LMFDB - Embedded newform 750.2.h.a.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(49,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("750.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.h (of order $10$, degree $4$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			199.1
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	750.199
Dual form			750.2.h.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} -2.00000i q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} -2.00000i q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.618034 - 0.449028i) q^{11} +(0.587785 - 0.809017i) q^{12} +(1.08981 - 1.50000i) q^{13} +(-1.61803 + 1.17557i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(1.08981 - 0.354102i) q^{17} -1.00000i q^{18} +(2.23607 + 6.88191i) q^{19} +(-0.618034 + 1.90211i) q^{21} +(-0.726543 - 0.236068i) q^{22} +(-3.52671 - 4.85410i) q^{23} -1.00000 q^{24} -1.85410 q^{26} +(-0.587785 - 0.809017i) q^{27} +(1.90211 + 0.618034i) q^{28} +(1.11803 - 3.44095i) q^{29} +(-3.00000 - 9.23305i) q^{31} +1.00000i q^{32} +(-0.726543 + 0.236068i) q^{33} +(-0.927051 - 0.673542i) q^{34} +(-0.809017 + 0.587785i) q^{36} +(5.20431 - 7.16312i) q^{37} +(4.25325 - 5.85410i) q^{38} +(-1.50000 + 1.08981i) q^{39} +(-4.11803 - 2.99193i) q^{41} +(1.90211 - 0.618034i) q^{42} +3.23607i q^{43} +(0.236068 + 0.726543i) q^{44} +(-1.85410 + 5.70634i) q^{46} +(-8.78402 - 2.85410i) q^{47} +(0.587785 + 0.809017i) q^{48} +3.00000 q^{49} -1.14590 q^{51} +(1.08981 + 1.50000i) q^{52} +(-10.9964 - 3.57295i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-0.618034 - 1.90211i) q^{56} -7.23607i q^{57} +(-3.44095 + 1.11803i) q^{58} +(-7.23607 - 5.25731i) q^{59} +(1.73607 - 1.26133i) q^{61} +(-5.70634 + 7.85410i) q^{62} +(1.17557 - 1.61803i) q^{63} +(0.809017 - 0.587785i) q^{64} +(0.618034 + 0.449028i) q^{66} +(3.52671 - 1.14590i) q^{67} +1.14590i q^{68} +(1.85410 + 5.70634i) q^{69} +(2.52786 - 7.77997i) q^{71} +(0.951057 + 0.309017i) q^{72} +(5.79210 + 7.97214i) q^{73} -8.85410 q^{74} -7.23607 q^{76} +(-0.898056 - 1.23607i) q^{77} +(1.76336 + 0.572949i) q^{78} +(0.309017 + 0.951057i) q^{81} +5.09017i q^{82} +(-5.70634 + 1.85410i) q^{83} +(-1.61803 - 1.17557i) q^{84} +(2.61803 - 1.90211i) q^{86} +(-2.12663 + 2.92705i) q^{87} +(0.449028 - 0.618034i) q^{88} +(2.92705 - 2.12663i) q^{89} +(-3.00000 - 2.17963i) q^{91} +(5.70634 - 1.85410i) q^{92} +9.70820i q^{93} +(2.85410 + 8.78402i) q^{94} +(0.309017 - 0.951057i) q^{96} +(6.79615 + 2.20820i) q^{97} +(-1.76336 - 2.42705i) q^{98} +0.763932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 2 q^{6} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^4 - 2 * q^6 + 2 * q^9	$ 8 q + 2 q^{4} - 2 q^{6} + 2 q^{9} - 4 q^{11} - 4 q^{14} - 2 q^{16} + 4 q^{21} - 8 q^{24} + 12 q^{26} - 24 q^{31} + 6 q^{34} - 2 q^{36} - 12 q^{39} - 24 q^{41} - 16 q^{44} + 12 q^{46} + 24 q^{49} - 36 q^{51} + 2 q^{54} + 4 q^{56} - 40 q^{59} - 4 q^{61} + 2 q^{64} - 4 q^{66} - 12 q^{69} + 56 q^{71} - 44 q^{74} - 40 q^{76} - 2 q^{81} - 4 q^{84} + 12 q^{86} + 10 q^{89} - 24 q^{91} - 4 q^{94} - 2 q^{96} + 24 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 - 2 * q^6 + 2 * q^9 - 4 * q^11 - 4 * q^14 - 2 * q^16 + 4 * q^21 - 8 * q^24 + 12 * q^26 - 24 * q^31 + 6 * q^34 - 2 * q^36 - 12 * q^39 - 24 * q^41 - 16 * q^44 + 12 * q^46 + 24 * q^49 - 36 * q^51 + 2 * q^54 + 4 * q^56 - 40 * q^59 - 4 * q^61 + 2 * q^64 - 4 * q^66 - 12 * q^69 + 56 * q^71 - 44 * q^74 - 40 * q^76 - 2 * q^81 - 4 * q^84 + 12 * q^86 + 10 * q^89 - 24 * q^91 - 4 * q^94 - 2 * q^96 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	0.309017	+	0.951057i	0.126156	+	0.388267i
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$		0			0
$11$	0.618034	−	0.449028i	0.186344	−	0.135387i	−0.490702	−	0.871327i	$-0.663260\pi$
$11$	0.618034	−	0.449028i	0.186344	−	0.135387i	0.677046	+	0.735940i	$0.263260\pi$
$12$	0.587785	−	0.809017i	0.169679	−	0.233543i
$13$	1.08981	−	1.50000i	0.302260	−	0.416025i	−0.630688	−	0.776037i	$-0.717227\pi$
$13$	1.08981	−	1.50000i	0.302260	−	0.416025i	0.932948	+	0.360011i	$0.117227\pi$
$14$	−1.61803	+	1.17557i	−0.432438	+	0.314184i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.08981	−	0.354102i	0.264319	−	0.0858823i	−0.173860	−	0.984770i	$-0.555624\pi$
$17$	1.08981	−	0.354102i	0.264319	−	0.0858823i	0.438178	+	0.898888i	$0.355624\pi$
$18$		−	1.00000i		−	0.235702i
$19$	2.23607	+	6.88191i	0.512989	+	1.57882i	0.786911	+	0.617066i	$0.211679\pi$
$19$	2.23607	+	6.88191i	0.512989	+	1.57882i	−0.273922	+	0.961752i	$0.588321\pi$
$20$		0			0
$21$	−0.618034	+	1.90211i	−0.134866	+	0.415075i
$22$	−0.726543	−	0.236068i	−0.154899	−	0.0503299i
$23$	−3.52671	−	4.85410i	−0.735370	−	1.01215i	−0.998872	−	0.0474912i	$-0.984877\pi$
$23$	−3.52671	−	4.85410i	−0.735370	−	1.01215i	0.263501	−	0.964659i	$-0.415123\pi$
$24$	−1.00000			−0.204124
$25$		0			0
$26$	−1.85410			−0.363619
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	1.90211	+	0.618034i	0.359466	+	0.116797i
$29$	1.11803	−	3.44095i	0.207614	−	0.638969i	−0.791982	−	0.610544i	$-0.790951\pi$
$29$	1.11803	−	3.44095i	0.207614	−	0.638969i	0.999596	−	0.0284251i	$-0.00904922\pi$
$30$		0			0
$31$	−3.00000	−	9.23305i	−0.538816	−	1.65830i	−0.735256	−	0.677789i	$-0.762938\pi$
$31$	−3.00000	−	9.23305i	−0.538816	−	1.65830i	0.196440	−	0.980516i	$-0.437062\pi$
$32$			1.00000i			0.176777i
$33$	−0.726543	+	0.236068i	−0.126475	+	0.0410942i
$34$	−0.927051	−	0.673542i	−0.158988	−	0.115511i
$35$		0			0
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	5.20431	−	7.16312i	0.855583	−	1.17761i	−0.127021	−	0.991900i	$-0.540542\pi$
$37$	5.20431	−	7.16312i	0.855583	−	1.17761i	0.982605	−	0.185710i	$-0.0594583\pi$
$38$	4.25325	−	5.85410i	0.689969	−	0.949661i
$39$	−1.50000	+	1.08981i	−0.240192	+	0.174510i
$40$		0			0
$41$	−4.11803	−	2.99193i	−0.643129	−	0.467260i	0.217795	−	0.975995i	$-0.430114\pi$
$41$	−4.11803	−	2.99193i	−0.643129	−	0.467260i	−0.860924	+	0.508734i	$0.830114\pi$
$42$	1.90211	−	0.618034i	0.293502	−	0.0953647i
$43$			3.23607i			0.493496i	0.969080	+	0.246748i	$0.0793619\pi$
$43$			3.23607i			0.493496i	−0.969080	+	0.246748i	$0.920638\pi$
$44$	0.236068	+	0.726543i	0.0355886	+	0.109530i
$45$		0			0
$46$	−1.85410	+	5.70634i	−0.273372	+	0.841354i
$47$	−8.78402	−	2.85410i	−1.28128	−	0.416314i	−0.412250	−	0.911071i	$-0.635257\pi$
$47$	−8.78402	−	2.85410i	−1.28128	−	0.416314i	−0.869031	+	0.494757i	$0.835257\pi$
$48$	0.587785	+	0.809017i	0.0848395	+	0.116772i
$49$	3.00000			0.428571
$50$		0			0
$51$	−1.14590			−0.160458
$52$	1.08981	+	1.50000i	0.151130	+	0.208013i
$53$	−10.9964	−	3.57295i	−1.51047	−	0.490782i	−0.567421	−	0.823428i	$-0.692059\pi$
$53$	−10.9964	−	3.57295i	−1.51047	−	0.490782i	−0.943052	+	0.332646i	$0.892059\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$		0			0
$56$	−0.618034	−	1.90211i	−0.0825883	−	0.254181i
$57$		−	7.23607i		−	0.958441i
$58$	−3.44095	+	1.11803i	−0.451820	+	0.146805i
$59$	−7.23607	−	5.25731i	−0.942056	−	0.684444i	0.00685884	−	0.999976i	$-0.497817\pi$
$59$	−7.23607	−	5.25731i	−0.942056	−	0.684444i	−0.948915	+	0.315533i	$0.897817\pi$
$60$		0			0
$61$	1.73607	−	1.26133i	0.222281	−	0.161496i	−0.471072	−	0.882095i	$-0.656133\pi$
$61$	1.73607	−	1.26133i	0.222281	−	0.161496i	0.693353	+	0.720598i	$0.256133\pi$
$62$	−5.70634	+	7.85410i	−0.724706	+	0.997472i
$63$	1.17557	−	1.61803i	0.148108	−	0.203853i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$		0			0
$66$	0.618034	+	0.449028i	0.0760747	+	0.0552715i
$67$	3.52671	−	1.14590i	0.430856	−	0.139994i	−0.0855568	−	0.996333i	$-0.527267\pi$
$67$	3.52671	−	1.14590i	0.430856	−	0.139994i	0.516413	+	0.856340i	$0.327267\pi$
$68$			1.14590i			0.138961i
$69$	1.85410	+	5.70634i	0.223208	+	0.686963i
$70$		0			0
$71$	2.52786	−	7.77997i	0.300002	−	0.923312i	−0.681493	−	0.731825i	$-0.738669\pi$
$71$	2.52786	−	7.77997i	0.300002	−	0.923312i	0.981495	−	0.191487i	$-0.0613311\pi$
$72$	0.951057	+	0.309017i	0.112083	+	0.0364180i
$73$	5.79210	+	7.97214i	0.677914	+	0.933068i	0.999907	−	0.0136741i	$-0.00435274\pi$
$73$	5.79210	+	7.97214i	0.677914	+	0.933068i	−0.321993	+	0.946742i	$0.604353\pi$
$74$	−8.85410			−1.02927
$75$		0			0
$76$	−7.23607			−0.830034
$77$	−0.898056	−	1.23607i	−0.102343	−	0.140863i
$78$	1.76336	+	0.572949i	0.199661	+	0.0648737i
$79$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$79$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$			5.09017i			0.562115i
$83$	−5.70634	+	1.85410i	−0.626352	+	0.203514i	−0.604959	−	0.796257i	$-0.706810\pi$
$83$	−5.70634	+	1.85410i	−0.626352	+	0.203514i	−0.0213936	+	0.999771i	$0.506810\pi$
$84$	−1.61803	−	1.17557i	−0.176542	−	0.128265i
$85$		0			0
$86$	2.61803	−	1.90211i	0.282310	−	0.205110i
$87$	−2.12663	+	2.92705i	−0.227998	+	0.313813i
$88$	0.449028	−	0.618034i	0.0478665	−	0.0658826i
$89$	2.92705	−	2.12663i	0.310267	−	0.225422i	−0.421744	−	0.906715i	$-0.638582\pi$
$89$	2.92705	−	2.12663i	0.310267	−	0.225422i	0.732011	+	0.681293i	$0.238582\pi$
$90$		0			0
$91$	−3.00000	−	2.17963i	−0.314485	−	0.228487i
$92$	5.70634	−	1.85410i	0.594927	−	0.193303i
$93$			9.70820i			1.00669i
$94$	2.85410	+	8.78402i	0.294378	+	0.906003i
$95$		0			0
$96$	0.309017	−	0.951057i	0.0315389	−	0.0970668i
$97$	6.79615	+	2.20820i	0.690045	+	0.224209i	0.632988	−	0.774162i	$-0.281828\pi$
$97$	6.79615	+	2.20820i	0.690045	+	0.224209i	0.0570570	+	0.998371i	$0.481828\pi$
$98$	−1.76336	−	2.42705i	−0.178126	−	0.245169i
$99$	0.763932			0.0767781
$100$		0			0
$101$	17.3262			1.72403			0.862013	−	0.506887i	$-0.169204\pi$
$101$	17.3262			1.72403			0.862013	+	0.506887i	$0.169204\pi$
$102$	0.673542	+	0.927051i	0.0666906	+	0.0917917i
$103$	−14.9394	−	4.85410i	−1.47202	−	0.478289i	−0.540303	−	0.841470i	$-0.681691\pi$
$103$	−14.9394	−	4.85410i	−1.47202	−	0.478289i	−0.931718	+	0.363181i	$0.881691\pi$
$104$	0.572949	−	1.76336i	0.0561823	−	0.172911i
$105$		0			0
$106$	3.57295	+	10.9964i	0.347035	+	1.06807i
$107$			6.94427i			0.671328i	0.941982	+	0.335664i	$0.108961\pi$
$107$			6.94427i			0.671328i	−0.941982	+	0.335664i	$0.891039\pi$
$108$	0.951057	−	0.309017i	0.0915155	−	0.0297352i
$109$	−14.2082	−	10.3229i	−1.36090	−	0.988751i	−0.998387	−	0.0567720i	$-0.981919\pi$
$109$	−14.2082	−	10.3229i	−1.36090	−	0.988751i	−0.362512	−	0.931979i	$-0.618081\pi$
$110$		0			0
$111$	−7.16312	+	5.20431i	−0.679893	+	0.493971i
$112$	−1.17557	+	1.61803i	−0.111081	+	0.152890i
$113$	5.03280	−	6.92705i	0.473446	−	0.651642i	−0.503783	−	0.863830i	$-0.668059\pi$
$113$	5.03280	−	6.92705i	0.473446	−	0.651642i	0.977229	+	0.212188i	$0.0680589\pi$
$114$	−5.85410	+	4.25325i	−0.548287	+	0.398354i
$115$		0			0
$116$	2.92705	+	2.12663i	0.271770	+	0.197452i
$117$	1.76336	−	0.572949i	0.163022	−	0.0529692i
$118$			8.94427i			0.823387i
$119$	−0.708204	−	2.17963i	−0.0649209	−	0.199806i
$120$		0			0
$121$	−3.21885	+	9.90659i	−0.292622	+	0.900599i
$122$	−2.04087	−	0.663119i	−0.184772	−	0.0600360i
$123$	2.99193	+	4.11803i	0.269773	+	0.371311i
$124$	9.70820			0.871822
$125$		0			0
$126$	−2.00000			−0.178174
$127$	8.05748	+	11.0902i	0.714986	+	0.984093i	0.999675	+	0.0254737i	$0.00810942\pi$
$127$	8.05748	+	11.0902i	0.714986	+	0.984093i	−0.284690	+	0.958620i	$0.591891\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	1.00000	−	3.07768i	0.0880451	−	0.270975i
$130$		0			0
$131$	−1.61803	−	4.97980i	−0.141368	−	0.435087i	0.855158	−	0.518368i	$-0.173460\pi$
$131$	−1.61803	−	4.97980i	−0.141368	−	0.435087i	−0.996526	+	0.0832809i	$0.973460\pi$
$132$		−	0.763932i		−	0.0664917i
$133$	13.7638	−	4.47214i	1.19347	−	0.387783i
$134$	−3.00000	−	2.17963i	−0.259161	−	0.188291i
$135$		0			0
$136$	0.927051	−	0.673542i	0.0794940	−	0.0577557i
$137$	−8.24924	+	11.3541i	−0.704780	+	0.970046i	0.295114	+	0.955462i	$0.404642\pi$
$137$	−8.24924	+	11.3541i	−0.704780	+	0.970046i	−0.999894	+	0.0145842i	$0.995358\pi$
$138$	3.52671	−	4.85410i	0.300214	−	0.413209i
$139$	10.8541	−	7.88597i	0.920633	−	0.668879i	−0.0230486	−	0.999734i	$-0.507337\pi$
$139$	10.8541	−	7.88597i	0.920633	−	0.668879i	0.943681	+	0.330855i	$0.107337\pi$
$140$		0			0
$141$	7.47214	+	5.42882i	0.629267	+	0.457190i
$142$	−7.77997	+	2.52786i	−0.652880	+	0.212134i
$143$		−	1.41641i		−	0.118446i
$144$	−0.309017	−	0.951057i	−0.0257514	−	0.0792547i
$145$		0			0
$146$	3.04508	−	9.37181i	0.252013	−	0.775616i
$147$	−2.85317	−	0.927051i	−0.235325	−	0.0764619i
$148$	5.20431	+	7.16312i	0.427792	+	0.588805i
$149$	22.0344			1.80513			0.902566	−	0.430552i	$-0.141681\pi$
$149$	22.0344			1.80513			0.902566	+	0.430552i	$0.141681\pi$
$150$		0			0
$151$	10.9443			0.890632			0.445316	−	0.895373i	$-0.353091\pi$
$151$	10.9443			0.890632			0.445316	+	0.895373i	$0.353091\pi$
$152$	4.25325	+	5.85410i	0.344984	+	0.474830i
$153$	1.08981	+	0.354102i	0.0881062	+	0.0286274i
$154$	−0.472136	+	1.45309i	−0.0380458	+	0.117093i
$155$		0			0
$156$	−0.572949	−	1.76336i	−0.0458726	−	0.141181i
$157$		−	11.1459i		−	0.889540i	−0.895645	−	0.444770i	$-0.853286\pi$
$157$		−	11.1459i		−	0.889540i	0.895645	−	0.444770i	$-0.146714\pi$
$158$		0			0
$159$	9.35410	+	6.79615i	0.741829	+	0.538970i
$160$		0			0
$161$	−9.70820	+	7.05342i	−0.765114	+	0.555888i
$162$	0.587785	−	0.809017i	0.0461808	−	0.0635624i
$163$	6.77591	−	9.32624i	0.530730	−	0.730487i	−0.456511	−	0.889718i	$-0.650901\pi$
$163$	6.77591	−	9.32624i	0.530730	−	0.730487i	0.987241	+	0.159230i	$0.0509012\pi$
$164$	4.11803	−	2.99193i	0.321564	−	0.233630i
$165$		0			0
$166$	4.85410	+	3.52671i	0.376751	+	0.273726i
$167$	−2.35114	+	0.763932i	−0.181937	+	0.0591148i	−0.398569	−	0.917139i	$-0.630493\pi$
$167$	−2.35114	+	0.763932i	−0.181937	+	0.0591148i	0.216632	+	0.976253i	$0.430493\pi$
$168$			2.00000i			0.154303i
$169$	2.95492	+	9.09429i	0.227301	+	0.699561i
$170$		0			0
$171$	−2.23607	+	6.88191i	−0.170996	+	0.526273i
$172$	−3.07768	−	1.00000i	−0.234671	−	0.0762493i
$173$	12.9843	+	17.8713i	0.987176	+	1.35873i	0.932872	+	0.360207i	$0.117294\pi$
$173$	12.9843	+	17.8713i	0.987176	+	1.35873i	0.0543039	+	0.998524i	$0.482706\pi$
$174$	3.61803			0.274282
$175$		0			0
$176$	−0.763932			−0.0575835
$177$	5.25731	+	7.23607i	0.395164	+	0.543896i
$178$	−3.44095	−	1.11803i	−0.257910	−	0.0838002i
$179$	8.09017	−	24.8990i	0.604688	−	1.86104i	0.105764	−	0.994391i	$-0.466271\pi$
$179$	8.09017	−	24.8990i	0.604688	−	1.86104i	0.498923	−	0.866646i	$-0.333729\pi$
$180$		0			0
$181$	2.79180	+	8.59226i	0.207513	+	0.638658i	0.999601	+	0.0282515i	$0.00899392\pi$
$181$	2.79180	+	8.59226i	0.207513	+	0.638658i	−0.792088	+	0.610407i	$0.791006\pi$
$182$			3.70820i			0.274870i
$183$	−2.04087	+	0.663119i	−0.150865	+	0.0490192i
$184$	−4.85410	−	3.52671i	−0.357849	−	0.259993i
$185$		0			0
$186$	7.85410	−	5.70634i	0.575891	−	0.418409i
$187$	0.514540	−	0.708204i	0.0376269	−	0.0517890i
$188$	5.42882	−	7.47214i	0.395938	−	0.544962i
$189$	−1.61803	+	1.17557i	−0.117695	+	0.0855102i
$190$		0			0
$191$	4.23607	+	3.07768i	0.306511	+	0.222693i	0.730398	−	0.683022i	$-0.239335\pi$
$191$	4.23607	+	3.07768i	0.306511	+	0.222693i	−0.423887	+	0.905715i	$0.639335\pi$
$192$	−0.951057	+	0.309017i	−0.0686366	+	0.0223014i
$193$			4.61803i			0.332413i	0.986091	+	0.166207i	$0.0531519\pi$
$193$			4.61803i			0.332413i	−0.986091	+	0.166207i	$0.946848\pi$
$194$	−2.20820	−	6.79615i	−0.158540	−	0.487935i
$195$		0			0
$196$	−0.927051	+	2.85317i	−0.0662179	+	0.203798i
$197$	−2.21238	−	0.718847i	−0.157626	−	0.0512157i	0.229141	−	0.973393i	$-0.426408\pi$
$197$	−2.21238	−	0.718847i	−0.157626	−	0.0512157i	−0.386767	+	0.922177i	$0.626408\pi$
$198$	−0.449028	−	0.618034i	−0.0319110	−	0.0439218i
$199$	−16.1803			−1.14699			−0.573497	−	0.819208i	$-0.694414\pi$
$199$	−16.1803			−1.14699			−0.573497	+	0.819208i	$0.694414\pi$
$200$		0			0
$201$	−3.70820			−0.261557
$202$	−10.1841	−	14.0172i	−0.716551	−	0.986248i
$203$	−6.88191	−	2.23607i	−0.483015	−	0.156941i
$204$	0.354102	−	1.08981i	0.0247921	−	0.0763022i
$205$		0			0
$206$	4.85410	+	14.9394i	0.338201	+	1.04088i
$207$		−	6.00000i		−	0.417029i
$208$	−1.76336	+	0.572949i	−0.122267	+	0.0397269i
$209$	4.47214	+	3.24920i	0.309344	+	0.224752i
$210$		0			0
$211$	6.47214	−	4.70228i	0.445560	−	0.323718i	−0.342280	−	0.939598i	$-0.611199\pi$
$211$	6.47214	−	4.70228i	0.445560	−	0.323718i	0.787840	+	0.615880i	$0.211199\pi$
$212$	6.79615	−	9.35410i	0.466762	−	0.642442i
$213$	−4.80828	+	6.61803i	−0.329458	+	0.453460i
$214$	5.61803	−	4.08174i	0.384041	−	0.279022i
$215$		0			0
$216$	−0.809017	−	0.587785i	−0.0550466	−	0.0399937i
$217$	−18.4661	+	6.00000i	−1.25356	+	0.407307i
$218$			17.5623i			1.18947i
$219$	−3.04508	−	9.37181i	−0.205768	−	0.633288i
$220$		0			0
$221$	0.656541	−	2.02063i	0.0441637	−	0.135922i
$222$	8.42075	+	2.73607i	0.565164	+	0.183633i
$223$	9.23305	+	12.7082i	0.618291	+	0.851004i	0.997227	−	0.0744185i	$-0.0237101\pi$
$223$	9.23305	+	12.7082i	0.618291	+	0.851004i	−0.378936	+	0.925423i	$0.623710\pi$
$224$	2.00000			0.133631
$225$		0			0
$226$	−8.56231			−0.569556
$227$	0.555029	+	0.763932i	0.0368386	+	0.0507039i	0.827039	−	0.562145i	$-0.190024\pi$
$227$	0.555029	+	0.763932i	0.0368386	+	0.0507039i	−0.790200	+	0.612849i	$0.790024\pi$
$228$	6.88191	+	2.23607i	0.455766	+	0.148087i
$229$	−2.86475	+	8.81678i	−0.189308	+	0.582629i	−0.999996	−	0.00284891i	$-0.999093\pi$
$229$	−2.86475	+	8.81678i	−0.189308	+	0.582629i	0.810688	+	0.585478i	$0.199093\pi$
$230$		0			0
$231$	0.472136	+	1.45309i	0.0310643	+	0.0956060i
$232$		−	3.61803i		−	0.237536i
$233$	10.3759	−	3.37132i	0.679746	−	0.220863i	0.0512616	−	0.998685i	$-0.483676\pi$
$233$	10.3759	−	3.37132i	0.679746	−	0.220863i	0.628484	+	0.777823i	$0.283676\pi$
$234$	−1.50000	−	1.08981i	−0.0980581	−	0.0712434i
$235$		0			0
$236$	7.23607	−	5.25731i	0.471028	−	0.342222i
$237$		0			0
$238$	−1.34708	+	1.85410i	−0.0873185	+	0.120184i
$239$	−21.7082	+	15.7719i	−1.40419	+	1.02020i	−0.410051	+	0.912063i	$0.634489\pi$
$239$	−21.7082	+	15.7719i	−1.40419	+	1.02020i	−0.994136	+	0.108139i	$0.965511\pi$
$240$		0			0
$241$	5.78115	+	4.20025i	0.372397	+	0.270562i	0.758204	−	0.652017i	$-0.226077\pi$
$241$	5.78115	+	4.20025i	0.372397	+	0.270562i	−0.385807	+	0.922579i	$0.626077\pi$
$242$	9.90659	−	3.21885i	0.636820	−	0.206915i
$243$		−	1.00000i		−	0.0641500i
$244$	0.663119	+	2.04087i	0.0424518	+	0.130653i
$245$		0			0
$246$	1.57295	−	4.84104i	0.100288	−	0.308653i
$247$	12.7598	+	4.14590i	0.811884	+	0.263797i
$248$	−5.70634	−	7.85410i	−0.362353	−	0.498736i
$249$	6.00000			0.380235
$250$		0			0
$251$	−3.52786			−0.222677			−0.111338	−	0.993783i	$-0.535514\pi$
$251$	−3.52786			−0.222677			−0.111338	+	0.993783i	$0.535514\pi$
$252$	1.17557	+	1.61803i	0.0740540	+	0.101927i
$253$	−4.35926	−	1.41641i	−0.274064	−	0.0890488i
$254$	4.23607	−	13.0373i	0.265795	−	0.818031i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			9.38197i			0.585231i	0.956230	+	0.292615i	$0.0945256\pi$
$257$			9.38197i			0.585231i	−0.956230	+	0.292615i	$0.905474\pi$
$258$	−3.07768	+	1.00000i	−0.191608	+	0.0622573i
$259$	−14.3262	−	10.4086i	−0.890189	−	0.646760i
$260$		0			0
$261$	2.92705	−	2.12663i	0.181180	−	0.131635i
$262$	−3.07768	+	4.23607i	−0.190140	+	0.261705i
$263$	−4.97980	+	6.85410i	−0.307067	+	0.422642i	−0.934464	−	0.356058i	$-0.884121\pi$
$263$	−4.97980	+	6.85410i	−0.307067	+	0.422642i	0.627396	+	0.778700i	$0.284121\pi$
$264$	−0.618034	+	0.449028i	−0.0380374	+	0.0276358i
$265$		0			0
$266$	−11.7082	−	8.50651i	−0.717876	−	0.521567i
$267$	−3.44095	+	1.11803i	−0.210583	+	0.0684226i
$268$			3.70820i			0.226515i
$269$	4.04508	+	12.4495i	0.246633	+	0.759059i	0.995364	+	0.0961842i	$0.0306638\pi$
$269$	4.04508	+	12.4495i	0.246633	+	0.759059i	−0.748730	+	0.662875i	$0.769336\pi$
$270$		0			0
$271$	1.79837	−	5.53483i	0.109243	−	0.336217i	−0.881460	−	0.472260i	$-0.843438\pi$
$271$	1.79837	−	5.53483i	0.109243	−	0.336217i	0.990703	+	0.136043i	$0.0434385\pi$
$272$	−1.08981	−	0.354102i	−0.0660797	−	0.0214706i
$273$	2.17963	+	3.00000i	0.131917	+	0.181568i
$274$	14.0344			0.847852
$275$		0			0
$276$	−6.00000			−0.361158
$277$	−16.9600	−	23.3435i	−1.01903	−	1.40257i	−0.912883	−	0.408222i	$-0.866149\pi$
$277$	−16.9600	−	23.3435i	−1.01903	−	1.40257i	−0.106146	−	0.994351i	$-0.533851\pi$
$278$	−12.7598	−	4.14590i	−0.765280	−	0.248654i
$279$	3.00000	−	9.23305i	0.179605	−	0.552768i
$280$		0			0
$281$	1.57295	+	4.84104i	0.0938343	+	0.288792i	0.986948	−	0.161038i	$-0.0514843\pi$
$281$	1.57295	+	4.84104i	0.0938343	+	0.288792i	−0.893114	+	0.449831i	$0.851484\pi$
$282$		−	9.23607i		−	0.550000i
$283$	1.17557	−	0.381966i	0.0698804	−	0.0227055i	−0.273868	−	0.961767i	$-0.588303\pi$
$283$	1.17557	−	0.381966i	0.0698804	−	0.0227055i	0.343749	+	0.939062i	$0.388303\pi$
$284$	6.61803	+	4.80828i	0.392708	+	0.285319i
$285$		0			0
$286$	−1.14590	+	0.832544i	−0.0677584	+	0.0492293i
$287$	−5.98385	+	8.23607i	−0.353216	+	0.486160i
$288$	−0.587785	+	0.809017i	−0.0346356	+	0.0476718i
$289$	−12.6910	+	9.22054i	−0.746528	+	0.542385i
$290$		0			0
$291$	−5.78115	−	4.20025i	−0.338897	−	0.246223i
$292$	−9.37181	+	3.04508i	−0.548444	+	0.178200i
$293$		−	4.20163i		−	0.245462i	−0.992440	−	0.122731i	$-0.960835\pi$
$293$		−	4.20163i		−	0.245462i	0.992440	−	0.122731i	$-0.0391652\pi$
$294$	0.927051	+	2.85317i	0.0540667	+	0.166400i
$295$		0			0
$296$	2.73607	−	8.42075i	0.159031	−	0.489446i
$297$	−0.726543	−	0.236068i	−0.0421583	−	0.0136981i
$298$	−12.9515	−	17.8262i	−0.750261	−	1.03265i
$299$	−11.1246			−0.643353
$300$		0			0
$301$	6.47214			0.373048
$302$	−6.43288	−	8.85410i	−0.370171	−	0.509496i
$303$	−16.4782	−	5.35410i	−0.946650	−	0.307585i
$304$	2.23607	−	6.88191i	0.128247	−	0.394705i
$305$		0			0
$306$	−0.354102	−	1.08981i	−0.0202427	−	0.0623005i
$307$			29.7082i			1.69554i	0.530367	+	0.847768i	$0.322054\pi$
$307$			29.7082i			1.69554i	−0.530367	+	0.847768i	$0.677946\pi$
$308$	1.45309	−	0.472136i	0.0827972	−	0.0269024i
$309$	12.7082	+	9.23305i	0.722944	+	0.525250i
$310$		0			0
$311$	−10.2361	+	7.43694i	−0.580434	+	0.421710i	−0.838881	−	0.544315i	$-0.816789\pi$
$311$	−10.2361	+	7.43694i	−0.580434	+	0.421710i	0.258446	+	0.966026i	$0.416789\pi$
$312$	−1.08981	+	1.50000i	−0.0616986	+	0.0849208i
$313$	10.7921	−	14.8541i	0.610008	−	0.839603i	−0.386570	−	0.922260i	$-0.626340\pi$
$313$	10.7921	−	14.8541i	0.610008	−	0.839603i	0.996578	+	0.0826564i	$0.0263404\pi$
$314$	−9.01722	+	6.55139i	−0.508871	+	0.369717i
$315$		0			0
$316$		0			0
$317$	10.4086	−	3.38197i	0.584606	−	0.189950i	−0.00175672	−	0.999998i	$-0.500559\pi$
$317$	10.4086	−	3.38197i	0.584606	−	0.189950i	0.586363	+	0.810048i	$0.300559\pi$
$318$		−	11.5623i		−	0.648382i
$319$	−0.854102	−	2.62866i	−0.0478205	−	0.147176i
$320$		0			0
$321$	2.14590	−	6.60440i	0.119772	−	0.368621i
$322$	11.4127	+	3.70820i	0.636004	+	0.206650i
$323$	4.87380	+	6.70820i	0.271185	+	0.373254i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−11.5279			−0.638469
$327$	10.3229	+	14.2082i	0.570856	+	0.785715i
$328$	−4.84104	−	1.57295i	−0.267302	−	0.0868516i
$329$	−5.70820	+	17.5680i	−0.314703	+	0.968558i
$330$		0			0
$331$	−7.27051	−	22.3763i	−0.399623	−	1.22991i	−0.925302	−	0.379231i	$-0.876189\pi$
$331$	−7.27051	−	22.3763i	−0.399623	−	1.22991i	0.525679	−	0.850683i	$-0.323811\pi$
$332$		−	6.00000i		−	0.329293i
$333$	8.42075	−	2.73607i	0.461454	−	0.149936i
$334$	2.00000	+	1.45309i	0.109435	+	0.0795093i
$335$		0			0
$336$	1.61803	−	1.17557i	0.0882710	−	0.0641326i
$337$	14.5964	−	20.0902i	0.795115	−	1.09438i	−0.198338	−	0.980134i	$-0.563554\pi$
$337$	14.5964	−	20.0902i	0.795115	−	1.09438i	0.993452	−	0.114248i	$-0.0364457\pi$
$338$	5.62058	−	7.73607i	0.305719	−	0.420787i
$339$	−6.92705	+	5.03280i	−0.376226	+	0.273344i
$340$		0			0
$341$	−6.00000	−	4.35926i	−0.324918	−	0.236067i
$342$	6.88191	−	2.23607i	0.372131	−	0.120913i
$343$		−	20.0000i		−	1.07990i
$344$	1.00000	+	3.07768i	0.0539164	+	0.165938i
$345$		0			0
$346$	6.82624	−	21.0090i	0.366981	−	1.12945i
$347$	0.726543	+	0.236068i	0.0390028	+	0.0126728i	0.328453	−	0.944520i	$-0.393473\pi$
$347$	0.726543	+	0.236068i	0.0390028	+	0.0126728i	−0.289451	+	0.957193i	$0.593473\pi$
$348$	−2.12663	−	2.92705i	−0.113999	−	0.156906i
$349$	9.79837			0.524495			0.262247	−	0.965001i	$-0.415536\pi$
$349$	9.79837			0.524495			0.262247	+	0.965001i	$0.415536\pi$
$350$		0			0
$351$	−1.85410			−0.0989646
$352$	0.449028	+	0.618034i	0.0239333	+	0.0329413i
$353$	10.9637	+	3.56231i	0.583536	+	0.189602i	0.585884	−	0.810395i	$-0.300747\pi$
$353$	10.9637	+	3.56231i	0.583536	+	0.189602i	−0.00234791	+	0.999997i	$0.500747\pi$
$354$	2.76393	−	8.50651i	0.146901	−	0.452116i
$355$		0			0
$356$	1.11803	+	3.44095i	0.0592557	+	0.182370i
$357$			2.29180i			0.121295i
$358$	−24.8990	+	8.09017i	−1.31595	+	0.427579i
$359$	6.38197	+	4.63677i	0.336827	+	0.244719i	0.743322	−	0.668934i	$-0.233249\pi$
$359$	6.38197	+	4.63677i	0.336827	+	0.244719i	−0.406495	+	0.913653i	$0.633249\pi$
$360$		0			0
$361$	−26.9894	+	19.6089i	−1.42049	+	1.03205i
$362$	5.31031	−	7.30902i	0.279104	−	0.384153i
$363$	6.12261	−	8.42705i	0.321354	−	0.442305i
$364$	3.00000	−	2.17963i	0.157243	−	0.114244i
$365$		0			0
$366$	1.73607	+	1.26133i	0.0907457	+	0.0659306i
$367$	−3.35520	+	1.09017i	−0.175140	+	0.0569064i	−0.395274	−	0.918563i	$-0.629350\pi$
$367$	−3.35520	+	1.09017i	−0.175140	+	0.0569064i	0.220134	+	0.975470i	$0.429350\pi$
$368$			6.00000i			0.312772i
$369$	−1.57295	−	4.84104i	−0.0818845	−	0.252014i
$370$		0			0
$371$	−7.14590	+	21.9928i	−0.370997	+	1.14181i
$372$	−9.23305	−	3.00000i	−0.478711	−	0.155543i
$373$	−17.2905	−	23.7984i	−0.895270	−	1.23223i	−0.971952	−	0.235178i	$-0.924433\pi$
$373$	−17.2905	−	23.7984i	−0.895270	−	1.23223i	0.0766827	−	0.997056i	$-0.475567\pi$
$374$	−0.875388			−0.0452652
$375$		0			0
$376$	−9.23607			−0.476314
$377$	−3.94298	−	5.42705i	−0.203074	−	0.279507i
$378$	1.90211	+	0.618034i	0.0978341	+	0.0317882i
$379$	−7.23607	+	22.2703i	−0.371692	+	1.14395i	0.573992	+	0.818861i	$0.305394\pi$
$379$	−7.23607	+	22.2703i	−0.371692	+	1.14395i	−0.945684	+	0.325089i	$0.894606\pi$
$380$		0			0
$381$	−4.23607	−	13.0373i	−0.217020	−	0.667920i
$382$		−	5.23607i		−	0.267901i
$383$	−10.9637	+	3.56231i	−0.560216	+	0.182025i	−0.575419	−	0.817859i	$-0.695161\pi$
$383$	−10.9637	+	3.56231i	−0.560216	+	0.182025i	0.0152022	+	0.999884i	$0.495161\pi$
$384$	0.809017	+	0.587785i	0.0412850	+	0.0299953i
$385$		0			0
$386$	3.73607	−	2.71441i	0.190161	−	0.138160i
$387$	−1.90211	+	2.61803i	−0.0966898	+	0.133082i
$388$	−4.20025	+	5.78115i	−0.213236	+	0.293494i
$389$	−25.0623	+	18.2088i	−1.27071	+	0.923224i	−0.999231	−	0.0392200i	$-0.987513\pi$
$389$	−25.0623	+	18.2088i	−1.27071	+	0.923224i	−0.271479	+	0.962444i	$0.587513\pi$
$390$		0			0
$391$	−5.56231	−	4.04125i	−0.281298	−	0.204375i
$392$	2.85317	−	0.927051i	0.144107	−	0.0468231i
$393$			5.23607i			0.264125i
$394$	0.718847	+	2.21238i	0.0362150	+	0.111458i
$395$		0			0
$396$	−0.236068	+	0.726543i	−0.0118629	+	0.0365101i
$397$	23.6174	+	7.67376i	1.18532	+	0.385135i	0.834342	−	0.551247i	$-0.185848\pi$
$397$	23.6174	+	7.67376i	1.18532	+	0.385135i	0.350982	+	0.936382i	$0.385848\pi$
$398$	9.51057	+	13.0902i	0.476722	+	0.656151i
$399$	−14.4721			−0.724513
$400$		0			0
$401$	−14.9098			−0.744561			−0.372281	−	0.928120i	$-0.621424\pi$
$401$	−14.9098			−0.744561			−0.372281	+	0.928120i	$0.621424\pi$
$402$	2.17963	+	3.00000i	0.108710	+	0.149626i
$403$	−17.1190	−	5.56231i	−0.852759	−	0.277078i
$404$	−5.35410	+	16.4782i	−0.266377	+	0.819823i
$405$		0			0
$406$	2.23607	+	6.88191i	0.110974	+	0.341543i
$407$		−	6.76393i		−	0.335276i
$408$	−1.08981	+	0.354102i	−0.0539538	+	0.0175307i
$409$	−21.0172	−	15.2699i	−1.03923	−	0.755048i	−0.0690987	−	0.997610i	$-0.522012\pi$
$409$	−21.0172	−	15.2699i	−1.03923	−	0.755048i	−0.970136	+	0.242562i	$0.922012\pi$
$410$		0			0
$411$	11.3541	−	8.24924i	0.560057	−	0.406905i
$412$	9.23305	−	12.7082i	0.454880	−	0.626088i
$413$	−10.5146	+	14.4721i	−0.517391	+	0.712127i
$414$	−4.85410	+	3.52671i	−0.238566	+	0.173328i
$415$		0			0
$416$	1.50000	+	1.08981i	0.0735436	+	0.0534325i
$417$	−12.7598	+	4.14590i	−0.624848	+	0.203026i
$418$		−	5.52786i		−	0.270377i
$419$	0.652476	+	2.00811i	0.0318755	+	0.0981028i	0.965729	−	0.259554i	$-0.0835757\pi$
$419$	0.652476	+	2.00811i	0.0318755	+	0.0981028i	−0.933853	+	0.357657i	$0.883576\pi$
$420$		0			0
$421$	0.0278640	−	0.0857567i	0.00135801	−	0.00417953i	−0.950375	−	0.311106i	$-0.899301\pi$
$421$	0.0278640	−	0.0857567i	0.00135801	−	0.00417953i	0.951733	+	0.306926i	$0.0993006\pi$
$422$	−7.60845	−	2.47214i	−0.370374	−	0.120342i
$423$	−5.42882	−	7.47214i	−0.263958	−	0.363308i
$424$	−11.5623			−0.561515
$425$		0			0
$426$	8.18034			0.396339
$427$	−2.52265	−	3.47214i	−0.122080	−	0.168028i
$428$	−6.60440	−	2.14590i	−0.319235	−	0.103726i
$429$	−0.437694	+	1.34708i	−0.0211321	+	0.0650378i
$430$		0			0
$431$	−3.00000	−	9.23305i	−0.144505	−	0.444740i	0.852442	−	0.522822i	$-0.175121\pi$
$431$	−3.00000	−	9.23305i	−0.144505	−	0.444740i	−0.996947	+	0.0780813i	$0.975121\pi$
$432$			1.00000i			0.0481125i
$433$	28.3929	−	9.22542i	1.36448	−	0.443346i	0.466942	−	0.884288i	$-0.345356\pi$
$433$	28.3929	−	9.22542i	1.36448	−	0.443346i	0.897535	+	0.440942i	$0.145356\pi$
$434$	15.7082	+	11.4127i	0.754018	+	0.547826i
$435$		0			0
$436$	14.2082	−	10.3229i	0.680450	−	0.494376i
$437$	25.5195	−	35.1246i	1.22076	−	1.68024i
$438$	−5.79210	+	7.97214i	−0.276757	+	0.380923i
$439$	12.2361	−	8.89002i	0.583996	−	0.424298i	−0.256167	−	0.966633i	$-0.582460\pi$
$439$	12.2361	−	8.89002i	0.583996	−	0.424298i	0.840162	+	0.542335i	$0.182460\pi$
$440$		0			0
$441$	2.42705	+	1.76336i	0.115574	+	0.0839693i
$442$	−2.02063	+	0.656541i	−0.0961114	+	0.0312285i
$443$		−	28.0689i		−	1.33359i	−0.745240	−	0.666796i	$-0.767665\pi$
$443$		−	28.0689i		−	1.33359i	0.745240	−	0.666796i	$-0.232335\pi$
$444$	−2.73607	−	8.42075i	−0.129848	−	0.399631i
$445$		0			0
$446$	4.85410	−	14.9394i	0.229848	−	0.707401i
$447$	−20.9560	−	6.80902i	−0.991185	−	0.322055i
$448$	−1.17557	−	1.61803i	−0.0555405	−	0.0764449i
$449$	19.7984			0.934343			0.467172	−	0.884167i	$-0.345273\pi$
$449$	19.7984			0.934343			0.467172	+	0.884167i	$0.345273\pi$
$450$		0			0
$451$	−3.88854			−0.183104
$452$	5.03280	+	6.92705i	0.236723	+	0.325821i
$453$	−10.4086	−	3.38197i	−0.489040	−	0.158899i
$454$	0.291796	−	0.898056i	0.0136947	−	0.0421479i
$455$		0			0
$456$	−2.23607	−	6.88191i	−0.104713	−	0.322275i
$457$			3.52786i			0.165027i	0.996590	+	0.0825133i	$0.0262947\pi$
$457$			3.52786i			0.165027i	−0.996590	+	0.0825133i	$0.973705\pi$
$458$	8.81678	−	2.86475i	0.411981	−	0.133861i
$459$	−0.927051	−	0.673542i	−0.0432710	−	0.0314382i
$460$		0			0
$461$	−11.2533	+	8.17599i	−0.524118	+	0.380794i	−0.818153	−	0.575001i	$-0.805002\pi$
$461$	−11.2533	+	8.17599i	−0.524118	+	0.380794i	0.294035	+	0.955795i	$0.405002\pi$
$462$	0.898056	−	1.23607i	0.0417813	−	0.0575071i
$463$	−15.1109	+	20.7984i	−0.702263	+	0.966582i	0.297666	+	0.954670i	$0.403792\pi$
$463$	−15.1109	+	20.7984i	−0.702263	+	0.966582i	−0.999929	+	0.0119123i	$0.996208\pi$
$464$	−2.92705	+	2.12663i	−0.135885	+	0.0987262i
$465$		0			0
$466$	−8.82624	−	6.41264i	−0.408868	−	0.297060i
$467$	36.3117	−	11.7984i	1.68030	−	0.545964i	0.695333	−	0.718688i	$-0.255257\pi$
$467$	36.3117	−	11.7984i	1.68030	−	0.545964i	0.984970	+	0.172724i	$0.0552569\pi$
$468$			1.85410i			0.0857059i
$469$	−2.29180	−	7.05342i	−0.105825	−	0.325697i
$470$		0			0
$471$	−3.44427	+	10.6004i	−0.158704	+	0.488440i
$472$	−8.50651	−	2.76393i	−0.391544	−	0.127220i
$473$	1.45309	+	2.00000i	0.0668129	+	0.0919601i
$474$		0			0
$475$		0			0
$476$	2.29180			0.105044
$477$	−6.79615	−	9.35410i	−0.311174	−	0.428295i
$478$	25.5195	+	8.29180i	1.16724	+	0.379258i
$479$	1.38197	−	4.25325i	0.0631436	−	0.194336i	−0.914508	−	0.404568i	$-0.867422\pi$
$479$	1.38197	−	4.25325i	0.0631436	−	0.194336i	0.977652	+	0.210232i	$0.0674219\pi$
$480$		0			0
$481$	−5.07295	−	15.6129i	−0.231307	−	0.711888i
$482$		−	7.14590i		−	0.325487i
$483$	11.4127	−	3.70820i	0.519295	−	0.168729i
$484$	−8.42705	−	6.12261i	−0.383048	−	0.278300i
$485$		0			0
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−13.9353	+	19.1803i	−0.631470	+	0.869144i	−0.998125	−	0.0612130i	$-0.980503\pi$
$487$	−13.9353	+	19.1803i	−0.631470	+	0.869144i	0.366655	+	0.930357i	$0.380503\pi$
$488$	1.26133	−	1.73607i	0.0570976	−	0.0785881i
$489$	−9.32624	+	6.77591i	−0.421747	+	0.306417i
$490$		0			0
$491$	4.76393	+	3.46120i	0.214993	+	0.156202i	0.690070	−	0.723743i	$-0.257580\pi$
$491$	4.76393	+	3.46120i	0.214993	+	0.156202i	−0.475077	+	0.879944i	$0.657580\pi$
$492$	−4.84104	+	1.57295i	−0.218251	+	0.0709140i
$493$		−	4.14590i		−	0.186722i
$494$	−4.14590	−	12.7598i	−0.186533	−	0.574089i
$495$		0			0
$496$	−3.00000	+	9.23305i	−0.134704	+	0.414576i
$497$	−15.5599	−	5.05573i	−0.697958	−	0.226780i
$498$	−3.52671	−	4.85410i	−0.158036	−	0.217518i
$499$	6.58359			0.294722			0.147361	−	0.989083i	$-0.452922\pi$
$499$	6.58359			0.294722			0.147361	+	0.989083i	$0.452922\pi$
$500$		0			0
$501$	2.47214			0.110447
$502$	2.07363	+	2.85410i	0.0925505	+	0.127385i
$503$	28.9807	+	9.41641i	1.29219	+	0.419857i	0.872857	−	0.487977i	$-0.162265\pi$
$503$	28.9807	+	9.41641i	1.29219	+	0.419857i	0.419330	+	0.907834i	$0.362265\pi$
$504$	0.618034	−	1.90211i	0.0275294	−	0.0847268i
$505$		0			0
$506$	1.41641	+	4.35926i	0.0629670	+	0.193793i
$507$		−	9.56231i		−	0.424677i
$508$	−13.0373	+	4.23607i	−0.578436	+	0.187945i
$509$	23.2533	+	16.8945i	1.03068	+	0.748836i	0.968445	−	0.249226i	$-0.0801761\pi$
$509$	23.2533	+	16.8945i	1.03068	+	0.748836i	0.0622385	+	0.998061i	$0.480176\pi$
$510$		0			0
$511$	15.9443	−	11.5842i	0.705333	−	0.512454i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	4.25325	−	5.85410i	0.187786	−	0.258465i
$514$	7.59017	−	5.51458i	0.334788	−	0.243238i
$515$		0			0
$516$	2.61803	+	1.90211i	0.115253	+	0.0837359i
$517$	−6.71040	+	2.18034i	−0.295123	+	0.0958912i
$518$			17.7082i			0.778054i
$519$	−6.82624	−	21.0090i	−0.299639	−	0.922193i
$520$		0			0
$521$	−8.42705	+	25.9358i	−0.369196	+	1.13627i	0.578116	+	0.815955i	$0.303788\pi$
$521$	−8.42705	+	25.9358i	−0.369196	+	1.13627i	−0.947312	+	0.320313i	$0.896212\pi$
$522$	−3.44095	−	1.11803i	−0.150607	−	0.0489350i
$523$	9.23305	+	12.7082i	0.403733	+	0.555691i	0.961676	−	0.274188i	$-0.0884092\pi$
$523$	9.23305	+	12.7082i	0.403733	+	0.555691i	−0.557943	+	0.829879i	$0.688409\pi$
$524$	5.23607			0.228739
$525$		0			0
$526$	8.47214			0.369403
$527$	−6.53888	−	9.00000i	−0.284838	−	0.392046i
$528$	0.726543	+	0.236068i	0.0316187	+	0.0102735i
$529$	−4.01722	+	12.3637i	−0.174662	+	0.537554i
$530$		0			0
$531$	−2.76393	−	8.50651i	−0.119944	−	0.369151i
$532$			14.4721i			0.627447i
$533$	−8.97578	+	2.91641i	−0.388784	+	0.126324i
$534$	2.92705	+	2.12663i	0.126666	+	0.0920282i
$535$		0			0
$536$	3.00000	−	2.17963i	0.129580	−	0.0941456i
$537$	−15.3884	+	21.1803i	−0.664059	+	0.913999i
$538$	7.69421	−	10.5902i	0.331721	−	0.456575i
$539$	1.85410	−	1.34708i	0.0798618	−	0.0580230i
$540$		0			0
$541$	9.92705	+	7.21242i	0.426797	+	0.310086i	0.780367	−	0.625322i	$-0.215032\pi$
$541$	9.92705	+	7.21242i	0.426797	+	0.310086i	−0.353570	+	0.935408i	$0.615032\pi$
$542$	−5.53483	+	1.79837i	−0.237741	+	0.0772468i
$543$		−	9.03444i		−	0.387705i
$544$	0.354102	+	1.08981i	0.0151820	+	0.0467254i
$545$		0			0
$546$	1.14590	−	3.52671i	0.0490399	−	0.150929i
$547$	−1.90211	−	0.618034i	−0.0813285	−	0.0264252i	0.268070	−	0.963399i	$-0.413614\pi$
$547$	−1.90211	−	0.618034i	−0.0813285	−	0.0264252i	−0.349399	+	0.936974i	$0.613614\pi$
$548$	−8.24924	−	11.3541i	−0.352390	−	0.485023i
$549$	2.14590			0.0915847
$550$		0			0
$551$	26.1803			1.11532
$552$	3.52671	+	4.85410i	0.150107	+	0.206604i
$553$		0			0
$554$	−8.91641	+	27.4419i	−0.378822	+	1.16589i
$555$		0			0
$556$	4.14590	+	12.7598i	0.175825	+	0.541134i
$557$		−	6.27051i		−	0.265690i	−0.991137	−	0.132845i	$-0.957589\pi$
$557$		−	6.27051i		−	0.265690i	0.991137	−	0.132845i	$-0.0424113\pi$
$558$	−9.23305	+	3.00000i	−0.390866	+	0.127000i
$559$	4.85410	+	3.52671i	0.205307	+	0.149164i
$560$		0			0
$561$	−0.708204	+	0.514540i	−0.0299004	+	0.0217239i
$562$	2.99193	−	4.11803i	0.126207	−	0.173709i
$563$	0.898056	−	1.23607i	0.0378485	−	0.0520941i	−0.789673	−	0.613528i	$-0.789750\pi$
$563$	0.898056	−	1.23607i	0.0378485	−	0.0520941i	0.827522	+	0.561434i	$0.189750\pi$
$564$	−7.47214	+	5.42882i	−0.314634	+	0.228595i
$565$		0			0
$566$	−1.00000	−	0.726543i	−0.0420331	−	0.0305389i
$567$	1.90211	−	0.618034i	0.0798812	−	0.0259550i
$568$		−	8.18034i		−	0.343239i
$569$	−7.29837	−	22.4621i	−0.305964	−	0.941660i	−0.979316	−	0.202338i	$-0.935146\pi$
$569$	−7.29837	−	22.4621i	−0.305964	−	0.941660i	0.673352	−	0.739322i	$-0.264854\pi$
$570$		0			0
$571$	6.27051	−	19.2986i	0.262413	−	0.807623i	−0.729866	−	0.683591i	$-0.760417\pi$
$571$	6.27051	−	19.2986i	0.262413	−	0.807623i	0.992278	−	0.124032i	$-0.0395827\pi$
$572$	1.34708	+	0.437694i	0.0563244	+	0.0183009i
$573$	−3.07768	−	4.23607i	−0.128572	−	0.176964i
$574$	10.1803			0.424919
$575$		0			0
$576$	1.00000			0.0416667
$577$	−14.5964	−	20.0902i	−0.607655	−	0.836365i	0.388727	−	0.921353i	$-0.372915\pi$
$577$	−14.5964	−	20.0902i	−0.607655	−	0.836365i	−0.996382	+	0.0849881i	$0.972915\pi$
$578$	14.9191	+	4.84752i	0.620555	+	0.201630i
$579$	1.42705	−	4.39201i	0.0593062	−	0.182526i
$580$		0			0
$581$	3.70820	+	11.4127i	0.153842	+	0.473478i
$582$			7.14590i			0.296207i
$583$	−8.40051	+	2.72949i	−0.347913	+	0.113044i
$584$	7.97214	+	5.79210i	0.329889	+	0.239679i
$585$		0			0
$586$	−3.39919	+	2.46965i	−0.140419	+	0.102020i
$587$	−11.6902	+	16.0902i	−0.482506	+	0.664112i	−0.978984	−	0.203937i	$-0.934626\pi$
$587$	−11.6902	+	16.0902i	−0.482506	+	0.664112i	0.496478	+	0.868049i	$0.334626\pi$
$588$	1.76336	−	2.42705i	0.0727196	−	0.100090i
$589$	56.8328	−	41.2915i	2.34176	−	1.70138i
$590$		0			0
$591$	1.88197	+	1.36733i	0.0774137	+	0.0562444i
$592$	−8.42075	+	2.73607i	−0.346091	+	0.112452i
$593$			23.0344i			0.945911i	0.881086	+	0.472956i	$0.156813\pi$
$593$			23.0344i			0.945911i	−0.881086	+	0.472956i	$0.843187\pi$
$594$	0.236068	+	0.726543i	0.00968599	+	0.0298104i
$595$		0			0
$596$	−6.80902	+	20.9560i	−0.278908	+	0.858391i
$597$	15.3884	+	5.00000i	0.629806	+	0.204636i
$598$	6.53888	+	9.00000i	0.267395	+	0.368037i
$599$	−18.9443			−0.774042			−0.387021	−	0.922071i	$-0.626496\pi$
$599$	−18.9443			−0.774042			−0.387021	+	0.922071i	$0.626496\pi$
$600$		0			0
$601$	−8.32624			−0.339634			−0.169817	−	0.985476i	$-0.554318\pi$
$601$	−8.32624			−0.339634			−0.169817	+	0.985476i	$0.554318\pi$
$602$	−3.80423	−	5.23607i	−0.155049	−	0.213406i
$603$	3.52671	+	1.14590i	0.143619	+	0.0466646i
$604$	−3.38197	+	10.4086i	−0.137610	+	0.423521i
$605$		0			0
$606$	5.35410	+	16.4782i	0.217496	+	0.669382i
$607$			24.1803i			0.981450i	0.871315	+	0.490725i	$0.163268\pi$
$607$			24.1803i			0.981450i	−0.871315	+	0.490725i	$0.836732\pi$
$608$	−6.88191	+	2.23607i	−0.279098	+	0.0906845i
$609$	5.85410	+	4.25325i	0.237220	+	0.172351i
$610$		0			0
$611$	−13.8541	+	10.0656i	−0.560477	+	0.407210i
$612$	−0.673542	+	0.927051i	−0.0272263	+	0.0374738i
$613$	−0.845055	+	1.16312i	−0.0341315	+	0.0469779i	−0.825742	−	0.564048i	$-0.809243\pi$
$613$	−0.845055	+	1.16312i	−0.0341315	+	0.0469779i	0.791610	+	0.611026i	$0.209243\pi$
$614$	24.0344	−	17.4620i	0.969951	−	0.704711i
$615$		0			0
$616$	−1.23607	−	0.898056i	−0.0498026	−	0.0361837i
$617$	10.0984	−	3.28115i	0.406544	−	0.132094i	−0.0986041	−	0.995127i	$-0.531438\pi$
$617$	10.0984	−	3.28115i	0.406544	−	0.132094i	0.505148	+	0.863032i	$0.331438\pi$
$618$		−	15.7082i		−	0.631877i
$619$	7.23607	+	22.2703i	0.290842	+	0.895120i	0.984586	+	0.174899i	$0.0559598\pi$
$619$	7.23607	+	22.2703i	0.290842	+	0.895120i	−0.693744	+	0.720221i	$0.744040\pi$
$620$		0			0
$621$	−1.85410	+	5.70634i	−0.0744025	+	0.228988i
$622$	12.0332	+	3.90983i	0.482488	+	0.156770i
$623$	−4.25325	−	5.85410i	−0.170403	−	0.234540i
$624$	1.85410			0.0742235
$625$		0			0
$626$	−18.3607			−0.733840
$627$	−3.24920	−	4.47214i	−0.129760	−	0.178600i
$628$	10.6004	+	3.44427i	0.423001	+	0.137441i
$629$	3.13525	−	9.64932i	0.125011	−	0.384744i
$630$		0			0
$631$	−0.888544	−	2.73466i	−0.0353724	−	0.108865i	0.931811	−	0.362943i	$-0.118228\pi$
$631$	−0.888544	−	2.73466i	−0.0353724	−	0.108865i	−0.967184	+	0.254078i	$0.918228\pi$
$632$		0			0
$633$	−7.60845	+	2.47214i	−0.302409	+	0.0982586i
$634$	−8.85410	−	6.43288i	−0.351641	−	0.255482i
$635$		0			0
$636$	−9.35410	+	6.79615i	−0.370914	+	0.269485i
$637$	3.26944	−	4.50000i	0.129540	−	0.178296i
$638$	−1.62460	+	2.23607i	−0.0643185	+	0.0885268i
$639$	6.61803	−	4.80828i	0.261805	−	0.190213i
$640$		0			0
$641$	7.32624	+	5.32282i	0.289369	+	0.210239i	0.722994	−	0.690855i	$-0.242766\pi$
$641$	7.32624	+	5.32282i	0.289369	+	0.210239i	−0.433625	+	0.901094i	$0.642766\pi$
$642$	−6.60440	+	2.14590i	−0.260655	+	0.0846918i
$643$			31.7771i			1.25317i	0.779355	+	0.626583i	$0.215547\pi$
$643$			31.7771i			1.25317i	−0.779355	+	0.626583i	$0.784453\pi$
$644$	−3.70820	−	11.4127i	−0.146124	−	0.449723i
$645$		0			0
$646$	2.56231	−	7.88597i	0.100813	−	0.310269i
$647$	0.106001	+	0.0344419i	0.00416733	+	0.00135405i	0.311100	−	0.950377i	$-0.399303\pi$
$647$	0.106001	+	0.0344419i	0.00416733	+	0.00135405i	−0.306933	+	0.951731i	$0.599303\pi$
$648$	0.587785	+	0.809017i	0.0230904	+	0.0317812i
$649$	−6.83282			−0.268211
$650$		0			0
$651$	19.4164			0.760989
$652$	6.77591	+	9.32624i	0.265365	+	0.365244i
$653$	18.2743	+	5.93769i	0.715130	+	0.232360i	0.643911	−	0.765101i	$-0.277311\pi$
$653$	18.2743	+	5.93769i	0.715130	+	0.232360i	0.0712197	+	0.997461i	$0.477311\pi$
$654$	5.42705	−	16.7027i	0.212214	−	0.653129i
$655$		0			0
$656$	1.57295	+	4.84104i	0.0614133	+	0.189011i
$657$			9.85410i			0.384445i
$658$	17.5680	−	5.70820i	0.684874	−	0.222529i
$659$	17.0344	+	12.3762i	0.663568	+	0.482110i	0.867866	−	0.496799i	$-0.165491\pi$
$659$	17.0344	+	12.3762i	0.663568	+	0.482110i	−0.204298	+	0.978909i	$0.565491\pi$
$660$		0			0
$661$	26.2705	−	19.0866i	1.02180	−	0.742384i	0.0551524	−	0.998478i	$-0.482436\pi$
$661$	26.2705	−	19.0866i	1.02180	−	0.742384i	0.966652	+	0.256094i	$0.0824355\pi$
$662$	−13.8293	+	19.0344i	−0.537492	+	0.739795i
$663$	−1.24882	+	1.71885i	−0.0485000	+	0.0667545i
$664$	−4.85410	+	3.52671i	−0.188376	+	0.136863i
$665$		0			0
$666$	−7.16312	−	5.20431i	−0.277565	−	0.201663i
$667$	−20.6457	+	6.70820i	−0.799406	+	0.259743i
$668$		−	2.47214i		−	0.0956498i
$669$	−4.85410	−	14.9394i	−0.187670	−	0.577590i
$670$		0			0
$671$	0.506578	−	1.55909i	0.0195562	−	0.0601879i
$672$	−1.90211	−	0.618034i	−0.0733756	−	0.0238412i
$673$	−3.40820	−	4.69098i	−0.131376	−	0.180824i	0.738261	−	0.674515i	$-0.235647\pi$
$673$	−3.40820	−	4.69098i	−0.131376	−	0.180824i	−0.869637	+	0.493691i	$0.835647\pi$
$674$	−24.8328			−0.956524
$675$		0			0
$676$	−9.56231			−0.367781
$677$	16.1805	+	22.2705i	0.621866	+	0.855925i	0.997487	−	0.0708481i	$-0.0225706\pi$
$677$	16.1805	+	22.2705i	0.621866	+	0.855925i	−0.375621	+	0.926773i	$0.622571\pi$
$678$	8.14324	+	2.64590i	0.312739	+	0.101615i
$679$	4.41641	−	13.5923i	0.169486	−	0.521625i
$680$		0			0
$681$	−0.291796	−	0.898056i	−0.0111816	−	0.0344136i
$682$			7.41641i			0.283989i
$683$	7.05342	−	2.29180i	0.269892	−	0.0876931i	−0.170945	−	0.985281i	$-0.554682\pi$
$683$	7.05342	−	2.29180i	0.269892	−	0.0876931i	0.440836	+	0.897588i	$0.354682\pi$
$684$	−5.85410	−	4.25325i	−0.223837	−	0.162627i
$685$		0			0
$686$	−16.1803	+	11.7557i	−0.617768	+	0.448835i
$687$	5.44907	−	7.50000i	0.207895	−	0.286143i
$688$	1.90211	−	2.61803i	0.0725174	−	0.0998116i
$689$	−17.3435	+	12.6008i	−0.660733	+	0.480051i
$690$		0			0
$691$	1.47214	+	1.06957i	0.0560027	+	0.0406883i	0.615434	−	0.788188i	$-0.288981\pi$
$691$	1.47214	+	1.06957i	0.0560027	+	0.0406883i	−0.559432	+	0.828876i	$0.688981\pi$
$692$	−21.0090	+	6.82624i	−0.798642	+	0.259495i
$693$		−	1.52786i		−	0.0580388i
$694$	−0.236068	−	0.726543i	−0.00896102	−	0.0275792i
$695$		0			0
$696$	−1.11803	+	3.44095i	−0.0423790	+	0.130429i
$697$	−5.54734	−	1.80244i	−0.210120	−	0.0682723i
$698$	−5.75934	−	7.92705i	−0.217994	−	0.300043i
$699$	−10.9098			−0.412648
$700$		0			0
$701$	49.1591			1.85671			0.928356	−	0.371692i	$-0.121222\pi$
$701$	49.1591			1.85671			0.928356	+	0.371692i	$0.121222\pi$
$702$	1.08981	+	1.50000i	0.0411324	+	0.0566139i
$703$	60.9331	+	19.7984i	2.29814	+	0.746710i
$704$	0.236068	−	0.726543i	0.00889715	−	0.0273826i
$705$		0			0
$706$	−3.56231	−	10.9637i	−0.134069	−	0.412622i
$707$		−	34.6525i		−	1.30324i
$708$	−8.50651	+	2.76393i	−0.319694	+	0.103875i
$709$	−4.20820	−	3.05744i	−0.158042	−	0.114825i	0.505953	−	0.862561i	$-0.331141\pi$
$709$	−4.20820	−	3.05744i	−0.158042	−	0.114825i	−0.663996	+	0.747736i	$0.731141\pi$
$710$		0			0
$711$		0			0
$712$	2.12663	−	2.92705i	0.0796987	−	0.109696i
$713$	−34.2380	+	47.1246i	−1.28222	+	1.76483i
$714$	1.85410	−	1.34708i	0.0693880	−	0.0504133i
$715$		0			0
$716$	21.1803	+	15.3884i	0.791546	+	0.575092i
$717$	25.5195	−	8.29180i	0.953044	−	0.309663i
$718$		−	7.88854i		−	0.294398i
$719$	6.90983	+	21.2663i	0.257693	+	0.793098i	0.993287	+	0.115675i	$0.0369032\pi$
$719$	6.90983	+	21.2663i	0.257693	+	0.793098i	−0.735594	+	0.677423i	$0.763097\pi$
$720$		0			0
$721$	−9.70820	+	29.8788i	−0.361552	+	1.11274i
$722$	31.7279	+	10.3090i	1.18079	+	0.383662i
$723$	−4.20025	−	5.78115i	−0.156209	−	0.215003i
$724$	−9.03444			−0.335762
$725$		0			0
$726$	−10.4164			−0.386589
$727$	13.9353	+	19.1803i	0.516833	+	0.711359i	0.985053	−	0.172253i	$-0.0551045\pi$
$727$	13.9353	+	19.1803i	0.516833	+	0.711359i	−0.468220	+	0.883612i	$0.655105\pi$
$728$	−3.52671	−	1.14590i	−0.130709	−	0.0424698i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$		0			0
$731$	1.14590	+	3.52671i	0.0423826	+	0.130440i
$732$		−	2.14590i		−	0.0793147i
$733$	−36.4832	+	11.8541i	−1.34754	+	0.437841i	−0.891863	−	0.452306i	$-0.850602\pi$
$733$	−36.4832	+	11.8541i	−1.34754	+	0.437841i	−0.455674	+	0.890147i	$0.650602\pi$
$734$	2.85410	+	2.07363i	0.105347	+	0.0765389i
$735$		0			0
$736$	4.85410	−	3.52671i	0.178925	−	0.129996i
$737$	1.66509	−	2.29180i	0.0613343	−	0.0844194i
$738$	−2.99193	+	4.11803i	−0.110134	+	0.151587i
$739$	17.5623	−	12.7598i	0.646040	−	0.469375i	−0.215880	−	0.976420i	$-0.569262\pi$
$739$	17.5623	−	12.7598i	0.646040	−	0.469375i	0.861920	+	0.507044i	$0.169262\pi$
$740$		0			0
$741$	−10.8541	−	7.88597i	−0.398735	−	0.289698i
$742$	21.9928	−	7.14590i	0.807382	−	0.262334i
$743$		−	24.6525i		−	0.904412i	−0.891914	−	0.452206i	$-0.850637\pi$
$743$		−	24.6525i		−	0.904412i	0.891914	−	0.452206i	$-0.149363\pi$
$744$	3.00000	+	9.23305i	0.109985	+	0.338500i
$745$		0			0
$746$	−9.09017	+	27.9767i	−0.332815	+	1.02430i
$747$	−5.70634	−	1.85410i	−0.208784	−	0.0678380i
$748$	0.514540	+	0.708204i	0.0188135	+	0.0258945i
$749$	13.8885			0.507476
$750$		0			0
$751$	19.2361			0.701934			0.350967	−	0.936388i	$-0.385853\pi$
$751$	19.2361			0.701934			0.350967	+	0.936388i	$0.385853\pi$
$752$	5.42882	+	7.47214i	0.197969	+	0.272481i
$753$	3.35520	+	1.09017i	0.122270	+	0.0397280i
$754$	−2.07295	+	6.37988i	−0.0754924	+	0.232342i
$755$		0			0
$756$	−0.618034	−	1.90211i	−0.0224777	−	0.0691792i
$757$			22.1459i			0.804906i	0.915441	+	0.402453i	$0.131842\pi$
$757$			22.1459i			0.804906i	−0.915441	+	0.402453i	$0.868158\pi$
$758$	22.2703	−	7.23607i	0.808895	−	0.262826i
$759$	3.70820	+	2.69417i	0.134599	+	0.0977921i
$760$		0			0
$761$	36.5344	−	26.5438i	1.32437	−	0.962213i	0.324506	−	0.945884i	$-0.394802\pi$
$761$	36.5344	−	26.5438i	1.32437	−	0.962213i	0.999867	−	0.0163292i	$-0.00519799\pi$
$762$	−8.05748	+	11.0902i	−0.291892	+	0.401754i
$763$	−20.6457	+	28.4164i	−0.747426	+	1.02874i
$764$	−4.23607	+	3.07768i	−0.153256	+	0.111347i
$765$		0			0
$766$	9.32624	+	6.77591i	0.336971	+	0.244824i
$767$	−15.7719	+	5.12461i	−0.569492	+	0.185039i
$768$		−	1.00000i		−	0.0360844i
$769$	−13.0902	−	40.2874i	−0.472044	−	1.45280i	−0.849904	−	0.526938i	$-0.823340\pi$
$769$	−13.0902	−	40.2874i	−0.472044	−	1.45280i	0.377860	−	0.925863i	$-0.376660\pi$
$770$		0			0
$771$	2.89919	−	8.92278i	0.104412	−	0.321346i
$772$	−4.39201	−	1.42705i	−0.158072	−	0.0513607i
$773$	−1.71036	−	2.35410i	−0.0615172	−	0.0846712i	0.777150	−	0.629315i	$-0.216665\pi$
$773$	−1.71036	−	2.35410i	−0.0615172	−	0.0846712i	−0.838667	+	0.544644i	$0.816665\pi$
$774$	3.23607			0.116318
$775$		0			0
$776$	7.14590			0.256523
$777$	10.4086	+	14.3262i	0.373407	+	0.513951i
$778$	29.4625	+	9.57295i	1.05628	+	0.343207i
$779$	11.3820	−	35.0301i	0.407801	−	1.25508i
$780$		0			0
$781$	−1.93112	−	5.94336i	−0.0691008	−	0.212670i
$782$			6.87539i			0.245863i
$783$	−3.44095	+	1.11803i	−0.122970	+	0.0399553i
$784$	−2.42705	−	1.76336i	−0.0866804	−	0.0629770i
$785$		0			0
$786$	4.23607	−	3.07768i	0.151096	−	0.109777i
$787$	21.4783	−	29.5623i	0.765618	−	1.05378i	−0.231108	−	0.972928i	$-0.574235\pi$
$787$	21.4783	−	29.5623i	0.765618	−	1.05378i	0.996726	−	0.0808543i	$-0.0257649\pi$
$788$	1.36733	−	1.88197i	0.0487091	−	0.0670423i
$789$	6.85410	−	4.97980i	0.244012	−	0.177285i
$790$		0			0
$791$	−13.8541	−	10.0656i	−0.492595	−	0.357891i
$792$	0.726543	−	0.236068i	0.0258166	−	0.00838831i
$793$		−	3.97871i		−	0.141288i
$794$	−7.67376	−	23.6174i	−0.272332	−	0.838151i
$795$		0			0
$796$	5.00000	−	15.3884i	0.177220	−	0.545428i
$797$	−2.21238	−	0.718847i	−0.0783667	−	0.0254629i	0.269571	−	0.962980i	$-0.413118\pi$
$797$	−2.21238	−	0.718847i	−0.0783667	−	0.0254629i	−0.347938	+	0.937518i	$0.613118\pi$
$798$	8.50651	+	11.7082i	0.301127	+	0.414466i
$799$	−10.5836			−0.374421
$800$		0			0
$801$	3.61803			0.127837
$802$	8.76378	+	12.0623i	0.309460	+	0.425935i
$803$	7.15942	+	2.32624i	0.252651	+	0.0820912i
$804$	1.14590	−	3.52671i	0.0404127	−	0.124378i
$805$		0			0
$806$	5.56231	+	17.1190i	0.195924	+	0.602992i
$807$		−	13.0902i		−	0.460796i
$808$	16.4782	−	5.35410i	0.579702	−	0.188357i
$809$	−34.9615	−	25.4010i	−1.22918	−	0.893052i	−0.232352	−	0.972632i	$-0.574642\pi$
$809$	−34.9615	−	25.4010i	−1.22918	−	0.893052i	−0.996829	+	0.0795797i	$0.974642\pi$
$810$		0			0
$811$	−19.1803	+	13.9353i	−0.673513	+	0.489336i	−0.871199	−	0.490930i	$-0.836657\pi$
$811$	−19.1803	+	13.9353i	−0.673513	+	0.489336i	0.197686	+	0.980265i	$0.436657\pi$
$812$	4.25325	−	5.85410i	0.149260	−	0.205439i
$813$	−3.42071	+	4.70820i	−0.119970	+	0.165124i
$814$	−5.47214	+	3.97574i	−0.191798	+	0.139350i
$815$		0			0
$816$	0.927051	+	0.673542i	0.0324533	+	0.0235787i
$817$	−22.2703	+	7.23607i	−0.779140	+	0.253158i
$818$			25.9787i			0.908324i
$819$	−1.14590	−	3.52671i	−0.0400409	−	0.123233i
$820$		0			0
$821$	2.72949	−	8.40051i	0.0952599	−	0.293180i	−0.892061	−	0.451914i	$-0.850741\pi$
$821$	2.72949	−	8.40051i	0.0952599	−	0.293180i	0.987321	+	0.158734i	$0.0507413\pi$
$822$	−13.3475	−	4.33688i	−0.465549	−	0.151266i
$823$	−15.0454	−	20.7082i	−0.524449	−	0.721843i	0.461822	−	0.886972i	$-0.347196\pi$
$823$	−15.0454	−	20.7082i	−0.524449	−	0.721843i	−0.986272	+	0.165130i	$0.947196\pi$
$824$	−15.7082			−0.547221
$825$		0			0
$826$	17.8885			0.622422
$827$	11.3067	+	15.5623i	0.393172	+	0.541154i	0.959014	−	0.283359i	$-0.0914489\pi$
$827$	11.3067	+	15.5623i	0.393172	+	0.541154i	−0.565842	+	0.824514i	$0.691449\pi$
$828$	5.70634	+	1.85410i	0.198309	+	0.0644345i
$829$	−14.1697	+	43.6098i	−0.492134	+	1.51463i	0.329242	+	0.944245i	$0.393207\pi$
$829$	−14.1697	+	43.6098i	−0.492134	+	1.51463i	−0.821376	+	0.570387i	$0.806793\pi$
$830$		0			0
$831$	8.91641	+	27.4419i	0.309307	+	0.951948i
$832$		−	1.85410i		−	0.0642794i
$833$	3.26944	−	1.06231i	0.113279	−	0.0368067i
$834$	10.8541	+	7.88597i	0.375847	+	0.273069i
$835$		0			0
$836$	−4.47214	+	3.24920i	−0.154672	+	0.112376i
$837$	−5.70634	+	7.85410i	−0.197240	+	0.271477i
$838$	1.24108	−	1.70820i	0.0428725	−	0.0590089i
$839$	28.4164	−	20.6457i	0.981043	−	0.712770i	0.0231018	−	0.999733i	$-0.492646\pi$
$839$	28.4164	−	20.6457i	0.981043	−	0.712770i	0.957942	+	0.286963i	$0.0926458\pi$
$840$		0			0
$841$	12.8713	+	9.35156i	0.443839	+	0.322468i
$842$	−0.0857567	+	0.0278640i	−0.00295537	+	0.000960258i
$843$		−	5.09017i		−	0.175315i
$844$	2.47214	+	7.60845i	0.0850944	+	0.261894i
$845$		0			0
$846$	−2.85410	+	8.78402i	−0.0981260	+	0.302001i
$847$	19.8132	+	6.43769i	0.680789	+	0.221202i
$848$	6.79615	+	9.35410i	0.233381	+	0.321221i
$849$	−1.23607			−0.0424217
$850$		0			0
$851$	−53.1246			−1.82109
$852$	−4.80828	−	6.61803i	−0.164729	−	0.226730i
$853$	−37.5200	−	12.1910i	−1.28466	−	0.417411i	−0.414441	−	0.910076i	$-0.636023\pi$
$853$	−37.5200	−	12.1910i	−1.28466	−	0.417411i	−0.870219	+	0.492665i	$0.836023\pi$
$854$	−1.32624	+	4.08174i	−0.0453829	+	0.139674i
$855$		0			0
$856$	2.14590	+	6.60440i	0.0733453	+	0.225734i
$857$			39.3050i			1.34263i	0.741171	+	0.671316i	$0.234271\pi$
$857$			39.3050i			1.34263i	−0.741171	+	0.671316i	$0.765729\pi$
$858$	1.34708	−	0.437694i	0.0459887	−	0.0149426i
$859$	44.0689	+	32.0179i	1.50361	+	1.09244i	0.968915	+	0.247393i	$0.0795737\pi$
$859$	44.0689	+	32.0179i	1.50361	+	1.09244i	0.534696	+	0.845045i	$0.320426\pi$
$860$		0			0
$861$	8.23607	−	5.98385i	0.280684	−	0.203929i
$862$	−5.70634	+	7.85410i	−0.194359	+	0.267512i
$863$	−5.98385	+	8.23607i	−0.203693	+	0.280359i	−0.898626	−	0.438715i	$-0.855434\pi$
$863$	−5.98385	+	8.23607i	−0.203693	+	0.280359i	0.694934	+	0.719074i	$0.255434\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$		0			0
$866$	−24.1525	−	17.5478i	−0.820735	−	0.596299i
$867$	14.9191	−	4.84752i	0.506681	−	0.164631i
$868$		−	19.4164i		−	0.659036i
$869$		0			0
$870$		0			0
$871$	2.12461	−	6.53888i	0.0719897	−	0.221562i
$872$	−16.7027	−	5.42705i	−0.565626	−	0.183783i
$873$	4.20025	+	5.78115i	0.142157	+	0.195662i
$874$	−43.4164			−1.46858
$875$		0			0
$876$	9.85410			0.332939
$877$	−17.0333	−	23.4443i	−0.575172	−	0.791657i	0.417983	−	0.908455i	$-0.362737\pi$
$877$	−17.0333	−	23.4443i	−0.575172	−	0.791657i	−0.993156	+	0.116798i	$0.962737\pi$
$878$	−14.3844	−	4.67376i	−0.485449	−	0.157732i
$879$	−1.29837	+	3.99598i	−0.0437931	+	0.134781i
$880$		0			0
$881$	−13.2016	−	40.6304i	−0.444774	−	1.36887i	−0.882731	−	0.469878i	$-0.844298\pi$
$881$	−13.2016	−	40.6304i	−0.444774	−	1.36887i	0.437957	−	0.898996i	$-0.355702\pi$
$882$		−	3.00000i		−	0.101015i
$883$	−18.8496	+	6.12461i	−0.634340	+	0.206110i	−0.608497	−	0.793556i	$-0.708227\pi$
$883$	−18.8496	+	6.12461i	−0.634340	+	0.206110i	−0.0258434	+	0.999666i	$0.508227\pi$
$884$	1.71885	+	1.24882i	0.0578111	+	0.0420022i
$885$		0			0
$886$	−22.7082	+	16.4985i	−0.762897	+	0.554277i
$887$	−28.3197	+	38.9787i	−0.950882	+	1.30878i	0.000252175		1.00000i	$0.499920\pi$
$887$	−28.3197	+	38.9787i	−0.950882	+	1.30878i	−0.951134	+	0.308777i	$0.900080\pi$
$888$	−5.20431	+	7.16312i	−0.174645	+	0.240379i
$889$	22.1803	−	16.1150i	0.743905	−	0.540478i
$890$		0			0
$891$	0.618034	+	0.449028i	0.0207049	+	0.0150430i
$892$	−14.9394	+	4.85410i	−0.500208	+	0.162527i
$893$		−	66.8328i		−	2.23647i
$894$	6.80902	+	20.9560i	0.227728	+	0.700873i
$895$		0			0
$896$	−0.618034	+	1.90211i	−0.0206471	+	0.0635451i
$897$	10.5801	+	3.43769i	0.353260	+	0.114781i
$898$	−11.6372	−	16.0172i	−0.388338	−	0.534502i
$899$	−35.1246			−1.17147
$900$		0			0
$901$	−13.2492			−0.441396
$902$	2.28563	+	3.14590i	0.0761031	+	0.104747i
$903$	−6.15537	−	2.00000i	−0.204838	−	0.0665558i
$904$	2.64590	−	8.14324i	0.0880013	−	0.270840i
$905$		0			0
$906$	3.38197	+	10.4086i	0.112358	+	0.345803i
$907$		−	33.7082i		−	1.11926i	−0.828742	−	0.559631i	$-0.810943\pi$
$907$		−	33.7082i		−	1.11926i	0.828742	−	0.559631i	$-0.189057\pi$
$908$	−0.898056	+	0.291796i	−0.0298030	+	0.00968359i
$909$	14.0172	+	10.1841i	0.464922	+	0.337786i
$910$		0			0
$911$	1.67376	−	1.21606i	0.0554542	−	0.0402898i	−0.559713	−	0.828687i	$-0.689089\pi$
$911$	1.67376	−	1.21606i	0.0554542	−	0.0402898i	0.615167	+	0.788397i	$0.289089\pi$
$912$	−4.25325	+	5.85410i	−0.140839	+	0.193849i
$913$	−2.69417	+	3.70820i	−0.0891639	+	0.122724i
$914$	2.85410	−	2.07363i	0.0944053	−	0.0685895i
$915$		0			0
$916$	−7.50000	−	5.44907i	−0.247807	−	0.180042i
$917$	−9.95959	+	3.23607i	−0.328895	+	0.106864i
$918$			1.14590i			0.0378203i
$919$	5.85410	+	18.0171i	0.193109	+	0.594328i	0.999993	+	0.00361909i	$0.00115200\pi$
$919$	5.85410	+	18.0171i	0.193109	+	0.594328i	−0.806884	+	0.590709i	$0.798848\pi$
$920$		0			0
$921$	9.18034	−	28.2542i	0.302502	−	0.931007i
$922$	13.2290	+	4.29837i	0.435675	+	0.141559i
$923$	−8.91505	−	12.2705i	−0.293442	−	0.403889i
$924$	−1.52786			−0.0502630
$925$		0			0
$926$	25.7082			0.844824
$927$	−9.23305	−	12.7082i	−0.303253	−	0.417392i
$928$	3.44095	+	1.11803i	0.112955	+	0.0367013i
$929$	−4.93769	+	15.1967i	−0.162000	+	0.498586i	−0.998803	−	0.0489190i	$-0.984422\pi$
$929$	−4.93769	+	15.1967i	−0.162000	+	0.498586i	0.836802	+	0.547505i	$0.184422\pi$
$930$		0			0
$931$	6.70820	+	20.6457i	0.219853	+	0.676636i
$932$			10.9098i			0.357363i
$933$	12.0332	−	3.90983i	0.393950	−	0.128002i
$934$	−30.8885	−	22.4418i	−1.01070	−	0.734319i
$935$		0			0
$936$	1.50000	−	1.08981i	0.0490290	−	0.0356217i
$937$	−14.0538	+	19.3435i	−0.459119	+	0.631923i	−0.974326	−	0.225143i	$-0.927715\pi$
$937$	−14.0538	+	19.3435i	−0.459119	+	0.631923i	0.515207	+	0.857066i	$0.327715\pi$
$938$	−4.35926	+	6.00000i	−0.142335	+	0.195907i
$939$	−14.8541	+	10.7921i	−0.484745	+	0.352188i
$940$		0			0
$941$	−30.1976	−	21.9398i	−0.984412	−	0.715217i	−0.0257220	−	0.999669i	$-0.508188\pi$
$941$	−30.1976	−	21.9398i	−0.984412	−	0.715217i	−0.958690	+	0.284452i	$0.908188\pi$
$942$	10.6004	−	3.44427i	0.345379	−	0.112220i
$943$			30.5410i			0.994552i
$944$	2.76393	+	8.50651i	0.0899583	+	0.276863i
$945$		0			0
$946$	0.763932	−	2.35114i	0.0248376	−	0.0764422i
$947$	6.60440	+	2.14590i	0.214614	+	0.0697323i	0.414351	−	0.910117i	$-0.364009\pi$
$947$	6.60440	+	2.14590i	0.214614	+	0.0697323i	−0.199737	+	0.979850i	$0.564009\pi$
$948$		0			0
$949$	18.2705			0.593086
$950$		0			0
$951$	−10.9443			−0.354892
$952$	−1.34708	−	1.85410i	−0.0436592	−	0.0600918i
$953$	47.4266	+	15.4098i	1.53630	+	0.499173i	0.950352	−	0.311177i	$-0.100723\pi$
$953$	47.4266	+	15.4098i	1.53630	+	0.499173i	0.585946	+	0.810350i	$0.300723\pi$
$954$	−3.57295	+	10.9964i	−0.115678	+	0.356022i
$955$		0			0
$956$	−8.29180	−	25.5195i	−0.268176	−	0.825360i
$957$			2.76393i			0.0893452i
$958$	−4.25325	+	1.38197i	−0.137416	+	0.0446493i
$959$	22.7082	+	16.4985i	0.733286	+	0.532764i
$960$		0			0
$961$	−51.1697	+	37.1770i	−1.65064	+	1.19926i
$962$	−9.64932	+	13.2812i	−0.311107	+	0.428202i
$963$	−4.08174	+	5.61803i	−0.131532	+	0.181039i
$964$	−5.78115	+	4.20025i	−0.186198	+	0.135281i
$965$		0			0
$966$	−9.70820	−	7.05342i	−0.312356	−	0.226940i
$967$	21.9273	−	7.12461i	0.705134	−	0.229112i	0.0655682	−	0.997848i	$-0.479114\pi$
$967$	21.9273	−	7.12461i	0.705134	−	0.229112i	0.639566	+	0.768736i	$0.279114\pi$
$968$			10.4164i			0.334796i
$969$	−2.56231	−	7.88597i	−0.0823131	−	0.253334i
$970$		0			0
$971$	11.6738	−	35.9281i	0.374629	−	1.15299i	−0.569100	−	0.822268i	$-0.692708\pi$
$971$	11.6738	−	35.9281i	0.374629	−	1.15299i	0.943729	−	0.330721i	$-0.107292\pi$
$972$	0.951057	+	0.309017i	0.0305052	+	0.00991172i
$973$	−15.7719	−	21.7082i	−0.505625	−	0.695933i
$974$	23.7082			0.759660
$975$		0			0
$976$	−2.14590			−0.0686885
$977$	−0.257270	−	0.354102i	−0.00823080	−	0.0113287i	0.804882	−	0.593435i	$-0.202229\pi$
$977$	−0.257270	−	0.354102i	−0.00823080	−	0.0113287i	−0.813113	+	0.582106i	$0.802229\pi$
$978$	10.9637	+	3.56231i	0.350579	+	0.113910i
$979$	0.854102	−	2.62866i	0.0272972	−	0.0840122i
$980$		0			0
$981$	−5.42705	−	16.7027i	−0.173272	−	0.533278i
$982$		−	5.88854i		−	0.187911i
$983$	−23.3399	+	7.58359i	−0.744427	+	0.241879i	−0.656582	−	0.754255i	$-0.727998\pi$
$983$	−23.3399	+	7.58359i	−0.744427	+	0.241879i	−0.0878456	+	0.996134i	$0.527998\pi$
$984$	4.11803	+	2.99193i	0.131278	+	0.0953791i
$985$		0			0
$986$	−3.35410	+	2.43690i	−0.106816	+	0.0776066i
$987$	10.8576	−	14.9443i	0.345603	−	0.475681i
$988$	−7.88597	+	10.8541i	−0.250886	+	0.345315i
$989$	15.7082	−	11.4127i	0.499492	−	0.362902i
$990$		0			0
$991$	5.29180	+	3.84471i	0.168099	+	0.122131i	0.668654	−	0.743573i	$-0.266871\pi$
$991$	5.29180	+	3.84471i	0.168099	+	0.122131i	−0.500555	+	0.865705i	$0.666871\pi$
$992$	9.23305	−	3.00000i	0.293150	−	0.0952501i
$993$			23.5279i			0.746634i
$994$	5.05573	+	15.5599i	0.160358	+	0.493531i
$995$		0			0
$996$	−1.85410	+	5.70634i	−0.0587495	+	0.180812i
$997$	−24.1724	−	7.85410i	−0.765549	−	0.248742i	−0.0998904	−	0.994998i	$-0.531849\pi$
$997$	−24.1724	−	7.85410i	−0.765549	−	0.248742i	−0.665658	+	0.746257i	$0.731849\pi$
$998$	−3.86974	−	5.32624i	−0.122494	−	0.168599i
$999$	−8.85410			−0.280131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.h.a.199.1		8
5.2	odd	4		150.2.g.b.61.1	✓	4
5.3	odd	4		750.2.g.a.301.1		4
5.4	even	2	inner	750.2.h.a.199.2		8
15.2	even	4		450.2.h.b.361.1		4
25.3	odd	20		3750.2.a.g.1.2		2
25.4	even	10		3750.2.c.c.1249.2		4
25.9	even	10	inner	750.2.h.a.49.1		8
25.12	odd	20		150.2.g.b.91.1	yes	4
25.13	odd	20		750.2.g.a.451.1		4
25.16	even	5	inner	750.2.h.a.49.2		8
25.21	even	5		3750.2.c.c.1249.4		4
25.22	odd	20		3750.2.a.b.1.2		2
75.62	even	20		450.2.h.b.91.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.b.61.1	✓	4	5.2	odd	4
150.2.g.b.91.1	yes	4	25.12	odd	20
450.2.h.b.91.1		4	75.62	even	20
450.2.h.b.361.1		4	15.2	even	4
750.2.g.a.301.1		4	5.3	odd	4
750.2.g.a.451.1		4	25.13	odd	20
750.2.h.a.49.1		8	25.9	even	10	inner
750.2.h.a.49.2		8	25.16	even	5	inner
750.2.h.a.199.1		8	1.1	even	1	trivial
750.2.h.a.199.2		8	5.4	even	2	inner
3750.2.a.b.1.2		2	25.22	odd	20
3750.2.a.g.1.2		2	25.3	odd	20
3750.2.c.c.1249.2		4	25.4	even	10
3750.2.c.c.1249.4		4	25.21	even	5

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} -2.00000i q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.309017 + 0.951057i) q^{6} -2.00000i q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.618034 - 0.449028i) q^{11} +(0.587785 - 0.809017i) q^{12} +(1.08981 - 1.50000i) q^{13} +(-1.61803 + 1.17557i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(1.08981 - 0.354102i) q^{17} -1.00000i q^{18} +(2.23607 + 6.88191i) q^{19} +(-0.618034 + 1.90211i) q^{21} +(-0.726543 - 0.236068i) q^{22} +(-3.52671 - 4.85410i) q^{23} -1.00000 q^{24} -1.85410 q^{26} +(-0.587785 - 0.809017i) q^{27} +(1.90211 + 0.618034i) q^{28} +(1.11803 - 3.44095i) q^{29} +(-3.00000 - 9.23305i) q^{31} +1.00000i q^{32} +(-0.726543 + 0.236068i) q^{33} +(-0.927051 - 0.673542i) q^{34} +(-0.809017 + 0.587785i) q^{36} +(5.20431 - 7.16312i) q^{37} +(4.25325 - 5.85410i) q^{38} +(-1.50000 + 1.08981i) q^{39} +(-4.11803 - 2.99193i) q^{41} +(1.90211 - 0.618034i) q^{42} +3.23607i q^{43} +(0.236068 + 0.726543i) q^{44} +(-1.85410 + 5.70634i) q^{46} +(-8.78402 - 2.85410i) q^{47} +(0.587785 + 0.809017i) q^{48} +3.00000 q^{49} -1.14590 q^{51} +(1.08981 + 1.50000i) q^{52} +(-10.9964 - 3.57295i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-0.618034 - 1.90211i) q^{56} -7.23607i q^{57} +(-3.44095 + 1.11803i) q^{58} +(-7.23607 - 5.25731i) q^{59} +(1.73607 - 1.26133i) q^{61} +(-5.70634 + 7.85410i) q^{62} +(1.17557 - 1.61803i) q^{63} +(0.809017 - 0.587785i) q^{64} +(0.618034 + 0.449028i) q^{66} +(3.52671 - 1.14590i) q^{67} +1.14590i q^{68} +(1.85410 + 5.70634i) q^{69} +(2.52786 - 7.77997i) q^{71} +(0.951057 + 0.309017i) q^{72} +(5.79210 + 7.97214i) q^{73} -8.85410 q^{74} -7.23607 q^{76} +(-0.898056 - 1.23607i) q^{77} +(1.76336 + 0.572949i) q^{78} +(0.309017 + 0.951057i) q^{81} +5.09017i q^{82} +(-5.70634 + 1.85410i) q^{83} +(-1.61803 - 1.17557i) q^{84} +(2.61803 - 1.90211i) q^{86} +(-2.12663 + 2.92705i) q^{87} +(0.449028 - 0.618034i) q^{88} +(2.92705 - 2.12663i) q^{89} +(-3.00000 - 2.17963i) q^{91} +(5.70634 - 1.85410i) q^{92} +9.70820i q^{93} +(2.85410 + 8.78402i) q^{94} +(0.309017 - 0.951057i) q^{96} +(6.79615 + 2.20820i) q^{97} +(-1.76336 - 2.42705i) q^{98} +0.763932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 2 q^{6} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^4 - 2 * q^6 + 2 * q^9	\( 8 q + 2 q^{4} - 2 q^{6} + 2 q^{9} - 4 q^{11} - 4 q^{14} - 2 q^{16} + 4 q^{21} - 8 q^{24} + 12 q^{26} - 24 q^{31} + 6 q^{34} - 2 q^{36} - 12 q^{39} - 24 q^{41} - 16 q^{44} + 12 q^{46} + 24 q^{49} - 36 q^{51} + 2 q^{54} + 4 q^{56} - 40 q^{59} - 4 q^{61} + 2 q^{64} - 4 q^{66} - 12 q^{69} + 56 q^{71} - 44 q^{74} - 40 q^{76} - 2 q^{81} - 4 q^{84} + 12 q^{86} + 10 q^{89} - 24 q^{91} - 4 q^{94} - 2 q^{96} + 24 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 - 2 * q^6 + 2 * q^9 - 4 * q^11 - 4 * q^14 - 2 * q^16 + 4 * q^21 - 8 * q^24 + 12 * q^26 - 24 * q^31 + 6 * q^34 - 2 * q^36 - 12 * q^39 - 24 * q^41 - 16 * q^44 + 12 * q^46 + 24 * q^49 - 36 * q^51 + 2 * q^54 + 4 * q^56 - 40 * q^59 - 4 * q^61 + 2 * q^64 - 4 * q^66 - 12 * q^69 + 56 * q^71 - 44 * q^74 - 40 * q^76 - 2 * q^81 - 4 * q^84 + 12 * q^86 + 10 * q^89 - 24 * q^91 - 4 * q^94 - 2 * q^96 + 24 * q^99

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