LMFDB - Embedded newform 867.2.i.e.131.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(65,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 9]))

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

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

chi := DirichletCharacter("867.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.i (of order $16$, degree $8$, 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:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			131.3
Character	$\chi$	$=$	867.131
Dual form			867.2.i.e.503.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.06586 - 0.855706i) q^{2} +(-0.921821 + 1.46637i) q^{3} +(2.12132 - 2.12132i) q^{4} +(-0.551799 + 2.77408i) q^{5} +(-0.649569 + 3.81812i) q^{6} +(3.10152 - 0.616930i) q^{7} +(0.855706 - 2.06586i) q^{8} +(-1.30049 - 2.70347i) q^{9} +O(q^{10})$	\(q+(2.06586 - 0.855706i) q^{2} +(-0.921821 + 1.46637i) q^{3} +(2.12132 - 2.12132i) q^{4} +(-0.551799 + 2.77408i) q^{5} +(-0.649569 + 3.81812i) q^{6} +(3.10152 - 0.616930i) q^{7} +(0.855706 - 2.06586i) q^{8} +(-1.30049 - 2.70347i) q^{9} +(1.23386 + 6.20303i) q^{10} +(-1.17588 - 0.785695i) q^{11} +(1.15517 + 5.06612i) q^{12} +(2.82843 + 2.82843i) q^{13} +(5.87938 - 3.92847i) q^{14} +(-3.55917 - 3.36635i) q^{15} +1.00000i q^{16} +(-5.00000 - 4.47214i) q^{18} +(4.71417 + 7.05525i) q^{20} +(-1.95440 + 5.11667i) q^{21} +(-3.10152 - 0.616930i) q^{22} +(-3.92847 + 5.87938i) q^{23} +(2.24051 + 3.15913i) q^{24} +(-2.77164 - 1.14805i) q^{25} +(8.26343 + 3.42282i) q^{26} +(5.16310 + 0.585110i) q^{27} +(5.27060 - 7.88801i) q^{28} +(-2.77408 - 0.551799i) q^{29} +(-10.2333 - 3.90879i) q^{30} +(1.75687 + 2.62934i) q^{31} +(2.56712 + 6.19757i) q^{32} +(2.23607 - 1.00000i) q^{33} +8.94427i q^{35} +(-8.49367 - 2.97616i) q^{36} +(5.25868 - 3.51373i) q^{37} +(-6.75483 + 1.54022i) q^{39} +(5.25868 + 3.51373i) q^{40} +(-1.10360 - 5.54816i) q^{41} +(0.340867 + 12.2427i) q^{42} +(-1.53073 + 3.69552i) q^{43} +(-4.16112 + 0.827698i) q^{44} +(8.21724 - 2.11590i) q^{45} +(-3.08465 + 15.5076i) q^{46} +(6.32456 - 6.32456i) q^{47} +(-1.46637 - 0.921821i) q^{48} +(2.77164 - 1.14805i) q^{49} -6.70820 q^{50} +12.0000 q^{52} +(11.1669 - 3.20935i) q^{54} +(2.82843 - 2.82843i) q^{55} +(1.37950 - 6.93520i) q^{56} +(-6.20303 + 1.23386i) q^{58} +(3.42282 - 8.26343i) q^{59} +(-14.6912 + 0.409040i) q^{60} +(-1.23386 - 6.20303i) q^{61} +(5.87938 + 3.92847i) q^{62} +(-5.70134 - 7.58253i) q^{63} +(9.19239 + 9.19239i) q^{64} +(-9.40700 + 6.28556i) q^{65} +(3.76369 - 3.97927i) q^{66} -8.00000i q^{67} +(-5.00000 - 11.1803i) q^{69} +(7.65367 + 18.4776i) q^{70} +(-7.07125 - 10.5829i) q^{71} +(-6.69781 + 0.373256i) q^{72} +(7.85695 - 11.7588i) q^{74} +(4.23842 - 3.00595i) q^{75} +(-4.13171 - 1.71141i) q^{77} +(-12.6365 + 8.96202i) q^{78} +(-1.75687 + 2.62934i) q^{79} +(-2.77408 - 0.551799i) q^{80} +(-5.61745 + 7.03166i) q^{81} +(-7.02747 - 10.5174i) q^{82} +(3.42282 + 8.26343i) q^{83} +(6.70820 + 15.0000i) q^{84} +8.94427i q^{86} +(3.36635 - 3.55917i) q^{87} +(-2.62934 + 1.75687i) q^{88} +(-9.48683 - 9.48683i) q^{89} +(15.1651 - 11.4027i) q^{90} +(10.5174 + 7.02747i) q^{91} +(4.13849 + 20.8056i) q^{92} +(-5.47510 + 0.152440i) q^{93} +(7.65367 - 18.4776i) q^{94} +(-11.4544 - 1.94871i) q^{96} +(2.46772 - 12.4061i) q^{97} +(4.74342 - 4.74342i) q^{98} +(-0.594884 + 4.20073i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 160 q^{18} + 384 q^{52} - 160 q^{69}+O(q^{100}) $ 32 * q - 160 * q^18 + 384 * q^52 - 160 * q^69

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{13}{16}\right)$

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 $

$2$	2.06586	−	0.855706i	1.46078	−	0.605076i	0.496046	−	0.868296i	$-0.334785\pi$
$2$	2.06586	−	0.855706i	1.46078	−	0.605076i	0.964736	+	0.263221i	$0.0847847\pi$
$3$	−0.921821	+	1.46637i	−0.532214	+	0.846610i
$3$	−0.921821	+	1.46637i	−0.532214	+	0.846610i
$4$	2.12132	−	2.12132i	1.06066	−	1.06066i
$5$	−0.551799	+	2.77408i	−0.246772	+	1.24061i	0.636327	+	0.771419i	$0.280453\pi$
$5$	−0.551799	+	2.77408i	−0.246772	+	1.24061i	−0.883099	+	0.469187i	$0.844547\pi$
$6$	−0.649569	+	3.81812i	−0.265185	+	1.55874i
$7$	3.10152	−	0.616930i	1.17226	−	0.233178i	0.429711	−	0.902966i	$-0.358615\pi$
$7$	3.10152	−	0.616930i	1.17226	−	0.233178i	0.742552	+	0.669789i	$0.233615\pi$
$8$	0.855706	−	2.06586i	0.302538	−	0.730391i
$9$	−1.30049	−	2.70347i	−0.433497	−	0.901155i
$10$	1.23386	+	6.20303i	0.390181	+	1.96157i
$11$	−1.17588	−	0.785695i	−0.354540	−	0.236896i	0.365527	−	0.930801i	$-0.380889\pi$
$11$	−1.17588	−	0.785695i	−0.354540	−	0.236896i	−0.720067	+	0.693905i	$0.755889\pi$
$12$	1.15517	+	5.06612i	0.333467	+	1.46246i
$13$	2.82843	+	2.82843i	0.784465	+	0.784465i	0.980581	−	0.196116i	$-0.0628330\pi$
$13$	2.82843	+	2.82843i	0.784465	+	0.784465i	−0.196116	+	0.980581i	$0.562833\pi$
$14$	5.87938	−	3.92847i	1.57133	−	1.04993i
$15$	−3.55917	−	3.36635i	−0.918974	−	0.869187i
$16$			1.00000i			0.250000i
$17$		0			0
$17$		0			0
$18$	−5.00000	−	4.47214i	−1.17851	−	1.05409i
$19$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$19$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$20$	4.71417	+	7.05525i	1.05412	+	1.57760i
$21$	−1.95440	+	5.11667i	−0.426484	+	1.11655i
$22$	−3.10152	−	0.616930i	−0.661245	−	0.131530i
$23$	−3.92847	+	5.87938i	−0.819144	+	1.22594i	0.152222	+	0.988346i	$0.451357\pi$
$23$	−3.92847	+	5.87938i	−0.819144	+	1.22594i	−0.971366	+	0.237589i	$0.923643\pi$
$24$	2.24051	+	3.15913i	0.457341	+	0.644856i
$25$	−2.77164	−	1.14805i	−0.554328	−	0.229610i
$26$	8.26343	+	3.42282i	1.62059	+	0.671271i
$27$	5.16310	+	0.585110i	0.993640	+	0.112604i
$28$	5.27060	−	7.88801i	0.996050	−	1.49069i
$29$	−2.77408	−	0.551799i	−0.515134	−	0.102466i	−0.0693239	−	0.997594i	$-0.522084\pi$
$29$	−2.77408	−	0.551799i	−0.515134	−	0.102466i	−0.445810	+	0.895128i	$0.647084\pi$
$30$	−10.2333	−	3.90879i	−1.86834	−	0.713644i
$31$	1.75687	+	2.62934i	0.315543	+	0.472243i	0.955009	−	0.296576i	$-0.0958448\pi$
$31$	1.75687	+	2.62934i	0.315543	+	0.472243i	−0.639467	+	0.768819i	$0.720845\pi$
$32$	2.56712	+	6.19757i	0.453807	+	1.09559i
$33$	2.23607	−	1.00000i	0.389249	−	0.174078i
$34$		0			0
$35$			8.94427i			1.51186i
$36$	−8.49367	−	2.97616i	−1.41561	−	0.496026i
$37$	5.25868	−	3.51373i	0.864521	−	0.577654i	−0.0423311	−	0.999104i	$-0.513478\pi$
$37$	5.25868	−	3.51373i	0.864521	−	0.577654i	0.906852	+	0.421449i	$0.138478\pi$
$38$		0			0
$39$	−6.75483	+	1.54022i	−1.08164	+	0.246633i
$40$	5.25868	+	3.51373i	0.831470	+	0.555570i
$41$	−1.10360	−	5.54816i	−0.172353	−	0.866477i	−0.966088	−	0.258213i	$-0.916866\pi$
$41$	−1.10360	−	5.54816i	−0.172353	−	0.866477i	0.793735	−	0.608264i	$-0.208134\pi$
$42$	0.340867	+	12.2427i	0.0525969	+	1.88909i
$43$	−1.53073	+	3.69552i	−0.233435	+	0.563561i	−0.996577	−	0.0826692i	$-0.973656\pi$
$43$	−1.53073	+	3.69552i	−0.233435	+	0.563561i	0.763142	+	0.646230i	$0.223656\pi$
$44$	−4.16112	+	0.827698i	−0.627312	+	0.124780i
$45$	8.21724	−	2.11590i	1.22495	−	0.315419i
$46$	−3.08465	+	15.5076i	−0.454807	+	2.28647i
$47$	6.32456	−	6.32456i	0.922531	−	0.922531i	−0.0746766	−	0.997208i	$-0.523792\pi$
$47$	6.32456	−	6.32456i	0.922531	−	0.922531i	0.997208	+	0.0746766i	$0.0237924\pi$
$48$	−1.46637	−	0.921821i	−0.211652	−	0.133053i
$49$	2.77164	−	1.14805i	0.395948	−	0.164007i
$50$	−6.70820			−0.948683
$51$		0			0
$52$	12.0000			1.66410
$53$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$53$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$54$	11.1669	−	3.20935i	1.51963	−	0.436737i
$55$	2.82843	−	2.82843i	0.381385	−	0.381385i
$56$	1.37950	−	6.93520i	0.184343	−	0.926755i
$57$		0			0
$58$	−6.20303	+	1.23386i	−0.814498	+	0.162014i
$59$	3.42282	−	8.26343i	0.445614	−	1.07581i	−0.528334	−	0.849036i	$-0.677183\pi$
$59$	3.42282	−	8.26343i	0.445614	−	1.07581i	0.973948	−	0.226771i	$-0.0728167\pi$
$60$	−14.6912	+	0.409040i	−1.89663	+	0.0528069i
$61$	−1.23386	−	6.20303i	−0.157980	−	0.794217i	−0.975787	−	0.218724i	$-0.929810\pi$
$61$	−1.23386	−	6.20303i	−0.157980	−	0.794217i	0.817807	−	0.575492i	$-0.195190\pi$
$62$	5.87938	+	3.92847i	0.746682	+	0.498917i
$63$	−5.70134	−	7.58253i	−0.718301	−	0.955309i
$64$	9.19239	+	9.19239i	1.14905	+	1.14905i
$65$	−9.40700	+	6.28556i	−1.16680	+	0.779628i
$66$	3.76369	−	3.97927i	0.463278	−	0.489815i
$67$		−	8.00000i		−	0.977356i	−0.872464	−	0.488678i	$-0.837479\pi$
$67$		−	8.00000i		−	0.977356i	0.872464	−	0.488678i	$-0.162521\pi$
$68$		0			0
$69$	−5.00000	−	11.1803i	−0.601929	−	1.34595i
$70$	7.65367	+	18.4776i	0.914788	+	2.20849i
$71$	−7.07125	−	10.5829i	−0.839204	−	1.25596i	−0.964565	−	0.263846i	$-0.915009\pi$
$71$	−7.07125	−	10.5829i	−0.839204	−	1.25596i	0.125361	−	0.992111i	$-0.459991\pi$
$72$	−6.69781	+	0.373256i	−0.789345	+	0.0439887i
$73$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$73$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$74$	7.85695	−	11.7588i	0.913352	−	1.36693i
$75$	4.23842	−	3.00595i	0.489411	−	0.347098i
$76$		0			0
$77$	−4.13171	−	1.71141i	−0.470853	−	0.195034i
$78$	−12.6365	+	8.96202i	−1.43081	+	1.01475i
$79$	−1.75687	+	2.62934i	−0.197663	+	0.295824i	−0.917039	−	0.398797i	$-0.869428\pi$
$79$	−1.75687	+	2.62934i	−0.197663	+	0.295824i	0.719376	+	0.694621i	$0.244428\pi$
$80$	−2.77408	−	0.551799i	−0.310152	−	0.0616930i
$81$	−5.61745	+	7.03166i	−0.624161	+	0.781296i
$82$	−7.02747	−	10.5174i	−0.776054	−	1.16145i
$83$	3.42282	+	8.26343i	0.375704	+	0.907029i	0.992761	+	0.120111i	$0.0383249\pi$
$83$	3.42282	+	8.26343i	0.375704	+	0.907029i	−0.617057	+	0.786919i	$0.711675\pi$
$84$	6.70820	+	15.0000i	0.731925	+	1.63663i
$85$		0			0
$86$			8.94427i			0.964486i
$87$	3.36635	−	3.55917i	0.360910	−	0.381583i
$88$	−2.62934	+	1.75687i	−0.280288	+	0.187283i
$89$	−9.48683	−	9.48683i	−1.00560	−	1.00560i	−0.999984	−	0.00561807i	$-0.998212\pi$
$89$	−9.48683	−	9.48683i	−1.00560	−	1.00560i	−0.00561807	−	0.999984i	$-0.501788\pi$
$90$	15.1651	−	11.4027i	1.59854	−	1.20195i
$91$	10.5174	+	7.02747i	1.10252	+	0.736679i
$92$	4.13849	+	20.8056i	0.431467	+	2.16913i
$93$	−5.47510	+	0.152440i	−0.567742	+	0.0158073i
$94$	7.65367	−	18.4776i	0.789416	−	1.90582i
$95$		0			0
$96$	−11.4544	−	1.94871i	−1.16906	−	0.198889i
$97$	2.46772	−	12.4061i	0.250559	−	1.25964i	−0.626561	−	0.779373i	$-0.715538\pi$
$97$	2.46772	−	12.4061i	0.250559	−	1.25964i	0.877120	−	0.480272i	$-0.159462\pi$
$98$	4.74342	−	4.74342i	0.479157	−	0.479157i
$99$	−0.594884	+	4.20073i	−0.0597881	+	0.422189i
$100$	−8.31492	+	3.44415i	−0.831492	+	0.344415i
$101$	4.47214			0.444994			0.222497	−	0.974933i	$-0.428579\pi$
$101$	4.47214			0.444994			0.222497	+	0.974933i	$0.428579\pi$
$102$		0			0
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$	8.26343	−	3.42282i	0.810296	−	0.335636i
$105$	−13.1156	−	8.24502i	−1.27995	−	0.804632i
$106$		0			0
$107$	0.827698	−	4.16112i	0.0800166	−	0.402271i	−0.919931	−	0.392079i	$-0.871756\pi$
$107$	0.827698	−	4.16112i	0.0800166	−	0.402271i	0.999948	−	0.0101914i	$-0.00324408\pi$
$108$	12.1938	−	9.71139i	1.17335	−	0.934479i
$109$	18.6091	−	3.70158i	1.78243	−	0.354547i	0.809762	−	0.586758i	$-0.199596\pi$
$109$	18.6091	−	3.70158i	1.78243	−	0.354547i	0.972665	+	0.232211i	$0.0745960\pi$
$110$	3.42282	−	8.26343i	0.326354	−	0.787887i
$111$	0.304881	+	10.9502i	0.0289380	+	1.03935i
$112$	0.616930	+	3.10152i	0.0582944	+	0.293066i
$113$	4.70350	+	3.14278i	0.442468	+	0.295648i	0.756777	−	0.653673i	$-0.226773\pi$
$113$	4.70350	+	3.14278i	0.442468	+	0.295648i	−0.314309	+	0.949321i	$0.601773\pi$
$114$		0			0
$115$	−14.1421	−	14.1421i	−1.31876	−	1.31876i
$116$	−7.05525	+	4.71417i	−0.655064	+	0.437700i
$117$	3.96821	−	11.3249i	0.366861	−	1.04699i
$118$		−	20.0000i		−	1.84115i
$119$		0			0
$120$	−10.0000	+	4.47214i	−0.912871	+	0.408248i
$121$	−3.44415	−	8.31492i	−0.313105	−	0.755901i
$122$	−7.85695	−	11.7588i	−0.711335	−	1.06459i
$123$	9.15298	+	3.49613i	0.825297	+	0.315235i
$124$	9.30455	+	1.85079i	0.835573	+	0.166206i
$125$	−3.14278	+	4.70350i	−0.281099	+	0.420694i
$126$	−18.2666	−	10.7857i	−1.62732	−	0.960871i
$127$	11.0866	+	4.59220i	0.983773	+	0.407492i	0.815822	−	0.578303i	$-0.196285\pi$
$127$	11.0866	+	4.59220i	0.983773	+	0.407492i	0.167951	+	0.985795i	$0.446285\pi$
$128$	14.4610	+	5.98994i	1.27818	+	0.529441i
$129$	−4.00794	−	5.65123i	−0.352879	−	0.497563i
$130$	−14.0549	+	21.0347i	−1.23270	+	1.84487i
$131$	−1.38704	−	0.275899i	−0.121186	−	0.0241054i	0.134125	−	0.990964i	$-0.457178\pi$
$131$	−1.38704	−	0.275899i	−0.121186	−	0.0241054i	−0.255311	+	0.966859i	$0.582178\pi$
$132$	2.62210	−	6.86474i	0.228224	−	0.597499i
$133$		0			0
$134$	−6.84565	−	16.5269i	−0.591374	−	1.42770i
$135$	−4.47214	+	14.0000i	−0.384900	+	1.20493i
$136$		0			0
$137$		−	4.47214i		−	0.382080i	−0.981582	−	0.191040i	$-0.938814\pi$
$137$		−	4.47214i		−	0.382080i	0.981582	−	0.191040i	$-0.0611861\pi$
$138$	−19.8964	−	18.8185i	−1.69369	−	1.60193i
$139$	−2.62934	+	1.75687i	−0.223018	+	0.149016i	−0.662060	−	0.749451i	$-0.730318\pi$
$139$	−2.62934	+	1.75687i	−0.223018	+	0.149016i	0.439043	+	0.898466i	$0.355318\pi$
$140$	18.9737	+	18.9737i	1.60357	+	1.60357i
$141$	3.44404	+	15.1043i	0.290040	+	1.27201i
$142$	−23.6640	−	15.8118i	−1.98584	−	1.32690i
$143$	−1.10360	−	5.54816i	−0.0922875	−	0.463960i
$144$	2.70347	−	1.30049i	0.225289	−	0.108374i
$145$	3.06147	−	7.39104i	0.254241	−	0.613792i
$146$		0			0
$147$	−0.871488	+	5.12255i	−0.0718791	+	0.422501i
$148$	3.70158	−	18.6091i	0.304268	−	1.52966i
$149$	−12.6491	+	12.6491i	−1.03626	+	1.03626i	−0.0369380	+	0.999318i	$0.511760\pi$
$149$	−12.6491	+	12.6491i	−1.03626	+	1.03626i	−0.999318	+	0.0369380i	$0.988240\pi$
$150$	6.18377	−	9.83672i	0.504902	−	0.803165i
$151$	−18.4776	+	7.65367i	−1.50369	+	0.622847i	−0.974243	−	0.225500i	$-0.927599\pi$
$151$	−18.4776	+	7.65367i	−1.50369	+	0.622847i	−0.529442	+	0.848346i	$0.677599\pi$
$152$		0			0
$153$		0			0
$154$	−10.0000			−0.805823
$155$	−8.26343	+	3.42282i	−0.663735	+	0.274928i
$156$	−11.0619	+	17.5965i	−0.885657	+	1.40884i
$157$	−1.41421	+	1.41421i	−0.112867	+	0.112867i	−0.761285	−	0.648418i	$-0.775431\pi$
$157$	−1.41421	+	1.41421i	−0.112867	+	0.112867i	0.648418	+	0.761285i	$0.275431\pi$
$158$	−1.37950	+	6.93520i	−0.109747	+	0.551735i
$159$		0			0
$160$	−18.6091	+	3.70158i	−1.47118	+	0.292635i
$161$	−8.55706	+	20.6586i	−0.674391	+	1.62812i
$162$	−5.58781	+	19.3333i	−0.439020	+	1.51897i
$163$	−1.85079	−	9.30455i	−0.144965	−	0.728788i	−0.983063	−	0.183268i	$-0.941332\pi$
$163$	−1.85079	−	9.30455i	−0.144965	−	0.728788i	0.838098	−	0.545520i	$-0.183668\pi$
$164$	−14.1105	−	9.42834i	−1.10185	−	0.736230i
$165$	1.54022	+	6.75483i	0.119906	+	0.525863i
$166$	14.1421	+	14.1421i	1.09764	+	1.09764i
$167$	−8.23113	+	5.49986i	−0.636944	+	0.425592i	−0.831674	−	0.555265i	$-0.812617\pi$
$167$	−8.23113	+	5.49986i	−0.636944	+	0.425592i	0.194730	+	0.980857i	$0.437617\pi$
$168$	8.89793	+	8.41587i	0.686490	+	0.649298i
$169$			3.00000i			0.230769i
$170$		0			0
$171$		0			0
$172$	4.59220	+	11.0866i	0.350152	+	0.845342i
$173$	7.85695	+	11.7588i	0.597353	+	0.894002i	0.999770	−	0.0214548i	$-0.00682980\pi$
$173$	7.85695	+	11.7588i	0.597353	+	0.894002i	−0.402417	+	0.915456i	$0.631830\pi$
$174$	3.90879	−	10.2333i	0.296325	−	0.775788i
$175$	−9.30455	−	1.85079i	−0.703358	−	0.139907i
$176$	0.785695	−	1.17588i	0.0592240	−	0.0886350i
$177$	8.96202	+	12.6365i	0.673627	+	0.949820i
$178$	−27.7164	−	11.4805i	−2.07743	−	0.860500i
$179$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$179$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$180$	12.9429	−	21.9199i	0.964707	−	1.63381i
$181$	10.5412	−	15.7760i	0.783522	−	1.17262i	−0.197799	−	0.980243i	$-0.563379\pi$
$181$	10.5412	−	15.7760i	0.783522	−	1.17262i	0.981320	−	0.192380i	$-0.0616207\pi$
$182$	27.7408	+	5.51799i	2.05628	+	0.409020i
$183$	10.2333	+	3.90879i	0.756471	+	0.288946i
$184$	8.78434	+	13.1467i	0.647590	+	0.969187i
$185$	6.84565	+	16.5269i	0.503302	+	1.21508i
$186$	−11.1803	+	5.00000i	−0.819782	+	0.366618i
$187$		0			0
$188$		−	26.8328i		−	1.95698i
$189$	16.3744	−	1.37055i	1.19106	−	0.0996925i
$190$		0			0
$191$	−6.32456	−	6.32456i	−0.457629	−	0.457629i	0.440248	−	0.897876i	$-0.354891\pi$
$191$	−6.32456	−	6.32456i	−0.457629	−	0.457629i	−0.897876	+	0.440248i	$0.854891\pi$
$192$	−21.9532	+	5.00572i	−1.58434	+	0.361256i
$193$	−10.5174	−	7.02747i	−0.757055	−	0.505848i	0.116131	−	0.993234i	$-0.462951\pi$
$193$	−10.5174	−	7.02747i	−0.757055	−	0.505848i	−0.873187	+	0.487386i	$0.837951\pi$
$194$	−5.51799	−	27.7408i	−0.396168	−	1.99167i
$195$	−0.545387	−	19.5883i	−0.0390560	−	1.40275i
$196$	3.44415	−	8.31492i	0.246011	−	0.593923i
$197$	24.9667	−	4.96619i	1.77880	−	0.353826i	0.807171	−	0.590317i	$-0.200997\pi$
$197$	24.9667	−	4.96619i	1.77880	−	0.353826i	0.971634	+	0.236491i	$0.0759974\pi$
$198$	2.36564	+	9.18715i	0.168119	+	0.652902i
$199$	1.85079	−	9.30455i	0.131199	−	0.659582i	−0.858077	−	0.513522i	$-0.828341\pi$
$199$	1.85079	−	9.30455i	0.131199	−	0.659582i	0.989276	−	0.146060i	$-0.0466593\pi$
$200$	−4.74342	+	4.74342i	−0.335410	+	0.335410i
$201$	11.7310	+	7.37457i	0.827439	+	0.520162i
$202$	9.23880	−	3.82683i	0.650039	−	0.269255i
$203$	−8.94427			−0.627765
$204$		0			0
$205$	16.0000			1.11749
$206$	8.26343	−	3.42282i	0.575740	−	0.238479i
$207$	21.0036	+	2.97442i	1.45985	+	0.206736i
$208$	−2.82843	+	2.82843i	−0.196116	+	0.196116i
$209$		0			0
$210$	−34.1503	−	5.80992i	−2.35660	−	0.400922i
$211$	−21.7106	+	4.31851i	−1.49462	+	0.297298i	−0.873657	−	0.486542i	$-0.838258\pi$
$211$	−21.7106	+	4.31851i	−1.49462	+	0.297298i	−0.620963	+	0.783840i	$0.713258\pi$
$212$		0			0
$213$	22.0369	−	0.613560i	1.50994	−	0.0420405i
$214$	−1.85079	−	9.30455i	−0.126517	−	0.636046i
$215$	−9.40700	−	6.28556i	−0.641552	−	0.428672i
$216$	5.62685	−	10.1656i	0.382859	−	0.691678i
$217$	7.07107	+	7.07107i	0.480015	+	0.480015i
$218$	35.2763	−	23.5708i	2.38921	−	1.59642i
$219$		0			0
$220$		−	12.0000i		−	0.809040i
$221$		0			0
$222$	10.0000	+	22.3607i	0.671156	+	1.50075i
$223$	6.12293	+	14.7821i	0.410022	+	0.989881i	0.985131	+	0.171804i	$0.0549596\pi$
$223$	6.12293	+	14.7821i	0.410022	+	0.989881i	−0.575109	+	0.818077i	$0.695040\pi$
$224$	11.7854	+	17.6381i	0.787447	+	1.17850i
$225$	0.500776	+	8.98606i	0.0333851	+	0.599070i
$226$	12.4061	+	2.46772i	0.825239	+	0.164150i
$227$	−3.92847	+	5.87938i	−0.260742	+	0.390228i	−0.938624	−	0.344943i	$-0.887898\pi$
$227$	−3.92847	+	5.87938i	−0.260742	+	0.390228i	0.677882	+	0.735171i	$0.262898\pi$
$228$		0			0
$229$	18.4776	+	7.65367i	1.22103	+	0.505769i	0.897738	−	0.440529i	$-0.145209\pi$
$229$	18.4776	+	7.65367i	1.22103	+	0.505769i	0.323295	+	0.946298i	$0.395209\pi$
$230$	−41.3171	−	17.1141i	−2.72437	−	1.12847i
$231$	6.31827	−	4.48101i	0.415712	−	0.294829i
$232$	−3.51373	+	5.25868i	−0.230688	+	0.345249i
$233$	5.54816	+	1.10360i	0.363472	+	0.0722991i	0.373448	−	0.927651i	$-0.378175\pi$
$233$	5.54816	+	1.10360i	0.363472	+	0.0722991i	−0.00997588	+	0.999950i	$0.503175\pi$
$234$	−1.49302	−	26.7912i	−0.0976021	−	1.75140i
$235$	14.0549	+	21.0347i	0.916843	+	1.37215i
$236$	−10.2685	−	24.7903i	−0.668421	−	1.61371i
$237$	−2.23607	−	5.00000i	−0.145248	−	0.324785i
$238$		0			0
$239$			8.94427i			0.578557i	0.957245	+	0.289278i	$0.0934153\pi$
$239$			8.94427i			0.578557i	−0.957245	+	0.289278i	$0.906585\pi$
$240$	3.36635	−	3.55917i	0.217297	−	0.229744i
$241$	−21.0347	+	14.0549i	−1.35496	+	0.905358i	−0.999569	−	0.0293579i	$-0.990654\pi$
$241$	−21.0347	+	14.0549i	−1.35496	+	0.905358i	−0.355395	+	0.934716i	$0.615654\pi$
$242$	−14.2302	−	14.2302i	−0.914755	−	0.914755i
$243$	−5.13274	−	14.7192i	−0.329266	−	0.944237i
$244$	−15.7760	−	10.5412i	−1.00996	−	0.674831i
$245$	1.65540	+	8.32224i	0.105759	+	0.531688i
$246$	21.9004	−	0.609761i	1.39632	−	0.0388769i
$247$		0			0
$248$	6.93520	−	1.37950i	0.440386	−	0.0875981i
$249$	−15.2725	−	2.59827i	−0.967855	−	0.164659i
$250$	−2.46772	+	12.4061i	−0.156072	+	0.784628i
$251$	12.6491	−	12.6491i	0.798405	−	0.798405i	−0.184439	−	0.982844i	$-0.559047\pi$
$251$	12.6491	−	12.6491i	0.798405	−	0.798405i	0.982844	+	0.184439i	$0.0590469\pi$
$252$	−28.1793	−	3.99060i	−1.77513	−	0.251384i
$253$	9.23880	−	3.82683i	0.580838	−	0.240591i
$254$	26.8328			1.68364
$255$		0			0
$256$	9.00000			0.562500
$257$	−20.6586	+	8.55706i	−1.28865	+	0.533775i	−0.918582	−	0.395231i	$-0.870665\pi$
$257$	−20.6586	+	8.55706i	−1.28865	+	0.533775i	−0.370065	+	0.929006i	$0.620665\pi$
$258$	−13.1156	−	8.24502i	−0.816543	−	0.513313i
$259$	14.1421	−	14.1421i	0.878750	−	0.878750i
$260$	−6.62159	+	33.2890i	−0.410653	+	2.06449i
$261$	2.11590	+	8.21724i	0.130971	+	0.508634i
$262$	−3.10152	+	0.616930i	−0.191612	+	0.0381140i
$263$	−6.84565	+	16.5269i	−0.422121	+	1.01909i	0.559600	+	0.828763i	$0.310955\pi$
$263$	−6.84565	+	16.5269i	−0.422121	+	1.01909i	−0.981721	+	0.190327i	$0.939045\pi$
$264$	−0.152440	−	5.47510i	−0.00938205	−	0.336969i
$265$		0			0
$266$		0			0
$267$	22.6564	−	5.16606i	1.38655	−	0.316157i
$268$	−16.9706	−	16.9706i	−1.03664	−	1.03664i
$269$	21.1658	−	14.1425i	1.29050	−	0.862284i	0.294857	−	0.955541i	$-0.404728\pi$
$269$	21.1658	−	14.1425i	1.29050	−	0.862284i	0.995642	+	0.0932573i	$0.0297279\pi$
$270$	2.74109	+	32.7488i	0.166817	+	1.99303i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$	−20.0000	+	8.94427i	−1.21046	+	0.541332i
$274$	−3.82683	−	9.23880i	−0.231188	−	0.558136i
$275$	2.35708	+	3.52763i	0.142138	+	0.212724i
$276$	−34.3237	−	13.1105i	−2.06604	−	0.789158i
$277$	6.20303	+	1.23386i	0.372704	+	0.0741354i	0.377888	−	0.925851i	$-0.376650\pi$
$277$	6.20303	+	1.23386i	0.372704	+	0.0741354i	−0.00518447	+	0.999987i	$0.501650\pi$
$278$	−3.92847	+	5.87938i	−0.235614	+	0.352622i
$279$	4.82353	−	8.16906i	0.288777	−	0.489069i
$280$	18.4776	+	7.65367i	1.10425	+	0.457394i
$281$	−16.5269	−	6.84565i	−0.985910	−	0.408377i	−0.169298	−	0.985565i	$-0.554150\pi$
$281$	−16.5269	−	6.84565i	−0.985910	−	0.408377i	−0.816612	+	0.577188i	$0.804150\pi$
$282$	20.0397	+	28.2562i	1.19335	+	1.68263i
$283$	−1.75687	+	2.62934i	−0.104435	+	0.156298i	−0.880006	−	0.474962i	$-0.842462\pi$
$283$	−1.75687	+	2.62934i	−0.104435	+	0.156298i	0.775571	+	0.631260i	$0.217462\pi$
$284$	−37.4501	−	7.44928i	−2.22225	−	0.442034i
$285$		0			0
$286$	−7.02747	−	10.5174i	−0.415543	−	0.621904i
$287$	−6.84565	−	16.5269i	−0.404086	−	0.975550i
$288$	13.4164	−	15.0000i	0.790569	−	0.883883i
$289$		0			0
$290$		−	17.8885i		−	1.05045i
$291$	15.9171	+	15.0548i	0.933077	+	0.882526i
$292$		0			0
$293$	12.6491	+	12.6491i	0.738969	+	0.738969i	0.972379	−	0.233410i	$-0.0749883\pi$
$293$	12.6491	+	12.6491i	0.738969	+	0.738969i	−0.233410	+	0.972379i	$0.574988\pi$
$294$	2.58303	+	11.3282i	0.150645	+	0.660674i
$295$	21.0347	+	14.0549i	1.22469	+	0.818310i
$296$	−2.75899	−	13.8704i	−0.160363	−	0.806201i
$297$	−5.61145	−	4.74464i	−0.325609	−	0.275312i
$298$	−15.3073	+	36.9552i	−0.886730	+	2.14076i
$299$	−27.7408	+	5.51799i	−1.60429	+	0.319113i
$300$	2.61446	−	15.3676i	0.150946	−	0.887252i
$301$	−2.46772	+	12.4061i	−0.142237	+	0.715073i
$302$	−31.6228	+	31.6228i	−1.81969	+	1.81969i
$303$	−4.12251	+	6.55781i	−0.236832	+	0.376736i
$304$		0			0
$305$	17.8885			1.02430
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$	−12.3951	+	5.13424i	−0.706279	+	0.292550i
$309$	−3.68729	+	5.86549i	−0.209762	+	0.333676i
$310$	−14.1421	+	14.1421i	−0.803219	+	0.803219i
$311$	−0.275899	+	1.38704i	−0.0156448	+	0.0786518i	−0.987819	−	0.155608i	$-0.950266\pi$
$311$	−0.275899	+	1.38704i	−0.0156448	+	0.0786518i	0.972174	+	0.234259i	$0.0752665\pi$
$312$	−2.59827	+	15.2725i	−0.147098	+	0.864635i
$313$	24.8121	−	4.93544i	1.40246	−	0.278967i	0.564834	−	0.825205i	$-0.308940\pi$
$313$	24.8121	−	4.93544i	1.40246	−	0.278967i	0.837630	+	0.546237i	$0.183940\pi$
$314$	−1.71141	+	4.13171i	−0.0965806	+	0.233166i
$315$	24.1805	−	11.6319i	1.36242	−	0.655386i
$316$	1.85079	+	9.30455i	0.104115	+	0.523422i
$317$	11.7588	+	7.85695i	0.660438	+	0.441290i	0.840095	−	0.542439i	$-0.182499\pi$
$317$	11.7588	+	7.85695i	0.660438	+	0.441290i	−0.179658	+	0.983729i	$0.557499\pi$
$318$		0			0
$319$	2.82843	+	2.82843i	0.158362	+	0.158362i
$320$	−30.5728	+	20.4281i	−1.70907	+	1.14196i
$321$	5.33876	+	5.04952i	0.297980	+	0.281837i
$322$			50.0000i			2.78639i
$323$		0			0
$324$	3.00000	+	26.8328i	0.166667	+	1.49071i
$325$	−4.59220	−	11.0866i	−0.254729	−	0.614971i
$326$	−11.7854	−	17.6381i	−0.652734	−	0.976886i
$327$	−11.7264	+	30.7000i	−0.648470	+	1.69772i
$328$	−12.4061	−	2.46772i	−0.685010	−	0.136257i
$329$	15.7139	−	23.5175i	0.866335	−	1.29656i
$330$	8.96202	+	12.6365i	0.493343	+	0.695619i
$331$	−25.8686	−	10.7151i	−1.42187	−	0.588957i	−0.466539	−	0.884501i	$-0.654499\pi$
$331$	−25.8686	−	10.7151i	−1.42187	−	0.588957i	−0.955329	+	0.295543i	$0.904499\pi$
$332$	24.7903	+	10.2685i	1.36054	+	0.563556i
$333$	−16.3381	−	9.64707i	−0.895323	−	0.528656i
$334$	−12.2981	+	18.4054i	−0.672921	+	1.00710i
$335$	22.1926	+	4.41439i	1.21251	+	0.241184i
$336$	−5.11667	−	1.95440i	−0.279137	−	0.106621i
$337$	−14.0549	−	21.0347i	−0.765621	−	1.14583i	−0.985395	−	0.170282i	$-0.945532\pi$
$337$	−14.0549	−	21.0347i	−0.765621	−	1.14583i	0.219774	−	0.975551i	$-0.429468\pi$
$338$	2.56712	+	6.19757i	0.139633	+	0.337103i
$339$	−8.94427	+	4.00000i	−0.485786	+	0.217250i
$340$		0			0
$341$		−	4.47214i		−	0.242180i
$342$		0			0
$343$	−10.5174	+	7.02747i	−0.567884	+	0.379448i
$344$	6.32456	+	6.32456i	0.340997	+	0.340997i
$345$	33.7741	−	7.70110i	1.81834	−	0.414613i
$346$	26.2934	+	17.5687i	1.41354	+	0.944498i
$347$	6.89748	+	34.6760i	0.370276	+	1.86151i	0.494395	+	0.869238i	$0.335390\pi$
$347$	6.89748	+	34.6760i	0.370276	+	1.86151i	−0.124118	+	0.992267i	$0.539610\pi$
$348$	−0.409040	−	14.6912i	−0.0219269	−	0.787533i
$349$	−5.35757	+	12.9343i	−0.286784	+	0.692358i	−0.999963	−	0.00862428i	$-0.997255\pi$
$349$	−5.35757	+	12.9343i	−0.286784	+	0.692358i	0.713179	+	0.700982i	$0.247255\pi$
$350$	−20.8056	+	4.13849i	−1.11211	+	0.221212i
$351$	12.9485	+	16.2584i	0.691141	+	0.867809i
$352$	1.85079	−	9.30455i	0.0986474	−	0.495934i
$353$	12.6491	−	12.6491i	0.673244	−	0.673244i	−0.285218	−	0.958463i	$-0.592066\pi$
$353$	12.6491	−	12.6491i	0.673244	−	0.673244i	0.958463	+	0.285218i	$0.0920661\pi$
$354$	29.3274	+	18.4364i	1.55874	+	0.979885i
$355$	33.2597	−	13.7766i	1.76524	−	0.731186i
$356$	−40.2492			−2.13320
$357$		0			0
$358$		0			0
$359$	−24.7903	+	10.2685i	−1.30838	+	0.541949i	−0.924412	−	0.381396i	$-0.875443\pi$
$359$	−24.7903	+	10.2685i	−1.30838	+	0.541949i	−0.383970	+	0.923346i	$0.625443\pi$
$360$	2.66040	−	18.7862i	0.140215	−	0.990121i
$361$	13.4350	−	13.4350i	0.707107	−	0.707107i
$362$	8.27698	−	41.6112i	0.435028	−	2.18704i
$363$	15.3676	+	2.61446i	0.806592	+	0.137224i
$364$	37.2182	−	7.40316i	1.95076	−	0.388031i
$365$		0			0
$366$	24.4854	−	0.681734i	1.27987	−	0.0356348i
$367$	3.08465	+	15.5076i	0.161017	+	0.809489i	0.973885	+	0.227041i	$0.0729051\pi$
$367$	3.08465	+	15.5076i	0.161017	+	0.809489i	−0.812868	+	0.582448i	$0.802095\pi$
$368$	−5.87938	−	3.92847i	−0.306484	−	0.204786i
$369$	−13.5640	+	10.1989i	−0.706116	+	0.530932i
$370$	28.2843	+	28.2843i	1.47043	+	1.47043i
$371$		0			0
$372$	−11.2911	+	11.9378i	−0.585415	+	0.618947i
$373$		−	4.00000i		−	0.207112i	−0.994624	−	0.103556i	$-0.966978\pi$
$373$		−	4.00000i		−	0.207112i	0.994624	−	0.103556i	$-0.0330221\pi$
$374$		0			0
$375$	−4.00000	−	8.94427i	−0.206559	−	0.461880i
$376$	−7.65367	−	18.4776i	−0.394708	−	0.952909i
$377$	−6.28556	−	9.40700i	−0.323723	−	0.484485i
$378$	32.6544	−	16.8430i	1.67956	−	0.866313i
$379$	−9.30455	−	1.85079i	−0.477942	−	0.0950687i	−0.0497604	−	0.998761i	$-0.515846\pi$
$379$	−9.30455	−	1.85079i	−0.477942	−	0.0950687i	−0.428182	+	0.903693i	$0.640846\pi$
$380$		0			0
$381$	−16.9537	+	12.0238i	−0.868564	+	0.615999i
$382$	−18.4776	−	7.65367i	−0.945396	−	0.391596i
$383$	−33.0537	−	13.6913i	−1.68897	−	0.699593i	−0.689276	−	0.724499i	$-0.742071\pi$
$383$	−33.0537	−	13.6913i	−1.68897	−	0.699593i	−0.999690	+	0.0249059i	$0.992071\pi$
$384$	−22.1139	+	15.6835i	−1.12850	+	0.800347i
$385$	7.02747	−	10.5174i	0.358153	−	0.536014i
$386$	−27.7408	−	5.51799i	−1.41197	−	0.280858i
$387$	11.9814	−	0.667701i	0.609049	−	0.0339412i
$388$	−21.0824	−	31.5521i	−1.07030	−	1.60181i
$389$	−1.71141	−	4.13171i	−0.0867720	−	0.209486i	0.874537	−	0.484959i	$-0.161166\pi$
$389$	−1.71141	−	4.13171i	−0.0867720	−	0.209486i	−0.961309	+	0.275473i	$0.911166\pi$
$390$	−17.8885	−	40.0000i	−0.905822	−	2.02548i
$391$		0			0
$392$		−	6.70820i		−	0.338815i
$393$	1.68317	−	1.77959i	0.0849049	−	0.0897682i
$394$	47.3281	−	31.6236i	2.38435	−	1.59317i
$395$	−6.32456	−	6.32456i	−0.318223	−	0.318223i
$396$	7.64915	+	10.1730i	0.384384	+	0.511214i
$397$	−15.7760	−	10.5412i	−0.791776	−	0.529048i	0.0926663	−	0.995697i	$-0.470461\pi$
$397$	−15.7760	−	10.5412i	−0.791776	−	0.529048i	−0.884442	+	0.466649i	$0.845461\pi$
$398$	−4.13849	−	20.8056i	−0.207444	−	1.04289i
$399$		0			0
$400$	1.14805	−	2.77164i	0.0574025	−	0.138582i
$401$	−5.54816	+	1.10360i	−0.277062	+	0.0551110i	−0.331665	−	0.943397i	$-0.607611\pi$
$401$	−5.54816	+	1.10360i	−0.277062	+	0.0551110i	0.0546036	+	0.998508i	$0.482611\pi$
$402$	30.5450	+	5.19655i	1.52345	+	0.259180i
$403$	−2.46772	+	12.4061i	−0.122926	+	0.617990i
$404$	9.48683	−	9.48683i	0.471988	−	0.471988i
$405$	−16.4067	−	19.4633i	−0.815255	−	0.967140i
$406$	−18.4776	+	7.65367i	−0.917027	+	0.379845i
$407$	−8.94427			−0.443351
$408$		0			0
$409$	14.0000			0.692255			0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000			0.692255			0.346128	+	0.938187i	$0.387496\pi$
$410$	33.0537	−	13.6913i	1.63241	−	0.676165i
$411$	6.55781	+	4.12251i	0.323473	+	0.203348i
$412$	8.48528	−	8.48528i	0.418040	−	0.418040i
$413$	5.51799	−	27.7408i	0.271522	−	1.36504i
$414$	45.9358	−	11.8282i	2.25762	−	0.581325i
$415$	−24.8121	+	4.93544i	−1.21798	+	0.242271i
$416$	−10.2685	+	24.7903i	−0.503453	+	1.21544i
$417$	−0.152440	−	5.47510i	−0.00746503	−	0.268117i
$418$		0			0
$419$	−8.23113	−	5.49986i	−0.402117	−	0.268686i	0.338024	−	0.941137i	$-0.390241\pi$
$419$	−8.23113	−	5.49986i	−0.402117	−	0.268686i	−0.740141	+	0.672451i	$0.765241\pi$
$420$	−45.3128	+	10.3321i	−2.21104	+	0.504155i
$421$	−14.1421	−	14.1421i	−0.689246	−	0.689246i	0.272820	−	0.962065i	$-0.412044\pi$
$421$	−14.1421	−	14.1421i	−0.689246	−	0.689246i	−0.962065	+	0.272820i	$0.912044\pi$
$422$	−41.1556	+	27.4993i	−2.00343	+	1.33865i
$423$	−25.3232	−	8.87319i	−1.23126	−	0.431429i
$424$		0			0
$425$		0			0
$426$	45.0000	−	20.1246i	2.18026	−	0.975041i
$427$	−7.65367	−	18.4776i	−0.370387	−	0.894193i
$428$	−7.07125	−	10.5829i	−0.341802	−	0.511543i
$429$	9.15298	+	3.49613i	0.441910	+	0.168795i
$430$	−24.8121	−	4.93544i	−1.19655	−	0.238008i
$431$	7.07125	−	10.5829i	0.340610	−	0.509759i	−0.621135	−	0.783703i	$-0.713328\pi$
$431$	7.07125	−	10.5829i	0.340610	−	0.509759i	0.961746	+	0.273944i	$0.0883283\pi$
$432$	−0.585110	+	5.16310i	−0.0281511	+	0.248410i
$433$	33.2597	+	13.7766i	1.59836	+	0.662061i	0.991182	−	0.132507i	$-0.0423026\pi$
$433$	33.2597	+	13.7766i	1.59836	+	0.662061i	0.607175	+	0.794568i	$0.292303\pi$
$434$	20.6586	+	8.55706i	0.991643	+	0.410752i
$435$	8.01588	+	11.3025i	0.384332	+	0.541912i
$436$	31.6236	−	47.3281i	1.51450	−	2.26660i
$437$		0			0
$438$		0			0
$439$	12.2981	+	18.4054i	0.586955	+	0.878440i	0.999471	−	0.0325100i	$-0.0103501\pi$
$439$	12.2981	+	18.4054i	0.586955	+	0.878440i	−0.412516	+	0.910950i	$0.635350\pi$
$440$	−3.42282	−	8.26343i	−0.163177	−	0.393944i
$441$	−6.70820	−	6.00000i	−0.319438	−	0.285714i
$442$		0			0
$443$		−	17.8885i		−	0.849910i	−0.905214	−	0.424955i	$-0.860290\pi$
$443$		−	17.8885i		−	0.849910i	0.905214	−	0.424955i	$-0.139710\pi$
$444$	23.8756	+	22.5821i	1.13309	+	1.07170i
$445$	31.5521	−	21.0824i	1.49571	−	0.999402i
$446$	25.2982	+	25.2982i	1.19791	+	1.19791i
$447$	−6.88807	−	30.2085i	−0.325795	−	1.42881i
$448$	34.1814	+	22.8393i	1.61492	+	1.07905i
$449$	3.31079	+	16.6445i	0.156246	+	0.785501i	0.976837	+	0.213985i	$0.0686445\pi$
$449$	3.31079	+	16.6445i	0.156246	+	0.785501i	−0.820591	+	0.571516i	$0.806355\pi$
$450$	8.72396	+	18.1354i	0.411251	+	0.854911i
$451$	−3.06147	+	7.39104i	−0.144159	+	0.348030i
$452$	16.6445	−	3.31079i	0.782890	−	0.155727i
$453$	5.80992	−	34.1503i	0.272974	−	1.60452i
$454$	−3.08465	+	15.5076i	−0.144770	+	0.727807i
$455$	−25.2982	+	25.2982i	−1.18600	+	1.18600i
$456$		0			0
$457$	−25.8686	+	10.7151i	−1.21008	+	0.501233i	−0.894244	−	0.447580i	$-0.852286\pi$
$457$	−25.8686	+	10.7151i	−1.21008	+	0.501233i	−0.315839	+	0.948813i	$0.602286\pi$
$458$	44.7214			2.08969
$459$		0			0
$460$	−60.0000			−2.79751
$461$	33.0537	−	13.6913i	1.53947	−	0.637667i	0.558092	−	0.829779i	$-0.311534\pi$
$461$	33.0537	−	13.6913i	1.53947	−	0.637667i	0.981373	+	0.192112i	$0.0615336\pi$
$462$	9.21821	−	14.6637i	0.428870	−	0.682218i
$463$	−2.82843	+	2.82843i	−0.131448	+	0.131448i	−0.769770	−	0.638322i	$-0.779629\pi$
$463$	−2.82843	+	2.82843i	−0.131448	+	0.131448i	0.638322	+	0.769770i	$0.279629\pi$
$464$	0.551799	−	2.77408i	0.0256166	−	0.128783i
$465$	2.59827	−	15.2725i	0.120492	−	0.708245i
$466$	12.4061	−	2.46772i	0.574700	−	0.114315i
$467$	6.84565	−	16.5269i	0.316779	−	0.764772i	−0.682642	−	0.730753i	$-0.739169\pi$
$467$	6.84565	−	16.5269i	0.316779	−	0.764772i	0.999421	−	0.0340192i	$-0.0108307\pi$
$468$	−15.6059	−	32.4416i	−0.721382	−	1.49961i
$469$	−4.93544	−	24.8121i	−0.227897	−	1.14572i
$470$	47.0350	+	31.4278i	2.16956	+	1.44966i
$471$	−0.770110	−	3.37741i	−0.0354848	−	0.155623i
$472$	−14.1421	−	14.1421i	−0.650945	−	0.650945i
$473$	4.70350	−	3.14278i	0.216267	−	0.144505i
$474$	−8.89793	−	8.41587i	−0.408695	−	0.386554i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	7.65367	+	18.4776i	0.350071	+	0.845145i
$479$	5.49986	+	8.23113i	0.251295	+	0.376090i	0.935574	−	0.353131i	$-0.114883\pi$
$479$	5.49986	+	8.23113i	0.251295	+	0.376090i	−0.684279	+	0.729220i	$0.739883\pi$
$480$	11.7264	−	30.7000i	0.535233	−	1.40126i
$481$	24.8121	+	4.93544i	1.13134	+	0.225037i
$482$	−31.4278	+	47.0350i	−1.43150	+	2.14239i
$483$	−22.4051	−	31.5913i	−1.01947	−	1.43746i
$484$	−24.9447	−	10.3325i	−1.13385	−	0.469657i
$485$	33.0537	+	13.6913i	1.50089	+	0.621690i
$486$	−23.1988	−	26.0157i	−1.05232	−	1.18009i
$487$	−15.8118	+	23.6640i	−0.716501	+	1.07232i	0.277260	+	0.960795i	$0.410574\pi$
$487$	−15.8118	+	23.6640i	−0.716501	+	1.07232i	−0.993762	+	0.111525i	$0.964426\pi$
$488$	−13.8704	−	2.75899i	−0.627883	−	0.124894i
$489$	15.3500	+	5.86319i	0.694152	+	0.265142i
$490$	10.5412	+	15.7760i	0.476203	+	0.712688i
$491$	6.84565	+	16.5269i	0.308940	+	0.745847i	0.999740	+	0.0228010i	$0.00725842\pi$
$491$	6.84565	+	16.5269i	0.308940	+	0.745847i	−0.690800	+	0.723046i	$0.742742\pi$
$492$	26.8328	−	12.0000i	1.20972	−	0.541002i
$493$		0			0
$494$		0			0
$495$	−11.3249	−	3.96821i	−0.509016	−	0.178358i
$496$	−2.62934	+	1.75687i	−0.118061	+	0.0788857i
$497$	−28.4605	−	28.4605i	−1.27663	−	1.27663i
$498$	−33.7741	+	7.70110i	−1.51346	+	0.345095i
$499$	2.62934	+	1.75687i	0.117705	+	0.0786482i	0.613029	−	0.790060i	$-0.289951\pi$
$499$	2.62934	+	1.75687i	0.117705	+	0.0786482i	−0.495324	+	0.868708i	$0.664951\pi$
$500$	3.31079	+	16.6445i	0.148063	+	0.744364i
$501$	−0.477214	−	17.1398i	−0.0213203	−	0.765749i
$502$	15.3073	−	36.9552i	0.683200	−	1.64939i
$503$	−12.4834	+	2.48309i	−0.556605	+	0.110716i	−0.465374	−	0.885114i	$-0.654080\pi$
$503$	−12.4834	+	2.48309i	−0.556605	+	0.110716i	−0.0912312	+	0.995830i	$0.529080\pi$
$504$	−20.5431	+	5.28974i	−0.915062	+	0.235624i
$505$	−2.46772	+	12.4061i	−0.109812	+	0.552062i
$506$	15.8114	−	15.8114i	0.702902	−	0.702902i
$507$	−4.39911	−	2.76546i	−0.195372	−	0.122819i
$508$	33.2597	−	13.7766i	1.47566	−	0.611238i
$509$	−17.8885			−0.792896			−0.396448	−	0.918057i	$-0.629757\pi$
$509$	−17.8885			−0.792896			−0.396448	+	0.918057i	$0.629757\pi$
$510$		0			0
$511$		0			0
$512$	−10.3293	+	4.27853i	−0.456494	+	0.189086i
$513$		0			0
$514$	−35.3553	+	35.3553i	−1.55946	+	1.55946i
$515$	−2.20720	+	11.0963i	−0.0972606	+	0.488962i
$516$	−20.4902	−	3.48595i	−0.902031	−	0.153460i
$517$	−12.4061	+	2.46772i	−0.545618	+	0.108530i
$518$	17.1141	−	41.3171i	0.751951	−	1.81537i
$519$	−24.4854	+	0.681734i	−1.07479	+	0.0299248i
$520$	4.93544	+	24.8121i	0.216433	+	1.08808i
$521$	28.2210	+	18.8567i	1.23639	+	0.826126i	0.989726	−	0.142976i	$-0.0456673\pi$
$521$	28.2210	+	18.8567i	1.23639	+	0.826126i	0.246659	+	0.969102i	$0.420667\pi$
$522$	11.4027	+	15.1651i	0.499082	+	0.663756i
$523$	−16.9706	−	16.9706i	−0.742071	−	0.742071i	0.230905	−	0.972976i	$-0.425831\pi$
$523$	−16.9706	−	16.9706i	−0.742071	−	0.742071i	−0.972976	+	0.230905i	$0.925831\pi$
$524$	−3.52763	+	2.35708i	−0.154105	+	0.102970i
$525$	11.2911	−	11.9378i	0.492783	−	0.521009i
$526$			40.0000i			1.74408i
$527$		0			0
$528$	1.00000	+	2.23607i	0.0435194	+	0.0973124i
$529$	−10.3325	−	24.9447i	−0.449237	−	1.08455i
$530$		0			0
$531$	−26.7912	+	1.49302i	−1.16264	+	0.0647918i
$532$		0			0
$533$	12.5711	−	18.8140i	0.544516	−	0.814925i
$534$	42.3842	−	30.0595i	1.83415	−	1.30080i
$535$	11.0866	+	4.59220i	0.479314	+	0.198538i
$536$	−16.5269	−	6.84565i	−0.713852	−	0.295687i
$537$		0			0
$538$	31.6236	−	47.3281i	1.36339	−	2.04046i
$539$	−4.16112	−	0.827698i	−0.179232	−	0.0356515i
$540$	20.2117	+	39.1853i	0.869771	+	1.68627i
$541$	3.51373	+	5.25868i	0.151067	+	0.226088i	0.899283	−	0.437368i	$-0.144089\pi$
$541$	3.51373	+	5.25868i	0.151067	+	0.226088i	−0.748216	+	0.663456i	$0.769089\pi$
$542$		0			0
$543$	13.4164	+	30.0000i	0.575753	+	1.28742i
$544$		0			0
$545$			53.6656i			2.29878i
$546$	−33.6635	+	35.5917i	−1.44066	+	1.52318i
$547$	2.62934	−	1.75687i	0.112422	−	0.0751182i	−0.498088	−	0.867126i	$-0.665964\pi$
$547$	2.62934	−	1.75687i	0.112422	−	0.0751182i	0.610510	+	0.792008i	$0.290964\pi$
$548$	−9.48683	−	9.48683i	−0.405257	−	0.405257i
$549$	−15.1651	+	11.4027i	−0.647229	+	0.486654i
$550$	7.88801	+	5.27060i	0.336346	+	0.224739i
$551$		0			0
$552$	−27.3755	+	0.762201i	−1.16518	+	0.0324414i
$553$	−3.82683	+	9.23880i	−0.162734	+	0.392874i
$554$	13.8704	−	2.75899i	0.589297	−	0.117218i
$555$	−30.5450	−	5.19655i	−1.29656	−	0.220581i
$556$	−1.85079	+	9.30455i	−0.0784909	+	0.394601i
$557$	9.48683	−	9.48683i	0.401970	−	0.401970i	−0.476957	−	0.878927i	$-0.658260\pi$
$557$	9.48683	−	9.48683i	0.401970	−	0.401970i	0.878927	+	0.476957i	$0.158260\pi$
$558$	2.97442	−	21.0036i	0.125917	−	0.889155i
$559$	−14.7821	+	6.12293i	−0.625215	+	0.258973i
$560$	−8.94427			−0.377964
$561$		0			0
$562$	−40.0000			−1.68730
$563$	8.26343	−	3.42282i	0.348262	−	0.144255i	−0.201694	−	0.979449i	$-0.564645\pi$
$563$	8.26343	−	3.42282i	0.348262	−	0.144255i	0.549956	+	0.835194i	$0.314645\pi$
$564$	39.3469	+	24.7351i	1.65680	+	1.04153i
$565$	−11.3137	+	11.3137i	−0.475971	+	0.475971i
$566$	−1.37950	+	6.93520i	−0.0579846	+	0.291508i
$567$	−13.0846	+	25.2744i	−0.549500	+	1.06142i
$568$	−27.9136	+	5.55237i	−1.17123	+	0.232972i
$569$	6.84565	−	16.5269i	0.286985	−	0.692842i	−0.712981	−	0.701184i	$-0.752655\pi$
$569$	6.84565	−	16.5269i	0.286985	−	0.692842i	0.999965	+	0.00834171i	$0.00265528\pi$
$570$		0			0
$571$	6.78623	+	34.1167i	0.283995	+	1.42774i	0.814553	+	0.580090i	$0.196982\pi$
$571$	6.78623	+	34.1167i	0.283995	+	1.42774i	−0.530558	+	0.847649i	$0.678018\pi$
$572$	−14.1105	−	9.42834i	−0.589990	−	0.394219i
$573$	15.1043	−	3.44404i	0.630989	−	0.143877i
$574$	−28.2843	−	28.2843i	−1.18056	−	1.18056i
$575$	17.6381	−	11.7854i	0.735561	−	0.491486i
$576$	12.8967	−	36.8059i	0.537362	−	1.53358i
$577$		−	12.0000i		−	0.499567i	−0.968302	−	0.249783i	$-0.919641\pi$
$577$		−	12.0000i		−	0.499567i	0.968302	−	0.249783i	$-0.0803594\pi$
$578$		0			0
$579$	20.0000	−	8.94427i	0.831172	−	0.371711i
$580$	−9.18440	−	22.1731i	−0.381362	−	0.920688i
$581$	15.7139	+	23.5175i	0.651922	+	0.975671i
$582$	45.7649	+	17.4806i	1.89702	+	0.724596i
$583$		0			0
$584$		0			0
$585$	29.2265	+	17.2572i	1.20837	+	0.713497i
$586$	36.9552	+	15.3073i	1.52660	+	0.632340i
$587$	16.5269	+	6.84565i	0.682136	+	0.282550i	0.696720	−	0.717343i	$-0.254642\pi$
$587$	16.5269	+	6.84565i	0.682136	+	0.282550i	−0.0145832	+	0.999894i	$0.504642\pi$
$588$	9.01786	+	12.7153i	0.371890	+	0.524369i
$589$		0			0
$590$	55.4816	+	11.0360i	2.28414	+	0.454344i
$591$	−15.7326	+	41.1884i	−0.647152	+	1.69427i
$592$	3.51373	+	5.25868i	0.144414	+	0.216130i
$593$	6.84565	+	16.5269i	0.281117	+	0.678677i	0.999862	−	0.0165969i	$-0.00528319\pi$
$593$	6.84565	+	16.5269i	0.281117	+	0.678677i	−0.718745	+	0.695274i	$0.755283\pi$
$594$	−15.6525	−	5.00000i	−0.642229	−	0.205152i
$595$		0			0
$596$			53.6656i			2.19823i
$597$	11.9378	+	11.2911i	0.488583	+	0.462113i
$598$	−52.5868	+	35.1373i	−2.15043	+	1.43687i
$599$	12.6491	+	12.6491i	0.516829	+	0.516829i	0.916610	−	0.399782i	$-0.130914\pi$
$599$	12.6491	+	12.6491i	0.516829	+	0.516829i	−0.399782	+	0.916610i	$0.630914\pi$
$600$	−2.58303	−	11.3282i	−0.105452	−	0.462472i
$601$	−10.5174	−	7.02747i	−0.429012	−	0.286656i	0.322258	−	0.946652i	$-0.395558\pi$
$601$	−10.5174	−	7.02747i	−0.429012	−	0.286656i	−0.751270	+	0.659995i	$0.770558\pi$
$602$	5.51799	+	27.7408i	0.224896	+	1.13063i
$603$	−21.6277	+	10.4039i	−0.880749	+	0.423681i
$604$	−22.9610	+	55.4328i	−0.934270	+	2.25553i
$605$	24.9667	−	4.96619i	1.01504	−	0.201904i
$606$	−2.90496	+	17.0752i	−0.118006	+	0.693631i
$607$	−4.31851	+	21.7106i	−0.175283	+	0.881206i	0.788605	+	0.614900i	$0.210803\pi$
$607$	−4.31851	+	21.7106i	−0.175283	+	0.881206i	−0.963888	+	0.266307i	$0.914197\pi$
$608$		0			0
$609$	8.24502	−	13.1156i	0.334105	−	0.531472i
$610$	36.9552	−	15.3073i	1.49627	−	0.619776i
$611$	35.7771			1.44739
$612$		0			0
$613$	6.00000			0.242338			0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000			0.242338			0.121169	+	0.992632i	$0.461336\pi$
$614$	−24.7903	+	10.2685i	−1.00045	+	0.414402i
$615$	−14.7491	+	23.4619i	−0.594743	+	0.946077i
$616$	−7.07107	+	7.07107i	−0.284901	+	0.284901i
$617$	−7.72518	+	38.8371i	−0.311004	+	1.56352i	0.436772	+	0.899572i	$0.356122\pi$
$617$	−7.72518	+	38.8371i	−0.311004	+	1.56352i	−0.747776	+	0.663951i	$0.768878\pi$
$618$	−2.59827	+	15.2725i	−0.104518	+	0.614350i
$619$	3.10152	−	0.616930i	0.124660	−	0.0247965i	−0.132366	−	0.991201i	$-0.542257\pi$
$619$	3.10152	−	0.616930i	0.124660	−	0.0247965i	0.257026	+	0.966404i	$0.417257\pi$
$620$	−10.2685	+	24.7903i	−0.412392	+	0.995602i
$621$	−23.7232	+	28.0573i	−0.951980	+	1.12590i
$622$	0.616930	+	3.10152i	0.0247366	+	0.124359i
$623$	−35.2763	−	23.5708i	−1.41331	−	0.944346i
$624$	−1.54022	−	6.75483i	−0.0616582	−	0.270410i
$625$	−21.9203	−	21.9203i	−0.876812	−	0.876812i
$626$	47.0350	−	31.4278i	1.87990	−	1.25611i
$627$		0			0
$628$			6.00000i			0.239426i
$629$		0			0
$630$	40.0000	−	44.7214i	1.59364	−	1.78174i
$631$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$631$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$632$	3.92847	+	5.87938i	0.156266	+	0.233869i
$633$	13.6808	−	35.8167i	0.543762	−	1.42359i
$634$	31.0152	+	6.16930i	1.23177	+	0.245014i
$635$	−18.8567	+	28.2210i	−0.748304	+	1.11992i
$636$		0			0
$637$	11.0866	+	4.59220i	0.439265	+	0.181950i
$638$	8.26343	+	3.42282i	0.327152	+	0.135511i
$639$	−19.4143	+	32.8798i	−0.768020	+	1.30071i
$640$	−24.5961	+	36.8107i	−0.972248	+	1.45507i
$641$	−22.1926	−	4.41439i	−0.876556	−	0.174358i	−0.263750	−	0.964591i	$-0.584959\pi$
$641$	−22.1926	−	4.41439i	−0.876556	−	0.174358i	−0.612806	+	0.790233i	$0.709959\pi$
$642$	15.3500	+	5.86319i	0.605817	+	0.231401i
$643$	−12.2981	−	18.4054i	−0.484989	−	0.725837i	0.505591	−	0.862773i	$-0.331274\pi$
$643$	−12.2981	−	18.4054i	−0.484989	−	0.725837i	−0.990580	+	0.136936i	$0.956274\pi$
$644$	25.6712	+	61.9757i	1.01159	+	2.44219i
$645$	17.8885	−	8.00000i	0.704361	−	0.315000i
$646$		0			0
$647$		−	26.8328i		−	1.05491i	−0.849584	−	0.527453i	$-0.823147\pi$
$647$		−	26.8328i		−	1.05491i	0.849584	−	0.527453i	$-0.176853\pi$
$648$	9.71953	+	17.6219i	0.381819	+	0.692253i
$649$	−10.5174	+	7.02747i	−0.412842	+	0.275852i
$650$	−18.9737	−	18.9737i	−0.744208	−	0.744208i
$651$	−16.8871	+	3.85055i	−0.661857	+	0.150915i
$652$	−23.6640	−	15.8118i	−0.926755	−	0.619238i
$653$	−7.17338	−	36.0630i	−0.280716	−	1.41126i	−0.821555	−	0.570129i	$-0.806893\pi$
$653$	−7.17338	−	36.0630i	−0.280716	−	1.41126i	0.540839	−	0.841126i	$-0.318107\pi$
$654$	2.04520	+	73.4562i	0.0799737	+	2.87237i
$655$	1.53073	−	3.69552i	0.0598107	−	0.144396i
$656$	5.54816	−	1.10360i	0.216619	−	0.0430882i
$657$		0			0
$658$	12.3386	−	62.0303i	0.481009	−	2.41819i
$659$	6.32456	−	6.32456i	0.246370	−	0.246370i	−0.573109	−	0.819479i	$-0.694263\pi$
$659$	6.32456	−	6.32456i	0.246370	−	0.246370i	0.819479	+	0.573109i	$0.194263\pi$
$660$	17.5965	+	11.0619i	0.684941	+	0.430582i
$661$	−35.1074	+	14.5420i	−1.36552	+	0.565617i	−0.940570	−	0.339600i	$-0.889708\pi$
$661$	−35.1074	+	14.5420i	−1.36552	+	0.565617i	−0.424950	+	0.905217i	$0.639708\pi$
$662$	−62.6099			−2.43340
$663$		0			0
$664$	20.0000			0.776151
$665$		0			0
$666$	−42.0073	−	5.94884i	−1.62775	−	0.230513i
$667$	14.1421	−	14.1421i	0.547586	−	0.547586i
$668$	−5.79389	+	29.1278i	−0.224172	+	1.12699i
$669$	−27.3203	−	4.64793i	−1.05626	−	0.179700i
$670$	49.6242	−	9.87088i	1.91715	−	0.381345i
$671$	−3.42282	+	8.26343i	−0.132137	+	0.319006i
$672$	−36.7281	+	1.02260i	−1.41682	+	0.0394477i
$673$	4.93544	+	24.8121i	0.190247	+	0.956437i	0.951422	+	0.307890i	$0.0996229\pi$
$673$	4.93544	+	24.8121i	0.190247	+	0.956437i	−0.761175	+	0.648547i	$0.775377\pi$
$674$	−47.0350	−	31.4278i	−1.81172	−	1.21055i
$675$	−13.6385	−	7.54922i	−0.524947	−	0.290569i
$676$	6.36396	+	6.36396i	0.244768	+	0.244768i
$677$	−11.7588	+	7.85695i	−0.451926	+	0.301967i	−0.760624	−	0.649193i	$-0.775107\pi$
$677$	−11.7588	+	7.85695i	−0.451926	+	0.301967i	0.308698	+	0.951160i	$0.400107\pi$
$678$	−15.0548	+	15.9171i	−0.578175	+	0.611292i
$679$		−	40.0000i		−	1.53506i
$680$		0			0
$681$	−5.00000	−	11.1803i	−0.191600	−	0.428432i
$682$	−3.82683	−	9.23880i	−0.146537	−	0.353772i
$683$	−3.92847	−	5.87938i	−0.150319	−	0.224968i	0.748666	−	0.662947i	$-0.230695\pi$
$683$	−3.92847	−	5.87938i	−0.150319	−	0.224968i	−0.898985	+	0.437979i	$0.855695\pi$
$684$		0			0
$685$	12.4061	+	2.46772i	0.474011	+	0.0942867i
$686$	−15.7139	+	23.5175i	−0.599959	+	0.897903i
$687$	−28.2562	+	20.0397i	−1.07804	+	0.764562i
$688$	−3.69552	−	1.53073i	−0.140890	−	0.0583587i
$689$		0			0
$690$	63.1827	−	44.8101i	2.40532	−	1.70589i
$691$	−22.8393	+	34.1814i	−0.868847	+	1.30032i	0.0838745	+	0.996476i	$0.473271\pi$
$691$	−22.8393	+	34.1814i	−0.868847	+	1.30032i	−0.952721	+	0.303845i	$0.901729\pi$
$692$	41.6112	+	8.27698i	1.58182	+	0.314644i
$693$	0.746512	+	13.3956i	0.0283577	+	0.508858i
$694$	43.9217	+	65.7334i	1.66724	+	2.49521i
$695$	−3.42282	−	8.26343i	−0.129835	−	0.313450i
$696$	−4.47214	−	10.0000i	−0.169516	−	0.379049i
$697$		0			0
$698$			31.3050i			1.18491i
$699$	−6.73270	+	7.11834i	−0.254654	+	0.269240i
$700$	−23.6640	+	15.8118i	−0.894417	+	0.597630i
$701$	9.48683	+	9.48683i	0.358313	+	0.358313i	0.863191	−	0.504878i	$-0.168463\pi$
$701$	9.48683	+	9.48683i	0.358313	+	0.358313i	−0.504878	+	0.863191i	$0.668463\pi$
$702$	40.6622	+	22.5074i	1.53470	+	0.849488i
$703$		0			0
$704$	−3.58669	−	18.0315i	−0.135179	−	0.679588i
$705$	−43.8008	+	1.21952i	−1.64963	+	0.0459299i
$706$	15.3073	−	36.9552i	0.576099	−	1.39083i
$707$	13.8704	−	2.75899i	0.521650	−	0.103763i
$708$	45.8175	+	7.79482i	1.72193	+	0.292947i
$709$	−1.23386	+	6.20303i	−0.0463386	+	0.232960i	−0.997013	−	0.0772298i	$-0.975392\pi$
$709$	−1.23386	+	6.20303i	−0.0463386	+	0.232960i	0.950675	+	0.310189i	$0.100392\pi$
$710$	56.9210	−	56.9210i	2.13621	−	2.13621i
$711$	9.39311	+	1.33020i	0.352269	+	0.0498864i
$712$	−27.7164	+	11.4805i	−1.03872	+	0.430250i
$713$	−22.3607			−0.837414
$714$		0			0
$715$	16.0000			0.598366
$716$		0			0
$717$	−13.1156	−	8.24502i	−0.489812	−	0.307916i
$718$	−42.4264	+	42.4264i	−1.58334	+	1.58334i
$719$	0.827698	−	4.16112i	0.0308679	−	0.155184i	−0.962277	−	0.272071i	$-0.912292\pi$
$719$	0.827698	−	4.16112i	0.0308679	−	0.155184i	0.993145	+	0.116887i	$0.0372916\pi$
$720$	2.11590	+	8.21724i	0.0788548	+	0.306238i
$721$	12.4061	−	2.46772i	0.462026	−	0.0919027i
$722$	16.2584	−	39.2513i	0.605076	−	1.46078i
$723$	−1.21952	−	43.8008i	−0.0453545	−	1.62897i
$724$	−11.1047	−	55.8273i	−0.412704	−	2.07480i
$725$	7.05525	+	4.71417i	0.262026	+	0.175080i
$726$	33.9846	−	7.74908i	1.26129	−	0.287595i
$727$	5.65685	+	5.65685i	0.209801	+	0.209801i	0.804183	−	0.594382i	$-0.202603\pi$
$727$	5.65685	+	5.65685i	0.209801	+	0.209801i	−0.594382	+	0.804183i	$0.702603\pi$
$728$	23.5175	−	15.7139i	0.871617	−	0.582396i
$729$	26.3153	+	6.04197i	0.974640	+	0.223777i
$730$		0			0
$731$		0			0
$732$	30.0000	−	13.4164i	1.10883	−	0.495885i
$733$	13.0112	+	31.4119i	0.480581	+	1.16023i	0.959333	+	0.282275i	$0.0910891\pi$
$733$	13.0112	+	31.4119i	0.480581	+	1.16023i	−0.478752	+	0.877950i	$0.658911\pi$
$734$	19.6424	+	29.3969i	0.725013	+	1.08506i
$735$	−13.7295	−	5.24419i	−0.506419	−	0.193435i
$736$	−46.5227	−	9.25395i	−1.71485	−	0.341105i
$737$	−6.28556	+	9.40700i	−0.231532	+	0.346511i
$738$	−19.2941	+	32.6762i	−0.710227	+	1.20283i
$739$	−22.1731	−	9.18440i	−0.815651	−	0.337854i	−0.0644448	−	0.997921i	$-0.520528\pi$
$739$	−22.1731	−	9.18440i	−0.815651	−	0.337854i	−0.751206	+	0.660068i	$0.770528\pi$
$740$	49.5806	+	20.5369i	1.82262	+	0.754953i
$741$		0			0
$742$		0			0
$743$	−6.93520	−	1.37950i	−0.254428	−	0.0506088i	0.0662284	−	0.997804i	$-0.478903\pi$
$743$	−6.93520	−	1.37950i	−0.254428	−	0.0506088i	−0.320656	+	0.947196i	$0.603903\pi$
$744$	−4.37016	+	11.4412i	−0.160218	+	0.419456i
$745$	−28.1099	−	42.0694i	−1.02987	−	1.54130i
$746$	−3.42282	−	8.26343i	−0.125319	−	0.302546i
$747$	17.8885	−	20.0000i	0.654508	−	0.731762i
$748$		0			0
$749$		−	13.4164i		−	0.490225i
$750$	−15.9171	−	15.0548i	−0.581210	−	0.549722i
$751$	28.9227	−	19.3255i	1.05540	−	0.705199i	0.0983636	−	0.995151i	$-0.468639\pi$
$751$	28.9227	−	19.3255i	1.05540	−	0.705199i	0.957041	+	0.289952i	$0.0936392\pi$
$752$	6.32456	+	6.32456i	0.230633	+	0.230633i
$753$	6.88807	+	30.2085i	0.251015	+	1.10086i
$754$	−21.0347	−	14.0549i	−0.766039	−	0.511851i
$755$	−11.0360	−	55.4816i	−0.401640	−	2.01918i
$756$	31.8280	−	37.6428i	1.15757	−	1.36905i
$757$	4.59220	−	11.0866i	0.166906	−	0.402948i	−0.818191	−	0.574947i	$-0.805023\pi$
$757$	4.59220	−	11.0866i	0.166906	−	0.402948i	0.985097	+	0.171999i	$0.0550227\pi$
$758$	−20.8056	+	4.13849i	−0.755693	+	0.150317i
$759$	−2.90496	+	17.0752i	−0.105443	+	0.619789i
$760$		0			0
$761$	−3.16228	+	3.16228i	−0.114632	+	0.114632i	−0.762096	−	0.647464i	$-0.775830\pi$
$761$	−3.16228	+	3.16228i	−0.114632	+	0.114632i	0.647464	+	0.762096i	$0.275830\pi$
$762$	−24.7351	+	39.3469i	−0.896057	+	1.42539i
$763$	55.4328	−	22.9610i	2.00680	−	0.831244i
$764$	−26.8328			−0.970777
$765$		0			0
$766$	−80.0000			−2.89052
$767$	33.0537	−	13.6913i	1.19350	−	0.494364i
$768$	−8.29639	+	13.1973i	−0.299370	+	0.476218i
$769$	−14.1421	+	14.1421i	−0.509978	+	0.509978i	−0.914520	−	0.404541i	$-0.867431\pi$
$769$	−14.1421	+	14.1421i	−0.509978	+	0.509978i	0.404541	+	0.914520i	$0.367431\pi$
$770$	5.51799	−	27.7408i	0.198854	−	0.999709i
$771$	6.49569	−	38.1812i	0.233936	−	1.37506i
$772$	−37.2182	+	7.40316i	−1.33951	+	0.266445i
$773$	15.4027	−	37.1854i	0.553997	−	1.33747i	−0.360456	−	0.932776i	$-0.617379\pi$
$773$	15.4027	−	37.1854i	0.553997	−	1.33747i	0.914453	−	0.404691i	$-0.132621\pi$
$774$	24.1805	−	11.6319i	0.869151	−	0.418101i
$775$	−1.85079	−	9.30455i	−0.0664823	−	0.334229i
$776$	−23.5175	−	15.7139i	−0.844229	−	0.564096i
$777$	7.70110	+	33.7741i	0.276275	+	1.21164i
$778$	−7.07107	−	7.07107i	−0.253510	−	0.253510i
$779$		0			0
$780$	−42.7101	−	40.3962i	−1.52927	−	1.44642i
$781$			18.0000i			0.644091i
$782$		0			0
$783$	−14.0000	−	4.47214i	−0.500319	−	0.159821i
$784$	1.14805	+	2.77164i	0.0410018	+	0.0989871i
$785$	−3.14278	−	4.70350i	−0.112171	−	0.167875i
$786$	1.95440	−	5.11667i	0.0697110	−	0.182506i
$787$	−34.1167	−	6.78623i	−1.21613	−	0.241903i	−0.454992	−	0.890495i	$-0.650358\pi$
$787$	−34.1167	−	6.78623i	−1.21613	−	0.241903i	−0.761136	+	0.648593i	$0.775358\pi$
$788$	42.4275	−	63.4973i	1.51142	−	2.26200i
$789$	−17.9240	−	25.2731i	−0.638113	−	0.899745i
$790$	−18.4776	−	7.65367i	−0.657403	−	0.272305i
$791$	16.5269	+	6.84565i	0.587627	+	0.243403i
$792$	8.16906	+	4.82353i	0.290275	+	0.171397i
$793$	14.0549	−	21.0347i	0.499106	−	0.746964i
$794$	−41.6112	−	8.27698i	−1.47673	−	0.293739i
$795$		0			0
$796$	−15.8118	−	23.6640i	−0.560435	−	0.838750i
$797$	−6.84565	−	16.5269i	−0.242485	−	0.585411i	0.755043	−	0.655675i	$-0.227616\pi$
$797$	−6.84565	−	16.5269i	−0.242485	−	0.585411i	−0.997528	+	0.0702638i	$0.977616\pi$
$798$		0			0
$799$		0			0
$800$		−	20.1246i		−	0.711512i
$801$	−13.3098	+	37.9849i	−0.470278	+	1.34213i
$802$	−10.5174	+	7.02747i	−0.371381	+	0.248149i
$803$		0			0
$804$	40.5290	−	9.24132i	1.42935	−	0.325916i
$805$	−52.5868	−	35.1373i	−1.85344	−	1.23843i
$806$	5.51799	+	27.7408i	0.194363	+	0.977128i
$807$	1.22712	+	44.0737i	0.0431967	+	1.55147i
$808$	3.82683	−	9.23880i	0.134628	−	0.325020i
$809$	−16.6445	+	3.31079i	−0.585189	+	0.116401i	−0.478801	−	0.877923i	$-0.658928\pi$
$809$	−16.6445	+	3.31079i	−0.585189	+	0.116401i	−0.106388	+	0.994325i	$0.533928\pi$
$810$	−50.5488	−	26.1691i	−1.77610	−	0.919489i
$811$	9.25395	−	46.5227i	0.324950	−	1.63363i	−0.380434	−	0.924808i	$-0.624225\pi$
$811$	9.25395	−	46.5227i	0.324950	−	1.63363i	0.705384	−	0.708826i	$-0.250775\pi$
$812$	−18.9737	+	18.9737i	−0.665845	+	0.665845i
$813$		0			0
$814$	−18.4776	+	7.65367i	−0.647639	+	0.268261i
$815$	26.8328			0.939913
$816$		0			0
$817$		0			0
$818$	28.9220	−	11.9799i	1.01123	−	0.418867i
$819$	5.32080	−	37.5725i	0.185924	−	1.31289i
$820$	33.9411	−	33.9411i	1.18528	−	1.18528i
$821$	−3.86259	+	19.4186i	−0.134805	+	0.677712i	0.852987	+	0.521933i	$0.174789\pi$
$821$	−3.86259	+	19.4186i	−0.134805	+	0.677712i	−0.987792	+	0.155779i	$0.950211\pi$
$822$	17.0752	+	2.90496i	0.595565	+	0.101322i
$823$	−34.1167	+	6.78623i	−1.18923	+	0.236553i	−0.749764	−	0.661705i	$-0.769833\pi$
$823$	−34.1167	+	6.78623i	−1.18923	+	0.236553i	−0.439468	+	0.898258i	$0.644833\pi$
$824$	3.42282	−	8.26343i	0.119240	−	0.287870i
$825$	−7.34562	+	0.204520i	−0.255742	+	0.00712048i
$826$	−12.3386	−	62.0303i	−0.429315	−	2.15831i
$827$	31.7486	+	21.2138i	1.10401	+	0.737675i	0.967477	−	0.252961i	$-0.0814044\pi$
$827$	31.7486	+	21.2138i	1.10401	+	0.737675i	0.136532	+	0.990636i	$0.456404\pi$
$828$	50.8651	−	38.2457i	1.76769	−	1.32913i
$829$	21.2132	+	21.2132i	0.736765	+	0.736765i	0.971951	−	0.235185i	$-0.0755698\pi$
$829$	21.2132	+	21.2132i	0.736765	+	0.736765i	−0.235185	+	0.971951i	$0.575570\pi$
$830$	−47.0350	+	31.4278i	−1.63261	+	1.09087i
$831$	−7.52738	+	7.95855i	−0.261122	+	0.276079i
$832$			52.0000i			1.80278i
$833$		0			0
$834$	−5.00000	−	11.1803i	−0.173136	−	0.387144i
$835$	−10.7151	−	25.8686i	−0.370813	−	0.895221i
$836$		0			0
$837$	7.53244	+	14.6035i	0.260359	+	0.504771i
$838$	−21.7106	−	4.31851i	−0.749980	−	0.149180i
$839$	5.49986	−	8.23113i	0.189876	−	0.284170i	−0.724301	−	0.689483i	$-0.757838\pi$
$839$	5.49986	−	8.23113i	0.189876	−	0.284170i	0.914178	+	0.405313i	$0.132838\pi$
$840$	−28.2562	+	20.0397i	−0.974930	+	0.691435i
$841$	−19.4015	−	8.03635i	−0.669016	−	0.277116i
$842$	−41.3171	−	17.1141i	−1.42388	−	0.589792i
$843$	25.2731	−	17.9240i	0.870451	−	0.617337i
$844$	−36.8942	+	55.2161i	−1.26995	+	1.90062i
$845$	−8.32224	−	1.65540i	−0.286294	−	0.0569474i
$846$	−59.9070	+	3.33851i	−2.05965	+	0.114780i
$847$	−15.8118	−	23.6640i	−0.543300	−	0.813106i
$848$		0			0
$849$	−2.23607	−	5.00000i	−0.0767417	−	0.171600i
$850$		0			0
$851$			44.7214i			1.53303i
$852$	45.4457	−	48.0488i	1.55694	−	1.64613i
$853$	5.25868	−	3.51373i	0.180054	−	0.120308i	−0.462277	−	0.886735i	$-0.652968\pi$
$853$	5.25868	−	3.51373i	0.180054	−	0.120308i	0.642331	+	0.766427i	$0.277968\pi$
$854$	−31.6228	−	31.6228i	−1.08211	−	1.08211i
$855$		0			0
$856$	−7.88801	−	5.27060i	−0.269607	−	0.180145i
$857$	−2.20720	−	11.0963i	−0.0753963	−	0.379043i	0.924602	−	0.380935i	$-0.124398\pi$
$857$	−2.20720	−	11.0963i	−0.0753963	−	0.379043i	−0.999998	+	0.00189186i	$0.999398\pi$
$858$	21.9004	−	0.609761i	0.747668	−	0.0208169i
$859$	−7.65367	+	18.4776i	−0.261140	+	0.630447i	−0.999010	−	0.0444959i	$-0.985832\pi$
$859$	−7.65367	+	18.4776i	−0.261140	+	0.630447i	0.737870	+	0.674943i	$0.235832\pi$
$860$	−33.2890	+	6.62159i	−1.13514	+	0.225794i
$861$	30.5450	+	5.19655i	1.04097	+	0.177098i
$862$	5.55237	−	27.9136i	0.189114	−	0.950742i
$863$	−12.6491	+	12.6491i	−0.430581	+	0.430581i	−0.888826	−	0.458245i	$-0.848478\pi$
$863$	−12.6491	+	12.6491i	−0.430581	+	0.430581i	0.458245	+	0.888826i	$0.348478\pi$
$864$	9.62804	+	33.5008i	0.327553	+	1.13972i
$865$	−36.9552	+	15.3073i	−1.25651	+	0.520465i
$866$	80.4984			2.73545
$867$		0			0
$868$	30.0000			1.01827
$869$	4.13171	−	1.71141i	0.140159	−	0.0580557i
$870$	26.2313	+	16.4900i	0.889323	+	0.559065i
$871$	22.6274	−	22.6274i	0.766701	−	0.766701i
$872$	8.27698	−	41.6112i	0.280294	−	1.40913i
$873$	−36.7486	+	9.46257i	−1.24375	+	0.320260i
$874$		0			0
$875$	−6.84565	+	16.5269i	−0.231425	+	0.558710i
$876$		0			0
$877$	−6.16930	−	31.0152i	−0.208322	−	1.04731i	−0.933454	−	0.358697i	$-0.883221\pi$
$877$	−6.16930	−	31.0152i	−0.208322	−	1.04731i	0.725132	−	0.688610i	$-0.241779\pi$
$878$	41.1556	+	27.4993i	1.38894	+	0.928057i
$879$	−30.2085	+	6.88807i	−1.01891	+	0.232329i
$880$	2.82843	+	2.82843i	0.0953463	+	0.0953463i
$881$	4.70350	−	3.14278i	0.158465	−	0.105883i	−0.473810	−	0.880627i	$-0.657121\pi$
$881$	4.70350	−	3.14278i	0.158465	−	0.105883i	0.632275	+	0.774744i	$0.282121\pi$
$882$	−18.9924	−	6.65489i	−0.639508	−	0.224082i
$883$			16.0000i			0.538443i	0.963078	+	0.269221i	$0.0867663\pi$
$883$			16.0000i			0.538443i	−0.963078	+	0.269221i	$0.913234\pi$
$884$		0			0
$885$	−40.0000	+	17.8885i	−1.34459	+	0.601317i
$886$	−15.3073	−	36.9552i	−0.514260	−	1.24153i
$887$	−27.4993	−	41.1556i	−0.923337	−	1.38187i	−0.924215	−	0.381872i	$-0.875280\pi$
$887$	−27.4993	−	41.1556i	−0.923337	−	1.38187i	0.000878410	−	1.00000i	$-0.499720\pi$
$888$	22.8825	+	8.74032i	0.767885	+	0.293306i
$889$	37.2182	+	7.40316i	1.24826	+	0.248294i
$890$	47.1417	−	70.5525i	1.58019	−	2.36493i
$891$	12.1302	−	3.85476i	0.406376	−	0.129139i
$892$	44.3462	+	18.3688i	1.48482	+	0.615033i
$893$		0			0
$894$	−40.0794	−	56.5123i	−1.34046	−	1.89005i
$895$		0			0
$896$	48.5464	+	9.65648i	1.62182	+	0.322600i
$897$	17.4806	−	45.7649i	0.583662	−	1.52805i
$898$	21.0824	+	31.5521i	0.703529	+	1.05291i
$899$	−3.42282	−	8.26343i	−0.114158	−	0.275601i
$900$	20.1246	+	18.0000i	0.670820	+	0.600000i
$901$		0			0
$902$			17.8885i			0.595623i
$903$	−15.9171	−	15.0548i	−0.529688	−	0.500991i
$904$	10.5174	−	7.02747i	0.349802	−	0.233730i
$905$	37.9473	+	37.9473i	1.26141	+	1.26141i
$906$	−17.2202	−	75.5213i	−0.572102	−	2.50903i
$907$	18.4054	+	12.2981i	0.611140	+	0.408351i	0.822262	−	0.569109i	$-0.192712\pi$
$907$	18.4054	+	12.2981i	0.611140	+	0.408351i	−0.211122	+	0.977460i	$0.567712\pi$
$908$	4.13849	+	20.8056i	0.137341	+	0.690458i
$909$	−5.81597	−	12.0903i	−0.192904	−	0.401009i
$910$	−30.6147	+	73.9104i	−1.01487	+	2.45010i
$911$	15.2574	−	3.03489i	0.505501	−	0.100550i	0.0642497	−	0.997934i	$-0.479535\pi$
$911$	15.2574	−	3.03489i	0.505501	−	0.100550i	0.441252	+	0.897383i	$0.354535\pi$
$912$		0			0
$913$	2.46772	−	12.4061i	0.0816696	−	0.410581i
$914$	−44.2719	+	44.2719i	−1.46438	+	1.46438i
$915$	−16.4900	+	26.2313i	−0.545144	+	0.867178i
$916$	55.4328	−	22.9610i	1.83155	−	0.758653i
$917$	−4.47214			−0.147683
$918$		0			0
$919$	−24.0000			−0.791687			−0.395843	−	0.918318i	$-0.629548\pi$
$919$	−24.0000			−0.791687			−0.395843	+	0.918318i	$0.629548\pi$
$920$	−41.3171	+	17.1141i	−1.36219	+	0.564236i
$921$	11.0619	−	17.5965i	0.364501	−	0.579823i
$922$	56.5685	−	56.5685i	1.86299	−	1.86299i
$923$	9.93238	−	49.9334i	0.326928	−	1.64358i
$924$	3.89741	−	22.9087i	0.128215	−	0.753642i
$925$	−18.6091	+	3.70158i	−0.611863	+	0.121707i
$926$	−3.42282	+	8.26343i	−0.112481	+	0.271553i
$927$	−5.20196	−	10.8139i	−0.170855	−	0.355174i
$928$	−3.70158	−	18.6091i	−0.121510	−	0.610873i
$929$	−32.9245	−	21.9995i	−1.08022	−	0.721779i	−0.117715	−	0.993047i	$-0.537557\pi$
$929$	−32.9245	−	21.9995i	−1.08022	−	0.721779i	−0.962504	+	0.271269i	$0.912557\pi$
$930$	−7.70110	−	33.7741i	−0.252529	−	1.10750i
$931$		0			0
$932$	14.1105	−	9.42834i	0.462205	−	0.308836i
$933$	−1.77959	−	1.68317i	−0.0582610	−	0.0551046i
$934$		−	40.0000i		−	1.30884i
$935$		0			0
$936$	−20.0000	−	17.8885i	−0.653720	−	0.584705i
$937$	0.765367	+	1.84776i	0.0250034	+	0.0603637i	0.935888	−	0.352297i	$-0.114599\pi$
$937$	0.765367	+	1.84776i	0.0250034	+	0.0603637i	−0.910885	+	0.412661i	$0.864599\pi$
$938$	−31.4278	−	47.0350i	−1.02615	−	1.53575i
$939$	−15.6352	+	40.9334i	−0.510234	+	1.33581i
$940$	74.4364	+	14.8063i	2.42785	+	0.482929i
$941$	20.4281	−	30.5728i	0.665936	−	0.996644i	−0.332627	−	0.943058i	$-0.607935\pi$
$941$	20.4281	−	30.5728i	0.665936	−	0.996644i	0.998563	−	0.0535853i	$-0.0170649\pi$
$942$	−4.48101	−	6.31827i	−0.145999	−	0.205860i
$943$	36.9552	+	15.3073i	1.20343	+	0.498475i
$944$	8.26343	+	3.42282i	0.268952	+	0.111403i
$945$	−5.23338	+	46.1802i	−0.170242	+	1.50224i
$946$	7.02747	−	10.5174i	0.228483	−	0.341949i
$947$	−48.5464	−	9.65648i	−1.57755	−	0.313793i	−0.672826	−	0.739801i	$-0.734920\pi$
$947$	−48.5464	−	9.65648i	−1.57755	−	0.313793i	−0.904720	+	0.426007i	$0.859920\pi$
$948$	−15.3500	−	5.86319i	−0.498545	−	0.190427i
$949$		0			0
$950$		0			0
$951$	−22.3607	+	10.0000i	−0.725095	+	0.324272i
$952$		0			0
$953$		−	13.4164i		−	0.434600i	−0.976105	−	0.217300i	$-0.930275\pi$
$953$		−	13.4164i		−	0.434600i	0.976105	−	0.217300i	$-0.0697250\pi$
$954$		0			0
$955$	21.0347	−	14.0549i	0.680667	−	0.454807i
$956$	18.9737	+	18.9737i	0.613652	+	0.613652i
$957$	−6.75483	+	1.54022i	−0.218353	+	0.0497882i
$958$	18.4054	+	12.2981i	0.594650	+	0.397333i
$959$	−2.75899	−	13.8704i	−0.0890926	−	0.447899i
$960$	−1.77251	−	63.6621i	−0.0572074	−	2.05468i
$961$	8.03635	−	19.4015i	0.259237	−	0.625854i
$962$	55.4816	−	11.0360i	1.78880	−	0.355814i
$963$	−12.3259	+	3.17384i	−0.397195	+	0.102276i
$964$	−14.8063	+	74.4364i	−0.476879	+	2.39743i
$965$	25.2982	−	25.2982i	0.814379	−	0.814379i
$966$	−73.3186	−	46.0911i	−2.35899	−	1.48296i
$967$	29.5641	−	12.2459i	0.950719	−	0.393801i	0.147218	−	0.989104i	$-0.452968\pi$
$967$	29.5641	−	12.2459i	0.950719	−	0.393801i	0.803501	+	0.595303i	$0.202968\pi$
$968$	−20.1246			−0.646830
$969$		0			0
$970$	80.0000			2.56865
$971$	24.7903	−	10.2685i	0.795558	−	0.329531i	0.0523823	−	0.998627i	$-0.483319\pi$
$971$	24.7903	−	10.2685i	0.795558	−	0.329531i	0.743176	+	0.669096i	$0.233319\pi$
$972$	−42.1123	−	20.3359i	−1.35075	−	0.652276i
$973$	−7.07107	+	7.07107i	−0.226688	+	0.226688i
$974$	−12.4155	+	62.4168i	−0.397817	+	1.99996i
$975$	20.4902	+	3.48595i	0.656211	+	0.111640i
$976$	6.20303	−	1.23386i	0.198554	−	0.0394949i
$977$	6.84565	−	16.5269i	0.219012	−	0.528741i	−0.775741	−	0.631052i	$-0.782624\pi$
$977$	6.84565	−	16.5269i	0.219012	−	0.528741i	0.994753	+	0.102311i	$0.0326236\pi$
$978$	36.7281	−	1.02260i	1.17444	−	0.0326992i
$979$	3.70158	+	18.6091i	0.118303	+	0.594749i
$980$	21.1658	+	14.1425i	0.676115	+	0.451766i
$981$	−34.2080	−	45.4952i	−1.09218	−	1.45255i
$982$	28.2843	+	28.2843i	0.902587	+	0.902587i
$983$	−29.3969	+	19.6424i	−0.937615	+	0.626494i	−0.927648	−	0.373456i	$-0.878173\pi$
$983$	−29.3969	+	19.6424i	−0.937615	+	0.626494i	−0.00996724	+	0.999950i	$0.503173\pi$
$984$	15.0548	−	15.9171i	0.479928	−	0.507419i
$985$			72.0000i			2.29411i
$986$		0			0
$987$	20.0000	+	44.7214i	0.636607	+	1.42350i
$988$		0			0
$989$	−15.7139	−	23.5175i	−0.499673	−	0.747813i
$990$	−26.7912	+	1.49302i	−0.851482	+	0.0474514i
$991$	−34.1167	−	6.78623i	−1.08375	−	0.215572i	−0.379265	−	0.925288i	$-0.623823\pi$
$991$	−34.1167	−	6.78623i	−1.08375	−	0.215572i	−0.704487	+	0.709717i	$0.748823\pi$
$992$	−11.7854	+	17.6381i	−0.374188	+	0.560011i
$993$	39.5586	−	28.0556i	1.25535	−	0.890317i
$994$	−83.1492	−	34.4415i	−2.63733	−	1.09242i
$995$	24.7903	+	10.2685i	0.785905	+	0.325533i
$996$	−37.9096	+	26.8861i	−1.20121	+	0.851918i
$997$	−3.51373	+	5.25868i	−0.111281	+	0.166544i	−0.882930	−	0.469505i	$-0.844432\pi$
$997$	−3.51373	+	5.25868i	−0.111281	+	0.166544i	0.771649	+	0.636049i	$0.219432\pi$
$998$	6.93520	+	1.37950i	0.219530	+	0.0436672i
$999$	29.2070	−	15.0649i	0.924069	−	0.476632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.i.e.131.3	yes	32
3.2	odd	2	inner	867.2.i.e.131.1	yes	32
17.2	even	8	inner	867.2.i.e.65.4	yes	32
17.3	odd	16	inner	867.2.i.e.329.3	yes	32
17.4	even	4	inner	867.2.i.e.158.2	yes	32
17.5	odd	16	inner	867.2.i.e.827.1	yes	32
17.6	odd	16	inner	867.2.i.e.653.3	yes	32
17.7	odd	16	inner	867.2.i.e.503.2	yes	32
17.8	even	8	inner	867.2.i.e.224.2	yes	32
17.9	even	8	inner	867.2.i.e.224.1	yes	32
17.10	odd	16	inner	867.2.i.e.503.1	yes	32
17.11	odd	16	inner	867.2.i.e.653.4	yes	32
17.12	odd	16	inner	867.2.i.e.827.2	yes	32
17.13	even	4	inner	867.2.i.e.158.1	yes	32
17.14	odd	16	inner	867.2.i.e.329.4	yes	32
17.15	even	8	inner	867.2.i.e.65.3	yes	32
17.16	even	2	inner	867.2.i.e.131.4	yes	32
51.2	odd	8	inner	867.2.i.e.65.1	✓	32
51.5	even	16	inner	867.2.i.e.827.4	yes	32
51.8	odd	8	inner	867.2.i.e.224.4	yes	32
51.11	even	16	inner	867.2.i.e.653.2	yes	32
51.14	even	16	inner	867.2.i.e.329.2	yes	32
51.20	even	16	inner	867.2.i.e.329.1	yes	32
51.23	even	16	inner	867.2.i.e.653.1	yes	32
51.26	odd	8	inner	867.2.i.e.224.3	yes	32
51.29	even	16	inner	867.2.i.e.827.3	yes	32
51.32	odd	8	inner	867.2.i.e.65.2	yes	32
51.38	odd	4	inner	867.2.i.e.158.4	yes	32
51.41	even	16	inner	867.2.i.e.503.4	yes	32
51.44	even	16	inner	867.2.i.e.503.3	yes	32
51.47	odd	4	inner	867.2.i.e.158.3	yes	32
51.50	odd	2	inner	867.2.i.e.131.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.i.e.65.1	✓	32	51.2	odd	8	inner
867.2.i.e.65.2	yes	32	51.32	odd	8	inner
867.2.i.e.65.3	yes	32	17.15	even	8	inner
867.2.i.e.65.4	yes	32	17.2	even	8	inner
867.2.i.e.131.1	yes	32	3.2	odd	2	inner
867.2.i.e.131.2	yes	32	51.50	odd	2	inner
867.2.i.e.131.3	yes	32	1.1	even	1	trivial
867.2.i.e.131.4	yes	32	17.16	even	2	inner
867.2.i.e.158.1	yes	32	17.13	even	4	inner
867.2.i.e.158.2	yes	32	17.4	even	4	inner
867.2.i.e.158.3	yes	32	51.47	odd	4	inner
867.2.i.e.158.4	yes	32	51.38	odd	4	inner
867.2.i.e.224.1	yes	32	17.9	even	8	inner
867.2.i.e.224.2	yes	32	17.8	even	8	inner
867.2.i.e.224.3	yes	32	51.26	odd	8	inner
867.2.i.e.224.4	yes	32	51.8	odd	8	inner
867.2.i.e.329.1	yes	32	51.20	even	16	inner
867.2.i.e.329.2	yes	32	51.14	even	16	inner
867.2.i.e.329.3	yes	32	17.3	odd	16	inner
867.2.i.e.329.4	yes	32	17.14	odd	16	inner
867.2.i.e.503.1	yes	32	17.10	odd	16	inner
867.2.i.e.503.2	yes	32	17.7	odd	16	inner
867.2.i.e.503.3	yes	32	51.44	even	16	inner
867.2.i.e.503.4	yes	32	51.41	even	16	inner
867.2.i.e.653.1	yes	32	51.23	even	16	inner
867.2.i.e.653.2	yes	32	51.11	even	16	inner
867.2.i.e.653.3	yes	32	17.6	odd	16	inner
867.2.i.e.653.4	yes	32	17.11	odd	16	inner
867.2.i.e.827.1	yes	32	17.5	odd	16	inner
867.2.i.e.827.2	yes	32	17.12	odd	16	inner
867.2.i.e.827.3	yes	32	51.29	even	16	inner
867.2.i.e.827.4	yes	32	51.5	even	16	inner

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.06586 - 0.855706i) q^{2} +(-0.921821 + 1.46637i) q^{3} +(2.12132 - 2.12132i) q^{4} +(-0.551799 + 2.77408i) q^{5} +(-0.649569 + 3.81812i) q^{6} +(3.10152 - 0.616930i) q^{7} +(0.855706 - 2.06586i) q^{8} +(-1.30049 - 2.70347i) q^{9} +O(q^{10})\)	\(q+(2.06586 - 0.855706i) q^{2} +(-0.921821 + 1.46637i) q^{3} +(2.12132 - 2.12132i) q^{4} +(-0.551799 + 2.77408i) q^{5} +(-0.649569 + 3.81812i) q^{6} +(3.10152 - 0.616930i) q^{7} +(0.855706 - 2.06586i) q^{8} +(-1.30049 - 2.70347i) q^{9} +(1.23386 + 6.20303i) q^{10} +(-1.17588 - 0.785695i) q^{11} +(1.15517 + 5.06612i) q^{12} +(2.82843 + 2.82843i) q^{13} +(5.87938 - 3.92847i) q^{14} +(-3.55917 - 3.36635i) q^{15} +1.00000i q^{16} +(-5.00000 - 4.47214i) q^{18} +(4.71417 + 7.05525i) q^{20} +(-1.95440 + 5.11667i) q^{21} +(-3.10152 - 0.616930i) q^{22} +(-3.92847 + 5.87938i) q^{23} +(2.24051 + 3.15913i) q^{24} +(-2.77164 - 1.14805i) q^{25} +(8.26343 + 3.42282i) q^{26} +(5.16310 + 0.585110i) q^{27} +(5.27060 - 7.88801i) q^{28} +(-2.77408 - 0.551799i) q^{29} +(-10.2333 - 3.90879i) q^{30} +(1.75687 + 2.62934i) q^{31} +(2.56712 + 6.19757i) q^{32} +(2.23607 - 1.00000i) q^{33} +8.94427i q^{35} +(-8.49367 - 2.97616i) q^{36} +(5.25868 - 3.51373i) q^{37} +(-6.75483 + 1.54022i) q^{39} +(5.25868 + 3.51373i) q^{40} +(-1.10360 - 5.54816i) q^{41} +(0.340867 + 12.2427i) q^{42} +(-1.53073 + 3.69552i) q^{43} +(-4.16112 + 0.827698i) q^{44} +(8.21724 - 2.11590i) q^{45} +(-3.08465 + 15.5076i) q^{46} +(6.32456 - 6.32456i) q^{47} +(-1.46637 - 0.921821i) q^{48} +(2.77164 - 1.14805i) q^{49} -6.70820 q^{50} +12.0000 q^{52} +(11.1669 - 3.20935i) q^{54} +(2.82843 - 2.82843i) q^{55} +(1.37950 - 6.93520i) q^{56} +(-6.20303 + 1.23386i) q^{58} +(3.42282 - 8.26343i) q^{59} +(-14.6912 + 0.409040i) q^{60} +(-1.23386 - 6.20303i) q^{61} +(5.87938 + 3.92847i) q^{62} +(-5.70134 - 7.58253i) q^{63} +(9.19239 + 9.19239i) q^{64} +(-9.40700 + 6.28556i) q^{65} +(3.76369 - 3.97927i) q^{66} -8.00000i q^{67} +(-5.00000 - 11.1803i) q^{69} +(7.65367 + 18.4776i) q^{70} +(-7.07125 - 10.5829i) q^{71} +(-6.69781 + 0.373256i) q^{72} +(7.85695 - 11.7588i) q^{74} +(4.23842 - 3.00595i) q^{75} +(-4.13171 - 1.71141i) q^{77} +(-12.6365 + 8.96202i) q^{78} +(-1.75687 + 2.62934i) q^{79} +(-2.77408 - 0.551799i) q^{80} +(-5.61745 + 7.03166i) q^{81} +(-7.02747 - 10.5174i) q^{82} +(3.42282 + 8.26343i) q^{83} +(6.70820 + 15.0000i) q^{84} +8.94427i q^{86} +(3.36635 - 3.55917i) q^{87} +(-2.62934 + 1.75687i) q^{88} +(-9.48683 - 9.48683i) q^{89} +(15.1651 - 11.4027i) q^{90} +(10.5174 + 7.02747i) q^{91} +(4.13849 + 20.8056i) q^{92} +(-5.47510 + 0.152440i) q^{93} +(7.65367 - 18.4776i) q^{94} +(-11.4544 - 1.94871i) q^{96} +(2.46772 - 12.4061i) q^{97} +(4.74342 - 4.74342i) q^{98} +(-0.594884 + 4.20073i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 160 q^{18} + 384 q^{52} - 160 q^{69}+O(q^{100}) \) 32 * q - 160 * q^18 + 384 * q^52 - 160 * q^69

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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