LMFDB - Embedded newform 504.2.q.c.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(25,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, 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("504.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (of order $3$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.4
Character	$\chi$	$=$	504.25
Dual form			504.2.q.c.121.4

$q$-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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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	−0.594766	−	0.803899i	$-0.702755\pi$
$5$	0.891774	−	1.54460i	0.398814	−	0.690765i	0.993580	+	0.113133i	$0.0360887\pi$
$6$		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	0.884435	+	0.466663i	$0.154544\pi$
$11$	2.80706	+	4.86196i	0.846359	+	1.46594i	−0.0380759	+	0.999275i	$0.512123\pi$
$12$		0			0
$13$	3.14009	+	5.43879i	0.870903	+	1.50845i	0.861064	+	0.508497i	$0.169799\pi$
$13$	3.14009	+	5.43879i	0.870903	+	1.50845i	0.00983976	+	0.999952i	$0.496868\pi$
$14$		0			0
$15$	1.45648	+	2.72430i	0.376062	+	0.703410i
$16$		0			0
$17$	0.646279	−	1.11939i	0.156746	−	0.271491i	−0.776948	−	0.629565i	$-0.783233\pi$
$17$	0.646279	−	1.11939i	0.156746	−	0.271491i	0.933693	+	0.358074i	$0.116566\pi$
$18$		0			0
$19$	0.559062	+	0.968324i	0.128258	+	0.222149i	0.923002	−	0.384796i	$-0.125728\pi$
$19$	0.559062	+	0.968324i	0.128258	+	0.222149i	−0.794744	+	0.606945i	$0.792395\pi$
$20$		0			0
$21$	3.39599	−	3.07689i	0.741065	−	0.671433i
$22$		0			0
$23$	−3.80857	+	6.59664i	−0.794142	+	1.37549i	0.129240	+	0.991613i	$0.458746\pi$
$23$	−3.80857	+	6.59664i	−0.794142	+	1.37549i	−0.923382	+	0.383882i	$0.874587\pi$
$24$		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	−0.974391	−	0.224859i	$-0.927808\pi$
$29$	−1.57496	+	2.72791i	−0.292462	+	0.506560i	0.681929	+	0.731418i	$0.261141\pi$
$30$		0			0
$31$	1.00311			0.180163			0.0900816	−	0.995934i	$-0.471287\pi$
$31$	1.00311			0.180163			0.0900816	+	0.995934i	$0.471287\pi$
$32$		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	−0.659642	−	0.751580i	$-0.729292\pi$
$37$	−5.96542	−	10.3324i	−0.980708	−	1.69864i	−0.321067	−	0.947057i	$-0.604041\pi$
$38$		0			0
$39$	−10.8718	−	0.354926i	−1.74088	−	0.0568336i
$40$		0			0
$41$	4.14160	+	7.17347i	0.646810	+	1.12031i	0.983880	+	0.178828i	$0.0572306\pi$
$41$	4.14160	+	7.17347i	0.646810	+	1.12031i	−0.337071	+	0.941479i	$0.609436\pi$
$42$		0			0
$43$	2.34804	−	4.06693i	0.358073	−	0.620200i	−0.629566	−	0.776947i	$-0.716767\pi$
$43$	2.34804	−	4.06693i	0.358073	−	0.620200i	0.987639	+	0.156747i	$0.0501006\pi$
$44$		0			0
$45$	−5.33925	−	0.348988i	−0.795929	−	0.0520240i
$46$		0			0
$47$	−1.94400			−0.283562			−0.141781	−	0.989898i	$-0.545283\pi$
$47$	−1.94400			−0.283562			−0.141781	+	0.989898i	$0.545283\pi$
$48$		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	0.378180	+	0.925732i	$0.376550\pi$
$53$	−4.45992	+	7.72481i	−0.612617	+	1.06108i	−0.990798	+	0.135352i	$0.956783\pi$
$54$		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	$-0.316175\pi$
$59$	8.38679			1.09187			0.545933	+	0.837829i	$0.316175\pi$
$60$		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	$-0.549908\pi$
$67$	−2.55628			−0.312299			−0.156150	+	0.987733i	$0.549908\pi$
$68$		0			0
$69$	−6.22032	−	11.6349i	−0.748838	−	1.40067i
$70$		0			0
$71$	−8.86178			−1.05170			−0.525850	−	0.850577i	$-0.676253\pi$
$71$	−8.86178			−1.05170			−0.525850	+	0.850577i	$0.676253\pi$
$72$		0			0
$73$	5.67598	−	9.83109i	0.664323	−	1.15064i	−0.315145	−	0.949044i	$-0.602053\pi$
$73$	5.67598	−	9.83109i	0.664323	−	1.15064i	0.979468	−	0.201598i	$-0.0646135\pi$
$74$		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	$-0.226639\pi$
$79$	13.4577			1.51410			0.757052	+	0.653354i	$0.226639\pi$
$80$		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	$-0.889599\pi$
$83$	−1.60203	+	2.77479i	−0.175845	+	0.304573i	0.764608	+	0.644495i	$0.222933\pi$
$84$		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	0.843782	−	0.536686i	$-0.180324\pi$
$89$	−0.404646	−	0.700867i	−0.0428924	−	0.0742917i	−0.886675	+	0.462394i	$0.846991\pi$
$90$		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	−0.804289	−	0.594238i	$-0.797454\pi$
$97$	1.10781	−	1.91879i	0.112481	−	0.194823i	0.916770	+	0.399415i	$0.130787\pi$
$98$		0			0
$99$	9.35458	−	14.0056i	0.940171	−	1.40761i
$100$		0			0
$101$	−4.70134	−	8.14296i	−0.467801	−	0.810254i	0.531522	−	0.847044i	$-0.321620\pi$
$101$	−4.70134	−	8.14296i	−0.467801	−	0.810254i	−0.999323	+	0.0367899i	$0.988287\pi$
$102$		0			0
$103$	1.76349	−	3.05446i	0.173762	−	0.300964i	−0.765970	−	0.642876i	$-0.777741\pi$
$103$	1.76349	−	3.05446i	0.173762	−	0.300964i	0.939732	+	0.341912i	$0.111074\pi$
$104$		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	$-0.273038\pi$
$107$	−3.39276	−	5.87644i	−0.327991	−	0.568097i	−0.982113	+	0.188292i	$0.939705\pi$
$108$		0			0
$109$	0.681848	−	1.18099i	0.0653092	−	0.113119i	−0.831522	−	0.555492i	$-0.812530\pi$
$109$	0.681848	−	1.18099i	0.0653092	−	0.113119i	0.896831	+	0.442373i	$0.145863\pi$
$110$		0			0
$111$	20.6538	+	0.674275i	1.96037	+	0.0639993i
$112$		0			0
$113$	−2.76458	−	4.78840i	−0.260070	−	0.450455i	0.706190	−	0.708022i	$-0.250412\pi$
$113$	−2.76458	−	4.78840i	−0.260070	−	0.450455i	−0.966260	+	0.257568i	$0.917079\pi$
$114$		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	$-0.692606\pi$
$127$	−12.8209			−1.13767			−0.568837	+	0.822450i	$0.692606\pi$
$128$		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	$-0.751518\pi$
$131$	2.90955	−	5.03948i	0.254208	−	0.440302i	0.964680	+	0.263424i	$0.0848518\pi$
$132$		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	0.981810	+	0.189864i	$0.0608046\pi$
$137$	7.67046	+	13.2856i	0.655332	+	1.13507i	−0.326479	+	0.945205i	$0.605862\pi$
$138$		0			0
$139$	−6.05803	−	10.4928i	−0.513835	−	0.889988i	−0.999871	−	0.0160496i	$-0.994891\pi$
$139$	−6.05803	−	10.4928i	−0.513835	−	0.889988i	0.486036	−	0.873939i	$-0.338442\pi$
$140$		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	−0.946584	−	0.322458i	$-0.895491\pi$
$149$	−2.36849	+	4.10235i	−0.194035	+	0.336078i	0.752549	+	0.658536i	$0.228824\pi$
$150$		0			0
$151$	−12.1845	−	21.1041i	−0.991559	−	1.71743i	−0.608066	−	0.793887i	$-0.708054\pi$
$151$	−12.1845	−	21.1041i	−0.991559	−	1.71743i	−0.383493	−	0.923544i	$-0.625279\pi$
$152$		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	$-0.157922\pi$
$163$	0.350678	+	0.607392i	0.0274672	+	0.0475746i	−0.851965	+	0.523599i	$0.824589\pi$
$164$		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	$-0.0783873\pi$
$167$	3.53822	+	6.12839i	0.273796	+	0.474229i	−0.696035	+	0.718008i	$0.745054\pi$
$168$		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	$-0.694943\pi$
$179$	5.63527	−	9.76057i	0.421200	−	0.729539i	0.996057	+	0.0887145i	$0.0282759\pi$
$180$		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	$-0.610955\pi$
$191$	−9.44088			−0.683118			−0.341559	+	0.939860i	$0.610955\pi$
$192$		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	$-0.783608\pi$
$199$	2.19477	−	3.80145i	0.155583	−	0.269478i	0.933271	+	0.359173i	$0.116941\pi$
$200$		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	0.998544	+	0.0539495i	$0.0171810\pi$
$211$	7.93101	+	13.7369i	0.545993	+	0.945688i	−0.452550	+	0.891739i	$0.649486\pi$
$212$		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	$-0.678216\pi$
$223$	6.99253	−	12.1114i	0.468254	−	0.811040i	0.999342	+	0.0362769i	$0.0115498\pi$
$224$		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	$-0.282978\pi$
$227$	−5.38364	−	9.32474i	−0.357325	−	0.618905i	−0.987513	+	0.157538i	$0.949644\pi$
$228$		0			0
$229$	0.805015	−	1.39433i	0.0531969	−	0.0921397i	−0.838201	−	0.545362i	$-0.816392\pi$
$229$	0.805015	−	1.39433i	0.0531969	−	0.0921397i	0.891398	+	0.453222i	$0.149726\pi$
$230$		0			0
$231$	24.4925	+	7.87414i	1.61149	+	0.518081i
$232$		0			0
$233$	−0.510606	−	0.884395i	−0.0334509	−	0.0579387i	0.848815	−	0.528690i	$-0.177316\pi$
$233$	−0.510606	−	0.884395i	−0.0334509	−	0.0579387i	−0.882266	+	0.470751i	$0.843983\pi$
$234$		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	$-0.315414\pi$
$239$	−6.96428	−	12.0625i	−0.450482	−	0.780258i	−0.998416	+	0.0562640i	$0.982081\pi$
$240$		0			0
$241$	7.28788	+	12.6230i	0.469454	+	0.813118i	0.999390	−	0.0349197i	$-0.0111175\pi$
$241$	7.28788	+	12.6230i	0.469454	+	0.813118i	−0.529936	+	0.848037i	$0.677784\pi$
$242$		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	$-0.307338\pi$
$251$	18.0287			1.13796			0.568981	+	0.822350i	$0.307338\pi$
$252$		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	0.0502291	+	0.998738i	$0.484005\pi$
$257$	−13.4633	+	23.3191i	−0.839818	+	1.45461i	−0.890047	+	0.455869i	$0.849328\pi$
$258$		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	$-0.181774\pi$
$263$	−0.769419	−	1.33267i	−0.0474444	−	0.0821761i	−0.888772	+	0.458349i	$0.848441\pi$
$264$		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	−0.749173	−	0.662374i	$-0.769549\pi$
$269$	3.26461	−	5.65446i	0.199047	−	0.344759i	0.948220	+	0.317616i	$0.102882\pi$
$270$		0			0
$271$	−5.64494	−	9.77733i	−0.342906	−	0.593930i	0.642065	−	0.766650i	$-0.278078\pi$
$271$	−5.64494	−	9.77733i	−0.342906	−	0.593930i	−0.984971	+	0.172720i	$0.944745\pi$
$272$		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	0.837525	−	0.546399i	$-0.184002\pi$
$277$	−0.905938	−	1.56913i	−0.0544325	−	0.0942799i	−0.891958	+	0.452119i	$0.850668\pi$
$278$		0			0
$279$	−1.33147	−	2.69874i	−0.0797133	−	0.161569i
$280$		0			0
$281$	−2.98798	+	5.17533i	−0.178248	+	0.308734i	−0.941280	−	0.337626i	$-0.890376\pi$
$281$	−2.98798	+	5.17533i	−0.178248	+	0.308734i	0.763033	+	0.646360i	$0.223710\pi$
$282$		0			0
$283$	−19.9952			−1.18859			−0.594295	−	0.804247i	$-0.702569\pi$
$283$	−19.9952			−1.18859			−0.594295	+	0.804247i	$0.702569\pi$
$284$		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	0.684359	−	0.729145i	$-0.260082\pi$
$293$	−4.95166	−	8.57652i	−0.289279	−	0.501046i	−0.973638	+	0.228099i	$0.926749\pi$
$294$		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	$-0.736574\pi$
$307$	−23.7122			−1.35332			−0.676662	+	0.736293i	$0.736574\pi$
$308$		0			0
$309$	2.88021	+	5.38732i	0.163849	+	0.306474i
$310$		0			0
$311$	20.3449			1.15365			0.576826	−	0.816867i	$-0.304291\pi$
$311$	20.3449			1.15365			0.576826	+	0.816867i	$0.304291\pi$
$312$		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	$-0.512554\pi$
$331$	−1.43469			−0.0788578			−0.0394289	+	0.999222i	$0.512554\pi$
$332$		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	0.866095	−	0.499879i	$-0.166622\pi$
$337$	0.00257316	+	0.00445685i	0.000140169	+	0.000242780i	−0.865955	+	0.500121i	$0.833289\pi$
$338$		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	$-0.287040\pi$
$347$	23.1072			1.24046			0.620229	+	0.784421i	$0.287040\pi$
$348$		0			0
$349$	6.09723	−	10.5607i	0.326377	−	0.565302i	−0.655413	−	0.755271i	$-0.727505\pi$
$349$	6.09723	−	10.5607i	0.326377	−	0.565302i	0.981790	+	0.189969i	$0.0608387\pi$
$350$		0			0
$351$	13.4758	+	29.7203i	0.719284	+	1.58635i
$352$		0			0
$353$	−12.3536	−	21.3970i	−0.657515	−	1.13885i	−0.981257	−	0.192704i	$-0.938274\pi$
$353$	−12.3536	−	21.3970i	−0.657515	−	1.13885i	0.323742	−	0.946145i	$-0.395059\pi$
$354$		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	$-0.0241321\pi$
$359$	8.20362	+	14.2091i	0.432970	+	0.749927i	−0.564157	+	0.825667i	$0.690799\pi$
$360$		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	$-0.118144\pi$
$367$	2.90900	+	5.03854i	0.151849	+	0.263010i	−0.780058	+	0.625707i	$0.784811\pi$
$368$		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	−0.957544	−	0.288286i	$-0.906915\pi$
$373$	−4.42483	+	7.66403i	−0.229109	+	0.396829i	0.728435	+	0.685115i	$0.240248\pi$
$374$		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	$-0.353171\pi$
$379$	17.3300			0.890181			0.445091	+	0.895486i	$0.353171\pi$
$380$		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	$-0.891320\pi$
$383$	−3.54545	+	6.14090i	−0.181164	+	0.313785i	0.761113	+	0.648619i	$0.224653\pi$
$384$		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	0.769463	−	0.638691i	$-0.220524\pi$
$389$	−3.32120	−	5.75249i	−0.168392	−	0.291663i	−0.937854	+	0.347029i	$0.887191\pi$
$390$		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	0.993057	−	0.117636i	$-0.0375315\pi$
$397$	7.86340	+	13.6198i	0.394653	+	0.683559i	−0.598404	+	0.801195i	$0.704198\pi$
$398$		0			0
$399$	4.87800	+	1.56824i	0.244205	+	0.0785101i
$400$		0			0
$401$	−2.98280	+	5.16635i	−0.148954	+	0.257995i	−0.930841	−	0.365424i	$-0.880924\pi$
$401$	−2.98280	+	5.16635i	−0.148954	+	0.257995i	0.781887	+	0.623420i	$0.214257\pi$
$402$		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	$-0.0109033\pi$
$419$	9.62164	+	16.6652i	0.470048	+	0.814147i	−0.529365	+	0.848394i	$0.677570\pi$
$420$		0			0
$421$	7.77999	−	13.4753i	0.379174	−	0.656748i	−0.611769	−	0.791037i	$-0.709542\pi$
$421$	7.77999	−	13.4753i	0.379174	−	0.656748i	0.990942	+	0.134289i	$0.0428750\pi$
$422$		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	0.0895020	+	0.995987i	$0.471472\pi$
$431$	−16.9779	+	29.4067i	−0.817799	+	1.41647i	−0.907301	+	0.420482i	$0.861861\pi$
$432$		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	$-0.378916\pi$
$439$	15.5588			0.742579			0.371290	+	0.928517i	$0.378916\pi$
$440$		0			0
$441$	2.06544	−	20.8982i	0.0983541	−	0.995151i
$442$		0			0
$443$	18.3242			0.870611			0.435305	−	0.900283i	$-0.356640\pi$
$443$	18.3242			0.870611			0.435305	+	0.900283i	$0.356640\pi$
$444$		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	−0.677378	−	0.735635i	$-0.736884\pi$
$461$	6.40670	−	11.0967i	0.298390	−	0.516826i	0.975768	+	0.218809i	$0.0702172\pi$
$462$		0			0
$463$	5.54704	+	9.60775i	0.257793	+	0.446510i	0.965650	−	0.259845i	$-0.0836715\pi$
$463$	5.54704	+	9.60775i	0.257793	+	0.446510i	−0.707858	+	0.706355i	$0.750338\pi$
$464$		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	$-0.0867684\pi$
$467$	5.36754	+	9.29686i	0.248380	+	0.430207i	−0.714696	+	0.699435i	$0.753435\pi$
$468$		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	$-0.109677\pi$
$479$	3.89754	+	6.75074i	0.178083	+	0.308449i	−0.763141	+	0.646232i	$0.776344\pi$
$480$		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	−0.352331	−	0.935875i	$-0.614611\pi$
$487$	13.9984	−	24.2459i	0.634326	−	1.09868i	0.986657	−	0.162810i	$-0.0520557\pi$
$488$		0			0
$489$	−1.21414	−	0.0396373i	−0.0549052	−	0.00179246i
$490$		0			0
$491$	−12.1227	−	20.9971i	−0.547089	−	0.947586i	−0.998472	−	0.0552556i	$-0.982403\pi$
$491$	−12.1227	−	20.9971i	−0.547089	−	0.947586i	0.451383	−	0.892330i	$-0.350931\pi$
$492$		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	−0.188899	−	0.981996i	$-0.560492\pi$
$499$	16.8874	−	29.2499i	0.755984	−	1.30940i	0.944883	−	0.327407i	$-0.106175\pi$
$500$		0			0
$501$	−12.2502	−	0.399928i	−0.547301	−	0.0178675i
$502$		0			0
$503$	−1.09819			−0.0489661			−0.0244830	−	0.999700i	$-0.507794\pi$
$503$	−1.09819			−0.0489661			−0.0244830	+	0.999700i	$0.507794\pi$
$504$		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	−0.987848	−	0.155423i	$-0.950326\pi$
$509$	−8.10672	+	14.0413i	−0.359324	+	0.622368i	0.628524	+	0.777790i	$0.283659\pi$
$510$		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	−0.0498617	−	0.998756i	$-0.515878\pi$
$521$	19.1738	−	33.2099i	0.840017	−	1.45495i	0.889879	−	0.456197i	$-0.150789\pi$
$522$		0			0
$523$	20.6021	+	35.6838i	0.900865	+	1.56034i	0.826374	+	0.563122i	$0.190400\pi$
$523$	20.6021	+	35.6838i	0.900865	+	1.56034i	0.0744911	+	0.997222i	$0.476267\pi$
$524$		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	0.601609	−	0.798791i	$-0.294527\pi$
$541$	−9.09371	−	15.7508i	−0.390969	−	0.677178i	−0.992578	+	0.121613i	$0.961193\pi$
$542$		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	$-0.828723\pi$
$547$	0.338699	−	0.586644i	0.0144817	−	0.0250831i	0.873175	+	0.487406i	$0.162057\pi$
$548$		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	−0.357687	−	0.933842i	$-0.616435\pi$
$557$	14.8659	−	25.7484i	0.629887	−	1.09100i	0.987574	−	0.157155i	$-0.0502322\pi$
$558$		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	$-0.351477\pi$
$563$	21.3478			0.899705			0.449852	+	0.893103i	$0.351477\pi$
$564$		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	$-0.363394\pi$
$571$	19.8863			0.832215			0.416107	+	0.909315i	$0.363394\pi$
$572$		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	−0.0775179	−	0.996991i	$-0.524700\pi$
$577$	19.8090	−	34.3102i	0.824661	−	1.42835i	0.902178	−	0.431363i	$-0.141967\pi$
$578$		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	$-0.818446\pi$
$587$	1.13275	−	1.96199i	0.0467537	−	0.0809798i	0.888455	+	0.458963i	$0.151779\pi$
$588$		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	0.962210	−	0.272308i	$-0.0877869\pi$
$593$	5.97295	+	10.3454i	0.245280	+	0.424837i	−0.716931	+	0.697145i	$0.754454\pi$
$594$		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	$-0.519213\pi$
$599$	−2.95272			−0.120645			−0.0603224	+	0.998179i	$0.519213\pi$
$600$		0			0
$601$	15.9751	−	27.6697i	0.651638	−	1.12867i	−0.331087	−	0.943600i	$-0.607415\pi$
$601$	15.9751	−	27.6697i	0.651638	−	1.12867i	0.982725	−	0.185071i	$-0.0592514\pi$
$602$		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	$-0.901034\pi$
$607$	−5.20069	+	9.00786i	−0.211089	+	0.365618i	0.740966	+	0.671542i	$0.234368\pi$
$608$		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	−0.712510	−	0.701662i	$-0.752442\pi$
$613$	6.22441	−	10.7810i	0.251402	−	0.435441i	0.963912	+	0.266221i	$0.0857751\pi$
$614$		0			0
$615$	−13.5105	+	21.7310i	−0.544795	+	0.876278i
$616$		0			0
$617$	−4.70100	−	8.14237i	−0.189255	−	0.327799i	0.755747	−	0.654864i	$-0.227274\pi$
$617$	−4.70100	−	8.14237i	−0.189255	−	0.327799i	−0.945002	+	0.327064i	$0.893941\pi$
$618$		0			0
$619$	11.0598	+	19.1561i	0.444531	+	0.769951i	0.998019	−	0.0629064i	$-0.0200370\pi$
$619$	11.0598	+	19.1561i	0.444531	+	0.769951i	−0.553488	+	0.832857i	$0.686704\pi$
$620$		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	$-0.380844\pi$
$631$	18.3705			0.731316			0.365658	+	0.930749i	$0.380844\pi$
$632$		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	0.979014	+	0.203791i	$0.0653262\pi$
$641$	16.8617	+	29.2052i	0.665995	+	1.15354i	−0.313019	+	0.949747i	$0.601340\pi$
$642$		0			0
$643$	10.0635	+	17.4306i	0.396867	+	0.687394i	0.993338	−	0.115241i	$-0.0367640\pi$
$643$	10.0635	+	17.4306i	0.396867	+	0.687394i	−0.596470	+	0.802635i	$0.703431\pi$
$644$		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	$-0.978315\pi$
$647$	−11.1891	+	19.3800i	−0.439887	+	0.761907i	0.557793	+	0.829980i	$0.311648\pi$
$648$		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	−0.126406	−	0.991979i	$-0.540344\pi$
$653$	20.3377	−	35.2259i	0.795875	−	1.37850i	0.922282	−	0.386518i	$-0.126322\pi$
$654$		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	$-0.736452\pi$
$659$	7.69321	−	13.3250i	0.299685	−	0.519070i	0.976064	+	0.217484i	$0.0697851\pi$
$660$		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	−0.968814	−	0.247789i	$-0.920296\pi$
$673$	−6.99961	+	12.1237i	−0.269815	+	0.467334i	0.698999	+	0.715123i	$0.253629\pi$
$674$		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	−0.0727571	−	0.997350i	$-0.523180\pi$
$683$	21.6222	−	37.4508i	0.827352	−	1.43302i	0.900109	−	0.435665i	$-0.143487\pi$
$684$		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	$-0.571569\pi$
$691$	−11.7214			−0.445905			−0.222952	+	0.974829i	$0.571569\pi$
$692$		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	$-0.00856140\pi$
$719$	12.7777	+	22.1317i	0.476529	+	0.825372i	−0.523109	+	0.852266i	$0.675228\pi$
$720$		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	$-0.759415\pi$
$727$	6.20522	−	10.7478i	0.230139	−	0.398612i	0.957849	+	0.287273i	$0.0927486\pi$
$728$		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	0.455405	+	0.890285i	$0.349495\pi$
$733$	−14.7095	+	25.4775i	−0.543307	+	0.941035i	−0.998711	+	0.0507502i	$0.983839\pi$
$734$		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	$-0.741199\pi$
$739$	7.75910	−	13.4392i	0.285423	−	0.494368i	0.972712	+	0.232017i	$0.0745325\pi$
$740$		0			0
$741$	−5.73432	−	10.7258i	−0.210656	−	0.394024i
$742$		0			0
$743$	−13.6333	−	23.6136i	−0.500159	−	0.866301i	−1.00000		0.000183414i	$-0.999942\pi$
$743$	−13.6333	−	23.6136i	−0.500159	−	0.866301i	0.499841	−	0.866117i	$-0.333392\pi$
$744$		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	$-0.779982\pi$
$751$	4.57176	−	7.91853i	0.166826	−	0.288951i	0.937302	+	0.348518i	$0.113315\pi$
$752$		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	−0.861657	−	0.507491i	$-0.830573\pi$
$761$	0.239208	−	0.414321i	0.00867130	−	0.0150191i	0.870328	+	0.492472i	$0.163906\pi$
$762$		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	0.518294	−	0.855202i	$-0.326567\pi$
$769$	−13.3518	−	23.1261i	−0.481480	−	0.833948i	−0.999774	+	0.0212548i	$0.993234\pi$
$770$		0			0
$771$	−21.9888	−	41.1293i	−0.791908	−	1.48123i
$772$		0			0
$773$	−13.5143	+	23.4074i	−0.486074	+	0.841905i	−0.999872	−	0.0160062i	$-0.994905\pi$
$773$	−13.5143	+	23.4074i	−0.486074	+	0.841905i	0.513798	+	0.857911i	$0.328238\pi$
$774$		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	$-0.159811\pi$
$787$	49.1830			1.75319			0.876593	+	0.481233i	$0.159811\pi$
$788$		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	0.929162	+	0.369674i	$0.120531\pi$
$797$	22.1538	+	38.3715i	0.784728	+	1.35919i	−0.144434	+	0.989514i	$0.546136\pi$
$798$		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	0.406040	+	0.913855i	$0.366909\pi$
$809$	−16.7359	+	28.9874i	−0.588402	+	1.01914i	−0.994442	+	0.105286i	$0.966424\pi$
$810$		0			0
$811$	−43.7383			−1.53586			−0.767929	−	0.640535i	$-0.778713\pi$
$811$	−43.7383			−1.53586			−0.767929	+	0.640535i	$0.778713\pi$
$812$		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	$-0.417680\pi$
$823$	14.6735			0.511485			0.255743	+	0.966745i	$0.417680\pi$
$824$		0			0
$825$	−8.33919	−	15.5981i	−0.290333	−	0.543058i
$826$		0			0
$827$	45.0520			1.56661			0.783306	−	0.621636i	$-0.213532\pi$
$827$	45.0520			1.56661			0.783306	+	0.621636i	$0.213532\pi$
$828$		0			0
$829$	20.6688	−	35.7993i	0.717856	−	1.24336i	−0.243992	−	0.969777i	$-0.578457\pi$
$829$	20.6688	−	35.7993i	0.717856	−	1.24336i	0.961848	−	0.273585i	$-0.0882095\pi$
$830$		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	$-0.810844\pi$
$839$	2.04477	−	3.54164i	0.0705932	−	0.122271i	0.899161	+	0.437617i	$0.144177\pi$
$840$		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	0.237507	+	0.971386i	$0.423670\pi$
$853$	−21.1012	+	36.5484i	−0.722491	+	1.25139i	−0.959998	+	0.280006i	$0.909664\pi$
$854$		0			0
$855$	−2.64704	−	5.36523i	−0.0905269	−	0.183487i
$856$		0			0
$857$	27.5623	+	47.7393i	0.941509	+	1.63074i	0.762594	+	0.646877i	$0.223925\pi$
$857$	27.5623	+	47.7393i	0.941509	+	1.63074i	0.178915	+	0.983864i	$0.442741\pi$
$858$		0			0
$859$	18.9767	−	32.8686i	0.647476	−	1.12146i	−0.336247	−	0.941774i	$-0.609158\pi$
$859$	18.9767	−	32.8686i	0.647476	−	1.12146i	0.983724	−	0.179688i	$-0.0575089\pi$
$860$		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	$-0.0981793\pi$
$863$	6.27205	+	10.8635i	0.213503	+	0.369798i	−0.739305	+	0.673370i	$0.764846\pi$
$864$		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	−0.936259	−	0.351310i	$-0.885736\pi$
$877$	−4.85337	+	8.40628i	−0.163887	+	0.283860i	0.772373	+	0.635169i	$0.219070\pi$
$878$		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	$-0.571161\pi$
$883$	−13.1758			−0.443401			−0.221701	+	0.975115i	$0.571161\pi$
$884$		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	$-0.828894\pi$
$887$	0.415361	−	0.719426i	0.0139464	−	0.0241560i	0.872914	+	0.487873i	$0.162227\pi$
$888$		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	−0.998045	−	0.0624962i	$-0.980094\pi$
$907$	−16.6588	−	28.8539i	−0.553146	−	0.958077i	0.444899	−	0.895581i	$-0.353239\pi$
$908$		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	$-0.953609\pi$
$911$	−11.1353	+	19.2870i	−0.368930	+	0.639006i	0.620469	+	0.784231i	$0.286942\pi$
$912$		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	$-0.0508243\pi$
$919$	10.7906	+	18.6899i	0.355949	+	0.616522i	−0.631331	+	0.775514i	$0.717491\pi$
$920$		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	$-0.512939\pi$
$947$	−2.50117			−0.0812771			−0.0406386	+	0.999174i	$0.512939\pi$
$948$		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	$-0.107302\pi$
$967$	5.76591	+	9.98684i	0.185419	+	0.321155i	−0.758299	+	0.651907i	$0.773969\pi$
$968$		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	$-0.261497\pi$
$971$	−9.14669	−	15.8425i	−0.293531	−	0.508411i	−0.974642	+	0.223769i	$0.928164\pi$
$972$		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	$-0.241177\pi$
$983$	−7.27224	−	12.5959i	−0.231948	−	0.401746i	−0.958381	+	0.285491i	$0.907843\pi$
$984$		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	$-0.984283\pi$
$991$	−14.3753	+	24.8987i	−0.456646	+	0.790935i	0.542135	+	0.840292i	$0.317616\pi$
$992$		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	−0.996726	−	0.0808539i	$-0.974235\pi$
$997$	−17.9469	−	31.0850i	−0.568384	−	0.984471i	0.428341	−	0.903617i	$-0.359098\pi$
$998$		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	504.2.q.c.25.4	✓	22
3.2	odd	2		1512.2.q.d.1369.4		22
4.3	odd	2		1008.2.q.l.529.8		22
7.2	even	3		504.2.t.c.457.5	yes	22
9.4	even	3		504.2.t.c.193.5	yes	22
9.5	odd	6		1512.2.t.c.361.8		22
12.11	even	2		3024.2.q.l.2881.4		22
21.2	odd	6		1512.2.t.c.289.8		22
28.23	odd	6		1008.2.t.l.961.7		22
36.23	even	6		3024.2.t.k.1873.8		22
36.31	odd	6		1008.2.t.l.193.7		22
63.23	odd	6		1512.2.q.d.793.4		22
63.58	even	3	inner	504.2.q.c.121.4	yes	22
84.23	even	6		3024.2.t.k.289.8		22
252.23	even	6		3024.2.q.l.2305.4		22
252.247	odd	6		1008.2.q.l.625.8		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.4	✓	22	1.1	even	1	trivial
504.2.q.c.121.4	yes	22	63.58	even	3	inner
504.2.t.c.193.5	yes	22	9.4	even	3
504.2.t.c.457.5	yes	22	7.2	even	3
1008.2.q.l.529.8		22	4.3	odd	2
1008.2.q.l.625.8		22	252.247	odd	6
1008.2.t.l.193.7		22	36.31	odd	6
1008.2.t.l.961.7		22	28.23	odd	6
1512.2.q.d.793.4		22	63.23	odd	6
1512.2.q.d.1369.4		22	3.2	odd	2
1512.2.t.c.289.8		22	21.2	odd	6
1512.2.t.c.361.8		22	9.5	odd	6
3024.2.q.l.2305.4		22	252.23	even	6
3024.2.q.l.2881.4		22	12.11	even	2
3024.2.t.k.289.8		22	84.23	even	6
3024.2.t.k.1873.8		22	36.23	even	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.q (of order \(3\), degree \(2\), 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

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