LMFDB - Embedded newform 950.2.q.f.107.3

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			107.3
Character	$\chi$	$=$	950.107
Dual form			950.2.q.f.293.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.206366 - 0.770169i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.398669 + 0.690515i) q^{6} +(-0.349095 - 0.349095i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.04750 + 1.18213i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.206366 - 0.770169i) 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} +(-6.55503 + 1.75642i) q^{13} +(0.246847 + 0.427552i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.57098 + 5.86296i) q^{17} +(-1.67178 - 1.67178i) q^{18} +(-4.09774 - 1.48612i) q^{19} +(-0.340903 + 0.196821i) q^{21} +(1.17781 + 0.315593i) q^{22} +(-2.37670 - 8.86996i) q^{23} +(-0.690515 + 0.398669i) q^{24} +6.78627 q^{26} +(3.02438 - 3.02438i) q^{27} +(-0.127777 - 0.476872i) q^{28} +(-3.16038 + 5.47393i) q^{29} +3.84404i q^{31} +(-0.258819 - 0.965926i) q^{32} +(-0.251634 + 0.939110i) q^{33} +(3.03489 - 5.25659i) q^{34} +(1.18213 + 2.04750i) q^{36} +(2.41973 - 2.41973i) q^{37} +(3.57347 + 2.49605i) q^{38} +5.41095i q^{39} +(-3.55111 + 2.05023i) q^{41} +(0.380228 - 0.101882i) q^{42} +(-5.62850 - 1.50815i) q^{43} +(-1.05599 - 0.609678i) q^{44} +9.18286i q^{46} +(0.201249 - 0.0539244i) q^{47} +(0.770169 - 0.206366i) q^{48} -6.75627i q^{49} +(4.19127 + 2.41983i) q^{51} +(-6.55503 - 1.75642i) q^{52} +(-13.1208 + 3.51570i) q^{53} +(-3.70410 + 2.13856i) q^{54} +0.493694i q^{56} +(-1.99020 + 2.84927i) q^{57} +(4.46945 - 4.46945i) q^{58} +(-0.0144572 - 0.0250407i) q^{59} +(3.90148 - 6.75757i) q^{61} +(0.994910 - 3.71305i) q^{62} +(-0.302098 - 1.12745i) q^{63} +1.00000i q^{64} +(0.486119 - 0.841983i) q^{66} +(3.56470 + 13.3037i) q^{67} +(-4.29198 + 4.29198i) q^{68} -7.32184 q^{69} +(-5.99527 + 3.46137i) q^{71} +(-0.611914 - 2.28369i) q^{72} +(7.53071 + 2.01785i) q^{73} +(-2.96355 + 1.71101i) q^{74} +(-2.80568 - 3.33589i) q^{76} +(0.425671 + 0.425671i) q^{77} +(1.40046 - 5.22658i) q^{78} +(2.17572 + 3.76846i) q^{79} +(1.84122 + 3.18909i) q^{81} +(3.96075 - 1.06128i) 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} +(2.37670 - 8.86996i) q^{92} +(2.96056 + 0.793279i) q^{93} -0.208348 q^{94} -0.797338 q^{96} +(3.06672 + 0.821725i) q^{97} +(-1.74865 + 6.52605i) 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	0.206366	−	0.770169i	0.119146	−	0.444657i	−0.880418	−	0.474198i	$-0.842738\pi$
$3$	0.206366	−	0.770169i	0.119146	−	0.444657i	0.999564	+	0.0295411i	$0.00940458\pi$
$4$	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
$13$	−6.55503	+	1.75642i	−1.81804	+	0.487142i	−0.996544	−	0.0830725i	$-0.973527\pi$
$13$	−6.55503	+	1.75642i	−1.81804	+	0.487142i	−0.821496	+	0.570215i	$0.806860\pi$
$14$	0.246847	+	0.427552i	0.0659727	+	0.114268i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.57098	+	5.86296i	−0.381017	+	1.42198i	0.463333	+	0.886185i	$0.346654\pi$
$17$	−1.57098	+	5.86296i	−0.381017	+	1.42198i	−0.844350	+	0.535792i	$0.820013\pi$
$18$	−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
$22$	1.17781	+	0.315593i	0.251109	+	0.0672846i
$23$	−2.37670	−	8.86996i	−0.495576	−	1.84952i	−0.526779	−	0.850002i	$-0.676600\pi$
$23$	−2.37670	−	8.86996i	−0.495576	−	1.84952i	0.0312028	−	0.999513i	$-0.490066\pi$
$24$	−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
$28$	−0.127777	−	0.476872i	−0.0241477	−	0.0901203i
$29$	−3.16038	+	5.47393i	−0.586867	+	1.01648i	0.407773	+	0.913083i	$0.366305\pi$
$29$	−3.16038	+	5.47393i	−0.586867	+	1.01648i	−0.994640	+	0.103400i	$0.967028\pi$
$30$		0			0
$31$			3.84404i			0.690409i	0.938527	+	0.345205i	$0.112191\pi$
$31$			3.84404i			0.690409i	−0.938527	+	0.345205i	$0.887809\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−0.251634	+	0.939110i	−0.0438038	+	0.163478i
$34$	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	−0.479655	−	0.877457i	$-0.659238\pi$
$37$	2.41973	−	2.41973i	0.397802	−	0.397802i	0.877457	+	0.479655i	$0.159238\pi$
$38$	3.57347	+	2.49605i	0.579694	+	0.404913i
$39$			5.41095i			0.866445i
$40$		0			0
$41$	−3.55111	+	2.05023i	−0.554590	+	0.320193i	−0.750971	−	0.660335i	$-0.770414\pi$
$41$	−3.55111	+	2.05023i	−0.554590	+	0.320193i	0.196381	+	0.980528i	$0.437081\pi$
$42$	0.380228	−	0.101882i	0.0586705	−	0.0157207i
$43$	−5.62850	−	1.50815i	−0.858339	−	0.229991i	−0.197300	−	0.980343i	$-0.563217\pi$
$43$	−5.62850	−	1.50815i	−0.858339	−	0.229991i	−0.661039	+	0.750352i	$0.729884\pi$
$44$	−1.05599	−	0.609678i	−0.159197	−	0.0919124i
$45$		0			0
$46$			9.18286i			1.35394i
$47$	0.201249	−	0.0539244i	0.0293551	−	0.00786568i	−0.244112	−	0.969747i	$-0.578496\pi$
$47$	0.201249	−	0.0539244i	0.0293551	−	0.00786568i	0.273467	+	0.961881i	$0.411830\pi$
$48$	0.770169	−	0.206366i	0.111164	−	0.0297864i
$49$		−	6.75627i		−	0.965181i
$50$		0			0
$51$	4.19127	+	2.41983i	0.586896	+	0.338844i
$52$	−6.55503	−	1.75642i	−0.909020	−	0.243571i
$53$	−13.1208	+	3.51570i	−1.80227	+	0.482918i	−0.994330	−	0.106340i	$-0.966087\pi$
$53$	−13.1208	+	3.51570i	−1.80227	+	0.482918i	−0.807945	+	0.589258i	$0.799420\pi$
$54$	−3.70410	+	2.13856i	−0.504064	+	0.291021i
$55$		0			0
$56$			0.493694i			0.0659727i
$57$	−1.99020	+	2.84927i	−0.263608	+	0.377395i
$58$	4.46945	−	4.46945i	0.586867	−	0.586867i
$59$	−0.0144572	−	0.0250407i	−0.00188217	−	0.00326002i	0.865083	−	0.501629i	$-0.167266\pi$
$59$	−0.0144572	−	0.0250407i	−0.00188217	−	0.00326002i	−0.866965	+	0.498369i	$0.833932\pi$
$60$		0			0
$61$	3.90148	−	6.75757i	0.499534	−	0.865218i	−0.500466	−	0.865756i	$-0.666838\pi$
$61$	3.90148	−	6.75757i	0.499534	−	0.865218i	1.00000		0.000538484i	$0.000171405\pi$
$62$	0.994910	−	3.71305i	0.126354	−	0.471558i
$63$	−0.302098	−	1.12745i	−0.0380608	−	0.142045i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	0.486119	−	0.841983i	0.0598372	−	0.103641i
$67$	3.56470	+	13.3037i	0.435498	+	1.62530i	0.739872	+	0.672748i	$0.234886\pi$
$67$	3.56470	+	13.3037i	0.435498	+	1.62530i	−0.304374	+	0.952553i	$0.598447\pi$
$68$	−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	−0.811619	−	0.584187i	$-0.801413\pi$
$71$	−5.99527	+	3.46137i	−0.711507	+	0.410789i	0.100112	+	0.994976i	$0.468080\pi$
$72$	−0.611914	−	2.28369i	−0.0721147	−	0.269136i
$73$	7.53071	+	2.01785i	0.881403	+	0.236171i	0.671013	−	0.741446i	$-0.265860\pi$
$73$	7.53071	+	2.01785i	0.881403	+	0.236171i	0.210391	+	0.977617i	$0.432526\pi$
$74$	−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
$78$	1.40046	−	5.22658i	0.158571	−	0.591793i
$79$	2.17572	+	3.76846i	0.244787	+	0.423984i	0.962072	−	0.272796i	$-0.0879485\pi$
$79$	2.17572	+	3.76846i	0.244787	+	0.423984i	−0.717284	+	0.696781i	$0.754615\pi$
$80$		0			0
$81$	1.84122	+	3.18909i	0.204580	+	0.354344i
$82$	3.96075	−	1.06128i	0.437392	−	0.117199i
$83$	−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	$-0.904939\pi$
$89$	−2.10438	+	3.64490i	−0.223064	+	0.386358i	0.732673	+	0.680581i	$0.238273\pi$
$90$		0			0
$91$	2.90148	+	1.67517i	0.304158	+	0.175606i
$92$	2.37670	−	8.86996i	0.247788	−	0.924758i
$93$	2.96056	+	0.793279i	0.306996	+	0.0822592i
$94$	−0.208348			−0.0214894
$95$		0			0
$96$	−0.797338			−0.0813780
$97$	3.06672	+	0.821725i	0.311378	+	0.0834335i	0.411124	−	0.911579i	$-0.365136\pi$
$97$	3.06672	+	0.821725i	0.311378	+	0.0834335i	−0.0997459	+	0.995013i	$0.531803\pi$
$98$	−1.74865	+	6.52605i	−0.176640	+	0.659231i
$99$	−2.49663	−	1.44143i	−0.250921	−	0.144869i
$100$		0			0
$101$	−4.27792	+	7.40958i	−0.425669	+	0.737281i	−0.996483	−	0.0837990i	$-0.973295\pi$
$101$	−4.27792	+	7.40958i	−0.425669	+	0.737281i	0.570813	+	0.821080i	$0.306628\pi$
$102$	−3.42216	−	3.42216i	−0.338844	−	0.338844i
$103$	8.22228	+	8.22228i	0.810166	+	0.810166i	0.984658	−	0.174493i	$-0.0558286\pi$
$103$	8.22228	+	8.22228i	0.810166	+	0.810166i	−0.174493	+	0.984658i	$0.555829\pi$
$104$	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	−0.955430	−	0.295218i	$-0.904608\pi$
$107$	−6.82929	+	6.82929i	−0.660212	+	0.660212i	0.295218	+	0.955430i	$0.404608\pi$
$108$	4.13138	−	1.10700i	0.397542	−	0.106521i
$109$	−7.79910	−	13.5084i	−0.747018	−	1.29387i	−0.949246	−	0.314535i	$-0.898151\pi$
$109$	−7.79910	−	13.5084i	−0.747018	−	1.29387i	0.202227	−	0.979339i	$-0.435182\pi$
$110$		0			0
$111$	−1.36425	−	2.36295i	−0.129489	−	0.224282i
$112$	0.127777	−	0.476872i	0.0120738	−	0.0450602i
$113$	−1.00393	−	1.00393i	−0.0944420	−	0.0944420i	0.658307	−	0.752749i	$-0.271273\pi$
$113$	−1.00393	−	1.00393i	−0.0944420	−	0.0944420i	−0.752749	+	0.658307i	$0.771273\pi$
$114$	2.65983	−	2.23708i	0.249116	−	0.209522i
$115$		0			0
$116$	−5.47393	+	3.16038i	−0.508242	+	0.293433i
$117$	−15.4978	−	4.15261i	−1.43277	−	0.383909i
$118$	0.00748361	+	0.0279292i	0.000688922	+	0.00257109i
$119$	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
$123$	0.846198	+	3.15806i	0.0762991	+	0.284752i
$124$	−1.92202	+	3.32903i	−0.172602	+	0.298956i
$125$		0			0
$126$			1.16722i			0.103984i
$127$	−1.12523	−	4.19942i	−0.0998481	−	0.372638i	0.897862	−	0.440278i	$-0.145120\pi$
$127$	−1.12523	−	4.19942i	−0.0998481	−	0.372638i	−0.997710	+	0.0676393i	$0.978453\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−2.32307	+	4.02367i	−0.204535	+	0.354264i
$130$		0			0
$131$	−9.48781	−	16.4334i	−0.828954	−	1.43579i	−0.898860	−	0.438237i	$-0.855603\pi$
$131$	−9.48781	−	16.4334i	−0.828954	−	1.43579i	0.0699057	−	0.997554i	$-0.477730\pi$
$132$	−0.687477	+	0.687477i	−0.0598372	+	0.0598372i
$133$	0.911702	+	1.94929i	0.0790546	+	0.169025i
$134$		−	13.7730i		−	1.18980i
$135$		0			0
$136$	5.25659	−	3.03489i	0.450748	−	0.260240i
$137$	6.47764	−	1.73568i	0.553422	−	0.148289i	0.0287397	−	0.999587i	$-0.490851\pi$
$137$	6.47764	−	1.73568i	0.553422	−	0.148289i	0.524683	+	0.851298i	$0.324184\pi$
$138$	7.07236	+	1.89503i	0.602039	+	0.161316i
$139$	13.6084	+	7.85680i	1.15425	+	0.666405i	0.949918	−	0.312498i	$-0.101166\pi$
$139$	13.6084	+	7.85680i	1.15425	+	0.666405i	0.204328	+	0.978902i	$0.434499\pi$
$140$		0			0
$141$		−	0.166124i		−	0.0139901i
$142$	6.68685	−	1.79174i	0.561148	−	0.150359i
$143$	7.99292	−	2.14170i	0.668401	−	0.179098i
$144$			2.36425i			0.197021i
$145$		0			0
$146$	−6.75185	−	3.89818i	−0.558787	−	0.322616i
$147$	−5.20347	−	1.39427i	−0.429175	−	0.114997i
$148$	3.30542	−	0.885683i	0.271703	−	0.0728027i
$149$	−9.44068	+	5.45058i	−0.773411	+	0.446529i	−0.834090	−	0.551628i	$-0.814007\pi$
$149$	−9.44068	+	5.45058i	−0.773411	+	0.446529i	0.0606791	+	0.998157i	$0.480673\pi$
$150$		0			0
$151$		−	16.8131i		−	1.36823i	−0.729374	−	0.684116i	$-0.760188\pi$
$151$		−	16.8131i		−	1.36823i	0.729374	−	0.684116i	$-0.239812\pi$
$152$	1.84669	+	3.94838i	0.149787	+	0.320256i
$153$	−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
$157$	−3.55544	+	13.2691i	−0.283755	+	1.05899i	0.665989	+	0.745962i	$0.268010\pi$
$157$	−3.55544	+	13.2691i	−0.283755	+	1.05899i	−0.949744	+	0.313028i	$0.898657\pi$
$158$	−1.12623	−	4.20317i	−0.0895984	−	0.334386i
$159$			10.8307i			0.858932i
$160$		0			0
$161$	−2.26676	+	3.92615i	−0.178646	+	0.309424i
$162$	−0.953087	−	3.55697i	−0.0748816	−	0.279462i
$163$	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
$167$	5.46639	+	20.4009i	0.423002	+	1.57867i	0.768247	+	0.640153i	$0.221129\pi$
$167$	5.46639	+	20.4009i	0.423002	+	1.57867i	−0.345245	+	0.938512i	$0.612204\pi$
$168$	0.380228	+	0.101882i	0.0293352	+	0.00786035i
$169$	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
$173$	−1.93247	+	7.21206i	−0.146923	+	0.548323i	0.852740	+	0.522336i	$0.174939\pi$
$173$	−1.93247	+	7.21206i	−0.146923	+	0.548323i	−0.999662	+	0.0259866i	$0.991727\pi$
$174$	−2.51989	−	4.36457i	−0.191032	−	0.330877i
$175$		0			0
$176$	−0.609678	−	1.05599i	−0.0459562	−	0.0795985i
$177$	−0.0222690	+	0.00596697i	−0.00167384	+	0.000448505i
$178$	2.97605	−	2.97605i	0.223064	−	0.223064i
$179$	10.5815			0.790897			0.395449	−	0.918488i	$-0.370589\pi$
$179$	10.5815			0.790897			0.395449	+	0.918488i	$0.370589\pi$
$180$		0			0
$181$	0.165201	+	0.0953786i	0.0122793	+	0.00708944i	0.506127	−	0.862459i	$-0.331077\pi$
$181$	0.165201	+	0.0953786i	0.0122793	+	0.00708944i	−0.493848	+	0.869548i	$0.664410\pi$
$182$	−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
$187$	1.91558	−	7.14903i	0.140081	−	0.522789i
$188$	0.201249	+	0.0539244i	0.0146776	+	0.00393284i
$189$	−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	$0.473773\pi$
$192$	0.770169	+	0.206366i	0.0555822	+	0.0148932i
$193$	1.25227	−	4.67355i	0.0901406	−	0.336409i	−0.906097	−	0.423069i	$-0.860953\pi$
$193$	1.25227	−	4.67355i	0.0901406	−	0.336409i	0.996238	+	0.0866600i	$0.0276194\pi$
$194$	−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	$-0.407980\pi$
$199$	−5.67753	−	3.27792i	−0.402469	−	0.232366i	−0.687549	+	0.726138i	$0.741313\pi$
$200$		0			0
$201$	10.9817			0.774590
$202$	6.04990	−	6.04990i	0.425669	−	0.425669i
$203$	3.01419	−	0.807650i	0.211555	−	0.0566859i
$204$	2.41983	+	4.19127i	0.169422	+	0.293448i
$205$		0			0
$206$	−5.81403	−	10.0702i	−0.405083	−	0.701624i
$207$	5.61912	−	20.9708i	0.390556	−	1.45757i
$208$	−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	−0.576047	−	0.817417i	$-0.695405\pi$
$211$	−2.26846	+	1.30969i	−0.156167	+	0.0901630i	0.419880	+	0.907580i	$0.362072\pi$
$212$	−13.1208	−	3.51570i	−0.901137	−	0.241459i
$213$	1.42862	+	5.33168i	0.0978874	+	0.365321i
$214$	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
$218$	4.03711	+	15.0667i	0.273428	+	1.02045i
$219$	3.10817	−	5.38351i	0.210031	−	0.363784i
$220$		0			0
$221$		−	41.1912i		−	2.77082i
$222$	0.706189	+	2.63553i	0.0473963	+	0.176885i
$223$	3.53106	−	13.1781i	0.236457	−	0.882471i	−0.741029	−	0.671473i	$-0.765662\pi$
$223$	3.53106	−	13.1781i	0.236457	−	0.882471i	0.977486	−	0.210998i	$-0.0676714\pi$
$224$	−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	−0.238472	−	0.971149i	$-0.576646\pi$
$227$	11.0389	−	11.0389i	0.732678	−	0.732678i	0.971149	+	0.238472i	$0.0766464\pi$
$228$	−3.14820	+	1.47244i	−0.208494	+	0.0975146i
$229$		−	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
$232$	6.10538	−	1.63593i	0.400838	−	0.107404i
$233$	14.3474	+	3.84438i	0.939931	+	0.251854i	0.696084	−	0.717960i	$-0.254924\pi$
$233$	14.3474	+	3.84438i	0.939931	+	0.251854i	0.243846	+	0.969814i	$0.421591\pi$
$234$	13.8949	+	8.02223i	0.908338	+	0.524429i
$235$		0			0
$236$		−	0.0289145i		−	0.00188217i
$237$	3.35134	−	0.897990i	0.217693	−	0.0583307i
$238$	−2.89451	+	0.775582i	−0.187623	+	0.0502735i
$239$		−	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	0.896400	−	0.443246i	$-0.146173\pi$
$241$	14.9147	+	8.61098i	0.960737	+	0.554682i	0.0643374	+	0.997928i	$0.479507\pi$
$242$	9.18902	+	2.46219i	0.590692	+	0.158276i
$243$	15.2303	−	4.08093i	0.977021	−	0.261792i
$244$	6.75757	−	3.90148i	0.432609	−	0.249767i
$245$		0			0
$246$		−	3.26946i		−	0.208453i
$247$	29.4710	+	2.54423i	1.87520	+	0.161886i
$248$	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	−0.948562	−	0.316591i	$-0.897462\pi$
$251$	−3.17026	+	5.49105i	−0.200105	+	0.346592i	0.748457	+	0.663183i	$0.230795\pi$
$252$	0.302098	−	1.12745i	0.0190304	−	0.0710224i
$253$	2.89804	+	10.8156i	0.182198	+	0.679974i
$254$			4.34756i			0.272790i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.22428	−	12.0332i	−0.201125	−	0.750608i	−0.990596	−	0.136820i	$-0.956312\pi$
$257$	−3.22428	−	12.0332i	−0.201125	−	0.750608i	0.789471	−	0.613788i	$-0.210355\pi$
$258$	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
$262$	4.91125	+	18.3290i	0.303418	+	1.13237i
$263$	−14.1130	−	3.78156i	−0.870243	−	0.233181i	−0.204050	−	0.978960i	$-0.565410\pi$
$263$	−14.1130	−	3.78156i	−0.870243	−	0.233181i	−0.666193	+	0.745780i	$0.732077\pi$
$264$	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
$268$	−3.56470	+	13.3037i	−0.217749	+	0.812650i
$269$	9.83761	+	17.0392i	0.599810	+	1.03890i	0.992849	+	0.119379i	$0.0380904\pi$
$269$	9.83761	+	17.0392i	0.599810	+	1.03890i	−0.393039	+	0.919522i	$0.628576\pi$
$270$		0			0
$271$	−1.93702	−	3.35502i	−0.117666	−	0.203803i	0.801177	−	0.598428i	$-0.204208\pi$
$271$	−1.93702	−	3.35502i	−0.117666	−	0.203803i	−0.918842	+	0.394625i	$0.870874\pi$
$272$	−5.86296	+	1.57098i	−0.355494	+	0.0952544i
$273$	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	−0.0298079	−	0.999556i	$-0.509490\pi$
$281$	−15.2603	−	8.81053i	−0.910352	−	0.525592i	−0.880545	+	0.473963i	$0.842823\pi$
$282$	−0.0429960	+	0.160463i	−0.00256037	+	0.00955544i
$283$	−10.3587	−	2.77562i	−0.615763	−	0.164993i	−0.0625622	−	0.998041i	$-0.519927\pi$
$283$	−10.3587	−	2.77562i	−0.615763	−	0.164993i	−0.553201	+	0.833048i	$0.686594\pi$
$284$	−6.92274			−0.410789
$285$		0			0
$286$	−8.27488			−0.489304
$287$	1.95540	+	0.523948i	0.115424	+	0.0309277i
$288$	0.611914	−	2.28369i	0.0360574	−	0.134568i
$289$	−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	0.592263	−	0.805745i	$-0.298235\pi$
$293$	−3.65423	−	3.65423i	−0.213482	−	0.213482i	−0.805745	+	0.592263i	$0.798235\pi$
$294$	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
$298$	10.5297	−	2.82143i	0.609970	−	0.163441i
$299$	31.1587	+	53.9684i	1.80195	+	3.12108i
$300$		0			0
$301$	1.43839	+	2.49137i	0.0829075	+	0.143600i
$302$	−4.35155	+	16.2402i	−0.250404	+	0.934519i
$303$	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
$307$	−16.3146	−	4.37148i	−0.931122	−	0.249493i	−0.238789	−	0.971071i	$-0.576750\pi$
$307$	−16.3146	−	4.37148i	−0.931122	−	0.249493i	−0.692333	+	0.721578i	$0.743417\pi$
$308$	0.155806	+	0.581477i	0.00887788	+	0.0331327i
$309$	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
$313$	6.15715	+	22.9788i	0.348023	+	1.29884i	0.889041	+	0.457827i	$0.151372\pi$
$313$	6.15715	+	22.9788i	0.348023	+	1.29884i	−0.541018	+	0.841011i	$0.681961\pi$
$314$	6.86859	−	11.8968i	0.387617	−	0.671372i
$315$		0			0
$316$			4.35144i			0.244787i
$317$	−5.95143	−	22.2110i	−0.334266	−	1.24750i	−0.904663	−	0.426127i	$-0.859878\pi$
$317$	−5.95143	−	22.2110i	−0.334266	−	1.24750i	0.570398	−	0.821369i	$-0.306789\pi$
$318$	2.80320	−	10.4617i	0.157196	−	0.586662i
$319$	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
$323$	15.1505	−	21.6902i	0.842996	−	1.20688i
$324$			3.68245i			0.204580i
$325$		0			0
$326$	−16.0440	+	9.26299i	−0.888594	+	0.513030i
$327$	−12.0133	+	3.21894i	−0.664335	+	0.178008i
$328$	3.96075	+	1.06128i	0.218696	+	0.0585994i
$329$	−0.0890795	−	0.0514301i	−0.00491111	−	0.00283543i
$330$		0			0
$331$			25.7959i			1.41787i	0.705274	+	0.708934i	$0.250824\pi$
$331$			25.7959i			1.41787i	−0.705274	+	0.708934i	$0.749176\pi$
$332$	−3.23618	+	0.867133i	−0.177609	+	0.0475901i
$333$	7.81484	−	2.09398i	0.428250	−	0.114749i
$334$		−	21.1205i		−	1.15566i
$335$		0			0
$336$	−0.340903	−	0.196821i	−0.0185978	−	0.0107374i
$337$	−7.96827	−	2.13509i	−0.434059	−	0.116306i	0.0351717	−	0.999381i	$-0.488802\pi$
$337$	−7.96827	−	2.13509i	−0.434059	−	0.116306i	−0.469231	+	0.883075i	$0.655469\pi$
$338$	−31.9272	+	8.55487i	−1.73661	+	0.465323i
$339$	−0.980376	+	0.566020i	−0.0532467	+	0.0307420i
$340$		0			0
$341$		−	4.68725i		−	0.253829i
$342$	4.36605	+	9.33497i	0.236089	+	0.504778i
$343$	−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
$347$	−1.83008	+	6.82994i	−0.0982437	+	0.366651i	−0.997491	−	0.0707896i	$-0.977448\pi$
$347$	−1.83008	+	6.82994i	−0.0982437	+	0.366651i	0.899248	+	0.437440i	$0.144115\pi$
$348$	1.30439	+	4.86805i	0.0699226	+	0.260955i
$349$		−	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
$352$	0.315593	+	1.17781i	0.0168211	+	0.0627773i
$353$	−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
$357$	−0.618401	−	2.30790i	−0.0327292	−	0.122147i
$358$	−10.2209	−	2.73869i	−0.540193	−	0.144744i
$359$	−10.7306	+	6.19530i	−0.566338	+	0.326975i	−0.755685	−	0.654935i	$-0.772696\pi$
$359$	−10.7306	+	6.19530i	−0.566338	+	0.326975i	0.189348	+	0.981910i	$0.439363\pi$
$360$		0			0
$361$	14.5829	+	12.1795i	0.767521	+	0.641024i
$362$	−0.134886	−	0.134886i	−0.00708944	−	0.00708944i
$363$	−1.96320	+	7.32675i	−0.103041	+	0.384555i
$364$	1.67517	+	2.90148i	0.0878028	+	0.152079i
$365$		0			0
$366$	3.11080	+	5.38806i	0.162604	+	0.281639i
$367$	5.81651	−	1.55853i	0.303620	−	0.0813546i	−0.103793	−	0.994599i	$-0.533098\pi$
$367$	5.81651	−	1.55853i	0.303620	−	0.0813546i	0.407412	+	0.913244i	$0.366431\pi$
$368$	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	0.964584	−	0.263774i	$-0.0849673\pi$
$373$	13.5349	+	13.5349i	0.700810	+	0.700810i	−0.263774	+	0.964584i	$0.584967\pi$
$374$	−3.70061	+	6.40965i	−0.191354	+	0.331435i
$375$		0			0
$376$	−0.180435	−	0.104174i	−0.00930520	−	0.00537236i
$377$	11.1019	−	41.4327i	0.571775	−	2.13389i
$378$	2.03964	+	0.546520i	0.104908	+	0.0281099i
$379$	−31.9024			−1.63872			−0.819358	−	0.573282i	$-0.805670\pi$
$379$	−31.9024			−1.63872			−0.819358	+	0.573282i	$0.805670\pi$
$380$		0			0
$381$	−3.46647			−0.177593
$382$	−2.19736	−	0.588782i	−0.112427	−	0.0301247i
$383$	8.70978	−	32.5053i	0.445049	−	1.66094i	−0.270759	−	0.962647i	$-0.587275\pi$
$383$	8.70978	−	32.5053i	0.445049	−	1.66094i	0.715808	−	0.698297i	$-0.246059\pi$
$384$	−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	$-0.443626\pi$
$389$	−11.6013	−	6.69802i	−0.588210	−	0.339603i	−0.764389	+	0.644755i	$0.776959\pi$
$390$		0			0
$391$	55.7380			2.81879
$392$	−4.77740	+	4.77740i	−0.241295	+	0.241295i
$393$	−14.6144	+	3.91593i	−0.737201	+	0.197532i
$394$	3.91462	+	6.78032i	0.197216	+	0.341588i
$395$		0			0
$396$	−1.44143	−	2.49663i	−0.0724347	−	0.125461i
$397$	−6.77935	+	25.3009i	−0.340246	+	1.26981i	0.557823	+	0.829960i	$0.311637\pi$
$397$	−6.77935	+	25.3009i	−0.340246	+	1.26981i	−0.898069	+	0.439855i	$0.855030\pi$
$398$	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	−0.787127	−	0.616791i	$-0.788432\pi$
$401$	−12.9468	+	7.47485i	−0.646534	+	0.373276i	0.140593	+	0.990067i	$0.455099\pi$
$402$	−10.6075	−	2.84227i	−0.529055	−	0.141760i
$403$	−6.75173	−	25.1978i	−0.336328	−	1.25519i
$404$	−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
$408$	−1.25260	−	4.67476i	−0.0620128	−	0.231435i
$409$	−1.11973	+	1.93942i	−0.0553669	+	0.0958982i	−0.892380	−	0.451284i	$-0.850966\pi$
$409$	−1.11973	+	1.93942i	−0.0553669	+	0.0958982i	0.837014	+	0.547182i	$0.184300\pi$
$410$		0			0
$411$		−	5.34707i		−	0.263751i
$412$	3.00956	+	11.2318i	0.148271	+	0.553353i
$413$	−0.00369462	+	0.0137885i	−0.000181800	+	0.000678487i
$414$	−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
$418$	−4.35734	−	3.04358i	−0.213124	−	0.148866i
$419$		−	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	−0.521896	−	0.853009i	$-0.674775\pi$
$421$	−0.905185	+	0.522609i	−0.0441160	+	0.0254704i	0.477780	+	0.878480i	$0.341442\pi$
$422$	2.53013	−	0.677947i	0.123165	−	0.0330019i
$423$	0.475802	+	0.127491i	0.0231343	+	0.00619882i
$424$	11.7637	+	6.79180i	0.571298	+	0.329839i
$425$		0			0
$426$		−	5.51976i		−	0.267433i
$427$	−3.72102	+	0.997043i	−0.180073	+	0.0482503i
$428$	−9.32898	+	2.49969i	−0.450933	+	0.120827i
$429$		−	6.59787i		−	0.318548i
$430$		0			0
$431$	−25.0325	−	14.4525i	−1.20577	−	0.696152i	−0.243938	−	0.969791i	$-0.578439\pi$
$431$	−25.0325	−	14.4525i	−1.20577	−	0.696152i	−0.961833	+	0.273639i	$0.911773\pi$
$432$	4.13138	+	1.10700i	0.198771	+	0.0532606i
$433$	−3.35379	+	0.898645i	−0.161173	+	0.0431861i	−0.338503	−	0.940965i	$-0.609921\pi$
$433$	−3.35379	+	0.898645i	−0.161173	+	0.0431861i	0.177330	+	0.984151i	$0.443254\pi$
$434$	−1.64352	+	0.948890i	−0.0788917	+	0.0455482i
$435$		0			0
$436$		−	15.5982i		−	0.747018i
$437$	−3.44273	+	39.8788i	−0.164688	+	1.90766i
$438$	−4.39562	+	4.39562i	−0.210031	+	0.210031i
$439$	−7.46725	−	12.9337i	−0.356392	−	0.617290i	0.630963	−	0.775813i	$-0.282660\pi$
$439$	−7.46725	−	12.9337i	−0.356392	−	0.617290i	−0.987355	+	0.158523i	$0.949327\pi$
$440$		0			0
$441$	7.98676	−	13.8335i	0.380322	−	0.658737i
$442$	−10.6611	+	39.7876i	−0.507095	+	1.89250i
$443$	5.18176	+	19.3386i	0.246193	+	0.918804i	0.972780	+	0.231730i	$0.0744386\pi$
$443$	5.18176	+	19.3386i	0.246193	+	0.918804i	−0.726587	+	0.687074i	$0.758895\pi$
$444$		−	2.72850i		−	0.129489i
$445$		0			0
$446$	−6.82149	+	11.8152i	−0.323007	+	0.559464i
$447$	2.24963	+	8.39574i	0.106404	+	0.397105i
$448$	0.349095	−	0.349095i	0.0164932	−	0.0164932i
$449$	−24.5286			−1.15758			−0.578788	−	0.815478i	$-0.696474\pi$
$449$	−24.5286			−1.15758			−0.578788	+	0.815478i	$0.696474\pi$
$450$		0			0
$451$	4.33007	−	2.49997i	0.203895	−	0.117719i
$452$	−0.367465	−	1.37140i	−0.0172841	−	0.0645051i
$453$	−12.9489	−	3.46966i	−0.608394	−	0.163019i
$454$	−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	$0.681348\pi$
$458$	−6.37567	+	23.7943i	−0.297915	+	1.11184i
$459$	12.9806	+	22.4831i	0.605882	+	1.04942i
$460$		0			0
$461$	13.8659	+	24.0165i	0.645801	+	1.11856i	0.984116	+	0.177528i	$0.0568099\pi$
$461$	13.8659	+	24.0165i	0.645801	+	1.11856i	−0.338314	+	0.941033i	$0.609857\pi$
$462$	−0.463633	+	0.124230i	−0.0215702	+	0.00577971i
$463$	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
$472$	−0.00748361	+	0.0279292i	−0.000344461	+	0.00128555i
$473$	6.86315	+	1.83898i	0.315568	+	0.0845562i
$474$	−3.46957			−0.159362
$475$		0			0
$476$	2.99662			0.137350
$477$	−31.0208	−	8.31199i	−1.42034	−	0.380580i
$478$	−4.88006	+	18.2126i	−0.223209	+	0.833026i
$479$	4.53649	+	2.61915i	0.207278	+	0.119672i	0.600046	−	0.799966i	$-0.295149\pi$
$479$	4.53649	+	2.61915i	0.207278	+	0.119672i	−0.392768	+	0.919638i	$0.628482\pi$
$480$		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	−0.126268	−	0.991996i	$-0.540300\pi$
$487$	19.1050	−	19.1050i	0.865728	−	0.865728i	0.991996	+	0.126268i	$0.0403000\pi$
$488$	−7.53708	+	2.01956i	−0.341188	+	0.0914210i
$489$	−7.38574	−	12.7925i	−0.333995	−	0.578496i
$490$		0			0
$491$	17.9282	+	31.0526i	0.809089	+	1.40138i	0.913496	+	0.406849i	$0.133372\pi$
$491$	17.9282	+	31.0526i	0.809089	+	1.40138i	−0.104407	+	0.994535i	$0.533294\pi$
$492$	−0.846198	+	3.15806i	−0.0381496	+	0.142376i
$493$	−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
$497$	3.30126	+	0.884570i	0.148082	+	0.0396784i
$498$	−0.691398	−	2.58033i	−0.0309823	−	0.115627i
$499$	4.98159	−	2.87612i	0.223007	−	0.128753i	−0.384335	−	0.923194i	$-0.625569\pi$
$499$	4.98159	−	2.87612i	0.223007	−	0.128753i	0.607342	+	0.794441i	$0.292236\pi$
$500$		0			0
$501$	16.8402			0.752364
$502$	4.48342	−	4.48342i	0.200105	−	0.200105i
$503$	3.39964	+	12.6876i	0.151582	+	0.565713i	0.999374	+	0.0353834i	$0.0112652\pi$
$503$	3.39964	+	12.6876i	0.151582	+	0.565713i	−0.847791	+	0.530330i	$0.822068\pi$
$504$	−0.583609	+	1.01084i	−0.0259960	+	0.0450264i
$505$		0			0
$506$		−	11.1972i		−	0.497775i
$507$	−6.82112	−	25.4568i	−0.302937	−	1.13057i
$508$	1.12523	−	4.19942i	0.0499241	−	0.186319i
$509$	0.486841	−	0.843234i	0.0215789	−	0.0373757i	−0.855034	−	0.518571i	$-0.826464\pi$
$509$	0.486841	−	0.843234i	0.0215789	−	0.0373757i	0.876613	+	0.481196i	$0.159797\pi$
$510$		0			0
$511$	−1.92451	−	3.33335i	−0.0851354	−	0.147459i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−16.8877	+	7.89853i	−0.745611	+	0.348729i
$514$			12.4576i			0.549483i
$515$		0			0
$516$	−4.02367	+	2.32307i	−0.177132	+	0.102267i
$517$	−0.245394	+	0.0657530i	−0.0107924	+	0.00289182i
$518$	1.63186	+	0.437257i	0.0717000	+	0.0192120i
$519$	5.15571	+	2.97665i	0.226311	+	0.130660i
$520$		0			0
$521$			39.3767i			1.72512i	0.505952	+	0.862562i	$0.331141\pi$
$521$			39.3767i			1.72512i	−0.505952	+	0.862562i	$0.668859\pi$
$522$	14.4346	−	3.86775i	0.631787	−	0.169287i
$523$	−11.9987	+	3.21505i	−0.524669	+	0.140585i	−0.511425	−	0.859328i	$-0.670882\pi$
$523$	−11.9987	+	3.21505i	−0.524669	+	0.140585i	−0.0132434	+	0.999912i	$0.504216\pi$
$524$		−	18.9756i		−	0.828954i
$525$		0			0
$526$	12.6533	+	7.30541i	0.551712	+	0.318531i
$527$	−22.5374	−	6.03889i	−0.981746	−	0.263058i
$528$	−0.939110	+	0.251634i	−0.0408695	+	0.0109510i
$529$	−53.1090	+	30.6625i	−2.30909	+	1.33315i
$530$		0			0
$531$		−	0.0683611i		−	0.00296662i
$532$	−0.185090	+	2.14399i	−0.00802468	+	0.0929537i
$533$	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
$537$	2.18366	−	8.14953i	0.0942319	−	0.351678i
$538$	−5.09232	−	19.0048i	−0.219546	−	0.819355i
$539$			8.23829i			0.354848i
$540$		0			0
$541$	1.47393	−	2.55292i	0.0633692	−	0.109759i	−0.832600	−	0.553874i	$-0.813149\pi$
$541$	1.47393	−	2.55292i	0.0633692	−	0.109759i	0.895969	+	0.444116i	$0.146482\pi$
$542$	1.00268	+	3.74204i	0.0430686	+	0.160734i
$543$	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
$547$	8.66691	+	32.3454i	0.370570	+	1.38299i	0.859710	+	0.510782i	$0.170644\pi$
$547$	8.66691	+	32.3454i	0.370570	+	1.38299i	−0.489140	+	0.872205i	$0.662689\pi$
$548$	6.47764	+	1.73568i	0.276711	+	0.0741445i
$549$	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
$553$	0.556016	−	2.07508i	0.0236442	−	0.0882413i
$554$	3.34349	+	5.79109i	0.142051	+	0.246040i
$555$		0			0
$556$	7.85680	+	13.6084i	0.333202	+	0.577123i
$557$	−34.9774	+	9.37215i	−1.48204	+	0.397111i	−0.907040	−	0.421044i	$-0.861664\pi$
$557$	−34.9774	+	9.37215i	−1.48204	+	0.397111i	−0.574998	+	0.818155i	$0.694997\pi$
$558$	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	0.614608	−	0.788833i	$-0.289314\pi$
$563$	−4.13394	−	4.13394i	−0.174225	−	0.174225i	−0.788833	+	0.614608i	$0.789314\pi$
$564$	0.0830618	−	0.143867i	0.00349753	−	0.00605791i
$565$		0			0
$566$	9.28739	+	5.36208i	0.390378	+	0.225385i
$567$	0.470534	−	1.75606i	0.0197606	−	0.0737474i
$568$	6.68685	+	1.79174i	0.280574	+	0.0751796i
$569$	−23.3672			−0.979605			−0.489803	−	0.871833i	$-0.662931\pi$
$569$	−23.3672			−0.979605			−0.489803	+	0.871833i	$0.662931\pi$
$570$		0			0
$571$	39.1225			1.63722			0.818612	−	0.574346i	$-0.194744\pi$
$571$	39.1225			1.63722			0.818612	+	0.574346i	$0.194744\pi$
$572$	7.99292	+	2.14170i	0.334201	+	0.0895488i
$573$	0.469458	−	1.75204i	0.0196119	−	0.0731926i
$574$	−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
$583$	15.9989	−	4.28689i	0.662606	−	0.177545i
$584$	−3.89818	−	6.75185i	−0.161308	−	0.279394i
$585$		0			0
$586$	2.58393	+	4.47549i	0.106741	+	0.184881i
$587$	2.25854	−	8.42898i	0.0932199	−	0.347901i	−0.903524	−	0.428538i	$-0.859029\pi$
$587$	2.25854	−	8.42898i	0.0932199	−	0.347901i	0.996744	+	0.0806369i	$0.0256954\pi$
$588$	−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
$592$	3.30542	+	0.885683i	0.135852	+	0.0364014i
$593$	−2.76469	−	10.3180i	−0.113532	−	0.423708i	0.885641	−	0.464371i	$-0.153720\pi$
$593$	−2.76469	−	10.3180i	−0.113532	−	0.423708i	−0.999173	+	0.0406634i	$0.987053\pi$
$594$	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
$598$	−16.1289	−	60.1940i	−0.659561	−	2.46151i
$599$	−23.4008	+	40.5314i	−0.956132	+	1.65607i	−0.224375	+	0.974503i	$0.572034\pi$
$599$	−23.4008	+	40.5314i	−0.956132	+	1.65607i	−0.731757	+	0.681566i	$0.761299\pi$
$600$		0			0
$601$			16.8381i			0.686839i	0.939182	+	0.343419i	$0.111585\pi$
$601$			16.8381i			0.686839i	−0.939182	+	0.343419i	$0.888415\pi$
$602$	−0.744567	−	2.77876i	−0.0303463	−	0.113254i
$603$	−8.42786	+	31.4532i	−0.343209	+	1.28087i
$604$	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	−0.418243	−	0.908335i	$-0.637354\pi$
$607$	12.0746	−	12.0746i	0.490093	−	0.490093i	0.908335	+	0.418243i	$0.137354\pi$
$608$	−0.374909	+	4.34275i	−0.0152046	+	0.176122i
$609$		−	2.48811i		−	0.100823i
$610$		0			0
$611$	−1.22448	+	0.706952i	−0.0495371	+	0.0286002i
$612$	−13.8615	+	3.71418i	−0.560319	+	0.150137i
$613$	−21.1498	−	5.66708i	−0.854233	−	0.228891i	−0.194975	−	0.980808i	$-0.562463\pi$
$613$	−21.1498	−	5.66708i	−0.854233	−	0.228891i	−0.659258	+	0.751917i	$0.729129\pi$
$614$	14.6273	+	8.44505i	0.590308	+	0.340814i
$615$		0			0
$616$		−	0.601989i		−	0.0242548i
$617$	32.7867	−	8.78516i	1.31994	−	0.353677i	0.470986	−	0.882141i	$-0.343898\pi$
$617$	32.7867	−	8.78516i	1.31994	−	0.353677i	0.848956	+	0.528464i	$0.177232\pi$
$618$	−8.95558	+	2.39964i	−0.360246	+	0.0965277i
$619$		−	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
$622$	−17.1283	−	4.58952i	−0.686782	−	0.184023i
$623$	2.00704	−	0.537785i	0.0804104	−	0.0215459i
$624$	−4.68602	+	2.70548i	−0.187591	+	0.108306i
$625$		0			0
$626$		−	23.7894i		−	0.950815i
$627$	2.42676	−	3.47427i	0.0969154	−	0.138749i
$628$	−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	−0.978741	−	0.205100i	$-0.934248\pi$
$631$	−7.83105	+	13.5638i	−0.311749	+	0.539965i	0.666992	+	0.745065i	$0.267581\pi$
$632$	1.12623	−	4.20317i	0.0447992	−	0.167193i
$633$	0.540553	+	2.01737i	0.0214850	+	0.0801833i
$634$			22.9946i			0.913231i
$635$		0			0
$636$	−5.41536	+	9.37968i	−0.214733	+	0.371929i
$637$	11.8668	+	44.2876i	0.470180	+	1.75474i
$638$	−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	−0.616335	−	0.787484i	$-0.711383\pi$
$641$	−6.14016	+	3.54502i	−0.242522	+	0.140020i	0.373813	+	0.927504i	$0.378050\pi$
$642$	−1.99310	−	7.43835i	−0.0786613	−	0.293568i
$643$	19.8340	+	5.31450i	0.782176	+	0.209583i	0.627744	−	0.778420i	$-0.283979\pi$
$643$	19.8340	+	5.31450i	0.782176	+	0.209583i	0.154432	+	0.988003i	$0.450645\pi$
$644$	−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	$0.804246\pi$
$648$	0.953087	−	3.55697i	0.0374408	−	0.139731i
$649$	0.0176285	+	0.0305335i	0.000691979	+	0.00119854i
$650$		0			0
$651$	−0.756586	−	1.31044i	−0.0296529	−	0.0513604i
$652$	17.8947	−	4.79488i	0.700812	−	0.187782i
$653$	−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	$-0.852588\pi$
$659$	−1.55187	+	2.68791i	−0.0604521	+	0.104706i	0.834215	+	0.551439i	$0.185921\pi$
$660$		0			0
$661$	−17.7163	−	10.2285i	−0.689085	−	0.397843i	0.114184	−	0.993460i	$-0.463575\pi$
$661$	−17.7163	−	10.2285i	−0.689085	−	0.397843i	−0.803269	+	0.595616i	$0.796908\pi$
$662$	6.67646	−	24.9169i	0.259488	−	0.968423i
$663$	−31.7242	−	8.50047i	−1.23207	−	0.330131i
$664$	3.35034			0.130019
$665$		0			0
$666$	−8.09051			−0.313501
$667$	56.0648	+	15.0225i	2.17084	+	0.581675i
$668$	−5.46639	+	20.4009i	−0.211501	+	0.789333i
$669$	−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	0.952619	−	0.304167i	$-0.0983782\pi$
$673$	16.8223	+	16.8223i	0.648451	+	0.648451i	−0.304167	+	0.952619i	$0.598378\pi$
$674$	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	−0.747129	−	0.664680i	$-0.768568\pi$
$677$	−2.14526	+	2.14526i	−0.0824489	+	0.0824489i	0.664680	+	0.747129i	$0.268568\pi$
$678$	1.09347	−	0.292994i	0.0419943	−	0.0112524i
$679$	−0.783715	−	1.35743i	−0.0300762	−	0.0520936i
$680$		0			0
$681$	−6.22377	−	10.7799i	−0.238495	−	0.413086i
$682$	−1.21315	+	4.52754i	−0.0464539	+	0.173368i
$683$	−28.7563	−	28.7563i	−1.10033	−	1.10033i	−0.994371	−	0.105958i	$-0.966209\pi$
$683$	−28.7563	−	28.7563i	−1.10033	−	1.10033i	−0.105958	−	0.994371i	$-0.533791\pi$
$684$	−1.80121	−	10.1469i	−0.0688710	−	0.387977i
$685$		0			0
$686$	5.88152	−	3.39569i	0.224557	−	0.129648i
$687$	−18.9721	−	5.08356i	−0.723831	−	0.193950i
$688$	−1.50815	−	5.62850i	−0.0574978	−	0.214585i
$689$	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
$693$	0.368365	+	1.37476i	0.0139930	+	0.0522227i
$694$	3.53544	−	6.12356i	0.134203	−	0.232447i
$695$		0			0
$696$		−	5.03977i		−	0.191032i
$697$	−6.44174	−	24.0409i	−0.243998	−	0.910613i
$698$	−5.34039	+	19.9306i	−0.202137	+	0.754385i
$699$	5.92165	−	10.2566i	0.223977	−	0.387940i
$700$		0			0
$701$	14.0812	+	24.3894i	0.531840	+	0.921174i	0.999309	+	0.0371643i	$0.0118325\pi$
$701$	14.0812	+	24.3894i	0.531840	+	0.921174i	−0.467469	+	0.884009i	$0.654834\pi$
$702$	20.5243	−	20.5243i	0.774639	−	0.774639i
$703$	−13.5114	+	6.31942i	−0.509593	+	0.238341i
$704$		−	1.21936i		−	0.0459562i
$705$		0			0
$706$	17.2081	−	9.93513i	0.647637	−	0.373914i
$707$	4.08004	−	1.09324i	0.153446	−	0.0411157i
$708$	−0.0222690	−	0.00596697i	−0.000836921	−	0.000224252i
$709$	28.3507	+	16.3683i	1.06473	+	0.614723i	0.926737	−	0.375709i	$-0.122601\pi$
$709$	28.3507	+	16.3683i	1.06473	+	0.614723i	0.137995	+	0.990433i	$0.455934\pi$
$710$		0			0
$711$			10.2879i			0.385826i
$712$	4.06535	−	1.08931i	0.152356	−	0.0408236i
$713$	34.0965	−	9.13612i	1.27692	−	0.342150i
$714$			2.38932i			0.0894179i
$715$		0			0
$716$	9.16383	+	5.29074i	0.342469	+	0.197724i
$717$	−14.5216	−	3.89106i	−0.542320	−	0.145314i
$718$	11.9684	−	3.20692i	0.446657	−	0.119681i
$719$	−19.9221	+	11.5020i	−0.742968	+	0.428953i	−0.823147	−	0.567828i	$-0.807784\pi$
$719$	−19.9221	+	11.5020i	−0.742968	+	0.428953i	0.0801796	+	0.996780i	$0.474451\pi$
$720$		0			0
$721$		−	5.74071i		−	0.213795i
$722$	−10.9337	−	15.5388i	−0.406911	−	0.578293i
$723$	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
$727$	−9.44145	+	35.2360i	−0.350164	+	1.30683i	0.536298	+	0.844029i	$0.319822\pi$
$727$	−9.44145	+	35.2360i	−0.350164	+	1.30683i	−0.886462	+	0.462802i	$0.846844\pi$
$728$	−0.867133	−	3.23618i	−0.0321381	−	0.119941i
$729$		−	1.52470i		−	0.0564705i
$730$		0			0
$731$	17.6845	−	30.6304i	0.654084	−	1.13291i
$732$	−1.61027	−	6.00960i	−0.0595172	−	0.222121i
$733$	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
$737$	−4.34664	−	16.2219i	−0.160111	−	0.597541i
$738$	9.36421	+	2.50913i	0.344701	+	0.0923624i
$739$	11.7878	−	6.80568i	0.433621	−	0.250351i	−0.267267	−	0.963622i	$-0.586121\pi$
$739$	11.7878	−	6.80568i	0.433621	−	0.250351i	0.700888	+	0.713271i	$0.252787\pi$
$740$		0			0
$741$	8.04132	−	22.1727i	0.295405	−	0.814533i
$742$	−4.74196	−	4.74196i	−0.174083	−	0.174083i
$743$	9.52951	−	35.5646i	0.349604	−	1.30474i	−0.537537	−	0.843240i	$-0.680645\pi$
$743$	9.52951	−	35.5646i	0.349604	−	1.30474i	0.887141	−	0.461499i	$-0.152688\pi$
$744$	−1.53250	−	2.65436i	−0.0561841	−	0.0973137i
$745$		0			0
$746$	−9.57062	−	16.5768i	−0.350405	−	0.606920i
$747$	−7.65115	+	2.05012i	−0.279941	+	0.0750100i
$748$	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	0.439584	−	0.898201i	$-0.355126\pi$
$751$	−3.24712	−	1.87472i	−0.118489	−	0.0684097i	−0.558073	+	0.829792i	$0.688459\pi$
$752$	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
$757$	3.99098	−	14.8945i	0.145055	−	0.541351i	−0.854698	−	0.519125i	$-0.826258\pi$
$757$	3.99098	−	14.8945i	0.145055	−	0.541351i	0.999753	−	0.0222261i	$-0.00707536\pi$
$758$	30.8154	+	8.25695i	1.11926	+	0.299906i
$759$	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	$0.561851\pi$
$762$	3.34836	+	0.897189i	0.121298	+	0.0325017i
$763$	−1.99310	+	7.43835i	−0.0721550	+	0.269286i
$764$	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	$-0.00232682\pi$
$769$	41.4196	+	23.9136i	1.49363	+	0.862347i	0.493656	+	0.869657i	$0.335660\pi$
$770$		0			0
$771$	−9.93296			−0.357727
$772$	3.42127	−	3.42127i	0.123134	−	0.123134i
$773$	−5.19588	+	1.39223i	−0.186883	+	0.0500751i	−0.351046	−	0.936358i	$-0.614174\pi$
$773$	−5.19588	+	1.39223i	−0.186883	+	0.0500751i	0.164164	+	0.986433i	$0.447507\pi$
$774$	6.88832	+	11.9309i	0.247595	+	0.428848i
$775$		0			0
$776$	−1.58745	−	2.74954i	−0.0569861	−	0.0987029i
$777$	−0.348641	+	1.30115i	−0.0125074	+	0.0466784i
$778$	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
$782$	−53.8388	−	14.4261i	−1.92527	−	0.515874i
$783$	6.99707	+	26.1134i	0.250055	+	0.933218i
$784$	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	−0.807417	−	0.589981i	$-0.799135\pi$
$787$	−6.09983	+	6.09983i	−0.217435	+	0.217435i	0.589981	+	0.807417i	$0.299135\pi$
$788$	−2.02636	−	7.56247i	−0.0721860	−	0.269402i
$789$	−5.82488	+	10.0890i	−0.207371	+	0.359177i
$790$		0			0
$791$			0.700935i			0.0249224i
$792$	0.746140	+	2.78463i	0.0265129	+	0.0989477i
$793$	−13.7053	+	51.1487i	−0.486688	+	1.81634i
$794$	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	−0.394028	−	0.919099i	$-0.628919\pi$
$797$	14.8234	−	14.8234i	0.525071	−	0.525071i	0.919099	+	0.394028i	$0.128919\pi$
$798$	−1.70948	−	0.147579i	−0.0605151	−	0.00522426i
$799$			1.26463i			0.0447393i
$800$		0			0
$801$	−8.61745	+	4.97529i	−0.304483	+	0.175793i
$802$	14.4403	−	3.86927i	0.509905	−	0.136629i
$803$	−9.18262	−	2.46048i	−0.324048	−	0.0868283i
$804$	9.51043	+	5.49085i	0.335407	+	0.193647i
$805$		0			0
$806$			26.0867i			0.918864i
$807$	15.1533	−	4.06030i	0.533420	−	0.142929i
$808$	8.26431	−	2.21442i	0.290738	−	0.0779029i
$809$		−	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	0.310186	−	0.950676i	$-0.399609\pi$
$811$	−10.1960	−	5.88667i	−0.358030	−	0.206709i	−0.668216	+	0.743967i	$0.732942\pi$
$812$	3.01419	+	0.807650i	0.105777	+	0.0283429i
$813$	−2.98367	+	0.799471i	−0.104642	+	0.0280387i
$814$	3.61363	−	2.08633i	0.126658	−	0.0731258i
$815$		0			0
$816$			4.83967i			0.169422i
$817$	20.8228	+	14.5446i	0.728499	+	0.508853i
$818$	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	−0.537670	−	0.843155i	$-0.680695\pi$
$821$	13.2194	−	22.8966i	0.461359	−	0.799097i	0.999029	+	0.0440585i	$0.0140288\pi$
$822$	−1.38392	+	5.16487i	−0.0482699	+	0.180146i
$823$	2.14817	+	8.01707i	0.0748804	+	0.279458i	0.993206	−	0.116368i	$-0.0371252\pi$
$823$	2.14817	+	8.01707i	0.0748804	+	0.279458i	−0.918326	+	0.395826i	$0.870459\pi$
$824$		−	11.6281i		−	0.405083i
$825$		0			0
$826$	0.00713745	−	0.0123624i	0.000248344	−	0.000430144i
$827$	−3.85372	−	14.3823i	−0.134007	−	0.500121i	−1.00000		6.47685e-5i	$-0.999979\pi$
$827$	−3.85372	−	14.3823i	−0.134007	−	0.500121i	0.865993	−	0.500056i	$-0.166687\pi$
$828$	15.3517	−	15.3517i	0.533509	−	0.533509i
$829$	−14.3540			−0.498535			−0.249267	−	0.968435i	$-0.580190\pi$
$829$	−14.3540			−0.498535			−0.249267	+	0.968435i	$0.580190\pi$
$830$		0			0
$831$	−4.61746	+	2.66589i	−0.160178	+	0.0924787i
$832$	−1.75642	−	6.55503i	−0.0608928	−	0.227255i
$833$	39.6117	+	10.6139i	1.37246	+	0.367751i
$834$	−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
$838$	−0.0760450	+	0.283804i	−0.00262693	+	0.00980384i
$839$	18.3046	+	31.7045i	0.631945	+	1.09456i	0.987154	+	0.159774i	$0.0510766\pi$
$839$	18.3046	+	31.7045i	0.631945	+	1.09456i	−0.355208	+	0.934787i	$0.615590\pi$
$840$		0			0
$841$	−5.47594	−	9.48461i	−0.188826	−	0.327055i
$842$	1.00960	−	0.270522i	0.0347932	−	0.00932281i
$843$	−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
$852$	−1.42862	+	5.33168i	−0.0489437	+	0.182660i
$853$	−20.8644	−	5.59060i	−0.714383	−	0.191418i	−0.116719	−	0.993165i	$-0.537238\pi$
$853$	−20.8644	−	5.59060i	−0.714383	−	0.191418i	−0.597664	+	0.801747i	$0.703904\pi$
$854$	3.85228			0.131822
$855$		0			0
$856$	9.65807			0.330106
$857$	−4.07232	−	1.09117i	−0.139108	−	0.0372738i	0.188593	−	0.982055i	$-0.439607\pi$
$857$	−4.07232	−	1.09117i	−0.139108	−	0.0372738i	−0.327701	+	0.944781i	$0.606274\pi$
$858$	−1.70766	+	6.37306i	−0.0582984	+	0.217573i
$859$	−31.3522	−	18.1012i	−1.06972	−	0.617605i	−0.141617	−	0.989922i	$-0.545230\pi$
$859$	−31.3522	−	18.1012i	−1.06972	−	0.617605i	−0.928106	+	0.372317i	$0.878563\pi$
$860$		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	0.491234	−	0.871028i	$-0.336546\pi$
$863$	−11.1571	−	11.1571i	−0.379794	−	0.379794i	−0.871028	+	0.491234i	$0.836546\pi$
$864$	−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
$868$	1.83311	−	0.491181i	0.0622199	−	0.0166718i
$869$	−2.65298	−	4.59509i	−0.0899960	−	0.155878i
$870$		0			0
$871$	−46.7335	−	80.9448i	−1.58350	−	2.74271i
$872$	−4.03711	+	15.0667i	−0.136714	+	0.510223i
$873$	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
$877$	−2.72557	−	0.730314i	−0.0920359	−	0.0246609i	0.212507	−	0.977159i	$-0.431837\pi$
$877$	−2.72557	−	0.730314i	−0.0920359	−	0.0246609i	−0.304543	+	0.952499i	$0.598504\pi$
$878$	3.86533	+	14.4256i	0.130449	+	0.486841i
$879$	−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
$883$	6.15826	+	22.9829i	0.207242	+	0.773437i	0.988755	+	0.149548i	$0.0477818\pi$
$883$	6.15826	+	22.9829i	0.207242	+	0.773437i	−0.781513	+	0.623889i	$0.785552\pi$
$884$	20.5956	−	35.6726i	0.692705	−	1.19980i
$885$		0			0
$886$		−	20.0208i		−	0.672611i
$887$	0.326105	+	1.21704i	0.0109495	+	0.0408642i	0.971184	−	0.238329i	$-0.0765997\pi$
$887$	0.326105	+	1.21704i	0.0109495	+	0.0408642i	−0.960235	+	0.279193i	$0.909933\pi$
$888$	−0.706189	+	2.63553i	−0.0236981	+	0.0884427i
$889$	−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
$893$	−0.904802	−	0.0781114i	−0.0302780	−	0.00261390i
$894$		−	8.69191i		−	0.290701i
$895$		0			0
$896$	−0.427552	+	0.246847i	−0.0142835	+	0.00824658i
$897$	47.9949	−	12.8602i	1.60250	−	0.429390i
$898$	23.6928	+	6.34847i	0.790639	+	0.211851i
$899$	−21.0420	−	12.1486i	−0.701790	−	0.405178i
$900$		0			0
$901$		−	82.4495i		−	2.74679i
$902$	−4.82956	+	1.29408i	−0.160807	+	0.0430881i
$903$	2.21561	−	0.593671i	0.0737309	−	0.0197561i
$904$			1.41978i			0.0472210i
$905$		0			0
$906$	11.6097	+	6.70286i	0.385706	+	0.222688i
$907$	−44.9084	−	12.0332i	−1.49116	−	0.399555i	−0.581032	−	0.813881i	$-0.697351\pi$
$907$	−44.9084	−	12.0332i	−1.49116	−	0.399555i	−0.910129	+	0.414326i	$0.864017\pi$
$908$	15.0794	−	4.04052i	0.500428	−	0.134089i
$909$	−17.5181	+	10.1141i	−0.581039	+	0.335463i
$910$		0			0
$911$		−	47.0550i		−	1.55900i	−0.626401	−	0.779501i	$-0.715473\pi$
$911$		−	47.0550i		−	1.55900i	0.626401	−	0.779501i	$-0.284527\pi$
$912$	−3.46264	−	0.298929i	−0.114659	−	0.00989852i
$913$	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
$917$	−2.42466	+	9.04894i	−0.0800692	+	0.298822i
$918$	−6.71925	−	25.0766i	−0.221768	−	0.827651i
$919$		−	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
$922$	−7.17754	−	26.7869i	−0.236380	−	0.882181i
$923$	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
$927$	7.11537	+	26.5549i	0.233699	+	0.872178i
$928$	6.10538	+	1.63593i	0.200419	+	0.0537021i
$929$	14.5037	−	8.37372i	0.475851	−	0.274733i	−0.242835	−	0.970068i	$-0.578077\pi$
$929$	14.5037	−	8.37372i	0.475851	−	0.274733i	0.718686	+	0.695335i	$0.244744\pi$
$930$		0			0
$931$	−10.0406	+	27.6854i	−0.329068	+	0.907352i
$932$	10.5030	+	10.5030i	0.344038	+	0.344038i
$933$	3.65939	−	13.6570i	0.119803	−	0.447112i
$934$	−11.8796	−	20.5762i	−0.388714	−	0.673272i
$935$		0			0
$936$	8.02223	+	13.8949i	0.262215	+	0.454169i
$937$	−34.1671	+	9.15504i	−1.11619	+	0.299082i	−0.769341	−	0.638839i	$-0.779415\pi$
$937$	−34.1671	+	9.15504i	−1.11619	+	0.299082i	−0.346849	+	0.937921i	$0.612748\pi$
$938$	−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	0.874608	−	0.484830i	$-0.161119\pi$
$941$	27.3639	+	15.7985i	0.892037	+	0.515018i	0.0174288	+	0.999848i	$0.494452\pi$
$942$	−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
$947$	−1.22030	+	4.55423i	−0.0396545	+	0.147993i	−0.982915	−	0.184062i	$-0.941075\pi$
$947$	−1.22030	+	4.55423i	−0.0396545	+	0.147993i	0.943260	+	0.332055i	$0.107742\pi$
$948$	3.35134	+	0.897990i	0.108847	+	0.0291653i
$949$	−52.9083			−1.71748
$950$		0			0
$951$	−18.3344			−0.594535
$952$	−2.89451	−	0.775582i	−0.0938116	−	0.0251367i
$953$	1.83819	−	6.86022i	0.0595448	−	0.222224i	−0.929741	−	0.368213i	$-0.879970\pi$
$953$	1.83819	−	6.86022i	0.0595448	−	0.222224i	0.989286	+	0.145989i	$0.0466364\pi$
$954$	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
$963$	−22.0561	+	5.90990i	−0.710746	+	0.190444i
$964$	8.61098	+	14.9147i	0.277341	+	0.480369i
$965$		0			0
$966$	−1.80738	−	3.13047i	−0.0581514	−	0.100721i
$967$	−7.76616	+	28.9837i	−0.249743	+	0.932053i	0.721197	+	0.692730i	$0.243592\pi$
$967$	−7.76616	+	28.9837i	−0.249743	+	0.932053i	−0.970940	+	0.239323i	$0.923075\pi$
$968$	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	−0.759713	−	0.650258i	$-0.774661\pi$
$971$	−17.9621	+	10.3704i	−0.576430	+	0.332802i	0.183283	+	0.983060i	$0.441327\pi$
$972$	15.2303	+	4.08093i	0.488511	+	0.130896i
$973$	−2.00784	−	7.49337i	−0.0643685	−	0.240226i
$974$	−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	−0.402694	−	0.915335i	$-0.631926\pi$
$977$	16.0236	−	16.0236i	0.512641	−	0.512641i	0.915335	+	0.402694i	$0.131926\pi$
$978$	3.82314	+	14.2681i	0.122250	+	0.456245i
$979$	2.56599	−	4.44443i	0.0820094	−	0.142044i
$980$		0			0
$981$		−	36.8781i		−	1.17743i
$982$	−9.28033	−	34.6347i	−0.296147	−	1.10524i
$983$	6.00592	−	22.4144i	0.191559	−	0.714908i	−0.801572	−	0.597899i	$-0.796003\pi$
$983$	6.00592	−	22.4144i	0.191559	−	0.714908i	0.993131	−	0.117010i	$-0.0373308\pi$
$984$	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
$988$	24.2506	+	16.9389i	0.771513	+	0.538898i
$989$			53.5091i			1.70149i
$990$		0			0
$991$	−40.6191	+	23.4515i	−1.29031	+	0.744960i	−0.978709	−	0.205254i	$-0.934198\pi$
$991$	−40.6191	+	23.4515i	−1.29031	+	0.744960i	−0.311600	+	0.950214i	$0.600865\pi$
$992$	3.71305	−	0.994910i	0.117890	−	0.0315884i
$993$	19.8672	+	5.32340i	0.630466	+	0.168933i
$994$	−2.95983	−	1.70886i	−0.0938801	−	0.0542017i
$995$		0			0
$996$			2.67136i			0.0846451i
$997$	−45.3300	+	12.1461i	−1.43562	+	0.384672i	−0.890996	−	0.454010i	$-0.849993\pi$
$997$	−45.3300	+	12.1461i	−1.43562	+	0.384672i	−0.544620	+	0.838683i	$0.683326\pi$
$998$	−5.55624	+	1.48879i	−0.175880	+	0.0471268i
$999$		−	14.6364i		−	0.463075i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.q.f.107.3	✓	32	1.1	even	1	trivial
950.2.q.f.107.6	yes	32	5.4	even	2	inner
950.2.q.f.293.3	yes	32	95.8	even	12	inner
950.2.q.f.293.6	yes	32	95.27	even	12	inner
950.2.q.f.407.3	yes	32	19.8	odd	6	inner
950.2.q.f.407.6	yes	32	95.84	odd	6	inner
950.2.q.f.943.3	yes	32	5.3	odd	4	inner
950.2.q.f.943.6	yes	32	5.2	odd	4	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)

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