LMFDB - Embedded newform 637.2.f.l.393.8

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:	16.0.468066644398978174550016.2
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			393.8
Root			$0.558788 - 0.967849i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.l.295.8

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

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	0.902442	+	0.430812i	$0.141773\pi$
$2$	1.16576	+	2.01915i	0.824315	+	1.42776i	−0.0781266	+	0.996943i	$0.524894\pi$
$3$	1.15450	+	1.99966i	0.666553	+	1.15450i	0.978862	+	0.204523i	$0.0655643\pi$
$3$	1.15450	+	1.99966i	0.666553	+	1.15450i	−0.312309	+	0.949981i	$0.601102\pi$
$4$	−1.71798	+	2.97563i	−0.858991	+	1.48782i
$5$	−3.37112			−1.50761			−0.753804	−	0.657099i	$-0.771783\pi$
$5$	−3.37112			−1.50761			−0.753804	+	0.657099i	$0.771783\pi$
$6$	−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	0.635021	−	0.772494i	$-0.280991\pi$
$11$	−1.16576	−	2.01915i	−0.351489	−	0.608797i	−0.986511	+	0.163697i	$0.947658\pi$
$12$	−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	0.318343	+	0.947976i	$0.396874\pi$
$17$	−2.72867	+	4.72620i	−0.661800	+	1.14627i	−0.980142	+	0.198295i	$0.936460\pi$
$18$	−5.43596			−1.28127
$19$	−3.58410	+	6.20784i	−0.822248	+	1.42418i	0.0817564	+	0.996652i	$0.473947\pi$
$19$	−3.58410	+	6.20784i	−0.822248	+	1.42418i	−0.904004	+	0.427523i	$0.859386\pi$
$20$	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	0.977132	+	0.212632i	$0.0682036\pi$
$23$	3.22621	+	5.58796i	0.672711	+	1.16517i	−0.304421	+	0.952537i	$0.598463\pi$
$24$	−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	0.929654	+	0.368434i	$0.120106\pi$
$29$	4.22143	+	7.31174i	0.783900	+	1.35776i	−0.145753	+	0.989321i	$0.546561\pi$
$30$	9.07418	−	15.7169i	1.65671	−	2.86951i
$31$	3.05121			0.548013			0.274007	−	0.961728i	$-0.411651\pi$
$31$	3.05121			0.548013			0.274007	+	0.961728i	$0.411651\pi$
$32$	−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	0.712623	−	0.701547i	$-0.247507\pi$
$37$	−1.52827	−	2.64704i	−0.251246	−	0.435170i	−0.963869	+	0.266377i	$0.914174\pi$
$38$	−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	$-0.189994\pi$
$41$	−0.468833	−	0.812043i	−0.0732194	−	0.126820i	−0.900311	+	0.435248i	$0.856661\pi$
$42$		0			0
$43$	2.04605	−	3.54385i	0.312019	−	0.540433i	−0.666780	−	0.745254i	$-0.732328\pi$
$43$	2.04605	−	3.54385i	0.312019	−	0.540433i	0.978799	+	0.204822i	$0.0656614\pi$
$44$	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	$-0.418717\pi$
$47$	3.46336			0.505183			0.252591	+	0.967573i	$0.418717\pi$
$48$	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	$-0.676961\pi$
$59$	3.62346	−	6.27602i	0.471735	−	0.817069i	0.999477	+	0.0323358i	$0.0102946\pi$
$60$	26.7453			3.45280
$61$	3.19506	−	5.53401i	0.409086	−	0.708558i	−0.585702	−	0.810527i	$-0.699181\pi$
$61$	3.19506	−	5.53401i	0.409086	−	0.708558i	0.994788	+	0.101969i	$0.0325143\pi$
$62$	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	0.690022	−	0.723788i	$-0.257601\pi$
$67$	−2.30670	−	3.99532i	−0.281808	−	0.488106i	−0.971830	+	0.235682i	$0.924268\pi$
$68$	−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	−0.548171	−	0.836366i	$-0.684676\pi$
$71$	3.79370	−	6.57088i	0.450229	−	0.779819i	0.998400	+	0.0565468i	$0.0180090\pi$
$72$	3.90292	−	6.76006i	0.459964	−	0.796680i
$73$	2.06996			0.242271			0.121136	−	0.992636i	$-0.461346\pi$
$73$	2.06996			0.242271			0.121136	+	0.992636i	$0.461346\pi$
$74$	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	$-0.449240\pi$
$83$	2.89335			0.317587			0.158793	+	0.987312i	$0.449240\pi$
$84$		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	0.969344	+	0.245708i	$0.0790205\pi$
$89$	6.57984	+	11.3966i	0.697461	+	1.20804i	−0.271882	+	0.962330i	$0.587646\pi$
$90$	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	$-0.891133\pi$
$97$	−1.77856	+	3.08056i	−0.180585	+	0.312783i	0.761495	+	0.648171i	$0.224466\pi$
$98$		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	$-0.0910728\pi$
$101$	2.36432	+	4.09513i	0.235259	+	0.407481i	−0.724089	+	0.689707i	$0.757740\pi$
$102$	−14.6898	−	25.4434i	−1.45450	−	2.51927i
$103$	5.98286			0.589508			0.294754	−	0.955573i	$-0.404762\pi$
$103$	5.98286			0.589508			0.294754	+	0.955573i	$0.404762\pi$
$104$	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	−0.986043	−	0.166490i	$-0.946757\pi$
$107$	−6.59131	−	11.4165i	−0.637206	−	1.10367i	0.348837	−	0.937183i	$-0.386577\pi$
$108$	−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	0.305723	+	0.952121i	$0.401102\pi$
$113$	−7.14026	+	12.3673i	−0.671699	+	1.16342i	−0.977422	+	0.211297i	$0.932231\pi$
$114$	−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	0.999952	−	0.00982616i	$-0.00312781\pi$
$127$	5.53854	+	9.59304i	0.491466	+	0.851244i	−0.508486	+	0.861071i	$0.669794\pi$
$128$	−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	$-0.490654\pi$
$131$	0.672012			0.0587139			0.0293570	+	0.999569i	$0.490654\pi$
$132$	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	−0.983457	−	0.181142i	$-0.942021\pi$
$137$	−3.91937	+	6.78855i	−0.334855	+	0.579985i	0.648602	+	0.761128i	$0.275354\pi$
$138$	−34.7365			−2.95697
$139$	1.63760	−	2.83641i	0.138900	−	0.240581i	−0.788181	−	0.615444i	$-0.788977\pi$
$139$	1.63760	−	2.83641i	0.138900	−	0.240581i	0.927080	+	0.374863i	$0.122310\pi$
$140$		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	−0.415290	−	0.909689i	$-0.636320\pi$
$149$	7.08186	−	12.2661i	0.580169	−	1.00488i	0.995459	−	0.0951925i	$-0.0303467\pi$
$150$	−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	$-0.325799\pi$
$157$	13.0401			1.04071			0.520357	+	0.853949i	$0.325799\pi$
$158$	−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	−0.946300	−	0.323289i	$-0.895211\pi$
$163$	−2.46628	+	4.27172i	−0.193174	+	0.334587i	0.753127	+	0.657876i	$0.228545\pi$
$164$	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	$-0.121656\pi$
$167$	1.82128	+	3.15455i	0.140935	+	0.244107i	−0.786914	+	0.617063i	$0.788322\pi$
$168$		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	$-0.673075\pi$
$173$	6.34584	−	10.9913i	0.482465	−	0.835654i	0.999797	+	0.0201306i	$0.00640819\pi$
$174$	−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	0.982209	−	0.187789i	$-0.0601321\pi$
$179$	4.39469	+	7.61183i	0.328475	+	0.568935i	−0.653735	+	0.756724i	$0.726799\pi$
$180$	13.5030	+	23.3879i	1.00645	+	1.74323i
$181$	17.1982			1.27833			0.639167	−	0.769068i	$-0.279279\pi$
$181$	17.1982			1.27833			0.639167	+	0.769068i	$0.279279\pi$
$182$		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	−0.884695	−	0.466171i	$-0.845633\pi$
$191$	−0.533902	+	0.924745i	−0.0386318	+	0.0669122i	0.846063	+	0.533083i	$0.178967\pi$
$192$	−14.3191	−	24.8013i	−1.03339	−	1.78988i
$193$	−1.57790	−	2.73300i	−0.113580	−	0.196726i	0.803631	−	0.595127i	$-0.202898\pi$
$193$	−1.57790	−	2.73300i	−0.113580	−	0.196726i	−0.917211	+	0.398402i	$0.869565\pi$
$194$	−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	0.987474	+	0.157784i	$0.0504351\pi$
$197$	8.84783	+	15.3249i	0.630382	+	1.09185i	−0.357092	+	0.934069i	$0.616232\pi$
$198$	6.33701	+	10.9760i	0.450352	+	0.780033i
$199$	6.49476	−	11.2493i	0.460402	−	0.797439i	−0.538579	−	0.842575i	$-0.681039\pi$
$199$	6.49476	−	11.2493i	0.460402	−	0.797439i	0.998981	+	0.0451359i	$0.0143721\pi$
$200$	−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	−0.749685	−	0.661795i	$-0.769795\pi$
$211$	−13.7701	−	23.8505i	−0.947974	−	1.64194i	−0.198289	−	0.980144i	$-0.563538\pi$
$212$	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	$-0.260776\pi$
$223$	−4.35098	−	7.53612i	−0.291363	−	0.504656i	−0.974132	+	0.225978i	$0.927442\pi$
$224$		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	0.228310	+	0.973589i	$0.426680\pi$
$227$	−10.9835	+	19.0239i	−0.728998	+	1.26266i	−0.957307	+	0.289072i	$0.906653\pi$
$228$	28.4350	−	49.2509i	1.88315	−	3.26172i
$229$	−20.5188			−1.35592			−0.677959	−	0.735100i	$-0.737135\pi$
$229$	−20.5188			−1.35592			−0.677959	+	0.735100i	$0.737135\pi$
$230$	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	$-0.818301\pi$
$241$	0.732856	−	1.26934i	0.0472074	−	0.0817657i	0.888664	+	0.458560i	$0.151634\pi$
$242$	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	0.459156	+	0.888356i	$0.348152\pi$
$251$	−8.55142	+	14.8115i	−0.539761	+	0.934894i	−0.998917	+	0.0465376i	$0.985181\pi$
$252$		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	$-0.204982\pi$
$257$	−1.92506	−	3.33430i	−0.120082	−	0.207988i	−0.919800	+	0.392388i	$0.871649\pi$
$258$	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	0.763866	+	0.645375i	$0.223299\pi$
$263$	15.2579	+	26.4275i	0.940844	+	1.62959i	0.176978	+	0.984215i	$0.443368\pi$
$264$	−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	0.488451	+	0.872591i	$0.337562\pi$
$269$	−8.38857	+	14.5294i	−0.511460	+	0.885875i	−0.999912	+	0.0132842i	$0.995771\pi$
$270$	−6.06595	−	10.5065i	−0.369162	−	0.639407i
$271$	−15.5886	−	27.0003i	−0.946941	−	1.64015i	−0.751817	−	0.659372i	$-0.770822\pi$
$271$	−15.5886	−	27.0003i	−0.946941	−	1.64015i	−0.195124	−	0.980779i	$-0.562511\pi$
$272$	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	−0.871911	−	0.489665i	$-0.837119\pi$
$277$	−0.197941	+	0.342844i	−0.0118931	+	0.0205995i	0.860018	+	0.510264i	$0.170452\pi$
$278$	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	−0.996024	−	0.0890873i	$-0.971605\pi$
$283$	−9.67575	−	16.7589i	−0.575164	−	0.996213i	0.420860	−	0.907126i	$-0.361728\pi$
$284$	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	$-0.680926\pi$
$293$	7.88616	−	13.6592i	0.460715	−	0.797981i	0.998997	+	0.0447835i	$0.0142598\pi$
$294$		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	$-0.314846\pi$
$307$	19.2535			1.09885			0.549427	+	0.835542i	$0.314846\pi$
$308$		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	$-0.472307\pi$
$311$	3.06464			0.173780			0.0868898	+	0.996218i	$0.472307\pi$
$312$	−22.4062	+	16.5785i	−1.26850	+	0.938571i
$313$	−35.2751			−1.99387			−0.996934	−	0.0782450i	$-0.975068\pi$
$313$	−35.2751			−1.99387			−0.996934	+	0.0782450i	$0.975068\pi$
$314$	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	−0.924172	−	0.381977i	$-0.875244\pi$
$331$	−2.38851	+	4.13703i	−0.131285	+	0.227392i	0.792887	+	0.609368i	$0.208577\pi$
$332$	−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	−0.691130	−	0.722730i	$-0.742887\pi$
$347$	5.22211	−	9.04496i	0.280338	−	0.485559i	0.971468	+	0.237171i	$0.0762202\pi$
$348$	−33.4914	−	58.0088i	−1.79533	−	3.10960i
$349$	−11.7344	−	20.3246i	−0.628128	−	1.08795i	−0.987927	−	0.154920i	$-0.950488\pi$
$349$	−11.7344	−	20.3246i	−0.628128	−	1.08795i	0.359799	−	0.933030i	$-0.382845\pi$
$350$		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	$-0.191523\pi$
$353$	−1.46567	−	2.53862i	−0.0780099	−	0.135117i	−0.902391	+	0.430918i	$0.858190\pi$
$354$	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	$-0.157954\pi$
$367$	0.524301	+	0.908115i	0.0273683	+	0.0474032i	−0.852017	+	0.523514i	$0.824621\pi$
$368$	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	−0.603650	−	0.797249i	$-0.706288\pi$
$373$	7.50536	−	12.9997i	0.388613	−	0.673098i	0.992263	+	0.124152i	$0.0396210\pi$
$374$	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	0.969401	+	0.245481i	$0.0789459\pi$
$379$	13.5749	+	23.5123i	0.697294	+	1.20775i	−0.272108	+	0.962267i	$0.587721\pi$
$380$	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	$-0.699052\pi$
$383$	8.01320	−	13.8793i	0.409455	−	0.709197i	0.994829	+	0.101566i	$0.0323854\pi$
$384$	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	$-0.734219\pi$
$397$	6.10435	−	10.5731i	0.306369	−	0.530646i	0.977565	+	0.210633i	$0.0675526\pi$
$398$	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	−0.756051	−	0.654513i	$-0.772874\pi$
$401$	−18.9206	−	32.7715i	−0.944850	−	1.63653i	−0.188799	−	0.982016i	$-0.560459\pi$
$402$	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	$-0.835183\pi$
$409$	−0.117537	+	0.203580i	−0.00581184	+	0.0100664i	0.863105	+	0.505025i	$0.168517\pi$
$410$	−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	$-0.170119\pi$
$419$	−0.222023	−	0.384555i	−0.0108465	−	0.0187868i	−0.871398	+	0.490577i	$0.836786\pi$
$420$		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	−0.999759	−	0.0219436i	$-0.993015\pi$
$431$	−10.7723	−	18.6582i	−0.518883	−	0.898732i	0.480876	−	0.876789i	$-0.340319\pi$
$432$	−0.720766	−	1.24840i	−0.0346778	−	0.0600638i
$433$	6.57949	−	11.3960i	0.316190	−	0.547657i	−0.663500	−	0.748176i	$-0.730930\pi$
$433$	6.57949	−	11.3960i	0.316190	−	0.547657i	0.979690	+	0.200519i	$0.0642630\pi$
$434$		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	0.964568	+	0.263836i	$0.0849878\pi$
$439$	14.8923	+	25.7943i	0.710773	+	1.23109i	−0.253795	+	0.967258i	$0.581679\pi$
$440$	−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	−0.370949	−	0.928653i	$-0.620968\pi$
$449$	13.1114	−	22.7095i	0.618763	−	1.07173i	0.989712	−	0.143075i	$-0.0456992\pi$
$450$	−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	0.989751	−	0.142804i	$-0.0456120\pi$
$457$	7.93542	+	13.7445i	0.371203	+	0.642943i	−0.618548	+	0.785747i	$0.712279\pi$
$458$	−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	0.485476	+	0.874250i	$0.338646\pi$
$461$	−11.0443	+	19.1293i	−0.514384	+	0.890940i	−0.999861	+	0.0166900i	$0.994687\pi$
$462$		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	$-0.466552\pi$
$467$	4.53318			0.209771			0.104885	+	0.994484i	$0.466552\pi$
$468$	−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	$-0.0899630\pi$
$479$	5.22303	+	9.04655i	0.238646	+	0.413347i	−0.721680	+	0.692227i	$0.756630\pi$
$480$	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	0.0965311	+	0.995330i	$0.469225\pi$
$487$	−17.9571	+	31.1027i	−0.813715	+	1.40940i	−0.910247	+	0.414067i	$0.864108\pi$
$488$	−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	0.765943	−	0.642909i	$-0.222273\pi$
$491$	−3.85124	−	6.67054i	−0.173804	−	0.301037i	−0.939747	+	0.341871i	$0.888939\pi$
$492$	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	0.297924	+	0.954589i	$0.403706\pi$
$503$	−15.2000	+	26.3272i	−0.677736	+	1.17387i	−0.975661	+	0.219285i	$0.929628\pi$
$504$		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	$-0.0544476\pi$
$509$	7.79007	+	13.4928i	0.345289	+	0.598058i	−0.640117	+	0.768277i	$0.721114\pi$
$510$	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	$-0.297194\pi$
$521$	27.1574			1.18979			0.594893	+	0.803805i	$0.297194\pi$
$522$	−22.9476	−	39.7463i	−1.00439	−	1.73965i
$523$	9.02874	+	15.6382i	0.394799	+	0.683812i	0.993076	−	0.117478i	$-0.0374808\pi$
$523$	9.02874	+	15.6382i	0.394799	+	0.683812i	−0.598276	+	0.801290i	$0.704147\pi$
$524$	−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	0.952122	−	0.305719i	$-0.0988969\pi$
$557$	4.98686	+	8.63750i	0.211300	+	0.365983i	−0.740822	+	0.671702i	$0.765564\pi$
$558$	−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	$-0.683456\pi$
$563$	10.7640	−	18.6437i	0.453647	−	0.785740i	0.998609	+	0.0527209i	$0.0167894\pi$
$564$	−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	0.970577	+	0.240791i	$0.0774068\pi$
$569$	16.5502	+	28.6657i	0.693819	+	1.20173i	−0.276758	+	0.960940i	$0.589260\pi$
$570$	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	$-0.289795\pi$
$577$	29.4695			1.22683			0.613416	+	0.789760i	$0.289795\pi$
$578$	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	$-0.212736\pi$
$587$	−3.49429	−	6.05229i	−0.144225	−	0.249805i	−0.929084	+	0.369870i	$0.879402\pi$
$588$		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	$-0.493658\pi$
$593$	0.970248			0.0398433			0.0199216	+	0.999802i	$0.493658\pi$
$594$	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	0.989371	+	0.145414i	$0.0464513\pi$
$601$	15.2146	+	26.3525i	0.620617	+	1.07494i	−0.368754	+	0.929527i	$0.620215\pi$
$602$		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	−0.329868	−	0.944027i	$-0.607004\pi$
$607$	16.0788	−	27.8493i	0.652618	−	1.13037i	0.982485	−	0.186340i	$-0.0596626\pi$
$608$	−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	0.690534	−	0.723300i	$-0.257376\pi$
$613$	−6.96043	−	12.0558i	−0.281129	−	0.486930i	−0.971663	+	0.236370i	$0.924042\pi$
$614$	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	−0.745356	−	0.666666i	$-0.767721\pi$
$617$	5.08394	−	8.80565i	0.204672	−	0.354502i	0.950028	+	0.312164i	$0.101054\pi$
$618$	−16.1043	+	27.8935i	−0.647810	+	1.12204i
$619$	−43.7905			−1.76009			−0.880044	−	0.474893i	$-0.842487\pi$
$619$	−43.7905			−1.76009			−0.880044	+	0.474893i	$0.842487\pi$
$620$	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	−0.980540	−	0.196320i	$-0.937101\pi$
$631$	−8.04464	+	13.9337i	−0.320252	+	0.554693i	0.660288	+	0.751013i	$0.270434\pi$
$632$	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	0.285148	−	0.958483i	$-0.407957\pi$
$641$	24.6254	−	42.6525i	0.972645	−	1.68467i	0.687497	−	0.726187i	$-0.258709\pi$
$642$	70.9684			2.80090
$643$	1.33579	−	2.31366i	0.0526784	−	0.0912417i	−0.838484	−	0.544927i	$-0.816558\pi$
$643$	1.33579	−	2.31366i	0.0526784	−	0.0912417i	0.891162	+	0.453685i	$0.149891\pi$
$644$		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	0.981689	+	0.190490i	$0.0610076\pi$
$647$	16.6814	+	28.8930i	0.655814	+	1.13590i	−0.325876	+	0.945413i	$0.605659\pi$
$648$	−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	0.532637	−	0.846344i	$-0.321201\pi$
$653$	−11.9244	−	20.6536i	−0.466637	−	0.808239i	−0.999274	+	0.0381052i	$0.987868\pi$
$654$	−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	−0.649071	−	0.760727i	$-0.724842\pi$
$659$	8.58114	−	14.8630i	0.334274	−	0.578979i	0.983345	+	0.181749i	$0.0581757\pi$
$660$	−31.1785	−	54.0028i	−1.21362	−	2.10206i
$661$	−0.233201	−	0.403917i	−0.00907048	−	0.0157105i	0.861455	−	0.507835i	$-0.169554\pi$
$661$	−0.233201	−	0.403917i	−0.00907048	−	0.0157105i	−0.870525	+	0.492124i	$0.836221\pi$
$662$	−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	0.645990	−	0.763346i	$-0.276445\pi$
$673$	−8.77061	−	15.1911i	−0.338082	−	0.585576i	−0.984072	+	0.177770i	$0.943112\pi$
$674$	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	$-0.440196\pi$
$677$	9.71961			0.373555			0.186777	+	0.982402i	$0.440196\pi$
$678$	−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	−0.280564	−	0.959835i	$-0.590522\pi$
$683$	18.0577	−	31.2769i	0.690960	−	1.19678i	0.971524	−	0.236942i	$-0.0761451\pi$
$684$	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	$-0.220031\pi$
$691$	−4.38634	−	7.59737i	−0.166864	−	0.289018i	−0.937316	+	0.348481i	$0.886698\pi$
$692$	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	−0.688681	−	0.725065i	$-0.741810\pi$
$709$	7.55100	−	13.0787i	0.283584	−	0.491182i	0.972265	+	0.233883i	$0.0751433\pi$
$710$	−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	$-0.949874\pi$
$719$	−9.59946	+	16.6267i	−0.357999	+	0.620073i	0.629627	+	0.776897i	$0.283208\pi$
$720$	−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	$-0.514236\pi$
$727$	−2.41101			−0.0894195			−0.0447098	+	0.999000i	$0.514236\pi$
$728$		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	$-0.580201\pi$
$733$	−13.4992			−0.498604			−0.249302	+	0.968426i	$0.580201\pi$
$734$	−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	0.866419	−	0.499318i	$-0.166416\pi$
$739$	0.0214096	+	0.0370824i	0.000787563	+	0.00136410i	−0.865631	+	0.500682i	$0.833083\pi$
$740$	−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	0.993372	−	0.114941i	$-0.0366678\pi$
$743$	10.8254	+	18.7501i	0.397145	+	0.687875i	−0.596228	+	0.802815i	$0.703334\pi$
$744$	−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	0.906454	+	0.422304i	$0.138779\pi$
$751$	22.4429	+	38.8723i	0.818953	+	1.41847i	−0.0875006	+	0.996164i	$0.527888\pi$
$752$	−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	0.926469	−	0.376372i	$-0.122828\pi$
$757$	3.77726	+	6.54240i	0.137287	+	0.237788i	−0.789182	+	0.614159i	$0.789495\pi$
$758$	−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	$-0.972682\pi$
$761$	−11.6946	+	20.2556i	−0.423928	+	0.734265i	0.572392	+	0.819980i	$0.306016\pi$
$762$	−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	0.925564	+	0.378592i	$0.123592\pi$
$769$	21.9255	+	37.9760i	0.790652	+	1.36945i	−0.134911	+	0.990858i	$0.543075\pi$
$770$		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	−0.159005	−	0.987278i	$-0.550829\pi$
$773$	21.5613	−	37.3452i	0.775505	−	1.34321i	0.934510	−	0.355936i	$-0.115838\pi$
$774$	−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

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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more