LMFDB - Embedded newform 528.2.y.d.433.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [528,2,Mod(49,528)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(528, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("528.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 528 = 2^{4} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	528.y (of order $5$, degree $4$, 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:	$4.21610122672$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			433.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	528.433
Dual form			528.2.y.d.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{3} +(3.11803 - 2.26538i) q^{5} +(-0.736068 - 2.26538i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{3} +(3.11803 - 2.26538i) q^{5} +(-0.736068 - 2.26538i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(3.23607 + 0.726543i) q^{11} +(-1.00000 - 0.726543i) q^{13} +(-1.19098 - 3.66547i) q^{15} +(-5.23607 + 3.80423i) q^{17} +(-0.381966 + 1.17557i) q^{19} -2.38197 q^{21} -1.23607 q^{23} +(3.04508 - 9.37181i) q^{25} +(-0.809017 + 0.587785i) q^{27} +(-0.809017 - 2.48990i) q^{29} +(5.16312 + 3.75123i) q^{31} +(1.69098 - 2.85317i) q^{33} +(-7.42705 - 5.39607i) q^{35} +(3.23607 + 9.95959i) q^{37} +(-1.00000 + 0.726543i) q^{39} +(0.381966 - 1.17557i) q^{41} -1.23607 q^{43} -3.85410 q^{45} +(2.00000 - 6.15537i) q^{47} +(1.07295 - 0.779543i) q^{49} +(2.00000 + 6.15537i) q^{51} +(-2.30902 - 1.67760i) q^{53} +(11.7361 - 5.06555i) q^{55} +(1.00000 + 0.726543i) q^{57} +(-0.881966 - 2.71441i) q^{59} +(9.09017 - 6.60440i) q^{61} +(-0.736068 + 2.26538i) q^{63} -4.76393 q^{65} -4.00000 q^{67} +(-0.381966 + 1.17557i) q^{69} +(2.85410 - 2.07363i) q^{71} +(1.33688 + 4.11450i) q^{73} +(-7.97214 - 5.79210i) q^{75} +(-0.736068 - 7.86572i) q^{77} +(5.11803 + 3.71847i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-13.2082 + 9.59632i) q^{83} +(-7.70820 + 23.7234i) q^{85} -2.61803 q^{87} +1.70820 q^{89} +(-0.909830 + 2.80017i) q^{91} +(5.16312 - 3.75123i) q^{93} +(1.47214 + 4.53077i) q^{95} +(3.50000 + 2.54290i) q^{97} +(-2.19098 - 2.48990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + 8 q^{5} + 6 q^{7} - q^{9}+O(q^{10}) $ 4 * q - q^3 + 8 * q^5 + 6 * q^7 - q^9	$ 4 q - q^{3} + 8 q^{5} + 6 q^{7} - q^{9} + 4 q^{11} - 4 q^{13} - 7 q^{15} - 12 q^{17} - 6 q^{19} - 14 q^{21} + 4 q^{23} + q^{25} - q^{27} - q^{29} + 5 q^{31} + 9 q^{33} - 23 q^{35} + 4 q^{37} - 4 q^{39} + 6 q^{41} + 4 q^{43} - 2 q^{45} + 8 q^{47} + 11 q^{49} + 8 q^{51} - 7 q^{53} + 38 q^{55} + 4 q^{57} - 8 q^{59} + 14 q^{61} + 6 q^{63} - 28 q^{65} - 16 q^{67} - 6 q^{69} - 2 q^{71} + 21 q^{73} - 14 q^{75} + 6 q^{77} + 16 q^{79} - q^{81} - 26 q^{83} - 4 q^{85} - 6 q^{87} - 20 q^{89} - 26 q^{91} + 5 q^{93} - 12 q^{95} + 14 q^{97} - 11 q^{99}+O(q^{100}) $ 4 * q - q^3 + 8 * q^5 + 6 * q^7 - q^9 + 4 * q^11 - 4 * q^13 - 7 * q^15 - 12 * q^17 - 6 * q^19 - 14 * q^21 + 4 * q^23 + q^25 - q^27 - q^29 + 5 * q^31 + 9 * q^33 - 23 * q^35 + 4 * q^37 - 4 * q^39 + 6 * q^41 + 4 * q^43 - 2 * q^45 + 8 * q^47 + 11 * q^49 + 8 * q^51 - 7 * q^53 + 38 * q^55 + 4 * q^57 - 8 * q^59 + 14 * q^61 + 6 * q^63 - 28 * q^65 - 16 * q^67 - 6 * q^69 - 2 * q^71 + 21 * q^73 - 14 * q^75 + 6 * q^77 + 16 * q^79 - q^81 - 26 * q^83 - 4 * q^85 - 6 * q^87 - 20 * q^89 - 26 * q^91 + 5 * q^93 - 12 * q^95 + 14 * q^97 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/528\mathbb{Z}\right)^\times$.

$n$	$133$	$145$	$353$	$463$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$		0			0
$5$	3.11803	−	2.26538i	1.39443	−	1.01311i	0.399064	−	0.916923i	$-0.369335\pi$
$5$	3.11803	−	2.26538i	1.39443	−	1.01311i	0.995363	−	0.0961876i	$-0.0306649\pi$
$6$		0			0
$7$	−0.736068	−	2.26538i	−0.278208	−	0.856235i	−0.988353	−	0.152180i	$-0.951371\pi$
$7$	−0.736068	−	2.26538i	−0.278208	−	0.856235i	0.710145	−	0.704055i	$-0.248629\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	3.23607	+	0.726543i	0.975711	+	0.219061i
$11$	3.23607	+	0.726543i	0.975711	+	0.219061i
$12$		0			0
$13$	−1.00000	−	0.726543i	−0.277350	−	0.201507i	0.440411	−	0.897796i	$-0.354833\pi$
$13$	−1.00000	−	0.726543i	−0.277350	−	0.201507i	−0.717761	+	0.696290i	$0.754833\pi$
$14$		0			0
$15$	−1.19098	−	3.66547i	−0.307510	−	0.946420i
$16$		0			0
$17$	−5.23607	+	3.80423i	−1.26993	+	0.922660i	−0.999200	−	0.0399941i	$-0.987266\pi$
$17$	−5.23607	+	3.80423i	−1.26993	+	0.922660i	−0.270733	+	0.962654i	$0.587266\pi$
$18$		0			0
$19$	−0.381966	+	1.17557i	−0.0876290	+	0.269694i	−0.985263	−	0.171048i	$-0.945285\pi$
$19$	−0.381966	+	1.17557i	−0.0876290	+	0.269694i	0.897634	+	0.440742i	$0.145285\pi$
$20$		0			0
$21$	−2.38197			−0.519788
$22$		0			0
$23$	−1.23607			−0.257738			−0.128869	−	0.991662i	$-0.541135\pi$
$23$	−1.23607			−0.257738			−0.128869	+	0.991662i	$0.541135\pi$
$24$		0			0
$25$	3.04508	−	9.37181i	0.609017	−	1.87436i
$26$		0			0
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$		0			0
$29$	−0.809017	−	2.48990i	−0.150231	−	0.462363i	0.847416	−	0.530930i	$-0.178157\pi$
$29$	−0.809017	−	2.48990i	−0.150231	−	0.462363i	−0.997646	+	0.0685673i	$0.978157\pi$
$30$		0			0
$31$	5.16312	+	3.75123i	0.927324	+	0.673740i	0.945336	−	0.326098i	$-0.105734\pi$
$31$	5.16312	+	3.75123i	0.927324	+	0.673740i	−0.0180125	+	0.999838i	$0.505734\pi$
$32$		0			0
$33$	1.69098	−	2.85317i	0.294362	−	0.496673i
$34$		0			0
$35$	−7.42705	−	5.39607i	−1.25540	−	0.912102i
$36$		0			0
$37$	3.23607	+	9.95959i	0.532006	+	1.63735i	0.750030	+	0.661404i	$0.230039\pi$
$37$	3.23607	+	9.95959i	0.532006	+	1.63735i	−0.218024	+	0.975943i	$0.569961\pi$
$38$		0			0
$39$	−1.00000	+	0.726543i	−0.160128	+	0.116340i
$40$		0			0
$41$	0.381966	−	1.17557i	0.0596531	−	0.183593i	−0.916789	−	0.399371i	$-0.869229\pi$
$41$	0.381966	−	1.17557i	0.0596531	−	0.183593i	0.976443	+	0.215778i	$0.0692286\pi$
$42$		0			0
$43$	−1.23607			−0.188499			−0.0942493	−	0.995549i	$-0.530045\pi$
$43$	−1.23607			−0.188499			−0.0942493	+	0.995549i	$0.530045\pi$
$44$		0			0
$45$	−3.85410			−0.574536
$46$		0			0
$47$	2.00000	−	6.15537i	0.291730	−	0.897853i	−0.692570	−	0.721350i	$-0.743522\pi$
$47$	2.00000	−	6.15537i	0.291730	−	0.897853i	0.984300	−	0.176502i	$-0.0564783\pi$
$48$		0			0
$49$	1.07295	−	0.779543i	0.153278	−	0.111363i
$50$		0			0
$51$	2.00000	+	6.15537i	0.280056	+	0.861924i
$52$		0			0
$53$	−2.30902	−	1.67760i	−0.317168	−	0.230436i	0.417798	−	0.908540i	$-0.362802\pi$
$53$	−2.30902	−	1.67760i	−0.317168	−	0.230436i	−0.734966	+	0.678104i	$0.762802\pi$
$54$		0			0
$55$	11.7361	−	5.06555i	1.58249	−	0.683039i
$56$		0			0
$57$	1.00000	+	0.726543i	0.132453	+	0.0962329i
$58$		0			0
$59$	−0.881966	−	2.71441i	−0.114822	−	0.353386i	0.877088	−	0.480330i	$-0.159483\pi$
$59$	−0.881966	−	2.71441i	−0.114822	−	0.353386i	−0.991910	+	0.126944i	$0.959483\pi$
$60$		0			0
$61$	9.09017	−	6.60440i	1.16388	−	0.845606i	0.173614	−	0.984814i	$-0.444456\pi$
$61$	9.09017	−	6.60440i	1.16388	−	0.845606i	0.990263	+	0.139208i	$0.0444556\pi$
$62$		0			0
$63$	−0.736068	+	2.26538i	−0.0927358	+	0.285412i
$64$		0			0
$65$	−4.76393			−0.590893
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$	−0.381966	+	1.17557i	−0.0459833	+	0.141522i
$70$		0			0
$71$	2.85410	−	2.07363i	0.338720	−	0.246094i	−0.405402	−	0.914139i	$-0.632868\pi$
$71$	2.85410	−	2.07363i	0.338720	−	0.246094i	0.744121	+	0.668044i	$0.232868\pi$
$72$		0			0
$73$	1.33688	+	4.11450i	0.156470	+	0.481565i	0.998307	−	0.0581668i	$-0.0185255\pi$
$73$	1.33688	+	4.11450i	0.156470	+	0.481565i	−0.841837	+	0.539732i	$0.818526\pi$
$74$		0			0
$75$	−7.97214	−	5.79210i	−0.920543	−	0.668814i
$76$		0			0
$77$	−0.736068	−	7.86572i	−0.0838827	−	0.896382i
$78$		0			0
$79$	5.11803	+	3.71847i	0.575824	+	0.418360i	0.837216	−	0.546872i	$-0.184182\pi$
$79$	5.11803	+	3.71847i	0.575824	+	0.418360i	−0.261392	+	0.965233i	$0.584182\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	−13.2082	+	9.59632i	−1.44979	+	1.05333i	−0.463908	+	0.885883i	$0.653553\pi$
$83$	−13.2082	+	9.59632i	−1.44979	+	1.05333i	−0.985881	+	0.167450i	$0.946447\pi$
$84$		0			0
$85$	−7.70820	+	23.7234i	−0.836072	+	2.57317i
$86$		0			0
$87$	−2.61803			−0.280683
$88$		0			0
$89$	1.70820			0.181069			0.0905346	−	0.995893i	$-0.471142\pi$
$89$	1.70820			0.181069			0.0905346	+	0.995893i	$0.471142\pi$
$90$		0			0
$91$	−0.909830	+	2.80017i	−0.0953761	+	0.293537i
$92$		0			0
$93$	5.16312	−	3.75123i	0.535390	−	0.388984i
$94$		0			0
$95$	1.47214	+	4.53077i	0.151038	+	0.464847i
$96$		0			0
$97$	3.50000	+	2.54290i	0.355371	+	0.258192i	0.751119	−	0.660167i	$-0.229515\pi$
$97$	3.50000	+	2.54290i	0.355371	+	0.258192i	−0.395748	+	0.918359i	$0.629515\pi$
$98$		0			0
$99$	−2.19098	−	2.48990i	−0.220202	−	0.250244i
$100$		0			0
$101$	11.8262	+	8.59226i	1.17675	+	0.854962i	0.991802	−	0.127785i	$-0.0407868\pi$
$101$	11.8262	+	8.59226i	1.17675	+	0.854962i	0.184953	+	0.982747i	$0.440787\pi$
$102$		0			0
$103$	5.26393	+	16.2007i	0.518671	+	1.59630i	0.776502	+	0.630114i	$0.216992\pi$
$103$	5.26393	+	16.2007i	0.518671	+	1.59630i	−0.257832	+	0.966190i	$0.583008\pi$
$104$		0			0
$105$	−7.42705	+	5.39607i	−0.724806	+	0.526602i
$106$		0			0
$107$	−2.35410	+	7.24518i	−0.227580	+	0.700418i	0.770440	+	0.637513i	$0.220037\pi$
$107$	−2.35410	+	7.24518i	−0.227580	+	0.700418i	−0.998019	+	0.0629054i	$0.979963\pi$
$108$		0			0
$109$	−9.41641			−0.901928			−0.450964	−	0.892542i	$-0.648920\pi$
$109$	−9.41641			−0.901928			−0.450964	+	0.892542i	$0.648920\pi$
$110$		0			0
$111$	10.4721			0.993971
$112$		0			0
$113$	−1.09017	+	3.35520i	−0.102555	+	0.315630i	−0.989149	−	0.146918i	$-0.953065\pi$
$113$	−1.09017	+	3.35520i	−0.102555	+	0.315630i	0.886594	+	0.462548i	$0.153065\pi$
$114$		0			0
$115$	−3.85410	+	2.80017i	−0.359397	+	0.261117i
$116$		0			0
$117$	0.381966	+	1.17557i	0.0353128	+	0.108682i
$118$		0			0
$119$	12.4721	+	9.06154i	1.14332	+	0.830670i
$120$		0			0
$121$	9.94427	+	4.70228i	0.904025	+	0.427480i
$122$		0			0
$123$	−1.00000	−	0.726543i	−0.0901670	−	0.0655101i
$124$		0			0
$125$	−5.78115	−	17.7926i	−0.517082	−	1.59141i
$126$		0			0
$127$	9.70820	−	7.05342i	0.861464	−	0.625890i	−0.0668190	−	0.997765i	$-0.521285\pi$
$127$	9.70820	−	7.05342i	0.861464	−	0.625890i	0.928283	+	0.371875i	$0.121285\pi$
$128$		0			0
$129$	−0.381966	+	1.17557i	−0.0336302	+	0.103503i
$130$		0			0
$131$	−18.2705			−1.59630			−0.798151	−	0.602458i	$-0.794188\pi$
$131$	−18.2705			−1.59630			−0.798151	+	0.602458i	$0.794188\pi$
$132$		0			0
$133$	2.94427			0.255301
$134$		0			0
$135$	−1.19098	+	3.66547i	−0.102503	+	0.315473i
$136$		0			0
$137$	−13.8541	+	10.0656i	−1.18364	+	0.859962i	−0.992577	−	0.121617i	$-0.961192\pi$
$137$	−13.8541	+	10.0656i	−1.18364	+	0.859962i	−0.191059	+	0.981579i	$0.561192\pi$
$138$		0			0
$139$	−2.70820	−	8.33499i	−0.229707	−	0.706965i	−0.997780	−	0.0666024i	$-0.978784\pi$
$139$	−2.70820	−	8.33499i	−0.229707	−	0.706965i	0.768073	−	0.640363i	$-0.221216\pi$
$140$		0			0
$141$	−5.23607	−	3.80423i	−0.440956	−	0.320374i
$142$		0			0
$143$	−2.70820	−	3.07768i	−0.226471	−	0.257369i
$144$		0			0
$145$	−8.16312	−	5.93085i	−0.677910	−	0.492531i
$146$		0			0
$147$	−0.409830	−	1.26133i	−0.0338022	−	0.104033i
$148$		0			0
$149$	−2.92705	+	2.12663i	−0.239793	+	0.174220i	−0.701191	−	0.712973i	$-0.747348\pi$
$149$	−2.92705	+	2.12663i	−0.239793	+	0.174220i	0.461398	+	0.887193i	$0.347348\pi$
$150$		0			0
$151$	1.95492	−	6.01661i	0.159089	−	0.489625i	−0.839463	−	0.543416i	$-0.817131\pi$
$151$	1.95492	−	6.01661i	0.159089	−	0.489625i	0.998552	+	0.0537914i	$0.0171306\pi$
$152$		0			0
$153$	6.47214			0.523241
$154$		0			0
$155$	24.5967			1.97566
$156$		0			0
$157$	−1.38197	+	4.25325i	−0.110293	+	0.339447i	−0.990936	−	0.134333i	$-0.957111\pi$
$157$	−1.38197	+	4.25325i	−0.110293	+	0.339447i	0.880643	+	0.473780i	$0.157111\pi$
$158$		0			0
$159$	−2.30902	+	1.67760i	−0.183117	+	0.133042i
$160$		0			0
$161$	0.909830	+	2.80017i	0.0717047	+	0.220684i
$162$		0			0
$163$	10.8541	+	7.88597i	0.850159	+	0.617677i	0.925190	−	0.379505i	$-0.123906\pi$
$163$	10.8541	+	7.88597i	0.850159	+	0.617677i	−0.0750310	+	0.997181i	$0.523906\pi$
$164$		0			0
$165$	−1.19098	−	12.7270i	−0.0927179	−	0.990796i
$166$		0			0
$167$	2.23607	+	1.62460i	0.173032	+	0.125715i	0.670931	−	0.741520i	$-0.265895\pi$
$167$	2.23607	+	1.62460i	0.173032	+	0.125715i	−0.497899	+	0.867235i	$0.665895\pi$
$168$		0			0
$169$	−3.54508	−	10.9106i	−0.272699	−	0.839281i
$170$		0			0
$171$	1.00000	−	0.726543i	0.0764719	−	0.0555601i
$172$		0			0
$173$	−3.35410	+	10.3229i	−0.255008	+	0.784833i	0.738821	+	0.673902i	$0.235383\pi$
$173$	−3.35410	+	10.3229i	−0.255008	+	0.784833i	−0.993828	+	0.110931i	$0.964617\pi$
$174$		0			0
$175$	−23.4721			−1.77433
$176$		0			0
$177$	−2.85410			−0.214527
$178$		0			0
$179$	2.66312	−	8.19624i	0.199051	−	0.612616i	−0.800855	−	0.598859i	$-0.795621\pi$
$179$	2.66312	−	8.19624i	0.199051	−	0.612616i	0.999905	−	0.0137566i	$-0.00437900\pi$
$180$		0			0
$181$	6.09017	−	4.42477i	0.452679	−	0.328890i	−0.337974	−	0.941156i	$-0.609742\pi$
$181$	6.09017	−	4.42477i	0.452679	−	0.328890i	0.790652	+	0.612265i	$0.209742\pi$
$182$		0			0
$183$	−3.47214	−	10.6861i	−0.256668	−	0.789942i
$184$		0			0
$185$	32.6525	+	23.7234i	2.40066	+	1.74418i
$186$		0			0
$187$	−19.7082	+	8.50651i	−1.44121	+	0.622057i
$188$		0			0
$189$	1.92705	+	1.40008i	0.140172	+	0.101841i
$190$		0			0
$191$	−4.18034	−	12.8658i	−0.302479	−	0.930934i	−0.980606	−	0.195989i	$-0.937208\pi$
$191$	−4.18034	−	12.8658i	−0.302479	−	0.930934i	0.678127	−	0.734945i	$-0.262792\pi$
$192$		0			0
$193$	12.3992	−	9.00854i	0.892513	−	0.648449i	−0.0440190	−	0.999031i	$-0.514016\pi$
$193$	12.3992	−	9.00854i	0.892513	−	0.648449i	0.936532	+	0.350582i	$0.114016\pi$
$194$		0			0
$195$	−1.47214	+	4.53077i	−0.105422	+	0.324455i
$196$		0			0
$197$	−5.09017			−0.362660			−0.181330	−	0.983422i	$-0.558040\pi$
$197$	−5.09017			−0.362660			−0.181330	+	0.983422i	$0.558040\pi$
$198$		0			0
$199$	−19.8541			−1.40742			−0.703710	−	0.710487i	$-0.748475\pi$
$199$	−19.8541			−1.40742			−0.703710	+	0.710487i	$0.748475\pi$
$200$		0			0
$201$	−1.23607	+	3.80423i	−0.0871855	+	0.268329i
$202$		0			0
$203$	−5.04508	+	3.66547i	−0.354096	+	0.257265i
$204$		0			0
$205$	−1.47214	−	4.53077i	−0.102818	−	0.316443i
$206$		0			0
$207$	1.00000	+	0.726543i	0.0695048	+	0.0504982i
$208$		0			0
$209$	−2.09017	+	3.52671i	−0.144580	+	0.243948i
$210$		0			0
$211$	21.5623	+	15.6659i	1.48441	+	1.07849i	0.976102	+	0.217312i	$0.0697289\pi$
$211$	21.5623	+	15.6659i	1.48441	+	1.07849i	0.508308	+	0.861175i	$0.330271\pi$
$212$		0			0
$213$	−1.09017	−	3.35520i	−0.0746972	−	0.229894i
$214$		0			0
$215$	−3.85410	+	2.80017i	−0.262848	+	0.190970i
$216$		0			0
$217$	4.69756	−	14.4576i	0.318891	−	0.981446i
$218$		0			0
$219$	4.32624			0.292340
$220$		0			0
$221$	8.00000			0.538138
$222$		0			0
$223$	4.04508	−	12.4495i	0.270879	−	0.833680i	−0.719402	−	0.694594i	$-0.755584\pi$
$223$	4.04508	−	12.4495i	0.270879	−	0.833680i	0.990280	−	0.139085i	$-0.0444162\pi$
$224$		0			0
$225$	−7.97214	+	5.79210i	−0.531476	+	0.386140i
$226$		0			0
$227$	4.28115	+	13.1760i	0.284150	+	0.874524i	0.986652	+	0.162842i	$0.0520662\pi$
$227$	4.28115	+	13.1760i	0.284150	+	0.874524i	−0.702502	+	0.711682i	$0.747934\pi$
$228$		0			0
$229$	−4.09017	−	2.97168i	−0.270286	−	0.196374i	0.444383	−	0.895837i	$-0.353423\pi$
$229$	−4.09017	−	2.97168i	−0.270286	−	0.196374i	−0.714669	+	0.699462i	$0.753423\pi$
$230$		0			0
$231$	−7.70820	−	1.73060i	−0.507163	−	0.113865i
$232$		0			0
$233$	−7.23607	−	5.25731i	−0.474051	−	0.344418i	0.324967	−	0.945725i	$-0.394647\pi$
$233$	−7.23607	−	5.25731i	−0.474051	−	0.344418i	−0.799018	+	0.601307i	$0.794647\pi$
$234$		0			0
$235$	−7.70820	−	23.7234i	−0.502828	−	1.54754i
$236$		0			0
$237$	5.11803	−	3.71847i	0.332452	−	0.241541i
$238$		0			0
$239$	2.32624	−	7.15942i	0.150472	−	0.463105i	−0.847202	−	0.531271i	$-0.821715\pi$
$239$	2.32624	−	7.15942i	0.150472	−	0.463105i	0.997674	+	0.0681660i	$0.0217147\pi$
$240$		0			0
$241$	−22.5623			−1.45337			−0.726683	−	0.686973i	$-0.758939\pi$
$241$	−22.5623			−1.45337			−0.726683	+	0.686973i	$0.758939\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	1.57953	−	4.86128i	0.100912	−	0.310576i
$246$		0			0
$247$	1.23607	−	0.898056i	0.0786491	−	0.0571419i
$248$		0			0
$249$	5.04508	+	15.5272i	0.319719	+	0.983995i
$250$		0			0
$251$	−2.97214	−	2.15938i	−0.187600	−	0.136299i	0.490021	−	0.871710i	$-0.336989\pi$
$251$	−2.97214	−	2.15938i	−0.187600	−	0.136299i	−0.677621	+	0.735411i	$0.736989\pi$
$252$		0			0
$253$	−4.00000	−	0.898056i	−0.251478	−	0.0564603i
$254$		0			0
$255$	20.1803	+	14.6619i	1.26374	+	0.918162i
$256$		0			0
$257$	−7.47214	−	22.9969i	−0.466099	−	1.43451i	−0.857595	−	0.514326i	$-0.828042\pi$
$257$	−7.47214	−	22.9969i	−0.466099	−	1.43451i	0.391496	−	0.920180i	$-0.371958\pi$
$258$		0			0
$259$	20.1803	−	14.6619i	1.25395	−	0.911045i
$260$		0			0
$261$	−0.809017	+	2.48990i	−0.0500769	+	0.154121i
$262$		0			0
$263$	5.70820			0.351983			0.175991	−	0.984392i	$-0.443687\pi$
$263$	5.70820			0.351983			0.175991	+	0.984392i	$0.443687\pi$
$264$		0			0
$265$	−11.0000			−0.675725
$266$		0			0
$267$	0.527864	−	1.62460i	0.0323048	−	0.0994238i
$268$		0			0
$269$	−12.0902	+	8.78402i	−0.737151	+	0.535571i	−0.891817	−	0.452395i	$-0.850570\pi$
$269$	−12.0902	+	8.78402i	−0.737151	+	0.535571i	0.154667	+	0.987967i	$0.450570\pi$
$270$		0			0
$271$	1.05573	+	3.24920i	0.0641309	+	0.197375i	0.977988	−	0.208662i	$-0.0669107\pi$
$271$	1.05573	+	3.24920i	0.0641309	+	0.197375i	−0.913857	+	0.406036i	$0.866911\pi$
$272$		0			0
$273$	2.38197	+	1.73060i	0.144163	+	0.104741i
$274$		0			0
$275$	16.6631	−	28.1154i	1.00482	−	1.69542i
$276$		0			0
$277$	23.5623	+	17.1190i	1.41572	+	1.02858i	0.992459	+	0.122575i	$0.0391152\pi$
$277$	23.5623	+	17.1190i	1.41572	+	1.02858i	0.423262	+	0.906007i	$0.360885\pi$
$278$		0			0
$279$	−1.97214	−	6.06961i	−0.118069	−	0.363378i
$280$		0			0
$281$	13.8541	−	10.0656i	0.826466	−	0.600463i	−0.0920910	−	0.995751i	$-0.529355\pi$
$281$	13.8541	−	10.0656i	0.826466	−	0.600463i	0.918557	+	0.395288i	$0.129355\pi$
$282$		0			0
$283$	−3.67376	+	11.3067i	−0.218382	+	0.672112i	0.780514	+	0.625139i	$0.214958\pi$
$283$	−3.67376	+	11.3067i	−0.218382	+	0.672112i	−0.998896	+	0.0469734i	$0.985042\pi$
$284$		0			0
$285$	4.76393			0.282191
$286$		0			0
$287$	−2.94427			−0.173795
$288$		0			0
$289$	7.69098	−	23.6704i	0.452411	−	1.39238i
$290$		0			0
$291$	3.50000	−	2.54290i	0.205174	−	0.149067i
$292$		0			0
$293$	−7.40983	−	22.8051i	−0.432887	−	1.33229i	−0.895237	−	0.445591i	$-0.852994\pi$
$293$	−7.40983	−	22.8051i	−0.432887	−	1.33229i	0.462350	−	0.886698i	$-0.347006\pi$
$294$		0			0
$295$	−8.89919	−	6.46564i	−0.518131	−	0.376444i
$296$		0			0
$297$	−3.04508	+	1.31433i	−0.176694	+	0.0762650i
$298$		0			0
$299$	1.23607	+	0.898056i	0.0714837	+	0.0519359i
$300$		0			0
$301$	0.909830	+	2.80017i	0.0524417	+	0.161399i
$302$		0			0
$303$	11.8262	−	8.59226i	0.679400	−	0.493613i
$304$		0			0
$305$	13.3820	−	41.1855i	0.766249	−	2.35827i
$306$		0			0
$307$	−14.6525			−0.836261			−0.418130	−	0.908387i	$-0.637315\pi$
$307$	−14.6525			−0.836261			−0.418130	+	0.908387i	$0.637315\pi$
$308$		0			0
$309$	17.0344			0.969056
$310$		0			0
$311$	−3.67376	+	11.3067i	−0.208320	+	0.641143i	0.791241	+	0.611505i	$0.209435\pi$
$311$	−3.67376	+	11.3067i	−0.208320	+	0.641143i	−0.999561	+	0.0296381i	$0.990565\pi$
$312$		0			0
$313$	−17.6803	+	12.8455i	−0.999352	+	0.726072i	−0.961949	−	0.273229i	$-0.911908\pi$
$313$	−17.6803	+	12.8455i	−0.999352	+	0.726072i	−0.0374028	+	0.999300i	$0.511908\pi$
$314$		0			0
$315$	2.83688	+	8.73102i	0.159840	+	0.491937i
$316$		0			0
$317$	−12.8541	−	9.33905i	−0.721958	−	0.524533i	0.165051	−	0.986285i	$-0.447221\pi$
$317$	−12.8541	−	9.33905i	−0.721958	−	0.524533i	−0.887009	+	0.461752i	$0.847221\pi$
$318$		0			0
$319$	−0.809017	−	8.64527i	−0.0452963	−	0.484042i
$320$		0			0
$321$	6.16312	+	4.47777i	0.343992	+	0.249925i
$322$		0			0
$323$	−2.47214	−	7.60845i	−0.137553	−	0.423346i
$324$		0			0
$325$	−9.85410	+	7.15942i	−0.546607	+	0.397133i
$326$		0			0
$327$	−2.90983	+	8.95554i	−0.160914	+	0.495242i
$328$		0			0
$329$	−15.4164			−0.849934
$330$		0			0
$331$	8.94427			0.491622			0.245811	−	0.969318i	$-0.420946\pi$
$331$	8.94427			0.491622			0.245811	+	0.969318i	$0.420946\pi$
$332$		0			0
$333$	3.23607	−	9.95959i	0.177335	−	0.545782i
$334$		0			0
$335$	−12.4721	+	9.06154i	−0.681426	+	0.495085i
$336$		0			0
$337$	−3.38197	−	10.4086i	−0.184227	−	0.566994i	0.815707	−	0.578466i	$-0.196348\pi$
$337$	−3.38197	−	10.4086i	−0.184227	−	0.566994i	−0.999934	+	0.0114719i	$0.996348\pi$
$338$		0			0
$339$	2.85410	+	2.07363i	0.155014	+	0.112624i
$340$		0			0
$341$	13.9828	+	15.8904i	0.757210	+	0.860516i
$342$		0			0
$343$	−16.0451	−	11.6574i	−0.866353	−	0.629442i
$344$		0			0
$345$	1.47214	+	4.53077i	0.0792571	+	0.243928i
$346$		0			0
$347$	4.16312	−	3.02468i	0.223488	−	0.162373i	−0.470407	−	0.882449i	$-0.655893\pi$
$347$	4.16312	−	3.02468i	0.223488	−	0.162373i	0.693895	+	0.720076i	$0.255893\pi$
$348$		0			0
$349$	−2.70820	+	8.33499i	−0.144967	+	0.446162i	−0.997007	−	0.0773148i	$-0.975365\pi$
$349$	−2.70820	+	8.33499i	−0.144967	+	0.446162i	0.852040	+	0.523477i	$0.175365\pi$
$350$		0			0
$351$	1.23607			0.0659764
$352$		0			0
$353$	27.5967			1.46883			0.734413	−	0.678702i	$-0.237457\pi$
$353$	27.5967			1.46883			0.734413	+	0.678702i	$0.237457\pi$
$354$		0			0
$355$	4.20163	−	12.9313i	0.222999	−	0.686321i
$356$		0			0
$357$	12.4721	−	9.06154i	0.660095	−	0.479587i
$358$		0			0
$359$	−5.32624	−	16.3925i	−0.281108	−	0.865162i	−0.987538	−	0.157379i	$-0.949696\pi$
$359$	−5.32624	−	16.3925i	−0.281108	−	0.865162i	0.706430	−	0.707783i	$-0.250304\pi$
$360$		0			0
$361$	14.1353	+	10.2699i	0.743961	+	0.540519i
$362$		0			0
$363$	7.54508	−	8.00448i	0.396014	−	0.420126i
$364$		0			0
$365$	13.4894	+	9.80059i	0.706065	+	0.512986i
$366$		0			0
$367$	−0.156541	−	0.481784i	−0.00817138	−	0.0251489i	0.946888	−	0.321564i	$-0.104209\pi$
$367$	−0.156541	−	0.481784i	−0.00817138	−	0.0251489i	−0.955059	+	0.296416i	$0.904209\pi$
$368$		0			0
$369$	−1.00000	+	0.726543i	−0.0520579	+	0.0378223i
$370$		0			0
$371$	−2.10081	+	6.46564i	−0.109069	+	0.335679i
$372$		0			0
$373$	−18.4721			−0.956451			−0.478225	−	0.878237i	$-0.658720\pi$
$373$	−18.4721			−0.956451			−0.478225	+	0.878237i	$0.658720\pi$
$374$		0			0
$375$	−18.7082			−0.966087
$376$		0			0
$377$	−1.00000	+	3.07768i	−0.0515026	+	0.158509i
$378$		0			0
$379$	−7.85410	+	5.70634i	−0.403438	+	0.293115i	−0.770940	−	0.636908i	$-0.780213\pi$
$379$	−7.85410	+	5.70634i	−0.403438	+	0.293115i	0.367502	+	0.930023i	$0.380213\pi$
$380$		0			0
$381$	−3.70820	−	11.4127i	−0.189977	−	0.584689i
$382$		0			0
$383$	7.09017	+	5.15131i	0.362291	+	0.263220i	0.754007	−	0.656866i	$-0.228118\pi$
$383$	7.09017	+	5.15131i	0.362291	+	0.263220i	−0.391716	+	0.920086i	$0.628118\pi$
$384$		0			0
$385$	−20.1140	−	22.8581i	−1.02510	−	1.16496i
$386$		0			0
$387$	1.00000	+	0.726543i	0.0508329	+	0.0369322i
$388$		0			0
$389$	6.50658	+	20.0252i	0.329897	+	1.01532i	0.969182	+	0.246347i	$0.0792304\pi$
$389$	6.50658	+	20.0252i	0.329897	+	1.01532i	−0.639285	+	0.768970i	$0.720770\pi$
$390$		0			0
$391$	6.47214	−	4.70228i	0.327310	−	0.237805i
$392$		0			0
$393$	−5.64590	+	17.3763i	−0.284798	+	0.876518i
$394$		0			0
$395$	24.3820			1.22679
$396$		0			0
$397$	−25.8885			−1.29931			−0.649654	−	0.760230i	$-0.725086\pi$
$397$	−25.8885			−1.29931			−0.649654	+	0.760230i	$0.725086\pi$
$398$		0			0
$399$	0.909830	−	2.80017i	0.0455485	−	0.140184i
$400$		0			0
$401$	−19.1803	+	13.9353i	−0.957820	+	0.695897i	−0.952644	−	0.304089i	$-0.901648\pi$
$401$	−19.1803	+	13.9353i	−0.957820	+	0.695897i	−0.00517693	+	0.999987i	$0.501648\pi$
$402$		0			0
$403$	−2.43769	−	7.50245i	−0.121430	−	0.373724i
$404$		0			0
$405$	3.11803	+	2.26538i	0.154936	+	0.112568i
$406$		0			0
$407$	3.23607	+	34.5811i	0.160406	+	1.71412i
$408$		0			0
$409$	0.736068	+	0.534785i	0.0363962	+	0.0264434i	0.605835	−	0.795591i	$-0.292839\pi$
$409$	0.736068	+	0.534785i	0.0363962	+	0.0264434i	−0.569438	+	0.822034i	$0.692839\pi$
$410$		0			0
$411$	5.29180	+	16.2865i	0.261025	+	0.803353i
$412$		0			0
$413$	−5.50000	+	3.99598i	−0.270637	+	0.196630i
$414$		0			0
$415$	−19.4443	+	59.8433i	−0.954482	+	2.93759i
$416$		0			0
$417$	−8.76393			−0.429172
$418$		0			0
$419$	−28.9787			−1.41570			−0.707851	−	0.706361i	$-0.750335\pi$
$419$	−28.9787			−1.41570			−0.707851	+	0.706361i	$0.750335\pi$
$420$		0			0
$421$	−1.58359	+	4.87380i	−0.0771796	+	0.237534i	−0.982201	−	0.187831i	$-0.939854\pi$
$421$	−1.58359	+	4.87380i	−0.0771796	+	0.237534i	0.905022	+	0.425365i	$0.139854\pi$
$422$		0			0
$423$	−5.23607	+	3.80423i	−0.254586	+	0.184968i
$424$		0			0
$425$	19.7082	+	60.6556i	0.955988	+	2.94223i
$426$		0			0
$427$	−21.6525	−	15.7314i	−1.04784	−	0.761298i
$428$		0			0
$429$	−3.76393	+	1.62460i	−0.181724	+	0.0784364i
$430$		0			0
$431$	−2.23607	−	1.62460i	−0.107708	−	0.0782542i	0.532628	−	0.846350i	$-0.321205\pi$
$431$	−2.23607	−	1.62460i	−0.107708	−	0.0782542i	−0.640335	+	0.768095i	$0.721205\pi$
$432$		0			0
$433$	−1.02786	−	3.16344i	−0.0493960	−	0.152025i	0.923316	−	0.384041i	$-0.125468\pi$
$433$	−1.02786	−	3.16344i	−0.0493960	−	0.152025i	−0.972712	+	0.232016i	$0.925468\pi$
$434$		0			0
$435$	−8.16312	+	5.93085i	−0.391392	+	0.284363i
$436$		0			0
$437$	0.472136	−	1.45309i	0.0225853	−	0.0695105i
$438$		0			0
$439$	13.0344			0.622100			0.311050	−	0.950394i	$-0.399319\pi$
$439$	13.0344			0.622100			0.311050	+	0.950394i	$0.399319\pi$
$440$		0			0
$441$	−1.32624			−0.0631542
$442$		0			0
$443$	5.35410	−	16.4782i	0.254381	−	0.782904i	−0.739570	−	0.673080i	$-0.764971\pi$
$443$	5.35410	−	16.4782i	0.254381	−	0.782904i	0.993951	−	0.109825i	$-0.0350289\pi$
$444$		0			0
$445$	5.32624	−	3.86974i	0.252488	−	0.183443i
$446$		0			0
$447$	1.11803	+	3.44095i	0.0528812	+	0.162752i
$448$		0			0
$449$	−0.0901699	−	0.0655123i	−0.00425538	−	0.00309172i	0.585656	−	0.810560i	$-0.300837\pi$
$449$	−0.0901699	−	0.0655123i	−0.00425538	−	0.00309172i	−0.589911	+	0.807468i	$0.700837\pi$
$450$		0			0
$451$	2.09017	−	3.52671i	0.0984223	−	0.166066i
$452$		0			0
$453$	−5.11803	−	3.71847i	−0.240466	−	0.174709i
$454$		0			0
$455$	3.50658	+	10.7921i	0.164391	+	0.505943i
$456$		0			0
$457$	−20.2082	+	14.6821i	−0.945300	+	0.686801i	−0.949691	−	0.313190i	$-0.898602\pi$
$457$	−20.2082	+	14.6821i	−0.945300	+	0.686801i	0.00439065	+	0.999990i	$0.498602\pi$
$458$		0			0
$459$	2.00000	−	6.15537i	0.0933520	−	0.287308i
$460$		0			0
$461$	−12.8328			−0.597684			−0.298842	−	0.954303i	$-0.596600\pi$
$461$	−12.8328			−0.597684			−0.298842	+	0.954303i	$0.596600\pi$
$462$		0			0
$463$	−7.90983			−0.367601			−0.183800	−	0.982964i	$-0.558840\pi$
$463$	−7.90983			−0.367601			−0.183800	+	0.982964i	$0.558840\pi$
$464$		0			0
$465$	7.60081	−	23.3929i	0.352479	−	1.08482i
$466$		0			0
$467$	−0.454915	+	0.330515i	−0.0210510	+	0.0152944i	−0.598261	−	0.801301i	$-0.704141\pi$
$467$	−0.454915	+	0.330515i	−0.0210510	+	0.0152944i	0.577210	+	0.816596i	$0.304141\pi$
$468$		0			0
$469$	2.94427	+	9.06154i	0.135954	+	0.418423i
$470$		0			0
$471$	3.61803	+	2.62866i	0.166710	+	0.121122i
$472$		0			0
$473$	−4.00000	−	0.898056i	−0.183920	−	0.0412927i
$474$		0			0
$475$	9.85410	+	7.15942i	0.452137	+	0.328497i
$476$		0			0
$477$	0.881966	+	2.71441i	0.0403824	+	0.124284i
$478$		0			0
$479$	−2.23607	+	1.62460i	−0.102169	+	0.0742298i	−0.637697	−	0.770288i	$-0.720113\pi$
$479$	−2.23607	+	1.62460i	−0.102169	+	0.0742298i	0.535528	+	0.844517i	$0.320113\pi$
$480$		0			0
$481$	4.00000	−	12.3107i	0.182384	−	0.561321i
$482$		0			0
$483$	2.94427			0.133969
$484$		0			0
$485$	16.6738			0.757117
$486$		0			0
$487$	6.79180	−	20.9030i	0.307766	−	0.947205i	−0.670865	−	0.741579i	$-0.734077\pi$
$487$	6.79180	−	20.9030i	0.307766	−	0.947205i	0.978631	−	0.205626i	$-0.0659230\pi$
$488$		0			0
$489$	10.8541	−	7.88597i	0.490839	−	0.356616i
$490$		0			0
$491$	11.8197	+	36.3772i	0.533414	+	1.64168i	0.747052	+	0.664766i	$0.231469\pi$
$491$	11.8197	+	36.3772i	0.533414	+	1.64168i	−0.213638	+	0.976913i	$0.568531\pi$
$492$		0			0
$493$	13.7082	+	9.95959i	0.617386	+	0.448558i
$494$		0			0
$495$	−12.4721	−	2.80017i	−0.560581	−	0.125858i
$496$		0			0
$497$	−6.79837	−	4.93931i	−0.304949	−	0.221558i
$498$		0			0
$499$	−6.00000	−	18.4661i	−0.268597	−	0.826656i	−0.990843	−	0.135020i	$-0.956890\pi$
$499$	−6.00000	−	18.4661i	−0.268597	−	0.826656i	0.722246	−	0.691636i	$-0.243110\pi$
$500$		0			0
$501$	2.23607	−	1.62460i	0.0999001	−	0.0725817i
$502$		0			0
$503$	12.4721	−	38.3853i	0.556105	−	1.71152i	−0.136902	−	0.990585i	$-0.543715\pi$
$503$	12.4721	−	38.3853i	0.556105	−	1.71152i	0.693007	−	0.720931i	$-0.256285\pi$
$504$		0			0
$505$	56.3394			2.50707
$506$		0			0
$507$	−11.4721			−0.509495
$508$		0			0
$509$	8.59017	−	26.4378i	0.380753	−	1.17184i	−0.558762	−	0.829328i	$-0.688724\pi$
$509$	8.59017	−	26.4378i	0.380753	−	1.17184i	0.939515	−	0.342508i	$-0.111276\pi$
$510$		0			0
$511$	8.33688	−	6.05710i	0.368802	−	0.267950i
$512$		0			0
$513$	−0.381966	−	1.17557i	−0.0168642	−	0.0519027i
$514$		0			0
$515$	53.1140	+	38.5896i	2.34048	+	1.70046i
$516$		0			0
$517$	10.9443	−	18.4661i	0.481329	−	0.812138i
$518$		0			0
$519$	8.78115	+	6.37988i	0.385450	+	0.280046i
$520$		0			0
$521$	1.41641	+	4.35926i	0.0620540	+	0.190982i	0.977277	−	0.211964i	$-0.0679860\pi$
$521$	1.41641	+	4.35926i	0.0620540	+	0.190982i	−0.915223	+	0.402947i	$0.867986\pi$
$522$		0			0
$523$	−23.9443	+	17.3965i	−1.04701	+	0.760697i	−0.971642	−	0.236459i	$-0.924013\pi$
$523$	−23.9443	+	17.3965i	−1.04701	+	0.760697i	−0.0753683	+	0.997156i	$0.524013\pi$
$524$		0			0
$525$	−7.25329	+	22.3233i	−0.316559	+	0.974270i
$526$		0			0
$527$	−41.3050			−1.79927
$528$		0			0
$529$	−21.4721			−0.933571
$530$		0			0
$531$	−0.881966	+	2.71441i	−0.0382741	+	0.117795i
$532$		0			0
$533$	−1.23607	+	0.898056i	−0.0535400	+	0.0388991i
$534$		0			0
$535$	9.07295	+	27.9237i	0.392258	+	1.20725i
$536$		0			0
$537$	−6.97214	−	5.06555i	−0.300870	−	0.218595i
$538$		0			0
$539$	4.03851	−	1.74311i	0.173951	−	0.0750811i
$540$		0			0
$541$	−13.3262	−	9.68208i	−0.572940	−	0.416265i	0.263232	−	0.964733i	$-0.415211\pi$
$541$	−13.3262	−	9.68208i	−0.572940	−	0.416265i	−0.836172	+	0.548467i	$0.815211\pi$
$542$		0			0
$543$	−2.32624	−	7.15942i	−0.0998284	−	0.307240i
$544$		0			0
$545$	−29.3607	+	21.3318i	−1.25767	+	0.913753i
$546$		0			0
$547$	1.29180	−	3.97574i	0.0552332	−	0.169990i	−0.919634	−	0.392776i	$-0.871515\pi$
$547$	1.29180	−	3.97574i	0.0552332	−	0.169990i	0.974868	+	0.222785i	$0.0715149\pi$
$548$		0			0
$549$	−11.2361			−0.479544
$550$		0			0
$551$	3.23607			0.137861
$552$		0			0
$553$	4.65654	−	14.3314i	0.198016	−	0.609431i
$554$		0			0
$555$	32.6525	−	23.7234i	1.38602	−	1.00700i
$556$		0			0
$557$	−4.00658	−	12.3310i	−0.169764	−	0.522480i	0.829592	−	0.558371i	$-0.188573\pi$
$557$	−4.00658	−	12.3310i	−0.169764	−	0.522480i	−0.999356	+	0.0358903i	$0.988573\pi$
$558$		0			0
$559$	1.23607	+	0.898056i	0.0522801	+	0.0379837i
$560$		0			0
$561$	2.00000	+	21.3723i	0.0844401	+	0.902338i
$562$		0			0
$563$	5.52786	+	4.01623i	0.232972	+	0.169264i	0.698146	−	0.715955i	$-0.254008\pi$
$563$	5.52786	+	4.01623i	0.232972	+	0.169264i	−0.465175	+	0.885219i	$0.654008\pi$
$564$		0			0
$565$	4.20163	+	12.9313i	0.176764	+	0.544023i
$566$		0			0
$567$	1.92705	−	1.40008i	0.0809285	−	0.0587980i
$568$		0			0
$569$	−5.20163	+	16.0090i	−0.218064	+	0.671130i	0.780858	+	0.624708i	$0.214782\pi$
$569$	−5.20163	+	16.0090i	−0.218064	+	0.671130i	−0.998922	+	0.0464224i	$0.985218\pi$
$570$		0			0
$571$	39.5967			1.65707			0.828536	−	0.559936i	$-0.189174\pi$
$571$	39.5967			1.65707			0.828536	+	0.559936i	$0.189174\pi$
$572$		0			0
$573$	−13.5279			−0.565135
$574$		0			0
$575$	−3.76393	+	11.5842i	−0.156967	+	0.483094i
$576$		0			0
$577$	3.30902	−	2.40414i	0.137756	−	0.100086i	−0.516773	−	0.856122i	$-0.672867\pi$
$577$	3.30902	−	2.40414i	0.137756	−	0.100086i	0.654529	+	0.756037i	$0.272867\pi$
$578$		0			0
$579$	−4.73607	−	14.5761i	−0.196824	−	0.605763i
$580$		0			0
$581$	31.4615	+	22.8581i	1.30524	+	0.948314i
$582$		0			0
$583$	−6.25329	−	7.10642i	−0.258985	−	0.294318i
$584$		0			0
$585$	3.85410	+	2.80017i	0.159348	+	0.115773i
$586$		0			0
$587$	3.98936	+	12.2780i	0.164658	+	0.506766i	0.999011	−	0.0444648i	$-0.0141582\pi$
$587$	3.98936	+	12.2780i	0.164658	+	0.506766i	−0.834353	+	0.551231i	$0.814158\pi$
$588$		0			0
$589$	−6.38197	+	4.63677i	−0.262964	+	0.191055i
$590$		0			0
$591$	−1.57295	+	4.84104i	−0.0647025	+	0.199134i
$592$		0			0
$593$	15.5279			0.637653			0.318826	−	0.947813i	$-0.396711\pi$
$593$	15.5279			0.637653			0.318826	+	0.947813i	$0.396711\pi$
$594$		0			0
$595$	59.4164			2.43584
$596$		0			0
$597$	−6.13525	+	18.8824i	−0.251099	+	0.772804i
$598$		0			0
$599$	−29.4164	+	21.3723i	−1.20192	+	0.873247i	−0.994472	−	0.104998i	$-0.966516\pi$
$599$	−29.4164	+	21.3723i	−1.20192	+	0.873247i	−0.207449	+	0.978246i	$0.566516\pi$
$600$		0			0
$601$	5.79180	+	17.8253i	0.236252	+	0.727110i	0.996953	+	0.0780068i	$0.0248556\pi$
$601$	5.79180	+	17.8253i	0.236252	+	0.727110i	−0.760701	+	0.649103i	$0.775144\pi$
$602$		0			0
$603$	3.23607	+	2.35114i	0.131783	+	0.0957459i
$604$		0			0
$605$	41.6591	−	7.86572i	1.69368	−	0.319787i
$606$		0			0
$607$	−38.6525	−	28.0827i	−1.56886	−	1.13984i	−0.928242	−	0.371977i	$-0.878680\pi$
$607$	−38.6525	−	28.0827i	−1.56886	−	1.13984i	−0.640614	−	0.767863i	$-0.721320\pi$
$608$		0			0
$609$	1.92705	+	5.93085i	0.0780880	+	0.240330i
$610$		0			0
$611$	−6.47214	+	4.70228i	−0.261835	+	0.190234i
$612$		0			0
$613$	−8.56231	+	26.3521i	−0.345828	+	1.06435i	0.615311	+	0.788285i	$0.289031\pi$
$613$	−8.56231	+	26.3521i	−0.345828	+	1.06435i	−0.961139	+	0.276065i	$0.910969\pi$
$614$		0			0
$615$	−4.76393			−0.192100
$616$		0			0
$617$	−43.7082			−1.75963			−0.879813	−	0.475320i	$-0.842332\pi$
$617$	−43.7082			−1.75963			−0.879813	+	0.475320i	$0.842332\pi$
$618$		0			0
$619$	−11.5279	+	35.4791i	−0.463344	+	1.42603i	0.397709	+	0.917511i	$0.369805\pi$
$619$	−11.5279	+	35.4791i	−0.463344	+	1.42603i	−0.861053	+	0.508515i	$0.830195\pi$
$620$		0			0
$621$	1.00000	−	0.726543i	0.0401286	−	0.0291551i
$622$		0			0
$623$	−1.25735	−	3.86974i	−0.0503748	−	0.155038i
$624$		0			0
$625$	−18.4721	−	13.4208i	−0.738885	−	0.536832i
$626$		0			0
$627$	2.70820	+	3.07768i	0.108155	+	0.122911i
$628$		0			0
$629$	−54.8328	−	39.8384i	−2.18633	−	1.58846i
$630$		0			0
$631$	7.37132	+	22.6866i	0.293448	+	0.903139i	0.983738	+	0.179607i	$0.0574826\pi$
$631$	7.37132	+	22.6866i	0.293448	+	0.903139i	−0.690291	+	0.723532i	$0.742517\pi$
$632$		0			0
$633$	21.5623	−	15.6659i	0.857025	−	0.622665i
$634$		0			0
$635$	14.2918	−	43.9856i	0.567153	−	1.74552i
$636$		0			0
$637$	−1.63932			−0.0649522
$638$		0			0
$639$	−3.52786			−0.139560
$640$		0			0
$641$	2.12461	−	6.53888i	0.0839171	−	0.258270i	−0.900290	−	0.435290i	$-0.856646\pi$
$641$	2.12461	−	6.53888i	0.0839171	−	0.258270i	0.984207	+	0.177020i	$0.0566457\pi$
$642$		0			0
$643$	−5.61803	+	4.08174i	−0.221554	+	0.160968i	−0.693026	−	0.720913i	$-0.743723\pi$
$643$	−5.61803	+	4.08174i	−0.221554	+	0.160968i	0.471472	+	0.881881i	$0.343723\pi$
$644$		0			0
$645$	1.47214	+	4.53077i	0.0579653	+	0.178399i
$646$		0			0
$647$	−34.8885	−	25.3480i	−1.37161	−	0.996533i	−0.997609	−	0.0691047i	$-0.977986\pi$
$647$	−34.8885	−	25.3480i	−1.37161	−	0.996533i	−0.374001	−	0.927428i	$-0.622014\pi$
$648$		0			0
$649$	−0.881966	−	9.42481i	−0.0346202	−	0.369956i
$650$		0			0
$651$	−12.2984	−	8.93529i	−0.482011	−	0.350202i
$652$		0			0
$653$	−8.60739	−	26.4908i	−0.336833	−	1.03667i	−0.965812	−	0.259244i	$-0.916527\pi$
$653$	−8.60739	−	26.4908i	−0.336833	−	1.03667i	0.628979	−	0.777423i	$-0.283473\pi$
$654$		0			0
$655$	−56.9681	+	41.3897i	−2.22593	+	1.61723i
$656$		0			0
$657$	1.33688	−	4.11450i	0.0521567	−	0.160522i
$658$		0			0
$659$	−49.8541			−1.94204			−0.971020	−	0.238998i	$-0.923181\pi$
$659$	−49.8541			−1.94204			−0.971020	+	0.238998i	$0.923181\pi$
$660$		0			0
$661$	28.1803			1.09609			0.548044	−	0.836449i	$-0.315373\pi$
$661$	28.1803			1.09609			0.548044	+	0.836449i	$0.315373\pi$
$662$		0			0
$663$	2.47214	−	7.60845i	0.0960098	−	0.295488i
$664$		0			0
$665$	9.18034	−	6.66991i	0.355998	−	0.258648i
$666$		0			0
$667$	1.00000	+	3.07768i	0.0387202	+	0.119168i
$668$		0			0
$669$	−10.5902	−	7.69421i	−0.409440	−	0.297475i
$670$		0			0
$671$	34.2148	−	14.7679i	1.32085	−	0.570108i
$672$		0			0
$673$	29.1525	+	21.1805i	1.12375	+	0.816449i	0.984773	−	0.173847i	$-0.0556200\pi$
$673$	29.1525	+	21.1805i	1.12375	+	0.816449i	0.138973	+	0.990296i	$0.455620\pi$
$674$		0			0
$675$	3.04508	+	9.37181i	0.117205	+	0.360721i
$676$		0			0
$677$	2.01722	−	1.46560i	0.0775281	−	0.0563275i	−0.548346	−	0.836252i	$-0.684742\pi$
$677$	2.01722	−	1.46560i	0.0775281	−	0.0563275i	0.625874	+	0.779924i	$0.284742\pi$
$678$		0			0
$679$	3.18441	−	9.80059i	0.122206	−	0.376112i
$680$		0			0
$681$	13.8541			0.530890
$682$		0			0
$683$	−3.25735			−0.124639			−0.0623196	−	0.998056i	$-0.519850\pi$
$683$	−3.25735			−0.124639			−0.0623196	+	0.998056i	$0.519850\pi$
$684$		0			0
$685$	−20.3951	+	62.7697i	−0.779258	+	2.39831i
$686$		0			0
$687$	−4.09017	+	2.97168i	−0.156050	+	0.113377i
$688$		0			0
$689$	1.09017	+	3.35520i	0.0415322	+	0.127823i
$690$		0			0
$691$	−11.0902	−	8.05748i	−0.421890	−	0.306521i	0.356508	−	0.934292i	$-0.383967\pi$
$691$	−11.0902	−	8.05748i	−0.421890	−	0.306521i	−0.778398	+	0.627771i	$0.783967\pi$
$692$		0			0
$693$	−4.02786	+	6.79615i	−0.153006	+	0.258165i
$694$		0			0
$695$	−27.3262	−	19.8537i	−1.03654	−	0.753093i
$696$		0			0
$697$	2.47214	+	7.60845i	0.0936388	+	0.288191i
$698$		0			0
$699$	−7.23607	+	5.25731i	−0.273693	+	0.198850i
$700$		0			0
$701$	5.85410	−	18.0171i	0.221106	−	0.680495i	−0.777557	−	0.628812i	$-0.783541\pi$
$701$	5.85410	−	18.0171i	0.221106	−	0.680495i	0.998664	−	0.0516832i	$-0.0164586\pi$
$702$		0			0
$703$	−12.9443			−0.488202
$704$		0			0
$705$	−24.9443			−0.939456
$706$		0			0
$707$	10.7599	−	33.1155i	0.404666	−	1.24544i
$708$		0			0
$709$	33.1803	−	24.1069i	1.24611	−	0.905355i	0.248124	−	0.968728i	$-0.420186\pi$
$709$	33.1803	−	24.1069i	1.24611	−	0.905355i	0.997990	+	0.0633736i	$0.0201860\pi$
$710$		0			0
$711$	−1.95492	−	6.01661i	−0.0733150	−	0.225640i
$712$		0			0
$713$	−6.38197	−	4.63677i	−0.239007	−	0.173648i
$714$		0			0
$715$	−15.4164	−	3.46120i	−0.576541	−	0.129442i
$716$		0			0
$717$	−6.09017	−	4.42477i	−0.227442	−	0.165246i
$718$		0			0
$719$	2.14590	+	6.60440i	0.0800285	+	0.246302i	0.983064	−	0.183264i	$-0.0586664\pi$
$719$	2.14590	+	6.60440i	0.0800285	+	0.246302i	−0.903035	+	0.429567i	$0.858666\pi$
$720$		0			0
$721$	32.8262	−	23.8497i	1.22251	−	0.888208i
$722$		0			0
$723$	−6.97214	+	21.4580i	−0.259297	+	0.798033i
$724$		0			0
$725$	−25.7984			−0.958128
$726$		0			0
$727$	23.4164			0.868466			0.434233	−	0.900800i	$-0.357019\pi$
$727$	23.4164			0.868466			0.434233	+	0.900800i	$0.357019\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	6.47214	−	4.70228i	0.239381	−	0.173920i
$732$		0			0
$733$	−9.36068	−	28.8092i	−0.345745	−	1.06409i	−0.961184	−	0.275908i	$-0.911021\pi$
$733$	−9.36068	−	28.8092i	−0.345745	−	1.06409i	0.615439	−	0.788184i	$-0.288979\pi$
$734$		0			0
$735$	−4.13525	−	3.00444i	−0.152531	−	0.110820i
$736$		0			0
$737$	−12.9443	−	2.90617i	−0.476808	−	0.107050i
$738$		0			0
$739$	26.6525	+	19.3642i	0.980427	+	0.712322i	0.957804	−	0.287422i	$-0.0927982\pi$
$739$	26.6525	+	19.3642i	0.980427	+	0.712322i	0.0226231	+	0.999744i	$0.492798\pi$
$740$		0			0
$741$	−0.472136	−	1.45309i	−0.0173443	−	0.0533804i
$742$		0			0
$743$	27.3262	−	19.8537i	1.00250	−	0.728361i	0.0398791	−	0.999205i	$-0.487303\pi$
$743$	27.3262	−	19.8537i	1.00250	−	0.728361i	0.962623	+	0.270844i	$0.0873027\pi$
$744$		0			0
$745$	−4.30902	+	13.2618i	−0.157870	+	0.485874i
$746$		0			0
$747$	16.3262			0.597346
$748$		0			0
$749$	18.1459			0.663037
$750$		0			0
$751$	14.1803	−	43.6426i	0.517448	−	1.59254i	−0.261335	−	0.965248i	$-0.584163\pi$
$751$	14.1803	−	43.6426i	0.517448	−	1.59254i	0.778783	−	0.627293i	$-0.215837\pi$
$752$		0			0
$753$	−2.97214	+	2.15938i	−0.108311	+	0.0786923i
$754$		0			0
$755$	−7.53444	−	23.1886i	−0.274206	−	0.843921i
$756$		0			0
$757$	−29.5623	−	21.4783i	−1.07446	−	0.780641i	−0.0977516	−	0.995211i	$-0.531165\pi$
$757$	−29.5623	−	21.4783i	−1.07446	−	0.780641i	−0.976709	+	0.214570i	$0.931165\pi$
$758$		0			0
$759$	−2.09017	+	3.52671i	−0.0758684	+	0.128012i
$760$		0			0
$761$	−19.1803	−	13.9353i	−0.695287	−	0.505155i	0.183107	−	0.983093i	$-0.441385\pi$
$761$	−19.1803	−	13.9353i	−0.695287	−	0.505155i	−0.878394	+	0.477938i	$0.841385\pi$
$762$		0			0
$763$	6.93112	+	21.3318i	0.250923	+	0.772262i
$764$		0			0
$765$	20.1803	−	14.6619i	0.729622	−	0.530101i
$766$		0			0
$767$	−1.09017	+	3.35520i	−0.0393638	+	0.121149i
$768$		0			0
$769$	29.2705			1.05552			0.527761	−	0.849393i	$-0.323032\pi$
$769$	29.2705			1.05552			0.527761	+	0.849393i	$0.323032\pi$
$770$		0			0
$771$	−24.1803			−0.870834
$772$		0			0
$773$	−8.80902	+	27.1114i	−0.316838	+	0.975128i	0.658153	+	0.752884i	$0.271338\pi$
$773$	−8.80902	+	27.1114i	−0.316838	+	0.975128i	−0.974991	+	0.222244i	$0.928662\pi$
$774$		0			0
$775$	50.8779	−	36.9650i	1.82759	−	1.32782i
$776$		0			0
$777$	−7.70820	−	23.7234i	−0.276530	−	0.851073i
$778$		0			0
$779$	1.23607	+	0.898056i	0.0442867	+	0.0321762i
$780$		0			0
$781$	10.7426	−	4.63677i	0.384402	−	0.165917i
$782$		0			0
$783$	2.11803	+	1.53884i	0.0756924	+	0.0549937i
$784$		0			0
$785$	5.32624	+	16.3925i	0.190102	+	0.585073i
$786$		0			0
$787$	38.4164	−	27.9112i	1.36940	−	0.994925i	0.371613	−	0.928388i	$-0.378805\pi$
$787$	38.4164	−	27.9112i	1.36940	−	0.994925i	0.997784	−	0.0665375i	$-0.0211952\pi$
$788$		0			0
$789$	1.76393	−	5.42882i	0.0627976	−	0.193271i
$790$		0			0
$791$	8.40325			0.298785
$792$		0			0
$793$	−13.8885			−0.493197
$794$		0			0
$795$	−3.39919	+	10.4616i	−0.120557	+	0.371035i
$796$		0			0
$797$	16.4894	−	11.9802i	0.584083	−	0.424361i	−0.256111	−	0.966647i	$-0.582441\pi$
$797$	16.4894	−	11.9802i	0.584083	−	0.424361i	0.840194	+	0.542286i	$0.182441\pi$
$798$		0			0
$799$	12.9443	+	39.8384i	0.457935	+	1.40938i
$800$		0			0
$801$	−1.38197	−	1.00406i	−0.0488294	−	0.0354766i
$802$		0			0
$803$	1.33688	+	14.2861i	0.0471775	+	0.504145i
$804$		0			0
$805$	9.18034	+	6.66991i	0.323564	+	0.235083i
$806$		0			0
$807$	4.61803	+	14.2128i	0.162562	+	0.500316i
$808$		0			0
$809$	40.6525	−	29.5358i	1.42926	−	1.03842i	0.439112	−	0.898432i	$-0.355293\pi$
$809$	40.6525	−	29.5358i	1.42926	−	1.03842i	0.990153	−	0.139989i	$-0.0447068\pi$
$810$		0			0
$811$	13.9787	−	43.0221i	0.490859	−	1.51071i	−0.332453	−	0.943120i	$-0.607876\pi$
$811$	13.9787	−	43.0221i	0.490859	−	1.51071i	0.823312	−	0.567589i	$-0.192124\pi$
$812$		0			0
$813$	3.41641			0.119819
$814$		0			0
$815$	51.7082			1.81126
$816$		0			0
$817$	0.472136	−	1.45309i	0.0165179	−	0.0508370i
$818$		0			0
$819$	2.38197	−	1.73060i	0.0832326	−	0.0604720i
$820$		0			0
$821$	3.06231	+	9.42481i	0.106875	+	0.328928i	0.990166	−	0.139897i	$-0.0446773\pi$
$821$	3.06231	+	9.42481i	0.106875	+	0.328928i	−0.883291	+	0.468826i	$0.844677\pi$
$822$		0			0
$823$	39.0066	+	28.3399i	1.35968	+	0.987868i	0.998465	+	0.0553871i	$0.0176393\pi$
$823$	39.0066	+	28.3399i	1.35968	+	0.987868i	0.361219	+	0.932481i	$0.382361\pi$
$824$		0			0
$825$	−21.5902	−	24.5357i	−0.751673	−	0.854224i
$826$		0			0
$827$	−40.1976	−	29.2052i	−1.39781	−	1.01557i	−0.994957	−	0.100299i	$-0.968020\pi$
$827$	−40.1976	−	29.2052i	−1.39781	−	1.01557i	−0.402849	−	0.915267i	$-0.631980\pi$
$828$		0			0
$829$	−17.0902	−	52.5981i	−0.593566	−	1.82681i	−0.561738	−	0.827315i	$-0.689867\pi$
$829$	−17.0902	−	52.5981i	−0.593566	−	1.82681i	−0.0318284	−	0.999493i	$-0.510133\pi$
$830$		0			0
$831$	23.5623	−	17.1190i	0.817367	−	0.593852i
$832$		0			0
$833$	−2.65248	+	8.16348i	−0.0919028	+	0.282848i
$834$		0			0
$835$	10.6525			0.368644
$836$		0			0
$837$	−6.38197			−0.220593
$838$		0			0
$839$	−11.4721	+	35.3076i	−0.396062	+	1.21895i	0.532069	+	0.846701i	$0.321415\pi$
$839$	−11.4721	+	35.3076i	−0.396062	+	1.21895i	−0.928131	+	0.372253i	$0.878585\pi$
$840$		0			0
$841$	17.9164	−	13.0170i	0.617807	−	0.448863i
$842$		0			0
$843$	−5.29180	−	16.2865i	−0.182259	−	0.560936i
$844$		0			0
$845$	−35.7705	−	25.9888i	−1.23054	−	0.894042i
$846$		0			0
$847$	3.33282	−	25.9888i	0.114517	−	0.892986i
$848$		0			0
$849$	9.61803	+	6.98791i	0.330090	+	0.239824i
$850$		0			0
$851$	−4.00000	−	12.3107i	−0.137118	−	0.422007i
$852$		0			0
$853$	−26.6525	+	19.3642i	−0.912563	+	0.663016i	−0.941662	−	0.336560i	$-0.890736\pi$
$853$	−26.6525	+	19.3642i	−0.912563	+	0.663016i	0.0290985	+	0.999577i	$0.490736\pi$
$854$		0			0
$855$	1.47214	−	4.53077i	0.0503460	−	0.154949i
$856$		0			0
$857$	13.2361			0.452135			0.226068	−	0.974112i	$-0.427413\pi$
$857$	13.2361			0.452135			0.226068	+	0.974112i	$0.427413\pi$
$858$		0			0
$859$	−53.5967			−1.82870			−0.914349	−	0.404928i	$-0.867297\pi$
$859$	−53.5967			−1.82870			−0.914349	+	0.404928i	$0.867297\pi$
$860$		0			0
$861$	−0.909830	+	2.80017i	−0.0310069	+	0.0954295i
$862$		0			0
$863$	5.85410	−	4.25325i	0.199276	−	0.144782i	−0.483672	−	0.875249i	$-0.660697\pi$
$863$	5.85410	−	4.25325i	0.199276	−	0.144782i	0.682948	+	0.730467i	$0.260697\pi$
$864$		0			0
$865$	12.9271	+	39.7854i	0.439533	+	1.35274i
$866$		0			0
$867$	−20.1353	−	14.6291i	−0.683829	−	0.496831i
$868$		0			0
$869$	13.8607	+	15.7517i	0.470191	+	0.534339i
$870$		0			0
$871$	4.00000	+	2.90617i	0.135535	+	0.0984718i
$872$		0			0
$873$	−1.33688	−	4.11450i	−0.0452466	−	0.139255i
$874$		0			0
$875$	−36.0517	+	26.1931i	−1.21877	+	0.885487i
$876$		0			0
$877$	4.43769	−	13.6578i	0.149850	−	0.461192i	−0.847753	−	0.530392i	$-0.822045\pi$
$877$	4.43769	−	13.6578i	0.149850	−	0.461192i	0.997603	+	0.0692003i	$0.0220447\pi$
$878$		0			0
$879$	−23.9787			−0.808782
$880$		0			0
$881$	−25.7082			−0.866131			−0.433066	−	0.901362i	$-0.642568\pi$
$881$	−25.7082			−0.866131			−0.433066	+	0.901362i	$0.642568\pi$
$882$		0			0
$883$	−15.5066	+	47.7243i	−0.521838	+	1.60605i	0.248647	+	0.968594i	$0.420014\pi$
$883$	−15.5066	+	47.7243i	−0.521838	+	1.60605i	−0.770485	+	0.637458i	$0.779986\pi$
$884$		0			0
$885$	−8.89919	+	6.46564i	−0.299143	+	0.217340i
$886$		0			0
$887$	−11.9098	−	36.6547i	−0.399893	−	1.23074i	−0.925085	−	0.379760i	$-0.876006\pi$
$887$	−11.9098	−	36.6547i	−0.399893	−	1.23074i	0.525192	−	0.850984i	$-0.323994\pi$
$888$		0			0
$889$	−23.1246	−	16.8010i	−0.775575	−	0.563488i
$890$		0			0
$891$	0.309017	+	3.30220i	0.0103525	+	0.110628i
$892$		0			0
$893$	6.47214	+	4.70228i	0.216582	+	0.157356i
$894$		0			0
$895$	−10.2639	−	31.5891i	−0.343085	−	1.05591i
$896$		0			0
$897$	1.23607	−	0.898056i	0.0412711	−	0.0299852i
$898$		0			0
$899$	5.16312	−	15.8904i	0.172200	−	0.529976i
$900$		0			0
$901$	18.4721			0.615396
$902$		0			0
$903$	2.94427			0.0979792
$904$		0			0
$905$	8.96556	−	27.5932i	0.298025	−	0.917227i
$906$		0			0
$907$	11.4721	−	8.33499i	0.380926	−	0.276759i	−0.380801	−	0.924657i	$-0.624352\pi$
$907$	11.4721	−	8.33499i	0.380926	−	0.276759i	0.761727	+	0.647898i	$0.224352\pi$
$908$		0			0
$909$	−4.51722	−	13.9026i	−0.149827	−	0.461119i
$910$		0			0
$911$	24.5066	+	17.8051i	0.811939	+	0.589908i	0.914392	−	0.404830i	$-0.132669\pi$
$911$	24.5066	+	17.8051i	0.811939	+	0.589908i	−0.102453	+	0.994738i	$0.532669\pi$
$912$		0			0
$913$	−49.7148	+	21.4580i	−1.64532	+	0.710157i
$914$		0			0
$915$	−35.0344	−	25.4540i	−1.15820	−	0.841484i
$916$		0			0
$917$	13.4483	+	41.3897i	0.444103	+	1.36681i
$918$		0			0
$919$	13.5344	−	9.83335i	0.446460	−	0.324372i	−0.341737	−	0.939796i	$-0.611015\pi$
$919$	13.5344	−	9.83335i	0.446460	−	0.324372i	0.788197	+	0.615424i	$0.211015\pi$
$920$		0			0
$921$	−4.52786	+	13.9353i	−0.149198	+	0.459185i
$922$		0			0
$923$	−4.36068			−0.143534
$924$		0			0
$925$	103.193			3.39298
$926$		0			0
$927$	5.26393	−	16.2007i	0.172890	−	0.532101i
$928$		0			0
$929$	−13.8541	+	10.0656i	−0.454538	+	0.330241i	−0.791385	−	0.611318i	$-0.790640\pi$
$929$	−13.8541	+	10.0656i	−0.454538	+	0.330241i	0.336847	+	0.941560i	$0.390640\pi$
$930$		0			0
$931$	0.506578	+	1.55909i	0.0166024	+	0.0510970i
$932$		0			0
$933$	9.61803	+	6.98791i	0.314880	+	0.228774i
$934$		0			0
$935$	−42.1803	+	71.1702i	−1.37944	+	2.32752i
$936$		0			0
$937$	23.0172	+	16.7230i	0.751940	+	0.546316i	0.896428	−	0.443190i	$-0.146153\pi$
$937$	23.0172	+	16.7230i	0.751940	+	0.546316i	−0.144488	+	0.989507i	$0.546153\pi$
$938$		0			0
$939$	6.75329	+	20.7845i	0.220385	+	0.678276i
$940$		0			0
$941$	−36.2705	+	26.3521i	−1.18238	+	0.859053i	−0.992439	−	0.122742i	$-0.960831\pi$
$941$	−36.2705	+	26.3521i	−1.18238	+	0.859053i	−0.189946	+	0.981795i	$0.560831\pi$
$942$		0			0
$943$	−0.472136	+	1.45309i	−0.0153749	+	0.0473190i
$944$		0			0
$945$	9.18034			0.298636
$946$		0			0
$947$	13.3262			0.433045			0.216522	−	0.976278i	$-0.430529\pi$
$947$	13.3262			0.433045			0.216522	+	0.976278i	$0.430529\pi$
$948$		0			0
$949$	1.65248	−	5.08580i	0.0536416	−	0.165092i
$950$		0			0
$951$	−12.8541	+	9.33905i	−0.416823	+	0.302840i
$952$		0			0
$953$	−12.5836	−	38.7283i	−0.407623	−	1.25453i	−0.918685	−	0.394990i	$-0.870748\pi$
$953$	−12.5836	−	38.7283i	−0.407623	−	1.25453i	0.511063	−	0.859543i	$-0.329252\pi$
$954$		0			0
$955$	−42.1803	−	30.6458i	−1.36492	−	0.991675i
$956$		0			0
$957$	−8.47214	−	1.90211i	−0.273865	−	0.0614866i
$958$		0			0
$959$	33.0000	+	23.9759i	1.06563	+	0.774222i
$960$		0			0
$961$	3.00658	+	9.25330i	0.0969864	+	0.298493i
$962$		0			0
$963$	6.16312	−	4.47777i	0.198604	−	0.144294i
$964$		0			0
$965$	18.2533	−	56.1778i	0.587594	−	1.80843i
$966$		0			0
$967$	46.6869			1.50135			0.750675	−	0.660672i	$-0.229728\pi$
$967$	46.6869			1.50135			0.750675	+	0.660672i	$0.229728\pi$
$968$		0			0
$969$	−8.00000			−0.256997
$970$		0			0
$971$	−16.4721	+	50.6960i	−0.528616	+	1.62691i	0.228437	+	0.973559i	$0.426639\pi$
$971$	−16.4721	+	50.6960i	−0.528616	+	1.62691i	−0.757053	+	0.653354i	$0.773361\pi$
$972$		0			0
$973$	−16.8885	+	12.2702i	−0.541422	+	0.393366i
$974$		0			0
$975$	3.76393	+	11.5842i	0.120542	+	0.370991i
$976$		0			0
$977$	33.3607	+	24.2380i	1.06730	+	0.775441i	0.975425	−	0.220330i	$-0.0707133\pi$
$977$	33.3607	+	24.2380i	1.06730	+	0.775441i	0.0918772	+	0.995770i	$0.470713\pi$
$978$		0			0
$979$	5.52786	+	1.24108i	0.176671	+	0.0396652i
$980$		0			0
$981$	7.61803	+	5.53483i	0.243225	+	0.176713i
$982$		0			0
$983$	−9.61803	−	29.6013i	−0.306768	−	0.944134i	−0.979012	−	0.203804i	$-0.934669\pi$
$983$	−9.61803	−	29.6013i	−0.306768	−	0.944134i	0.672244	−	0.740330i	$-0.265331\pi$
$984$		0			0
$985$	−15.8713	+	11.5312i	−0.505702	+	0.367414i
$986$		0			0
$987$	−4.76393	+	14.6619i	−0.151638	+	0.466693i
$988$		0			0
$989$	1.52786			0.0485833
$990$		0			0
$991$	−14.6869			−0.466545			−0.233273	−	0.972411i	$-0.574943\pi$
$991$	−14.6869			−0.466545			−0.233273	+	0.972411i	$0.574943\pi$
$992$		0			0
$993$	2.76393	−	8.50651i	0.0877107	−	0.269946i
$994$		0			0
$995$	−61.9058	+	44.9772i	−1.96254	+	1.42587i
$996$		0			0
$997$	−11.1115	−	34.1975i	−0.351903	−	1.08305i	−0.957783	−	0.287491i	$-0.907179\pi$
$997$	−11.1115	−	34.1975i	−0.351903	−	1.08305i	0.605880	−	0.795556i	$-0.292821\pi$
$998$		0			0
$999$	−8.47214	−	6.15537i	−0.268047	−	0.194747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	528.2.y.d.433.1		4
4.3	odd	2		66.2.e.a.37.1	yes	4
11.3	even	5	inner	528.2.y.d.289.1		4
11.5	even	5		5808.2.a.cb.1.1		2
11.6	odd	10		5808.2.a.cg.1.1		2
12.11	even	2		198.2.f.c.37.1		4
44.3	odd	10		66.2.e.a.25.1	✓	4
44.7	even	10		726.2.e.n.493.1		4
44.15	odd	10		726.2.e.f.493.1		4
44.19	even	10		726.2.e.r.487.1		4
44.27	odd	10		726.2.a.l.1.1		2
44.31	odd	10		726.2.e.f.511.1		4
44.35	even	10		726.2.e.n.511.1		4
44.39	even	10		726.2.a.j.1.1		2
44.43	even	2		726.2.e.r.565.1		4
132.47	even	10		198.2.f.c.91.1		4
132.71	even	10		2178.2.a.t.1.2		2
132.83	odd	10		2178.2.a.bb.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.e.a.25.1	✓	4	44.3	odd	10
66.2.e.a.37.1	yes	4	4.3	odd	2
198.2.f.c.37.1		4	12.11	even	2
198.2.f.c.91.1		4	132.47	even	10
528.2.y.d.289.1		4	11.3	even	5	inner
528.2.y.d.433.1		4	1.1	even	1	trivial
726.2.a.j.1.1		2	44.39	even	10
726.2.a.l.1.1		2	44.27	odd	10
726.2.e.f.493.1		4	44.15	odd	10
726.2.e.f.511.1		4	44.31	odd	10
726.2.e.n.493.1		4	44.7	even	10
726.2.e.n.511.1		4	44.35	even	10
726.2.e.r.487.1		4	44.19	even	10
726.2.e.r.565.1		4	44.43	even	2
2178.2.a.t.1.2		2	132.71	even	10
2178.2.a.bb.1.2		2	132.83	odd	10
5808.2.a.cb.1.1		2	11.5	even	5
5808.2.a.cg.1.1		2	11.6	odd	10

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:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	528.y (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{3} +(3.11803 - 2.26538i) q^{5} +(-0.736068 - 2.26538i) q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{3} +(3.11803 - 2.26538i) q^{5} +(-0.736068 - 2.26538i) q^{7} +(-0.809017 - 0.587785i) q^{9} +(3.23607 + 0.726543i) q^{11} +(-1.00000 - 0.726543i) q^{13} +(-1.19098 - 3.66547i) q^{15} +(-5.23607 + 3.80423i) q^{17} +(-0.381966 + 1.17557i) q^{19} -2.38197 q^{21} -1.23607 q^{23} +(3.04508 - 9.37181i) q^{25} +(-0.809017 + 0.587785i) q^{27} +(-0.809017 - 2.48990i) q^{29} +(5.16312 + 3.75123i) q^{31} +(1.69098 - 2.85317i) q^{33} +(-7.42705 - 5.39607i) q^{35} +(3.23607 + 9.95959i) q^{37} +(-1.00000 + 0.726543i) q^{39} +(0.381966 - 1.17557i) q^{41} -1.23607 q^{43} -3.85410 q^{45} +(2.00000 - 6.15537i) q^{47} +(1.07295 - 0.779543i) q^{49} +(2.00000 + 6.15537i) q^{51} +(-2.30902 - 1.67760i) q^{53} +(11.7361 - 5.06555i) q^{55} +(1.00000 + 0.726543i) q^{57} +(-0.881966 - 2.71441i) q^{59} +(9.09017 - 6.60440i) q^{61} +(-0.736068 + 2.26538i) q^{63} -4.76393 q^{65} -4.00000 q^{67} +(-0.381966 + 1.17557i) q^{69} +(2.85410 - 2.07363i) q^{71} +(1.33688 + 4.11450i) q^{73} +(-7.97214 - 5.79210i) q^{75} +(-0.736068 - 7.86572i) q^{77} +(5.11803 + 3.71847i) q^{79} +(0.309017 + 0.951057i) q^{81} +(-13.2082 + 9.59632i) q^{83} +(-7.70820 + 23.7234i) q^{85} -2.61803 q^{87} +1.70820 q^{89} +(-0.909830 + 2.80017i) q^{91} +(5.16312 - 3.75123i) q^{93} +(1.47214 + 4.53077i) q^{95} +(3.50000 + 2.54290i) q^{97} +(-2.19098 - 2.48990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 8 q^{5} + 6 q^{7} - q^{9}+O(q^{10}) \) 4 * q - q^3 + 8 * q^5 + 6 * q^7 - q^9	\( 4 q - q^{3} + 8 q^{5} + 6 q^{7} - q^{9} + 4 q^{11} - 4 q^{13} - 7 q^{15} - 12 q^{17} - 6 q^{19} - 14 q^{21} + 4 q^{23} + q^{25} - q^{27} - q^{29} + 5 q^{31} + 9 q^{33} - 23 q^{35} + 4 q^{37} - 4 q^{39} + 6 q^{41} + 4 q^{43} - 2 q^{45} + 8 q^{47} + 11 q^{49} + 8 q^{51} - 7 q^{53} + 38 q^{55} + 4 q^{57} - 8 q^{59} + 14 q^{61} + 6 q^{63} - 28 q^{65} - 16 q^{67} - 6 q^{69} - 2 q^{71} + 21 q^{73} - 14 q^{75} + 6 q^{77} + 16 q^{79} - q^{81} - 26 q^{83} - 4 q^{85} - 6 q^{87} - 20 q^{89} - 26 q^{91} + 5 q^{93} - 12 q^{95} + 14 q^{97} - 11 q^{99}+O(q^{100}) \) 4 * q - q^3 + 8 * q^5 + 6 * q^7 - q^9 + 4 * q^11 - 4 * q^13 - 7 * q^15 - 12 * q^17 - 6 * q^19 - 14 * q^21 + 4 * q^23 + q^25 - q^27 - q^29 + 5 * q^31 + 9 * q^33 - 23 * q^35 + 4 * q^37 - 4 * q^39 + 6 * q^41 + 4 * q^43 - 2 * q^45 + 8 * q^47 + 11 * q^49 + 8 * q^51 - 7 * q^53 + 38 * q^55 + 4 * q^57 - 8 * q^59 + 14 * q^61 + 6 * q^63 - 28 * q^65 - 16 * q^67 - 6 * q^69 - 2 * q^71 + 21 * q^73 - 14 * q^75 + 6 * q^77 + 16 * q^79 - q^81 - 26 * q^83 - 4 * q^85 - 6 * q^87 - 20 * q^89 - 26 * q^91 + 5 * q^93 - 12 * q^95 + 14 * q^97 - 11 * q^99

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