LMFDB - Embedded newform 414.2.i.c.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 46)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	414.127
Dual form			414.2.i.c.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 - 0.540641i) q^{2} +(0.415415 - 0.909632i) q^{4} +(1.34125 - 0.393828i) q^{5} +(2.81051 + 3.24350i) q^{7} +(-0.142315 - 0.989821i) q^{8} +O(q^{10})$	\(q+(0.841254 - 0.540641i) q^{2} +(0.415415 - 0.909632i) q^{4} +(1.34125 - 0.393828i) q^{5} +(2.81051 + 3.24350i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(0.915415 - 1.05645i) q^{10} +(-0.186393 - 0.119787i) q^{11} +(-1.30185 + 1.50242i) q^{13} +(4.11792 + 1.20913i) q^{14} +(-0.654861 - 0.755750i) q^{16} +(-0.0462003 - 0.101165i) q^{17} +(1.34422 - 2.94343i) q^{19} +(0.198939 - 1.38365i) q^{20} -0.221566 q^{22} +(0.936621 - 4.70348i) q^{23} +(-2.56241 + 1.64676i) q^{25} +(-0.282920 + 1.96775i) q^{26} +(4.11792 - 1.20913i) q^{28} +(1.48246 + 3.24614i) q^{29} +(-0.876357 - 6.09519i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-0.0935599 - 0.0601273i) q^{34} +(5.04699 + 3.24350i) q^{35} +(-4.05681 - 1.19119i) q^{37} +(-0.460509 - 3.20291i) q^{38} +(-0.580699 - 1.27155i) q^{40} +(3.27491 - 0.961600i) q^{41} +(0.462235 - 3.21491i) q^{43} +(-0.186393 + 0.119787i) q^{44} +(-1.75496 - 4.46320i) q^{46} -7.73852 q^{47} +(-1.62514 + 11.3031i) q^{49} +(-1.26533 + 2.77068i) q^{50} +(0.825838 + 1.80833i) q^{52} +(0.0956823 + 0.110423i) q^{53} +(-0.297176 - 0.0872586i) q^{55} +(2.81051 - 3.24350i) q^{56} +(3.00212 + 1.92935i) q^{58} +(-8.62403 + 9.95266i) q^{59} +(0.809721 + 5.63174i) q^{61} +(-4.03255 - 4.65381i) q^{62} +(-0.959493 + 0.281733i) q^{64} +(-1.15442 + 2.52783i) q^{65} +(-12.0623 + 7.75194i) q^{67} -0.111215 q^{68} +5.99937 q^{70} +(4.91722 - 3.16011i) q^{71} +(-1.57542 + 3.44970i) q^{73} +(-4.05681 + 1.19119i) q^{74} +(-2.11903 - 2.44549i) q^{76} +(-0.135328 - 0.941230i) q^{77} +(5.71616 - 6.59680i) q^{79} +(-1.17597 - 0.755750i) q^{80} +(2.23515 - 2.57950i) q^{82} +(-15.0155 - 4.40894i) q^{83} +(-0.101808 - 0.117492i) q^{85} +(-1.34926 - 2.95446i) q^{86} +(-0.0920417 + 0.201543i) q^{88} +(0.145067 - 1.00896i) q^{89} -8.53197 q^{91} +(-3.88935 - 2.80588i) q^{92} +(-6.51006 + 4.18376i) q^{94} +(0.643736 - 4.47728i) q^{95} +(17.4754 - 5.13124i) q^{97} +(4.74375 + 10.3874i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{4} + 4 q^{5} - 7 q^{7} - q^{8}+O(q^{10}) $ 10 * q - q^2 - q^4 + 4 * q^5 - 7 * q^7 - q^8	$ 10 q - q^{2} - q^{4} + 4 q^{5} - 7 q^{7} - q^{8} + 4 q^{10} + 2 q^{11} + 2 q^{13} + 15 q^{14} - q^{16} + 9 q^{17} + 2 q^{19} - 7 q^{20} + 2 q^{22} - 21 q^{23} - 11 q^{25} - 9 q^{26} + 15 q^{28} + 2 q^{29} + 11 q^{31} - q^{32} - 13 q^{34} + 17 q^{35} - 18 q^{37} + 13 q^{38} + 4 q^{40} - 5 q^{41} - 21 q^{43} + 2 q^{44} - 10 q^{46} + 22 q^{47} + 24 q^{49} + 22 q^{50} - 20 q^{52} + 7 q^{53} + 3 q^{55} - 7 q^{56} + 24 q^{58} - 43 q^{59} - 3 q^{61} - 33 q^{62} - q^{64} - 41 q^{65} - q^{67} - 2 q^{68} + 6 q^{70} + 11 q^{71} - 28 q^{73} - 18 q^{74} + 2 q^{76} - 30 q^{77} + 34 q^{79} - 7 q^{80} + 6 q^{82} + 3 q^{83} + 8 q^{85} + 34 q^{86} - 9 q^{88} + 49 q^{89} - 52 q^{91} + q^{92} - 11 q^{94} + 36 q^{95} + 16 q^{97} - 20 q^{98}+O(q^{100}) $ 10 * q - q^2 - q^4 + 4 * q^5 - 7 * q^7 - q^8 + 4 * q^10 + 2 * q^11 + 2 * q^13 + 15 * q^14 - q^16 + 9 * q^17 + 2 * q^19 - 7 * q^20 + 2 * q^22 - 21 * q^23 - 11 * q^25 - 9 * q^26 + 15 * q^28 + 2 * q^29 + 11 * q^31 - q^32 - 13 * q^34 + 17 * q^35 - 18 * q^37 + 13 * q^38 + 4 * q^40 - 5 * q^41 - 21 * q^43 + 2 * q^44 - 10 * q^46 + 22 * q^47 + 24 * q^49 + 22 * q^50 - 20 * q^52 + 7 * q^53 + 3 * q^55 - 7 * q^56 + 24 * q^58 - 43 * q^59 - 3 * q^61 - 33 * q^62 - q^64 - 41 * q^65 - q^67 - 2 * q^68 + 6 * q^70 + 11 * q^71 - 28 * q^73 - 18 * q^74 + 2 * q^76 - 30 * q^77 + 34 * q^79 - 7 * q^80 + 6 * q^82 + 3 * q^83 + 8 * q^85 + 34 * q^86 - 9 * q^88 + 49 * q^89 - 52 * q^91 + q^92 - 11 * q^94 + 36 * q^95 + 16 * q^97 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$3$		0			0
$3$		0			0
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	1.34125	−	0.393828i	0.599827	−	0.176125i	0.0322976	−	0.999478i	$-0.489718\pi$
$5$	1.34125	−	0.393828i	0.599827	−	0.176125i	0.567529	+	0.823353i	$0.307899\pi$
$6$		0			0
$7$	2.81051	+	3.24350i	1.06227	+	1.22593i	0.973213	+	0.229903i	$0.0738410\pi$
$7$	2.81051	+	3.24350i	1.06227	+	1.22593i	0.0890604	+	0.996026i	$0.471614\pi$
$8$	−0.142315	−	0.989821i	−0.0503159	−	0.349955i
$9$		0			0
$10$	0.915415	−	1.05645i	0.289480	−	0.334077i
$11$	−0.186393	−	0.119787i	−0.0561995	−	0.0361173i	0.512239	−	0.858843i	$-0.328816\pi$
$11$	−0.186393	−	0.119787i	−0.0561995	−	0.0361173i	−0.568439	+	0.822725i	$0.692452\pi$
$12$		0			0
$13$	−1.30185	+	1.50242i	−0.361069	+	0.416696i	−0.906998	−	0.421136i	$-0.861632\pi$
$13$	−1.30185	+	1.50242i	−0.361069	+	0.416696i	0.545929	+	0.837832i	$0.316177\pi$
$14$	4.11792	+	1.20913i	1.10056	+	0.323154i
$15$		0			0
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−0.0462003	−	0.101165i	−0.0112052	−	0.0245360i	0.903947	−	0.427645i	$-0.140657\pi$
$17$	−0.0462003	−	0.101165i	−0.0112052	−	0.0245360i	−0.915152	+	0.403109i	$0.867929\pi$
$18$		0			0
$19$	1.34422	−	2.94343i	0.308385	−	0.675270i	−0.690457	−	0.723373i	$-0.742591\pi$
$19$	1.34422	−	2.94343i	0.308385	−	0.675270i	0.998842	+	0.0481038i	$0.0153178\pi$
$20$	0.198939	−	1.38365i	0.0444840	−	0.309393i
$21$		0			0
$22$	−0.221566			−0.0472379
$23$	0.936621	−	4.70348i	0.195299	−	0.980744i
$23$	0.936621	−	4.70348i	0.195299	−	0.980744i
$24$		0			0
$25$	−2.56241	+	1.64676i	−0.512481	+	0.329352i
$26$	−0.282920	+	1.96775i	−0.0554851	+	0.385907i
$27$		0			0
$28$	4.11792	−	1.20913i	0.778215	−	0.228504i
$29$	1.48246	+	3.24614i	0.275286	+	0.602793i	0.995892	−	0.0905524i	$-0.0288633\pi$
$29$	1.48246	+	3.24614i	0.275286	+	0.602793i	−0.720605	+	0.693345i	$0.756136\pi$
$30$		0			0
$31$	−0.876357	−	6.09519i	−0.157398	−	1.09473i	−0.903404	−	0.428790i	$-0.858940\pi$
$31$	−0.876357	−	6.09519i	−0.157398	−	1.09473i	0.746006	−	0.665939i	$-0.231969\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$		0			0
$34$	−0.0935599	−	0.0601273i	−0.0160454	−	0.0103118i
$35$	5.04699	+	3.24350i	0.853097	+	0.548252i
$36$		0			0
$37$	−4.05681	−	1.19119i	−0.666936	−	0.195830i	−0.0692976	−	0.997596i	$-0.522076\pi$
$37$	−4.05681	−	1.19119i	−0.666936	−	0.195830i	−0.597638	+	0.801766i	$0.703894\pi$
$38$	−0.460509	−	3.20291i	−0.0747045	−	0.519581i
$39$		0			0
$40$	−0.580699	−	1.27155i	−0.0918166	−	0.201050i
$41$	3.27491	−	0.961600i	0.511455	−	0.150177i	−0.0158145	−	0.999875i	$-0.505034\pi$
$41$	3.27491	−	0.961600i	0.511455	−	0.150177i	0.527269	+	0.849698i	$0.323216\pi$
$42$		0			0
$43$	0.462235	−	3.21491i	0.0704901	−	0.490270i	−0.923742	−	0.383016i	$-0.874885\pi$
$43$	0.462235	−	3.21491i	0.0704901	−	0.490270i	0.994232	−	0.107253i	$-0.0342056\pi$
$44$	−0.186393	+	0.119787i	−0.0280998	+	0.0180586i
$45$		0			0
$46$	−1.75496	−	4.46320i	−0.258755	−	0.658062i
$47$	−7.73852			−1.12878			−0.564389	−	0.825509i	$-0.690888\pi$
$47$	−7.73852			−1.12878			−0.564389	+	0.825509i	$0.690888\pi$
$48$		0			0
$49$	−1.62514	+	11.3031i	−0.232162	+	1.61472i
$50$	−1.26533	+	2.77068i	−0.178945	+	0.391834i
$51$		0			0
$52$	0.825838	+	1.80833i	0.114523	+	0.250771i
$53$	0.0956823	+	0.110423i	0.0131430	+	0.0151678i	0.762283	−	0.647244i	$-0.224078\pi$
$53$	0.0956823	+	0.110423i	0.0131430	+	0.0151678i	−0.749140	+	0.662412i	$0.769533\pi$
$54$		0			0
$55$	−0.297176	−	0.0872586i	−0.0400711	−	0.0117660i
$56$	2.81051	−	3.24350i	0.375571	−	0.433432i
$57$		0			0
$58$	3.00212	+	1.92935i	0.394198	+	0.253336i
$59$	−8.62403	+	9.95266i	−1.12275	+	1.29573i	−0.172235	+	0.985056i	$0.555099\pi$
$59$	−8.62403	+	9.95266i	−1.12275	+	1.29573i	−0.950518	+	0.310670i	$0.899446\pi$
$60$		0			0
$61$	0.809721	+	5.63174i	0.103674	+	0.721070i	0.973662	+	0.227997i	$0.0732175\pi$
$61$	0.809721	+	5.63174i	0.103674	+	0.721070i	−0.869988	+	0.493073i	$0.835873\pi$
$62$	−4.03255	−	4.65381i	−0.512134	−	0.591034i
$63$		0			0
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	−1.15442	+	2.52783i	−0.143188	+	0.313539i
$66$		0			0
$67$	−12.0623	+	7.75194i	−1.47364	+	0.947050i	−0.475924	+	0.879486i	$0.657886\pi$
$67$	−12.0623	+	7.75194i	−1.47364	+	0.947050i	−0.997715	+	0.0675637i	$0.978477\pi$
$68$	−0.111215			−0.0134868
$69$		0			0
$70$	5.99937			0.717062
$71$	4.91722	−	3.16011i	0.583567	−	0.375036i	−0.215296	−	0.976549i	$-0.569072\pi$
$71$	4.91722	−	3.16011i	0.583567	−	0.375036i	0.798863	+	0.601513i	$0.205435\pi$
$72$		0			0
$73$	−1.57542	+	3.44970i	−0.184389	+	0.403756i	−0.979142	−	0.203177i	$-0.934873\pi$
$73$	−1.57542	+	3.44970i	−0.184389	+	0.403756i	0.794753	+	0.606933i	$0.207601\pi$
$74$	−4.05681	+	1.19119i	−0.471595	+	0.138473i
$75$		0			0
$76$	−2.11903	−	2.44549i	−0.243069	−	0.280517i
$77$	−0.135328	−	0.941230i	−0.0154221	−	0.107263i
$78$		0			0
$79$	5.71616	−	6.59680i	0.643118	−	0.742198i	−0.336805	−	0.941575i	$-0.609346\pi$
$79$	5.71616	−	6.59680i	0.643118	−	0.742198i	0.979923	+	0.199376i	$0.0638916\pi$
$80$	−1.17597	−	0.755750i	−0.131477	−	0.0844954i
$81$		0			0
$82$	2.23515	−	2.57950i	0.246831	−	0.284858i
$83$	−15.0155	−	4.40894i	−1.64816	−	0.483944i	−0.679781	−	0.733415i	$-0.737925\pi$
$83$	−15.0155	−	4.40894i	−1.64816	−	0.483944i	−0.968382	+	0.249471i	$0.919743\pi$
$84$		0			0
$85$	−0.101808	−	0.117492i	−0.0110426	−	0.0127438i
$86$	−1.34926	−	2.95446i	−0.145494	−	0.318588i
$87$		0			0
$88$	−0.0920417	+	0.201543i	−0.00981167	+	0.0214846i
$89$	0.145067	−	1.00896i	0.0153771	−	0.106950i	−0.980687	−	0.195582i	$-0.937340\pi$
$89$	0.145067	−	1.00896i	0.0153771	−	0.106950i	0.996064	+	0.0886321i	$0.0282496\pi$
$90$		0			0
$91$	−8.53197			−0.894394
$92$	−3.88935	−	2.80588i	−0.405493	−	0.292533i
$93$		0			0
$94$	−6.51006	+	4.18376i	−0.671461	+	0.431522i
$95$	0.643736	−	4.47728i	0.0660459	−	0.459359i
$96$		0			0
$97$	17.4754	−	5.13124i	1.77436	−	0.520999i	0.779879	−	0.625930i	$-0.215281\pi$
$97$	17.4754	−	5.13124i	1.77436	−	0.520999i	0.994479	+	0.104932i	$0.0334624\pi$
$98$	4.74375	+	10.3874i	0.479191	+	1.04928i
$99$		0			0
$100$	0.433482	+	3.01494i	0.0433482	+	0.301494i
$101$	3.12690	+	0.918141i	0.311138	+	0.0913584i	0.433574	−	0.901118i	$-0.357252\pi$
$101$	3.12690	+	0.918141i	0.311138	+	0.0913584i	−0.122436	+	0.992476i	$0.539071\pi$
$102$		0			0
$103$	−8.50723	−	5.46726i	−0.838242	−	0.538706i	0.0496449	−	0.998767i	$-0.484191\pi$
$103$	−8.50723	−	5.46726i	−0.838242	−	0.538706i	−0.887887	+	0.460061i	$0.847827\pi$
$104$	1.67240	+	1.07479i	0.163992	+	0.105391i
$105$		0			0
$106$	0.140192	+	0.0411642i	0.0136167	+	0.00399822i
$107$	−0.0677199	−	0.471002i	−0.00654673	−	0.0455335i	0.986286	−	0.165044i	$-0.0527766\pi$
$107$	−0.0677199	−	0.471002i	−0.00654673	−	0.0455335i	−0.992833	+	0.119510i	$0.961868\pi$
$108$		0			0
$109$	4.07469	+	8.92233i	0.390285	+	0.854604i	0.998164	+	0.0605745i	$0.0192933\pi$
$109$	4.07469	+	8.92233i	0.390285	+	0.854604i	−0.607879	+	0.794030i	$0.707979\pi$
$110$	−0.297176	+	0.0872586i	−0.0283346	+	0.00831978i
$111$		0			0
$112$	0.610783	−	4.24809i	0.0577135	−	0.401407i
$113$	−7.46023	+	4.79440i	−0.701799	+	0.451019i	−0.842263	−	0.539067i	$-0.818777\pi$
$113$	−7.46023	+	4.79440i	−0.701799	+	0.451019i	0.140464	+	0.990086i	$0.455141\pi$
$114$		0			0
$115$	−0.596114	−	6.67743i	−0.0555880	−	0.622673i
$116$	3.56863			0.331339
$117$		0			0
$118$	−1.87418	+	13.0352i	−0.172532	+	1.19999i
$119$	0.198281	−	0.434176i	0.0181764	−	0.0398008i
$120$		0			0
$121$	−4.54917	−	9.96130i	−0.413561	−	0.905572i
$122$	3.72593	+	4.29995i	0.337330	+	0.389299i
$123$		0			0
$124$	−5.90843	−	1.73487i	−0.530593	−	0.155796i
$125$	−7.36537	+	8.50009i	−0.658779	+	0.760271i
$126$		0			0
$127$	2.20377	+	1.41627i	0.195553	+	0.125674i	0.634753	−	0.772715i	$-0.281102\pi$
$127$	2.20377	+	1.41627i	0.195553	+	0.125674i	−0.439200	+	0.898389i	$0.644738\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$		0			0
$130$	0.395487	+	2.75067i	0.0346865	+	0.241250i
$131$	10.0329	+	11.5786i	0.876578	+	1.01163i	0.999815	+	0.0192479i	$0.00612719\pi$
$131$	10.0329	+	11.5786i	0.876578	+	1.01163i	−0.123236	+	0.992377i	$0.539327\pi$
$132$		0			0
$133$	13.3250	−	3.91257i	1.15542	−	0.339263i
$134$	−5.95640	+	13.0427i	−0.514554	+	1.12672i
$135$		0			0
$136$	−0.0935599	+	0.0601273i	−0.00802270	+	0.00515588i
$137$	10.3092			0.880771			0.440386	−	0.897809i	$-0.354842\pi$
$137$	10.3092			0.880771			0.440386	+	0.897809i	$0.354842\pi$
$138$		0			0
$139$	−0.569454			−0.0483005			−0.0241502	−	0.999708i	$-0.507688\pi$
$139$	−0.569454			−0.0483005			−0.0241502	+	0.999708i	$0.507688\pi$
$140$	5.04699	−	3.24350i	0.426549	−	0.274126i
$141$		0			0
$142$	2.42815	−	5.31690i	0.203766	−	0.446185i
$143$	0.422627	−	0.124094i	0.0353418	−	0.0103773i
$144$		0			0
$145$	3.26678	+	3.77006i	0.271291	+	0.313087i
$146$	0.539716	+	3.75381i	0.0446672	+	0.310667i
$147$		0			0
$148$	−2.76880	+	3.19537i	−0.227594	+	0.262658i
$149$	−11.0753	−	7.11764i	−0.907321	−	0.583100i	0.00163183	−	0.999999i	$-0.499481\pi$
$149$	−11.0753	−	7.11764i	−0.907321	−	0.583100i	−0.908953	+	0.416899i	$0.863117\pi$
$150$		0			0
$151$	5.95136	−	6.86823i	0.484315	−	0.558929i	−0.460023	−	0.887907i	$-0.652159\pi$
$151$	5.95136	−	6.86823i	0.484315	−	0.558929i	0.944338	+	0.328978i	$0.106704\pi$
$152$	−3.10477	−	0.911644i	−0.251830	−	0.0739441i
$153$		0			0
$154$	−0.622713	−	0.718649i	−0.0501796	−	0.0579104i
$155$	−3.57587	−	7.83007i	−0.287221	−	0.628926i
$156$		0			0
$157$	−3.61916	+	7.92485i	−0.288840	+	0.632472i	−0.997312	−	0.0732667i	$-0.976658\pi$
$157$	−3.61916	+	7.92485i	−0.288840	+	0.632472i	0.708472	+	0.705739i	$0.249385\pi$
$158$	1.24224	−	8.63997i	0.0988274	−	0.687359i
$159$		0			0
$160$	−1.39788			−0.110512
$161$	17.8881	−	10.1813i	1.40978	−	0.802396i
$162$		0			0
$163$	8.98559	−	5.77469i	0.703806	−	0.452309i	−0.139164	−	0.990269i	$-0.544442\pi$
$163$	8.98559	−	5.77469i	0.703806	−	0.452309i	0.842970	+	0.537961i	$0.180805\pi$
$164$	0.485744	−	3.37842i	0.0379302	−	0.263811i
$165$		0			0
$166$	−15.0155	+	4.40894i	−1.16543	+	0.342200i
$167$	−3.29765	−	7.22084i	−0.255180	−	0.558765i	0.738075	−	0.674719i	$-0.235735\pi$
$167$	−3.29765	−	7.22084i	−0.255180	−	0.558765i	−0.993255	+	0.115953i	$0.963008\pi$
$168$		0			0
$169$	1.28765	+	8.95583i	0.0990503	+	0.688910i
$170$	−0.149167	−	0.0437995i	−0.0114406	−	0.00335927i
$171$		0			0
$172$	−2.73237	−	1.75599i	−0.208341	−	0.133893i
$173$	6.27506	+	4.03274i	0.477084	+	0.306603i	0.756993	−	0.653423i	$-0.226668\pi$
$173$	6.27506	+	4.03274i	0.477084	+	0.306603i	−0.279909	+	0.960027i	$0.590304\pi$
$174$		0			0
$175$	−12.5429	−	3.68294i	−0.948158	−	0.278404i
$176$	0.0315321	+	0.219310i	0.00237682	+	0.0165311i
$177$		0			0
$178$	−0.423448	−	0.927222i	−0.0317388	−	0.0694982i
$179$	19.9940	−	5.87078i	1.49442	−	0.438802i	0.570474	−	0.821316i	$-0.306760\pi$
$179$	19.9940	−	5.87078i	1.49442	−	0.438802i	0.923950	+	0.382513i	$0.124941\pi$
$180$		0			0
$181$	0.600884	−	4.17924i	0.0446634	−	0.310641i	−0.955228	−	0.295872i	$-0.904390\pi$
$181$	0.600884	−	4.17924i	0.0446634	−	0.310641i	0.999891	−	0.0147685i	$-0.00470112\pi$
$182$	−7.17755	+	4.61273i	−0.532036	+	0.341918i
$183$		0			0
$184$	−4.78890	−	0.257712i	−0.353043	−	0.0189988i
$185$	−5.91033			−0.434536
$186$		0			0
$187$	−0.00350684	+	0.0243906i	−0.000256445	+	0.00178362i
$188$	−3.21470	+	7.03920i	−0.234456	+	0.513387i
$189$		0			0
$190$	−1.87906	−	4.11456i	−0.136321	−	0.298501i
$191$	−9.29189	−	10.7234i	−0.672337	−	0.775919i	0.312403	−	0.949950i	$-0.398866\pi$
$191$	−9.29189	−	10.7234i	−0.672337	−	0.775919i	−0.984740	+	0.174031i	$0.944321\pi$
$192$		0			0
$193$	−1.92476	−	0.565162i	−0.138548	−	0.0406812i	0.211724	−	0.977330i	$-0.432092\pi$
$193$	−1.92476	−	0.565162i	−0.138548	−	0.0406812i	−0.350271	+	0.936648i	$0.613911\pi$
$194$	11.9271	−	13.7646i	0.856315	−	0.988240i
$195$		0			0
$196$	9.60653	+	6.17374i	0.686181	+	0.440982i
$197$	8.49273	−	9.80113i	0.605082	−	0.698302i	−0.367721	−	0.929936i	$-0.619862\pi$
$197$	8.49273	−	9.80113i	0.605082	−	0.698302i	0.972803	+	0.231635i	$0.0744074\pi$
$198$		0			0
$199$	1.68909	+	11.7479i	0.119736	+	0.832783i	0.957846	+	0.287282i	$0.0927516\pi$
$199$	1.68909	+	11.7479i	0.119736	+	0.832783i	−0.838110	+	0.545501i	$0.816339\pi$
$200$	1.99467	+	2.30197i	0.141044	+	0.162774i
$201$		0			0
$202$	3.12690	−	0.918141i	0.220008	−	0.0646001i
$203$	−6.36239	+	13.9317i	−0.446552	+	0.977813i
$204$		0			0
$205$	4.01378	−	2.57950i	0.280334	−	0.180160i
$206$	−10.1126			−0.704576
$207$		0			0
$208$	1.98798			0.137842
$209$	−0.603139	+	0.387614i	−0.0417200	+	0.0268118i
$210$		0			0
$211$	8.14282	−	17.8303i	0.560575	−	1.22749i	−0.391091	−	0.920352i	$-0.627902\pi$
$211$	8.14282	−	17.8303i	0.560575	−	1.22749i	0.951666	−	0.307136i	$-0.0993706\pi$
$212$	0.140192	−	0.0411642i	0.00962846	−	0.00282717i
$213$		0			0
$214$	−0.311613	−	0.359620i	−0.0213014	−	0.0245831i
$215$	−0.646147	−	4.49405i	−0.0440669	−	0.306492i
$216$		0			0
$217$	17.3068	−	19.9731i	1.17486	−	1.35586i
$218$	8.25162	+	5.30300i	0.558870	+	0.359164i
$219$		0			0
$220$	−0.202824	+	0.234072i	−0.0136744	+	0.0157811i
$221$	0.212138	+	0.0622892i	0.0142699	+	0.00419003i
$222$		0			0
$223$	10.9510	+	12.6381i	0.733330	+	0.846308i	0.992842	−	0.119432i	$-0.0381073\pi$
$223$	10.9510	+	12.6381i	0.733330	+	0.846308i	−0.259512	+	0.965740i	$0.583562\pi$
$224$	−1.78287	−	3.90393i	−0.119123	−	0.260842i
$225$		0			0
$226$	−3.68390	+	8.06661i	−0.245049	+	0.536583i
$227$	2.01346	−	14.0039i	0.133638	−	0.929471i	−0.807119	−	0.590389i	$-0.798974\pi$
$227$	2.01346	−	14.0039i	0.133638	−	0.929471i	0.940757	−	0.339082i	$-0.110116\pi$
$228$		0			0
$229$	−23.3847			−1.54531			−0.772653	−	0.634828i	$-0.781071\pi$
$229$	−23.3847			−1.54531			−0.772653	+	0.634828i	$0.781071\pi$
$230$	−4.11157	−	5.29513i	−0.271109	−	0.349150i
$231$		0			0
$232$	3.00212	−	1.92935i	0.197099	−	0.126668i
$233$	−1.23046	+	8.55801i	−0.0806098	+	0.560654i	0.908991	+	0.416815i	$0.136854\pi$
$233$	−1.23046	+	8.55801i	−0.0806098	+	0.560654i	−0.989601	+	0.143839i	$0.954055\pi$
$234$		0			0
$235$	−10.3793	+	3.04764i	−0.677072	+	0.198806i
$236$	5.47071	+	11.9792i	0.356113	+	0.779778i
$237$		0			0
$238$	−0.0679282	−	0.472451i	−0.00440313	−	0.0306244i
$239$	8.49017	+	2.49294i	0.549183	+	0.161255i	0.544541	−	0.838734i	$-0.316704\pi$
$239$	8.49017	+	2.49294i	0.549183	+	0.161255i	0.00464274	+	0.999989i	$0.498522\pi$
$240$		0			0
$241$	4.70043	+	3.02078i	0.302781	+	0.194586i	0.683205	−	0.730227i	$-0.260585\pi$
$241$	4.70043	+	3.02078i	0.302781	+	0.194586i	−0.380424	+	0.924812i	$0.624222\pi$
$242$	−9.21249	−	5.92051i	−0.592201	−	0.380585i
$243$		0			0
$244$	5.45918	+	1.60296i	0.349488	+	0.102619i
$245$	2.27174	+	15.8003i	0.145136	+	1.00944i
$246$		0			0
$247$	2.67229	+	5.85150i	0.170034	+	0.372322i
$248$	−5.90843	+	1.73487i	−0.375186	+	0.110165i
$249$		0			0
$250$	−1.60065	+	11.1328i	−0.101234	+	0.704097i
$251$	16.1491	−	10.3784i	1.01932	−	0.655077i	0.0795311	−	0.996832i	$-0.474658\pi$
$251$	16.1491	−	10.3784i	1.01932	−	0.655077i	0.939789	+	0.341755i	$0.111021\pi$
$252$		0			0
$253$	−0.737997	+	0.764500i	−0.0463975	+	0.0480637i
$254$	2.61962			0.164370
$255$		0			0
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−3.50421	+	7.67316i	−0.218587	+	0.478639i	−0.986879	−	0.161461i	$-0.948380\pi$
$257$	−3.50421	+	7.67316i	−0.218587	+	0.478639i	0.768292	+	0.640099i	$0.221107\pi$
$258$		0			0
$259$	−7.53810	−	16.5061i	−0.468395	−	1.02564i
$260$	1.81983	+	2.10020i	0.112861	+	0.130249i
$261$		0			0
$262$	14.7001	+	4.31633i	0.908173	+	0.266664i
$263$	14.0492	−	16.2137i	0.866313	−	0.999779i	−0.133649	−	0.991029i	$-0.542669\pi$
$263$	14.0492	−	16.2137i	0.866313	−	0.999779i	0.999962	−	0.00874993i	$-0.00278523\pi$
$264$		0			0
$265$	0.171822	+	0.110423i	0.0105549	+	0.00678325i
$266$	9.09440	−	10.4955i	0.557613	−	0.643520i
$267$		0			0
$268$	2.04057	+	14.1925i	0.124648	+	0.866944i
$269$	−14.1348	−	16.3124i	−0.861812	−	0.994584i	−0.999991	−	0.00417692i	$-0.998670\pi$
$269$	−14.1348	−	16.3124i	−0.861812	−	0.994584i	0.138179	−	0.990407i	$-0.455875\pi$
$270$		0			0
$271$	12.2876	−	3.60796i	0.746419	−	0.219168i	0.113662	−	0.993519i	$-0.463742\pi$
$271$	12.2876	−	3.60796i	0.746419	−	0.219168i	0.632756	+	0.774351i	$0.281924\pi$
$272$	−0.0462003	+	0.101165i	−0.00280131	+	0.00613401i
$273$		0			0
$274$	8.67262	−	5.57356i	0.523932	−	0.336711i
$275$	0.674875			0.0406965
$276$		0			0
$277$	−15.6781			−0.942007			−0.471004	−	0.882131i	$-0.656108\pi$
$277$	−15.6781			−0.942007			−0.471004	+	0.882131i	$0.656108\pi$
$278$	−0.479055	+	0.307870i	−0.0287318	+	0.0184648i
$279$		0			0
$280$	2.49223	−	5.45722i	0.148939	−	0.326131i
$281$	−9.02973	+	2.65137i	−0.538668	+	0.158167i	−0.539739	−	0.841832i	$-0.681477\pi$
$281$	−9.02973	+	2.65137i	−0.538668	+	0.158167i	0.00107113	+	0.999999i	$0.499659\pi$
$282$		0			0
$283$	−4.63869	−	5.35333i	−0.275742	−	0.318223i	0.600940	−	0.799294i	$-0.294793\pi$
$283$	−4.63869	−	5.35333i	−0.275742	−	0.318223i	−0.876681	+	0.481072i	$0.840248\pi$
$284$	−0.831846	−	5.78562i	−0.0493610	−	0.343313i
$285$		0			0
$286$	0.288446	−	0.332884i	0.0170561	−	0.0196838i
$287$	12.3231	+	7.91959i	0.727411	+	0.467479i
$288$		0			0
$289$	11.1245	−	12.8384i	0.654384	−	0.755200i
$290$	4.78644	+	1.40542i	0.281069	+	0.0825294i
$291$		0			0
$292$	2.48350	+	2.86611i	0.145336	+	0.167726i
$293$	10.9804	+	24.0437i	0.641482	+	1.40465i	0.898816	+	0.438327i	$0.144429\pi$
$293$	10.9804	+	24.0437i	0.641482	+	1.40465i	−0.257334	+	0.966323i	$0.582844\pi$
$294$		0			0
$295$	−7.64738	+	16.7454i	−0.445248	+	0.974956i
$296$	−0.601718	+	4.18504i	−0.0349742	+	0.243251i
$297$		0			0
$298$	−13.1652			−0.762639
$299$	5.84725	+	7.53044i	0.338155	+	0.435496i
$300$		0			0
$301$	11.7267	−	7.53629i	0.675916	−	0.434385i
$302$	1.29335	−	8.99547i	0.0744241	−	0.517631i
$303$		0			0
$304$	−3.10477	+	0.911644i	−0.178071	+	0.0522864i
$305$	3.30397	+	7.23470i	0.189185	+	0.414257i
$306$		0			0
$307$	−1.60723	−	11.1785i	−0.0917296	−	0.637993i	−0.982875	−	0.184275i	$-0.941006\pi$
$307$	−1.60723	−	11.1785i	−0.0917296	−	0.637993i	0.891145	−	0.453718i	$-0.149903\pi$
$308$	−0.912390	−	0.267902i	−0.0519883	−	0.0152651i
$309$		0			0
$310$	−7.24147	−	4.65381i	−0.411288	−	0.264319i
$311$	6.87135	+	4.41595i	0.389639	+	0.250406i	0.720763	−	0.693182i	$-0.243792\pi$
$311$	6.87135	+	4.41595i	0.389639	+	0.250406i	−0.331124	+	0.943587i	$0.607428\pi$
$312$		0			0
$313$	7.53633	+	2.21287i	0.425978	+	0.125079i	0.487693	−	0.873015i	$-0.337839\pi$
$313$	7.53633	+	2.21287i	0.425978	+	0.125079i	−0.0617144	+	0.998094i	$0.519657\pi$
$314$	1.23987	+	8.62348i	0.0699698	+	0.486651i
$315$		0			0
$316$	−3.62608	−	7.94001i	−0.203983	−	0.446661i
$317$	12.7418	−	3.74132i	0.715649	−	0.210133i	0.0964162	−	0.995341i	$-0.469262\pi$
$317$	12.7418	−	3.74132i	0.715649	−	0.210133i	0.619232	+	0.785208i	$0.287444\pi$
$318$		0			0
$319$	0.112526	−	0.782637i	0.00630026	−	0.0438193i
$320$	−1.17597	+	0.755750i	−0.0657387	+	0.0422477i
$321$		0			0
$322$	9.54406	−	18.2361i	0.531870	−	1.01626i
$323$	−0.359875			−0.0200240
$324$		0			0
$325$	0.861756	−	5.99364i	0.0478016	−	0.332467i
$326$	4.43713	−	9.71595i	0.245750	−	0.538117i
$327$		0			0
$328$	−1.41788	−	3.10472i	−0.0782893	−	0.171430i
$329$	−21.7492	−	25.0999i	−1.19907	−	1.38380i
$330$		0			0
$331$	−1.25777	−	0.369313i	−0.0691330	−	0.0202993i	0.246983	−	0.969020i	$-0.420561\pi$
$331$	−1.25777	−	0.369313i	−0.0691330	−	0.0202993i	−0.316116	+	0.948720i	$0.602379\pi$
$332$	−10.2482	+	11.8270i	−0.562441	+	0.649092i
$333$		0			0
$334$	−6.67804	−	4.29171i	−0.365406	−	0.234832i
$335$	−13.1256	+	15.1478i	−0.717129	+	0.827611i
$336$		0			0
$337$	4.87689	+	33.9195i	0.265661	+	1.84772i	0.488124	+	0.872774i	$0.337681\pi$
$337$	4.87689	+	33.9195i	0.265661	+	1.84772i	−0.222463	+	0.974941i	$0.571410\pi$
$338$	5.92513	+	6.83796i	0.322284	+	0.371936i
$339$		0			0
$340$	−0.149167	+	0.0437995i	−0.00808974	+	0.00237536i
$341$	−0.566781	+	1.24108i	−0.0306929	+	0.0672081i
$342$		0			0
$343$	−15.9558	+	10.2541i	−0.861530	+	0.553671i
$344$	−3.24797			−0.175119
$345$		0			0
$346$	7.45918			0.401008
$347$	−20.7117	+	13.3106i	−1.11186	+	0.714552i	−0.961699	−	0.274109i	$-0.911617\pi$
$347$	−20.7117	+	13.3106i	−1.11186	+	0.714552i	−0.150166	+	0.988661i	$0.547981\pi$
$348$		0			0
$349$	−8.55401	+	18.7307i	−0.457886	+	1.00263i	0.530079	+	0.847949i	$0.322162\pi$
$349$	−8.55401	+	18.7307i	−0.457886	+	1.00263i	−0.987964	+	0.154682i	$0.950565\pi$
$350$	−12.5429	+	3.68294i	−0.670449	+	0.196861i
$351$		0			0
$352$	0.145095	+	0.167448i	0.00773357	+	0.00892501i
$353$	3.88704	+	27.0350i	0.206886	+	1.43893i	0.783237	+	0.621724i	$0.213567\pi$
$353$	3.88704	+	27.0350i	0.206886	+	1.43893i	−0.576350	+	0.817203i	$0.695524\pi$
$354$		0			0
$355$	5.35070	−	6.17504i	0.283986	−	0.327737i
$356$	−0.857521	−	0.551095i	−0.0454485	−	0.0292080i
$357$		0			0
$358$	13.6461	−	15.7484i	0.721217	−	0.832329i
$359$	−36.0677	−	10.5904i	−1.90358	−	0.558941i	−0.987419	−	0.158125i	$-0.949455\pi$
$359$	−36.0677	−	10.5904i	−1.90358	−	0.558941i	−0.916159	−	0.400816i	$-0.868727\pi$
$360$		0			0
$361$	5.58549	+	6.44600i	0.293973	+	0.339263i
$362$	−1.75397	−	3.84066i	−0.0921867	−	0.201861i
$363$		0			0
$364$	−3.54431	+	7.76095i	−0.185772	+	0.406785i
$365$	−0.754457	+	5.24736i	−0.0394901	+	0.274659i
$366$		0			0
$367$	−22.3474			−1.16653			−0.583263	−	0.812283i	$-0.698224\pi$
$367$	−22.3474			−1.16653			−0.583263	+	0.812283i	$0.698224\pi$
$368$	−4.16801	+	2.37227i	−0.217273	+	0.123663i
$369$		0			0
$370$	−4.97209	+	3.19537i	−0.258487	+	0.166119i
$371$	−0.0892421	+	0.620692i	−0.00463322	+	0.0322247i
$372$		0			0
$373$	−28.5850	+	8.39331i	−1.48007	+	0.434589i	−0.919359	−	0.393420i	$-0.871292\pi$
$373$	−28.5850	+	8.39331i	−1.48007	+	0.434589i	−0.560715	+	0.828009i	$0.689474\pi$
$374$	0.0102364	+	0.0224146i	0.000529312	+	0.00115903i
$375$		0			0
$376$	1.10131	+	7.65975i	0.0567955	+	0.395021i
$377$	−6.80701	−	1.99872i	−0.350579	−	0.102939i
$378$		0			0
$379$	18.1294	+	11.6511i	0.931247	+	0.598476i	0.915900	−	0.401406i	$-0.131478\pi$
$379$	18.1294	+	11.6511i	0.931247	+	0.598476i	0.0153469	+	0.999882i	$0.495115\pi$
$380$	−3.80526	−	2.44549i	−0.195206	−	0.125451i
$381$		0			0
$382$	−13.6143	−	3.99753i	−0.696570	−	0.204532i
$383$	1.82892	+	12.7204i	0.0934537	+	0.649985i	0.981674	+	0.190567i	$0.0610327\pi$
$383$	1.82892	+	12.7204i	0.0934537	+	0.649985i	−0.888221	+	0.459417i	$0.848058\pi$
$384$		0			0
$385$	−0.552192	−	1.20913i	−0.0281423	−	0.0616231i
$386$	−1.92476	+	0.565162i	−0.0979679	+	0.0287660i
$387$		0			0
$388$	2.59200	−	18.0278i	0.131589	−	0.915222i
$389$	0.412167	−	0.264884i	0.0208977	−	0.0134301i	−0.530150	−	0.847904i	$-0.677864\pi$
$389$	0.412167	−	0.264884i	0.0208977	−	0.0134301i	0.551048	+	0.834474i	$0.314228\pi$
$390$		0			0
$391$	−0.519098	+	0.122550i	−0.0262519	+	0.00619760i
$392$	11.4193			0.576762
$393$		0			0
$394$	1.84565	−	12.8367i	0.0929823	−	0.646706i
$395$	5.06882	−	11.0992i	0.255040	−	0.558460i
$396$		0			0
$397$	6.20105	+	13.5784i	0.311222	+	0.681481i	0.999013	−	0.0444281i	$-0.0141466\pi$
$397$	6.20105	+	13.5784i	0.311222	+	0.681481i	−0.687791	+	0.725909i	$0.741419\pi$
$398$	7.77232	+	8.96973i	0.389591	+	0.449612i
$399$		0			0
$400$	2.92256	+	0.858140i	0.146128	+	0.0429070i
$401$	24.1069	−	27.8209i	1.20384	−	1.38931i	0.304242	−	0.952595i	$-0.401597\pi$
$401$	24.1069	−	27.8209i	1.20384	−	1.38931i	0.899600	−	0.436714i	$-0.143858\pi$
$402$		0			0
$403$	10.2984	+	6.61839i	0.513001	+	0.329685i
$404$	2.13413	−	2.46292i	0.106177	−	0.122535i
$405$		0			0
$406$	2.17966	+	15.1599i	0.108175	+	0.752371i
$407$	0.613471	+	0.707983i	0.0304086	+	0.0350934i
$408$		0			0
$409$	26.1942	−	7.69133i	1.29522	−	0.380312i	0.439731	−	0.898129i	$-0.355074\pi$
$409$	26.1942	−	7.69133i	1.29522	−	0.380312i	0.855491	+	0.517818i	$0.173255\pi$
$410$	1.98202	−	4.34002i	0.0978851	−	0.214338i
$411$		0			0
$412$	−8.50723	+	5.46726i	−0.419121	+	0.269353i
$413$	−56.5194			−2.78114
$414$		0			0
$415$	−21.8759			−1.07385
$416$	1.67240	−	1.07479i	0.0819961	−	0.0526957i
$417$		0			0
$418$	−0.297833	+	0.652163i	−0.0145675	+	0.0318983i
$419$	−16.2218	+	4.76315i	−0.792487	+	0.232695i	−0.652830	−	0.757505i	$-0.726418\pi$
$419$	−16.2218	+	4.76315i	−0.792487	+	0.232695i	−0.139657	+	0.990200i	$0.544600\pi$
$420$		0			0
$421$	−2.90278	−	3.34999i	−0.141473	−	0.163268i	0.680591	−	0.732663i	$-0.261723\pi$
$421$	−2.90278	−	3.34999i	−0.141473	−	0.163268i	−0.822064	+	0.569395i	$0.807178\pi$
$422$	−2.78961	−	19.4021i	−0.135796	−	0.944481i
$423$		0			0
$424$	0.0956823	−	0.110423i	0.00464675	−	0.00536263i
$425$	0.284978	+	0.183144i	0.0138235	+	0.00888380i
$426$		0			0
$427$	−15.9908	+	18.4544i	−0.773851	+	0.893071i
$428$	−0.456570	−	0.134061i	−0.0220692	−	0.00648009i
$429$		0			0
$430$	−2.97324	−	3.43130i	−0.143382	−	0.165472i
$431$	−11.6311	−	25.4685i	−0.560248	−	1.22677i	−0.951829	−	0.306629i	$-0.900799\pi$
$431$	−11.6311	−	25.4685i	−0.560248	−	1.22677i	0.391581	−	0.920144i	$-0.371928\pi$
$432$		0			0
$433$	−5.07970	+	11.1230i	−0.244115	+	0.534537i	−0.991539	−	0.129810i	$-0.958563\pi$
$433$	−5.07970	+	11.1230i	−0.244115	+	0.534537i	0.747424	+	0.664347i	$0.231290\pi$
$434$	3.76112	−	26.1592i	0.180540	−	1.25568i
$435$		0			0
$436$	9.80872			0.469753
$437$	−12.5854	−	9.07940i	−0.602039	−	0.434326i
$438$		0			0
$439$	12.8757	−	8.27473i	0.614525	−	0.394931i	−0.196026	−	0.980599i	$-0.562804\pi$
$439$	12.8757	−	8.27473i	0.614525	−	0.394931i	0.810552	+	0.585667i	$0.199167\pi$
$440$	−0.0440780	+	0.306569i	−0.00210133	+	0.0146151i
$441$		0			0
$442$	0.212138	−	0.0622892i	0.0100904	−	0.00296280i
$443$	−3.13249	−	6.85920i	−0.148829	−	0.325890i	0.820504	−	0.571641i	$-0.193693\pi$
$443$	−3.13249	−	6.85920i	−0.148829	−	0.325890i	−0.969333	+	0.245750i	$0.920966\pi$
$444$		0			0
$445$	−0.202786	−	1.41041i	−0.00961296	−	0.0668596i
$446$	16.0452	+	4.71129i	0.759762	+	0.223086i
$447$		0			0
$448$	−3.61047	−	2.32031i	−0.170579	−	0.109624i
$449$	10.5102	+	6.75451i	0.496008	+	0.318765i	0.764618	−	0.644484i	$-0.222928\pi$
$449$	10.5102	+	6.75451i	0.496008	+	0.318765i	−0.268609	+	0.963249i	$0.586564\pi$
$450$		0			0
$451$	−0.725607	−	0.213057i	−0.0341675	−	0.0100325i
$452$	1.26205	+	8.77773i	0.0593617	+	0.412870i
$453$		0			0
$454$	−5.87725	−	12.8694i	−0.275833	−	0.603990i
$455$	−11.4435	+	3.36013i	−0.536481	+	0.157525i
$456$		0			0
$457$	3.93686	−	27.3814i	0.184158	−	1.28085i	−0.662641	−	0.748937i	$-0.730564\pi$
$457$	3.93686	−	27.3814i	0.184158	−	1.28085i	0.846799	−	0.531913i	$-0.178527\pi$
$458$	−19.6725	+	12.6427i	−0.919235	+	0.590756i
$459$		0			0
$460$	−6.32164	−	2.23166i	−0.294748	−	0.104052i
$461$	−11.2174			−0.522445			−0.261223	−	0.965279i	$-0.584126\pi$
$461$	−11.2174			−0.522445			−0.261223	+	0.965279i	$0.584126\pi$
$462$		0			0
$463$	−1.34849	+	9.37894i	−0.0626696	+	0.435876i	0.934196	+	0.356761i	$0.116119\pi$
$463$	−1.34849	+	9.37894i	−0.0626696	+	0.435876i	−0.996865	+	0.0791159i	$0.974790\pi$
$464$	1.48246	−	3.24614i	0.0688216	−	0.150698i
$465$		0			0
$466$	3.59168	+	7.86469i	0.166381	+	0.364325i
$467$	6.11571	+	7.05791i	0.283001	+	0.326601i	0.879397	−	0.476090i	$-0.157946\pi$
$467$	6.11571	+	7.05791i	0.283001	+	0.326601i	−0.596395	+	0.802691i	$0.703401\pi$
$468$		0			0
$469$	−59.0446	−	17.3370i	−2.72642	−	0.800551i
$470$	−7.08396	+	8.17532i	−0.326758	+	0.377099i
$471$		0			0
$472$	11.0787	+	7.11984i	0.509938	+	0.327717i
$473$	−0.471263	+	0.543867i	−0.0216687	+	0.0250070i
$474$		0			0
$475$	1.40268	+	9.75588i	0.0643595	+	0.447630i
$476$	−0.312571	−	0.360726i	−0.0143267	−	0.0165339i
$477$		0			0
$478$	8.49017	−	2.49294i	0.388331	−	0.114024i
$479$	−0.499775	+	1.09436i	−0.0228353	+	0.0500024i	−0.920706	−	0.390257i	$-0.872386\pi$
$479$	−0.499775	+	1.09436i	−0.0228353	+	0.0500024i	0.897871	+	0.440259i	$0.145113\pi$
$480$		0			0
$481$	7.07103	−	4.54428i	0.322411	−	0.207201i
$482$	5.58741			0.254500
$483$		0			0
$484$	−10.9509			−0.497769
$485$	21.4181	−	13.7646i	0.972547	−	0.625018i
$486$		0			0
$487$	−1.85793	+	4.06831i	−0.0841910	+	0.184353i	−0.947045	−	0.321100i	$-0.895947\pi$
$487$	−1.85793	+	4.06831i	−0.0841910	+	0.184353i	0.862854	+	0.505453i	$0.168675\pi$
$488$	5.45918	−	1.60296i	0.247125	−	0.0725626i
$489$		0			0
$490$	10.4534	+	12.0639i	0.472237	+	0.544990i
$491$	1.71595	+	11.9347i	0.0774396	+	0.538604i	0.991202	+	0.132356i	$0.0422542\pi$
$491$	1.71595	+	11.9347i	0.0774396	+	0.538604i	−0.913763	+	0.406248i	$0.866837\pi$
$492$		0			0
$493$	0.259904	−	0.299946i	0.0117055	−	0.0135089i
$494$	5.41163	+	3.47784i	0.243481	+	0.156476i
$495$		0			0
$496$	−4.03255	+	4.65381i	−0.181067	+	0.208962i
$497$	24.0697	+	7.06751i	1.07968	+	0.317021i
$498$		0			0
$499$	−2.38745	−	2.75527i	−0.106877	−	0.123343i	0.699791	−	0.714348i	$-0.253277\pi$
$499$	−2.38745	−	2.75527i	−0.106877	−	0.123343i	−0.806668	+	0.591005i	$0.798731\pi$
$500$	4.67227	+	10.2308i	0.208950	+	0.457537i
$501$		0			0
$502$	7.97449	−	17.4617i	0.355919	−	0.779353i
$503$	−5.27651	+	36.6989i	−0.235268	+	1.63632i	0.439464	+	0.898260i	$0.355168\pi$
$503$	−5.27651	+	36.6989i	−0.235268	+	1.63632i	−0.674732	+	0.738063i	$0.735741\pi$
$504$		0			0
$505$	4.55555			0.202720
$506$	−0.207523	+	1.04213i	−0.00922552	+	0.0463283i
$507$		0			0
$508$	2.20377	−	1.41627i	0.0977763	−	0.0628370i
$509$	−5.05731	+	35.1743i	−0.224161	+	1.55907i	0.497893	+	0.867238i	$0.334107\pi$
$509$	−5.05731	+	35.1743i	−0.224161	+	1.55907i	−0.722054	+	0.691836i	$0.756802\pi$
$510$		0			0
$511$	−15.6168	+	4.58552i	−0.690849	+	0.202851i
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$		0			0
$514$	1.20049	+	8.34959i	0.0529514	+	0.368285i
$515$	−13.5635	−	3.98261i	−0.597680	−	0.175495i
$516$		0			0
$517$	1.44240	+	0.926977i	0.0634369	+	0.0407684i
$518$	−15.2653	−	9.81044i	−0.670721	−	0.431046i
$519$		0			0
$520$	2.66639	+	0.782923i	0.116929	+	0.0343334i
$521$	−0.805718	−	5.60389i	−0.0352992	−	0.245511i	0.964530	−	0.263972i	$-0.0850326\pi$
$521$	−0.805718	−	5.60389i	−0.0352992	−	0.245511i	−0.999830	+	0.0184606i	$0.994123\pi$
$522$		0			0
$523$	1.57610	+	3.45118i	0.0689180	+	0.150909i	0.940956	−	0.338529i	$-0.109929\pi$
$523$	1.57610	+	3.45118i	0.0689180	+	0.150909i	−0.872038	+	0.489438i	$0.837202\pi$
$524$	14.7001	−	4.31633i	0.642175	−	0.188560i
$525$		0			0
$526$	3.05319	−	21.2354i	0.133125	−	0.925908i
$527$	−0.576130	+	0.370256i	−0.0250966	+	0.0161286i
$528$		0			0
$529$	−21.2455	−	8.81076i	−0.923717	−	0.383077i
$530$	0.204245			0.00887185
$531$		0			0
$532$	1.97640	−	13.7462i	0.0856879	−	0.595972i
$533$	−2.81872	+	6.17214i	−0.122092	+	0.267345i
$534$		0			0
$535$	−0.276323	−	0.605063i	−0.0119465	−	0.0261592i
$536$	9.38967	+	10.8363i	0.405572	+	0.468055i
$537$		0			0
$538$	−20.7101	−	6.08103i	−0.892875	−	0.262172i
$539$	1.65688	−	1.91214i	0.0713668	−	0.0823617i
$540$		0			0
$541$	8.81571	+	5.66551i	0.379017	+	0.243579i	0.716253	−	0.697841i	$-0.245856\pi$
$541$	8.81571	+	5.66551i	0.379017	+	0.243579i	−0.337236	+	0.941420i	$0.609492\pi$
$542$	8.38637	−	9.67839i	0.360226	−	0.415723i
$543$		0			0
$544$	0.0158275	+	0.110083i	0.000678600	+	0.00471977i
$545$	8.97905	+	10.3624i	0.384620	+	0.443876i
$546$		0			0
$547$	27.5274	−	8.08279i	1.17699	−	0.345595i	0.365976	−	0.930624i	$-0.380735\pi$
$547$	27.5274	−	8.08279i	1.17699	−	0.345595i	0.811012	+	0.585029i	$0.198917\pi$
$548$	4.28258	−	9.37755i	0.182943	−	0.400589i
$549$		0			0
$550$	0.567741	−	0.364865i	0.0242086	−	0.0155579i
$551$	11.5475			0.491942
$552$		0			0
$553$	37.4621			1.59305
$554$	−13.1893	+	8.47623i	−0.560359	+	0.360121i
$555$		0			0
$556$	−0.236560	+	0.517994i	−0.0100324	+	0.0219678i
$557$	39.3349	−	11.5498i	1.66667	−	0.489380i	0.693694	−	0.720270i	$-0.255982\pi$
$557$	39.3349	−	11.5498i	1.66667	−	0.489380i	0.972980	+	0.230890i	$0.0741639\pi$
$558$		0			0
$559$	4.22838	+	4.87981i	0.178841	+	0.206394i
$560$	−0.853799	−	5.93831i	−0.0360796	−	0.250939i
$561$		0			0
$562$	−6.16285	+	7.11231i	−0.259964	+	0.300015i
$563$	−9.56189	−	6.14506i	−0.402986	−	0.258983i	0.323411	−	0.946258i	$-0.395170\pi$
$563$	−9.56189	−	6.14506i	−0.402986	−	0.258983i	−0.726397	+	0.687275i	$0.758807\pi$
$564$		0			0
$565$	−8.11789	+	9.36855i	−0.341522	+	0.394138i
$566$	−6.79655	−	1.99565i	−0.285680	−	0.0838833i
$567$		0			0
$568$	−3.82774	−	4.41744i	−0.160608	−	0.185352i
$569$	14.6664	+	32.1150i	0.614849	+	1.34633i	0.919208	+	0.393773i	$0.128831\pi$
$569$	14.6664	+	32.1150i	0.614849	+	1.34633i	−0.304359	+	0.952557i	$0.598442\pi$
$570$		0			0
$571$	5.97126	−	13.0752i	0.249890	−	0.547182i	−0.742568	−	0.669771i	$-0.766392\pi$
$571$	5.97126	−	13.0752i	0.249890	−	0.547182i	0.992458	+	0.122589i	$0.0391197\pi$
$572$	0.0626852	−	0.435985i	0.00262100	−	0.0182295i
$573$		0			0
$574$	14.6485			0.611418
$575$	5.34550	+	13.5946i	0.222923	+	0.566935i
$576$		0			0
$577$	−16.0760	+	10.3314i	−0.669251	+	0.430101i	−0.830655	−	0.556787i	$-0.812034\pi$
$577$	−16.0760	+	10.3314i	−0.669251	+	0.430101i	0.161405	+	0.986888i	$0.448398\pi$
$578$	2.41759	−	16.8147i	0.100559	−	0.699400i
$579$		0			0
$580$	4.78644	−	1.40542i	0.198746	−	0.0583571i
$581$	−27.9008	−	61.0942i	−1.15752	−	2.53461i
$582$		0			0
$583$	−0.00460718	−	0.0320436i	−0.000190810	−	0.00132711i
$584$	3.63879	+	1.06844i	0.150574	+	0.0442126i
$585$		0			0
$586$	22.2363	+	14.2904i	0.918574	+	0.590332i
$587$	35.6448	+	22.9075i	1.47122	+	0.945494i	0.997911	+	0.0645964i	$0.0205760\pi$
$587$	35.6448	+	22.9075i	1.47122	+	0.945494i	0.473306	+	0.880898i	$0.343060\pi$
$588$		0			0
$589$	−19.1188	−	5.61379i	−0.787777	−	0.231312i
$590$	2.61988	+	18.2216i	0.107859	+	0.750173i
$591$		0			0
$592$	1.75641	+	3.84599i	0.0721879	+	0.158069i
$593$	31.2352	−	9.17149i	1.28268	−	0.376628i	0.431789	−	0.901975i	$-0.357883\pi$
$593$	31.2352	−	9.17149i	1.28268	−	0.376628i	0.850888	+	0.525347i	$0.176064\pi$
$594$		0			0
$595$	0.0949552	−	0.660428i	0.00389279	−	0.0270749i
$596$	−11.0753	+	7.11764i	−0.453661	+	0.291550i
$597$		0			0
$598$	8.99028	+	3.17374i	0.367640	+	0.129784i
$599$	35.4803			1.44969			0.724843	−	0.688914i	$-0.241912\pi$
$599$	35.4803			1.44969			0.724843	+	0.688914i	$0.241912\pi$
$600$		0			0
$601$	−1.99090	+	13.8470i	−0.0812107	+	0.564833i	0.908071	+	0.418815i	$0.137555\pi$
$601$	−1.99090	+	13.8470i	−0.0812107	+	0.564833i	−0.989282	+	0.146017i	$0.953355\pi$
$602$	5.79070	−	12.6799i	0.236011	−	0.516793i
$603$		0			0
$604$	−3.77528	−	8.26671i	−0.153614	−	0.336368i
$605$	−10.0246	−	11.5690i	−0.407559	−	0.470348i
$606$		0			0
$607$	29.1012	+	8.54490i	1.18118	+	0.346827i	0.812630	−	0.582780i	$-0.198035\pi$
$607$	29.1012	+	8.54490i	1.18118	+	0.346827i	0.368553	+	0.929607i	$0.379853\pi$
$608$	−2.11903	+	2.44549i	−0.0859380	+	0.0991778i
$609$		0			0
$610$	6.69085	+	4.29995i	0.270905	+	0.174100i
$611$	10.0744	−	11.6265i	0.407567	−	0.470357i
$612$		0			0
$613$	−1.97112	−	13.7094i	−0.0796127	−	0.553719i	−0.990120	−	0.140225i	$-0.955217\pi$
$613$	−1.97112	−	13.7094i	−0.0796127	−	0.553719i	0.910507	−	0.413494i	$-0.135692\pi$
$614$	−7.39567	−	8.53505i	−0.298465	−	0.344447i
$615$		0			0
$616$	−0.912390	+	0.267902i	−0.0367612	+	0.0107941i
$617$	19.4829	−	42.6617i	0.784353	−	1.71749i	0.0922035	−	0.995740i	$-0.470609\pi$
$617$	19.4829	−	42.6617i	0.784353	−	1.71749i	0.692150	−	0.721754i	$-0.256664\pi$
$618$		0			0
$619$	12.9488	−	8.32166i	0.520455	−	0.334476i	−0.253897	−	0.967231i	$-0.581712\pi$
$619$	12.9488	−	8.32166i	0.520455	−	0.334476i	0.774352	+	0.632755i	$0.218076\pi$
$620$	−8.60795			−0.345704
$621$		0			0
$622$	8.16799			0.327507
$623$	3.68028	−	2.36518i	0.147447	−	0.0947588i
$624$		0			0
$625$	−0.204618	+	0.448051i	−0.00818472	+	0.0179220i
$626$	7.53633	−	2.21287i	0.301212	−	0.0884439i
$627$		0			0
$628$	5.70525	+	6.58421i	0.227664	+	0.262738i
$629$	0.0669200	+	0.465439i	0.00266828	+	0.0185583i
$630$		0			0
$631$	17.1724	−	19.8180i	0.683621	−	0.788941i	−0.302822	−	0.953047i	$-0.597929\pi$
$631$	17.1724	−	19.8180i	0.683621	−	0.788941i	0.986443	+	0.164107i	$0.0524741\pi$
$632$	−7.34315	−	4.71916i	−0.292095	−	0.187718i
$633$		0			0
$634$	8.69634	−	10.0361i	0.345376	−	0.398585i
$635$	3.51358	+	1.03168i	0.139432	+	0.0409409i
$636$		0			0
$637$	−14.8662	−	17.1566i	−0.589022	−	0.679768i
$638$	−0.328463	−	0.719233i	−0.0130040	−	0.0284747i
$639$		0			0
$640$	−0.580699	+	1.27155i	−0.0229542	+	0.0502626i
$641$	3.03853	−	21.1335i	0.120015	−	0.834722i	−0.837520	−	0.546406i	$-0.815996\pi$
$641$	3.03853	−	21.1335i	0.120015	−	0.834722i	0.957535	−	0.288316i	$-0.0930953\pi$
$642$		0			0
$643$	21.3545			0.842139			0.421069	−	0.907028i	$-0.361655\pi$
$643$	21.3545			0.842139			0.421069	+	0.907028i	$0.361655\pi$
$644$	−1.83019	−	20.5011i	−0.0721198	−	0.807856i
$645$		0			0
$646$	−0.302746	+	0.194563i	−0.0119114	+	0.00765498i
$647$	−1.52796	+	10.6272i	−0.0600704	+	0.417798i	0.937491	+	0.348009i	$0.113142\pi$
$647$	−1.52796	+	10.6272i	−0.0600704	+	0.417798i	−0.997562	+	0.0697899i	$0.977767\pi$
$648$		0			0
$649$	2.79966	−	0.822054i	0.109896	−	0.0322685i
$650$	−2.51545	−	5.50807i	−0.0986642	−	0.216044i
$651$		0			0
$652$	−1.52009	−	10.5725i	−0.0595314	−	0.414050i
$653$	−20.7677	−	6.09796i	−0.812705	−	0.238632i	−0.151133	−	0.988513i	$-0.548292\pi$
$653$	−20.7677	−	6.09796i	−0.812705	−	0.238632i	−0.661572	+	0.749882i	$0.730110\pi$
$654$		0			0
$655$	18.0166	+	11.5786i	0.703968	+	0.452413i
$656$	−2.87134	−	1.84530i	−0.112107	−	0.0720467i
$657$		0			0
$658$	−31.8666	−	9.35689i	−1.24229	−	0.364769i
$659$	−1.21005	−	8.41609i	−0.0471369	−	0.327844i	−0.999722	−	0.0235725i	$-0.992496\pi$
$659$	−1.21005	−	8.41609i	−0.0471369	−	0.327844i	0.952585	−	0.304272i	$-0.0984131\pi$
$660$		0			0
$661$	−11.0970	−	24.2991i	−0.431625	−	0.945127i	−0.993060	−	0.117606i	$-0.962478\pi$
$661$	−11.0970	−	24.2991i	−0.431625	−	0.945127i	0.561435	−	0.827521i	$-0.310249\pi$
$662$	−1.25777	+	0.369313i	−0.0488844	+	0.0143538i
$663$		0			0
$664$	−2.22714	+	15.4901i	−0.0864298	+	0.601132i
$665$	16.3313	−	10.4955i	0.633301	−	0.406998i
$666$		0			0
$667$	16.6567	−	3.93233i	0.644949	−	0.152260i
$668$	−7.93820			−0.307138
$669$		0			0
$670$	−2.85247	+	19.8394i	−0.110200	+	0.766461i
$671$	0.523685	−	1.14671i	0.0202166	−	0.0442682i
$672$		0			0
$673$	−0.665476	−	1.45719i	−0.0256522	−	0.0561706i	0.896372	−	0.443302i	$-0.146193\pi$
$673$	−0.665476	−	1.45719i	−0.0256522	−	0.0561706i	−0.922024	+	0.387132i	$0.873466\pi$
$674$	22.4410	+	25.8983i	0.864395	+	0.997565i
$675$		0			0
$676$	8.68142	+	2.54909i	0.333901	+	0.0980421i
$677$	−11.2793	+	13.0170i	−0.433497	+	0.500283i	−0.929901	−	0.367809i	$-0.880108\pi$
$677$	−11.2793	+	13.0170i	−0.433497	+	0.500283i	0.496404	+	0.868092i	$0.334653\pi$
$678$		0			0
$679$	65.7580	+	42.2601i	2.52356	+	1.62179i
$680$	−0.101808	+	0.117492i	−0.00390415	+	0.00450563i
$681$		0			0
$682$	0.194170	+	1.35048i	0.00743517	+	0.0517127i
$683$	−6.20568	−	7.16174i	−0.237454	−	0.274036i	0.624498	−	0.781026i	$-0.285304\pi$
$683$	−6.20568	−	7.16174i	−0.237454	−	0.274036i	−0.861952	+	0.506990i	$0.830758\pi$
$684$		0			0
$685$	13.8272	−	4.06003i	0.528310	−	0.155126i
$686$	−7.87903	+	17.2527i	−0.300823	+	0.658710i
$687$		0			0
$688$	−2.73237	+	1.75599i	−0.104171	+	0.0669463i
$689$	−0.290466			−0.0110659
$690$		0			0
$691$	−21.3629			−0.812685			−0.406342	−	0.913721i	$-0.633196\pi$
$691$	−21.3629			−0.812685			−0.406342	+	0.913721i	$0.633196\pi$
$692$	6.27506	−	4.03274i	0.238542	−	0.153302i
$693$		0			0
$694$	−10.2276	+	22.3952i	−0.388233	+	0.850111i
$695$	−0.763783	+	0.224267i	−0.0289719	+	0.00850693i
$696$		0			0
$697$	−0.248582	−	0.286879i	−0.00941571	−	0.0108663i
$698$	2.93047	+	20.3819i	0.110920	+	0.771466i
$699$		0			0
$700$	−8.56065	+	9.87952i	−0.323562	+	0.373411i
$701$	−4.66438	−	2.99761i	−0.176171	−	0.113218i	0.449583	−	0.893238i	$-0.351572\pi$
$701$	−4.66438	−	2.99761i	−0.176171	−	0.113218i	−0.625754	+	0.780020i	$0.715209\pi$
$702$		0			0
$703$	−8.95943	+	10.3397i	−0.337911	+	0.389970i
$704$	0.212591	+	0.0624222i	0.00801231	+	0.00235263i
$705$		0			0
$706$	17.8862	+	20.6418i	0.673156	+	0.776863i
$707$	5.81020	+	12.7226i	0.218515	+	0.478481i
$708$		0			0
$709$	1.66381	−	3.64323i	0.0624855	−	0.136824i	−0.875813	−	0.482651i	$-0.839674\pi$
$709$	1.66381	−	3.64323i	0.0624855	−	0.136824i	0.938299	+	0.345826i	$0.112401\pi$
$710$	1.16282	−	8.08759i	0.0436398	−	0.303522i
$711$		0			0
$712$	−1.01934			−0.0382013
$713$	−29.4894	−	1.58696i	−1.10439	−	0.0594321i
$714$		0			0
$715$	0.517978	−	0.332884i	0.0193713	−	0.0124492i
$716$	2.96557	−	20.6260i	0.110829	−	0.770830i
$717$		0			0
$718$	−36.0677	+	10.5904i	−1.34603	+	0.395231i
$719$	9.39965	+	20.5824i	0.350548	+	0.767592i	0.999974	+	0.00716803i	$0.00228167\pi$
$719$	9.39965	+	20.5824i	0.350548	+	0.767592i	−0.649427	+	0.760424i	$0.724991\pi$
$720$		0			0
$721$	−6.17658	−	42.9591i	−0.230028	−	1.59988i
$722$	8.18378	+	2.40298i	0.304569	+	0.0894295i
$723$		0			0
$724$	−3.55195	−	2.28270i	−0.132007	−	0.0848360i
$725$	−9.14428	−	5.87667i	−0.339610	−	0.218254i
$726$		0			0
$727$	−35.8427	−	10.5244i	−1.32933	−	0.390327i	−0.461479	−	0.887151i	$-0.652681\pi$
$727$	−35.8427	−	10.5244i	−1.32933	−	0.390327i	−0.867851	+	0.496824i	$0.834499\pi$
$728$	1.21423	+	8.44513i	0.0450022	+	0.312997i
$729$		0			0
$730$	2.20225	+	4.82225i	0.0815089	+	0.178480i
$731$	−0.346591	+	0.101768i	−0.0128191	+	0.00376404i
$732$		0			0
$733$	−0.298094	+	2.07329i	−0.0110103	+	0.0765786i	−0.994586	−	0.103919i	$-0.966862\pi$
$733$	−0.298094	+	2.07329i	−0.0110103	+	0.0765786i	0.983575	+	0.180498i	$0.0577708\pi$
$734$	−18.7999	+	12.0819i	−0.693916	+	0.445952i
$735$		0			0
$736$	−2.22381	+	4.24908i	−0.0819706	+	0.156623i
$737$	3.17690			0.117023
$738$		0			0
$739$	−2.66340	+	18.5243i	−0.0979746	+	0.681429i	0.880346	+	0.474332i	$0.157310\pi$
$739$	−2.66340	+	18.5243i	−0.0979746	+	0.681429i	−0.978321	+	0.207096i	$0.933599\pi$
$740$	−2.45524	+	5.37623i	−0.0902565	+	0.197634i
$741$		0			0
$742$	0.260496	+	0.570407i	0.00956312	+	0.0209403i
$743$	20.4961	+	23.6537i	0.751928	+	0.867772i	0.994754	−	0.102298i	$-0.0326197\pi$
$743$	20.4961	+	23.6537i	0.751928	+	0.867772i	−0.242825	+	0.970070i	$0.578074\pi$
$744$		0			0
$745$	−17.6579	−	5.18482i	−0.646934	−	0.189957i
$746$	−19.5095	+	22.5151i	−0.714292	+	0.824337i
$747$		0			0
$748$	0.0207297	+	0.0133221i	0.000757951	+	0.000487106i
$749$	1.33737	−	1.54341i	0.0488664	−	0.0563949i
$750$		0			0
$751$	−6.86265	−	47.7308i	−0.250422	−	1.74172i	−0.595687	−	0.803217i	$-0.703120\pi$
$751$	−6.86265	−	47.7308i	−0.250422	−	1.74172i	0.345265	−	0.938505i	$-0.387789\pi$
$752$	5.06765	+	5.84838i	0.184798	+	0.213269i
$753$		0			0
$754$	−6.80701	+	1.99872i	−0.247897	+	0.0727890i
$755$	5.27738	−	11.5558i	0.192063	−	0.420560i
$756$		0			0
$757$	−15.5239	+	9.97660i	−0.564226	+	0.362606i	−0.791447	−	0.611237i	$-0.790672\pi$
$757$	−15.5239	+	9.97660i	−0.564226	+	0.362606i	0.227222	+	0.973843i	$0.427036\pi$
$758$	21.5505			0.782750
$759$		0			0
$760$	−4.52332			−0.164078
$761$	−15.5061	+	9.96519i	−0.562097	+	0.361238i	−0.790626	−	0.612299i	$-0.790245\pi$
$761$	−15.5061	+	9.96519i	−0.562097	+	0.361238i	0.228529	+	0.973537i	$0.426608\pi$
$762$		0			0
$763$	−17.4876	+	38.2926i	−0.633095	+	1.38629i
$764$	−13.6143	+	3.99753i	−0.492550	+	0.144626i
$765$		0			0
$766$	8.41578	+	9.71233i	0.304075	+	0.350921i
$767$	−3.72584	−	25.9138i	−0.134532	−	0.935693i
$768$		0			0
$769$	22.5489	−	26.0228i	0.813135	−	0.938408i	−0.185889	−	0.982571i	$-0.559517\pi$
$769$	22.5489	−	26.0228i	0.813135	−	0.938408i	0.999024	+	0.0441629i	$0.0140621\pi$
$770$	−1.11824	−	0.718649i	−0.0402986	−	0.0258983i
$771$		0			0
$772$	−1.31367	+	1.51605i	−0.0472798	+	0.0545638i
$773$	5.60920	+	1.64701i	0.201749	+	0.0592388i	0.381046	−	0.924556i	$-0.375564\pi$
$773$	5.60920	+	1.64701i	0.201749	+	0.0592388i	−0.179297	+	0.983795i	$0.557382\pi$
$774$		0			0
$775$	12.2829	+	14.1752i	0.441215	+	0.509189i
$776$	−7.56602	−	16.5673i	−0.271604	−	0.594731i
$777$		0			0
$778$	0.203530	−	0.445668i	0.00729690	−	0.0159780i
$779$	1.57179	−	10.9321i	0.0563154	−	0.391682i
$780$		0			0
$781$	−1.29508			−0.0463415
$782$	−0.370438	+	0.383741i	−0.0132468	+	0.0137225i
$783$		0			0
$784$	9.60653	−	6.17374i	0.343090	−	0.220491i
$785$	−1.73318	+	12.0546i	−0.0618600	+	0.430246i
$786$		0			0
$787$	−5.25324	+	1.54249i	−0.187258	+	0.0549838i	−0.374017	−	0.927422i	$-0.622020\pi$
$787$	−5.25324	+	1.54249i	−0.187258	+	0.0549838i	0.186759	+	0.982406i	$0.440202\pi$
$788$	−5.38741	−	11.7968i	−0.191919	−	0.420243i
$789$		0			0
$790$	−1.73650	−	12.0776i	−0.0617819	−	0.429703i
$791$	−36.5177	−	10.7226i	−1.29842	−	0.381251i
$792$		0			0
$793$	−9.51536	−	6.11515i	−0.337900	−	0.217155i
$794$	12.5577	+	8.07034i	0.445656	+	0.286406i
$795$		0			0
$796$	11.3879	+	3.34379i	0.403633	+	0.118517i
$797$	0.319893	+	2.22491i	0.0113312	+	0.0788103i	0.994702	−	0.102797i	$-0.0327792\pi$
$797$	0.319893	+	2.22491i	0.0113312	+	0.0788103i	−0.983371	+	0.181607i	$0.941870\pi$
$798$		0			0
$799$	0.357522	+	0.782864i	0.0126482	+	0.0276958i
$800$	2.92256	−	0.858140i	0.103328	−	0.0303398i
$801$		0			0
$802$	5.23894	−	36.4376i	0.184993	−	1.28666i
$803$	0.706877	−	0.454283i	0.0249452	−	0.0160313i
$804$		0			0
$805$	19.9829	−	20.7005i	0.704304	−	0.729597i
$806$	12.2417			0.431197
$807$		0			0
$808$	0.463791	−	3.22574i	0.0163161	−	0.113481i
$809$	−5.17789	+	11.3380i	−0.182045	+	0.398623i	−0.978550	−	0.206009i	$-0.933952\pi$
$809$	−5.17789	+	11.3380i	−0.182045	+	0.398623i	0.796505	+	0.604632i	$0.206680\pi$
$810$		0			0
$811$	9.96038	+	21.8102i	0.349756	+	0.765859i	0.999981	+	0.00611758i	$0.00194730\pi$
$811$	9.96038	+	21.8102i	0.349756	+	0.765859i	−0.650225	+	0.759742i	$0.725325\pi$
$812$	10.0297	+	11.5749i	0.351973	+	0.406198i
$813$		0			0
$814$	0.898850	+	0.263926i	0.0315047	+	0.00925060i
$815$	9.77772	−	11.2841i	0.342499	−	0.395265i
$816$		0			0
$817$	−8.84153	−	5.68211i	−0.309326	−	0.198792i
$818$	17.8778	−	20.6320i	0.625081	−	0.721382i
$819$		0			0
$820$	−0.679011	−	4.72262i	−0.0237121	−	0.164921i
$821$	−19.5728	−	22.5882i	−0.683095	−	0.788333i	0.303270	−	0.952905i	$-0.401921\pi$
$821$	−19.5728	−	22.5882i	−0.683095	−	0.788333i	−0.986365	+	0.164571i	$0.947376\pi$
$822$		0			0
$823$	−10.3151	+	3.02878i	−0.359561	+	0.105577i	−0.456523	−	0.889711i	$-0.650906\pi$
$823$	−10.3151	+	3.02878i	−0.359561	+	0.105577i	0.0969623	+	0.995288i	$0.469087\pi$
$824$	−4.20091	+	9.19871i	−0.146346	+	0.320452i
$825$		0			0
$826$	−47.5472	+	30.5567i	−1.65438	+	1.06320i
$827$	−4.42943			−0.154026			−0.0770132	−	0.997030i	$-0.524538\pi$
$827$	−4.42943			−0.154026			−0.0770132	+	0.997030i	$0.524538\pi$
$828$		0			0
$829$	−7.87479			−0.273503			−0.136751	−	0.990605i	$-0.543666\pi$
$829$	−7.87479			−0.273503			−0.136751	+	0.990605i	$0.543666\pi$
$830$	−18.4032	+	11.8270i	−0.638784	+	0.410522i
$831$		0			0
$832$	0.825838	−	1.80833i	0.0286308	−	0.0626927i
$833$	1.21855	−	0.357799i	0.0422204	−	0.0123970i
$834$		0			0
$835$	−7.26675	−	8.38627i	−0.251476	−	0.290219i
$836$	0.102033	+	0.709655i	0.00352889	+	0.0245439i
$837$		0			0
$838$	−11.0715	+	12.7772i	−0.382458	+	0.441381i
$839$	10.0086	+	6.43215i	0.345536	+	0.222063i	0.701885	−	0.712290i	$-0.252342\pi$
$839$	10.0086	+	6.43215i	0.345536	+	0.222063i	−0.356349	+	0.934353i	$0.615978\pi$
$840$		0			0
$841$	10.6512	−	12.2922i	0.367284	−	0.423868i
$842$	−4.25311	−	1.24883i	−0.146572	−	0.0430374i
$843$		0			0
$844$	−12.8364	−	14.8139i	−0.441846	−	0.509917i
$845$	5.25412	+	11.5049i	0.180747	+	0.395781i
$846$		0			0
$847$	19.5240	−	42.7516i	0.670853	−	1.46896i
$848$	0.0207938	−	0.144624i	0.000714061	−	0.00496640i
$849$		0			0
$850$	0.338754			0.0116192
$851$	−9.40242	+	17.9654i	−0.322311	+	0.615848i
$852$		0			0
$853$	−28.6153	+	18.3899i	−0.979768	+	0.629659i	−0.929401	−	0.369072i	$-0.879676\pi$
$853$	−28.6153	+	18.3899i	−0.979768	+	0.629659i	−0.0503673	+	0.998731i	$0.516039\pi$
$854$	−3.47514	+	24.1701i	−0.118917	+	0.827085i
$855$		0			0
$856$	−0.456570	+	0.134061i	−0.0156053	+	0.00458212i
$857$	−15.4802	−	33.8970i	−0.528795	−	1.15790i	−0.966001	−	0.258538i	$-0.916759\pi$
$857$	−15.4802	−	33.8970i	−0.528795	−	1.15790i	0.437206	−	0.899361i	$-0.355968\pi$
$858$		0			0
$859$	5.37040	+	37.3520i	0.183236	+	1.27443i	0.849049	+	0.528314i	$0.177176\pi$
$859$	5.37040	+	37.3520i	0.183236	+	1.27443i	−0.665813	+	0.746119i	$0.731915\pi$
$860$	−4.35635	−	1.27914i	−0.148550	−	0.0436183i
$861$		0			0
$862$	−23.5540	−	15.1372i	−0.802251	−	0.515575i
$863$	−11.3975	−	7.32473i	−0.387976	−	0.249337i	0.332083	−	0.943250i	$-0.392249\pi$
$863$	−11.3975	−	7.32473i	−0.387976	−	0.249337i	−0.720058	+	0.693913i	$0.755885\pi$
$864$		0			0
$865$	10.0046	+	2.93763i	0.340168	+	0.0998824i
$866$	1.74023	+	12.1035i	0.0591353	+	0.411295i
$867$		0			0
$868$	−10.9787	−	24.0399i	−0.372640	−	0.815968i
$869$	−1.85566	+	0.544872i	−0.0629491	+	0.0184835i
$870$		0			0
$871$	4.05662	−	28.2144i	0.137453	−	0.956009i
$872$	8.25162	−	5.30300i	0.279435	−	0.179582i
$873$		0			0
$874$	−15.4962	−	0.833918i	−0.524166	−	0.0282077i
$875$	−48.2706			−1.63184
$876$		0			0
$877$	−1.00627	+	6.99877i	−0.0339794	+	0.236332i	−0.999732	−	0.0231313i	$-0.992636\pi$
$877$	−1.00627	+	6.99877i	−0.0339794	+	0.236332i	0.965753	+	0.259463i	$0.0835455\pi$
$878$	6.35810	−	13.9223i	0.214575	−	0.469855i
$879$		0			0
$880$	0.128663	+	0.281733i	0.00433723	+	0.00949720i
$881$	5.36772	+	6.19468i	0.180843	+	0.208704i	0.838932	−	0.544236i	$-0.183180\pi$
$881$	5.36772	+	6.19468i	0.180843	+	0.208704i	−0.658089	+	0.752940i	$0.728635\pi$
$882$		0			0
$883$	−7.43828	−	2.18408i	−0.250318	−	0.0735000i	0.154166	−	0.988045i	$-0.450731\pi$
$883$	−7.43828	−	2.18408i	−0.250318	−	0.0735000i	−0.404484	+	0.914545i	$0.632549\pi$
$884$	0.144785	−	0.167091i	0.00486966	−	0.00561989i
$885$		0			0
$886$	−6.34358	−	4.07677i	−0.213117	−	0.136962i
$887$	−29.6380	+	34.2040i	−0.995146	+	1.14846i	−0.00622994	+	0.999981i	$0.501983\pi$
$887$	−29.6380	+	34.2040i	−0.995146	+	1.14846i	−0.988916	+	0.148479i	$0.952562\pi$
$888$		0			0
$889$	1.60002	+	11.1284i	0.0536630	+	0.373234i
$890$	−0.933117	−	1.07687i	−0.0312781	−	0.0360969i
$891$		0			0
$892$	16.0452	−	4.71129i	0.537233	−	0.157746i
$893$	−10.4023	+	22.7778i	−0.348099	+	0.762230i
$894$		0			0
$895$	24.5050	−	15.7484i	0.819111	−	0.526411i
$896$	−4.29177			−0.143378
$897$		0			0
$898$	12.4935			0.416915
$899$	18.4867	−	11.8807i	0.616565	−	0.396243i
$900$		0			0
$901$	0.00675038	−	0.0147813i	0.000224888	−	0.000492435i
$902$	−0.725607	+	0.213057i	−0.0241601	+	0.00709403i
$903$		0			0
$904$	5.80730	+	6.70198i	0.193148	+	0.222905i
$905$	−0.839962	−	5.84207i	−0.0279213	−	0.194197i
$906$		0			0
$907$	−35.5758	+	41.0567i	−1.18128	+	1.36326i	−0.264241	+	0.964457i	$0.585121\pi$
$907$	−35.5758	+	41.0567i	−1.18128	+	1.36326i	−0.917034	+	0.398808i	$0.869424\pi$
$908$	−11.9020	−	7.64893i	−0.394981	−	0.253839i
$909$		0			0
$910$	−7.81030	+	9.01356i	−0.258909	+	0.298797i
$911$	24.0218	+	7.05343i	0.795877	+	0.233691i	0.654299	−	0.756236i	$-0.272964\pi$
$911$	24.0218	+	7.05343i	0.795877	+	0.233691i	0.141579	+	0.989927i	$0.454782\pi$
$912$		0			0
$913$	2.27064	+	2.62046i	0.0751473	+	0.0867246i
$914$	−11.4916	−	25.1632i	−0.380109	−	0.832323i
$915$		0			0
$916$	−9.71437	+	21.2715i	−0.320972	+	0.702830i
$917$	−9.35759	+	65.0835i	−0.309015	+	2.14925i
$918$		0			0
$919$	−23.8024			−0.785170			−0.392585	−	0.919716i	$-0.628419\pi$
$919$	−23.8024			−0.785170			−0.392585	+	0.919716i	$0.628419\pi$
$920$	−6.52463	+	1.54034i	−0.215111	+	0.0507836i
$921$		0			0
$922$	−9.43666	+	6.06457i	−0.310780	+	0.199726i
$923$	−1.65370	+	11.5017i	−0.0544321	+	0.378584i
$924$		0			0
$925$	12.3568	−	3.62828i	0.406289	−	0.119297i
$926$	3.93622	+	8.61912i	0.129352	+	0.283242i
$927$		0			0
$928$	−0.507869	−	3.53231i	−0.0166716	−	0.115954i
$929$	−13.7404	−	4.03453i	−0.450806	−	0.132369i	0.0484450	−	0.998826i	$-0.484573\pi$
$929$	−13.7404	−	4.03453i	−0.450806	−	0.132369i	−0.499251	+	0.866457i	$0.666392\pi$
$930$		0			0
$931$	31.0853	+	19.9773i	1.01878	+	0.654729i
$932$	7.27349	+	4.67439i	0.238251	+	0.153115i
$933$		0			0
$934$	8.96066	+	2.63109i	0.293202	+	0.0860918i
$935$	0.00490213	+	0.0340950i	0.000160317	+	0.00111503i
$936$		0			0
$937$	15.7422	+	34.4706i	0.514274	+	1.12610i	0.971562	+	0.236785i	$0.0760937\pi$
$937$	15.7422	+	34.4706i	0.514274	+	1.12610i	−0.457288	+	0.889319i	$0.651179\pi$
$938$	−59.0446	+	17.3370i	−1.92787	+	0.566075i
$939$		0			0
$940$	−1.53949	+	10.7074i	−0.0502126	+	0.349237i
$941$	22.1682	−	14.2466i	0.722663	−	0.464427i	−0.126899	−	0.991916i	$-0.540502\pi$
$941$	22.1682	−	14.2466i	0.722663	−	0.464427i	0.849562	+	0.527488i	$0.176866\pi$
$942$		0			0
$943$	−1.45552	−	16.3041i	−0.0473982	−	0.530935i
$944$	13.1693			0.428623
$945$		0			0
$946$	−0.102415	+	0.712314i	−0.00332981	+	0.0231593i
$947$	5.36945	−	11.7575i	0.174484	−	0.382066i	−0.802104	−	0.597184i	$-0.796286\pi$
$947$	5.36945	−	11.7575i	0.174484	−	0.382066i	0.976588	+	0.215118i	$0.0690135\pi$
$948$		0			0
$949$	−3.13192	−	6.85794i	−0.101666	−	0.222618i
$950$	6.45444	+	7.44882i	0.209410	+	0.241672i
$951$		0			0
$952$	−0.457975	−	0.134473i	−0.0148430	−	0.00435831i
$953$	6.44759	−	7.44091i	0.208858	−	0.241035i	−0.641649	−	0.766998i	$-0.721750\pi$
$953$	6.44759	−	7.44091i	0.208858	−	0.241035i	0.850507	+	0.525963i	$0.176295\pi$
$954$		0			0
$955$	−16.6859	−	10.7234i	−0.539945	−	0.347001i
$956$	5.79460	−	6.68733i	0.187411	−	0.216284i
$957$		0			0
$958$	0.171215	+	1.19083i	0.00553172	+	0.0384739i
$959$	28.9740	+	33.4378i	0.935620	+	1.07976i
$960$		0			0
$961$	−6.63910	+	1.94942i	−0.214165	+	0.0628844i
$962$	3.49171	−	7.64578i	0.112577	−	0.246510i
$963$		0			0
$964$	4.70043	−	3.02078i	0.151391	−	0.0972929i
$965$	−2.80417			−0.0902695
$966$		0			0
$967$	−59.2387			−1.90499			−0.952495	−	0.304555i	$-0.901492\pi$
$967$	−59.2387			−1.90499			−0.952495	+	0.304555i	$0.901492\pi$
$968$	−9.21249	+	5.92051i	−0.296101	+	0.190292i
$969$		0			0
$970$	10.5764	−	23.1590i	0.339587	−	0.743591i
$971$	−6.45523	+	1.89543i	−0.207158	+	0.0608271i	−0.383665	−	0.923472i	$-0.625338\pi$
$971$	−6.45523	+	1.89543i	−0.207158	+	0.0608271i	0.176507	+	0.984299i	$0.443520\pi$
$972$		0			0
$973$	−1.60046	−	1.84703i	−0.0513083	−	0.0592130i
$974$	0.636500	+	4.42695i	0.0203948	+	0.141849i
$975$		0			0
$976$	3.72593	−	4.29995i	0.119264	−	0.137638i
$977$	−27.5632	−	17.7138i	−0.881824	−	0.566714i	0.0195241	−	0.999809i	$-0.493785\pi$
$977$	−27.5632	−	17.7138i	−0.881824	−	0.566714i	−0.901348	+	0.433096i	$0.857421\pi$
$978$		0			0
$979$	−0.147900	+	0.170686i	−0.00472691	+	0.00545515i
$980$	15.3162	+	4.49724i	0.489257	+	0.143659i
$981$		0			0
$982$	7.89592	+	9.11238i	0.251969	+	0.290788i
$983$	−10.4605	−	22.9053i	−0.333639	−	0.730567i	0.666246	−	0.745732i	$-0.267900\pi$
$983$	−10.4605	−	22.9053i	−0.333639	−	0.730567i	−0.999885	+	0.0151648i	$0.995173\pi$
$984$		0			0
$985$	7.53094	−	16.4905i	0.239956	−	0.525430i
$986$	0.0564826	−	0.392845i	0.00179877	−	0.0125107i
$987$		0			0
$988$	6.43282			0.204655
$989$	−14.6883	−	5.18527i	−0.467062	−	0.164882i
$990$		0			0
$991$	30.0608	−	19.3189i	0.954914	−	0.613686i	0.0323277	−	0.999477i	$-0.489708\pi$
$991$	30.0608	−	19.3189i	0.954914	−	0.613686i	0.922586	+	0.385792i	$0.126072\pi$
$992$	−0.876357	+	6.09519i	−0.0278243	+	0.193523i
$993$		0			0
$994$	24.0697	−	7.06751i	0.763446	−	0.224168i
$995$	6.89212	+	15.0916i	0.218495	+	0.478437i
$996$		0			0
$997$	−0.835232	−	5.80917i	−0.0264521	−	0.183978i	0.972312	−	0.233688i	$-0.0750794\pi$
$997$	−0.835232	−	5.80917i	−0.0264521	−	0.183978i	−0.998764	+	0.0497099i	$0.984170\pi$
$998$	−3.49806	−	1.02712i	−0.110729	−	0.0325131i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.c.127.1		10
3.2	odd	2		46.2.c.b.35.1	yes	10
12.11	even	2		368.2.m.a.81.1		10
23.2	even	11	inner	414.2.i.c.163.1		10
23.5	odd	22		9522.2.a.bw.1.5		5
23.18	even	11		9522.2.a.bz.1.1		5
69.2	odd	22		46.2.c.b.25.1	✓	10
69.5	even	22		1058.2.a.k.1.1		5
69.41	odd	22		1058.2.a.j.1.1		5
276.71	even	22		368.2.m.a.209.1		10
276.143	odd	22		8464.2.a.bv.1.5		5
276.179	even	22		8464.2.a.bu.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.b.25.1	✓	10	69.2	odd	22
46.2.c.b.35.1	yes	10	3.2	odd	2
368.2.m.a.81.1		10	12.11	even	2
368.2.m.a.209.1		10	276.71	even	22
414.2.i.c.127.1		10	1.1	even	1	trivial
414.2.i.c.163.1		10	23.2	even	11	inner
1058.2.a.j.1.1		5	69.41	odd	22
1058.2.a.k.1.1		5	69.5	even	22
8464.2.a.bu.1.5		5	276.179	even	22
8464.2.a.bv.1.5		5	276.143	odd	22
9522.2.a.bw.1.5		5	23.5	odd	22
9522.2.a.bz.1.1		5	23.18	even	11

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.415415 - 0.909632i) q^{4} +(1.34125 - 0.393828i) q^{5} +(2.81051 + 3.24350i) q^{7} +(-0.142315 - 0.989821i) q^{8} +O(q^{10})\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.415415 - 0.909632i) q^{4} +(1.34125 - 0.393828i) q^{5} +(2.81051 + 3.24350i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(0.915415 - 1.05645i) q^{10} +(-0.186393 - 0.119787i) q^{11} +(-1.30185 + 1.50242i) q^{13} +(4.11792 + 1.20913i) q^{14} +(-0.654861 - 0.755750i) q^{16} +(-0.0462003 - 0.101165i) q^{17} +(1.34422 - 2.94343i) q^{19} +(0.198939 - 1.38365i) q^{20} -0.221566 q^{22} +(0.936621 - 4.70348i) q^{23} +(-2.56241 + 1.64676i) q^{25} +(-0.282920 + 1.96775i) q^{26} +(4.11792 - 1.20913i) q^{28} +(1.48246 + 3.24614i) q^{29} +(-0.876357 - 6.09519i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-0.0935599 - 0.0601273i) q^{34} +(5.04699 + 3.24350i) q^{35} +(-4.05681 - 1.19119i) q^{37} +(-0.460509 - 3.20291i) q^{38} +(-0.580699 - 1.27155i) q^{40} +(3.27491 - 0.961600i) q^{41} +(0.462235 - 3.21491i) q^{43} +(-0.186393 + 0.119787i) q^{44} +(-1.75496 - 4.46320i) q^{46} -7.73852 q^{47} +(-1.62514 + 11.3031i) q^{49} +(-1.26533 + 2.77068i) q^{50} +(0.825838 + 1.80833i) q^{52} +(0.0956823 + 0.110423i) q^{53} +(-0.297176 - 0.0872586i) q^{55} +(2.81051 - 3.24350i) q^{56} +(3.00212 + 1.92935i) q^{58} +(-8.62403 + 9.95266i) q^{59} +(0.809721 + 5.63174i) q^{61} +(-4.03255 - 4.65381i) q^{62} +(-0.959493 + 0.281733i) q^{64} +(-1.15442 + 2.52783i) q^{65} +(-12.0623 + 7.75194i) q^{67} -0.111215 q^{68} +5.99937 q^{70} +(4.91722 - 3.16011i) q^{71} +(-1.57542 + 3.44970i) q^{73} +(-4.05681 + 1.19119i) q^{74} +(-2.11903 - 2.44549i) q^{76} +(-0.135328 - 0.941230i) q^{77} +(5.71616 - 6.59680i) q^{79} +(-1.17597 - 0.755750i) q^{80} +(2.23515 - 2.57950i) q^{82} +(-15.0155 - 4.40894i) q^{83} +(-0.101808 - 0.117492i) q^{85} +(-1.34926 - 2.95446i) q^{86} +(-0.0920417 + 0.201543i) q^{88} +(0.145067 - 1.00896i) q^{89} -8.53197 q^{91} +(-3.88935 - 2.80588i) q^{92} +(-6.51006 + 4.18376i) q^{94} +(0.643736 - 4.47728i) q^{95} +(17.4754 - 5.13124i) q^{97} +(4.74375 + 10.3874i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{4} + 4 q^{5} - 7 q^{7} - q^{8}+O(q^{10}) \) 10 * q - q^2 - q^4 + 4 * q^5 - 7 * q^7 - q^8	\( 10 q - q^{2} - q^{4} + 4 q^{5} - 7 q^{7} - q^{8} + 4 q^{10} + 2 q^{11} + 2 q^{13} + 15 q^{14} - q^{16} + 9 q^{17} + 2 q^{19} - 7 q^{20} + 2 q^{22} - 21 q^{23} - 11 q^{25} - 9 q^{26} + 15 q^{28} + 2 q^{29} + 11 q^{31} - q^{32} - 13 q^{34} + 17 q^{35} - 18 q^{37} + 13 q^{38} + 4 q^{40} - 5 q^{41} - 21 q^{43} + 2 q^{44} - 10 q^{46} + 22 q^{47} + 24 q^{49} + 22 q^{50} - 20 q^{52} + 7 q^{53} + 3 q^{55} - 7 q^{56} + 24 q^{58} - 43 q^{59} - 3 q^{61} - 33 q^{62} - q^{64} - 41 q^{65} - q^{67} - 2 q^{68} + 6 q^{70} + 11 q^{71} - 28 q^{73} - 18 q^{74} + 2 q^{76} - 30 q^{77} + 34 q^{79} - 7 q^{80} + 6 q^{82} + 3 q^{83} + 8 q^{85} + 34 q^{86} - 9 q^{88} + 49 q^{89} - 52 q^{91} + q^{92} - 11 q^{94} + 36 q^{95} + 16 q^{97} - 20 q^{98}+O(q^{100}) \) 10 * q - q^2 - q^4 + 4 * q^5 - 7 * q^7 - q^8 + 4 * q^10 + 2 * q^11 + 2 * q^13 + 15 * q^14 - q^16 + 9 * q^17 + 2 * q^19 - 7 * q^20 + 2 * q^22 - 21 * q^23 - 11 * q^25 - 9 * q^26 + 15 * q^28 + 2 * q^29 + 11 * q^31 - q^32 - 13 * q^34 + 17 * q^35 - 18 * q^37 + 13 * q^38 + 4 * q^40 - 5 * q^41 - 21 * q^43 + 2 * q^44 - 10 * q^46 + 22 * q^47 + 24 * q^49 + 22 * q^50 - 20 * q^52 + 7 * q^53 + 3 * q^55 - 7 * q^56 + 24 * q^58 - 43 * q^59 - 3 * q^61 - 33 * q^62 - q^64 - 41 * q^65 - q^67 - 2 * q^68 + 6 * q^70 + 11 * q^71 - 28 * q^73 - 18 * q^74 + 2 * q^76 - 30 * q^77 + 34 * q^79 - 7 * q^80 + 6 * q^82 + 3 * q^83 + 8 * q^85 + 34 * q^86 - 9 * q^88 + 49 * q^89 - 52 * q^91 + q^92 - 11 * q^94 + 36 * q^95 + 16 * q^97 - 20 * q^98

Introduction

L-functions

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