LMFDB - Embedded newform 536.2.q.a.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [536,2,Mod(9,536)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(536, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([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("536.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 536 = 2^{3} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	536.q (of order $11$, degree $10$, 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:	$4.27998154834$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	536.25
Dual form			536.2.q.a.193.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0837208 + 0.0966190i) q^{3} +(-1.91873 + 1.23309i) q^{5} +(-0.0678491 - 0.471901i) q^{7} +(0.424618 + 2.95329i) q^{9} +O(q^{10})$	\(q+(-0.0837208 + 0.0966190i) q^{3} +(-1.91873 + 1.23309i) q^{5} +(-0.0678491 - 0.471901i) q^{7} +(0.424618 + 2.95329i) q^{9} +(1.90666 - 1.22534i) q^{11} +(-0.0421648 + 0.0923281i) q^{13} +(0.0414976 - 0.288622i) q^{15} +(-6.98735 - 2.05167i) q^{17} +(-0.924017 + 6.42668i) q^{19} +(0.0512750 + 0.0329524i) q^{21} +(-4.99260 + 5.76176i) q^{23} +(0.0839382 - 0.183799i) q^{25} +(-0.643544 - 0.413581i) q^{27} -3.72350 q^{29} +(3.37298 + 7.38579i) q^{31} +(-0.0412366 + 0.286807i) q^{33} +(0.712083 + 0.821787i) q^{35} -7.40784 q^{37} +(-0.00539058 - 0.0118037i) q^{39} +(9.80987 + 2.88044i) q^{41} +(1.60308 + 0.470707i) q^{43} +(-4.45641 - 5.14297i) q^{45} +(8.47072 - 9.77573i) q^{47} +(6.49836 - 1.90809i) q^{49} +(0.783218 - 0.503343i) q^{51} +(-10.3176 + 3.02952i) q^{53} +(-2.14742 + 4.70220i) q^{55} +(-0.543580 - 0.627325i) q^{57} +(-0.863986 - 1.89186i) q^{59} +(-9.36127 - 6.01612i) q^{61} +(1.36485 - 0.400756i) q^{63} +(-0.0329463 - 0.229146i) q^{65} +(7.97017 + 1.86452i) q^{67} +(-0.138712 - 0.964760i) q^{69} +(11.8910 - 3.49151i) q^{71} +(5.23294 + 3.36301i) q^{73} +(0.0107311 + 0.0234978i) q^{75} +(-0.707604 - 0.816619i) q^{77} +(-2.83565 + 6.20920i) q^{79} +(-8.49455 + 2.49423i) q^{81} +(-3.92100 + 2.51987i) q^{83} +(15.9368 - 4.67946i) q^{85} +(0.311734 - 0.359760i) q^{87} +(-4.42813 - 5.11033i) q^{89} +(0.0464306 + 0.0136332i) q^{91} +(-0.995996 - 0.292451i) q^{93} +(-6.15176 - 13.4705i) q^{95} +16.1422 q^{97} +(4.42838 + 5.11063i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{3} + q^{5} - 6 q^{7} - 7 q^{9}+O(q^{10}) $ 80 * q - q^3 + q^5 - 6 * q^7 - 7 * q^9	$ 80 q - q^{3} + q^{5} - 6 q^{7} - 7 q^{9} - q^{11} - q^{13} - 6 q^{15} + 8 q^{17} + 7 q^{19} + 71 q^{21} - 18 q^{23} - 5 q^{25} - 4 q^{27} - 14 q^{29} - 34 q^{31} - 24 q^{33} + 20 q^{35} - 40 q^{37} + 21 q^{39} - 70 q^{41} + 10 q^{43} + 34 q^{45} - 8 q^{47} + 10 q^{49} + 10 q^{51} - 39 q^{53} - 50 q^{55} + 35 q^{57} - 66 q^{59} + 4 q^{61} + 21 q^{63} + 20 q^{65} - 24 q^{67} - 8 q^{69} - 13 q^{71} + 25 q^{73} + 44 q^{75} + 15 q^{77} + 59 q^{79} + 16 q^{81} - 51 q^{83} + 59 q^{85} - 26 q^{87} + 58 q^{89} + 16 q^{91} + 87 q^{93} - 56 q^{95} - 30 q^{97} + 93 q^{99}+O(q^{100}) $ 80 * q - q^3 + q^5 - 6 * q^7 - 7 * q^9 - q^11 - q^13 - 6 * q^15 + 8 * q^17 + 7 * q^19 + 71 * q^21 - 18 * q^23 - 5 * q^25 - 4 * q^27 - 14 * q^29 - 34 * q^31 - 24 * q^33 + 20 * q^35 - 40 * q^37 + 21 * q^39 - 70 * q^41 + 10 * q^43 + 34 * q^45 - 8 * q^47 + 10 * q^49 + 10 * q^51 - 39 * q^53 - 50 * q^55 + 35 * q^57 - 66 * q^59 + 4 * q^61 + 21 * q^63 + 20 * q^65 - 24 * q^67 - 8 * q^69 - 13 * q^71 + 25 * q^73 + 44 * q^75 + 15 * q^77 + 59 * q^79 + 16 * q^81 - 51 * q^83 + 59 * q^85 - 26 * q^87 + 58 * q^89 + 16 * q^91 + 87 * q^93 - 56 * q^95 - 30 * q^97 + 93 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/536\mathbb{Z}\right)^\times$.

$n$	$135$	$269$	$337$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{11}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0837208	+	0.0966190i	−0.0483363	+	0.0557830i	−0.779403	−	0.626523i	$-0.784477\pi$
$3$	−0.0837208	+	0.0966190i	−0.0483363	+	0.0557830i	0.731067	+	0.682306i	$0.239023\pi$
$4$		0			0
$5$	−1.91873	+	1.23309i	−0.858083	+	0.551457i	−0.894086	−	0.447895i	$-0.852174\pi$
$5$	−1.91873	+	1.23309i	−0.858083	+	0.551457i	0.0360028	+	0.999352i	$0.488537\pi$
$6$		0			0
$7$	−0.0678491	−	0.471901i	−0.0256445	−	0.178362i	0.972973	−	0.230917i	$-0.0741726\pi$
$7$	−0.0678491	−	0.471901i	−0.0256445	−	0.178362i	−0.998618	+	0.0525552i	$0.983263\pi$
$8$		0			0
$9$	0.424618	+	2.95329i	0.141539	+	0.984429i
$10$		0			0
$11$	1.90666	−	1.22534i	0.574881	−	0.369454i	−0.220662	−	0.975350i	$-0.570822\pi$
$11$	1.90666	−	1.22534i	0.574881	−	0.369454i	0.795543	+	0.605897i	$0.207185\pi$
$12$		0			0
$13$	−0.0421648	+	0.0923281i	−0.0116944	+	0.0256072i	−0.915389	−	0.402570i	$-0.868117\pi$
$13$	−0.0421648	+	0.0923281i	−0.0116944	+	0.0256072i	0.903695	+	0.428177i	$0.140844\pi$
$14$		0			0
$15$	0.0414976	−	0.288622i	0.0107146	−	0.0745218i
$16$		0			0
$17$	−6.98735	−	2.05167i	−1.69468	−	0.497603i	−0.715163	−	0.698957i	$-0.753648\pi$
$17$	−6.98735	−	2.05167i	−1.69468	−	0.497603i	−0.979519	+	0.201354i	$0.935466\pi$
$18$		0			0
$19$	−0.924017	+	6.42668i	−0.211984	+	1.47438i	0.554535	+	0.832160i	$0.312896\pi$
$19$	−0.924017	+	6.42668i	−0.211984	+	1.47438i	−0.766519	+	0.642221i	$0.778013\pi$
$20$		0			0
$21$	0.0512750	+	0.0329524i	0.0111891	+	0.00719081i
$22$		0			0
$23$	−4.99260	+	5.76176i	−1.04103	+	1.20141i	−0.0619183	+	0.998081i	$0.519722\pi$
$23$	−4.99260	+	5.76176i	−1.04103	+	1.20141i	−0.979110	+	0.203330i	$0.934824\pi$
$24$		0			0
$25$	0.0839382	−	0.183799i	0.0167876	−	0.0367598i
$26$		0			0
$27$	−0.643544	−	0.413581i	−0.123850	−	0.0795936i
$28$		0			0
$29$	−3.72350			−0.691436			−0.345718	−	0.938338i	$-0.612365\pi$
$29$	−3.72350			−0.691436			−0.345718	+	0.938338i	$0.612365\pi$
$30$		0			0
$31$	3.37298	+	7.38579i	0.605805	+	1.32653i	0.925407	+	0.378975i	$0.123723\pi$
$31$	3.37298	+	7.38579i	0.605805	+	1.32653i	−0.319602	+	0.947552i	$0.603549\pi$
$32$		0			0
$33$	−0.0412366	+	0.286807i	−0.00717836	+	0.0499266i
$34$		0			0
$35$	0.712083	+	0.821787i	0.120364	+	0.138907i
$36$		0			0
$37$	−7.40784			−1.21784			−0.608921	−	0.793231i	$-0.708397\pi$
$37$	−7.40784			−1.21784			−0.608921	+	0.793231i	$0.708397\pi$
$38$		0			0
$39$	−0.00539058	−	0.0118037i	−0.000863183	−	0.00189011i
$40$		0			0
$41$	9.80987	+	2.88044i	1.53204	+	0.449849i	0.935675	−	0.352862i	$-0.114792\pi$
$41$	9.80987	+	2.88044i	1.53204	+	0.449849i	0.596368	+	0.802711i	$0.296610\pi$
$42$		0			0
$43$	1.60308	+	0.470707i	0.244468	+	0.0717822i	0.401671	−	0.915784i	$-0.368430\pi$
$43$	1.60308	+	0.470707i	0.244468	+	0.0717822i	−0.157203	+	0.987566i	$0.550248\pi$
$44$		0			0
$45$	−4.45641	−	5.14297i	−0.664323	−	0.766669i
$46$		0			0
$47$	8.47072	−	9.77573i	1.23558	−	1.42594i	0.367126	−	0.930171i	$-0.380342\pi$
$47$	8.47072	−	9.77573i	1.23558	−	1.42594i	0.868456	−	0.495766i	$-0.165113\pi$
$48$		0			0
$49$	6.49836	−	1.90809i	0.928338	−	0.272585i
$50$		0			0
$51$	0.783218	−	0.503343i	0.109672	−	0.0704822i
$52$		0			0
$53$	−10.3176	+	3.02952i	−1.41723	+	0.416137i	−0.898565	−	0.438840i	$-0.855390\pi$
$53$	−10.3176	+	3.02952i	−1.41723	+	0.416137i	−0.518667	+	0.854977i	$0.673571\pi$
$54$		0			0
$55$	−2.14742	+	4.70220i	−0.289558	+	0.634044i
$56$		0			0
$57$	−0.543580	−	0.627325i	−0.0719989	−	0.0830912i
$58$		0			0
$59$	−0.863986	−	1.89186i	−0.112481	−	0.246300i	0.845016	−	0.534740i	$-0.179591\pi$
$59$	−0.863986	−	1.89186i	−0.112481	−	0.246300i	−0.957498	+	0.288440i	$0.906863\pi$
$60$		0			0
$61$	−9.36127	−	6.01612i	−1.19859	−	0.770286i	−0.219877	−	0.975528i	$-0.570565\pi$
$61$	−9.36127	−	6.01612i	−1.19859	−	0.770286i	−0.978711	+	0.205242i	$0.934202\pi$
$62$		0			0
$63$	1.36485	−	0.400756i	0.171955	−	0.0504905i
$64$		0			0
$65$	−0.0329463	−	0.229146i	−0.00408648	−	0.0284221i
$66$		0			0
$67$	7.97017	+	1.86452i	0.973711	+	0.227787i
$67$	7.97017	+	1.86452i	0.973711	+	0.227787i
$68$		0			0
$69$	−0.138712	−	0.964760i	−0.0166989	−	0.116143i
$70$		0			0
$71$	11.8910	−	3.49151i	1.41120	−	0.414366i	0.514687	−	0.857378i	$-0.327908\pi$
$71$	11.8910	−	3.49151i	1.41120	−	0.414366i	0.896516	+	0.443012i	$0.146090\pi$
$72$		0			0
$73$	5.23294	+	3.36301i	0.612470	+	0.393610i	0.809782	−	0.586730i	$-0.199585\pi$
$73$	5.23294	+	3.36301i	0.612470	+	0.393610i	−0.197313	+	0.980341i	$0.563221\pi$
$74$		0			0
$75$	0.0107311	+	0.0234978i	0.00123912	+	0.00271329i
$76$		0			0
$77$	−0.707604	−	0.816619i	−0.0806390	−	0.0930623i
$78$		0			0
$79$	−2.83565	+	6.20920i	−0.319035	+	0.698590i	−0.999413	−	0.0342723i	$-0.989089\pi$
$79$	−2.83565	+	6.20920i	−0.319035	+	0.698590i	0.680377	+	0.732862i	$0.261816\pi$
$80$		0			0
$81$	−8.49455	+	2.49423i	−0.943839	+	0.277136i
$82$		0			0
$83$	−3.92100	+	2.51987i	−0.430385	+	0.276592i	−0.737846	−	0.674969i	$-0.764157\pi$
$83$	−3.92100	+	2.51987i	−0.430385	+	0.276592i	0.307461	+	0.951561i	$0.400521\pi$
$84$		0			0
$85$	15.9368	−	4.67946i	1.72859	−	0.507558i
$86$		0			0
$87$	0.311734	−	0.359760i	0.0334214	−	0.0385704i
$88$		0			0
$89$	−4.42813	−	5.11033i	−0.469381	−	0.541694i	0.470859	−	0.882209i	$-0.343944\pi$
$89$	−4.42813	−	5.11033i	−0.469381	−	0.541694i	−0.940239	+	0.340514i	$0.889399\pi$
$90$		0			0
$91$	0.0464306	+	0.0136332i	0.00486724	+	0.00142915i
$92$		0			0
$93$	−0.995996	−	0.292451i	−0.103280	−	0.0303257i
$94$		0			0
$95$	−6.15176	−	13.4705i	−0.631158	−	1.38204i
$96$		0			0
$97$	16.1422			1.63899			0.819494	−	0.573088i	$-0.194255\pi$
$97$	16.1422			1.63899			0.819494	+	0.573088i	$0.194255\pi$
$98$		0			0
$99$	4.42838	+	5.11063i	0.445069	+	0.513637i
$100$		0			0
$101$	0.772309	−	5.37152i	0.0768476	−	0.534487i	−0.914638	−	0.404273i	$-0.867525\pi$
$101$	0.772309	−	5.37152i	0.0768476	−	0.534487i	0.991486	−	0.130214i	$-0.0415663\pi$
$102$		0			0
$103$	−1.84750	−	4.04547i	−0.182040	−	0.398612i	0.796509	−	0.604627i	$-0.206678\pi$
$103$	−1.84750	−	4.04547i	−0.182040	−	0.398612i	−0.978549	+	0.206015i	$0.933950\pi$
$104$		0			0
$105$	−0.139016			−0.0135666
$106$		0			0
$107$	−9.56347	−	6.14607i	−0.924536	−	0.594163i	−0.0105655	−	0.999944i	$-0.503363\pi$
$107$	−9.56347	−	6.14607i	−0.924536	−	0.594163i	−0.913970	+	0.405781i	$0.867000\pi$
$108$		0			0
$109$	−1.71137	+	3.74738i	−0.163920	+	0.358934i	−0.973712	−	0.227782i	$-0.926853\pi$
$109$	−1.71137	+	3.74738i	−0.163920	+	0.358934i	0.809792	+	0.586717i	$0.199580\pi$
$110$		0			0
$111$	0.620191	−	0.715738i	0.0588659	−	0.0679349i
$112$		0			0
$113$	2.19352	+	1.40969i	0.206349	+	0.132613i	0.639734	−	0.768596i	$-0.279045\pi$
$113$	2.19352	+	1.40969i	0.206349	+	0.132613i	−0.433385	+	0.901209i	$0.642681\pi$
$114$		0			0
$115$	2.47466	−	17.2116i	0.230763	−	1.60499i
$116$		0			0
$117$	−0.290575	−	0.0853206i	−0.0268637	−	0.00788789i
$118$		0			0
$119$	−0.494100	+	3.43654i	−0.0452941	+	0.315027i
$120$		0			0
$121$	−2.43565	+	5.33333i	−0.221423	+	0.484848i
$122$		0			0
$123$	−1.09960	+	0.706667i	−0.0991472	+	0.0637180i
$124$		0			0
$125$	−1.55737	−	10.8318i	−0.139296	−	0.968823i
$126$		0			0
$127$	1.49648	+	10.4082i	0.132791	+	0.923581i	0.941893	+	0.335913i	$0.109045\pi$
$127$	1.49648	+	10.4082i	0.132791	+	0.923581i	−0.809102	+	0.587668i	$0.800046\pi$
$128$		0			0
$129$	−0.179691	+	0.115480i	−0.0158209	+	0.0101675i
$130$		0			0
$131$	1.05667	−	1.21946i	0.0923218	−	0.106545i	−0.707709	−	0.706504i	$-0.750271\pi$
$131$	1.05667	−	1.21946i	0.0923218	−	0.106545i	0.800031	+	0.599959i	$0.204817\pi$
$132$		0			0
$133$	3.09545			0.268409
$134$		0			0
$135$	1.74477			0.150166
$136$		0			0
$137$	−4.54920	+	5.25005i	−0.388664	+	0.448542i	−0.916038	−	0.401091i	$-0.868631\pi$
$137$	−4.54920	+	5.25005i	−0.388664	+	0.448542i	0.527374	+	0.849633i	$0.323177\pi$
$138$		0			0
$139$	15.6107	−	10.0324i	1.32408	−	0.850934i	0.328468	−	0.944515i	$-0.393468\pi$
$139$	15.6107	−	10.0324i	1.32408	−	0.850934i	0.995612	+	0.0935809i	$0.0298314\pi$
$140$		0			0
$141$	0.235346	+	1.63687i	0.0198197	+	0.137849i
$142$		0			0
$143$	0.0327390	+	0.227705i	0.00273778	+	0.0190416i
$144$		0			0
$145$	7.14439	−	4.59142i	0.593310	−	0.381297i
$146$		0			0
$147$	−0.359691	+	0.787613i	−0.0296668	+	0.0649612i
$148$		0			0
$149$	−0.427448	+	2.97297i	−0.0350179	+	0.243555i	−0.999811	−	0.0194561i	$-0.993807\pi$
$149$	−0.427448	+	2.97297i	−0.0350179	+	0.243555i	0.964793	+	0.263011i	$0.0847156\pi$
$150$		0			0
$151$	−3.21181	−	0.943074i	−0.261374	−	0.0767463i	0.148420	−	0.988924i	$-0.452581\pi$
$151$	−3.21181	−	0.943074i	−0.261374	−	0.0767463i	−0.409794	+	0.912178i	$0.634399\pi$
$152$		0			0
$153$	3.09222	−	21.5068i	0.249991	−	1.73872i
$154$		0			0
$155$	−15.5792	−	10.0122i	−1.25135	−	0.804196i
$156$		0			0
$157$	5.37868	−	6.20733i	0.429265	−	0.495399i	−0.499372	−	0.866388i	$-0.666436\pi$
$157$	5.37868	−	6.20733i	0.429265	−	0.495399i	0.928637	+	0.370989i	$0.120981\pi$
$158$		0			0
$159$	0.571089	−	1.25051i	0.0452903	−	0.0991720i
$160$		0			0
$161$	3.05772	+	1.96508i	0.240982	+	0.154870i
$162$		0			0
$163$	12.7641			0.999762			0.499881	−	0.866094i	$-0.333377\pi$
$163$	12.7641			0.999762			0.499881	+	0.866094i	$0.333377\pi$
$164$		0			0
$165$	−0.274538	−	0.601154i	−0.0213727	−	0.0467997i
$166$		0			0
$167$	1.29942	−	9.03768i	0.100552	−	0.699356i	−0.875722	−	0.482817i	$-0.839614\pi$
$167$	1.29942	−	9.03768i	0.100552	−	0.699356i	0.976274	−	0.216540i	$-0.0694771\pi$
$168$		0			0
$169$	8.50644	+	9.81696i	0.654342	+	0.755151i
$170$		0			0
$171$	−19.3722			−1.48143
$172$		0			0
$173$	10.4747	+	22.9363i	0.796373	+	1.74381i	0.657433	+	0.753513i	$0.271642\pi$
$173$	10.4747	+	22.9363i	0.796373	+	1.74381i	0.138941	+	0.990301i	$0.455630\pi$
$174$		0			0
$175$	−0.0924300	−	0.0271399i	−0.00698705	−	0.00205158i
$176$		0			0
$177$	0.255124	+	0.0749111i	0.0191763	+	0.00563066i
$178$		0			0
$179$	16.5020	+	19.0444i	1.23342	+	1.42344i	0.870894	+	0.491470i	$0.163540\pi$
$179$	16.5020	+	19.0444i	1.23342	+	1.42344i	0.362526	+	0.931973i	$0.381914\pi$
$180$		0			0
$181$	4.42999	−	5.11248i	0.329279	−	0.380008i	−0.566836	−	0.823831i	$-0.691833\pi$
$181$	4.42999	−	5.11248i	0.329279	−	0.380008i	0.896115	+	0.443823i	$0.146378\pi$
$182$		0			0
$183$	1.36501	−	0.400802i	0.100904	−	0.0296281i
$184$		0			0
$185$	14.2137	−	9.13457i	1.04501	−	0.671587i
$186$		0			0
$187$	−15.8365	+	4.65003i	−1.15808	+	0.340044i
$188$		0			0
$189$	−0.151505	+	0.331750i	−0.0110204	+	0.0241313i
$190$		0			0
$191$	7.84921	+	9.05847i	0.567949	+	0.655448i	0.964970	−	0.262362i	$-0.0845014\pi$
$191$	7.84921	+	9.05847i	0.567949	+	0.655448i	−0.397021	+	0.917810i	$0.629956\pi$
$192$		0			0
$193$	0.245347	+	0.537235i	0.0176605	+	0.0386710i	0.918257	−	0.395986i	$-0.129597\pi$
$193$	0.245347	+	0.537235i	0.0176605	+	0.0386710i	−0.900596	+	0.434657i	$0.856870\pi$
$194$		0			0
$195$	0.0248982	+	0.0160011i	0.00178300	+	0.00114586i
$196$		0			0
$197$	−17.9146	+	5.26019i	−1.27636	+	0.374773i	−0.848560	−	0.529100i	$-0.822530\pi$
$197$	−17.9146	+	5.26019i	−1.27636	+	0.374773i	−0.427801	+	0.903873i	$0.640712\pi$
$198$		0			0
$199$	−1.69802	−	11.8100i	−0.120369	−	0.837187i	−0.957138	−	0.289631i	$-0.906467\pi$
$199$	−1.69802	−	11.8100i	−0.120369	−	0.837187i	0.836769	−	0.547556i	$-0.184442\pi$
$200$		0			0
$201$	−0.847417	+	0.613971i	−0.0597722	+	0.0433062i
$202$		0			0
$203$	0.252636	+	1.75712i	0.0177316	+	0.123326i
$204$		0			0
$205$	−22.3744	+	6.56971i	−1.56269	+	0.458848i
$206$		0			0
$207$	−19.1361	−	12.2980i	−1.33005	−	0.854771i
$208$		0			0
$209$	6.11307	+	13.3858i	0.422850	+	0.925912i
$210$		0			0
$211$	3.09650	+	3.57356i	0.213172	+	0.246014i	0.852258	−	0.523122i	$-0.175233\pi$
$211$	3.09650	+	3.57356i	0.213172	+	0.246014i	−0.639086	+	0.769135i	$0.720687\pi$
$212$		0			0
$213$	−0.658178	+	1.44121i	−0.0450976	+	0.0987500i
$214$		0			0
$215$	−3.65631	+	1.07359i	−0.249358	+	0.0732182i
$216$		0			0
$217$	3.25651	−	2.09283i	0.221066	−	0.142071i
$218$		0			0
$219$	−0.763037	+	0.224048i	−0.0515612	+	0.0151397i
$220$		0			0
$221$	0.484048	−	0.558621i	0.0325606	−	0.0375769i
$222$		0			0
$223$	2.87626	+	3.31938i	0.192609	+	0.222282i	0.843837	−	0.536600i	$-0.180291\pi$
$223$	2.87626	+	3.31938i	0.192609	+	0.222282i	−0.651228	+	0.758882i	$0.725746\pi$
$224$		0			0
$225$	0.578453	+	0.169849i	0.0385635	+	0.0113233i
$226$		0			0
$227$	1.06845	+	0.313724i	0.0709153	+	0.0208226i	0.316998	−	0.948426i	$-0.397325\pi$
$227$	1.06845	+	0.313724i	0.0709153	+	0.0208226i	−0.246082	+	0.969249i	$0.579143\pi$
$228$		0			0
$229$	−4.17480	−	9.14154i	−0.275879	−	0.604090i	0.720081	−	0.693890i	$-0.244104\pi$
$229$	−4.17480	−	9.14154i	−0.275879	−	0.604090i	−0.995960	+	0.0898000i	$0.971377\pi$
$230$		0			0
$231$	0.138142			0.00908908
$232$		0			0
$233$	−3.38769	−	3.90960i	−0.221935	−	0.256126i	0.633853	−	0.773454i	$-0.281472\pi$
$233$	−3.38769	−	3.90960i	−0.221935	−	0.256126i	−0.855788	+	0.517327i	$0.826927\pi$
$234$		0			0
$235$	−4.19865	+	29.2022i	−0.273889	+	1.90494i
$236$		0			0
$237$	−0.362524	−	0.793817i	−0.0235485	−	0.0515640i
$238$		0			0
$239$	−21.7684			−1.40808			−0.704040	−	0.710160i	$-0.748623\pi$
$239$	−21.7684			−1.40808			−0.704040	+	0.710160i	$0.748623\pi$
$240$		0			0
$241$	−3.71977	−	2.39055i	−0.239612	−	0.153989i	0.415324	−	0.909673i	$-0.363668\pi$
$241$	−3.71977	−	2.39055i	−0.239612	−	0.153989i	−0.654936	+	0.755684i	$0.727304\pi$
$242$		0			0
$243$	1.42354	−	3.11711i	0.0913199	−	0.199963i
$244$		0			0
$245$	−10.1158	+	11.6742i	−0.646273	+	0.745838i
$246$		0			0
$247$	−0.554402	−	0.356293i	−0.0352758	−	0.0226704i
$248$		0			0
$249$	0.0848017	−	0.589809i	0.00537409	−	0.0373776i
$250$		0			0
$251$	−25.2724	−	7.42066i	−1.59518	−	0.468388i	−0.640982	−	0.767556i	$-0.721473\pi$
$251$	−25.2724	−	7.42066i	−1.59518	−	0.468388i	−0.954200	+	0.299168i	$0.903291\pi$
$252$		0			0
$253$	−2.45909	+	17.1034i	−0.154602	+	1.07528i
$254$		0			0
$255$	−0.882115	+	1.93156i	−0.0552402	+	0.120959i
$256$		0			0
$257$	−4.83081	+	3.10458i	−0.301338	+	0.193658i	−0.682568	−	0.730822i	$-0.739137\pi$
$257$	−4.83081	+	3.10458i	−0.301338	+	0.193658i	0.381230	+	0.924480i	$0.375501\pi$
$258$		0			0
$259$	0.502615	+	3.49576i	0.0312310	+	0.217216i
$260$		0			0
$261$	−1.58107	−	10.9965i	−0.0978655	−	0.680669i
$262$		0			0
$263$	15.4624	−	9.93711i	0.953455	−	0.612748i	0.0312755	−	0.999511i	$-0.490043\pi$
$263$	15.4624	−	9.93711i	0.953455	−	0.612748i	0.922179	+	0.386763i	$0.126407\pi$
$264$		0			0
$265$	16.0610	−	18.5354i	0.986622	−	1.13862i
$266$		0			0
$267$	0.864482			0.0529054
$268$		0			0
$269$	8.91592			0.543613			0.271807	−	0.962352i	$-0.412379\pi$
$269$	8.91592			0.543613			0.271807	+	0.962352i	$0.412379\pi$
$270$		0			0
$271$	−11.4669	+	13.2335i	−0.696566	+	0.803880i	−0.988284	−	0.152625i	$-0.951227\pi$
$271$	−11.4669	+	13.2335i	−0.696566	+	0.803880i	0.291719	+	0.956504i	$0.405773\pi$
$272$		0			0
$273$	−0.00520444	+	0.00334469i	−0.000314987	+	0.000202430i
$274$		0			0
$275$	−0.0651741	−	0.453296i	−0.00393014	−	0.0273348i
$276$		0			0
$277$	2.34534	+	16.3122i	0.140918	+	0.980103i	0.930456	+	0.366402i	$0.119411\pi$
$277$	2.34534	+	16.3122i	0.140918	+	0.980103i	−0.789539	+	0.613700i	$0.789680\pi$
$278$		0			0
$279$	−20.3801	+	13.0975i	−1.22013	+	0.784127i
$280$		0			0
$281$	−8.51851	+	18.6529i	−0.508172	+	1.11274i	0.465555	+	0.885019i	$0.345855\pi$
$281$	−8.51851	+	18.6529i	−0.508172	+	1.11274i	−0.973726	+	0.227721i	$0.926872\pi$
$282$		0			0
$283$	−1.31843	+	9.16985i	−0.0783723	+	0.545091i	0.912373	+	0.409359i	$0.134248\pi$
$283$	−1.31843	+	9.16985i	−0.0783723	+	0.545091i	−0.990746	+	0.135732i	$0.956661\pi$
$284$		0			0
$285$	1.81654	+	0.533383i	0.107602	+	0.0315949i
$286$		0			0
$287$	0.693690	−	4.82472i	0.0409472	−	0.284794i
$288$		0			0
$289$	30.3124	+	19.4806i	1.78308	+	1.14592i
$290$		0			0
$291$	−1.35143	+	1.55964i	−0.0792225	+	0.0914276i
$292$		0			0
$293$	−10.0410	+	21.9867i	−0.586602	+	1.28448i	0.350872	+	0.936423i	$0.385885\pi$
$293$	−10.0410	+	21.9867i	−0.586602	+	1.28448i	−0.937474	+	0.348055i	$0.886842\pi$
$294$		0			0
$295$	3.99061	+	2.56461i	0.232342	+	0.149317i
$296$		0			0
$297$	−1.73380			−0.100605
$298$		0			0
$299$	−0.321461	−	0.703901i	−0.0185906	−	0.0407076i
$300$		0			0
$301$	0.113359	−	0.788432i	0.00653393	−	0.0454445i
$302$		0			0
$303$	0.454333	+	0.524328i	0.0261008	+	0.0301219i
$304$		0			0
$305$	25.3802			1.45327
$306$		0			0
$307$	−9.79117	−	21.4397i	−0.558812	−	1.22363i	−0.952544	−	0.304401i	$-0.901544\pi$
$307$	−9.79117	−	21.4397i	−0.558812	−	1.22363i	0.393732	−	0.919225i	$-0.371184\pi$
$308$		0			0
$309$	0.545544	+	0.160186i	0.0310349	+	0.00911267i
$310$		0			0
$311$	10.7670	+	3.16148i	0.610541	+	0.179271i	0.572364	−	0.820000i	$-0.306027\pi$
$311$	10.7670	+	3.16148i	0.610541	+	0.179271i	0.0381775	+	0.999271i	$0.487845\pi$
$312$		0			0
$313$	16.5044	+	19.0471i	0.932883	+	1.07660i	0.996902	+	0.0786559i	$0.0250629\pi$
$313$	16.5044	+	19.0471i	0.932883	+	1.07660i	−0.0640186	+	0.997949i	$0.520392\pi$
$314$		0			0
$315$	−2.12461	+	2.45193i	−0.119708	+	0.138151i
$316$		0			0
$317$	4.27314	−	1.25471i	0.240004	−	0.0704714i	−0.159519	−	0.987195i	$-0.550994\pi$
$317$	4.27314	−	1.25471i	0.240004	−	0.0704714i	0.399522	+	0.916723i	$0.369176\pi$
$318$		0			0
$319$	−7.09946	+	4.56255i	−0.397493	+	0.255453i
$320$		0			0
$321$	1.39449	−	0.409459i	0.0778328	−	0.0228538i
$322$		0			0
$323$	19.6419	−	43.0097i	1.09290	−	2.39312i
$324$		0			0
$325$	0.0134306	+	0.0154997i	0.000744994	+	0.000859769i
$326$		0			0
$327$	−0.218791	−	0.479085i	−0.0120992	−	0.0264935i
$328$		0			0
$329$	−5.18791	−	3.33407i	−0.286019	−	0.183813i
$330$		0			0
$331$	12.3880	−	3.63745i	0.680908	−	0.199933i	0.0770530	−	0.997027i	$-0.475449\pi$
$331$	12.3880	−	3.63745i	0.680908	−	0.199933i	0.603855	+	0.797094i	$0.293631\pi$
$332$		0			0
$333$	−3.14551	−	21.8775i	−0.172373	−	1.19888i
$334$		0			0
$335$	−17.5917	+	6.25046i	−0.961140	+	0.341499i
$336$		0			0
$337$	−3.45089	−	24.0015i	−0.187982	−	1.30744i	−0.837223	−	0.546862i	$-0.815822\pi$
$337$	−3.45089	−	24.0015i	−0.187982	−	1.30744i	0.649241	−	0.760583i	$-0.275087\pi$
$338$		0			0
$339$	−0.319846	+	0.0939154i	−0.0173717	+	0.00510078i
$340$		0			0
$341$	15.4812	+	9.94919i	0.838356	+	0.538779i
$342$		0			0
$343$	−2.72769	−	5.97281i	−0.147282	−	0.322502i
$344$		0			0
$345$	1.45579	+	1.68007i	0.0783771	+	0.0904520i
$346$		0			0
$347$	2.50826	−	5.49233i	0.134651	−	0.294844i	−0.830281	−	0.557345i	$-0.811820\pi$
$347$	2.50826	−	5.49233i	0.134651	−	0.294844i	0.964932	+	0.262501i	$0.0845474\pi$
$348$		0			0
$349$	−8.40409	+	2.46766i	−0.449861	+	0.132091i	−0.498812	−	0.866710i	$-0.666230\pi$
$349$	−8.40409	+	2.46766i	−0.449861	+	0.132091i	0.0489514	+	0.998801i	$0.484412\pi$
$350$		0			0
$351$	0.0653200	−	0.0419786i	0.00348653	−	0.00224065i
$352$		0			0
$353$	−30.0926	+	8.83597i	−1.60166	+	0.470291i	−0.956009	−	0.293337i	$-0.905234\pi$
$353$	−30.0926	+	8.83597i	−1.60166	+	0.470291i	−0.645656	+	0.763628i	$0.723416\pi$
$354$		0			0
$355$	−18.5103	+	21.3620i	−0.982424	+	1.13378i
$356$		0			0
$357$	−0.290669	−	0.335450i	−0.0153838	−	0.0177539i
$358$		0			0
$359$	−4.84736	−	1.42331i	−0.255834	−	0.0751196i	0.151301	−	0.988488i	$-0.451654\pi$
$359$	−4.84736	−	1.42331i	−0.255834	−	0.0751196i	−0.407135	+	0.913368i	$0.633472\pi$
$360$		0			0
$361$	−22.2181	−	6.52381i	−1.16937	−	0.343358i
$362$		0			0
$363$	−0.311386	−	0.681841i	−0.0163435	−	0.0357874i
$364$		0			0
$365$	−14.1875			−0.742609
$366$		0			0
$367$	9.86718	+	11.3873i	0.515062	+	0.594414i	0.952388	−	0.304890i	$-0.0986196\pi$
$367$	9.86718	+	11.3873i	0.515062	+	0.594414i	−0.437325	+	0.899303i	$0.644074\pi$
$368$		0			0
$369$	−4.34130	+	30.1944i	−0.225999	+	1.57186i
$370$		0			0
$371$	2.12967	+	4.66334i	0.110567	+	0.242108i
$372$		0			0
$373$	−18.1828			−0.941471			−0.470736	−	0.882274i	$-0.656011\pi$
$373$	−18.1828			−0.941471			−0.470736	+	0.882274i	$0.656011\pi$
$374$		0			0
$375$	1.17694	+	0.756373i	0.0607769	+	0.0390589i
$376$		0			0
$377$	0.157001	−	0.343783i	0.00808594	−	0.0177057i
$378$		0			0
$379$	−10.2952	+	11.8813i	−0.528828	+	0.610300i	−0.955819	−	0.293956i	$-0.905028\pi$
$379$	−10.2952	+	11.8813i	−0.528828	+	0.610300i	0.426991	+	0.904256i	$0.359574\pi$
$380$		0			0
$381$	−1.13092	−	0.726798i	−0.0579388	−	0.0372350i
$382$		0			0
$383$	−1.10085	+	7.65656i	−0.0562506	+	0.391232i	0.942174	+	0.335124i	$0.108778\pi$
$383$	−1.10085	+	7.65656i	−0.0562506	+	0.391232i	−0.998425	+	0.0561079i	$0.982131\pi$
$384$		0			0
$385$	2.36467	+	0.694330i	0.120515	+	0.0353863i
$386$		0			0
$387$	−0.709435	+	4.93423i	−0.0360626	+	0.250821i
$388$		0			0
$389$	9.97081	−	21.8330i	0.505540	−	1.10698i	−0.469089	−	0.883151i	$-0.655418\pi$
$389$	9.97081	−	21.8330i	0.505540	−	1.10698i	0.974629	−	0.223827i	$-0.0718551\pi$
$390$		0			0
$391$	46.7063	−	30.0163i	2.36204	−	1.51799i
$392$		0			0
$393$	0.0293580	+	0.204189i	0.00148091	+	0.0103000i
$394$		0			0
$395$	−2.21568	−	15.4104i	−0.111483	−	0.775382i
$396$		0			0
$397$	14.5250	−	9.33466i	0.728990	−	0.468493i	−0.122764	−	0.992436i	$-0.539176\pi$
$397$	14.5250	−	9.33466i	0.728990	−	0.468493i	0.851754	+	0.523943i	$0.175539\pi$
$398$		0			0
$399$	−0.259154	+	0.299079i	−0.0129739	+	0.0149727i
$400$		0			0
$401$	−7.84379			−0.391700			−0.195850	−	0.980634i	$-0.562747\pi$
$401$	−7.84379			−0.391700			−0.195850	+	0.980634i	$0.562747\pi$
$402$		0			0
$403$	−0.824137			−0.0410532
$404$		0			0
$405$	13.2232	−	15.2603i	0.657064	−	0.758292i
$406$		0			0
$407$	−14.1243	+	9.07712i	−0.700114	+	0.449936i
$408$		0			0
$409$	2.79503	+	19.4398i	0.138205	+	0.961238i	0.934407	+	0.356207i	$0.115930\pi$
$409$	2.79503	+	19.4398i	0.138205	+	0.961238i	−0.796202	+	0.605031i	$0.793161\pi$
$410$		0			0
$411$	−0.126392	−	0.879077i	−0.00623447	−	0.0433617i
$412$		0			0
$413$	−0.834152	+	0.536077i	−0.0410459	+	0.0263786i
$414$		0			0
$415$	4.41610	−	9.66992i	0.216778	−	0.474678i
$416$		0			0
$417$	−0.337621	+	2.34821i	−0.0165334	+	0.114992i
$418$		0			0
$419$	9.56335	+	2.80805i	0.467200	+	0.137182i	0.506856	−	0.862031i	$-0.330808\pi$
$419$	9.56335	+	2.80805i	0.467200	+	0.137182i	−0.0396551	+	0.999213i	$0.512626\pi$
$420$		0			0
$421$	−0.539904	+	3.75511i	−0.0263133	+	0.183013i	−0.998739	−	0.0501989i	$-0.984014\pi$
$421$	−0.539904	+	3.75511i	−0.0263133	+	0.183013i	0.972426	+	0.233212i	$0.0749236\pi$
$422$		0			0
$423$	32.4674	+	20.8655i	1.57862	+	1.01452i
$424$		0			0
$425$	−0.963601	+	1.11205i	−0.0467415	+	0.0539426i
$426$		0			0
$427$	−2.20386	+	4.82578i	−0.106652	+	0.233536i
$428$		0			0
$429$	−0.0247416	−	0.0159004i	−0.00119453	−	0.000767681i
$430$		0			0
$431$	−18.9027			−0.910513			−0.455257	−	0.890360i	$-0.650452\pi$
$431$	−18.9027			−0.910513			−0.455257	+	0.890360i	$0.650452\pi$
$432$		0			0
$433$	−11.0367	−	24.1671i	−0.530392	−	1.16140i	−0.965353	−	0.260948i	$-0.915965\pi$
$433$	−11.0367	−	24.1671i	−0.530392	−	1.16140i	0.434961	−	0.900449i	$-0.356762\pi$
$434$		0			0
$435$	−0.154516	+	1.07468i	−0.00740847	+	0.0515271i
$436$		0			0
$437$	−32.4158	−	37.4098i	−1.55066	−	1.78955i
$438$		0			0
$439$	−1.98097			−0.0945467			−0.0472734	−	0.998882i	$-0.515053\pi$
$439$	−1.98097			−0.0945467			−0.0472734	+	0.998882i	$0.515053\pi$
$440$		0			0
$441$	8.39447	+	18.3813i	0.399737	+	0.875301i
$442$		0			0
$443$	−19.3643	−	5.68587i	−0.920025	−	0.270144i	−0.212770	−	0.977102i	$-0.568249\pi$
$443$	−19.3643	−	5.68587i	−0.920025	−	0.270144i	−0.707255	+	0.706958i	$0.750067\pi$
$444$		0			0
$445$	14.7979	+	4.34506i	0.701489	+	0.205976i
$446$		0			0
$447$	−0.251459	−	0.290199i	−0.0118936	−	0.0137259i
$448$		0			0
$449$	23.1247	−	26.6874i	1.09132	−	1.25945i	0.127809	−	0.991799i	$-0.459206\pi$
$449$	23.1247	−	26.6874i	1.09132	−	1.25945i	0.963515	−	0.267655i	$-0.0862489\pi$
$450$		0			0
$451$	22.2336	−	6.52839i	1.04694	−	0.307410i
$452$		0			0
$453$	0.360015	−	0.231367i	0.0169150	−	0.0108706i
$454$		0			0
$455$	−0.105899	+	0.0310947i	−0.00496462	+	0.00145774i
$456$		0			0
$457$	4.27675	−	9.36477i	0.200058	−	0.438065i	−0.782839	−	0.622225i	$-0.786229\pi$
$457$	4.27675	−	9.36477i	0.200058	−	0.438065i	0.982896	+	0.184159i	$0.0589563\pi$
$458$		0			0
$459$	3.64814	+	4.21017i	0.170280	+	0.196514i
$460$		0			0
$461$	−5.82672	−	12.7587i	−0.271377	−	0.594233i	0.724051	−	0.689747i	$-0.242278\pi$
$461$	−5.82672	−	12.7587i	−0.271377	−	0.594233i	−0.995428	+	0.0955132i	$0.969551\pi$
$462$		0			0
$463$	15.6362	+	10.0488i	0.726676	+	0.467006i	0.850953	−	0.525241i	$-0.176025\pi$
$463$	15.6362	+	10.0488i	0.726676	+	0.467006i	−0.124277	+	0.992248i	$0.539661\pi$
$464$		0			0
$465$	2.27167	−	0.667023i	0.105346	−	0.0309324i
$466$		0			0
$467$	−1.84778	−	12.8516i	−0.0855053	−	0.594702i	−0.986855	−	0.161610i	$-0.948331\pi$
$467$	−1.84778	−	12.8516i	−0.0855053	−	0.594702i	0.901349	−	0.433093i	$-0.142578\pi$
$468$		0			0
$469$	0.339098	−	3.88763i	0.0156581	−	0.179514i
$470$		0			0
$471$	0.149438	+	1.03937i	0.00688575	+	0.0478914i
$472$		0			0
$473$	3.63331	−	1.06684i	0.167060	−	0.0490532i
$474$		0			0
$475$	1.10366	+	0.709277i	0.0506392	+	0.0325439i
$476$		0			0
$477$	−13.3281	−	29.1845i	−0.610251	−	1.33626i
$478$		0			0
$479$	14.9604	+	17.2652i	0.683557	+	0.788867i	0.986433	−	0.164163i	$-0.0524924\pi$
$479$	14.9604	+	17.2652i	0.683557	+	0.788867i	−0.302876	+	0.953030i	$0.597947\pi$
$480$		0			0
$481$	0.312350	−	0.683952i	0.0142419	−	0.0311855i
$482$		0			0
$483$	−0.445859	+	0.130916i	−0.0202873	+	0.00595689i
$484$		0			0
$485$	−30.9725	+	19.9048i	−1.40639	+	0.903830i
$486$		0			0
$487$	1.14650	−	0.336642i	0.0519528	−	0.0152547i	−0.255653	−	0.966769i	$-0.582290\pi$
$487$	1.14650	−	0.336642i	0.0519528	−	0.0152547i	0.307606	+	0.951514i	$0.400472\pi$
$488$		0			0
$489$	−1.06862	+	1.23326i	−0.0483248	+	0.0557698i
$490$		0			0
$491$	25.9828	+	29.9857i	1.17259	+	1.35324i	0.922961	+	0.384893i	$0.125762\pi$
$491$	25.9828	+	29.9857i	1.17259	+	1.35324i	0.249624	+	0.968343i	$0.419693\pi$
$492$		0			0
$493$	26.0174	+	7.63939i	1.17176	+	0.344061i
$494$		0			0
$495$	−14.7988	−	4.34531i	−0.665155	−	0.195307i
$496$		0			0
$497$	−2.45444	−	5.37448i	−0.110097	−	0.241078i
$498$		0			0
$499$	12.1245			0.542767			0.271384	−	0.962471i	$-0.412519\pi$
$499$	12.1245			0.542767			0.271384	+	0.962471i	$0.412519\pi$
$500$		0			0
$501$	0.764423	+	0.882191i	0.0341519	+	0.0394134i
$502$		0			0
$503$	3.18914	−	22.1810i	0.142197	−	0.989000i	−0.786349	−	0.617782i	$-0.788031\pi$
$503$	3.18914	−	22.1810i	0.142197	−	0.989000i	0.928546	−	0.371218i	$-0.121060\pi$
$504$		0			0
$505$	5.14174	+	11.2588i	0.228805	+	0.501012i
$506$		0			0
$507$	−1.66067			−0.0737530
$508$		0			0
$509$	13.9318	+	8.95344i	0.617517	+	0.396854i	0.811669	−	0.584117i	$-0.198559\pi$
$509$	13.9318	+	8.95344i	0.617517	+	0.396854i	−0.194152	+	0.980971i	$0.562195\pi$
$510$		0			0
$511$	1.23196	−	2.69761i	0.0544985	−	0.119335i
$512$		0			0
$513$	3.25260	−	3.75370i	0.143606	−	0.165730i
$514$		0			0
$515$	8.53331	+	5.48403i	0.376023	+	0.241655i
$516$		0			0
$517$	4.17224	−	29.0186i	0.183495	−	1.27623i
$518$		0			0
$519$	−3.09303	−	0.908195i	−0.135769	−	0.0398653i
$520$		0			0
$521$	−2.02486	+	14.0832i	−0.0887106	+	0.616996i	0.896163	+	0.443724i	$0.146343\pi$
$521$	−2.02486	+	14.0832i	−0.0887106	+	0.616996i	−0.984874	+	0.173272i	$0.944566\pi$
$522$		0			0
$523$	−2.95418	+	6.46876i	−0.129177	+	0.282859i	−0.963159	−	0.268934i	$-0.913329\pi$
$523$	−2.95418	+	6.46876i	−0.129177	+	0.282859i	0.833981	+	0.551793i	$0.186056\pi$
$524$		0			0
$525$	0.0103605	−	0.00665832i	0.000452171	−	0.000290593i
$526$		0			0
$527$	−8.41496	−	58.5274i	−0.366562	−	2.54949i
$528$		0			0
$529$	−4.99866	−	34.7665i	−0.217333	−	1.51159i
$530$		0			0
$531$	5.22035	−	3.35492i	0.226544	−	0.145591i
$532$		0			0
$533$	−0.679577	+	0.784273i	−0.0294357	+	0.0339706i
$534$		0			0
$535$	25.9284			1.12098
$536$		0			0
$537$	−3.22161			−0.139023
$538$		0			0
$539$	10.0521	−	11.6008i	0.432976	−	0.499681i
$540$		0			0
$541$	−16.6594	+	10.7064i	−0.716244	+	0.460302i	−0.847329	−	0.531069i	$-0.821791\pi$
$541$	−16.6594	+	10.7064i	−0.716244	+	0.460302i	0.131084	+	0.991371i	$0.458154\pi$
$542$		0			0
$543$	0.123080	+	0.856043i	0.00528188	+	0.0367363i
$544$		0			0
$545$	−1.33721	−	9.30052i	−0.0572799	−	0.398390i
$546$		0			0
$547$	5.98792	−	3.84821i	0.256025	−	0.164537i	−0.406332	−	0.913725i	$-0.633192\pi$
$547$	5.98792	−	3.84821i	0.256025	−	0.164537i	0.662357	+	0.749188i	$0.269556\pi$
$548$		0			0
$549$	13.7924	−	30.2011i	0.588644	−	1.28895i
$550$		0			0
$551$	3.44057	−	23.9297i	0.146573	−	1.01944i
$552$		0			0
$553$	3.12252	+	0.916855i	0.132783	+	0.0389887i
$554$		0			0
$555$	−0.307407	+	2.13806i	−0.0130487	+	0.0907558i
$556$		0			0
$557$	−5.31223	−	3.41396i	−0.225086	−	0.144654i	0.423238	−	0.906019i	$-0.360894\pi$
$557$	−5.31223	−	3.41396i	−0.225086	−	0.144654i	−0.648324	+	0.761364i	$0.724530\pi$
$558$		0			0
$559$	−0.111053	+	0.128162i	−0.00469705	+	0.00542068i
$560$		0			0
$561$	0.876567	−	1.91941i	0.0370087	−	0.0810377i
$562$		0			0
$563$	32.3216	+	20.7718i	1.36219	+	0.875429i	0.998427	−	0.0560612i	$-0.0178542\pi$
$563$	32.3216	+	20.7718i	1.36219	+	0.875429i	0.363767	+	0.931490i	$0.381491\pi$
$564$		0			0
$565$	−5.94707			−0.250195
$566$		0			0
$567$	1.75337	+	3.83935i	0.0736348	+	0.161238i
$568$		0			0
$569$	0.121221	−	0.843109i	0.00508184	−	0.0353450i	−0.987123	−	0.159965i	$-0.948862\pi$
$569$	0.121221	−	0.843109i	0.00508184	−	0.0353450i	0.992205	+	0.124620i	$0.0397711\pi$
$570$		0			0
$571$	7.96661	+	9.19396i	0.333392	+	0.384755i	0.897551	−	0.440911i	$-0.145345\pi$
$571$	7.96661	+	9.19396i	0.333392	+	0.384755i	−0.564158	+	0.825667i	$0.690799\pi$
$572$		0			0
$573$	−1.53236			−0.0640154
$574$		0			0
$575$	0.639937	+	1.40127i	0.0266872	+	0.0584368i
$576$		0			0
$577$	−35.7099	−	10.4854i	−1.48662	−	0.436512i	−0.565160	−	0.824981i	$-0.691186\pi$
$577$	−35.7099	−	10.4854i	−1.48662	−	0.436512i	−0.921461	+	0.388470i	$0.873004\pi$
$578$		0			0
$579$	−0.0724478	−	0.0212726i	−0.00301083	−	0.000884059i
$580$		0			0
$581$	1.45517	+	1.67935i	0.0603704	+	0.0696712i
$582$		0			0
$583$	−15.9600	+	18.4188i	−0.660997	+	0.762831i
$584$		0			0
$585$	0.662745	−	0.194599i	0.0274011	−	0.00804570i
$586$		0			0
$587$	34.0469	−	21.8806i	1.40526	−	0.903109i	0.405326	−	0.914172i	$-0.367158\pi$
$587$	34.0469	−	21.8806i	1.40526	−	0.903109i	0.999939	+	0.0110634i	$0.00352165\pi$
$588$		0			0
$589$	−50.5828	+	14.8525i	−2.08423	+	0.611985i
$590$		0			0
$591$	0.991588	−	2.17128i	0.0407885	−	0.0893144i
$592$		0			0
$593$	5.09361	+	5.87834i	0.209170	+	0.241395i	0.850634	−	0.525758i	$-0.176218\pi$
$593$	5.09361	+	5.87834i	0.209170	+	0.241395i	−0.641465	+	0.767153i	$0.721673\pi$
$594$		0			0
$595$	−3.28953	−	7.20308i	−0.134858	−	0.295297i
$596$		0			0
$597$	1.28323	+	0.824680i	0.0525190	+	0.0337519i
$598$		0			0
$599$	35.3783	−	10.3880i	1.44552	−	0.424442i	0.537461	−	0.843289i	$-0.319383\pi$
$599$	35.3783	−	10.3880i	1.44552	−	0.424442i	0.908057	+	0.418846i	$0.137565\pi$
$600$		0			0
$601$	−1.33525	−	9.28687i	−0.0544660	−	0.378819i	−0.998763	−	0.0497248i	$-0.984166\pi$
$601$	−1.33525	−	9.28687i	−0.0544660	−	0.378819i	0.944297	−	0.329095i	$-0.106744\pi$
$602$		0			0
$603$	−2.12217	+	24.3299i	−0.0864215	+	0.990790i
$604$		0			0
$605$	−1.90314	−	13.2366i	−0.0773736	−	0.538145i
$606$		0			0
$607$	−21.2087	+	6.22745i	−0.860836	+	0.252764i	−0.682213	−	0.731153i	$-0.738982\pi$
$607$	−21.2087	+	6.22745i	−0.860836	+	0.252764i	−0.178623	+	0.983918i	$0.557164\pi$
$608$		0			0
$609$	−0.190922	−	0.122698i	−0.00773656	−	0.00497198i
$610$		0			0
$611$	0.545409	+	1.19428i	0.0220649	+	0.0483153i
$612$		0			0
$613$	10.3022	+	11.8894i	0.416102	+	0.480208i	0.924646	−	0.380829i	$-0.124361\pi$
$613$	10.3022	+	11.8894i	0.416102	+	0.480208i	−0.508543	+	0.861036i	$0.669816\pi$
$614$		0			0
$615$	1.23844	−	2.71181i	0.0499388	−	0.109351i
$616$		0			0
$617$	23.8909	−	7.01501i	0.961813	−	0.282414i	0.237116	−	0.971481i	$-0.423798\pi$
$617$	23.8909	−	7.01501i	0.961813	−	0.282414i	0.724697	+	0.689068i	$0.241980\pi$
$618$		0			0
$619$	−19.1621	+	12.3147i	−0.770190	+	0.494971i	−0.865765	−	0.500451i	$-0.833168\pi$
$619$	−19.1621	+	12.3147i	−0.770190	+	0.494971i	0.0955745	+	0.995422i	$0.469531\pi$
$620$		0			0
$621$	5.59591	−	1.64311i	0.224556	−	0.0659356i
$622$		0			0
$623$	−2.11113	+	2.43637i	−0.0845805	+	0.0976111i
$624$		0			0
$625$	17.0064	+	19.6264i	0.680255	+	0.785056i
$626$		0			0
$627$	−1.80511	−	0.530028i	−0.0720892	−	0.0211673i
$628$		0			0
$629$	51.7612	+	15.1985i	2.06385	+	0.606002i
$630$		0			0
$631$	2.54037	+	5.56263i	0.101131	+	0.221445i	0.953433	−	0.301604i	$-0.0975219\pi$
$631$	2.54037	+	5.56263i	0.101131	+	0.221445i	−0.852303	+	0.523049i	$0.824795\pi$
$632$		0			0
$633$	−0.604516			−0.0240273
$634$		0			0
$635$	−15.7057	−	18.1253i	−0.623261	−	0.719281i
$636$		0			0
$637$	−0.0978319	+	0.680436i	−0.00387624	+	0.0269599i
$638$		0			0
$639$	15.3606	+	33.6350i	0.607655	+	1.33058i
$640$		0			0
$641$	−37.5130			−1.48168			−0.740838	−	0.671684i	$-0.765571\pi$
$641$	−37.5130			−1.48168			−0.740838	+	0.671684i	$0.765571\pi$
$642$		0			0
$643$	−17.0523	−	10.9589i	−0.672478	−	0.432176i	0.159340	−	0.987224i	$-0.449063\pi$
$643$	−17.0523	−	10.9589i	−0.672478	−	0.432176i	−0.831818	+	0.555048i	$0.812700\pi$
$644$		0			0
$645$	0.202380	−	0.443151i	0.00796872	−	0.0174491i
$646$		0			0
$647$	−15.9928	+	18.4567i	−0.628743	+	0.725608i	−0.977343	−	0.211663i	$-0.932112\pi$
$647$	−15.9928	+	18.4567i	−0.628743	+	0.725608i	0.348599	+	0.937272i	$0.386657\pi$
$648$		0			0
$649$	−3.96551	−	2.54848i	−0.155660	−	0.100036i
$650$		0			0
$651$	−0.0704304	+	0.489854i	−0.00276038	+	0.0191989i
$652$		0			0
$653$	9.57691	+	2.81204i	0.374774	+	0.110043i	0.463694	−	0.885995i	$-0.346524\pi$
$653$	9.57691	+	2.81204i	0.374774	+	0.110043i	−0.0889208	+	0.996039i	$0.528342\pi$
$654$		0			0
$655$	−0.523756	+	3.64280i	−0.0204648	+	0.142336i
$656$		0			0
$657$	−7.70992	+	16.8824i	−0.300793	+	0.658644i
$658$		0			0
$659$	−21.1194	+	13.5726i	−0.822696	+	0.528714i	−0.882949	−	0.469469i	$-0.844445\pi$
$659$	−21.1194	+	13.5726i	−0.822696	+	0.528714i	0.0602535	+	0.998183i	$0.480809\pi$
$660$		0			0
$661$	0.977820	+	6.80089i	0.0380328	+	0.264524i	0.999961	−	0.00877663i	$-0.00279372\pi$
$661$	0.977820	+	6.80089i	0.0380328	+	0.264524i	−0.961929	+	0.273301i	$0.911885\pi$
$662$		0			0
$663$	0.0134485	+	0.0935364i	0.000522297	+	0.00363265i
$664$		0			0
$665$	−5.93934	+	3.81698i	−0.230318	+	0.148016i
$666$		0			0
$667$	18.5899	−	21.4539i	0.719804	−	0.830699i
$668$		0			0
$669$	−0.561518			−0.0217095
$670$		0			0
$671$	−25.2206			−0.973630
$672$		0			0
$673$	−13.9791	+	16.1328i	−0.538855	+	0.621872i	−0.958250	−	0.285932i	$-0.907697\pi$
$673$	−13.9791	+	16.1328i	−0.538855	+	0.621872i	0.419395	+	0.907804i	$0.362242\pi$
$674$		0			0
$675$	−0.130034	+	0.0835675i	−0.00500499	+	0.00321651i
$676$		0			0
$677$	6.52200	+	45.3615i	0.250661	+	1.74338i	0.594265	+	0.804269i	$0.297443\pi$
$677$	6.52200	+	45.3615i	0.250661	+	1.74338i	−0.343604	+	0.939115i	$0.611648\pi$
$678$		0			0
$679$	−1.09523	−	7.61749i	−0.0420311	−	0.292333i
$680$		0			0
$681$	−0.119763	+	0.0769670i	−0.00458933	+	0.00294938i
$682$		0			0
$683$	−0.334567	+	0.732601i	−0.0128019	+	0.0280322i	−0.915925	−	0.401350i	$-0.868541\pi$
$683$	−0.334567	+	0.732601i	−0.0128019	+	0.0280322i	0.903123	+	0.429382i	$0.141269\pi$
$684$		0			0
$685$	2.25488	−	15.6830i	0.0861545	−	0.599218i
$686$		0			0
$687$	1.23276	+	0.361972i	0.0470329	+	0.0138101i
$688$		0			0
$689$	0.155330	−	1.08034i	0.00591760	−	0.0411578i
$690$		0			0
$691$	−36.5011	−	23.4578i	−1.38857	−	0.892378i	−0.388985	−	0.921244i	$-0.627174\pi$
$691$	−36.5011	−	23.4578i	−1.38857	−	0.892378i	−0.999583	+	0.0288657i	$0.990810\pi$
$692$		0			0
$693$	2.11125	−	2.43651i	0.0801996	−	0.0925553i
$694$		0			0
$695$	−17.5818	+	38.4989i	−0.666917	+	1.46035i
$696$		0			0
$697$	−62.6353	−	40.2533i	−2.37248	−	1.52470i
$698$		0			0
$699$	0.661361			0.0250150
$700$		0			0
$701$	9.96030	+	21.8100i	0.376195	+	0.823753i	0.999139	+	0.0414861i	$0.0132092\pi$
$701$	9.96030	+	21.8100i	0.376195	+	0.823753i	−0.622944	+	0.782267i	$0.714063\pi$
$702$		0			0
$703$	6.84497	−	47.6078i	0.258163	−	1.79556i
$704$		0			0
$705$	−2.46998	−	2.85050i	−0.0930247	−	0.107356i
$706$		0			0
$707$	−2.58723			−0.0973027
$708$		0			0
$709$	13.9087	+	30.4557i	0.522351	+	1.14379i	0.968542	+	0.248851i	$0.0800531\pi$
$709$	13.9087	+	30.4557i	0.522351	+	1.14379i	−0.446191	+	0.894938i	$0.647220\pi$
$710$		0			0
$711$	−19.5416	−	5.73794i	−0.732868	−	0.215189i
$712$		0			0
$713$	−59.3951	−	17.4400i	−2.22436	−	0.653132i
$714$		0			0
$715$	−0.343599	−	0.396535i	−0.0128499	−	0.0148296i
$716$		0			0
$717$	1.82247	−	2.10324i	0.0680613	−	0.0785470i
$718$		0			0
$719$	23.4692	−	6.89118i	0.875253	−	0.256998i	0.186905	−	0.982378i	$-0.440154\pi$
$719$	23.4692	−	6.89118i	0.875253	−	0.256998i	0.688348	+	0.725380i	$0.258336\pi$
$720$		0			0
$721$	−1.78371	+	1.14632i	−0.0664288	+	0.0426912i
$722$		0			0
$723$	0.542395	−	0.159262i	0.0201719	−	0.00592300i
$724$		0			0
$725$	−0.312543	+	0.684375i	−0.0116076	+	0.0254170i
$726$		0			0
$727$	28.0440	+	32.3645i	1.04009	+	1.20033i	0.979348	+	0.202180i	$0.0648024\pi$
$727$	28.0440	+	32.3645i	1.04009	+	1.20033i	0.0607458	+	0.998153i	$0.480652\pi$
$728$		0			0
$729$	−10.8512	−	23.7609i	−0.401897	−	0.880032i
$730$		0			0
$731$	−10.2356	−	6.57799i	−0.378576	−	0.243296i
$732$		0			0
$733$	7.27133	−	2.13506i	0.268573	−	0.0788601i	−0.144673	−	0.989479i	$-0.546213\pi$
$733$	7.27133	−	2.13506i	0.268573	−	0.0788601i	0.413246	+	0.910619i	$0.364395\pi$
$734$		0			0
$735$	−0.281051	−	1.95475i	−0.0103667	−	0.0721021i
$736$		0			0
$737$	17.4811	−	6.21115i	0.643925	−	0.228791i
$738$		0			0
$739$	1.46758	+	10.2073i	0.0539860	+	0.375481i	0.998847	+	0.0480088i	$0.0152876\pi$
$739$	1.46758	+	10.2073i	0.0539860	+	0.375481i	−0.944861	+	0.327472i	$0.893803\pi$
$740$		0			0
$741$	0.0808397	−	0.0237367i	0.00296972	−	0.000871988i
$742$		0			0
$743$	35.8060	+	23.0111i	1.31359	+	0.844195i	0.994622	−	0.103569i	$-0.0330264\pi$
$743$	35.8060	+	23.0111i	1.31359	+	0.844195i	0.318971	+	0.947764i	$0.396663\pi$
$744$		0			0
$745$	−2.84579	−	6.23142i	−0.104262	−	0.228301i
$746$		0			0
$747$	−9.10683	−	10.5098i	−0.333201	−	0.384535i
$748$		0			0
$749$	−2.25146	+	4.93002i	−0.0822667	+	0.180139i
$750$		0			0
$751$	−0.702210	+	0.206188i	−0.0256240	+	0.00752389i	−0.294519	−	0.955645i	$-0.595160\pi$
$751$	−0.702210	+	0.206188i	−0.0256240	+	0.00752389i	0.268895	+	0.963169i	$0.413341\pi$
$752$		0			0
$753$	2.83281	−	1.82053i	0.103233	−	0.0663440i
$754$		0			0
$755$	7.32551	−	2.15096i	0.266603	−	0.0782816i
$756$		0			0
$757$	8.48300	−	9.78990i	0.308320	−	0.355820i	−0.580350	−	0.814367i	$-0.697084\pi$
$757$	8.48300	−	9.78990i	0.308320	−	0.355820i	0.888670	+	0.458547i	$0.151630\pi$
$758$		0			0
$759$	−1.44663	−	1.66950i	−0.0525095	−	0.0605992i
$760$		0			0
$761$	−11.3929	−	3.34525i	−0.412992	−	0.121265i	0.0686348	−	0.997642i	$-0.478136\pi$
$761$	−11.3929	−	3.34525i	−0.412992	−	0.121265i	−0.481627	+	0.876377i	$0.659954\pi$
$762$		0			0
$763$	1.88451	+	0.553342i	0.0682238	+	0.0200323i
$764$		0			0
$765$	20.5868	+	45.0789i	0.744318	+	1.62983i
$766$		0			0
$767$	0.211102			0.00762245
$768$		0			0
$769$	22.8202	+	26.3359i	0.822918	+	0.949698i	0.999401	−	0.0346053i	$-0.0110174\pi$
$769$	22.8202	+	26.3359i	0.822918	+	0.949698i	−0.176483	+	0.984304i	$0.556472\pi$
$770$		0			0
$771$	0.104479	−	0.726666i	0.00376271	−	0.0261702i
$772$		0			0
$773$	5.86386	+	12.8401i	0.210909	+	0.461825i	0.985289	−	0.170895i	$-0.0546658\pi$
$773$	5.86386	+	12.8401i	0.210909	+	0.461825i	−0.774381	+	0.632720i	$0.781938\pi$
$774$		0			0
$775$	1.64062			0.0589329
$776$		0			0
$777$	−0.379837	−	0.244106i	−0.0136266	−	0.00875726i
$778$		0			0
$779$	−27.5761	+	60.3833i	−0.988017	+	2.16346i
$780$		0			0
$781$	18.3939	−	21.2277i	0.658184	−	0.759585i
$782$		0			0
$783$	2.39623	+	1.53997i	0.0856344	+	0.0550339i
$784$		0			0
$785$	−2.66603	+	18.5426i	−0.0951546	+	0.661815i
$786$		0			0
$787$	30.5175	+	8.96074i	1.08783	+	0.319416i	0.776007	−	0.630724i	$-0.217242\pi$
$787$	30.5175	+	8.96074i	1.08783	+	0.319416i	0.311824	+	0.950140i	$0.399060\pi$
$788$		0			0
$789$	−0.334415	+	2.32591i	−0.0119055	+	0.0828045i
$790$		0			0
$791$	0.516406	−	1.13077i	0.0183613	−	0.0402056i
$792$		0			0
$793$	0.950174	−	0.610640i	0.0337417	−	0.0216844i
$794$		0			0
$795$	0.446231	+	3.10360i	0.0158262	+	0.110073i
$796$		0			0
$797$	2.89342	+	20.1242i	0.102490	+	0.712836i	0.974670	+	0.223649i	$0.0717971\pi$
$797$	2.89342	+	20.1242i	0.102490	+	0.712836i	−0.872179	+	0.489186i	$0.837294\pi$
$798$		0			0
$799$	−79.2445	+	50.9274i	−2.80347	+	1.80168i
$800$		0			0
$801$	13.2120	−	15.2475i	0.466823	−	0.538743i
$802$		0			0
$803$	14.0983			0.497518
$804$		0			0
$805$	−8.29009			−0.292187
$806$		0			0
$807$	−0.746449	+	0.861448i	−0.0262762	+	0.0303244i
$808$		0			0
$809$	25.0285	−	16.0849i	0.879957	−	0.565514i	−0.0208264	−	0.999783i	$-0.506630\pi$
$809$	25.0285	−	16.0849i	0.879957	−	0.565514i	0.900783	+	0.434269i	$0.142993\pi$
$810$		0			0
$811$	−4.12918	−	28.7191i	−0.144995	−	1.00846i	−0.924259	−	0.381767i	$-0.875316\pi$
$811$	−4.12918	−	28.7191i	−0.144995	−	1.00846i	0.779264	−	0.626696i	$-0.215593\pi$
$812$		0			0
$813$	−0.318590	−	2.21584i	−0.0111735	−	0.0777131i
$814$		0			0
$815$	−24.4909	+	15.7394i	−0.857879	+	0.551326i
$816$		0			0
$817$	−4.50636	+	9.86755i	−0.157658	+	0.345222i
$818$		0			0
$819$	−0.0205476	+	0.142912i	−0.000717991	+	0.00499374i
$820$		0			0
$821$	22.4203	+	6.58318i	0.782473	+	0.229755i	0.648484	−	0.761228i	$-0.275403\pi$
$821$	22.4203	+	6.58318i	0.782473	+	0.229755i	0.133989	+	0.990983i	$0.457221\pi$
$822$		0			0
$823$	7.27148	−	50.5743i	0.253468	−	1.76291i	−0.323583	−	0.946200i	$-0.604887\pi$
$823$	7.27148	−	50.5743i	0.253468	−	1.76291i	0.577051	−	0.816708i	$-0.304204\pi$
$824$		0			0
$825$	0.0492534	+	0.0316532i	0.00171478	+	0.00110202i
$826$		0			0
$827$	−22.5142	+	25.9828i	−0.782897	+	0.903511i	−0.997315	−	0.0732311i	$-0.976669\pi$
$827$	−22.5142	+	25.9828i	−0.782897	+	0.903511i	0.214418	+	0.976742i	$0.431214\pi$
$828$		0			0
$829$	20.4167	−	44.7064i	0.709103	−	1.55272i	−0.119470	−	0.992838i	$-0.538120\pi$
$829$	20.4167	−	44.7064i	0.709103	−	1.55272i	0.828573	−	0.559881i	$-0.189153\pi$
$830$		0			0
$831$	−1.77242	−	1.13906i	−0.0614845	−	0.0395137i
$832$		0			0
$833$	−49.3211			−1.70888
$834$		0			0
$835$	8.65107	+	18.9432i	0.299383	+	0.655556i
$836$		0			0
$837$	0.883960	−	6.14808i	0.0305541	−	0.212509i
$838$		0			0
$839$	36.2640	+	41.8509i	1.25197	+	1.44485i	0.847926	+	0.530115i	$0.177851\pi$
$839$	36.2640	+	41.8509i	1.25197	+	1.44485i	0.404047	+	0.914738i	$0.367603\pi$
$840$		0			0
$841$	−15.1356			−0.521917
$842$		0			0
$843$	−1.08905	−	2.38469i	−0.0375089	−	0.0821331i
$844$		0			0
$845$	−28.4268	−	8.34687i	−0.977913	−	0.287141i
$846$		0			0
$847$	2.68206	+	0.787524i	0.0921566	+	0.0270596i
$848$		0			0
$849$	−0.775602	−	0.895093i	−0.0266186	−	0.0307195i
$850$		0			0
$851$	36.9844	−	42.6822i	1.26781	−	1.46313i
$852$		0			0
$853$	−28.1304	+	8.25983i	−0.963167	+	0.282811i	−0.725259	−	0.688477i	$-0.758280\pi$
$853$	−28.1304	+	8.25983i	−0.963167	+	0.282811i	−0.237908	+	0.971288i	$0.576462\pi$
$854$		0			0
$855$	37.1700	−	23.8877i	1.27119	−	0.816943i
$856$		0			0
$857$	−21.0935	+	6.19361i	−0.720540	+	0.211570i	−0.621388	−	0.783503i	$-0.713431\pi$
$857$	−21.0935	+	6.19361i	−0.720540	+	0.211570i	−0.0991516	+	0.995072i	$0.531613\pi$
$858$		0			0
$859$	−9.18153	+	20.1047i	−0.313270	+	0.685965i	−0.999127	−	0.0417709i	$-0.986700\pi$
$859$	−9.18153	+	20.1047i	−0.313270	+	0.685965i	0.685858	+	0.727736i	$0.259427\pi$
$860$		0			0
$861$	0.408083	+	0.470953i	0.0139074	+	0.0160500i
$862$		0			0
$863$	−8.73191	−	19.1202i	−0.297238	−	0.650859i	0.700808	−	0.713350i	$-0.252823\pi$
$863$	−8.73191	−	19.1202i	−0.297238	−	0.650859i	−0.998046	+	0.0624905i	$0.980096\pi$
$864$		0			0
$865$	−48.3807	−	31.0924i	−1.64499	−	1.05717i
$866$		0			0
$867$	−4.41998	+	1.29782i	−0.150110	+	0.0440764i
$868$		0			0
$869$	2.20175	+	15.3135i	0.0746892	+	0.519475i
$870$		0			0
$871$	−0.508208	+	0.657254i	−0.0172200	+	0.0222702i
$872$		0			0
$873$	6.85426	+	47.6724i	0.231981	+	1.61347i
$874$		0			0
$875$	−5.00585	+	1.46985i	−0.169229	+	0.0496900i
$876$		0			0
$877$	−11.6520	−	7.48826i	−0.393459	−	0.252861i	0.328921	−	0.944358i	$-0.393315\pi$
$877$	−11.6520	−	7.48826i	−0.393459	−	0.252861i	−0.722379	+	0.691497i	$0.756951\pi$
$878$		0			0
$879$	−1.28370	−	2.81090i	−0.0432980	−	0.0948093i
$880$		0			0
$881$	7.19637	+	8.30506i	0.242452	+	0.279805i	0.863914	−	0.503640i	$-0.168006\pi$
$881$	7.19637	+	8.30506i	0.242452	+	0.279805i	−0.621462	+	0.783445i	$0.713461\pi$
$882$		0			0
$883$	−11.0742	+	24.2491i	−0.372676	+	0.816048i	0.626648	+	0.779302i	$0.284426\pi$
$883$	−11.0742	+	24.2491i	−0.372676	+	0.816048i	−0.999325	+	0.0367454i	$0.988301\pi$
$884$		0			0
$885$	−0.581887	+	0.170857i	−0.0195599	+	0.00574331i
$886$		0			0
$887$	12.6082	−	8.10283i	0.423344	−	0.272066i	−0.311575	−	0.950221i	$-0.600857\pi$
$887$	12.6082	−	8.10283i	0.423344	−	0.272066i	0.734919	+	0.678155i	$0.237220\pi$
$888$		0			0
$889$	4.81012	−	1.41238i	0.161326	−	0.0473696i
$890$		0			0
$891$	−13.1400	+	15.1644i	−0.440206	+	0.508025i
$892$		0			0
$893$	54.9984	+	63.4716i	1.84045	+	2.12400i
$894$		0			0
$895$	−55.1465	−	16.1925i	−1.84335	−	0.541255i
$896$		0			0
$897$	0.0949232	+	0.0278720i	0.00316939	+	0.000930618i
$898$		0			0
$899$	−12.5593	−	27.5010i	−0.418875	−	0.917208i
$900$		0			0
$901$	78.3083			2.60883
$902$		0			0
$903$	0.0666870	+	0.0769609i	0.00221920	+	0.00256110i
$904$		0			0
$905$	−2.19579	+	15.2721i	−0.0729907	+	0.507661i
$906$		0			0
$907$	−15.9330	−	34.8883i	−0.529045	−	1.15845i	−0.965900	−	0.258916i	$-0.916635\pi$
$907$	−15.9330	−	34.8883i	−0.529045	−	1.15845i	0.436855	−	0.899532i	$-0.356092\pi$
$908$		0			0
$909$	16.1916			0.537041
$910$		0			0
$911$	−17.6105	−	11.3176i	−0.583462	−	0.374968i	0.215361	−	0.976535i	$-0.430907\pi$
$911$	−17.6105	−	11.3176i	−0.583462	−	0.374968i	−0.798823	+	0.601566i	$0.794544\pi$
$912$		0			0
$913$	−4.38833	+	9.60910i	−0.145233	+	0.318015i
$914$		0			0
$915$	−2.12485	+	2.45221i	−0.0702455	+	0.0810676i
$916$		0			0
$917$	−0.647160	−	0.415904i	−0.0213711	−	0.0137344i
$918$		0			0
$919$	−4.55518	+	31.6820i	−0.150262	+	1.04509i	0.765519	+	0.643413i	$0.222482\pi$
$919$	−4.55518	+	31.6820i	−0.150262	+	1.04509i	−0.915781	+	0.401679i	$0.868427\pi$
$920$		0			0
$921$	2.89120	+	0.848934i	0.0952684	+	0.0279733i
$922$		0			0
$923$	−0.179017	+	1.24509i	−0.00589243	+	0.0409827i
$924$		0			0
$925$	−0.621800	+	1.36155i	−0.0204447	+	0.0447676i
$926$		0			0
$927$	11.1629	−	7.17399i	0.366639	−	0.235625i
$928$		0			0
$929$	0.936777	+	6.51543i	0.0307347	+	0.213764i	0.999401	−	0.0346006i	$-0.0110159\pi$
$929$	0.936777	+	6.51543i	0.0307347	+	0.213764i	−0.968667	+	0.248365i	$0.920107\pi$
$930$		0			0
$931$	6.25810	+	43.5260i	0.205101	+	1.42651i
$932$		0			0
$933$	−1.20688	+	0.775616i	−0.0395116	+	0.0253925i
$934$		0			0
$935$	24.6522	−	28.4501i	0.806212	−	0.930418i
$936$		0			0
$937$	−1.11005			−0.0362638			−0.0181319	−	0.999836i	$-0.505772\pi$
$937$	−1.11005			−0.0362638			−0.0181319	+	0.999836i	$0.505772\pi$
$938$		0			0
$939$	−3.22207			−0.105148
$940$		0			0
$941$	−9.80311	+	11.3134i	−0.319572	+	0.368806i	−0.892693	−	0.450665i	$-0.851187\pi$
$941$	−9.80311	+	11.3134i	−0.319572	+	0.368806i	0.573121	+	0.819471i	$0.305732\pi$
$942$		0			0
$943$	−65.5731	+	42.1413i	−2.13535	+	1.37231i
$944$		0			0
$945$	−0.118381	−	0.823360i	−0.00385094	−	0.0267839i
$946$		0			0
$947$	−2.08878	−	14.5278i	−0.0678763	−	0.472090i	−0.995203	−	0.0978362i	$-0.968808\pi$
$947$	−2.08878	−	14.5278i	−0.0678763	−	0.472090i	0.927326	−	0.374254i	$-0.122101\pi$
$948$		0			0
$949$	−0.531146	+	0.341347i	−0.0172417	+	0.0110806i
$950$		0			0
$951$	−0.236523	+	0.517912i	−0.00766977	+	0.0167944i
$952$		0			0
$953$	3.84052	−	26.7114i	0.124407	−	0.865268i	−0.828063	−	0.560635i	$-0.810557\pi$
$953$	3.84052	−	26.7114i	0.124407	−	0.865268i	0.952470	−	0.304633i	$-0.0985338\pi$
$954$		0			0
$955$	−26.2305	−	7.70197i	−0.848799	−	0.249230i
$956$		0			0
$957$	0.153544	−	1.06792i	0.00496338	−	0.0345210i
$958$		0			0
$959$	2.78616	+	1.79056i	0.0899699	+	0.0578201i
$960$		0			0
$961$	−22.8722	+	26.3960i	−0.737814	+	0.851483i
$962$		0			0
$963$	14.0903	−	30.8534i	0.454053	−	0.994237i
$964$		0			0
$965$	−1.13322	−	0.728275i	−0.0364796	−	0.0234440i
$966$		0			0
$967$	−6.83555			−0.219817			−0.109908	−	0.993942i	$-0.535056\pi$
$967$	−6.83555			−0.219817			−0.109908	+	0.993942i	$0.535056\pi$
$968$		0			0
$969$	2.51112	+	5.49859i	0.0806688	+	0.176640i
$970$		0			0
$971$	1.62043	−	11.2703i	0.0520021	−	0.361683i	−0.947160	−	0.320761i	$-0.896061\pi$
$971$	1.62043	−	11.2703i	0.0520021	−	0.361683i	0.999162	−	0.0409219i	$-0.0130295\pi$
$972$		0			0
$973$	−5.79345	−	6.68600i	−0.185730	−	0.214343i
$974$		0			0
$975$	−0.00262198			−8.39707e−5
$976$		0			0
$977$	−8.21689	−	17.9925i	−0.262882	−	0.575630i	0.731457	−	0.681887i	$-0.238841\pi$
$977$	−8.21689	−	17.9925i	−0.262882	−	0.575630i	−0.994339	+	0.106257i	$0.966113\pi$
$978$		0			0
$979$	−14.7049	−	4.31773i	−0.469969	−	0.137995i
$980$		0			0
$981$	−11.7938	−	3.46297i	−0.376546	−	0.110564i
$982$		0			0
$983$	−8.65995	−	9.99412i	−0.276210	−	0.318763i	0.600648	−	0.799514i	$-0.294909\pi$
$983$	−8.65995	−	9.99412i	−0.276210	−	0.318763i	−0.876857	+	0.480751i	$0.840364\pi$
$984$		0			0
$985$	27.8870	−	32.1833i	0.888552	−	1.02544i
$986$		0			0
$987$	0.756470	−	0.222120i	0.0240787	−	0.00707015i
$988$		0			0
$989$	−10.7156	+	6.88653i	−0.340738	+	0.218979i
$990$		0			0
$991$	−0.395567	+	0.116149i	−0.0125656	+	0.00368959i	−0.288009	−	0.957628i	$-0.592993\pi$
$991$	−0.395567	+	0.116149i	−0.0125656	+	0.00368959i	0.275444	+	0.961317i	$0.411175\pi$
$992$		0			0
$993$	−0.685689	+	1.50145i	−0.0217597	+	0.0476471i
$994$		0			0
$995$	17.8209	+	20.5664i	0.564959	+	0.651998i
$996$		0			0
$997$	−6.50067	−	14.2345i	−0.205878	−	0.450810i	0.778323	−	0.627864i	$-0.216071\pi$
$997$	−6.50067	−	14.2345i	−0.205878	−	0.450810i	−0.984201	+	0.177054i	$0.943343\pi$
$998$		0			0
$999$	4.76727	+	3.06374i	0.150830	+	0.0969324i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	536.2.q.a.25.3	✓	80
67.59	even	11	inner	536.2.q.a.193.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
536.2.q.a.25.3	✓	80	1.1	even	1	trivial
536.2.q.a.193.3	yes	80	67.59	even	11	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:	\( N \)	\(=\)	\( 536 = 2^{3} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	536.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0837208 + 0.0966190i) q^{3} +(-1.91873 + 1.23309i) q^{5} +(-0.0678491 - 0.471901i) q^{7} +(0.424618 + 2.95329i) q^{9} +O(q^{10})\)	\(q+(-0.0837208 + 0.0966190i) q^{3} +(-1.91873 + 1.23309i) q^{5} +(-0.0678491 - 0.471901i) q^{7} +(0.424618 + 2.95329i) q^{9} +(1.90666 - 1.22534i) q^{11} +(-0.0421648 + 0.0923281i) q^{13} +(0.0414976 - 0.288622i) q^{15} +(-6.98735 - 2.05167i) q^{17} +(-0.924017 + 6.42668i) q^{19} +(0.0512750 + 0.0329524i) q^{21} +(-4.99260 + 5.76176i) q^{23} +(0.0839382 - 0.183799i) q^{25} +(-0.643544 - 0.413581i) q^{27} -3.72350 q^{29} +(3.37298 + 7.38579i) q^{31} +(-0.0412366 + 0.286807i) q^{33} +(0.712083 + 0.821787i) q^{35} -7.40784 q^{37} +(-0.00539058 - 0.0118037i) q^{39} +(9.80987 + 2.88044i) q^{41} +(1.60308 + 0.470707i) q^{43} +(-4.45641 - 5.14297i) q^{45} +(8.47072 - 9.77573i) q^{47} +(6.49836 - 1.90809i) q^{49} +(0.783218 - 0.503343i) q^{51} +(-10.3176 + 3.02952i) q^{53} +(-2.14742 + 4.70220i) q^{55} +(-0.543580 - 0.627325i) q^{57} +(-0.863986 - 1.89186i) q^{59} +(-9.36127 - 6.01612i) q^{61} +(1.36485 - 0.400756i) q^{63} +(-0.0329463 - 0.229146i) q^{65} +(7.97017 + 1.86452i) q^{67} +(-0.138712 - 0.964760i) q^{69} +(11.8910 - 3.49151i) q^{71} +(5.23294 + 3.36301i) q^{73} +(0.0107311 + 0.0234978i) q^{75} +(-0.707604 - 0.816619i) q^{77} +(-2.83565 + 6.20920i) q^{79} +(-8.49455 + 2.49423i) q^{81} +(-3.92100 + 2.51987i) q^{83} +(15.9368 - 4.67946i) q^{85} +(0.311734 - 0.359760i) q^{87} +(-4.42813 - 5.11033i) q^{89} +(0.0464306 + 0.0136332i) q^{91} +(-0.995996 - 0.292451i) q^{93} +(-6.15176 - 13.4705i) q^{95} +16.1422 q^{97} +(4.42838 + 5.11063i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{3} + q^{5} - 6 q^{7} - 7 q^{9}+O(q^{10}) \) 80 * q - q^3 + q^5 - 6 * q^7 - 7 * q^9	\( 80 q - q^{3} + q^{5} - 6 q^{7} - 7 q^{9} - q^{11} - q^{13} - 6 q^{15} + 8 q^{17} + 7 q^{19} + 71 q^{21} - 18 q^{23} - 5 q^{25} - 4 q^{27} - 14 q^{29} - 34 q^{31} - 24 q^{33} + 20 q^{35} - 40 q^{37} + 21 q^{39} - 70 q^{41} + 10 q^{43} + 34 q^{45} - 8 q^{47} + 10 q^{49} + 10 q^{51} - 39 q^{53} - 50 q^{55} + 35 q^{57} - 66 q^{59} + 4 q^{61} + 21 q^{63} + 20 q^{65} - 24 q^{67} - 8 q^{69} - 13 q^{71} + 25 q^{73} + 44 q^{75} + 15 q^{77} + 59 q^{79} + 16 q^{81} - 51 q^{83} + 59 q^{85} - 26 q^{87} + 58 q^{89} + 16 q^{91} + 87 q^{93} - 56 q^{95} - 30 q^{97} + 93 q^{99}+O(q^{100}) \) 80 * q - q^3 + q^5 - 6 * q^7 - 7 * q^9 - q^11 - q^13 - 6 * q^15 + 8 * q^17 + 7 * q^19 + 71 * q^21 - 18 * q^23 - 5 * q^25 - 4 * q^27 - 14 * q^29 - 34 * q^31 - 24 * q^33 + 20 * q^35 - 40 * q^37 + 21 * q^39 - 70 * q^41 + 10 * q^43 + 34 * q^45 - 8 * q^47 + 10 * q^49 + 10 * q^51 - 39 * q^53 - 50 * q^55 + 35 * q^57 - 66 * q^59 + 4 * q^61 + 21 * q^63 + 20 * q^65 - 24 * q^67 - 8 * q^69 - 13 * q^71 + 25 * q^73 + 44 * q^75 + 15 * q^77 + 59 * q^79 + 16 * q^81 - 51 * q^83 + 59 * q^85 - 26 * q^87 + 58 * q^89 + 16 * q^91 + 87 * q^93 - 56 * q^95 - 30 * q^97 + 93 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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