LMFDB - Embedded newform 637.2.bb.b.227.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(227,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("637.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bb (of order $12$, degree $4$, not 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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.2
Character	$\chi$	$=$	637.227
Dual form			637.2.bb.b.362.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.65980 + 1.65980i) q^{2} +(2.39046 - 1.38013i) q^{3} -3.50987i q^{4} +(0.412430 - 1.53921i) q^{5} +(-1.67694 + 6.25841i) q^{6} +(2.50608 + 2.50608i) q^{8} +(2.30952 - 4.00020i) q^{9} +(1.87023 + 3.23933i) q^{10} +(0.813080 - 3.03446i) q^{11} +(-4.84407 - 8.39018i) q^{12} +(-1.04831 - 3.44979i) q^{13} +(-1.13841 - 4.24862i) q^{15} -1.29944 q^{16} -0.641590 q^{17} +(2.80620 + 10.4729i) q^{18} +(-7.61472 + 2.04036i) q^{19} +(-5.40242 - 1.44757i) q^{20} +(3.68704 + 6.38614i) q^{22} +0.146149i q^{23} +(9.44938 + 2.53195i) q^{24} +(2.13106 + 1.23037i) q^{25} +(7.46594 + 3.98598i) q^{26} -4.46896i q^{27} +(1.49412 - 2.58790i) q^{29} +(8.94139 + 5.16231i) q^{30} +(-6.46586 + 1.73252i) q^{31} +(-2.85535 + 2.85535i) q^{32} +(-2.24431 - 8.37589i) q^{33} +(1.06491 - 1.06491i) q^{34} +(-14.0402 - 8.10610i) q^{36} +(-2.75050 - 2.75050i) q^{37} +(9.25232 - 16.0255i) q^{38} +(-7.26709 - 6.79977i) q^{39} +(4.89096 - 2.82380i) q^{40} +(5.60356 - 1.50147i) q^{41} +(2.42713 - 1.40130i) q^{43} +(-10.6505 - 2.85380i) q^{44} +(-5.20463 - 5.20463i) q^{45} +(-0.242578 - 0.242578i) q^{46} +(3.04537 + 0.816005i) q^{47} +(-3.10624 + 1.79339i) q^{48} +(-5.57930 + 1.49497i) q^{50} +(-1.53369 + 0.885477i) q^{51} +(-12.1083 + 3.67942i) q^{52} +(3.66059 - 6.34033i) q^{53} +(7.41757 + 7.41757i) q^{54} +(-4.33533 - 2.50300i) q^{55} +(-15.3867 + 15.3867i) q^{57} +(1.81545 + 6.77534i) q^{58} +(2.93283 - 2.93283i) q^{59} +(-14.9121 + 3.99568i) q^{60} +(3.90292 + 2.25335i) q^{61} +(7.85639 - 13.6077i) q^{62} -12.0775i q^{64} +(-5.74230 + 0.190767i) q^{65} +(17.6274 + 10.1772i) q^{66} +(1.36775 + 0.366486i) q^{67} +2.25190i q^{68} +(0.201704 + 0.349362i) q^{69} +(13.8300 + 3.70574i) q^{71} +(15.8126 - 4.23699i) q^{72} +(1.82677 + 6.81760i) q^{73} +9.13055 q^{74} +6.79227 q^{75} +(7.16138 + 26.7267i) q^{76} +(23.3482 - 0.775656i) q^{78} +(0.316458 + 0.548121i) q^{79} +(-0.535926 + 2.00010i) q^{80} +(0.760810 + 1.31776i) q^{81} +(-6.80865 + 11.7929i) q^{82} +(1.07813 + 1.07813i) q^{83} +(-0.264611 + 0.987541i) q^{85} +(-1.70266 + 6.35443i) q^{86} -8.24834i q^{87} +(9.64223 - 5.56694i) q^{88} +(9.60471 - 9.60471i) q^{89} +17.2773 q^{90} +0.512963 q^{92} +(-13.0652 + 13.0652i) q^{93} +(-6.40911 + 3.70030i) q^{94} +12.5621i q^{95} +(-2.88483 + 10.7663i) q^{96} +(0.0487160 - 0.181811i) q^{97} +(-10.2606 - 10.2606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9} - 16 q^{11} - 8 q^{15} - 24 q^{16} + 68 q^{18} + 4 q^{22} + 4 q^{29} - 12 q^{30} - 68 q^{32} - 8 q^{37} - 48 q^{43} + 60 q^{44} + 24 q^{46} - 44 q^{50} - 12 q^{51} - 36 q^{53}+ \cdots - 60 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9 - 16 * q^11 - 8 * q^15 - 24 * q^16 + 68 * q^18 + 4 * q^22 + 4 * q^29 - 12 * q^30 - 68 * q^32 - 8 * q^37 - 48 * q^43 + 60 * q^44 + 24 * q^46 - 44 * q^50 - 12 * q^51 - 36 * q^53 - 92 * q^57 - 28 * q^58 - 104 * q^60 - 32 * q^65 - 8 * q^67 + 84 * q^71 + 124 * q^72 + 48 * q^74 + 148 * q^78 + 40 * q^79 + 28 * q^81 + 36 * q^85 - 60 * q^86 + 228 * q^88 + 24 * q^92 - 84 * q^93 - 60 * q^99

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.65980	+	1.65980i	−1.17366	+	1.17366i	−0.192324	+	0.981332i	$0.561602\pi$
$2$	−1.65980	+	1.65980i	−1.17366	+	1.17366i	−0.981332	+	0.192324i	$0.938398\pi$
$3$	2.39046	−	1.38013i	1.38013	−	0.796818i	0.387956	−	0.921678i	$-0.373181\pi$
$3$	2.39046	−	1.38013i	1.38013	−	0.796818i	0.992174	+	0.124860i	$0.0398481\pi$
$4$		−	3.50987i		−	1.75493i
$5$	0.412430	−	1.53921i	0.184444	−	0.688355i	−0.810305	−	0.586009i	$-0.800698\pi$
$5$	0.412430	−	1.53921i	0.184444	−	0.688355i	0.994749	−	0.102346i	$-0.0326350\pi$
$6$	−1.67694	+	6.25841i	−0.684607	+	2.55499i
$7$		0			0
$7$		0			0
$8$	2.50608	+	2.50608i	0.886032	+	0.886032i
$9$	2.30952	−	4.00020i	0.769839	−	1.33340i
$10$	1.87023	+	3.23933i	0.591418	+	1.02437i
$11$	0.813080	−	3.03446i	0.245153	−	0.914923i	−0.728154	−	0.685414i	$-0.759621\pi$
$11$	0.813080	−	3.03446i	0.245153	−	0.914923i	0.973306	−	0.229509i	$-0.0737121\pi$
$12$	−4.84407	−	8.39018i	−1.39836	−	2.42204i
$13$	−1.04831	−	3.44979i	−0.290748	−	0.956800i
$13$	−1.04831	−	3.44979i	−0.290748	−	0.956800i
$14$		0			0
$15$	−1.13841	−	4.24862i	−0.293937	−	1.09699i
$16$	−1.29944			−0.324859
$17$	−0.641590			−0.155608			−0.0778042	−	0.996969i	$-0.524791\pi$
$17$	−0.641590			−0.155608			−0.0778042	+	0.996969i	$0.524791\pi$
$18$	2.80620	+	10.4729i	0.661427	+	2.46848i
$19$	−7.61472	+	2.04036i	−1.74694	+	0.468090i	−0.983968	−	0.178346i	$-0.942925\pi$
$19$	−7.61472	+	2.04036i	−1.74694	+	0.468090i	−0.762968	+	0.646436i	$0.776259\pi$
$20$	−5.40242	−	1.44757i	−1.20802	−	0.323687i
$21$		0			0
$22$	3.68704	+	6.38614i	0.786080	+	1.36153i
$23$			0.146149i			0.0304741i	0.999884	+	0.0152371i	$0.00485029\pi$
$23$			0.146149i			0.0304741i	−0.999884	+	0.0152371i	$0.995150\pi$
$24$	9.44938	+	2.53195i	1.92885	+	0.516833i
$25$	2.13106	+	1.23037i	0.426212	+	0.246074i
$26$	7.46594	+	3.98598i	1.46419	+	0.781715i
$27$		−	4.46896i		−	0.860051i
$28$		0			0
$29$	1.49412	−	2.58790i	0.277452	−	0.480561i	−0.693299	−	0.720650i	$-0.743843\pi$
$29$	1.49412	−	2.58790i	0.277452	−	0.480561i	0.970751	+	0.240089i	$0.0771768\pi$
$30$	8.94139	+	5.16231i	1.63247	+	0.942505i
$31$	−6.46586	+	1.73252i	−1.16130	+	0.311170i	−0.787486	−	0.616333i	$-0.788618\pi$
$31$	−6.46586	+	1.73252i	−1.16130	+	0.311170i	−0.373817	+	0.927503i	$0.621951\pi$
$32$	−2.85535	+	2.85535i	−0.504760	+	0.504760i
$33$	−2.24431	−	8.37589i	−0.390685	−	1.45806i
$34$	1.06491	−	1.06491i	0.182631	−	0.182631i
$35$		0			0
$36$	−14.0402	−	8.10610i	−2.34003	−	1.35102i
$37$	−2.75050	−	2.75050i	−0.452179	−	0.452179i	0.443898	−	0.896077i	$-0.353595\pi$
$37$	−2.75050	−	2.75050i	−0.452179	−	0.452179i	−0.896077	+	0.443898i	$0.853595\pi$
$38$	9.25232	−	16.0255i	1.50092	−	2.59968i
$39$	−7.26709	−	6.79977i	−1.16367	−	1.08883i
$40$	4.89096	−	2.82380i	0.773328	−	0.446481i
$41$	5.60356	−	1.50147i	0.875129	−	0.234490i	0.206825	−	0.978378i	$-0.433687\pi$
$41$	5.60356	−	1.50147i	0.875129	−	0.234490i	0.668305	+	0.743888i	$0.267020\pi$
$42$		0			0
$43$	2.42713	−	1.40130i	0.370133	−	0.213697i	−0.303383	−	0.952869i	$-0.598116\pi$
$43$	2.42713	−	1.40130i	0.370133	−	0.213697i	0.673517	+	0.739172i	$0.264783\pi$
$44$	−10.6505	−	2.85380i	−1.60563	−	0.430227i
$45$	−5.20463	−	5.20463i	−0.775861	−	0.775861i
$46$	−0.242578	−	0.242578i	−0.0357661	−	0.0357661i
$47$	3.04537	+	0.816005i	0.444213	+	0.119027i	0.473990	−	0.880530i	$-0.342813\pi$
$47$	3.04537	+	0.816005i	0.444213	+	0.119027i	−0.0297773	+	0.999557i	$0.509480\pi$
$48$	−3.10624	+	1.79339i	−0.448348	+	0.258854i
$49$		0			0
$50$	−5.57930	+	1.49497i	−0.789032	+	0.211420i
$51$	−1.53369	+	0.885477i	−0.214760	+	0.123992i
$52$	−12.1083	+	3.67942i	−1.67912	+	0.510243i
$53$	3.66059	−	6.34033i	0.502821	−	0.870912i	−0.497173	−	0.867651i	$-0.665629\pi$
$53$	3.66059	−	6.34033i	0.502821	−	0.870912i	0.999995	−	0.00326078i	$-0.00103794\pi$
$54$	7.41757	+	7.41757i	1.00940	+	1.00940i
$55$	−4.33533	−	2.50300i	−0.584575	−	0.337505i
$56$		0			0
$57$	−15.3867	+	15.3867i	−2.03802	+	2.03802i
$58$	1.81545	+	6.77534i	0.238380	+	0.889646i
$59$	2.93283	−	2.93283i	0.381821	−	0.381821i	−0.489937	−	0.871758i	$-0.662980\pi$
$59$	2.93283	−	2.93283i	0.381821	−	0.381821i	0.871758	+	0.489937i	$0.162980\pi$
$60$	−14.9121	+	3.99568i	−1.92514	+	0.515840i
$61$	3.90292	+	2.25335i	0.499718	+	0.288512i	0.728597	−	0.684942i	$-0.240173\pi$
$61$	3.90292	+	2.25335i	0.499718	+	0.288512i	−0.228879	+	0.973455i	$0.573506\pi$
$62$	7.85639	−	13.6077i	0.997763	−	1.72818i
$63$		0			0
$64$		−	12.0775i		−	1.50969i
$65$	−5.74230	+	0.190767i	−0.712245	+	0.0236617i
$66$	17.6274	+	10.1772i	2.16978	+	1.25273i
$67$	1.36775	+	0.366486i	0.167097	+	0.0447734i	0.341397	−	0.939919i	$-0.389100\pi$
$67$	1.36775	+	0.366486i	0.167097	+	0.0447734i	−0.174301	+	0.984692i	$0.555766\pi$
$68$			2.25190i			0.273082i
$69$	0.201704	+	0.349362i	0.0242823	+	0.0420582i
$70$		0			0
$71$	13.8300	+	3.70574i	1.64132	+	0.439791i	0.957165	−	0.289544i	$-0.0935038\pi$
$71$	13.8300	+	3.70574i	1.64132	+	0.439791i	0.684157	+	0.729335i	$0.260170\pi$
$72$	15.8126	−	4.23699i	1.86354	−	0.499334i
$73$	1.82677	+	6.81760i	0.213807	+	0.797940i	0.986583	+	0.163261i	$0.0522011\pi$
$73$	1.82677	+	6.81760i	0.213807	+	0.797940i	−0.772776	+	0.634679i	$0.781132\pi$
$74$	9.13055			1.06140
$75$	6.79227			0.784304
$76$	7.16138	+	26.7267i	0.821467	+	3.06576i
$77$		0			0
$78$	23.3482	−	0.775656i	2.64366	−	0.0878258i
$79$	0.316458	+	0.548121i	0.0356043	+	0.0616685i	0.883278	−	0.468849i	$-0.155331\pi$
$79$	0.316458	+	0.548121i	0.0356043	+	0.0616685i	−0.847674	+	0.530517i	$0.821998\pi$
$80$	−0.535926	+	2.00010i	−0.0599184	+	0.223618i
$81$	0.760810	+	1.31776i	0.0845344	+	0.146418i
$82$	−6.80865	+	11.7929i	−0.751890	+	1.30231i
$83$	1.07813	+	1.07813i	0.118340	+	0.118340i	0.763797	−	0.645457i	$-0.223333\pi$
$83$	1.07813	+	1.07813i	0.118340	+	0.118340i	−0.645457	+	0.763797i	$0.723333\pi$
$84$		0			0
$85$	−0.264611	+	0.987541i	−0.0287011	+	0.107114i
$86$	−1.70266	+	6.35443i	−0.183603	+	0.685215i
$87$		−	8.24834i		−	0.884315i
$88$	9.64223	−	5.56694i	1.02786	−	0.593438i
$89$	9.60471	−	9.60471i	1.01810	−	1.01810i	0.0182641	−	0.999833i	$-0.494186\pi$
$89$	9.60471	−	9.60471i	1.01810	−	1.01810i	0.999833	−	0.0182641i	$-0.00581396\pi$
$90$	17.2773			1.82119
$91$		0			0
$92$	0.512963			0.0534801
$93$	−13.0652	+	13.0652i	−1.35480	+	1.35480i
$94$	−6.40911	+	3.70030i	−0.661049	+	0.381657i
$95$			12.5621i			1.28885i
$96$	−2.88483	+	10.7663i	−0.294432	+	1.09884i
$97$	0.0487160	−	0.181811i	0.00494637	−	0.0184601i	−0.963409	−	0.268037i	$-0.913625\pi$
$97$	0.0487160	−	0.181811i	0.00494637	−	0.0184601i	0.968355	+	0.249577i	$0.0802916\pi$
$98$		0			0
$99$	−10.2606	−	10.2606i	−1.03123	−	1.03123i
$100$	4.31843	−	7.47974i	0.431843	−	0.747974i
$101$	−0.596904	−	1.03387i	−0.0593942	−	0.102874i	0.834799	−	0.550554i	$-0.185584\pi$
$101$	−0.596904	−	1.03387i	−0.0593942	−	0.102874i	−0.894194	+	0.447680i	$0.852250\pi$
$102$	1.07591	−	4.01534i	0.106531	−	0.397577i
$103$	−2.39792	−	4.15331i	−0.236274	−	0.409238i	0.723368	−	0.690462i	$-0.242593\pi$
$103$	−2.39792	−	4.15331i	−0.236274	−	0.409238i	−0.959642	+	0.281224i	$0.909260\pi$
$104$	6.01830	−	11.2726i	0.590143	−	1.10537i
$105$		0			0
$106$	4.44783	+	16.5995i	0.432012	+	1.61229i
$107$	15.2964			1.47876			0.739378	−	0.673290i	$-0.235120\pi$
$107$	15.2964			1.47876			0.739378	+	0.673290i	$0.235120\pi$
$108$	−15.6855			−1.50933
$109$	3.33967	+	12.4638i	0.319883	+	1.19382i	0.919357	+	0.393424i	$0.128710\pi$
$109$	3.33967	+	12.4638i	0.319883	+	1.19382i	−0.599475	+	0.800394i	$0.704624\pi$
$110$	11.3503	−	3.04129i	1.08220	−	0.289976i
$111$	−10.3710	−	2.77890i	−0.984370	−	0.263761i
$112$		0			0
$113$	−0.770731	−	1.33494i	−0.0725042	−	0.125581i	0.827494	−	0.561475i	$-0.189766\pi$
$113$	−0.770731	−	1.33494i	−0.0725042	−	0.125581i	−0.899998	+	0.435894i	$0.856432\pi$
$114$		−	51.0776i		−	4.78386i
$115$	0.224953	+	0.0602761i	0.0209770	+	0.00562078i
$116$	−9.08318	−	5.24418i	−0.843352	−	0.486910i
$117$	−16.2209	−	3.77391i	−1.49963	−	0.348898i
$118$			9.73580i			0.896253i
$119$		0			0
$120$	7.79441	−	13.5003i	0.711529	−	1.23240i
$121$	0.979449	+	0.565485i	0.0890408	+	0.0514077i
$122$	−10.2182	+	2.73796i	−0.925111	+	0.247883i
$123$	11.3228	−	11.3228i	1.02095	−	1.02095i
$124$	6.08092	+	22.6943i	0.546083	+	2.03801i
$125$	8.40660	−	8.40660i	0.751910	−	0.751910i
$126$		0			0
$127$	2.81842	+	1.62722i	0.250095	+	0.144392i	0.619808	−	0.784754i	$-0.287211\pi$
$127$	2.81842	+	1.62722i	0.250095	+	0.144392i	−0.369713	+	0.929146i	$0.620544\pi$
$128$	14.3355	+	14.3355i	1.26709	+	1.26709i
$129$	3.86796	−	6.69950i	0.340555	−	0.589858i
$130$	9.21443	−	9.84770i	0.808159	−	0.863701i
$131$	−14.2615	+	8.23390i	−1.24604	+	0.719400i	−0.970317	−	0.241838i	$-0.922250\pi$
$131$	−14.2615	+	8.23390i	−1.24604	+	0.719400i	−0.275720	+	0.961238i	$0.588916\pi$
$132$	−29.3983	+	7.87724i	−2.55879	+	0.685626i
$133$		0			0
$134$	−2.87848	+	1.66189i	−0.248663	+	0.143565i
$135$	−6.87866	−	1.84313i	−0.592021	−	0.158632i
$136$	−1.60787	−	1.60787i	−0.137874	−	0.137874i
$137$	−0.267239	−	0.267239i	−0.0228318	−	0.0228318i	0.695599	−	0.718431i	$-0.255139\pi$
$137$	−0.267239	−	0.267239i	−0.0228318	−	0.0228318i	−0.718431	+	0.695599i	$0.755139\pi$
$138$	−0.914659	−	0.245082i	−0.0778610	−	0.0208628i
$139$	−8.52132	+	4.91978i	−0.722769	+	0.417291i	−0.815771	−	0.578375i	$-0.803687\pi$
$139$	−8.52132	+	4.91978i	−0.722769	+	0.417291i	0.0930022	+	0.995666i	$0.470354\pi$
$140$		0			0
$141$	8.40602	−	2.25239i	0.707914	−	0.189685i
$142$	−29.1058	+	16.8043i	−2.44251	+	1.41018i
$143$	−11.3206	+	0.376085i	−0.946676	+	0.0314498i
$144$	−3.00107	+	5.19801i	−0.250089	+	0.433167i
$145$	−3.36710	−	3.36710i	−0.279622	−	0.279622i
$146$	−14.3479	−	8.28378i	−1.18744	−	0.685570i
$147$		0			0
$148$	−9.65388	+	9.65388i	−0.793544	+	0.793544i
$149$	1.43738	+	5.36436i	0.117754	+	0.439465i	0.999478	−	0.0323006i	$-0.0102834\pi$
$149$	1.43738	+	5.36436i	0.117754	+	0.439465i	−0.881724	+	0.471766i	$0.843617\pi$
$150$	−11.2738	+	11.2738i	−0.920503	+	0.920503i
$151$	−4.58330	+	1.22809i	−0.372983	+	0.0999406i	−0.440441	−	0.897782i	$-0.645178\pi$
$151$	−4.58330	+	1.22809i	−0.372983	+	0.0999406i	0.0674576	+	0.997722i	$0.478511\pi$
$152$	−24.1964	−	13.9698i	−1.96258	−	1.13310i
$153$	−1.48176	+	2.56649i	−0.119793	+	0.207488i
$154$		0			0
$155$			10.6669i			0.856782i
$156$	−23.8663	+	25.5065i	−1.91083	+	2.04216i
$157$	−10.9293	−	6.31006i	−0.872257	−	0.503598i	−0.00415919	−	0.999991i	$-0.501324\pi$
$157$	−10.9293	−	6.31006i	−0.872257	−	0.503598i	−0.868098	+	0.496394i	$0.834657\pi$
$158$	−1.43503	−	0.384515i	−0.114165	−	0.0305904i
$159$		−	20.2084i		−	1.60263i
$160$	3.21735	+	5.57262i	0.254354	+	0.440554i
$161$		0			0
$162$	−3.45001	−	0.924428i	−0.271058	−	0.0726299i
$163$	12.6085	−	3.37843i	0.987571	−	0.264619i	0.271341	−	0.962483i	$-0.412533\pi$
$163$	12.6085	−	3.37843i	0.987571	−	0.264619i	0.716230	+	0.697864i	$0.245866\pi$
$164$	−5.26996	−	19.6678i	−0.411515	−	1.53579i
$165$	−13.8179			−1.07572
$166$	−3.57897			−0.277782
$167$	−4.79697	−	17.9025i	−0.371201	−	1.38534i	−0.858817	−	0.512282i	$-0.828800\pi$
$167$	−4.79697	−	17.9025i	−0.371201	−	1.38534i	0.487616	−	0.873058i	$-0.337867\pi$
$168$		0			0
$169$	−10.8021	+	7.23288i	−0.830931	+	0.556375i
$170$	−1.19992	−	2.07832i	−0.0920296	−	0.159400i
$171$	−9.42448	+	35.1726i	−0.720708	+	2.68972i
$172$	−4.91839	−	8.51890i	−0.375024	−	0.649560i
$173$	−2.79684	+	4.84427i	−0.212640	+	0.368303i	−0.952540	−	0.304414i	$-0.901540\pi$
$173$	−2.79684	+	4.84427i	−0.212640	+	0.368303i	0.739900	+	0.672717i	$0.234873\pi$
$174$	13.6906	+	13.6906i	1.03788	+	1.03788i
$175$		0			0
$176$	−1.05655	+	3.94308i	−0.0796402	+	0.297221i
$177$	2.96311	−	11.0585i	0.222721	−	0.831205i
$178$			31.8838i			2.38979i
$179$	−8.21928	+	4.74540i	−0.614338	+	0.354688i	−0.774661	−	0.632377i	$-0.782080\pi$
$179$	−8.21928	+	4.74540i	−0.614338	+	0.354688i	0.160324	+	0.987065i	$0.448746\pi$
$180$	−18.2676	+	18.2676i	−1.36158	+	1.36158i
$181$	6.91516			0.514000			0.257000	−	0.966411i	$-0.417266\pi$
$181$	6.91516			0.514000			0.257000	+	0.966411i	$0.417266\pi$
$182$		0			0
$183$	12.4397			0.919568
$184$	−0.366260	+	0.366260i	−0.0270011	+	0.0270011i
$185$	−5.36798	+	3.09920i	−0.394662	+	0.227858i
$186$		−	43.3714i		−	3.18014i
$187$	−0.521664	+	1.94688i	−0.0381479	+	0.142370i
$188$	2.86407	−	10.6889i	0.208884	−	0.779565i
$189$		0			0
$190$	−20.8506	−	20.8506i	−1.51266	−	1.51266i
$191$	1.25251	−	2.16942i	0.0906287	−	0.156974i	−0.817147	−	0.576429i	$-0.804446\pi$
$191$	1.25251	−	2.16942i	0.0906287	−	0.156974i	0.907776	+	0.419456i	$0.137779\pi$
$192$	−16.6685	−	28.8707i	−1.20295	−	2.08356i
$193$	−5.83813	+	21.7882i	−0.420238	+	1.56835i	0.353870	+	0.935295i	$0.384866\pi$
$193$	−5.83813	+	21.7882i	−0.420238	+	1.56835i	−0.774108	+	0.633054i	$0.781801\pi$
$194$	0.220911	+	0.382628i	0.0158605	+	0.0274711i
$195$	−13.4634	+	8.38114i	−0.964136	+	0.600186i
$196$		0			0
$197$	−4.63560	−	17.3003i	−0.330273	−	1.23259i	−0.908904	−	0.417005i	$-0.863080\pi$
$197$	−4.63560	−	17.3003i	−0.330273	−	1.23259i	0.578631	−	0.815589i	$-0.303587\pi$
$198$	34.0611			2.42062
$199$	16.4123			1.16344			0.581720	−	0.813389i	$-0.302380\pi$
$199$	16.4123			1.16344			0.581720	+	0.813389i	$0.302380\pi$
$200$	2.25720	+	8.42400i	0.159608	+	0.595667i
$201$	3.77533	−	1.01160i	0.266291	−	0.0713526i
$202$	2.70675	+	0.725273i	0.190447	+	0.0510300i
$203$		0			0
$204$	3.10791	+	5.38306i	0.217597	+	0.376889i
$205$		−	9.24430i		−	0.645650i
$206$	10.8737	+	2.91361i	0.757609	+	0.203001i
$207$	0.584624	+	0.337533i	0.0406342	+	0.0234602i
$208$	1.36221	+	4.48278i	0.0944521	+	0.310825i
$209$			24.7655i			1.71307i
$210$		0			0
$211$	4.93176	−	8.54207i	0.339517	−	0.588060i	−0.644825	−	0.764330i	$-0.723070\pi$
$211$	4.93176	−	8.54207i	0.339517	−	0.588060i	0.984342	+	0.176270i	$0.0564032\pi$
$212$	−22.2537	−	12.8482i	−1.52839	−	0.882418i
$213$	38.1744	−	10.2288i	2.61567	−	0.700867i
$214$	−25.3889	+	25.3889i	−1.73555	+	1.73555i
$215$	−1.15588	−	4.31380i	−0.0788302	−	0.294198i
$216$	11.1996	−	11.1996i	0.762033	−	0.762033i
$217$		0			0
$218$	−26.2306	−	15.1443i	−1.77656	−	1.02570i
$219$	13.7760	+	13.7760i	0.930895	+	0.930895i
$220$	−8.78520	+	15.2164i	−0.592298	+	1.02589i
$221$	0.672583	+	2.21335i	0.0452428	+	0.148886i
$222$	21.8262	−	12.6013i	1.46488	−	0.845747i
$223$	−8.41926	+	2.25594i	−0.563796	+	0.151069i	−0.529450	−	0.848341i	$-0.677602\pi$
$223$	−8.41926	+	2.25594i	−0.563796	+	0.151069i	−0.0343461	+	0.999410i	$0.510935\pi$
$224$		0			0
$225$	9.84344	−	5.68312i	0.656230	−	0.378874i
$226$	3.49500	+	0.936482i	0.232484	+	0.0622939i
$227$	11.9452	+	11.9452i	0.792834	+	0.792834i	0.981954	−	0.189120i	$-0.0605636\pi$
$227$	11.9452	+	11.9452i	0.792834	+	0.792834i	−0.189120	+	0.981954i	$0.560564\pi$
$228$	54.0052	+	54.0052i	3.57658	+	3.57658i
$229$	−2.36198	−	0.632892i	−0.156084	−	0.0418227i	0.179931	−	0.983679i	$-0.442413\pi$
$229$	−2.36198	−	0.632892i	−0.156084	−	0.0418227i	−0.336015	+	0.941857i	$0.609079\pi$
$230$	−0.473424	+	0.273331i	−0.0312166	+	0.0180229i
$231$		0			0
$232$	10.2299	−	2.74108i	0.671624	−	0.179961i
$233$	4.65474	−	2.68741i	0.304942	−	0.176058i	−0.339719	−	0.940527i	$-0.610332\pi$
$233$	4.65474	−	2.68741i	0.304942	−	0.176058i	0.644661	+	0.764469i	$0.276999\pi$
$234$	33.1874	−	20.6596i	2.16953	−	1.35056i
$235$	2.51200	−	4.35092i	0.163865	−	0.283823i
$236$	−10.2938	−	10.2938i	−0.670071	−	0.670071i
$237$	1.51296	+	0.873507i	0.0982772	+	0.0567404i
$238$		0			0
$239$	−11.9572	+	11.9572i	−0.773448	+	0.773448i	−0.978708	−	0.205260i	$-0.934196\pi$
$239$	−11.9572	+	11.9572i	−0.773448	+	0.773448i	0.205260	+	0.978708i	$0.434196\pi$
$240$	1.47930	+	5.52081i	0.0954882	+	0.356367i
$241$	−9.50881	+	9.50881i	−0.612516	+	0.612516i	−0.943601	−	0.331085i	$-0.892585\pi$
$241$	−9.50881	+	9.50881i	−0.612516	+	0.612516i	0.331085	+	0.943601i	$0.392585\pi$
$242$	−2.56428	+	0.687097i	−0.164838	+	0.0441682i
$243$	15.2481	+	8.80347i	0.978163	+	0.564743i
$244$	7.90898	−	13.6987i	0.506320	−	0.876972i
$245$		0			0
$246$			37.5873i			2.39648i
$247$	15.0214	+	24.1303i	0.955786	+	1.53537i
$248$	−20.5458	−	11.8621i	−1.30466	−	0.753245i
$249$	4.06519	+	1.08926i	0.257621	+	0.0690293i
$250$			27.9066i			1.76497i
$251$	6.40248	+	11.0894i	0.404121	+	0.699958i	0.994219	−	0.107374i	$-0.0342441\pi$
$251$	6.40248	+	11.0894i	0.404121	+	0.699958i	−0.590098	+	0.807332i	$0.700911\pi$
$252$		0			0
$253$	0.443482	+	0.118831i	0.0278815	+	0.00747082i
$254$	−7.37887	+	1.97716i	−0.462992	+	0.124058i
$255$	0.730395	+	2.72587i	0.0457391	+	0.170701i
$256$	−23.4332			−1.46457
$257$	−10.3807			−0.647532			−0.323766	−	0.946137i	$-0.604949\pi$
$257$	−10.3807			−0.647532			−0.323766	+	0.946137i	$0.604949\pi$
$258$	4.69979	+	17.5399i	0.292596	+	1.09198i
$259$		0			0
$260$	0.669566	+	20.1547i	0.0415247	+	1.24994i
$261$	−6.90141	−	11.9536i	−0.427187	−	0.739909i
$262$	10.0047	−	37.3379i	0.618090	−	2.30674i
$263$	2.18977	+	3.79279i	0.135027	+	0.233873i	0.925608	−	0.378484i	$-0.123555\pi$
$263$	2.18977	+	3.79279i	0.135027	+	0.233873i	−0.790581	+	0.612358i	$0.790221\pi$
$264$	15.3662	−	26.6151i	0.945725	−	1.63804i
$265$	−8.24936	−	8.24936i	−0.506754	−	0.506754i
$266$		0			0
$267$	9.70388	−	36.2154i	0.593868	−	2.21635i
$268$	1.28632	−	4.80061i	0.0785744	−	0.293244i
$269$		−	11.6847i		−	0.712427i	−0.934405	−	0.356213i	$-0.884068\pi$
$269$		−	11.6847i		−	0.712427i	0.934405	−	0.356213i	$-0.115932\pi$
$270$	14.4764	−	8.35797i	0.881007	−	0.508650i
$271$	21.7031	−	21.7031i	1.31837	−	1.31837i	0.403303	−	0.915066i	$-0.367862\pi$
$271$	21.7031	−	21.7031i	1.31837	−	1.31837i	0.915066	−	0.403303i	$-0.132138\pi$
$272$	0.833705			0.0505508
$273$		0			0
$274$	0.887127			0.0535933
$275$	5.46622	−	5.46622i	0.329626	−	0.329626i
$276$	1.22621	−	0.707955i	0.0738094	−	0.0426139i
$277$		−	19.0652i		−	1.14552i	−0.819724	−	0.572758i	$-0.805873\pi$
$277$		−	19.0652i		−	1.14552i	0.819724	−	0.572758i	$-0.194127\pi$
$278$	5.97782	−	22.3095i	0.358526	−	1.33804i
$279$	−8.00258	+	29.8660i	−0.479102	+	1.78803i
$280$		0			0
$281$	11.8671	+	11.8671i	0.707931	+	0.707931i	0.966100	−	0.258169i	$-0.0831190\pi$
$281$	11.8671	+	11.8671i	0.707931	+	0.707931i	−0.258169	+	0.966100i	$0.583119\pi$
$282$	−10.2138	+	17.6908i	−0.608223	+	1.05347i
$283$	4.21864	+	7.30690i	0.250772	+	0.434350i	0.963739	−	0.266848i	$-0.0859821\pi$
$283$	4.21864	+	7.30690i	0.250772	+	0.434350i	−0.712966	+	0.701198i	$0.752649\pi$
$284$	13.0067	−	48.5415i	0.771804	−	2.88041i
$285$	17.3374	+	30.0292i	1.02698	+	1.77878i
$286$	18.1657	−	19.4141i	1.07416	−	1.14798i
$287$		0			0
$288$	4.82750	+	18.0165i	0.284463	+	1.06163i
$289$	−16.5884			−0.975786
$290$	11.1774			0.656360
$291$	−0.134469	−	0.501845i	−0.00788271	−	0.0294187i
$292$	23.9289	−	6.41172i	1.40033	−	0.375218i
$293$	−8.00676	−	2.14541i	−0.467760	−	0.125336i	0.0172376	−	0.999851i	$-0.494513\pi$
$293$	−8.00676	−	2.14541i	−0.467760	−	0.125336i	−0.484998	+	0.874516i	$0.661180\pi$
$294$		0			0
$295$	−3.30465	−	5.72382i	−0.192404	−	0.333253i
$296$		−	13.7859i		−	0.801290i
$297$	−13.5609	−	3.63362i	−0.786881	−	0.210844i
$298$	−11.2895	−	6.51800i	−0.653984	−	0.377578i
$299$	0.504183	−	0.153209i	0.0291576	−	0.00886029i
$300$		−	23.8400i		−	1.37640i
$301$		0			0
$302$	5.56897	−	9.64574i	0.320458	−	0.555050i
$303$	−2.85375	−	1.64761i	−0.163943	−	0.0946528i
$304$	9.89484	−	2.65131i	0.567508	−	0.152063i
$305$	5.07807	−	5.07807i	0.290769	−	0.290769i
$306$	−1.80043	−	6.71929i	−0.102924	−	0.384116i
$307$	−17.3438	+	17.3438i	−0.989863	+	0.989863i	−0.999949	−	0.0100865i	$-0.996789\pi$
$307$	−17.3438	+	17.3438i	−0.989863	+	0.989863i	0.0100865	+	0.999949i	$0.496789\pi$
$308$		0			0
$309$	−11.4642	−	6.61887i	−0.652177	−	0.376535i
$310$	−17.7048	−	17.7048i	−1.00557	−	1.00557i
$311$	−11.8560	+	20.5353i	−0.672294	+	1.16445i	0.304958	+	0.952366i	$0.401358\pi$
$311$	−11.8560	+	20.5353i	−0.672294	+	1.16445i	−0.977252	+	0.212082i	$0.931976\pi$
$312$	−1.17114	−	35.2526i	−0.0663026	−	1.99579i
$313$	−12.1862	+	7.03573i	−0.688808	+	0.397683i	−0.803165	−	0.595756i	$-0.796852\pi$
$313$	−12.1862	+	7.03573i	−0.688808	+	0.397683i	0.114358	+	0.993440i	$0.463519\pi$
$314$	28.6140	−	7.66709i	1.61478	−	0.432679i
$315$		0			0
$316$	1.92383	−	1.11073i	0.108224	−	0.0624832i
$317$	−16.1695	−	4.33262i	−0.908172	−	0.243344i	−0.225649	−	0.974209i	$-0.572450\pi$
$317$	−16.1695	−	4.33262i	−0.908172	−	0.243344i	−0.682522	+	0.730865i	$0.739117\pi$
$318$	33.5419	+	33.5419i	1.88093	+	1.88093i
$319$	−6.63803	−	6.63803i	−0.371658	−	0.371658i
$320$	−18.5898	−	4.98112i	−1.03920	−	0.278453i
$321$	36.5653	−	21.1110i	2.04088	−	1.17830i
$322$		0			0
$323$	4.88553	−	1.30907i	0.271838	−	0.0728388i
$324$	4.62517	−	2.67034i	0.256954	−	0.148352i
$325$	2.01051	−	8.64152i	0.111523	−	0.479345i
$326$	−15.3200	+	26.5350i	−0.848497	+	1.46964i
$327$	25.1850	+	25.1850i	1.39274	+	1.39274i
$328$	17.8058	+	10.2802i	0.983159	+	0.567627i
$329$		0			0
$330$	22.9349	−	22.9349i	1.26252	−	1.26252i
$331$	−2.50489	−	9.34837i	−0.137681	−	0.513833i	−0.999972	−	0.00742049i	$-0.997638\pi$
$331$	−2.50489	−	9.34837i	−0.137681	−	0.513833i	0.862291	−	0.506413i	$-0.169029\pi$
$332$	3.78410	−	3.78410i	0.207680	−	0.207680i
$333$	−17.3549	+	4.65022i	−0.951041	+	0.254831i
$334$	37.6766	+	21.7526i	2.06157	+	1.19025i
$335$	1.12820	−	1.95410i	0.0616401	−	0.106764i
$336$		0			0
$337$			20.0838i			1.09403i	0.837122	+	0.547016i	$0.184236\pi$
$337$			20.0838i			1.09403i	−0.837122	+	0.547016i	$0.815764\pi$
$338$	5.92421	−	29.9345i	0.322234	−	1.62822i
$339$	−3.68479	−	2.12742i	−0.200131	−	0.115545i
$340$	3.46614	+	0.928749i	0.187978	+	0.0503685i
$341$			21.0291i			1.13879i
$342$	−42.7368	−	74.0223i	−2.31094	−	4.00267i
$343$		0			0
$344$	9.59434	+	2.57080i	0.517292	+	0.138608i
$345$	0.620930	−	0.166378i	0.0334298	−	0.00895748i
$346$	−3.39833	−	12.6827i	−0.182695	−	0.681827i
$347$	−22.2015			−1.19184			−0.595920	−	0.803044i	$-0.703212\pi$
$347$	−22.2015			−1.19184			−0.595920	+	0.803044i	$0.703212\pi$
$348$	−28.9506			−1.55191
$349$	−1.38593	−	5.17235i	−0.0741869	−	0.276869i	0.918861	−	0.394582i	$-0.129111\pi$
$349$	−1.38593	−	5.17235i	−0.0741869	−	0.276869i	−0.993048	+	0.117713i	$0.962444\pi$
$350$		0			0
$351$	−15.4170	+	4.68484i	−0.822897	+	0.250058i
$352$	6.34281	+	10.9861i	0.338073	+	0.585560i
$353$	6.75514	−	25.2105i	0.359540	−	1.34182i	−0.515134	−	0.857110i	$-0.672258\pi$
$353$	6.75514	−	25.2105i	0.359540	−	1.34182i	0.874674	−	0.484712i	$-0.161075\pi$
$354$	13.4367	+	23.2730i	0.714151	+	1.23695i
$355$	11.4078	−	19.7589i	0.605465	−	1.04870i
$356$	−33.7113	−	33.7113i	−1.78669	−	1.78669i
$357$		0			0
$358$	5.76594	−	21.5188i	0.304739	−	1.13730i
$359$	−5.86066	+	21.8723i	−0.309314	+	1.15437i	0.619854	+	0.784717i	$0.287192\pi$
$359$	−5.86066	+	21.8723i	−0.309314	+	1.15437i	−0.929168	+	0.369658i	$0.879475\pi$
$360$		−	26.0864i		−	1.37488i
$361$	37.3664	−	21.5735i	1.96665	−	1.13545i
$362$	−11.4778	+	11.4778i	−0.603258	+	0.603258i
$363$	3.12177			0.163850
$364$		0			0
$365$	11.2471			0.588702
$366$	−20.6474	+	20.6474i	−1.07926	+	1.07926i
$367$	−12.2942	+	7.09806i	−0.641752	+	0.370516i	−0.785289	−	0.619129i	$-0.787486\pi$
$367$	−12.2942	+	7.09806i	−0.641752	+	0.370516i	0.143537	+	0.989645i	$0.454152\pi$
$368$		−	0.189911i		−	0.00989980i
$369$	6.93534	−	25.8831i	0.361040	−	1.34742i
$370$	3.76571	−	14.0538i	0.195770	−	0.730624i
$371$		0			0
$372$	45.8573	+	45.8573i	2.37759	+	2.37759i
$373$	−1.75321	+	3.03665i	−0.0907778	+	0.157232i	−0.907839	−	0.419320i	$-0.862269\pi$
$373$	−1.75321	+	3.03665i	−0.0907778	+	0.157232i	0.817061	+	0.576551i	$0.195602\pi$
$374$	−2.36557	−	4.09728i	−0.122321	−	0.211865i
$375$	8.49340	−	31.6978i	0.438598	−	1.63687i
$376$	5.58697	+	9.67691i	0.288126	+	0.499048i
$377$	−10.4940	−	2.44150i	−0.540469	−	0.125744i
$378$		0			0
$379$	6.94797	+	25.9302i	0.356893	+	1.33194i	0.878085	+	0.478504i	$0.158821\pi$
$379$	6.94797	+	25.9302i	0.356893	+	1.33194i	−0.521192	+	0.853439i	$0.674513\pi$
$380$	44.0915			2.26184
$381$	8.98309			0.460217
$382$	1.52188	+	5.67972i	0.0778660	+	0.290600i
$383$	−32.9891	+	8.83941i	−1.68567	+	0.451673i	−0.969266	−	0.246017i	$-0.920878\pi$
$383$	−32.9891	+	8.83941i	−1.68567	+	0.451673i	−0.716400	+	0.697690i	$0.754211\pi$
$384$	54.0533	+	14.4835i	2.75839	+	0.739110i
$385$		0			0
$386$	−26.4739	−	45.8542i	−1.34749	−	2.33392i
$387$		−	12.9453i		−	0.658048i
$388$	−0.638132	−	0.170987i	−0.0323962	−	0.00868054i
$389$	23.7849	+	13.7322i	1.20594	+	0.696251i	0.961870	−	0.273506i	$-0.0881834\pi$
$389$	23.7849	+	13.7322i	1.20594	+	0.696251i	0.244072	+	0.969757i	$0.421517\pi$
$390$	8.43558	−	36.2576i	0.427152	−	1.83598i
$391$		−	0.0937676i		−	0.00474203i
$392$		0			0
$393$	−22.7277	+	39.3656i	−1.14646	+	1.98573i
$394$	36.4092	+	21.0208i	1.83427	+	1.05901i
$395$	0.974190	−	0.261034i	0.0490168	−	0.0131340i
$396$	−36.0134	+	36.0134i	−1.80974	+	1.80974i
$397$	−9.59343	−	35.8032i	−0.481480	−	1.79691i	−0.595412	−	0.803420i	$-0.703011\pi$
$397$	−9.59343	−	35.8032i	−0.481480	−	1.79691i	0.113932	−	0.993489i	$-0.463655\pi$
$398$	−27.2412	+	27.2412i	−1.36548	+	1.36548i
$399$		0			0
$400$	−2.76918	−	1.59879i	−0.138459	−	0.0799393i
$401$	12.2868	+	12.2868i	0.613574	+	0.613574i	0.943876	−	0.330301i	$-0.107150\pi$
$401$	12.2868	+	12.2868i	0.613574	+	0.613574i	−0.330301	+	0.943876i	$0.607150\pi$
$402$	−4.58725	+	7.94535i	−0.228791	+	0.396278i
$403$	12.7550	+	20.4896i	0.635374	+	1.02066i
$404$	−3.62874	+	2.09505i	−0.180537	+	0.104233i
$405$	2.34209	−	0.627561i	0.116379	−	0.0311838i
$406$		0			0
$407$	−10.5826	+	6.10989i	−0.524562	+	0.302856i
$408$	−6.06263	−	1.62448i	−0.300145	−	0.0804235i
$409$	7.97850	+	7.97850i	0.394512	+	0.394512i	0.876292	−	0.481780i	$-0.160010\pi$
$409$	7.97850	+	7.97850i	0.394512	+	0.394512i	−0.481780	+	0.876292i	$0.660010\pi$
$410$	15.3437	+	15.3437i	0.757771	+	0.757771i
$411$	−1.00765	−	0.269999i	−0.0497036	−	0.0133180i
$412$	−14.5776	+	8.41637i	−0.718186	+	0.414645i
$413$		0			0
$414$	−1.53060	+	0.410122i	−0.0752247	+	0.0201564i
$415$	2.10413	−	1.21482i	0.103287	−	0.0596330i
$416$	12.8436	+	6.85708i	0.629712	+	0.336196i
$417$	−13.5799	+	23.5211i	−0.665010	+	1.15183i
$418$	−41.1058	−	41.1058i	−2.01055	−	2.01055i
$419$	16.1248	+	9.30964i	0.787747	+	0.454806i	0.839169	−	0.543871i	$-0.183042\pi$
$419$	16.1248	+	9.30964i	0.787747	+	0.454806i	−0.0514220	+	0.998677i	$0.516375\pi$
$420$		0			0
$421$	18.9024	−	18.9024i	0.921247	−	0.921247i	−0.0758709	−	0.997118i	$-0.524174\pi$
$421$	18.9024	−	18.9024i	0.921247	−	0.921247i	0.997118	+	0.0758709i	$0.0241737\pi$
$422$	5.99238	+	22.3639i	0.291704	+	1.08866i
$423$	10.2975	−	10.2975i	0.500683	−	0.500683i
$424$	25.0631	−	6.71564i	1.21717	−	0.326140i
$425$	−1.36727	−	0.789392i	−0.0663222	−	0.0382911i
$426$	−46.3841	+	80.3397i	−2.24732	+	3.89247i
$427$		0			0
$428$		−	53.6883i		−	2.59512i
$429$	−26.5423	+	16.5229i	−1.28148	+	0.797734i
$430$	9.07856	+	5.24151i	0.437807	+	0.252768i
$431$	28.5158	+	7.64079i	1.37356	+	0.368044i	0.868777	−	0.495203i	$-0.164906\pi$
$431$	28.5158	+	7.64079i	1.37356	+	0.368044i	0.504782	+	0.863247i	$0.331573\pi$
$432$			5.80713i			0.279396i
$433$	17.9660	+	31.1180i	0.863390	+	1.49543i	0.868637	+	0.495449i	$0.164996\pi$
$433$	17.9660	+	31.1180i	0.863390	+	1.49543i	−0.00524758	+	0.999986i	$0.501670\pi$
$434$		0			0
$435$	−12.6959	−	3.40186i	−0.608723	−	0.163107i
$436$	43.7464	−	11.7218i	2.09507	−	0.561373i
$437$	−0.298196	−	1.11288i	−0.0142646	−	0.0532363i
$438$	−45.7308			−2.18510
$439$	9.75982			0.465811			0.232906	−	0.972499i	$-0.425177\pi$
$439$	9.75982			0.465811			0.232906	+	0.972499i	$0.425177\pi$
$440$	−4.59195	−	17.1374i	−0.218912	−	0.816992i
$441$		0			0
$442$	−4.79007	−	2.55737i	−0.227840	−	0.121641i
$443$	−19.3899	−	33.5843i	−0.921241	−	1.59564i	−0.797497	−	0.603323i	$-0.793843\pi$
$443$	−19.3899	−	33.5843i	−0.921241	−	1.59564i	−0.123744	−	0.992314i	$-0.539490\pi$
$444$	−9.75356	+	36.4008i	−0.462884	+	1.72751i
$445$	−10.8224	−	18.7449i	−0.513030	−	0.888595i
$446$	10.2299	−	17.7187i	0.484399	−	0.839004i
$447$	10.8395	+	10.8395i	0.512690	+	0.512690i
$448$		0			0
$449$	−2.42216	+	9.03963i	−0.114309	+	0.426606i	−0.999234	−	0.0391263i	$-0.987543\pi$
$449$	−2.42216	+	9.03963i	−0.114309	+	0.426606i	0.884925	+	0.465733i	$0.154209\pi$
$450$	−6.90531	+	25.7710i	−0.325520	+	1.21486i
$451$		−	18.2246i		−	0.858162i
$452$	−4.68548	+	2.70516i	−0.220386	+	0.127240i
$453$	−9.26124	+	9.26124i	−0.435131	+	0.435131i
$454$	−39.6534			−1.86103
$455$		0			0
$456$	−77.1204			−3.61150
$457$	13.5913	−	13.5913i	0.635775	−	0.635775i	−0.313735	−	0.949511i	$-0.601580\pi$
$457$	13.5913	−	13.5913i	0.635775	−	0.635775i	0.949511	+	0.313735i	$0.101580\pi$
$458$	4.97089	−	2.86995i	0.232275	−	0.134104i
$459$			2.86724i			0.133831i
$460$	0.211561	−	0.789557i	0.00986409	−	0.0368133i
$461$	3.50466	−	13.0796i	0.163228	−	0.609175i	−0.835031	−	0.550202i	$-0.814551\pi$
$461$	3.50466	−	13.0796i	0.163228	−	0.609175i	0.998260	−	0.0589733i	$-0.0187827\pi$
$462$		0			0
$463$	−14.6336	−	14.6336i	−0.680081	−	0.680081i	0.279937	−	0.960018i	$-0.409686\pi$
$463$	−14.6336	−	14.6336i	−0.680081	−	0.680081i	−0.960018	+	0.279937i	$0.909686\pi$
$464$	−1.94152	+	3.36281i	−0.0901328	+	0.156115i
$465$	14.7216	+	25.4986i	0.682700	+	1.18247i
$466$	−3.26536	+	12.1865i	−0.151265	+	0.564529i
$467$	15.4866	+	26.8236i	0.716634	+	1.24125i	0.962326	+	0.271899i	$0.0876515\pi$
$467$	15.4866	+	26.8236i	0.716634	+	1.24125i	−0.245692	+	0.969348i	$0.579015\pi$
$468$	−13.2459	+	56.9334i	−0.612294	+	2.63175i
$469$		0			0
$470$	3.05223	+	11.3911i	0.140789	+	0.525431i
$471$	−34.8348			−1.60510
$472$	14.6998			0.676612
$473$	−2.27874	−	8.50439i	−0.104777	−	0.391032i
$474$	−3.96105	+	1.06136i	−0.181937	+	0.0487499i
$475$	−18.7378	−	5.02078i	−0.859750	−	0.230369i
$476$		0			0
$477$	−16.9084	−	29.2862i	−0.774183	−	1.34092i
$478$		−	39.6932i		−	1.81552i
$479$	7.09483	+	1.90105i	0.324171	+	0.0868613i	0.417235	−	0.908799i	$-0.362999\pi$
$479$	7.09483	+	1.90105i	0.324171	+	0.0868613i	−0.0930636	+	0.995660i	$0.529666\pi$
$480$	15.3819	+	8.88072i	0.702083	+	0.405348i
$481$	−6.60528	+	12.3720i	−0.301175	+	0.564115i
$482$		−	31.5654i		−	1.43777i
$483$		0			0
$484$	1.98478	−	3.43773i	0.0902171	−	0.156261i
$485$	−0.259753	−	0.149968i	−0.0117948	−	0.00680971i
$486$	−39.9207	+	10.6967i	−1.81084	+	0.485213i
$487$	−6.97359	+	6.97359i	−0.316004	+	0.316004i	−0.847230	−	0.531226i	$-0.821731\pi$
$487$	−6.97359	+	6.97359i	−0.316004	+	0.316004i	0.531226	+	0.847230i	$0.321731\pi$
$488$	4.13395	+	15.4281i	0.187135	+	0.698398i
$489$	25.4773	−	25.4773i	1.15212	−	1.15212i
$490$		0			0
$491$	33.1372	+	19.1318i	1.49546	+	0.863404i	0.999986	−	0.00521946i	$-0.00166141\pi$
$491$	33.1372	+	19.1318i	1.49546	+	0.863404i	0.495473	+	0.868623i	$0.334995\pi$
$492$	−39.7417	−	39.7417i	−1.79169	−	1.79169i
$493$	−0.958615	+	1.66037i	−0.0431738	+	0.0747793i
$494$	−64.9838	−	15.1189i	−2.92376	−	0.680233i
$495$	−20.0250	+	11.5615i	−0.900058	+	0.519649i
$496$	8.40197	−	2.25130i	0.377260	−	0.101086i
$497$		0			0
$498$	−8.55536	+	4.93944i	−0.383375	+	0.221342i
$499$	−0.00140307		0.000375951i	−6.28100e−5		1.68299e-5i	0.258788	−	0.965934i	$-0.416677\pi$
$499$	−0.00140307		0.000375951i	−6.28100e−5		1.68299e-5i	−0.258850	+	0.965917i	$0.583344\pi$
$500$	−29.5061	−	29.5061i	−1.31955	−	1.31955i
$501$	−36.1748	−	36.1748i	−1.61617	−	1.61617i
$502$	−29.0331	−	7.77938i	−1.29581	−	0.347211i
$503$	−21.6205	+	12.4826i	−0.964012	+	0.556573i	−0.897406	−	0.441206i	$-0.854551\pi$
$503$	−21.6205	+	12.4826i	−0.964012	+	0.556573i	−0.0666068	+	0.997779i	$0.521217\pi$
$504$		0			0
$505$	−1.83752	+	0.492362i	−0.0817686	+	0.0219098i
$506$	−0.933326	+	0.538856i	−0.0414914	+	0.0239551i
$507$	−15.8396	+	32.1982i	−0.703463	+	1.42997i
$508$	5.71132	−	9.89229i	0.253399	−	0.438900i
$509$	−1.85338	−	1.85338i	−0.0821495	−	0.0821495i	0.664838	−	0.746988i	$-0.268501\pi$
$509$	−1.85338	−	1.85338i	−0.0821495	−	0.0821495i	−0.746988	+	0.664838i	$0.768501\pi$
$510$	−5.73671	−	3.31209i	−0.254026	−	0.146662i
$511$		0			0
$512$	10.2233	−	10.2233i	0.451811	−	0.451811i
$513$	9.11827	+	34.0299i	0.402582	+	1.50245i
$514$	17.2299	−	17.2299i	0.759979	−	0.759979i
$515$	−7.38179	+	1.97795i	−0.325281	+	0.0871587i
$516$	−23.5144	−	13.5760i	−1.03516	−	0.597651i
$517$	4.95226	−	8.57757i	0.217800	−	0.377241i
$518$		0			0
$519$			15.4400i			0.677742i
$520$	−14.8687	−	13.9126i	−0.652037	−	0.610107i
$521$	−25.8598	−	14.9302i	−1.13294	−	0.654102i	−0.188266	−	0.982118i	$-0.560287\pi$
$521$	−25.8598	−	14.9302i	−1.13294	−	0.654102i	−0.944672	+	0.328016i	$0.893620\pi$
$522$	31.2955	+	8.38561i	1.36977	+	0.367028i
$523$		−	16.0812i		−	0.703184i	−0.936153	−	0.351592i	$-0.885640\pi$
$523$		−	16.0812i		−	0.703184i	0.936153	−	0.351592i	$-0.114360\pi$
$524$	28.8999	+	50.0561i	1.26250	+	2.18671i
$525$		0			0
$526$	−9.92985	−	2.66069i	−0.432962	−	0.116012i
$527$	4.14843	−	1.11157i	0.180708	−	0.0484207i
$528$	2.91634	+	10.8839i	0.126918	+	0.473663i
$529$	22.9786			0.999071
$530$	27.3846			1.18951
$531$	−4.95848	−	18.5053i	−0.215180	−	0.803062i
$532$		0			0
$533$	−11.0540	−	17.7571i	−0.478802	−	0.769146i
$534$	44.0038	+	76.2168i	1.90423	+	3.29822i
$535$	6.30868	−	23.5443i	0.272748	−	1.01791i
$536$	2.50923	+	4.34612i	0.108382	+	0.187724i
$537$	−13.0985	+	22.6873i	−0.565244	+	0.979031i
$538$	19.3942	+	19.3942i	0.836143	+	0.836143i
$539$		0			0
$540$	−6.46915	+	24.1432i	−0.278388	+	1.03896i
$541$	4.55572	−	17.0022i	0.195866	−	0.730980i	−0.796176	−	0.605066i	$-0.793147\pi$
$541$	4.55572	−	17.0022i	0.195866	−	0.730980i	0.992041	−	0.125915i	$-0.0401865\pi$
$542$			72.0456i			3.09462i
$543$	16.5304	−	9.54381i	0.709386	−	0.409564i
$544$	1.83196	−	1.83196i	0.0785448	−	0.0785448i
$545$	20.5618			0.880771
$546$		0			0
$547$	−15.8734			−0.678698			−0.339349	−	0.940661i	$-0.610207\pi$
$547$	−15.8734			−0.678698			−0.339349	+	0.940661i	$0.610207\pi$
$548$	−0.937974	+	0.937974i	−0.0400683	+	0.0400683i
$549$	18.0277	−	10.4083i	0.769405	−	0.444216i
$550$			18.1457i			0.773734i
$551$	−6.09709	+	22.7547i	−0.259745	+	0.969381i
$552$	−0.370042	+	1.38101i	−0.0157500	+	0.0587799i
$553$		0			0
$554$	31.6444	+	31.6444i	1.34444	+	1.34444i
$555$	−8.55461	+	14.8170i	−0.363123	+	0.628947i
$556$	17.2678	+	29.9087i	0.732318	+	1.26841i
$557$	0.655582	−	2.44666i	0.0277779	−	0.103668i	−0.950645	−	0.310280i	$-0.899577\pi$
$557$	0.655582	−	2.44666i	0.0277779	−	0.103668i	0.978423	+	0.206612i	$0.0662437\pi$
$558$	−36.2889	−	62.8543i	−1.53623	−	2.66083i
$559$	−7.37857	−	6.90409i	−0.312080	−	0.292012i
$560$		0			0
$561$	1.43993	+	5.37389i	0.0607938	+	0.226886i
$562$	−39.3940			−1.66173
$563$	−20.2319			−0.852673			−0.426336	−	0.904565i	$-0.640196\pi$
$563$	−20.2319			−0.852673			−0.426336	+	0.904565i	$0.640196\pi$
$564$	−7.90558	−	29.5040i	−0.332885	−	1.24234i
$565$	−2.37263	+	0.635745i	−0.0998174	+	0.0267460i
$566$	−19.1301	−	5.12589i	−0.804098	−	0.215457i
$567$		0			0
$568$	25.3722	+	43.9460i	1.06459	+	1.84393i
$569$			14.8726i			0.623493i	0.950165	+	0.311747i	$0.100914\pi$
$569$			14.8726i			0.623493i	−0.950165	+	0.311747i	$0.899086\pi$
$570$	−78.6191	−	21.0659i	−3.29299	−	0.882355i
$571$	−31.9767	−	18.4617i	−1.33818	−	0.772600i	−0.351645	−	0.936133i	$-0.614378\pi$
$571$	−31.9767	−	18.4617i	−1.33818	−	0.772600i	−0.986538	+	0.163533i	$0.947711\pi$
$572$	1.32001	+	39.7338i	0.0551923	+	1.66135i
$573$		−	6.91453i		−	0.288859i
$574$		0			0
$575$	−0.179817	+	0.311452i	−0.00749888	+	0.0129884i
$576$	−48.3124	−	27.8932i	−2.01302	−	1.16222i
$577$	19.8217	−	5.31122i	0.825189	−	0.221109i	0.178575	−	0.983926i	$-0.442851\pi$
$577$	19.8217	−	5.31122i	0.825189	−	0.221109i	0.646614	+	0.762817i	$0.276184\pi$
$578$	27.5334	−	27.5334i	1.14524	−	1.14524i
$579$	16.1148	+	60.1411i	0.669706	+	2.49938i
$580$	−11.8181	+	11.8181i	−0.490718	+	0.490718i
$581$		0			0
$582$	1.05615	+	0.609771i	0.0437790	+	0.0252758i
$583$	−16.2631	−	16.2631i	−0.673550	−	0.673550i
$584$	−12.5074	+	21.6635i	−0.517560	+	0.896441i
$585$	−12.4988	+	23.4109i	−0.516764	+	0.967923i
$586$	16.8506	−	9.72867i	0.696090	−	0.401888i
$587$	19.8321	−	5.31399i	0.818557	−	0.219332i	0.174842	−	0.984597i	$-0.444059\pi$
$587$	19.8321	−	5.31399i	0.818557	−	0.219332i	0.643715	+	0.765265i	$0.277392\pi$
$588$		0			0
$589$	45.7007	−	26.3853i	1.88307	−	1.08719i
$590$	14.9854	+	4.01534i	0.616941	+	0.165309i
$591$	−34.9578	−	34.9578i	−1.43797	−	1.43797i
$592$	3.57410	+	3.57410i	0.146894	+	0.146894i
$593$	40.1793	+	10.7660i	1.64997	+	0.442107i	0.959603	−	0.281357i	$-0.0907844\pi$
$593$	40.1793	+	10.7660i	1.64997	+	0.442107i	0.690362	+	0.723464i	$0.257451\pi$
$594$	28.5394	−	16.4772i	1.17099	−	0.676069i
$595$		0			0
$596$	18.8282	−	5.04500i	0.771233	−	0.206651i
$597$	39.2330	−	22.6512i	1.60570	−	0.927050i
$598$	−0.582546	+	1.09114i	−0.0238221	+	0.0446199i
$599$	2.16999	−	3.75853i	0.0886634	−	0.153569i	−0.818283	−	0.574816i	$-0.805074\pi$
$599$	2.16999	−	3.75853i	0.0886634	−	0.153569i	0.906946	+	0.421246i	$0.138407\pi$
$600$	17.0220	+	17.0220i	0.694919	+	0.694919i
$601$	−5.72067	−	3.30283i	−0.233351	−	0.134725i	0.378766	−	0.925492i	$-0.376348\pi$
$601$	−5.72067	−	3.30283i	−0.233351	−	0.134725i	−0.612117	+	0.790767i	$0.709682\pi$
$602$		0			0
$603$	4.62485	−	4.62485i	0.188339	−	0.188339i
$604$	4.31044	+	16.0868i	0.175389	+	0.654561i
$605$	1.27435	−	1.27435i	0.0518098	−	0.0518098i
$606$	7.47135	−	2.00194i	0.303503	−	0.0813233i
$607$	−39.8777	−	23.0234i	−1.61859	−	0.934492i	−0.987286	−	0.158954i	$-0.949188\pi$
$607$	−39.8777	−	23.0234i	−1.61859	−	0.934492i	−0.631301	−	0.775538i	$-0.717479\pi$
$608$	15.9168	−	27.5686i	0.645510	−	1.11806i
$609$		0			0
$610$			16.8571i			0.682526i
$611$	−0.377438	−	11.3613i	−0.0152695	−	0.459630i
$612$	9.00804	+	5.20079i	0.364128	+	0.210230i
$613$	−27.7207	−	7.42773i	−1.11963	−	0.300003i	−0.348895	−	0.937162i	$-0.613443\pi$
$613$	−27.7207	−	7.42773i	−1.11963	−	0.300003i	−0.770733	+	0.637159i	$0.780110\pi$
$614$		−	57.5744i		−	2.32352i
$615$	−12.7583	−	22.0981i	−0.514466	−	0.891081i
$616$		0			0
$617$	0.0947548	+	0.0253895i	0.00381469	+	0.00102214i	0.260726	−	0.965413i	$-0.416038\pi$
$617$	0.0947548	+	0.0253895i	0.00381469	+	0.00102214i	−0.256911	+	0.966435i	$0.582705\pi$
$618$	30.0143	−	8.04231i	1.20735	−	0.323509i
$619$	10.9468	+	40.8542i	0.439991	+	1.64207i	0.728834	+	0.684691i	$0.240063\pi$
$619$	10.9468	+	40.8542i	0.439991	+	1.64207i	−0.288843	+	0.957376i	$0.593271\pi$
$620$	37.4392			1.50360
$621$	0.653133			0.0262093
$622$	−14.4058	−	53.7630i	−0.577619	−	2.15570i
$623$		0			0
$624$	9.44312	+	8.83587i	0.378027	+	0.353718i
$625$	−3.32054	−	5.75135i	−0.132822	−	0.230054i
$626$	8.54882	−	31.9046i	0.341680	−	1.27517i
$627$	34.1796	+	59.2008i	1.36500	+	2.36425i
$628$	−22.1475	+	38.3606i	−0.883781	+	1.53075i
$629$	1.76469	+	1.76469i	0.0703629	+	0.0703629i
$630$		0			0
$631$	2.02584	−	7.56053i	0.0806473	−	0.300980i	−0.913807	−	0.406148i	$-0.866872\pi$
$631$	2.02584	−	7.56053i	0.0806473	−	0.300980i	0.994454	+	0.105169i	$0.0335383\pi$
$632$	−0.580566	+	2.16670i	−0.0230937	+	0.0861868i
$633$		−	27.2259i		−	1.08213i
$634$	34.0295	−	19.6469i	1.35148	−	0.780279i
$635$	3.66703	−	3.66703i	0.145522	−	0.145522i
$636$	−70.9288			−2.81251
$637$		0			0
$638$	22.0356			0.872397
$639$	46.7644	−	46.7644i	1.84997	−	1.84997i
$640$	27.9777	−	16.1530i	1.10592	−	0.638502i
$641$		−	33.4026i		−	1.31932i	−0.751563	−	0.659661i	$-0.770700\pi$
$641$		−	33.4026i		−	1.31932i	0.751563	−	0.659661i	$-0.229300\pi$
$642$	−25.6511	+	95.7311i	−1.01237	+	3.77820i
$643$	4.94009	−	18.4367i	0.194818	−	0.727071i	−0.797496	−	0.603324i	$-0.793842\pi$
$643$	4.94009	−	18.4367i	0.194818	−	0.727071i	0.992314	−	0.123746i	$-0.0394909\pi$
$644$		0			0
$645$	−8.71667	−	8.71667i	−0.343219	−	0.343219i
$646$	−5.93619	+	10.2818i	−0.233556	+	0.404532i
$647$	−16.4522	−	28.4961i	−0.646804	−	1.12030i	−0.983882	−	0.178821i	$-0.942772\pi$
$647$	−16.4522	−	28.4961i	−0.646804	−	1.12030i	0.337078	−	0.941477i	$-0.390561\pi$
$648$	−1.39576	+	5.20906i	−0.0548308	+	0.204631i
$649$	−6.51491	−	11.2842i	−0.255733	−	0.442942i
$650$	11.0061	+	17.6802i	0.431696	+	0.693475i
$651$		0			0
$652$	−11.8578	−	44.2541i	−0.464389	−	1.73312i
$653$	27.9965			1.09559			0.547793	−	0.836614i	$-0.315468\pi$
$653$	27.9965			1.09559			0.547793	+	0.836614i	$0.315468\pi$
$654$	−83.6042			−3.26918
$655$	6.79182	+	25.3474i	0.265378	+	0.990405i
$656$	−7.28147	+	1.95106i	−0.284294	+	0.0761763i
$657$	31.4907	+	8.43792i	1.22857	+	0.329195i
$658$		0			0
$659$	−5.35203	−	9.27000i	−0.208486	−	0.361108i	0.742752	−	0.669567i	$-0.233520\pi$
$659$	−5.35203	−	9.27000i	−0.208486	−	0.361108i	−0.951238	+	0.308459i	$0.900187\pi$
$660$			48.4989i			1.88782i
$661$	23.2066	+	6.21818i	0.902631	+	0.241859i	0.680146	−	0.733077i	$-0.261916\pi$
$661$	23.2066	+	6.21818i	0.902631	+	0.241859i	0.222485	+	0.974936i	$0.428583\pi$
$662$	19.6740	+	11.3588i	0.764653	+	0.441473i
$663$	4.66249	+	4.36266i	0.181076	+	0.169432i
$664$			5.40377i			0.209707i
$665$		0			0
$666$	21.0872	−	36.5240i	0.817111	−	1.41528i
$667$	0.378218	+	0.218364i	0.0146447	+	0.00845510i
$668$	−62.8356	+	16.8367i	−2.43118	+	0.651433i
$669$	−17.0124	+	17.0124i	−0.657737	+	0.657737i
$670$	1.37083	+	5.11599i	0.0529596	+	0.197648i
$671$	10.0111	−	10.0111i	0.386474	−	0.386474i
$672$		0			0
$673$	4.79792	+	2.77008i	0.184946	+	0.106779i	0.589615	−	0.807685i	$-0.299280\pi$
$673$	4.79792	+	2.77008i	0.184946	+	0.106779i	−0.404668	+	0.914464i	$0.632613\pi$
$674$	−33.3350	−	33.3350i	−1.28402	−	1.28402i
$675$	5.49846	−	9.52362i	0.211636	−	0.366564i
$676$	25.3864	+	37.9140i	0.976402	+	1.45823i
$677$	38.1640	−	22.0340i	1.46676	−	0.846835i	0.467454	−	0.884018i	$-0.345172\pi$
$677$	38.1640	−	22.0340i	1.46676	−	0.846835i	0.999309	+	0.0371822i	$0.0118382\pi$
$678$	9.64710	−	2.58493i	0.370495	−	0.0992738i
$679$		0			0
$680$	−3.13799	+	1.81172i	−0.120336	+	0.0694763i
$681$	45.0406	+	12.0686i	1.72596	+	0.462469i
$682$	−34.9040	−	34.9040i	−1.33654	−	1.33654i
$683$	3.64259	+	3.64259i	0.139380	+	0.139380i	0.773354	−	0.633974i	$-0.218578\pi$
$683$	3.64259	+	3.64259i	0.139380	+	0.139380i	−0.633974	+	0.773354i	$0.718578\pi$
$684$	123.451	+	33.0787i	4.72028	+	1.26480i
$685$	−0.521554	+	0.301120i	−0.0199276	+	0.0115052i
$686$		0			0
$687$	−6.51969	+	1.74695i	−0.248742	+	0.0666501i
$688$	−3.15390	+	1.82090i	−0.120241	+	0.0694213i
$689$	−25.7103	−	5.98167i	−0.979483	−	0.227883i
$690$	−0.754466	+	1.30677i	−0.0287220	+	0.0497480i
$691$	2.16091	+	2.16091i	0.0822048	+	0.0822048i	0.747014	−	0.664809i	$-0.231487\pi$
$691$	2.16091	+	2.16091i	0.0822048	+	0.0822048i	−0.664809	+	0.747014i	$0.731487\pi$
$692$	17.0028	+	9.81655i	0.646348	+	0.373169i
$693$		0			0
$694$	36.8501	−	36.8501i	1.39881	−	1.39881i
$695$	4.05813	+	15.1452i	0.153934	+	0.574489i
$696$	20.6710	−	20.6710i	0.783532	−	0.783532i
$697$	−3.59519	+	0.963328i	−0.136177	+	0.0364886i
$698$	10.8854	+	6.28470i	0.412019	+	0.237879i
$699$	7.41796	−	12.8483i	0.280573	−	0.485967i
$700$		0			0
$701$		−	11.0158i		−	0.416061i	−0.978122	−	0.208031i	$-0.933295\pi$
$701$		−	11.0158i		−	0.416061i	0.978122	−	0.208031i	$-0.0667054\pi$
$702$	17.8132	−	33.3650i	0.672315	−	1.25928i
$703$	26.5563	+	15.3323i	1.00159	+	0.578267i
$704$	−36.6486	−	9.81997i	−1.38125	−	0.370104i
$705$		−	13.8676i		−	0.522283i
$706$	30.6322	+	53.0566i	1.15286	+	1.99681i
$707$		0			0
$708$	−38.8138	−	10.4001i	−1.45871	−	0.390860i
$709$	−27.2109	+	7.29113i	−1.02192	+	0.273824i	−0.730604	−	0.682801i	$-0.760761\pi$
$709$	−27.2109	+	7.29113i	−1.02192	+	0.273824i	−0.291321	+	0.956625i	$0.594095\pi$
$710$	13.8612	+	51.7306i	0.520200	+	1.94141i
$711$	2.92346			0.109638
$712$	48.1403			1.80413
$713$	−0.253206	−	0.944977i	−0.00948263	−	0.0353897i
$714$		0			0
$715$	−4.09008	+	17.5799i	−0.152960	+	0.657450i
$716$	16.6557	+	28.8486i	0.622454	+	1.07812i
$717$	−12.0807	+	45.0857i	−0.451161	+	1.68376i
$718$	−26.5761	−	46.0311i	−0.991811	−	1.71787i
$719$	−21.0559	+	36.4699i	−0.785252	+	1.36010i	0.143596	+	0.989636i	$0.454133\pi$
$719$	−21.0559	+	36.4699i	−0.785252	+	1.36010i	−0.928848	+	0.370460i	$0.879200\pi$
$720$	6.76309	+	6.76309i	0.252045	+	0.252045i
$721$		0			0
$722$	−26.2130	+	97.8284i	−0.975548	+	3.64079i
$723$	−9.60699	+	35.8538i	−0.357288	+	1.33342i
$724$		−	24.2713i		−	0.902035i
$725$	6.36814	−	3.67665i	0.236507	−	0.136547i
$726$	−5.18151	+	5.18151i	−0.192304	+	0.192304i
$727$	−10.0901			−0.374223			−0.187111	−	0.982339i	$-0.559913\pi$
$727$	−10.0901			−0.374223			−0.187111	+	0.982339i	$0.559913\pi$
$728$		0			0
$729$	44.0349			1.63092
$730$	−18.6680	+	18.6680i	−0.690933	+	0.690933i
$731$	−1.55722	+	0.899062i	−0.0575959	+	0.0332530i
$732$		−	43.6617i		−	1.61378i
$733$	6.87790	−	25.6687i	0.254041	−	0.948093i	−0.714581	−	0.699553i	$-0.753382\pi$
$733$	6.87790	−	25.6687i	0.254041	−	0.948093i	0.968622	−	0.248540i	$-0.0799509\pi$
$734$	8.62455	−	32.1873i	0.318338	−	1.18805i
$735$		0			0
$736$	−0.417306	−	0.417306i	−0.0153821	−	0.0153821i
$737$	2.22417	−	3.85238i	0.0819285	−	0.141904i
$738$	31.4494	+	54.4719i	1.15767	+	2.00514i
$739$	6.51146	−	24.3011i	0.239528	−	0.893930i	−0.736528	−	0.676407i	$-0.763536\pi$
$739$	6.51146	−	24.3011i	0.239528	−	0.893930i	0.976055	−	0.217522i	$-0.0697975\pi$
$740$	10.8778	+	18.8409i	0.399876	+	0.692605i
$741$	69.2108	+	36.9509i	2.54252	+	1.35742i
$742$		0			0
$743$	−2.81817	−	10.5175i	−0.103388	−	0.385851i	0.894769	−	0.446530i	$-0.147340\pi$
$743$	−2.81817	−	10.5175i	−0.103388	−	0.385851i	−0.998157	+	0.0606785i	$0.980674\pi$
$744$	−65.4850			−2.40080
$745$	8.84969			0.324227
$746$	−2.13025	−	7.95021i	−0.0779941	−	0.291078i
$747$	6.80271	−	1.82278i	0.248898	−	0.0666921i
$748$	6.83328	+	1.83097i	0.249850	+	0.0669470i
$749$		0			0
$750$	38.5147	+	66.7094i	1.40636	+	2.43588i
$751$			32.2340i			1.17623i	0.808776	+	0.588117i	$0.200131\pi$
$751$			32.2340i			1.17623i	−0.808776	+	0.588117i	$0.799869\pi$
$752$	−3.95727	−	1.06035i	−0.144307	−	0.0386669i
$753$	30.6097	+	17.6725i	1.11548	+	0.644022i
$754$	21.4704	−	13.3655i	0.781904	−	0.486744i
$755$			7.56115i			0.275179i
$756$		0			0
$757$	−16.9609	+	29.3771i	−0.616453	+	1.06773i	0.373675	+	0.927560i	$0.378098\pi$
$757$	−16.9609	+	29.3771i	−0.616453	+	1.06773i	−0.990128	+	0.140168i	$0.955236\pi$
$758$	−54.5711	−	31.5066i	−1.98211	−	1.14437i
$759$	1.22413	−	0.328004i	0.0444330	−	0.0119058i
$760$	−31.4817	+	31.4817i	−1.14196	+	1.14196i
$761$	2.50812	+	9.36045i	0.0909194	+	0.339316i	0.996369	−	0.0851375i	$-0.0271329\pi$
$761$	2.50812	+	9.36045i	0.0909194	+	0.339316i	−0.905450	+	0.424453i	$0.860466\pi$
$762$	−14.9101	+	14.9101i	−0.540137	+	0.540137i
$763$		0			0
$764$	−7.61437	−	4.39616i	−0.275478	−	0.159047i
$765$	3.33924	+	3.33924i	0.120730	+	0.120730i
$766$	40.0837	−	69.4270i	1.44828	−	2.50850i
$767$	−13.1921	−	7.04313i	−0.476340	−	0.254313i
$768$	−56.0159	+	32.3408i	−2.02130	+	1.16700i
$769$	14.6001	−	3.91210i	0.526495	−	0.141074i	0.0142256	−	0.999899i	$-0.495472\pi$
$769$	14.6001	−	3.91210i	0.526495	−	0.141074i	0.512269	+	0.858825i	$0.328805\pi$
$770$		0			0
$771$	−24.8147	+	14.3268i	−0.893678	+	0.515965i
$772$	76.4737	+	20.4911i	2.75235	+	0.737490i
$773$	−27.6552	−	27.6552i	−0.994687	−	0.994687i	0.00529914	−	0.999986i	$-0.498313\pi$
$773$	−27.6552	−	27.6552i	−0.994687	−	0.994687i	−0.999986	+	0.00529914i	$0.998313\pi$
$774$	21.4867	+	21.4867i	0.772322	+	0.772322i
$775$	−15.9108	−	4.26328i	−0.571532	−	0.153142i
$776$	0.577718	−	0.333546i	0.0207389	−	0.0119736i
$777$		0			0
$778$	−62.2709	+	16.6854i	−2.23252	+	0.598202i
$779$	−39.6060	+	22.8665i	−1.41903	+	0.819279i
$780$	29.4167	+	47.2549i	1.05329	+	1.69200i
$781$	22.4898	−	38.9535i	0.804750	−	1.39387i
$782$	0.155635	+	0.155635i	0.00556551	+	0.00556551i
$783$	−11.5652	−	6.67718i	−0.413307	−	0.238623i
$784$		0			0
$785$	−14.2201	+	14.2201i	−0.507537	+	0.507537i
$786$	−27.6155	−	103.062i	−0.985012	−	3.67611i
$787$	1.23354	−	1.23354i	0.0439711	−	0.0439711i	−0.684779	−	0.728750i	$-0.740101\pi$
$787$	1.23354	−	1.23354i	0.0439711	−	0.0439711i	0.728750	+	0.684779i	$0.240101\pi$
$788$	−60.7217	+	16.2703i	−2.16312	+	0.579607i
$789$	10.4691	+	6.04433i	0.372709	+	0.215184i
$790$	−1.18370	+	2.05022i	−0.0421141	+	0.0729437i
$791$		0			0
$792$		−	51.4278i		−	1.82741i
$793$	3.68214	−	15.8265i	0.130757	−	0.562015i
$794$	75.3492	+	43.5029i	2.67404	+	1.54386i
$795$	−31.1049	−	8.33454i	−1.10318	−	0.295596i
$796$		−	57.6051i		−	2.04176i
$797$	−12.2921	−	21.2905i	−0.435407	−	0.754148i	0.561921	−	0.827191i	$-0.310062\pi$
$797$	−12.2921	−	21.2905i	−0.435407	−	0.754148i	−0.997329	+	0.0730430i	$0.976729\pi$
$798$		0			0
$799$	−1.95388	−	0.523540i	−0.0691233	−	0.0185215i
$800$	−9.59806	+	2.57179i	−0.339343	+	0.0909266i
$801$	−16.2385	−	60.6030i	−0.573760	−	2.14130i
$802$	−40.7873			−1.44025
$803$	22.1730			0.782469
$804$	−3.55057	−	13.2509i	−0.125219	−	0.467324i
$805$		0			0
$806$	−55.1795	−	12.8379i	−1.94362	−	0.452195i
$807$	−16.1264	−	27.9317i	−0.567675	−	0.983241i
$808$	1.09507	−	4.08684i	0.0385243	−	0.143775i
$809$	1.41467	+	2.45029i	0.0497373	+	0.0861475i	0.889822	−	0.456307i	$-0.150828\pi$
$809$	1.41467	+	2.45029i	0.0497373	+	0.0861475i	−0.840085	+	0.542455i	$0.817495\pi$
$810$	−2.84577	+	4.92903i	−0.0999903	+	0.173188i
$811$	−6.39483	−	6.39483i	−0.224553	−	0.224553i	0.585860	−	0.810412i	$-0.300757\pi$
$811$	−6.39483	−	6.39483i	−0.224553	−	0.224553i	−0.810412	+	0.585860i	$0.800757\pi$
$812$		0			0
$813$	21.9272	−	81.8334i	0.769020	−	2.87002i
$814$	7.42387	−	27.7063i	0.260207	−	0.971104i
$815$		−	20.8004i		−	0.728607i
$816$	1.99294	−	1.15062i	0.0697667	−	0.0402798i
$817$	−15.6227	+	15.6227i	−0.546570	+	0.546570i
$818$	−26.4854			−0.926041
$819$		0			0
$820$	−32.4463			−1.13307
$821$	26.3858	−	26.3858i	0.920872	−	0.920872i	−0.0762190	−	0.997091i	$-0.524285\pi$
$821$	26.3858	−	26.3858i	0.920872	−	0.920872i	0.997091	+	0.0762190i	$0.0242848\pi$
$822$	2.12064	−	1.22435i	0.0739657	−	0.0427041i
$823$			39.4868i			1.37642i	0.725510	+	0.688212i	$0.241604\pi$
$823$			39.4868i			1.37642i	−0.725510	+	0.688212i	$0.758396\pi$
$824$	4.39916	−	16.4179i	0.153252	−	0.571944i
$825$	5.52266	−	20.6109i	0.192274	−	0.717578i
$826$		0			0
$827$	−24.4804	−	24.4804i	−0.851267	−	0.851267i	0.139022	−	0.990289i	$-0.455604\pi$
$827$	−24.4804	−	24.4804i	−0.851267	−	0.851267i	−0.990289	+	0.139022i	$0.955604\pi$
$828$	1.18470	−	2.05195i	0.0411711	−	0.0713104i
$829$	−6.73903	−	11.6723i	−0.234056	−	0.405397i	0.724942	−	0.688810i	$-0.241867\pi$
$829$	−6.73903	−	11.6723i	−0.234056	−	0.405397i	−0.958998	+	0.283413i	$0.908533\pi$
$830$	−1.47607	+	5.50878i	−0.0512352	+	0.191212i
$831$	−26.3125	−	45.5745i	−0.912769	−	1.58096i
$832$	−41.6648	+	12.6609i	−1.44447	+	0.438938i
$833$		0			0
$834$	−16.5003	−	61.5801i	−0.571360	−	2.13234i
$835$	−29.5342			−1.02207
$836$	86.9237			3.00632
$837$	7.74257	+	28.8957i	0.267622	+	0.998780i
$838$	−42.2160	+	11.3118i	−1.45833	+	0.390758i
$839$	48.1190	+	12.8935i	1.66125	+	0.445132i	0.962732	−	0.270457i	$-0.0871749\pi$
$839$	48.1190	+	12.8935i	1.66125	+	0.445132i	0.698522	+	0.715589i	$0.253842\pi$
$840$		0			0
$841$	10.0352	+	17.3815i	0.346041	+	0.599360i
$842$			62.7484i			2.16245i
$843$	44.7459	+	11.9896i	1.54113	+	0.412944i
$844$	−29.9815	−	17.3098i	−1.03201	−	0.595829i
$845$	6.67780	+	19.6098i	0.229723	+	0.674596i
$846$			34.1836i			1.17526i
$847$		0			0
$848$	−4.75671	+	8.23886i	−0.163346	+	0.282924i
$849$	20.1690	+	11.6445i	0.692197	+	0.399640i
$850$	3.57962	−	0.959157i	0.122780	−	0.0328988i
$851$	0.401982	−	0.401982i	0.0137798	−	0.0137798i
$852$	−35.9018	−	133.987i	−1.22997	−	4.59033i
$853$	−15.4604	+	15.4604i	−0.529355	+	0.529355i	−0.920380	−	0.391025i	$-0.872121\pi$
$853$	−15.4604	+	15.4604i	−0.529355	+	0.529355i	0.391025	+	0.920380i	$0.372121\pi$
$854$		0			0
$855$	50.2511	+	29.0125i	1.71855	+	0.992207i
$856$	38.3339	+	38.3339i	1.31023	+	1.31023i
$857$	−12.5050	+	21.6594i	−0.427164	+	0.739869i	−0.996620	−	0.0821525i	$-0.973821\pi$
$857$	−12.5050	+	21.6594i	−0.427164	+	0.739869i	0.569456	+	0.822022i	$0.307154\pi$
$858$	16.6302	−	71.4797i	0.567747	−	2.44028i
$859$	30.9754	−	17.8837i	1.05687	−	0.610183i	0.132304	−	0.991209i	$-0.457762\pi$
$859$	30.9754	−	17.8837i	1.05687	−	0.610183i	0.924564	+	0.381026i	$0.124429\pi$
$860$	−15.1409	+	4.05698i	−0.516299	+	0.138342i
$861$		0			0
$862$	−60.0127	+	34.6484i	−2.04404	+	1.18013i
$863$	−39.9815	−	10.7130i	−1.36099	−	0.364675i	−0.496807	−	0.867861i	$-0.665494\pi$
$863$	−39.9815	−	10.7130i	−1.36099	−	0.364675i	−0.864178	+	0.503186i	$0.832161\pi$
$864$	12.7604	+	12.7604i	0.434119	+	0.434119i
$865$	6.30285	+	6.30285i	0.214303	+	0.214303i
$866$	−81.4695	−	21.8297i	−2.76845	−	0.741803i
$867$	−39.6537	+	22.8941i	−1.34671	+	0.777524i
$868$		0			0
$869$	1.92056	−	0.514612i	0.0651504	−	0.0174570i
$870$	26.7191	−	15.4263i	0.905862	−	0.523000i
$871$	−0.169516	−	5.10263i	−0.00574382	−	0.172896i
$872$	−22.8658	+	39.6048i	−0.774335	+	1.34119i
$873$	−0.614769	−	0.614769i	−0.0208068	−	0.0208068i
$874$	2.34210	+	1.35221i	0.0792229	+	0.0457393i
$875$		0			0
$876$	48.3519	−	48.3519i	1.63366	−	1.63366i
$877$	6.49432	+	24.2371i	0.219298	+	0.818430i	0.984609	+	0.174770i	$0.0559183\pi$
$877$	6.49432	+	24.2371i	0.219298	+	0.818430i	−0.765312	+	0.643660i	$0.777415\pi$
$878$	−16.1994	+	16.1994i	−0.546702	+	0.546702i
$879$	−22.1007	+	5.92188i	−0.745440	+	0.199740i
$880$	5.63348	+	3.25249i	0.189905	+	0.109641i
$881$	−18.7477	+	32.4719i	−0.631624	+	1.09401i	0.355595	+	0.934640i	$0.384278\pi$
$881$	−18.7477	+	32.4719i	−0.631624	+	1.09401i	−0.987220	+	0.159365i	$0.949055\pi$
$882$		0			0
$883$			19.9652i			0.671881i	0.941883	+	0.335941i	$0.109054\pi$
$883$			19.9652i			0.671881i	−0.941883	+	0.335941i	$0.890946\pi$
$884$	7.76857	−	2.36068i	0.261285	−	0.0793982i
$885$	−15.7992	−	9.12168i	−0.531085	−	0.306622i
$886$	87.9265	+	23.5598i	2.95395	+	0.791508i
$887$			51.4854i			1.72871i	0.502882	+	0.864355i	$0.332273\pi$
$887$			51.4854i			1.72871i	−0.502882	+	0.864355i	$0.667727\pi$
$888$	−19.0264	−	32.9546i	−0.638483	−	1.10588i
$889$		0			0
$890$	49.0758	+	13.1498i	1.64502	+	0.440783i
$891$	4.61729	−	1.23720i	0.154685	−	0.0414477i
$892$	7.91803	+	29.5505i	0.265115	+	0.989424i
$893$	−24.8546			−0.831727
$894$	−35.9828			−1.20344
$895$	3.91429	+	14.6083i	0.130840	+	0.488303i
$896$		0			0
$897$	0.993778	−	1.06208i	0.0331813	−	0.0354617i
$898$	−10.9837	−	19.0243i	−0.366530	−	0.634848i
$899$	−5.17720	+	19.3216i	−0.172669	+	0.644411i
$900$	−19.9470	−	34.5492i	−0.664899	−	1.15164i
$901$	−2.34860	+	4.06789i	−0.0782432	+	0.135521i
$902$	30.2492	+	30.2492i	1.00719	+	1.00719i
$903$		0			0
$904$	1.41396	−	5.27699i	0.0470277	−	0.175510i
$905$	2.85202	−	10.6439i	0.0948042	−	0.353814i
$906$		−	30.7436i		−	1.02139i
$907$	−25.0770	+	14.4782i	−0.832669	+	0.480742i	−0.854766	−	0.519014i	$-0.826299\pi$
$907$	−25.0770	+	14.4782i	−0.832669	+	0.480742i	0.0220968	+	0.999756i	$0.492966\pi$
$908$	41.9262	−	41.9262i	1.39137	−	1.39137i
$909$	−5.51424			−0.182896
$910$		0			0
$911$	3.65299			0.121029			0.0605144	−	0.998167i	$-0.480726\pi$
$911$	3.65299			0.121029			0.0605144	+	0.998167i	$0.480726\pi$
$912$	19.9940	−	19.9940i	0.662068	−	0.662068i
$913$	4.14815	−	2.39494i	0.137284	−	0.0792609i
$914$			45.1178i			1.49236i
$915$	5.13050	−	19.1473i	0.169609	−	0.632990i
$916$	−2.22137	+	8.29025i	−0.0733960	+	0.273918i
$917$		0			0
$918$	−4.75904	−	4.75904i	−0.157072	−	0.157072i
$919$	−21.3670	+	37.0087i	−0.704831	+	1.22080i	0.261922	+	0.965089i	$0.415644\pi$
$919$	−21.3670	+	37.0087i	−0.704831	+	1.22080i	−0.966753	+	0.255714i	$0.917690\pi$
$920$	0.412694	+	0.714807i	0.0136061	+	0.0235665i
$921$	−17.5229	+	65.3963i	−0.577398	+	2.15488i
$922$	15.8924	+	27.5265i	0.523389	+	0.906536i
$923$	−1.71407	−	51.5954i	−0.0564192	−	1.69828i
$924$		0			0
$925$	−2.47735	−	9.24560i	−0.0814548	−	0.303994i
$926$	48.5777			1.59636
$927$	−22.1521			−0.727571
$928$	3.12311	+	11.6556i	0.102521	+	0.382614i
$929$	16.3504	−	4.38107i	0.536438	−	0.143738i	0.0195786	−	0.999808i	$-0.493768\pi$
$929$	16.3504	−	4.38107i	0.536438	−	0.143738i	0.516860	+	0.856070i	$0.327101\pi$
$930$	−66.7576	−	17.8876i	−2.18907	−	0.586559i
$931$		0			0
$932$	−9.43247	−	16.3375i	−0.308971	−	0.535153i
$933$			65.4515i			2.14279i
$934$	−70.2264	−	18.8171i	−2.29788	−	0.615714i
$935$	2.78150	+	1.60590i	0.0909648	+	0.0525186i
$936$	−31.1932	−	50.1087i	−1.01958	−	1.63785i
$937$		−	46.5686i		−	1.52133i	−0.649145	−	0.760665i	$-0.724873\pi$
$937$		−	46.5686i		−	1.52133i	0.649145	−	0.760665i	$-0.275127\pi$
$938$		0			0
$939$	−19.4205	+	33.6372i	−0.633763	+	1.09771i
$940$	−15.2712	−	8.81680i	−0.498090	−	0.287572i
$941$	−11.4955	+	3.08022i	−0.374744	+	0.100412i	−0.441275	−	0.897372i	$-0.645474\pi$
$941$	−11.4955	+	3.08022i	−0.374744	+	0.100412i	0.0665310	+	0.997784i	$0.478807\pi$
$942$	57.8188	−	57.8188i	1.88384	−	1.88384i
$943$	0.219438	+	0.818954i	0.00714588	+	0.0266688i
$944$	−3.81102	+	3.81102i	−0.124038	+	0.124038i
$945$		0			0
$946$	17.8978	+	10.3333i	0.581909	+	0.335965i
$947$	30.5491	+	30.5491i	0.992714	+	0.992714i	0.999974	−	0.00726000i	$-0.00231095\pi$
$947$	30.5491	+	30.5491i	0.992714	+	0.992714i	−0.00726000	+	0.999974i	$0.502311\pi$
$948$	3.06589	−	5.31028i	0.0995756	−	0.172470i
$949$	21.6043	−	13.4489i	0.701305	−	0.436570i
$950$	39.4345	−	22.7675i	1.27942	−	0.738676i
$951$	−44.6321	+	11.9591i	−1.44730	+	0.387802i
$952$		0			0
$953$	−50.8066	+	29.3332i	−1.64579	+	0.950195i	−0.667066	+	0.744999i	$0.732450\pi$
$953$	−50.8066	+	29.3332i	−1.64579	+	0.950195i	−0.978721	+	0.205196i	$0.934217\pi$
$954$	76.6738	+	20.5447i	2.48241	+	0.665159i
$955$	−2.82261	−	2.82261i	−0.0913376	−	0.0913376i
$956$	41.9682	+	41.9682i	1.35735	+	1.35735i
$957$	−25.0292	−	6.70657i	−0.809080	−	0.216792i
$958$	−14.9314	+	8.62062i	−0.482410	+	0.278520i
$959$		0			0
$960$	−51.3127	+	13.7492i	−1.65611	+	0.443753i
$961$	11.9589	−	6.90448i	0.385771	−	0.222725i
$962$	−9.57161	−	31.4985i	−0.308601	−	1.01555i
$963$	35.3273	−	61.1886i	1.13840	−	1.97178i
$964$	33.3747	+	33.3747i	1.07493	+	1.07493i
$965$	31.1288	+	17.9722i	1.00207	+	0.578546i
$966$		0			0
$967$	−7.53769	+	7.53769i	−0.242396	+	0.242396i	−0.817841	−	0.575445i	$-0.804829\pi$
$967$	−7.53769	+	7.53769i	−0.242396	+	0.242396i	0.575445	+	0.817841i	$0.304829\pi$
$968$	1.03743	+	3.87172i	0.0333441	+	0.124442i
$969$	9.87194	−	9.87194i	0.317132	−	0.317132i
$970$	0.680055	−	0.182220i	0.0218353	−	0.00585074i
$971$	−27.3314	−	15.7798i	−0.877107	−	0.506398i	−0.00740334	−	0.999973i	$-0.502357\pi$
$971$	−27.3314	−	15.7798i	−0.877107	−	0.506398i	−0.869703	+	0.493575i	$0.835690\pi$
$972$	30.8990	−	53.5187i	0.991086	−	1.71661i
$973$		0			0
$974$		−	23.1495i		−	0.741759i
$975$	−7.12039	−	23.4319i	−0.228035	−	0.750422i
$976$	−5.07160	−	2.92809i	−0.162338	−	0.0937259i
$977$	1.10312	+	0.295580i	0.0352919	+	0.00945644i	0.276422	−	0.961036i	$-0.410851\pi$
$977$	1.10312	+	0.295580i	0.0352919	+	0.00945644i	−0.241130	+	0.970493i	$0.577518\pi$
$978$			84.5744i			2.70439i
$979$	−21.3357	−	36.9545i	−0.681891	−	1.18107i
$980$		0			0
$981$	57.5708	+	15.4261i	1.83810	+	0.492516i
$982$	−86.7559	+	23.2462i	−2.76849	+	0.741815i
$983$	7.63569	+	28.4968i	0.243541	+	0.908907i	0.974111	+	0.226069i	$0.0725876\pi$
$983$	7.63569	+	28.4968i	0.243541	+	0.908907i	−0.730570	+	0.682837i	$0.760746\pi$
$984$	56.7518			1.80918
$985$	−28.5406			−0.909380
$986$	−1.16477	−	4.34699i	−0.0370939	−	0.138436i
$987$		0			0
$988$	84.6940	−	52.7230i	2.69448	−	1.67734i
$989$	0.204799	+	0.354722i	0.00651222	+	0.0112795i
$990$	14.0478	−	52.4272i	0.446469	−	1.66625i
$991$	22.8046	+	39.4987i	0.724412	+	1.25472i	0.959216	+	0.282675i	$0.0912219\pi$
$991$	22.8046	+	39.4987i	0.724412	+	1.25472i	−0.234804	+	0.972043i	$0.575445\pi$
$992$	13.5153	−	23.4093i	0.429113	−	0.743245i
$993$	−18.8898	−	18.8898i	−0.599450	−	0.599450i
$994$		0			0
$995$	6.76894	−	25.2620i	0.214590	−	0.800860i
$996$	3.82317	−	14.2683i	0.121142	−	0.452108i
$997$			26.0713i			0.825686i	0.910802	+	0.412843i	$0.135464\pi$
$997$			26.0713i			0.825686i	−0.910802	+	0.412843i	$0.864536\pi$
$998$	0.00295282	−	0.00170481i	9.34698e−5	−	5.39648e-5i
$999$	−12.2919	+	12.2919i	−0.388897	+	0.388897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bb.b.227.2		32
7.2	even	3		637.2.x.b.19.8		32
7.3	odd	6		91.2.bc.a.6.2	yes	32
7.4	even	3		91.2.bc.a.6.1	✓	32
7.5	odd	6		637.2.x.b.19.7		32
7.6	odd	2	inner	637.2.bb.b.227.1		32
13.11	odd	12		637.2.x.b.570.8		32
21.11	odd	6		819.2.fm.g.370.7		32
21.17	even	6		819.2.fm.g.370.8		32
91.11	odd	12		91.2.bc.a.76.2	yes	32
91.24	even	12		91.2.bc.a.76.1	yes	32
91.37	odd	12	inner	637.2.bb.b.362.1		32
91.76	even	12		637.2.x.b.570.7		32
91.89	even	12	inner	637.2.bb.b.362.2		32
273.11	even	12		819.2.fm.g.622.8		32
273.206	odd	12		819.2.fm.g.622.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.6.1	✓	32	7.4	even	3
91.2.bc.a.6.2	yes	32	7.3	odd	6
91.2.bc.a.76.1	yes	32	91.24	even	12
91.2.bc.a.76.2	yes	32	91.11	odd	12
637.2.x.b.19.7		32	7.5	odd	6
637.2.x.b.19.8		32	7.2	even	3
637.2.x.b.570.7		32	91.76	even	12
637.2.x.b.570.8		32	13.11	odd	12
637.2.bb.b.227.1		32	7.6	odd	2	inner
637.2.bb.b.227.2		32	1.1	even	1	trivial
637.2.bb.b.362.1		32	91.37	odd	12	inner
637.2.bb.b.362.2		32	91.89	even	12	inner
819.2.fm.g.370.7		32	21.11	odd	6
819.2.fm.g.370.8		32	21.17	even	6
819.2.fm.g.622.7		32	273.206	odd	12
819.2.fm.g.622.8		32	273.11	even	12

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.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.65980 + 1.65980i) q^{2} +(2.39046 - 1.38013i) q^{3} -3.50987i q^{4} +(0.412430 - 1.53921i) q^{5} +(-1.67694 + 6.25841i) q^{6} +(2.50608 + 2.50608i) q^{8} +(2.30952 - 4.00020i) q^{9} +(1.87023 + 3.23933i) q^{10} +(0.813080 - 3.03446i) q^{11} +(-4.84407 - 8.39018i) q^{12} +(-1.04831 - 3.44979i) q^{13} +(-1.13841 - 4.24862i) q^{15} -1.29944 q^{16} -0.641590 q^{17} +(2.80620 + 10.4729i) q^{18} +(-7.61472 + 2.04036i) q^{19} +(-5.40242 - 1.44757i) q^{20} +(3.68704 + 6.38614i) q^{22} +0.146149i q^{23} +(9.44938 + 2.53195i) q^{24} +(2.13106 + 1.23037i) q^{25} +(7.46594 + 3.98598i) q^{26} -4.46896i q^{27} +(1.49412 - 2.58790i) q^{29} +(8.94139 + 5.16231i) q^{30} +(-6.46586 + 1.73252i) q^{31} +(-2.85535 + 2.85535i) q^{32} +(-2.24431 - 8.37589i) q^{33} +(1.06491 - 1.06491i) q^{34} +(-14.0402 - 8.10610i) q^{36} +(-2.75050 - 2.75050i) q^{37} +(9.25232 - 16.0255i) q^{38} +(-7.26709 - 6.79977i) q^{39} +(4.89096 - 2.82380i) q^{40} +(5.60356 - 1.50147i) q^{41} +(2.42713 - 1.40130i) q^{43} +(-10.6505 - 2.85380i) q^{44} +(-5.20463 - 5.20463i) q^{45} +(-0.242578 - 0.242578i) q^{46} +(3.04537 + 0.816005i) q^{47} +(-3.10624 + 1.79339i) q^{48} +(-5.57930 + 1.49497i) q^{50} +(-1.53369 + 0.885477i) q^{51} +(-12.1083 + 3.67942i) q^{52} +(3.66059 - 6.34033i) q^{53} +(7.41757 + 7.41757i) q^{54} +(-4.33533 - 2.50300i) q^{55} +(-15.3867 + 15.3867i) q^{57} +(1.81545 + 6.77534i) q^{58} +(2.93283 - 2.93283i) q^{59} +(-14.9121 + 3.99568i) q^{60} +(3.90292 + 2.25335i) q^{61} +(7.85639 - 13.6077i) q^{62} -12.0775i q^{64} +(-5.74230 + 0.190767i) q^{65} +(17.6274 + 10.1772i) q^{66} +(1.36775 + 0.366486i) q^{67} +2.25190i q^{68} +(0.201704 + 0.349362i) q^{69} +(13.8300 + 3.70574i) q^{71} +(15.8126 - 4.23699i) q^{72} +(1.82677 + 6.81760i) q^{73} +9.13055 q^{74} +6.79227 q^{75} +(7.16138 + 26.7267i) q^{76} +(23.3482 - 0.775656i) q^{78} +(0.316458 + 0.548121i) q^{79} +(-0.535926 + 2.00010i) q^{80} +(0.760810 + 1.31776i) q^{81} +(-6.80865 + 11.7929i) q^{82} +(1.07813 + 1.07813i) q^{83} +(-0.264611 + 0.987541i) q^{85} +(-1.70266 + 6.35443i) q^{86} -8.24834i q^{87} +(9.64223 - 5.56694i) q^{88} +(9.60471 - 9.60471i) q^{89} +17.2773 q^{90} +0.512963 q^{92} +(-13.0652 + 13.0652i) q^{93} +(-6.40911 + 3.70030i) q^{94} +12.5621i q^{95} +(-2.88483 + 10.7663i) q^{96} +(0.0487160 - 0.181811i) q^{97} +(-10.2606 - 10.2606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9} - 16 q^{11} - 8 q^{15} - 24 q^{16} + 68 q^{18} + 4 q^{22} + 4 q^{29} - 12 q^{30} - 68 q^{32} - 8 q^{37} - 48 q^{43} + 60 q^{44} + 24 q^{46} - 44 q^{50} - 12 q^{51} - 36 q^{53}+ \cdots - 60 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9 - 16 * q^11 - 8 * q^15 - 24 * q^16 + 68 * q^18 + 4 * q^22 + 4 * q^29 - 12 * q^30 - 68 * q^32 - 8 * q^37 - 48 * q^43 + 60 * q^44 + 24 * q^46 - 44 * q^50 - 12 * q^51 - 36 * q^53 - 92 * q^57 - 28 * q^58 - 104 * q^60 - 32 * q^65 - 8 * q^67 + 84 * q^71 + 124 * q^72 + 48 * q^74 + 148 * q^78 + 40 * q^79 + 28 * q^81 + 36 * q^85 - 60 * q^86 + 228 * q^88 + 24 * q^92 - 84 * q^93 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more