LMFDB - Embedded newform 370.2.v.a.289.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(99,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("370.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.v (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:	$2.95446487479$
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			289.6
Character	$\chi$	$=$	370.289
Dual form			370.2.v.a.169.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(0.362370 - 0.995603i) q^{3} +(0.766044 - 0.642788i) q^{4} +(2.23443 - 0.0855581i) q^{5} +1.05950i q^{6} +(1.06185 - 0.187234i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.43822 + 1.20681i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(0.362370 - 0.995603i) q^{3} +(0.766044 - 0.642788i) q^{4} +(2.23443 - 0.0855581i) q^{5} +1.05950i q^{6} +(1.06185 - 0.187234i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.43822 + 1.20681i) q^{9} +(-2.07042 + 0.844619i) q^{10} +(0.436261 - 0.755627i) q^{11} +(-0.362370 - 0.995603i) q^{12} +(-1.18263 + 0.992348i) q^{13} +(-0.933779 + 0.539117i) q^{14} +(0.724508 - 2.25561i) q^{15} +(0.173648 - 0.984808i) q^{16} +(0.626355 + 0.525574i) q^{17} +(-1.76424 - 0.642130i) q^{18} +(-0.570090 + 1.56631i) q^{19} +(1.65668 - 1.50181i) q^{20} +(0.198374 - 1.12503i) q^{21} +(-0.151512 + 0.859267i) q^{22} +(-2.32537 - 4.02766i) q^{23} +(0.681032 + 0.811623i) q^{24} +(4.98536 - 0.382347i) q^{25} +(0.771910 - 1.33699i) q^{26} +(4.47533 - 2.58383i) q^{27} +(0.693076 - 0.825976i) q^{28} +(-1.84171 - 1.06331i) q^{29} +(0.0906487 + 2.36738i) q^{30} -2.18324i q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.594216 - 0.708159i) q^{33} +(-0.768338 - 0.279652i) q^{34} +(2.35662 - 0.509210i) q^{35} +1.87746 q^{36} +(4.86631 + 3.64952i) q^{37} -1.66683i q^{38} +(0.559434 + 1.53703i) q^{39} +(-1.04312 + 1.97785i) q^{40} +(1.27193 - 1.06727i) q^{41} +(0.198374 + 1.12503i) q^{42} +2.12972 q^{43} +(-0.151512 - 0.859267i) q^{44} +(3.31686 + 2.57348i) q^{45} +(3.56267 + 2.98944i) q^{46} +(4.23630 - 2.44583i) q^{47} +(-0.917552 - 0.529749i) q^{48} +(-5.48537 + 1.99651i) q^{49} +(-4.55394 + 2.06438i) q^{50} +(0.750235 - 0.433149i) q^{51} +(-0.268082 + 1.52037i) q^{52} +(-4.91073 - 0.865893i) q^{53} +(-3.32171 + 3.95866i) q^{54} +(0.910145 - 1.72572i) q^{55} +(-0.368778 + 1.01321i) q^{56} +(1.35284 + 1.13517i) q^{57} +(2.09432 + 0.369284i) q^{58} +(-10.8290 - 1.90944i) q^{59} +(-0.894872 - 2.19360i) q^{60} +(1.22233 + 1.45671i) q^{61} +(0.746712 + 2.05157i) q^{62} +(1.75314 + 1.01217i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.55761 + 2.31852i) q^{65} +(0.800585 + 0.462218i) q^{66} +(5.75930 - 1.01552i) q^{67} +0.817648 q^{68} +(-4.85259 + 0.855643i) q^{69} +(-2.04034 + 1.28451i) q^{70} +(-10.2016 - 3.71309i) q^{71} +(-1.76424 + 0.642130i) q^{72} +10.5379i q^{73} +(-5.82105 - 1.76505i) q^{74} +(1.42588 - 5.10199i) q^{75} +(0.570090 + 1.56631i) q^{76} +(0.321767 - 0.884048i) q^{77} +(-1.05139 - 1.25300i) q^{78} +(-4.86694 + 0.858174i) q^{79} +(0.303747 - 2.21534i) q^{80} +(0.0273076 + 0.154869i) q^{81} +(-0.830191 + 1.43793i) q^{82} +(-2.61137 + 3.11211i) q^{83} +(-0.571194 - 0.989337i) q^{84} +(1.44451 + 1.12077i) q^{85} +(-2.00128 + 0.728408i) q^{86} +(-1.72602 + 1.44830i) q^{87} +(0.436261 + 0.755627i) q^{88} +(-15.0870 - 2.66025i) q^{89} +(-3.99701 - 1.28385i) q^{90} +(-1.06998 + 1.27516i) q^{91} +(-4.37026 - 1.59065i) q^{92} +(-2.17364 - 0.791140i) q^{93} +(-3.14430 + 3.74723i) q^{94} +(-1.13982 + 3.54859i) q^{95} +(1.04340 + 0.183980i) q^{96} +(-5.51919 - 9.55952i) q^{97} +(4.47172 - 3.75221i) q^{98} +(1.53934 - 0.560273i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{5} - 30 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q - 3 * q^5 - 30 * q^8 - 6 * q^9	$ 60 q - 3 q^{5} - 30 q^{8} - 6 q^{9} + 9 q^{10} + 6 q^{11} - 3 q^{13} + 9 q^{14} + 18 q^{15} + 3 q^{17} + 12 q^{18} + 3 q^{19} - 6 q^{20} + 12 q^{21} - 3 q^{22} - 18 q^{23} - 15 q^{25} - 27 q^{26} + 6 q^{30} - 66 q^{33} + 21 q^{34} - 3 q^{35} - 72 q^{36} + 6 q^{37} + 12 q^{39} + 6 q^{40} - 57 q^{41} + 12 q^{42} + 60 q^{43} - 3 q^{44} + 45 q^{45} - 21 q^{46} - 18 q^{47} - 6 q^{49} + 36 q^{50} - 3 q^{52} - 6 q^{53} + 3 q^{55} + 30 q^{57} + 15 q^{58} - 12 q^{59} + 9 q^{60} + 42 q^{61} - 12 q^{62} - 9 q^{63} - 30 q^{64} - 30 q^{65} - 18 q^{67} - 24 q^{68} + 36 q^{69} + 18 q^{71} + 12 q^{72} + 3 q^{74} - 78 q^{75} - 3 q^{76} + 21 q^{77} + 6 q^{78} - 24 q^{79} - 36 q^{81} + 27 q^{82} + 30 q^{83} + 12 q^{84} + 33 q^{85} - 18 q^{86} - 30 q^{87} + 6 q^{88} + 3 q^{89} - 3 q^{90} + 57 q^{91} + 15 q^{92} + 60 q^{93} + 3 q^{94} - 150 q^{95} + 84 q^{97} - 6 q^{98} - 45 q^{99}+O(q^{100}) $ 60 * q - 3 * q^5 - 30 * q^8 - 6 * q^9 + 9 * q^10 + 6 * q^11 - 3 * q^13 + 9 * q^14 + 18 * q^15 + 3 * q^17 + 12 * q^18 + 3 * q^19 - 6 * q^20 + 12 * q^21 - 3 * q^22 - 18 * q^23 - 15 * q^25 - 27 * q^26 + 6 * q^30 - 66 * q^33 + 21 * q^34 - 3 * q^35 - 72 * q^36 + 6 * q^37 + 12 * q^39 + 6 * q^40 - 57 * q^41 + 12 * q^42 + 60 * q^43 - 3 * q^44 + 45 * q^45 - 21 * q^46 - 18 * q^47 - 6 * q^49 + 36 * q^50 - 3 * q^52 - 6 * q^53 + 3 * q^55 + 30 * q^57 + 15 * q^58 - 12 * q^59 + 9 * q^60 + 42 * q^61 - 12 * q^62 - 9 * q^63 - 30 * q^64 - 30 * q^65 - 18 * q^67 - 24 * q^68 + 36 * q^69 + 18 * q^71 + 12 * q^72 + 3 * q^74 - 78 * q^75 - 3 * q^76 + 21 * q^77 + 6 * q^78 - 24 * q^79 - 36 * q^81 + 27 * q^82 + 30 * q^83 + 12 * q^84 + 33 * q^85 - 18 * q^86 - 30 * q^87 + 6 * q^88 + 3 * q^89 - 3 * q^90 + 57 * q^91 + 15 * q^92 + 60 * q^93 + 3 * q^94 - 150 * q^95 + 84 * q^97 - 6 * q^98 - 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	0.362370	−	0.995603i	0.209214	−	0.574812i	−0.790055	−	0.613036i	$-0.789948\pi$
$3$	0.362370	−	0.995603i	0.209214	−	0.574812i	0.999269	+	0.0382246i	$0.0121702\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	2.23443	−	0.0855581i	0.999268	−	0.0382627i
$5$	2.23443	−	0.0855581i	0.999268	−	0.0382627i
$6$			1.05950i			0.432538i
$7$	1.06185	−	0.187234i	0.401343	−	0.0707676i	0.0306666	−	0.999530i	$-0.490237\pi$
$7$	1.06185	−	0.187234i	0.401343	−	0.0707676i	0.370676	+	0.928762i	$0.379126\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	1.43822	+	1.20681i	0.479407	+	0.402270i
$10$	−2.07042	+	0.844619i	−0.654723	+	0.267092i
$11$	0.436261	−	0.755627i	0.131538	−	0.227830i	−0.792732	−	0.609571i	$-0.791342\pi$
$11$	0.436261	−	0.755627i	0.131538	−	0.227830i	0.924270	+	0.381741i	$0.124675\pi$
$12$	−0.362370	−	0.995603i	−0.104607	−	0.287406i
$13$	−1.18263	+	0.992348i	−0.328004	+	0.275228i	−0.791886	−	0.610669i	$-0.790901\pi$
$13$	−1.18263	+	0.992348i	−0.328004	+	0.275228i	0.463882	+	0.885897i	$0.346456\pi$
$14$	−0.933779	+	0.539117i	−0.249563	+	0.144085i
$15$	0.724508	−	2.25561i	0.187067	−	0.582396i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	0.626355	+	0.525574i	0.151913	+	0.127470i	0.715577	−	0.698534i	$-0.246164\pi$
$17$	0.626355	+	0.525574i	0.151913	+	0.127470i	−0.563663	+	0.826005i	$0.690608\pi$
$18$	−1.76424	−	0.642130i	−0.415835	−	0.151352i
$19$	−0.570090	+	1.56631i	−0.130788	+	0.359336i	−0.987750	−	0.156042i	$-0.950126\pi$
$19$	−0.570090	+	1.56631i	−0.130788	+	0.359336i	0.856963	+	0.515378i	$0.172349\pi$
$20$	1.65668	−	1.50181i	0.370444	−	0.335814i
$21$	0.198374	−	1.12503i	0.0432887	−	0.245502i
$22$	−0.151512	+	0.859267i	−0.0323025	+	0.183196i
$23$	−2.32537	−	4.02766i	−0.484873	−	0.839825i	0.514976	−	0.857205i	$-0.327801\pi$
$23$	−2.32537	−	4.02766i	−0.484873	−	0.839825i	−0.999849	+	0.0173800i	$0.994468\pi$
$24$	0.681032	+	0.811623i	0.139015	+	0.165672i
$25$	4.98536	−	0.382347i	0.997072	−	0.0764695i
$26$	0.771910	−	1.33699i	0.151384	−	0.262205i
$27$	4.47533	−	2.58383i	0.861277	−	0.497259i
$28$	0.693076	−	0.825976i	0.130979	−	0.156095i
$29$	−1.84171	−	1.06331i	−0.341997	−	0.197452i	0.319158	−	0.947702i	$-0.396600\pi$
$29$	−1.84171	−	1.06331i	−0.341997	−	0.197452i	−0.661155	+	0.750249i	$0.729933\pi$
$30$	0.0906487	+	2.36738i	0.0165501	+	0.432222i
$31$		−	2.18324i		−	0.392122i	−0.980592	−	0.196061i	$-0.937185\pi$
$31$		−	2.18324i		−	0.392122i	0.980592	−	0.196061i	$-0.0628150\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−0.594216	−	0.708159i	−0.103440	−	0.123275i
$34$	−0.768338	−	0.279652i	−0.131769	−	0.0479600i
$35$	2.35662	−	0.509210i	0.398341	−	0.0860723i
$36$	1.87746			0.312911
$37$	4.86631	+	3.64952i	0.800017	+	0.599977i
$37$	4.86631	+	3.64952i	0.800017	+	0.599977i
$38$		−	1.66683i		−	0.270396i
$39$	0.559434	+	1.53703i	0.0895811	+	0.246122i
$40$	−1.04312	+	1.97785i	−0.164932	+	0.312726i
$41$	1.27193	−	1.06727i	0.198642	−	0.166680i	−0.538041	−	0.842919i	$-0.680836\pi$
$41$	1.27193	−	1.06727i	0.198642	−	0.166680i	0.736683	+	0.676238i	$0.236391\pi$
$42$	0.198374	+	1.12503i	0.0306097	+	0.173596i
$43$	2.12972			0.324780			0.162390	−	0.986727i	$-0.448080\pi$
$43$	2.12972			0.324780			0.162390	+	0.986727i	$0.448080\pi$
$44$	−0.151512	−	0.859267i	−0.0228413	−	0.129539i
$45$	3.31686	+	2.57348i	0.494448	+	0.383632i
$46$	3.56267	+	2.98944i	0.525287	+	0.440768i
$47$	4.23630	−	2.44583i	0.617928	−	0.356761i	−0.158134	−	0.987418i	$-0.550548\pi$
$47$	4.23630	−	2.44583i	0.617928	−	0.356761i	0.776062	+	0.630657i	$0.217214\pi$
$48$	−0.917552	−	0.529749i	−0.132437	−	0.0764627i
$49$	−5.48537	+	1.99651i	−0.783624	+	0.285216i
$50$	−4.55394	+	2.06438i	−0.644024	+	0.291948i
$51$	0.750235	−	0.433149i	0.105054	−	0.0606529i
$52$	−0.268082	+	1.52037i	−0.0371762	+	0.210837i
$53$	−4.91073	−	0.865893i	−0.674540	−	0.118940i	−0.174123	−	0.984724i	$-0.555709\pi$
$53$	−4.91073	−	0.865893i	−0.674540	−	0.118940i	−0.500417	+	0.865784i	$0.666820\pi$
$54$	−3.32171	+	3.95866i	−0.452028	+	0.538705i
$55$	0.910145	−	1.72572i	0.122724	−	0.232696i
$56$	−0.368778	+	1.01321i	−0.0492800	+	0.135396i
$57$	1.35284	+	1.13517i	0.179188	+	0.150357i
$58$	2.09432	+	0.369284i	0.274997	+	0.0484894i
$59$	−10.8290	−	1.90944i	−1.40981	−	0.248588i	−0.583642	−	0.812011i	$-0.698373\pi$
$59$	−10.8290	−	1.90944i	−1.40981	−	0.248588i	−0.826168	+	0.563423i	$0.809484\pi$
$60$	−0.894872	−	2.19360i	−0.115527	−	0.283193i
$61$	1.22233	+	1.45671i	0.156503	+	0.186513i	0.838598	−	0.544750i	$-0.183376\pi$
$61$	1.22233	+	1.45671i	0.156503	+	0.186513i	−0.682095	+	0.731263i	$0.738931\pi$
$62$	0.746712	+	2.05157i	0.0948325	+	0.260550i
$63$	1.75314	+	1.01217i	0.220874	+	0.127522i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.55761	+	2.31852i	−0.317233	+	0.287577i
$66$	0.800585	+	0.462218i	0.0985452	+	0.0568951i
$67$	5.75930	−	1.01552i	0.703610	−	0.124065i	0.189615	−	0.981859i	$-0.439276\pi$
$67$	5.75930	−	1.01552i	0.703610	−	0.124065i	0.513995	+	0.857793i	$0.328165\pi$
$68$	0.817648			0.0991544
$69$	−4.85259	+	0.855643i	−0.584183	+	0.103007i
$70$	−2.04034	+	1.28451i	−0.243867	+	0.153529i
$71$	−10.2016	−	3.71309i	−1.21071	−	0.440663i	−0.343761	−	0.939057i	$-0.611701\pi$
$71$	−10.2016	−	3.71309i	−1.21071	−	0.440663i	−0.866951	+	0.498394i	$0.833923\pi$
$72$	−1.76424	+	0.642130i	−0.207917	+	0.0756758i
$73$			10.5379i			1.23336i	0.787212	+	0.616682i	$0.211523\pi$
$73$			10.5379i			1.23336i	−0.787212	+	0.616682i	$0.788477\pi$
$74$	−5.82105	−	1.76505i	−0.676683	−	0.205183i
$75$	1.42588	−	5.10199i	0.164646	−	0.589127i
$76$	0.570090	+	1.56631i	0.0653938	+	0.179668i
$77$	0.321767	−	0.884048i	0.0366688	−	0.100747i
$78$	−1.05139	−	1.25300i	−0.119047	−	0.141874i
$79$	−4.86694	+	0.858174i	−0.547574	+	0.0965521i	−0.440590	−	0.897709i	$-0.645231\pi$
$79$	−4.86694	+	0.858174i	−0.547574	+	0.0965521i	−0.106984	+	0.994261i	$0.534119\pi$
$80$	0.303747	−	2.21534i	0.0339599	−	0.247683i
$81$	0.0273076	+	0.154869i	0.00303418	+	0.0172077i
$82$	−0.830191	+	1.43793i	−0.0916793	+	0.158793i
$83$	−2.61137	+	3.11211i	−0.286635	+	0.341598i	−0.890078	−	0.455808i	$-0.849350\pi$
$83$	−2.61137	+	3.11211i	−0.286635	+	0.341598i	0.603443	+	0.797406i	$0.293795\pi$
$84$	−0.571194	−	0.989337i	−0.0623224	−	0.107946i
$85$	1.44451	+	1.12077i	0.156680	+	0.121565i
$86$	−2.00128	+	0.728408i	−0.215804	+	0.0785463i
$87$	−1.72602	+	1.44830i	−0.185048	+	0.155274i
$88$	0.436261	+	0.755627i	0.0465056	+	0.0805501i
$89$	−15.0870	−	2.66025i	−1.59922	−	0.281986i	−0.698247	−	0.715857i	$-0.746036\pi$
$89$	−15.0870	−	2.66025i	−1.59922	−	0.281986i	−0.900975	+	0.433871i	$0.857147\pi$
$90$	−3.99701	−	1.28385i	−0.421322	−	0.135330i
$91$	−1.06998	+	1.27516i	−0.112165	+	0.133673i
$92$	−4.37026	−	1.59065i	−0.455632	−	0.165836i
$93$	−2.17364	−	0.791140i	−0.225396	−	0.0820374i
$94$	−3.14430	+	3.74723i	−0.324309	+	0.386497i
$95$	−1.13982	+	3.54859i	−0.116943	+	0.364077i
$96$	1.04340	+	0.183980i	0.106492	+	0.0187774i
$97$	−5.51919	−	9.55952i	−0.560389	−	0.970622i	−0.997462	−	0.0711965i	$-0.977318\pi$
$97$	−5.51919	−	9.55952i	−0.560389	−	0.970622i	0.437073	−	0.899426i	$-0.356015\pi$
$98$	4.47172	−	3.75221i	0.451711	−	0.379031i
$99$	1.53934	−	0.560273i	0.154709	−	0.0563096i
$100$	3.57324	−	3.49742i	0.357324	−	0.349742i
$101$	1.28806	+	2.23099i	0.128167	+	0.221992i	0.922966	−	0.384881i	$-0.125757\pi$
$101$	1.28806	+	2.23099i	0.128167	+	0.221992i	−0.794800	+	0.606872i	$0.792424\pi$
$102$	−0.556845	+	0.663622i	−0.0551359	+	0.0657084i
$103$	−2.51846	+	4.36211i	−0.248152	+	0.429811i	−0.963013	−	0.269455i	$-0.913156\pi$
$103$	−2.51846	+	4.36211i	−0.248152	+	0.429811i	0.714861	+	0.699266i	$0.246490\pi$
$104$	−0.268082	−	1.52037i	−0.0262876	−	0.149084i
$105$	0.346996	−	2.53078i	0.0338634	−	0.246979i
$106$	4.91073	−	0.865893i	0.476972	−	0.0841030i
$107$	−1.57623	−	1.87848i	−0.152380	−	0.181599i	0.684454	−	0.729056i	$-0.260041\pi$
$107$	−1.57623	−	1.87848i	−0.152380	−	0.181599i	−0.836834	+	0.547457i	$0.815596\pi$
$108$	1.76745	−	4.85602i	0.170072	−	0.467270i
$109$	3.11601	+	8.56118i	0.298460	+	0.820012i	0.994758	+	0.102259i	$0.0326071\pi$
$109$	3.11601	+	8.56118i	0.298460	+	0.820012i	−0.696298	+	0.717753i	$0.745171\pi$
$110$	−0.265026	+	1.93294i	−0.0252692	+	0.184298i
$111$	5.39688	−	3.52244i	0.512249	−	0.334335i
$112$		−	1.07823i		−	0.101884i
$113$	−9.25336	+	3.36795i	−0.870483	+	0.316830i	−0.738363	−	0.674404i	$-0.764401\pi$
$113$	−9.25336	+	3.36795i	−0.870483	+	0.316830i	−0.132120	+	0.991234i	$0.542178\pi$
$114$	−1.65950	−	0.604010i	−0.155427	−	0.0565707i
$115$	−5.54047	−	8.80057i	−0.516652	−	0.820657i
$116$	−2.09432	+	0.369284i	−0.194452	+	0.0342872i
$117$	−2.89847			−0.267963
$118$	10.8290	−	1.90944i	0.996886	−	0.175778i
$119$	0.763503	+	0.440809i	0.0699902	+	0.0404088i
$120$	1.59116	+	1.75525i	0.145252	+	0.160231i
$121$	5.11935	+	8.86698i	0.465396	+	0.806089i
$122$	−1.64684	−	0.950801i	−0.149097	−	0.0860815i
$123$	−0.601672	−	1.65308i	−0.0542510	−	0.149053i
$124$	−1.40336	−	1.67246i	−0.126025	−	0.150191i
$125$	11.1067	−	1.28087i	0.993416	−	0.114564i
$126$	−1.99359	−	0.351524i	−0.177603	−	0.0313162i
$127$	−17.5015	−	3.08598i	−1.55300	−	0.273836i	−0.669697	−	0.742634i	$-0.733576\pi$
$127$	−17.5015	−	3.08598i	−1.55300	−	0.273836i	−0.883305	+	0.468798i	$0.844687\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	0.771747	−	2.12036i	0.0679485	−	0.186687i
$130$	1.61039	−	3.05345i	0.141240	−	0.267805i
$131$	−4.45501	+	5.30927i	−0.389236	+	0.463873i	−0.924707	−	0.380680i	$-0.875690\pi$
$131$	−4.45501	+	5.30927i	−0.389236	+	0.463873i	0.535471	+	0.844554i	$0.320134\pi$
$132$	−0.910392	−	0.160527i	−0.0792394	−	0.0139721i
$133$	−0.312087	+	1.76993i	−0.0270614	+	0.153473i
$134$	−5.06464	+	2.92407i	−0.437518	+	0.252601i
$135$	9.77874	−	6.15629i	0.841620	−	0.529849i
$136$	−0.768338	+	0.279652i	−0.0658845	+	0.0239800i
$137$	5.53751	+	3.19708i	0.473101	+	0.273145i	0.717537	−	0.696520i	$-0.245269\pi$
$137$	5.53751	+	3.19708i	0.473101	+	0.273145i	−0.244436	+	0.969665i	$0.578603\pi$
$138$	4.26730	−	2.46372i	0.363256	−	0.209726i
$139$	6.69739	+	5.61978i	0.568065	+	0.476663i	0.881003	−	0.473110i	$-0.156869\pi$
$139$	6.69739	+	5.61978i	0.568065	+	0.476663i	−0.312938	+	0.949774i	$0.601313\pi$
$140$	1.47796	−	1.90488i	0.124911	−	0.160992i
$141$	−0.899967	−	5.10396i	−0.0757909	−	0.429831i
$142$	10.8564			0.911045
$143$	0.233907	+	1.32655i	0.0195603	+	0.110932i
$144$	1.43822	−	1.20681i	0.119852	−	0.100568i
$145$	−4.20615	−	2.21832i	−0.349302	−	0.184222i
$146$	−3.60416	−	9.90235i	−0.298283	−	0.819525i
$147$			6.18473i			0.510108i
$148$	6.07368	−	0.332312i	0.499253	−	0.0273159i
$149$	2.57942			0.211314			0.105657	−	0.994403i	$-0.466305\pi$
$149$	2.57942			0.211314			0.105657	+	0.994403i	$0.466305\pi$
$150$	0.405096	+	5.28198i	0.0330760	+	0.431272i
$151$	20.9296	+	7.61777i	1.70323	+	0.619925i	0.996187	−	0.0872457i	$-0.0278065\pi$
$151$	20.9296	+	7.61777i	1.70323	+	0.619925i	0.707043	+	0.707171i	$0.250029\pi$
$152$	−1.07142	−	1.27687i	−0.0869036	−	0.103568i
$153$	0.266568	+	1.51178i	0.0215508	+	0.122220i
$154$			0.940784i			0.0758105i
$155$	−0.186794	−	4.87830i	−0.0150036	−	0.391834i
$156$	1.41654	+	0.817837i	0.113414	+	0.0654794i
$157$	−4.13022	+	4.92220i	−0.329627	+	0.392834i	−0.905249	−	0.424882i	$-0.860316\pi$
$157$	−4.13022	+	4.92220i	−0.329627	+	0.392834i	0.575622	+	0.817716i	$0.304760\pi$
$158$	4.27992	−	2.47101i	0.340492	−	0.196583i
$159$	−2.64158	+	4.57536i	−0.209491	+	0.362850i
$160$	0.472263	+	2.18563i	0.0373357	+	0.172789i
$161$	−3.22331	−	3.84140i	−0.254033	−	0.302744i
$162$	−0.0786291	−	0.136190i	−0.00617769	−	0.0107001i
$163$	−0.526085	+	2.98357i	−0.0412061	+	0.233692i	−0.998454	−	0.0555758i	$-0.982301\pi$
$163$	−0.526085	+	2.98357i	−0.0412061	+	0.233692i	0.957248	+	0.289267i	$0.0934117\pi$
$164$	0.288322	−	1.63516i	0.0225142	−	0.127684i
$165$	−1.38832	−	1.53149i	−0.108081	−	0.119227i
$166$	1.38948	−	3.81756i	0.107845	−	0.296300i
$167$	0.265056	+	0.0964724i	0.0205106	+	0.00746526i	0.352255	−	0.935904i	$-0.385415\pi$
$167$	0.265056	+	0.0964724i	0.0205106	+	0.00746526i	−0.331744	+	0.943369i	$0.607637\pi$
$168$	0.875120	+	0.734313i	0.0675170	+	0.0566535i
$169$	−1.84356	+	10.4553i	−0.141812	+	0.804256i
$170$	−1.74072	−	0.559126i	−0.133508	−	0.0428830i
$171$	−2.71015	+	1.56471i	−0.207251	+	0.119656i
$172$	1.63146	−	1.36896i	0.124398	−	0.104382i
$173$	5.80274	+	15.9429i	0.441174	+	1.21212i	0.938721	+	0.344679i	$0.112012\pi$
$173$	5.80274	+	15.9429i	0.441174	+	1.21212i	−0.497546	+	0.867438i	$0.665765\pi$
$174$	1.12658	−	1.95129i	0.0854056	−	0.147927i
$175$	5.22214	−	1.33942i	0.394756	−	0.101251i
$176$	−0.668391	−	0.560847i	−0.0503819	−	0.0422754i
$177$	−5.82513	+	10.0894i	−0.437843	+	0.758367i
$178$	15.0870	−	2.66025i	1.13082	−	0.199394i
$179$		−	14.3771i		−	1.07459i	−0.843393	−	0.537297i	$-0.819446\pi$
$179$		−	14.3771i		−	1.07459i	0.843393	−	0.537297i	$-0.180554\pi$
$180$	4.19506	−	0.160632i	0.312681	−	0.0119728i
$181$	11.8298	−	9.92638i	0.879302	−	0.737822i	−0.0867336	−	0.996232i	$-0.527643\pi$
$181$	11.8298	−	9.92638i	0.879302	−	0.737822i	0.966035	+	0.258410i	$0.0831985\pi$
$182$	0.569327	−	1.56421i	0.0422013	−	0.115947i
$183$	1.89324	−	0.689083i	0.139952	−	0.0509385i
$184$	4.65074			0.342857
$185$	11.1857	+	7.73825i	0.822388	+	0.568927i
$186$	2.31314			0.169608
$187$	0.670392	−	0.244003i	0.0490239	−	0.0178433i
$188$	1.67304	−	4.59665i	0.122019	−	0.335245i
$189$	4.26837	−	3.58158i	0.310478	−	0.260522i
$190$	−0.142611	−	3.72442i	−0.0103461	−	0.270198i
$191$		−	3.30124i		−	0.238869i	−0.992842	−	0.119435i	$-0.961892\pi$
$191$		−	3.30124i		−	0.238869i	0.992842	−	0.119435i	$-0.0381082\pi$
$192$	−1.04340	+	0.183980i	−0.0753011	+	0.0132776i
$193$	−5.47500	+	9.48298i	−0.394099	+	0.682600i	−0.992986	−	0.118234i	$-0.962277\pi$
$193$	−5.47500	+	9.48298i	−0.394099	+	0.682600i	0.598886	+	0.800834i	$0.295610\pi$
$194$	8.45589	+	7.09534i	0.607098	+	0.509416i
$195$	1.38152	+	3.38653i	0.0989328	+	0.242514i
$196$	−2.91870	+	5.05535i	−0.208479	+	0.361096i
$197$	−6.48938	−	17.8294i	−0.462349	−	1.27029i	−0.923714	−	0.383084i	$-0.874862\pi$
$197$	−6.48938	−	17.8294i	−0.462349	−	1.27029i	0.461364	−	0.887211i	$-0.347360\pi$
$198$	−1.25488	+	1.05297i	−0.0891804	+	0.0748312i
$199$	7.88126	−	4.55025i	0.558688	−	0.322558i	−0.193931	−	0.981015i	$-0.562124\pi$
$199$	7.88126	−	4.55025i	0.558688	−	0.322558i	0.752619	+	0.658457i	$0.228790\pi$
$200$	−2.16156	+	4.50862i	−0.152845	+	0.318808i
$201$	1.07594	−	6.10197i	0.0758910	−	0.430399i
$202$	−1.97342	−	1.65590i	−0.138850	−	0.116509i
$203$	−2.15472	−	0.784252i	−0.151231	−	0.0550437i
$204$	0.296291	−	0.814053i	0.0207445	−	0.0569951i
$205$	2.75072	−	2.49357i	0.192118	−	0.174159i
$206$	0.874653	−	4.96041i	0.0609400	−	0.345608i
$207$	1.51622	−	8.59894i	0.105385	−	0.597667i
$208$	0.771910	+	1.33699i	0.0535223	+	0.0927034i
$209$	0.934838	+	1.11410i	0.0646641	+	0.0770636i
$210$	0.539508	+	2.49683i	0.0372296	+	0.172298i
$211$	7.52679	−	13.0368i	0.518165	−	0.897489i	−0.481612	−	0.876385i	$-0.659949\pi$
$211$	7.52679	−	13.0368i	0.518165	−	0.897489i	0.999777	−	0.0211041i	$-0.00671815\pi$
$212$	−4.31842	+	2.49324i	−0.296590	+	0.171236i
$213$	−7.39353	+	8.81127i	−0.506596	+	0.603738i
$214$	2.12365	+	1.22609i	0.145170	+	0.0838137i
$215$	4.75872	−	0.182215i	0.324542	−	0.0124270i
$216$			5.16766i			0.351615i
$217$	−0.408776	−	2.31828i	−0.0277495	−	0.157375i
$218$	−5.85619	−	6.97914i	−0.396631	−	0.472687i
$219$	10.4915	+	3.81860i	0.708952	+	0.258037i
$220$	−0.412060	−	1.90701i	−0.0277811	−	0.128571i
$221$	−1.26230			−0.0849116
$222$	−3.86666	+	5.15585i	−0.259513	+	0.346038i
$223$		−	21.7384i		−	1.45571i	−0.685730	−	0.727856i	$-0.740517\pi$
$223$		−	21.7384i		−	1.45571i	0.685730	−	0.727856i	$-0.259483\pi$
$224$	0.368778	+	1.01321i	0.0246400	+	0.0676979i
$225$	7.63147	+	5.46648i	0.508764	+	0.364432i
$226$	7.54341	−	6.32967i	0.501780	−	0.421043i
$227$	2.20438	+	12.5017i	0.146310	+	0.829764i	0.966306	+	0.257395i	$0.0828642\pi$
$227$	2.20438	+	12.5017i	0.146310	+	0.829764i	−0.819996	+	0.572369i	$0.806025\pi$
$228$	1.76601			0.116957
$229$	−1.74813	−	9.91413i	−0.115520	−	0.655144i	−0.986492	−	0.163812i	$-0.947621\pi$
$229$	−1.74813	−	9.91413i	−0.115520	−	0.655144i	0.870972	−	0.491332i	$-0.163490\pi$
$230$	8.21631	+	6.37487i	0.541768	+	0.420347i
$231$	−0.763562	−	0.640704i	−0.0502387	−	0.0421553i
$232$	1.84171	−	1.06331i	0.120914	−	0.0698099i
$233$	−6.64095	−	3.83415i	−0.435063	−	0.251184i	0.266438	−	0.963852i	$-0.414153\pi$
$233$	−6.64095	−	3.83415i	−0.435063	−	0.251184i	−0.701501	+	0.712668i	$0.747487\pi$
$234$	2.72367	−	0.991333i	0.178052	−	0.0648055i
$235$	9.25645	−	5.82748i	0.603824	−	0.380143i
$236$	−9.52283	+	5.49801i	−0.619883	+	0.357890i
$237$	−0.909234	+	5.15652i	−0.0590611	+	0.334952i
$238$	−0.868223	−	0.153091i	−0.0562786	−	0.00992343i
$239$	−4.23812	+	5.05080i	−0.274141	+	0.326709i	−0.885495	−	0.464648i	$-0.846181\pi$
$239$	−4.23812	+	5.05080i	−0.274141	+	0.326709i	0.611354	+	0.791357i	$0.290625\pi$
$240$	−2.09553	−	1.10518i	−0.135266	−	0.0713393i
$241$	−9.22443	+	25.3439i	−0.594197	+	1.63254i	0.168435	+	0.985713i	$0.446129\pi$
$241$	−9.22443	+	25.3439i	−0.594197	+	1.63254i	−0.762633	+	0.646832i	$0.776094\pi$
$242$	−7.84330	−	6.58131i	−0.504187	−	0.423063i
$243$	15.4316	+	2.72100i	0.989934	+	0.174552i
$244$	1.87271	+	0.330210i	0.119888	+	0.0211395i
$245$	−12.0859	+	4.93038i	−0.772137	+	0.314991i
$246$	1.13077	+	1.34760i	0.0720955	+	0.0859201i
$247$	−0.880117	−	2.41810i	−0.0560005	−	0.153860i
$248$	1.89074	+	1.09162i	0.120062	+	0.0693179i
$249$	2.15214	+	3.72762i	0.136386	+	0.236228i
$250$	−9.99883	+	5.00235i	−0.632381	+	0.316376i
$251$	4.49165	+	2.59325i	0.283510	+	0.163685i	0.635011	−	0.772503i	$-0.280995\pi$
$251$	4.49165	+	2.59325i	0.283510	+	0.163685i	−0.351501	+	0.936187i	$0.614329\pi$
$252$	1.99359	−	0.351524i	0.125584	−	0.0221439i
$253$	−4.05787			−0.255116
$254$	17.5015	−	3.08598i	1.09814	−	0.193631i
$255$	1.63929	−	1.03203i	0.102656	−	0.0646282i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	19.8471	−	7.22375i	1.23803	−	0.450605i	0.361689	−	0.932299i	$-0.382200\pi$
$257$	19.8471	−	7.22375i	1.23803	−	0.450605i	0.876340	+	0.481694i	$0.159978\pi$
$258$			2.25644i			0.140480i
$259$	5.85063	+	2.96412i	0.363540	+	0.184181i
$260$	−0.468930	+	3.42009i	−0.0290818	+	0.212105i
$261$	−1.36557	−	3.75187i	−0.0845267	−	0.232235i
$262$	2.37046	−	6.51279i	0.146448	−	0.402361i
$263$	−19.4723	−	23.2062i	−1.20072	−	1.43096i	−0.874062	−	0.485814i	$-0.838523\pi$
$263$	−19.4723	−	23.2062i	−1.20072	−	1.43096i	−0.326654	−	0.945144i	$-0.605921\pi$
$264$	0.910392	−	0.160527i	0.0560307	−	0.00987973i
$265$	−11.0468	−	1.51463i	−0.678597	−	0.0930428i
$266$	−0.312087	−	1.76993i	−0.0191353	−	0.108522i
$267$	−8.11564	+	14.0567i	−0.496669	+	0.860256i
$268$	3.75911	−	4.47994i	0.229624	−	0.273656i
$269$	−4.54723	−	7.87603i	−0.277250	−	0.480210i	0.693451	−	0.720504i	$-0.256090\pi$
$269$	−4.54723	−	7.87603i	−0.277250	−	0.480210i	−0.970700	+	0.240294i	$0.922756\pi$
$270$	−7.08344	+	9.12955i	−0.431084	+	0.555607i
$271$	−12.8176	+	4.66521i	−0.778612	+	0.283391i	−0.700594	−	0.713561i	$-0.747081\pi$
$271$	−12.8176	+	4.66521i	−0.778612	+	0.283391i	−0.0780180	+	0.996952i	$0.524859\pi$
$272$	0.626355	−	0.525574i	0.0379784	−	0.0318676i
$273$	0.881821	+	1.52736i	0.0533702	+	0.0924399i
$274$	−6.29702	−	1.11033i	−0.380417	−	0.0670778i
$275$	1.88601	−	3.93387i	0.113731	−	0.237222i
$276$	−3.16730	+	3.77465i	−0.190649	+	0.227207i
$277$	−22.5852	−	8.22034i	−1.35701	−	0.493913i	−0.441884	−	0.897072i	$-0.645690\pi$
$277$	−22.5852	−	8.22034i	−1.35701	−	0.493913i	−0.915130	+	0.403160i	$0.867912\pi$
$278$	−8.21557	−	2.99022i	−0.492737	−	0.179342i
$279$	2.63476	−	3.13998i	0.157739	−	0.187986i
$280$	−0.737321	+	2.29550i	−0.0440633	+	0.137182i
$281$	−9.23169	−	1.62780i	−0.550716	−	0.0971061i	−0.108636	−	0.994082i	$-0.534648\pi$
$281$	−9.23169	−	1.62780i	−0.550716	−	0.0971061i	−0.442080	+	0.896975i	$0.645759\pi$
$282$	2.59135	+	4.48835i	0.154313	+	0.267277i
$283$	−8.38991	+	7.03997i	−0.498729	+	0.418483i	−0.857142	−	0.515080i	$-0.827762\pi$
$283$	−8.38991	+	7.03997i	−0.498729	+	0.418483i	0.358414	+	0.933563i	$0.383318\pi$
$284$	−10.2016	+	3.71309i	−0.605356	+	0.220332i
$285$	3.11995	+	2.42071i	0.184810	+	0.143390i
$286$	−0.673509	−	1.16655i	−0.0398254	−	0.0689796i
$287$	1.15077	−	1.37144i	0.0679279	−	0.0809533i
$288$	−0.938732	+	1.62593i	−0.0553153	+	0.0958089i
$289$	−2.83593	−	16.0833i	−0.166819	−	0.946079i
$290$	4.71120	+	0.645955i	0.276651	+	0.0379318i
$291$	−11.5175	+	2.03084i	−0.675166	+	0.119050i
$292$	6.77361	+	8.07247i	0.396395	+	0.472406i
$293$	−1.24458	+	3.41945i	−0.0727090	+	0.199766i	−0.970724	−	0.240199i	$-0.922787\pi$
$293$	−1.24458	+	3.41945i	−0.0727090	+	0.199766i	0.898015	+	0.439966i	$0.145009\pi$
$294$	−2.11530	−	5.81174i	−0.123367	−	0.338948i
$295$	−24.3599	−	3.34000i	−1.41829	−	0.194462i
$296$	−5.59373	+	2.38959i	−0.325129	+	0.138892i
$297$		−	4.50890i		−	0.261633i
$298$	−2.42386	+	0.882214i	−0.140411	+	0.0511053i
$299$	6.74690	+	2.45567i	0.390183	+	0.142015i
$300$	−2.18721	−	4.82489i	−0.126279	−	0.278565i
$301$	2.26145	−	0.398755i	0.130348	−	0.0229839i
$302$	−22.2729			−1.28166
$303$	2.68793	−	0.473955i	0.154418	−	0.0272280i
$304$	1.44352	+	0.833416i	0.0827915	+	0.0477997i
$305$	2.85584	+	3.15034i	0.163525	+	0.180388i
$306$	−0.767552	−	1.32944i	−0.0438781	−	0.0759990i
$307$	−0.732784	−	0.423073i	−0.0418222	−	0.0241461i	0.478943	−	0.877846i	$-0.341020\pi$
$307$	−0.732784	−	0.423073i	−0.0418222	−	0.0241461i	−0.520765	+	0.853700i	$0.674353\pi$
$308$	−0.321767	−	0.884048i	−0.0183344	−	0.0503733i
$309$	3.43031	+	4.08809i	0.195144	+	0.232563i
$310$	1.84401	+	4.52021i	0.104732	+	0.256731i
$311$	−12.8692	−	2.26918i	−0.729745	−	0.128674i	−0.203582	−	0.979058i	$-0.565258\pi$
$311$	−12.8692	−	2.26918i	−0.729745	−	0.128674i	−0.526162	+	0.850384i	$0.676370\pi$
$312$	−1.61083	−	0.284032i	−0.0911950	−	0.0160801i
$313$	−4.47117	−	3.75176i	−0.252726	−	0.212062i	0.507619	−	0.861581i	$-0.330526\pi$
$313$	−4.47117	−	3.75176i	−0.252726	−	0.212062i	−0.760345	+	0.649520i	$0.774970\pi$
$314$	2.19764	−	6.03797i	0.124020	−	0.340743i
$315$	4.00386	+	2.11164i	0.225592	+	0.118977i
$316$	−3.17667	+	3.78581i	−0.178702	+	0.212968i
$317$	18.3987	+	3.24419i	1.03338	+	0.182212i	0.664517	−	0.747273i	$-0.268637\pi$
$317$	18.3987	+	3.24419i	1.03338	+	0.182212i	0.368859	+	0.929485i	$0.379748\pi$
$318$	0.917413	−	5.20291i	0.0514460	−	0.291764i
$319$	−1.60693	+	0.927764i	−0.0899710	+	0.0519448i
$320$	−1.19131	−	1.89229i	−0.0665963	−	0.105782i
$321$	−2.44139	+	0.888595i	−0.136265	+	0.0495965i
$322$	4.34276	+	2.50729i	0.242013	+	0.139726i
$323$	−1.18029	+	0.681442i	−0.0656732	+	0.0379164i
$324$	0.120467	+	0.101084i	0.00669260	+	0.00561576i
$325$	−5.51644	+	5.39939i	−0.305997	+	0.299504i
$326$	−0.526085	−	2.98357i	−0.0291371	−	0.165245i
$327$	9.65268			0.533795
$328$	0.288322	+	1.63516i	0.0159199	+	0.0902865i
$329$	4.04039	−	3.39029i	0.222754	−	0.186913i
$330$	1.82840	+	0.964298i	0.100650	+	0.0530828i
$331$	2.62689	+	7.21733i	0.144387	+	0.396700i	0.990714	−	0.135964i	$-0.0434131\pi$
$331$	2.62689	+	7.21733i	0.144387	+	0.396700i	−0.846327	+	0.532664i	$0.821191\pi$
$332$			4.06257i			0.222962i
$333$	2.59455	+	11.1215i	0.142181	+	0.609456i
$334$	−0.282066			−0.0154340
$335$	12.7819	−	2.76186i	0.698348	−	0.150897i
$336$	−1.07349	−	0.390720i	−0.0585639	−	0.0213155i
$337$	−10.3303	−	12.3112i	−0.562728	−	0.670633i	0.407394	−	0.913253i	$-0.366438\pi$
$337$	−10.3303	−	12.3112i	−0.562728	−	0.670633i	−0.970121	+	0.242620i	$0.921993\pi$
$338$	−1.84356	−	10.4553i	−0.100276	−	0.568695i
$339$			10.4331i			0.566649i
$340$	1.82698	−	0.0699565i	0.0990818	−	0.00379392i
$341$	−1.64971	−	0.952463i	−0.0893371	−	0.0515788i
$342$	2.01155	−	2.39727i	0.108772	−	0.129630i
$343$	−11.9873	+	6.92087i	−0.647253	+	0.373692i
$344$	−1.06486	+	1.84439i	−0.0574135	+	0.0994431i
$345$	−10.7696	+	2.32705i	−0.579814	+	0.125284i
$346$	−10.9056	−	12.9968i	−0.586288	−	0.698711i
$347$	10.0777	+	17.4551i	0.541001	+	0.937041i	0.998847	+	0.0480094i	$0.0152878\pi$
$347$	10.0777	+	17.4551i	0.541001	+	0.937041i	−0.457846	+	0.889031i	$0.651379\pi$
$348$	−0.391256	+	2.21892i	−0.0209735	+	0.118947i
$349$	−0.0949475	+	0.538474i	−0.00508242	+	0.0288239i	−0.987244	−	0.159218i	$-0.949103\pi$
$349$	−0.0949475	+	0.538474i	−0.00508242	+	0.0288239i	0.982161	+	0.188042i	$0.0602140\pi$
$350$	−4.44909	+	3.04472i	−0.237814	+	0.162747i
$351$	−2.72862	+	7.49681i	−0.145643	+	0.400150i
$352$	0.819903	+	0.298420i	0.0437010	+	0.0159059i
$353$	9.42472	+	7.90828i	0.501627	+	0.420915i	0.858171	−	0.513363i	$-0.171601\pi$
$353$	9.42472	+	7.90828i	0.501627	+	0.420915i	−0.356544	+	0.934278i	$0.616045\pi$
$354$	2.02305	−	11.4733i	0.107524	−	0.609797i
$355$	−23.1125	−	7.42381i	−1.22669	−	0.394015i
$356$	−13.2673	+	7.65989i	−0.703166	+	0.405973i
$357$	0.715540	−	0.600410i	0.0378704	−	0.0317771i
$358$	4.91725	+	13.5100i	0.259885	+	0.714028i
$359$	13.2940	−	23.0258i	0.701629	−	1.21526i	−0.266265	−	0.963900i	$-0.585790\pi$
$359$	13.2940	−	23.0258i	0.701629	−	1.21526i	0.967894	−	0.251358i	$-0.0808771\pi$
$360$	−3.88713	+	1.58574i	−0.204870	+	0.0835759i
$361$	12.4265	+	10.4271i	0.654027	+	0.548794i
$362$	−7.72135	+	13.3738i	−0.405825	+	0.702910i
$363$	10.6831	−	1.88372i	0.560717	−	0.0988695i
$364$			1.66460i			0.0872488i
$365$	0.901600	+	23.5461i	0.0471919	+	1.23246i
$366$	−1.54338	+	1.29505i	−0.0806739	+	0.0676935i
$367$	−3.36052	+	9.23295i	−0.175418	+	0.481956i	−0.995977	−	0.0896048i	$-0.971440\pi$
$367$	−3.36052	+	9.23295i	−0.175418	+	0.481956i	0.820560	+	0.571561i	$0.193662\pi$
$368$	−4.37026	+	1.59065i	−0.227816	+	0.0829182i
$369$	3.11731			0.162280
$370$	−13.1577	−	3.44584i	−0.684038	−	0.179141i
$371$	−5.37660			−0.279139
$372$	−2.17364	+	0.791140i	−0.112698	+	0.0410187i
$373$	8.97241	−	24.6515i	0.464574	−	1.27641i	−0.457437	−	0.889242i	$-0.651233\pi$
$373$	8.97241	−	24.6515i	0.464574	−	1.27641i	0.922011	−	0.387164i	$-0.126545\pi$
$374$	−0.546509	+	0.458575i	−0.0282593	+	0.0237124i
$375$	2.74951	−	11.5220i	0.141984	−	0.594995i
$376$			4.89166i			0.252268i
$377$	3.23325	−	0.570109i	0.166521	−	0.0293621i
$378$	−2.78598	+	4.82545i	−0.143295	+	0.248195i
$379$	−3.82454	−	3.20917i	−0.196453	−	0.164844i	0.539255	−	0.842143i	$-0.318706\pi$
$379$	−3.82454	−	3.20917i	−0.196453	−	0.164844i	−0.735708	+	0.677299i	$0.763150\pi$
$380$	1.40784	+	3.45104i	0.0722206	+	0.177034i
$381$	−9.41440	+	16.3062i	−0.482315	+	0.835393i
$382$	1.12909	+	3.10215i	0.0577692	+	0.158720i
$383$	24.8001	−	20.8097i	1.26722	−	1.06333i	0.272351	−	0.962198i	$-0.412199\pi$
$383$	24.8001	−	20.8097i	1.26722	−	1.06333i	0.994873	−	0.101130i	$-0.0322457\pi$
$384$	0.917552	−	0.529749i	0.0468237	−	0.0270336i
$385$	0.643329	−	2.00287i	0.0327871	−	0.102076i
$386$	1.90145	−	10.7837i	0.0967812	−	0.548873i
$387$	3.06301	+	2.57017i	0.155702	+	0.130649i
$388$	−10.3727	−	3.77535i	−0.526594	−	0.191664i
$389$	−6.55864	+	18.0197i	−0.332536	+	0.913636i	0.654914	+	0.755704i	$0.272705\pi$
$389$	−6.55864	+	18.0197i	−0.332536	+	0.913636i	−0.987450	+	0.157932i	$0.949517\pi$
$390$	−2.45647	−	2.70979i	−0.124388	−	0.137215i
$391$	0.660327	−	3.74490i	0.0333941	−	0.189388i
$392$	1.01366	−	5.74873i	0.0511973	−	0.290355i
$393$	3.67157	+	6.35934i	0.185206	+	0.320786i
$394$	12.1961	+	14.5347i	0.614428	+	0.732247i
$395$	−10.8014	+	2.33394i	−0.543479	+	0.117433i
$396$	0.819064	−	1.41866i	0.0411595	−	0.0712904i
$397$	28.7635	−	16.6066i	1.44360	−	0.833461i	0.445510	−	0.895277i	$-0.353022\pi$
$397$	28.7635	−	16.6066i	1.44360	−	0.833461i	0.998088	+	0.0618156i	$0.0196891\pi$
$398$	−5.84969	+	6.97138i	−0.293218	+	0.349444i
$399$	1.64906	+	0.952085i	0.0825562	+	0.0476639i
$400$	0.489160	−	4.97601i	0.0244580	−	0.248801i
$401$		−	6.78294i		−	0.338724i	−0.985554	−	0.169362i	$-0.945829\pi$
$401$		−	6.78294i		−	0.338724i	0.985554	−	0.169362i	$-0.0541707\pi$
$402$	1.07594	+	6.10197i	0.0536631	+	0.304338i
$403$	2.16653	+	2.58198i	0.107923	+	0.128617i
$404$	2.42076	+	0.881086i	0.120437	+	0.0438357i
$405$	0.0742673	+	0.343708i	0.00369037	+	0.0170790i
$406$	2.29300			0.113800
$407$	4.88066	−	2.08497i	0.241925	−	0.103348i
$408$			0.866297i			0.0428881i
$409$	−3.95396	−	10.8634i	−0.195511	−	0.537161i	0.802737	−	0.596333i	$-0.203376\pi$
$409$	−3.95396	−	10.8634i	−0.195511	−	0.537161i	−0.998248	+	0.0591720i	$0.981154\pi$
$410$	−1.73198	+	3.28399i	−0.0855363	+	0.162185i
$411$	5.18965	−	4.35463i	0.255986	−	0.214798i
$412$	0.874653	+	4.96041i	0.0430911	+	0.244382i
$413$	−11.8563			−0.583410
$414$	1.51622	+	8.59894i	0.0745184	+	0.422615i
$415$	−5.56865	+	7.17721i	−0.273354	+	0.352315i
$416$	−1.18263	−	0.992348i	−0.0579834	−	0.0486539i
$417$	8.02200	−	4.63150i	0.392839	−	0.226806i
$418$	−1.25950	−	0.727174i	−0.0616043	−	0.0355673i
$419$	16.0572	−	5.84436i	0.784448	−	0.285516i	0.0814217	−	0.996680i	$-0.474054\pi$
$419$	16.0572	−	5.84436i	0.784448	−	0.285516i	0.703026	+	0.711164i	$0.251832\pi$
$420$	−1.36094	−	2.16173i	−0.0664070	−	0.105482i
$421$	1.95703	−	1.12989i	0.0953798	−	0.0550675i	−0.451551	−	0.892245i	$-0.649129\pi$
$421$	1.95703	−	1.12989i	0.0953798	−	0.0550675i	0.546931	+	0.837178i	$0.315796\pi$
$422$	−2.61403	+	14.8249i	−0.127249	+	0.721664i
$423$	9.04438	+	1.59477i	0.439753	+	0.0775403i
$424$	3.20525	−	3.81987i	0.155661	−	0.185509i
$425$	3.32356	+	2.38069i	0.161216	+	0.115481i
$426$	3.93402	−	10.8086i	0.190604	−	0.523679i
$427$	1.57068	+	1.31795i	0.0760104	+	0.0637803i
$428$	−2.41492	−	0.425816i	−0.116730	−	0.0205826i
$429$	1.40548	+	0.247824i	0.0678573	+	0.0119651i
$430$	−4.40941	+	1.79880i	−0.212641	+	0.0867460i
$431$	−9.25962	−	11.0352i	−0.446020	−	0.531546i	0.495453	−	0.868635i	$-0.335002\pi$
$431$	−9.25962	−	11.0352i	−0.446020	−	0.531546i	−0.941473	+	0.337089i	$0.890558\pi$
$432$	−1.76745	−	4.85602i	−0.0850362	−	0.233635i
$433$	8.73101	+	5.04085i	0.419586	+	0.242248i	0.694900	−	0.719106i	$-0.255449\pi$
$433$	8.73101	+	5.04085i	0.419586	+	0.242248i	−0.275314	+	0.961354i	$0.588782\pi$
$434$	1.17702	+	2.03866i	0.0564989	+	0.0978590i
$435$	−3.73275	+	3.38380i	−0.178972	+	0.162241i
$436$	7.89003	+	4.55531i	0.377864	+	0.218160i
$437$	7.63423	−	1.34612i	0.365195	−	0.0643937i
$438$	−11.1648			−0.533477
$439$	−9.15624	+	1.61449i	−0.437003	+	0.0770555i	−0.387822	−	0.921734i	$-0.626772\pi$
$439$	−9.15624	+	1.61449i	−0.437003	+	0.0770555i	−0.0491815	+	0.998790i	$0.515661\pi$
$440$	1.03945	+	1.65107i	0.0495536	+	0.0787117i
$441$	−10.2986	−	3.74838i	−0.490409	−	0.178494i
$442$	1.18618	−	0.431733i	0.0564206	−	0.0205354i
$443$			35.7351i			1.69783i	0.528531	+	0.848914i	$0.322743\pi$
$443$			35.7351i			1.69783i	−0.528531	+	0.848914i	$0.677257\pi$
$444$	1.87007	−	6.16739i	0.0887494	−	0.292691i
$445$	−33.9385	−	4.65333i	−1.60884	−	0.220589i
$446$	7.43498	+	20.4274i	0.352056	+	0.967267i
$447$	0.934704	−	2.56808i	0.0442100	−	0.121466i
$448$	−0.693076	−	0.825976i	−0.0327448	−	0.0390237i
$449$	18.1541	−	3.20105i	0.856743	−	0.151067i	0.272012	−	0.962294i	$-0.412311\pi$
$449$	18.1541	−	3.20105i	0.856743	−	0.151067i	0.584731	+	0.811227i	$0.301200\pi$
$450$	−9.04088	−	2.52670i	−0.426191	−	0.119110i
$451$	−0.251568	−	1.42671i	−0.0118459	−	0.0671812i
$452$	−4.92361	+	8.52794i	−0.231587	+	0.401121i
$453$	15.1685	−	18.0772i	0.712680	−	0.849339i
$454$	−6.34726	−	10.9938i	−0.297891	−	0.515963i
$455$	−2.28171	+	2.94080i	−0.106968	+	0.137867i
$456$	−1.65950	+	0.604010i	−0.0777134	+	0.0282853i
$457$	25.8346	−	21.6778i	1.20849	−	1.01404i	0.209144	−	0.977885i	$-0.432932\pi$
$457$	25.8346	−	21.6778i	1.20849	−	1.01404i	0.999346	−	0.0361587i	$-0.0115122\pi$
$458$	5.03353	+	8.71834i	0.235202	+	0.407381i
$459$	4.16114	+	0.733721i	0.194225	+	0.0342472i
$460$	−9.90114	−	3.18028i	−0.461643	−	0.148281i
$461$	19.5455	−	23.2934i	0.910323	−	1.08488i	−0.0857480	−	0.996317i	$-0.527328\pi$
$461$	19.5455	−	23.2934i	0.910323	−	1.08488i	0.996071	−	0.0885633i	$-0.0282276\pi$
$462$	0.936647	+	0.340912i	0.0435768	+	0.0158606i
$463$	−31.3726	−	11.4187i	−1.45801	−	0.530672i	−0.513194	−	0.858273i	$-0.671538\pi$
$463$	−31.3726	−	11.4187i	−1.45801	−	0.530672i	−0.944816	+	0.327600i	$0.893760\pi$
$464$	−1.36697	+	1.62909i	−0.0634599	+	0.0756286i
$465$	−4.92454	−	1.58178i	−0.228370	−	0.0733531i
$466$	7.55181	+	1.33159i	0.349831	+	0.0616846i
$467$	9.94276	+	17.2214i	0.460096	+	0.796910i	0.998965	−	0.0454795i	$-0.0144816\pi$
$467$	9.94276	+	17.2214i	0.460096	+	0.796910i	−0.538869	+	0.842390i	$0.681148\pi$
$468$	−2.22035	+	1.86310i	−0.102636	+	0.0861217i
$469$	5.92539	−	2.15667i	0.273609	−	0.0995856i
$470$	−6.70511	+	8.64194i	−0.309283	+	0.398623i
$471$	3.40389	+	5.89571i	0.156843	+	0.271660i
$472$	7.06810	−	8.42343i	0.325336	−	0.387720i
$473$	0.929115	−	1.60928i	0.0427208	−	0.0739946i
$474$	−0.909234	−	5.15652i	−0.0417625	−	0.236847i
$475$	−2.24323	+	8.02659i	−0.102926	+	0.368285i
$476$	0.868223	−	0.153091i	0.0397949	−	0.00701692i
$477$	−6.01774	−	7.17166i	−0.275533	−	0.328368i
$478$	2.25506	−	6.19572i	0.103144	−	0.283386i
$479$	7.41314	+	20.3674i	0.338715	+	0.930612i	0.985760	+	0.168160i	$0.0537824\pi$
$479$	7.41314	+	20.3674i	0.338715	+	0.930612i	−0.647045	+	0.762452i	$0.723995\pi$
$480$	2.34715	+	0.321819i	0.107132	+	0.0146890i
$481$	−9.37667	+	0.513030i	−0.427539	+	0.0233921i
$482$		−	26.9704i		−	1.22847i
$483$	−4.99254	+	1.81713i	−0.227168	+	0.0826825i
$484$	9.62124	+	3.50184i	0.437329	+	0.159175i
$485$	−13.1501	−	20.8879i	−0.597117	−	0.948470i
$486$	−15.4316	+	2.72100i	−0.699989	+	0.123427i
$487$	−36.5419			−1.65587			−0.827937	−	0.560822i	$-0.810485\pi$
$487$	−36.5419			−1.65587			−0.827937	+	0.560822i	$0.810485\pi$
$488$	−1.87271	+	0.330210i	−0.0847737	+	0.0149479i
$489$	2.77982	+	1.60493i	0.125708	+	0.0725774i
$490$	9.67070	−	8.76665i	0.436878	−	0.396037i
$491$	11.9230	+	20.6513i	0.538078	+	0.931979i	0.999008	+	0.0445419i	$0.0141828\pi$
$491$	11.9230	+	20.6513i	0.538078	+	0.931979i	−0.460929	+	0.887437i	$0.652484\pi$
$492$	−1.52349	−	0.879586i	−0.0686841	−	0.0396548i
$493$	−0.594715	−	1.63397i	−0.0267846	−	0.0735902i
$494$	1.65408	+	1.97125i	0.0744205	+	0.0886909i
$495$	3.39161	−	1.38359i	0.152441	−	0.0621879i
$496$	−2.15007	−	0.379116i	−0.0965411	−	0.0170228i
$497$	−11.5279	−	2.03267i	−0.517095	−	0.0911779i
$498$	−3.29727	−	2.76674i	−0.147754	−	0.123981i
$499$	12.9665	−	35.6251i	0.580458	−	1.59480i	−0.206941	−	0.978353i	$-0.566351\pi$
$499$	12.9665	−	35.6251i	0.580458	−	1.59480i	0.787399	−	0.616443i	$-0.211427\pi$
$500$	7.68492	−	8.12047i	0.343680	−	0.363158i
$501$	0.192096	−	0.228932i	0.00858223	−	0.0102279i
$502$	−5.10771	−	0.900627i	−0.227968	−	0.0401970i
$503$	6.98751	−	39.6282i	0.311558	−	1.76693i	−0.279346	−	0.960191i	$-0.590118\pi$
$503$	6.98751	−	39.6282i	0.311558	−	1.76693i	0.590904	−	0.806742i	$-0.298771\pi$
$504$	−1.75314	+	1.01217i	−0.0780909	+	0.0450858i
$505$	3.06896	+	4.87478i	0.136567	+	0.216925i
$506$	3.81315	−	1.38787i	0.169515	−	0.0616985i
$507$	9.74131	+	5.62415i	0.432627	+	0.249777i
$508$	−15.3905	+	8.88572i	−0.682844	+	0.394240i
$509$	15.7389	+	13.2065i	0.697617	+	0.585370i	0.921094	−	0.389339i	$-0.127297\pi$
$509$	15.7389	+	13.2065i	0.697617	+	0.585370i	−0.223478	+	0.974709i	$0.571741\pi$
$510$	−1.18745	+	1.53046i	−0.0525813	+	0.0677699i
$511$	1.97304	+	11.1897i	0.0872822	+	0.495002i
$512$	1.00000			0.0441942
$513$	1.49574	+	8.48277i	0.0660386	+	0.374523i
$514$	−16.1795	+	13.5762i	−0.713647	+	0.598821i
$515$	−5.25412	+	9.96230i	−0.231524	+	0.438991i
$516$	−0.771747	−	2.12036i	−0.0339743	−	0.0933435i
$517$		−	4.26808i		−	0.187710i
$518$	−6.51158	−	0.784329i	−0.286102	−	0.0344615i
$519$	17.9755			0.789039
$520$	−0.729089	−	3.37422i	−0.0319727	−	0.147969i
$521$	−7.39970	−	2.69327i	−0.324187	−	0.117994i	0.174800	−	0.984604i	$-0.444072\pi$
$521$	−7.39970	−	2.69327i	−0.324187	−	0.117994i	−0.498987	+	0.866610i	$0.666294\pi$
$522$	2.56643	+	3.05855i	0.112330	+	0.133869i
$523$	2.06053	+	11.6858i	0.0901006	+	0.510986i	0.996139	+	0.0877905i	$0.0279806\pi$
$523$	2.06053	+	11.6858i	0.0901006	+	0.510986i	−0.906038	+	0.423196i	$0.860908\pi$
$524$			6.93076i			0.302772i
$525$	0.558811	−	5.68454i	0.0243885	−	0.248094i
$526$	26.2350	+	15.1468i	1.14390	+	0.660432i
$527$	1.14745	−	1.36748i	0.0499839	−	0.0595685i
$528$	−0.800585	+	0.462218i	−0.0348410	+	0.0201155i
$529$	0.685317	−	1.18700i	0.0297964	−	0.0516089i
$530$	10.8986	−	2.35493i	0.473405	−	0.102292i
$531$	−13.2701	−	15.8147i	−0.575873	−	0.686299i
$532$	0.898618	+	1.55645i	0.0389601	+	0.0674808i
$533$	−0.445118	+	2.52439i	−0.0192802	+	0.109343i
$534$	2.81853	−	15.9847i	0.121970	−	0.691725i
$535$	−3.68269	−	4.06247i	−0.159217	−	0.175636i
$536$	−2.00018	+	5.49546i	−0.0863947	+	0.237368i
$537$	−14.3139	−	5.20982i	−0.617689	−	0.224820i
$538$	6.96676	+	5.84581i	0.300358	+	0.252031i
$539$	−0.884437	+	5.01589i	−0.0380954	+	0.216050i
$540$	3.53376	−	11.0016i	0.152069	−	0.473436i
$541$	36.1647	−	20.8797i	1.55484	−	0.897689i	0.557106	−	0.830441i	$-0.311912\pi$
$541$	36.1647	−	20.8797i	1.55484	−	0.897689i	0.997736	−	0.0672476i	$-0.0214217\pi$
$542$	10.4490	−	8.76773i	0.448822	−	0.376606i
$543$	−5.59597	−	15.3748i	−0.240146	−	0.659796i
$544$	−0.408824	+	0.708104i	−0.0175282	+	0.0303597i
$545$	7.69500	+	18.8628i	0.329617	+	0.807992i
$546$	−1.35103	−	1.13365i	−0.0578186	−	0.0485156i
$547$	−21.5669	+	37.3550i	−0.922135	+	1.59718i	−0.126030	+	0.992026i	$0.540223\pi$
$547$	−21.5669	+	37.3550i	−0.922135	+	1.59718i	−0.796105	+	0.605158i	$0.793110\pi$
$548$	6.29702	−	1.11033i	0.268995	−	0.0474311i
$549$			3.57019i			0.152372i
$550$	−0.426803	+	4.34168i	−0.0181989	+	0.185130i
$551$	2.71542	−	2.27851i	0.115681	−	0.0970677i
$552$	1.68529	−	4.63029i	0.0717306	−	0.197078i
$553$	−5.00731	+	1.82251i	−0.212932	+	0.0775010i
$554$	24.0347			1.02114
$555$	11.7576	−	8.33239i	0.499081	−	0.353690i
$556$	8.74282			0.370778
$557$	25.8419	−	9.40569i	1.09496	−	0.398532i	0.269502	−	0.963000i	$-0.413141\pi$
$557$	25.8419	−	9.40569i	1.09496	−	0.398532i	0.825455	+	0.564468i	$0.190919\pi$
$558$	−1.40192	+	3.85176i	−0.0593482	+	0.163058i
$559$	−2.51868	+	2.11343i	−0.106529	+	0.0893884i
$560$	−0.0922517	−	2.40924i	−0.00389835	−	0.101809i
$561$		−	0.755864i		−	0.0319126i
$562$	9.23169	−	1.62780i	0.389415	−	0.0686644i
$563$	−14.0675	+	24.3656i	−0.592873	+	1.02689i	0.400970	+	0.916091i	$0.368673\pi$
$563$	−14.0675	+	24.3656i	−0.592873	+	1.02689i	−0.993843	+	0.110795i	$0.964660\pi$
$564$	−3.97018	−	3.33138i	−0.167175	−	0.140276i
$565$	−20.3878	+	8.31715i	−0.857723	+	0.349905i
$566$	5.47613	−	9.48493i	0.230179	−	0.398681i
$567$	0.0579934	+	0.159336i	0.00243549	+	0.00669146i
$568$	8.31645	−	6.97833i	0.348951	−	0.292804i
$569$	31.5420	−	18.2108i	1.32231	−	0.763437i	0.338214	−	0.941069i	$-0.390177\pi$
$569$	31.5420	−	18.2108i	1.32231	−	0.763437i	0.984097	+	0.177633i	$0.0568439\pi$
$570$	−3.75972	−	1.20763i	−0.157477	−	0.0505822i
$571$	−2.64393	+	14.9945i	−0.110645	+	0.627499i	0.878170	+	0.478349i	$0.158765\pi$
$571$	−2.64393	+	14.9945i	−0.110645	+	0.627499i	−0.988815	+	0.149150i	$0.952346\pi$
$572$	1.03188	+	0.865846i	0.0431449	+	0.0362028i
$573$	−3.28672	−	1.19627i	−0.137305	−	0.0499748i
$574$	−0.612312	+	1.68231i	−0.0255574	+	0.0702185i
$575$	−13.1328	−	19.1902i	−0.547674	−	0.800288i
$576$	0.326018	−	1.84894i	0.0135841	−	0.0770392i
$577$	4.51304	−	25.5947i	0.187880	−	1.06552i	−0.734318	−	0.678805i	$-0.762498\pi$
$577$	4.51304	−	25.5947i	0.187880	−	1.06552i	0.922199	−	0.386716i	$-0.126391\pi$
$578$	8.16573	+	14.1435i	0.339649	+	0.588290i
$579$	7.45731	+	8.88728i	0.309915	+	0.369343i
$580$	−4.64801	+	1.00433i	−0.192998	+	0.0417024i
$581$	−2.19020	+	3.79354i	−0.0908648	+	0.157382i
$582$	10.1283	−	5.84758i	0.419831	−	0.242390i
$583$	−2.79665	+	3.33292i	−0.115825	+	0.138035i
$584$	−9.12606	−	5.26893i	−0.377639	−	0.218030i
$585$	−6.47642	+	0.247987i	−0.267767	+	0.0102530i
$586$		−	3.63890i		−	0.150322i
$587$	7.24062	+	41.0636i	0.298852	+	1.69488i	0.651119	+	0.758976i	$0.274300\pi$
$587$	7.24062	+	41.0636i	0.298852	+	1.69488i	−0.352267	+	0.935900i	$0.614589\pi$
$588$	3.97547	+	4.73777i	0.163945	+	0.195383i
$589$	3.41963	+	1.24464i	0.140903	+	0.0512847i
$590$	24.0332	−	5.19301i	0.989431	−	0.213793i
$591$	−20.1026			−0.826910
$592$	4.43910	−	4.15865i	0.182446	−	0.170919i
$593$		−	28.6164i		−	1.17514i	−0.809175	−	0.587568i	$-0.800085\pi$
$593$		−	28.6164i		−	1.17514i	0.809175	−	0.587568i	$-0.199915\pi$
$594$	1.54214	+	4.23698i	0.0632746	+	0.173846i
$595$	1.74371	+	0.919632i	0.0714851	+	0.0377012i
$596$	1.97595	−	1.65802i	0.0809381	−	0.0679152i
$597$	−1.67431	−	9.49548i	−0.0685249	−	0.388624i
$598$	−7.17990			−0.293608
$599$	−4.18335	−	23.7249i	−0.170927	−	0.969375i	−0.942741	−	0.333526i	$-0.891761\pi$
$599$	−4.18335	−	23.7249i	−0.170927	−	0.969375i	0.771814	−	0.635849i	$-0.219350\pi$
$600$	3.70551	+	3.78584i	0.151277	+	0.154556i
$601$	3.35161	+	2.81234i	0.136715	+	0.114718i	0.708581	−	0.705630i	$-0.249336\pi$
$601$	3.35161	+	2.81234i	0.136715	+	0.114718i	−0.571866	+	0.820347i	$0.693780\pi$
$602$	−1.98869	+	1.14817i	−0.0810529	+	0.0467959i
$603$	9.50868	+	5.48984i	0.387223	+	0.223563i
$604$	20.9296	−	7.61777i	0.851615	−	0.309962i
$605$	12.1975	+	19.3746i	0.495898	+	0.787691i
$606$	−2.36373	+	1.36470i	−0.0960199	+	0.0554371i
$607$	−4.77849	+	27.1002i	−0.193953	+	1.09996i	0.719949	+	0.694027i	$0.244165\pi$
$607$	−4.77849	+	27.1002i	−0.193953	+	1.09996i	−0.913902	+	0.405935i	$0.866946\pi$
$608$	−1.64151	−	0.289442i	−0.0665720	−	0.0117384i
$609$	−1.56161	+	1.86105i	−0.0632795	+	0.0754136i
$610$	−3.76109	−	1.98360i	−0.152282	−	0.0803135i
$611$	−2.58288	+	7.09640i	−0.104492	+	0.287090i
$612$	1.17596	+	0.986746i	0.0475353	+	0.0398869i
$613$	17.8488	+	3.14722i	0.720906	+	0.127115i	0.522052	−	0.852914i	$-0.325167\pi$
$613$	17.8488	+	3.14722i	0.720906	+	0.127115i	0.198854	+	0.980029i	$0.436278\pi$
$614$	0.833291	+	0.146932i	0.0336289	+	0.00592968i
$615$	−1.48583	−	3.64222i	−0.0599144	−	0.146868i
$616$	0.604724	+	0.720682i	0.0243650	+	0.0290371i
$617$	−3.72701	−	10.2399i	−0.150044	−	0.412242i	0.841786	−	0.539812i	$-0.181505\pi$
$617$	−3.72701	−	10.2399i	−0.150044	−	0.412242i	−0.991830	+	0.127570i	$0.959282\pi$
$618$	−4.62165	−	2.66831i	−0.185910	−	0.107335i
$619$	−1.39499	−	2.41619i	−0.0560692	−	0.0971148i	0.836628	−	0.547771i	$-0.184523\pi$
$619$	−1.39499	−	2.41619i	−0.0560692	−	0.0971148i	−0.892698	+	0.450656i	$0.851190\pi$
$620$	−3.27880	−	3.61692i	−0.131680	−	0.145259i
$621$	−20.8136	−	12.0167i	−0.835220	−	0.482215i
$622$	12.8692	−	2.26918i	0.516007	−	0.0909860i
$623$	−16.5183			−0.661792
$624$	1.61083	−	0.284032i	0.0644846	−	0.0113704i
$625$	24.7076	−	3.81228i	0.988305	−	0.152491i
$626$	5.48470	+	1.99627i	0.219213	+	0.0797869i
$627$	1.44795	−	0.527012i	0.0578257	−	0.0210468i
$628$			6.42548i			0.256404i
$629$	1.12995	+	4.84350i	0.0450539	+	0.193123i
$630$	−4.48462	−	0.614888i	−0.178671	−	0.0244977i
$631$	5.08822	+	13.9798i	0.202559	+	0.556525i	0.998827	−	0.0484180i	$-0.0154180\pi$
$631$	5.08822	+	13.9798i	0.202559	+	0.556525i	−0.796268	+	0.604943i	$0.793196\pi$
$632$	1.69027	−	4.64398i	0.0672354	−	0.184728i
$633$	−10.2520	−	12.2178i	−0.407479	−	0.485615i
$634$	−18.3987	+	3.24419i	−0.730707	+	0.128843i
$635$	−39.3698	−	5.39801i	−1.56234	−	0.214214i
$636$	0.917413	+	5.20291i	0.0363778	+	0.206309i
$637$	4.50595	−	7.80454i	0.178532	−	0.309227i
$638$	1.19271	−	1.42142i	0.0472199	−	0.0562744i
$639$	−10.1912	−	17.6517i	−0.403158	−	0.698290i
$640$	1.76667	+	1.37072i	0.0698337	+	0.0541826i
$641$	−21.3389	+	7.76672i	−0.842835	+	0.306767i	−0.727116	−	0.686515i	$-0.759140\pi$
$641$	−21.3389	+	7.76672i	−0.842835	+	0.306767i	−0.115720	+	0.993282i	$0.536917\pi$
$642$	1.99024	−	1.67001i	0.0785486	−	0.0659101i
$643$	14.1824	+	24.5646i	0.559298	+	0.968733i	0.997555	+	0.0698834i	$0.0222627\pi$
$643$	14.1824	+	24.5646i	0.559298	+	0.968733i	−0.438257	+	0.898850i	$0.644404\pi$
$644$	−4.93840	−	0.870774i	−0.194600	−	0.0343133i
$645$	1.54300	−	4.80382i	0.0607556	−	0.189150i
$646$	0.876044	−	1.04403i	0.0344675	−	0.0410768i
$647$	−7.84861	−	2.85666i	−0.308561	−	0.112307i	0.183099	−	0.983095i	$-0.441387\pi$
$647$	−7.84861	−	2.85666i	−0.308561	−	0.112307i	−0.491659	+	0.870788i	$0.663609\pi$
$648$	−0.147774	−	0.0537855i	−0.00580513	−	0.00211289i
$649$	−6.16708	+	7.34964i	−0.242079	+	0.288498i
$650$	3.33706	−	6.96050i	0.130890	−	0.273013i
$651$	−2.45622	−	0.433097i	−0.0962667	−	0.0169744i
$652$	1.51480	+	2.62371i	0.0593242	+	0.102752i
$653$	−9.84771	+	8.26321i	−0.385371	+	0.323364i	−0.814807	−	0.579733i	$-0.803157\pi$
$653$	−9.84771	+	8.26321i	−0.385371	+	0.323364i	0.429436	+	0.903097i	$0.358712\pi$
$654$	−9.07056	+	3.30141i	−0.354687	+	0.129095i
$655$	−9.50016	+	12.2444i	−0.371202	+	0.478427i
$656$	−0.830191	−	1.43793i	−0.0324135	−	0.0561419i
$657$	−12.7172	+	15.1558i	−0.496145	+	0.591283i
$658$	−2.63718	+	4.56772i	−0.102808	+	0.178068i
$659$	3.18898	+	18.0856i	0.124225	+	0.704515i	0.981765	+	0.190098i	$0.0608805\pi$
$659$	3.18898	+	18.0856i	0.124225	+	0.704515i	−0.857540	+	0.514417i	$0.828008\pi$
$660$	−2.04794	−	0.280794i	−0.0797160	−	0.0109299i
$661$	−0.545303	+	0.0961516i	−0.0212098	+	0.00373987i	−0.184243	−	0.982881i	$-0.558983\pi$
$661$	−0.545303	+	0.0961516i	−0.0212098	+	0.00373987i	0.163033	+	0.986621i	$0.447872\pi$
$662$	−4.93694	−	5.88362i	−0.191880	−	0.228673i
$663$	−0.457420	+	1.25675i	−0.0177647	+	0.0488082i
$664$	−1.38948	−	3.81756i	−0.0539223	−	0.148150i
$665$	−0.545904	+	3.98149i	−0.0211693	+	0.154396i
$666$	−6.24187	−	9.56343i	−0.241868	−	0.370575i
$667$			9.89037i			0.382957i
$668$	0.265056	−	0.0964724i	0.0102553	−	0.00373263i
$669$	−21.6428	−	7.87735i	−0.836760	−	0.304556i
$670$	−11.0664	+	6.96696i	−0.427533	+	0.269157i
$671$	1.63398	−	0.288115i	0.0630792	−	0.0111226i
$672$	1.14239			0.0440686
$673$	34.0710	−	6.00764i	1.31334	−	0.231577i	0.527261	−	0.849703i	$-0.323219\pi$
$673$	34.0710	−	6.00764i	1.31334	−	0.231577i	0.786079	+	0.618126i	$0.212108\pi$
$674$	13.9180	+	8.03556i	0.536101	+	0.309518i
$675$	21.3232	−	14.5925i	0.820730	−	0.561664i
$676$	5.30831	+	9.19426i	0.204166	+	0.353625i
$677$	−25.8495	−	14.9242i	−0.993477	−	0.573584i	−0.0871652	−	0.996194i	$-0.527781\pi$
$677$	−25.8495	−	14.9242i	−0.993477	−	0.573584i	−0.906312	+	0.422610i	$0.861114\pi$
$678$	−3.56834	−	9.80392i	−0.137041	−	0.376517i
$679$	−7.65044	−	9.11744i	−0.293597	−	0.349895i
$680$	−1.69287	+	0.690601i	−0.0649187	+	0.0264833i
$681$	13.2455	+	2.33554i	0.507568	+	0.0894979i
$682$	1.87599	+	0.330787i	0.0718352	+	0.0126665i
$683$	23.6104	+	19.8115i	0.903428	+	0.758066i	0.970857	−	0.239658i	$-0.0770352\pi$
$683$	23.6104	+	19.8115i	0.903428	+	0.758066i	−0.0674291	+	0.997724i	$0.521480\pi$
$684$	−1.07032	+	2.94069i	−0.0409248	+	0.112440i
$685$	12.6467	+	6.66988i	0.483206	+	0.254843i
$686$	8.89730	−	10.6034i	0.339700	−	0.404839i
$687$	−10.5040	−	1.85214i	−0.400753	−	0.0706635i
$688$	0.369822	−	2.09737i	0.0140993	−	0.0799614i
$689$	6.66686	−	3.84912i	0.253987	−	0.146640i
$690$	9.32419	−	5.87012i	0.354966	−	0.223472i
$691$	16.7698	−	6.10370i	0.637952	−	0.232196i	−0.00273673	−	0.999996i	$-0.500871\pi$
$691$	16.7698	−	6.10370i	0.637952	−	0.232196i	0.640689	+	0.767801i	$0.278649\pi$
$692$	14.6931	+	8.48304i	0.558546	+	0.322477i
$693$	1.52965	−	0.883144i	0.0581066	−	0.0335479i
$694$	−15.4400	−	12.9557i	−0.586093	−	0.491791i
$695$	15.4457	+	11.9840i	0.585888	+	0.454579i
$696$	−0.391256	−	2.21892i	−0.0148305	−	0.0841081i
$697$	1.35761			0.0514231
$698$	−0.0949475	−	0.538474i	−0.00359382	−	0.0203815i
$699$	−6.22378	+	5.22237i	−0.235405	+	0.197528i
$700$	3.13942	−	4.38278i	0.118659	−	0.165654i
$701$	−3.08447	−	8.47452i	−0.116499	−	0.320078i	0.867715	−	0.497063i	$-0.165588\pi$
$701$	−3.08447	−	8.47452i	−0.116499	−	0.320078i	−0.984214	+	0.176984i	$0.943366\pi$
$702$		−	7.97794i		−	0.301108i
$703$	−8.49052	+	5.54160i	−0.320226	+	0.209005i
$704$	−0.872522			−0.0328844
$705$	−2.44760	−	11.3275i	−0.0921819	−	0.426617i
$706$	−11.5611	−	4.20791i	−0.435109	−	0.158367i
$707$	1.78545	+	2.12781i	0.0671487	+	0.0800247i
$708$	2.02305	+	11.4733i	0.0760307	+	0.431192i
$709$			34.7424i			1.30478i	0.757884	+	0.652389i	$0.226233\pi$
$709$			34.7424i			1.30478i	−0.757884	+	0.652389i	$0.773767\pi$
$710$	24.2578	−	0.928849i	0.910378	−	0.0348591i
$711$	−8.03539	−	4.63924i	−0.301351	−	0.173985i
$712$	9.84736	−	11.7356i	0.369045	−	0.439811i
$713$	−8.79334	+	5.07684i	−0.329313	+	0.190129i
$714$	−0.467036	+	0.808930i	−0.0174784	+	0.0302734i
$715$	0.636147	+	2.94408i	0.0237905	+	0.110102i
$716$	−9.24141	−	11.0135i	−0.345368	−	0.411593i
$717$	3.49282	+	6.04974i	0.130442	+	0.225932i
$718$	−4.61695	+	26.1840i	−0.172303	+	0.977179i
$719$	−7.62793	+	43.2601i	−0.284474	+	1.61333i	0.422686	+	0.906276i	$0.361087\pi$
$719$	−7.62793	+	43.2601i	−0.284474	+	1.61333i	−0.707160	+	0.707054i	$0.750024\pi$
$720$	3.11035	−	2.81958i	0.115916	−	0.105080i
$721$	−1.85751	+	5.10346i	−0.0691772	+	0.190063i
$722$	−15.2434	−	5.54814i	−0.567300	−	0.206480i
$723$	21.8898	+	18.3677i	0.814091	+	0.683103i
$724$	2.68160	−	15.2081i	0.0996608	−	0.565204i
$725$	−9.58815	−	4.59682i	−0.356095	−	0.170722i
$726$	−9.39455	+	5.42395i	−0.348664	+	0.201301i
$727$	−16.3714	+	13.7372i	−0.607180	+	0.509484i	−0.893744	−	0.448577i	$-0.851931\pi$
$727$	−16.3714	+	13.7372i	−0.607180	+	0.509484i	0.286565	+	0.958061i	$0.407487\pi$
$728$	−0.569327	−	1.56421i	−0.0211007	−	0.0579736i
$729$	8.06507	−	13.9691i	0.298706	−	0.517375i
$730$	−8.90048	−	21.8178i	−0.329421	−	0.807511i
$731$	1.33396	+	1.11933i	0.0493384	+	0.0413998i
$732$	1.00737	−	1.74482i	0.0372335	−	0.0644904i
$733$	49.0798	−	8.65409i	1.81280	−	0.319646i	0.838503	−	0.544897i	$-0.183431\pi$
$733$	49.0798	−	8.65409i	1.81280	−	0.319646i	0.974301	+	0.225251i	$0.0723201\pi$
$734$		−	9.82550i		−	0.362666i
$735$	0.529153	+	13.8193i	0.0195181	+	0.509734i
$736$	3.56267	−	2.98944i	0.131322	−	0.110192i
$737$	1.74520	−	4.79491i	0.0642854	−	0.176623i
$738$	−2.92931	+	1.06618i	−0.107829	+	0.0392467i
$739$	−28.3679			−1.04353			−0.521765	−	0.853089i	$-0.674726\pi$
$739$	−28.3679			−1.04353			−0.521765	+	0.853089i	$0.674726\pi$
$740$	13.5428	−	1.26218i	0.497843	−	0.0463987i
$741$	−2.72640			−0.100157
$742$	5.05235	−	1.83890i	0.185478	−	0.0675083i
$743$	14.5077	−	39.8595i	0.532235	−	1.46230i	−0.324170	−	0.945999i	$-0.605085\pi$
$743$	14.5077	−	39.8595i	0.532235	−	1.46230i	0.856405	−	0.516305i	$-0.172693\pi$
$744$	1.77197	−	1.48686i	0.0649635	−	0.0545108i
$745$	5.76354	−	0.220690i	0.211160	−	0.00808547i
$746$			26.2336i			0.960479i
$747$	−7.51144	+	1.32447i	−0.274829	+	0.0484598i
$748$	0.356708	−	0.617837i	0.0130425	−	0.0225904i
$749$	−2.02544	−	1.69954i	−0.0740079	−	0.0621000i
$750$	1.35708	+	11.7676i	0.0495534	+	0.429690i
$751$	13.4911	−	23.3673i	0.492297	−	0.852683i	−0.507664	−	0.861555i	$-0.669491\pi$
$751$	13.4911	−	23.3673i	0.492297	−	0.852683i	0.999961	+	0.00887216i	$0.00282413\pi$
$752$	−1.67304	−	4.59665i	−0.0610097	−	0.167623i
$753$	4.20949	−	3.53218i	0.153402	−	0.128720i
$754$	−2.84327	+	1.64156i	−0.103546	+	0.0597822i
$755$	47.4176	+	15.2307i	1.72570	+	0.554301i
$756$	0.967560	−	5.48730i	0.0351898	−	0.199571i
$757$	−26.1873	−	21.9738i	−0.951795	−	0.798651i	0.0278040	−	0.999613i	$-0.491149\pi$
$757$	−26.1873	−	21.9738i	−0.951795	−	0.798651i	−0.979599	+	0.200963i	$0.935593\pi$
$758$	4.69149	+	1.70756i	0.170403	+	0.0620215i
$759$	−1.47045	+	4.04003i	−0.0533740	+	0.146644i
$760$	−2.50326	−	2.76140i	−0.0908027	−	0.100167i
$761$	−2.73193	+	15.4935i	−0.0990322	+	0.561640i	0.894405	+	0.447259i	$0.147600\pi$
$761$	−2.73193	+	15.4935i	−0.0990322	+	0.561640i	−0.993437	+	0.114381i	$0.963511\pi$
$762$	3.26959	−	18.5428i	0.118445	−	0.671733i
$763$	4.91169	+	8.50730i	0.177815	+	0.307985i
$764$	−2.12199	−	2.52889i	−0.0767710	−	0.0914922i
$765$	0.724973	+	3.35517i	0.0262115	+	0.121306i
$766$	−16.1871	+	28.0369i	−0.584864	+	1.01301i
$767$	14.7015	−	8.48793i	0.530841	−	0.306481i
$768$	−0.681032	+	0.811623i	−0.0245746	+	0.0292869i
$769$	−20.7470	−	11.9783i	−0.748157	−	0.431949i	0.0768704	−	0.997041i	$-0.475507\pi$
$769$	−20.7470	−	11.9783i	−0.748157	−	0.431949i	−0.825028	+	0.565092i	$0.808841\pi$
$770$	0.0804917	+	2.10212i	0.00290072	+	0.0757550i
$771$		−	22.3775i		−	0.805906i
$772$	1.90145	+	10.7837i	0.0684346	+	0.388112i
$773$	−26.1595	−	31.1757i	−0.940892	−	1.12131i	−0.992451	−	0.122642i	$-0.960863\pi$
$773$	−26.1595	−	31.1757i	−0.940892	−	1.12131i	0.0515586	−	0.998670i	$-0.483581\pi$
$774$	−3.75734	−	1.36756i	−0.135055	−	0.0491559i
$775$	−0.834756	−	10.8842i	−0.0299853	−	0.390973i
$776$	11.0384			0.396255
$777$	5.07118	−	4.75079i	0.181927	−	0.170434i
$778$		−	19.1762i		−	0.687500i
$779$	0.946568	+	2.60067i	0.0339143	+	0.0931788i
$780$	3.23512	+	1.70620i	0.115836	+	0.0610919i
$781$	−7.25629	+	6.08875i	−0.259650	+	0.217873i
$782$	0.660327	+	3.74490i	0.0236132	+	0.133917i
$783$	−10.9897			−0.392739
$784$	1.01366	+	5.74873i	0.0362020	+	0.205312i
$785$	−8.80755	+	11.3517i	−0.314355	+	0.405159i
$786$	−5.62517	−	4.72007i	−0.200643	−	0.168359i
$787$	−28.3359	+	16.3598i	−1.01007	+	0.583162i	−0.911211	−	0.411940i	$-0.864851\pi$
$787$	−28.3359	+	16.3598i	−1.01007	+	0.583162i	−0.0988555	+	0.995102i	$0.531518\pi$
$788$	−16.4317	−	9.48684i	−0.585355	−	0.337955i
$789$	−30.1604	+	10.9775i	−1.07374	+	0.390809i
$790$	9.35177	−	5.88749i	0.332721	−	0.209467i
$791$	−9.19512	+	5.30881i	−0.326941	+	0.188759i
$792$	−0.284458	+	1.61324i	−0.0101078	+	0.0573241i
$793$	−2.89113	−	0.509784i	−0.102667	−	0.0181030i
$794$	−21.3490	+	25.4428i	−0.757649	+	0.902931i
$795$	−5.51098	+	10.4493i	−0.195454	+	0.370600i
$796$	3.11255	−	8.55167i	0.110322	−	0.303106i
$797$	12.3686	+	10.3785i	0.438118	+	0.367625i	0.835005	−	0.550243i	$-0.185465\pi$
$797$	12.3686	+	10.3785i	0.438118	+	0.367625i	−0.396886	+	0.917868i	$0.629909\pi$
$798$	−1.87524	−	0.330656i	−0.0663828	−	0.0117051i
$799$	3.93889	+	0.694533i	0.139348	+	0.0245708i
$800$	1.24224	+	4.84323i	0.0439197	+	0.171234i
$801$	−18.4881	−	22.0332i	−0.653243	−	0.778505i
$802$	2.31990	+	6.37388i	0.0819186	+	0.225070i
$803$	7.96269	+	4.59726i	0.280997	+	0.162234i
$804$	−3.09805	−	5.36598i	−0.109260	−	0.189243i
$805$	−7.53094	−	8.30755i	−0.265431	−	0.292803i
$806$	−2.91896	−	1.68526i	−0.102816	−	0.0593609i
$807$	−9.48918	+	1.67320i	−0.334035	+	0.0588994i
$808$	−2.57612			−0.0906277
$809$	−3.01409	+	0.531466i	−0.105970	+	0.0186853i	−0.226382	−	0.974039i	$-0.572690\pi$
$809$	−3.01409	+	0.531466i	−0.105970	+	0.0186853i	0.120412	+	0.992724i	$0.461579\pi$
$810$	−0.187343	−	0.297579i	−0.00658258	−	0.0104559i
$811$	16.3747	+	5.95991i	0.574994	+	0.209281i	0.613117	−	0.789992i	$-0.289916\pi$
$811$	16.3747	+	5.95991i	0.574994	+	0.209281i	−0.0381226	+	0.999273i	$0.512138\pi$
$812$	−2.15472	+	0.784252i	−0.0756157	+	0.0275219i
$813$			14.4517i			0.506844i
$814$	−3.87322	+	3.62852i	−0.135756	+	0.127179i
$815$	−0.920231	+	6.71160i	−0.0322343	+	0.235097i
$816$	−0.296291	−	0.814053i	−0.0103723	−	0.0284976i
$817$	−1.21413	+	3.33581i	−0.0424772	+	0.116705i
$818$	7.43101	+	8.85593i	0.259819	+	0.309640i
$819$	−3.07775	+	0.542690i	−0.107545	+	0.0189631i
$820$	0.504335	−	3.67831i	0.0176122	−	0.128452i
$821$	−0.251379	−	1.42564i	−0.00877319	−	0.0497553i	0.980107	−	0.198470i	$-0.0635974\pi$
$821$	−0.251379	−	1.42564i	−0.00877319	−	0.0497553i	−0.988880	+	0.148715i	$0.952486\pi$
$822$	−3.38730	+	5.86698i	−0.118146	+	0.204634i
$823$	11.0717	−	13.1948i	0.385936	−	0.459941i	−0.537742	−	0.843109i	$-0.680723\pi$
$823$	11.0717	−	13.1948i	0.385936	−	0.459941i	0.923679	+	0.383168i	$0.125167\pi$
$824$	−2.51846	−	4.36211i	−0.0877348	−	0.151961i
$825$	−3.23314	−	3.30323i	−0.112564	−	0.115004i
$826$	11.1413	−	4.05509i	0.387654	−	0.141095i
$827$	−3.68473	+	3.09185i	−0.128131	+	0.107514i	−0.704601	−	0.709604i	$-0.748874\pi$
$827$	−3.68473	+	3.09185i	−0.128131	+	0.107514i	0.576470	+	0.817118i	$0.304430\pi$
$828$	−4.36580	−	7.56178i	−0.151722	−	0.262790i
$829$	−15.9631	−	2.81473i	−0.554423	−	0.0977596i	−0.110585	−	0.993867i	$-0.535272\pi$
$829$	−15.9631	−	2.81473i	−0.554423	−	0.0977596i	−0.443838	+	0.896107i	$0.646383\pi$
$830$	2.77807	−	8.64896i	0.0964283	−	0.300210i
$831$	−16.3684	+	19.5071i	−0.567813	+	0.676693i
$832$	1.45072	+	0.528018i	0.0502945	+	0.0183057i
$833$	−4.48511	−	1.63244i	−0.155400	−	0.0565609i
$834$	−5.95415	+	7.09587i	−0.206175	+	0.245710i
$835$	0.600503	+	0.192883i	0.0207812	+	0.00667500i
$836$	1.43225	+	0.252545i	0.0495355	+	0.00873445i
$837$	−5.64113	−	9.77072i	−0.194986	−	0.337725i
$838$	−13.0900	+	10.9838i	−0.452186	+	0.379429i
$839$	−30.5392	+	11.1153i	−1.05433	+	0.383744i	−0.810295	−	0.586022i	$-0.800693\pi$
$839$	−30.5392	+	11.1153i	−1.05433	+	0.383744i	−0.244034	+	0.969767i	$0.578471\pi$
$840$	2.01822	+	1.56590i	0.0696352	+	0.0540286i
$841$	−12.2387	−	21.1981i	−0.422025	−	0.730969i
$842$	−1.45256	+	1.73109i	−0.0500585	+	0.0596575i
$843$	−4.96592	+	8.60123i	−0.171035	+	0.296242i
$844$	−2.61403	−	14.8249i	−0.0899785	−	0.510293i
$845$	−3.22476	+	23.5194i	−0.110935	+	0.809093i
$846$	−9.04438	+	1.59477i	−0.310952	+	0.0548293i
$847$	7.09620	+	8.45692i	0.243828	+	0.290583i
$848$	−1.70548	+	4.68576i	−0.0585663	+	0.160910i
$849$	3.96877	+	10.9041i	0.136208	+	0.374228i
$850$	−3.93737	−	1.10039i	−0.135051	−	0.0377432i
$851$	3.38304	−	28.0863i	0.115969	−	0.962787i
$852$			11.5023i			0.394062i
$853$	−24.4129	+	8.88557i	−0.835881	+	0.304236i	−0.724270	−	0.689516i	$-0.757823\pi$
$853$	−24.4129	+	8.88557i	−0.835881	+	0.304236i	−0.111611	+	0.993752i	$0.535601\pi$
$854$	−1.92672	−	0.701269i	−0.0659310	−	0.0239969i
$855$	−5.92178	+	3.72811i	−0.202521	+	0.127499i
$856$	2.41492	−	0.425816i	0.0825403	−	0.0145541i
$857$	−34.7901			−1.18841			−0.594204	−	0.804314i	$-0.702533\pi$
$857$	−34.7901			−1.18841			−0.594204	+	0.804314i	$0.702533\pi$
$858$	−1.40548	+	0.247824i	−0.0479823	+	0.00846058i
$859$	−46.6988	−	26.9616i	−1.59334	−	0.919917i	−0.992728	−	0.120379i	$-0.961589\pi$
$859$	−46.6988	−	26.9616i	−1.59334	−	0.919917i	−0.600615	−	0.799538i	$-0.705078\pi$
$860$	3.52826	−	3.19843i	0.120313	−	0.109066i
$861$	−0.948400	−	1.64268i	−0.0323214	−	0.0559823i
$862$	12.4755	+	7.20271i	0.424916	+	0.245325i
$863$	−17.7620	−	48.8008i	−0.604627	−	1.66120i	−0.741776	−	0.670648i	$-0.766016\pi$
$863$	−17.7620	−	48.8008i	−0.604627	−	1.66120i	0.137149	−	0.990550i	$-0.456206\pi$
$864$	3.32171	+	3.95866i	0.113007	+	0.134676i
$865$	14.3299	+	35.1268i	0.487230	+	1.19435i
$866$	−9.92854	−	1.75067i	−0.337385	−	0.0594902i
$867$	−17.0403	−	3.00466i	−0.578718	−	0.102044i
$868$	−1.80330	−	1.51315i	−0.0612081	−	0.0513597i
$869$	−1.47480	+	4.05198i	−0.0500292	+	0.137454i
$870$	2.35031	−	4.45641i	0.0796830	−	0.151086i
$871$	−5.80340	+	6.91622i	−0.196641	+	0.234347i
$872$	−8.97221	−	1.58204i	−0.303837	−	0.0535747i
$873$	3.59871	−	20.4093i	0.121798	−	0.690751i
$874$	−6.71343	+	3.87600i	−0.227085	+	0.131108i
$875$	11.5539	−	3.43964i	0.390593	−	0.116281i
$876$	10.4915	−	3.81860i	0.354476	−	0.129019i
$877$	3.13287	+	1.80876i	0.105790	+	0.0610776i	0.551961	−	0.833870i	$-0.313880\pi$
$877$	3.13287	+	1.80876i	0.105790	+	0.0610776i	−0.446172	+	0.894947i	$0.647213\pi$
$878$	8.05186	−	4.64874i	0.271737	−	0.156887i
$879$	2.95342	+	2.47821i	0.0996163	+	0.0835880i
$880$	−1.54146	−	1.19599i	−0.0519625	−	0.0403167i
$881$	8.69325	+	49.3019i	0.292883	+	1.66102i	0.675684	+	0.737191i	$0.263848\pi$
$881$	8.69325	+	49.3019i	0.292883	+	1.66102i	−0.382801	+	0.923831i	$0.625041\pi$
$882$	10.9595			0.369026
$883$	−2.65222	−	15.0415i	−0.0892542	−	0.506186i	−0.996357	−	0.0852772i	$-0.972822\pi$
$883$	−2.65222	−	15.0415i	−0.0892542	−	0.506186i	0.907103	−	0.420909i	$-0.138289\pi$
$884$	−0.966979	+	0.811392i	−0.0325230	+	0.0272901i
$885$	−12.1526	+	23.0425i	−0.408506	+	0.774565i
$886$	−12.2221	−	33.5801i	−0.410611	−	1.12814i
$887$			23.5038i			0.789181i	0.918857	+	0.394591i	$0.129114\pi$
$887$			23.5038i			0.789181i	−0.918857	+	0.394591i	$0.870886\pi$
$888$	0.352084	+	6.43505i	0.0118152	+	0.215946i
$889$	−19.1618			−0.642666
$890$	33.4833	−	7.23496i	1.12236	−	0.242516i
$891$	0.128937	+	0.0469291i	0.00431954	+	0.00157218i
$892$	−13.9732	−	16.6526i	−0.467857	−	0.557570i
$893$	1.41585	+	8.02970i	0.0473797	+	0.268704i
$894$			2.73289i			0.0914016i
$895$	−1.23008	−	32.1246i	−0.0411169	−	1.07381i
$896$	0.933779	+	0.539117i	0.0311954	+	0.0180106i
$897$	4.88975	−	5.82737i	0.163264	−	0.194570i
$898$	−15.9644	+	9.21706i	−0.532739	+	0.307577i
$899$	−2.32147	+	4.02090i	−0.0774252	+	0.134104i
$900$	9.35983	−	0.717843i	0.311994	−	0.0239281i
$901$	−2.62077	−	3.12331i	−0.0873104	−	0.104052i
$902$	0.724360	+	1.25463i	0.0241186	+	0.0417746i
$903$	0.422481	−	2.39601i	0.0140593	−	0.0797341i
$904$	1.70995	−	9.69762i	0.0568722	−	0.322538i
$905$	25.5836	−	23.1919i	0.850427	−	0.770926i
$906$	−8.07101	+	22.1749i	−0.268141	+	0.736712i
$907$	−7.86850	−	2.86390i	−0.261269	−	0.0950942i	0.208064	−	0.978115i	$-0.433284\pi$
$907$	−7.86850	−	2.86390i	−0.261269	−	0.0950942i	−0.469334	+	0.883021i	$0.655506\pi$
$908$	9.72456	+	8.15987i	0.322721	+	0.270795i
$909$	−0.839862	+	4.76310i	−0.0278565	+	0.157982i
$910$	1.13829	−	3.54384i	0.0377340	−	0.117477i
$911$	45.8295	−	26.4597i	1.51840	−	0.876648i	0.518633	−	0.854997i	$-0.326441\pi$
$911$	45.8295	−	26.4597i	1.51840	−	0.876648i	0.999766	−	0.0216508i	$-0.00689220\pi$
$912$	1.35284	−	1.13517i	0.0447970	−	0.0375891i
$913$	1.21235	+	3.33091i	0.0401230	+	0.110237i
$914$	−16.8623	+	29.2064i	−0.557756	+	0.966061i
$915$	4.17136	−	1.70169i	0.137901	−	0.0562561i
$916$	−7.71182	−	6.47099i	−0.254806	−	0.213807i
$917$	−3.73650	+	6.47180i	−0.123390	+	0.213718i
$918$	−4.16114	+	0.733721i	−0.137338	+	0.0242164i
$919$			25.9125i			0.854773i	0.904069	+	0.427387i	$0.140566\pi$
$919$			25.9125i			0.854773i	−0.904069	+	0.427387i	$0.859434\pi$
$920$	10.3918	−	0.397908i	0.342606	−	0.0131187i
$921$	−0.686752	+	0.576253i	−0.0226292	+	0.0189882i
$922$	−10.3999	+	28.5735i	−0.342503	+	0.941019i
$923$	15.7495	−	5.73235i	0.518401	−	0.188682i
$924$	−0.996759			−0.0327910
$925$	25.6557	+	16.3335i	0.843554	+	0.537044i
$926$	33.3861			1.09713
$927$	−8.88634	+	3.23436i	−0.291866	+	0.106230i
$928$	0.727348	−	1.99837i	0.0238764	−	0.0655998i
$929$	−6.55154	+	5.49740i	−0.214949	+	0.180364i	−0.743905	−	0.668286i	$-0.767028\pi$
$929$	−6.55154	+	5.49740i	−0.214949	+	0.180364i	0.528955	+	0.848650i	$0.322584\pi$
$930$	5.16855	−	0.197908i	0.169483	−	0.00648965i
$931$		−	9.72999i		−	0.318887i
$932$	−7.55181	+	1.33159i	−0.247368	+	0.0436176i
$933$	−6.92261	+	11.9903i	−0.226636	+	0.392545i
$934$	−15.2332	−	12.7822i	−0.498445	−	0.418245i
$935$	1.47707	−	0.602565i	0.0483053	−	0.0197060i
$936$	1.44923	−	2.51014i	0.0473696	−	0.0820466i
$937$	11.6912	+	32.1214i	0.381936	+	1.04936i	0.970540	+	0.240940i	$0.0774556\pi$
$937$	11.6912	+	32.1214i	0.381936	+	1.04936i	−0.588604	+	0.808422i	$0.700322\pi$
$938$	−4.83042	+	4.05321i	−0.157719	+	0.132342i
$939$	−5.35548	+	3.09199i	−0.174769	+	0.100903i
$940$	3.34502	−	10.4140i	0.109103	−	0.339669i
$941$	−5.69881	+	32.3196i	−0.185776	+	1.05359i	0.739178	+	0.673510i	$0.235214\pi$
$941$	−5.69881	+	32.3196i	−0.185776	+	1.05359i	−0.924954	+	0.380078i	$0.875897\pi$
$942$	−5.21506	−	4.37596i	−0.169916	−	0.142576i
$943$	−7.25631	−	2.64108i	−0.236298	−	0.0860054i
$944$	−3.76086	+	10.3329i	−0.122405	+	0.336306i
$945$	9.23093	−	8.36799i	0.300282	−	0.272211i
$946$	−0.322678	+	1.83000i	−0.0104912	+	0.0594984i
$947$	5.11925	−	29.0327i	0.166353	−	0.943436i	−0.781305	−	0.624150i	$-0.785446\pi$
$947$	5.11925	−	29.0327i	0.166353	−	0.943436i	0.947658	−	0.319287i	$-0.103443\pi$
$948$	2.61803	+	4.53457i	0.0850298	+	0.147276i
$949$	−10.4572	−	12.4624i	−0.339456	−	0.404548i
$950$	−0.637309	−	8.30976i	−0.0206770	−	0.269604i
$951$	9.89708	−	17.1422i	0.320935	−	0.555875i
$952$	−0.763503	+	0.440809i	−0.0247453	+	0.0142867i
$953$	−13.1824	+	15.7102i	−0.427020	+	0.508902i	−0.936060	−	0.351841i	$-0.885556\pi$
$953$	−13.1824	+	15.7102i	−0.427020	+	0.508902i	0.509040	+	0.860743i	$0.330000\pi$
$954$	8.10767	+	4.68097i	0.262496	+	0.151552i
$955$	−0.282448	−	7.37638i	−0.00913979	−	0.238694i
$956$			6.59335i			0.213244i
$957$	0.341380	+	1.93606i	0.0110352	+	0.0625840i
$958$	−13.9321	−	16.6037i	−0.450127	−	0.536441i
$959$	6.47862	+	2.35803i	0.209206	+	0.0761446i
$960$	−2.31567	+	0.500362i	−0.0747379	+	0.0161491i
$961$	26.2335			0.846241
$962$	8.63572	−	3.68910i	0.278427	−	0.118941i
$963$		−	4.60387i		−	0.148358i
$964$	9.22443	+	25.3439i	0.297099	+	0.816272i
$965$	−11.4222	+	21.6575i	−0.367693	+	0.697180i
$966$	4.06995	−	3.41510i	0.130949	−	0.109879i
$967$	2.60568	+	14.7775i	0.0837930	+	0.475214i	0.997611	+	0.0690888i	$0.0220092\pi$
$967$	2.60568	+	14.7775i	0.0837930	+	0.475214i	−0.913817	+	0.406125i	$0.866880\pi$
$968$	−10.2387			−0.329084
$969$	0.250743	+	1.42204i	0.00805503	+	0.0456824i
$970$	19.5012	+	15.1306i	0.626145	+	0.485813i
$971$	−7.81074	−	6.55399i	−0.250659	−	0.210327i	0.508797	−	0.860886i	$-0.330090\pi$
$971$	−7.81074	−	6.55399i	−0.250659	−	0.210327i	−0.759456	+	0.650559i	$0.774535\pi$
$972$	13.5703	−	7.83480i	0.435267	−	0.251301i
$973$	8.16386	+	4.71341i	0.261721	+	0.151105i
$974$	34.3382	−	12.4981i	1.10027	−	0.400464i
$975$	3.37666	+	7.44876i	0.108140	+	0.238551i
$976$	1.64684	−	0.950801i	0.0527139	−	0.0304344i
$977$	3.07787	−	17.4554i	0.0984697	−	0.558449i	−0.895159	−	0.445747i	$-0.852938\pi$
$977$	3.07787	−	17.4554i	0.0984697	−	0.558449i	0.993629	−	0.112703i	$-0.0359507\pi$
$978$	−3.16109	−	0.557386i	−0.101081	−	0.0178232i
$979$	−8.59204	+	10.2396i	−0.274603	+	0.327259i
$980$	−6.08912	+	11.5455i	−0.194510	+	0.368809i
$981$	−5.85020	+	16.0733i	−0.186783	+	0.513181i
$982$	−18.2671	−	15.3279i	−0.582927	−	0.489134i
$983$	22.5758	+	3.98072i	0.720056	+	0.126965i	0.521656	−	0.853156i	$-0.325314\pi$
$983$	22.5758	+	3.98072i	0.720056	+	0.126965i	0.198400	+	0.980121i	$0.436425\pi$
$984$	1.73245	+	0.305477i	0.0552284	+	0.00973825i
$985$	−16.0255	−	39.2834i	−0.510616	−	1.25167i
$986$	1.11770	+	1.33202i	0.0355948	+	0.0424202i
$987$	−1.91127	−	5.25116i	−0.0608363	−	0.167146i
$988$	−2.22853	−	1.28664i	−0.0708991	−	0.0409336i
$989$	−4.95239	−	8.57779i	−0.157477	−	0.272758i
$990$	−2.71385	+	2.46015i	−0.0862519	+	0.0781887i
$991$	37.5341	+	21.6703i	1.19231	+	0.688380i	0.958830	−	0.283982i	$-0.0916556\pi$
$991$	37.5341	+	21.6703i	1.19231	+	0.688380i	0.233479	+	0.972362i	$0.424989\pi$
$992$	2.15007	−	0.379116i	0.0682649	−	0.0120369i
$993$	8.13750			0.258236
$994$	11.5279	−	2.03267i	0.365642	−	0.0644725i
$995$	17.2208	−	10.8415i	0.545937	−	0.343699i
$996$	4.04470	+	1.47215i	0.128161	+	0.0466469i
$997$	23.0591	−	8.39284i	0.730290	−	0.265804i	0.0500023	−	0.998749i	$-0.484077\pi$
$997$	23.0591	−	8.39284i	0.730290	−	0.265804i	0.680288	+	0.732945i	$0.261855\pi$
$998$			37.9114i			1.20006i
$999$	31.2081	+	3.75906i	0.987381	+	0.118931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.v.a.289.6	yes	60
5.4	even	2		370.2.v.b.289.5	yes	60
37.21	even	18		370.2.v.b.169.5	yes	60
185.169	even	18	inner	370.2.v.a.169.6	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.v.a.169.6	✓	60	185.169	even	18	inner
370.2.v.a.289.6	yes	60	1.1	even	1	trivial
370.2.v.b.169.5	yes	60	37.21	even	18
370.2.v.b.289.5	yes	60	5.4	even	2

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(0.362370 - 0.995603i) q^{3} +(0.766044 - 0.642788i) q^{4} +(2.23443 - 0.0855581i) q^{5} +1.05950i q^{6} +(1.06185 - 0.187234i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.43822 + 1.20681i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(0.362370 - 0.995603i) q^{3} +(0.766044 - 0.642788i) q^{4} +(2.23443 - 0.0855581i) q^{5} +1.05950i q^{6} +(1.06185 - 0.187234i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.43822 + 1.20681i) q^{9} +(-2.07042 + 0.844619i) q^{10} +(0.436261 - 0.755627i) q^{11} +(-0.362370 - 0.995603i) q^{12} +(-1.18263 + 0.992348i) q^{13} +(-0.933779 + 0.539117i) q^{14} +(0.724508 - 2.25561i) q^{15} +(0.173648 - 0.984808i) q^{16} +(0.626355 + 0.525574i) q^{17} +(-1.76424 - 0.642130i) q^{18} +(-0.570090 + 1.56631i) q^{19} +(1.65668 - 1.50181i) q^{20} +(0.198374 - 1.12503i) q^{21} +(-0.151512 + 0.859267i) q^{22} +(-2.32537 - 4.02766i) q^{23} +(0.681032 + 0.811623i) q^{24} +(4.98536 - 0.382347i) q^{25} +(0.771910 - 1.33699i) q^{26} +(4.47533 - 2.58383i) q^{27} +(0.693076 - 0.825976i) q^{28} +(-1.84171 - 1.06331i) q^{29} +(0.0906487 + 2.36738i) q^{30} -2.18324i q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.594216 - 0.708159i) q^{33} +(-0.768338 - 0.279652i) q^{34} +(2.35662 - 0.509210i) q^{35} +1.87746 q^{36} +(4.86631 + 3.64952i) q^{37} -1.66683i q^{38} +(0.559434 + 1.53703i) q^{39} +(-1.04312 + 1.97785i) q^{40} +(1.27193 - 1.06727i) q^{41} +(0.198374 + 1.12503i) q^{42} +2.12972 q^{43} +(-0.151512 - 0.859267i) q^{44} +(3.31686 + 2.57348i) q^{45} +(3.56267 + 2.98944i) q^{46} +(4.23630 - 2.44583i) q^{47} +(-0.917552 - 0.529749i) q^{48} +(-5.48537 + 1.99651i) q^{49} +(-4.55394 + 2.06438i) q^{50} +(0.750235 - 0.433149i) q^{51} +(-0.268082 + 1.52037i) q^{52} +(-4.91073 - 0.865893i) q^{53} +(-3.32171 + 3.95866i) q^{54} +(0.910145 - 1.72572i) q^{55} +(-0.368778 + 1.01321i) q^{56} +(1.35284 + 1.13517i) q^{57} +(2.09432 + 0.369284i) q^{58} +(-10.8290 - 1.90944i) q^{59} +(-0.894872 - 2.19360i) q^{60} +(1.22233 + 1.45671i) q^{61} +(0.746712 + 2.05157i) q^{62} +(1.75314 + 1.01217i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.55761 + 2.31852i) q^{65} +(0.800585 + 0.462218i) q^{66} +(5.75930 - 1.01552i) q^{67} +0.817648 q^{68} +(-4.85259 + 0.855643i) q^{69} +(-2.04034 + 1.28451i) q^{70} +(-10.2016 - 3.71309i) q^{71} +(-1.76424 + 0.642130i) q^{72} +10.5379i q^{73} +(-5.82105 - 1.76505i) q^{74} +(1.42588 - 5.10199i) q^{75} +(0.570090 + 1.56631i) q^{76} +(0.321767 - 0.884048i) q^{77} +(-1.05139 - 1.25300i) q^{78} +(-4.86694 + 0.858174i) q^{79} +(0.303747 - 2.21534i) q^{80} +(0.0273076 + 0.154869i) q^{81} +(-0.830191 + 1.43793i) q^{82} +(-2.61137 + 3.11211i) q^{83} +(-0.571194 - 0.989337i) q^{84} +(1.44451 + 1.12077i) q^{85} +(-2.00128 + 0.728408i) q^{86} +(-1.72602 + 1.44830i) q^{87} +(0.436261 + 0.755627i) q^{88} +(-15.0870 - 2.66025i) q^{89} +(-3.99701 - 1.28385i) q^{90} +(-1.06998 + 1.27516i) q^{91} +(-4.37026 - 1.59065i) q^{92} +(-2.17364 - 0.791140i) q^{93} +(-3.14430 + 3.74723i) q^{94} +(-1.13982 + 3.54859i) q^{95} +(1.04340 + 0.183980i) q^{96} +(-5.51919 - 9.55952i) q^{97} +(4.47172 - 3.75221i) q^{98} +(1.53934 - 0.560273i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{5} - 30 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q - 3 * q^5 - 30 * q^8 - 6 * q^9	\( 60 q - 3 q^{5} - 30 q^{8} - 6 q^{9} + 9 q^{10} + 6 q^{11} - 3 q^{13} + 9 q^{14} + 18 q^{15} + 3 q^{17} + 12 q^{18} + 3 q^{19} - 6 q^{20} + 12 q^{21} - 3 q^{22} - 18 q^{23} - 15 q^{25} - 27 q^{26} + 6 q^{30} - 66 q^{33} + 21 q^{34} - 3 q^{35} - 72 q^{36} + 6 q^{37} + 12 q^{39} + 6 q^{40} - 57 q^{41} + 12 q^{42} + 60 q^{43} - 3 q^{44} + 45 q^{45} - 21 q^{46} - 18 q^{47} - 6 q^{49} + 36 q^{50} - 3 q^{52} - 6 q^{53} + 3 q^{55} + 30 q^{57} + 15 q^{58} - 12 q^{59} + 9 q^{60} + 42 q^{61} - 12 q^{62} - 9 q^{63} - 30 q^{64} - 30 q^{65} - 18 q^{67} - 24 q^{68} + 36 q^{69} + 18 q^{71} + 12 q^{72} + 3 q^{74} - 78 q^{75} - 3 q^{76} + 21 q^{77} + 6 q^{78} - 24 q^{79} - 36 q^{81} + 27 q^{82} + 30 q^{83} + 12 q^{84} + 33 q^{85} - 18 q^{86} - 30 q^{87} + 6 q^{88} + 3 q^{89} - 3 q^{90} + 57 q^{91} + 15 q^{92} + 60 q^{93} + 3 q^{94} - 150 q^{95} + 84 q^{97} - 6 q^{98} - 45 q^{99}+O(q^{100}) \) 60 * q - 3 * q^5 - 30 * q^8 - 6 * q^9 + 9 * q^10 + 6 * q^11 - 3 * q^13 + 9 * q^14 + 18 * q^15 + 3 * q^17 + 12 * q^18 + 3 * q^19 - 6 * q^20 + 12 * q^21 - 3 * q^22 - 18 * q^23 - 15 * q^25 - 27 * q^26 + 6 * q^30 - 66 * q^33 + 21 * q^34 - 3 * q^35 - 72 * q^36 + 6 * q^37 + 12 * q^39 + 6 * q^40 - 57 * q^41 + 12 * q^42 + 60 * q^43 - 3 * q^44 + 45 * q^45 - 21 * q^46 - 18 * q^47 - 6 * q^49 + 36 * q^50 - 3 * q^52 - 6 * q^53 + 3 * q^55 + 30 * q^57 + 15 * q^58 - 12 * q^59 + 9 * q^60 + 42 * q^61 - 12 * q^62 - 9 * q^63 - 30 * q^64 - 30 * q^65 - 18 * q^67 - 24 * q^68 + 36 * q^69 + 18 * q^71 + 12 * q^72 + 3 * q^74 - 78 * q^75 - 3 * q^76 + 21 * q^77 + 6 * q^78 - 24 * q^79 - 36 * q^81 + 27 * q^82 + 30 * q^83 + 12 * q^84 + 33 * q^85 - 18 * q^86 - 30 * q^87 + 6 * q^88 + 3 * q^89 - 3 * q^90 + 57 * q^91 + 15 * q^92 + 60 * q^93 + 3 * q^94 - 150 * q^95 + 84 * q^97 - 6 * q^98 - 45 * q^99

Introduction

L-functions

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