LMFDB - Embedded newform 950.2.l.k.351.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			351.4
Character	$\chi$	$=$	950.351
Dual form			950.2.l.k.701.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(2.49196 - 2.09100i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.49196 + 2.09100i) q^{6} +(0.556842 - 0.964479i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.31663 - 7.46696i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(2.49196 - 2.09100i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.49196 + 2.09100i) q^{6} +(0.556842 - 0.964479i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.31663 - 7.46696i) q^{9} +(0.0761417 + 0.131881i) q^{11} +(-1.62651 + 2.81720i) q^{12} +(2.66310 + 2.23460i) q^{13} +(1.04652 + 0.380902i) q^{14} +(0.766044 - 0.642788i) q^{16} +(0.0290288 + 0.164631i) q^{17} +7.58215 q^{18} +(-3.08288 + 3.08154i) q^{19} +(-0.629099 - 3.56780i) q^{21} +(-0.116656 + 0.0978859i) q^{22} +(5.83492 - 2.12374i) q^{23} +(-3.05684 - 1.11260i) q^{24} +(-1.73821 + 3.01067i) q^{26} +(-7.45291 - 12.9088i) q^{27} +(-0.193389 + 1.09676i) q^{28} +(0.881569 - 4.99963i) q^{29} +(4.34624 - 7.52791i) q^{31} +(0.766044 + 0.642788i) q^{32} +(0.465506 + 0.169430i) q^{33} +(-0.157089 + 0.0571756i) q^{34} +(1.31663 + 7.46696i) q^{36} -3.71015 q^{37} +(-3.57006 - 2.50094i) q^{38} +11.3089 q^{39} +(3.70091 - 3.10544i) q^{41} +(3.40435 - 1.23908i) q^{42} +(-9.50662 - 3.46013i) q^{43} +(-0.116656 - 0.0978859i) q^{44} +(3.10470 + 5.37749i) q^{46} +(-1.46019 + 8.28114i) q^{47} +(0.564881 - 3.20360i) q^{48} +(2.87985 + 4.98805i) q^{49} +(0.416582 + 0.349553i) q^{51} +(-3.26677 - 1.18901i) q^{52} +(-13.3964 + 4.87588i) q^{53} +(11.4185 - 9.58128i) q^{54} -1.11368 q^{56} +(-1.23891 + 14.1254i) q^{57} +5.07676 q^{58} +(2.35406 + 13.3505i) q^{59} +(-4.92653 + 1.79311i) q^{61} +(8.16827 + 2.97301i) q^{62} +(-6.46857 - 5.42778i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.0860220 + 0.487855i) q^{66} +(0.450563 - 2.55527i) q^{67} +(-0.0835852 - 0.144774i) q^{68} +(10.0996 - 17.4931i) q^{69} +(1.70994 + 0.622369i) q^{71} +(-7.12489 + 2.59325i) q^{72} +(7.79099 - 6.53742i) q^{73} +(-0.644261 - 3.65379i) q^{74} +(1.84301 - 3.95010i) q^{76} +0.169596 q^{77} +(1.96377 + 11.1371i) q^{78} +(4.00343 - 3.35927i) q^{79} +(-24.1901 - 8.80446i) q^{81} +(3.70091 + 3.10544i) q^{82} +(-3.03770 + 5.26145i) q^{83} +(1.81142 + 3.13747i) q^{84} +(1.75675 - 9.96304i) q^{86} +(-8.25740 - 14.3022i) q^{87} +(0.0761417 - 0.131881i) q^{88} +(9.18716 + 7.70894i) q^{89} +(3.63815 - 1.32418i) q^{91} +(-4.75667 + 3.99132i) q^{92} +(-4.91022 - 27.8473i) q^{93} -8.40889 q^{94} +3.25302 q^{96} +(2.16512 + 12.2790i) q^{97} +(-4.41219 + 3.70227i) q^{98} +(1.08500 - 0.394909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{7} - 12 q^{8}+O(q^{10}) $ 24 * q + 3 * q^7 - 12 * q^8	$ 24 q + 3 q^{7} - 12 q^{8} - 6 q^{11} - 3 q^{12} + 24 q^{13} - 15 q^{14} - 9 q^{17} + 30 q^{18} - 15 q^{19} - 18 q^{21} + 12 q^{23} - 9 q^{26} - 21 q^{27} + 12 q^{28} - 12 q^{29} + 9 q^{31} - 42 q^{33} - 9 q^{34} + 66 q^{37} + 6 q^{38} + 66 q^{39} + 18 q^{41} + 9 q^{42} - 3 q^{43} - 3 q^{46} - 12 q^{47} - 27 q^{49} - 3 q^{51} - 12 q^{52} - 45 q^{53} + 27 q^{54} - 6 q^{56} - 27 q^{57} - 18 q^{58} + 36 q^{59} + 12 q^{61} - 24 q^{62} - 63 q^{63} - 12 q^{64} + 48 q^{66} - 54 q^{67} + 3 q^{68} + 21 q^{69} - 39 q^{71} + 48 q^{73} + 18 q^{74} + 6 q^{76} + 48 q^{77} - 12 q^{78} - 42 q^{79} - 36 q^{81} + 18 q^{82} - 3 q^{83} + 9 q^{84} - 39 q^{86} - 24 q^{87} - 6 q^{88} - 36 q^{89} + 12 q^{91} - 15 q^{92} - 6 q^{93} + 12 q^{94} + 6 q^{96} - 54 q^{97} + 3 q^{98} + 51 q^{99}+O(q^{100}) $ 24 * q + 3 * q^7 - 12 * q^8 - 6 * q^11 - 3 * q^12 + 24 * q^13 - 15 * q^14 - 9 * q^17 + 30 * q^18 - 15 * q^19 - 18 * q^21 + 12 * q^23 - 9 * q^26 - 21 * q^27 + 12 * q^28 - 12 * q^29 + 9 * q^31 - 42 * q^33 - 9 * q^34 + 66 * q^37 + 6 * q^38 + 66 * q^39 + 18 * q^41 + 9 * q^42 - 3 * q^43 - 3 * q^46 - 12 * q^47 - 27 * q^49 - 3 * q^51 - 12 * q^52 - 45 * q^53 + 27 * q^54 - 6 * q^56 - 27 * q^57 - 18 * q^58 + 36 * q^59 + 12 * q^61 - 24 * q^62 - 63 * q^63 - 12 * q^64 + 48 * q^66 - 54 * q^67 + 3 * q^68 + 21 * q^69 - 39 * q^71 + 48 * q^73 + 18 * q^74 + 6 * q^76 + 48 * q^77 - 12 * q^78 - 42 * q^79 - 36 * q^81 + 18 * q^82 - 3 * q^83 + 9 * q^84 - 39 * q^86 - 24 * q^87 - 6 * q^88 - 36 * q^89 + 12 * q^91 - 15 * q^92 - 6 * q^93 + 12 * q^94 + 6 * q^96 - 54 * q^97 + 3 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	2.49196	−	2.09100i	1.43873	−	1.20724i	0.498417	−	0.866937i	$-0.333915\pi$
$3$	2.49196	−	2.09100i	1.43873	−	1.20724i	0.940316	−	0.340303i	$-0.110530\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$		0			0
$5$		0			0
$6$	2.49196	+	2.09100i	1.01734	+	0.853648i
$7$	0.556842	−	0.964479i	0.210467	−	0.364539i	−0.741394	−	0.671070i	$-0.765835\pi$
$7$	0.556842	−	0.964479i	0.210467	−	0.364539i	0.951861	+	0.306531i	$0.0991684\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	1.31663	−	7.46696i	0.438875	−	2.48899i
$10$		0			0
$11$	0.0761417	+	0.131881i	0.0229576	+	0.0397637i	0.877276	−	0.479986i	$-0.159358\pi$
$11$	0.0761417	+	0.131881i	0.0229576	+	0.0397637i	−0.854318	+	0.519750i	$0.826025\pi$
$12$	−1.62651	+	2.81720i	−0.469533	+	0.813255i
$13$	2.66310	+	2.23460i	0.738610	+	0.619767i	0.932464	−	0.361263i	$-0.117654\pi$
$13$	2.66310	+	2.23460i	0.738610	+	0.619767i	−0.193854	+	0.981030i	$0.562099\pi$
$14$	1.04652	+	0.380902i	0.279694	+	0.101800i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.0290288	+	0.164631i	0.00704052	+	0.0399288i	0.988126	−	0.153648i	$-0.0491022\pi$
$17$	0.0290288	+	0.164631i	0.00704052	+	0.0399288i	−0.981085	+	0.193577i	$0.937991\pi$
$18$	7.58215			1.78713
$19$	−3.08288	+	3.08154i	−0.707261	+	0.706953i
$19$	−3.08288	+	3.08154i	−0.707261	+	0.706953i
$20$		0			0
$21$	−0.629099	−	3.56780i	−0.137281	−	0.778558i
$22$	−0.116656	+	0.0978859i	−0.0248711	+	0.0208693i
$23$	5.83492	−	2.12374i	1.21667	−	0.442830i	0.347654	−	0.937623i	$-0.386978\pi$
$23$	5.83492	−	2.12374i	1.21667	−	0.442830i	0.869011	+	0.494793i	$0.164756\pi$
$24$	−3.05684	−	1.11260i	−0.623975	−	0.227108i
$25$		0			0
$26$	−1.73821	+	3.01067i	−0.340891	+	0.590441i
$27$	−7.45291	−	12.9088i	−1.43431	−	2.48430i
$28$	−0.193389	+	1.09676i	−0.0365471	+	0.207269i
$29$	0.881569	−	4.99963i	0.163703	−	0.928408i	−0.786688	−	0.617351i	$-0.788206\pi$
$29$	0.881569	−	4.99963i	0.163703	−	0.928408i	0.950391	−	0.311057i	$-0.100683\pi$
$30$		0			0
$31$	4.34624	−	7.52791i	0.780608	−	1.35205i	−0.150979	−	0.988537i	$-0.548243\pi$
$31$	4.34624	−	7.52791i	0.780608	−	1.35205i	0.931588	−	0.363517i	$-0.118424\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	0.465506	+	0.169430i	0.0810342	+	0.0294940i
$34$	−0.157089	+	0.0571756i	−0.0269405	+	0.00980554i
$35$		0			0
$36$	1.31663	+	7.46696i	0.219438	+	1.24449i
$37$	−3.71015			−0.609945			−0.304973	−	0.952361i	$-0.598647\pi$
$37$	−3.71015			−0.609945			−0.304973	+	0.952361i	$0.598647\pi$
$38$	−3.57006	−	2.50094i	−0.579140	−	0.405706i
$39$	11.3089			1.81087
$40$		0			0
$41$	3.70091	−	3.10544i	0.577986	−	0.484988i	−0.306299	−	0.951935i	$-0.599091\pi$
$41$	3.70091	−	3.10544i	0.577986	−	0.484988i	0.884285	+	0.466948i	$0.154646\pi$
$42$	3.40435	−	1.23908i	0.525303	−	0.191195i
$43$	−9.50662	−	3.46013i	−1.44975	−	0.527665i	−0.507226	−	0.861813i	$-0.669329\pi$
$43$	−9.50662	−	3.46013i	−1.44975	−	0.527665i	−0.942520	+	0.334149i	$0.891551\pi$
$44$	−0.116656	−	0.0978859i	−0.0175865	−	0.0147569i
$45$		0			0
$46$	3.10470	+	5.37749i	0.457763	+	0.792868i
$47$	−1.46019	+	8.28114i	−0.212990	+	1.20793i	0.671370	+	0.741123i	$0.265706\pi$
$47$	−1.46019	+	8.28114i	−0.212990	+	1.20793i	−0.884360	+	0.466806i	$0.845405\pi$
$48$	0.564881	−	3.20360i	0.0815336	−	0.462400i
$49$	2.87985	+	4.98805i	0.411408	+	0.712579i
$50$		0			0
$51$	0.416582	+	0.349553i	0.0583331	+	0.0489473i
$52$	−3.26677	−	1.18901i	−0.453020	−	0.164886i
$53$	−13.3964	+	4.87588i	−1.84013	+	0.669754i	−0.850531	+	0.525925i	$0.823719\pi$
$53$	−13.3964	+	4.87588i	−1.84013	+	0.669754i	−0.989603	+	0.143829i	$0.954059\pi$
$54$	11.4185	−	9.58128i	1.55386	−	1.30385i
$55$		0			0
$56$	−1.11368			−0.148822
$57$	−1.23891	+	14.1254i	−0.164098	+	1.87095i
$58$	5.07676			0.666611
$59$	2.35406	+	13.3505i	0.306472	+	1.73809i	0.616493	+	0.787360i	$0.288553\pi$
$59$	2.35406	+	13.3505i	0.306472	+	1.73809i	−0.310021	+	0.950730i	$0.600336\pi$
$60$		0			0
$61$	−4.92653	+	1.79311i	−0.630777	+	0.229584i	−0.637570	−	0.770393i	$-0.720060\pi$
$61$	−4.92653	+	1.79311i	−0.630777	+	0.229584i	0.00679218	+	0.999977i	$0.497838\pi$
$62$	8.16827	+	2.97301i	1.03737	+	0.377572i
$63$	−6.46857	−	5.42778i	−0.814963	−	0.683835i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	−0.0860220	+	0.487855i	−0.0105886	+	0.0600508i
$67$	0.450563	−	2.55527i	0.0550450	−	0.312176i	−0.944837	−	0.327541i	$-0.893780\pi$
$67$	0.450563	−	2.55527i	0.0550450	−	0.312176i	0.999882	+	0.0153653i	$0.00489111\pi$
$68$	−0.0835852	−	0.144774i	−0.0101362	−	0.0175564i
$69$	10.0996	−	17.4931i	1.21585	−	2.10592i
$70$		0			0
$71$	1.70994	+	0.622369i	0.202933	+	0.0738616i	0.441487	−	0.897268i	$-0.354451\pi$
$71$	1.70994	+	0.622369i	0.202933	+	0.0738616i	−0.238554	+	0.971129i	$0.576673\pi$
$72$	−7.12489	+	2.59325i	−0.839676	+	0.305617i
$73$	7.79099	−	6.53742i	0.911866	−	0.765147i	−0.0606068	−	0.998162i	$-0.519304\pi$
$73$	7.79099	−	6.53742i	0.911866	−	0.765147i	0.972473	+	0.233015i	$0.0748591\pi$
$74$	−0.644261	−	3.65379i	−0.0748938	−	0.424744i
$75$		0			0
$76$	1.84301	−	3.95010i	0.211408	−	0.453108i
$77$	0.169596			0.0193272
$78$	1.96377	+	11.1371i	0.222353	+	1.26103i
$79$	4.00343	−	3.35927i	0.450421	−	0.377948i	−0.389171	−	0.921165i	$-0.627239\pi$
$79$	4.00343	−	3.35927i	0.450421	−	0.377948i	0.839592	+	0.543218i	$0.182794\pi$
$80$		0			0
$81$	−24.1901	−	8.80446i	−2.68778	−	0.978274i
$82$	3.70091	+	3.10544i	0.408698	+	0.342938i
$83$	−3.03770	+	5.26145i	−0.333431	+	0.577520i	−0.983182	−	0.182627i	$-0.941540\pi$
$83$	−3.03770	+	5.26145i	−0.333431	+	0.577520i	0.649751	+	0.760147i	$0.274873\pi$
$84$	1.81142	+	3.13747i	0.197642	+	0.342326i
$85$		0			0
$86$	1.75675	−	9.96304i	0.189436	−	1.07434i
$87$	−8.25740	−	14.3022i	−0.885286	−	1.53336i
$88$	0.0761417	−	0.131881i	0.00811673	−	0.0140586i
$89$	9.18716	+	7.70894i	0.973837	+	0.817146i	0.983148	−	0.182811i	$-0.0585195\pi$
$89$	9.18716	+	7.70894i	0.973837	+	0.817146i	−0.00931144	+	0.999957i	$0.502964\pi$
$90$		0			0
$91$	3.63815	−	1.32418i	0.381382	−	0.138812i
$92$	−4.75667	+	3.99132i	−0.495917	+	0.416124i
$93$	−4.91022	−	27.8473i	−0.509166	−	2.88763i
$94$	−8.40889			−0.867311
$95$		0			0
$96$	3.25302			0.332010
$97$	2.16512	+	12.2790i	0.219835	+	1.24674i	0.872317	+	0.488940i	$0.162616\pi$
$97$	2.16512	+	12.2790i	0.219835	+	1.24674i	−0.652483	+	0.757804i	$0.726272\pi$
$98$	−4.41219	+	3.70227i	−0.445699	+	0.373986i
$99$	1.08500	−	0.394909i	0.109047	−	0.0396898i
$100$		0			0
$101$	−5.27210	−	4.42381i	−0.524593	−	0.440186i	0.341636	−	0.939832i	$-0.389019\pi$
$101$	−5.27210	−	4.42381i	−0.524593	−	0.440186i	−0.866230	+	0.499646i	$0.833463\pi$
$102$	−0.271904	+	0.470952i	−0.0269225	+	0.0466312i
$103$	10.0009	+	17.3221i	0.985420	+	1.70680i	0.640056	+	0.768329i	$0.278911\pi$
$103$	10.0009	+	17.3221i	0.985420	+	1.70680i	0.345364	+	0.938469i	$0.387755\pi$
$104$	0.603675	−	3.42361i	0.0591952	−	0.335713i
$105$		0			0
$106$	−7.12806	−	12.3462i	−0.692339	−	1.19917i
$107$	−8.42290	+	14.5889i	−0.814273	+	1.41036i	0.0955766	+	0.995422i	$0.469531\pi$
$107$	−8.42290	+	14.5889i	−0.814273	+	1.41036i	−0.909849	+	0.414939i	$0.863803\pi$
$108$	11.4185	+	9.58128i	1.09875	+	0.921959i
$109$	0.719820	+	0.261993i	0.0689463	+	0.0250944i	0.376263	−	0.926513i	$-0.377209\pi$
$109$	0.719820	+	0.261993i	0.0689463	+	0.0250944i	−0.307317	+	0.951607i	$0.599431\pi$
$110$		0			0
$111$	−9.24555	+	7.75793i	−0.877548	+	0.736350i
$112$	−0.193389	−	1.09676i	−0.0182736	−	0.103635i
$113$	−4.30310			−0.404801			−0.202401	−	0.979303i	$-0.564874\pi$
$113$	−4.30310			−0.404801			−0.202401	+	0.979303i	$0.564874\pi$
$114$	−14.1259	+	1.23275i	−1.32301	+	0.115458i
$115$		0			0
$116$	0.881569	+	4.99963i	0.0818517	+	0.464204i
$117$	20.1920	−	16.9431i	1.86675	−	1.56639i
$118$	−12.7389	+	4.63659i	−1.17271	+	0.426833i
$119$	0.174947	+	0.0636756i	0.0160374	+	0.00583713i
$120$		0			0
$121$	5.48840	−	9.50620i	0.498946	−	0.864200i
$122$	−2.62135	−	4.54031i	−0.237326	−	0.411061i
$123$	2.72905	−	15.4772i	0.246071	−	1.39554i
$124$	−1.50943	+	8.56043i	−0.135551	+	0.768749i
$125$		0			0
$126$	4.22206	−	7.31282i	0.376131	−	0.651478i
$127$	−8.22449	−	6.90116i	−0.729805	−	0.612379i	0.200273	−	0.979740i	$-0.435817\pi$
$127$	−8.22449	−	6.90116i	−0.729805	−	0.612379i	−0.930078	+	0.367361i	$0.880261\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	−30.9252	+	11.2559i	−2.72282	+	0.991024i
$130$		0			0
$131$	3.17506	+	18.0067i	0.277406	+	1.57325i	0.731213	+	0.682150i	$0.238955\pi$
$131$	3.17506	+	18.0067i	0.277406	+	1.57325i	−0.453806	+	0.891100i	$0.649934\pi$
$132$	−0.495381			−0.0431174
$133$	1.25540	+	4.68930i	0.108857	+	0.406614i
$134$	2.59469			0.224147
$135$		0			0
$136$	0.128060	−	0.107455i	0.0109810	−	0.00921419i
$137$	1.55026	−	0.564247i	0.132447	−	0.0482069i	−0.274946	−	0.961460i	$-0.588660\pi$
$137$	1.55026	−	0.564247i	0.132447	−	0.0482069i	0.407393	+	0.913253i	$0.366438\pi$
$138$	18.9811	+	6.90857i	1.61578	+	0.588096i
$139$	4.89098	+	4.10402i	0.414847	+	0.348098i	0.826199	−	0.563378i	$-0.190499\pi$
$139$	4.89098	+	4.10402i	0.414847	+	0.348098i	−0.411352	+	0.911477i	$0.634943\pi$
$140$		0			0
$141$	13.6771	+	23.6895i	1.15182	+	1.99502i
$142$	−0.315985	+	1.79204i	−0.0265169	+	0.150385i
$143$	−0.0919296	+	0.521359i	−0.00768754	+	0.0435982i
$144$	−3.79107	−	6.56633i	−0.315923	−	0.547194i
$145$		0			0
$146$	7.79099	+	6.53742i	0.644787	+	0.541040i
$147$	17.6065	+	6.40824i	1.45216	+	0.528543i
$148$	3.48640	−	1.26895i	0.286580	−	0.104307i
$149$	1.51331	−	1.26982i	0.123976	−	0.104028i	−0.578692	−	0.815546i	$-0.696437\pi$
$149$	1.51331	−	1.26982i	0.123976	−	0.104028i	0.702667	+	0.711518i	$0.251992\pi$
$150$		0			0
$151$	−0.819838			−0.0667175			−0.0333587	−	0.999443i	$-0.510620\pi$
$151$	−0.819838			−0.0667175			−0.0333587	+	0.999443i	$0.510620\pi$
$152$	4.21013	+	1.12908i	0.341486	+	0.0915808i
$153$	1.26751			0.102472
$154$	0.0294500	+	0.167019i	0.00237315	+	0.0134588i
$155$		0			0
$156$	−10.6269	+	3.86787i	−0.850831	+	0.309677i
$157$	8.40779	+	3.06019i	0.671015	+	0.244229i	0.654985	−	0.755642i	$-0.272675\pi$
$157$	8.40779	+	3.06019i	0.671015	+	0.244229i	0.0160301	+	0.999872i	$0.494897\pi$
$158$	4.00343	+	3.35927i	0.318496	+	0.267250i
$159$	−23.1877	+	40.1623i	−1.83891	+	3.18508i
$160$		0			0
$161$	1.20083	−	6.81025i	0.0946387	−	0.536723i
$162$	4.47014	−	25.3514i	0.351208	−	1.99180i
$163$	6.13765	+	10.6307i	0.480738	+	0.832662i	0.999756	−	0.0221013i	$-0.00703565\pi$
$163$	6.13765	+	10.6307i	0.480738	+	0.832662i	−0.519018	+	0.854763i	$0.673702\pi$
$164$	−2.41560	+	4.18394i	−0.188627	+	0.326711i
$165$		0			0
$166$	−5.70901	−	2.07791i	−0.443105	−	0.161277i
$167$	−10.8060	+	3.93306i	−0.836193	+	0.304349i	−0.724398	−	0.689382i	$-0.757882\pi$
$167$	−10.8060	+	3.93306i	−0.836193	+	0.304349i	−0.111795	+	0.993731i	$0.535660\pi$
$168$	−2.77526	+	2.32872i	−0.214116	+	0.179664i
$169$	−0.158797	−	0.900582i	−0.0122151	−	0.0692755i
$170$		0			0
$171$	18.9507	+	27.0770i	1.44920	+	2.07063i
$172$	10.1167			0.771394
$173$	−1.81970	−	10.3201i	−0.138350	−	0.784620i	−0.972468	−	0.233035i	$-0.925134\pi$
$173$	−1.81970	−	10.3201i	−0.138350	−	0.784620i	0.834119	−	0.551585i	$-0.185977\pi$
$174$	12.6511	−	10.6155i	0.959075	−	0.804759i
$175$		0			0
$176$	0.143100	+	0.0520840i	0.0107865	+	0.00392598i
$177$	33.7822	+	28.3466i	2.53922	+	2.13066i
$178$	−5.99649	+	10.3862i	−0.449456	+	0.778481i
$179$	−2.28771	−	3.96243i	−0.170991	−	0.296166i	0.767775	−	0.640719i	$-0.221364\pi$
$179$	−2.28771	−	3.96243i	−0.170991	−	0.296166i	−0.938767	+	0.344553i	$0.888030\pi$
$180$		0			0
$181$	1.65446	−	9.38289i	0.122975	−	0.697425i	−0.859515	−	0.511110i	$-0.829234\pi$
$181$	1.65446	−	9.38289i	0.122975	−	0.697425i	0.982490	−	0.186315i	$-0.0596545\pi$
$182$	1.93582	+	3.35294i	0.143492	+	0.248536i
$183$	−8.52731	+	14.7697i	−0.630357	+	1.09181i
$184$	−4.75667	−	3.99132i	−0.350667	−	0.294244i
$185$		0			0
$186$	26.5715	−	9.67125i	1.94832	−	0.709131i
$187$	−0.0195014	+	0.0163636i	−0.00142608	+	0.00119663i
$188$	−1.46019	−	8.28114i	−0.106495	−	0.603964i
$189$	−16.6004			−1.20750
$190$		0			0
$191$	−8.49290			−0.614525			−0.307262	−	0.951625i	$-0.599413\pi$
$191$	−8.49290			−0.614525			−0.307262	+	0.951625i	$0.599413\pi$
$192$	0.564881	+	3.20360i	0.0407668	+	0.231200i
$193$	1.59233	−	1.33612i	0.114618	−	0.0961762i	−0.583677	−	0.811986i	$-0.698387\pi$
$193$	1.59233	−	1.33612i	0.114618	−	0.0961762i	0.698295	+	0.715810i	$0.253942\pi$
$194$	−11.7165	+	4.26445i	−0.841195	+	0.306170i
$195$		0			0
$196$	−4.41219	−	3.70227i	−0.315157	−	0.264448i
$197$	−4.08717	+	7.07919i	−0.291199	+	0.504371i	−0.974094	−	0.226146i	$-0.927388\pi$
$197$	−4.08717	+	7.07919i	−0.291199	+	0.504371i	0.682895	+	0.730517i	$0.260721\pi$
$198$	0.577318	+	0.999943i	0.0410282	+	0.0710629i
$199$	−0.209332	+	1.18718i	−0.0148392	+	0.0841572i	−0.991328	−	0.131411i	$-0.958049\pi$
$199$	−0.209332	+	1.18718i	−0.0148392	+	0.0841572i	0.976489	+	0.215568i	$0.0691603\pi$
$200$		0			0
$201$	−4.22029	−	7.30975i	−0.297676	−	0.515590i
$202$	3.44112	−	5.96019i	0.242116	−	0.419357i
$203$	−4.33114	−	3.63426i	−0.303986	−	0.255075i
$204$	−0.511013	−	0.185994i	−0.0357781	−	0.0130222i
$205$		0			0
$206$	−15.3223	+	12.8569i	−1.06756	+	0.895785i
$207$	−8.17545	−	46.3653i	−0.568233	−	3.22261i
$208$	3.47642			0.241047
$209$	−0.641132	−	0.171941i	−0.0443481	−	0.0118934i
$210$		0			0
$211$	−1.52354	−	8.64040i	−0.104885	−	0.594830i	−0.991266	−	0.131875i	$-0.957900\pi$
$211$	−1.52354	−	8.64040i	−0.104885	−	0.594830i	0.886382	−	0.462955i	$-0.153211\pi$
$212$	10.9208	−	9.16366i	0.750045	−	0.629363i
$213$	5.56249	−	2.02458i	0.381135	−	0.138722i
$214$	−15.8299	−	5.76160i	−1.08211	−	0.393855i
$215$		0			0
$216$	−7.45291	+	12.9088i	−0.507106	+	0.878334i
$217$	−4.84034	−	8.38372i	−0.328584	−	0.569124i
$218$	−0.133017	+	0.754379i	−0.00900908	+	0.0510930i
$219$	5.74508	−	32.5819i	0.388216	−	2.20168i
$220$		0			0
$221$	−0.290577	+	0.503295i	−0.0195464	+	0.0338553i
$222$	−9.24555	−	7.75793i	−0.620520	−	0.520678i
$223$	15.5349	+	5.65425i	1.04030	+	0.378637i	0.804992	−	0.593285i	$-0.202169\pi$
$223$	15.5349	+	5.65425i	1.04030	+	0.378637i	0.235304	+	0.971922i	$0.424392\pi$
$224$	1.04652	−	0.380902i	0.0699236	−	0.0254501i
$225$		0			0
$226$	−0.747225	−	4.23772i	−0.0497047	−	0.281889i
$227$	−24.8268			−1.64781			−0.823907	−	0.566726i	$-0.808210\pi$
$227$	−24.8268			−1.64781			−0.823907	+	0.566726i	$0.808210\pi$
$228$	−3.66696	−	13.6972i	−0.242851	−	0.907121i
$229$	−13.6959			−0.905053			−0.452527	−	0.891751i	$-0.649477\pi$
$229$	−13.6959			−0.905053			−0.452527	+	0.891751i	$0.649477\pi$
$230$		0			0
$231$	0.422625	−	0.354625i	0.0278067	−	0.0233326i
$232$	−4.77059	+	1.73635i	−0.313205	+	0.113997i
$233$	5.64942	+	2.05622i	0.370106	+	0.134708i	0.520376	−	0.853937i	$-0.325792\pi$
$233$	5.64942	+	2.05622i	0.370106	+	0.134708i	−0.150270	+	0.988645i	$0.548014\pi$
$234$	20.1920	+	16.9431i	1.31999	+	1.10760i
$235$		0			0
$236$	−6.77824	−	11.7403i	−0.441226	−	0.764225i
$237$	2.95213	−	16.7423i	0.191761	−	1.08753i
$238$	−0.0323289	+	0.183347i	−0.00209557	+	0.0118846i
$239$	−1.63902	−	2.83887i	−0.106019	−	0.183631i	0.808135	−	0.588998i	$-0.200477\pi$
$239$	−1.63902	−	2.83887i	−0.106019	−	0.183631i	−0.914154	+	0.405367i	$0.867144\pi$
$240$		0			0
$241$	−2.85594	−	2.39642i	−0.183967	−	0.154367i	0.546153	−	0.837685i	$-0.316092\pi$
$241$	−2.85594	−	2.39642i	−0.183967	−	0.154367i	−0.730121	+	0.683318i	$0.760536\pi$
$242$	10.3148	+	3.75429i	0.663062	+	0.241335i
$243$	−36.6701	+	13.3468i	−2.35239	+	0.856199i
$244$	4.01614	−	3.36994i	0.257107	−	0.215739i
$245$		0			0
$246$	15.7160			1.00202
$247$	−15.0960	+	1.31741i	−0.960536	+	0.0838250i
$248$	−8.69249			−0.551974
$249$	3.43188	+	19.4632i	0.217487	+	1.23343i
$250$		0			0
$251$	18.6292	−	6.78049i	1.17587	−	0.427981i	0.321127	−	0.947036i	$-0.395938\pi$
$251$	18.6292	−	6.78049i	1.17587	−	0.427981i	0.854741	+	0.519055i	$0.173716\pi$
$252$	7.93488	+	2.88806i	0.499850	+	0.181931i
$253$	0.724362	+	0.607812i	0.0455403	+	0.0382128i
$254$	5.36815	−	9.29791i	0.336828	−	0.583403i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−2.64648	+	15.0089i	−0.165083	+	0.936231i	0.783896	+	0.620892i	$0.213229\pi$
$257$	−2.64648	+	15.0089i	−0.165083	+	0.936231i	−0.948979	+	0.315339i	$0.897882\pi$
$258$	−16.4550	−	28.5009i	−1.02444	−	1.77439i
$259$	−2.06597	+	3.57836i	−0.128373	+	0.222349i
$260$		0			0
$261$	−36.1713	−	13.1653i	−2.23895	−	0.814911i
$262$	−17.1818	+	6.25365i	−1.06149	+	0.386352i
$263$	−18.6204	+	15.6244i	−1.14818	+	0.963441i	−0.999676	−	0.0254695i	$-0.991892\pi$
$263$	−18.6204	+	15.6244i	−1.14818	+	0.963441i	−0.148509	+	0.988911i	$0.547447\pi$
$264$	−0.0860220	−	0.487855i	−0.00529429	−	0.0300254i
$265$		0			0
$266$	−4.40006	+	2.05061i	−0.269785	+	0.125731i
$267$	39.0134			2.38758
$268$	0.450563	+	2.55527i	0.0275225	+	0.156088i
$269$	−2.17895	+	1.82836i	−0.132853	+	0.111477i	−0.706793	−	0.707420i	$-0.749859\pi$
$269$	−2.17895	+	1.82836i	−0.132853	+	0.111477i	0.573940	+	0.818897i	$0.305414\pi$
$270$		0			0
$271$	−28.9899	−	10.5515i	−1.76101	−	0.640956i	−0.761043	−	0.648702i	$-0.775312\pi$
$271$	−28.9899	−	10.5515i	−1.76101	−	0.640956i	−0.999970	+	0.00774568i	$0.997534\pi$
$272$	0.128060	+	0.107455i	0.00776477	+	0.00651542i
$273$	6.29726	−	10.9072i	0.381128	−	0.660132i
$274$	0.824875	+	1.42872i	0.0498325	+	0.0863124i
$275$		0			0
$276$	−3.50757	+	19.8924i	−0.211131	+	1.19738i
$277$	−11.1260	−	19.2709i	−0.668499	−	1.15787i	−0.978324	−	0.207081i	$-0.933604\pi$
$277$	−11.1260	−	19.2709i	−0.668499	−	1.15787i	0.309824	−	0.950794i	$-0.399730\pi$
$278$	−3.19236	+	5.52933i	−0.191465	+	0.331627i
$279$	−50.4882	−	42.3647i	−3.02265	−	2.53631i
$280$		0			0
$281$	6.95277	−	2.53060i	0.414768	−	0.150963i	−0.126203	−	0.992004i	$-0.540279\pi$
$281$	6.95277	−	2.53060i	0.414768	−	0.150963i	0.540971	+	0.841041i	$0.318057\pi$
$282$	−20.9546	+	17.5830i	−1.24783	+	1.04705i
$283$	−1.55556	−	8.82202i	−0.0924685	−	0.524415i	−0.995494	−	0.0948274i	$-0.969770\pi$
$283$	−1.55556	−	8.82202i	−0.0924685	−	0.524415i	0.903025	−	0.429587i	$-0.141341\pi$
$284$	−1.81969			−0.107978
$285$		0			0
$286$	−0.529402			−0.0313042
$287$	−0.934302	−	5.29869i	−0.0551501	−	0.312772i
$288$	5.80826	−	4.87371i	0.342255	−	0.287186i
$289$	15.9485	−	5.80478i	0.938148	−	0.341458i
$290$		0			0
$291$	31.0708	+	26.0715i	1.82140	+	1.52834i
$292$	−5.08521	+	8.80784i	−0.297589	+	0.515440i
$293$	−8.43085	−	14.6027i	−0.492536	−	0.853097i	0.507428	−	0.861694i	$-0.330596\pi$
$293$	−8.43085	−	14.6027i	−0.492536	−	0.853097i	−0.999963	+	0.00859792i	$0.997263\pi$
$294$	−3.25355	+	18.4518i	−0.189751	+	1.07613i
$295$		0			0
$296$	1.85508	+	3.21309i	0.107824	+	0.186757i
$297$	1.13495	−	1.96580i	0.0658568	−	0.114067i
$298$	1.51331	+	1.26982i	0.0876639	+	0.0735588i
$299$	20.2847	+	7.38301i	1.17309	+	0.426971i
$300$		0			0
$301$	−8.63091	+	7.24219i	−0.497477	+	0.417433i
$302$	−0.142363	−	0.807383i	−0.00819209	−	0.0464597i
$303$	−22.3880			−1.28616
$304$	−0.380850	+	4.34223i	−0.0218432	+	0.249044i
$305$		0			0
$306$	0.220101	+	1.24825i	0.0125823	+	0.0713579i
$307$	17.7995	−	14.9356i	1.01587	−	0.852418i	0.0267691	−	0.999642i	$-0.491478\pi$
$307$	17.7995	−	14.9356i	1.01587	−	0.852418i	0.989103	+	0.147224i	$0.0470337\pi$
$308$	−0.159368	+	0.0580051i	−0.00908082	+	0.00330515i
$309$	61.1424	+	22.2540i	3.47827	+	1.26599i
$310$		0			0
$311$	−3.22769	+	5.59053i	−0.183026	+	0.317010i	−0.942909	−	0.333049i	$-0.891922\pi$
$311$	−3.22769	+	5.59053i	−0.183026	+	0.317010i	0.759884	+	0.650059i	$0.225256\pi$
$312$	−5.65444	−	9.79378i	−0.320120	−	0.554464i
$313$	−4.13990	+	23.4785i	−0.234001	+	1.32709i	0.610706	+	0.791857i	$0.290886\pi$
$313$	−4.13990	+	23.4785i	−0.234001	+	1.32709i	−0.844707	+	0.535228i	$0.820226\pi$
$314$	−1.55370	+	8.81146i	−0.0876802	+	0.497259i
$315$		0			0
$316$	−2.61305	+	4.52594i	−0.146996	+	0.254604i
$317$	3.33416	+	2.79769i	0.187265	+	0.157134i	0.731601	−	0.681734i	$-0.238774\pi$
$317$	3.33416	+	2.79769i	0.187265	+	0.157134i	−0.544335	+	0.838868i	$0.683218\pi$
$318$	−43.5787	−	15.8613i	−2.44377	−	0.889460i
$319$	0.726482	−	0.264418i	0.0406752	−	0.0148045i
$320$		0			0
$321$	9.51588	+	53.9672i	0.531124	+	3.01216i
$322$	6.91531			0.385375
$323$	−0.596807	−	0.418083i	−0.0332073	−	0.0232628i
$324$	25.7425			1.43014
$325$		0			0
$326$	−9.40342	+	7.89041i	−0.520807	+	0.437009i
$327$	2.34159	−	0.852269i	0.129490	−	0.0471306i
$328$	−4.53984	−	1.65237i	−0.250671	−	0.0912367i
$329$	7.17389	+	6.01961i	0.395509	+	0.331872i
$330$		0			0
$331$	−5.66535	−	9.81267i	−0.311396	−	0.539353i	0.667269	−	0.744817i	$-0.267463\pi$
$331$	−5.66535	−	9.81267i	−0.311396	−	0.539353i	−0.978665	+	0.205464i	$0.934130\pi$
$332$	1.05498	−	5.98310i	0.0578997	−	0.328365i
$333$	−4.88488	+	27.7035i	−0.267690	+	1.51815i
$334$	−5.74975	−	9.95886i	−0.314612	−	0.544925i
$335$		0			0
$336$	−2.77526	−	2.32872i	−0.151403	−	0.127042i
$337$	4.50143	+	1.63839i	0.245209	+	0.0892486i	0.461701	−	0.887036i	$-0.347239\pi$
$337$	4.50143	+	1.63839i	0.245209	+	0.0892486i	−0.216492	+	0.976284i	$0.569462\pi$
$338$	0.859325	−	0.312769i	0.0467411	−	0.0170124i
$339$	−10.7231	+	8.99778i	−0.582401	+	0.488692i
$340$		0			0
$341$	1.32372			0.0716835
$342$	−23.3748	+	23.3647i	−1.26397	+	1.26342i
$343$	14.2103			0.767283
$344$	1.75675	+	9.96304i	0.0947178	+	0.537171i
$345$		0			0
$346$	9.84729	−	3.58412i	0.529393	−	0.192683i
$347$	−12.2580	−	4.46154i	−0.658043	−	0.239508i	−0.00865172	−	0.999963i	$-0.502754\pi$
$347$	−12.2580	−	4.46154i	−0.658043	−	0.239508i	−0.649391	+	0.760455i	$0.724976\pi$
$348$	12.6511	+	10.6155i	0.678168	+	0.569051i
$349$	9.17384	−	15.8896i	0.491064	−	0.850549i	−0.508883	−	0.860836i	$-0.669941\pi$
$349$	9.17384	−	15.8896i	0.491064	−	0.850549i	0.999947	+	0.0102874i	$0.00327463\pi$
$350$		0			0
$351$	8.99827	−	51.0317i	0.480292	−	2.72387i
$352$	−0.0264437	+	0.149970i	−0.00140946	+	0.00799342i
$353$	8.26649	+	14.3180i	0.439981	+	0.762070i	0.997687	−	0.0679687i	$-0.0216518\pi$
$353$	8.26649	+	14.3180i	0.439981	+	0.762070i	−0.557706	+	0.830038i	$0.688318\pi$
$354$	−22.0498	+	38.1913i	−1.17193	+	2.02984i
$355$		0			0
$356$	−11.2697	−	4.10184i	−0.597294	−	0.217397i
$357$	0.569107	−	0.207138i	0.0301203	−	0.0109629i
$358$	3.50498	−	2.94102i	0.185244	−	0.155438i
$359$	−0.213524	−	1.21096i	−0.0112694	−	0.0639118i	0.978654	−	0.205513i	$-0.0658862\pi$
$359$	−0.213524	−	1.21096i	−0.0112694	−	0.0639118i	−0.989924	+	0.141601i	$0.954775\pi$
$360$		0			0
$361$	0.00828280	−	19.0000i	0.000435937	−	1.00000i
$362$	9.52764			0.500762
$363$	−6.20059	−	35.1653i	−0.325447	−	1.84570i
$364$	−2.96585	+	2.48864i	−0.155453	+	0.130440i
$365$		0			0
$366$	−16.0261	−	5.83303i	−0.837698	−	0.304897i
$367$	−13.9273	−	11.6864i	−0.726998	−	0.610024i	0.202313	−	0.979321i	$-0.435154\pi$
$367$	−13.9273	−	11.6864i	−0.726998	−	0.610024i	−0.929312	+	0.369297i	$0.879599\pi$
$368$	3.10470	−	5.37749i	0.161844	−	0.280321i
$369$	−18.3154	−	31.7233i	−0.953464	−	1.65145i
$370$		0			0
$371$	−2.75698	+	15.6356i	−0.143135	+	0.811761i
$372$	14.1384	+	24.4885i	0.733043	+	1.26967i
$373$	−10.2694	+	17.7870i	−0.531727	+	0.920978i	0.467587	+	0.883947i	$0.345123\pi$
$373$	−10.2694	+	17.7870i	−0.531727	+	0.920978i	−0.999314	+	0.0370312i	$0.988210\pi$
$374$	−0.0195014	−	0.0163636i	−0.00100839	−	0.000846142i
$375$		0			0
$376$	7.90177	−	2.87601i	0.407503	−	0.148319i
$377$	13.5199	−	11.3445i	0.696309	−	0.584273i
$378$	−2.88263	−	16.3482i	−0.148266	−	0.840860i
$379$	−17.7716			−0.912864			−0.456432	−	0.889758i	$-0.650873\pi$
$379$	−17.7716			−0.912864			−0.456432	+	0.889758i	$0.650873\pi$
$380$		0			0
$381$	−34.9254			−1.78928
$382$	−1.47478	−	8.36388i	−0.0754561	−	0.427933i
$383$	13.3969	−	11.2414i	0.684551	−	0.574406i	−0.232781	−	0.972529i	$-0.574783\pi$
$383$	13.3969	−	11.2414i	0.684551	−	0.574406i	0.917332	+	0.398123i	$0.130338\pi$
$384$	−3.05684	+	1.11260i	−0.155994	+	0.0567771i
$385$		0			0
$386$	1.59233	+	1.33612i	0.0810474	+	0.0680069i
$387$	−38.3533	+	66.4299i	−1.94961	+	3.37682i
$388$	−6.23421	−	10.7980i	−0.316494	−	0.548184i
$389$	−0.283038	+	1.60519i	−0.0143506	+	0.0813862i	−0.991142	−	0.132807i	$-0.957601\pi$
$389$	−0.283038	+	1.60519i	−0.0143506	+	0.0813862i	0.976791	+	0.214193i	$0.0687121\pi$
$390$		0			0
$391$	0.519013	+	0.898957i	0.0262476	+	0.0454622i
$392$	2.87985	−	4.98805i	0.145455	−	0.251935i
$393$	45.5641	+	38.2328i	2.29841	+	1.92859i
$394$	−7.68137	−	2.79579i	−0.386982	−	0.140850i
$395$		0			0
$396$	−0.884502	+	0.742185i	−0.0444479	+	0.0372962i
$397$	−4.99194	−	28.3107i	−0.250538	−	1.42087i	−0.807271	−	0.590181i	$-0.799056\pi$
$397$	−4.99194	−	28.3107i	−0.250538	−	1.42087i	0.556733	−	0.830692i	$-0.312055\pi$
$398$	−1.20550			−0.0604261
$399$	12.9337	+	9.06050i	0.647497	+	0.453592i
$400$		0			0
$401$	−3.20094	−	18.1534i	−0.159847	−	0.906539i	−0.954219	−	0.299107i	$-0.903311\pi$
$401$	−3.20094	−	18.1534i	−0.159847	−	0.906539i	0.794372	−	0.607431i	$-0.207800\pi$
$402$	6.46586	−	5.42550i	0.322488	−	0.270599i
$403$	28.3964	−	10.3354i	1.41452	−	0.514844i
$404$	6.46718	+	2.35386i	0.321754	+	0.117109i
$405$		0			0
$406$	2.82695	−	4.89642i	0.140299	−	0.243005i
$407$	−0.282497	−	0.489300i	−0.0140029	−	0.0242537i
$408$	0.0944314	−	0.535547i	0.00467505	−	0.0265135i
$409$	3.79907	−	21.5456i	0.187852	−	1.06536i	−0.734384	−	0.678734i	$-0.762529\pi$
$409$	3.79907	−	21.5456i	0.187852	−	1.06536i	0.922236	−	0.386627i	$-0.126360\pi$
$410$		0			0
$411$	2.68333	−	4.64767i	0.132359	−	0.229253i
$412$	−15.3223	−	12.8569i	−0.754875	−	0.633416i
$413$	14.1871	+	5.16370i	0.698103	+	0.254089i
$414$	44.2412	−	16.1025i	2.17434	−	0.791395i
$415$		0			0
$416$	0.603675	+	3.42361i	0.0295976	+	0.167856i
$417$	20.7696			1.01709
$418$	0.0579971	−	0.661249i	0.00283673	−	0.0323428i
$419$	−27.9242			−1.36419			−0.682093	−	0.731266i	$-0.738930\pi$
$419$	−27.9242			−1.36419			−0.682093	+	0.731266i	$0.738930\pi$
$420$		0			0
$421$	22.0785	−	18.5261i	1.07604	−	0.902905i	0.0804538	−	0.996758i	$-0.474363\pi$
$421$	22.0785	−	18.5261i	1.07604	−	0.902905i	0.995586	+	0.0938538i	$0.0299186\pi$
$422$	8.24457	−	3.00078i	0.401340	−	0.146076i
$423$	59.9124	+	21.8063i	2.91304	+	1.06026i
$424$	10.9208	+	9.16366i	0.530362	+	0.445027i
$425$		0			0
$426$	2.95974	+	5.12642i	0.143400	+	0.248376i
$427$	−1.01388	+	5.75001i	−0.0490652	+	0.278263i
$428$	2.92524	−	16.5899i	0.141397	−	0.801902i
$429$	0.861078	+	1.49143i	0.0415732	+	0.0720069i
$430$		0			0
$431$	−14.3787	−	12.0651i	−0.692597	−	0.581158i	0.227060	−	0.973881i	$-0.427089\pi$
$431$	−14.3787	−	12.0651i	−0.692597	−	0.581158i	−0.919657	+	0.392723i	$0.871533\pi$
$432$	−14.0069	−	5.09809i	−0.673907	−	0.245282i
$433$	−4.50126	+	1.63832i	−0.216317	+	0.0787328i	−0.447905	−	0.894081i	$-0.647830\pi$
$433$	−4.50126	+	1.63832i	−0.216317	+	0.0787328i	0.231589	+	0.972814i	$0.425608\pi$
$434$	7.41584	−	6.22263i	0.355972	−	0.298696i
$435$		0			0
$436$	−0.766017			−0.0366856
$437$	−11.4440	+	24.5277i	−0.547440	+	1.17332i
$438$	33.0846			1.58084
$439$	−6.69068	−	37.9447i	−0.319329	−	1.81100i	−0.546852	−	0.837230i	$-0.684174\pi$
$439$	−6.69068	−	37.9447i	−0.319329	−	1.81100i	0.227523	−	0.973773i	$-0.426937\pi$
$440$		0			0
$441$	41.0373	−	14.9363i	1.95416	−	0.711255i
$442$	−0.546107	−	0.198767i	−0.0259757	−	0.00945437i
$443$	−2.99699	−	2.51477i	−0.142391	−	0.119480i	0.568810	−	0.822469i	$-0.307404\pi$
$443$	−2.99699	−	2.51477i	−0.142391	−	0.119480i	−0.711201	+	0.702989i	$0.751848\pi$
$444$	6.03460	−	10.4522i	0.286389	−	0.496041i
$445$		0			0
$446$	−2.87074	+	16.2808i	−0.135933	+	0.770917i
$447$	1.11592	−	6.32869i	0.0527811	−	0.299337i
$448$	0.556842	+	0.964479i	0.0263083	+	0.0455673i
$449$	−12.8929	+	22.3311i	−0.608451	+	1.05387i	0.383044	+	0.923730i	$0.374876\pi$
$449$	−12.8929	+	22.3311i	−0.608451	+	1.05387i	−0.991496	+	0.130139i	$0.958458\pi$
$450$		0			0
$451$	0.691343	+	0.251628i	0.0325541	+	0.0118487i
$452$	4.04359	−	1.47175i	0.190194	−	0.0692251i
$453$	−2.04300	+	1.71428i	−0.0959886	+	0.0805440i
$454$	−4.31113	−	24.4496i	−0.202331	−	1.14748i
$455$		0			0
$456$	12.8524	−	5.98975i	0.601868	−	0.280496i
$457$	1.97813			0.0925329			0.0462665	−	0.998929i	$-0.485268\pi$
$457$	1.97813			0.0925329			0.0462665	+	0.998929i	$0.485268\pi$
$458$	−2.37828	−	13.4879i	−0.111130	−	0.630247i
$459$	1.90884	−	1.60171i	0.0890970	−	0.0747612i
$460$		0			0
$461$	35.6621	+	12.9800i	1.66095	+	0.604537i	0.990512	−	0.137427i	$-0.0438832\pi$
$461$	35.6621	+	12.9800i	1.66095	+	0.604537i	0.670440	+	0.741964i	$0.266105\pi$
$462$	0.422625	+	0.354625i	0.0196623	+	0.0164986i
$463$	3.75740	−	6.50802i	0.174621	−	0.302453i	−0.765409	−	0.643544i	$-0.777463\pi$
$463$	3.75740	−	6.50802i	0.174621	−	0.302453i	0.940030	+	0.341091i	$0.110797\pi$
$464$	−2.53838	−	4.39660i	−0.117841	−	0.204107i
$465$		0			0
$466$	−1.04397	+	5.92065i	−0.0483610	+	0.274269i
$467$	9.91503	+	17.1733i	0.458813	+	0.794687i	0.998899	−	0.0469230i	$-0.0149415\pi$
$467$	9.91503	+	17.1733i	0.458813	+	0.794687i	−0.540086	+	0.841610i	$0.681608\pi$
$468$	−13.1794	+	22.8274i	−0.609217	+	1.05520i
$469$	−2.21361	−	1.85744i	−0.102215	−	0.0857686i
$470$		0			0
$471$	27.3507	−	9.95485i	1.26026	−	0.458695i
$472$	10.3849	−	8.71394i	0.478002	−	0.401091i
$473$	−0.267524	−	1.51721i	−0.0123008	−	0.0697612i
$474$	17.0006			0.780865
$475$		0			0
$476$	−0.186175			−0.00853332
$477$	18.7700	+	106.450i	0.859419	+	4.87401i
$478$	2.51112	−	2.10708i	0.114856	−	0.0963758i
$479$	33.3726	−	12.1466i	1.52483	−	0.554994i	0.562485	−	0.826808i	$-0.309846\pi$
$479$	33.3726	−	12.1466i	1.52483	−	0.554994i	0.962350	+	0.271813i	$0.0876233\pi$
$480$		0			0
$481$	−9.88049	−	8.29071i	−0.450511	−	0.378024i
$482$	1.86408	−	3.22869i	0.0849067	−	0.147063i
$483$	−11.2478	−	19.4818i	−0.511793	−	0.886452i
$484$	−1.90610	+	10.8100i	−0.0866410	+	0.491366i
$485$		0			0
$486$	−19.5118	−	33.7954i	−0.885071	−	1.53299i
$487$	−7.51774	+	13.0211i	−0.340661	+	0.590043i	−0.984556	−	0.175072i	$-0.943984\pi$
$487$	−7.51774	+	13.0211i	−0.340661	+	0.590043i	0.643894	+	0.765114i	$0.277318\pi$
$488$	4.01614	+	3.36994i	0.181802	+	0.152550i
$489$	37.5236	+	13.6575i	1.69688	+	0.617612i
$490$		0			0
$491$	−7.84707	+	6.58448i	−0.354133	+	0.297153i	−0.802447	−	0.596723i	$-0.796469\pi$
$491$	−7.84707	+	6.58448i	−0.354133	+	0.297153i	0.448314	+	0.893876i	$0.352025\pi$
$492$	2.72905	+	15.4772i	0.123035	+	0.697768i
$493$	0.848683			0.0382228
$494$	−3.91879	−	14.6379i	−0.176315	−	0.658590i
$495$		0			0
$496$	−1.50943	−	8.56043i	−0.0677756	−	0.384375i
$497$	1.55243	−	1.30264i	0.0696360	−	0.0584316i
$498$	−18.5715	+	6.75949i	−0.832210	+	0.302900i
$499$	14.5418	+	5.29279i	0.650982	+	0.236938i	0.646338	−	0.763051i	$-0.276300\pi$
$499$	14.5418	+	5.29279i	0.650982	+	0.236938i	0.00464370	+	0.999989i	$0.498522\pi$
$500$		0			0
$501$	−18.7041	+	32.3964i	−0.835636	+	1.44736i
$502$	9.91241	+	17.1688i	0.442413	+	0.766281i
$503$	3.15334	−	17.8835i	0.140600	−	0.797384i	−0.830195	−	0.557474i	$-0.811771\pi$
$503$	3.15334	−	17.8835i	0.140600	−	0.797384i	0.970795	−	0.239911i	$-0.0771182\pi$
$504$	−1.46631	+	8.31583i	−0.0653145	+	0.370417i
$505$		0			0
$506$	−0.472794	+	0.818903i	−0.0210183	+	0.0364047i
$507$	−2.27883	−	1.91217i	−0.101207	−	0.0849224i
$508$	10.0888	+	3.67203i	0.447619	+	0.162920i
$509$	−7.26057	+	2.64263i	−0.321819	+	0.117133i	−0.497878	−	0.867247i	$-0.665887\pi$
$509$	−7.26057	+	2.64263i	−0.321819	+	0.117133i	0.176059	+	0.984380i	$0.443665\pi$
$510$		0			0
$511$	−1.96685	−	11.1546i	−0.0870083	−	0.493448i
$512$	1.00000			0.0441942
$513$	62.7554	+	16.8299i	2.77072	+	0.743059i
$514$	−15.2405			−0.672228
$515$		0			0
$516$	25.2105	−	21.1541i	1.10983	−	0.931258i
$517$	−1.20331	+	0.437968i	−0.0529214	+	0.0192618i
$518$	−3.88275	−	1.41321i	−0.170598	−	0.0620927i
$519$	−26.1139	−	21.9122i	−1.14627	−	0.961837i
$520$		0			0
$521$	18.8868	+	32.7129i	0.827445	+	1.43318i	0.900036	+	0.435816i	$0.143540\pi$
$521$	18.8868	+	32.7129i	0.827445	+	1.43318i	−0.0725907	+	0.997362i	$0.523127\pi$
$522$	6.68419	−	37.9079i	0.292559	−	1.65918i
$523$	4.40242	−	24.9674i	0.192505	−	1.09175i	−0.723423	−	0.690405i	$-0.757432\pi$
$523$	4.40242	−	24.9674i	0.192505	−	1.09175i	0.915928	−	0.401343i	$-0.131456\pi$
$524$	−9.14223	−	15.8348i	−0.399380	−	0.691747i
$525$		0			0
$526$	−18.6204	−	15.6244i	−0.811889	−	0.681256i
$527$	1.36549	+	0.496998i	0.0594818	+	0.0216496i
$528$	0.465506	−	0.169430i	0.0202585	−	0.00737351i
$529$	11.9170	−	9.99958i	0.518132	−	0.434764i
$530$		0			0
$531$	102.787			4.46059
$532$	−2.78352	−	3.97713i	−0.120681	−	0.172430i
$533$	16.7953			0.727485
$534$	6.77461	+	38.4207i	0.293166	+	1.66263i
$535$		0			0
$536$	−2.43821	+	0.887436i	−0.105315	+	0.0383314i
$537$	−13.9863	−	5.09061i	−0.603555	−	0.219676i
$538$	−2.17895	−	1.82836i	−0.0939413	−	0.0788261i
$539$	−0.438554	+	0.759598i	−0.0188899	+	0.0327182i
$540$		0			0
$541$	−1.60850	+	9.12224i	−0.0691547	+	0.392196i	0.930509	+	0.366269i	$0.119365\pi$
$541$	−1.60850	+	9.12224i	−0.0691547	+	0.392196i	−0.999664	+	0.0259272i	$0.991746\pi$
$542$	5.35712	−	30.3817i	0.230108	−	1.30501i
$543$	−15.4968	−	26.8413i	−0.665032	−	1.15187i
$544$	−0.0835852	+	0.144774i	−0.00358368	+	0.00620712i
$545$		0			0
$546$	11.8350	+	4.30758i	0.506490	+	0.184347i
$547$	35.7435	−	13.0096i	1.52828	−	0.556250i	0.565083	−	0.825034i	$-0.308844\pi$
$547$	35.7435	−	13.0096i	1.52828	−	0.556250i	0.963200	+	0.268784i	$0.0866219\pi$
$548$	−1.26378	+	1.06044i	−0.0539861	+	0.0452997i
$549$	6.90268	+	39.1470i	0.294599	+	1.67076i
$550$		0			0
$551$	12.6888	+	18.1298i	0.540559	+	0.772357i
$552$	−20.1993			−0.859739
$553$	−1.01067	−	5.73181i	−0.0429782	−	0.243741i
$554$	17.0461	−	14.3034i	0.724219	−	0.607692i
$555$		0			0
$556$	−5.99967	−	2.18370i	−0.254443	−	0.0926096i
$557$	−12.4171	−	10.4192i	−0.526130	−	0.441475i	0.340633	−	0.940196i	$-0.389359\pi$
$557$	−12.4171	−	10.4192i	−0.526130	−	0.441475i	−0.866763	+	0.498721i	$0.833803\pi$
$558$	32.9539	−	57.0778i	1.39505	−	2.41629i
$559$	−17.5850	−	30.4582i	−0.743768	−	1.28824i
$560$		0			0
$561$	−0.0143803	+	0.0815549i	−0.000607138	+	0.00344325i
$562$	3.69949	+	6.40771i	0.156054	+	0.270293i
$563$	−0.419520	+	0.726630i	−0.0176807	+	0.0306238i	−0.874730	−	0.484610i	$-0.838962\pi$
$563$	−0.419520	+	0.726630i	−0.0176807	+	0.0306238i	0.857050	+	0.515234i	$0.172295\pi$
$564$	−20.9546	−	17.5830i	−0.882348	−	0.740378i
$565$		0			0
$566$	8.41788	−	3.06386i	0.353830	−	0.128783i
$567$	−21.9618	+	18.4281i	−0.922307	+	0.773908i
$568$	−0.315985	−	1.79204i	−0.0132584	−	0.0751923i
$569$	16.7155			0.700749			0.350375	−	0.936610i	$-0.386054\pi$
$569$	16.7155			0.700749			0.350375	+	0.936610i	$0.386054\pi$
$570$		0			0
$571$	−15.0248			−0.628769			−0.314385	−	0.949296i	$-0.601798\pi$
$571$	−15.0248			−0.628769			−0.314385	+	0.949296i	$0.601798\pi$
$572$	−0.0919296	−	0.521359i	−0.00384377	−	0.0217991i
$573$	−21.1640	+	17.7587i	−0.884137	+	0.741879i
$574$	5.05595	−	1.84022i	0.211031	−	0.0768091i
$575$		0			0
$576$	5.80826	+	4.87371i	0.242011	+	0.203071i
$577$	8.85391	−	15.3354i	0.368593	−	0.638422i	−0.620753	−	0.784006i	$-0.713173\pi$
$577$	8.85391	−	15.3354i	0.368593	−	0.638422i	0.989346	+	0.145584i	$0.0465062\pi$
$578$	8.48603	+	14.6982i	0.352972	+	0.611366i
$579$	1.17418	−	6.65913i	0.0487974	−	0.276744i
$580$		0			0
$581$	3.38304	+	5.85960i	0.140352	+	0.243097i
$582$	−20.2800	+	35.1260i	−0.840634	+	1.45602i
$583$	−1.66306	−	1.39547i	−0.0688769	−	0.0577946i
$584$	−9.55706	−	3.47849i	−0.395474	−	0.143941i
$585$		0			0
$586$	12.9168	−	10.8385i	0.533589	−	0.447734i
$587$	−1.42130	−	8.06057i	−0.0586632	−	0.332695i	0.941325	−	0.337501i	$-0.109582\pi$
$587$	−1.42130	−	8.06057i	−0.0586632	−	0.332695i	−0.999988	+	0.00480525i	$0.998470\pi$
$588$	−18.7365			−0.772678
$589$	9.79859	+	36.6008i	0.403744	+	1.50811i
$590$		0			0
$591$	4.61753	+	26.1873i	0.189940	+	1.07720i
$592$	−2.84214	+	2.38484i	−0.116811	+	0.0980163i
$593$	−30.5313	+	11.1125i	−1.25377	+	0.456334i	−0.881673	−	0.471860i	$-0.843583\pi$
$593$	−30.5313	+	11.1125i	−1.25377	+	0.456334i	−0.372095	+	0.928195i	$0.621360\pi$
$594$	2.13302	+	0.776355i	0.0875188	+	0.0318542i
$595$		0			0
$596$	−0.987746	+	1.71083i	−0.0404596	+	0.0700782i
$597$	1.96075	+	3.39613i	0.0802483	+	0.138994i
$598$	−3.74845	+	21.2585i	−0.153286	+	0.869327i
$599$	2.31538	−	13.1312i	0.0946041	−	0.536526i	−0.900264	−	0.435345i	$-0.856627\pi$
$599$	2.31538	−	13.1312i	0.0946041	−	0.536526i	0.994868	−	0.101182i	$-0.0322623\pi$
$600$		0			0
$601$	−22.1899	+	38.4341i	−0.905147	+	1.56776i	−0.0844266	+	0.996430i	$0.526906\pi$
$601$	−22.1899	+	38.4341i	−0.905147	+	1.56776i	−0.820720	+	0.571330i	$0.806427\pi$
$602$	−8.63091	−	7.24219i	−0.351770	−	0.295170i
$603$	−18.4869	−	6.72867i	−0.752843	−	0.274013i
$604$	0.770396	−	0.280401i	0.0313470	−	0.0114094i
$605$		0			0
$606$	−3.88764	−	22.0479i	−0.157925	−	0.895636i
$607$	−2.26302			−0.0918533			−0.0459266	−	0.998945i	$-0.514624\pi$
$607$	−2.26302			−0.0918533			−0.0459266	+	0.998945i	$0.514624\pi$
$608$	−4.34239	+	0.378957i	−0.176107	+	0.0153687i
$609$	−18.3923			−0.745292
$610$		0			0
$611$	−22.3937	+	18.7905i	−0.905951	+	0.760183i
$612$	−1.19107	+	0.433514i	−0.0481462	+	0.0175238i
$613$	17.5267	+	6.37919i	0.707896	+	0.257653i	0.670778	−	0.741658i	$-0.265960\pi$
$613$	17.5267	+	6.37919i	0.707896	+	0.257653i	0.0371176	+	0.999311i	$0.488182\pi$
$614$	17.7995	+	14.9356i	0.718330	+	0.602751i
$615$		0			0
$616$	−0.0847978	−	0.146874i	−0.00341660	−	0.00591773i
$617$	7.85208	−	44.5314i	0.316113	−	1.79277i	−0.249796	−	0.968298i	$-0.580364\pi$
$617$	7.85208	−	44.5314i	0.316113	−	1.79277i	0.565909	−	0.824467i	$-0.308525\pi$
$618$	−11.2987	+	64.0779i	−0.454499	+	2.57759i
$619$	8.05129	+	13.9453i	0.323609	+	0.560507i	0.981230	−	0.192842i	$-0.0617705\pi$
$619$	8.05129	+	13.9453i	0.323609	+	0.560507i	−0.657621	+	0.753349i	$0.728437\pi$
$620$		0			0
$621$	−70.9021	−	59.4940i	−2.84520	−	2.38741i
$622$	−6.06608	−	2.20787i	−0.243227	−	0.0885276i
$623$	12.5509	−	4.56816i	0.502841	−	0.183019i
$624$	8.66311	−	7.26921i	0.346802	−	0.291001i
$625$		0			0
$626$	−23.8407			−0.952867
$627$	−1.95720	+	0.912140i	−0.0781632	+	0.0364274i
$628$	−8.94739			−0.357040
$629$	−0.107701	−	0.610805i	−0.00429433	−	0.0243544i
$630$		0			0
$631$	−32.6820	+	11.8953i	−1.30105	+	0.473544i	−0.897339	−	0.441343i	$-0.854502\pi$
$631$	−32.6820	+	11.8953i	−1.30105	+	0.473544i	−0.403712	+	0.914886i	$0.632280\pi$
$632$	−4.91093	−	1.78743i	−0.195346	−	0.0711003i
$633$	−21.8637	−	18.3458i	−0.869003	−	0.729180i
$634$	−2.17622	+	3.76932i	−0.0864287	+	0.149699i
$635$		0			0
$636$	8.05302	−	45.6709i	0.319323	−	1.81097i
$637$	−3.47699	+	19.7190i	−0.137763	+	0.781295i
$638$	0.386553	+	0.669529i	0.0153038	+	0.0265069i
$639$	6.89856	−	11.9487i	0.272903	−	0.472682i
$640$		0			0
$641$	31.9450	+	11.6270i	1.26175	+	0.459241i	0.884357	−	0.466811i	$-0.154597\pi$
$641$	31.9450	+	11.6270i	1.26175	+	0.459241i	0.377396	+	0.926052i	$0.376819\pi$
$642$	−51.4949	+	18.7426i	−2.03234	+	0.739712i
$643$	−18.6938	+	15.6860i	−0.737212	+	0.618595i	−0.932087	−	0.362234i	$-0.882014\pi$
$643$	−18.6938	+	15.6860i	−0.737212	+	0.618595i	0.194875	+	0.980828i	$0.437570\pi$
$644$	1.20083	+	6.81025i	0.0473193	+	0.268361i
$645$		0			0
$646$	0.308097	−	0.660340i	0.0121219	−	0.0259807i
$647$	25.1558			0.988977			0.494488	−	0.869184i	$-0.335355\pi$
$647$	25.1558			0.988977			0.494488	+	0.869184i	$0.335355\pi$
$648$	4.47014	+	25.3514i	0.175604	+	0.995899i
$649$	−1.58144	+	1.32699i	−0.0620770	+	0.0520888i
$650$		0			0
$651$	−29.5923	−	10.7707i	−1.15981	−	0.422138i
$652$	−9.40342	−	7.89041i	−0.368266	−	0.309012i
$653$	−5.40821	+	9.36730i	−0.211640	+	0.366571i	−0.952228	−	0.305388i	$-0.901214\pi$
$653$	−5.40821	+	9.36730i	−0.211640	+	0.366571i	0.740588	+	0.671959i	$0.234547\pi$
$654$	1.24593	+	2.15802i	0.0487199	+	0.0843853i
$655$		0			0
$656$	0.838929	−	4.75780i	0.0327547	−	0.185761i
$657$	−38.5568	−	66.7823i	−1.50424	−	2.60543i
$658$	−4.68242	+	8.11020i	−0.182540	+	0.316168i
$659$	0.812323	+	0.681620i	0.0316436	+	0.0265521i	0.658472	−	0.752605i	$-0.271203\pi$
$659$	0.812323	+	0.681620i	0.0316436	+	0.0265521i	−0.626829	+	0.779157i	$0.715647\pi$
$660$		0			0
$661$	22.6497	−	8.24381i	0.880970	−	0.320647i	0.138369	−	0.990381i	$-0.455814\pi$
$661$	22.6497	−	8.24381i	0.880970	−	0.320647i	0.742601	+	0.669734i	$0.233592\pi$
$662$	8.67981	−	7.28323i	0.337351	−	0.283071i
$663$	0.328284	+	1.86179i	0.0127495	+	0.0723059i
$664$	6.07540			0.235771
$665$		0			0
$666$	−28.1309			−1.09005
$667$	−5.47401	−	31.0447i	−0.211955	−	1.20205i
$668$	8.80913	−	7.39174i	0.340835	−	0.285995i
$669$	50.5355	−	18.3934i	1.95381	−	0.711130i
$670$		0			0
$671$	−0.611592	−	0.513187i	−0.0236102	−	0.0198114i
$672$	1.81142	−	3.13747i	0.0698770	−	0.121031i
$673$	3.72297	+	6.44837i	0.143510	+	0.248567i	0.928816	−	0.370541i	$-0.120828\pi$
$673$	3.72297	+	6.44837i	0.143510	+	0.248567i	−0.785306	+	0.619108i	$0.787494\pi$
$674$	−0.831831	+	4.71755i	−0.0320409	+	0.181713i
$675$		0			0
$676$	0.457237	+	0.791958i	0.0175861	+	0.0304599i
$677$	1.06800	−	1.84983i	0.0410465	−	0.0710947i	−0.844772	−	0.535126i	$-0.820264\pi$
$677$	1.06800	−	1.84983i	0.0410465	−	0.0710947i	0.885819	+	0.464031i	$0.153597\pi$
$678$	−10.7231	−	8.99778i	−0.411820	−	0.345558i
$679$	13.0485	+	4.74926i	0.500754	+	0.182260i
$680$		0			0
$681$	−61.8674	+	51.9129i	−2.37076	+	1.98931i
$682$	0.229862	+	1.30361i	0.00880186	+	0.0499179i
$683$	−45.9563			−1.75847			−0.879234	−	0.476389i	$-0.841945\pi$
$683$	−45.9563			−1.75847			−0.879234	+	0.476389i	$0.841945\pi$
$684$	−27.0687	−	18.9625i	−1.03500	−	0.725049i
$685$		0			0
$686$	2.46759	+	13.9944i	0.0942130	+	0.534309i
$687$	−34.1297	+	28.6382i	−1.30213	+	1.09262i
$688$	−9.50662	+	3.46013i	−0.362437	+	0.131916i
$689$	−46.5715	−	16.9506i	−1.77423	−	0.645768i
$690$		0			0
$691$	−14.5426	+	25.1886i	−0.553228	+	0.958218i	0.444812	+	0.895624i	$0.353271\pi$
$691$	−14.5426	+	25.1886i	−0.553228	+	0.958218i	−0.998039	+	0.0625940i	$0.980063\pi$
$692$	5.23963	+	9.07531i	0.199181	+	0.344991i
$693$	0.223294	−	1.26636i	0.00848224	−	0.0481052i
$694$	2.26518	−	12.8465i	0.0859852	−	0.487646i
$695$		0			0
$696$	−8.25740	+	14.3022i	−0.312996	+	0.542125i
$697$	0.618683	+	0.519137i	0.0234343	+	0.0196637i
$698$	17.2412	+	6.27528i	0.652588	+	0.237523i
$699$	18.3777	−	6.68893i	0.695108	−	0.252999i
$700$		0			0
$701$	−6.02338	−	34.1603i	−0.227500	−	1.29022i	−0.857848	−	0.513903i	$-0.828199\pi$
$701$	−6.02338	−	34.1603i	−0.227500	−	1.29022i	0.630348	−	0.776312i	$-0.282912\pi$
$702$	51.8190			1.95578
$703$	11.4379	−	11.4330i	0.431390	−	0.431202i
$704$	−0.152283			−0.00573940
$705$		0			0
$706$	−12.6650	+	10.6272i	−0.476654	+	0.399960i
$707$	−7.20240	+	2.62146i	−0.270874	+	0.0985901i
$708$	−41.4400	−	15.0829i	−1.55741	−	0.566851i
$709$	18.6361	+	15.6376i	0.699894	+	0.587281i	0.921744	−	0.387800i	$-0.126765\pi$
$709$	18.6361	+	15.6376i	0.699894	+	0.587281i	−0.221849	+	0.975081i	$0.571209\pi$
$710$		0			0
$711$	−19.8125	−	34.3163i	−0.743029	−	1.28696i
$712$	2.08256	−	11.8108i	0.0780472	−	0.442628i
$713$	9.37268	−	53.1551i	0.351009	−	1.99067i
$714$	0.302816	+	0.524492i	0.0113326	+	0.0196286i
$715$		0			0
$716$	3.50498	+	2.94102i	0.130987	+	0.109911i
$717$	−10.0204	−	3.64714i	−0.374220	−	0.136205i
$718$	1.15548	−	0.420561i	0.0431222	−	0.0156952i
$719$	−13.2721	+	11.1366i	−0.494965	+	0.415325i	−0.855802	−	0.517304i	$-0.826936\pi$
$719$	−13.2721	+	11.1366i	−0.494965	+	0.415325i	0.360837	+	0.932629i	$0.382491\pi$
$720$		0			0
$721$	22.2757			0.829592
$722$	18.7128	−	3.29116i	0.696418	−	0.122484i
$723$	−12.1278			−0.451038
$724$	1.65446	+	9.38289i	0.0614874	+	0.348713i
$725$		0			0
$726$	33.5544	−	12.2128i	1.24532	−	0.453259i
$727$	−17.3188	−	6.30353i	−0.642319	−	0.233785i	0.000265506	−	1.00000i	$-0.499915\pi$
$727$	−17.3188	−	6.30353i	−0.642319	−	0.233785i	−0.642584	+	0.766215i	$0.722138\pi$
$728$	−2.96585	−	2.48864i	−0.109922	−	0.0922352i
$729$	−24.8584	+	43.0560i	−0.920680	+	1.59467i
$730$		0			0
$731$	0.293677	−	1.66552i	0.0108620	−	0.0616017i
$732$	2.96150	−	16.7955i	0.109460	−	0.620781i
$733$	−10.1669	−	17.6095i	−0.375522	−	0.650423i	0.614883	−	0.788618i	$-0.289203\pi$
$733$	−10.1669	−	17.6095i	−0.375522	−	0.650423i	−0.990405	+	0.138195i	$0.955870\pi$
$734$	9.09039	−	15.7450i	0.335532	−	0.581159i
$735$		0			0
$736$	5.83492	+	2.12374i	0.215078	+	0.0782820i
$737$	0.371299	−	0.135142i	0.0136770	−	0.00497801i
$738$	28.0609	−	23.5459i	1.03294	−	0.866736i
$739$	−6.29815	−	35.7186i	−0.231681	−	1.31393i	−0.849492	−	0.527602i	$-0.823091\pi$
$739$	−6.29815	−	35.7186i	−0.231681	−	1.31393i	0.617811	−	0.786327i	$-0.288020\pi$
$740$		0			0
$741$	−34.8639	+	34.8487i	−1.28076	+	1.28020i
$742$	−15.8768			−0.582856
$743$	2.65630	+	15.0646i	0.0974503	+	0.552668i	0.993969	+	0.109662i	$0.0349769\pi$
$743$	2.65630	+	15.0646i	0.0974503	+	0.552668i	−0.896519	+	0.443006i	$0.853912\pi$
$744$	−21.6613	+	18.1760i	−0.794143	+	0.666365i
$745$		0			0
$746$	−19.3001	−	7.02465i	−0.706626	−	0.257191i
$747$	35.2875	+	29.6098i	1.29110	+	1.08336i
$748$	0.0127286	−	0.0220466i	0.000465405	−	0.000806105i
$749$	9.38045	+	16.2474i	0.342754	+	0.593668i
$750$		0			0
$751$	6.31318	−	35.8038i	0.230371	−	1.30650i	−0.621775	−	0.783196i	$-0.713588\pi$
$751$	6.31318	−	35.8038i	0.230371	−	1.30650i	0.852146	−	0.523303i	$-0.175301\pi$
$752$	4.20444	+	7.28231i	0.153320	+	0.265559i
$753$	32.2453	−	55.8505i	1.17508	−	2.03531i
$754$	13.5199	+	11.3445i	0.492365	+	0.413143i
$755$		0			0
$756$	15.5993	−	5.67767i	0.567340	−	0.206495i
$757$	20.4185	−	17.1332i	0.742124	−	0.622716i	−0.191283	−	0.981535i	$-0.561265\pi$
$757$	20.4185	−	17.1332i	0.742124	−	0.622716i	0.933407	+	0.358819i	$0.116821\pi$
$758$	−3.08600	−	17.5016i	−0.112089	−	0.635686i
$759$	3.07602			0.111652
$760$		0			0
$761$	38.6389			1.40066			0.700329	−	0.713820i	$-0.253037\pi$
$761$	38.6389			1.40066			0.700329	+	0.713820i	$0.253037\pi$
$762$	−6.06474	−	34.3948i	−0.219702	−	1.24599i
$763$	0.653513	−	0.548363i	0.0236588	−	0.0198521i
$764$	7.98072	−	2.90474i	0.288732	−	0.105090i
$765$		0			0
$766$	13.3969	+	11.2414i	0.484051	+	0.406167i
$767$	−23.5640	+	40.8141i	−0.850848	+	1.47371i
$768$	−1.62651	−	2.81720i	−0.0586916	−	0.101657i
$769$	7.40411	−	41.9908i	0.266999	−	1.51423i	−0.496282	−	0.868161i	$-0.665302\pi$
$769$	7.40411	−	41.9908i	0.266999	−	1.51423i	0.763281	−	0.646066i	$-0.223587\pi$
$770$		0			0
$771$	24.7888	+	42.9354i	0.892746	+	1.54628i
$772$	−1.03932	+	1.80015i	−0.0374059	+	0.0647889i
$773$	0.210260	+	0.176429i	0.00756254	+	0.00634572i	0.646561	−	0.762862i	$-0.276207\pi$
$773$	0.210260	+	0.176429i	0.00756254	+	0.00634572i	−0.638999	+	0.769208i	$0.720651\pi$
$774$	−72.0806	−	26.2352i	−2.59088	−	0.943005i
$775$		0			0
$776$	9.55137	−	8.01455i	0.342874	−	0.287706i
$777$	2.33405	+	13.2371i	0.0837337	+	0.474878i
$778$	−1.62995			−0.0584365
$779$	−1.83996	+	20.9782i	−0.0659234	+	0.751621i
$780$		0			0
$781$	0.0481193	+	0.272898i	0.00172184	+	0.00976506i
$782$	−0.795175	+	0.667231i	−0.0284354	+	0.0238601i
$783$	−71.1096	+	25.8818i	−2.54125	+	0.924939i
$784$	5.41235	+	1.96994i	0.193298	+	0.0703549i
$785$		0			0
$786$	−29.7399	+	51.5109i	−1.06079	+	1.83733i
$787$	0.610341	+	1.05714i	0.0217563	+	0.0376830i	0.876699	−	0.481040i	$-0.159741\pi$
$787$	0.610341	+	1.05714i	0.0217563	+	0.0376830i	−0.854942	+	0.518723i	$0.826408\pi$
$788$	1.41946	−	8.05016i	0.0505662	−	0.286775i
$789$	−13.7307	+	77.8707i	−0.488826	+	2.77227i
$790$		0			0
$791$	−2.39615	+	4.15025i	−0.0851971	+	0.147566i
$792$	−0.884502	−	0.742185i	−0.0314294	−	0.0263724i
$793$	−17.1267	−	6.23361i	−0.608187	−	0.221362i
$794$	27.0137	−	9.83220i	0.958682	−	0.348932i
$795$		0			0
$796$	−0.209332	−	1.18718i	−0.00741959	−	0.0420786i
$797$	32.1696			1.13950			0.569752	−	0.821817i	$-0.307039\pi$
$797$	32.1696			1.13950			0.569752	+	0.821817i	$0.307039\pi$
$798$	−6.67693	+	14.3106i	−0.236361	+	0.506589i
$799$	−1.40572			−0.0497307
$800$		0			0
$801$	69.6584	−	58.4503i	2.46126	−	2.06524i
$802$	17.3218	−	6.30462i	0.611654	−	0.222624i
$803$	1.45538	+	0.529716i	0.0513593	+	0.0186933i
$804$	6.46586	+	5.42550i	0.228033	+	0.191343i
$805$		0			0
$806$	15.1094	+	26.1702i	0.532205	+	0.921807i
$807$	−1.60676	+	9.11239i	−0.0565606	+	0.320771i
$808$	−1.19509	+	6.77768i	−0.0420430	+	0.238438i
$809$	7.73400	+	13.3957i	0.271913	+	0.470967i	0.969352	−	0.245678i	$-0.0790104\pi$
$809$	7.73400	+	13.3957i	0.271913	+	0.470967i	−0.697439	+	0.716644i	$0.745677\pi$
$810$		0			0
$811$	12.4771	+	10.4695i	0.438130	+	0.367634i	0.835009	−	0.550236i	$-0.185462\pi$
$811$	12.4771	+	10.4695i	0.438130	+	0.367634i	−0.396879	+	0.917871i	$0.629907\pi$
$812$	5.31293	+	1.93375i	0.186447	+	0.0678613i
$813$	−94.3049	+	34.3242i	−3.30742	+	1.20380i
$814$	0.432811	−	0.363171i	0.0151700	−	0.0127292i
$815$		0			0
$816$	0.543809			0.0190371
$817$	39.9703	−	18.6278i	1.39838	−	0.651706i
$818$	21.8780			0.764945
$819$	−5.09750	−	28.9094i	−0.178121	−	1.01017i
$820$		0			0
$821$	18.7800	−	6.83535i	0.655425	−	0.238555i	0.00716519	−	0.999974i	$-0.497719\pi$
$821$	18.7800	−	6.83535i	0.655425	−	0.238555i	0.648260	+	0.761419i	$0.275497\pi$
$822$	5.04302	+	1.83551i	0.175896	+	0.0640207i
$823$	−28.3826	−	23.8158i	−0.989356	−	0.830168i	−0.00388158	−	0.999992i	$-0.501236\pi$
$823$	−28.3826	−	23.8158i	−0.989356	−	0.830168i	−0.985474	+	0.169824i	$0.945680\pi$
$824$	10.0009	−	17.3221i	0.348399	−	0.603444i
$825$		0			0
$826$	−2.62168	+	14.8683i	−0.0912198	+	0.517333i
$827$	−3.54837	+	20.1238i	−0.123389	+	0.699774i	0.858863	+	0.512206i	$0.171172\pi$
$827$	−3.54837	+	20.1238i	−0.123389	+	0.699774i	−0.982252	+	0.187568i	$0.939939\pi$
$828$	23.5403	+	40.7730i	0.818081	+	1.41696i
$829$	21.5683	−	37.3574i	0.749098	−	1.29748i	−0.199157	−	0.979968i	$-0.563820\pi$
$829$	21.5683	−	37.3574i	0.749098	−	1.29748i	0.948255	−	0.317509i	$-0.102846\pi$
$830$		0			0
$831$	−68.0211	−	24.7577i	−2.35963	−	0.858833i
$832$	−3.26677	+	1.18901i	−0.113255	+	0.0412214i
$833$	−0.737588	+	0.618909i	−0.0255559	+	0.0214439i
$834$	3.60661	+	20.4541i	0.124887	+	0.708267i
$835$		0			0
$836$	0.661275	−	0.0577088i	0.0228707	−	0.00199590i
$837$	−129.569			−4.47855
$838$	−4.84898	−	27.5000i	−0.167505	−	0.949970i
$839$	−12.6386	+	10.6051i	−0.436334	+	0.366128i	−0.834335	−	0.551257i	$-0.814148\pi$
$839$	−12.6386	+	10.6051i	−0.436334	+	0.366128i	0.398001	+	0.917385i	$0.369704\pi$
$840$		0			0
$841$	3.03197	+	1.10355i	0.104551	+	0.0380533i
$842$	22.0785	+	18.5261i	0.760875	+	0.638450i
$843$	12.0345	−	20.8444i	0.414491	−	0.717920i
$844$	4.38685	+	7.59824i	0.151001	+	0.261542i
$845$		0			0
$846$	−11.0714	+	62.7888i	−0.380641	+	2.15872i
$847$	−6.11235	−	10.5869i	−0.210023	−	0.363770i
$848$	−7.12806	+	12.3462i	−0.244779	+	0.423969i
$849$	−22.3233	−	18.7314i	−0.766132	−	0.642861i
$850$		0			0
$851$	−21.6484	+	7.87939i	−0.742099	+	0.270102i
$852$	−4.53458	+	3.80497i	−0.155352	+	0.130356i
$853$	4.30870	+	24.4359i	0.147527	+	0.836669i	0.965303	+	0.261132i	$0.0840957\pi$
$853$	4.30870	+	24.4359i	0.147527	+	0.836669i	−0.817776	+	0.575537i	$0.804793\pi$
$854$	−5.83872			−0.199797
$855$		0			0
$856$	16.8458			0.575778
$857$	1.49962	+	8.50475i	0.0512259	+	0.290517i	0.999649	−	0.0264906i	$-0.00843319\pi$
$857$	1.49962	+	8.50475i	0.0512259	+	0.290517i	−0.948423	+	0.317007i	$0.897322\pi$
$858$	−1.31925	+	1.10698i	−0.0450384	+	0.0377917i
$859$	−51.8239	+	18.8624i	−1.76821	+	0.643575i	−0.768214	+	0.640193i	$0.778854\pi$
$859$	−51.8239	+	18.8624i	−1.76821	+	0.643575i	−0.999994	+	0.00338162i	$0.998924\pi$
$860$		0			0
$861$	−13.4078	−	11.2505i	−0.456937	−	0.383416i
$862$	9.38502	−	16.2553i	0.319655	−	0.553659i
$863$	22.9876	+	39.8156i	0.782506	+	1.35534i	0.930478	+	0.366349i	$0.119392\pi$
$863$	22.9876	+	39.8156i	0.782506	+	1.35534i	−0.147972	+	0.988992i	$0.547274\pi$
$864$	2.58837	−	14.6794i	0.0880581	−	0.499402i
$865$		0			0
$866$	−2.39507	−	4.14838i	−0.0813877	−	0.140968i
$867$	27.6052	−	47.8137i	0.937523	−	1.62384i
$868$	7.41584	+	6.22263i	0.251710	+	0.211210i
$869$	0.747853	+	0.272196i	0.0253692	+	0.00923363i
$870$		0			0
$871$	6.90990	−	5.79810i	0.234133	−	0.196461i
$872$	−0.133017	−	0.754379i	−0.00450454	−	0.0255465i
$873$	94.5375			3.19961
$874$	−26.1423	−	7.01093i	−0.884278	−	0.237148i
$875$		0			0
$876$	5.74508	+	32.5819i	0.194108	+	1.10084i
$877$	27.3240	−	22.9276i	0.922667	−	0.774210i	−0.0518190	−	0.998656i	$-0.516502\pi$
$877$	27.3240	−	22.9276i	0.922667	−	0.774210i	0.974486	+	0.224447i	$0.0720575\pi$
$878$	36.2064	−	13.1781i	1.22191	−	0.444738i
$879$	−51.5435	−	18.7603i	−1.73852	−	0.632769i
$880$		0			0
$881$	−15.6962	+	27.1867i	−0.528820	+	0.915943i	0.470615	+	0.882339i	$0.344032\pi$
$881$	−15.6962	+	27.1867i	−0.528820	+	0.915943i	−0.999435	+	0.0336046i	$0.989301\pi$
$882$	21.8355	+	37.8202i	0.735239	+	1.27347i
$883$	−9.23557	+	52.3775i	−0.310802	+	1.76264i	0.284050	+	0.958809i	$0.408322\pi$
$883$	−9.23557	+	52.3775i	−0.310802	+	1.76264i	−0.594852	+	0.803835i	$0.702789\pi$
$884$	0.100917	−	0.572326i	0.00339419	−	0.0192494i
$885$		0			0
$886$	1.95615	−	3.38814i	0.0657180	−	0.113827i
$887$	−38.1940	−	32.0486i	−1.28243	−	1.07609i	−0.992904	−	0.118917i	$-0.962058\pi$
$887$	−38.1940	−	32.0486i	−1.28243	−	1.07609i	−0.289526	−	0.957170i	$-0.593498\pi$
$888$	11.3413	+	4.12791i	0.380590	+	0.138524i
$889$	−11.2358	+	4.08948i	−0.376835	+	0.137157i
$890$		0			0
$891$	−0.680729	−	3.86060i	−0.0228053	−	0.129335i
$892$	−16.5319			−0.553530
$893$	−21.0170	−	30.0294i	−0.703308	−	1.00489i
$894$	6.42632			0.214928
$895$		0			0
$896$	−0.853132	+	0.715862i	−0.0285011	+	0.0239153i
$897$	65.9865	−	24.0171i	2.20322	−	0.801908i
$898$	−24.2306	−	8.81923i	−0.808587	−	0.294302i
$899$	−33.8053	−	28.3660i	−1.12747	−	0.946058i
$900$		0			0
$901$	−1.19160	−	2.06391i	−0.0396980	−	0.0687589i
$902$	−0.127755	+	0.724534i	−0.00425378	+	0.0241244i
$903$	−6.36443	+	36.0945i	−0.211795	+	1.20115i
$904$	2.15155	+	3.72659i	0.0715594	+	0.123945i
$905$		0			0
$906$	−2.04300	−	1.71428i	−0.0678742	−	0.0569532i
$907$	−27.7827	−	10.1121i	−0.922508	−	0.335765i	−0.163272	−	0.986581i	$-0.552205\pi$
$907$	−27.7827	−	10.1121i	−0.922508	−	0.335765i	−0.759236	+	0.650816i	$0.774427\pi$
$908$	23.3296	−	8.49127i	0.774219	−	0.281793i
$909$	−39.9738	+	33.5420i	−1.32585	+	1.11252i
$910$		0			0
$911$	39.6035			1.31212			0.656061	−	0.754708i	$-0.272222\pi$
$911$	39.6035			1.31212			0.656061	+	0.754708i	$0.272222\pi$
$912$	8.13055	+	11.6170i	0.269229	+	0.384678i
$913$	−0.925183			−0.0306191
$914$	0.343498	+	1.94808i	0.0113619	+	0.0644366i
$915$		0			0
$916$	12.8700	−	4.68429i	0.425236	−	0.154773i
$917$	19.1351	+	6.96459i	0.631895	+	0.229991i
$918$	1.90884	+	1.60171i	0.0630011	+	0.0528642i
$919$	−10.5711	+	18.3097i	−0.348708	+	0.603981i	−0.986020	−	0.166625i	$-0.946713\pi$
$919$	−10.5711	+	18.3097i	−0.348708	+	0.603981i	0.637312	+	0.770606i	$0.280046\pi$
$920$		0			0
$921$	13.1254	−	74.4377i	0.432496	−	2.45280i
$922$	−6.59010	+	37.3743i	−0.217033	+	1.23086i
$923$	3.16300	+	5.47847i	0.104111	+	0.180326i
$924$	−0.275849	+	0.477785i	−0.00907477	+	0.0157180i
$925$		0			0
$926$	7.06161	+	2.57022i	0.232059	+	0.0844625i
$927$	142.511	−	51.8697i	4.68067	−	1.70363i
$928$	3.88902	−	3.26328i	0.127663	−	0.107122i
$929$	0.110092	+	0.624361i	0.00361199	+	0.0204846i	0.986560	−	0.163396i	$-0.0522450\pi$
$929$	0.110092	+	0.624361i	0.00361199	+	0.0204846i	−0.982948	+	0.183881i	$0.941134\pi$
$930$		0			0
$931$	−24.2491	−	6.50319i	−0.794732	−	0.213134i
$932$	−6.01199			−0.196929
$933$	3.64652	+	20.6805i	0.119382	+	0.677048i
$934$	−15.1907	+	12.7465i	−0.497055	+	0.417079i
$935$		0			0
$936$	−24.7691	−	9.01523i	−0.809605	−	0.294672i
$937$	−10.3940	−	8.72163i	−0.339558	−	0.284923i	0.457023	−	0.889455i	$-0.348916\pi$
$937$	−10.3940	−	8.72163i	−0.339558	−	0.284923i	−0.796581	+	0.604532i	$0.793360\pi$
$938$	1.44483	−	2.50252i	0.0471754	−	0.0817102i
$939$	38.7772	+	67.1641i	1.26545	+	2.19182i
$940$		0			0
$941$	6.64131	−	37.6648i	0.216501	−	1.22784i	−0.661783	−	0.749696i	$-0.730200\pi$
$941$	6.64131	−	37.6648i	0.216501	−	1.22784i	0.878283	−	0.478140i	$-0.158689\pi$
$942$	14.5530	+	25.2066i	0.474163	+	0.821274i
$943$	14.9994	−	25.9797i	0.488448	−	0.846017i
$944$	10.3849	+	8.71394i	0.337999	+	0.283614i
$945$		0			0
$946$	1.44770	−	0.526920i	0.0470688	−	0.0171316i
$947$	−24.2614	+	20.3577i	−0.788390	+	0.661538i	−0.945346	−	0.326068i	$-0.894276\pi$
$947$	−24.2614	+	20.3577i	−0.788390	+	0.661538i	0.156956	+	0.987606i	$0.449832\pi$
$948$	2.95213	+	16.7423i	0.0958807	+	0.543766i
$949$	35.3567			1.14773
$950$		0			0
$951$	14.1586			0.459123
$952$	−0.0323289	−	0.183347i	−0.00104779	−	0.00594230i
$953$	4.05531	−	3.40281i	0.131364	−	0.110228i	−0.574738	−	0.818337i	$-0.694896\pi$
$953$	4.05531	−	3.40281i	0.131364	−	0.110228i	0.706103	+	0.708109i	$0.250452\pi$
$954$	−101.573	+	36.9697i	−3.28856	+	1.19694i
$955$		0			0
$956$	2.51112	+	2.10708i	0.0812156	+	0.0681480i
$957$	1.25746	−	2.17799i	0.0406481	−	0.0704045i
$958$	17.7572	+	30.7564i	0.573709	+	0.993694i
$959$	0.319044	−	1.80939i	0.0103025	−	0.0584282i
$960$		0			0
$961$	−22.2797	−	38.5895i	−0.718699	−	1.24482i
$962$	6.44903	−	11.1700i	0.207925	−	0.360137i
$963$	97.8448	+	82.1016i	3.15301	+	2.64569i
$964$	3.50333	+	1.27511i	0.112835	+	0.0410685i
$965$		0			0
$966$	17.2327	−	14.4599i	0.554452	−	0.465240i
$967$	8.54518	+	48.4621i	0.274794	+	1.55844i	0.739614	+	0.673031i	$0.235008\pi$
$967$	8.54518	+	48.4621i	0.274794	+	1.55844i	−0.464820	+	0.885405i	$0.653881\pi$
$968$	−10.9768			−0.352808
$969$	−2.36143	+	0.206080i	−0.0758601	+	0.00662024i
$970$		0			0
$971$	−4.04703	−	22.9519i	−0.129875	−	0.736560i	−0.978292	−	0.207231i	$-0.933555\pi$
$971$	−4.04703	−	22.9519i	−0.129875	−	0.736560i	0.848417	−	0.529329i	$-0.177556\pi$
$972$	29.8937	−	25.0838i	0.958842	−	0.804564i
$973$	6.68174	−	2.43196i	0.214207	−	0.0779649i
$974$	−14.1287	−	5.14244i	−0.452714	−	0.164774i
$975$		0			0
$976$	−2.62135	+	4.54031i	−0.0839074	+	0.145332i
$977$	−11.1445	−	19.3028i	−0.356543	−	0.617550i	0.630838	−	0.775914i	$-0.282711\pi$
$977$	−11.1445	−	19.3028i	−0.356543	−	0.617550i	−0.987381	+	0.158365i	$0.949378\pi$
$978$	−6.93408	+	39.3251i	−0.221728	+	1.25748i
$979$	−0.317139	+	1.79859i	−0.0101358	+	0.0574831i
$980$		0			0
$981$	2.90403	−	5.02992i	0.0927184	−	0.160593i
$982$	−7.84707	−	6.58448i	−0.250410	−	0.210119i
$983$	1.64198	+	0.597631i	0.0523710	+	0.0190615i	0.368073	−	0.929797i	$-0.380018\pi$
$983$	1.64198	+	0.597631i	0.0523710	+	0.0190615i	−0.315702	+	0.948858i	$0.602240\pi$
$984$	−14.7682	+	5.37519i	−0.470793	+	0.171355i
$985$		0			0
$986$	0.147372	+	0.835790i	0.00469329	+	0.0266170i
$987$	30.4640			0.969681
$988$	13.7350	−	6.40110i	0.436969	−	0.203646i
$989$	−62.8188			−1.99752
$990$		0			0
$991$	−33.8989	+	28.4445i	−1.07683	+	0.903571i	−0.995654	−	0.0931289i	$-0.970313\pi$
$991$	−33.8989	+	28.4445i	−1.07683	+	0.903571i	−0.0811794	+	0.996700i	$0.525869\pi$
$992$	8.16827	−	2.97301i	0.259343	−	0.0943930i
$993$	−34.6361	−	12.6065i	−1.09914	−	0.400056i
$994$	1.55243	+	1.30264i	0.0492401	+	0.0413174i
$995$		0			0
$996$	−9.88171	−	17.1156i	−0.313114	−	0.542329i
$997$	−4.97878	+	28.2360i	−0.157679	+	0.894244i	0.798616	+	0.601841i	$0.205566\pi$
$997$	−4.97878	+	28.2360i	−0.157679	+	0.894244i	−0.956295	+	0.292403i	$0.905545\pi$
$998$	−2.68722	+	15.2400i	−0.0850625	+	0.482413i
$999$	27.6514	+	47.8937i	0.874853	+	1.51529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.k.351.4	yes	24
5.2	odd	4		950.2.u.h.199.1		48
5.3	odd	4		950.2.u.h.199.8		48
5.4	even	2		950.2.l.j.351.1	✓	24
19.17	even	9	inner	950.2.l.k.701.4	yes	24
95.17	odd	36		950.2.u.h.549.8		48
95.74	even	18		950.2.l.j.701.1	yes	24
95.93	odd	36		950.2.u.h.549.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.351.1	✓	24	5.4	even	2
950.2.l.j.701.1	yes	24	95.74	even	18
950.2.l.k.351.4	yes	24	1.1	even	1	trivial
950.2.l.k.701.4	yes	24	19.17	even	9	inner
950.2.u.h.199.1		48	5.2	odd	4
950.2.u.h.199.8		48	5.3	odd	4
950.2.u.h.549.1		48	95.93	odd	36
950.2.u.h.549.8		48	95.17	odd	36

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.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(2.49196 - 2.09100i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.49196 + 2.09100i) q^{6} +(0.556842 - 0.964479i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.31663 - 7.46696i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(2.49196 - 2.09100i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.49196 + 2.09100i) q^{6} +(0.556842 - 0.964479i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.31663 - 7.46696i) q^{9} +(0.0761417 + 0.131881i) q^{11} +(-1.62651 + 2.81720i) q^{12} +(2.66310 + 2.23460i) q^{13} +(1.04652 + 0.380902i) q^{14} +(0.766044 - 0.642788i) q^{16} +(0.0290288 + 0.164631i) q^{17} +7.58215 q^{18} +(-3.08288 + 3.08154i) q^{19} +(-0.629099 - 3.56780i) q^{21} +(-0.116656 + 0.0978859i) q^{22} +(5.83492 - 2.12374i) q^{23} +(-3.05684 - 1.11260i) q^{24} +(-1.73821 + 3.01067i) q^{26} +(-7.45291 - 12.9088i) q^{27} +(-0.193389 + 1.09676i) q^{28} +(0.881569 - 4.99963i) q^{29} +(4.34624 - 7.52791i) q^{31} +(0.766044 + 0.642788i) q^{32} +(0.465506 + 0.169430i) q^{33} +(-0.157089 + 0.0571756i) q^{34} +(1.31663 + 7.46696i) q^{36} -3.71015 q^{37} +(-3.57006 - 2.50094i) q^{38} +11.3089 q^{39} +(3.70091 - 3.10544i) q^{41} +(3.40435 - 1.23908i) q^{42} +(-9.50662 - 3.46013i) q^{43} +(-0.116656 - 0.0978859i) q^{44} +(3.10470 + 5.37749i) q^{46} +(-1.46019 + 8.28114i) q^{47} +(0.564881 - 3.20360i) q^{48} +(2.87985 + 4.98805i) q^{49} +(0.416582 + 0.349553i) q^{51} +(-3.26677 - 1.18901i) q^{52} +(-13.3964 + 4.87588i) q^{53} +(11.4185 - 9.58128i) q^{54} -1.11368 q^{56} +(-1.23891 + 14.1254i) q^{57} +5.07676 q^{58} +(2.35406 + 13.3505i) q^{59} +(-4.92653 + 1.79311i) q^{61} +(8.16827 + 2.97301i) q^{62} +(-6.46857 - 5.42778i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.0860220 + 0.487855i) q^{66} +(0.450563 - 2.55527i) q^{67} +(-0.0835852 - 0.144774i) q^{68} +(10.0996 - 17.4931i) q^{69} +(1.70994 + 0.622369i) q^{71} +(-7.12489 + 2.59325i) q^{72} +(7.79099 - 6.53742i) q^{73} +(-0.644261 - 3.65379i) q^{74} +(1.84301 - 3.95010i) q^{76} +0.169596 q^{77} +(1.96377 + 11.1371i) q^{78} +(4.00343 - 3.35927i) q^{79} +(-24.1901 - 8.80446i) q^{81} +(3.70091 + 3.10544i) q^{82} +(-3.03770 + 5.26145i) q^{83} +(1.81142 + 3.13747i) q^{84} +(1.75675 - 9.96304i) q^{86} +(-8.25740 - 14.3022i) q^{87} +(0.0761417 - 0.131881i) q^{88} +(9.18716 + 7.70894i) q^{89} +(3.63815 - 1.32418i) q^{91} +(-4.75667 + 3.99132i) q^{92} +(-4.91022 - 27.8473i) q^{93} -8.40889 q^{94} +3.25302 q^{96} +(2.16512 + 12.2790i) q^{97} +(-4.41219 + 3.70227i) q^{98} +(1.08500 - 0.394909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{7} - 12 q^{8}+O(q^{10}) \) 24 * q + 3 * q^7 - 12 * q^8	\( 24 q + 3 q^{7} - 12 q^{8} - 6 q^{11} - 3 q^{12} + 24 q^{13} - 15 q^{14} - 9 q^{17} + 30 q^{18} - 15 q^{19} - 18 q^{21} + 12 q^{23} - 9 q^{26} - 21 q^{27} + 12 q^{28} - 12 q^{29} + 9 q^{31} - 42 q^{33} - 9 q^{34} + 66 q^{37} + 6 q^{38} + 66 q^{39} + 18 q^{41} + 9 q^{42} - 3 q^{43} - 3 q^{46} - 12 q^{47} - 27 q^{49} - 3 q^{51} - 12 q^{52} - 45 q^{53} + 27 q^{54} - 6 q^{56} - 27 q^{57} - 18 q^{58} + 36 q^{59} + 12 q^{61} - 24 q^{62} - 63 q^{63} - 12 q^{64} + 48 q^{66} - 54 q^{67} + 3 q^{68} + 21 q^{69} - 39 q^{71} + 48 q^{73} + 18 q^{74} + 6 q^{76} + 48 q^{77} - 12 q^{78} - 42 q^{79} - 36 q^{81} + 18 q^{82} - 3 q^{83} + 9 q^{84} - 39 q^{86} - 24 q^{87} - 6 q^{88} - 36 q^{89} + 12 q^{91} - 15 q^{92} - 6 q^{93} + 12 q^{94} + 6 q^{96} - 54 q^{97} + 3 q^{98} + 51 q^{99}+O(q^{100}) \) 24 * q + 3 * q^7 - 12 * q^8 - 6 * q^11 - 3 * q^12 + 24 * q^13 - 15 * q^14 - 9 * q^17 + 30 * q^18 - 15 * q^19 - 18 * q^21 + 12 * q^23 - 9 * q^26 - 21 * q^27 + 12 * q^28 - 12 * q^29 + 9 * q^31 - 42 * q^33 - 9 * q^34 + 66 * q^37 + 6 * q^38 + 66 * q^39 + 18 * q^41 + 9 * q^42 - 3 * q^43 - 3 * q^46 - 12 * q^47 - 27 * q^49 - 3 * q^51 - 12 * q^52 - 45 * q^53 + 27 * q^54 - 6 * q^56 - 27 * q^57 - 18 * q^58 + 36 * q^59 + 12 * q^61 - 24 * q^62 - 63 * q^63 - 12 * q^64 + 48 * q^66 - 54 * q^67 + 3 * q^68 + 21 * q^69 - 39 * q^71 + 48 * q^73 + 18 * q^74 + 6 * q^76 + 48 * q^77 - 12 * q^78 - 42 * q^79 - 36 * q^81 + 18 * q^82 - 3 * q^83 + 9 * q^84 - 39 * q^86 - 24 * q^87 - 6 * q^88 - 36 * q^89 + 12 * q^91 - 15 * q^92 - 6 * q^93 + 12 * q^94 + 6 * q^96 - 54 * q^97 + 3 * q^98 + 51 * q^99

Introduction

L-functions

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