LMFDB - Embedded newform 351.2.bd.e.215.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,2,Mod(80,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

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

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

chi := DirichletCharacter("351.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.bd (of order $12$, degree $4$, 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:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 88 x^{16} - 6 x^{15} + 48 x^{13} + 1980 x^{12} - 204 x^{11} + 18 x^{10} + 2076 x^{9} + \cdots + 81 $ x^20 + 88x^16 - 6x^15 + 48x^13 + 1980x^12 - 204x^11 + 18x^10 + 2076x^9 + 8020x^8 + 2220x^7 + 792x^6 + 4350x^5 + 10936x^4 + 6648x^3 + 1800x^2 - 540*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			215.3
Root			$-0.561693 + 0.561693i$ of defining polynomial
Character	$\chi$	$=$	351.215
Dual form			351.2.bd.e.80.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.205594 + 0.767287i) q^{2} +(1.18559 - 0.684501i) q^{4} +(-2.75236 + 2.75236i) q^{5} +(1.54508 + 0.414002i) q^{7} +(1.89235 + 1.89235i) q^{8} +O(q^{10})$	\(q+(0.205594 + 0.767287i) q^{2} +(1.18559 - 0.684501i) q^{4} +(-2.75236 + 2.75236i) q^{5} +(1.54508 + 0.414002i) q^{7} +(1.89235 + 1.89235i) q^{8} +(-2.67772 - 1.54598i) q^{10} +(1.42638 - 0.382196i) q^{11} +(-1.55939 + 3.25089i) q^{13} +1.27063i q^{14} +(0.306084 - 0.530153i) q^{16} +(-1.22700 - 2.12522i) q^{17} +(-2.03606 + 7.59867i) q^{19} +(-1.37918 + 5.14717i) q^{20} +(0.586509 + 1.01586i) q^{22} +(0.0635456 - 0.110064i) q^{23} -10.1510i q^{25} +(-2.81497 - 0.528136i) q^{26} +(2.11521 - 0.566769i) q^{28} +(7.00921 + 4.04677i) q^{29} +(1.87990 + 1.87990i) q^{31} +(5.63969 + 1.51115i) q^{32} +(1.37839 - 1.37839i) q^{34} +(-5.39210 + 3.11313i) q^{35} +(-1.26053 - 4.70437i) q^{37} -6.24897 q^{38} -10.4168 q^{40} +(-1.07198 - 4.00068i) q^{41} +(9.87623 - 5.70204i) q^{43} +(1.42948 - 1.42948i) q^{44} +(0.0975154 + 0.0261292i) q^{46} +(-5.41270 - 5.41270i) q^{47} +(-3.84632 - 2.22067i) q^{49} +(7.78875 - 2.08699i) q^{50} +(0.376441 + 4.92163i) q^{52} -7.39660i q^{53} +(-2.87396 + 4.97785i) q^{55} +(2.14038 + 3.70725i) q^{56} +(-1.66398 + 6.21007i) q^{58} +(-0.0877466 + 0.327475i) q^{59} +(-0.120262 - 0.208299i) q^{61} +(-1.05593 + 1.82892i) q^{62} +3.41361i q^{64} +(-4.65563 - 13.2397i) q^{65} +(-5.41185 + 1.45010i) q^{67} +(-2.90943 - 1.67976i) q^{68} +(-3.49725 - 3.49725i) q^{70} +(-0.902351 - 0.241784i) q^{71} +(4.50619 - 4.50619i) q^{73} +(3.35044 - 1.93438i) q^{74} +(2.78737 + 10.4026i) q^{76} +2.36209 q^{77} -0.351919 q^{79} +(0.616719 + 2.30163i) q^{80} +(2.84928 - 1.64503i) q^{82} +(10.6691 - 10.6691i) q^{83} +(9.22654 + 2.47224i) q^{85} +(6.40560 + 6.40560i) q^{86} +(3.42244 + 1.97595i) q^{88} +(13.1675 - 3.52822i) q^{89} +(-3.75525 + 4.37729i) q^{91} -0.173988i q^{92} +(3.04028 - 5.26591i) q^{94} +(-15.3103 - 26.5183i) q^{95} +(2.88713 - 10.7749i) q^{97} +(0.913113 - 3.40779i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{5}+O(q^{10}) $ 20 * q + 6 * q^5	$ 20 q + 6 q^{5} - 12 q^{10} - 8 q^{13} + 24 q^{16} - 12 q^{17} - 12 q^{19} + 36 q^{20} + 8 q^{22} - 42 q^{26} + 2 q^{28} - 6 q^{29} - 22 q^{31} - 36 q^{32} - 6 q^{34} - 36 q^{35} + 8 q^{37} + 72 q^{38} - 36 q^{40} + 30 q^{41} - 30 q^{43} + 36 q^{44} - 48 q^{46} + 6 q^{47} + 30 q^{49} + 54 q^{50} + 4 q^{52} - 28 q^{55} - 60 q^{56} + 44 q^{58} + 30 q^{59} - 16 q^{61} - 30 q^{62} - 78 q^{65} + 18 q^{67} + 6 q^{68} + 38 q^{70} - 60 q^{71} - 72 q^{74} - 8 q^{76} - 12 q^{77} - 16 q^{79} + 126 q^{80} + 78 q^{82} + 12 q^{83} + 12 q^{85} + 18 q^{86} + 84 q^{89} + 30 q^{91} - 22 q^{94} - 66 q^{95} + 26 q^{97} + 42 q^{98}+O(q^{100}) $ 20 * q + 6 * q^5 - 12 * q^10 - 8 * q^13 + 24 * q^16 - 12 * q^17 - 12 * q^19 + 36 * q^20 + 8 * q^22 - 42 * q^26 + 2 * q^28 - 6 * q^29 - 22 * q^31 - 36 * q^32 - 6 * q^34 - 36 * q^35 + 8 * q^37 + 72 * q^38 - 36 * q^40 + 30 * q^41 - 30 * q^43 + 36 * q^44 - 48 * q^46 + 6 * q^47 + 30 * q^49 + 54 * q^50 + 4 * q^52 - 28 * q^55 - 60 * q^56 + 44 * q^58 + 30 * q^59 - 16 * q^61 - 30 * q^62 - 78 * q^65 + 18 * q^67 + 6 * q^68 + 38 * q^70 - 60 * q^71 - 72 * q^74 - 8 * q^76 - 12 * q^77 - 16 * q^79 + 126 * q^80 + 78 * q^82 + 12 * q^83 + 12 * q^85 + 18 * q^86 + 84 * q^89 + 30 * q^91 - 22 * q^94 - 66 * q^95 + 26 * q^97 + 42 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.205594	+	0.767287i	0.145377	+	0.542554i	0.999738	+	0.0228747i	$0.00728189\pi$
$2$	0.205594	+	0.767287i	0.145377	+	0.542554i	−0.854361	+	0.519679i	$0.826051\pi$
$3$		0			0
$3$		0			0
$4$	1.18559	−	0.684501i	0.592795	−	0.342250i
$5$	−2.75236	+	2.75236i	−1.23089	+	1.23089i	−0.267274	+	0.963620i	$0.586123\pi$
$5$	−2.75236	+	2.75236i	−1.23089	+	1.23089i	−0.963620	+	0.267274i	$0.913877\pi$
$6$		0			0
$7$	1.54508	+	0.414002i	0.583984	+	0.156478i	0.538702	−	0.842496i	$-0.318915\pi$
$7$	1.54508	+	0.414002i	0.583984	+	0.156478i	0.0452816	+	0.998974i	$0.485581\pi$
$8$	1.89235	+	1.89235i	0.669045	+	0.669045i
$9$		0			0
$10$	−2.67772	−	1.54598i	−0.846771	−	0.488883i
$11$	1.42638	−	0.382196i	0.430069	−	0.115237i	−0.0372897	−	0.999304i	$-0.511872\pi$
$11$	1.42638	−	0.382196i	0.430069	−	0.115237i	0.467358	+	0.884068i	$0.345206\pi$
$12$		0			0
$13$	−1.55939	+	3.25089i	−0.432497	+	0.901635i
$13$	−1.55939	+	3.25089i	−0.432497	+	0.901635i
$14$			1.27063i			0.339591i
$15$		0			0
$16$	0.306084	−	0.530153i	0.0765210	−	0.132538i
$17$	−1.22700	−	2.12522i	−0.297591	−	0.515442i	0.677993	−	0.735068i	$-0.262850\pi$
$17$	−1.22700	−	2.12522i	−0.297591	−	0.515442i	−0.975584	+	0.219626i	$0.929516\pi$
$18$		0			0
$19$	−2.03606	+	7.59867i	−0.467104	+	1.74326i	0.182715	+	0.983166i	$0.441511\pi$
$19$	−2.03606	+	7.59867i	−0.467104	+	1.74326i	−0.649819	+	0.760089i	$0.725155\pi$
$20$	−1.37918	+	5.14717i	−0.308394	+	1.15094i
$21$		0			0
$22$	0.586509	+	1.01586i	0.125044	+	0.216583i
$23$	0.0635456	−	0.110064i	0.0132502	−	0.0229500i	−0.859324	−	0.511431i	$-0.829116\pi$
$23$	0.0635456	−	0.110064i	0.0132502	−	0.0229500i	0.872574	+	0.488481i	$0.162449\pi$
$24$		0			0
$25$		−	10.1510i		−	2.03020i
$26$	−2.81497	−	0.528136i	−0.552061	−	0.103576i
$27$		0			0
$28$	2.11521	−	0.566769i	0.399737	−	0.107109i
$29$	7.00921	+	4.04677i	1.30158	+	0.751466i	0.980675	−	0.195646i	$-0.0626802\pi$
$29$	7.00921	+	4.04677i	1.30158	+	0.751466i	0.320903	+	0.947112i	$0.396014\pi$
$30$		0			0
$31$	1.87990	+	1.87990i	0.337641	+	0.337641i	0.855479	−	0.517838i	$-0.173263\pi$
$31$	1.87990	+	1.87990i	0.337641	+	0.337641i	−0.517838	+	0.855479i	$0.673263\pi$
$32$	5.63969	+	1.51115i	0.996966	+	0.267136i
$33$		0			0
$34$	1.37839	−	1.37839i	0.236393	−	0.236393i
$35$	−5.39210	+	3.11313i	−0.911431	+	0.526215i
$36$		0			0
$37$	−1.26053	−	4.70437i	−0.207230	−	0.773393i	−0.988758	−	0.149523i	$-0.952226\pi$
$37$	−1.26053	−	4.70437i	−0.207230	−	0.773393i	0.781528	−	0.623870i	$-0.214440\pi$
$38$	−6.24897			−1.01372
$39$		0			0
$40$	−10.4168			−1.64705
$41$	−1.07198	−	4.00068i	−0.167415	−	0.624801i	−0.997720	−	0.0674918i	$-0.978500\pi$
$41$	−1.07198	−	4.00068i	−0.167415	−	0.624801i	0.830305	−	0.557309i	$-0.188166\pi$
$42$		0			0
$43$	9.87623	−	5.70204i	1.50611	−	0.869553i	0.506136	−	0.862454i	$-0.331074\pi$
$43$	9.87623	−	5.70204i	1.50611	−	0.869553i	0.999975	−	0.00709934i	$-0.00225981\pi$
$44$	1.42948	−	1.42948i	0.215503	−	0.215503i
$45$		0			0
$46$	0.0975154	+	0.0261292i	0.0143779	+	0.00385254i
$47$	−5.41270	−	5.41270i	−0.789523	−	0.789523i	0.191892	−	0.981416i	$-0.438538\pi$
$47$	−5.41270	−	5.41270i	−0.789523	−	0.789523i	−0.981416	+	0.191892i	$0.938538\pi$
$48$		0			0
$49$	−3.84632	−	2.22067i	−0.549474	−	0.317239i
$50$	7.78875	−	2.08699i	1.10150	−	0.295145i
$51$		0			0
$52$	0.376441	+	4.92163i	0.0522030	+	0.682507i
$53$		−	7.39660i		−	1.01600i	−0.861357	−	0.508001i	$-0.830385\pi$
$53$		−	7.39660i		−	1.01600i	0.861357	−	0.508001i	$-0.169615\pi$
$54$		0			0
$55$	−2.87396	+	4.97785i	−0.387525	+	0.671213i
$56$	2.14038	+	3.70725i	0.286021	+	0.495402i
$57$		0			0
$58$	−1.66398	+	6.21007i	−0.218492	+	0.815422i
$59$	−0.0877466	+	0.327475i	−0.0114236	+	0.0426336i	−0.971402	−	0.237439i	$-0.923692\pi$
$59$	−0.0877466	+	0.327475i	−0.0114236	+	0.0426336i	0.959979	+	0.280073i	$0.0903586\pi$
$60$		0			0
$61$	−0.120262	−	0.208299i	−0.0153979	−	0.0266700i	0.858224	−	0.513276i	$-0.171568\pi$
$61$	−0.120262	−	0.208299i	−0.0153979	−	0.0266700i	−0.873622	+	0.486606i	$0.838235\pi$
$62$	−1.05593	+	1.82892i	−0.134103	+	0.232274i
$63$		0			0
$64$			3.41361i			0.426701i
$65$	−4.65563	−	13.2397i	−0.577460	−	1.64218i
$66$		0			0
$67$	−5.41185	+	1.45010i	−0.661163	+	0.177158i	−0.573771	−	0.819016i	$-0.694520\pi$
$67$	−5.41185	+	1.45010i	−0.661163	+	0.177158i	−0.0873923	+	0.996174i	$0.527853\pi$
$68$	−2.90943	−	1.67976i	−0.352821	−	0.203701i
$69$		0			0
$70$	−3.49725	−	3.49725i	−0.418001	−	0.418001i
$71$	−0.902351	−	0.241784i	−0.107089	−	0.0286945i	0.204876	−	0.978788i	$-0.434321\pi$
$71$	−0.902351	−	0.241784i	−0.107089	−	0.0286945i	−0.311966	+	0.950093i	$0.600987\pi$
$72$		0			0
$73$	4.50619	−	4.50619i	0.527409	−	0.527409i	−0.392390	−	0.919799i	$-0.628352\pi$
$73$	4.50619	−	4.50619i	0.527409	−	0.527409i	0.919799	+	0.392390i	$0.128352\pi$
$74$	3.35044	−	1.93438i	0.389481	−	0.224867i
$75$		0			0
$76$	2.78737	+	10.4026i	0.319733	+	1.19326i
$77$	2.36209			0.269185
$78$		0			0
$79$	−0.351919			−0.0395940			−0.0197970	−	0.999804i	$-0.506302\pi$
$79$	−0.351919			−0.0395940			−0.0197970	+	0.999804i	$0.506302\pi$
$80$	0.616719	+	2.30163i	0.0689513	+	0.257330i
$81$		0			0
$82$	2.84928	−	1.64503i	0.314650	−	0.181663i
$83$	10.6691	−	10.6691i	1.17109	−	1.17109i	0.189138	−	0.981951i	$-0.439431\pi$
$83$	10.6691	−	10.6691i	1.17109	−	1.17109i	0.981951	−	0.189138i	$-0.0605692\pi$
$84$		0			0
$85$	9.22654	+	2.47224i	1.00076	+	0.268152i
$86$	6.40560	+	6.40560i	0.690733	+	0.690733i
$87$		0			0
$88$	3.42244	+	1.97595i	0.364834	+	0.210637i
$89$	13.1675	−	3.52822i	1.39575	−	0.373990i	0.518934	−	0.854814i	$-0.326329\pi$
$89$	13.1675	−	3.52822i	1.39575	−	0.373990i	0.876817	+	0.480824i	$0.159662\pi$
$90$		0			0
$91$	−3.75525	+	4.37729i	−0.393657	+	0.458864i
$92$		−	0.173988i		−	0.0181395i
$93$		0			0
$94$	3.04028	−	5.26591i	0.313581	−	0.543138i
$95$	−15.3103	−	26.5183i	−1.57081	−	2.72072i
$96$		0			0
$97$	2.88713	−	10.7749i	0.293143	−	1.09403i	−0.649537	−	0.760330i	$-0.725037\pi$
$97$	2.88713	−	10.7749i	0.293143	−	1.09403i	0.942681	−	0.333697i	$-0.108296\pi$
$98$	0.913113	−	3.40779i	0.0922384	−	0.344238i
$99$		0			0
$100$	−6.94838	−	12.0349i	−0.694838	−	1.20349i
$101$	−4.37119	+	7.57113i	−0.434950	+	0.753356i	−0.997292	−	0.0735496i	$-0.976567\pi$
$101$	−4.37119	+	7.57113i	−0.434950	+	0.753356i	0.562342	+	0.826905i	$0.309901\pi$
$102$		0			0
$103$		−	5.77354i		−	0.568884i	−0.958693	−	0.284442i	$-0.908192\pi$
$103$		−	5.77354i		−	0.568884i	0.958693	−	0.284442i	$-0.0918083\pi$
$104$	−9.10272	+	3.20091i	−0.892595	+	0.313875i
$105$		0			0
$106$	5.67532	−	1.52070i	0.551236	−	0.147703i
$107$	−4.39109	−	2.53520i	−0.424503	−	0.245087i	0.272499	−	0.962156i	$-0.412150\pi$
$107$	−4.39109	−	2.53520i	−0.424503	−	0.245087i	−0.697002	+	0.717069i	$0.745483\pi$
$108$		0			0
$109$	9.69280	+	9.69280i	0.928402	+	0.928402i	0.997603	−	0.0692012i	$-0.0220450\pi$
$109$	9.69280	+	9.69280i	0.928402	+	0.928402i	−0.0692012	+	0.997603i	$0.522045\pi$
$110$	−4.41031	−	1.18174i	−0.420507	−	0.112674i
$111$		0			0
$112$	0.692407	−	0.692407i	0.0654263	−	0.0654263i
$113$	−11.8168	+	6.82246i	−1.11164	+	0.641803i	−0.939253	−	0.343227i	$-0.888480\pi$
$113$	−11.8168	+	6.82246i	−1.11164	+	0.641803i	−0.172383	+	0.985030i	$0.555147\pi$
$114$		0			0
$115$	0.128036	+	0.477837i	0.0119394	+	0.0445586i
$116$	11.0801			1.02876
$117$		0			0
$118$	−0.269307			−0.0247918
$119$	−1.01596	−	3.79161i	−0.0931328	−	0.347576i
$120$		0			0
$121$	−7.63780	+	4.40969i	−0.694346	+	0.400881i
$122$	0.135100	−	0.135100i	0.0122314	−	0.0122314i
$123$		0			0
$124$	3.51559	+	0.942000i	0.315709	+	0.0845941i
$125$	14.1775	+	14.1775i	1.26807	+	1.26807i
$126$		0			0
$127$	12.9255	+	7.46255i	1.14695	+	0.662194i	0.948143	−	0.317844i	$-0.102959\pi$
$127$	12.9255	+	7.46255i	1.14695	+	0.662194i	0.198811	+	0.980038i	$0.436292\pi$
$128$	8.66016	−	2.32048i	0.765458	−	0.205104i
$129$		0			0
$130$	9.20145	−	6.29420i	0.807020	−	0.552038i
$131$			2.21920i			0.193892i	0.995290	+	0.0969461i	$0.0309074\pi$
$131$			2.21920i			0.193892i	−0.995290	+	0.0969461i	$0.969093\pi$
$132$		0			0
$133$	−6.29173	+	10.8976i	−0.545562	+	0.944941i
$134$	−2.22529	−	3.85431i	−0.192236	−	0.332962i
$135$		0			0
$136$	1.69975	−	6.34356i	0.145753	−	0.543956i
$137$	−5.00500	+	18.6789i	−0.427606	+	1.59585i	0.330558	+	0.943786i	$0.392763\pi$
$137$	−5.00500	+	18.6789i	−0.427606	+	1.59585i	−0.758165	+	0.652063i	$0.773904\pi$
$138$		0			0
$139$	−4.35562	−	7.54416i	−0.369439	−	0.639887i	0.620039	−	0.784571i	$-0.287117\pi$
$139$	−4.35562	−	7.54416i	−0.369439	−	0.639887i	−0.989478	+	0.144684i	$0.953783\pi$
$140$	−4.26188	+	7.38179i	−0.360194	+	0.623875i
$141$		0			0
$142$		−	0.742072i		−	0.0622733i
$143$	−0.981798	+	5.23299i	−0.0821021	+	0.437605i
$144$		0			0
$145$	−30.4301	+	8.15372i	−2.52708	+	0.677129i
$146$	4.38399	+	2.53110i	0.362821	+	0.209475i
$147$		0			0
$148$	−4.71461	−	4.71461i	−0.387539	−	0.387539i
$149$	15.1274	+	4.05338i	1.23929	+	0.332066i	0.818188	−	0.574950i	$-0.194979\pi$
$149$	15.1274	+	4.05338i	1.23929	+	0.332066i	0.421097	+	0.907016i	$0.361645\pi$
$150$		0			0
$151$	−14.2162	+	14.2162i	−1.15690	+	1.15690i	−0.171756	+	0.985139i	$0.554944\pi$
$151$	−14.2162	+	14.2162i	−1.15690	+	1.15690i	−0.985139	+	0.171756i	$0.945056\pi$
$152$	−18.2322	+	10.5264i	−1.47883	+	0.853803i
$153$		0			0
$154$	0.485632	+	1.81240i	0.0391333	+	0.146047i
$155$	−10.3484			−0.831201
$156$		0			0
$157$	10.4197			0.831586			0.415793	−	0.909459i	$-0.363504\pi$
$157$	10.4197			0.831586			0.415793	+	0.909459i	$0.363504\pi$
$158$	−0.0723524	−	0.270023i	−0.00575605	−	0.0214819i
$159$		0			0
$160$	−19.6817	+	11.3632i	−1.55598	+	0.898344i
$161$	0.143750	−	0.143750i	0.0113291	−	0.0113291i
$162$		0			0
$163$	−16.1273	−	4.32129i	−1.26318	−	0.338469i	−0.435768	−	0.900059i	$-0.643523\pi$
$163$	−16.1273	−	4.32129i	−1.26318	−	0.338469i	−0.827416	+	0.561590i	$0.810190\pi$
$164$	−4.00940	−	4.00940i	−0.313081	−	0.313081i
$165$		0			0
$166$	10.3798	+	5.99277i	0.805628	+	0.465129i
$167$	−2.28699	+	0.612796i	−0.176972	+	0.0474196i	−0.346217	−	0.938154i	$-0.612534\pi$
$167$	−2.28699	+	0.612796i	−0.176972	+	0.0474196i	0.169245	+	0.985574i	$0.445867\pi$
$168$		0			0
$169$	−8.13660	−	10.1388i	−0.625893	−	0.779909i
$170$			7.58768i			0.581949i
$171$		0			0
$172$	7.80610	−	13.5206i	0.595210	−	1.03093i
$173$	4.87703	+	8.44726i	0.370793	+	0.642233i	0.989688	−	0.143241i	$-0.0457525\pi$
$173$	4.87703	+	8.44726i	0.370793	+	0.642233i	−0.618894	+	0.785474i	$0.712419\pi$
$174$		0			0
$175$	4.20254	−	15.6841i	0.317682	−	1.18561i
$176$	0.233968	−	0.873182i	0.0176360	−	0.0658186i
$177$		0			0
$178$	5.41431	+	9.37787i	0.405820	+	0.702901i
$179$	1.70298	−	2.94965i	0.127287	−	0.220467i	−0.795338	−	0.606167i	$-0.792706\pi$
$179$	1.70298	−	2.94965i	0.127287	−	0.220467i	0.922625	+	0.385699i	$0.126040\pi$
$180$		0			0
$181$			10.3133i			0.766584i	0.923627	+	0.383292i	$0.125210\pi$
$181$			10.3133i			0.766584i	−0.923627	+	0.383292i	$0.874790\pi$
$182$	−4.13069	−	1.98141i	−0.306187	−	0.146872i
$183$		0			0
$184$	0.328530	−	0.0880293i	0.0242195	−	0.00648960i
$185$	16.4176	+	9.47869i	1.20704	+	0.696887i
$186$		0			0
$187$	−2.56241	−	2.56241i	−0.187382	−	0.187382i
$188$	−10.1222	−	2.71225i	−0.738240	−	0.197811i
$189$		0			0
$190$	17.1994	−	17.1994i	1.24778	−	1.24778i
$191$	−8.60515	+	4.96819i	−0.622647	+	0.359485i	−0.777899	−	0.628389i	$-0.783714\pi$
$191$	−8.60515	+	4.96819i	−0.622647	+	0.359485i	0.155252	+	0.987875i	$0.450381\pi$
$192$		0			0
$193$	−0.370570	−	1.38299i	−0.0266742	−	0.0995495i	0.951305	−	0.308250i	$-0.0997433\pi$
$193$	−0.370570	−	1.38299i	−0.0266742	−	0.0995495i	−0.977980	+	0.208700i	$0.933077\pi$
$194$	8.86103			0.636185
$195$		0			0
$196$	−6.08020			−0.434300
$197$	−4.60073	−	17.1702i	−0.327789	−	1.22332i	−0.911479	−	0.411348i	$-0.865058\pi$
$197$	−4.60073	−	17.1702i	−0.327789	−	1.22332i	0.583690	−	0.811977i	$-0.301608\pi$
$198$		0			0
$199$	9.62946	−	5.55957i	0.682615	−	0.394108i	−0.118225	−	0.992987i	$-0.537720\pi$
$199$	9.62946	−	5.55957i	0.682615	−	0.394108i	0.800839	+	0.598879i	$0.204387\pi$
$200$	19.2092	−	19.2092i	1.35830	−	1.35830i
$201$		0			0
$202$	−6.70792	−	1.79738i	−0.471968	−	0.126463i
$203$	9.15439	+	9.15439i	0.642512	+	0.642512i
$204$		0			0
$205$	13.9618	+	8.06085i	0.975135	+	0.562994i
$206$	4.42996	−	1.18701i	0.308650	−	0.0827026i
$207$		0			0
$208$	1.24617	+	1.82176i	0.0864060	+	0.126316i
$209$			11.6167i			0.803547i
$210$		0			0
$211$	4.05396	−	7.02166i	0.279086	−	0.483391i	−0.692072	−	0.721829i	$-0.743302\pi$
$211$	4.05396	−	7.02166i	0.279086	−	0.483391i	0.971158	+	0.238438i	$0.0766353\pi$
$212$	−5.06298	−	8.76934i	−0.347727	−	0.602280i
$213$		0			0
$214$	1.04244	−	3.89045i	0.0712599	−	0.265946i
$215$	−11.4889	+	42.8771i	−0.783535	+	2.92419i
$216$		0			0
$217$	2.12631	+	3.68288i	0.144343	+	0.250010i
$218$	−5.44438	+	9.42994i	−0.368740	+	0.638676i
$219$		0			0
$220$			7.86892i			0.530523i
$221$	8.82224	−	0.674787i	0.593448	−	0.0453911i
$222$		0			0
$223$	3.04625	−	0.816241i	0.203992	−	0.0546595i	−0.155376	−	0.987855i	$-0.549659\pi$
$223$	3.04625	−	0.816241i	0.203992	−	0.0546595i	0.359368	+	0.933196i	$0.382992\pi$
$224$	8.08813	+	4.66969i	0.540411	+	0.312006i
$225$		0			0
$226$	−7.66426	−	7.66426i	−0.509819	−	0.509819i
$227$	−23.5610	−	6.31315i	−1.56380	−	0.419018i	−0.629934	−	0.776648i	$-0.716918\pi$
$227$	−23.5610	−	6.31315i	−1.56380	−	0.419018i	−0.933863	+	0.357630i	$0.883585\pi$
$228$		0			0
$229$	0.945623	−	0.945623i	0.0624885	−	0.0624885i	−0.675172	−	0.737660i	$-0.735931\pi$
$229$	0.945623	−	0.945623i	0.0624885	−	0.0624885i	0.737660	+	0.675172i	$0.235931\pi$
$230$	−0.340315	+	0.196481i	−0.0224397	+	0.0129556i
$231$		0			0
$232$	5.60596	+	20.9217i	0.368049	+	1.37358i
$233$	−3.62616			−0.237558			−0.118779	−	0.992921i	$-0.537898\pi$
$233$	−3.62616			−0.237558			−0.118779	+	0.992921i	$0.537898\pi$
$234$		0			0
$235$	29.7954			1.94364
$236$	0.120125	+	0.448314i	0.00781949	+	0.0291827i
$237$		0			0
$238$	2.70038	−	1.55906i	0.175040	−	0.101059i
$239$	−1.04328	+	1.04328i	−0.0674842	+	0.0674842i	−0.740043	−	0.672559i	$-0.765195\pi$
$239$	−1.04328	+	1.04328i	−0.0674842	+	0.0674842i	0.672559	+	0.740043i	$0.265195\pi$
$240$		0			0
$241$	−6.32118	−	1.69375i	−0.407183	−	0.109104i	0.0494133	−	0.998778i	$-0.484265\pi$
$241$	−6.32118	−	1.69375i	−0.407183	−	0.109104i	−0.456596	+	0.889674i	$0.650932\pi$
$242$	−4.95378	−	4.95378i	−0.318441	−	0.318441i
$243$		0			0
$244$	−0.285162	−	0.164638i	−0.0182556	−	0.0105399i
$245$	16.6986	−	4.47437i	1.06683	−	0.285857i
$246$		0			0
$247$	−21.5275	−	18.4683i	−1.36976	−	1.17511i
$248$			7.11486i			0.451794i
$249$		0			0
$250$	−7.96340	+	13.7930i	−0.503649	+	0.872346i
$251$	−12.3112	−	21.3237i	−0.777079	−	1.34594i	−0.933619	−	0.358269i	$-0.883367\pi$
$251$	−12.3112	−	21.3237i	−0.777079	−	1.34594i	0.156539	−	0.987672i	$-0.449966\pi$
$252$		0			0
$253$	0.0485738	−	0.181280i	0.00305381	−	0.0113970i
$254$	−3.06851	+	11.4518i	−0.192535	+	0.718552i
$255$		0			0
$256$	6.97457	+	12.0803i	0.435910	+	0.755019i
$257$	−6.23916	+	10.8066i	−0.389188	+	0.674094i	−0.992341	−	0.123532i	$-0.960578\pi$
$257$	−6.23916	+	10.8066i	−0.389188	+	0.674094i	0.603152	+	0.797626i	$0.293911\pi$
$258$		0			0
$259$		−	7.79046i		−	0.484076i
$260$	−14.5822	−	12.5100i	−0.904351	−	0.775838i
$261$		0			0
$262$	−1.70276	+	0.456254i	−0.105197	+	0.0281874i
$263$	19.4401	+	11.2238i	1.19873	+	0.692087i	0.960272	−	0.279066i	$-0.0900248\pi$
$263$	19.4401	+	11.2238i	1.19873	+	0.692087i	0.238458	+	0.971153i	$0.423358\pi$
$264$		0			0
$265$	20.3581	+	20.3581i	1.25059	+	1.25059i
$266$	−9.65513	−	2.58708i	−0.591994	−	0.158624i
$267$		0			0
$268$	−5.42364	+	5.42364i	−0.331302	+	0.331302i
$269$	20.7591	−	11.9853i	1.26571	−	0.730756i	0.291534	−	0.956560i	$-0.405834\pi$
$269$	20.7591	−	11.9853i	1.26571	−	0.730756i	0.974173	+	0.225804i	$0.0725010\pi$
$270$		0			0
$271$	−0.714098	−	2.66505i	−0.0433783	−	0.161890i	0.940839	−	0.338854i	$-0.110039\pi$
$271$	−0.714098	−	2.66505i	−0.0433783	−	0.161890i	−0.984217	+	0.176964i	$0.943373\pi$
$272$	−1.50226			−0.0910878
$273$		0			0
$274$	−15.3611			−0.927998
$275$	−3.87968	−	14.4792i	−0.233954	−	0.873127i
$276$		0			0
$277$	−15.1680	+	8.75727i	−0.911359	+	0.526173i	−0.880868	−	0.473362i	$-0.843040\pi$
$277$	−15.1680	+	8.75727i	−0.911359	+	0.526173i	−0.0304909	+	0.999535i	$0.509707\pi$
$278$	4.89305	−	4.89305i	0.293465	−	0.293465i
$279$		0			0
$280$	−16.0948	−	4.31259i	−0.961849	−	0.257727i
$281$	14.8429	+	14.8429i	0.885454	+	0.885454i	0.994082	−	0.108628i	$-0.0346457\pi$
$281$	14.8429	+	14.8429i	0.885454	+	0.885454i	−0.108628	+	0.994082i	$0.534646\pi$
$282$		0			0
$283$	−5.60392	−	3.23543i	−0.333119	−	0.192326i	0.324106	−	0.946021i	$-0.394936\pi$
$283$	−5.60392	−	3.23543i	−0.333119	−	0.192326i	−0.657225	+	0.753695i	$0.728270\pi$
$284$	−1.23532	+	0.331003i	−0.0733028	+	0.0196414i
$285$		0			0
$286$	−4.21706	+	0.322550i	−0.249360	+	0.0190728i
$287$		−	6.62516i		−	0.391071i
$288$		0			0
$289$	5.48895	−	9.50714i	0.322879	−	0.559244i
$290$	−12.5125	−	21.6723i	−0.734759	−	1.27264i
$291$		0			0
$292$	2.25800	−	8.42698i	0.132140	−	0.493152i
$293$	1.40538	−	5.24495i	0.0821032	−	0.306413i	−0.912647	−	0.408749i	$-0.865965\pi$
$293$	1.40538	−	5.24495i	0.0821032	−	0.306413i	0.994750	+	0.102336i	$0.0326317\pi$
$294$		0			0
$295$	−0.659819	−	1.14284i	−0.0384162	−	0.0665388i
$296$	6.51692	−	11.2876i	0.378789	−	0.656081i
$297$		0			0
$298$			12.4404i			0.720654i
$299$	0.258714	+	0.378213i	0.0149618	+	0.0218726i
$300$		0			0
$301$	17.6202	−	4.72131i	1.01561	−	0.272132i
$302$	−13.8306	−	7.98513i	−0.795864	−	0.459493i
$303$		0			0
$304$	3.40525	+	3.40525i	0.195305	+	0.195305i
$305$	0.904318	+	0.242311i	0.0517811	+	0.0138747i
$306$		0			0
$307$	−7.27550	+	7.27550i	−0.415235	+	0.415235i	−0.883558	−	0.468323i	$-0.844859\pi$
$307$	−7.27550	+	7.27550i	−0.415235	+	0.415235i	0.468323	+	0.883558i	$0.344859\pi$
$308$	2.80047	−	1.61685i	0.159572	−	0.0921287i
$309$		0			0
$310$	−2.12756	−	7.94017i	−0.120837	−	0.450971i
$311$	−4.40180			−0.249603			−0.124802	−	0.992182i	$-0.539829\pi$
$311$	−4.40180			−0.249603			−0.124802	+	0.992182i	$0.539829\pi$
$312$		0			0
$313$	3.50602			0.198172			0.0990861	−	0.995079i	$-0.468408\pi$
$313$	3.50602			0.198172			0.0990861	+	0.995079i	$0.468408\pi$
$314$	2.14224	+	7.99494i	0.120893	+	0.451180i
$315$		0			0
$316$	−0.417232	+	0.240889i	−0.0234711	+	0.0135511i
$317$	−8.78842	+	8.78842i	−0.493607	+	0.493607i	−0.909441	−	0.415834i	$-0.863490\pi$
$317$	−8.78842	+	8.78842i	−0.493607	+	0.493607i	0.415834	+	0.909441i	$0.363490\pi$
$318$		0			0
$319$	11.5444	+	3.09332i	0.646364	+	0.173193i
$320$	−9.39550	−	9.39550i	−0.525225	−	0.525225i
$321$		0			0
$322$	0.139851	+	0.0807431i	0.00779360	+	0.00449964i
$323$	18.6471	−	4.99648i	1.03755	−	0.278012i
$324$		0			0
$325$	32.9999	+	15.8294i	1.83050	+	0.878057i
$326$		−	13.2627i		−	0.734551i
$327$		0			0
$328$	5.54211	−	9.59922i	0.306012	−	0.530028i
$329$	−6.12216	−	10.6039i	−0.337526	−	0.584612i
$330$		0			0
$331$	−4.41989	+	16.4952i	−0.242939	+	0.906661i	0.731469	+	0.681875i	$0.238835\pi$
$331$	−4.41989	+	16.4952i	−0.242939	+	0.906661i	−0.974408	+	0.224786i	$0.927832\pi$
$332$	5.34618	−	19.9522i	0.293410	−	1.09502i
$333$		0			0
$334$	−0.940381	−	1.62879i	−0.0514554	−	0.0891233i
$335$	10.9042	−	18.8866i	0.595759	−	1.03189i
$336$		0			0
$337$		−	19.5394i		−	1.06438i	−0.846625	−	0.532191i	$-0.821369\pi$
$337$		−	19.5394i		−	1.06438i	0.846625	−	0.532191i	$-0.178631\pi$
$338$	6.10655	−	8.32759i	0.332153	−	0.452961i
$339$		0			0
$340$	12.6311	−	3.38450i	0.685020	−	0.183551i
$341$	3.39994	+	1.96296i	0.184117	+	0.106300i
$342$		0			0
$343$	−12.9410	−	12.9410i	−0.698749	−	0.698749i
$344$	29.4795	+	7.89900i	1.58943	+	0.425885i
$345$		0			0
$346$	−5.47879	+	5.47879i	−0.294541	+	0.294541i
$347$	−14.5598	+	8.40611i	−0.781611	+	0.451263i	−0.837001	−	0.547201i	$-0.815693\pi$
$347$	−14.5598	+	8.40611i	−0.781611	+	0.451263i	0.0553898	+	0.998465i	$0.482360\pi$
$348$		0			0
$349$	−0.900657	−	3.36130i	−0.0482111	−	0.179926i	0.937622	−	0.347657i	$-0.113023\pi$
$349$	−0.900657	−	3.36130i	−0.0482111	−	0.179926i	−0.985833	+	0.167731i	$0.946356\pi$
$350$	12.8982			0.689439
$351$		0			0
$352$	8.62188			0.459548
$353$	−4.68448	−	17.4827i	−0.249330	−	0.930511i	−0.971158	−	0.238438i	$-0.923365\pi$
$353$	−4.68448	−	17.4827i	−0.249330	−	0.930511i	0.721828	−	0.692072i	$-0.243302\pi$
$354$		0			0
$355$	3.14908	−	1.81812i	0.167136	−	0.0964959i
$356$	13.1962	−	13.1962i	0.699396	−	0.699396i
$357$		0			0
$358$	2.61335	+	0.700246i	0.138120	+	0.0370091i
$359$	−14.4587	−	14.4587i	−0.763101	−	0.763101i	0.213781	−	0.976882i	$-0.431422\pi$
$359$	−14.4587	−	14.4587i	−0.763101	−	0.763101i	−0.976882	+	0.213781i	$0.931422\pi$
$360$		0			0
$361$	−37.1398	−	21.4427i	−1.95473	−	1.12856i
$362$	−7.91329	+	2.12036i	−0.415913	+	0.111444i
$363$		0			0
$364$	−1.45593	+	7.76014i	−0.0763117	+	0.406742i
$365$			24.8053i			1.29837i
$366$		0			0
$367$	11.8449	−	20.5160i	0.618300	−	1.07093i	−0.371496	−	0.928434i	$-0.621155\pi$
$367$	11.8449	−	20.5160i	0.618300	−	1.07093i	0.989796	−	0.142492i	$-0.0455116\pi$
$368$	−0.0389006	−	0.0673777i	−0.00202783	−	0.00351231i
$369$		0			0
$370$	−3.89752	+	14.5458i	−0.202623	+	0.756198i
$371$	3.06221	−	11.4283i	0.158982	−	0.593328i
$372$		0			0
$373$	0.993763	+	1.72125i	0.0514551	+	0.0891228i	0.890606	−	0.454776i	$-0.150281\pi$
$373$	0.993763	+	1.72125i	0.0514551	+	0.0891228i	−0.839151	+	0.543899i	$0.816947\pi$
$374$	1.43929	−	2.49293i	0.0744240	−	0.128906i
$375$		0			0
$376$		−	20.4854i		−	1.05645i
$377$	−24.0857	+	16.4757i	−1.24048	+	0.848542i
$378$		0			0
$379$	6.53547	−	1.75117i	0.335704	−	0.0899517i	−0.0870291	−	0.996206i	$-0.527737\pi$
$379$	6.53547	−	1.75117i	0.335704	−	0.0899517i	0.422733	+	0.906254i	$0.361071\pi$
$380$	−36.3036	−	20.9599i	−1.86233	−	1.07522i
$381$		0			0
$382$	−5.58120	−	5.58120i	−0.285559	−	0.285559i
$383$	2.75402	+	0.737937i	0.140724	+	0.0377068i	0.328493	−	0.944506i	$-0.393459\pi$
$383$	2.75402	+	0.737937i	0.140724	+	0.0377068i	−0.187770	+	0.982213i	$0.560126\pi$
$384$		0			0
$385$	−6.50133	+	6.50133i	−0.331339	+	0.331339i
$386$	0.984960	−	0.568667i	0.0501332	−	0.0289444i
$387$		0			0
$388$	−3.95248	−	14.7509i	−0.200657	−	0.748862i
$389$	33.4065			1.69377			0.846887	−	0.531772i	$-0.178474\pi$
$389$	33.4065			1.69377			0.846887	+	0.531772i	$0.178474\pi$
$390$		0			0
$391$	−0.311881			−0.0157725
$392$	−3.07628	−	11.4808i	−0.155376	−	0.579870i
$393$		0			0
$394$	12.2286	−	7.06017i	0.616067	−	0.355686i
$395$	0.968609	−	0.968609i	0.0487360	−	0.0487360i
$396$		0			0
$397$	−17.2479	−	4.62157i	−0.865650	−	0.231950i	−0.201444	−	0.979500i	$-0.564563\pi$
$397$	−17.2479	−	4.62157i	−0.865650	−	0.231950i	−0.664206	+	0.747550i	$0.731230\pi$
$398$	6.24555	+	6.24555i	0.313061	+	0.313061i
$399$		0			0
$400$	−5.38159	−	3.10706i	−0.269080	−	0.155353i
$401$	15.5864	−	4.17636i	0.778347	−	0.208557i	0.152291	−	0.988336i	$-0.451335\pi$
$401$	15.5864	−	4.17636i	0.778347	−	0.208557i	0.626056	+	0.779778i	$0.284668\pi$
$402$		0			0
$403$	−9.04287	+	3.17986i	−0.450458	+	0.158400i
$404$			11.9683i			0.595447i
$405$		0			0
$406$	−5.14196	+	8.90614i	−0.255191	+	0.442004i
$407$	−3.59598	−	6.22843i	−0.178246	−	0.308732i
$408$		0			0
$409$	−6.31725	+	23.5763i	−0.312368	+	1.16577i	0.614047	+	0.789269i	$0.289540\pi$
$409$	−6.31725	+	23.5763i	−0.312368	+	1.16577i	−0.926415	+	0.376504i	$0.877126\pi$
$410$	−3.31453	+	12.3700i	−0.163693	+	0.610910i
$411$		0			0
$412$	−3.95199	−	6.84505i	−0.194701	−	0.337232i
$413$	−0.271150	+	0.469646i	−0.0133424	+	0.0231098i
$414$		0			0
$415$			58.7306i			2.88297i
$416$	−13.7071	+	15.9776i	−0.672044	+	0.783364i
$417$		0			0
$418$	−8.91338	+	2.38833i	−0.435968	+	0.116817i
$419$	31.3143	+	18.0793i	1.52980	+	0.883231i	0.999370	+	0.0355041i	$0.0113037\pi$
$419$	31.3143	+	18.0793i	1.52980	+	0.883231i	0.530432	+	0.847727i	$0.322030\pi$
$420$		0			0
$421$	−5.23855	−	5.23855i	−0.255311	−	0.255311i	0.567833	−	0.823144i	$-0.307782\pi$
$421$	−5.23855	−	5.23855i	−0.255311	−	0.255311i	−0.823144	+	0.567833i	$0.807782\pi$
$422$	6.22110	+	1.66694i	0.302838	+	0.0811453i
$423$		0			0
$424$	13.9969	−	13.9969i	0.679751	−	0.679751i
$425$	−21.5732	+	12.4553i	−1.04645	+	0.604170i
$426$		0			0
$427$	−0.0995770	−	0.371626i	−0.00481887	−	0.0179843i
$428$	−6.94138			−0.335524
$429$		0			0
$430$	−35.2611			−1.70044
$431$	3.80867	+	14.2142i	0.183457	+	0.684672i	0.994956	+	0.100317i	$0.0319857\pi$
$431$	3.80867	+	14.2142i	0.183457	+	0.684672i	−0.811498	+	0.584355i	$0.801348\pi$
$432$		0			0
$433$	10.9100	−	6.29888i	0.524300	−	0.302705i	−0.214392	−	0.976748i	$-0.568777\pi$
$433$	10.9100	−	6.29888i	0.524300	−	0.302705i	0.738692	+	0.674043i	$0.235444\pi$
$434$	−2.38867	+	2.38867i	−0.114660	+	0.114660i
$435$		0			0
$436$	18.1264	+	4.85696i	0.868098	+	0.232606i
$437$	0.706959	+	0.706959i	0.0338184	+	0.0338184i
$438$		0			0
$439$	−20.9172	−	12.0765i	−0.998322	−	0.576382i	−0.0905707	−	0.995890i	$-0.528869\pi$
$439$	−20.9172	−	12.0765i	−0.998322	−	0.576382i	−0.907751	+	0.419508i	$0.862202\pi$
$440$	−14.8583	+	3.98128i	−0.708344	+	0.189800i
$441$		0			0
$442$	2.33156	+	6.63046i	0.110901	+	0.315379i
$443$		−	18.8052i		−	0.893463i	−0.894668	−	0.446731i	$-0.852588\pi$
$443$		−	18.8052i		−	0.893463i	0.894668	−	0.446731i	$-0.147412\pi$
$444$		0			0
$445$	−26.5308	+	45.9527i	−1.25768	+	2.17837i
$446$	1.25258	+	2.16954i	0.0593115	+	0.102731i
$447$		0			0
$448$	−1.41324	+	5.27429i	−0.0667694	+	0.249187i
$449$	−5.23342	+	19.5314i	−0.246980	+	0.921743i	0.725397	+	0.688330i	$0.241656\pi$
$449$	−5.23342	+	19.5314i	−0.246980	+	0.921743i	−0.972378	+	0.233413i	$0.925011\pi$
$450$		0			0
$451$	−3.05809	−	5.29677i	−0.144000	−	0.249415i
$452$	−9.33996	+	16.1773i	−0.439315	+	0.760915i
$453$		0			0
$454$		−	19.3760i		−	0.909360i
$455$	−1.71206	−	22.3837i	−0.0802628	−	1.04936i
$456$		0			0
$457$	29.2298	−	7.83210i	1.36731	−	0.366370i	0.500815	−	0.865554i	$-0.333034\pi$
$457$	29.2298	−	7.83210i	1.36731	−	0.366370i	0.866496	+	0.499184i	$0.166367\pi$
$458$	0.919979	+	0.531150i	0.0429878	+	0.0248190i
$459$		0			0
$460$	0.478878	+	0.478878i	0.0223278	+	0.0223278i
$461$	−17.7596	−	4.75867i	−0.827148	−	0.221634i	−0.179679	−	0.983725i	$-0.557506\pi$
$461$	−17.7596	−	4.75867i	−0.827148	−	0.221634i	−0.647469	+	0.762092i	$0.724172\pi$
$462$		0			0
$463$	−5.86314	+	5.86314i	−0.272483	+	0.272483i	−0.830099	−	0.557616i	$-0.811716\pi$
$463$	−5.86314	+	5.86314i	−0.272483	+	0.272483i	0.557616	+	0.830099i	$0.311716\pi$
$464$	4.29081	−	2.47730i	0.199196	−	0.115006i
$465$		0			0
$466$	−0.745517	−	2.78231i	−0.0345354	−	0.128888i
$467$	−25.8432			−1.19588			−0.597939	−	0.801541i	$-0.704014\pi$
$467$	−25.8432			−1.19588			−0.597939	+	0.801541i	$0.704014\pi$
$468$		0			0
$469$	−8.96207			−0.413830
$470$	6.12576	+	22.8617i	0.282560	+	1.05453i
$471$		0			0
$472$	−0.785742	+	0.453649i	−0.0361667	+	0.0208809i
$473$	11.9079	−	11.9079i	0.547527	−	0.547527i
$474$		0			0
$475$	77.1343	+	20.6681i	3.53916	+	0.948316i
$476$	−3.79987	−	3.79987i	−0.174167	−	0.174167i
$477$		0			0
$478$	−1.01499	−	0.586004i	−0.0464245	−	0.0268032i
$479$	−6.40241	+	1.71552i	−0.292534	+	0.0783841i	−0.402101	−	0.915595i	$-0.631720\pi$
$479$	−6.40241	+	1.71552i	−0.292534	+	0.0783841i	0.109568	+	0.993979i	$0.465053\pi$
$480$		0			0
$481$	17.2590	+	3.23809i	0.786945	+	0.147644i
$482$		−	5.19838i		−	0.236780i
$483$		0			0
$484$	−6.03687	+	10.4562i	−0.274403	+	0.475280i
$485$	21.7101	+	37.6029i	0.985803	+	1.70746i
$486$		0			0
$487$	−2.89650	+	10.8099i	−0.131253	+	0.489843i	−0.999985	−	0.00543914i	$-0.998269\pi$
$487$	−2.89650	+	10.8099i	−0.131253	+	0.489843i	0.868732	+	0.495282i	$0.164935\pi$
$488$	0.166597	−	0.621750i	0.00754151	−	0.0281453i
$489$		0			0
$490$	6.86625	+	11.8927i	0.310185	+	0.537257i
$491$	−14.1823	+	24.5645i	−0.640038	+	1.10858i	0.345386	+	0.938461i	$0.387748\pi$
$491$	−14.1823	+	24.5645i	−0.640038	+	1.10858i	−0.985424	+	0.170118i	$0.945585\pi$
$492$		0			0
$493$		−	19.8615i		−	0.894518i
$494$	9.74458	−	20.3147i	0.438429	−	0.914002i
$495$		0			0
$496$	1.57205	−	0.421228i	0.0705869	−	0.0189137i
$497$	−1.29410	−	0.747150i	−0.0580484	−	0.0335143i
$498$		0			0
$499$	−25.0922	−	25.0922i	−1.12328	−	1.12328i	−0.991245	−	0.132034i	$-0.957849\pi$
$499$	−25.0922	−	25.0922i	−1.12328	−	1.12328i	−0.132034	−	0.991245i	$-0.542151\pi$
$500$	26.5132	+	7.10418i	1.18571	+	0.317709i
$501$		0			0
$502$	13.8303	−	13.8303i	0.617276	−	0.617276i
$503$	11.1968	−	6.46448i	0.499241	−	0.288237i	−0.229159	−	0.973389i	$-0.573598\pi$
$503$	11.1968	−	6.46448i	0.499241	−	0.288237i	0.728400	+	0.685152i	$0.240264\pi$
$504$		0			0
$505$	−8.80739	−	32.8696i	−0.391924	−	1.46268i
$506$	0.149080			0.00662742
$507$		0			0
$508$	20.4325			0.906544
$509$	5.21410	+	19.4593i	0.231111	+	0.862517i	0.979864	+	0.199668i	$0.0639863\pi$
$509$	5.21410	+	19.4593i	0.231111	+	0.862517i	−0.748753	+	0.662849i	$0.769347\pi$
$510$		0			0
$511$	8.82797	−	5.09683i	0.390527	−	0.225471i
$512$	4.84423	−	4.84423i	0.214087	−	0.214087i
$513$		0			0
$514$	−9.57446	−	2.56547i	−0.422311	−	0.113158i
$515$	15.8909	+	15.8909i	0.700236	+	0.700236i
$516$		0			0
$517$	−9.78926	−	5.65183i	−0.430531	−	0.248567i
$518$	5.97752	−	1.60167i	0.262637	−	0.0703734i
$519$		0			0
$520$	16.2439	−	33.8641i	0.712343	−	1.48504i
$521$			2.32517i			0.101868i	0.998702	+	0.0509338i	$0.0162197\pi$
$521$			2.32517i			0.101868i	−0.998702	+	0.0509338i	$0.983780\pi$
$522$		0			0
$523$	4.10483	−	7.10977i	0.179492	−	0.310888i	−0.762215	−	0.647324i	$-0.775888\pi$
$523$	4.10483	−	7.10977i	0.179492	−	0.310888i	0.941706	+	0.336436i	$0.109221\pi$
$524$	1.51904	+	2.63106i	0.0663597	+	0.114938i
$525$		0			0
$526$	−4.61508	+	17.2237i	−0.201227	+	0.750989i
$527$	1.68858	−	6.30186i	0.0735556	−	0.274513i
$528$		0			0
$529$	11.4919	+	19.9046i	0.499649	+	0.865417i
$530$	−11.4350	+	19.8061i	−0.496706	+	0.860320i
$531$		0			0
$532$			17.2268i			0.746875i
$533$	14.6774	+	2.75373i	0.635749	+	0.119277i
$534$		0			0
$535$	19.0637	−	5.10809i	0.824194	−	0.220842i
$536$	−12.9852	−	7.49700i	−0.560875	−	0.323821i
$537$		0			0
$538$	13.4641	+	13.4641i	0.580479	+	0.580479i
$539$	−6.33503	−	1.69747i	−0.272869	−	0.0731150i
$540$		0			0
$541$	20.7070	−	20.7070i	0.890265	−	0.890265i	−0.104283	−	0.994548i	$-0.533255\pi$
$541$	20.7070	−	20.7070i	0.890265	−	0.890265i	0.994548	+	0.104283i	$0.0332547\pi$
$542$	1.89804	−	1.09584i	0.0815280	−	0.0470702i
$543$		0			0
$544$	−3.70836	−	13.8398i	−0.158995	−	0.593376i
$545$	−53.3562			−2.28553
$546$		0			0
$547$	−30.8903			−1.32078			−0.660388	−	0.750925i	$-0.729608\pi$
$547$	−30.8903			−1.32078			−0.660388	+	0.750925i	$0.729608\pi$
$548$	6.85186	+	25.5715i	0.292697	+	1.09236i
$549$		0			0
$550$	10.3120	−	5.95366i	0.439707	−	0.253865i
$551$	−45.0212	+	45.0212i	−1.91797	+	1.91797i
$552$		0			0
$553$	−0.543741	−	0.145695i	−0.0231222	−	0.00619559i
$554$	−9.83780	−	9.83780i	−0.417968	−	0.417968i
$555$		0			0
$556$	−10.3280	−	5.96285i	−0.438003	−	0.252881i
$557$	−4.49583	+	1.20465i	−0.190494	+	0.0510428i	−0.352805	−	0.935697i	$-0.614772\pi$
$557$	−4.49583	+	1.20465i	−0.190494	+	0.0510428i	0.162310	+	0.986740i	$0.448105\pi$
$558$		0			0
$559$	3.13584	+	40.9983i	0.132632	+	1.73404i
$560$			3.81151i			0.161066i
$561$		0			0
$562$	−8.33717	+	14.4404i	−0.351682	+	0.609132i
$563$	21.6843	+	37.5583i	0.913885	+	1.58289i	0.808526	+	0.588460i	$0.200266\pi$
$563$	21.6843	+	37.5583i	0.913885	+	1.58289i	0.105359	+	0.994434i	$0.466401\pi$
$564$		0			0
$565$	13.7464	−	51.3022i	0.578314	−	2.15830i
$566$	1.33037	−	4.96500i	0.0559195	−	0.208695i
$567$		0			0
$568$	−1.25002	−	2.16510i	−0.0524497	−	0.0908456i
$569$	18.6114	−	32.2359i	0.780231	−	1.35140i	−0.151577	−	0.988445i	$-0.548435\pi$
$569$	18.6114	−	32.2359i	0.780231	−	1.35140i	0.931807	−	0.362953i	$-0.118232\pi$
$570$		0			0
$571$			18.1841i			0.760980i	0.924785	+	0.380490i	$0.124245\pi$
$571$			18.1841i			0.760980i	−0.924785	+	0.380490i	$0.875755\pi$
$572$	2.41798	+	6.87622i	0.101101	+	0.287509i
$573$		0			0
$574$	5.08340	−	1.36209i	0.212177	−	0.0568526i
$575$	−1.11726	−	0.645052i	−0.0465931	−	0.0269005i
$576$		0			0
$577$	16.4668	+	16.4668i	0.685523	+	0.685523i	0.961239	−	0.275716i	$-0.0889149\pi$
$577$	16.4668	+	16.4668i	0.685523	+	0.685523i	−0.275716	+	0.961239i	$0.588915\pi$
$578$	8.42320	+	2.25699i	0.350359	+	0.0938784i
$579$		0			0
$580$	−30.4964	+	30.4964i	−1.26629	+	1.26629i
$581$	20.9016	−	12.0676i	0.867146	−	0.500647i
$582$		0			0
$583$	−2.82695	−	10.5503i	−0.117080	−	0.436950i
$584$	17.0545			0.705721
$585$		0			0
$586$	4.31332			0.178182
$587$	−0.333222	−	1.24360i	−0.0137536	−	0.0513290i	0.958708	−	0.284392i	$-0.0917918\pi$
$587$	−0.333222	−	1.24360i	−0.0137536	−	0.0513290i	−0.972462	+	0.233063i	$0.925125\pi$
$588$		0			0
$589$	−18.1124	+	10.4572i	−0.746307	+	0.430881i
$590$	0.741232	−	0.741232i	0.0305160	−	0.0305160i
$591$		0			0
$592$	−2.87986	−	0.771656i	−0.118362	−	0.0317149i
$593$	7.64836	+	7.64836i	0.314080	+	0.314080i	0.846488	−	0.532408i	$-0.178713\pi$
$593$	7.64836	+	7.64836i	0.314080	+	0.314080i	−0.532408	+	0.846488i	$0.678713\pi$
$594$		0			0
$595$	13.2322	+	7.63961i	0.542467	+	0.313193i
$596$	20.7094	−	5.54908i	0.848292	−	0.227299i
$597$		0			0
$598$	−0.237008	+	0.276267i	−0.00969197	+	0.0112974i
$599$		−	44.2262i		−	1.80704i	−0.428551	−	0.903518i	$-0.640976\pi$
$599$		−	44.2262i		−	1.80704i	0.428551	−	0.903518i	$-0.359024\pi$
$600$		0			0
$601$	12.6644	−	21.9353i	0.516590	−	0.894761i	−0.483224	−	0.875497i	$-0.660534\pi$
$601$	12.6644	−	21.9353i	0.516590	−	0.894761i	0.999814	−	0.0192641i	$-0.00613233\pi$
$602$	7.24520	+	12.5491i	0.295292	+	0.511462i
$603$		0			0
$604$	−7.12357	+	26.5855i	−0.289854	+	1.08175i
$605$	8.88495	−	33.1591i	0.361225	−	1.34811i
$606$		0			0
$607$	−2.46383	−	4.26749i	−0.100004	−	0.173212i	0.811682	−	0.584099i	$-0.198552\pi$
$607$	−2.46383	−	4.26749i	−0.100004	−	0.173212i	−0.911686	+	0.410888i	$0.865219\pi$
$608$	−22.9655	+	39.7774i	−0.931373	+	1.61319i
$609$		0			0
$610$			0.743690i			0.0301111i
$611$	26.0366	−	9.15560i	1.05333	−	0.370396i
$612$		0			0
$613$	−10.4249	+	2.79334i	−0.421057	+	0.112822i	−0.463125	−	0.886293i	$-0.653272\pi$
$613$	−10.4249	+	2.79334i	−0.421057	+	0.112822i	0.0420682	+	0.999115i	$0.486605\pi$
$614$	−7.07820	−	4.08660i	−0.285653	−	0.164922i
$615$		0			0
$616$	4.46989	+	4.46989i	0.180097	+	0.180097i
$617$	−33.9359	−	9.09310i	−1.36621	−	0.366074i	−0.500116	−	0.865958i	$-0.666709\pi$
$617$	−33.9359	−	9.09310i	−1.36621	−	0.366074i	−0.866092	+	0.499884i	$0.833376\pi$
$618$		0			0
$619$	−27.2332	+	27.2332i	−1.09459	+	1.09459i	−0.0995626	+	0.995031i	$0.531744\pi$
$619$	−27.2332	+	27.2332i	−1.09459	+	1.09459i	−0.995031	+	0.0995626i	$0.968256\pi$
$620$	−12.2689	+	7.08346i	−0.492732	+	0.284479i
$621$		0			0
$622$	−0.904983	−	3.37744i	−0.0362865	−	0.135423i
$623$	21.8055			0.873617
$624$		0			0
$625$	−27.2881			−1.09152
$626$	0.720817	+	2.69013i	0.0288097	+	0.107519i
$627$		0			0
$628$	12.3535	−	7.13232i	0.492960	−	0.284611i
$629$	−8.45116	+	8.45116i	−0.336970	+	0.336970i
$630$		0			0
$631$	−35.3657	−	9.47620i	−1.40788	−	0.377242i	−0.526715	−	0.850042i	$-0.676577\pi$
$631$	−35.3657	−	9.47620i	−1.40788	−	0.377242i	−0.881170	+	0.472800i	$0.843243\pi$
$632$	−0.665952	−	0.665952i	−0.0264902	−	0.0264902i
$633$		0			0
$634$	−8.55009	−	4.93640i	−0.339567	−	0.196049i
$635$	−56.1154	+	15.0361i	−2.22687	+	0.596688i
$636$		0			0
$637$	13.2171	−	9.04107i	0.523679	−	0.358220i
$638$			9.49387i			0.375866i
$639$		0			0
$640$	−17.4491	+	30.2227i	−0.689737	+	1.19466i
$641$	−18.7159	−	32.4169i	−0.739234	−	1.28039i	−0.952840	−	0.303472i	$-0.901854\pi$
$641$	−18.7159	−	32.4169i	−0.739234	−	1.28039i	0.213606	−	0.976920i	$-0.431479\pi$
$642$		0			0
$643$	−1.10595	+	4.12746i	−0.0436144	+	0.162771i	−0.984298	−	0.176513i	$-0.943518\pi$
$643$	−1.10595	+	4.12746i	−0.0436144	+	0.162771i	0.940684	+	0.339284i	$0.110185\pi$
$644$	0.0720314	−	0.268825i	0.00283843	−	0.0105932i
$645$		0			0
$646$	7.66747	+	13.2804i	0.301673	+	0.522512i
$647$	19.9930	−	34.6289i	0.786007	−	1.36140i	−0.142388	−	0.989811i	$-0.545478\pi$
$647$	19.9930	−	34.6289i	0.786007	−	1.36140i	0.928396	−	0.371593i	$-0.121188\pi$
$648$		0			0
$649$			0.500639i			0.0196518i
$650$	−5.36112	+	28.5748i	−0.210280	+	1.12080i
$651$		0			0
$652$	−22.0782	+	5.91585i	−0.864651	+	0.231682i
$653$	11.7612	+	6.79035i	0.460253	+	0.265727i	0.712151	−	0.702027i	$-0.247721\pi$
$653$	11.7612	+	6.79035i	0.460253	+	0.265727i	−0.251898	+	0.967754i	$0.581055\pi$
$654$		0			0
$655$	−6.10804	−	6.10804i	−0.238661	−	0.238661i
$656$	−2.44909	−	0.656231i	−0.0956208	−	0.0256215i
$657$		0			0
$658$	6.87756	−	6.87756i	0.268115	−	0.268115i
$659$	−28.8666	+	16.6661i	−1.12448	+	0.649220i	−0.942541	−	0.334089i	$-0.891571\pi$
$659$	−28.8666	+	16.6661i	−1.12448	+	0.649220i	−0.181941	+	0.983309i	$0.558238\pi$
$660$		0			0
$661$	2.02088	+	7.54201i	0.0786029	+	0.293350i	0.994026	−	0.109143i	$-0.0348105\pi$
$661$	2.02088	+	7.54201i	0.0786029	+	0.293350i	−0.915423	+	0.402493i	$0.868144\pi$
$662$	−13.5653			−0.527230
$663$		0			0
$664$	40.3793			1.56702
$665$	−12.6770	−	47.3113i	−0.491594	−	1.83465i
$666$		0			0
$667$	0.890809	−	0.514309i	0.0344923	−	0.0199141i
$668$	−2.29197	+	2.29197i	−0.0886789	+	0.0886789i
$669$		0			0
$670$	16.7333	+	4.48367i	0.646463	+	0.173219i
$671$	−0.251149	−	0.251149i	−0.00969551	−	0.00969551i
$672$		0			0
$673$	−22.8114	−	13.1702i	−0.879316	−	0.507673i	−0.00888322	−	0.999961i	$-0.502828\pi$
$673$	−22.8114	−	13.1702i	−0.879316	−	0.507673i	−0.870433	+	0.492287i	$0.836161\pi$
$674$	14.9924	−	4.01719i	0.577484	−	0.154736i
$675$		0			0
$676$	−16.5867	−	6.45097i	−0.637950	−	0.248114i
$677$			5.45329i			0.209587i	0.994494	+	0.104793i	$0.0334181\pi$
$677$			5.45329i			0.209587i	−0.994494	+	0.104793i	$0.966582\pi$
$678$		0			0
$679$	8.92167	−	15.4528i	0.342382	−	0.593023i
$680$	12.7815	+	22.1381i	0.490146	+	0.848959i
$681$		0			0
$682$	−0.807145	+	3.01231i	−0.0309072	+	0.115347i
$683$	−0.462889	+	1.72753i	−0.0177120	+	0.0661019i	−0.974216	−	0.225617i	$-0.927560\pi$
$683$	−0.462889	+	1.72753i	−0.0177120	+	0.0661019i	0.956504	+	0.291718i	$0.0942270\pi$
$684$		0			0
$685$	−37.6356	−	65.1868i	−1.43798	−	2.49066i
$686$	7.26888	−	12.5901i	0.277527	−	0.480691i
$687$		0			0
$688$		−	6.98121i		−	0.266156i
$689$	24.0456	+	11.5342i	0.916063	+	0.439418i
$690$		0			0
$691$	3.03133	−	0.812242i	0.115317	−	0.0308991i	−0.200699	−	0.979653i	$-0.564321\pi$
$691$	3.03133	−	0.812242i	0.115317	−	0.0308991i	0.316016	+	0.948754i	$0.397655\pi$
$692$	11.5643	+	6.67666i	0.439609	+	0.253808i
$693$		0			0
$694$	−9.44331	−	9.44331i	−0.358463	−	0.358463i
$695$	32.7525	+	8.77601i	1.24237	+	0.332893i
$696$		0			0
$697$	−7.18702	+	7.18702i	−0.272228	+	0.272228i
$698$	2.39391	−	1.38212i	0.0906109	−	0.0523142i
$699$		0			0
$700$	−5.75328	−	21.4715i	−0.217454	−	0.811548i
$701$	−23.3688			−0.882629			−0.441315	−	0.897352i	$-0.645488\pi$
$701$	−23.3688			−0.882629			−0.441315	+	0.897352i	$0.645488\pi$
$702$		0			0
$703$	38.3134			1.44502
$704$	1.30467	+	4.86910i	0.0491716	+	0.183511i
$705$		0			0
$706$	12.4512	−	7.18868i	0.468606	−	0.270550i
$707$	−9.88829	+	9.88829i	−0.371887	+	0.371887i
$708$		0			0
$709$	−6.62430	−	1.77498i	−0.248781	−	0.0666606i	0.132274	−	0.991213i	$-0.457772\pi$
$709$	−6.62430	−	1.77498i	−0.248781	−	0.0666606i	−0.381054	+	0.924553i	$0.624439\pi$
$710$	2.04245	+	2.04245i	0.0766519	+	0.0766519i
$711$		0			0
$712$	31.5940	+	18.2408i	1.18404	+	0.683604i
$713$	0.326370	−	0.0874505i	0.0122226	−	0.00327505i
$714$		0			0
$715$	−11.7008	−	17.1054i	−0.437586	−	0.639704i
$716$		−	4.66277i		−	0.174256i
$717$		0			0
$718$	8.12135	−	14.0666i	0.303086	−	0.524961i
$719$	2.72338	+	4.71703i	0.101565	+	0.175916i	0.912330	−	0.409457i	$-0.134282\pi$
$719$	2.72338	+	4.71703i	0.101565	+	0.175916i	−0.810765	+	0.585372i	$0.800948\pi$
$720$		0			0
$721$	2.39026	−	8.92056i	0.0890178	−	0.332219i
$722$	8.81697	−	32.9054i	0.328134	−	1.22461i
$723$		0			0
$724$	7.05949	+	12.2274i	0.262364	+	0.454427i
$725$	41.0788	−	71.1506i	1.52563	−	2.64247i
$726$		0			0
$727$			18.8286i			0.698316i	0.937064	+	0.349158i	$0.113532\pi$
$727$			18.8286i			0.698316i	−0.937064	+	0.349158i	$0.886468\pi$
$728$	−15.3896	+	1.17710i	−0.570375	+	0.0436263i
$729$		0			0
$730$	−19.0328	+	5.09983i	−0.704436	+	0.188753i
$731$	−24.2362	−	13.9928i	−0.896409	−	0.517542i
$732$		0			0
$733$	13.0612	+	13.0612i	0.482427	+	0.482427i	0.905906	−	0.423479i	$-0.139191\pi$
$733$	13.0612	+	13.0612i	0.482427	+	0.482427i	−0.423479	+	0.905906i	$0.639191\pi$
$734$	18.1769	+	4.87049i	0.670922	+	0.179773i
$735$		0			0
$736$	0.524701	−	0.524701i	0.0193407	−	0.0193407i
$737$	−7.16512	+	4.13678i	−0.263931	+	0.152380i
$738$		0			0
$739$	6.11762	+	22.8313i	0.225040	+	0.839862i	0.982388	+	0.186851i	$0.0598280\pi$
$739$	6.11762	+	22.8313i	0.225040	+	0.839862i	−0.757348	+	0.653012i	$0.773505\pi$
$740$	25.9527			0.954039
$741$		0			0
$742$	9.39837			0.345025
$743$	−5.89718	−	22.0086i	−0.216347	−	0.807417i	−0.985688	−	0.168579i	$-0.946082\pi$
$743$	−5.89718	−	22.0086i	−0.216347	−	0.807417i	0.769342	−	0.638838i	$-0.220584\pi$
$744$		0			0
$745$	−52.7925	+	30.4798i	−1.93417	+	1.11669i
$746$	−1.11638	+	1.11638i	−0.0408736	+	0.0408736i
$747$		0			0
$748$	−4.79195	−	1.28400i	−0.175211	−	0.0469476i
$749$	−5.73499	−	5.73499i	−0.209552	−	0.209552i
$750$		0			0
$751$	22.7803	+	13.1522i	0.831266	+	0.479931i	0.854286	−	0.519804i	$-0.173995\pi$
$751$	22.7803	+	13.1522i	0.831266	+	0.479931i	−0.0230202	+	0.999735i	$0.507328\pi$
$752$	−4.52630	+	1.21282i	−0.165057	+	0.0442269i
$753$		0			0
$754$	−17.5935	−	15.0934i	−0.640716	−	0.549668i
$755$		−	78.2562i		−	2.84803i
$756$		0			0
$757$	5.61207	−	9.72038i	0.203974	−	0.353293i	−0.745831	−	0.666135i	$-0.767948\pi$
$757$	5.61207	−	9.72038i	0.203974	−	0.353293i	0.949805	+	0.312842i	$0.101281\pi$
$758$	2.68731	+	4.65455i	0.0976073	+	0.169061i
$759$		0			0
$760$	21.2093	−	79.1542i	0.769342	−	2.87123i
$761$	2.36137	−	8.81276i	0.0855997	−	0.319462i	−0.909827	−	0.414987i	$-0.863786\pi$
$761$	2.36137	−	8.81276i	0.0855997	−	0.319462i	0.995427	+	0.0955245i	$0.0304528\pi$
$762$		0			0
$763$	10.9633	+	18.9889i	0.396897	+	0.687446i
$764$	−6.80146	+	11.7805i	−0.246068	+	0.426202i
$765$		0			0
$766$			2.26484i			0.0818319i
$767$	−0.927754	−	0.795916i	−0.0334993	−	0.0287389i
$768$		0			0
$769$	49.2388	−	13.1935i	1.77560	−	0.475770i	0.785828	−	0.618445i	$-0.212237\pi$
$769$	49.2388	−	13.1935i	1.77560	−	0.475770i	0.989770	+	0.142675i	$0.0455703\pi$
$770$	−6.32502	−	3.65175i	−0.227938	−	0.131600i
$771$		0			0
$772$	−1.38600	−	1.38600i	−0.0498832	−	0.0498832i
$773$	−15.3153	−	4.10372i	−0.550852	−	0.147600i	−0.0273518	−	0.999626i	$-0.508707\pi$
$773$	−15.3153	−	4.10372i	−0.550852	−	0.147600i	−0.523500	+	0.852025i	$0.675374\pi$
$774$		0			0
$775$	19.0829	−	19.0829i	0.685480	−	0.685480i
$776$	25.8533	−	14.9264i	0.928079	−	0.535827i
$777$		0			0
$778$	6.86817	+	25.6324i	0.246236	+	0.918964i
$779$	32.5825			1.16739
$780$		0			0
$781$	−1.37950			−0.0493625
$782$	−0.0641209	−	0.239303i	−0.00229296	−	0.00855744i
$783$		0			0
$784$	−2.35459	+	1.35942i	−0.0840925	+	0.0485508i
$785$	−28.6789	+	28.6789i	−1.02359	+	1.02359i
$786$		0			0
$787$	−28.9551	−	7.75850i	−1.03214	−	0.276561i	−0.297286	−	0.954788i	$-0.596082\pi$
$787$	−28.9551	−	7.75850i	−1.03214	−	0.276561i	−0.734852	+	0.678228i	$0.762748\pi$
$788$	−17.2076	−	17.2076i	−0.612995	−	0.612995i
$789$		0			0
$790$	0.942342	+	0.544061i	0.0335270	+	0.0193568i
$791$	−21.0824	+	5.64902i	−0.749605	+	0.200856i
$792$		0			0
$793$	0.864692	−	0.0661378i	0.0307061	−	0.00234862i
$794$		−	14.1843i		−	0.503382i
$795$		0			0
$796$	7.61106	−	13.1827i	0.269767	−	0.467250i
$797$	1.19542	+	2.07053i	0.0423439	+	0.0733418i	0.886421	−	0.462881i	$-0.153184\pi$
$797$	1.19542	+	2.07053i	0.0423439	+	0.0733418i	−0.844077	+	0.536222i	$0.819851\pi$
$798$		0			0
$799$	−4.86182	+	18.1446i	−0.171999	+	0.641909i
$800$	15.3397	−	57.2486i	0.542341	−	2.02404i
$801$		0			0
$802$	6.40894	+	11.1006i	0.226307	+	0.391976i
$803$	4.70527	−	8.14977i	0.166045	−	0.287599i
$804$		0			0
$805$			0.791302i			0.0278897i
$806$	−4.29903	−	6.28472i	−0.151427	−	0.221370i
$807$		0			0
$808$	−22.5990	+	6.05538i	−0.795030	+	0.213028i
$809$	−27.2960	−	15.7594i	−0.959678	−	0.554070i	−0.0636037	−	0.997975i	$-0.520259\pi$
$809$	−27.2960	−	15.7594i	−0.959678	−	0.554070i	−0.896074	+	0.443905i	$0.853593\pi$
$810$		0			0
$811$	−17.2928	−	17.2928i	−0.607232	−	0.607232i	0.334990	−	0.942222i	$-0.391267\pi$
$811$	−17.2928	−	17.2928i	−0.607232	−	0.607232i	−0.942222	+	0.334990i	$0.891267\pi$
$812$	17.1195	+	4.58717i	0.600778	+	0.160978i
$813$		0			0
$814$	4.03968	−	4.03968i	0.141591	−	0.141591i
$815$	56.2818	−	32.4943i	1.97147	−	1.13823i
$816$		0			0
$817$	23.2194	+	86.6559i	0.812343	+	3.03171i
$818$	−19.3886			−0.677906
$819$		0			0
$820$	22.0706			0.770740
$821$	1.10028	+	4.10629i	0.0383999	+	0.143310i	0.982464	−	0.186451i	$-0.0596985\pi$
$821$	1.10028	+	4.10629i	0.0383999	+	0.143310i	−0.944064	+	0.329761i	$0.893032\pi$
$822$		0			0
$823$	−28.7990	+	16.6271i	−1.00387	+	0.579585i	−0.909391	−	0.415942i	$-0.863452\pi$
$823$	−28.7990	+	16.6271i	−1.00387	+	0.579585i	−0.0944794	+	0.995527i	$0.530119\pi$
$824$	10.9255	−	10.9255i	0.380609	−	0.380609i
$825$		0			0
$826$	−0.416100	−	0.111494i	−0.0144780	−	0.00387936i
$827$	−17.6567	−	17.6567i	−0.613984	−	0.613984i	0.329997	−	0.943982i	$-0.392952\pi$
$827$	−17.6567	−	17.6567i	−0.613984	−	0.613984i	−0.943982	+	0.329997i	$0.892952\pi$
$828$		0			0
$829$	5.19452	+	2.99906i	0.180413	+	0.104162i	0.587487	−	0.809234i	$-0.300117\pi$
$829$	5.19452	+	2.99906i	0.180413	+	0.104162i	−0.407074	+	0.913395i	$0.633451\pi$
$830$	−45.0633	+	12.0747i	−1.56417	+	0.419118i
$831$		0			0
$832$	−11.0973	−	5.32315i	−0.384729	−	0.184547i
$833$			10.8990i			0.377629i
$834$		0			0
$835$	4.60798	−	7.98126i	0.159466	−	0.276203i
$836$	7.95167	+	13.7727i	0.275014	+	0.476339i
$837$		0			0
$838$	−7.43399	+	27.7440i	−0.256803	+	0.958401i
$839$	−3.75035	+	13.9965i	−0.129477	+	0.483213i	−0.999960	−	0.00898522i	$-0.997140\pi$
$839$	−3.75035	+	13.9965i	−0.129477	+	0.483213i	0.870483	+	0.492198i	$0.163807\pi$
$840$		0			0
$841$	18.2527	+	31.6146i	0.629403	+	1.09016i
$842$	2.94246	−	5.09649i	0.101404	−	0.175637i
$843$		0			0
$844$		−	11.0997i		−	0.382069i
$845$	50.3006	+	5.51082i	1.73039	+	0.189578i
$846$		0			0
$847$	−13.6266	+	3.65124i	−0.468216	+	0.125458i
$848$	−3.92133	−	2.26398i	−0.134659	−	0.0777454i
$849$		0			0
$850$	−13.9921	−	13.9921i	−0.479925	−	0.479925i
$851$	−0.597883	−	0.160202i	−0.0204952	−	0.00549167i
$852$		0			0
$853$	−6.04887	+	6.04887i	−0.207110	+	0.207110i	−0.803038	−	0.595928i	$-0.796784\pi$
$853$	−6.04887	+	6.04887i	−0.207110	+	0.207110i	0.595928	+	0.803038i	$0.296784\pi$
$854$	0.264672	−	0.152808i	0.00905688	−	0.00522899i
$855$		0			0
$856$	−3.51199	−	13.1069i	−0.120037	−	0.447985i
$857$	−26.6863			−0.911588			−0.455794	−	0.890085i	$-0.650645\pi$
$857$	−26.6863			−0.911588			−0.455794	+	0.890085i	$0.650645\pi$
$858$		0			0
$859$	−14.3033			−0.488022			−0.244011	−	0.969773i	$-0.578463\pi$
$859$	−14.3033			−0.488022			−0.244011	+	0.969773i	$0.578463\pi$
$860$	15.7283	+	58.6988i	0.536330	+	2.00161i
$861$		0			0
$862$	−10.1233	+	5.84469i	−0.344801	+	0.199071i
$863$	−1.53000	+	1.53000i	−0.0520819	+	0.0520819i	−0.732668	−	0.680586i	$-0.761725\pi$
$863$	−1.53000	+	1.53000i	−0.0520819	+	0.0520819i	0.680586	+	0.732668i	$0.261725\pi$
$864$		0			0
$865$	−36.6733	−	9.82658i	−1.24693	−	0.334114i
$866$	7.07608	+	7.07608i	0.240455	+	0.240455i
$867$		0			0
$868$	5.04187	+	2.91092i	0.171132	+	0.0988032i
$869$	−0.501969	+	0.134502i	−0.0170281	+	0.00456267i
$870$		0			0
$871$	3.72507	−	19.8546i	0.126219	−	0.672749i
$872$			36.6842i			1.24228i
$873$		0			0
$874$	−0.397094	+	0.687787i	−0.0134319	+	0.0232648i
$875$	16.0358	+	27.7748i	0.542108	+	0.938959i
$876$		0			0
$877$	3.83843	−	14.3252i	0.129614	−	0.483728i	−0.870348	−	0.492438i	$-0.836106\pi$
$877$	3.83843	−	14.3252i	0.129614	−	0.483728i	0.999962	+	0.00871020i	$0.00277258\pi$
$878$	4.96573	−	18.5323i	0.167585	−	0.625436i
$879$		0			0
$880$	1.75935	+	3.04728i	0.0593076	+	0.102724i
$881$	−16.0129	+	27.7351i	−0.539488	+	0.934420i	0.459444	+	0.888207i	$0.348049\pi$
$881$	−16.0129	+	27.7351i	−0.539488	+	0.934420i	−0.998932	+	0.0462131i	$0.985285\pi$
$882$		0			0
$883$			3.05381i			0.102769i	0.998679	+	0.0513844i	$0.0163634\pi$
$883$			3.05381i			0.102769i	−0.998679	+	0.0513844i	$0.983637\pi$
$884$	9.99767	−	6.83885i	0.336258	−	0.230015i
$885$		0			0
$886$	14.4290	−	3.86624i	0.484752	−	0.129889i
$887$	−7.75681	−	4.47840i	−0.260448	−	0.150370i	0.364091	−	0.931363i	$-0.381380\pi$
$887$	−7.75681	−	4.47840i	−0.260448	−	0.150370i	−0.624539	+	0.780994i	$0.714713\pi$
$888$		0			0
$889$	16.8814	+	16.8814i	0.566184	+	0.566184i
$890$	−40.7135	−	10.9091i	−1.36472	−	0.365675i
$891$		0			0
$892$	3.05289	−	3.05289i	0.102218	−	0.102218i
$893$	52.1499	−	30.1088i	1.74513	−	1.00755i
$894$		0			0
$895$	3.43129	+	12.8057i	0.114695	+	0.428049i
$896$	14.3413			0.479109
$897$		0			0
$898$	−16.0621			−0.536001
$899$	5.56911	+	20.7842i	0.185740	+	0.693192i
$900$		0			0
$901$	−15.7194	+	9.07562i	−0.523690	+	0.302353i
$902$	3.43542	−	3.43542i	0.114387	−	0.114387i
$903$		0			0
$904$	−35.2720	−	9.45111i	−1.17313	−	0.314339i
$905$	−28.3861	−	28.3861i	−0.943584	−	0.943584i
$906$		0			0
$907$	31.7841	+	18.3506i	1.05537	+	0.609320i	0.924149	−	0.382033i	$-0.124776\pi$
$907$	31.7841	+	18.3506i	1.05537	+	0.609320i	0.131224	+	0.991353i	$0.458109\pi$
$908$	−32.2550	+	8.64271i	−1.07042	+	0.286818i
$909$		0			0
$910$	16.8227	−	5.91560i	0.557668	−	0.196100i
$911$			40.1992i			1.33186i	0.746014	+	0.665930i	$0.231965\pi$
$911$			40.1992i			1.33186i	−0.746014	+	0.665930i	$0.768035\pi$
$912$		0			0
$913$	11.1405	−	19.2959i	0.368696	−	0.638601i
$914$	12.0189	+	20.8174i	0.397551	+	0.688579i
$915$		0			0
$916$	0.473842	−	1.76840i	0.0156562	−	0.0584296i
$917$	−0.918752	+	3.42883i	−0.0303399	+	0.113230i
$918$		0			0
$919$	4.46542	+	7.73433i	0.147301	+	0.255132i	0.930229	−	0.366980i	$-0.119608\pi$
$919$	4.46542	+	7.73433i	0.147301	+	0.255132i	−0.782928	+	0.622112i	$0.786275\pi$
$920$	−0.661945	+	1.14652i	−0.0218237	+	0.0377997i
$921$		0			0
$922$		−	14.6051i		−	0.480993i
$923$	2.19313	−	2.55641i	0.0721878	−	0.0841453i
$924$		0			0
$925$	−47.7541	+	12.7957i	−1.57015	+	0.420719i
$926$	−5.70414	−	3.29328i	−0.187450	−	0.108224i
$927$		0			0
$928$	33.4145	+	33.4145i	1.09689	+	1.09689i
$929$	−34.3628	−	9.20749i	−1.12741	−	0.302088i	−0.353530	−	0.935423i	$-0.615019\pi$
$929$	−34.3628	−	9.20749i	−1.12741	−	0.302088i	−0.773877	+	0.633335i	$0.781685\pi$
$930$		0			0
$931$	24.7055	−	24.7055i	0.809689	−	0.809689i
$932$	−4.29914	+	2.48211i	−0.140823	+	0.0813043i
$933$		0			0
$934$	−5.31320	−	19.8291i	−0.173853	−	0.648829i
$935$	14.1054			0.461296
$936$		0			0
$937$	50.6097			1.65335			0.826673	−	0.562682i	$-0.190231\pi$
$937$	50.6097			1.65335			0.826673	+	0.562682i	$0.190231\pi$
$938$	−1.84255	−	6.87648i	−0.0601613	−	0.224525i
$939$		0			0
$940$	35.3252	−	20.3950i	1.15218	−	0.665212i
$941$	−9.82184	+	9.82184i	−0.320183	+	0.320183i	−0.848837	−	0.528654i	$-0.822697\pi$
$941$	−9.82184	+	9.82184i	−0.320183	+	0.320183i	0.528654	+	0.848837i	$0.322697\pi$
$942$		0			0
$943$	−0.508451	−	0.136239i	−0.0165574	−	0.00443655i
$944$	0.146754	+	0.146754i	0.00477643	+	0.00477643i
$945$		0			0
$946$	11.5850	+	6.68860i	0.376661	+	0.217465i
$947$	−11.4112	+	3.05763i	−0.370815	+	0.0993597i	−0.439414	−	0.898285i	$-0.644814\pi$
$947$	−11.4112	+	3.05763i	−0.370815	+	0.0993597i	0.0685986	+	0.997644i	$0.478147\pi$
$948$		0			0
$949$	7.62223	+	21.6760i	0.247428	+	0.703634i
$950$			63.4334i			2.05805i
$951$		0			0
$952$	5.25249	−	9.09758i	0.170234	−	0.294854i
$953$	3.32064	+	5.75152i	0.107566	+	0.186310i	0.914784	−	0.403944i	$-0.132361\pi$
$953$	3.32064	+	5.75152i	0.107566	+	0.186310i	−0.807218	+	0.590254i	$0.799028\pi$
$954$		0			0
$955$	10.0103	−	37.3588i	0.323924	−	1.20890i
$956$	−0.522777	+	1.95103i	−0.0169078	+	0.0631008i
$957$		0			0
$958$	−2.63259	−	4.55979i	−0.0850553	−	0.147320i
$959$	−15.4662	+	26.7883i	−0.499430	+	0.865039i
$960$		0			0
$961$		−	23.9319i		−	0.771997i
$962$	1.06381	+	13.9084i	0.0342986	+	0.448424i
$963$		0			0
$964$	−8.65370	+	2.31875i	−0.278717	+	0.0746820i
$965$	4.82642	+	2.78654i	0.155368	+	0.0897018i
$966$		0			0
$967$	−12.4796	−	12.4796i	−0.401318	−	0.401318i	0.477380	−	0.878697i	$-0.341587\pi$
$967$	−12.4796	−	12.4796i	−0.401318	−	0.401318i	−0.878697	+	0.477380i	$0.841587\pi$
$968$	−22.7980	−	6.10871i	−0.732756	−	0.196341i
$969$		0			0
$970$	−24.3888	+	24.3888i	−0.783076	+	0.783076i
$971$	28.4284	−	16.4132i	0.912312	−	0.526724i	0.0311377	−	0.999515i	$-0.490087\pi$
$971$	28.4284	−	16.4132i	0.912312	−	0.526724i	0.881174	+	0.472792i	$0.156754\pi$
$972$		0			0
$973$	−3.60647	−	13.4595i	−0.115618	−	0.431493i
$974$	−8.88980			−0.284847
$975$		0			0
$976$	−0.147240			−0.00471305
$977$	−1.29137	−	4.81947i	−0.0413147	−	0.154189i	0.942187	−	0.335088i	$-0.108766\pi$
$977$	−1.29137	−	4.81947i	−0.0413147	−	0.154189i	−0.983502	+	0.180899i	$0.942099\pi$
$978$		0			0
$979$	17.4333	−	10.0651i	0.557172	−	0.321683i
$980$	16.7349	−	16.7349i	0.534578	−	0.534578i
$981$		0			0
$982$	−21.7638	−	5.83159i	−0.694510	−	0.186094i
$983$	−33.3284	−	33.3284i	−1.06301	−	1.06301i	−0.997877	−	0.0651332i	$-0.979253\pi$
$983$	−33.3284	−	33.3284i	−1.06301	−	1.06301i	−0.0651332	−	0.997877i	$-0.520747\pi$
$984$		0			0
$985$	59.9215	+	34.5957i	1.90926	+	1.10231i
$986$	15.2395	−	4.08341i	0.485324	−	0.130042i
$987$		0			0
$988$	−38.1643	−	7.16027i	−1.21417	−	0.227799i
$989$		−	1.44936i		−	0.0460869i
$990$		0			0
$991$	27.1712	−	47.0620i	0.863123	−	1.49497i	−0.00577642	−	0.999983i	$-0.501839\pi$
$991$	27.1712	−	47.0620i	0.863123	−	1.49497i	0.868899	−	0.494989i	$-0.164828\pi$
$992$	7.76126	+	13.4429i	0.246420	+	0.426813i
$993$		0			0
$994$	0.307219	−	1.14656i	0.00974440	−	0.0363666i
$995$	−11.2018	+	41.8058i	−0.355122	+	1.32533i
$996$		0			0
$997$	0.900561	+	1.55982i	0.0285211	+	0.0493999i	0.879934	−	0.475097i	$-0.157587\pi$
$997$	0.900561	+	1.55982i	0.0285211	+	0.0493999i	−0.851413	+	0.524497i	$0.824254\pi$
$998$	14.0941	−	24.4117i	0.446141	−	0.772739i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.bd.e.215.3	yes	20
3.2	odd	2		351.2.bd.d.215.3	yes	20
13.2	odd	12		351.2.bd.d.80.3	✓	20
39.2	even	12	inner	351.2.bd.e.80.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
351.2.bd.d.80.3	✓	20	13.2	odd	12
351.2.bd.d.215.3	yes	20	3.2	odd	2
351.2.bd.e.80.3	yes	20	39.2	even	12	inner
351.2.bd.e.215.3	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.205594 + 0.767287i) q^{2} +(1.18559 - 0.684501i) q^{4} +(-2.75236 + 2.75236i) q^{5} +(1.54508 + 0.414002i) q^{7} +(1.89235 + 1.89235i) q^{8} +O(q^{10})\)	\(q+(0.205594 + 0.767287i) q^{2} +(1.18559 - 0.684501i) q^{4} +(-2.75236 + 2.75236i) q^{5} +(1.54508 + 0.414002i) q^{7} +(1.89235 + 1.89235i) q^{8} +(-2.67772 - 1.54598i) q^{10} +(1.42638 - 0.382196i) q^{11} +(-1.55939 + 3.25089i) q^{13} +1.27063i q^{14} +(0.306084 - 0.530153i) q^{16} +(-1.22700 - 2.12522i) q^{17} +(-2.03606 + 7.59867i) q^{19} +(-1.37918 + 5.14717i) q^{20} +(0.586509 + 1.01586i) q^{22} +(0.0635456 - 0.110064i) q^{23} -10.1510i q^{25} +(-2.81497 - 0.528136i) q^{26} +(2.11521 - 0.566769i) q^{28} +(7.00921 + 4.04677i) q^{29} +(1.87990 + 1.87990i) q^{31} +(5.63969 + 1.51115i) q^{32} +(1.37839 - 1.37839i) q^{34} +(-5.39210 + 3.11313i) q^{35} +(-1.26053 - 4.70437i) q^{37} -6.24897 q^{38} -10.4168 q^{40} +(-1.07198 - 4.00068i) q^{41} +(9.87623 - 5.70204i) q^{43} +(1.42948 - 1.42948i) q^{44} +(0.0975154 + 0.0261292i) q^{46} +(-5.41270 - 5.41270i) q^{47} +(-3.84632 - 2.22067i) q^{49} +(7.78875 - 2.08699i) q^{50} +(0.376441 + 4.92163i) q^{52} -7.39660i q^{53} +(-2.87396 + 4.97785i) q^{55} +(2.14038 + 3.70725i) q^{56} +(-1.66398 + 6.21007i) q^{58} +(-0.0877466 + 0.327475i) q^{59} +(-0.120262 - 0.208299i) q^{61} +(-1.05593 + 1.82892i) q^{62} +3.41361i q^{64} +(-4.65563 - 13.2397i) q^{65} +(-5.41185 + 1.45010i) q^{67} +(-2.90943 - 1.67976i) q^{68} +(-3.49725 - 3.49725i) q^{70} +(-0.902351 - 0.241784i) q^{71} +(4.50619 - 4.50619i) q^{73} +(3.35044 - 1.93438i) q^{74} +(2.78737 + 10.4026i) q^{76} +2.36209 q^{77} -0.351919 q^{79} +(0.616719 + 2.30163i) q^{80} +(2.84928 - 1.64503i) q^{82} +(10.6691 - 10.6691i) q^{83} +(9.22654 + 2.47224i) q^{85} +(6.40560 + 6.40560i) q^{86} +(3.42244 + 1.97595i) q^{88} +(13.1675 - 3.52822i) q^{89} +(-3.75525 + 4.37729i) q^{91} -0.173988i q^{92} +(3.04028 - 5.26591i) q^{94} +(-15.3103 - 26.5183i) q^{95} +(2.88713 - 10.7749i) q^{97} +(0.913113 - 3.40779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{5}+O(q^{10}) \) 20 * q + 6 * q^5	\( 20 q + 6 q^{5} - 12 q^{10} - 8 q^{13} + 24 q^{16} - 12 q^{17} - 12 q^{19} + 36 q^{20} + 8 q^{22} - 42 q^{26} + 2 q^{28} - 6 q^{29} - 22 q^{31} - 36 q^{32} - 6 q^{34} - 36 q^{35} + 8 q^{37} + 72 q^{38} - 36 q^{40} + 30 q^{41} - 30 q^{43} + 36 q^{44} - 48 q^{46} + 6 q^{47} + 30 q^{49} + 54 q^{50} + 4 q^{52} - 28 q^{55} - 60 q^{56} + 44 q^{58} + 30 q^{59} - 16 q^{61} - 30 q^{62} - 78 q^{65} + 18 q^{67} + 6 q^{68} + 38 q^{70} - 60 q^{71} - 72 q^{74} - 8 q^{76} - 12 q^{77} - 16 q^{79} + 126 q^{80} + 78 q^{82} + 12 q^{83} + 12 q^{85} + 18 q^{86} + 84 q^{89} + 30 q^{91} - 22 q^{94} - 66 q^{95} + 26 q^{97} + 42 q^{98}+O(q^{100}) \) 20 * q + 6 * q^5 - 12 * q^10 - 8 * q^13 + 24 * q^16 - 12 * q^17 - 12 * q^19 + 36 * q^20 + 8 * q^22 - 42 * q^26 + 2 * q^28 - 6 * q^29 - 22 * q^31 - 36 * q^32 - 6 * q^34 - 36 * q^35 + 8 * q^37 + 72 * q^38 - 36 * q^40 + 30 * q^41 - 30 * q^43 + 36 * q^44 - 48 * q^46 + 6 * q^47 + 30 * q^49 + 54 * q^50 + 4 * q^52 - 28 * q^55 - 60 * q^56 + 44 * q^58 + 30 * q^59 - 16 * q^61 - 30 * q^62 - 78 * q^65 + 18 * q^67 + 6 * q^68 + 38 * q^70 - 60 * q^71 - 72 * q^74 - 8 * q^76 - 12 * q^77 - 16 * q^79 + 126 * q^80 + 78 * q^82 + 12 * q^83 + 12 * q^85 + 18 * q^86 + 84 * q^89 + 30 * q^91 - 22 * q^94 - 66 * q^95 + 26 * q^97 + 42 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more