LMFDB - Embedded newform 567.2.ba.a.143.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(143,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 3]))

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

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

chi := DirichletCharacter("567.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (of order $18$, degree $6$, not 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			143.17
Character	$\chi$	$=$	567.143
Dual form			567.2.ba.a.341.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07972 - 1.28676i) q^{2} +(-0.142658 - 0.809053i) q^{4} +(-2.87107 + 2.40911i) q^{5} +(-1.86335 - 1.87828i) q^{7} +(1.71431 + 0.989760i) q^{8} +O(q^{10})$	\(q+(1.07972 - 1.28676i) q^{2} +(-0.142658 - 0.809053i) q^{4} +(-2.87107 + 2.40911i) q^{5} +(-1.86335 - 1.87828i) q^{7} +(1.71431 + 0.989760i) q^{8} +6.29553i q^{10} +(-3.07307 + 3.66234i) q^{11} +(-1.10865 + 3.04598i) q^{13} +(-4.42878 + 0.369659i) q^{14} +(4.66853 - 1.69921i) q^{16} -3.86831 q^{17} +1.52130i q^{19} +(2.35868 + 1.97917i) q^{20} +(1.39450 + 7.90859i) q^{22} +(-0.124554 + 0.342208i) q^{23} +(1.57097 - 8.90940i) q^{25} +(2.72242 + 4.71536i) q^{26} +(-1.25381 + 1.77550i) q^{28} +(2.29492 + 6.30525i) q^{29} +(-0.692139 + 0.122043i) q^{31} +(1.50016 - 4.12165i) q^{32} +(-4.17668 + 4.97757i) q^{34} +(9.87478 + 0.903668i) q^{35} +(2.75197 - 4.76655i) q^{37} +(1.95755 + 1.64258i) q^{38} +(-7.30635 + 1.28831i) q^{40} +(-0.793900 - 0.288956i) q^{41} +(0.0136704 - 0.0775288i) q^{43} +(3.40143 + 1.96381i) q^{44} +(0.305856 + 0.529758i) q^{46} +(-0.617436 + 3.50165i) q^{47} +(-0.0558886 + 6.99978i) q^{49} +(-9.76803 - 11.6411i) q^{50} +(2.62252 + 0.462421i) q^{52} +(-7.25668 - 4.18964i) q^{53} -17.9182i q^{55} +(-1.33531 - 5.06423i) q^{56} +(10.5912 + 3.85488i) q^{58} +(-1.36168 - 0.495612i) q^{59} +(2.82040 + 0.497313i) q^{61} +(-0.590275 + 1.02239i) q^{62} +(1.28433 + 2.22452i) q^{64} +(-4.15511 - 11.4161i) q^{65} +(3.09944 - 2.60074i) q^{67} +(0.551844 + 3.12967i) q^{68} +(11.8248 - 11.7307i) q^{70} +(14.1956 - 8.19580i) q^{71} +(-10.4351 + 6.02468i) q^{73} +(-3.16204 - 8.68764i) q^{74} +(1.23082 - 0.217026i) q^{76} +(12.6051 - 1.05212i) q^{77} +(1.00589 + 0.844043i) q^{79} +(-9.31009 + 16.1256i) q^{80} +(-1.22900 + 0.709566i) q^{82} +(12.7610 - 4.64462i) q^{83} +(11.1062 - 9.31918i) q^{85} +(-0.0850005 - 0.101300i) q^{86} +(-8.89304 + 3.23680i) q^{88} -8.72878 q^{89} +(7.78701 - 3.59337i) q^{91} +(0.294633 + 0.0519517i) q^{92} +(3.83912 + 4.57528i) q^{94} +(-3.66499 - 4.36777i) q^{95} +(-4.18960 - 0.738740i) q^{97} +(8.94667 + 7.62970i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$

Coefficient data

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

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

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

$2$	1.07972	−	1.28676i	0.763476	−	0.909875i	−0.234587	−	0.972095i	$-0.575374\pi$
$2$	1.07972	−	1.28676i	0.763476	−	0.909875i	0.998062	+	0.0622204i	$0.0198182\pi$
$3$		0			0
$3$		0			0
$4$	−0.142658	−	0.809053i	−0.0713289	−	0.404527i
$5$	−2.87107	+	2.40911i	−1.28398	+	1.07739i	−0.291298	+	0.956632i	$0.594087\pi$
$5$	−2.87107	+	2.40911i	−1.28398	+	1.07739i	−0.992682	+	0.120755i	$0.961469\pi$
$6$		0			0
$7$	−1.86335	−	1.87828i	−0.704278	−	0.709924i
$7$	−1.86335	−	1.87828i	−0.704278	−	0.709924i
$8$	1.71431	+	0.989760i	0.606101	+	0.349933i
$9$		0			0
$10$			6.29553i			1.99082i
$11$	−3.07307	+	3.66234i	−0.926565	+	1.10424i	0.0677435	+	0.997703i	$0.478420\pi$
$11$	−3.07307	+	3.66234i	−0.926565	+	1.10424i	−0.994309	+	0.106535i	$0.966024\pi$
$12$		0			0
$13$	−1.10865	+	3.04598i	−0.307483	+	0.844804i	0.685662	+	0.727920i	$0.259513\pi$
$13$	−1.10865	+	3.04598i	−0.307483	+	0.844804i	−0.993146	+	0.116884i	$0.962709\pi$
$14$	−4.42878	+	0.369659i	−1.18364	+	0.0987955i
$15$		0			0
$16$	4.66853	−	1.69921i	1.16713	−	0.424802i
$17$	−3.86831			−0.938202			−0.469101	−	0.883144i	$-0.655422\pi$
$17$	−3.86831			−0.938202			−0.469101	+	0.883144i	$0.655422\pi$
$18$		0			0
$19$			1.52130i			0.349011i	0.984656	+	0.174506i	$0.0558327\pi$
$19$			1.52130i			0.349011i	−0.984656	+	0.174506i	$0.944167\pi$
$20$	2.35868	+	1.97917i	0.527417	+	0.442555i
$21$		0			0
$22$	1.39450	+	7.90859i	0.297308	+	1.68612i
$23$	−0.124554	+	0.342208i	−0.0259712	+	0.0713553i	−0.952001	−	0.306096i	$-0.900977\pi$
$23$	−0.124554	+	0.342208i	−0.0259712	+	0.0713553i	0.926029	+	0.377451i	$0.123199\pi$
$24$		0			0
$25$	1.57097	−	8.90940i	0.314194	−	1.78188i
$26$	2.72242	+	4.71536i	0.533910	+	0.924758i
$27$		0			0
$28$	−1.25381	+	1.77550i	−0.236948	+	0.335537i
$29$	2.29492	+	6.30525i	0.426157	+	1.17086i	0.948127	+	0.317892i	$0.102975\pi$
$29$	2.29492	+	6.30525i	0.426157	+	1.17086i	−0.521970	+	0.852964i	$0.674803\pi$
$30$		0			0
$31$	−0.692139	+	0.122043i	−0.124312	+	0.0219195i	−0.235458	−	0.971885i	$-0.575659\pi$
$31$	−0.692139	+	0.122043i	−0.124312	+	0.0219195i	0.111146	+	0.993804i	$0.464548\pi$
$32$	1.50016	−	4.12165i	0.265193	−	0.728612i
$33$		0			0
$34$	−4.17668	+	4.97757i	−0.716294	+	0.853647i
$35$	9.87478	+	0.903668i	1.66914	+	0.152748i
$36$		0			0
$37$	2.75197	−	4.76655i	0.452421	−	0.783616i	−0.546115	−	0.837710i	$-0.683894\pi$
$37$	2.75197	−	4.76655i	0.452421	−	0.783616i	0.998536	+	0.0540945i	$0.0172272\pi$
$38$	1.95755	+	1.64258i	0.317556	+	0.266461i
$39$		0			0
$40$	−7.30635	+	1.28831i	−1.15524	+	0.203699i
$41$	−0.793900	−	0.288956i	−0.123986	−	0.0451273i	0.279282	−	0.960209i	$-0.409904\pi$
$41$	−0.793900	−	0.288956i	−0.123986	−	0.0451273i	−0.403268	+	0.915082i	$0.632126\pi$
$42$		0			0
$43$	0.0136704	−	0.0775288i	0.00208472	−	0.0118230i	−0.983748	−	0.179557i	$-0.942534\pi$
$43$	0.0136704	−	0.0775288i	0.00208472	−	0.0118230i	0.985832	+	0.167734i	$0.0536448\pi$
$44$	3.40143	+	1.96381i	0.512784	+	0.296056i
$45$		0			0
$46$	0.305856	+	0.529758i	0.0450960	+	0.0781086i
$47$	−0.617436	+	3.50165i	−0.0900622	+	0.510768i	0.906087	+	0.423092i	$0.139055\pi$
$47$	−0.617436	+	3.50165i	−0.0900622	+	0.510768i	−0.996149	+	0.0876764i	$0.972056\pi$
$48$		0			0
$49$	−0.0558886	+	6.99978i	−0.00798409	+	0.999968i
$50$	−9.76803	−	11.6411i	−1.38141	−	1.64630i
$51$		0			0
$52$	2.62252	+	0.462421i	0.363678	+	0.0641262i
$53$	−7.25668	−	4.18964i	−0.996781	−	0.575492i	−0.0894868	−	0.995988i	$-0.528523\pi$
$53$	−7.25668	−	4.18964i	−0.996781	−	0.575492i	−0.907294	+	0.420496i	$0.861856\pi$
$54$		0			0
$55$		−	17.9182i		−	2.41609i
$56$	−1.33531	−	5.06423i	−0.178438	−	0.676736i
$57$		0			0
$58$	10.5912	+	3.85488i	1.39069	+	0.506170i
$59$	−1.36168	−	0.495612i	−0.177276	−	0.0645231i	0.251857	−	0.967764i	$-0.418959\pi$
$59$	−1.36168	−	0.495612i	−0.177276	−	0.0645231i	−0.429133	+	0.903241i	$0.641181\pi$
$60$		0			0
$61$	2.82040	+	0.497313i	0.361116	+	0.0636745i	0.351263	−	0.936277i	$-0.385752\pi$
$61$	2.82040	+	0.497313i	0.361116	+	0.0636745i	0.00985324	+	0.999951i	$0.496864\pi$
$62$	−0.590275	+	1.02239i	−0.0749650	+	0.129843i
$63$		0			0
$64$	1.28433	+	2.22452i	0.160541	+	0.278066i
$65$	−4.15511	−	11.4161i	−0.515378	−	1.41599i
$66$		0			0
$67$	3.09944	−	2.60074i	0.378657	−	0.317731i	−0.433518	−	0.901145i	$-0.642728\pi$
$67$	3.09944	−	2.60074i	0.378657	−	0.317731i	0.812175	+	0.583414i	$0.198284\pi$
$68$	0.551844	+	3.12967i	0.0669210	+	0.379528i
$69$		0			0
$70$	11.8248	−	11.7307i	1.41333	−	1.40209i
$71$	14.1956	−	8.19580i	1.68470	−	0.972663i	0.726240	−	0.687441i	$-0.241266\pi$
$71$	14.1956	−	8.19580i	1.68470	−	0.972663i	0.958461	−	0.285222i	$-0.0920674\pi$
$72$		0			0
$73$	−10.4351	+	6.02468i	−1.22133	+	0.705136i	−0.965202	−	0.261507i	$-0.915781\pi$
$73$	−10.4351	+	6.02468i	−1.22133	+	0.705136i	−0.256129	+	0.966643i	$0.582447\pi$
$74$	−3.16204	−	8.68764i	−0.367580	−	1.00992i
$75$		0			0
$76$	1.23082	−	0.217026i	0.141184	−	0.0248946i
$77$	12.6051	−	1.05212i	1.43648	−	0.119900i
$78$		0			0
$79$	1.00589	+	0.844043i	0.113172	+	0.0949623i	0.697617	−	0.716471i	$-0.254244\pi$
$79$	1.00589	+	0.844043i	0.113172	+	0.0949623i	−0.584446	+	0.811433i	$0.698688\pi$
$80$	−9.31009	+	16.1256i	−1.04090	+	1.80289i
$81$		0			0
$82$	−1.22900	+	0.709566i	−0.135721	+	0.0783584i
$83$	12.7610	−	4.64462i	1.40070	−	0.509814i	0.472315	−	0.881430i	$-0.343419\pi$
$83$	12.7610	−	4.64462i	1.40070	−	0.509814i	0.928386	+	0.371616i	$0.121196\pi$
$84$		0			0
$85$	11.1062	−	9.31918i	1.20463	−	1.01081i
$86$	−0.0850005	−	0.101300i	−0.00916584	−	0.0109234i
$87$		0			0
$88$	−8.89304	+	3.23680i	−0.948002	+	0.345044i
$89$	−8.72878			−0.925248			−0.462624	−	0.886555i	$-0.653092\pi$
$89$	−8.72878			−0.925248			−0.462624	+	0.886555i	$0.653092\pi$
$90$		0			0
$91$	7.78701	−	3.59337i	0.816300	−	0.376687i
$92$	0.294633	+	0.0519517i	0.0307176	+	0.00541634i
$93$		0			0
$94$	3.83912	+	4.57528i	0.395975	+	0.471904i
$95$	−3.66499	−	4.36777i	−0.376020	−	0.448123i
$96$		0			0
$97$	−4.18960	−	0.738740i	−0.425390	−	0.0750077i	−0.0431451	−	0.999069i	$-0.513738\pi$
$97$	−4.18960	−	0.738740i	−0.425390	−	0.0750077i	−0.382245	+	0.924061i	$0.624849\pi$
$98$	8.94667	+	7.62970i	0.903750	+	0.770716i
$99$		0			0
$100$	−7.43229			−0.743229
$101$	6.58764	−	2.39771i	0.655495	−	0.238581i	0.00720487	−	0.999974i	$-0.497707\pi$
$101$	6.58764	−	2.39771i	0.655495	−	0.238581i	0.648290	+	0.761393i	$0.275484\pi$
$102$		0			0
$103$	4.60791	+	5.49149i	0.454031	+	0.541093i	0.943694	−	0.330818i	$-0.107325\pi$
$103$	4.60791	+	5.49149i	0.454031	+	0.541093i	−0.489663	+	0.871912i	$0.662880\pi$
$104$	−4.91536	+	4.12448i	−0.481991	+	0.404438i
$105$		0			0
$106$	−13.2262	+	4.81395i	−1.28464	+	0.467572i
$107$	−15.4107	+	8.89738i	−1.48981	+	0.860142i	−0.999932	−	0.0116497i	$-0.996292\pi$
$107$	−15.4107	+	8.89738i	−1.48981	+	0.860142i	−0.489877	+	0.871792i	$0.662958\pi$
$108$		0			0
$109$	−8.73677	+	15.1325i	−0.836831	+	1.44943i	0.0557007	+	0.998448i	$0.482261\pi$
$109$	−8.73677	+	15.1325i	−0.836831	+	1.44943i	−0.892531	+	0.450986i	$0.851073\pi$
$110$	−23.0564	−	19.3466i	−2.19834	−	1.84463i
$111$		0			0
$112$	−11.8907	−	5.60261i	−1.12356	−	0.529397i
$113$	−11.6574	+	2.05551i	−1.09663	+	0.193366i	−0.692561	−	0.721360i	$-0.743517\pi$
$113$	−11.6574	+	2.05551i	−1.09663	+	0.193366i	−0.404074	+	0.914726i	$0.632406\pi$
$114$		0			0
$115$	−0.466816	−	1.28257i	−0.0435308	−	0.119600i
$116$	4.77389	−	2.75621i	0.443245	−	0.255908i
$117$		0			0
$118$	−2.10796	+	1.21703i	−0.194054	+	0.112037i
$119$	7.20799	+	7.26577i	0.660755	+	0.666052i
$120$		0			0
$121$	−2.05886	−	11.6764i	−0.187169	−	1.06149i
$122$	3.68516	−	3.09222i	0.333639	−	0.279956i
$123$		0			0
$124$	0.197478	+	0.542567i	0.0177341	+	0.0487240i
$125$	7.58360	+	13.1352i	0.678298	+	1.17485i
$126$		0			0
$127$	−0.317649	+	0.550185i	−0.0281868	+	0.0488210i	−0.879775	−	0.475391i	$-0.842307\pi$
$127$	−0.317649	+	0.550185i	−0.0281868	+	0.0488210i	0.851588	+	0.524212i	$0.175640\pi$
$128$	12.8882	+	2.27254i	1.13917	+	0.200866i
$129$		0			0
$130$	−19.1761	−	6.97952i	−1.68185	−	0.612144i
$131$	−1.92871	−	0.701993i	−0.168512	−	0.0613334i	0.256386	−	0.966574i	$-0.417468\pi$
$131$	−1.92871	−	0.701993i	−0.168512	−	0.0613334i	−0.424899	+	0.905241i	$0.639690\pi$
$132$		0			0
$133$	2.85744	−	2.83471i	0.247771	−	0.245801i
$134$		−	6.79629i		−	0.587110i
$135$		0			0
$136$	−6.63149	−	3.82869i	−0.568646	−	0.328308i
$137$	15.4247	+	2.71978i	1.31782	+	0.232367i	0.787964	−	0.615722i	$-0.211136\pi$
$137$	15.4247	+	2.71978i	1.31782	+	0.232367i	0.529854	+	0.848089i	$0.322247\pi$
$138$		0			0
$139$	14.5992	+	17.3986i	1.23829	+	1.47573i	0.824999	+	0.565133i	$0.191175\pi$
$139$	14.5992	+	17.3986i	1.23829	+	1.47573i	0.413288	+	0.910600i	$0.364380\pi$
$140$	−0.677600	−	8.11814i	−0.0572676	−	0.686108i
$141$		0			0
$142$	4.78117	−	27.1154i	0.401227	−	2.27547i
$143$	−7.74848	−	13.4208i	−0.647961	−	1.12230i
$144$		0			0
$145$	−21.7789	−	12.5741i	−1.80864	−	1.04422i
$146$	−3.51461	+	19.9323i	−0.290871	+	1.64961i
$147$		0			0
$148$	−4.24898	−	1.54650i	−0.349264	−	0.127122i
$149$	11.5651	−	2.03925i	0.947454	−	0.167062i	0.321489	−	0.946913i	$-0.395817\pi$
$149$	11.5651	−	2.03925i	0.947454	−	0.167062i	0.625964	+	0.779852i	$0.284706\pi$
$150$		0			0
$151$	1.20396	+	1.01025i	0.0979771	+	0.0822126i	0.690460	−	0.723370i	$-0.257408\pi$
$151$	1.20396	+	1.01025i	0.0979771	+	0.0822126i	−0.592483	+	0.805583i	$0.701852\pi$
$152$	−1.50572	+	2.60799i	−0.122130	+	0.211536i
$153$		0			0
$154$	12.2561	−	17.3557i	0.987627	−	1.39856i
$155$	1.69316	−	2.01783i	0.135998	−	0.162076i
$156$		0			0
$157$	−3.19698	+	8.78364i	−0.255147	+	0.701011i	0.744303	+	0.667842i	$0.232782\pi$
$157$	−3.19698	+	8.78364i	−0.255147	+	0.701011i	−0.999450	+	0.0331683i	$0.989440\pi$
$158$	2.17216	−	0.383010i	0.172808	−	0.0304706i
$159$		0			0
$160$	5.62247	+	15.4476i	0.444495	+	1.22124i
$161$	0.874849	−	0.403705i	0.0689478	−	0.0318164i
$162$		0			0
$163$	7.03192	+	12.1796i	0.550783	+	0.953983i	0.998218	+	0.0596673i	$0.0190040\pi$
$163$	7.03192	+	12.1796i	0.550783	+	0.953983i	−0.447436	+	0.894316i	$0.647663\pi$
$164$	−0.120525	+	0.683529i	−0.00941139	+	0.0533747i
$165$		0			0
$166$	7.80177	−	21.4352i	0.605535	−	1.66369i
$167$	−0.663852	−	3.76489i	−0.0513704	−	0.291336i	0.948290	−	0.317406i	$-0.102812\pi$
$167$	−0.663852	−	3.76489i	−0.0513704	−	0.291336i	−0.999660	+	0.0260700i	$0.991701\pi$
$168$		0			0
$169$	1.90966	+	1.60240i	0.146897	+	0.123261i
$170$		−	24.3530i		−	1.86779i
$171$		0			0
$172$	−0.0646751			−0.00493143
$173$	10.8746	−	3.95802i	0.826777	−	0.300922i	0.106242	−	0.994340i	$-0.466118\pi$
$173$	10.8746	−	3.95802i	0.826777	−	0.300922i	0.720536	+	0.693418i	$0.243896\pi$
$174$		0			0
$175$	−19.6616	+	13.6506i	−1.48628	+	1.03189i
$176$	−8.12365	+	22.3196i	−0.612343	+	1.68240i
$177$		0			0
$178$	−9.42461	+	11.2318i	−0.706404	+	0.841860i
$179$			9.11384i			0.681200i	0.940208	+	0.340600i	$0.110630\pi$
$179$			9.11384i			0.681200i	−0.940208	+	0.340600i	$0.889370\pi$
$180$		0			0
$181$	6.15516	+	3.55368i	0.457509	+	0.264143i	0.710996	−	0.703196i	$-0.248244\pi$
$181$	6.15516	+	3.55368i	0.457509	+	0.264143i	−0.253487	+	0.967339i	$0.581578\pi$
$182$	3.78398	−	13.8998i	0.280487	−	1.03032i
$183$		0			0
$184$	−0.552227	+	0.463374i	−0.0407107	+	0.0341604i
$185$	3.58206	+	20.3149i	0.263358	+	1.49358i
$186$		0			0
$187$	11.8876	−	14.1671i	0.869306	−	1.03600i
$188$	2.92110			0.213043
$189$		0			0
$190$	−9.57741			−0.694818
$191$	−7.87297	+	9.38264i	−0.569668	+	0.678904i	−0.971563	−	0.236782i	$-0.923907\pi$
$191$	−7.87297	+	9.38264i	−0.569668	+	0.678904i	0.401895	+	0.915686i	$0.368352\pi$
$192$		0			0
$193$	−2.88238	−	16.3468i	−0.207478	−	1.17667i	−0.893493	−	0.449078i	$-0.851753\pi$
$193$	−2.88238	−	16.3468i	−0.207478	−	1.17667i	0.686015	−	0.727588i	$-0.259359\pi$
$194$	−5.47417	+	4.59337i	−0.393022	+	0.329785i
$195$		0			0
$196$	5.67116	−	0.953357i	0.405083	−	0.0680969i
$197$	−7.93030	−	4.57856i	−0.565011	−	0.326209i	0.190144	−	0.981756i	$-0.439105\pi$
$197$	−7.93030	−	4.57856i	−0.565011	−	0.326209i	−0.755154	+	0.655547i	$0.772438\pi$
$198$		0			0
$199$		−	6.56017i		−	0.465038i	−0.972592	−	0.232519i	$-0.925303\pi$
$199$		−	6.56017i		−	0.465038i	0.972592	−	0.232519i	$-0.0746968\pi$
$200$	11.5113	−	13.7186i	0.813971	−	0.970053i
$201$		0			0
$202$	4.02753	−	11.0655i	0.283376	−	0.778569i
$203$	7.56680	−	16.0594i	0.531086	−	1.12715i
$204$		0			0
$205$	2.97547	−	1.08298i	0.207816	−	0.0756387i
$206$	12.0415			0.838968
$207$		0			0
$208$			16.1041i			1.11662i
$209$	−5.57154	−	4.67507i	−0.385391	−	0.323382i
$210$		0			0
$211$	2.58385	+	14.6538i	0.177880	+	1.00881i	0.934767	+	0.355261i	$0.115608\pi$
$211$	2.58385	+	14.6538i	0.177880	+	1.00881i	−0.756888	+	0.653545i	$0.773281\pi$
$212$	−2.35442	+	6.46872i	−0.161702	+	0.444274i
$213$		0			0
$214$	−5.19045	+	29.4365i	−0.354812	+	2.01224i
$215$	0.147527	+	0.255524i	0.0100612	+	0.0174266i
$216$		0			0
$217$	1.51893	+	1.07262i	0.103111	+	0.0728145i
$218$	10.0386	+	27.5810i	0.679903	+	1.86802i
$219$		0			0
$220$	−14.4968	+	2.55617i	−0.977372	+	0.172337i
$221$	4.28859	−	11.7828i	0.288482	−	0.792597i
$222$		0			0
$223$	0.651794	−	0.776778i	0.0436474	−	0.0520169i	−0.743779	−	0.668425i	$-0.766969\pi$
$223$	0.651794	−	0.776778i	0.0436474	−	0.0520169i	0.787426	+	0.616409i	$0.211413\pi$
$224$	−10.5369	+	4.86234i	−0.704029	+	0.324879i
$225$		0			0
$226$	−9.94174	+	17.2196i	−0.661315	+	1.14543i
$227$	−17.6041	−	14.7716i	−1.16843	−	0.980428i	−0.168442	−	0.985712i	$-0.553874\pi$
$227$	−17.6041	−	14.7716i	−1.16843	−	0.980428i	−0.999986	+	0.00528399i	$0.998318\pi$
$228$		0			0
$229$	0.352295	−	0.0621191i	0.0232803	−	0.00410495i	−0.161996	−	0.986791i	$-0.551793\pi$
$229$	0.352295	−	0.0621191i	0.0232803	−	0.00410495i	0.185276	+	0.982686i	$0.440682\pi$
$230$	−2.15438	−	0.784130i	−0.142056	−	0.0517040i
$231$		0			0
$232$	−2.30646	+	13.0806i	−0.151427	+	0.858783i
$233$	−17.2582	−	9.96402i	−1.13062	−	0.652764i	−0.186530	−	0.982449i	$-0.559724\pi$
$233$	−17.2582	−	9.96402i	−1.13062	−	0.652764i	−0.944091	+	0.329685i	$0.893058\pi$
$234$		0			0
$235$	−6.66317	−	11.5409i	−0.434657	−	0.752848i
$236$	−0.206721	+	1.17238i	−0.0134564	+	0.0763152i
$237$		0			0
$238$	17.1319	−	1.42995i	1.11049	−	0.0926901i
$239$	8.88553	+	10.5894i	0.574757	+	0.684969i	0.972600	−	0.232485i	$-0.0746855\pi$
$239$	8.88553	+	10.5894i	0.574757	+	0.684969i	−0.397843	+	0.917454i	$0.630241\pi$
$240$		0			0
$241$	−3.32597	−	0.586458i	−0.214244	−	0.0377770i	0.0654957	−	0.997853i	$-0.479137\pi$
$241$	−3.32597	−	0.586458i	−0.214244	−	0.0377770i	−0.279740	+	0.960076i	$0.590248\pi$
$242$	−17.2477	−	9.95794i	−1.10872	−	0.640121i
$243$		0			0
$244$		−	2.35280i		−	0.150623i
$245$	−16.7028	−	20.2315i	−1.06710	−	1.29254i
$246$		0			0
$247$	−4.63387	−	1.68659i	−0.294846	−	0.107315i
$248$	−1.30734	−	0.475832i	−0.0830160	−	0.0302153i
$249$		0			0
$250$	25.0899	+	4.42403i	1.58683	+	0.279800i
$251$	−0.197747	+	0.342507i	−0.0124817	+	0.0216189i	−0.872199	−	0.489152i	$-0.837306\pi$
$251$	−0.197747	+	0.342507i	−0.0124817	+	0.0216189i	0.859717	+	0.510770i	$0.170640\pi$
$252$		0			0
$253$	−0.870521	−	1.50779i	−0.0547292	−	0.0947937i
$254$	0.364983	+	1.00278i	0.0229010	+	0.0629201i
$255$		0			0
$256$	12.9044	−	10.8281i	0.806526	−	0.676756i
$257$	5.15739	+	29.2490i	0.321709	+	1.82450i	0.531857	+	0.846834i	$0.321495\pi$
$257$	5.15739	+	29.2490i	0.321709	+	1.82450i	−0.210147	+	0.977670i	$0.567394\pi$
$258$		0			0
$259$	−14.0808	+	3.71275i	−0.874938	+	0.230699i
$260$	−8.64345	+	4.99030i	−0.536044	+	0.309485i
$261$		0			0
$262$	−2.98576	+	1.72383i	−0.184461	+	0.106498i
$263$	4.12604	+	11.3362i	0.254422	+	0.699020i	0.999487	+	0.0320276i	$0.0101964\pi$
$263$	4.12604	+	11.3362i	0.254422	+	0.699020i	−0.745065	+	0.666992i	$0.767581\pi$
$264$		0			0
$265$	30.9277	−	5.45339i	1.89987	−	0.334999i
$266$	−0.562363	−	6.73752i	−0.0344807	−	0.413104i
$267$		0			0
$268$	−2.54629	−	2.13659i	−0.155540	−	0.130513i
$269$	1.78062	−	3.08412i	0.108566	−	0.188042i	−0.806624	−	0.591066i	$-0.798707\pi$
$269$	1.78062	−	3.08412i	0.108566	−	0.188042i	0.915190	+	0.403024i	$0.132041\pi$
$270$		0			0
$271$	6.59196	−	3.80587i	0.400433	−	0.231190i	−0.286238	−	0.958159i	$-0.592405\pi$
$271$	6.59196	−	3.80587i	0.400433	−	0.231190i	0.686671	+	0.726969i	$0.259071\pi$
$272$	−18.0593	+	6.57306i	−1.09501	+	0.398550i
$273$		0			0
$274$	20.1540	−	16.9112i	1.21755	−	1.02164i
$275$	27.8016	+	33.1326i	1.67650	+	1.99797i
$276$		0			0
$277$	10.1541	−	3.69580i	0.610103	−	0.222059i	−0.0184453	−	0.999830i	$-0.505872\pi$
$277$	10.1541	−	3.69580i	0.610103	−	0.222059i	0.628548	+	0.777771i	$0.283649\pi$
$278$	38.1508			2.28814
$279$		0			0
$280$	16.0341	+	11.3228i	0.958218	+	0.676668i
$281$	−3.59151	−	0.633280i	−0.214252	−	0.0377783i	0.0654920	−	0.997853i	$-0.479138\pi$
$281$	−3.59151	−	0.633280i	−0.214252	−	0.0377783i	−0.279744	+	0.960075i	$0.590249\pi$
$282$		0			0
$283$	16.0737	+	19.1559i	0.955484	+	1.13870i	0.990249	+	0.139306i	$0.0444870\pi$
$283$	16.0737	+	19.1559i	0.955484	+	1.13870i	−0.0347657	+	0.999395i	$0.511069\pi$
$284$	−8.65595	−	10.3158i	−0.513636	−	0.612128i
$285$		0			0
$286$	−25.6354	−	4.52022i	−1.51586	−	0.267286i
$287$	0.936569	+	2.02959i	0.0552839	+	0.119803i
$288$		0			0
$289$	−2.03620			−0.119777
$290$	−39.6949	+	14.4477i	−2.33096	+	0.848401i
$291$		0			0
$292$	6.36293	+	7.58305i	0.372362	+	0.443764i
$293$	23.0690	−	19.3572i	1.34770	−	1.13086i	0.368131	−	0.929774i	$-0.379998\pi$
$293$	23.0690	−	19.3572i	1.34770	−	1.13086i	0.979574	−	0.201084i	$-0.0644465\pi$
$294$		0			0
$295$	5.10346	−	1.85751i	0.297135	−	0.108148i
$296$	9.43547	−	5.44757i	0.548426	−	0.316634i
$297$		0			0
$298$	9.86307	−	17.0833i	0.571352	−	0.989612i
$299$	−0.904274	−	0.758776i	−0.0522955	−	0.0438811i
$300$		0			0
$301$	−0.171094	+	0.118786i	−0.00986168	+	0.00684671i
$302$	2.59988	−	0.458429i	0.149606	−	0.0263796i
$303$		0			0
$304$	2.58501	+	7.10226i	0.148261	+	0.407342i
$305$	−9.29565	+	5.36685i	−0.532268	+	0.307305i
$306$		0			0
$307$	21.5000	−	12.4130i	1.22707	−	0.708449i	0.260654	−	0.965432i	$-0.416062\pi$
$307$	21.5000	−	12.4130i	1.22707	−	0.708449i	0.966416	+	0.256983i	$0.0827284\pi$
$308$	−2.64943	−	10.0481i	−0.150966	−	0.572544i
$309$		0			0
$310$	−0.768324	−	4.35738i	−0.0436379	−	0.247483i
$311$	−6.04946	+	5.07610i	−0.343034	+	0.287839i	−0.797985	−	0.602677i	$-0.794101\pi$
$311$	−6.04946	+	5.07610i	−0.343034	+	0.287839i	0.454952	+	0.890516i	$0.349656\pi$
$312$		0			0
$313$	6.61039	+	18.1619i	0.373641	+	1.02657i	0.973942	+	0.226797i	$0.0728253\pi$
$313$	6.61039	+	18.1619i	0.373641	+	1.02657i	−0.600301	+	0.799774i	$0.704952\pi$
$314$	7.85057	+	13.5976i	0.443033	+	0.767356i
$315$		0			0
$316$	0.539377	−	0.934229i	0.0303424	−	0.0525545i
$317$	−13.9204	−	2.45453i	−0.781845	−	0.137860i	−0.231541	−	0.972825i	$-0.574377\pi$
$317$	−13.9204	−	2.45453i	−0.781845	−	0.137860i	−0.550304	+	0.834965i	$0.685488\pi$
$318$		0			0
$319$	−30.1444	−	10.9717i	−1.68776	−	0.614296i
$320$	−9.04652	−	3.29266i	−0.505716	−	0.184066i
$321$		0			0
$322$	0.425120	−	1.56161i	0.0236910	−	0.0870249i
$323$		−	5.88487i		−	0.327443i
$324$		0			0
$325$	25.3962	+	14.6625i	1.40873	+	0.813330i
$326$	23.2647	+	4.10220i	1.28851	+	0.227200i
$327$		0			0
$328$	−1.07500	−	1.28113i	−0.0593568	−	0.0707386i
$329$	7.72758	−	5.36507i	0.426036	−	0.295786i
$330$		0			0
$331$	−2.53135	+	14.3560i	−0.139135	+	0.789077i	0.832755	+	0.553642i	$0.186762\pi$
$331$	−2.53135	+	14.3560i	−0.139135	+	0.789077i	−0.971890	+	0.235435i	$0.924349\pi$
$332$	−5.57820	−	9.66173i	−0.306144	−	0.530256i
$333$		0			0
$334$	−5.56127	−	3.21080i	−0.304299	−	0.175687i
$335$	−2.63323	+	14.9338i	−0.143869	+	0.815920i
$336$		0			0
$337$	−25.3341	−	9.22085i	−1.38003	−	0.502291i	−0.457846	−	0.889032i	$-0.651379\pi$
$337$	−25.3341	−	9.22085i	−1.38003	−	0.502291i	−0.922189	+	0.386740i	$0.873601\pi$
$338$	4.12379	−	0.727136i	0.224305	−	0.0395510i
$339$		0			0
$340$	−9.12410	−	7.65602i	−0.494824	−	0.415206i
$341$	1.68003	−	2.90990i	0.0909787	−	0.157580i
$342$		0			0
$343$	13.2517	−	12.9380i	0.715524	−	0.698588i
$344$	0.100170	−	0.119378i	0.00540082	−	0.00643644i
$345$		0			0
$346$	6.64845	−	18.2665i	0.357423	−	0.982011i
$347$	−19.7224	+	3.47759i	−1.05875	+	0.186687i	−0.675803	−	0.737082i	$-0.736203\pi$
$347$	−19.7224	+	3.47759i	−1.05875	+	0.186687i	−0.382950	+	0.923769i	$0.625092\pi$
$348$		0			0
$349$	−3.59306	−	9.87186i	−0.192332	−	0.528429i	0.805617	−	0.592437i	$-0.201834\pi$
$349$	−3.59306	−	9.87186i	−0.192332	−	0.528429i	−0.997949	+	0.0640080i	$0.979612\pi$
$350$	−3.66403	+	40.0385i	−0.195851	+	2.14015i
$351$		0			0
$352$	10.4848	+	18.1602i	0.558842	+	0.967944i
$353$	0.572625	−	3.24752i	0.0304778	−	0.172848i	−0.965769	−	0.259402i	$-0.916474\pi$
$353$	0.572625	−	3.24752i	0.0304778	−	0.172848i	0.996247	+	0.0865542i	$0.0275856\pi$
$354$		0			0
$355$	−21.0118	+	57.7294i	−1.11519	+	3.06396i
$356$	1.24523	+	7.06204i	0.0659970	+	0.374288i
$357$		0			0
$358$	11.7273	+	9.84037i	0.619807	+	0.520080i
$359$		−	11.0679i		−	0.584139i	−0.956397	−	0.292070i	$-0.905656\pi$
$359$		−	11.0679i		−	0.584139i	0.956397	−	0.292070i	$-0.0943439\pi$
$360$		0			0
$361$	16.6856			0.878191
$362$	11.2186	−	4.08322i	0.589634	−	0.214609i
$363$		0			0
$364$	−4.01810	−	5.78748i	−0.210606	−	0.303346i
$365$	15.4456	−	42.4365i	0.808461	−	2.22123i
$366$		0			0
$367$	12.7217	−	15.1611i	0.664066	−	0.791404i	−0.323897	−	0.946092i	$-0.604993\pi$
$367$	12.7217	−	15.1611i	0.664066	−	0.791404i	0.987963	+	0.154689i	$0.0494375\pi$
$368$			1.80925i			0.0943138i
$369$		0			0
$370$	30.0079	+	17.3251i	1.56004	+	0.900688i
$371$	5.65236	+	21.4368i	0.293456	+	1.11295i
$372$		0			0
$373$	−3.34599	+	2.80762i	−0.173249	+	0.145373i	−0.725289	−	0.688444i	$-0.758294\pi$
$373$	−3.34599	+	2.80762i	−0.173249	+	0.145373i	0.552040	+	0.833817i	$0.313849\pi$
$374$	−5.39435	−	30.5929i	−0.278935	−	1.58192i
$375$		0			0
$376$	−4.52427	+	5.39182i	−0.233321	+	0.278062i
$377$	−21.7499			−1.12018
$378$		0			0
$379$	−5.24775			−0.269559			−0.134780	−	0.990876i	$-0.543033\pi$
$379$	−5.24775			−0.269559			−0.134780	+	0.990876i	$0.543033\pi$
$380$	−3.01091	+	3.58827i	−0.154457	+	0.184074i
$381$		0			0
$382$	3.57260	+	20.2612i	0.182790	+	1.03665i
$383$	3.10858	−	2.60841i	0.158841	−	0.133283i	−0.559903	−	0.828558i	$-0.689162\pi$
$383$	3.10858	−	2.60841i	0.158841	−	0.133283i	0.718744	+	0.695275i	$0.244717\pi$
$384$		0			0
$385$	−33.6554	+	33.3878i	−1.71524	+	1.70160i
$386$	−24.1465	−	13.9410i	−1.22902	−	0.709577i
$387$		0			0
$388$			3.49500i			0.177432i
$389$	5.26118	−	6.27003i	0.266753	−	0.317903i	−0.615996	−	0.787749i	$-0.711246\pi$
$389$	5.26118	−	6.27003i	0.266753	−	0.317903i	0.882748	+	0.469846i	$0.155691\pi$
$390$		0			0
$391$	0.481811	−	1.32377i	0.0243662	−	0.0669457i
$392$	−7.02391	+	11.9445i	−0.354761	+	0.603288i
$393$		0			0
$394$	−14.4540	+	5.26082i	−0.728181	+	0.265036i
$395$	−4.92138			−0.247621
$396$		0			0
$397$		−	6.76990i		−	0.339771i	−0.985464	−	0.169886i	$-0.945660\pi$
$397$		−	6.76990i		−	0.339771i	0.985464	−	0.169886i	$-0.0543399\pi$
$398$	−8.44135	−	7.08313i	−0.423127	−	0.355045i
$399$		0			0
$400$	−7.80480	−	44.2632i	−0.390240	−	2.21316i
$401$	−1.24382	+	3.41736i	−0.0621133	+	0.170655i	−0.966867	−	0.255280i	$-0.917832\pi$
$401$	−1.24382	+	3.41736i	−0.0621133	+	0.170655i	0.904754	+	0.425935i	$0.140055\pi$
$402$		0			0
$403$	0.395598	−	2.24355i	0.0197061	−	0.111759i
$404$	−2.87965	−	4.98770i	−0.143268	−	0.248147i
$405$		0			0
$406$	−12.4945	−	27.0762i	−0.620092	−	1.34377i
$407$	8.99974	+	24.7266i	0.446101	+	1.22565i
$408$		0			0
$409$	−36.1958	+	6.38230i	−1.78977	+	0.315584i	−0.967377	−	0.253340i	$-0.918471\pi$
$409$	−36.1958	+	6.38230i	−1.78977	+	0.315584i	−0.822390	+	0.568925i	$0.807360\pi$
$410$	1.81913	−	4.99802i	0.0898404	−	0.246835i
$411$		0			0
$412$	3.78556	−	4.51145i	0.186501	−	0.222263i
$413$	1.60638	+	3.48112i	0.0790450	+	0.171295i
$414$		0			0
$415$	−25.4483	+	44.0777i	−1.24921	+	2.16369i
$416$	10.8913	+	9.13892i	0.533992	+	0.448073i
$417$		0			0
$418$	−12.0314	+	2.12145i	−0.588473	+	0.103764i
$419$	−11.4760	−	4.17694i	−0.560642	−	0.204057i	0.0461267	−	0.998936i	$-0.485312\pi$
$419$	−11.4760	−	4.17694i	−0.560642	−	0.204057i	−0.606768	+	0.794879i	$0.707534\pi$
$420$		0			0
$421$	0.755733	−	4.28598i	0.0368322	−	0.208886i	−0.960838	−	0.277112i	$-0.910623\pi$
$421$	0.755733	−	4.28598i	0.0368322	−	0.208886i	0.997670	+	0.0682260i	$0.0217339\pi$
$422$	21.6457	+	12.4971i	1.05369	+	0.608350i
$423$		0			0
$424$	−8.29348	−	14.3647i	−0.402767	−	0.697613i
$425$	−6.07698	+	34.4643i	−0.294777	+	1.67176i
$426$		0			0
$427$	−4.32129	−	6.22418i	−0.209122	−	0.301209i
$428$	9.39691	+	11.1988i	0.454217	+	0.541314i
$429$		0			0
$430$	0.488085	+	0.0860625i	0.0235375	+	0.00415030i
$431$	7.21480	+	4.16547i	0.347525	+	0.200644i	0.663595	−	0.748092i	$-0.269030\pi$
$431$	7.21480	+	4.16547i	0.347525	+	0.200644i	−0.316070	+	0.948736i	$0.602363\pi$
$432$		0			0
$433$		−	23.0129i		−	1.10593i	−0.833205	−	0.552965i	$-0.813496\pi$
$433$		−	23.0129i		−	1.10593i	0.833205	−	0.552965i	$-0.186504\pi$
$434$	3.02022	−	0.796356i	0.144975	−	0.0382263i
$435$		0			0
$436$	13.4894	+	4.90973i	0.646024	+	0.235134i
$437$	−0.520602	−	0.189484i	−0.0249038	−	0.00906424i
$438$		0			0
$439$	−17.9478	−	3.16469i	−0.856603	−	0.151042i	−0.271936	−	0.962315i	$-0.587664\pi$
$439$	−17.9478	−	3.16469i	−0.856603	−	0.151042i	−0.584667	+	0.811273i	$0.698775\pi$
$440$	17.7347	−	30.7174i	0.845469	−	1.46440i
$441$		0			0
$442$	−10.5311	−	18.2405i	−0.500915	−	0.867610i
$443$	5.16749	+	14.1975i	0.245515	+	0.674546i	0.999837	+	0.0180420i	$0.00574325\pi$
$443$	5.16749	+	14.1975i	0.245515	+	0.674546i	−0.754323	+	0.656504i	$0.772035\pi$
$444$		0			0
$445$	25.0609	−	21.0286i	1.18800	−	0.996851i
$446$	−0.295771	−	1.67740i	−0.0140052	−	0.0794273i
$447$		0			0
$448$	1.78513	−	6.55739i	0.0843397	−	0.309808i
$449$	19.1172	−	11.0373i	0.902197	−	0.520884i	0.0242848	−	0.999705i	$-0.492269\pi$
$449$	19.1172	−	11.0373i	0.902197	−	0.520884i	0.877912	+	0.478821i	$0.158936\pi$
$450$		0			0
$451$	3.49797	−	2.01955i	0.164713	−	0.0950970i
$452$	3.32604	+	9.13821i	0.156444	+	0.429825i
$453$		0			0
$454$	−38.0150	+	6.70307i	−1.78413	+	0.314591i
$455$	−13.7002	+	29.0766i	−0.642276	+	1.36313i
$456$		0			0
$457$	−29.7824	−	24.9904i	−1.39316	−	1.16900i	−0.964040	−	0.265756i	$-0.914379\pi$
$457$	−29.7824	−	24.9904i	−1.39316	−	1.16900i	−0.429122	−	0.903246i	$-0.641177\pi$
$458$	0.300447	−	0.520389i	0.0140390	−	0.0243162i
$459$		0			0
$460$	−0.971069	+	0.560647i	−0.0452763	+	0.0261403i
$461$	−6.46360	+	2.35256i	−0.301040	+	0.109570i	−0.488124	−	0.872774i	$-0.662319\pi$
$461$	−6.46360	+	2.35256i	−0.301040	+	0.109570i	0.187084	+	0.982344i	$0.440096\pi$
$462$		0			0
$463$	7.23069	−	6.06727i	0.336039	−	0.281970i	−0.459116	−	0.888376i	$-0.651834\pi$
$463$	7.23069	−	6.06727i	0.336039	−	0.281970i	0.795155	+	0.606406i	$0.207389\pi$
$464$	21.4279	+	25.5367i	0.994763	+	1.18551i
$465$		0			0
$466$	−31.4552	+	11.4488i	−1.45714	+	0.530354i
$467$	19.3403			0.894962			0.447481	−	0.894293i	$-0.352321\pi$
$467$	19.3403			0.894962			0.447481	+	0.894293i	$0.352321\pi$
$468$		0			0
$469$	−10.6602	−	0.975548i	−0.492244	−	0.0450466i
$470$	−22.0447	−	3.88708i	−1.01685	−	0.179298i
$471$		0			0
$472$	−1.84381	−	2.19737i	−0.0848684	−	0.101142i
$473$	0.241927	+	0.288317i	0.0111238	+	0.0132568i
$474$		0			0
$475$	13.5539	+	2.38992i	0.621896	+	0.109657i
$476$	4.85012	−	6.86817i	0.222305	−	0.314802i
$477$		0			0
$478$	23.2198			1.06205
$479$	16.0915	−	5.85683i	0.735240	−	0.267606i	0.0528590	−	0.998602i	$-0.483167\pi$
$479$	16.0915	−	5.85683i	0.735240	−	0.267606i	0.682381	+	0.730996i	$0.260944\pi$
$480$		0			0
$481$	11.4679	+	13.6669i	0.522890	+	0.623155i
$482$	−4.34573	+	3.64650i	−0.197943	+	0.166094i
$483$		0			0
$484$	−9.15310	+	3.33146i	−0.416050	+	0.151430i
$485$	13.8083	−	7.97225i	0.627005	−	0.362001i
$486$		0			0
$487$	−20.1639	+	34.9249i	−0.913713	+	1.58260i	−0.104939	+	0.994479i	$0.533465\pi$
$487$	−20.1639	+	34.9249i	−0.913713	+	1.58260i	−0.808774	+	0.588119i	$0.799869\pi$
$488$	4.34284	+	3.64407i	0.196591	+	0.164959i
$489$		0			0
$490$	−44.0673	−	0.351848i	−1.99076	−	0.0158949i
$491$	−4.14445	+	0.730778i	−0.187036	+	0.0329795i	−0.266382	−	0.963868i	$-0.585828\pi$
$491$	−4.14445	+	0.730778i	−0.187036	+	0.0329795i	0.0793453	+	0.996847i	$0.474717\pi$
$492$		0			0
$493$	−8.87747	−	24.3906i	−0.399821	−	1.09850i
$494$	−7.17350	+	4.14162i	−0.322751	+	0.186340i
$495$		0			0
$496$	−3.02390	+	1.74585i	−0.135777	+	0.0783909i
$497$	−41.8452	−	11.3916i	−1.87702	−	0.510985i
$498$		0			0
$499$	2.17385	+	12.3285i	0.0973149	+	0.551900i	0.994013	+	0.109258i	$0.0348476\pi$
$499$	2.17385	+	12.3285i	0.0973149	+	0.551900i	−0.896698	+	0.442642i	$0.854041\pi$
$500$	9.54520	−	8.00938i	0.426874	−	0.358190i
$501$		0			0
$502$	0.227213	+	0.624263i	0.0101410	+	0.0278622i
$503$	17.2248	+	29.8343i	0.768016	+	1.33024i	0.938637	+	0.344907i	$0.112089\pi$
$503$	17.2248	+	29.8343i	0.768016	+	1.33024i	−0.170621	+	0.985337i	$0.554577\pi$
$504$		0			0
$505$	−13.1372	+	22.7543i	−0.584599	+	1.01255i
$506$	−2.88007	−	0.507834i	−0.128035	−	0.0225760i
$507$		0			0
$508$	0.490444	+	0.178507i	0.0217599	+	0.00791996i
$509$	−9.42273	−	3.42959i	−0.417655	−	0.152014i	0.124640	−	0.992202i	$-0.460222\pi$
$509$	−9.42273	−	3.42959i	−0.417655	−	0.152014i	−0.542295	+	0.840188i	$0.682445\pi$
$510$		0			0
$511$	30.7602	+	8.37392i	1.36075	+	0.370440i
$512$		−	2.12207i		−	0.0937832i
$513$		0			0
$514$	43.2049	+	24.9444i	1.90569	+	1.10025i
$515$	−26.4592	−	4.66548i	−1.16593	−	0.205586i
$516$		0			0
$517$	−10.9268	−	13.0221i	−0.480561	−	0.572710i
$518$	−10.4259	+	22.1273i	−0.458086	+	0.972217i
$519$		0			0
$520$	4.17600	−	23.6833i	0.183130	−	1.03858i
$521$	−16.0296	−	27.7641i	−0.702270	−	1.21637i	−0.967668	−	0.252228i	$-0.918837\pi$
$521$	−16.0296	−	27.7641i	−0.702270	−	1.21637i	0.265398	−	0.964139i	$-0.414497\pi$
$522$		0			0
$523$	−3.61939	−	2.08966i	−0.158265	−	0.0913742i	0.418776	−	0.908090i	$-0.362459\pi$
$523$	−3.61939	−	2.08966i	−0.158265	−	0.0913742i	−0.577041	+	0.816715i	$0.695793\pi$
$524$	−0.292804	+	1.66057i	−0.0127912	+	0.0725425i
$525$		0			0
$526$	19.0419	+	6.93068i	0.830266	+	0.302192i
$527$	2.67741	−	0.472099i	0.116630	−	0.0205650i
$528$		0			0
$529$	17.5174	+	14.6989i	0.761627	+	0.639081i
$530$	26.3760	−	45.6846i	1.14570	−	1.98441i
$531$		0			0
$532$	−2.70107	−	1.90742i	−0.117106	−	0.0826974i
$533$	1.76031	−	2.09786i	0.0762475	−	0.0908682i
$534$		0			0
$535$	22.8104	−	62.6711i	0.986180	−	2.70951i
$536$	7.88752	−	1.39078i	0.340689	−	0.0600726i
$537$		0			0
$538$	−2.04595	−	5.62119i	−0.0882070	−	0.242347i
$539$	−25.4638	−	21.7155i	−1.09680	−	0.935352i
$540$		0			0
$541$	−1.91792	−	3.32193i	−0.0824578	−	0.142821i	0.821847	−	0.569708i	$-0.192944\pi$
$541$	−1.91792	−	3.32193i	−0.0824578	−	0.142821i	−0.904305	+	0.426887i	$0.859610\pi$
$542$	2.22022	−	12.5915i	0.0953667	−	0.540852i
$543$		0			0
$544$	−5.80308	+	15.9438i	−0.248805	+	0.683586i
$545$	−11.3721	−	64.4943i	−0.487127	−	2.76263i
$546$		0			0
$547$	3.29856	+	2.76782i	0.141036	+	0.118344i	0.710576	−	0.703620i	$-0.248434\pi$
$547$	3.29856	+	2.76782i	0.141036	+	0.118344i	−0.569540	+	0.821964i	$0.692879\pi$
$548$		−	12.8674i		−	0.549667i
$549$		0			0
$550$	72.6515			3.09787
$551$	−9.59220	+	3.49128i	−0.408641	+	0.148733i
$552$		0			0
$553$	−0.288972	−	3.46209i	−0.0122883	−	0.147223i
$554$	6.20800	−	17.0563i	0.263753	−	0.724654i
$555$		0			0
$556$	11.9937	−	14.2936i	0.508648	−	0.606183i
$557$		−	33.8656i		−	1.43493i	−0.696594	−	0.717465i	$-0.745302\pi$
$557$		−	33.8656i		−	1.43493i	0.696594	−	0.717465i	$-0.254698\pi$
$558$		0			0
$559$	0.220996	+	0.127592i	0.00934712	+	0.00539656i
$560$	47.6363	−	12.5605i	2.01300	−	0.530778i
$561$		0			0
$562$	−4.69270	+	3.93764i	−0.197949	+	0.166099i
$563$	0.780886	+	4.42862i	0.0329104	+	0.186644i	0.996831	−	0.0795446i	$-0.0253466\pi$
$563$	0.780886	+	4.42862i	0.0329104	+	0.186644i	−0.963921	+	0.266189i	$0.914236\pi$
$564$		0			0
$565$	28.5172	−	33.9855i	1.19973	−	1.42978i
$566$	42.0041			1.76556
$567$		0			0
$568$	32.4475			1.36147
$569$	−2.17293	+	2.58959i	−0.0910938	+	0.108561i	−0.809666	−	0.586891i	$-0.800352\pi$
$569$	−2.17293	+	2.58959i	−0.0910938	+	0.108561i	0.718572	+	0.695453i	$0.244796\pi$
$570$		0			0
$571$	3.32678	+	18.8671i	0.139222	+	0.789565i	0.971826	+	0.235697i	$0.0757374\pi$
$571$	3.32678	+	18.8671i	0.139222	+	0.789565i	−0.832605	+	0.553867i	$0.813151\pi$
$572$	−9.75273	+	8.18351i	−0.407782	+	0.342170i
$573$		0			0
$574$	3.62282	+	0.986250i	0.151214	+	0.0411653i
$575$	2.85320	+	1.64729i	0.118987	+	0.0686969i
$576$		0			0
$577$		−	45.8713i		−	1.90965i	−0.297175	−	0.954823i	$-0.596045\pi$
$577$		−	45.8713i		−	1.90965i	0.297175	−	0.954823i	$-0.403955\pi$
$578$	−2.19852	+	2.62010i	−0.0914465	+	0.108982i
$579$		0			0
$580$	−7.06615	+	19.4141i	−0.293406	+	0.806127i
$581$	−32.5021	−	15.3142i	−1.34841	−	0.635341i
$582$		0			0
$583$	37.6442	−	13.7014i	1.55906	−	0.567452i
$584$	−23.8519			−0.987001
$585$		0			0
$586$		−	50.5845i		−	2.08963i
$587$	−30.9328	−	25.9557i	−1.27673	−	1.07131i	−0.993686	−	0.112201i	$-0.964210\pi$
$587$	−30.9328	−	25.9557i	−1.27673	−	1.07131i	−0.283048	−	0.959106i	$-0.591346\pi$
$588$		0			0
$589$	−0.185664	−	1.05295i	−0.00765016	−	0.0433862i
$590$	3.12014	−	8.57250i	0.128454	−	0.352924i
$591$		0			0
$592$	4.74830	−	26.9290i	0.195154	−	1.10677i
$593$	2.27065	+	3.93289i	0.0932446	+	0.161504i	0.908875	−	0.417069i	$-0.136943\pi$
$593$	2.27065	+	3.93289i	0.0932446	+	0.161504i	−0.815630	+	0.578574i	$0.803609\pi$
$594$		0			0
$595$	−38.1987	−	3.49567i	−1.56599	−	0.143308i
$596$	−3.29972	−	9.06590i	−0.135162	−	0.371354i
$597$		0			0
$598$	−1.95272	+	0.344317i	−0.0798527	+	0.0140802i
$599$	−3.36732	+	9.25164i	−0.137585	+	0.378012i	−0.989281	−	0.146025i	$-0.953352\pi$
$599$	−3.36732	+	9.25164i	−0.137585	+	0.378012i	0.851696	+	0.524036i	$0.175574\pi$
$600$		0			0
$601$	−13.1479	+	15.6690i	−0.536313	+	0.639153i	−0.964357	−	0.264605i	$-0.914758\pi$
$601$	−13.1479	+	15.6690i	−0.536313	+	0.639153i	0.428044	+	0.903758i	$0.359203\pi$
$602$	−0.0318841	+	0.348411i	−0.00129950	+	0.0142002i
$603$		0			0
$604$	0.645587	−	1.11819i	0.0262686	−	0.0454985i
$605$	34.0408	+	28.5636i	1.38396	+	1.16128i
$606$		0			0
$607$	16.5784	−	2.92322i	0.672897	−	0.118650i	0.173249	−	0.984878i	$-0.444574\pi$
$607$	16.5784	−	2.92322i	0.672897	−	0.118650i	0.499649	+	0.866228i	$0.333462\pi$
$608$	6.27029	+	2.28220i	0.254294	+	0.0925554i
$609$		0			0
$610$	−3.13085	+	17.7559i	−0.126764	+	0.718917i
$611$	−9.98145	−	5.76279i	−0.403806	−	0.233138i
$612$		0			0
$613$	7.28280	+	12.6142i	0.294150	+	0.509482i	0.974787	−	0.223139i	$-0.0716303\pi$
$613$	7.28280	+	12.6142i	0.294150	+	0.509482i	−0.680637	+	0.732621i	$0.738297\pi$
$614$	7.24137	−	41.0679i	0.292238	−	1.65736i
$615$		0			0
$616$	22.6504	+	10.6724i	0.912612	+	0.430002i
$617$	−6.20042	−	7.38938i	−0.249620	−	0.297485i	0.626655	−	0.779297i	$-0.284423\pi$
$617$	−6.20042	−	7.38938i	−0.249620	−	0.297485i	−0.876275	+	0.481811i	$0.839979\pi$
$618$		0			0
$619$	−31.9542	−	5.63438i	−1.28435	−	0.226465i	−0.510522	−	0.859865i	$-0.670548\pi$
$619$	−31.9542	−	5.63438i	−1.28435	−	0.226465i	−0.773825	+	0.633400i	$0.781659\pi$
$620$	−1.87408	−	1.08200i	−0.0752648	−	0.0434541i
$621$		0			0
$622$			13.2649i			0.531876i
$623$	16.2647	+	16.3951i	0.651632	+	0.656856i
$624$		0			0
$625$	−10.9109	−	3.97124i	−0.436436	−	0.158850i
$626$	30.5073	+	11.1037i	1.21932	+	0.443795i
$627$		0			0
$628$	7.56251	+	1.33347i	0.301777	+	0.0532114i
$629$	−10.6455	+	18.4385i	−0.424462	+	0.735190i
$630$		0			0
$631$	1.22037	+	2.11374i	0.0485821	+	0.0841467i	0.889294	−	0.457336i	$-0.151196\pi$
$631$	1.22037	+	2.11374i	0.0485821	+	0.0841467i	−0.840712	+	0.541483i	$0.817863\pi$
$632$	0.889014	+	2.44255i	0.0353631	+	0.0971593i
$633$		0			0
$634$	−18.1884	+	15.2619i	−0.722355	+	0.606128i
$635$	−0.413464	−	2.34487i	−0.0164078	−	0.0930533i
$636$		0			0
$637$	−21.2592	−	7.93052i	−0.842322	−	0.314219i
$638$	−46.6654	+	26.9423i	−1.84750	+	1.06665i
$639$		0			0
$640$	−42.4777	+	24.5245i	−1.67908	+	0.969417i
$641$	6.48762	+	17.8246i	0.256245	+	0.704029i	0.999391	+	0.0348986i	$0.0111108\pi$
$641$	6.48762	+	17.8246i	0.256245	+	0.704029i	−0.743145	+	0.669130i	$0.766667\pi$
$642$		0			0
$643$	−30.7254	+	5.41772i	−1.21169	+	0.213654i	−0.742746	−	0.669573i	$-0.766477\pi$
$643$	−30.7254	+	5.41772i	−1.21169	+	0.213654i	−0.468946	+	0.883227i	$0.655366\pi$
$644$	−0.451423	−	0.650208i	−0.0177886	−	0.0256218i
$645$		0			0
$646$	−7.57240	−	6.35400i	−0.297932	−	0.249995i
$647$	18.3923	−	31.8564i	0.723076	−	1.25240i	−0.236685	−	0.971587i	$-0.576061\pi$
$647$	18.3923	−	31.8564i	0.723076	−	1.25240i	0.959761	−	0.280818i	$-0.0906058\pi$
$648$		0			0
$649$	5.99964	−	3.46390i	0.235507	−	0.135970i
$650$	46.2879	−	16.8474i	1.81556	−	0.660810i
$651$		0			0
$652$	8.85082	−	7.42672i	0.346625	−	0.290853i
$653$	−10.1406	−	12.0851i	−0.396832	−	0.472926i	0.530220	−	0.847860i	$-0.322110\pi$
$653$	−10.1406	−	12.0851i	−0.396832	−	0.472926i	−0.927051	+	0.374935i	$0.877665\pi$
$654$		0			0
$655$	7.22864	−	2.63101i	0.282446	−	0.102802i
$656$	−4.19735			−0.163879
$657$		0			0
$658$	1.44007	−	15.7363i	0.0561398	−	0.613464i
$659$	14.0350	+	2.47474i	0.546725	+	0.0964023i	0.440187	−	0.897906i	$-0.354912\pi$
$659$	14.0350	+	2.47474i	0.546725	+	0.0964023i	0.106538	+	0.994309i	$0.466023\pi$
$660$		0			0
$661$	−15.3589	−	18.3041i	−0.597394	−	0.711946i	0.379615	−	0.925144i	$-0.376056\pi$
$661$	−15.3589	−	18.3041i	−0.597394	−	0.711946i	−0.977009	+	0.213198i	$0.931612\pi$
$662$	15.7395	+	18.7576i	0.611734	+	0.729037i
$663$		0			0
$664$	26.4734	+	4.66798i	1.02737	+	0.181153i
$665$	−1.37475	+	15.0225i	−0.0533107	+	0.582549i
$666$		0			0
$667$	−2.44355			−0.0946145
$668$	−2.95129	+	1.07418i	−0.114189	+	0.0415614i
$669$		0			0
$670$	16.3730	+	19.5126i	0.632545	+	0.753837i
$671$	−10.4886	+	8.80101i	−0.404909	+	0.339759i
$672$		0			0
$673$	−2.30855	+	0.840244i	−0.0889881	+	0.0323890i	−0.386131	−	0.922444i	$-0.626189\pi$
$673$	−2.30855	+	0.840244i	−0.0889881	+	0.0323890i	0.297142	+	0.954833i	$0.403966\pi$
$674$	−39.2186	+	22.6429i	−1.51064	+	0.872171i
$675$		0			0
$676$	1.02400	−	1.77361i	0.0393845	−	0.0682159i
$677$	2.08260	+	1.74751i	0.0800409	+	0.0671623i	0.681930	−	0.731417i	$-0.261141\pi$
$677$	2.08260	+	1.74751i	0.0800409	+	0.0671623i	−0.601889	+	0.798579i	$0.705585\pi$
$678$		0			0
$679$	6.41912	+	9.24579i	0.246343	+	0.354821i
$680$	28.2632	−	4.98357i	1.08384	−	0.191111i
$681$		0			0
$682$	−1.93037	−	5.30366i	−0.0739178	−	0.203088i
$683$	−18.8189	+	10.8651i	−0.720086	+	0.415742i	−0.814784	−	0.579764i	$-0.803145\pi$
$683$	−18.8189	+	10.8651i	−0.720086	+	0.415742i	0.0946982	+	0.995506i	$0.469811\pi$
$684$		0			0
$685$	−50.8375	+	29.3510i	−1.94240	+	1.12145i
$686$	−2.34001	−	31.0211i	−0.0893420	−	1.18439i
$687$		0			0
$688$	−0.0679167	−	0.385175i	−0.00258930	−	0.0146846i
$689$	20.8067	−	17.4589i	0.792671	−	0.665130i
$690$		0			0
$691$	4.34469	+	11.9369i	0.165280	+	0.454103i	0.994490	−	0.104835i	$-0.0334314\pi$
$691$	4.34469	+	11.9369i	0.165280	+	0.454103i	−0.829210	+	0.558937i	$0.811209\pi$
$692$	−4.75359	−	8.23345i	−0.180704	−	0.312989i
$693$		0			0
$694$	−16.8198	+	29.1327i	−0.638471	+	1.10586i
$695$	−83.8305	−	14.7816i	−3.17987	−	0.560698i
$696$		0			0
$697$	3.07105	+	1.11777i	0.116324	+	0.0423386i
$698$	−16.5822	−	6.03542i	−0.627645	−	0.228444i
$699$		0			0
$700$	13.8489	+	13.9599i	0.523440	+	0.527636i
$701$			23.3250i			0.880973i	0.897759	+	0.440487i	$0.145194\pi$
$701$			23.3250i			0.880973i	−0.897759	+	0.440487i	$0.854806\pi$
$702$		0			0
$703$	7.25137	+	4.18658i	0.273490	+	0.157900i
$704$	−12.0938	−	2.13246i	−0.455802	−	0.0803703i
$705$		0			0
$706$	−3.56050	−	4.24323i	−0.134001	−	0.159696i
$707$	−16.7786	−	7.90570i	−0.631025	−	0.297324i
$708$		0			0
$709$	−3.99399	+	22.6510i	−0.149997	+	0.850677i	0.813221	+	0.581955i	$0.197712\pi$
$709$	−3.99399	+	22.6510i	−0.149997	+	0.850677i	−0.963218	+	0.268721i	$0.913399\pi$
$710$	51.5969	+	89.3684i	1.93640	+	3.35394i
$711$		0			0
$712$	−14.9639	−	8.63939i	−0.560794	−	0.323775i
$713$	0.0444444	−	0.252056i	0.00166445	−	0.00943959i
$714$		0			0
$715$	54.5785	+	19.8650i	2.04112	+	0.742907i
$716$	7.37358	−	1.30016i	0.275563	−	0.0485893i
$717$		0			0
$718$	−14.2417	−	11.9502i	−0.531494	−	0.445976i
$719$	−9.22441	+	15.9772i	−0.344013	+	0.595847i	−0.985174	−	0.171559i	$-0.945120\pi$
$719$	−9.22441	+	15.9772i	−0.344013	+	0.595847i	0.641161	+	0.767406i	$0.278453\pi$
$720$		0			0
$721$	1.72845	−	18.8875i	0.0643708	−	0.703408i
$722$	18.0158	−	21.4704i	0.670478	−	0.799044i
$723$		0			0
$724$	1.99704	−	5.48681i	0.0742193	−	0.203916i
$725$	59.7812	−	10.5410i	2.22022	−	0.391485i
$726$		0			0
$727$	−0.912501	−	2.50708i	−0.0338428	−	0.0929823i	0.921620	−	0.388092i	$-0.126866\pi$
$727$	−0.912501	−	2.50708i	−0.0338428	−	0.0929823i	−0.955463	+	0.295110i	$0.904644\pi$
$728$	16.9059	+	1.54711i	0.626576	+	0.0573397i
$729$		0			0
$730$	−37.9285	−	65.6942i	−1.40380	−	2.43145i
$731$	−0.0528814	+	0.299905i	−0.00195589	+	0.0110924i
$732$		0			0
$733$	11.9877	−	32.9359i	0.442775	−	1.21651i	−0.494884	−	0.868959i	$-0.664790\pi$
$733$	11.9877	−	32.9359i	0.442775	−	1.21651i	0.937659	−	0.347556i	$-0.112988\pi$
$734$	−5.77285	−	32.7394i	−0.213080	−	1.20843i
$735$		0			0
$736$	1.22361	+	1.02673i	0.0451030	+	0.0378459i
$737$			19.3435i			0.712525i
$738$		0			0
$739$	−6.84534			−0.251810			−0.125905	−	0.992042i	$-0.540183\pi$
$739$	−6.84534			−0.251810			−0.125905	+	0.992042i	$0.540183\pi$
$740$	15.9248	−	5.79615i	0.585407	−	0.213071i
$741$		0			0
$742$	33.6870	+	15.8725i	1.23669	+	0.582698i
$743$	−7.09106	+	19.4825i	−0.260146	+	0.714744i	0.739011	+	0.673693i	$0.235293\pi$
$743$	−7.09106	+	19.4825i	−0.260146	+	0.714744i	−0.999157	+	0.0410513i	$0.986929\pi$
$744$		0			0
$745$	−28.2915	+	33.7165i	−1.03652	+	1.23528i
$746$			7.33692i			0.268624i
$747$		0			0
$748$	−13.1578	−	7.59664i	−0.481095	−	0.277761i
$749$	45.4273	+	12.3668i	1.65988	+	0.451872i
$750$		0			0
$751$	22.5351	−	18.9092i	0.822316	−	0.690005i	−0.131197	−	0.991356i	$-0.541882\pi$
$751$	22.5351	−	18.9092i	0.822316	−	0.690005i	0.953513	+	0.301351i	$0.0974376\pi$
$752$	3.06751	+	17.3967i	0.111861	+	0.634393i
$753$		0			0
$754$	−23.4838	+	27.9869i	−0.855229	+	1.01922i
$755$	−5.89045			−0.214376
$756$		0			0
$757$	−41.4656			−1.50709			−0.753546	−	0.657396i	$-0.771658\pi$
$757$	−41.4656			−1.50709			−0.753546	+	0.657396i	$0.771658\pi$
$758$	−5.66609	+	6.75259i	−0.205802	+	0.245265i
$759$		0			0
$760$	−1.95991	−	11.1152i	−0.0710933	−	0.403190i
$761$	−35.0006	+	29.3690i	−1.26877	+	1.06463i	−0.274082	+	0.961706i	$0.588374\pi$
$761$	−35.0006	+	29.3690i	−1.26877	+	1.06463i	−0.994690	+	0.102920i	$0.967181\pi$
$762$		0			0
$763$	44.7028	−	11.7870i	1.61835	−	0.426718i
$764$	8.71420	+	5.03115i	0.315269	+	0.182020i
$765$		0			0
$766$		−	6.81633i		−	0.246284i
$767$	3.01925	−	3.59820i	0.109019	−	0.129924i
$768$		0			0
$769$	−3.17805	+	8.73163i	−0.114604	+	0.314871i	−0.983712	−	0.179750i	$-0.942471\pi$
$769$	−3.17805	+	8.73163i	−0.114604	+	0.314871i	0.869109	+	0.494621i	$0.164693\pi$
$770$	6.62362	+	79.3557i	0.238699	+	2.85978i
$771$		0			0
$772$	−12.8142	+	4.66399i	−0.461193	+	0.167861i
$773$	−3.25512			−0.117079			−0.0585393	−	0.998285i	$-0.518644\pi$
$773$	−3.25512			−0.117079			−0.0585393	+	0.998285i	$0.518644\pi$
$774$		0			0
$775$			6.35827i			0.228396i
$776$	−6.45112	−	5.41313i	−0.231582	−	0.194320i
$777$		0			0
$778$	−2.38742	−	13.5397i	−0.0855931	−	0.485423i
$779$	0.439590	−	1.20776i	0.0157499	−	0.0432726i
$780$		0			0
$781$	−13.6081	+	77.1752i	−0.486935	+	2.76155i
$782$	−1.18314	−	2.04927i	−0.0423092	−	0.0732816i
$783$		0			0
$784$	11.6332	+	32.7737i	0.415470	+	1.17049i
$785$	−11.9820	−	32.9203i	−0.427656	−	1.17498i
$786$		0			0
$787$	36.7086	−	6.47272i	1.30852	−	0.230728i	0.524472	−	0.851427i	$-0.324263\pi$
$787$	36.7086	−	6.47272i	1.30852	−	0.230728i	0.784048	+	0.620700i	$0.213151\pi$
$788$	−2.57298	+	7.06920i	−0.0916586	+	0.251830i
$789$		0			0
$790$	−5.31370	+	6.33262i	−0.189053	+	0.225304i
$791$	25.5826	+	18.0657i	0.909612	+	0.642344i
$792$		0			0
$793$	−4.64164	+	8.03956i	−0.164830	+	0.285493i
$794$	−8.71122	−	7.30958i	−0.309149	−	0.259407i
$795$		0			0
$796$	−5.30753	+	0.935860i	−0.188120	+	0.0331707i
$797$	24.8403	+	9.04114i	0.879889	+	0.320253i	0.742165	−	0.670217i	$-0.233799\pi$
$797$	24.8403	+	9.04114i	0.879889	+	0.320253i	0.137724	+	0.990471i	$0.456021\pi$
$798$		0			0
$799$	2.38843	−	13.5455i	0.0844966	−	0.479204i
$800$	−34.3648	−	19.8405i	−1.21498	−	0.701468i
$801$		0			0
$802$	3.05434	+	5.29028i	0.107853	+	0.186806i
$803$	10.0032	−	56.7310i	0.353006	−	2.00199i
$804$		0			0
$805$	−1.53918	+	3.26667i	−0.0542490	+	0.115135i
$806$	−2.45977	−	2.93144i	−0.0866416	−	0.103255i
$807$		0			0
$808$	13.6664	+	2.40976i	0.480784	+	0.0847751i
$809$	5.51222	+	3.18248i	0.193799	+	0.111890i	0.593760	−	0.804642i	$-0.297643\pi$
$809$	5.51222	+	3.18248i	0.193799	+	0.111890i	−0.399961	+	0.916532i	$0.630976\pi$
$810$		0			0
$811$		−	37.5618i		−	1.31897i	−0.751716	−	0.659487i	$-0.770773\pi$
$811$		−	37.5618i		−	1.31897i	0.751716	−	0.659487i	$-0.229227\pi$
$812$	−14.0723	−	3.83095i	−0.493843	−	0.134440i
$813$		0			0
$814$	41.5343	+	15.1172i	1.45578	+	0.529859i
$815$	−49.5312	−	18.0279i	−1.73500	−	0.631490i
$816$		0			0
$817$	0.117945	+	0.0207969i	0.00412637	+	0.000727590i
$818$	−30.8688	+	53.4663i	−1.07930	+	1.86940i
$819$		0			0
$820$	−1.30066	−	2.25282i	−0.0454211	−	0.0786717i
$821$	14.9344	+	41.0321i	0.521216	+	1.43203i	0.869168	+	0.494517i	$0.164655\pi$
$821$	14.9344	+	41.0321i	0.521216	+	1.43203i	−0.347952	+	0.937512i	$0.613123\pi$
$822$		0			0
$823$	18.2144	−	15.2837i	0.634914	−	0.532756i	−0.267538	−	0.963547i	$-0.586210\pi$
$823$	18.2144	−	15.2837i	0.634914	−	0.532756i	0.902452	+	0.430791i	$0.141766\pi$
$824$	2.46415	+	13.9749i	0.0858426	+	0.486838i
$825$		0			0
$826$	6.21380	+	1.69160i	0.216206	+	0.0588582i
$827$	−1.91398	+	1.10504i	−0.0665558	+	0.0384260i	−0.532909	−	0.846173i	$-0.678901\pi$
$827$	−1.91398	+	1.10504i	−0.0665558	+	0.0384260i	0.466353	+	0.884599i	$0.345568\pi$
$828$		0			0
$829$	7.55608	−	4.36250i	0.262433	−	0.151516i	−0.363011	−	0.931785i	$-0.618251\pi$
$829$	7.55608	−	4.36250i	0.262433	−	0.151516i	0.625444	+	0.780269i	$0.284918\pi$
$830$	29.2403	+	80.3372i	1.01495	+	2.78854i
$831$		0			0
$832$	−8.19973	+	1.44583i	−0.284275	+	0.0501253i
$833$	0.216194	−	27.0773i	0.00749069	−	0.938172i
$834$		0			0
$835$	10.9760	+	9.20996i	0.379840	+	0.318724i
$836$	−2.98756	+	5.17460i	−0.103327	+	0.178967i
$837$		0			0
$838$	−17.7656	+	10.2570i	−0.613702	+	0.354321i
$839$	22.6010	−	8.22611i	0.780275	−	0.283997i	0.0789874	−	0.996876i	$-0.474831\pi$
$839$	22.6010	−	8.22611i	0.780275	−	0.283997i	0.701287	+	0.712879i	$0.252609\pi$
$840$		0			0
$841$	−12.2742	+	10.2993i	−0.423249	+	0.355148i
$842$	−4.69903	−	5.60009i	−0.161939	−	0.192992i
$843$		0			0
$844$	11.4871	−	4.18095i	0.395401	−	0.143914i
$845$	−9.34312			−0.321413
$846$		0			0
$847$	−18.0952	+	25.6243i	−0.621757	+	0.880460i
$848$	−40.9971	−	7.22890i	−1.40785	−	0.248241i
$849$		0			0
$850$	37.7858	+	45.0313i	1.29604	+	1.54456i
$851$	1.28838	+	1.53544i	0.0441652	+	0.0526341i
$852$		0			0
$853$	13.6366	+	2.40451i	0.466910	+	0.0823287i	0.402153	−	0.915572i	$-0.368262\pi$
$853$	13.6366	+	2.40451i	0.466910	+	0.0823287i	0.0647563	+	0.997901i	$0.479373\pi$
$854$	−12.6748	−	1.15990i	−0.433722	−	0.0396911i
$855$		0			0
$856$	−35.2250			−1.20397
$857$	9.93166	−	3.61483i	0.339259	−	0.123480i	−0.166772	−	0.985996i	$-0.553334\pi$
$857$	9.93166	−	3.61483i	0.339259	−	0.123480i	0.506031	+	0.862515i	$0.331112\pi$
$858$		0			0
$859$	−29.2486	−	34.8571i	−0.997950	−	1.18931i	−0.981892	−	0.189439i	$-0.939333\pi$
$859$	−29.2486	−	34.8571i	−0.997950	−	1.18931i	−0.0160572	−	0.999871i	$-0.505111\pi$
$860$	0.185687	−	0.155810i	0.00633186	−	0.00531306i
$861$		0			0
$862$	13.1499	−	4.78617i	0.447887	−	0.163018i
$863$	42.6896	−	24.6469i	1.45317	−	0.838989i	0.454511	−	0.890741i	$-0.349814\pi$
$863$	42.6896	−	24.6469i	1.45317	−	0.838989i	0.998660	+	0.0517521i	$0.0164806\pi$
$864$		0			0
$865$	−21.6863	+	37.5618i	−0.737356	+	1.27714i
$866$	−29.6120	−	24.8474i	−1.00626	−	0.844350i
$867$		0			0
$868$	0.651124	−	1.38191i	0.0221006	−	0.0469051i
$869$	−6.18235	+	1.09012i	−0.209722	+	0.0369796i
$870$		0			0
$871$	4.48562	+	12.3241i	0.151989	+	0.417588i
$872$	−29.9551	+	17.2946i	−1.01441	+	0.585669i
$873$		0			0
$874$	−0.805923	+	0.465300i	−0.0272608	+	0.0157390i
$875$	10.5407	−	38.7195i	0.356341	−	1.30896i
$876$		0			0
$877$	6.82630	+	38.7139i	0.230508	+	1.30727i	0.851871	+	0.523752i	$0.175468\pi$
$877$	6.82630	+	38.7139i	0.230508	+	1.30727i	−0.621363	+	0.783523i	$0.713421\pi$
$878$	−23.4508	+	19.6775i	−0.791425	+	0.664085i
$879$		0			0
$880$	−30.4467	−	83.6517i	−1.02636	−	2.81990i
$881$	−20.9452	−	36.2781i	−0.705660	−	1.22224i	−0.966453	−	0.256845i	$-0.917317\pi$
$881$	−20.9452	−	36.2781i	−0.705660	−	1.22224i	0.260792	−	0.965395i	$-0.416016\pi$
$882$		0			0
$883$	3.31527	−	5.74221i	0.111568	−	0.193241i	−0.804835	−	0.593499i	$-0.797746\pi$
$883$	3.31527	−	5.74221i	0.111568	−	0.193241i	0.916402	+	0.400258i	$0.131080\pi$
$884$	−10.1447	−	1.78879i	−0.341204	−	0.0601634i
$885$		0			0
$886$	23.8482	+	8.68004i	0.801197	+	0.291612i
$887$	37.6426	+	13.7008i	1.26392	+	0.460028i	0.885081	−	0.465436i	$-0.154103\pi$
$887$	37.6426	+	13.7008i	1.26392	+	0.460028i	0.378835	+	0.925464i	$0.376325\pi$
$888$		0			0
$889$	1.62529	−	0.428549i	0.0545105	−	0.0143731i
$890$		−	54.9522i		−	1.84200i
$891$		0			0
$892$	−0.721438	−	0.416523i	−0.0241555	−	0.0139462i
$893$	−5.32707	−	0.939307i	−0.178264	−	0.0314327i
$894$		0			0
$895$	−21.9562	−	26.1664i	−0.733916	−	0.874647i
$896$	−19.7467	−	28.4422i	−0.659691	−	0.950188i
$897$		0			0
$898$	6.43883	−	36.5164i	0.214867	−	1.21857i
$899$	−2.35792	−	4.08403i	−0.0786409	−	0.136210i
$900$		0			0
$901$	28.0710	+	16.2068i	0.935182	+	0.539928i
$902$	1.17814	−	6.68158i	0.0392279	−	0.222472i
$903$		0			0
$904$	−22.0189	−	8.01422i	−0.732337	−	0.266549i
$905$	−26.2331	+	4.62560i	−0.872017	+	0.153760i
$906$		0			0
$907$	35.7631	+	30.0088i	1.18749	+	0.996426i	0.999899	+	0.0141799i	$0.00451377\pi$
$907$	35.7631	+	30.0088i	1.18749	+	0.996426i	0.187595	+	0.982246i	$0.439931\pi$
$908$	−9.43966	+	16.3500i	−0.313266	+	0.542593i
$909$		0			0
$910$	22.6221	+	49.0233i	0.749916	+	1.62511i
$911$	11.2903	−	13.4553i	0.374066	−	0.445794i	−0.545866	−	0.837872i	$-0.683799\pi$
$911$	11.2903	−	13.4553i	0.374066	−	0.445794i	0.919932	+	0.392078i	$0.128244\pi$
$912$		0			0
$913$	−22.2052	+	61.0084i	−0.734886	+	2.01908i
$914$	−64.3132	+	11.3402i	−2.12729	+	0.375099i
$915$		0			0
$916$	−0.100515	−	0.276164i	−0.00332112	−	0.00912470i
$917$	2.27531	+	4.93072i	0.0751374	+	0.162827i
$918$		0			0
$919$	−0.970359	−	1.68071i	−0.0320092	−	0.0554416i	0.849577	−	0.527465i	$-0.176857\pi$
$919$	−0.970359	−	1.68071i	−0.0320092	−	0.0554416i	−0.881586	+	0.472023i	$0.843524\pi$
$920$	0.469163	−	2.66075i	0.0154678	−	0.0877225i
$921$		0			0
$922$	−3.95169	+	10.8572i	−0.130142	+	0.357562i
$923$	9.22643	+	52.3257i	0.303692	+	1.72232i
$924$		0			0
$925$	−38.1438	−	32.0065i	−1.25416	−	1.05237i
$926$		−	15.8551i		−	0.521030i
$927$		0			0
$928$	29.4308			0.966114
$929$	−4.71446	+	1.71592i	−0.154676	+	0.0562976i	−0.418198	−	0.908356i	$-0.637338\pi$
$929$	−4.71446	+	1.71592i	−0.154676	+	0.0562976i	0.263522	+	0.964653i	$0.415116\pi$
$930$		0			0
$931$	−10.6488	−	0.0850236i	−0.349000	−	0.00278654i
$932$	−5.59940	+	15.3842i	−0.183415	+	0.503927i
$933$		0			0
$934$	20.8820	−	24.8863i	0.683282	−	0.814303i
$935$			69.3131i			2.26678i
$936$		0			0
$937$	25.9158	+	14.9625i	0.846632	+	0.488803i	0.859513	−	0.511114i	$-0.170767\pi$
$937$	25.9158	+	14.9625i	0.846632	+	0.488803i	−0.0128808	+	0.999917i	$0.504100\pi$
$938$	−12.7653	+	12.6638i	−0.416803	+	0.413489i
$939$		0			0
$940$	−8.38668	+	7.03726i	−0.273543	+	0.229530i
$941$	7.13638	+	40.4724i	0.232639	+	1.31936i	0.847529	+	0.530750i	$0.178090\pi$
$941$	7.13638	+	40.4724i	0.232639	+	1.31936i	−0.614889	+	0.788613i	$0.710799\pi$
$942$		0			0
$943$	0.197766	−	0.235688i	0.00644015	−	0.00767507i
$944$	−7.19920			−0.234314
$945$		0			0
$946$	0.632207			0.0205548
$947$	12.6597	−	15.0873i	0.411386	−	0.490270i	−0.520071	−	0.854123i	$-0.674094\pi$
$947$	12.6597	−	15.0873i	0.411386	−	0.490270i	0.931456	+	0.363853i	$0.118539\pi$
$948$		0			0
$949$	−6.78229	−	38.4643i	−0.220162	−	1.24860i
$950$	17.7096	−	14.8601i	0.574576	−	0.482127i
$951$		0			0
$952$	5.16539	+	19.5900i	0.167411	+	0.634915i
$953$	11.1121	+	6.41558i	0.359956	+	0.207821i	0.669062	−	0.743207i	$-0.266696\pi$
$953$	11.1121	+	6.41558i	0.359956	+	0.207821i	−0.309105	+	0.951028i	$0.600030\pi$
$954$		0			0
$955$		−	45.9051i		−	1.48545i
$956$	7.29977	−	8.69952i	0.236091	−	0.281363i
$957$		0			0
$958$	9.83797	−	27.0296i	0.317850	−	0.873287i
$959$	−23.6329	−	34.0398i	−0.763148	−	1.09920i
$960$		0			0
$961$	−28.6663	+	10.4337i	−0.924720	+	0.336570i
$962$	29.9680			0.966207
$963$		0			0
$964$			2.77455i			0.0893621i
$965$	47.6567	+	39.9887i	1.53412	+	1.28728i
$966$		0			0
$967$	10.1442	+	57.5307i	0.326216	+	1.85006i	0.500987	+	0.865455i	$0.332971\pi$
$967$	10.1442	+	57.5307i	0.326216	+	1.85006i	−0.174771	+	0.984609i	$0.555918\pi$
$968$	8.02728	−	22.0548i	0.258006	−	0.708867i
$969$		0			0
$970$	4.65076	−	26.3758i	0.149327	−	0.846875i
$971$	28.5180	+	49.3946i	0.915186	+	1.58515i	0.806629	+	0.591059i	$0.201290\pi$
$971$	28.5180	+	49.3946i	0.915186	+	1.58515i	0.108558	+	0.994090i	$0.465377\pi$
$972$		0			0
$973$	5.47622	−	59.8411i	0.175560	−	1.91842i
$974$	23.1685	+	63.6551i	0.742368	+	2.03964i
$975$		0			0
$976$	14.0122	−	2.47073i	0.448519	−	0.0790861i
$977$	−7.13483	+	19.6028i	−0.228263	+	0.627148i	−0.999961	−	0.00884128i	$-0.997186\pi$
$977$	−7.13483	+	19.6028i	−0.228263	+	0.627148i	0.771698	+	0.635990i	$0.219408\pi$
$978$		0			0
$979$	26.8241	−	31.9678i	0.857303	−	1.02169i
$980$	−13.9856	+	16.3996i	−0.446752	+	0.523867i
$981$		0			0
$982$	−3.53450	+	6.12193i	−0.112790	+	0.195359i
$983$	29.7422	+	24.9567i	0.948630	+	0.795995i	0.979066	−	0.203541i	$-0.0652451\pi$
$983$	29.7422	+	24.9567i	0.948630	+	0.795995i	−0.0304360	+	0.999537i	$0.509690\pi$
$984$		0			0
$985$	33.7987	−	5.95962i	1.07692	−	0.189889i
$986$	−40.9700	−	14.9119i	−1.30475	−	0.474890i
$987$		0			0
$988$	−0.703483	+	3.98965i	−0.0223808	+	0.126928i
$989$	0.0248283	+	0.0143346i	0.000789493	+	0.000455814i
$990$		0			0
$991$	−30.3659	−	52.5952i	−0.964603	−	1.67074i	−0.710677	−	0.703518i	$-0.751611\pi$
$991$	−30.3659	−	52.5952i	−0.964603	−	1.67074i	−0.253926	−	0.967224i	$-0.581722\pi$
$992$	−0.535301	+	3.03584i	−0.0169958	+	0.0963881i
$993$		0			0
$994$	−59.8393	+	41.5449i	−1.89799	+	1.31772i
$995$	15.8042	+	18.8347i	0.501026	+	0.597100i
$996$		0			0
$997$	45.0811	+	7.94902i	1.42773	+	0.251748i	0.833489	−	0.552536i	$-0.186340\pi$
$997$	45.0811	+	7.94902i	1.42773	+	0.251748i	0.594245	+	0.804284i	$0.297451\pi$
$998$	18.2110	+	10.5141i	0.576458	+	0.332818i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.143.17		132
3.2	odd	2		189.2.ba.a.101.6	✓	132
7.5	odd	6		567.2.bd.a.467.6		132
21.5	even	6		189.2.bd.a.47.17	yes	132
27.4	even	9		189.2.bd.a.185.17	yes	132
27.23	odd	18		567.2.bd.a.17.6		132
189.131	even	18	inner	567.2.ba.a.341.17		132
189.166	odd	18		189.2.ba.a.131.6	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.6	✓	132	3.2	odd	2
189.2.ba.a.131.6	yes	132	189.166	odd	18
189.2.bd.a.47.17	yes	132	21.5	even	6
189.2.bd.a.185.17	yes	132	27.4	even	9
567.2.ba.a.143.17		132	1.1	even	1	trivial
567.2.ba.a.341.17		132	189.131	even	18	inner
567.2.bd.a.17.6		132	27.23	odd	18
567.2.bd.a.467.6		132	7.5	odd	6

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.07972 - 1.28676i) q^{2} +(-0.142658 - 0.809053i) q^{4} +(-2.87107 + 2.40911i) q^{5} +(-1.86335 - 1.87828i) q^{7} +(1.71431 + 0.989760i) q^{8} +O(q^{10})\)	\(q+(1.07972 - 1.28676i) q^{2} +(-0.142658 - 0.809053i) q^{4} +(-2.87107 + 2.40911i) q^{5} +(-1.86335 - 1.87828i) q^{7} +(1.71431 + 0.989760i) q^{8} +6.29553i q^{10} +(-3.07307 + 3.66234i) q^{11} +(-1.10865 + 3.04598i) q^{13} +(-4.42878 + 0.369659i) q^{14} +(4.66853 - 1.69921i) q^{16} -3.86831 q^{17} +1.52130i q^{19} +(2.35868 + 1.97917i) q^{20} +(1.39450 + 7.90859i) q^{22} +(-0.124554 + 0.342208i) q^{23} +(1.57097 - 8.90940i) q^{25} +(2.72242 + 4.71536i) q^{26} +(-1.25381 + 1.77550i) q^{28} +(2.29492 + 6.30525i) q^{29} +(-0.692139 + 0.122043i) q^{31} +(1.50016 - 4.12165i) q^{32} +(-4.17668 + 4.97757i) q^{34} +(9.87478 + 0.903668i) q^{35} +(2.75197 - 4.76655i) q^{37} +(1.95755 + 1.64258i) q^{38} +(-7.30635 + 1.28831i) q^{40} +(-0.793900 - 0.288956i) q^{41} +(0.0136704 - 0.0775288i) q^{43} +(3.40143 + 1.96381i) q^{44} +(0.305856 + 0.529758i) q^{46} +(-0.617436 + 3.50165i) q^{47} +(-0.0558886 + 6.99978i) q^{49} +(-9.76803 - 11.6411i) q^{50} +(2.62252 + 0.462421i) q^{52} +(-7.25668 - 4.18964i) q^{53} -17.9182i q^{55} +(-1.33531 - 5.06423i) q^{56} +(10.5912 + 3.85488i) q^{58} +(-1.36168 - 0.495612i) q^{59} +(2.82040 + 0.497313i) q^{61} +(-0.590275 + 1.02239i) q^{62} +(1.28433 + 2.22452i) q^{64} +(-4.15511 - 11.4161i) q^{65} +(3.09944 - 2.60074i) q^{67} +(0.551844 + 3.12967i) q^{68} +(11.8248 - 11.7307i) q^{70} +(14.1956 - 8.19580i) q^{71} +(-10.4351 + 6.02468i) q^{73} +(-3.16204 - 8.68764i) q^{74} +(1.23082 - 0.217026i) q^{76} +(12.6051 - 1.05212i) q^{77} +(1.00589 + 0.844043i) q^{79} +(-9.31009 + 16.1256i) q^{80} +(-1.22900 + 0.709566i) q^{82} +(12.7610 - 4.64462i) q^{83} +(11.1062 - 9.31918i) q^{85} +(-0.0850005 - 0.101300i) q^{86} +(-8.89304 + 3.23680i) q^{88} -8.72878 q^{89} +(7.78701 - 3.59337i) q^{91} +(0.294633 + 0.0519517i) q^{92} +(3.83912 + 4.57528i) q^{94} +(-3.66499 - 4.36777i) q^{95} +(-4.18960 - 0.738740i) q^{97} +(8.94667 + 7.62970i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more