LMFDB - Embedded newform 775.2.bf.a.624.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(349,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 4]))

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

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

chi := DirichletCharacter("775.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.bf (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:	$6.18840615665$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			624.1
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	775.624
Dual form			775.2.bf.a.349.1

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

Character values

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

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$

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 $

$2$	−0.587785	+	0.190983i	−0.415627	+	0.135045i	−0.509363	−	0.860552i	$-0.670119\pi$
$2$	−0.587785	+	0.190983i	−0.415627	+	0.135045i	0.0937362	+	0.995597i	$0.470119\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i	0.0213149	−	0.999773i	$-0.493215\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i	−0.570408	+	0.821362i	$0.693215\pi$
$4$	−1.30902	+	0.951057i	−0.654508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	0.618034			0.252311
$7$	1.76336	+	2.42705i	0.666486	+	0.917339i	0.999674	−	0.0255212i	$-0.00812453\pi$
$7$	1.76336	+	2.42705i	0.666486	+	0.917339i	−0.333188	+	0.942860i	$0.608125\pi$
$8$	1.31433	−	1.80902i	0.464685	−	0.639584i
$9$	−1.61803	−	1.17557i	−0.539345	−	0.391857i
$10$		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	$0.263260\pi$
$12$	1.53884	−	0.500000i	0.444225	−	0.144338i
$13$	4.61653	+	1.50000i	1.28039	+	0.416025i	0.868719	−	0.495306i	$-0.164944\pi$
$13$	4.61653	+	1.50000i	1.28039	+	0.416025i	0.411675	+	0.911331i	$0.364944\pi$
$14$	−1.50000	−	1.08981i	−0.400892	−	0.291265i
$15$		0			0
$16$	0.572949	−	1.76336i	0.143237	−	0.440839i
$17$	−0.138757	+	0.190983i	−0.0336536	+	0.0463202i	−0.825512	−	0.564384i	$-0.809114\pi$
$17$	−0.138757	+	0.190983i	−0.0336536	+	0.0463202i	0.791859	+	0.610704i	$0.209114\pi$
$18$	1.17557	+	0.381966i	0.277085	+	0.0900303i
$19$	−1.54508	−	4.75528i	−0.354467	−	1.09094i	−0.956318	−	0.292328i	$-0.905570\pi$
$19$	−1.54508	−	4.75528i	−0.354467	−	1.09094i	0.601851	−	0.798608i	$-0.294430\pi$
$20$		0			0
$21$	−0.927051	−	2.85317i	−0.202299	−	0.622613i
$22$	−0.277515	+	0.381966i	−0.0591663	+	0.0814354i
$23$	−3.21644	+	4.42705i	−0.670674	+	0.923104i	−0.999775	−	0.0211907i	$-0.993254\pi$
$23$	−3.21644	+	4.42705i	−0.670674	+	0.923104i	0.329101	+	0.944295i	$0.393254\pi$
$24$	−1.80902	+	1.31433i	−0.369264	+	0.268286i
$25$		0			0
$26$	−3.00000			−0.588348
$27$	2.93893	+	4.04508i	0.565597	+	0.778477i
$28$	−4.61653	−	1.50000i	−0.872441	−	0.283473i
$29$	2.66312	+	8.19624i	0.494529	+	1.52200i	0.817690	+	0.575659i	$0.195254\pi$
$29$	2.66312	+	8.19624i	0.494529	+	1.52200i	−0.323161	+	0.946344i	$0.604746\pi$
$30$		0			0
$31$	−5.54508	+	0.502029i	−0.995927	+	0.0901670i
$31$	−5.54508	+	0.502029i	−0.995927	+	0.0901670i
$32$			5.61803i			0.993137i
$33$	−0.726543	+	0.236068i	−0.126475	+	0.0410942i
$34$	0.0450850	−	0.138757i	0.00773201	−	0.0237967i
$35$		0			0
$36$	3.23607			0.539345
$37$		−	0.236068i		−	0.0388093i	−0.999812	−	0.0194047i	$-0.993823\pi$
$37$		−	0.236068i		−	0.0388093i	0.999812	−	0.0194047i	$-0.00617709\pi$
$38$	1.81636	+	2.50000i	0.294652	+	0.405554i
$39$	−3.92705	−	2.85317i	−0.628831	−	0.456873i
$40$		0			0
$41$	2.00000	+	6.15537i	0.312348	+	0.961307i	0.976833	+	0.214005i	$0.0686510\pi$
$41$	2.00000	+	6.15537i	0.312348	+	0.961307i	−0.664485	+	0.747302i	$0.731349\pi$
$42$	1.08981	+	1.50000i	0.168162	+	0.231455i
$43$	4.39201	−	1.42705i	0.669775	−	0.217623i	0.0456620	−	0.998957i	$-0.485460\pi$
$43$	4.39201	−	1.42705i	0.669775	−	0.217623i	0.624113	+	0.781334i	$0.285460\pi$
$44$	−0.381966	+	1.17557i	−0.0575835	+	0.177224i
$45$		0			0
$46$	1.04508	−	3.21644i	0.154089	−	0.474238i
$47$	3.21644	+	1.04508i	0.469166	+	0.152441i	0.534052	−	0.845451i	$-0.320668\pi$
$47$	3.21644	+	1.04508i	0.469166	+	0.152441i	−0.0648863	+	0.997893i	$0.520668\pi$
$48$	−1.08981	+	1.50000i	−0.157301	+	0.216506i
$49$	−0.618034	+	1.90211i	−0.0882906	+	0.271730i
$50$		0			0
$51$	0.190983	−	0.138757i	0.0267430	−	0.0194299i
$52$	−7.46969	+	2.42705i	−1.03586	+	0.336571i
$53$	−7.46969	+	10.2812i	−1.02604	+	1.41222i	−0.118162	+	0.992994i	$0.537700\pi$
$53$	−7.46969	+	10.2812i	−1.02604	+	1.41222i	−0.907880	+	0.419231i	$0.862300\pi$
$54$	−2.50000	−	1.81636i	−0.340207	−	0.247175i
$55$		0			0
$56$	6.70820			0.896421
$57$			5.00000i			0.662266i
$58$	−3.13068	−	4.30902i	−0.411079	−	0.565802i
$59$	−2.92705	+	9.00854i	−0.381070	+	1.17281i	0.558222	+	0.829692i	$0.311484\pi$
$59$	−2.92705	+	9.00854i	−0.381070	+	1.17281i	−0.939292	+	0.343120i	$0.888516\pi$
$60$		0			0
$61$	−6.94427			−0.889123			−0.444561	−	0.895748i	$-0.646640\pi$
$61$	−6.94427			−0.889123			−0.444561	+	0.895748i	$0.646640\pi$
$62$	3.16344	−	1.35410i	0.401757	−	0.171971i
$63$		−	6.00000i		−	0.755929i
$64$	0.0729490	+	0.224514i	0.00911863	+	0.0280642i
$65$		0			0
$66$	0.381966	−	0.277515i	0.0470168	−	0.0341597i
$67$			4.23607i			0.517518i	0.965942	+	0.258759i	$0.0833136\pi$
$67$			4.23607i			0.517518i	−0.965942	+	0.258759i	$0.916686\pi$
$68$		−	0.381966i		−	0.0463202i
$69$	4.42705	−	3.21644i	0.532954	−	0.387214i
$70$		0			0
$71$	−0.0729490	−	0.0530006i	−0.00865746	−	0.00629001i	0.583448	−	0.812150i	$-0.301703\pi$
$71$	−0.0729490	−	0.0530006i	−0.00865746	−	0.00629001i	−0.592106	+	0.805860i	$0.701703\pi$
$72$	−4.25325	+	1.38197i	−0.501251	+	0.162866i
$73$	5.03280	+	6.92705i	0.589044	+	0.810750i	0.994650	−	0.103298i	$-0.0329395\pi$
$73$	5.03280	+	6.92705i	0.589044	+	0.810750i	−0.405606	+	0.914048i	$0.632940\pi$
$74$	0.0450850	+	0.138757i	0.00524102	+	0.0161302i
$75$		0			0
$76$	6.54508	+	4.75528i	0.750773	+	0.545468i
$77$	2.17963	+	0.708204i	0.248392	+	0.0807073i
$78$	2.85317	+	0.927051i	0.323058	+	0.104968i
$79$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$79$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−2.35114	−	3.23607i	−0.259640	−	0.357364i
$83$	3.88998	−	1.26393i	0.426981	−	0.138735i	−0.0876401	−	0.996152i	$-0.527933\pi$
$83$	3.88998	−	1.26393i	0.426981	−	0.138735i	0.514621	+	0.857418i	$0.327933\pi$
$84$	3.92705	+	2.85317i	0.428476	+	0.311306i
$85$		0			0
$86$	−2.30902	+	1.67760i	−0.248988	+	0.180900i
$87$		−	8.61803i		−	0.923950i
$88$		−	1.70820i		−	0.182095i
$89$	−5.16312	+	3.75123i	−0.547290	+	0.397629i	−0.826785	−	0.562518i	$-0.809833\pi$
$89$	−5.16312	+	3.75123i	−0.547290	+	0.397629i	0.279496	+	0.960147i	$0.409833\pi$
$90$		0			0
$91$	4.50000	+	13.8496i	0.471728	+	1.45183i
$92$		−	8.85410i		−	0.923104i
$93$	5.42882	+	1.23607i	0.562943	+	0.128174i
$94$	−2.09017			−0.215585
$95$		0			0
$96$	1.73607	−	5.34307i	0.177187	−	0.545325i
$97$	−3.11044	−	4.28115i	−0.315817	−	0.434685i	0.621367	−	0.783520i	$-0.286578\pi$
$97$	−3.11044	−	4.28115i	−0.315817	−	0.434685i	−0.937184	+	0.348834i	$0.886578\pi$
$98$		−	1.23607i		−	0.124862i
$99$	−1.52786			−0.153556
$100$		0			0
$101$	−3.85410	−	2.80017i	−0.383497	−	0.278627i	0.379288	−	0.925279i	$-0.376169\pi$
$101$	−3.85410	−	2.80017i	−0.383497	−	0.278627i	−0.762786	+	0.646651i	$0.776169\pi$
$102$	−0.0857567	+	0.118034i	−0.00849118	+	0.0116871i
$103$	0.138757	−	0.0450850i	0.0136722	−	0.00444235i	−0.302173	−	0.953253i	$-0.597712\pi$
$103$	0.138757	−	0.0450850i	0.0136722	−	0.00444235i	0.315845	+	0.948811i	$0.397712\pi$
$104$	8.78115	−	6.37988i	0.861063	−	0.625599i
$105$		0			0
$106$	2.42705	−	7.46969i	0.235736	−	0.725521i
$107$	−0.640786	+	0.881966i	−0.0619471	+	0.0852629i	−0.838867	−	0.544337i	$-0.816781\pi$
$107$	−0.640786	+	0.881966i	−0.0619471	+	0.0852629i	0.776919	+	0.629600i	$0.216781\pi$
$108$	−7.69421	−	2.50000i	−0.740376	−	0.240563i
$109$	2.60081	−	8.00448i	0.249113	−	0.766690i	−0.745820	−	0.666147i	$-0.767942\pi$
$109$	2.60081	−	8.00448i	0.249113	−	0.766690i	0.994933	−	0.100543i	$-0.0320579\pi$
$110$		0			0
$111$	−0.0729490	+	0.224514i	−0.00692401	+	0.0213099i
$112$	5.29007	−	1.71885i	0.499864	−	0.162416i
$113$	1.08981	+	1.50000i	0.102521	+	0.141108i	0.857195	−	0.514992i	$-0.172205\pi$
$113$	1.08981	+	1.50000i	0.102521	+	0.141108i	−0.754674	+	0.656100i	$0.772205\pi$
$114$	−0.954915	−	2.93893i	−0.0894360	−	0.275256i
$115$		0			0
$116$	−11.2812	−	8.19624i	−1.04743	−	0.761002i
$117$	−5.70634	−	7.85410i	−0.527551	−	0.726112i
$118$		−	5.85410i		−	0.538914i
$119$	−0.708204			−0.0649209
$120$		0			0
$121$	−3.21885	+	9.90659i	−0.292622	+	0.900599i
$122$	4.08174	−	1.32624i	0.369543	−	0.120072i
$123$		−	6.47214i		−	0.583573i
$124$	6.78115	−	5.93085i	0.608966	−	0.532606i
$125$		0			0
$126$	1.14590	+	3.52671i	0.102085	+	0.314184i
$127$	−9.73508	−	3.16312i	−0.863849	−	0.280681i	−0.156614	−	0.987660i	$-0.550058\pi$
$127$	−9.73508	−	3.16312i	−0.863849	−	0.280681i	−0.707235	+	0.706979i	$0.750058\pi$
$128$	−6.69015	−	9.20820i	−0.591331	−	0.813898i
$129$	−4.61803			−0.406595
$130$		0			0
$131$	−0.0729490	+	0.0530006i	−0.00637359	+	0.00463068i	−0.590967	−	0.806695i	$-0.701254\pi$
$131$	−0.0729490	+	0.0530006i	−0.00637359	+	0.00463068i	0.584594	+	0.811326i	$0.301254\pi$
$132$	0.726543	−	1.00000i	0.0632374	−	0.0870388i
$133$	8.81678	−	12.1353i	0.764512	−	1.05226i
$134$	−0.809017	−	2.48990i	−0.0698884	−	0.215094i
$135$		0			0
$136$	0.163119	+	0.502029i	0.0139873	+	0.0430486i
$137$	6.15537	+	2.00000i	0.525888	+	0.170872i	0.559916	−	0.828549i	$-0.310833\pi$
$137$	6.15537	+	2.00000i	0.525888	+	0.170872i	−0.0340275	+	0.999421i	$0.510833\pi$
$138$	−1.98787	+	2.73607i	−0.169219	+	0.232910i
$139$	−1.80902	+	5.56758i	−0.153439	+	0.472236i	−0.997999	−	0.0632239i	$-0.979862\pi$
$139$	−1.80902	+	5.56758i	−0.153439	+	0.472236i	0.844561	+	0.535460i	$0.179862\pi$
$140$		0			0
$141$	−2.73607	−	1.98787i	−0.230418	−	0.167409i
$142$	0.0530006	+	0.0172209i	0.00444771	+	0.00144515i
$143$	3.52671	−	1.14590i	0.294918	−	0.0958248i
$144$	−3.00000	+	2.17963i	−0.250000	+	0.181636i
$145$		0			0
$146$	−4.28115	−	3.11044i	−0.354311	−	0.257422i
$147$	1.17557	−	1.61803i	0.0969594	−	0.133453i
$148$	0.224514	+	0.309017i	0.0184549	+	0.0254010i
$149$	17.0344			1.39552			0.697758	−	0.716334i	$-0.254181\pi$
$149$	17.0344			1.39552			0.697758	+	0.716334i	$0.254181\pi$
$150$		0			0
$151$	15.7812	−	11.4657i	1.28425	−	0.933064i	0.284579	−	0.958652i	$-0.408146\pi$
$151$	15.7812	−	11.4657i	1.28425	−	0.933064i	0.999673	+	0.0255888i	$0.00814604\pi$
$152$	−10.6331	−	3.45492i	−0.862461	−	0.280231i
$153$	0.449028	−	0.145898i	0.0363018	−	0.0117952i
$154$	−1.41641			−0.114137
$155$		0			0
$156$	7.85410			0.628831
$157$	9.23305	−	3.00000i	0.736878	−	0.239426i	0.0835524	−	0.996503i	$-0.473373\pi$
$157$	9.23305	−	3.00000i	0.736878	−	0.239426i	0.653325	+	0.757077i	$0.273373\pi$
$158$		0			0
$159$	10.2812	−	7.46969i	0.815348	−	0.592385i
$160$		0			0
$161$	−16.4164			−1.29379
$162$	−0.363271	−	0.500000i	−0.0285413	−	0.0392837i
$163$	−7.46969	+	10.2812i	−0.585072	+	0.805282i	−0.994240	−	0.107177i	$-0.965819\pi$
$163$	−7.46969	+	10.2812i	−0.585072	+	0.805282i	0.409168	+	0.912459i	$0.365819\pi$
$164$	−8.47214	−	6.15537i	−0.661563	−	0.480653i
$165$		0			0
$166$	−2.04508	+	1.48584i	−0.158729	+	0.115324i
$167$	−8.78402	+	2.85410i	−0.679728	+	0.220857i	−0.628476	−	0.777829i	$-0.716321\pi$
$167$	−8.78402	+	2.85410i	−0.679728	+	0.220857i	−0.0512518	+	0.998686i	$0.516321\pi$
$168$	−6.37988	−	2.07295i	−0.492219	−	0.159931i
$169$	8.54508	+	6.20837i	0.657314	+	0.477567i
$170$		0			0
$171$	−3.09017	+	9.51057i	−0.236311	+	0.727291i
$172$	−4.39201	+	6.04508i	−0.334888	+	0.460933i
$173$	0.865300	+	0.281153i	0.0657875	+	0.0213757i	0.341726	−	0.939800i	$-0.388989\pi$
$173$	0.865300	+	0.281153i	0.0657875	+	0.0213757i	−0.275938	+	0.961175i	$0.588989\pi$
$174$	1.64590	+	5.06555i	0.124775	+	0.384019i
$175$		0			0
$176$	−0.437694	−	1.34708i	−0.0329924	−	0.101540i
$177$	5.56758	−	7.66312i	0.418485	−	0.575995i
$178$	2.31838	−	3.19098i	0.173770	−	0.239174i
$179$	16.0172	−	11.6372i	1.19718	−	0.869805i	0.203179	−	0.979142i	$-0.434873\pi$
$179$	16.0172	−	11.6372i	1.19718	−	0.869805i	0.994005	+	0.109337i	$0.0348728\pi$
$180$		0			0
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$	−5.29007	−	7.28115i	−0.392126	−	0.539715i
$183$	6.60440	+	2.14590i	0.488211	+	0.158629i
$184$	3.78115	+	11.6372i	0.278750	+	0.857905i
$185$		0			0
$186$	−3.42705	+	0.310271i	−0.251284	+	0.0227502i
$187$			0.180340i			0.0131878i
$188$	−5.20431	+	1.69098i	−0.379563	+	0.123328i
$189$	−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	$0.697777\pi$
$192$		−	0.236068i		−	0.0170367i
$193$	1.40008	+	1.92705i	0.100780	+	0.138712i	0.856429	−	0.516265i	$-0.172678\pi$
$193$	1.40008	+	1.92705i	0.100780	+	0.138712i	−0.755648	+	0.654977i	$0.772678\pi$
$194$	2.64590	+	1.92236i	0.189964	+	0.138017i
$195$		0			0
$196$	−1.00000	−	3.07768i	−0.0714286	−	0.219835i
$197$	9.64932	+	13.2812i	0.687486	+	0.946243i	0.999993	−	0.00367232i	$-0.00116894\pi$
$197$	9.64932	+	13.2812i	0.687486	+	0.946243i	−0.312507	+	0.949915i	$0.601169\pi$
$198$	0.898056	−	0.291796i	0.0638221	−	0.0207370i
$199$	8.25329	−	25.4010i	0.585060	−	1.80063i	−0.0139686	−	0.999902i	$-0.504446\pi$
$199$	8.25329	−	25.4010i	0.585060	−	1.80063i	0.599029	−	0.800728i	$-0.295554\pi$
$200$		0			0
$201$	1.30902	−	4.02874i	0.0923309	−	0.284165i
$202$	2.80017	+	0.909830i	0.197019	+	0.0640154i
$203$	−15.1967	+	20.9164i	−1.06660	+	1.46804i
$204$	−0.118034	+	0.363271i	−0.00826403	+	0.0254341i
$205$		0			0
$206$	−0.0729490	+	0.0530006i	−0.00508260	+	0.00369272i
$207$	10.4086	−	3.38197i	0.723449	−	0.235063i
$208$	5.29007	−	7.28115i	0.366800	−	0.504857i
$209$	−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	$0.588801\pi$
$212$		−	20.5623i		−	1.41222i
$213$	0.0530006	+	0.0729490i	0.00363154	+	0.00499838i
$214$	0.208204	−	0.640786i	0.0142325	−	0.0438032i
$215$		0			0
$216$	11.1803			0.760726
$217$	−10.9964	−	12.5729i	−0.746485	−	0.853507i
$218$			5.20163i			0.352299i
$219$	−2.64590	−	8.14324i	−0.178793	−	0.550269i
$220$		0			0
$221$	−0.927051	+	0.673542i	−0.0623602	+	0.0453073i
$222$		−	0.145898i		−	0.00979203i
$223$			0.708204i			0.0474248i	0.999719	+	0.0237124i	$0.00754861\pi$
$223$			0.708204i			0.0474248i	−0.999719	+	0.0237124i	$0.992451\pi$
$224$	−13.6353	+	9.90659i	−0.911044	+	0.661912i
$225$		0			0
$226$	−0.927051	−	0.673542i	−0.0616665	−	0.0448033i
$227$	−19.7274	+	6.40983i	−1.30936	+	0.425435i	−0.878827	−	0.477141i	$-0.841673\pi$
$227$	−19.7274	+	6.40983i	−1.30936	+	0.425435i	−0.430529	+	0.902577i	$0.641673\pi$
$228$	−4.75528	−	6.54508i	−0.314926	−	0.433459i
$229$	2.23607	+	6.88191i	0.147764	+	0.454769i	0.997356	−	0.0726703i	$-0.0231521\pi$
$229$	2.23607	+	6.88191i	0.147764	+	0.454769i	−0.849592	+	0.527440i	$0.823152\pi$
$230$		0			0
$231$	−1.85410	−	1.34708i	−0.121991	−	0.0886316i
$232$	18.3273	+	5.95492i	1.20325	+	0.390959i
$233$	17.8783	+	5.80902i	1.17125	+	0.380561i	0.829108	−	0.559088i	$-0.188849\pi$
$233$	17.8783	+	5.80902i	1.17125	+	0.380561i	0.342139	+	0.939649i	$0.388849\pi$
$234$	4.85410	+	3.52671i	0.317323	+	0.230548i
$235$		0			0
$236$	−4.73607	−	14.5761i	−0.308292	−	0.948824i
$237$		0			0
$238$	0.416272	−	0.135255i	0.0269829	−	0.00876727i
$239$	−10.8541	−	7.88597i	−0.702093	−	0.510101i	0.178520	−	0.983936i	$-0.442869\pi$
$239$	−10.8541	−	7.88597i	−0.702093	−	0.510101i	−0.880613	+	0.473836i	$0.842869\pi$
$240$		0			0
$241$	6.89919	−	5.01255i	0.444416	−	0.322887i	−0.342971	−	0.939346i	$-0.611433\pi$
$241$	6.89919	−	5.01255i	0.444416	−	0.322887i	0.787387	+	0.616459i	$0.211433\pi$
$242$		−	6.43769i		−	0.413831i
$243$		−	16.0000i		−	1.02640i
$244$	9.09017	−	6.60440i	0.581938	−	0.422803i
$245$		0			0
$246$	1.23607	+	3.80423i	0.0788088	+	0.242549i
$247$		−	24.2705i		−	1.54430i
$248$	−6.37988	+	10.6910i	−0.405123	+	0.678878i
$249$	−4.09017			−0.259204
$250$		0			0
$251$	0.291796	−	0.898056i	0.0184180	−	0.0566848i	−0.941425	−	0.337222i	$-0.890513\pi$
$251$	0.291796	−	0.898056i	0.0184180	−	0.0566848i	0.959843	+	0.280537i	$0.0905127\pi$
$252$	5.70634	+	7.85410i	0.359466	+	0.494762i
$253$			4.18034i			0.262816i
$254$	6.32624			0.396943
$255$		0			0
$256$	5.30902	+	3.85723i	0.331814	+	0.241077i
$257$	−0.832544	+	1.14590i	−0.0519326	+	0.0714792i	−0.834194	−	0.551472i	$-0.814066\pi$
$257$	−0.832544	+	1.14590i	−0.0519326	+	0.0714792i	0.782261	+	0.622951i	$0.214066\pi$
$258$	2.71441	−	0.881966i	0.168992	−	0.0549088i
$259$	0.572949	−	0.416272i	0.0356013	−	0.0258659i
$260$		0			0
$261$	5.32624	−	16.3925i	0.329686	−	1.01467i
$262$	0.0327561	−	0.0450850i	0.00202368	−	0.00278536i
$263$	−10.2699	−	3.33688i	−0.633267	−	0.205761i	−0.0252452	−	0.999681i	$-0.508037\pi$
$263$	−10.2699	−	3.33688i	−0.633267	−	0.205761i	−0.608022	+	0.793920i	$0.708037\pi$
$264$	−0.527864	+	1.62460i	−0.0324878	+	0.0999871i
$265$		0			0
$266$	−2.86475	+	8.81678i	−0.175649	+	0.540591i
$267$	6.06961	−	1.97214i	0.371454	−	0.120693i
$268$	−4.02874	−	5.54508i	−0.246094	−	0.338720i
$269$	0.427051	+	1.31433i	0.0260378	+	0.0801360i	0.963231	−	0.268675i	$-0.0865856\pi$
$269$	0.427051	+	1.31433i	0.0260378	+	0.0801360i	−0.937193	+	0.348811i	$0.886586\pi$
$270$		0			0
$271$	−7.73607	−	5.62058i	−0.469933	−	0.341426i	0.327482	−	0.944857i	$-0.393800\pi$
$271$	−7.73607	−	5.62058i	−0.469933	−	0.341426i	−0.797415	+	0.603431i	$0.793800\pi$
$272$	0.257270	+	0.354102i	0.0155993	+	0.0214706i
$273$		−	14.5623i		−	0.881351i
$274$	−4.00000			−0.241649
$275$		0			0
$276$	−2.73607	+	8.42075i	−0.164692	+	0.506870i
$277$	12.6740	−	4.11803i	0.761507	−	0.247429i	0.0975818	−	0.995228i	$-0.468889\pi$
$277$	12.6740	−	4.11803i	0.761507	−	0.247429i	0.663925	+	0.747799i	$0.268889\pi$
$278$		−	3.61803i		−	0.216995i
$279$	9.56231	+	5.70634i	0.572480	+	0.341630i
$280$		0			0
$281$	5.88197	+	18.1028i	0.350889	+	1.07992i	0.958355	+	0.285579i	$0.0921859\pi$
$281$	5.88197	+	18.1028i	0.350889	+	1.07992i	−0.607466	+	0.794345i	$0.707814\pi$
$282$	1.98787	+	0.645898i	0.118376	+	0.0384627i
$283$	−3.85723	−	5.30902i	−0.229288	−	0.315588i	0.678835	−	0.734291i	$-0.262485\pi$
$283$	−3.85723	−	5.30902i	−0.229288	−	0.315588i	−0.908124	+	0.418702i	$0.862485\pi$
$284$	0.145898			0.00865746
$285$		0			0
$286$	−1.85410	+	1.34708i	−0.109635	+	0.0796547i
$287$	−11.4127	+	15.7082i	−0.673669	+	0.927226i
$288$	6.60440	−	9.09017i	0.389168	−	0.535643i
$289$	5.23607	+	16.1150i	0.308004	+	0.947939i
$290$		0			0
$291$	1.63525	+	5.03280i	0.0958603	+	0.295028i
$292$	−13.1760	−	4.28115i	−0.771069	−	0.250536i
$293$	−4.84104	+	6.66312i	−0.282817	+	0.389264i	−0.926664	−	0.375890i	$-0.877337\pi$
$293$	−4.84104	+	6.66312i	−0.282817	+	0.389264i	0.643848	+	0.765154i	$0.277337\pi$
$294$	−0.381966	+	1.17557i	−0.0222767	+	0.0685607i
$295$		0			0
$296$	−0.427051	−	0.310271i	−0.0248218	−	0.0180341i
$297$	3.63271	+	1.18034i	0.210791	+	0.0684903i
$298$	−10.0126	+	3.25329i	−0.580014	+	0.188458i
$299$	−21.4894	+	15.6129i	−1.24276	+	0.902919i
$300$		0			0
$301$	11.2082	+	8.14324i	0.646030	+	0.469368i
$302$	−7.08618	+	9.75329i	−0.407764	+	0.561239i
$303$	2.80017	+	3.85410i	0.160866	+	0.221412i
$304$	−9.27051			−0.531700
$305$		0			0
$306$	−0.236068	+	0.171513i	−0.0134951	+	0.00980477i
$307$	−5.79210	−	1.88197i	−0.330572	−	0.107409i	0.139028	−	0.990288i	$-0.455602\pi$
$307$	−5.79210	−	1.88197i	−0.330572	−	0.107409i	−0.469601	+	0.882879i	$0.655602\pi$
$308$	−3.52671	+	1.14590i	−0.200953	+	0.0652936i
$309$	−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	$0.345326\pi$
$312$	−10.3229	+	3.35410i	−0.584417	+	0.189889i
$313$	1.17557	+	0.381966i	0.0664472	+	0.0215900i	0.342052	−	0.939681i	$-0.388878\pi$
$313$	1.17557	+	0.381966i	0.0664472	+	0.0215900i	−0.275605	+	0.961271i	$0.588878\pi$
$314$	−4.85410	+	3.52671i	−0.273933	+	0.199024i
$315$		0			0
$316$		0			0
$317$	15.2169	+	20.9443i	0.854666	+	1.17635i	0.982815	+	0.184593i	$0.0590965\pi$
$317$	15.2169	+	20.9443i	0.854666	+	1.17635i	−0.128149	+	0.991755i	$0.540903\pi$
$318$	−4.61653	+	6.35410i	−0.258882	+	0.356320i
$319$	5.32624	+	3.86974i	0.298212	+	0.216664i
$320$		0			0
$321$	0.881966	−	0.640786i	0.0492265	−	0.0357652i
$322$	9.64932	−	3.13525i	0.537736	−	0.174721i
$323$	1.12257	+	0.364745i	0.0624615	+	0.0202950i
$324$	−1.30902	−	0.951057i	−0.0727232	−	0.0528365i
$325$		0			0
$326$	2.42705	−	7.46969i	0.134422	−	0.413708i
$327$	−4.94704	+	6.80902i	−0.273572	+	0.376540i
$328$	13.7638	+	4.47214i	0.759980	+	0.246932i
$329$	3.13525	+	9.64932i	0.172852	+	0.531984i
$330$		0			0
$331$	3.48278	+	10.7189i	0.191431	+	0.589164i	1.00000		0.000762014i	$0.000242557\pi$
$331$	3.48278	+	10.7189i	0.191431	+	0.589164i	−0.808569	+	0.588402i	$0.799757\pi$
$332$	−3.88998	+	5.35410i	−0.213491	+	0.293845i
$333$	−0.277515	+	0.381966i	−0.0152077	+	0.0209316i
$334$	4.61803	−	3.35520i	0.252688	−	0.183588i
$335$		0			0
$336$	−5.56231			−0.303449
$337$	11.1554	+	15.3541i	0.607674	+	0.836391i	0.996384	−	0.0849690i	$-0.0270791\pi$
$337$	11.1554	+	15.3541i	0.607674	+	0.836391i	−0.388710	+	0.921360i	$0.627079\pi$
$338$	−6.20837	−	2.01722i	−0.337691	−	0.109722i
$339$	−0.572949	−	1.76336i	−0.0311183	−	0.0957723i
$340$		0			0
$341$	−3.20163	+	2.80017i	−0.173378	+	0.151638i
$342$		−	6.18034i		−	0.334195i
$343$	14.2658	−	4.63525i	0.770283	−	0.250280i
$344$	3.19098	−	9.82084i	0.172046	−	0.529504i
$345$		0			0
$346$	−0.562306			−0.0302298
$347$		−	8.12461i		−	0.436152i	−0.975932	−	0.218076i	$-0.930022\pi$
$347$		−	8.12461i		−	0.436152i	0.975932	−	0.218076i	$-0.0699781\pi$
$348$	8.19624	+	11.2812i	0.439364	+	0.604733i
$349$	−13.5172	−	9.82084i	−0.723560	−	0.525697i	0.163959	−	0.986467i	$-0.447573\pi$
$349$	−13.5172	−	9.82084i	−0.723560	−	0.525697i	−0.887520	+	0.460770i	$0.847573\pi$
$350$		0			0
$351$	7.50000	+	23.0826i	0.400320	+	1.23206i
$352$	2.52265	+	3.47214i	0.134458	+	0.185065i
$353$	30.7971	−	10.0066i	1.63916	−	0.532596i	0.662812	−	0.748786i	$-0.269363\pi$
$353$	30.7971	−	10.0066i	1.63916	−	0.532596i	0.976351	+	0.216190i	$0.0693630\pi$
$354$	−1.80902	+	5.56758i	−0.0961482	+	0.295914i
$355$		0			0
$356$	3.19098	−	9.82084i	0.169122	−	0.520503i
$357$	0.673542	+	0.218847i	0.0356476	+	0.0115826i
$358$	−7.19218	+	9.89919i	−0.380119	+	0.523188i
$359$	7.82624	−	24.0867i	0.413053	−	1.27125i	−0.500928	−	0.865489i	$-0.667008\pi$
$359$	7.82624	−	24.0867i	0.413053	−	1.27125i	0.913981	−	0.405757i	$-0.132992\pi$
$360$		0			0
$361$	−4.85410	+	3.52671i	−0.255479	+	0.185616i
$362$	−9.99235	+	3.24671i	−0.525186	+	0.170643i
$363$	6.12261	−	8.42705i	0.321354	−	0.442305i
$364$	−19.0623	−	13.8496i	−0.999136	−	0.725915i
$365$		0			0
$366$	−4.29180			−0.224336
$367$			36.2705i			1.89331i	0.322256	+	0.946653i	$0.395559\pi$
$367$			36.2705i			1.89331i	−0.322256	+	0.946653i	$0.604441\pi$
$368$	5.96361	+	8.20820i	0.310875	+	0.427882i
$369$	4.00000	−	12.3107i	0.208232	−	0.640871i
$370$		0			0
$371$	−38.1246			−1.97933
$372$	−8.28199	+	3.54508i	−0.429401	+	0.183804i
$373$		−	0.347524i		−	0.0179941i	−0.999960	−	0.00899706i	$-0.997136\pi$
$373$		−	0.347524i		−	0.0179941i	0.999960	−	0.00899706i	$-0.00286389\pi$
$374$	−0.0344419	−	0.106001i	−0.00178095	−	0.00548119i
$375$		0			0
$376$	6.11803	−	4.44501i	0.315514	−	0.229234i
$377$			41.8328i			2.15450i
$378$		−	9.27051i		−	0.476824i
$379$	−14.8992	+	10.8249i	−0.765320	+	0.556037i	−0.900537	−	0.434779i	$-0.856827\pi$
$379$	−14.8992	+	10.8249i	−0.765320	+	0.556037i	0.135218	+	0.990816i	$0.456827\pi$
$380$		0			0
$381$	8.28115	+	6.01661i	0.424256	+	0.308240i
$382$	9.45756	−	3.07295i	0.483891	−	0.157226i
$383$	9.90659	+	13.6353i	0.506203	+	0.696729i	0.983273	−	0.182136i	$-0.0583012\pi$
$383$	9.90659	+	13.6353i	0.506203	+	0.696729i	−0.477070	+	0.878865i	$0.658301\pi$
$384$	3.51722	+	10.8249i	0.179487	+	0.552406i
$385$		0			0
$386$	−1.19098	−	0.865300i	−0.0606194	−	0.0440426i
$387$	−8.78402	−	2.85410i	−0.446517	−	0.145082i
$388$	8.14324	+	2.64590i	0.413410	+	0.134325i
$389$	−23.5172	−	17.0863i	−1.19237	−	0.866308i	−0.198858	−	0.980028i	$-0.563723\pi$
$389$	−23.5172	−	17.0863i	−1.19237	−	0.866308i	−0.993513	+	0.113721i	$0.963723\pi$
$390$		0			0
$391$	−0.399187	−	1.22857i	−0.0201878	−	0.0621315i
$392$	2.62866	+	3.61803i	0.132767	+	0.182738i
$393$	0.0857567	−	0.0278640i	0.00432585	−	0.00140556i
$394$	−8.20820	−	5.96361i	−0.413523	−	0.300442i
$395$		0			0
$396$	2.00000	−	1.45309i	0.100504	−	0.0730203i
$397$		−	16.2918i		−	0.817662i	−0.912610	−	0.408831i	$-0.865937\pi$
$397$		−	16.2918i		−	0.817662i	0.912610	−	0.408831i	$-0.134063\pi$
$398$			16.5066i			0.827400i
$399$	−12.1353	+	8.81678i	−0.607523	+	0.441391i
$400$		0			0
$401$	−9.21885	−	28.3727i	−0.460367	−	1.41686i	−0.864717	−	0.502260i	$-0.832502\pi$
$401$	−9.21885	−	28.3727i	−0.460367	−	1.41686i	0.404349	−	0.914605i	$-0.367498\pi$
$402$			2.61803i			0.130576i
$403$	−26.3521	−	6.00000i	−1.31269	−	0.298881i
$404$	7.70820			0.383497
$405$		0			0
$406$	4.93769	−	15.1967i	0.245054	−	0.754198i
$407$	−0.106001	−	0.145898i	−0.00525428	−	0.00723190i
$408$		−	0.527864i		−	0.0261332i
$409$	6.18034			0.305598			0.152799	−	0.988257i	$-0.451171\pi$
$409$	6.18034			0.305598			0.152799	+	0.988257i	$0.451171\pi$
$410$		0			0
$411$	−5.23607	−	3.80423i	−0.258276	−	0.187649i
$412$	−0.138757	+	0.190983i	−0.00683608	+	0.00940906i
$413$	−27.0256	+	8.78115i	−1.32984	+	0.432092i
$414$	−5.47214	+	3.97574i	−0.268941	+	0.195397i
$415$		0			0
$416$	−8.42705	+	25.9358i	−0.413170	+	1.27161i
$417$	3.44095	−	4.73607i	0.168504	−	0.231926i
$418$	2.24514	+	0.729490i	0.109813	+	0.0356805i
$419$	−1.38197	+	4.25325i	−0.0675135	+	0.207785i	−0.979122	−	0.203275i	$-0.934841\pi$
$419$	−1.38197	+	4.25325i	−0.0675135	+	0.207785i	0.911608	+	0.411060i	$0.134841\pi$
$420$		0			0
$421$	4.56231	−	14.0413i	0.222353	−	0.684333i	−0.776196	−	0.630491i	$-0.782853\pi$
$421$	4.56231	−	14.0413i	0.222353	−	0.684333i	0.998549	−	0.0538414i	$-0.0171466\pi$
$422$	4.70228	−	1.52786i	0.228904	−	0.0743753i
$423$	−3.97574	−	5.47214i	−0.193307	−	0.266064i
$424$	8.78115	+	27.0256i	0.426450	+	1.31248i
$425$		0			0
$426$	−0.0450850	−	0.0327561i	−0.00218437	−	0.00158704i
$427$	−12.2452	−	16.8541i	−0.592588	−	0.815627i
$428$		−	1.76393i		−	0.0852629i
$429$	−3.70820			−0.179034
$430$		0			0
$431$	9.03444	−	27.8052i	0.435174	−	1.33933i	−0.457735	−	0.889089i	$-0.651339\pi$
$431$	9.03444	−	27.8052i	0.435174	−	1.33933i	0.892908	−	0.450238i	$-0.148661\pi$
$432$	8.81678	−	2.86475i	0.424197	−	0.137830i
$433$			0.583592i			0.0280456i	0.999902	+	0.0140228i	$0.00446375\pi$
$433$			0.583592i			0.0280456i	−0.999902	+	0.0140228i	$0.995536\pi$
$434$	8.86475	+	5.29007i	0.425521	+	0.253931i
$435$		0			0
$436$	4.20820	+	12.9515i	0.201536	+	0.620265i
$437$	26.0216	+	8.45492i	1.24478	+	0.404453i
$438$	3.11044	+	4.28115i	0.148623	+	0.204561i
$439$	−41.8328			−1.99657			−0.998286	−	0.0585295i	$-0.981359\pi$
$439$	−41.8328			−1.99657			−0.998286	+	0.0585295i	$0.981359\pi$
$440$		0			0
$441$	3.23607	−	2.35114i	0.154098	−	0.111959i
$442$	0.416272	−	0.572949i	0.0198000	−	0.0272524i
$443$	−24.1724	+	33.2705i	−1.14847	+	1.58073i	−0.401514	+	0.915853i	$0.631516\pi$
$443$	−24.1724	+	33.2705i	−1.14847	+	1.58073i	−0.746953	+	0.664877i	$0.768484\pi$
$444$	−0.118034	−	0.363271i	−0.00560165	−	0.0172401i
$445$		0			0
$446$	−0.135255	−	0.416272i	−0.00640451	−	0.0197110i
$447$	−16.2007	−	5.26393i	−0.766268	−	0.248975i
$448$	−0.416272	+	0.572949i	−0.0196670	+	0.0270693i
$449$	−7.43769	+	22.8909i	−0.351006	+	1.08029i	0.607283	+	0.794486i	$0.292260\pi$
$449$	−7.43769	+	22.8909i	−0.351006	+	1.08029i	−0.958289	+	0.285801i	$0.907740\pi$
$450$		0			0
$451$	4.00000	+	2.90617i	0.188353	+	0.136846i
$452$	−2.85317	−	0.927051i	−0.134202	−	0.0436048i
$453$	−18.5519	+	6.02786i	−0.871642	+	0.283214i
$454$	10.3713	−	7.53521i	0.486750	−	0.353645i
$455$		0			0
$456$	9.04508	+	6.57164i	0.423575	+	0.307745i
$457$	9.25330	−	12.7361i	0.432851	−	0.595768i	−0.535754	−	0.844374i	$-0.679972\pi$
$457$	9.25330	−	12.7361i	0.432851	−	0.595768i	0.968605	+	0.248606i	$0.0799725\pi$
$458$	−2.62866	−	3.61803i	−0.122829	−	0.169060i
$459$	−1.18034			−0.0550935
$460$		0			0
$461$	−8.69098	+	6.31437i	−0.404779	+	0.294089i	−0.771485	−	0.636248i	$-0.780486\pi$
$461$	−8.69098	+	6.31437i	−0.404779	+	0.294089i	0.366705	+	0.930337i	$0.380486\pi$
$462$	1.34708	+	0.437694i	0.0626720	+	0.0203634i
$463$	29.6013	−	9.61803i	1.37569	−	0.446988i	0.474438	−	0.880289i	$-0.342651\pi$
$463$	29.6013	−	9.61803i	1.37569	−	0.446988i	0.901249	+	0.433301i	$0.142651\pi$
$464$	15.9787			0.741793
$465$		0			0
$466$	−11.6180			−0.538195
$467$	−31.1729	+	10.1287i	−1.44251	+	0.468699i	−0.922678	−	0.385571i	$-0.874005\pi$
$467$	−31.1729	+	10.1287i	−1.44251	+	0.468699i	−0.519830	+	0.854270i	$0.674005\pi$
$468$	14.9394	+	4.85410i	0.690574	+	0.224381i
$469$	−10.2812	+	7.46969i	−0.474740	+	0.344918i
$470$		0			0
$471$	−9.70820			−0.447330
$472$	12.4495	+	17.1353i	0.573034	+	0.788714i
$473$	2.07363	−	2.85410i	0.0953454	−	0.131232i
$474$		0			0
$475$		0			0
$476$	0.927051	−	0.673542i	0.0424913	−	0.0308717i
$477$	24.1724	−	7.85410i	1.10678	−	0.359615i
$478$	7.88597	+	2.56231i	0.360696	+	0.117197i
$479$	−7.23607	−	5.25731i	−0.330624	−	0.240213i	0.410071	−	0.912054i	$-0.365504\pi$
$479$	−7.23607	−	5.25731i	−0.330624	−	0.240213i	−0.740696	+	0.671841i	$0.765504\pi$
$480$		0			0
$481$	0.354102	−	1.08981i	0.0161457	−	0.0496912i
$482$	−3.09793	+	4.26393i	−0.141107	+	0.194217i
$483$	15.6129	+	5.07295i	0.710413	+	0.230827i
$484$	−5.20820	−	16.0292i	−0.236737	−	0.728600i
$485$		0			0
$486$	3.05573	+	9.40456i	0.138611	+	0.426600i
$487$	−13.4738	+	18.5451i	−0.610556	+	0.840358i	−0.996623	−	0.0821126i	$-0.973833\pi$
$487$	−13.4738	+	18.5451i	−0.610556	+	0.840358i	0.386067	+	0.922471i	$0.373833\pi$
$488$	−9.12705	+	12.5623i	−0.413162	+	0.568669i
$489$	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	$0.713969\pi$
$492$	6.15537	+	8.47214i	0.277505	+	0.381953i
$493$	−1.93487	−	0.628677i	−0.0871421	−	0.0283142i
$494$	4.63525	+	14.2658i	0.208550	+	0.641851i
$495$		0			0
$496$	−2.29180	+	10.0656i	−0.102905	+	0.451959i
$497$		−	0.270510i		−	0.0121340i
$498$	2.40414	−	0.781153i	0.107732	−	0.0350043i
$499$	−1.28115	+	3.94298i	−0.0573523	+	0.176512i	−0.975629	−	0.219427i	$-0.929581\pi$
$499$	−1.28115	+	3.94298i	−0.0573523	+	0.176512i	0.918277	+	0.395940i	$0.129581\pi$
$500$		0			0
$501$	9.23607			0.412637
$502$			0.583592i			0.0260470i
$503$	−7.72696	−	10.6353i	−0.344528	−	0.474203i	0.601229	−	0.799077i	$-0.294678\pi$
$503$	−7.72696	−	10.6353i	−0.344528	−	0.474203i	−0.945757	+	0.324874i	$0.894678\pi$
$504$	−10.8541	−	7.88597i	−0.483480	−	0.351269i
$505$		0			0
$506$	−0.798374	−	2.45714i	−0.0354920	−	0.109233i
$507$	−6.20837	−	8.54508i	−0.275723	−	0.379501i
$508$	15.7517	−	5.11803i	0.698868	−	0.227076i
$509$	0.590170	−	1.81636i	0.0261588	−	0.0805086i	−0.937125	−	0.348994i	$-0.886523\pi$
$509$	0.590170	−	1.81636i	0.0261588	−	0.0805086i	0.963284	+	0.268486i	$0.0865232\pi$
$510$		0			0
$511$	−7.93769	+	24.4297i	−0.351143	+	1.08071i
$512$	17.7926	+	5.78115i	0.786327	+	0.255493i
$513$	14.6946	−	20.2254i	0.648784	−	0.892974i
$514$	0.270510	−	0.832544i	0.0119317	−	0.0367219i
$515$		0			0
$516$	6.04508	−	4.39201i	0.266120	−	0.193348i
$517$	2.45714	−	0.798374i	0.108065	−	0.0351124i
$518$	−0.257270	+	0.354102i	−0.0113038	+	0.0155583i
$519$	−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	$0.261729\pi$
$522$			10.6525i			0.466246i
$523$	−20.0579	−	27.6074i	−0.877073	−	1.20719i	−0.977223	−	0.212215i	$-0.931932\pi$
$523$	−20.0579	−	27.6074i	−0.877073	−	1.20719i	0.100150	−	0.994972i	$-0.468068\pi$
$524$	0.0450850	−	0.138757i	0.00196955	−	0.00606164i
$525$		0			0
$526$	6.67376			0.290990
$527$	0.673542	−	1.12868i	0.0293399	−	0.0491659i
$528$			1.41641i			0.0616412i
$529$	−2.14590	−	6.60440i	−0.0932999	−	0.287148i
$530$		0			0
$531$	15.3262	−	11.1352i	0.665102	−	0.483225i
$532$			24.2705i			1.05226i
$533$			31.4164i			1.36080i
$534$	−3.19098	+	2.31838i	−0.138087	+	0.100326i
$535$		0			0
$536$	7.66312	+	5.56758i	0.330996	+	0.240483i
$537$	−18.8294	+	6.11803i	−0.812547	+	0.264013i
$538$	−0.502029	−	0.690983i	−0.0216440	−	0.0297904i
$539$	0.472136	+	1.45309i	0.0203363	+	0.0625888i
$540$		0			0
$541$	−17.7984	−	12.9313i	−0.765212	−	0.555959i	0.135293	−	0.990806i	$-0.456803\pi$
$541$	−17.7984	−	12.9313i	−0.765212	−	0.555959i	−0.900504	+	0.434847i	$0.856803\pi$
$542$	5.62058	+	1.82624i	0.241425	+	0.0784436i
$543$	−16.1680	−	5.25329i	−0.693834	−	0.225440i
$544$	−1.07295	−	0.779543i	−0.0460023	−	0.0334226i
$545$		0			0
$546$	2.78115	+	8.55951i	0.119022	+	0.366313i
$547$	−13.9353	−	19.1803i	−0.595832	−	0.820092i	0.399487	−	0.916739i	$-0.369188\pi$
$547$	−13.9353	−	19.1803i	−0.595832	−	0.820092i	−0.995319	+	0.0966468i	$0.969188\pi$
$548$	−9.95959	+	3.23607i	−0.425453	+	0.138238i
$549$	11.2361	+	8.16348i	0.479544	+	0.348409i
$550$		0			0
$551$	34.8607	−	25.3278i	1.48511	−	1.07900i
$552$		−	12.2361i		−	0.520802i
$553$		0			0
$554$	−6.66312	+	4.84104i	−0.283089	+	0.205676i
$555$		0			0
$556$	−2.92705	−	9.00854i	−0.124135	−	0.382047i
$557$		−	35.8885i		−	1.52065i	−0.649545	−	0.760323i	$-0.725041\pi$
$557$		−	35.8885i		−	1.52065i	0.649545	−	0.760323i	$-0.274959\pi$
$558$	−6.71040	−	1.52786i	−0.284074	−	0.0646796i
$559$	22.4164			0.948113
$560$		0			0
$561$	0.0557281	−	0.171513i	0.00235284	−	0.00724130i
$562$	−6.91467	−	9.51722i	−0.291678	−	0.401460i
$563$		−	8.56231i		−	0.360858i	−0.983588	−	0.180429i	$-0.942251\pi$
$563$		−	8.56231i		−	0.360858i	0.983588	−	0.180429i	$-0.0577486\pi$
$564$	5.47214			0.230418
$565$		0			0
$566$	3.28115	+	2.38390i	0.137917	+	0.100203i
$567$	−1.76336	+	2.42705i	−0.0740540	+	0.101927i
$568$	−0.191758	+	0.0623059i	−0.00804598	+	0.00261430i
$569$	12.5623	−	9.12705i	0.526639	−	0.382626i	−0.292460	−	0.956278i	$-0.594474\pi$
$569$	12.5623	−	9.12705i	0.526639	−	0.382626i	0.819099	+	0.573652i	$0.194474\pi$
$570$		0			0
$571$	2.16312	−	6.65740i	0.0905237	−	0.278603i	−0.895538	−	0.444986i	$-0.853209\pi$
$571$	2.16312	−	6.65740i	0.0905237	−	0.278603i	0.986061	+	0.166383i	$0.0532087\pi$
$572$	−3.52671	+	4.85410i	−0.147459	+	0.202960i
$573$	15.3027	+	4.97214i	0.639278	+	0.207714i
$574$	3.70820	−	11.4127i	0.154777	−	0.476356i
$575$		0			0
$576$	0.145898	−	0.449028i	0.00607908	−	0.0187095i
$577$	37.0710	−	12.0451i	1.54328	−	0.501443i	0.591004	−	0.806669i	$-0.298732\pi$
$577$	37.0710	−	12.0451i	1.54328	−	0.501443i	0.952280	+	0.305225i	$0.0987317\pi$
$578$	−6.15537	−	8.47214i	−0.256030	−	0.352394i
$579$	−0.736068	−	2.26538i	−0.0305899	−	0.0941462i
$580$		0			0
$581$	9.92705	+	7.21242i	0.411843	+	0.299222i
$582$	−1.92236	−	2.64590i	−0.0796843	−	0.109676i
$583$			9.70820i			0.402073i
$584$	19.1459			0.792263
$585$		0			0
$586$	1.57295	−	4.84104i	0.0649779	−	0.199981i
$587$	34.2505	−	11.1287i	1.41367	−	0.459330i	0.500086	−	0.865976i	$-0.333302\pi$
$587$	34.2505	−	11.1287i	1.41367	−	0.459330i	0.913586	+	0.406646i	$0.133302\pi$
$588$			3.23607i			0.133453i
$589$	10.9549	+	25.5928i	0.451389	+	1.05453i
$590$		0			0
$591$	−5.07295	−	15.6129i	−0.208673	−	0.642230i
$592$	−0.416272	−	0.135255i	−0.0171087	−	0.00555894i
$593$	−3.59222	−	4.94427i	−0.147515	−	0.203037i	0.728865	−	0.684658i	$-0.240048\pi$
$593$	−3.59222	−	4.94427i	−0.147515	−	0.203037i	−0.876380	+	0.481621i	$0.840048\pi$
$594$	−2.36068			−0.0968599
$595$		0			0
$596$	−22.2984	+	16.2007i	−0.913377	+	0.663607i
$597$	−15.6987	+	21.6074i	−0.642505	+	0.884332i
$598$	9.64932	−	13.2812i	0.394590	−	0.543107i
$599$	−9.20820	−	28.3399i	−0.376237	−	1.15794i	−0.942640	−	0.333810i	$-0.891666\pi$
$599$	−9.20820	−	28.3399i	−0.376237	−	1.15794i	0.566403	−	0.824128i	$-0.308334\pi$
$600$		0			0
$601$	6.79837	+	20.9232i	0.277311	+	0.853477i	0.988599	+	0.150575i	$0.0481126\pi$
$601$	6.79837	+	20.9232i	0.277311	+	0.853477i	−0.711287	+	0.702902i	$0.751887\pi$
$602$	−8.14324	−	2.64590i	−0.331894	−	0.107839i
$603$	4.97980	−	6.85410i	0.202793	−	0.279121i
$604$	−9.75329	+	30.0175i	−0.396856	+	1.22140i
$605$		0			0
$606$	−2.38197	−	1.73060i	−0.0967608	−	0.0703008i
$607$	24.1724	+	7.85410i	0.981129	+	0.318788i	0.755300	−	0.655379i	$-0.227491\pi$
$607$	24.1724	+	7.85410i	0.981129	+	0.318788i	0.225829	+	0.974167i	$0.427491\pi$
$608$	26.7153	−	8.68034i	1.08345	−	0.352034i
$609$	20.9164	−	15.1967i	0.847576	−	0.615800i
$610$		0			0
$611$	13.2812	+	9.64932i	0.537298	+	0.390370i
$612$	−0.449028	+	0.618034i	−0.0181509	+	0.0249825i
$613$	−14.7274	−	20.2705i	−0.594834	−	0.818718i	0.400390	−	0.916345i	$-0.368875\pi$
$613$	−14.7274	−	20.2705i	−0.594834	−	0.818718i	−0.995223	+	0.0976269i	$0.968875\pi$
$614$	3.76393			0.151900
$615$		0			0
$616$	4.14590	−	3.01217i	0.167043	−	0.121364i
$617$	13.5393	+	4.39919i	0.545072	+	0.177105i	0.568593	−	0.822619i	$-0.307488\pi$
$617$	13.5393	+	4.39919i	0.545072	+	0.177105i	−0.0235215	+	0.999723i	$0.507488\pi$
$618$	0.0857567	−	0.0278640i	0.00344964	−	0.00112086i
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$		0			0
$621$	−27.3607			−1.09795
$622$	−9.68208	+	3.14590i	−0.388216	+	0.126139i
$623$	−18.2088	−	5.91641i	−0.729521	−	0.237036i
$624$	−7.28115	+	5.29007i	−0.291479	+	0.211772i
$625$		0			0
$626$	−0.763932			−0.0305329
$627$	2.24514	+	3.09017i	0.0896623	+	0.123410i
$628$	−9.23305	+	12.7082i	−0.368439	+	0.507113i
$629$	0.0450850	+	0.0327561i	0.00179766	+	0.00130607i
$630$		0			0
$631$	7.06231	−	5.13107i	0.281146	−	0.204264i	−0.438271	−	0.898843i	$-0.644409\pi$
$631$	7.06231	−	5.13107i	0.281146	−	0.204264i	0.719417	+	0.694578i	$0.244409\pi$
$632$		0			0
$633$	7.60845	+	2.47214i	0.302409	+	0.0982586i
$634$	−12.9443	−	9.40456i	−0.514083	−	0.373503i
$635$		0			0
$636$	−6.35410	+	19.5559i	−0.251957	+	0.775442i
$637$	−5.70634	+	7.85410i	−0.226093	+	0.311191i
$638$	−3.86974	−	1.25735i	−0.153204	−	0.0497791i
$639$	0.0557281	+	0.171513i	0.00220457	+	0.00678497i
$640$		0			0
$641$	−12.6976	−	39.0791i	−0.501523	−	1.54353i	−0.806538	−	0.591183i	$-0.798661\pi$
$641$	−12.6976	−	39.0791i	−0.501523	−	1.54353i	0.305014	−	0.952348i	$-0.401339\pi$
$642$	−0.396027	+	0.545085i	−0.0156300	+	0.0215128i
$643$	4.78804	−	6.59017i	0.188822	−	0.259891i	−0.704102	−	0.710099i	$-0.748650\pi$
$643$	4.78804	−	6.59017i	0.188822	−	0.259891i	0.892924	+	0.450208i	$0.148650\pi$
$644$	21.4894	−	15.6129i	0.846799	−	0.615236i
$645$		0			0
$646$	−0.729490			−0.0287014
$647$	−17.5680	−	24.1803i	−0.690671	−	0.950627i	0.309329	−	0.950955i	$-0.399896\pi$
$647$	−17.5680	−	24.1803i	−0.690671	−	0.950627i	−1.00000		0.000327889i	$0.999896\pi$
$648$	2.12663	+	0.690983i	0.0835418	+	0.0271444i
$649$	2.23607	+	6.88191i	0.0877733	+	0.270139i
$650$		0			0
$651$	6.57295	+	15.3557i	0.257614	+	0.601836i
$652$		−	20.5623i		−	0.805282i
$653$	−37.7117	+	12.2533i	−1.47577	+	0.479508i	−0.932847	−	0.360272i	$-0.882684\pi$
$653$	−37.7117	+	12.2533i	−1.47577	+	0.479508i	−0.542927	+	0.839780i	$0.682684\pi$
$654$	1.60739	−	4.94704i	0.0628540	−	0.193445i
$655$		0			0
$656$	12.0000			0.468521
$657$		−	17.1246i		−	0.668095i
$658$	−3.68571	−	5.07295i	−0.143684	−	0.197764i
$659$	18.3541	+	13.3350i	0.714974	+	0.519459i	0.884775	−	0.466019i	$-0.154312\pi$
$659$	18.3541	+	13.3350i	0.714974	+	0.519459i	−0.169800	+	0.985478i	$0.554312\pi$
$660$		0			0
$661$	−5.13525	−	15.8047i	−0.199738	−	0.614731i	−0.999889	−	0.0149316i	$-0.995247\pi$
$661$	−5.13525	−	15.8047i	−0.199738	−	0.614731i	0.800150	−	0.599800i	$-0.204753\pi$
$662$	−4.09425	−	5.63525i	−0.159128	−	0.219020i
$663$	1.08981	−	0.354102i	0.0423249	−	0.0137522i
$664$	2.82624	−	8.69827i	0.109679	−	0.337558i
$665$		0			0
$666$	0.0901699	−	0.277515i	0.00349401	−	0.0107535i
$667$	−44.8509	−	14.5729i	−1.73663	−	0.564267i
$668$	8.78402	−	12.0902i	0.339864	−	0.467783i
$669$	0.218847	−	0.673542i	0.00846112	−	0.0260406i
$670$		0			0
$671$	−4.29180	+	3.11817i	−0.165683	+	0.120376i
$672$	16.0292	−	5.20820i	0.618340	−	0.200911i
$673$	−2.59590	+	3.57295i	−0.100065	+	0.137727i	−0.856113	−	0.516788i	$-0.827127\pi$
$673$	−2.59590	+	3.57295i	−0.100065	+	0.137727i	0.756049	+	0.654516i	$0.227127\pi$
$674$	−9.48936	−	6.89442i	−0.365516	−	0.265563i
$675$		0			0
$676$	−17.0902			−0.657314
$677$		−	28.6525i		−	1.10120i	−0.834768	−	0.550602i	$-0.814398\pi$
$677$		−	28.6525i		−	1.10120i	0.834768	−	0.550602i	$-0.185602\pi$
$678$	0.673542	+	0.927051i	0.0258672	+	0.0356032i
$679$	4.90576	−	15.0984i	0.188266	−	0.579423i
$680$		0			0
$681$	20.7426			0.794860
$682$	1.34708	−	2.25735i	0.0515825	−	0.0864386i
$683$			10.0557i			0.384772i	0.981319	+	0.192386i	$0.0616225\pi$
$683$			10.0557i			0.384772i	−0.981319	+	0.192386i	$0.938377\pi$
$684$	−5.00000	−	15.3884i	−0.191180	−	0.588391i
$685$		0			0
$686$	−7.50000	+	5.44907i	−0.286351	+	0.208046i
$687$		−	7.23607i		−	0.276073i
$688$		−	8.56231i		−	0.326435i
$689$	−49.9058	+	36.2587i	−1.90126	+	1.38134i
$690$		0			0
$691$	−3.10081	−	2.25287i	−0.117960	−	0.0857033i	0.527241	−	0.849716i	$-0.323227\pi$
$691$	−3.10081	−	2.25287i	−0.117960	−	0.0857033i	−0.645201	+	0.764013i	$0.723227\pi$
$692$	−1.40008	+	0.454915i	−0.0532232	+	0.0172933i
$693$	−2.69417	−	3.70820i	−0.102343	−	0.140863i
$694$	1.55166	+	4.77553i	0.0589003	+	0.181277i
$695$		0			0
$696$	−15.5902	−	11.3269i	−0.590944	−	0.429346i
$697$	−1.45309	−	0.472136i	−0.0550395	−	0.0178834i
$698$	9.82084	+	3.19098i	0.371724	+	0.120780i
$699$	−15.2082	−	11.0494i	−0.575227	−	0.417927i
$700$		0			0
$701$	−9.28115	−	28.5645i	−0.350544	−	1.07886i	−0.958548	−	0.284930i	$-0.908030\pi$
$701$	−9.28115	−	28.5645i	−0.350544	−	1.07886i	0.608004	−	0.793934i	$-0.291970\pi$
$702$	−8.81678	−	12.1353i	−0.332768	−	0.458016i
$703$	−1.12257	+	0.364745i	−0.0423385	+	0.0137566i
$704$	0.145898	+	0.106001i	0.00549874	+	0.00399507i
$705$		0			0
$706$	−16.1910	+	11.7634i	−0.609356	+	0.442723i
$707$		−	14.2918i		−	0.537498i
$708$			15.3262i			0.575995i
$709$	3.35410	−	2.43690i	0.125966	−	0.0915196i	−0.523018	−	0.852321i	$-0.675194\pi$
$709$	3.35410	−	2.43690i	0.125966	−	0.0915196i	0.648984	+	0.760802i	$0.275194\pi$
$710$		0			0
$711$		0			0
$712$			14.2705i			0.534810i
$713$	15.6129	−	26.1631i	0.584709	−	0.979817i
$714$	−0.437694			−0.0163803
$715$		0			0
$716$	−9.89919	+	30.4666i	−0.369950	+	1.13859i
$717$	7.88597	+	10.8541i	0.294507	+	0.405354i
$718$			15.6525i			0.584145i
$719$	41.3820			1.54329			0.771643	−	0.636055i	$-0.219435\pi$
$719$	41.3820			1.54329			0.771643	+	0.636055i	$0.219435\pi$
$720$		0			0
$721$	0.354102	+	0.257270i	0.0131874	+	0.00958124i
$722$	2.17963	−	3.00000i	0.0811173	−	0.111648i
$723$	−8.11048	+	2.63525i	−0.301632	+	0.0980062i
$724$	−22.2533	+	16.1680i	−0.827037	+	0.600878i
$725$		0			0
$726$	−1.98936	+	6.12261i	−0.0738320	+	0.227231i
$727$	14.0086	−	19.2812i	0.519549	−	0.715098i	−0.465944	−	0.884814i	$-0.654285\pi$
$727$	14.0086	−	19.2812i	0.519549	−	0.715098i	0.985493	+	0.169716i	$0.0542850\pi$
$728$	30.9686	+	10.0623i	1.14777	+	0.372934i
$729$	−4.01722	+	12.3637i	−0.148786	+	0.457916i
$730$		0			0
$731$	−0.336881	+	1.03681i	−0.0124600	+	0.0383479i
$732$	−10.6861	+	3.47214i	−0.394971	+	0.128334i
$733$	−16.4252	−	22.6074i	−0.606680	−	0.835023i	0.389619	−	0.920976i	$-0.372607\pi$
$733$	−16.4252	−	22.6074i	−0.606680	−	0.835023i	−0.996299	+	0.0859529i	$0.972607\pi$
$734$	−6.92705	−	21.3193i	−0.255682	−	0.786909i
$735$		0			0
$736$	−24.8713	−	18.0701i	−0.916769	−	0.666072i
$737$	1.90211	+	2.61803i	0.0700652	+	0.0964365i
$738$			8.00000i			0.294484i
$739$	−21.7082			−0.798549			−0.399275	−	0.916831i	$-0.630738\pi$
$739$	−21.7082			−0.798549			−0.399275	+	0.916831i	$0.630738\pi$
$740$		0			0
$741$	−7.50000	+	23.0826i	−0.275519	+	0.847961i
$742$	22.4091	−	7.28115i	0.822663	−	0.267300i
$743$		−	3.43769i		−	0.126117i	−0.998010	−	0.0630584i	$-0.979915\pi$
$743$		−	3.43769i		−	0.126117i	0.998010	−	0.0630584i	$-0.0200854\pi$
$744$	9.37132	−	8.19624i	0.343569	−	0.300489i
$745$		0			0
$746$	0.0663712	+	0.204270i	0.00243002	+	0.00747884i
$747$	−7.77997	−	2.52786i	−0.284654	−	0.0924897i
$748$	−0.171513	−	0.236068i	−0.00627115	−	0.00863150i
$749$	−3.27051			−0.119502
$750$		0			0
$751$	32.2254	−	23.4131i	1.17592	−	0.854358i	0.184217	−	0.982886i	$-0.441025\pi$
$751$	32.2254	−	23.4131i	1.17592	−	0.854358i	0.991706	+	0.128528i	$0.0410252\pi$
$752$	3.68571	−	5.07295i	0.134404	−	0.184991i
$753$	−0.555029	+	0.763932i	−0.0202264	+	0.0278392i
$754$	−7.98936	−	24.5887i	−0.290955	−	0.895468i
$755$		0			0
$756$	−7.50000	−	23.0826i	−0.272772	−	0.839507i
$757$	−41.0139	−	13.3262i	−1.49068	−	0.484350i	−0.553394	−	0.832920i	$-0.686668\pi$
$757$	−41.0139	−	13.3262i	−1.49068	−	0.484350i	−0.937283	+	0.348569i	$0.886668\pi$
$758$	6.69015	−	9.20820i	0.242997	−	0.334457i
$759$	1.29180	−	3.97574i	0.0468892	−	0.144310i
$760$		0			0
$761$	−2.83688	−	2.06111i	−0.102837	−	0.0747154i	0.535178	−	0.844739i	$-0.320244\pi$
$761$	−2.83688	−	2.06111i	−0.102837	−	0.0747154i	−0.638015	+	0.770024i	$0.720244\pi$
$762$	−6.01661	−	1.95492i	−0.217959	−	0.0708191i
$763$	24.0134	−	7.80244i	0.869345	−	0.282467i
$764$	21.0623	−	15.3027i	0.762007	−	0.553631i
$765$		0			0
$766$	−8.42705	−	6.12261i	−0.304482	−	0.221219i
$767$	−27.0256	+	37.1976i	−0.975838	+	1.34313i
$768$	−3.85723	−	5.30902i	−0.139186	−	0.191573i
$769$	53.7426			1.93801			0.969005	−	0.247042i	$-0.0794587\pi$
$769$	53.7426			1.93801			0.969005	+	0.247042i	$0.0794587\pi$
$770$		0			0
$771$	1.14590	−	0.832544i	0.0412685	−	0.0299833i
$772$	−3.66547	−	1.19098i	−0.131923	−	0.0428644i
$773$	18.1558	−	5.89919i	0.653020	−	0.212179i	0.0362746	−	0.999342i	$-0.488451\pi$
$773$	18.1558	−	5.89919i	0.653020	−	0.212179i	0.616745	+	0.787163i	$0.288451\pi$
$774$	5.70820			0.205177
$775$		0			0
$776$	−11.8328			−0.424773
$777$	−0.673542	+	0.218847i	−0.0241632	+	0.00785109i
$778$	17.0863	+	5.55166i	0.612572	+	0.199037i
$779$	26.1803	−	19.0211i	0.938008	−	0.681503i
$780$		0			0
$781$	−0.0688837			−0.00246485
$782$	0.469272	+	0.645898i	0.0167811	+	0.0230973i
$783$	−25.3278	+	34.8607i	−0.905141	+	1.24582i
$784$	3.00000	+	2.17963i	0.107143	+	0.0778438i
$785$		0			0
$786$	−0.0450850	+	0.0327561i	−0.00160813	+	0.00116837i
$787$	29.7603	−	9.66970i	1.06084	−	0.344687i	0.273926	−	0.961751i	$-0.411678\pi$
$787$	29.7603	−	9.66970i	1.06084	−	0.344687i	0.786913	+	0.617063i	$0.211678\pi$
$788$	−25.2623	−	8.20820i	−0.899931	−	0.292405i
$789$	8.73607	+	6.34712i	0.311012	+	0.225964i
$790$		0			0
$791$	−1.71885	+	5.29007i	−0.0611152	+	0.188093i
$792$	−2.00811	+	2.76393i	−0.0713552	+	0.0982120i
$793$	−32.0584	−	10.4164i	−1.13843	−	0.369897i
$794$	3.11146	+	9.57608i	0.110421	+	0.339842i
$795$		0			0
$796$	13.3541	+	41.0997i	0.473324	+	1.45674i
$797$	−5.32282	+	7.32624i	−0.188544	+	0.259509i	−0.892816	−	0.450422i	$-0.851274\pi$
$797$	−5.32282	+	7.32624i	−0.188544	+	0.259509i	0.704272	+	0.709930i	$0.251274\pi$
$798$	5.44907	−	7.50000i	0.192895	−	0.265497i
$799$	−0.645898	+	0.469272i	−0.0228502	+	0.0166017i
$800$		0			0
$801$	12.7639			0.450991
$802$	10.8374	+	14.9164i	0.382682	+	0.526717i
$803$	6.22088	+	2.02129i	0.219530	+	0.0713296i
$804$	2.11803	+	6.51864i	0.0746973	+	0.229895i
$805$		0			0
$806$	16.6353	−	1.50609i	0.585952	−	0.0530496i
$807$		−	1.38197i		−	0.0486475i
$808$	−10.1311	+	3.29180i	−0.356411	+	0.115805i
$809$	−16.9336	+	52.1164i	−0.595355	+	1.83231i	−0.0424020	+	0.999101i	$0.513501\pi$
$809$	−16.9336	+	52.1164i	−0.595355	+	1.83231i	−0.552953	+	0.833213i	$0.686499\pi$
$810$		0			0
$811$	42.7771			1.50211			0.751053	−	0.660242i	$-0.229546\pi$
$811$	42.7771			1.50211			0.751053	+	0.660242i	$0.229546\pi$
$812$		−	41.8328i		−	1.46804i
$813$	5.62058	+	7.73607i	0.197122	+	0.271316i
$814$	0.0901699	+	0.0655123i	0.00316045	+	0.00229620i
$815$		0			0
$816$	−0.135255	−	0.416272i	−0.00473487	−	0.0145724i
$817$	−13.5721	−	18.6803i	−0.474826	−	0.653542i
$818$	−3.63271	+	1.18034i	−0.127015	+	0.0412696i
$819$	9.00000	−	27.6992i	0.314485	−	0.967887i
$820$		0			0
$821$	−10.0344	+	30.8828i	−0.350204	+	1.07782i	0.608534	+	0.793528i	$0.291758\pi$
$821$	−10.0344	+	30.8828i	−0.350204	+	1.07782i	−0.958738	+	0.284290i	$0.908242\pi$
$822$	3.80423	+	1.23607i	0.132688	+	0.0431128i
$823$	−3.59996	+	4.95492i	−0.125487	+	0.172717i	−0.867138	−	0.498068i	$-0.834043\pi$
$823$	−3.59996	+	4.95492i	−0.125487	+	0.172717i	0.741651	+	0.670786i	$0.234043\pi$
$824$	0.100813	−	0.310271i	0.00351199	−	0.0108088i
$825$		0			0
$826$	14.2082	−	10.3229i	0.494367	−	0.359178i
$827$	2.54290	−	0.826238i	0.0884253	−	0.0287311i	−0.264470	−	0.964394i	$-0.585197\pi$
$827$	2.54290	−	0.826238i	0.0884253	−	0.0287311i	0.352896	+	0.935663i	$0.385197\pi$
$828$	−10.4086	+	14.3262i	−0.361725	+	0.497871i
$829$	−17.5623	−	12.7598i	−0.609964	−	0.443165i	0.239438	−	0.970912i	$-0.423037\pi$
$829$	−17.5623	−	12.7598i	−0.609964	−	0.443165i	−0.849402	+	0.527747i	$0.823037\pi$
$830$		0			0
$831$	−13.3262			−0.462282
$832$			1.14590i			0.0397269i
$833$	−0.277515	−	0.381966i	−0.00961531	−	0.0132343i
$834$	−1.11803	+	3.44095i	−0.0387144	+	0.119151i
$835$		0			0
$836$	6.18034			0.213752
$837$	−18.3273	−	20.9549i	−0.633486	−	0.724308i
$838$		−	2.76393i		−	0.0954784i
$839$	−3.45492	−	10.6331i	−0.119277	−	0.367097i	0.873538	−	0.486756i	$-0.161820\pi$
$839$	−3.45492	−	10.6331i	−0.119277	−	0.367097i	−0.992815	+	0.119659i	$0.961820\pi$
$840$		0			0
$841$	−36.6246	+	26.6093i	−1.26292	+	0.917563i
$842$			9.12461i			0.314455i
$843$		−	19.0344i		−	0.655581i
$844$	10.4721	−	7.60845i	0.360466	−	0.261894i
$845$		0			0
$846$	3.38197	+	2.45714i	0.116274	+	0.0844783i
$847$	−29.7198	+	9.65654i	−1.02118	+	0.331803i
$848$	13.8496	+	19.0623i	0.475596	+	0.654602i
$849$	2.02786	+	6.24112i	0.0695961	+	0.214195i
$850$		0			0
$851$	1.04508	+	0.759299i	0.0358251	+	0.0260284i
$852$	−0.138757	−	0.0450850i	−0.00475375	−	0.00154459i
$853$	3.80423	+	1.23607i	0.130254	+	0.0423222i	0.373419	−	0.927663i	$-0.378185\pi$
$853$	3.80423	+	1.23607i	0.130254	+	0.0423222i	−0.243164	+	0.969985i	$0.578185\pi$
$854$	10.4164	+	7.56796i	0.356442	+	0.258970i
$855$		0			0
$856$	0.753289	+	2.31838i	0.0257469	+	0.0792408i
$857$	−4.80828	−	6.61803i	−0.164248	−	0.226068i	0.718958	−	0.695054i	$-0.244619\pi$
$857$	−4.80828	−	6.61803i	−0.164248	−	0.226068i	−0.883206	+	0.468986i	$0.844619\pi$
$858$	2.17963	−	0.708204i	0.0744113	−	0.0241777i
$859$	35.0238	+	25.4463i	1.19500	+	0.868216i	0.993783	−	0.111332i	$-0.0355116\pi$
$859$	35.0238	+	25.4463i	1.19500	+	0.868216i	0.201213	+	0.979547i	$0.435512\pi$
$860$		0			0
$861$	15.7082	−	11.4127i	0.535334	−	0.388943i
$862$			18.0689i			0.615429i
$863$			2.49342i			0.0848771i	0.999099	+	0.0424385i	$0.0135127\pi$
$863$			2.49342i			0.0848771i	−0.999099	+	0.0424385i	$0.986487\pi$
$864$	−22.7254	+	16.5110i	−0.773135	+	0.561715i
$865$		0			0
$866$	−0.111456	−	0.343027i	−0.00378744	−	0.0116565i
$867$		−	16.9443i		−	0.575458i
$868$	26.3521	+	6.00000i	0.894447	+	0.203653i
$869$		0			0
$870$		0			0
$871$	−6.35410	+	19.5559i	−0.215301	+	0.662627i
$872$	−11.0619	−	15.2254i	−0.374604	−	0.515598i
$873$			10.5836i			0.358200i
$874$	−16.9098			−0.571984
$875$		0			0
$876$	11.2082	+	8.14324i	0.378690	+	0.275134i
$877$	−9.57608	+	13.1803i	−0.323361	+	0.445068i	−0.939490	−	0.342577i	$-0.888700\pi$
$877$	−9.57608	+	13.1803i	−0.323361	+	0.445068i	0.616129	+	0.787646i	$0.288700\pi$
$878$	24.5887	−	7.98936i	0.829829	−	0.269628i
$879$	6.66312	−	4.84104i	0.224741	−	0.163284i
$880$		0			0
$881$	−4.74671	+	14.6089i	−0.159921	+	0.492185i	−0.998626	−	0.0523999i	$-0.983313\pi$
$881$	−4.74671	+	14.6089i	−0.159921	+	0.492185i	0.838705	+	0.544585i	$0.183313\pi$
$882$	−1.45309	+	2.00000i	−0.0489279	+	0.0673435i
$883$	−0.951057	−	0.309017i	−0.0320056	−	0.0103992i	0.292970	−	0.956121i	$-0.405356\pi$
$883$	−0.951057	−	0.309017i	−0.0320056	−	0.0103992i	−0.324976	+	0.945722i	$0.605356\pi$
$884$	0.572949	−	1.76336i	0.0192704	−	0.0593081i
$885$		0			0
$886$	7.85410	−	24.1724i	0.263864	−	0.812089i
$887$	37.1895	−	12.0836i	1.24870	−	0.405727i	0.391245	−	0.920286i	$-0.372044\pi$
$887$	37.1895	−	12.0836i	1.24870	−	0.405727i	0.857455	+	0.514559i	$0.172044\pi$
$888$	0.310271	+	0.427051i	0.0104120	+	0.0143309i
$889$	−9.48936	−	29.2052i	−0.318263	−	0.979512i
$890$		0			0
$891$	0.618034	+	0.449028i	0.0207049	+	0.0150430i
$892$	−0.673542	−	0.927051i	−0.0225519	−	0.0310400i
$893$		−	16.9098i		−	0.565866i
$894$	10.5279			0.352104
$895$		0			0
$896$	10.5517	−	32.4747i	0.352506	−	1.08490i
$897$	25.2623	−	8.20820i	0.843482	−	0.274064i
$898$		−	14.8754i		−	0.496398i
$899$	−18.8820	−	44.1119i	−0.629749	−	1.47121i
$900$		0			0
$901$	−0.927051	−	2.85317i	−0.0308845	−	0.0950529i
$902$	−2.90617	−	0.944272i	−0.0967649	−	0.0314408i
$903$	−8.14324	−	11.2082i	−0.270990	−	0.372986i
$904$	4.14590			0.137891
$905$		0			0
$906$	9.75329	−	7.08618i	0.324031	−	0.235423i
$907$	−31.1074	+	42.8156i	−1.03290	+	1.42167i	−0.130157	+	0.991493i	$0.541548\pi$
$907$	−31.1074	+	42.8156i	−1.03290	+	1.42167i	−0.902745	+	0.430175i	$0.858452\pi$
$908$	19.7274	−	27.1525i	0.654678	−	0.901087i
$909$	2.94427	+	9.06154i	0.0976553	+	0.300552i
$910$		0			0
$911$	2.52786	+	7.77997i	0.0837519	+	0.257762i	0.984159	−	0.177286i	$-0.0567316\pi$
$911$	2.52786	+	7.77997i	0.0837519	+	0.257762i	−0.900408	+	0.435047i	$0.856732\pi$
$912$	8.81678	+	2.86475i	0.291953	+	0.0948612i
$913$	1.83660	−	2.52786i	0.0607826	−	0.0836601i
$914$	−3.00658	+	9.25330i	−0.0994488	+	0.306072i
$915$		0			0
$916$	−9.47214	−	6.88191i	−0.312968	−	0.227385i
$917$	−0.257270	−	0.0835921i	−0.00849581	−	0.00276046i
$918$	0.693786	−	0.225425i	0.0228984	−	0.00744013i
$919$	7.98936	−	5.80461i	0.263545	−	0.191476i	−0.448164	−	0.893952i	$-0.647922\pi$
$919$	7.98936	−	5.80461i	0.263545	−	0.191476i	0.711708	+	0.702475i	$0.247922\pi$
$920$		0			0
$921$	4.92705	+	3.57971i	0.162352	+	0.117956i
$922$	3.90249	−	5.37132i	0.128522	−	0.176895i
$923$	−0.257270	−	0.354102i	−0.00846815	−	0.0116554i
$924$	3.70820			0.121991
$925$		0			0
$926$	−15.5623	+	11.3067i	−0.511409	+	0.371560i
$927$	−0.277515	−	0.0901699i	−0.00911477	−	0.00296157i
$928$	−46.0467	+	14.9615i	−1.51156	+	0.491135i
$929$	−33.5410			−1.10045			−0.550223	−	0.835018i	$-0.685457\pi$
$929$	−33.5410			−1.10045			−0.550223	+	0.835018i	$0.685457\pi$
$930$		0			0
$931$	10.0000			0.327737
$932$	−28.9277	+	9.39919i	−0.947559	+	0.307881i
$933$	−15.6659	−	5.09017i	−0.512880	−	0.166645i
$934$	16.3885	−	11.9070i	0.536250	−	0.389608i
$935$		0			0
$936$	−21.7082			−0.709555
$937$	23.7967	+	32.7533i	0.777403	+	1.07000i	0.995564	+	0.0940905i	$0.0299943\pi$
$937$	23.7967	+	32.7533i	0.777403	+	1.07000i	−0.218161	+	0.975913i	$0.570006\pi$
$938$	4.61653	−	6.35410i	0.150735	−	0.207469i
$939$	−1.00000	−	0.726543i	−0.0326338	−	0.0237098i
$940$		0			0
$941$	−23.1246	+	16.8010i	−0.753841	+	0.547697i	−0.897015	−	0.442000i	$-0.854269\pi$
$941$	−23.1246	+	16.8010i	−0.753841	+	0.547697i	0.143174	+	0.989698i	$0.454269\pi$
$942$	5.70634	−	1.85410i	0.185923	−	0.0604099i
$943$	−33.6830	−	10.9443i	−1.09687	−	0.356395i
$944$	14.2082	+	10.3229i	0.462438	+	0.335981i
$945$		0			0
$946$	−0.673762	+	2.07363i	−0.0219059	+	0.0674194i
$947$	−12.9718	+	17.8541i	−0.421526	+	0.580180i	−0.965982	−	0.258609i	$-0.916736\pi$
$947$	−12.9718	+	17.8541i	−0.421526	+	0.580180i	0.544456	+	0.838789i	$0.316736\pi$
$948$		0			0
$949$	12.8435	+	39.5281i	0.416916	+	1.28314i
$950$		0			0
$951$	−8.00000	−	24.6215i	−0.259418	−	0.798406i
$952$	−0.930812	+	1.28115i	−0.0301678	+	0.0415224i
$953$	24.8132	−	34.1525i	0.803779	−	1.10631i	−0.188474	−	0.982078i	$-0.560354\pi$
$953$	24.8132	−	34.1525i	0.803779	−	1.10631i	0.992254	−	0.124229i	$-0.0396458\pi$
$954$	−12.7082	+	9.23305i	−0.411443	+	0.298931i
$955$		0			0
$956$	21.7082			0.702093
$957$	−3.86974	−	5.32624i	−0.125091	−	0.172173i
$958$	5.25731	+	1.70820i	0.169856	+	0.0551896i
$959$	6.00000	+	18.4661i	0.193750	+	0.596302i
$960$		0			0
$961$	30.4959	−	5.56758i	0.983740	−	0.179599i
$962$			0.708204i			0.0228334i
$963$	2.07363	−	0.673762i	0.0668217	−	0.0217117i
$964$	−4.26393	+	13.1230i	−0.137332	+	0.422664i
$965$		0			0
$966$	−10.1459			−0.326439
$967$		−	43.6525i		−	1.40377i	−0.712291	−	0.701884i	$-0.752342\pi$
$967$		−	43.6525i		−	1.40377i	0.712291	−	0.701884i	$-0.247658\pi$
$968$	13.6906	+	18.8435i	0.440032	+	0.605652i
$969$	−0.954915	−	0.693786i	−0.0306763	−	0.0222876i
$970$		0			0
$971$	−6.35410	−	19.5559i	−0.203913	−	0.627579i	−0.999756	−	0.0220767i	$-0.992972\pi$
$971$	−6.35410	−	19.5559i	−0.203913	−	0.627579i	0.795843	−	0.605502i	$-0.207028\pi$
$972$	15.2169	+	20.9443i	0.488082	+	0.671788i
$973$	−16.7027	+	5.42705i	−0.535465	+	0.173983i
$974$	4.37790	−	13.4738i	0.140277	−	0.431728i
$975$		0			0
$976$	−3.97871	+	12.2452i	−0.127356	+	0.391960i
$977$	5.77185	+	1.87539i	0.184658	+	0.0599990i	0.399886	−	0.916565i	$-0.369050\pi$
$977$	5.77185	+	1.87539i	0.184658	+	0.0599990i	−0.215228	+	0.976564i	$0.569050\pi$
$978$	−4.61653	+	6.35410i	−0.147620	+	0.203182i
$979$	−1.50658	+	4.63677i	−0.0481504	+	0.148192i
$980$		0			0
$981$	−13.6180	+	9.89408i	−0.434790	+	0.315894i
$982$	16.2210	−	5.27051i	0.517632	−	0.168189i
$983$	12.3637	−	17.0172i	0.394342	−	0.542765i	−0.564971	−	0.825111i	$-0.691113\pi$
$983$	12.3637	−	17.0172i	0.394342	−	0.542765i	0.959313	+	0.282346i	$0.0911126\pi$
$984$	−11.7082	−	8.50651i	−0.373244	−	0.271178i
$985$		0			0
$986$	1.25735			0.0400423
$987$		−	10.1459i		−	0.322947i
$988$	23.0826	+	31.7705i	0.734356	+	1.01075i
$989$	−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	$0.588449\pi$
$992$	−2.82041	−	31.1525i	−0.0895482	−	0.989092i
$993$		−	11.2705i		−	0.357659i
$994$	0.0516628	+	0.159002i	0.00163864	+	0.00504323i
$995$		0			0
$996$	5.35410	−	3.88998i	0.169651	−	0.123259i
$997$			27.2492i			0.862992i	0.902115	+	0.431496i	$0.142014\pi$
$997$			27.2492i			0.862992i	−0.902115	+	0.431496i	$0.857986\pi$
$998$		−	2.56231i		−	0.0811084i
$999$	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.bf.a.624.1		8
5.2	odd	4		31.2.d.a.4.1	✓	4
5.3	odd	4		775.2.k.c.376.1		4
5.4	even	2	inner	775.2.bf.a.624.2		8
15.2	even	4		279.2.i.a.190.1		4
20.7	even	4		496.2.n.b.97.1		4
31.8	even	5	inner	775.2.bf.a.349.2		8
155.2	odd	20		961.2.d.f.388.1		4
155.7	odd	60		961.2.g.f.816.1		8
155.8	odd	20		775.2.k.c.101.1		4
155.12	even	60		961.2.g.g.235.1		8
155.17	even	60		961.2.g.c.846.1		8
155.22	even	60		961.2.g.c.448.1		8
155.27	even	20		961.2.d.e.374.1		4
155.37	even	12		961.2.g.c.547.1		8
155.39	even	10	inner	775.2.bf.a.349.1		8
155.42	even	60		961.2.g.g.732.1		8
155.47	odd	20		961.2.a.d.1.1		2
155.52	even	60		961.2.g.g.338.1		8
155.57	even	12		961.2.g.c.844.1		8
155.67	odd	12		961.2.g.b.844.1		8
155.72	odd	60		961.2.g.f.338.1		8
155.77	even	20		961.2.a.e.1.1		2
155.82	odd	60		961.2.g.f.732.1		8
155.87	odd	12		961.2.g.b.547.1		8
155.92	even	4		961.2.d.b.531.1		4
155.97	odd	20		961.2.d.f.374.1		4
155.102	odd	60		961.2.g.b.448.1		8
155.107	odd	60		961.2.g.b.846.1		8
155.112	odd	60		961.2.g.f.235.1		8
155.117	even	60		961.2.g.g.816.1		8
155.122	even	20		961.2.d.e.388.1		4
155.127	even	60		961.2.c.d.439.1		4
155.132	odd	20		31.2.d.a.8.1	yes	4
155.137	even	60		961.2.c.d.521.1		4
155.142	odd	60		961.2.c.f.521.1		4
155.147	even	20		961.2.d.b.628.1		4
155.152	odd	60		961.2.c.f.439.1		4
465.47	even	20		8649.2.a.g.1.2		2
465.77	odd	20		8649.2.a.f.1.2		2
465.287	even	20		279.2.i.a.163.1		4
620.287	even	20		496.2.n.b.225.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.d.a.4.1	✓	4	5.2	odd	4
31.2.d.a.8.1	yes	4	155.132	odd	20
279.2.i.a.163.1		4	465.287	even	20
279.2.i.a.190.1		4	15.2	even	4
496.2.n.b.97.1		4	20.7	even	4
496.2.n.b.225.1		4	620.287	even	20
775.2.k.c.101.1		4	155.8	odd	20
775.2.k.c.376.1		4	5.3	odd	4
775.2.bf.a.349.1		8	155.39	even	10	inner
775.2.bf.a.349.2		8	31.8	even	5	inner
775.2.bf.a.624.1		8	1.1	even	1	trivial
775.2.bf.a.624.2		8	5.4	even	2	inner
961.2.a.d.1.1		2	155.47	odd	20
961.2.a.e.1.1		2	155.77	even	20
961.2.c.d.439.1		4	155.127	even	60
961.2.c.d.521.1		4	155.137	even	60
961.2.c.f.439.1		4	155.152	odd	60
961.2.c.f.521.1		4	155.142	odd	60
961.2.d.b.531.1		4	155.92	even	4
961.2.d.b.628.1		4	155.147	even	20
961.2.d.e.374.1		4	155.27	even	20
961.2.d.e.388.1		4	155.122	even	20
961.2.d.f.374.1		4	155.97	odd	20
961.2.d.f.388.1		4	155.2	odd	20
961.2.g.b.448.1		8	155.102	odd	60
961.2.g.b.547.1		8	155.87	odd	12
961.2.g.b.844.1		8	155.67	odd	12
961.2.g.b.846.1		8	155.107	odd	60
961.2.g.c.448.1		8	155.22	even	60
961.2.g.c.547.1		8	155.37	even	12
961.2.g.c.844.1		8	155.57	even	12
961.2.g.c.846.1		8	155.17	even	60
961.2.g.f.235.1		8	155.112	odd	60
961.2.g.f.338.1		8	155.72	odd	60
961.2.g.f.732.1		8	155.82	odd	60
961.2.g.f.816.1		8	155.7	odd	60
961.2.g.g.235.1		8	155.12	even	60
961.2.g.g.338.1		8	155.52	even	60
961.2.g.g.732.1		8	155.42	even	60
961.2.g.g.816.1		8	155.117	even	60
8649.2.a.f.1.2		2	465.77	odd	20
8649.2.a.g.1.2		2	465.47	even	20

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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.bf (of order \(10\), degree \(4\), not minimal)

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

Introduction

L-functions

Modular forms

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Database

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