LMFDB - Embedded newform 273.2.bt.b.136.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(136,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("273.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bt (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			136.10
Character	$\chi$	$=$	273.136
Dual form			273.2.bt.b.271.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93326 - 1.93326i) q^{2} +(-0.866025 + 0.500000i) q^{3} -5.47495i q^{4} +(-0.212233 + 0.792066i) q^{5} +(-0.707621 + 2.64088i) q^{6} +(2.21517 - 1.44673i) q^{7} +(-6.71797 - 6.71797i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.93326 - 1.93326i) q^{2} +(-0.866025 + 0.500000i) q^{3} -5.47495i q^{4} +(-0.212233 + 0.792066i) q^{5} +(-0.707621 + 2.64088i) q^{6} +(2.21517 - 1.44673i) q^{7} +(-6.71797 - 6.71797i) q^{8} +(0.500000 - 0.866025i) q^{9} +(1.12096 + 1.94157i) q^{10} +(0.207489 - 0.774358i) q^{11} +(2.73748 + 4.74145i) q^{12} +(-2.33034 + 2.75128i) q^{13} +(1.48557 - 7.07939i) q^{14} +(-0.212233 - 0.792066i) q^{15} -15.0252 q^{16} +0.290651 q^{17} +(-0.707621 - 2.64088i) q^{18} +(2.05764 - 0.551342i) q^{19} +(4.33652 + 1.16197i) q^{20} +(-1.19502 + 2.36049i) q^{21} +(-1.09590 - 1.89816i) q^{22} +9.32871i q^{23} +(9.17692 + 2.45895i) q^{24} +(3.74780 + 2.16379i) q^{25} +(0.813775 + 9.82406i) q^{26} +1.00000i q^{27} +(-7.92080 - 12.1279i) q^{28} +(2.87091 - 4.97256i) q^{29} +(-1.94157 - 1.12096i) q^{30} +(5.03926 - 1.35027i) q^{31} +(-15.6116 + 15.6116i) q^{32} +(0.207489 + 0.774358i) q^{33} +(0.561903 - 0.561903i) q^{34} +(0.675777 + 2.06160i) q^{35} +(-4.74145 - 2.73748i) q^{36} +(1.61650 + 1.61650i) q^{37} +(2.91205 - 5.04382i) q^{38} +(0.642496 - 3.54784i) q^{39} +(6.74685 - 3.89530i) q^{40} +(-8.80575 + 2.35949i) q^{41} +(2.25315 + 6.87372i) q^{42} +(2.71857 - 1.56956i) q^{43} +(-4.23957 - 1.13599i) q^{44} +(0.579832 + 0.579832i) q^{45} +(18.0348 + 18.0348i) q^{46} +(4.70196 + 1.25989i) q^{47} +(13.0122 - 7.51260i) q^{48} +(2.81392 - 6.40951i) q^{49} +(11.4286 - 3.06229i) q^{50} +(-0.251711 + 0.145326i) q^{51} +(15.0631 + 12.7585i) q^{52} +(-2.69075 + 4.66051i) q^{53} +(1.93326 + 1.93326i) q^{54} +(0.569307 + 0.328689i) q^{55} +(-24.6005 - 5.16230i) q^{56} +(-1.50629 + 1.50629i) q^{57} +(-4.06302 - 15.1634i) q^{58} +(-8.80521 + 8.80521i) q^{59} +(-4.33652 + 1.16197i) q^{60} +(-5.06274 - 2.92297i) q^{61} +(7.13177 - 12.3526i) q^{62} +(-0.145326 - 2.64176i) q^{63} +30.3120i q^{64} +(-1.68461 - 2.42970i) q^{65} +(1.89816 + 1.09590i) q^{66} +(-12.2581 - 3.28455i) q^{67} -1.59130i q^{68} +(-4.66436 - 8.07890i) q^{69} +(5.29205 + 2.67916i) q^{70} +(-6.43570 - 1.72444i) q^{71} +(-9.17692 + 2.45895i) q^{72} +(-2.07411 - 7.74069i) q^{73} +6.25021 q^{74} -4.32759 q^{75} +(-3.01857 - 11.2655i) q^{76} +(-0.660669 - 2.01551i) q^{77} +(-5.61678 - 8.10100i) q^{78} +(2.75101 + 4.76489i) q^{79} +(3.18885 - 11.9009i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-12.4623 + 21.5853i) q^{82} +(3.51255 + 3.51255i) q^{83} +(12.9236 + 6.54269i) q^{84} +(-0.0616859 + 0.230215i) q^{85} +(2.22131 - 8.29005i) q^{86} +5.74181i q^{87} +(-6.59602 + 3.80821i) q^{88} +(-3.11778 + 3.11778i) q^{89} +2.24193 q^{90} +(-1.18173 + 9.46591i) q^{91} +51.0743 q^{92} +(-3.68899 + 3.68899i) q^{93} +(11.5258 - 6.65440i) q^{94} +1.74680i q^{95} +(5.71424 - 21.3259i) q^{96} +(3.20349 - 11.9556i) q^{97} +(-6.95120 - 17.8313i) q^{98} +(-0.566870 - 0.566870i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q - 2 * q^7 + 20 * q^9	$ 40 q - 2 q^{7} + 20 q^{9} - 8 q^{11} + 24 q^{12} - 18 q^{14} - 64 q^{16} + 8 q^{17} - 14 q^{19} - 14 q^{20} - 8 q^{21} + 4 q^{22} + 18 q^{24} - 24 q^{25} - 10 q^{26} - 2 q^{28} + 8 q^{29} - 8 q^{31} + 10 q^{32} - 8 q^{33} + 24 q^{34} - 22 q^{35} + 12 q^{37} + 8 q^{38} - 24 q^{39} - 30 q^{40} + 2 q^{41} + 6 q^{42} - 66 q^{43} + 28 q^{44} + 40 q^{46} + 10 q^{47} - 24 q^{48} + 38 q^{49} - 20 q^{50} + 40 q^{52} - 8 q^{53} + 42 q^{55} + 20 q^{56} - 14 q^{57} - 48 q^{58} - 26 q^{59} + 14 q^{60} - 12 q^{61} - 24 q^{62} - 4 q^{63} - 44 q^{65} - 18 q^{66} + 46 q^{67} - 4 q^{69} + 32 q^{70} - 6 q^{71} - 18 q^{72} + 10 q^{73} + 40 q^{74} + 48 q^{75} + 64 q^{76} - 24 q^{77} + 8 q^{78} + 34 q^{80} - 20 q^{81} + 24 q^{82} + 12 q^{83} + 20 q^{84} + 2 q^{85} + 12 q^{86} - 84 q^{88} - 16 q^{89} + 26 q^{91} + 236 q^{92} + 22 q^{93} + 30 q^{94} + 26 q^{96} + 62 q^{97} - 14 q^{98} - 4 q^{99}+O(q^{100}) $ 40 * q - 2 * q^7 + 20 * q^9 - 8 * q^11 + 24 * q^12 - 18 * q^14 - 64 * q^16 + 8 * q^17 - 14 * q^19 - 14 * q^20 - 8 * q^21 + 4 * q^22 + 18 * q^24 - 24 * q^25 - 10 * q^26 - 2 * q^28 + 8 * q^29 - 8 * q^31 + 10 * q^32 - 8 * q^33 + 24 * q^34 - 22 * q^35 + 12 * q^37 + 8 * q^38 - 24 * q^39 - 30 * q^40 + 2 * q^41 + 6 * q^42 - 66 * q^43 + 28 * q^44 + 40 * q^46 + 10 * q^47 - 24 * q^48 + 38 * q^49 - 20 * q^50 + 40 * q^52 - 8 * q^53 + 42 * q^55 + 20 * q^56 - 14 * q^57 - 48 * q^58 - 26 * q^59 + 14 * q^60 - 12 * q^61 - 24 * q^62 - 4 * q^63 - 44 * q^65 - 18 * q^66 + 46 * q^67 - 4 * q^69 + 32 * q^70 - 6 * q^71 - 18 * q^72 + 10 * q^73 + 40 * q^74 + 48 * q^75 + 64 * q^76 - 24 * q^77 + 8 * q^78 + 34 * q^80 - 20 * q^81 + 24 * q^82 + 12 * q^83 + 20 * q^84 + 2 * q^85 + 12 * q^86 - 84 * q^88 - 16 * q^89 + 26 * q^91 + 236 * q^92 + 22 * q^93 + 30 * q^94 + 26 * q^96 + 62 * q^97 - 14 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.93326	−	1.93326i	1.36702	−	1.36702i	0.502359	−	0.864659i	$-0.332466\pi$
$2$	1.93326	−	1.93326i	1.36702	−	1.36702i	0.864659	−	0.502359i	$-0.167534\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$		−	5.47495i		−	2.73748i
$5$	−0.212233	+	0.792066i	−0.0949137	+	0.354223i	−0.997006	−	0.0773197i	$-0.975364\pi$
$5$	−0.212233	+	0.792066i	−0.0949137	+	0.354223i	0.902093	+	0.431542i	$0.142030\pi$
$6$	−0.707621	+	2.64088i	−0.288885	+	1.07813i
$7$	2.21517	−	1.44673i	0.837254	−	0.546814i
$7$	2.21517	−	1.44673i	0.837254	−	0.546814i
$8$	−6.71797	−	6.71797i	−2.37516	−	2.37516i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.12096	+	1.94157i	0.354480	+	0.613977i
$11$	0.207489	−	0.774358i	0.0625602	−	0.233478i	−0.927565	−	0.373661i	$-0.878102\pi$
$11$	0.207489	−	0.774358i	0.0625602	−	0.233478i	0.990126	+	0.140183i	$0.0447691\pi$
$12$	2.73748	+	4.74145i	0.790241	+	1.36874i
$13$	−2.33034	+	2.75128i	−0.646320	+	0.763066i
$13$	−2.33034	+	2.75128i	−0.646320	+	0.763066i
$14$	1.48557	−	7.07939i	0.397037	−	1.89205i
$15$	−0.212233	−	0.792066i	−0.0547984	−	0.204511i
$16$	−15.0252			−3.75630
$17$	0.290651			0.0704933			0.0352466	−	0.999379i	$-0.488778\pi$
$17$	0.290651			0.0704933			0.0352466	+	0.999379i	$0.488778\pi$
$18$	−0.707621	−	2.64088i	−0.166788	−	0.622460i
$19$	2.05764	−	0.551342i	0.472054	−	0.126487i	−0.0149462	−	0.999888i	$-0.504758\pi$
$19$	2.05764	−	0.551342i	0.472054	−	0.126487i	0.487000	+	0.873402i	$0.338091\pi$
$20$	4.33652	+	1.16197i	0.969676	+	0.259824i
$21$	−1.19502	+	2.36049i	−0.260775	+	0.515101i
$22$	−1.09590	−	1.89816i	−0.233647	−	0.404689i
$23$			9.32871i			1.94517i	0.232545	+	0.972586i	$0.425295\pi$
$23$			9.32871i			1.94517i	−0.232545	+	0.972586i	$0.574705\pi$
$24$	9.17692	+	2.45895i	1.87323	+	0.501931i
$25$	3.74780	+	2.16379i	0.749560	+	0.432759i
$26$	0.813775	+	9.82406i	0.159594	+	1.92666i
$27$			1.00000i			0.192450i
$28$	−7.92080	−	12.1279i	−1.49689	−	2.29196i
$29$	2.87091	−	4.97256i	0.533114	−	0.923380i	−0.466138	−	0.884712i	$-0.654355\pi$
$29$	2.87091	−	4.97256i	0.533114	−	0.923380i	0.999252	−	0.0386684i	$-0.0123116\pi$
$30$	−1.94157	−	1.12096i	−0.354480	−	0.204659i
$31$	5.03926	−	1.35027i	0.905078	−	0.242515i	0.223882	−	0.974616i	$-0.428127\pi$
$31$	5.03926	−	1.35027i	0.905078	−	0.242515i	0.681196	+	0.732101i	$0.261460\pi$
$32$	−15.6116	+	15.6116i	−2.75977	+	2.75977i
$33$	0.207489	+	0.774358i	0.0361191	+	0.134798i
$34$	0.561903	−	0.561903i	0.0963656	−	0.0963656i
$35$	0.675777	+	2.06160i	0.114227	+	0.348474i
$36$	−4.74145	−	2.73748i	−0.790241	−	0.456246i
$37$	1.61650	+	1.61650i	0.265751	+	0.265751i	0.827385	−	0.561635i	$-0.189827\pi$
$37$	1.61650	+	1.61650i	0.265751	+	0.265751i	−0.561635	+	0.827385i	$0.689827\pi$
$38$	2.91205	−	5.04382i	0.472397	−	0.818216i
$39$	0.642496	−	3.54784i	0.102882	−	0.568110i
$40$	6.74685	−	3.89530i	1.06677	−	0.615901i
$41$	−8.80575	+	2.35949i	−1.37523	+	0.368491i	−0.869385	−	0.494135i	$-0.835485\pi$
$41$	−8.80575	+	2.35949i	−1.37523	+	0.368491i	−0.505842	+	0.862626i	$0.668818\pi$
$42$	2.25315	+	6.87372i	0.347668	+	1.06064i
$43$	2.71857	−	1.56956i	0.414577	−	0.239356i	−0.278177	−	0.960530i	$-0.589730\pi$
$43$	2.71857	−	1.56956i	0.414577	−	0.239356i	0.692755	+	0.721173i	$0.256397\pi$
$44$	−4.23957	−	1.13599i	−0.639140	−	0.171257i
$45$	0.579832	+	0.579832i	0.0864363	+	0.0864363i
$46$	18.0348	+	18.0348i	2.65908	+	2.65908i
$47$	4.70196	+	1.25989i	0.685851	+	0.183773i	0.584884	−	0.811117i	$-0.301140\pi$
$47$	4.70196	+	1.25989i	0.685851	+	0.183773i	0.100966	+	0.994890i	$0.467807\pi$
$48$	13.0122	−	7.51260i	1.87815	−	1.08435i
$49$	2.81392	−	6.40951i	0.401989	−	0.915645i
$50$	11.4286	−	3.06229i	1.61625	−	0.433073i
$51$	−0.251711	+	0.145326i	−0.0352466	+	0.0203497i
$52$	15.0631	+	12.7585i	2.08888	+	1.76929i
$53$	−2.69075	+	4.66051i	−0.369602	+	0.640170i	−0.989503	−	0.144510i	$-0.953839\pi$
$53$	−2.69075	+	4.66051i	−0.369602	+	0.640170i	0.619901	+	0.784680i	$0.287173\pi$
$54$	1.93326	+	1.93326i	0.263083	+	0.263083i
$55$	0.569307	+	0.328689i	0.0767653	+	0.0443205i
$56$	−24.6005	−	5.16230i	−3.28738	−	0.689842i
$57$	−1.50629	+	1.50629i	−0.199514	+	0.199514i
$58$	−4.06302	−	15.1634i	−0.533501	−	1.99105i
$59$	−8.80521	+	8.80521i	−1.14634	+	1.14634i	−0.159073	+	0.987267i	$0.550851\pi$
$59$	−8.80521	+	8.80521i	−1.14634	+	1.14634i	−0.987267	+	0.159073i	$0.949149\pi$
$60$	−4.33652	+	1.16197i	−0.559843	+	0.150009i
$61$	−5.06274	−	2.92297i	−0.648217	−	0.374248i	0.139556	−	0.990214i	$-0.455433\pi$
$61$	−5.06274	−	2.92297i	−0.648217	−	0.374248i	−0.787773	+	0.615966i	$0.788766\pi$
$62$	7.13177	−	12.3526i	0.905735	−	1.56878i
$63$	−0.145326	−	2.64176i	−0.0183093	−	0.332830i
$64$			30.3120i			3.78901i
$65$	−1.68461	−	2.42970i	−0.208951	−	0.301367i
$66$	1.89816	+	1.09590i	0.233647	+	0.134896i
$67$	−12.2581	−	3.28455i	−1.49757	−	0.401272i	−0.585282	−	0.810830i	$-0.699016\pi$
$67$	−12.2581	−	3.28455i	−1.49757	−	0.401272i	−0.912284	+	0.409558i	$0.865683\pi$
$68$		−	1.59130i		−	0.192974i
$69$	−4.66436	−	8.07890i	−0.561523	−	0.972586i
$70$	5.29205	+	2.67916i	0.632521	+	0.320220i
$71$	−6.43570	−	1.72444i	−0.763778	−	0.204654i	−0.144157	−	0.989555i	$-0.546047\pi$
$71$	−6.43570	−	1.72444i	−0.763778	−	0.204654i	−0.619621	+	0.784901i	$0.712714\pi$
$72$	−9.17692	+	2.45895i	−1.08151	+	0.289790i
$73$	−2.07411	−	7.74069i	−0.242756	−	0.905979i	−0.974498	−	0.224397i	$-0.927959\pi$
$73$	−2.07411	−	7.74069i	−0.242756	−	0.905979i	0.731742	−	0.681582i	$-0.238708\pi$
$74$	6.25021			0.726572
$75$	−4.32759			−0.499707
$76$	−3.01857	−	11.2655i	−0.346254	−	1.29224i
$77$	−0.660669	−	2.01551i	−0.0752902	−	0.229689i
$78$	−5.61678	−	8.10100i	−0.635975	−	0.917257i
$79$	2.75101	+	4.76489i	0.309513	+	0.536092i	0.978256	−	0.207402i	$-0.0665008\pi$
$79$	2.75101	+	4.76489i	0.309513	+	0.536092i	−0.668743	+	0.743493i	$0.733167\pi$
$80$	3.18885	−	11.9009i	0.356524	−	1.33057i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−12.4623	+	21.5853i	−1.37623	+	2.38370i
$83$	3.51255	+	3.51255i	0.385552	+	0.385552i	0.873098	−	0.487546i	$-0.162108\pi$
$83$	3.51255	+	3.51255i	0.385552	+	0.385552i	−0.487546	+	0.873098i	$0.662108\pi$
$84$	12.9236	+	6.54269i	1.41008	+	0.713866i
$85$	−0.0616859	+	0.230215i	−0.00669078	+	0.0249703i
$86$	2.22131	−	8.29005i	0.239530	−	0.893939i
$87$			5.74181i			0.615587i
$88$	−6.59602	+	3.80821i	−0.703138	+	0.405957i
$89$	−3.11778	+	3.11778i	−0.330484	+	0.330484i	−0.852770	−	0.522286i	$-0.825079\pi$
$89$	−3.11778	+	3.11778i	−0.330484	+	0.330484i	0.522286	+	0.852770i	$0.325079\pi$
$90$	2.24193			0.236320
$91$	−1.18173	+	9.46591i	−0.123879	+	0.992297i
$92$	51.0743			5.32486
$93$	−3.68899	+	3.68899i	−0.382531	+	0.382531i
$94$	11.5258	−	6.65440i	1.18879	−	0.686349i
$95$			1.74680i			0.179218i
$96$	5.71424	−	21.3259i	0.583208	−	2.17656i
$97$	3.20349	−	11.9556i	0.325265	−	1.21391i	−0.588780	−	0.808293i	$-0.700392\pi$
$97$	3.20349	−	11.9556i	0.325265	−	1.21391i	0.914045	−	0.405612i	$-0.132942\pi$
$98$	−6.95120	−	17.8313i	−0.702177	−	1.80123i
$99$	−0.566870	−	0.566870i	−0.0569725	−	0.0569725i
$100$	11.8467	−	20.5190i	1.18467	−	2.05190i
$101$	−6.10374	−	10.5720i	−0.607345	−	1.05195i	−0.991676	−	0.128757i	$-0.958901\pi$
$101$	−6.10374	−	10.5720i	−0.607345	−	1.05195i	0.384331	−	0.923195i	$-0.374432\pi$
$102$	−0.205671	+	0.767574i	−0.0203644	+	0.0760011i
$103$	8.55111	+	14.8110i	0.842566	+	1.45937i	0.887719	+	0.460387i	$0.152289\pi$
$103$	8.55111	+	14.8110i	0.842566	+	1.45937i	−0.0451528	+	0.998980i	$0.514377\pi$
$104$	34.1381	−	2.82783i	3.34752	−	0.277291i
$105$	−1.61604	−	1.44751i	−0.157709	−	0.141263i
$106$	3.80806	+	14.2119i	0.369871	+	1.38038i
$107$	−6.61923			−0.639905			−0.319953	−	0.947434i	$-0.603667\pi$
$107$	−6.61923			−0.639905			−0.319953	+	0.947434i	$0.603667\pi$
$108$	5.47495			0.526828
$109$	−1.91381	−	7.14245i	−0.183310	−	0.684123i	−0.994986	−	0.100014i	$-0.968111\pi$
$109$	−1.91381	−	7.14245i	−0.183310	−	0.684123i	0.811676	−	0.584108i	$-0.198556\pi$
$110$	1.73606	−	0.465175i	0.165526	−	0.0443527i
$111$	−2.20818	−	0.591680i	−0.209591	−	0.0561598i
$112$	−33.2833	+	21.7375i	−3.14498	+	2.05400i
$113$	−5.57880	−	9.66277i	−0.524810	−	0.908997i	−0.999583	−	0.0288885i	$-0.990803\pi$
$113$	−5.57880	−	9.66277i	−0.524810	−	0.908997i	0.474773	−	0.880108i	$-0.342530\pi$
$114$			5.82410i			0.545477i
$115$	−7.38895	−	1.97986i	−0.689024	−	0.184623i
$116$	−27.2245	−	15.7181i	−2.52773	−	1.45939i
$117$	1.21750	+	3.39377i	0.112558	+	0.313754i
$118$			34.0454i			3.13414i
$119$	0.643841	−	0.420495i	0.0590208	−	0.0385467i
$120$	−3.89530	+	6.74685i	−0.355590	+	0.615901i
$121$	8.96970	+	5.17866i	0.815427	+	0.470787i
$122$	−15.4384	+	4.13671i	−1.39773	+	0.374520i
$123$	6.44626	−	6.44626i	0.581240	−	0.581240i
$124$	−7.39264	−	27.5897i	−0.663879	−	2.47763i
$125$	−5.40844	+	5.40844i	−0.483745	+	0.483745i
$126$	−5.38814	−	4.82624i	−0.480014	−	0.429956i
$127$	6.08635	+	3.51395i	0.540076	+	0.311813i	0.745110	−	0.666942i	$-0.232397\pi$
$127$	6.08635	+	3.51395i	0.540076	+	0.311813i	−0.205034	+	0.978755i	$0.565730\pi$
$128$	27.3777	+	27.3777i	2.41987	+	2.41987i
$129$	−1.56956	+	2.71857i	−0.138192	+	0.239356i
$130$	−7.95401	−	1.44043i	−0.697613	−	0.126334i
$131$	1.77697	−	1.02593i	0.155254	−	0.0896361i	−0.420360	−	0.907357i	$-0.638096\pi$
$131$	1.77697	−	1.02593i	0.155254	−	0.0896361i	0.575614	+	0.817721i	$0.304763\pi$
$132$	4.23957	−	1.13599i	0.369008	−	0.0988753i
$133$	3.76036	−	4.19817i	0.326065	−	0.364027i
$134$	−30.0479	+	17.3482i	−2.59575	+	1.49865i
$135$	−0.792066	−	0.212233i	−0.0681702	−	0.0182661i
$136$	−1.95259	−	1.95259i	−0.167433	−	0.167433i
$137$	6.67688	+	6.67688i	0.570445	+	0.570445i	0.932253	−	0.361808i	$-0.117840\pi$
$137$	6.67688	+	6.67688i	0.570445	+	0.570445i	−0.361808	+	0.932253i	$0.617840\pi$
$138$	−24.6360	−	6.60119i	−2.09715	−	0.561931i
$139$	−11.2360	+	6.48710i	−0.953024	+	0.550229i	−0.894019	−	0.448029i	$-0.852126\pi$
$139$	−11.2360	+	6.48710i	−0.953024	+	0.550229i	−0.0590051	+	0.998258i	$0.518793\pi$
$140$	11.2872	−	3.69984i	0.953940	−	0.312694i
$141$	−4.70196	+	1.25989i	−0.395976	+	0.106101i
$142$	−15.7756	+	9.10807i	−1.32386	+	0.764333i
$143$	1.64695	+	2.37538i	0.137725	+	0.198639i
$144$	−7.51260	+	13.0122i	−0.626050	+	1.08435i
$145$	3.32929	+	3.32929i	0.276482	+	0.276482i
$146$	−18.9745	−	10.9549i	−1.57034	−	0.906637i
$147$	0.767830	+	6.95776i	0.0633295	+	0.573866i
$148$	8.85026	−	8.85026i	0.727487	−	0.727487i
$149$	−0.610901	−	2.27991i	−0.0500469	−	0.186778i	0.936377	−	0.350995i	$-0.114157\pi$
$149$	−0.610901	−	2.27991i	−0.0500469	−	0.186778i	−0.986424	+	0.164218i	$0.947490\pi$
$150$	−8.36633	+	8.36633i	−0.683108	+	0.683108i
$151$	13.7829	−	3.69311i	1.12164	−	0.300541i	0.350091	−	0.936716i	$-0.386151\pi$
$151$	13.7829	−	3.69311i	1.12164	−	0.300541i	0.771545	+	0.636174i	$0.219484\pi$
$152$	−17.5270	−	10.1192i	−1.42163	−	0.820779i
$153$	0.145326	−	0.251711i	0.0117489	−	0.0203497i
$154$	−5.17374	−	2.61926i	−0.416912	−	0.211066i
$155$			4.27800i			0.343617i
$156$	−19.4243	−	3.51764i	−1.55519	−	0.281636i
$157$	−19.5507	−	11.2876i	−1.56031	−	0.900848i	−0.997225	−	0.0744522i	$-0.976279\pi$
$157$	−19.5507	−	11.2876i	−1.56031	−	0.900848i	−0.563090	−	0.826396i	$-0.690387\pi$
$158$	14.5301	+	3.89334i	1.15596	+	0.309738i
$159$		−	5.38149i		−	0.426780i
$160$	−9.05212	−	15.6787i	−0.715633	−	1.23951i
$161$	13.4962	+	20.6646i	1.06365	+	1.62860i
$162$	−2.64088	−	0.707621i	−0.207487	−	0.0555959i
$163$	13.6702	−	3.66293i	1.07073	−	0.286903i	0.319940	−	0.947438i	$-0.396337\pi$
$163$	13.6702	−	3.66293i	1.07073	−	0.286903i	0.750795	+	0.660535i	$0.229671\pi$
$164$	12.9181	+	48.2111i	1.00874	+	3.76465i
$165$	−0.657379			−0.0511769
$166$	13.5813			1.05411
$167$	−3.99207	−	14.8986i	−0.308916	−	1.15289i	−0.929522	−	0.368767i	$-0.879780\pi$
$167$	−3.99207	−	14.8986i	−0.308916	−	1.15289i	0.620606	−	0.784123i	$-0.286887\pi$
$168$	23.8858	−	7.82958i	1.84283	−	0.604066i
$169$	−2.13903	−	12.8228i	−0.164541	−	0.986370i
$170$	0.325810	+	0.564319i	0.0249885	+	0.0432813i
$171$	0.551342	−	2.05764i	0.0421622	−	0.157351i
$172$	−8.59329	−	14.8840i	−0.655232	−	1.13490i
$173$	−1.53213	+	2.65372i	−0.116485	+	0.201759i	−0.918373	−	0.395717i	$-0.870496\pi$
$173$	−1.53213	+	2.65372i	−0.116485	+	0.201759i	0.801887	+	0.597476i	$0.203829\pi$
$174$	11.1004	+	11.1004i	0.841518	+	0.841518i
$175$	11.4324	−	0.628910i	0.864211	−	0.0475411i
$176$	−3.11756	+	11.6349i	−0.234995	+	0.877012i
$177$	3.22293	−	12.0281i	0.242250	−	0.904090i
$178$			12.0549i			0.903555i
$179$	1.11637	−	0.644537i	0.0834415	−	0.0481749i	−0.457699	−	0.889107i	$-0.651326\pi$
$179$	1.11637	−	0.644537i	0.0834415	−	0.0481749i	0.541140	+	0.840932i	$0.317993\pi$
$180$	3.17455	−	3.17455i	0.236617	−	0.236617i
$181$	−14.2160			−1.05667			−0.528335	−	0.849036i	$-0.677183\pi$
$181$	−14.2160			−1.05667			−0.528335	+	0.849036i	$0.677183\pi$
$182$	16.0154	+	20.5846i	1.18714	+	1.52583i
$183$	5.84594			0.432145
$184$	62.6700	−	62.6700i	4.62009	−	4.62009i
$185$	−1.62345	+	0.937299i	−0.119358	+	0.0689116i
$186$			14.2635i			1.04585i
$187$	0.0603068	−	0.225068i	0.00441007	−	0.0164586i
$188$	6.89781	−	25.7430i	0.503075	−	1.87750i
$189$	1.44673	+	2.21517i	0.105234	+	0.161130i
$190$	3.37700	+	3.37700i	0.244994	+	0.244994i
$191$	−10.1407	+	17.5643i	−0.733758	+	1.27091i	0.221508	+	0.975159i	$0.428902\pi$
$191$	−10.1407	+	17.5643i	−0.733758	+	1.27091i	−0.955266	+	0.295748i	$0.904431\pi$
$192$	−15.1560	−	26.2510i	−1.09379	−	1.89450i
$193$	−1.88513	+	7.03538i	−0.135694	+	0.506418i	0.864300	+	0.502977i	$0.167762\pi$
$193$	−1.88513	+	7.03538i	−0.135694	+	0.506418i	−0.999994	+	0.00344097i	$0.998905\pi$
$194$	−16.9200	−	29.3064i	−1.21479	−	2.10407i
$195$	2.67377	+	1.26187i	0.191472	+	0.0903644i
$196$	−35.0918	−	15.4061i	−2.50656	−	1.10043i
$197$	−4.20373	−	15.6885i	−0.299504	−	1.11776i	−0.937574	−	0.347785i	$-0.886934\pi$
$197$	−4.20373	−	15.6885i	−0.299504	−	1.11776i	0.638071	−	0.769978i	$-0.279733\pi$
$198$	−2.19181			−0.155765
$199$	1.05711			0.0749364			0.0374682	−	0.999298i	$-0.488071\pi$
$199$	1.05711			0.0749364			0.0374682	+	0.999298i	$0.488071\pi$
$200$	−10.6413	−	39.7139i	−0.752455	−	2.80820i
$201$	12.2581	−	3.28455i	0.864620	−	0.231674i
$202$	−32.2384	−	8.63826i	−2.26829	−	0.607786i
$203$	−0.834432	−	15.1685i	−0.0585657	−	1.06462i
$204$	0.795651	+	1.37811i	0.0557067	+	0.0964868i
$205$		−	7.47550i		−	0.522112i
$206$	45.1648	+	12.1019i	3.14678	+	0.843178i
$207$	8.07890	+	4.66436i	0.561523	+	0.324195i
$208$	35.0138	−	41.3385i	2.42777	−	2.86631i
$209$		−	1.70774i		−	0.118127i
$210$	−5.92263	+	0.325810i	−0.408700	+	0.0224830i
$211$	0.948161	−	1.64226i	0.0652741	−	0.113058i	−0.831541	−	0.555463i	$-0.812541\pi$
$211$	0.948161	−	1.64226i	0.0652741	−	0.113058i	0.896816	+	0.442405i	$0.145875\pi$
$212$	25.5161	+	14.7317i	1.75245	+	1.01178i
$213$	6.43570	−	1.72444i	0.440967	−	0.118157i
$214$	−12.7967	+	12.7967i	−0.874762	+	0.874762i
$215$	0.666228	+	2.48640i	0.0454364	+	0.169571i
$216$	6.71797	−	6.71797i	0.457100	−	0.457100i
$217$	9.20932	−	10.2815i	0.625170	−	0.697956i
$218$	−17.5081	−	10.1083i	−1.18580	−	0.684620i
$219$	5.66658	+	5.66658i	0.382912	+	0.382912i
$220$	1.79956	−	3.11693i	0.121326	−	0.210143i
$221$	−0.677316	+	0.799662i	−0.0455612	+	0.0537911i
$222$	−5.41284	+	3.12511i	−0.363286	+	0.209743i
$223$	−5.32451	+	1.42670i	−0.356556	+	0.0955388i	−0.432650	−	0.901562i	$-0.642422\pi$
$223$	−5.32451	+	1.42670i	−0.356556	+	0.0955388i	0.0760947	+	0.997101i	$0.475755\pi$
$224$	−11.9965	+	57.1681i	−0.801547	+	3.81971i
$225$	3.74780	−	2.16379i	0.249853	−	0.144253i
$226$	−29.4658	−	7.89535i	−1.96004	−	0.525191i
$227$	11.2940	+	11.2940i	0.749612	+	0.749612i	0.974406	−	0.224795i	$-0.0721711\pi$
$227$	11.2940	+	11.2940i	0.749612	+	0.749612i	−0.224795	+	0.974406i	$0.572171\pi$
$228$	8.24689	+	8.24689i	0.546164	+	0.546164i
$229$	11.9695	+	3.20721i	0.790966	+	0.211939i	0.631614	−	0.775283i	$-0.282393\pi$
$229$	11.9695	+	3.20721i	0.790966	+	0.211939i	0.159352	+	0.987222i	$0.449059\pi$
$230$	−18.1123	+	10.4572i	−1.19429	+	0.689524i
$231$	1.57991	+	1.41515i	0.103951	+	0.0931101i
$232$	−52.6921	+	14.1188i	−3.45941	+	0.926946i
$233$	2.95409	−	1.70554i	0.193529	−	0.111734i	−0.400105	−	0.916469i	$-0.631026\pi$
$233$	2.95409	−	1.70554i	0.193529	−	0.111734i	0.593633	+	0.804736i	$0.297693\pi$
$234$	8.91477	+	4.20728i	0.582777	+	0.275039i
$235$	−1.99582	+	3.45687i	−0.130193	+	0.225501i
$236$	48.2081	+	48.2081i	3.13808	+	3.13808i
$237$	−4.76489	−	2.75101i	−0.309513	−	0.178697i
$238$	0.431784	−	2.05763i	0.0279884	−	0.133377i
$239$	0.615965	−	0.615965i	0.0398435	−	0.0398435i	−0.686904	−	0.726748i	$-0.741031\pi$
$239$	0.615965	−	0.615965i	0.0398435	−	0.0398435i	0.726748	+	0.686904i	$0.241031\pi$
$240$	3.18885	+	11.9009i	0.205839	+	0.768203i
$241$	−5.13129	+	5.13129i	−0.330536	+	0.330536i	−0.852790	−	0.522254i	$-0.825091\pi$
$241$	−5.13129	+	5.13129i	−0.330536	+	0.330536i	0.522254	+	0.852790i	$0.325091\pi$
$242$	27.3524	−	7.32905i	1.75828	−	0.471129i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−16.0031	+	27.7182i	−1.02450	+	1.77448i
$245$	4.47955	+	3.58912i	0.286188	+	0.229301i
$246$		−	24.9245i		−	1.58913i
$247$	−3.27810	+	6.94594i	−0.208580	+	0.441960i
$248$	−42.9246	−	24.7826i	−2.72572	−	1.57369i
$249$	−4.79823	−	1.28568i	−0.304075	−	0.0814767i
$250$			20.9118i			1.32258i
$251$	7.68725	+	13.3147i	0.485215	+	0.840417i	0.999856	−	0.0169888i	$-0.00540797\pi$
$251$	7.68725	+	13.3147i	0.485215	+	0.840417i	−0.514641	+	0.857406i	$0.672075\pi$
$252$	−14.4635	+	0.795651i	−0.911115	+	0.0501213i
$253$	7.22376	+	1.93560i	0.454154	+	0.121690i
$254$	18.5598	−	4.97309i	1.16455	−	0.312040i
$255$	−0.0616859	−	0.230215i	−0.00386292	−	0.0144166i
$256$	45.2321			2.82701
$257$	22.2627			1.38871			0.694354	−	0.719633i	$-0.255690\pi$
$257$	22.2627			1.38871			0.694354	+	0.719633i	$0.255690\pi$
$258$	2.22131	+	8.29005i	0.138293	+	0.516116i
$259$	5.91946	+	1.24217i	0.367817	+	0.0771847i
$260$	−13.3025	+	9.22319i	−0.824984	+	0.571998i
$261$	−2.87091	−	4.97256i	−0.177705	−	0.307793i
$262$	1.45194	−	5.41872i	0.0897012	−	0.334770i
$263$	−6.59022	−	11.4146i	−0.406370	−	0.703854i	0.588110	−	0.808781i	$-0.299872\pi$
$263$	−6.59022	−	11.4146i	−0.406370	−	0.703854i	−0.994480	+	0.104927i	$0.966539\pi$
$264$	3.80821	−	6.59602i	0.234379	−	0.405957i
$265$	−3.12036	−	3.12036i	−0.191682	−	0.191682i
$266$	−0.846392	−	15.3859i	−0.0518956	−	0.943368i
$267$	1.14119	−	4.25897i	0.0698395	−	0.260645i
$268$	−17.9828	+	67.1126i	−1.09847	+	4.09955i
$269$			2.02949i			0.123740i	0.998084	+	0.0618702i	$0.0197065\pi$
$269$			2.02949i			0.123740i	−0.998084	+	0.0618702i	$0.980294\pi$
$270$	−1.94157	+	1.12096i	−0.118160	+	0.0682197i
$271$	19.8188	−	19.8188i	1.20391	−	1.20391i	0.230940	−	0.972968i	$-0.425820\pi$
$271$	19.8188	−	19.8188i	1.20391	−	1.20391i	0.972968	−	0.230940i	$-0.0741801\pi$
$272$	−4.36709			−0.264794
$273$	−3.70955	−	8.78858i	−0.224512	−	0.531909i
$274$	25.8162			1.55962
$275$	2.45318	−	2.45318i	0.147932	−	0.147932i
$276$	−44.2316	+	25.5371i	−2.66243	+	1.53715i
$277$			10.8734i			0.653322i	0.945142	+	0.326661i	$0.105924\pi$
$277$			10.8734i			0.653322i	−0.945142	+	0.326661i	$0.894076\pi$
$278$	−9.18081	+	34.2633i	−0.550629	+	2.05497i
$279$	1.35027	−	5.03926i	0.0808383	−	0.301693i
$280$	9.30994	−	18.3896i	0.556375	−	1.09899i
$281$	−5.00498	−	5.00498i	−0.298572	−	0.298572i	0.541882	−	0.840454i	$-0.317712\pi$
$281$	−5.00498	−	5.00498i	−0.298572	−	0.298572i	−0.840454	+	0.541882i	$0.817712\pi$
$282$	−6.65440	+	11.5258i	−0.396264	+	0.686349i
$283$	−0.461081	−	0.798615i	−0.0274084	−	0.0474727i	0.851996	−	0.523549i	$-0.175392\pi$
$283$	−0.461081	−	0.798615i	−0.0274084	−	0.0474727i	−0.879404	+	0.476076i	$0.842059\pi$
$284$	−9.44124	+	35.2352i	−0.560234	+	2.09082i
$285$	−0.873398	−	1.51277i	−0.0517357	−	0.0896088i
$286$	7.77619	+	1.40823i	0.459816	+	0.0832702i
$287$	−16.0926	+	17.9663i	−0.949919	+	1.06051i
$288$	5.71424	+	21.3259i	0.336715	+	1.25664i
$289$	−16.9155			−0.995031
$290$	12.8727			0.755913
$291$	3.20349	+	11.9556i	0.187792	+	0.700849i
$292$	−42.3799	+	11.3557i	−2.48010	+	0.664540i
$293$	14.3112	+	3.83466i	0.836067	+	0.224023i	0.651359	−	0.758770i	$-0.274199\pi$
$293$	14.3112	+	3.83466i	0.836067	+	0.224023i	0.184708	+	0.982793i	$0.440866\pi$
$294$	14.9355	+	11.9667i	0.871058	+	0.697913i
$295$	−5.10554	−	8.84306i	−0.297256	−	0.514863i
$296$		−	21.7192i		−	1.26240i
$297$	0.774358	+	0.207489i	0.0449328	+	0.0120397i
$298$	−5.58868	−	3.22663i	−0.323744	−	0.186913i
$299$	−25.6659	−	21.7391i	−1.48429	−	1.25720i
$300$			23.6933i			1.36794i
$301$	3.75133	−	7.40989i	0.216223	−	0.427099i
$302$	19.5061	−	33.7856i	1.12245	−	1.94414i
$303$	10.5720	+	6.10374i	0.607345	+	0.350651i
$304$	−30.9164	+	8.28402i	−1.77318	+	0.475121i
$305$	3.38967	−	3.38967i	0.194092	−	0.194092i
$306$	−0.205671	−	0.767574i	−0.0117574	−	0.0438793i
$307$	−2.59247	+	2.59247i	−0.147960	+	0.147960i	−0.777206	−	0.629246i	$-0.783364\pi$
$307$	−2.59247	+	2.59247i	−0.147960	+	0.147960i	0.629246	+	0.777206i	$0.283364\pi$
$308$	−11.0348	+	3.61713i	−0.628768	+	0.206105i
$309$	−14.8110	−	8.55111i	−0.842566	−	0.486456i
$310$	8.27046	+	8.27046i	0.469731	+	0.469731i
$311$	4.16328	−	7.21101i	0.236078	−	0.408899i	−0.723508	−	0.690316i	$-0.757471\pi$
$311$	4.16328	−	7.21101i	0.236078	−	0.408899i	0.959585	+	0.281418i	$0.0908047\pi$
$312$	−28.1506	+	19.5180i	−1.59371	+	1.10499i
$313$	8.01564	−	4.62783i	0.453071	−	0.261580i	−0.256056	−	0.966662i	$-0.582423\pi$
$313$	8.01564	−	4.62783i	0.453071	−	0.261580i	0.709126	+	0.705082i	$0.249090\pi$
$314$	−59.6183	+	15.9747i	−3.36445	+	0.901502i
$315$	2.12329	+	0.445562i	0.119634	+	0.0251046i
$316$	26.0875	−	15.0616i	1.46754	−	0.847284i
$317$	15.8649	+	4.25100i	0.891064	+	0.238760i	0.675175	−	0.737658i	$-0.264068\pi$
$317$	15.8649	+	4.25100i	0.891064	+	0.238760i	0.215889	+	0.976418i	$0.430735\pi$
$318$	−10.4038	−	10.4038i	−0.583416	−	0.583416i
$319$	−3.25486	−	3.25486i	−0.182237	−	0.182237i
$320$	−24.0091	−	6.43323i	−1.34215	−	0.359628i
$321$	5.73242	−	3.30962i	0.319953	−	0.184725i
$322$	66.0416	+	13.8585i	3.68035	+	0.772304i
$323$	0.598055	−	0.160248i	0.0332767	−	0.00891645i
$324$	−4.74145	+	2.73748i	−0.263414	+	0.152082i
$325$	−14.6868	+	5.26886i	−0.814680	+	0.292264i
$326$	19.3467	−	33.5094i	1.07151	−	1.85591i
$327$	5.22864	+	5.22864i	0.289144	+	0.289144i
$328$	75.0078	+	43.3058i	4.14161	+	2.39116i
$329$	12.2383	−	4.01162i	0.674721	−	0.221168i
$330$	−1.27088	+	1.27088i	−0.0699597	+	0.0699597i
$331$	5.60236	+	20.9083i	0.307934	+	1.14922i	0.930390	+	0.366570i	$0.119468\pi$
$331$	5.60236	+	20.9083i	0.307934	+	1.14922i	−0.622457	+	0.782654i	$0.713865\pi$
$332$	19.2310	−	19.2310i	1.05544	−	1.05544i
$333$	2.20818	−	0.591680i	0.121007	−	0.0324239i
$334$	−36.5205	−	21.0851i	−1.99832	−	1.15373i
$335$	5.20316	−	9.01214i	0.284279	−	0.492386i
$336$	17.9555	−	35.4669i	0.979550	−	1.93488i
$337$			29.6410i			1.61465i	0.590110	+	0.807323i	$0.299084\pi$
$337$			29.6410i			1.61465i	−0.590110	+	0.807323i	$0.700916\pi$
$338$	−28.9251	−	20.6545i	−1.57332	−	1.12346i
$339$	9.66277	+	5.57880i	0.524810	+	0.302999i
$340$	1.26042	+	0.337727i	0.0683556	+	0.0183158i
$341$		−	4.18236i		−	0.226487i
$342$	−2.91205	−	5.04382i	−0.157466	−	0.272739i
$343$	−3.03956	−	18.2691i	−0.164121	−	0.986440i
$344$	−28.8075	−	7.71896i	−1.55320	−	0.416178i
$345$	7.38895	−	1.97986i	0.397808	−	0.106592i
$346$	2.16833	+	8.09231i	0.116570	+	0.435045i
$347$	21.3480			1.14602			0.573011	−	0.819548i	$-0.305775\pi$
$347$	21.3480			1.14602			0.573011	+	0.819548i	$0.305775\pi$
$348$	31.4361			1.68515
$349$	−0.717765	−	2.67873i	−0.0384211	−	0.143389i	0.944051	−	0.329800i	$-0.106981\pi$
$349$	−0.717765	−	2.67873i	−0.0384211	−	0.143389i	−0.982472	+	0.186410i	$0.940315\pi$
$350$	20.8860	−	23.3177i	1.11640	−	1.24638i
$351$	−2.75128	−	2.33034i	−0.146852	−	0.124384i
$352$	8.84974	+	15.3282i	0.471693	+	0.816996i
$353$	−2.38143	+	8.88762i	−0.126751	+	0.473040i	−0.999896	−	0.0144198i	$-0.995410\pi$
$353$	−2.38143	+	8.88762i	−0.126751	+	0.473040i	0.873145	+	0.487460i	$0.162077\pi$
$354$	−17.0227	−	29.4842i	−0.904747	−	1.56707i
$355$	2.73174	−	4.73152i	0.144986	−	0.251123i
$356$	17.0697	+	17.0697i	0.904692	+	0.904692i
$357$	−0.347335	+	0.686080i	−0.0183829	+	0.0363112i
$358$	0.912175	−	3.40428i	0.0482100	−	0.179922i
$359$	5.48985	−	20.4884i	0.289743	−	1.08134i	−0.655560	−	0.755143i	$-0.727567\pi$
$359$	5.48985	−	20.4884i	0.289743	−	1.08134i	0.945303	−	0.326193i	$-0.105766\pi$
$360$		−	7.79059i		−	0.410600i
$361$	−12.5246	+	7.23108i	−0.659189	+	0.380583i
$362$	−27.4832	+	27.4832i	−1.44449	+	1.44449i
$363$	−10.3573			−0.543618
$364$	51.8254	+	6.46989i	2.71639	+	0.339115i
$365$	6.57133			0.343959
$366$	11.3017	−	11.3017i	0.590749	−	0.590749i
$367$	4.28504	−	2.47397i	0.223677	−	0.129140i	−0.383975	−	0.923344i	$-0.625445\pi$
$367$	4.28504	−	2.47397i	0.223677	−	0.129140i	0.607652	+	0.794204i	$0.292112\pi$
$368$		−	140.166i		−	7.30665i
$369$	−2.35949	+	8.80575i	−0.122830	+	0.458409i
$370$	−1.32650	+	4.95058i	−0.0689616	+	0.257368i
$371$	0.782069	+	14.2166i	0.0406030	+	0.738089i
$372$	20.1971	+	20.1971i	1.04717	+	1.04717i
$373$	−7.89279	+	13.6707i	−0.408673	+	0.707843i	−0.994741	−	0.102419i	$-0.967342\pi$
$373$	−7.89279	+	13.6707i	−0.408673	+	0.707843i	0.586068	+	0.810262i	$0.300675\pi$
$374$	−0.318526	−	0.551703i	−0.0164706	−	0.0285279i
$375$	1.97963	−	7.38806i	0.102227	−	0.381518i
$376$	−23.1237	−	40.0515i	−1.19252	−	2.06550i
$377$	6.99068	+	19.4864i	0.360038	+	1.00360i
$378$	7.07939	+	1.48557i	0.364124	+	0.0764097i
$379$	4.90908	+	18.3209i	0.252163	+	0.941084i	0.969647	+	0.244509i	$0.0786268\pi$
$379$	4.90908	+	18.3209i	0.252163	+	0.941084i	−0.717484	+	0.696575i	$0.754707\pi$
$380$	9.56363			0.490604
$381$	−7.02791			−0.360051
$382$	14.3516	+	53.5609i	0.734291	+	2.74041i
$383$	32.9336	−	8.82454i	1.68283	−	0.450913i	0.714306	−	0.699834i	$-0.246743\pi$
$383$	32.9336	−	8.82454i	1.68283	−	0.450913i	0.968524	+	0.248921i	$0.0800759\pi$
$384$	−37.3986	−	10.0209i	−1.90849	−	0.511379i
$385$	1.73663	−	0.0955340i	0.0885071	−	0.00486886i
$386$	9.95676	+	17.2456i	0.506786	+	0.877779i
$387$		−	3.13913i		−	0.159571i
$388$	−65.4562	−	17.5389i	−3.32304	−	0.890405i
$389$	13.4365	+	7.75759i	0.681260	+	0.393325i	0.800330	−	0.599560i	$-0.204658\pi$
$389$	13.4365	+	7.75759i	0.681260	+	0.393325i	−0.119070	+	0.992886i	$0.537991\pi$
$390$	7.60859	−	2.72956i	0.385276	−	0.138216i
$391$			2.71140i			0.137121i
$392$	−61.9627	+	24.1551i	−3.12959	+	1.22002i
$393$	−1.02593	+	1.77697i	−0.0517514	+	0.0896361i
$394$	−38.4569	−	22.2031i	−1.93743	−	1.11858i
$395$	−4.35796	+	1.16771i	−0.219273	+	0.0587540i
$396$	−3.10358	+	3.10358i	−0.155961	+	0.155961i
$397$	3.43406	+	12.8161i	0.172350	+	0.643220i	0.996988	+	0.0775586i	$0.0247125\pi$
$397$	3.43406	+	12.8161i	0.172350	+	0.643220i	−0.824637	+	0.565662i	$0.808621\pi$
$398$	2.04366	−	2.04366i	0.102439	−	0.102439i
$399$	−1.15748	+	5.51590i	−0.0579467	+	0.276140i
$400$	−56.3115	−	32.5114i	−2.81557	−	1.62557i
$401$	−11.7436	−	11.7436i	−0.586446	−	0.586446i	0.350221	−	0.936667i	$-0.386106\pi$
$401$	−11.7436	−	11.7436i	−0.586446	−	0.586446i	−0.936667	+	0.350221i	$0.886106\pi$
$402$	17.3482	−	30.0479i	0.865249	−	1.49865i
$403$	−8.02824	+	17.0110i	−0.399915	+	0.847377i
$404$	−57.8811	+	33.4177i	−2.87969	+	1.66259i
$405$	0.792066	−	0.212233i	0.0393581	−	0.0105460i
$406$	−30.9377	−	27.7114i	−1.53541	−	1.37529i
$407$	1.58715	−	0.916344i	0.0786723	−	0.0454215i
$408$	2.66728	+	0.714696i	0.132050	+	0.0353827i
$409$	−25.4290	−	25.4290i	−1.25738	−	1.25738i	−0.952338	−	0.305046i	$-0.901328\pi$
$409$	−25.4290	−	25.4290i	−1.25738	−	1.25738i	−0.305046	−	0.952338i	$-0.598672\pi$
$410$	−14.4521	−	14.4521i	−0.713736	−	0.713736i
$411$	−9.12079	−	2.44391i	−0.449895	−	0.120549i
$412$	81.0893	−	46.8169i	3.99498	−	2.30650i
$413$	−6.76620	+	32.2438i	−0.332943	+	1.58661i
$414$	24.6360	−	6.60119i	1.21079	−	0.324431i
$415$	−3.52765	+	2.03669i	−0.173165	+	0.0999771i
$416$	−6.57147	−	79.3322i	−0.322193	−	3.88958i
$417$	6.48710	−	11.2360i	0.317675	−	0.550229i
$418$	−3.30151	−	3.30151i	−0.161482	−	0.161482i
$419$	−17.3534	−	10.0190i	−0.847767	−	0.489459i	0.0121297	−	0.999926i	$-0.496139\pi$
$419$	−17.3534	−	10.0190i	−0.847767	−	0.489459i	−0.859897	+	0.510468i	$0.829472\pi$
$420$	−7.92506	+	8.84775i	−0.386703	+	0.431726i
$421$	9.14971	−	9.14971i	0.445929	−	0.445929i	−0.448069	−	0.893999i	$-0.647888\pi$
$421$	9.14971	−	9.14971i	0.445929	−	0.445929i	0.893999	+	0.448069i	$0.147888\pi$
$422$	−1.34188	−	5.00795i	−0.0653215	−	0.243783i
$423$	3.44207	−	3.44207i	0.167359	−	0.167359i
$424$	49.3855	−	13.2328i	2.39837	−	0.642642i
$425$	1.08930	+	0.628910i	0.0528390	+	0.0305066i
$426$	9.10807	−	15.7756i	0.441288	−	0.764333i
$427$	−15.4436	+	0.849565i	−0.747366	+	0.0411134i
$428$			36.2400i			1.75173i
$429$	−2.61399	−	1.23366i	−0.126205	−	0.0595616i
$430$	6.09483	+	3.51885i	0.293919	+	0.169694i
$431$	−11.8750	−	3.18191i	−0.572001	−	0.153267i	−0.0387867	−	0.999248i	$-0.512349\pi$
$431$	−11.8750	−	3.18191i	−0.572001	−	0.153267i	−0.533214	+	0.845980i	$0.679016\pi$
$432$		−	15.0252i		−	0.722900i
$433$	−11.2493	−	19.4844i	−0.540609	−	0.936362i	−0.998869	−	0.0475437i	$-0.984861\pi$
$433$	−11.2493	−	19.4844i	−0.540609	−	0.936362i	0.458261	−	0.888818i	$-0.348473\pi$
$434$	−2.07286	−	37.6808i	−0.0995003	−	1.80874i
$435$	−4.54789	−	1.21860i	−0.218055	−	0.0584276i
$436$	−39.1046	+	10.4780i	−1.87277	+	0.501807i
$437$	5.14331	+	19.1951i	0.246038	+	0.918226i
$438$	21.9099			1.04689
$439$	−16.8443			−0.803935			−0.401967	−	0.915654i	$-0.631673\pi$
$439$	−16.8443			−0.803935			−0.401967	+	0.915654i	$0.631673\pi$
$440$	−1.61646	−	6.03271i	−0.0770617	−	0.287598i
$441$	−4.14384	−	5.64168i	−0.197326	−	0.268652i
$442$	0.236525	+	2.85538i	0.0112503	+	0.135816i
$443$	−6.31905	−	10.9449i	−0.300227	−	0.520008i	0.675960	−	0.736938i	$-0.263729\pi$
$443$	−6.31905	−	10.9449i	−0.300227	−	0.520008i	−0.976187	+	0.216930i	$0.930396\pi$
$444$	−3.23942	+	12.0897i	−0.153736	+	0.573751i
$445$	−1.80779	−	3.13118i	−0.0856975	−	0.148432i
$446$	−7.53547	+	13.0518i	−0.356815	+	0.618021i
$447$	1.66901	+	1.66901i	0.0789416	+	0.0789416i
$448$	43.8535	+	67.1462i	2.07188	+	3.17236i
$449$	−2.81967	+	10.5232i	−0.133069	+	0.496618i	−0.999998	−	0.00181175i	$-0.999423\pi$
$449$	−2.81967	+	10.5232i	−0.133069	+	0.496618i	0.866930	+	0.498430i	$0.166090\pi$
$450$	3.06229	−	11.4286i	0.144358	−	0.538751i
$451$			7.30838i			0.344138i
$452$	−52.9032	+	30.5437i	−2.48836	+	1.43665i
$453$	−10.0898	+	10.0898i	−0.474059	+	0.474059i
$454$	43.6685			2.04947
$455$	−7.24682	−	2.94499i	−0.339736	−	0.138063i
$456$	20.2385			0.947754
$457$	−0.189763	+	0.189763i	−0.00887676	+	0.00887676i	−0.711531	−	0.702654i	$-0.751998\pi$
$457$	−0.189763	+	0.189763i	−0.00887676	+	0.00887676i	0.702654	+	0.711531i	$0.251998\pi$
$458$	29.3404	−	16.9397i	1.37099	−	0.791541i
$459$			0.290651i			0.0135664i
$460$	−10.8397	+	40.4542i	−0.505402	+	1.88619i
$461$	8.32642	−	31.0746i	0.387800	−	1.44729i	−0.445906	−	0.895080i	$-0.647118\pi$
$461$	8.32642	−	31.0746i	0.387800	−	1.44729i	0.833706	−	0.552209i	$-0.186215\pi$
$462$	5.79022	−	0.318526i	0.269385	−	0.0148192i
$463$	23.1731	+	23.1731i	1.07695	+	1.07695i	0.996782	+	0.0801653i	$0.0255448\pi$
$463$	23.1731	+	23.1731i	1.07695	+	1.07695i	0.0801653	+	0.996782i	$0.474455\pi$
$464$	−43.1359	+	74.7136i	−2.00254	+	3.46849i
$465$	−2.13900	−	3.70485i	−0.0991937	−	0.171809i
$466$	2.41376	−	9.00826i	0.111815	−	0.417300i
$467$	3.81254	+	6.60352i	0.176423	+	0.305574i	0.940653	−	0.339370i	$-0.110214\pi$
$467$	3.81254	+	6.60352i	0.176423	+	0.305574i	−0.764230	+	0.644944i	$0.776881\pi$
$468$	18.5807	−	6.66578i	0.858895	−	0.308126i
$469$	−31.9056	+	10.4584i	−1.47326	+	0.482924i
$470$	2.82457	+	10.5414i	0.130288	+	0.486241i
$471$	22.5752			1.04021
$472$	118.306			5.44549
$473$	−0.651334	−	2.43081i	−0.0299484	−	0.111769i
$474$	−14.5301	+	3.89334i	−0.667392	+	0.178827i
$475$	8.90461	+	2.38598i	0.408571	+	0.109476i
$476$	−2.30219	−	3.52500i	−0.105521	−	0.161568i
$477$	2.69075	+	4.66051i	0.123201	+	0.213390i
$478$		−	2.38164i		−	0.108933i
$479$	−5.55037	−	1.48722i	−0.253603	−	0.0679527i	0.129778	−	0.991543i	$-0.458574\pi$
$479$	−5.55037	−	1.48722i	−0.253603	−	0.0679527i	−0.383381	+	0.923590i	$0.625240\pi$
$480$	15.6787	+	9.05212i	0.715633	+	0.413171i
$481$	−8.21443	+	0.680441i	−0.374546	+	0.0310254i
$482$			19.8402i			0.903697i
$483$	−22.0203	−	11.1480i	−1.00196	−	0.507253i
$484$	28.3529	−	49.1087i	1.28877	−	2.23221i
$485$	8.78972	+	5.07475i	0.399121	+	0.230432i
$486$	2.64088	−	0.707621i	0.119793	−	0.0320983i
$487$	2.73539	−	2.73539i	0.123952	−	0.123952i	−0.642409	−	0.766362i	$-0.722065\pi$
$487$	2.73539	−	2.73539i	0.123952	−	0.123952i	0.766362	+	0.642409i	$0.222065\pi$
$488$	14.3749	+	53.6478i	0.650720	+	2.42852i
$489$	−10.0073	+	10.0073i	−0.452546	+	0.452546i
$490$	15.5988	−	1.72142i	0.704682	−	0.0777658i
$491$	−33.9925	−	19.6256i	−1.53406	−	0.885691i	−0.999169	−	0.0407714i	$-0.987018\pi$
$491$	−33.9925	−	19.6256i	−1.53406	−	0.885691i	−0.534893	−	0.844920i	$-0.679648\pi$
$492$	−35.2930	−	35.2930i	−1.59113	−	1.59113i
$493$	0.834432	−	1.44528i	0.0375809	−	0.0650921i
$494$	7.09087	+	19.7657i	0.319033	+	0.889300i
$495$	0.569307	−	0.328689i	0.0255884	−	0.0147735i
$496$	−75.7159	+	20.2880i	−3.39974	+	0.910959i
$497$	−16.7510	+	5.49083i	−0.751383	+	0.246297i
$498$	−11.7617	+	6.79065i	−0.527056	+	0.304296i
$499$	−11.1203	−	2.97967i	−0.497811	−	0.133388i	0.00117270	−	0.999999i	$-0.499627\pi$
$499$	−11.1203	−	2.97967i	−0.497811	−	0.133388i	−0.498984	+	0.866611i	$0.666293\pi$
$500$	29.6109	+	29.6109i	1.32424	+	1.32424i
$501$	10.9065	+	10.9065i	0.487269	+	0.487269i
$502$	40.6022	+	10.8793i	1.81216	+	0.485568i
$503$	12.9603	−	7.48266i	0.577873	−	0.333635i	−0.182414	−	0.983222i	$-0.558391\pi$
$503$	12.9603	−	7.48266i	0.577873	−	0.333635i	0.760288	+	0.649586i	$0.225058\pi$
$504$	−16.7710	+	18.7235i	−0.747038	+	0.834013i
$505$	9.66913	−	2.59083i	0.430271	−	0.115291i
$506$	17.7074	−	10.2234i	0.787190	−	0.454484i
$507$	8.26386	+	10.0354i	0.367011	+	0.445686i
$508$	19.2387	−	33.3225i	0.853581	−	1.47845i
$509$	−19.3349	−	19.3349i	−0.857004	−	0.857004i	0.133980	−	0.990984i	$-0.457224\pi$
$509$	−19.3349	−	19.3349i	−0.857004	−	0.857004i	−0.990984	+	0.133980i	$0.957224\pi$
$510$	−0.564319	−	0.325810i	−0.0249885	−	0.0144271i
$511$	−15.7932	−	14.1462i	−0.698651	−	0.625792i
$512$	32.6898	−	32.6898i	1.44470	−	1.44470i
$513$	0.551342	+	2.05764i	0.0243423	+	0.0908469i
$514$	43.0395	−	43.0395i	1.89839	−	1.89839i
$515$	−13.5461	+	3.62966i	−0.596912	+	0.159942i
$516$	14.8840	+	8.59329i	0.655232	+	0.378299i
$517$	1.95120	−	3.37959i	0.0858139	−	0.148634i
$518$	13.8453	−	9.04240i	0.608326	−	0.397300i
$519$		−	3.06425i		−	0.134506i
$520$	−5.00543	+	27.6398i	−0.219502	+	1.21209i
$521$	6.87190	+	3.96750i	0.301064	+	0.173819i	0.642921	−	0.765933i	$-0.277723\pi$
$521$	6.87190	+	3.96750i	0.301064	+	0.173819i	−0.341857	+	0.939752i	$0.611056\pi$
$522$	−15.1634	−	4.06302i	−0.663685	−	0.177834i
$523$			3.44793i			0.150767i	0.997155	+	0.0753837i	$0.0240182\pi$
$523$			3.44793i			0.150767i	−0.997155	+	0.0753837i	$0.975982\pi$
$524$	−5.61693	−	9.72881i	−0.245377	−	0.425005i
$525$	−9.58633	+	6.26087i	−0.418382	+	0.273247i
$526$	−34.8079	−	9.32675i	−1.51770	−	0.406665i
$527$	1.46467	−	0.392456i	0.0638019	−	0.0170957i
$528$	−3.11756	−	11.6349i	−0.135674	−	0.506343i
$529$	−64.0249			−2.78369
$530$	−12.0649			−0.524067
$531$	3.22293	+	12.0281i	0.139863	+	0.521977i
$532$	−22.9848	−	20.5878i	−0.996516	−	0.892594i
$533$	14.0288	−	29.7255i	0.607654	−	1.28755i
$534$	−6.02747	−	10.4399i	−0.260834	−	0.451778i
$535$	1.40482	−	5.24287i	0.0607357	−	0.226669i
$536$	60.2841	+	104.415i	2.60388	+	4.51005i
$537$	−0.644537	+	1.11637i	−0.0278138	+	0.0481749i
$538$	3.92353	+	3.92353i	0.169155	+	0.169155i
$539$	−4.37940	−	3.50888i	−0.188634	−	0.151138i
$540$	−1.16197	+	4.33652i	−0.0500031	+	0.186614i
$541$	0.692633	−	2.58494i	0.0297786	−	0.111135i	−0.949437	−	0.313958i	$-0.898345\pi$
$541$	0.692633	−	2.58494i	0.0297786	−	0.111135i	0.979215	+	0.202823i	$0.0650115\pi$
$542$		−	76.6297i		−	3.29153i
$543$	12.3114	−	7.10802i	0.528335	−	0.305034i
$544$	−4.53753	+	4.53753i	−0.194545	+	0.194545i
$545$	6.06346			0.259730
$546$	−24.1621	−	9.81907i	−1.03404	−	0.420217i
$547$	−34.9374			−1.49382			−0.746908	−	0.664927i	$-0.768463\pi$
$547$	−34.9374			−1.49382			−0.746908	+	0.664927i	$0.768463\pi$
$548$	36.5556	−	36.5556i	1.56158	−	1.56158i
$549$	−5.06274	+	2.92297i	−0.216072	+	0.124749i
$550$		−	9.48524i		−	0.404452i
$551$	3.16570	−	11.8146i	0.134863	−	0.503317i
$552$	−22.9388	+	85.6088i	−0.976341	+	3.64375i
$553$	12.9875	+	6.57504i	0.552283	+	0.279599i
$554$	21.0211	+	21.0211i	0.893103	+	0.893103i
$555$	0.937299	−	1.62345i	0.0397861	−	0.0689116i
$556$	35.5166	+	61.5165i	1.50624	+	2.60888i
$557$	−0.437852	+	1.63409i	−0.0185524	+	0.0692385i	−0.974581	−	0.224034i	$-0.928077\pi$
$557$	−0.437852	+	1.63409i	−0.0185524	+	0.0692385i	0.956029	+	0.293272i	$0.0947442\pi$
$558$	−7.13177	−	12.3526i	−0.301912	−	0.522927i
$559$	−2.01688	+	11.1371i	−0.0853049	+	0.471051i
$560$	−10.1537	−	30.9760i	−0.429071	−	1.30897i
$561$	0.0603068	+	0.225068i	0.00254616	+	0.00950239i
$562$	−19.3518			−0.816307
$563$	−18.3449			−0.773147			−0.386574	−	0.922259i	$-0.626342\pi$
$563$	−18.3449			−0.773147			−0.386574	+	0.922259i	$0.626342\pi$
$564$	6.89781	+	25.7430i	0.290450	+	1.08398i
$565$	8.83756	−	2.36802i	0.371799	−	0.0996232i
$566$	−2.43531	−	0.652540i	−0.102364	−	0.0274283i
$567$	−2.36049	−	1.19502i	−0.0991313	−	0.0501862i
$568$	31.6501	+	54.8196i	1.32801	+	2.30018i
$569$			14.3470i			0.601457i	0.953710	+	0.300728i	$0.0972298\pi$
$569$			14.3470i			0.601457i	−0.953710	+	0.300728i	$0.902770\pi$
$570$	−4.61307	−	1.23607i	−0.193220	−	0.0517732i
$571$	5.06747	+	2.92571i	0.212067	+	0.122437i	0.602272	−	0.798291i	$-0.294262\pi$
$571$	5.06747	+	2.92571i	0.212067	+	0.122437i	−0.390205	+	0.920728i	$0.627596\pi$
$572$	13.0051	−	9.01699i	0.543769	−	0.377019i
$573$		−	20.2815i		−	0.847271i
$574$	3.62217	+	65.8446i	0.151187	+	2.74830i
$575$	−20.1854	+	34.9622i	−0.841790	+	1.45802i
$576$	26.2510	+	15.1560i	1.09379	+	0.631501i
$577$	9.98937	−	2.67664i	0.415863	−	0.111430i	−0.0448197	−	0.998995i	$-0.514271\pi$
$577$	9.98937	−	2.67664i	0.415863	−	0.111430i	0.460683	+	0.887565i	$0.347605\pi$
$578$	−32.7020	+	32.7020i	−1.36022	+	1.36022i
$579$	−1.88513	−	7.03538i	−0.0783431	−	0.292381i
$580$	18.2277	−	18.2277i	0.756864	−	0.756864i
$581$	12.8626	+	2.69915i	0.533630	+	0.111980i
$582$	29.3064	+	16.9200i	1.21479	+	0.701358i
$583$	3.05060	+	3.05060i	0.126343	+	0.126343i
$584$	−38.0679	+	65.9355i	−1.57526	+	2.72843i
$585$	−2.94649	+	0.244072i	−0.121822	+	0.0100911i
$586$	35.0805	−	20.2537i	1.44916	−	0.836674i
$587$	28.5050	−	7.63789i	1.17653	−	0.315250i	0.382979	−	0.923757i	$-0.374898\pi$
$587$	28.5050	−	7.63789i	1.17653	−	0.315250i	0.793548	+	0.608507i	$0.208231\pi$
$588$	38.0934	−	4.20383i	1.57095	−	0.173363i
$589$	9.62451	−	5.55671i	0.396571	−	0.228960i
$590$	−26.9662	−	7.22558i	−1.11018	−	0.297472i
$591$	11.4848	+	11.4848i	0.472422	+	0.472422i
$592$	−24.2882	−	24.2882i	−0.998240	−	0.998240i
$593$	−26.2560	−	7.03528i	−1.07821	−	0.288904i	−0.324345	−	0.945939i	$-0.605144\pi$
$593$	−26.2560	−	7.03528i	−1.07821	−	0.288904i	−0.753861	+	0.657034i	$0.771811\pi$
$594$	1.89816	−	1.09590i	0.0778825	−	0.0449655i
$595$	0.196415	+	0.599207i	0.00805224	+	0.0245651i
$596$	−12.4824	+	3.34465i	−0.511300	+	0.137002i
$597$	−0.915483	+	0.528554i	−0.0374682	+	0.0216323i
$598$	−91.6458	+	7.59147i	−3.74768	+	0.310438i
$599$	14.5684	−	25.2331i	0.595247	−	1.03100i	−0.398265	−	0.917270i	$-0.630388\pi$
$599$	14.5684	−	25.2331i	0.595247	−	1.03100i	0.993512	−	0.113727i	$-0.0362790\pi$
$600$	29.0726	+	29.0726i	1.18688	+	1.18688i
$601$	−22.2556	−	12.8493i	−0.907826	−	0.524133i	−0.0280947	−	0.999605i	$-0.508944\pi$
$601$	−22.2556	−	12.8493i	−0.907826	−	0.524133i	−0.879731	+	0.475472i	$0.842277\pi$
$602$	−7.07292	−	21.5775i	−0.288271	−	0.879433i
$603$	−8.97356	+	8.97356i	−0.365432	+	0.365432i
$604$	−20.2196	−	75.4607i	−0.822725	−	3.07045i
$605$	−6.00551	+	6.00551i	−0.244159	+	0.244159i
$606$	32.2384	−	8.63826i	1.30960	−	0.350905i
$607$	−18.0619	−	10.4281i	−0.733111	−	0.423262i	0.0864483	−	0.996256i	$-0.472448\pi$
$607$	−18.0619	−	10.4281i	−0.733111	−	0.423262i	−0.819559	+	0.572995i	$0.805782\pi$
$608$	−23.5157	+	40.7303i	−0.953687	+	1.65183i
$609$	8.30688	+	12.7191i	0.336612	+	0.515403i
$610$		−	13.1062i		−	0.530654i
$611$	−14.4234	+	10.0004i	−0.583510	+	0.404573i
$612$	−1.37811	−	0.795651i	−0.0557067	−	0.0321623i
$613$	2.72979	+	0.731444i	0.110255	+	0.0295428i	0.313525	−	0.949580i	$-0.398490\pi$
$613$	2.72979	+	0.731444i	0.110255	+	0.0295428i	−0.203270	+	0.979123i	$0.565157\pi$
$614$			10.0238i			0.404528i
$615$	3.73775	+	6.47397i	0.150721	+	0.261056i
$616$	−9.10180	+	17.9785i	−0.366722	+	0.724375i
$617$	28.1706	+	7.54830i	1.13411	+	0.303883i	0.776579	−	0.630019i	$-0.216953\pi$
$617$	28.1706	+	7.54830i	1.13411	+	0.303883i	0.357528	+	0.933902i	$0.383620\pi$
$618$	−45.1648	+	12.1019i	−1.81680	+	0.486809i
$619$	−11.9376	−	44.5517i	−0.479813	−	1.79069i	−0.602362	−	0.798223i	$-0.705774\pi$
$619$	−11.9376	−	44.5517i	−0.479813	−	1.79069i	0.122549	−	0.992462i	$-0.460893\pi$
$620$	23.4218			0.940643
$621$	−9.32871			−0.374348
$622$	−5.89204	−	21.9894i	−0.236249	−	0.881694i
$623$	−2.39580	+	11.4170i	−0.0959857	+	0.457412i
$624$	−9.65363	+	53.3071i	−0.386455	+	2.13399i
$625$	7.68298	+	13.3073i	0.307319	+	0.532293i
$626$	6.54950	−	24.4430i	0.261770	−	0.976941i
$627$	0.853872	+	1.47895i	0.0341004	+	0.0590636i
$628$	−61.7990	+	107.039i	−2.46605	+	4.27132i
$629$	0.469838	+	0.469838i	0.0187337	+	0.0187337i
$630$	4.96624	−	3.24347i	0.197860	−	0.129223i
$631$	−3.87044	+	14.4447i	−0.154080	+	0.575034i	0.845102	+	0.534604i	$0.179539\pi$
$631$	−3.87044	+	14.4447i	−0.154080	+	0.575034i	−0.999182	+	0.0404298i	$0.987127\pi$
$632$	13.5292	−	50.4916i	0.538162	−	2.00845i
$633$			1.89632i			0.0753720i
$634$	38.8892	−	22.4527i	1.54449	−	0.891711i
$635$	−4.07501	+	4.07501i	−0.161712	+	0.161712i
$636$	−29.4634			−1.16830
$637$	11.0769	+	22.6782i	0.438884	+	0.898544i
$638$	−12.5849			−0.498243
$639$	−4.71126	+	4.71126i	−0.186375	+	0.186375i
$640$	−27.4954	+	15.8745i	−1.08685	+	0.627494i
$641$		−	16.8755i		−	0.666541i	−0.942831	−	0.333270i	$-0.891848\pi$
$641$		−	16.8755i		−	0.666541i	0.942831	−	0.333270i	$-0.108152\pi$
$642$	4.68390	−	17.4806i	0.184859	−	0.689903i
$643$	−4.07102	+	15.1933i	−0.160545	+	0.599164i	0.838021	+	0.545638i	$0.183713\pi$
$643$	−4.07102	+	15.1933i	−0.160545	+	0.599164i	−0.998566	+	0.0535258i	$0.982954\pi$
$644$	113.138	−	73.8909i	4.45826	−	2.91171i
$645$	−1.82017	−	1.82017i	−0.0716691	−	0.0716691i
$646$	0.846392	−	1.46599i	0.0333008	−	0.0576787i
$647$	4.90222	+	8.49089i	0.192726	+	0.333811i	0.946153	−	0.323721i	$-0.104934\pi$
$647$	4.90222	+	8.49089i	0.192726	+	0.333811i	−0.753427	+	0.657532i	$0.771600\pi$
$648$	−2.45895	+	9.17692i	−0.0965966	+	0.360503i
$649$	4.99140	+	8.64536i	0.195930	+	0.339360i
$650$	−18.2074	+	38.5795i	−0.714152	+	1.51321i
$651$	−2.83474	+	13.5087i	−0.111102	+	0.529449i
$652$	−20.0543	−	74.8438i	−0.785389	−	2.93111i
$653$	−3.62937			−0.142028			−0.0710140	−	0.997475i	$-0.522624\pi$
$653$	−3.62937			−0.142028			−0.0710140	+	0.997475i	$0.522624\pi$
$654$	20.2166			0.790531
$655$	0.435474	+	1.62521i	0.0170154	+	0.0635023i
$656$	132.308	−	35.4519i	5.16577	−	1.38416i
$657$	−7.74069	−	2.07411i	−0.301993	−	0.0809188i
$658$	15.9043	−	31.4153i	0.620015	−	1.22470i
$659$	5.04765	+	8.74278i	0.196628	+	0.340570i	0.947433	−	0.319954i	$-0.103667\pi$
$659$	5.04765	+	8.74278i	0.196628	+	0.340570i	−0.750805	+	0.660524i	$0.770334\pi$
$660$			3.59912i			0.140095i
$661$	29.7036	+	7.95906i	1.15534	+	0.309572i	0.785102	−	0.619366i	$-0.212610\pi$
$661$	29.7036	+	7.95906i	1.15534	+	0.309572i	0.370235	+	0.928938i	$0.379277\pi$
$662$	51.2519	+	29.5903i	1.99196	+	1.15006i
$663$	0.186742	−	1.03119i	0.00725247	−	0.0400479i
$664$		−	47.1944i		−	1.83150i
$665$	2.52715	+	3.86944i	0.0979987	+	0.150051i
$666$	3.12511	−	5.41284i	0.121095	−	0.209743i
$667$	46.3875	+	26.7819i	1.79613	+	1.03700i
$668$	−81.5693	+	21.8564i	−3.15601	+	0.845650i
$669$	3.89781	−	3.89781i	0.150698	−	0.150698i
$670$	−7.36373	−	27.4818i	−0.284486	−	1.06171i
$671$	−3.31389	+	3.31389i	−0.127931	+	0.127931i
$672$	−18.1948	−	55.5073i	−0.701881	−	2.14124i
$673$	−6.14654	−	3.54871i	−0.236932	−	0.136793i	0.376834	−	0.926281i	$-0.377013\pi$
$673$	−6.14654	−	3.54871i	−0.236932	−	0.136793i	−0.613766	+	0.789488i	$0.710346\pi$
$674$	57.3036	+	57.3036i	2.20725	+	2.20725i
$675$	−2.16379	+	3.74780i	−0.0832845	+	0.144253i
$676$	−70.2043	+	11.7111i	−2.70017	+	0.450426i
$677$	11.0871	−	6.40112i	0.426111	−	0.246015i	−0.271578	−	0.962417i	$-0.587545\pi$
$677$	11.0871	−	6.40112i	0.426111	−	0.246015i	0.697688	+	0.716401i	$0.254212\pi$
$678$	29.4658	−	7.89535i	1.13163	−	0.303219i
$679$	−10.2003	−	31.1182i	−0.391451	−	1.19421i
$680$	1.96098	−	1.13217i	0.0752002	−	0.0434168i
$681$	−15.4279	−	4.13390i	−0.591200	−	0.158412i
$682$	−8.08556	−	8.08556i	−0.309612	−	0.309612i
$683$	−15.6324	−	15.6324i	−0.598157	−	0.598157i	0.341665	−	0.939822i	$-0.389009\pi$
$683$	−15.6324	−	15.6324i	−0.598157	−	0.598157i	−0.939822	+	0.341665i	$0.889009\pi$
$684$	−11.2655	−	3.01857i	−0.430746	−	0.115418i
$685$	−6.70559	+	3.87147i	−0.256207	+	0.147921i
$686$	−41.1951	−	29.4426i	−1.57284	−	1.12413i
$687$	−11.9695	+	3.20721i	−0.456664	+	0.122363i
$688$	−40.8470	+	23.5830i	−1.55728	+	0.899094i
$689$	−6.55199	−	18.2636i	−0.249611	−	0.695786i
$690$	10.4572	−	18.1123i	0.398097	−	0.689524i
$691$	8.84754	+	8.84754i	0.336576	+	0.336576i	0.855077	−	0.518501i	$-0.173510\pi$
$691$	8.84754	+	8.84754i	0.336576	+	0.336576i	−0.518501	+	0.855077i	$0.673510\pi$
$692$	14.5290	+	8.38832i	0.552310	+	0.318876i
$693$	−2.07582	−	0.435601i	−0.0788539	−	0.0165471i
$694$	41.2712	−	41.2712i	1.56663	−	1.56663i
$695$	−2.75356	−	10.2764i	−0.104448	−	0.389807i
$696$	38.5733	−	38.5733i	1.46212	−	1.46212i
$697$	−2.55940	+	0.685790i	−0.0969443	+	0.0259762i
$698$	−6.56630	−	3.79105i	−0.248538	−	0.143494i
$699$	−1.70554	+	2.95409i	−0.0645096	+	0.111734i
$700$	−3.44325	−	62.5921i	−0.130143	−	2.36576i
$701$		−	35.5823i		−	1.34393i	−0.740585	−	0.671963i	$-0.765451\pi$
$701$		−	35.5823i		−	1.34393i	0.740585	−	0.671963i	$-0.234549\pi$
$702$	−9.82406	+	0.813775i	−0.370785	+	0.0307140i
$703$	4.21741	+	2.43492i	0.159063	+	0.0918349i
$704$	23.4724	+	6.28940i	0.884649	+	0.237041i
$705$		−	3.99165i		−	0.150334i
$706$	12.5781	+	21.7860i	0.473384	+	0.819925i
$707$	−28.8157	−	14.5882i	−1.08372	−	0.548646i
$708$	−65.8535	−	17.6454i	−2.47492	−	0.663154i
$709$	14.1954	−	3.80364i	0.533118	−	0.142849i	0.0177902	−	0.999842i	$-0.494337\pi$
$709$	14.1954	−	3.80364i	0.533118	−	0.142849i	0.515328	+	0.856993i	$0.327670\pi$
$710$	−3.86607	−	14.4284i	−0.145091	−	0.541488i
$711$	5.50202			0.206342
$712$	41.8903			1.56991
$713$	12.5962	+	47.0098i	0.471733	+	1.76053i
$714$	0.654880	+	1.99785i	0.0245083	+	0.0747678i
$715$	−2.23099	+	0.800361i	−0.0834344	+	0.0299318i
$716$	−3.52881	−	6.11208i	−0.131878	−	0.228419i
$717$	−0.225459	+	0.841424i	−0.00841992	+	0.0314236i
$718$	−28.9960	−	50.2226i	−1.08212	−	1.87429i
$719$	−9.69831	+	16.7980i	−0.361686	+	0.626458i	−0.988238	−	0.152921i	$-0.951132\pi$
$719$	−9.69831	+	16.7980i	−0.361686	+	0.626458i	0.626552	+	0.779379i	$0.284465\pi$
$720$	−8.71210	−	8.71210i	−0.324681	−	0.324681i
$721$	40.3696	+	20.4375i	1.50344	+	0.761134i
$722$	−10.2337	+	38.1928i	−0.380860	+	1.42139i
$723$	1.87818	−	7.00948i	0.0698504	−	0.260685i
$724$			77.8321i			2.89261i
$725$	21.5192	−	12.4241i	0.799202	−	0.461420i
$726$	−20.0233	+	20.0233i	−0.743136	+	0.743136i
$727$	48.0775			1.78309			0.891547	−	0.452928i	$-0.149621\pi$
$727$	48.0775			1.78309			0.891547	+	0.452928i	$0.149621\pi$
$728$	71.5305	−	55.6529i	2.65110	−	2.06263i
$729$	−1.00000			−0.0370370
$730$	12.7041	−	12.7041i	0.470198	−	0.470198i
$731$	0.790155	−	0.456196i	0.0292249	−	0.0168730i
$732$		−	32.0063i		−	1.18299i
$733$	5.53194	−	20.6455i	0.204327	−	0.762558i	−0.785327	−	0.619082i	$-0.787505\pi$
$733$	5.53194	−	20.6455i	0.204327	−	0.762558i	0.989654	−	0.143477i	$-0.0458283\pi$
$734$	3.50126	−	13.0669i	0.129234	−	0.482307i
$735$	−5.67396	−	0.868497i	−0.209287	−	0.0320350i
$736$	−145.636	−	145.636i	−5.36822	−	5.36822i
$737$	−5.08684	+	8.81066i	−0.187376	+	0.324545i
$738$	12.4623	+	21.5853i	0.458742	+	0.794565i
$739$	4.02305	−	15.0142i	0.147990	−	0.552307i	−0.851614	−	0.524170i	$-0.824376\pi$
$739$	4.02305	−	15.0142i	0.147990	−	0.552307i	0.999604	−	0.0281375i	$-0.00895764\pi$
$740$	5.13167	+	8.88831i	0.188644	+	0.326741i
$741$	−0.634052	−	7.65441i	−0.0232925	−	0.281192i
$742$	28.9963	+	25.9724i	1.06449	+	0.953476i
$743$	−1.89512	−	7.07267i	−0.0695250	−	0.259471i	0.922411	−	0.386209i	$-0.126216\pi$
$743$	−1.89512	−	7.07267i	−0.0695250	−	0.259471i	−0.991936	+	0.126738i	$0.959549\pi$
$744$	49.5651			1.81715
$745$	1.93549			0.0709110
$746$	11.1702	+	41.6878i	0.408970	+	1.52630i
$747$	4.79823	−	1.28568i	0.175558	−	0.0470406i
$748$	−1.23224	−	0.330177i	−0.0450551	−	0.0120725i
$749$	−14.6627	+	9.57627i	−0.535763	+	0.349909i
$750$	−10.4559	−	18.1101i	−0.381795	−	0.661289i
$751$			15.2637i			0.556979i	0.960439	+	0.278490i	$0.0898338\pi$
$751$			15.2637i			0.556979i	−0.960439	+	0.278490i	$0.910166\pi$
$752$	−70.6478	−	18.9300i	−2.57626	−	0.690307i
$753$	−13.3147	−	7.68725i	−0.485215	−	0.280139i
$754$	51.1870	+	24.1574i	1.86412	+	0.879761i
$755$			11.7008i			0.425834i
$756$	12.1279	−	7.92080i	0.441088	−	0.288077i
$757$	−14.8601	+	25.7384i	−0.540098	+	0.935477i	0.458800	+	0.888540i	$0.348280\pi$
$757$	−14.8601	+	25.7384i	−0.540098	+	0.935477i	−0.998898	+	0.0469377i	$0.985054\pi$
$758$	44.9096	+	25.9286i	1.63119	+	0.941768i
$759$	−7.22376	+	1.93560i	−0.262206	+	0.0702579i
$760$	11.7349	−	11.7349i	0.425671	−	0.425671i
$761$	−0.631743	−	2.35770i	−0.0229007	−	0.0854664i	0.953530	−	0.301299i	$-0.0974202\pi$
$761$	−0.631743	−	2.35770i	−0.0229007	−	0.0854664i	−0.976430	+	0.215832i	$0.930754\pi$
$762$	−13.5867	+	13.5867i	−0.492196	+	0.492196i
$763$	−14.5726	−	13.0529i	−0.527565	−	0.472548i
$764$	96.1636	+	55.5201i	3.47908	+	2.00865i
$765$	0.168529	+	0.168529i	0.00609318	+	0.00609318i
$766$	46.6090	−	80.7292i	1.68405	−	2.91686i
$767$	−3.70642	−	44.7447i	−0.133831	−	1.61564i
$768$	−39.1722	+	22.6161i	−1.41350	+	0.816087i
$769$	39.3287	−	10.5381i	1.41823	−	0.380013i	0.533374	−	0.845880i	$-0.320924\pi$
$769$	39.3287	−	10.5381i	1.41823	−	0.380013i	0.884855	+	0.465867i	$0.154257\pi$
$770$	3.17267	−	3.54205i	0.114335	−	0.127647i
$771$	−19.2801	+	11.1313i	−0.694354	+	0.400886i
$772$	38.5184	+	10.3210i	1.38631	+	0.371460i
$773$	19.8835	+	19.8835i	0.715159	+	0.715159i	0.967610	−	0.252451i	$-0.0812367\pi$
$773$	19.8835	+	19.8835i	0.715159	+	0.715159i	−0.252451	+	0.967610i	$0.581237\pi$
$774$	−6.06874	−	6.06874i	−0.218136	−	0.218136i
$775$	21.8078	+	5.84339i	0.783361	+	0.209901i
$776$	−101.838	+	58.7963i	−3.65578	+	2.11066i
$777$	−5.74749	+	1.88398i	−0.206190	+	0.0675874i
$778$	40.9737	−	10.9789i	1.46898	−	0.393611i
$779$	−16.8182	+	9.70997i	−0.602573	+	0.347896i
$780$	6.90868	−	14.6387i	0.247370	−	0.524151i
$781$	−2.67067	+	4.62574i	−0.0955641	+	0.165522i
$782$	5.24183	+	5.24183i	0.187448	+	0.187448i
$783$	4.97256	+	2.87091i	0.177705	+	0.102598i
$784$	−42.2797	+	96.3042i	−1.50999	+	3.43944i
$785$	13.0898	−	13.0898i	0.467196	−	0.467196i
$786$	1.45194	+	5.41872i	0.0517890	+	0.193279i
$787$	−1.46512	+	1.46512i	−0.0522259	+	0.0522259i	−0.732737	−	0.680512i	$-0.761758\pi$
$787$	−1.46512	+	1.46512i	−0.0522259	+	0.0522259i	0.680512	+	0.732737i	$0.261758\pi$
$788$	−85.8941	+	23.0152i	−3.05985	+	0.819884i
$789$	11.4146	+	6.59022i	0.406370	+	0.234618i
$790$	−6.16756	+	10.6825i	−0.219432	+	0.380068i
$791$	−26.3374	−	13.3336i	−0.936451	−	0.474088i
$792$			7.61643i			0.270638i
$793$	19.8398	−	7.11746i	0.704532	−	0.252748i
$794$	31.4157	+	18.1378i	1.11490	+	0.643688i
$795$	4.26250	+	1.14213i	0.151175	+	0.0405073i
$796$		−	5.78762i		−	0.205137i
$797$	−11.7487	−	20.3493i	−0.416159	−	0.720809i	0.579390	−	0.815050i	$-0.303291\pi$
$797$	−11.7487	−	20.3493i	−0.416159	−	0.720809i	−0.995549	+	0.0942412i	$0.969958\pi$
$798$	8.42593	+	12.9014i	0.298275	+	0.456703i
$799$	1.36663	+	0.366187i	0.0483479	+	0.0129548i
$800$	−92.2895	+	24.7289i	−3.26293	+	0.874299i
$801$	1.14119	+	4.25897i	0.0403219	+	0.150483i
$802$	−45.4066			−1.60336
$803$	−6.42442			−0.226713
$804$	−17.9828	−	67.1126i	−0.634203	−	2.36688i
$805$	−19.2321	+	6.30413i	−0.677842	+	0.222191i
$806$	17.3659	+	48.4072i	0.611688	+	1.70507i
$807$	−1.01475	−	1.75759i	−0.0357207	−	0.0618702i
$808$	−30.0176	+	112.027i	−1.05601	+	3.94110i
$809$	21.7852	+	37.7331i	0.765927	+	1.32662i	0.939755	+	0.341848i	$0.111053\pi$
$809$	21.7852	+	37.7331i	0.765927	+	1.32662i	−0.173828	+	0.984776i	$0.555614\pi$
$810$	1.12096	−	1.94157i	0.0393867	−	0.0682197i
$811$	9.71904	+	9.71904i	0.341282	+	0.341282i	0.856849	−	0.515567i	$-0.172419\pi$
$811$	9.71904	+	9.71904i	0.341282	+	0.341282i	−0.515567	+	0.856849i	$0.672419\pi$
$812$	−83.0467	+	4.56848i	−2.91437	+	0.160322i
$813$	−7.25419	+	27.0730i	−0.254416	+	0.949492i
$814$	1.29685	−	4.83990i	0.0454545	−	0.169639i
$815$			11.6051i			0.406509i
$816$	3.78201	−	2.18355i	0.132397	−	0.0764394i
$817$	4.72845	−	4.72845i	0.165428	−	0.165428i
$818$	−98.3215			−3.43773
$819$	7.60686	+	5.75636i	0.265805	+	0.201144i
$820$	−40.9280			−1.42927
$821$	−5.83662	+	5.83662i	−0.203700	+	0.203700i	−0.801583	−	0.597883i	$-0.796009\pi$
$821$	−5.83662	+	5.83662i	−0.203700	+	0.203700i	0.597883	+	0.801583i	$0.296009\pi$
$822$	−22.3575	+	12.9081i	−0.779808	+	0.450222i
$823$		−	6.64495i		−	0.231629i	−0.993271	−	0.115814i	$-0.963052\pi$
$823$		−	6.64495i		−	0.231629i	0.993271	−	0.115814i	$-0.0369477\pi$
$824$	42.0535	−	156.946i	1.46500	−	5.46746i
$825$	−0.897926	+	3.35110i	−0.0312618	+	0.116670i
$826$	49.2547	+	75.4163i	1.71379	+	2.62407i
$827$	31.3947	+	31.3947i	1.09170	+	1.09170i	0.995347	+	0.0963527i	$0.0307177\pi$
$827$	31.3947	+	31.3947i	1.09170	+	1.09170i	0.0963527	+	0.995347i	$0.469282\pi$
$828$	25.5371	−	44.2316i	0.887477	−	1.53715i
$829$	−8.58319	−	14.8665i	−0.298106	−	0.516336i	0.677596	−	0.735434i	$-0.263022\pi$
$829$	−8.58319	−	14.8665i	−0.298106	−	0.516336i	−0.975703	+	0.219099i	$0.929688\pi$
$830$	−2.88240	+	10.7573i	−0.100050	+	0.373391i
$831$	−5.43672	−	9.41668i	−0.188598	−	0.326661i
$832$	−83.3968	−	70.6374i	−2.89126	−	2.44891i
$833$	0.817869	−	1.86293i	0.0283375	−	0.0645468i
$834$	−9.18081	−	34.2633i	−0.317906	−	1.18644i
$835$	12.6479			0.437700
$836$	−9.34982			−0.323370
$837$	1.35027	+	5.03926i	0.0466720	+	0.174182i
$838$	−52.9177	+	14.1793i	−1.82801	+	0.489814i
$839$	−2.14438	−	0.574586i	−0.0740324	−	0.0198369i	0.221613	−	0.975135i	$-0.428868\pi$
$839$	−2.14438	−	0.574586i	−0.0740324	−	0.0198369i	−0.295645	+	0.955298i	$0.595535\pi$
$840$	1.13217	+	20.5809i	0.0390637	+	0.710107i
$841$	−1.98420	−	3.43674i	−0.0684208	−	0.118508i
$842$		−	35.3774i		−	1.21919i
$843$	6.83694	+	1.83195i	0.235477	+	0.0630958i
$844$	−8.99131	−	5.19113i	−0.309494	−	0.178686i
$845$	10.6105	+	1.02718i	0.365012	+	0.0353360i
$846$		−	13.3088i		−	0.457566i
$847$	27.3615	−	1.50518i	0.940153	−	0.0517187i
$848$	40.4290	−	70.0251i	1.38834	−	2.40467i
$849$	0.798615	+	0.461081i	0.0274084	+	0.0158242i
$850$	3.32174	−	0.890059i	0.113935	−	0.0305288i
$851$	−15.0799	+	15.0799i	−0.516931	+	0.516931i
$852$	−9.44124	−	35.2352i	−0.323451	−	1.20714i
$853$	−20.3713	+	20.3713i	−0.697499	+	0.697499i	−0.963870	−	0.266371i	$-0.914175\pi$
$853$	−20.3713	+	20.3713i	−0.697499	+	0.697499i	0.266371	+	0.963870i	$0.414175\pi$
$854$	−28.2139	+	31.4988i	−0.965461	+	1.07787i
$855$	1.51277	+	0.873398i	0.0517357	+	0.0298696i
$856$	44.4678	+	44.4678i	1.51988	+	1.51988i
$857$	−21.8286	+	37.8083i	−0.745652	+	1.29151i	0.204238	+	0.978921i	$0.434528\pi$
$857$	−21.8286	+	37.8083i	−0.745652	+	1.29151i	−0.949890	+	0.312585i	$0.898805\pi$
$858$	−7.43849	+	2.66853i	−0.253946	+	0.0911022i
$859$	−34.3572	+	19.8362i	−1.17225	+	0.676801i	−0.954210	−	0.299138i	$-0.903301\pi$
$859$	−34.3572	+	19.8362i	−1.17225	+	0.676801i	−0.218044	+	0.975939i	$0.569968\pi$
$860$	13.6129	−	3.64757i	0.464196	−	0.124381i
$861$	4.95351	−	23.6056i	0.168815	−	0.804475i
$862$	−29.1089	+	16.8060i	−0.991454	+	0.572416i
$863$	28.0540	+	7.51704i	0.954968	+	0.255883i	0.702469	−	0.711714i	$-0.252081\pi$
$863$	28.0540	+	7.51704i	0.954968	+	0.255883i	0.252499	+	0.967597i	$0.418748\pi$
$864$	−15.6116	−	15.6116i	−0.531118	−	0.531118i
$865$	−1.77675	−	1.77675i	−0.0604114	−	0.0604114i
$866$	−59.4162	−	15.9205i	−2.01904	−	0.541001i
$867$	14.6493	−	8.45776i	0.497515	−	0.287241i
$868$	−56.2909	−	50.4206i	−1.91064	−	1.71139i
$869$	4.26053	−	1.14161i	0.144529	−	0.0387263i
$870$	−11.1481	+	6.43637i	−0.377956	+	0.218213i
$871$	37.6023	−	26.0713i	1.27410	−	0.883393i
$872$	−35.1258	+	60.8397i	−1.18951	+	2.06029i
$873$	−8.75209	−	8.75209i	−0.296214	−	0.296214i
$874$	47.0524	+	27.1657i	1.59157	+	0.918893i
$875$	−4.15602	+	19.8052i	−0.140499	+	0.669537i
$876$	31.0242	−	31.0242i	1.04821	−	1.04821i
$877$	−6.23297	−	23.2618i	−0.210472	−	0.785494i	−0.987711	−	0.156288i	$-0.950047\pi$
$877$	−6.23297	−	23.2618i	−0.210472	−	0.785494i	0.777239	−	0.629205i	$-0.216620\pi$
$878$	−32.5643	+	32.5643i	−1.09899	+	1.09899i
$879$	−14.3112	+	3.83466i	−0.482703	+	0.129340i
$880$	−8.55395	−	4.93862i	−0.288353	−	0.166481i
$881$	16.4202	−	28.4406i	0.553209	−	0.958187i	−0.444831	−	0.895615i	$-0.646736\pi$
$881$	16.4202	−	28.4406i	0.553209	−	0.958187i	0.998040	−	0.0625724i	$-0.0199304\pi$
$882$	−18.9179	−	2.89571i	−0.636999	−	0.0975037i
$883$			23.2851i			0.783606i	0.920049	+	0.391803i	$0.128149\pi$
$883$			23.2851i			0.783606i	−0.920049	+	0.391803i	$0.871851\pi$
$884$	4.37811	+	3.70827i	0.147252	+	0.124723i
$885$	8.84306	+	5.10554i	0.297256	+	0.171621i
$886$	−33.3756	−	8.94297i	−1.12128	−	0.300445i
$887$		−	39.8653i		−	1.33854i	−0.743017	−	0.669272i	$-0.766606\pi$
$887$		−	39.8653i		−	1.33854i	0.743017	−	0.669272i	$-0.233394\pi$
$888$	10.8596	+	18.8094i	0.364424	+	0.631201i
$889$	18.5660	−	1.02134i	0.622685	−	0.0342545i
$890$	−9.54830	−	2.55846i	−0.320060	−	0.0857597i
$891$	−0.774358	+	0.207489i	−0.0259420	+	0.00695113i
$892$	7.81111	+	29.1514i	0.261535	+	0.976063i
$893$	10.3695			0.347004
$894$	6.45325			0.215829
$895$	0.273585	+	1.02103i	0.00914492	+	0.0341293i
$896$	100.254	+	21.0379i	3.34927	+	0.702827i
$897$	33.0968	+	5.99366i	1.10507	+	0.200123i
$898$	14.8928	+	25.7951i	0.496979	+	0.860793i
$899$	7.75297	−	28.9345i	0.258576	−	0.965019i
$900$	−11.8467	−	20.5190i	−0.394889	−	0.683968i
$901$	−0.782069	+	1.35458i	−0.0260545	+	0.0451277i
$902$	14.1290	+	14.1290i	0.470443	+	0.470443i
$903$	0.456196	+	8.29282i	0.0151812	+	0.275968i
$904$	−27.4360	+	102.392i	−0.912507	+	3.40552i
$905$	3.01712	−	11.2600i	0.100292	−	0.374296i
$906$			39.0122i			1.29609i
$907$	−12.1536	+	7.01690i	−0.403555	+	0.232992i	−0.688017	−	0.725695i	$-0.741518\pi$
$907$	−12.1536	+	7.01690i	−0.403555	+	0.232992i	0.284462	+	0.958687i	$0.408185\pi$
$908$	61.8343	−	61.8343i	2.05204	−	2.05204i
$909$	−12.2075			−0.404897
$910$	−19.7034	+	8.31655i	−0.653161	+	0.275691i
$911$	−11.6160			−0.384856			−0.192428	−	0.981311i	$-0.561636\pi$
$911$	−11.6160			−0.384856			−0.192428	+	0.981311i	$0.561636\pi$
$912$	22.6324	−	22.6324i	0.749433	−	0.749433i
$913$	3.44878	−	1.99115i	0.114138	−	0.0658976i
$914$			0.733722i			0.0242694i
$915$	−1.24070	+	4.63037i	−0.0410164	+	0.153075i
$916$	17.5593	−	65.5324i	0.580177	−	2.16525i
$917$	2.45202	−	4.84341i	0.0809730	−	0.159943i
$918$	0.561903	+	0.561903i	0.0185456	+	0.0185456i
$919$	9.42513	−	16.3248i	0.310906	−	0.538505i	−0.667653	−	0.744473i	$-0.732701\pi$
$919$	9.42513	−	16.3248i	0.310906	−	0.538505i	0.978559	+	0.205968i	$0.0660341\pi$
$920$	36.3381	+	62.9394i	1.19803	+	2.07505i
$921$	0.948910	−	3.54138i	0.0312676	−	0.116692i
$922$	−43.9781	−	76.1722i	−1.44834	−	2.50860i
$923$	19.7418	−	13.6879i	0.649809	−	0.450541i
$924$	7.74788	−	8.64994i	0.254887	−	0.284562i
$925$	2.56055	+	9.55609i	0.0841903	+	0.314202i
$926$	89.5992			2.94441
$927$	17.1022			0.561710
$928$	32.8101	+	122.449i	1.07704	+	4.01959i
$929$	22.6089	−	6.05803i	0.741773	−	0.198757i	0.131907	−	0.991262i	$-0.457890\pi$
$929$	22.6089	−	6.05803i	0.741773	−	0.198757i	0.609866	+	0.792505i	$0.291223\pi$
$930$	−11.2977	−	3.02720i	−0.370465	−	0.0992658i
$931$	2.25619	−	14.7399i	0.0739437	−	0.483080i
$932$	−9.33777	−	16.1735i	−0.305869	−	0.529781i
$933$			8.32655i			0.272599i
$934$	20.1369	+	5.39567i	0.658899	+	0.176552i
$935$	0.165470	+	0.0955340i	0.00541144	+	0.00312429i
$936$	14.6201	−	30.9784i	0.477873	−	1.01256i
$937$			6.34230i			0.207194i	0.994619	+	0.103597i	$0.0330352\pi$
$937$			6.34230i			0.207194i	−0.994619	+	0.103597i	$0.966965\pi$
$938$	−41.4629	+	81.9005i	−1.35381	+	2.67415i
$939$	−4.62783	+	8.01564i	−0.151024	+	0.261580i
$940$	18.9262	+	10.9270i	0.617304	+	0.356401i
$941$	42.3526	−	11.3483i	1.38065	−	0.369945i	0.509295	−	0.860592i	$-0.329906\pi$
$941$	42.3526	−	11.3483i	1.38065	−	0.369945i	0.871359	+	0.490647i	$0.163239\pi$
$942$	43.6436	−	43.6436i	1.42199	−	1.42199i
$943$	−22.0110	−	82.1464i	−0.716778	−	2.67505i
$944$	132.300	−	132.300i	4.30600	−	4.30600i
$945$	−2.06160	+	0.675777i	−0.0670639	+	0.0219830i
$946$	−5.95857	−	3.44018i	−0.193730	−	0.111850i
$947$	−39.6852	−	39.6852i	−1.28960	−	1.28960i	−0.935031	−	0.354566i	$-0.884629\pi$
$947$	−39.6852	−	39.6852i	−1.28960	−	1.28960i	−0.354566	−	0.935031i	$-0.615371\pi$
$948$	−15.0616	+	26.0875i	−0.489179	+	0.847284i
$949$	26.1301	+	12.3320i	0.848220	+	0.400313i
$950$	21.8276	−	12.6022i	0.708180	−	0.408868i
$951$	−15.8649	+	4.25100i	−0.514456	+	0.137848i
$952$	−7.15018	−	1.50043i	−0.231739	−	0.0486292i
$953$	2.39079	−	1.38032i	0.0774453	−	0.0447130i	−0.460777	−	0.887516i	$-0.652429\pi$
$953$	2.39079	−	1.38032i	0.0774453	−	0.0447130i	0.538223	+	0.842803i	$0.319096\pi$
$954$	14.2119	+	3.80806i	0.460126	+	0.123290i
$955$	−11.7599	−	11.7599i	−0.380540	−	0.380540i
$956$	−3.37238	−	3.37238i	−0.109071	−	0.109071i
$957$	4.44622	+	1.19136i	0.143726	+	0.0385112i
$958$	−13.6055	+	7.85511i	−0.439572	+	0.253787i
$959$	24.4501	+	5.13073i	0.789534	+	0.165680i
$960$	24.0091	−	6.43323i	0.774891	−	0.207632i
$961$	−3.27586	+	1.89132i	−0.105673	+	0.0610103i
$962$	−14.5651	+	17.1961i	−0.469598	+	0.554423i
$963$	−3.30962	+	5.73242i	−0.106651	+	0.184725i
$964$	28.0936	+	28.0936i	0.904834	+	0.904834i
$965$	−5.17240	−	2.98629i	−0.166505	−	0.0961320i
$966$	−64.1229	+	21.0190i	−2.06312	+	0.676274i
$967$	3.57988	−	3.57988i	0.115121	−	0.115121i	−0.647200	−	0.762321i	$-0.724060\pi$
$967$	3.57988	−	3.57988i	0.115121	−	0.115121i	0.762321	+	0.647200i	$0.224060\pi$
$968$	−25.4681	−	95.0483i	−0.818576	−	3.05497i
$969$	−0.437806	+	0.437806i	−0.0140644	+	0.0140644i
$970$	26.8036	−	7.18199i	0.860610	−	0.230600i
$971$	−14.4013	−	8.31458i	−0.462159	−	0.266828i	0.250793	−	0.968041i	$-0.419309\pi$
$971$	−14.4013	−	8.31458i	−0.462159	−	0.266828i	−0.712952	+	0.701213i	$0.752642\pi$
$972$	2.73748	−	4.74145i	0.0878046	−	0.152082i
$973$	−15.5045	+	30.6255i	−0.497050	+	0.981808i
$974$		−	10.5764i		−	0.338891i
$975$	10.0848	−	11.9064i	0.322971	−	0.381310i
$976$	76.0686	+	43.9182i	2.43490	+	1.40579i
$977$	−2.82477	−	0.756896i	−0.0903725	−	0.0242152i	0.213349	−	0.976976i	$-0.431563\pi$
$977$	−2.82477	−	0.756896i	−0.0903725	−	0.0242152i	−0.303722	+	0.952761i	$0.598229\pi$
$978$			38.6933i			1.23728i
$979$	1.76737	+	3.06118i	0.0564855	+	0.0978358i
$980$	19.6503	−	24.5253i	0.627705	−	0.783432i
$981$	−7.14245	−	1.91381i	−0.228041	−	0.0611034i
$982$	−103.658	+	27.7750i	−3.30785	+	0.886335i
$983$	−14.1988	−	52.9906i	−0.452871	−	1.69014i	−0.694272	−	0.719713i	$-0.744273\pi$
$983$	−14.1988	−	52.9906i	−0.452871	−	1.69014i	0.241401	−	0.970426i	$-0.422393\pi$
$984$	−86.6116			−2.76108
$985$	13.3185			0.424364
$986$	−1.18092	−	4.40726i	−0.0376083	−	0.140356i
$987$	−8.59289	+	9.59333i	−0.273515	+	0.305359i
$988$	38.0287	+	17.9474i	1.20985	+	0.570984i
$989$	14.6420	+	25.3607i	0.465589	+	0.806424i
$990$	0.465175	−	1.73606i	0.0147842	−	0.0551755i
$991$	27.3314	+	47.3393i	0.868209	+	1.50378i	0.863825	+	0.503792i	$0.168062\pi$
$991$	27.3314	+	47.3393i	0.868209	+	1.50378i	0.00438397	+	0.999990i	$0.498605\pi$
$992$	−57.5911	+	99.7508i	−1.82852	+	3.16709i
$993$	−15.3059	−	15.3059i	−0.485719	−	0.485719i
$994$	−21.7687	+	42.9991i	−0.690462	+	1.36385i
$995$	−0.224354	+	0.837299i	−0.00711249	+	0.0265442i
$996$	−7.03904	+	26.2701i	−0.223041	+	0.832399i
$997$		−	31.0895i		−	0.984614i	−0.870422	−	0.492307i	$-0.836154\pi$
$997$		−	31.0895i		−	0.984614i	0.870422	−	0.492307i	$-0.163846\pi$
$998$	−27.2588	+	15.7379i	−0.862861	+	0.498173i
$999$	−1.61650	+	1.61650i	−0.0511438	+	0.0511438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bt.b.136.10	✓	40
3.2	odd	2		819.2.et.d.136.1		40
7.5	odd	6		273.2.cg.b.19.1	yes	40
13.11	odd	12		273.2.cg.b.115.1	yes	40
21.5	even	6		819.2.gh.d.19.10		40
39.11	even	12		819.2.gh.d.388.10		40
91.89	even	12	inner	273.2.bt.b.271.10	yes	40
273.89	odd	12		819.2.et.d.271.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.136.10	✓	40	1.1	even	1	trivial
273.2.bt.b.271.10	yes	40	91.89	even	12	inner
273.2.cg.b.19.1	yes	40	7.5	odd	6
273.2.cg.b.115.1	yes	40	13.11	odd	12
819.2.et.d.136.1		40	3.2	odd	2
819.2.et.d.271.1		40	273.89	odd	12
819.2.gh.d.19.10		40	21.5	even	6
819.2.gh.d.388.10		40	39.11	even	12

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.93326 - 1.93326i) q^{2} +(-0.866025 + 0.500000i) q^{3} -5.47495i q^{4} +(-0.212233 + 0.792066i) q^{5} +(-0.707621 + 2.64088i) q^{6} +(2.21517 - 1.44673i) q^{7} +(-6.71797 - 6.71797i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.93326 - 1.93326i) q^{2} +(-0.866025 + 0.500000i) q^{3} -5.47495i q^{4} +(-0.212233 + 0.792066i) q^{5} +(-0.707621 + 2.64088i) q^{6} +(2.21517 - 1.44673i) q^{7} +(-6.71797 - 6.71797i) q^{8} +(0.500000 - 0.866025i) q^{9} +(1.12096 + 1.94157i) q^{10} +(0.207489 - 0.774358i) q^{11} +(2.73748 + 4.74145i) q^{12} +(-2.33034 + 2.75128i) q^{13} +(1.48557 - 7.07939i) q^{14} +(-0.212233 - 0.792066i) q^{15} -15.0252 q^{16} +0.290651 q^{17} +(-0.707621 - 2.64088i) q^{18} +(2.05764 - 0.551342i) q^{19} +(4.33652 + 1.16197i) q^{20} +(-1.19502 + 2.36049i) q^{21} +(-1.09590 - 1.89816i) q^{22} +9.32871i q^{23} +(9.17692 + 2.45895i) q^{24} +(3.74780 + 2.16379i) q^{25} +(0.813775 + 9.82406i) q^{26} +1.00000i q^{27} +(-7.92080 - 12.1279i) q^{28} +(2.87091 - 4.97256i) q^{29} +(-1.94157 - 1.12096i) q^{30} +(5.03926 - 1.35027i) q^{31} +(-15.6116 + 15.6116i) q^{32} +(0.207489 + 0.774358i) q^{33} +(0.561903 - 0.561903i) q^{34} +(0.675777 + 2.06160i) q^{35} +(-4.74145 - 2.73748i) q^{36} +(1.61650 + 1.61650i) q^{37} +(2.91205 - 5.04382i) q^{38} +(0.642496 - 3.54784i) q^{39} +(6.74685 - 3.89530i) q^{40} +(-8.80575 + 2.35949i) q^{41} +(2.25315 + 6.87372i) q^{42} +(2.71857 - 1.56956i) q^{43} +(-4.23957 - 1.13599i) q^{44} +(0.579832 + 0.579832i) q^{45} +(18.0348 + 18.0348i) q^{46} +(4.70196 + 1.25989i) q^{47} +(13.0122 - 7.51260i) q^{48} +(2.81392 - 6.40951i) q^{49} +(11.4286 - 3.06229i) q^{50} +(-0.251711 + 0.145326i) q^{51} +(15.0631 + 12.7585i) q^{52} +(-2.69075 + 4.66051i) q^{53} +(1.93326 + 1.93326i) q^{54} +(0.569307 + 0.328689i) q^{55} +(-24.6005 - 5.16230i) q^{56} +(-1.50629 + 1.50629i) q^{57} +(-4.06302 - 15.1634i) q^{58} +(-8.80521 + 8.80521i) q^{59} +(-4.33652 + 1.16197i) q^{60} +(-5.06274 - 2.92297i) q^{61} +(7.13177 - 12.3526i) q^{62} +(-0.145326 - 2.64176i) q^{63} +30.3120i q^{64} +(-1.68461 - 2.42970i) q^{65} +(1.89816 + 1.09590i) q^{66} +(-12.2581 - 3.28455i) q^{67} -1.59130i q^{68} +(-4.66436 - 8.07890i) q^{69} +(5.29205 + 2.67916i) q^{70} +(-6.43570 - 1.72444i) q^{71} +(-9.17692 + 2.45895i) q^{72} +(-2.07411 - 7.74069i) q^{73} +6.25021 q^{74} -4.32759 q^{75} +(-3.01857 - 11.2655i) q^{76} +(-0.660669 - 2.01551i) q^{77} +(-5.61678 - 8.10100i) q^{78} +(2.75101 + 4.76489i) q^{79} +(3.18885 - 11.9009i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-12.4623 + 21.5853i) q^{82} +(3.51255 + 3.51255i) q^{83} +(12.9236 + 6.54269i) q^{84} +(-0.0616859 + 0.230215i) q^{85} +(2.22131 - 8.29005i) q^{86} +5.74181i q^{87} +(-6.59602 + 3.80821i) q^{88} +(-3.11778 + 3.11778i) q^{89} +2.24193 q^{90} +(-1.18173 + 9.46591i) q^{91} +51.0743 q^{92} +(-3.68899 + 3.68899i) q^{93} +(11.5258 - 6.65440i) q^{94} +1.74680i q^{95} +(5.71424 - 21.3259i) q^{96} +(3.20349 - 11.9556i) q^{97} +(-6.95120 - 17.8313i) q^{98} +(-0.566870 - 0.566870i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q - 2 * q^7 + 20 * q^9	\( 40 q - 2 q^{7} + 20 q^{9} - 8 q^{11} + 24 q^{12} - 18 q^{14} - 64 q^{16} + 8 q^{17} - 14 q^{19} - 14 q^{20} - 8 q^{21} + 4 q^{22} + 18 q^{24} - 24 q^{25} - 10 q^{26} - 2 q^{28} + 8 q^{29} - 8 q^{31} + 10 q^{32} - 8 q^{33} + 24 q^{34} - 22 q^{35} + 12 q^{37} + 8 q^{38} - 24 q^{39} - 30 q^{40} + 2 q^{41} + 6 q^{42} - 66 q^{43} + 28 q^{44} + 40 q^{46} + 10 q^{47} - 24 q^{48} + 38 q^{49} - 20 q^{50} + 40 q^{52} - 8 q^{53} + 42 q^{55} + 20 q^{56} - 14 q^{57} - 48 q^{58} - 26 q^{59} + 14 q^{60} - 12 q^{61} - 24 q^{62} - 4 q^{63} - 44 q^{65} - 18 q^{66} + 46 q^{67} - 4 q^{69} + 32 q^{70} - 6 q^{71} - 18 q^{72} + 10 q^{73} + 40 q^{74} + 48 q^{75} + 64 q^{76} - 24 q^{77} + 8 q^{78} + 34 q^{80} - 20 q^{81} + 24 q^{82} + 12 q^{83} + 20 q^{84} + 2 q^{85} + 12 q^{86} - 84 q^{88} - 16 q^{89} + 26 q^{91} + 236 q^{92} + 22 q^{93} + 30 q^{94} + 26 q^{96} + 62 q^{97} - 14 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 2 * q^7 + 20 * q^9 - 8 * q^11 + 24 * q^12 - 18 * q^14 - 64 * q^16 + 8 * q^17 - 14 * q^19 - 14 * q^20 - 8 * q^21 + 4 * q^22 + 18 * q^24 - 24 * q^25 - 10 * q^26 - 2 * q^28 + 8 * q^29 - 8 * q^31 + 10 * q^32 - 8 * q^33 + 24 * q^34 - 22 * q^35 + 12 * q^37 + 8 * q^38 - 24 * q^39 - 30 * q^40 + 2 * q^41 + 6 * q^42 - 66 * q^43 + 28 * q^44 + 40 * q^46 + 10 * q^47 - 24 * q^48 + 38 * q^49 - 20 * q^50 + 40 * q^52 - 8 * q^53 + 42 * q^55 + 20 * q^56 - 14 * q^57 - 48 * q^58 - 26 * q^59 + 14 * q^60 - 12 * q^61 - 24 * q^62 - 4 * q^63 - 44 * q^65 - 18 * q^66 + 46 * q^67 - 4 * q^69 + 32 * q^70 - 6 * q^71 - 18 * q^72 + 10 * q^73 + 40 * q^74 + 48 * q^75 + 64 * q^76 - 24 * q^77 + 8 * q^78 + 34 * q^80 - 20 * q^81 + 24 * q^82 + 12 * q^83 + 20 * q^84 + 2 * q^85 + 12 * q^86 - 84 * q^88 - 16 * q^89 + 26 * q^91 + 236 * q^92 + 22 * q^93 + 30 * q^94 + 26 * q^96 + 62 * q^97 - 14 * q^98 - 4 * q^99

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