LMFDB - Embedded newform 684.2.o.a.11.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(11,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 4]))

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

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

chi := DirichletCharacter("684.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$684 = 2^{2} \cdot 3^{2} \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	684.o (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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$232$
Relative dimension:	$116$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	684.11
Dual form			684.2.o.a.311.19

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23750 - 0.684543i) q^{2} +(-0.706340 - 1.58148i) q^{3} +(1.06280 + 1.69424i) q^{4} -3.02562i q^{5} +(-0.208498 + 2.44060i) q^{6} +(-3.37115 - 1.94633i) q^{7} +(-0.155435 - 2.82415i) q^{8} +(-2.00217 + 2.23413i) q^{9} +(-2.07117 + 3.74420i) q^{10} +(-1.50566 + 2.60787i) q^{11} +(1.92871 - 2.87751i) q^{12} +(-2.00787 + 3.47774i) q^{13} +(2.83944 + 4.71628i) q^{14} +(-4.78496 + 2.13712i) q^{15} +(-1.74090 + 3.60129i) q^{16} +(4.32629 + 2.49779i) q^{17} +(4.00703 - 1.39416i) q^{18} +(-2.72273 - 3.40393i) q^{19} +(5.12613 - 3.21563i) q^{20} +(-0.696914 + 6.70618i) q^{21} +(3.64845 - 2.19655i) q^{22} +(2.39004 - 4.13967i) q^{23} +(-4.35656 + 2.24063i) q^{24} -4.15438 q^{25} +(4.86540 - 2.92922i) q^{26} +(4.94744 + 1.58834i) q^{27} +(-0.285305 - 7.78010i) q^{28} +0.434362i q^{29} +(7.38433 + 0.630836i) q^{30} +(-2.21690 + 1.27993i) q^{31} +(4.61960 - 3.26486i) q^{32} +(5.18781 + 0.539123i) q^{33} +(-3.64394 - 6.05254i) q^{34} +(-5.88886 + 10.1998i) q^{35} +(-5.91306 - 1.01772i) q^{36} -3.09614 q^{37} +(1.03924 + 6.07618i) q^{38} +(6.91822 + 0.718950i) q^{39} +(-8.54481 + 0.470286i) q^{40} -0.413929i q^{41} +(5.45309 - 7.82181i) q^{42} +(1.63331 - 0.942994i) q^{43} +(-6.01858 + 0.220709i) q^{44} +(6.75962 + 6.05780i) q^{45} +(-5.79146 + 3.48675i) q^{46} -12.3628 q^{47} +(6.92504 + 0.209477i) q^{48} +(4.07641 + 7.06056i) q^{49} +(5.14103 + 2.84385i) q^{50} +(0.894370 - 8.60624i) q^{51} +(-8.02610 + 0.294327i) q^{52} +(9.32144 - 5.38174i) q^{53} +(-5.03516 - 5.35230i) q^{54} +(7.89043 + 4.55554i) q^{55} +(-4.97275 + 9.82316i) q^{56} +(-3.46008 + 6.71028i) q^{57} +(0.297339 - 0.537522i) q^{58} +10.5919 q^{59} +(-8.70626 - 5.83555i) q^{60} -6.42411 q^{61} +(3.61958 - 0.0663448i) q^{62} +(11.0980 - 3.63468i) q^{63} +(-7.95168 + 0.877943i) q^{64} +(10.5223 + 6.07506i) q^{65} +(-6.05085 - 4.21844i) q^{66} +(11.1698 + 6.44889i) q^{67} +(0.366141 + 9.98443i) q^{68} +(-8.23500 - 0.855791i) q^{69} +(14.2697 - 8.59106i) q^{70} +(-4.86918 + 8.43367i) q^{71} +(6.62072 + 5.30717i) q^{72} +(0.298078 - 0.516286i) q^{73} +(3.83146 + 2.11944i) q^{74} +(2.93440 + 6.57007i) q^{75} +(2.87335 - 8.23067i) q^{76} +(10.1516 - 5.86101i) q^{77} +(-8.06913 - 5.62552i) q^{78} +(-11.6679 + 6.73648i) q^{79} +(10.8961 + 5.26731i) q^{80} +(-0.982644 - 8.94620i) q^{81} +(-0.283352 + 0.512236i) q^{82} +(-1.87399 + 3.24584i) q^{83} +(-12.1026 + 5.94660i) q^{84} +(7.55735 - 13.0897i) q^{85} +(-2.66674 + 0.0488799i) q^{86} +(0.686935 - 0.306807i) q^{87} +(7.59906 + 3.84685i) q^{88} +(-12.3615 + 7.13690i) q^{89} +(-4.21819 - 12.1238i) q^{90} +(13.5377 - 7.81597i) q^{91} +(9.55374 - 0.350347i) q^{92} +(3.59007 + 2.60193i) q^{93} +(15.2989 + 8.46284i) q^{94} +(-10.2990 + 8.23795i) q^{95} +(-8.42632 - 4.99971i) q^{96} +(-1.43496 - 2.48542i) q^{97} +(-0.211300 - 11.5279i) q^{98} +(-2.81174 - 8.58523i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$232 q - 3 q^{2} + q^{4} + 3 q^{6} + 2 q^{10} - q^{12} + 2 q^{13} + q^{16} - 12 q^{17} - 16 q^{18} - 27 q^{20} - 14 q^{21} + 6 q^{22} - 10 q^{24} - 204 q^{25} - 6 q^{28} - 9 q^{30} - 3 q^{32} - 12 q^{33}+ \cdots - 162 q^{98}+O(q^{100})$ 232 * q - 3 * q^2 + q^4 + 3 * q^6 + 2 * q^10 - q^12 + 2 * q^13 + q^16 - 12 * q^17 - 16 * q^18 - 27 * q^20 - 14 * q^21 + 6 * q^22 - 10 * q^24 - 204 * q^25 - 6 * q^28 - 9 * q^30 - 3 * q^32 - 12 * q^33 + 2 * q^34 + 13 * q^36 - 16 * q^37 - 3 * q^38 - 16 * q^40 - 43 * q^42 + 21 * q^44 + 2 * q^45 - 24 * q^46 + 58 * q^48 + 88 * q^49 + 9 * q^50 + 17 * q^52 + 41 * q^54 - 48 * q^56 - 12 * q^57 + 2 * q^58 + 16 * q^60 - 4 * q^61 + 6 * q^62 + 16 * q^64 + 12 * q^65 - 27 * q^66 - 18 * q^68 - 14 * q^69 + 60 * q^70 + 15 * q^72 + 2 * q^73 - 30 * q^74 + 3 * q^76 - 12 * q^77 - 64 * q^78 + 54 * q^80 + 4 * q^81 + 2 * q^82 - 10 * q^84 + 22 * q^85 + 51 * q^86 - 18 * q^88 + 14 * q^90 + 57 * q^92 + 4 * q^93 - 6 * q^94 - 17 * q^96 - 4 * q^97 - 162 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$ .

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

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

)

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

$2$	−1.23750	−	0.684543i	−0.875043	−	0.484045i
$2$	−1.23750	−	0.684543i	−0.875043	−	0.484045i
$3$	−0.706340	−	1.58148i	−0.407805	−	0.913069i
$3$	−0.706340	−	1.58148i	−0.407805	−	0.913069i
$4$	1.06280	+	1.69424i	0.531401	+	0.847120i
$5$		−	3.02562i		−	1.35310i	−0.736397	−	0.676549i	$-0.763475\pi$
$5$		−	3.02562i		−	1.35310i	0.736397	−	0.676549i	$-0.236525\pi$
$6$	−0.208498	+	2.44060i	−0.0851190	+	0.996371i
$7$	−3.37115	−	1.94633i	−1.27417	−	0.735644i	−0.298403	−	0.954440i	$-0.596454\pi$
$7$	−3.37115	−	1.94633i	−1.27417	−	0.735644i	−0.975771	+	0.218796i	$0.929787\pi$
$8$	−0.155435	−	2.82415i	−0.0549545	−	0.998489i
$9$	−2.00217	+	2.23413i	−0.667389	+	0.744709i
$10$	−2.07117	+	3.74420i	−0.654960	+	1.18402i
$11$	−1.50566	+	2.60787i	−0.453972	+	0.786303i	−0.998628	−	0.0523562i	$-0.983327\pi$
$11$	−1.50566	+	2.60787i	−0.453972	+	0.786303i	0.544656	+	0.838660i	$0.316660\pi$
$12$	1.92871	−	2.87751i	0.556771	−	0.830666i
$13$	−2.00787	+	3.47774i	−0.556884	+	0.964551i	0.440870	+	0.897571i	$0.354670\pi$
$13$	−2.00787	+	3.47774i	−0.556884	+	0.964551i	−0.997754	+	0.0669803i	$0.978664\pi$
$14$	2.83944	+	4.71628i	0.758872	+	1.26048i
$15$	−4.78496	+	2.13712i	−1.23547	+	0.551801i
$16$	−1.74090	+	3.60129i	−0.435226	+	0.900321i
$17$	4.32629	+	2.49779i	1.04928	+	0.605802i	0.922448	−	0.386122i	$-0.126186\pi$
$17$	4.32629	+	2.49779i	1.04928	+	0.605802i	0.126832	+	0.991924i	$0.459519\pi$
$18$	4.00703	−	1.39416i	0.944467	−	0.328606i
$19$	−2.72273	−	3.40393i	−0.624637	−	0.780915i
$19$	−2.72273	−	3.40393i	−0.624637	−	0.780915i
$20$	5.12613	−	3.21563i	1.14624	−	0.719038i
$21$	−0.696914	+	6.70618i	−0.152079	+	1.46341i
$22$	3.64845	−	2.19655i	0.777852	−	0.468306i
$23$	2.39004	−	4.13967i	0.498358	−	0.863182i	−0.501640	−	0.865076i	$-0.667270\pi$
$23$	2.39004	−	4.13967i	0.498358	−	0.863182i	0.999998	+	0.00189485i	$0.000603151\pi$
$24$	−4.35656	+	2.24063i	−0.889278	+	0.457366i
$25$	−4.15438			−0.830875
$26$	4.86540	−	2.92922i	0.954183	−	0.574467i
$27$	4.94744	+	1.58834i	0.952136	+	0.305676i
$28$	−0.285305	−	7.78010i	−0.0539177	−	1.47030i
$29$			0.434362i			0.0806590i	0.999186	+	0.0403295i	$0.0128408\pi$
$29$			0.434362i			0.0806590i	−0.999186	+	0.0403295i	$0.987159\pi$
$30$	7.38433	+	0.630836i	1.34819	+	0.115174i
$31$	−2.21690	+	1.27993i	−0.398167	+	0.229882i	−0.685693	−	0.727891i	$-0.740501\pi$
$31$	−2.21690	+	1.27993i	−0.398167	+	0.229882i	0.287525	+	0.957773i	$0.407167\pi$
$32$	4.61960	−	3.26486i	0.816637	−	0.577151i
$33$	5.18781	+	0.539123i	0.903081	+	0.0938493i
$34$	−3.64394	−	6.05254i	−0.624930	−	1.03800i
$35$	−5.88886	+	10.1998i	−0.995399	+	1.72408i
$36$	−5.91306	−	1.01772i	−0.985510	−	0.169620i
$37$	−3.09614			−0.509002			−0.254501	−	0.967073i	$-0.581911\pi$
$37$	−3.09614			−0.509002			−0.254501	+	0.967073i	$0.581911\pi$
$38$	1.03924	+	6.07618i	0.168587	+	0.985687i
$39$	6.91822	+	0.718950i	1.10780	+	0.115124i
$40$	−8.54481	+	0.470286i	−1.35105	+	0.0743588i
$41$		−	0.413929i		−	0.0646449i	−0.999477	−	0.0323224i	$-0.989710\pi$
$41$		−	0.413929i		−	0.0646449i	0.999477	−	0.0323224i	$-0.0102903\pi$
$42$	5.45309	−	7.82181i	0.841431	−	1.20693i
$43$	1.63331	−	0.942994i	0.249078	−	0.143805i	−0.370264	−	0.928927i	$-0.620733\pi$
$43$	1.63331	−	0.942994i	0.249078	−	0.143805i	0.619342	+	0.785121i	$0.287399\pi$
$44$	−6.01858	+	0.220709i	−0.907335	+	0.0332731i
$45$	6.75962	+	6.05780i	1.00766	+	0.903044i
$46$	−5.79146	+	3.48675i	−0.853904	+	0.514093i
$47$	−12.3628			−1.80329			−0.901647	−	0.432474i	$-0.857641\pi$
$47$	−12.3628			−1.80329			−0.901647	+	0.432474i	$0.857641\pi$
$48$	6.92504	+	0.209477i	0.999543	+	0.0302353i
$49$	4.07641	+	7.06056i	0.582345	+	1.00865i
$50$	5.14103	+	2.84385i	0.727052	+	0.402181i
$51$	0.894370	−	8.60624i	0.125237	−	1.20511i
$52$	−8.02610	+	0.294327i	−1.11302	+	0.0408158i
$53$	9.32144	−	5.38174i	1.28040	−	0.739238i	0.303477	−	0.952839i	$-0.401852\pi$
$53$	9.32144	−	5.38174i	1.28040	−	0.739238i	0.976921	+	0.213600i	$0.0685190\pi$
$54$	−5.03516	−	5.35230i	−0.685199	−	0.728356i
$55$	7.89043	+	4.55554i	1.06395	+	0.614269i
$56$	−4.97275	+	9.82316i	−0.664511	+	1.31267i
$57$	−3.46008	+	6.71028i	−0.458299	+	0.888798i
$58$	0.297339	−	0.537522i	0.0390426	−	0.0705801i
$59$	10.5919			1.37895			0.689477	−	0.724308i	$-0.257840\pi$
$59$	10.5919			1.37895			0.689477	+	0.724308i	$0.257840\pi$
$60$	−8.70626	−	5.83555i	−1.12397	−	0.753366i
$61$	−6.42411			−0.822524			−0.411262	−	0.911517i	$-0.634912\pi$
$61$	−6.42411			−0.822524			−0.411262	+	0.911517i	$0.634912\pi$
$62$	3.61958	−	0.0663448i	0.459687	−	0.00842580i
$63$	11.0980	−	3.63468i	1.39821	−	0.457927i
$64$	−7.95168	+	0.877943i	−0.993960	+	0.109743i
$65$	10.5223	+	6.07506i	1.30513	+	0.753519i
$66$	−6.05085	−	4.21844i	−0.744808	−	0.519254i
$67$	11.1698	+	6.44889i	1.36461	+	0.787858i	0.990233	−	0.139420i	$-0.0445237\pi$
$67$	11.1698	+	6.44889i	1.36461	+	0.787858i	0.374376	+	0.927277i	$0.377857\pi$
$68$	0.366141	+	9.98443i	0.0444011	+	1.21079i
$69$	−8.23500	−	0.855791i	−0.991377	−	0.103025i
$70$	14.2697	−	8.59106i	1.70555	−	1.02683i
$71$	−4.86918	+	8.43367i	−0.577866	+	1.00089i	0.417858	+	0.908512i	$0.362781\pi$
$71$	−4.86918	+	8.43367i	−0.577866	+	1.00089i	−0.995724	+	0.0923804i	$0.970552\pi$
$72$	6.62072	+	5.30717i	0.780260	+	0.625456i
$73$	0.298078	−	0.516286i	0.0348874	−	0.0604267i	−0.848055	−	0.529909i	$-0.822226\pi$
$73$	0.298078	−	0.516286i	0.0348874	−	0.0604267i	0.882942	+	0.469482i	$0.155559\pi$
$74$	3.83146	+	2.11944i	0.445398	+	0.246380i
$75$	2.93440	+	6.57007i	0.338835	+	0.758646i
$76$	2.87335	−	8.23067i	0.329596	−	0.944122i
$77$	10.1516	−	5.86101i	1.15688	−	0.667924i
$78$	−8.06913	−	5.62552i	−0.913649	−	0.636964i
$79$	−11.6679	+	6.73648i	−1.31274	+	0.757913i	−0.982550	−	0.185999i	$-0.940448\pi$
$79$	−11.6679	+	6.73648i	−1.31274	+	0.757913i	−0.330195	+	0.943913i	$0.607114\pi$
$80$	10.8961	+	5.26731i	1.21822	+	0.588904i
$81$	−0.982644	−	8.94620i	−0.109183	−	0.994022i
$82$	−0.283352	+	0.512236i	−0.0312910	+	0.0565670i
$83$	−1.87399	+	3.24584i	−0.205697	+	0.356277i	−0.950354	−	0.311169i	$-0.899279\pi$
$83$	−1.87399	+	3.24584i	−0.205697	+	0.356277i	0.744658	+	0.667446i	$0.232613\pi$
$84$	−12.1026	+	5.94660i	−1.32050	+	0.648827i
$85$	7.55735	−	13.0897i	0.819710	−	1.41978i
$86$	−2.66674	+	0.0488799i	−0.287562	+	0.00527085i
$87$	0.686935	−	0.306807i	0.0736472	−	0.0328932i
$88$	7.59906	+	3.84685i	0.810063	+	0.410076i
$89$	−12.3615	+	7.13690i	−1.31031	+	0.756510i	−0.982148	−	0.188111i	$-0.939764\pi$
$89$	−12.3615	+	7.13690i	−1.31031	+	0.756510i	−0.328165	+	0.944620i	$0.606430\pi$
$90$	−4.21819	−	12.1238i	−0.444636	−	1.27796i
$91$	13.5377	−	7.81597i	1.41913	−	0.819337i
$92$	9.55374	−	0.350347i	0.996047	−	0.0365262i
$93$	3.59007	+	2.60193i	0.372273	+	0.269807i
$94$	15.2989	+	8.46284i	1.57796	+	0.872875i
$95$	−10.2990	+	8.23795i	−1.05665	+	0.845196i
$96$	−8.42632	−	4.99971i	−0.860008	−	0.510281i
$97$	−1.43496	−	2.48542i	−0.145698	−	0.252357i	0.783935	−	0.620843i	$-0.213210\pi$
$97$	−1.43496	−	2.48542i	−0.145698	−	0.252357i	−0.929633	+	0.368486i	$0.879876\pi$
$98$	−0.211300	−	11.5279i	−0.0213445	−	1.16449i
$99$	−2.81174	−	8.58523i	−0.282591	−	0.862848i
$100$	−4.41528	−	7.03851i	−0.441528	−	0.703851i
$101$			5.37149i			0.534483i	0.963630	+	0.267241i	$0.0861121\pi$
$101$			5.37149i			0.534483i	−0.963630	+	0.267241i	$0.913888\pi$
$102$	−6.99812	+	10.0380i	−0.692917	+	0.993907i
$103$	−7.02928	+	4.05836i	−0.692615	+	0.399882i	−0.804591	−	0.593829i	$-0.797615\pi$
$103$	−7.02928	+	4.05836i	−0.692615	+	0.399882i	0.111976	+	0.993711i	$0.464282\pi$
$104$	10.1338	+	5.12998i	0.993697	+	0.503036i
$105$	20.2903	+	2.10860i	1.98013	+	0.205778i
$106$	−15.2193	+	0.278961i	−1.47823	+	0.0270951i
$107$	6.23445			0.602707			0.301354	−	0.953512i	$-0.402562\pi$
$107$	6.23445			0.602707			0.301354	+	0.953512i	$0.402562\pi$
$108$	2.56712	+	10.0702i	0.247021	+	0.969010i
$109$	−8.83890	+	15.3094i	−0.846613	+	1.46638i	0.0376005	+	0.999293i	$0.488029\pi$
$109$	−8.83890	+	15.3094i	−0.846613	+	1.46638i	−0.884213	+	0.467083i	$0.845305\pi$
$110$	−6.64593	−	11.0388i	−0.633664	−	1.05251i
$111$	2.18692	+	4.89648i	0.207574	+	0.464754i
$112$	12.8781	−	8.75208i	1.21687	−	0.826994i
$113$	−10.0674	+	5.81240i	−0.947058	+	0.546784i	−0.892166	−	0.451708i	$-0.850815\pi$
$113$	−10.0674	+	5.81240i	−0.947058	+	0.546784i	−0.0548923	+	0.998492i	$0.517482\pi$
$114$	8.87531	−	5.93539i	0.831249	−	0.555900i
$115$	−12.5251	−	7.23136i	−1.16797	−	0.674328i
$116$	−0.735914	+	0.461641i	−0.0683279	+	0.0428623i
$117$	−3.74961	−	11.4489i	−0.346651	−	1.05845i
$118$	−13.1075	−	7.25064i	−1.20664	−	0.667476i
$119$	−9.72304	−	16.8408i	−0.891310	−	1.54379i
$120$	6.77929	+	13.1813i	0.618862	+	1.20328i
$121$	0.965999	+	1.67316i	0.0878181	+	0.152105i
$122$	7.94983	+	4.39758i	0.719744	+	0.398138i
$123$	−0.654621	+	0.292375i	−0.0590252	+	0.0263625i
$124$	−4.52464	−	2.39566i	−0.406324	−	0.215136i
$125$		−	2.55854i		−	0.228843i
$126$	−16.2218	−	3.09911i	−1.44515	−	0.276091i
$127$	−5.52271	+	3.18854i	−0.490062	+	0.282937i	−0.724600	−	0.689170i	$-0.757975\pi$
$127$	−5.52271	+	3.18854i	−0.490062	+	0.282937i	0.234538	+	0.972107i	$0.424642\pi$
$128$	10.4412	+	4.35681i	0.922878	+	0.385092i
$129$	−2.64500	−	1.91698i	−0.232880	−	0.168781i
$130$	−8.86270	−	14.7209i	−0.777310	−	1.29110i
$131$	−9.96122			−0.870316			−0.435158	−	0.900354i	$-0.643307\pi$
$131$	−9.96122			−0.870316			−0.435158	+	0.900354i	$0.643307\pi$
$132$	4.60021	+	9.36238i	0.400397	+	0.814890i
$133$	2.55355	+	16.7745i	0.221421	+	1.45453i
$134$	−9.40807	−	15.6267i	−0.812734	−	1.34994i
$135$	4.80571	−	14.9691i	0.413610	−	1.28833i
$136$	6.38167	−	12.6064i	0.547224	−	1.08099i
$137$		−	17.9170i		−	1.53075i	−0.643585	−	0.765375i	$-0.722554\pi$
$137$		−	17.9170i		−	1.53075i	0.643585	−	0.765375i	$-0.277446\pi$
$138$	9.60497	+	6.69625i	0.817629	+	0.570023i
$139$	−12.9933	−	7.50170i	−1.10208	−	0.636286i	−0.165313	−	0.986241i	$-0.552863\pi$
$139$	−12.9933	−	7.50170i	−1.10208	−	0.636286i	−0.936766	+	0.349955i	$0.886197\pi$
$140$	−23.5396	+	0.863226i	−1.98946	+	0.0729559i
$141$	8.73231	+	19.5515i	0.735393	+	1.64653i
$142$	11.7988	−	7.10349i	0.990134	−	0.596111i
$143$	−6.04633	−	10.4726i	−0.505620	−	0.875759i
$144$	−4.56014	−	11.0998i	−0.380012	−	0.924982i
$145$	1.31421			0.109140
$146$	−0.722290	+	0.434856i	−0.0597772	+	0.0359889i
$147$	8.28681	−	11.4339i	0.683484	−	0.943054i
$148$	−3.29058	−	5.24560i	−0.270484	−	0.431186i
$149$		−	17.7470i		−	1.45389i	−0.686695	−	0.726946i	$-0.740939\pi$
$149$		−	17.7470i		−	1.45389i	0.686695	−	0.726946i	$-0.259061\pi$
$150$	0.866179	−	10.1392i	0.0707233	−	0.827860i
$151$	−2.78743	−	1.60932i	−0.226838	−	0.130965i	0.382275	−	0.924049i	$-0.375141\pi$
$151$	−2.78743	−	1.60932i	−0.226838	−	0.130965i	−0.609112	+	0.793084i	$0.708474\pi$
$152$	−9.19001	+	8.21850i	−0.745408	+	0.666608i
$153$	−14.2423	+	4.66450i	−1.15142	+	0.377102i
$154$	−16.5747	+	0.303804i	−1.33562	+	0.0244812i
$155$	3.87258	+	6.70751i	0.311053	+	0.538760i
$156$	6.13462	+	12.4852i	0.491163	+	0.999619i
$157$	−2.50724			−0.200100			−0.100050	−	0.994982i	$-0.531900\pi$
$157$	−2.50724			−0.200100			−0.100050	+	0.994982i	$0.531900\pi$
$158$	19.0504	−	0.349184i	1.51557	−	0.0277796i
$159$	−15.0952	−	10.9404i	−1.19713	−	0.867626i
$160$	−9.87822	−	13.9772i	−0.780942	−	1.10499i
$161$	−16.1144	+	9.30363i	−1.26999	+	0.733229i
$162$	−4.90803	+	11.7436i	−0.385612	+	0.922661i
$163$			18.7315i			1.46717i	0.679600	+	0.733583i	$0.262153\pi$
$163$			18.7315i			1.46717i	−0.679600	+	0.733583i	$0.737847\pi$
$164$	0.701296	−	0.439925i	0.0547620	−	0.0343523i
$165$	1.63118	−	15.6963i	0.126987	−	1.22196i
$166$	4.54097	−	2.73389i	0.352448	−	0.212191i
$167$	−8.16353	+	14.1397i	−0.631713	+	1.09416i	0.355488	+	0.934681i	$0.384315\pi$
$167$	−8.16353	+	14.1397i	−0.631713	+	1.09416i	−0.987201	+	0.159479i	$0.949019\pi$
$168$	19.0476	+	0.925819i	1.46955	+	0.0714285i
$169$	−1.56311	−	2.70738i	−0.120239	−	0.208260i
$170$	−18.3127	+	11.0252i	−1.40452	+	0.845592i
$171$	13.0562	+	0.732312i	0.998431	+	0.0560013i
$172$	3.33355	+	1.76501i	0.254181	+	0.134581i
$173$	−4.54638	+	2.62485i	−0.345655	+	0.199564i	−0.662770	−	0.748823i	$-0.730619\pi$
$173$	−4.54638	+	2.62485i	−0.345655	+	0.199564i	0.317115	+	0.948387i	$0.397286\pi$
$174$	−1.06010	−	0.0905636i	−0.0803662	−	0.00686561i
$175$	14.0050	+	8.08579i	1.05868	+	0.611229i
$176$	−6.77049	−	9.96235i	−0.510345	−	0.750941i
$177$	−7.48151	−	16.7510i	−0.562345	−	1.25908i
$178$	20.1828	−	0.369939i	1.51277	−	0.0277281i
$179$	9.00022			0.672708			0.336354	−	0.941736i	$-0.390806\pi$
$179$	9.00022			0.672708			0.336354	+	0.941736i	$0.390806\pi$
$180$	−3.07924	+	17.8907i	−0.229513	+	1.33349i
$181$	6.89054	+	11.9348i	0.512170	+	0.887104i	0.999900	+	0.0141097i	$0.00449141\pi$
$181$	6.89054	+	11.9348i	0.512170	+	0.887104i	−0.487731	+	0.872994i	$0.662175\pi$
$182$	−22.1032	+	0.405139i	−1.63840	+	0.0300309i
$183$	4.53761	+	10.1596i	0.335430	+	0.751021i
$184$	−12.0626	−	6.10639i	−0.889264	−	0.450169i
$185$			9.36773i			0.688729i
$186$	−2.66158	−	5.67744i	−0.195156	−	0.416290i
$187$	−13.0278	+	7.52161i	−0.952688	+	0.550035i
$188$	−13.1392	−	20.9455i	−0.958272	−	1.52761i
$189$	−13.5871	−	14.9839i	−0.988317	−	1.08992i
$190$	18.3842	−	3.14434i	1.33373	−	0.228115i
$191$	7.15070	−	12.3854i	0.517406	−	0.896174i	−0.482389	−	0.875957i	$-0.660231\pi$
$191$	7.15070	−	12.3854i	0.517406	−	0.896174i	0.999796	−	0.0202169i	$-0.00643569\pi$
$192$	7.00504	+	11.9553i	0.505545	+	0.862800i
$193$	−4.54467			−0.327132			−0.163566	−	0.986532i	$-0.552300\pi$
$193$	−4.54467			−0.327132			−0.163566	+	0.986532i	$0.552300\pi$
$194$	0.0743809	+	4.05800i	0.00534023	+	0.291347i
$195$	2.17527	−	20.9319i	0.155774	−	1.49896i
$196$	−7.62986	+	14.4104i	−0.544990	+	1.02931i
$197$		−	19.3601i		−	1.37935i	−0.724121	−	0.689673i	$-0.757754\pi$
$197$		−	19.3601i		−	1.37935i	0.724121	−	0.689673i	$-0.242246\pi$
$198$	−2.39743	+	12.5490i	−0.170378	+	0.891816i
$199$	5.50195	−	3.17655i	0.390023	−	0.225180i	−0.292147	−	0.956373i	$-0.594370\pi$
$199$	5.50195	−	3.17655i	0.390023	−	0.225180i	0.682170	+	0.731194i	$0.261036\pi$
$200$	0.645734	+	11.7326i	0.0456603	+	0.829620i
$201$	2.30912	−	22.2200i	0.162873	−	1.56727i
$202$	3.67701	−	6.64720i	0.258714	−	0.467695i
$203$	0.845412	−	1.46430i	0.0593363	−	0.102774i
$204$	15.5316	−	7.63145i	1.08743	−	0.534308i
$205$	−1.25239			−0.0874709
$206$	11.4768	−	0.210364i	0.799629	−	0.0146568i
$207$	4.46329	+	13.6280i	0.310220	+	0.947210i
$208$	−9.02881	−	13.2853i	−0.626036	−	0.921172i
$209$	12.9765	−	1.97539i	0.897604	−	0.136641i
$210$	−23.6658	−	16.4990i	−1.63310	−	1.13854i
$211$			3.70510i			0.255070i	0.991834	+	0.127535i	$0.0407065\pi$
$211$			3.70510i			0.255070i	−0.991834	+	0.127535i	$0.959294\pi$
$212$	19.0248	+	10.0730i	1.30663	+	0.691820i
$213$	16.7770	+	1.74349i	1.14954	+	0.119462i
$214$	−7.71512	−	4.26775i	−0.527395	−	0.291737i
$215$	−2.85314	−	4.94179i	−0.194583	−	0.337027i
$216$	3.71671	−	14.2192i	0.252890	−	0.967495i
$217$	9.96467			0.676446
$218$	21.4181	−	12.8948i	1.45061	−	0.873344i
$219$	−1.02704	−	0.106731i	−0.0694010	−	0.00721223i
$220$	0.667780	+	18.2099i	0.0450217	+	1.22771i
$221$	−17.3733	+	10.0305i	−1.16865	+	0.674723i
$222$	0.645538	−	7.55643i	0.0433257	−	0.507154i
$223$	10.0726	−	5.81541i	0.674511	−	0.389429i	−0.123273	−	0.992373i	$-0.539339\pi$
$223$	10.0726	−	5.81541i	0.674511	−	0.389429i	0.797784	+	0.602944i	$0.206006\pi$
$224$	−21.9278	+	2.01504i	−1.46512	+	0.134636i
$225$	8.31776	−	9.28140i	0.554517	−	0.618760i
$226$	16.4372	−	0.301284i	1.09338	−	0.0200411i
$227$	1.26292	−	2.18744i	0.0838227	−	0.145185i	−0.821066	−	0.570833i	$-0.806620\pi$
$227$	1.26292	−	2.18744i	0.0838227	−	0.145185i	0.904889	+	0.425648i	$0.139954\pi$
$228$	−15.0462	+	1.26949i	−0.996459	+	0.0840743i
$229$	−13.4497	−	23.2956i	−0.888782	−	1.53942i	−0.841316	−	0.540544i	$-0.818219\pi$
$229$	−13.4497	−	23.2956i	−0.888782	−	1.53942i	−0.0474665	−	0.998873i	$-0.515115\pi$
$230$	10.5496	+	17.5227i	0.695619	+	1.15542i
$231$	−16.4395	−	11.9147i	−1.08164	−	0.783927i
$232$	1.22670	−	0.0675149i	0.0805371	−	0.00443257i
$233$	4.82101	+	2.78341i	0.315835	+	0.182347i	0.649534	−	0.760332i	$-0.274964\pi$
$233$	4.82101	+	2.78341i	0.315835	+	0.182347i	−0.333700	+	0.942679i	$0.608297\pi$
$234$	−3.19710	+	16.7347i	−0.209001	+	1.09398i
$235$			37.4050i			2.44003i
$236$	11.2571	+	17.9453i	0.732778	+	1.16814i
$237$	18.8951	+	13.6944i	1.22737	+	0.889545i
$238$	0.503992	+	27.4963i	0.0326689	+	1.78232i
$239$	−0.139802	−	0.242144i	−0.00904302	−	0.0156630i	0.861468	−	0.507811i	$-0.169545\pi$
$239$	−0.139802	−	0.242144i	−0.00904302	−	0.0156630i	−0.870512	+	0.492148i	$0.836212\pi$
$240$	0.633797	−	20.9525i	0.0409114	−	1.35248i
$241$	−14.7801			−0.952069			−0.476034	−	0.879427i	$-0.657926\pi$
$241$	−14.7801			−0.952069			−0.476034	+	0.879427i	$0.657926\pi$
$242$	−0.0500723	−	2.73180i	−0.00321877	−	0.175607i
$243$	−13.4542	+	7.87309i	−0.863085	+	0.505059i
$244$	−6.82756	−	10.8840i	−0.437090	−	0.696777i
$245$	21.3626	−	12.3337i	1.36480	−	0.787970i
$246$	1.01024	+	0.0863034i	0.0644103	+	0.00550251i
$247$	17.3049	−	2.63429i	1.10108	−	0.167616i
$248$	3.95930	+	6.06193i	0.251416	+	0.384933i
$249$	6.45690	+	0.671009i	0.409190	+	0.0425235i
$250$	−1.75143	+	3.16619i	−0.110770	+	0.200247i
$251$	3.57806	+	6.19739i	0.225845	+	0.391176i	0.956573	−	0.291494i	$-0.0941522\pi$
$251$	3.57806	+	6.19739i	0.225845	+	0.391176i	−0.730727	+	0.682669i	$0.760819\pi$
$252$	17.9530	+	14.9397i	1.13093	+	0.941110i
$253$	7.19716	+	12.4658i	0.452482	+	0.783721i
$254$	9.01704	−	0.165277i	0.565779	−	0.0103704i
$255$	−26.0392	−	2.70602i	−1.63064	−	0.169458i
$256$	−9.93851	−	12.5390i	−0.621157	−	0.783686i
$257$	−18.0122	−	10.3993i	−1.12357	−	0.648693i	−0.181260	−	0.983435i	$-0.558018\pi$
$257$	−18.0122	−	10.3993i	−1.12357	−	0.648693i	−0.942310	+	0.334742i	$0.891351\pi$
$258$	1.96093	+	4.18288i	0.122082	+	0.260415i
$259$	10.4375	+	6.02611i	0.648556	+	0.374444i
$260$	0.890520	+	24.2839i	0.0552277	+	1.50602i
$261$	−0.970419	−	0.869666i	−0.0600675	−	0.0538309i
$262$	12.3270	+	6.81888i	0.761564	+	0.421272i
$263$	−4.49769	−	7.79022i	−0.277339	−	0.480366i	0.693383	−	0.720569i	$-0.256119\pi$
$263$	−4.49769	−	7.79022i	−0.277339	−	0.480366i	−0.970723	+	0.240203i	$0.922786\pi$
$264$	0.716201	−	14.7350i	0.0440791	−	0.906874i
$265$	−16.2831	−	28.2031i	−1.00026	−	1.73251i
$266$	8.32284	−	22.5064i	0.510306	−	1.37996i
$267$	20.0183	+	14.5084i	1.22510	+	0.887897i
$268$	0.945319	+	25.7782i	0.0577445	+	1.57466i
$269$	−9.99790	−	5.77229i	−0.609583	−	0.351943i	0.163219	−	0.986590i	$-0.447812\pi$
$269$	−9.99790	−	5.77229i	−0.609583	−	0.351943i	−0.772802	+	0.634647i	$0.781146\pi$
$270$	−16.1940	+	15.2345i	−0.985538	+	0.927141i
$271$	−0.0117891	−	0.00680646i	−0.000716139	−	0.000413463i	0.499642	−	0.866232i	$-0.333465\pi$
$271$	−0.0117891	−	0.00680646i	−0.000716139	−	0.000413463i	−0.500358	+	0.865819i	$0.666798\pi$
$272$	−16.5269	+	11.2318i	−1.00209	+	0.681028i
$273$	−21.9230	−	15.8888i	−1.32684	−	0.961636i
$274$	−12.2649	+	22.1722i	−0.740951	+	1.33947i
$275$	6.25506	−	10.8341i	0.377194	−	0.653320i
$276$	−7.30226	−	14.8616i	−0.439544	−	0.894564i
$277$	4.86773	−	8.43115i	0.292473	−	0.506579i	−0.681921	−	0.731426i	$-0.738855\pi$
$277$	4.86773	−	8.43115i	0.292473	−	0.506579i	0.974394	+	0.224847i	$0.0721883\pi$
$278$	10.9440	+	18.1778i	0.656376	+	1.09023i
$279$	1.57909	−	7.51548i	0.0945375	−	0.449940i
$280$	29.7211	+	15.0456i	1.77618	+	0.899149i
$281$			11.5527i			0.689174i	0.938754	+	0.344587i	$0.111981\pi$
$281$			11.5527i			0.689174i	−0.938754	+	0.344587i	$0.888019\pi$
$282$	2.57761	−	30.1725i	0.153494	−	1.79675i
$283$			22.5259i			1.33902i	0.742802	+	0.669511i	$0.233496\pi$
$283$			22.5259i			1.33902i	−0.742802	+	0.669511i	$0.766504\pi$
$284$	−19.4636	+	0.713755i	−1.15495	+	0.0423536i
$285$	20.3028	+	10.4689i	1.20263	+	0.620123i
$286$	0.313410	+	17.0987i	0.0185323	+	1.01107i
$287$	−0.805643	+	1.39542i	−0.0475556	+	0.0823688i
$288$	−1.95511	+	16.8576i	−0.115206	+	0.993342i
$289$	3.97787	+	6.88987i	0.233992	+	0.405287i
$290$	−1.62634	−	0.899636i	−0.0955018	−	0.0528284i
$291$	−2.91708	+	4.02492i	−0.171002	+	0.235945i
$292$	1.19151	−	0.0436941i	0.0697279	−	0.00255700i
$293$	16.3725	−	9.45267i	0.956492	−	0.552231i	0.0614006	−	0.998113i	$-0.480443\pi$
$293$	16.3725	−	9.45267i	0.956492	−	0.552231i	0.895092	+	0.445882i	$0.147110\pi$
$294$	−18.0819	+	8.47678i	−1.05456	+	0.494376i
$295$		−	32.0472i		−	1.86586i
$296$	0.481247	+	8.74396i	0.0279719	+	0.508232i
$297$	−11.5913	+	10.5108i	−0.672597	+	0.609899i
$298$	−12.1486	+	21.9619i	−0.703749	+	1.27222i
$299$	9.59780	+	16.6239i	0.555055	+	0.961384i
$300$	−8.01259	+	11.9543i	−0.462607	+	0.690180i
$301$	−7.34152			−0.423158
$302$	2.34778	+	3.89964i	0.135100	+	0.224399i
$303$	8.49491	−	3.79409i	0.488020	−	0.217965i
$304$	16.9985	−	3.87942i	0.974933	−	0.222500i
$305$			19.4369i			1.11296i
$306$	20.8179	+	3.97718i	1.19008	+	0.227361i
$307$	−24.8145	−	14.3266i	−1.41624	−	0.817664i	−0.420270	−	0.907399i	$-0.638065\pi$
$307$	−24.8145	−	14.3266i	−1.41624	−	0.817664i	−0.995966	+	0.0897351i	$0.971398\pi$
$308$	20.7191	+	10.9701i	1.18058	+	0.625080i
$309$	11.3833	+	8.25010i	0.647572	+	0.469332i
$310$	−0.200734	−	10.9515i	−0.0114009	−	0.622002i
$311$	−0.926512	−	1.60477i	−0.0525377	−	0.0909979i	0.838561	−	0.544808i	$-0.183398\pi$
$311$	−0.926512	−	1.60477i	−0.0525377	−	0.0909979i	−0.891098	+	0.453811i	$0.850064\pi$
$312$	0.955092	−	19.6499i	0.0540715	−	1.11245i
$313$	−4.47592			−0.252994			−0.126497	−	0.991967i	$-0.540373\pi$
$313$	−4.47592			−0.252994			−0.126497	+	0.991967i	$0.540373\pi$
$314$	3.10271	+	1.71631i	0.175096	+	0.0968572i
$315$	−10.9972	−	33.5782i	−0.619620	−	1.89192i
$316$	−23.8139	−	12.6087i	−1.33964	−	0.709297i
$317$		−	26.9184i		−	1.51189i	−0.654638	−	0.755943i	$-0.727179\pi$
$317$		−	26.9184i		−	1.51189i	0.654638	−	0.755943i	$-0.272821\pi$
$318$	11.1912	+	23.8720i	0.627569	+	1.33867i
$319$	−1.13276	−	0.654000i	−0.0634224	−	0.0366169i
$320$	2.65632	+	24.0588i	0.148493	+	1.34493i
$321$	−4.40364	−	9.85967i	−0.245787	−	0.550313i
$322$	26.3102	−	0.482251i	1.46621	−	0.0268748i
$323$	−3.27705	−	21.5272i	−0.182340	−	1.19781i
$324$	14.1127	−	11.1729i	0.784036	−	0.620715i
$325$	8.34146	−	14.4478i	0.462701	−	0.801421i
$326$	12.8225	−	23.1802i	0.710174	−	1.28383i
$327$	30.4548	+	3.16490i	1.68416	+	0.175019i
$328$	−1.16900	+	0.0643389i	−0.0645472	+	0.00355252i
$329$	41.6766	+	24.0620i	2.29771	+	1.32658i
$330$	−12.7634	+	18.3076i	−0.702602	+	1.00780i
$331$	24.8192	+	14.3294i	1.36419	+	0.787613i	0.990178	−	0.139813i	$-0.0446501\pi$
$331$	24.8192	+	14.3294i	1.36419	+	0.787613i	0.374007	+	0.927426i	$0.377983\pi$
$332$	−7.49091	+	0.274701i	−0.411117	+	0.0150761i
$333$	6.19899	−	6.91716i	0.339702	−	0.379058i
$334$	19.7816	−	11.9095i	1.08240	−	0.651659i
$335$	19.5119	−	33.7956i	1.06605	−	1.84645i
$336$	−22.9376	−	14.1846i	−1.25135	−	0.773833i
$337$	−28.4780			−1.55129			−0.775647	−	0.631167i	$-0.782576\pi$
$337$	−28.4780			−1.55129			−0.775647	+	0.631167i	$0.782576\pi$
$338$	0.0810234	+	4.42040i	0.00440709	+	0.240438i
$339$	16.3032	+	11.8158i	0.885467	+	0.641748i
$340$	30.2091	−	1.10780i	1.63832	−	0.0600791i
$341$		−	7.70853i		−	0.417441i
$342$	−15.6557	−	9.84375i	−0.846563	−	0.532289i
$343$		−	4.48757i		−	0.242306i
$344$	−2.91703	−	4.46615i	−0.157276	−	0.240799i
$345$	−2.58930	+	24.9160i	−0.139403	+	1.34143i
$346$	7.42296	−	0.136059i	0.399061	−	0.00731456i
$347$	−5.79778			−0.311241			−0.155621	−	0.987817i	$-0.549738\pi$
$347$	−5.79778			−0.311241			−0.155621	+	0.987817i	$0.549738\pi$
$348$	1.24988	+	0.837759i	0.0670007	+	0.0449086i
$349$	0.0557583	−	0.0965762i	0.00298467	−	0.00516961i	−0.864529	−	0.502583i	$-0.832383\pi$
$349$	0.0557583	−	0.0965762i	0.00298467	−	0.00516961i	0.867514	+	0.497413i	$0.165717\pi$
$350$	−11.7961	−	19.5932i	−0.630528	−	1.04730i
$351$	−15.4577	+	14.0167i	−0.825069	+	0.748157i
$352$	1.55881	+	16.9631i	0.0830849	+	0.904135i
$353$	−31.2249	−	18.0277i	−1.66194	−	0.959519i	−0.971790	−	0.235849i	$-0.924213\pi$
$353$	−31.2249	−	18.0277i	−1.66194	−	0.959519i	−0.690146	−	0.723670i	$-0.742454\pi$
$354$	−2.20840	+	25.8507i	−0.117375	+	1.37395i
$355$	25.5171	+	14.7323i	1.35431	+	0.781909i
$356$	−25.2294	−	13.3582i	−1.33716	−	0.707983i
$357$	−19.7656	+	27.2721i	−1.04611	+	1.44339i
$358$	−11.1377	−	6.16103i	−0.588648	−	0.325621i
$359$	−12.7970	+	22.1650i	−0.675399	+	1.16983i	0.300953	+	0.953639i	$0.402695\pi$
$359$	−12.7970	+	22.1650i	−0.675399	+	1.16983i	−0.976352	+	0.216186i	$0.930638\pi$
$360$	16.0575	−	20.0318i	0.846303	−	1.05577i
$361$	−4.17347	+	18.5360i	−0.219656	+	0.975577i
$362$	−0.357169	−	19.4861i	−0.0187724	−	1.02417i
$363$	1.96375	−	2.70953i	0.103070	−	0.142213i
$364$	27.6300	+	14.6292i	1.44821	+	0.766780i
$365$	−1.56208	−	0.901870i	−0.0817633	−	0.0472060i
$366$	1.33942	−	15.6787i	0.0700124	−	0.819539i
$367$		−	11.6822i		−	0.609804i	−0.952384	−	0.304902i	$-0.901376\pi$
$367$		−	11.6822i		−	0.609804i	0.952384	−	0.304902i	$-0.0986238\pi$
$368$	10.7473	+	15.8140i	0.560242	+	0.824361i
$369$	0.924770	+	0.828756i	0.0481416	+	0.0431433i
$370$	6.41261	−	11.5925i	0.333376	−	0.602668i
$371$	−41.8986			−2.17527
$372$	−0.592754	+	8.84778i	−0.0307329	+	0.458736i
$373$	13.7257	+	23.7736i	0.710691	+	1.23095i	0.964598	+	0.263724i	$0.0849508\pi$
$373$	13.7257	+	23.7736i	0.710691	+	1.23095i	−0.253908	+	0.967228i	$0.581716\pi$
$374$	21.2708	−	0.389881i	1.09989	−	0.0201603i
$375$	−4.04628	+	1.80720i	−0.208949	+	0.0933232i
$376$	1.92160	+	34.9143i	0.0990990	+	1.80057i
$377$	−1.51060	−	0.872144i	−0.0777997	−	0.0449177i
$378$	6.55690	+	27.8435i	0.337251	+	1.43211i
$379$		−	8.84686i		−	0.454433i	−0.973844	−	0.227216i	$-0.927038\pi$
$379$		−	8.84686i		−	0.454433i	0.973844	−	0.227216i	$-0.0729624\pi$
$380$	−24.9029	−	8.69367i	−1.27749	−	0.445976i
$381$	8.94353	+	6.48188i	0.458191	+	0.332077i
$382$	−17.3273	+	10.4319i	−0.886541	+	0.533743i
$383$	1.37298			0.0701560			0.0350780	−	0.999385i	$-0.488832\pi$
$383$	1.37298			0.0701560			0.0350780	+	0.999385i	$0.488832\pi$
$384$	−0.484797	−	19.5899i	−0.0247397	−	0.999694i
$385$	−17.7332	−	30.7148i	−0.903767	−	1.56537i
$386$	5.62402	+	3.11102i	0.286255	+	0.158347i
$387$	−1.16340	+	5.53706i	−0.0591390	+	0.281465i
$388$	2.68583	−	5.07268i	0.136352	−	0.257526i
$389$			32.5422i			1.64995i	0.565166	+	0.824977i	$0.308812\pi$
$389$			32.5422i			1.64995i	−0.565166	+	0.824977i	$0.691188\pi$
$390$	−17.0207	+	24.4141i	−0.861875	+	1.23626i
$391$	20.6800	−	11.9396i	1.04583	−	0.603813i
$392$	19.3065	−	12.6099i	0.975124	−	0.636895i
$393$	7.03600	+	15.7535i	0.354919	+	0.794658i
$394$	−13.2528	+	23.9580i	−0.667666	+	1.20699i
$395$	20.3820	+	35.3027i	1.02553	+	1.77627i
$396$	11.5571	−	13.8882i	0.580767	−	0.697907i
$397$	8.64308	−	14.9703i	0.433784	−	0.751335i	−0.563412	−	0.826176i	$-0.690512\pi$
$397$	8.64308	−	14.9703i	0.433784	−	0.751335i	0.997195	+	0.0748408i	$0.0238449\pi$
$398$	−8.98313	+	0.164656i	−0.450284	+	0.00825345i
$399$	24.7249	−	15.8869i	1.23779	−	0.795338i
$400$	7.23237	−	14.9611i	0.361618	−	0.748055i
$401$			14.8592i			0.742031i	0.928627	+	0.371015i	$0.120990\pi$
$401$			14.8592i			0.742031i	−0.928627	+	0.371015i	$0.879010\pi$
$402$	−18.0680	+	25.9165i	−0.901152	+	1.29260i
$403$		−	10.2797i		−	0.512070i
$404$	−9.10059	+	5.70883i	−0.452771	+	0.284025i
$405$	−27.0678	+	2.97311i	−1.34501	+	0.147735i
$406$	−2.04857	+	1.23334i	−0.101669	+	0.0612098i
$407$	4.66172	−	8.07433i	0.231073	−	0.400230i
$408$	−24.4443	−	1.18813i	−1.21018	−	0.0588213i
$409$	0.0451886	−	0.0782689i	0.00223443	−	0.00387015i	−0.864906	−	0.501934i	$-0.832622\pi$
$409$	0.0451886	−	0.0782689i	0.00223443	−	0.00387015i	0.867140	+	0.498064i	$0.165955\pi$
$410$	1.54983	+	0.857316i	0.0765408	+	0.0423398i
$411$	−28.3353	+	12.6555i	−1.39768	+	0.624248i
$412$	−14.3466	−	7.59606i	−0.706804	−	0.374231i
$413$	−35.7070	−	20.6154i	−1.75703	−	1.01442i
$414$	3.80562	−	19.9199i	0.187036	−	0.979010i
$415$	9.82067	+	5.66997i	0.482078	+	0.278328i
$416$	2.07876	+	22.6212i	0.101919	+	1.10909i
$417$	−2.68610	+	25.8475i	−0.131539	+	1.26576i
$418$	−17.4106	−	6.43844i	−0.851583	−	0.314914i
$419$	6.82563	+	11.8223i	0.333454	+	0.577559i	0.983187	−	0.182604i	$-0.0584525\pi$
$419$	6.82563	+	11.8223i	0.333454	+	0.577559i	−0.649733	+	0.760163i	$0.725119\pi$
$420$	17.9921	+	36.6177i	0.877927	+	1.78676i
$421$	9.05530	+	15.6842i	0.441328	+	0.764403i	0.997788	−	0.0664712i	$-0.0211741\pi$
$421$	9.05530	+	15.6842i	0.441328	+	0.764403i	−0.556460	+	0.830874i	$0.687841\pi$
$422$	2.53630	−	4.58506i	0.123465	−	0.223197i
$423$	24.7523	−	27.6200i	1.20350	−	1.34293i
$424$	−16.6477	−	25.4887i	−0.808485	−	1.23784i
$425$	−17.9730	−	10.3767i	−0.871821	−	0.503346i
$426$	−19.5680	−	13.6421i	−0.948073	−	0.660963i
$427$	21.6566	+	12.5035i	1.04804	+	0.605085i
$428$	6.62599	+	10.5627i	0.320279	+	0.510566i
$429$	−12.2914	+	16.9593i	−0.593434	+	0.818805i
$430$	0.147892	+	8.06855i	0.00713199	+	0.389100i
$431$	6.32209	+	10.9502i	0.304525	+	0.527452i	0.977155	−	0.212526i	$-0.0681691\pi$
$431$	6.32209	+	10.9502i	0.304525	+	0.527452i	−0.672631	+	0.739978i	$0.734836\pi$
$432$	−14.3331	+	15.0520i	−0.689601	+	0.724190i
$433$	10.3116	+	17.8602i	0.495544	+	0.858307i	0.999987	−	0.00513780i	$-0.00163542\pi$
$433$	10.3116	+	17.8602i	0.495544	+	0.858307i	−0.504443	+	0.863445i	$0.668302\pi$
$434$	−12.3313	−	6.82124i	−0.591919	−	0.327430i
$435$	−0.928282	−	2.07841i	−0.0445077	−	0.0996519i
$436$	−35.3318	+	1.29566i	−1.69209	+	0.0620509i
$437$	−20.5986	+	3.13569i	−0.985364	+	0.150000i
$438$	1.19790	+	0.835133i	0.0572378	+	0.0399042i
$439$	10.6777	−	6.16477i	0.509618	−	0.294228i	−0.223058	−	0.974805i	$-0.571604\pi$
$439$	10.6777	−	6.16477i	0.509618	−	0.294228i	0.732677	+	0.680577i	$0.238271\pi$
$440$	11.6391	−	22.9919i	0.554873	−	1.09609i
$441$	−23.9358	−	5.02920i	−1.13980	−	0.239486i
$442$	28.3657	−	0.519927i	1.34922	−	0.0247304i
$443$	−3.25827			−0.154805			−0.0774026	−	0.997000i	$-0.524663\pi$
$443$	−3.25827			−0.154805			−0.0774026	+	0.997000i	$0.524663\pi$
$444$	−5.97155	+	8.90917i	−0.283397	+	0.422810i
$445$	21.5935	+	37.4011i	1.02363	+	1.77298i
$446$	−16.4457	+	0.301441i	−0.778727	+	0.0142736i
$447$	−28.0666	+	12.5354i	−1.32750	+	0.592905i
$448$	28.5150	+	12.5169i	1.34721	+	0.591370i
$449$		−	19.0008i		−	0.896701i	−0.893858	−	0.448351i	$-0.852012\pi$
$449$		−	19.0008i		−	0.896701i	0.893858	−	0.448351i	$-0.147988\pi$
$450$	−16.6467	+	5.79185i	−0.784734	+	0.273031i
$451$	1.07947	+	0.623235i	0.0508305	+	0.0293470i
$452$	−20.5472	−	10.8791i	−0.966460	−	0.511711i
$453$	−0.576242	+	5.54499i	−0.0270742	+	0.260526i
$454$	−3.06025	+	1.84243i	−0.143625	+	0.0864693i
$455$	−23.6482	−	40.9598i	−1.10864	−	1.92023i
$456$	19.4887	+	8.72878i	0.912641	+	0.408763i
$457$	7.55453	−	13.0848i	0.353386	−	0.612083i	−0.633454	−	0.773780i	$-0.718363\pi$
$457$	7.55453	−	13.0848i	0.353386	−	0.612083i	0.986840	+	0.161697i	$0.0516968\pi$
$458$	0.697163	+	38.0352i	0.0325763	+	1.77727i
$459$	17.4367	+	19.2293i	0.813878	+	0.897546i
$460$	−1.06002	−	28.9060i	−0.0494236	−	1.34775i
$461$	−7.38699	+	4.26488i	−0.344046	+	0.198635i	−0.662060	−	0.749451i	$-0.730318\pi$
$461$	−7.38699	+	4.26488i	−0.344046	+	0.198635i	0.318014	+	0.948086i	$0.396984\pi$
$462$	12.1878	+	25.9979i	0.567028	+	1.20953i
$463$	−8.79687	+	5.07887i	−0.408825	+	0.236035i	−0.690285	−	0.723538i	$-0.742515\pi$
$463$	−8.79687	+	5.07887i	−0.408825	+	0.236035i	0.281460	+	0.959573i	$0.409181\pi$
$464$	−1.56426	−	0.756182i	−0.0726190	−	0.0351049i
$465$	7.87244	−	10.8622i	0.365076	−	0.503722i
$466$	−4.06062	−	6.74465i	−0.188105	−	0.312440i
$467$	6.04500			0.279729			0.139865	−	0.990171i	$-0.455333\pi$
$467$	6.04500			0.279729			0.139865	+	0.990171i	$0.455333\pi$
$468$	15.4120	−	18.5206i	0.712422	−	0.856116i
$469$	−25.1034	−	43.4803i	−1.15917	−	2.00773i
$470$	25.6053	−	46.2886i	1.18109	−	2.13513i
$471$	1.77096	+	3.96516i	0.0816017	+	0.182705i
$472$	−1.64636	−	29.9133i	−0.0757797	−	1.37687i
$473$			5.67930i			0.261135i
$474$	−14.0083	−	29.8813i	−0.643423	−	1.37249i
$475$	11.3112	+	14.1412i	0.518996	+	0.648843i
$476$	18.1987	−	34.3716i	0.834136	−	1.57542i
$477$	−6.63961	+	31.6004i	−0.304007	+	1.44688i
$478$	0.00724659	+	0.395353i	0.000331451	+	0.0180830i
$479$	10.9343			0.499601			0.249800	−	0.968297i	$-0.419635\pi$
$479$	10.9343			0.499601			0.249800	+	0.968297i	$0.419635\pi$
$480$	−15.1272	+	25.4948i	−0.690460	+	1.16368i
$481$	6.21665	−	10.7676i	0.283455	−	0.490958i
$482$	18.2903	+	10.1176i	0.833101	+	0.460844i
$483$	26.0957	+	18.9130i	1.18740	+	0.860573i
$484$	−1.80807	+	3.41487i	−0.0821849	+	0.155221i
$485$	−7.51995	+	4.34165i	−0.341463	+	0.197144i
$486$	22.0390	−	0.532977i	0.999708	−	0.0241763i
$487$		−	31.2745i		−	1.41718i	−0.705619	−	0.708592i	$-0.749331\pi$
$487$		−	31.2745i		−	1.41718i	0.705619	−	0.708592i	$-0.250669\pi$
$488$	0.998530	+	18.1427i	0.0452013	+	0.821281i
$489$	29.6236	−	13.2308i	1.33962	−	0.598318i
$490$	−34.8791	+	0.639314i	−1.57568	+	0.0288812i
$491$	7.16052			0.323150			0.161575	−	0.986860i	$-0.448343\pi$
$491$	7.16052			0.323150			0.161575	+	0.986860i	$0.448343\pi$
$492$	−1.19109	−	0.798350i	−0.0536983	−	0.0359924i
$493$	−1.08494	+	1.87918i	−0.0488634	+	0.0846338i
$494$	−23.2180	−	8.58600i	−1.04463	−	0.386302i
$495$	−25.9756	+	8.50726i	−1.16752	+	0.382373i
$496$	−0.749976	−	10.2119i	−0.0336749	−	0.458529i
$497$	32.8294	−	18.9541i	1.47260	−	0.850207i
$498$	−7.53107	−	5.25040i	−0.337475	−	0.235276i
$499$		−	33.9896i		−	1.52158i	−0.648997	−	0.760791i	$-0.724811\pi$
$499$		−	33.9896i		−	1.52158i	0.648997	−	0.760791i	$-0.275189\pi$
$500$	4.33478	−	2.71922i	0.193857	−	0.121607i
$501$	28.1278	+	2.92308i	1.25666	+	0.130594i
$502$	−0.185468	−	10.1186i	−0.00827785	−	0.451615i
$503$	−21.1844	−	36.6924i	−0.944565	−	1.63603i	−0.756619	−	0.653855i	$-0.773150\pi$
$503$	−21.1844	−	36.6924i	−0.944565	−	1.63603i	−0.187946	−	0.982179i	$-0.560183\pi$
$504$	−11.9899	−	30.7774i	−0.534073	−	1.37093i
$505$	16.2521			0.723208
$506$	−0.373063	−	20.3532i	−0.0165847	−	0.904811i
$507$	−3.17759	+	4.38436i	−0.141122	+	0.194716i
$508$	−11.2717	−	5.96802i	−0.500101	−	0.264788i
$509$	−6.44054	−	3.71845i	−0.285472	−	0.164817i	0.350426	−	0.936590i	$-0.386037\pi$
$509$	−6.44054	−	3.71845i	−0.285472	−	0.164817i	−0.635898	+	0.771773i	$0.719370\pi$
$510$	30.3711	+	21.1737i	1.34485	+	0.937585i
$511$	−2.00973	+	1.16032i	−0.0889051	+	0.0513294i
$512$	3.71541	+	22.3203i	0.164200	+	0.986427i
$513$	−8.06396	−	21.1654i	−0.356032	−	0.934474i
$514$	15.1713	+	25.1993i	0.669175	+	1.11149i
$515$	12.2790	+	21.2679i	0.541079	+	0.937177i
$516$	0.436714	−	6.51864i	0.0192253	−	0.286967i
$517$	18.6141	−	32.2405i	0.818645	−	1.41794i
$518$	−8.79129	−	14.6022i	−0.386267	−	0.641585i
$519$	7.36245	+	5.33598i	0.323176	+	0.234223i
$520$	15.5214	−	30.6609i	0.680657	−	1.34457i
$521$			1.07049i			0.0468992i	0.999725	+	0.0234496i	$0.00746492\pi$
$521$			1.07049i			0.0468992i	−0.999725	+	0.0234496i	$0.992535\pi$
$522$	0.605569	+	1.74050i	0.0265050	+	0.0761797i
$523$	−7.38254	+	4.26231i	−0.322816	+	0.186378i	−0.652647	−	0.757662i	$-0.726342\pi$
$523$	−7.38254	+	4.26231i	−0.322816	+	0.186378i	0.329831	+	0.944040i	$0.393008\pi$
$524$	−10.5868	−	16.8767i	−0.462487	−	0.737262i
$525$	2.89524	−	27.8600i	0.126359	−	1.21591i
$526$	0.233137	+	12.7192i	0.0101652	+	0.554585i
$527$	−12.7880			−0.557052
$528$	−10.9730	+	17.7442i	−0.477539	+	0.772218i
$529$	0.0754029	+	0.130602i	0.00327839	+	0.00567833i
$530$	0.844030	+	46.0478i	0.0366623	+	2.00019i
$531$	−21.2069	+	23.6638i	−0.920299	+	1.02692i
$532$	−25.7061	+	22.1543i	−1.11450	+	0.960510i
$533$	1.43954	+	0.831117i	0.0623533	+	0.0359997i
$534$	−14.8410	−	31.6574i	−0.642232	−	1.36995i
$535$		−	18.8631i		−	0.815522i
$536$	16.4765	−	32.5476i	0.711676	−	1.40584i
$537$	−6.35721	−	14.2337i	−0.274334	−	0.614229i
$538$	8.42100	+	13.9872i	0.363055	+	0.603031i
$539$	−24.5507			−1.05747
$540$	30.4687	−	7.76713i	1.31117	−	0.334244i
$541$	0.207415	+	0.359253i	0.00891746	+	0.0154455i	0.870450	−	0.492257i	$-0.163828\pi$
$541$	0.207415	+	0.359253i	0.00891746	+	0.0154455i	−0.861532	+	0.507703i	$0.830495\pi$
$542$	0.00992972	+	0.0164932i	0.000426518	+	0.000708442i
$543$	14.0075	−	19.3273i	0.601121	−	0.829412i
$544$	28.1407	−	2.58597i	1.20652	−	0.110872i
$545$	46.3205	+	26.7431i	1.98415	+	1.14555i
$546$	16.2531	+	34.6696i	0.695568	+	1.48372i
$547$		−	27.9073i		−	1.19323i	−0.802528	−	0.596614i	$-0.796512\pi$
$547$		−	27.9073i		−	1.19323i	0.802528	−	0.596614i	$-0.203488\pi$
$548$	30.3556	−	19.0422i	1.29673	−	0.813442i
$549$	12.8622	−	14.3523i	0.548944	−	0.612541i
$550$	−15.1570	+	9.12530i	−0.646298	+	0.389104i
$551$	1.47854	−	1.18265i	0.0629878	−	0.0503826i
$552$	−1.13688	+	23.3899i	−0.0483888	+	0.995541i
$553$	52.4457			2.23022
$554$	−11.7953	+	7.10137i	−0.501134	+	0.301708i
$555$	14.8149	−	6.61680i	0.628857	−	0.280868i
$556$	−1.09965	−	29.9866i	−0.0466354	−	1.27172i
$557$	9.40864	−	5.43208i	0.398657	−	0.230165i	−0.287247	−	0.957856i	$-0.592740\pi$
$557$	9.40864	−	5.43208i	0.398657	−	0.230165i	0.685904	+	0.727692i	$0.259407\pi$
$558$	−7.09878	+	8.21943i	−0.300515	+	0.347956i
$559$			7.57365i			0.320331i
$560$	−26.4805	−	38.9643i	−1.11900	−	1.64654i
$561$	21.0974	+	15.2904i	0.890731	+	0.645563i
$562$	7.90830	−	14.2964i	0.333591	−	0.603057i
$563$	6.07143	+	10.5160i	0.255880	+	0.443198i	0.965134	−	0.261755i	$-0.0843013\pi$
$563$	6.07143	+	10.5160i	0.255880	+	0.443198i	−0.709254	+	0.704953i	$0.750968\pi$
$564$	−23.8442	+	35.5740i	−1.00402	+	1.49793i
$565$	17.5861	+	30.4600i	0.739853	+	1.28146i
$566$	15.4199	−	27.8757i	0.648147	−	1.17170i
$567$	−14.0996	+	32.0715i	−0.592129	+	1.34688i
$568$	24.5748	+	12.4404i	1.03114	+	0.521989i
$569$	−10.8712	−	6.27649i	−0.455745	−	0.263124i	0.254509	−	0.967071i	$-0.418086\pi$
$569$	−10.8712	−	6.27649i	−0.455745	−	0.263124i	−0.710253	+	0.703946i	$0.751420\pi$
$570$	−17.9582	−	26.8533i	−0.752187	−	1.12476i
$571$	−27.6064	+	15.9386i	−1.15529	+	0.667008i	−0.950171	−	0.311729i	$-0.899092\pi$
$571$	−27.6064	+	15.9386i	−1.15529	+	0.667008i	−0.205120	+	0.978737i	$0.565759\pi$
$572$	11.3170	−	21.3742i	0.473187	−	0.893700i
$573$	−24.6381	−	2.56042i	−1.02927	−	0.106963i
$574$	1.95220	−	1.17533i	0.0814834	−	0.0490572i
$575$	−9.92913	+	17.1978i	−0.414073	+	0.717196i
$576$	13.9592	−	19.5228i	0.581632	−	0.813452i
$577$	16.0365			0.667607			0.333803	−	0.942643i	$-0.391668\pi$
$577$	16.0365			0.667607			0.333803	+	0.942643i	$0.391668\pi$
$578$	−0.206192	−	11.2492i	−0.00857646	−	0.467906i
$579$	3.21008	+	7.18731i	0.133406	+	0.298694i
$580$	1.39675	+	2.22659i	0.0579969	+	0.0924543i
$581$	12.6350	−	7.29479i	0.524186	−	0.302639i
$582$	6.36511	−	2.98396i	0.263842	−	0.123689i
$583$			32.4122i			1.34238i
$584$	−1.50440	−	0.761569i	−0.0622526	−	0.0315139i
$585$	−34.6399	+	11.3449i	−1.43218	+	0.469053i
$586$	−26.7317	+	0.489977i	−1.10428	+	0.0202408i
$587$	−18.9447	−	32.8132i	−0.781932	−	1.35435i	−0.930815	−	0.365491i	$-0.880901\pi$
$587$	−18.9447	−	32.8132i	−0.781932	−	1.35435i	0.148883	−	0.988855i	$-0.452432\pi$
$588$	28.1791	+	1.88785i	1.16208	+	0.0778535i
$589$	10.3928	+	4.06128i	0.428229	+	0.167342i
$590$	−21.9377	+	39.6583i	−0.903160	+	1.63271i
$591$	−30.6176	+	13.6748i	−1.25944	+	0.562505i
$592$	5.39008	−	11.1501i	0.221531	−	0.458265i
$593$	−0.224349	+	0.129528i	−0.00921292	+	0.00531908i	−0.504599	−	0.863354i	$-0.668360\pi$
$593$	−0.224349	+	0.129528i	−0.00921292	+	0.00531908i	0.495386	+	0.868673i	$0.335026\pi$
$594$	21.5393	−	5.07233i	0.883770	−	0.208120i
$595$	−50.9539	+	29.4182i	−2.08890	+	1.20603i
$596$	30.0677	−	18.8616i	1.23162	−	0.772600i
$597$	−8.90990	−	6.45750i	−0.364658	−	0.264288i
$598$	−0.497500	−	27.1421i	−0.0203443	−	1.10992i
$599$	−5.98755	+	10.3707i	−0.244645	+	0.423737i	−0.962032	−	0.272938i	$-0.912005\pi$
$599$	−5.98755	+	10.3707i	−0.244645	+	0.423737i	0.717387	+	0.696675i	$0.245338\pi$
$600$	18.0988	−	9.30841i	0.738879	−	0.380014i
$601$	12.1188	−	20.9904i	0.494337	−	0.856216i	−0.505642	−	0.862743i	$-0.668744\pi$
$601$	12.1188	−	20.9904i	0.494337	−	0.856216i	0.999979	+	0.00652730i	$0.00207772\pi$
$602$	9.08511	+	5.02558i	0.370282	+	0.204828i
$603$	−36.7715	+	12.0430i	−1.49745	+	0.490429i
$604$	−0.235904	−	6.43296i	−0.00959881	−	0.261753i
$605$	5.06234	−	2.92275i	0.205814	−	0.118826i
$606$	−13.1096	−	1.11994i	−0.532543	−	0.0454946i
$607$	−8.98311	+	5.18640i	−0.364613	+	0.210510i	−0.671103	−	0.741365i	$-0.734179\pi$
$607$	−8.98311	+	5.18640i	−0.364613	+	0.210510i	0.306489	+	0.951874i	$0.400846\pi$
$608$	−23.6913	−	6.83545i	−0.960808	−	0.277214i
$609$	−2.91291	−	0.302713i	−0.118037	−	0.0122665i
$610$	13.3054	−	24.0532i	0.538720	−	0.973884i
$611$	24.8228	−	42.9944i	1.00422	−	1.73937i
$612$	−23.0396	−	19.1725i	−0.931319	−	0.775003i
$613$	−17.3644	+	30.0761i	−0.701343	+	1.21476i	0.266652	+	0.963793i	$0.414083\pi$
$613$	−17.3644	+	30.0761i	−0.701343	+	1.21476i	−0.967995	+	0.250969i	$0.919251\pi$
$614$	20.9006	+	34.7157i	0.843481	+	1.40101i
$615$	0.884614	+	1.98064i	0.0356711	+	0.0798669i
$616$	−18.1303	−	27.7586i	−0.730491	−	1.11843i
$617$	−22.8372	−	13.1851i	−0.919393	−	0.530812i	−0.0359516	−	0.999354i	$-0.511446\pi$
$617$	−22.8372	−	13.1851i	−0.919393	−	0.530812i	−0.883441	+	0.468542i	$0.844780\pi$
$618$	−8.43923	−	18.0018i	−0.339476	−	0.724139i
$619$	−13.0555	−	7.53759i	−0.524745	−	0.302961i	0.214129	−	0.976805i	$-0.431309\pi$
$619$	−13.0555	−	7.53759i	−0.524745	−	0.302961i	−0.738874	+	0.673844i	$0.764642\pi$
$620$	−7.24834	+	13.6898i	−0.291100	+	0.549797i
$621$	18.3998	−	16.6846i	0.738358	−	0.669530i
$622$	0.0480255	+	2.62013i	0.00192565	+	0.105058i
$623$	55.5631			2.22609
$624$	−14.6331	+	23.6629i	−0.585793	+	0.947272i
$625$	−28.5130			−1.14052
$626$	5.53895	+	3.06396i	0.221381	+	0.122461i
$627$	−12.2899	−	19.1268i	−0.490810	−	0.763852i
$628$	−2.66470	−	4.24787i	−0.106333	−	0.169508i
$629$	−13.3948	−	7.73349i	−0.534085	−	0.308354i
$630$	−9.37674	+	49.0810i	−0.373578	+	1.95543i
$631$	−20.8654	+	12.0466i	−0.830638	+	0.479569i	−0.854071	−	0.520156i	$-0.825874\pi$
$631$	−20.8654	+	12.0466i	−0.830638	+	0.479569i	0.0234332	+	0.999725i	$0.492540\pi$
$632$	20.8385	+	31.9049i	0.828909	+	1.26911i
$633$	5.85955	−	2.61706i	0.232896	−	0.104019i
$634$	−18.4268	+	33.3114i	−0.731820	+	1.32296i
$635$	9.64731	+	16.7096i	0.382842	+	0.663102i
$636$	2.49236	−	37.2024i	0.0988285	−	1.47517i
$637$	−32.7397			−1.29719
$638$	0.954098	+	1.58475i	0.0377731	+	0.0627407i
$639$	−9.09297	−	27.7640i	−0.359712	−	1.09833i
$640$	13.1821	−	31.5910i	0.521067	−	1.24875i
$641$	31.1331	−	17.9747i	1.22969	−	0.709959i	0.262721	−	0.964872i	$-0.415380\pi$
$641$	31.1331	−	17.9747i	1.22969	−	0.709959i	0.966964	+	0.254913i	$0.0820467\pi$
$642$	−1.29987	+	15.2158i	−0.0513018	+	0.600520i
$643$		−	29.5252i		−	1.16436i	−0.813060	−	0.582180i	$-0.802200\pi$
$643$		−	29.5252i		−	1.16436i	0.813060	−	0.582180i	$-0.197800\pi$
$644$	−32.8890	−	17.4137i	−1.29601	−	0.686195i
$645$	−5.80006	+	8.00277i	−0.228377	+	0.315109i
$646$	−10.6810	+	28.8831i	−0.420236	+	1.13639i
$647$	−20.2868			−0.797555			−0.398778	−	0.917048i	$-0.630565\pi$
$647$	−20.2868			−0.797555			−0.398778	+	0.917048i	$0.630565\pi$
$648$	−25.1127	+	4.16569i	−0.986520	+	0.163644i
$649$	−15.9478	+	27.6225i	−0.626007	+	1.08428i
$650$	−20.2127	+	12.1691i	−0.792807	+	0.477310i
$651$	−7.03844	−	15.7589i	−0.275858	−	0.617642i
$652$	−31.7357	+	19.9079i	−1.24287	+	0.779653i
$653$	−41.8593	+	24.1675i	−1.63808	+	0.945746i	−0.656587	+	0.754250i	$0.728001\pi$
$653$	−41.8593	+	24.1675i	−1.63808	+	0.945746i	−0.981493	+	0.191496i	$0.938666\pi$
$654$	−35.5213	−	24.7642i	−1.38899	−	0.968357i
$655$			30.1389i			1.17762i
$656$	1.49068	+	0.720611i	0.0582011	+	0.0281351i
$657$	0.556646	+	1.69963i	0.0217168	+	0.0663091i
$658$	−35.1033	−	58.3062i	−1.36847	−	2.27301i
$659$	−9.78463			−0.381155			−0.190578	−	0.981672i	$-0.561036\pi$
$659$	−9.78463			−0.381155			−0.190578	+	0.981672i	$0.561036\pi$
$660$	28.3270	−	13.9185i	1.10263	−	0.541776i
$661$	23.8165	−	41.2514i	0.926355	−	1.60449i	0.136987	−	0.990573i	$-0.456258\pi$
$661$	23.8165	−	41.2514i	0.926355	−	1.60449i	0.789367	−	0.613921i	$-0.210409\pi$
$662$	−20.9046	−	34.7223i	−0.812481	−	1.34952i
$663$	28.1345	+	20.3906i	1.09265	+	0.791906i
$664$	9.45803	+	4.78791i	0.367043	+	0.185807i
$665$	50.7532	−	7.72607i	1.96812	−	0.299604i
$666$	−12.4063	+	4.31650i	−0.480735	+	0.167261i
$667$	1.79812	+	1.03814i	0.0696233	+	0.0401971i
$668$	−32.6322	+	1.19666i	−1.26258	+	0.0463002i
$669$	−16.3116	−	11.8220i	−0.630645	−	0.457063i
$670$	−47.2805	+	28.4652i	−1.82660	+	1.09971i
$671$	9.67251	−	16.7533i	0.373403	−	0.646753i
$672$	18.6753	+	33.2552i	0.720414	+	1.28285i
$673$	−18.5127	+	32.0650i	−0.713614	+	1.23602i	0.249878	+	0.968277i	$0.419610\pi$
$673$	−18.5127	+	32.0650i	−0.713614	+	1.23602i	−0.963492	+	0.267738i	$0.913724\pi$
$674$	35.2414	+	19.4944i	1.35745	+	0.750896i
$675$	−20.5535	−	6.59856i	−0.791106	−	0.253979i
$676$	2.92569	−	5.52570i	0.112526	−	0.212527i
$677$	11.5974	+	6.69576i	0.445724	+	0.257339i	0.706023	−	0.708189i	$-0.250488\pi$
$677$	11.5974	+	6.69576i	0.445724	+	0.257339i	−0.260298	+	0.965528i	$0.583821\pi$
$678$	−12.0867	−	25.7823i	−0.464187	−	0.990163i
$679$			11.1716i			0.428728i
$680$	−38.1420	−	19.3085i	−1.46268	−	0.740448i
$681$	−4.35144	−	0.452206i	−0.166747	−	0.0173286i
$682$	−5.27682	+	9.53930i	−0.202060	+	0.365278i
$683$	17.3858			0.665251			0.332625	−	0.943059i	$-0.392066\pi$
$683$	17.3858			0.665251			0.332625	+	0.943059i	$0.392066\pi$
$684$	12.6354	+	22.8986i	0.483127	+	0.875550i
$685$	−54.2099			−2.07125
$686$	−3.07194	+	5.55336i	−0.117287	+	0.212028i
$687$	−27.3415	+	37.7251i	−1.04314	+	1.43930i
$688$	0.552549	+	7.52369i	0.0210657	+	0.286838i
$689$			43.2234i			1.64668i
$690$	20.2603	−	29.0610i	0.771297	−	1.10633i
$691$	−10.2721	−	5.93061i	−0.390770	−	0.225611i	0.291724	−	0.956503i	$-0.405771\pi$
$691$	−10.2721	−	5.93061i	−0.390770	−	0.225611i	−0.682494	+	0.730892i	$0.739105\pi$
$692$	−9.27904	−	4.91296i	−0.352736	−	0.186763i
$693$	−7.23091	+	34.4146i	−0.274680	+	1.30730i
$694$	7.17474	+	3.96883i	0.272349	+	0.150655i
$695$	−22.6973	+	39.3129i	−0.860957	+	1.49122i
$696$	−0.973244	−	1.89232i	−0.0368907	−	0.0717283i
$697$	1.03391	−	1.79078i	0.0391620	−	0.0678306i
$698$	−0.135111	+	0.0813439i	−0.00511404	+	0.00307891i
$699$	0.996643	−	9.59037i	0.0376965	−	0.362741i
$700$	1.18527	+	32.3214i	0.0447988	+	1.22164i
$701$	34.5702	+	19.9591i	1.30570	+	0.753846i	0.981375	−	0.192101i	$-0.0615300\pi$
$701$	34.5702	+	19.9591i	1.30570	+	0.753846i	0.324324	+	0.945946i	$0.394863\pi$
$702$	28.7239	−	6.76423i	1.08411	−	0.255299i
$703$	8.42995	+	10.5390i	0.317941	+	0.397487i
$704$	9.68293	−	22.0589i	0.364939	−	0.831374i
$705$	59.1553	−	26.4206i	2.22792	−	0.995059i
$706$	26.3000	+	43.6841i	0.989815	+	1.64407i
$707$	10.4547	−	18.1081i	0.393189	−	0.681024i
$708$	20.4288	−	30.4784i	0.767762	−	1.14545i
$709$	−11.7027			−0.439505			−0.219753	−	0.975556i	$-0.570525\pi$
$709$	−11.7027			−0.439505			−0.219753	+	0.975556i	$0.570525\pi$
$710$	−21.4924	−	35.6987i	−0.806597	−	1.33975i
$711$	8.31100	−	39.5552i	0.311687	−	1.48344i
$712$	22.0771	+	33.8014i	0.827374	+	1.26676i
$713$			12.2363i			0.458254i
$714$	43.1289	−	20.2188i	1.61406	−	0.756669i
$715$	−31.6860	+	18.2939i	−1.18499	+	0.684153i
$716$	9.56545	+	15.2485i	0.357478	+	0.569864i
$717$	−0.284198	+	0.392130i	−0.0106136	+	0.0146443i
$718$	31.0092	−	18.6691i	1.15725	−	0.696724i
$719$	19.9654	−	34.5812i	0.744585	−	1.28966i	−0.205803	−	0.978593i	$-0.565981\pi$
$719$	19.9654	−	34.5812i	0.744585	−	1.28966i	0.950388	−	0.311066i	$-0.100686\pi$
$720$	−33.5837	+	13.7973i	−1.25159	+	0.514194i
$721$	31.5956			1.17668
$722$	17.8533	−	20.0813i	0.664432	−	0.747349i
$723$	10.4398	+	23.3744i	0.388259	+	0.869304i
$724$	−12.8971	+	24.3585i	−0.479316	+	0.905277i
$725$		−	1.80450i		−	0.0670175i
$726$	−4.28492	+	2.00877i	−0.159028	+	0.0745523i
$727$	−2.26330	+	1.30672i	−0.0839410	+	0.0484634i	−0.541383	−	0.840776i	$-0.682099\pi$
$727$	−2.26330	+	1.30672i	−0.0839410	+	0.0484634i	0.457442	+	0.889239i	$0.348766\pi$
$728$	−24.1777	−	37.0176i	−0.896086	−	1.37196i
$729$	21.9544	+	15.7164i	0.813124	+	0.582090i
$730$	1.31571	+	2.18538i	0.0486965	+	0.0808844i
$731$	9.42159			0.348470
$732$	−12.3903	+	18.4855i	−0.457957	+	0.683242i
$733$	−16.7836	−	29.0701i	−0.619918	−	1.07373i	−0.989500	−	0.144532i	$-0.953832\pi$
$733$	−16.7836	−	29.0701i	−0.619918	−	1.07373i	0.369582	−	0.929198i	$-0.379501\pi$
$734$	−7.99695	+	14.4567i	−0.295173	+	0.533605i
$735$	−34.5947	−	25.0727i	−1.27605	−	0.924822i
$736$	−2.47442	−	26.9268i	−0.0912082	−	0.992534i
$737$	−33.6358	+	19.4196i	−1.23899	+	0.715331i
$738$	−0.577082	−	1.65863i	−0.0212427	−	0.0610549i
$739$	15.2623	+	8.81167i	0.561431	+	0.324142i	0.753720	−	0.657196i	$-0.228258\pi$
$739$	15.2623	+	8.81167i	0.561431	+	0.324142i	−0.192288	+	0.981338i	$0.561591\pi$
$740$	−15.8712	+	9.95604i	−0.583437	+	0.365991i
$741$	−16.3892	−	25.5066i	−0.602072	−	0.937010i
$742$	51.8494	+	28.6814i	1.90345	+	1.05293i
$743$	18.2705			0.670281			0.335141	−	0.942168i	$-0.391216\pi$
$743$	18.2705			0.670281			0.335141	+	0.942168i	$0.391216\pi$
$744$	6.79022	−	10.5433i	0.248941	−	0.386538i
$745$	−53.6957			−1.96726
$746$	−0.711469	−	38.8157i	−0.0260487	−	1.42114i
$747$	−3.49958	−	10.6854i	−0.128043	−	0.390960i
$748$	−26.5894	−	14.0783i	−0.972205	−	0.514753i
$749$	−21.0172	−	12.1343i	−0.767954	−	0.443378i
$750$	6.24437	+	0.533450i	0.228012	+	0.0194788i
$751$	−36.8395	−	21.2693i	−1.34429	−	0.776127i	−0.356857	−	0.934159i	$-0.616152\pi$
$751$	−36.8395	−	21.2693i	−1.34429	−	0.776127i	−0.987434	+	0.158032i	$0.949485\pi$
$752$	21.5224	−	44.5218i	0.784840	−	1.62354i
$753$	7.27373	−	10.0361i	0.265069	−	0.365736i
$754$	1.27234	+	2.11334i	0.0463359	+	0.0769635i
$755$	−4.86919	+	8.43369i	−0.177208	+	0.306933i
$756$	10.9459	−	38.9447i	0.398099	−	1.41641i
$757$	14.5044	−	25.1223i	0.527171	−	0.913087i	−0.472328	−	0.881423i	$-0.656586\pi$
$757$	14.5044	−	25.1223i	0.527171	−	0.913087i	0.999499	−	0.0316637i	$-0.0100805\pi$
$758$	−6.05606	+	10.9480i	−0.219966	+	0.397648i
$759$	14.6309	−	20.1873i	0.531067	−	0.732753i
$760$	24.8661	+	27.8055i	0.901987	+	1.00861i
$761$	−8.77550	+	5.06654i	−0.318112	+	0.183662i	−0.650551	−	0.759463i	$-0.725462\pi$
$761$	−8.77550	+	5.06654i	−0.318112	+	0.183662i	0.332439	+	0.943125i	$0.392128\pi$
$762$	−6.63048	−	14.1435i	−0.240197	−	0.512366i
$763$	59.5944	−	34.4068i	2.15746	−	1.24561i
$764$	28.5836	−	1.04819i	1.03412	−	0.0379223i
$765$	14.1130	+	43.0919i	0.510256	+	1.55799i
$766$	−1.69906	−	0.939864i	−0.0613896	−	0.0339587i
$767$	−21.2673	+	36.8360i	−0.767917	+	1.33007i
$768$	−12.8102	+	24.5743i	−0.462248	+	0.886750i
$769$	7.21239	−	12.4922i	0.260086	−	0.450481i	−0.706179	−	0.708033i	$-0.749583\pi$
$769$	7.21239	−	12.4922i	0.260086	−	0.450481i	0.966264	+	0.257552i	$0.0829159\pi$
$770$	0.919196	+	50.1486i	0.0331255	+	1.80723i
$771$	−3.72365	+	35.8314i	−0.134104	+	1.29044i
$772$	−4.83008	−	7.69976i	−0.173839	−	0.277121i
$773$	−20.1732	+	11.6470i	−0.725580	+	0.418914i	−0.816803	−	0.576916i	$-0.804256\pi$
$773$	−20.1732	+	11.6470i	−0.725580	+	0.418914i	0.0912227	+	0.995831i	$0.470922\pi$
$774$	5.23006	−	6.05571i	0.187991	−	0.217668i
$775$	9.20985	−	5.31731i	0.330827	−	0.191003i
$776$	−6.79618	+	4.43887i	−0.243969	+	0.159346i
$777$	2.15774	−	20.7632i	0.0774085	−	0.744877i
$778$	22.2765	−	40.2709i	0.798652	−	1.44378i
$779$	−1.40899	+	1.12702i	−0.0504821	+	0.0403796i
$780$	37.7756	−	18.5610i	1.35258	−	0.664592i
$781$	−14.6626	−	25.3964i	−0.524670	−	0.908755i
$782$	−33.7647	+	0.618888i	−1.20742	+	0.0221314i
$783$	−0.689914	+	2.14898i	−0.0246555	+	0.0767983i
$784$	−32.5237	+	2.38858i	−1.16156	+	0.0853064i
$785$			7.58596i			0.270754i
$786$	2.07689	−	24.3113i	0.0740804	−	0.867157i
$787$	−41.3050	+	23.8474i	−1.47236	+	0.850069i	−0.999517	−	0.0310765i	$-0.990106\pi$
$787$	−41.3050	+	23.8474i	−1.47236	+	0.850069i	−0.472845	+	0.881145i	$0.656773\pi$
$788$	32.8006	−	20.5759i	1.16847	−	0.732986i
$789$	−9.14320	+	12.6156i	−0.325506	+	0.449126i
$790$	−1.05650	−	57.6394i	−0.0375885	−	2.05072i
$791$	45.2514			1.60895
$792$	−23.8090	+	9.27523i	−0.846014	+	0.329581i
$793$	12.8988	−	22.3414i	0.458050	−	0.793366i
$794$	−20.9436	+	12.6091i	−0.743260	+	0.447480i
$795$	−33.1014	+	45.6724i	−1.17398	+	1.61983i
$796$	11.2293	+	5.94558i	0.398013	+	0.210735i
$797$	17.5689	−	10.1434i	0.622323	−	0.359299i	−0.155450	−	0.987844i	$-0.549683\pi$
$797$	17.5689	−	10.1434i	0.622323	−	0.359299i	0.777773	+	0.628545i	$0.216349\pi$
$798$	−41.4722	+	2.73474i	−1.46810	+	0.0968089i
$799$	−53.4849	−	30.8795i	−1.89216	−	1.09244i
$800$	−19.1915	+	13.5635i	−0.678524	+	0.479540i
$801$	8.80501	−	41.9064i	0.311110	−	1.48069i
$802$	10.1717	−	18.3882i	0.359176	−	0.649309i
$803$	0.897605	+	1.55470i	0.0316758	+	0.0548641i
$804$	40.1001	−	19.7032i	1.41422	−	0.694878i
$805$	28.1492	+	48.7559i	0.992130	+	1.71842i
$806$	−7.03693	+	12.7212i	−0.247865	+	0.448084i
$807$	−2.06686	+	19.8887i	−0.0727568	+	0.700115i
$808$	15.1699	−	0.834915i	0.533675	−	0.0293722i
$809$			14.0970i			0.495624i	0.968808	+	0.247812i	$0.0797116\pi$
$809$			14.0970i			0.495624i	−0.968808	+	0.247812i	$0.920288\pi$
$810$	35.5315	+	14.8498i	1.24845	+	0.521770i
$811$	−5.19959	+	3.00199i	−0.182582	+	0.105414i	−0.588505	−	0.808493i	$-0.700283\pi$
$811$	−5.19959	+	3.00199i	−0.182582	+	0.105414i	0.405923	+	0.913907i	$0.366950\pi$
$812$	3.37938	−	0.123926i	0.118593	−	0.00434894i
$813$	−0.00243716	+	0.0234520i	−8.54749e−5	+	0.000822497i
$814$	−11.2961	+	6.80082i	−0.395928	+	0.238369i
$815$	56.6745			1.98522
$816$	29.4365	+	18.2035i	1.03048	+	0.637250i
$817$	−7.65696	−	2.99217i	−0.267883	−	0.104683i
$818$	−0.109499	+	0.0659241i	−0.00382855	+	0.00230498i
$819$	−9.64281	+	45.8938i	−0.336947	+	1.60366i
$820$	−1.33104	−	2.12185i	−0.0464821	−	0.0740983i
$821$			25.4733i			0.889023i	0.895773	+	0.444511i	$0.146623\pi$
$821$			25.4733i			0.889023i	−0.895773	+	0.444511i	$0.853377\pi$
$822$	43.7281	+	3.73565i	1.52519	+	0.130296i
$823$	16.0564	+	9.27019i	0.559692	+	0.323139i	0.753022	−	0.657995i	$-0.228595\pi$
$823$	16.0564	+	9.27019i	0.559692	+	0.323139i	−0.193330	+	0.981134i	$0.561929\pi$
$824$	12.5540	+	19.2209i	0.437340	+	0.669593i
$825$	−21.5521	−	2.23972i	−0.750348	−	0.0779771i
$826$	30.0752	+	49.9545i	1.04645	+	1.73814i
$827$	1.50477	+	2.60634i	0.0523261	+	0.0906314i	0.891002	−	0.453999i	$-0.150003\pi$
$827$	1.50477	+	2.60634i	0.0523261	+	0.0906314i	−0.838676	+	0.544631i	$0.816670\pi$
$828$	−18.3455	+	22.0457i	−0.637550	+	0.766142i
$829$	28.3457			0.984487			0.492244	−	0.870457i	$-0.336177\pi$
$829$	28.3457			0.984487			0.492244	+	0.870457i	$0.336177\pi$
$830$	−8.27173	−	13.7392i	−0.287116	−	0.476896i
$831$	−16.7720	−	1.74296i	−0.581814	−	0.0604628i
$832$	12.9127	−	29.4167i	0.447668	−	1.01984i
$833$			40.7280i			1.41114i
$834$	21.0177	−	30.1474i	0.727785	−	1.04392i
$835$	42.7812	+	24.6998i	1.48051	+	0.854770i
$836$	17.1383	+	19.8859i	0.592739	+	0.687768i
$837$	−13.0010	+	2.81118i	−0.449379	+	0.0971686i
$838$	−0.353805	−	19.3026i	−0.0122220	−	0.666796i
$839$	21.4490	+	37.1508i	0.740502	+	1.28259i	0.952267	+	0.305266i	$0.0987454\pi$
$839$	21.4490	+	37.1508i	0.740502	+	1.28259i	−0.211765	+	0.977321i	$0.567921\pi$
$840$	2.80118	−	57.6308i	0.0966498	−	1.98845i
$841$	28.8113			0.993494
$842$	−0.469380	−	25.6080i	−0.0161759	−	0.882509i
$843$	18.2703	−	8.16011i	0.629264	−	0.281049i
$844$	−6.27734	+	3.93779i	−0.216075	+	0.135544i
$845$	−8.19152	+	4.72937i	−0.281797	+	0.162695i
$846$	−49.5380	+	17.2356i	−1.70315	+	0.592573i
$847$		−	7.52062i		−	0.258411i
$848$	3.15343	+	42.9383i	0.108289	+	1.47451i
$849$	35.6242	−	15.9109i	1.22262	−	0.546061i
$850$	15.1383	+	25.1445i	0.519239	+	0.862450i
$851$	−7.39989	+	12.8170i	−0.253665	+	0.439361i
$852$	14.8767	+	30.2772i	0.509669	+	1.03728i
$853$	12.7676	+	22.1141i	0.437155	+	0.757174i	0.997469	−	0.0711062i	$-0.0226529\pi$
$853$	12.7676	+	22.1141i	0.437155	+	0.757174i	−0.560314	+	0.828280i	$0.689320\pi$
$854$	−18.2409	−	30.2979i	−0.624190	−	1.03677i
$855$	2.21570	−	39.5030i	0.0757752	−	1.35097i
$856$	−0.969050	−	17.6071i	−0.0331215	−	0.601797i
$857$	−17.8659	+	10.3149i	−0.610288	+	0.352350i	−0.773078	−	0.634311i	$-0.781284\pi$
$857$	−17.8659	+	10.3149i	−0.610288	+	0.352350i	0.162790	+	0.986661i	$0.447951\pi$
$858$	26.8200	−	12.5732i	0.915619	−	0.429241i
$859$	44.1631	+	25.4976i	1.50683	+	0.869967i	0.999969	+	0.00793693i	$0.00252643\pi$
$859$	44.1631	+	25.4976i	1.50683	+	0.869967i	0.506858	+	0.862030i	$0.330807\pi$
$860$	5.34025	−	10.0861i	0.182101	−	0.343932i
$861$	2.77588	+	0.288473i	0.0946018	+	0.00983113i
$862$	−0.327704	−	17.8786i	−0.0111617	−	0.608947i
$863$	−0.580286			−0.0197532			−0.00987658	−	0.999951i	$-0.503144\pi$
$863$	−0.580286			−0.0197532			−0.00987658	+	0.999951i	$0.503144\pi$
$864$	28.0409	−	8.81521i	0.953971	−	0.299899i
$865$	7.94181	+	13.7556i	0.270030	+	0.467705i
$866$	−0.534500	−	29.1607i	−0.0181630	−	0.990921i
$867$	8.08648	−	11.1575i	0.274631	−	0.378929i
$868$	10.5905	+	16.8825i	0.359464	+	0.573031i
$869$		−	40.5713i		−	1.37629i
$870$	−0.274011	+	3.20747i	−0.00928985	+	0.108743i
$871$	−44.8551	+	25.8971i	−1.51986	+	0.877490i
$872$	44.6100	+	22.5828i	1.51069	+	0.764749i
$873$	8.42579	+	1.77035i	0.285170	+	0.0599174i
$874$	27.6372	+	10.2202i	0.934843	+	0.345704i
$875$	−4.97976	+	8.62520i	−0.168347	+	0.291585i
$876$	−0.910712	−	1.85349i	−0.0307701	−	0.0626236i
$877$	−23.2433			−0.784870			−0.392435	−	0.919780i	$-0.628367\pi$
$877$	−23.2433			−0.784870			−0.392435	+	0.919780i	$0.628367\pi$
$878$	−17.4337	+	0.319549i	−0.588358	+	0.0107843i
$879$	−26.5138	−	19.2160i	−0.894288	−	0.648140i
$880$	−30.1423	+	20.4849i	−1.01610	+	0.690547i
$881$			7.48812i			0.252281i	0.992012	+	0.126141i	$0.0402590\pi$
$881$			7.48812i			0.252281i	−0.992012	+	0.126141i	$0.959741\pi$
$882$	26.1779	+	22.6087i	0.881454	+	0.761276i
$883$	24.9720	−	14.4176i	0.840374	−	0.485190i	−0.0170172	−	0.999855i	$-0.505417\pi$
$883$	24.9720	−	14.4176i	0.840374	−	0.485190i	0.857391	+	0.514665i	$0.172084\pi$
$884$	−35.4584	−	18.7741i	−1.19260	−	0.631442i
$885$	−50.6821	+	22.6362i	−1.70366	+	0.760908i
$886$	4.03210	+	2.23043i	0.135461	+	0.0749326i
$887$	14.8290	−	25.6846i	0.497909	−	0.862403i	−0.502088	−	0.864816i	$-0.667435\pi$
$887$	14.8290	−	25.6846i	0.497909	−	0.862403i	0.999997	+	0.00241298i	$0.000768076\pi$
$888$	13.4885	−	6.93729i	0.452644	−	0.232800i
$889$	24.8238			0.832565
$890$	−1.11930	−	61.0655i	−0.0375189	−	2.04692i
$891$	24.8101	+	10.9073i	0.831168	+	0.365408i
$892$	20.5579	+	10.8848i	0.688329	+	0.364449i
$893$	33.6605	+	42.0819i	1.12640	+	1.40822i
$894$	43.3134	+	3.70022i	1.44862	+	0.123754i
$895$		−	27.2312i		−	0.910240i
$896$	−26.7189	−	35.0094i	−0.892616	−	1.16958i
$897$	19.5110	−	26.9209i	0.651455	−	0.898861i
$898$	−13.0068	+	23.5134i	−0.434044	+	0.784652i
$899$	−0.555953	−	0.962938i	−0.0185421	−	0.0321158i
$900$	24.5651	+	4.22799i	0.818835	+	0.140933i
$901$	53.7697			1.79133
$902$	−0.909216	−	1.51020i	−0.0302736	−	0.0502841i
$903$	5.18561	+	11.6105i	0.172566	+	0.386373i
$904$	17.9799	+	27.5283i	0.598003	+	0.915579i
$905$	36.1100	−	20.8481i	1.20034	−	0.693016i
$906$	4.50888	−	6.46745i	0.149798	−	0.214867i
$907$	31.9137	−	18.4254i	1.05968	−	0.611804i	0.134333	−	0.990936i	$-0.457111\pi$
$907$	31.9137	−	18.4254i	1.05968	−	0.611804i	0.925342	+	0.379132i	$0.123778\pi$
$908$	5.04827	−	0.185126i	0.167533	−	0.00614363i
$909$	−12.0006	−	10.7546i	−0.398034	−	0.356708i
$910$	1.22580	+	66.8759i	0.0406348	+	2.21691i
$911$	−5.88938	+	10.2007i	−0.195124	+	0.337965i	−0.946941	−	0.321407i	$-0.895844\pi$
$911$	−5.88938	+	10.2007i	−0.195124	+	0.337965i	0.751817	+	0.659372i	$0.229178\pi$
$912$	−18.1420	−	24.1427i	−0.600741	−	0.799444i
$913$	−5.64316	−	9.77423i	−0.186761	−	0.323480i
$914$	−18.3059	+	11.0211i	−0.605504	+	0.364544i
$915$	30.7391	−	13.7291i	1.01620	−	0.453869i
$916$	25.1740	−	47.5457i	0.831771	−	1.57095i
$917$	33.5807	+	19.3878i	1.10893	+	0.640243i
$918$	−8.41467	−	35.7324i	−0.277726	−	1.17934i
$919$		−	48.5036i		−	1.59999i	−0.600010	−	0.799993i	$-0.704837\pi$
$919$		−	48.5036i		−	1.59999i	0.600010	−	0.799993i	$-0.295163\pi$
$920$	−18.4756	+	36.4967i	−0.609123	+	1.20326i
$921$	−5.12987	+	49.3631i	−0.169035	+	1.62657i
$922$	12.0609	−	0.221069i	0.397204	−	0.00728052i
$923$	−19.5534	−	33.8675i	−0.643608	−	1.11476i
$924$	2.71432	−	40.5155i	0.0892946	−	1.33286i
$925$	12.8625			0.422917
$926$	14.3628	−	0.263262i	0.471991	−	0.00865134i
$927$	5.00692	−	23.8298i	0.164449	−	0.782674i
$928$	1.41813	+	2.00658i	0.0465524	+	0.0658691i
$929$	13.9413	−	8.04901i	0.457399	−	0.264079i	−0.253551	−	0.967322i	$-0.581599\pi$
$929$	13.9413	−	8.04901i	0.457399	−	0.264079i	0.710950	+	0.703243i	$0.248265\pi$
$930$	−17.1778	+	8.05292i	−0.563281	+	0.264066i
$931$	12.9347	−	33.0998i	0.423916	−	1.08480i
$932$	0.408010	+	11.1262i	0.0133648	+	0.364450i
$933$	−1.88348	+	2.59877i	−0.0616622	+	0.0850799i
$934$	−7.48067	−	4.13806i	−0.244775	−	0.135401i
$935$	22.7575	+	39.4172i	0.744251	+	1.28908i
$936$	−31.7505	+	12.3690i	−1.03780	+	0.404294i
$937$	−2.32881	−	4.03361i	−0.0760788	−	0.131772i	0.825476	−	0.564437i	$-0.190907\pi$
$937$	−2.32881	−	4.03361i	−0.0760788	−	0.131772i	−0.901555	+	0.432665i	$0.857573\pi$
$938$	1.30123	+	70.9911i	0.0424866	+	2.31794i
$939$	3.16152	+	7.07859i	0.103172	+	0.231001i
$940$	−63.3731	+	39.7541i	−2.06700	+	1.29664i
$941$	−39.8576	−	23.0118i	−1.29932	−	0.750163i	−0.319034	−	0.947743i	$-0.603358\pi$
$941$	−39.8576	−	23.0118i	−1.29932	−	0.750163i	−0.980287	+	0.197580i	$0.936692\pi$
$942$	0.522755	−	6.11917i	0.0170323	−	0.199373i
$943$	−1.71353	−	0.989308i	−0.0558003	−	0.0322163i
$944$	−18.4396	+	38.1446i	−0.600157	+	1.24150i
$945$	−45.3355	+	41.1094i	−1.47477	+	1.33729i
$946$	3.88773	−	7.02812i	0.126401	−	0.228504i
$947$	7.16391	+	12.4083i	0.232796	+	0.403214i	0.958630	−	0.284656i	$-0.0918793\pi$
$947$	7.16391	+	12.4083i	0.232796	+	0.403214i	−0.725834	+	0.687870i	$0.758546\pi$
$948$	−3.11976	+	46.5673i	−0.101325	+	1.51244i
$949$	1.19700	+	2.07327i	0.0388564	+	0.0673013i
$950$	−4.31739	−	25.2427i	−0.140075	−	0.818983i
$951$	−42.5709	+	19.0135i	−1.38046	+	0.616555i
$952$	−46.0497	+	30.0770i	−1.49248	+	0.974801i
$953$	26.2384	+	15.1488i	0.849946	+	0.490717i	0.860633	−	0.509226i	$-0.170068\pi$
$953$	26.2384	+	15.1488i	0.849946	+	0.490717i	−0.0106866	+	0.999943i	$0.503402\pi$
$954$	29.8484	−	34.5604i	0.966376	−	1.11893i
$955$	−37.4734	−	21.6353i	−1.21261	−	0.700101i
$956$	0.261668	−	0.494209i	0.00846295	−	0.0159838i
$957$	−0.234175	+	2.25339i	−0.00756979	+	0.0728416i
$958$	−13.5312	−	7.48499i	−0.437172	−	0.241829i
$959$	−34.8723	+	60.4007i	−1.12609	+	1.95044i
$960$	36.1722	−	21.1946i	1.16745	−	0.684052i
$961$	−12.2236	+	21.1718i	−0.394308	+	0.682962i
$962$	−15.0639	+	9.06926i	−0.485681	+	0.292405i
$963$	−12.4824	+	13.9286i	−0.402241	+	0.448842i
$964$	−15.7083	−	25.0410i	−0.505930	−	0.806517i
$965$			13.7504i			0.442642i
$966$	−19.3466	−	41.2685i	−0.622467	−	1.32779i
$967$		−	49.3216i		−	1.58608i	−0.609172	−	0.793038i	$-0.708498\pi$
$967$		−	49.3216i		−	1.58608i	0.609172	−	0.793038i	$-0.291502\pi$
$968$	4.57511	−	2.98820i	0.147050	−	0.0960442i
$969$	−31.7302	+	20.3881i	−1.01932	+	0.654960i
$970$	12.2780	−	0.225048i	0.394222	−	0.00722586i
$971$	14.3746	−	24.8975i	0.461303	−	0.798999i	−0.537724	−	0.843121i	$-0.680716\pi$
$971$	14.3746	−	24.8975i	0.461303	−	0.798999i	0.999026	+	0.0441217i	$0.0140489\pi$
$972$	−27.6380	−	14.4271i	−0.886490	−	0.462748i
$973$	29.2016	+	50.5786i	0.936160	+	1.62148i
$974$	−21.4087	+	38.7021i	−0.685981	+	1.24010i
$975$	−28.7409	−	2.98679i	−0.920445	−	0.0956537i
$976$	11.1838	−	23.1351i	0.357984	−	0.740536i
$977$	−7.76297	+	4.48195i	−0.248359	+	0.143390i	−0.619013	−	0.785381i	$-0.712467\pi$
$977$	−7.76297	+	4.48195i	−0.248359	+	0.143390i	0.370653	+	0.928771i	$0.379134\pi$
$978$	−45.7162	−	3.90549i	−1.46184	−	0.124884i
$979$		−	42.9829i		−	1.37374i
$980$	43.6004	+	23.0851i	1.39276	+	0.737425i
$981$	−16.5062	−	50.3992i	−0.527003	−	1.60912i
$982$	−8.86113	−	4.90168i	−0.282770	−	0.156419i
$983$	13.1412	+	22.7612i	0.419139	+	0.725970i	0.995853	−	0.0909759i	$-0.0289986\pi$
$983$	13.1412	+	22.7612i	0.419139	+	0.725970i	−0.576714	+	0.816946i	$0.695665\pi$
$984$	0.927461	+	1.80331i	0.0295664	+	0.0574873i
$985$	−58.5762			−1.86639
$986$	2.62899	−	1.58279i	0.0837241	−	0.0504062i
$987$	8.61577	−	82.9068i	0.274243	−	2.63895i
$988$	22.8548	+	26.5189i	0.727107	+	0.843678i
$989$		−	9.01518i		−	0.286666i
$990$	37.9684	+	7.25372i	1.20671	+	0.230538i
$991$	−17.2201	−	9.94205i	−0.547016	−	0.315820i	0.200902	−	0.979611i	$-0.435613\pi$
$991$	−17.2201	−	9.94205i	−0.547016	−	0.315820i	−0.747918	+	0.663792i	$0.768946\pi$
$992$	−6.06241	+	13.1506i	−0.192482	+	0.417533i
$993$	5.13085	−	49.3725i	0.162822	−	1.56679i
$994$	−53.6013	+	0.982481i	−1.70013	+	0.0311624i
$995$	−9.61103	−	16.6468i	−0.304690	−	0.527739i
$996$	5.72556	+	11.6527i	0.181421	+	0.369230i
$997$	−40.3929			−1.27926			−0.639629	−	0.768684i	$-0.720912\pi$
$997$	−40.3929			−1.27926			−0.639629	+	0.768684i	$0.720912\pi$
$998$	−23.2673	+	42.0620i	−0.736514	+	1.33145i
$999$	−15.3180	−	4.91772i	−0.484639	−	0.155590i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.o.a.11.19	✓	232
4.3	odd	2	inner	684.2.o.a.11.59	yes	232
9.5	odd	6		684.2.bi.a.239.20	yes	232
19.7	even	3		684.2.bi.a.83.97	yes	232
36.23	even	6		684.2.bi.a.239.97	yes	232
76.7	odd	6		684.2.bi.a.83.20	yes	232
171.140	odd	6	inner	684.2.o.a.311.59	yes	232
684.311	even	6	inner	684.2.o.a.311.19	yes	232

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.o.a.11.19	✓	232	1.1	even	1	trivial
684.2.o.a.11.59	yes	232	4.3	odd	2	inner
684.2.o.a.311.19	yes	232	684.311	even	6	inner
684.2.o.a.311.59	yes	232	171.140	odd	6	inner
684.2.bi.a.83.20	yes	232	76.7	odd	6
684.2.bi.a.83.97	yes	232	19.7	even	3
684.2.bi.a.239.20	yes	232	9.5	odd	6
684.2.bi.a.239.97	yes	232	36.23	even	6

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	684.2.o.a.11.19

Level	$684$
Weight	$2$
Character	684.11
Analytic conductor	$5.462$
Analytic rank	$0$
Dimension	$232$
Inner twists	$4$