LMFDB - Embedded newform 608.2.s.c.559.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [608,2,Mod(335,608)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(608, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("608.335"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 608 = 2^{5} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	608.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.85490444289$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.11
Character	$\chi$	$=$	608.559
Dual form			608.2.s.c.335.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.03079 + 1.17247i) q^{3} +(-1.50560 - 0.869259i) q^{5} -2.63359i q^{7} +(1.24939 + 2.16401i) q^{9} +3.51485 q^{11} +(3.13303 + 5.42656i) q^{13} +(-2.03837 - 3.53056i) q^{15} +(-0.535037 + 0.926710i) q^{17} +(3.79871 + 2.13770i) q^{19} +(3.08781 - 5.34825i) q^{21} +(5.79041 - 3.34309i) q^{23} +(-0.988779 - 1.71262i) q^{25} -1.17531i q^{27} +(-0.579314 - 1.00340i) q^{29} +3.82638 q^{31} +(7.13790 + 4.12107i) q^{33} +(-2.28927 + 3.96513i) q^{35} -3.55090 q^{37} +14.6936i q^{39} +(-4.54864 - 2.62616i) q^{41} +(0.164324 - 0.284617i) q^{43} -4.34419i q^{45} +(-6.68209 + 3.85791i) q^{47} +0.0642261 q^{49} +(-2.17309 + 1.25463i) q^{51} +(-0.526815 - 0.912471i) q^{53} +(-5.29195 - 3.05531i) q^{55} +(5.20797 + 8.79511i) q^{57} +(-8.45232 - 4.87995i) q^{59} +(-11.2916 + 6.51920i) q^{61} +(5.69912 - 3.29039i) q^{63} -10.8936i q^{65} +(-12.3705 + 7.14213i) q^{67} +15.6788 q^{69} +(0.554279 - 0.960040i) q^{71} +(-5.98385 + 10.3643i) q^{73} -4.63727i q^{75} -9.25665i q^{77} +(-1.02065 + 1.76782i) q^{79} +(5.12621 - 8.87886i) q^{81} +11.0796 q^{83} +(1.61110 - 0.930170i) q^{85} -2.71693i q^{87} +(2.18737 - 1.26288i) q^{89} +(14.2913 - 8.25110i) q^{91} +(7.77056 + 4.48634i) q^{93} +(-3.86113 - 6.52059i) q^{95} +(0.354186 + 0.204489i) q^{97} +(4.39143 + 7.60618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 6 q^{3} + 8 q^{9} + 16 q^{11} - 22 q^{17} - 4 q^{19} + 16 q^{25} + 36 q^{33} + 28 q^{35} + 6 q^{41} - 30 q^{43} - 68 q^{49} + 42 q^{51} - 26 q^{57} + 18 q^{59} - 78 q^{67} + 14 q^{73} + 6 q^{81}+ \cdots + 28 q^{99}+O(q^{100}) $ 28 * q + 6 * q^3 + 8 * q^9 + 16 * q^11 - 22 * q^17 - 4 * q^19 + 16 * q^25 + 36 * q^33 + 28 * q^35 + 6 * q^41 - 30 * q^43 - 68 * q^49 + 42 * q^51 - 26 * q^57 + 18 * q^59 - 78 * q^67 + 14 * q^73 + 6 * q^81 + 32 * q^83 - 18 * q^89 + 12 * q^91 + 30 * q^97 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/608\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.03079	+	1.17247i	1.17247	+	0.676929i	0.954262	−	0.298972i	$-0.0966439\pi$
$3$	2.03079	+	1.17247i	1.17247	+	0.676929i	0.218213	+	0.975901i	$0.429977\pi$
$4$		0			0
$5$	−1.50560	−	0.869259i	−0.673325	−	0.388744i	0.124010	−	0.992281i	$-0.460424\pi$
$5$	−1.50560	−	0.869259i	−0.673325	−	0.388744i	−0.797335	+	0.603537i	$0.793758\pi$
$6$		0			0
$7$		−	2.63359i		−	0.995402i	−0.867349	−	0.497701i	$-0.834178\pi$
$7$		−	2.63359i		−	0.995402i	0.867349	−	0.497701i	$-0.165822\pi$
$8$		0			0
$9$	1.24939	+	2.16401i	0.416465	+	0.721338i
$10$		0			0
$11$	3.51485			1.05977			0.529883	−	0.848071i	$-0.322236\pi$
$11$	3.51485			1.05977			0.529883	+	0.848071i	$0.322236\pi$
$12$		0			0
$13$	3.13303	+	5.42656i	0.868946	+	1.50506i	0.863075	+	0.505075i	$0.168535\pi$
$13$	3.13303	+	5.42656i	0.868946	+	1.50506i	0.00587005	+	0.999983i	$0.498131\pi$
$14$		0			0
$15$	−2.03837	−	3.53056i	−0.526304	−	0.911586i
$16$		0			0
$17$	−0.535037	+	0.926710i	−0.129765	+	0.224760i	−0.923586	−	0.383392i	$-0.874756\pi$
$17$	−0.535037	+	0.926710i	−0.129765	+	0.224760i	0.793820	+	0.608153i	$0.208089\pi$
$18$		0			0
$19$	3.79871	+	2.13770i	0.871485	+	0.490422i
$19$	3.79871	+	2.13770i	0.871485	+	0.490422i
$20$		0			0
$21$	3.08781	−	5.34825i	0.673816	−	1.16708i
$22$		0			0
$23$	5.79041	−	3.34309i	1.20738	−	0.697083i	0.245196	−	0.969473i	$-0.421148\pi$
$23$	5.79041	−	3.34309i	1.20738	−	0.697083i	0.962187	+	0.272390i	$0.0878142\pi$
$24$		0			0
$25$	−0.988779	−	1.71262i	−0.197756	−	0.342523i
$26$		0			0
$27$		−	1.17531i		−	0.226189i
$28$		0			0
$29$	−0.579314	−	1.00340i	−0.107576	−	0.186327i	0.807212	−	0.590262i	$-0.200976\pi$
$29$	−0.579314	−	1.00340i	−0.107576	−	0.186327i	−0.914788	+	0.403935i	$0.867642\pi$
$30$		0			0
$31$	3.82638			0.687238			0.343619	−	0.939109i	$-0.388347\pi$
$31$	3.82638			0.687238			0.343619	+	0.939109i	$0.388347\pi$
$32$		0			0
$33$	7.13790	+	4.12107i	1.24255	+	0.717386i
$34$		0			0
$35$	−2.28927	+	3.96513i	−0.386957	+	0.670229i
$36$		0			0
$37$	−3.55090			−0.583764			−0.291882	−	0.956454i	$-0.594281\pi$
$37$	−3.55090			−0.583764			−0.291882	+	0.956454i	$0.594281\pi$
$38$		0			0
$39$			14.6936i			2.35286i
$40$		0			0
$41$	−4.54864	−	2.62616i	−0.710378	−	0.410137i	0.100823	−	0.994904i	$-0.467852\pi$
$41$	−4.54864	−	2.62616i	−0.710378	−	0.410137i	−0.811201	+	0.584767i	$0.801186\pi$
$42$		0			0
$43$	0.164324	−	0.284617i	0.0250591	−	0.0434036i	−0.853224	−	0.521545i	$-0.825356\pi$
$43$	0.164324	−	0.284617i	0.0250591	−	0.0434036i	0.878283	+	0.478141i	$0.158689\pi$
$44$		0			0
$45$		−	4.34419i		−	0.647593i
$46$		0			0
$47$	−6.68209	+	3.85791i	−0.974683	+	0.562733i	−0.900661	−	0.434523i	$-0.856917\pi$
$47$	−6.68209	+	3.85791i	−0.974683	+	0.562733i	−0.0740221	+	0.997257i	$0.523584\pi$
$48$		0			0
$49$	0.0642261			0.00917515
$50$		0			0
$51$	−2.17309	+	1.25463i	−0.304293	+	0.175684i
$52$		0			0
$53$	−0.526815	−	0.912471i	−0.0723636	−	0.125338i	0.827573	−	0.561358i	$-0.189721\pi$
$53$	−0.526815	−	0.912471i	−0.0723636	−	0.125338i	−0.899937	+	0.436020i	$0.856388\pi$
$54$		0			0
$55$	−5.29195	−	3.05531i	−0.713567	−	0.411978i
$56$		0			0
$57$	5.20797	+	8.79511i	0.689813	+	1.16494i
$58$		0			0
$59$	−8.45232	−	4.87995i	−1.10040	−	0.635315i	−0.164073	−	0.986448i	$-0.552463\pi$
$59$	−8.45232	−	4.87995i	−1.10040	−	0.635315i	−0.936326	+	0.351133i	$0.885796\pi$
$60$		0			0
$61$	−11.2916	+	6.51920i	−1.44574	+	0.834698i	−0.998224	−	0.0595773i	$-0.981025\pi$
$61$	−11.2916	+	6.51920i	−1.44574	+	0.834698i	−0.447516	+	0.894276i	$0.647691\pi$
$62$		0			0
$63$	5.69912	−	3.29039i	0.718021	−	0.414550i
$64$		0			0
$65$		−	10.8936i		−	1.35119i
$66$		0			0
$67$	−12.3705	+	7.14213i	−1.51130	+	0.872549i	−0.511387	+	0.859350i	$0.670868\pi$
$67$	−12.3705	+	7.14213i	−1.51130	+	0.872549i	−0.999913	+	0.0131990i	$0.995798\pi$
$68$		0			0
$69$	15.6788			1.88750
$70$		0			0
$71$	0.554279	−	0.960040i	0.0657808	−	0.113936i	−0.831259	−	0.555885i	$-0.812380\pi$
$71$	0.554279	−	0.960040i	0.0657808	−	0.113936i	0.897040	+	0.441949i	$0.145713\pi$
$72$		0			0
$73$	−5.98385	+	10.3643i	−0.700356	+	1.21305i	0.267985	+	0.963423i	$0.413642\pi$
$73$	−5.98385	+	10.3643i	−0.700356	+	1.21305i	−0.968341	+	0.249630i	$0.919691\pi$
$74$		0			0
$75$		−	4.63727i		−	0.535466i
$76$		0			0
$77$		−	9.25665i		−	1.05489i
$78$		0			0
$79$	−1.02065	+	1.76782i	−0.114832	+	0.198895i	−0.917713	−	0.397245i	$-0.869966\pi$
$79$	−1.02065	+	1.76782i	−0.114832	+	0.198895i	0.802881	+	0.596140i	$0.203300\pi$
$80$		0			0
$81$	5.12621	−	8.87886i	0.569579	−	0.986540i
$82$		0			0
$83$	11.0796			1.21615			0.608073	−	0.793881i	$-0.291943\pi$
$83$	11.0796			1.21615			0.608073	+	0.793881i	$0.291943\pi$
$84$		0			0
$85$	1.61110	−	0.930170i	0.174749	−	0.100891i
$86$		0			0
$87$		−	2.71693i		−	0.291285i
$88$		0			0
$89$	2.18737	−	1.26288i	0.231861	−	0.133865i	−0.379569	−	0.925163i	$-0.623928\pi$
$89$	2.18737	−	1.26288i	0.231861	−	0.133865i	0.611430	+	0.791298i	$0.290594\pi$
$90$		0			0
$91$	14.2913	−	8.25110i	1.49814	−	0.864950i
$92$		0			0
$93$	7.77056	+	4.48634i	0.805770	+	0.465211i
$94$		0			0
$95$	−3.86113	−	6.52059i	−0.396143	−	0.668998i
$96$		0			0
$97$	0.354186	+	0.204489i	0.0359622	+	0.0207628i	0.517873	−	0.855457i	$-0.326724\pi$
$97$	0.354186	+	0.204489i	0.0359622	+	0.0207628i	−0.481911	+	0.876220i	$0.660057\pi$
$98$		0			0
$99$	4.39143	+	7.60618i	0.441355	+	0.764450i
$100$		0			0
$101$	−14.9614	+	8.63798i	−1.48872	+	0.859511i	−0.999917	−	0.0128855i	$-0.995898\pi$
$101$	−14.9614	+	8.63798i	−1.48872	+	0.859511i	−0.488799	+	0.872396i	$0.662565\pi$
$102$		0			0
$103$	−1.22345			−0.120551			−0.0602753	−	0.998182i	$-0.519198\pi$
$103$	−1.22345			−0.120551			−0.0602753	+	0.998182i	$0.519198\pi$
$104$		0			0
$105$	−9.29802	+	5.36822i	−0.907394	+	0.523884i
$106$		0			0
$107$		−	9.53314i		−	0.921604i	−0.887503	−	0.460802i	$-0.847562\pi$
$107$		−	9.53314i		−	0.921604i	0.887503	−	0.460802i	$-0.152438\pi$
$108$		0			0
$109$	8.32099	−	14.4124i	0.797006	−	1.38045i	−0.124552	−	0.992213i	$-0.539749\pi$
$109$	8.32099	−	14.4124i	0.797006	−	1.38045i	0.921558	−	0.388241i	$-0.126917\pi$
$110$		0			0
$111$	−7.21111	−	4.16334i	−0.684448	−	0.395166i
$112$		0			0
$113$		−	11.1836i		−	1.05206i	−0.850465	−	0.526032i	$-0.823679\pi$
$113$		−	11.1836i		−	1.05206i	0.850465	−	0.526032i	$-0.176321\pi$
$114$		0			0
$115$	−11.6240			−1.08395
$116$		0			0
$117$	−7.82877	+	13.5598i	−0.723770	+	1.25361i
$118$		0			0
$119$	2.44057	+	1.40906i	0.223727	+	0.129169i
$120$		0			0
$121$	1.35414			0.123104
$122$		0			0
$123$	−6.15821	−	10.6663i	−0.555267	−	0.961750i
$124$		0			0
$125$			12.1306i			1.08499i
$126$		0			0
$127$	6.15278	+	10.6569i	0.545971	+	0.945650i	0.998545	+	0.0539229i	$0.0171725\pi$
$127$	6.15278	+	10.6569i	0.545971	+	0.945650i	−0.452574	+	0.891727i	$0.649494\pi$
$128$		0			0
$129$	0.667412	−	0.385330i	0.0587623	−	0.0339264i
$130$		0			0
$131$	−2.13527	+	3.69840i	−0.186560	+	0.323131i	−0.944101	−	0.329656i	$-0.893067\pi$
$131$	−2.13527	+	3.69840i	−0.186560	+	0.323131i	0.757541	+	0.652787i	$0.226400\pi$
$132$		0			0
$133$	5.62982	−	10.0042i	0.488167	−	0.867478i
$134$		0			0
$135$	−1.02165	+	1.76955i	−0.0879299	+	0.152299i
$136$		0			0
$137$	−4.80955	−	8.33038i	−0.410907	−	0.711712i	0.584082	−	0.811695i	$-0.301455\pi$
$137$	−4.80955	−	8.33038i	−0.410907	−	0.711712i	−0.994989	+	0.0999823i	$0.968121\pi$
$138$		0			0
$139$	1.71132	+	2.96409i	0.145152	+	0.251411i	0.929430	−	0.368999i	$-0.120300\pi$
$139$	1.71132	+	2.96409i	0.145152	+	0.251411i	−0.784278	+	0.620410i	$0.786966\pi$
$140$		0			0
$141$	−18.0932			−1.52372
$142$		0			0
$143$	11.0121	+	19.0735i	0.920879	+	1.59501i
$144$		0			0
$145$			2.01430i			0.167278i
$146$		0			0
$147$	0.130429	+	0.0753035i	0.0107576	+	0.00621092i
$148$		0			0
$149$	−4.61838	−	2.66643i	−0.378353	−	0.218442i	0.298749	−	0.954332i	$-0.403431\pi$
$149$	−4.61838	−	2.66643i	−0.378353	−	0.218442i	−0.677101	+	0.735890i	$0.736764\pi$
$150$		0			0
$151$	12.8756			1.04780			0.523899	−	0.851780i	$-0.324477\pi$
$151$	12.8756			1.04780			0.523899	+	0.851780i	$0.324477\pi$
$152$		0			0
$153$	−2.67389			−0.216171
$154$		0			0
$155$	−5.76100	−	3.32611i	−0.462735	−	0.267160i
$156$		0			0
$157$	10.7727	+	6.21961i	0.859754	+	0.496379i	0.863930	−	0.503612i	$-0.167996\pi$
$157$	10.7727	+	6.21961i	0.859754	+	0.496379i	−0.00417613	+	0.999991i	$0.501329\pi$
$158$		0			0
$159$		−	2.47071i		−	0.195940i
$160$		0			0
$161$	−8.80432	−	15.2495i	−0.693878	−	1.20183i
$162$		0			0
$163$	−12.0962			−0.947449			−0.473724	−	0.880673i	$-0.657091\pi$
$163$	−12.0962			−0.947449			−0.473724	+	0.880673i	$0.657091\pi$
$164$		0			0
$165$	−7.16455	−	12.4094i	−0.557759	−	0.966067i
$166$		0			0
$167$	−12.3200	−	21.3389i	−0.953352	−	1.65125i	−0.738094	−	0.674698i	$-0.764274\pi$
$167$	−12.3200	−	21.3389i	−0.953352	−	1.65125i	−0.215258	−	0.976557i	$-0.569059\pi$
$168$		0			0
$169$	−13.1317	+	22.7448i	−1.01013	+	1.74960i
$170$		0			0
$171$	0.120074	+	10.8913i	0.00918232	+	0.832879i
$172$		0			0
$173$	−1.29936	+	2.25057i	−0.0987889	+	0.171107i	−0.911184	−	0.412001i	$-0.864830\pi$
$173$	−1.29936	+	2.25057i	−0.0987889	+	0.171107i	0.812395	+	0.583108i	$0.198164\pi$
$174$		0			0
$175$	−4.51032	+	2.60403i	−0.340948	+	0.196846i
$176$		0			0
$177$	−11.4432	−	19.8203i	−0.860126	−	1.48978i
$178$		0			0
$179$			1.92541i			0.143912i	0.997408	+	0.0719559i	$0.0229241\pi$
$179$			1.92541i			0.143912i	−0.997408	+	0.0719559i	$0.977076\pi$
$180$		0			0
$181$	8.78786	+	15.2210i	0.653196	+	1.13137i	0.982343	+	0.187091i	$0.0599058\pi$
$181$	8.78786	+	15.2210i	0.653196	+	1.13137i	−0.329146	+	0.944279i	$0.606761\pi$
$182$		0			0
$183$	−30.5744			−2.26013
$184$		0			0
$185$	5.34623	+	3.08665i	0.393063	+	0.226935i
$186$		0			0
$187$	−1.88057	+	3.25724i	−0.137521	+	0.238193i
$188$		0			0
$189$	−3.09529			−0.225149
$190$		0			0
$191$		−	3.45229i		−	0.249799i	−0.992169	−	0.124900i	$-0.960139\pi$
$191$		−	3.45229i		−	0.249799i	0.992169	−	0.124900i	$-0.0398609\pi$
$192$		0			0
$193$	6.81683	+	3.93570i	0.490686	+	0.283298i	0.724859	−	0.688897i	$-0.241905\pi$
$193$	6.81683	+	3.93570i	0.490686	+	0.283298i	−0.234173	+	0.972195i	$0.575238\pi$
$194$		0			0
$195$	12.7725	−	22.1227i	0.914659	−	1.58424i
$196$		0			0
$197$			14.5485i			1.03653i	0.855219	+	0.518267i	$0.173423\pi$
$197$			14.5485i			1.03653i	−0.855219	+	0.518267i	$0.826577\pi$
$198$		0			0
$199$	−4.90638	+	2.83270i	−0.347804	+	0.200805i	−0.663718	−	0.747983i	$-0.731022\pi$
$199$	−4.90638	+	2.83270i	−0.347804	+	0.200805i	0.315914	+	0.948788i	$0.397689\pi$
$200$		0			0
$201$	−33.4958			−2.36261
$202$		0			0
$203$	−2.64254	+	1.52567i	−0.185470	+	0.107081i
$204$		0			0
$205$	4.56562	+	7.90789i	0.318877	+	0.552311i
$206$		0			0
$207$	14.4690	+	8.35368i	1.00567	+	0.580621i
$208$		0			0
$209$	13.3519	+	7.51369i	0.923570	+	0.519733i
$210$		0			0
$211$	1.22935	+	0.709763i	0.0846317	+	0.0488621i	0.541719	−	0.840560i	$-0.317774\pi$
$211$	1.22935	+	0.709763i	0.0846317	+	0.0488621i	−0.457087	+	0.889422i	$0.651107\pi$
$212$		0			0
$213$	2.25124	−	1.29976i	0.154253	−	0.0890579i
$214$		0			0
$215$	−0.494811	+	0.285679i	−0.0337458	+	0.0194832i
$216$		0			0
$217$		−	10.0771i		−	0.684078i
$218$		0			0
$219$	−24.3038	+	14.0318i	−1.64230	+	0.948182i
$220$		0			0
$221$	−6.70514			−0.451036
$222$		0			0
$223$	9.02397	−	15.6300i	0.604290	−	1.04666i	−0.387874	−	0.921713i	$-0.626790\pi$
$223$	9.02397	−	15.6300i	0.604290	−	1.04666i	0.992163	−	0.124948i	$-0.0398764\pi$
$224$		0			0
$225$	2.47075	−	4.27946i	0.164717	−	0.285298i
$226$		0			0
$227$		−	17.6838i		−	1.17371i	−0.809691	−	0.586857i	$-0.800365\pi$
$227$		−	17.6838i		−	1.17371i	0.809691	−	0.586857i	$-0.199635\pi$
$228$		0			0
$229$		−	5.53546i		−	0.365793i	−0.983132	−	0.182897i	$-0.941453\pi$
$229$		−	5.53546i		−	0.365793i	0.983132	−	0.182897i	$-0.0585474\pi$
$230$		0			0
$231$	10.8532	−	18.7983i	0.714087	−	1.23684i
$232$		0			0
$233$	−9.43030	+	16.3338i	−0.617799	+	1.07006i	0.372087	+	0.928198i	$0.378642\pi$
$233$	−9.43030	+	16.3338i	−0.617799	+	1.07006i	−0.989886	+	0.141862i	$0.954691\pi$
$234$		0			0
$235$	13.4141			0.875037
$236$		0			0
$237$	−4.14544	+	2.39337i	−0.269275	+	0.155466i
$238$		0			0
$239$		−	8.91252i		−	0.576503i	−0.957555	−	0.288251i	$-0.906926\pi$
$239$		−	8.91252i		−	0.576503i	0.957555	−	0.288251i	$-0.0930739\pi$
$240$		0			0
$241$	10.6275	−	6.13581i	0.684580	−	0.395242i	−0.116999	−	0.993132i	$-0.537327\pi$
$241$	10.6275	−	6.13581i	0.684580	−	0.395242i	0.801578	+	0.597890i	$0.203994\pi$
$242$		0			0
$243$	17.7669	−	10.2577i	1.13975	−	0.658034i
$244$		0			0
$245$	−0.0966988	−	0.0558291i	−0.00617786	−	0.00356679i
$246$		0			0
$247$	0.301103	+	27.3114i	0.0191587	+	1.73779i
$248$		0			0
$249$	22.5003	+	12.9906i	1.42590	+	0.823244i
$250$		0			0
$251$	6.34526	+	10.9903i	0.400510	+	0.693703i	0.993787	−	0.111295i	$-0.0354998\pi$
$251$	6.34526	+	10.9903i	0.400510	+	0.693703i	−0.593278	+	0.804998i	$0.702166\pi$
$252$		0			0
$253$	20.3524	−	11.7505i	1.27954	−	0.738745i
$254$		0			0
$255$	4.36240			0.273184
$256$		0			0
$257$	−15.8394	+	9.14489i	−0.988035	+	0.570442i	−0.904686	−	0.426078i	$-0.859895\pi$
$257$	−15.8394	+	9.14489i	−0.988035	+	0.570442i	−0.0833488	+	0.996520i	$0.526562\pi$
$258$		0			0
$259$			9.35159i			0.581080i
$260$		0			0
$261$	1.44758	−	2.50729i	0.0896032	−	0.155197i
$262$		0			0
$263$	17.6630	+	10.1978i	1.08915	+	0.628821i	0.933350	−	0.358968i	$-0.116871\pi$
$263$	17.6630	+	10.1978i	1.08915	+	0.628821i	0.155799	+	0.987789i	$0.450205\pi$
$264$		0			0
$265$			1.83175i			0.112524i
$266$		0			0
$267$	5.92279			0.362469
$268$		0			0
$269$	2.66106	−	4.60909i	0.162248	−	0.281021i	−0.773427	−	0.633886i	$-0.781459\pi$
$269$	2.66106	−	4.60909i	0.162248	−	0.281021i	0.935674	+	0.352864i	$0.114792\pi$
$270$		0			0
$271$	−18.8199	−	10.8657i	−1.14323	−	0.660044i	−0.196002	−	0.980604i	$-0.562796\pi$
$271$	−18.8199	−	10.8657i	−1.14323	−	0.660044i	−0.947228	+	0.320559i	$0.896129\pi$
$272$		0			0
$273$	38.6968			2.34204
$274$		0			0
$275$	−3.47541	−	6.01958i	−0.209575	−	0.362994i
$276$		0			0
$277$		−	5.64662i		−	0.339273i	−0.985507	−	0.169636i	$-0.945741\pi$
$277$		−	5.64662i		−	0.339273i	0.985507	−	0.169636i	$-0.0542593\pi$
$278$		0			0
$279$	4.78066	+	8.28034i	0.286211	+	0.495731i
$280$		0			0
$281$	21.8341	−	12.6059i	1.30251	−	0.752005i	0.321677	−	0.946849i	$-0.395753\pi$
$281$	21.8341	−	12.6059i	1.30251	−	0.752005i	0.980834	+	0.194844i	$0.0624201\pi$
$282$		0			0
$283$	−15.2893	+	26.4818i	−0.908852	+	1.57418i	−0.0931914	+	0.995648i	$0.529707\pi$
$283$	−15.2893	+	26.4818i	−0.908852	+	1.57418i	−0.815661	+	0.578530i	$0.803627\pi$
$284$		0			0
$285$	−0.195900	−	17.7690i	−0.0116041	−	1.05254i
$286$		0			0
$287$	−6.91621	+	11.9792i	−0.408251	+	0.707112i
$288$		0			0
$289$	7.92747	+	13.7308i	0.466322	+	0.807693i
$290$		0			0
$291$	0.479518	+	0.830549i	0.0281098	+	0.0486876i
$292$		0			0
$293$	6.91254			0.403835			0.201918	−	0.979403i	$-0.435283\pi$
$293$	6.91254			0.403835			0.201918	+	0.979403i	$0.435283\pi$
$294$		0			0
$295$	8.48387	+	14.6945i	0.493950	+	0.855547i
$296$		0			0
$297$		−	4.13105i		−	0.239708i
$298$		0			0
$299$	36.2830	+	20.9480i	2.09830	+	1.21145i
$300$		0			0
$301$	−0.749562	−	0.432760i	−0.0432041	−	0.0249439i
$302$		0			0
$303$	−40.5112			−2.32731
$304$		0			0
$305$	22.6675			1.29794
$306$		0			0
$307$	4.83749	+	2.79293i	0.276090	+	0.159401i	0.631652	−	0.775252i	$-0.282377\pi$
$307$	4.83749	+	2.79293i	0.276090	+	0.159401i	−0.355562	+	0.934653i	$0.615711\pi$
$308$		0			0
$309$	−2.48457	−	1.43447i	−0.141342	−	0.0816041i
$310$		0			0
$311$		−	3.40979i		−	0.193351i	−0.995316	−	0.0966757i	$-0.969179\pi$
$311$		−	3.40979i		−	0.193351i	0.995316	−	0.0966757i	$-0.0308210\pi$
$312$		0			0
$313$	6.98982	+	12.1067i	0.395088	+	0.684313i	0.993112	−	0.117165i	$-0.0373808\pi$
$313$	6.98982	+	12.1067i	0.395088	+	0.684313i	−0.598024	+	0.801478i	$0.704047\pi$
$314$		0			0
$315$	−11.4408			−0.644615
$316$		0			0
$317$	−12.9318	−	22.3986i	−0.726323	−	1.25803i	−0.958427	−	0.285338i	$-0.907894\pi$
$317$	−12.9318	−	22.3986i	−0.726323	−	1.25803i	0.232104	−	0.972691i	$-0.425439\pi$
$318$		0			0
$319$	−2.03620	−	3.52680i	−0.114005	−	0.197463i
$320$		0			0
$321$	11.1774	−	19.3598i	0.623860	−	1.08056i
$322$		0			0
$323$	−4.01348	+	2.37656i	−0.223316	+	0.132235i
$324$		0			0
$325$	6.19574	−	10.7313i	0.343678	−	0.595268i
$326$		0			0
$327$	33.7963	−	19.5123i	1.86894	−	1.07903i
$328$		0			0
$329$	10.1601	+	17.5979i	0.560146	+	0.970201i
$330$		0			0
$331$		−	7.70618i		−	0.423570i	−0.977316	−	0.211785i	$-0.932072\pi$
$331$		−	7.70618i		−	0.423570i	0.977316	−	0.211785i	$-0.0679276\pi$
$332$		0			0
$333$	−4.43647	−	7.68419i	−0.243117	−	0.421091i
$334$		0			0
$335$	24.8334			1.35679
$336$		0			0
$337$	16.5941	+	9.58062i	0.903939	+	0.521889i	0.878476	−	0.477786i	$-0.158561\pi$
$337$	16.5941	+	9.58062i	0.903939	+	0.521889i	0.0254629	+	0.999676i	$0.491894\pi$
$338$		0			0
$339$	13.1125	−	22.7115i	0.712172	−	1.23352i
$340$		0			0
$341$	13.4491			0.728312
$342$		0			0
$343$		−	18.6042i		−	1.00453i
$344$		0			0
$345$	−23.6060	−	13.6289i	−1.27090	−	0.733756i
$346$		0			0
$347$	0.244410	−	0.423330i	0.0131206	−	0.0227255i	−0.859391	−	0.511320i	$-0.829157\pi$
$347$	0.244410	−	0.423330i	0.0131206	−	0.0227255i	0.872511	+	0.488594i	$0.162490\pi$
$348$		0			0
$349$		−	23.0553i		−	1.23412i	−0.786916	−	0.617060i	$-0.788324\pi$
$349$		−	23.0553i		−	1.23412i	0.786916	−	0.617060i	$-0.211676\pi$
$350$		0			0
$351$	6.37792	−	3.68229i	0.340428	−	0.196546i
$352$		0			0
$353$	−18.1384			−0.965407			−0.482704	−	0.875784i	$-0.660345\pi$
$353$	−18.1384			−0.965407			−0.482704	+	0.875784i	$0.660345\pi$
$354$		0			0
$355$	−1.66905	+	0.963624i	−0.0885837	+	0.0511438i
$356$		0			0
$357$	3.30419	+	5.72302i	0.174876	+	0.302894i
$358$		0			0
$359$	−1.99616	−	1.15248i	−0.105353	−	0.0608257i	0.446398	−	0.894835i	$-0.352707\pi$
$359$	−1.99616	−	1.15248i	−0.105353	−	0.0608257i	−0.551751	+	0.834009i	$0.686040\pi$
$360$		0			0
$361$	9.86046	+	16.2410i	0.518972	+	0.854791i
$362$		0			0
$363$	2.74997	+	1.58770i	0.144336	+	0.0833325i
$364$		0			0
$365$	18.0186	−	10.4030i	0.943135	−	0.544519i
$366$		0			0
$367$	6.22808	−	3.59578i	0.325103	−	0.187698i	−0.328562	−	0.944482i	$-0.606564\pi$
$367$	6.22808	−	3.59578i	0.325103	−	0.187698i	0.653665	+	0.756784i	$0.273231\pi$
$368$		0			0
$369$		−	13.1244i		−	0.683230i
$370$		0			0
$371$	−2.40307	+	1.38741i	−0.124761	+	0.0720309i
$372$		0			0
$373$	−36.8480			−1.90792			−0.953958	−	0.299940i	$-0.903033\pi$
$373$	−36.8480			−1.90792			−0.953958	+	0.299940i	$0.903033\pi$
$374$		0			0
$375$	−14.2228	+	24.6347i	−0.734464	+	1.27213i
$376$		0			0
$377$	3.63001	−	6.28737i	0.186955	−	0.323816i
$378$		0			0
$379$			13.7966i			0.708683i	0.935116	+	0.354342i	$0.115295\pi$
$379$			13.7966i			0.708683i	−0.935116	+	0.354342i	$0.884705\pi$
$380$		0			0
$381$			28.8559i			1.47833i
$382$		0			0
$383$	−10.3391	+	17.9079i	−0.528304	+	0.915049i	0.471152	+	0.882052i	$0.343838\pi$
$383$	−10.3391	+	17.9079i	−0.528304	+	0.915049i	−0.999455	+	0.0329968i	$0.989495\pi$
$384$		0			0
$385$	−8.04642	+	13.9368i	−0.410084	+	0.710286i
$386$		0			0
$387$	0.821220			0.0417449
$388$		0			0
$389$	−4.94700	+	2.85615i	−0.250823	+	0.144813i	−0.620141	−	0.784490i	$-0.712925\pi$
$389$	−4.94700	+	2.85615i	−0.250823	+	0.144813i	0.369318	+	0.929303i	$0.379591\pi$
$390$		0			0
$391$			7.15471i			0.361829i
$392$		0			0
$393$	−8.67256	+	5.00711i	−0.437473	+	0.252575i
$394$		0			0
$395$	3.07338	−	1.77442i	0.154639	−	0.0892806i
$396$		0			0
$397$	3.60511	+	2.08141i	0.180935	+	0.104463i	0.587732	−	0.809056i	$-0.300021\pi$
$397$	3.60511	+	2.08141i	0.180935	+	0.104463i	−0.406797	+	0.913519i	$0.633354\pi$
$398$		0			0
$399$	23.1627	−	13.7156i	1.15958	−	0.686641i
$400$		0			0
$401$	−11.9448	−	6.89632i	−0.596494	−	0.344386i	0.171167	−	0.985242i	$-0.445246\pi$
$401$	−11.9448	−	6.89632i	−0.596494	−	0.344386i	−0.767661	+	0.640856i	$0.778579\pi$
$402$		0			0
$403$	11.9882	+	20.7641i	0.597173	+	1.03433i
$404$		0			0
$405$	−15.4360	+	8.91200i	−0.767023	+	0.442841i
$406$		0			0
$407$	−12.4809			−0.618653
$408$		0			0
$409$	−23.9196	+	13.8100i	−1.18275	+	0.682859i	−0.956648	−	0.291246i	$-0.905930\pi$
$409$	−23.9196	+	13.8100i	−1.18275	+	0.682859i	−0.226098	+	0.974105i	$0.572597\pi$
$410$		0			0
$411$		−	22.5563i		−	1.11262i
$412$		0			0
$413$	−12.8518	+	22.2599i	−0.632394	+	1.09534i
$414$		0			0
$415$	−16.6815	−	9.63106i	−0.818862	−	0.472770i
$416$		0			0
$417$			8.02591i			0.393031i
$418$		0			0
$419$	−5.29106			−0.258485			−0.129243	−	0.991613i	$-0.541255\pi$
$419$	−5.29106			−0.258485			−0.129243	+	0.991613i	$0.541255\pi$
$420$		0			0
$421$	0.257440	−	0.445898i	0.0125468	−	0.0217318i	−0.859684	−	0.510827i	$-0.829339\pi$
$421$	0.257440	−	0.445898i	0.0125468	−	0.0217318i	0.872231	+	0.489095i	$0.162673\pi$
$422$		0			0
$423$	−16.6971	−	9.64009i	−0.811842	−	0.468717i
$424$		0			0
$425$	2.11613			0.102647
$426$		0			0
$427$	17.1689	+	29.7374i	0.830860	+	1.43909i
$428$		0			0
$429$			51.6457i			2.49348i
$430$		0			0
$431$	−3.98898	−	6.90912i	−0.192143	−	0.332801i	0.753817	−	0.657084i	$-0.228210\pi$
$431$	−3.98898	−	6.90912i	−0.192143	−	0.332801i	−0.945960	+	0.324283i	$0.894877\pi$
$432$		0			0
$433$	−23.3608	+	13.4874i	−1.12265	+	0.648161i	−0.942075	−	0.335401i	$-0.891128\pi$
$433$	−23.3608	+	13.4874i	−1.12265	+	0.648161i	−0.180572	+	0.983562i	$0.557795\pi$
$434$		0			0
$435$	−2.36171	+	4.09060i	−0.113235	+	0.196129i
$436$		0			0
$437$	29.1426	−	0.321292i	1.39408	−	0.0153695i
$438$		0			0
$439$	12.1104	−	20.9758i	0.577996	−	1.00112i	−0.417713	−	0.908579i	$-0.637168\pi$
$439$	12.1104	−	20.9758i	0.577996	−	1.00112i	0.995709	−	0.0925395i	$-0.0294984\pi$
$440$		0			0
$441$	0.0802437	+	0.138986i	0.00382113	+	0.00661839i
$442$		0			0
$443$	−9.46404	−	16.3922i	−0.449650	−	0.778817i	0.548713	−	0.836011i	$-0.315118\pi$
$443$	−9.46404	−	16.3922i	−0.449650	−	0.778817i	−0.998363	+	0.0571938i	$0.981785\pi$
$444$		0			0
$445$	−4.39108			−0.208157
$446$		0			0
$447$	−6.25263	−	10.8299i	−0.295739	−	0.512236i
$448$		0			0
$449$		−	26.8822i		−	1.26865i	−0.773067	−	0.634325i	$-0.781278\pi$
$449$		−	26.8822i		−	1.26865i	0.773067	−	0.634325i	$-0.218722\pi$
$450$		0			0
$451$	−15.9878	−	9.23054i	−0.752834	−	0.434649i
$452$		0			0
$453$	26.1475	+	15.0963i	1.22852	+	0.709285i
$454$		0			0
$455$	−28.6893			−1.34498
$456$		0			0
$457$	−20.7685			−0.971510			−0.485755	−	0.874095i	$-0.661455\pi$
$457$	−20.7685			−0.971510			−0.485755	+	0.874095i	$0.661455\pi$
$458$		0			0
$459$	1.08918	+	0.628836i	0.0508384	+	0.0293516i
$460$		0			0
$461$	−1.43067	−	0.825996i	−0.0666328	−	0.0384705i	0.466313	−	0.884620i	$-0.345582\pi$
$461$	−1.43067	−	0.825996i	−0.0666328	−	0.0384705i	−0.532946	+	0.846149i	$0.678915\pi$
$462$		0			0
$463$			1.67704i			0.0779389i	0.999240	+	0.0389694i	$0.0124075\pi$
$463$			1.67704i			0.0779389i	−0.999240	+	0.0389694i	$0.987592\pi$
$464$		0			0
$465$	−7.79957	−	13.5093i	−0.361696	−	0.626477i
$466$		0			0
$467$	−11.9357			−0.552316			−0.276158	−	0.961112i	$-0.589061\pi$
$467$	−11.9357			−0.552316			−0.276158	+	0.961112i	$0.589061\pi$
$468$		0			0
$469$	18.8094	+	32.5788i	0.868537	+	1.50435i
$470$		0			0
$471$	14.5847	+	25.2614i	0.672026	+	1.16398i
$472$		0			0
$473$	0.577572	−	1.00038i	0.0265568	−	0.0459977i
$474$		0			0
$475$	−0.0950277	−	8.61945i	−0.00436017	−	0.395488i
$476$		0			0
$477$	1.31640	−	2.28007i	0.0602738	−	0.104397i
$478$		0			0
$479$	−1.63885	+	0.946189i	−0.0748808	+	0.0432325i	−0.536973	−	0.843599i	$-0.680432\pi$
$479$	−1.63885	+	0.946189i	−0.0748808	+	0.0432325i	0.462092	+	0.886832i	$0.347099\pi$
$480$		0			0
$481$	−11.1251	−	19.2692i	−0.507259	−	0.878598i
$482$		0			0
$483$		−	41.2914i		−	1.87882i
$484$		0			0
$485$	−0.355508	−	0.615759i	−0.0161428	−	0.0279602i
$486$		0			0
$487$	7.47813			0.338866			0.169433	−	0.985542i	$-0.445806\pi$
$487$	7.47813			0.338866			0.169433	+	0.985542i	$0.445806\pi$
$488$		0			0
$489$	−24.5648	−	14.1825i	−1.11086	−	0.641355i
$490$		0			0
$491$	14.3418	−	24.8407i	0.647236	−	1.12105i	−0.336544	−	0.941668i	$-0.609258\pi$
$491$	14.3418	−	24.8407i	0.647236	−	1.12105i	0.983780	−	0.179378i	$-0.0574087\pi$
$492$		0			0
$493$	1.23982			0.0558386
$494$		0			0
$495$		−	15.2691i		−	0.686297i
$496$		0			0
$497$	−2.52835	−	1.45974i	−0.113412	−	0.0654784i
$498$		0			0
$499$	−6.66818	+	11.5496i	−0.298509	+	0.517033i	−0.975795	−	0.218687i	$-0.929823\pi$
$499$	−6.66818	+	11.5496i	−0.298509	+	0.517033i	0.677286	+	0.735720i	$0.263156\pi$
$500$		0			0
$501$		−	57.7797i		−	2.58141i
$502$		0			0
$503$	31.7044	−	18.3046i	1.41363	−	0.816160i	0.417902	−	0.908492i	$-0.362765\pi$
$503$	31.7044	−	18.3046i	1.41363	−	0.816160i	0.995728	+	0.0923320i	$0.0294321\pi$
$504$		0			0
$505$	30.0345			1.33652
$506$		0			0
$507$	−53.3354	+	30.7932i	−2.36871	+	1.36758i
$508$		0			0
$509$	4.86878	+	8.43297i	0.215805	+	0.373785i	0.953521	−	0.301326i	$-0.0974292\pi$
$509$	4.86878	+	8.43297i	0.215805	+	0.373785i	−0.737716	+	0.675111i	$0.764096\pi$
$510$		0			0
$511$	27.2953	+	15.7590i	1.20747	+	0.697136i
$512$		0			0
$513$	2.51247	−	4.46469i	0.110928	−	0.197121i
$514$		0			0
$515$	1.84203	+	1.06350i	0.0811697	+	0.0468633i
$516$		0			0
$517$	−23.4865	+	13.5599i	−1.03294	+	0.596366i
$518$		0			0
$519$	−5.27746	+	3.04695i	−0.231655	+	0.133746i
$520$		0			0
$521$		−	10.4196i		−	0.456489i	−0.973604	−	0.228244i	$-0.926701\pi$
$521$		−	10.4196i		−	0.456489i	0.973604	−	0.228244i	$-0.0732985\pi$
$522$		0			0
$523$	−7.69425	+	4.44228i	−0.336446	+	0.194247i	−0.658699	−	0.752406i	$-0.728893\pi$
$523$	−7.69425	+	4.44228i	−0.336446	+	0.194247i	0.322253	+	0.946653i	$0.395560\pi$
$524$		0			0
$525$	−12.2127			−0.533004
$526$		0			0
$527$	−2.04725	+	3.54595i	−0.0891798	+	0.154464i
$528$		0			0
$529$	10.8525	−	18.7972i	0.471850	−	0.817267i
$530$		0			0
$531$		−	24.3879i		−	1.05835i
$532$		0			0
$533$		−	32.9113i		−	1.42555i
$534$		0			0
$535$	−8.28677	+	14.3531i	−0.358268	+	0.620539i
$536$		0			0
$537$	−2.25749	+	3.91009i	−0.0974180	+	0.168733i
$538$		0			0
$539$	0.225745			0.00972351
$540$		0			0
$541$	−13.0499	+	7.53435i	−0.561058	+	0.323927i	−0.753570	−	0.657367i	$-0.771670\pi$
$541$	−13.0499	+	7.53435i	−0.561058	+	0.323927i	0.192512	+	0.981295i	$0.438337\pi$
$542$		0			0
$543$			41.2142i			1.76867i
$544$		0			0
$545$	−25.0562	+	14.4662i	−1.07329	+	0.619663i
$546$		0			0
$547$	13.6000	−	7.85196i	0.581494	−	0.335725i	−0.180233	−	0.983624i	$-0.557685\pi$
$547$	13.6000	−	7.85196i	0.581494	−	0.335725i	0.761727	+	0.647898i	$0.224352\pi$
$548$		0			0
$549$	−28.2153	−	16.2901i	−1.20420	−	0.695245i
$550$		0			0
$551$	−0.0556756	−	5.05004i	−0.00237186	−	0.215139i
$552$		0			0
$553$	4.65570	+	2.68797i	0.197980	+	0.114304i
$554$		0			0
$555$	7.23803	+	12.5366i	0.307237	+	0.532151i
$556$		0			0
$557$	−5.29879	+	3.05926i	−0.224517	+	0.129625i	−0.608040	−	0.793906i	$-0.708044\pi$
$557$	−5.29879	+	3.05926i	−0.224517	+	0.129625i	0.383523	+	0.923531i	$0.374711\pi$
$558$		0			0
$559$	2.05932			0.0871000
$560$		0			0
$561$	−7.63807	+	4.40984i	−0.322480	+	0.186184i
$562$		0			0
$563$			7.15012i			0.301342i	0.988584	+	0.150671i	$0.0481433\pi$
$563$			7.15012i			0.301342i	−0.988584	+	0.150671i	$0.951857\pi$
$564$		0			0
$565$	−9.72143	+	16.8380i	−0.408984	+	0.708380i
$566$		0			0
$567$	−23.3832	−	13.5003i	−0.982003	−	0.566960i
$568$		0			0
$569$			17.0049i			0.712881i	0.934318	+	0.356440i	$0.116010\pi$
$569$			17.0049i			0.712881i	−0.934318	+	0.356440i	$0.883990\pi$
$570$		0			0
$571$	24.7475			1.03565			0.517826	−	0.855486i	$-0.326741\pi$
$571$	24.7475			1.03565			0.517826	+	0.855486i	$0.326741\pi$
$572$		0			0
$573$	4.04773	−	7.01087i	0.169096	−	0.292883i
$574$		0			0
$575$	−11.4509	−	6.61116i	−0.477534	−	0.275704i
$576$		0			0
$577$	4.20132			0.174903			0.0874515	−	0.996169i	$-0.472128\pi$
$577$	4.20132			0.174903			0.0874515	+	0.996169i	$0.472128\pi$
$578$		0			0
$579$	9.22902	+	15.9851i	0.383545	+	0.664319i
$580$		0			0
$581$		−	29.1791i		−	1.21055i
$582$		0			0
$583$	−1.85167	−	3.20719i	−0.0766885	−	0.132828i
$584$		0			0
$585$	23.5740	−	13.6105i	0.974665	−	0.562723i
$586$		0			0
$587$	−2.00696	+	3.47616i	−0.0828361	+	0.143476i	−0.904467	−	0.426543i	$-0.859731\pi$
$587$	−2.00696	+	3.47616i	−0.0828361	+	0.143476i	0.821631	+	0.570020i	$0.193064\pi$
$588$		0			0
$589$	14.5353	+	8.17966i	0.598918	+	0.337037i
$590$		0			0
$591$	−17.0577	+	29.5448i	−0.701660	+	1.21531i
$592$		0			0
$593$	20.6458	+	35.7596i	0.847821	+	1.46847i	0.883148	+	0.469094i	$0.155419\pi$
$593$	20.6458	+	35.7596i	0.847821	+	1.46847i	−0.0353273	+	0.999376i	$0.511247\pi$
$594$		0			0
$595$	−2.44968	−	4.24298i	−0.100427	−	0.173945i
$596$		0			0
$597$	−13.2851			−0.543722
$598$		0			0
$599$	−16.4449	−	28.4833i	−0.671919	−	1.16380i	−0.977359	−	0.211586i	$-0.932137\pi$
$599$	−16.4449	−	28.4833i	−0.671919	−	1.16380i	0.305440	−	0.952211i	$-0.401196\pi$
$600$		0			0
$601$		−	36.2387i		−	1.47821i	−0.673591	−	0.739104i	$-0.735249\pi$
$601$		−	36.2387i		−	1.47821i	0.673591	−	0.739104i	$-0.264751\pi$
$602$		0			0
$603$	−30.9113	−	17.8467i	−1.25881	−	0.726772i
$604$		0			0
$605$	−2.03880	−	1.17710i	−0.0828889	−	0.0478559i
$606$		0			0
$607$	31.1439			1.26409			0.632046	−	0.774931i	$-0.282215\pi$
$607$	31.1439			1.26409			0.632046	+	0.774931i	$0.282215\pi$
$608$		0			0
$609$	−7.15526			−0.289946
$610$		0			0
$611$	−41.8703	−	24.1738i	−1.69389	−	0.977969i
$612$		0			0
$613$	19.0102	+	10.9755i	0.767813	+	0.443297i	0.832094	−	0.554635i	$-0.187142\pi$
$613$	19.0102	+	10.9755i	0.767813	+	0.443297i	−0.0642809	+	0.997932i	$0.520475\pi$
$614$		0			0
$615$			21.4123i			0.863427i
$616$		0			0
$617$	13.2947	+	23.0270i	0.535222	+	0.927033i	0.999153	+	0.0411607i	$0.0131056\pi$
$617$	13.2947	+	23.0270i	0.535222	+	0.927033i	−0.463930	+	0.885872i	$0.653561\pi$
$618$		0			0
$619$	10.1699			0.408765			0.204382	−	0.978891i	$-0.434481\pi$
$619$	10.1699			0.408765			0.204382	+	0.978891i	$0.434481\pi$
$620$		0			0
$621$	−3.92919	−	6.80555i	−0.157673	−	0.273097i
$622$		0			0
$623$	−3.32591	−	5.76064i	−0.133250	−	0.230795i
$624$		0			0
$625$	5.60074	−	9.70076i	0.224029	−	0.388030i
$626$		0			0
$627$	18.3052	+	30.9135i	0.731040	+	1.23456i
$628$		0			0
$629$	1.89986	−	3.29065i	0.0757524	−	0.131207i
$630$		0			0
$631$	−1.60265	+	0.925289i	−0.0638004	+	0.0368352i	−0.531561	−	0.847020i	$-0.678394\pi$
$631$	−1.60265	+	0.925289i	−0.0638004	+	0.0368352i	0.467760	+	0.883855i	$0.345061\pi$
$632$		0			0
$633$	1.66436	+	2.88275i	0.0661523	+	0.114579i
$634$		0			0
$635$		−	21.3934i		−	0.848973i
$636$		0			0
$637$	0.201222	+	0.348527i	0.00797271	+	0.0138091i
$638$		0			0
$639$	2.77005			0.109582
$640$		0			0
$641$	14.0043	+	8.08541i	0.553138	+	0.319354i	0.750387	−	0.660999i	$-0.229867\pi$
$641$	14.0043	+	8.08541i	0.553138	+	0.319354i	−0.197249	+	0.980353i	$0.563201\pi$
$642$		0			0
$643$	3.77472	−	6.53800i	0.148860	−	0.257834i	−0.781946	−	0.623346i	$-0.785773\pi$
$643$	3.77472	−	6.53800i	0.148860	−	0.257834i	0.930806	+	0.365512i	$0.119106\pi$
$644$		0			0
$645$	−1.33981			−0.0527548
$646$		0			0
$647$			26.6043i			1.04592i	0.852356	+	0.522962i	$0.175173\pi$
$647$			26.6043i			1.04592i	−0.852356	+	0.522962i	$0.824827\pi$
$648$		0			0
$649$	−29.7086	−	17.1523i	−1.16616	−	0.673285i
$650$		0			0
$651$	11.8151	−	20.4644i	0.463072	−	0.802065i
$652$		0			0
$653$			44.5639i			1.74392i	0.489576	+	0.871961i	$0.337152\pi$
$653$			44.5639i			1.74392i	−0.489576	+	0.871961i	$0.662848\pi$
$654$		0			0
$655$	6.42973	−	3.71221i	0.251230	−	0.145048i
$656$		0			0
$657$	−29.9047			−1.16669
$658$		0			0
$659$	−7.12914	+	4.11601i	−0.277712	+	0.160337i	−0.632387	−	0.774653i	$-0.717925\pi$
$659$	−7.12914	+	4.11601i	−0.277712	+	0.160337i	0.354675	+	0.934990i	$0.384591\pi$
$660$		0			0
$661$	−12.0523	−	20.8752i	−0.468780	−	0.811952i	0.530583	−	0.847633i	$-0.321973\pi$
$661$	−12.0523	−	20.8752i	−0.468780	−	0.811952i	−0.999363	+	0.0356816i	$0.988640\pi$
$662$		0			0
$663$	−13.6167	−	7.86160i	−0.528829	−	0.305319i
$664$		0			0
$665$	−17.1725	+	10.1686i	−0.665922	+	0.394322i
$666$		0			0
$667$	−6.70893	−	3.87340i	−0.259771	−	0.149979i
$668$		0			0
$669$	36.6515	−	21.1608i	1.41703	−	0.818122i
$670$		0			0
$671$	−39.6882	+	22.9140i	−1.53215	+	0.884585i
$672$		0			0
$673$		−	20.9382i		−	0.807109i	−0.914956	−	0.403555i	$-0.867775\pi$
$673$		−	20.9382i		−	0.807109i	0.914956	−	0.403555i	$-0.132225\pi$
$674$		0			0
$675$	−2.01286	+	1.16213i	−0.0774751	+	0.0447303i
$676$		0			0
$677$	−1.42054			−0.0545958			−0.0272979	−	0.999627i	$-0.508690\pi$
$677$	−1.42054			−0.0545958			−0.0272979	+	0.999627i	$0.508690\pi$
$678$		0			0
$679$	0.538541	−	0.932780i	0.0206673	−	0.0357968i
$680$		0			0
$681$	20.7338	−	35.9120i	0.794521	−	1.37615i
$682$		0			0
$683$			5.61433i			0.214826i	0.994214	+	0.107413i	$0.0342567\pi$
$683$			5.61433i			0.214826i	−0.994214	+	0.107413i	$0.965743\pi$
$684$		0			0
$685$			16.7230i			0.638952i
$686$		0			0
$687$	6.49018	−	11.2413i	0.247616	−	0.428883i
$688$		0			0
$689$	3.30105	−	5.71759i	0.125760	−	0.217823i
$690$		0			0
$691$	−14.4545			−0.549874			−0.274937	−	0.961462i	$-0.588657\pi$
$691$	−14.4545			−0.549874			−0.274937	+	0.961462i	$0.588657\pi$
$692$		0			0
$693$	20.0315	−	11.5652i	0.760935	−	0.439326i
$694$		0			0
$695$		−	5.95031i		−	0.225708i
$696$		0			0
$697$	4.86738	−	2.81018i	0.184365	−	0.106443i
$698$		0			0
$699$	−38.3018	+	22.1136i	−1.44871	+	0.836412i
$700$		0			0
$701$	−19.3056	−	11.1461i	−0.729162	−	0.420982i	0.0889537	−	0.996036i	$-0.471648\pi$
$701$	−19.3056	−	11.1461i	−0.729162	−	0.420982i	−0.818115	+	0.575054i	$0.804981\pi$
$702$		0			0
$703$	−13.4888	−	7.59076i	−0.508741	−	0.286291i
$704$		0			0
$705$	27.2411	+	15.7277i	1.02596	+	0.592338i
$706$		0			0
$707$	22.7489	+	39.4022i	0.855559	+	1.48187i
$708$		0			0
$709$	3.96340	−	2.28827i	0.148849	−	0.0859379i	−0.423726	−	0.905790i	$-0.639278\pi$
$709$	3.96340	−	2.28827i	0.148849	−	0.0859379i	0.572575	+	0.819853i	$0.305945\pi$
$710$		0			0
$711$	−5.10078			−0.191294
$712$		0			0
$713$	22.1563	−	12.7919i	0.829760	−	0.479062i
$714$		0			0
$715$		−	38.2895i		−	1.43195i
$716$		0			0
$717$	10.4497	−	18.0994i	0.390251	−	0.675935i
$718$		0			0
$719$	27.0082	+	15.5932i	1.00724	+	0.581529i	0.910382	−	0.413770i	$-0.135788\pi$
$719$	27.0082	+	15.5932i	1.00724	+	0.581529i	0.0968558	+	0.995298i	$0.469121\pi$
$720$		0			0
$721$			3.22207i			0.119996i
$722$		0			0
$723$	28.7763			1.07020
$724$		0			0
$725$	−1.14563	+	1.98428i	−0.0425475	+	0.0736945i
$726$		0			0
$727$	23.9867	+	13.8487i	0.889616	+	0.513620i	0.873817	−	0.486255i	$-0.161637\pi$
$727$	23.9867	+	13.8487i	0.889616	+	0.513620i	0.0157989	+	0.999875i	$0.494971\pi$
$728$		0			0
$729$	17.3505			0.642610
$730$		0			0
$731$	0.175838	+	0.304561i	0.00650361	+	0.0112646i
$732$		0			0
$733$		−	39.4678i		−	1.45778i	−0.684633	−	0.728888i	$-0.740038\pi$
$733$		−	39.4678i		−	1.45778i	0.684633	−	0.728888i	$-0.259962\pi$
$734$		0			0
$735$	−0.130916	−	0.226754i	−0.00482892	−	0.00836394i
$736$		0			0
$737$	−43.4805	+	25.1035i	−1.60162	+	0.924698i
$738$		0			0
$739$	9.60431	−	16.6352i	0.353300	−	0.611934i	−0.633525	−	0.773722i	$-0.718393\pi$
$739$	9.60431	−	16.6352i	0.353300	−	0.611934i	0.986826	+	0.161788i	$0.0517260\pi$
$740$		0			0
$741$	−31.4105	+	55.8167i	−1.15389	+	2.05048i
$742$		0			0
$743$	−12.5887	+	21.8042i	−0.461834	+	0.799920i	−0.999052	−	0.0435235i	$-0.986142\pi$
$743$	−12.5887	+	21.8042i	−0.461834	+	0.799920i	0.537219	+	0.843443i	$0.319475\pi$
$744$		0			0
$745$	4.63563	+	8.02914i	0.169836	+	0.294165i
$746$		0			0
$747$	13.8428	+	23.9765i	0.506482	+	0.877253i
$748$		0			0
$749$	−25.1063			−0.917366
$750$		0			0
$751$	6.81951	+	11.8117i	0.248848	+	0.431017i	0.963206	−	0.268763i	$-0.0866149\pi$
$751$	6.81951	+	11.8117i	0.248848	+	0.431017i	−0.714359	+	0.699780i	$0.753282\pi$
$752$		0			0
$753$			29.7587i			1.08447i
$754$		0			0
$755$	−19.3854	−	11.1922i	−0.705508	−	0.407325i
$756$		0			0
$757$	−11.9944	−	6.92497i	−0.435944	−	0.251692i	0.265932	−	0.963992i	$-0.414320\pi$
$757$	−11.9944	−	6.92497i	−0.435944	−	0.251692i	−0.701876	+	0.712299i	$0.747654\pi$
$758$		0			0
$759$	55.1085			2.00031
$760$		0			0
$761$	30.7993			1.11647			0.558237	−	0.829682i	$-0.311478\pi$
$761$	30.7993			1.11647			0.558237	+	0.829682i	$0.311478\pi$
$762$		0			0
$763$	−37.9562	−	21.9140i	−1.37411	−	0.793341i
$764$		0			0
$765$	4.02580	+	2.32430i	0.145553	+	0.0840352i
$766$		0			0
$767$		−	61.1560i		−	2.20822i
$768$		0			0
$769$	13.8221	+	23.9405i	0.498437	+	0.863318i	0.999998	−	0.00180408i	$-0.000574256\pi$
$769$	13.8221	+	23.9405i	0.498437	+	0.863318i	−0.501562	+	0.865122i	$0.667241\pi$
$770$		0			0
$771$	−42.8886			−1.54460
$772$		0			0
$773$	8.10943	+	14.0459i	0.291676	+	0.505198i	0.974206	−	0.225660i	$-0.0724538\pi$
$773$	8.10943	+	14.0459i	0.291676	+	0.505198i	−0.682530	+	0.730857i	$0.739120\pi$
$774$		0			0
$775$	−3.78344	−	6.55312i	−0.135905	−	0.235395i
$776$		0			0
$777$	−10.9645	+	18.9911i	−0.393349	+	0.681301i
$778$		0			0
$779$	−11.6650	−	19.6997i	−0.417943	−	0.705813i
$780$		0			0
$781$	1.94821	−	3.37439i	0.0697123	−	0.120745i
$782$		0			0
$783$	−1.17931	+	0.680877i	−0.0421452	+	0.0243325i
$784$		0			0
$785$	−10.8129	−	18.7285i	−0.385929	−	0.668449i
$786$		0			0
$787$			5.50219i			0.196132i	0.995180	+	0.0980660i	$0.0312656\pi$
$787$			5.50219i			0.196132i	−0.995180	+	0.0980660i	$0.968734\pi$
$788$		0			0
$789$	23.9132	+	41.4189i	0.851333	+	1.47455i
$790$		0			0
$791$	−29.4529			−1.04723
$792$		0			0
$793$	−70.7537	−	40.8497i	−2.51254	−	1.45061i
$794$		0			0
$795$	−2.14769	+	3.71990i	−0.0761706	+	0.131931i
$796$		0			0
$797$	49.6076			1.75719			0.878596	−	0.477565i	$-0.158481\pi$
$797$	49.6076			1.75719			0.878596	+	0.477565i	$0.158481\pi$
$798$		0			0
$799$		−	8.25648i		−	0.292093i
$800$		0			0
$801$	5.46579	+	3.15567i	0.193124	+	0.111500i
$802$		0			0
$803$	−21.0323	+	36.4290i	−0.742214	+	1.28555i
$804$		0			0
$805$			30.6129i			1.07896i
$806$		0			0
$807$	10.8081	−	6.24005i	0.380463	−	0.219660i
$808$		0			0
$809$	1.83016			0.0643449			0.0321725	−	0.999482i	$-0.489757\pi$
$809$	1.83016			0.0643449			0.0321725	+	0.999482i	$0.489757\pi$
$810$		0			0
$811$	35.5280	−	20.5121i	1.24756	−	0.720278i	0.276936	−	0.960888i	$-0.410681\pi$
$811$	35.5280	−	20.5121i	1.24756	−	0.720278i	0.970622	+	0.240610i	$0.0773476\pi$
$812$		0			0
$813$	−25.4795	−	44.1318i	−0.893606	−	1.54777i
$814$		0			0
$815$	18.2121	+	10.5147i	0.637941	+	0.368315i
$816$		0			0
$817$	1.23264	−	0.729903i	0.0431247	−	0.0255361i
$818$		0			0
$819$	35.7110	+	20.6177i	1.24784	+	0.720442i
$820$		0			0
$821$	43.4002	−	25.0571i	1.51468	−	0.874500i	0.514827	−	0.857294i	$-0.327856\pi$
$821$	43.4002	−	25.0571i	1.51468	−	0.874500i	0.999852	−	0.0172064i	$-0.00547725\pi$
$822$		0			0
$823$	15.6404	−	9.02998i	0.545190	−	0.314765i	−0.201990	−	0.979388i	$-0.564741\pi$
$823$	15.6404	−	9.02998i	0.545190	−	0.314765i	0.747180	+	0.664622i	$0.231408\pi$
$824$		0			0
$825$		−	16.2993i		−	0.567469i
$826$		0			0
$827$	9.58340	−	5.53298i	0.333247	−	0.192400i	−0.324035	−	0.946045i	$-0.605039\pi$
$827$	9.58340	−	5.53298i	0.333247	−	0.192400i	0.657282	+	0.753645i	$0.271706\pi$
$828$		0			0
$829$	−12.1712			−0.422722			−0.211361	−	0.977408i	$-0.567790\pi$
$829$	−12.1712			−0.422722			−0.211361	+	0.977408i	$0.567790\pi$
$830$		0			0
$831$	6.62052	−	11.4671i	0.229663	−	0.397789i
$832$		0			0
$833$	−0.0343633	+	0.0595190i	−0.00119062	+	0.00206221i
$834$		0			0
$835$			42.8372i			1.48244i
$836$		0			0
$837$		−	4.49720i		−	0.155446i
$838$		0			0
$839$	−16.4497	+	28.4917i	−0.567906	+	0.983642i	0.428867	+	0.903368i	$0.358913\pi$
$839$	−16.4497	+	28.4917i	−0.567906	+	0.983642i	−0.996773	+	0.0802744i	$0.974420\pi$
$840$		0			0
$841$	13.8288	−	23.9522i	0.476855	−	0.825937i
$842$		0			0
$843$	59.1204			2.03622
$844$		0			0
$845$	39.5422	−	22.8297i	1.36029	−	0.785366i
$846$		0			0
$847$		−	3.56625i		−	0.122538i
$848$		0			0
$849$	−62.0984	+	35.8526i	−2.13121	+	1.23046i
$850$		0			0
$851$	−20.5611	+	11.8710i	−0.704827	+	0.406932i
$852$		0			0
$853$	8.52099	+	4.91960i	0.291753	+	0.168444i	0.638732	−	0.769429i	$-0.279459\pi$
$853$	8.52099	+	4.91960i	0.291753	+	0.168444i	−0.346979	+	0.937873i	$0.612793\pi$
$854$		0			0
$855$	9.28658	−	16.5023i	0.317594	−	0.564368i
$856$		0			0
$857$	13.0633	+	7.54208i	0.446233	+	0.257633i	0.706238	−	0.707975i	$-0.250391\pi$
$857$	13.0633	+	7.54208i	0.446233	+	0.257633i	−0.260005	+	0.965607i	$0.583724\pi$
$858$		0			0
$859$	−19.2316	−	33.3101i	−0.656173	−	1.13653i	−0.981598	−	0.190958i	$-0.938841\pi$
$859$	−19.2316	−	33.3101i	−0.656173	−	1.13653i	0.325425	−	0.945568i	$-0.394493\pi$
$860$		0			0
$861$	−28.0907	+	16.2182i	−0.957328	+	0.552714i
$862$		0			0
$863$	−5.27487			−0.179559			−0.0897794	−	0.995962i	$-0.528616\pi$
$863$	−5.27487			−0.179559			−0.0897794	+	0.995962i	$0.528616\pi$
$864$		0			0
$865$	3.91265	−	2.25897i	0.133034	−	0.0768072i
$866$		0			0
$867$			37.1790i			1.26267i
$868$		0			0
$869$	−3.58743	+	6.21360i	−0.121695	+	0.210782i
$870$		0			0
$871$	−77.5144	−	44.7530i	−2.62647	−	1.51640i
$872$		0			0
$873$			1.02195i			0.0345878i
$874$		0			0
$875$	31.9470			1.08001
$876$		0			0
$877$	−12.9910	+	22.5011i	−0.438676	+	0.759810i	−0.997588	−	0.0694177i	$-0.977886\pi$
$877$	−12.9910	+	22.5011i	−0.438676	+	0.759810i	0.558911	+	0.829227i	$0.311219\pi$
$878$		0			0
$879$	14.0379	+	8.10478i	0.473487	+	0.273368i
$880$		0			0
$881$	−53.7653			−1.81140			−0.905699	−	0.423920i	$-0.860654\pi$
$881$	−53.7653			−1.81140			−0.905699	+	0.423920i	$0.860654\pi$
$882$		0			0
$883$	6.64678	+	11.5126i	0.223682	+	0.387428i	0.955923	−	0.293617i	$-0.0948590\pi$
$883$	6.64678	+	11.5126i	0.223682	+	0.387428i	−0.732241	+	0.681045i	$0.761526\pi$
$884$		0			0
$885$			39.7885i			1.33748i
$886$		0			0
$887$	17.6190	+	30.5170i	0.591587	+	1.02466i	0.994019	+	0.109209i	$0.0348318\pi$
$887$	17.6190	+	30.5170i	0.591587	+	1.02466i	−0.402432	+	0.915450i	$0.631835\pi$
$888$		0			0
$889$	28.0659	−	16.2039i	0.941302	−	0.543461i
$890$		0			0
$891$	18.0178	−	31.2078i	0.603620	−	1.04550i
$892$		0			0
$893$	−33.6304	+	0.370768i	−1.12540	+	0.0124073i
$894$		0			0
$895$	1.67368	−	2.89889i	0.0559449	−	0.0968993i
$896$		0			0
$897$	49.1220	+	85.0818i	1.64014	+	2.84080i
$898$		0			0
$899$	−2.21668	−	3.83940i	−0.0739303	−	0.128051i
$900$		0			0
$901$	1.12746			0.0375612
$902$		0			0
$903$	−1.01480	−	1.75769i	−0.0337705	−	0.0584921i
$904$		0			0
$905$		−	30.5557i		−	1.01571i
$906$		0			0
$907$	5.23790	+	3.02410i	0.173922	+	0.100414i	0.584434	−	0.811441i	$-0.301317\pi$
$907$	5.23790	+	3.02410i	0.173922	+	0.100414i	−0.410512	+	0.911855i	$0.634650\pi$
$908$		0			0
$909$	−37.3854	−	21.5845i	−1.24000	−	0.715912i
$910$		0			0
$911$	8.93239			0.295943			0.147972	−	0.988992i	$-0.452726\pi$
$911$	8.93239			0.295943			0.147972	+	0.988992i	$0.452726\pi$
$912$		0			0
$913$	38.9432			1.28883
$914$		0			0
$915$	46.0328	+	26.5771i	1.52180	+	0.878611i
$916$		0			0
$917$	9.74006	+	5.62342i	0.321645	+	0.185702i
$918$		0			0
$919$		−	5.38284i		−	0.177563i	−0.996051	−	0.0887817i	$-0.971703\pi$
$919$		−	5.38284i		−	0.177563i	0.996051	−	0.0887817i	$-0.0282974\pi$
$920$		0			0
$921$	6.54927	+	11.3437i	0.215806	+	0.373787i
$922$		0			0
$923$	6.94629			0.228640
$924$		0			0
$925$	3.51105	+	6.08132i	0.115443	+	0.199953i
$926$		0			0
$927$	−1.52858	−	2.64757i	−0.0502051	−	0.0869577i
$928$		0			0
$929$	7.20302	−	12.4760i	0.236323	−	0.409324i	−0.723333	−	0.690499i	$-0.757391\pi$
$929$	7.20302	−	12.4760i	0.236323	−	0.409324i	0.959656	+	0.281175i	$0.0907242\pi$
$930$		0			0
$931$	0.243976	+	0.137296i	0.00799601	+	0.00449970i
$932$		0			0
$933$	3.99789	−	6.92455i	0.130885	−	0.226700i
$934$		0			0
$935$	5.66278	−	3.26941i	0.185193	−	0.106921i
$936$		0			0
$937$	22.6784	+	39.2801i	0.740871	+	1.28323i	0.952099	+	0.305789i	$0.0989202\pi$
$937$	22.6784	+	39.2801i	0.740871	+	1.28323i	−0.211229	+	0.977437i	$0.567746\pi$
$938$		0			0
$939$			32.7816i			1.06979i
$940$		0			0
$941$	−1.14512	−	1.98340i	−0.0373298	−	0.0646571i	0.846757	−	0.531980i	$-0.178552\pi$
$941$	−1.14512	−	1.98340i	−0.0373298	−	0.0646571i	−0.884087	+	0.467323i	$0.845219\pi$
$942$		0			0
$943$	−35.1180			−1.14360
$944$		0			0
$945$	4.66027	+	2.69061i	0.151599	+	0.0875255i
$946$		0			0
$947$	19.1593	−	33.1850i	0.622595	−	1.07837i	−0.366406	−	0.930455i	$-0.619412\pi$
$947$	19.1593	−	33.1850i	0.622595	−	1.07837i	0.989001	−	0.147911i	$-0.0472549\pi$
$948$		0			0
$949$	−74.9902			−2.43429
$950$		0			0
$951$		−	60.6489i		−	1.96668i
$952$		0			0
$953$	23.6158	+	13.6346i	0.764991	+	0.441668i	0.831085	−	0.556146i	$-0.187720\pi$
$953$	23.6158	+	13.6346i	0.764991	+	0.441668i	−0.0660939	+	0.997813i	$0.521054\pi$
$954$		0			0
$955$	−3.00094	+	5.19777i	−0.0971080	+	0.168196i
$956$		0			0
$957$		−	9.54957i		−	0.308694i
$958$		0			0
$959$	−21.9388	+	12.6664i	−0.708440	+	0.409018i
$960$		0			0
$961$	−16.3588			−0.527704
$962$		0			0
$963$	20.6299	−	11.9107i	0.664788	−	0.383815i
$964$		0			0
$965$	−6.84228	−	11.8512i	−0.220261	−	0.381503i
$966$		0			0
$967$	14.8285	+	8.56126i	0.476854	+	0.275312i	0.719104	−	0.694902i	$-0.244552\pi$
$967$	14.8285	+	8.56126i	0.476854	+	0.275312i	−0.242251	+	0.970214i	$0.577886\pi$
$968$		0			0
$969$	−10.9370	+	0.120578i	−0.351346	+	0.00387352i
$970$		0			0
$971$	30.1925	+	17.4317i	0.968924	+	0.559409i	0.898908	−	0.438137i	$-0.144362\pi$
$971$	30.1925	+	17.4317i	0.968924	+	0.559409i	0.0700160	+	0.997546i	$0.477695\pi$
$972$		0			0
$973$	7.80619	−	4.50690i	0.250255	−	0.144485i
$974$		0			0
$975$	25.1645	−	14.5287i	0.805908	−	0.465291i
$976$		0			0
$977$			44.3910i			1.42019i	0.704104	+	0.710097i	$0.251349\pi$
$977$			44.3910i			1.42019i	−0.704104	+	0.710097i	$0.748651\pi$
$978$		0			0
$979$	7.68828	−	4.43883i	0.245719	−	0.141866i
$980$		0			0
$981$	41.5848			1.32770
$982$		0			0
$983$	9.40482	−	16.2896i	0.299967	−	0.519558i	−0.676161	−	0.736754i	$-0.736358\pi$
$983$	9.40482	−	16.2896i	0.299967	−	0.519558i	0.976128	+	0.217196i	$0.0696910\pi$
$984$		0			0
$985$	12.6464	−	21.9042i	0.402947	−	0.697925i
$986$		0			0
$987$			47.6500i			1.51671i
$988$		0			0
$989$		−	2.19740i		−	0.0698731i
$990$		0			0
$991$	−1.81524	+	3.14409i	−0.0576630	+	0.0998753i	−0.893416	−	0.449230i	$-0.851698\pi$
$991$	−1.81524	+	3.14409i	−0.0576630	+	0.0998753i	0.835753	+	0.549106i	$0.185032\pi$
$992$		0			0
$993$	9.03530	−	15.6496i	0.286727	−	0.496625i
$994$		0			0
$995$	9.84939			0.312247
$996$		0			0
$997$	33.8520	−	19.5445i	1.07210	−	0.618980i	0.143349	−	0.989672i	$-0.454213\pi$
$997$	33.8520	−	19.5445i	1.07210	−	0.618980i	0.928756	+	0.370693i	$0.120880\pi$
$998$		0			0
$999$			4.17342i			0.132041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	608.2.s.c.559.11		28
4.3	odd	2		152.2.o.c.27.6	yes	28
8.3	odd	2	inner	608.2.s.c.559.12		28
8.5	even	2		152.2.o.c.27.1	✓	28
19.12	odd	6	inner	608.2.s.c.335.12		28
76.31	even	6		152.2.o.c.107.1	yes	28
152.69	odd	6		152.2.o.c.107.6	yes	28
152.107	even	6	inner	608.2.s.c.335.11		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.1	✓	28	8.5	even	2
152.2.o.c.27.6	yes	28	4.3	odd	2
152.2.o.c.107.1	yes	28	76.31	even	6
152.2.o.c.107.6	yes	28	152.69	odd	6
608.2.s.c.335.11		28	152.107	even	6	inner
608.2.s.c.335.12		28	19.12	odd	6	inner
608.2.s.c.559.11		28	1.1	even	1	trivial
608.2.s.c.559.12		28	8.3	odd	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	608.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.03079 + 1.17247i) q^{3} +(-1.50560 - 0.869259i) q^{5} -2.63359i q^{7} +(1.24939 + 2.16401i) q^{9} +3.51485 q^{11} +(3.13303 + 5.42656i) q^{13} +(-2.03837 - 3.53056i) q^{15} +(-0.535037 + 0.926710i) q^{17} +(3.79871 + 2.13770i) q^{19} +(3.08781 - 5.34825i) q^{21} +(5.79041 - 3.34309i) q^{23} +(-0.988779 - 1.71262i) q^{25} -1.17531i q^{27} +(-0.579314 - 1.00340i) q^{29} +3.82638 q^{31} +(7.13790 + 4.12107i) q^{33} +(-2.28927 + 3.96513i) q^{35} -3.55090 q^{37} +14.6936i q^{39} +(-4.54864 - 2.62616i) q^{41} +(0.164324 - 0.284617i) q^{43} -4.34419i q^{45} +(-6.68209 + 3.85791i) q^{47} +0.0642261 q^{49} +(-2.17309 + 1.25463i) q^{51} +(-0.526815 - 0.912471i) q^{53} +(-5.29195 - 3.05531i) q^{55} +(5.20797 + 8.79511i) q^{57} +(-8.45232 - 4.87995i) q^{59} +(-11.2916 + 6.51920i) q^{61} +(5.69912 - 3.29039i) q^{63} -10.8936i q^{65} +(-12.3705 + 7.14213i) q^{67} +15.6788 q^{69} +(0.554279 - 0.960040i) q^{71} +(-5.98385 + 10.3643i) q^{73} -4.63727i q^{75} -9.25665i q^{77} +(-1.02065 + 1.76782i) q^{79} +(5.12621 - 8.87886i) q^{81} +11.0796 q^{83} +(1.61110 - 0.930170i) q^{85} -2.71693i q^{87} +(2.18737 - 1.26288i) q^{89} +(14.2913 - 8.25110i) q^{91} +(7.77056 + 4.48634i) q^{93} +(-3.86113 - 6.52059i) q^{95} +(0.354186 + 0.204489i) q^{97} +(4.39143 + 7.60618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{3} + 8 q^{9} + 16 q^{11} - 22 q^{17} - 4 q^{19} + 16 q^{25} + 36 q^{33} + 28 q^{35} + 6 q^{41} - 30 q^{43} - 68 q^{49} + 42 q^{51} - 26 q^{57} + 18 q^{59} - 78 q^{67} + 14 q^{73} + 6 q^{81}+ \cdots + 28 q^{99}+O(q^{100}) \) 28 * q + 6 * q^3 + 8 * q^9 + 16 * q^11 - 22 * q^17 - 4 * q^19 + 16 * q^25 + 36 * q^33 + 28 * q^35 + 6 * q^41 - 30 * q^43 - 68 * q^49 + 42 * q^51 - 26 * q^57 + 18 * q^59 - 78 * q^67 + 14 * q^73 + 6 * q^81 + 32 * q^83 - 18 * q^89 + 12 * q^91 + 30 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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