LMFDB - Embedded newform 588.2.e.c.491.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(491,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("588.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.2593100598870016.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} + x^{8} + 4x^{6} + 4x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 + x^8 + 4x^6 + 4x^4 - 32x^2 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			491.2
Root			$0.430469 + 1.34711i$ of defining polynomial
Character	$\chi$	$=$	588.491
Dual form			588.2.e.c.491.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34711 + 0.430469i) q^{2} +(-0.916638 - 1.46962i) q^{3} +(1.62939 - 1.15978i) q^{4} -0.348612i q^{5} +(1.86743 + 1.58515i) q^{6} +(-1.69572 + 2.26374i) q^{8} +(-1.31955 + 2.69421i) q^{9} +O(q^{10})$	\(q+(-1.34711 + 0.430469i) q^{2} +(-0.916638 - 1.46962i) q^{3} +(1.62939 - 1.15978i) q^{4} -0.348612i q^{5} +(1.86743 + 1.58515i) q^{6} +(-1.69572 + 2.26374i) q^{8} +(-1.31955 + 2.69421i) q^{9} +(0.150067 + 0.469617i) q^{10} +3.90376 q^{11} +(-3.19799 - 1.33149i) q^{12} +2.93923 q^{13} +(-0.512326 + 0.319551i) q^{15} +(1.30984 - 3.77946i) q^{16} +3.90376i q^{17} +(0.617800 - 4.19742i) q^{18} +5.57834i q^{19} +(-0.404312 - 0.568026i) q^{20} +(-5.25879 + 1.68045i) q^{22} -2.18189 q^{23} +(4.88120 + 0.417024i) q^{24} +4.87847 q^{25} +(-3.95946 + 1.26525i) q^{26} +(5.16901 - 0.530383i) q^{27} -9.75220i q^{29} +(0.552601 - 0.651010i) q^{30} -2.63910i q^{31} +(-0.137557 + 5.65518i) q^{32} +(-3.57834 - 5.73704i) q^{33} +(-1.68045 - 5.25879i) q^{34} +(0.974616 + 5.92031i) q^{36} +0.639102 q^{37} +(-2.40130 - 7.51461i) q^{38} +(-2.69421 - 4.31955i) q^{39} +(0.789168 + 0.591148i) q^{40} -7.57031i q^{41} +2.51757i q^{43} +(6.36076 - 4.52749i) q^{44} +(0.939235 + 0.460011i) q^{45} +(2.93923 - 0.939235i) q^{46} +4.36377 q^{47} +(-6.75501 + 1.53943i) q^{48} +(-6.57182 + 2.10003i) q^{50} +(5.73704 - 3.57834i) q^{51} +(4.78917 - 3.40885i) q^{52} +1.72188i q^{53} +(-6.73490 + 2.93958i) q^{54} -1.36090i q^{55} +(8.19802 - 5.11331i) q^{57} +(4.19802 + 13.1373i) q^{58} +8.24635 q^{59} +(-0.464173 + 1.11486i) q^{60} +14.0959 q^{61} +(1.13605 + 3.55515i) q^{62} +(-2.24908 - 7.67735i) q^{64} -1.02465i q^{65} +(7.29002 + 6.18804i) q^{66} +0.639102i q^{67} +(4.52749 + 6.36076i) q^{68} +(2.00000 + 3.20654i) q^{69} +11.9341 q^{71} +(-3.86142 - 7.55575i) q^{72} -7.87847 q^{73} +(-0.860938 + 0.275113i) q^{74} +(-4.47179 - 7.16948i) q^{75} +(6.46962 + 9.08930i) q^{76} +(5.48883 + 4.65912i) q^{78} +4.00000i q^{79} +(-1.31756 - 0.456627i) q^{80} +(-5.51757 - 7.11030i) q^{81} +(3.25879 + 10.1980i) q^{82} -8.94358 q^{83} +1.36090 q^{85} +(-1.08374 - 3.39144i) q^{86} +(-14.3320 + 8.93923i) q^{87} +(-6.61968 + 8.83712i) q^{88} -10.5396i q^{89} +(-1.46327 - 0.215373i) q^{90} +(-3.55515 + 2.53050i) q^{92} +(-3.87847 + 2.41910i) q^{93} +(-5.87847 + 1.87847i) q^{94} +1.94467 q^{95} +(8.43704 - 4.98160i) q^{96} +2.00000 q^{97} +(-5.15121 + 10.5176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4} + 6 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^4 + 6 * q^6 - 4 * q^9	$ 12 q - 4 q^{4} + 6 q^{6} - 4 q^{9} - 4 q^{10} + 6 q^{12} + 4 q^{16} - 8 q^{18} - 16 q^{22} - 2 q^{24} - 12 q^{25} + 20 q^{30} + 16 q^{33} - 32 q^{34} - 20 q^{36} - 16 q^{37} - 20 q^{40} - 24 q^{45} - 46 q^{48} + 28 q^{52} - 10 q^{54} + 16 q^{57} - 32 q^{58} + 28 q^{60} + 16 q^{61} + 20 q^{64} + 12 q^{66} + 24 q^{69} - 32 q^{72} - 24 q^{73} + 60 q^{76} + 20 q^{78} + 28 q^{81} - 8 q^{82} + 40 q^{85} - 56 q^{88} + 80 q^{90} + 24 q^{93} + 34 q^{96} + 24 q^{97}+O(q^{100}) $ 12 * q - 4 * q^4 + 6 * q^6 - 4 * q^9 - 4 * q^10 + 6 * q^12 + 4 * q^16 - 8 * q^18 - 16 * q^22 - 2 * q^24 - 12 * q^25 + 20 * q^30 + 16 * q^33 - 32 * q^34 - 20 * q^36 - 16 * q^37 - 20 * q^40 - 24 * q^45 - 46 * q^48 + 28 * q^52 - 10 * q^54 + 16 * q^57 - 32 * q^58 + 28 * q^60 + 16 * q^61 + 20 * q^64 + 12 * q^66 + 24 * q^69 - 32 * q^72 - 24 * q^73 + 60 * q^76 + 20 * q^78 + 28 * q^81 - 8 * q^82 + 40 * q^85 - 56 * q^88 + 80 * q^90 + 24 * q^93 + 34 * q^96 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.34711	+	0.430469i	−0.952548	+	0.304388i
$2$	−1.34711	+	0.430469i	−0.952548	+	0.304388i
$3$	−0.916638	−	1.46962i	−0.529221	−	0.848484i
$3$	−0.916638	−	1.46962i	−0.529221	−	0.848484i
$4$	1.62939	−	1.15978i	0.814696	−	0.579888i
$5$		−	0.348612i		−	0.155904i	−0.996957	−	0.0779520i	$-0.975162\pi$
$5$		−	0.348612i		−	0.155904i	0.996957	−	0.0779520i	$-0.0248381\pi$
$6$	1.86743	+	1.58515i	0.762377	+	0.647134i
$7$		0			0
$7$		0			0
$8$	−1.69572	+	2.26374i	−0.599527	+	0.800354i
$9$	−1.31955	+	2.69421i	−0.439850	+	0.898071i
$10$	0.150067	+	0.469617i	0.0474552	+	0.148506i
$11$	3.90376			1.17703			0.588514	−	0.808487i	$-0.299713\pi$
$11$	3.90376			1.17703			0.588514	+	0.808487i	$0.299713\pi$
$12$	−3.19799	−	1.33149i	−0.923180	−	0.384368i
$13$	2.93923			0.815197			0.407599	−	0.913161i	$-0.366366\pi$
$13$	2.93923			0.815197			0.407599	+	0.913161i	$0.366366\pi$
$14$		0			0
$15$	−0.512326	+	0.319551i	−0.132282	+	0.0825077i
$16$	1.30984	−	3.77946i	0.327461	−	0.944865i
$17$			3.90376i			0.946802i	0.880847	+	0.473401i	$0.156974\pi$
$17$			3.90376i			0.946802i	−0.880847	+	0.473401i	$0.843026\pi$
$18$	0.617800	−	4.19742i	0.145617	−	0.989341i
$19$			5.57834i			1.27976i	0.768476	+	0.639879i	$0.221016\pi$
$19$			5.57834i			1.27976i	−0.768476	+	0.639879i	$0.778984\pi$
$20$	−0.404312	−	0.568026i	−0.0904068	−	0.127014i
$21$		0			0
$22$	−5.25879	+	1.68045i	−1.12118	+	0.358273i
$23$	−2.18189			−0.454955			−0.227477	−	0.973783i	$-0.573048\pi$
$23$	−2.18189			−0.454955			−0.227477	+	0.973783i	$0.573048\pi$
$24$	4.88120	+	0.417024i	0.996370	+	0.0851247i
$25$	4.87847			0.975694
$26$	−3.95946	+	1.26525i	−0.776515	+	0.248136i
$27$	5.16901	−	0.530383i	0.994777	−	0.102072i
$28$		0			0
$29$		−	9.75220i		−	1.81094i	−0.424412	−	0.905469i	$-0.639519\pi$
$29$		−	9.75220i		−	1.81094i	0.424412	−	0.905469i	$-0.360481\pi$
$30$	0.552601	−	0.651010i	0.100891	−	0.118858i
$31$		−	2.63910i		−	0.473997i	−0.971510	−	0.236998i	$-0.923836\pi$
$31$		−	2.63910i		−	0.473997i	0.971510	−	0.236998i	$-0.0761636\pi$
$32$	−0.137557	+	5.65518i	−0.0243168	+	0.999704i
$33$	−3.57834	−	5.73704i	−0.622908	−	0.998690i
$34$	−1.68045	−	5.25879i	−0.288195	−	0.901874i
$35$		0			0
$36$	0.974616	+	5.92031i	0.162436	+	0.986719i
$37$	0.639102			0.105068			0.0525338	−	0.998619i	$-0.483270\pi$
$37$	0.639102			0.105068			0.0525338	+	0.998619i	$0.483270\pi$
$38$	−2.40130	−	7.51461i	−0.389542	−	1.21903i
$39$	−2.69421	−	4.31955i	−0.431419	−	0.691682i
$40$	0.789168	+	0.591148i	0.124778	+	0.0934687i
$41$		−	7.57031i		−	1.18228i	−0.806567	−	0.591142i	$-0.798677\pi$
$41$		−	7.57031i		−	1.18228i	0.806567	−	0.591142i	$-0.201323\pi$
$42$		0			0
$43$			2.51757i			0.383926i	0.981402	+	0.191963i	$0.0614854\pi$
$43$			2.51757i			0.383926i	−0.981402	+	0.191963i	$0.938515\pi$
$44$	6.36076	−	4.52749i	0.958921	−	0.682545i
$45$	0.939235	+	0.460011i	0.140013	+	0.0685744i
$46$	2.93923	−	0.939235i	0.433367	−	0.138483i
$47$	4.36377			0.636522			0.318261	−	0.948003i	$-0.396901\pi$
$47$	4.36377			0.636522			0.318261	+	0.948003i	$0.396901\pi$
$48$	−6.75501	+	1.53943i	−0.975002	+	0.222197i
$49$		0			0
$50$	−6.57182	+	2.10003i	−0.929396	+	0.296989i
$51$	5.73704	−	3.57834i	0.803346	−	0.501067i
$52$	4.78917	−	3.40885i	0.664138	−	0.472723i
$53$			1.72188i			0.236518i	0.992983	+	0.118259i	$0.0377313\pi$
$53$			1.72188i			0.236518i	−0.992983	+	0.118259i	$0.962269\pi$
$54$	−6.73490	+	2.93958i	−0.916504	+	0.400026i
$55$		−	1.36090i		−	0.183504i
$56$		0			0
$57$	8.19802	−	5.11331i	1.08585	−	0.677275i
$58$	4.19802	+	13.1373i	0.551227	+	1.72501i
$59$	8.24635			1.07358			0.536792	−	0.843715i	$-0.319636\pi$
$59$	8.24635			1.07358			0.536792	+	0.843715i	$0.319636\pi$
$60$	−0.464173	+	1.11486i	−0.0599245	+	0.143927i
$61$	14.0959			1.80480			0.902398	−	0.430903i	$-0.141805\pi$
$61$	14.0959			1.80480			0.902398	+	0.430903i	$0.141805\pi$
$62$	1.13605	+	3.55515i	0.144279	+	0.451505i
$63$		0			0
$64$	−2.24908	−	7.67735i	−0.281135	−	0.959668i
$65$		−	1.02465i		−	0.127092i
$66$	7.29002	+	6.18804i	0.897339	+	0.761695i
$67$			0.639102i			0.0780787i	0.999238	+	0.0390393i	$0.0124298\pi$
$67$			0.639102i			0.0780787i	−0.999238	+	0.0390393i	$0.987570\pi$
$68$	4.52749	+	6.36076i	0.549039	+	0.771356i
$69$	2.00000	+	3.20654i	0.240772	+	0.386022i
$70$		0			0
$71$	11.9341			1.41632			0.708158	−	0.706054i	$-0.249526\pi$
$71$	11.9341			1.41632			0.708158	+	0.706054i	$0.249526\pi$
$72$	−3.86142	−	7.55575i	−0.455073	−	0.890454i
$73$	−7.87847			−0.922105			−0.461053	−	0.887373i	$-0.652528\pi$
$73$	−7.87847			−0.922105			−0.461053	+	0.887373i	$0.652528\pi$
$74$	−0.860938	+	0.275113i	−0.100082	+	0.0319813i
$75$	−4.47179	−	7.16948i	−0.516358	−	0.827861i
$76$	6.46962	+	9.08930i	0.742116	+	1.04261i
$77$		0			0
$78$	5.48883	+	4.65912i	0.621487	+	0.527541i
$79$			4.00000i			0.450035i	0.974355	+	0.225018i	$0.0722440\pi$
$79$			4.00000i			0.450035i	−0.974355	+	0.225018i	$0.927756\pi$
$80$	−1.31756	−	0.456627i	−0.147308	−	0.0510524i
$81$	−5.51757	−	7.11030i	−0.613063	−	0.790034i
$82$	3.25879	+	10.1980i	0.359873	+	1.12618i
$83$	−8.94358			−0.981685			−0.490843	−	0.871248i	$-0.663311\pi$
$83$	−8.94358			−0.981685			−0.490843	+	0.871248i	$0.663311\pi$
$84$		0			0
$85$	1.36090			0.147610
$86$	−1.08374	−	3.39144i	−0.116862	−	0.365708i
$87$	−14.3320	+	8.93923i	−1.53655	+	0.958387i
$88$	−6.61968	+	8.83712i	−0.705661	+	0.942040i
$89$		−	10.5396i		−	1.11720i	−0.829437	−	0.558600i	$-0.811339\pi$
$89$		−	10.5396i		−	1.11720i	0.829437	−	0.558600i	$-0.188661\pi$
$90$	−1.46327	−	0.215373i	−0.154242	−	0.0227023i
$91$		0			0
$92$	−3.55515	+	2.53050i	−0.370650	+	0.263823i
$93$	−3.87847	+	2.41910i	−0.402179	+	0.250849i
$94$	−5.87847	+	1.87847i	−0.606318	+	0.193749i
$95$	1.94467			0.199519
$96$	8.43704	−	4.98160i	0.861102	−	0.508432i
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		0			0
$99$	−5.15121	+	10.5176i	−0.517716	+	1.05706i
$100$	7.94894	−	5.65793i	0.794894	−	0.565793i
$101$			3.09514i			0.307978i	0.988073	+	0.153989i	$0.0492120\pi$
$101$			3.09514i			0.307978i	−0.988073	+	0.153989i	$0.950788\pi$
$102$	−6.18804	+	7.29002i	−0.612707	+	0.721819i
$103$		−	7.23937i		−	0.713316i	−0.934235	−	0.356658i	$-0.883916\pi$
$103$		−	7.23937i		−	0.713316i	0.934235	−	0.356658i	$-0.116084\pi$
$104$	−4.98412	+	6.65368i	−0.488733	+	0.652447i
$105$		0			0
$106$	−0.741214	−	2.31955i	−0.0719931	−	0.225295i
$107$	−11.0141			−1.06477			−0.532385	−	0.846502i	$-0.678704\pi$
$107$	−11.0141			−1.06477			−0.532385	+	0.846502i	$0.678704\pi$
$108$	7.80723	−	6.85910i	0.751251	−	0.660017i
$109$	1.39973			0.134070			0.0670351	−	0.997751i	$-0.478646\pi$
$109$	1.39973			0.134070			0.0670351	+	0.997751i	$0.478646\pi$
$110$	0.585825	+	1.83328i	0.0558562	+	0.174796i
$111$	−0.585825	−	0.939235i	−0.0556040	−	0.0891482i
$112$		0			0
$113$			8.83218i			0.830862i	0.909625	+	0.415431i	$0.136369\pi$
$113$			8.83218i			0.830862i	−0.909625	+	0.415431i	$0.863631\pi$
$114$	−8.84249	+	10.4172i	−0.828175	+	0.975658i
$115$			0.760632i			0.0709293i
$116$	−11.3104	−	15.8902i	−1.05014	−	1.47536i
$117$	−3.87847	+	7.91893i	−0.358565	+	0.732105i
$118$	−11.1087	+	3.54980i	−1.02264	+	0.326786i
$119$		0			0
$120$	0.145380	−	1.70164i	0.0132713	−	0.155338i
$121$	4.23937			0.385397
$122$	−18.9887	+	6.06785i	−1.71916	+	0.549357i
$123$	−11.1255	+	6.93923i	−1.00315	+	0.625690i
$124$	−3.06077	−	4.30013i	−0.274865	−	0.386163i
$125$		−	3.44375i		−	0.308019i
$126$		0			0
$127$		−	12.3960i		−	1.09997i	−0.835174	−	0.549985i	$-0.814633\pi$
$127$		−	12.3960i		−	1.09997i	0.835174	−	0.549985i	$-0.185367\pi$
$128$	6.33461	+	9.37405i	0.559905	+	0.828557i
$129$	3.69987	−	2.30770i	0.325755	−	0.203182i
$130$	0.441081	+	1.38032i	0.0386854	+	0.121062i
$131$	1.61048			0.140708			0.0703540	−	0.997522i	$-0.477587\pi$
$131$	1.61048			0.140708			0.0703540	+	0.997522i	$0.477587\pi$
$132$	−12.4842	−	5.19782i	−1.08661	−	0.452412i
$133$		0			0
$134$	−0.275113	−	0.860938i	−0.0237662	−	0.0743737i
$135$	−0.184898	−	1.80198i	−0.0159135	−	0.155090i
$136$	−8.83712	−	6.61968i	−0.757777	−	0.567633i
$137$		−	4.36377i		−	0.372822i	−0.982472	−	0.186411i	$-0.940314\pi$
$137$		−	4.36377i		−	0.372822i	0.982472	−	0.186411i	$-0.0596857\pi$
$138$	−4.07453	−	3.45861i	−0.346847	−	0.294417i
$139$			16.8177i			1.42646i	0.700931	+	0.713230i	$0.252768\pi$
$139$			16.8177i			1.42646i	−0.700931	+	0.713230i	$0.747232\pi$
$140$		0			0
$141$	−4.00000	−	6.41308i	−0.336861	−	0.540079i
$142$	−16.0765	+	5.13726i	−1.34911	+	0.431109i
$143$	11.4741			0.959511
$144$	8.45427	+	8.51618i	0.704522	+	0.709682i
$145$	−3.39973			−0.282332
$146$	10.6131	−	3.39144i	0.878350	−	0.280677i
$147$		0			0
$148$	1.04135	−	0.741214i	0.0855982	−	0.0609274i
$149$			7.66053i			0.627575i	0.949493	+	0.313788i	$0.101598\pi$
$149$			7.66053i			0.627575i	−0.949493	+	0.313788i	$0.898402\pi$
$150$	9.11022	+	7.73309i	0.743846	+	0.631404i
$151$			12.6391i			1.02856i	0.857624	+	0.514278i	$0.171940\pi$
$151$			12.6391i			1.02856i	−0.857624	+	0.514278i	$0.828060\pi$
$152$	−12.6279	−	9.45929i	−1.02426	−	0.767250i
$153$	−10.5176	−	5.15121i	−0.850295	−	0.416451i
$154$		0			0
$155$	−0.920022			−0.0738980
$156$	−9.39964	−	3.91356i	−0.752574	−	0.313336i
$157$	−0.217438			−0.0173534			−0.00867672	−	0.999962i	$-0.502762\pi$
$157$	−0.217438			−0.0173534			−0.00867672	+	0.999962i	$0.502762\pi$
$158$	−1.72188	−	5.38843i	−0.136985	−	0.428680i
$159$	2.53050	−	1.57834i	0.200682	−	0.125170i
$160$	1.97146	+	0.0479539i	0.155858	+	0.00379109i
$161$		0			0
$162$	10.4935	+	7.20319i	0.824449	+	0.565936i
$163$		−	5.23937i		−	0.410379i	−0.978722	−	0.205189i	$-0.934219\pi$
$163$		−	5.23937i		−	0.410379i	0.978722	−	0.205189i	$-0.0657811\pi$
$164$	−8.77986	−	12.3350i	−0.685592	−	0.963203i
$165$	−2.00000	+	1.24745i	−0.155700	+	0.0971139i
$166$	12.0480	−	3.84993i	0.935103	−	0.298813i
$167$	11.4741			0.887891			0.443945	−	0.896054i	$-0.353578\pi$
$167$	11.4741			0.887891			0.443945	+	0.896054i	$0.353578\pi$
$168$		0			0
$169$	−4.36090			−0.335454
$170$	−1.83328	+	0.585825i	−0.140606	+	0.0449307i
$171$	−15.0292	−	7.36090i	−1.14931	−	0.562902i
$172$	2.91982	+	4.10211i	0.222634	+	0.312783i
$173$			21.2051i			1.61219i	0.591784	+	0.806097i	$0.298424\pi$
$173$			21.2051i			1.61219i	−0.591784	+	0.806097i	$0.701576\pi$
$174$	15.4587	−	18.2116i	1.17192	−	1.38062i
$175$		0			0
$176$	5.11331	−	14.7541i	0.385430	−	1.11213i
$177$	−7.55892	−	12.1190i	−0.568163	−	0.910919i
$178$	4.53699	+	14.1980i	0.340062	+	1.06419i
$179$	1.81209			0.135442			0.0677211	−	0.997704i	$-0.478427\pi$
$179$	1.81209			0.135442			0.0677211	+	0.997704i	$0.478427\pi$
$180$	2.06389	−	0.339763i	0.153833	−	0.0253244i
$181$	−7.53950			−0.560407			−0.280203	−	0.959941i	$-0.590402\pi$
$181$	−7.53950			−0.560407			−0.280203	+	0.959941i	$0.590402\pi$
$182$		0			0
$183$	−12.9208	−	20.7156i	−0.955136	−	1.53134i
$184$	3.69987	−	4.93923i	0.272758	−	0.364125i
$185$		−	0.222798i		−	0.0163805i
$186$	4.18336	−	4.92835i	0.306739	−	0.361364i
$187$			15.2394i			1.11441i
$188$	7.11030	−	5.06100i	0.518572	−	0.369111i
$189$		0			0
$190$	−2.61968	+	0.837122i	−0.190052	+	0.0607312i
$191$	1.63166			0.118063			0.0590314	−	0.998256i	$-0.481199\pi$
$191$	1.63166			0.118063			0.0590314	+	0.998256i	$0.481199\pi$
$192$	−9.22117	+	10.3426i	−0.665481	+	0.746415i
$193$	−15.1567			−1.09100			−0.545501	−	0.838110i	$-0.683660\pi$
$193$	−15.1567			−1.09100			−0.545501	+	0.838110i	$0.683660\pi$
$194$	−2.69421	+	0.860938i	−0.193433	+	0.0618117i
$195$	−1.50585	+	0.939235i	−0.107836	+	0.0672600i
$196$		0			0
$197$			21.2263i			1.51231i	0.654393	+	0.756155i	$0.272924\pi$
$197$			21.2263i			1.51231i	−0.654393	+	0.756155i	$0.727076\pi$
$198$	2.41175	−	16.3857i	0.171395	−	1.16448i
$199$			3.75694i			0.266322i	0.991094	+	0.133161i	$0.0425128\pi$
$199$			3.75694i			0.266322i	−0.991094	+	0.133161i	$0.957487\pi$
$200$	−8.27251	+	11.0436i	−0.584955	+	0.780901i
$201$	0.939235	−	0.585825i	0.0662485	−	0.0413209i
$202$	−1.33236	−	4.16948i	−0.0937447	−	0.293364i
$203$		0			0
$204$	5.19782	−	12.4842i	0.363920	−	0.874068i
$205$	−2.63910			−0.184323
$206$	3.11632	+	9.75220i	0.217125	+	0.679468i
$207$	2.87911	−	5.87847i	0.200112	−	0.408582i
$208$	3.84993	−	11.1087i	0.266945	−	0.770251i
$209$			21.7765i			1.50631i
$210$		0			0
$211$			9.83963i			0.677388i	0.940897	+	0.338694i	$0.109985\pi$
$211$			9.83963i			0.677388i	−0.940897	+	0.338694i	$0.890015\pi$
$212$	1.99699	+	2.80561i	0.137154	+	0.192690i
$213$	−10.9392	−	17.5385i	−0.749544	−	1.20172i
$214$	14.8371	−	4.74121i	1.01424	−	0.324103i
$215$	0.877655			0.0598556
$216$	−7.56454	+	12.6007i	−0.514702	+	0.857369i
$217$		0			0
$218$	−1.88559	+	0.602542i	−0.127708	+	0.0408093i
$219$	7.22170	+	11.5783i	0.487997	+	0.782391i
$220$	−1.57834	−	2.21744i	−0.106411	−	0.149500i
$221$			11.4741i			0.771830i
$222$	1.19348	+	1.01307i	0.0801011	+	0.0679928i
$223$		−	22.9136i		−	1.53441i	−0.641403	−	0.767204i	$-0.721647\pi$
$223$		−	22.9136i		−	1.53441i	0.641403	−	0.767204i	$-0.278353\pi$
$224$		0			0
$225$	−6.43739	+	13.1436i	−0.429159	+	0.876243i
$226$	−3.80198	−	11.8979i	−0.252904	−	0.791436i
$227$	13.5302			0.898028			0.449014	−	0.893525i	$-0.351775\pi$
$227$	13.5302			0.898028			0.449014	+	0.893525i	$0.351775\pi$
$228$	7.42750	−	17.8395i	0.491898	−	1.18145i
$229$	−14.6962			−0.971151			−0.485575	−	0.874195i	$-0.661390\pi$
$229$	−14.6962			−0.971151			−0.485575	+	0.874195i	$0.661390\pi$
$230$	−0.327428	−	1.02465i	−0.0215900	−	0.0675636i
$231$		0			0
$232$	22.0765	+	16.5370i	1.44939	+	1.08571i
$233$		−	17.1899i		−	1.12615i	−0.826406	−	0.563075i	$-0.809618\pi$
$233$		−	17.1899i		−	1.12615i	0.826406	−	0.563075i	$-0.190382\pi$
$234$	1.81586	−	12.3372i	0.118706	−	0.806508i
$235$		−	1.52126i		−	0.0992363i
$236$	13.4366	−	9.56392i	0.874645	−	0.622558i
$237$	5.87847	−	3.66655i	0.381848	−	0.238168i
$238$		0			0
$239$	14.5336			0.940102			0.470051	−	0.882639i	$-0.344236\pi$
$239$	14.5336			0.940102			0.470051	+	0.882639i	$0.344236\pi$
$240$	0.536663	+	2.35488i	0.0346414	+	0.152007i
$241$	18.7921			1.21050			0.605252	−	0.796034i	$-0.293072\pi$
$241$	18.7921			1.21050			0.605252	+	0.796034i	$0.293072\pi$
$242$	−5.71088	+	1.82492i	−0.367109	+	0.117310i
$243$	−5.39181	+	14.6263i	−0.345885	+	0.938277i
$244$	22.9678	−	16.3481i	1.47036	−	1.04658i
$245$		0			0
$246$	12.0001	−	14.1371i	0.765096	−	0.901346i
$247$			16.3960i			1.04326i
$248$	5.97425	+	4.47517i	0.379365	+	0.284174i
$249$	8.19802	+	13.1436i	0.519528	+	0.832944i
$250$	1.48243	+	4.63910i	0.0937570	+	0.293403i
$251$	−20.6405			−1.30281			−0.651407	−	0.758729i	$-0.725821\pi$
$251$	−20.6405			−1.30281			−0.651407	+	0.758729i	$0.725821\pi$
$252$		0			0
$253$	−8.51757			−0.535495
$254$	5.33611	+	16.6988i	0.334817	+	1.04778i
$255$	−1.24745	−	2.00000i	−0.0781184	−	0.125245i
$256$	−12.5686	−	9.90099i	−0.785539	−	0.618812i
$257$			4.82379i			0.300899i	0.988618	+	0.150450i	$0.0480722\pi$
$257$			4.82379i			0.300899i	−0.988618	+	0.150450i	$0.951928\pi$
$258$	−3.99072	+	4.70140i	−0.248451	+	0.292696i
$259$		0			0
$260$	−1.18837	−	1.66956i	−0.0736994	−	0.103542i
$261$	26.2745	+	12.8685i	1.62635	+	0.796542i
$262$	−2.16948	+	0.693260i	−0.134031	+	0.0428298i
$263$	14.4578			0.891507			0.445754	−	0.895156i	$-0.352936\pi$
$263$	14.4578			0.891507			0.445754	+	0.895156i	$0.352936\pi$
$264$	19.0550	+	1.62796i	1.17276	+	0.100194i
$265$	0.600267			0.0368741
$266$		0			0
$267$	−15.4892	+	9.66103i	−0.947926	+	0.591246i
$268$	0.741214	+	1.04135i	0.0452769	+	0.0636104i
$269$		−	4.71239i		−	0.287319i	−0.989627	−	0.143660i	$-0.954113\pi$
$269$		−	4.71239i		−	0.287319i	0.989627	−	0.143660i	$-0.0458871\pi$
$270$	1.02477	+	2.34787i	0.0623657	+	0.142887i
$271$		−	15.6742i		−	0.952143i	−0.879407	−	0.476071i	$-0.842060\pi$
$271$		−	15.6742i		−	0.952143i	0.879407	−	0.476071i	$-0.157940\pi$
$272$	14.7541	+	5.11331i	0.894600	+	0.310040i
$273$		0			0
$274$	1.87847	+	5.87847i	0.113483	+	0.355131i
$275$	19.0444			1.14842
$276$	6.97765	+	2.90516i	0.420005	+	0.174870i
$277$	16.9963			1.02121			0.510605	−	0.859816i	$-0.329422\pi$
$277$	16.9963			1.02121			0.510605	+	0.859816i	$0.329422\pi$
$278$	−7.23950	−	22.6552i	−0.434196	−	1.35877i
$279$	7.11030	+	3.48243i	0.425683	+	0.208488i
$280$		0			0
$281$			5.75822i			0.343507i	0.985140	+	0.171753i	$0.0549432\pi$
$281$			5.75822i			0.343507i	−0.985140	+	0.171753i	$0.945057\pi$
$282$	8.14906	+	6.91723i	0.485269	+	0.411915i
$283$		−	5.57834i		−	0.331598i	−0.986160	−	0.165799i	$-0.946980\pi$
$283$		−	5.57834i		−	0.331598i	0.986160	−	0.165799i	$-0.0530202\pi$
$284$	19.4453	−	13.8409i	1.15387	−	0.821304i
$285$	−1.78256	−	2.85793i	−0.105590	−	0.169289i
$286$	−15.4568	+	4.93923i	−0.913980	+	0.292063i
$287$		0			0
$288$	−15.0548	−	7.83291i	−0.887110	−	0.461558i
$289$	1.76063			0.103567
$290$	4.57980	−	1.46348i	0.268935	−	0.0859385i
$291$	−1.83328	−	2.93923i	−0.107469	−	0.172301i
$292$	−12.8371	+	9.13726i	−0.751236	+	0.534717i
$293$			23.7712i			1.38873i	0.719624	+	0.694364i	$0.244314\pi$
$293$			23.7712i			1.38873i	−0.719624	+	0.694364i	$0.755686\pi$
$294$		0			0
$295$		−	2.87478i		−	0.167376i
$296$	−1.08374	+	1.44676i	−0.0629909	+	0.0840914i
$297$	20.1786	−	2.07049i	1.17088	−	0.120142i
$298$	−3.29762	−	10.3196i	−0.191026	−	0.597796i
$299$	−6.41308			−0.370878
$300$	−15.6013	−	6.49564i	−0.900741	−	0.375026i
$301$		0			0
$302$	−5.44074	−	17.0262i	−0.313080	−	0.979749i
$303$	4.54867	−	2.83712i	0.261314	−	0.162988i
$304$	21.0831	+	7.30674i	1.20920	+	0.419070i
$305$		−	4.91400i		−	0.281375i
$306$	16.3857	+	2.41175i	0.936710	+	0.137870i
$307$		−	3.69987i		−	0.211163i	−0.994411	−	0.105581i	$-0.966330\pi$
$307$		−	3.69987i		−	0.211163i	0.994411	−	0.105581i	$-0.0336703\pi$
$308$		0			0
$309$	−10.6391	+	6.63588i	−0.605237	+	0.377502i
$310$	1.23937	−	0.396041i	0.0703914	−	0.0224936i
$311$	7.58473			0.430090			0.215045	−	0.976604i	$-0.431010\pi$
$311$	7.58473			0.430090			0.215045	+	0.976604i	$0.431010\pi$
$312$	14.3470	+	1.22573i	0.812238	+	0.0693934i
$313$	−15.6354			−0.883766			−0.441883	−	0.897073i	$-0.645689\pi$
$313$	−15.6354			−0.883766			−0.441883	+	0.897073i	$0.645689\pi$
$314$	0.292912	−	0.0936004i	0.0165300	−	0.00528217i
$315$		0			0
$316$	4.63910	+	6.51757i	0.260970	+	0.366642i
$317$		−	13.8932i		−	0.780319i	−0.920747	−	0.390159i	$-0.872420\pi$
$317$		−	13.8932i		−	0.780319i	0.920747	−	0.390159i	$-0.127580\pi$
$318$	−2.72943	+	3.21549i	−0.153059	+	0.180316i
$319$		−	38.0703i		−	2.13153i
$320$	−2.67641	+	0.784055i	−0.149616	+	0.0438300i
$321$	10.0959	+	16.1865i	0.563499	+	0.903440i
$322$		0			0
$323$	−21.7765			−1.21168
$324$	−17.2366	−	5.18633i	−0.957591	−	0.288130i
$325$	14.3390			0.795383
$326$	2.25539	+	7.05799i	0.124914	+	0.390906i
$327$	−1.28305	−	2.05707i	−0.0709527	−	0.113756i
$328$	17.1373	+	12.8371i	0.946247	+	0.708811i
$329$		0			0
$330$	2.15722	−	2.54139i	0.118751	−	0.139899i
$331$		−	31.7958i		−	1.74765i	−0.486237	−	0.873827i	$-0.661631\pi$
$331$		−	31.7958i		−	1.74765i	0.486237	−	0.873827i	$-0.338369\pi$
$332$	−14.5726	+	10.3725i	−0.799775	+	0.569267i
$333$	−0.843327	+	1.72188i	−0.0462140	+	0.0943582i
$334$	−15.4568	+	4.93923i	−0.845759	+	0.270263i
$335$	0.222798			0.0121728
$336$		0			0
$337$	−17.1178			−0.932468			−0.466234	−	0.884661i	$-0.654390\pi$
$337$	−17.1178			−0.932468			−0.466234	+	0.884661i	$0.654390\pi$
$338$	5.87460	−	1.87723i	0.319536	−	0.102108i
$339$	12.9799	−	8.09591i	0.704973	−	0.439709i
$340$	2.21744	−	1.57834i	0.120257	−	0.0855973i
$341$		−	10.3024i		−	0.557908i
$342$	23.4146	+	3.44630i	1.26612	+	0.186354i
$343$		0			0
$344$	−5.69914	−	4.26909i	−0.307277	−	0.230174i
$345$	1.11784	−	0.697224i	0.0601824	−	0.0375373i
$346$	−9.12814	−	28.5655i	−0.490732	−	1.53569i
$347$	−8.44797			−0.453511			−0.226755	−	0.973952i	$-0.572812\pi$
$347$	−8.44797			−0.453511			−0.226755	+	0.973952i	$0.572812\pi$
$348$	−12.9850	+	31.1874i	−0.696067	+	1.67182i
$349$	−17.4956			−0.936520			−0.468260	−	0.883591i	$-0.655119\pi$
$349$	−17.4956			−0.936520			−0.468260	+	0.883591i	$0.655119\pi$
$350$		0			0
$351$	15.1929	−	1.55892i	0.810939	−	0.0832089i
$352$	−0.536989	+	22.0765i	−0.0286216	+	1.17668i
$353$			8.26754i			0.440037i	0.975496	+	0.220018i	$0.0706117\pi$
$353$			8.26754i			0.440037i	−0.975496	+	0.220018i	$0.929388\pi$
$354$	15.3995	+	13.0717i	0.818475	+	0.694752i
$355$		−	4.16037i		−	0.220809i
$356$	−12.2236	−	17.1732i	−0.647850	−	0.910179i
$357$		0			0
$358$	−2.44108	+	0.780049i	−0.129015	+	0.0412269i
$359$	−25.1300			−1.32631			−0.663156	−	0.748481i	$-0.730784\pi$
$359$	−25.1300			−1.32631			−0.663156	+	0.748481i	$0.730784\pi$
$360$	−2.63403	+	1.34614i	−0.138825	+	0.0709477i
$361$	−12.1178			−0.637781
$362$	10.1565	−	3.24552i	0.533814	−	0.170581i
$363$	−3.88596	−	6.23025i	−0.203960	−	0.327003i
$364$		0			0
$365$			2.74653i			0.143760i
$366$	26.3232	+	22.3441i	1.37593	+	1.16794i
$367$			21.7131i			1.13341i	0.823920	+	0.566707i	$0.191783\pi$
$367$			21.7131i			1.13341i	−0.823920	+	0.566707i	$0.808217\pi$
$368$	−2.85793	+	8.24635i	−0.148980	+	0.429871i
$369$	20.3960	+	9.98941i	1.06178	+	0.520028i
$370$	0.0959078	+	0.300133i	0.00498601	+	0.0156032i
$371$		0			0
$372$	−3.51394	+	8.43982i	−0.182189	+	0.437584i
$373$	−0.721797			−0.0373732			−0.0186866	−	0.999825i	$-0.505948\pi$
$373$	−0.721797			−0.0373732			−0.0186866	+	0.999825i	$0.505948\pi$
$374$	−6.56008	−	20.5291i	−0.339213	−	1.06153i
$375$	−5.06100	+	3.15667i	−0.261349	+	0.163010i
$376$	−7.39973	+	9.87847i	−0.381612	+	0.509443i
$377$		−	28.6640i		−	1.47627i
$378$		0			0
$379$			18.2745i			0.938699i	0.883013	+	0.469349i	$0.155511\pi$
$379$			18.2745i			0.938699i	−0.883013	+	0.469349i	$0.844489\pi$
$380$	3.16864	−	2.25539i	0.162548	−	0.115699i
$381$	−18.2174	+	11.3627i	−0.933308	+	0.582128i
$382$	−2.19802	+	0.702379i	−0.112461	+	0.0359368i
$383$	−2.04930			−0.104715			−0.0523573	−	0.998628i	$-0.516673\pi$
$383$	−2.04930			−0.104715			−0.0523573	+	0.998628i	$0.516673\pi$
$384$	7.96972	−	17.9021i	0.406703	−	0.913560i
$385$		0			0
$386$	20.4177	−	6.52448i	1.03923	−	0.332087i
$387$	−6.78287	−	3.32206i	−0.344793	−	0.168870i
$388$	3.25879	−	2.31955i	0.165440	−	0.117757i
$389$			11.1466i			0.565158i	0.959244	+	0.282579i	$0.0911899\pi$
$389$			11.1466i			0.565158i	−0.959244	+	0.282579i	$0.908810\pi$
$390$	1.62422	−	1.91347i	0.0822458	−	0.0968923i
$391$		−	8.51757i		−	0.430752i
$392$		0			0
$393$	−1.47622	−	2.36678i	−0.0744656	−	0.119389i
$394$	−9.13726	−	28.5941i	−0.460328	−	1.44055i
$395$	1.39445			0.0701623
$396$	3.80467	+	23.1115i	0.191192	+	1.16140i
$397$	−7.97438			−0.400223			−0.200111	−	0.979773i	$-0.564130\pi$
$397$	−7.97438			−0.400223			−0.200111	+	0.979773i	$0.564130\pi$
$398$	−1.61725	−	5.06100i	−0.0810652	−	0.253685i
$399$		0			0
$400$	6.39002	−	18.4380i	0.319501	−	0.921899i
$401$			21.4779i			1.07256i	0.844042	+	0.536278i	$0.180170\pi$
$401$			21.4779i			1.07256i	−0.844042	+	0.536278i	$0.819830\pi$
$402$	−1.01307	+	1.19348i	−0.0505274	+	0.0595254i
$403$		−	7.75694i		−	0.386401i
$404$	3.58967	+	5.04320i	0.178593	+	0.250909i
$405$	−2.47874	+	1.92349i	−0.123169	+	0.0955790i
$406$		0			0
$407$	2.49490			0.123668
$408$	−1.62796	+	19.0550i	−0.0805962	+	0.943365i
$409$	−36.9136			−1.82526			−0.912630	−	0.408786i	$-0.865952\pi$
$409$	−36.9136			−1.82526			−0.912630	+	0.408786i	$0.865952\pi$
$410$	3.55515	−	1.13605i	0.175576	−	0.0561056i
$411$	−6.41308	+	4.00000i	−0.316334	+	0.197305i
$412$	−8.39604	−	11.7958i	−0.413643	−	0.581136i
$413$		0			0
$414$	−1.34797	+	9.15829i	−0.0662491	+	0.450106i
$415$			3.11784i			0.153049i
$416$	−0.404312	+	16.6219i	−0.0198230	+	0.814956i
$417$	24.7156	−	15.4157i	1.21033	−	0.754912i
$418$	−9.37411	−	29.3353i	−0.458503	−	1.43484i
$419$	29.5773			1.44494			0.722472	−	0.691400i	$-0.243006\pi$
$419$	29.5773			1.44494			0.722472	+	0.691400i	$0.243006\pi$
$420$		0			0
$421$	36.8309			1.79503			0.897515	−	0.440985i	$-0.145371\pi$
$421$	36.8309			1.79503			0.897515	+	0.440985i	$0.145371\pi$
$422$	−4.23566	−	13.2550i	−0.206189	−	0.645245i
$423$	−5.75822	+	11.7569i	−0.279974	+	0.571642i
$424$	−3.89789	−	2.91982i	−0.189298	−	0.141799i
$425$			19.0444i			0.923789i
$426$	22.2861	+	18.9173i	1.07977	+	0.916546i
$427$		0			0
$428$	−17.9462	+	12.7738i	−0.867464	+	0.617447i
$429$	−10.5176	−	16.8625i	−0.507793	−	0.814129i
$430$	−1.18230	+	0.377803i	−0.0570153	+	0.0182193i
$431$	4.67679			0.225273			0.112636	−	0.993636i	$-0.464070\pi$
$431$	4.67679			0.225273			0.112636	+	0.993636i	$0.464070\pi$
$432$	4.76603	−	20.2308i	0.229306	−	0.973354i
$433$	16.5564			0.795650			0.397825	−	0.917461i	$-0.369765\pi$
$433$	16.5564			0.795650			0.397825	+	0.917461i	$0.369765\pi$
$434$		0			0
$435$	3.11632	+	4.99631i	0.149416	+	0.239555i
$436$	2.28072	−	1.62338i	0.109226	−	0.0777456i
$437$		−	12.1713i		−	0.582232i
$438$	−14.7125	−	12.4885i	−0.702991	−	0.596725i
$439$		−	26.4787i		−	1.26376i	−0.775066	−	0.631881i	$-0.782283\pi$
$439$		−	26.4787i		−	1.26376i	0.775066	−	0.631881i	$-0.217717\pi$
$440$	3.08073	+	2.30770i	0.146868	+	0.110015i
$441$		0			0
$442$	−4.93923	−	15.4568i	−0.234935	−	0.735205i
$443$	−4.60099			−0.218599			−0.109300	−	0.994009i	$-0.534861\pi$
$443$	−4.60099			−0.218599			−0.109300	+	0.994009i	$0.534861\pi$
$444$	−2.04384	−	0.850958i	−0.0969963	−	0.0403847i
$445$	−3.67424			−0.174176
$446$	9.86360	+	30.8671i	0.467055	+	1.46160i
$447$	11.2580	−	7.02193i	0.532487	−	0.332126i
$448$		0			0
$449$		−	17.0095i		−	0.802728i	−0.915919	−	0.401364i	$-0.868536\pi$
$449$		−	17.0095i		−	0.802728i	0.915919	−	0.401364i	$-0.131464\pi$
$450$	3.01392	−	20.4770i	0.142078	−	0.965294i
$451$		−	29.5527i		−	1.39158i
$452$	10.2433	+	14.3911i	0.481806	+	0.676900i
$453$	18.5746	−	11.5855i	0.872713	−	0.544333i
$454$	−18.2266	+	5.82431i	−0.855415	+	0.273348i
$455$		0			0
$456$	−2.32630	+	27.2290i	−0.108939	+	1.27511i
$457$	−15.4312			−0.721840			−0.360920	−	0.932597i	$-0.617537\pi$
$457$	−15.4312			−0.721840			−0.360920	+	0.932597i	$0.617537\pi$
$458$	19.7973	−	6.32625i	0.925068	−	0.295606i
$459$	2.07049	+	20.1786i	0.0966421	+	0.941857i
$460$	0.882162	+	1.23937i	0.0411310	+	0.0577858i
$461$		−	33.3764i		−	1.55449i	−0.629196	−	0.777247i	$-0.716616\pi$
$461$		−	33.3764i		−	1.55449i	0.629196	−	0.777247i	$-0.283384\pi$
$462$		0			0
$463$		−	26.4787i		−	1.23057i	−0.788304	−	0.615286i	$-0.789041\pi$
$463$		−	26.4787i		−	1.23057i	0.788304	−	0.615286i	$-0.210959\pi$
$464$	−36.8580	−	12.7738i	−1.71109	−	0.593011i
$465$	0.843327	+	1.35208i	0.0391084	+	0.0627012i
$466$	7.39973	+	23.1567i	0.342786	+	1.07271i
$467$	−18.5911			−0.860296			−0.430148	−	0.902758i	$-0.641539\pi$
$467$	−18.5911			−0.860296			−0.430148	+	0.902758i	$0.641539\pi$
$468$	2.86462	+	17.4012i	0.132417	+	0.804371i
$469$		0			0
$470$	0.654857	+	2.04930i	0.0302063	+	0.0945274i
$471$	0.199312	+	0.319551i	0.00918381	+	0.0147241i
$472$	−13.9835	+	18.6676i	−0.643643	+	0.859248i
$473$			9.82800i			0.451892i
$474$	−6.34059	+	7.46973i	−0.291233	+	0.343096i
$475$			27.2137i			1.24865i
$476$		0			0
$477$	−4.63910	−	2.27210i	−0.212410	−	0.104032i
$478$	−19.5783	+	6.25627i	−0.895492	+	0.286155i
$479$	−40.8777			−1.86775			−0.933874	−	0.357601i	$-0.883595\pi$
$479$	−40.8777			−1.86775			−0.933874	+	0.357601i	$0.883595\pi$
$480$	−1.73664	−	2.94125i	−0.0792666	−	0.134249i
$481$	1.87847			0.0856508
$482$	−25.3149	+	8.08941i	−1.15306	+	0.368462i
$483$		0			0
$484$	6.90760	−	4.91671i	0.313982	−	0.223487i
$485$		−	0.697224i		−	0.0316593i
$486$	0.967180	−	22.0242i	0.0438722	−	0.999037i
$487$			21.4312i			0.971140i	0.874198	+	0.485570i	$0.161388\pi$
$487$			21.4312i			0.971140i	−0.874198	+	0.485570i	$0.838612\pi$
$488$	−23.9027	+	31.9095i	−1.08202	+	1.44448i
$489$	−7.69987	+	4.80260i	−0.348200	+	0.217181i
$490$		0			0
$491$	1.63166			0.0736358			0.0368179	−	0.999322i	$-0.488278\pi$
$491$	1.63166			0.0736358			0.0368179	+	0.999322i	$0.488278\pi$
$492$	−10.0798	+	24.2098i	−0.454432	+	1.09146i
$493$	38.0703			1.71460
$494$	−7.05799	−	22.0872i	−0.317554	−	0.993751i
$495$	3.66655	+	1.79577i	0.164799	+	0.0807141i
$496$	−9.97438	−	3.45681i	−0.447863	−	0.155215i
$497$		0			0
$498$	−16.7015	−	14.1769i	−0.748414	−	0.635282i
$499$			8.88216i			0.397620i	0.980038	+	0.198810i	$0.0637077\pi$
$499$			8.88216i			0.397620i	−0.980038	+	0.198810i	$0.936292\pi$
$500$	−3.99398	−	5.61123i	−0.178616	−	0.250942i
$501$	−10.5176	−	16.8625i	−0.469890	−	0.753361i
$502$	27.8049	−	8.88508i	1.24099	−	0.396560i
$503$	−34.8967			−1.55597			−0.777983	−	0.628286i	$-0.783757\pi$
$503$	−34.8967			−1.55597			−0.777983	+	0.628286i	$0.783757\pi$
$504$		0			0
$505$	1.07900			0.0480150
$506$	11.4741	−	3.66655i	0.510085	−	0.162998i
$507$	3.99736	+	6.40885i	0.177529	+	0.284627i
$508$	−14.3766	−	20.1980i	−0.637860	−	0.896142i
$509$		−	23.7712i		−	1.05364i	−0.849977	−	0.526820i	$-0.823384\pi$
$509$		−	23.7712i		−	1.05364i	0.849977	−	0.526820i	$-0.176616\pi$
$510$	2.54139	+	2.15722i	0.112535	+	0.0955235i
$511$		0			0
$512$	21.1934	+	7.92728i	0.936623	+	0.350340i
$513$	2.95865	+	28.8345i	0.130628	+	1.27307i
$514$	−2.07649	−	6.49815i	−0.0915901	−	0.286621i
$515$	−2.52373			−0.111209
$516$	3.35212	−	8.05117i	0.147569	−	0.354433i
$517$	17.0351			0.749205
$518$		0			0
$519$	31.1634	−	19.4374i	1.36792	−	0.853207i
$520$	2.31955	+	1.73752i	0.101719	+	0.0761954i
$521$		−	5.73027i		−	0.251048i	−0.992091	−	0.125524i	$-0.959939\pi$
$521$		−	5.73027i		−	0.251048i	0.992091	−	0.125524i	$-0.0400612\pi$
$522$	−40.9341	−	6.02491i	−1.79164	−	0.263703i
$523$			4.81770i			0.210664i	0.994437	+	0.105332i	$0.0335904\pi$
$523$			4.81770i			0.210664i	−0.994437	+	0.105332i	$0.966410\pi$
$524$	2.62410	−	1.86779i	0.114634	−	0.0815948i
$525$		0			0
$526$	−19.4762	+	6.22364i	−0.849204	+	0.271364i
$527$	10.3024			0.448781
$528$	−26.3700	+	6.00956i	−1.14761	+	0.261533i
$529$	−18.2394			−0.793016
$530$	−0.808623	+	0.258396i	−0.0351243	+	0.0112240i
$531$	−10.8815	+	22.2174i	−0.472216	+	0.964155i
$532$		0			0
$533$		−	22.2509i		−	0.963795i
$534$	16.7069	−	19.6821i	0.722978	−	0.851727i
$535$			3.83963i			0.166002i
$536$	−1.44676	−	1.08374i	−0.0624906	−	0.0468103i
$537$	−1.66103	−	2.66308i	−0.0716788	−	0.114920i
$538$	2.02854	+	6.34809i	0.0874564	+	0.273685i
$539$		0			0
$540$	−2.39116	−	2.72169i	−0.102899	−	0.117123i
$541$	−12.0388			−0.517590			−0.258795	−	0.965932i	$-0.583325\pi$
$541$	−12.0388			−0.517590			−0.258795	+	0.965932i	$0.583325\pi$
$542$	6.74728	+	21.1149i	0.289820	+	0.906962i
$543$	6.91099	+	11.0802i	0.296579	+	0.475496i
$544$	−22.0765	−	0.536989i	−0.946522	−	0.0230232i
$545$		−	0.487964i		−	0.0209021i
$546$		0			0
$547$			35.3097i			1.50973i	0.655879	+	0.754866i	$0.272298\pi$
$547$			35.3097i			1.50973i	−0.655879	+	0.754866i	$0.727702\pi$
$548$	−5.06100	−	7.11030i	−0.216195	−	0.303737i
$549$	−18.6003	+	37.9774i	−0.793840	+	1.62084i
$550$	−25.6548	+	8.19802i	−1.09393	+	0.349565i
$551$	54.4011			2.31756
$552$	−10.6502	−	0.909900i	−0.453304	−	0.0387279i
$553$		0			0
$554$	−22.8958	+	7.31638i	−0.972751	+	0.310843i
$555$	−0.327428	+	0.204225i	−0.0138986	+	0.00866889i
$556$	19.5048	+	27.4026i	0.827186	+	1.16213i
$557$		−	34.7920i		−	1.47419i	−0.675792	−	0.737093i	$-0.736198\pi$
$557$		−	34.7920i		−	1.47419i	0.675792	−	0.737093i	$-0.263802\pi$
$558$	−11.0774	−	1.63044i	−0.468944	−	0.0690219i
$559$			7.39973i			0.312975i
$560$		0			0
$561$	22.3960	−	13.9690i	0.945562	−	0.589771i
$562$	−2.47874	−	7.75694i	−0.104559	−	0.327207i
$563$	−12.8618			−0.542058			−0.271029	−	0.962571i	$-0.587364\pi$
$563$	−12.8618			−0.542058			−0.271029	+	0.962571i	$0.587364\pi$
$564$	−13.9553	−	5.81032i	−0.587624	−	0.244659i
$565$	3.07900			0.129535
$566$	2.40130	+	7.51461i	0.100934	+	0.315863i
$567$		0			0
$568$	−20.2369	+	27.0157i	−0.849120	+	1.13355i
$569$			15.6909i			0.657795i	0.944366	+	0.328897i	$0.106677\pi$
$569$			15.6909i			0.657795i	−0.944366	+	0.328897i	$0.893323\pi$
$570$	3.63155	+	3.08260i	0.152109	+	0.129116i
$571$			42.0315i			1.75896i	0.475935	+	0.879481i	$0.342110\pi$
$571$			42.0315i			1.75896i	−0.475935	+	0.879481i	$0.657890\pi$
$572$	18.6958	−	13.3074i	0.781710	−	0.556408i
$573$	−1.49564	−	2.39792i	−0.0624813	−	0.100174i
$574$		0			0
$575$	−10.6443			−0.443897
$576$	23.6522	+	4.07116i	0.985508	+	0.169632i
$577$	−38.7921			−1.61494			−0.807468	−	0.589912i	$-0.799163\pi$
$577$	−38.7921			−1.61494			−0.807468	+	0.589912i	$0.799163\pi$
$578$	−2.37176	+	0.757897i	−0.0986522	+	0.0315244i
$579$	13.8932	+	22.2745i	0.577381	+	0.925697i
$580$	−5.53950	+	3.94293i	−0.230015	+	0.163721i
$581$		0			0
$582$	3.73487	+	3.17029i	0.154815	+	0.131413i
$583$			6.72180i			0.278388i
$584$	13.3597	−	17.8348i	0.552827	−	0.738011i
$585$	2.76063	+	1.35208i	0.114138	+	0.0559017i
$586$	−10.2328	−	32.0223i	−0.422711	−	1.32283i
$587$	−7.07471			−0.292004			−0.146002	−	0.989284i	$-0.546641\pi$
$587$	−7.07471			−0.292004			−0.146002	+	0.989284i	$0.546641\pi$
$588$		0			0
$589$	14.7218			0.606601
$590$	1.23750	+	3.87263i	0.0509472	+	0.159434i
$591$	31.1945	−	19.4568i	1.28317	−	0.800346i
$592$	0.837122	−	2.41546i	0.0344055	−	0.0992747i
$593$		−	18.3895i		−	0.755168i	−0.925975	−	0.377584i	$-0.876755\pi$
$593$		−	18.3895i		−	0.755168i	0.925975	−	0.377584i	$-0.123245\pi$
$594$	−26.2915	+	11.4754i	−1.07875	+	0.470843i
$595$		0			0
$596$	8.88449	+	12.4820i	0.363923	+	0.511283i
$597$	5.52126	−	3.44375i	0.225970	−	0.140943i
$598$	8.63910	−	2.76063i	0.353279	−	0.112891i
$599$	−37.8516			−1.54657			−0.773287	−	0.634057i	$-0.781389\pi$
$599$	−37.8516			−1.54657			−0.773287	+	0.634057i	$0.781389\pi$
$600$	23.8128	+	2.03444i	0.972152	+	0.0830557i
$601$	−21.9488			−0.895308			−0.447654	−	0.894207i	$-0.647740\pi$
$601$	−21.9488			−0.895308			−0.447654	+	0.894207i	$0.647740\pi$
$602$		0			0
$603$	−1.72188	−	0.843327i	−0.0701202	−	0.0343429i
$604$	14.6585	+	20.5941i	0.596447	+	0.837960i
$605$		−	1.47789i		−	0.0600849i
$606$	−4.90625	+	5.77997i	−0.199303	+	0.234795i
$607$			25.8785i			1.05037i	0.850987	+	0.525187i	$0.176005\pi$
$607$			25.8785i			1.05037i	−0.850987	+	0.525187i	$0.823995\pi$
$608$	−31.5465	−	0.767338i	−1.27938	−	0.0311197i
$609$		0			0
$610$	2.11533	+	6.61968i	0.0856470	+	0.268023i
$611$	12.8262			0.518891
$612$	−23.1115	+	3.80467i	−0.934227	+	0.153795i
$613$	−12.9136			−0.521576			−0.260788	−	0.965396i	$-0.583982\pi$
$613$	−12.9136			−0.521576			−0.260788	+	0.965396i	$0.583982\pi$
$614$	1.59268	+	4.98412i	0.0642753	+	0.201143i
$615$	2.41910	+	3.87847i	0.0975475	+	0.156395i
$616$		0			0
$617$		−	26.4677i		−	1.06555i	−0.846257	−	0.532775i	$-0.821149\pi$
$617$		−	26.4677i		−	1.06555i	0.846257	−	0.532775i	$-0.178851\pi$
$618$	11.4755	−	13.5190i	0.461611	−	0.543815i
$619$			34.3390i			1.38020i	0.723714	+	0.690100i	$0.242433\pi$
$619$			34.3390i			1.38020i	−0.723714	+	0.690100i	$0.757567\pi$
$620$	−1.49908	+	1.06702i	−0.0602044	+	0.0428525i
$621$	−11.2782	+	1.15723i	−0.452579	+	0.0464382i
$622$	−10.2174	+	3.26499i	−0.409682	+	0.130914i
$623$		0			0
$624$	−19.8546	+	4.52474i	−0.794819	+	0.181135i
$625$	23.1918			0.927673
$626$	21.0626	−	6.73056i	0.841829	−	0.269007i
$627$	32.0031	−	19.9612i	1.27808	−	0.797172i
$628$	−0.354292	+	0.252179i	−0.0141378	+	0.0100631i
$629$			2.49490i			0.0994782i
$630$		0			0
$631$		−	27.7569i		−	1.10499i	−0.833517	−	0.552493i	$-0.813677\pi$
$631$		−	27.7569i		−	1.10499i	0.833517	−	0.552493i	$-0.186323\pi$
$632$	−9.05498	−	6.78287i	−0.360188	−	0.269808i
$633$	14.4605	−	9.01938i	0.574753	−	0.358488i
$634$	5.98058	+	18.7156i	0.237519	+	0.743291i
$635$	−4.32141			−0.171490
$636$	2.29266	−	5.50654i	0.0909099	−	0.218349i
$637$		0			0
$638$	16.3881	+	51.2847i	0.648810	+	2.03038i
$639$	−15.7476	+	32.1530i	−0.622967	+	1.27195i
$640$	3.26790	−	2.20832i	0.129175	−	0.0872915i
$641$			6.96331i			0.275034i	0.990499	+	0.137517i	$0.0439122\pi$
$641$			6.96331i			0.275034i	−0.990499	+	0.137517i	$0.956088\pi$
$642$	−20.5680	−	17.4589i	−0.811756	−	0.689049i
$643$		−	9.74373i		−	0.384255i	−0.981370	−	0.192128i	$-0.938461\pi$
$643$		−	9.74373i		−	0.384255i	0.981370	−	0.192128i	$-0.0615387\pi$
$644$		0			0
$645$	−0.804492	−	1.28982i	−0.0316768	−	0.0507865i
$646$	29.3353	−	9.37411i	1.15418	−	0.368819i
$647$	−28.1896			−1.10825			−0.554123	−	0.832434i	$-0.686946\pi$
$647$	−28.1896			−1.10825			−0.554123	+	0.832434i	$0.686946\pi$
$648$	25.4522	−	0.433298i	0.999855	−	0.0170216i
$649$	32.1918			1.26364
$650$	−19.3161	+	6.17248i	−0.757641	+	0.242105i
$651$		0			0
$652$	−6.07649	−	8.53699i	−0.237974	−	0.334334i
$653$		−	10.8527i		−	0.424697i	−0.977194	−	0.212349i	$-0.931889\pi$
$653$		−	10.8527i		−	0.424697i	0.977194	−	0.212349i	$-0.0681112\pi$
$654$	2.61391	+	2.21878i	0.102212	+	0.0867613i
$655$		−	0.561431i		−	0.0219369i
$656$	−28.6117	−	9.91592i	−1.11710	−	0.387151i
$657$	10.3960	−	21.2263i	0.405588	−	0.828116i
$658$		0			0
$659$	−19.2248			−0.748893			−0.374446	−	0.927249i	$-0.622167\pi$
$659$	−19.2248			−0.748893			−0.374446	+	0.927249i	$0.622167\pi$
$660$	−1.81202	+	4.35214i	−0.0705329	+	0.169407i
$661$	2.74742			0.106862			0.0534311	−	0.998572i	$-0.482984\pi$
$661$	2.74742			0.106862			0.0534311	+	0.998572i	$0.482984\pi$
$662$	13.6871	+	42.8323i	0.531964	+	1.66472i
$663$	16.8625	−	10.5176i	0.654885	−	0.408469i
$664$	15.1658	−	20.2460i	0.588547	−	0.785696i
$665$		0			0
$666$	0.394837	−	2.68258i	0.0152996	−	0.103948i
$667$			21.2782i			0.823895i
$668$	18.6958	−	13.3074i	0.723361	−	0.514877i
$669$	−33.6742	+	21.0035i	−1.30192	+	0.812041i
$670$	−0.300133	+	0.0959078i	−0.0115952	+	0.00370524i
$671$	55.0271			2.12430
$672$		0			0
$673$	31.3097			1.20690			0.603449	−	0.797401i	$-0.293793\pi$
$673$	31.3097			1.20690			0.603449	+	0.797401i	$0.293793\pi$
$674$	23.0596	−	7.36870i	0.888221	−	0.283832i
$675$	25.2169	−	2.58746i	0.970598	−	0.0995912i
$676$	−7.10562	+	5.05766i	−0.273293	+	0.194525i
$677$		−	20.9823i		−	0.806415i	−0.915109	−	0.403208i	$-0.867895\pi$
$677$		−	20.9823i		−	0.806415i	0.915109	−	0.403208i	$-0.132105\pi$
$678$	−14.0003	+	16.4935i	−0.537678	+	0.633429i
$679$		0			0
$680$	−2.30770	+	3.08073i	−0.0884963	+	0.118140i
$681$	−12.4022	−	19.8841i	−0.475255	−	0.761962i
$682$	4.43488	+	13.8785i	0.169820	+	0.531434i
$683$	−15.8234			−0.605467			−0.302734	−	0.953075i	$-0.597899\pi$
$683$	−15.8234			−0.605467			−0.302734	+	0.953075i	$0.597899\pi$
$684$	−33.0255	+	5.43673i	−1.26276	+	0.207879i
$685$	−1.52126			−0.0581245
$686$		0			0
$687$	13.4711	+	21.5978i	0.513953	+	0.824006i
$688$	9.51506	+	3.29762i	0.362758	+	0.125721i
$689$			5.06100i			0.192809i
$690$	−1.20571	+	1.42043i	−0.0459007	+	0.0540748i
$691$			24.4093i			0.928572i	0.885685	+	0.464286i	$0.153689\pi$
$691$			24.4093i			0.928572i	−0.885685	+	0.464286i	$0.846311\pi$
$692$	24.5931	+	34.5514i	0.934891	+	1.31345i
$693$		0			0
$694$	11.3803	−	3.63659i	0.431991	−	0.138043i
$695$	5.86285			0.222391
$696$	4.06690	−	47.6024i	0.154156	−	1.80437i
$697$	29.5527			1.11939
$698$	23.5685	−	7.53133i	0.892081	−	0.285065i
$699$	−25.2626	+	15.7569i	−0.955520	+	0.595982i
$700$		0			0
$701$		−	21.4779i		−	0.811209i	−0.914049	−	0.405605i	$-0.867061\pi$
$701$		−	21.4779i		−	0.811209i	0.914049	−	0.405605i	$-0.132939\pi$
$702$	−19.7954	+	8.64012i	−0.747131	+	0.326100i
$703$			3.56512i			0.134461i
$704$	−8.77986	−	29.9705i	−0.330904	−	1.12956i
$705$	−2.23568	+	1.39445i	−0.0842004	+	0.0525179i
$706$	−3.55892	−	11.1373i	−0.133942	−	0.419156i
$707$		0			0
$708$	−26.3718	−	10.9799i	−0.991111	−	0.412651i
$709$	−42.1918			−1.58455			−0.792273	−	0.610166i	$-0.791103\pi$
$709$	−42.1918			−1.58455			−0.792273	+	0.610166i	$0.791103\pi$
$710$	1.79091	+	5.60446i	0.0672116	+	0.210331i
$711$	−10.7769	−	5.27820i	−0.404164	−	0.197948i
$712$	23.8591	+	17.8723i	0.894156	+	0.669791i
$713$			5.75822i			0.215647i
$714$		0			0
$715$		−	4.00000i		−	0.149592i
$716$	2.95261	−	2.10162i	0.110344	−	0.0785412i
$717$	−13.3221	−	21.3589i	−0.497522	−	0.797661i
$718$	33.8528	−	10.8177i	1.26338	−	0.403713i
$719$	−19.0588			−0.710774			−0.355387	−	0.934719i	$-0.615651\pi$
$719$	−19.0588			−0.710774			−0.355387	+	0.934719i	$0.615651\pi$
$720$	2.96884	−	2.94726i	0.110642	−	0.109838i
$721$		0			0
$722$	16.3240	−	5.21635i	0.607517	−	0.194133i
$723$	−17.2255	−	27.6172i	−0.640624	−	1.02709i
$724$	−12.2848	+	8.74413i	−0.456561	+	0.324973i
$725$		−	47.5758i		−	1.76692i
$726$	7.91674	+	6.72002i	0.293818	+	0.249403i
$727$		−	3.72549i		−	0.138171i	−0.997611	−	0.0690854i	$-0.977992\pi$
$727$		−	3.72549i		−	0.138171i	0.997611	−	0.0690854i	$-0.0220081\pi$
$728$		0			0
$729$	26.4374	−	5.48311i	0.979163	−	0.203078i
$730$	−1.18230	−	3.69987i	−0.0437587	−	0.136938i
$731$	−9.82800			−0.363502
$732$	−45.0786	−	18.7686i	−1.66615	−	0.693706i
$733$	25.4180			0.938834			0.469417	−	0.882977i	$-0.344464\pi$
$733$	25.4180			0.938834			0.469417	+	0.882977i	$0.344464\pi$
$734$	−9.34681	−	29.2498i	−0.344997	−	1.07963i
$735$		0			0
$736$	0.300133	−	12.3390i	0.0110631	−	0.454820i
$737$			2.49490i			0.0919009i
$738$	−31.7758	−	4.67694i	−1.16968	−	0.172161i
$739$		−	23.3097i		−	0.857459i	−0.903433	−	0.428730i	$-0.858961\pi$
$739$		−	23.3097i		−	0.857459i	0.903433	−	0.428730i	$-0.141039\pi$
$740$	−0.258396	−	0.363026i	−0.00949883	−	0.0133451i
$741$	24.0959	−	15.0292i	0.885185	−	0.552113i
$742$		0			0
$743$	33.8576			1.24211			0.621057	−	0.783765i	$-0.286703\pi$
$743$	33.8576			1.24211			0.621057	+	0.783765i	$0.286703\pi$
$744$	1.10057	−	12.8820i	0.0403488	−	0.472276i
$745$	2.67055			0.0978415
$746$	0.972337	−	0.310711i	0.0355998	−	0.0113759i
$747$	11.8015	−	24.0959i	0.431795	−	0.881623i
$748$	17.6742	+	24.8309i	0.646234	+	0.907908i
$749$		0			0
$750$	5.45885	−	6.43098i	0.199329	−	0.234826i
$751$		−	48.1530i		−	1.75713i	−0.477625	−	0.878564i	$-0.658502\pi$
$751$		−	48.1530i		−	1.75713i	0.477625	−	0.878564i	$-0.341498\pi$
$752$	5.71586	−	16.4927i	0.208436	−	0.601427i
$753$	18.9198	+	30.3336i	0.689476	+	1.10542i
$754$	12.3390	+	38.6135i	0.449359	+	1.40622i
$755$	4.40614			0.160356
$756$		0			0
$757$	−11.3923			−0.414062			−0.207031	−	0.978334i	$-0.566380\pi$
$757$	−11.3923			−0.414062			−0.207031	+	0.978334i	$0.566380\pi$
$758$	−7.86661	−	24.6177i	−0.285728	−	0.894156i
$759$	7.80753	+	12.5176i	0.283395	+	0.454359i
$760$	−3.29762	+	4.40225i	−0.119617	+	0.159686i
$761$			27.5491i			0.998656i	0.866413	+	0.499328i	$0.166420\pi$
$761$			27.5491i			0.998656i	−0.866413	+	0.499328i	$0.833580\pi$
$762$	19.6496	−	23.1488i	0.711828	−	0.838592i
$763$		0			0
$764$	2.65862	−	1.89236i	0.0961853	−	0.0684632i
$765$	−1.79577	+	3.66655i	−0.0649264	+	0.132564i
$766$	2.76063	−	0.882162i	0.0997457	−	0.0318738i
$767$	24.2380			0.875182
$768$	−3.02979	+	27.5467i	−0.109328	+	0.994006i
$769$	5.83461			0.210401			0.105201	−	0.994451i	$-0.466451\pi$
$769$	5.83461			0.210401			0.105201	+	0.994451i	$0.466451\pi$
$770$		0			0
$771$	7.08912	−	4.42166i	0.255308	−	0.159242i
$772$	−24.6962	+	17.5783i	−0.888835	+	0.632658i
$773$			47.5682i			1.71091i	0.517879	+	0.855454i	$0.326722\pi$
$773$			47.5682i			1.71091i	−0.517879	+	0.855454i	$0.673278\pi$
$774$	10.5673	+	1.55536i	0.379834	+	0.0559061i
$775$		−	12.8748i		−	0.462476i
$776$	−3.39144	+	4.52749i	−0.121745	+	0.162527i
$777$		0			0
$778$	−4.79829	−	15.0157i	−0.172027	−	0.538340i
$779$	42.2298			1.51304
$780$	−1.36431	+	3.27683i	−0.0488503	+	0.117329i
$781$	46.5879			1.66704
$782$	3.66655	+	11.4741i	0.131116	+	0.410312i
$783$	−5.17240	−	50.4093i	−0.184846	−	1.80148i
$784$		0			0
$785$			0.0758015i			0.00270547i
$786$	3.00746	+	2.55284i	0.107272	+	0.0910569i
$787$		−	48.8177i		−	1.74016i	−0.492908	−	0.870082i	$-0.664066\pi$
$787$		−	48.8177i		−	1.74016i	0.492908	−	0.870082i	$-0.335934\pi$
$788$	24.6177	+	34.5859i	0.876970	+	1.23207i
$789$	−13.2526	−	21.2475i	−0.471804	−	0.756430i
$790$	−1.87847	+	0.600267i	−0.0668330	+	0.0213565i
$791$		0			0
$792$	−15.0741	−	29.4959i	−0.535634	−	1.04809i
$793$	41.4312			1.47126
$794$	10.7423	−	3.43272i	0.381231	−	0.121823i
$795$	−0.550227	−	0.882162i	−0.0195145	−	0.0312871i
$796$	4.35721	+	6.12153i	0.154437	+	0.216972i
$797$			12.7292i			0.450890i	0.974256	+	0.225445i	$0.0723837\pi$
$797$			12.7292i			0.450890i	−0.974256	+	0.225445i	$0.927616\pi$
$798$		0			0
$799$			17.0351i			0.602660i
$800$	−0.671066	+	27.5886i	−0.0237258	+	0.975405i
$801$	28.3960	+	13.9076i	1.00332	+	0.491401i
$802$	−9.24557	−	28.9330i	−0.326473	−	1.02166i
$803$	−30.7557			−1.08534
$804$	0.850958	−	2.04384i	0.0300110	−	0.0720807i
$805$		0			0
$806$	3.33912	+	10.4494i	0.117616	+	0.368065i
$807$	−6.92541	+	4.31955i	−0.243786	+	0.152055i
$808$	−7.00661	−	5.24849i	−0.246492	−	0.184641i
$809$			26.5813i			0.934548i	0.884113	+	0.467274i	$0.154764\pi$
$809$			26.5813i			0.934548i	−0.884113	+	0.467274i	$0.845236\pi$
$810$	2.51112	−	3.65817i	0.0882317	−	0.128535i
$811$			4.13977i			0.145367i	0.997355	+	0.0726835i	$0.0231563\pi$
$811$			4.13977i			0.145367i	−0.997355	+	0.0726835i	$0.976844\pi$
$812$		0			0
$813$	−23.0351	+	14.3676i	−0.807878	+	0.503894i
$814$	−3.36090	+	1.07398i	−0.117799	+	0.0376429i
$815$	−1.82651			−0.0639797
$816$	−6.00956	−	26.3700i	−0.210377	−	0.923133i
$817$	−14.0439			−0.491332
$818$	49.7266	−	15.8902i	1.73865	−	0.555587i
$819$		0			0
$820$	−4.30013	+	3.06077i	−0.150167	+	0.106887i
$821$			29.5082i			1.02984i	0.857237	+	0.514922i	$0.172179\pi$
$821$			29.5082i			1.02984i	−0.857237	+	0.514922i	$0.827821\pi$
$822$	6.91723	−	8.14906i	0.241266	−	0.284231i
$823$		−	12.0777i		−	0.421001i	−0.977594	−	0.210501i	$-0.932491\pi$
$823$		−	12.0777i		−	0.421001i	0.977594	−	0.210501i	$-0.0675094\pi$
$824$	16.3881	+	12.2759i	0.570906	+	0.427652i
$825$	−17.4568	−	27.9880i	−0.607768	−	0.974416i
$826$		0			0
$827$	−11.9341			−0.414989			−0.207494	−	0.978236i	$-0.566531\pi$
$827$	−11.9341			−0.414989			−0.207494	+	0.978236i	$0.566531\pi$
$828$	−2.12650	−	12.9175i	−0.0739010	−	0.448913i
$829$	2.50436			0.0869800			0.0434900	−	0.999054i	$-0.486152\pi$
$829$	2.50436			0.0869800			0.0434900	+	0.999054i	$0.486152\pi$
$830$	−1.34213	−	4.20006i	−0.0465861	−	0.145786i
$831$	−15.5795	−	24.9781i	−0.540445	−	0.866480i
$832$	−6.61057	−	22.5655i	−0.229180	−	0.782319i
$833$		0			0
$834$	−26.6585	+	31.4059i	−0.923110	+	1.08750i
$835$		−	4.00000i		−	0.138426i
$836$	25.2559	+	35.4825i	0.873492	+	1.22719i
$837$	−1.39973	−	13.6416i	−0.0483819	−	0.471521i
$838$	−39.8437	+	12.7321i	−1.37638	+	0.439823i
$839$	1.64607			0.0568288			0.0284144	−	0.999596i	$-0.490954\pi$
$839$	1.64607			0.0568288			0.0284144	+	0.999596i	$0.490954\pi$
$840$		0			0
$841$	−66.1054			−2.27950
$842$	−49.6152	+	15.8546i	−1.70985	+	0.546385i
$843$	8.46238	−	5.27820i	0.291460	−	0.181791i
$844$	11.4118	+	16.0326i	0.392809	+	0.551866i
$845$			1.52026i			0.0522986i
$846$	2.69594	−	18.3166i	0.0926884	−	0.629737i
$847$		0			0
$848$	6.50776	+	2.25539i	0.223477	+	0.0774503i
$849$	−8.19802	+	5.11331i	−0.281355	+	0.175488i
$850$	−8.19802	−	25.6548i	−0.281190	−	0.879953i
$851$	−1.39445			−0.0478010
$852$	−38.1651	−	15.8901i	−1.30751	−	0.544387i
$853$	15.1311			0.518077			0.259039	−	0.965867i	$-0.416594\pi$
$853$	15.1311			0.518077			0.259039	+	0.965867i	$0.416594\pi$
$854$		0			0
$855$	−2.56610	+	5.23937i	−0.0877587	+	0.179183i
$856$	18.6768	−	24.9330i	0.638358	−	0.852193i
$857$		−	48.9224i		−	1.67116i	−0.549370	−	0.835579i	$-0.685132\pi$
$857$		−	48.9224i		−	1.67116i	0.549370	−	0.835579i	$-0.314868\pi$
$858$	21.4271	+	18.1881i	0.731508	+	0.620932i
$859$		−	16.0571i		−	0.547860i	−0.961750	−	0.273930i	$-0.911676\pi$
$859$		−	16.0571i		−	0.547860i	0.961750	−	0.273930i	$-0.0883237\pi$
$860$	1.43005	−	1.01788i	0.0487641	−	0.0347095i
$861$		0			0
$862$	−6.30013	+	2.01321i	−0.214583	+	0.0685703i
$863$	−14.9034			−0.507318			−0.253659	−	0.967294i	$-0.581634\pi$
$863$	−14.9034			−0.507318			−0.253659	+	0.967294i	$0.581634\pi$
$864$	2.28838	+	29.3047i	0.0778522	+	0.996965i
$865$	7.39235			0.251347
$866$	−22.3032	+	7.12702i	−0.757895	+	0.242186i
$867$	−1.61386	−	2.58746i	−0.0548096	−	0.0878746i
$868$		0			0
$869$			15.6151i			0.529704i
$870$	−6.34878	−	5.38908i	−0.215244	−	0.182707i
$871$			1.87847i			0.0636495i
$872$	−2.37355	+	3.16864i	−0.0803787	+	0.107304i
$873$	−2.63910	+	5.38843i	−0.0893201	+	0.182371i
$874$	5.23937	+	16.3960i	0.177224	+	0.554604i
$875$		0			0
$876$	25.1953	+	10.4901i	0.851269	+	0.354428i
$877$	11.8785			0.401107			0.200554	−	0.979683i	$-0.435726\pi$
$877$	11.8785			0.401107			0.200554	+	0.979683i	$0.435726\pi$
$878$	11.3983	+	35.6697i	0.384673	+	1.20379i
$879$	34.9346	−	21.7896i	1.17831	−	0.734944i
$880$	−5.14346	−	1.78256i	−0.173386	−	0.0600901i
$881$			36.4995i			1.22970i	0.788644	+	0.614850i	$0.210783\pi$
$881$			36.4995i			1.22970i	−0.788644	+	0.614850i	$0.789217\pi$
$882$		0			0
$883$			31.1178i			1.04720i	0.851965	+	0.523599i	$0.175411\pi$
$883$			31.1178i			1.04720i	−0.851965	+	0.523599i	$0.824589\pi$
$884$	13.3074	+	18.6958i	0.447575	+	0.628807i
$885$	−4.22482	+	2.63513i	−0.142016	+	0.0885789i
$886$	6.19802	−	1.98058i	0.208227	−	0.0665390i
$887$	−56.9248			−1.91135			−0.955674	−	0.294428i	$-0.904871\pi$
$887$	−56.9248			−1.91135			−0.955674	+	0.294428i	$0.904871\pi$
$888$	3.11958	+	0.266521i	0.104686	+	0.00894386i
$889$		0			0
$890$	4.94960	−	1.58165i	0.165911	−	0.0530170i
$891$	−21.5393	−	27.7569i	−0.721593	−	0.929892i
$892$	−26.5746	−	37.3353i	−0.889785	−	1.25008i
$893$			24.3426i			0.814594i
$894$	−12.1431	+	14.3055i	−0.406125	+	0.478448i
$895$		−	0.631717i		−	0.0211160i
$896$		0			0
$897$	5.87847	+	9.42477i	0.196276	+	0.314684i
$898$	7.32206	+	22.9136i	0.244340	+	0.764637i
$899$	−25.7370			−0.858379
$900$	4.75463	+	28.8821i	0.158488	+	0.962736i
$901$	−6.72180			−0.223936
$902$	12.7215	+	39.8107i	0.423581	+	1.32555i
$903$		0			0
$904$	−19.9938	−	14.9769i	−0.664984	−	0.498124i
$905$			2.62836i			0.0873696i
$906$	−20.0348	+	23.6027i	−0.665613	+	0.784147i
$907$			6.70939i			0.222782i	0.993777	+	0.111391i	$0.0355305\pi$
$907$			6.70939i			0.222782i	−0.993777	+	0.111391i	$0.964469\pi$
$908$	22.0459	−	15.6919i	0.731620	−	0.520755i
$909$	−8.33897	−	4.08419i	−0.276586	−	0.135464i
$910$		0			0
$911$	−50.1275			−1.66080			−0.830399	−	0.557169i	$-0.811888\pi$
$911$	−50.1275			−1.66080			−0.830399	+	0.557169i	$0.811888\pi$
$912$	−8.58745	−	37.6817i	−0.284359	−	1.24777i
$913$	−34.9136			−1.15547
$914$	20.7875	−	6.64265i	0.687588	−	0.219719i
$915$	−7.22170	+	4.50436i	−0.238742	+	0.148910i
$916$	−23.9458	+	17.0443i	−0.791193	+	0.563158i
$917$		0			0
$918$	−11.4754	−	26.2915i	−0.378746	−	0.867747i
$919$			17.0351i			0.561938i	0.959717	+	0.280969i	$0.0906557\pi$
$919$			17.0351i			0.561938i	−0.959717	+	0.280969i	$0.909344\pi$
$920$	−1.72188	−	1.28982i	−0.0567686	−	0.0425240i
$921$	−5.43739	+	3.39144i	−0.179168	+	0.111752i
$922$	14.3675	+	44.9616i	0.473169	+	1.48073i
$923$	35.0771			1.15458
$924$		0			0
$925$	3.11784			0.102514
$926$	11.3983	+	35.6697i	0.374571	+	1.17218i
$927$	19.5044	+	9.55271i	0.640609	+	0.313752i
$928$	55.1505	+	1.34148i	1.81040	+	0.0440363i
$929$		−	23.4082i		−	0.767997i	−0.923334	−	0.383999i	$-0.874547\pi$
$929$		−	23.4082i		−	0.767997i	0.923334	−	0.383999i	$-0.125453\pi$
$930$	−1.71808	−	1.45837i	−0.0563381	−	0.0478219i
$931$		0			0
$932$	−19.9365	−	28.0092i	−0.653040	−	0.917470i
$933$	−6.95245	−	11.1466i	−0.227613	−	0.364925i
$934$	25.0443	−	8.00291i	0.819473	−	0.261863i
$935$	5.31263			0.173741
$936$	−11.3496	−	22.2081i	−0.370974	−	0.725896i
$937$	48.5929			1.58746			0.793730	−	0.608270i	$-0.208136\pi$
$937$	48.5929			1.58746			0.793730	+	0.608270i	$0.208136\pi$
$938$		0			0
$939$	14.3320	+	22.9781i	0.467707	+	0.749861i
$940$	−1.76432	−	2.47874i	−0.0575459	−	0.0808475i
$941$			14.6116i			0.476324i	0.971225	+	0.238162i	$0.0765449\pi$
$941$			14.6116i			0.476324i	−0.971225	+	0.238162i	$0.923455\pi$
$942$	−0.406051	−	0.344671i	−0.0132299	−	0.0112300i
$943$			16.5176i			0.537886i
$944$	10.8014	−	31.1668i	0.351556	−	1.01439i
$945$		0			0
$946$	−4.23065	−	13.2394i	−0.137550	−	0.430449i
$947$	−31.4250			−1.02117			−0.510587	−	0.859826i	$-0.670572\pi$
$947$	−31.4250			−1.02117			−0.510587	+	0.859826i	$0.670572\pi$
$948$	5.32596	−	12.7920i	0.172979	−	0.415463i
$949$	−23.1567			−0.751697
$950$	−11.7147	−	36.6598i	−0.380074	−	1.18940i
$951$	−20.4177	+	12.7350i	−0.662088	+	0.412961i
$952$		0			0
$953$			14.0113i			0.453872i	0.973910	+	0.226936i	$0.0728708\pi$
$953$			14.0113i			0.453872i	−0.973910	+	0.226936i	$0.927129\pi$
$954$	7.22743	+	1.06378i	0.233997	+	0.0344410i
$955$		−	0.568816i		−	0.0184065i
$956$	23.6810	−	16.8557i	0.765898	−	0.545153i
$957$	−55.9488	+	34.8967i	−1.80857	+	1.12805i
$958$	55.0666	−	17.5966i	1.77912	−	0.568520i
$959$		0			0
$960$	3.60556	+	3.21461i	0.116369	+	0.103751i
$961$	24.0351			0.775327
$962$	−2.53050	+	0.808623i	−0.0815866	+	0.0260711i
$963$	14.5336	−	29.6742i	0.468339	−	0.956239i
$964$	30.6197	−	21.7946i	0.986194	−	0.701957i
$965$			5.28380i			0.170091i
$966$		0			0
$967$		−	35.9876i		−	1.15728i	−0.815582	−	0.578641i	$-0.803583\pi$
$967$		−	35.9876i		−	1.15728i	0.815582	−	0.578641i	$-0.196417\pi$
$968$	−7.18878	+	9.59685i	−0.231056	+	0.308454i
$969$	19.9612	+	32.0031i	0.641245	+	1.02809i
$970$	0.300133	+	0.939235i	0.00963670	+	0.0301570i
$971$	48.3844			1.55273			0.776365	−	0.630283i	$-0.217061\pi$
$971$	48.3844			1.55273			0.776365	+	0.630283i	$0.217061\pi$
$972$	8.17783	+	30.0853i	0.262304	+	0.964985i
$973$		0			0
$974$	−9.22546	−	28.8701i	−0.295603	−	0.925057i
$975$	−13.1436	−	21.0728i	−0.420933	−	0.674870i
$976$	18.4634	−	53.2749i	0.590999	−	1.70529i
$977$		−	37.6432i		−	1.20431i	−0.798378	−	0.602156i	$-0.794308\pi$
$977$		−	37.6432i		−	1.20431i	0.798378	−	0.602156i	$-0.205692\pi$
$978$	8.30517	−	9.78417i	0.265570	−	0.312863i
$979$		−	41.1443i		−	1.31498i
$980$		0			0
$981$	−1.84702	+	3.77118i	−0.0589708	+	0.120405i
$982$	−2.19802	+	0.702379i	−0.0701417	+	0.0224138i
$983$	5.35499			0.170798			0.0853989	−	0.996347i	$-0.472784\pi$
$983$	5.35499			0.170798			0.0853989	+	0.996347i	$0.472784\pi$
$984$	3.15700	−	36.9522i	0.100642	−	1.17799i
$985$	7.39973			0.235775
$986$	−51.2847	+	16.3881i	−1.63324	+	0.521903i
$987$		0			0
$988$	19.0157	+	26.7156i	0.604971	+	0.849936i
$989$		−	5.49306i		−	0.174669i
$990$	−5.71226	−	0.840763i	−0.181548	−	0.0267212i
$991$		−	51.0278i		−	1.62095i	−0.585773	−	0.810475i	$-0.699209\pi$
$991$		−	51.0278i		−	1.62095i	0.585773	−	0.810475i	$-0.300791\pi$
$992$	14.9246	+	0.363026i	0.473856	+	0.0115261i
$993$	−46.7276	+	29.1452i	−1.48286	+	0.924895i
$994$		0			0
$995$	1.30971			0.0415207
$996$	28.6015	+	11.9083i	0.906272	+	0.377329i
$997$	53.9305			1.70800			0.853998	−	0.520276i	$-0.174171\pi$
$997$	53.9305			1.70800			0.853998	+	0.520276i	$0.174171\pi$
$998$	−3.82350	−	11.9652i	−0.121031	−	0.378752i
$999$	3.30352	−	0.338968i	0.104519	−	0.0107245i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.e.c.491.2		12
3.2	odd	2	inner	588.2.e.c.491.11		12
4.3	odd	2	inner	588.2.e.c.491.12		12
7.2	even	3		588.2.n.g.263.10		24
7.3	odd	6		588.2.n.f.275.7		24
7.4	even	3		588.2.n.g.275.7		24
7.5	odd	6		588.2.n.f.263.10		24
7.6	odd	2		84.2.e.a.71.2	yes	12
12.11	even	2	inner	588.2.e.c.491.1		12
21.2	odd	6		588.2.n.g.263.3		24
21.5	even	6		588.2.n.f.263.3		24
21.11	odd	6		588.2.n.g.275.6		24
21.17	even	6		588.2.n.f.275.6		24
21.20	even	2		84.2.e.a.71.11	yes	12
28.3	even	6		588.2.n.f.275.3		24
28.11	odd	6		588.2.n.g.275.3		24
28.19	even	6		588.2.n.f.263.6		24
28.23	odd	6		588.2.n.g.263.6		24
28.27	even	2		84.2.e.a.71.12	yes	12
56.13	odd	2		1344.2.h.h.575.3		12
56.27	even	2		1344.2.h.h.575.10		12
84.11	even	6		588.2.n.g.275.10		24
84.23	even	6		588.2.n.g.263.7		24
84.47	odd	6		588.2.n.f.263.7		24
84.59	odd	6		588.2.n.f.275.10		24
84.83	odd	2		84.2.e.a.71.1	✓	12
168.83	odd	2		1344.2.h.h.575.4		12
168.125	even	2		1344.2.h.h.575.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.e.a.71.1	✓	12	84.83	odd	2
84.2.e.a.71.2	yes	12	7.6	odd	2
84.2.e.a.71.11	yes	12	21.20	even	2
84.2.e.a.71.12	yes	12	28.27	even	2
588.2.e.c.491.1		12	12.11	even	2	inner
588.2.e.c.491.2		12	1.1	even	1	trivial
588.2.e.c.491.11		12	3.2	odd	2	inner
588.2.e.c.491.12		12	4.3	odd	2	inner
588.2.n.f.263.3		24	21.5	even	6
588.2.n.f.263.6		24	28.19	even	6
588.2.n.f.263.7		24	84.47	odd	6
588.2.n.f.263.10		24	7.5	odd	6
588.2.n.f.275.3		24	28.3	even	6
588.2.n.f.275.6		24	21.17	even	6
588.2.n.f.275.7		24	7.3	odd	6
588.2.n.f.275.10		24	84.59	odd	6
588.2.n.g.263.3		24	21.2	odd	6
588.2.n.g.263.6		24	28.23	odd	6
588.2.n.g.263.7		24	84.23	even	6
588.2.n.g.263.10		24	7.2	even	3
588.2.n.g.275.3		24	28.11	odd	6
588.2.n.g.275.6		24	21.11	odd	6
588.2.n.g.275.7		24	7.4	even	3
588.2.n.g.275.10		24	84.11	even	6
1344.2.h.h.575.3		12	56.13	odd	2
1344.2.h.h.575.4		12	168.83	odd	2
1344.2.h.h.575.9		12	168.125	even	2
1344.2.h.h.575.10		12	56.27	even	2

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34711 + 0.430469i) q^{2} +(-0.916638 - 1.46962i) q^{3} +(1.62939 - 1.15978i) q^{4} -0.348612i q^{5} +(1.86743 + 1.58515i) q^{6} +(-1.69572 + 2.26374i) q^{8} +(-1.31955 + 2.69421i) q^{9} +O(q^{10})\)	\(q+(-1.34711 + 0.430469i) q^{2} +(-0.916638 - 1.46962i) q^{3} +(1.62939 - 1.15978i) q^{4} -0.348612i q^{5} +(1.86743 + 1.58515i) q^{6} +(-1.69572 + 2.26374i) q^{8} +(-1.31955 + 2.69421i) q^{9} +(0.150067 + 0.469617i) q^{10} +3.90376 q^{11} +(-3.19799 - 1.33149i) q^{12} +2.93923 q^{13} +(-0.512326 + 0.319551i) q^{15} +(1.30984 - 3.77946i) q^{16} +3.90376i q^{17} +(0.617800 - 4.19742i) q^{18} +5.57834i q^{19} +(-0.404312 - 0.568026i) q^{20} +(-5.25879 + 1.68045i) q^{22} -2.18189 q^{23} +(4.88120 + 0.417024i) q^{24} +4.87847 q^{25} +(-3.95946 + 1.26525i) q^{26} +(5.16901 - 0.530383i) q^{27} -9.75220i q^{29} +(0.552601 - 0.651010i) q^{30} -2.63910i q^{31} +(-0.137557 + 5.65518i) q^{32} +(-3.57834 - 5.73704i) q^{33} +(-1.68045 - 5.25879i) q^{34} +(0.974616 + 5.92031i) q^{36} +0.639102 q^{37} +(-2.40130 - 7.51461i) q^{38} +(-2.69421 - 4.31955i) q^{39} +(0.789168 + 0.591148i) q^{40} -7.57031i q^{41} +2.51757i q^{43} +(6.36076 - 4.52749i) q^{44} +(0.939235 + 0.460011i) q^{45} +(2.93923 - 0.939235i) q^{46} +4.36377 q^{47} +(-6.75501 + 1.53943i) q^{48} +(-6.57182 + 2.10003i) q^{50} +(5.73704 - 3.57834i) q^{51} +(4.78917 - 3.40885i) q^{52} +1.72188i q^{53} +(-6.73490 + 2.93958i) q^{54} -1.36090i q^{55} +(8.19802 - 5.11331i) q^{57} +(4.19802 + 13.1373i) q^{58} +8.24635 q^{59} +(-0.464173 + 1.11486i) q^{60} +14.0959 q^{61} +(1.13605 + 3.55515i) q^{62} +(-2.24908 - 7.67735i) q^{64} -1.02465i q^{65} +(7.29002 + 6.18804i) q^{66} +0.639102i q^{67} +(4.52749 + 6.36076i) q^{68} +(2.00000 + 3.20654i) q^{69} +11.9341 q^{71} +(-3.86142 - 7.55575i) q^{72} -7.87847 q^{73} +(-0.860938 + 0.275113i) q^{74} +(-4.47179 - 7.16948i) q^{75} +(6.46962 + 9.08930i) q^{76} +(5.48883 + 4.65912i) q^{78} +4.00000i q^{79} +(-1.31756 - 0.456627i) q^{80} +(-5.51757 - 7.11030i) q^{81} +(3.25879 + 10.1980i) q^{82} -8.94358 q^{83} +1.36090 q^{85} +(-1.08374 - 3.39144i) q^{86} +(-14.3320 + 8.93923i) q^{87} +(-6.61968 + 8.83712i) q^{88} -10.5396i q^{89} +(-1.46327 - 0.215373i) q^{90} +(-3.55515 + 2.53050i) q^{92} +(-3.87847 + 2.41910i) q^{93} +(-5.87847 + 1.87847i) q^{94} +1.94467 q^{95} +(8.43704 - 4.98160i) q^{96} +2.00000 q^{97} +(-5.15121 + 10.5176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4} + 6 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^4 + 6 * q^6 - 4 * q^9	\( 12 q - 4 q^{4} + 6 q^{6} - 4 q^{9} - 4 q^{10} + 6 q^{12} + 4 q^{16} - 8 q^{18} - 16 q^{22} - 2 q^{24} - 12 q^{25} + 20 q^{30} + 16 q^{33} - 32 q^{34} - 20 q^{36} - 16 q^{37} - 20 q^{40} - 24 q^{45} - 46 q^{48} + 28 q^{52} - 10 q^{54} + 16 q^{57} - 32 q^{58} + 28 q^{60} + 16 q^{61} + 20 q^{64} + 12 q^{66} + 24 q^{69} - 32 q^{72} - 24 q^{73} + 60 q^{76} + 20 q^{78} + 28 q^{81} - 8 q^{82} + 40 q^{85} - 56 q^{88} + 80 q^{90} + 24 q^{93} + 34 q^{96} + 24 q^{97}+O(q^{100}) \) 12 * q - 4 * q^4 + 6 * q^6 - 4 * q^9 - 4 * q^10 + 6 * q^12 + 4 * q^16 - 8 * q^18 - 16 * q^22 - 2 * q^24 - 12 * q^25 + 20 * q^30 + 16 * q^33 - 32 * q^34 - 20 * q^36 - 16 * q^37 - 20 * q^40 - 24 * q^45 - 46 * q^48 + 28 * q^52 - 10 * q^54 + 16 * q^57 - 32 * q^58 + 28 * q^60 + 16 * q^61 + 20 * q^64 + 12 * q^66 + 24 * q^69 - 32 * q^72 - 24 * q^73 + 60 * q^76 + 20 * q^78 + 28 * q^81 - 8 * q^82 + 40 * q^85 - 56 * q^88 + 80 * q^90 + 24 * q^93 + 34 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more