\pi$
$432$	−4.34015	−	2.85711i	−0.208816	−	0.137463i
$433$	13.3457	−	15.9048i	0.641354	−	0.764336i	−0.343229	−	0.939252i	$-0.611521\pi$
$433$	13.3457	−	15.9048i	0.641354	−	0.764336i	0.984583	+	0.174915i	$0.0559652\pi$
$434$	−0.298108	+	0.819044i	−0.0143096	+	0.0393154i
$435$	−2.22654	+	28.5954i	−0.106754	+	1.37105i
$436$	−11.2463	+	6.49303i	−0.538598	+	0.310960i
$437$	0.591220	+	4.52975i	0.0282819	+	0.216687i
$438$	4.92695	−	19.1168i	0.235419	−	0.913436i
$439$	−7.30539	−	8.70622i	−0.348667	−	0.415525i	0.562999	−	0.826458i	$-0.309648\pi$
$439$	−7.30539	−	8.70622i	−0.348667	−	0.415525i	−0.911666	+	0.410933i	$0.865203\pi$
$440$	−1.26425	−	7.16991i	−0.0602707	−	0.341812i
$441$	7.34014	+	19.0269i	0.349531	+	0.906042i
$442$	6.48263	−	5.43957i	0.308347	−	0.258734i
$443$	22.4482	−	26.7527i	1.06655	−	1.27106i	0.105577	−	0.994411i	$-0.466331\pi$
$443$	22.4482	−	26.7527i	1.06655	−	1.27106i	0.960971	−	0.276650i	$-0.0892244\pi$
$444$	0.891554	+	3.20447i	0.0423113	+	0.152077i
$445$	−48.1494	−	27.7991i	−2.28250	−	1.31780i
$446$	2.36706	−	2.82095i	0.112084	−	0.133576i
$447$	5.68129	−	12.4940i	0.268716	−	0.590948i
$448$	−0.449583			−0.0212408
$449$	0.694714	−	1.20328i	0.0327856	−	0.0567863i	−0.849167	−	0.528124i	$-0.822895\pi$
$449$	0.694714	−	1.20328i	0.0327856	−	0.0567863i	0.881953	+	0.471338i	$0.156229\pi$
$450$	22.5749	−	27.9728i	1.06419	−	1.31865i
$451$	2.87843	+	3.43038i	0.135540	+	0.161530i
$452$	−1.76699	+	0.643133i	−0.0831124	+	0.0302504i
$453$	0.795147	−	10.2121i	0.0373593	−	0.479806i
$454$	0.495474	+	2.80997i	0.0232538	+	0.131879i
$455$	2.69110	+	4.66112i	0.126161	+	0.218517i
$456$	−7.21932	−	2.20938i	−0.338076	−	0.103464i
$457$	10.6225	−	18.3987i	0.496899	−	0.860654i	−0.503095	−	0.864231i	$-0.667805\pi$
$457$	10.6225	−	18.3987i	0.496899	−	0.860654i	0.999994	+	0.00357692i	$0.00113857\pi$
$458$	−1.42440	−	0.518438i	−0.0665576	−	0.0242250i
$459$	8.32276	−	12.6429i	0.388473	−	0.590119i
$460$	−3.30836	−	2.77605i	−0.154253	−	0.129434i
$461$	−7.65658	+	1.35006i	−0.356602	+	0.0628786i	−0.349080	−	0.937093i	$-0.613506\pi$
$461$	−7.65658	+	1.35006i	−0.356602	+	0.0628786i	−0.00752280	+	0.999972i	$0.502395\pi$
$462$	1.36930	−	0.133000i	0.0637057	−	0.00618774i
$463$	−7.06539			−0.328357			−0.164178	−	0.986431i	$-0.552497\pi$
$463$	−7.06539			−0.328357			−0.164178	+	0.986431i	$0.552497\pi$
$464$	−2.00921	+	3.48005i	−0.0932752	+	0.161557i
$465$	−1.33777	−	13.7730i	−0.0620376	−	0.638706i
$466$	1.74299	+	0.307337i	0.0807427	+	0.0142371i
$467$	13.8785	−	8.01273i	0.642218	−	0.370785i	−0.143250	−	0.989686i	$-0.545755\pi$
$467$	13.8785	−	8.01273i	0.642218	−	0.370785i	0.785469	+	0.618902i	$0.212422\pi$
$468$	−4.21251	+	7.62953i	−0.194723	+	0.352675i
$469$	3.72126	+	0.656158i	0.171832	+	0.0302985i
$470$	1.94211	+	11.0143i	0.0895829	+	0.508050i
$471$	−1.91769	−	19.7436i	−0.0883627	−	0.909735i
$472$	11.1180	−	9.32912i	0.511748	−	0.429407i
$473$	10.5328	−	1.85722i	0.484300	−	0.0853951i
$474$	20.2417	−	20.6324i	0.929731	−	0.947679i
$475$	20.0406	−	48.2302i	0.919524	−	2.21295i
$476$		−	1.30963i		−	0.0600270i
$477$	−35.9081	+	7.04195i	−1.64412	+	0.322429i
$478$	−23.6615	+	4.17216i	−1.08225	+	0.190830i
$479$	−5.40898	−	14.8611i	−0.247143	−	0.679019i	−0.999788	−	0.0205927i	$-0.993445\pi$
$479$	−5.40898	−	14.8611i	−0.247143	−	0.679019i	0.752645	−	0.658426i	$-0.228778\pi$
$480$	6.43976	−	3.07820i	0.293934	−	0.140500i
$481$	5.24237	−	1.90807i	0.239032	−	0.0870004i
$482$			0.348328i			0.0158659i
$483$	0.571516	−	0.582549i	0.0260049	−	0.0265069i
$484$	1.36812	−	7.75900i	0.0621873	−	0.352682i
$485$	−43.9470	+	15.9954i	−1.99553	+	0.726313i
$486$	−3.31052	+	15.2329i	−0.150168	+	0.690977i
$487$	−24.0351	−	13.8767i	−1.08913	−	0.628812i	−0.155788	−	0.987790i	$-0.549792\pi$
$487$	−24.0351	−	13.8767i	−1.08913	−	0.628812i	−0.933346	+	0.358978i	$0.883125\pi$
$488$	11.4851	+	9.63711i	0.519904	+	0.436251i
$489$	9.50476	−	13.8542i	0.429820	−	0.626510i
$490$	−27.5879	−	4.86449i	−1.24629	−	0.219755i
$491$	−5.82711	−	6.94448i	−0.262974	−	0.313400i	0.618359	−	0.785896i	$-0.287798\pi$
$491$	−5.82711	−	6.94448i	−0.262974	−	0.313400i	−0.881333	+	0.472496i	$0.843353\pi$
$492$	−2.48360	+	3.62012i	−0.111969	+	0.163208i
$493$	−10.1374	−	5.85283i	−0.456565	−	0.263598i
$494$	−2.75452	+	12.3597i	−0.123932	+	0.556089i
$495$	−18.7031	+	11.2804i	−0.840641	+	0.507017i
$496$	0.663077	−	1.82179i	0.0297730	−	0.0818007i
$497$	3.31008	+	1.20477i	0.148477	+	0.0540414i
$498$	−3.64474	+	0.354014i	−0.163325	+	0.0158637i
$499$	−23.1951	−	8.44232i	−1.03835	−	0.377930i	−0.234099	−	0.972213i	$-0.575214\pi$
$499$	−23.1951	−	8.44232i	−1.03835	−	0.377930i	−0.804256	+	0.594283i	$0.797436\pi$
$500$	9.84060	+	27.0368i	0.440085	+	1.20912i
$501$	−16.5547	+	4.60589i	−0.739610	+	0.205776i
$502$		−	14.4696i		−	0.645812i
$503$	−6.79369	−	18.6655i	−0.302916	−	0.832254i	−0.993990	−	0.109470i	$-0.965085\pi$
$503$	−6.79369	−	18.6655i	−0.302916	−	0.832254i	0.691075	−	0.722784i	$-0.257138\pi$
$504$	0.485446	+	1.25836i	0.0216235	+	0.0560517i
$505$	−7.94917	−	13.7684i	−0.353734	−	0.612685i
$506$	0.925771	+	1.60348i	0.0411556	+	0.0712835i
$507$	−7.19063	−	3.26973i	−0.319347	−	0.145214i
$508$	−3.20430	+	8.80374i	−0.142168	+	0.390603i
$509$	1.96903	−	11.1669i	0.0872757	−	0.494965i	−0.909567	−	0.415558i	$-0.863586\pi$
$509$	1.96903	−	11.1669i	0.0872757	−	0.494965i	0.996842	−	0.0794070i	$-0.0253027\pi$
$510$	8.96680	+	18.7590i	0.397056	+	0.830664i
$511$	−3.92539	+	3.29380i	−0.173649	+	0.145709i
$512$	1.00000			0.0441942
$513$	1.61126	+	22.5921i	0.0711389	+	0.997466i
$514$	24.0904			1.06258
$515$	50.6846	−	42.5294i	2.23343	−	1.87407i
$516$	4.52197	+	9.46021i	0.199069	+	0.416463i
$517$	0.832623	−	4.72204i	0.0366187	−	0.207675i
$518$	0.295288	−	0.811298i	0.0129742	−	0.0356464i
$519$	19.7328	+	8.97289i	0.866172	+	0.393866i
$520$	−5.98577	−	10.3677i	−0.262494	−	0.454652i
$521$	−1.47082	−	2.54754i	−0.0644380	−	0.111610i	0.832007	−	0.554766i	$-0.187192\pi$
$521$	−1.47082	−	2.54754i	−0.0644380	−	0.111610i	−0.896445	+	0.443156i	$0.853859\pi$
$522$	11.9100	+	1.86601i	0.521285	+	0.0816731i
$523$	1.58892	+	4.36552i	0.0694785	+	0.190891i	0.969572	−	0.244806i	$-0.0787243\pi$
$523$	1.58892	+	4.36552i	0.0694785	+	0.190891i	−0.900094	+	0.435697i	$0.856502\pi$
$524$			14.2546i			0.622713i
$525$	−8.98891	+	2.50091i	−0.392308	+	0.109149i
$526$	3.84222	+	10.5564i	0.167529	+	0.460282i
$527$	5.30687	+	1.93154i	0.231171	+	0.0841394i
$528$	−3.04572	+	0.295831i	−0.132548	+	0.0128744i
$529$	−20.5808	−	7.49081i	−0.894819	−	0.325688i
$530$	17.1914	−	47.2330i	0.746746	−	2.05167i
$531$	−38.1166	−	21.0454i	−1.65412	−	0.913293i
$532$	1.19125	+	1.55605i	0.0516471	+	0.0674633i
$533$	6.37687	+	3.68169i	0.276213	+	0.159472i
$534$	−13.2199	+	19.2695i	−0.572081	+	0.833871i
$535$	12.0762	+	14.3918i	0.522099	+	0.622213i
$536$	−8.27714	−	1.45948i	−0.357518	−	0.0630400i
$537$	8.93350	−	13.0216i	0.385509	−	0.561922i
$538$	−10.6433	−	8.93083i	−0.458867	−	0.385035i
$539$	10.4009	+	6.00498i	0.448000	+	0.258653i
$540$	−15.5692	−	14.7008i	−0.669990	−	0.632622i
$541$	23.0936	−	8.40538i	0.992871	−	0.361376i	0.206040	−	0.978544i	$-0.433942\pi$
$541$	23.0936	−	8.40538i	0.992871	−	0.361376i	0.786831	+	0.617168i	$0.211720\pi$
$542$	−2.65369	+	15.0498i	−0.113986	+	0.646446i
$543$	29.7908	−	30.3659i	1.27845	−	1.30313i
$544$			2.91300i			0.124894i
$545$	−50.2871	+	18.3030i	−2.15406	+	0.784015i
$546$	2.04100	−	0.975594i	0.0873466	−	0.0417516i
$547$	3.00540	+	8.25727i	0.128502	+	0.353056i	0.987214	−	0.159403i	$-0.0509570\pi$
$547$	3.00540	+	8.25727i	0.128502	+	0.353056i	−0.858712	+	0.512459i	$0.828735\pi$
$548$	4.11479	−	0.725549i	0.175775	−	0.0309939i
$549$	14.5725	−	42.5519i	0.621940	−	1.81607i
$550$		−	21.1688i		−	0.902639i
$551$	17.3686	−	2.26693i	0.739926	−	0.0965747i
$552$	−1.27122	+	1.29576i	−0.0541065	+	0.0551511i
$553$	−7.38845	+	1.30278i	−0.314189	+	0.0554000i
$554$	−3.92412	+	3.29273i	−0.166720	+	0.139895i
$555$	1.32512	+	13.6427i	0.0562481	+	0.579101i
$556$	2.98731	+	16.9419i	0.126690	+	0.718495i
$557$	−20.8606	−	3.67829i	−0.883894	−	0.155854i	−0.286766	−	0.958001i	$-0.592580\pi$
$557$	−20.8606	−	3.67829i	−0.883894	−	0.155854i	−0.597128	+	0.802146i	$0.703691\pi$
$558$	−5.81506	+	0.111196i	−0.246171	+	0.00470731i
$559$	15.2304	−	8.79329i	0.644179	−	0.371917i
$560$	−1.82454	−	0.321716i	−0.0771011	−	0.0135950i
$561$	−0.861756	−	8.87219i	−0.0363834	−	0.374584i
$562$	−4.08347	+	7.07278i	−0.172251	+	0.298347i
$563$	−22.1508			−0.933547			−0.466773	−	0.884377i	$-0.654584\pi$
$563$	−22.1508			−0.933547			−0.466773	+	0.884377i	$0.654584\pi$
$564$	4.67877	−	0.454449i	0.197012	−	0.0191358i
$565$	−7.63122	+	1.34559i	−0.321048	+	0.0566094i
$566$	15.5717	+	13.0662i	0.654528	+	0.549214i
$567$	2.99790	−	2.71747i	0.125900	−	0.114123i
$568$	−7.36257	−	2.67976i	−0.308927	−	0.112440i
$569$	21.9089	−	37.9473i	0.918467	−	1.59083i	0.116723	−	0.993165i	$-0.462761\pi$
$569$	21.9089	−	37.9473i	0.918467	−	1.59083i	0.801744	−	0.597667i	$-0.203906\pi$
$570$	−27.7172	−	14.1324i	−1.16095	−	0.591943i
$571$	−2.72607	−	4.72169i	−0.114082	−	0.197597i	0.803330	−	0.595534i	$-0.203059\pi$
$571$	−2.72607	−	4.72169i	−0.114082	−	0.197597i	−0.917413	+	0.397937i	$0.869726\pi$
$572$	0.891241	+	5.05448i	0.0372647	+	0.211338i
$573$	−2.57586	+	33.0818i	−0.107608	+	1.38201i
$574$	1.07082	−	0.389746i	0.0446950	−	0.0162677i
$575$	−8.07161	−	9.61937i	−0.336609	−	0.401155i
$576$	−1.07977	−	2.79895i	−0.0449904	−	0.116623i
$577$	−9.76210	+	16.9084i	−0.406401	+	0.703908i	−0.994483	−	0.104893i	$-0.966550\pi$
$577$	−9.76210	+	16.9084i	−0.406401	+	0.703908i	0.588082	+	0.808801i	$0.299883\pi$
$578$	8.51442			0.354153
$579$	9.10115	−	20.0148i	0.378231	−	0.831788i
$580$	−10.6443	+	12.6854i	−0.441980	+	0.526731i
$581$	0.823161	+	0.475252i	0.0341505	+	0.0197168i
$582$	5.26880	+	18.9374i	0.218399	+	0.784980i
$583$	−13.8516	+	16.5078i	−0.573677	+	0.683681i
$584$	8.73120	−	7.32634i	0.361299	−	0.303166i
$585$	−22.5553	+	27.9486i	−0.932546	+	1.15553i
$586$	−0.280797	−	1.59248i	−0.0115996	−	0.0657846i
$587$	2.79339	+	3.32903i	0.115295	+	0.137404i	0.820605	−	0.571495i	$-0.193637\pi$
$587$	2.79339	+	3.32903i	0.115295	+	0.137404i	−0.705310	+	0.708899i	$0.749192\pi$
$588$	−2.93854	+	11.4017i	−0.121183	+	0.470197i
$589$	−8.06233	+	2.53217i	−0.332203	+	0.104336i
$590$	51.7961	−	29.9045i	2.13241	−	1.23115i
$591$	−2.17046	+	27.8752i	−0.0892807	+	1.14663i
$592$	−0.656806	+	1.80456i	−0.0269945	+	0.0741669i
$593$	−13.0725	+	15.5792i	−0.536822	+	0.639760i	−0.964472	−	0.264185i	$-0.914897\pi$
$593$	−13.0725	+	15.5792i	−0.536822	+	0.639760i	0.427650	+	0.903944i	$0.359342\pi$
$594$	4.11669	+	8.20537i	0.168910	+	0.336671i
$595$	0.937161	−	5.31490i	0.0384198	−	0.217890i
$596$	6.86254	−	3.96209i	0.281101	−	0.162294i
$597$	−6.19893	−	6.08152i	−0.253705	−	0.248900i
$598$	2.33226	+	1.95699i	0.0953730	+	0.0800275i
$599$	−5.64537	−	4.73703i	−0.230664	−	0.193550i	0.520129	−	0.854088i	$-0.325884\pi$
$599$	−5.64537	−	4.73703i	−0.230664	−	0.193550i	−0.750793	+	0.660538i	$0.770328\pi$
$600$	19.9939	−	5.56275i	0.816248	−	0.227098i
$601$	−25.1066	+	14.4953i	−1.02412	+	0.591276i	−0.915295	−	0.402785i	$-0.868042\pi$
$601$	−25.1066	+	14.4953i	−1.02412	+	0.591276i	−0.108825	+	0.994061i	$0.534709\pi$
$602$	0.472612	−	2.68031i	0.0192622	−	0.109241i
$603$	4.85239	+	24.7432i	0.197605	+	1.00762i
$604$	3.80132	−	4.53023i	0.154673	−	0.184333i
$605$	11.1045	−	30.5094i	0.451463	−	1.24038i
$606$	−6.02885	+	2.88178i	−0.244905	+	0.117064i
$607$	6.75488	−	3.89993i	0.274172	−	0.158293i	−0.356610	−	0.934253i	$-0.616067\pi$
$607$	6.75488	−	3.89993i	0.274172	−	0.158293i	0.630782	+	0.775960i	$0.282734\pi$
$608$	−2.64968	−	3.46110i	−0.107459	−	0.140366i
$609$	−2.23369	−	2.19138i	−0.0905136	−	0.0887993i
$610$	39.7137	+	47.3290i	1.60796	+	1.91629i
$611$	−1.36911	−	7.76458i	−0.0553881	−	0.314121i
$612$	8.15333	−	3.14537i	0.329579	−	0.127144i
$613$	15.5598	−	13.0562i	0.628453	−	0.527334i	−0.271995	−	0.962299i	$-0.587683\pi$
$613$	15.5598	−	13.0562i	0.628453	−	0.527334i	0.900448	+	0.434964i	$0.143239\pi$
$614$	16.5107	−	19.6767i	0.666319	−	0.794088i
$615$	−12.6697	+	12.9143i	−0.510893	+	0.520756i
$616$	0.687873	+	0.397144i	0.0277152	+	0.0160014i
$617$	24.4674	−	29.1591i	0.985022	−	1.17390i	0.000258917	−	1.00000i	$-0.499918\pi$
$617$	24.4674	−	29.1591i	0.985022	−	1.17390i	0.984763	−	0.173903i	$-0.0556380\pi$
$618$	−16.1678	−	22.6265i	−0.650362	−	0.910169i
$619$	1.19000			0.0478300			0.0239150	−	0.999714i	$-0.492387\pi$
$619$	1.19000			0.0478300			0.0239150	+	0.999714i	$0.492387\pi$
$620$	3.99462	−	6.91889i	0.160428	−	0.277869i
$621$	4.99937	+	2.15895i	0.200618	+	0.0866355i
$622$	−18.3569	−	21.8769i	−0.736045	−	0.877184i
$623$	5.69983	−	2.07457i	0.228359	−	0.0831158i
$624$	−4.53976	+	2.17000i	−0.181736	+	0.0868695i
$625$	10.1857	+	57.7661i	0.407429	+	2.31064i
$626$	13.1527	+	22.7811i	0.525686	+	0.910514i
$627$	9.09407	+	9.75769i	0.363182	+	0.389684i
$628$	5.72630	−	9.91824i	0.228504	−	0.395781i
$629$	−5.25668	−	1.91328i	−0.209598	−	0.0762873i
$630$	1.06962	+	5.45418i	0.0426147	+	0.217300i
$631$	4.47258	+	3.75294i	0.178051	+	0.149402i	0.727458	−	0.686153i	$-0.240702\pi$
$631$	4.47258	+	3.75294i	0.178051	+	0.149402i	−0.549407	+	0.835555i	$0.685146\pi$
$632$	16.4340	−	2.89776i	0.653710	−	0.115267i
$633$	21.1361	+	29.5795i	0.840083	+	1.17568i
$634$	25.5360			1.01416
$635$	−19.3039	+	33.4353i	−0.766052	+	1.32684i
$636$	−19.2315	−	8.74497i	−0.762580	−	0.346761i
$637$	19.4483	+	3.42926i	0.770569	+	0.135872i
$638$	6.14829	−	3.54971i	0.243413	−	0.140535i
$639$	0.449388	+	23.5009i	0.0177775	+	0.929683i
$640$	4.05831	+	0.715589i	0.160419	+	0.0282862i
$641$	0.615570	+	3.49107i	0.0243136	+	0.137889i	0.994548	−	0.104278i	$-0.0332530\pi$
$641$	0.615570	+	3.49107i	0.0243136	+	0.137889i	−0.970235	+	0.242167i	$0.922142\pi$
$642$	6.42476	−	4.59082i	0.253565	−	0.181185i
$643$	15.3264	−	12.8604i	0.604415	−	0.507164i	−0.288447	−	0.957496i	$-0.593139\pi$
$643$	15.3264	−	12.8604i	0.604415	−	0.507164i	0.892861	+	0.450332i	$0.148694\pi$
$644$	0.464009	−	0.0818173i	0.0182845	−	0.00322405i
$645$	11.5819	+	41.6283i	0.456038	+	1.63911i
$646$	10.0822	−	7.71851i	0.396679	−	0.303681i
$647$		−	14.6375i		−	0.575458i	−0.957712	−	0.287729i	$-0.907100\pi$
$647$		−	14.6375i		−	0.575458i	0.957712	−	0.287729i	$-0.0929002\pi$
$648$	−6.66819	+	6.04443i	−0.261951	+	0.237448i
$649$	−25.2518	+	4.45258i	−0.991221	+	0.174779i
$650$	−11.9052	−	32.7092i	−0.466959	−	1.28296i
$651$	1.24487	+	0.854050i	0.0487903	+	0.0334728i
$652$	9.11518	−	3.31766i	0.356978	−	0.129929i
$653$			7.08532i			0.277270i	0.990344	+	0.138635i	$0.0442715\pi$
$653$			7.08532i			0.277270i	−0.990344	+	0.138635i	$0.955729\pi$
$654$	6.02892	+	21.6695i	0.235750	+	0.847343i
$655$	−10.2004	+	57.8494i	−0.398563	+	2.26036i
$656$	−2.38180	+	0.866906i	−0.0929938	+	0.0338470i
$657$	−29.9337	−	16.5274i	−1.16783	−	0.644794i
$658$	−1.05670	−	0.610084i	−0.0411943	−	0.0237835i
$659$	−2.64623	−	2.22045i	−0.103083	−	0.0864966i	0.589790	−	0.807557i	$-0.299211\pi$
$659$	−2.64623	−	2.22045i	−0.103083	−	0.0864966i	−0.692872	+	0.721060i	$0.743655\pi$
$660$	−12.5722	−	0.978911i	−0.489371	−	0.0381041i
$661$	−47.9700	−	8.45841i	−1.86582	−	0.328994i	−0.877281	−	0.479978i	$-0.840645\pi$
$661$	−47.9700	−	8.45841i	−1.86582	−	0.328994i	−0.988536	+	0.150984i	$0.951756\pi$
$662$	4.60071	+	5.48292i	0.178812	+	0.213100i
$663$	−6.32121	−	13.2243i	−0.245496	−	0.513590i
$664$	−1.83095	−	1.05710i	−0.0710545	−	0.0410233i
$665$	3.72096	+	7.16738i	0.144293	+	0.277939i
$666$	5.76006	−	0.110145i	0.223198	−	0.00426802i
$667$	1.44036	−	3.95737i	0.0557711	−	0.153230i
$668$	−9.32260	−	3.39315i	−0.360702	−	0.131285i
$669$	−3.70820	−	5.18955i	−0.143367	−	0.200640i
$670$	−32.5468	−	11.8461i	−1.25739	−	0.457653i
$671$	−9.05940	−	24.8905i	−0.349734	−	0.960887i
$672$	−0.194343	+	0.754059i	−0.00749693	+	0.0290884i
$673$		−	18.4784i		−	0.712289i	−0.934431	−	0.356144i	$-0.884091\pi$
$673$		−	18.4784i		−	0.712289i	0.934431	−	0.356144i	$-0.115909\pi$
$674$	−1.76597	−	4.85195i	−0.0680224	−	0.186890i
$675$	−37.1587	−	49.9554i	−1.43024	−	1.92278i
$676$	−2.28028	−	3.94957i	−0.0877032	−	0.151906i
$677$	21.6684	+	37.5307i	0.832783	+	1.44242i	0.895823	+	0.444411i	$0.146587\pi$
$677$	21.6684	+	37.5307i	0.832783	+	1.44242i	−0.0630399	+	0.998011i	$0.520080\pi$
$678$	0.314865	+	3.24168i	0.0120923	+	0.124496i
$679$	1.74506	−	4.79451i	0.0669693	−	0.183997i
$680$	−2.08451	+	11.8219i	−0.0799374	+	0.453348i
$681$	4.92719	+	0.383647i	0.188810	+	0.0147014i
$682$	−2.62382	+	2.20165i	−0.100471	+	0.0843055i
$683$	−9.98777			−0.382171			−0.191086	−	0.981573i	$-0.561201\pi$
$683$	−9.98777			−0.382171			−0.191086	+	0.981573i	$0.561201\pi$
$684$	−6.82639	+	11.1535i	−0.261014	+	0.426464i
$685$	17.2183			0.657877
$686$	4.75199	−	3.98739i	0.181432	−	0.152239i
$687$	−1.48527	+	2.16495i	−0.0566667	+	0.0825980i
$688$	−1.05122	+	5.96178i	−0.0400775	+	0.227291i
$689$	−12.1192	+	33.2972i	−0.461705	+	1.26852i
$690$	−6.08622	+	4.34891i	−0.231698	+	0.165560i
$691$	17.9069	+	31.0156i	0.681210	+	1.17989i	0.974612	+	0.223901i	$0.0718792\pi$
$691$	17.9069	+	31.0156i	0.681210	+	1.17989i	−0.293402	+	0.955989i	$0.594787\pi$
$692$	6.25763	+	10.8385i	0.237879	+	0.412019i
$693$	0.368839	−	2.35414i	0.0140110	−	0.0894265i
$694$	−7.60051	−	20.8822i	−0.288511	−	0.792678i
$695$			70.8930i			2.68912i
$696$	4.96836	+	4.87426i	0.188325	+	0.184758i
$697$	−2.52530	−	6.93820i	−0.0956525	−	0.262803i
$698$	0.712071	+	0.259173i	0.0269523	+	0.00980982i
$699$	1.26893	−	2.79057i	0.0479953	−	0.105549i
$700$	−5.06200	−	1.84242i	−0.191326	−	0.0696369i
$701$	13.1368	−	36.0930i	0.496170	−	1.36322i	−0.398779	−	0.917047i	$-0.630566\pi$
$701$	13.1368	−	36.0930i	0.496170	−	1.36322i	0.894949	−	0.446169i	$-0.147212\pi$
$702$	10.9756	+	10.3634i	0.414247	+	0.391143i
$703$	7.98608	−	2.50822i	0.301201	−	0.0945995i
$704$	−1.53003	−	0.883361i	−0.0576650	−	0.0332929i
$705$	19.3131	+	1.50378i	0.727373	+	0.0566357i
$706$	4.94556	+	5.89389i	0.186129	+	0.221819i
$707$	1.70812	+	0.301188i	0.0642406	+	0.0113273i
$708$	−10.8412	−	22.6803i	−0.407436	−	0.852379i
$709$	28.8393	+	24.1990i	1.08308	+	0.908813i	0.996173	−	0.0874031i	$-0.0278568\pi$
$709$	28.8393	+	24.1990i	1.08308	+	0.908813i	0.0869084	+	0.996216i	$0.472301\pi$
$710$	−27.9620	−	16.1439i	−1.04939	−	0.605868i
$711$	−25.8556	−	42.8690i	−0.969662	−	1.60771i
$712$	−12.6781	+	4.61443i	−0.475130	+	0.172933i
$713$	−0.352816	+	2.00092i	−0.0132130	+	0.0749349i
$714$	−2.19657	−	0.566120i	−0.0822047	−	0.0211865i
$715$			21.1504i			0.790980i
$716$	8.56734	−	3.11826i	0.320176	−	0.116535i
$717$	−3.23052	+	41.4896i	−0.120646	+	1.54946i
$718$	−7.39702	−	20.3231i	−0.276054	−	0.758453i
$719$	6.26841	−	1.10529i	0.233772	−	0.0412203i	−0.0555347	−	0.998457i	$-0.517686\pi$
$719$	6.26841	−	1.10529i	0.233772	−	0.0412203i	0.289307	+	0.957236i	$0.406575\pi$
$720$	−2.37914	−	12.1317i	−0.0886655	−	0.452120i
$721$			7.21834i			0.268825i
$722$	−4.95844	+	18.3416i	−0.184534	+	0.682603i
$723$	0.584231	+	0.150573i	0.0217278	+	0.00559987i
$724$	24.1869	−	4.26480i	0.898898	−	0.158500i
$725$	−36.8839	+	30.9492i	−1.36983	+	1.14943i
$726$	−12.4223	−	5.64868i	−0.461035	−	0.209642i
$727$	−6.86471	−	38.9317i	−0.254598	−	1.44390i	−0.797102	−	0.603844i	$-0.793635\pi$
$727$	−6.86471	−	38.9317i	−0.254598	−	1.44390i	0.542504	−	0.840053i	$-0.317476\pi$
$728$	1.28623	+	0.226796i	0.0476707	+	0.00840564i
$729$	24.1182	+	12.1373i	0.893265	+	0.449530i
$730$	40.6765	−	23.4846i	1.50551	−	0.869205i
$731$	−17.3667	−	3.06222i	−0.642330	−	0.113260i
$732$	21.1285	−	15.0974i	0.780930	−	0.558014i
$733$	−9.32507	+	16.1515i	−0.344429	+	0.596569i	−0.985250	−	0.171122i	$-0.945261\pi$
$733$	−9.32507	+	16.1515i	−0.344429	+	0.596569i	0.640821	+	0.767691i	$0.278594\pi$
$734$	−13.9653			−0.515467
$735$	−20.0844	+	44.1688i	−0.740825	+	1.62919i
$736$	−1.03209	+	0.181985i	−0.0380433	+	0.00670806i
$737$	11.3750	+	9.54475i	0.419003	+	0.351585i
$738$	4.99822	+	5.73048i	0.183987	+	0.210942i
$739$	−1.17299	−	0.426932i	−0.0431490	−	0.0157050i	0.320355	−	0.947297i	$-0.396198\pi$
$739$	−1.17299	−	0.426932i	−0.0431490	−	0.0157050i	−0.363505	+	0.931592i	$0.618420\pi$
$740$	−3.95684	+	6.85345i	−0.145456	+	0.251938i
$741$	19.5395	+	9.96277i	0.717801	+	0.365991i
$742$	2.74186	+	4.74904i	0.100657	+	0.174343i
$743$	−4.06927	−	23.0780i	−0.149287	−	0.846649i	−0.963824	−	0.266538i	$-0.914120\pi$
$743$	−4.06927	−	23.0780i	−0.149287	−	0.846649i	0.814537	−	0.580111i	$-0.196991\pi$
$744$	−2.76895	−	1.89965i	−0.101515	−	0.0696446i
$745$	30.6856	−	11.1686i	1.12423	−	0.409187i
$746$	11.0481	+	13.1666i	0.404498	+	0.482062i
$747$	−0.981758	+	6.26614i	−0.0359206	+	0.229266i
$748$	2.57323	−	4.45697i	0.0940867	−	0.162963i
$749$	−2.04964			−0.0748923
$750$	49.6011	−	4.81776i	1.81118	−	0.175920i
$751$	8.37951	−	9.98631i	0.305773	−	0.364406i	−0.591174	−	0.806544i	$-0.701335\pi$
$751$	8.37951	−	9.98631i	0.305773	−	0.364406i	0.896947	+	0.442138i	$0.145780\pi$
$752$	2.35039	+	1.35700i	0.0857101	+	0.0494847i
$753$	−24.2691	−	6.25484i	−0.884414	−	0.227939i
$754$	7.50377	−	8.94264i	0.273271	−	0.325672i
$755$	18.6687	−	15.6649i	0.679424	−	0.570104i
$756$	2.32041	−	0.270255i	0.0843926	−	0.00982909i
$757$	1.29941	+	7.36931i	0.0472278	+	0.267842i	0.999273	−	0.0381140i	$-0.0121350\pi$
$757$	1.29941	+	7.36931i	0.0472278	+	0.267842i	−0.952046	+	0.305956i	$0.901024\pi$
$758$	2.65762	+	3.16723i	0.0965290	+	0.115039i
$759$	3.08961	−	0.859599i	0.112146	−	0.0312015i
$760$	−8.27648	−	15.9423i	−0.300219	−	0.578288i
$761$	27.4980	−	15.8760i	0.996801	−	0.575503i	0.0895008	−	0.995987i	$-0.471473\pi$
$761$	27.4980	−	15.8760i	0.996801	−	0.575503i	0.907300	+	0.420483i	$0.138140\pi$
$762$	13.3809	+	9.18001i	0.484738	+	0.332557i
$763$	1.99682	−	5.48621i	0.0722897	−	0.198614i
$764$	−12.3143	+	14.6756i	−0.445515	+	0.530944i
$765$	35.3395	−	6.93045i	1.27770	−	0.250571i
$766$	−5.13772	+	29.1375i	−0.185634	+	1.05278i
$767$	−36.5141	+	21.0814i	−1.31845	+	0.761206i
$768$	0.432273	−	1.67724i	0.0155983	−	0.0605222i
$769$	26.9987	+	22.6546i	0.973597	+	0.816945i	0.983111	−	0.183010i	$-0.0585839\pi$
$769$	26.9987	+	22.6546i	0.973597	+	0.816945i	−0.00951376	+	0.999955i	$0.503028\pi$
$770$	2.50741	+	2.10397i	0.0903608	+	0.0758217i
$771$	10.4136	−	40.4054i	0.375038	−	1.45517i
$772$	10.9935	−	6.34707i	0.395663	−	0.228436i
$773$	0.194313	−	1.10200i	0.00698895	−	0.0396363i	−0.981114	−	0.193431i	$-0.938038\pi$
$773$	0.194313	−	1.10200i	0.00698895	−	0.0396363i	0.988103	+	0.153795i	$0.0491495\pi$
$774$	17.8218	−	3.49504i	0.640591	−	0.125627i
$775$	14.9316	−	17.7948i	0.536359	−	0.639208i
$776$	−3.88151	+	10.6644i	−0.139338	+	0.382829i
$777$	−1.23310	−	0.845973i	−0.0442371	−	0.0303491i
$778$	−29.8274	+	17.2208i	−1.06936	+	0.617397i
$779$	9.31146	+	5.94664i	0.333618	+	0.213061i
$780$	−19.9766	+	5.55792i	−0.715276	+	0.199006i
$781$	8.89773	+	10.6039i	0.318386	+	0.379438i
$782$	−0.530123	−	3.00648i	−0.0189571	−	0.107511i
$783$	8.27811	−	19.1693i	0.295836	−	0.685053i
$784$	−5.20747	+	4.36959i	−0.185981	+	0.156057i
$785$	30.3365	−	36.1536i	1.08275	−	1.29038i
$786$	23.9083	+	6.16187i	0.852782	+	0.219786i
$787$	−20.4415	−	11.8019i	−0.728662	−	0.420693i	0.0892705	−	0.996007i	$-0.471546\pi$
$787$	−20.4415	−	11.8019i	−0.728662	−	0.420693i	−0.817932	+	0.575314i	$0.804880\pi$
$788$	−10.3762	+	12.3659i	−0.369636	+	0.440515i
$789$	19.3665	−	1.88107i	0.689467	−	0.0669680i
$790$	68.7680			2.44665
$791$	0.422696	−	0.732131i	0.0150294	−	0.0260316i
$792$	−0.820404	+	5.23629i	−0.0291518	+	0.186063i
$793$	−27.9965	−	33.3649i	−0.994184	−	1.18482i
$794$	−25.3495	+	9.22645i	−0.899619	+	0.327435i
$795$	−71.7897	−	49.2517i	−2.54612	−	1.74678i
$796$	−0.870620	−	4.93753i	−0.0308583	−	0.175006i
$797$	20.6365	+	35.7435i	0.730983	+	1.26610i	0.956464	+	0.291852i	$0.0942714\pi$
$797$	20.6365	+	35.7435i	0.730983	+	1.26610i	−0.225481	+	0.974248i	$0.572395\pi$
$798$	3.12482	−	1.32537i	0.110617	−	0.0469176i
$799$	−3.95295	+	6.84670i	−0.139845	+	0.242219i
$800$	11.2593	+	4.09807i	0.398078	+	0.144888i
$801$	26.6049	+	30.5027i	0.940039	+	1.07776i
$802$	8.37281	+	7.02563i	0.295654	+	0.248083i
$803$	−19.8308	+	3.49670i	−0.699813	+	0.123396i
$804$	−6.02589	+	13.2519i	−0.212517	+	0.467357i
$805$	1.94164			0.0684338
$806$	−2.81604	+	4.87752i	−0.0991908	+	0.171803i
$807$	−19.5800	+	13.9909i	−0.689249	+	0.492503i
$808$	−3.79935	−	0.669929i	−0.133661	−	0.0235680i
$809$	0.255074	−	0.147267i	0.00896791	−	0.00517763i	−0.495509	−	0.868603i	$-0.665019\pi$
$809$	0.255074	−	0.147267i	0.00896791	−	0.00517763i	0.504477	+	0.863425i	$0.331685\pi$
$810$	−31.3869	+	19.7585i	−1.10282	+	0.694243i
$811$	2.79552	+	0.492925i	0.0981639	+	0.0173089i	0.222514	−	0.974929i	$-0.428574\pi$
$811$	2.79552	+	0.492925i	0.0981639	+	0.0173089i	−0.124350	+	0.992238i	$0.539685\pi$
$812$	−0.313715	−	1.77916i	−0.0110092	−	0.0624364i
$813$	24.0951	+	10.9565i	0.845052	+	0.384262i
$814$	2.59901	−	2.18083i	0.0910952	−	0.0764379i
$815$	39.3663	−	6.94134i	1.37894	−	0.243145i
$816$	4.88581	+	1.25921i	0.171037	+	0.0440813i
$817$	23.4197	−	12.1584i	0.819353	−	0.425369i
$818$			6.53585i			0.228521i
$819$	−0.754038	−	3.84497i	−0.0263482	−	0.134354i
$820$	−10.2864	+	1.81378i	−0.359218	+	0.0633399i
$821$	6.92089	+	19.0150i	0.241541	+	0.663628i	0.999930	+	0.0118259i	$0.00376439\pi$
$821$	6.92089	+	19.0150i	0.241541	+	0.663628i	−0.758389	+	0.651802i	$0.774013\pi$
$822$	0.561795	−	7.21514i	0.0195948	−	0.251657i
$823$	25.3485	−	9.22611i	0.883594	−	0.321602i	0.139935	−	0.990161i	$-0.455311\pi$
$823$	25.3485	−	9.22611i	0.883594	−	0.321602i	0.743659	+	0.668559i	$0.233088\pi$
$824$		−	16.0557i		−	0.559325i
$825$	−35.5051	−	9.15070i	−1.23613	−	0.318586i
$826$	−1.13306	+	6.42590i	−0.0394242	+	0.223586i
$827$	5.37473	−	1.95624i	0.186898	−	0.0680252i	−0.246876	−	0.969047i	$-0.579404\pi$
$827$	5.37473	−	1.95624i	0.186898	−	0.0680252i	0.433774	+	0.901022i	$0.357182\pi$
$828$	1.62378	+	2.69226i	0.0564304	+	0.0935624i
$829$	−27.8706	−	16.0911i	−0.967988	−	0.558868i	−0.0693655	−	0.997591i	$-0.522097\pi$
$829$	−27.8706	−	16.0911i	−0.967988	−	0.558868i	−0.898622	+	0.438723i	$0.855431\pi$
$830$	−6.67410	−	5.60023i	−0.231661	−	0.194387i
$831$	3.82641	+	8.00506i	0.132737	+	0.277692i
$832$	−2.86094	−	0.504460i	−0.0991851	−	0.0174890i
$833$	−12.7286	−	15.1694i	−0.441021	−	0.525588i
$834$	29.7069	+	2.31308i	1.02867	+	0.0800954i
$835$	−35.4059	−	20.4416i	−1.22527	−	0.707411i
$836$	0.996672	+	7.63620i	0.0344706	+	0.264103i
$837$	−2.32719	+	9.80132i	−0.0804395	+	0.338783i
$838$	−9.15824	+	25.1621i	−0.316366	+	0.869209i
$839$	−22.8355	−	8.31146i	−0.788370	−	0.286943i	−0.0837120	−	0.996490i	$-0.526678\pi$
$839$	−22.8355	−	8.31146i	−0.788370	−	0.286943i	−0.704659	+	0.709547i	$0.748900\pi$
$840$	−1.32830	+	2.92113i	−0.0458307	+	0.100789i
$841$	12.0772	+	4.39575i	0.416456	+	0.151578i
$842$	−7.21828	−	19.8321i	−0.248758	−	0.683458i
$843$	10.0976	+	9.90634i	0.347779	+	0.341192i
$844$			20.9895i			0.722489i
$845$	−6.42782	−	17.6603i	−0.221124	−	0.607533i
$846$	1.26029	−	8.04387i	0.0433296	−	0.276554i
$847$	1.77106	+	3.06757i	0.0608544	+	0.105403i
$848$	−6.09868	−	10.5632i	−0.209429	−	0.362742i
$849$	28.6465	−	20.4694i	0.983144	−	0.702506i
$850$	−11.9377	+	32.7985i	−0.409459	+	1.12498i
$851$	0.349479	−	1.98199i	0.0119800	−	0.0679418i
$852$	−7.67724	+	11.1904i	−0.263018	+	0.383377i
$853$	−29.9626	+	25.1416i	−1.02590	+	0.860833i	−0.990357	−	0.138536i	$-0.955760\pi$
$853$	−29.9626	+	25.1416i	−1.02590	+	0.860833i	−0.0355428	+	0.999368i	$0.511316\pi$
$854$	−6.74045			−0.230653
$855$	−35.6849	+	40.3794i	−1.22040	+	1.38095i
$856$	4.55899			0.155823
$857$	−22.2026	+	18.6302i	−0.758426	+	0.636395i	−0.937717	−	0.347401i	$-0.887064\pi$
$857$	−22.2026	+	18.6302i	−0.758426	+	0.636395i	0.179290	+	0.983796i	$0.442620\pi$
$858$	8.86284	+	0.690091i	0.302573	+	0.0235593i
$859$	−1.48476	+	8.42050i	−0.0506594	+	0.287304i	−0.999604	−	0.0281390i	$-0.991042\pi$
$859$	−1.48476	+	8.42050i	−0.0506594	+	0.287304i	0.948945	+	0.315443i	$0.102153\pi$
$860$	−8.53238	+	23.4425i	−0.290952	+	0.799383i
$861$	−0.190812	−	1.96450i	−0.00650284	−	0.0669498i
$862$	6.11019	+	10.5832i	0.208114	+	0.360464i
$863$	−1.62682	−	2.81774i	−0.0553777	−	0.0959169i	0.837008	−	0.547191i	$-0.184303\pi$
$863$	−1.62682	−	2.81774i	−0.0553777	−	0.0959169i	−0.892385	+	0.451274i	$0.850970\pi$
$864$	−5.16126	+	0.601125i	−0.175590	+	0.0204507i
$865$	17.6394	+	48.4640i	0.599759	+	1.64782i
$866$		−	20.7623i		−	0.705530i
$867$	3.68056	−	14.2807i	0.124998	−	0.484999i
$868$	0.298108	+	0.819044i	0.0101184	+	0.0278002i
$869$	−27.7043	−	10.0835i	−0.939803	−	0.342060i
$870$	16.6752	+	23.3366i	0.565341	+	0.791184i
$871$	22.9441	+	8.35097i	0.777431	+	0.282962i
$872$	−4.44149	+	12.2029i	−0.150408	+	0.413243i
$873$	34.0401	−	0.650920i	1.15208	−	0.0220303i
$874$	3.36457	+	3.08996i	0.113808	+	0.104519i
$875$	−11.2024	−	6.46769i	−0.378709	−	0.218648i
$876$	−8.51378	−	17.8113i	−0.287654	−	0.601788i
$877$	−30.7353	−	36.6289i	−1.03786	−	1.23687i	−0.970993	−	0.239107i	$-0.923145\pi$
$877$	−30.7353	−	36.6289i	−1.03786	−	1.23687i	−0.0668635	−	0.997762i	$-0.521299\pi$
$878$	−11.1925	−	1.97354i	−0.377729	−	0.0666037i
$879$	−2.79235	−	0.217422i	−0.0941837	−	0.00733345i
$880$	−5.57720	−	4.67982i	−0.188007	−	0.157757i
$881$	19.6269	+	11.3316i	0.661248	+	0.381772i	0.792752	−	0.609544i	$-0.208647\pi$
$881$	19.6269	+	11.3316i	0.661248	+	0.381772i	−0.131505	+	0.991316i	$0.541981\pi$
$882$	17.8531	+	9.85729i	0.601146	+	0.331912i
$883$	1.88608	−	0.686479i	0.0634718	−	0.0231018i	−0.310089	−	0.950707i	$-0.600359\pi$
$883$	1.88608	−	0.686479i	0.0634718	−	0.0231018i	0.373561	+	0.927606i	$0.378137\pi$
$884$	1.46949	−	8.33391i	0.0494244	−	0.280300i
$885$	−27.7670	−	99.8016i	−0.933377	−	3.35479i
$886$		−	34.9232i		−	1.17327i
$887$	−47.3943	+	17.2501i	−1.59134	+	0.579202i	−0.977631	−	0.210328i	$-0.932547\pi$
$887$	−47.3943	+	17.2501i	−1.59134	+	0.579202i	−0.613712	+	0.789530i	$0.710325\pi$
$888$	2.74276	+	1.88168i	0.0920410	+	0.0631452i
$889$	−1.44060	−	3.95801i	−0.0483161	−	0.132747i
$890$	−54.7535	+	9.65452i	−1.83534	+	0.323620i
$891$	15.5419	−	3.35772i	0.520674	−	0.112488i
$892$		−	3.68249i		−	0.123299i
$893$	−1.53107	−	11.7306i	−0.0512352	−	0.392548i
$894$	−3.67889	−	13.2228i	−0.123040	−	0.442238i
$895$	37.0003	−	6.52415i	1.23678	−	0.218078i
$896$	−0.344400	+	0.288986i	−0.0115056	+	0.00965435i
$897$	4.29052	−	3.06580i	0.143256	−	0.102364i
$898$	−0.241272	−	1.36832i	−0.00805134	−	0.0456614i
$899$	7.67218	+	1.35281i	0.255881	+	0.0451188i
$900$	−0.687235	−	35.9393i	−0.0229078	−	1.19798i
$901$	30.7707	−	17.7655i	1.02512	−	0.591853i
$902$	4.41001	+	0.777604i	0.146837	+	0.0258914i
$903$	−4.29124	−	1.95131i	−0.142803	−	0.0649356i
$904$	−0.940197	+	1.62847i	−0.0312705	+	0.0541621i
$905$	101.210			3.36432
$906$	−5.95509	−	8.33402i	−0.197844	−	0.276879i
$907$	11.9049	−	2.09915i	0.395295	−	0.0697012i	0.0275324	−	0.999621i	$-0.491235\pi$
$907$	11.9049	−	2.09915i	0.395295	−	0.0697012i	0.367763	+	0.929920i	$0.380124\pi$
$908$	2.18577	+	1.83408i	0.0725374	+	0.0608661i
$909$	2.22733	+	11.3576i	0.0738760	+	0.376706i
$910$	5.05761	+	1.84082i	0.167658	+	0.0610226i
$911$	1.09402	−	1.89489i	0.0362464	−	0.0627806i	−0.847333	−	0.531062i	$-0.821793\pi$
$911$	1.09402	−	1.89489i	0.0362464	−	0.0627806i	0.883580	+	0.468281i	$0.155127\pi$
$912$	−6.95049	+	2.94800i	−0.230154	+	0.0976182i
$913$	1.86760	+	3.23477i	0.0618085	+	0.107055i
$914$	−3.68915	−	20.9222i	−0.122026	−	0.692046i
$915$	96.5493	−	46.1504i	3.19182	−	1.52569i
$916$	−1.42440	+	0.518438i	−0.0470634	+	0.0171297i
$917$	−4.11937	−	4.90927i	−0.136033	−	0.162118i
$918$	−1.75108	−	15.0348i	−0.0577942	−	0.496221i
$919$	10.6068	−	18.3715i	0.349885	−	0.606019i	−0.636343	−	0.771406i	$-0.719554\pi$
$919$	10.6068	−	18.3715i	0.349885	−	0.606019i	0.986229	+	0.165387i	$0.0528872\pi$
$920$	−4.31876			−0.142385
$921$	−25.8655	−	36.1982i	−0.852296	−	1.19277i
$922$	−4.99748	+	5.95576i	−0.164583	+	0.196143i
$923$	19.7120	+	11.3807i	0.648829	+	0.374601i
$924$	0.963455	−	0.982055i	0.0316954	−	0.0323072i
$925$	−14.7904	+	17.6265i	−0.486305	+	0.579556i
$926$	−5.41240	+	4.54155i	−0.177863	+	0.149244i
$927$	−44.9389	+	17.3364i	−1.47599	+	0.569403i
$928$	0.697791	+	3.95737i	0.0229061	+	0.129907i
$929$	−0.554500	−	0.660827i	−0.0181926	−	0.0216810i	0.756871	−	0.653564i	$-0.226727\pi$
$929$	−0.554500	−	0.660827i	−0.0181926	−	0.0216810i	−0.775064	+	0.631883i	$0.782282\pi$
$930$	−9.87788	−	9.69080i	−0.323908	−	0.317774i
$931$	28.9217	+	6.44560i	0.947871	+	0.211246i
$932$	1.53276	−	0.884942i	0.0502074	−	0.0289872i
$933$	−44.6281	+	21.3322i	−1.46106	+	0.698383i
$934$	5.48103	−	15.0590i	0.179345	−	0.492746i
$935$	13.6323	−	16.2464i	0.445825	−	0.531314i
$936$	1.67720	+	8.55231i	0.0548209	+	0.279541i
$937$	8.52318	−	48.3373i	0.278440	−	1.57911i	−0.449378	−	0.893342i	$-0.648354\pi$
$937$	8.52318	−	48.3373i	0.278440	−	1.57911i	0.727818	−	0.685770i	$-0.240534\pi$
$938$	3.27242	−	1.88933i	0.106848	−	0.0616888i
$939$	43.8949	−	12.2125i	1.43246	−	0.398541i
$940$	8.56757	+	7.18905i	0.279443	+	0.234481i
$941$	−18.2750	−	15.3346i	−0.595749	−	0.499892i	0.294327	−	0.955705i	$-0.404904\pi$
$941$	−18.2750	−	15.3346i	−0.595749	−	0.499892i	−0.890076	+	0.455812i	$0.849349\pi$
$942$	−14.1600	−	13.8918i	−0.461356	−	0.452618i
$943$	2.30047	−	1.32818i	0.0749135	−	0.0432514i
$944$	2.52025	−	14.2930i	0.0820271	−	0.465199i
$945$	9.61035	+	0.563684i	0.312625	+	0.0183367i
$946$	6.87481	−	8.19308i	0.223519	−	0.266380i
$947$	−20.2276	+	55.5748i	−0.657307	+	1.80594i	−0.0685185	+	0.997650i	$0.521827\pi$
$947$	−20.2276	+	55.5748i	−0.657307	+	1.80594i	−0.588789	+	0.808287i	$0.700395\pi$
$948$	2.24375	−	28.8165i	0.0728735	−	0.935915i
$949$	−28.6752	+	16.5557i	−0.930838	+	0.537419i
$950$	−15.6498	−	49.8283i	−0.507746	−	1.61664i
$951$	11.0385	−	42.8301i	0.357949	−	1.38886i
$952$	−0.841817	−	1.00324i	−0.0272834	−	0.0325151i
$953$	−7.62054	−	43.2182i	−0.246853	−	1.39998i	−0.816148	−	0.577842i	$-0.803895\pi$
$953$	−7.62054	−	43.2182i	−0.246853	−	1.39998i	0.569295	−	0.822133i	$-0.307216\pi$
$954$	−22.9807	+	28.4757i	−0.744028	+	0.921935i
$955$	−60.4768	+	50.7461i	−1.95698	+	1.64210i
$956$	−15.4439	+	18.4054i	−0.499493	+	0.595272i
$957$	−3.29599	−	11.8466i	−0.106544	−	0.382946i
$958$	−13.6960	−	7.90740i	−0.442498	−	0.255477i
$959$	−1.20746	+	1.43900i	−0.0389910	+	0.0464676i
$960$	2.95452	−	6.49744i	0.0953566	−	0.209704i
$961$	27.2414			0.878755
$962$	2.78941	−	4.83139i	0.0899341	−	0.155770i
$963$	−4.92266	−	12.7604i	−0.158630	−	0.411197i
$964$	0.223901	+	0.266835i	0.00721137	+	0.00859418i
$965$	49.1567	−	17.8916i	1.58241	−	0.575951i
$966$	0.0633514	−	0.813622i	0.00203830	−	0.0261779i
$967$	−1.31262	−	7.44426i	−0.0422111	−	0.239391i	0.956401	−	0.292056i	$-0.0943395\pi$
$967$	−1.31262	−	7.44426i	−0.0422111	−	0.239391i	−0.998612	+	0.0526651i	$0.983228\pi$
$968$	−3.93935	−	6.82315i	−0.126615	−	0.219304i
$969$	−8.58754	−	20.2468i	−0.275872	−	0.650420i
$970$	−23.3837	+	40.5017i	−0.750805	+	1.30043i
$971$	−24.6461	−	8.97044i	−0.790931	−	0.287875i	−0.0852078	−	0.996363i	$-0.527155\pi$
$971$	−24.6461	−	8.97044i	−0.790931	−	0.287875i	−0.705723	+	0.708488i	$0.749378\pi$
$972$	7.25549	+	13.7970i	0.232720	+	0.442540i
$973$	−5.92479	−	4.97149i	−0.189940	−	0.159379i
$974$	−27.3317	+	4.81932i	−0.875764	+	0.154421i
$975$	−60.0075	+	5.82853i	−1.92178	+	0.186662i
$976$	14.9927			0.479904
$977$	27.6439	−	47.8806i	0.884406	−	1.53184i	0.0380122	−	0.999277i	$-0.487897\pi$
$977$	27.6439	−	47.8806i	0.884406	−	1.53184i	0.846393	−	0.532558i	$-0.178769\pi$
$978$	−1.62426	−	16.7225i	−0.0519381	−	0.534727i
$979$	23.4740	+	4.13909i	0.750231	+	0.132286i
$980$	−24.2604	+	14.0067i	−0.774969	+	0.447429i
$981$	38.9511	−	0.744827i	1.24361	−	0.0237805i
$982$	−8.92765	−	1.57419i	−0.284893	−	0.0502343i
$983$	−0.870583	−	4.93732i	−0.0277673	−	0.157476i	0.967771	−	0.251830i	$-0.0810325\pi$
$983$	−0.870583	−	4.93732i	−0.0277673	−	0.157476i	−0.995539	+	0.0943542i	$0.969921\pi$
$984$	0.424420	+	4.36960i	0.0135300	+	0.139298i
$985$	−50.9586	+	42.7594i	−1.62368	+	1.36243i
$986$	−11.5278	+	2.03267i	−0.367121	+	0.0647333i
$987$	−1.48004	+	1.50861i	−0.0471102	+	0.0480196i
$988$	5.83457	+	11.2386i	0.185622	+	0.357549i
$989$		−	6.34440i		−	0.201740i
$990$	−7.07648	+	20.6634i	−0.224905	+	0.656726i
$991$	5.58885	−	0.985465i	0.177536	−	0.0313043i	−0.0841735	−	0.996451i	$-0.526825\pi$
$991$	5.58885	−	0.985465i	0.177536	−	0.0313043i	0.261709	+	0.965147i	$0.415714\pi$
$992$	−0.663077	−	1.82179i	−0.0210527	−	0.0578418i
$993$	11.1849	−	5.34639i	0.354943	−	0.169662i
$994$	3.31008	−	1.20477i	0.104989	−	0.0382130i
$995$		−	20.6610i		−	0.654999i
$996$	−2.56448	+	2.61398i	−0.0812586	+	0.0828273i
$997$	−4.48767	+	25.4508i	−0.142126	+	0.806036i	0.827504	+	0.561460i	$0.189760\pi$
$997$	−4.48767	+	25.4508i	−0.142126	+	0.806036i	−0.969630	+	0.244576i	$0.921351\pi$
$998$	−23.1951	+	8.44232i	−0.734228	+	0.267237i
$999$	2.30518	−	9.70863i	0.0729327	−	0.307167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.x.c.281.4	yes	60
9.5	odd	6		342.2.bf.c.167.5	yes	60
19.14	odd	18		342.2.bf.c.299.5	yes	60
171.14	even	18	inner	342.2.x.c.185.4	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.x.c.185.4	✓	60	171.14	even	18	inner
342.2.x.c.281.4	yes	60	1.1	even	1	trivial
342.2.bf.c.167.5	yes	60	9.5	odd	6
342.2.bf.c.299.5	yes	60	19.14	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-0.746969 - 1.56270i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.40944 - 3.87239i) q^{5} +(-1.57670 - 0.716956i) q^{6} +(0.224791 + 0.389350i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.88407 + 2.33458i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(-0.746969 - 1.56270i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.40944 - 3.87239i) q^{5} +(-1.57670 - 0.716956i) q^{6} +(0.224791 + 0.389350i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.88407 + 2.33458i) q^{9} +(-1.40944 - 3.87239i) q^{10} +1.76672i q^{11} +(-1.66867 + 0.464261i) q^{12} +(0.993593 + 2.72987i) q^{13} +(0.422469 + 0.153766i) q^{14} +(-7.10420 + 0.690032i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.996305 - 2.73733i) q^{17} +(0.0573559 + 2.99945i) q^{18} +(1.30611 + 4.15861i) q^{19} +(-3.56882 - 2.06046i) q^{20} +(0.440526 - 0.642114i) q^{21} +(1.13563 + 1.35339i) q^{22} +(1.03209 + 0.181985i) q^{23} +(-0.979855 + 1.42825i) q^{24} +(-9.17870 - 7.70184i) q^{25} +(2.51586 + 1.45254i) q^{26} +(5.05560 + 1.20038i) q^{27} +(0.422469 - 0.153766i) q^{28} +(0.697791 - 3.95737i) q^{29} +(-4.99859 + 5.09509i) q^{30} +1.93871i q^{31} +(-0.939693 + 0.342020i) q^{32} +(2.76086 - 1.31969i) q^{33} +(-0.996305 - 2.73733i) q^{34} +(1.82454 - 0.321716i) q^{35} +(1.97195 + 2.26085i) q^{36} -1.92037i q^{37} +(3.67365 + 2.34613i) q^{38} +(3.52379 - 3.59182i) q^{39} +(-4.05831 + 0.715589i) q^{40} +(1.94166 - 1.62925i) q^{41} +(-0.0752809 - 0.775052i) q^{42} +(-1.05122 - 5.96178i) q^{43} +(1.73988 + 0.306788i) q^{44} +(6.38494 + 10.5863i) q^{45} +(0.907603 - 0.524005i) q^{46} +(-2.67277 - 0.471281i) q^{47} +(0.167446 + 1.72394i) q^{48} +(3.39894 - 5.88713i) q^{49} -11.9819 q^{50} +(-5.02183 + 0.487771i) q^{51} +(2.86094 - 0.504460i) q^{52} +(9.34372 + 7.84031i) q^{53} +(4.64441 - 2.33013i) q^{54} +(6.84144 + 2.49008i) q^{55} +(0.224791 - 0.389350i) q^{56} +(5.52304 - 5.14742i) q^{57} +(-2.00921 - 3.48005i) q^{58} +(2.52025 + 14.2930i) q^{59} +(-0.554083 + 7.11610i) q^{60} +(-14.0885 + 5.12780i) q^{61} +(1.24618 + 1.48514i) q^{62} +(-1.33249 - 0.208770i) q^{63} +(-0.500000 + 0.866025i) q^{64} +11.9715 q^{65} +(1.26666 - 2.78559i) q^{66} +(5.40252 - 6.43847i) q^{67} +(-2.52273 - 1.45650i) q^{68} +(-0.486550 - 1.74878i) q^{69} +(1.19089 - 1.41924i) q^{70} +(6.00202 - 5.03629i) q^{71} +(2.96384 + 0.464365i) q^{72} +(1.97920 + 11.2246i) q^{73} +(-1.23439 - 1.47109i) q^{74} +(-5.17948 + 20.0966i) q^{75} +(4.32224 - 0.564136i) q^{76} +(-0.687873 + 0.397144i) q^{77} +(0.390605 - 5.01655i) q^{78} +(-5.70748 + 15.6812i) q^{79} +(-2.64887 + 3.15680i) q^{80} +(-1.90054 - 8.79704i) q^{81} +(0.440140 - 2.49616i) q^{82} +(1.83095 - 1.05710i) q^{83} +(-0.555863 - 0.545335i) q^{84} +(-9.19578 - 7.71617i) q^{85} +(-4.63745 - 3.89128i) q^{86} +(-6.70542 + 1.86559i) q^{87} +(1.53003 - 0.883361i) q^{88} +(2.34281 - 13.2867i) q^{89} +(11.6959 + 4.00543i) q^{90} +(-0.839525 + 1.00051i) q^{91} +(0.358441 - 0.984807i) q^{92} +(3.02962 - 1.44815i) q^{93} +(-2.35039 + 1.35700i) q^{94} +(17.9447 + 0.803509i) q^{95} +(1.23640 + 1.21298i) q^{96} +(-7.29486 - 8.69367i) q^{97} +(-1.18044 - 6.69460i) q^{98} +(-4.12456 - 3.32863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9}+O(q^{10}) \) 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9	\( 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9} + 3 q^{13} + 3 q^{14} + 27 q^{15} - 27 q^{17} - 18 q^{18} + 3 q^{19} + 18 q^{23} + 3 q^{24} - 6 q^{27} + 3 q^{28} + 57 q^{33} + 27 q^{34} + 9 q^{38} - 30 q^{39} + 9 q^{41} - 3 q^{43} - 9 q^{44} + 27 q^{45} - 30 q^{49} - 132 q^{50} - 66 q^{51} + 6 q^{52} + 27 q^{54} + 102 q^{57} - 54 q^{59} + 6 q^{60} - 24 q^{61} - 3 q^{62} - 30 q^{64} + 36 q^{65} - 63 q^{66} + 51 q^{67} - 18 q^{68} + 3 q^{69} - 18 q^{71} - 3 q^{72} - 66 q^{73} - 6 q^{74} + 3 q^{78} - 51 q^{79} - 30 q^{81} - 36 q^{83} + 60 q^{84} - 3 q^{86} + 54 q^{87} - 27 q^{89} + 36 q^{90} - 69 q^{91} + 69 q^{93} + 18 q^{94} - 27 q^{95} + 81 q^{97} + 60 q^{98} + 51 q^{99}+O(q^{100}) \) 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9 + 3 * q^13 + 3 * q^14 + 27 * q^15 - 27 * q^17 - 18 * q^18 + 3 * q^19 + 18 * q^23 + 3 * q^24 - 6 * q^27 + 3 * q^28 + 57 * q^33 + 27 * q^34 + 9 * q^38 - 30 * q^39 + 9 * q^41 - 3 * q^43 - 9 * q^44 + 27 * q^45 - 30 * q^49 - 132 * q^50 - 66 * q^51 + 6 * q^52 + 27 * q^54 + 102 * q^57 - 54 * q^59 + 6 * q^60 - 24 * q^61 - 3 * q^62 - 30 * q^64 + 36 * q^65 - 63 * q^66 + 51 * q^67 - 18 * q^68 + 3 * q^69 - 18 * q^71 - 3 * q^72 - 66 * q^73 - 6 * q^74 + 3 * q^78 - 51 * q^79 - 30 * q^81 - 36 * q^83 + 60 * q^84 - 3 * q^86 + 54 * q^87 - 27 * q^89 + 36 * q^90 - 69 * q^91 + 69 * q^93 + 18 * q^94 - 27 * q^95 + 81 * q^97 + 60 * q^98 + 51 * q^99

Introduction

L-functions

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