LMFDB - Embedded newform 1008.2.q.l.625.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(529,1008)]

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([0, 0, 4, 4]))

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

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

chi := DirichletCharacter("1008.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.q (of order $3$, degree $2$, not 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:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.8
Character	$\chi$	$=$	1008.625
Dual form			1008.2.q.l.529.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.914508 + 1.47094i) q^{3} +(0.891774 + 1.54460i) q^{5} +(2.54386 - 0.727153i) q^{7} +(-1.32735 + 2.69038i) q^{9} +O(q^{10})$	\(q+(0.914508 + 1.47094i) q^{3} +(0.891774 + 1.54460i) q^{5} +(2.54386 - 0.727153i) q^{7} +(-1.32735 + 2.69038i) q^{9} +(-2.80706 + 4.86196i) q^{11} +(3.14009 - 5.43879i) q^{13} +(-1.45648 + 2.72430i) q^{15} +(0.646279 + 1.11939i) q^{17} +(-0.559062 + 0.968324i) q^{19} +(3.39599 + 3.07689i) q^{21} +(3.80857 + 6.59664i) q^{23} +(0.909478 - 1.57526i) q^{25} +(-5.17127 + 0.507916i) q^{27} +(-1.57496 - 2.72791i) q^{29} -1.00311 q^{31} +(-9.71875 + 0.317283i) q^{33} +(3.39171 + 3.28079i) q^{35} +(-5.96542 + 10.3324i) q^{37} +(10.8718 - 0.354926i) q^{39} +(4.14160 - 7.17347i) q^{41} +(-2.34804 - 4.06693i) q^{43} +(-5.33925 + 0.348988i) q^{45} +1.94400 q^{47} +(5.94250 - 3.69956i) q^{49} +(-1.05553 + 1.97433i) q^{51} +(-4.45992 - 7.72481i) q^{53} -10.0130 q^{55} +(-1.93562 + 0.0631911i) q^{57} -8.38679 q^{59} +4.82576 q^{61} +(-1.42028 + 7.80915i) q^{63} +11.2010 q^{65} +2.55628 q^{67} +(-6.22032 + 11.6349i) q^{69} +8.86178 q^{71} +(5.67598 + 9.83109i) q^{73} +(3.14885 - 0.102799i) q^{75} +(-3.60538 + 14.4093i) q^{77} -13.4577 q^{79} +(-5.47628 - 7.14215i) q^{81} +(1.60203 + 2.77479i) q^{83} +(-1.15267 + 1.99648i) q^{85} +(2.57229 - 4.81137i) q^{87} +(-0.404646 + 0.700867i) q^{89} +(4.03312 - 16.1189i) q^{91} +(-0.917349 - 1.47551i) q^{93} -1.99423 q^{95} +(1.10781 + 1.91879i) q^{97} +(-9.35458 - 14.0056i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} + q^{5} - 5 q^{7} + 6 q^{9}+O(q^{10}) $ 22 * q + 2 * q^3 + q^5 - 5 * q^7 + 6 * q^9	$ 22 q + 2 q^{3} + q^{5} - 5 q^{7} + 6 q^{9} - 3 q^{11} + 7 q^{13} + q^{15} - q^{17} - 13 q^{19} - 22 q^{25} + 2 q^{27} - 7 q^{29} + 12 q^{31} - 3 q^{33} - 2 q^{35} + 6 q^{37} + 4 q^{39} + 4 q^{41} - 2 q^{43} - 3 q^{45} + 34 q^{47} - 25 q^{49} - 53 q^{51} + q^{53} - 2 q^{55} - 21 q^{57} - 42 q^{59} - 62 q^{61} + 22 q^{63} + 6 q^{65} - 52 q^{67} - 40 q^{69} + 32 q^{71} + 17 q^{73} - 53 q^{75} - q^{77} - 32 q^{79} - 6 q^{81} + 36 q^{83} + 28 q^{85} + 5 q^{87} - 2 q^{89} - 15 q^{91} - 11 q^{93} - 48 q^{95} + 19 q^{97} - 24 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 + q^5 - 5 * q^7 + 6 * q^9 - 3 * q^11 + 7 * q^13 + q^15 - q^17 - 13 * q^19 - 22 * q^25 + 2 * q^27 - 7 * q^29 + 12 * q^31 - 3 * q^33 - 2 * q^35 + 6 * q^37 + 4 * q^39 + 4 * q^41 - 2 * q^43 - 3 * q^45 + 34 * q^47 - 25 * q^49 - 53 * q^51 + q^53 - 2 * q^55 - 21 * q^57 - 42 * q^59 - 62 * q^61 + 22 * q^63 + 6 * q^65 - 52 * q^67 - 40 * q^69 + 32 * q^71 + 17 * q^73 - 53 * q^75 - q^77 - 32 * q^79 - 6 * q^81 + 36 * q^83 + 28 * q^85 + 5 * q^87 - 2 * q^89 - 15 * q^91 - 11 * q^93 - 48 * q^95 + 19 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.914508	+	1.47094i	0.527991	+	0.849250i
$3$	0.914508	+	1.47094i	0.527991	+	0.849250i
$4$		0			0
$5$	0.891774	+	1.54460i	0.398814	+	0.690765i	0.993580	−	0.113133i	$-0.0360887\pi$
$5$	0.891774	+	1.54460i	0.398814	+	0.690765i	−0.594766	+	0.803899i	$0.702755\pi$
$6$		0			0
$7$	2.54386	−	0.727153i	0.961491	−	0.274838i
$7$	2.54386	−	0.727153i	0.961491	−	0.274838i
$8$		0			0
$9$	−1.32735	+	2.69038i	−0.442450	+	0.896793i
$10$		0			0
$11$	−2.80706	+	4.86196i	−0.846359	+	1.46594i	0.0380759	+	0.999275i	$0.487877\pi$
$11$	−2.80706	+	4.86196i	−0.846359	+	1.46594i	−0.884435	+	0.466663i	$0.845456\pi$
$12$		0			0
$13$	3.14009	−	5.43879i	0.870903	−	1.50845i	0.00983976	−	0.999952i	$-0.496868\pi$
$13$	3.14009	−	5.43879i	0.870903	−	1.50845i	0.861064	−	0.508497i	$-0.169799\pi$
$14$		0			0
$15$	−1.45648	+	2.72430i	−0.376062	+	0.703410i
$16$		0			0
$17$	0.646279	+	1.11939i	0.156746	+	0.271491i	0.933693	−	0.358074i	$-0.116566\pi$
$17$	0.646279	+	1.11939i	0.156746	+	0.271491i	−0.776948	+	0.629565i	$0.783233\pi$
$18$		0			0
$19$	−0.559062	+	0.968324i	−0.128258	+	0.222149i	−0.923002	−	0.384796i	$-0.874272\pi$
$19$	−0.559062	+	0.968324i	−0.128258	+	0.222149i	0.794744	+	0.606945i	$0.207605\pi$
$20$		0			0
$21$	3.39599	+	3.07689i	0.741065	+	0.671433i
$22$		0			0
$23$	3.80857	+	6.59664i	0.794142	+	1.37549i	0.923382	+	0.383882i	$0.125413\pi$
$23$	3.80857	+	6.59664i	0.794142	+	1.37549i	−0.129240	+	0.991613i	$0.541254\pi$
$24$		0			0
$25$	0.909478	−	1.57526i	0.181896	−	0.315052i
$26$		0			0
$27$	−5.17127	+	0.507916i	−0.995211	+	0.0977485i
$28$		0			0
$29$	−1.57496	−	2.72791i	−0.292462	−	0.506560i	0.681929	−	0.731418i	$-0.261141\pi$
$29$	−1.57496	−	2.72791i	−0.292462	−	0.506560i	−0.974391	+	0.224859i	$0.927808\pi$
$30$		0			0
$31$	−1.00311			−0.180163			−0.0900816	−	0.995934i	$-0.528713\pi$
$31$	−1.00311			−0.180163			−0.0900816	+	0.995934i	$0.528713\pi$
$32$		0			0
$33$	−9.71875	+	0.317283i	−1.69182	+	0.0552320i
$34$		0			0
$35$	3.39171	+	3.28079i	0.573304	+	0.554555i
$36$		0			0
$37$	−5.96542	+	10.3324i	−0.980708	+	1.69864i	−0.321067	+	0.947057i	$0.604041\pi$
$37$	−5.96542	+	10.3324i	−0.980708	+	1.69864i	−0.659642	+	0.751580i	$0.729292\pi$
$38$		0			0
$39$	10.8718	−	0.354926i	1.74088	−	0.0568336i
$40$		0			0
$41$	4.14160	−	7.17347i	0.646810	−	1.12031i	−0.337071	−	0.941479i	$-0.609436\pi$
$41$	4.14160	−	7.17347i	0.646810	−	1.12031i	0.983880	−	0.178828i	$-0.0572306\pi$
$42$		0			0
$43$	−2.34804	−	4.06693i	−0.358073	−	0.620200i	0.629566	−	0.776947i	$-0.283233\pi$
$43$	−2.34804	−	4.06693i	−0.358073	−	0.620200i	−0.987639	+	0.156747i	$0.949899\pi$
$44$		0			0
$45$	−5.33925	+	0.348988i	−0.795929	+	0.0520240i
$46$		0			0
$47$	1.94400			0.283562			0.141781	−	0.989898i	$-0.454717\pi$
$47$	1.94400			0.283562			0.141781	+	0.989898i	$0.454717\pi$
$48$		0			0
$49$	5.94250	−	3.69956i	0.848928	−	0.528508i
$50$		0			0
$51$	−1.05553	+	1.97433i	−0.147804	+	0.276461i
$52$		0			0
$53$	−4.45992	−	7.72481i	−0.612617	−	1.06108i	−0.990798	−	0.135352i	$-0.956783\pi$
$53$	−4.45992	−	7.72481i	−0.612617	−	1.06108i	0.378180	−	0.925732i	$-0.376550\pi$
$54$		0			0
$55$	−10.0130			−1.35016
$56$		0			0
$57$	−1.93562	+	0.0631911i	−0.256379	+	0.00836987i
$58$		0			0
$59$	−8.38679			−1.09187			−0.545933	−	0.837829i	$-0.683825\pi$
$59$	−8.38679			−1.09187			−0.545933	+	0.837829i	$0.683825\pi$
$60$		0			0
$61$	4.82576			0.617875			0.308937	−	0.951082i	$-0.400027\pi$
$61$	4.82576			0.617875			0.308937	+	0.951082i	$0.400027\pi$
$62$		0			0
$63$	−1.42028	+	7.80915i	−0.178939	+	0.983860i
$64$		0			0
$65$	11.2010			1.38931
$66$		0			0
$67$	2.55628			0.312299			0.156150	−	0.987733i	$-0.450092\pi$
$67$	2.55628			0.312299			0.156150	+	0.987733i	$0.450092\pi$
$68$		0			0
$69$	−6.22032	+	11.6349i	−0.748838	+	1.40067i
$70$		0			0
$71$	8.86178			1.05170			0.525850	−	0.850577i	$-0.323747\pi$
$71$	8.86178			1.05170			0.525850	+	0.850577i	$0.323747\pi$
$72$		0			0
$73$	5.67598	+	9.83109i	0.664323	+	1.15064i	0.979468	+	0.201598i	$0.0646135\pi$
$73$	5.67598	+	9.83109i	0.664323	+	1.15064i	−0.315145	+	0.949044i	$0.602053\pi$
$74$		0			0
$75$	3.14885	−	0.102799i	0.363597	−	0.0118702i
$76$		0			0
$77$	−3.60538	+	14.4093i	−0.410871	+	1.64210i
$78$		0			0
$79$	−13.4577			−1.51410			−0.757052	−	0.653354i	$-0.773361\pi$
$79$	−13.4577			−1.51410			−0.757052	+	0.653354i	$0.773361\pi$
$80$		0			0
$81$	−5.47628	−	7.14215i	−0.608476	−	0.793572i
$82$		0			0
$83$	1.60203	+	2.77479i	0.175845	+	0.304573i	0.940453	−	0.339922i	$-0.110401\pi$
$83$	1.60203	+	2.77479i	0.175845	+	0.304573i	−0.764608	+	0.644495i	$0.777067\pi$
$84$		0			0
$85$	−1.15267	+	1.99648i	−0.125025	+	0.216549i
$86$		0			0
$87$	2.57229	−	4.81137i	0.275778	−	0.515833i
$88$		0			0
$89$	−0.404646	+	0.700867i	−0.0428924	+	0.0742917i	−0.886675	−	0.462394i	$-0.846991\pi$
$89$	−0.404646	+	0.700867i	−0.0428924	+	0.0742917i	0.843782	+	0.536686i	$0.180324\pi$
$90$		0			0
$91$	4.03312	−	16.1189i	0.422786	−	1.68972i
$92$		0			0
$93$	−0.917349	−	1.47551i	−0.0951247	−	0.153004i
$94$		0			0
$95$	−1.99423			−0.204604
$96$		0			0
$97$	1.10781	+	1.91879i	0.112481	+	0.194823i	0.916770	−	0.399415i	$-0.130787\pi$
$97$	1.10781	+	1.91879i	0.112481	+	0.194823i	−0.804289	+	0.594238i	$0.797454\pi$
$98$		0			0
$99$	−9.35458	−	14.0056i	−0.940171	−	1.40761i
$100$		0			0
$101$	−4.70134	+	8.14296i	−0.467801	+	0.810254i	−0.999323	−	0.0367899i	$-0.988287\pi$
$101$	−4.70134	+	8.14296i	−0.467801	+	0.810254i	0.531522	+	0.847044i	$0.321620\pi$
$102$		0			0
$103$	−1.76349	−	3.05446i	−0.173762	−	0.300964i	0.765970	−	0.642876i	$-0.222259\pi$
$103$	−1.76349	−	3.05446i	−0.173762	−	0.300964i	−0.939732	+	0.341912i	$0.888926\pi$
$104$		0			0
$105$	−1.72411	+	7.98933i	−0.168256	+	0.779679i
$106$		0			0
$107$	3.39276	−	5.87644i	0.327991	−	0.568097i	−0.654122	−	0.756389i	$-0.726962\pi$
$107$	3.39276	−	5.87644i	0.327991	−	0.568097i	0.982113	+	0.188292i	$0.0602951\pi$
$108$		0			0
$109$	0.681848	+	1.18099i	0.0653092	+	0.113119i	0.896831	−	0.442373i	$-0.145863\pi$
$109$	0.681848	+	1.18099i	0.0653092	+	0.113119i	−0.831522	+	0.555492i	$0.812530\pi$
$110$		0			0
$111$	−20.6538	+	0.674275i	−1.96037	+	0.0639993i
$112$		0			0
$113$	−2.76458	+	4.78840i	−0.260070	+	0.450455i	−0.966260	−	0.257568i	$-0.917079\pi$
$113$	−2.76458	+	4.78840i	−0.260070	+	0.450455i	0.706190	+	0.708022i	$0.250412\pi$
$114$		0			0
$115$	−6.79277	+	11.7654i	−0.633429	+	1.09713i
$116$		0			0
$117$	10.4644	+	15.6672i	0.967435	+	1.44843i
$118$		0			0
$119$	2.45801	+	2.37763i	0.225326	+	0.217957i
$120$		0			0
$121$	−10.2591	−	17.7693i	−0.932649	−	1.61539i
$122$		0			0
$123$	14.3393	−	0.468128i	1.29293	−	0.0422097i
$124$		0			0
$125$	12.1619			1.08780
$126$		0			0
$127$	12.8209			1.13767			0.568837	−	0.822450i	$-0.307394\pi$
$127$	12.8209			1.13767			0.568837	+	0.822450i	$0.307394\pi$
$128$		0			0
$129$	3.83492	−	7.17307i	0.337646	−	0.631554i
$130$		0			0
$131$	−2.90955	−	5.03948i	−0.254208	−	0.440302i	0.710472	−	0.703726i	$-0.248482\pi$
$131$	−2.90955	−	5.03948i	−0.254208	−	0.440302i	−0.964680	+	0.263424i	$0.915148\pi$
$132$		0			0
$133$	−0.718059	+	2.86981i	−0.0622636	+	0.248844i
$134$		0			0
$135$	−5.39613	−	7.53459i	−0.464425	−	0.648474i
$136$		0			0
$137$	7.67046	−	13.2856i	0.655332	−	1.13507i	−0.326479	−	0.945205i	$-0.605862\pi$
$137$	7.67046	−	13.2856i	0.655332	−	1.13507i	0.981810	−	0.189864i	$-0.0608046\pi$
$138$		0			0
$139$	6.05803	−	10.4928i	0.513835	−	0.889988i	−0.486036	−	0.873939i	$-0.661558\pi$
$139$	6.05803	−	10.4928i	0.513835	−	0.889988i	0.999871	−	0.0160496i	$-0.00510897\pi$
$140$		0			0
$141$	1.77781	+	2.85952i	0.149718	+	0.240815i
$142$		0			0
$143$	17.6288	+	30.5340i	1.47419	+	2.55338i
$144$		0			0
$145$	2.80901	−	4.86535i	0.233276	−	0.404046i
$146$		0			0
$147$	10.8763	+	5.35780i	0.897062	+	0.441904i
$148$		0			0
$149$	−2.36849	−	4.10235i	−0.194035	−	0.336078i	0.752549	−	0.658536i	$-0.228824\pi$
$149$	−2.36849	−	4.10235i	−0.194035	−	0.336078i	−0.946584	+	0.322458i	$0.895491\pi$
$150$		0			0
$151$	12.1845	−	21.1041i	0.991559	−	1.71743i	0.383493	−	0.923544i	$-0.374721\pi$
$151$	12.1845	−	21.1041i	0.991559	−	1.71743i	0.608066	−	0.793887i	$-0.291946\pi$
$152$		0			0
$153$	−3.86942	+	0.252916i	−0.312824	+	0.0204470i
$154$		0			0
$155$	−0.894545	−	1.54940i	−0.0718516	−	0.124451i
$156$		0			0
$157$	−6.30458			−0.503160			−0.251580	−	0.967836i	$-0.580950\pi$
$157$	−6.30458			−0.503160			−0.251580	+	0.967836i	$0.580950\pi$
$158$		0			0
$159$	7.28413	−	13.6247i	0.577669	−	1.08051i
$160$		0			0
$161$	14.4853	+	14.0116i	1.14160	+	1.10426i
$162$		0			0
$163$	−0.350678	+	0.607392i	−0.0274672	+	0.0475746i	−0.879432	−	0.476024i	$-0.842078\pi$
$163$	−0.350678	+	0.607392i	−0.0274672	+	0.0475746i	0.851965	+	0.523599i	$0.175411\pi$
$164$		0			0
$165$	−9.15701	−	14.7286i	−0.712872	−	1.14662i
$166$		0			0
$167$	−3.53822	+	6.12839i	−0.273796	+	0.474229i	−0.969831	−	0.243780i	$-0.921613\pi$
$167$	−3.53822	+	6.12839i	−0.273796	+	0.474229i	0.696035	+	0.718008i	$0.254946\pi$
$168$		0			0
$169$	−13.2203	−	22.8982i	−1.01695	−	1.76140i
$170$		0			0
$171$	−1.86309	−	2.78939i	−0.142474	−	0.213310i
$172$		0			0
$173$	6.63534			0.504476			0.252238	−	0.967665i	$-0.418833\pi$
$173$	6.63534			0.504476			0.252238	+	0.967665i	$0.418833\pi$
$174$		0			0
$175$	1.16813	−	4.66858i	0.0883025	−	0.352912i
$176$		0			0
$177$	−7.66978	−	12.3365i	−0.576496	−	0.927267i
$178$		0			0
$179$	−5.63527	−	9.76057i	−0.421200	−	0.729539i	0.574858	−	0.818253i	$-0.305057\pi$
$179$	−5.63527	−	9.76057i	−0.421200	−	0.729539i	−0.996057	+	0.0887145i	$0.971724\pi$
$180$		0			0
$181$	21.1800			1.57430			0.787149	−	0.616762i	$-0.211556\pi$
$181$	21.1800			1.57430			0.787149	+	0.616762i	$0.211556\pi$
$182$		0			0
$183$	4.41319	+	7.09841i	0.326233	+	0.524730i
$184$		0			0
$185$	−21.2792			−1.56448
$186$		0			0
$187$	−7.25657			−0.530653
$188$		0			0
$189$	−12.7857	+	5.05237i	−0.930021	+	0.367506i
$190$		0			0
$191$	9.44088			0.683118			0.341559	−	0.939860i	$-0.389045\pi$
$191$	9.44088			0.683118			0.341559	+	0.939860i	$0.389045\pi$
$192$		0			0
$193$	−6.28042			−0.452074			−0.226037	−	0.974119i	$-0.572577\pi$
$193$	−6.28042			−0.452074			−0.226037	+	0.974119i	$0.572577\pi$
$194$		0			0
$195$	10.2434	+	16.4760i	0.733545	+	1.17987i
$196$		0			0
$197$	15.4780			1.10276			0.551382	−	0.834253i	$-0.314101\pi$
$197$	15.4780			1.10276			0.551382	+	0.834253i	$0.314101\pi$
$198$		0			0
$199$	−2.19477	−	3.80145i	−0.155583	−	0.269478i	0.777688	−	0.628650i	$-0.216392\pi$
$199$	−2.19477	−	3.80145i	−0.155583	−	0.269478i	−0.933271	+	0.359173i	$0.883059\pi$
$200$		0			0
$201$	2.33774	+	3.76014i	0.164891	+	0.265220i
$202$		0			0
$203$	−5.99009	−	5.79419i	−0.420422	−	0.406673i
$204$		0			0
$205$	14.7735			1.03183
$206$		0			0
$207$	−22.8028	+	1.49045i	−1.58490	+	0.103594i
$208$		0			0
$209$	−3.13864	−	5.43628i	−0.217104	−	0.376035i
$210$		0			0
$211$	−7.93101	+	13.7369i	−0.545993	+	0.945688i	0.452550	+	0.891739i	$0.350514\pi$
$211$	−7.93101	+	13.7369i	−0.545993	+	0.945688i	−0.998544	+	0.0539495i	$0.982819\pi$
$212$		0			0
$213$	8.10417	+	13.0352i	0.555289	+	0.893156i
$214$		0			0
$215$	4.18784	−	7.25356i	0.285609	−	0.494689i
$216$		0			0
$217$	−2.55177	+	0.729412i	−0.173225	+	0.0495157i
$218$		0			0
$219$	−9.27025	+	17.3397i	−0.626425	+	1.17171i
$220$		0			0
$221$	8.11749			0.546041
$222$		0			0
$223$	−6.99253	−	12.1114i	−0.468254	−	0.811040i	0.531088	−	0.847317i	$-0.321784\pi$
$223$	−6.99253	−	12.1114i	−0.468254	−	0.811040i	−0.999342	+	0.0362769i	$0.988450\pi$
$224$		0			0
$225$	3.03086	+	4.53776i	0.202057	+	0.302518i
$226$		0			0
$227$	5.38364	−	9.32474i	0.357325	−	0.618905i	−0.630188	−	0.776443i	$-0.717022\pi$
$227$	5.38364	−	9.32474i	0.357325	−	0.618905i	0.987513	+	0.157538i	$0.0503555\pi$
$228$		0			0
$229$	0.805015	+	1.39433i	0.0531969	+	0.0921397i	0.891398	−	0.453222i	$-0.149726\pi$
$229$	0.805015	+	1.39433i	0.0531969	+	0.0921397i	−0.838201	+	0.545362i	$0.816392\pi$
$230$		0			0
$231$	−24.4925	+	7.87414i	−1.61149	+	0.518081i
$232$		0			0
$233$	−0.510606	+	0.884395i	−0.0334509	+	0.0579387i	−0.882266	−	0.470751i	$-0.843983\pi$
$233$	−0.510606	+	0.884395i	−0.0334509	+	0.0579387i	0.848815	+	0.528690i	$0.177316\pi$
$234$		0			0
$235$	1.73361	+	3.00270i	0.113088	+	0.195875i
$236$		0			0
$237$	−12.3071	−	19.7955i	−0.799434	−	1.28585i
$238$		0			0
$239$	6.96428	−	12.0625i	0.450482	−	0.780258i	−0.547934	−	0.836522i	$-0.684586\pi$
$239$	6.96428	−	12.0625i	0.450482	−	0.780258i	0.998416	+	0.0562640i	$0.0179189\pi$
$240$		0			0
$241$	7.28788	−	12.6230i	0.469454	−	0.813118i	−0.529936	−	0.848037i	$-0.677784\pi$
$241$	7.28788	−	12.6230i	0.469454	−	0.813118i	0.999390	+	0.0349197i	$0.0111175\pi$
$242$		0			0
$243$	5.49760	−	14.5869i	0.352671	−	0.935747i
$244$		0			0
$245$	11.0137	+	5.87960i	0.703639	+	0.375634i
$246$		0			0
$247$	3.51101	+	6.08124i	0.223400	+	0.386940i
$248$		0			0
$249$	−2.61650	+	4.89406i	−0.165814	+	0.310148i
$250$		0			0
$251$	−18.0287			−1.13796			−0.568981	−	0.822350i	$-0.692662\pi$
$251$	−18.0287			−1.13796			−0.568981	+	0.822350i	$0.692662\pi$
$252$		0			0
$253$	−42.7635			−2.68852
$254$		0			0
$255$	−3.99084	+	0.130287i	−0.249916	+	0.00815889i
$256$		0			0
$257$	−13.4633	−	23.3191i	−0.839818	−	1.45461i	−0.890047	−	0.455869i	$-0.849328\pi$
$257$	−13.4633	−	23.3191i	−0.839818	−	1.45461i	0.0502291	−	0.998738i	$-0.484005\pi$
$258$		0			0
$259$	−7.66198	+	30.6220i	−0.476092	+	1.90276i
$260$		0			0
$261$	9.42963	−	0.616346i	0.583679	−	0.0381508i
$262$		0			0
$263$	0.769419	−	1.33267i	0.0474444	−	0.0821761i	−0.841328	−	0.540525i	$-0.818226\pi$
$263$	0.769419	−	1.33267i	0.0474444	−	0.0821761i	0.888772	+	0.458349i	$0.151559\pi$
$264$		0			0
$265$	7.95448	−	13.7776i	0.488640	−	0.846349i
$266$		0			0
$267$	−1.40099	+	0.0457374i	−0.0857390	+	0.00279908i
$268$		0			0
$269$	3.26461	+	5.65446i	0.199047	+	0.344759i	0.948220	−	0.317616i	$-0.102882\pi$
$269$	3.26461	+	5.65446i	0.199047	+	0.344759i	−0.749173	+	0.662374i	$0.769549\pi$
$270$		0			0
$271$	5.64494	−	9.77733i	0.342906	−	0.593930i	−0.642065	−	0.766650i	$-0.721922\pi$
$271$	5.64494	−	9.77733i	0.342906	−	0.593930i	0.984971	+	0.172720i	$0.0552555\pi$
$272$		0			0
$273$	27.3983	−	8.80834i	1.65822	−	0.533105i
$274$		0			0
$275$	5.10591	+	8.84370i	0.307898	+	0.533295i
$276$		0			0
$277$	−0.905938	+	1.56913i	−0.0544325	+	0.0942799i	−0.891958	−	0.452119i	$-0.850668\pi$
$277$	−0.905938	+	1.56913i	−0.0544325	+	0.0942799i	0.837525	+	0.546399i	$0.184002\pi$
$278$		0			0
$279$	1.33147	−	2.69874i	0.0797133	−	0.161569i
$280$		0			0
$281$	−2.98798	−	5.17533i	−0.178248	−	0.308734i	0.763033	−	0.646360i	$-0.223710\pi$
$281$	−2.98798	−	5.17533i	−0.178248	−	0.308734i	−0.941280	+	0.337626i	$0.890376\pi$
$282$		0			0
$283$	19.9952			1.18859			0.594295	−	0.804247i	$-0.297431\pi$
$283$	19.9952			1.18859			0.594295	+	0.804247i	$0.297431\pi$
$284$		0			0
$285$	−1.82374	−	2.93340i	−0.108029	−	0.173759i
$286$		0			0
$287$	5.31947	−	21.2599i	0.313998	−	1.25493i
$288$		0			0
$289$	7.66465	−	13.2756i	0.450862	−	0.780915i
$290$		0			0
$291$	−1.80932	+	3.38427i	−0.106064	+	0.198390i
$292$		0			0
$293$	−4.95166	+	8.57652i	−0.289279	+	0.501046i	−0.973638	−	0.228099i	$-0.926749\pi$
$293$	−4.95166	+	8.57652i	−0.289279	+	0.501046i	0.684359	+	0.729145i	$0.260082\pi$
$294$		0			0
$295$	−7.47912	−	12.9542i	−0.435451	−	0.754224i
$296$		0			0
$297$	12.0466	−	26.5683i	0.699013	−	1.54165i
$298$		0			0
$299$	47.8370			2.76649
$300$		0			0
$301$	−8.93038	−	8.63833i	−0.514738	−	0.497905i
$302$		0			0
$303$	−16.2772	+	0.531395i	−0.935103	+	0.0305279i
$304$		0			0
$305$	4.30348	+	7.45385i	0.246417	+	0.426806i
$306$		0			0
$307$	23.7122			1.35332			0.676662	−	0.736293i	$-0.263426\pi$
$307$	23.7122			1.35332			0.676662	+	0.736293i	$0.263426\pi$
$308$		0			0
$309$	2.88021	−	5.38732i	0.163849	−	0.306474i
$310$		0			0
$311$	−20.3449			−1.15365			−0.576826	−	0.816867i	$-0.695709\pi$
$311$	−20.3449			−1.15365			−0.576826	+	0.816867i	$0.695709\pi$
$312$		0			0
$313$	9.71871			0.549334			0.274667	−	0.961539i	$-0.411432\pi$
$313$	9.71871			0.549334			0.274667	+	0.961539i	$0.411432\pi$
$314$		0			0
$315$	−13.3286	+	4.77023i	−0.750980	+	0.268772i
$316$		0			0
$317$	−3.32838			−0.186941			−0.0934703	−	0.995622i	$-0.529796\pi$
$317$	−3.32838			−0.186941			−0.0934703	+	0.995622i	$0.529796\pi$
$318$		0			0
$319$	17.6840			0.990113
$320$		0			0
$321$	11.7466	−	0.383486i	0.655633	−	0.0214041i
$322$		0			0
$323$	−1.44524			−0.0804153
$324$		0			0
$325$	−5.71168	−	9.89292i	−0.316827	−	0.548760i
$326$		0			0
$327$	−1.11362	+	2.08299i	−0.0615834	+	0.115190i
$328$		0			0
$329$	4.94528	−	1.41359i	0.272642	−	0.0779335i
$330$		0			0
$331$	1.43469			0.0788578			0.0394289	−	0.999222i	$-0.487446\pi$
$331$	1.43469			0.0788578			0.0394289	+	0.999222i	$0.487446\pi$
$332$		0			0
$333$	−19.8799	−	29.7640i	−1.08941	−	1.63105i
$334$		0			0
$335$	2.27962	+	3.94843i	0.124549	+	0.215726i
$336$		0			0
$337$	0.00257316	−	0.00445685i	0.000140169	−	0.000242780i	−0.865955	−	0.500121i	$-0.833289\pi$
$337$	0.00257316	−	0.00445685i	0.000140169	−	0.000242780i	0.866095	+	0.499879i	$0.166622\pi$
$338$		0			0
$339$	−9.57170	+	0.312483i	−0.519863	+	0.0169717i
$340$		0			0
$341$	2.81578	−	4.87707i	0.152483	−	0.264108i
$342$		0			0
$343$	12.4268	−	13.7323i	0.670982	−	0.741473i
$344$		0			0
$345$	−23.5183	+	0.767792i	−1.26618	+	0.0413365i
$346$		0			0
$347$	−23.1072			−1.24046			−0.620229	−	0.784421i	$-0.712960\pi$
$347$	−23.1072			−1.24046			−0.620229	+	0.784421i	$0.712960\pi$
$348$		0			0
$349$	6.09723	+	10.5607i	0.326377	+	0.565302i	0.981790	−	0.189969i	$-0.0608387\pi$
$349$	6.09723	+	10.5607i	0.326377	+	0.565302i	−0.655413	+	0.755271i	$0.727505\pi$
$350$		0			0
$351$	−13.4758	+	29.7203i	−0.719284	+	1.58635i
$352$		0			0
$353$	−12.3536	+	21.3970i	−0.657515	+	1.13885i	0.323742	+	0.946145i	$0.395059\pi$
$353$	−12.3536	+	21.3970i	−0.657515	+	1.13885i	−0.981257	+	0.192704i	$0.938274\pi$
$354$		0			0
$355$	7.90271	+	13.6879i	0.419432	+	0.726478i
$356$		0			0
$357$	−1.24948	+	5.78996i	−0.0661298	+	0.306437i
$358$		0			0
$359$	−8.20362	+	14.2091i	−0.432970	+	0.749927i	−0.997128	−	0.0757407i	$-0.975868\pi$
$359$	−8.20362	+	14.2091i	−0.432970	+	0.749927i	0.564157	+	0.825667i	$0.309201\pi$
$360$		0			0
$361$	8.87490	+	15.3718i	0.467100	+	0.809041i
$362$		0			0
$363$	16.7556	−	31.3408i	0.879443	−	1.64497i
$364$		0			0
$365$	−10.1234	+	17.5342i	−0.529882	+	0.917783i
$366$		0			0
$367$	−2.90900	+	5.03854i	−0.151849	+	0.263010i	−0.931907	−	0.362697i	$-0.881856\pi$
$367$	−2.90900	+	5.03854i	−0.151849	+	0.263010i	0.780058	+	0.625707i	$0.215189\pi$
$368$		0			0
$369$	13.8020	+	20.6642i	0.718503	+	1.07573i
$370$		0			0
$371$	−16.9626	−	16.4078i	−0.880652	−	0.851852i
$372$		0			0
$373$	−4.42483	−	7.66403i	−0.229109	−	0.396829i	0.728435	−	0.685115i	$-0.240248\pi$
$373$	−4.42483	−	7.66403i	−0.229109	−	0.396829i	−0.957544	+	0.288286i	$0.906915\pi$
$374$		0			0
$375$	11.1222	+	17.8895i	0.574347	+	0.923811i
$376$		0			0
$377$	−19.7820			−1.01883
$378$		0			0
$379$	−17.3300			−0.890181			−0.445091	−	0.895486i	$-0.646829\pi$
$379$	−17.3300			−0.890181			−0.445091	+	0.895486i	$0.646829\pi$
$380$		0			0
$381$	11.7248	+	18.8589i	0.600682	+	0.966169i
$382$		0			0
$383$	3.54545	+	6.14090i	0.181164	+	0.313785i	0.942277	−	0.334834i	$-0.108680\pi$
$383$	3.54545	+	6.14090i	0.181164	+	0.313785i	−0.761113	+	0.648619i	$0.775347\pi$
$384$		0			0
$385$	−25.4718	+	7.28101i	−1.29816	+	0.371075i
$386$		0			0
$387$	14.0582	−	0.918885i	0.714621	−	0.0467095i
$388$		0			0
$389$	−3.32120	+	5.75249i	−0.168392	+	0.291663i	−0.937854	−	0.347029i	$-0.887191\pi$
$389$	−3.32120	+	5.75249i	−0.168392	+	0.291663i	0.769463	+	0.638691i	$0.220524\pi$
$390$		0			0
$391$	−4.92280	+	8.52654i	−0.248957	+	0.431206i
$392$		0			0
$393$	4.75199	−	8.88843i	0.239706	−	0.448362i
$394$		0			0
$395$	−12.0012	−	20.7867i	−0.603845	−	1.04589i
$396$		0			0
$397$	7.86340	−	13.6198i	0.394653	−	0.683559i	−0.598404	−	0.801195i	$-0.704198\pi$
$397$	7.86340	−	13.6198i	0.394653	−	0.683559i	0.993057	+	0.117636i	$0.0375315\pi$
$398$		0			0
$399$	−4.87800	+	1.56824i	−0.244205	+	0.0785101i
$400$		0			0
$401$	−2.98280	−	5.16635i	−0.148954	−	0.257995i	0.781887	−	0.623420i	$-0.214257\pi$
$401$	−2.98280	−	5.16635i	−0.148954	−	0.257995i	−0.930841	+	0.365424i	$0.880924\pi$
$402$		0			0
$403$	−3.14984	+	5.45569i	−0.156905	+	0.271767i
$404$		0			0
$405$	6.14815	−	14.8278i	0.305504	−	0.736801i
$406$		0			0
$407$	−33.4905	−	58.0073i	−1.66006	−	2.87531i
$408$		0			0
$409$	−17.6189			−0.871197			−0.435598	−	0.900141i	$-0.643463\pi$
$409$	−17.6189			−0.871197			−0.435598	+	0.900141i	$0.643463\pi$
$410$		0			0
$411$	26.5571	−	0.866997i	1.30997	−	0.0427658i
$412$		0			0
$413$	−21.3349	+	6.09848i	−1.04982	+	0.300086i
$414$		0			0
$415$	−2.85729	+	4.94897i	−0.140259	+	0.242936i
$416$		0			0
$417$	20.9744	−	0.684742i	1.02712	−	0.0335320i
$418$		0			0
$419$	−9.62164	+	16.6652i	−0.470048	+	0.814147i	−0.999413	−	0.0342470i	$-0.989097\pi$
$419$	−9.62164	+	16.6652i	−0.470048	+	0.814147i	0.529365	+	0.848394i	$0.322430\pi$
$420$		0			0
$421$	7.77999	+	13.4753i	0.379174	+	0.656748i	0.990942	−	0.134289i	$-0.0428750\pi$
$421$	7.77999	+	13.4753i	0.379174	+	0.656748i	−0.611769	+	0.791037i	$0.709542\pi$
$422$		0			0
$423$	−2.58037	+	5.23010i	−0.125462	+	0.254296i
$424$		0			0
$425$	2.35111			0.114045
$426$		0			0
$427$	12.2761	−	3.50906i	0.594081	−	0.169815i
$428$		0			0
$429$	−28.7921	+	53.8545i	−1.39010	+	2.60012i
$430$		0			0
$431$	16.9779	+	29.4067i	0.817799	+	1.41647i	0.907301	+	0.420482i	$0.138139\pi$
$431$	16.9779	+	29.4067i	0.817799	+	1.41647i	−0.0895020	+	0.995987i	$0.528528\pi$
$432$		0			0
$433$	−34.8338			−1.67401			−0.837004	−	0.547197i	$-0.815695\pi$
$433$	−34.8338			−1.67401			−0.837004	+	0.547197i	$0.815695\pi$
$434$		0			0
$435$	9.72553	−	0.317505i	0.466303	−	0.0152232i
$436$		0			0
$437$	−8.51692			−0.407419
$438$		0			0
$439$	−15.5588			−0.742579			−0.371290	−	0.928517i	$-0.621084\pi$
$439$	−15.5588			−0.742579			−0.371290	+	0.928517i	$0.621084\pi$
$440$		0			0
$441$	2.06544	+	20.8982i	0.0983541	+	0.995151i
$442$		0			0
$443$	−18.3242			−0.870611			−0.435305	−	0.900283i	$-0.643360\pi$
$443$	−18.3242			−0.870611			−0.435305	+	0.900283i	$0.643360\pi$
$444$		0			0
$445$	−1.44341			−0.0684242
$446$		0			0
$447$	3.86832	−	7.23555i	0.182965	−	0.342230i
$448$		0			0
$449$	−2.75072			−0.129815			−0.0649073	−	0.997891i	$-0.520675\pi$
$449$	−2.75072			−0.129815			−0.0649073	+	0.997891i	$0.520675\pi$
$450$		0			0
$451$	23.2514	+	40.2727i	1.09487	+	1.89637i
$452$		0			0
$453$	42.1858	−	1.37722i	1.98206	−	0.0647074i
$454$		0			0
$455$	28.4938	−	8.14483i	1.33581	−	0.381836i
$456$		0			0
$457$	20.6813			0.967433			0.483716	−	0.875225i	$-0.339287\pi$
$457$	20.6813			0.967433			0.483716	+	0.875225i	$0.339287\pi$
$458$		0			0
$459$	−3.91064	−	5.46040i	−0.182533	−	0.254870i
$460$		0			0
$461$	6.40670	+	11.0967i	0.298390	+	0.516826i	0.975768	−	0.218809i	$-0.0702172\pi$
$461$	6.40670	+	11.0967i	0.298390	+	0.516826i	−0.677378	+	0.735635i	$0.736884\pi$
$462$		0			0
$463$	−5.54704	+	9.60775i	−0.257793	+	0.446510i	−0.965650	−	0.259845i	$-0.916328\pi$
$463$	−5.54704	+	9.60775i	−0.257793	+	0.446510i	0.707858	+	0.706355i	$0.249662\pi$
$464$		0			0
$465$	1.46101	−	2.73276i	0.0677526	−	0.126729i
$466$		0			0
$467$	−5.36754	+	9.29686i	−0.248380	+	0.430207i	−0.963077	−	0.269228i	$-0.913232\pi$
$467$	−5.36754	+	9.29686i	−0.248380	+	0.430207i	0.714696	+	0.699435i	$0.246565\pi$
$468$		0			0
$469$	6.50283	−	1.85881i	0.300273	−	0.0858317i
$470$		0			0
$471$	−5.76559	−	9.27368i	−0.265664	−	0.427309i
$472$		0			0
$473$	26.3643			1.21223
$474$		0			0
$475$	1.01691	+	1.76134i	0.0466590	+	0.0808157i
$476$		0			0
$477$	26.7025	−	1.74535i	1.22263	−	0.0799141i
$478$		0			0
$479$	−3.89754	+	6.75074i	−0.178083	+	0.308449i	−0.941224	−	0.337783i	$-0.890323\pi$
$479$	−3.89754	+	6.75074i	−0.178083	+	0.308449i	0.763141	+	0.646232i	$0.223656\pi$
$480$		0			0
$481$	37.4639	+	64.8893i	1.70820	+	2.95870i
$482$		0			0
$483$	−7.36331	+	34.1207i	−0.335042	+	1.55254i
$484$		0			0
$485$	−1.97583	+	3.42225i	−0.0897180	+	0.155396i
$486$		0			0
$487$	−13.9984	−	24.2459i	−0.634326	−	1.09868i	−0.986657	−	0.162810i	$-0.947944\pi$
$487$	−13.9984	−	24.2459i	−0.634326	−	1.09868i	0.352331	−	0.935875i	$-0.385389\pi$
$488$		0			0
$489$	−1.21414	+	0.0396373i	−0.0549052	+	0.00179246i
$490$		0			0
$491$	12.1227	−	20.9971i	0.547089	−	0.947586i	−0.451383	−	0.892330i	$-0.649069\pi$
$491$	12.1227	−	20.9971i	0.547089	−	0.947586i	0.998472	−	0.0552556i	$-0.0175974\pi$
$492$		0			0
$493$	2.03572	−	3.52598i	0.0916844	−	0.158802i
$494$		0			0
$495$	13.2908	−	26.9389i	0.597378	−	1.21081i
$496$		0			0
$497$	22.5432	−	6.44387i	1.01120	−	0.289047i
$498$		0			0
$499$	−16.8874	−	29.2499i	−0.755984	−	1.30940i	−0.944883	−	0.327407i	$-0.893825\pi$
$499$	−16.8874	−	29.2499i	−0.755984	−	1.30940i	0.188899	−	0.981996i	$-0.439508\pi$
$500$		0			0
$501$	−12.2502	+	0.399928i	−0.547301	+	0.0178675i
$502$		0			0
$503$	1.09819			0.0489661			0.0244830	−	0.999700i	$-0.492206\pi$
$503$	1.09819			0.0489661			0.0244830	+	0.999700i	$0.492206\pi$
$504$		0			0
$505$	−16.7701			−0.746261
$506$		0			0
$507$	21.5919	−	40.3869i	0.958931	−	1.79365i
$508$		0			0
$509$	−8.10672	−	14.0413i	−0.359324	−	0.622368i	0.628524	−	0.777790i	$-0.283659\pi$
$509$	−8.10672	−	14.0413i	−0.359324	−	0.622368i	−0.987848	+	0.155423i	$0.950326\pi$
$510$		0			0
$511$	21.5876	+	20.8817i	0.954981	+	0.923750i
$512$		0			0
$513$	2.39923	−	5.29142i	0.105929	−	0.233622i
$514$		0			0
$515$	3.14527	−	5.44777i	0.138597	−	0.240057i
$516$		0			0
$517$	−5.45692	+	9.45167i	−0.239995	+	0.415684i
$518$		0			0
$519$	6.06807	+	9.76021i	0.266359	+	0.428426i
$520$		0			0
$521$	19.1738	+	33.2099i	0.840017	+	1.45495i	0.889879	+	0.456197i	$0.150789\pi$
$521$	19.1738	+	33.2099i	0.840017	+	1.45495i	−0.0498617	+	0.998756i	$0.515878\pi$
$522$		0			0
$523$	−20.6021	+	35.6838i	−0.900865	+	1.56034i	−0.0744911	+	0.997222i	$0.523733\pi$
$523$	−20.6021	+	35.6838i	−0.900865	+	1.56034i	−0.826374	+	0.563122i	$0.809600\pi$
$524$		0			0
$525$	7.93549	−	2.55120i	0.346333	−	0.111343i
$526$		0			0
$527$	−0.648287	−	1.12287i	−0.0282398	−	0.0489128i
$528$		0			0
$529$	−17.5105	+	30.3290i	−0.761324	+	1.31865i
$530$		0			0
$531$	11.1322	−	22.5636i	0.483097	−	0.979178i
$532$		0			0
$533$	−26.0100	−	45.0506i	−1.12662	−	1.95136i
$534$		0			0
$535$	12.1023			0.523229
$536$		0			0
$537$	9.20375	−	17.2153i	0.397171	−	0.742894i
$538$		0			0
$539$	1.30619	+	39.2771i	0.0562616	+	1.69178i
$540$		0			0
$541$	−9.09371	+	15.7508i	−0.390969	+	0.677178i	−0.992578	−	0.121613i	$-0.961193\pi$
$541$	−9.09371	+	15.7508i	−0.390969	+	0.677178i	0.601609	+	0.798791i	$0.294527\pi$
$542$		0			0
$543$	19.3693	+	31.1546i	0.831216	+	1.33697i
$544$		0			0
$545$	−1.21611	+	2.10636i	−0.0520924	+	0.0902266i
$546$		0			0
$547$	−0.338699	−	0.586644i	−0.0144817	−	0.0250831i	0.858694	−	0.512489i	$-0.171277\pi$
$547$	−0.338699	−	0.586644i	−0.0144817	−	0.0250831i	−0.873175	+	0.487406i	$0.837943\pi$
$548$		0			0
$549$	−6.40547	+	12.9831i	−0.273379	+	0.554106i
$550$		0			0
$551$	3.52200			0.150042
$552$		0			0
$553$	−34.2345	+	9.78577i	−1.45580	+	0.416133i
$554$		0			0
$555$	−19.4600	−	31.3005i	−0.826032	−	1.32863i
$556$		0			0
$557$	14.8659	+	25.7484i	0.629887	+	1.09100i	0.987574	+	0.157155i	$0.0502322\pi$
$557$	14.8659	+	25.7484i	0.629887	+	1.09100i	−0.357687	+	0.933842i	$0.616435\pi$
$558$		0			0
$559$	−29.4922			−1.24739
$560$		0			0
$561$	−6.63619	−	10.6740i	−0.280180	−	0.450657i
$562$		0			0
$563$	−21.3478			−0.899705			−0.449852	−	0.893103i	$-0.648523\pi$
$563$	−21.3478			−0.899705			−0.449852	+	0.893103i	$0.648523\pi$
$564$		0			0
$565$	−9.86153			−0.414878
$566$		0			0
$567$	−19.1244	−	14.1866i	−0.803148	−	0.595780i
$568$		0			0
$569$	−15.1242			−0.634041			−0.317021	−	0.948419i	$-0.602682\pi$
$569$	−15.1242			−0.634041			−0.317021	+	0.948419i	$0.602682\pi$
$570$		0			0
$571$	−19.8863			−0.832215			−0.416107	−	0.909315i	$-0.636606\pi$
$571$	−19.8863			−0.832215			−0.416107	+	0.909315i	$0.636606\pi$
$572$		0			0
$573$	8.63376	+	13.8870i	0.360681	+	0.580138i
$574$		0			0
$575$	13.8553			0.577804
$576$		0			0
$577$	19.8090	+	34.3102i	0.824661	+	1.42835i	0.902178	+	0.431363i	$0.141967\pi$
$577$	19.8090	+	34.3102i	0.824661	+	1.42835i	−0.0775179	+	0.996991i	$0.524700\pi$
$578$		0			0
$579$	−5.74349	−	9.23814i	−0.238691	−	0.383924i
$580$		0			0
$581$	6.09304	+	5.89378i	0.252782	+	0.244515i
$582$		0			0
$583$	50.0770			2.07398
$584$		0			0
$585$	−14.8676	+	30.1349i	−0.614701	+	1.24593i
$586$		0			0
$587$	−1.13275	−	1.96199i	−0.0467537	−	0.0809798i	0.841701	−	0.539943i	$-0.181554\pi$
$587$	−1.13275	−	1.96199i	−0.0467537	−	0.0809798i	−0.888455	+	0.458963i	$0.848221\pi$
$588$		0			0
$589$	0.560799	−	0.971332i	0.0231073	−	0.0400230i
$590$		0			0
$591$	14.1548	+	22.7673i	0.582250	+	0.936522i
$592$		0			0
$593$	5.97295	−	10.3454i	0.245280	−	0.424837i	−0.716931	−	0.697145i	$-0.754454\pi$
$593$	5.97295	−	10.3454i	0.245280	−	0.424837i	0.962210	+	0.272308i	$0.0877869\pi$
$594$		0			0
$595$	−1.48049	+	5.91695i	−0.0606941	+	0.242571i
$596$		0			0
$597$	3.58458	−	6.70483i	0.146707	−	0.274411i
$598$		0			0
$599$	2.95272			0.120645			0.0603224	−	0.998179i	$-0.480787\pi$
$599$	2.95272			0.120645			0.0603224	+	0.998179i	$0.480787\pi$
$600$		0			0
$601$	15.9751	+	27.6697i	0.651638	+	1.12867i	0.982725	+	0.185071i	$0.0592514\pi$
$601$	15.9751	+	27.6697i	0.651638	+	1.12867i	−0.331087	+	0.943600i	$0.607415\pi$
$602$		0			0
$603$	−3.39308	+	6.87736i	−0.138177	+	0.280068i
$604$		0			0
$605$	18.2977	−	31.6925i	0.743906	−	1.28848i
$606$		0			0
$607$	5.20069	+	9.00786i	0.211089	+	0.365618i	0.952056	−	0.305925i	$-0.0989655\pi$
$607$	5.20069	+	9.00786i	0.211089	+	0.365618i	−0.740966	+	0.671542i	$0.765632\pi$
$608$		0			0
$609$	3.04495	−	14.1099i	0.123388	−	0.571762i
$610$		0			0
$611$	6.10433	−	10.5730i	0.246955	−	0.427739i
$612$		0			0
$613$	6.22441	+	10.7810i	0.251402	+	0.435441i	0.963912	−	0.266221i	$-0.0857751\pi$
$613$	6.22441	+	10.7810i	0.251402	+	0.435441i	−0.712510	+	0.701662i	$0.752442\pi$
$614$		0			0
$615$	13.5105	+	21.7310i	0.544795	+	0.876278i
$616$		0			0
$617$	−4.70100	+	8.14237i	−0.189255	+	0.327799i	−0.945002	−	0.327064i	$-0.893941\pi$
$617$	−4.70100	+	8.14237i	−0.189255	+	0.327799i	0.755747	+	0.654864i	$0.227274\pi$
$618$		0			0
$619$	−11.0598	+	19.1561i	−0.444531	+	0.769951i	−0.998019	−	0.0629064i	$-0.979963\pi$
$619$	−11.0598	+	19.1561i	−0.444531	+	0.769951i	0.553488	+	0.832857i	$0.313296\pi$
$620$		0			0
$621$	−23.0457	−	32.1786i	−0.924792	−	1.29128i
$622$		0			0
$623$	−0.519727	+	2.07715i	−0.0208224	+	0.0832193i
$624$		0			0
$625$	6.29831	+	10.9090i	0.251932	+	0.436360i
$626$		0			0
$627$	5.12615	−	9.58828i	0.204719	−	0.382919i
$628$		0			0
$629$	−15.4213			−0.614887
$630$		0			0
$631$	−18.3705			−0.731316			−0.365658	−	0.930749i	$-0.619156\pi$
$631$	−18.3705			−0.731316			−0.365658	+	0.930749i	$0.619156\pi$
$632$		0			0
$633$	−27.4592	+	0.896448i	−1.09141	+	0.0356306i
$634$		0			0
$635$	11.4334	+	19.8032i	0.453720	+	0.785866i
$636$		0			0
$637$	−1.46116	−	43.9369i	−0.0578932	−	1.74084i
$638$		0			0
$639$	−11.7627	+	23.8416i	−0.465325	+	0.943157i
$640$		0			0
$641$	16.8617	−	29.2052i	0.665995	−	1.15354i	−0.313019	−	0.949747i	$-0.601340\pi$
$641$	16.8617	−	29.2052i	0.665995	−	1.15354i	0.979014	−	0.203791i	$-0.0653262\pi$
$642$		0			0
$643$	−10.0635	+	17.4306i	−0.396867	+	0.687394i	−0.993338	−	0.115241i	$-0.963236\pi$
$643$	−10.0635	+	17.4306i	−0.396867	+	0.687394i	0.596470	+	0.802635i	$0.296569\pi$
$644$		0			0
$645$	14.4994	−	0.473355i	0.570913	−	0.0186383i
$646$		0			0
$647$	11.1891	+	19.3800i	0.439887	+	0.761907i	0.997680	−	0.0680731i	$-0.0216851\pi$
$647$	11.1891	+	19.3800i	0.439887	+	0.761907i	−0.557793	+	0.829980i	$0.688352\pi$
$648$		0			0
$649$	23.5422	−	40.7763i	0.924112	−	1.60061i
$650$		0			0
$651$	−3.40654	−	3.08645i	−0.133513	−	0.120968i
$652$		0			0
$653$	20.3377	+	35.2259i	0.795875	+	1.37850i	0.922282	+	0.386518i	$0.126322\pi$
$653$	20.3377	+	35.2259i	0.795875	+	1.37850i	−0.126406	+	0.991979i	$0.540344\pi$
$654$		0			0
$655$	5.18932	−	8.98816i	0.202763	−	0.351197i
$656$		0			0
$657$	−33.9834	+	2.22124i	−1.32582	+	0.0866590i
$658$		0			0
$659$	−7.69321	−	13.3250i	−0.299685	−	0.519070i	0.676379	−	0.736554i	$-0.263548\pi$
$659$	−7.69321	−	13.3250i	−0.299685	−	0.519070i	−0.976064	+	0.217484i	$0.930215\pi$
$660$		0			0
$661$	49.1473			1.91161			0.955804	−	0.294006i	$-0.0949885\pi$
$661$	49.1473			1.91161			0.955804	+	0.294006i	$0.0949885\pi$
$662$		0			0
$663$	7.42351	+	11.9404i	0.288305	+	0.463725i
$664$		0			0
$665$	−5.07305	+	1.45011i	−0.196724	+	0.0562328i
$666$		0			0
$667$	11.9967	−	20.7789i	0.464513	−	0.804561i
$668$		0			0
$669$	11.4205	−	21.3616i	0.441541	−	0.825887i
$670$		0			0
$671$	−13.5462	+	23.4627i	−0.522944	+	0.905766i
$672$		0			0
$673$	−6.99961	−	12.1237i	−0.269815	−	0.467334i	0.698999	−	0.715123i	$-0.253629\pi$
$673$	−6.99961	−	12.1237i	−0.269815	−	0.467334i	−0.968814	+	0.247789i	$0.920296\pi$
$674$		0			0
$675$	−3.90305	+	8.60804i	−0.150229	+	0.331324i
$676$		0			0
$677$	−46.7740			−1.79767			−0.898836	−	0.438285i	$-0.855586\pi$
$677$	−46.7740			−1.79767			−0.898836	+	0.438285i	$0.855586\pi$
$678$		0			0
$679$	4.21337	+	4.07558i	0.161694	+	0.156406i
$680$		0			0
$681$	18.6396	−	0.608517i	0.714269	−	0.0233184i
$682$		0			0
$683$	−21.6222	−	37.4508i	−0.827352	−	1.43302i	−0.900109	−	0.435665i	$-0.856513\pi$
$683$	−21.6222	−	37.4508i	−0.827352	−	1.43302i	0.0727571	−	0.997350i	$-0.476820\pi$
$684$		0			0
$685$	27.3613			1.04542
$686$		0			0
$687$	−1.31478	+	2.45925i	−0.0501621	+	0.0938264i
$688$		0			0
$689$	−56.0181			−2.13412
$690$		0			0
$691$	11.7214			0.445905			0.222952	−	0.974829i	$-0.428431\pi$
$691$	11.7214			0.445905			0.222952	+	0.974829i	$0.428431\pi$
$692$		0			0
$693$	−33.9810	−	28.8261i	−1.29083	−	1.09501i
$694$		0			0
$695$	21.6096			0.819697
$696$		0			0
$697$	10.7065			0.405538
$698$		0			0
$699$	−1.76785	+	0.0577141i	−0.0668662	+	0.00218295i
$700$		0			0
$701$	0.0120975			0.000456915			0.000228458	−	1.00000i	$-0.499927\pi$
$701$	0.0120975			0.000456915			0.000228458		1.00000i	$0.499927\pi$
$702$		0			0
$703$	−6.67008	−	11.5529i	−0.251567	−	0.435726i
$704$		0			0
$705$	−2.83140	+	5.29604i	−0.106637	+	0.199460i
$706$		0			0
$707$	−6.03839	+	24.1332i	−0.227097	+	0.907621i
$708$		0			0
$709$	1.07478			0.0403640			0.0201820	−	0.999796i	$-0.493575\pi$
$709$	1.07478			0.0403640			0.0201820	+	0.999796i	$0.493575\pi$
$710$		0			0
$711$	17.8630	−	36.2062i	0.669916	−	1.35784i
$712$		0			0
$713$	−3.82041	−	6.61714i	−0.143075	−	0.247814i
$714$		0			0
$715$	−31.4418	+	54.4588i	−1.17586	+	2.03664i
$716$		0			0
$717$	24.1121	−	0.787177i	0.900484	−	0.0293977i
$718$		0			0
$719$	−12.7777	+	22.1317i	−0.476529	+	0.825372i	−0.999638	−	0.0268932i	$-0.991439\pi$
$719$	−12.7777	+	22.1317i	−0.476529	+	0.825372i	0.523109	+	0.852266i	$0.324772\pi$
$720$		0			0
$721$	−6.70714	−	6.48779i	−0.249787	−	0.241618i
$722$		0			0
$723$	25.2325	−	0.823754i	0.938408	−	0.0306357i
$724$		0			0
$725$	−5.72956			−0.212790
$726$		0			0
$727$	−6.20522	−	10.7478i	−0.230139	−	0.398612i	0.727710	−	0.685885i	$-0.240585\pi$
$727$	−6.20522	−	10.7478i	−0.230139	−	0.398612i	−0.957849	+	0.287273i	$0.907251\pi$
$728$		0			0
$729$	26.4840	−	5.25314i	0.980890	−	0.194561i
$730$		0			0
$731$	3.03498	−	5.25674i	0.112253	−	0.194427i
$732$		0			0
$733$	−14.7095	−	25.4775i	−0.543307	−	0.941035i	−0.998711	−	0.0507502i	$-0.983839\pi$
$733$	−14.7095	−	25.4775i	−0.543307	−	0.941035i	0.455405	−	0.890285i	$-0.349495\pi$
$734$		0			0
$735$	1.42355	+	21.5775i	0.0525084	+	0.795897i
$736$		0			0
$737$	−7.17562	+	12.4285i	−0.264317	+	0.457811i
$738$		0			0
$739$	−7.75910	−	13.4392i	−0.285423	−	0.494368i	0.687288	−	0.726385i	$-0.258801\pi$
$739$	−7.75910	−	13.4392i	−0.285423	−	0.494368i	−0.972712	+	0.232017i	$0.925468\pi$
$740$		0			0
$741$	−5.73432	+	10.7258i	−0.210656	+	0.394024i
$742$		0			0
$743$	13.6333	−	23.6136i	0.500159	−	0.866301i	−0.499841	−	0.866117i	$-0.666608\pi$
$743$	13.6333	−	23.6136i	0.500159	−	0.866301i	1.00000		0.000183414i	$-5.83824e-5\pi$
$744$		0			0
$745$	4.22432	−	7.31674i	0.154767	−	0.268065i
$746$		0			0
$747$	−9.59169	+	0.626939i	−0.350942	+	0.0229385i
$748$		0			0
$749$	4.35766	−	17.4159i	0.159226	−	0.636364i
$750$		0			0
$751$	−4.57176	−	7.91853i	−0.166826	−	0.288951i	0.770476	−	0.637469i	$-0.220018\pi$
$751$	−4.57176	−	7.91853i	−0.166826	−	0.288951i	−0.937302	+	0.348518i	$0.886685\pi$
$752$		0			0
$753$	−16.4874	−	26.5192i	−0.600835	−	0.966415i
$754$		0			0
$755$	43.4632			1.58179
$756$		0			0
$757$	−20.6307			−0.749834			−0.374917	−	0.927058i	$-0.622329\pi$
$757$	−20.6307			−0.749834			−0.374917	+	0.927058i	$0.622329\pi$
$758$		0			0
$759$	−39.1076	−	62.9027i	−1.41952	−	2.28322i
$760$		0			0
$761$	0.239208	+	0.414321i	0.00867130	+	0.0150191i	0.870328	−	0.492472i	$-0.163906\pi$
$761$	0.239208	+	0.414321i	0.00867130	+	0.0150191i	−0.861657	+	0.507491i	$0.830573\pi$
$762$		0			0
$763$	2.59329	+	2.50848i	0.0938835	+	0.0908132i
$764$		0			0
$765$	−3.84130	−	5.75115i	−0.138882	−	0.207933i
$766$		0			0
$767$	−26.3352	+	45.6140i	−0.950910	+	1.64702i
$768$		0			0
$769$	−13.3518	+	23.1261i	−0.481480	+	0.833948i	−0.999774	−	0.0212548i	$-0.993234\pi$
$769$	−13.3518	+	23.1261i	−0.481480	+	0.833948i	0.518294	+	0.855202i	$0.326567\pi$
$770$		0			0
$771$	21.9888	−	41.1293i	0.791908	−	1.48123i
$772$		0			0
$773$	−13.5143	−	23.4074i	−0.486074	−	0.841905i	0.513798	−	0.857911i	$-0.328238\pi$
$773$	−13.5143	−	23.4074i	−0.486074	−	0.841905i	−0.999872	+	0.0160062i	$0.994905\pi$
$774$		0			0
$775$	−0.912303	+	1.58016i	−0.0327709	+	0.0567609i
$776$		0			0
$777$	−52.0502	+	16.7337i	−1.86729	+	0.600320i
$778$		0			0
$779$	4.63083	+	8.02083i	0.165917	+	0.287376i
$780$		0			0
$781$	−24.8755	+	43.0857i	−0.890116	+	1.54173i
$782$		0			0
$783$	9.53008	+	13.3068i	0.340577	+	0.475546i
$784$		0			0
$785$	−5.62226	−	9.73804i	−0.200667	−	0.347566i
$786$		0			0
$787$	−49.1830			−1.75319			−0.876593	−	0.481233i	$-0.840189\pi$
$787$	−49.1830			−1.75319			−0.876593	+	0.481233i	$0.840189\pi$
$788$		0			0
$789$	2.66393	−	0.0869679i	0.0948382	−	0.00309614i
$790$		0			0
$791$	−3.55083	+	14.1913i	−0.126253	+	0.504585i
$792$		0			0
$793$	15.1533	−	26.2463i	0.538109	−	0.932032i
$794$		0			0
$795$	27.5405	−	0.899100i	0.976760	−	0.0318878i
$796$		0			0
$797$	22.1538	−	38.3715i	0.784728	−	1.35919i	−0.144434	−	0.989514i	$-0.546136\pi$
$797$	22.1538	−	38.3715i	0.784728	−	1.35919i	0.929162	−	0.369674i	$-0.120531\pi$
$798$		0			0
$799$	1.25637	+	2.17609i	0.0444471	+	0.0769846i
$800$		0			0
$801$	−1.34849	−	2.01895i	−0.0476466	−	0.0713360i
$802$		0			0
$803$	−63.7312			−2.24903
$804$		0			0
$805$	−8.72463	+	34.8690i	−0.307503	+	1.22897i
$806$		0			0
$807$	−5.33189	+	9.97310i	−0.187691	+	0.351070i
$808$		0			0
$809$	−16.7359	−	28.9874i	−0.588402	−	1.01914i	−0.994442	−	0.105286i	$-0.966424\pi$
$809$	−16.7359	−	28.9874i	−0.588402	−	1.01914i	0.406040	−	0.913855i	$-0.366909\pi$
$810$		0			0
$811$	43.7383			1.53586			0.767929	−	0.640535i	$-0.221287\pi$
$811$	43.7383			1.53586			0.767929	+	0.640535i	$0.221287\pi$
$812$		0			0
$813$	19.5442	−	0.638051i	0.685446	−	0.0223774i
$814$		0			0
$815$	−1.25090			−0.0438172
$816$		0			0
$817$	5.25080			0.183702
$818$		0			0
$819$	38.0125	+	32.2460i	1.32826	+	1.12677i
$820$		0			0
$821$	−22.5132			−0.785714			−0.392857	−	0.919599i	$-0.628513\pi$
$821$	−22.5132			−0.785714			−0.392857	+	0.919599i	$0.628513\pi$
$822$		0			0
$823$	−14.6735			−0.511485			−0.255743	−	0.966745i	$-0.582320\pi$
$823$	−14.6735			−0.511485			−0.255743	+	0.966745i	$0.582320\pi$
$824$		0			0
$825$	−8.33919	+	15.5981i	−0.290333	+	0.543058i
$826$		0			0
$827$	−45.0520			−1.56661			−0.783306	−	0.621636i	$-0.786468\pi$
$827$	−45.0520			−1.56661			−0.783306	+	0.621636i	$0.786468\pi$
$828$		0			0
$829$	20.6688	+	35.7993i	0.717856	+	1.24336i	0.961848	+	0.273585i	$0.0882095\pi$
$829$	20.6688	+	35.7993i	0.717856	+	1.24336i	−0.243992	+	0.969777i	$0.578457\pi$
$830$		0			0
$831$	−3.13659	+	0.102399i	−0.108807	+	0.00355217i
$832$		0			0
$833$	7.98175	+	4.26101i	0.276551	+	0.147635i
$834$		0			0
$835$	−12.6212			−0.436774
$836$		0			0
$837$	5.18733	−	0.509494i	0.179301	−	0.0176107i
$838$		0			0
$839$	−2.04477	−	3.54164i	−0.0705932	−	0.122271i	0.828568	−	0.559888i	$-0.189156\pi$
$839$	−2.04477	−	3.54164i	−0.0705932	−	0.122271i	−0.899161	+	0.437617i	$0.855823\pi$
$840$		0			0
$841$	9.53902	−	16.5221i	0.328932	−	0.569726i
$842$		0			0
$843$	4.88009	−	9.12802i	0.168079	−	0.314386i
$844$		0			0
$845$	23.5790	−	40.8401i	0.811143	−	1.40494i
$846$		0			0
$847$	−39.0189	−	37.7428i	−1.34070	−	1.29686i
$848$		0			0
$849$	18.2858	+	29.4118i	0.627566	+	1.00941i
$850$		0			0
$851$	−90.8789			−3.11529
$852$		0			0
$853$	−21.1012	−	36.5484i	−0.722491	−	1.25139i	−0.959998	−	0.280006i	$-0.909664\pi$
$853$	−21.1012	−	36.5484i	−0.722491	−	1.25139i	0.237507	−	0.971386i	$-0.423670\pi$
$854$		0			0
$855$	2.64704	−	5.36523i	0.0905269	−	0.183487i
$856$		0			0
$857$	27.5623	−	47.7393i	0.941509	−	1.63074i	0.178915	−	0.983864i	$-0.442741\pi$
$857$	27.5623	−	47.7393i	0.941509	−	1.63074i	0.762594	−	0.646877i	$-0.223925\pi$
$858$		0			0
$859$	−18.9767	−	32.8686i	−0.647476	−	1.12146i	−0.983724	−	0.179688i	$-0.942491\pi$
$859$	−18.9767	−	32.8686i	−0.647476	−	1.12146i	0.336247	−	0.941774i	$-0.390842\pi$
$860$		0			0
$861$	36.1368	−	11.6177i	1.23154	−	0.395931i
$862$		0			0
$863$	−6.27205	+	10.8635i	−0.213503	+	0.369798i	−0.952809	−	0.303572i	$-0.901821\pi$
$863$	−6.27205	+	10.8635i	−0.213503	+	0.369798i	0.739305	+	0.673370i	$0.235154\pi$
$864$		0			0
$865$	5.91723	+	10.2489i	0.201192	+	0.348474i
$866$		0			0
$867$	26.5370	−	0.866340i	0.901243	−	0.0294224i
$868$		0			0
$869$	37.7764	−	65.4306i	1.28148	−	2.21958i
$870$		0			0
$871$	8.02694	−	13.9031i	0.271983	−	0.471088i
$872$		0			0
$873$	−6.63271	+	0.433532i	−0.224483	+	0.0146728i
$874$		0			0
$875$	30.9383	−	8.84359i	1.04591	−	0.298968i
$876$		0			0
$877$	−4.85337	−	8.40628i	−0.163887	−	0.283860i	0.772373	−	0.635169i	$-0.219070\pi$
$877$	−4.85337	−	8.40628i	−0.163887	−	0.283860i	−0.936259	+	0.351310i	$0.885736\pi$
$878$		0			0
$879$	−17.1439	+	0.559689i	−0.578250	+	0.0188778i
$880$		0			0
$881$	−11.6652			−0.393012			−0.196506	−	0.980503i	$-0.562959\pi$
$881$	−11.6652			−0.393012			−0.196506	+	0.980503i	$0.562959\pi$
$882$		0			0
$883$	13.1758			0.443401			0.221701	−	0.975115i	$-0.428839\pi$
$883$	13.1758			0.443401			0.221701	+	0.975115i	$0.428839\pi$
$884$		0			0
$885$	12.2152	−	22.8481i	0.410610	−	0.768030i
$886$		0			0
$887$	−0.415361	−	0.719426i	−0.0139464	−	0.0241560i	0.858968	−	0.512029i	$-0.171106\pi$
$887$	−0.415361	−	0.719426i	−0.0139464	−	0.0241560i	−0.872914	+	0.487873i	$0.837773\pi$
$888$		0			0
$889$	32.6147	−	9.32278i	1.09386	−	0.312676i
$890$		0			0
$891$	50.0971	−	6.57707i	1.67832	−	0.220340i
$892$		0			0
$893$	−1.08682	+	1.88242i	−0.0363690	+	0.0629929i
$894$		0			0
$895$	10.0508	−	17.4084i	0.335960	−	0.581900i
$896$		0			0
$897$	43.7473	+	70.3655i	1.46068	+	2.34944i
$898$		0			0
$899$	1.57985	+	2.73638i	0.0526910	+	0.0912634i
$900$		0			0
$901$	5.76470	−	9.98476i	0.192050	−	0.332641i
$902$		0			0
$903$	4.53959	−	21.0359i	0.151068	−	0.700031i
$904$		0			0
$905$	18.8878	+	32.7146i	0.627852	+	1.08747i
$906$		0			0
$907$	16.6588	−	28.8539i	0.553146	−	0.958077i	−0.444899	−	0.895581i	$-0.646761\pi$
$907$	16.6588	−	28.8539i	0.553146	−	0.958077i	0.998045	−	0.0624962i	$-0.0199061\pi$
$908$		0			0
$909$	−15.6673	−	23.4569i	−0.519652	−	0.778017i
$910$		0			0
$911$	11.1353	+	19.2870i	0.368930	+	0.639006i	0.989399	−	0.145226i	$-0.0463909\pi$
$911$	11.1353	+	19.2870i	0.368930	+	0.639006i	−0.620469	+	0.784231i	$0.713058\pi$
$912$		0			0
$913$	−17.9879			−0.595313
$914$		0			0
$915$	−7.02863	+	13.1468i	−0.232359	+	0.434619i
$916$		0			0
$917$	−11.0660	−	10.7041i	−0.365431	−	0.353480i
$918$		0			0
$919$	−10.7906	+	18.6899i	−0.355949	+	0.616522i	−0.987280	−	0.158992i	$-0.949176\pi$
$919$	−10.7906	+	18.6899i	−0.355949	+	0.616522i	0.631331	+	0.775514i	$0.282509\pi$
$920$		0			0
$921$	21.6850	+	34.8793i	0.714544	+	1.14931i
$922$		0			0
$923$	27.8268	−	48.1974i	0.915929	−	1.58644i
$924$		0			0
$925$	10.8508	+	18.7942i	0.356773	+	0.617949i
$926$		0			0
$927$	10.5584	−	0.690126i	0.346784	−	0.0226667i
$928$		0			0
$929$	−37.1559			−1.21905			−0.609523	−	0.792768i	$-0.708639\pi$
$929$	−37.1559			−1.21905			−0.609523	+	0.792768i	$0.708639\pi$
$930$		0			0
$931$	0.260145	+	7.82255i	0.00852591	+	0.256374i
$932$		0			0
$933$	−18.6055	−	29.9262i	−0.609118	−	0.979738i
$934$		0			0
$935$	−6.47122	−	11.2085i	−0.211631	−	0.366556i
$936$		0			0
$937$	21.5238			0.703152			0.351576	−	0.936159i	$-0.385646\pi$
$937$	21.5238			0.703152			0.351576	+	0.936159i	$0.385646\pi$
$938$		0			0
$939$	8.88784	+	14.2957i	0.290044	+	0.466522i
$940$		0			0
$941$	−47.4064			−1.54540			−0.772702	−	0.634769i	$-0.781095\pi$
$941$	−47.4064			−1.54540			−0.772702	+	0.634769i	$0.781095\pi$
$942$		0			0
$943$	63.0944			2.05464
$944$		0			0
$945$	−19.2058	−	15.2432i	−0.624765	−	0.495860i
$946$		0			0
$947$	2.50117			0.0812771			0.0406386	−	0.999174i	$-0.487061\pi$
$947$	2.50117			0.0812771			0.0406386	+	0.999174i	$0.487061\pi$
$948$		0			0
$949$	71.2923			2.31425
$950$		0			0
$951$	−3.04383	−	4.89586i	−0.0987031	−	0.158759i
$952$		0			0
$953$	−7.89914			−0.255878			−0.127939	−	0.991782i	$-0.540836\pi$
$953$	−7.89914			−0.255878			−0.127939	+	0.991782i	$0.540836\pi$
$954$		0			0
$955$	8.41913	+	14.5824i	0.272437	+	0.471874i
$956$		0			0
$957$	16.1721	+	26.0121i	0.522771	+	0.840853i
$958$		0			0
$959$	9.85194	−	39.3745i	0.318136	−	1.27147i
$960$		0			0
$961$	−29.9938			−0.967541
$962$		0			0
$963$	11.3065	+	16.9279i	0.364346	+	0.545495i
$964$		0			0
$965$	−5.60071	−	9.70072i	−0.180293	−	0.312277i
$966$		0			0
$967$	−5.76591	+	9.98684i	−0.185419	+	0.321155i	−0.943718	−	0.330752i	$-0.892698\pi$
$967$	−5.76591	+	9.98684i	−0.185419	+	0.321155i	0.758299	+	0.651907i	$0.226031\pi$
$968$		0			0
$969$	−1.32168	−	2.12587i	−0.0424586	−	0.0682927i
$970$		0			0
$971$	9.14669	−	15.8425i	0.293531	−	0.508411i	−0.681111	−	0.732180i	$-0.738503\pi$
$971$	9.14669	−	15.8425i	0.293531	−	0.508411i	0.974642	+	0.223769i	$0.0718362\pi$
$972$		0			0
$973$	7.78092	−	31.0974i	0.249445	−	0.996937i
$974$		0			0
$975$	9.32855	−	17.4487i	0.298753	−	0.558806i
$976$		0			0
$977$	−29.9083			−0.956850			−0.478425	−	0.878128i	$-0.658792\pi$
$977$	−29.9083			−0.956850			−0.478425	+	0.878128i	$0.658792\pi$
$978$		0			0
$979$	−2.27173	−	3.93475i	−0.0726047	−	0.125755i
$980$		0			0
$981$	−4.08238	+	0.266835i	−0.130340	+	0.00851939i
$982$		0			0
$983$	7.27224	−	12.5959i	0.231948	−	0.401746i	−0.726433	−	0.687237i	$-0.758823\pi$
$983$	7.27224	−	12.5959i	0.231948	−	0.401746i	0.958381	+	0.285491i	$0.0921566\pi$
$984$		0			0
$985$	13.8029	+	23.9073i	0.439797	+	0.761751i
$986$		0			0
$987$	6.60180	+	5.98149i	0.210138	+	0.190393i
$988$		0			0
$989$	17.8854	−	30.9784i	0.568722	−	0.985055i
$990$		0			0
$991$	14.3753	+	24.8987i	0.456646	+	0.790935i	0.998781	−	0.0493567i	$-0.0157171\pi$
$991$	14.3753	+	24.8987i	0.456646	+	0.790935i	−0.542135	+	0.840292i	$0.682384\pi$
$992$		0			0
$993$	1.31204	+	2.11035i	0.0416363	+	0.0669700i
$994$		0			0
$995$	3.91447	−	6.78007i	0.124097	−	0.214943i
$996$		0			0
$997$	−17.9469	+	31.0850i	−0.568384	+	0.984471i	0.428341	+	0.903617i	$0.359098\pi$
$997$	−17.9469	+	31.0850i	−0.568384	+	0.984471i	−0.996726	+	0.0808539i	$0.974235\pi$
$998$		0			0
$999$	25.6008	−	56.4616i	0.809973	−	1.78637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.q.l.625.8		22
3.2	odd	2		3024.2.q.l.2305.4		22
4.3	odd	2		504.2.q.c.121.4	yes	22
7.4	even	3		1008.2.t.l.193.7		22
9.2	odd	6		3024.2.t.k.289.8		22
9.7	even	3		1008.2.t.l.961.7		22
12.11	even	2		1512.2.q.d.793.4		22
21.11	odd	6		3024.2.t.k.1873.8		22
28.11	odd	6		504.2.t.c.193.5	yes	22
36.7	odd	6		504.2.t.c.457.5	yes	22
36.11	even	6		1512.2.t.c.289.8		22
63.11	odd	6		3024.2.q.l.2881.4		22
63.25	even	3	inner	1008.2.q.l.529.8		22
84.11	even	6		1512.2.t.c.361.8		22
252.11	even	6		1512.2.q.d.1369.4		22
252.151	odd	6		504.2.q.c.25.4	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.4	✓	22	252.151	odd	6
504.2.q.c.121.4	yes	22	4.3	odd	2
504.2.t.c.193.5	yes	22	28.11	odd	6
504.2.t.c.457.5	yes	22	36.7	odd	6
1008.2.q.l.529.8		22	63.25	even	3	inner
1008.2.q.l.625.8		22	1.1	even	1	trivial
1008.2.t.l.193.7		22	7.4	even	3
1008.2.t.l.961.7		22	9.7	even	3
1512.2.q.d.793.4		22	12.11	even	2
1512.2.q.d.1369.4		22	252.11	even	6
1512.2.t.c.289.8		22	36.11	even	6
1512.2.t.c.361.8		22	84.11	even	6
3024.2.q.l.2305.4		22	3.2	odd	2
3024.2.q.l.2881.4		22	63.11	odd	6
3024.2.t.k.289.8		22	9.2	odd	6
3024.2.t.k.1873.8		22	21.11	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.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.914508 + 1.47094i) q^{3} +(0.891774 + 1.54460i) q^{5} +(2.54386 - 0.727153i) q^{7} +(-1.32735 + 2.69038i) q^{9} +O(q^{10})\)	\(q+(0.914508 + 1.47094i) q^{3} +(0.891774 + 1.54460i) q^{5} +(2.54386 - 0.727153i) q^{7} +(-1.32735 + 2.69038i) q^{9} +(-2.80706 + 4.86196i) q^{11} +(3.14009 - 5.43879i) q^{13} +(-1.45648 + 2.72430i) q^{15} +(0.646279 + 1.11939i) q^{17} +(-0.559062 + 0.968324i) q^{19} +(3.39599 + 3.07689i) q^{21} +(3.80857 + 6.59664i) q^{23} +(0.909478 - 1.57526i) q^{25} +(-5.17127 + 0.507916i) q^{27} +(-1.57496 - 2.72791i) q^{29} -1.00311 q^{31} +(-9.71875 + 0.317283i) q^{33} +(3.39171 + 3.28079i) q^{35} +(-5.96542 + 10.3324i) q^{37} +(10.8718 - 0.354926i) q^{39} +(4.14160 - 7.17347i) q^{41} +(-2.34804 - 4.06693i) q^{43} +(-5.33925 + 0.348988i) q^{45} +1.94400 q^{47} +(5.94250 - 3.69956i) q^{49} +(-1.05553 + 1.97433i) q^{51} +(-4.45992 - 7.72481i) q^{53} -10.0130 q^{55} +(-1.93562 + 0.0631911i) q^{57} -8.38679 q^{59} +4.82576 q^{61} +(-1.42028 + 7.80915i) q^{63} +11.2010 q^{65} +2.55628 q^{67} +(-6.22032 + 11.6349i) q^{69} +8.86178 q^{71} +(5.67598 + 9.83109i) q^{73} +(3.14885 - 0.102799i) q^{75} +(-3.60538 + 14.4093i) q^{77} -13.4577 q^{79} +(-5.47628 - 7.14215i) q^{81} +(1.60203 + 2.77479i) q^{83} +(-1.15267 + 1.99648i) q^{85} +(2.57229 - 4.81137i) q^{87} +(-0.404646 + 0.700867i) q^{89} +(4.03312 - 16.1189i) q^{91} +(-0.917349 - 1.47551i) q^{93} -1.99423 q^{95} +(1.10781 + 1.91879i) q^{97} +(-9.35458 - 14.0056i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} + q^{5} - 5 q^{7} + 6 q^{9}+O(q^{10}) \) 22 * q + 2 * q^3 + q^5 - 5 * q^7 + 6 * q^9	\( 22 q + 2 q^{3} + q^{5} - 5 q^{7} + 6 q^{9} - 3 q^{11} + 7 q^{13} + q^{15} - q^{17} - 13 q^{19} - 22 q^{25} + 2 q^{27} - 7 q^{29} + 12 q^{31} - 3 q^{33} - 2 q^{35} + 6 q^{37} + 4 q^{39} + 4 q^{41} - 2 q^{43} - 3 q^{45} + 34 q^{47} - 25 q^{49} - 53 q^{51} + q^{53} - 2 q^{55} - 21 q^{57} - 42 q^{59} - 62 q^{61} + 22 q^{63} + 6 q^{65} - 52 q^{67} - 40 q^{69} + 32 q^{71} + 17 q^{73} - 53 q^{75} - q^{77} - 32 q^{79} - 6 q^{81} + 36 q^{83} + 28 q^{85} + 5 q^{87} - 2 q^{89} - 15 q^{91} - 11 q^{93} - 48 q^{95} + 19 q^{97} - 24 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 + q^5 - 5 * q^7 + 6 * q^9 - 3 * q^11 + 7 * q^13 + q^15 - q^17 - 13 * q^19 - 22 * q^25 + 2 * q^27 - 7 * q^29 + 12 * q^31 - 3 * q^33 - 2 * q^35 + 6 * q^37 + 4 * q^39 + 4 * q^41 - 2 * q^43 - 3 * q^45 + 34 * q^47 - 25 * q^49 - 53 * q^51 + q^53 - 2 * q^55 - 21 * q^57 - 42 * q^59 - 62 * q^61 + 22 * q^63 + 6 * q^65 - 52 * q^67 - 40 * q^69 + 32 * q^71 + 17 * q^73 - 53 * q^75 - q^77 - 32 * q^79 - 6 * q^81 + 36 * q^83 + 28 * q^85 + 5 * q^87 - 2 * q^89 - 15 * q^91 - 11 * q^93 - 48 * q^95 + 19 * q^97 - 24 * q^99

Introduction

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