LMFDB - Embedded newform 945.2.p.b.622.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(433,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("945.433");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.p (of order $4$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			622.7
Character	$\chi$	$=$	945.622
Dual form			945.2.p.b.433.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.834614 - 0.834614i) q^{2} -0.606840i q^{4} +(-1.65237 + 1.50655i) q^{5} +(-2.61358 - 0.411321i) q^{7} +(-2.17570 + 2.17570i) q^{8} +O(q^{10})$	\(q+(-0.834614 - 0.834614i) q^{2} -0.606840i q^{4} +(-1.65237 + 1.50655i) q^{5} +(-2.61358 - 0.411321i) q^{7} +(-2.17570 + 2.17570i) q^{8} +(2.63647 + 0.121701i) q^{10} +5.36829 q^{11} +(-0.211233 - 0.211233i) q^{13} +(1.83804 + 2.52463i) q^{14} +2.41806 q^{16} +(-4.64565 + 4.64565i) q^{17} +4.27159 q^{19} +(0.914234 + 1.00272i) q^{20} +(-4.48045 - 4.48045i) q^{22} +(4.44100 - 4.44100i) q^{23} +(0.460626 - 4.97874i) q^{25} +0.352597i q^{26} +(-0.249607 + 1.58603i) q^{28} +4.03028i q^{29} -6.55561i q^{31} +(2.33326 + 2.33326i) q^{32} +7.75465 q^{34} +(4.93827 - 3.25783i) q^{35} +(-4.85693 - 4.85693i) q^{37} +(-3.56513 - 3.56513i) q^{38} +(0.317256 - 6.87286i) q^{40} -1.91696i q^{41} +(5.01165 - 5.01165i) q^{43} -3.25769i q^{44} -7.41304 q^{46} +(7.26539 - 7.26539i) q^{47} +(6.66163 + 2.15005i) q^{49} +(-4.53977 + 3.77088i) q^{50} +(-0.128185 + 0.128185i) q^{52} +(-1.40312 + 1.40312i) q^{53} +(-8.87037 + 8.08758i) q^{55} +(6.58130 - 4.79147i) q^{56} +(3.36373 - 3.36373i) q^{58} +1.34247 q^{59} -1.03926i q^{61} +(-5.47140 + 5.47140i) q^{62} -8.73087i q^{64} +(0.667268 + 0.0308016i) q^{65} +(7.23733 + 7.23733i) q^{67} +(2.81917 + 2.81917i) q^{68} +(-6.84058 - 1.40251i) q^{70} -2.92647 q^{71} +(9.72270 + 9.72270i) q^{73} +8.10732i q^{74} -2.59217i q^{76} +(-14.0305 - 2.20809i) q^{77} -2.78130i q^{79} +(-3.99553 + 3.64293i) q^{80} +(-1.59992 + 1.59992i) q^{82} +(-4.47936 - 4.47936i) q^{83} +(0.677418 - 14.6752i) q^{85} -8.36558 q^{86} +(-11.6798 + 11.6798i) q^{88} +2.53502 q^{89} +(0.465191 + 0.638961i) q^{91} +(-2.69498 - 2.69498i) q^{92} -12.1276 q^{94} +(-7.05823 + 6.43536i) q^{95} +(13.1398 - 13.1398i) q^{97} +(-3.76543 - 7.35434i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{7}+O(q^{10}) $ 48 * q - 8 * q^7	$ 48 q - 8 q^{7} + 40 q^{16} + 8 q^{22} - 48 q^{25} - 20 q^{28} - 24 q^{37} - 40 q^{43} + 40 q^{46} - 80 q^{58} - 64 q^{67} - 4 q^{70} - 8 q^{85} - 48 q^{88} + 48 q^{91}+O(q^{100}) $ 48 * q - 8 * q^7 + 40 * q^16 + 8 * q^22 - 48 * q^25 - 20 * q^28 - 24 * q^37 - 40 * q^43 + 40 * q^46 - 80 * q^58 - 64 * q^67 - 4 * q^70 - 8 * q^85 - 48 * q^88 + 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.834614	−	0.834614i	−0.590161	−	0.590161i	0.347514	−	0.937675i	$-0.387026\pi$
$2$	−0.834614	−	0.834614i	−0.590161	−	0.590161i	−0.937675	+	0.347514i	$0.887026\pi$
$3$		0			0
$3$		0			0
$4$		−	0.606840i		−	0.303420i
$5$	−1.65237	+	1.50655i	−0.738960	+	0.673749i
$5$	−1.65237	+	1.50655i	−0.738960	+	0.673749i
$6$		0			0
$7$	−2.61358	−	0.411321i	−0.987841	−	0.155465i
$7$	−2.61358	−	0.411321i	−0.987841	−	0.155465i
$8$	−2.17570	+	2.17570i	−0.769228	+	0.769228i
$9$		0			0
$10$	2.63647	+	0.121701i	0.833726	+	0.0384854i
$11$	5.36829			1.61860			0.809300	−	0.587396i	$-0.199847\pi$
$11$	5.36829			1.61860			0.809300	+	0.587396i	$0.199847\pi$
$12$		0			0
$13$	−0.211233	−	0.211233i	−0.0585856	−	0.0585856i	0.677207	−	0.735793i	$-0.263190\pi$
$13$	−0.211233	−	0.211233i	−0.0585856	−	0.0585856i	−0.735793	+	0.677207i	$0.763190\pi$
$14$	1.83804	+	2.52463i	0.491236	+	0.674735i
$15$		0			0
$16$	2.41806			0.604516
$17$	−4.64565	+	4.64565i	−1.12674	+	1.12674i	−0.136032	+	0.990705i	$0.543435\pi$
$17$	−4.64565	+	4.64565i	−1.12674	+	1.12674i	−0.990705	+	0.136032i	$0.956565\pi$
$18$		0			0
$19$	4.27159			0.979970			0.489985	−	0.871731i	$-0.337002\pi$
$19$	4.27159			0.979970			0.489985	+	0.871731i	$0.337002\pi$
$20$	0.914234	+	1.00272i	0.204429	+	0.224216i
$21$		0			0
$22$	−4.48045	−	4.48045i	−0.955234	−	0.955234i
$23$	4.44100	−	4.44100i	0.926013	−	0.926013i	−0.0714324	−	0.997445i	$-0.522757\pi$
$23$	4.44100	−	4.44100i	0.926013	−	0.926013i	0.997445	+	0.0714324i	$0.0227570\pi$
$24$		0			0
$25$	0.460626	−	4.97874i	0.0921251	−	0.995747i
$26$			0.352597i			0.0691499i
$27$		0			0
$28$	−0.249607	+	1.58603i	−0.0471712	+	0.299731i
$29$			4.03028i			0.748404i	0.927347	+	0.374202i	$0.122083\pi$
$29$			4.03028i			0.748404i	−0.927347	+	0.374202i	$0.877917\pi$
$30$		0			0
$31$		−	6.55561i		−	1.17742i	−0.808344	−	0.588711i	$-0.799636\pi$
$31$		−	6.55561i		−	1.17742i	0.808344	−	0.588711i	$-0.200364\pi$
$32$	2.33326	+	2.33326i	0.412466	+	0.412466i
$33$		0			0
$34$	7.75465			1.32991
$35$	4.93827	−	3.25783i	0.834720	−	0.550675i
$36$		0			0
$37$	−4.85693	−	4.85693i	−0.798475	−	0.798475i	0.184380	−	0.982855i	$-0.440972\pi$
$37$	−4.85693	−	4.85693i	−0.798475	−	0.798475i	−0.982855	+	0.184380i	$0.940972\pi$
$38$	−3.56513	−	3.56513i	−0.578340	−	0.578340i
$39$		0			0
$40$	0.317256	−	6.87286i	0.0501626	−	1.08670i
$41$		−	1.91696i		−	0.299378i	−0.988733	−	0.149689i	$-0.952173\pi$
$41$		−	1.91696i		−	0.299378i	0.988733	−	0.149689i	$-0.0478273\pi$
$42$		0			0
$43$	5.01165	−	5.01165i	0.764269	−	0.764269i	−0.212822	−	0.977091i	$-0.568265\pi$
$43$	5.01165	−	5.01165i	0.764269	−	0.764269i	0.977091	+	0.212822i	$0.0682654\pi$
$44$		−	3.25769i		−	0.491116i
$45$		0			0
$46$	−7.41304			−1.09299
$47$	7.26539	−	7.26539i	1.05977	−	1.05977i	0.0616689	−	0.998097i	$-0.480358\pi$
$47$	7.26539	−	7.26539i	1.05977	−	1.05977i	0.998097	−	0.0616689i	$-0.0196423\pi$
$48$		0			0
$49$	6.66163	+	2.15005i	0.951661	+	0.307149i
$50$	−4.53977	+	3.77088i	−0.642020	+	0.533283i
$51$		0			0
$52$	−0.128185	+	0.128185i	−0.0177761	+	0.0177761i
$53$	−1.40312	+	1.40312i	−0.192733	+	0.192733i	−0.796876	−	0.604143i	$-0.793516\pi$
$53$	−1.40312	+	1.40312i	−0.192733	+	0.192733i	0.604143	+	0.796876i	$0.293516\pi$
$54$		0			0
$55$	−8.87037	+	8.08758i	−1.19608	+	1.09053i
$56$	6.58130	−	4.79147i	0.879463	−	0.640287i
$57$		0			0
$58$	3.36373	−	3.36373i	0.441679	−	0.441679i
$59$	1.34247			0.174774			0.0873872	−	0.996174i	$-0.472148\pi$
$59$	1.34247			0.174774			0.0873872	+	0.996174i	$0.472148\pi$
$60$		0			0
$61$		−	1.03926i		−	0.133063i	−0.997784	−	0.0665317i	$-0.978807\pi$
$61$		−	1.03926i		−	0.133063i	0.997784	−	0.0665317i	$-0.0211934\pi$
$62$	−5.47140	+	5.47140i	−0.694868	+	0.694868i
$63$		0			0
$64$		−	8.73087i		−	1.09136i
$65$	0.667268	+	0.0308016i	0.0827644	+	0.00382047i
$66$		0			0
$67$	7.23733	+	7.23733i	0.884181	+	0.884181i	0.993956	−	0.109776i	$-0.0350133\pi$
$67$	7.23733	+	7.23733i	0.884181	+	0.884181i	−0.109776	+	0.993956i	$0.535013\pi$
$68$	2.81917	+	2.81917i	0.341875	+	0.341875i
$69$		0			0
$70$	−6.84058	−	1.40251i	−0.817606	−	0.167633i
$71$	−2.92647			−0.347309			−0.173654	−	0.984807i	$-0.555558\pi$
$71$	−2.92647			−0.347309			−0.173654	+	0.984807i	$0.555558\pi$
$72$		0			0
$73$	9.72270	+	9.72270i	1.13796	+	1.13796i	0.988816	+	0.149140i	$0.0476505\pi$
$73$	9.72270	+	9.72270i	1.13796	+	1.13796i	0.149140	+	0.988816i	$0.452349\pi$
$74$			8.10732i			0.942457i
$75$		0			0
$76$		−	2.59217i		−	0.297343i
$77$	−14.0305	−	2.20809i	−1.59892	−	0.251635i
$78$		0			0
$79$		−	2.78130i		−	0.312920i	−0.987684	−	0.156460i	$-0.949992\pi$
$79$		−	2.78130i		−	0.312920i	0.987684	−	0.156460i	$-0.0500083\pi$
$80$	−3.99553	+	3.64293i	−0.446713	+	0.407292i
$81$		0			0
$82$	−1.59992	+	1.59992i	−0.176681	+	0.176681i
$83$	−4.47936	−	4.47936i	−0.491674	−	0.491674i	0.417159	−	0.908833i	$-0.363026\pi$
$83$	−4.47936	−	4.47936i	−0.491674	−	0.491674i	−0.908833	+	0.417159i	$0.863026\pi$
$84$		0			0
$85$	0.677418	−	14.6752i	0.0734764	−	1.59175i
$86$	−8.36558			−0.902084
$87$		0			0
$88$	−11.6798	+	11.6798i	−1.24507	+	1.24507i
$89$	2.53502			0.268711			0.134356	−	0.990933i	$-0.457104\pi$
$89$	2.53502			0.268711			0.134356	+	0.990933i	$0.457104\pi$
$90$		0			0
$91$	0.465191	+	0.638961i	0.0487653	+	0.0669813i
$92$	−2.69498	−	2.69498i	−0.280971	−	0.280971i
$93$		0			0
$94$	−12.1276			−1.25086
$95$	−7.05823	+	6.43536i	−0.724159	+	0.660254i
$96$		0			0
$97$	13.1398	−	13.1398i	1.33415	−	1.33415i	0.432527	−	0.901621i	$-0.357622\pi$
$97$	13.1398	−	13.1398i	1.33415	−	1.33415i	0.901621	−	0.432527i	$-0.142378\pi$
$98$	−3.76543	−	7.35434i	−0.380366	−	0.742901i
$99$		0			0
$100$	−3.02130	−	0.279526i	−0.302130	−	0.0279526i
$101$		−	2.63557i		−	0.262249i	−0.991366	−	0.131124i	$-0.958141\pi$
$101$		−	2.63557i		−	0.262249i	0.991366	−	0.131124i	$-0.0418587\pi$
$102$		0			0
$103$	8.70224	+	8.70224i	0.857457	+	0.857457i	0.991038	−	0.133581i	$-0.0426475\pi$
$103$	8.70224	+	8.70224i	0.857457	+	0.857457i	−0.133581	+	0.991038i	$0.542647\pi$
$104$	0.919163			0.0901314
$105$		0			0
$106$	2.34212			0.227487
$107$	−10.4154	−	10.4154i	−1.00690	−	1.00690i	−0.999976	−	0.00692307i	$-0.997796\pi$
$107$	−10.4154	−	10.4154i	−1.00690	−	1.00690i	−0.00692307	−	0.999976i	$-0.502204\pi$
$108$		0			0
$109$			6.59594i			0.631776i	0.948796	+	0.315888i	$0.102302\pi$
$109$			6.59594i			0.631776i	−0.948796	+	0.315888i	$0.897698\pi$
$110$	14.1533	+	0.653328i	1.34947	+	0.0622924i
$111$		0			0
$112$	−6.31981	−	0.994601i	−0.597166	−	0.0939810i
$113$	10.7735	−	10.7735i	1.01348	−	1.01348i	0.0135748	−	0.999908i	$-0.495679\pi$
$113$	10.7735	−	10.7735i	1.01348	−	1.01348i	0.999908	−	0.0135748i	$-0.00432112\pi$
$114$		0			0
$115$	−0.647577	+	14.0287i	−0.0603869	+	1.30819i
$116$	2.44574			0.227081
$117$		0			0
$118$	−1.12044	−	1.12044i	−0.103145	−	0.103145i
$119$	14.0527	−	10.2309i	1.28820	−	0.937869i
$120$		0			0
$121$	17.8185			1.61986
$122$	−0.867380	+	0.867380i	−0.0785289	+	0.0785289i
$123$		0			0
$124$	−3.97821			−0.357254
$125$	6.73958	+	8.92065i	0.602807	+	0.797887i
$126$		0			0
$127$	7.88309	+	7.88309i	0.699511	+	0.699511i	0.964305	−	0.264794i	$-0.0853039\pi$
$127$	7.88309	+	7.88309i	0.699511	+	0.699511i	−0.264794	+	0.964305i	$0.585304\pi$
$128$	−2.62038	+	2.62038i	−0.231611	+	0.231611i
$129$		0			0
$130$	−0.531204	−	0.582619i	−0.0465897	−	0.0510990i
$131$		−	9.63252i		−	0.841598i	−0.907154	−	0.420799i	$-0.861750\pi$
$131$		−	9.63252i		−	0.841598i	0.907154	−	0.420799i	$-0.138250\pi$
$132$		0			0
$133$	−11.1642	−	1.75700i	−0.968055	−	0.152351i
$134$		−	12.0807i		−	1.04362i
$135$		0			0
$136$		−	20.2151i		−	1.73343i
$137$	2.81008	+	2.81008i	0.240081	+	0.240081i	0.816884	−	0.576803i	$-0.195700\pi$
$137$	2.81008	+	2.81008i	0.240081	+	0.240081i	−0.576803	+	0.816884i	$0.695700\pi$
$138$		0			0
$139$	−8.83253			−0.749166			−0.374583	−	0.927193i	$-0.622214\pi$
$139$	−8.83253			−0.749166			−0.374583	+	0.927193i	$0.622214\pi$
$140$	−1.97699	−	2.99674i	−0.167086	−	0.253271i
$141$		0			0
$142$	2.44247	+	2.44247i	0.204968	+	0.204968i
$143$	−1.13396	−	1.13396i	−0.0948267	−	0.0948267i
$144$		0			0
$145$	−6.07181	−	6.65950i	−0.504236	−	0.553041i
$146$		−	16.2294i		−	1.34315i
$147$		0			0
$148$	−2.94738	+	2.94738i	−0.242273	+	0.242273i
$149$			2.30798i			0.189077i	0.995521	+	0.0945387i	$0.0301376\pi$
$149$			2.30798i			0.189077i	−0.995521	+	0.0945387i	$0.969862\pi$
$150$		0			0
$151$	7.65488			0.622945			0.311472	−	0.950255i	$-0.399178\pi$
$151$	7.65488			0.622945			0.311472	+	0.950255i	$0.399178\pi$
$152$	−9.29372	+	9.29372i	−0.753820	+	0.753820i
$153$		0			0
$154$	9.86711	+	13.5529i	0.795114	+	1.09213i
$155$	9.87634	+	10.8323i	0.793286	+	0.870068i
$156$		0			0
$157$	1.31345	−	1.31345i	0.104824	−	0.104824i	−0.652749	−	0.757574i	$-0.726385\pi$
$157$	1.31345	−	1.31345i	0.104824	−	0.104824i	0.757574	+	0.652749i	$0.226385\pi$
$158$	−2.32131	+	2.32131i	−0.184673	+	0.184673i
$159$		0			0
$160$	−7.37057	−	0.340231i	−0.582695	−	0.0268976i
$161$	−13.4336	+	9.78025i	−1.05872	+	0.770791i
$162$		0			0
$163$	0.0280160	−	0.0280160i	0.00219438	−	0.00219438i	−0.706009	−	0.708203i	$-0.749506\pi$
$163$	0.0280160	−	0.0280160i	0.00219438	−	0.00219438i	0.708203	+	0.706009i	$0.249506\pi$
$164$	−1.16329			−0.0908375
$165$		0			0
$166$			7.47707i			0.580333i
$167$	−6.11313	+	6.11313i	−0.473048	+	0.473048i	−0.902900	−	0.429851i	$-0.858566\pi$
$167$	−6.11313	+	6.11313i	−0.473048	+	0.473048i	0.429851	+	0.902900i	$0.358566\pi$
$168$		0			0
$169$		−	12.9108i		−	0.993135i
$170$	−12.8135	+	11.6827i	−0.982752	+	0.896026i
$171$		0			0
$172$	−3.04127	−	3.04127i	−0.231895	−	0.231895i
$173$	−10.1230	−	10.1230i	−0.769636	−	0.769636i	0.208406	−	0.978042i	$-0.433172\pi$
$173$	−10.1230	−	10.1230i	−0.769636	−	0.769636i	−0.978042	+	0.208406i	$0.933172\pi$
$174$		0			0
$175$	−3.25174	+	12.8229i	−0.245809	+	0.969318i
$176$	12.9809			0.978469
$177$		0			0
$178$	−2.11576	−	2.11576i	−0.158583	−	0.158583i
$179$			22.9115i			1.71249i	0.516571	+	0.856244i	$0.327208\pi$
$179$			22.9115i			1.71249i	−0.516571	+	0.856244i	$0.672792\pi$
$180$		0			0
$181$			10.7359i			0.797997i	0.916952	+	0.398998i	$0.130642\pi$
$181$			10.7359i			0.797997i	−0.916952	+	0.398998i	$0.869358\pi$
$182$	0.145031	−	0.921540i	0.0107504	−	0.0683091i
$183$		0			0
$184$			19.3246i			1.42463i
$185$	15.3426	+	0.708227i	1.12801	+	0.0520699i
$186$		0			0
$187$	−24.9392	+	24.9392i	−1.82373	+	1.82373i
$188$	−4.40893	−	4.40893i	−0.321554	−	0.321554i
$189$		0			0
$190$	11.2619	+	0.519859i	0.817026	+	0.0377145i
$191$	17.1890			1.24375			0.621874	−	0.783117i	$-0.286371\pi$
$191$	17.1890			1.24375			0.621874	+	0.783117i	$0.286371\pi$
$192$		0			0
$193$	−11.2279	+	11.2279i	−0.808200	+	0.808200i	−0.984361	−	0.176162i	$-0.943632\pi$
$193$	−11.2279	+	11.2279i	−0.808200	+	0.808200i	0.176162	+	0.984361i	$0.443632\pi$
$194$	−21.9334			−1.57472
$195$		0			0
$196$	1.30473	−	4.04255i	0.0931953	−	0.288753i
$197$	4.92276	+	4.92276i	0.350732	+	0.350732i	0.860382	−	0.509650i	$-0.170225\pi$
$197$	4.92276	+	4.92276i	0.350732	+	0.350732i	−0.509650	+	0.860382i	$0.670225\pi$
$198$		0			0
$199$	−8.83915			−0.626591			−0.313295	−	0.949656i	$-0.601433\pi$
$199$	−8.83915			−0.626591			−0.313295	+	0.949656i	$0.601433\pi$
$200$	9.83007	+	11.8344i	0.695091	+	0.836822i
$201$		0			0
$202$	−2.19968	+	2.19968i	−0.154769	+	0.154769i
$203$	1.65774	−	10.5335i	0.116351	−	0.739305i
$204$		0			0
$205$	2.88799	+	3.16751i	0.201706	+	0.221229i
$206$		−	14.5260i		−	1.01208i
$207$		0			0
$208$	−0.510776	−	0.510776i	−0.0354159	−	0.0354159i
$209$	22.9311			1.58618
$210$		0			0
$211$	23.3053			1.60440			0.802202	−	0.597053i	$-0.203662\pi$
$211$	23.3053			1.60440			0.802202	+	0.597053i	$0.203662\pi$
$212$	0.851469	+	0.851469i	0.0584791	+	0.0584791i
$213$		0			0
$214$			17.3857i			1.18846i
$215$	−0.730787	+	15.8314i	−0.0498393	+	1.07969i
$216$		0			0
$217$	−2.69646	+	17.1336i	−0.183048	+	1.16311i
$218$	5.50506	−	5.50506i	0.372850	−	0.372850i
$219$		0			0
$220$	4.90787	+	5.38290i	0.330889	+	0.362915i
$221$	1.96263			0.132021
$222$		0			0
$223$	0.433366	+	0.433366i	0.0290203	+	0.0290203i	0.721468	−	0.692448i	$-0.243468\pi$
$223$	0.433366	+	0.433366i	0.0290203	+	0.0290203i	−0.692448	+	0.721468i	$0.743468\pi$
$224$	−5.13845	−	7.05789i	−0.343327	−	0.471575i
$225$		0			0
$226$	−17.9834			−1.19624
$227$	−5.94890	+	5.94890i	−0.394842	+	0.394842i	−0.876409	−	0.481567i	$-0.840068\pi$
$227$	−5.94890	+	5.94890i	−0.394842	+	0.394842i	0.481567	+	0.876409i	$0.340068\pi$
$228$		0			0
$229$	−1.75108			−0.115714			−0.0578572	−	0.998325i	$-0.518427\pi$
$229$	−1.75108			−0.115714			−0.0578572	+	0.998325i	$0.518427\pi$
$230$	12.2491	−	11.1681i	0.807679	−	0.736403i
$231$		0			0
$232$	−8.76870	−	8.76870i	−0.575693	−	0.575693i
$233$	14.2334	−	14.2334i	0.932463	−	0.932463i	−0.0653964	−	0.997859i	$-0.520831\pi$
$233$	14.2334	−	14.2334i	0.932463	−	0.932463i	0.997859	+	0.0653964i	$0.0208312\pi$
$234$		0			0
$235$	−1.05942	+	22.9507i	−0.0691091	+	1.49714i
$236$		−	0.814663i		−	0.0530301i
$237$		0			0
$238$	−20.2674	−	3.18965i	−1.31374	−	0.206754i
$239$			17.1339i			1.10830i	0.832416	+	0.554151i	$0.186957\pi$
$239$			17.1339i			1.10830i	−0.832416	+	0.554151i	$0.813043\pi$
$240$		0			0
$241$			1.10083i			0.0709106i	0.999371	+	0.0354553i	$0.0112881\pi$
$241$			1.10083i			0.0709106i	−0.999371	+	0.0354553i	$0.988712\pi$
$242$	−14.8716	−	14.8716i	−0.955980	−	0.955980i
$243$		0			0
$244$	−0.630664			−0.0403741
$245$	−14.2466	+	6.48340i	−0.910182	+	0.414209i
$246$		0			0
$247$	−0.902303	−	0.902303i	−0.0574122	−	0.0574122i
$248$	14.2631	+	14.2631i	0.905705	+	0.905705i
$249$		0			0
$250$	1.82035	−	13.0702i	0.115129	−	0.826635i
$251$			17.9236i			1.13133i	0.824636	+	0.565664i	$0.191380\pi$
$251$			17.9236i			1.13133i	−0.824636	+	0.565664i	$0.808620\pi$
$252$		0			0
$253$	23.8406	−	23.8406i	1.49884	−	1.49884i
$254$		−	13.1587i		−	0.825648i
$255$		0			0
$256$	−13.0877			−0.817983
$257$	−15.8529	+	15.8529i	−0.988877	+	0.988877i	−0.999939	−	0.0110616i	$-0.996479\pi$
$257$	−15.8529	+	15.8529i	−0.988877	+	0.988877i	0.0110616	+	0.999939i	$0.496479\pi$
$258$		0			0
$259$	10.6962	+	14.6918i	0.664632	+	0.912901i
$260$	0.0186917	−	0.404925i	0.00115921	−	0.0251124i
$261$		0			0
$262$	−8.03944	+	8.03944i	−0.496678	+	0.496678i
$263$	−2.67848	+	2.67848i	−0.165162	+	0.165162i	−0.784849	−	0.619687i	$-0.787260\pi$
$263$	−2.67848	+	2.67848i	−0.165162	+	0.165162i	0.619687	+	0.784849i	$0.287260\pi$
$264$		0			0
$265$	0.204600	−	4.43233i	0.0125685	−	0.272276i
$266$	7.85134	+	10.7842i	0.481397	+	0.661220i
$267$		0			0
$268$	4.39191	−	4.39191i	0.268278	−	0.268278i
$269$	7.81764			0.476650			0.238325	−	0.971186i	$-0.423402\pi$
$269$	7.81764			0.476650			0.238325	+	0.971186i	$0.423402\pi$
$270$		0			0
$271$		−	31.7453i		−	1.92839i	−0.265193	−	0.964195i	$-0.585436\pi$
$271$		−	31.7453i		−	1.92839i	0.265193	−	0.964195i	$-0.414564\pi$
$272$	−11.2335	+	11.2335i	−0.681130	+	0.681130i
$273$		0			0
$274$		−	4.69066i		−	0.283373i
$275$	2.47277	−	26.7273i	0.149114	−	1.61172i
$276$		0			0
$277$	8.79671	+	8.79671i	0.528543	+	0.528543i	0.920138	−	0.391595i	$-0.128076\pi$
$277$	8.79671	+	8.79671i	0.528543	+	0.528543i	−0.391595	+	0.920138i	$0.628076\pi$
$278$	7.37175	+	7.37175i	0.442128	+	0.442128i
$279$		0			0
$280$	−3.65613	+	17.8323i	−0.218496	+	1.06568i
$281$	−1.93492			−0.115428			−0.0577138	−	0.998333i	$-0.518381\pi$
$281$	−1.93492			−0.115428			−0.0577138	+	0.998333i	$0.518381\pi$
$282$		0			0
$283$	−7.96846	−	7.96846i	−0.473676	−	0.473676i	0.429426	−	0.903102i	$-0.358716\pi$
$283$	−7.96846	−	7.96846i	−0.473676	−	0.473676i	−0.903102	+	0.429426i	$0.858716\pi$
$284$			1.77590i			0.105380i
$285$		0			0
$286$			1.89284i			0.111926i
$287$	−0.788485	+	5.01013i	−0.0465428	+	0.295738i
$288$		0			0
$289$		−	26.1642i		−	1.53907i
$290$	−0.490491	+	10.6257i	−0.0288026	+	0.623964i
$291$		0			0
$292$	5.90013	−	5.90013i	0.345279	−	0.345279i
$293$	−4.45089	−	4.45089i	−0.260024	−	0.260024i	0.565040	−	0.825064i	$-0.308861\pi$
$293$	−4.45089	−	4.45089i	−0.260024	−	0.260024i	−0.825064	+	0.565040i	$0.808861\pi$
$294$		0			0
$295$	−2.21825	+	2.02249i	−0.129151	+	0.117754i
$296$	21.1345			1.22842
$297$		0			0
$298$	1.92627	−	1.92627i	0.111586	−	0.111586i
$299$	−1.87618			−0.108502
$300$		0			0
$301$	−15.1598	+	11.0370i	−0.873794	+	0.636160i
$302$	−6.38886	−	6.38886i	−0.367638	−	0.367638i
$303$		0			0
$304$	10.3290			0.592408
$305$	1.56569	+	1.71724i	0.0896513	+	0.0983286i
$306$		0			0
$307$	6.48304	−	6.48304i	0.370007	−	0.370007i	−0.497473	−	0.867480i	$-0.665739\pi$
$307$	6.48304	−	6.48304i	0.370007	−	0.370007i	0.867480	+	0.497473i	$0.165739\pi$
$308$	−1.33996	+	8.51425i	−0.0763513	+	0.485145i
$309$		0			0
$310$	0.797827	−	17.2837i	0.0453135	−	0.981647i
$311$		−	23.3314i		−	1.32300i	−0.749944	−	0.661501i	$-0.769920\pi$
$311$		−	23.3314i		−	1.32300i	0.749944	−	0.661501i	$-0.230080\pi$
$312$		0			0
$313$	16.2566	+	16.2566i	0.918879	+	0.918879i	0.996948	−	0.0780691i	$-0.0248755\pi$
$313$	16.2566	+	16.2566i	0.918879	+	0.918879i	−0.0780691	+	0.996948i	$0.524875\pi$
$314$	−2.19244			−0.123727
$315$		0			0
$316$	−1.68780			−0.0949464
$317$	−5.31536	−	5.31536i	−0.298540	−	0.298540i	0.541902	−	0.840442i	$-0.317705\pi$
$317$	−5.31536	−	5.31536i	−0.298540	−	0.298540i	−0.840442	+	0.541902i	$0.817705\pi$
$318$		0			0
$319$			21.6357i			1.21137i
$320$	13.1535	+	14.4266i	0.735301	+	0.806471i
$321$		0			0
$322$	19.3746	+	3.04914i	1.07970	+	0.169922i
$323$	−19.8443	+	19.8443i	−1.10417	+	1.10417i
$324$		0			0
$325$	−1.14898	+	0.954376i	−0.0637337	+	0.0529393i
$326$	−0.0467651			−0.00259008
$327$		0			0
$328$	4.17073	+	4.17073i	0.230290	+	0.230290i
$329$	−21.9771	+	16.0003i	−1.21164	+	0.882124i
$330$		0			0
$331$	−2.24110			−0.123182			−0.0615910	−	0.998101i	$-0.519617\pi$
$331$	−2.24110			−0.123182			−0.0615910	+	0.998101i	$0.519617\pi$
$332$	−2.71826	+	2.71826i	−0.149184	+	0.149184i
$333$		0			0
$334$	10.2042			0.558349
$335$	−22.8621	−	1.05533i	−1.24909	−	0.0576589i
$336$		0			0
$337$	−9.05299	−	9.05299i	−0.493148	−	0.493148i	0.416149	−	0.909297i	$-0.363380\pi$
$337$	−9.05299	−	9.05299i	−0.493148	−	0.493148i	−0.909297	+	0.416149i	$0.863380\pi$
$338$	−10.7755	+	10.7755i	−0.586110	+	0.586110i
$339$		0			0
$340$	−8.90551	−	0.411085i	−0.482969	−	0.0222942i
$341$		−	35.1924i		−	1.90577i
$342$		0			0
$343$	−16.5264	−	8.35939i	−0.892340	−	0.451365i
$344$			21.8077i			1.17579i
$345$		0			0
$346$			16.8976i			0.908419i
$347$	14.2565	+	14.2565i	0.765331	+	0.765331i	0.977281	−	0.211950i	$-0.0679813\pi$
$347$	14.2565	+	14.2565i	0.765331	+	0.765331i	−0.211950	+	0.977281i	$0.567981\pi$
$348$		0			0
$349$	−25.0031			−1.33838			−0.669192	−	0.743090i	$-0.733360\pi$
$349$	−25.0031			−1.33838			−0.669192	+	0.743090i	$0.733360\pi$
$350$	13.4161	−	7.98820i	0.717121	−	0.426987i
$351$		0			0
$352$	12.5256	+	12.5256i	0.667617	+	0.667617i
$353$	−14.1339	−	14.1339i	−0.752272	−	0.752272i	0.222631	−	0.974903i	$-0.428536\pi$
$353$	−14.1339	−	14.1339i	−0.752272	−	0.752272i	−0.974903	+	0.222631i	$0.928536\pi$
$354$		0			0
$355$	4.83561	−	4.40887i	0.256647	−	0.233999i
$356$		−	1.53835i		−	0.0815325i
$357$		0			0
$358$	19.1223	−	19.1223i	1.01064	−	1.01064i
$359$			4.56436i			0.240898i	0.992720	+	0.120449i	$0.0384334\pi$
$359$			4.56436i			0.240898i	−0.992720	+	0.120449i	$0.961567\pi$
$360$		0			0
$361$	−0.753512			−0.0396585
$362$	8.96037	−	8.96037i	0.470947	−	0.470947i
$363$		0			0
$364$	0.387747	−	0.282297i	0.0203235	−	0.0147964i
$365$	−30.7132	−	1.41774i	−1.60760	−	0.0742080i
$366$		0			0
$367$	−1.77553	+	1.77553i	−0.0926819	+	0.0926819i	−0.751928	−	0.659246i	$-0.770876\pi$
$367$	−1.77553	+	1.77553i	−0.0926819	+	0.0926819i	0.659246	+	0.751928i	$0.270876\pi$
$368$	10.7386	−	10.7386i	0.559790	−	0.559790i
$369$		0			0
$370$	−12.2141	−	13.3963i	−0.634980	−	0.696439i
$371$	4.24430	−	3.09003i	0.220353	−	0.160427i
$372$		0			0
$373$	−9.44065	+	9.44065i	−0.488818	+	0.488818i	−0.907933	−	0.419115i	$-0.862340\pi$
$373$	−9.44065	+	9.44065i	−0.488818	+	0.488818i	0.419115	+	0.907933i	$0.362340\pi$
$374$	41.6292			2.15259
$375$		0			0
$376$			31.6147i			1.63040i
$377$	0.851330	−	0.851330i	0.0438457	−	0.0438457i
$378$		0			0
$379$		−	16.1510i		−	0.829619i	−0.909908	−	0.414809i	$-0.863848\pi$
$379$		−	16.1510i		−	0.829619i	0.909908	−	0.414809i	$-0.136152\pi$
$380$	3.90524	+	4.28322i	0.200334	+	0.219725i
$381$		0			0
$382$	−14.3461	−	14.3461i	−0.734012	−	0.734012i
$383$	−14.1980	−	14.1980i	−0.725482	−	0.725482i	0.244234	−	0.969716i	$-0.421464\pi$
$383$	−14.1980	−	14.1980i	−0.725482	−	0.725482i	−0.969716	+	0.244234i	$0.921464\pi$
$384$		0			0
$385$	26.5101	−	17.4890i	1.35108	−	0.891322i
$386$	18.7419			0.953936
$387$		0			0
$388$	−7.97378	−	7.97378i	−0.404807	−	0.404807i
$389$		−	26.2759i		−	1.33224i	−0.745844	−	0.666121i	$-0.767954\pi$
$389$		−	26.2759i		−	1.33224i	0.745844	−	0.666121i	$-0.232046\pi$
$390$		0			0
$391$			41.2627i			2.08674i
$392$	−19.1716	+	9.81587i	−0.968312	+	0.495776i
$393$		0			0
$394$		−	8.21721i		−	0.413977i
$395$	4.19016	+	4.59572i	0.210830	+	0.231236i
$396$		0			0
$397$	25.5891	−	25.5891i	1.28428	−	1.28428i	0.346068	−	0.938209i	$-0.387517\pi$
$397$	25.5891	−	25.5891i	1.28428	−	1.28428i	0.938209	−	0.346068i	$-0.112483\pi$
$398$	7.37727	+	7.37727i	0.369789	+	0.369789i
$399$		0			0
$400$	1.11382	−	12.0389i	0.0556911	−	0.601945i
$401$	−7.82242			−0.390633			−0.195317	−	0.980740i	$-0.562573\pi$
$401$	−7.82242			−0.390633			−0.195317	+	0.980740i	$0.562573\pi$
$402$		0			0
$403$	−1.38476	+	1.38476i	−0.0689800	+	0.0689800i
$404$	−1.59937			−0.0795716
$405$		0			0
$406$	−10.1749	+	7.40780i	−0.504974	+	0.367643i
$407$	−26.0734	−	26.0734i	−1.29241	−	1.29241i
$408$		0			0
$409$	19.9780			0.987848			0.493924	−	0.869505i	$-0.335562\pi$
$409$	19.9780			0.987848			0.493924	+	0.869505i	$0.335562\pi$
$410$	0.233296	−	5.05400i	0.0115217	−	0.249599i
$411$		0			0
$412$	5.28087	−	5.28087i	0.260170	−	0.260170i
$413$	−3.50865	−	0.552185i	−0.172649	−	0.0271713i
$414$		0			0
$415$	14.1499	+	0.653170i	0.694592	+	0.0320629i
$416$		−	0.985725i		−	0.0483292i
$417$		0			0
$418$	−19.1386	−	19.1386i	−0.936101	−	0.936101i
$419$	24.0861			1.17668			0.588341	−	0.808613i	$-0.299781\pi$
$419$	24.0861			1.17668			0.588341	+	0.808613i	$0.299781\pi$
$420$		0			0
$421$	10.9909			0.535662			0.267831	−	0.963466i	$-0.413693\pi$
$421$	10.9909			0.535662			0.267831	+	0.963466i	$0.413693\pi$
$422$	−19.4509	−	19.4509i	−0.946857	−	0.946857i
$423$		0			0
$424$		−	6.10554i		−	0.296511i
$425$	20.9896	+	25.2694i	1.01814	+	1.22575i
$426$		0			0
$427$	−0.427469	+	2.71619i	−0.0206867	+	0.131446i
$428$	−6.32051	+	6.32051i	−0.305514	+	0.305514i
$429$		0			0
$430$	13.8230	−	12.6031i	0.666604	−	0.607778i
$431$	15.5845			0.750681			0.375340	−	0.926887i	$-0.377526\pi$
$431$	15.5845			0.750681			0.375340	+	0.926887i	$0.377526\pi$
$432$		0			0
$433$	26.9396	+	26.9396i	1.29464	+	1.29464i	0.931887	+	0.362748i	$0.118161\pi$
$433$	26.9396	+	26.9396i	1.29464	+	1.29464i	0.362748	+	0.931887i	$0.381839\pi$
$434$	16.5505	−	12.0494i	0.794447	−	0.578392i
$435$		0			0
$436$	4.00268			0.191694
$437$	18.9701	−	18.9701i	0.907465	−	0.907465i
$438$		0			0
$439$	−31.4369			−1.50040			−0.750201	−	0.661210i	$-0.770043\pi$
$439$	−31.4369			−1.50040			−0.750201	+	0.661210i	$0.770043\pi$
$440$	1.70312	−	36.8955i	0.0811932	−	1.75892i
$441$		0			0
$442$	−1.63804	−	1.63804i	−0.0779137	−	0.0779137i
$443$	−2.32611	+	2.32611i	−0.110517	+	0.110517i	−0.760203	−	0.649686i	$-0.774900\pi$
$443$	−2.32611	+	2.32611i	−0.110517	+	0.110517i	0.649686	+	0.760203i	$0.274900\pi$
$444$		0			0
$445$	−4.18878	+	3.81913i	−0.198567	+	0.181044i
$446$		−	0.723386i		−	0.0342533i
$447$		0			0
$448$	−3.59119	+	22.8188i	−0.169668	+	1.07809i
$449$		−	10.7504i		−	0.507344i	−0.967290	−	0.253672i	$-0.918362\pi$
$449$		−	10.7504i		−	0.507344i	0.967290	−	0.253672i	$-0.0816384\pi$
$450$		0			0
$451$		−	10.2908i		−	0.484574i
$452$	−6.53778	−	6.53778i	−0.307511	−	0.307511i
$453$		0			0
$454$	9.93007			0.466041
$455$	−1.73129	−	0.354964i	−0.0811642	−	0.0166410i
$456$		0			0
$457$	−17.9180	−	17.9180i	−0.838170	−	0.838170i	0.150448	−	0.988618i	$-0.451929\pi$
$457$	−17.9180	−	17.9180i	−0.838170	−	0.838170i	−0.988618	+	0.150448i	$0.951929\pi$
$458$	1.46147	+	1.46147i	0.0682901	+	0.0682901i
$459$		0			0
$460$	8.51321	+	0.392976i	0.396930	+	0.0183226i
$461$			14.6856i			0.683974i	0.939705	+	0.341987i	$0.111100\pi$
$461$			14.6856i			0.683974i	−0.939705	+	0.341987i	$0.888900\pi$
$462$		0			0
$463$	5.08950	−	5.08950i	0.236529	−	0.236529i	−0.578882	−	0.815411i	$-0.696511\pi$
$463$	5.08950	−	5.08950i	0.236529	−	0.236529i	0.815411	+	0.578882i	$0.196511\pi$
$464$			9.74547i			0.452422i
$465$		0			0
$466$	−23.7588			−1.10061
$467$	22.3186	−	22.3186i	1.03278	−	1.03278i	0.0333391	−	0.999444i	$-0.489386\pi$
$467$	22.3186	−	22.3186i	1.03278	−	1.03278i	0.999444	−	0.0333391i	$-0.0106141\pi$
$468$		0			0
$469$	−15.9385	−	21.8922i	−0.735971	−	1.01089i
$470$	20.0392	−	18.2708i	0.924339	−	0.842768i
$471$		0			0
$472$	−2.92081	+	2.92081i	−0.134441	+	0.134441i
$473$	26.9040	−	26.9040i	1.23705	−	1.23705i
$474$		0			0
$475$	1.96760	−	21.2671i	0.0902799	−	0.975803i
$476$	−6.20855	−	8.52772i	−0.284568	−	0.390867i
$477$		0			0
$478$	14.3002	−	14.3002i	0.654076	−	0.654076i
$479$	−37.1494			−1.69740			−0.848700	−	0.528874i	$-0.822614\pi$
$479$	−37.1494			−1.69740			−0.848700	+	0.528874i	$0.822614\pi$
$480$		0			0
$481$			2.05189i			0.0935583i
$482$	0.918767	−	0.918767i	0.0418487	−	0.0418487i
$483$		0			0
$484$		−	10.8130i		−	0.491500i
$485$	−1.91602	+	41.5076i	−0.0870020	+	1.88476i
$486$		0			0
$487$	−4.41260	−	4.41260i	−0.199954	−	0.199954i	0.600026	−	0.799980i	$-0.295157\pi$
$487$	−4.41260	−	4.41260i	−0.199954	−	0.199954i	−0.799980	+	0.600026i	$0.795157\pi$
$488$	2.26112	+	2.26112i	0.102356	+	0.102356i
$489$		0			0
$490$	17.3015	+	6.47926i	0.781604	+	0.292703i
$491$	−14.8666			−0.670922			−0.335461	−	0.942054i	$-0.608892\pi$
$491$	−14.8666			−0.670922			−0.335461	+	0.942054i	$0.608892\pi$
$492$		0			0
$493$	−18.7233	−	18.7233i	−0.843254	−	0.843254i
$494$			1.50615i			0.0677648i
$495$		0			0
$496$		−	15.8519i		−	0.711770i
$497$	7.64858	+	1.20372i	0.343086	+	0.0539943i
$498$		0			0
$499$		−	31.4873i		−	1.40956i	−0.709424	−	0.704782i	$-0.751045\pi$
$499$		−	31.4873i		−	1.40956i	0.709424	−	0.704782i	$-0.248955\pi$
$500$	5.41341	−	4.08985i	0.242095	−	0.182904i
$501$		0			0
$502$	14.9593	−	14.9593i	0.667665	−	0.667665i
$503$	−8.21640	−	8.21640i	−0.366351	−	0.366351i	0.499794	−	0.866145i	$-0.333409\pi$
$503$	−8.21640	−	8.21640i	−0.366351	−	0.366351i	−0.866145	+	0.499794i	$0.833409\pi$
$504$		0			0
$505$	3.97061	+	4.35492i	0.176690	+	0.193791i
$506$	−39.7953			−1.76912
$507$		0			0
$508$	4.78378	−	4.78378i	0.212246	−	0.212246i
$509$	−34.3815			−1.52393			−0.761966	−	0.647616i	$-0.775766\pi$
$509$	−34.3815			−1.52393			−0.761966	+	0.647616i	$0.775766\pi$
$510$		0			0
$511$	−21.4119	−	29.4102i	−0.947208	−	1.30103i
$512$	16.1640	+	16.1640i	0.714353	+	0.714353i
$513$		0			0
$514$	26.4621			1.16719
$515$	−27.4896	−	1.26894i	−1.21134	−	0.0559162i
$516$		0			0
$517$	39.0027	−	39.0027i	1.71534	−	1.71534i
$518$	3.33472	−	21.1892i	0.146519	−	0.930998i
$519$		0			0
$520$	−1.51879	+	1.38476i	−0.0666035	+	0.0607259i
$521$			9.07830i			0.397727i	0.980027	+	0.198864i	$0.0637251\pi$
$521$			9.07830i			0.397727i	−0.980027	+	0.198864i	$0.936275\pi$
$522$		0			0
$523$	16.1622	+	16.1622i	0.706724	+	0.706724i	0.965845	−	0.259121i	$-0.0834327\pi$
$523$	16.1622	+	16.1622i	0.706724	+	0.706724i	−0.259121	+	0.965845i	$0.583433\pi$
$524$	−5.84541			−0.255358
$525$		0			0
$526$	4.47100			0.194945
$527$	30.4551	+	30.4551i	1.32664	+	1.32664i
$528$		0			0
$529$		−	16.4450i		−	0.715000i
$530$	−3.87004	+	3.52852i	−0.168104	+	0.153269i
$531$		0			0
$532$	−1.06622	+	6.77486i	−0.0462264	+	0.293728i
$533$	−0.404925	+	0.404925i	−0.0175393	+	0.0175393i
$534$		0			0
$535$	32.9015	+	1.51876i	1.42246	+	0.0656616i
$536$	−31.4926			−1.36027
$537$		0			0
$538$	−6.52470	−	6.52470i	−0.281300	−	0.281300i
$539$	35.7615	+	11.5421i	1.54036	+	0.497152i
$540$		0			0
$541$	−41.1554			−1.76941			−0.884704	−	0.466152i	$-0.845640\pi$
$541$	−41.1554			−1.76941			−0.884704	+	0.466152i	$0.845640\pi$
$542$	−26.4951	+	26.4951i	−1.13806	+	1.13806i
$543$		0			0
$544$	−21.6790			−0.929481
$545$	−9.93709	−	10.8989i	−0.425658	−	0.466858i
$546$		0			0
$547$	0.803089	+	0.803089i	0.0343376	+	0.0343376i	0.724067	−	0.689730i	$-0.242271\pi$
$547$	0.803089	+	0.803089i	0.0343376	+	0.0343376i	−0.689730	+	0.724067i	$0.742271\pi$
$548$	1.70527	−	1.70527i	0.0728455	−	0.0728455i
$549$		0			0
$550$	−24.3708	+	20.2432i	−1.03917	+	0.863171i
$551$			17.2157i			0.733414i
$552$		0			0
$553$	−1.14401	+	7.26915i	−0.0486481	+	0.309116i
$554$		−	14.6837i		−	0.623851i
$555$		0			0
$556$			5.35994i			0.227312i
$557$	−6.69005	−	6.69005i	−0.283466	−	0.283466i	0.551023	−	0.834490i	$-0.314238\pi$
$557$	−6.69005	−	6.69005i	−0.283466	−	0.283466i	−0.834490	+	0.551023i	$0.814238\pi$
$558$		0			0
$559$	−2.11726			−0.0895504
$560$	11.9411	−	7.87765i	0.504602	−	0.332892i
$561$		0			0
$562$	1.61491	+	1.61491i	0.0681209	+	0.0681209i
$563$	13.5785	+	13.5785i	0.572267	+	0.572267i	0.932761	−	0.360494i	$-0.117392\pi$
$563$	13.5785	+	13.5785i	0.572267	+	0.572267i	−0.360494	+	0.932761i	$0.617392\pi$
$564$		0			0
$565$	−1.57096	+	34.0325i	−0.0660909	+	1.43176i
$566$			13.3012i			0.559090i
$567$		0			0
$568$	6.36714	−	6.36714i	0.267159	−	0.267159i
$569$			22.3363i			0.936388i	0.883626	+	0.468194i	$0.155095\pi$
$569$			22.3363i			0.936388i	−0.883626	+	0.468194i	$0.844905\pi$
$570$		0			0
$571$	36.9515			1.54637			0.773186	−	0.634179i	$-0.218662\pi$
$571$	36.9515			1.54637			0.773186	+	0.634179i	$0.218662\pi$
$572$	−0.688134	+	0.688134i	−0.0287723	+	0.0287723i
$573$		0			0
$574$	4.83960	−	3.52344i	0.202001	−	0.147065i
$575$	−20.0649	−	24.1562i	−0.836766	−	1.00738i
$576$		0			0
$577$	−14.2142	+	14.2142i	−0.591745	+	0.591745i	−0.938103	−	0.346357i	$-0.887418\pi$
$577$	−14.2142	+	14.2142i	−0.591745	+	0.591745i	0.346357	+	0.938103i	$0.387418\pi$
$578$	−21.8370	+	21.8370i	−0.908298	+	0.908298i
$579$		0			0
$580$	−4.04125	+	3.68462i	−0.167804	+	0.152996i
$581$	9.86473	+	13.5496i	0.409258	+	0.562134i
$582$		0			0
$583$	−7.53234	+	7.53234i	−0.311958	+	0.311958i
$584$	−42.3074			−1.75069
$585$		0			0
$586$			7.42955i			0.306912i
$587$	−15.4368	+	15.4368i	−0.637146	+	0.637146i	−0.949851	−	0.312704i	$-0.898765\pi$
$587$	−15.4368	+	15.4368i	−0.637146	+	0.637146i	0.312704	+	0.949851i	$0.398765\pi$
$588$		0			0
$589$		−	28.0029i		−	1.15384i
$590$	3.53938	+	0.163380i	0.145714	+	0.00672626i
$591$		0			0
$592$	−11.7444	−	11.7444i	−0.482691	−	0.482691i
$593$	10.3544	+	10.3544i	0.425205	+	0.425205i	0.886991	−	0.461786i	$-0.152791\pi$
$593$	10.3544	+	10.3544i	0.425205	+	0.425205i	−0.461786	+	0.886991i	$0.652791\pi$
$594$		0			0
$595$	−7.80672	+	38.0762i	−0.320044	+	1.56097i
$596$	1.40058			0.0573699
$597$		0			0
$598$	1.56588	+	1.56588i	0.0640337	+	0.0640337i
$599$		−	26.9396i		−	1.10072i	−0.834927	−	0.550361i	$-0.814490\pi$
$599$		−	26.9396i		−	1.10072i	0.834927	−	0.550361i	$-0.185510\pi$
$600$		0			0
$601$			0.0891997i			0.00363853i	0.999998	+	0.00181926i	$0.000579090\pi$
$601$			0.0891997i			0.00363853i	−0.999998	+	0.00181926i	$0.999421\pi$
$602$	21.8641	+	3.44094i	0.891116	+	0.140242i
$603$		0			0
$604$		−	4.64529i		−	0.189014i
$605$	−29.4427	+	26.8444i	−1.19702	+	1.09138i
$606$		0			0
$607$	10.0616	−	10.0616i	0.408389	−	0.408389i	−0.472787	−	0.881177i	$-0.656752\pi$
$607$	10.0616	−	10.0616i	0.408389	−	0.408389i	0.881177	+	0.472787i	$0.156752\pi$
$608$	9.96673	+	9.96673i	0.404204	+	0.404204i
$609$		0			0
$610$	0.126479	−	2.73998i	0.00512100	−	0.110938i
$611$	−3.06939			−0.124174
$612$		0			0
$613$	16.0621	−	16.0621i	0.648743	−	0.648743i	−0.303946	−	0.952689i	$-0.598304\pi$
$613$	16.0621	−	16.0621i	0.648743	−	0.648743i	0.952689	+	0.303946i	$0.0983044\pi$
$614$	−10.8217			−0.436727
$615$		0			0
$616$	35.3303	−	25.7220i	1.42350	−	1.03637i
$617$	2.97487	+	2.97487i	0.119764	+	0.119764i	0.764448	−	0.644685i	$-0.223011\pi$
$617$	2.97487	+	2.97487i	0.119764	+	0.119764i	−0.644685	+	0.764448i	$0.723011\pi$
$618$		0			0
$619$	−2.85389			−0.114707			−0.0573537	−	0.998354i	$-0.518266\pi$
$619$	−2.85389			−0.114707			−0.0573537	+	0.998354i	$0.518266\pi$
$620$	6.57345	−	5.99336i	0.263996	−	0.240699i
$621$		0			0
$622$	−19.4727	+	19.4727i	−0.780784	+	0.780784i
$623$	−6.62548	−	1.04271i	−0.265444	−	0.0417752i
$624$		0			0
$625$	−24.5756	−	4.58667i	−0.983026	−	0.183467i
$626$		−	27.1360i		−	1.08457i
$627$		0			0
$628$	−0.797053	−	0.797053i	−0.0318059	−	0.0318059i
$629$	45.1272			1.79934
$630$		0			0
$631$	−43.5592			−1.73406			−0.867031	−	0.498253i	$-0.833975\pi$
$631$	−43.5592			−1.73406			−0.867031	+	0.498253i	$0.833975\pi$
$632$	6.05128	+	6.05128i	0.240707	+	0.240707i
$633$		0			0
$634$			8.87254i			0.352374i
$635$	−24.9020	−	1.14949i	−0.988206	−	0.0456163i
$636$		0			0
$637$	−0.952998	−	1.86132i	−0.0377591	−	0.0737482i
$638$	18.0574	−	18.0574i	0.714901	−	0.714901i
$639$		0			0
$640$	0.382098	−	8.27756i	0.0151038	−	0.327199i
$641$	−3.15773			−0.124723			−0.0623615	−	0.998054i	$-0.519863\pi$
$641$	−3.15773			−0.124723			−0.0623615	+	0.998054i	$0.519863\pi$
$642$		0			0
$643$	−20.6478	−	20.6478i	−0.814270	−	0.814270i	0.171001	−	0.985271i	$-0.445300\pi$
$643$	−20.6478	−	20.6478i	−0.814270	−	0.814270i	−0.985271	+	0.171001i	$0.945300\pi$
$644$	5.93505	+	8.15206i	0.233874	+	0.321236i
$645$		0			0
$646$	33.1247			1.30327
$647$	15.9052	−	15.9052i	0.625299	−	0.625299i	−0.321583	−	0.946882i	$-0.604215\pi$
$647$	15.9052	−	15.9052i	0.625299	−	0.625299i	0.946882	+	0.321583i	$0.104215\pi$
$648$		0			0
$649$	7.20675			0.282890
$650$	1.75549	+	0.162415i	0.0688558	+	0.00637044i
$651$		0			0
$652$	−0.0170012	−	0.0170012i	−0.000665820	−	0.000665820i
$653$	−1.09464	+	1.09464i	−0.0428366	+	0.0428366i	−0.728201	−	0.685364i	$-0.759643\pi$
$653$	−1.09464	+	1.09464i	−0.0428366	+	0.0428366i	0.685364	+	0.728201i	$0.259643\pi$
$654$		0			0
$655$	14.5119	+	15.9165i	0.567025	+	0.621907i
$656$		−	4.63532i		−	0.180979i
$657$		0			0
$658$	31.6964	+	4.98833i	1.23566	+	0.194465i
$659$		−	10.3823i		−	0.404438i	−0.979340	−	0.202219i	$-0.935185\pi$
$659$		−	10.3823i		−	0.404438i	0.979340	−	0.202219i	$-0.0648153\pi$
$660$		0			0
$661$		−	1.17964i		−	0.0458826i	−0.999737	−	0.0229413i	$-0.992697\pi$
$661$		−	1.17964i		−	0.0458826i	0.999737	−	0.0229413i	$-0.00730308\pi$
$662$	1.87045	+	1.87045i	0.0726972	+	0.0726972i
$663$		0			0
$664$	19.4915			0.756418
$665$	21.0943	−	13.9161i	0.818001	−	0.539645i
$666$		0			0
$667$	17.8985	+	17.8985i	0.693032	+	0.693032i
$668$	3.70970	+	3.70970i	0.143532	+	0.143532i
$669$		0			0
$670$	18.2002	+	19.9618i	0.703136	+	0.771192i
$671$		−	5.57904i		−	0.215376i
$672$		0			0
$673$	5.04729	−	5.04729i	0.194559	−	0.194559i	−0.603104	−	0.797663i	$-0.706070\pi$
$673$	5.04729	−	5.04729i	0.194559	−	0.194559i	0.797663	+	0.603104i	$0.206070\pi$
$674$			15.1115i			0.582073i
$675$		0			0
$676$	−7.83477			−0.301337
$677$	35.4227	−	35.4227i	1.36140	−	1.36140i	0.489272	−	0.872131i	$-0.337262\pi$
$677$	35.4227	−	35.4227i	1.36140	−	1.36140i	0.872131	−	0.489272i	$-0.162738\pi$
$678$		0			0
$679$	−39.7467	+	28.9373i	−1.52534	+	1.11051i
$680$	30.4551	+	33.4028i	1.16790	+	1.28094i
$681$		0			0
$682$	−29.3720	+	29.3720i	−1.12471	+	1.12471i
$683$	−15.7912	+	15.7912i	−0.604235	+	0.604235i	−0.941433	−	0.337199i	$-0.890521\pi$
$683$	−15.7912	+	15.7912i	−0.604235	+	0.604235i	0.337199	+	0.941433i	$0.390521\pi$
$684$		0			0
$685$	−8.87679	−	0.409759i	−0.339165	−	0.0156561i
$686$	6.81626	+	20.7700i	0.260246	+	0.793002i
$687$		0			0
$688$	12.1185	−	12.1185i	0.462013	−	0.462013i
$689$	0.592771			0.0225828
$690$		0			0
$691$			12.7766i			0.486043i	0.970021	+	0.243022i	$0.0781386\pi$
$691$			12.7766i			0.486043i	−0.970021	+	0.243022i	$0.921861\pi$
$692$	−6.14304	+	6.14304i	−0.233523	+	0.233523i
$693$		0			0
$694$		−	23.7974i		−	0.903337i
$695$	14.5946	−	13.3066i	0.553604	−	0.504749i
$696$		0			0
$697$	8.90551	+	8.90551i	0.337320	+	0.337320i
$698$	20.8679	+	20.8679i	0.789862	+	0.789862i
$699$		0			0
$700$	7.78144	+	1.97329i	0.294111	+	0.0745834i
$701$	−0.236603			−0.00893637			−0.00446819	−	0.999990i	$-0.501422\pi$
$701$	−0.236603			−0.00893637			−0.00446819	+	0.999990i	$0.501422\pi$
$702$		0			0
$703$	−20.7468	−	20.7468i	−0.782482	−	0.782482i
$704$		−	46.8698i		−	1.76647i
$705$		0			0
$706$			23.5927i			0.887923i
$707$	−1.08407	+	6.88827i	−0.0407705	+	0.259060i
$708$		0			0
$709$			21.9016i			0.822531i	0.911516	+	0.411266i	$0.134913\pi$
$709$			21.9016i			0.822531i	−0.911516	+	0.411266i	$0.865087\pi$
$710$	−7.71557	−	0.356156i	−0.289560	−	0.0133663i
$711$		0			0
$712$	−5.51545	+	5.51545i	−0.206700	+	0.206700i
$713$	−29.1135	−	29.1135i	−1.09031	−	1.09031i
$714$		0			0
$715$	3.58209	+	0.165352i	0.133962	+	0.00618381i
$716$	13.9036			0.519604
$717$		0			0
$718$	3.80948	−	3.80948i	0.142168	−	0.142168i
$719$	−22.0183			−0.821143			−0.410571	−	0.911829i	$-0.634671\pi$
$719$	−22.0183			−0.821143			−0.410571	+	0.911829i	$0.634671\pi$
$720$		0			0
$721$	−19.1646	−	26.3234i	−0.713727	−	0.980336i
$722$	0.628891	+	0.628891i	0.0234049	+	0.0234049i
$723$		0			0
$724$	6.51501			0.242128
$725$	20.0657	+	1.85645i	0.745222	+	0.0689468i
$726$		0			0
$727$	20.8625	−	20.8625i	0.773748	−	0.773748i	−0.205012	−	0.978760i	$-0.565723\pi$
$727$	20.8625	−	20.8625i	0.773748	−	0.773748i	0.978760	+	0.205012i	$0.0657233\pi$
$728$	−2.40231	−	0.378072i	−0.0890355	−	0.0140123i
$729$		0			0
$730$	24.4504	+	26.8169i	0.904949	+	0.992538i
$731$			46.5647i			1.72226i
$732$		0			0
$733$	−24.6466	−	24.6466i	−0.910342	−	0.910342i	0.0859573	−	0.996299i	$-0.472605\pi$
$733$	−24.6466	−	24.6466i	−0.910342	−	0.910342i	−0.996299	+	0.0859573i	$0.972605\pi$
$734$	2.96376			0.109394
$735$		0			0
$736$	20.7240			0.763898
$737$	38.8521	+	38.8521i	1.43113	+	1.43113i
$738$		0			0
$739$			13.8298i			0.508738i	0.967107	+	0.254369i	$0.0818678\pi$
$739$			13.8298i			0.508738i	−0.967107	+	0.254369i	$0.918132\pi$
$740$	0.429781	−	9.31053i	0.0157991	−	0.342262i
$741$		0			0
$742$	−6.12133	−	0.963365i	−0.224721	−	0.0353663i
$743$	23.9640	−	23.9640i	0.879156	−	0.879156i	−0.114292	−	0.993447i	$-0.536460\pi$
$743$	23.9640	−	23.9640i	0.879156	−	0.879156i	0.993447	+	0.114292i	$0.0364598\pi$
$744$		0			0
$745$	−3.47709	−	3.81363i	−0.127391	−	0.139721i
$746$	15.7586			0.576963
$747$		0			0
$748$	15.1341	+	15.1341i	0.553358	+	0.553358i
$749$	22.9375	+	31.5057i	0.838119	+	1.15119i
$750$		0			0
$751$	−19.8695			−0.725049			−0.362525	−	0.931974i	$-0.618085\pi$
$751$	−19.8695			−0.725049			−0.362525	+	0.931974i	$0.618085\pi$
$752$	17.5682	−	17.5682i	0.640645	−	0.640645i
$753$		0			0
$754$	−1.42106			−0.0517521
$755$	−12.6487	+	11.5324i	−0.460332	+	0.419708i
$756$		0			0
$757$	12.3668	+	12.3668i	0.449480	+	0.449480i	0.895182	−	0.445701i	$-0.147046\pi$
$757$	12.3668	+	12.3668i	0.449480	+	0.449480i	−0.445701	+	0.895182i	$0.647046\pi$
$758$	−13.4798	+	13.4798i	−0.489609	+	0.489609i
$759$		0			0
$760$	1.35519	−	29.3581i	0.0491579	−	1.06493i
$761$			5.77211i			0.209239i	0.994512	+	0.104619i	$0.0333624\pi$
$761$			5.77211i			0.209239i	−0.994512	+	0.104619i	$0.966638\pi$
$762$		0			0
$763$	2.71305	−	17.2390i	0.0982190	−	0.624095i
$764$		−	10.4310i		−	0.377379i
$765$		0			0
$766$			23.6996i			0.856303i
$767$	−0.283574	−	0.283574i	−0.0102393	−	0.0102393i
$768$		0			0
$769$	−33.2996			−1.20081			−0.600407	−	0.799694i	$-0.704995\pi$
$769$	−33.2996			−1.20081			−0.600407	+	0.799694i	$0.704995\pi$
$770$	−36.7222	−	7.52910i	−1.32338	−	0.271330i
$771$		0			0
$772$	6.81353	+	6.81353i	0.245224	+	0.245224i
$773$	−16.3711	−	16.3711i	−0.588829	−	0.588829i	0.348485	−	0.937314i	$-0.386696\pi$
$773$	−16.3711	−	16.3711i	−0.588829	−	0.588829i	−0.937314	+	0.348485i	$0.886696\pi$
$774$		0			0
$775$	−32.6386	−	3.01968i	−1.17241	−	0.108470i
$776$			57.1768i			2.05253i
$777$		0			0
$778$	−21.9302	+	21.9302i	−0.786237	+	0.786237i
$779$		−	8.18846i		−	0.293382i
$780$		0			0
$781$	−15.7102			−0.562153
$782$	34.4384	−	34.4384i	1.23151	−	1.23151i
$783$		0			0
$784$	16.1082	+	5.19895i	0.575294	+	0.185677i
$785$	−0.191524	+	4.14907i	−0.00683578	+	0.148087i
$786$		0			0
$787$	−25.5165	+	25.5165i	−0.909564	+	0.909564i	−0.996237	−	0.0866724i	$-0.972377\pi$
$787$	−25.5165	+	25.5165i	−0.909564	+	0.909564i	0.0866724	+	0.996237i	$0.472377\pi$
$788$	2.98733	−	2.98733i	0.106419	−	0.106419i
$789$		0			0
$790$	0.338488	−	7.33281i	0.0120429	−	0.260890i
$791$	−32.5887	+	23.7260i	−1.15872	+	0.843599i
$792$		0			0
$793$	−0.219526	+	0.219526i	−0.00779561	+	0.00779561i
$794$	−42.7139			−1.51586
$795$		0			0
$796$			5.36395i			0.190120i
$797$	−4.81872	+	4.81872i	−0.170688	+	0.170688i	−0.787281	−	0.616594i	$-0.788512\pi$
$797$	−4.81872	+	4.81872i	−0.170688	+	0.170688i	0.616594	+	0.787281i	$0.288512\pi$
$798$		0			0
$799$			67.5049i			2.38815i
$800$	12.6914	−	10.5419i	0.448710	−	0.372713i
$801$		0			0
$802$	6.52870	+	6.52870i	0.230536	+	0.230536i
$803$	52.1943	+	52.1943i	1.84190	+	1.84190i
$804$		0			0
$805$	7.46282	−	36.3989i	0.263030	−	1.28289i
$806$	2.31148			0.0814186
$807$		0			0
$808$	5.73421	+	5.73421i	0.201729	+	0.201729i
$809$			11.9948i			0.421715i	0.977517	+	0.210858i	$0.0676256\pi$
$809$			11.9948i			0.421715i	−0.977517	+	0.210858i	$0.932374\pi$
$810$		0			0
$811$			45.1121i			1.58410i	0.610457	+	0.792049i	$0.290986\pi$
$811$			45.1121i			1.58410i	−0.610457	+	0.792049i	$0.709014\pi$
$812$	−6.39214	−	1.00598i	−0.224320	−	0.0353031i
$813$		0			0
$814$			43.5224i			1.52546i
$815$	−0.00408523	+	0.0885001i	−0.000143099	+	0.00310002i
$816$		0			0
$817$	21.4077	−	21.4077i	0.748961	−	0.748961i
$818$	−16.6739	−	16.6739i	−0.582989	−	0.582989i
$819$		0			0
$820$	1.92218	−	1.75255i	0.0671253	−	0.0612016i
$821$	19.1184			0.667237			0.333619	−	0.942708i	$-0.391730\pi$
$821$	19.1184			0.667237			0.333619	+	0.942708i	$0.391730\pi$
$822$		0			0
$823$	−26.7028	+	26.7028i	−0.930802	+	0.930802i	−0.997756	−	0.0669541i	$-0.978672\pi$
$823$	−26.7028	+	26.7028i	−0.930802	+	0.930802i	0.0669541	+	0.997756i	$0.478672\pi$
$824$	−37.8670			−1.31916
$825$		0			0
$826$	2.46750	+	3.38923i	0.0858554	+	0.117926i
$827$	38.9060	+	38.9060i	1.35289	+	1.35289i	0.882406	+	0.470489i	$0.155922\pi$
$827$	38.9060	+	38.9060i	1.35289	+	1.35289i	0.470489	+	0.882406i	$0.344078\pi$
$828$		0			0
$829$	50.9527			1.76966			0.884830	−	0.465915i	$-0.154275\pi$
$829$	50.9527			1.76966			0.884830	+	0.465915i	$0.154275\pi$
$830$	−11.2646	−	12.3549i	−0.390999	−	0.428843i
$831$		0			0
$832$	−1.84425	+	1.84425i	−0.0639379	+	0.0639379i
$833$	−40.9360	+	20.9592i	−1.41835	+	0.726195i
$834$		0			0
$835$	0.891403	−	19.3109i	0.0308483	−	0.668280i
$836$		−	13.9155i		−	0.481279i
$837$		0			0
$838$	−20.1026	−	20.1026i	−0.694432	−	0.694432i
$839$	−18.9255			−0.653382			−0.326691	−	0.945131i	$-0.605934\pi$
$839$	−18.9255			−0.653382			−0.326691	+	0.945131i	$0.605934\pi$
$840$		0			0
$841$	12.7568			0.439891
$842$	−9.17313	−	9.17313i	−0.316127	−	0.316127i
$843$		0			0
$844$		−	14.1426i		−	0.486809i
$845$	19.4507	+	21.3333i	0.669124	+	0.733888i
$846$		0			0
$847$	−46.5701	−	7.32913i	−1.60017	−	0.251832i
$848$	−3.39283	+	3.39283i	−0.116510	+	0.116510i
$849$		0			0
$850$	3.57199	−	38.6084i	0.122518	−	1.32426i
$851$	−43.1393			−1.47880
$852$		0			0
$853$	10.3473	+	10.3473i	0.354285	+	0.354285i	0.861701	−	0.507416i	$-0.169399\pi$
$853$	10.3473	+	10.3473i	0.354285	+	0.354285i	−0.507416	+	0.861701i	$0.669399\pi$
$854$	2.62374	−	1.91020i	0.0897825	−	0.0653656i
$855$		0			0
$856$	45.3219			1.54907
$857$	−6.66606	+	6.66606i	−0.227708	+	0.227708i	−0.811735	−	0.584026i	$-0.801476\pi$
$857$	−6.66606	+	6.66606i	−0.227708	+	0.227708i	0.584026	+	0.811735i	$0.301476\pi$
$858$		0			0
$859$	8.54137			0.291428			0.145714	−	0.989327i	$-0.453452\pi$
$859$	8.54137			0.291428			0.145714	+	0.989327i	$0.453452\pi$
$860$	9.60711	+	0.443471i	0.327600	+	0.0151222i
$861$		0			0
$862$	−13.0071	−	13.0071i	−0.443023	−	0.443023i
$863$	15.3649	−	15.3649i	0.523026	−	0.523026i	−0.395458	−	0.918484i	$-0.629414\pi$
$863$	15.3649	−	15.3649i	0.523026	−	0.523026i	0.918484	+	0.395458i	$0.129414\pi$
$864$		0			0
$865$	31.9776	+	1.47611i	1.08727	+	0.0501893i
$866$		−	44.9683i		−	1.52809i
$867$		0			0
$868$	10.3974	+	1.63632i	0.352910	+	0.0555404i
$869$		−	14.9308i		−	0.506493i
$870$		0			0
$871$		−	3.05753i		−	0.103601i
$872$	−14.3508	−	14.3508i	−0.485980	−	0.485980i
$873$		0			0
$874$	−31.6655			−1.07110
$875$	−13.9452	−	26.0870i	−0.471434	−	0.881901i
$876$		0			0
$877$	−13.4460	−	13.4460i	−0.454040	−	0.454040i	0.442653	−	0.896693i	$-0.354037\pi$
$877$	−13.4460	−	13.4460i	−0.454040	−	0.454040i	−0.896693	+	0.442653i	$0.854037\pi$
$878$	26.2377	+	26.2377i	0.885478	+	0.885478i
$879$		0			0
$880$	−21.4491	+	19.5563i	−0.723050	+	0.659242i
$881$		−	38.9446i		−	1.31208i	−0.754727	−	0.656039i	$-0.772231\pi$
$881$		−	38.9446i		−	1.31208i	0.754727	−	0.656039i	$-0.227769\pi$
$882$		0			0
$883$	−41.0363	+	41.0363i	−1.38098	+	1.38098i	−0.538104	+	0.842878i	$0.680859\pi$
$883$	−41.0363	+	41.0363i	−1.38098	+	1.38098i	−0.842878	+	0.538104i	$0.819141\pi$
$884$		−	1.19101i		−	0.0400579i
$885$		0			0
$886$	3.88280			0.130445
$887$	24.0739	−	24.0739i	0.808321	−	0.808321i	−0.176058	−	0.984380i	$-0.556335\pi$
$887$	24.0739	−	24.0739i	0.808321	−	0.808321i	0.984380	+	0.176058i	$0.0563348\pi$
$888$		0			0
$889$	−17.3606	−	23.8456i	−0.582257	−	0.799756i
$890$	6.68350	+	0.308515i	0.224032	+	0.0103415i
$891$		0			0
$892$	0.262984	−	0.262984i	0.00880535	−	0.00880535i
$893$	31.0348	−	31.0348i	1.03854	−	1.03854i
$894$		0			0
$895$	−34.5173	−	37.8582i	−1.15379	−	1.26546i
$896$	7.92640	−	5.77076i	0.264802	−	0.192788i
$897$		0			0
$898$	−8.97246	+	8.97246i	−0.299415	+	0.299415i
$899$	26.4209			0.881187
$900$		0			0
$901$		−	13.0368i		−	0.434319i
$902$	−8.58882	+	8.58882i	−0.285976	+	0.285976i
$903$		0			0
$904$			46.8798i			1.55920i
$905$	−16.1742	−	17.7397i	−0.537649	−	0.589688i
$906$		0			0
$907$	39.8310	+	39.8310i	1.32257	+	1.32257i	0.911692	+	0.410874i	$0.134776\pi$
$907$	39.8310	+	39.8310i	1.32257	+	1.32257i	0.410874	+	0.911692i	$0.365224\pi$
$908$	3.61003	+	3.61003i	0.119803	+	0.119803i
$909$		0			0
$910$	1.14870	+	1.74122i	0.0380791	+	0.0577208i
$911$	−43.1171			−1.42853			−0.714267	−	0.699874i	$-0.753240\pi$
$911$	−43.1171			−1.42853			−0.714267	+	0.699874i	$0.753240\pi$
$912$		0			0
$913$	−24.0465	−	24.0465i	−0.795823	−	0.795823i
$914$			29.9093i			0.989311i
$915$		0			0
$916$			1.06262i			0.0351101i
$917$	−3.96206	+	25.1754i	−0.130839	+	0.831365i
$918$		0			0
$919$			18.4346i			0.608101i	0.952656	+	0.304051i	$0.0983392\pi$
$919$			18.4346i			0.608101i	−0.952656	+	0.304051i	$0.901661\pi$
$920$	−29.1135	−	31.9313i	−0.959842	−	1.05274i
$921$		0			0
$922$	12.2568	−	12.2568i	0.403655	−	0.403655i
$923$	0.618169	+	0.618169i	0.0203473	+	0.0203473i
$924$		0			0
$925$	−26.4186	+	21.9442i	−0.868639	+	0.721520i
$926$	−8.49552			−0.279180
$927$		0			0
$928$	−9.40369	+	9.40369i	−0.308691	+	0.308691i
$929$	7.44762			0.244349			0.122174	−	0.992509i	$-0.461013\pi$
$929$	7.44762			0.244349			0.122174	+	0.992509i	$0.461013\pi$
$930$		0			0
$931$	28.4558	+	9.18411i	0.932600	+	0.300997i
$932$	−8.63742	−	8.63742i	−0.282928	−	0.282928i
$933$		0			0
$934$	−37.2549			−1.21902
$935$	3.63658	−	78.7808i	0.118929	−	2.57641i
$936$		0			0
$937$	2.21948	−	2.21948i	0.0725073	−	0.0725073i	−0.669923	−	0.742430i	$-0.733673\pi$
$937$	2.21948	−	2.21948i	0.0725073	−	0.0725073i	0.742430	+	0.669923i	$0.233673\pi$
$938$	−4.96907	+	31.5740i	−0.162246	+	1.03093i
$939$		0			0
$940$	13.9274	+	0.642900i	0.454263	+	0.0209691i
$941$			39.7630i			1.29624i	0.761540	+	0.648118i	$0.224443\pi$
$941$			39.7630i			1.29624i	−0.761540	+	0.648118i	$0.775557\pi$
$942$		0			0
$943$	−8.51321	−	8.51321i	−0.277228	−	0.277228i
$944$	3.24617			0.105654
$945$		0			0
$946$	−44.9088			−1.46011
$947$	−15.8124	−	15.8124i	−0.513835	−	0.513835i	0.401864	−	0.915699i	$-0.368362\pi$
$947$	−15.8124	−	15.8124i	−0.513835	−	0.513835i	−0.915699	+	0.401864i	$0.868362\pi$
$948$		0			0
$949$		−	4.10752i		−	0.133336i
$950$	−19.3920	+	16.1076i	−0.629160	+	0.522601i
$951$		0			0
$952$	−8.31492	+	52.8339i	−0.269488	+	1.71236i
$953$	−24.9374	+	24.9374i	−0.807803	+	0.807803i	−0.984301	−	0.176498i	$-0.943523\pi$
$953$	−24.9374	+	24.9374i	−0.807803	+	0.807803i	0.176498	+	0.984301i	$0.443523\pi$
$954$		0			0
$955$	−28.4024	+	25.8960i	−0.919081	+	0.837974i
$956$	10.3976			0.336281
$957$		0			0
$958$	31.0054	+	31.0054i	1.00174	+	1.00174i
$959$	−6.18852	−	8.50021i	−0.199838	−	0.274486i
$960$		0			0
$961$	−11.9760			−0.386322
$962$	1.71254	−	1.71254i	0.0552145	−	0.0552145i
$963$		0			0
$964$	0.668028			0.0215157
$965$	1.63722	−	35.4679i	0.0527041	−	1.14175i
$966$		0			0
$967$	32.3820	+	32.3820i	1.04133	+	1.04133i	0.999108	+	0.0422262i	$0.0134450\pi$
$967$	32.3820	+	32.3820i	1.04133	+	1.04133i	0.0422262	+	0.999108i	$0.486555\pi$
$968$	−38.7678	+	38.7678i	−1.24604	+	1.24604i
$969$		0			0
$970$	36.2419	−	33.0437i	1.16366	−	1.06097i
$971$			12.9902i			0.416877i	0.978036	+	0.208438i	$0.0668380\pi$
$971$			12.9902i			0.416877i	−0.978036	+	0.208438i	$0.933162\pi$
$972$		0			0
$973$	23.0846	+	3.63301i	0.740057	+	0.116469i
$974$			7.36563i			0.236010i
$975$		0			0
$976$		−	2.51299i		−	0.0804390i
$977$	−35.1310	−	35.1310i	−1.12394	−	1.12394i	−0.991143	−	0.132798i	$-0.957604\pi$
$977$	−35.1310	−	35.1310i	−1.12394	−	1.12394i	−0.132798	−	0.991143i	$-0.542396\pi$
$978$		0			0
$979$	13.6087			0.434936
$980$	3.93439	+	8.64541i	0.125680	+	0.276168i
$981$		0			0
$982$	12.4079	+	12.4079i	0.395952	+	0.395952i
$983$	4.28795	+	4.28795i	0.136764	+	0.136764i	0.772175	−	0.635410i	$-0.219169\pi$
$983$	4.28795	+	4.28795i	0.136764	+	0.136764i	−0.635410	+	0.772175i	$0.719169\pi$
$984$		0			0
$985$	−15.5506	−	0.717826i	−0.495483	−	0.0228719i
$986$			31.2534i			0.995311i
$987$		0			0
$988$	−0.547554	+	0.547554i	−0.0174200	+	0.0174200i
$989$		−	44.5135i		−	1.41545i
$990$		0			0
$991$	−2.67606			−0.0850080			−0.0425040	−	0.999096i	$-0.513534\pi$
$991$	−2.67606			−0.0850080			−0.0425040	+	0.999096i	$0.513534\pi$
$992$	15.2959	−	15.2959i	0.485646	−	0.485646i
$993$		0			0
$994$	−5.37897	−	7.38825i	−0.170610	−	0.234341i
$995$	14.6055	−	13.3166i	0.463026	−	0.422165i
$996$		0			0
$997$	−3.09258	+	3.09258i	−0.0979429	+	0.0979429i	−0.754380	−	0.656437i	$-0.772063\pi$
$997$	−3.09258	+	3.09258i	−0.0979429	+	0.0979429i	0.656437	+	0.754380i	$0.272063\pi$
$998$	−26.2797	+	26.2797i	−0.831869	+	0.831869i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.p.b.622.7	yes	48
3.2	odd	2	inner	945.2.p.b.622.18	yes	48
5.3	odd	4	inner	945.2.p.b.433.8	yes	48
7.6	odd	2	inner	945.2.p.b.622.8	yes	48
15.8	even	4	inner	945.2.p.b.433.17	yes	48
21.20	even	2	inner	945.2.p.b.622.17	yes	48
35.13	even	4	inner	945.2.p.b.433.7	✓	48
105.83	odd	4	inner	945.2.p.b.433.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.p.b.433.7	✓	48	35.13	even	4	inner
945.2.p.b.433.8	yes	48	5.3	odd	4	inner
945.2.p.b.433.17	yes	48	15.8	even	4	inner
945.2.p.b.433.18	yes	48	105.83	odd	4	inner
945.2.p.b.622.7	yes	48	1.1	even	1	trivial
945.2.p.b.622.8	yes	48	7.6	odd	2	inner
945.2.p.b.622.17	yes	48	21.20	even	2	inner
945.2.p.b.622.18	yes	48	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.834614 - 0.834614i) q^{2} -0.606840i q^{4} +(-1.65237 + 1.50655i) q^{5} +(-2.61358 - 0.411321i) q^{7} +(-2.17570 + 2.17570i) q^{8} +O(q^{10})\)	\(q+(-0.834614 - 0.834614i) q^{2} -0.606840i q^{4} +(-1.65237 + 1.50655i) q^{5} +(-2.61358 - 0.411321i) q^{7} +(-2.17570 + 2.17570i) q^{8} +(2.63647 + 0.121701i) q^{10} +5.36829 q^{11} +(-0.211233 - 0.211233i) q^{13} +(1.83804 + 2.52463i) q^{14} +2.41806 q^{16} +(-4.64565 + 4.64565i) q^{17} +4.27159 q^{19} +(0.914234 + 1.00272i) q^{20} +(-4.48045 - 4.48045i) q^{22} +(4.44100 - 4.44100i) q^{23} +(0.460626 - 4.97874i) q^{25} +0.352597i q^{26} +(-0.249607 + 1.58603i) q^{28} +4.03028i q^{29} -6.55561i q^{31} +(2.33326 + 2.33326i) q^{32} +7.75465 q^{34} +(4.93827 - 3.25783i) q^{35} +(-4.85693 - 4.85693i) q^{37} +(-3.56513 - 3.56513i) q^{38} +(0.317256 - 6.87286i) q^{40} -1.91696i q^{41} +(5.01165 - 5.01165i) q^{43} -3.25769i q^{44} -7.41304 q^{46} +(7.26539 - 7.26539i) q^{47} +(6.66163 + 2.15005i) q^{49} +(-4.53977 + 3.77088i) q^{50} +(-0.128185 + 0.128185i) q^{52} +(-1.40312 + 1.40312i) q^{53} +(-8.87037 + 8.08758i) q^{55} +(6.58130 - 4.79147i) q^{56} +(3.36373 - 3.36373i) q^{58} +1.34247 q^{59} -1.03926i q^{61} +(-5.47140 + 5.47140i) q^{62} -8.73087i q^{64} +(0.667268 + 0.0308016i) q^{65} +(7.23733 + 7.23733i) q^{67} +(2.81917 + 2.81917i) q^{68} +(-6.84058 - 1.40251i) q^{70} -2.92647 q^{71} +(9.72270 + 9.72270i) q^{73} +8.10732i q^{74} -2.59217i q^{76} +(-14.0305 - 2.20809i) q^{77} -2.78130i q^{79} +(-3.99553 + 3.64293i) q^{80} +(-1.59992 + 1.59992i) q^{82} +(-4.47936 - 4.47936i) q^{83} +(0.677418 - 14.6752i) q^{85} -8.36558 q^{86} +(-11.6798 + 11.6798i) q^{88} +2.53502 q^{89} +(0.465191 + 0.638961i) q^{91} +(-2.69498 - 2.69498i) q^{92} -12.1276 q^{94} +(-7.05823 + 6.43536i) q^{95} +(13.1398 - 13.1398i) q^{97} +(-3.76543 - 7.35434i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{7}+O(q^{10}) \) 48 * q - 8 * q^7	\( 48 q - 8 q^{7} + 40 q^{16} + 8 q^{22} - 48 q^{25} - 20 q^{28} - 24 q^{37} - 40 q^{43} + 40 q^{46} - 80 q^{58} - 64 q^{67} - 4 q^{70} - 8 q^{85} - 48 q^{88} + 48 q^{91}+O(q^{100}) \) 48 * q - 8 * q^7 + 40 * q^16 + 8 * q^22 - 48 * q^25 - 20 * q^28 - 24 * q^37 - 40 * q^43 + 40 * q^46 - 80 * q^58 - 64 * q^67 - 4 * q^70 - 8 * q^85 - 48 * q^88 + 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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