LMFDB - Embedded newform 1008.2.cz.g.607.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(367,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4, 1]))

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

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

chi := DirichletCharacter("1008.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			607.12
Character	$\chi$	$=$	1008.607
Dual form			1008.2.cz.g.367.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.69672 - 0.348077i) q^{3} +(-2.08545 + 1.20403i) q^{5} +(-2.53309 - 0.763830i) q^{7} +(2.75769 - 1.18117i) q^{9} +O(q^{10})$	\(q+(1.69672 - 0.348077i) q^{3} +(-2.08545 + 1.20403i) q^{5} +(-2.53309 - 0.763830i) q^{7} +(2.75769 - 1.18117i) q^{9} +(2.81055 + 1.62267i) q^{11} +(4.35943 + 2.51692i) q^{13} +(-3.11931 + 2.76880i) q^{15} +(0.795645 - 0.459366i) q^{17} +(-3.22136 + 5.57956i) q^{19} +(-4.56381 - 0.414291i) q^{21} +(5.31720 - 3.06988i) q^{23} +(0.399389 - 0.691762i) q^{25} +(4.26787 - 2.96400i) q^{27} +(1.22793 + 2.12684i) q^{29} -3.21891 q^{31} +(5.33352 + 1.77493i) q^{33} +(6.20231 - 1.45700i) q^{35} +(-4.08685 + 7.07863i) q^{37} +(8.27280 + 2.75308i) q^{39} +(10.3845 + 5.99550i) q^{41} +(10.2187 - 5.89979i) q^{43} +(-4.32883 + 5.78362i) q^{45} -4.84127 q^{47} +(5.83313 + 3.86971i) q^{49} +(1.19009 - 1.05636i) q^{51} +(-1.56472 - 2.71017i) q^{53} -7.81500 q^{55} +(-3.52362 + 10.5882i) q^{57} +9.86072 q^{59} +9.49187i q^{61} +(-7.88769 + 0.885623i) q^{63} -12.1218 q^{65} +0.359208i q^{67} +(7.95321 - 7.05951i) q^{69} -2.32616i q^{71} +(-4.01081 + 2.31564i) q^{73} +(0.436863 - 1.31274i) q^{75} +(-5.87994 - 6.25717i) q^{77} -4.36153i q^{79} +(6.20965 - 6.51461i) q^{81} +(-8.68159 - 15.0370i) q^{83} +(-1.10618 + 1.91596i) q^{85} +(2.82375 + 3.18122i) q^{87} +(-9.68778 - 5.59324i) q^{89} +(-9.12036 - 9.70546i) q^{91} +(-5.46157 + 1.12043i) q^{93} -15.5145i q^{95} +(-9.79041 + 5.65250i) q^{97} +(9.66728 + 1.15507i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9}+O(q^{10}) $ 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9	$ 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9} - 9 q^{11} - 3 q^{13} - 6 q^{15} - 3 q^{17} - 4 q^{19} + 13 q^{21} - 6 q^{23} + 15 q^{25} + 9 q^{27} + 18 q^{29} + 34 q^{31} - 21 q^{33} - 42 q^{35} - 3 q^{37} + 27 q^{39} + 36 q^{41} + 24 q^{43} + 21 q^{45} - 42 q^{47} + 30 q^{49} - 6 q^{51} - 12 q^{53} - 30 q^{55} - 13 q^{57} - 12 q^{59} - 3 q^{63} + 6 q^{69} + 48 q^{73} + 36 q^{75} - 48 q^{77} - 31 q^{81} - 48 q^{83} - 21 q^{85} + 15 q^{87} + 39 q^{89} + 9 q^{91} + 10 q^{93} + 3 q^{97} + 30 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9 - 9 * q^11 - 3 * q^13 - 6 * q^15 - 3 * q^17 - 4 * q^19 + 13 * q^21 - 6 * q^23 + 15 * q^25 + 9 * q^27 + 18 * q^29 + 34 * q^31 - 21 * q^33 - 42 * q^35 - 3 * q^37 + 27 * q^39 + 36 * q^41 + 24 * q^43 + 21 * q^45 - 42 * q^47 + 30 * q^49 - 6 * q^51 - 12 * q^53 - 30 * q^55 - 13 * q^57 - 12 * q^59 - 3 * q^63 + 6 * q^69 + 48 * q^73 + 36 * q^75 - 48 * q^77 - 31 * q^81 - 48 * q^83 - 21 * q^85 + 15 * q^87 + 39 * q^89 + 9 * q^91 + 10 * q^93 + 3 * q^97 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.69672	−	0.348077i	0.979599	−	0.200962i
$3$	1.69672	−	0.348077i	0.979599	−	0.200962i
$4$		0			0
$5$	−2.08545	+	1.20403i	−0.932640	+	0.538460i	−0.887645	−	0.460528i	$-0.847660\pi$
$5$	−2.08545	+	1.20403i	−0.932640	+	0.538460i	−0.0449942	+	0.998987i	$0.514327\pi$
$6$		0			0
$7$	−2.53309	−	0.763830i	−0.957419	−	0.288701i
$7$	−2.53309	−	0.763830i	−0.957419	−	0.288701i
$8$		0			0
$9$	2.75769	−	1.18117i	0.919228	−	0.393725i
$10$		0			0
$11$	2.81055	+	1.62267i	0.847413	+	0.489254i	0.859777	−	0.510669i	$-0.170602\pi$
$11$	2.81055	+	1.62267i	0.847413	+	0.489254i	−0.0123640	+	0.999924i	$0.503936\pi$
$12$		0			0
$13$	4.35943	+	2.51692i	1.20909	+	0.698068i	0.962560	−	0.271067i	$-0.0873765\pi$
$13$	4.35943	+	2.51692i	1.20909	+	0.698068i	0.246529	+	0.969135i	$0.420710\pi$
$14$		0			0
$15$	−3.11931	+	2.76880i	−0.805403	+	0.714900i
$16$		0			0
$17$	0.795645	−	0.459366i	0.192972	−	0.111413i	−0.400401	−	0.916340i	$-0.631129\pi$
$17$	0.795645	−	0.459366i	0.192972	−	0.111413i	0.593373	+	0.804927i	$0.297796\pi$
$18$		0			0
$19$	−3.22136	+	5.57956i	−0.739031	+	1.28004i	0.213901	+	0.976855i	$0.431383\pi$
$19$	−3.22136	+	5.57956i	−0.739031	+	1.28004i	−0.952932	+	0.303184i	$0.901950\pi$
$20$		0			0
$21$	−4.56381	−	0.414291i	−0.995905	−	0.0904057i
$22$		0			0
$23$	5.31720	−	3.06988i	1.10871	−	0.640115i	0.170217	−	0.985407i	$-0.445553\pi$
$23$	5.31720	−	3.06988i	1.10871	−	0.640115i	0.938496	+	0.345291i	$0.112220\pi$
$24$		0			0
$25$	0.399389	−	0.691762i	0.0798777	−	0.138352i
$26$		0			0
$27$	4.26787	−	2.96400i	0.821351	−	0.570423i
$28$		0			0
$29$	1.22793	+	2.12684i	0.228021	+	0.394944i	0.957221	−	0.289356i	$-0.0934412\pi$
$29$	1.22793	+	2.12684i	0.228021	+	0.394944i	−0.729201	+	0.684300i	$0.760108\pi$
$30$		0			0
$31$	−3.21891			−0.578133			−0.289067	−	0.957309i	$-0.593345\pi$
$31$	−3.21891			−0.578133			−0.289067	+	0.957309i	$0.593345\pi$
$32$		0			0
$33$	5.33352	+	1.77493i	0.928447	+	0.308975i
$34$		0			0
$35$	6.20231	−	1.45700i	1.04838	−	0.246278i
$36$		0			0
$37$	−4.08685	+	7.07863i	−0.671874	+	1.16372i	0.305498	+	0.952193i	$0.401177\pi$
$37$	−4.08685	+	7.07863i	−0.671874	+	1.16372i	−0.977372	+	0.211528i	$0.932156\pi$
$38$		0			0
$39$	8.27280	+	2.75308i	1.32471	+	0.440846i
$40$		0			0
$41$	10.3845	+	5.99550i	1.62179	+	0.936340i	0.986441	+	0.164114i	$0.0524764\pi$
$41$	10.3845	+	5.99550i	1.62179	+	0.936340i	0.635347	+	0.772226i	$0.280857\pi$
$42$		0			0
$43$	10.2187	−	5.89979i	1.55834	−	0.899709i	0.560926	−	0.827866i	$-0.310445\pi$
$43$	10.2187	−	5.89979i	1.55834	−	0.899709i	0.997416	−	0.0718430i	$-0.0228880\pi$
$44$		0			0
$45$	−4.32883	+	5.78362i	−0.645304	+	0.862171i
$46$		0			0
$47$	−4.84127			−0.706172			−0.353086	−	0.935591i	$-0.614868\pi$
$47$	−4.84127			−0.706172			−0.353086	+	0.935591i	$0.614868\pi$
$48$		0			0
$49$	5.83313	+	3.86971i	0.833304	+	0.552815i
$50$		0			0
$51$	1.19009	−	1.05636i	0.166646	−	0.147920i
$52$		0			0
$53$	−1.56472	−	2.71017i	−0.214930	−	0.372270i	0.738321	−	0.674450i	$-0.235619\pi$
$53$	−1.56472	−	2.71017i	−0.214930	−	0.372270i	−0.953251	+	0.302179i	$0.902286\pi$
$54$		0			0
$55$	−7.81500			−1.05377
$56$		0			0
$57$	−3.52362	+	10.5882i	−0.466715	+	1.40244i
$58$		0			0
$59$	9.86072			1.28376			0.641878	−	0.766807i	$-0.278155\pi$
$59$	9.86072			1.28376			0.641878	+	0.766807i	$0.278155\pi$
$60$		0			0
$61$			9.49187i			1.21531i	0.794201	+	0.607655i	$0.207890\pi$
$61$			9.49187i			1.21531i	−0.794201	+	0.607655i	$0.792110\pi$
$62$		0			0
$63$	−7.88769	+	0.885623i	−0.993756	+	0.111578i
$64$		0			0
$65$	−12.1218			−1.50353
$66$		0			0
$67$			0.359208i			0.0438842i	0.999759	+	0.0219421i	$0.00698495\pi$
$67$			0.359208i			0.0438842i	−0.999759	+	0.0219421i	$0.993015\pi$
$68$		0			0
$69$	7.95321	−	7.05951i	0.957454	−	0.849865i
$70$		0			0
$71$		−	2.32616i		−	0.276064i	−0.990428	−	0.138032i	$-0.955922\pi$
$71$		−	2.32616i		−	0.276064i	0.990428	−	0.138032i	$-0.0440777\pi$
$72$		0			0
$73$	−4.01081	+	2.31564i	−0.469429	+	0.271025i	−0.716001	−	0.698099i	$-0.754029\pi$
$73$	−4.01081	+	2.31564i	−0.469429	+	0.271025i	0.246571	+	0.969125i	$0.420696\pi$
$74$		0			0
$75$	0.436863	−	1.31274i	0.0504446	−	0.151582i
$76$		0			0
$77$	−5.87994	−	6.25717i	−0.670082	−	0.713070i
$78$		0			0
$79$		−	4.36153i		−	0.490711i	−0.969433	−	0.245355i	$-0.921095\pi$
$79$		−	4.36153i		−	0.490711i	0.969433	−	0.245355i	$-0.0789047\pi$
$80$		0			0
$81$	6.20965	−	6.51461i	0.689962	−	0.723846i
$82$		0			0
$83$	−8.68159	−	15.0370i	−0.952928	−	1.65052i	−0.739040	−	0.673662i	$-0.764720\pi$
$83$	−8.68159	−	15.0370i	−0.952928	−	1.65052i	−0.213889	−	0.976858i	$-0.568613\pi$
$84$		0			0
$85$	−1.10618	+	1.91596i	−0.119982	+	0.207815i
$86$		0			0
$87$	2.82375	+	3.18122i	0.302738	+	0.341063i
$88$		0			0
$89$	−9.68778	−	5.59324i	−1.02690	−	0.592882i	−0.110807	−	0.993842i	$-0.535343\pi$
$89$	−9.68778	−	5.59324i	−1.02690	−	0.592882i	−0.916096	+	0.400960i	$0.868677\pi$
$90$		0			0
$91$	−9.12036	−	9.70546i	−0.956073	−	1.01741i
$92$		0			0
$93$	−5.46157	+	1.12043i	−0.566339	+	0.116183i
$94$		0			0
$95$		−	15.5145i		−	1.59175i
$96$		0			0
$97$	−9.79041	+	5.65250i	−0.994066	+	0.573924i	−0.906487	−	0.422233i	$-0.861246\pi$
$97$	−9.79041	+	5.65250i	−0.994066	+	0.573924i	−0.0875786	+	0.996158i	$0.527913\pi$
$98$		0			0
$99$	9.66728	+	1.15507i	0.971598	+	0.116089i
$100$		0			0
$101$	8.64458	+	4.99095i	0.860168	+	0.496618i	0.864068	−	0.503374i	$-0.167908\pi$
$101$	8.64458	+	4.99095i	0.860168	+	0.496618i	−0.00390076	+	0.999992i	$0.501242\pi$
$102$		0			0
$103$	0.396129	+	0.686115i	0.0390317	+	0.0676049i	0.884881	−	0.465817i	$-0.154239\pi$
$103$	0.396129	+	0.686115i	0.0390317	+	0.0676049i	−0.845850	+	0.533421i	$0.820906\pi$
$104$		0			0
$105$	10.0164	−	4.63099i	0.977500	−	0.451939i
$106$		0			0
$107$	−9.47378	−	5.46969i	−0.915865	−	0.528775i	−0.0335517	−	0.999437i	$-0.510682\pi$
$107$	−9.47378	−	5.46969i	−0.915865	−	0.528775i	−0.882314	+	0.470662i	$0.844015\pi$
$108$		0			0
$109$	−3.09619	−	5.36276i	−0.296562	−	0.513660i	0.678785	−	0.734337i	$-0.262507\pi$
$109$	−3.09619	−	5.36276i	−0.296562	−	0.513660i	−0.975347	+	0.220677i	$0.929173\pi$
$110$		0			0
$111$	−4.47031	+	13.4330i	−0.424303	+	1.27500i
$112$		0			0
$113$	2.85750	−	4.94934i	0.268811	−	0.465595i	−0.699744	−	0.714394i	$-0.746702\pi$
$113$	2.85750	−	4.94934i	0.268811	−	0.465595i	0.968555	+	0.248799i	$0.0800358\pi$
$114$		0			0
$115$	−7.39248	+	12.8042i	−0.689353	+	1.19399i
$116$		0			0
$117$	14.9949	+	1.79162i	1.38628	+	0.165636i
$118$		0			0
$119$	−2.36632	+	0.555879i	−0.216920	+	0.0509573i
$120$		0			0
$121$	−0.233866	−	0.405068i	−0.0212606	−	0.0368244i
$122$		0			0
$123$	19.7065	+	6.55805i	1.77687	+	0.591320i
$124$		0			0
$125$		−	10.1168i		−	0.904876i
$126$		0			0
$127$			7.50003i			0.665520i	0.943012	+	0.332760i	$0.107980\pi$
$127$			7.50003i			0.665520i	−0.943012	+	0.332760i	$0.892020\pi$
$128$		0			0
$129$	15.2847	−	13.5672i	1.34574	−	1.19452i
$130$		0			0
$131$	−1.02386	−	1.77338i	−0.0894551	−	0.154941i	0.817826	−	0.575466i	$-0.195179\pi$
$131$	−1.02386	−	1.77338i	−0.0894551	−	0.154941i	−0.907281	+	0.420525i	$0.861846\pi$
$132$		0			0
$133$	12.4218	−	11.6730i	1.07711	−	1.01218i
$134$		0			0
$135$	−5.33165	+	11.3199i	−0.458875	+	0.974263i
$136$		0			0
$137$	−8.05512	+	13.9519i	−0.688195	+	1.19199i	0.284226	+	0.958757i	$0.408263\pi$
$137$	−8.05512	+	13.9519i	−0.688195	+	1.19199i	−0.972421	+	0.233232i	$0.925070\pi$
$138$		0			0
$139$	−4.60386	+	7.97411i	−0.390494	+	0.676356i	−0.992515	−	0.122125i	$-0.961029\pi$
$139$	−4.60386	+	7.97411i	−0.390494	+	0.676356i	0.602021	+	0.798480i	$0.294362\pi$
$140$		0			0
$141$	−8.21426	+	1.68514i	−0.691766	+	0.141914i
$142$		0			0
$143$	8.16828	+	14.1479i	0.683066	+	1.18310i
$144$		0			0
$145$	−5.12156	−	2.95693i	−0.425322	−	0.245560i
$146$		0			0
$147$	11.2441	+	4.53541i	0.927399	+	0.374075i
$148$		0			0
$149$	−3.98935	−	6.90976i	−0.326820	−	0.566070i	0.655059	−	0.755578i	$-0.272644\pi$
$149$	−3.98935	−	6.90976i	−0.326820	−	0.566070i	−0.981879	+	0.189508i	$0.939311\pi$
$150$		0			0
$151$	−6.94588	−	4.01021i	−0.565248	−	0.326346i	0.190001	−	0.981784i	$-0.439151\pi$
$151$	−6.94588	−	4.01021i	−0.565248	−	0.326346i	−0.755249	+	0.655438i	$0.772484\pi$
$152$		0			0
$153$	1.65155	−	2.20658i	0.133520	−	0.178391i
$154$		0			0
$155$	6.71286	−	3.87567i	0.539190	−	0.311301i
$156$		0			0
$157$		−	13.0289i		−	1.03982i	−0.854220	−	0.519912i	$-0.825965\pi$
$157$		−	13.0289i		−	1.03982i	0.854220	−	0.519912i	$-0.174035\pi$
$158$		0			0
$159$	−3.59823	−	4.05374i	−0.285358	−	0.321483i
$160$		0			0
$161$	−15.8138	+	3.71487i	−1.24630	+	0.292773i
$162$		0			0
$163$	−7.57235	−	4.37190i	−0.593112	−	0.342434i	0.173215	−	0.984884i	$-0.444585\pi$
$163$	−7.57235	−	4.37190i	−0.593112	−	0.342434i	−0.766327	+	0.642450i	$0.777918\pi$
$164$		0			0
$165$	−13.2598	+	2.72022i	−1.03228	+	0.211769i
$166$		0			0
$167$	7.49367	−	12.9794i	0.579877	−	1.00438i	−0.415616	−	0.909540i	$-0.636434\pi$
$167$	7.49367	−	12.9794i	0.579877	−	1.00438i	0.995493	−	0.0948365i	$-0.0302328\pi$
$168$		0			0
$169$	6.16978	+	10.6864i	0.474599	+	0.822029i
$170$		0			0
$171$	−2.29307	+	19.1917i	−0.175355	+	1.46762i
$172$		0			0
$173$			10.1258i			0.769854i	0.922947	+	0.384927i	$0.125773\pi$
$173$			10.1258i			0.769854i	−0.922947	+	0.384927i	$0.874227\pi$
$174$		0			0
$175$	−1.54008	+	1.44723i	−0.116419	+	0.109400i
$176$		0			0
$177$	16.7308	−	3.43229i	1.25757	−	0.257987i
$178$		0			0
$179$	1.50241	−	0.867414i	0.112295	−	0.0648336i	−0.442801	−	0.896620i	$-0.646015\pi$
$179$	1.50241	−	0.867414i	0.112295	−	0.0648336i	0.555096	+	0.831787i	$0.312682\pi$
$180$		0			0
$181$			7.36133i			0.547163i	0.961849	+	0.273582i	$0.0882084\pi$
$181$			7.36133i			0.547163i	−0.961849	+	0.273582i	$0.911792\pi$
$182$		0			0
$183$	3.30390	+	16.1050i	0.244231	+	1.19052i
$184$		0			0
$185$		−	19.6828i		−	1.44711i
$186$		0			0
$187$	2.98160			0.218036
$188$		0			0
$189$	−13.0749	+	4.24817i	−0.951059	+	0.309009i
$190$		0			0
$191$			2.40493i			0.174014i	0.996208	+	0.0870071i	$0.0277303\pi$
$191$			2.40493i			0.174014i	−0.996208	+	0.0870071i	$0.972270\pi$
$192$		0			0
$193$	0.914227			0.0658075			0.0329037	−	0.999459i	$-0.489525\pi$
$193$	0.914227			0.0658075			0.0329037	+	0.999459i	$0.489525\pi$
$194$		0			0
$195$	−20.5673	+	4.21932i	−1.47285	+	0.302152i
$196$		0			0
$197$	20.0330			1.42730			0.713648	−	0.700505i	$-0.247042\pi$
$197$	20.0330			1.42730			0.713648	+	0.700505i	$0.247042\pi$
$198$		0			0
$199$	−2.75624	−	4.77395i	−0.195385	−	0.338416i	0.751642	−	0.659571i	$-0.229262\pi$
$199$	−2.75624	−	4.77395i	−0.195385	−	0.338416i	−0.947027	+	0.321155i	$0.895929\pi$
$200$		0			0
$201$	0.125032	+	0.609473i	0.00881907	+	0.0429889i
$202$		0			0
$203$	−1.48592	−	6.32541i	−0.104291	−	0.443956i
$204$		0			0
$205$	−28.8751			−2.01673
$206$		0			0
$207$	11.0371	−	14.7463i	0.767130	−	1.02494i
$208$		0			0
$209$	−18.1076	+	10.4544i	−1.25253	+	0.723148i
$210$		0			0
$211$	−4.04293	−	2.33418i	−0.278327	−	0.160692i	0.354339	−	0.935117i	$-0.384706\pi$
$211$	−4.04293	−	2.33418i	−0.278327	−	0.160692i	−0.632666	+	0.774425i	$0.718039\pi$
$212$		0			0
$213$	−0.809681	−	3.94682i	−0.0554784	−	0.270432i
$214$		0			0
$215$	−14.2071	+	24.6074i	−0.968914	+	1.67821i
$216$		0			0
$217$	8.15380	+	2.45870i	0.553516	+	0.166907i
$218$		0			0
$219$	−5.99918	+	5.32505i	−0.405387	+	0.359834i
$220$		0			0
$221$	4.62475			0.311094
$222$		0			0
$223$	−4.85402	−	8.40740i	−0.325049	−	0.563001i	0.656473	−	0.754349i	$-0.272047\pi$
$223$	−4.85402	−	8.40740i	−0.325049	−	0.563001i	−0.981522	+	0.191348i	$0.938714\pi$
$224$		0			0
$225$	0.284297	−	2.37941i	0.0189532	−	0.158627i
$226$		0			0
$227$	−0.173234	+	0.300051i	−0.0114980	+	0.0199151i	−0.871717	−	0.490009i	$-0.836993\pi$
$227$	−0.173234	+	0.300051i	−0.0114980	+	0.0199151i	0.860219	+	0.509924i	$0.170327\pi$
$228$		0			0
$229$	17.5315	−	10.1218i	1.15851	−	0.668867i	0.207565	−	0.978221i	$-0.433446\pi$
$229$	17.5315	−	10.1218i	1.15851	−	0.668867i	0.950947	+	0.309354i	$0.100113\pi$
$230$		0			0
$231$	−12.1546	−	8.56996i	−0.799712	−	0.563862i
$232$		0			0
$233$	11.3381	−	19.6382i	0.742786	−	1.28654i	−0.208436	−	0.978036i	$-0.566837\pi$
$233$	11.3381	−	19.6382i	0.742786	−	1.28654i	0.951222	−	0.308507i	$-0.0998293\pi$
$234$		0			0
$235$	10.0962	−	5.82905i	0.658604	−	0.380245i
$236$		0			0
$237$	−1.51815	−	7.40028i	−0.0986143	−	0.480700i
$238$		0			0
$239$	−15.1991	−	8.77520i	−0.983148	−	0.567621i	−0.0799289	−	0.996801i	$-0.525469\pi$
$239$	−15.1991	−	8.77520i	−0.983148	−	0.567621i	−0.903219	+	0.429180i	$0.858803\pi$
$240$		0			0
$241$	−3.12877	−	1.80640i	−0.201542	−	0.116360i	0.395832	−	0.918323i	$-0.370456\pi$
$241$	−3.12877	−	1.80640i	−0.201542	−	0.116360i	−0.597375	+	0.801962i	$0.703789\pi$
$242$		0			0
$243$	8.26843	−	13.2149i	0.530420	−	0.847735i
$244$		0			0
$245$	−16.8239	−	1.04679i	−1.07484	−	0.0668768i
$246$		0			0
$247$	−28.0866	+	16.2158i	−1.78711	+	1.03179i
$248$		0			0
$249$	−19.9642	−	22.4916i	−1.26518	−	1.42535i
$250$		0			0
$251$	10.9138			0.688875			0.344437	−	0.938809i	$-0.388070\pi$
$251$	10.9138			0.688875			0.344437	+	0.938809i	$0.388070\pi$
$252$		0			0
$253$	19.9257			1.25272
$254$		0			0
$255$	−1.20997	+	3.63588i	−0.0757715	+	0.227688i
$256$		0			0
$257$	−15.8202	+	9.13378i	−0.986836	+	0.569750i	−0.904327	−	0.426841i	$-0.859627\pi$
$257$	−15.8202	+	9.13378i	−0.986836	+	0.569750i	−0.0825087	+	0.996590i	$0.526293\pi$
$258$		0			0
$259$	15.7593	−	14.8092i	0.979232	−	0.920198i
$260$		0			0
$261$	5.89841	+	4.41475i	0.365102	+	0.273266i
$262$		0			0
$263$	25.0834	+	14.4819i	1.54671	+	0.892993i	0.998390	+	0.0567248i	$0.0180658\pi$
$263$	25.0834	+	14.4819i	1.54671	+	0.892993i	0.548320	+	0.836269i	$0.315268\pi$
$264$		0			0
$265$	6.52627	+	3.76794i	0.400905	+	0.231463i
$266$		0			0
$267$	−18.3843	−	6.11805i	−1.12510	−	0.374418i
$268$		0			0
$269$	7.83478	−	4.52341i	0.477695	−	0.275797i	−0.241760	−	0.970336i	$-0.577725\pi$
$269$	7.83478	−	4.52341i	0.477695	−	0.275797i	0.719455	+	0.694539i	$0.244391\pi$
$270$		0			0
$271$	−3.58752	+	6.21376i	−0.217926	+	0.377459i	−0.954174	−	0.299253i	$-0.903263\pi$
$271$	−3.58752	+	6.21376i	−0.217926	+	0.377459i	0.736248	+	0.676712i	$0.236596\pi$
$272$		0			0
$273$	−18.8529	−	13.2928i	−1.14103	−	0.804518i
$274$		0			0
$275$	2.24501	−	1.29615i	0.135379	−	0.0781611i
$276$		0			0
$277$	9.84559	−	17.0531i	0.591564	−	1.02462i	−0.402457	−	0.915439i	$-0.631844\pi$
$277$	9.84559	−	17.0531i	0.591564	−	1.02462i	0.994022	−	0.109181i	$-0.0348228\pi$
$278$		0			0
$279$	−8.87674	+	3.80209i	−0.531436	+	0.227625i
$280$		0			0
$281$	−12.7045	−	22.0049i	−0.757889	−	1.31270i	−0.943925	−	0.330160i	$-0.892897\pi$
$281$	−12.7045	−	22.0049i	−0.757889	−	1.31270i	0.186036	−	0.982543i	$-0.440436\pi$
$282$		0			0
$283$	25.2310			1.49983			0.749914	−	0.661535i	$-0.230095\pi$
$283$	25.2310			1.49983			0.749914	+	0.661535i	$0.230095\pi$
$284$		0			0
$285$	−5.40024	−	26.3237i	−0.319882	−	1.55928i
$286$		0			0
$287$	−21.7254	−	23.1192i	−1.28241	−	1.36468i
$288$		0			0
$289$	−8.07797	+	13.9914i	−0.475175	+	0.823026i
$290$		0			0
$291$	−14.6440	+	12.9985i	−0.858449	+	0.761985i
$292$		0			0
$293$	21.5402	+	12.4363i	1.25839	+	0.726534i	0.972762	−	0.231805i	$-0.0744631\pi$
$293$	21.5402	+	12.4363i	1.25839	+	0.726534i	0.285632	+	0.958339i	$0.407796\pi$
$294$		0			0
$295$	−20.5640	+	11.8726i	−1.19728	+	0.691251i
$296$		0			0
$297$	16.8047	−	1.40513i	0.975106	−	0.0815340i
$298$		0			0
$299$	30.9066			1.78738
$300$		0			0
$301$	−30.3914	+	7.13934i	−1.75173	+	0.411505i
$302$		0			0
$303$	16.4046	+	5.45924i	0.942421	+	0.313625i
$304$		0			0
$305$	−11.4285	−	19.7948i	−0.654395	−	1.13345i
$306$		0			0
$307$	−30.7557			−1.75532			−0.877661	−	0.479281i	$-0.840897\pi$
$307$	−30.7557			−1.75532			−0.877661	+	0.479281i	$0.840897\pi$
$308$		0			0
$309$	0.910939	+	1.02626i	0.0518215	+	0.0583818i
$310$		0			0
$311$	−4.97412			−0.282056			−0.141028	−	0.990006i	$-0.545041\pi$
$311$	−4.97412			−0.282056			−0.141028	+	0.990006i	$0.545041\pi$
$312$		0			0
$313$			4.57758i			0.258740i	0.991596	+	0.129370i	$0.0412955\pi$
$313$			4.57758i			0.258740i	−0.991596	+	0.129370i	$0.958704\pi$
$314$		0			0
$315$	15.3830	−	11.3440i	0.866736	−	0.639159i
$316$		0			0
$317$	26.2253			1.47296			0.736479	−	0.676460i	$-0.236487\pi$
$317$	26.2253			1.47296			0.736479	+	0.676460i	$0.236487\pi$
$318$		0			0
$319$			7.97011i			0.446241i
$320$		0			0
$321$	−17.9782	−	5.98291i	−1.00344	−	0.333933i
$322$		0			0
$323$			5.91913i			0.329349i
$324$		0			0
$325$	3.48222	−	2.01046i	0.193159	−	0.111520i
$326$		0			0
$327$	−7.12001	−	8.02137i	−0.393738	−	0.443583i
$328$		0			0
$329$	12.2634	+	3.69791i	0.676103	+	0.203872i
$330$		0			0
$331$			10.8238i			0.594932i	0.954732	+	0.297466i	$0.0961415\pi$
$331$			10.8238i			0.594932i	−0.954732	+	0.297466i	$0.903858\pi$
$332$		0			0
$333$	−2.90915	+	24.3479i	−0.159420	+	1.33426i
$334$		0			0
$335$	−0.432498	−	0.749108i	−0.0236299	−	0.0409282i
$336$		0			0
$337$	−8.72115	+	15.1055i	−0.475071	+	0.822848i	−0.999592	−	0.0285498i	$-0.990911\pi$
$337$	−8.72115	+	15.1055i	−0.475071	+	0.822848i	0.524521	+	0.851397i	$0.324244\pi$
$338$		0			0
$339$	3.12562	−	9.39226i	0.169760	−	0.510117i
$340$		0			0
$341$	−9.04691	−	5.22324i	−0.489918	−	0.282854i
$342$		0			0
$343$	−11.8201	−	14.2578i	−0.638223	−	0.769851i
$344$		0			0
$345$	−8.08611	+	24.2982i	−0.435341	+	1.30817i
$346$		0			0
$347$		−	28.6423i		−	1.53760i	−0.639490	−	0.768799i	$-0.720855\pi$
$347$		−	28.6423i		−	1.53760i	0.639490	−	0.768799i	$-0.279145\pi$
$348$		0			0
$349$	−5.69708	+	3.28921i	−0.304958	+	0.176067i	−0.644668	−	0.764463i	$-0.723004\pi$
$349$	−5.69708	+	3.28921i	−0.304958	+	0.176067i	0.339710	+	0.940530i	$0.389671\pi$
$350$		0			0
$351$	26.0656	−	2.17949i	1.39128	−	0.116333i
$352$		0			0
$353$	−5.48131	−	3.16463i	−0.291741	−	0.168437i	0.346986	−	0.937870i	$-0.387205\pi$
$353$	−5.48131	−	3.16463i	−0.291741	−	0.168437i	−0.638727	+	0.769434i	$0.720538\pi$
$354$		0			0
$355$	2.80077	+	4.85107i	0.148649	+	0.257468i
$356$		0			0
$357$	−3.82148	+	1.76683i	−0.202254	+	0.0935105i
$358$		0			0
$359$	−15.7202	−	9.07605i	−0.829679	−	0.479015i	0.0240637	−	0.999710i	$-0.492340\pi$
$359$	−15.7202	−	9.07605i	−0.829679	−	0.479015i	−0.853743	+	0.520695i	$0.825673\pi$
$360$		0			0
$361$	−11.2543	−	19.4931i	−0.592334	−	1.02595i
$362$		0			0
$363$	−0.537799	−	0.605882i	−0.0282271	−	0.0318006i
$364$		0			0
$365$	5.57621	−	9.65828i	0.291872	−	0.505538i
$366$		0			0
$367$	−3.48682	+	6.03934i	−0.182010	+	0.315251i	−0.942565	−	0.334023i	$-0.891594\pi$
$367$	−3.48682	+	6.03934i	−0.182010	+	0.315251i	0.760555	+	0.649274i	$0.224927\pi$
$368$		0			0
$369$	35.7190	+	4.26778i	1.85945	+	0.222172i
$370$		0			0
$371$	1.89347	+	8.06029i	0.0983039	+	0.418470i
$372$		0			0
$373$	−12.6055	−	21.8333i	−0.652687	−	1.13049i	−0.982468	−	0.186430i	$-0.940308\pi$
$373$	−12.6055	−	21.8333i	−0.652687	−	1.13049i	0.329781	−	0.944057i	$-0.393025\pi$
$374$		0			0
$375$	−3.52143	−	17.1654i	−0.181846	−	0.886415i
$376$		0			0
$377$			12.3624i			0.636696i
$378$		0			0
$379$		−	6.73528i		−	0.345968i	−0.984925	−	0.172984i	$-0.944659\pi$
$379$		−	6.73528i		−	0.345968i	0.984925	−	0.172984i	$-0.0553409\pi$
$380$		0			0
$381$	2.61059	+	12.7254i	0.133744	+	0.651943i
$382$		0			0
$383$	4.23777	+	7.34003i	0.216540	+	0.375058i	0.953748	−	0.300608i	$-0.0971895\pi$
$383$	4.23777	+	7.34003i	0.216540	+	0.375058i	−0.737208	+	0.675666i	$0.763856\pi$
$384$		0			0
$385$	19.7961	+	5.96933i	1.00890	+	0.304225i
$386$		0			0
$387$	21.2114	−	28.3399i	1.07823	−	1.44060i
$388$		0			0
$389$	−4.85307	+	8.40576i	−0.246060	+	0.426189i	−0.962429	−	0.271533i	$-0.912469\pi$
$389$	−4.85307	+	8.40576i	−0.246060	+	0.426189i	0.716369	+	0.697722i	$0.245803\pi$
$390$		0			0
$391$	2.82040	−	4.88507i	0.142634	−	0.247049i
$392$		0			0
$393$	−2.35447	−	2.65254i	−0.118767	−	0.133803i
$394$		0			0
$395$	5.25143	+	9.09574i	0.264228	+	0.457656i
$396$		0			0
$397$	25.1157	+	14.5005i	1.26052	+	0.727761i	0.973175	−	0.230066i	$-0.0738942\pi$
$397$	25.1157	+	14.5005i	1.26052	+	0.727761i	0.287344	+	0.957827i	$0.407228\pi$
$398$		0			0
$399$	17.0132	−	24.1295i	0.851728	−	1.20799i
$400$		0			0
$401$	5.04905	+	8.74520i	0.252137	+	0.436715i	0.964114	−	0.265488i	$-0.0855332\pi$
$401$	5.04905	+	8.74520i	0.252137	+	0.436715i	−0.711977	+	0.702203i	$0.752200\pi$
$402$		0			0
$403$	−14.0326	−	8.10174i	−0.699015	−	0.403576i
$404$		0			0
$405$	−5.10609	+	21.0625i	−0.253724	+	1.04660i
$406$		0			0
$407$	−22.9726	+	13.2632i	−1.13871	+	0.657435i
$408$		0			0
$409$			20.5202i			1.01466i	0.861752	+	0.507330i	$0.169367\pi$
$409$			20.5202i			1.01466i	−0.861752	+	0.507330i	$0.830633\pi$
$410$		0			0
$411$	−8.81092	+	26.4762i	−0.434610	+	1.30597i
$412$		0			0
$413$	−24.9781	−	7.53192i	−1.22909	−	0.370621i
$414$		0			0
$415$	36.2100	+	20.9058i	1.77748	+	1.02623i
$416$		0			0
$417$	−5.03583	+	15.1323i	−0.246606	+	0.741032i
$418$		0			0
$419$	−16.1828	+	28.0295i	−0.790583	+	1.36933i	0.135024	+	0.990842i	$0.456889\pi$
$419$	−16.1828	+	28.0295i	−0.790583	+	1.36933i	−0.925606	+	0.378487i	$0.876444\pi$
$420$		0			0
$421$	−18.8498	−	32.6488i	−0.918683	−	1.59121i	−0.801418	−	0.598104i	$-0.795921\pi$
$421$	−18.8498	−	32.6488i	−0.918683	−	1.59121i	−0.117264	−	0.993101i	$-0.537413\pi$
$422$		0			0
$423$	−13.3507	+	5.71839i	−0.649134	+	0.278038i
$424$		0			0
$425$		−	0.733862i		−	0.0355975i
$426$		0			0
$427$	7.25018	−	24.0438i	0.350861	−	1.16356i
$428$		0			0
$429$	18.7838	+	21.1617i	0.906890	+	1.02170i
$430$		0			0
$431$	25.1267	−	14.5069i	1.21031	−	0.698773i	0.247483	−	0.968892i	$-0.420396\pi$
$431$	25.1267	−	14.5069i	1.21031	−	0.698773i	0.962827	+	0.270119i	$0.0870631\pi$
$432$		0			0
$433$			14.1188i			0.678507i	0.940695	+	0.339254i	$0.110175\pi$
$433$			14.1188i			0.678507i	−0.940695	+	0.339254i	$0.889825\pi$
$434$		0			0
$435$	−9.71907	−	3.23438i	−0.465994	−	0.155077i
$436$		0			0
$437$			39.5568i			1.89226i
$438$		0			0
$439$	21.4404			1.02329			0.511646	−	0.859196i	$-0.329036\pi$
$439$	21.4404			1.02329			0.511646	+	0.859196i	$0.329036\pi$
$440$		0			0
$441$	20.6567	+	3.78149i	0.983654	+	0.180071i
$442$		0			0
$443$		−	1.75440i		−	0.0833540i	−0.999131	−	0.0416770i	$-0.986730\pi$
$443$		−	1.75440i		−	0.0833540i	0.999131	−	0.0416770i	$-0.0132700\pi$
$444$		0			0
$445$	26.9378			1.27697
$446$		0			0
$447$	−9.17392	−	10.3353i	−0.433912	−	0.488843i
$448$		0			0
$449$	−4.85151			−0.228957			−0.114478	−	0.993426i	$-0.536520\pi$
$449$	−4.85151			−0.228957			−0.114478	+	0.993426i	$0.536520\pi$
$450$		0			0
$451$	19.4575	+	33.7013i	0.916217	+	1.58693i
$452$		0			0
$453$	−13.1810	−	4.38648i	−0.619299	−	0.206095i
$454$		0			0
$455$	30.7057	+	9.25901i	1.43951	+	0.434069i
$456$		0			0
$457$	20.9862			0.981693			0.490846	−	0.871246i	$-0.336688\pi$
$457$	20.9862			0.981693			0.490846	+	0.871246i	$0.336688\pi$
$458$		0			0
$459$	2.03414	−	4.31880i	0.0949457	−	0.201584i
$460$		0			0
$461$	−16.3326	+	9.42964i	−0.760686	+	0.439182i	−0.829542	−	0.558444i	$-0.811398\pi$
$461$	−16.3326	+	9.42964i	−0.760686	+	0.439182i	0.0688562	+	0.997627i	$0.478065\pi$
$462$		0			0
$463$	1.91609	+	1.10625i	0.0890481	+	0.0514120i	0.543863	−	0.839174i	$-0.316961\pi$
$463$	1.91609	+	1.10625i	0.0890481	+	0.0514120i	−0.454815	+	0.890586i	$0.650295\pi$
$464$		0			0
$465$	10.0408	−	8.91250i	0.465630	−	0.413307i
$466$		0			0
$467$	−17.0552	+	29.5404i	−0.789220	+	1.36697i	0.137226	+	0.990540i	$0.456181\pi$
$467$	−17.0552	+	29.5404i	−0.789220	+	1.36697i	−0.926445	+	0.376429i	$0.877152\pi$
$468$		0			0
$469$	0.274374	−	0.909907i	0.0126694	−	0.0420156i
$470$		0			0
$471$	−4.53507	−	22.1064i	−0.208965	−	1.01861i
$472$		0			0
$473$	38.2937			1.76075
$474$		0			0
$475$	2.57315	+	4.45683i	0.118064	+	0.204493i
$476$		0			0
$477$	−7.51618	−	5.62559i	−0.344142	−	0.257578i
$478$		0			0
$479$	−3.84432	+	6.65856i	−0.175652	+	0.304237i	−0.940387	−	0.340107i	$-0.889537\pi$
$479$	−3.84432	+	6.65856i	−0.175652	+	0.304237i	0.764735	+	0.644345i	$0.222870\pi$
$480$		0			0
$481$	−35.6327	+	20.5726i	−1.62471	+	0.938028i
$482$		0			0
$483$	−25.5385	+	11.8075i	−1.16204	+	0.537260i
$484$		0			0
$485$	13.6116	−	23.5760i	0.618070	−	1.07053i
$486$		0			0
$487$	21.1767	−	12.2264i	0.959610	−	0.554031i	0.0635571	−	0.997978i	$-0.479756\pi$
$487$	21.1767	−	12.2264i	0.959610	−	0.554031i	0.896053	+	0.443947i	$0.146422\pi$
$488$		0			0
$489$	−14.3699	−	4.78211i	−0.649829	−	0.216254i
$490$		0			0
$491$	11.5981	+	6.69616i	0.523414	+	0.302193i	0.738331	−	0.674439i	$-0.235614\pi$
$491$	11.5981	+	6.69616i	0.523414	+	0.302193i	−0.214916	+	0.976633i	$0.568948\pi$
$492$		0			0
$493$	1.95399	+	1.12814i	0.0880033	+	0.0508087i
$494$		0			0
$495$	−21.5513	+	9.23088i	−0.968660	+	0.414897i
$496$		0			0
$497$	−1.77679	+	5.89237i	−0.0796998	+	0.264309i
$498$		0			0
$499$	4.62958	−	2.67289i	0.207248	−	0.119655i	−0.392784	−	0.919631i	$-0.628488\pi$
$499$	4.62958	−	2.67289i	0.207248	−	0.119655i	0.600032	+	0.799976i	$0.295155\pi$
$500$		0			0
$501$	8.19678	−	24.6307i	0.366205	−	1.10042i
$502$		0			0
$503$	−29.5727			−1.31858			−0.659292	−	0.751887i	$-0.729144\pi$
$503$	−29.5727			−1.31858			−0.659292	+	0.751887i	$0.729144\pi$
$504$		0			0
$505$	−24.0371			−1.06964
$506$		0			0
$507$	14.1880	+	15.9842i	0.630113	+	0.709882i
$508$		0			0
$509$	18.2788	−	10.5532i	0.810192	−	0.467764i	−0.0368307	−	0.999322i	$-0.511726\pi$
$509$	18.2788	−	10.5532i	0.810192	−	0.467764i	0.847022	+	0.531557i	$0.178393\pi$
$510$		0			0
$511$	11.9285	−	2.80216i	0.527686	−	0.123960i
$512$		0			0
$513$	2.78950	+	33.3610i	0.123159	+	1.47292i
$514$		0			0
$515$	−1.65221	−	0.953904i	−0.0728051	−	0.0420340i
$516$		0			0
$517$	−13.6067	−	7.85580i	−0.598420	−	0.345498i
$518$		0			0
$519$	3.52457	+	17.1807i	0.154712	+	0.754148i
$520$		0			0
$521$	2.00231	−	1.15604i	0.0877230	−	0.0506469i	−0.455497	−	0.890237i	$-0.650538\pi$
$521$	2.00231	−	1.15604i	0.0877230	−	0.0506469i	0.543220	+	0.839591i	$0.317205\pi$
$522$		0			0
$523$	10.0437	−	17.3961i	0.439179	−	0.760680i	−0.558448	−	0.829540i	$-0.688603\pi$
$523$	10.0437	−	17.3961i	0.439179	−	0.760680i	0.997626	+	0.0688601i	$0.0219362\pi$
$524$		0			0
$525$	−2.10932	+	2.99161i	−0.0920585	+	0.130564i
$526$		0			0
$527$	−2.56111	+	1.47866i	−0.111564	+	0.0644113i
$528$		0			0
$529$	7.34839	−	12.7278i	0.319495	−	0.553382i
$530$		0			0
$531$	27.1928	−	11.6472i	1.18007	−	0.505447i
$532$		0			0
$533$	30.1804	+	52.2740i	1.30726	+	2.26424i
$534$		0			0
$535$	26.3427			1.13890
$536$		0			0
$537$	2.24723	−	1.99471i	0.0969750	−	0.0860780i
$538$		0			0
$539$	10.1150	+	20.3413i	0.435686	+	0.876160i
$540$		0			0
$541$	4.55369	−	7.88722i	0.195778	−	0.339098i	−0.751377	−	0.659873i	$-0.770610\pi$
$541$	4.55369	−	7.88722i	0.195778	−	0.339098i	0.947155	+	0.320775i	$0.103943\pi$
$542$		0			0
$543$	2.56231	+	12.4901i	0.109959	+	0.536001i
$544$		0			0
$545$	12.9139	+	7.45584i	0.553170	+	0.319373i
$546$		0			0
$547$	17.4031	−	10.0477i	0.744105	−	0.429609i	−0.0794552	−	0.996838i	$-0.525318\pi$
$547$	17.4031	−	10.0477i	0.744105	−	0.429609i	0.823560	+	0.567229i	$0.191985\pi$
$548$		0			0
$549$	11.2116	+	26.1756i	0.478498	+	1.11715i
$550$		0			0
$551$	−15.8224			−0.674058
$552$		0			0
$553$	−3.33147	+	11.0482i	−0.141669	+	0.469816i
$554$		0			0
$555$	−6.85113	−	33.3961i	−0.290814	−	1.41759i
$556$		0			0
$557$	16.6814	+	28.8930i	0.706814	+	1.22424i	0.966033	+	0.258419i	$0.0832015\pi$
$557$	16.6814	+	28.8930i	0.706814	+	1.22424i	−0.259219	+	0.965819i	$0.583465\pi$
$558$		0			0
$559$	59.3972			2.51223
$560$		0			0
$561$	5.05893	−	1.03783i	0.213588	−	0.0438170i
$562$		0			0
$563$	−20.1630			−0.849770			−0.424885	−	0.905247i	$-0.639685\pi$
$563$	−20.1630			−0.849770			−0.424885	+	0.905247i	$0.639685\pi$
$564$		0			0
$565$			13.7621i			0.578976i
$566$		0			0
$567$	−20.7057	+	11.7590i	−0.869557	+	0.493832i
$568$		0			0
$569$	6.42561			0.269376			0.134688	−	0.990888i	$-0.456997\pi$
$569$	6.42561			0.269376			0.134688	+	0.990888i	$0.456997\pi$
$570$		0			0
$571$		−	18.4781i		−	0.773285i	−0.922230	−	0.386642i	$-0.873635\pi$
$571$		−	18.4781i		−	0.773285i	0.922230	−	0.386642i	$-0.126365\pi$
$572$		0			0
$573$	0.837099	+	4.08047i	0.0349703	+	0.170464i
$574$		0			0
$575$		−	4.90431i		−	0.204524i
$576$		0			0
$577$	23.2756	−	13.4382i	0.968976	−	0.559439i	0.0700521	−	0.997543i	$-0.477683\pi$
$577$	23.2756	−	13.4382i	0.968976	−	0.559439i	0.898924	+	0.438105i	$0.144350\pi$
$578$		0			0
$579$	1.55118	−	0.318221i	0.0644649	−	0.0132248i
$580$		0			0
$581$	10.5056	+	44.7213i	0.435846	+	1.85535i
$582$		0			0
$583$		−	10.1561i		−	0.420623i
$584$		0			0
$585$	−33.4282	+	14.3180i	−1.38208	+	0.591976i
$586$		0			0
$587$	7.57329	+	13.1173i	0.312583	+	0.541410i	0.978921	−	0.204240i	$-0.0654724\pi$
$587$	7.57329	+	13.1173i	0.312583	+	0.541410i	−0.666338	+	0.745650i	$0.732139\pi$
$588$		0			0
$589$	10.3693	−	17.9601i	0.427258	−	0.740033i
$590$		0			0
$591$	33.9904	−	6.97304i	1.39818	−	0.286832i
$592$		0			0
$593$	−31.7966	−	18.3578i	−1.30573	−	0.753863i	−0.324349	−	0.945938i	$-0.605145\pi$
$593$	−31.7966	−	18.3578i	−1.30573	−	0.753863i	−0.981380	+	0.192074i	$0.938478\pi$
$594$		0			0
$595$	4.26553	−	4.00838i	0.174870	−	0.164328i
$596$		0			0
$597$	−6.33825	−	7.14065i	−0.259407	−	0.292247i
$598$		0			0
$599$		−	2.33017i		−	0.0952082i	−0.998866	−	0.0476041i	$-0.984841\pi$
$599$		−	2.33017i		−	0.0952082i	0.998866	−	0.0476041i	$-0.0151586\pi$
$600$		0			0
$601$	27.6094	−	15.9403i	1.12621	−	0.650217i	0.183231	−	0.983070i	$-0.441344\pi$
$601$	27.6094	−	15.9403i	1.12621	−	0.650217i	0.942979	+	0.332853i	$0.108011\pi$
$602$		0			0
$603$	0.424287	+	0.990582i	0.0172783	+	0.0403396i
$604$		0			0
$605$	0.975431	+	0.563165i	0.0396569	+	0.0228959i
$606$		0			0
$607$	−13.0074	−	22.5295i	−0.527955	−	0.914446i	−0.999469	−	0.0325868i	$-0.989625\pi$
$607$	−13.0074	−	22.5295i	−0.527955	−	0.914446i	0.471513	−	0.881859i	$-0.343708\pi$
$608$		0			0
$609$	−4.72291	−	10.2152i	−0.191382	−	0.413941i
$610$		0			0
$611$	−21.1052	−	12.1851i	−0.853826	−	0.492957i
$612$		0			0
$613$	−23.1369	−	40.0742i	−0.934489	−	1.61858i	−0.775543	−	0.631295i	$-0.782524\pi$
$613$	−23.1369	−	40.0742i	−0.934489	−	1.61858i	−0.158946	−	0.987287i	$-0.550810\pi$
$614$		0			0
$615$	−48.9929	+	10.0508i	−1.97558	+	0.405286i
$616$		0			0
$617$	23.5659	−	40.8174i	0.948729	−	1.64325i	0.200621	−	0.979669i	$-0.435704\pi$
$617$	23.5659	−	40.8174i	0.948729	−	1.64325i	0.748107	−	0.663578i	$-0.230963\pi$
$618$		0			0
$619$	−19.5066	+	33.7865i	−0.784038	+	1.35799i	0.145534	+	0.989353i	$0.453510\pi$
$619$	−19.5066	+	33.7865i	−0.784038	+	1.35799i	−0.929572	+	0.368641i	$0.879823\pi$
$620$		0			0
$621$	13.5939	−	28.8620i	0.545506	−	1.15819i
$622$		0			0
$623$	20.2678	+	21.5680i	0.812011	+	0.864105i
$624$		0			0
$625$	14.1779	+	24.5569i	0.567117	+	0.982275i
$626$		0			0
$627$	−27.0845	+	24.0410i	−1.08165	+	0.960106i
$628$		0			0
$629$			7.50944i			0.299421i
$630$		0			0
$631$			29.3621i			1.16889i	0.811435	+	0.584443i	$0.198687\pi$
$631$			29.3621i			1.16889i	−0.811435	+	0.584443i	$0.801313\pi$
$632$		0			0
$633$	−7.67217	−	2.55320i	−0.304941	−	0.101481i
$634$		0			0
$635$	−9.03028	−	15.6409i	−0.358356	−	0.620690i
$636$		0			0
$637$	15.6894	+	31.5513i	0.621636	+	1.25011i
$638$		0			0
$639$	−2.74760	−	6.41480i	−0.108693	−	0.253766i
$640$		0			0
$641$	5.02022	−	8.69527i	0.198287	−	0.343443i	−0.749686	−	0.661793i	$-0.769796\pi$
$641$	5.02022	−	8.69527i	0.198287	−	0.343443i	0.947973	+	0.318351i	$0.103129\pi$
$642$		0			0
$643$	−2.91261	+	5.04478i	−0.114862	+	0.198947i	−0.917725	−	0.397217i	$-0.869976\pi$
$643$	−2.91261	+	5.04478i	−0.114862	+	0.198947i	0.802863	+	0.596164i	$0.203309\pi$
$644$		0			0
$645$	−15.5401	+	46.6968i	−0.611891	+	1.83869i
$646$		0			0
$647$	−12.4035	−	21.4836i	−0.487634	−	0.844606i	0.512265	−	0.858827i	$-0.328807\pi$
$647$	−12.4035	−	21.4836i	−0.487634	−	0.844606i	−0.999899	+	0.0142209i	$0.995473\pi$
$648$		0			0
$649$	27.7141	+	16.0007i	1.08787	+	0.628083i
$650$		0			0
$651$	14.6905	+	1.33356i	0.575766	+	0.0522665i
$652$		0			0
$653$	−1.23851	−	2.14516i	−0.0484665	−	0.0839465i	0.840774	−	0.541386i	$-0.182100\pi$
$653$	−1.23851	−	2.14516i	−0.0484665	−	0.0839465i	−0.889241	+	0.457439i	$0.848767\pi$
$654$		0			0
$655$	4.27041	+	2.46552i	0.166859	+	0.0963360i
$656$		0			0
$657$	−8.32537	+	11.1233i	−0.324803	+	0.433960i
$658$		0			0
$659$	6.89259	−	3.97944i	0.268497	−	0.155017i	−0.359707	−	0.933065i	$-0.617123\pi$
$659$	6.89259	−	3.97944i	0.268497	−	0.155017i	0.628205	+	0.778048i	$0.283790\pi$
$660$		0			0
$661$		−	19.0229i		−	0.739903i	−0.929051	−	0.369952i	$-0.879374\pi$
$661$		−	19.0229i		−	0.739903i	0.929051	−	0.369952i	$-0.120626\pi$
$662$		0			0
$663$	7.84688	−	1.60977i	0.304748	−	0.0625182i
$664$		0			0
$665$	−11.8504	+	39.2997i	−0.459540	+	1.52398i
$666$		0			0
$667$	13.0583	+	7.53920i	0.505619	+	0.291919i
$668$		0			0
$669$	−11.1623	−	12.5754i	−0.431560	−	0.486193i
$670$		0			0
$671$	−15.4022	+	26.6774i	−0.594595	+	1.02987i
$672$		0			0
$673$	−17.7573	−	30.7565i	−0.684492	−	1.18558i	−0.973596	−	0.228278i	$-0.926691\pi$
$673$	−17.7573	−	30.7565i	−0.684492	−	1.18558i	0.289104	−	0.957298i	$-0.406643\pi$
$674$		0			0
$675$	−0.345845	−	4.13614i	−0.0133116	−	0.159200i
$676$		0			0
$677$		−	17.6527i		−	0.678449i	−0.940705	−	0.339224i	$-0.889835\pi$
$677$		−	17.6527i		−	0.678449i	0.940705	−	0.339224i	$-0.110165\pi$
$678$		0			0
$679$	29.1176	−	6.84009i	1.11743	−	0.262499i
$680$		0			0
$681$	−0.189489	+	0.569400i	−0.00726123	+	0.0218194i
$682$		0			0
$683$	−2.43776	+	1.40744i	−0.0932782	+	0.0538542i	−0.545913	−	0.837842i	$-0.683817\pi$
$683$	−2.43776	+	1.40744i	−0.0932782	+	0.0538542i	0.452635	+	0.891696i	$0.350484\pi$
$684$		0			0
$685$		−	38.7945i		−	1.48226i
$686$		0			0
$687$	26.2227	−	23.2761i	1.00046	−	0.888039i
$688$		0			0
$689$		−	15.7531i		−	0.600144i
$690$		0			0
$691$	−8.65706			−0.329330			−0.164665	−	0.986350i	$-0.552654\pi$
$691$	−8.65706			−0.329330			−0.164665	+	0.986350i	$0.552654\pi$
$692$		0			0
$693$	−23.6058	−	10.3101i	−0.896712	−	0.391647i
$694$		0			0
$695$		−	22.1728i		−	0.841061i
$696$		0			0
$697$	11.0165			0.417280
$698$		0			0
$699$	12.4020	−	37.2670i	0.469086	−	1.40957i
$700$		0			0
$701$	−51.0401			−1.92776			−0.963879	−	0.266341i	$-0.914185\pi$
$701$	−51.0401			−1.92776			−0.963879	+	0.266341i	$0.914185\pi$
$702$		0			0
$703$	−26.3305	−	45.6057i	−0.993072	−	1.72005i
$704$		0			0
$705$	15.1014	−	13.4045i	0.568753	−	0.504843i
$706$		0			0
$707$	−18.0853	−	19.2455i	−0.680167	−	0.723803i
$708$		0			0
$709$	−50.4538			−1.89483			−0.947417	−	0.320003i	$-0.896316\pi$
$709$	−50.4538			−1.89483			−0.947417	+	0.320003i	$0.896316\pi$
$710$		0			0
$711$	−5.15173	−	12.0277i	−0.193205	−	0.451075i
$712$		0			0
$713$	−17.1156	+	9.88168i	−0.640983	+	0.370072i
$714$		0			0
$715$	−34.0690	−	19.6697i	−1.27411	−	0.735607i
$716$		0			0
$717$	−28.8430	−	9.59857i	−1.07716	−	0.358465i
$718$		0			0
$719$	−1.34602	+	2.33138i	−0.0501982	+	0.0869459i	−0.890033	−	0.455897i	$-0.849319\pi$
$719$	−1.34602	+	2.33138i	−0.0501982	+	0.0869459i	0.839834	+	0.542843i	$0.182652\pi$
$720$		0			0
$721$	−0.479356	−	2.04057i	−0.0178521	−	0.0759948i
$722$		0			0
$723$	−5.93741	−	1.97589i	−0.220814	−	0.0734842i
$724$		0			0
$725$	1.96168			0.0728551
$726$		0			0
$727$	−6.12746	−	10.6131i	−0.227255	−	0.393617i	0.729739	−	0.683726i	$-0.239642\pi$
$727$	−6.12746	−	10.6131i	−0.227255	−	0.393617i	−0.956994	+	0.290109i	$0.906308\pi$
$728$		0			0
$729$	9.42937	−	25.2999i	0.349236	−	0.937035i
$730$		0			0
$731$	5.42032	−	9.38827i	0.200478	−	0.347238i
$732$		0			0
$733$	−9.26773	+	5.35073i	−0.342311	+	0.197634i	−0.661294	−	0.750127i	$-0.729992\pi$
$733$	−9.26773	+	5.35073i	−0.342311	+	0.197634i	0.318982	+	0.947761i	$0.396659\pi$
$734$		0			0
$735$	−28.9098	+	4.07992i	−1.06635	+	0.150490i
$736$		0			0
$737$	−0.582877	+	1.00957i	−0.0214705	+	0.0371881i
$738$		0			0
$739$	20.6947	−	11.9481i	0.761266	−	0.439517i	−0.0684841	−	0.997652i	$-0.521816\pi$
$739$	20.6947	−	11.9481i	0.761266	−	0.439517i	0.829750	+	0.558135i	$0.188483\pi$
$740$		0			0
$741$	−42.0107	+	37.2899i	−1.54330	+	1.36988i
$742$		0			0
$743$	22.5547	+	13.0220i	0.827451	+	0.477729i	0.852979	−	0.521945i	$-0.174793\pi$
$743$	22.5547	+	13.0220i	0.827451	+	0.477729i	−0.0255279	+	0.999674i	$0.508127\pi$
$744$		0			0
$745$	16.6392	+	9.60662i	0.609611	+	0.351959i
$746$		0			0
$747$	−41.7024	−	31.2127i	−1.52581	−	1.14201i
$748$		0			0
$749$	19.8201	+	21.0916i	0.724210	+	0.770670i
$750$		0			0
$751$	23.7555	−	13.7153i	0.866851	−	0.500477i	0.000550503	−	1.00000i	$-0.499825\pi$
$751$	23.7555	−	13.7153i	0.866851	−	0.500477i	0.866301	+	0.499523i	$0.166491\pi$
$752$		0			0
$753$	18.5177	−	3.79885i	0.674821	−	0.138438i
$754$		0			0
$755$	19.3137			0.702897
$756$		0			0
$757$	−18.6436			−0.677613			−0.338807	−	0.940856i	$-0.610023\pi$
$757$	−18.6436			−0.677613			−0.338807	+	0.940856i	$0.610023\pi$
$758$		0			0
$759$	33.8082	−	6.93566i	1.22716	−	0.251749i
$760$		0			0
$761$	−30.6015	+	17.6678i	−1.10930	+	0.640458i	−0.938649	−	0.344873i	$-0.887922\pi$
$761$	−30.6015	+	17.6678i	−1.10930	+	0.640458i	−0.170656	+	0.985331i	$0.554589\pi$
$762$		0			0
$763$	3.74671	+	15.9494i	0.135640	+	0.577405i
$764$		0			0
$765$	−0.787415	+	6.59022i	−0.0284690	+	0.238270i
$766$		0			0
$767$	42.9872	+	24.8187i	1.55218	+	0.896150i
$768$		0			0
$769$	1.19508	+	0.689979i	0.0430956	+	0.0248813i	0.521393	−	0.853317i	$-0.325413\pi$
$769$	1.19508	+	0.689979i	0.0430956	+	0.0248813i	−0.478297	+	0.878198i	$0.658746\pi$
$770$		0			0
$771$	−23.6631	+	21.0041i	−0.852205	+	0.756443i
$772$		0			0
$773$	41.1864	−	23.7790i	1.48137	−	0.855270i	0.481594	−	0.876394i	$-0.340058\pi$
$773$	41.1864	−	23.7790i	1.48137	−	0.855270i	0.999777	+	0.0211243i	$0.00672458\pi$
$774$		0			0
$775$	−1.28560	+	2.22672i	−0.0461800	+	0.0799861i
$776$		0			0
$777$	21.5842	−	30.6124i	0.774330	−	1.09821i
$778$		0			0
$779$	−66.9046	+	38.6274i	−2.39710	+	1.38397i
$780$		0			0
$781$	3.77459	−	6.53778i	0.135065	−	0.233940i
$782$		0			0
$783$	11.5446	+	5.43747i	0.412570	+	0.194319i
$784$		0			0
$785$	15.6873	+	27.1712i	0.559903	+	0.969780i
$786$		0			0
$787$	21.1490			0.753881			0.376941	−	0.926237i	$-0.376976\pi$
$787$	21.1490			0.753881			0.376941	+	0.926237i	$0.376976\pi$
$788$		0			0
$789$	47.6002	+	15.8407i	1.69461	+	0.563945i
$790$		0			0
$791$	−11.0188	+	10.3545i	−0.391783	+	0.368164i
$792$		0			0
$793$	−23.8903	+	41.3792i	−0.848369	+	1.46942i
$794$		0			0
$795$	12.3847	+	4.12148i	0.439242	+	0.146174i
$796$		0			0
$797$	13.6500	+	7.88083i	0.483508	+	0.279153i	0.721877	−	0.692021i	$-0.243280\pi$
$797$	13.6500	+	7.88083i	0.483508	+	0.279153i	−0.238369	+	0.971175i	$0.576613\pi$
$798$		0			0
$799$	−3.85193	+	2.22391i	−0.136272	+	0.0786764i
$800$		0			0
$801$	−33.3224	−	3.98144i	−1.17739	−	0.140677i
$802$		0			0
$803$	−15.0301			−0.530401
$804$		0			0
$805$	28.5060	−	26.7875i	1.00471	−	0.944136i
$806$		0			0
$807$	11.7189	−	10.4020i	0.412525	−	0.366169i
$808$		0			0
$809$	12.6913	+	21.9820i	0.446203	+	0.772846i	0.998135	−	0.0610430i	$-0.0194427\pi$
$809$	12.6913	+	21.9820i	0.446203	+	0.772846i	−0.551932	+	0.833889i	$0.686109\pi$
$810$		0			0
$811$	−6.10807			−0.214483			−0.107242	−	0.994233i	$-0.534202\pi$
$811$	−6.10807			−0.214483			−0.107242	+	0.994233i	$0.534202\pi$
$812$		0			0
$813$	−3.92413	+	11.7917i	−0.137625	+	0.413554i
$814$		0			0
$815$	21.0556			0.737547
$816$		0			0
$817$			76.0214i			2.65965i
$818$		0			0
$819$	−36.6149	−	15.9919i	−1.27943	−	0.558802i
$820$		0			0
$821$	−18.4740			−0.644746			−0.322373	−	0.946613i	$-0.604481\pi$
$821$	−18.4740			−0.644746			−0.322373	+	0.946613i	$0.604481\pi$
$822$		0			0
$823$			10.0524i			0.350406i	0.984532	+	0.175203i	$0.0560581\pi$
$823$			10.0524i			0.350406i	−0.984532	+	0.175203i	$0.943942\pi$
$824$		0			0
$825$	3.35797	−	2.98064i	0.116910	−	0.103773i
$826$		0			0
$827$		−	26.8216i		−	0.932677i	−0.884606	−	0.466338i	$-0.845573\pi$
$827$		−	26.8216i		−	0.932677i	0.884606	−	0.466338i	$-0.154427\pi$
$828$		0			0
$829$	−21.8538	+	12.6173i	−0.759013	+	0.438216i	−0.828941	−	0.559336i	$-0.811056\pi$
$829$	−21.8538	+	12.6173i	−0.759013	+	0.438216i	0.0699285	+	0.997552i	$0.477723\pi$
$830$		0			0
$831$	10.7694	−	32.3612i	0.373586	−	1.12260i
$832$		0			0
$833$	6.41871	+	0.399373i	0.222395	+	0.0138374i
$834$		0			0
$835$			36.0905i			1.24896i
$836$		0			0
$837$	−13.7379	+	9.54085i	−0.474850	+	0.329780i
$838$		0			0
$839$	13.1834	+	22.8343i	0.455141	+	0.788327i	0.998696	−	0.0510462i	$-0.0162556\pi$
$839$	13.1834	+	22.8343i	0.455141	+	0.788327i	−0.543555	+	0.839373i	$0.682922\pi$
$840$		0			0
$841$	11.4844	−	19.8915i	0.396013	−	0.685915i
$842$		0			0
$843$	−29.2154	−	32.9139i	−1.00623	−	1.13362i
$844$		0			0
$845$	−25.7335	−	14.8572i	−0.885259	−	0.511105i
$846$		0			0
$847$	0.283002	+	1.20471i	0.00972406	+	0.0413943i
$848$		0			0
$849$	42.8099	−	8.78234i	1.46923	−	0.301409i
$850$		0			0
$851$			50.1847i			1.72031i
$852$		0			0
$853$	23.1926	−	13.3903i	0.794100	−	0.458474i	−0.0473041	−	0.998881i	$-0.515063\pi$
$853$	23.1926	−	13.3903i	0.794100	−	0.458474i	0.841404	+	0.540407i	$0.181730\pi$
$854$		0			0
$855$	−18.3253	−	42.7841i	−0.626713	−	1.46319i
$856$		0			0
$857$	−15.9755	−	9.22343i	−0.545711	−	0.315066i	0.201679	−	0.979452i	$-0.435360\pi$
$857$	−15.9755	−	9.22343i	−0.545711	−	0.315066i	−0.747390	+	0.664385i	$0.768693\pi$
$858$		0			0
$859$	14.0243	+	24.2908i	0.478502	+	0.828790i	0.999696	−	0.0246479i	$-0.00784647\pi$
$859$	14.0243	+	24.2908i	0.478502	+	0.828790i	−0.521194	+	0.853438i	$0.674513\pi$
$860$		0			0
$861$	−44.9091	−	31.6645i	−1.53050	−	1.07912i
$862$		0			0
$863$	0.137388	+	0.0793209i	0.00467674	+	0.00270012i	0.502337	−	0.864672i	$-0.332474\pi$
$863$	0.137388	+	0.0793209i	0.00467674	+	0.00270012i	−0.497660	+	0.867372i	$0.665807\pi$
$864$		0			0
$865$	−12.1918	−	21.1169i	−0.414535	−	0.717996i
$866$		0			0
$867$	−8.83591	+	26.5513i	−0.300083	+	0.901728i
$868$		0			0
$869$	7.07734	−	12.2583i	0.240082	−	0.415835i
$870$		0			0
$871$	−0.904098	+	1.56594i	−0.0306342	+	0.0530600i
$872$		0			0
$873$	−20.3223	+	27.1520i	−0.687805	+	0.918956i
$874$		0			0
$875$	−7.72753	+	25.6268i	−0.261238	+	0.866346i
$876$		0			0
$877$	−18.6664	−	32.3311i	−0.630319	−	1.09174i	−0.987486	−	0.157704i	$-0.949591\pi$
$877$	−18.6664	−	32.3311i	−0.630319	−	1.09174i	0.357168	−	0.934040i	$-0.383742\pi$
$878$		0			0
$879$	40.8764	+	13.6031i	1.37873	+	0.458823i
$880$		0			0
$881$		−	50.2119i		−	1.69168i	−0.533436	−	0.845840i	$-0.679100\pi$
$881$		−	50.2119i		−	1.69168i	0.533436	−	0.845840i	$-0.320900\pi$
$882$		0			0
$883$			40.3508i			1.35791i	0.734179	+	0.678955i	$0.237567\pi$
$883$			40.3508i			1.35791i	−0.734179	+	0.678955i	$0.762433\pi$
$884$		0			0
$885$	−30.7587	+	27.3023i	−1.03394	+	0.917758i
$886$		0			0
$887$	3.10313	+	5.37477i	0.104193	+	0.180467i	0.913408	−	0.407045i	$-0.133441\pi$
$887$	3.10313	+	5.37477i	0.104193	+	0.180467i	−0.809215	+	0.587512i	$0.800107\pi$
$888$		0			0
$889$	5.72875	−	18.9983i	0.192136	−	0.637182i
$890$		0			0
$891$	28.0236	−	8.23342i	0.938827	−	0.275830i
$892$		0			0
$893$	15.5955	−	27.0122i	0.521883	−	0.903928i
$894$		0			0
$895$	−2.08879	+	3.61789i	−0.0698205	+	0.120933i
$896$		0			0
$897$	52.4397	−	10.7579i	1.75091	−	0.359195i
$898$		0			0
$899$	−3.95259	−	6.84609i	−0.131826	−	0.228330i
$900$		0			0
$901$	−2.48992	−	1.43755i	−0.0829512	−	0.0478919i
$902$		0			0
$903$	−49.0806	+	22.6920i	−1.63330	+	0.755142i
$904$		0			0
$905$	−8.86328	−	15.3517i	−0.294625	−	0.510306i
$906$		0			0
$907$	−9.54195	−	5.50905i	−0.316835	−	0.182925i	0.333146	−	0.942875i	$-0.391890\pi$
$907$	−9.54195	−	5.50905i	−0.316835	−	0.182925i	−0.649981	+	0.759950i	$0.725223\pi$
$908$		0			0
$909$	29.7342	+	3.55271i	0.986221	+	0.117836i
$910$		0			0
$911$	−0.991689	+	0.572552i	−0.0328561	+	0.0189695i	−0.516338	−	0.856385i	$-0.672705\pi$
$911$	−0.991689	+	0.572552i	−0.0328561	+	0.0189695i	0.483482	+	0.875354i	$0.339372\pi$
$912$		0			0
$913$		−	56.3495i		−	1.86490i
$914$		0			0
$915$	−26.2811	−	29.6081i	−0.868825	−	0.978814i
$916$		0			0
$917$	1.23898	+	5.27419i	0.0409146	+	0.174169i
$918$		0			0
$919$	−23.0364	−	13.3001i	−0.759900	−	0.438729i	0.0693596	−	0.997592i	$-0.477904\pi$
$919$	−23.0364	−	13.3001i	−0.759900	−	0.438729i	−0.829260	+	0.558863i	$0.811238\pi$
$920$		0			0
$921$	−52.1837	+	10.7054i	−1.71951	+	0.352754i
$922$		0			0
$923$	5.85475	−	10.1407i	0.192711	−	0.333786i
$924$		0			0
$925$	3.26449	+	5.65425i	0.107336	+	0.185911i
$926$		0			0
$927$	1.90282	+	1.42419i	0.0624968	+	0.0467766i
$928$		0			0
$929$		−	52.0006i		−	1.70608i	−0.521843	−	0.853042i	$-0.674755\pi$
$929$		−	52.0006i		−	1.70608i	0.521843	−	0.853042i	$-0.325245\pi$
$930$		0			0
$931$	−40.3819	+	20.0806i	−1.32346	+	0.658114i
$932$		0			0
$933$	−8.43966	+	1.73137i	−0.276302	+	0.0566827i
$934$		0			0
$935$	−6.21796	+	3.58994i	−0.203349	+	0.117404i
$936$		0			0
$937$		−	54.3180i		−	1.77449i	−0.461297	−	0.887246i	$-0.652616\pi$
$937$		−	54.3180i		−	1.77449i	0.461297	−	0.887246i	$-0.347384\pi$
$938$		0			0
$939$	1.59335	+	7.76685i	0.0519970	+	0.253462i
$940$		0			0
$941$			1.85203i			0.0603744i	0.999544	+	0.0301872i	$0.00961034\pi$
$941$			1.85203i			0.0603744i	−0.999544	+	0.0301872i	$0.990390\pi$
$942$		0			0
$943$	73.6220			2.39746
$944$		0			0
$945$	22.1521	−	24.6019i	0.720606	−	0.800301i
$946$		0			0
$947$			20.7245i			0.673457i	0.941602	+	0.336728i	$0.109320\pi$
$947$			20.7245i			0.673457i	−0.941602	+	0.336728i	$0.890680\pi$
$948$		0			0
$949$	−23.3131			−0.756776
$950$		0			0
$951$	44.4968	−	9.12841i	1.44291	−	0.296009i
$952$		0			0
$953$	12.4979			0.404847			0.202423	−	0.979298i	$-0.435118\pi$
$953$	12.4979			0.404847			0.202423	+	0.979298i	$0.435118\pi$
$954$		0			0
$955$	−2.89561	−	5.01534i	−0.0936997	−	0.162293i
$956$		0			0
$957$	2.77421	+	13.5230i	0.0896775	+	0.437137i
$958$		0			0
$959$	31.0612	−	29.1887i	1.00302	−	0.942551i
$960$		0			0
$961$	−20.6386			−0.665762
$962$		0			0
$963$	−32.5864	−	3.89350i	−1.05008	−	0.125466i
$964$		0			0
$965$	−1.90657	+	1.10076i	−0.0613747	+	0.0354347i
$966$		0			0
$967$	4.01390	+	2.31742i	0.129078	+	0.0745234i	0.563149	−	0.826356i	$-0.309590\pi$
$967$	4.01390	+	2.31742i	0.129078	+	0.0745234i	−0.434071	+	0.900879i	$0.642923\pi$
$968$		0			0
$969$	2.06031	+	10.0431i	0.0661868	+	0.322630i
$970$		0			0
$971$	−20.9286	+	36.2494i	−0.671631	+	1.16330i	0.305811	+	0.952092i	$0.401072\pi$
$971$	−20.9286	+	36.2494i	−0.671631	+	1.16330i	−0.977442	+	0.211206i	$0.932261\pi$
$972$		0			0
$973$	17.7529	−	16.6826i	0.569131	−	0.534820i
$974$		0			0
$975$	5.20854	−	4.62326i	0.166807	−	0.148063i
$976$		0			0
$977$	31.5651			1.00986			0.504929	−	0.863161i	$-0.331519\pi$
$977$	31.5651			1.00986			0.504929	+	0.863161i	$0.331519\pi$
$978$		0			0
$979$	−18.1520	−	31.4402i	−0.580141	−	1.00483i
$980$		0			0
$981$	−14.8727	−	11.1317i	−0.474848	−	0.355407i
$982$		0			0
$983$	−23.4360	+	40.5924i	−0.747493	+	1.29470i	0.201528	+	0.979483i	$0.435409\pi$
$983$	−23.4360	+	40.5924i	−0.747493	+	1.29470i	−0.949021	+	0.315213i	$0.897924\pi$
$984$		0			0
$985$	−41.7778	+	24.1204i	−1.33115	+	0.768541i
$986$		0			0
$987$	22.0947	+	2.00570i	0.703281	+	0.0638420i
$988$		0			0
$989$	36.2233	−	62.7406i	1.15183	−	1.99504i
$990$		0			0
$991$	−52.2849	+	30.1867i	−1.66088	+	0.958912i	−0.688589	+	0.725152i	$0.741770\pi$
$991$	−52.2849	+	30.1867i	−1.66088	+	0.958912i	−0.972294	+	0.233760i	$0.924897\pi$
$992$		0			0
$993$	3.76753	+	18.3650i	0.119559	+	0.582795i
$994$		0			0
$995$	11.4960	+	6.63720i	0.364447	+	0.210414i
$996$		0			0
$997$	−19.0480	−	10.9973i	−0.603255	−	0.348289i	0.167066	−	0.985946i	$-0.446571\pi$
$997$	−19.0480	−	10.9973i	−0.603255	−	0.348289i	−0.770321	+	0.637656i	$0.779904\pi$
$998$		0			0
$999$	3.53895	+	42.3241i	0.111968	+	1.33908i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.g.607.12	yes	24
3.2	odd	2		3024.2.cz.h.1279.9		24
4.3	odd	2		1008.2.cz.h.607.1	yes	24
7.3	odd	6		1008.2.bf.g.31.10	✓	24
9.2	odd	6		3024.2.bf.g.2287.9		24
9.7	even	3		1008.2.bf.h.943.3	yes	24
12.11	even	2		3024.2.cz.g.1279.9		24
21.17	even	6		3024.2.bf.h.1711.4		24
28.3	even	6		1008.2.bf.h.31.3	yes	24
36.7	odd	6		1008.2.bf.g.943.10	yes	24
36.11	even	6		3024.2.bf.h.2287.9		24
63.38	even	6		3024.2.cz.g.2719.9		24
63.52	odd	6		1008.2.cz.h.367.1	yes	24
84.59	odd	6		3024.2.bf.g.1711.4		24
252.115	even	6	inner	1008.2.cz.g.367.12	yes	24
252.227	odd	6		3024.2.cz.h.2719.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.10	✓	24	7.3	odd	6
1008.2.bf.g.943.10	yes	24	36.7	odd	6
1008.2.bf.h.31.3	yes	24	28.3	even	6
1008.2.bf.h.943.3	yes	24	9.7	even	3
1008.2.cz.g.367.12	yes	24	252.115	even	6	inner
1008.2.cz.g.607.12	yes	24	1.1	even	1	trivial
1008.2.cz.h.367.1	yes	24	63.52	odd	6
1008.2.cz.h.607.1	yes	24	4.3	odd	2
3024.2.bf.g.1711.4		24	84.59	odd	6
3024.2.bf.g.2287.9		24	9.2	odd	6
3024.2.bf.h.1711.4		24	21.17	even	6
3024.2.bf.h.2287.9		24	36.11	even	6
3024.2.cz.g.1279.9		24	12.11	even	2
3024.2.cz.g.2719.9		24	63.38	even	6
3024.2.cz.h.1279.9		24	3.2	odd	2
3024.2.cz.h.2719.9		24	252.227	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.69672 - 0.348077i) q^{3} +(-2.08545 + 1.20403i) q^{5} +(-2.53309 - 0.763830i) q^{7} +(2.75769 - 1.18117i) q^{9} +O(q^{10})\)	\(q+(1.69672 - 0.348077i) q^{3} +(-2.08545 + 1.20403i) q^{5} +(-2.53309 - 0.763830i) q^{7} +(2.75769 - 1.18117i) q^{9} +(2.81055 + 1.62267i) q^{11} +(4.35943 + 2.51692i) q^{13} +(-3.11931 + 2.76880i) q^{15} +(0.795645 - 0.459366i) q^{17} +(-3.22136 + 5.57956i) q^{19} +(-4.56381 - 0.414291i) q^{21} +(5.31720 - 3.06988i) q^{23} +(0.399389 - 0.691762i) q^{25} +(4.26787 - 2.96400i) q^{27} +(1.22793 + 2.12684i) q^{29} -3.21891 q^{31} +(5.33352 + 1.77493i) q^{33} +(6.20231 - 1.45700i) q^{35} +(-4.08685 + 7.07863i) q^{37} +(8.27280 + 2.75308i) q^{39} +(10.3845 + 5.99550i) q^{41} +(10.2187 - 5.89979i) q^{43} +(-4.32883 + 5.78362i) q^{45} -4.84127 q^{47} +(5.83313 + 3.86971i) q^{49} +(1.19009 - 1.05636i) q^{51} +(-1.56472 - 2.71017i) q^{53} -7.81500 q^{55} +(-3.52362 + 10.5882i) q^{57} +9.86072 q^{59} +9.49187i q^{61} +(-7.88769 + 0.885623i) q^{63} -12.1218 q^{65} +0.359208i q^{67} +(7.95321 - 7.05951i) q^{69} -2.32616i q^{71} +(-4.01081 + 2.31564i) q^{73} +(0.436863 - 1.31274i) q^{75} +(-5.87994 - 6.25717i) q^{77} -4.36153i q^{79} +(6.20965 - 6.51461i) q^{81} +(-8.68159 - 15.0370i) q^{83} +(-1.10618 + 1.91596i) q^{85} +(2.82375 + 3.18122i) q^{87} +(-9.68778 - 5.59324i) q^{89} +(-9.12036 - 9.70546i) q^{91} +(-5.46157 + 1.12043i) q^{93} -15.5145i q^{95} +(-9.79041 + 5.65250i) q^{97} +(9.66728 + 1.15507i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9}+O(q^{10}) \) 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9	\( 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9} - 9 q^{11} - 3 q^{13} - 6 q^{15} - 3 q^{17} - 4 q^{19} + 13 q^{21} - 6 q^{23} + 15 q^{25} + 9 q^{27} + 18 q^{29} + 34 q^{31} - 21 q^{33} - 42 q^{35} - 3 q^{37} + 27 q^{39} + 36 q^{41} + 24 q^{43} + 21 q^{45} - 42 q^{47} + 30 q^{49} - 6 q^{51} - 12 q^{53} - 30 q^{55} - 13 q^{57} - 12 q^{59} - 3 q^{63} + 6 q^{69} + 48 q^{73} + 36 q^{75} - 48 q^{77} - 31 q^{81} - 48 q^{83} - 21 q^{85} + 15 q^{87} + 39 q^{89} + 9 q^{91} + 10 q^{93} + 3 q^{97} + 30 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9 - 9 * q^11 - 3 * q^13 - 6 * q^15 - 3 * q^17 - 4 * q^19 + 13 * q^21 - 6 * q^23 + 15 * q^25 + 9 * q^27 + 18 * q^29 + 34 * q^31 - 21 * q^33 - 42 * q^35 - 3 * q^37 + 27 * q^39 + 36 * q^41 + 24 * q^43 + 21 * q^45 - 42 * q^47 + 30 * q^49 - 6 * q^51 - 12 * q^53 - 30 * q^55 - 13 * q^57 - 12 * q^59 - 3 * q^63 + 6 * q^69 + 48 * q^73 + 36 * q^75 - 48 * q^77 - 31 * q^81 - 48 * q^83 - 21 * q^85 + 15 * q^87 + 39 * q^89 + 9 * q^91 + 10 * q^93 + 3 * q^97 + 30 * q^99

Introduction

L-functions

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