LMFDB - Embedded newform 990.2.i.j.331.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(331,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.331"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,-7,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 3 x^{12} - 4 x^{11} + 4 x^{10} - 27 x^{8} - 9 x^{7} - 81 x^{6} + 108 x^{4} + \cdots + 2187 $ x^14 - x^13 + 3x^12 - 4x^11 + 4x^10 - 27x^8 - 9x^7 - 81x^6 + 108x^4 - 324x^3 + 729x^2 - 729x + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.3
Root			$1.01796 + 1.40134i$ of defining polynomial
Character	$\chi$	$=$	990.331
Dual form			990.2.i.j.661.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.01796 + 1.40134i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.704617 - 1.58225i) q^{6} +(0.170965 - 0.296120i) q^{7} +1.00000 q^{8} +(-0.927514 - 2.85302i) q^{9} +1.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.72258 + 0.180909i) q^{12} +(3.25957 + 5.64575i) q^{13} +(0.170965 + 0.296120i) q^{14} +(1.72258 + 0.180909i) q^{15} +(-0.500000 + 0.866025i) q^{16} +4.62820 q^{17} +(2.93454 + 0.623258i) q^{18} -4.74612 q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.240930 + 0.541019i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(-3.02499 - 5.23944i) q^{23} +(-1.01796 + 1.40134i) q^{24} +(-0.500000 + 0.866025i) q^{25} -6.51915 q^{26} +(4.94223 + 1.60450i) q^{27} -0.341930 q^{28} +(-4.54403 + 7.87048i) q^{29} +(-1.01796 + 1.40134i) q^{30} +(2.53454 + 4.38995i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.704617 - 1.58225i) q^{33} +(-2.31410 + 4.00814i) q^{34} -0.341930 q^{35} +(-2.00703 + 2.22976i) q^{36} -9.02949 q^{37} +(2.37306 - 4.11026i) q^{38} +(-11.2297 - 1.17937i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-1.23458 - 2.13836i) q^{41} +(-0.589001 - 0.0618582i) q^{42} +(-3.93674 + 6.81864i) q^{43} +1.00000 q^{44} +(-2.00703 + 2.22976i) q^{45} +6.04998 q^{46} +(0.573169 - 0.992759i) q^{47} +(-0.704617 - 1.58225i) q^{48} +(3.44154 + 5.96093i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-4.71132 + 6.48569i) q^{51} +(3.25957 - 5.64575i) q^{52} +0.392415 q^{53} +(-3.86065 + 3.47785i) q^{54} +1.00000 q^{55} +(0.170965 - 0.296120i) q^{56} +(4.83136 - 6.65094i) q^{57} +(-4.54403 - 7.87048i) q^{58} +(-7.48911 - 12.9715i) q^{59} +(-0.704617 - 1.58225i) q^{60} +(-5.54512 + 9.60443i) q^{61} -5.06908 q^{62} +(-1.00341 - 0.213111i) q^{63} +1.00000 q^{64} +(3.25957 - 5.64575i) q^{65} +(1.72258 + 0.180909i) q^{66} +(-6.04372 - 10.4680i) q^{67} +(-2.31410 - 4.00814i) q^{68} +(10.4216 + 1.09449i) q^{69} +(0.170965 - 0.296120i) q^{70} +0.850693 q^{71} +(-0.927514 - 2.85302i) q^{72} +6.30335 q^{73} +(4.51474 - 7.81976i) q^{74} +(-0.704617 - 1.58225i) q^{75} +(2.37306 + 4.11026i) q^{76} +(0.170965 + 0.296120i) q^{77} +(6.63623 - 9.13555i) q^{78} +(2.00334 - 3.46990i) q^{79} +1.00000 q^{80} +(-7.27943 + 5.29243i) q^{81} +2.46917 q^{82} +(0.999607 - 1.73137i) q^{83} +(0.348071 - 0.479161i) q^{84} +(-2.31410 - 4.00814i) q^{85} +(-3.93674 - 6.81864i) q^{86} +(-6.40360 - 14.3796i) q^{87} +(-0.500000 + 0.866025i) q^{88} +0.823380 q^{89} +(-0.927514 - 2.85302i) q^{90} +2.22909 q^{91} +(-3.02499 + 5.23944i) q^{92} +(-8.73188 - 0.917041i) q^{93} +(0.573169 + 0.992759i) q^{94} +(2.37306 + 4.11026i) q^{95} +(1.72258 + 0.180909i) q^{96} +(-9.65280 + 16.7191i) q^{97} -6.88308 q^{98} +(2.93454 + 0.623258i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 7 q^{2} - q^{3} - 7 q^{4} - 7 q^{5} + 2 q^{6} - 5 q^{7} + 14 q^{8} - 5 q^{9} + 14 q^{10} - 7 q^{11} - q^{12} - 5 q^{13} - 5 q^{14} - q^{15} - 7 q^{16} + 6 q^{17} + 7 q^{18} + 22 q^{19} - 7 q^{20}+ \cdots + 7 q^{99}+O(q^{100}) $ 14 * q - 7 * q^2 - q^3 - 7 * q^4 - 7 * q^5 + 2 * q^6 - 5 * q^7 + 14 * q^8 - 5 * q^9 + 14 * q^10 - 7 * q^11 - q^12 - 5 * q^13 - 5 * q^14 - q^15 - 7 * q^16 + 6 * q^17 + 7 * q^18 + 22 * q^19 - 7 * q^20 - 21 * q^21 - 7 * q^22 - 3 * q^23 - q^24 - 7 * q^25 + 10 * q^26 - 4 * q^27 + 10 * q^28 - 12 * q^29 - q^30 - 5 * q^31 - 7 * q^32 + 2 * q^33 - 3 * q^34 + 10 * q^35 - 2 * q^36 + 4 * q^37 - 11 * q^38 - 33 * q^39 - 7 * q^40 - 6 * q^41 + 21 * q^42 - 17 * q^43 + 14 * q^44 - 2 * q^45 + 6 * q^46 + 3 * q^47 + 2 * q^48 - 12 * q^49 - 7 * q^50 + 4 * q^51 - 5 * q^52 + 6 * q^53 + 2 * q^54 + 14 * q^55 - 5 * q^56 - 2 * q^57 - 12 * q^58 - 18 * q^59 + 2 * q^60 - 11 * q^61 + 10 * q^62 - 3 * q^63 + 14 * q^64 - 5 * q^65 - q^66 - 20 * q^67 - 3 * q^68 + 24 * q^69 - 5 * q^70 + 24 * q^71 - 5 * q^72 + 4 * q^73 - 2 * q^74 + 2 * q^75 - 11 * q^76 - 5 * q^77 + 24 * q^78 + 7 * q^79 + 14 * q^80 + 7 * q^81 + 12 * q^82 - 3 * q^85 - 17 * q^86 + 19 * q^87 - 7 * q^88 - 6 * q^89 - 5 * q^90 + 14 * q^91 - 3 * q^92 - 24 * q^93 + 3 * q^94 - 11 * q^95 - q^96 - 23 * q^97 + 24 * q^98 + 7 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.01796	+	1.40134i	−0.587720	+	0.809065i
$3$	−1.01796	+	1.40134i	−0.587720	+	0.809065i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.704617	−	1.58225i	−0.287659	−	0.645951i
$7$	0.170965	−	0.296120i	0.0646188	−	0.111923i	−0.831906	−	0.554916i	$-0.812750\pi$
$7$	0.170965	−	0.296120i	0.0646188	−	0.111923i	0.896525	+	0.442994i	$0.146084\pi$
$8$	1.00000			0.353553
$9$	−0.927514	−	2.85302i	−0.309171	−	0.951006i
$10$	1.00000			0.316228
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	1.72258	+	0.180909i	0.497265	+	0.0522239i
$13$	3.25957	+	5.64575i	0.904043	+	1.56585i	0.822197	+	0.569204i	$0.192748\pi$
$13$	3.25957	+	5.64575i	0.904043	+	1.56585i	0.0818466	+	0.996645i	$0.473918\pi$
$14$	0.170965	+	0.296120i	0.0456924	+	0.0791415i
$15$	1.72258	+	0.180909i	0.444768	+	0.0467104i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.62820			1.12250			0.561252	−	0.827645i	$-0.310320\pi$
$17$	4.62820			1.12250			0.561252	+	0.827645i	$0.310320\pi$
$18$	2.93454	+	0.623258i	0.691679	+	0.146903i
$19$	−4.74612			−1.08884			−0.544418	−	0.838814i	$-0.683249\pi$
$19$	−4.74612			−1.08884			−0.544418	+	0.838814i	$0.683249\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	0.240930	+	0.541019i	0.0525752	+	0.118060i
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	−3.02499	−	5.23944i	−0.630754	−	1.09250i	−0.987398	−	0.158258i	$-0.949412\pi$
$23$	−3.02499	−	5.23944i	−0.630754	−	1.09250i	0.356644	−	0.934240i	$-0.383921\pi$
$24$	−1.01796	+	1.40134i	−0.207790	+	0.286048i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−6.51915			−1.27851
$27$	4.94223	+	1.60450i	0.951132	+	0.308785i
$28$	−0.341930			−0.0646188
$29$	−4.54403	+	7.87048i	−0.843805	+	1.46151i	0.0428508	+	0.999081i	$0.486356\pi$
$29$	−4.54403	+	7.87048i	−0.843805	+	1.46151i	−0.886655	+	0.462431i	$0.846977\pi$
$30$	−1.01796	+	1.40134i	−0.185853	+	0.255849i
$31$	2.53454	+	4.38995i	0.455217	+	0.788459i	0.998701	−	0.0509609i	$-0.0162284\pi$
$31$	2.53454	+	4.38995i	0.455217	+	0.788459i	−0.543484	+	0.839420i	$0.682895\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.704617	−	1.58225i	−0.122658	−	0.275434i
$34$	−2.31410	+	4.00814i	−0.396865	+	0.687390i
$35$	−0.341930			−0.0577968
$36$	−2.00703	+	2.22976i	−0.334505	+	0.371627i
$37$	−9.02949			−1.48444			−0.742219	−	0.670157i	$-0.766227\pi$
$37$	−9.02949			−1.48444			−0.742219	+	0.670157i	$0.766227\pi$
$38$	2.37306	−	4.11026i	0.384961	−	0.666773i
$39$	−11.2297	−	1.17937i	−1.79820	−	0.188850i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−1.23458	−	2.13836i	−0.192810	−	0.333956i	0.753371	−	0.657596i	$-0.228427\pi$
$41$	−1.23458	−	2.13836i	−0.192810	−	0.333956i	−0.946180	+	0.323640i	$0.895093\pi$
$42$	−0.589001	−	0.0618582i	−0.0908849	−	0.00954492i
$43$	−3.93674	+	6.81864i	−0.600348	+	1.03983i	0.392420	+	0.919786i	$0.371638\pi$
$43$	−3.93674	+	6.81864i	−0.600348	+	1.03983i	−0.992768	+	0.120047i	$0.961695\pi$
$44$	1.00000			0.150756
$45$	−2.00703	+	2.22976i	−0.299190	+	0.332393i
$46$	6.04998			0.892021
$47$	0.573169	−	0.992759i	0.0836054	−	0.144809i	−0.821191	−	0.570654i	$-0.806690\pi$
$47$	0.573169	−	0.992759i	0.0836054	−	0.144809i	0.904796	+	0.425845i	$0.140023\pi$
$48$	−0.704617	−	1.58225i	−0.101703	−	0.228378i
$49$	3.44154	+	5.96093i	0.491649	+	0.851561i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−4.71132	+	6.48569i	−0.659717	+	0.908178i
$52$	3.25957	−	5.64575i	0.452022	−	0.782924i
$53$	0.392415			0.0539023			0.0269512	−	0.999637i	$-0.491420\pi$
$53$	0.392415			0.0539023			0.0269512	+	0.999637i	$0.491420\pi$
$54$	−3.86065	+	3.47785i	−0.525367	+	0.473275i
$55$	1.00000			0.134840
$56$	0.170965	−	0.296120i	0.0228462	−	0.0395707i
$57$	4.83136	−	6.65094i	0.639930	−	0.880938i
$58$	−4.54403	−	7.87048i	−0.596660	−	1.03345i
$59$	−7.48911	−	12.9715i	−0.974999	−	1.68875i	−0.679939	−	0.733269i	$-0.737994\pi$
$59$	−7.48911	−	12.9715i	−0.974999	−	1.68875i	−0.295060	−	0.955479i	$-0.595340\pi$
$60$	−0.704617	−	1.58225i	−0.0909657	−	0.204268i
$61$	−5.54512	+	9.60443i	−0.709980	+	1.22972i	0.254885	+	0.966971i	$0.417963\pi$
$61$	−5.54512	+	9.60443i	−0.709980	+	1.22972i	−0.964864	+	0.262749i	$0.915371\pi$
$62$	−5.06908			−0.643774
$63$	−1.00341	−	0.213111i	−0.126418	−	0.0268495i
$64$	1.00000			0.125000
$65$	3.25957	−	5.64575i	0.404300	−	0.700269i
$66$	1.72258	+	0.180909i	0.212035	+	0.0222683i
$67$	−6.04372	−	10.4680i	−0.738358	−	1.27887i	−0.953234	−	0.302233i	$-0.902268\pi$
$67$	−6.04372	−	10.4680i	−0.738358	−	1.27887i	0.214876	−	0.976641i	$-0.431065\pi$
$68$	−2.31410	−	4.00814i	−0.280626	−	0.486058i
$69$	10.4216	+	1.09449i	1.25461	+	0.131762i
$70$	0.170965	−	0.296120i	0.0204342	−	0.0353931i
$71$	0.850693			0.100959			0.0504793	−	0.998725i	$-0.483925\pi$
$71$	0.850693			0.100959			0.0504793	+	0.998725i	$0.483925\pi$
$72$	−0.927514	−	2.85302i	−0.109309	−	0.336232i
$73$	6.30335			0.737752			0.368876	−	0.929479i	$-0.379743\pi$
$73$	6.30335			0.737752			0.368876	+	0.929479i	$0.379743\pi$
$74$	4.51474	−	7.81976i	0.524828	−	0.909029i
$75$	−0.704617	−	1.58225i	−0.0813622	−	0.182702i
$76$	2.37306	+	4.11026i	0.272209	+	0.471479i
$77$	0.170965	+	0.296120i	0.0194833	+	0.0337460i
$78$	6.63623	−	9.13555i	0.751405	−	1.03440i
$79$	2.00334	−	3.46990i	0.225394	−	0.390394i	−0.731044	−	0.682331i	$-0.760966\pi$
$79$	2.00334	−	3.46990i	0.225394	−	0.390394i	0.956438	+	0.291937i	$0.0942998\pi$
$80$	1.00000			0.111803
$81$	−7.27943	+	5.29243i	−0.808826	+	0.588048i
$82$	2.46917			0.272674
$83$	0.999607	−	1.73137i	0.109721	−	0.190043i	−0.805936	−	0.592003i	$-0.798338\pi$
$83$	0.999607	−	1.73137i	0.109721	−	0.190043i	0.915657	+	0.401960i	$0.131671\pi$
$84$	0.348071	−	0.479161i	0.0379777	−	0.0522808i
$85$	−2.31410	−	4.00814i	−0.250999	−	0.434744i
$86$	−3.93674	−	6.81864i	−0.424510	−	0.735273i
$87$	−6.40360	−	14.3796i	−0.686538	−	1.54165i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	0.823380			0.0872782			0.0436391	−	0.999047i	$-0.486105\pi$
$89$	0.823380			0.0872782			0.0436391	+	0.999047i	$0.486105\pi$
$90$	−0.927514	−	2.85302i	−0.0977686	−	0.300735i
$91$	2.22909			0.233673
$92$	−3.02499	+	5.23944i	−0.315377	+	0.546249i
$93$	−8.73188	−	0.917041i	−0.905454	−	0.0950927i
$94$	0.573169	+	0.992759i	0.0591179	+	0.102395i
$95$	2.37306	+	4.11026i	0.243471	+	0.421704i
$96$	1.72258	+	0.180909i	0.175810	+	0.0184639i
$97$	−9.65280	+	16.7191i	−0.980093	+	1.69757i	−0.318106	+	0.948055i	$0.603047\pi$
$97$	−9.65280	+	16.7191i	−0.980093	+	1.69757i	−0.661987	+	0.749516i	$0.730286\pi$
$98$	−6.88308			−0.695296
$99$	2.93454	+	0.623258i	0.294933	+	0.0626398i
$100$	1.00000			0.100000
$101$	−9.56562	+	16.5681i	−0.951815	+	1.64859i	−0.210321	+	0.977632i	$0.567451\pi$
$101$	−9.56562	+	16.5681i	−0.951815	+	1.64859i	−0.741494	+	0.670960i	$0.765882\pi$
$102$	−3.26111	−	7.32297i	−0.322898	−	0.725082i
$103$	1.01656	+	1.76074i	0.100165	+	0.173491i	0.911753	−	0.410740i	$-0.134730\pi$
$103$	1.01656	+	1.76074i	0.100165	+	0.173491i	−0.811588	+	0.584231i	$0.801396\pi$
$104$	3.25957	+	5.64575i	0.319628	+	0.553611i
$105$	0.348071	−	0.479161i	0.0339683	−	0.0467613i
$106$	−0.196208	+	0.339841i	−0.0190574	+	0.0330083i
$107$	−13.9835			−1.35184			−0.675920	−	0.736975i	$-0.736254\pi$
$107$	−13.9835			−1.35184			−0.675920	+	0.736975i	$0.736254\pi$
$108$	−1.08158	−	5.08234i	−0.104075	−	0.489048i
$109$	−11.4527			−1.09697			−0.548486	−	0.836160i	$-0.684795\pi$
$109$	−11.4527			−1.09697			−0.548486	+	0.836160i	$0.684795\pi$
$110$	−0.500000	+	0.866025i	−0.0476731	+	0.0825723i
$111$	9.19166	−	12.6534i	0.872433	−	1.20101i
$112$	0.170965	+	0.296120i	0.0161547	+	0.0279807i
$113$	4.49455	+	7.78479i	0.422812	+	0.732331i	0.996213	−	0.0869431i	$-0.0277098\pi$
$113$	4.49455	+	7.78479i	0.422812	+	0.732331i	−0.573402	+	0.819274i	$0.694376\pi$
$114$	3.34420	+	7.50955i	0.313213	+	0.703334i
$115$	−3.02499	+	5.23944i	−0.282082	+	0.488580i
$116$	9.08805			0.843805
$117$	13.0841	−	14.5361i	1.20963	−	1.34387i
$118$	14.9782			1.37886
$119$	0.791261	−	1.37050i	0.0725347	−	0.125634i
$120$	1.72258	+	0.180909i	0.157249	+	0.0165146i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−5.54512	−	9.60443i	−0.502031	−	0.869544i
$123$	4.25333	+	0.446694i	0.383510	+	0.0402770i
$124$	2.53454	−	4.38995i	0.227608	−	0.394229i
$125$	1.00000			0.0894427
$126$	0.686264	−	0.762423i	0.0611373	−	0.0679220i
$127$	15.1160			1.34132			0.670662	−	0.741763i	$-0.266010\pi$
$127$	15.1160			1.34132			0.670662	+	0.741763i	$0.266010\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−5.54779	−	12.4578i	−0.488456	−	1.09685i
$130$	3.25957	+	5.64575i	0.285884	+	0.495165i
$131$	3.13808	+	5.43532i	0.274176	+	0.474886i	0.969927	−	0.243397i	$-0.0782617\pi$
$131$	3.13808	+	5.43532i	0.274176	+	0.474886i	−0.695751	+	0.718283i	$0.744928\pi$
$132$	−1.01796	+	1.40134i	−0.0886021	+	0.121971i
$133$	−0.811422	+	1.40542i	−0.0703592	+	0.121866i
$134$	12.0874			1.04420
$135$	−1.08158	−	5.08234i	−0.0930875	−	0.437418i
$136$	4.62820			0.396865
$137$	3.37535	−	5.84627i	0.288375	−	0.499481i	−0.685047	−	0.728499i	$-0.740218\pi$
$137$	3.37535	−	5.84627i	0.288375	−	0.499481i	0.973422	+	0.229018i	$0.0735516\pi$
$138$	−6.15864	+	8.47809i	−0.524258	+	0.721703i
$139$	3.29001	+	5.69847i	0.279055	+	0.483338i	0.971150	−	0.238469i	$-0.0766454\pi$
$139$	3.29001	+	5.69847i	0.279055	+	0.483338i	−0.692095	+	0.721806i	$0.743312\pi$
$140$	0.170965	+	0.296120i	0.0144492	+	0.0250267i
$141$	0.807730	+	1.81379i	0.0680231	+	0.152749i
$142$	−0.425346	+	0.736722i	−0.0356943	+	0.0618243i
$143$	−6.51915			−0.545159
$144$	2.93454	+	0.623258i	0.244545	+	0.0519382i
$145$	9.08805			0.754722
$146$	−3.15168	+	5.45886i	−0.260835	+	0.451779i
$147$	−11.8566	−	1.24521i	−0.977919	−	0.102703i
$148$	4.51474	+	7.81976i	0.371110	+	0.642781i
$149$	−6.91485	−	11.9769i	−0.566486	−	0.981183i	−0.996910	−	0.0785560i	$-0.974969\pi$
$149$	−6.91485	−	11.9769i	−0.566486	−	0.981183i	0.430423	−	0.902627i	$-0.358364\pi$
$150$	1.72258	+	0.180909i	0.140648	+	0.0147711i
$151$	−3.04273	+	5.27016i	−0.247614	+	0.428880i	−0.962863	−	0.269990i	$-0.912980\pi$
$151$	−3.04273	+	5.27016i	−0.247614	+	0.428880i	0.715249	+	0.698869i	$0.246313\pi$
$152$	−4.74612			−0.384961
$153$	−4.29272	−	13.2043i	−0.347046	−	1.06751i
$154$	−0.341930			−0.0275535
$155$	2.53454	−	4.38995i	0.203579	−	0.352610i
$156$	4.59350	+	10.3149i	0.367775	+	0.825855i
$157$	8.05263	+	13.9476i	0.642670	+	1.11314i	0.984834	+	0.173497i	$0.0555066\pi$
$157$	8.05263	+	13.9476i	0.642670	+	1.11314i	−0.342165	+	0.939640i	$0.611160\pi$
$158$	2.00334	+	3.46990i	0.159378	+	0.276050i
$159$	−0.399463	+	0.549907i	−0.0316795	+	0.0436105i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−2.06867			−0.163034
$162$	−0.943663	−	8.95039i	−0.0741412	−	0.703209i
$163$	14.5582			1.14029			0.570145	−	0.821544i	$-0.306887\pi$
$163$	14.5582			1.14029			0.570145	+	0.821544i	$0.306887\pi$
$164$	−1.23458	+	2.13836i	−0.0964048	+	0.166978i
$165$	−1.01796	+	1.40134i	−0.0792481	+	0.109094i
$166$	0.999607	+	1.73137i	0.0775846	+	0.134380i
$167$	−7.42739	−	12.8646i	−0.574749	−	0.995495i	−0.996069	−	0.0885824i	$-0.971766\pi$
$167$	−7.42739	−	12.8646i	−0.574749	−	0.995495i	0.421320	−	0.906912i	$-0.361567\pi$
$168$	0.240930	+	0.541019i	0.0185881	+	0.0417405i
$169$	−14.7496	+	25.5471i	−1.13459	+	1.96516i
$170$	4.62820			0.354967
$171$	4.40210	+	13.5408i	0.336637	+	1.03549i
$172$	7.87349			0.600348
$173$	4.82513	−	8.35738i	0.366848	−	0.635400i	−0.622223	−	0.782840i	$-0.713770\pi$
$173$	4.82513	−	8.35738i	0.366848	−	0.635400i	0.989071	+	0.147441i	$0.0471035\pi$
$174$	15.6549	+	1.64411i	1.18679	+	0.124640i
$175$	0.170965	+	0.296120i	0.0129238	+	0.0223846i
$176$	−0.500000	−	0.866025i	−0.0376889	−	0.0652791i
$177$	25.8011	+	2.70969i	1.93933	+	0.203673i
$178$	−0.411690	+	0.713068i	−0.0308575	+	0.0534467i
$179$	−21.7265			−1.62391			−0.811956	−	0.583719i	$-0.801597\pi$
$179$	−21.7265			−1.62391			−0.811956	+	0.583719i	$0.801597\pi$
$180$	2.93454	+	0.623258i	0.218728	+	0.0464549i
$181$	5.95042			0.442291			0.221146	−	0.975241i	$-0.429020\pi$
$181$	5.95042			0.442291			0.221146	+	0.975241i	$0.429020\pi$
$182$	−1.11455	+	1.93045i	−0.0826157	+	0.143095i
$183$	−7.81437	−	17.5475i	−0.577655	−	1.29715i
$184$	−3.02499	−	5.23944i	−0.223005	−	0.386256i
$185$	4.51474	+	7.81976i	0.331931	+	0.574921i
$186$	5.16012	−	7.10351i	0.378359	−	0.520855i
$187$	−2.31410	+	4.00814i	−0.169224	+	0.293104i
$188$	−1.14634			−0.0836054
$189$	1.32007	−	1.18918i	0.0960211	−	0.0865002i
$190$	−4.74612			−0.344320
$191$	−12.4479	+	21.5604i	−0.900698	+	1.56005i	−0.0741074	+	0.997250i	$0.523611\pi$
$191$	−12.4479	+	21.5604i	−0.900698	+	1.56005i	−0.826590	+	0.562804i	$0.809723\pi$
$192$	−1.01796	+	1.40134i	−0.0734649	+	0.101133i
$193$	4.94115	+	8.55832i	0.355672	+	0.616041i	0.987233	−	0.159285i	$-0.0509188\pi$
$193$	4.94115	+	8.55832i	0.355672	+	0.616041i	−0.631561	+	0.775326i	$0.717585\pi$
$194$	−9.65280	−	16.7191i	−0.693030	−	1.20036i
$195$	4.59350	+	10.3149i	0.328948	+	0.738667i
$196$	3.44154	−	5.96093i	0.245824	−	0.425780i
$197$	25.5227			1.81842			0.909210	−	0.416337i	$-0.136686\pi$
$197$	25.5227			1.81842			0.909210	+	0.416337i	$0.136686\pi$
$198$	−2.00703	+	2.22976i	−0.142633	+	0.158462i
$199$	5.03309			0.356786			0.178393	−	0.983959i	$-0.442910\pi$
$199$	5.03309			0.356786			0.178393	+	0.983959i	$0.442910\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	20.8216	+	2.18672i	1.46864	+	0.154240i
$202$	−9.56562	−	16.5681i	−0.673035	−	1.16573i
$203$	1.55374	+	2.69116i	0.109051	+	0.188882i
$204$	7.97243	+	0.837282i	0.558182	+	0.0586214i
$205$	−1.23458	+	2.13836i	−0.0862271	+	0.149350i
$206$	−2.03313			−0.141655
$207$	−12.1425	+	13.4900i	−0.843961	+	0.937620i
$208$	−6.51915			−0.452022
$209$	2.37306	−	4.11026i	0.164148	−	0.284313i
$210$	0.240930	+	0.541019i	0.0166257	+	0.0373339i
$211$	2.01027	+	3.48190i	0.138393	+	0.239704i	0.926888	−	0.375337i	$-0.122473\pi$
$211$	2.01027	+	3.48190i	0.138393	+	0.239704i	−0.788495	+	0.615041i	$0.789140\pi$
$212$	−0.196208	−	0.339841i	−0.0134756	−	0.0233404i
$213$	−0.865971	+	1.19211i	−0.0593354	+	0.0816821i
$214$	6.99177	−	12.1101i	0.477948	−	0.827830i
$215$	7.87349			0.536968
$216$	4.94223	+	1.60450i	0.336276	+	0.109172i
$217$	1.73327			0.117662
$218$	5.72636	−	9.91834i	0.387838	−	0.671755i
$219$	−6.41656	+	8.83315i	−0.433591	+	0.596889i
$220$	−0.500000	−	0.866025i	−0.0337100	−	0.0583874i
$221$	15.0860	+	26.1296i	1.01479	+	1.75767i
$222$	6.36233	+	14.2869i	0.427012	+	0.958874i
$223$	−5.40299	+	9.35826i	−0.361811	+	0.626675i	−0.988259	−	0.152788i	$-0.951175\pi$
$223$	−5.40299	+	9.35826i	−0.361811	+	0.626675i	0.626448	+	0.779463i	$0.284508\pi$
$224$	−0.341930			−0.0228462
$225$	2.93454	+	0.623258i	0.195636	+	0.0415506i
$226$	−8.98910			−0.597946
$227$	−9.54374	+	16.5303i	−0.633441	+	1.09715i	0.353403	+	0.935471i	$0.385025\pi$
$227$	−9.54374	+	16.5303i	−0.633441	+	1.09715i	−0.986843	+	0.161680i	$0.948309\pi$
$228$	−8.17556	−	0.858615i	−0.541440	−	0.0568632i
$229$	−11.1559	−	19.3226i	−0.737203	−	1.27687i	−0.953750	−	0.300601i	$-0.902813\pi$
$229$	−11.1559	−	19.3226i	−0.737203	−	1.27687i	0.216547	−	0.976272i	$-0.430520\pi$
$230$	−3.02499	−	5.23944i	−0.199462	−	0.345478i
$231$	−0.589001	−	0.0618582i	−0.0387534	−	0.00406997i
$232$	−4.54403	+	7.87048i	−0.298330	+	0.516723i
$233$	4.69942			0.307869			0.153935	−	0.988081i	$-0.450805\pi$
$233$	4.69942			0.307869			0.153935	+	0.988081i	$0.450805\pi$
$234$	6.04660	+	18.5993i	0.395279	+	1.21587i
$235$	−1.14634			−0.0747789
$236$	−7.48911	+	12.9715i	−0.487499	+	0.844374i
$237$	2.82318	+	6.33958i	0.183385	+	0.411800i
$238$	0.791261	+	1.37050i	0.0512898	+	0.0888366i
$239$	5.58240	+	9.66901i	0.361096	+	0.625436i	0.988141	−	0.153546i	$-0.0490695\pi$
$239$	5.58240	+	9.66901i	0.361096	+	0.625436i	−0.627046	+	0.778982i	$0.715736\pi$
$240$	−1.01796	+	1.40134i	−0.0657090	+	0.0904562i
$241$	7.93318	−	13.7407i	0.511021	−	0.885114i	−0.488898	−	0.872341i	$-0.662601\pi$
$241$	7.93318	−	13.7407i	0.511021	−	0.885114i	0.999918	−	0.0127728i	$-0.00406582\pi$
$242$	1.00000			0.0642824
$243$	−0.00632911	−	15.5885i	−0.000406013	−	1.00000i
$244$	11.0902			0.709980
$245$	3.44154	−	5.96093i	0.219872	−	0.380830i
$246$	−2.51351	+	3.46015i	−0.160256	+	0.220611i
$247$	−15.4703	−	26.7954i	−0.984354	−	1.70495i
$248$	2.53454	+	4.38995i	0.160943	+	0.278762i
$249$	1.40868	+	3.16326i	0.0892715	+	0.200463i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	11.2471			0.709910			0.354955	−	0.934883i	$-0.384496\pi$
$251$	11.2471			0.709910			0.354955	+	0.934883i	$0.384496\pi$
$252$	0.317145	+	0.975534i	0.0199783	+	0.0614528i
$253$	6.04998			0.380359
$254$	−7.55798	+	13.0908i	−0.474230	+	0.821390i
$255$	7.97243	+	0.837282i	0.499253	+	0.0524326i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.98710	−	3.44176i	−0.123952	−	0.214691i	0.797371	−	0.603490i	$-0.206224\pi$
$257$	−1.98710	−	3.44176i	−0.123952	−	0.214691i	−0.921323	+	0.388799i	$0.872890\pi$
$258$	13.5627	+	1.42438i	0.844376	+	0.0886782i
$259$	−1.54373	+	2.67381i	−0.0959226	+	0.166143i
$260$	−6.51915			−0.404300
$261$	26.6693	+	5.66421i	1.65079	+	0.350606i
$262$	−6.27617			−0.387743
$263$	1.80954	−	3.13422i	0.111581	−	0.193264i	−0.804827	−	0.593510i	$-0.797742\pi$
$263$	1.80954	−	3.13422i	0.111581	−	0.193264i	0.916408	+	0.400246i	$0.131075\pi$
$264$	−0.704617	−	1.58225i	−0.0433662	−	0.0973808i
$265$	−0.196208	−	0.339841i	−0.0120529	−	0.0208763i
$266$	−0.811422	−	1.40542i	−0.0497514	−	0.0861720i
$267$	−0.838169	+	1.15384i	−0.0512951	+	0.0706137i
$268$	−6.04372	+	10.4680i	−0.369179	+	0.639437i
$269$	14.9521			0.911643			0.455821	−	0.890071i	$-0.349346\pi$
$269$	14.9521			0.911643			0.455821	+	0.890071i	$0.349346\pi$
$270$	4.94223	+	1.60450i	0.300774	+	0.0976465i
$271$	−11.2316			−0.682273			−0.341137	−	0.940014i	$-0.610812\pi$
$271$	−11.2316			−0.682273			−0.341137	+	0.940014i	$0.610812\pi$
$272$	−2.31410	+	4.00814i	−0.140313	+	0.243029i
$273$	−2.26913	+	3.12372i	−0.137334	+	0.189056i
$274$	3.37535	+	5.84627i	0.203912	+	0.353186i
$275$	−0.500000	−	0.866025i	−0.0301511	−	0.0522233i
$276$	−4.26292	−	9.57258i	−0.256598	−	0.576202i
$277$	6.80210	−	11.7816i	0.408699	−	0.707887i	−0.586045	−	0.810278i	$-0.699316\pi$
$277$	6.80210	−	11.7816i	0.408699	−	0.707887i	0.994744	+	0.102391i	$0.0326493\pi$
$278$	−6.58003			−0.394644
$279$	10.1738	−	11.3028i	0.609089	−	0.676683i
$280$	−0.341930			−0.0204342
$281$	−0.349163	+	0.604768i	−0.0208293	+	0.0360774i	−0.876252	−	0.481853i	$-0.839964\pi$
$281$	−0.349163	+	0.604768i	−0.0208293	+	0.0360774i	0.855423	+	0.517930i	$0.173297\pi$
$282$	−1.97466	−	0.207383i	−0.117589	−	0.0123495i
$283$	14.9959	+	25.9736i	0.891412	+	1.54397i	0.838183	+	0.545389i	$0.183618\pi$
$283$	14.9959	+	25.9736i	0.891412	+	1.54397i	0.0532296	+	0.998582i	$0.483048\pi$
$284$	−0.425346	−	0.736722i	−0.0252397	−	0.0437164i
$285$	−8.17556	−	0.858615i	−0.484279	−	0.0508600i
$286$	3.25957	−	5.64575i	0.192743	−	0.333840i
$287$	−0.844283			−0.0498365
$288$	−2.00703	+	2.22976i	−0.118265	+	0.131390i
$289$	4.42022			0.260013
$290$	−4.54403	+	7.87048i	−0.266834	+	0.462171i
$291$	−13.6030	−	30.5463i	−0.797425	−	1.79065i
$292$	−3.15168	−	5.45886i	−0.184438	−	0.319456i
$293$	1.65341	+	2.86379i	0.0965934	+	0.167305i	0.910273	−	0.414010i	$-0.135872\pi$
$293$	1.65341	+	2.86379i	0.0965934	+	0.167305i	−0.813679	+	0.581314i	$0.802539\pi$
$294$	7.00670	−	9.64555i	0.408639	−	0.562540i
$295$	−7.48911	+	12.9715i	−0.436033	+	0.755231i
$296$	−9.02949			−0.524828
$297$	−3.86065	+	3.47785i	−0.224017	+	0.201805i
$298$	13.8297			0.801133
$299$	19.7204	−	34.1567i	1.14046	−	1.97533i
$300$	−1.01796	+	1.40134i	−0.0587720	+	0.0809065i
$301$	1.34609	+	2.33150i	0.0775875	+	0.134385i
$302$	−3.04273	−	5.27016i	−0.175089	−	0.303264i
$303$	−13.4802	−	30.2704i	−0.774417	−	1.73899i
$304$	2.37306	−	4.11026i	0.136104	−	0.235740i
$305$	11.0902			0.635025
$306$	13.5817	+	2.88456i	0.776411	+	0.164900i
$307$	6.04837			0.345198			0.172599	−	0.984992i	$-0.444783\pi$
$307$	6.04837			0.345198			0.172599	+	0.984992i	$0.444783\pi$
$308$	0.170965	−	0.296120i	0.00974164	−	0.0168730i
$309$	−3.50222	−	0.367810i	−0.199234	−	0.0209240i
$310$	2.53454	+	4.38995i	0.143952	+	0.249333i
$311$	−1.30782	−	2.26521i	−0.0741596	−	0.128448i	0.826561	−	0.562847i	$-0.190294\pi$
$311$	−1.30782	−	2.26521i	−0.0741596	−	0.128448i	−0.900720	+	0.434399i	$0.856961\pi$
$312$	−11.2297	−	1.17937i	−0.635759	−	0.0667687i
$313$	13.2700	−	22.9842i	0.750062	−	1.29915i	−0.197729	−	0.980257i	$-0.563357\pi$
$313$	13.2700	−	22.9842i	0.750062	−	1.29915i	0.947792	−	0.318890i	$-0.103310\pi$
$314$	−16.1053			−0.908872
$315$	0.317145	+	0.975534i	0.0178691	+	0.0549651i
$316$	−4.00669			−0.225394
$317$	−0.520712	+	0.901900i	−0.0292461	+	0.0506558i	−0.880278	−	0.474458i	$-0.842644\pi$
$317$	−0.520712	+	0.901900i	−0.0292461	+	0.0506558i	0.851032	+	0.525114i	$0.175977\pi$
$318$	−0.276502	−	0.620899i	−0.0155055	−	0.0348183i
$319$	−4.54403	−	7.87048i	−0.254417	−	0.440663i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	14.2347	−	19.5957i	0.794503	−	1.09373i
$322$	1.03434	−	1.79152i	0.0576413	−	0.0998376i
$323$	−21.9660			−1.22222
$324$	8.22310	+	3.65796i	0.456839	+	0.203220i
$325$	−6.51915			−0.361617
$326$	−7.27912	+	12.6078i	−0.403153	+	0.698282i
$327$	11.6584	−	16.0492i	0.644711	−	0.887521i
$328$	−1.23458	−	2.13836i	−0.0681685	−	0.118071i
$329$	−0.195984	−	0.339454i	−0.0108049	−	0.0187147i
$330$	−0.704617	−	1.58225i	−0.0387879	−	0.0871000i
$331$	−6.70843	+	11.6193i	−0.368728	+	0.638656i	−0.989367	−	0.145440i	$-0.953540\pi$
$331$	−6.70843	+	11.6193i	−0.368728	+	0.638656i	0.620639	+	0.784097i	$0.286873\pi$
$332$	−1.99921			−0.109721
$333$	8.37498	+	25.7613i	0.458946	+	1.41171i
$334$	14.8548			0.812818
$335$	−6.04372	+	10.4680i	−0.330204	+	0.571930i
$336$	−0.589001	−	0.0618582i	−0.0321327	−	0.00337464i
$337$	5.09519	+	8.82513i	0.277553	+	0.480735i	0.970776	−	0.239988i	$-0.0771434\pi$
$337$	5.09519	+	8.82513i	0.277553	+	0.480735i	−0.693223	+	0.720723i	$0.743810\pi$
$338$	−14.7496	−	25.5471i	−0.802275	−	1.38958i
$339$	−15.4844	−	1.62621i	−0.840998	−	0.0883234i
$340$	−2.31410	+	4.00814i	−0.125500	+	0.217372i
$341$	−5.06908			−0.274506
$342$	−13.9277	−	2.95806i	−0.753124	−	0.159954i
$343$	4.74705			0.256316
$344$	−3.93674	+	6.81864i	−0.212255	+	0.367637i
$345$	−4.26292	−	9.57258i	−0.229508	−	0.515370i
$346$	4.82513	+	8.35738i	0.259401	+	0.449295i
$347$	4.52500	+	7.83753i	0.242915	+	0.420740i	0.961543	−	0.274654i	$-0.0885632\pi$
$347$	4.52500	+	7.83753i	0.242915	+	0.420740i	−0.718629	+	0.695394i	$0.755230\pi$
$348$	−9.25128	+	12.7355i	−0.495920	+	0.682692i
$349$	16.3023	−	28.2364i	0.872642	−	1.51146i	0.0133891	−	0.999910i	$-0.495738\pi$
$349$	16.3023	−	28.2364i	0.872642	−	1.51146i	0.859253	−	0.511550i	$-0.170929\pi$
$350$	−0.341930			−0.0182769
$351$	7.05097	+	33.1325i	0.376353	+	1.76848i
$352$	1.00000			0.0533002
$353$	12.6341	−	21.8830i	0.672447	−	1.16471i	−0.304761	−	0.952429i	$-0.598577\pi$
$353$	12.6341	−	21.8830i	0.672447	−	1.16471i	0.977208	−	0.212284i	$-0.0680901\pi$
$354$	−15.2472	+	20.9896i	−0.810381	+	1.11558i
$355$	−0.425346	−	0.736722i	−0.0225750	−	0.0391011i
$356$	−0.411690	−	0.713068i	−0.0218195	−	0.0377926i
$357$	1.11507	+	2.50394i	0.0590158	+	0.132523i
$358$	10.8632	−	18.8157i	0.574139	−	0.994439i
$359$	30.2888			1.59858			0.799291	−	0.600944i	$-0.205208\pi$
$359$	30.2888			1.59858			0.799291	+	0.600944i	$0.205208\pi$
$360$	−2.00703	+	2.22976i	−0.105780	+	0.117519i
$361$	3.52568			0.185562
$362$	−2.97521	+	5.15322i	−0.156374	+	0.270847i
$363$	1.72258	+	0.180909i	0.0904119	+	0.00949525i
$364$	−1.11455	−	1.93045i	−0.0584181	−	0.101183i
$365$	−3.15168	−	5.45886i	−0.164966	−	0.285730i
$366$	19.1038	+	2.00632i	0.998571	+	0.104872i
$367$	2.03594	−	3.52636i	0.106275	−	0.184074i	−0.807983	−	0.589206i	$-0.799441\pi$
$367$	2.03594	−	3.52636i	0.106275	−	0.184074i	0.914259	+	0.405131i	$0.132774\pi$
$368$	6.04998			0.315377
$369$	−4.95569	+	5.50565i	−0.257983	+	0.286613i
$370$	−9.02949			−0.469421
$371$	0.0670893	−	0.116202i	0.00348310	−	0.00603291i
$372$	3.57176	+	8.02055i	0.185187	+	0.415846i
$373$	−9.92038	−	17.1826i	−0.513658	−	0.889682i	−0.999874	−	0.0158432i	$-0.994957\pi$
$373$	−9.92038	−	17.1826i	−0.513658	−	0.889682i	0.486217	−	0.873838i	$-0.338377\pi$
$374$	−2.31410	−	4.00814i	−0.119659	−	0.207256i
$375$	−1.01796	+	1.40134i	−0.0525672	+	0.0723649i
$376$	0.573169	−	0.992759i	0.0295590	−	0.0511976i
$377$	−59.2464			−3.05134
$378$	0.369825	+	1.73781i	0.0190217	+	0.0893831i
$379$	−17.9227			−0.920626			−0.460313	−	0.887757i	$-0.652263\pi$
$379$	−17.9227			−0.920626			−0.460313	+	0.887757i	$0.652263\pi$
$380$	2.37306	−	4.11026i	0.121735	−	0.210852i
$381$	−15.3874	+	21.1826i	−0.788323	+	1.08522i
$382$	−12.4479	−	21.5604i	−0.636889	−	1.10312i
$383$	8.97127	+	15.5387i	0.458410	+	0.793990i	0.998877	−	0.0473755i	$-0.0150857\pi$
$383$	8.97127	+	15.5387i	0.458410	+	0.793990i	−0.540467	+	0.841365i	$0.681752\pi$
$384$	−0.704617	−	1.58225i	−0.0359573	−	0.0807439i
$385$	0.170965	−	0.296120i	0.00871319	−	0.0150917i
$386$	−9.88230			−0.502996
$387$	23.1051	+	4.90722i	1.17450	+	0.249448i
$388$	19.3056			0.980093
$389$	0.0739301	−	0.128051i	0.00374841	−	0.00649243i	−0.864145	−	0.503243i	$-0.832140\pi$
$389$	0.0739301	−	0.128051i	0.00374841	−	0.00649243i	0.867894	+	0.496750i	$0.165474\pi$
$390$	−11.2297	−	1.17937i	−0.568640	−	0.0597198i
$391$	−14.0003	−	24.2492i	−0.708023	−	1.22633i
$392$	3.44154	+	5.96093i	0.173824	+	0.301072i
$393$	−10.8112	−	1.13541i	−0.545352	−	0.0572741i
$394$	−12.7614	+	22.1033i	−0.642909	+	1.11355i
$395$	−4.00669			−0.201598
$396$	−0.927514	−	2.85302i	−0.0466093	−	0.143370i
$397$	11.9339			0.598944			0.299472	−	0.954105i	$-0.403189\pi$
$397$	11.9339			0.598944			0.299472	+	0.954105i	$0.403189\pi$
$398$	−2.51654	+	4.35878i	−0.126143	+	0.218486i
$399$	−1.14348	−	2.56774i	−0.0572457	−	0.128548i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	8.25631	+	14.3003i	0.412300	+	0.714125i	0.995141	−	0.0984614i	$-0.0313921\pi$
$401$	8.25631	+	14.3003i	0.412300	+	0.714125i	−0.582841	+	0.812587i	$0.698059\pi$
$402$	−12.3045	+	16.9386i	−0.613695	+	0.844822i
$403$	−16.5230	+	28.6188i	−0.823071	+	1.42560i
$404$	19.1312			0.951815
$405$	8.22310	+	3.65796i	0.408609	+	0.181765i
$406$	−3.10748			−0.154222
$407$	4.51474	−	7.81976i	0.223788	−	0.387611i
$408$	−4.71132	+	6.48569i	−0.233245	+	0.321089i
$409$	−11.5738	−	20.0464i	−0.572288	−	0.991233i	−0.996330	−	0.0855901i	$-0.972722\pi$
$409$	−11.5738	−	20.0464i	−0.572288	−	0.991233i	0.424042	−	0.905642i	$-0.360611\pi$
$410$	−1.23458	−	2.13836i	−0.0609718	−	0.105606i
$411$	4.75665	+	10.6813i	0.234628	+	0.526869i
$412$	1.01656	−	1.76074i	0.0500825	−	0.0867454i
$413$	−5.12151			−0.252013
$414$	−5.61144	−	17.2607i	−0.275787	−	0.848317i
$415$	−1.99921			−0.0981376
$416$	3.25957	−	5.64575i	0.159814	−	0.276806i
$417$	−11.3346	−	1.19038i	−0.555058	−	0.0582934i
$418$	2.37306	+	4.11026i	0.116070	+	0.201040i
$419$	−15.9157	−	27.5669i	−0.777535	−	1.34673i	−0.933359	−	0.358945i	$-0.883136\pi$
$419$	−15.9157	−	27.5669i	−0.777535	−	1.34673i	0.155823	−	0.987785i	$-0.450197\pi$
$420$	−0.589001	−	0.0618582i	−0.0287403	−	0.00301837i
$421$	4.58954	−	7.94932i	0.223681	−	0.387426i	−0.732242	−	0.681044i	$-0.761526\pi$
$421$	4.58954	−	7.94932i	0.223681	−	0.387426i	0.955923	+	0.293618i	$0.0948594\pi$
$422$	−4.02055			−0.195717
$423$	−3.36398	−	0.714465i	−0.163562	−	0.0347385i
$424$	0.392415			0.0190574
$425$	−2.31410	+	4.00814i	−0.112250	+	0.194423i
$426$	−0.599413	−	1.34601i	−0.0290416	−	0.0652143i
$427$	1.89604	+	3.28404i	0.0917560	+	0.158926i
$428$	6.99177	+	12.1101i	0.337960	+	0.585364i
$429$	6.63623	−	9.13555i	0.320400	−	0.441069i
$430$	−3.93674	+	6.81864i	−0.189847	+	0.328824i
$431$	−6.08652			−0.293177			−0.146589	−	0.989198i	$-0.546829\pi$
$431$	−6.08652			−0.293177			−0.146589	+	0.989198i	$0.546829\pi$
$432$	−3.86065	+	3.47785i	−0.185745	+	0.167328i
$433$	−40.5802			−1.95016			−0.975080	−	0.221854i	$-0.928789\pi$
$433$	−40.5802			−1.95016			−0.975080	+	0.221854i	$0.928789\pi$
$434$	−0.866636	+	1.50106i	−0.0415999	+	0.0720531i
$435$	−9.25128	+	12.7355i	−0.443565	+	0.610619i
$436$	5.72636	+	9.91834i	0.274243	+	0.475002i
$437$	14.3570	+	24.8670i	0.686787	+	1.18955i
$438$	−4.44145	−	9.97348i	−0.212221	−	0.476551i
$439$	11.3914	−	19.7304i	0.543680	−	0.941681i	−0.455009	−	0.890487i	$-0.650364\pi$
$439$	11.3914	−	19.7304i	0.543680	−	0.941681i	0.998689	−	0.0511942i	$-0.0163027\pi$
$440$	1.00000			0.0476731
$441$	13.8146	−	15.3476i	0.657836	−	0.730839i
$442$	−30.1719			−1.43513
$443$	−2.24947	+	3.89619i	−0.106875	+	0.185114i	−0.914503	−	0.404579i	$-0.867418\pi$
$443$	−2.24947	+	3.89619i	−0.106875	+	0.185114i	0.807627	+	0.589693i	$0.200751\pi$
$444$	−15.5540	−	1.63351i	−0.738160	−	0.0775231i
$445$	−0.411690	−	0.713068i	−0.0195160	−	0.0338027i
$446$	−5.40299	−	9.35826i	−0.255839	−	0.443126i
$447$	23.8227	+	2.50191i	1.12678	+	0.118336i
$448$	0.170965	−	0.296120i	0.00807734	−	0.0139904i
$449$	12.8049			0.604299			0.302149	−	0.953261i	$-0.402296\pi$
$449$	12.8049			0.604299			0.302149	+	0.953261i	$0.402296\pi$
$450$	−2.00703	+	2.22976i	−0.0946123	+	0.105112i
$451$	2.46917			0.116269
$452$	4.49455	−	7.78479i	0.211406	−	0.366166i
$453$	−4.28792	−	9.62872i	−0.201464	−	0.452397i
$454$	−9.54374	−	16.5303i	−0.447910	−	0.775803i
$455$	−1.11455	−	1.93045i	−0.0522508	−	0.0905010i
$456$	4.83136	−	6.65094i	0.226249	−	0.311459i
$457$	3.66247	−	6.34359i	0.171323	−	0.296741i	−0.767559	−	0.640978i	$-0.778529\pi$
$457$	3.66247	−	6.34359i	0.171323	−	0.296741i	0.938883	+	0.344237i	$0.111862\pi$
$458$	22.3118			1.04256
$459$	22.8736	+	7.42592i	1.06765	+	0.346612i
$460$	6.04998			0.282082
$461$	0.112855	−	0.195471i	0.00525619	−	0.00910398i	−0.863385	−	0.504545i	$-0.831660\pi$
$461$	0.112855	−	0.195471i	0.00525619	−	0.00910398i	0.868642	+	0.495441i	$0.164994\pi$
$462$	0.348071	−	0.479161i	0.0161937	−	0.0222926i
$463$	14.0500	+	24.3353i	0.652959	+	1.13096i	0.982401	+	0.186782i	$0.0598059\pi$
$463$	14.0500	+	24.3353i	0.652959	+	1.13096i	−0.329442	+	0.944176i	$0.606861\pi$
$464$	−4.54403	−	7.87048i	−0.210951	−	0.365378i
$465$	3.57176	+	8.02055i	0.165636	+	0.371944i
$466$	−2.34971	+	4.06982i	−0.108848	+	0.188531i
$467$	6.65716			0.308056			0.154028	−	0.988066i	$-0.450775\pi$
$467$	6.65716			0.308056			0.154028	+	0.988066i	$0.450775\pi$
$468$	−19.1307	−	4.06311i	−0.884318	−	0.187818i
$469$	−4.13306			−0.190847
$470$	0.573169	−	0.992759i	0.0264383	−	0.0457925i
$471$	−27.7425	−	2.91358i	−1.27831	−	0.134251i
$472$	−7.48911	−	12.9715i	−0.344714	−	0.597062i
$473$	−3.93674	−	6.81864i	−0.181012	−	0.313521i
$474$	−6.90183	−	0.724845i	−0.317012	−	0.0332932i
$475$	2.37306	−	4.11026i	0.108884	−	0.188592i
$476$	−1.58252			−0.0725347
$477$	−0.363971	−	1.11957i	−0.0166651	−	0.0512615i
$478$	−11.1648			−0.510666
$479$	0.125108	−	0.216694i	0.00571635	−	0.00990100i	−0.863153	−	0.504942i	$-0.831514\pi$
$479$	0.125108	−	0.216694i	0.00571635	−	0.00990100i	0.868869	+	0.495041i	$0.164847\pi$
$480$	−0.704617	−	1.58225i	−0.0321612	−	0.0722195i
$481$	−29.4323	−	50.9782i	−1.34200	−	2.32441i
$482$	7.93318	+	13.7407i	0.361346	+	0.625870i
$483$	2.10582	−	2.89891i	0.0958184	−	0.131905i
$484$	−0.500000	+	0.866025i	−0.0227273	+	0.0393648i
$485$	19.3056			0.876622
$486$	13.5032	+	7.78875i	0.612516	+	0.353305i
$487$	8.39142			0.380252			0.190126	−	0.981760i	$-0.439110\pi$
$487$	8.39142			0.380252			0.190126	+	0.981760i	$0.439110\pi$
$488$	−5.54512	+	9.60443i	−0.251016	+	0.434772i
$489$	−14.8197	+	20.4011i	−0.670170	+	0.922568i
$490$	3.44154	+	5.96093i	0.155473	+	0.269287i
$491$	−9.25409	−	16.0286i	−0.417631	−	0.723359i	0.578069	−	0.815988i	$-0.303806\pi$
$491$	−9.25409	−	16.0286i	−0.417631	−	0.723359i	−0.995701	+	0.0926290i	$0.970473\pi$
$492$	−1.73982	−	3.90684i	−0.0784370	−	0.176134i
$493$	−21.0307	+	36.4262i	−0.947173	+	1.64055i
$494$	30.9407			1.39209
$495$	−0.927514	−	2.85302i	−0.0416887	−	0.128234i
$496$	−5.06908			−0.227608
$497$	0.145439	−	0.251907i	0.00652382	−	0.0112996i
$498$	−3.44380	−	0.361675i	−0.154320	−	0.0162071i
$499$	−1.60582	−	2.78136i	−0.0718862	−	0.124511i	0.827842	−	0.560962i	$-0.189569\pi$
$499$	−1.60582	−	2.78136i	−0.0718862	−	0.124511i	−0.899728	+	0.436451i	$0.856235\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	25.5885	+	2.68736i	1.14321	+	0.120062i
$502$	−5.62354	+	9.74026i	−0.250991	+	0.434729i
$503$	21.0230			0.937368			0.468684	−	0.883366i	$-0.344728\pi$
$503$	21.0230			0.937368			0.468684	+	0.883366i	$0.344728\pi$
$504$	−1.00341	−	0.213111i	−0.0446954	−	0.00949272i
$505$	19.1312			0.851329
$506$	−3.02499	+	5.23944i	−0.134477	+	0.232921i
$507$	−20.7857	−	46.6752i	−0.923125	−	2.07292i
$508$	−7.55798	−	13.0908i	−0.335331	−	0.580811i
$509$	13.7034	+	23.7349i	0.607391	+	1.05203i	0.991669	+	0.128815i	$0.0411174\pi$
$509$	13.7034	+	23.7349i	0.607391	+	1.05203i	−0.384277	+	0.923218i	$0.625549\pi$
$510$	−4.71132	+	6.48569i	−0.208621	+	0.287191i
$511$	1.07765	−	1.86655i	0.0476726	−	0.0825713i
$512$	1.00000			0.0441942
$513$	−23.4564	−	7.61513i	−1.03563	−	0.336216i
$514$	3.97420			0.175294
$515$	1.01656	−	1.76074i	0.0447951	−	0.0775875i
$516$	−8.01490	+	11.0334i	−0.352836	+	0.485720i
$517$	0.573169	+	0.992759i	0.0252080	+	0.0436615i
$518$	−1.54373	−	2.67381i	−0.0678275	−	0.117481i
$519$	6.79974	+	15.2691i	0.298476	+	0.670241i
$520$	3.25957	−	5.64575i	0.142942	−	0.247582i
$521$	−12.4239			−0.544300			−0.272150	−	0.962255i	$-0.587735\pi$
$521$	−12.4239			−0.544300			−0.272150	+	0.962255i	$0.587735\pi$
$522$	−18.2400	+	20.2642i	−0.798343	+	0.886939i
$523$	−14.5774			−0.637425			−0.318712	−	0.947851i	$-0.603250\pi$
$523$	−14.5774			−0.637425			−0.318712	+	0.947851i	$0.603250\pi$
$524$	3.13808	−	5.43532i	0.137088	−	0.237443i
$525$	−0.589001	−	0.0618582i	−0.0257061	−	0.00269971i
$526$	1.80954	+	3.13422i	0.0788997	+	0.136658i
$527$	11.7304	+	20.3176i	0.510982	+	0.885047i
$528$	1.72258	+	0.180909i	0.0749655	+	0.00787304i
$529$	−6.80113	+	11.7799i	−0.295701	+	0.512169i
$530$	0.392415			0.0170454
$531$	−30.0617	+	33.3978i	−1.30457	+	1.44934i
$532$	1.62284			0.0703592
$533$	8.04844	−	13.9403i	0.348616	−	0.603821i
$534$	−0.580168	−	1.30279i	−0.0251063	−	0.0563774i
$535$	6.99177	+	12.1101i	0.302281	+	0.523566i
$536$	−6.04372	−	10.4680i	−0.261049	−	0.452150i
$537$	22.1167	−	30.4462i	0.954405	−	1.31385i
$538$	−7.47603	+	12.9489i	−0.322314	+	0.558265i
$539$	−6.88308			−0.296475
$540$	−3.86065	+	3.47785i	−0.166136	+	0.149663i
$541$	27.7784			1.19429			0.597144	−	0.802134i	$-0.296302\pi$
$541$	27.7784			1.19429			0.597144	+	0.802134i	$0.296302\pi$
$542$	5.61582	−	9.72688i	0.241220	−	0.417805i
$543$	−6.05729	+	8.33857i	−0.259943	+	0.357842i
$544$	−2.31410	−	4.00814i	−0.0992162	−	0.171847i
$545$	5.72636	+	9.91834i	0.245290	+	0.424855i
$546$	−1.57066	−	3.52698i	−0.0672179	−	0.150941i
$547$	11.9469	−	20.6926i	0.510813	−	0.884754i	−0.489109	−	0.872223i	$-0.662678\pi$
$547$	11.9469	−	20.6926i	0.510813	−	0.884754i	0.999921	−	0.0125309i	$-0.00398881\pi$
$548$	−6.75069			−0.288375
$549$	32.5448	+	6.91208i	1.38898	+	0.295001i
$550$	1.00000			0.0426401
$551$	21.5665	−	37.3543i	0.918764	−	1.59135i
$552$	10.4216	+	1.09449i	0.443571	+	0.0465848i
$553$	−0.685004	−	1.18646i	−0.0291293	−	0.0504535i
$554$	6.80210	+	11.7816i	0.288994	+	0.500552i
$555$	−15.5540	−	1.63351i	−0.660230	−	0.0693388i
$556$	3.29001	−	5.69847i	0.139528	−	0.241669i
$557$	14.3933			0.609862			0.304931	−	0.952374i	$-0.401367\pi$
$557$	14.3933			0.609862			0.304931	+	0.952374i	$0.401367\pi$
$558$	4.70165	+	14.4622i	0.199037	+	0.612233i
$559$	−51.3284			−2.17096
$560$	0.170965	−	0.296120i	0.00722460	−	0.0125134i
$561$	−3.26111	−	7.32297i	−0.137684	−	0.309176i
$562$	−0.349163	−	0.604768i	−0.0147286	−	0.0255106i
$563$	−5.57890	−	9.66293i	−0.235123	−	0.407244i	0.724186	−	0.689605i	$-0.242216\pi$
$563$	−5.57890	−	9.66293i	−0.235123	−	0.407244i	−0.959308	+	0.282361i	$0.908882\pi$
$564$	1.16693	−	1.60641i	0.0491365	−	0.0676421i
$565$	4.49455	−	7.78479i	0.189087	−	0.327509i
$566$	−29.9918			−1.26065
$567$	0.322667	+	3.06041i	0.0135507	+	0.128525i
$568$	0.850693			0.0356943
$569$	−21.8161	+	37.7866i	−0.914578	+	1.58410i	−0.107061	+	0.994252i	$0.534144\pi$
$569$	−21.8161	+	37.7866i	−0.914578	+	1.58410i	−0.807517	+	0.589844i	$0.799189\pi$
$570$	4.83136	−	6.65094i	0.202364	−	0.278577i
$571$	−22.4431	−	38.8725i	−0.939213	−	1.62676i	−0.766944	−	0.641714i	$-0.778223\pi$
$571$	−22.4431	−	38.8725i	−0.939213	−	1.62676i	−0.172269	−	0.985050i	$-0.555110\pi$
$572$	3.25957	+	5.64575i	0.136290	+	0.236061i
$573$	−17.5420	−	39.3913i	−0.732827	−	1.64560i
$574$	0.422142	−	0.731171i	0.0176199	−	0.0305185i
$575$	6.04998			0.252302
$576$	−0.927514	−	2.85302i	−0.0386464	−	0.118876i
$577$	−26.7049			−1.11174			−0.555870	−	0.831269i	$-0.687615\pi$
$577$	−26.7049			−1.11174			−0.555870	+	0.831269i	$0.687615\pi$
$578$	−2.21011	+	3.82803i	−0.0919285	+	0.159225i
$579$	−17.0230	−	1.78779i	−0.707453	−	0.0742982i
$580$	−4.54403	−	7.87048i	−0.188680	−	0.326804i
$581$	−0.341796	−	0.592008i	−0.0141801	−	0.0245606i
$582$	33.2554	+	3.49255i	1.37848	+	0.144771i
$583$	−0.196208	+	0.339841i	−0.00812608	+	0.0140748i
$584$	6.30335			0.260835
$585$	−19.1307	−	4.06311i	−0.790958	−	0.167989i
$586$	−3.30683			−0.136604
$587$	4.95379	−	8.58021i	0.204465	−	0.354143i	−0.745497	−	0.666509i	$-0.767788\pi$
$587$	4.95379	−	8.58021i	0.204465	−	0.354143i	0.949962	+	0.312365i	$0.101121\pi$
$588$	4.84994	+	10.8908i	0.200008	+	0.449127i
$589$	−12.0292	−	20.8353i	−0.495656	−	0.858502i
$590$	−7.48911	−	12.9715i	−0.308322	−	0.534029i
$591$	−25.9811	+	35.7661i	−1.06872	+	1.47122i
$592$	4.51474	−	7.81976i	0.185555	−	0.321390i
$593$	15.9871			0.656511			0.328255	−	0.944589i	$-0.393539\pi$
$593$	15.9871			0.656511			0.328255	+	0.944589i	$0.393539\pi$
$594$	−1.08158	−	5.08234i	−0.0443777	−	0.208531i
$595$	−1.58252			−0.0648770
$596$	−6.91485	+	11.9769i	−0.283243	+	0.490592i
$597$	−5.12348	+	7.05307i	−0.209690	+	0.288663i
$598$	19.7204	+	34.1567i	0.806425	+	1.39677i
$599$	1.48203	+	2.56696i	0.0605542	+	0.104883i	0.894713	−	0.446641i	$-0.147380\pi$
$599$	1.48203	+	2.56696i	0.0605542	+	0.104883i	−0.834159	+	0.551524i	$0.814047\pi$
$600$	−0.704617	−	1.58225i	−0.0287659	−	0.0645951i
$601$	−9.29940	+	16.1070i	−0.379330	+	0.657020i	−0.990965	−	0.134121i	$-0.957179\pi$
$601$	−9.29940	+	16.1070i	−0.379330	+	0.657020i	0.611635	+	0.791140i	$0.290512\pi$
$602$	−2.69218			−0.109725
$603$	−24.2599	+	26.9521i	−0.987938	+	1.09757i
$604$	6.08546			0.247614
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$	32.9550	+	3.46101i	1.33871	+	0.140594i
$607$	−11.7851	−	20.4124i	−0.478343	−	0.828514i	0.521349	−	0.853344i	$-0.325429\pi$
$607$	−11.7851	−	20.4124i	−0.478343	−	0.828514i	−0.999692	+	0.0248298i	$0.992096\pi$
$608$	2.37306	+	4.11026i	0.0962403	+	0.166693i
$609$	−5.35288	−	0.562170i	−0.216909	−	0.0227803i
$610$	−5.54512	+	9.60443i	−0.224515	+	0.388872i
$611$	7.47315			0.302331
$612$	−9.28893	+	10.3198i	−0.375483	+	0.417152i
$613$	13.1149			0.529707			0.264853	−	0.964289i	$-0.414676\pi$
$613$	13.1149			0.529707			0.264853	+	0.964289i	$0.414676\pi$
$614$	−3.02418	+	5.23804i	−0.122046	+	0.211390i
$615$	−1.73982	−	3.90684i	−0.0701562	−	0.157539i
$616$	0.170965	+	0.296120i	0.00688838	+	0.0119310i
$617$	7.92102	+	13.7196i	0.318888	+	0.552331i	0.980256	−	0.197731i	$-0.0633572\pi$
$617$	7.92102	+	13.7196i	0.318888	+	0.552331i	−0.661368	+	0.750061i	$0.730024\pi$
$618$	2.06964	−	2.84910i	0.0832532	−	0.114608i
$619$	−7.86675	+	13.6256i	−0.316191	+	0.547660i	−0.979690	−	0.200518i	$-0.935738\pi$
$619$	−7.86675	+	13.6256i	−0.316191	+	0.547660i	0.663499	+	0.748178i	$0.269071\pi$
$620$	−5.06908			−0.203579
$621$	−6.54353	−	30.7481i	−0.262583	−	1.23388i
$622$	2.61564			0.104877
$623$	0.140769	−	0.243820i	0.00563981	−	0.00976843i
$624$	6.63623	−	9.13555i	0.265662	−	0.365715i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	13.2700	+	22.9842i	0.530374	+	0.918635i
$627$	3.34420	+	7.50955i	0.133554	+	0.299903i
$628$	8.05263	−	13.9476i	0.321335	−	0.556568i
$629$	−41.7903			−1.66629
$630$	−1.00341	−	0.213111i	−0.0399768	−	0.00849054i
$631$	7.66327			0.305070			0.152535	−	0.988298i	$-0.451256\pi$
$631$	7.66327			0.305070			0.152535	+	0.988298i	$0.451256\pi$
$632$	2.00334	−	3.46990i	0.0796888	−	0.138025i
$633$	−6.92570	−	0.727352i	−0.275272	−	0.0289097i
$634$	−0.520712	−	0.901900i	−0.0206801	−	0.0358190i
$635$	−7.55798	−	13.0908i	−0.299929	−	0.519493i
$636$	0.675965	+	0.0709913i	0.0268038	+	0.00281499i
$637$	−22.4359	+	38.8602i	−0.888943	+	1.53970i
$638$	9.08805			0.359799
$639$	−0.789030	−	2.42704i	−0.0312135	−	0.0960123i
$640$	1.00000			0.0395285
$641$	8.95567	−	15.5117i	0.353728	−	0.612674i	−0.633172	−	0.774011i	$-0.718247\pi$
$641$	8.95567	−	15.5117i	0.353728	−	0.612674i	0.986899	+	0.161337i	$0.0515807\pi$
$642$	9.85305	+	22.1255i	0.388869	+	0.873223i
$643$	2.18779	+	3.78936i	0.0862779	+	0.149438i	0.905935	−	0.423417i	$-0.139169\pi$
$643$	2.18779	+	3.78936i	0.0862779	+	0.149438i	−0.819657	+	0.572854i	$0.805836\pi$
$644$	1.03434	+	1.79152i	0.0407585	+	0.0705959i
$645$	−8.01490	+	11.0334i	−0.315586	+	0.434441i
$646$	10.9830	−	19.0231i	0.432120	−	0.748454i
$647$	−31.6184			−1.24305			−0.621524	−	0.783395i	$-0.713486\pi$
$647$	−31.6184			−1.24305			−0.621524	+	0.783395i	$0.713486\pi$
$648$	−7.27943	+	5.29243i	−0.285963	+	0.207906i
$649$	14.9782			0.587946
$650$	3.25957	−	5.64575i	0.127851	−	0.221444i
$651$	−1.76440	+	2.42891i	−0.0691524	+	0.0951963i
$652$	−7.27912	−	12.6078i	−0.285072	−	0.493760i
$653$	3.39512	+	5.88052i	0.132861	+	0.230122i	0.924778	−	0.380506i	$-0.124250\pi$
$653$	3.39512	+	5.88052i	0.132861	+	0.230122i	−0.791917	+	0.610629i	$0.790917\pi$
$654$	8.06978	+	18.1211i	0.315553	+	0.708589i
$655$	3.13808	−	5.43532i	0.122615	−	0.212376i
$656$	2.46917			0.0964048
$657$	−5.84645	−	17.9836i	−0.228092	−	0.701606i
$658$	0.391968			0.0152805
$659$	3.07140	−	5.31982i	0.119645	−	0.207231i	−0.799982	−	0.600024i	$-0.795158\pi$
$659$	3.07140	−	5.31982i	0.119645	−	0.207231i	0.919627	+	0.392793i	$0.128491\pi$
$660$	1.72258	+	0.180909i	0.0670512	+	0.00704186i
$661$	10.3682	+	17.9582i	0.403276	+	0.698494i	0.994119	−	0.108292i	$-0.0345383\pi$
$661$	10.3682	+	17.9582i	0.403276	+	0.698494i	−0.590843	+	0.806786i	$0.701205\pi$
$662$	−6.70843	−	11.6193i	−0.260730	−	0.451598i
$663$	−51.9734	−	5.45836i	−2.01848	−	0.211985i
$664$	0.999607	−	1.73137i	0.0387923	−	0.0671902i
$665$	1.62284			0.0629312
$666$	−26.4974	−	5.62770i	−1.02675	−	0.218069i
$667$	54.9825			2.12893
$668$	−7.42739	+	12.8646i	−0.287375	+	0.497747i
$669$	−7.61408	−	17.0978i	−0.294377	−	0.661038i
$670$	−6.04372	−	10.4680i	−0.233489	−	0.404415i
$671$	−5.54512	−	9.60443i	−0.214067	−	0.370775i
$672$	0.348071	−	0.479161i	0.0134271	−	0.0184840i
$673$	18.8458	−	32.6418i	0.726451	−	1.25825i	−0.231924	−	0.972734i	$-0.574502\pi$
$673$	18.8458	−	32.6418i	0.726451	−	1.25825i	0.958374	−	0.285515i	$-0.0921647\pi$
$674$	−10.1904			−0.392519
$675$	−3.86065	+	3.47785i	−0.148596	+	0.133862i
$676$	29.4993			1.13459
$677$	−16.8547	+	29.1932i	−0.647779	+	1.12199i	0.335874	+	0.941907i	$0.390969\pi$
$677$	−16.8547	+	29.1932i	−0.647779	+	1.12199i	−0.983652	+	0.180079i	$0.942365\pi$
$678$	9.15055	−	12.5968i	0.351425	−	0.483777i
$679$	3.30058	+	5.71678i	0.126665	+	0.219390i
$680$	−2.31410	−	4.00814i	−0.0887417	−	0.153705i
$681$	−13.4494	−	30.2012i	−0.515381	−	1.15731i
$682$	2.53454	−	4.38995i	0.0970526	−	0.168100i
$683$	16.2605			0.622189			0.311094	−	0.950379i	$-0.399304\pi$
$683$	16.2605			0.622189			0.311094	+	0.950379i	$0.399304\pi$
$684$	9.52561	−	10.5827i	0.364221	−	0.404640i
$685$	−6.75069			−0.257931
$686$	−2.37352	+	4.11106i	−0.0906215	+	0.156961i
$687$	38.4338	+	4.03640i	1.46634	+	0.153998i
$688$	−3.93674	−	6.81864i	−0.150087	−	0.259958i
$689$	1.27911	+	2.21548i	0.0487300	+	0.0844029i
$690$	10.4216	+	1.09449i	0.396742	+	0.0416667i
$691$	17.6033	−	30.4898i	0.669660	−	1.15989i	−0.308339	−	0.951276i	$-0.599773\pi$
$691$	17.6033	−	30.4898i	0.669660	−	1.15989i	0.977999	−	0.208609i	$-0.0668935\pi$
$692$	−9.65027			−0.366848
$693$	0.686264	−	0.762423i	0.0260690	−	0.0289620i
$694$	−9.05000			−0.343533
$695$	3.29001	−	5.69847i	0.124797	−	0.216155i
$696$	−6.40360	−	14.3796i	−0.242728	−	0.545056i
$697$	−5.71390	−	9.89677i	−0.216429	−	0.374867i
$698$	16.3023	+	28.2364i	0.617051	+	1.06876i
$699$	−4.78383	+	6.58550i	−0.180941	+	0.249086i
$700$	0.170965	−	0.296120i	0.00646188	−	0.0111923i
$701$	49.5189			1.87030			0.935151	−	0.354248i	$-0.115263\pi$
$701$	49.5189			1.87030			0.935151	+	0.354248i	$0.115263\pi$
$702$	−32.2191	−	10.4599i	−1.21603	−	0.394785i
$703$	42.8550			1.61631
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$	1.16693	−	1.60641i	0.0439490	−	0.0605010i
$706$	12.6341	+	21.8830i	0.475492	+	0.823576i
$707$	3.27078	+	5.66515i	0.123010	+	0.213060i
$708$	−10.5539	−	23.6993i	−0.396640	−	0.890674i
$709$	−23.8956	+	41.3885i	−0.897419	+	1.55438i	−0.0666381	+	0.997777i	$0.521227\pi$
$709$	−23.8956	+	41.3885i	−0.897419	+	1.55438i	−0.830781	+	0.556599i	$0.812106\pi$
$710$	0.850693			0.0319259
$711$	−11.7578	−	2.49720i	−0.440952	−	0.0936524i
$712$	0.823380			0.0308575
$713$	15.3339	−	26.5591i	0.574260	−	0.994647i
$714$	−2.72602	−	0.286292i	−0.102019	−	0.0107142i
$715$	3.25957	+	5.64575i	0.121901	+	0.211139i
$716$	10.8632	+	18.8157i	0.405978	+	0.703174i
$717$	−19.2322	−	2.01981i	−0.718241	−	0.0754312i
$718$	−15.1444	+	26.2309i	−0.565184	+	0.978928i
$719$	−0.191464			−0.00714038			−0.00357019	−	0.999994i	$-0.501136\pi$
$719$	−0.191464			−0.00714038			−0.00357019	+	0.999994i	$0.501136\pi$
$720$	−0.927514	−	2.85302i	−0.0345664	−	0.106326i
$721$	0.695188			0.0258901
$722$	−1.76284	+	3.05333i	−0.0656061	+	0.113633i
$723$	11.1797	+	25.1045i	0.415778	+	0.933648i
$724$	−2.97521	−	5.15322i	−0.110573	−	0.191518i
$725$	−4.54403	−	7.87048i	−0.168761	−	0.292302i
$726$	−1.01796	+	1.40134i	−0.0377800	+	0.0520087i
$727$	−18.5806	+	32.1825i	−0.689115	+	1.19358i	0.283010	+	0.959117i	$0.408667\pi$
$727$	−18.5806	+	32.1825i	−0.689115	+	1.19358i	−0.972125	+	0.234465i	$0.924666\pi$
$728$	2.22909			0.0826157
$729$	21.8512	+	15.8596i	0.809303	+	0.587391i
$730$	6.30335			0.233298
$731$	−18.2200	+	31.5580i	−0.673892	+	1.16722i
$732$	−11.2894	+	15.5412i	−0.417269	+	0.574419i
$733$	5.14789	+	8.91641i	0.190142	+	0.329335i	0.945297	−	0.326211i	$-0.105772\pi$
$733$	5.14789	+	8.91641i	0.190142	+	0.329335i	−0.755155	+	0.655546i	$0.772439\pi$
$734$	2.03594	+	3.52636i	0.0751481	+	0.130160i
$735$	4.84994	+	10.8908i	0.178893	+	0.401712i
$736$	−3.02499	+	5.23944i	−0.111503	+	0.193128i
$737$	12.0874			0.445247
$738$	−2.29019	−	7.04458i	−0.0843030	−	0.259315i
$739$	8.56279			0.314987			0.157494	−	0.987520i	$-0.449659\pi$
$739$	8.56279			0.314987			0.157494	+	0.987520i	$0.449659\pi$
$740$	4.51474	−	7.81976i	0.165965	−	0.287460i
$741$	53.2977	+	5.59744i	1.95794	+	0.205627i
$742$	0.0670893	+	0.116202i	0.00246293	+	0.00426591i
$743$	−9.82196	−	17.0121i	−0.360333	−	0.624115i	0.627683	−	0.778469i	$-0.284004\pi$
$743$	−9.82196	−	17.0121i	−0.360333	−	0.624115i	−0.988016	+	0.154354i	$0.950670\pi$
$744$	−8.73188	−	0.917041i	−0.320126	−	0.0336204i
$745$	−6.91485	+	11.9769i	−0.253340	+	0.438798i
$746$	19.8408			0.726422
$747$	−5.86678	−	1.24603i	−0.214654	−	0.0455898i
$748$	4.62820			0.169224
$749$	−2.39070	+	4.14081i	−0.0873543	+	0.151302i
$750$	−0.704617	−	1.58225i	−0.0257290	−	0.0577756i
$751$	−12.9493	−	22.4288i	−0.472525	−	0.818438i	0.526980	−	0.849877i	$-0.323324\pi$
$751$	−12.9493	−	22.4288i	−0.472525	−	0.818438i	−0.999506	+	0.0314396i	$0.989991\pi$
$752$	0.573169	+	0.992759i	0.0209013	+	0.0362022i
$753$	−11.4491	+	15.7610i	−0.417228	+	0.574363i
$754$	29.6232	−	51.3089i	1.07881	−	1.86856i
$755$	6.08546			0.221473
$756$	−1.68990	−	0.548626i	−0.0614609	−	0.0199533i
$757$	21.2937			0.773933			0.386967	−	0.922094i	$-0.373523\pi$
$757$	21.2937			0.773933			0.386967	+	0.922094i	$0.373523\pi$
$758$	8.96134	−	15.5215i	0.325491	−	0.563766i
$759$	−6.15864	+	8.47809i	−0.223544	+	0.307735i
$760$	2.37306	+	4.11026i	0.0860800	+	0.149095i
$761$	1.39177	+	2.41062i	0.0504517	+	0.0873849i	0.890148	−	0.455671i	$-0.150601\pi$
$761$	1.39177	+	2.41062i	0.0504517	+	0.0873849i	−0.839697	+	0.543056i	$0.817267\pi$
$762$	−10.6510	−	23.9172i	−0.385844	−	0.866430i
$763$	−1.95802	+	3.39138i	−0.0708849	+	0.122776i
$764$	24.8958			0.900698
$765$	−9.28893	+	10.3198i	−0.335842	+	0.373112i
$766$	−17.9425			−0.648290
$767$	48.8226	−	84.5632i	1.76288	−	3.05340i
$768$	1.72258	+	0.180909i	0.0621581	+	0.00652798i
$769$	2.97443	+	5.15186i	0.107261	+	0.185781i	0.914660	−	0.404225i	$-0.132459\pi$
$769$	2.97443	+	5.15186i	0.107261	+	0.185781i	−0.807399	+	0.590006i	$0.799125\pi$
$770$	0.170965	+	0.296120i	0.00616116	+	0.0106714i
$771$	6.84587	+	0.718968i	0.246548	+	0.0258930i
$772$	4.94115	−	8.55832i	0.177836	−	0.308021i
$773$	−4.24185			−0.152569			−0.0762844	−	0.997086i	$-0.524306\pi$
$773$	−4.24185			−0.152569			−0.0762844	+	0.997086i	$0.524306\pi$
$774$	−15.8023	+	17.5560i	−0.568003	+	0.631037i
$775$	−5.06908			−0.182087
$776$	−9.65280	+	16.7191i	−0.346515	+	0.600182i
$777$	−2.17547	−	4.88513i	−0.0780447	−	0.175253i
$778$	0.0739301	+	0.128051i	0.00265052	+	0.00459084i
$779$	5.85949	+	10.1489i	0.209938	+	0.363623i
$780$	6.63623	−	9.13555i	0.237615	−	0.327105i
$781$	−0.425346	+	0.736722i	−0.0152201	+	0.0263620i
$782$	28.0005			1.00130
$783$	−35.0858	+	31.6068i	−1.25386	+	1.12954i
$784$	−6.88308			−0.245824
$785$	8.05263	−	13.9476i	0.287411	−	0.497810i
$786$	6.38889	−	8.79505i	0.227884	−	0.313709i
$787$	16.1751	+	28.0162i	0.576582	+	0.998669i	0.995868	+	0.0908146i	$0.0289471\pi$
$787$	16.1751	+	28.0162i	0.576582	+	0.998669i	−0.419286	+	0.907854i	$0.637720\pi$
$788$	−12.7614	−	22.1033i	−0.454605	−	0.787399i
$789$	2.55007	+	5.72629i	0.0907848	+	0.203861i
$790$	2.00334	−	3.46990i	0.0712758	−	0.123453i
$791$	3.07365			0.109286
$792$	2.93454	+	0.623258i	0.104274	+	0.0221465i
$793$	−72.2989			−2.56741
$794$	−5.96694	+	10.3350i	−0.211759	+	0.366777i
$795$	0.675965	+	0.0709913i	0.0239740	+	0.00251780i
$796$	−2.51654	−	4.35878i	−0.0891965	−	0.154493i
$797$	−8.97667	−	15.5480i	−0.317970	−	0.550740i	0.662094	−	0.749420i	$-0.269668\pi$
$797$	−8.97667	−	15.5480i	−0.317970	−	0.550740i	−0.980064	+	0.198680i	$0.936334\pi$
$798$	2.79547	+	0.293586i	0.0989586	+	0.0103928i
$799$	2.65274	−	4.59468i	0.0938473	−	0.162548i
$800$	1.00000			0.0353553
$801$	−0.763697	−	2.34912i	−0.0269839	−	0.0830021i
$802$	−16.5126			−0.583081
$803$	−3.15168	+	5.45886i	−0.111220	+	0.192639i
$804$	−8.51702	−	19.1254i	−0.300372	−	0.674499i
$805$	1.03434	+	1.79152i	0.0364555	+	0.0631429i
$806$	−16.5230	−	28.6188i	−0.581999	−	1.00805i
$807$	−15.2206	+	20.9529i	−0.535790	+	0.737578i
$808$	−9.56562	+	16.5681i	−0.336517	+	0.582865i
$809$	5.96281			0.209641			0.104821	−	0.994491i	$-0.466573\pi$
$809$	5.96281			0.209641			0.104821	+	0.994491i	$0.466573\pi$
$810$	−7.27943	+	5.29243i	−0.255773	+	0.185957i
$811$	11.9034			0.417983			0.208992	−	0.977917i	$-0.432982\pi$
$811$	11.9034			0.417983			0.208992	+	0.977917i	$0.432982\pi$
$812$	1.55374	−	2.69116i	0.0545256	−	0.0944411i
$813$	11.4334	−	15.7394i	0.400985	−	0.552003i
$814$	4.51474	+	7.81976i	0.158242	+	0.274083i
$815$	−7.27912	−	12.6078i	−0.254976	−	0.441632i
$816$	−3.26111	−	7.32297i	−0.114162	−	0.256355i
$817$	18.6843	−	32.3621i	0.653680	−	1.13221i
$818$	23.1476			0.809338
$819$	−2.06752	−	6.35965i	−0.0722449	−	0.222224i
$820$	2.46917			0.0862271
$821$	−3.46404	+	5.99989i	−0.120896	+	0.209398i	−0.920121	−	0.391634i	$-0.871910\pi$
$821$	−3.46404	+	5.99989i	−0.120896	+	0.209398i	0.799225	+	0.601031i	$0.205243\pi$
$822$	−11.6286	−	1.22126i	−0.405594	−	0.0425963i
$823$	13.2286	+	22.9126i	0.461120	+	0.798683i	0.999017	−	0.0443276i	$-0.0141146\pi$
$823$	13.2286	+	22.9126i	0.461120	+	0.798683i	−0.537897	+	0.843010i	$0.680781\pi$
$824$	1.01656	+	1.76074i	0.0354137	+	0.0613383i
$825$	1.72258	+	0.180909i	0.0599724	+	0.00629843i
$826$	2.56075	−	4.43535i	0.0891000	−	0.154326i
$827$	−9.64401			−0.335355			−0.167677	−	0.985842i	$-0.553627\pi$
$827$	−9.64401			−0.335355			−0.167677	+	0.985842i	$0.553627\pi$
$828$	17.7539	+	3.77070i	0.616992	+	0.131041i
$829$	−27.5168			−0.955699			−0.477850	−	0.878442i	$-0.658584\pi$
$829$	−27.5168			−0.955699			−0.477850	+	0.878442i	$0.658584\pi$
$830$	0.999607	−	1.73137i	0.0346969	−	0.0600968i
$831$	9.58576	+	21.5253i	0.332526	+	0.746703i
$832$	3.25957	+	5.64575i	0.113005	+	0.195731i
$833$	15.9281	+	27.5883i	0.551877	+	0.955880i
$834$	6.69820	−	9.22086i	0.231940	−	0.319292i
$835$	−7.42739	+	12.8646i	−0.257036	+	0.445199i
$836$	−4.74612			−0.164148
$837$	5.48261	+	25.7628i	0.189507	+	0.890493i
$838$	31.8315			1.09960
$839$	−5.97432	+	10.3478i	−0.206256	+	0.357247i	−0.950532	−	0.310626i	$-0.899461\pi$
$839$	−5.97432	+	10.3478i	−0.206256	+	0.357247i	0.744276	+	0.667872i	$0.232795\pi$
$840$	0.348071	−	0.479161i	0.0120096	−	0.0165326i
$841$	−26.7964	−	46.4126i	−0.924012	−	1.60044i
$842$	4.58954	+	7.94932i	0.158166	+	0.273952i
$843$	−0.492052	−	1.10493i	−0.0169472	−	0.0380557i
$844$	2.01027	−	3.48190i	0.0691965	−	0.119852i
$845$	29.4993			1.01481
$846$	2.30074	−	2.55606i	0.0791009	−	0.0878792i
$847$	−0.341930			−0.0117489
$848$	−0.196208	+	0.339841i	−0.00673779	+	0.0116702i
$849$	−51.6631	−	5.42577i	−1.77307	−	0.186212i
$850$	−2.31410	−	4.00814i	−0.0793730	−	0.137478i
$851$	27.3141	+	47.3094i	0.936315	+	1.62175i
$852$	1.46538	+	0.153898i	0.0502032	+	0.00527245i
$853$	9.44223	−	16.3544i	0.323296	−	0.559965i	−0.657870	−	0.753131i	$-0.728542\pi$
$853$	9.44223	−	16.3544i	0.323296	−	0.559965i	0.981166	+	0.193166i	$0.0618757\pi$
$854$	−3.79209			−0.129763
$855$	9.52561	−	10.5827i	0.325769	−	0.361921i
$856$	−13.9835			−0.477948
$857$	0.168677	−	0.292157i	0.00576190	−	0.00997990i	−0.863130	−	0.504982i	$-0.831499\pi$
$857$	0.168677	−	0.292157i	0.00576190	−	0.00997990i	0.868892	+	0.495002i	$0.164833\pi$
$858$	4.59350	+	10.3149i	0.156820	+	0.352146i
$859$	26.9505	+	46.6796i	0.919538	+	1.59269i	0.800118	+	0.599843i	$0.204770\pi$
$859$	26.9505	+	46.6796i	0.919538	+	1.59269i	0.119420	+	0.992844i	$0.461896\pi$
$860$	−3.93674	−	6.81864i	−0.134242	−	0.232514i
$861$	0.859447	−	1.18313i	0.0292899	−	0.0403209i
$862$	3.04326	−	5.27108i	0.103654	−	0.179534i
$863$	40.0758			1.36419			0.682097	−	0.731261i	$-0.261068\pi$
$863$	40.0758			1.36419			0.682097	+	0.731261i	$0.261068\pi$
$864$	−1.08158	−	5.08234i	−0.0367961	−	0.172905i
$865$	−9.65027			−0.328119
$866$	20.2901	−	35.1435i	0.689486	−	1.19422i
$867$	−4.49961	+	6.19424i	−0.152815	+	0.210367i
$868$	−0.866636	−	1.50106i	−0.0294155	−	0.0509492i
$869$	2.00334	+	3.46990i	0.0679588	+	0.117708i
$870$	−6.40360	−	14.3796i	−0.217102	−	0.487513i
$871$	39.3999	−	68.2427i	1.33502	−	2.31231i
$872$	−11.4527			−0.387838
$873$	56.6531	+	12.0324i	1.91742	+	0.407234i
$874$	−28.7139			−0.971264
$875$	0.170965	−	0.296120i	0.00577968	−	0.0100107i
$876$	10.8580	+	1.14033i	0.366858	+	0.0385282i
$877$	0.767873	+	1.33000i	0.0259292	+	0.0449108i	0.878699	−	0.477377i	$-0.158412\pi$
$877$	0.767873	+	1.33000i	0.0259292	+	0.0449108i	−0.852770	+	0.522287i	$0.825079\pi$
$878$	11.3914	+	19.7304i	0.384440	+	0.665869i
$879$	−5.69626	−	0.598234i	−0.192130	−	0.0201779i
$880$	−0.500000	+	0.866025i	−0.0168550	+	0.0291937i
$881$	−22.0850			−0.744062			−0.372031	−	0.928220i	$-0.621339\pi$
$881$	−22.0850			−0.744062			−0.372031	+	0.928220i	$0.621339\pi$
$882$	6.38416	+	19.6376i	0.214966	+	0.661231i
$883$	55.3080			1.86126			0.930631	−	0.365958i	$-0.119259\pi$
$883$	55.3080			1.86126			0.930631	+	0.365958i	$0.119259\pi$
$884$	15.0860	−	26.1296i	0.507396	−	0.878835i
$885$	−10.5539	−	23.6993i	−0.354766	−	0.796643i
$886$	−2.24947	−	3.89619i	−0.0755723	−	0.130895i
$887$	8.83810	+	15.3080i	0.296754	+	0.513993i	0.975391	−	0.220480i	$-0.0707625\pi$
$887$	8.83810	+	15.3080i	0.296754	+	0.513993i	−0.678637	+	0.734474i	$0.737429\pi$
$888$	9.19166	−	12.6534i	0.308452	−	0.424620i
$889$	2.58430	−	4.47614i	0.0866747	−	0.150125i
$890$	0.823380			0.0275998
$891$	−0.943663	−	8.95039i	−0.0316139	−	0.299849i
$892$	10.8060			0.361811
$893$	−2.72033	+	4.71175i	−0.0910325	+	0.157673i
$894$	−14.0781	+	19.3801i	−0.470841	+	0.648168i
$895$	10.8632	+	18.8157i	0.363118	+	0.628938i
$896$	0.170965	+	0.296120i	0.00571154	+	0.00989269i
$897$	27.7906	+	62.4051i	0.927901	+	2.08364i
$898$	−6.40243	+	11.0893i	−0.213652	+	0.370056i
$899$	−46.0681			−1.53646
$900$	−0.927514	−	2.85302i	−0.0309171	−	0.0951006i
$901$	1.81617			0.0605056
$902$	−1.23458	+	2.13836i	−0.0411072	+	0.0711997i
$903$	−4.63750	−	0.487040i	−0.154326	−	0.0162077i
$904$	4.49455	+	7.78479i	0.149487	+	0.258918i
$905$	−2.97521	−	5.15322i	−0.0988993	−	0.171299i
$906$	10.4827	+	1.10091i	0.348264	+	0.0365754i
$907$	8.71014	−	15.0864i	0.289216	−	0.500936i	−0.684407	−	0.729100i	$-0.739939\pi$
$907$	8.71014	−	15.0864i	0.289216	−	0.500936i	0.973623	+	0.228164i	$0.0732722\pi$
$908$	19.0875			0.633441
$909$	56.1415	+	11.9237i	1.86210	+	0.395485i
$910$	2.22909			0.0738937
$911$	−11.0560	+	19.1496i	−0.366302	+	0.634454i	−0.988984	−	0.148021i	$-0.952710\pi$
$911$	−11.0560	+	19.1496i	−0.366302	+	0.634454i	0.622682	+	0.782475i	$0.286043\pi$
$912$	3.34420	+	7.50955i	0.110737	+	0.248666i
$913$	0.999607	+	1.73137i	0.0330822	+	0.0573000i
$914$	3.66247	+	6.34359i	0.121144	+	0.209827i
$915$	−11.2894	+	15.5412i	−0.373217	+	0.513776i
$916$	−11.1559	+	19.3226i	−0.368601	+	0.638436i
$917$	2.14601			0.0708676
$918$	−17.8678	+	16.0962i	−0.589727	+	0.531252i
$919$	2.35200			0.0775854			0.0387927	−	0.999247i	$-0.487649\pi$
$919$	2.35200			0.0775854			0.0387927	+	0.999247i	$0.487649\pi$
$920$	−3.02499	+	5.23944i	−0.0997310	+	0.172739i
$921$	−6.15699	+	8.47582i	−0.202880	+	0.279288i
$922$	0.112855	+	0.195471i	0.00371669	+	0.00643749i
$923$	2.77290	+	4.80280i	0.0912710	+	0.158086i
$924$	0.240930	+	0.541019i	0.00792601	+	0.0177982i
$925$	4.51474	−	7.81976i	0.148444	−	0.257112i
$926$	−28.1000			−0.923423
$927$	4.08055	−	4.53339i	0.134023	−	0.148896i
$928$	9.08805			0.298330
$929$	14.7721	−	25.5860i	0.484657	−	0.839451i	−0.515187	−	0.857078i	$-0.672278\pi$
$929$	14.7721	−	25.5860i	0.484657	−	0.839451i	0.999845	+	0.0176267i	$0.00561104\pi$
$930$	−8.73188	−	0.917041i	−0.286330	−	0.0300710i
$931$	−16.3340	−	28.2913i	−0.535325	−	0.927209i
$932$	−2.34971	−	4.06982i	−0.0769674	−	0.133311i
$933$	4.50564	+	0.473191i	0.147508	+	0.0154916i
$934$	−3.32858	+	5.76527i	−0.108914	+	0.188645i
$935$	4.62820			0.151358
$936$	13.0841	−	14.5361i	0.427668	−	0.475129i
$937$	−5.02273			−0.164085			−0.0820426	−	0.996629i	$-0.526144\pi$
$937$	−5.02273			−0.164085			−0.0820426	+	0.996629i	$0.526144\pi$
$938$	2.06653	−	3.57934i	0.0674747	−	0.116870i
$939$	18.7005	+	41.9928i	0.610267	+	1.37038i
$940$	0.573169	+	0.992759i	0.0186947	+	0.0323802i
$941$	6.09508	+	10.5570i	0.198694	+	0.344148i	0.948105	−	0.317957i	$-0.102997\pi$
$941$	6.09508	+	10.5570i	0.198694	+	0.344148i	−0.749411	+	0.662105i	$0.769663\pi$
$942$	16.3945	−	22.5690i	0.534162	−	0.735336i
$943$	−7.46921	+	12.9370i	−0.243231	+	0.421288i
$944$	14.9782			0.487499
$945$	−1.68990	−	0.548626i	−0.0549723	−	0.0178468i
$946$	7.87349			0.255989
$947$	−10.6157	+	18.3870i	−0.344965	+	0.597497i	−0.985347	−	0.170559i	$-0.945443\pi$
$947$	−10.6157	+	18.3870i	−0.344965	+	0.597497i	0.640382	+	0.768056i	$0.278776\pi$
$948$	4.07865	−	5.61474i	0.132468	−	0.182358i
$949$	20.5462	+	35.5871i	0.666959	+	1.15521i
$950$	2.37306	+	4.11026i	0.0769923	+	0.133355i
$951$	−0.733805	−	1.64779i	−0.0237953	−	0.0534334i
$952$	0.791261	−	1.37050i	0.0256449	−	0.0444183i
$953$	−60.5205			−1.96045			−0.980226	−	0.197879i	$-0.936595\pi$
$953$	−60.5205			−1.96045			−0.980226	+	0.197879i	$0.936595\pi$
$954$	1.15156	+	0.244576i	0.0372831	+	0.00791844i
$955$	24.8958			0.805609
$956$	5.58240	−	9.66901i	0.180548	−	0.312718i
$957$	15.6549	+	1.64411i	0.506050	+	0.0531465i
$958$	0.125108	+	0.216694i	0.00404207	+	0.00700107i
$959$	−1.15413	−	1.99902i	−0.0372689	−	0.0645516i
$960$	1.72258	+	0.180909i	0.0555959	+	0.00583880i
$961$	2.65221	−	4.59376i	0.0855551	−	0.148186i
$962$	58.8646			1.89787
$963$	12.9699	+	39.8953i	0.417951	+	1.28561i
$964$	−15.8664			−0.511021
$965$	4.94115	−	8.55832i	0.159061	−	0.275502i
$966$	1.45762	+	3.27316i	0.0468982	+	0.105312i
$967$	6.54203	+	11.3311i	0.210378	+	0.364385i	0.951833	−	0.306618i	$-0.0991973\pi$
$967$	6.54203	+	11.3311i	0.210378	+	0.364385i	−0.741455	+	0.671002i	$0.765864\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$	22.3605	−	30.7819i	0.718323	−	0.988856i
$970$	−9.65280	+	16.7191i	−0.309933	+	0.536819i
$971$	−44.1202			−1.41588			−0.707942	−	0.706271i	$-0.750376\pi$
$971$	−44.1202			−1.41588			−0.707942	+	0.706271i	$0.750376\pi$
$972$	−13.4968	+	7.79971i	−0.432911	+	0.250176i
$973$	2.24991			0.0721288
$974$	−4.19571	+	7.26718i	−0.134439	+	0.232856i
$975$	6.63623	−	9.13555i	0.212530	−	0.292572i
$976$	−5.54512	−	9.60443i	−0.177495	−	0.307430i
$977$	5.96736	+	10.3358i	0.190913	+	0.330671i	0.945553	−	0.325468i	$-0.105522\pi$
$977$	5.96736	+	10.3358i	0.190913	+	0.330671i	−0.754640	+	0.656139i	$0.772189\pi$
$978$	−10.2580	−	23.0348i	−0.328014	−	0.736571i
$979$	−0.411690	+	0.713068i	−0.0131577	+	0.0227898i
$980$	−6.88308			−0.219872
$981$	10.6226	+	32.6748i	0.339152	+	1.04323i
$982$	18.5082			0.590620
$983$	23.6319	−	40.9317i	0.753741	−	1.30552i	−0.192257	−	0.981345i	$-0.561581\pi$
$983$	23.6319	−	40.9317i	0.753741	−	1.30552i	0.945998	−	0.324173i	$-0.105086\pi$
$984$	4.25333	+	0.446694i	0.135591	+	0.0142401i
$985$	−12.7614	−	22.1033i	−0.406611	−	0.704271i
$986$	−21.0307	−	36.4262i	−0.669753	−	1.16005i
$987$	0.675195	+	0.0709104i	0.0214917	+	0.00225710i
$988$	−15.4703	+	26.7954i	−0.492177	+	0.852476i
$989$	47.6345			1.51469
$990$	2.93454	+	0.623258i	0.0932659	+	0.0198085i
$991$	−17.3542			−0.551274			−0.275637	−	0.961262i	$-0.588889\pi$
$991$	−17.3542			−0.551274			−0.275637	+	0.961262i	$0.588889\pi$
$992$	2.53454	−	4.38995i	0.0804717	−	0.139381i
$993$	−9.45374	−	21.2288i	−0.300005	−	0.673676i
$994$	0.145439	+	0.251907i	0.00461304	+	0.00799002i
$995$	−2.51654	−	4.35878i	−0.0797798	−	0.138183i
$996$	2.03512	−	2.80158i	0.0644853	−	0.0887715i
$997$	−4.99850	+	8.65766i	−0.158304	+	0.274191i	−0.934257	−	0.356600i	$-0.883936\pi$
$997$	−4.99850	+	8.65766i	−0.158304	+	0.274191i	0.775953	+	0.630791i	$0.217269\pi$
$998$	3.21163			0.101662
$999$	−44.6258	−	14.4878i	−1.41190	−	0.458373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.i.j.331.3	✓	14
3.2	odd	2		2970.2.i.k.991.5		14
9.2	odd	6		8910.2.a.ca.1.3		7
9.4	even	3	inner	990.2.i.j.661.3	yes	14
9.5	odd	6		2970.2.i.k.1981.5		14
9.7	even	3		8910.2.a.cd.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.i.j.331.3	✓	14	1.1	even	1	trivial
990.2.i.j.661.3	yes	14	9.4	even	3	inner
2970.2.i.k.991.5		14	3.2	odd	2
2970.2.i.k.1981.5		14	9.5	odd	6
8910.2.a.ca.1.3		7	9.2	odd	6
8910.2.a.cd.1.3		7	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.01796 + 1.40134i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.704617 - 1.58225i) q^{6} +(0.170965 - 0.296120i) q^{7} +1.00000 q^{8} +(-0.927514 - 2.85302i) q^{9} +1.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.72258 + 0.180909i) q^{12} +(3.25957 + 5.64575i) q^{13} +(0.170965 + 0.296120i) q^{14} +(1.72258 + 0.180909i) q^{15} +(-0.500000 + 0.866025i) q^{16} +4.62820 q^{17} +(2.93454 + 0.623258i) q^{18} -4.74612 q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.240930 + 0.541019i) q^{21} +(-0.500000 - 0.866025i) q^{22} +(-3.02499 - 5.23944i) q^{23} +(-1.01796 + 1.40134i) q^{24} +(-0.500000 + 0.866025i) q^{25} -6.51915 q^{26} +(4.94223 + 1.60450i) q^{27} -0.341930 q^{28} +(-4.54403 + 7.87048i) q^{29} +(-1.01796 + 1.40134i) q^{30} +(2.53454 + 4.38995i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.704617 - 1.58225i) q^{33} +(-2.31410 + 4.00814i) q^{34} -0.341930 q^{35} +(-2.00703 + 2.22976i) q^{36} -9.02949 q^{37} +(2.37306 - 4.11026i) q^{38} +(-11.2297 - 1.17937i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-1.23458 - 2.13836i) q^{41} +(-0.589001 - 0.0618582i) q^{42} +(-3.93674 + 6.81864i) q^{43} +1.00000 q^{44} +(-2.00703 + 2.22976i) q^{45} +6.04998 q^{46} +(0.573169 - 0.992759i) q^{47} +(-0.704617 - 1.58225i) q^{48} +(3.44154 + 5.96093i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-4.71132 + 6.48569i) q^{51} +(3.25957 - 5.64575i) q^{52} +0.392415 q^{53} +(-3.86065 + 3.47785i) q^{54} +1.00000 q^{55} +(0.170965 - 0.296120i) q^{56} +(4.83136 - 6.65094i) q^{57} +(-4.54403 - 7.87048i) q^{58} +(-7.48911 - 12.9715i) q^{59} +(-0.704617 - 1.58225i) q^{60} +(-5.54512 + 9.60443i) q^{61} -5.06908 q^{62} +(-1.00341 - 0.213111i) q^{63} +1.00000 q^{64} +(3.25957 - 5.64575i) q^{65} +(1.72258 + 0.180909i) q^{66} +(-6.04372 - 10.4680i) q^{67} +(-2.31410 - 4.00814i) q^{68} +(10.4216 + 1.09449i) q^{69} +(0.170965 - 0.296120i) q^{70} +0.850693 q^{71} +(-0.927514 - 2.85302i) q^{72} +6.30335 q^{73} +(4.51474 - 7.81976i) q^{74} +(-0.704617 - 1.58225i) q^{75} +(2.37306 + 4.11026i) q^{76} +(0.170965 + 0.296120i) q^{77} +(6.63623 - 9.13555i) q^{78} +(2.00334 - 3.46990i) q^{79} +1.00000 q^{80} +(-7.27943 + 5.29243i) q^{81} +2.46917 q^{82} +(0.999607 - 1.73137i) q^{83} +(0.348071 - 0.479161i) q^{84} +(-2.31410 - 4.00814i) q^{85} +(-3.93674 - 6.81864i) q^{86} +(-6.40360 - 14.3796i) q^{87} +(-0.500000 + 0.866025i) q^{88} +0.823380 q^{89} +(-0.927514 - 2.85302i) q^{90} +2.22909 q^{91} +(-3.02499 + 5.23944i) q^{92} +(-8.73188 - 0.917041i) q^{93} +(0.573169 + 0.992759i) q^{94} +(2.37306 + 4.11026i) q^{95} +(1.72258 + 0.180909i) q^{96} +(-9.65280 + 16.7191i) q^{97} -6.88308 q^{98} +(2.93454 + 0.623258i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 7 q^{2} - q^{3} - 7 q^{4} - 7 q^{5} + 2 q^{6} - 5 q^{7} + 14 q^{8} - 5 q^{9} + 14 q^{10} - 7 q^{11} - q^{12} - 5 q^{13} - 5 q^{14} - q^{15} - 7 q^{16} + 6 q^{17} + 7 q^{18} + 22 q^{19} - 7 q^{20}+ \cdots + 7 q^{99}+O(q^{100}) \) 14 * q - 7 * q^2 - q^3 - 7 * q^4 - 7 * q^5 + 2 * q^6 - 5 * q^7 + 14 * q^8 - 5 * q^9 + 14 * q^10 - 7 * q^11 - q^12 - 5 * q^13 - 5 * q^14 - q^15 - 7 * q^16 + 6 * q^17 + 7 * q^18 + 22 * q^19 - 7 * q^20 - 21 * q^21 - 7 * q^22 - 3 * q^23 - q^24 - 7 * q^25 + 10 * q^26 - 4 * q^27 + 10 * q^28 - 12 * q^29 - q^30 - 5 * q^31 - 7 * q^32 + 2 * q^33 - 3 * q^34 + 10 * q^35 - 2 * q^36 + 4 * q^37 - 11 * q^38 - 33 * q^39 - 7 * q^40 - 6 * q^41 + 21 * q^42 - 17 * q^43 + 14 * q^44 - 2 * q^45 + 6 * q^46 + 3 * q^47 + 2 * q^48 - 12 * q^49 - 7 * q^50 + 4 * q^51 - 5 * q^52 + 6 * q^53 + 2 * q^54 + 14 * q^55 - 5 * q^56 - 2 * q^57 - 12 * q^58 - 18 * q^59 + 2 * q^60 - 11 * q^61 + 10 * q^62 - 3 * q^63 + 14 * q^64 - 5 * q^65 - q^66 - 20 * q^67 - 3 * q^68 + 24 * q^69 - 5 * q^70 + 24 * q^71 - 5 * q^72 + 4 * q^73 - 2 * q^74 + 2 * q^75 - 11 * q^76 - 5 * q^77 + 24 * q^78 + 7 * q^79 + 14 * q^80 + 7 * q^81 + 12 * q^82 - 3 * q^85 - 17 * q^86 + 19 * q^87 - 7 * q^88 - 6 * q^89 - 5 * q^90 + 14 * q^91 - 3 * q^92 - 24 * q^93 + 3 * q^94 - 11 * q^95 - q^96 - 23 * q^97 + 24 * q^98 + 7 * q^99

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