LMFDB - Embedded newform 637.2.f.l.295.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(295,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("637.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 8x^{14} + 45x^{12} + 124x^{10} + 248x^{8} + 250x^{6} + 177x^{4} + 14x^{2} + 1 $ x^16 + 8x^14 + 45x^12 + 124x^10 + 248x^8 + 250x^6 + 177x^4 + 14*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.7
Root			$-0.558788 - 0.967849i$ of defining polynomial
Character	$\chi$	$=$	637.295
Dual form			637.2.f.l.393.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16576 - 2.01915i) q^{2} +(-1.15450 + 1.99966i) q^{3} +(-1.71798 - 2.97563i) q^{4} +3.37112 q^{5} +(2.69174 + 4.66224i) q^{6} -3.34797 q^{8} +(-1.16576 - 2.01915i) q^{9} +O(q^{10})$	\(q+(1.16576 - 2.01915i) q^{2} +(-1.15450 + 1.99966i) q^{3} +(-1.71798 - 2.97563i) q^{4} +3.37112 q^{5} +(2.69174 + 4.66224i) q^{6} -3.34797 q^{8} +(-1.16576 - 2.01915i) q^{9} +(3.92990 - 6.80679i) q^{10} +(-1.16576 + 2.01915i) q^{11} +7.93366 q^{12} +(0.408029 - 3.58239i) q^{13} +(-3.89197 + 6.74108i) q^{15} +(-0.466957 + 0.808794i) q^{16} +(2.72867 + 4.72620i) q^{17} -5.43596 q^{18} +(3.58410 + 6.20784i) q^{19} +(-5.79151 - 10.0312i) q^{20} +(2.71798 + 4.70768i) q^{22} +(3.22621 - 5.58796i) q^{23} +(3.86524 - 6.69480i) q^{24} +6.36442 q^{25} +(-6.75772 - 5.00007i) q^{26} -1.54354 q^{27} +(4.22143 - 7.31174i) q^{29} +(9.07418 + 15.7169i) q^{30} -3.05121 q^{31} +(-2.25925 - 3.91314i) q^{32} +(-2.69174 - 4.66224i) q^{33} +12.7239 q^{34} +(-4.00550 + 6.93773i) q^{36} +(-1.52827 + 2.64704i) q^{37} +16.7127 q^{38} +(6.69249 + 4.95180i) q^{39} -11.2864 q^{40} +(0.468833 - 0.812043i) q^{41} +(2.04605 + 3.54385i) q^{43} +8.01100 q^{44} +(-3.92990 - 6.80679i) q^{45} +(-7.52195 - 13.0284i) q^{46} -3.46336 q^{47} +(-1.07821 - 1.86751i) q^{48} +(7.41937 - 12.8507i) q^{50} -12.6010 q^{51} +(-11.3609 + 4.94034i) q^{52} -2.34387 q^{53} +(-1.79939 + 3.11663i) q^{54} +(-3.92990 + 6.80679i) q^{55} -16.5514 q^{57} +(-9.84233 - 17.0474i) q^{58} +(-3.62346 - 6.27602i) q^{59} +26.7453 q^{60} +(-3.19506 - 5.53401i) q^{61} +(-3.55697 + 6.16085i) q^{62} -12.4028 q^{64} +(1.37551 - 12.0766i) q^{65} -12.5517 q^{66} +(-2.30670 + 3.99532i) q^{67} +(9.37561 - 16.2390i) q^{68} +(7.44934 + 12.9026i) q^{69} +(3.79370 + 6.57088i) q^{71} +(3.90292 + 6.76006i) q^{72} -2.06996 q^{73} +(3.56318 + 6.17161i) q^{74} +(-7.34775 + 12.7267i) q^{75} +(12.3148 - 21.3299i) q^{76} +(17.8002 - 7.74054i) q^{78} -7.58868 q^{79} +(-1.57417 + 2.72654i) q^{80} +(5.27929 - 9.14400i) q^{81} +(-1.09309 - 1.89329i) q^{82} -2.89335 q^{83} +(9.19866 + 15.9326i) q^{85} +9.54077 q^{86} +(9.74732 + 16.8829i) q^{87} +(3.90292 - 6.76006i) q^{88} +(-6.57984 + 11.3966i) q^{89} -18.3253 q^{90} -22.1703 q^{92} +(3.52263 - 6.10138i) q^{93} +(-4.03744 + 6.99305i) q^{94} +(12.0824 + 20.9273i) q^{95} +10.4333 q^{96} +(1.77856 + 3.08056i) q^{97} +5.43596 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 - 4 * q^9	$ 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} - 4 q^{16} - 56 q^{18} + 28 q^{22} + 12 q^{23} - 24 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} - 8 q^{37} - 4 q^{39} + 32 q^{43} - 8 q^{44} - 4 q^{46} + 36 q^{50} - 88 q^{51} - 8 q^{53} - 96 q^{57} - 48 q^{58} + 128 q^{60} - 64 q^{64} + 16 q^{65} + 20 q^{67} + 8 q^{71} + 28 q^{72} + 76 q^{74} + 28 q^{78} - 8 q^{79} + 56 q^{81} + 36 q^{85} + 8 q^{86} + 28 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 - 4 * q^9 - 4 * q^11 - 8 * q^15 - 4 * q^16 - 56 * q^18 + 28 * q^22 + 12 * q^23 - 24 * q^25 + 8 * q^29 + 28 * q^30 + 4 * q^36 - 8 * q^37 - 4 * q^39 + 32 * q^43 - 8 * q^44 - 4 * q^46 + 36 * q^50 - 88 * q^51 - 8 * q^53 - 96 * q^57 - 48 * q^58 + 128 * q^60 - 64 * q^64 + 16 * q^65 + 20 * q^67 + 8 * q^71 + 28 * q^72 + 76 * q^74 + 28 * q^78 - 8 * q^79 + 56 * q^81 + 36 * q^85 + 8 * q^86 + 28 * q^88 - 160 * q^92 + 8 * q^93 + 52 * q^95 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.16576	−	2.01915i	0.824315	−	1.42776i	−0.0781266	−	0.996943i	$-0.524894\pi$
$2$	1.16576	−	2.01915i	0.824315	−	1.42776i	0.902442	−	0.430812i	$-0.141773\pi$
$3$	−1.15450	+	1.99966i	−0.666553	+	1.15450i	0.312309	+	0.949981i	$0.398898\pi$
$3$	−1.15450	+	1.99966i	−0.666553	+	1.15450i	−0.978862	+	0.204523i	$0.934436\pi$
$4$	−1.71798	−	2.97563i	−0.858991	−	1.48782i
$5$	3.37112			1.50761			0.753804	−	0.657099i	$-0.228217\pi$
$5$	3.37112			1.50761			0.753804	+	0.657099i	$0.228217\pi$
$6$	2.69174	+	4.66224i	1.09890	+	1.90335i
$7$		0			0
$7$		0			0
$8$	−3.34797			−1.18369
$9$	−1.16576	−	2.01915i	−0.388586	−	0.673050i
$10$	3.92990	−	6.80679i	1.24274	−	2.15250i
$11$	−1.16576	+	2.01915i	−0.351489	+	0.608797i	−0.986511	−	0.163697i	$-0.947658\pi$
$11$	−1.16576	+	2.01915i	−0.351489	+	0.608797i	0.635021	+	0.772494i	$0.280991\pi$
$12$	7.93366			2.29025
$13$	0.408029	−	3.58239i	0.113167	−	0.993576i
$13$	0.408029	−	3.58239i	0.113167	−	0.993576i
$14$		0			0
$15$	−3.89197	+	6.74108i	−1.00490	+	1.74054i
$16$	−0.466957	+	0.808794i	−0.116739	+	0.202198i
$17$	2.72867	+	4.72620i	0.661800	+	1.14627i	0.980142	+	0.198295i	$0.0635405\pi$
$17$	2.72867	+	4.72620i	0.661800	+	1.14627i	−0.318343	+	0.947976i	$0.603126\pi$
$18$	−5.43596			−1.28127
$19$	3.58410	+	6.20784i	0.822248	+	1.42418i	0.904004	+	0.427523i	$0.140614\pi$
$19$	3.58410	+	6.20784i	0.822248	+	1.42418i	−0.0817564	+	0.996652i	$0.526053\pi$
$20$	−5.79151	−	10.0312i	−1.29502	−	2.24304i
$21$		0			0
$22$	2.71798	+	4.70768i	0.579476	+	1.00368i
$23$	3.22621	−	5.58796i	0.672711	−	1.16517i	−0.304421	−	0.952537i	$-0.598463\pi$
$23$	3.22621	−	5.58796i	0.672711	−	1.16517i	0.977132	−	0.212632i	$-0.0682036\pi$
$24$	3.86524	−	6.69480i	0.788989	−	1.36657i
$25$	6.36442			1.27288
$26$	−6.75772	−	5.00007i	−1.32530	−	0.980594i
$27$	−1.54354			−0.297054
$28$		0			0
$29$	4.22143	−	7.31174i	0.783900	−	1.35776i	−0.145753	−	0.989321i	$-0.546561\pi$
$29$	4.22143	−	7.31174i	0.783900	−	1.35776i	0.929654	−	0.368434i	$-0.120106\pi$
$30$	9.07418	+	15.7169i	1.65671	+	2.86951i
$31$	−3.05121			−0.548013			−0.274007	−	0.961728i	$-0.588349\pi$
$31$	−3.05121			−0.548013			−0.274007	+	0.961728i	$0.588349\pi$
$32$	−2.25925	−	3.91314i	−0.399383	−	0.691752i
$33$	−2.69174	−	4.66224i	−0.468572	−	0.811591i
$34$	12.7239			2.18213
$35$		0			0
$36$	−4.00550	+	6.93773i	−0.667583	+	1.15629i
$37$	−1.52827	+	2.64704i	−0.251246	+	0.435170i	−0.963869	−	0.266377i	$-0.914174\pi$
$37$	−1.52827	+	2.64704i	−0.251246	+	0.435170i	0.712623	+	0.701547i	$0.247507\pi$
$38$	16.7127			2.71117
$39$	6.69249	+	4.95180i	1.07166	+	0.792923i
$40$	−11.2864			−1.78454
$41$	0.468833	−	0.812043i	0.0732194	−	0.126820i	−0.827091	−	0.562068i	$-0.810006\pi$
$41$	0.468833	−	0.812043i	0.0732194	−	0.126820i	0.900311	+	0.435248i	$0.143339\pi$
$42$		0			0
$43$	2.04605	+	3.54385i	0.312019	+	0.540433i	0.978799	−	0.204822i	$-0.0656614\pi$
$43$	2.04605	+	3.54385i	0.312019	+	0.540433i	−0.666780	+	0.745254i	$0.732328\pi$
$44$	8.01100			1.20770
$45$	−3.92990	−	6.80679i	−0.585835	−	1.01470i
$46$	−7.52195	−	13.0284i	−1.10905	−	1.92093i
$47$	−3.46336			−0.505183			−0.252591	−	0.967573i	$-0.581283\pi$
$47$	−3.46336			−0.505183			−0.252591	+	0.967573i	$0.581283\pi$
$48$	−1.07821	−	1.86751i	−0.155626	−	0.269552i
$49$		0			0
$50$	7.41937	−	12.8507i	1.04926	−	1.81737i
$51$	−12.6010			−1.76450
$52$	−11.3609	+	4.94034i	−1.57547	+	0.685101i
$53$	−2.34387			−0.321956			−0.160978	−	0.986958i	$-0.551465\pi$
$53$	−2.34387			−0.321956			−0.160978	+	0.986958i	$0.551465\pi$
$54$	−1.79939	+	3.11663i	−0.244866	+	0.424120i
$55$	−3.92990	+	6.80679i	−0.529908	+	0.917828i
$56$		0			0
$57$	−16.5514			−2.19229
$58$	−9.84233	−	17.0474i	−1.29236	−	2.23844i
$59$	−3.62346	−	6.27602i	−0.471735	−	0.817069i	0.527742	−	0.849405i	$-0.323039\pi$
$59$	−3.62346	−	6.27602i	−0.471735	−	0.817069i	−0.999477	+	0.0323358i	$0.989705\pi$
$60$	26.7453			3.45280
$61$	−3.19506	−	5.53401i	−0.409086	−	0.708558i	0.585702	−	0.810527i	$-0.300819\pi$
$61$	−3.19506	−	5.53401i	−0.409086	−	0.708558i	−0.994788	+	0.101969i	$0.967486\pi$
$62$	−3.55697	+	6.16085i	−0.451736	+	0.782429i
$63$		0			0
$64$	−12.4028			−1.55035
$65$	1.37551	−	12.0766i	0.170611	−	1.49792i
$66$	−12.5517			−1.54500
$67$	−2.30670	+	3.99532i	−0.281808	+	0.488106i	−0.971830	−	0.235682i	$-0.924268\pi$
$67$	−2.30670	+	3.99532i	−0.281808	+	0.488106i	0.690022	+	0.723788i	$0.257601\pi$
$68$	9.37561	−	16.2390i	1.13696	−	1.96927i
$69$	7.44934	+	12.9026i	0.896795	+	1.55329i
$70$		0			0
$71$	3.79370	+	6.57088i	0.450229	+	0.779819i	0.998400	−	0.0565468i	$-0.0180090\pi$
$71$	3.79370	+	6.57088i	0.450229	+	0.779819i	−0.548171	+	0.836366i	$0.684676\pi$
$72$	3.90292	+	6.76006i	0.459964	+	0.796680i
$73$	−2.06996			−0.242271			−0.121136	−	0.992636i	$-0.538654\pi$
$73$	−2.06996			−0.242271			−0.121136	+	0.992636i	$0.538654\pi$
$74$	3.56318	+	6.17161i	0.414211	+	0.717435i
$75$	−7.34775	+	12.7267i	−0.848445	+	1.46955i
$76$	12.3148	−	21.3299i	1.41261	−	2.44671i
$77$		0			0
$78$	17.8002	−	7.74054i	2.01548	−	0.876444i
$79$	−7.58868			−0.853794			−0.426897	−	0.904300i	$-0.640393\pi$
$79$	−7.58868			−0.853794			−0.426897	+	0.904300i	$0.640393\pi$
$80$	−1.57417	+	2.72654i	−0.175997	+	0.304836i
$81$	5.27929	−	9.14400i	0.586588	−	1.01600i
$82$	−1.09309	−	1.89329i	−0.120712	−	0.209079i
$83$	−2.89335			−0.317587			−0.158793	−	0.987312i	$-0.550760\pi$
$83$	−2.89335			−0.317587			−0.158793	+	0.987312i	$0.550760\pi$
$84$		0			0
$85$	9.19866	+	15.9326i	0.997735	+	1.72813i
$86$	9.54077			1.02881
$87$	9.74732	+	16.8829i	1.04502	+	1.81003i
$88$	3.90292	−	6.76006i	0.416053	−	0.720624i
$89$	−6.57984	+	11.3966i	−0.697461	+	1.20804i	0.271882	+	0.962330i	$0.412354\pi$
$89$	−6.57984	+	11.3966i	−0.697461	+	1.20804i	−0.969344	+	0.245708i	$0.920980\pi$
$90$	−18.3253			−1.93165
$91$		0			0
$92$	−22.1703			−2.31141
$93$	3.52263	−	6.10138i	0.365280	−	0.632683i
$94$	−4.03744	+	6.99305i	−0.416430	+	0.721278i
$95$	12.0824	+	20.9273i	1.23963	+	2.14710i
$96$	10.4333			1.06484
$97$	1.77856	+	3.08056i	0.180585	+	0.312783i	0.942080	−	0.335388i	$-0.108867\pi$
$97$	1.77856	+	3.08056i	0.180585	+	0.312783i	−0.761495	+	0.648171i	$0.775534\pi$
$98$		0			0
$99$	5.43596			0.546335
$100$	−10.9340	−	18.9382i	−1.09340	−	1.89382i
$101$	−2.36432	+	4.09513i	−0.235259	+	0.407481i	−0.959348	−	0.282226i	$-0.908927\pi$
$101$	−2.36432	+	4.09513i	−0.235259	+	0.407481i	0.724089	+	0.689707i	$0.242260\pi$
$102$	−14.6898	+	25.4434i	−1.45450	+	2.51927i
$103$	−5.98286			−0.589508			−0.294754	−	0.955573i	$-0.595238\pi$
$103$	−5.98286			−0.589508			−0.294754	+	0.955573i	$0.595238\pi$
$104$	−1.36607	+	11.9937i	−0.133954	+	1.17608i
$105$		0			0
$106$	−2.73239	+	4.73263i	−0.265393	+	0.459674i
$107$	−6.59131	+	11.4165i	−0.637206	+	1.10367i	0.348837	+	0.937183i	$0.386577\pi$
$107$	−6.59131	+	11.4165i	−0.637206	+	1.10367i	−0.986043	+	0.166490i	$0.946757\pi$
$108$	2.65177	+	4.59300i	0.255166	+	0.441961i
$109$	4.11545			0.394188			0.197094	−	0.980385i	$-0.436850\pi$
$109$	4.11545			0.394188			0.197094	+	0.980385i	$0.436850\pi$
$110$	9.16263	+	15.8701i	0.873623	+	1.51316i
$111$	−3.52878	−	6.11203i	−0.334937	−	0.580128i
$112$		0			0
$113$	−7.14026	−	12.3673i	−0.671699	−	1.16342i	−0.977422	−	0.211297i	$-0.932231\pi$
$113$	−7.14026	−	12.3673i	−0.671699	−	1.16342i	0.305723	−	0.952121i	$-0.401102\pi$
$114$	−19.2949	+	33.4198i	−1.80714	+	3.13005i
$115$	10.8759	−	18.8376i	1.01418	−	1.75662i
$116$	−29.0094			−2.69345
$117$	−7.70905	+	3.35233i	−0.712702	+	0.309923i
$118$	−16.8963			−1.55543
$119$		0			0
$120$	13.0302	−	22.5689i	1.18949	−	2.06025i
$121$	2.78202	+	4.81860i	0.252911	+	0.438054i
$122$	−14.8987			−1.34886
$123$	1.08254	+	1.87501i	0.0976093	+	0.169064i
$124$	5.24192	+	9.07927i	0.470738	+	0.815343i
$125$	4.59963			0.411403
$126$		0			0
$127$	5.53854	−	9.59304i	0.491466	−	0.851244i	−0.508486	−	0.861071i	$-0.669794\pi$
$127$	5.53854	−	9.59304i	0.491466	−	0.851244i	0.999952	+	0.00982616i	$0.00312781\pi$
$128$	−9.94014	+	17.2168i	−0.878592	+	1.52177i
$129$	−9.44867			−0.831909
$130$	−22.7811	−	16.8558i	−1.99803	−	1.47835i
$131$	−0.672012			−0.0587139			−0.0293570	−	0.999569i	$-0.509346\pi$
$131$	−0.672012			−0.0587139			−0.0293570	+	0.999569i	$0.509346\pi$
$132$	−9.24873	+	16.0193i	−0.804998	+	1.39430i
$133$		0			0
$134$	5.37810	+	9.31515i	0.464597	+	0.804706i
$135$	−5.20344			−0.447841
$136$	−9.13550	−	15.8232i	−0.783363	−	1.35682i
$137$	−3.91937	−	6.78855i	−0.334855	−	0.579985i	0.648602	−	0.761128i	$-0.275354\pi$
$137$	−3.91937	−	6.78855i	−0.334855	−	0.579985i	−0.983457	+	0.181142i	$0.942021\pi$
$138$	34.7365			2.95697
$139$	−1.63760	−	2.83641i	−0.138900	−	0.240581i	0.788181	−	0.615444i	$-0.211023\pi$
$139$	−1.63760	−	2.83641i	−0.138900	−	0.240581i	−0.927080	+	0.374863i	$0.877690\pi$
$140$		0			0
$141$	3.99846	−	6.92554i	0.336731	−	0.583236i
$142$	17.6901			1.48452
$143$	6.75772	+	5.00007i	0.565109	+	0.418127i
$144$	2.17744			0.181453
$145$	14.2309	−	24.6487i	1.18182	−	2.04696i
$146$	−2.41308	+	4.17957i	−0.199708	+	0.345904i
$147$		0			0
$148$	10.5021			0.863270
$149$	7.08186	+	12.2661i	0.580169	+	1.00488i	0.995459	+	0.0951925i	$0.0303467\pi$
$149$	7.08186	+	12.2661i	0.580169	+	1.00488i	−0.415290	+	0.909689i	$0.636320\pi$
$150$	17.1314	+	29.6724i	1.39877	+	2.42274i
$151$	−1.34625			−0.109556			−0.0547781	−	0.998499i	$-0.517445\pi$
$151$	−1.34625			−0.109556			−0.0547781	+	0.998499i	$0.517445\pi$
$152$	−11.9994	−	20.7836i	−0.973283	−	1.68578i
$153$	6.36194	−	11.0192i	0.514332	−	0.890849i
$154$		0			0
$155$	−10.2860			−0.826190
$156$	3.23716	−	28.4215i	0.259180	−	2.27554i
$157$	−13.0401			−1.04071			−0.520357	−	0.853949i	$-0.674201\pi$
$157$	−13.0401			−1.04071			−0.520357	+	0.853949i	$0.674201\pi$
$158$	−8.84657	+	15.3227i	−0.703795	+	1.21901i
$159$	2.70601	−	4.68695i	0.214600	−	0.371699i
$160$	−7.61620	−	13.1916i	−0.602113	−	1.04289i
$161$		0			0
$162$	−12.3087	−	21.3194i	−0.967067	−	1.67501i
$163$	−2.46628	−	4.27172i	−0.193174	−	0.334587i	0.753127	−	0.657876i	$-0.228545\pi$
$163$	−2.46628	−	4.27172i	−0.193174	−	0.334587i	−0.946300	+	0.323289i	$0.895211\pi$
$164$	−3.22179			−0.251579
$165$	−9.07418	−	15.7169i	−0.706424	−	1.22356i
$166$	−3.37295	+	5.84212i	−0.261792	+	0.453436i
$167$	−1.82128	+	3.15455i	−0.140935	+	0.244107i	−0.927849	−	0.372956i	$-0.878344\pi$
$167$	−1.82128	+	3.15455i	−0.140935	+	0.244107i	0.786914	+	0.617063i	$0.211678\pi$
$168$		0			0
$169$	−12.6670	−	2.92344i	−0.974387	−	0.224880i
$170$	42.8937			3.28979
$171$	8.35637	−	14.4737i	0.639028	−	1.10683i
$172$	7.03014	−	12.1766i	0.536043	−	0.928453i
$173$	−6.34584	−	10.9913i	−0.482465	−	0.835654i	0.517332	−	0.855785i	$-0.326925\pi$
$173$	−6.34584	−	10.9913i	−0.482465	−	0.835654i	−0.999797	+	0.0201306i	$0.993592\pi$
$174$	45.4520			3.44571
$175$		0			0
$176$	−1.08872	−	1.88571i	−0.0820652	−	0.142141i
$177$	16.7332			1.25775
$178$	15.3410	+	26.5714i	1.14986	+	1.99161i
$179$	4.39469	−	7.61183i	0.328475	−	0.568935i	−0.653735	−	0.756724i	$-0.726799\pi$
$179$	4.39469	−	7.61183i	0.328475	−	0.568935i	0.982209	+	0.187789i	$0.0601321\pi$
$180$	−13.5030	+	23.3879i	−1.00645	+	1.74323i
$181$	−17.1982			−1.27833			−0.639167	−	0.769068i	$-0.720721\pi$
$181$	−17.1982			−1.27833			−0.639167	+	0.769068i	$0.720721\pi$
$182$		0			0
$183$	14.7548			1.09071
$184$	−10.8012	+	18.7083i	−0.796278	+	1.37919i
$185$	−5.15197	+	8.92347i	−0.378780	+	0.656066i
$186$	−8.21307	−	14.2255i	−0.602212	−	1.04306i
$187$	−12.7239			−0.930462
$188$	5.94999	+	10.3057i	0.433947	+	0.751619i
$189$		0			0
$190$	56.3406			4.08738
$191$	−0.533902	−	0.924745i	−0.0386318	−	0.0669122i	0.846063	−	0.533083i	$-0.178967\pi$
$191$	−0.533902	−	0.924745i	−0.0386318	−	0.0669122i	−0.884695	+	0.466171i	$0.845633\pi$
$192$	14.3191	−	24.8013i	1.03339	−	1.78988i
$193$	−1.57790	+	2.73300i	−0.113580	+	0.196726i	−0.917211	−	0.398402i	$-0.869565\pi$
$193$	−1.57790	+	2.73300i	−0.113580	+	0.196726i	0.803631	+	0.595127i	$0.202898\pi$
$194$	8.29348			0.595437
$195$	22.5611	+	16.6931i	1.61564	+	1.19542i
$196$		0			0
$197$	8.84783	−	15.3249i	0.630382	−	1.09185i	−0.357092	−	0.934069i	$-0.616232\pi$
$197$	8.84783	−	15.3249i	0.630382	−	1.09185i	0.987474	−	0.157784i	$-0.0504351\pi$
$198$	6.33701	−	10.9760i	0.450352	−	0.780033i
$199$	−6.49476	−	11.2493i	−0.460402	−	0.797439i	0.538579	−	0.842575i	$-0.318961\pi$
$199$	−6.49476	−	11.2493i	−0.460402	−	0.797439i	−0.998981	+	0.0451359i	$0.985628\pi$
$200$	−21.3079			−1.50670
$201$	−5.32619	−	9.22522i	−0.375680	−	0.650697i
$202$	5.51246	+	9.54785i	0.387855	+	0.671785i
$203$		0			0
$204$	21.6484	+	37.4960i	1.51569	+	2.62525i
$205$	1.58049	−	2.73749i	0.110386	−	0.191195i
$206$	−6.97456	+	12.0803i	−0.485941	+	0.841674i
$207$	−15.0439			−1.04562
$208$	2.70688	+	2.00283i	0.187688	+	0.138872i
$209$	−16.7127			−1.15605
$210$		0			0
$211$	−13.7701	+	23.8505i	−0.947974	+	1.64194i	−0.198289	+	0.980144i	$0.563538\pi$
$211$	−13.7701	+	23.8505i	−0.947974	+	1.64194i	−0.749685	+	0.661795i	$0.769795\pi$
$212$	4.02673	+	6.97450i	0.276557	+	0.479011i
$213$	−17.5193			−1.20041
$214$	15.3677	+	26.6177i	1.05052	+	1.81955i
$215$	6.89746	+	11.9467i	0.470403	+	0.814761i
$216$	5.16771			0.351618
$217$		0			0
$218$	4.79761	−	8.30971i	0.324935	−	0.562805i
$219$	2.38978	−	4.13922i	0.161487	−	0.279703i
$220$	27.0060			1.82074
$221$	18.0445	−	7.84674i	1.21380	−	0.527829i
$222$	−16.4548			−1.10437
$223$	4.35098	−	7.53612i	0.291363	−	0.504656i	−0.682769	−	0.730634i	$-0.739224\pi$
$223$	4.35098	−	7.53612i	0.291363	−	0.504656i	0.974132	+	0.225978i	$0.0725578\pi$
$224$		0			0
$225$	−7.41937	−	12.8507i	−0.494625	−	0.856715i
$226$	−33.2953			−2.21477
$227$	10.9835	+	19.0239i	0.728998	+	1.26266i	0.957307	+	0.289072i	$0.0933468\pi$
$227$	10.9835	+	19.0239i	0.728998	+	1.26266i	−0.228310	+	0.973589i	$0.573320\pi$
$228$	28.4350	+	49.2509i	1.88315	+	3.26172i
$229$	20.5188			1.35592			0.677959	−	0.735100i	$-0.262865\pi$
$229$	20.5188			1.35592			0.677959	+	0.735100i	$0.262865\pi$
$230$	−25.3574	−	43.9203i	−1.67202	−	2.89602i
$231$		0			0
$232$	−14.1332	+	24.4795i	−0.927892	+	1.60716i
$233$	−17.2888			−1.13263			−0.566313	−	0.824190i	$-0.691631\pi$
$233$	−17.2888			−1.13263			−0.566313	+	0.824190i	$0.691631\pi$
$234$	−2.21803	+	19.4737i	−0.144997	+	1.27304i
$235$	−11.6754			−0.761618
$236$	−12.4501	+	21.5642i	−0.810432	+	1.40371i
$237$	8.76116	−	15.1748i	0.569099	−	0.985708i
$238$		0			0
$239$	3.25961			0.210847			0.105423	−	0.994427i	$-0.466380\pi$
$239$	3.25961			0.210847			0.105423	+	0.994427i	$0.466380\pi$
$240$	−3.63476	−	6.29559i	−0.234623	−	0.406379i
$241$	−0.732856	−	1.26934i	−0.0472074	−	0.0817657i	0.841456	−	0.540325i	$-0.181699\pi$
$241$	−0.732856	−	1.26934i	−0.0472074	−	0.0817657i	−0.888664	+	0.458560i	$0.848366\pi$
$242$	12.9726			0.833913
$243$	9.87462	+	17.1033i	0.633457	+	1.09718i
$244$	−10.9781	+	19.0147i	−0.702802	+	1.21729i
$245$		0			0
$246$	5.04791			0.321843
$247$	23.7013	−	10.3067i	1.50808	−	0.655797i
$248$	10.2154			0.648676
$249$	3.34039	−	5.78572i	0.211688	−	0.366655i
$250$	5.36205	−	9.28734i	0.339126	−	0.587383i
$251$	8.55142	+	14.8115i	0.539761	+	0.934894i	0.998917	+	0.0465376i	$0.0148187\pi$
$251$	8.55142	+	14.8115i	0.539761	+	0.934894i	−0.459156	+	0.888356i	$0.651848\pi$
$252$		0			0
$253$	7.52195	+	13.0284i	0.472901	+	0.819089i
$254$	−12.9132	−	22.3663i	−0.810246	−	1.40339i
$255$	−42.4796			−2.66017
$256$	10.7728	+	18.6590i	0.673300	+	1.16619i
$257$	1.92506	−	3.33430i	0.120082	−	0.207988i	−0.799718	−	0.600376i	$-0.795018\pi$
$257$	1.92506	−	3.33430i	0.120082	−	0.207988i	0.919800	+	0.392388i	$0.128351\pi$
$258$	−11.0149	+	19.0783i	−0.685755	+	1.18776i
$259$		0			0
$260$	−38.2988	+	16.6544i	−2.37519	+	1.03286i
$261$	−19.6847			−1.21845
$262$	−0.783403	+	1.35689i	−0.0483988	+	0.0838292i
$263$	15.2579	−	26.4275i	0.940844	−	1.62959i	0.176978	−	0.984215i	$-0.443368\pi$
$263$	15.2579	−	26.4275i	0.940844	−	1.62959i	0.763866	−	0.645375i	$-0.223299\pi$
$264$	9.01187	+	15.6090i	0.554642	+	0.960669i
$265$	−7.90147			−0.485383
$266$		0			0
$267$	−15.1929	−	26.3149i	−0.929790	−	1.61044i
$268$	15.8515			0.968282
$269$	8.38857	+	14.5294i	0.511460	+	0.885875i	0.999912	+	0.0132842i	$0.00422861\pi$
$269$	8.38857	+	14.5294i	0.511460	+	0.885875i	−0.488451	+	0.872591i	$0.662438\pi$
$270$	−6.06595	+	10.5065i	−0.369162	+	0.639407i
$271$	15.5886	−	27.0003i	0.946941	−	1.64015i	0.195124	−	0.980779i	$-0.437489\pi$
$271$	15.5886	−	27.0003i	0.946941	−	1.64015i	0.751817	−	0.659372i	$-0.229178\pi$
$272$	−5.09669			−0.309032
$273$		0			0
$274$	−18.2762			−1.10410
$275$	−7.41937	+	12.8507i	−0.447405	+	0.774928i
$276$	25.5956	−	44.3330i	1.54068	−	2.66853i
$277$	−0.197941	−	0.342844i	−0.0118931	−	0.0205995i	0.860018	−	0.510264i	$-0.170452\pi$
$277$	−0.197941	−	0.342844i	−0.0118931	−	0.0205995i	−0.871911	+	0.489665i	$0.837119\pi$
$278$	−7.63619			−0.457988
$279$	3.55697	+	6.16085i	0.212950	+	0.368841i
$280$		0			0
$281$	−22.9459			−1.36884			−0.684420	−	0.729088i	$-0.739944\pi$
$281$	−22.9459			−1.36884			−0.684420	+	0.729088i	$0.739944\pi$
$282$	−9.32247	−	16.1470i	−0.555145	−	0.961540i
$283$	9.67575	−	16.7589i	0.575164	−	0.996213i	−0.420860	−	0.907126i	$-0.638272\pi$
$283$	9.67575	−	16.7589i	0.575164	−	0.996213i	0.996024	−	0.0890873i	$-0.0283950\pi$
$284$	13.0350	−	22.5773i	0.773485	−	1.33972i
$285$	−55.7967			−3.30511
$286$	17.9738	−	7.81600i	1.06281	−	0.462170i
$287$		0			0
$288$	−5.26748	+	9.12354i	−0.310389	+	0.537610i
$289$	−6.39129	+	11.0700i	−0.375958	+	0.651178i
$290$	−33.1796	−	57.4688i	−1.94838	−	3.37469i
$291$	−8.21342			−0.481479
$292$	3.55616	+	6.15945i	0.208109	+	0.360455i
$293$	−7.88616	−	13.6592i	−0.460715	−	0.797981i	0.538282	−	0.842765i	$-0.319074\pi$
$293$	−7.88616	−	13.6592i	−0.460715	−	0.797981i	−0.998997	+	0.0447835i	$0.985740\pi$
$294$		0			0
$295$	−12.2151	−	21.1572i	−0.711192	−	1.23182i
$296$	5.11659	−	8.86220i	0.297396	−	0.515105i
$297$	1.79939	−	3.11663i	0.104411	−	0.180845i
$298$	33.0229			1.91297
$299$	−18.7018	−	13.8376i	−1.08156	−	0.800248i
$300$	50.4932			2.91523
$301$		0			0
$302$	−1.56940	+	2.71828i	−0.0903089	+	0.156420i
$303$	−5.45924	−	9.45568i	−0.313625	−	0.543215i
$304$	−6.69448			−0.383955
$305$	−10.7709	−	18.6558i	−0.616742	−	1.06823i
$306$	−14.8330	−	25.6914i	−0.847943	−	1.46868i
$307$	−19.2535			−1.09885			−0.549427	−	0.835542i	$-0.685154\pi$
$307$	−19.2535			−1.09885			−0.549427	+	0.835542i	$0.685154\pi$
$308$		0			0
$309$	6.90723	−	11.9637i	0.392939	−	0.680590i
$310$	−11.9910	+	20.7689i	−0.681041	+	1.17960i
$311$	−3.06464			−0.173780			−0.0868898	−	0.996218i	$-0.527693\pi$
$311$	−3.06464			−0.173780			−0.0868898	+	0.996218i	$0.527693\pi$
$312$	−22.4062	−	16.5785i	−1.26850	−	0.938571i
$313$	35.2751			1.99387			0.996934	−	0.0782450i	$-0.0249316\pi$
$313$	35.2751			1.99387			0.996934	+	0.0782450i	$0.0249316\pi$
$314$	−15.2016	+	26.3300i	−0.857877	+	1.48589i
$315$		0			0
$316$	13.0372	+	22.5811i	0.733401	+	1.27029i
$317$	32.7065			1.83698			0.918490	−	0.395444i	$-0.129409\pi$
$317$	32.7065			1.83698			0.918490	+	0.395444i	$0.129409\pi$
$318$	−6.30910	−	10.9277i	−0.353797	−	0.612794i
$319$	9.84233	+	17.0474i	0.551065	+	0.954472i
$320$	−41.8112			−2.33732
$321$	−15.2194	−	26.3607i	−0.849463	−	1.47131i
$322$		0			0
$323$	−19.5596	+	33.8783i	−1.08833	+	1.88504i
$324$	−36.2789			−2.01549
$325$	2.59687	−	22.7998i	0.144048	−	1.26471i
$326$	−11.5003			−0.636944
$327$	−4.75130	+	8.22949i	−0.262747	+	0.455092i
$328$	−1.56964	+	2.71869i	−0.0866688	+	0.150115i
$329$		0			0
$330$	−42.3132			−2.32926
$331$	−2.38851	−	4.13703i	−0.131285	−	0.227392i	0.792887	−	0.609368i	$-0.208577\pi$
$331$	−2.38851	−	4.13703i	−0.131285	−	0.227392i	−0.924172	+	0.381977i	$0.875244\pi$
$332$	4.97073	+	8.60955i	0.272804	+	0.472511i
$333$	7.12636			0.390522
$334$	4.24635	+	7.35489i	0.232350	+	0.402442i
$335$	−7.77615	+	13.4687i	−0.424856	+	0.735873i
$336$		0			0
$337$	26.2392			1.42934			0.714669	−	0.699463i	$-0.246577\pi$
$337$	26.2392			1.42934			0.714669	+	0.699463i	$0.246577\pi$
$338$	−20.6695	+	22.1686i	−1.12427	+	1.20581i
$339$	32.9738			1.79089
$340$	31.6063	−	54.7437i	1.71409	−	2.96889i
$341$	3.55697	−	6.16085i	0.192621	−	0.333629i
$342$	−19.4830	−	33.7456i	−1.05352	−	1.82475i
$343$		0			0
$344$	−6.85010	−	11.8647i	−0.369332	−	0.639702i
$345$	25.1126	+	43.4963i	1.35202	+	2.34176i
$346$	−29.5908			−1.59081
$347$	5.22211	+	9.04496i	0.280338	+	0.485559i	0.971468	−	0.237171i	$-0.0762202\pi$
$347$	5.22211	+	9.04496i	0.280338	+	0.485559i	−0.691130	+	0.722730i	$0.742887\pi$
$348$	33.4914	−	58.0088i	1.79533	−	3.10960i
$349$	11.7344	−	20.3246i	0.628128	−	1.08795i	−0.359799	−	0.933030i	$-0.617155\pi$
$349$	11.7344	−	20.3246i	0.628128	−	1.08795i	0.987927	−	0.154920i	$-0.0495118\pi$
$350$		0			0
$351$	−0.629807	+	5.52955i	−0.0336166	+	0.295145i
$352$	10.5350			0.561515
$353$	1.46567	−	2.53862i	0.0780099	−	0.135117i	−0.824381	−	0.566035i	$-0.808477\pi$
$353$	1.46567	−	2.53862i	0.0780099	−	0.135117i	0.902391	+	0.430918i	$0.141810\pi$
$354$	19.5069	−	33.7869i	1.03678	−	1.79575i
$355$	12.7890	+	22.1512i	0.678769	+	1.17566i
$356$	45.2162			2.39645
$357$		0			0
$358$	−10.2463	−	17.7471i	−0.541533	−	0.937963i
$359$	−17.1014			−0.902576			−0.451288	−	0.892378i	$-0.649035\pi$
$359$	−17.1014			−0.902576			−0.451288	+	0.892378i	$0.649035\pi$
$360$	13.1572	+	22.7889i	0.693445	+	1.20108i
$361$	−16.1915	+	28.0445i	−0.852184	+	1.47603i
$362$	−20.0490	+	34.7258i	−1.05375	+	1.82515i
$363$	−12.8474			−0.674314
$364$		0			0
$365$	−6.97809			−0.365250
$366$	17.2006	−	29.7923i	0.899089	−	1.55727i
$367$	−0.524301	+	0.908115i	−0.0273683	+	0.0474032i	−0.879385	−	0.476111i	$-0.842046\pi$
$367$	−0.524301	+	0.908115i	−0.0273683	+	0.0474032i	0.852017	+	0.523514i	$0.175379\pi$
$368$	3.01300	+	5.21867i	0.157064	+	0.272042i
$369$	−2.18618			−0.113808
$370$	12.0119	+	20.8052i	0.624468	+	1.08161i
$371$		0			0
$372$	−24.2073			−1.25509
$373$	7.50536	+	12.9997i	0.388613	+	0.673098i	0.992263	−	0.124152i	$-0.0396210\pi$
$373$	7.50536	+	12.9997i	0.388613	+	0.673098i	−0.603650	+	0.797249i	$0.706288\pi$
$374$	−14.8330	+	25.6914i	−0.766994	+	1.32847i
$375$	−5.31029	+	9.19768i	−0.274222	+	0.474966i
$376$	11.5952			0.597978
$377$	−24.4710	−	18.1062i	−1.26032	−	0.932517i
$378$		0			0
$379$	13.5749	−	23.5123i	0.697294	−	1.20775i	−0.272108	−	0.962267i	$-0.587721\pi$
$379$	13.5749	−	23.5123i	0.697294	−	1.20775i	0.969401	−	0.245481i	$-0.0789459\pi$
$380$	41.5147	−	71.9056i	2.12966	−	3.68868i
$381$	12.7885	+	22.1504i	0.655177	+	1.13480i
$382$	−2.48960			−0.127379
$383$	−8.01320	−	13.8793i	−0.409455	−	0.709197i	0.585373	−	0.810764i	$-0.300948\pi$
$383$	−8.01320	−	13.8793i	−0.409455	−	0.709197i	−0.994829	+	0.101566i	$0.967615\pi$
$384$	−22.9519	−	39.7538i	−1.17126	−	2.02868i
$385$		0			0
$386$	3.67890	+	6.37203i	0.187251	+	0.324328i
$387$	4.77039	−	8.26255i	0.242492	−	0.420009i
$388$	6.11107	−	10.5847i	0.310242	−	0.537356i
$389$	7.99427			0.405326			0.202663	−	0.979249i	$-0.435040\pi$
$389$	7.99427			0.405326			0.202663	+	0.979249i	$0.435040\pi$
$390$	60.0067	−	26.0943i	3.03856	−	1.32133i
$391$	35.2130			1.78080
$392$		0			0
$393$	0.775840	−	1.34379i	0.0391360	−	0.0677855i
$394$	−20.6289	−	35.7302i	−1.03927	−	1.80006i
$395$	−25.5823			−1.28719
$396$	−9.33888	−	16.1754i	−0.469297	−	0.812845i
$397$	−6.10435	−	10.5731i	−0.306369	−	0.530646i	0.671196	−	0.741280i	$-0.265781\pi$
$397$	−6.10435	−	10.5731i	−0.306369	−	0.530646i	−0.977565	+	0.210633i	$0.932447\pi$
$398$	−30.2853			−1.51806
$399$		0			0
$400$	−2.97191	+	5.14750i	−0.148596	+	0.257375i
$401$	−18.9206	+	32.7715i	−0.944850	+	1.63653i	−0.188799	+	0.982016i	$0.560459\pi$
$401$	−18.9206	+	32.7715i	−0.944850	+	1.63653i	−0.756051	+	0.654513i	$0.772874\pi$
$402$	−24.8362			−1.23872
$403$	−1.24498	+	10.9306i	−0.0620169	+	0.544493i
$404$	16.2475			0.808341
$405$	17.7971	−	30.8255i	0.884345	−	1.53173i
$406$		0			0
$407$	−3.56318	−	6.17161i	−0.176620	−	0.305915i
$408$	42.1879			2.08861
$409$	0.117537	+	0.203580i	0.00581184	+	0.0100664i	0.868917	−	0.494958i	$-0.164817\pi$
$409$	0.117537	+	0.203580i	0.00581184	+	0.0100664i	−0.863105	+	0.505025i	$0.831483\pi$
$410$	−3.68494	−	6.38250i	−0.181986	−	0.315209i
$411$	18.0997			0.892794
$412$	10.2784	+	17.8028i	0.506382	+	0.877080i
$413$		0			0
$414$	−17.5375	+	30.3759i	−0.861923	+	1.49290i
$415$	−9.75383			−0.478797
$416$	−14.9402	+	6.49684i	−0.732505	+	0.318534i
$417$	7.56248			0.370336
$418$	−19.4830	+	33.7456i	−0.952945	+	1.65055i
$419$	0.222023	−	0.384555i	0.0108465	−	0.0187868i	−0.860551	−	0.509364i	$-0.829881\pi$
$419$	0.222023	−	0.384555i	0.0108465	−	0.0187868i	0.871398	+	0.490577i	$0.163214\pi$
$420$		0			0
$421$	9.45998			0.461051			0.230526	−	0.973066i	$-0.425955\pi$
$421$	9.45998			0.461051			0.230526	+	0.973066i	$0.425955\pi$
$422$	32.1052	+	55.6079i	1.56286	+	2.70695i
$423$	4.03744	+	6.99305i	0.196307	+	0.340014i
$424$	7.84721			0.381094
$425$	17.3664	+	30.0795i	0.842395	+	1.45907i
$426$	−20.4233	+	35.3742i	−0.989513	+	1.71389i
$427$		0			0
$428$	45.2950			2.18942
$429$	−17.8002	+	7.74054i	−0.859404	+	0.373717i
$430$	32.1630			1.55104
$431$	−10.7723	+	18.6582i	−0.518883	+	0.898732i	0.480876	+	0.876789i	$0.340319\pi$
$431$	−10.7723	+	18.6582i	−0.518883	+	0.898732i	−0.999759	+	0.0219436i	$0.993015\pi$
$432$	0.720766	−	1.24840i	0.0346778	−	0.0600638i
$433$	−6.57949	−	11.3960i	−0.316190	−	0.547657i	0.663500	−	0.748176i	$-0.269070\pi$
$433$	−6.57949	−	11.3960i	−0.316190	−	0.547657i	−0.979690	+	0.200519i	$0.935737\pi$
$434$		0			0
$435$	32.8593	+	56.9141i	1.57548	+	2.72882i
$436$	−7.07026	−	12.2461i	−0.338604	−	0.586479i
$437$	46.2522			2.21254
$438$	−5.57181	−	9.65066i	−0.266232	−	0.461127i
$439$	−14.8923	+	25.7943i	−0.710773	+	1.23109i	0.253795	+	0.967258i	$0.418321\pi$
$439$	−14.8923	+	25.7943i	−0.710773	+	1.23109i	−0.964568	+	0.263836i	$0.915012\pi$
$440$	13.1572	−	22.7889i	0.627245	−	1.08642i
$441$		0			0
$442$	5.19171	−	45.5819i	0.246944	−	2.16811i
$443$	14.8467			0.705387			0.352693	−	0.935739i	$-0.385266\pi$
$443$	14.8467			0.705387			0.352693	+	0.935739i	$0.385266\pi$
$444$	−12.1248	+	21.0007i	−0.575416	+	0.996649i
$445$	−22.1814	+	38.4193i	−1.05150	+	1.82125i
$446$	−10.1444	−	17.5706i	−0.480351	−	0.831992i
$447$	−32.7041			−1.54685
$448$		0			0
$449$	13.1114	+	22.7095i	0.618763	+	1.07173i	0.989712	+	0.143075i	$0.0456992\pi$
$449$	13.1114	+	22.7095i	0.618763	+	1.07173i	−0.370949	+	0.928653i	$0.620968\pi$
$450$	−34.5968			−1.63091
$451$	1.09309	+	1.89329i	0.0514717	+	0.0891516i
$452$	−24.5337	+	42.4936i	−1.15397	+	1.99873i
$453$	1.55425	−	2.69204i	0.0730251	−	0.126483i
$454$	51.2162			2.40369
$455$		0			0
$456$	55.4136			2.59498
$457$	7.93542	−	13.7445i	0.371203	−	0.642943i	−0.618548	−	0.785747i	$-0.712279\pi$
$457$	7.93542	−	13.7445i	0.371203	−	0.642943i	0.989751	+	0.142804i	$0.0456120\pi$
$458$	23.9199	−	41.4305i	1.11770	−	1.93592i
$459$	−4.21180	−	7.29506i	−0.196590	−	0.340504i
$460$	−74.7385			−3.48470
$461$	11.0443	+	19.1293i	0.514384	+	0.890940i	0.999861	+	0.0166900i	$0.00531285\pi$
$461$	11.0443	+	19.1293i	0.514384	+	0.890940i	−0.485476	+	0.874250i	$0.661354\pi$
$462$		0			0
$463$	18.2887			0.849949			0.424974	−	0.905205i	$-0.360283\pi$
$463$	18.2887			0.849949			0.424974	+	0.905205i	$0.360283\pi$
$464$	3.94246	+	6.82854i	0.183024	+	0.317007i
$465$	11.8752	−	20.5685i	0.550699	−	0.953839i
$466$	−20.1545	+	34.9087i	−0.933641	+	1.61711i
$467$	−4.53318			−0.209771			−0.104885	−	0.994484i	$-0.533448\pi$
$467$	−4.53318			−0.209771			−0.104885	+	0.994484i	$0.533448\pi$
$468$	23.2193	+	17.1801i	1.07331	+	0.794148i
$469$		0			0
$470$	−13.6107	+	23.5744i	−0.627813	+	1.08740i
$471$	15.0549	−	26.0758i	0.693691	−	1.20151i
$472$	12.1312	+	21.0119i	0.558386	+	0.967153i
$473$	−9.54077			−0.438685
$474$	−20.4268	−	35.3802i	−0.938233	−	1.62507i
$475$	22.8107	+	39.5093i	1.04663	+	1.81281i
$476$		0			0
$477$	2.73239	+	4.73263i	0.125107	+	0.216692i
$478$	3.79992	−	6.58165i	0.173804	−	0.301038i
$479$	−5.22303	+	9.04655i	−0.238646	+	0.413347i	−0.960326	−	0.278880i	$-0.910037\pi$
$479$	−5.22303	+	9.04655i	−0.238646	+	0.413347i	0.721680	+	0.692227i	$0.243370\pi$
$480$	35.1717			1.60536
$481$	8.85914	+	6.55491i	0.403942	+	0.298878i
$482$	−3.41733			−0.155655
$483$		0			0
$484$	9.55891	−	16.5565i	0.434496	−	0.752569i
$485$	5.99573	+	10.3849i	0.272252	+	0.471555i
$486$	46.0456			2.08867
$487$	−17.9571	−	31.1027i	−0.813715	−	1.40940i	−0.910247	−	0.414067i	$-0.864108\pi$
$487$	−17.9571	−	31.1027i	−0.813715	−	1.40940i	0.0965311	−	0.995330i	$-0.469225\pi$
$488$	10.6970	+	18.5277i	0.484229	+	0.838710i
$489$	11.3893			0.515042
$490$		0			0
$491$	−3.85124	+	6.67054i	−0.173804	+	0.301037i	−0.939747	−	0.341871i	$-0.888939\pi$
$491$	−3.85124	+	6.67054i	−0.173804	+	0.301037i	0.765943	+	0.642909i	$0.222273\pi$
$492$	3.71956	−	6.44247i	0.167691	−	0.290449i
$493$	46.0756			2.07514
$494$	6.81928	−	59.8716i	0.306814	−	2.69375i
$495$	18.3253			0.823659
$496$	1.42478	−	2.46780i	0.0639747	−	0.110807i
$497$		0			0
$498$	−7.78816	−	13.4895i	−0.348996	−	0.604479i
$499$	8.49078			0.380099			0.190050	−	0.981774i	$-0.439135\pi$
$499$	8.49078			0.380099			0.190050	+	0.981774i	$0.439135\pi$
$500$	−7.90207	−	13.6868i	−0.353391	−	0.612092i
$501$	−4.20535	−	7.28389i	−0.187881	−	0.325420i
$502$	39.8755			1.77973
$503$	15.2000	+	26.3272i	0.677736	+	1.17387i	0.975661	+	0.219285i	$0.0703723\pi$
$503$	15.2000	+	26.3272i	0.677736	+	1.17387i	−0.297924	+	0.954589i	$0.596294\pi$
$504$		0			0
$505$	−7.97041	+	13.8052i	−0.354679	+	0.614321i
$506$	35.0751			1.55928
$507$	20.4700	−	21.9546i	0.909105	−	0.975039i
$508$	−38.0604			−1.68866
$509$	−7.79007	+	13.4928i	−0.345289	+	0.598058i	−0.985406	−	0.170219i	$-0.945552\pi$
$509$	−7.79007	+	13.4928i	−0.345289	+	0.598058i	0.640117	+	0.768277i	$0.278886\pi$
$510$	−49.5209	+	85.7727i	−2.19282	+	3.79808i
$511$		0			0
$512$	10.4733			0.462860
$513$	−5.53218	−	9.58202i	−0.244252	−	0.423057i
$514$	−4.48830	−	7.77396i	−0.197970	−	0.342895i
$515$	−20.1689			−0.888748
$516$	16.2326	+	28.1157i	0.714602	+	1.23773i
$517$	4.03744	−	6.99305i	0.177566	−	0.307554i
$518$		0			0
$519$	29.3052			1.28635
$520$	−4.60517	+	40.4322i	−0.201950	+	1.77307i
$521$	−27.1574			−1.18979			−0.594893	−	0.803805i	$-0.702806\pi$
$521$	−27.1574			−1.18979			−0.594893	+	0.803805i	$0.702806\pi$
$522$	−22.9476	+	39.7463i	−1.00439	+	1.73965i
$523$	−9.02874	+	15.6382i	−0.394799	+	0.683812i	−0.993076	−	0.117478i	$-0.962519\pi$
$523$	−9.02874	+	15.6382i	−0.394799	+	0.683812i	0.598276	+	0.801290i	$0.295853\pi$
$524$	1.15450	+	1.99966i	0.0504347	+	0.0873555i
$525$		0			0
$526$	−35.5741	−	61.6161i	−1.55110	−	2.68659i
$527$	−8.32574	−	14.4206i	−0.362675	−	0.628172i
$528$	5.02772			0.218803
$529$	−9.31684	−	16.1372i	−0.405080	−	0.701619i
$530$	−9.21119	+	15.9543i	−0.400109	+	0.693008i
$531$	−8.44816	+	14.6326i	−0.366619	+	0.635003i
$532$		0			0
$533$	−2.71776	−	2.01088i	−0.117719	−	0.0871009i
$534$	−70.8449			−3.06576
$535$	−22.2201	+	38.4863i	−0.960657	+	1.66391i
$536$	7.72276	−	13.3762i	0.333572	−	0.577764i
$537$	10.1474	+	17.5758i	0.437892	+	0.758451i
$538$	39.1162			1.68642
$539$		0			0
$540$	8.93941	+	15.4835i	0.384691	+	0.666305i
$541$	39.9882			1.71923			0.859613	−	0.510945i	$-0.170705\pi$
$541$	39.9882			1.71923			0.859613	+	0.510945i	$0.170705\pi$
$542$	−36.3451	−	62.9516i	−1.56116	−	2.70400i
$543$	19.8554	−	34.3906i	0.852077	−	1.47584i
$544$	12.3295	−	21.3553i	0.528623	−	0.915602i
$545$	13.8736			0.594282
$546$		0			0
$547$	−22.6124			−0.966836			−0.483418	−	0.875390i	$-0.660605\pi$
$547$	−22.6124			−0.966836			−0.483418	+	0.875390i	$0.660605\pi$
$548$	−13.4668	+	23.3252i	−0.575274	+	0.996404i
$549$	−7.44934	+	12.9026i	−0.317930	+	0.550671i
$550$	17.2984	+	29.9617i	0.737605	+	1.27757i
$551$	60.5201			2.57824
$552$	−24.9402	−	43.1976i	−1.06152	−	1.83861i
$553$		0			0
$554$	−0.923005			−0.0392147
$555$	−11.8959	−	20.6043i	−0.504954	−	0.874606i
$556$	−5.62674	+	9.74581i	−0.238627	+	0.413314i
$557$	4.98686	−	8.63750i	0.211300	−	0.365983i	−0.740822	−	0.671702i	$-0.765564\pi$
$557$	4.98686	−	8.63750i	0.211300	−	0.365983i	0.952122	+	0.305719i	$0.0988969\pi$
$558$	16.5863			0.702152
$559$	13.5303	−	5.88374i	0.572271	−	0.248856i
$560$		0			0
$561$	14.6898	−	25.4434i	0.620202	−	1.07422i
$562$	−26.7494	+	46.3313i	−1.12836	+	1.95437i
$563$	−10.7640	−	18.6437i	−0.453647	−	0.785740i	0.544962	−	0.838461i	$-0.316544\pi$
$563$	−10.7640	−	18.6437i	−0.453647	−	0.785740i	−0.998609	+	0.0527209i	$0.983211\pi$
$564$	−27.4771			−1.15700
$565$	−24.0707	−	41.6916i	−1.01266	−	1.75398i
$566$	−22.5592	−	39.0736i	−0.948232	−	1.64239i
$567$		0			0
$568$	−12.7012	−	21.9991i	−0.532930	−	0.923061i
$569$	16.5502	−	28.6657i	0.693819	−	1.20173i	−0.276758	−	0.960940i	$-0.589260\pi$
$569$	16.5502	−	28.6657i	0.693819	−	1.20173i	0.970577	−	0.240791i	$-0.0774068\pi$
$570$	−65.0454	+	112.662i	−2.72445	+	4.71889i
$571$	19.9357			0.834284			0.417142	−	0.908841i	$-0.363032\pi$
$571$	19.9357			0.834284			0.417142	+	0.908841i	$0.363032\pi$
$572$	3.26872	−	28.6985i	0.136672	−	1.19995i
$573$	2.46557			0.103001
$574$		0			0
$575$	20.5330	−	35.5641i	0.856283	−	1.48313i
$576$	14.4586	+	25.0431i	0.602443	+	1.04346i
$577$	−29.4695			−1.22683			−0.613416	−	0.789760i	$-0.710205\pi$
$577$	−29.4695			−1.22683			−0.613416	+	0.789760i	$0.710205\pi$
$578$	14.9014	+	25.8100i	0.619816	+	1.07355i
$579$	−3.64338	−	6.31052i	−0.151414	−	0.262256i
$580$	−97.7939			−4.06067
$581$		0			0
$582$	−9.57486	+	16.5841i	−0.396891	+	0.687435i
$583$	2.73239	−	4.73263i	0.113164	−	0.196006i
$584$	6.93018			0.286773
$585$	−25.9881	+	11.3011i	−1.07448	+	0.467242i
$586$	−36.7734			−1.51910
$587$	3.49429	−	6.05229i	0.144225	−	0.249805i	−0.784859	−	0.619675i	$-0.787264\pi$
$587$	3.49429	−	6.05229i	0.144225	−	0.249805i	0.929084	+	0.369870i	$0.120598\pi$
$588$		0			0
$589$	−10.9358	−	18.9414i	−0.450603	−	0.780467i
$590$	−56.9595			−2.34498
$591$	20.4297	+	35.3853i	0.840366	+	1.45556i
$592$	−1.42727	−	2.47211i	−0.0586605	−	0.101603i
$593$	−0.970248			−0.0398433			−0.0199216	−	0.999802i	$-0.506342\pi$
$593$	−0.970248			−0.0398433			−0.0199216	+	0.999802i	$0.506342\pi$
$594$	−4.19530	−	7.26648i	−0.172135	−	0.298147i
$595$		0			0
$596$	24.3330	−	42.1460i	0.996719	−	1.72637i
$597$	29.9929			1.22753
$598$	−49.7420	+	21.6306i	−2.03410	+	0.884541i
$599$	−22.5998			−0.923404			−0.461702	−	0.887035i	$-0.652761\pi$
$599$	−22.5998			−0.923404			−0.461702	+	0.887035i	$0.652761\pi$
$600$	24.6000	−	42.6085i	1.00429	−	1.73949i
$601$	−15.2146	+	26.3525i	−0.620617	+	1.07494i	0.368754	+	0.929527i	$0.379785\pi$
$601$	−15.2146	+	26.3525i	−0.620617	+	1.07494i	−0.989371	+	0.145414i	$0.953549\pi$
$602$		0			0
$603$	10.7562			0.438027
$604$	2.31283	+	4.00594i	0.0941078	+	0.163000i
$605$	9.37851	+	16.2441i	0.381291	+	0.660415i
$606$	−25.4566			−1.03410
$607$	−16.0788	−	27.8493i	−0.652618	−	1.13037i	−0.982485	−	0.186340i	$-0.940337\pi$
$607$	−16.0788	−	27.8493i	−0.652618	−	1.13037i	0.329868	−	0.944027i	$-0.392996\pi$
$608$	16.1947	−	28.0501i	0.656784	−	1.13758i
$609$		0			0
$610$	−50.2252			−2.03356
$611$	−1.41315	+	12.4071i	−0.0571699	+	0.501938i
$612$	−43.7188			−1.76723
$613$	−6.96043	+	12.0558i	−0.281129	+	0.486930i	−0.971663	−	0.236370i	$-0.924042\pi$
$613$	−6.96043	+	12.0558i	−0.281129	+	0.486930i	0.690534	+	0.723300i	$0.257376\pi$
$614$	−22.4449	+	38.8757i	−0.905801	+	1.56889i
$615$	3.64937	+	6.32089i	0.147157	+	0.254883i
$616$		0			0
$617$	5.08394	+	8.80565i	0.204672	+	0.354502i	0.950028	−	0.312164i	$-0.101054\pi$
$617$	5.08394	+	8.80565i	0.204672	+	0.354502i	−0.745356	+	0.666666i	$0.767721\pi$
$618$	−16.1043	−	27.8935i	−0.647810	−	1.12204i
$619$	43.7905			1.76009			0.880044	−	0.474893i	$-0.157513\pi$
$619$	43.7905			1.76009			0.880044	+	0.474893i	$0.157513\pi$
$620$	17.6711	+	30.6073i	0.709689	+	1.22922i
$621$	−4.97977	+	8.62522i	−0.199831	+	0.346118i
$622$	−3.57262	+	6.18796i	−0.143249	+	0.248115i
$623$		0			0
$624$	−7.13009	+	3.10056i	−0.285432	+	0.124122i
$625$	−16.3162			−0.652650
$626$	41.1223	−	71.2258i	1.64358	−	2.84676i
$627$	19.2949	−	33.4198i	0.770565	−	1.33466i
$628$	22.4027	+	38.8026i	0.893964	+	1.54839i
$629$	−16.6806			−0.665097
$630$		0			0
$631$	−8.04464	−	13.9337i	−0.320252	−	0.554693i	0.660288	−	0.751013i	$-0.270434\pi$
$631$	−8.04464	−	13.9337i	−0.320252	−	0.554693i	−0.980540	+	0.196320i	$0.937101\pi$
$632$	25.4067			1.01062
$633$	−31.7953	−	55.0711i	−1.26375	−	2.18888i
$634$	38.1279	−	66.0394i	1.51425	−	2.62276i
$635$	18.6711	−	32.3392i	0.740939	−	1.28334i
$636$	−18.5955			−0.737359
$637$		0			0
$638$	45.8951			1.81700
$639$	8.84506	−	15.3201i	0.349905	−	0.606054i
$640$	−33.5094	+	58.0399i	−1.32457	+	2.29423i
$641$	24.6254	+	42.6525i	0.972645	+	1.68467i	0.687497	+	0.726187i	$0.258709\pi$
$641$	24.6254	+	42.6525i	0.972645	+	1.68467i	0.285148	+	0.958483i	$0.407957\pi$
$642$	−70.9684			−2.80090
$643$	−1.33579	−	2.31366i	−0.0526784	−	0.0912417i	0.838484	−	0.544927i	$-0.183442\pi$
$643$	−1.33579	−	2.31366i	−0.0526784	−	0.0912417i	−0.891162	+	0.453685i	$0.850109\pi$
$644$		0			0
$645$	−31.8526			−1.25419
$646$	45.6036	+	78.9877i	1.79425	+	3.10773i
$647$	−16.6814	+	28.8930i	−0.655814	+	1.13590i	0.325876	+	0.945413i	$0.394341\pi$
$647$	−16.6814	+	28.8930i	−0.655814	+	1.13590i	−0.981689	+	0.190490i	$0.938992\pi$
$648$	−17.6749	+	30.6138i	−0.694336	+	1.20262i
$649$	16.8963			0.663239
$650$	−43.0090	−	31.8226i	−1.68695	−	1.24818i
$651$		0			0
$652$	−8.47404	+	14.6775i	−0.331869	+	0.574814i
$653$	−11.9244	+	20.6536i	−0.466637	+	0.808239i	−0.999274	−	0.0381052i	$-0.987868\pi$
$653$	−11.9244	+	20.6536i	−0.466637	+	0.808239i	0.532637	+	0.846344i	$0.321201\pi$
$654$	11.0777	+	19.1872i	0.433173	+	0.750278i
$655$	−2.26543			−0.0885177
$656$	0.437850	+	0.758379i	0.0170952	+	0.0296097i
$657$	2.41308	+	4.17957i	0.0941431	+	0.163061i
$658$		0			0
$659$	8.58114	+	14.8630i	0.334274	+	0.578979i	0.983345	−	0.181749i	$-0.0581757\pi$
$659$	8.58114	+	14.8630i	0.334274	+	0.578979i	−0.649071	+	0.760727i	$0.724842\pi$
$660$	−31.1785	+	54.0028i	−1.21362	+	2.10206i
$661$	0.233201	−	0.403917i	0.00907048	−	0.0157105i	−0.861455	−	0.507835i	$-0.830446\pi$
$661$	0.233201	−	0.403917i	0.00907048	−	0.0157105i	0.870525	+	0.492124i	$0.163779\pi$
$662$	−11.1377			−0.432880
$663$	−5.14159	+	45.1418i	−0.199683	+	1.75316i
$664$	9.68686			0.375923
$665$		0			0
$666$	8.30760	−	14.3892i	0.321913	−	0.557570i
$667$	−27.2384	−	47.1784i	−1.05468	−	1.82675i
$668$	12.5157			0.484248
$669$	10.0465	+	17.4010i	0.388418	+	0.672760i
$670$	18.1302	+	31.4024i	0.700431	+	1.21318i
$671$	14.8987			0.575157
$672$		0			0
$673$	−8.77061	+	15.1911i	−0.338082	+	0.585576i	−0.984072	−	0.177770i	$-0.943112\pi$
$673$	−8.77061	+	15.1911i	−0.338082	+	0.585576i	0.645990	+	0.763346i	$0.276445\pi$
$674$	30.5885	−	52.9808i	1.17822	−	2.04075i
$675$	−9.82372			−0.378115
$676$	13.0626	+	42.7148i	0.502410	+	1.64288i
$677$	−9.71961			−0.373555			−0.186777	−	0.982402i	$-0.559804\pi$
$677$	−9.71961			−0.373555			−0.186777	+	0.982402i	$0.559804\pi$
$678$	38.4395	−	66.5792i	1.47626	−	2.55696i
$679$		0			0
$680$	−30.7968	−	53.3417i	−1.18101	−	2.04556i
$681$	−50.7218			−1.94366
$682$	−8.29313	−	14.3641i	−0.317560	−	0.550031i
$683$	18.0577	+	31.2769i	0.690960	+	1.19678i	0.971524	+	0.236942i	$0.0761451\pi$
$683$	18.0577	+	31.2769i	0.690960	+	1.19678i	−0.280564	+	0.959835i	$0.590522\pi$
$684$	−57.4244			−2.19568
$685$	−13.2127	−	22.8850i	−0.504830	−	0.874391i
$686$		0			0
$687$	−23.6890	+	41.0305i	−0.903791	+	1.56541i
$688$	−3.82166			−0.145700
$689$	−0.956367	+	8.39666i	−0.0364347	+	0.319887i
$690$	117.101			4.45795
$691$	4.38634	−	7.59737i	0.166864	−	0.289018i	−0.770451	−	0.637499i	$-0.779969\pi$
$691$	4.38634	−	7.59737i	0.166864	−	0.289018i	0.937316	+	0.348481i	$0.113302\pi$
$692$	−21.8041	+	37.7657i	−0.828866	+	1.43564i
$693$		0			0
$694$	24.3509			0.924346
$695$	−5.52055	−	9.56187i	−0.209406	−	0.362703i
$696$	−32.6337	−	56.5233i	−1.23698	−	2.14251i
$697$	5.11717			0.193826
$698$	−27.3589	−	47.3870i	−1.03555	−	1.79363i
$699$	19.9600	−	34.5717i	0.754955	−	1.30762i
$700$		0			0
$701$	1.51585			0.0572530			0.0286265	−	0.999590i	$-0.490887\pi$
$701$	1.51585			0.0572530			0.0286265	+	0.999590i	$0.490887\pi$
$702$	10.4308	+	7.71779i	0.393685	+	0.291289i
$703$	−21.9098			−0.826345
$704$	14.4586	−	25.0431i	0.544930	−	0.943847i
$705$	13.4793	−	23.3468i	0.507659	−	0.879291i
$706$	−3.41724	−	5.91883i	−0.128609	−	0.222758i
$707$		0			0
$708$	−28.7473	−	49.7919i	−1.08039	−	1.87129i
$709$	7.55100	+	13.0787i	0.283584	+	0.491182i	0.972265	−	0.233883i	$-0.0751433\pi$
$709$	7.55100	+	13.0787i	0.283584	+	0.491182i	−0.688681	+	0.725065i	$0.741810\pi$
$710$	59.6355			2.23808
$711$	8.84657	+	15.3227i	0.331772	+	0.574646i
$712$	22.0291	−	38.1555i	0.825575	−	1.42994i
$713$	−9.84384	+	17.0500i	−0.368655	+	0.638528i
$714$		0			0
$715$	22.7811	+	16.8558i	0.851964	+	0.630372i
$716$	−30.2000			−1.12863
$717$	−3.76324	+	6.51812i	−0.140541	+	0.243424i
$718$	−19.9361	+	34.5303i	−0.744007	+	1.28866i
$719$	9.59946	+	16.6267i	0.357999	+	0.620073i	0.987626	−	0.156824i	$-0.0501257\pi$
$719$	9.59946	+	16.6267i	0.357999	+	0.620073i	−0.629627	+	0.776897i	$0.716792\pi$
$720$	7.34039			0.273560
$721$		0			0
$722$	37.7507	+	65.3861i	1.40494	+	2.43342i
$723$	3.38434			0.125865
$724$	29.5462	+	51.1756i	1.09808	+	1.90193i
$725$	26.8670	−	46.5350i	0.997815	−	1.72827i
$726$	−14.9770	+	25.9409i	−0.555847	+	0.962755i
$727$	2.41101			0.0894195			0.0447098	−	0.999000i	$-0.485764\pi$
$727$	2.41101			0.0894195			0.0447098	+	0.999000i	$0.485764\pi$
$728$		0			0
$729$	−13.9254			−0.515755
$730$	−8.13476	+	14.0898i	−0.301081	+	0.521488i
$731$	−11.1660	+	19.3400i	−0.412988	+	0.715317i
$732$	−25.3486	−	43.9050i	−0.936910	−	1.62278i
$733$	13.4992			0.498604			0.249302	−	0.968426i	$-0.419799\pi$
$733$	13.4992			0.498604			0.249302	+	0.968426i	$0.419799\pi$
$734$	1.22241	+	2.11728i	0.0451201	+	0.0781504i
$735$		0			0
$736$	−29.1553			−1.07468
$737$	−5.37810	−	9.31515i	−0.198105	−	0.343128i
$738$	−2.54856	+	4.41423i	−0.0938138	+	0.162490i
$739$	0.0214096	−	0.0370824i	0.000787563	−	0.00136410i	−0.865631	−	0.500682i	$-0.833083\pi$
$739$	0.0214096	−	0.0370824i	0.000787563	−	0.00136410i	0.866419	+	0.499318i	$0.166416\pi$
$740$	35.4039			1.30147
$741$	−6.75345	+	59.2936i	−0.248094	+	2.17820i
$742$		0			0
$743$	10.8254	−	18.7501i	0.397145	−	0.687875i	−0.596228	−	0.802815i	$-0.703334\pi$
$743$	10.8254	−	18.7501i	0.397145	−	0.687875i	0.993372	+	0.114941i	$0.0366678\pi$
$744$	−11.7937	+	20.4272i	−0.432377	+	0.748898i
$745$	23.8738	+	41.3506i	0.874667	+	1.51497i
$746$	34.9977			1.28136
$747$	3.37295	+	5.84212i	0.123410	+	0.213752i
$748$	21.8594	+	37.8616i	0.799258	+	1.38436i
$749$		0			0
$750$	12.3810	+	21.4445i	0.452091	+	0.783044i
$751$	22.4429	−	38.8723i	0.818953	−	1.41847i	−0.0875006	−	0.996164i	$-0.527888\pi$
$751$	22.4429	−	38.8723i	0.818953	−	1.41847i	0.906454	−	0.422304i	$-0.138779\pi$
$752$	1.61724	−	2.80114i	0.0589747	−	0.102147i
$753$	−39.4906			−1.43912
$754$	−65.0865	+	28.3032i	−2.37031	+	1.03074i
$755$	−4.53837			−0.165168
$756$		0			0
$757$	3.77726	−	6.54240i	0.137287	−	0.237788i	−0.789182	−	0.614159i	$-0.789495\pi$
$757$	3.77726	−	6.54240i	0.137287	−	0.237788i	0.926469	+	0.376372i	$0.122828\pi$
$758$	−31.6500	−	54.8194i	−1.14958	−	1.99113i
$759$	−34.7365			−1.26085
$760$	−40.4515	−	70.0641i	−1.46733	−	2.54149i
$761$	11.6946	+	20.2556i	0.423928	+	0.734265i	0.996320	−	0.0857157i	$-0.0273177\pi$
$761$	11.6946	+	20.2556i	0.423928	+	0.734265i	−0.572392	+	0.819980i	$0.693984\pi$
$762$	59.6333			2.16029
$763$		0			0
$764$	−1.83447	+	3.17739i	−0.0663687	+	0.114954i
$765$	21.4468	−	37.1470i	0.775412	−	1.34305i
$766$	−37.3658			−1.35008
$767$	−23.9616	+	10.4199i	−0.865205	+	0.376239i
$768$	−49.7489			−1.79516
$769$	−21.9255	+	37.9760i	−0.790652	+	1.36945i	0.134911	+	0.990858i	$0.456925\pi$
$769$	−21.9255	+	37.9760i	−0.790652	+	1.36945i	−0.925564	+	0.378592i	$0.876408\pi$
$770$		0			0
$771$	4.44497	+	7.69891i	0.160082	+	0.277270i
$772$	10.8432			0.390255
$773$	−21.5613	−	37.3452i	−0.775505	−	1.34321i	−0.934510	−	0.355936i	$-0.884162\pi$
$773$	−21.5613	−	37.3452i	−0.775505	−	1.34321i	0.159005	−	0.987278i	$-0.449171\pi$
$774$	−11.1222	−	19.2643i	−0.399780	−	0.692440i
$775$	−19.4192			−0.697558
$776$	−5.95457	−	10.3136i	−0.213756	−	0.370237i
$777$		0			0
$778$	9.31939	−	16.1417i	0.334116	−	0.578706i
$779$	6.72137			0.240818
$780$	10.9128	−	95.8121i	0.390743	−	3.43062i
$781$	−17.6901			−0.633002
$782$	41.0499	−	71.1005i	1.46794	−	2.54255i
$783$	−6.51594	+	11.2859i	−0.232861	+	0.403326i
$784$		0			0
$785$	−43.9597			−1.56899
$786$	−1.80888	−	3.13308i	−0.0645207	−	0.111753i
$787$	−12.4480	−	21.5606i	−0.443723	−	0.768551i	0.554239	−	0.832357i	$-0.313009\pi$
$787$	−12.4480	−	21.5606i	−0.443723	−	0.768551i	−0.997962	+	0.0638066i	$0.979676\pi$
$788$	−60.8017			−2.16597
$789$	35.2307	+	61.0213i	1.25424	+	2.17242i
$790$	−29.8228	+	51.6546i	−1.06105	+	1.83779i
$791$		0			0
$792$	−18.1994			−0.646689
$793$	−21.1287	+	9.18792i	−0.750301	+	0.326273i
$794$	−28.4648			−1.01018
$795$	9.12227	−	15.8002i	0.323534	−	0.560377i
$796$	−22.3158	+	38.6520i	−0.790961	+	1.36999i
$797$	15.6211	+	27.0565i	0.553327	+	0.958391i	0.998032	+	0.0627134i	$0.0199754\pi$
$797$	15.6211	+	27.0565i	0.553327	+	0.958391i	−0.444704	+	0.895677i	$0.646691\pi$
$798$		0			0
$799$	−9.45037	−	16.3685i	−0.334330	−	0.579077i
$800$	−14.3788	−	24.9049i	−0.508368	−	0.880520i
$801$	30.6820			1.08409
$802$	44.1137	+	76.4071i	1.55771	+	2.69803i
$803$	2.41308	−	4.17957i	0.0851556	−	0.147494i
$804$	−18.3006	+	31.6975i	−0.645412	+	1.11789i
$805$		0			0
$806$	20.6192	+	15.2563i	0.726281	+	0.537379i
$807$	−38.7386			−1.36366
$808$	7.91568	−	13.7104i	0.278473	−	0.482329i
$809$	−19.7729	+	34.2477i	−0.695179	+	1.20409i	0.274941	+	0.961461i	$0.411342\pi$
$809$	−19.7729	+	34.2477i	−0.695179	+	1.20409i	−0.970120	+	0.242624i	$0.921992\pi$
$810$	−41.4942	−	71.8701i	−1.45796	−	2.52526i
$811$	43.8260			1.53894			0.769470	−	0.638683i	$-0.220520\pi$
$811$	43.8260			1.53894			0.769470	+	0.638683i	$0.220520\pi$
$812$		0			0
$813$	35.9942	+	62.3439i	1.26237	+	2.18649i
$814$	−16.6152			−0.582363
$815$	−8.31411	−	14.4005i	−0.291231	−	0.504426i
$816$	5.88415	−	10.1916i	0.205986	−	0.356779i
$817$	−14.6664	+	25.4030i	−0.513114	+	0.888740i
$818$	0.548079			0.0191631
$819$		0			0
$820$	−10.8610			−0.379283
$821$	−22.5162	+	38.9992i	−0.785820	+	1.36108i	0.142688	+	0.989768i	$0.454426\pi$
$821$	−22.5162	+	38.9992i	−0.785820	+	1.36108i	−0.928508	+	0.371313i	$0.878908\pi$
$822$	21.0999	−	36.5461i	0.735943	−	1.27469i
$823$	−12.5994	−	21.8227i	−0.439186	−	0.760693i	0.558441	−	0.829545i	$-0.311400\pi$
$823$	−12.5994	−	21.8227i	−0.439186	−	0.760693i	−0.997627	+	0.0688515i	$0.978067\pi$
$824$	20.0304			0.697793
$825$	−17.1314	−	29.6724i	−0.596438	−	1.03306i
$826$		0			0
$827$	−22.3091			−0.775762			−0.387881	−	0.921709i	$-0.626793\pi$
$827$	−22.3091			−0.775762			−0.387881	+	0.921709i	$0.626793\pi$
$828$	25.8452	+	44.7651i	0.898181	+	1.55570i
$829$	13.0981	−	22.6866i	0.454917	−	0.787939i	−0.543766	−	0.839237i	$-0.683002\pi$
$829$	13.0981	−	22.6866i	0.454917	−	0.787939i	0.998683	+	0.0512972i	$0.0163356\pi$
$830$	−11.3706	+	19.6945i	−0.394679	+	0.683605i
$831$	0.914095			0.0317096
$832$	−5.06069	+	44.4316i	−0.175448	+	1.54039i
$833$		0			0
$834$	8.81601	−	15.2698i	0.305274	−	0.528749i
$835$	−6.13975	+	10.6344i	−0.212475	+	0.368017i
$836$	28.7122	+	49.7310i	0.993032	+	1.71998i
$837$	4.70965			0.162789
$838$	−0.517650	−	0.896597i	−0.0178819	−	0.0309724i
$839$	21.7207	+	37.6214i	0.749882	+	1.29883i	0.947879	+	0.318631i	$0.103223\pi$
$839$	21.7207	+	37.6214i	0.749882	+	1.29883i	−0.197997	+	0.980203i	$0.563443\pi$
$840$		0			0
$841$	−21.1410	−	36.6173i	−0.729000	−	1.26266i
$842$	11.0280	−	19.1011i	0.380051	−	0.658268i
$843$	26.4912	−	45.8840i	0.912404	−	1.58033i
$844$	94.6272			3.25720
$845$	−42.7020	−	9.85524i	−1.46899	−	0.339031i
$846$	18.8267			0.647275
$847$		0			0
$848$	1.09449	−	1.89571i	0.0375849	−	0.0650989i
$849$	22.3414	+	38.6964i	0.766754	+	1.32806i
$850$	80.9801			2.77759
$851$	9.86102	+	17.0798i	0.338031	+	0.585487i
$852$	30.0979	+	52.1311i	1.03114	+	1.78598i
$853$	−1.15312			−0.0394820			−0.0197410	−	0.999805i	$-0.506284\pi$
$853$	−1.15312			−0.0394820			−0.0197410	+	0.999805i	$0.506284\pi$
$854$		0			0
$855$	28.1703	−	48.7924i	0.963404	−	1.66866i
$856$	22.0675	−	38.2220i	0.754252	−	1.30640i
$857$	25.0087			0.854280			0.427140	−	0.904185i	$-0.359521\pi$
$857$	25.0087			0.854280			0.427140	+	0.904185i	$0.359521\pi$
$858$	−5.12145	+	44.9650i	−0.174843	+	1.53508i
$859$	4.08914			0.139520			0.0697598	−	0.997564i	$-0.477777\pi$
$859$	4.08914			0.139520			0.0697598	+	0.997564i	$0.477777\pi$
$860$	23.6994	−	41.0486i	0.808143	−	1.39974i
$861$		0			0
$862$	25.1158	+	43.5018i	0.855447	+	1.48168i
$863$	17.3929			0.592060			0.296030	−	0.955179i	$-0.404337\pi$
$863$	17.3929			0.592060			0.296030	+	0.955179i	$0.404337\pi$
$864$	3.48724	+	6.04007i	0.118638	+	0.205487i
$865$	−21.3926	−	37.0530i	−0.727369	−	1.25984i
$866$	−30.6803			−1.04256
$867$	−14.7575	−	25.5608i	−0.501192	−	0.868090i
$868$		0			0
$869$	8.84657	−	15.3227i	0.300099	−	0.519787i
$870$	153.224			5.19478
$871$	13.3716	+	9.89370i	0.453079	+	0.335235i
$872$	−13.7784			−0.466595
$873$	4.14674	−	7.18237i	0.140346	−	0.243086i
$874$	53.9188	−	93.3901i	1.82383	−	3.15897i
$875$		0			0
$876$	−16.4224			−0.554862
$877$	7.49082	+	12.9745i	0.252947	+	0.438117i	0.964336	−	0.264681i	$-0.0852668\pi$
$877$	7.49082	+	12.9745i	0.252947	+	0.438117i	−0.711389	+	0.702799i	$0.751933\pi$
$878$	34.7217	+	60.1398i	1.17180	+	2.02962i
$879$	36.4184			1.22836
$880$	−3.67019	−	6.35696i	−0.123722	−	0.214293i
$881$	21.3382	−	36.9588i	0.718901	−	1.24517i	−0.242534	−	0.970143i	$-0.577979\pi$
$881$	21.3382	−	36.9588i	0.718901	−	1.24517i	0.961436	−	0.275030i	$-0.0886879\pi$
$882$		0			0
$883$	35.8874			1.20771			0.603854	−	0.797095i	$-0.293631\pi$
$883$	35.8874			1.20771			0.603854	+	0.797095i	$0.293631\pi$
$884$	−54.3490	−	40.2131i	−1.82796	−	1.35251i
$885$	56.4096			1.89619
$886$	17.3076	−	29.9777i	0.581461	−	1.00712i
$887$	13.8336	−	23.9605i	0.464488	−	0.804516i	−0.534691	−	0.845048i	$-0.679572\pi$
$887$	13.8336	−	23.9605i	0.464488	−	0.804516i	0.999178	+	0.0405317i	$0.0129052\pi$
$888$	11.8142	+	20.4629i	0.396460	+	0.686689i
$889$		0			0
$890$	51.7163	+	89.5752i	1.73353	+	3.00257i
$891$	12.3087	+	21.3194i	0.412359	+	0.714226i
$892$	−29.8996			−1.00111
$893$	−12.4130	−	21.5000i	−0.415386	−	0.719469i
$894$	−38.1251	+	66.0346i	−1.27509	+	2.20853i
$895$	14.8150	−	25.6604i	0.495211	−	0.857731i
$896$		0			0
$897$	49.2618	−	21.4218i	1.64480	−	0.715253i
$898$	61.1386			2.04022
$899$	−12.8805	+	22.3096i	−0.429588	+	0.744068i
$900$	−25.4927	+	44.1546i	−0.849756	+	1.47182i
$901$	−6.39566	−	11.0776i	−0.213070	−	0.369048i
$902$	5.09712			0.169716
$903$		0			0
$904$	23.9054	+	41.4053i	0.795081	+	1.37712i
$905$	−57.9772			−1.92723
$906$	−3.62376	−	6.27654i	−0.120391	−	0.208524i
$907$	−9.09663	+	15.7558i	−0.302049	+	0.523164i	−0.976600	−	0.215064i	$-0.931004\pi$
$907$	−9.09663	+	15.7558i	−0.302049	+	0.523164i	0.674551	+	0.738228i	$0.264337\pi$
$908$	37.7387	−	65.3654i	1.25240	−	2.16923i
$909$	11.0249			0.365673
$910$		0			0
$911$	−33.1527			−1.09840			−0.549199	−	0.835691i	$-0.685067\pi$
$911$	−33.1527			−1.09840			−0.549199	+	0.835691i	$0.685067\pi$
$912$	7.72880	−	13.3867i	0.255926	−	0.443277i
$913$	3.37295	−	5.84212i	0.111628	−	0.193346i
$914$	−18.5015	−	32.0456i	−0.611977	−	1.05998i
$915$	49.7403			1.64436
$916$	−35.2508	−	61.0562i	−1.16472	−	2.01736i
$917$		0			0
$918$	−19.6398			−0.648209
$919$	−1.49164	−	2.58359i	−0.0492046	−	0.0852249i	0.840374	−	0.542007i	$-0.182335\pi$
$919$	−1.49164	−	2.58359i	−0.0492046	−	0.0852249i	−0.889579	+	0.456782i	$0.849002\pi$
$920$	−36.4122	+	63.0679i	−1.20048	+	2.07929i
$921$	22.2282	−	38.5004i	0.732444	−	1.26863i
$922$	51.4999			1.69606
$923$	25.0874	−	10.9094i	0.825761	−	0.359087i
$924$		0			0
$925$	−9.72654	+	16.8469i	−0.319807	+	0.553921i
$926$	21.3202	−	36.9277i	0.700626	−	1.21352i
$927$	6.97456	+	12.0803i	0.229075	+	0.396769i
$928$	−38.1491			−1.25231
$929$	−16.6990	−	28.9235i	−0.547876	−	0.948948i	−0.998420	−	0.0561943i	$-0.982103\pi$
$929$	−16.6990	−	28.9235i	−0.547876	−	0.948948i	0.450544	−	0.892754i	$-0.351230\pi$
$930$	−27.6872	−	47.9557i	−0.907899	−	1.57253i
$931$		0			0
$932$	29.7018	+	51.4450i	0.972915	+	1.68514i
$933$	3.53813	−	6.12823i	0.115833	−	0.200629i
$934$	−5.28459	+	9.15318i	−0.172917	+	0.299501i
$935$	−42.8937			−1.40277
$936$	25.8097	−	11.2235i	0.843615	−	0.366851i
$937$	−51.3187			−1.67651			−0.838254	−	0.545279i	$-0.816424\pi$
$937$	−51.3187			−1.67651			−0.838254	+	0.545279i	$0.816424\pi$
$938$		0			0
$939$	−40.7253	+	70.5382i	−1.32902	+	2.30193i
$940$	20.0581	+	34.7416i	0.654223	+	1.13315i
$941$	19.0039			0.619509			0.309755	−	0.950817i	$-0.399753\pi$
$941$	19.0039			0.619509			0.309755	+	0.950817i	$0.399753\pi$
$942$	−35.1006	−	60.7961i	−1.14364	−	1.98084i
$943$	−3.02511	−	5.23964i	−0.0985110	−	0.170626i
$944$	6.76801			0.220280
$945$		0			0
$946$	−11.1222	+	19.2643i	−0.361615	+	0.626335i
$947$	23.3540	−	40.4503i	0.758902	−	1.31446i	−0.184508	−	0.982831i	$-0.559069\pi$
$947$	23.3540	−	40.4503i	0.758902	−	1.31446i	0.943411	−	0.331626i	$-0.107597\pi$
$948$	−60.2061			−1.95540
$949$	−0.844605	+	7.41542i	−0.0274170	+	0.240715i
$950$	106.367			3.45100
$951$	−37.7598	+	65.4019i	−1.22444	+	2.12080i
$952$		0			0
$953$	0.865567	+	1.49921i	0.0280385	+	0.0485640i	0.879704	−	0.475521i	$-0.157741\pi$
$953$	0.865567	+	1.49921i	0.0280385	+	0.0485640i	−0.851666	+	0.524085i	$0.824407\pi$
$954$	12.7412			0.412512
$955$	−1.79985	−	3.11742i	−0.0582416	−	0.100877i
$956$	−5.59996	−	9.69941i	−0.181116	−	0.313701i
$957$	−45.4520			−1.46926
$958$	12.1776	+	21.0922i	0.393439	+	0.681457i
$959$		0			0
$960$	48.2712	−	83.6082i	1.55795	−	2.69844i
$961$	−21.6901			−0.699681
$962$	23.5630	−	10.2465i	0.759701	−	0.330360i
$963$	30.7355			0.990437
$964$	−2.51807	+	4.36142i	−0.0811015	+	0.140472i
$965$	−5.31928	+	9.21326i	−0.171234	+	0.296585i
$966$		0			0
$967$	−4.88811			−0.157191			−0.0785955	−	0.996907i	$-0.525044\pi$
$967$	−4.88811			−0.157191			−0.0785955	+	0.996907i	$0.525044\pi$
$968$	−9.31411	−	16.1325i	−0.299367	−	0.518519i
$969$	−45.1633	−	78.2252i	−1.45086	−	2.51296i
$970$	27.9583			0.897687
$971$	−4.28576	−	7.42316i	−0.137537	−	0.238220i	0.789027	−	0.614359i	$-0.210585\pi$
$971$	−4.28576	−	7.42316i	−0.137537	−	0.238220i	−0.926564	+	0.376138i	$0.877252\pi$
$972$	33.9288	−	58.7664i	1.08827	−	1.88493i
$973$		0			0
$974$	−83.7347			−2.68303
$975$	42.5938	+	31.5153i	1.36409	+	1.00930i
$976$	5.96783			0.191026
$977$	20.0191	−	34.6741i	0.640467	−	1.10932i	−0.344861	−	0.938654i	$-0.612074\pi$
$977$	20.0191	−	34.6741i	0.640467	−	1.10932i	0.985329	−	0.170668i	$-0.0545927\pi$
$978$	13.2772	−	22.9967i	0.424557	−	0.735355i
$979$	−15.3410	−	26.5714i	−0.490300	−	0.849225i
$980$		0			0
$981$	−4.79761	−	8.30971i	−0.153176	−	0.265309i
$982$	8.97922	+	15.5525i	0.286539	+	0.496299i
$983$	23.9120			0.762675			0.381337	−	0.924436i	$-0.375464\pi$
$983$	23.9120			0.762675			0.381337	+	0.924436i	$0.375464\pi$
$984$	−3.62431	−	6.27749i	−0.115539	−	0.200119i
$985$	29.8271	−	51.6620i	0.950370	−	1.64609i
$986$	53.7130	−	93.0336i	1.71057	−	2.96279i
$987$		0			0
$988$	−71.3872	−	52.8197i	−2.27113	−	1.68042i
$989$	26.4039			0.839594
$990$	21.3628	−	37.0015i	0.678955	−	1.17598i
$991$	−20.5069	+	35.5190i	−0.651424	+	1.12830i	0.331354	+	0.943506i	$0.392495\pi$
$991$	−20.5069	+	35.5190i	−0.651424	+	1.12830i	−0.982778	+	0.184792i	$0.940839\pi$
$992$	6.89345	+	11.9398i	0.218867	+	0.379089i
$993$	11.0302			0.350033
$994$		0			0
$995$	−21.8946	−	37.9226i	−0.694106	−	1.20223i
$996$	−22.9549			−0.727354
$997$	−12.7122	−	22.0182i	−0.402600	−	0.697324i	0.591439	−	0.806350i	$-0.298560\pi$
$997$	−12.7122	−	22.0182i	−0.402600	−	0.697324i	−0.994039	+	0.109026i	$0.965227\pi$
$998$	9.89819	−	17.1442i	0.313322	−	0.542689i
$999$	2.35894	−	4.08580i	0.0746334	−	0.129269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.f.l.295.7	✓	16
7.2	even	3		637.2.h.m.165.1		16
7.3	odd	6		637.2.g.m.373.7		16
7.4	even	3		637.2.g.m.373.8		16
7.5	odd	6		637.2.h.m.165.2		16
7.6	odd	2	inner	637.2.f.l.295.8	yes	16
13.3	even	3	inner	637.2.f.l.393.7	yes	16
13.4	even	6		8281.2.a.cl.1.8		8
13.9	even	3		8281.2.a.ci.1.2		8
91.3	odd	6		637.2.h.m.471.2		16
91.16	even	3		637.2.g.m.263.8		16
91.48	odd	6		8281.2.a.ci.1.1		8
91.55	odd	6	inner	637.2.f.l.393.8	yes	16
91.68	odd	6		637.2.g.m.263.7		16
91.69	odd	6		8281.2.a.cl.1.7		8
91.81	even	3		637.2.h.m.471.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.l.295.7	✓	16	1.1	even	1	trivial
637.2.f.l.295.8	yes	16	7.6	odd	2	inner
637.2.f.l.393.7	yes	16	13.3	even	3	inner
637.2.f.l.393.8	yes	16	91.55	odd	6	inner
637.2.g.m.263.7		16	91.68	odd	6
637.2.g.m.263.8		16	91.16	even	3
637.2.g.m.373.7		16	7.3	odd	6
637.2.g.m.373.8		16	7.4	even	3
637.2.h.m.165.1		16	7.2	even	3
637.2.h.m.165.2		16	7.5	odd	6
637.2.h.m.471.1		16	91.81	even	3
637.2.h.m.471.2		16	91.3	odd	6
8281.2.a.ci.1.1		8	91.48	odd	6
8281.2.a.ci.1.2		8	13.9	even	3
8281.2.a.cl.1.7		8	91.69	odd	6
8281.2.a.cl.1.8		8	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16576 - 2.01915i) q^{2} +(-1.15450 + 1.99966i) q^{3} +(-1.71798 - 2.97563i) q^{4} +3.37112 q^{5} +(2.69174 + 4.66224i) q^{6} -3.34797 q^{8} +(-1.16576 - 2.01915i) q^{9} +O(q^{10})\)	\(q+(1.16576 - 2.01915i) q^{2} +(-1.15450 + 1.99966i) q^{3} +(-1.71798 - 2.97563i) q^{4} +3.37112 q^{5} +(2.69174 + 4.66224i) q^{6} -3.34797 q^{8} +(-1.16576 - 2.01915i) q^{9} +(3.92990 - 6.80679i) q^{10} +(-1.16576 + 2.01915i) q^{11} +7.93366 q^{12} +(0.408029 - 3.58239i) q^{13} +(-3.89197 + 6.74108i) q^{15} +(-0.466957 + 0.808794i) q^{16} +(2.72867 + 4.72620i) q^{17} -5.43596 q^{18} +(3.58410 + 6.20784i) q^{19} +(-5.79151 - 10.0312i) q^{20} +(2.71798 + 4.70768i) q^{22} +(3.22621 - 5.58796i) q^{23} +(3.86524 - 6.69480i) q^{24} +6.36442 q^{25} +(-6.75772 - 5.00007i) q^{26} -1.54354 q^{27} +(4.22143 - 7.31174i) q^{29} +(9.07418 + 15.7169i) q^{30} -3.05121 q^{31} +(-2.25925 - 3.91314i) q^{32} +(-2.69174 - 4.66224i) q^{33} +12.7239 q^{34} +(-4.00550 + 6.93773i) q^{36} +(-1.52827 + 2.64704i) q^{37} +16.7127 q^{38} +(6.69249 + 4.95180i) q^{39} -11.2864 q^{40} +(0.468833 - 0.812043i) q^{41} +(2.04605 + 3.54385i) q^{43} +8.01100 q^{44} +(-3.92990 - 6.80679i) q^{45} +(-7.52195 - 13.0284i) q^{46} -3.46336 q^{47} +(-1.07821 - 1.86751i) q^{48} +(7.41937 - 12.8507i) q^{50} -12.6010 q^{51} +(-11.3609 + 4.94034i) q^{52} -2.34387 q^{53} +(-1.79939 + 3.11663i) q^{54} +(-3.92990 + 6.80679i) q^{55} -16.5514 q^{57} +(-9.84233 - 17.0474i) q^{58} +(-3.62346 - 6.27602i) q^{59} +26.7453 q^{60} +(-3.19506 - 5.53401i) q^{61} +(-3.55697 + 6.16085i) q^{62} -12.4028 q^{64} +(1.37551 - 12.0766i) q^{65} -12.5517 q^{66} +(-2.30670 + 3.99532i) q^{67} +(9.37561 - 16.2390i) q^{68} +(7.44934 + 12.9026i) q^{69} +(3.79370 + 6.57088i) q^{71} +(3.90292 + 6.76006i) q^{72} -2.06996 q^{73} +(3.56318 + 6.17161i) q^{74} +(-7.34775 + 12.7267i) q^{75} +(12.3148 - 21.3299i) q^{76} +(17.8002 - 7.74054i) q^{78} -7.58868 q^{79} +(-1.57417 + 2.72654i) q^{80} +(5.27929 - 9.14400i) q^{81} +(-1.09309 - 1.89329i) q^{82} -2.89335 q^{83} +(9.19866 + 15.9326i) q^{85} +9.54077 q^{86} +(9.74732 + 16.8829i) q^{87} +(3.90292 - 6.76006i) q^{88} +(-6.57984 + 11.3966i) q^{89} -18.3253 q^{90} -22.1703 q^{92} +(3.52263 - 6.10138i) q^{93} +(-4.03744 + 6.99305i) q^{94} +(12.0824 + 20.9273i) q^{95} +10.4333 q^{96} +(1.77856 + 3.08056i) q^{97} +5.43596 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 - 4 * q^9	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} - 4 q^{16} - 56 q^{18} + 28 q^{22} + 12 q^{23} - 24 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} - 8 q^{37} - 4 q^{39} + 32 q^{43} - 8 q^{44} - 4 q^{46} + 36 q^{50} - 88 q^{51} - 8 q^{53} - 96 q^{57} - 48 q^{58} + 128 q^{60} - 64 q^{64} + 16 q^{65} + 20 q^{67} + 8 q^{71} + 28 q^{72} + 76 q^{74} + 28 q^{78} - 8 q^{79} + 56 q^{81} + 36 q^{85} + 8 q^{86} + 28 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 - 4 * q^9 - 4 * q^11 - 8 * q^15 - 4 * q^16 - 56 * q^18 + 28 * q^22 + 12 * q^23 - 24 * q^25 + 8 * q^29 + 28 * q^30 + 4 * q^36 - 8 * q^37 - 4 * q^39 + 32 * q^43 - 8 * q^44 - 4 * q^46 + 36 * q^50 - 88 * q^51 - 8 * q^53 - 96 * q^57 - 48 * q^58 + 128 * q^60 - 64 * q^64 + 16 * q^65 + 20 * q^67 + 8 * q^71 + 28 * q^72 + 76 * q^74 + 28 * q^78 - 8 * q^79 + 56 * q^81 + 36 * q^85 + 8 * q^86 + 28 * q^88 - 160 * q^92 + 8 * q^93 + 52 * q^95 + 56 * q^99

Introduction

L-functions

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