LMFDB - Embedded newform 950.2.q.f.407.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(107,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("950.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.q (of order $12$, degree $4$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			407.3
Character	$\chi$	$=$	950.407
Dual form			950.2.q.f.943.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(0.770169 - 0.206366i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.398669 - 0.690515i) q^{6} +(-0.349095 - 0.349095i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.04750 + 1.18213i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(0.770169 - 0.206366i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.398669 - 0.690515i) q^{6} +(-0.349095 - 0.349095i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.04750 + 1.18213i) q^{9} -1.21936 q^{11} +(-0.563803 + 0.563803i) q^{12} +(-1.75642 + 6.55503i) q^{13} +(-0.246847 + 0.427552i) q^{14} +(0.500000 - 0.866025i) q^{16} +(5.86296 - 1.57098i) q^{17} +(1.67178 + 1.67178i) q^{18} +(4.09774 - 1.48612i) q^{19} +(-0.340903 - 0.196821i) q^{21} +(0.315593 + 1.17781i) q^{22} +(8.86996 + 2.37670i) q^{23} +(0.690515 + 0.398669i) q^{24} +6.78627 q^{26} +(-3.02438 + 3.02438i) q^{27} +(0.476872 + 0.127777i) q^{28} +(3.16038 + 5.47393i) q^{29} -3.84404i q^{31} +(-0.965926 - 0.258819i) q^{32} +(-0.939110 + 0.251634i) q^{33} +(-3.03489 - 5.25659i) q^{34} +(1.18213 - 2.04750i) q^{36} +(-2.41973 + 2.41973i) q^{37} +(-2.49605 - 3.57347i) q^{38} +5.41095i q^{39} +(-3.55111 - 2.05023i) q^{41} +(-0.101882 + 0.380228i) q^{42} +(1.50815 + 5.62850i) q^{43} +(1.05599 - 0.609678i) q^{44} -9.18286i q^{46} +(-0.0539244 + 0.201249i) q^{47} +(0.206366 - 0.770169i) q^{48} -6.75627i q^{49} +(4.19127 - 2.41983i) q^{51} +(-1.75642 - 6.55503i) q^{52} +(-3.51570 + 13.1208i) q^{53} +(3.70410 + 2.13856i) q^{54} -0.493694i q^{56} +(2.84927 - 1.99020i) q^{57} +(4.46945 - 4.46945i) q^{58} +(0.0144572 - 0.0250407i) q^{59} +(3.90148 + 6.75757i) q^{61} +(-3.71305 + 0.994910i) q^{62} +(1.12745 + 0.302098i) q^{63} +1.00000i q^{64} +(0.486119 + 0.841983i) q^{66} +(13.3037 + 3.56470i) q^{67} +(-4.29198 + 4.29198i) q^{68} +7.32184 q^{69} +(-5.99527 - 3.46137i) q^{71} +(-2.28369 - 0.611914i) q^{72} +(-2.01785 - 7.53071i) q^{73} +(2.96355 + 1.71101i) q^{74} +(-2.80568 + 3.33589i) q^{76} +(0.425671 + 0.425671i) q^{77} +(5.22658 - 1.40046i) q^{78} +(-2.17572 + 3.76846i) q^{79} +(1.84122 - 3.18909i) q^{81} +(-1.06128 + 3.96075i) q^{82} +(-2.36905 + 2.36905i) q^{83} +0.393641 q^{84} +(5.04638 - 2.91353i) q^{86} +(3.56366 + 3.56366i) q^{87} +(-0.862215 - 0.862215i) q^{88} +(2.10438 + 3.64490i) q^{89} +(2.90148 - 1.67517i) q^{91} +(-8.86996 + 2.37670i) q^{92} +(-0.793279 - 2.96056i) q^{93} +0.208348 q^{94} -0.797338 q^{96} +(0.821725 + 3.06672i) q^{97} +(-6.52605 + 1.74865i) q^{98} +(2.49663 - 1.44143i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{6}+O(q^{10}) $ 32 * q + 4 * q^6	$ 32 q + 4 q^{6} + 72 q^{11} + 16 q^{16} + 60 q^{21} + 8 q^{26} - 28 q^{36} - 84 q^{41} - 84 q^{51} - 52 q^{61} - 24 q^{71} + 16 q^{76} + 64 q^{81} - 36 q^{86} - 84 q^{91} + 8 q^{96}+O(q^{100}) $ 32 * q + 4 * q^6 + 72 * q^11 + 16 * q^16 + 60 * q^21 + 8 * q^26 - 28 * q^36 - 84 * q^41 - 84 * q^51 - 52 * q^61 - 24 * q^71 + 16 * q^76 + 64 * q^81 - 36 * q^86 - 84 * q^91 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	0.770169	−	0.206366i	0.444657	−	0.119146i	−0.0295411	−	0.999564i	$-0.509405\pi$
$3$	0.770169	−	0.206366i	0.444657	−	0.119146i	0.474198	+	0.880418i	$0.342738\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−0.398669	−	0.690515i	−0.162756	−	0.281902i
$7$	−0.349095	−	0.349095i	−0.131945	−	0.131945i	0.638050	−	0.769995i	$-0.279741\pi$
$7$	−0.349095	−	0.349095i	−0.131945	−	0.131945i	−0.769995	+	0.638050i	$0.779741\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.04750	+	1.18213i	−0.682501	+	0.394042i
$10$		0			0
$11$	−1.21936			−0.367650			−0.183825	−	0.982959i	$-0.558848\pi$
$11$	−1.21936			−0.367650			−0.183825	+	0.982959i	$0.558848\pi$
$12$	−0.563803	+	0.563803i	−0.162756	+	0.162756i
$13$	−1.75642	+	6.55503i	−0.487142	+	1.81804i	0.0830725	+	0.996544i	$0.473527\pi$
$13$	−1.75642	+	6.55503i	−0.487142	+	1.81804i	−0.570215	+	0.821496i	$0.693140\pi$
$14$	−0.246847	+	0.427552i	−0.0659727	+	0.114268i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	5.86296	−	1.57098i	1.42198	−	0.381017i	0.535792	−	0.844350i	$-0.320013\pi$
$17$	5.86296	−	1.57098i	1.42198	−	0.381017i	0.886185	+	0.463333i	$0.153346\pi$
$18$	1.67178	+	1.67178i	0.394042	+	0.394042i
$19$	4.09774	−	1.48612i	0.940085	−	0.340939i
$19$	4.09774	−	1.48612i	0.940085	−	0.340939i
$20$		0			0
$21$	−0.340903	−	0.196821i	−0.0743912	−	0.0429498i
$22$	0.315593	+	1.17781i	0.0672846	+	0.251109i
$23$	8.86996	+	2.37670i	1.84952	+	0.495576i	0.999513	−	0.0312028i	$-0.00993376\pi$
$23$	8.86996	+	2.37670i	1.84952	+	0.495576i	0.850002	+	0.526779i	$0.176600\pi$
$24$	0.690515	+	0.398669i	0.140951	+	0.0813780i
$25$		0			0
$26$	6.78627			1.33090
$27$	−3.02438	+	3.02438i	−0.582043	+	0.582043i
$28$	0.476872	+	0.127777i	0.0901203	+	0.0241477i
$29$	3.16038	+	5.47393i	0.586867	+	1.01648i	0.994640	+	0.103400i	$0.0329722\pi$
$29$	3.16038	+	5.47393i	0.586867	+	1.01648i	−0.407773	+	0.913083i	$0.633695\pi$
$30$		0			0
$31$		−	3.84404i		−	0.690409i	−0.938527	−	0.345205i	$-0.887809\pi$
$31$		−	3.84404i		−	0.690409i	0.938527	−	0.345205i	$-0.112191\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−0.939110	+	0.251634i	−0.163478	+	0.0438038i
$34$	−3.03489	−	5.25659i	−0.520480	−	0.901497i
$35$		0			0
$36$	1.18213	−	2.04750i	0.197021	−	0.341250i
$37$	−2.41973	+	2.41973i	−0.397802	+	0.397802i	−0.877457	−	0.479655i	$-0.840762\pi$
$37$	−2.41973	+	2.41973i	−0.397802	+	0.397802i	0.479655	+	0.877457i	$0.340762\pi$
$38$	−2.49605	−	3.57347i	−0.404913	−	0.579694i
$39$			5.41095i			0.866445i
$40$		0			0
$41$	−3.55111	−	2.05023i	−0.554590	−	0.320193i	0.196381	−	0.980528i	$-0.437081\pi$
$41$	−3.55111	−	2.05023i	−0.554590	−	0.320193i	−0.750971	+	0.660335i	$0.770414\pi$
$42$	−0.101882	+	0.380228i	−0.0157207	+	0.0586705i
$43$	1.50815	+	5.62850i	0.229991	+	0.858339i	0.980343	+	0.197300i	$0.0632174\pi$
$43$	1.50815	+	5.62850i	0.229991	+	0.858339i	−0.750352	+	0.661039i	$0.770116\pi$
$44$	1.05599	−	0.609678i	0.159197	−	0.0919124i
$45$		0			0
$46$		−	9.18286i		−	1.35394i
$47$	−0.0539244	+	0.201249i	−0.00786568	+	0.0293551i	−0.969747	−	0.244112i	$-0.921504\pi$
$47$	−0.0539244	+	0.201249i	−0.00786568	+	0.0293551i	0.961881	+	0.273467i	$0.0881703\pi$
$48$	0.206366	−	0.770169i	0.0297864	−	0.111164i
$49$		−	6.75627i		−	0.965181i
$50$		0			0
$51$	4.19127	−	2.41983i	0.586896	−	0.338844i
$52$	−1.75642	−	6.55503i	−0.243571	−	0.909020i
$53$	−3.51570	+	13.1208i	−0.482918	+	1.80227i	0.106340	+	0.994330i	$0.466087\pi$
$53$	−3.51570	+	13.1208i	−0.482918	+	1.80227i	−0.589258	+	0.807945i	$0.700580\pi$
$54$	3.70410	+	2.13856i	0.504064	+	0.291021i
$55$		0			0
$56$		−	0.493694i		−	0.0659727i
$57$	2.84927	−	1.99020i	0.377395	−	0.263608i
$58$	4.46945	−	4.46945i	0.586867	−	0.586867i
$59$	0.0144572	−	0.0250407i	0.00188217	−	0.00326002i	−0.865083	−	0.501629i	$-0.832734\pi$
$59$	0.0144572	−	0.0250407i	0.00188217	−	0.00326002i	0.866965	+	0.498369i	$0.166068\pi$
$60$		0			0
$61$	3.90148	+	6.75757i	0.499534	+	0.865218i	1.00000		0.000538484i	$-0.000171405\pi$
$61$	3.90148	+	6.75757i	0.499534	+	0.865218i	−0.500466	+	0.865756i	$0.666838\pi$
$62$	−3.71305	+	0.994910i	−0.471558	+	0.126354i
$63$	1.12745	+	0.302098i	0.142045	+	0.0380608i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	0.486119	+	0.841983i	0.0598372	+	0.103641i
$67$	13.3037	+	3.56470i	1.62530	+	0.435498i	0.952553	−	0.304374i	$-0.0984472\pi$
$67$	13.3037	+	3.56470i	1.62530	+	0.435498i	0.672748	+	0.739872i	$0.265114\pi$
$68$	−4.29198	+	4.29198i	−0.520480	+	0.520480i
$69$	7.32184			0.881446
$70$		0			0
$71$	−5.99527	−	3.46137i	−0.711507	−	0.410789i	0.100112	−	0.994976i	$-0.468080\pi$
$71$	−5.99527	−	3.46137i	−0.711507	−	0.410789i	−0.811619	+	0.584187i	$0.801413\pi$
$72$	−2.28369	−	0.611914i	−0.269136	−	0.0721147i
$73$	−2.01785	−	7.53071i	−0.236171	−	0.881403i	−0.977617	−	0.210391i	$-0.932526\pi$
$73$	−2.01785	−	7.53071i	−0.236171	−	0.881403i	0.741446	−	0.671013i	$-0.234140\pi$
$74$	2.96355	+	1.71101i	0.344506	+	0.198901i
$75$		0			0
$76$	−2.80568	+	3.33589i	−0.321834	+	0.382652i
$77$	0.425671	+	0.425671i	0.0485097	+	0.0485097i
$78$	5.22658	−	1.40046i	0.591793	−	0.158571i
$79$	−2.17572	+	3.76846i	−0.244787	+	0.423984i	−0.962072	−	0.272796i	$-0.912052\pi$
$79$	−2.17572	+	3.76846i	−0.244787	+	0.423984i	0.717284	+	0.696781i	$0.245385\pi$
$80$		0			0
$81$	1.84122	−	3.18909i	0.204580	−	0.354344i
$82$	−1.06128	+	3.96075i	−0.117199	+	0.437392i
$83$	−2.36905	+	2.36905i	−0.260037	+	0.260037i	−0.825069	−	0.565032i	$-0.808864\pi$
$83$	−2.36905	+	2.36905i	−0.260037	+	0.260037i	0.565032	+	0.825069i	$0.308864\pi$
$84$	0.393641			0.0429498
$85$		0			0
$86$	5.04638	−	2.91353i	0.544165	−	0.314174i
$87$	3.56366	+	3.56366i	0.382064	+	0.382064i
$88$	−0.862215	−	0.862215i	−0.0919124	−	0.0919124i
$89$	2.10438	+	3.64490i	0.223064	+	0.386358i	0.955737	−	0.294223i	$-0.0950608\pi$
$89$	2.10438	+	3.64490i	0.223064	+	0.386358i	−0.732673	+	0.680581i	$0.761727\pi$
$90$		0			0
$91$	2.90148	−	1.67517i	0.304158	−	0.175606i
$92$	−8.86996	+	2.37670i	−0.924758	+	0.247788i
$93$	−0.793279	−	2.96056i	−0.0822592	−	0.306996i
$94$	0.208348			0.0214894
$95$		0			0
$96$	−0.797338			−0.0813780
$97$	0.821725	+	3.06672i	0.0834335	+	0.311378i	0.995013	−	0.0997459i	$-0.0318030\pi$
$97$	0.821725	+	3.06672i	0.0834335	+	0.311378i	−0.911579	+	0.411124i	$0.865136\pi$
$98$	−6.52605	+	1.74865i	−0.659231	+	0.176640i
$99$	2.49663	−	1.44143i	0.250921	−	0.144869i
$100$		0			0
$101$	−4.27792	−	7.40958i	−0.425669	−	0.737281i	0.570813	−	0.821080i	$-0.306628\pi$
$101$	−4.27792	−	7.40958i	−0.425669	−	0.737281i	−0.996483	+	0.0837990i	$0.973295\pi$
$102$	−3.42216	−	3.42216i	−0.338844	−	0.338844i
$103$	−8.22228	−	8.22228i	−0.810166	−	0.810166i	0.174493	−	0.984658i	$-0.444171\pi$
$103$	−8.22228	−	8.22228i	−0.810166	−	0.810166i	−0.984658	+	0.174493i	$0.944171\pi$
$104$	−5.87708	+	3.39314i	−0.576295	+	0.332724i
$105$		0			0
$106$	13.5836			1.31936
$107$	6.82929	−	6.82929i	0.660212	−	0.660212i	−0.295218	−	0.955430i	$-0.595392\pi$
$107$	6.82929	−	6.82929i	0.660212	−	0.660212i	0.955430	+	0.295218i	$0.0953923\pi$
$108$	1.10700	−	4.13138i	0.106521	−	0.397542i
$109$	7.79910	−	13.5084i	0.747018	−	1.29387i	−0.202227	−	0.979339i	$-0.564818\pi$
$109$	7.79910	−	13.5084i	0.747018	−	1.29387i	0.949246	−	0.314535i	$-0.101849\pi$
$110$		0			0
$111$	−1.36425	+	2.36295i	−0.129489	+	0.224282i
$112$	−0.476872	+	0.127777i	−0.0450602	+	0.0120738i
$113$	1.00393	+	1.00393i	0.0944420	+	0.0944420i	0.752749	−	0.658307i	$-0.228727\pi$
$113$	1.00393	+	1.00393i	0.0944420	+	0.0944420i	−0.658307	+	0.752749i	$0.728727\pi$
$114$	−2.65983	−	2.23708i	−0.249116	−	0.209522i
$115$		0			0
$116$	−5.47393	−	3.16038i	−0.508242	−	0.293433i
$117$	−4.15261	−	15.4978i	−0.383909	−	1.43277i
$118$	−0.0279292	−	0.00748361i	−0.00257109	−	0.000688922i
$119$	−2.59515	−	1.49831i	−0.237897	−	0.137350i
$120$		0			0
$121$	−9.51317			−0.864834
$122$	5.51753	−	5.51753i	0.499534	−	0.499534i
$123$	−3.15806	−	0.846198i	−0.284752	−	0.0762991i
$124$	1.92202	+	3.32903i	0.172602	+	0.298956i
$125$		0			0
$126$		−	1.16722i		−	0.103984i
$127$	−4.19942	−	1.12523i	−0.372638	−	0.0998481i	0.0676393	−	0.997710i	$-0.478453\pi$
$127$	−4.19942	−	1.12523i	−0.372638	−	0.0998481i	−0.440278	+	0.897862i	$0.645120\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	2.32307	+	4.02367i	0.204535	+	0.354264i
$130$		0			0
$131$	−9.48781	+	16.4334i	−0.828954	+	1.43579i	0.0699057	+	0.997554i	$0.477730\pi$
$131$	−9.48781	+	16.4334i	−0.828954	+	1.43579i	−0.898860	+	0.438237i	$0.855603\pi$
$132$	0.687477	−	0.687477i	0.0598372	−	0.0598372i
$133$	−1.94929	−	0.911702i	−0.169025	−	0.0790546i
$134$		−	13.7730i		−	1.18980i
$135$		0			0
$136$	5.25659	+	3.03489i	0.450748	+	0.260240i
$137$	−1.73568	+	6.47764i	−0.148289	+	0.553422i	0.851298	+	0.524683i	$0.175816\pi$
$137$	−1.73568	+	6.47764i	−0.148289	+	0.553422i	−0.999587	+	0.0287397i	$0.990851\pi$
$138$	−1.89503	−	7.07236i	−0.161316	−	0.602039i
$139$	−13.6084	+	7.85680i	−1.15425	+	0.666405i	−0.949918	−	0.312498i	$-0.898834\pi$
$139$	−13.6084	+	7.85680i	−1.15425	+	0.666405i	−0.204328	+	0.978902i	$0.565501\pi$
$140$		0			0
$141$			0.166124i			0.0139901i
$142$	−1.79174	+	6.68685i	−0.150359	+	0.561148i
$143$	2.14170	−	7.99292i	0.179098	−	0.668401i
$144$			2.36425i			0.197021i
$145$		0			0
$146$	−6.75185	+	3.89818i	−0.558787	+	0.322616i
$147$	−1.39427	−	5.20347i	−0.114997	−	0.429175i
$148$	0.885683	−	3.30542i	0.0728027	−	0.271703i
$149$	9.44068	+	5.45058i	0.773411	+	0.446529i	0.834090	−	0.551628i	$-0.185993\pi$
$149$	9.44068	+	5.45058i	0.773411	+	0.446529i	−0.0606791	+	0.998157i	$0.519327\pi$
$150$		0			0
$151$			16.8131i			1.36823i	0.729374	+	0.684116i	$0.239812\pi$
$151$			16.8131i			1.36823i	−0.729374	+	0.684116i	$0.760188\pi$
$152$	3.94838	+	1.84669i	0.320256	+	0.149787i
$153$	−10.1473	+	10.1473i	−0.820363	+	0.820363i
$154$	0.300995	−	0.521338i	0.0242548	−	0.0420106i
$155$		0			0
$156$	−2.70548	−	4.68602i	−0.216611	−	0.375182i
$157$	13.2691	−	3.55544i	1.05899	−	0.283755i	0.313028	−	0.949744i	$-0.398657\pi$
$157$	13.2691	−	3.55544i	1.05899	−	0.283755i	0.745962	+	0.665989i	$0.231990\pi$
$158$	4.20317	+	1.12623i	0.334386	+	0.0895984i
$159$			10.8307i			0.858932i
$160$		0			0
$161$	−2.26676	−	3.92615i	−0.178646	−	0.309424i
$162$	−3.55697	−	0.953087i	−0.279462	−	0.0748816i
$163$	13.0999	−	13.0999i	1.02606	−	1.02606i	0.0264084	−	0.999651i	$-0.491593\pi$
$163$	13.0999	−	13.0999i	1.02606	−	1.02606i	0.999651	−	0.0264084i	$-0.00840704\pi$
$164$	4.10047			0.320193
$165$		0			0
$166$	2.90148	+	1.67517i	0.225199	+	0.130019i
$167$	20.4009	+	5.46639i	1.57867	+	0.423002i	0.938512	−	0.345245i	$-0.112204\pi$
$167$	20.4009	+	5.46639i	1.57867	+	0.423002i	0.640153	+	0.768247i	$0.278871\pi$
$168$	−0.101882	−	0.380228i	−0.00786035	−	0.0293352i
$169$	−28.6251	−	16.5267i	−2.20193	−	1.27129i
$170$		0			0
$171$	−6.63335	+	7.88688i	−0.507265	+	0.603124i
$172$	−4.12035	−	4.12035i	−0.314174	−	0.314174i
$173$	−7.21206	+	1.93247i	−0.548323	+	0.146923i	−0.522336	−	0.852740i	$-0.674939\pi$
$173$	−7.21206	+	1.93247i	−0.548323	+	0.146923i	−0.0259866	+	0.999662i	$0.508273\pi$
$174$	2.51989	−	4.36457i	0.191032	−	0.330877i
$175$		0			0
$176$	−0.609678	+	1.05599i	−0.0459562	+	0.0795985i
$177$	0.00596697	−	0.0222690i	0.000448505	−	0.00167384i
$178$	2.97605	−	2.97605i	0.223064	−	0.223064i
$179$	−10.5815			−0.790897			−0.395449	−	0.918488i	$-0.629411\pi$
$179$	−10.5815			−0.790897			−0.395449	+	0.918488i	$0.629411\pi$
$180$		0			0
$181$	0.165201	−	0.0953786i	0.0122793	−	0.00708944i	−0.493848	−	0.869548i	$-0.664410\pi$
$181$	0.165201	−	0.0953786i	0.0122793	−	0.00708944i	0.506127	+	0.862459i	$0.331077\pi$
$182$	−2.36905	−	2.36905i	−0.175606	−	0.175606i
$183$	4.39933	+	4.39933i	0.325208	+	0.325208i
$184$	4.59143	+	7.95259i	0.338485	+	0.586273i
$185$		0			0
$186$	−2.65436	+	1.53250i	−0.194627	+	0.112368i
$187$	−7.14903	+	1.91558i	−0.522789	+	0.140081i
$188$	−0.0539244	−	0.201249i	−0.00393284	−	0.0146776i
$189$	2.11159			0.153596
$190$		0			0
$191$	2.27488			0.164604			0.0823022	−	0.996607i	$-0.473773\pi$
$191$	2.27488			0.164604			0.0823022	+	0.996607i	$0.473773\pi$
$192$	0.206366	+	0.770169i	0.0148932	+	0.0555822i
$193$	4.67355	−	1.25227i	0.336409	−	0.0901406i	−0.0866600	−	0.996238i	$-0.527619\pi$
$193$	4.67355	−	1.25227i	0.336409	−	0.0901406i	0.423069	+	0.906097i	$0.360953\pi$
$194$	2.74954	−	1.58745i	0.197406	−	0.113972i
$195$		0			0
$196$	3.37813	+	5.85110i	0.241295	+	0.417936i
$197$	−5.53611	−	5.53611i	−0.394432	−	0.394432i	0.481832	−	0.876264i	$-0.339972\pi$
$197$	−5.53611	−	5.53611i	−0.394432	−	0.394432i	−0.876264	+	0.481832i	$0.839972\pi$
$198$	−2.03849	−	2.03849i	−0.144869	−	0.144869i
$199$	5.67753	−	3.27792i	0.402469	−	0.232366i	−0.285080	−	0.958504i	$-0.592020\pi$
$199$	5.67753	−	3.27792i	0.402469	−	0.232366i	0.687549	+	0.726138i	$0.258687\pi$
$200$		0			0
$201$	10.9817			0.774590
$202$	−6.04990	+	6.04990i	−0.425669	+	0.425669i
$203$	0.807650	−	3.01419i	0.0566859	−	0.211555i
$204$	−2.41983	+	4.19127i	−0.169422	+	0.293448i
$205$		0			0
$206$	−5.81403	+	10.0702i	−0.405083	+	0.701624i
$207$	−20.9708	+	5.61912i	−1.45757	+	0.390556i
$208$	4.79862	+	4.79862i	0.332724	+	0.332724i
$209$	−4.99660	+	1.81211i	−0.345622	+	0.125346i
$210$		0			0
$211$	−2.26846	−	1.30969i	−0.156167	−	0.0901630i	0.419880	−	0.907580i	$-0.362072\pi$
$211$	−2.26846	−	1.30969i	−0.156167	−	0.0901630i	−0.576047	+	0.817417i	$0.695405\pi$
$212$	−3.51570	−	13.1208i	−0.241459	−	0.901137i
$213$	−5.33168	−	1.42862i	−0.365321	−	0.0978874i
$214$	−8.36413	−	4.82903i	−0.571760	−	0.330106i
$215$		0			0
$216$	−4.27712			−0.291021
$217$	−1.34193	+	1.34193i	−0.0910963	+	0.0910963i
$218$	−15.0667	−	4.03711i	−1.02045	−	0.273428i
$219$	−3.10817	−	5.38351i	−0.210031	−	0.363784i
$220$		0			0
$221$			41.1912i			2.77082i
$222$	2.63553	+	0.706189i	0.176885	+	0.0473963i
$223$	13.1781	−	3.53106i	0.882471	−	0.236457i	0.210998	−	0.977486i	$-0.432329\pi$
$223$	13.1781	−	3.53106i	0.882471	−	0.236457i	0.671473	+	0.741029i	$0.265662\pi$
$224$	0.246847	+	0.427552i	0.0164932	+	0.0285670i
$225$		0			0
$226$	0.709888	−	1.22956i	0.0472210	−	0.0817892i
$227$	−11.0389	+	11.0389i	−0.732678	+	0.732678i	−0.971149	−	0.238472i	$-0.923354\pi$
$227$	−11.0389	+	11.0389i	−0.732678	+	0.732678i	0.238472	+	0.971149i	$0.423354\pi$
$228$	−1.47244	+	3.14820i	−0.0975146	+	0.208494i
$229$		−	24.6337i		−	1.62784i	−0.580977	−	0.813920i	$-0.697329\pi$
$229$		−	24.6337i		−	1.62784i	0.580977	−	0.813920i	$-0.302671\pi$
$230$		0			0
$231$	0.415682	+	0.239994i	0.0273499	+	0.0157905i
$232$	−1.63593	+	6.10538i	−0.107404	+	0.400838i
$233$	−3.84438	−	14.3474i	−0.251854	−	0.939931i	−0.969814	−	0.243846i	$-0.921591\pi$
$233$	−3.84438	−	14.3474i	−0.251854	−	0.939931i	0.717960	−	0.696084i	$-0.245076\pi$
$234$	−13.8949	+	8.02223i	−0.908338	+	0.524429i
$235$		0			0
$236$			0.0289145i			0.00188217i
$237$	−0.897990	+	3.35134i	−0.0583307	+	0.217693i
$238$	−0.775582	+	2.89451i	−0.0502735	+	0.187623i
$239$		−	18.8551i		−	1.21964i	−0.792542	−	0.609818i	$-0.791243\pi$
$239$		−	18.8551i		−	1.21964i	0.792542	−	0.609818i	$-0.208757\pi$
$240$		0			0
$241$	14.9147	−	8.61098i	0.960737	−	0.554682i	0.0643374	−	0.997928i	$-0.479507\pi$
$241$	14.9147	−	8.61098i	0.960737	−	0.554682i	0.896400	+	0.443246i	$0.146173\pi$
$242$	2.46219	+	9.18902i	0.158276	+	0.590692i
$243$	4.08093	−	15.2303i	0.261792	−	0.977021i
$244$	−6.75757	−	3.90148i	−0.432609	−	0.249767i
$245$		0			0
$246$			3.26946i			0.208453i
$247$	2.54423	+	29.4710i	0.161886	+	1.87520i
$248$	2.71814	−	2.71814i	0.172602	−	0.172602i
$249$	−1.33568	+	2.31346i	−0.0846451	+	0.146610i
$250$		0			0
$251$	−3.17026	−	5.49105i	−0.200105	−	0.346592i	0.748457	−	0.663183i	$-0.230795\pi$
$251$	−3.17026	−	5.49105i	−0.200105	−	0.346592i	−0.948562	+	0.316591i	$0.897462\pi$
$252$	−1.12745	+	0.302098i	−0.0710224	+	0.0190304i
$253$	−10.8156	−	2.89804i	−0.679974	−	0.182198i
$254$			4.34756i			0.272790i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.0332	−	3.22428i	−0.750608	−	0.201125i	−0.136820	−	0.990596i	$-0.543688\pi$
$257$	−12.0332	−	3.22428i	−0.750608	−	0.201125i	−0.613788	+	0.789471i	$0.710355\pi$
$258$	3.28531	−	3.28531i	0.204535	−	0.204535i
$259$	1.68943			0.104976
$260$		0			0
$261$	−12.9418	−	7.47192i	−0.801074	−	0.462500i
$262$	18.3290	+	4.91125i	1.13237	+	0.303418i
$263$	3.78156	+	14.1130i	0.233181	+	0.870243i	0.978960	+	0.204050i	$0.0654105\pi$
$263$	3.78156	+	14.1130i	0.233181	+	0.870243i	−0.745780	+	0.666193i	$0.767923\pi$
$264$	−0.841983	−	0.486119i	−0.0518205	−	0.0299186i
$265$		0			0
$266$	−0.376122	+	2.11884i	−0.0230615	+	0.129914i
$267$	2.37291	+	2.37291i	0.145220	+	0.145220i
$268$	−13.3037	+	3.56470i	−0.812650	+	0.217749i
$269$	−9.83761	+	17.0392i	−0.599810	+	1.03890i	0.393039	+	0.919522i	$0.371424\pi$
$269$	−9.83761	+	17.0392i	−0.599810	+	1.03890i	−0.992849	+	0.119379i	$0.961910\pi$
$270$		0			0
$271$	−1.93702	+	3.35502i	−0.117666	+	0.203803i	−0.918842	−	0.394625i	$-0.870874\pi$
$271$	−1.93702	+	3.35502i	−0.117666	+	0.203803i	0.801177	+	0.598428i	$0.204208\pi$
$272$	1.57098	−	5.86296i	0.0952544	−	0.355494i
$273$	1.88893	−	1.88893i	0.114323	−	0.114323i
$274$	6.70615			0.405133
$275$		0			0
$276$	−6.34090	+	3.66092i	−0.381678	+	0.220362i
$277$	−4.72841	−	4.72841i	−0.284103	−	0.284103i	0.550640	−	0.834743i	$-0.314384\pi$
$277$	−4.72841	−	4.72841i	−0.284103	−	0.284103i	−0.834743	+	0.550640i	$0.814384\pi$
$278$	11.1112	+	11.1112i	0.666405	+	0.666405i
$279$	4.54414	+	7.87068i	0.272050	+	0.471205i
$280$		0			0
$281$	−15.2603	+	8.81053i	−0.910352	+	0.525592i	−0.880545	−	0.473963i	$-0.842823\pi$
$281$	−15.2603	+	8.81053i	−0.910352	+	0.525592i	−0.0298079	+	0.999556i	$0.509490\pi$
$282$	0.160463	−	0.0429960i	0.00955544	−	0.00256037i
$283$	2.77562	+	10.3587i	0.164993	+	0.615763i	0.998041	+	0.0625622i	$0.0199272\pi$
$283$	2.77562	+	10.3587i	0.164993	+	0.615763i	−0.833048	+	0.553201i	$0.813406\pi$
$284$	6.92274			0.410789
$285$		0			0
$286$	−8.27488			−0.489304
$287$	0.523948	+	1.95540i	0.0309277	+	0.115424i
$288$	2.28369	−	0.611914i	0.134568	−	0.0360574i
$289$	17.1839	−	9.92113i	1.01082	−	0.583596i
$290$		0			0
$291$	1.26573	+	2.19232i	0.0741987	+	0.128516i
$292$	5.51287	+	5.51287i	0.322616	+	0.322616i
$293$	3.65423	+	3.65423i	0.213482	+	0.213482i	0.805745	−	0.592263i	$-0.201765\pi$
$293$	3.65423	+	3.65423i	0.213482	+	0.213482i	−0.592263	+	0.805745i	$0.701765\pi$
$294$	−4.66530	+	2.69351i	−0.272086	+	0.157089i
$295$		0			0
$296$	−3.42202			−0.198901
$297$	3.68780	−	3.68780i	0.213988	−	0.213988i
$298$	2.82143	−	10.5297i	0.163441	−	0.609970i
$299$	−31.1587	+	53.9684i	−1.80195	+	3.12108i
$300$		0			0
$301$	1.43839	−	2.49137i	0.0829075	−	0.143600i
$302$	16.2402	−	4.35155i	0.934519	−	0.250404i
$303$	−4.82381	−	4.82381i	−0.277121	−	0.277121i
$304$	0.761851	−	4.29180i	0.0436952	−	0.246152i
$305$		0			0
$306$	12.4279	+	7.17525i	0.710455	+	0.410182i
$307$	−4.37148	−	16.3146i	−0.249493	−	0.931122i	−0.971071	−	0.238789i	$-0.923250\pi$
$307$	−4.37148	−	16.3146i	−0.249493	−	0.931122i	0.721578	−	0.692333i	$-0.243417\pi$
$308$	−0.581477	−	0.155806i	−0.0331327	−	0.00887788i
$309$	−8.02935	−	4.63575i	−0.456774	−	0.263718i
$310$		0			0
$311$	17.7325			1.00552			0.502760	−	0.864426i	$-0.332318\pi$
$311$	17.7325			1.00552			0.502760	+	0.864426i	$0.332318\pi$
$312$	−3.82612	+	3.82612i	−0.216611	+	0.216611i
$313$	−22.9788	−	6.15715i	−1.29884	−	0.348023i	−0.457827	−	0.889041i	$-0.651372\pi$
$313$	−22.9788	−	6.15715i	−1.29884	−	0.348023i	−0.841011	+	0.541018i	$0.818039\pi$
$314$	−6.86859	−	11.8968i	−0.387617	−	0.671372i
$315$		0			0
$316$		−	4.35144i		−	0.244787i
$317$	−22.2110	−	5.95143i	−1.24750	−	0.334266i	−0.426127	−	0.904663i	$-0.640122\pi$
$317$	−22.2110	−	5.95143i	−1.24750	−	0.334266i	−0.821369	+	0.570398i	$0.806789\pi$
$318$	10.4617	−	2.80320i	0.586662	−	0.157196i
$319$	−3.85362	−	6.67467i	−0.215761	−	0.373710i
$320$		0			0
$321$	3.85037	−	6.66904i	0.214907	−	0.372229i
$322$	−3.20569	+	3.20569i	−0.178646	+	0.178646i
$323$	21.6902	−	15.1505i	1.20688	−	0.842996i
$324$			3.68245i			0.204580i
$325$		0			0
$326$	−16.0440	−	9.26299i	−0.888594	−	0.513030i
$327$	3.21894	−	12.0133i	0.178008	−	0.664335i
$328$	−1.06128	−	3.96075i	−0.0585994	−	0.218696i
$329$	0.0890795	−	0.0514301i	0.00491111	−	0.00283543i
$330$		0			0
$331$		−	25.7959i		−	1.41787i	−0.705274	−	0.708934i	$-0.749176\pi$
$331$		−	25.7959i		−	1.41787i	0.705274	−	0.708934i	$-0.250824\pi$
$332$	0.867133	−	3.23618i	0.0475901	−	0.177609i
$333$	2.09398	−	7.81484i	0.114749	−	0.428250i
$334$		−	21.1205i		−	1.15566i
$335$		0			0
$336$	−0.340903	+	0.196821i	−0.0185978	+	0.0107374i
$337$	−2.13509	−	7.96827i	−0.116306	−	0.434059i	0.883075	−	0.469231i	$-0.155469\pi$
$337$	−2.13509	−	7.96827i	−0.116306	−	0.434059i	−0.999381	+	0.0351717i	$0.988802\pi$
$338$	−8.55487	+	31.9272i	−0.465323	+	1.73661i
$339$	0.980376	+	0.566020i	0.0532467	+	0.0307420i
$340$		0			0
$341$			4.68725i			0.253829i
$342$	9.33497	+	4.36605i	0.504778	+	0.236089i
$343$	−4.80224	+	4.80224i	−0.259296	+	0.259296i
$344$	−2.91353	+	5.04638i	−0.157087	+	0.272082i
$345$		0			0
$346$	3.73324	+	6.46616i	0.200700	+	0.347623i
$347$	6.82994	−	1.83008i	0.366651	−	0.0982437i	−0.0707896	−	0.997491i	$-0.522552\pi$
$347$	6.82994	−	1.83008i	0.366651	−	0.0982437i	0.437440	+	0.899248i	$0.355885\pi$
$348$	−4.86805	−	1.30439i	−0.260955	−	0.0699226i
$349$		−	20.6337i		−	1.10450i	−0.833680	−	0.552248i	$-0.813770\pi$
$349$		−	20.6337i		−	1.10450i	0.833680	−	0.552248i	$-0.186230\pi$
$350$		0			0
$351$	−14.5129	−	25.1370i	−0.774639	−	1.34171i
$352$	1.17781	+	0.315593i	0.0627773	+	0.0168211i
$353$	−14.0504	+	14.0504i	−0.747827	+	0.747827i	−0.974071	−	0.226244i	$-0.927355\pi$
$353$	−14.0504	+	14.0504i	−0.747827	+	0.747827i	0.226244	+	0.974071i	$0.427355\pi$
$354$	−0.0230546			−0.00122534
$355$		0			0
$356$	−3.64490	−	2.10438i	−0.193179	−	0.111532i
$357$	−2.30790	−	0.618401i	−0.122147	−	0.0327292i
$358$	2.73869	+	10.2209i	0.144744	+	0.540193i
$359$	10.7306	+	6.19530i	0.566338	+	0.326975i	0.755685	−	0.654935i	$-0.227304\pi$
$359$	10.7306	+	6.19530i	0.566338	+	0.326975i	−0.189348	+	0.981910i	$0.560637\pi$
$360$		0			0
$361$	14.5829	−	12.1795i	0.767521	−	0.641024i
$362$	−0.134886	−	0.134886i	−0.00708944	−	0.00708944i
$363$	−7.32675	+	1.96320i	−0.384555	+	0.103041i
$364$	−1.67517	+	2.90148i	−0.0878028	+	0.152079i
$365$		0			0
$366$	3.11080	−	5.38806i	0.162604	−	0.281639i
$367$	−1.55853	+	5.81651i	−0.0813546	+	0.303620i	−0.994599	−	0.103793i	$-0.966902\pi$
$367$	−1.55853	+	5.81651i	−0.0813546	+	0.303620i	0.913244	+	0.407412i	$0.133569\pi$
$368$	6.49326	−	6.49326i	0.338485	−	0.338485i
$369$	9.69454			0.504678
$370$		0			0
$371$	5.80770	−	3.35307i	0.301521	−	0.174083i
$372$	2.16728	+	2.16728i	0.112368	+	0.112368i
$373$	−13.5349	−	13.5349i	−0.700810	−	0.700810i	0.263774	−	0.964584i	$-0.415033\pi$
$373$	−13.5349	−	13.5349i	−0.700810	−	0.700810i	−0.964584	+	0.263774i	$0.915033\pi$
$374$	3.70061	+	6.40965i	0.191354	+	0.331435i
$375$		0			0
$376$	−0.180435	+	0.104174i	−0.00930520	+	0.00537236i
$377$	−41.4327	+	11.1019i	−2.13389	+	0.571775i
$378$	−0.546520	−	2.03964i	−0.0281099	−	0.104908i
$379$	31.9024			1.63872			0.819358	−	0.573282i	$-0.194330\pi$
$379$	31.9024			1.63872			0.819358	+	0.573282i	$0.194330\pi$
$380$		0			0
$381$	−3.46647			−0.177593
$382$	−0.588782	−	2.19736i	−0.0301247	−	0.112427i
$383$	32.5053	−	8.70978i	1.66094	−	0.445049i	0.698297	−	0.715808i	$-0.253941\pi$
$383$	32.5053	−	8.70978i	1.66094	−	0.445049i	0.962647	+	0.270759i	$0.0872747\pi$
$384$	0.690515	−	0.398669i	0.0352377	−	0.0203445i
$385$		0			0
$386$	−2.41920	−	4.19019i	−0.123134	−	0.213275i
$387$	−9.74155	−	9.74155i	−0.495191	−	0.495191i
$388$	−2.24499	−	2.24499i	−0.113972	−	0.113972i
$389$	11.6013	−	6.69802i	0.588210	−	0.339603i	−0.176180	−	0.984358i	$-0.556374\pi$
$389$	11.6013	−	6.69802i	0.588210	−	0.339603i	0.764389	+	0.644755i	$0.223041\pi$
$390$		0			0
$391$	55.7380			2.81879
$392$	4.77740	−	4.77740i	0.241295	−	0.241295i
$393$	−3.91593	+	14.6144i	−0.197532	+	0.737201i
$394$	−3.91462	+	6.78032i	−0.197216	+	0.341588i
$395$		0			0
$396$	−1.44143	+	2.49663i	−0.0724347	+	0.125461i
$397$	25.3009	−	6.77935i	1.26981	−	0.340246i	0.439855	−	0.898069i	$-0.355030\pi$
$397$	25.3009	−	6.77935i	1.26981	−	0.340246i	0.829960	+	0.557823i	$0.188363\pi$
$398$	−4.63568	−	4.63568i	−0.232366	−	0.232366i
$399$	−1.68943	−	0.299896i	−0.0845773	−	0.0150136i
$400$		0			0
$401$	−12.9468	−	7.47485i	−0.646534	−	0.373276i	0.140593	−	0.990067i	$-0.455099\pi$
$401$	−12.9468	−	7.47485i	−0.646534	−	0.373276i	−0.787127	+	0.616791i	$0.788432\pi$
$402$	−2.84227	−	10.6075i	−0.141760	−	0.529055i
$403$	25.1978	+	6.75173i	1.25519	+	0.336328i
$404$	7.40958	+	4.27792i	0.368640	+	0.212835i
$405$		0			0
$406$	−3.12052			−0.154869
$407$	2.95051	−	2.95051i	0.146252	−	0.146252i
$408$	4.67476	+	1.25260i	0.231435	+	0.0620128i
$409$	1.11973	+	1.93942i	0.0553669	+	0.0958982i	0.892380	−	0.451284i	$-0.149034\pi$
$409$	1.11973	+	1.93942i	0.0553669	+	0.0958982i	−0.837014	+	0.547182i	$0.815700\pi$
$410$		0			0
$411$			5.34707i			0.263751i
$412$	11.2318	+	3.00956i	0.553353	+	0.148271i
$413$	−0.0137885	+	0.00369462i	−0.000678487	+	0.000181800i
$414$	10.8553	+	18.8019i	0.533509	+	0.924065i
$415$		0			0
$416$	3.39314	−	5.87708i	0.166362	−	0.288148i
$417$	−8.85937	+	8.85937i	−0.433845	+	0.433845i
$418$	3.04358	+	4.35734i	0.148866	+	0.213124i
$419$		−	0.293815i		−	0.0143538i	−0.999974	−	0.00717691i	$-0.997715\pi$
$419$		−	0.293815i		−	0.0143538i	0.999974	−	0.00717691i	$-0.00228450\pi$
$420$		0			0
$421$	−0.905185	−	0.522609i	−0.0441160	−	0.0254704i	0.477780	−	0.878480i	$-0.341442\pi$
$421$	−0.905185	−	0.522609i	−0.0441160	−	0.0254704i	−0.521896	+	0.853009i	$0.674775\pi$
$422$	−0.677947	+	2.53013i	−0.0330019	+	0.123165i
$423$	−0.127491	−	0.475802i	−0.00619882	−	0.0231343i
$424$	−11.7637	+	6.79180i	−0.571298	+	0.329839i
$425$		0			0
$426$			5.51976i			0.267433i
$427$	0.997043	−	3.72102i	0.0482503	−	0.180073i
$428$	−2.49969	+	9.32898i	−0.120827	+	0.450933i
$429$		−	6.59787i		−	0.318548i
$430$		0			0
$431$	−25.0325	+	14.4525i	−1.20577	+	0.696152i	−0.961833	−	0.273639i	$-0.911773\pi$
$431$	−25.0325	+	14.4525i	−1.20577	+	0.696152i	−0.243938	+	0.969791i	$0.578439\pi$
$432$	1.10700	+	4.13138i	0.0532606	+	0.198771i
$433$	−0.898645	+	3.35379i	−0.0431861	+	0.161173i	−0.984151	−	0.177330i	$-0.943254\pi$
$433$	−0.898645	+	3.35379i	−0.0431861	+	0.161173i	0.940965	+	0.338503i	$0.109921\pi$
$434$	1.64352	+	0.948890i	0.0788917	+	0.0455482i
$435$		0			0
$436$			15.5982i			0.747018i
$437$	39.8788	−	3.44273i	1.90766	−	0.164688i
$438$	−4.39562	+	4.39562i	−0.210031	+	0.210031i
$439$	7.46725	−	12.9337i	0.356392	−	0.617290i	−0.630963	−	0.775813i	$-0.717340\pi$
$439$	7.46725	−	12.9337i	0.356392	−	0.617290i	0.987355	+	0.158523i	$0.0506733\pi$
$440$		0			0
$441$	7.98676	+	13.8335i	0.380322	+	0.658737i
$442$	39.7876	−	10.6611i	1.89250	−	0.507095i
$443$	−19.3386	−	5.18176i	−0.918804	−	0.246193i	−0.231730	−	0.972780i	$-0.574439\pi$
$443$	−19.3386	−	5.18176i	−0.918804	−	0.246193i	−0.687074	+	0.726587i	$0.741105\pi$
$444$		−	2.72850i		−	0.129489i
$445$		0			0
$446$	−6.82149	−	11.8152i	−0.323007	−	0.559464i
$447$	8.39574	+	2.24963i	0.397105	+	0.106404i
$448$	0.349095	−	0.349095i	0.0164932	−	0.0164932i
$449$	24.5286			1.15758			0.578788	−	0.815478i	$-0.303526\pi$
$449$	24.5286			1.15758			0.578788	+	0.815478i	$0.303526\pi$
$450$		0			0
$451$	4.33007	+	2.49997i	0.203895	+	0.117719i
$452$	−1.37140	−	0.367465i	−0.0645051	−	0.0172841i
$453$	3.46966	+	12.9489i	0.163019	+	0.608394i
$454$	13.5198	+	7.80568i	0.634518	+	0.366339i
$455$		0			0
$456$	3.42202	+	0.607453i	0.160251	+	0.0284466i
$457$	6.47002	+	6.47002i	0.302655	+	0.302655i	0.842052	−	0.539397i	$-0.181348\pi$
$457$	6.47002	+	6.47002i	0.302655	+	0.302655i	−0.539397	+	0.842052i	$0.681348\pi$
$458$	−23.7943	+	6.37567i	−1.11184	+	0.297915i
$459$	−12.9806	+	22.4831i	−0.605882	+	1.04942i
$460$		0			0
$461$	13.8659	−	24.0165i	0.645801	−	1.11856i	−0.338314	−	0.941033i	$-0.609857\pi$
$461$	13.8659	−	24.0165i	0.645801	−	1.11856i	0.984116	−	0.177528i	$-0.0568099\pi$
$462$	0.124230	−	0.463633i	0.00577971	−	0.0215702i
$463$	0.815656	−	0.815656i	0.0379068	−	0.0379068i	−0.687899	−	0.725806i	$-0.741467\pi$
$463$	0.815656	−	0.815656i	0.0379068	−	0.0379068i	0.725806	+	0.687899i	$0.241467\pi$
$464$	6.32075			0.293433
$465$		0			0
$466$	−12.8635	+	7.42677i	−0.595892	+	0.344038i
$467$	16.8004	+	16.8004i	0.777428	+	0.777428i	0.979393	−	0.201965i	$-0.0647327\pi$
$467$	16.8004	+	16.8004i	0.777428	+	0.777428i	−0.201965	+	0.979393i	$0.564733\pi$
$468$	11.3451	+	11.3451i	0.524429	+	0.524429i
$469$	−3.39982	−	5.88865i	−0.156989	−	0.271913i
$470$		0			0
$471$	9.48573	−	5.47659i	0.437079	−	0.252348i
$472$	0.0279292	−	0.00748361i	0.00128555	−	0.000344461i
$473$	−1.83898	−	6.86315i	−0.0845562	−	0.315568i
$474$	3.46957			0.159362
$475$		0			0
$476$	2.99662			0.137350
$477$	−8.31199	−	31.0208i	−0.380580	−	1.42034i
$478$	−18.2126	+	4.88006i	−0.833026	+	0.223209i
$479$	−4.53649	+	2.61915i	−0.207278	+	0.119672i	−0.600046	−	0.799966i	$-0.704851\pi$
$479$	−4.53649	+	2.61915i	−0.207278	+	0.119672i	0.392768	+	0.919638i	$0.371518\pi$
$480$		0			0
$481$	−11.6114	−	20.1115i	−0.529433	−	0.917005i
$482$	−12.1778	−	12.1778i	−0.554682	−	0.554682i
$483$	−2.55602	−	2.55602i	−0.116303	−	0.116303i
$484$	8.23865	−	4.75659i	0.374484	−	0.216208i
$485$		0			0
$486$	−15.7675			−0.715229
$487$	−19.1050	+	19.1050i	−0.865728	+	0.865728i	−0.991996	−	0.126268i	$-0.959700\pi$
$487$	−19.1050	+	19.1050i	−0.865728	+	0.865728i	0.126268	+	0.991996i	$0.459700\pi$
$488$	−2.01956	+	7.53708i	−0.0914210	+	0.341188i
$489$	7.38574	−	12.7925i	0.333995	−	0.578496i
$490$		0			0
$491$	17.9282	−	31.0526i	0.809089	−	1.40138i	−0.104407	−	0.994535i	$-0.533294\pi$
$491$	17.9282	−	31.0526i	0.809089	−	1.40138i	0.913496	−	0.406849i	$-0.133372\pi$
$492$	3.15806	−	0.846198i	0.142376	−	0.0381496i
$493$	27.1286	+	27.1286i	1.22181	+	1.22181i
$494$	27.8084	−	10.0852i	1.25116	−	0.453755i
$495$		0			0
$496$	−3.32903	−	1.92202i	−0.149478	−	0.0863012i
$497$	0.884570	+	3.30126i	0.0396784	+	0.148082i
$498$	2.58033	+	0.691398i	0.115627	+	0.0309823i
$499$	−4.98159	−	2.87612i	−0.223007	−	0.128753i	0.384335	−	0.923194i	$-0.374431\pi$
$499$	−4.98159	−	2.87612i	−0.223007	−	0.128753i	−0.607342	+	0.794441i	$0.707764\pi$
$500$		0			0
$501$	16.8402			0.752364
$502$	−4.48342	+	4.48342i	−0.200105	+	0.200105i
$503$	−12.6876	−	3.39964i	−0.565713	−	0.151582i	−0.0353834	−	0.999374i	$-0.511265\pi$
$503$	−12.6876	−	3.39964i	−0.565713	−	0.151582i	−0.530330	+	0.847791i	$0.677932\pi$
$504$	0.583609	+	1.01084i	0.0259960	+	0.0450264i
$505$		0			0
$506$			11.1972i			0.497775i
$507$	−25.4568	−	6.82112i	−1.13057	−	0.302937i
$508$	4.19942	−	1.12523i	0.186319	−	0.0499241i
$509$	−0.486841	−	0.843234i	−0.0215789	−	0.0373757i	0.855034	−	0.518571i	$-0.173536\pi$
$509$	−0.486841	−	0.843234i	−0.0215789	−	0.0373757i	−0.876613	+	0.481196i	$0.840203\pi$
$510$		0			0
$511$	−1.92451	+	3.33335i	−0.0851354	+	0.147459i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−7.89853	+	16.8877i	−0.348729	+	0.745611i
$514$			12.4576i			0.549483i
$515$		0			0
$516$	−4.02367	−	2.32307i	−0.177132	−	0.102267i
$517$	0.0657530	−	0.245394i	0.00289182	−	0.0107924i
$518$	−0.437257	−	1.63186i	−0.0192120	−	0.0717000i
$519$	−5.15571	+	2.97665i	−0.226311	+	0.130660i
$520$		0			0
$521$		−	39.3767i		−	1.72512i	−0.505952	−	0.862562i	$-0.668859\pi$
$521$		−	39.3767i		−	1.72512i	0.505952	−	0.862562i	$-0.331141\pi$
$522$	−3.86775	+	14.4346i	−0.169287	+	0.631787i
$523$	−3.21505	+	11.9987i	−0.140585	+	0.524669i	0.859328	+	0.511425i	$0.170882\pi$
$523$	−3.21505	+	11.9987i	−0.140585	+	0.524669i	−0.999912	+	0.0132434i	$0.995784\pi$
$524$		−	18.9756i		−	0.828954i
$525$		0			0
$526$	12.6533	−	7.30541i	0.551712	−	0.318531i
$527$	−6.03889	−	22.5374i	−0.263058	−	0.981746i
$528$	−0.251634	+	0.939110i	−0.0109510	+	0.0408695i
$529$	53.1090	+	30.6625i	2.30909	+	1.33315i
$530$		0			0
$531$			0.0683611i			0.00296662i
$532$	2.14399	−	0.185090i	0.0929537	−	0.00802468i
$533$	19.6766	−	19.6766i	0.852287	−	0.852287i
$534$	1.67790	−	2.90621i	0.0726100	−	0.125764i
$535$		0			0
$536$	6.88648	+	11.9277i	0.297451	+	0.515200i
$537$	−8.14953	+	2.18366i	−0.351678	+	0.0942319i
$538$	19.0048	+	5.09232i	0.819355	+	0.219546i
$539$			8.23829i			0.354848i
$540$		0			0
$541$	1.47393	+	2.55292i	0.0633692	+	0.109759i	0.895969	−	0.444116i	$-0.146482\pi$
$541$	1.47393	+	2.55292i	0.0633692	+	0.109759i	−0.832600	+	0.553874i	$0.813149\pi$
$542$	3.74204	+	1.00268i	0.160734	+	0.0430686i
$543$	0.107550	−	0.107550i	0.00461539	−	0.00461539i
$544$	−6.06978			−0.260240
$545$		0			0
$546$	−2.31346	−	1.33568i	−0.0990070	−	0.0571617i
$547$	32.3454	+	8.66691i	1.38299	+	0.370570i	0.872205	−	0.489140i	$-0.162689\pi$
$547$	32.3454	+	8.66691i	1.38299	+	0.370570i	0.510782	+	0.859710i	$0.329356\pi$
$548$	−1.73568	−	6.47764i	−0.0741445	−	0.276711i
$549$	−15.9766	−	9.22409i	−0.681864	−	0.393674i
$550$		0			0
$551$	21.0853	+	17.7340i	0.898264	+	0.755495i
$552$	5.17733	+	5.17733i	0.220362	+	0.220362i
$553$	2.07508	−	0.556016i	0.0882413	−	0.0236442i
$554$	−3.34349	+	5.79109i	−0.142051	+	0.246040i
$555$		0			0
$556$	7.85680	−	13.6084i	0.333202	−	0.577123i
$557$	9.37215	−	34.9774i	0.397111	−	1.48204i	−0.421044	−	0.907040i	$-0.638336\pi$
$557$	9.37215	−	34.9774i	0.397111	−	1.48204i	0.818155	−	0.574998i	$-0.194997\pi$
$558$	6.42638	−	6.42638i	0.272050	−	0.272050i
$559$	−39.5440			−1.67253
$560$		0			0
$561$	−5.11066	+	2.95064i	−0.215772	+	0.124576i
$562$	12.4600	+	12.4600i	0.525592	+	0.525592i
$563$	4.13394	+	4.13394i	0.174225	+	0.174225i	0.788833	−	0.614608i	$-0.210686\pi$
$563$	4.13394	+	4.13394i	0.174225	+	0.174225i	−0.614608	+	0.788833i	$0.710686\pi$
$564$	−0.0830618	−	0.143867i	−0.00349753	−	0.00605791i
$565$		0			0
$566$	9.28739	−	5.36208i	0.390378	−	0.225385i
$567$	−1.75606	+	0.470534i	−0.0737474	+	0.0197606i
$568$	−1.79174	−	6.68685i	−0.0751796	−	0.280574i
$569$	23.3672			0.979605			0.489803	−	0.871833i	$-0.337069\pi$
$569$	23.3672			0.979605			0.489803	+	0.871833i	$0.337069\pi$
$570$		0			0
$571$	39.1225			1.63722			0.818612	−	0.574346i	$-0.194744\pi$
$571$	39.1225			1.63722			0.818612	+	0.574346i	$0.194744\pi$
$572$	2.14170	+	7.99292i	0.0895488	+	0.334201i
$573$	1.75204	−	0.469458i	0.0731926	−	0.0196119i
$574$	1.75316	−	1.01219i	0.0731756	−	0.0422480i
$575$		0			0
$576$	−1.18213	−	2.04750i	−0.0492553	−	0.0853126i
$577$	−27.1530	−	27.1530i	−1.13040	−	1.13040i	−0.990111	−	0.140285i	$-0.955198\pi$
$577$	−27.1530	−	27.1530i	−1.13040	−	1.13040i	−0.140285	−	0.990111i	$-0.544802\pi$
$578$	−14.0306	−	14.0306i	−0.583596	−	0.583596i
$579$	3.34099	−	1.92892i	0.138847	−	0.0801633i
$580$		0			0
$581$	1.65405			0.0686214
$582$	1.79002	−	1.79002i	0.0741987	−	0.0741987i
$583$	4.28689	−	15.9989i	0.177545	−	0.662606i
$584$	3.89818	−	6.75185i	0.161308	−	0.279394i
$585$		0			0
$586$	2.58393	−	4.47549i	0.106741	−	0.184881i
$587$	−8.42898	+	2.25854i	−0.347901	+	0.0932199i	−0.428538	−	0.903524i	$-0.640971\pi$
$587$	−8.42898	+	2.25854i	−0.347901	+	0.0932199i	0.0806369	+	0.996744i	$0.474305\pi$
$588$	3.80920	+	3.80920i	0.157089	+	0.157089i
$589$	−5.71270	−	15.7519i	−0.235388	−	0.649044i
$590$		0			0
$591$	−5.40621	−	3.12128i	−0.222382	−	0.128392i
$592$	0.885683	+	3.30542i	0.0364014	+	0.135852i
$593$	10.3180	+	2.76469i	0.423708	+	0.113532i	0.464371	−	0.885641i	$-0.346280\pi$
$593$	10.3180	+	2.76469i	0.423708	+	0.113532i	−0.0406634	+	0.999173i	$0.512947\pi$
$594$	−4.51661	−	2.60767i	−0.185319	−	0.106994i
$595$		0			0
$596$	−10.9012			−0.446529
$597$	3.69621	−	3.69621i	0.151276	−	0.151276i
$598$	60.1940	+	16.1289i	2.46151	+	0.659561i
$599$	23.4008	+	40.5314i	0.956132	+	1.65607i	0.731757	+	0.681566i	$0.238701\pi$
$599$	23.4008	+	40.5314i	0.956132	+	1.65607i	0.224375	+	0.974503i	$0.427966\pi$
$600$		0			0
$601$		−	16.8381i		−	0.686839i	−0.939182	−	0.343419i	$-0.888415\pi$
$601$		−	16.8381i		−	0.686839i	0.939182	−	0.343419i	$-0.111585\pi$
$602$	−2.77876	−	0.744567i	−0.113254	−	0.0303463i
$603$	−31.4532	+	8.42786i	−1.28087	+	0.343209i
$604$	−8.40655	−	14.5606i	−0.342058	−	0.592462i
$605$		0			0
$606$	−3.41095	+	5.90794i	−0.138560	+	0.239994i
$607$	−12.0746	+	12.0746i	−0.490093	+	0.490093i	−0.908335	−	0.418243i	$-0.862646\pi$
$607$	−12.0746	+	12.0746i	−0.490093	+	0.490093i	0.418243	+	0.908335i	$0.362646\pi$
$608$	−4.34275	+	0.374909i	−0.176122	+	0.0152046i
$609$		−	2.48811i		−	0.100823i
$610$		0			0
$611$	−1.22448	−	0.706952i	−0.0495371	−	0.0286002i
$612$	3.71418	−	13.8615i	0.150137	−	0.560319i
$613$	5.66708	+	21.1498i	0.228891	+	0.854233i	0.980808	+	0.194975i	$0.0624627\pi$
$613$	5.66708	+	21.1498i	0.228891	+	0.854233i	−0.751917	+	0.659258i	$0.770871\pi$
$614$	−14.6273	+	8.44505i	−0.590308	+	0.340814i
$615$		0			0
$616$			0.601989i			0.0242548i
$617$	−8.78516	+	32.7867i	−0.353677	+	1.31994i	0.528464	+	0.848956i	$0.322768\pi$
$617$	−8.78516	+	32.7867i	−0.353677	+	1.31994i	−0.882141	+	0.470986i	$0.843898\pi$
$618$	−2.39964	+	8.95558i	−0.0965277	+	0.360246i
$619$		−	30.7197i		−	1.23473i	−0.786678	−	0.617364i	$-0.788201\pi$
$619$		−	30.7197i		−	1.23473i	0.786678	−	0.617364i	$-0.211799\pi$
$620$		0			0
$621$	−34.0142	+	19.6381i	−1.36494	+	0.788050i
$622$	−4.58952	−	17.1283i	−0.184023	−	0.686782i
$623$	0.537785	−	2.00704i	0.0215459	−	0.0804104i
$624$	4.68602	+	2.70548i	0.187591	+	0.108306i
$625$		0			0
$626$			23.7894i			0.950815i
$627$	−3.47427	+	2.42676i	−0.138749	+	0.0969154i
$628$	−9.71366	+	9.71366i	−0.387617	+	0.387617i
$629$	−10.3855	+	17.9881i	−0.414095	+	0.717234i
$630$		0			0
$631$	−7.83105	−	13.5638i	−0.311749	−	0.539965i	0.666992	−	0.745065i	$-0.267581\pi$
$631$	−7.83105	−	13.5638i	−0.311749	−	0.539965i	−0.978741	+	0.205100i	$0.934248\pi$
$632$	−4.20317	+	1.12623i	−0.167193	+	0.0447992i
$633$	−2.01737	−	0.540553i	−0.0801833	−	0.0214850i
$634$			22.9946i			0.913231i
$635$		0			0
$636$	−5.41536	−	9.37968i	−0.214733	−	0.371929i
$637$	44.2876	+	11.8668i	1.75474	+	0.470180i
$638$	−5.44984	+	5.44984i	−0.215761	+	0.215761i
$639$	16.3671			0.647473
$640$		0			0
$641$	−6.14016	−	3.54502i	−0.242522	−	0.140020i	0.373813	−	0.927504i	$-0.378050\pi$
$641$	−6.14016	−	3.54502i	−0.242522	−	0.140020i	−0.616335	+	0.787484i	$0.711383\pi$
$642$	−7.43835	−	1.99310i	−0.293568	−	0.0786613i
$643$	−5.31450	−	19.8340i	−0.209583	−	0.782176i	−0.988003	−	0.154432i	$-0.950645\pi$
$643$	−5.31450	−	19.8340i	−0.209583	−	0.782176i	0.778420	−	0.627744i	$-0.216021\pi$
$644$	3.92615	+	2.26676i	0.154712	+	0.0893230i
$645$		0			0
$646$	−20.2481	−	17.0299i	−0.796651	−	0.670032i
$647$	−6.10076	−	6.10076i	−0.239846	−	0.239846i	0.576941	−	0.816786i	$-0.304246\pi$
$647$	−6.10076	−	6.10076i	−0.239846	−	0.239846i	−0.816786	+	0.576941i	$0.804246\pi$
$648$	3.55697	−	0.953087i	0.139731	−	0.0374408i
$649$	−0.0176285	+	0.0305335i	−0.000691979	+	0.00119854i
$650$		0			0
$651$	−0.756586	+	1.31044i	−0.0296529	+	0.0513604i
$652$	−4.79488	+	17.8947i	−0.187782	+	0.700812i
$653$	−10.4826	+	10.4826i	−0.410216	+	0.410216i	−0.881814	−	0.471598i	$-0.843677\pi$
$653$	−10.4826	+	10.4826i	−0.410216	+	0.410216i	0.471598	+	0.881814i	$0.343677\pi$
$654$	−12.4370			−0.486327
$655$		0			0
$656$	−3.55111	+	2.05023i	−0.138648	+	0.0800482i
$657$	13.0338	+	13.0338i	0.508497	+	0.508497i
$658$	−0.0727331	−	0.0727331i	−0.00283543	−	0.00283543i
$659$	1.55187	+	2.68791i	0.0604521	+	0.104706i	0.894668	−	0.446732i	$-0.147412\pi$
$659$	1.55187	+	2.68791i	0.0604521	+	0.104706i	−0.834215	+	0.551439i	$0.814079\pi$
$660$		0			0
$661$	−17.7163	+	10.2285i	−0.689085	+	0.397843i	−0.803269	−	0.595616i	$-0.796908\pi$
$661$	−17.7163	+	10.2285i	−0.689085	+	0.397843i	0.114184	+	0.993460i	$0.463575\pi$
$662$	−24.9169	+	6.67646i	−0.968423	+	0.259488i
$663$	8.50047	+	31.7242i	0.330131	+	1.23207i
$664$	−3.35034			−0.130019
$665$		0			0
$666$	−8.09051			−0.313501
$667$	15.0225	+	56.0648i	0.581675	+	2.17084i
$668$	−20.4009	+	5.46639i	−0.789333	+	0.211501i
$669$	9.42068	−	5.43903i	0.364224	−	0.210285i
$670$		0			0
$671$	−4.75730	−	8.23988i	−0.183653	−	0.318097i
$672$	0.278346	+	0.278346i	0.0107374	+	0.0107374i
$673$	−16.8223	−	16.8223i	−0.648451	−	0.648451i	0.304167	−	0.952619i	$-0.401622\pi$
$673$	−16.8223	−	16.8223i	−0.648451	−	0.648451i	−0.952619	+	0.304167i	$0.901622\pi$
$674$	−7.14416	+	4.12468i	−0.275183	+	0.158877i
$675$		0			0
$676$	33.0535			1.27129
$677$	2.14526	−	2.14526i	0.0824489	−	0.0824489i	−0.664680	−	0.747129i	$-0.731432\pi$
$677$	2.14526	−	2.14526i	0.0824489	−	0.0824489i	0.747129	+	0.664680i	$0.231432\pi$
$678$	0.292994	−	1.09347i	0.0112524	−	0.0419943i
$679$	0.783715	−	1.35743i	0.0300762	−	0.0520936i
$680$		0			0
$681$	−6.22377	+	10.7799i	−0.238495	+	0.413086i
$682$	4.52754	−	1.21315i	0.173368	−	0.0464539i
$683$	28.7563	+	28.7563i	1.10033	+	1.10033i	0.994371	+	0.105958i	$0.0337910\pi$
$683$	28.7563	+	28.7563i	1.10033	+	1.10033i	0.105958	+	0.994371i	$0.466209\pi$
$684$	1.80121	−	10.1469i	0.0688710	−	0.387977i
$685$		0			0
$686$	5.88152	+	3.39569i	0.224557	+	0.129648i
$687$	−5.08356	−	18.9721i	−0.193950	−	0.723831i
$688$	5.62850	+	1.50815i	0.214585	+	0.0574978i
$689$	−79.8320	−	46.0910i	−3.04136	−	1.75593i
$690$		0			0
$691$	−18.7806			−0.714449			−0.357225	−	0.934018i	$-0.616277\pi$
$691$	−18.7806			−0.714449			−0.357225	+	0.934018i	$0.616277\pi$
$692$	5.27959	−	5.27959i	0.200700	−	0.200700i
$693$	−1.37476	−	0.368365i	−0.0522227	−	0.0139930i
$694$	−3.53544	−	6.12356i	−0.134203	−	0.232447i
$695$		0			0
$696$			5.03977i			0.191032i
$697$	−24.0409	−	6.44174i	−0.910613	−	0.243998i
$698$	−19.9306	+	5.34039i	−0.754385	+	0.202137i
$699$	−5.92165	−	10.2566i	−0.223977	−	0.387940i
$700$		0			0
$701$	14.0812	−	24.3894i	0.531840	−	0.921174i	−0.467469	−	0.884009i	$-0.654834\pi$
$701$	14.0812	−	24.3894i	0.531840	−	0.921174i	0.999309	−	0.0371643i	$-0.0118325\pi$
$702$	−20.5243	+	20.5243i	−0.774639	+	0.774639i
$703$	−6.31942	+	13.5114i	−0.238341	+	0.509593i
$704$		−	1.21936i		−	0.0459562i
$705$		0			0
$706$	17.2081	+	9.93513i	0.647637	+	0.373914i
$707$	−1.09324	+	4.08004i	−0.0411157	+	0.153446i
$708$	0.00596697	+	0.0222690i	0.000224252	+	0.000836921i
$709$	−28.3507	+	16.3683i	−1.06473	+	0.614723i	−0.926737	−	0.375709i	$-0.877399\pi$
$709$	−28.3507	+	16.3683i	−1.06473	+	0.614723i	−0.137995	+	0.990433i	$0.544066\pi$
$710$		0			0
$711$		−	10.2879i		−	0.385826i
$712$	−1.08931	+	4.06535i	−0.0408236	+	0.152356i
$713$	9.13612	−	34.0965i	0.342150	−	1.27692i
$714$			2.38932i			0.0894179i
$715$		0			0
$716$	9.16383	−	5.29074i	0.342469	−	0.197724i
$717$	−3.89106	−	14.5216i	−0.145314	−	0.542320i
$718$	3.20692	−	11.9684i	0.119681	−	0.446657i
$719$	19.9221	+	11.5020i	0.742968	+	0.428953i	0.823147	−	0.567828i	$-0.192216\pi$
$719$	19.9221	+	11.5020i	0.742968	+	0.428953i	−0.0801796	+	0.996780i	$0.525549\pi$
$720$		0			0
$721$			5.74071i			0.213795i
$722$	−15.5388	−	10.9337i	−0.578293	−	0.406911i
$723$	9.70979	−	9.70979i	0.361111	−	0.361111i
$724$	−0.0953786	+	0.165201i	−0.00354472	+	0.00613963i
$725$		0			0
$726$	3.79261	+	6.56899i	0.140757	+	0.243798i
$727$	35.2360	−	9.44145i	1.30683	−	0.350164i	0.462802	−	0.886462i	$-0.346844\pi$
$727$	35.2360	−	9.44145i	1.30683	−	0.350164i	0.844029	+	0.536298i	$0.180178\pi$
$728$	3.23618	+	0.867133i	0.119941	+	0.0321381i
$729$		−	1.52470i		−	0.0564705i
$730$		0			0
$731$	17.6845	+	30.6304i	0.654084	+	1.13291i
$732$	−6.00960	−	1.61027i	−0.222121	−	0.0595172i
$733$	28.0599	−	28.0599i	1.03642	−	1.03642i	0.0371046	−	0.999311i	$-0.488187\pi$
$733$	28.0599	−	28.0599i	1.03642	−	1.03642i	0.999311	−	0.0371046i	$-0.0118135\pi$
$734$	6.02170			0.222265
$735$		0			0
$736$	−7.95259	−	4.59143i	−0.293136	−	0.169242i
$737$	−16.2219	−	4.34664i	−0.597541	−	0.160111i
$738$	−2.50913	−	9.36421i	−0.0923624	−	0.344701i
$739$	−11.7878	−	6.80568i	−0.433621	−	0.250351i	0.267267	−	0.963622i	$-0.413879\pi$
$739$	−11.7878	−	6.80568i	−0.433621	−	0.250351i	−0.700888	+	0.713271i	$0.747213\pi$
$740$		0			0
$741$	8.04132	+	22.1727i	0.295405	+	0.814533i
$742$	−4.74196	−	4.74196i	−0.174083	−	0.174083i
$743$	35.5646	−	9.52951i	1.30474	−	0.349604i	0.461499	−	0.887141i	$-0.347312\pi$
$743$	35.5646	−	9.52951i	1.30474	−	0.349604i	0.843240	+	0.537537i	$0.180645\pi$
$744$	1.53250	−	2.65436i	0.0561841	−	0.0973137i
$745$		0			0
$746$	−9.57062	+	16.5768i	−0.350405	+	0.606920i
$747$	2.05012	−	7.65115i	0.0750100	−	0.279941i
$748$	5.23346	−	5.23346i	0.191354	−	0.191354i
$749$	−4.76813			−0.174224
$750$		0			0
$751$	−3.24712	+	1.87472i	−0.118489	+	0.0684097i	−0.558073	−	0.829792i	$-0.688459\pi$
$751$	−3.24712	+	1.87472i	−0.118489	+	0.0684097i	0.439584	+	0.898201i	$0.355126\pi$
$752$	0.147324	+	0.147324i	0.00537236	+	0.00537236i
$753$	−3.57480	−	3.57480i	−0.130273	−	0.130273i
$754$	21.4472	+	37.1476i	0.781059	+	1.35283i
$755$		0			0
$756$	−1.82869	+	1.05580i	−0.0665088	+	0.0383989i
$757$	−14.8945	+	3.99098i	−0.541351	+	0.145055i	−0.519125	−	0.854698i	$-0.673742\pi$
$757$	−14.8945	+	3.99098i	−0.541351	+	0.145055i	−0.0222261	+	0.999753i	$0.507075\pi$
$758$	−8.25695	−	30.8154i	−0.299906	−	1.11926i
$759$	−8.92793			−0.324063
$760$		0			0
$761$	−10.6533			−0.386181			−0.193090	−	0.981181i	$-0.561851\pi$
$761$	−10.6533			−0.386181			−0.193090	+	0.981181i	$0.561851\pi$
$762$	0.897189	+	3.34836i	0.0325017	+	0.121298i
$763$	−7.43835	+	1.99310i	−0.269286	+	0.0721550i
$764$	−1.97010	+	1.13744i	−0.0712758	+	0.0411511i
$765$		0			0
$766$	−16.8260	−	29.1435i	−0.607948	−	1.05300i
$767$	0.138749	+	0.138749i	0.00500995	+	0.00500995i
$768$	−0.563803	−	0.563803i	−0.0203445	−	0.0203445i
$769$	−41.4196	+	23.9136i	−1.49363	+	0.862347i	−0.999973	−	0.00730985i	$-0.997673\pi$
$769$	−41.4196	+	23.9136i	−1.49363	+	0.862347i	−0.493656	+	0.869657i	$0.664340\pi$
$770$		0			0
$771$	−9.93296			−0.357727
$772$	−3.42127	+	3.42127i	−0.123134	+	0.123134i
$773$	−1.39223	+	5.19588i	−0.0500751	+	0.186883i	−0.986433	−	0.164164i	$-0.947507\pi$
$773$	−1.39223	+	5.19588i	−0.0500751	+	0.186883i	0.936358	+	0.351046i	$0.114174\pi$
$774$	−6.88832	+	11.9309i	−0.247595	+	0.428848i
$775$		0			0
$776$	−1.58745	+	2.74954i	−0.0569861	+	0.0987029i
$777$	1.30115	−	0.348641i	0.0466784	−	0.0125074i
$778$	−9.47243	−	9.47243i	−0.339603	−	0.339603i
$779$	−17.5984	−	3.12395i	−0.630528	−	0.111927i
$780$		0			0
$781$	7.31037	+	4.22064i	0.261585	+	0.151026i
$782$	−14.4261	−	53.8388i	−0.515874	−	1.92527i
$783$	−26.1134	−	6.99707i	−0.933218	−	0.250055i
$784$	−5.85110	−	3.37813i	−0.208968	−	0.120648i
$785$		0			0
$786$	15.1300			0.539669
$787$	6.09983	−	6.09983i	0.217435	−	0.217435i	−0.589981	−	0.807417i	$-0.700865\pi$
$787$	6.09983	−	6.09983i	0.217435	−	0.217435i	0.807417	+	0.589981i	$0.200865\pi$
$788$	7.56247	+	2.02636i	0.269402	+	0.0721860i
$789$	5.82488	+	10.0890i	0.207371	+	0.359177i
$790$		0			0
$791$		−	0.700935i		−	0.0249224i
$792$	2.78463	+	0.746140i	0.0989477	+	0.0265129i
$793$	−51.1487	+	13.7053i	−1.81634	+	0.486688i
$794$	−13.0967	−	22.6841i	−0.464784	−	0.805030i
$795$		0			0
$796$	−3.27792	+	5.67753i	−0.116183	+	0.201235i
$797$	−14.8234	+	14.8234i	−0.525071	+	0.525071i	−0.919099	−	0.394028i	$-0.871081\pi$
$797$	−14.8234	+	14.8234i	−0.525071	+	0.525071i	0.394028	+	0.919099i	$0.371081\pi$
$798$	0.147579	+	1.70948i	0.00522426	+	0.0605151i
$799$			1.26463i			0.0447393i
$800$		0			0
$801$	−8.61745	−	4.97529i	−0.304483	−	0.175793i
$802$	−3.86927	+	14.4403i	−0.136629	+	0.509905i
$803$	2.46048	+	9.18262i	0.0868283	+	0.324048i
$804$	−9.51043	+	5.49085i	−0.335407	+	0.193647i
$805$		0			0
$806$		−	26.0867i		−	0.918864i
$807$	−4.06030	+	15.1533i	−0.142929	+	0.533420i
$808$	2.21442	−	8.26431i	0.0779029	−	0.290738i
$809$		−	23.3920i		−	0.822419i	−0.911541	−	0.411210i	$-0.865106\pi$
$809$		−	23.3920i		−	0.822419i	0.911541	−	0.411210i	$-0.134894\pi$
$810$		0			0
$811$	−10.1960	+	5.88667i	−0.358030	+	0.206709i	−0.668216	−	0.743967i	$-0.732942\pi$
$811$	−10.1960	+	5.88667i	−0.358030	+	0.206709i	0.310186	+	0.950676i	$0.399609\pi$
$812$	0.807650	+	3.01419i	0.0283429	+	0.105777i
$813$	−0.799471	+	2.98367i	−0.0280387	+	0.104642i
$814$	−3.61363	−	2.08633i	−0.126658	−	0.0731258i
$815$		0			0
$816$		−	4.83967i		−	0.169422i
$817$	14.5446	+	20.8228i	0.508853	+	0.728499i
$818$	1.58353	−	1.58353i	0.0553669	−	0.0553669i
$819$	−3.96053	+	6.85984i	−0.138392	+	0.239702i
$820$		0			0
$821$	13.2194	+	22.8966i	0.461359	+	0.799097i	0.999029	−	0.0440585i	$-0.0140288\pi$
$821$	13.2194	+	22.8966i	0.461359	+	0.799097i	−0.537670	+	0.843155i	$0.680695\pi$
$822$	5.16487	−	1.38392i	0.180146	−	0.0482699i
$823$	−8.01707	−	2.14817i	−0.279458	−	0.0748804i	0.116368	−	0.993206i	$-0.462875\pi$
$823$	−8.01707	−	2.14817i	−0.279458	−	0.0748804i	−0.395826	+	0.918326i	$0.629541\pi$
$824$		−	11.6281i		−	0.405083i
$825$		0			0
$826$	0.00713745	+	0.0123624i	0.000248344	+	0.000430144i
$827$	−14.3823	−	3.85372i	−0.500121	−	0.134007i	−6.47685e−5	−	1.00000i	$-0.500021\pi$
$827$	−14.3823	−	3.85372i	−0.500121	−	0.134007i	−0.500056	+	0.865993i	$0.666687\pi$
$828$	15.3517	−	15.3517i	0.533509	−	0.533509i
$829$	14.3540			0.498535			0.249267	−	0.968435i	$-0.419810\pi$
$829$	14.3540			0.498535			0.249267	+	0.968435i	$0.419810\pi$
$830$		0			0
$831$	−4.61746	−	2.66589i	−0.160178	−	0.0924787i
$832$	−6.55503	−	1.75642i	−0.227255	−	0.0608928i
$833$	−10.6139	−	39.6117i	−0.367751	−	1.37246i
$834$	10.8505	+	6.26452i	0.375721	+	0.216923i
$835$		0			0
$836$	3.42113	−	4.06763i	0.118322	−	0.140682i
$837$	11.6258	+	11.6258i	0.401848	+	0.401848i
$838$	−0.283804	+	0.0760450i	−0.00980384	+	0.00262693i
$839$	−18.3046	+	31.7045i	−0.631945	+	1.09456i	0.355208	+	0.934787i	$0.384410\pi$
$839$	−18.3046	+	31.7045i	−0.631945	+	1.09456i	−0.987154	+	0.159774i	$0.948923\pi$
$840$		0			0
$841$	−5.47594	+	9.48461i	−0.188826	+	0.327055i
$842$	−0.270522	+	1.00960i	−0.00932281	+	0.0347932i
$843$	−9.93481	+	9.93481i	−0.342173	+	0.342173i
$844$	2.61939			0.0901630
$845$		0			0
$846$	−0.426593	+	0.246293i	−0.0146666	+	0.00846774i
$847$	3.32100	+	3.32100i	0.114111	+	0.114111i
$848$	9.60506	+	9.60506i	0.329839	+	0.329839i
$849$	4.27539	+	7.40519i	0.146731	+	0.254145i
$850$		0			0
$851$	−27.2139	+	15.7120i	−0.932881	+	0.538599i
$852$	5.33168	−	1.42862i	0.182660	−	0.0489437i
$853$	5.59060	+	20.8644i	0.191418	+	0.714383i	0.993165	+	0.116719i	$0.0372377\pi$
$853$	5.59060	+	20.8644i	0.191418	+	0.714383i	−0.801747	+	0.597664i	$0.796096\pi$
$854$	−3.85228			−0.131822
$855$		0			0
$856$	9.65807			0.330106
$857$	−1.09117	−	4.07232i	−0.0372738	−	0.139108i	0.944781	−	0.327701i	$-0.106274\pi$
$857$	−1.09117	−	4.07232i	−0.0372738	−	0.139108i	−0.982055	+	0.188593i	$0.939607\pi$
$858$	−6.37306	+	1.70766i	−0.217573	+	0.0582984i
$859$	31.3522	−	18.1012i	1.06972	−	0.617605i	0.141617	−	0.989922i	$-0.454770\pi$
$859$	31.3522	−	18.1012i	1.06972	−	0.617605i	0.928106	+	0.372317i	$0.121437\pi$
$860$		0			0
$861$	0.807057	+	1.39786i	0.0275044	+	0.0476391i
$862$	20.4389	+	20.4389i	0.696152	+	0.696152i
$863$	11.1571	+	11.1571i	0.379794	+	0.379794i	0.871028	−	0.491234i	$-0.163454\pi$
$863$	11.1571	+	11.1571i	0.379794	+	0.379794i	−0.491234	+	0.871028i	$0.663454\pi$
$864$	3.70410	−	2.13856i	0.126016	−	0.0727553i
$865$		0			0
$866$	3.47210			0.117987
$867$	11.1871	−	11.1871i	0.379935	−	0.379935i
$868$	0.491181	−	1.83311i	0.0166718	−	0.0622199i
$869$	2.65298	−	4.59509i	0.0899960	−	0.155878i
$870$		0			0
$871$	−46.7335	+	80.9448i	−1.58350	+	2.74271i
$872$	15.0667	−	4.03711i	0.510223	−	0.136714i
$873$	−5.30773	−	5.30773i	−0.179640	−	0.179640i
$874$	−13.6468	−	37.6290i	−0.461611	−	1.27282i
$875$		0			0
$876$	5.38351	+	3.10817i	0.181892	+	0.105015i
$877$	−0.730314	−	2.72557i	−0.0246609	−	0.0920359i	0.952499	−	0.304543i	$-0.0985038\pi$
$877$	−0.730314	−	2.72557i	−0.0246609	−	0.0920359i	−0.977159	+	0.212507i	$0.931837\pi$
$878$	−14.4256	−	3.86533i	−0.486841	−	0.130449i
$879$	3.56848	+	2.06026i	0.120362	+	0.0694910i
$880$		0			0
$881$	−11.6425			−0.392246			−0.196123	−	0.980579i	$-0.562835\pi$
$881$	−11.6425			−0.392246			−0.196123	+	0.980579i	$0.562835\pi$
$882$	11.2950	−	11.2950i	0.380322	−	0.380322i
$883$	−22.9829	−	6.15826i	−0.773437	−	0.207242i	−0.149548	−	0.988755i	$-0.547782\pi$
$883$	−22.9829	−	6.15826i	−0.773437	−	0.207242i	−0.623889	+	0.781513i	$0.714448\pi$
$884$	−20.5956	−	35.6726i	−0.692705	−	1.19980i
$885$		0			0
$886$			20.0208i			0.672611i
$887$	1.21704	+	0.326105i	0.0408642	+	0.0109495i	0.279193	−	0.960235i	$-0.409933\pi$
$887$	1.21704	+	0.326105i	0.0408642	+	0.0109495i	−0.238329	+	0.971184i	$0.576600\pi$
$888$	−2.63553	+	0.706189i	−0.0884427	+	0.0236981i
$889$	1.07318	+	1.85881i	0.0359934	+	0.0623424i
$890$		0			0
$891$	−2.24511	+	3.88864i	−0.0752139	+	0.130274i
$892$	−9.64704	+	9.64704i	−0.323007	+	0.323007i
$893$	0.0781114	+	0.904802i	0.00261390	+	0.0302780i
$894$		−	8.69191i		−	0.290701i
$895$		0			0
$896$	−0.427552	−	0.246847i	−0.0142835	−	0.00824658i
$897$	−12.8602	+	47.9949i	−0.429390	+	1.60250i
$898$	−6.34847	−	23.6928i	−0.211851	−	0.790639i
$899$	21.0420	−	12.1486i	0.701790	−	0.405178i
$900$		0			0
$901$			82.4495i			2.74679i
$902$	1.29408	−	4.82956i	0.0430881	−	0.160807i
$903$	0.593671	−	2.21561i	0.0197561	−	0.0737309i
$904$			1.41978i			0.0472210i
$905$		0			0
$906$	11.6097	−	6.70286i	0.385706	−	0.222688i
$907$	−12.0332	−	44.9084i	−0.399555	−	1.49116i	−0.813881	−	0.581032i	$-0.802649\pi$
$907$	−12.0332	−	44.9084i	−0.399555	−	1.49116i	0.414326	−	0.910129i	$-0.364017\pi$
$908$	4.04052	−	15.0794i	0.134089	−	0.500428i
$909$	17.5181	+	10.1141i	0.581039	+	0.335463i
$910$		0			0
$911$			47.0550i			1.55900i	0.626401	+	0.779501i	$0.284527\pi$
$911$			47.0550i			1.55900i	−0.626401	+	0.779501i	$0.715473\pi$
$912$	−0.298929	−	3.46264i	−0.00989852	−	0.114659i
$913$	2.88872	−	2.88872i	0.0956025	−	0.0956025i
$914$	4.57499	−	7.92412i	0.151327	−	0.262107i
$915$		0			0
$916$	12.3168	+	21.3334i	0.406960	+	0.704875i
$917$	9.04894	−	2.42466i	0.298822	−	0.0800692i
$918$	25.0766	+	6.71925i	0.827651	+	0.221768i
$919$		−	24.4556i		−	0.806715i	−0.915042	−	0.403358i	$-0.867843\pi$
$919$		−	24.4556i		−	0.806715i	0.915042	−	0.403358i	$-0.132157\pi$
$920$		0			0
$921$	−6.73356	−	11.6629i	−0.221878	−	0.384304i
$922$	−26.7869	−	7.17754i	−0.882181	−	0.236380i
$923$	33.2196	−	33.2196i	1.09344	−	1.09344i
$924$	−0.479989			−0.0157905
$925$		0			0
$926$	−0.998971	−	0.576756i	−0.0328282	−	0.0189534i
$927$	26.5549	+	7.11537i	0.872178	+	0.233699i
$928$	−1.63593	−	6.10538i	−0.0537021	−	0.200419i
$929$	−14.5037	−	8.37372i	−0.475851	−	0.274733i	0.242835	−	0.970068i	$-0.421923\pi$
$929$	−14.5037	−	8.37372i	−0.475851	−	0.274733i	−0.718686	+	0.695335i	$0.755256\pi$
$930$		0			0
$931$	−10.0406	−	27.6854i	−0.329068	−	0.907352i
$932$	10.5030	+	10.5030i	0.344038	+	0.344038i
$933$	13.6570	−	3.65939i	0.447112	−	0.119803i
$934$	11.8796	−	20.5762i	0.388714	−	0.673272i
$935$		0			0
$936$	8.02223	−	13.8949i	0.262215	−	0.454169i
$937$	9.15504	−	34.1671i	0.299082	−	1.11619i	−0.638839	−	0.769341i	$-0.720585\pi$
$937$	9.15504	−	34.1671i	0.299082	−	1.11619i	0.937921	−	0.346849i	$-0.112748\pi$
$938$	−4.80807	+	4.80807i	−0.156989	+	0.156989i
$939$	−18.9682			−0.619003
$940$		0			0
$941$	27.3639	−	15.7985i	0.892037	−	0.515018i	0.0174288	−	0.999848i	$-0.494452\pi$
$941$	27.3639	−	15.7985i	0.892037	−	0.515018i	0.874608	+	0.484830i	$0.161119\pi$
$942$	−7.74507	−	7.74507i	−0.252348	−	0.252348i
$943$	−26.6254	−	26.6254i	−0.867043	−	0.867043i
$944$	−0.0144572	−	0.0250407i	−0.000470543	−	0.000815004i
$945$		0			0
$946$	−6.15333	+	3.55263i	−0.200062	+	0.115506i
$947$	4.55423	−	1.22030i	0.147993	−	0.0396545i	−0.184062	−	0.982915i	$-0.558925\pi$
$947$	4.55423	−	1.22030i	0.147993	−	0.0396545i	0.332055	+	0.943260i	$0.392258\pi$
$948$	−0.897990	−	3.35134i	−0.0291653	−	0.108847i
$949$	52.9083			1.71748
$950$		0			0
$951$	−18.3344			−0.594535
$952$	−0.775582	−	2.89451i	−0.0251367	−	0.0938116i
$953$	6.86022	−	1.83819i	0.222224	−	0.0595448i	−0.145989	−	0.989286i	$-0.546636\pi$
$953$	6.86022	−	1.83819i	0.222224	−	0.0595448i	0.368213	+	0.929741i	$0.379970\pi$
$954$	−27.8125	+	16.0575i	−0.900462	+	0.519882i
$955$		0			0
$956$	9.42755	+	16.3290i	0.304909	+	0.528118i
$957$	−4.34537	−	4.34537i	−0.140466	−	0.140466i
$958$	3.70403	+	3.70403i	0.119672	+	0.119672i
$959$	2.86723	−	1.65539i	0.0925876	−	0.0534555i
$960$		0			0
$961$	16.2234			0.523335
$962$	−16.4210	+	16.4210i	−0.529433	+	0.529433i
$963$	−5.90990	+	22.0561i	−0.190444	+	0.710746i
$964$	−8.61098	+	14.9147i	−0.277341	+	0.480369i
$965$		0			0
$966$	−1.80738	+	3.13047i	−0.0581514	+	0.100721i
$967$	28.9837	−	7.76616i	0.932053	−	0.249743i	0.239323	−	0.970940i	$-0.423075\pi$
$967$	28.9837	−	7.76616i	0.932053	−	0.249743i	0.692730	+	0.721197i	$0.256408\pi$
$968$	−6.72683	−	6.72683i	−0.216208	−	0.216208i
$969$	13.5786	−	16.1446i	0.436207	−	0.518639i
$970$		0			0
$971$	−17.9621	−	10.3704i	−0.576430	−	0.332802i	0.183283	−	0.983060i	$-0.441327\pi$
$971$	−17.9621	−	10.3704i	−0.576430	−	0.332802i	−0.759713	+	0.650258i	$0.774661\pi$
$972$	4.08093	+	15.2303i	0.130896	+	0.488511i
$973$	7.49337	+	2.00784i	0.240226	+	0.0643685i
$974$	23.3987	+	13.5092i	0.749742	+	0.432864i
$975$		0			0
$976$	7.80296			0.249767
$977$	−16.0236	+	16.0236i	−0.512641	+	0.512641i	−0.915335	−	0.402694i	$-0.868074\pi$
$977$	−16.0236	+	16.0236i	−0.512641	+	0.512641i	0.402694	+	0.915335i	$0.368074\pi$
$978$	−14.2681	−	3.82314i	−0.456245	−	0.122250i
$979$	−2.56599	−	4.44443i	−0.0820094	−	0.142044i
$980$		0			0
$981$			36.8781i			1.17743i
$982$	−34.6347	−	9.28033i	−1.10524	−	0.296147i
$983$	22.4144	−	6.00592i	0.714908	−	0.191559i	0.117010	−	0.993131i	$-0.462669\pi$
$983$	22.4144	−	6.00592i	0.714908	−	0.191559i	0.597899	+	0.801572i	$0.296003\pi$
$984$	−1.63473	−	2.83143i	−0.0521133	−	0.0902628i
$985$		0			0
$986$	19.1828	−	33.2256i	0.610904	−	1.05812i
$987$	0.0579929	−	0.0579929i	0.00184593	−	0.00184593i
$988$	−16.9389	−	24.2506i	−0.538898	−	0.771513i
$989$			53.5091i			1.70149i
$990$		0			0
$991$	−40.6191	−	23.4515i	−1.29031	−	0.744960i	−0.311600	−	0.950214i	$-0.600865\pi$
$991$	−40.6191	−	23.4515i	−1.29031	−	0.744960i	−0.978709	+	0.205254i	$0.934198\pi$
$992$	−0.994910	+	3.71305i	−0.0315884	+	0.117890i
$993$	−5.32340	−	19.8672i	−0.168933	−	0.630466i
$994$	2.95983	−	1.70886i	0.0938801	−	0.0542017i
$995$		0			0
$996$		−	2.67136i		−	0.0846451i
$997$	12.1461	−	45.3300i	0.384672	−	1.43562i	−0.454010	−	0.890996i	$-0.650007\pi$
$997$	12.1461	−	45.3300i	0.384672	−	1.43562i	0.838683	−	0.544620i	$-0.183326\pi$
$998$	−1.48879	+	5.55624i	−0.0471268	+	0.175880i
$999$		−	14.6364i		−	0.463075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.f.407.3	yes	32
5.2	odd	4	inner	950.2.q.f.293.6	yes	32
5.3	odd	4	inner	950.2.q.f.293.3	yes	32
5.4	even	2	inner	950.2.q.f.407.6	yes	32
19.12	odd	6	inner	950.2.q.f.107.3	✓	32
95.12	even	12	inner	950.2.q.f.943.6	yes	32
95.69	odd	6	inner	950.2.q.f.107.6	yes	32
95.88	even	12	inner	950.2.q.f.943.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.q.f.107.3	✓	32	19.12	odd	6	inner
950.2.q.f.107.6	yes	32	95.69	odd	6	inner
950.2.q.f.293.3	yes	32	5.3	odd	4	inner
950.2.q.f.293.6	yes	32	5.2	odd	4	inner
950.2.q.f.407.3	yes	32	1.1	even	1	trivial
950.2.q.f.407.6	yes	32	5.4	even	2	inner
950.2.q.f.943.3	yes	32	95.88	even	12	inner
950.2.q.f.943.6	yes	32	95.12	even	12	inner

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.770169 - 0.206366i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.398669 - 0.690515i) q^{6} +(-0.349095 - 0.349095i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.04750 + 1.18213i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.770169 - 0.206366i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.398669 - 0.690515i) q^{6} +(-0.349095 - 0.349095i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.04750 + 1.18213i) q^{9} -1.21936 q^{11} +(-0.563803 + 0.563803i) q^{12} +(-1.75642 + 6.55503i) q^{13} +(-0.246847 + 0.427552i) q^{14} +(0.500000 - 0.866025i) q^{16} +(5.86296 - 1.57098i) q^{17} +(1.67178 + 1.67178i) q^{18} +(4.09774 - 1.48612i) q^{19} +(-0.340903 - 0.196821i) q^{21} +(0.315593 + 1.17781i) q^{22} +(8.86996 + 2.37670i) q^{23} +(0.690515 + 0.398669i) q^{24} +6.78627 q^{26} +(-3.02438 + 3.02438i) q^{27} +(0.476872 + 0.127777i) q^{28} +(3.16038 + 5.47393i) q^{29} -3.84404i q^{31} +(-0.965926 - 0.258819i) q^{32} +(-0.939110 + 0.251634i) q^{33} +(-3.03489 - 5.25659i) q^{34} +(1.18213 - 2.04750i) q^{36} +(-2.41973 + 2.41973i) q^{37} +(-2.49605 - 3.57347i) q^{38} +5.41095i q^{39} +(-3.55111 - 2.05023i) q^{41} +(-0.101882 + 0.380228i) q^{42} +(1.50815 + 5.62850i) q^{43} +(1.05599 - 0.609678i) q^{44} -9.18286i q^{46} +(-0.0539244 + 0.201249i) q^{47} +(0.206366 - 0.770169i) q^{48} -6.75627i q^{49} +(4.19127 - 2.41983i) q^{51} +(-1.75642 - 6.55503i) q^{52} +(-3.51570 + 13.1208i) q^{53} +(3.70410 + 2.13856i) q^{54} -0.493694i q^{56} +(2.84927 - 1.99020i) q^{57} +(4.46945 - 4.46945i) q^{58} +(0.0144572 - 0.0250407i) q^{59} +(3.90148 + 6.75757i) q^{61} +(-3.71305 + 0.994910i) q^{62} +(1.12745 + 0.302098i) q^{63} +1.00000i q^{64} +(0.486119 + 0.841983i) q^{66} +(13.3037 + 3.56470i) q^{67} +(-4.29198 + 4.29198i) q^{68} +7.32184 q^{69} +(-5.99527 - 3.46137i) q^{71} +(-2.28369 - 0.611914i) q^{72} +(-2.01785 - 7.53071i) q^{73} +(2.96355 + 1.71101i) q^{74} +(-2.80568 + 3.33589i) q^{76} +(0.425671 + 0.425671i) q^{77} +(5.22658 - 1.40046i) q^{78} +(-2.17572 + 3.76846i) q^{79} +(1.84122 - 3.18909i) q^{81} +(-1.06128 + 3.96075i) q^{82} +(-2.36905 + 2.36905i) q^{83} +0.393641 q^{84} +(5.04638 - 2.91353i) q^{86} +(3.56366 + 3.56366i) q^{87} +(-0.862215 - 0.862215i) q^{88} +(2.10438 + 3.64490i) q^{89} +(2.90148 - 1.67517i) q^{91} +(-8.86996 + 2.37670i) q^{92} +(-0.793279 - 2.96056i) q^{93} +0.208348 q^{94} -0.797338 q^{96} +(0.821725 + 3.06672i) q^{97} +(-6.52605 + 1.74865i) q^{98} +(2.49663 - 1.44143i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{6}+O(q^{10}) \) 32 * q + 4 * q^6	\( 32 q + 4 q^{6} + 72 q^{11} + 16 q^{16} + 60 q^{21} + 8 q^{26} - 28 q^{36} - 84 q^{41} - 84 q^{51} - 52 q^{61} - 24 q^{71} + 16 q^{76} + 64 q^{81} - 36 q^{86} - 84 q^{91} + 8 q^{96}+O(q^{100}) \) 32 * q + 4 * q^6 + 72 * q^11 + 16 * q^16 + 60 * q^21 + 8 * q^26 - 28 * q^36 - 84 * q^41 - 84 * q^51 - 52 * q^61 - 24 * q^71 + 16 * q^76 + 64 * q^81 - 36 * q^86 - 84 * q^91 + 8 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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