LMFDB - Embedded newform 930.2.r.b.119.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(119,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("930.119");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.r (of order $6$, degree $2$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			119.16
Character	$\chi$	$=$	930.119
Dual form			930.2.r.b.719.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.180653 + 1.72260i) q^{3} +1.00000 q^{4} +(0.550525 - 2.16724i) q^{5} +(0.180653 + 1.72260i) q^{6} +(2.86191 + 1.65233i) q^{7} +1.00000 q^{8} +(-2.93473 + 0.622388i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.180653 + 1.72260i) q^{3} +1.00000 q^{4} +(0.550525 - 2.16724i) q^{5} +(0.180653 + 1.72260i) q^{6} +(2.86191 + 1.65233i) q^{7} +1.00000 q^{8} +(-2.93473 + 0.622388i) q^{9} +(0.550525 - 2.16724i) q^{10} +(2.78549 + 4.82461i) q^{11} +(0.180653 + 1.72260i) q^{12} +(-1.20794 - 2.09222i) q^{13} +(2.86191 + 1.65233i) q^{14} +(3.83275 + 0.556818i) q^{15} +1.00000 q^{16} +(-3.46854 - 2.00256i) q^{17} +(-2.93473 + 0.622388i) q^{18} +(2.21704 - 3.84003i) q^{19} +(0.550525 - 2.16724i) q^{20} +(-2.32929 + 5.22844i) q^{21} +(2.78549 + 4.82461i) q^{22} +6.85192i q^{23} +(0.180653 + 1.72260i) q^{24} +(-4.39384 - 2.38624i) q^{25} +(-1.20794 - 2.09222i) q^{26} +(-1.60230 - 4.94294i) q^{27} +(2.86191 + 1.65233i) q^{28} +7.83840 q^{29} +(3.83275 + 0.556818i) q^{30} +(5.44595 - 1.15829i) q^{31} +1.00000 q^{32} +(-7.80769 + 5.66988i) q^{33} +(-3.46854 - 2.00256i) q^{34} +(5.15654 - 5.29280i) q^{35} +(-2.93473 + 0.622388i) q^{36} +(-0.592220 + 1.02576i) q^{37} +(2.21704 - 3.84003i) q^{38} +(3.38584 - 2.45877i) q^{39} +(0.550525 - 2.16724i) q^{40} +(-7.88355 + 4.55157i) q^{41} +(-2.32929 + 5.22844i) q^{42} +(-1.62936 + 2.82213i) q^{43} +(2.78549 + 4.82461i) q^{44} +(-0.266779 + 6.70290i) q^{45} +6.85192i q^{46} +3.16650 q^{47} +(0.180653 + 1.72260i) q^{48} +(1.96037 + 3.39546i) q^{49} +(-4.39384 - 2.38624i) q^{50} +(2.82302 - 6.33669i) q^{51} +(-1.20794 - 2.09222i) q^{52} +(-1.34776 + 0.778128i) q^{53} +(-1.60230 - 4.94294i) q^{54} +(11.9896 - 3.38075i) q^{55} +(2.86191 + 1.65233i) q^{56} +(7.01537 + 3.12537i) q^{57} +7.83840 q^{58} +(-6.34470 - 3.66312i) q^{59} +(3.83275 + 0.556818i) q^{60} -11.1591i q^{61} +(5.44595 - 1.15829i) q^{62} +(-9.42733 - 3.06791i) q^{63} +1.00000 q^{64} +(-5.19933 + 1.46608i) q^{65} +(-7.80769 + 5.66988i) q^{66} +(1.47147 - 0.849552i) q^{67} +(-3.46854 - 2.00256i) q^{68} +(-11.8031 + 1.23782i) q^{69} +(5.15654 - 5.29280i) q^{70} +(-9.82808 + 5.67425i) q^{71} +(-2.93473 + 0.622388i) q^{72} +(-3.89097 - 6.73935i) q^{73} +(-0.592220 + 1.02576i) q^{74} +(3.31678 - 7.99994i) q^{75} +(2.21704 - 3.84003i) q^{76} +18.4102i q^{77} +(3.38584 - 2.45877i) q^{78} +(10.6582 + 6.15354i) q^{79} +(0.550525 - 2.16724i) q^{80} +(8.22527 - 3.65308i) q^{81} +(-7.88355 + 4.55157i) q^{82} +(-11.3161 + 6.53335i) q^{83} +(-2.32929 + 5.22844i) q^{84} +(-6.24955 + 6.41469i) q^{85} +(-1.62936 + 2.82213i) q^{86} +(1.41603 + 13.5025i) q^{87} +(2.78549 + 4.82461i) q^{88} +6.52903 q^{89} +(-0.266779 + 6.70290i) q^{90} -7.98366i q^{91} +6.85192i q^{92} +(2.97911 + 9.17196i) q^{93} +3.16650 q^{94} +(-7.10172 - 6.91889i) q^{95} +(0.180653 + 1.72260i) q^{96} -5.20680i q^{97} +(1.96037 + 3.39546i) q^{98} +(-11.1774 - 12.4253i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) $ 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9	$ 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) $ 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^20 + 2 * q^25 + 18 * q^31 + 64 * q^32 - 8 * q^33 + 6 * q^34 + 16 * q^35 - 4 * q^36 + 4 * q^38 - 8 * q^39 + 2 * q^40 + 9 * q^45 - 4 * q^47 + 30 * q^49 + 2 * q^50 - 8 * q^51 - 6 * q^53 + 6 * q^57 + 18 * q^62 + 12 * q^63 + 64 * q^64 - 8 * q^66 + 6 * q^68 - 10 * q^69 + 16 * q^70 - 4 * q^72 - 63 * q^75 + 4 * q^76 - 8 * q^78 - 30 * q^79 + 2 * q^80 - 12 * q^81 - 54 * q^83 - 16 * q^87 + 9 * q^90 - 18 * q^93 - 4 * q^94 - 56 * q^95 + 30 * q^98 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.180653	+	1.72260i	0.104300	+	0.994546i
$3$	0.180653	+	1.72260i	0.104300	+	0.994546i
$4$	1.00000			0.500000
$5$	0.550525	−	2.16724i	0.246202	−	0.969218i
$5$	0.550525	−	2.16724i	0.246202	−	0.969218i
$6$	0.180653	+	1.72260i	0.0737514	+	0.703250i
$7$	2.86191	+	1.65233i	1.08170	+	0.624521i	0.931355	−	0.364112i	$-0.118628\pi$
$7$	2.86191	+	1.65233i	1.08170	+	0.624521i	0.150347	+	0.988633i	$0.451961\pi$
$8$	1.00000			0.353553
$9$	−2.93473	+	0.622388i	−0.978243	+	0.207463i
$10$	0.550525	−	2.16724i	0.174091	−	0.685341i
$11$	2.78549	+	4.82461i	0.839857	+	1.45467i	0.890014	+	0.455933i	$0.150694\pi$
$11$	2.78549	+	4.82461i	0.839857	+	1.45467i	−0.0501570	+	0.998741i	$0.515972\pi$
$12$	0.180653	+	1.72260i	0.0521501	+	0.497273i
$13$	−1.20794	−	2.09222i	−0.335023	−	0.580276i	0.648466	−	0.761243i	$-0.275411\pi$
$13$	−1.20794	−	2.09222i	−0.335023	−	0.580276i	−0.983489	+	0.180967i	$0.942077\pi$
$14$	2.86191	+	1.65233i	0.764879	+	0.441603i
$15$	3.83275	+	0.556818i	0.989611	+	0.143770i
$16$	1.00000			0.250000
$17$	−3.46854	−	2.00256i	−0.841244	−	0.485693i	0.0164427	−	0.999865i	$-0.494766\pi$
$17$	−3.46854	−	2.00256i	−0.841244	−	0.485693i	−0.857687	+	0.514172i	$0.828099\pi$
$18$	−2.93473	+	0.622388i	−0.691722	+	0.146698i
$19$	2.21704	−	3.84003i	0.508624	−	0.880963i	−0.491326	−	0.870976i	$-0.663488\pi$
$19$	2.21704	−	3.84003i	0.508624	−	0.880963i	0.999950	−	0.00998742i	$-0.00317915\pi$
$20$	0.550525	−	2.16724i	0.123101	−	0.484609i
$21$	−2.32929	+	5.22844i	−0.508293	+	1.14094i
$22$	2.78549	+	4.82461i	0.593868	+	1.02861i
$23$			6.85192i			1.42872i	0.699776	+	0.714362i	$0.253283\pi$
$23$			6.85192i			1.42872i	−0.699776	+	0.714362i	$0.746717\pi$
$24$	0.180653	+	1.72260i	0.0368757	+	0.351625i
$25$	−4.39384	−	2.38624i	−0.878769	−	0.477248i
$26$	−1.20794	−	2.09222i	−0.236897	−	0.410317i
$27$	−1.60230	−	4.94294i	−0.308362	−	0.951269i
$28$	2.86191	+	1.65233i	0.540851	+	0.312260i
$29$	7.83840			1.45555			0.727777	−	0.685813i	$-0.240553\pi$
$29$	7.83840			1.45555			0.727777	+	0.685813i	$0.240553\pi$
$30$	3.83275	+	0.556818i	0.699761	+	0.101661i
$31$	5.44595	−	1.15829i	0.978121	−	0.208036i
$31$	5.44595	−	1.15829i	0.978121	−	0.208036i
$32$	1.00000			0.176777
$33$	−7.80769	+	5.66988i	−1.35914	+	0.986999i
$34$	−3.46854	−	2.00256i	−0.594850	−	0.343437i
$35$	5.15654	−	5.29280i	0.871615	−	0.894647i
$36$	−2.93473	+	0.622388i	−0.489121	+	0.103731i
$37$	−0.592220	+	1.02576i	−0.0973604	+	0.168633i	−0.910591	−	0.413308i	$-0.864373\pi$
$37$	−0.592220	+	1.02576i	−0.0973604	+	0.168633i	0.813231	+	0.581941i	$0.197707\pi$
$38$	2.21704	−	3.84003i	0.359652	−	0.622935i
$39$	3.38584	−	2.45877i	0.542169	−	0.393718i
$40$	0.550525	−	2.16724i	0.0870457	−	0.342670i
$41$	−7.88355	+	4.55157i	−1.23120	+	0.710836i	−0.967281	−	0.253708i	$-0.918350\pi$
$41$	−7.88355	+	4.55157i	−1.23120	+	0.710836i	−0.263923	+	0.964544i	$0.585016\pi$
$42$	−2.32929	+	5.22844i	−0.359417	+	0.806766i
$43$	−1.62936	+	2.82213i	−0.248474	+	0.430370i	−0.963103	−	0.269134i	$-0.913263\pi$
$43$	−1.62936	+	2.82213i	−0.248474	+	0.430370i	0.714628	+	0.699504i	$0.246596\pi$
$44$	2.78549	+	4.82461i	0.419928	+	0.727337i
$45$	−0.266779	+	6.70290i	−0.0397690	+	0.999209i
$46$			6.85192i			1.01026i
$47$	3.16650			0.461881			0.230940	−	0.972968i	$-0.425820\pi$
$47$	3.16650			0.461881			0.230940	+	0.972968i	$0.425820\pi$
$48$	0.180653	+	1.72260i	0.0260750	+	0.248636i
$49$	1.96037	+	3.39546i	0.280053	+	0.485066i
$50$	−4.39384	−	2.38624i	−0.621383	−	0.337465i
$51$	2.82302	−	6.33669i	0.395302	−	0.887314i
$52$	−1.20794	−	2.09222i	−0.167511	−	0.290138i
$53$	−1.34776	+	0.778128i	−0.185129	+	0.106884i	−0.589700	−	0.807622i	$-0.700754\pi$
$53$	−1.34776	+	0.778128i	−0.185129	+	0.106884i	0.404571	+	0.914506i	$0.367421\pi$
$54$	−1.60230	−	4.94294i	−0.218045	−	0.672649i
$55$	11.9896	−	3.38075i	1.61667	−	0.455861i
$56$	2.86191	+	1.65233i	0.382439	+	0.220801i
$57$	7.01537	+	3.12537i	0.929208	+	0.413966i
$58$	7.83840			1.02923
$59$	−6.34470	−	3.66312i	−0.826010	−	0.476897i	0.0264745	−	0.999649i	$-0.491572\pi$
$59$	−6.34470	−	3.66312i	−0.826010	−	0.476897i	−0.852485	+	0.522752i	$0.824905\pi$
$60$	3.83275	+	0.556818i	0.494806	+	0.0718849i
$61$		−	11.1591i		−	1.42878i	−0.699748	−	0.714390i	$-0.746704\pi$
$61$		−	11.1591i		−	1.42878i	0.699748	−	0.714390i	$-0.253296\pi$
$62$	5.44595	−	1.15829i	0.691636	−	0.147104i
$63$	−9.42733	−	3.06791i	−1.18773	−	0.386520i
$64$	1.00000			0.125000
$65$	−5.19933	+	1.46608i	−0.644898	+	0.181845i
$66$	−7.80769	+	5.66988i	−0.961060	+	0.697914i
$67$	1.47147	−	0.849552i	0.179768	−	0.103789i	−0.407416	−	0.913243i	$-0.633570\pi$
$67$	1.47147	−	0.849552i	0.179768	−	0.103789i	0.587184	+	0.809454i	$0.300237\pi$
$68$	−3.46854	−	2.00256i	−0.420622	−	0.242846i
$69$	−11.8031	+	1.23782i	−1.42093	+	0.149016i
$70$	5.15654	−	5.29280i	0.616325	−	0.632611i
$71$	−9.82808	+	5.67425i	−1.16638	+	0.673409i	−0.952824	−	0.303522i	$-0.901837\pi$
$71$	−9.82808	+	5.67425i	−1.16638	+	0.673409i	−0.213555	+	0.976931i	$0.568504\pi$
$72$	−2.93473	+	0.622388i	−0.345861	+	0.0733491i
$73$	−3.89097	−	6.73935i	−0.455403	−	0.788781i	0.543308	−	0.839533i	$-0.317171\pi$
$73$	−3.89097	−	6.73935i	−0.455403	−	0.788781i	−0.998711	+	0.0507521i	$0.983838\pi$
$74$	−0.592220	+	1.02576i	−0.0688442	+	0.119242i
$75$	3.31678	−	7.99994i	0.382989	−	0.923753i
$76$	2.21704	−	3.84003i	0.254312	−	0.440482i
$77$			18.4102i			2.09803i
$78$	3.38584	−	2.45877i	0.383371	−	0.278401i
$79$	10.6582	+	6.15354i	1.19915	+	0.692327i	0.960365	−	0.278746i	$-0.0899188\pi$
$79$	10.6582	+	6.15354i	1.19915	+	0.692327i	0.238781	+	0.971073i	$0.423252\pi$
$80$	0.550525	−	2.16724i	0.0615506	−	0.242305i
$81$	8.22527	−	3.65308i	0.913918	−	0.405898i
$82$	−7.88355	+	4.55157i	−0.870593	+	0.502637i
$83$	−11.3161	+	6.53335i	−1.24210	+	0.717129i	−0.969522	−	0.245004i	$-0.921211\pi$
$83$	−11.3161	+	6.53335i	−1.24210	+	0.717129i	−0.272581	+	0.962133i	$0.587877\pi$
$84$	−2.32929	+	5.22844i	−0.254146	+	0.570470i
$85$	−6.24955	+	6.41469i	−0.677858	+	0.695771i
$86$	−1.62936	+	2.82213i	−0.175698	+	0.304318i
$87$	1.41603	+	13.5025i	0.151815	+	1.44762i
$88$	2.78549	+	4.82461i	0.296934	+	0.514305i
$89$	6.52903			0.692075			0.346038	−	0.938221i	$-0.387527\pi$
$89$	6.52903			0.692075			0.346038	+	0.938221i	$0.387527\pi$
$90$	−0.266779	+	6.70290i	−0.0281209	+	0.706547i
$91$		−	7.98366i		−	0.836915i
$92$			6.85192i			0.714362i
$93$	2.97911	+	9.17196i	0.308919	+	0.951088i
$94$	3.16650			0.326599
$95$	−7.10172	−	6.91889i	−0.728621	−	0.709863i
$96$	0.180653	+	1.72260i	0.0184378	+	0.175813i
$97$		−	5.20680i		−	0.528670i	−0.964431	−	0.264335i	$-0.914847\pi$
$97$		−	5.20680i		−	0.528670i	0.964431	−	0.264335i	$-0.0851525\pi$
$98$	1.96037	+	3.39546i	0.198027	+	0.342993i
$99$	−11.1774	−	12.4253i	−1.12337	−	1.24879i
$100$	−4.39384	−	2.38624i	−0.439384	−	0.238624i
$101$		−	19.0964i		−	1.90016i	−0.312000	−	0.950082i	$-0.600999\pi$
$101$		−	19.0964i		−	1.90016i	0.312000	−	0.950082i	$-0.399001\pi$
$102$	2.82302	−	6.33669i	0.279520	−	0.627426i
$103$	−7.70085	+	4.44609i	−0.758787	+	0.438086i	−0.828860	−	0.559456i	$-0.811010\pi$
$103$	−7.70085	+	4.44609i	−0.758787	+	0.438086i	0.0700730	+	0.997542i	$0.477677\pi$
$104$	−1.20794	−	2.09222i	−0.118448	−	0.205159i
$105$	10.0489	+	7.92652i	0.980677	+	0.773549i
$106$	−1.34776	+	0.778128i	−0.130906	+	0.0755785i
$107$	−1.07526	+	1.86240i	−0.103949	+	0.180045i	−0.913308	−	0.407269i	$-0.866481\pi$
$107$	−1.07526	+	1.86240i	−0.103949	+	0.180045i	0.809359	+	0.587314i	$0.199815\pi$
$108$	−1.60230	−	4.94294i	−0.154181	−	0.475635i
$109$	0.373734			0.0357972			0.0178986	−	0.999840i	$-0.494302\pi$
$109$	0.373734			0.0357972			0.0178986	+	0.999840i	$0.494302\pi$
$110$	11.9896	−	3.38075i	1.14316	−	0.322342i
$111$	−1.87396	−	0.834855i	−0.177868	−	0.0792409i
$112$	2.86191	+	1.65233i	0.270425	+	0.156130i
$113$	−5.04948	−	8.74596i	−0.475015	−	0.822750i	0.524575	−	0.851364i	$-0.324224\pi$
$113$	−5.04948	−	8.74596i	−0.475015	−	0.822750i	−0.999591	+	0.0286137i	$0.990891\pi$
$114$	7.01537	+	3.12537i	0.657049	+	0.292718i
$115$	14.8498	+	3.77216i	1.38475	+	0.351755i
$116$	7.83840			0.727777
$117$	4.84715	+	5.38828i	0.448119	+	0.498147i
$118$	−6.34470	−	3.66312i	−0.584077	−	0.337217i
$119$	−6.61777	−	11.4623i	−0.606650	−	1.05075i
$120$	3.83275	+	0.556818i	0.349880	+	0.0508303i
$121$	−10.0179	+	17.3515i	−0.910719	+	1.57741i
$122$		−	11.1591i		−	1.01030i
$123$	−9.26474	−	12.7580i	−0.835374	−	1.15035i
$124$	5.44595	−	1.15829i	0.489061	−	0.104018i
$125$	−7.59047	+	8.20882i	−0.678912	+	0.734220i
$126$	−9.42733	−	3.06791i	−0.839853	−	0.273311i
$127$	1.33639	−	2.31469i	0.118585	−	0.205395i	−0.800622	−	0.599170i	$-0.795498\pi$
$127$	1.33639	−	2.31469i	0.118585	−	0.205395i	0.919207	+	0.393774i	$0.128831\pi$
$128$	1.00000			0.0883883
$129$	−5.15576	−	2.29691i	−0.453939	−	0.202232i
$130$	−5.19933	+	1.46608i	−0.456012	+	0.128584i
$131$	0.418042	+	0.241356i	0.0365245	+	0.0210874i	0.518151	−	0.855289i	$-0.326621\pi$
$131$	0.418042	+	0.241356i	0.0365245	+	0.0210874i	−0.481627	+	0.876377i	$0.659954\pi$
$132$	−7.80769	+	5.66988i	−0.679572	+	0.493500i
$133$	12.6900	−	7.32656i	1.10036	−	0.635293i
$134$	1.47147	−	0.849552i	0.127115	−	0.0733901i
$135$	−11.5946	+	0.751346i	−0.997907	+	0.0646656i
$136$	−3.46854	−	2.00256i	−0.297425	−	0.171718i
$137$	13.4336	−	7.75587i	1.14771	−	0.662629i	0.199380	−	0.979922i	$-0.436107\pi$
$137$	13.4336	−	7.75587i	1.14771	−	0.662629i	0.948327	+	0.317293i	$0.102774\pi$
$138$	−11.8031	+	1.23782i	−1.00475	+	0.105370i
$139$			1.12995i			0.0958408i	0.998851	+	0.0479204i	$0.0152594\pi$
$139$			1.12995i			0.0958408i	−0.998851	+	0.0479204i	$0.984741\pi$
$140$	5.15654	−	5.29280i	0.435807	−	0.447324i
$141$	0.572038	+	5.45462i	0.0481743	+	0.459362i
$142$	−9.82808	+	5.67425i	−0.824754	+	0.476172i
$143$	6.72942	−	11.6557i	0.562742	−	0.974698i
$144$	−2.93473	+	0.622388i	−0.244561	+	0.0518657i
$145$	4.31524	−	16.9877i	0.358361	−	1.41075i
$146$	−3.89097	−	6.73935i	−0.322019	−	0.557753i
$147$	−5.49488	+	3.99034i	−0.453210	+	0.329118i
$148$	−0.592220	+	1.02576i	−0.0486802	+	0.0843166i
$149$	−1.16540	−	0.672843i	−0.0954731	−	0.0551214i	0.451503	−	0.892269i	$-0.350888\pi$
$149$	−1.16540	−	0.672843i	−0.0954731	−	0.0551214i	−0.546976	+	0.837148i	$0.684221\pi$
$150$	3.31678	−	7.99994i	0.270814	−	0.653192i
$151$		−	18.3802i		−	1.49576i	−0.663835	−	0.747879i	$-0.731072\pi$
$151$		−	18.3802i		−	1.49576i	0.663835	−	0.747879i	$-0.268928\pi$
$152$	2.21704	−	3.84003i	0.179826	−	0.311468i
$153$	11.4256	+	3.71820i	0.923704	+	0.300599i
$154$			18.4102i			1.48353i
$155$	0.487830	−	12.4403i	0.0391834	−	0.999232i
$156$	3.38584	−	2.45877i	0.271084	−	0.196859i
$157$		−	12.0822i		−	0.964263i	−0.876099	−	0.482131i	$-0.839863\pi$
$157$		−	12.0822i		−	0.964263i	0.876099	−	0.482131i	$-0.160137\pi$
$158$	10.6582	+	6.15354i	0.847924	+	0.489549i
$159$	−1.58388	−	2.18108i	−0.125610	−	0.172971i
$160$	0.550525	−	2.16724i	0.0435228	−	0.171335i
$161$	−11.3216	+	19.6096i	−0.892268	+	1.54545i
$162$	8.22527	−	3.65308i	0.646238	−	0.287013i
$163$		−	3.19393i		−	0.250168i	−0.992146	−	0.125084i	$-0.960080\pi$
$163$		−	3.19393i		−	0.250168i	0.992146	−	0.125084i	$-0.0399200\pi$
$164$	−7.88355	+	4.55157i	−0.615602	+	0.355418i
$165$	7.98965	+	20.0425i	0.621993	+	1.56031i
$166$	−11.3161	+	6.53335i	−0.878300	+	0.507086i
$167$	−15.1583	−	8.75165i	−1.17298	−	0.677223i	−0.218603	−	0.975814i	$-0.570150\pi$
$167$	−15.1583	−	8.75165i	−1.17298	−	0.677223i	−0.954381	+	0.298591i	$0.903483\pi$
$168$	−2.32929	+	5.22844i	−0.179709	+	0.403383i
$169$	3.58175	−	6.20378i	0.275520	−	0.477214i
$170$	−6.24955	+	6.41469i	−0.479318	+	0.491984i
$171$	−4.11643	+	12.6493i	−0.314791	+	0.967317i
$172$	−1.62936	+	2.82213i	−0.124237	+	0.215185i
$173$	−9.24593	−	16.0144i	−0.702955	−	1.21755i	−0.967425	−	0.253159i	$-0.918530\pi$
$173$	−9.24593	−	16.0144i	−0.702955	−	1.21755i	0.264470	−	0.964394i	$-0.414803\pi$
$174$	1.41603	+	13.5025i	0.107349	+	1.02362i
$175$	−8.63196	−	14.0893i	−0.652515	−	1.06505i
$176$	2.78549	+	4.82461i	0.209964	+	0.363669i
$177$	5.16391	−	11.5912i	0.388143	−	0.871245i
$178$	6.52903			0.489371
$179$	−1.26319	+	2.18791i	−0.0944152	+	0.163532i	−0.909364	−	0.416000i	$-0.863431\pi$
$179$	−1.26319	+	2.18791i	−0.0944152	+	0.163532i	0.814949	+	0.579532i	$0.196765\pi$
$180$	−0.266779	+	6.70290i	−0.0198845	+	0.499604i
$181$	−8.88208	+	5.12807i	−0.660200	+	0.381167i	−0.792353	−	0.610063i	$-0.791144\pi$
$181$	−8.88208	+	5.12807i	−0.660200	+	0.381167i	0.132153	+	0.991229i	$0.457811\pi$
$182$		−	7.98366i		−	0.591788i
$183$	19.2228	−	2.01593i	1.42099	−	0.149022i
$184$			6.85192i			0.505130i
$185$	1.89702	+	1.84819i	0.139472	+	0.135881i
$186$	2.97911	+	9.17196i	0.218439	+	0.672521i
$187$		−	22.3125i		−	1.63165i
$188$	3.16650			0.230940
$189$	3.58172	−	16.7938i	0.260532	−	1.22157i
$190$	−7.10172	−	6.91889i	−0.515213	−	0.501949i
$191$	1.15070	−	0.664357i	0.0832618	−	0.0480712i	−0.457791	−	0.889060i	$-0.651359\pi$
$191$	1.15070	−	0.664357i	0.0832618	−	0.0480712i	0.541053	+	0.840989i	$0.318026\pi$
$192$	0.180653	+	1.72260i	0.0130375	+	0.124318i
$193$	−2.06771	−	1.19379i	−0.148837	−	0.0859311i	0.423732	−	0.905788i	$-0.360720\pi$
$193$	−2.06771	−	1.19379i	−0.148837	−	0.0859311i	−0.572569	+	0.819856i	$0.694053\pi$
$194$		−	5.20680i		−	0.373826i
$195$	−3.46475	−	8.69154i	−0.248116	−	0.622414i
$196$	1.96037	+	3.39546i	0.140026	+	0.242533i
$197$	17.8245	−	10.2910i	1.26994	−	0.733203i	0.294967	−	0.955507i	$-0.404691\pi$
$197$	17.8245	−	10.2910i	1.26994	−	0.733203i	0.974977	+	0.222304i	$0.0713579\pi$
$198$	−11.1774	−	12.4253i	−0.794346	−	0.883025i
$199$	−7.88469	+	4.55223i	−0.558931	+	0.322699i	−0.752716	−	0.658345i	$-0.771257\pi$
$199$	−7.88469	+	4.55223i	−0.558931	+	0.322699i	0.193785	+	0.981044i	$0.437923\pi$
$200$	−4.39384	−	2.38624i	−0.310692	−	0.168733i
$201$	1.72927	+	2.38128i	0.121973	+	0.167963i
$202$		−	19.0964i		−	1.34362i
$203$	22.4328	+	12.9516i	1.57448	+	0.909024i
$204$	2.82302	−	6.33669i	0.197651	−	0.443657i
$205$	5.52425	+	19.5913i	0.385830	+	1.36832i
$206$	−7.70085	+	4.44609i	−0.536544	+	0.309774i
$207$	−4.26455	−	20.1085i	−0.296407	−	1.39764i
$208$	−1.20794	−	2.09222i	−0.0837557	−	0.145069i
$209$	24.7022			1.70869
$210$	10.0489	+	7.92652i	0.693443	+	0.546982i
$211$	1.20286	−	2.08341i	0.0828082	−	0.143428i	−0.821647	−	0.569997i	$-0.806944\pi$
$211$	1.20286	−	2.08341i	0.0828082	−	0.143428i	0.904455	+	0.426569i	$0.140278\pi$
$212$	−1.34776	+	0.778128i	−0.0925643	+	0.0534420i
$213$	−11.5500	−	15.9048i	−0.791390	−	1.08978i
$214$	−1.07526	+	1.86240i	−0.0735030	+	0.127311i
$215$	5.21922	+	5.08486i	0.355948	+	0.346784i
$216$	−1.60230	−	4.94294i	−0.109022	−	0.336324i
$217$	17.4997	+	5.68355i	1.18796	+	0.385824i
$218$	0.373734			0.0253124
$219$	10.9063	−	7.92008i	0.736980	−	0.535189i
$220$	11.9896	−	3.38075i	0.808336	−	0.227930i
$221$			9.67591i			0.650872i
$222$	−1.87396	−	0.834855i	−0.125772	−	0.0560318i
$223$	−0.590667	+	1.02306i	−0.0395540	+	0.0685095i	−0.885125	−	0.465354i	$-0.845927\pi$
$223$	−0.590667	+	1.02306i	−0.0395540	+	0.0685095i	0.845571	+	0.533863i	$0.179260\pi$
$224$	2.86191	+	1.65233i	0.191220	+	0.110401i
$225$	14.3799	+	4.26829i	0.958660	+	0.284552i
$226$	−5.04948	−	8.74596i	−0.335886	−	0.581772i
$227$	11.6653	+	20.2050i	0.774255	+	1.34105i	0.935212	+	0.354088i	$0.115209\pi$
$227$	11.6653	+	20.2050i	0.774255	+	1.34105i	−0.160957	+	0.986961i	$0.551458\pi$
$228$	7.01537	+	3.12537i	0.464604	+	0.206983i
$229$	24.3330	+	14.0487i	1.60797	+	0.928362i	0.989824	+	0.142298i	$0.0454491\pi$
$229$	24.3330	+	14.0487i	1.60797	+	0.928362i	0.618146	+	0.786064i	$0.287884\pi$
$230$	14.8498	+	3.77216i	0.979164	+	0.248729i
$231$	−31.7134	+	3.32586i	−2.08659	+	0.218825i
$232$	7.83840			0.514616
$233$	−1.85618			−0.121602			−0.0608012	−	0.998150i	$-0.519366\pi$
$233$	−1.85618			−0.121602			−0.0608012	+	0.998150i	$0.519366\pi$
$234$	4.84715	+	5.38828i	0.316868	+	0.352243i
$235$	1.74324	−	6.86255i	0.113716	−	0.447663i
$236$	−6.34470	−	3.66312i	−0.413005	−	0.238449i
$237$	−8.67466	+	19.4716i	−0.563480	+	1.26482i
$238$	−6.61777	−	11.4623i	−0.428967	−	0.742992i
$239$	−10.6369	−	18.4237i	−0.688045	−	1.19173i	−0.972470	−	0.233030i	$-0.925136\pi$
$239$	−10.6369	−	18.4237i	−0.688045	−	1.19173i	0.284425	−	0.958698i	$-0.408197\pi$
$240$	3.83275	+	0.556818i	0.247403	+	0.0359424i
$241$	−25.2426	−	14.5738i	−1.62602	−	0.938781i	−0.985266	−	0.171032i	$-0.945290\pi$
$241$	−25.2426	−	14.5738i	−1.62602	−	0.938781i	−0.640751	−	0.767749i	$-0.721377\pi$
$242$	−10.0179	+	17.3515i	−0.643976	+	1.11540i
$243$	7.77873	+	13.5089i	0.499006	+	0.866599i
$244$		−	11.1591i		−	0.714390i
$245$	8.43800	−	2.37930i	0.539084	−	0.152008i
$246$	−9.26474	−	12.7580i	−0.590698	−	0.813419i
$247$	−10.7122			−0.681603
$248$	5.44595	−	1.15829i	0.345818	−	0.0735518i
$249$	−13.2987	−	18.3129i	−0.842769	−	1.16053i
$250$	−7.59047	+	8.20882i	−0.480063	+	0.519172i
$251$	−13.8668	+	24.0180i	−0.875264	+	1.51600i	−0.0187823	+	0.999824i	$0.505979\pi$
$251$	−13.8668	+	24.0180i	−0.875264	+	1.51600i	−0.856481	+	0.516178i	$0.827354\pi$
$252$	−9.42733	−	3.06791i	−0.593866	−	0.193260i
$253$	−33.0579	+	19.0860i	−2.07833	+	1.19992i
$254$	1.33639	−	2.31469i	0.0838523	−	0.145236i
$255$	−12.1790	−	9.60666i	−0.762677	−	0.601592i
$256$	1.00000			0.0625000
$257$	−1.72588	−	2.98931i	−0.107657	−	0.186468i	0.807163	−	0.590328i	$-0.201002\pi$
$257$	−1.72588	−	2.98931i	−0.107657	−	0.186468i	−0.914821	+	0.403860i	$0.867668\pi$
$258$	−5.15576	−	2.29691i	−0.320983	−	0.142999i
$259$	−3.38977	+	1.95708i	−0.210630	+	0.121607i
$260$	−5.19933	+	1.46608i	−0.322449	+	0.0909224i
$261$	−23.0036	+	4.87853i	−1.42389	+	0.301973i
$262$	0.418042	+	0.241356i	0.0258267	+	0.0149111i
$263$			18.7126i			1.15387i	0.816791	+	0.576934i	$0.195751\pi$
$263$			18.7126i			1.15387i	−0.816791	+	0.576934i	$0.804249\pi$
$264$	−7.80769	+	5.66988i	−0.480530	+	0.348957i
$265$	0.944415	+	3.34929i	0.0580149	+	0.205745i
$266$	12.6900	−	7.32656i	0.778072	−	0.449220i
$267$	1.17949	+	11.2469i	0.0721836	+	0.688301i
$268$	1.47147	−	0.849552i	0.0898841	−	0.0518946i
$269$	9.22902	+	15.9851i	0.562703	+	0.974631i	0.997259	+	0.0739860i	$0.0235720\pi$
$269$	9.22902	+	15.9851i	0.562703	+	0.974631i	−0.434556	+	0.900645i	$0.643095\pi$
$270$	−11.5946	+	0.751346i	−0.705627	+	0.0457255i
$271$			24.2153i			1.47097i	0.677540	+	0.735486i	$0.263046\pi$
$271$			24.2153i			1.47097i	−0.677540	+	0.735486i	$0.736954\pi$
$272$	−3.46854	−	2.00256i	−0.210311	−	0.121423i
$273$	13.7527	−	1.44227i	0.832350	−	0.0872904i
$274$	13.4336	−	7.75587i	0.811552	−	0.468550i
$275$	−0.726341	−	27.8454i	−0.0438000	−	1.67914i
$276$	−11.8031	+	1.23782i	−0.710466	+	0.0745081i
$277$	−5.60736			−0.336914			−0.168457	−	0.985709i	$-0.553878\pi$
$277$	−5.60736			−0.336914			−0.168457	+	0.985709i	$0.553878\pi$
$278$			1.12995i			0.0677697i
$279$	−15.2615	+	6.78877i	−0.913680	+	0.406433i
$280$	5.15654	−	5.29280i	0.308162	−	0.316305i
$281$			1.25229i			0.0747053i	0.999302	+	0.0373526i	$0.0118925\pi$
$281$			1.25229i			0.0747053i	−0.999302	+	0.0373526i	$0.988108\pi$
$282$	0.572038	+	5.45462i	0.0340644	+	0.324818i
$283$		−	9.29538i		−	0.552553i	−0.961078	−	0.276276i	$-0.910899\pi$
$283$		−	9.29538i		−	0.552553i	0.961078	−	0.276276i	$-0.0891005\pi$
$284$	−9.82808	+	5.67425i	−0.583189	+	0.336705i
$285$	10.6356	−	13.4834i	0.629996	−	0.798686i
$286$	6.72942	−	11.6557i	0.397919	−	0.689216i
$287$	−30.0827			−1.77573
$288$	−2.93473	+	0.622388i	−0.172931	+	0.0366746i
$289$	−0.479492	−	0.830505i	−0.0282054	−	0.0488532i
$290$	4.31524	−	16.9877i	0.253399	−	0.997551i
$291$	8.96926	−	0.940625i	0.525787	−	0.0551404i
$292$	−3.89097	−	6.73935i	−0.227702	−	0.394391i
$293$	−9.76669	+	16.9164i	−0.570576	+	0.988267i	0.425930	+	0.904756i	$0.359947\pi$
$293$	−9.76669	+	16.9164i	−0.570576	+	0.988267i	−0.996507	+	0.0835113i	$0.973387\pi$
$294$	−5.49488	+	3.99034i	−0.320468	+	0.232721i
$295$	−11.4318	+	11.7338i	−0.665583	+	0.683171i
$296$	−0.592220	+	1.02576i	−0.0344221	+	0.0596208i
$297$	19.3846	−	21.4990i	1.12481	−	1.24750i
$298$	−1.16540	−	0.672843i	−0.0675097	−	0.0389767i
$299$	14.3357	−	8.27672i	0.829055	−	0.478655i
$300$	3.31678	−	7.99994i	0.191494	−	0.461876i
$301$	−9.32616	+	5.38446i	−0.537551	+	0.310355i
$302$		−	18.3802i		−	1.05766i
$303$	32.8956	−	3.44983i	1.88980	−	0.198188i
$304$	2.21704	−	3.84003i	0.127156	−	0.220241i
$305$	−24.1845	−	6.14338i	−1.38480	−	0.351769i
$306$	11.4256	+	3.71820i	0.653158	+	0.212555i
$307$	7.18208	+	4.14657i	0.409903	+	0.236657i	0.690748	−	0.723096i	$-0.257281\pi$
$307$	7.18208	+	4.14657i	0.409903	+	0.236657i	−0.280845	+	0.959753i	$0.590615\pi$
$308$			18.4102i			1.04902i
$309$	−9.05003	−	12.4623i	−0.514838	−	0.708956i
$310$	0.487830	−	12.4403i	0.0277069	−	0.706564i
$311$			15.4408i			0.875567i	0.899080	+	0.437784i	$0.144236\pi$
$311$			15.4408i			0.875567i	−0.899080	+	0.437784i	$0.855764\pi$
$312$	3.38584	−	2.45877i	0.191686	−	0.139200i
$313$	−4.71257	+	8.16241i	−0.266370	+	0.461367i	−0.967922	−	0.251252i	$-0.919158\pi$
$313$	−4.71257	+	8.16241i	−0.266370	+	0.461367i	0.701552	+	0.712619i	$0.252491\pi$
$314$		−	12.0822i		−	0.681837i
$315$	−11.8389	+	18.7423i	−0.667045	+	1.05601i
$316$	10.6582	+	6.15354i	0.599573	+	0.346164i
$317$	1.09170	−	1.89088i	0.0613161	−	0.106203i	−0.833738	−	0.552160i	$-0.813804\pi$
$317$	1.09170	−	1.89088i	0.0613161	−	0.106203i	0.895054	+	0.445958i	$0.147137\pi$
$318$	−1.58388	−	2.18108i	−0.0888197	−	0.122309i
$319$	21.8338	+	37.8172i	1.22246	+	2.11736i
$320$	0.550525	−	2.16724i	0.0307753	−	0.121152i
$321$	−3.40242	−	1.51579i	−0.189905	−	0.0846032i
$322$	−11.3216	+	19.6096i	−0.630929	+	1.09280i
$323$	−15.3798	+	8.87953i	−0.855755	+	0.494070i
$324$	8.22527	−	3.65308i	0.456959	−	0.202949i
$325$	0.314981	+	12.0753i	0.0174720	+	0.669818i
$326$		−	3.19393i		−	0.176896i
$327$	0.0675162	+	0.643795i	0.00373366	+	0.0356020i
$328$	−7.88355	+	4.55157i	−0.435296	+	0.251318i
$329$	9.06224	+	5.23209i	0.499617	+	0.288454i
$330$	7.98965	+	20.0425i	0.439816	+	1.10330i
$331$	11.8419	−	6.83691i	0.650888	−	0.375791i	−0.137908	−	0.990445i	$-0.544038\pi$
$331$	11.8419	−	6.83691i	0.650888	−	0.375791i	0.788797	+	0.614654i	$0.210705\pi$
$332$	−11.3161	+	6.53335i	−0.621052	+	0.358564i
$333$	1.09959	−	3.37891i	0.0602570	−	0.185163i
$334$	−15.1583	−	8.75165i	−0.829425	−	0.478869i
$335$	−1.03110	−	3.65672i	−0.0563351	−	0.199788i
$336$	−2.32929	+	5.22844i	−0.127073	+	0.285235i
$337$	5.64290			0.307388			0.153694	−	0.988118i	$-0.450883\pi$
$337$	5.64290			0.307388			0.153694	+	0.988118i	$0.450883\pi$
$338$	3.58175	−	6.20378i	0.194822	−	0.337441i
$339$	14.1536	−	10.2782i	0.768719	−	0.558237i
$340$	−6.24955	+	6.41469i	−0.338929	+	0.347885i
$341$	20.7580	+	23.0482i	1.12411	+	1.24813i
$342$	−4.11643	+	12.6493i	−0.222591	+	0.683996i
$343$		−	10.1759i		−	0.549447i
$344$	−1.62936	+	2.82213i	−0.0878490	+	0.152159i
$345$	−3.81527	+	26.2617i	−0.205407	+	1.41388i
$346$	−9.24593	−	16.0144i	−0.497064	−	0.860940i
$347$	−1.93242	−	1.11569i	−0.103738	−	0.0598931i	0.447233	−	0.894417i	$-0.352409\pi$
$347$	−1.93242	−	1.11569i	−0.103738	−	0.0598931i	−0.550971	+	0.834524i	$0.685743\pi$
$348$	1.41603	+	13.5025i	0.0759073	+	0.723808i
$349$	−25.9566			−1.38943			−0.694713	−	0.719287i	$-0.744469\pi$
$349$	−25.9566			−1.38943			−0.694713	+	0.719287i	$0.744469\pi$
$350$	−8.63196	−	14.0893i	−0.461398	−	0.753103i
$351$	−8.40622	+	9.32313i	−0.448691	+	0.497632i
$352$	2.78549	+	4.82461i	0.148467	+	0.257153i
$353$	28.7787	+	16.6154i	1.53173	+	0.884347i	0.999282	+	0.0378878i	$0.0120629\pi$
$353$	28.7787	+	16.6154i	1.53173	+	0.884347i	0.532453	+	0.846460i	$0.321270\pi$
$354$	5.16391	−	11.5912i	0.274459	−	0.616064i
$355$	6.88684	+	24.4236i	0.365515	+	1.29627i
$356$	6.52903			0.346038
$357$	18.5495	−	13.4705i	0.981745	−	0.712935i
$358$	−1.26319	+	2.18791i	−0.0667616	+	0.115635i
$359$	−17.1377	+	9.89444i	−0.904492	+	0.522209i	−0.878655	−	0.477457i	$-0.841559\pi$
$359$	−17.1377	+	9.89444i	−0.904492	+	0.522209i	−0.0258373	+	0.999666i	$0.508225\pi$
$360$	−0.266779	+	6.70290i	−0.0140605	+	0.353274i
$361$	−0.330555	−	0.572537i	−0.0173976	−	0.0301335i
$362$	−8.88208	+	5.12807i	−0.466832	+	0.269525i
$363$	−31.6996	−	14.1223i	−1.66380	−	0.741228i
$364$		−	7.98366i		−	0.418457i
$365$	−16.7479	+	4.72247i	−0.876623	+	0.247185i
$366$	19.2228	−	2.01593i	1.00479	−	0.105375i
$367$	−15.9406	−	27.6100i	−0.832095	−	1.44123i	−0.896374	−	0.443299i	$-0.853808\pi$
$367$	−15.9406	−	27.6100i	−0.832095	−	1.44123i	0.0642788	−	0.997932i	$-0.479525\pi$
$368$			6.85192i			0.357181i
$369$	20.3032	−	18.2643i	1.05694	−	0.950799i
$370$	1.89702	+	1.84819i	0.0986216	+	0.0960826i
$371$	−5.14289			−0.267005
$372$	2.97911	+	9.17196i	0.154460	+	0.475544i
$373$			31.4578i			1.62882i	0.580289	+	0.814411i	$0.302940\pi$
$373$			31.4578i			1.62882i	−0.580289	+	0.814411i	$0.697060\pi$
$374$		−	22.3125i		−	1.15375i
$375$	−15.5118	−	11.5924i	−0.801026	−	0.598630i
$376$	3.16650			0.163300
$377$	−9.46833	−	16.3996i	−0.487644	−	0.844624i
$378$	3.58172	−	16.7938i	0.184224	−	0.863779i
$379$	2.82127	−	4.88658i	0.144919	−	0.251007i	−0.784424	−	0.620225i	$-0.787041\pi$
$379$	2.82127	−	4.88658i	0.144919	−	0.251007i	0.929343	+	0.369218i	$0.120375\pi$
$380$	−7.10172	−	6.91889i	−0.364311	−	0.354932i
$381$	4.22871	+	1.88391i	0.216644	+	0.0965155i
$382$	1.15070	−	0.664357i	0.0588750	−	0.0339915i
$383$	5.87647	−	3.39278i	0.300273	−	0.173363i	−0.342292	−	0.939594i	$-0.611203\pi$
$383$	5.87647	−	3.39278i	0.300273	−	0.173363i	0.642566	+	0.766231i	$0.277870\pi$
$384$	0.180653	+	1.72260i	0.00921892	+	0.0879063i
$385$	39.8992	+	10.1353i	2.03345	+	0.516540i
$386$	−2.06771	−	1.19379i	−0.105244	−	0.0607625i
$387$	3.02526	−	9.29627i	0.153783	−	0.472556i
$388$		−	5.20680i		−	0.264335i
$389$	−14.6999	+	25.4610i	−0.745315	+	1.29092i	0.204733	+	0.978818i	$0.434367\pi$
$389$	−14.6999	+	25.4610i	−0.745315	+	1.29092i	−0.950048	+	0.312105i	$0.898966\pi$
$390$	−3.46475	−	8.69154i	−0.175445	−	0.440113i
$391$	13.7214	−	23.7662i	0.693921	−	1.20191i
$392$	1.96037	+	3.39546i	0.0990136	+	0.171497i
$393$	−0.340241	+	0.763722i	−0.0171629	+	0.0385247i
$394$	17.8245	−	10.2910i	0.897987	−	0.518453i
$395$	19.2038	−	19.7113i	0.966249	−	0.991782i
$396$	−11.1774	−	12.4253i	−0.561687	−	0.624393i
$397$	12.5146	+	7.22528i	0.628087	+	0.362626i	0.780011	−	0.625766i	$-0.215213\pi$
$397$	12.5146	+	7.22528i	0.628087	+	0.362626i	−0.151924	+	0.988392i	$0.548547\pi$
$398$	−7.88469	+	4.55223i	−0.395224	+	0.228183i
$399$	14.9132	+	20.5362i	0.746596	+	1.02810i
$400$	−4.39384	−	2.38624i	−0.219692	−	0.119312i
$401$	−6.38334			−0.318769			−0.159384	−	0.987217i	$-0.550951\pi$
$401$	−6.38334			−0.318769			−0.159384	+	0.987217i	$0.550951\pi$
$402$	1.72927	+	2.38128i	0.0862480	+	0.118767i
$403$	−9.00179	−	9.99495i	−0.448411	−	0.497884i
$404$		−	19.0964i		−	0.950082i
$405$	−3.38888	−	19.8372i	−0.168395	−	0.985720i
$406$	22.4328	+	12.9516i	1.11332	+	0.642777i
$407$	−6.59849			−0.327075
$408$	2.82302	−	6.33669i	0.139760	−	0.313713i
$409$	−4.24890	−	2.45311i	−0.210095	−	0.121298i	0.391261	−	0.920280i	$-0.372039\pi$
$409$	−4.24890	−	2.45311i	−0.210095	−	0.121298i	−0.601355	+	0.798982i	$0.705372\pi$
$410$	5.52425	+	19.5913i	0.272823	+	0.967545i
$411$	15.7871	+	21.7396i	0.778721	+	1.07234i
$412$	−7.70085	+	4.44609i	−0.379394	+	0.219043i
$413$	−12.1053	−	20.9671i	−0.595664	−	1.03172i
$414$	−4.26455	−	20.1085i	−0.209591	−	0.988281i
$415$	7.92954	+	28.1215i	0.389246	+	1.38043i
$416$	−1.20794	−	2.09222i	−0.0592242	−	0.102579i
$417$	−1.94645	+	0.204128i	−0.0953181	+	0.00999621i
$418$	24.7022			1.20822
$419$		−	9.80896i		−	0.479199i	−0.970872	−	0.239599i	$-0.922984\pi$
$419$		−	9.80896i		−	0.479199i	0.970872	−	0.239599i	$-0.0770161\pi$
$420$	10.0489	+	7.92652i	0.490339	+	0.386774i
$421$	−3.94712	−	6.83662i	−0.192371	−	0.333196i	0.753665	−	0.657259i	$-0.228284\pi$
$421$	−3.94712	−	6.83662i	−0.192371	−	0.333196i	−0.946036	+	0.324063i	$0.894951\pi$
$422$	1.20286	−	2.08341i	0.0585543	−	0.101419i
$423$	−9.29281	+	1.97079i	−0.451832	+	0.0958230i
$424$	−1.34776	+	0.778128i	−0.0654529	+	0.0377892i
$425$	10.4616	+	17.0757i	0.507464	+	0.828293i
$426$	−11.5500	−	15.9048i	−0.559597	−	0.770591i
$427$	18.4385	−	31.9365i	0.892303	−	1.54551i
$428$	−1.07526	+	1.86240i	−0.0519744	+	0.0900224i
$429$	21.2938	+	9.48648i	1.02808	+	0.458012i
$430$	5.21922	+	5.08486i	0.251693	+	0.245213i
$431$	5.03759	+	2.90845i	0.242652	+	0.140095i	0.616395	−	0.787437i	$-0.288592\pi$
$431$	5.03759	+	2.90845i	0.242652	+	0.140095i	−0.373743	+	0.927532i	$0.621926\pi$
$432$	−1.60230	−	4.94294i	−0.0770905	−	0.237817i
$433$	27.3374			1.31375			0.656877	−	0.753998i	$-0.271877\pi$
$433$	27.3374			1.31375			0.656877	+	0.753998i	$0.271877\pi$
$434$	17.4997	+	5.68355i	0.840013	+	0.272819i
$435$	30.0426	+	4.36456i	1.44043	+	0.209265i
$436$	0.373734			0.0178986
$437$	26.3116	+	15.1910i	1.25865	+	0.726684i
$438$	10.9063	−	7.92008i	0.521124	−	0.378436i
$439$	11.3452	+	19.6505i	0.541477	+	0.937866i	0.998820	+	0.0485752i	$0.0154681\pi$
$439$	11.3452	+	19.6505i	0.541477	+	0.937866i	−0.457342	+	0.889291i	$0.651199\pi$
$440$	11.9896	−	3.38075i	0.571580	−	0.161171i
$441$	−7.86644	−	8.74464i	−0.374593	−	0.416411i
$442$			9.67591i			0.460236i
$443$	9.72814	+	16.8496i	0.462198	+	0.800550i	0.999070	−	0.0431134i	$-0.0137277\pi$
$443$	9.72814	+	16.8496i	0.462198	+	0.800550i	−0.536872	+	0.843663i	$0.680394\pi$
$444$	−1.87396	−	0.834855i	−0.0889341	−	0.0396205i
$445$	3.59439	−	14.1500i	0.170391	−	0.670772i
$446$	−0.590667	+	1.02306i	−0.0279689	+	0.0484435i
$447$	0.948509	−	2.12907i	0.0448629	−	0.100702i
$448$	2.86191	+	1.65233i	0.135213	+	0.0780651i
$449$	−10.3186			−0.486967			−0.243483	−	0.969905i	$-0.578290\pi$
$449$	−10.3186			−0.486967			−0.243483	+	0.969905i	$0.578290\pi$
$450$	14.3799	+	4.26829i	0.677875	+	0.201209i
$451$	−43.9191	−	25.3567i	−2.06807	−	1.19400i
$452$	−5.04948	−	8.74596i	−0.237508	−	0.411375i
$453$	31.6618	−	3.32044i	1.48760	−	0.156008i
$454$	11.6653	+	20.2050i	0.547481	+	0.948265i
$455$	−17.3025	−	4.39520i	−0.811153	−	0.206050i
$456$	7.01537	+	3.12537i	0.328525	+	0.146359i
$457$	4.31019			0.201622			0.100811	−	0.994906i	$-0.467856\pi$
$457$	4.31019			0.201622			0.100811	+	0.994906i	$0.467856\pi$
$458$	24.3330	+	14.0487i	1.13701	+	0.656451i
$459$	−4.34091	+	20.3535i	−0.202617	+	0.950019i
$460$	14.8498	+	3.77216i	0.692373	+	0.175878i
$461$	24.1218			1.12347			0.561733	−	0.827319i	$-0.310135\pi$
$461$	24.1218			1.12347			0.561733	+	0.827319i	$0.310135\pi$
$462$	−31.7134	+	3.32586i	−1.47544	+	0.154733i
$463$	13.1532			0.611279			0.305639	−	0.952147i	$-0.401130\pi$
$463$	13.1532			0.611279			0.305639	+	0.952147i	$0.401130\pi$
$464$	7.83840			0.363889
$465$	21.5179	−	1.40705i	0.997869	−	0.0652504i
$466$	−1.85618			−0.0859859
$467$	28.4663			1.31726			0.658631	−	0.752466i	$-0.271136\pi$
$467$	28.4663			1.31726			0.658631	+	0.752466i	$0.271136\pi$
$468$	4.84715	+	5.38828i	0.224060	+	0.249073i
$469$	5.61495			0.259274
$470$	1.74324	−	6.86255i	0.0804095	−	0.316546i
$471$	20.8128	−	2.18269i	0.959004	−	0.100573i
$472$	−6.34470	−	3.66312i	−0.292039	−	0.168609i
$473$	−18.1542			−0.834732
$474$	−8.67466	+	19.4716i	−0.398441	+	0.894360i
$475$	−18.9046	+	11.5821i	−0.867401	+	0.531423i
$476$	−6.61777	−	11.4623i	−0.303325	−	0.525375i
$477$	3.47100	−	3.12242i	0.158926	−	0.142966i
$478$	−10.6369	−	18.4237i	−0.486521	−	0.842679i
$479$	−31.9232	−	18.4309i	−1.45861	−	0.842128i	−0.459666	−	0.888092i	$-0.652031\pi$
$479$	−31.9232	−	18.4309i	−1.45861	−	0.842128i	−0.998943	+	0.0459634i	$0.985364\pi$
$480$	3.83275	+	0.556818i	0.174940	+	0.0254151i
$481$	2.86147			0.130472
$482$	−25.2426	−	14.5738i	−1.14977	−	0.663818i
$483$	−35.8249	−	15.9601i	−1.63009	−	0.726211i
$484$	−10.0179	+	17.3515i	−0.455360	+	0.788706i
$485$	−11.2844	−	2.86647i	−0.512397	−	0.130160i
$486$	7.77873	+	13.5089i	0.352850	+	0.612778i
$487$	16.7504	+	29.0126i	0.759035	+	1.31469i	0.943343	+	0.331818i	$0.107662\pi$
$487$	16.7504	+	29.0126i	0.759035	+	1.31469i	−0.184309	+	0.982868i	$0.559005\pi$
$488$		−	11.1591i		−	0.505150i
$489$	5.50188	−	0.576994i	0.248804	−	0.0260926i
$490$	8.43800	−	2.37930i	0.381190	−	0.107486i
$491$	6.16407	+	10.6765i	0.278181	+	0.481823i	0.970933	−	0.239353i	$-0.0769353\pi$
$491$	6.16407	+	10.6765i	0.278181	+	0.481823i	−0.692752	+	0.721176i	$0.743602\pi$
$492$	−9.26474	−	12.7580i	−0.417687	−	0.575174i
$493$	−27.1878	−	15.6969i	−1.22448	−	0.706952i
$494$	−10.7122			−0.481966
$495$	−33.0820	+	17.3838i	−1.48692	+	0.781341i
$496$	5.44595	−	1.15829i	0.244530	−	0.0520090i
$497$	−37.5028			−1.68223
$498$	−13.2987	−	18.3129i	−0.595928	−	0.820620i
$499$	−20.8127	−	12.0162i	−0.931705	−	0.537920i	−0.0443546	−	0.999016i	$-0.514123\pi$
$499$	−20.8127	−	12.0162i	−0.931705	−	0.537920i	−0.887350	+	0.461096i	$0.847456\pi$
$500$	−7.59047	+	8.20882i	−0.339456	+	0.367110i
$501$	12.3372	−	27.6928i	0.551187	−	1.23722i
$502$	−13.8668	+	24.0180i	−0.618905	+	1.07197i
$503$	2.18795	−	3.78965i	0.0975560	−	0.168972i	−0.813116	−	0.582101i	$-0.802231\pi$
$503$	2.18795	−	3.78965i	0.0975560	−	0.168972i	0.910673	+	0.413129i	$0.135564\pi$
$504$	−9.42733	−	3.06791i	−0.419927	−	0.136656i
$505$	−41.3865	−	10.5131i	−1.84167	−	0.467825i
$506$	−33.0579	+	19.0860i	−1.46960	+	0.848475i
$507$	11.3337	+	5.04921i	0.503348	+	0.224243i
$508$	1.33639	−	2.31469i	0.0592925	−	0.102698i
$509$	−1.65386	−	2.86457i	−0.0733062	−	0.126970i	0.827042	−	0.562140i	$-0.190022\pi$
$509$	−1.65386	−	2.86457i	−0.0733062	−	0.126970i	−0.900348	+	0.435170i	$0.856688\pi$
$510$	−12.1790	−	9.60666i	−0.539294	−	0.425390i
$511$		−	25.7166i		−	1.13763i
$512$	1.00000			0.0441942
$513$	−22.5334	−	4.80584i	−0.994874	−	0.212183i
$514$	−1.72588	−	2.98931i	−0.0761253	−	0.131853i
$515$	5.39622	+	19.1373i	0.237786	+	0.843288i
$516$	−5.15576	−	2.29691i	−0.226970	−	0.101116i
$517$	8.82024	+	15.2771i	0.387914	+	0.671886i
$518$	−3.38977	+	1.95708i	−0.148938	+	0.0859893i
$519$	25.9162	−	18.8201i	1.13759	−	0.826112i
$520$	−5.19933	+	1.46608i	−0.228006	+	0.0642919i
$521$	12.8717	+	7.43148i	0.563920	+	0.325579i	0.754717	−	0.656050i	$-0.227774\pi$
$521$	12.8717	+	7.43148i	0.563920	+	0.325579i	−0.190798	+	0.981629i	$0.561107\pi$
$522$	−23.0036	+	4.87853i	−1.00684	+	0.213527i
$523$	21.9651			0.960465			0.480232	−	0.877141i	$-0.340552\pi$
$523$	21.9651			0.960465			0.480232	+	0.877141i	$0.340552\pi$
$524$	0.418042	+	0.241356i	0.0182622	+	0.0105437i
$525$	22.7109	−	17.4147i	0.991183	−	0.760041i
$526$			18.7126i			0.815908i
$527$	−21.2090	−	6.88826i	−0.923880	−	0.300057i
$528$	−7.80769	+	5.66988i	−0.339786	+	0.246750i
$529$	−23.9488			−1.04125
$530$	0.944415	+	3.34929i	0.0410228	+	0.145484i
$531$	20.8999	+	6.80139i	0.906977	+	0.295155i
$532$	12.6900	−	7.32656i	0.550180	−	0.317647i
$533$	19.0457	+	10.9961i	0.824963	+	0.476292i
$534$	1.17949	+	11.2469i	0.0510415	+	0.486702i
$535$	3.44430	+	3.35563i	0.148910	+	0.145077i
$536$	1.47147	−	0.849552i	0.0635577	−	0.0366950i
$537$	−3.99710	−	1.78072i	−0.172488	−	0.0768438i
$538$	9.22902	+	15.9851i	0.397891	+	0.689168i
$539$	−10.9212	+	18.9160i	−0.470408	+	0.814771i
$540$	−11.5946	+	0.751346i	−0.498953	+	0.0323328i
$541$	14.6790	−	25.4247i	0.631098	−	1.09309i	−0.356229	−	0.934399i	$-0.615938\pi$
$541$	14.6790	−	25.4247i	0.631098	−	1.09309i	0.987328	−	0.158696i	$-0.0507288\pi$
$542$			24.2153i			1.04013i
$543$	−10.4382	−	14.3739i	−0.447947	−	0.616843i
$544$	−3.46854	−	2.00256i	−0.148712	−	0.0858591i
$545$	0.205750	−	0.809970i	0.00881335	−	0.0346953i
$546$	13.7527	−	1.44227i	0.588560	−	0.0617236i
$547$	−12.4554	+	7.19114i	−0.532555	+	0.307471i	−0.742056	−	0.670337i	$-0.766149\pi$
$547$	−12.4554	+	7.19114i	−0.532555	+	0.307471i	0.209501	+	0.977808i	$0.432816\pi$
$548$	13.4336	−	7.75587i	0.573854	−	0.331315i
$549$	6.94531	+	32.7490i	0.296419	+	1.39769i
$550$	−0.726341	−	27.8454i	−0.0309713	−	1.18733i
$551$	17.3781	−	30.0997i	0.740331	−	1.28229i
$552$	−11.8031	+	1.23782i	−0.502375	+	0.0526852i
$553$	20.3353	+	35.2218i	0.864746	+	1.49778i
$554$	−5.60736			−0.238234
$555$	−2.84099	+	3.60170i	−0.120593	+	0.152884i
$556$			1.12995i			0.0479204i
$557$			2.67416i			0.113308i	0.998394	+	0.0566539i	$0.0180432\pi$
$557$			2.67416i			0.113308i	−0.998394	+	0.0566539i	$0.981957\pi$
$558$	−15.2615	+	6.78877i	−0.646070	+	0.287392i
$559$	7.87267			0.332978
$560$	5.15654	−	5.29280i	0.217904	−	0.223662i
$561$	38.4355	−	4.03082i	1.62275	−	0.170181i
$562$			1.25229i			0.0528246i
$563$	15.8858	+	27.5151i	0.669509	+	1.15962i	0.978042	+	0.208409i	$0.0668286\pi$
$563$	15.8858	+	27.5151i	0.669509	+	1.15962i	−0.308533	+	0.951214i	$0.599838\pi$
$564$	0.572038	+	5.45462i	0.0240871	+	0.229681i
$565$	−21.7344	+	6.12856i	−0.914375	+	0.257830i
$566$		−	9.29538i		−	0.390714i
$567$	29.5761	+	3.13603i	1.24208	+	0.131701i
$568$	−9.82808	+	5.67425i	−0.412377	+	0.238086i
$569$	12.9668	+	22.4592i	0.543598	+	0.941539i	0.998694	+	0.0510968i	$0.0162717\pi$
$569$	12.9668	+	22.4592i	0.543598	+	0.941539i	−0.455096	+	0.890443i	$0.650395\pi$
$570$	10.6356	−	13.4834i	0.445475	−	0.564757i
$571$	−30.5159	+	17.6184i	−1.27705	+	0.737305i	−0.976305	−	0.216399i	$-0.930569\pi$
$571$	−30.5159	+	17.6184i	−1.27705	+	0.737305i	−0.300746	+	0.953704i	$0.597235\pi$
$572$	6.72942	−	11.6557i	0.281371	−	0.487349i
$573$	1.35230	+	1.86218i	0.0564932	+	0.0777938i
$574$	−30.0827			−1.25563
$575$	16.3503	−	30.1063i	0.681855	−	1.25552i
$576$	−2.93473	+	0.622388i	−0.122280	+	0.0259328i
$577$	−18.8795	−	10.9001i	−0.785964	−	0.453776i	0.0525760	−	0.998617i	$-0.483257\pi$
$577$	−18.8795	−	10.9001i	−0.785964	−	0.453776i	−0.838540	+	0.544841i	$0.816590\pi$
$578$	−0.479492	−	0.830505i	−0.0199442	−	0.0345444i
$579$	1.68289	−	3.77751i	0.0699387	−	0.156988i
$580$	4.31524	−	16.9877i	0.179180	−	0.705375i
$581$	−43.1809			−1.79145
$582$	8.96926	−	0.940625i	0.371788	−	0.0389902i
$583$	−7.50833	−	4.33494i	−0.310963	−	0.179535i
$584$	−3.89097	−	6.73935i	−0.161009	−	0.278876i
$585$	14.3462	−	7.53855i	0.593141	−	0.311681i
$586$	−9.76669	+	16.9164i	−0.403458	+	0.698810i
$587$			4.40580i			0.181847i	0.995858	+	0.0909233i	$0.0289818\pi$
$587$			4.40580i			0.181847i	−0.995858	+	0.0909233i	$0.971018\pi$
$588$	−5.49488	+	3.99034i	−0.226605	+	0.164559i
$589$	7.62601	−	23.4806i	0.314224	−	0.967501i
$590$	−11.4318	+	11.7338i	−0.470638	+	0.483075i
$591$	20.9474	+	28.8455i	0.861659	+	1.18655i
$592$	−0.592220	+	1.02576i	−0.0243401	+	0.0421583i
$593$	34.1655			1.40301			0.701505	−	0.712665i	$-0.252512\pi$
$593$	34.1655			1.40301			0.701505	+	0.712665i	$0.252512\pi$
$594$	19.3846	−	21.4990i	0.795359	−	0.882113i
$595$	−28.4848	+	8.03200i	−1.16776	+	0.329280i
$596$	−1.16540	−	0.672843i	−0.0477365	−	0.0275607i
$597$	−9.26608	−	12.7598i	−0.379235	−	0.522225i
$598$	14.3357	−	8.27672i	0.586231	−	0.338460i
$599$	−1.81258	+	1.04649i	−0.0740599	+	0.0427585i	−0.536573	−	0.843854i	$-0.680281\pi$
$599$	−1.81258	+	1.04649i	−0.0740599	+	0.0427585i	0.462513	+	0.886613i	$0.346948\pi$
$600$	3.31678	−	7.99994i	0.135407	−	0.326596i
$601$	19.7245	+	11.3879i	0.804578	+	0.464524i	0.845070	−	0.534656i	$-0.179559\pi$
$601$	19.7245	+	11.3879i	0.804578	+	0.464524i	−0.0404912	+	0.999180i	$0.512892\pi$
$602$	−9.32616	+	5.38446i	−0.380106	+	0.219454i
$603$	−3.78961	+	3.40903i	−0.154325	+	0.138826i
$604$		−	18.3802i		−	0.747879i
$605$	32.0898	+	31.2636i	1.30464	+	1.27105i
$606$	32.8956	−	3.44983i	1.33629	−	0.140140i
$607$	−8.10906	+	4.68177i	−0.329137	+	0.190027i	−0.655458	−	0.755232i	$-0.727524\pi$
$607$	−8.10906	+	4.68177i	−0.329137	+	0.190027i	0.326321	+	0.945259i	$0.394191\pi$
$608$	2.21704	−	3.84003i	0.0899129	−	0.155734i
$609$	−18.2579	+	40.9826i	−0.739848	+	1.66070i
$610$	−24.1845	−	6.14338i	−0.979202	−	0.248738i
$611$	−3.82494	−	6.62499i	−0.154741	−	0.268019i
$612$	11.4256	+	3.71820i	0.461852	+	0.150299i
$613$	4.05011	−	7.01500i	0.163582	−	0.283333i	−0.772569	−	0.634931i	$-0.781028\pi$
$613$	4.05011	−	7.01500i	0.163582	−	0.283333i	0.936151	+	0.351598i	$0.114362\pi$
$614$	7.18208	+	4.14657i	0.289845	+	0.167342i
$615$	−32.7501	+	13.0553i	−1.32061	+	0.526441i
$616$			18.4102i			0.741767i
$617$	14.4279	−	24.9899i	0.580847	−	1.00606i	−0.414532	−	0.910035i	$-0.636055\pi$
$617$	14.4279	−	24.9899i	0.580847	−	1.00606i	0.995379	−	0.0960220i	$-0.0306119\pi$
$618$	−9.05003	−	12.4623i	−0.364046	−	0.501308i
$619$			16.3790i			0.658328i	0.944273	+	0.329164i	$0.106767\pi$
$619$			16.3790i			0.658328i	−0.944273	+	0.329164i	$0.893233\pi$
$620$	0.487830	−	12.4403i	0.0195917	−	0.499616i
$621$	33.8686	−	10.9788i	1.35910	−	0.440564i
$622$			15.4408i			0.619119i
$623$	18.6855	+	10.7881i	0.748619	+	0.432215i
$624$	3.38584	−	2.45877i	0.135542	−	0.0984296i
$625$	13.6117	+	20.9695i	0.544469	+	0.838781i
$626$	−4.71257	+	8.16241i	−0.188352	+	0.326235i
$627$	4.46253	+	42.5521i	0.178216	+	1.69937i
$628$		−	12.0822i		−	0.482131i
$629$	4.10828	−	2.37192i	0.163808	−	0.0945745i
$630$	−11.8389	+	18.7423i	−0.471672	+	0.746712i
$631$	−18.7554	+	10.8284i	−0.746640	+	0.431073i	−0.824478	−	0.565893i	$-0.808531\pi$
$631$	−18.7554	+	10.8284i	−0.746640	+	0.431073i	0.0778388	+	0.996966i	$0.475198\pi$
$632$	10.6582	+	6.15354i	0.423962	+	0.244775i
$633$	3.80620	+	1.69567i	0.151283	+	0.0673970i
$634$	1.09170	−	1.89088i	0.0433570	−	0.0750965i
$635$	−4.28077	−	4.17056i	−0.169877	−	0.165504i
$636$	−1.58388	−	2.18108i	−0.0628050	−	0.0864855i
$637$	4.73602	−	8.20303i	0.187648	−	0.325016i
$638$	21.8338	+	37.8172i	0.864408	+	1.49720i
$639$	25.3112	−	22.7693i	1.00129	−	0.900738i
$640$	0.550525	−	2.16724i	0.0217614	−	0.0856676i
$641$	−21.5225	−	37.2780i	−0.850086	−	1.47239i	−0.881130	−	0.472875i	$-0.843216\pi$
$641$	−21.5225	−	37.2780i	−0.850086	−	1.47239i	0.0310435	−	0.999518i	$-0.490117\pi$
$642$	−3.40242	−	1.51579i	−0.134283	−	0.0598235i
$643$	26.5851			1.04842			0.524208	−	0.851590i	$-0.324361\pi$
$643$	26.5851			1.04842			0.524208	+	0.851590i	$0.324361\pi$
$644$	−11.3216	+	19.6096i	−0.446134	+	0.772727i
$645$	−7.81632	+	9.90925i	−0.307767	+	0.390176i
$646$	−15.3798	+	8.87953i	−0.605110	+	0.349360i
$647$		−	3.55246i		−	0.139662i	−0.997559	−	0.0698308i	$-0.977754\pi$
$647$		−	3.55246i		−	0.139662i	0.997559	−	0.0698308i	$-0.0222459\pi$
$648$	8.22527	−	3.65308i	0.323119	−	0.143507i
$649$		−	40.8143i		−	1.60210i
$650$	0.314981	+	12.0753i	0.0123546	+	0.473633i
$651$	−6.62912	+	31.1718i	−0.259816	+	1.22172i
$652$		−	3.19393i		−	0.125084i
$653$	−24.8690			−0.973200			−0.486600	−	0.873625i	$-0.661763\pi$
$653$	−24.8690			−0.973200			−0.486600	+	0.873625i	$0.661763\pi$
$654$	0.0675162	+	0.643795i	0.00264009	+	0.0251744i
$655$	0.753219	−	0.773123i	0.0294307	−	0.0302084i
$656$	−7.88355	+	4.55157i	−0.307801	+	0.177709i
$657$	15.6134	+	17.3565i	0.609137	+	0.677141i
$658$	9.06224	+	5.23209i	0.353283	+	0.203968i
$659$		−	17.8288i		−	0.694510i	−0.937771	−	0.347255i	$-0.887114\pi$
$659$		−	17.8288i		−	0.694510i	0.937771	−	0.347255i	$-0.112886\pi$
$660$	7.98965	+	20.0425i	0.310997	+	0.780154i
$661$	21.5773	+	37.3730i	0.839261	+	1.45364i	0.890514	+	0.454957i	$0.150345\pi$
$661$	21.5773	+	37.3730i	0.839261	+	1.45364i	−0.0512527	+	0.998686i	$0.516321\pi$
$662$	11.8419	−	6.83691i	0.460248	−	0.265724i
$663$	−16.6678	+	1.74798i	−0.647322	+	0.0678861i
$664$	−11.3161	+	6.53335i	−0.439150	+	0.253543i
$665$	−8.89225	−	31.5356i	−0.344827	−	1.22290i
$666$	1.09959	−	3.37891i	0.0426082	−	0.130930i
$667$			53.7081i			2.07959i
$668$	−15.1583	−	8.75165i	−0.586492	−	0.338611i
$669$	−1.86904	−	0.832665i	−0.0722613	−	0.0321927i
$670$	−1.03110	−	3.65672i	−0.0398349	−	0.141271i
$671$	53.8385	−	31.0837i	2.07841	−	1.19997i
$672$	−2.32929	+	5.22844i	−0.0898543	+	0.201692i
$673$	19.0627	+	33.0175i	0.734811	+	1.27273i	0.954806	+	0.297229i	$0.0960626\pi$
$673$	19.0627	+	33.0175i	0.734811	+	1.27273i	−0.219995	+	0.975501i	$0.570604\pi$
$674$	5.64290			0.217356
$675$	−4.75479	+	25.5420i	−0.183012	+	0.983111i
$676$	3.58175	−	6.20378i	0.137760	−	0.238607i
$677$	−13.0001	+	7.50559i	−0.499633	+	0.288463i	−0.728562	−	0.684980i	$-0.759811\pi$
$677$	−13.0001	+	7.50559i	−0.499633	+	0.288463i	0.228929	+	0.973443i	$0.426478\pi$
$678$	14.1536	−	10.2782i	0.543566	−	0.394733i
$679$	8.60334	−	14.9014i	0.330166	−	0.571864i
$680$	−6.24955	+	6.41469i	−0.239659	+	0.245992i
$681$	−32.6978	+	23.7448i	−1.25298	+	0.909904i
$682$	20.7580	+	23.0482i	0.794863	+	0.882560i
$683$	−23.7656			−0.909365			−0.454682	−	0.890654i	$-0.650247\pi$
$683$	−23.7656			−0.909365			−0.454682	+	0.890654i	$0.650247\pi$
$684$	−4.11643	+	12.6493i	−0.157396	+	0.483658i
$685$	−9.41331	−	33.3836i	−0.359664	−	1.27552i
$686$		−	10.1759i		−	0.388518i
$687$	−19.8044	+	44.4540i	−0.755587	+	1.69603i
$688$	−1.62936	+	2.82213i	−0.0621186	+	0.107593i
$689$	3.25602	+	1.87987i	0.124045	+	0.0716172i
$690$	−3.81527	+	26.2617i	−0.145245	+	0.999765i
$691$	18.2700	+	31.6445i	0.695022	+	1.20381i	0.970173	+	0.242413i	$0.0779388\pi$
$691$	18.2700	+	31.6445i	0.695022	+	1.20381i	−0.275151	+	0.961401i	$0.588728\pi$
$692$	−9.24593	−	16.0144i	−0.351477	−	0.608777i
$693$	−11.4583	−	54.0288i	−0.435263	−	2.05239i
$694$	−1.93242	−	1.11569i	−0.0733538	−	0.0423508i
$695$	2.44886	+	0.622064i	0.0928907	+	0.0235962i
$696$	1.41603	+	13.5025i	0.0536746	+	0.511810i
$697$	36.4592			1.38099
$698$	−25.9566			−0.982473
$699$	−0.335325	−	3.19746i	−0.0126832	−	0.120939i
$700$	−8.63196	−	14.0893i	−0.326257	−	0.532525i
$701$	10.3655	+	5.98450i	0.391498	+	0.226031i	0.682809	−	0.730597i	$-0.260758\pi$
$701$	10.3655	+	5.98450i	0.391498	+	0.226031i	−0.291311	+	0.956628i	$0.594091\pi$
$702$	−8.40622	+	9.32313i	−0.317272	+	0.351879i
$703$	2.62595	+	4.54829i	0.0990398	+	0.171542i
$704$	2.78549	+	4.82461i	0.104982	+	0.181834i
$705$	12.1364	+	1.76316i	0.457082	+	0.0664045i
$706$	28.7787	+	16.6154i	1.08310	+	0.625328i
$707$	31.5535	−	54.6523i	1.18669	−	2.05541i
$708$	5.16391	−	11.5912i	0.194072	−	0.435623i
$709$			31.7469i			1.19228i	0.802881	+	0.596140i	$0.203300\pi$
$709$			31.7469i			1.19228i	−0.802881	+	0.596140i	$0.796700\pi$
$710$	6.88684	+	24.4236i	0.258458	+	0.916602i
$711$	−35.1089	−	11.4254i	−1.31669	−	0.428486i
$712$	6.52903			0.244686
$713$	7.93655	+	37.3152i	0.297226	+	1.39747i
$714$	18.5495	−	13.4705i	0.694198	−	0.504121i
$715$	−21.5560	−	21.0010i	−0.806147	−	0.785393i
$716$	−1.26319	+	2.18791i	−0.0472076	+	0.0817660i
$717$	29.8151	−	21.6515i	1.11347	−	0.808589i
$718$	−17.1377	+	9.89444i	−0.639573	+	0.369257i
$719$	−7.44580	+	12.8965i	−0.277682	+	0.480959i	−0.970808	−	0.239857i	$-0.922899\pi$
$719$	−7.44580	+	12.8965i	−0.277682	+	0.480959i	0.693127	+	0.720816i	$0.256233\pi$
$720$	−0.266779	+	6.70290i	−0.00994225	+	0.249802i
$721$	−29.3856			−1.09438
$722$	−0.330555	−	0.572537i	−0.0123020	−	0.0213076i
$723$	20.5447	−	46.1157i	0.764067	−	1.71506i
$724$	−8.88208	+	5.12807i	−0.330100	+	0.190583i
$725$	−34.4407	−	18.7043i	−1.27910	−	0.694660i
$726$	−31.6996	−	14.1223i	−1.17648	−	0.524127i
$727$	−40.8082	−	23.5606i	−1.51349	−	0.873814i	−0.999875	−	0.0157935i	$-0.994973\pi$
$727$	−40.8082	−	23.5606i	−1.51349	−	0.873814i	−0.513615	−	0.858021i	$-0.671694\pi$
$728$		−	7.98366i		−	0.295894i
$729$	−21.8653	+	15.8401i	−0.809826	+	0.586671i
$730$	−16.7479	+	4.72247i	−0.619866	+	0.174786i
$731$	11.3030	−	6.52577i	0.418055	−	0.241364i
$732$	19.2228	−	2.01593i	0.710494	−	0.0745110i
$733$	44.1203	−	25.4729i	1.62962	−	0.940862i	0.645416	−	0.763832i	$-0.276684\pi$
$733$	44.1203	−	25.4729i	1.62962	−	0.940862i	0.984205	−	0.177031i	$-0.0566492\pi$
$734$	−15.9406	−	27.6100i	−0.588380	−	1.01910i
$735$	5.62295	+	14.1055i	0.207406	+	0.520289i
$736$			6.85192i			0.252565i
$737$	8.19751	+	4.73284i	0.301959	+	0.174336i
$738$	20.3032	−	18.2643i	0.747373	−	0.672316i
$739$	12.6250	−	7.28903i	0.464417	−	0.268131i	−0.249483	−	0.968379i	$-0.580261\pi$
$739$	12.6250	−	7.28903i	0.464417	−	0.268131i	0.713900	+	0.700248i	$0.246927\pi$
$740$	1.89702	+	1.84819i	0.0697360	+	0.0679407i
$741$	−1.93520	−	18.4529i	−0.0710913	−	0.677885i
$742$	−5.14289			−0.188801
$743$		−	13.1396i		−	0.482044i	−0.970520	−	0.241022i	$-0.922517\pi$
$743$		−	13.1396i		−	0.482044i	0.970520	−	0.241022i	$-0.0774825\pi$
$744$	2.97911	+	9.17196i	0.109220	+	0.336260i
$745$	−2.09979	+	2.15528i	−0.0769304	+	0.0789633i
$746$			31.4578i			1.15175i
$747$	29.1434	−	26.2166i	1.06630	−	0.959216i
$748$		−	22.3125i		−	0.815825i
$749$	−6.15458	+	3.55335i	−0.224883	+	0.129837i
$750$	−15.5118	−	11.5924i	−0.566411	−	0.423295i
$751$	12.8502	−	22.2572i	0.468911	−	0.812178i	−0.530457	−	0.847712i	$-0.677980\pi$
$751$	12.8502	−	22.2572i	0.468911	−	0.812178i	0.999368	+	0.0355335i	$0.0113130\pi$
$752$	3.16650			0.115470
$753$	−43.8785	−	19.5481i	−1.59902	−	0.712371i
$754$	−9.46833	−	16.3996i	−0.344816	−	0.597239i
$755$	−39.8342	−	10.1187i	−1.44972	−	0.368259i
$756$	3.58172	−	16.7938i	0.130266	−	0.610784i
$757$	7.82839	+	13.5592i	0.284528	+	0.492817i	0.972495	−	0.232926i	$-0.0748298\pi$
$757$	7.82839	+	13.5592i	0.284528	+	0.492817i	−0.687967	+	0.725742i	$0.741497\pi$
$758$	2.82127	−	4.88658i	0.102473	−	0.177488i
$759$	−38.8496	−	53.4977i	−1.41015	−	1.94184i
$760$	−7.10172	−	6.91889i	−0.257607	−	0.250975i
$761$	6.26230	−	10.8466i	0.227008	−	0.393190i	−0.729912	−	0.683541i	$-0.760439\pi$
$761$	6.26230	−	10.8466i	0.227008	−	0.393190i	0.956920	+	0.290352i	$0.0937723\pi$
$762$	4.22871	+	1.88391i	0.153190	+	0.0682468i
$763$	1.06959	+	0.617530i	0.0387219	+	0.0223561i
$764$	1.15070	−	0.664357i	0.0416309	−	0.0240356i
$765$	14.3483	−	22.7150i	0.518764	−	0.821263i
$766$	5.87647	−	3.39278i	0.212325	−	0.122586i
$767$			17.6993i			0.639086i
$768$	0.180653	+	1.72260i	0.00651876	+	0.0621591i
$769$	−14.0671	+	24.3650i	−0.507274	+	0.878624i	0.492691	+	0.870205i	$0.336013\pi$
$769$	−14.0671	+	24.3650i	−0.507274	+	0.878624i	−0.999965	+	0.00841962i	$0.997320\pi$
$770$	39.8992	+	10.1353i	1.43787	+	0.365249i
$771$	4.83761	−	3.51303i	0.174222	−	0.126519i
$772$	−2.06771	−	1.19379i	−0.0744185	−	0.0429656i
$773$			30.7951i			1.10762i	0.832643	+	0.553811i	$0.186827\pi$
$773$			30.7951i			1.10762i	−0.832643	+	0.553811i	$0.813173\pi$
$774$	3.02526	−	9.29627i	0.108741	−	0.334148i
$775$	−26.6926	−	7.90596i	−0.958827	−	0.283991i
$776$		−	5.20680i		−	0.186913i
$777$	−3.98365	−	5.48567i	−0.142913	−	0.196797i
$778$	−14.6999	+	25.4610i	−0.527017	+	0.912820i
$779$			40.3641i			1.44619i
$780$	−3.46475	−	8.69154i	−0.124058	−	0.311207i
$781$	−54.7521	−	31.6111i	−1.95918	−	1.13113i
$782$	13.7214	−	23.7662i	0.490676	−	0.849876i
$783$	−12.5594	−	38.7447i	−0.448838	−	1.38462i
$784$	1.96037	+	3.39546i	0.0700132	+	0.121266i
$785$	−26.1850	−	6.65154i	−0.934582	−	0.237404i
$786$	−0.340241	+	0.763722i	−0.0121360	+	0.0272411i
$787$	−19.3224	+	33.4674i	−0.688769	+	1.19298i	0.283468	+	0.958982i	$0.408515\pi$
$787$	−19.3224	+	33.4674i	−0.688769	+	1.19298i	−0.972236	+	0.234001i	$0.924818\pi$
$788$	17.8245	−	10.2910i	0.634972	−	0.366601i
$789$	−32.2344	+	3.38049i	−1.14757	+	0.120349i
$790$	19.2038	−	19.7113i	0.683241	−	0.701296i
$791$		−	33.3736i		−	1.18663i
$792$	−11.1774	−	12.4253i	−0.397173	−	0.441513i
$793$	−23.3473	+	13.4796i	−0.829088	+	0.478674i
$794$	12.5146	+	7.22528i	0.444125	+	0.256416i
$795$	−5.59889	+	2.23191i	−0.198572	+	0.0791578i
$796$	−7.88469	+	4.55223i	−0.279465	+	0.161349i
$797$	−26.3740	+	15.2270i	−0.934216	+	0.539370i	−0.888142	−	0.459568i	$-0.848004\pi$
$797$	−26.3740	+	15.2270i	−0.934216	+	0.539370i	−0.0460733	+	0.998938i	$0.514671\pi$
$798$	14.9132	+	20.5362i	0.527923	+	0.726975i
$799$	−10.9831	−	6.34110i	−0.388555	−	0.224332i
$800$	−4.39384	−	2.38624i	−0.155346	−	0.0843663i
$801$	−19.1609	+	4.06359i	−0.677018	+	0.143580i
$802$	−6.38334			−0.225403
$803$	21.6765	−	37.5448i	0.764947	−	1.32493i
$804$	1.72927	+	2.38128i	0.0609865	+	0.0839813i
$805$	36.2659	+	35.3322i	1.27820	+	1.24530i
$806$	−9.00179	−	9.99495i	−0.317075	−	0.352057i
$807$	−25.8688	+	18.7857i	−0.910625	+	0.661288i
$808$		−	19.0964i		−	0.671810i
$809$	9.48886	−	16.4352i	0.333611	−	0.577831i	−0.649606	−	0.760271i	$-0.725066\pi$
$809$	9.48886	−	16.4352i	0.333611	−	0.577831i	0.983217	+	0.182440i	$0.0583996\pi$
$810$	−3.38888	−	19.8372i	−0.119073	−	0.697009i
$811$	−10.6157	−	18.3870i	−0.372768	−	0.645653i	0.617222	−	0.786789i	$-0.288258\pi$
$811$	−10.6157	−	18.3870i	−0.372768	−	0.645653i	−0.989990	+	0.141136i	$0.954925\pi$
$812$	22.4328	+	12.9516i	0.787238	+	0.454512i
$813$	−41.7133	+	4.37457i	−1.46295	+	0.153423i
$814$	−6.59849			−0.231277
$815$	−6.92201	−	1.75834i	−0.242467	−	0.0615919i
$816$	2.82302	−	6.33669i	0.0988254	−	0.221828i
$817$	7.22470	+	12.5136i	0.252760	+	0.437794i
$818$	−4.24890	−	2.45311i	−0.148559	−	0.0857708i
$819$	4.96893	+	23.4299i	0.173629	+	0.818706i
$820$	5.52425	+	19.5913i	0.192915	+	0.684158i
$821$	25.3107			0.883351			0.441676	−	0.897175i	$-0.354384\pi$
$821$	25.3107			0.883351			0.441676	+	0.897175i	$0.354384\pi$
$822$	15.7871	+	21.7396i	0.550639	+	0.758255i
$823$	23.0657	−	39.9510i	0.804021	−	1.39261i	−0.112929	−	0.993603i	$-0.536023\pi$
$823$	23.0657	−	39.9510i	0.804021	−	1.39261i	0.916950	−	0.399002i	$-0.130643\pi$
$824$	−7.70085	+	4.44609i	−0.268272	+	0.154887i
$825$	47.8354	−	6.28156i	1.66542	−	0.218696i
$826$	−12.1053	−	20.9671i	−0.421198	−	0.729537i
$827$	33.4212	−	19.2957i	1.16217	−	0.670978i	0.210346	−	0.977627i	$-0.432541\pi$
$827$	33.4212	−	19.2957i	1.16217	−	0.670978i	0.951823	+	0.306649i	$0.0992077\pi$
$828$	−4.26455	−	20.1085i	−0.148204	−	0.698820i
$829$			12.5198i			0.434829i	0.976079	+	0.217415i	$0.0697624\pi$
$829$			12.5198i			0.434829i	−0.976079	+	0.217415i	$0.930238\pi$
$830$	7.92954	+	28.1215i	0.275238	+	0.976110i
$831$	−1.01299	−	9.65927i	−0.0351402	−	0.335076i
$832$	−1.20794	−	2.09222i	−0.0418778	−	0.0725345i
$833$		−	15.7030i		−	0.544078i
$834$	−1.94645	+	0.204128i	−0.0674001	+	0.00706839i
$835$	−27.3119	+	28.0336i	−0.945168	+	0.970144i
$836$	24.7022			0.854343
$837$	−14.4514	−	25.0631i	−0.499514	−	0.866306i
$838$		−	9.80896i		−	0.338845i
$839$		−	38.3794i		−	1.32500i	−0.749060	−	0.662502i	$-0.769495\pi$
$839$		−	38.3794i		−	1.32500i	0.749060	−	0.662502i	$-0.230505\pi$
$840$	10.0489	+	7.92652i	0.346722	+	0.273491i
$841$	32.4405			1.11864
$842$	−3.94712	−	6.83662i	−0.136027	−	0.235605i
$843$	−2.15720	+	0.226230i	−0.0742978	+	0.00779177i
$844$	1.20286	−	2.08341i	0.0414041	−	0.0717140i
$845$	−11.4732	−	11.1779i	−0.394691	−	0.384530i
$846$	−9.29281	+	1.97079i	−0.319493	+	0.0677571i
$847$	−57.3408	+	33.1057i	−1.97025	+	1.13753i
$848$	−1.34776	+	0.778128i	−0.0462822	+	0.0267210i
$849$	16.0123	−	1.67924i	0.549539	−	0.0576314i
$850$	10.4616	+	17.0757i	0.358831	+	0.585692i
$851$	−7.02840	−	4.05785i	−0.240930	−	0.139101i
$852$	−11.5500	−	15.9048i	−0.395695	−	0.544890i
$853$			20.8163i			0.712737i	0.934346	+	0.356368i	$0.115985\pi$
$853$			20.8163i			0.712737i	−0.934346	+	0.356368i	$0.884015\pi$
$854$	18.4385	−	31.9365i	0.630954	−	1.09284i
$855$	25.1479	+	15.8850i	0.860039	+	0.543257i
$856$	−1.07526	+	1.86240i	−0.0367515	+	0.0636554i
$857$	4.26864	+	7.39350i	0.145814	+	0.252557i	0.929676	−	0.368377i	$-0.120087\pi$
$857$	4.26864	+	7.39350i	0.145814	+	0.252557i	−0.783862	+	0.620935i	$0.786753\pi$
$858$	21.2938	+	9.48648i	0.726960	+	0.323863i
$859$	−16.2675	+	9.39206i	−0.555041	+	0.320453i	−0.751153	−	0.660129i	$-0.770502\pi$
$859$	−16.2675	+	9.39206i	−0.555041	+	0.320453i	0.196112	+	0.980582i	$0.437168\pi$
$860$	5.21922	+	5.08486i	0.177974	+	0.173392i
$861$	−5.43454	−	51.8206i	−0.185209	−	1.76604i
$862$	5.03759	+	2.90845i	0.171581	+	0.0990623i
$863$	27.9444	−	16.1337i	0.951240	−	0.549199i	0.0577739	−	0.998330i	$-0.481600\pi$
$863$	27.9444	−	16.1337i	0.951240	−	0.549199i	0.893466	+	0.449131i	$0.148266\pi$
$864$	−1.60230	−	4.94294i	−0.0545112	−	0.168162i
$865$	−39.7972	+	11.2218i	−1.35314	+	0.381552i
$866$	27.3374			0.928964
$867$	1.34401	−	0.976008i	0.0456449	−	0.0331470i
$868$	17.4997	+	5.68355i	0.593979	+	0.192912i
$869$			68.5625i			2.32582i
$870$	30.0426	+	4.36456i	1.01854	+	0.147973i
$871$	−3.55489	−	2.05242i	−0.120453	−	0.0695435i
$872$	0.373734			0.0126562
$873$	3.24065	+	15.2805i	0.109679	+	0.517168i
$874$	26.3116	+	15.1910i	0.890003	+	0.513843i
$875$	−35.2869	+	10.9510i	−1.19292	+	0.370212i
$876$	10.9063	−	7.92008i	0.368490	−	0.267595i
$877$	−33.9269	+	19.5877i	−1.14563	+	0.661430i	−0.947819	−	0.318810i	$-0.896717\pi$
$877$	−33.9269	+	19.5877i	−1.14563	+	0.661430i	−0.197812	+	0.980240i	$0.563383\pi$
$878$	11.3452	+	19.6505i	0.382882	+	0.663171i
$879$	−30.9047	−	13.7681i	−1.04239	−	0.464388i
$880$	11.9896	−	3.38075i	0.404168	−	0.113965i
$881$	−20.9257	−	36.2444i	−0.705005	−	1.22110i	−0.966690	−	0.255951i	$-0.917612\pi$
$881$	−20.9257	−	36.2444i	−0.705005	−	1.22110i	0.261685	−	0.965153i	$-0.415722\pi$
$882$	−7.86644	−	8.74464i	−0.264877	−	0.294447i
$883$	−26.9336			−0.906388			−0.453194	−	0.891412i	$-0.649715\pi$
$883$	−26.9336			−0.906388			−0.453194	+	0.891412i	$0.649715\pi$
$884$			9.67591i			0.325436i
$885$	−22.2780	−	17.5726i	−0.748865	−	0.590698i
$886$	9.72814	+	16.8496i	0.326823	+	0.566074i
$887$	1.56971	−	2.71882i	0.0527057	−	0.0912890i	−0.838469	−	0.544950i	$-0.816549\pi$
$887$	1.56971	−	2.71882i	0.0527057	−	0.0912890i	0.891175	+	0.453661i	$0.149882\pi$
$888$	−1.87396	−	0.834855i	−0.0628859	−	0.0280159i
$889$	7.64924	−	4.41629i	0.256547	−	0.148118i
$890$	3.59439	−	14.1500i	0.120484	−	0.474308i
$891$	40.5361	+	29.5081i	1.35801	+	0.988558i
$892$	−0.590667	+	1.02306i	−0.0197770	+	0.0342547i
$893$	7.02026	−	12.1594i	0.234924	−	0.406900i
$894$	0.948509	−	2.12907i	0.0317229	−	0.0712067i
$895$	4.04630	+	3.94213i	0.135253	+	0.131771i
$896$	2.86191	+	1.65233i	0.0956098	+	0.0552004i
$897$	16.8473	+	23.1995i	0.562515	+	0.774610i
$898$	−10.3186			−0.344337
$899$	42.6875	−	9.07918i	1.42371	−	0.302808i
$900$	14.3799	+	4.26829i	0.479330	+	0.142276i
$901$	6.23300			0.207651
$902$	−43.9191	−	25.3567i	−1.46235	−	0.844286i
$903$	−10.9601	−	15.0926i	−0.364729	−	0.502249i
$904$	−5.04948	−	8.74596i	−0.167943	−	0.290886i
$905$	6.22395	+	22.0727i	0.206891	+	0.733722i
$906$	31.6618	−	3.32044i	1.05189	−	0.110314i
$907$		−	41.8040i		−	1.38808i	−0.719938	−	0.694039i	$-0.755830\pi$
$907$		−	41.8040i		−	1.38808i	0.719938	−	0.694039i	$-0.244170\pi$
$908$	11.6653	+	20.2050i	0.387128	+	0.670525i
$909$	11.8854	+	56.0428i	0.394213	+	1.85882i
$910$	−17.3025	−	4.39520i	−0.573572	−	0.145700i
$911$	11.8099	−	20.4553i	0.391278	−	0.677713i	−0.601340	−	0.798993i	$-0.705366\pi$
$911$	11.8099	−	20.4553i	0.391278	−	0.677713i	0.992618	+	0.121280i	$0.0386997\pi$
$912$	7.01537	+	3.12537i	0.232302	+	0.103491i
$913$	−63.0418	−	36.3972i	−2.08638	−	1.20457i
$914$	4.31019			0.142568
$915$	6.21361	−	42.7701i	0.205415	−	1.41394i
$916$	24.3330	+	14.0487i	0.803985	+	0.464181i
$917$	0.797599	+	1.38148i	0.0263391	+	0.0456206i
$918$	−4.34091	+	20.3535i	−0.143272	+	0.671765i
$919$	−7.86679	−	13.6257i	−0.259502	−	0.449470i	0.706607	−	0.707606i	$-0.250225\pi$
$919$	−7.86679	−	13.6257i	−0.259502	−	0.449470i	−0.966108	+	0.258136i	$0.916892\pi$
$920$	14.8498	+	3.77216i	0.489582	+	0.124364i
$921$	−5.84544	+	13.1210i	−0.192614	+	0.432351i
$922$	24.1218			0.794410
$923$	23.7435	+	13.7083i	0.781527	+	0.451215i
$924$	−31.7134	+	3.32586i	−1.04329	+	0.109413i
$925$	5.04982	−	3.09383i	0.166037	−	0.101725i
$926$	13.1532			0.432239
$927$	19.8327	−	17.8410i	0.651392	−	0.585975i
$928$	7.83840			0.257308
$929$	−17.9204			−0.587950			−0.293975	−	0.955813i	$-0.594978\pi$
$929$	−17.9204			−0.587950			−0.293975	+	0.955813i	$0.594978\pi$
$930$	21.5179	−	1.40705i	0.705600	−	0.0461390i
$931$	17.3849			0.569767
$932$	−1.85618			−0.0608012
$933$	−26.5984	+	2.78943i	−0.870792	+	0.0913218i
$934$	28.4663			0.931445
$935$	−48.3564	−	12.2836i	−1.58142	−	0.401716i
$936$	4.84715	+	5.38828i	0.158434	+	0.176121i
$937$	−20.0137	−	11.5549i	−0.653820	−	0.377483i	0.136098	−	0.990695i	$-0.456544\pi$
$937$	−20.0137	−	11.5549i	−0.653820	−	0.377483i	−0.789918	+	0.613212i	$0.789877\pi$
$938$	5.61495			0.183335
$939$	−14.9119	−	6.64332i	−0.486633	−	0.216797i
$940$	1.74324	−	6.86255i	0.0568581	−	0.223832i
$941$	−18.3804	−	31.8358i	−0.599183	−	1.03782i	−0.992942	−	0.118602i	$-0.962159\pi$
$941$	−18.3804	−	31.8358i	−0.599183	−	1.03782i	0.393758	−	0.919214i	$-0.371175\pi$
$942$	20.8128	−	2.18269i	0.678118	−	0.0711157i
$943$	−31.1870	−	54.0175i	−1.01559	−	1.75905i
$944$	−6.34470	−	3.66312i	−0.206503	−	0.119224i
$945$	−34.4243	−	17.0078i	−1.11982	−	0.553265i
$946$	−18.1542			−0.590245
$947$	29.0255	+	16.7579i	0.943201	+	0.544557i	0.890962	−	0.454078i	$-0.150031\pi$
$947$	29.0255	+	16.7579i	0.943201	+	0.544557i	0.0522384	+	0.998635i	$0.483364\pi$
$948$	−8.67466	+	19.4716i	−0.281740	+	0.632408i
$949$	−9.40012	+	16.2815i	−0.305141	+	0.528519i
$950$	−18.9046	+	11.5821i	−0.613345	+	0.375773i
$951$	3.45446	+	1.53898i	0.112019	+	0.0499047i
$952$	−6.61777	−	11.4623i	−0.214483	−	0.371496i
$953$			23.6471i			0.766004i	0.923748	+	0.383002i	$0.125110\pi$
$953$			23.6471i			0.766004i	−0.923748	+	0.383002i	$0.874890\pi$
$954$	3.47100	−	3.12242i	0.112378	−	0.101092i
$955$	−0.806331	−	2.85959i	−0.0260923	−	0.0925341i
$956$	−10.6369	−	18.4237i	−0.344022	−	0.595864i
$957$	−61.1998	+	44.4428i	−1.97831	+	1.43663i
$958$	−31.9232	−	18.4309i	−1.03139	−	0.595475i
$959$	51.2610			1.65530
$960$	3.83275	+	0.556818i	0.123701	+	0.0179712i
$961$	28.3167	−	12.6160i	0.913442	−	0.406969i
$962$	2.86147			0.0922575
$963$	1.99645	−	6.13486i	0.0643347	−	0.197693i
$964$	−25.2426	−	14.5738i	−0.813008	−	0.469390i
$965$	−3.72556	+	3.82401i	−0.119930	+	0.123099i
$966$	−35.8249	−	15.9601i	−1.15265	−	0.513509i
$967$	26.6045	−	46.0803i	0.855543	−	1.48184i	−0.0205973	−	0.999788i	$-0.506557\pi$
$967$	26.6045	−	46.0803i	0.855543	−	1.48184i	0.876140	−	0.482056i	$-0.160110\pi$
$968$	−10.0179	+	17.3515i	−0.321988	+	0.557699i
$969$	−18.0743	−	24.8892i	−0.580631	−	0.799556i
$970$	−11.2844	−	2.86647i	−0.362320	−	0.0920369i
$971$	−20.0716	+	11.5883i	−0.644128	+	0.371888i	−0.786203	−	0.617968i	$-0.787956\pi$
$971$	−20.0716	+	11.5883i	−0.644128	+	0.371888i	0.142075	+	0.989856i	$0.454623\pi$
$972$	7.77873	+	13.5089i	0.249503	+	0.433299i
$973$	−1.86704	+	3.23381i	−0.0598546	+	0.103671i
$974$	16.7504	+	29.0126i	0.536719	+	0.929624i
$975$	−20.7441	+	2.72403i	−0.664342	+	0.0872388i
$976$		−	11.1591i		−	0.357195i
$977$	2.63050			0.0841571			0.0420786	−	0.999114i	$-0.486602\pi$
$977$	2.63050			0.0841571			0.0420786	+	0.999114i	$0.486602\pi$
$978$	5.50188	−	0.576994i	0.175931	−	0.0184502i
$979$	18.1865	+	31.5000i	0.581244	+	1.00674i
$980$	8.43800	−	2.37930i	0.269542	−	0.0760040i
$981$	−1.09681	+	0.232607i	−0.0350184	+	0.00742658i
$982$	6.16407	+	10.6765i	0.196703	+	0.340700i
$983$	2.24131	−	1.29402i	0.0714867	−	0.0412729i	−0.463831	−	0.885924i	$-0.653525\pi$
$983$	2.24131	−	1.29402i	0.0714867	−	0.0412729i	0.535317	+	0.844651i	$0.320192\pi$
$984$	−9.26474	−	12.7580i	−0.295349	−	0.406710i
$985$	−12.4902	−	44.2954i	−0.397971	−	1.41137i
$986$	−27.1878	−	15.6969i	−0.865836	−	0.499891i
$987$	−7.37569	+	16.5558i	−0.234771	+	0.526978i
$988$	−10.7122			−0.340801
$989$	−19.3370	−	11.1642i	−0.614881	−	0.355002i
$990$	−33.0820	+	17.3838i	−1.05141	+	0.552492i
$991$			11.9614i			0.379966i	0.981787	+	0.189983i	$0.0608433\pi$
$991$			11.9614i			0.379966i	−0.981787	+	0.189983i	$0.939157\pi$
$992$	5.44595	−	1.15829i	0.172909	−	0.0367759i
$993$	13.9166	+	19.1638i	0.441629	+	0.608143i
$994$	−37.5028			−1.18952
$995$	5.52504	+	19.5941i	0.175156	+	0.621175i
$996$	−13.2987	−	18.3129i	−0.421384	−	0.580266i
$997$	50.3545	−	29.0722i	1.59474	−	0.920725i	0.602266	−	0.798296i	$-0.294265\pi$
$997$	50.3545	−	29.0722i	1.59474	−	0.920725i	0.992477	−	0.122430i	$-0.0390686\pi$
$998$	−20.8127	−	12.0162i	−0.658815	−	0.380367i
$999$	6.01916	+	1.28374i	0.190438	+	0.0406159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.r.b.119.16	yes	64
3.2	odd	2		930.2.r.a.119.6	✓	64
5.4	even	2		930.2.r.a.119.17	yes	64
15.14	odd	2	inner	930.2.r.b.119.27	yes	64
31.6	odd	6	inner	930.2.r.b.719.27	yes	64
93.68	even	6		930.2.r.a.719.17	yes	64
155.99	odd	6		930.2.r.a.719.6	yes	64
465.254	even	6	inner	930.2.r.b.719.16	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.r.a.119.6	✓	64	3.2	odd	2
930.2.r.a.119.17	yes	64	5.4	even	2
930.2.r.a.719.6	yes	64	155.99	odd	6
930.2.r.a.719.17	yes	64	93.68	even	6
930.2.r.b.119.16	yes	64	1.1	even	1	trivial
930.2.r.b.119.27	yes	64	15.14	odd	2	inner
930.2.r.b.719.16	yes	64	465.254	even	6	inner
930.2.r.b.719.27	yes	64	31.6	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.180653 + 1.72260i) q^{3} +1.00000 q^{4} +(0.550525 - 2.16724i) q^{5} +(0.180653 + 1.72260i) q^{6} +(2.86191 + 1.65233i) q^{7} +1.00000 q^{8} +(-2.93473 + 0.622388i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.180653 + 1.72260i) q^{3} +1.00000 q^{4} +(0.550525 - 2.16724i) q^{5} +(0.180653 + 1.72260i) q^{6} +(2.86191 + 1.65233i) q^{7} +1.00000 q^{8} +(-2.93473 + 0.622388i) q^{9} +(0.550525 - 2.16724i) q^{10} +(2.78549 + 4.82461i) q^{11} +(0.180653 + 1.72260i) q^{12} +(-1.20794 - 2.09222i) q^{13} +(2.86191 + 1.65233i) q^{14} +(3.83275 + 0.556818i) q^{15} +1.00000 q^{16} +(-3.46854 - 2.00256i) q^{17} +(-2.93473 + 0.622388i) q^{18} +(2.21704 - 3.84003i) q^{19} +(0.550525 - 2.16724i) q^{20} +(-2.32929 + 5.22844i) q^{21} +(2.78549 + 4.82461i) q^{22} +6.85192i q^{23} +(0.180653 + 1.72260i) q^{24} +(-4.39384 - 2.38624i) q^{25} +(-1.20794 - 2.09222i) q^{26} +(-1.60230 - 4.94294i) q^{27} +(2.86191 + 1.65233i) q^{28} +7.83840 q^{29} +(3.83275 + 0.556818i) q^{30} +(5.44595 - 1.15829i) q^{31} +1.00000 q^{32} +(-7.80769 + 5.66988i) q^{33} +(-3.46854 - 2.00256i) q^{34} +(5.15654 - 5.29280i) q^{35} +(-2.93473 + 0.622388i) q^{36} +(-0.592220 + 1.02576i) q^{37} +(2.21704 - 3.84003i) q^{38} +(3.38584 - 2.45877i) q^{39} +(0.550525 - 2.16724i) q^{40} +(-7.88355 + 4.55157i) q^{41} +(-2.32929 + 5.22844i) q^{42} +(-1.62936 + 2.82213i) q^{43} +(2.78549 + 4.82461i) q^{44} +(-0.266779 + 6.70290i) q^{45} +6.85192i q^{46} +3.16650 q^{47} +(0.180653 + 1.72260i) q^{48} +(1.96037 + 3.39546i) q^{49} +(-4.39384 - 2.38624i) q^{50} +(2.82302 - 6.33669i) q^{51} +(-1.20794 - 2.09222i) q^{52} +(-1.34776 + 0.778128i) q^{53} +(-1.60230 - 4.94294i) q^{54} +(11.9896 - 3.38075i) q^{55} +(2.86191 + 1.65233i) q^{56} +(7.01537 + 3.12537i) q^{57} +7.83840 q^{58} +(-6.34470 - 3.66312i) q^{59} +(3.83275 + 0.556818i) q^{60} -11.1591i q^{61} +(5.44595 - 1.15829i) q^{62} +(-9.42733 - 3.06791i) q^{63} +1.00000 q^{64} +(-5.19933 + 1.46608i) q^{65} +(-7.80769 + 5.66988i) q^{66} +(1.47147 - 0.849552i) q^{67} +(-3.46854 - 2.00256i) q^{68} +(-11.8031 + 1.23782i) q^{69} +(5.15654 - 5.29280i) q^{70} +(-9.82808 + 5.67425i) q^{71} +(-2.93473 + 0.622388i) q^{72} +(-3.89097 - 6.73935i) q^{73} +(-0.592220 + 1.02576i) q^{74} +(3.31678 - 7.99994i) q^{75} +(2.21704 - 3.84003i) q^{76} +18.4102i q^{77} +(3.38584 - 2.45877i) q^{78} +(10.6582 + 6.15354i) q^{79} +(0.550525 - 2.16724i) q^{80} +(8.22527 - 3.65308i) q^{81} +(-7.88355 + 4.55157i) q^{82} +(-11.3161 + 6.53335i) q^{83} +(-2.32929 + 5.22844i) q^{84} +(-6.24955 + 6.41469i) q^{85} +(-1.62936 + 2.82213i) q^{86} +(1.41603 + 13.5025i) q^{87} +(2.78549 + 4.82461i) q^{88} +6.52903 q^{89} +(-0.266779 + 6.70290i) q^{90} -7.98366i q^{91} +6.85192i q^{92} +(2.97911 + 9.17196i) q^{93} +3.16650 q^{94} +(-7.10172 - 6.91889i) q^{95} +(0.180653 + 1.72260i) q^{96} -5.20680i q^{97} +(1.96037 + 3.39546i) q^{98} +(-11.1774 - 12.4253i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) \) 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9	\( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) \) 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^20 + 2 * q^25 + 18 * q^31 + 64 * q^32 - 8 * q^33 + 6 * q^34 + 16 * q^35 - 4 * q^36 + 4 * q^38 - 8 * q^39 + 2 * q^40 + 9 * q^45 - 4 * q^47 + 30 * q^49 + 2 * q^50 - 8 * q^51 - 6 * q^53 + 6 * q^57 + 18 * q^62 + 12 * q^63 + 64 * q^64 - 8 * q^66 + 6 * q^68 - 10 * q^69 + 16 * q^70 - 4 * q^72 - 63 * q^75 + 4 * q^76 - 8 * q^78 - 30 * q^79 + 2 * q^80 - 12 * q^81 - 54 * q^83 - 16 * q^87 + 9 * q^90 - 18 * q^93 - 4 * q^94 - 56 * q^95 + 30 * q^98 - 102 * q^99

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