LMFDB - Embedded newform 775.2.k.c.101.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(101,775)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("775.101"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			101.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	775.101
Dual form			775.2.k.c.376.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.190983 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.30902 + 0.951057i) q^{4} +0.618034 q^{6} +(2.42705 + 1.76336i) q^{7} +(1.80902 - 1.31433i) q^{8} +(1.61803 - 1.17557i) q^{9} +(0.618034 + 0.449028i) q^{11} +(-0.500000 + 1.53884i) q^{12} +(-1.50000 - 4.61653i) q^{13} +(1.50000 - 1.08981i) q^{14} +(0.572949 + 1.76336i) q^{16} +(0.190983 - 0.138757i) q^{17} +(-0.381966 - 1.17557i) q^{18} +(1.54508 - 4.75528i) q^{19} +(-0.927051 + 2.85317i) q^{21} +(0.381966 - 0.277515i) q^{22} +(-4.42705 + 3.21644i) q^{23} +(1.80902 + 1.31433i) q^{24} -3.00000 q^{26} +(4.04508 + 2.93893i) q^{27} +(1.50000 + 4.61653i) q^{28} +(-2.66312 + 8.19624i) q^{29} +(-5.54508 - 0.502029i) q^{31} +5.61803 q^{32} +(-0.236068 + 0.726543i) q^{33} +(-0.0450850 - 0.138757i) q^{34} +3.23607 q^{36} -0.236068 q^{37} +(-2.50000 - 1.81636i) q^{38} +(3.92705 - 2.85317i) q^{39} +(2.00000 - 6.15537i) q^{41} +(1.50000 + 1.08981i) q^{42} +(1.42705 - 4.39201i) q^{43} +(0.381966 + 1.17557i) q^{44} +(1.04508 + 3.21644i) q^{46} +(1.04508 + 3.21644i) q^{47} +(-1.50000 + 1.08981i) q^{48} +(0.618034 + 1.90211i) q^{49} +(0.190983 + 0.138757i) q^{51} +(2.42705 - 7.46969i) q^{52} +(-10.2812 + 7.46969i) q^{53} +(2.50000 - 1.81636i) q^{54} +6.70820 q^{56} +5.00000 q^{57} +(4.30902 + 3.13068i) q^{58} +(2.92705 + 9.00854i) q^{59} -6.94427 q^{61} +(-1.35410 + 3.16344i) q^{62} +6.00000 q^{63} +(-0.0729490 + 0.224514i) q^{64} +(0.381966 + 0.277515i) q^{66} +4.23607 q^{67} +0.381966 q^{68} +(-4.42705 - 3.21644i) q^{69} +(-0.0729490 + 0.0530006i) q^{71} +(1.38197 - 4.25325i) q^{72} +(-6.92705 - 5.03280i) q^{73} +(-0.0450850 + 0.138757i) q^{74} +(6.54508 - 4.75528i) q^{76} +(0.708204 + 2.17963i) q^{77} +(-0.927051 - 2.85317i) q^{78} +(0.309017 - 0.951057i) q^{81} +(-3.23607 - 2.35114i) q^{82} +(1.26393 - 3.88998i) q^{83} +(-3.92705 + 2.85317i) q^{84} +(-2.30902 - 1.67760i) q^{86} -8.61803 q^{87} +1.70820 q^{88} +(5.16312 + 3.75123i) q^{89} +(4.50000 - 13.8496i) q^{91} -8.85410 q^{92} +(-1.23607 - 5.42882i) q^{93} +2.09017 q^{94} +(1.73607 + 5.34307i) q^{96} +(-4.28115 - 3.11044i) q^{97} +1.23607 q^{98} +1.52786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - q^{3} + 3 q^{4} - 2 q^{6} + 3 q^{7} + 5 q^{8} + 2 q^{9} - 2 q^{11} - 2 q^{12} - 6 q^{13} + 6 q^{14} + 9 q^{16} + 3 q^{17} - 6 q^{18} - 5 q^{19} + 3 q^{21} + 6 q^{22} - 11 q^{23} + 5 q^{24}+ \cdots + 24 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 - q^3 + 3 * q^4 - 2 * q^6 + 3 * q^7 + 5 * q^8 + 2 * q^9 - 2 * q^11 - 2 * q^12 - 6 * q^13 + 6 * q^14 + 9 * q^16 + 3 * q^17 - 6 * q^18 - 5 * q^19 + 3 * q^21 + 6 * q^22 - 11 * q^23 + 5 * q^24 - 12 * q^26 + 5 * q^27 + 6 * q^28 + 5 * q^29 - 11 * q^31 + 18 * q^32 + 8 * q^33 + 11 * q^34 + 4 * q^36 + 8 * q^37 - 10 * q^38 + 9 * q^39 + 8 * q^41 + 6 * q^42 - q^43 + 6 * q^44 - 7 * q^46 - 7 * q^47 - 6 * q^48 - 2 * q^49 + 3 * q^51 + 3 * q^52 - 21 * q^53 + 10 * q^54 + 20 * q^57 + 15 * q^58 + 5 * q^59 + 8 * q^61 + 8 * q^62 + 24 * q^63 - 7 * q^64 + 6 * q^66 + 8 * q^67 + 6 * q^68 - 11 * q^69 - 7 * q^71 + 10 * q^72 - 21 * q^73 + 11 * q^74 + 15 * q^76 - 24 * q^77 + 3 * q^78 - q^81 - 4 * q^82 + 14 * q^83 - 9 * q^84 - 7 * q^86 - 30 * q^87 - 20 * q^88 + 5 * q^89 + 18 * q^91 - 22 * q^92 + 4 * q^93 - 14 * q^94 - 2 * q^96 + 3 * q^97 - 4 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.190983	−	0.587785i	0.135045	−	0.415627i	−0.860552	−	0.509363i	$-0.829881\pi$
$2$	0.190983	−	0.587785i	0.135045	−	0.415627i	0.995597	+	0.0937362i	$0.0298810\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i	0.999773	−	0.0213149i	$-0.00678525\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i	−0.821362	+	0.570408i	$0.806785\pi$
$4$	1.30902	+	0.951057i	0.654508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	0.618034			0.252311
$7$	2.42705	+	1.76336i	0.917339	+	0.666486i	0.942860	−	0.333188i	$-0.108125\pi$
$7$	2.42705	+	1.76336i	0.917339	+	0.666486i	−0.0255212	+	0.999674i	$0.508125\pi$
$8$	1.80902	−	1.31433i	0.639584	−	0.464685i
$9$	1.61803	−	1.17557i	0.539345	−	0.391857i
$10$		0			0
$11$	0.618034	+	0.449028i	0.186344	+	0.135387i	0.677046	−	0.735940i	$-0.263260\pi$
$11$	0.618034	+	0.449028i	0.186344	+	0.135387i	−0.490702	+	0.871327i	$0.663260\pi$
$12$	−0.500000	+	1.53884i	−0.144338	+	0.444225i
$13$	−1.50000	−	4.61653i	−0.416025	−	1.28039i	−0.911331	−	0.411675i	$-0.864944\pi$
$13$	−1.50000	−	4.61653i	−0.416025	−	1.28039i	0.495306	−	0.868719i	$-0.335056\pi$
$14$	1.50000	−	1.08981i	0.400892	−	0.291265i
$15$		0			0
$16$	0.572949	+	1.76336i	0.143237	+	0.440839i
$17$	0.190983	−	0.138757i	0.0463202	−	0.0336536i	−0.564384	−	0.825512i	$-0.690886\pi$
$17$	0.190983	−	0.138757i	0.0463202	−	0.0336536i	0.610704	+	0.791859i	$0.290886\pi$
$18$	−0.381966	−	1.17557i	−0.0900303	−	0.277085i
$19$	1.54508	−	4.75528i	0.354467	−	1.09094i	−0.601851	−	0.798608i	$-0.705570\pi$
$19$	1.54508	−	4.75528i	0.354467	−	1.09094i	0.956318	−	0.292328i	$-0.0944300\pi$
$20$		0			0
$21$	−0.927051	+	2.85317i	−0.202299	+	0.622613i
$22$	0.381966	−	0.277515i	0.0814354	−	0.0591663i
$23$	−4.42705	+	3.21644i	−0.923104	+	0.670674i	−0.944295	−	0.329101i	$-0.893254\pi$
$23$	−4.42705	+	3.21644i	−0.923104	+	0.670674i	0.0211907	+	0.999775i	$0.493254\pi$
$24$	1.80902	+	1.31433i	0.369264	+	0.268286i
$25$		0			0
$26$	−3.00000			−0.588348
$27$	4.04508	+	2.93893i	0.778477	+	0.565597i
$28$	1.50000	+	4.61653i	0.283473	+	0.872441i
$29$	−2.66312	+	8.19624i	−0.494529	+	1.52200i	0.323161	+	0.946344i	$0.395254\pi$
$29$	−2.66312	+	8.19624i	−0.494529	+	1.52200i	−0.817690	+	0.575659i	$0.804746\pi$
$30$		0			0
$31$	−5.54508	−	0.502029i	−0.995927	−	0.0901670i
$31$	−5.54508	−	0.502029i	−0.995927	−	0.0901670i
$32$	5.61803			0.993137
$33$	−0.236068	+	0.726543i	−0.0410942	+	0.126475i
$34$	−0.0450850	−	0.138757i	−0.00773201	−	0.0237967i
$35$		0			0
$36$	3.23607			0.539345
$37$	−0.236068			−0.0388093			−0.0194047	−	0.999812i	$-0.506177\pi$
$37$	−0.236068			−0.0388093			−0.0194047	+	0.999812i	$0.506177\pi$
$38$	−2.50000	−	1.81636i	−0.405554	−	0.294652i
$39$	3.92705	−	2.85317i	0.628831	−	0.456873i
$40$		0			0
$41$	2.00000	−	6.15537i	0.312348	−	0.961307i	−0.664485	−	0.747302i	$-0.731349\pi$
$41$	2.00000	−	6.15537i	0.312348	−	0.961307i	0.976833	−	0.214005i	$-0.0686510\pi$
$42$	1.50000	+	1.08981i	0.231455	+	0.168162i
$43$	1.42705	−	4.39201i	0.217623	−	0.669775i	−0.781334	−	0.624113i	$-0.785460\pi$
$43$	1.42705	−	4.39201i	0.217623	−	0.669775i	0.998957	−	0.0456620i	$-0.0145397\pi$
$44$	0.381966	+	1.17557i	0.0575835	+	0.177224i
$45$		0			0
$46$	1.04508	+	3.21644i	0.154089	+	0.474238i
$47$	1.04508	+	3.21644i	0.152441	+	0.469166i	0.997893	−	0.0648863i	$-0.0206685\pi$
$47$	1.04508	+	3.21644i	0.152441	+	0.469166i	−0.845451	+	0.534052i	$0.820668\pi$
$48$	−1.50000	+	1.08981i	−0.216506	+	0.157301i
$49$	0.618034	+	1.90211i	0.0882906	+	0.271730i
$50$		0			0
$51$	0.190983	+	0.138757i	0.0267430	+	0.0194299i
$52$	2.42705	−	7.46969i	0.336571	−	1.03586i
$53$	−10.2812	+	7.46969i	−1.41222	+	1.02604i	−0.419231	+	0.907880i	$0.637700\pi$
$53$	−10.2812	+	7.46969i	−1.41222	+	1.02604i	−0.992994	+	0.118162i	$0.962300\pi$
$54$	2.50000	−	1.81636i	0.340207	−	0.247175i
$55$		0			0
$56$	6.70820			0.896421
$57$	5.00000			0.662266
$58$	4.30902	+	3.13068i	0.565802	+	0.411079i
$59$	2.92705	+	9.00854i	0.381070	+	1.17281i	0.939292	+	0.343120i	$0.111484\pi$
$59$	2.92705	+	9.00854i	0.381070	+	1.17281i	−0.558222	+	0.829692i	$0.688516\pi$
$60$		0			0
$61$	−6.94427			−0.889123			−0.444561	−	0.895748i	$-0.646640\pi$
$61$	−6.94427			−0.889123			−0.444561	+	0.895748i	$0.646640\pi$
$62$	−1.35410	+	3.16344i	−0.171971	+	0.401757i
$63$	6.00000			0.755929
$64$	−0.0729490	+	0.224514i	−0.00911863	+	0.0280642i
$65$		0			0
$66$	0.381966	+	0.277515i	0.0470168	+	0.0341597i
$67$	4.23607			0.517518			0.258759	−	0.965942i	$-0.416686\pi$
$67$	4.23607			0.517518			0.258759	+	0.965942i	$0.416686\pi$
$68$	0.381966			0.0463202
$69$	−4.42705	−	3.21644i	−0.532954	−	0.387214i
$70$		0			0
$71$	−0.0729490	+	0.0530006i	−0.00865746	+	0.00629001i	−0.592106	−	0.805860i	$-0.701703\pi$
$71$	−0.0729490	+	0.0530006i	−0.00865746	+	0.00629001i	0.583448	+	0.812150i	$0.301703\pi$
$72$	1.38197	−	4.25325i	0.162866	−	0.501251i
$73$	−6.92705	−	5.03280i	−0.810750	−	0.589044i	0.103298	−	0.994650i	$-0.467060\pi$
$73$	−6.92705	−	5.03280i	−0.810750	−	0.589044i	−0.914048	+	0.405606i	$0.867060\pi$
$74$	−0.0450850	+	0.138757i	−0.00524102	+	0.0161302i
$75$		0			0
$76$	6.54508	−	4.75528i	0.750773	−	0.545468i
$77$	0.708204	+	2.17963i	0.0807073	+	0.248392i
$78$	−0.927051	−	2.85317i	−0.104968	−	0.323058i
$79$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$79$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−3.23607	−	2.35114i	−0.357364	−	0.259640i
$83$	1.26393	−	3.88998i	0.138735	−	0.426981i	−0.857418	−	0.514621i	$-0.827933\pi$
$83$	1.26393	−	3.88998i	0.138735	−	0.426981i	0.996152	+	0.0876401i	$0.0279326\pi$
$84$	−3.92705	+	2.85317i	−0.428476	+	0.311306i
$85$		0			0
$86$	−2.30902	−	1.67760i	−0.248988	−	0.180900i
$87$	−8.61803			−0.923950
$88$	1.70820			0.182095
$89$	5.16312	+	3.75123i	0.547290	+	0.397629i	0.826785	−	0.562518i	$-0.190167\pi$
$89$	5.16312	+	3.75123i	0.547290	+	0.397629i	−0.279496	+	0.960147i	$0.590167\pi$
$90$		0			0
$91$	4.50000	−	13.8496i	0.471728	−	1.45183i
$92$	−8.85410			−0.923104
$93$	−1.23607	−	5.42882i	−0.128174	−	0.562943i
$94$	2.09017			0.215585
$95$		0			0
$96$	1.73607	+	5.34307i	0.177187	+	0.545325i
$97$	−4.28115	−	3.11044i	−0.434685	−	0.315817i	0.348834	−	0.937184i	$-0.386578\pi$
$97$	−4.28115	−	3.11044i	−0.434685	−	0.315817i	−0.783520	+	0.621367i	$0.786578\pi$
$98$	1.23607			0.124862
$99$	1.52786			0.153556
$100$		0			0
$101$	−3.85410	+	2.80017i	−0.383497	+	0.278627i	−0.762786	−	0.646651i	$-0.776169\pi$
$101$	−3.85410	+	2.80017i	−0.383497	+	0.278627i	0.379288	+	0.925279i	$0.376169\pi$
$102$	0.118034	−	0.0857567i	0.0116871	−	0.00849118i
$103$	0.0450850	−	0.138757i	0.00444235	−	0.0136722i	−0.948811	−	0.315845i	$-0.897712\pi$
$103$	0.0450850	−	0.138757i	0.00444235	−	0.0136722i	0.953253	+	0.302173i	$0.0977120\pi$
$104$	−8.78115	−	6.37988i	−0.861063	−	0.625599i
$105$		0			0
$106$	2.42705	+	7.46969i	0.235736	+	0.725521i
$107$	0.881966	−	0.640786i	0.0852629	−	0.0619471i	−0.544337	−	0.838867i	$-0.683219\pi$
$107$	0.881966	−	0.640786i	0.0852629	−	0.0619471i	0.629600	+	0.776919i	$0.283219\pi$
$108$	2.50000	+	7.69421i	0.240563	+	0.740376i
$109$	−2.60081	−	8.00448i	−0.249113	−	0.766690i	−0.994933	−	0.100543i	$-0.967942\pi$
$109$	−2.60081	−	8.00448i	−0.249113	−	0.766690i	0.745820	−	0.666147i	$-0.232058\pi$
$110$		0			0
$111$	−0.0729490	−	0.224514i	−0.00692401	−	0.0213099i
$112$	−1.71885	+	5.29007i	−0.162416	+	0.499864i
$113$	−1.50000	−	1.08981i	−0.141108	−	0.102521i	0.514992	−	0.857195i	$-0.327795\pi$
$113$	−1.50000	−	1.08981i	−0.141108	−	0.102521i	−0.656100	+	0.754674i	$0.727795\pi$
$114$	0.954915	−	2.93893i	0.0894360	−	0.275256i
$115$		0			0
$116$	−11.2812	+	8.19624i	−1.04743	+	0.761002i
$117$	−7.85410	−	5.70634i	−0.726112	−	0.527551i
$118$	5.85410			0.538914
$119$	0.708204			0.0649209
$120$		0			0
$121$	−3.21885	−	9.90659i	−0.292622	−	0.900599i
$122$	−1.32624	+	4.08174i	−0.120072	+	0.369543i
$123$	6.47214			0.583573
$124$	−6.78115	−	5.93085i	−0.608966	−	0.532606i
$125$		0			0
$126$	1.14590	−	3.52671i	0.102085	−	0.314184i
$127$	−3.16312	−	9.73508i	−0.280681	−	0.863849i	−0.987660	−	0.156614i	$-0.949942\pi$
$127$	−3.16312	−	9.73508i	−0.280681	−	0.863849i	0.706979	−	0.707235i	$-0.250058\pi$
$128$	9.20820	+	6.69015i	0.813898	+	0.591331i
$129$	4.61803			0.406595
$130$		0			0
$131$	−0.0729490	−	0.0530006i	−0.00637359	−	0.00463068i	0.584594	−	0.811326i	$-0.301254\pi$
$131$	−0.0729490	−	0.0530006i	−0.00637359	−	0.00463068i	−0.590967	+	0.806695i	$0.701254\pi$
$132$	−1.00000	+	0.726543i	−0.0870388	+	0.0632374i
$133$	12.1353	−	8.81678i	1.05226	−	0.764512i
$134$	0.809017	−	2.48990i	0.0698884	−	0.215094i
$135$		0			0
$136$	0.163119	−	0.502029i	0.0139873	−	0.0430486i
$137$	2.00000	+	6.15537i	0.170872	+	0.525888i	0.999421	−	0.0340275i	$-0.0108334\pi$
$137$	2.00000	+	6.15537i	0.170872	+	0.525888i	−0.828549	+	0.559916i	$0.810833\pi$
$138$	−2.73607	+	1.98787i	−0.232910	+	0.169219i
$139$	1.80902	+	5.56758i	0.153439	+	0.472236i	0.997999	−	0.0632239i	$-0.0201382\pi$
$139$	1.80902	+	5.56758i	0.153439	+	0.472236i	−0.844561	+	0.535460i	$0.820138\pi$
$140$		0			0
$141$	−2.73607	+	1.98787i	−0.230418	+	0.167409i
$142$	0.0172209	+	0.0530006i	0.00144515	+	0.00444771i
$143$	1.14590	−	3.52671i	0.0958248	−	0.294918i
$144$	3.00000	+	2.17963i	0.250000	+	0.181636i
$145$		0			0
$146$	−4.28115	+	3.11044i	−0.354311	+	0.257422i
$147$	−1.61803	+	1.17557i	−0.133453	+	0.0969594i
$148$	−0.309017	−	0.224514i	−0.0254010	−	0.0184549i
$149$	−17.0344			−1.39552			−0.697758	−	0.716334i	$-0.745819\pi$
$149$	−17.0344			−1.39552			−0.697758	+	0.716334i	$0.745819\pi$
$150$		0			0
$151$	15.7812	+	11.4657i	1.28425	+	0.933064i	0.999673	−	0.0255888i	$-0.00814604\pi$
$151$	15.7812	+	11.4657i	1.28425	+	0.933064i	0.284579	+	0.958652i	$0.408146\pi$
$152$	−3.45492	−	10.6331i	−0.280231	−	0.862461i
$153$	0.145898	−	0.449028i	0.0117952	−	0.0363018i
$154$	1.41641			0.114137
$155$		0			0
$156$	7.85410			0.628831
$157$	−3.00000	+	9.23305i	−0.239426	+	0.736878i	0.757077	+	0.653325i	$0.226627\pi$
$157$	−3.00000	+	9.23305i	−0.239426	+	0.736878i	−0.996503	+	0.0835524i	$0.973373\pi$
$158$		0			0
$159$	−10.2812	−	7.46969i	−0.815348	−	0.592385i
$160$		0			0
$161$	−16.4164			−1.29379
$162$	−0.500000	−	0.363271i	−0.0392837	−	0.0285413i
$163$	−10.2812	+	7.46969i	−0.805282	+	0.585072i	−0.912459	−	0.409168i	$-0.865819\pi$
$163$	−10.2812	+	7.46969i	−0.805282	+	0.585072i	0.107177	+	0.994240i	$0.465819\pi$
$164$	8.47214	−	6.15537i	0.661563	−	0.480653i
$165$		0			0
$166$	−2.04508	−	1.48584i	−0.158729	−	0.115324i
$167$	2.85410	−	8.78402i	0.220857	−	0.679728i	−0.777829	−	0.628476i	$-0.783679\pi$
$167$	2.85410	−	8.78402i	0.220857	−	0.679728i	0.998686	−	0.0512518i	$-0.0163211\pi$
$168$	2.07295	+	6.37988i	0.159931	+	0.492219i
$169$	−8.54508	+	6.20837i	−0.657314	+	0.477567i
$170$		0			0
$171$	−3.09017	−	9.51057i	−0.236311	−	0.727291i
$172$	6.04508	−	4.39201i	0.460933	−	0.334888i
$173$	−0.281153	−	0.865300i	−0.0213757	−	0.0657875i	0.939800	−	0.341726i	$-0.111011\pi$
$173$	−0.281153	−	0.865300i	−0.0213757	−	0.0657875i	−0.961175	+	0.275938i	$0.911011\pi$
$174$	−1.64590	+	5.06555i	−0.124775	+	0.384019i
$175$		0			0
$176$	−0.437694	+	1.34708i	−0.0329924	+	0.101540i
$177$	−7.66312	+	5.56758i	−0.575995	+	0.418485i
$178$	3.19098	−	2.31838i	0.239174	−	0.173770i
$179$	−16.0172	−	11.6372i	−1.19718	−	0.869805i	−0.203179	−	0.979142i	$-0.565127\pi$
$179$	−16.0172	−	11.6372i	−1.19718	−	0.869805i	−0.994005	+	0.109337i	$0.965127\pi$
$180$		0			0
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$	−7.28115	−	5.29007i	−0.539715	−	0.392126i
$183$	−2.14590	−	6.60440i	−0.158629	−	0.488211i
$184$	−3.78115	+	11.6372i	−0.278750	+	0.857905i
$185$		0			0
$186$	−3.42705	−	0.310271i	−0.251284	−	0.0227502i
$187$	0.180340			0.0131878
$188$	−1.69098	+	5.20431i	−0.123328	+	0.379563i
$189$	4.63525	+	14.2658i	0.337165	+	1.03769i
$190$		0			0
$191$	−16.0902			−1.16424			−0.582122	−	0.813102i	$-0.697777\pi$
$191$	−16.0902			−1.16424			−0.582122	+	0.813102i	$0.697777\pi$
$192$	−0.236068			−0.0170367
$193$	−1.92705	−	1.40008i	−0.138712	−	0.100780i	0.516265	−	0.856429i	$-0.327322\pi$
$193$	−1.92705	−	1.40008i	−0.138712	−	0.100780i	−0.654977	+	0.755648i	$0.727322\pi$
$194$	−2.64590	+	1.92236i	−0.189964	+	0.138017i
$195$		0			0
$196$	−1.00000	+	3.07768i	−0.0714286	+	0.219835i
$197$	13.2812	+	9.64932i	0.946243	+	0.687486i	0.949915	−	0.312507i	$-0.101169\pi$
$197$	13.2812	+	9.64932i	0.946243	+	0.687486i	−0.00367232	+	0.999993i	$0.501169\pi$
$198$	0.291796	−	0.898056i	0.0207370	−	0.0638221i
$199$	−8.25329	−	25.4010i	−0.585060	−	1.80063i	−0.599029	−	0.800728i	$-0.704446\pi$
$199$	−8.25329	−	25.4010i	−0.585060	−	1.80063i	0.0139686	−	0.999902i	$-0.495554\pi$
$200$		0			0
$201$	1.30902	+	4.02874i	0.0923309	+	0.284165i
$202$	0.909830	+	2.80017i	0.0640154	+	0.197019i
$203$	−20.9164	+	15.1967i	−1.46804	+	1.06660i
$204$	0.118034	+	0.363271i	0.00826403	+	0.0254341i
$205$		0			0
$206$	−0.0729490	−	0.0530006i	−0.00508260	−	0.00369272i
$207$	−3.38197	+	10.4086i	−0.235063	+	0.723449i
$208$	7.28115	−	5.29007i	0.504857	−	0.366800i
$209$	3.09017	−	2.24514i	0.213752	−	0.155300i
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	−20.5623			−1.41222
$213$	−0.0729490	−	0.0530006i	−0.00499838	−	0.00363154i
$214$	−0.208204	−	0.640786i	−0.0142325	−	0.0438032i
$215$		0			0
$216$	11.1803			0.760726
$217$	−12.5729	−	10.9964i	−0.853507	−	0.746485i
$218$	−5.20163			−0.352299
$219$	2.64590	−	8.14324i	0.178793	−	0.550269i
$220$		0			0
$221$	−0.927051	−	0.673542i	−0.0623602	−	0.0453073i
$222$	−0.145898			−0.00979203
$223$	−0.708204			−0.0474248			−0.0237124	−	0.999719i	$-0.507549\pi$
$223$	−0.708204			−0.0474248			−0.0237124	+	0.999719i	$0.507549\pi$
$224$	13.6353	+	9.90659i	0.911044	+	0.661912i
$225$		0			0
$226$	−0.927051	+	0.673542i	−0.0616665	+	0.0448033i
$227$	6.40983	−	19.7274i	0.425435	−	1.30936i	−0.477141	−	0.878827i	$-0.658327\pi$
$227$	6.40983	−	19.7274i	0.425435	−	1.30936i	0.902577	−	0.430529i	$-0.141673\pi$
$228$	6.54508	+	4.75528i	0.433459	+	0.314926i
$229$	−2.23607	+	6.88191i	−0.147764	+	0.454769i	−0.997356	−	0.0726703i	$-0.976848\pi$
$229$	−2.23607	+	6.88191i	−0.147764	+	0.454769i	0.849592	+	0.527440i	$0.176848\pi$
$230$		0			0
$231$	−1.85410	+	1.34708i	−0.121991	+	0.0886316i
$232$	5.95492	+	18.3273i	0.390959	+	1.20325i
$233$	−5.80902	−	17.8783i	−0.380561	−	1.17125i	−0.939649	−	0.342139i	$-0.888849\pi$
$233$	−5.80902	−	17.8783i	−0.380561	−	1.17125i	0.559088	−	0.829108i	$-0.311151\pi$
$234$	−4.85410	+	3.52671i	−0.317323	+	0.230548i
$235$		0			0
$236$	−4.73607	+	14.5761i	−0.308292	+	0.948824i
$237$		0			0
$238$	0.135255	−	0.416272i	0.00876727	−	0.0269829i
$239$	10.8541	−	7.88597i	0.702093	−	0.510101i	−0.178520	−	0.983936i	$-0.557131\pi$
$239$	10.8541	−	7.88597i	0.702093	−	0.510101i	0.880613	+	0.473836i	$0.157131\pi$
$240$		0			0
$241$	6.89919	+	5.01255i	0.444416	+	0.322887i	0.787387	−	0.616459i	$-0.211433\pi$
$241$	6.89919	+	5.01255i	0.444416	+	0.322887i	−0.342971	+	0.939346i	$0.611433\pi$
$242$	−6.43769			−0.413831
$243$	16.0000			1.02640
$244$	−9.09017	−	6.60440i	−0.581938	−	0.422803i
$245$		0			0
$246$	1.23607	−	3.80423i	0.0788088	−	0.242549i
$247$	−24.2705			−1.54430
$248$	−10.6910	+	6.37988i	−0.678878	+	0.405123i
$249$	4.09017			0.259204
$250$		0			0
$251$	0.291796	+	0.898056i	0.0184180	+	0.0566848i	0.959843	−	0.280537i	$-0.0905127\pi$
$251$	0.291796	+	0.898056i	0.0184180	+	0.0566848i	−0.941425	+	0.337222i	$0.890513\pi$
$252$	7.85410	+	5.70634i	0.494762	+	0.359466i
$253$	−4.18034			−0.262816
$254$	−6.32624			−0.396943
$255$		0			0
$256$	5.30902	−	3.85723i	0.331814	−	0.241077i
$257$	1.14590	−	0.832544i	0.0714792	−	0.0519326i	−0.551472	−	0.834194i	$-0.685934\pi$
$257$	1.14590	−	0.832544i	0.0714792	−	0.0519326i	0.622951	+	0.782261i	$0.285934\pi$
$258$	0.881966	−	2.71441i	0.0549088	−	0.168992i
$259$	−0.572949	−	0.416272i	−0.0356013	−	0.0258659i
$260$		0			0
$261$	5.32624	+	16.3925i	0.329686	+	1.01467i
$262$	−0.0450850	+	0.0327561i	−0.00278536	+	0.00202368i
$263$	3.33688	+	10.2699i	0.205761	+	0.633267i	0.999681	+	0.0252452i	$0.00803665\pi$
$263$	3.33688	+	10.2699i	0.205761	+	0.633267i	−0.793920	+	0.608022i	$0.791963\pi$
$264$	0.527864	+	1.62460i	0.0324878	+	0.0999871i
$265$		0			0
$266$	−2.86475	−	8.81678i	−0.175649	−	0.540591i
$267$	−1.97214	+	6.06961i	−0.120693	+	0.371454i
$268$	5.54508	+	4.02874i	0.338720	+	0.246094i
$269$	−0.427051	+	1.31433i	−0.0260378	+	0.0801360i	−0.963231	−	0.268675i	$-0.913414\pi$
$269$	−0.427051	+	1.31433i	−0.0260378	+	0.0801360i	0.937193	+	0.348811i	$0.113414\pi$
$270$		0			0
$271$	−7.73607	+	5.62058i	−0.469933	+	0.341426i	−0.797415	−	0.603431i	$-0.793800\pi$
$271$	−7.73607	+	5.62058i	−0.469933	+	0.341426i	0.327482	+	0.944857i	$0.393800\pi$
$272$	0.354102	+	0.257270i	0.0214706	+	0.0155993i
$273$	14.5623			0.881351
$274$	4.00000			0.241649
$275$		0			0
$276$	−2.73607	−	8.42075i	−0.164692	−	0.506870i
$277$	−4.11803	+	12.6740i	−0.247429	+	0.761507i	0.747799	+	0.663925i	$0.231111\pi$
$277$	−4.11803	+	12.6740i	−0.247429	+	0.761507i	−0.995228	+	0.0975818i	$0.968889\pi$
$278$	3.61803			0.216995
$279$	−9.56231	+	5.70634i	−0.572480	+	0.341630i
$280$		0			0
$281$	5.88197	−	18.1028i	0.350889	−	1.07992i	−0.607466	−	0.794345i	$-0.707814\pi$
$281$	5.88197	−	18.1028i	0.350889	−	1.07992i	0.958355	−	0.285579i	$-0.0921859\pi$
$282$	0.645898	+	1.98787i	0.0384627	+	0.118376i
$283$	5.30902	+	3.85723i	0.315588	+	0.229288i	0.734291	−	0.678835i	$-0.237515\pi$
$283$	5.30902	+	3.85723i	0.315588	+	0.229288i	−0.418702	+	0.908124i	$0.637515\pi$
$284$	−0.145898			−0.00865746
$285$		0			0
$286$	−1.85410	−	1.34708i	−0.109635	−	0.0796547i
$287$	15.7082	−	11.4127i	0.927226	−	0.673669i
$288$	9.09017	−	6.60440i	0.535643	−	0.389168i
$289$	−5.23607	+	16.1150i	−0.308004	+	0.947939i
$290$		0			0
$291$	1.63525	−	5.03280i	0.0958603	−	0.295028i
$292$	−4.28115	−	13.1760i	−0.250536	−	0.771069i
$293$	−6.66312	+	4.84104i	−0.389264	+	0.282817i	−0.765154	−	0.643848i	$-0.777337\pi$
$293$	−6.66312	+	4.84104i	−0.389264	+	0.282817i	0.375890	+	0.926664i	$0.377337\pi$
$294$	0.381966	+	1.17557i	0.0222767	+	0.0685607i
$295$		0			0
$296$	−0.427051	+	0.310271i	−0.0248218	+	0.0180341i
$297$	1.18034	+	3.63271i	0.0684903	+	0.210791i
$298$	−3.25329	+	10.0126i	−0.188458	+	0.580014i
$299$	21.4894	+	15.6129i	1.24276	+	0.902919i
$300$		0			0
$301$	11.2082	−	8.14324i	0.646030	−	0.469368i
$302$	9.75329	−	7.08618i	0.561239	−	0.407764i
$303$	−3.85410	−	2.80017i	−0.221412	−	0.160866i
$304$	9.27051			0.531700
$305$		0			0
$306$	−0.236068	−	0.171513i	−0.0134951	−	0.00980477i
$307$	−1.88197	−	5.79210i	−0.107409	−	0.330572i	0.882879	−	0.469601i	$-0.155602\pi$
$307$	−1.88197	−	5.79210i	−0.107409	−	0.330572i	−0.990288	+	0.139028i	$0.955602\pi$
$308$	−1.14590	+	3.52671i	−0.0652936	+	0.200953i
$309$	0.145898			0.00829985
$310$		0			0
$311$	16.4721			0.934049			0.467025	−	0.884244i	$-0.345326\pi$
$311$	16.4721			0.934049			0.467025	+	0.884244i	$0.345326\pi$
$312$	3.35410	−	10.3229i	0.189889	−	0.584417i
$313$	−0.381966	−	1.17557i	−0.0215900	−	0.0664472i	0.939681	−	0.342052i	$-0.111122\pi$
$313$	−0.381966	−	1.17557i	−0.0215900	−	0.0664472i	−0.961271	+	0.275605i	$0.911122\pi$
$314$	4.85410	+	3.52671i	0.273933	+	0.199024i
$315$		0			0
$316$		0			0
$317$	20.9443	+	15.2169i	1.17635	+	0.854666i	0.991755	−	0.128149i	$-0.0409035\pi$
$317$	20.9443	+	15.2169i	1.17635	+	0.854666i	0.184593	+	0.982815i	$0.440903\pi$
$318$	−6.35410	+	4.61653i	−0.356320	+	0.258882i
$319$	−5.32624	+	3.86974i	−0.298212	+	0.216664i
$320$		0			0
$321$	0.881966	+	0.640786i	0.0492265	+	0.0357652i
$322$	−3.13525	+	9.64932i	−0.174721	+	0.537736i
$323$	−0.364745	−	1.12257i	−0.0202950	−	0.0624615i
$324$	1.30902	−	0.951057i	0.0727232	−	0.0528365i
$325$		0			0
$326$	2.42705	+	7.46969i	0.134422	+	0.413708i
$327$	6.80902	−	4.94704i	0.376540	−	0.273572i
$328$	−4.47214	−	13.7638i	−0.246932	−	0.759980i
$329$	−3.13525	+	9.64932i	−0.172852	+	0.531984i
$330$		0			0
$331$	3.48278	−	10.7189i	0.191431	−	0.589164i	−0.808569	−	0.588402i	$-0.799757\pi$
$331$	3.48278	−	10.7189i	0.191431	−	0.589164i	1.00000		0.000762014i	$-0.000242557\pi$
$332$	5.35410	−	3.88998i	0.293845	−	0.213491i
$333$	−0.381966	+	0.277515i	−0.0209316	+	0.0152077i
$334$	−4.61803	−	3.35520i	−0.252688	−	0.183588i
$335$		0			0
$336$	−5.56231			−0.303449
$337$	15.3541	+	11.1554i	0.836391	+	0.607674i	0.921360	−	0.388710i	$-0.127079\pi$
$337$	15.3541	+	11.1554i	0.836391	+	0.607674i	−0.0849690	+	0.996384i	$0.527079\pi$
$338$	2.01722	+	6.20837i	0.109722	+	0.337691i
$339$	0.572949	−	1.76336i	0.0311183	−	0.0957723i
$340$		0			0
$341$	−3.20163	−	2.80017i	−0.173378	−	0.151638i
$342$	−6.18034			−0.334195
$343$	4.63525	−	14.2658i	0.250280	−	0.770283i
$344$	−3.19098	−	9.82084i	−0.172046	−	0.529504i
$345$		0			0
$346$	−0.562306			−0.0302298
$347$	−8.12461			−0.436152			−0.218076	−	0.975932i	$-0.569978\pi$
$347$	−8.12461			−0.436152			−0.218076	+	0.975932i	$0.569978\pi$
$348$	−11.2812	−	8.19624i	−0.604733	−	0.439364i
$349$	13.5172	−	9.82084i	0.723560	−	0.525697i	−0.163959	−	0.986467i	$-0.552427\pi$
$349$	13.5172	−	9.82084i	0.723560	−	0.525697i	0.887520	+	0.460770i	$0.152427\pi$
$350$		0			0
$351$	7.50000	−	23.0826i	0.400320	−	1.23206i
$352$	3.47214	+	2.52265i	0.185065	+	0.134458i
$353$	10.0066	−	30.7971i	0.532596	−	1.63916i	−0.216190	−	0.976351i	$-0.569363\pi$
$353$	10.0066	−	30.7971i	0.532596	−	1.63916i	0.748786	−	0.662812i	$-0.230637\pi$
$354$	1.80902	+	5.56758i	0.0961482	+	0.295914i
$355$		0			0
$356$	3.19098	+	9.82084i	0.169122	+	0.520503i
$357$	0.218847	+	0.673542i	0.0115826	+	0.0356476i
$358$	−9.89919	+	7.19218i	−0.523188	+	0.380119i
$359$	−7.82624	−	24.0867i	−0.413053	−	1.27125i	−0.913981	−	0.405757i	$-0.867008\pi$
$359$	−7.82624	−	24.0867i	−0.413053	−	1.27125i	0.500928	−	0.865489i	$-0.332992\pi$
$360$		0			0
$361$	−4.85410	−	3.52671i	−0.255479	−	0.185616i
$362$	3.24671	−	9.99235i	0.170643	−	0.525186i
$363$	8.42705	−	6.12261i	0.442305	−	0.321354i
$364$	19.0623	−	13.8496i	0.999136	−	0.725915i
$365$		0			0
$366$	−4.29180			−0.224336
$367$	36.2705			1.89331			0.946653	−	0.322256i	$-0.104441\pi$
$367$	36.2705			1.89331			0.946653	+	0.322256i	$0.104441\pi$
$368$	−8.20820	−	5.96361i	−0.427882	−	0.310875i
$369$	−4.00000	−	12.3107i	−0.208232	−	0.640871i
$370$		0			0
$371$	−38.1246			−1.97933
$372$	3.54508	−	8.28199i	0.183804	−	0.429401i
$373$	0.347524			0.0179941			0.00899706	−	0.999960i	$-0.497136\pi$
$373$	0.347524			0.0179941			0.00899706	+	0.999960i	$0.497136\pi$
$374$	0.0344419	−	0.106001i	0.00178095	−	0.00548119i
$375$		0			0
$376$	6.11803	+	4.44501i	0.315514	+	0.229234i
$377$	41.8328			2.15450
$378$	9.27051			0.476824
$379$	14.8992	+	10.8249i	0.765320	+	0.556037i	0.900537	−	0.434779i	$-0.143173\pi$
$379$	14.8992	+	10.8249i	0.765320	+	0.556037i	−0.135218	+	0.990816i	$0.543173\pi$
$380$		0			0
$381$	8.28115	−	6.01661i	0.424256	−	0.308240i
$382$	−3.07295	+	9.45756i	−0.157226	+	0.483891i
$383$	−13.6353	−	9.90659i	−0.696729	−	0.506203i	0.182136	−	0.983273i	$-0.441699\pi$
$383$	−13.6353	−	9.90659i	−0.696729	−	0.506203i	−0.878865	+	0.477070i	$0.841699\pi$
$384$	−3.51722	+	10.8249i	−0.179487	+	0.552406i
$385$		0			0
$386$	−1.19098	+	0.865300i	−0.0606194	+	0.0440426i
$387$	−2.85410	−	8.78402i	−0.145082	−	0.446517i
$388$	−2.64590	−	8.14324i	−0.134325	−	0.413410i
$389$	23.5172	−	17.0863i	1.19237	−	0.866308i	0.198858	−	0.980028i	$-0.436277\pi$
$389$	23.5172	−	17.0863i	1.19237	−	0.866308i	0.993513	+	0.113721i	$0.0362769\pi$
$390$		0			0
$391$	−0.399187	+	1.22857i	−0.0201878	+	0.0621315i
$392$	3.61803	+	2.62866i	0.182738	+	0.132767i
$393$	0.0278640	−	0.0857567i	0.00140556	−	0.00432585i
$394$	8.20820	−	5.96361i	0.413523	−	0.300442i
$395$		0			0
$396$	2.00000	+	1.45309i	0.100504	+	0.0730203i
$397$	−16.2918			−0.817662			−0.408831	−	0.912610i	$-0.634063\pi$
$397$	−16.2918			−0.817662			−0.408831	+	0.912610i	$0.634063\pi$
$398$	−16.5066			−0.827400
$399$	12.1353	+	8.81678i	0.607523	+	0.441391i
$400$		0			0
$401$	−9.21885	+	28.3727i	−0.460367	+	1.41686i	0.404349	+	0.914605i	$0.367498\pi$
$401$	−9.21885	+	28.3727i	−0.460367	+	1.41686i	−0.864717	+	0.502260i	$0.832502\pi$
$402$	2.61803			0.130576
$403$	6.00000	+	26.3521i	0.298881	+	1.31269i
$404$	−7.70820			−0.383497
$405$		0			0
$406$	4.93769	+	15.1967i	0.245054	+	0.754198i
$407$	−0.145898	−	0.106001i	−0.00723190	−	0.00525428i
$408$	0.527864			0.0261332
$409$	−6.18034			−0.305598			−0.152799	−	0.988257i	$-0.548829\pi$
$409$	−6.18034			−0.305598			−0.152799	+	0.988257i	$0.548829\pi$
$410$		0			0
$411$	−5.23607	+	3.80423i	−0.258276	+	0.187649i
$412$	0.190983	−	0.138757i	0.00940906	−	0.00683608i
$413$	−8.78115	+	27.0256i	−0.432092	+	1.32984i
$414$	5.47214	+	3.97574i	0.268941	+	0.195397i
$415$		0			0
$416$	−8.42705	−	25.9358i	−0.413170	−	1.27161i
$417$	−4.73607	+	3.44095i	−0.231926	+	0.168504i
$418$	−0.729490	−	2.24514i	−0.0356805	−	0.109813i
$419$	1.38197	+	4.25325i	0.0675135	+	0.207785i	0.979122	−	0.203275i	$-0.0651586\pi$
$419$	1.38197	+	4.25325i	0.0675135	+	0.207785i	−0.911608	+	0.411060i	$0.865159\pi$
$420$		0			0
$421$	4.56231	+	14.0413i	0.222353	+	0.684333i	0.998549	+	0.0538414i	$0.0171466\pi$
$421$	4.56231	+	14.0413i	0.222353	+	0.684333i	−0.776196	+	0.630491i	$0.782853\pi$
$422$	−1.52786	+	4.70228i	−0.0743753	+	0.228904i
$423$	5.47214	+	3.97574i	0.266064	+	0.193307i
$424$	−8.78115	+	27.0256i	−0.426450	+	1.31248i
$425$		0			0
$426$	−0.0450850	+	0.0327561i	−0.00218437	+	0.00158704i
$427$	−16.8541	−	12.2452i	−0.815627	−	0.592588i
$428$	1.76393			0.0852629
$429$	3.70820			0.179034
$430$		0			0
$431$	9.03444	+	27.8052i	0.435174	+	1.33933i	0.892908	+	0.450238i	$0.148661\pi$
$431$	9.03444	+	27.8052i	0.435174	+	1.33933i	−0.457735	+	0.889089i	$0.651339\pi$
$432$	−2.86475	+	8.81678i	−0.137830	+	0.424197i
$433$	−0.583592			−0.0280456			−0.0140228	−	0.999902i	$-0.504464\pi$
$433$	−0.583592			−0.0280456			−0.0140228	+	0.999902i	$0.504464\pi$
$434$	−8.86475	+	5.29007i	−0.425521	+	0.253931i
$435$		0			0
$436$	4.20820	−	12.9515i	0.201536	−	0.620265i
$437$	8.45492	+	26.0216i	0.404453	+	1.24478i
$438$	−4.28115	−	3.11044i	−0.204561	−	0.148623i
$439$	41.8328			1.99657			0.998286	−	0.0585295i	$-0.0186412\pi$
$439$	41.8328			1.99657			0.998286	+	0.0585295i	$0.0186412\pi$
$440$		0			0
$441$	3.23607	+	2.35114i	0.154098	+	0.111959i
$442$	−0.572949	+	0.416272i	−0.0272524	+	0.0198000i
$443$	−33.2705	+	24.1724i	−1.58073	+	1.14847i	−0.664877	+	0.746953i	$0.731516\pi$
$443$	−33.2705	+	24.1724i	−1.58073	+	1.14847i	−0.915853	+	0.401514i	$0.868484\pi$
$444$	0.118034	−	0.363271i	0.00560165	−	0.0172401i
$445$		0			0
$446$	−0.135255	+	0.416272i	−0.00640451	+	0.0197110i
$447$	−5.26393	−	16.2007i	−0.248975	−	0.766268i
$448$	−0.572949	+	0.416272i	−0.0270693	+	0.0196670i
$449$	7.43769	+	22.8909i	0.351006	+	1.08029i	0.958289	+	0.285801i	$0.0922596\pi$
$449$	7.43769	+	22.8909i	0.351006	+	1.08029i	−0.607283	+	0.794486i	$0.707740\pi$
$450$		0			0
$451$	4.00000	−	2.90617i	0.188353	−	0.136846i
$452$	−0.927051	−	2.85317i	−0.0436048	−	0.134202i
$453$	−6.02786	+	18.5519i	−0.283214	+	0.871642i
$454$	−10.3713	−	7.53521i	−0.486750	−	0.353645i
$455$		0			0
$456$	9.04508	−	6.57164i	0.423575	−	0.307745i
$457$	−12.7361	+	9.25330i	−0.595768	+	0.432851i	−0.844374	−	0.535754i	$-0.820028\pi$
$457$	−12.7361	+	9.25330i	−0.595768	+	0.432851i	0.248606	+	0.968605i	$0.420028\pi$
$458$	3.61803	+	2.62866i	0.169060	+	0.122829i
$459$	1.18034			0.0550935
$460$		0			0
$461$	−8.69098	−	6.31437i	−0.404779	−	0.294089i	0.366705	−	0.930337i	$-0.380486\pi$
$461$	−8.69098	−	6.31437i	−0.404779	−	0.294089i	−0.771485	+	0.636248i	$0.780486\pi$
$462$	0.437694	+	1.34708i	0.0203634	+	0.0626720i
$463$	9.61803	−	29.6013i	0.446988	−	1.37569i	−0.433301	−	0.901249i	$-0.642651\pi$
$463$	9.61803	−	29.6013i	0.446988	−	1.37569i	0.880289	−	0.474438i	$-0.157349\pi$
$464$	−15.9787			−0.741793
$465$		0			0
$466$	−11.6180			−0.538195
$467$	10.1287	−	31.1729i	0.468699	−	1.44251i	−0.385571	−	0.922678i	$-0.625995\pi$
$467$	10.1287	−	31.1729i	0.468699	−	1.44251i	0.854270	−	0.519830i	$-0.174005\pi$
$468$	−4.85410	−	14.9394i	−0.224381	−	0.690574i
$469$	10.2812	+	7.46969i	0.474740	+	0.344918i
$470$		0			0
$471$	−9.70820			−0.447330
$472$	17.1353	+	12.4495i	0.788714	+	0.573034i
$473$	2.85410	−	2.07363i	0.131232	−	0.0953454i
$474$		0			0
$475$		0			0
$476$	0.927051	+	0.673542i	0.0424913	+	0.0308717i
$477$	−7.85410	+	24.1724i	−0.359615	+	1.10678i
$478$	−2.56231	−	7.88597i	−0.117197	−	0.360696i
$479$	7.23607	−	5.25731i	0.330624	−	0.240213i	−0.410071	−	0.912054i	$-0.634496\pi$
$479$	7.23607	−	5.25731i	0.330624	−	0.240213i	0.740696	+	0.671841i	$0.234496\pi$
$480$		0			0
$481$	0.354102	+	1.08981i	0.0161457	+	0.0496912i
$482$	4.26393	−	3.09793i	0.194217	−	0.141107i
$483$	−5.07295	−	15.6129i	−0.230827	−	0.710413i
$484$	5.20820	−	16.0292i	0.236737	−	0.728600i
$485$		0			0
$486$	3.05573	−	9.40456i	0.138611	−	0.426600i
$487$	18.5451	−	13.4738i	0.840358	−	0.610556i	−0.0821126	−	0.996623i	$-0.526167\pi$
$487$	18.5451	−	13.4738i	0.840358	−	0.610556i	0.922471	+	0.386067i	$0.126167\pi$
$488$	−12.5623	+	9.12705i	−0.568669	+	0.413162i
$489$	−10.2812	−	7.46969i	−0.464930	−	0.337791i
$490$		0			0
$491$	−27.5967			−1.24542			−0.622712	−	0.782451i	$-0.713969\pi$
$491$	−27.5967			−1.24542			−0.622712	+	0.782451i	$0.713969\pi$
$492$	8.47214	+	6.15537i	0.381953	+	0.277505i
$493$	0.628677	+	1.93487i	0.0283142	+	0.0871421i
$494$	−4.63525	+	14.2658i	−0.208550	+	0.641851i
$495$		0			0
$496$	−2.29180	−	10.0656i	−0.102905	−	0.451959i
$497$	−0.270510			−0.0121340
$498$	0.781153	−	2.40414i	0.0350043	−	0.107732i
$499$	1.28115	+	3.94298i	0.0573523	+	0.176512i	0.975629	−	0.219427i	$-0.0704189\pi$
$499$	1.28115	+	3.94298i	0.0573523	+	0.176512i	−0.918277	+	0.395940i	$0.870419\pi$
$500$		0			0
$501$	9.23607			0.412637
$502$	0.583592			0.0260470
$503$	10.6353	+	7.72696i	0.474203	+	0.344528i	0.799077	−	0.601229i	$-0.205322\pi$
$503$	10.6353	+	7.72696i	0.474203	+	0.344528i	−0.324874	+	0.945757i	$0.605322\pi$
$504$	10.8541	−	7.88597i	0.483480	−	0.351269i
$505$		0			0
$506$	−0.798374	+	2.45714i	−0.0354920	+	0.109233i
$507$	−8.54508	−	6.20837i	−0.379501	−	0.275723i
$508$	5.11803	−	15.7517i	0.227076	−	0.698868i
$509$	−0.590170	−	1.81636i	−0.0261588	−	0.0805086i	0.937125	−	0.348994i	$-0.113477\pi$
$509$	−0.590170	−	1.81636i	−0.0261588	−	0.0805086i	−0.963284	+	0.268486i	$0.913477\pi$
$510$		0			0
$511$	−7.93769	−	24.4297i	−0.351143	−	1.08071i
$512$	5.78115	+	17.7926i	0.255493	+	0.786327i
$513$	20.2254	−	14.6946i	0.892974	−	0.648784i
$514$	−0.270510	−	0.832544i	−0.0119317	−	0.0367219i
$515$		0			0
$516$	6.04508	+	4.39201i	0.266120	+	0.193348i
$517$	−0.798374	+	2.45714i	−0.0351124	+	0.108065i
$518$	−0.354102	+	0.257270i	−0.0155583	+	0.0113038i
$519$	0.736068	−	0.534785i	0.0323098	−	0.0234744i
$520$		0			0
$521$	31.0689			1.36115			0.680576	−	0.732677i	$-0.261729\pi$
$521$	31.0689			1.36115			0.680576	+	0.732677i	$0.261729\pi$
$522$	10.6525			0.466246
$523$	27.6074	+	20.0579i	1.20719	+	0.877073i	0.994972	−	0.100150i	$-0.0319324\pi$
$523$	27.6074	+	20.0579i	1.20719	+	0.877073i	0.212215	+	0.977223i	$0.431932\pi$
$524$	−0.0450850	−	0.138757i	−0.00196955	−	0.00606164i
$525$		0			0
$526$	6.67376			0.290990
$527$	−1.12868	+	0.673542i	−0.0491659	+	0.0293399i
$528$	−1.41641			−0.0616412
$529$	2.14590	−	6.60440i	0.0932999	−	0.287148i
$530$		0			0
$531$	15.3262	+	11.1352i	0.665102	+	0.483225i
$532$	24.2705			1.05226
$533$	−31.4164			−1.36080
$534$	3.19098	+	2.31838i	0.138087	+	0.100326i
$535$		0			0
$536$	7.66312	−	5.56758i	0.330996	−	0.240483i
$537$	6.11803	−	18.8294i	0.264013	−	0.812547i
$538$	0.690983	+	0.502029i	0.0297904	+	0.0216440i
$539$	−0.472136	+	1.45309i	−0.0203363	+	0.0625888i
$540$		0			0
$541$	−17.7984	+	12.9313i	−0.765212	+	0.555959i	−0.900504	−	0.434847i	$-0.856803\pi$
$541$	−17.7984	+	12.9313i	−0.765212	+	0.555959i	0.135293	+	0.990806i	$0.456803\pi$
$542$	1.82624	+	5.62058i	0.0784436	+	0.241425i
$543$	5.25329	+	16.1680i	0.225440	+	0.693834i
$544$	1.07295	−	0.779543i	0.0460023	−	0.0334226i
$545$		0			0
$546$	2.78115	−	8.55951i	0.119022	−	0.366313i
$547$	−19.1803	−	13.9353i	−0.820092	−	0.595832i	0.0966468	−	0.995319i	$-0.469188\pi$
$547$	−19.1803	−	13.9353i	−0.820092	−	0.595832i	−0.916739	+	0.399487i	$0.869188\pi$
$548$	−3.23607	+	9.95959i	−0.138238	+	0.425453i
$549$	−11.2361	+	8.16348i	−0.479544	+	0.348409i
$550$		0			0
$551$	34.8607	+	25.3278i	1.48511	+	1.07900i
$552$	−12.2361			−0.520802
$553$		0			0
$554$	6.66312	+	4.84104i	0.283089	+	0.205676i
$555$		0			0
$556$	−2.92705	+	9.00854i	−0.124135	+	0.382047i
$557$	−35.8885			−1.52065			−0.760323	−	0.649545i	$-0.774959\pi$
$557$	−35.8885			−1.52065			−0.760323	+	0.649545i	$0.774959\pi$
$558$	1.52786	+	6.71040i	0.0646796	+	0.284074i
$559$	−22.4164			−0.948113
$560$		0			0
$561$	0.0557281	+	0.171513i	0.00235284	+	0.00724130i
$562$	−9.51722	−	6.91467i	−0.401460	−	0.291678i
$563$	8.56231			0.360858			0.180429	−	0.983588i	$-0.442251\pi$
$563$	8.56231			0.360858			0.180429	+	0.983588i	$0.442251\pi$
$564$	−5.47214			−0.230418
$565$		0			0
$566$	3.28115	−	2.38390i	0.137917	−	0.100203i
$567$	2.42705	−	1.76336i	0.101927	−	0.0740540i
$568$	−0.0623059	+	0.191758i	−0.00261430	+	0.00804598i
$569$	−12.5623	−	9.12705i	−0.526639	−	0.382626i	0.292460	−	0.956278i	$-0.405526\pi$
$569$	−12.5623	−	9.12705i	−0.526639	−	0.382626i	−0.819099	+	0.573652i	$0.805526\pi$
$570$		0			0
$571$	2.16312	+	6.65740i	0.0905237	+	0.278603i	0.986061	−	0.166383i	$-0.0532087\pi$
$571$	2.16312	+	6.65740i	0.0905237	+	0.278603i	−0.895538	+	0.444986i	$0.853209\pi$
$572$	4.85410	−	3.52671i	0.202960	−	0.147459i
$573$	−4.97214	−	15.3027i	−0.207714	−	0.639278i
$574$	−3.70820	−	11.4127i	−0.154777	−	0.476356i
$575$		0			0
$576$	0.145898	+	0.449028i	0.00607908	+	0.0187095i
$577$	−12.0451	+	37.0710i	−0.501443	+	1.54328i	0.305225	+	0.952280i	$0.401268\pi$
$577$	−12.0451	+	37.0710i	−0.501443	+	1.54328i	−0.806669	+	0.591004i	$0.798732\pi$
$578$	8.47214	+	6.15537i	0.352394	+	0.256030i
$579$	0.736068	−	2.26538i	0.0305899	−	0.0941462i
$580$		0			0
$581$	9.92705	−	7.21242i	0.411843	−	0.299222i
$582$	−2.64590	−	1.92236i	−0.109676	−	0.0796843i
$583$	−9.70820			−0.402073
$584$	−19.1459			−0.792263
$585$		0			0
$586$	1.57295	+	4.84104i	0.0649779	+	0.199981i
$587$	−11.1287	+	34.2505i	−0.459330	+	1.41367i	0.406646	+	0.913586i	$0.366698\pi$
$587$	−11.1287	+	34.2505i	−0.459330	+	1.41367i	−0.865976	+	0.500086i	$0.833302\pi$
$588$	−3.23607			−0.133453
$589$	−10.9549	+	25.5928i	−0.451389	+	1.05453i
$590$		0			0
$591$	−5.07295	+	15.6129i	−0.208673	+	0.642230i
$592$	−0.135255	−	0.416272i	−0.00555894	−	0.0171087i
$593$	4.94427	+	3.59222i	0.203037	+	0.147515i	0.684658	−	0.728865i	$-0.259952\pi$
$593$	4.94427	+	3.59222i	0.203037	+	0.147515i	−0.481621	+	0.876380i	$0.659952\pi$
$594$	2.36068			0.0968599
$595$		0			0
$596$	−22.2984	−	16.2007i	−0.913377	−	0.663607i
$597$	21.6074	−	15.6987i	0.884332	−	0.642505i
$598$	13.2812	−	9.64932i	0.543107	−	0.394590i
$599$	9.20820	−	28.3399i	0.376237	−	1.15794i	−0.566403	−	0.824128i	$-0.691666\pi$
$599$	9.20820	−	28.3399i	0.376237	−	1.15794i	0.942640	−	0.333810i	$-0.108334\pi$
$600$		0			0
$601$	6.79837	−	20.9232i	0.277311	−	0.853477i	−0.711287	−	0.702902i	$-0.751887\pi$
$601$	6.79837	−	20.9232i	0.277311	−	0.853477i	0.988599	−	0.150575i	$-0.0481126\pi$
$602$	−2.64590	−	8.14324i	−0.107839	−	0.331894i
$603$	6.85410	−	4.97980i	0.279121	−	0.202793i
$604$	9.75329	+	30.0175i	0.396856	+	1.22140i
$605$		0			0
$606$	−2.38197	+	1.73060i	−0.0967608	+	0.0703008i
$607$	7.85410	+	24.1724i	0.318788	+	0.981129i	0.974167	+	0.225829i	$0.0725090\pi$
$607$	7.85410	+	24.1724i	0.318788	+	0.981129i	−0.655379	+	0.755300i	$0.727491\pi$
$608$	8.68034	−	26.7153i	0.352034	−	1.08345i
$609$	−20.9164	−	15.1967i	−0.847576	−	0.615800i
$610$		0			0
$611$	13.2812	−	9.64932i	0.537298	−	0.390370i
$612$	0.618034	−	0.449028i	0.0249825	−	0.0181509i
$613$	20.2705	+	14.7274i	0.818718	+	0.594834i	0.916345	−	0.400390i	$-0.131125\pi$
$613$	20.2705	+	14.7274i	0.818718	+	0.594834i	−0.0976269	+	0.995223i	$0.531125\pi$
$614$	−3.76393			−0.151900
$615$		0			0
$616$	4.14590	+	3.01217i	0.167043	+	0.121364i
$617$	4.39919	+	13.5393i	0.177105	+	0.545072i	0.999723	−	0.0235215i	$-0.00748780\pi$
$617$	4.39919	+	13.5393i	0.177105	+	0.545072i	−0.822619	+	0.568593i	$0.807488\pi$
$618$	0.0278640	−	0.0857567i	0.00112086	−	0.00344964i
$619$	−40.0000			−1.60774			−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000			−1.60774			−0.803868	+	0.594808i	$0.797228\pi$
$620$		0			0
$621$	−27.3607			−1.09795
$622$	3.14590	−	9.68208i	0.126139	−	0.388216i
$623$	5.91641	+	18.2088i	0.237036	+	0.729521i
$624$	7.28115	+	5.29007i	0.291479	+	0.211772i
$625$		0			0
$626$	−0.763932			−0.0305329
$627$	3.09017	+	2.24514i	0.123410	+	0.0896623i
$628$	−12.7082	+	9.23305i	−0.507113	+	0.368439i
$629$	−0.0450850	+	0.0327561i	−0.00179766	+	0.00130607i
$630$		0			0
$631$	7.06231	+	5.13107i	0.281146	+	0.204264i	0.719417	−	0.694578i	$-0.244409\pi$
$631$	7.06231	+	5.13107i	0.281146	+	0.204264i	−0.438271	+	0.898843i	$0.644409\pi$
$632$		0			0
$633$	−2.47214	−	7.60845i	−0.0982586	−	0.302409i
$634$	12.9443	−	9.40456i	0.514083	−	0.373503i
$635$		0			0
$636$	−6.35410	−	19.5559i	−0.251957	−	0.775442i
$637$	7.85410	−	5.70634i	0.311191	−	0.226093i
$638$	1.25735	+	3.86974i	0.0497791	+	0.153204i
$639$	−0.0557281	+	0.171513i	−0.00220457	+	0.00678497i
$640$		0			0
$641$	−12.6976	+	39.0791i	−0.501523	+	1.54353i	0.305014	+	0.952348i	$0.401339\pi$
$641$	−12.6976	+	39.0791i	−0.501523	+	1.54353i	−0.806538	+	0.591183i	$0.798661\pi$
$642$	0.545085	−	0.396027i	0.0215128	−	0.0156300i
$643$	6.59017	−	4.78804i	0.259891	−	0.188822i	−0.450208	−	0.892924i	$-0.648650\pi$
$643$	6.59017	−	4.78804i	0.259891	−	0.188822i	0.710099	+	0.704102i	$0.248650\pi$
$644$	−21.4894	−	15.6129i	−0.846799	−	0.615236i
$645$		0			0
$646$	−0.729490			−0.0287014
$647$	−24.1803	−	17.5680i	−0.950627	−	0.690671i	0.000327889	−	1.00000i	$-0.499896\pi$
$647$	−24.1803	−	17.5680i	−0.950627	−	0.690671i	−0.950955	+	0.309329i	$0.899896\pi$
$648$	−0.690983	−	2.12663i	−0.0271444	−	0.0835418i
$649$	−2.23607	+	6.88191i	−0.0877733	+	0.270139i
$650$		0			0
$651$	6.57295	−	15.3557i	0.257614	−	0.601836i
$652$	−20.5623			−0.805282
$653$	−12.2533	+	37.7117i	−0.479508	+	1.47577i	0.360272	+	0.932847i	$0.382684\pi$
$653$	−12.2533	+	37.7117i	−0.479508	+	1.47577i	−0.839780	+	0.542927i	$0.817316\pi$
$654$	−1.60739	−	4.94704i	−0.0628540	−	0.193445i
$655$		0			0
$656$	12.0000			0.468521
$657$	−17.1246			−0.668095
$658$	5.07295	+	3.68571i	0.197764	+	0.143684i
$659$	−18.3541	+	13.3350i	−0.714974	+	0.519459i	−0.884775	−	0.466019i	$-0.845688\pi$
$659$	−18.3541	+	13.3350i	−0.714974	+	0.519459i	0.169800	+	0.985478i	$0.445688\pi$
$660$		0			0
$661$	−5.13525	+	15.8047i	−0.199738	+	0.614731i	0.800150	+	0.599800i	$0.204753\pi$
$661$	−5.13525	+	15.8047i	−0.199738	+	0.614731i	−0.999889	+	0.0149316i	$0.995247\pi$
$662$	−5.63525	−	4.09425i	−0.219020	−	0.159128i
$663$	0.354102	−	1.08981i	0.0137522	−	0.0423249i
$664$	−2.82624	−	8.69827i	−0.109679	−	0.337558i
$665$		0			0
$666$	0.0901699	+	0.277515i	0.00349401	+	0.0107535i
$667$	−14.5729	−	44.8509i	−0.564267	−	1.73663i
$668$	12.0902	−	8.78402i	0.467783	−	0.339864i
$669$	−0.218847	−	0.673542i	−0.00846112	−	0.0260406i
$670$		0			0
$671$	−4.29180	−	3.11817i	−0.165683	−	0.120376i
$672$	−5.20820	+	16.0292i	−0.200911	+	0.618340i
$673$	−3.57295	+	2.59590i	−0.137727	+	0.100065i	−0.654516	−	0.756049i	$-0.727127\pi$
$673$	−3.57295	+	2.59590i	−0.137727	+	0.100065i	0.516788	+	0.856113i	$0.327127\pi$
$674$	9.48936	−	6.89442i	0.365516	−	0.265563i
$675$		0			0
$676$	−17.0902			−0.657314
$677$	−28.6525			−1.10120			−0.550602	−	0.834768i	$-0.685602\pi$
$677$	−28.6525			−1.10120			−0.550602	+	0.834768i	$0.685602\pi$
$678$	−0.927051	−	0.673542i	−0.0356032	−	0.0258672i
$679$	−4.90576	−	15.0984i	−0.188266	−	0.579423i
$680$		0			0
$681$	20.7426			0.794860
$682$	−2.25735	+	1.34708i	−0.0864386	+	0.0515825i
$683$	−10.0557			−0.384772			−0.192386	−	0.981319i	$-0.561623\pi$
$683$	−10.0557			−0.384772			−0.192386	+	0.981319i	$0.561623\pi$
$684$	5.00000	−	15.3884i	0.191180	−	0.588391i
$685$		0			0
$686$	−7.50000	−	5.44907i	−0.286351	−	0.208046i
$687$	−7.23607			−0.276073
$688$	8.56231			0.326435
$689$	49.9058	+	36.2587i	1.90126	+	1.38134i
$690$		0			0
$691$	−3.10081	+	2.25287i	−0.117960	+	0.0857033i	−0.645201	−	0.764013i	$-0.723227\pi$
$691$	−3.10081	+	2.25287i	−0.117960	+	0.0857033i	0.527241	+	0.849716i	$0.323227\pi$
$692$	0.454915	−	1.40008i	0.0172933	−	0.0532232i
$693$	3.70820	+	2.69417i	0.140863	+	0.102343i
$694$	−1.55166	+	4.77553i	−0.0589003	+	0.181277i
$695$		0			0
$696$	−15.5902	+	11.3269i	−0.590944	+	0.429346i
$697$	−0.472136	−	1.45309i	−0.0178834	−	0.0550395i
$698$	−3.19098	−	9.82084i	−0.120780	−	0.371724i
$699$	15.2082	−	11.0494i	0.575227	−	0.417927i
$700$		0			0
$701$	−9.28115	+	28.5645i	−0.350544	+	1.07886i	0.608004	+	0.793934i	$0.291970\pi$
$701$	−9.28115	+	28.5645i	−0.350544	+	1.07886i	−0.958548	+	0.284930i	$0.908030\pi$
$702$	−12.1353	−	8.81678i	−0.458016	−	0.332768i
$703$	−0.364745	+	1.12257i	−0.0137566	+	0.0423385i
$704$	−0.145898	+	0.106001i	−0.00549874	+	0.00399507i
$705$		0			0
$706$	−16.1910	−	11.7634i	−0.609356	−	0.442723i
$707$	−14.2918			−0.537498
$708$	−15.3262			−0.575995
$709$	−3.35410	−	2.43690i	−0.125966	−	0.0915196i	0.523018	−	0.852321i	$-0.324806\pi$
$709$	−3.35410	−	2.43690i	−0.125966	−	0.0915196i	−0.648984	+	0.760802i	$0.724806\pi$
$710$		0			0
$711$		0			0
$712$	14.2705			0.534810
$713$	26.1631	−	15.6129i	0.979817	−	0.584709i
$714$	0.437694			0.0163803
$715$		0			0
$716$	−9.89919	−	30.4666i	−0.369950	−	1.13859i
$717$	10.8541	+	7.88597i	0.405354	+	0.294507i
$718$	−15.6525			−0.584145
$719$	−41.3820			−1.54329			−0.771643	−	0.636055i	$-0.780565\pi$
$719$	−41.3820			−1.54329			−0.771643	+	0.636055i	$0.780565\pi$
$720$		0			0
$721$	0.354102	−	0.257270i	0.0131874	−	0.00958124i
$722$	−3.00000	+	2.17963i	−0.111648	+	0.0811173i
$723$	−2.63525	+	8.11048i	−0.0980062	+	0.301632i
$724$	22.2533	+	16.1680i	0.827037	+	0.600878i
$725$		0			0
$726$	−1.98936	−	6.12261i	−0.0738320	−	0.227231i
$727$	−19.2812	+	14.0086i	−0.715098	+	0.519549i	−0.884814	−	0.465944i	$-0.845715\pi$
$727$	−19.2812	+	14.0086i	−0.715098	+	0.519549i	0.169716	+	0.985493i	$0.445715\pi$
$728$	−10.0623	−	30.9686i	−0.372934	−	1.14777i
$729$	4.01722	+	12.3637i	0.148786	+	0.457916i
$730$		0			0
$731$	−0.336881	−	1.03681i	−0.0124600	−	0.0383479i
$732$	3.47214	−	10.6861i	0.128334	−	0.394971i
$733$	22.6074	+	16.4252i	0.835023	+	0.606680i	0.920976	−	0.389619i	$-0.127393\pi$
$733$	22.6074	+	16.4252i	0.835023	+	0.606680i	−0.0859529	+	0.996299i	$0.527393\pi$
$734$	6.92705	−	21.3193i	0.255682	−	0.786909i
$735$		0			0
$736$	−24.8713	+	18.0701i	−0.916769	+	0.666072i
$737$	2.61803	+	1.90211i	0.0964365	+	0.0700652i
$738$	−8.00000			−0.294484
$739$	21.7082			0.798549			0.399275	−	0.916831i	$-0.369262\pi$
$739$	21.7082			0.798549			0.399275	+	0.916831i	$0.369262\pi$
$740$		0			0
$741$	−7.50000	−	23.0826i	−0.275519	−	0.847961i
$742$	−7.28115	+	22.4091i	−0.267300	+	0.822663i
$743$	3.43769			0.126117			0.0630584	−	0.998010i	$-0.479915\pi$
$743$	3.43769			0.126117			0.0630584	+	0.998010i	$0.479915\pi$
$744$	−9.37132	−	8.19624i	−0.343569	−	0.300489i
$745$		0			0
$746$	0.0663712	−	0.204270i	0.00243002	−	0.00747884i
$747$	−2.52786	−	7.77997i	−0.0924897	−	0.284654i
$748$	0.236068	+	0.171513i	0.00863150	+	0.00627115i
$749$	3.27051			0.119502
$750$		0			0
$751$	32.2254	+	23.4131i	1.17592	+	0.854358i	0.991706	−	0.128528i	$-0.0410252\pi$
$751$	32.2254	+	23.4131i	1.17592	+	0.854358i	0.184217	+	0.982886i	$0.441025\pi$
$752$	−5.07295	+	3.68571i	−0.184991	+	0.134404i
$753$	−0.763932	+	0.555029i	−0.0278392	+	0.0202264i
$754$	7.98936	−	24.5887i	0.290955	−	0.895468i
$755$		0			0
$756$	−7.50000	+	23.0826i	−0.272772	+	0.839507i
$757$	−13.3262	−	41.0139i	−0.484350	−	1.49068i	−0.832920	−	0.553394i	$-0.813332\pi$
$757$	−13.3262	−	41.0139i	−0.484350	−	1.49068i	0.348569	−	0.937283i	$-0.386668\pi$
$758$	9.20820	−	6.69015i	0.334457	−	0.242997i
$759$	−1.29180	−	3.97574i	−0.0468892	−	0.144310i
$760$		0			0
$761$	−2.83688	+	2.06111i	−0.102837	+	0.0747154i	−0.638015	−	0.770024i	$-0.720244\pi$
$761$	−2.83688	+	2.06111i	−0.102837	+	0.0747154i	0.535178	+	0.844739i	$0.320244\pi$
$762$	−1.95492	−	6.01661i	−0.0708191	−	0.217959i
$763$	7.80244	−	24.0134i	0.282467	−	0.869345i
$764$	−21.0623	−	15.3027i	−0.762007	−	0.553631i
$765$		0			0
$766$	−8.42705	+	6.12261i	−0.304482	+	0.221219i
$767$	37.1976	−	27.0256i	1.34313	−	0.975838i
$768$	5.30902	+	3.85723i	0.191573	+	0.139186i
$769$	−53.7426			−1.93801			−0.969005	−	0.247042i	$-0.920541\pi$
$769$	−53.7426			−1.93801			−0.969005	+	0.247042i	$0.920541\pi$
$770$		0			0
$771$	1.14590	+	0.832544i	0.0412685	+	0.0299833i
$772$	−1.19098	−	3.66547i	−0.0428644	−	0.131923i
$773$	5.89919	−	18.1558i	0.212179	−	0.653020i	−0.787163	−	0.616745i	$-0.788451\pi$
$773$	5.89919	−	18.1558i	0.212179	−	0.653020i	0.999342	−	0.0362746i	$-0.0115491\pi$
$774$	−5.70820			−0.205177
$775$		0			0
$776$	−11.8328			−0.424773
$777$	0.218847	−	0.673542i	0.00785109	−	0.0241632i
$778$	−5.55166	−	17.0863i	−0.199037	−	0.612572i
$779$	−26.1803	−	19.0211i	−0.938008	−	0.681503i
$780$		0			0
$781$	−0.0688837			−0.00246485
$782$	0.645898	+	0.469272i	0.0230973	+	0.0167811i
$783$	−34.8607	+	25.3278i	−1.24582	+	0.905141i
$784$	−3.00000	+	2.17963i	−0.107143	+	0.0778438i
$785$		0			0
$786$	−0.0450850	−	0.0327561i	−0.00160813	−	0.00116837i
$787$	−9.66970	+	29.7603i	−0.344687	+	1.06084i	0.617063	+	0.786913i	$0.288322\pi$
$787$	−9.66970	+	29.7603i	−0.344687	+	1.06084i	−0.961751	+	0.273926i	$0.911678\pi$
$788$	8.20820	+	25.2623i	0.292405	+	0.899931i
$789$	−8.73607	+	6.34712i	−0.311012	+	0.225964i
$790$		0			0
$791$	−1.71885	−	5.29007i	−0.0611152	−	0.188093i
$792$	2.76393	−	2.00811i	0.0982120	−	0.0713552i
$793$	10.4164	+	32.0584i	0.369897	+	1.13843i
$794$	−3.11146	+	9.57608i	−0.110421	+	0.339842i
$795$		0			0
$796$	13.3541	−	41.0997i	0.473324	−	1.45674i
$797$	7.32624	−	5.32282i	0.259509	−	0.188544i	−0.450422	−	0.892816i	$-0.648726\pi$
$797$	7.32624	−	5.32282i	0.259509	−	0.188544i	0.709930	+	0.704272i	$0.248726\pi$
$798$	7.50000	−	5.44907i	0.265497	−	0.192895i
$799$	0.645898	+	0.469272i	0.0228502	+	0.0166017i
$800$		0			0
$801$	12.7639			0.450991
$802$	14.9164	+	10.8374i	0.526717	+	0.382682i
$803$	−2.02129	−	6.22088i	−0.0713296	−	0.219530i
$804$	−2.11803	+	6.51864i	−0.0746973	+	0.229895i
$805$		0			0
$806$	16.6353	+	1.50609i	0.585952	+	0.0530496i
$807$	−1.38197			−0.0486475
$808$	−3.29180	+	10.1311i	−0.115805	+	0.356411i
$809$	16.9336	+	52.1164i	0.595355	+	1.83231i	0.552953	+	0.833213i	$0.313501\pi$
$809$	16.9336	+	52.1164i	0.595355	+	1.83231i	0.0424020	+	0.999101i	$0.486499\pi$
$810$		0			0
$811$	42.7771			1.50211			0.751053	−	0.660242i	$-0.229546\pi$
$811$	42.7771			1.50211			0.751053	+	0.660242i	$0.229546\pi$
$812$	−41.8328			−1.46804
$813$	−7.73607	−	5.62058i	−0.271316	−	0.197122i
$814$	−0.0901699	+	0.0655123i	−0.00316045	+	0.00229620i
$815$		0			0
$816$	−0.135255	+	0.416272i	−0.00473487	+	0.0145724i
$817$	−18.6803	−	13.5721i	−0.653542	−	0.474826i
$818$	−1.18034	+	3.63271i	−0.0412696	+	0.127015i
$819$	−9.00000	−	27.6992i	−0.314485	−	0.967887i
$820$		0			0
$821$	−10.0344	−	30.8828i	−0.350204	−	1.07782i	−0.958738	−	0.284290i	$-0.908242\pi$
$821$	−10.0344	−	30.8828i	−0.350204	−	1.07782i	0.608534	−	0.793528i	$-0.291758\pi$
$822$	1.23607	+	3.80423i	0.0431128	+	0.132688i
$823$	−4.95492	+	3.59996i	−0.172717	+	0.125487i	−0.670786	−	0.741651i	$-0.734043\pi$
$823$	−4.95492	+	3.59996i	−0.172717	+	0.125487i	0.498068	+	0.867138i	$0.334043\pi$
$824$	−0.100813	−	0.310271i	−0.00351199	−	0.0108088i
$825$		0			0
$826$	14.2082	+	10.3229i	0.494367	+	0.359178i
$827$	−0.826238	+	2.54290i	−0.0287311	+	0.0884253i	−0.964394	−	0.264470i	$-0.914803\pi$
$827$	−0.826238	+	2.54290i	−0.0287311	+	0.0884253i	0.935663	+	0.352896i	$0.114803\pi$
$828$	−14.3262	+	10.4086i	−0.497871	+	0.361725i
$829$	17.5623	−	12.7598i	0.609964	−	0.443165i	−0.239438	−	0.970912i	$-0.576963\pi$
$829$	17.5623	−	12.7598i	0.609964	−	0.443165i	0.849402	+	0.527747i	$0.176963\pi$
$830$		0			0
$831$	−13.3262			−0.462282
$832$	1.14590			0.0397269
$833$	0.381966	+	0.277515i	0.0132343	+	0.00961531i
$834$	1.11803	+	3.44095i	0.0387144	+	0.119151i
$835$		0			0
$836$	6.18034			0.213752
$837$	−20.9549	−	18.3273i	−0.724308	−	0.633486i
$838$	2.76393			0.0954784
$839$	3.45492	−	10.6331i	0.119277	−	0.367097i	−0.873538	−	0.486756i	$-0.838180\pi$
$839$	3.45492	−	10.6331i	0.119277	−	0.367097i	0.992815	+	0.119659i	$0.0381802\pi$
$840$		0			0
$841$	−36.6246	−	26.6093i	−1.26292	−	0.917563i
$842$	9.12461			0.314455
$843$	19.0344			0.655581
$844$	−10.4721	−	7.60845i	−0.360466	−	0.261894i
$845$		0			0
$846$	3.38197	−	2.45714i	0.116274	−	0.0844783i
$847$	9.65654	−	29.7198i	0.331803	−	1.02118i
$848$	−19.0623	−	13.8496i	−0.654602	−	0.475596i
$849$	−2.02786	+	6.24112i	−0.0695961	+	0.214195i
$850$		0			0
$851$	1.04508	−	0.759299i	0.0358251	−	0.0260284i
$852$	−0.0450850	−	0.138757i	−0.00154459	−	0.00475375i
$853$	−1.23607	−	3.80423i	−0.0423222	−	0.130254i	0.927663	−	0.373419i	$-0.121815\pi$
$853$	−1.23607	−	3.80423i	−0.0423222	−	0.130254i	−0.969985	+	0.243164i	$0.921815\pi$
$854$	−10.4164	+	7.56796i	−0.356442	+	0.258970i
$855$		0			0
$856$	0.753289	−	2.31838i	0.0257469	−	0.0792408i
$857$	−6.61803	−	4.80828i	−0.226068	−	0.164248i	0.468986	−	0.883206i	$-0.344619\pi$
$857$	−6.61803	−	4.80828i	−0.226068	−	0.164248i	−0.695054	+	0.718958i	$0.744619\pi$
$858$	0.708204	−	2.17963i	0.0241777	−	0.0744113i
$859$	−35.0238	+	25.4463i	−1.19500	+	0.868216i	−0.993783	−	0.111332i	$-0.964488\pi$
$859$	−35.0238	+	25.4463i	−1.19500	+	0.868216i	−0.201213	+	0.979547i	$0.564488\pi$
$860$		0			0
$861$	15.7082	+	11.4127i	0.535334	+	0.388943i
$862$	18.0689			0.615429
$863$	−2.49342			−0.0848771			−0.0424385	−	0.999099i	$-0.513513\pi$
$863$	−2.49342			−0.0848771			−0.0424385	+	0.999099i	$0.513513\pi$
$864$	22.7254	+	16.5110i	0.773135	+	0.561715i
$865$		0			0
$866$	−0.111456	+	0.343027i	−0.00378744	+	0.0116565i
$867$	−16.9443			−0.575458
$868$	−6.00000	−	26.3521i	−0.203653	−	0.894447i
$869$		0			0
$870$		0			0
$871$	−6.35410	−	19.5559i	−0.215301	−	0.662627i
$872$	−15.2254	−	11.0619i	−0.515598	−	0.374604i
$873$	−10.5836			−0.358200
$874$	16.9098			0.571984
$875$		0			0
$876$	11.2082	−	8.14324i	0.378690	−	0.275134i
$877$	13.1803	−	9.57608i	0.445068	−	0.323361i	−0.342577	−	0.939490i	$-0.611300\pi$
$877$	13.1803	−	9.57608i	0.445068	−	0.323361i	0.787646	+	0.616129i	$0.211300\pi$
$878$	7.98936	−	24.5887i	0.269628	−	0.829829i
$879$	−6.66312	−	4.84104i	−0.224741	−	0.163284i
$880$		0			0
$881$	−4.74671	−	14.6089i	−0.159921	−	0.492185i	0.838705	−	0.544585i	$-0.183313\pi$
$881$	−4.74671	−	14.6089i	−0.159921	−	0.492185i	−0.998626	+	0.0523999i	$0.983313\pi$
$882$	2.00000	−	1.45309i	0.0673435	−	0.0489279i
$883$	0.309017	+	0.951057i	0.0103992	+	0.0320056i	0.956121	−	0.292970i	$-0.0946438\pi$
$883$	0.309017	+	0.951057i	0.0103992	+	0.0320056i	−0.945722	+	0.324976i	$0.894644\pi$
$884$	−0.572949	−	1.76336i	−0.0192704	−	0.0593081i
$885$		0			0
$886$	7.85410	+	24.1724i	0.263864	+	0.812089i
$887$	−12.0836	+	37.1895i	−0.405727	+	1.24870i	0.514559	+	0.857455i	$0.327956\pi$
$887$	−12.0836	+	37.1895i	−0.405727	+	1.24870i	−0.920286	+	0.391245i	$0.872044\pi$
$888$	−0.427051	−	0.310271i	−0.0143309	−	0.0104120i
$889$	9.48936	−	29.2052i	0.318263	−	0.979512i
$890$		0			0
$891$	0.618034	−	0.449028i	0.0207049	−	0.0150430i
$892$	−0.927051	−	0.673542i	−0.0310400	−	0.0225519i
$893$	16.9098			0.565866
$894$	−10.5279			−0.352104
$895$		0			0
$896$	10.5517	+	32.4747i	0.352506	+	1.08490i
$897$	−8.20820	+	25.2623i	−0.274064	+	0.843482i
$898$	14.8754			0.496398
$899$	18.8820	−	44.1119i	0.629749	−	1.47121i
$900$		0			0
$901$	−0.927051	+	2.85317i	−0.0308845	+	0.0950529i
$902$	−0.944272	−	2.90617i	−0.0314408	−	0.0967649i
$903$	11.2082	+	8.14324i	0.372986	+	0.270990i
$904$	−4.14590			−0.137891
$905$		0			0
$906$	9.75329	+	7.08618i	0.324031	+	0.235423i
$907$	42.8156	−	31.1074i	1.42167	−	1.03290i	0.430175	−	0.902745i	$-0.358452\pi$
$907$	42.8156	−	31.1074i	1.42167	−	1.03290i	0.991493	−	0.130157i	$-0.0415482\pi$
$908$	27.1525	−	19.7274i	0.901087	−	0.654678i
$909$	−2.94427	+	9.06154i	−0.0976553	+	0.300552i
$910$		0			0
$911$	2.52786	−	7.77997i	0.0837519	−	0.257762i	−0.900408	−	0.435047i	$-0.856732\pi$
$911$	2.52786	−	7.77997i	0.0837519	−	0.257762i	0.984159	+	0.177286i	$0.0567316\pi$
$912$	2.86475	+	8.81678i	0.0948612	+	0.291953i
$913$	2.52786	−	1.83660i	0.0836601	−	0.0607826i
$914$	3.00658	+	9.25330i	0.0994488	+	0.306072i
$915$		0			0
$916$	−9.47214	+	6.88191i	−0.312968	+	0.227385i
$917$	−0.0835921	−	0.257270i	−0.00276046	−	0.00849581i
$918$	0.225425	−	0.693786i	0.00744013	−	0.0228984i
$919$	−7.98936	−	5.80461i	−0.263545	−	0.191476i	0.448164	−	0.893952i	$-0.352078\pi$
$919$	−7.98936	−	5.80461i	−0.263545	−	0.191476i	−0.711708	+	0.702475i	$0.752078\pi$
$920$		0			0
$921$	4.92705	−	3.57971i	0.162352	−	0.117956i
$922$	−5.37132	+	3.90249i	−0.176895	+	0.128522i
$923$	0.354102	+	0.257270i	0.0116554	+	0.00846815i
$924$	−3.70820			−0.121991
$925$		0			0
$926$	−15.5623	−	11.3067i	−0.511409	−	0.371560i
$927$	−0.0901699	−	0.277515i	−0.00296157	−	0.00911477i
$928$	−14.9615	+	46.0467i	−0.491135	+	1.51156i
$929$	33.5410			1.10045			0.550223	−	0.835018i	$-0.314543\pi$
$929$	33.5410			1.10045			0.550223	+	0.835018i	$0.314543\pi$
$930$		0			0
$931$	10.0000			0.327737
$932$	9.39919	−	28.9277i	0.307881	−	0.947559i
$933$	5.09017	+	15.6659i	0.166645	+	0.512880i
$934$	−16.3885	−	11.9070i	−0.536250	−	0.389608i
$935$		0			0
$936$	−21.7082			−0.709555
$937$	32.7533	+	23.7967i	1.07000	+	0.777403i	0.975913	−	0.218161i	$-0.0700057\pi$
$937$	32.7533	+	23.7967i	1.07000	+	0.777403i	0.0940905	+	0.995564i	$0.470006\pi$
$938$	6.35410	−	4.61653i	0.207469	−	0.150735i
$939$	1.00000	−	0.726543i	0.0326338	−	0.0237098i
$940$		0			0
$941$	−23.1246	−	16.8010i	−0.753841	−	0.547697i	0.143174	−	0.989698i	$-0.454269\pi$
$941$	−23.1246	−	16.8010i	−0.753841	−	0.547697i	−0.897015	+	0.442000i	$0.854269\pi$
$942$	−1.85410	+	5.70634i	−0.0604099	+	0.185923i
$943$	10.9443	+	33.6830i	0.356395	+	1.09687i
$944$	−14.2082	+	10.3229i	−0.462438	+	0.335981i
$945$		0			0
$946$	−0.673762	−	2.07363i	−0.0219059	−	0.0674194i
$947$	17.8541	−	12.9718i	0.580180	−	0.421526i	−0.258609	−	0.965982i	$-0.583264\pi$
$947$	17.8541	−	12.9718i	0.580180	−	0.421526i	0.838789	+	0.544456i	$0.183264\pi$
$948$		0			0
$949$	−12.8435	+	39.5281i	−0.416916	+	1.28314i
$950$		0			0
$951$	−8.00000	+	24.6215i	−0.259418	+	0.798406i
$952$	1.28115	−	0.930812i	0.0415224	−	0.0301678i
$953$	34.1525	−	24.8132i	1.10631	−	0.803779i	0.124229	−	0.992254i	$-0.460354\pi$
$953$	34.1525	−	24.8132i	1.10631	−	0.803779i	0.982078	+	0.188474i	$0.0603542\pi$
$954$	12.7082	+	9.23305i	0.411443	+	0.298931i
$955$		0			0
$956$	21.7082			0.702093
$957$	−5.32624	−	3.86974i	−0.172173	−	0.125091i
$958$	−1.70820	−	5.25731i	−0.0551896	−	0.169856i
$959$	−6.00000	+	18.4661i	−0.193750	+	0.596302i
$960$		0			0
$961$	30.4959	+	5.56758i	0.983740	+	0.179599i
$962$	0.708204			0.0228334
$963$	0.673762	−	2.07363i	0.0217117	−	0.0668217i
$964$	4.26393	+	13.1230i	0.137332	+	0.422664i
$965$		0			0
$966$	−10.1459			−0.326439
$967$	−43.6525			−1.40377			−0.701884	−	0.712291i	$-0.747658\pi$
$967$	−43.6525			−1.40377			−0.701884	+	0.712291i	$0.747658\pi$
$968$	−18.8435	−	13.6906i	−0.605652	−	0.440032i
$969$	0.954915	−	0.693786i	0.0306763	−	0.0222876i
$970$		0			0
$971$	−6.35410	+	19.5559i	−0.203913	+	0.627579i	0.795843	+	0.605502i	$0.207028\pi$
$971$	−6.35410	+	19.5559i	−0.203913	+	0.627579i	−0.999756	+	0.0220767i	$0.992972\pi$
$972$	20.9443	+	15.2169i	0.671788	+	0.488082i
$973$	−5.42705	+	16.7027i	−0.173983	+	0.535465i
$974$	−4.37790	−	13.4738i	−0.140277	−	0.431728i
$975$		0			0
$976$	−3.97871	−	12.2452i	−0.127356	−	0.391960i
$977$	1.87539	+	5.77185i	0.0599990	+	0.184658i	0.976564	−	0.215228i	$-0.0690496\pi$
$977$	1.87539	+	5.77185i	0.0599990	+	0.184658i	−0.916565	+	0.399886i	$0.869050\pi$
$978$	−6.35410	+	4.61653i	−0.203182	+	0.147620i
$979$	1.50658	+	4.63677i	0.0481504	+	0.148192i
$980$		0			0
$981$	−13.6180	−	9.89408i	−0.434790	−	0.315894i
$982$	−5.27051	+	16.2210i	−0.168189	+	0.517632i
$983$	17.0172	−	12.3637i	0.542765	−	0.394342i	−0.282346	−	0.959313i	$-0.591113\pi$
$983$	17.0172	−	12.3637i	0.542765	−	0.394342i	0.825111	+	0.564971i	$0.191113\pi$
$984$	11.7082	−	8.50651i	0.373244	−	0.271178i
$985$		0			0
$986$	1.25735			0.0400423
$987$	−10.1459			−0.322947
$988$	−31.7705	−	23.0826i	−1.01075	−	0.734356i
$989$	7.80902	+	24.0337i	0.248312	+	0.764227i
$990$		0			0
$991$	−17.2705			−0.548616			−0.274308	−	0.961642i	$-0.588449\pi$
$991$	−17.2705			−0.548616			−0.274308	+	0.961642i	$0.588449\pi$
$992$	−31.1525	−	2.82041i	−0.989092	−	0.0895482i
$993$	11.2705			0.357659
$994$	−0.0516628	+	0.159002i	−0.00163864	+	0.00504323i
$995$		0			0
$996$	5.35410	+	3.88998i	0.169651	+	0.123259i
$997$	27.2492			0.862992			0.431496	−	0.902115i	$-0.357986\pi$
$997$	27.2492			0.862992			0.431496	+	0.902115i	$0.357986\pi$
$998$	2.56231			0.0811084
$999$	−0.954915	−	0.693786i	−0.0302122	−	0.0219504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.k.c.101.1		4
5.2	odd	4		775.2.bf.a.349.2		8
5.3	odd	4		775.2.bf.a.349.1		8
5.4	even	2		31.2.d.a.8.1	yes	4
15.14	odd	2		279.2.i.a.163.1		4
20.19	odd	2		496.2.n.b.225.1		4
31.4	even	5	inner	775.2.k.c.376.1		4
155.4	even	10		31.2.d.a.4.1	✓	4
155.9	even	30		961.2.g.f.338.1		8
155.14	even	30		961.2.g.f.235.1		8
155.19	even	30		961.2.c.f.439.1		4
155.24	odd	30		961.2.g.c.547.1		8
155.29	odd	10		961.2.a.e.1.1		2
155.34	odd	30		961.2.g.g.816.1		8
155.39	even	10		961.2.d.f.388.1		4
155.44	odd	30		961.2.g.g.732.1		8
155.49	even	30		961.2.g.f.732.1		8
155.54	odd	10		961.2.d.e.388.1		4
155.59	even	30		961.2.g.f.816.1		8
155.64	even	10		961.2.a.d.1.1		2
155.69	even	30		961.2.g.b.547.1		8
155.74	odd	30		961.2.c.d.439.1		4
155.79	odd	30		961.2.g.g.235.1		8
155.84	odd	30		961.2.g.g.338.1		8
155.89	odd	10		961.2.d.b.531.1		4
155.97	odd	20		775.2.bf.a.624.1		8
155.99	odd	6		961.2.g.c.846.1		8
155.104	odd	30		961.2.g.c.844.1		8
155.109	even	10		961.2.d.f.374.1		4
155.114	odd	30		961.2.c.d.521.1		4
155.119	odd	6		961.2.g.c.448.1		8
155.128	odd	20		775.2.bf.a.624.2		8
155.129	even	6		961.2.g.b.448.1		8
155.134	even	30		961.2.c.f.521.1		4
155.139	odd	10		961.2.d.e.374.1		4
155.144	even	30		961.2.g.b.844.1		8
155.149	even	6		961.2.g.b.846.1		8
155.154	odd	2		961.2.d.b.628.1		4
465.29	even	10		8649.2.a.f.1.2		2
465.314	odd	10		279.2.i.a.190.1		4
465.374	odd	10		8649.2.a.g.1.2		2
620.159	odd	10		496.2.n.b.97.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.d.a.4.1	✓	4	155.4	even	10
31.2.d.a.8.1	yes	4	5.4	even	2
279.2.i.a.163.1		4	15.14	odd	2
279.2.i.a.190.1		4	465.314	odd	10
496.2.n.b.97.1		4	620.159	odd	10
496.2.n.b.225.1		4	20.19	odd	2
775.2.k.c.101.1		4	1.1	even	1	trivial
775.2.k.c.376.1		4	31.4	even	5	inner
775.2.bf.a.349.1		8	5.3	odd	4
775.2.bf.a.349.2		8	5.2	odd	4
775.2.bf.a.624.1		8	155.97	odd	20
775.2.bf.a.624.2		8	155.128	odd	20
961.2.a.d.1.1		2	155.64	even	10
961.2.a.e.1.1		2	155.29	odd	10
961.2.c.d.439.1		4	155.74	odd	30
961.2.c.d.521.1		4	155.114	odd	30
961.2.c.f.439.1		4	155.19	even	30
961.2.c.f.521.1		4	155.134	even	30
961.2.d.b.531.1		4	155.89	odd	10
961.2.d.b.628.1		4	155.154	odd	2
961.2.d.e.374.1		4	155.139	odd	10
961.2.d.e.388.1		4	155.54	odd	10
961.2.d.f.374.1		4	155.109	even	10
961.2.d.f.388.1		4	155.39	even	10
961.2.g.b.448.1		8	155.129	even	6
961.2.g.b.547.1		8	155.69	even	30
961.2.g.b.844.1		8	155.144	even	30
961.2.g.b.846.1		8	155.149	even	6
961.2.g.c.448.1		8	155.119	odd	6
961.2.g.c.547.1		8	155.24	odd	30
961.2.g.c.844.1		8	155.104	odd	30
961.2.g.c.846.1		8	155.99	odd	6
961.2.g.f.235.1		8	155.14	even	30
961.2.g.f.338.1		8	155.9	even	30
961.2.g.f.732.1		8	155.49	even	30
961.2.g.f.816.1		8	155.59	even	30
961.2.g.g.235.1		8	155.79	odd	30
961.2.g.g.338.1		8	155.84	odd	30
961.2.g.g.732.1		8	155.44	odd	30
961.2.g.g.816.1		8	155.34	odd	30
8649.2.a.f.1.2		2	465.29	even	10
8649.2.a.g.1.2		2	465.374	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.190983 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.30902 + 0.951057i) q^{4} +0.618034 q^{6} +(2.42705 + 1.76336i) q^{7} +(1.80902 - 1.31433i) q^{8} +(1.61803 - 1.17557i) q^{9} +(0.618034 + 0.449028i) q^{11} +(-0.500000 + 1.53884i) q^{12} +(-1.50000 - 4.61653i) q^{13} +(1.50000 - 1.08981i) q^{14} +(0.572949 + 1.76336i) q^{16} +(0.190983 - 0.138757i) q^{17} +(-0.381966 - 1.17557i) q^{18} +(1.54508 - 4.75528i) q^{19} +(-0.927051 + 2.85317i) q^{21} +(0.381966 - 0.277515i) q^{22} +(-4.42705 + 3.21644i) q^{23} +(1.80902 + 1.31433i) q^{24} -3.00000 q^{26} +(4.04508 + 2.93893i) q^{27} +(1.50000 + 4.61653i) q^{28} +(-2.66312 + 8.19624i) q^{29} +(-5.54508 - 0.502029i) q^{31} +5.61803 q^{32} +(-0.236068 + 0.726543i) q^{33} +(-0.0450850 - 0.138757i) q^{34} +3.23607 q^{36} -0.236068 q^{37} +(-2.50000 - 1.81636i) q^{38} +(3.92705 - 2.85317i) q^{39} +(2.00000 - 6.15537i) q^{41} +(1.50000 + 1.08981i) q^{42} +(1.42705 - 4.39201i) q^{43} +(0.381966 + 1.17557i) q^{44} +(1.04508 + 3.21644i) q^{46} +(1.04508 + 3.21644i) q^{47} +(-1.50000 + 1.08981i) q^{48} +(0.618034 + 1.90211i) q^{49} +(0.190983 + 0.138757i) q^{51} +(2.42705 - 7.46969i) q^{52} +(-10.2812 + 7.46969i) q^{53} +(2.50000 - 1.81636i) q^{54} +6.70820 q^{56} +5.00000 q^{57} +(4.30902 + 3.13068i) q^{58} +(2.92705 + 9.00854i) q^{59} -6.94427 q^{61} +(-1.35410 + 3.16344i) q^{62} +6.00000 q^{63} +(-0.0729490 + 0.224514i) q^{64} +(0.381966 + 0.277515i) q^{66} +4.23607 q^{67} +0.381966 q^{68} +(-4.42705 - 3.21644i) q^{69} +(-0.0729490 + 0.0530006i) q^{71} +(1.38197 - 4.25325i) q^{72} +(-6.92705 - 5.03280i) q^{73} +(-0.0450850 + 0.138757i) q^{74} +(6.54508 - 4.75528i) q^{76} +(0.708204 + 2.17963i) q^{77} +(-0.927051 - 2.85317i) q^{78} +(0.309017 - 0.951057i) q^{81} +(-3.23607 - 2.35114i) q^{82} +(1.26393 - 3.88998i) q^{83} +(-3.92705 + 2.85317i) q^{84} +(-2.30902 - 1.67760i) q^{86} -8.61803 q^{87} +1.70820 q^{88} +(5.16312 + 3.75123i) q^{89} +(4.50000 - 13.8496i) q^{91} -8.85410 q^{92} +(-1.23607 - 5.42882i) q^{93} +2.09017 q^{94} +(1.73607 + 5.34307i) q^{96} +(-4.28115 - 3.11044i) q^{97} +1.23607 q^{98} +1.52786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - q^{3} + 3 q^{4} - 2 q^{6} + 3 q^{7} + 5 q^{8} + 2 q^{9} - 2 q^{11} - 2 q^{12} - 6 q^{13} + 6 q^{14} + 9 q^{16} + 3 q^{17} - 6 q^{18} - 5 q^{19} + 3 q^{21} + 6 q^{22} - 11 q^{23} + 5 q^{24}+ \cdots + 24 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - q^3 + 3 * q^4 - 2 * q^6 + 3 * q^7 + 5 * q^8 + 2 * q^9 - 2 * q^11 - 2 * q^12 - 6 * q^13 + 6 * q^14 + 9 * q^16 + 3 * q^17 - 6 * q^18 - 5 * q^19 + 3 * q^21 + 6 * q^22 - 11 * q^23 + 5 * q^24 - 12 * q^26 + 5 * q^27 + 6 * q^28 + 5 * q^29 - 11 * q^31 + 18 * q^32 + 8 * q^33 + 11 * q^34 + 4 * q^36 + 8 * q^37 - 10 * q^38 + 9 * q^39 + 8 * q^41 + 6 * q^42 - q^43 + 6 * q^44 - 7 * q^46 - 7 * q^47 - 6 * q^48 - 2 * q^49 + 3 * q^51 + 3 * q^52 - 21 * q^53 + 10 * q^54 + 20 * q^57 + 15 * q^58 + 5 * q^59 + 8 * q^61 + 8 * q^62 + 24 * q^63 - 7 * q^64 + 6 * q^66 + 8 * q^67 + 6 * q^68 - 11 * q^69 - 7 * q^71 + 10 * q^72 - 21 * q^73 + 11 * q^74 + 15 * q^76 - 24 * q^77 + 3 * q^78 - q^81 - 4 * q^82 + 14 * q^83 - 9 * q^84 - 7 * q^86 - 30 * q^87 - 20 * q^88 + 5 * q^89 + 18 * q^91 - 22 * q^92 + 4 * q^93 - 14 * q^94 - 2 * q^96 + 3 * q^97 - 4 * q^98 + 24 * q^99

Introduction

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