LMFDB - Embedded newform 680.2.cg.b.73.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(57,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 0, 4, 15])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.57"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.cg (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [112] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			73.3
Character	$\chi$	$=$	680.73
Dual form			680.2.cg.b.177.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.446513 + 2.24477i) q^{3} +(0.682045 - 2.12951i) q^{5} +(-1.62658 - 1.08684i) q^{7} +(-2.06799 - 0.856589i) q^{9} +(-3.24910 - 2.17098i) q^{11} -0.242367i q^{13} +(4.47572 + 2.48189i) q^{15} +(-4.12252 + 0.0694971i) q^{17} +(-6.48434 + 2.68590i) q^{19} +(3.16600 - 3.16600i) q^{21} +(-9.03529 + 1.79723i) q^{23} +(-4.06963 - 2.90484i) q^{25} +(-0.968454 + 1.44939i) q^{27} +(1.52506 - 7.66700i) q^{29} +(4.24674 - 2.83758i) q^{31} +(6.32413 - 6.32413i) q^{33} +(-3.42384 + 2.72253i) q^{35} +(2.25031 + 0.447614i) q^{37} +(0.544060 + 0.108220i) q^{39} +(0.789503 + 3.96910i) q^{41} +(9.56951 - 3.96382i) q^{43} +(-3.23457 + 3.81957i) q^{45} +7.19997 q^{47} +(-1.21426 - 2.93149i) q^{49} +(1.68475 - 9.28515i) q^{51} +(-4.13058 + 9.97210i) q^{53} +(-6.83916 + 5.43829i) q^{55} +(-3.13390 - 15.7552i) q^{57} +(2.44267 - 5.89712i) q^{59} +(4.60449 - 0.915891i) q^{61} +(2.43276 + 3.64088i) q^{63} +(-0.516124 - 0.165305i) q^{65} +(3.29080 + 3.29080i) q^{67} -21.0847i q^{69} +(-5.28418 - 7.90834i) q^{71} +(-10.4326 + 6.97086i) q^{73} +(8.33785 - 7.83834i) q^{75} +(2.92540 + 7.06253i) q^{77} +(-5.04210 + 7.54604i) q^{79} +(-7.56944 - 7.56944i) q^{81} +(2.46878 + 1.02260i) q^{83} +(-2.66375 + 8.82635i) q^{85} +(16.5297 + 6.84683i) q^{87} +(-4.74058 - 4.74058i) q^{89} +(-0.263415 + 0.394229i) q^{91} +(4.47350 + 10.8000i) q^{93} +(1.29704 + 15.6404i) q^{95} +(1.83285 - 1.22467i) q^{97} +(4.85947 + 7.27271i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 16 q^{15} - 24 q^{27} - 8 q^{29} + 16 q^{31} - 48 q^{33} - 32 q^{35} - 16 q^{37} - 16 q^{41} + 48 q^{43} - 24 q^{45} - 16 q^{47} - 80 q^{49} + 32 q^{51} - 8 q^{53} + 24 q^{55} - 80 q^{59} - 24 q^{61}+ \cdots + 48 q^{99}+O(q^{100}) $ 112 * q + 16 * q^15 - 24 * q^27 - 8 * q^29 + 16 * q^31 - 48 * q^33 - 32 * q^35 - 16 * q^37 - 16 * q^41 + 48 * q^43 - 24 * q^45 - 16 * q^47 - 80 * q^49 + 32 * q^51 - 8 * q^53 + 24 * q^55 - 80 * q^59 - 24 * q^61 - 72 * q^63 + 16 * q^65 - 48 * q^67 - 40 * q^71 - 16 * q^73 + 16 * q^75 + 24 * q^77 + 40 * q^79 - 24 * q^83 + 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^93 - 8 * q^95 + 64 * q^97 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{16}\right)$	$1$	$1$

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
$3$	−0.446513	+	2.24477i	−0.257794	+	1.29602i	0.607325	+	0.794453i	$0.292243\pi$
$3$	−0.446513	+	2.24477i	−0.257794	+	1.29602i	−0.865119	+	0.501566i	$0.832757\pi$
$4$		0			0
$5$	0.682045	−	2.12951i	0.305020	−	0.952346i
$5$	0.682045	−	2.12951i	0.305020	−	0.952346i
$6$		0			0
$7$	−1.62658	−	1.08684i	−0.614788	−	0.410788i	0.208815	−	0.977955i	$-0.433039\pi$
$7$	−1.62658	−	1.08684i	−0.614788	−	0.410788i	−0.823603	+	0.567167i	$0.808039\pi$
$8$		0			0
$9$	−2.06799	−	0.856589i	−0.689329	−	0.285530i
$10$		0			0
$11$	−3.24910	−	2.17098i	−0.979642	−	0.654576i	−0.0408879	−	0.999164i	$-0.513019\pi$
$11$	−3.24910	−	2.17098i	−0.979642	−	0.654576i	−0.938754	+	0.344588i	$0.888019\pi$
$12$		0			0
$13$		−	0.242367i		−	0.0672206i	−0.999435	−	0.0336103i	$-0.989299\pi$
$13$		−	0.242367i		−	0.0672206i	0.999435	−	0.0336103i	$-0.0107005\pi$
$14$		0			0
$15$	4.47572	+	2.48189i	1.15563	+	0.640821i
$16$		0			0
$17$	−4.12252	+	0.0694971i	−0.999858	+	0.0168555i
$17$	−4.12252	+	0.0694971i	−0.999858	+	0.0168555i
$18$		0			0
$19$	−6.48434	+	2.68590i	−1.48761	+	0.616188i	−0.970795	−	0.239909i	$-0.922882\pi$
$19$	−6.48434	+	2.68590i	−1.48761	+	0.616188i	−0.516814	+	0.856097i	$0.672882\pi$
$20$		0			0
$21$	3.16600	−	3.16600i	0.690878	−	0.690878i
$22$		0			0
$23$	−9.03529	+	1.79723i	−1.88399	+	0.374749i	−0.996318	−	0.0857316i	$-0.972677\pi$
$23$	−9.03529	+	1.79723i	−1.88399	+	0.374749i	−0.887670	+	0.460480i	$0.847677\pi$
$24$		0			0
$25$	−4.06963	−	2.90484i	−0.813926	−	0.580969i
$26$		0			0
$27$	−0.968454	+	1.44939i	−0.186379	+	0.278936i
$28$		0			0
$29$	1.52506	−	7.66700i	0.283197	−	1.42373i	−0.533080	−	0.846065i	$-0.678965\pi$
$29$	1.52506	−	7.66700i	0.283197	−	1.42373i	0.816276	−	0.577662i	$-0.196035\pi$
$30$		0			0
$31$	4.24674	−	2.83758i	0.762737	−	0.509645i	−0.112315	−	0.993673i	$-0.535827\pi$
$31$	4.24674	−	2.83758i	0.762737	−	0.509645i	0.875053	+	0.484028i	$0.160827\pi$
$32$		0			0
$33$	6.32413	−	6.32413i	1.10089	−	1.10089i
$34$		0			0
$35$	−3.42384	+	2.72253i	−0.578735	+	0.460192i
$36$		0			0
$37$	2.25031	+	0.447614i	0.369948	+	0.0735873i	0.376563	−	0.926391i	$-0.377106\pi$
$37$	2.25031	+	0.447614i	0.369948	+	0.0735873i	−0.00661524	+	0.999978i	$0.502106\pi$
$38$		0			0
$39$	0.544060	+	0.108220i	0.0871193	+	0.0173291i
$40$		0			0
$41$	0.789503	+	3.96910i	0.123300	+	0.619869i	0.992177	+	0.124841i	$0.0398422\pi$
$41$	0.789503	+	3.96910i	0.123300	+	0.619869i	−0.868877	+	0.495028i	$0.835158\pi$
$42$		0			0
$43$	9.56951	−	3.96382i	1.45934	−	0.604477i	0.494937	−	0.868929i	$-0.335191\pi$
$43$	9.56951	−	3.96382i	1.45934	−	0.604477i	0.964399	+	0.264452i	$0.0851911\pi$
$44$		0			0
$45$	−3.23457	+	3.81957i	−0.482182	+	0.569388i
$46$		0			0
$47$	7.19997			1.05022			0.525111	−	0.851033i	$-0.324024\pi$
$47$	7.19997			1.05022			0.525111	+	0.851033i	$0.324024\pi$
$48$		0			0
$49$	−1.21426	−	2.93149i	−0.173466	−	0.418785i
$50$		0			0
$51$	1.68475	−	9.28515i	0.235913	−	1.30018i
$52$		0			0
$53$	−4.13058	+	9.97210i	−0.567378	+	1.36977i	0.336379	+	0.941727i	$0.390798\pi$
$53$	−4.13058	+	9.97210i	−0.567378	+	1.36977i	−0.903757	+	0.428046i	$0.859202\pi$
$54$		0			0
$55$	−6.83916	+	5.43829i	−0.922193	+	0.733300i
$56$		0			0
$57$	−3.13390	−	15.7552i	−0.415095	−	2.08682i
$58$		0			0
$59$	2.44267	−	5.89712i	0.318008	−	0.767739i	−0.681352	−	0.731956i	$-0.738608\pi$
$59$	2.44267	−	5.89712i	0.318008	−	0.767739i	0.999360	−	0.0357829i	$-0.0113925\pi$
$60$		0			0
$61$	4.60449	−	0.915891i	0.589545	−	0.117268i	0.108702	−	0.994074i	$-0.465331\pi$
$61$	4.60449	−	0.915891i	0.589545	−	0.117268i	0.480843	+	0.876807i	$0.340331\pi$
$62$		0			0
$63$	2.43276	+	3.64088i	0.306499	+	0.458708i
$64$		0			0
$65$	−0.516124	−	0.165305i	−0.0640173	−	0.0205036i
$66$		0			0
$67$	3.29080	+	3.29080i	0.402035	+	0.402035i	0.878950	−	0.476915i	$-0.158245\pi$
$67$	3.29080	+	3.29080i	0.402035	+	0.402035i	−0.476915	+	0.878950i	$0.658245\pi$
$68$		0			0
$69$		−	21.0847i		−	2.53829i
$70$		0			0
$71$	−5.28418	−	7.90834i	−0.627117	−	0.938547i	−0.999943	−	0.0106456i	$-0.996611\pi$
$71$	−5.28418	−	7.90834i	−0.627117	−	0.938547i	0.372826	−	0.927901i	$-0.378389\pi$
$72$		0			0
$73$	−10.4326	+	6.97086i	−1.22105	+	0.815877i	−0.987676	−	0.156510i	$-0.949976\pi$
$73$	−10.4326	+	6.97086i	−1.22105	+	0.815877i	−0.233371	+	0.972388i	$0.574976\pi$
$74$		0			0
$75$	8.33785	−	7.83834i	0.962772	−	0.905093i
$76$		0			0
$77$	2.92540	+	7.06253i	0.333380	+	0.804850i
$78$		0			0
$79$	−5.04210	+	7.54604i	−0.567281	+	0.848995i	−0.998583	−	0.0532119i	$-0.983054\pi$
$79$	−5.04210	+	7.54604i	−0.567281	+	0.848995i	0.431303	+	0.902207i	$0.358054\pi$
$80$		0			0
$81$	−7.56944	−	7.56944i	−0.841049	−	0.841049i
$82$		0			0
$83$	2.46878	+	1.02260i	0.270984	+	0.112245i	0.514038	−	0.857768i	$-0.328149\pi$
$83$	2.46878	+	1.02260i	0.270984	+	0.112245i	−0.243054	+	0.970013i	$0.578149\pi$
$84$		0			0
$85$	−2.66375	+	8.82635i	−0.288924	+	0.957352i
$86$		0			0
$87$	16.5297	+	6.84683i	1.77217	+	0.734057i
$88$		0			0
$89$	−4.74058	−	4.74058i	−0.502501	−	0.502501i	0.409714	−	0.912214i	$-0.365629\pi$
$89$	−4.74058	−	4.74058i	−0.502501	−	0.502501i	−0.912214	+	0.409714i	$0.865629\pi$
$90$		0			0
$91$	−0.263415	+	0.394229i	−0.0276134	+	0.0413264i
$92$		0			0
$93$	4.47350	+	10.8000i	0.463880	+	1.11991i
$94$		0			0
$95$	1.29704	+	15.6404i	0.133074	+	1.60467i
$96$		0			0
$97$	1.83285	−	1.22467i	0.186097	−	0.124346i	−0.459032	−	0.888420i	$-0.651804\pi$
$97$	1.83285	−	1.22467i	0.186097	−	0.124346i	0.645129	+	0.764074i	$0.276804\pi$
$98$		0			0
$99$	4.85947	+	7.27271i	0.488395	+	0.730935i
$100$		0			0
$101$			7.91783i			0.787853i	0.919142	+	0.393927i	$0.128884\pi$
$101$			7.91783i			0.787853i	−0.919142	+	0.393927i	$0.871116\pi$
$102$		0			0
$103$	0.622052	+	0.622052i	0.0612926	+	0.0612926i	0.737089	−	0.675796i	$-0.236200\pi$
$103$	0.622052	+	0.622052i	0.0612926	+	0.0612926i	−0.675796	+	0.737089i	$0.736200\pi$
$104$		0			0
$105$	−4.58268	−	8.90139i	−0.447224	−	0.868686i
$106$		0			0
$107$	−6.81525	−	10.1997i	−0.658856	−	0.986047i	−0.998957	−	0.0456583i	$-0.985461\pi$
$107$	−6.81525	−	10.1997i	−0.658856	−	0.986047i	0.340102	−	0.940389i	$-0.389539\pi$
$108$		0			0
$109$	3.16026	−	0.628614i	0.302698	−	0.0602103i	−0.0414046	−	0.999142i	$-0.513183\pi$
$109$	3.16026	−	0.628614i	0.302698	−	0.0602103i	0.344102	+	0.938932i	$0.388183\pi$
$110$		0			0
$111$	−2.00958	+	4.85156i	−0.190741	+	0.460490i
$112$		0			0
$113$	−0.0346850	−	0.174373i	−0.00326289	−	0.0164037i	0.979120	−	0.203285i	$-0.0651619\pi$
$113$	−0.0346850	−	0.174373i	−0.00326289	−	0.0164037i	−0.982382	+	0.186882i	$0.940162\pi$
$114$		0			0
$115$	−2.33525	+	20.4665i	−0.217763	+	1.90851i
$116$		0			0
$117$	−0.207609	+	0.501213i	−0.0191935	+	0.0463371i
$118$		0			0
$119$	6.78112	+	4.36749i	0.621624	+	0.400367i
$120$		0			0
$121$	1.63400	+	3.94482i	0.148545	+	0.358620i
$122$		0			0
$123$	−9.26225			−0.835149
$124$		0			0
$125$	−8.96156	+	6.68508i	−0.801547	+	0.597932i
$126$		0			0
$127$	−4.24739	+	1.75933i	−0.376895	+	0.156115i	−0.563085	−	0.826399i	$-0.690386\pi$
$127$	−4.24739	+	1.75933i	−0.376895	+	0.156115i	0.186191	+	0.982514i	$0.440386\pi$
$128$		0			0
$129$	4.62496	+	23.2513i	0.407205	+	2.04716i
$130$		0			0
$131$	−10.5485	−	2.09822i	−0.921624	−	0.183322i	−0.288596	−	0.957451i	$-0.593188\pi$
$131$	−10.5485	−	2.09822i	−0.921624	−	0.183322i	−0.633028	+	0.774129i	$0.718188\pi$
$132$		0			0
$133$	13.4664	+	2.67864i	1.16769	+	0.232267i
$134$		0			0
$135$	2.42597	+	3.05089i	0.208794	+	0.262578i
$136$		0			0
$137$	−7.55598	+	7.55598i	−0.645551	+	0.645551i	−0.951914	−	0.306364i	$-0.900888\pi$
$137$	−7.55598	+	7.55598i	−0.645551	+	0.645551i	0.306364	+	0.951914i	$0.400888\pi$
$138$		0			0
$139$	10.5761	−	7.06674i	0.897055	−	0.599393i	−0.0192763	−	0.999814i	$-0.506136\pi$
$139$	10.5761	−	7.06674i	0.897055	−	0.599393i	0.916331	+	0.400421i	$0.131136\pi$
$140$		0			0
$141$	−3.21488	+	16.1623i	−0.270741	+	1.36111i
$142$		0			0
$143$	−0.526175	+	0.787477i	−0.0440010	+	0.0658521i
$144$		0			0
$145$	−15.2868	−	8.47688i	−1.26950	−	0.703966i
$146$		0			0
$147$	7.12272	−	1.41680i	0.587472	−	0.116855i
$148$		0			0
$149$	9.42922	−	9.42922i	0.772472	−	0.772472i	−0.206066	−	0.978538i	$-0.566066\pi$
$149$	9.42922	−	9.42922i	0.772472	−	0.772472i	0.978538	+	0.206066i	$0.0660663\pi$
$150$		0			0
$151$	−11.6910	+	4.84257i	−0.951399	+	0.394082i	−0.803757	−	0.594958i	$-0.797169\pi$
$151$	−11.6910	+	4.84257i	−0.951399	+	0.394082i	−0.147643	+	0.989041i	$0.547169\pi$
$152$		0			0
$153$	8.58485	+	3.38758i	0.694044	+	0.273870i
$154$		0			0
$155$	−3.14619	−	10.9788i	−0.252708	−	0.881842i
$156$		0			0
$157$			6.73305i			0.537356i	0.963230	+	0.268678i	$0.0865868\pi$
$157$			6.73305i			0.537356i	−0.963230	+	0.268678i	$0.913413\pi$
$158$		0			0
$159$	−20.5407	−	13.7249i	−1.62899	−	1.08845i
$160$		0			0
$161$	16.6499	+	6.89661i	1.31220	+	0.543529i
$162$		0			0
$163$	14.8431	+	9.91787i	1.16260	+	0.776828i	0.978534	−	0.206085i	$-0.0660725\pi$
$163$	14.8431	+	9.91787i	1.16260	+	0.776828i	0.184071	+	0.982913i	$0.441072\pi$
$164$		0			0
$165$	−9.15396	−	17.7806i	−0.712634	−	1.38422i
$166$		0			0
$167$	−0.0356861	+	0.179406i	−0.00276147	+	0.0138829i	−0.982141	−	0.188144i	$-0.939753\pi$
$167$	−0.0356861	+	0.179406i	−0.00276147	+	0.0138829i	0.979380	+	0.202027i	$0.0647528\pi$
$168$		0			0
$169$	12.9413			0.995481
$170$		0			0
$171$	15.7102			1.20139
$172$		0			0
$173$	2.96809	−	14.9216i	0.225659	−	1.13447i	−0.687287	−	0.726386i	$-0.741198\pi$
$173$	2.96809	−	14.9216i	0.225659	−	1.13447i	0.912946	−	0.408080i	$-0.133802\pi$
$174$		0			0
$175$	3.46245	+	9.14800i	0.261737	+	0.691523i
$176$		0			0
$177$	12.1470	+	8.11636i	0.913024	+	0.610063i
$178$		0			0
$179$	8.84537	+	3.66387i	0.661134	+	0.273851i	0.687916	−	0.725791i	$-0.258526\pi$
$179$	8.84537	+	3.66387i	0.661134	+	0.273851i	−0.0267815	+	0.999641i	$0.508526\pi$
$180$		0			0
$181$	−3.69371	−	2.46806i	−0.274552	−	0.183450i	0.410670	−	0.911784i	$-0.365295\pi$
$181$	−3.69371	−	2.46806i	−0.274552	−	0.183450i	−0.685222	+	0.728334i	$0.740295\pi$
$182$		0			0
$183$			10.7450i			0.794293i
$184$		0			0
$185$	2.48801	−	4.48676i	0.182922	−	0.329873i
$186$		0			0
$187$	13.5454	+	8.72411i	0.990536	+	0.637970i
$188$		0			0
$189$	3.15053	−	1.30499i	0.229167	−	0.0949242i
$190$		0			0
$191$	−8.45149	+	8.45149i	−0.611528	+	0.611528i	−0.943344	−	0.331816i	$-0.892339\pi$
$191$	−8.45149	+	8.45149i	−0.611528	+	0.611528i	0.331816	+	0.943344i	$0.392339\pi$
$192$		0			0
$193$	−18.3107	+	3.64222i	−1.31803	+	0.262173i	−0.803503	−	0.595300i	$-0.797033\pi$
$193$	−18.3107	+	3.64222i	−1.31803	+	0.262173i	−0.514529	+	0.857473i	$0.672033\pi$
$194$		0			0
$195$	0.601529	−	1.08477i	0.0430764	−	0.0776820i
$196$		0			0
$197$	13.6688	−	20.4568i	0.973863	−	1.45749i	0.0865907	−	0.996244i	$-0.472403\pi$
$197$	13.6688	−	20.4568i	0.973863	−	1.45749i	0.887273	−	0.461245i	$-0.152597\pi$
$198$		0			0
$199$	1.18714	−	5.96817i	0.0841543	−	0.423072i	−0.915624	−	0.402035i	$-0.868303\pi$
$199$	1.18714	−	5.96817i	0.0841543	−	0.423072i	0.999779	−	0.0210375i	$-0.00669693\pi$
$200$		0			0
$201$	−8.85647	+	5.91771i	−0.624687	+	0.417403i
$202$		0			0
$203$	−10.8135	+	10.8135i	−0.758956	+	0.758956i
$204$		0			0
$205$	8.99072	+	1.02585i	0.627939	+	0.0716484i
$206$		0			0
$207$	20.2244	+	4.02287i	1.40569	+	0.279609i
$208$		0			0
$209$	26.8993	+	5.35061i	1.86067	+	0.370110i
$210$		0			0
$211$	−3.58864	−	18.0413i	−0.247052	−	1.24202i	−0.882663	−	0.470006i	$-0.844252\pi$
$211$	−3.58864	−	18.0413i	−0.247052	−	1.24202i	0.635611	−	0.772010i	$-0.280748\pi$
$212$		0			0
$213$	20.1119	−	8.33061i	1.37804	−	0.570804i
$214$		0			0
$215$	−1.91416	−	23.0819i	−0.130545	−	1.57417i
$216$		0			0
$217$	−9.99165			−0.678278
$218$		0			0
$219$	−10.9897	−	26.5315i	−0.742614	−	1.79283i
$220$		0			0
$221$	0.0168438	+	0.999165i	0.00113304	+	0.0672111i
$222$		0			0
$223$	−7.21593	+	17.4208i	−0.483214	+	1.16658i	0.474859	+	0.880062i	$0.342499\pi$
$223$	−7.21593	+	17.4208i	−0.483214	+	1.16658i	−0.958074	+	0.286521i	$0.907501\pi$
$224$		0			0
$225$	5.92769	+	9.49318i	0.395179	+	0.632879i
$226$		0			0
$227$	−4.46150	−	22.4295i	−0.296120	−	1.48870i	−0.786719	−	0.617311i	$-0.788222\pi$
$227$	−4.46150	−	22.4295i	−0.296120	−	1.48870i	0.490599	−	0.871386i	$-0.336778\pi$
$228$		0			0
$229$	−7.72032	+	18.6385i	−0.510173	+	1.23167i	0.433610	+	0.901101i	$0.357240\pi$
$229$	−7.72032	+	18.6385i	−0.510173	+	1.23167i	−0.943783	+	0.330566i	$0.892760\pi$
$230$		0			0
$231$	−17.1600	+	3.41334i	−1.12905	+	0.224581i
$232$		0			0
$233$	−5.09119	−	7.61951i	−0.333535	−	0.499171i	0.626358	−	0.779535i	$-0.284545\pi$
$233$	−5.09119	−	7.61951i	−0.333535	−	0.499171i	−0.959894	+	0.280365i	$0.909545\pi$
$234$		0			0
$235$	4.91070	−	15.3324i	0.320339	−	1.00018i
$236$		0			0
$237$	−14.6878	−	14.6878i	−0.954073	−	0.954073i
$238$		0			0
$239$		−	8.77753i		−	0.567771i	−0.958858	−	0.283886i	$-0.908376\pi$
$239$		−	8.77753i		−	0.567771i	0.958858	−	0.283886i	$-0.0916236\pi$
$240$		0			0
$241$	−0.316852	−	0.474203i	−0.0204102	−	0.0305461i	0.821124	−	0.570750i	$-0.193347\pi$
$241$	−0.316852	−	0.474203i	−0.0204102	−	0.0305461i	−0.841534	+	0.540203i	$0.818347\pi$
$242$		0			0
$243$	16.0233	−	10.7064i	1.02790	−	0.686819i
$244$		0			0
$245$	−7.07083	+	0.586378i	−0.451739	+	0.0374623i
$246$		0			0
$247$	0.650975	+	1.57159i	0.0414206	+	0.0999981i
$248$		0			0
$249$	−3.39785	+	5.08524i	−0.215330	+	0.322264i
$250$		0			0
$251$	−11.5855	−	11.5855i	−0.731273	−	0.731273i	0.239599	−	0.970872i	$-0.422984\pi$
$251$	−11.5855	−	11.5855i	−0.731273	−	0.731273i	−0.970872	+	0.239599i	$0.922984\pi$
$252$		0			0
$253$	33.2584	+	13.7761i	2.09094	+	0.866094i
$254$		0			0
$255$	−18.6237	−	9.92059i	−1.16626	−	0.621251i
$256$		0			0
$257$	−0.448980	−	0.185974i	−0.0280066	−	0.0116007i	0.368636	−	0.929574i	$-0.379825\pi$
$257$	−0.448980	−	0.185974i	−0.0280066	−	0.0116007i	−0.396643	+	0.917973i	$0.629825\pi$
$258$		0			0
$259$	−3.17381	−	3.17381i	−0.197211	−	0.197211i
$260$		0			0
$261$	−9.72128	+	14.5489i	−0.601732	+	0.900555i
$262$		0			0
$263$	−5.58255	−	13.4775i	−0.344235	−	0.831056i	−0.997278	−	0.0737355i	$-0.976508\pi$
$263$	−5.58255	−	13.4775i	−0.344235	−	0.831056i	0.653043	−	0.757321i	$-0.273492\pi$
$264$		0			0
$265$	18.4184	+	15.5975i	1.13144	+	0.958148i
$266$		0			0
$267$	12.7583	−	8.52479i	0.780792	−	0.521709i
$268$		0			0
$269$	−3.42146	−	5.12058i	−0.208610	−	0.312207i	0.712379	−	0.701795i	$-0.247618\pi$
$269$	−3.42146	−	5.12058i	−0.208610	−	0.312207i	−0.920990	+	0.389587i	$0.872618\pi$
$270$		0			0
$271$			14.5780i			0.885552i	0.896632	+	0.442776i	$0.146006\pi$
$271$			14.5780i			0.885552i	−0.896632	+	0.442776i	$0.853994\pi$
$272$		0			0
$273$	−0.767336	−	0.767336i	−0.0464413	−	0.0464413i
$274$		0			0
$275$	6.91629	+	18.2732i	0.417068	+	1.10192i
$276$		0			0
$277$	−0.938813	−	1.40503i	−0.0564078	−	0.0844202i	0.802194	−	0.597064i	$-0.203666\pi$
$277$	−0.938813	−	1.40503i	−0.0564078	−	0.0844202i	−0.858601	+	0.512644i	$0.828666\pi$
$278$		0			0
$279$	−11.2128	+	2.23037i	−0.671296	+	0.133529i
$280$		0			0
$281$	−11.8884	+	28.7012i	−0.709204	+	1.71217i	−0.00722295	+	0.999974i	$0.502299\pi$
$281$	−11.8884	+	28.7012i	−0.709204	+	1.71217i	−0.701981	+	0.712196i	$0.747701\pi$
$282$		0			0
$283$	5.52694	+	27.7858i	0.328543	+	1.65170i	0.693341	+	0.720609i	$0.256138\pi$
$283$	5.52694	+	27.7858i	0.328543	+	1.65170i	−0.364799	+	0.931086i	$0.618862\pi$
$284$		0			0
$285$	−35.6882	−	4.07206i	−2.11399	−	0.241208i
$286$		0			0
$287$	3.02960	−	7.31411i	0.178832	−	0.431738i
$288$		0			0
$289$	16.9903	−	0.573007i	0.999432	−	0.0337063i
$290$		0			0
$291$	1.93071	+	4.66115i	0.113180	+	0.273242i
$292$		0			0
$293$	22.4715			1.31280			0.656400	−	0.754413i	$-0.272078\pi$
$293$	22.4715			1.31280			0.656400	+	0.754413i	$0.272078\pi$
$294$		0			0
$295$	−10.8920	−	9.22378i	−0.634155	−	0.537029i
$296$		0			0
$297$	6.29322	−	2.60674i	0.365170	−	0.151258i
$298$		0			0
$299$	0.435590	+	2.18986i	0.0251908	+	0.126643i
$300$		0			0
$301$	−19.8736	−	3.95310i	−1.14549	−	0.227853i
$302$		0			0
$303$	−17.7737	−	3.53541i	−1.02107	−	0.203104i
$304$		0			0
$305$	1.19007	−	10.4300i	0.0681434	−	0.597220i
$306$		0			0
$307$	−0.750014	+	0.750014i	−0.0428056	+	0.0428056i	−0.728186	−	0.685380i	$-0.759636\pi$
$307$	−0.750014	+	0.750014i	−0.0428056	+	0.0428056i	0.685380	+	0.728186i	$0.259636\pi$
$308$		0			0
$309$	−1.67412	+	1.11861i	−0.0952373	+	0.0636356i
$310$		0			0
$311$	2.36845	−	11.9070i	0.134302	−	0.675183i	−0.853703	−	0.520761i	$-0.825648\pi$
$311$	2.36845	−	11.9070i	0.134302	−	0.675183i	0.988005	−	0.154422i	$-0.0493516\pi$
$312$		0			0
$313$	1.99635	−	2.98775i	0.112840	−	0.168877i	−0.770751	−	0.637137i	$-0.780119\pi$
$313$	1.99635	−	2.98775i	0.112840	−	0.168877i	0.883591	+	0.468259i	$0.155119\pi$
$314$		0			0
$315$	9.41255	−	2.69734i	0.530337	−	0.151978i
$316$		0			0
$317$	−30.8374	+	6.13394i	−1.73200	+	0.344516i	−0.957583	−	0.288158i	$-0.906957\pi$
$317$	−30.8374	+	6.13394i	−1.73200	+	0.344516i	−0.774418	+	0.632675i	$0.781957\pi$
$318$		0			0
$319$	−21.6000	+	21.6000i	−1.20937	+	1.20937i
$320$		0			0
$321$	25.9392	−	10.7444i	1.44779	−	0.599692i
$322$		0			0
$323$	26.5452	−	11.5233i	1.47701	−	0.641175i
$324$		0			0
$325$	−0.704039	+	0.986346i	−0.0390531	+	0.0547126i
$326$		0			0
$327$			7.37474i			0.407824i
$328$		0			0
$329$	−11.7113	−	7.82523i	−0.645664	−	0.431419i
$330$		0			0
$331$	−14.2998	−	5.92318i	−0.785989	−	0.325567i	−0.0466595	−	0.998911i	$-0.514858\pi$
$331$	−14.2998	−	5.92318i	−0.785989	−	0.325567i	−0.739330	+	0.673343i	$0.764858\pi$
$332$		0			0
$333$	−4.27019	−	2.85325i	−0.234005	−	0.156357i
$334$		0			0
$335$	9.25226	−	4.76332i	0.505505	−	0.260248i
$336$		0			0
$337$	−0.152117	+	0.764745i	−0.00828635	+	0.0416583i	−0.984707	−	0.174217i	$-0.944261\pi$
$337$	−0.152117	+	0.764745i	−0.00828635	+	0.0416583i	0.976421	+	0.215875i	$0.0692605\pi$
$338$		0			0
$339$	0.406915			0.0221006
$340$		0			0
$341$	−19.9584			−1.08081
$342$		0			0
$343$	−3.88252	+	19.5187i	−0.209636	+	1.05391i
$344$		0			0
$345$	−44.9000	−	14.3807i	−2.41733	−	0.774230i
$346$		0			0
$347$	−29.3885	−	19.6368i	−1.57766	−	1.05416i	−0.964461	−	0.264227i	$-0.914883\pi$
$347$	−29.3885	−	19.6368i	−1.57766	−	1.05416i	−0.613197	−	0.789930i	$-0.710117\pi$
$348$		0			0
$349$	−18.1629	−	7.52330i	−0.972235	−	0.402713i	−0.160691	−	0.987005i	$-0.551372\pi$
$349$	−18.1629	−	7.52330i	−0.972235	−	0.402713i	−0.811544	+	0.584292i	$0.801372\pi$
$350$		0			0
$351$	0.351286	+	0.234722i	0.0187503	+	0.0125285i
$352$		0			0
$353$			3.42082i			0.182072i	0.995848	+	0.0910359i	$0.0290178\pi$
$353$			3.42082i			0.182072i	−0.995848	+	0.0910359i	$0.970982\pi$
$354$		0			0
$355$	−20.4449	+	5.85888i	−1.08510	+	0.310957i
$356$		0			0
$357$	−12.8319	+	13.2719i	−0.679135	+	0.702425i
$358$		0			0
$359$	6.54897	−	2.71267i	0.345642	−	0.143169i	−0.203108	−	0.979156i	$-0.565104\pi$
$359$	6.54897	−	2.71267i	0.345642	−	0.143169i	0.548749	+	0.835987i	$0.315104\pi$
$360$		0			0
$361$	21.3976	−	21.3976i	1.12619	−	1.12619i
$362$		0			0
$363$	−9.58483	+	1.90654i	−0.503073	+	0.100067i
$364$		0			0
$365$	7.72900	+	26.9708i	0.404554	+	1.41172i
$366$		0			0
$367$	4.31427	−	6.45676i	0.225203	−	0.337040i	−0.701612	−	0.712560i	$-0.747536\pi$
$367$	4.31427	−	6.45676i	0.225203	−	0.337040i	0.926814	+	0.375520i	$0.122536\pi$
$368$		0			0
$369$	1.76720	−	8.88433i	0.0919969	−	0.462500i
$370$		0			0
$371$	17.5568	−	11.7311i	0.911504	−	0.609047i
$372$		0			0
$373$	−1.82294	+	1.82294i	−0.0943884	+	0.0943884i	−0.752724	−	0.658336i	$-0.771261\pi$
$373$	−1.82294	+	1.82294i	−0.0943884	+	0.0943884i	0.658336	+	0.752724i	$0.271261\pi$
$374$		0			0
$375$	−11.0050	−	23.1016i	−0.568298	−	1.19296i
$376$		0			0
$377$	−1.85823	−	0.369625i	−0.0957038	−	0.0190367i
$378$		0			0
$379$	−4.60801	−	0.916591i	−0.236698	−	0.0470821i	0.0753159	−	0.997160i	$-0.476003\pi$
$379$	−4.60801	−	0.916591i	−0.236698	−	0.0470821i	−0.312014	+	0.950078i	$0.601003\pi$
$380$		0			0
$381$	−2.05277	−	10.3200i	−0.105167	−	0.528709i
$382$		0			0
$383$	24.4665	−	10.1344i	1.25018	−	0.517841i	0.343298	−	0.939227i	$-0.388456\pi$
$383$	24.4665	−	10.1344i	1.25018	−	0.517841i	0.906882	+	0.421385i	$0.138456\pi$
$384$		0			0
$385$	17.0350	−	1.41270i	0.868183	−	0.0719978i
$386$		0			0
$387$	−23.1850			−1.17856
$388$		0			0
$389$	9.48911	+	22.9087i	0.481117	+	1.16152i	0.959079	+	0.283139i	$0.0913756\pi$
$389$	9.48911	+	22.9087i	0.481117	+	1.16152i	−0.477962	+	0.878380i	$0.658624\pi$
$390$		0			0
$391$	37.1233	−	8.03705i	1.87740	−	0.406451i
$392$		0			0
$393$	9.42005	−	22.7420i	0.475179	−	1.14718i
$394$		0			0
$395$	12.6304	+	15.8839i	0.635506	+	0.799208i
$396$		0			0
$397$	−0.761180	−	3.82671i	−0.0382025	−	0.192057i	0.956972	−	0.290182i	$-0.0937157\pi$
$397$	−0.761180	−	3.82671i	−0.0382025	−	0.192057i	−0.995174	+	0.0981244i	$0.968716\pi$
$398$		0			0
$399$	−12.0259	+	29.0330i	−0.602046	+	1.45347i
$400$		0			0
$401$	−20.0915	+	3.99644i	−1.00332	+	0.199573i	−0.669299	−	0.742993i	$-0.733406\pi$
$401$	−20.0915	+	3.99644i	−1.00332	+	0.199573i	−0.334021	+	0.942566i	$0.608406\pi$
$402$		0			0
$403$	−0.687738	−	1.02927i	−0.0342586	−	0.0512717i
$404$		0			0
$405$	−21.2819	+	10.9565i	−1.05751	+	0.544433i
$406$		0			0
$407$	−6.33972	−	6.33972i	−0.314248	−	0.314248i
$408$		0			0
$409$		−	1.29942i		−	0.0642523i	−0.999484	−	0.0321262i	$-0.989772\pi$
$409$		−	1.29942i		−	0.0642523i	0.999484	−	0.0321262i	$-0.0102278\pi$
$410$		0			0
$411$	−13.5876	−	20.3353i	−0.670227	−	1.00307i
$412$		0			0
$413$	−10.3824	+	6.93731i	−0.510885	+	0.341363i
$414$		0			0
$415$	3.86146	−	4.55983i	0.189552	−	0.223833i
$416$		0			0
$417$	11.1408	+	26.8964i	0.545569	+	1.31712i
$418$		0			0
$419$	2.53289	−	3.79074i	0.123740	−	0.185190i	−0.764428	−	0.644709i	$-0.776978\pi$
$419$	2.53289	−	3.79074i	0.123740	−	0.185190i	0.888168	+	0.459520i	$0.151978\pi$
$420$		0			0
$421$	13.4301	+	13.4301i	0.654542	+	0.654542i	0.954083	−	0.299541i	$-0.0968336\pi$
$421$	13.4301	+	13.4301i	0.654542	+	0.654542i	−0.299541	+	0.954083i	$0.596834\pi$
$422$		0			0
$423$	−14.8894	−	6.16741i	−0.723949	−	0.299870i
$424$		0			0
$425$	16.9790	+	11.6924i	0.823603	+	0.567167i
$426$		0			0
$427$	−8.48499	−	3.51460i	−0.410617	−	0.170083i
$428$		0			0
$429$	−1.53276	−	1.53276i	−0.0740025	−	0.0740025i
$430$		0			0
$431$	16.2956	−	24.3881i	0.784932	−	1.17473i	−0.196042	−	0.980595i	$-0.562809\pi$
$431$	16.2956	−	24.3881i	0.784932	−	1.17473i	0.980974	−	0.194138i	$-0.0621910\pi$
$432$		0			0
$433$	−1.75589	−	4.23908i	−0.0843825	−	0.203717i	0.876056	−	0.482209i	$-0.160165\pi$
$433$	−1.75589	−	4.23908i	−0.0843825	−	0.203717i	−0.960439	+	0.278492i	$0.910165\pi$
$434$		0			0
$435$	25.8544	−	30.5303i	1.23962	−	1.46382i
$436$		0			0
$437$	53.7607	−	35.9218i	2.57172	−	1.71837i
$438$		0			0
$439$	−8.18943	−	12.2563i	−0.390860	−	0.584963i	0.582899	−	0.812545i	$-0.301918\pi$
$439$	−8.18943	−	12.2563i	−0.390860	−	0.584963i	−0.973759	+	0.227581i	$0.926918\pi$
$440$		0			0
$441$			7.10241i			0.338210i
$442$		0			0
$443$	−18.8865	−	18.8865i	−0.897323	−	0.897323i	0.0978753	−	0.995199i	$-0.468795\pi$
$443$	−18.8865	−	18.8865i	−0.897323	−	0.897323i	−0.995199	+	0.0978753i	$0.968795\pi$
$444$		0			0
$445$	−13.3284	+	6.86183i	−0.631827	+	0.325282i
$446$		0			0
$447$	16.9562	+	25.3767i	0.802000	+	1.20028i
$448$		0			0
$449$	−8.53680	+	1.69808i	−0.402877	+	0.0801371i	−0.392370	−	0.919808i	$-0.628345\pi$
$449$	−8.53680	+	1.69808i	−0.402877	+	0.0801371i	−0.0105070	+	0.999945i	$0.503345\pi$
$450$		0			0
$451$	6.05167	−	14.6100i	0.284962	−	0.687959i
$452$		0			0
$453$	−5.65028	−	28.4059i	−0.265473	−	1.33462i
$454$		0			0
$455$	0.659854	+	0.829828i	0.0309344	+	0.0389029i
$456$		0			0
$457$	3.80799	−	9.19330i	0.178130	−	0.430044i	−0.809444	−	0.587197i	$-0.800231\pi$
$457$	3.80799	−	9.19330i	0.178130	−	0.430044i	0.987574	+	0.157152i	$0.0502314\pi$
$458$		0			0
$459$	3.89174	−	6.04246i	0.181651	−	0.282038i
$460$		0			0
$461$	0.501341	+	1.21035i	0.0233498	+	0.0563714i	0.935124	−	0.354320i	$-0.115288\pi$
$461$	0.501341	+	1.21035i	0.0233498	+	0.0563714i	−0.911775	+	0.410691i	$0.865288\pi$
$462$		0			0
$463$	−28.7687			−1.33700			−0.668498	−	0.743714i	$-0.733062\pi$
$463$	−28.7687			−1.33700			−0.668498	+	0.743714i	$0.733062\pi$
$464$		0			0
$465$	26.0498	−	2.16029i	1.20803	−	0.100181i
$466$		0			0
$467$	3.91817	−	1.62296i	0.181311	−	0.0751015i	−0.290181	−	0.956972i	$-0.593716\pi$
$467$	3.91817	−	1.62296i	0.181311	−	0.0751015i	0.471492	+	0.881870i	$0.343716\pi$
$468$		0			0
$469$	−1.77615	−	8.92931i	−0.0820150	−	0.412317i
$470$		0			0
$471$	−15.1142	−	3.00640i	−0.696424	−	0.138527i
$472$		0			0
$473$	−39.6977	−	7.89637i	−1.82530	−	0.363075i
$474$		0			0
$475$	34.1910	+	7.90537i	1.56879	+	0.362723i
$476$		0			0
$477$	17.0840	−	17.0840i	0.782221	−	0.782221i
$478$		0			0
$479$	8.59431	−	5.74254i	0.392684	−	0.262383i	−0.343516	−	0.939147i	$-0.611618\pi$
$479$	8.59431	−	5.74254i	0.392684	−	0.262383i	0.736200	+	0.676764i	$0.236618\pi$
$480$		0			0
$481$	0.108487	−	0.545401i	0.00494658	−	0.0248681i
$482$		0			0
$483$	−22.9157	+	34.2958i	−1.04270	+	1.56051i
$484$		0			0
$485$	−1.35786	−	4.73835i	−0.0616573	−	0.215157i
$486$		0			0
$487$	−16.2419	+	3.23072i	−0.735992	+	0.146398i	−0.548833	−	0.835932i	$-0.684928\pi$
$487$	−16.2419	+	3.23072i	−0.735992	+	0.146398i	−0.187159	+	0.982330i	$0.559928\pi$
$488$		0			0
$489$	−28.8910	+	28.8910i	−1.30650	+	1.30650i
$490$		0			0
$491$	27.4389	−	11.3656i	1.23830	−	0.512921i	0.335117	−	0.942176i	$-0.391224\pi$
$491$	27.4389	−	11.3656i	1.23830	−	0.512921i	0.903183	+	0.429255i	$0.141224\pi$
$492$		0			0
$493$	−5.75426	+	31.7134i	−0.259159	+	1.42830i
$494$		0			0
$495$	18.8017	−	5.38798i	0.845073	−	0.242172i
$496$		0			0
$497$			18.6066i			0.834619i
$498$		0			0
$499$	15.1407	+	10.1167i	0.677790	+	0.452885i	0.846224	−	0.532828i	$-0.178871\pi$
$499$	15.1407	+	10.1167i	0.677790	+	0.452885i	−0.168433	+	0.985713i	$0.553871\pi$
$500$		0			0
$501$	−0.386792	−	0.160214i	−0.0172806	−	0.00715785i
$502$		0			0
$503$	−10.7055	−	7.15320i	−0.477336	−	0.318946i	0.293523	−	0.955952i	$-0.405172\pi$
$503$	−10.7055	−	7.15320i	−0.477336	−	0.318946i	−0.770858	+	0.637007i	$0.780172\pi$
$504$		0			0
$505$	16.8611	+	5.40031i	0.750309	+	0.240311i
$506$		0			0
$507$	−5.77844	+	29.0502i	−0.256629	+	1.29016i
$508$		0			0
$509$	36.0005			1.59570			0.797848	−	0.602859i	$-0.205972\pi$
$509$	36.0005			1.59570			0.797848	+	0.602859i	$0.205972\pi$
$510$		0			0
$511$	24.5457			1.08584
$512$		0			0
$513$	2.38686	−	11.9995i	0.105382	−	0.529793i
$514$		0			0
$515$	1.74893	−	0.900399i	0.0770673	−	0.0396763i
$516$		0			0
$517$	−23.3934	−	15.6310i	−1.02884	−	0.687450i
$518$		0			0
$519$	32.1702	+	13.3253i	1.41212	+	0.584918i
$520$		0			0
$521$	4.28825	+	2.86532i	0.187872	+	0.125532i	0.645949	−	0.763380i	$-0.276462\pi$
$521$	4.28825	+	2.86532i	0.187872	+	0.125532i	−0.458077	+	0.888912i	$0.651462\pi$
$522$		0			0
$523$		−	15.8575i		−	0.693399i	−0.937976	−	0.346700i	$-0.887302\pi$
$523$		−	15.8575i		−	0.693399i	0.937976	−	0.346700i	$-0.112698\pi$
$524$		0			0
$525$	−22.0812	+	3.68771i	−0.963702	+	0.160945i
$526$		0			0
$527$	−17.3101	+	11.9931i	−0.754039	+	0.522429i
$528$		0			0
$529$	57.1572	−	23.6753i	2.48510	−	1.02936i
$530$		0			0
$531$	−10.1028	+	10.1028i	−0.438424	+	0.438424i
$532$		0			0
$533$	0.961980	−	0.191350i	0.0416680	−	0.00828828i
$534$		0			0
$535$	−26.3688	+	7.55647i	−1.14002	+	0.326695i
$536$		0			0
$537$	−12.1741	+	18.2199i	−0.525353	+	0.786246i
$538$		0			0
$539$	−2.41895	+	12.1609i	−0.104191	+	0.523806i
$540$		0			0
$541$	23.4522	−	15.6703i	1.00829	−	0.673718i	0.0623484	−	0.998054i	$-0.480141\pi$
$541$	23.4522	−	15.6703i	1.00829	−	0.673718i	0.945942	+	0.324337i	$0.105141\pi$
$542$		0			0
$543$	7.18953	−	7.18953i	0.308532	−	0.308532i
$544$		0			0
$545$	0.816797	−	7.15854i	0.0349877	−	0.306638i
$546$		0			0
$547$	4.48522	+	0.892165i	0.191774	+	0.0381462i	0.290043	−	0.957014i	$-0.406330\pi$
$547$	4.48522	+	0.892165i	0.191774	+	0.0381462i	−0.0982687	+	0.995160i	$0.531330\pi$
$548$		0			0
$549$	−10.3066	−	2.05011i	−0.439874	−	0.0874964i
$550$		0			0
$551$	10.7038	+	53.8116i	0.455997	+	2.29245i
$552$		0			0
$553$	16.4027	−	6.79423i	0.697514	−	0.288920i
$554$		0			0
$555$	8.96082	+	7.58841i	0.380366	+	0.322110i
$556$		0			0
$557$	−13.0068			−0.551117			−0.275558	−	0.961284i	$-0.588863\pi$
$557$	−13.0068			−0.551117			−0.275558	+	0.961284i	$0.588863\pi$
$558$		0			0
$559$	−0.960701	−	2.31934i	−0.0406333	−	0.0980975i
$560$		0			0
$561$	−25.6318	+	26.5108i	−1.08218	+	1.11929i
$562$		0			0
$563$	−7.11276	+	17.1717i	−0.299767	+	0.723701i	0.700186	+	0.713961i	$0.253101\pi$
$563$	−7.11276	+	17.1717i	−0.299767	+	0.723701i	−0.999953	+	0.00974053i	$0.996899\pi$
$564$		0			0
$565$	−0.394986	−	0.0450683i	−0.0166172	−	0.00189604i
$566$		0			0
$567$	4.08547	+	20.5391i	0.171574	+	0.862559i
$568$		0			0
$569$	−6.89001	+	16.6340i	−0.288844	+	0.697332i	−0.999984	−	0.00571919i	$-0.998180\pi$
$569$	−6.89001	+	16.6340i	−0.288844	+	0.697332i	0.711139	+	0.703051i	$0.248180\pi$
$570$		0			0
$571$	−24.1455	+	4.80283i	−1.01046	+	0.200992i	−0.672443	−	0.740149i	$-0.734755\pi$
$571$	−24.1455	+	4.80283i	−1.01046	+	0.200992i	−0.338013	+	0.941141i	$0.609755\pi$
$572$		0			0
$573$	−15.1980	−	22.7454i	−0.634904	−	0.950201i
$574$		0			0
$575$	41.9910	+	18.9320i	1.75114	+	0.789521i
$576$		0			0
$577$	−23.3705	−	23.3705i	−0.972928	−	0.972928i	0.0267154	−	0.999643i	$-0.491495\pi$
$577$	−23.3705	−	23.3705i	−0.972928	−	0.972928i	−0.999643	+	0.0267154i	$0.991495\pi$
$578$		0			0
$579$		−	42.7296i		−	1.77578i
$580$		0			0
$581$	−2.90425	−	4.34651i	−0.120489	−	0.180324i
$582$		0			0
$583$	35.0699	−	23.4330i	1.45245	−	0.970495i
$584$		0			0
$585$	0.925739	+	0.783956i	0.0382746	+	0.0324126i
$586$		0			0
$587$	−6.40421	−	15.4611i	−0.264330	−	0.638149i	0.734867	−	0.678211i	$-0.237244\pi$
$587$	−6.40421	−	15.4611i	−0.264330	−	0.638149i	−0.999197	+	0.0400621i	$0.987244\pi$
$588$		0			0
$589$	−19.9159	+	29.8062i	−0.820618	+	1.22814i
$590$		0			0
$591$	39.8176	+	39.8176i	1.63788	+	1.63788i
$592$		0			0
$593$	−44.6466	−	18.4932i	−1.83342	−	0.759426i	−0.964296	−	0.264825i	$-0.914686\pi$
$593$	−44.6466	−	18.4932i	−1.83342	−	0.759426i	−0.869120	−	0.494601i	$-0.835314\pi$
$594$		0			0
$595$	13.9256	−	11.4616i	0.570896	−	0.469882i
$596$		0			0
$597$	12.8671	+	5.32973i	0.526615	+	0.218131i
$598$		0			0
$599$	−18.5662	−	18.5662i	−0.758595	−	0.758595i	0.217471	−	0.976067i	$-0.430219\pi$
$599$	−18.5662	−	18.5662i	−0.758595	−	0.758595i	−0.976067	+	0.217471i	$0.930219\pi$
$600$		0			0
$601$	3.30596	−	4.94773i	0.134853	−	0.201822i	−0.757897	−	0.652374i	$-0.773773\pi$
$601$	3.30596	−	4.94773i	0.134853	−	0.201822i	0.892750	+	0.450552i	$0.148773\pi$
$602$		0			0
$603$	−3.98647	−	9.62419i	−0.162342	−	0.391927i
$604$		0			0
$605$	9.51500	−	0.789072i	0.386840	−	0.0320803i
$606$		0			0
$607$	5.98598	−	3.99971i	0.242964	−	0.162343i	−0.428127	−	0.903719i	$-0.640826\pi$
$607$	5.98598	−	3.99971i	0.242964	−	0.162343i	0.671090	+	0.741376i	$0.265826\pi$
$608$		0			0
$609$	−19.4454	−	29.1021i	−0.787967	−	1.17928i
$610$		0			0
$611$		−	1.74504i		−	0.0705966i
$612$		0			0
$613$	−8.32227	−	8.32227i	−0.336133	−	0.336133i	0.518776	−	0.854910i	$-0.326388\pi$
$613$	−8.32227	−	8.32227i	−0.336133	−	0.336133i	−0.854910	+	0.518776i	$0.826388\pi$
$614$		0			0
$615$	−6.31727	+	19.7240i	−0.254737	+	0.795350i
$616$		0			0
$617$	17.4113	+	26.0579i	0.700953	+	1.04905i	0.995624	+	0.0934511i	$0.0297899\pi$
$617$	17.4113	+	26.0579i	0.700953	+	1.04905i	−0.294671	+	0.955599i	$0.595210\pi$
$618$		0			0
$619$	−5.55912	+	1.10578i	−0.223440	+	0.0444450i	−0.305540	−	0.952179i	$-0.598837\pi$
$619$	−5.55912	+	1.10578i	−0.223440	+	0.0444450i	0.0821006	+	0.996624i	$0.473837\pi$
$620$		0			0
$621$	6.14537	−	14.8362i	0.246605	−	0.595358i
$622$		0			0
$623$	2.55865	+	12.8632i	0.102510	+	0.515352i
$624$		0			0
$625$	8.12377	+	23.6433i	0.324951	+	0.945731i
$626$		0			0
$627$	−24.0218	+	57.9938i	−0.959339	+	2.31605i
$628$		0			0
$629$	−9.30804	−	1.68891i	−0.371136	−	0.0673411i
$630$		0			0
$631$	3.14931	+	7.60310i	0.125372	+	0.302675i	0.974086	−	0.226177i	$-0.0726228\pi$
$631$	3.14931	+	7.60310i	0.125372	+	0.302675i	−0.848714	+	0.528852i	$0.822623\pi$
$632$		0			0
$633$	42.1010			1.67337
$634$		0			0
$635$	0.849593	+	10.2448i	0.0337151	+	0.406553i
$636$		0			0
$637$	−0.710498	+	0.294298i	−0.0281510	+	0.0116605i
$638$		0			0
$639$	4.15343	+	20.8807i	0.164307	+	0.826028i
$640$		0			0
$641$	5.64693	+	1.12324i	0.223040	+	0.0443655i	0.305345	−	0.952242i	$-0.401228\pi$
$641$	5.64693	+	1.12324i	0.223040	+	0.0443655i	−0.0823049	+	0.996607i	$0.526228\pi$
$642$		0			0
$643$	−5.21426	−	1.03718i	−0.205630	−	0.0409024i	0.0912002	−	0.995833i	$-0.470930\pi$
$643$	−5.21426	−	1.03718i	−0.205630	−	0.0409024i	−0.296831	+	0.954930i	$0.595930\pi$
$644$		0			0
$645$	52.6682	+	6.00949i	2.07381	+	0.236624i
$646$		0			0
$647$	−0.898766	+	0.898766i	−0.0353341	+	0.0353341i	−0.724553	−	0.689219i	$-0.757954\pi$
$647$	−0.898766	+	0.898766i	−0.0353341	+	0.0353341i	0.689219	+	0.724553i	$0.257954\pi$
$648$		0			0
$649$	−20.7390	+	13.8574i	−0.814077	+	0.543949i
$650$		0			0
$651$	4.46140	−	22.4290i	0.174856	−	0.879061i
$652$		0			0
$653$	−16.1226	+	24.1292i	−0.630926	+	0.944247i	0.368965	+	0.929443i	$0.379712\pi$
$653$	−16.1226	+	24.1292i	−0.630926	+	0.944247i	−0.999890	+	0.0148035i	$0.995288\pi$
$654$		0			0
$655$	−11.6627	+	21.0320i	−0.455700	+	0.821788i
$656$		0			0
$657$	27.5457	−	5.47918i	1.07466	−	0.213763i
$658$		0			0
$659$	−23.1025	+	23.1025i	−0.899944	+	0.899944i	−0.995431	−	0.0954867i	$-0.969559\pi$
$659$	−23.1025	+	23.1025i	−0.899944	+	0.899944i	0.0954867	+	0.995431i	$0.469559\pi$
$660$		0			0
$661$	−12.5069	+	5.18051i	−0.486461	+	0.201499i	−0.612414	−	0.790538i	$-0.709801\pi$
$661$	−12.5069	+	5.18051i	−0.486461	+	0.201499i	0.125953	+	0.992036i	$0.459801\pi$
$662$		0			0
$663$	−2.25042	−	0.408329i	−0.0873990	−	0.0158582i
$664$		0			0
$665$	14.8889	−	26.8499i	0.577367	−	1.04120i
$666$		0			0
$667$			72.0145i			2.78841i
$668$		0			0
$669$	−35.8837	−	23.9767i	−1.38734	−	0.926994i
$670$		0			0
$671$	−16.9489	−	7.02045i	−0.654304	−	0.271021i
$672$		0			0
$673$	−14.2554	−	9.52518i	−0.549507	−	0.367169i	0.249608	−	0.968347i	$-0.419698\pi$
$673$	−14.2554	−	9.52518i	−0.549507	−	0.367169i	−0.799115	+	0.601178i	$0.794698\pi$
$674$		0			0
$675$	8.15151	−	3.08529i	0.313752	−	0.118753i
$676$		0			0
$677$	−3.71425	+	18.6728i	−0.142750	+	0.717653i	0.841414	+	0.540392i	$0.181724\pi$
$677$	−3.71425	+	18.6728i	−0.142750	+	0.717653i	−0.984164	+	0.177262i	$0.943276\pi$
$678$		0			0
$679$	−4.31229			−0.165490
$680$		0			0
$681$	52.3412			2.00572
$682$		0			0
$683$	−3.93332	+	19.7741i	−0.150504	+	0.756637i	0.829632	+	0.558311i	$0.188550\pi$
$683$	−3.93332	+	19.7741i	−0.150504	+	0.756637i	−0.980136	+	0.198326i	$0.936450\pi$
$684$		0			0
$685$	10.9370	+	21.2440i	0.417882	+	0.811693i
$686$		0			0
$687$	−38.3920	−	25.6527i	−1.46474	−	0.978711i
$688$		0			0
$689$	2.41691	+	1.00112i	0.0920770	+	0.0381395i
$690$		0			0
$691$	18.8779	+	12.6138i	0.718149	+	0.479852i	0.860167	−	0.510012i	$-0.170359\pi$
$691$	18.8779	+	12.6138i	0.718149	+	0.479852i	−0.142018	+	0.989864i	$0.545359\pi$
$692$		0			0
$693$		−	17.1111i		−	0.649997i
$694$		0			0
$695$	−7.83530	−	27.3418i	−0.297210	−	1.03713i
$696$		0			0
$697$	−3.53058	−	16.3078i	−0.133730	−	0.617703i
$698$		0			0
$699$	19.3773	−	8.02636i	0.732918	−	0.303585i
$700$		0			0
$701$	25.0022	−	25.0022i	0.944322	−	0.944322i	−0.0542080	−	0.998530i	$-0.517263\pi$
$701$	25.0022	−	25.0022i	0.944322	−	0.944322i	0.998530	+	0.0542080i	$0.0172634\pi$
$702$		0			0
$703$	−15.7940	+	3.14162i	−0.595682	+	0.118489i
$704$		0			0
$705$	32.2251	+	17.8695i	1.21367	+	0.673005i
$706$		0			0
$707$	8.60544	−	12.8789i	0.323641	−	0.484363i
$708$		0			0
$709$	2.04697	−	10.2908i	0.0768756	−	0.386480i	−0.923122	−	0.384506i	$-0.874372\pi$
$709$	2.04697	−	10.2908i	0.0768756	−	0.386480i	0.999998	−	0.00197357i	$-0.000628206\pi$
$710$		0			0
$711$	16.8908	−	11.2861i	0.633456	−	0.423262i
$712$		0			0
$713$	−33.2708	+	33.2708i	−1.24600	+	1.24600i
$714$		0			0
$715$	1.31807	+	1.65759i	0.0492929	+	0.0619904i
$716$		0			0
$717$	19.7035	+	3.91928i	0.735842	+	0.146368i
$718$		0			0
$719$	27.5120	+	5.47248i	1.02603	+	0.204089i	0.679287	−	0.733873i	$-0.262289\pi$
$719$	27.5120	+	5.47248i	1.02603	+	0.204089i	0.346738	+	0.937962i	$0.387289\pi$
$720$		0			0
$721$	−0.335742	−	1.68789i	−0.0125037	−	0.0628602i
$722$		0			0
$723$	1.20596	−	0.499523i	0.0448500	−	0.0185775i
$724$		0			0
$725$	−28.4779	+	26.7718i	−1.05764	+	0.994280i
$726$		0			0
$727$	29.0104			1.07594			0.537968	−	0.842965i	$-0.319192\pi$
$727$	29.0104			1.07594			0.537968	+	0.842965i	$0.319192\pi$
$728$		0			0
$729$	4.58926	+	11.0794i	0.169972	+	0.410350i
$730$		0			0
$731$	−39.1750	+	17.0060i	−1.44894	+	0.628989i
$732$		0			0
$733$	15.9067	−	38.4022i	0.587528	−	1.41842i	−0.298331	−	0.954462i	$-0.596430\pi$
$733$	15.9067	−	38.4022i	0.587528	−	1.41842i	0.885859	−	0.463955i	$-0.153570\pi$
$734$		0			0
$735$	1.84093	−	16.1342i	0.0679037	−	0.595120i
$736$		0			0
$737$	−3.54788	−	17.8364i	−0.130688	−	0.657013i
$738$		0			0
$739$	−2.84036	+	6.85724i	−0.104484	+	0.252248i	−0.967472	−	0.252977i	$-0.918590\pi$
$739$	−2.84036	+	6.85724i	−0.104484	+	0.252248i	0.862988	+	0.505225i	$0.168590\pi$
$740$		0			0
$741$	−3.81854	+	0.759554i	−0.140277	+	0.0279029i
$742$		0			0
$743$	1.72985	+	2.58891i	0.0634621	+	0.0949778i	0.861843	−	0.507174i	$-0.169310\pi$
$743$	1.72985	+	2.58891i	0.0634621	+	0.0949778i	−0.798381	+	0.602152i	$0.794310\pi$
$744$		0			0
$745$	−13.6485	−	26.5108i	−0.500041	−	0.971280i
$746$		0			0
$747$	−4.22946	−	4.22946i	−0.154748	−	0.154748i
$748$		0			0
$749$			23.9978i			0.876860i
$750$		0			0
$751$	−14.2315	−	21.2990i	−0.519316	−	0.777211i	0.475412	−	0.879763i	$-0.342299\pi$
$751$	−14.2315	−	21.2990i	−0.519316	−	0.777211i	−0.994728	+	0.102553i	$0.967299\pi$
$752$		0			0
$753$	31.1800	−	20.8338i	1.13626	−	0.759226i
$754$		0			0
$755$	2.33852	+	28.1989i	0.0851073	+	1.02626i
$756$		0			0
$757$	19.8457	+	47.9116i	0.721303	+	1.74138i	0.669607	+	0.742715i	$0.266462\pi$
$757$	19.8457	+	47.9116i	0.721303	+	1.74138i	0.0516954	+	0.998663i	$0.483538\pi$
$758$		0			0
$759$	−45.7744	+	68.5062i	−1.66151	+	2.48662i
$760$		0			0
$761$	−33.1219	−	33.1219i	−1.20067	−	1.20067i	−0.973964	−	0.226705i	$-0.927205\pi$
$761$	−33.1219	−	33.1219i	−1.20067	−	1.20067i	−0.226705	−	0.973964i	$-0.572795\pi$
$762$		0			0
$763$	−5.82360	−	2.41221i	−0.210829	−	0.0873280i
$764$		0			0
$765$	13.0691	−	15.9710i	0.472516	−	0.577434i
$766$		0			0
$767$	−1.42927	−	0.592023i	−0.0516079	−	0.0213767i
$768$		0			0
$769$	26.9212	+	26.9212i	0.970804	+	0.970804i	0.999586	−	0.0287816i	$-0.00916272\pi$
$769$	26.9212	+	26.9212i	0.970804	+	0.970804i	−0.0287816	+	0.999586i	$0.509163\pi$
$770$		0			0
$771$	0.617944	−	0.924818i	0.0222547	−	0.0333065i
$772$		0			0
$773$	−5.65367	−	13.6492i	−0.203348	−	0.490926i	0.789000	−	0.614393i	$-0.210599\pi$
$773$	−5.65367	−	13.6492i	−0.203348	−	0.490926i	−0.992349	+	0.123466i	$0.960599\pi$
$774$		0			0
$775$	−25.5254	−	0.788213i	−0.916899	−	0.0283134i
$776$		0			0
$777$	8.54162	−	5.70733i	0.306429	−	0.204749i
$778$		0			0
$779$	−15.7800	−	23.6165i	−0.565378	−	0.846148i
$780$		0			0
$781$			37.1669i			1.32994i
$782$		0			0
$783$	9.63556	+	9.63556i	0.344347	+	0.344347i
$784$		0			0
$785$	14.3381	+	4.59225i	0.511749	+	0.163904i
$786$		0			0
$787$	−2.26970	−	3.39685i	−0.0809062	−	0.121085i	0.788809	−	0.614638i	$-0.210698\pi$
$787$	−2.26970	−	3.39685i	−0.0809062	−	0.121085i	−0.869716	+	0.493553i	$0.835698\pi$
$788$		0			0
$789$	32.7465	−	6.51369i	1.16581	−	0.231893i
$790$		0			0
$791$	−0.133099	+	0.321328i	−0.00473244	+	0.0114251i
$792$		0			0
$793$	−0.221982	−	1.11598i	−0.00788282	−	0.0396296i
$794$		0			0
$795$	−43.2370	+	34.3807i	−1.53346	+	1.21936i
$796$		0			0
$797$	14.7563	−	35.6248i	0.522694	−	1.26189i	−0.413530	−	0.910490i	$-0.635704\pi$
$797$	14.7563	−	35.6248i	0.522694	−	1.26189i	0.936224	−	0.351404i	$-0.114296\pi$
$798$		0			0
$799$	−29.6820	+	0.500377i	−1.05007	+	0.0177021i
$800$		0			0
$801$	5.74274	+	13.8642i	0.202910	+	0.489867i
$802$		0			0
$803$	49.0303			1.73024
$804$		0			0
$805$	26.0424	−	30.7523i	0.917873	−	1.08388i
$806$		0			0
$807$	13.0223	−	5.39400i	0.458406	−	0.189878i
$808$		0			0
$809$	−2.22998	−	11.2109i	−0.0784020	−	0.394153i	−0.999982	−	0.00596546i	$-0.998101\pi$
$809$	−2.22998	−	11.2109i	−0.0784020	−	0.394153i	0.921580	−	0.388188i	$-0.126899\pi$
$810$		0			0
$811$	42.4483	+	8.44349i	1.49056	+	0.296491i	0.872101	−	0.489325i	$-0.162757\pi$
$811$	42.4483	+	8.44349i	1.49056	+	0.296491i	0.618460	+	0.785816i	$0.287757\pi$
$812$		0			0
$813$	−32.7243	−	6.50928i	−1.14769	−	0.228290i
$814$		0			0
$815$	31.2439	−	24.8442i	1.09443	−	0.870254i
$816$		0			0
$817$	−51.4055	+	51.4055i	−1.79845	+	1.79845i
$818$		0			0
$819$	0.882432	−	0.589622i	0.0308347	−	0.0206031i
$820$		0			0
$821$	−7.05965	+	35.4913i	−0.246383	+	1.23865i	0.637317	+	0.770601i	$0.280044\pi$
$821$	−7.05965	+	35.4913i	−0.246383	+	1.23865i	−0.883701	+	0.468052i	$0.844956\pi$
$822$		0			0
$823$	3.26171	−	4.88149i	0.113696	−	0.170158i	−0.770257	−	0.637733i	$-0.779872\pi$
$823$	3.26171	−	4.88149i	0.113696	−	0.170158i	0.883953	+	0.467575i	$0.154872\pi$
$824$		0			0
$825$	−44.1074	+	7.36625i	−1.53562	+	0.256460i
$826$		0			0
$827$	−21.6895	+	4.31431i	−0.754218	+	0.150023i	−0.557202	−	0.830377i	$-0.688125\pi$
$827$	−21.6895	+	4.31431i	−0.754218	+	0.150023i	−0.197016	+	0.980400i	$0.563125\pi$
$828$		0			0
$829$	32.3188	−	32.3188i	1.12248	−	1.12248i	0.131109	−	0.991368i	$-0.458146\pi$
$829$	32.3188	−	32.3188i	1.12248	−	1.12248i	0.991368	−	0.131109i	$-0.0418538\pi$
$830$		0			0
$831$	3.57317	−	1.48006i	0.123952	−	0.0513425i
$832$		0			0
$833$	5.20956	+	12.0007i	0.180500	+	0.415801i
$834$		0			0
$835$	0.357708	+	0.198357i	0.0123790	+	0.00686443i
$836$		0			0
$837$			8.90327i			0.307742i
$838$		0			0
$839$	19.1088	+	12.7681i	0.659710	+	0.440804i	0.839837	−	0.542839i	$-0.182651\pi$
$839$	19.1088	+	12.7681i	0.659710	+	0.440804i	−0.180127	+	0.983643i	$0.557651\pi$
$840$		0			0
$841$	−29.6646	−	12.2875i	−1.02292	−	0.423706i
$842$		0			0
$843$	−59.1193	−	39.5022i	−2.03618	−	1.36053i
$844$		0			0
$845$	8.82652	−	27.5585i	0.303641	−	0.948043i
$846$		0			0
$847$	1.62958	−	8.19245i	0.0559930	−	0.281496i
$848$		0			0
$849$	−64.8407			−2.22533
$850$		0			0
$851$	−21.1366			−0.724555
$852$		0			0
$853$	3.79265	−	19.0669i	0.129858	−	0.652839i	−0.859944	−	0.510388i	$-0.829502\pi$
$853$	3.79265	−	19.0669i	0.129858	−	0.652839i	0.989802	−	0.142451i	$-0.0454982\pi$
$854$		0			0
$855$	10.7151	−	33.4551i	0.366449	−	1.14414i
$856$		0			0
$857$	−21.8762	−	14.6172i	−0.747276	−	0.499314i	0.122678	−	0.992447i	$-0.460852\pi$
$857$	−21.8762	−	14.6172i	−0.747276	−	0.499314i	−0.869954	+	0.493133i	$0.835852\pi$
$858$		0			0
$859$	40.0729	+	16.5987i	1.36727	+	0.566341i	0.941046	−	0.338277i	$-0.109844\pi$
$859$	40.0729	+	16.5987i	1.36727	+	0.566341i	0.426222	+	0.904618i	$0.359844\pi$
$860$		0			0
$861$	15.0657	+	10.0666i	0.513439	+	0.343069i
$862$		0			0
$863$		−	16.7008i		−	0.568501i	−0.958750	−	0.284250i	$-0.908255\pi$
$863$		−	16.7008i		−	0.568501i	0.958750	−	0.284250i	$-0.0917447\pi$
$864$		0			0
$865$	−29.7513	−	16.4978i	−1.01157	−	0.560940i
$866$		0			0
$867$	−6.30014	+	38.3953i	−0.213964	+	1.30397i
$868$		0			0
$869$	32.7646	−	13.5716i	1.11146	−	0.460383i
$870$		0			0
$871$	0.797582	−	0.797582i	0.0270250	−	0.0270250i
$872$		0			0
$873$	−4.83934	+	0.962605i	−0.163787	+	0.0325793i
$874$		0			0
$875$	21.8423	−	1.13398i	0.738404	−	0.0383356i
$876$		0			0
$877$	9.88365	−	14.7919i	0.333747	−	0.499488i	−0.626202	−	0.779661i	$-0.715392\pi$
$877$	9.88365	−	14.7919i	0.333747	−	0.499488i	0.959950	+	0.280172i	$0.0903916\pi$
$878$		0			0
$879$	−10.0338	+	50.4434i	−0.338432	+	1.70141i
$880$		0			0
$881$	33.7775	−	22.5694i	1.13799	−	0.760382i	0.163887	−	0.986479i	$-0.447597\pi$
$881$	33.7775	−	22.5694i	1.13799	−	0.760382i	0.974105	+	0.226097i	$0.0725966\pi$
$882$		0			0
$883$	14.4104	−	14.4104i	0.484947	−	0.484947i	−0.421760	−	0.906707i	$-0.638588\pi$
$883$	14.4104	−	14.4104i	0.484947	−	0.484947i	0.906707	+	0.421760i	$0.138588\pi$
$884$		0			0
$885$	25.5687	−	20.3314i	0.859482	−	0.683434i
$886$		0			0
$887$	37.2711	+	7.41369i	1.25144	+	0.248927i	0.775951	−	0.630793i	$-0.217270\pi$
$887$	37.2711	+	7.41369i	1.25144	+	0.248927i	0.475491	+	0.879721i	$0.342270\pi$
$888$		0			0
$889$	8.82081	+	1.75457i	0.295841	+	0.0588463i
$890$		0			0
$891$	8.16078	+	41.0270i	0.273396	+	1.37446i
$892$		0			0
$893$	−46.6870	+	19.3384i	−1.56232	+	0.647135i
$894$		0			0
$895$	13.8352	−	16.3374i	0.462460	−	0.546099i
$896$		0			0
$897$	−5.11023			−0.170626
$898$		0			0
$899$	−15.2792	−	36.8873i	−0.509590	−	1.23026i
$900$		0			0
$901$	16.3354	−	41.3972i	0.544210	−	1.37914i
$902$		0			0
$903$	17.7476	−	42.8465i	0.590604	−	1.42584i
$904$		0			0
$905$	−7.77504	+	6.18248i	−0.258451	+	0.205512i
$906$		0			0
$907$	−11.5062	−	57.8457i	−0.382058	−	1.92074i	−0.390112	−	0.920767i	$-0.627564\pi$
$907$	−11.5062	−	57.8457i	−0.382058	−	1.92074i	0.00805392	−	0.999968i	$-0.497436\pi$
$908$		0			0
$909$	6.78232	−	16.3740i	0.224955	−	0.543090i
$910$		0			0
$911$	−43.3510	+	8.62304i	−1.43628	+	0.285694i	−0.851013	−	0.525145i	$-0.824011\pi$
$911$	−43.3510	+	8.62304i	−1.43628	+	0.285694i	−0.585269	+	0.810839i	$0.699011\pi$
$912$		0			0
$913$	−5.80127	−	8.68222i	−0.191994	−	0.287339i
$914$		0			0
$915$	22.8816	+	7.32857i	0.756442	+	0.242275i
$916$		0			0
$917$	14.8774	+	14.8774i	0.491296	+	0.491296i
$918$		0			0
$919$		−	8.47263i		−	0.279486i	−0.990188	−	0.139743i	$-0.955372\pi$
$919$		−	8.47263i		−	0.279486i	0.990188	−	0.139743i	$-0.0446277\pi$
$920$		0			0
$921$	−1.34872	−	2.01850i	−0.0444418	−	0.0665119i
$922$		0			0
$923$	−1.91672	+	1.28071i	−0.0630897	+	0.0421552i
$924$		0			0
$925$	−7.85767	−	8.35841i	−0.258358	−	0.274823i
$926$		0			0
$927$	−0.753554	−	1.81924i	−0.0247499	−	0.0597517i
$928$		0			0
$929$	22.9385	−	34.3299i	0.752589	−	1.12633i	−0.235415	−	0.971895i	$-0.575645\pi$
$929$	22.9385	−	34.3299i	0.752589	−	1.12633i	0.988003	−	0.154433i	$-0.0493552\pi$
$930$		0			0
$931$	15.7474	+	15.7474i	0.516100	+	0.516100i
$932$		0			0
$933$	25.6709	+	10.6332i	0.840428	+	0.348117i
$934$		0			0
$935$	27.8166	−	22.8948i	0.909702	−	0.748739i
$936$		0			0
$937$	−26.9375	−	11.1579i	−0.880009	−	0.364512i	−0.103508	−	0.994629i	$-0.533007\pi$
$937$	−26.9375	−	11.1579i	−0.880009	−	0.364512i	−0.776500	+	0.630117i	$0.783007\pi$
$938$		0			0
$939$	5.81541	+	5.81541i	0.189779	+	0.189779i
$940$		0			0
$941$	−14.1630	+	21.1965i	−0.461702	+	0.690985i	−0.987142	−	0.159845i	$-0.948901\pi$
$941$	−14.1630	+	21.1965i	−0.461702	+	0.690985i	0.525440	+	0.850830i	$0.323901\pi$
$942$		0			0
$943$	−14.2668	−	34.4430i	−0.464590	−	1.12162i
$944$		0			0
$945$	−0.630191	−	7.59915i	−0.0205001	−	0.247200i
$946$		0			0
$947$	−31.9561	+	21.3524i	−1.03843	+	0.693858i	−0.953150	−	0.302499i	$-0.902179\pi$
$947$	−31.9561	+	21.3524i	−1.03843	+	0.693858i	−0.0852824	+	0.996357i	$0.527179\pi$
$948$		0			0
$949$	1.68951	+	2.52853i	0.0548438	+	0.0820795i
$950$		0			0
$951$		−	71.9618i		−	2.33352i
$952$		0			0
$953$	−9.57028	−	9.57028i	−0.310012	−	0.310012i	0.534902	−	0.844914i	$-0.320348\pi$
$953$	−9.57028	−	9.57028i	−0.310012	−	0.310012i	−0.844914	+	0.534902i	$0.820348\pi$
$954$		0			0
$955$	12.2332	+	23.7618i	0.395858	+	0.768915i
$956$		0			0
$957$	−38.8424	−	58.1318i	−1.25560	−	1.87913i
$958$		0			0
$959$	20.5025	−	4.07821i	0.662061	−	0.131692i
$960$		0			0
$961$	−1.88024	+	4.53931i	−0.0606530	+	0.146429i
$962$		0			0
$963$	5.35687	+	26.9308i	0.172623	+	0.867834i
$964$		0			0
$965$	−4.73256	+	41.4770i	−0.152347	+	1.33519i
$966$		0			0
$967$	2.24232	−	5.41343i	0.0721081	−	0.174084i	−0.883716	−	0.468023i	$-0.844966\pi$
$967$	2.24232	−	5.41343i	0.0721081	−	0.174084i	0.955824	+	0.293939i	$0.0949663\pi$
$968$		0			0
$969$	14.0145	+	64.7331i	0.450210	+	2.07953i
$970$		0			0
$971$	−10.6655	−	25.7488i	−0.342272	−	0.826317i	−0.997485	−	0.0708734i	$-0.977421\pi$
$971$	−10.6655	−	25.7488i	−0.342272	−	0.826317i	0.655214	−	0.755444i	$-0.272579\pi$
$972$		0			0
$973$	−24.8833			−0.797722
$974$		0			0
$975$	−1.89976	−	2.02082i	−0.0608410	−	0.0647182i
$976$		0			0
$977$	−43.6535	+	18.0819i	−1.39660	+	0.578490i	−0.948867	−	0.315678i	$-0.897768\pi$
$977$	−43.6535	+	18.0819i	−1.39660	+	0.578490i	−0.447732	+	0.894168i	$0.647768\pi$
$978$		0			0
$979$	5.11093	+	25.6944i	0.163346	+	0.821195i
$980$		0			0
$981$	−7.07384	−	1.40707i	−0.225850	−	0.0449244i
$982$		0			0
$983$	−2.37586	−	0.472589i	−0.0757783	−	0.0150732i	0.157056	−	0.987590i	$-0.449800\pi$
$983$	−2.37586	−	0.472589i	−0.0757783	−	0.0150732i	−0.232834	+	0.972517i	$0.574800\pi$
$984$		0			0
$985$	−34.2403	−	43.0604i	−1.09099	−	1.37202i
$986$		0			0
$987$	22.7951	−	22.7951i	0.725576	−	0.725576i
$988$		0			0
$989$	−79.3394	+	53.0129i	−2.52285	+	1.68571i
$990$		0			0
$991$	−9.55435	+	48.0330i	−0.303504	+	1.52582i	0.464617	+	0.885512i	$0.346192\pi$
$991$	−9.55435	+	48.0330i	−0.303504	+	1.52582i	−0.768121	+	0.640305i	$0.778808\pi$
$992$		0			0
$993$	19.6812	−	29.4551i	0.624565	−	0.934728i
$994$		0			0
$995$	−11.8996	−	6.59859i	−0.377242	−	0.209189i
$996$		0			0
$997$	−1.64406	+	0.327024i	−0.0520680	+	0.0103570i	−0.221056	−	0.975261i	$-0.570950\pi$
$997$	−1.64406	+	0.327024i	−0.0520680	+	0.0103570i	0.168988	+	0.985618i	$0.445950\pi$
$998$		0			0
$999$	−2.82809	+	2.82809i	−0.0894768	+	0.0894768i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.cg.b.73.3	✓	112
5.2	odd	4		680.2.cq.b.617.12	yes	112
17.7	odd	16		680.2.cq.b.313.12	yes	112
85.7	even	16	inner	680.2.cg.b.177.3	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.cg.b.73.3	✓	112	1.1	even	1	trivial
680.2.cg.b.177.3	yes	112	85.7	even	16	inner
680.2.cq.b.313.12	yes	112	17.7	odd	16
680.2.cq.b.617.12	yes	112	5.2	odd	4

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.cg (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.446513 + 2.24477i) q^{3} +(0.682045 - 2.12951i) q^{5} +(-1.62658 - 1.08684i) q^{7} +(-2.06799 - 0.856589i) q^{9} +(-3.24910 - 2.17098i) q^{11} -0.242367i q^{13} +(4.47572 + 2.48189i) q^{15} +(-4.12252 + 0.0694971i) q^{17} +(-6.48434 + 2.68590i) q^{19} +(3.16600 - 3.16600i) q^{21} +(-9.03529 + 1.79723i) q^{23} +(-4.06963 - 2.90484i) q^{25} +(-0.968454 + 1.44939i) q^{27} +(1.52506 - 7.66700i) q^{29} +(4.24674 - 2.83758i) q^{31} +(6.32413 - 6.32413i) q^{33} +(-3.42384 + 2.72253i) q^{35} +(2.25031 + 0.447614i) q^{37} +(0.544060 + 0.108220i) q^{39} +(0.789503 + 3.96910i) q^{41} +(9.56951 - 3.96382i) q^{43} +(-3.23457 + 3.81957i) q^{45} +7.19997 q^{47} +(-1.21426 - 2.93149i) q^{49} +(1.68475 - 9.28515i) q^{51} +(-4.13058 + 9.97210i) q^{53} +(-6.83916 + 5.43829i) q^{55} +(-3.13390 - 15.7552i) q^{57} +(2.44267 - 5.89712i) q^{59} +(4.60449 - 0.915891i) q^{61} +(2.43276 + 3.64088i) q^{63} +(-0.516124 - 0.165305i) q^{65} +(3.29080 + 3.29080i) q^{67} -21.0847i q^{69} +(-5.28418 - 7.90834i) q^{71} +(-10.4326 + 6.97086i) q^{73} +(8.33785 - 7.83834i) q^{75} +(2.92540 + 7.06253i) q^{77} +(-5.04210 + 7.54604i) q^{79} +(-7.56944 - 7.56944i) q^{81} +(2.46878 + 1.02260i) q^{83} +(-2.66375 + 8.82635i) q^{85} +(16.5297 + 6.84683i) q^{87} +(-4.74058 - 4.74058i) q^{89} +(-0.263415 + 0.394229i) q^{91} +(4.47350 + 10.8000i) q^{93} +(1.29704 + 15.6404i) q^{95} +(1.83285 - 1.22467i) q^{97} +(4.85947 + 7.27271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 16 q^{15} - 24 q^{27} - 8 q^{29} + 16 q^{31} - 48 q^{33} - 32 q^{35} - 16 q^{37} - 16 q^{41} + 48 q^{43} - 24 q^{45} - 16 q^{47} - 80 q^{49} + 32 q^{51} - 8 q^{53} + 24 q^{55} - 80 q^{59} - 24 q^{61}+ \cdots + 48 q^{99}+O(q^{100}) \) 112 * q + 16 * q^15 - 24 * q^27 - 8 * q^29 + 16 * q^31 - 48 * q^33 - 32 * q^35 - 16 * q^37 - 16 * q^41 + 48 * q^43 - 24 * q^45 - 16 * q^47 - 80 * q^49 + 32 * q^51 - 8 * q^53 + 24 * q^55 - 80 * q^59 - 24 * q^61 - 72 * q^63 + 16 * q^65 - 48 * q^67 - 40 * q^71 - 16 * q^73 + 16 * q^75 + 24 * q^77 + 40 * q^79 - 24 * q^83 + 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^93 - 8 * q^95 + 64 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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