LMFDB - Embedded newform 867.2.i.e.503.2

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			503.2
Character	$\chi$	$=$	867.503
Dual form			867.2.i.e.131.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.06586 - 0.855706i) q^{2} +(1.70752 + 0.290496i) q^{3} +(2.12132 + 2.12132i) q^{4} +(-0.551799 - 2.77408i) q^{5} +(-3.27891 - 2.06126i) q^{6} +(-3.10152 - 0.616930i) q^{7} +(-0.855706 - 2.06586i) q^{8} +(2.83122 + 0.992053i) q^{9} +O(q^{10})$	\(q+(-2.06586 - 0.855706i) q^{2} +(1.70752 + 0.290496i) q^{3} +(2.12132 + 2.12132i) q^{4} +(-0.551799 - 2.77408i) q^{5} +(-3.27891 - 2.06126i) q^{6} +(-3.10152 - 0.616930i) q^{7} +(-0.855706 - 2.06586i) q^{8} +(2.83122 + 0.992053i) q^{9} +(-1.23386 + 6.20303i) q^{10} +(-1.17588 + 0.785695i) q^{11} +(3.00595 + 4.23842i) q^{12} +(2.82843 - 2.82843i) q^{13} +(5.87938 + 3.92847i) q^{14} +(-0.136347 - 4.89708i) q^{15} -1.00000i q^{16} +(-5.00000 - 4.47214i) q^{18} +(4.71417 - 7.05525i) q^{20} +(-5.11667 - 1.95440i) q^{21} +(3.10152 - 0.616930i) q^{22} +(-3.92847 - 5.87938i) q^{23} +(-0.861009 - 3.77606i) q^{24} +(-2.77164 + 1.14805i) q^{25} +(-8.26343 + 3.42282i) q^{26} +(4.54617 + 2.51641i) q^{27} +(-5.27060 - 7.88801i) q^{28} +(-2.77408 + 0.551799i) q^{29} +(-3.90879 + 10.2333i) q^{30} +(-1.75687 + 2.62934i) q^{31} +(-2.56712 + 6.19757i) q^{32} +(-2.23607 + 1.00000i) q^{33} +8.94427i q^{35} +(3.90147 + 8.11040i) q^{36} +(-5.25868 - 3.51373i) q^{37} +(5.65123 - 4.00794i) q^{39} +(-5.25868 + 3.51373i) q^{40} +(-1.10360 + 5.54816i) q^{41} +(8.89793 + 8.41587i) q^{42} +(-1.53073 - 3.69552i) q^{43} +(-4.16112 - 0.827698i) q^{44} +(1.18977 - 8.40146i) q^{45} +(3.08465 + 15.5076i) q^{46} +(-6.32456 - 6.32456i) q^{47} +(0.290496 - 1.70752i) q^{48} +(2.77164 + 1.14805i) q^{49} +6.70820 q^{50} +12.0000 q^{52} +(-7.23844 - 9.08872i) 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} +(10.0990 - 10.6775i) q^{60} +(1.23386 - 6.20303i) q^{61} +(5.87938 - 3.92847i) q^{62} +(-8.16906 - 4.82353i) q^{63} +(9.19239 - 9.19239i) q^{64} +(-9.40700 - 6.28556i) q^{65} +(5.47510 - 0.152440i) q^{66} +8.00000i q^{67} +(-5.00000 - 11.1803i) q^{69} +(7.65367 - 18.4776i) q^{70} +(-7.07125 + 10.5829i) q^{71} +(-0.373256 - 6.69781i) q^{72} +(7.85695 + 11.7588i) q^{74} +(-5.06612 + 1.15517i) q^{75} +(4.13171 - 1.71141i) q^{77} +(-15.1043 + 3.44404i) q^{78} +(1.75687 + 2.62934i) q^{79} +(-2.77408 + 0.551799i) q^{80} +(7.03166 + 5.61745i) q^{81} +(7.02747 - 10.5174i) q^{82} +(-3.42282 + 8.26343i) q^{83} +(-6.70820 - 15.0000i) q^{84} +8.94427i q^{86} +(-4.89708 + 0.136347i) q^{87} +(2.62934 + 1.75687i) q^{88} +(9.48683 - 9.48683i) q^{89} +(-9.64707 + 16.3381i) q^{90} +(-10.5174 + 7.02747i) q^{91} +(4.13849 - 20.8056i) q^{92} +(-3.76369 + 3.97927i) q^{93} +(7.65367 + 18.4776i) q^{94} +(-6.18377 + 9.83672i) q^{96} +(-2.46772 - 12.4061i) q^{97} +(-4.74342 - 4.74342i) q^{98} +(-4.10862 + 1.05795i) 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 $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{3}{16}\right)$

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	$-0.665215\pi$
$2$	−2.06586	−	0.855706i	−1.46078	−	0.605076i	−0.964736	+	0.263221i	$0.915215\pi$
$3$	1.70752	+	0.290496i	0.985835	+	0.167718i
$3$	1.70752	+	0.290496i	0.985835	+	0.167718i
$4$	2.12132	+	2.12132i	1.06066	+	1.06066i
$5$	−0.551799	−	2.77408i	−0.246772	−	1.24061i	−0.883099	−	0.469187i	$-0.844547\pi$
$5$	−0.551799	−	2.77408i	−0.246772	−	1.24061i	0.636327	−	0.771419i	$-0.280453\pi$
$6$	−3.27891	−	2.06126i	−1.33861	−	0.841504i
$7$	−3.10152	−	0.616930i	−1.17226	−	0.233178i	−0.429711	−	0.902966i	$-0.641385\pi$
$7$	−3.10152	−	0.616930i	−1.17226	−	0.233178i	−0.742552	+	0.669789i	$0.766385\pi$
$8$	−0.855706	−	2.06586i	−0.302538	−	0.730391i
$9$	2.83122	+	0.992053i	0.943741	+	0.330684i
$10$	−1.23386	+	6.20303i	−0.390181	+	1.96157i
$11$	−1.17588	+	0.785695i	−0.354540	+	0.236896i	−0.720067	−	0.693905i	$-0.755889\pi$
$11$	−1.17588	+	0.785695i	−0.354540	+	0.236896i	0.365527	+	0.930801i	$0.380889\pi$
$12$	3.00595	+	4.23842i	0.867744	+	1.22353i
$13$	2.82843	−	2.82843i	0.784465	−	0.784465i	−0.196116	−	0.980581i	$-0.562833\pi$
$13$	2.82843	−	2.82843i	0.784465	−	0.784465i	0.980581	+	0.196116i	$0.0628330\pi$
$14$	5.87938	+	3.92847i	1.57133	+	1.04993i
$15$	−0.136347	−	4.89708i	−0.0352046	−	1.26442i
$16$		−	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	$-0.875000\pi$
$19$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$20$	4.71417	−	7.05525i	1.05412	−	1.57760i
$21$	−5.11667	−	1.95440i	−1.11655	−	0.426484i
$22$	3.10152	−	0.616930i	0.661245	−	0.131530i
$23$	−3.92847	−	5.87938i	−0.819144	−	1.22594i	−0.971366	−	0.237589i	$-0.923643\pi$
$23$	−3.92847	−	5.87938i	−0.819144	−	1.22594i	0.152222	−	0.988346i	$-0.451357\pi$
$24$	−0.861009	−	3.77606i	−0.175753	−	0.770786i
$25$	−2.77164	+	1.14805i	−0.554328	+	0.229610i
$26$	−8.26343	+	3.42282i	−1.62059	+	0.671271i
$27$	4.54617	+	2.51641i	0.874912	+	0.484282i
$28$	−5.27060	−	7.88801i	−0.996050	−	1.49069i
$29$	−2.77408	+	0.551799i	−0.515134	+	0.102466i	−0.445810	−	0.895128i	$-0.647084\pi$
$29$	−2.77408	+	0.551799i	−0.515134	+	0.102466i	−0.0693239	+	0.997594i	$0.522084\pi$
$30$	−3.90879	+	10.2333i	−0.713644	+	1.86834i
$31$	−1.75687	+	2.62934i	−0.315543	+	0.472243i	−0.955009	−	0.296576i	$-0.904155\pi$
$31$	−1.75687	+	2.62934i	−0.315543	+	0.472243i	0.639467	+	0.768819i	$0.279155\pi$
$32$	−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
$36$	3.90147	+	8.11040i	0.650245	+	1.35173i
$37$	−5.25868	−	3.51373i	−0.864521	−	0.577654i	0.0423311	−	0.999104i	$-0.486522\pi$
$37$	−5.25868	−	3.51373i	−0.864521	−	0.577654i	−0.906852	+	0.421449i	$0.861522\pi$
$38$		0			0
$39$	5.65123	−	4.00794i	0.904921	−	0.641784i
$40$	−5.25868	+	3.51373i	−0.831470	+	0.555570i
$41$	−1.10360	+	5.54816i	−0.172353	+	0.866477i	0.793735	+	0.608264i	$0.208134\pi$
$41$	−1.10360	+	5.54816i	−0.172353	+	0.866477i	−0.966088	+	0.258213i	$0.916866\pi$
$42$	8.89793	+	8.41587i	1.37298	+	1.29860i
$43$	−1.53073	−	3.69552i	−0.233435	−	0.563561i	0.763142	−	0.646230i	$-0.223656\pi$
$43$	−1.53073	−	3.69552i	−0.233435	−	0.563561i	−0.996577	+	0.0826692i	$0.973656\pi$
$44$	−4.16112	−	0.827698i	−0.627312	−	0.124780i
$45$	1.18977	−	8.40146i	0.177360	−	1.25242i
$46$	3.08465	+	15.5076i	0.454807	+	2.28647i
$47$	−6.32456	−	6.32456i	−0.922531	−	0.922531i	0.0746766	−	0.997208i	$-0.476208\pi$
$47$	−6.32456	−	6.32456i	−0.922531	−	0.922531i	−0.997208	+	0.0746766i	$0.976208\pi$
$48$	0.290496	−	1.70752i	0.0419295	−	0.246459i
$49$	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	$-0.375000\pi$
$53$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$54$	−7.23844	−	9.08872i	−0.985028	−	1.23682i
$55$	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	−0.973948	−	0.226771i	$-0.927183\pi$
$59$	−3.42282	−	8.26343i	−0.445614	−	1.07581i	0.528334	−	0.849036i	$-0.322817\pi$
$60$	10.0990	−	10.6775i	1.30378	−	1.37846i
$61$	1.23386	−	6.20303i	0.157980	−	0.794217i	−0.817807	−	0.575492i	$-0.804810\pi$
$61$	1.23386	−	6.20303i	0.157980	−	0.794217i	0.975787	−	0.218724i	$-0.0701896\pi$
$62$	5.87938	−	3.92847i	0.746682	−	0.498917i
$63$	−8.16906	−	4.82353i	−1.02920	−	0.607708i
$64$	9.19239	−	9.19239i	1.14905	−	1.14905i
$65$	−9.40700	−	6.28556i	−1.16680	−	0.779628i
$66$	5.47510	−	0.152440i	0.673939	−	0.0187641i
$67$			8.00000i			0.977356i	0.872464	+	0.488678i	$0.162521\pi$
$67$			8.00000i			0.977356i	−0.872464	+	0.488678i	$0.837479\pi$
$68$		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	0.125361	+	0.992111i	$0.459991\pi$
$71$	−7.07125	+	10.5829i	−0.839204	+	1.25596i	−0.964565	+	0.263846i	$0.915009\pi$
$72$	−0.373256	−	6.69781i	−0.0439887	−	0.789345i
$73$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$73$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$74$	7.85695	+	11.7588i	0.913352	+	1.36693i
$75$	−5.06612	+	1.15517i	−0.584985	+	0.133387i
$76$		0			0
$77$	4.13171	−	1.71141i	0.470853	−	0.195034i
$78$	−15.1043	+	3.44404i	−1.71022	+	0.389960i
$79$	1.75687	+	2.62934i	0.197663	+	0.295824i	0.917039	−	0.398797i	$-0.130572\pi$
$79$	1.75687	+	2.62934i	0.197663	+	0.295824i	−0.719376	+	0.694621i	$0.755572\pi$
$80$	−2.77408	+	0.551799i	−0.310152	+	0.0616930i
$81$	7.03166	+	5.61745i	0.781296	+	0.624161i
$82$	7.02747	−	10.5174i	0.776054	−	1.16145i
$83$	−3.42282	+	8.26343i	−0.375704	+	0.907029i	0.617057	+	0.786919i	$0.288325\pi$
$83$	−3.42282	+	8.26343i	−0.375704	+	0.907029i	−0.992761	+	0.120111i	$0.961675\pi$
$84$	−6.70820	−	15.0000i	−0.731925	−	1.63663i
$85$		0			0
$86$			8.94427i			0.964486i
$87$	−4.89708	+	0.136347i	−0.525022	+	0.0146179i
$88$	2.62934	+	1.75687i	0.280288	+	0.187283i
$89$	9.48683	−	9.48683i	1.00560	−	1.00560i	0.00561807	−	0.999984i	$-0.498212\pi$
$89$	9.48683	−	9.48683i	1.00560	−	1.00560i	0.999984	−	0.00561807i	$-0.00178830\pi$
$90$	−9.64707	+	16.3381i	−1.01689	+	1.72219i
$91$	−10.5174	+	7.02747i	−1.10252	+	0.736679i
$92$	4.13849	−	20.8056i	0.431467	−	2.16913i
$93$	−3.76369	+	3.97927i	−0.390277	+	0.412632i
$94$	7.65367	+	18.4776i	0.789416	+	1.90582i
$95$		0			0
$96$	−6.18377	+	9.83672i	−0.631128	+	1.00396i
$97$	−2.46772	−	12.4061i	−0.250559	−	1.25964i	−0.877120	−	0.480272i	$-0.840538\pi$
$97$	−2.46772	−	12.4061i	−0.250559	−	1.25964i	0.626561	−	0.779373i	$-0.284462\pi$
$98$	−4.74342	−	4.74342i	−0.479157	−	0.479157i
$99$	−4.10862	+	1.05795i	−0.412932	+	0.106328i
$100$	−8.31492	−	3.44415i	−0.831492	−	0.344415i
$101$	−4.47214			−0.444994			−0.222497	−	0.974933i	$-0.571421\pi$
$101$	−4.47214			−0.444994			−0.222497	+	0.974933i	$0.571421\pi$
$102$		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
$105$	−2.59827	+	15.2725i	−0.253566	+	1.49044i
$106$		0			0
$107$	0.827698	+	4.16112i	0.0800166	+	0.402271i	0.999948	+	0.0101914i	$0.00324408\pi$
$107$	0.827698	+	4.16112i	0.0800166	+	0.402271i	−0.919931	+	0.392079i	$0.871756\pi$
$108$	4.30579	+	14.9820i	0.414325	+	1.44164i
$109$	−18.6091	−	3.70158i	−1.78243	−	0.354547i	−0.809762	−	0.586758i	$-0.800404\pi$
$109$	−18.6091	−	3.70158i	−1.78243	−	0.354547i	−0.972665	+	0.232211i	$0.925404\pi$
$110$	−3.42282	−	8.26343i	−0.326354	−	0.787887i
$111$	−7.95855	−	7.52738i	−0.755392	−	0.714468i
$112$	−0.616930	+	3.10152i	−0.0582944	+	0.293066i
$113$	4.70350	−	3.14278i	0.442468	−	0.295648i	−0.314309	−	0.949321i	$-0.601773\pi$
$113$	4.70350	−	3.14278i	0.442468	−	0.295648i	0.756777	+	0.653673i	$0.226773\pi$
$114$		0			0
$115$	−14.1421	+	14.1421i	−1.31876	+	1.31876i
$116$	−7.05525	−	4.71417i	−0.655064	−	0.437700i
$117$	10.8139	−	5.20196i	0.999742	−	0.480922i
$118$			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
$123$	−3.49613	+	9.15298i	−0.315235	+	0.825297i
$124$	−9.30455	+	1.85079i	−0.835573	+	0.166206i
$125$	−3.14278	−	4.70350i	−0.281099	−	0.420694i
$126$	12.7486	+	16.9550i	1.13573	+	1.51048i
$127$	11.0866	−	4.59220i	0.983773	−	0.407492i	0.167951	−	0.985795i	$-0.446285\pi$
$127$	11.0866	−	4.59220i	0.983773	−	0.407492i	0.815822	+	0.578303i	$0.196285\pi$
$128$	−14.4610	+	5.98994i	−1.27818	+	0.529441i
$129$	−1.54022	−	6.75483i	−0.135609	−	0.594730i
$130$	14.0549	+	21.0347i	1.23270	+	1.84487i
$131$	−1.38704	+	0.275899i	−0.121186	+	0.0241054i	−0.255311	−	0.966859i	$-0.582178\pi$
$131$	−1.38704	+	0.275899i	−0.121186	+	0.0241054i	0.134125	+	0.990964i	$0.457178\pi$
$132$	−6.86474	−	2.62210i	−0.597499	−	0.228224i
$133$		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	$-0.0611861\pi$
$138$	0.762201	+	27.3755i	0.0648829	+	2.33036i
$139$	2.62934	+	1.75687i	0.223018	+	0.149016i	0.662060	−	0.749451i	$-0.269682\pi$
$139$	2.62934	+	1.75687i	0.223018	+	0.149016i	−0.439043	+	0.898466i	$0.644682\pi$
$140$	−18.9737	+	18.9737i	−1.60357	+	1.60357i
$141$	−8.96202	−	12.6365i	−0.754739	−	1.06419i
$142$	23.6640	−	15.8118i	1.98584	−	1.32690i
$143$	−1.10360	+	5.54816i	−0.0922875	+	0.463960i
$144$	0.992053	−	2.83122i	0.0826711	−	0.235935i
$145$	3.06147	+	7.39104i	0.254241	+	0.613792i
$146$		0			0
$147$	4.39911	+	2.76546i	0.362833	+	0.228092i
$148$	−3.70158	−	18.6091i	−0.304268	−	1.52966i
$149$	12.6491	+	12.6491i	1.03626	+	1.03626i	0.999318	+	0.0369380i	$0.0117604\pi$
$149$	12.6491	+	12.6491i	1.03626	+	1.03626i	0.0369380	+	0.999318i	$0.488240\pi$
$150$	11.4544	+	1.94871i	0.935245	+	0.159111i
$151$	−18.4776	−	7.65367i	−1.50369	−	0.622847i	−0.529442	−	0.848346i	$-0.677599\pi$
$151$	−18.4776	−	7.65367i	−1.50369	−	0.622847i	−0.974243	+	0.225500i	$0.927599\pi$
$152$		0			0
$153$		0			0
$154$	−10.0000			−0.805823
$155$	8.26343	+	3.42282i	0.663735	+	0.274928i
$156$	20.4902	+	3.48595i	1.64053	+	0.279099i
$157$	−1.41421	−	1.41421i	−0.112867	−	0.112867i	0.648418	−	0.761285i	$-0.275431\pi$
$157$	−1.41421	−	1.41421i	−0.112867	−	0.112867i	−0.761285	+	0.648418i	$0.775431\pi$
$158$	−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
$162$	−9.71953	−	17.6219i	−0.763638	−	1.38451i
$163$	1.85079	−	9.30455i	0.144965	−	0.728788i	−0.838098	−	0.545520i	$-0.816332\pi$
$163$	1.85079	−	9.30455i	0.144965	−	0.728788i	0.983063	−	0.183268i	$-0.0586678\pi$
$164$	−14.1105	+	9.42834i	−1.10185	+	0.736230i
$165$	4.00794	+	5.65123i	0.312018	+	0.439948i
$166$	14.1421	−	14.1421i	1.09764	−	1.09764i
$167$	−8.23113	−	5.49986i	−0.636944	−	0.425592i	0.194730	−	0.980857i	$-0.437617\pi$
$167$	−8.23113	−	5.49986i	−0.636944	−	0.425592i	−0.831674	+	0.555265i	$0.812617\pi$
$168$	0.340867	+	12.2427i	0.0262984	+	0.944545i
$169$		−	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	−0.402417	−	0.915456i	$-0.631830\pi$
$173$	7.85695	−	11.7588i	0.597353	−	0.894002i	0.999770	+	0.0214548i	$0.00682980\pi$
$174$	10.2333	+	3.90879i	0.775788	+	0.296325i
$175$	9.30455	−	1.85079i	0.703358	−	0.139907i
$176$	0.785695	+	1.17588i	0.0592240	+	0.0886350i
$177$	−3.44404	−	15.1043i	−0.258870	−	1.13531i
$178$	−27.7164	+	11.4805i	−2.07743	+	0.860500i
$179$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$179$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$180$	20.3461	−	15.2983i	1.51651	−	1.14027i
$181$	−10.5412	−	15.7760i	−0.783522	−	1.17262i	−0.981320	−	0.192380i	$-0.938379\pi$
$181$	−10.5412	−	15.7760i	−0.783522	−	1.17262i	0.197799	−	0.980243i	$-0.436621\pi$
$182$	27.7408	−	5.51799i	2.05628	−	0.409020i
$183$	3.90879	−	10.2333i	0.288946	−	0.756471i
$184$	−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
$189$	−12.5476	−	10.6093i	−0.912703	−	0.771716i
$190$		0			0
$191$	6.32456	−	6.32456i	0.457629	−	0.457629i	−0.440248	−	0.897876i	$-0.645109\pi$
$191$	6.32456	−	6.32456i	0.457629	−	0.457629i	0.897876	+	0.440248i	$0.145109\pi$
$192$	18.3665	−	13.0258i	1.32549	−	0.940056i
$193$	10.5174	−	7.02747i	0.757055	−	0.505848i	−0.116131	−	0.993234i	$-0.537049\pi$
$193$	10.5174	−	7.02747i	0.757055	−	0.505848i	0.873187	+	0.487386i	$0.162049\pi$
$194$	−5.51799	+	27.7408i	−0.396168	+	1.99167i
$195$	−14.2367	−	13.4654i	−1.01951	−	0.964277i
$196$	3.44415	+	8.31492i	0.246011	+	0.593923i
$197$	24.9667	+	4.96619i	1.77880	+	0.353826i	0.971634	−	0.236491i	$-0.0759974\pi$
$197$	24.9667	+	4.96619i	1.77880	+	0.353826i	0.807171	+	0.590317i	$0.200997\pi$
$198$	9.39311	+	1.33020i	0.667539	+	0.0945333i
$199$	−1.85079	−	9.30455i	−0.131199	−	0.659582i	−0.989276	−	0.146060i	$-0.953341\pi$
$199$	−1.85079	−	9.30455i	−0.131199	−	0.659582i	0.858077	−	0.513522i	$-0.171659\pi$
$200$	4.74342	+	4.74342i	0.335410	+	0.335410i
$201$	−2.32397	+	13.6601i	−0.163920	+	0.963511i
$202$	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
$207$	−5.28974	−	20.5431i	−0.367662	−	1.42784i
$208$	−2.82843	−	2.82843i	−0.196116	−	0.196116i
$209$		0			0
$210$	18.4364	−	29.3274i	1.27223	−	2.02378i
$211$	21.7106	+	4.31851i	1.49462	+	0.297298i	0.873657	−	0.486542i	$-0.161742\pi$
$211$	21.7106	+	4.31851i	1.49462	+	0.297298i	0.620963	+	0.783840i	$0.286742\pi$
$212$		0			0
$213$	−15.1486	+	16.0163i	−1.03796	+	1.09742i
$214$	1.85079	−	9.30455i	0.126517	−	0.636046i
$215$	−9.40700	+	6.28556i	−0.641552	+	0.428672i
$216$	1.30835	−	11.5451i	0.0890216	−	0.785541i
$217$	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	−0.575109	−	0.818077i	$-0.695040\pi$
$223$	6.12293	−	14.7821i	0.410022	−	0.989881i	0.985131	−	0.171804i	$-0.0549596\pi$
$224$	11.7854	−	17.6381i	0.787447	−	1.17850i
$225$	−8.98606	+	0.500776i	−0.599070	+	0.0333851i
$226$	−12.4061	+	2.46772i	−0.825239	+	0.164150i
$227$	−3.92847	−	5.87938i	−0.260742	−	0.390228i	0.677882	−	0.735171i	$-0.262898\pi$
$227$	−3.92847	−	5.87938i	−0.260742	−	0.390228i	−0.938624	+	0.344943i	$0.887898\pi$
$228$		0			0
$229$	18.4776	−	7.65367i	1.22103	−	0.505769i	0.323295	−	0.946298i	$-0.395209\pi$
$229$	18.4776	−	7.65367i	1.22103	−	0.505769i	0.897738	+	0.440529i	$0.145209\pi$
$230$	41.3171	−	17.1141i	2.72437	−	1.12847i
$231$	7.55213	−	1.72202i	0.496894	−	0.113300i
$232$	3.51373	+	5.25868i	0.230688	+	0.345249i
$233$	5.54816	−	1.10360i	0.363472	−	0.0722991i	−0.00997588	−	0.999950i	$-0.503175\pi$
$233$	5.54816	−	1.10360i	0.363472	−	0.0722991i	0.373448	+	0.927651i	$0.378175\pi$
$234$	−26.7912	+	1.49302i	−1.75140	+	0.0976021i
$235$	−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	$0.906585\pi$
$240$	−4.89708	+	0.136347i	−0.316105	+	0.00880114i
$241$	21.0347	+	14.0549i	1.35496	+	0.905358i	0.999569	−	0.0293579i	$-0.00934625\pi$
$241$	21.0347	+	14.0549i	1.35496	+	0.905358i	0.355395	+	0.934716i	$0.384346\pi$
$242$	14.2302	−	14.2302i	0.914755	−	0.914755i
$243$	10.3748	+	11.6346i	0.665546	+	0.746357i
$244$	15.7760	−	10.5412i	1.00996	−	0.674831i
$245$	1.65540	−	8.32224i	0.105759	−	0.531688i
$246$	15.0548	−	15.9171i	0.959857	−	1.01484i
$247$		0			0
$248$	6.93520	+	1.37950i	0.440386	+	0.0875981i
$249$	−8.24502	+	13.1156i	−0.522507	+	0.831169i
$250$	2.46772	+	12.4061i	0.156072	+	0.784628i
$251$	−12.6491	−	12.6491i	−0.798405	−	0.798405i	0.184439	−	0.982844i	$-0.440953\pi$
$251$	−12.6491	−	12.6491i	−0.798405	−	0.798405i	−0.982844	+	0.184439i	$0.940953\pi$
$252$	−7.09693	−	27.5615i	−0.447065	−	1.73621i
$253$	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	$-0.129335\pi$
$257$	20.6586	+	8.55706i	1.28865	+	0.533775i	0.370065	+	0.929006i	$0.379335\pi$
$258$	−2.59827	+	15.2725i	−0.161761	+	0.950824i
$259$	14.1421	+	14.1421i	0.878750	+	0.878750i
$260$	−6.62159	−	33.2890i	−0.410653	−	2.06449i
$261$	−8.40146	−	1.18977i	−0.520037	−	0.0736448i
$262$	3.10152	+	0.616930i	0.191612	+	0.0381140i
$263$	6.84565	+	16.5269i	0.422121	+	1.01909i	0.981721	+	0.190327i	$0.0609548\pi$
$263$	6.84565	+	16.5269i	0.422121	+	1.01909i	−0.559600	+	0.828763i	$0.689045\pi$
$264$	3.97927	+	3.76369i	0.244907	+	0.231639i
$265$		0			0
$266$		0			0
$267$	18.9548	−	13.4430i	1.16002	−	0.822700i
$268$	−16.9706	+	16.9706i	−1.03664	+	1.03664i
$269$	21.1658	+	14.1425i	1.29050	+	0.862284i	0.995642	−	0.0932573i	$-0.0297279\pi$
$269$	21.1658	+	14.1425i	1.29050	+	0.862284i	0.294857	+	0.955541i	$0.404728\pi$
$270$	−21.2187	+	25.0952i	−1.29133	+	1.52724i
$271$		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
$276$	13.1105	−	34.3237i	0.789158	−	2.06604i
$277$	−6.20303	+	1.23386i	−0.372704	+	0.0741354i	−0.377888	−	0.925851i	$-0.623350\pi$
$277$	−6.20303	+	1.23386i	−0.372704	+	0.0741354i	0.00518447	+	0.999987i	$0.498350\pi$
$278$	−3.92847	−	5.87938i	−0.235614	−	0.352622i
$279$	−7.58253	+	5.70134i	−0.453954	+	0.341330i
$280$	18.4776	−	7.65367i	1.10425	−	0.457394i
$281$	16.5269	−	6.84565i	0.985910	−	0.408377i	0.169298	−	0.985565i	$-0.445850\pi$
$281$	16.5269	−	6.84565i	0.985910	−	0.408377i	0.816612	+	0.577188i	$0.195850\pi$
$282$	7.70110	+	33.7741i	0.458594	+	2.01122i
$283$	1.75687	+	2.62934i	0.104435	+	0.156298i	0.880006	−	0.474962i	$-0.157538\pi$
$283$	1.75687	+	2.62934i	0.104435	+	0.156298i	−0.775571	+	0.631260i	$0.782538\pi$
$284$	−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
$291$	−0.609761	−	21.9004i	−0.0357448	−	1.28383i
$292$		0			0
$293$	−12.6491	+	12.6491i	−0.738969	+	0.738969i	−0.972379	−	0.233410i	$-0.925012\pi$
$293$	−12.6491	+	12.6491i	−0.738969	+	0.738969i	0.233410	+	0.972379i	$0.425012\pi$
$294$	−6.72152	−	9.47740i	−0.392007	−	0.552733i
$295$	−21.0347	+	14.0549i	−1.22469	+	0.818310i
$296$	−2.75899	+	13.8704i	−0.160363	+	0.806201i
$297$	−7.32286	+	0.612927i	−0.424916	+	0.0355656i
$298$	−15.3073	−	36.9552i	−0.886730	−	2.14076i
$299$	−27.7408	−	5.51799i	−1.60429	−	0.319113i
$300$	−13.1973	−	8.29639i	−0.761949	−	0.478992i
$301$	2.46772	+	12.4061i	0.142237	+	0.715073i
$302$	31.6228	+	31.6228i	1.81969	+	1.81969i
$303$	−7.63625	−	1.29914i	−0.438691	−	0.0746335i
$304$		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
$309$	6.83007	+	1.16198i	0.388549	+	0.0661029i
$310$	−14.1421	−	14.1421i	−0.803219	−	0.803219i
$311$	−0.275899	−	1.38704i	−0.0156448	−	0.0786518i	0.972174	−	0.234259i	$-0.0752665\pi$
$311$	−0.275899	−	1.38704i	−0.0156448	−	0.0786518i	−0.987819	+	0.155608i	$0.950266\pi$
$312$	−13.1156	−	8.24502i	−0.742526	−	0.466782i
$313$	−24.8121	−	4.93544i	−1.40246	−	0.278967i	−0.564834	−	0.825205i	$-0.691060\pi$
$313$	−24.8121	−	4.93544i	−1.40246	−	0.278967i	−0.837630	+	0.546237i	$0.816060\pi$
$314$	1.71141	+	4.13171i	0.0965806	+	0.233166i
$315$	−8.87319	+	25.3232i	−0.499948	+	1.42680i
$316$	−1.85079	+	9.30455i	−0.104115	+	0.523422i
$317$	11.7588	−	7.85695i	0.660438	−	0.441290i	−0.179658	−	0.983729i	$-0.557499\pi$
$317$	11.7588	−	7.85695i	0.660438	−	0.441290i	0.840095	+	0.542439i	$0.182499\pi$
$318$		0			0
$319$	2.82843	−	2.82843i	0.158362	−	0.158362i
$320$	−30.5728	−	20.4281i	−1.70907	−	1.14196i
$321$	0.204520	+	7.34562i	0.0114152	+	0.409993i
$322$		−	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
$327$	−30.7000	−	11.7264i	−1.69772	−	0.648470i
$328$	12.4061	−	2.46772i	0.685010	−	0.136257i
$329$	15.7139	+	23.5175i	0.866335	+	1.29656i
$330$	−3.44404	−	15.1043i	−0.189588	−	0.831462i
$331$	−25.8686	+	10.7151i	−1.42187	+	0.588957i	−0.955329	−	0.295543i	$-0.904499\pi$
$331$	−25.8686	+	10.7151i	−1.42187	+	0.588957i	−0.466539	+	0.884501i	$0.654499\pi$
$332$	−24.7903	+	10.2685i	−1.36054	+	0.563556i
$333$	−11.4027	−	15.1651i	−0.624863	−	0.831040i
$334$	12.2981	+	18.4054i	0.672921	+	1.00710i
$335$	22.1926	−	4.41439i	1.21251	−	0.241184i
$336$	−1.95440	+	5.11667i	−0.106621	+	0.279137i
$337$	14.0549	−	21.0347i	0.765621	−	1.14583i	−0.219774	−	0.975551i	$-0.570532\pi$
$337$	14.0549	−	21.0347i	0.765621	−	1.14583i	0.985395	−	0.170282i	$-0.0544680\pi$
$338$	−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
$345$	−28.2562	+	20.0397i	−1.52126	+	1.07890i
$346$	−26.2934	+	17.5687i	−1.41354	+	0.944498i
$347$	6.89748	−	34.6760i	0.370276	−	1.86151i	−0.124118	−	0.992267i	$-0.539610\pi$
$347$	6.89748	−	34.6760i	0.370276	−	1.86151i	0.494395	−	0.869238i	$-0.335390\pi$
$348$	−10.6775	−	10.0990i	−0.572375	−	0.541366i
$349$	−5.35757	−	12.9343i	−0.286784	−	0.692358i	0.713179	−	0.700982i	$-0.247255\pi$
$349$	−5.35757	−	12.9343i	−0.286784	−	0.692358i	−0.999963	+	0.00862428i	$0.997255\pi$
$350$	−20.8056	−	4.13849i	−1.11211	−	0.221212i
$351$	19.9760	−	5.74105i	1.06624	−	0.306435i
$352$	−1.85079	−	9.30455i	−0.0986474	−	0.495934i
$353$	−12.6491	−	12.6491i	−0.673244	−	0.673244i	0.285218	−	0.958463i	$-0.407934\pi$
$353$	−12.6491	−	12.6491i	−0.673244	−	0.673244i	−0.958463	+	0.285218i	$0.907934\pi$
$354$	−5.80992	+	34.1503i	−0.308794	+	1.81507i
$355$	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	$-0.124557\pi$
$359$	24.7903	+	10.2685i	1.30838	+	0.541949i	0.383970	+	0.923346i	$0.374557\pi$
$360$	−18.3743	+	4.73129i	−0.968411	+	0.249361i
$361$	13.4350	+	13.4350i	0.707107	+	0.707107i
$362$	8.27698	+	41.6112i	0.435028	+	2.18704i
$363$	−8.29639	+	13.1973i	−0.435448	+	0.692681i
$364$	−37.2182	−	7.40316i	−1.95076	−	0.388031i
$365$		0			0
$366$	−16.8317	+	17.7959i	−0.879809	+	0.930204i
$367$	−3.08465	+	15.5076i	−0.161017	+	0.809489i	0.812868	+	0.582448i	$0.197905\pi$
$367$	−3.08465	+	15.5076i	−0.161017	+	0.809489i	−0.973885	+	0.227041i	$0.927095\pi$
$368$	−5.87938	+	3.92847i	−0.306484	+	0.204786i
$369$	−8.62860	+	14.6133i	−0.449187	+	0.760736i
$370$	28.2843	−	28.2843i	1.47043	−	1.47043i
$371$		0			0
$372$	−16.4253	+	0.457321i	−0.851613	+	0.0237110i
$373$			4.00000i			0.207112i	0.994624	+	0.103556i	$0.0330221\pi$
$373$			4.00000i			0.207112i	−0.994624	+	0.103556i	$0.966978\pi$
$374$		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
$378$	16.8430	+	32.6544i	0.866313	+	1.67956i
$379$	9.30455	−	1.85079i	0.477942	−	0.0950687i	0.0497604	−	0.998761i	$-0.484154\pi$
$379$	9.30455	−	1.85079i	0.477942	−	0.0950687i	0.428182	+	0.903693i	$0.359154\pi$
$380$		0			0
$381$	20.2645	−	4.62066i	1.03818	−	0.236724i
$382$	−18.4776	+	7.65367i	−0.945396	+	0.391596i
$383$	33.0537	−	13.6913i	1.68897	−	0.699593i	0.689276	−	0.724499i	$-0.257929\pi$
$383$	33.0537	−	13.6913i	1.68897	−	0.699593i	0.999690	+	0.0249059i	$0.00792860\pi$
$384$	−26.4325	+	6.02706i	−1.34888	+	0.307567i
$385$	−7.02747	−	10.5174i	−0.358153	−	0.536014i
$386$	−27.7408	+	5.51799i	−1.41197	+	0.280858i
$387$	−0.667701	−	11.9814i	−0.0339412	−	0.609049i
$388$	21.0824	−	31.5521i	1.07030	−	1.60181i
$389$	1.71141	−	4.13171i	0.0867720	−	0.209486i	−0.874537	−	0.484959i	$-0.838834\pi$
$389$	1.71141	−	4.13171i	0.0867720	−	0.209486i	0.961309	+	0.275473i	$0.0888344\pi$
$390$	17.8885	+	40.0000i	0.905822	+	2.02548i
$391$		0			0
$392$		−	6.70820i		−	0.338815i
$393$	−2.44854	+	0.0681734i	−0.123513	+	0.00343889i
$394$	−47.3281	−	31.6236i	−2.38435	−	1.59317i
$395$	6.32456	−	6.32456i	0.318223	−	0.318223i
$396$	−10.9599	−	6.47145i	−0.550758	−	0.325203i
$397$	15.7760	−	10.5412i	0.791776	−	0.529048i	−0.0926663	−	0.995697i	$-0.529539\pi$
$397$	15.7760	−	10.5412i	0.791776	−	0.529048i	0.884442	+	0.466649i	$0.154539\pi$
$398$	−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	0.0546036	−	0.998508i	$-0.482611\pi$
$401$	−5.54816	−	1.10360i	−0.277062	−	0.0551110i	−0.331665	+	0.943397i	$0.607611\pi$
$402$	16.4900	−	26.2313i	0.822449	−	1.30830i
$403$	2.46772	+	12.4061i	0.122926	+	0.617990i
$404$	−9.48683	−	9.48683i	−0.471988	−	0.471988i
$405$	11.7032	−	22.6061i	0.581536	−	1.12331i
$406$	−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
$411$	1.29914	−	7.63625i	0.0640817	−	0.376668i
$412$	8.48528	+	8.48528i	0.418040	+	0.418040i
$413$	5.51799	+	27.7408i	0.271522	+	1.36504i
$414$	−6.65100	+	46.9656i	−0.326879	+	2.30823i
$415$	24.8121	+	4.93544i	1.21798	+	0.242271i
$416$	10.2685	+	24.7903i	0.503453	+	1.21544i
$417$	3.97927	+	3.76369i	0.194866	+	0.184309i
$418$		0			0
$419$	−8.23113	+	5.49986i	−0.402117	+	0.268686i	−0.740141	−	0.672451i	$-0.765241\pi$
$419$	−8.23113	+	5.49986i	−0.402117	+	0.268686i	0.338024	+	0.941137i	$0.390241\pi$
$420$	−37.9096	+	26.8861i	−1.84980	+	1.31191i
$421$	−14.1421	+	14.1421i	−0.689246	+	0.689246i	−0.962065	−	0.272820i	$-0.912044\pi$
$421$	−14.1421	+	14.1421i	−0.689246	+	0.689246i	0.272820	+	0.962065i	$0.412044\pi$
$422$	−41.1556	−	27.4993i	−2.00343	−	1.33865i
$423$	−11.6319	−	24.1805i	−0.565564	−	1.17570i
$424$		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
$429$	−3.49613	+	9.15298i	−0.168795	+	0.441910i
$430$	24.8121	−	4.93544i	1.19655	−	0.238008i
$431$	7.07125	+	10.5829i	0.340610	+	0.509759i	0.961746	−	0.273944i	$-0.0883283\pi$
$431$	7.07125	+	10.5829i	0.340610	+	0.509759i	−0.621135	+	0.783703i	$0.713328\pi$
$432$	2.51641	−	4.54617i	0.121071	−	0.218728i
$433$	33.2597	−	13.7766i	1.59836	−	0.662061i	0.607175	−	0.794568i	$-0.292303\pi$
$433$	33.2597	−	13.7766i	1.59836	−	0.662061i	0.991182	+	0.132507i	$0.0423026\pi$
$434$	−20.6586	+	8.55706i	−0.991643	+	0.410752i
$435$	3.08044	+	13.5097i	0.147696	+	0.647739i
$436$	−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	$-0.989650\pi$
$439$	−12.2981	+	18.4054i	−0.586955	+	0.878440i	0.412516	+	0.910950i	$0.364650\pi$
$440$	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	$-0.139710\pi$
$444$	−0.914642	−	32.8506i	−0.0434070	−	1.55902i
$445$	−31.5521	−	21.0824i	−1.49571	−	0.999402i
$446$	−25.2982	+	25.2982i	−1.19791	+	1.19791i
$447$	17.9240	+	25.2731i	0.847778	+	1.19538i
$448$	−34.1814	+	22.8393i	−1.61492	+	1.07905i
$449$	3.31079	−	16.6445i	0.156246	−	0.785501i	−0.820591	−	0.571516i	$-0.806355\pi$
$449$	3.31079	−	16.6445i	0.156246	−	0.785501i	0.976837	−	0.213985i	$-0.0686445\pi$
$450$	18.9924	+	6.65489i	0.895312	+	0.313715i
$451$	−3.06147	−	7.39104i	−0.144159	−	0.348030i
$452$	16.6445	+	3.31079i	0.782890	+	0.155727i
$453$	−29.3274	−	18.4364i	−1.37792	−	0.866219i
$454$	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	−0.315839	−	0.948813i	$-0.602286\pi$
$457$	−25.8686	−	10.7151i	−1.21008	−	0.501233i	−0.894244	+	0.447580i	$0.852286\pi$
$458$	−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	$-0.688466\pi$
$461$	−33.0537	−	13.6913i	−1.53947	−	0.637667i	−0.981373	+	0.192112i	$0.938466\pi$
$462$	−17.0752	−	2.90496i	−0.794409	−	0.135151i
$463$	−2.82843	−	2.82843i	−0.131448	−	0.131448i	0.638322	−	0.769770i	$-0.279629\pi$
$463$	−2.82843	−	2.82843i	−0.131448	−	0.131448i	−0.769770	+	0.638322i	$0.779629\pi$
$464$	0.551799	+	2.77408i	0.0256166	+	0.128783i
$465$	13.1156	+	8.24502i	0.608223	+	0.382354i
$466$	−12.4061	−	2.46772i	−0.574700	−	0.114315i
$467$	−6.84565	−	16.5269i	−0.316779	−	0.764772i	−0.999421	−	0.0340192i	$-0.989169\pi$
$467$	−6.84565	−	16.5269i	−0.316779	−	0.764772i	0.682642	−	0.730753i	$-0.260831\pi$
$468$	33.9747	+	11.9046i	1.57048	+	0.550292i
$469$	4.93544	−	24.8121i	0.227897	−	1.14572i
$470$	47.0350	−	31.4278i	2.16956	−	1.44966i
$471$	−2.00397	−	2.82562i	−0.0923380	−	0.130198i
$472$	−14.1421	+	14.1421i	−0.650945	+	0.650945i
$473$	4.70350	+	3.14278i	0.216267	+	0.144505i
$474$	−0.340867	−	12.2427i	−0.0156565	−	0.562326i
$475$		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	−0.684279	−	0.729220i	$-0.739883\pi$
$479$	5.49986	−	8.23113i	0.251295	−	0.376090i	0.935574	+	0.353131i	$0.114883\pi$
$480$	30.7000	+	11.7264i	1.40126	+	0.535233i
$481$	−24.8121	+	4.93544i	−1.13134	+	0.225037i
$482$	−31.4278	−	47.0350i	−1.43150	−	2.14239i
$483$	8.61009	+	37.7606i	0.391773	+	1.71817i
$484$	−24.9447	+	10.3325i	−1.13385	+	0.469657i
$485$	−33.0537	+	13.6913i	−1.50089	+	0.621690i
$486$	−11.4772	−	32.9131i	−0.520615	−	1.49297i
$487$	15.8118	+	23.6640i	0.716501	+	1.07232i	0.993762	+	0.111525i	$0.0355736\pi$
$487$	15.8118	+	23.6640i	0.716501	+	1.07232i	−0.277260	+	0.960795i	$0.589426\pi$
$488$	−13.8704	+	2.75899i	−0.627883	+	0.124894i
$489$	5.86319	−	15.3500i	0.265142	−	0.694152i
$490$	−10.5412	+	15.7760i	−0.476203	+	0.712688i
$491$	−6.84565	+	16.5269i	−0.308940	+	0.745847i	0.690800	+	0.723046i	$0.257258\pi$
$491$	−6.84565	+	16.5269i	−0.308940	+	0.745847i	−0.999740	+	0.0228010i	$0.992742\pi$
$492$	−26.8328	+	12.0000i	−1.20972	+	0.541002i
$493$		0			0
$494$		0			0
$495$	5.20196	+	10.8139i	0.233811	+	0.486047i
$496$	2.62934	+	1.75687i	0.118061	+	0.0788857i
$497$	28.4605	−	28.4605i	1.27663	−	1.27663i
$498$	28.2562	−	20.0397i	1.26619	−	0.898000i
$499$	−2.62934	+	1.75687i	−0.117705	+	0.0786482i	−0.613029	−	0.790060i	$-0.710049\pi$
$499$	−2.62934	+	1.75687i	−0.117705	+	0.0786482i	0.495324	+	0.868708i	$0.335049\pi$
$500$	3.31079	−	16.6445i	0.148063	−	0.744364i
$501$	−12.4571	−	11.7822i	−0.556542	−	0.526391i
$502$	15.3073	+	36.9552i	0.683200	+	1.64939i
$503$	−12.4834	−	2.48309i	−0.556605	−	0.110716i	−0.0912312	−	0.995830i	$-0.529080\pi$
$503$	−12.4834	−	2.48309i	−0.556605	−	0.110716i	−0.465374	+	0.885114i	$0.654080\pi$
$504$	−2.97442	+	21.0036i	−0.132491	+	0.935576i
$505$	2.46772	+	12.4061i	0.109812	+	0.552062i
$506$	−15.8114	−	15.8114i	−0.702902	−	0.702902i
$507$	0.871488	−	5.12255i	0.0387041	−	0.227500i
$508$	33.2597	+	13.7766i	1.47566	+	0.611238i
$509$	17.8885			0.792896			0.396448	−	0.918057i	$-0.370243\pi$
$509$	17.8885			0.792896			0.396448	+	0.918057i	$0.370243\pi$
$510$		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
$516$	11.0619	−	17.5965i	0.486971	−	0.774641i
$517$	12.4061	+	2.46772i	0.545618	+	0.108530i
$518$	−17.1141	−	41.3171i	−0.751951	−	1.81537i
$519$	16.8317	−	17.7959i	0.738831	−	0.781151i
$520$	−4.93544	+	24.8121i	−0.216433	+	1.08808i
$521$	28.2210	−	18.8567i	1.23639	−	0.826126i	0.246659	−	0.969102i	$-0.420667\pi$
$521$	28.2210	−	18.8567i	1.23639	−	0.826126i	0.989726	+	0.142976i	$0.0456673\pi$
$522$	16.3381	+	9.64707i	0.715100	+	0.422241i
$523$	−16.9706	+	16.9706i	−0.742071	+	0.742071i	−0.972976	−	0.230905i	$-0.925831\pi$
$523$	−16.9706	+	16.9706i	−0.742071	+	0.742071i	0.230905	+	0.972976i	$0.425831\pi$
$524$	−3.52763	−	2.35708i	−0.154105	−	0.102970i
$525$	16.4253	−	0.457321i	0.716859	−	0.0199591i
$526$		−	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
$531$	−1.49302	−	26.7912i	−0.0647918	−	1.16264i
$532$		0			0
$533$	12.5711	+	18.8140i	0.544516	+	0.814925i
$534$	−50.6612	+	11.5517i	−2.19233	+	0.499889i
$535$	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
$540$	39.1853	−	20.2117i	1.68627	−	0.869771i
$541$	−3.51373	+	5.25868i	−0.151067	+	0.226088i	−0.899283	−	0.437368i	$-0.855911\pi$
$541$	−3.51373	+	5.25868i	−0.151067	+	0.226088i	0.748216	+	0.663456i	$0.230911\pi$
$542$		0			0
$543$	−13.4164	−	30.0000i	−0.575753	−	1.28742i
$544$		0			0
$545$			53.6656i			2.29878i
$546$	48.9708	−	1.36347i	2.09576	−	0.0583510i
$547$	−2.62934	−	1.75687i	−0.112422	−	0.0751182i	0.498088	−	0.867126i	$-0.334036\pi$
$547$	−2.62934	−	1.75687i	−0.112422	−	0.0751182i	−0.610510	+	0.792008i	$0.709036\pi$
$548$	9.48683	−	9.48683i	0.405257	−	0.405257i
$549$	9.64707	−	16.3381i	0.411727	−	0.697294i
$550$	−7.88801	+	5.27060i	−0.336346	+	0.224739i
$551$		0			0
$552$	−18.8185	+	19.8964i	−0.800967	+	0.846846i
$553$	−3.82683	−	9.23880i	−0.162734	−	0.392874i
$554$	13.8704	+	2.75899i	0.589297	+	0.117218i
$555$	−16.4900	+	26.2313i	−0.699963	+	1.11345i
$556$	1.85079	+	9.30455i	0.0784909	+	0.394601i
$557$	−9.48683	−	9.48683i	−0.401970	−	0.401970i	0.476957	−	0.878927i	$-0.341740\pi$
$557$	−9.48683	−	9.48683i	−0.401970	−	0.401970i	−0.878927	+	0.476957i	$0.841740\pi$
$558$	20.5431	−	5.28974i	0.869658	−	0.223933i
$559$	−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	$-0.435355\pi$
$563$	−8.26343	−	3.42282i	−0.348262	−	0.144255i	−0.549956	+	0.835194i	$0.685355\pi$
$564$	7.79482	−	45.8175i	0.328221	−	1.92926i
$565$	−11.3137	−	11.3137i	−0.475971	−	0.475971i
$566$	−1.37950	−	6.93520i	−0.0579846	−	0.291508i
$567$	−18.3432	−	21.7606i	−0.770344	−	0.913861i
$568$	27.9136	+	5.55237i	1.17123	+	0.232972i
$569$	−6.84565	−	16.5269i	−0.286985	−	0.692842i	0.712981	−	0.701184i	$-0.247345\pi$
$569$	−6.84565	−	16.5269i	−0.286985	−	0.692842i	−0.999965	+	0.00834171i	$0.997345\pi$
$570$		0			0
$571$	−6.78623	+	34.1167i	−0.283995	+	1.42774i	0.530558	+	0.847649i	$0.321982\pi$
$571$	−6.78623	+	34.1167i	−0.283995	+	1.42774i	−0.814553	+	0.580090i	$0.803018\pi$
$572$	−14.1105	+	9.42834i	−0.589990	+	0.394219i
$573$	12.6365	−	8.96202i	0.527899	−	0.374394i
$574$	−28.2843	+	28.2843i	−1.18056	+	1.18056i
$575$	17.6381	+	11.7854i	0.735561	+	0.491486i
$576$	35.1450	−	16.9064i	1.46438	−	0.704432i
$577$			12.0000i			0.499567i	0.968302	+	0.249783i	$0.0803594\pi$
$577$			12.0000i			0.499567i	−0.968302	+	0.249783i	$0.919641\pi$
$578$		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
$582$	−17.4806	+	45.7649i	−0.724596	+	1.89702i
$583$		0			0
$584$		0			0
$585$	−20.3977	−	27.1281i	−0.843342	−	1.12161i
$586$	36.9552	−	15.3073i	1.52660	−	0.632340i
$587$	−16.5269	+	6.84565i	−0.682136	+	0.282550i	−0.696720	−	0.717343i	$-0.745358\pi$
$587$	−16.5269	+	6.84565i	−0.682136	+	0.282550i	0.0145832	+	0.999894i	$0.495358\pi$
$588$	3.46550	+	15.1984i	0.142915	+	0.626770i
$589$		0			0
$590$	55.4816	−	11.0360i	2.28414	−	0.454344i
$591$	41.1884	+	15.7326i	1.69427	+	0.647152i
$592$	−3.51373	+	5.25868i	−0.144414	+	0.216130i
$593$	−6.84565	+	16.5269i	−0.281117	+	0.678677i	−0.999862	−	0.0165969i	$-0.994717\pi$
$593$	−6.84565	+	16.5269i	−0.281117	+	0.678677i	0.718745	+	0.695274i	$0.244717\pi$
$594$	15.6525	+	5.00000i	0.642229	+	0.205152i
$595$		0			0
$596$			53.6656i			2.19823i
$597$	−0.457321	−	16.4253i	−0.0187169	−	0.672243i
$598$	52.5868	+	35.1373i	2.15043	+	1.43687i
$599$	−12.6491	+	12.6491i	−0.516829	+	0.516829i	−0.916610	−	0.399782i	$-0.869086\pi$
$599$	−12.6491	+	12.6491i	−0.516829	+	0.516829i	0.399782	+	0.916610i	$0.369086\pi$
$600$	6.72152	+	9.47740i	0.274405	+	0.386913i
$601$	10.5174	−	7.02747i	0.429012	−	0.286656i	−0.322258	−	0.946652i	$-0.604442\pi$
$601$	10.5174	−	7.02747i	0.429012	−	0.286656i	0.751270	+	0.659995i	$0.229442\pi$
$602$	5.51799	−	27.7408i	0.224896	−	1.13063i
$603$	−7.93642	+	22.6498i	−0.323196	+	0.922371i
$604$	−22.9610	−	55.4328i	−0.934270	−	2.25553i
$605$	24.9667	+	4.96619i	1.01504	+	0.201904i
$606$	14.6637	+	9.21821i	0.595673	+	0.374464i
$607$	4.31851	+	21.7106i	0.175283	+	0.881206i	0.963888	+	0.266307i	$0.0858034\pi$
$607$	4.31851	+	21.7106i	0.175283	+	0.881206i	−0.788605	+	0.614900i	$0.789197\pi$
$608$		0			0
$609$	15.2725	+	2.59827i	0.618873	+	0.105287i
$610$	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
$615$	27.3203	+	4.64793i	1.10166	+	0.187423i
$616$	−7.07107	−	7.07107i	−0.284901	−	0.284901i
$617$	−7.72518	−	38.8371i	−0.311004	−	1.56352i	−0.747776	−	0.663951i	$-0.768878\pi$
$617$	−7.72518	−	38.8371i	−0.311004	−	1.56352i	0.436772	−	0.899572i	$-0.356122\pi$
$618$	−13.1156	−	8.24502i	−0.527588	−	0.331663i
$619$	−3.10152	−	0.616930i	−0.124660	−	0.0247965i	0.132366	−	0.991201i	$-0.457743\pi$
$619$	−3.10152	−	0.616930i	−0.124660	−	0.0247965i	−0.257026	+	0.966404i	$0.582743\pi$
$620$	10.2685	+	24.7903i	0.412392	+	0.995602i
$621$	−3.06463	−	36.6143i	−0.122979	−	1.46928i
$622$	−0.616930	+	3.10152i	−0.0247366	+	0.124359i
$623$	−35.2763	+	23.5708i	−1.41331	+	0.944346i
$624$	−4.00794	−	5.65123i	−0.160446	−	0.226230i
$625$	−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	$-0.875000\pi$
$631$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$632$	3.92847	−	5.87938i	0.156266	−	0.233869i
$633$	35.8167	+	13.6808i	1.42359	+	0.543762i
$634$	−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
$639$	−30.5191	+	22.9474i	−1.20732	+	0.907787i
$640$	24.5961	+	36.8107i	0.972248	+	1.45507i
$641$	−22.1926	+	4.41439i	−0.876556	+	0.174358i	−0.612806	−	0.790233i	$-0.709959\pi$
$641$	−22.1926	+	4.41439i	−0.876556	+	0.174358i	−0.263750	+	0.964591i	$0.584959\pi$
$642$	5.86319	−	15.3500i	0.231401	−	0.605817i
$643$	12.2981	−	18.4054i	0.484989	−	0.725837i	−0.505591	−	0.862773i	$-0.668726\pi$
$643$	12.2981	−	18.4054i	0.484989	−	0.725837i	0.990580	+	0.136936i	$0.0437256\pi$
$644$	−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	$-0.176853\pi$
$648$	5.58781	−	19.3333i	0.219510	−	0.759484i
$649$	10.5174	+	7.02747i	0.412842	+	0.275852i
$650$	18.9737	−	18.9737i	0.744208	−	0.744208i
$651$	14.1281	−	10.0198i	0.553723	−	0.392709i
$652$	23.6640	−	15.8118i	0.926755	−	0.619238i
$653$	−7.17338	+	36.0630i	−0.280716	+	1.41126i	0.540839	+	0.841126i	$0.318107\pi$
$653$	−7.17338	+	36.0630i	−0.280716	+	1.41126i	−0.821555	+	0.570129i	$0.806893\pi$
$654$	53.3876	+	50.4952i	2.08762	+	1.97452i
$655$	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	$-0.305737\pi$
$659$	−6.32456	−	6.32456i	−0.246370	−	0.246370i	−0.819479	+	0.573109i	$0.805737\pi$
$660$	−3.48595	+	20.4902i	−0.135690	+	0.797580i
$661$	−35.1074	−	14.5420i	−1.36552	−	0.565617i	−0.424950	−	0.905217i	$-0.639708\pi$
$661$	−35.1074	−	14.5420i	−1.36552	−	0.565617i	−0.940570	+	0.339600i	$0.889708\pi$
$662$	62.6099			2.43340
$663$		0			0
$664$	20.0000			0.776151
$665$		0			0
$666$	10.5795	+	41.0862i	0.409946	+	1.59206i
$667$	14.1421	+	14.1421i	0.547586	+	0.547586i
$668$	−5.79389	−	29.1278i	−0.224172	−	1.12699i
$669$	14.7491	−	23.4619i	0.570235	−	0.907091i
$670$	−49.6242	−	9.87088i	−1.91715	−	0.381345i
$671$	3.42282	+	8.26343i	0.132137	+	0.319006i
$672$	25.2476	−	26.6938i	0.973948	−	1.02974i
$673$	−4.93544	+	24.8121i	−0.190247	+	0.956437i	0.761175	+	0.648547i	$0.224623\pi$
$673$	−4.93544	+	24.8121i	−0.190247	+	0.956437i	−0.951422	+	0.307890i	$0.900377\pi$
$674$	−47.0350	+	31.4278i	−1.81172	+	1.21055i
$675$	−15.4893	−	1.75533i	−0.596184	−	0.0675627i
$676$	6.36396	−	6.36396i	0.244768	−	0.244768i
$677$	−11.7588	−	7.85695i	−0.451926	−	0.301967i	0.308698	−	0.951160i	$-0.400107\pi$
$677$	−11.7588	−	7.85695i	−0.451926	−	0.301967i	−0.760624	+	0.649193i	$0.775107\pi$
$678$	−21.9004	+	0.609761i	−0.841080	+	0.0234177i
$679$			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	−0.898985	−	0.437979i	$-0.855695\pi$
$683$	−3.92847	+	5.87938i	−0.150319	+	0.224968i	0.748666	+	0.662947i	$0.230695\pi$
$684$		0			0
$685$	−12.4061	+	2.46772i	−0.474011	+	0.0942867i
$686$	−15.7139	−	23.5175i	−0.599959	−	0.897903i
$687$	33.7741	−	7.70110i	1.28856	−	0.293815i
$688$	−3.69552	+	1.53073i	−0.140890	+	0.0583587i
$689$		0			0
$690$	75.5213	−	17.2202i	2.87505	−	0.655561i
$691$	22.8393	+	34.1814i	0.868847	+	1.30032i	0.952721	+	0.303845i	$0.0982705\pi$
$691$	22.8393	+	34.1814i	0.868847	+	1.30032i	−0.0838745	+	0.996476i	$0.526729\pi$
$692$	41.6112	−	8.27698i	1.58182	−	0.314644i
$693$	13.3956	−	0.746512i	0.508858	−	0.0283577i
$694$	−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
$699$	9.79416	−	0.272693i	0.370449	−	0.0103142i
$700$	23.6640	+	15.8118i	0.894417	+	0.597630i
$701$	−9.48683	+	9.48683i	−0.358313	+	0.358313i	−0.863191	−	0.504878i	$-0.831537\pi$
$701$	−9.48683	+	9.48683i	−0.358313	+	0.358313i	0.504878	+	0.863191i	$0.331537\pi$
$702$	−46.1802	−	5.23338i	−1.74296	−	0.197521i
$703$		0			0
$704$	−3.58669	+	18.0315i	−0.135179	+	0.679588i
$705$	−30.1095	+	31.8342i	−1.13399	+	1.19895i
$706$	15.3073	+	36.9552i	0.576099	+	1.39083i
$707$	13.8704	+	2.75899i	0.521650	+	0.103763i
$708$	24.7351	−	39.3469i	0.929601	−	1.47875i
$709$	1.23386	+	6.20303i	0.0463386	+	0.232960i	0.997013	−	0.0772298i	$-0.0246075\pi$
$709$	1.23386	+	6.20303i	0.0463386	+	0.232960i	−0.950675	+	0.310189i	$0.899608\pi$
$710$	−56.9210	−	56.9210i	−2.13621	−	2.13621i
$711$	2.36564	+	9.18715i	0.0887186	+	0.344545i
$712$	−27.7164	−	11.4805i	−1.03872	−	0.430250i
$713$	22.3607			0.837414
$714$		0			0
$715$	16.0000			0.598366
$716$		0			0
$717$	−2.59827	+	15.2725i	−0.0970343	+	0.570362i
$718$	−42.4264	−	42.4264i	−1.58334	−	1.58334i
$719$	0.827698	+	4.16112i	0.0308679	+	0.155184i	0.993145	−	0.116887i	$-0.0372916\pi$
$719$	0.827698	+	4.16112i	0.0308679	+	0.155184i	−0.962277	+	0.272071i	$0.912292\pi$
$720$	−8.40146	−	1.18977i	−0.313104	−	0.0443400i
$721$	−12.4061	−	2.46772i	−0.462026	−	0.0919027i
$722$	−16.2584	−	39.2513i	−0.605076	−	1.46078i
$723$	31.8342	+	30.1095i	1.18393	+	1.11979i
$724$	11.1047	−	55.8273i	0.412704	−	2.07480i
$725$	7.05525	−	4.71417i	0.262026	−	0.175080i
$726$	28.4322	−	20.1646i	1.05522	−	0.748377i
$727$	5.65685	−	5.65685i	0.209801	−	0.209801i	−0.594382	−	0.804183i	$-0.702603\pi$
$727$	5.65685	−	5.65685i	0.209801	−	0.209801i	0.804183	+	0.594382i	$0.202603\pi$
$728$	23.5175	+	15.7139i	0.871617	+	0.582396i
$729$	14.3354	+	22.8800i	0.530941	+	0.847409i
$730$		0			0
$731$		0			0
$732$	30.0000	−	13.4164i	1.10883	−	0.495885i
$733$	13.0112	−	31.4119i	0.480581	−	1.16023i	−0.478752	−	0.877950i	$-0.658911\pi$
$733$	13.0112	−	31.4119i	0.480581	−	1.16023i	0.959333	−	0.282275i	$-0.0910891\pi$
$734$	19.6424	−	29.3969i	0.725013	−	1.08506i
$735$	5.24419	−	13.7295i	0.193435	−	0.506419i
$736$	46.5227	−	9.25395i	1.71485	−	0.341105i
$737$	−6.28556	−	9.40700i	−0.231532	−	0.346511i
$738$	30.3301	−	22.8054i	1.11647	−	0.839477i
$739$	−22.1731	+	9.18440i	−0.815651	+	0.337854i	−0.751206	−	0.660068i	$-0.770528\pi$
$739$	−22.1731	+	9.18440i	−0.815651	+	0.337854i	−0.0644448	+	0.997921i	$0.520528\pi$
$740$	−49.5806	+	20.5369i	−1.82262	+	0.754953i
$741$		0			0
$742$		0			0
$743$	−6.93520	+	1.37950i	−0.254428	+	0.0506088i	−0.320656	−	0.947196i	$-0.603903\pi$
$743$	−6.93520	+	1.37950i	−0.254428	+	0.0506088i	0.0662284	+	0.997804i	$0.478903\pi$
$744$	11.4412	+	4.37016i	0.419456	+	0.160218i
$745$	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
$750$	0.609761	+	21.9004i	0.0222653	+	0.799690i
$751$	−28.9227	−	19.3255i	−1.05540	−	0.705199i	−0.0983636	−	0.995151i	$-0.531361\pi$
$751$	−28.9227	−	19.3255i	−1.05540	−	0.705199i	−0.957041	+	0.289952i	$0.906361\pi$
$752$	−6.32456	+	6.32456i	−0.230633	+	0.230633i
$753$	−17.9240	−	25.2731i	−0.653189	−	0.921002i
$754$	21.0347	−	14.0549i	0.766039	−	0.511851i
$755$	−11.0360	+	55.4816i	−0.401640	+	2.01918i
$756$	−4.11164	−	49.1233i	−0.149539	−	1.78660i
$757$	4.59220	+	11.0866i	0.166906	+	0.402948i	0.985097	−	0.171999i	$-0.0550227\pi$
$757$	4.59220	+	11.0866i	0.166906	+	0.402948i	−0.818191	+	0.574947i	$0.805023\pi$
$758$	−20.8056	−	4.13849i	−0.755693	−	0.150317i
$759$	14.6637	+	9.21821i	0.532259	+	0.334600i
$760$		0			0
$761$	3.16228	+	3.16228i	0.114632	+	0.114632i	0.762096	−	0.647464i	$-0.224170\pi$
$761$	3.16228	+	3.16228i	0.114632	+	0.114632i	−0.647464	+	0.762096i	$0.724170\pi$
$762$	−45.8175	−	7.79482i	−1.65979	−	0.282377i
$763$	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
$768$	15.3676	+	2.61446i	0.554532	+	0.0943413i
$769$	−14.1421	−	14.1421i	−0.509978	−	0.509978i	0.404541	−	0.914520i	$-0.367431\pi$
$769$	−14.1421	−	14.1421i	−0.509978	−	0.509978i	−0.914520	+	0.404541i	$0.867431\pi$
$770$	5.51799	+	27.7408i	0.198854	+	0.999709i
$771$	32.7891	+	20.6126i	1.18087	+	0.742343i
$772$	37.2182	+	7.40316i	1.33951	+	0.266445i
$773$	−15.4027	−	37.1854i	−0.553997	−	1.33747i	−0.914453	−	0.404691i	$-0.867379\pi$
$773$	−15.4027	−	37.1854i	−0.553997	−	1.33747i	0.360456	−	0.932776i	$-0.382621\pi$
$774$	−8.87319	+	25.3232i	−0.318940	+	0.910225i
$775$	1.85079	−	9.30455i	0.0664823	−	0.334229i
$776$	−23.5175	+	15.7139i	−0.844229	+	0.564096i
$777$	20.0397	+	28.2562i	0.718920	+	1.01368i
$778$	−7.07107	+	7.07107i	−0.253510	+	0.253510i
$779$		0			0
$780$	−1.63616	−	58.7650i	−0.0585840	−	2.10412i
$781$		−	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
$786$	5.11667	+	1.95440i	0.182506	+	0.0697110i
$787$	34.1167	−	6.78623i	1.21613	−	0.241903i	0.454992	−	0.890495i	$-0.349642\pi$
$787$	34.1167	−	6.78623i	1.21613	−	0.241903i	0.761136	+	0.648593i	$0.224642\pi$
$788$	42.4275	+	63.4973i	1.51142	+	2.26200i
$789$	6.88807	+	30.2085i	0.245222	+	1.07545i
$790$	−18.4776	+	7.65367i	−0.657403	+	0.272305i
$791$	−16.5269	+	6.84565i	−0.587627	+	0.243403i
$792$	5.70134	+	7.58253i	0.202588	+	0.269433i
$793$	−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	$-0.772384\pi$
$797$	6.84565	−	16.5269i	0.242485	−	0.585411i	0.997528	+	0.0702638i	$0.0223841\pi$
$798$		0			0
$799$		0			0
$800$		−	20.1246i		−	0.711512i
$801$	36.2708	−	17.4479i	1.28157	−	0.616492i
$802$	10.5174	+	7.02747i	0.371381	+	0.248149i
$803$		0			0
$804$	−33.9074	+	24.0476i	−1.19582	+	0.848095i
$805$	52.5868	−	35.1373i	1.85344	−	1.23843i
$806$	5.51799	−	27.7408i	0.194363	−	0.977128i
$807$	32.0325	+	30.2971i	1.12760	+	1.06651i
$808$	3.82683	+	9.23880i	0.134628	+	0.325020i
$809$	−16.6445	−	3.31079i	−0.585189	−	0.116401i	−0.106388	−	0.994325i	$-0.533928\pi$
$809$	−16.6445	−	3.31079i	−0.585189	−	0.116401i	−0.478801	+	0.877923i	$0.658928\pi$
$810$	−43.5213	+	36.6865i	−1.52918	+	1.28903i
$811$	−9.25395	−	46.5227i	−0.324950	−	1.63363i	−0.705384	−	0.708826i	$-0.749225\pi$
$811$	−9.25395	−	46.5227i	−0.324950	−	1.63363i	0.380434	−	0.924808i	$-0.375775\pi$
$812$	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
$819$	−36.7486	+	9.46257i	−1.28410	+	0.330649i
$820$	33.9411	+	33.9411i	1.18528	+	1.18528i
$821$	−3.86259	−	19.4186i	−0.134805	−	0.677712i	−0.987792	−	0.155779i	$-0.950211\pi$
$821$	−3.86259	−	19.4186i	−0.134805	−	0.677712i	0.852987	−	0.521933i	$-0.174789\pi$
$822$	−9.21821	+	14.6637i	−0.321522	+	0.511456i
$823$	34.1167	+	6.78623i	1.18923	+	0.236553i	0.749764	−	0.661705i	$-0.230167\pi$
$823$	34.1167	+	6.78623i	1.18923	+	0.236553i	0.439468	+	0.898258i	$0.355167\pi$
$824$	−3.42282	−	8.26343i	−0.119240	−	0.287870i
$825$	5.04952	−	5.33876i	0.175802	−	0.185872i
$826$	12.3386	−	62.0303i	0.429315	−	2.15831i
$827$	31.7486	−	21.2138i	1.10401	−	0.737675i	0.136532	−	0.990636i	$-0.456404\pi$
$827$	31.7486	−	21.2138i	1.10401	−	0.737675i	0.967477	+	0.252961i	$0.0814044\pi$
$828$	32.3572	−	54.7997i	1.12449	−	1.90442i
$829$	21.2132	−	21.2132i	0.736765	−	0.736765i	−0.235185	−	0.971951i	$-0.575570\pi$
$829$	21.2132	−	21.2132i	0.736765	−	0.736765i	0.971951	+	0.235185i	$0.0755698\pi$
$830$	−47.0350	−	31.4278i	−1.63261	−	1.09087i
$831$	−10.9502	+	0.304881i	−0.379858	+	0.0105762i
$832$		−	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
$837$	−14.6035	+	7.53244i	−0.504771	+	0.260359i
$838$	21.7106	−	4.31851i	0.749980	−	0.149180i
$839$	5.49986	+	8.23113i	0.189876	+	0.284170i	0.914178	−	0.405313i	$-0.132838\pi$
$839$	5.49986	+	8.23113i	0.189876	+	0.284170i	−0.724301	+	0.689483i	$0.757838\pi$
$840$	33.7741	−	7.70110i	1.16532	−	0.265713i
$841$	−19.4015	+	8.03635i	−0.669016	+	0.277116i
$842$	41.3171	−	17.1141i	1.42388	−	0.589792i
$843$	30.2085	−	6.88807i	1.04044	−	0.237238i
$844$	36.8942	+	55.2161i	1.26995	+	1.90062i
$845$	−8.32224	+	1.65540i	−0.286294	+	0.0569474i
$846$	3.33851	+	59.9070i	0.114780	+	2.05965i
$847$	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
$852$	−66.1106	+	1.84068i	−2.26491	+	0.0630607i
$853$	−5.25868	−	3.51373i	−0.180054	−	0.120308i	0.462277	−	0.886735i	$-0.347032\pi$
$853$	−5.25868	−	3.51373i	−0.180054	−	0.120308i	−0.642331	+	0.766427i	$0.722032\pi$
$854$	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	−0.999998	−	0.00189186i	$-0.999398\pi$
$857$	−2.20720	+	11.0963i	−0.0753963	+	0.379043i	0.924602	+	0.380935i	$0.124398\pi$
$858$	15.0548	−	15.9171i	0.513961	−	0.543401i
$859$	−7.65367	−	18.4776i	−0.261140	−	0.630447i	0.737870	−	0.674943i	$-0.235832\pi$
$859$	−7.65367	−	18.4776i	−0.261140	−	0.630447i	−0.999010	+	0.0444959i	$0.985832\pi$
$860$	−33.2890	−	6.62159i	−1.13514	−	0.225794i
$861$	16.4900	−	26.2313i	0.561979	−	0.893959i
$862$	−5.55237	−	27.9136i	−0.189114	−	0.950742i
$863$	12.6491	+	12.6491i	0.430581	+	0.430581i	0.888826	−	0.458245i	$-0.151522\pi$
$863$	12.6491	+	12.6491i	0.430581	+	0.430581i	−0.458245	+	0.888826i	$0.651522\pi$
$864$	−27.2662	+	21.7153i	−0.927614	+	0.738771i
$865$	−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
$870$	5.19655	−	30.5450i	0.176179	−	1.03557i
$871$	22.6274	+	22.6274i	0.766701	+	0.766701i
$872$	8.27698	+	41.6112i	0.280294	+	1.40913i
$873$	5.32080	−	37.5725i	0.180082	−	1.27163i
$874$		0			0
$875$	6.84565	+	16.5269i	0.231425	+	0.558710i
$876$		0			0
$877$	6.16930	−	31.0152i	0.208322	−	1.04731i	−0.725132	−	0.688610i	$-0.758221\pi$
$877$	6.16930	−	31.0152i	0.208322	−	1.04731i	0.933454	−	0.358697i	$-0.116779\pi$
$878$	41.1556	−	27.4993i	1.38894	−	0.928057i
$879$	−25.2731	+	17.9240i	−0.852440	+	0.604563i
$880$	2.82843	−	2.82843i	0.0953463	−	0.0953463i
$881$	4.70350	+	3.14278i	0.158465	+	0.105883i	0.632275	−	0.774744i	$-0.282121\pi$
$881$	4.70350	+	3.14278i	0.158465	+	0.105883i	−0.473810	+	0.880627i	$0.657121\pi$
$882$	−8.72396	−	18.1354i	−0.293751	−	0.610651i
$883$		−	16.0000i		−	0.538443i	−0.963078	−	0.269221i	$-0.913234\pi$
$883$		−	16.0000i		−	0.538443i	0.963078	−	0.269221i	$-0.0867663\pi$
$884$		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	0.000878410		1.00000i	$0.499720\pi$
$887$	−27.4993	+	41.1556i	−0.923337	+	1.38187i	−0.924215	+	0.381872i	$0.875280\pi$
$888$	−8.74032	+	22.8825i	−0.293306	+	0.767885i
$889$	−37.2182	+	7.40316i	−1.24826	+	0.248294i
$890$	47.1417	+	70.5525i	1.58019	+	2.36493i
$891$	−12.6820	−	1.08068i	−0.424862	−	0.0362041i
$892$	44.3462	−	18.3688i	1.48482	−	0.615033i
$893$		0			0
$894$	−15.4022	−	67.5483i	−0.515127	−	2.25915i
$895$		0			0
$896$	48.5464	−	9.65648i	1.62182	−	0.322600i
$897$	−45.7649	−	17.4806i	−1.52805	−	0.583662i
$898$	−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
$903$	0.609761	+	21.9004i	0.0202916	+	0.728800i
$904$	−10.5174	−	7.02747i	−0.349802	−	0.233730i
$905$	−37.9473	+	37.9473i	−1.26141	+	1.26141i
$906$	44.8101	+	63.1827i	1.48872	+	2.09910i
$907$	−18.4054	+	12.2981i	−0.611140	+	0.408351i	−0.822262	−	0.569109i	$-0.807288\pi$
$907$	−18.4054	+	12.2981i	−0.611140	+	0.408351i	0.211122	+	0.977460i	$0.432288\pi$
$908$	4.13849	−	20.8056i	0.137341	−	0.690458i
$909$	−12.6616	−	4.43660i	−0.419959	−	0.147153i
$910$	−30.6147	−	73.9104i	−1.01487	−	2.45010i
$911$	15.2574	+	3.03489i	0.505501	+	0.100550i	0.441252	−	0.897383i	$-0.354535\pi$
$911$	15.2574	+	3.03489i	0.505501	+	0.100550i	0.0642497	+	0.997934i	$0.479535\pi$
$912$		0			0
$913$	−2.46772	−	12.4061i	−0.0816696	−	0.410581i
$914$	44.2719	+	44.2719i	1.46438	+	1.46438i
$915$	−30.5450	−	5.19655i	−1.00979	−	0.171793i
$916$	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
$921$	−20.4902	−	3.48595i	−0.675175	−	0.114866i
$922$	56.5685	+	56.5685i	1.86299	+	1.86299i
$923$	9.93238	+	49.9334i	0.326928	+	1.64358i
$924$	19.6734	+	12.3675i	0.647209	+	0.406862i
$925$	18.6091	+	3.70158i	0.611863	+	0.121707i
$926$	3.42282	+	8.26343i	0.112481	+	0.271553i
$927$	11.3249	+	3.96821i	0.371958	+	0.130333i
$928$	3.70158	−	18.6091i	0.121510	−	0.610873i
$929$	−32.9245	+	21.9995i	−1.08022	+	0.721779i	−0.962504	−	0.271269i	$-0.912557\pi$
$929$	−32.9245	+	21.9995i	−1.08022	+	0.721779i	−0.117715	+	0.993047i	$0.537557\pi$
$930$	−20.0397	−	28.2562i	−0.657128	−	0.926556i
$931$		0			0
$932$	14.1105	+	9.42834i	0.462205	+	0.308836i
$933$	−0.0681734	−	2.44854i	−0.00223190	−	0.0801616i
$934$			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	−0.910885	−	0.412661i	$-0.864599\pi$
$937$	0.765367	−	1.84776i	0.0250034	−	0.0603637i	0.935888	+	0.352297i	$0.114599\pi$
$938$	−31.4278	+	47.0350i	−1.02615	+	1.53575i
$939$	−40.9334	−	15.6352i	−1.33581	−	0.510234i
$940$	−74.4364	+	14.8063i	−2.42785	+	0.482929i
$941$	20.4281	+	30.5728i	0.665936	+	0.996644i	0.998563	+	0.0535853i	$0.0170649\pi$
$941$	20.4281	+	30.5728i	0.665936	+	0.996644i	−0.332627	+	0.943058i	$0.607935\pi$
$942$	1.72202	+	7.55213i	0.0561064	+	0.246062i
$943$	36.9552	−	15.3073i	1.20343	−	0.498475i
$944$	−8.26343	+	3.42282i	−0.268952	+	0.111403i
$945$	−22.5074	+	40.6622i	−0.732166	+	1.32274i
$946$	−7.02747	−	10.5174i	−0.228483	−	0.341949i
$947$	−48.5464	+	9.65648i	−1.57755	+	0.313793i	−0.904720	−	0.426007i	$-0.859920\pi$
$947$	−48.5464	+	9.65648i	−1.57755	+	0.313793i	−0.672826	+	0.739801i	$0.734920\pi$
$948$	−5.86319	+	15.3500i	−0.190427	+	0.498545i
$949$		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
$957$	5.65123	−	4.00794i	0.182678	−	0.129558i
$958$	−18.4054	+	12.2981i	−0.594650	+	0.397333i
$959$	−2.75899	+	13.8704i	−0.0890926	+	0.447899i
$960$	−46.2692	−	43.7625i	−1.49333	−	1.41243i
$961$	8.03635	+	19.4015i	0.259237	+	0.625854i
$962$	55.4816	+	11.0360i	1.78880	+	0.355814i
$963$	−1.78465	+	12.6022i	−0.0575096	+	0.406100i
$964$	14.8063	+	74.4364i	0.476879	+	2.39743i
$965$	−25.2982	−	25.2982i	−0.814379	−	0.814379i
$966$	14.5248	−	85.3758i	0.467328	−	2.74692i
$967$	29.5641	+	12.2459i	0.950719	+	0.393801i	0.803501	−	0.595303i	$-0.202968\pi$
$967$	29.5641	+	12.2459i	0.950719	+	0.393801i	0.147218	+	0.989104i	$0.452968\pi$
$968$	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	$-0.516681\pi$
$971$	−24.7903	−	10.2685i	−0.795558	−	0.329531i	−0.743176	+	0.669096i	$0.766681\pi$
$972$	−2.67227	+	46.6890i	−0.0857132	+	1.49755i
$973$	−7.07107	−	7.07107i	−0.226688	−	0.226688i
$974$	−12.4155	−	62.4168i	−0.397817	−	1.99996i
$975$	−11.0619	+	17.5965i	−0.354263	+	0.563538i
$976$	−6.20303	−	1.23386i	−0.198554	−	0.0394949i
$977$	−6.84565	−	16.5269i	−0.219012	−	0.528741i	0.775741	−	0.631052i	$-0.217376\pi$
$977$	−6.84565	−	16.5269i	−0.219012	−	0.528741i	−0.994753	+	0.102311i	$0.967376\pi$
$978$	−25.2476	+	26.6938i	−0.807330	+	0.853573i
$979$	−3.70158	+	18.6091i	−0.118303	+	0.594749i
$980$	21.1658	−	14.1425i	0.676115	−	0.451766i
$981$	−49.0144	−	28.9412i	−1.56491	−	0.924022i
$982$	28.2843	−	28.2843i	0.902587	−	0.902587i
$983$	−29.3969	−	19.6424i	−0.937615	−	0.626494i	−0.00996724	−	0.999950i	$-0.503173\pi$
$983$	−29.3969	−	19.6424i	−0.937615	−	0.626494i	−0.927648	+	0.373456i	$0.878173\pi$
$984$	21.9004	−	0.609761i	0.698160	−	0.0194385i
$985$		−	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
$990$	−1.49302	−	26.7912i	−0.0474514	−	0.851482i
$991$	34.1167	−	6.78623i	1.08375	−	0.215572i	0.379265	−	0.925288i	$-0.376177\pi$
$991$	34.1167	−	6.78623i	1.08375	−	0.215572i	0.704487	+	0.709717i	$0.251177\pi$
$992$	−11.7854	−	17.6381i	−0.374188	−	0.560011i
$993$	−47.2838	+	10.7815i	−1.50051	+	0.342142i
$994$	−83.1492	+	34.4415i	−2.63733	+	1.09242i
$995$	−24.7903	+	10.2685i	−0.785905	+	0.325533i
$996$	−45.3128	+	10.3321i	−1.43579	+	0.327385i
$997$	3.51373	+	5.25868i	0.111281	+	0.166544i	0.882930	−	0.469505i	$-0.155568\pi$
$997$	3.51373	+	5.25868i	0.111281	+	0.166544i	−0.771649	+	0.636049i	$0.780568\pi$
$998$	6.93520	−	1.37950i	0.219530	−	0.0436672i
$999$	−15.0649	−	29.2070i	−0.476632	−	0.924069i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-2.06586 - 0.855706i) q^{2} +(1.70752 + 0.290496i) q^{3} +(2.12132 + 2.12132i) q^{4} +(-0.551799 - 2.77408i) q^{5} +(-3.27891 - 2.06126i) q^{6} +(-3.10152 - 0.616930i) q^{7} +(-0.855706 - 2.06586i) q^{8} +(2.83122 + 0.992053i) q^{9} +O(q^{10})\)	\(q+(-2.06586 - 0.855706i) q^{2} +(1.70752 + 0.290496i) q^{3} +(2.12132 + 2.12132i) q^{4} +(-0.551799 - 2.77408i) q^{5} +(-3.27891 - 2.06126i) q^{6} +(-3.10152 - 0.616930i) q^{7} +(-0.855706 - 2.06586i) q^{8} +(2.83122 + 0.992053i) q^{9} +(-1.23386 + 6.20303i) q^{10} +(-1.17588 + 0.785695i) q^{11} +(3.00595 + 4.23842i) q^{12} +(2.82843 - 2.82843i) q^{13} +(5.87938 + 3.92847i) q^{14} +(-0.136347 - 4.89708i) q^{15} -1.00000i q^{16} +(-5.00000 - 4.47214i) q^{18} +(4.71417 - 7.05525i) q^{20} +(-5.11667 - 1.95440i) q^{21} +(3.10152 - 0.616930i) q^{22} +(-3.92847 - 5.87938i) q^{23} +(-0.861009 - 3.77606i) q^{24} +(-2.77164 + 1.14805i) q^{25} +(-8.26343 + 3.42282i) q^{26} +(4.54617 + 2.51641i) q^{27} +(-5.27060 - 7.88801i) q^{28} +(-2.77408 + 0.551799i) q^{29} +(-3.90879 + 10.2333i) q^{30} +(-1.75687 + 2.62934i) q^{31} +(-2.56712 + 6.19757i) q^{32} +(-2.23607 + 1.00000i) q^{33} +8.94427i q^{35} +(3.90147 + 8.11040i) q^{36} +(-5.25868 - 3.51373i) q^{37} +(5.65123 - 4.00794i) q^{39} +(-5.25868 + 3.51373i) q^{40} +(-1.10360 + 5.54816i) q^{41} +(8.89793 + 8.41587i) q^{42} +(-1.53073 - 3.69552i) q^{43} +(-4.16112 - 0.827698i) q^{44} +(1.18977 - 8.40146i) q^{45} +(3.08465 + 15.5076i) q^{46} +(-6.32456 - 6.32456i) q^{47} +(0.290496 - 1.70752i) q^{48} +(2.77164 + 1.14805i) q^{49} +6.70820 q^{50} +12.0000 q^{52} +(-7.23844 - 9.08872i) 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} +(10.0990 - 10.6775i) q^{60} +(1.23386 - 6.20303i) q^{61} +(5.87938 - 3.92847i) q^{62} +(-8.16906 - 4.82353i) q^{63} +(9.19239 - 9.19239i) q^{64} +(-9.40700 - 6.28556i) q^{65} +(5.47510 - 0.152440i) q^{66} +8.00000i q^{67} +(-5.00000 - 11.1803i) q^{69} +(7.65367 - 18.4776i) q^{70} +(-7.07125 + 10.5829i) q^{71} +(-0.373256 - 6.69781i) q^{72} +(7.85695 + 11.7588i) q^{74} +(-5.06612 + 1.15517i) q^{75} +(4.13171 - 1.71141i) q^{77} +(-15.1043 + 3.44404i) q^{78} +(1.75687 + 2.62934i) q^{79} +(-2.77408 + 0.551799i) q^{80} +(7.03166 + 5.61745i) q^{81} +(7.02747 - 10.5174i) q^{82} +(-3.42282 + 8.26343i) q^{83} +(-6.70820 - 15.0000i) q^{84} +8.94427i q^{86} +(-4.89708 + 0.136347i) q^{87} +(2.62934 + 1.75687i) q^{88} +(9.48683 - 9.48683i) q^{89} +(-9.64707 + 16.3381i) q^{90} +(-10.5174 + 7.02747i) q^{91} +(4.13849 - 20.8056i) q^{92} +(-3.76369 + 3.97927i) q^{93} +(7.65367 + 18.4776i) q^{94} +(-6.18377 + 9.83672i) q^{96} +(-2.46772 - 12.4061i) q^{97} +(-4.74342 - 4.74342i) q^{98} +(-4.10862 + 1.05795i) 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

Related objects

Downloads

Learn more