LMFDB - Embedded newform 684.2.o.a.11.59

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			11.59
Character	$\chi$	$=$	684.11
Dual form			684.2.o.a.311.59

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0259174 + 1.41398i) q^{2} +(0.706340 + 1.58148i) q^{3} +(-1.99866 - 0.0732931i) q^{4} -3.02562i q^{5} +(-2.25448 + 0.957760i) q^{6} +(3.37115 + 1.94633i) q^{7} +(0.155435 - 2.82415i) q^{8} +(-2.00217 + 2.23413i) q^{9} +(4.27815 + 0.0784162i) q^{10} +(1.50566 - 2.60787i) q^{11} +(-1.29582 - 3.21261i) q^{12} +(-2.00787 + 3.47774i) q^{13} +(-2.83944 + 4.71628i) q^{14} +(4.78496 - 2.13712i) q^{15} +(3.98926 + 0.292976i) q^{16} +(4.32629 + 2.49779i) q^{17} +(-3.10711 - 2.88892i) q^{18} +(2.72273 + 3.40393i) q^{19} +(-0.221757 + 6.04718i) q^{20} +(-0.696914 + 6.70618i) q^{21} +(3.64845 + 2.19655i) q^{22} +(-2.39004 + 4.13967i) q^{23} +(4.57614 - 1.74899i) q^{24} -4.15438 q^{25} +(-4.86540 - 2.92922i) q^{26} +(-4.94744 - 1.58834i) q^{27} +(-6.59511 - 4.13713i) q^{28} +0.434362i q^{29} +(2.89782 + 6.82121i) q^{30} +(2.21690 - 1.27993i) q^{31} +(-0.517652 + 5.63312i) q^{32} +(5.18781 + 0.539123i) q^{33} +(-3.64394 + 6.05254i) q^{34} +(5.88886 - 10.1998i) q^{35} +(4.16539 - 4.31851i) q^{36} -3.09614 q^{37} +(-4.88364 + 3.76166i) q^{38} +(-6.91822 - 0.718950i) q^{39} +(-8.54481 - 0.470286i) q^{40} -0.413929i q^{41} +(-9.46431 - 1.15923i) q^{42} +(-1.63331 + 0.942994i) q^{43} +(-3.20043 + 5.10189i) q^{44} +(6.75962 + 6.05780i) q^{45} +(-5.79146 - 3.48675i) q^{46} +12.3628 q^{47} +(2.35443 + 6.51588i) q^{48} +(4.07641 + 7.06056i) q^{49} +(0.107671 - 5.87419i) q^{50} +(-0.894370 + 8.60624i) q^{51} +(4.26794 - 6.80364i) q^{52} +(9.32144 - 5.38174i) q^{53} +(2.37410 - 6.95440i) q^{54} +(-7.89043 - 4.55554i) q^{55} +(6.02073 - 9.21810i) q^{56} +(-3.46008 + 6.71028i) q^{57} +(-0.614177 - 0.0112575i) q^{58} -10.5919 q^{59} +(-9.72013 + 3.92066i) q^{60} -6.42411 q^{61} +(1.75233 + 3.16782i) q^{62} +(-11.0980 + 3.63468i) q^{63} +(-7.95168 - 0.877943i) q^{64} +(10.5223 + 6.07506i) q^{65} +(-0.896762 + 7.32146i) q^{66} +(-11.1698 - 6.44889i) q^{67} +(-8.46370 - 5.30930i) q^{68} +(-8.23500 - 0.855791i) q^{69} +(14.2697 + 8.59106i) q^{70} +(4.86918 - 8.43367i) q^{71} +(5.99831 + 6.00169i) q^{72} +(0.298078 - 0.516286i) q^{73} +(0.0802438 - 4.37786i) q^{74} +(-2.93440 - 6.57007i) q^{75} +(-5.19232 - 7.00284i) q^{76} +(10.1516 - 5.86101i) q^{77} +(1.19588 - 9.76356i) q^{78} +(11.6679 - 6.73648i) q^{79} +(0.886433 - 12.0700i) q^{80} +(-0.982644 - 8.94620i) q^{81} +(0.585286 + 0.0107280i) q^{82} +(1.87399 - 3.24584i) q^{83} +(1.88441 - 13.3523i) q^{84} +(7.55735 - 13.0897i) q^{85} +(-1.29104 - 2.33391i) q^{86} +(-0.686935 + 0.306807i) q^{87} +(-7.13100 - 4.65756i) q^{88} +(-12.3615 + 7.13690i) q^{89} +(-8.74078 + 9.40094i) q^{90} +(-13.5377 + 7.81597i) q^{91} +(5.08028 - 8.09861i) q^{92} +(3.59007 + 2.60193i) q^{93} +(-0.320410 + 17.4806i) q^{94} +(10.2990 - 8.23795i) q^{95} +(-9.27431 + 3.16024i) q^{96} +(-1.43496 - 2.48542i) q^{97} +(-10.0891 + 5.58096i) 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 $

$2$	−0.0259174	+	1.41398i	−0.0183264	+	0.999832i
$2$	−0.0259174	+	1.41398i	−0.0183264	+	0.999832i
$3$	0.706340	+	1.58148i	0.407805	+	0.913069i
$3$	0.706340	+	1.58148i	0.407805	+	0.913069i
$4$	−1.99866	−	0.0732931i	−0.999328	−	0.0366466i
$5$		−	3.02562i		−	1.35310i	−0.736397	−	0.676549i	$-0.763475\pi$
$5$		−	3.02562i		−	1.35310i	0.736397	−	0.676549i	$-0.236525\pi$
$6$	−2.25448	+	0.957760i	−0.920389	+	0.391004i
$7$	3.37115	+	1.94633i	1.27417	+	0.735644i	0.975771	−	0.218796i	$-0.0702129\pi$
$7$	3.37115	+	1.94633i	1.27417	+	0.735644i	0.298403	+	0.954440i	$0.403546\pi$
$8$	0.155435	−	2.82415i	0.0549545	−	0.998489i
$9$	−2.00217	+	2.23413i	−0.667389	+	0.744709i
$10$	4.27815	+	0.0784162i	1.35287	+	0.0247974i
$11$	1.50566	−	2.60787i	0.453972	−	0.786303i	−0.544656	−	0.838660i	$-0.683340\pi$
$11$	1.50566	−	2.60787i	0.453972	−	0.786303i	0.998628	+	0.0523562i	$0.0166731\pi$
$12$	−1.29582	−	3.21261i	−0.374071	−	0.927400i
$13$	−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
$16$	3.98926	+	0.292976i	0.997314	+	0.0732439i
$17$	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	$0.459519\pi$
$18$	−3.10711	−	2.88892i	−0.732353	−	0.680925i
$19$	2.72273	+	3.40393i	0.624637	+	0.780915i
$19$	2.72273	+	3.40393i	0.624637	+	0.780915i
$20$	−0.221757	+	6.04718i	−0.0495864	+	1.35219i
$21$	−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	−0.999998	−	0.00189485i	$-0.999397\pi$
$23$	−2.39004	+	4.13967i	−0.498358	+	0.863182i	0.501640	+	0.865076i	$0.332730\pi$
$24$	4.57614	−	1.74899i	0.934100	−	0.357012i
$25$	−4.15438			−0.830875
$26$	−4.86540	−	2.92922i	−0.954183	−	0.574467i
$27$	−4.94744	−	1.58834i	−0.952136	−	0.305676i
$28$	−6.59511	−	4.13713i	−1.24636	−	0.781844i
$29$			0.434362i			0.0806590i	0.999186	+	0.0403295i	$0.0128408\pi$
$29$			0.434362i			0.0806590i	−0.999186	+	0.0403295i	$0.987159\pi$
$30$	2.89782	+	6.82121i	0.529067	+	1.24538i
$31$	2.21690	−	1.27993i	0.398167	−	0.229882i	−0.287525	−	0.957773i	$-0.592833\pi$
$31$	2.21690	−	1.27993i	0.398167	−	0.229882i	0.685693	+	0.727891i	$0.259499\pi$
$32$	−0.517652	+	5.63312i	−0.0915087	+	0.995804i
$33$	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
$36$	4.16539	−	4.31851i	0.694232	−	0.719751i
$37$	−3.09614			−0.509002			−0.254501	−	0.967073i	$-0.581911\pi$
$37$	−3.09614			−0.509002			−0.254501	+	0.967073i	$0.581911\pi$
$38$	−4.88364	+	3.76166i	−0.792231	+	0.610221i
$39$	−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	$-0.0102903\pi$
$42$	−9.46431	−	1.15923i	−1.46037	−	0.178872i
$43$	−1.63331	+	0.942994i	−0.249078	+	0.143805i	−0.619342	−	0.785121i	$-0.712601\pi$
$43$	−1.63331	+	0.942994i	−0.249078	+	0.143805i	0.370264	+	0.928927i	$0.379267\pi$
$44$	−3.20043	+	5.10189i	−0.482483	+	0.769139i
$45$	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	$-0.142359\pi$
$47$	12.3628			1.80329			0.901647	+	0.432474i	$0.142359\pi$
$48$	2.35443	+	6.51588i	0.339833	+	0.940486i
$49$	4.07641	+	7.06056i	0.582345	+	1.00865i
$50$	0.107671	−	5.87419i	0.0152269	−	0.830736i
$51$	−0.894370	+	8.60624i	−0.125237	+	1.20511i
$52$	4.26794	−	6.80364i	0.591857	−	0.943495i
$53$	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	$0.0685190\pi$
$54$	2.37410	−	6.95440i	0.323074	−	0.946374i
$55$	−7.89043	−	4.55554i	−1.06395	−	0.614269i
$56$	6.02073	−	9.21810i	0.804554	−	1.23182i
$57$	−3.46008	+	6.71028i	−0.458299	+	0.888798i
$58$	−0.614177	−	0.0112575i	−0.0806454	−	0.00147819i
$59$	−10.5919			−1.37895			−0.689477	−	0.724308i	$-0.742160\pi$
$59$	−10.5919			−1.37895			−0.689477	+	0.724308i	$0.742160\pi$
$60$	−9.72013	+	3.92066i	−1.25486	+	0.506154i
$61$	−6.42411			−0.822524			−0.411262	−	0.911517i	$-0.634912\pi$
$61$	−6.42411			−0.822524			−0.411262	+	0.911517i	$0.634912\pi$
$62$	1.75233	+	3.16782i	0.222547	+	0.402314i
$63$	−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
$66$	−0.896762	+	7.32146i	−0.110384	+	0.901210i
$67$	−11.1698	−	6.44889i	−1.36461	−	0.787858i	−0.374376	−	0.927277i	$-0.622143\pi$
$67$	−11.1698	−	6.44889i	−1.36461	−	0.787858i	−0.990233	+	0.139420i	$0.955476\pi$
$68$	−8.46370	−	5.30930i	−1.02637	−	0.643848i
$69$	−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	$-0.637219\pi$
$71$	4.86918	−	8.43367i	0.577866	−	1.00089i	0.995724	−	0.0923804i	$-0.0294476\pi$
$72$	5.99831	+	6.00169i	0.706908	+	0.707306i
$73$	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	$0.155559\pi$
$74$	0.0802438	−	4.37786i	0.00932815	−	0.508916i
$75$	−2.93440	−	6.57007i	−0.338835	−	0.758646i
$76$	−5.19232	−	7.00284i	−0.595600	−	0.803281i
$77$	10.1516	−	5.86101i	1.15688	−	0.667924i
$78$	1.19588	−	9.76356i	0.135407	−	1.10551i
$79$	11.6679	−	6.73648i	1.31274	−	0.757913i	0.330195	−	0.943913i	$-0.392886\pi$
$79$	11.6679	−	6.73648i	1.31274	−	0.757913i	0.982550	+	0.185999i	$0.0595522\pi$
$80$	0.886433	−	12.0700i	0.0991062	−	1.34946i
$81$	−0.982644	−	8.94620i	−0.109183	−	0.994022i
$82$	0.585286	+	0.0107280i	0.0646340	+	0.00118471i
$83$	1.87399	−	3.24584i	0.205697	−	0.356277i	−0.744658	−	0.667446i	$-0.767387\pi$
$83$	1.87399	−	3.24584i	0.205697	−	0.356277i	0.950354	+	0.311169i	$0.100721\pi$
$84$	1.88441	−	13.3523i	0.205606	−	1.45685i
$85$	7.55735	−	13.0897i	0.819710	−	1.41978i
$86$	−1.29104	−	2.33391i	−0.139216	−	0.251672i
$87$	−0.686935	+	0.306807i	−0.0736472	+	0.0328932i
$88$	−7.13100	−	4.65756i	−0.760167	−	0.496497i
$89$	−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	$0.606430\pi$
$90$	−8.74078	+	9.40094i	−0.921359	+	0.990946i
$91$	−13.5377	+	7.81597i	−1.41913	+	0.819337i
$92$	5.08028	−	8.09861i	0.529656	−	0.844339i
$93$	3.59007	+	2.60193i	0.372273	+	0.269807i
$94$	−0.320410	+	17.4806i	−0.0330478	+	1.80299i
$95$	10.2990	−	8.23795i	1.05665	−	0.845196i
$96$	−9.27431	+	3.16024i	−0.946556	+	0.322541i
$97$	−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	$0.879876\pi$
$98$	−10.0891	+	5.58096i	−1.01915	+	0.563762i
$99$	2.81174	+	8.58523i	0.282591	+	0.862848i
$100$	8.30317	+	0.304487i	0.830317	+	0.0304487i
$101$			5.37149i			0.534483i	0.963630	+	0.267241i	$0.0861121\pi$
$101$			5.37149i			0.534483i	−0.963630	+	0.267241i	$0.913888\pi$
$102$	−12.1458	−	1.48767i	−1.20262	−	0.147301i
$103$	7.02928	−	4.05836i	0.692615	−	0.399882i	−0.111976	−	0.993711i	$-0.535718\pi$
$103$	7.02928	−	4.05836i	0.692615	−	0.399882i	0.804591	+	0.593829i	$0.202385\pi$
$104$	9.50957	+	6.21110i	0.932490	+	0.609049i
$105$	20.2903	+	2.10860i	1.98013	+	0.205778i
$106$	7.36806	+	13.3198i	0.715649	+	1.29373i
$107$	−6.23445			−0.602707			−0.301354	−	0.953512i	$-0.597438\pi$
$107$	−6.23445			−0.602707			−0.301354	+	0.953512i	$0.597438\pi$
$108$	9.77182	+	3.53716i	0.940294	+	0.340363i
$109$	−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	$0.517482\pi$
$114$	−9.39850	−	5.06638i	−0.880250	−	0.474510i
$115$	12.5251	+	7.23136i	1.16797	+	0.674328i
$116$	0.0318357	−	0.868140i	0.00295587	−	0.0806048i
$117$	−3.74961	−	11.4489i	−0.346651	−	1.05845i
$118$	0.274516	−	14.9768i	0.0252712	−	1.37872i
$119$	9.72304	+	16.8408i	0.891310	+	1.54379i
$120$	−5.29179	−	13.8456i	−0.483072	−	1.26393i
$121$	0.965999	+	1.67316i	0.0878181	+	0.152105i
$122$	0.166496	−	9.08354i	0.0150739	−	0.822385i
$123$	0.654621	−	0.292375i	0.0590252	−	0.0263625i
$124$	−4.52464	+	2.39566i	−0.406324	+	0.215136i
$125$		−	2.55854i		−	0.228843i
$126$	−4.85172	−	15.7864i	−0.432226	−	1.40637i
$127$	5.52271	−	3.18854i	0.490062	−	0.282937i	−0.234538	−	0.972107i	$-0.575358\pi$
$127$	5.52271	−	3.18854i	0.490062	−	0.282937i	0.724600	+	0.689170i	$0.242025\pi$
$128$	1.44748	−	11.2207i	0.127940	−	0.991782i
$129$	−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	$-0.356693\pi$
$131$	9.96122			0.870316			0.435158	+	0.900354i	$0.356693\pi$
$132$	−10.3291	−	1.45775i	−0.899036	−	0.126881i
$133$	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
$136$	7.72659	−	11.8299i	0.662549	−	1.01440i
$137$		−	17.9170i		−	1.53075i	−0.643585	−	0.765375i	$-0.722554\pi$
$137$		−	17.9170i		−	1.53075i	0.643585	−	0.765375i	$-0.277446\pi$
$138$	1.42350	−	11.6219i	0.121176	−	0.989323i
$139$	12.9933	+	7.50170i	1.10208	+	0.636286i	0.936766	−	0.349955i	$-0.113803\pi$
$139$	12.9933	+	7.50170i	1.10208	+	0.636286i	0.165313	+	0.986241i	$0.447137\pi$
$140$	−12.5174	+	19.9543i	−1.05791	+	1.68645i
$141$	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
$144$	−8.64171	+	8.32592i	−0.720142	+	0.693826i
$145$	1.31421			0.109140
$146$	0.722290	+	0.434856i	0.0597772	+	0.0359889i
$147$	−8.28681	+	11.4339i	−0.683484	+	0.943054i
$148$	6.18811	+	0.226926i	0.508660	+	0.0186532i
$149$		−	17.7470i		−	1.45389i	−0.686695	−	0.726946i	$-0.740939\pi$
$149$		−	17.7470i		−	1.45389i	0.686695	−	0.726946i	$-0.259061\pi$
$150$	9.36597	−	3.97889i	0.764728	−	0.324875i
$151$	2.78743	+	1.60932i	0.226838	+	0.130965i	0.609112	−	0.793084i	$-0.291526\pi$
$151$	2.78743	+	1.60932i	0.226838	+	0.130965i	−0.382275	+	0.924049i	$0.624859\pi$
$152$	10.0364	−	7.16032i	0.814061	−	0.580779i
$153$	−14.2423	+	4.66450i	−1.15142	+	0.377102i
$154$	8.02423	+	14.5060i	0.646611	+	1.16893i
$155$	−3.87258	−	6.70751i	−0.311053	−	0.538760i
$156$	13.7745	+	1.94399i	1.10284	+	0.155644i
$157$	−2.50724			−0.200100			−0.100050	−	0.994982i	$-0.531900\pi$
$157$	−2.50724			−0.200100			−0.100050	+	0.994982i	$0.531900\pi$
$158$	9.22282	+	16.6728i	0.733728	+	1.32641i
$159$	15.0952	+	10.9404i	1.19713	+	0.867626i
$160$	17.0437	+	1.56622i	1.34742	+	0.123820i
$161$	−16.1144	+	9.30363i	−1.26999	+	0.733229i
$162$	12.6752	−	1.15757i	0.995856	−	0.0909476i
$163$		−	18.7315i		−	1.46717i	−0.679600	−	0.733583i	$-0.737847\pi$
$163$		−	18.7315i		−	1.46717i	0.679600	−	0.733583i	$-0.262153\pi$
$164$	−0.0303382	+	0.827302i	−0.00236901	+	0.0646014i
$165$	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	$-0.615685\pi$
$167$	8.16353	−	14.1397i	0.631713	−	1.09416i	0.987201	−	0.159479i	$-0.0509813\pi$
$168$	18.8309	+	3.01056i	1.45284	+	0.232270i
$169$	−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	$0.397286\pi$
$174$	−0.416014	−	0.979262i	−0.0315380	−	0.0742376i
$175$	−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
$178$	−9.77103	−	17.6638i	−0.732369	−	1.32396i
$179$	−9.00022			−0.672708			−0.336354	−	0.941736i	$-0.609194\pi$
$179$	−9.00022			−0.672708			−0.336354	+	0.941736i	$0.609194\pi$
$180$	−13.0662	−	12.6029i	−0.973894	−	0.939364i
$181$	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	$0.662175\pi$
$182$	−10.7007	−	19.3445i	−0.793192	−	1.43391i
$183$	−4.53761	−	10.1596i	−0.335430	−	0.751021i
$184$	11.3196	+	7.39329i	0.834490	+	0.545041i
$185$			9.36773i			0.688729i
$186$	−3.77211	+	5.00884i	−0.276584	+	0.367266i
$187$	13.0278	−	7.52161i	0.952688	−	0.550035i
$188$	−24.7089	−	0.906105i	−1.80208	−	0.0660845i
$189$	−13.5871	−	14.9839i	−0.988317	−	1.08992i
$190$	11.3813	+	14.7760i	0.825689	+	1.07197i
$191$	−7.15070	+	12.3854i	−0.517406	+	0.896174i	0.482389	+	0.875957i	$0.339769\pi$
$191$	−7.15070	+	12.3854i	−0.517406	+	0.896174i	−0.999796	+	0.0202169i	$0.993564\pi$
$192$	−4.22814	−	13.1956i	−0.305140	−	0.952308i
$193$	−4.54467			−0.327132			−0.163566	−	0.986532i	$-0.552300\pi$
$193$	−4.54467			−0.327132			−0.163566	+	0.986532i	$0.552300\pi$
$194$	3.55152	−	1.96458i	0.254984	−	0.141049i
$195$	−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	$-0.242246\pi$
$198$	−12.2122	+	3.75323i	−0.867882	+	0.266730i
$199$	−5.50195	+	3.17655i	−0.390023	+	0.225180i	−0.682170	−	0.731194i	$-0.738964\pi$
$199$	−5.50195	+	3.17655i	−0.390023	+	0.225180i	0.292147	+	0.956373i	$0.405630\pi$
$200$	−0.645734	+	11.7326i	−0.0456603	+	0.829620i
$201$	2.30912	−	22.2200i	0.162873	−	1.56727i
$202$	−7.59515	−	0.139215i	−0.534393	−	0.00979512i
$203$	−0.845412	+	1.46430i	−0.0593363	+	0.102774i
$204$	2.41832	−	17.1354i	0.169316	−	1.19972i
$205$	−1.25239			−0.0874709
$206$	5.55624	+	10.0444i	0.387121	+	0.699827i
$207$	−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
$210$	−3.50738	+	28.6354i	−0.242032	+	1.97603i
$211$		−	3.70510i		−	0.255070i	−0.991834	−	0.127535i	$-0.959294\pi$
$211$		−	3.70510i		−	0.255070i	0.991834	−	0.127535i	$-0.0407065\pi$
$212$	−19.0248	+	10.0730i	−1.30663	+	0.691820i
$213$	16.7770	+	1.74349i	1.14954	+	0.119462i
$214$	0.161581	−	8.81537i	0.0110454	−	0.602606i
$215$	2.85314	+	4.94179i	0.194583	+	0.337027i
$216$	−5.25472	+	13.7254i	−0.357538	+	0.933898i
$217$	9.96467			0.676446
$218$	−21.4181	−	12.8948i	−1.45061	−	0.873344i
$219$	1.02704	+	0.106731i	0.0694010	+	0.00721223i
$220$	15.4364	+	9.68328i	1.04072	+	0.652847i
$221$	−17.3733	+	10.0305i	−1.16865	+	0.674723i
$222$	6.98019	−	2.96535i	0.468480	−	0.199022i
$223$	−10.0726	+	5.81541i	−0.674511	+	0.389429i	−0.797784	−	0.602944i	$-0.793994\pi$
$223$	−10.0726	+	5.81541i	−0.674511	+	0.389429i	0.123273	+	0.992373i	$0.460661\pi$
$224$	−12.7090	+	17.9825i	−0.849156	+	1.20151i
$225$	8.31776	−	9.28140i	0.554517	−	0.618760i
$226$	−7.95767	−	14.3857i	−0.529336	−	0.956920i
$227$	−1.26292	+	2.18744i	−0.0838227	+	0.145185i	−0.904889	−	0.425648i	$-0.860046\pi$
$227$	−1.26292	+	2.18744i	−0.0838227	+	0.145185i	0.821066	+	0.570833i	$0.193380\pi$
$228$	7.40732	−	13.1579i	0.490562	−	0.871406i
$229$	−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	$0.608297\pi$
$234$	16.2856	−	5.00513i	1.06462	−	0.327196i
$235$		−	37.4050i		−	2.44003i
$236$	21.1697	+	0.776317i	1.37803	+	0.0505339i
$237$	18.8951	+	13.6944i	1.22737	+	0.889545i
$238$	−24.0645	+	13.3117i	−1.55987	+	0.862868i
$239$	0.139802	+	0.242144i	0.00904302	+	0.0156630i	0.870512	−	0.492148i	$-0.163788\pi$
$239$	0.139802	+	0.242144i	0.00904302	+	0.0156630i	−0.861468	+	0.507811i	$0.830455\pi$
$240$	19.7146	−	7.12362i	1.27257	−	0.459828i
$241$	−14.7801			−0.952069			−0.476034	−	0.879427i	$-0.657926\pi$
$241$	−14.7801			−0.952069			−0.476034	+	0.879427i	$0.657926\pi$
$242$	−2.39084	+	1.32254i	−0.153689	+	0.0850158i
$243$	13.4542	−	7.87309i	0.863085	−	0.505059i
$244$	12.8396	+	0.470843i	0.821971	+	0.0301427i
$245$	21.3626	−	12.3337i	1.36480	−	0.787970i
$246$	0.396445	+	0.933196i	0.0252764	+	0.0594984i
$247$	−17.3049	+	2.63429i	−1.10108	+	0.167616i
$248$	−3.27013	−	6.45982i	−0.207654	−	0.410199i
$249$	6.45690	+	0.671009i	0.409190	+	0.0425235i
$250$	3.61771	+	0.0663106i	0.228804	+	0.00419385i
$251$	−3.57806	−	6.19739i	−0.225845	−	0.391176i	0.730727	−	0.682669i	$-0.239181\pi$
$251$	−3.57806	−	6.19739i	−0.225845	−	0.391176i	−0.956573	+	0.291494i	$0.905848\pi$
$252$	22.4474	−	6.45108i	1.41405	−	0.406380i
$253$	7.19716	+	12.4658i	0.452482	+	0.783721i
$254$	4.36539	+	7.89163i	0.273909	+	0.495165i
$255$	26.0392	+	2.70602i	1.63064	+	0.169458i
$256$	15.8283	+	2.33751i	0.989271	+	0.146094i
$257$	−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	$0.891351\pi$
$258$	2.77912	−	3.69029i	0.173020	−	0.229747i
$259$	−10.4375	−	6.02611i	−0.648556	−	0.374444i
$260$	−20.5852	−	12.9132i	−1.27664	−	0.800841i
$261$	−0.970419	−	0.869666i	−0.0600675	−	0.0538309i
$262$	−0.258169	+	14.0849i	−0.0159497	+	0.870169i
$263$	4.49769	+	7.79022i	0.277339	+	0.480366i	0.970723	−	0.240203i	$-0.0772141\pi$
$263$	4.49769	+	7.79022i	0.277339	+	0.480366i	−0.693383	+	0.720569i	$0.743881\pi$
$264$	2.32893	−	14.5674i	0.143336	−	0.896559i
$265$	−16.2831	−	28.2031i	−1.00026	−	1.73251i
$266$	−23.7849	+	3.17591i	−1.45835	+	0.194727i
$267$	−20.0183	−	14.5084i	−1.22510	−	0.887897i
$268$	21.8520	+	13.7078i	1.33482	+	0.837337i
$269$	−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	$0.781146\pi$
$270$	−21.0414	−	7.18312i	−1.28054	−	0.437151i
$271$	0.0117891	+	0.00680646i	0.000716139	+	0.000413463i	0.500358	−	0.865819i	$-0.333202\pi$
$271$	0.0117891	+	0.00680646i	0.000716139	+	0.000413463i	−0.499642	+	0.866232i	$0.666535\pi$
$272$	16.5269	+	11.2318i	1.00209	+	0.681028i
$273$	−21.9230	−	15.8888i	−1.32684	−	0.961636i
$274$	25.3342	+	0.464361i	1.53049	+	0.0280531i
$275$	−6.25506	+	10.8341i	−0.377194	+	0.653320i
$276$	16.3962	+	2.31400i	0.986936	+	0.139286i
$277$	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
$280$	−27.8905	−	18.2164i	−1.66677	−	1.08864i
$281$			11.5527i			0.689174i	0.938754	+	0.344587i	$0.111981\pi$
$281$			11.5527i			0.689174i	−0.938754	+	0.344587i	$0.888019\pi$
$282$	−27.8716	+	11.8405i	−1.65973	+	0.705094i
$283$		−	22.5259i		−	1.33902i	−0.742802	−	0.669511i	$-0.766504\pi$
$283$		−	22.5259i		−	1.33902i	0.742802	−	0.669511i	$-0.233496\pi$
$284$	−10.3500	+	16.4991i	−0.614157	+	0.979044i
$285$	20.3028	+	10.4689i	1.20263	+	0.620123i
$286$	−14.9646	+	8.27795i	−0.884878	+	0.489485i
$287$	0.805643	−	1.39542i	0.0475556	−	0.0823688i
$288$	−11.5487	−	12.4350i	−0.680512	−	0.732737i
$289$	3.97787	+	6.88987i	0.233992	+	0.405287i
$290$	−0.0340610	+	1.85827i	−0.00200013	+	0.109121i
$291$	2.91708	−	4.02492i	0.171002	−	0.235945i
$292$	−0.633595	+	1.01003i	−0.0370784	+	0.0591076i
$293$	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	$0.147110\pi$
$294$	−15.9525	−	12.0137i	−0.930370	−	0.700652i
$295$			32.0472i			1.86586i
$296$	−0.481247	+	8.74396i	−0.0279719	+	0.508232i
$297$	−11.5913	+	10.5108i	−0.672597	+	0.609899i
$298$	25.0938	+	0.459956i	1.45365	+	0.0266445i
$299$	−9.59780	−	16.6239i	−0.555055	−	0.961384i
$300$	5.38332	+	13.3464i	0.310806	+	0.770554i
$301$	−7.34152			−0.423158
$302$	−2.34778	+	3.89964i	−0.135100	+	0.224399i
$303$	−8.49491	+	3.79409i	−0.488020	+	0.217965i
$304$	9.86441	+	14.3768i	0.565762	+	0.824568i
$305$			19.4369i			1.11296i
$306$	−6.22636	−	20.2592i	−0.355937	−	1.15814i
$307$	24.8145	+	14.3266i	1.41624	+	0.817664i	0.995966	−	0.0897351i	$-0.0286020\pi$
$307$	24.8145	+	14.3266i	1.41624	+	0.817664i	0.420270	+	0.907399i	$0.361935\pi$
$308$	−20.7191	+	10.9701i	−1.18058	+	0.625080i
$309$	11.3833	+	8.25010i	0.647572	+	0.469332i
$310$	9.58462	−	5.30189i	0.544370	−	0.301127i
$311$	0.926512	+	1.60477i	0.0525377	+	0.0909979i	0.891098	−	0.453811i	$-0.149936\pi$
$311$	0.926512	+	1.60477i	0.0525377	+	0.0909979i	−0.838561	+	0.544808i	$0.816602\pi$
$312$	−3.10576	+	19.4264i	−0.175829	+	1.09980i
$313$	−4.47592			−0.252994			−0.126497	−	0.991967i	$-0.540373\pi$
$313$	−4.47592			−0.252994			−0.126497	+	0.991967i	$0.540373\pi$
$314$	0.0649811	−	3.54518i	0.00366710	−	0.200066i
$315$	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	$-0.272821\pi$
$318$	−15.8606	+	21.0607i	−0.889420	+	1.18103i
$319$	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
$322$	−12.7375	−	23.0264i	−0.709831	−	1.28321i
$323$	3.27705	+	21.5272i	0.182340	+	1.19781i
$324$	1.30827	+	17.9524i	0.0726819	+	0.997355i
$325$	8.34146	−	14.4478i	0.462701	−	0.801421i
$326$	26.4859	+	0.485472i	1.46692	+	0.0268878i
$327$	−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
$330$	22.1520	+	2.71326i	1.21943	+	0.149360i
$331$	−24.8192	−	14.3294i	−1.36419	−	0.787613i	−0.374007	−	0.927426i	$-0.622017\pi$
$331$	−24.8192	−	14.3294i	−1.36419	−	0.787613i	−0.990178	+	0.139813i	$0.955350\pi$
$332$	−3.98335	+	6.34997i	−0.218615	+	0.348500i
$333$	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
$336$	−4.74491	+	26.5485i	−0.258856	+	1.44834i
$337$	−28.4780			−1.55129			−0.775647	−	0.631167i	$-0.782576\pi$
$337$	−28.4780			−1.55129			−0.775647	+	0.631167i	$0.782576\pi$
$338$	3.86869	−	2.14003i	0.210429	−	0.116402i
$339$	−16.3032	−	11.8158i	−0.885467	−	0.641748i
$340$	−16.0639	+	25.6079i	−0.871189	+	1.38879i
$341$		−	7.70853i		−	0.417441i
$342$	1.37385	−	18.4421i	0.0742895	−	0.997237i
$343$			4.48757i			0.242306i
$344$	2.40929	+	4.75930i	0.129900	+	0.256604i
$345$	−2.58930	+	24.9160i	−0.139403	+	1.34143i
$346$	−3.59365	−	6.49650i	−0.193196	−	0.349254i
$347$	5.79778			0.311241			0.155621	−	0.987817i	$-0.450262\pi$
$347$	5.79778			0.311241			0.155621	+	0.987817i	$0.450262\pi$
$348$	1.39543	−	0.562854i	0.0748031	−	0.0301722i
$349$	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
$352$	13.9111	+	9.83151i	0.741462	+	0.524021i
$353$	−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	$-0.742454\pi$
$354$	23.8794	−	10.1445i	1.26917	−	0.539176i
$355$	−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
$358$	0.233262	−	12.7261i	0.0123283	−	0.672595i
$359$	12.7970	−	22.1650i	0.675399	−	1.16983i	−0.300953	−	0.953639i	$-0.597305\pi$
$359$	12.7970	−	22.1650i	0.675399	−	1.16983i	0.976352	−	0.216186i	$-0.0693619\pi$
$360$	18.1588	−	18.1486i	0.957055	−	0.956515i
$361$	−4.17347	+	18.5360i	−0.219656	+	0.975577i
$362$	−17.0540	+	9.43374i	−0.896341	+	0.495826i
$363$	−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
$366$	14.4831	−	6.15276i	0.757042	−	0.321610i
$367$			11.6822i			0.609804i	0.952384	+	0.304902i	$0.0986238\pi$
$367$			11.6822i			0.609804i	−0.952384	+	0.304902i	$0.901376\pi$
$368$	−10.7473	+	15.8140i	−0.560242	+	0.824361i
$369$	0.924770	+	0.828756i	0.0481416	+	0.0431433i
$370$	−13.2457	−	0.242787i	−0.688614	−	0.0126219i
$371$	41.8986			2.17527
$372$	−6.98462	−	5.46348i	−0.362135	−	0.283268i
$373$	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	$0.581716\pi$
$374$	10.2977	+	18.6160i	0.532483	+	0.962609i
$375$	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
$378$	21.5390	−	18.8235i	1.10785	−	0.968177i
$379$			8.84686i			0.454433i	0.973844	+	0.227216i	$0.0729624\pi$
$379$			8.84686i			0.454433i	−0.973844	+	0.227216i	$0.927038\pi$
$380$	−21.1879	+	15.7100i	−1.08692	+	0.805905i
$381$	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	$-0.511168\pi$
$383$	−1.37298			−0.0701560			−0.0350780	+	0.999385i	$0.511168\pi$
$384$	18.7678	−	5.63649i	0.957740	−	0.287636i
$385$	−17.7332	−	30.7148i	−0.903767	−	1.56537i
$386$	0.117786	−	6.42605i	0.00599515	−	0.327078i
$387$	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	$0.691188\pi$
$390$	−29.5408	−	3.61828i	−1.49586	−	0.183219i
$391$	−20.6800	+	11.9396i	−1.04583	+	0.603813i
$392$	20.5737	−	10.4150i	1.03913	−	0.526035i
$393$	7.03600	+	15.7535i	0.354919	+	0.794658i
$394$	27.3747	+	0.501762i	1.37912	+	0.0252784i
$395$	−20.3820	−	35.3027i	−1.02553	−	1.77627i
$396$	−4.99047	−	17.3650i	−0.250780	−	0.872624i
$397$	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	$0.0238449\pi$
$398$	−4.34897	−	7.86195i	−0.217994	−	0.394084i
$399$	−24.7249	+	15.8869i	−1.23779	+	0.795338i
$400$	−16.5729	−	1.21713i	−0.828643	−	0.0608565i
$401$			14.8592i			0.742031i	0.928627	+	0.371015i	$0.120990\pi$
$401$			14.8592i			0.742031i	−0.928627	+	0.371015i	$0.879010\pi$
$402$	31.3586	+	3.84093i	1.56403	+	0.191568i
$403$			10.2797i			0.512070i
$404$	0.393693	−	10.7358i	0.0195870	−	0.534124i
$405$	−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
$408$	24.1663	+	3.86355i	1.19641	+	0.191274i
$409$	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	$0.165955\pi$
$410$	0.0324587	−	1.77085i	0.00160302	−	0.0874562i
$411$	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
$414$	19.3853	−	5.95778i	0.952736	−	0.292809i
$415$	−9.82067	−	5.66997i	−0.482078	−	0.278328i
$416$	−18.5511	−	13.1108i	−0.909544	−	0.642812i
$417$	−2.68610	+	25.8475i	−0.131539	+	1.26576i
$418$	2.45684	+	18.3997i	0.120168	+	0.899958i
$419$	−6.82563	−	11.8223i	−0.333454	−	0.577559i	0.649733	−	0.760163i	$-0.274881\pi$
$419$	−6.82563	−	11.8223i	−0.333454	−	0.577559i	−0.983187	+	0.182604i	$0.941547\pi$
$420$	−40.3989	−	5.70150i	−1.97126	−	0.278205i
$421$	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	$0.687841\pi$
$422$	5.23893	+	0.0960266i	0.255027	+	0.00467450i
$423$	−24.7523	+	27.6200i	−1.20350	+	1.34293i
$424$	−13.7500	−	27.1617i	−0.667758	−	1.31909i
$425$	−17.9730	−	10.3767i	−0.871821	−	0.503346i
$426$	−2.90006	+	23.6771i	−0.140508	+	1.14716i
$427$	−21.6566	−	12.5035i	−1.04804	−	0.605085i
$428$	12.4605	+	0.456943i	0.602303	+	0.0220872i
$429$	−12.2914	+	16.9593i	−0.593434	+	0.818805i
$430$	−7.06152	+	3.90620i	−0.340537	+	0.188374i
$431$	−6.32209	−	10.9502i	−0.304525	−	0.527452i	0.672631	−	0.739978i	$-0.265164\pi$
$431$	−6.32209	−	10.9502i	−0.304525	−	0.527452i	−0.977155	+	0.212526i	$0.931831\pi$
$432$	−19.2713	−	7.78577i	−0.927189	−	0.374593i
$433$	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	$0.668302\pi$
$434$	−0.258258	+	14.0898i	−0.0123968	+	0.676332i
$435$	0.928282	+	2.07841i	0.0445077	+	0.0996519i
$436$	18.7880	−	29.9504i	0.899782	−	1.43437i
$437$	−20.5986	+	3.13569i	−0.985364	+	0.150000i
$438$	−0.177534	+	1.44944i	−0.00848289	+	0.0692572i
$439$	−10.6777	+	6.16477i	−0.509618	+	0.294228i	−0.732677	−	0.680577i	$-0.761729\pi$
$439$	−10.6777	+	6.16477i	−0.509618	+	0.294228i	0.223058	+	0.974805i	$0.428396\pi$
$440$	−14.0920	+	21.5757i	−0.671810	+	1.02858i
$441$	−23.9358	−	5.02920i	−1.13980	−	0.239486i
$442$	−13.7326	−	24.8254i	−0.653192	−	1.18082i
$443$	3.25827			0.154805			0.0774026	−	0.997000i	$-0.475337\pi$
$443$	3.25827			0.154805			0.0774026	+	0.997000i	$0.475337\pi$
$444$	4.01203	+	9.94667i	0.190403	+	0.472048i
$445$	21.5935	+	37.4011i	1.02363	+	1.77298i
$446$	−7.96180	−	14.3931i	−0.377002	−	0.681534i
$447$	28.0666	−	12.5354i	1.32750	−	0.592905i
$448$	−25.0975	−	18.4363i	−1.18575	−	0.871032i
$449$		−	19.0008i		−	0.896701i	−0.893858	−	0.448351i	$-0.852012\pi$
$449$		−	19.0008i		−	0.896701i	0.893858	−	0.448351i	$-0.147988\pi$
$450$	12.9081	+	12.0017i	0.608494	+	0.565764i
$451$	−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
$456$	18.4130	+	10.8148i	0.862270	+	0.506449i
$457$	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	$0.0516968\pi$
$458$	33.2880	−	18.4138i	1.55545	−	0.860421i
$459$	−17.4367	−	19.2293i	−0.813878	−	0.897546i
$460$	−24.5033	−	15.3710i	−1.14247	−	0.716677i
$461$	−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	$0.396984\pi$
$462$	−17.2731	+	22.9363i	−0.803618	+	1.06709i
$463$	8.79687	−	5.07887i	0.408825	−	0.236035i	−0.281460	−	0.959573i	$-0.590819\pi$
$463$	8.79687	−	5.07887i	0.408825	−	0.236035i	0.690285	+	0.723538i	$0.257485\pi$
$464$	−0.127257	+	1.73278i	−0.00590778	+	0.0804423i
$465$	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	$-0.544667\pi$
$467$	−6.04500			−0.279729			−0.139865	+	0.990171i	$0.544667\pi$
$468$	6.65506	+	23.1572i	0.307630	+	1.07044i
$469$	−25.1034	−	43.4803i	−1.15917	−	2.00773i
$470$	52.8898	+	0.969440i	2.43962	+	0.0447169i
$471$	−1.77096	−	3.96516i	−0.0816017	−	0.182705i
$472$	−1.64636	+	29.9133i	−0.0757797	+	1.37687i
$473$			5.67930i			0.261135i
$474$	−19.8532	+	26.3624i	−0.911889	+	1.21086i
$475$	−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
$478$	−0.346009	+	0.191401i	−0.0158261	+	0.00875446i
$479$	−10.9343			−0.499601			−0.249800	−	0.968297i	$-0.580365\pi$
$479$	−10.9343			−0.499601			−0.249800	+	0.968297i	$0.580365\pi$
$480$	9.56168	+	28.0605i	0.436429	+	1.28078i
$481$	6.21665	−	10.7676i	0.283455	−	0.490958i
$482$	0.383061	−	20.8987i	0.0174480	−	0.951909i
$483$	−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
$486$	10.7837	+	19.2279i	0.489157	+	0.872196i
$487$			31.2745i			1.41718i	0.705619	+	0.708592i	$0.250669\pi$
$487$			31.2745i			1.41718i	−0.705619	+	0.708592i	$0.749331\pi$
$488$	−0.998530	+	18.1427i	−0.0452013	+	0.821281i
$489$	29.6236	−	13.2308i	1.33962	−	0.598318i
$490$	16.8859	+	30.5258i	0.762826	+	1.37902i
$491$	−7.16052			−0.323150			−0.161575	−	0.986860i	$-0.551657\pi$
$491$	−7.16052			−0.323150			−0.161575	+	0.986860i	$0.551657\pi$
$492$	−1.32979	+	0.536377i	−0.0599517	+	0.0241817i
$493$	−1.08494	+	1.87918i	−0.0488634	+	0.0846338i
$494$	−3.27633	−	24.5370i	−0.147409	−	1.10397i
$495$	25.9756	−	8.50726i	1.16752	−	0.382373i
$496$	9.21878	−	4.45647i	0.413935	−	0.200101i
$497$	32.8294	−	18.9541i	1.47260	−	0.850207i
$498$	−1.11614	+	9.11252i	−0.0500153	+	0.408342i
$499$			33.9896i			1.52158i	0.648997	+	0.760791i	$0.275189\pi$
$499$			33.9896i			1.52158i	−0.648997	+	0.760791i	$0.724811\pi$
$500$	−0.187523	+	5.11364i	−0.00838629	+	0.228689i
$501$	28.1278	+	2.92308i	1.25666	+	0.130594i
$502$	8.85569	−	4.89868i	0.395249	−	0.218639i
$503$	21.1844	+	36.6924i	0.944565	+	1.63603i	0.756619	+	0.653855i	$0.226850\pi$
$503$	21.1844	+	36.6924i	0.944565	+	1.63603i	0.187946	+	0.982179i	$0.439817\pi$
$504$	8.53989	+	31.9073i	0.380397	+	1.42126i
$505$	16.2521			0.723208
$506$	−17.8129	+	9.85353i	−0.791882	+	0.438043i
$507$	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	$0.719370\pi$
$510$	−4.50112	+	36.7487i	−0.199313	+	1.62726i
$511$	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
$516$	5.14595	+	4.02525i	0.226538	+	0.177202i
$517$	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
$520$	18.7924	−	28.7723i	0.824103	−	1.26175i
$521$			1.07049i			0.0468992i	0.999725	+	0.0234496i	$0.00746492\pi$
$521$			1.07049i			0.0468992i	−0.999725	+	0.0234496i	$0.992535\pi$
$522$	1.25484	−	1.34961i	0.0549227	−	0.0590708i
$523$	7.38254	−	4.26231i	0.322816	−	0.186378i	−0.329831	−	0.944040i	$-0.606992\pi$
$523$	7.38254	−	4.26231i	0.322816	−	0.186378i	0.652647	+	0.757662i	$0.273658\pi$
$524$	−19.9091	−	0.730089i	−0.869731	−	0.0318941i
$525$	2.89524	−	27.8600i	0.126359	−	1.21591i
$526$	−11.1318	+	6.15772i	−0.485368	+	0.268489i
$527$	12.7880			0.557052
$528$	20.5375	+	3.67060i	0.893782	+	0.159742i
$529$	0.0754029	+	0.130602i	0.00327839	+	0.00567833i
$530$	40.3006	−	22.2929i	1.75055	−	0.968344i
$531$	21.2069	−	23.6638i	0.920299	−	1.02692i
$532$	−3.87421	−	33.7136i	−0.167968	−	1.46167i
$533$	1.43954	+	0.831117i	0.0623533	+	0.0359997i
$534$	21.0333	−	27.9293i	0.910200	−	1.20862i
$535$			18.8631i			0.815522i
$536$	−19.9488	+	30.5429i	−0.861658	+	1.31925i
$537$	−6.35721	−	14.2337i	−0.274334	−	0.614229i
$538$	8.42100	−	13.9872i	0.363055	−	0.603031i
$539$	24.5507			1.05747
$540$	10.7021	−	29.5658i	0.460545	−	1.27231i
$541$	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
$544$	−16.3098	+	23.0775i	−0.699279	+	0.989441i
$545$	46.3205	+	26.7431i	1.98415	+	1.14555i
$546$	23.0346	−	30.5868i	0.985791	−	1.30899i
$547$			27.9073i			1.19323i	0.802528	+	0.596614i	$0.203488\pi$
$547$			27.9073i			1.19323i	−0.802528	+	0.596614i	$0.796512\pi$
$548$	−1.31319	+	35.8099i	−0.0560967	+	1.52972i
$549$	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
$552$	−3.69689	+	23.1239i	−0.157350	+	0.984218i
$553$	52.4457			2.23022
$554$	11.7953	+	7.10137i	0.501134	+	0.301708i
$555$	−14.8149	+	6.61680i	−0.628857	+	0.280868i
$556$	−25.4194	−	15.9456i	−1.07802	−	0.676246i
$557$	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	$0.259407\pi$
$558$	−10.5858	−	2.42757i	−0.448132	−	0.102767i
$559$		−	7.57365i		−	0.320331i
$560$	26.4805	−	38.9643i	1.11900	−	1.64654i
$561$	21.0974	+	15.2904i	0.890731	+	0.645563i
$562$	−16.3352	−	0.299415i	−0.689059	−	0.0126301i
$563$	−6.07143	−	10.5160i	−0.255880	−	0.443198i	0.709254	−	0.704953i	$-0.249032\pi$
$563$	−6.07143	−	10.5160i	−0.255880	−	0.443198i	−0.965134	+	0.261755i	$0.915699\pi$
$564$	−16.0199	−	39.7167i	−0.674559	−	1.67237i
$565$	17.5861	+	30.4600i	0.739853	+	1.28146i
$566$	31.8510	+	0.583811i	1.33880	+	0.0245394i
$567$	14.0996	−	32.0715i	0.592129	−	1.34688i
$568$	−23.0611	−	15.0622i	−0.967624	−	0.631996i
$569$	−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	$0.751420\pi$
$570$	−15.3289	+	28.4363i	−0.642059	+	1.19106i
$571$	27.6064	−	15.9386i	1.15529	−	0.667008i	0.205120	−	0.978737i	$-0.434241\pi$
$571$	27.6064	−	15.9386i	1.15529	−	0.667008i	0.950171	+	0.311729i	$0.100908\pi$
$572$	−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
$576$	17.8820	−	16.0073i	0.745085	−	0.666970i
$577$	16.0365			0.667607			0.333803	−	0.942643i	$-0.391668\pi$
$577$	16.0365			0.667607			0.333803	+	0.942643i	$0.391668\pi$
$578$	−9.84521	+	5.44605i	−0.409507	+	0.226526i
$579$	−3.21008	−	7.18731i	−0.133406	−	0.298694i
$580$	−2.62666	−	0.0963228i	−0.109066	−	0.00399959i
$581$	12.6350	−	7.29479i	0.524186	−	0.302639i
$582$	5.61554	+	4.22900i	0.232771	+	0.175298i
$583$		−	32.4122i		−	1.34238i
$584$	−1.41174	−	0.922066i	−0.0584182	−	0.0381554i
$585$	−34.6399	+	11.3449i	−1.43218	+	0.469053i
$586$	12.9415	+	23.3953i	0.534609	+	0.966452i
$587$	18.9447	+	32.8132i	0.781932	+	1.35435i	0.930815	+	0.365491i	$0.119099\pi$
$587$	18.9447	+	32.8132i	0.781932	+	1.35435i	−0.148883	+	0.988855i	$0.547568\pi$
$588$	17.4005	−	22.2451i	0.717585	−	0.917374i
$589$	10.3928	+	4.06128i	0.428229	+	0.167342i
$590$	−45.3140	−	0.830580i	−1.86555	−	0.0341944i
$591$	30.6176	−	13.6748i	1.25944	−	0.562505i
$592$	−12.3513	−	0.907092i	−0.507635	−	0.0372813i
$593$	−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	$0.335026\pi$
$594$	−14.5616	−	16.6623i	−0.597470	−	0.683662i
$595$	50.9539	−	29.4182i	2.08890	−	1.20603i
$596$	−1.30073	+	35.4702i	−0.0532801	+	1.45292i
$597$	−8.90990	−	6.45750i	−0.364658	−	0.264288i
$598$	23.7545	−	13.1402i	0.971394	−	0.537343i
$599$	5.98755	−	10.3707i	0.244645	−	0.423737i	−0.717387	−	0.696675i	$-0.754662\pi$
$599$	5.98755	−	10.3707i	0.244645	−	0.423737i	0.962032	+	0.272938i	$0.0879954\pi$
$600$	−19.0110	+	7.26598i	−0.776120	+	0.296632i
$601$	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	$0.00207772\pi$
$602$	0.190273	−	10.3807i	0.00775495	−	0.423087i
$603$	36.7715	−	12.0430i	1.49745	−	0.490429i
$604$	−5.45316	−	3.42078i	−0.221886	−	0.139190i
$605$	5.06234	−	2.92275i	0.205814	−	0.118826i
$606$	−5.14459	−	12.1099i	−0.208985	−	0.491932i
$607$	8.98311	−	5.18640i	0.364613	−	0.210510i	−0.306489	−	0.951874i	$-0.599154\pi$
$607$	8.98311	−	5.18640i	0.364613	−	0.210510i	0.671103	+	0.741365i	$0.265821\pi$
$608$	−20.5842	+	13.5754i	−0.834798	+	0.550556i
$609$	−2.91291	−	0.302713i	−0.118037	−	0.0122665i
$610$	−27.4834	−	0.503754i	−1.11277	−	0.0203964i
$611$	−24.8228	+	42.9944i	−1.00422	+	1.73937i
$612$	28.8074	−	8.27886i	1.16447	−	0.334653i
$613$	−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
$616$	−14.9745	−	29.5806i	−0.603339	−	1.19184i
$617$	−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	$0.844780\pi$
$618$	−11.9605	+	15.8819i	−0.481120	+	0.638862i
$619$	13.0555	+	7.53759i	0.524745	+	0.302961i	0.738874	−	0.673844i	$-0.235358\pi$
$619$	13.0555	+	7.53759i	0.524745	+	0.302961i	−0.214129	+	0.976805i	$0.568691\pi$
$620$	7.24834	+	13.6898i	0.291100	+	0.549797i
$621$	18.3998	−	16.6846i	0.738358	−	0.669530i
$622$	−2.29311	+	1.26847i	−0.0919454	+	0.0508612i
$623$	−55.5631			−2.22609
$624$	−27.3879	−	4.89494i	−1.09639	−	0.195955i
$625$	−28.5130			−1.14052
$626$	0.116004	−	6.32885i	0.00463646	−	0.252952i
$627$	12.2899	+	19.1268i	0.490810	+	0.763852i
$628$	5.01111	+	0.183764i	0.199965	+	0.00733296i
$629$	−13.3948	−	7.73349i	−0.534085	−	0.308354i
$630$	−47.7638	+	14.6795i	−1.90295	+	0.584844i
$631$	20.8654	−	12.0466i	0.830638	−	0.479569i	−0.0234332	−	0.999725i	$-0.507460\pi$
$631$	20.8654	−	12.0466i	0.830638	−	0.479569i	0.854071	+	0.520156i	$0.174126\pi$
$632$	−17.2113	−	33.9991i	−0.684627	−	1.35241i
$633$	5.85955	−	2.61706i	0.232896	−	0.104019i
$634$	38.0619	+	0.697653i	1.51163	+	0.0277074i
$635$	−9.64731	−	16.7096i	−0.382842	−	0.663102i
$636$	−29.3683	−	22.9724i	−1.16453	−	0.910914i
$637$	−32.7397			−1.29719
$638$	−0.954098	+	1.58475i	−0.0377731	+	0.0627407i
$639$	9.09297	+	27.7640i	0.359712	+	1.09833i
$640$	−33.9497	−	4.37951i	−1.34198	−	0.173115i
$641$	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	$0.0820467\pi$
$642$	14.0555	−	5.97111i	0.554725	−	0.235661i
$643$			29.5252i			1.16436i	0.813060	+	0.582180i	$0.197800\pi$
$643$			29.5252i			1.16436i	−0.813060	+	0.582180i	$0.802200\pi$
$644$	32.8890	−	17.4137i	1.29601	−	0.686195i
$645$	−5.80006	+	8.00277i	−0.228377	+	0.315109i
$646$	−30.5239	+	4.07574i	−1.20095	+	0.160358i
$647$	20.2868			0.797555			0.398778	−	0.917048i	$-0.369435\pi$
$647$	20.2868			0.797555			0.398778	+	0.917048i	$0.369435\pi$
$648$	−25.4182	+	1.38459i	−0.998520	+	0.0543918i
$649$	−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
$652$	−1.37289	+	37.4379i	−0.0537666	+	1.46618i
$653$	−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	$0.938666\pi$
$654$	5.26441	−	42.9804i	0.205855	−	1.68067i
$655$		−	30.1389i		−	1.17762i
$656$	0.121271	−	1.65127i	0.00473484	−	0.0644712i
$657$	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	$-0.438964\pi$
$659$	9.78463			0.381155			0.190578	+	0.981672i	$0.438964\pi$
$660$	−4.41061	+	31.2520i	−0.171683	+	1.21648i
$661$	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
$664$	−8.87546	−	5.79694i	−0.344435	−	0.224965i
$665$	50.7532	−	7.72607i	1.96812	−	0.299604i
$666$	9.62004	+	8.94449i	0.372769	+	0.346592i
$667$	−1.79812	−	1.03814i	−0.0696233	−	0.0401971i
$668$	−17.3524	+	27.6620i	−0.671386	+	1.07027i
$669$	−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
$672$	−37.4159	−	7.39726i	−1.44335	−	0.285356i
$673$	−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	$0.913724\pi$
$674$	0.738075	−	40.2672i	0.0284296	−	1.55103i
$675$	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	$0.583821\pi$
$678$	17.1298	−	22.7461i	0.657867	−	0.873557i
$679$		−	11.1716i		−	0.428728i
$680$	−35.7927	−	23.3777i	−1.37259	−	0.896494i
$681$	−4.35144	−	0.452206i	−0.166747	−	0.0173286i
$682$	10.8997	+	0.199785i	0.417370	+	0.00765017i
$683$	−17.3858			−0.665251			−0.332625	−	0.943059i	$-0.607934\pi$
$683$	−17.3858			−0.665251			−0.332625	+	0.943059i	$0.607934\pi$
$684$	26.0411	+	2.42057i	0.995708	+	0.0925527i
$685$	−54.2099			−2.07125
$686$	−6.34532	−	0.116306i	−0.242266	−	0.00444059i
$687$	27.3415	−	37.7251i	1.04314	−	1.43930i
$688$	−6.79198	+	3.28332i	−0.258942	+	0.125176i
$689$			43.2234i			1.64668i
$690$	−35.1635	−	4.30696i	−1.33865	−	0.163963i
$691$	10.2721	+	5.93061i	0.390770	+	0.225611i	0.682494	−	0.730892i	$-0.260895\pi$
$691$	10.2721	+	5.93061i	0.390770	+	0.225611i	−0.291724	+	0.956503i	$0.594229\pi$
$692$	9.27904	−	4.91296i	0.352736	−	0.186763i
$693$	−7.23091	+	34.4146i	−0.274680	+	1.30730i
$694$	−0.150263	+	8.19792i	−0.00570392	+	0.311189i
$695$	22.6973	−	39.3129i	0.860957	−	1.49122i
$696$	0.759696	+	1.98770i	0.0287962	+	0.0753435i
$697$	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
$700$	27.3986	+	17.1872i	1.03557	+	0.649615i
$701$	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	$0.394863\pi$
$702$	19.4187	+	22.2200i	0.732911	+	0.838642i
$703$	−8.42995	−	10.5390i	−0.317941	−	0.397487i
$704$	−14.2621	+	19.4151i	−0.537522	+	0.731734i
$705$	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
$708$	13.7252	+	34.0278i	0.515826	+	1.27884i
$709$	−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
$712$	18.2343	+	36.0200i	0.683359	+	1.34991i
$713$			12.2363i			0.458254i
$714$	−38.0499	−	28.6550i	−1.42398	−	1.07239i
$715$	31.6860	−	18.2939i	1.18499	−	0.684153i
$716$	17.9883	+	0.659654i	0.672256	+	0.0246524i
$717$	−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	$0.434019\pi$
$719$	−19.9654	+	34.5812i	−0.744585	+	1.28966i	−0.950388	+	0.311066i	$0.899314\pi$
$720$	25.1911	+	26.1465i	0.938815	+	0.974423i
$721$	31.5956			1.17668
$722$	−26.1013	−	6.38159i	−0.971388	−	0.237498i
$723$	−10.4398	−	23.3744i	−0.388259	−	0.869304i
$724$	−12.8971	−	24.3585i	−0.479316	−	0.905277i
$725$		−	1.80450i		−	0.0670175i
$726$	−3.78031	−	2.84691i	−0.140301	−	0.105659i
$727$	2.26330	−	1.30672i	0.0839410	−	0.0484634i	−0.457442	−	0.889239i	$-0.651234\pi$
$727$	2.26330	−	1.30672i	0.0839410	−	0.0484634i	0.541383	+	0.840776i	$0.317901\pi$
$728$	19.9693	+	39.4473i	0.740111	+	1.46201i
$729$	21.9544	+	15.7164i	0.813124	+	0.582090i
$730$	1.31571	−	2.18538i	0.0486965	−	0.0808844i
$731$	−9.42159			−0.348470
$732$	8.32449	+	20.6382i	0.307682	+	0.762809i
$733$	−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	$-0.379501\pi$
$734$	−16.5183	−	0.302771i	−0.609702	−	0.0111755i
$735$	34.5947	+	25.0727i	1.27605	+	0.924822i
$736$	−22.0821	−	15.6063i	−0.813956	−	0.575256i
$737$	−33.6358	+	19.4196i	−1.23899	+	0.715331i
$738$	−1.19581	+	1.28612i	−0.0440183	+	0.0473429i
$739$	−15.2623	−	8.81167i	−0.561431	−	0.324142i	0.192288	−	0.981338i	$-0.438409\pi$
$739$	−15.2623	−	8.81167i	−0.561431	−	0.324142i	−0.753720	+	0.657196i	$0.771742\pi$
$740$	0.686590	−	18.7229i	0.0252396	−	0.688267i
$741$	−16.3892	−	25.5066i	−0.602072	−	0.937010i
$742$	−1.08590	+	59.2436i	−0.0398647	+	2.17490i
$743$	−18.2705			−0.670281			−0.335141	−	0.942168i	$-0.608784\pi$
$743$	−18.2705			−0.670281			−0.335141	+	0.942168i	$0.608784\pi$
$744$	7.90626	−	9.73448i	0.289858	−	0.356883i
$745$	−53.6957			−1.96726
$746$	−33.9711	+	18.7917i	−1.24377	+	0.688012i
$747$	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
$750$	2.45046	+	5.76818i	0.0894783	+	0.210624i
$751$	36.8395	+	21.2693i	1.34429	+	0.776127i	0.987434	−	0.158032i	$-0.0505151\pi$
$751$	36.8395	+	21.2693i	1.34429	+	0.776127i	0.356857	+	0.934159i	$0.383848\pi$
$752$	49.3182	+	3.62199i	1.79845	+	0.132080i
$753$	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
$756$	26.0577	+	30.9435i	0.947711	+	1.12540i
$757$	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	$-0.0100805\pi$
$758$	−12.5092	−	0.229287i	−0.454356	−	0.00832810i
$759$	−14.6309	+	20.1873i	−0.531067	+	0.732753i
$760$	−21.6644	−	30.3664i	−0.785851	−	1.10151i
$761$	−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	$0.392128\pi$
$762$	−9.39701	+	12.4779i	−0.340418	+	0.452028i
$763$	−59.5944	+	34.4068i	−2.15746	+	1.24561i
$764$	15.1995	−	24.2300i	0.549900	−	0.876611i
$765$	14.1130	+	43.0919i	0.510256	+	1.55799i
$766$	0.0355841	−	1.94136i	0.00128570	−	0.0701443i
$767$	21.2673	−	36.8360i	0.767917	−	1.33007i
$768$	7.48345	+	26.6833i	0.270036	+	0.962850i
$769$	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	$0.0829159\pi$
$770$	43.8896	−	24.2783i	1.58167	−	0.874928i
$771$	3.72365	−	35.8314i	0.134104	−	1.29044i
$772$	9.08323	+	0.333093i	0.326913	+	0.0119883i
$773$	−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	$0.470922\pi$
$774$	7.79912	+	1.78853i	0.280334	+	0.0642873i
$775$	−9.20985	+	5.31731i	−0.330827	+	0.191003i
$776$	−7.24226	+	3.66623i	−0.259982	+	0.131610i
$777$	2.15774	−	20.7632i	0.0774085	−	0.744877i
$778$	−46.0139	−	0.843408i	−1.64968	−	0.0302377i
$779$	1.40899	−	1.12702i	0.0504821	−	0.0403796i
$780$	5.88178	−	41.6763i	0.210601	−	1.49225i
$781$	−14.6626	−	25.3964i	−0.524670	−	0.908755i
$782$	−16.3464	−	29.5505i	−0.584545	−	1.05672i
$783$	0.689914	−	2.14898i	0.0246555	−	0.0767983i
$784$	14.1933	+	29.3607i	0.506903	+	1.04859i
$785$			7.58596i			0.270754i
$786$	−22.4574	+	9.54045i	−0.801029	+	0.340297i
$787$	41.3050	−	23.8474i	1.47236	−	0.850069i	0.472845	−	0.881145i	$-0.343227\pi$
$787$	41.3050	−	23.8474i	1.47236	−	0.850069i	0.999517	+	0.0310765i	$0.00989354\pi$
$788$	−1.41896	+	38.6941i	−0.0505483	+	1.37842i
$789$	−9.14320	+	12.6156i	−0.325506	+	0.449126i
$790$	50.4454	−	27.9048i	1.79477	−	0.992807i
$791$	−45.2514			−1.60895
$792$	24.6830	−	6.60635i	0.877074	−	0.234746i
$793$	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	$0.216349\pi$
$798$	−21.8229	−	35.3721i	−0.772521	−	1.25216i
$799$	53.4849	+	30.8795i	1.89216	+	1.09244i
$800$	2.15052	−	23.4021i	0.0760323	−	0.827389i
$801$	8.80501	−	41.9064i	0.311110	−	1.48069i
$802$	−21.0105	−	0.385111i	−0.741906	−	0.0135987i
$803$	−0.897605	−	1.55470i	−0.0316758	−	0.0548641i
$804$	−6.24372	+	44.2408i	−0.220199	+	1.56025i
$805$	28.1492	+	48.7559i	0.992130	+	1.71842i
$806$	−14.5353	−	0.266424i	−0.511984	−	0.00938439i
$807$	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	$0.920288\pi$
$810$	−3.50238	−	38.3503i	−0.123061	−	1.34749i
$811$	5.19959	−	3.00199i	0.182582	−	0.105414i	−0.405923	−	0.913907i	$-0.633050\pi$
$811$	5.19959	−	3.00199i	0.182582	−	0.105414i	0.588505	+	0.808493i	$0.299717\pi$
$812$	1.79701	−	2.86466i	0.0630627	−	0.100530i
$813$	−0.00243716	+	0.0234520i	−8.54749e−5	+	0.000822497i
$814$	−11.2961	−	6.80082i	−0.395928	−	0.238369i
$815$	−56.6745			−1.98522
$816$	−6.08929	+	34.0705i	−0.213168	+	1.19270i
$817$	−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
$820$	2.50310	+	0.0917917i	0.0874121	+	0.00320551i
$821$			25.4733i			0.889023i	0.895773	+	0.444511i	$0.146623\pi$
$821$			25.4733i			0.889023i	−0.895773	+	0.444511i	$0.853377\pi$
$822$	17.1601	+	40.3935i	0.598529	+	1.40888i
$823$	−16.0564	−	9.27019i	−0.559692	−	0.323139i	0.193330	−	0.981134i	$-0.438071\pi$
$823$	−16.0564	−	9.27019i	−0.559692	−	0.323139i	−0.753022	+	0.657995i	$0.771405\pi$
$824$	−10.3688	−	20.4826i	−0.361215	−	0.713544i
$825$	−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	0.838676	−	0.544631i	$-0.183330\pi$
$827$	−1.50477	−	2.60634i	−0.0523261	−	0.0906314i	−0.891002	+	0.453999i	$0.849997\pi$
$828$	7.92175	+	27.5648i	0.275300	+	0.957942i
$829$	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
$832$	19.0192	−	25.8911i	0.659373	−	0.897611i
$833$			40.7280i			1.41114i
$834$	−36.4781	−	4.46798i	−1.26313	−	0.154713i
$835$	−42.7812	−	24.6998i	−1.48051	−	0.854770i
$836$	−26.0804	+	2.99704i	−0.902009	+	0.103655i
$837$	−13.0010	+	2.81118i	−0.449379	+	0.0971686i
$838$	16.8934	−	9.34487i	0.583573	−	0.322813i
$839$	−21.4490	−	37.1508i	−0.740502	−	1.28259i	−0.952267	−	0.305266i	$-0.901255\pi$
$839$	−21.4490	−	37.1508i	−0.740502	−	1.28259i	0.211765	−	0.977321i	$-0.432079\pi$
$840$	9.10882	−	56.9753i	0.314284	−	1.96583i
$841$	28.8113			0.993494
$842$	−22.4118	+	12.3975i	−0.772363	+	0.427246i
$843$	−18.2703	+	8.16011i	−0.629264	+	0.281049i
$844$	−0.271559	+	7.40523i	−0.00934743	+	0.254899i
$845$	−8.19152	+	4.72937i	−0.281797	+	0.162695i
$846$	−38.4124	−	35.7150i	−1.32065	−	1.22791i
$847$			7.52062i			0.258411i
$848$	38.7623	−	18.7382i	1.33110	−	0.643471i
$849$	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
$852$	−33.4037	−	4.71427i	−1.14439	−	0.161508i
$853$	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	$0.447951\pi$
$858$	−23.6616	−	17.8193i	−0.807792	−	0.608340i
$859$	−44.1631	−	25.4976i	−1.50683	−	0.869967i	−0.999969	−	0.00793693i	$-0.997474\pi$
$859$	−44.1631	−	25.4976i	−1.50683	−	0.869967i	−0.506858	−	0.862030i	$-0.669193\pi$
$860$	−5.34025	−	10.0861i	−0.182101	−	0.343932i
$861$	2.77588	+	0.288473i	0.0946018	+	0.00983113i
$862$	15.6472	−	8.65549i	0.532944	−	0.294807i
$863$	0.580286			0.0197532			0.00987658	−	0.999951i	$-0.496856\pi$
$863$	0.580286			0.0197532			0.00987658	+	0.999951i	$0.496856\pi$
$864$	11.5084	−	27.0473i	0.391522	−	0.920169i
$865$	7.94181	+	13.7556i	0.270030	+	0.467705i
$866$	−25.5212	+	14.1175i	−0.867245	+	0.479731i
$867$	−8.08648	+	11.1575i	−0.274631	+	0.378929i
$868$	−19.9160	−	0.730342i	−0.675991	−	0.0247894i
$869$		−	40.5713i		−	1.37629i
$870$	−2.96287	+	1.25870i	−0.100451	+	0.0426740i
$871$	44.8551	−	25.8971i	1.51986	−	0.877490i
$872$	41.8623	+	27.3420i	1.41764	+	0.925917i
$873$	8.42579	+	1.77035i	0.285170	+	0.0599174i
$874$	−3.89992	−	29.2072i	−0.131917	−	0.987948i
$875$	4.97976	−	8.62520i	0.168347	−	0.291585i
$876$	−2.04488	−	0.288594i	−0.0690901	−	0.00975070i
$877$	−23.2433			−0.784870			−0.392435	−	0.919780i	$-0.628367\pi$
$877$	−23.2433			−0.784870			−0.392435	+	0.919780i	$0.628367\pi$
$878$	−8.44010	−	15.2578i	−0.284840	−	0.514925i
$879$	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	$0.959741\pi$
$882$	7.73152	−	33.7144i	0.260334	−	1.13522i
$883$	−24.9720	+	14.4176i	−0.840374	+	0.485190i	−0.857391	−	0.514665i	$-0.827916\pi$
$883$	−24.9720	+	14.4176i	−0.840374	+	0.485190i	0.0170172	+	0.999855i	$0.494583\pi$
$884$	35.4584	−	18.7741i	1.19260	−	0.631442i
$885$	−50.6821	+	22.6362i	−1.70366	+	0.760908i
$886$	−0.0844459	+	4.60712i	−0.00283701	+	0.154779i
$887$	−14.8290	+	25.6846i	−0.497909	+	0.862403i	−0.999997	−	0.00241298i	$-0.999232\pi$
$887$	−14.8290	+	25.6846i	−0.497909	+	0.862403i	0.502088	+	0.864816i	$0.332565\pi$
$888$	−14.1683	+	5.41513i	−0.475458	+	0.181720i
$889$	24.8238			0.832565
$890$	−53.4439	+	29.5634i	−1.79144	+	0.990968i
$891$	−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
$894$	16.9974	+	40.0103i	0.568477	+	1.33815i
$895$			27.2312i			0.910240i
$896$	26.7189	−	35.0094i	0.892616	−	1.16958i
$897$	19.5110	−	26.9209i	0.651455	−	0.898861i
$898$	26.8666	+	0.492450i	0.896551	+	0.0164333i
$899$	0.555953	+	0.962938i	0.0185421	+	0.0321158i
$900$	−17.3046	+	17.9407i	−0.576820	+	0.598023i
$901$	53.7697			1.79133
$902$	0.909216	−	1.51020i	0.0302736	−	0.0502841i
$903$	−5.18561	−	11.6105i	−0.172566	−	0.386373i
$904$	14.8503	+	29.3352i	0.493913	+	0.975675i
$905$	36.1100	−	20.8481i	1.20034	−	0.693016i
$906$	−7.82555	−	0.958504i	−0.259986	−	0.0318442i
$907$	−31.9137	+	18.4254i	−1.05968	+	0.611804i	−0.925342	−	0.379132i	$-0.876222\pi$
$907$	−31.9137	+	18.4254i	−1.05968	+	0.611804i	−0.134333	+	0.990936i	$0.542889\pi$
$908$	2.68446	−	4.27937i	0.0890869	−	0.142016i
$909$	−12.0006	−	10.7546i	−0.398034	−	0.356708i
$910$	−58.5291	+	32.3764i	−1.94022	+	1.07327i
$911$	5.88938	−	10.2007i	0.195124	−	0.337965i	−0.751817	−	0.659372i	$-0.770822\pi$
$911$	5.88938	−	10.2007i	0.195124	−	0.337965i	0.946941	+	0.321407i	$0.104156\pi$
$912$	−15.7691	+	25.7553i	−0.522167	+	0.852844i
$913$	−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
$918$	27.6416	−	24.1568i	0.912310	−	0.797292i
$919$			48.5036i			1.59999i	0.600010	+	0.799993i	$0.295163\pi$
$919$			48.5036i			1.59999i	−0.600010	+	0.799993i	$0.704837\pi$
$920$	22.3693	−	34.2487i	0.737494	−	1.12915i
$921$	−5.12987	+	49.3631i	−0.169035	+	1.62657i
$922$	−5.83899	−	10.5556i	−0.192297	−	0.347629i
$923$	19.5534	+	33.8675i	0.643608	+	1.11476i
$924$	−31.9837	−	25.0182i	−1.05219	−	0.823039i
$925$	12.8625			0.422917
$926$	6.95341	+	12.5702i	0.228503	+	0.413082i
$927$	−5.00692	+	23.8298i	−0.164449	+	0.782674i
$928$	−2.44681	−	0.224848i	−0.0803205	−	0.00738100i
$929$	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	$0.248265\pi$
$930$	15.1548	+	11.4130i	0.496947	+	0.374246i
$931$	−12.9347	+	33.0998i	−0.423916	+	1.08480i
$932$	−9.43154	−	5.91643i	−0.308940	−	0.193799i
$933$	−1.88348	+	2.59877i	−0.0616622	+	0.0850799i
$934$	0.156671	−	8.54748i	0.00512642	−	0.279682i
$935$	−22.7575	−	39.4172i	−0.744251	−	1.28908i
$936$	−32.9162	+	8.80992i	−1.07590	+	0.287961i
$937$	−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	$0.857573\pi$
$938$	62.1307	−	34.3687i	2.02864	−	1.12218i
$939$	−3.16152	−	7.07859i	−0.103172	−	0.231001i
$940$	−2.74153	+	74.7597i	−0.0894188	+	2.43839i
$941$	−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	$0.936692\pi$
$942$	5.65253	−	2.40133i	0.184170	−	0.0782397i
$943$	1.71353	+	0.989308i	0.0558003	+	0.0322163i
$944$	−42.2540	−	3.10318i	−1.37525	−	0.101000i
$945$	−45.3355	+	41.1094i	−1.47477	+	1.33729i
$946$	−8.03040	−	0.147193i	−0.261091	−	0.00478565i
$947$	−7.16391	−	12.4083i	−0.232796	−	0.403214i	0.725834	−	0.687870i	$-0.241454\pi$
$947$	−7.16391	−	12.4083i	−0.232796	−	0.403214i	−0.958630	+	0.284656i	$0.908121\pi$
$948$	−36.7612	−	28.7552i	−1.19395	−	0.933926i
$949$	1.19700	+	2.07327i	0.0388564	+	0.0673013i
$950$	20.2885	−	15.6273i	0.658245	−	0.507018i
$951$	42.5709	−	19.0135i	1.38046	−	0.616555i
$952$	49.0723	−	24.8417i	1.59044	−	0.805124i
$953$	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	$0.503402\pi$
$954$	−44.5102	−	10.2073i	−1.44107	−	0.330472i
$955$	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
$958$	0.283388	−	15.4608i	0.00915586	−	0.499517i
$959$	34.8723	−	60.4007i	1.12609	−	1.95044i
$960$	−39.9248	+	12.7927i	−1.28857	+	0.412884i
$961$	−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
$964$	29.5403	+	1.08328i	0.951429	+	0.0348900i
$965$			13.7504i			0.442642i
$966$	27.4189	−	36.4086i	0.882189	−	1.17143i
$967$			49.3216i			1.58608i	0.609172	+	0.793038i	$0.291502\pi$
$967$			49.3216i			1.58608i	−0.609172	+	0.793038i	$0.708498\pi$
$968$	4.87541	−	2.46806i	0.156702	−	0.0793265i
$969$	−31.7302	+	20.3881i	−1.01932	+	0.654960i
$970$	−5.94409	−	10.7456i	−0.190853	−	0.345019i
$971$	−14.3746	+	24.8975i	−0.461303	+	0.798999i	−0.999026	−	0.0441217i	$-0.985951\pi$
$971$	−14.3746	+	24.8975i	−0.461303	+	0.798999i	0.537724	+	0.843121i	$0.319284\pi$
$972$	−27.4673	+	14.7495i	−0.881014	+	0.473090i
$973$	29.2016	+	50.5786i	0.936160	+	1.62148i
$974$	−44.2214	−	0.810554i	−1.41695	−	0.0259718i
$975$	28.7409	+	2.98679i	0.920445	+	0.0956537i
$976$	−25.6274	−	1.88211i	−0.820314	−	0.0602448i
$977$	−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	$0.379134\pi$
$978$	17.9403	+	42.2299i	0.573667	+	1.35036i
$979$			42.9829i			1.37374i
$980$	−43.6004	+	23.0851i	−1.39276	+	0.737425i
$981$	−16.5062	−	50.3992i	−0.527003	−	1.60912i
$982$	0.185582	−	10.1248i	0.00592216	−	0.323095i
$983$	−13.1412	−	22.7612i	−0.419139	−	0.725970i	0.576714	−	0.816946i	$-0.304335\pi$
$983$	−13.1412	−	22.7612i	−0.419139	−	0.725970i	−0.995853	+	0.0909759i	$0.971001\pi$
$984$	−0.723960	−	1.89420i	−0.0230790	−	0.0603848i
$985$	−58.5762			−1.86639
$986$	−2.62899	−	1.58279i	−0.0837241	−	0.0504062i
$987$	−8.61577	+	82.9068i	−0.274243	+	2.63895i
$988$	34.7796	−	3.99671i	1.10649	−	0.127152i
$989$		−	9.01518i		−	0.286666i
$990$	11.3558	+	36.9494i	0.360912	+	1.17433i
$991$	17.2201	+	9.94205i	0.547016	+	0.315820i	0.747918	−	0.663792i	$-0.231054\pi$
$991$	17.2201	+	9.94205i	0.547016	+	0.315820i	−0.200902	+	0.979611i	$0.564387\pi$
$992$	6.06241	+	13.1506i	0.192482	+	0.417533i
$993$	5.13085	−	49.3725i	0.162822	−	1.56679i
$994$	25.9498	+	46.9113i	0.823077	+	1.48794i
$995$	9.61103	+	16.6468i	0.304690	+	0.527739i
$996$	−12.8560	−	1.81436i	−0.407356	−	0.0574903i
$997$	−40.3929			−1.27926			−0.639629	−	0.768684i	$-0.720912\pi$
$997$	−40.3929			−1.27926			−0.639629	+	0.768684i	$0.720912\pi$
$998$	−48.0605	−	0.880921i	−1.52133	−	0.0278851i
$999$	15.3180	+	4.91772i	0.484639	+	0.155590i

Twists

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

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

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0259174 + 1.41398i) q^{2} +(0.706340 + 1.58148i) q^{3} +(-1.99866 - 0.0732931i) q^{4} -3.02562i q^{5} +(-2.25448 + 0.957760i) q^{6} +(3.37115 + 1.94633i) q^{7} +(0.155435 - 2.82415i) q^{8} +(-2.00217 + 2.23413i) q^{9} +(4.27815 + 0.0784162i) q^{10} +(1.50566 - 2.60787i) q^{11} +(-1.29582 - 3.21261i) q^{12} +(-2.00787 + 3.47774i) q^{13} +(-2.83944 + 4.71628i) q^{14} +(4.78496 - 2.13712i) q^{15} +(3.98926 + 0.292976i) q^{16} +(4.32629 + 2.49779i) q^{17} +(-3.10711 - 2.88892i) q^{18} +(2.72273 + 3.40393i) q^{19} +(-0.221757 + 6.04718i) q^{20} +(-0.696914 + 6.70618i) q^{21} +(3.64845 + 2.19655i) q^{22} +(-2.39004 + 4.13967i) q^{23} +(4.57614 - 1.74899i) q^{24} -4.15438 q^{25} +(-4.86540 - 2.92922i) q^{26} +(-4.94744 - 1.58834i) q^{27} +(-6.59511 - 4.13713i) q^{28} +0.434362i q^{29} +(2.89782 + 6.82121i) q^{30} +(2.21690 - 1.27993i) q^{31} +(-0.517652 + 5.63312i) q^{32} +(5.18781 + 0.539123i) q^{33} +(-3.64394 + 6.05254i) q^{34} +(5.88886 - 10.1998i) q^{35} +(4.16539 - 4.31851i) q^{36} -3.09614 q^{37} +(-4.88364 + 3.76166i) q^{38} +(-6.91822 - 0.718950i) q^{39} +(-8.54481 - 0.470286i) q^{40} -0.413929i q^{41} +(-9.46431 - 1.15923i) q^{42} +(-1.63331 + 0.942994i) q^{43} +(-3.20043 + 5.10189i) q^{44} +(6.75962 + 6.05780i) q^{45} +(-5.79146 - 3.48675i) q^{46} +12.3628 q^{47} +(2.35443 + 6.51588i) q^{48} +(4.07641 + 7.06056i) q^{49} +(0.107671 - 5.87419i) q^{50} +(-0.894370 + 8.60624i) q^{51} +(4.26794 - 6.80364i) q^{52} +(9.32144 - 5.38174i) q^{53} +(2.37410 - 6.95440i) q^{54} +(-7.89043 - 4.55554i) q^{55} +(6.02073 - 9.21810i) q^{56} +(-3.46008 + 6.71028i) q^{57} +(-0.614177 - 0.0112575i) q^{58} -10.5919 q^{59} +(-9.72013 + 3.92066i) q^{60} -6.42411 q^{61} +(1.75233 + 3.16782i) q^{62} +(-11.0980 + 3.63468i) q^{63} +(-7.95168 - 0.877943i) q^{64} +(10.5223 + 6.07506i) q^{65} +(-0.896762 + 7.32146i) q^{66} +(-11.1698 - 6.44889i) q^{67} +(-8.46370 - 5.30930i) q^{68} +(-8.23500 - 0.855791i) q^{69} +(14.2697 + 8.59106i) q^{70} +(4.86918 - 8.43367i) q^{71} +(5.99831 + 6.00169i) q^{72} +(0.298078 - 0.516286i) q^{73} +(0.0802438 - 4.37786i) q^{74} +(-2.93440 - 6.57007i) q^{75} +(-5.19232 - 7.00284i) q^{76} +(10.1516 - 5.86101i) q^{77} +(1.19588 - 9.76356i) q^{78} +(11.6679 - 6.73648i) q^{79} +(0.886433 - 12.0700i) q^{80} +(-0.982644 - 8.94620i) q^{81} +(0.585286 + 0.0107280i) q^{82} +(1.87399 - 3.24584i) q^{83} +(1.88441 - 13.3523i) q^{84} +(7.55735 - 13.0897i) q^{85} +(-1.29104 - 2.33391i) q^{86} +(-0.686935 + 0.306807i) q^{87} +(-7.13100 - 4.65756i) q^{88} +(-12.3615 + 7.13690i) q^{89} +(-8.74078 + 9.40094i) q^{90} +(-13.5377 + 7.81597i) q^{91} +(5.08028 - 8.09861i) q^{92} +(3.59007 + 2.60193i) q^{93} +(-0.320410 + 17.4806i) q^{94} +(10.2990 - 8.23795i) q^{95} +(-9.27431 + 3.16024i) q^{96} +(-1.43496 - 2.48542i) q^{97} +(-10.0891 + 5.58096i) 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

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