LMFDB - Embedded newform 273.2.cc.a.50.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(50,273)]

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([6, 0, 7]))

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

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

chi := DirichletCharacter("273.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cc (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:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.7
Character	$\chi$	$=$	273.50
Dual form			273.2.cc.a.71.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.78824 - 0.479158i) q^{2} +(-1.54238 + 0.788082i) q^{3} +(1.23617 + 0.713702i) q^{4} +(0.0341444 - 0.0341444i) q^{5} +(3.13576 - 0.670240i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.749576 + 0.749576i) q^{8} +(1.75785 - 2.43104i) q^{9} +O(q^{10})$	\(q+(-1.78824 - 0.479158i) q^{2} +(-1.54238 + 0.788082i) q^{3} +(1.23617 + 0.713702i) q^{4} +(0.0341444 - 0.0341444i) q^{5} +(3.13576 - 0.670240i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.749576 + 0.749576i) q^{8} +(1.75785 - 2.43104i) q^{9} +(-0.0774191 + 0.0446979i) q^{10} +(0.593688 - 2.21567i) q^{11} +(-2.46909 - 0.126596i) q^{12} +(-2.82144 + 2.24487i) q^{13} -1.85133i q^{14} +(-0.0257549 + 0.0795721i) q^{15} +(-2.40866 - 4.17193i) q^{16} +(-1.35027 + 2.33874i) q^{17} +(-4.30832 + 3.50500i) q^{18} +(-3.57887 + 0.958956i) q^{19} +(0.0665772 - 0.0178393i) q^{20} +(-1.16043 - 1.28585i) q^{21} +(-2.12332 + 3.67769i) q^{22} +(-3.77557 - 6.53948i) q^{23} +(-1.74686 - 0.565401i) q^{24} +4.99767i q^{25} +(6.12107 - 2.66246i) q^{26} +(-0.795414 + 5.13491i) q^{27} +(-0.369439 + 1.37877i) q^{28} +(-4.84979 + 2.80003i) q^{29} +(0.0841837 - 0.129954i) q^{30} +(-7.53697 - 7.53697i) q^{31} +(1.75953 + 6.56667i) q^{32} +(0.830442 + 3.88528i) q^{33} +(3.53524 - 3.53524i) q^{34} +(0.0418182 + 0.0241437i) q^{35} +(3.90804 - 1.75059i) q^{36} +(-7.04136 - 1.88673i) q^{37} +6.85939 q^{38} +(2.58258 - 5.68597i) q^{39} +0.0511877 q^{40} +(-1.06090 - 0.284266i) q^{41} +(1.45900 + 2.85544i) q^{42} +(7.18359 + 4.14745i) q^{43} +(2.31523 - 2.31523i) q^{44} +(-0.0229855 - 0.143027i) q^{45} +(3.61819 + 13.5033i) q^{46} +(-0.532347 - 0.532347i) q^{47} +(7.00289 + 4.53646i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(2.39467 - 8.93704i) q^{50} +(0.239510 - 4.67135i) q^{51} +(-5.08995 + 0.761372i) q^{52} +1.25773i q^{53} +(3.88283 - 8.80134i) q^{54} +(-0.0553817 - 0.0959239i) q^{55} +(-0.530030 + 0.918039i) q^{56} +(4.76424 - 4.29952i) q^{57} +(10.0143 - 2.68331i) q^{58} +(-0.918551 + 0.246125i) q^{59} +(-0.0886283 + 0.0799832i) q^{60} +(-0.722037 + 1.25060i) q^{61} +(9.86653 + 17.0893i) q^{62} +(2.80317 + 1.06876i) q^{63} -2.95124i q^{64} +(-0.0196866 + 0.172986i) q^{65} +(0.376631 - 7.34573i) q^{66} +(2.72551 - 10.1717i) q^{67} +(-3.33833 + 1.92739i) q^{68} +(10.9770 + 7.11088i) q^{69} +(-0.0632124 - 0.0632124i) q^{70} +(-2.64960 - 9.88844i) q^{71} +(3.13989 - 0.504604i) q^{72} +(3.34308 - 3.34308i) q^{73} +(11.6876 + 6.74785i) q^{74} +(-3.93857 - 7.70829i) q^{75} +(-5.10850 - 1.36882i) q^{76} +2.29383 q^{77} +(-7.34277 + 8.93043i) q^{78} -2.36122 q^{79} +(-0.224690 - 0.0602056i) q^{80} +(-2.81990 - 8.54682i) q^{81} +(1.76093 + 1.01667i) q^{82} +(-8.80818 + 8.80818i) q^{83} +(-0.516767 - 2.41773i) q^{84} +(0.0337507 + 0.125959i) q^{85} +(-10.8587 - 10.8587i) q^{86} +(5.27356 - 8.14074i) q^{87} +(2.10583 - 1.21580i) q^{88} +(-1.21816 + 4.54622i) q^{89} +(-0.0274290 + 0.266781i) q^{90} +(-2.89862 - 2.14429i) q^{91} -10.7785i q^{92} +(17.5646 + 5.68510i) q^{93} +(0.696888 + 1.20704i) q^{94} +(-0.0894555 + 0.154942i) q^{95} +(-7.88894 - 8.74162i) q^{96} +(-7.22276 + 1.93533i) q^{97} +(1.78824 - 0.479158i) q^{98} +(-4.34277 - 5.33811i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{6}+O(q^{10}) $ 112 * q - 12 * q^6	$ 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) $ 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$1$

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 $

$2$	−1.78824	−	0.479158i	−1.26448	−	0.338816i	−0.436565	−	0.899672i	$-0.643805\pi$
$2$	−1.78824	−	0.479158i	−1.26448	−	0.338816i	−0.827913	+	0.560856i	$0.810472\pi$
$3$	−1.54238	+	0.788082i	−0.890492	+	0.454999i
$3$	−1.54238	+	0.788082i	−0.890492	+	0.454999i
$4$	1.23617	+	0.713702i	0.618084	+	0.356851i
$5$	0.0341444	−	0.0341444i	0.0152698	−	0.0152698i	−0.699431	−	0.714700i	$-0.746563\pi$
$5$	0.0341444	−	0.0341444i	0.0152698	−	0.0152698i	0.714700	+	0.699431i	$0.246563\pi$
$6$	3.13576	−	0.670240i	1.28017	−	0.273624i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$8$	0.749576	+	0.749576i	0.265015	+	0.265015i
$9$	1.75785	−	2.43104i	0.585951	−	0.810346i
$10$	−0.0774191	+	0.0446979i	−0.0244821	+	0.0141347i
$11$	0.593688	−	2.21567i	0.179004	−	0.668050i	−0.816831	−	0.576876i	$-0.804271\pi$
$11$	0.593688	−	2.21567i	0.179004	−	0.668050i	0.995835	−	0.0911739i	$-0.0290619\pi$
$12$	−2.46909	−	0.126596i	−0.712766	−	0.0365450i
$13$	−2.82144	+	2.24487i	−0.782527	+	0.622616i
$13$	−2.82144	+	2.24487i	−0.782527	+	0.622616i
$14$		−	1.85133i		−	0.494787i
$15$	−0.0257549	+	0.0795721i	−0.00664990	+	0.0205454i
$16$	−2.40866	−	4.17193i	−0.602166	−	1.04298i
$17$	−1.35027	+	2.33874i	−0.327489	+	0.567228i	−0.982013	−	0.188813i	$-0.939536\pi$
$17$	−1.35027	+	2.33874i	−0.327489	+	0.567228i	0.654524	+	0.756042i	$0.272869\pi$
$18$	−4.30832	+	3.50500i	−1.01548	+	0.826136i
$19$	−3.57887	+	0.958956i	−0.821050	+	0.220000i	−0.644805	−	0.764347i	$-0.723062\pi$
$19$	−3.57887	+	0.958956i	−0.821050	+	0.220000i	−0.176245	+	0.984346i	$0.556395\pi$
$20$	0.0665772	−	0.0178393i	0.0148871	−	0.00398899i
$21$	−1.16043	−	1.28585i	−0.253226	−	0.280596i
$22$	−2.12332	+	3.67769i	−0.452692	+	0.784086i
$23$	−3.77557	−	6.53948i	−0.787261	−	1.36358i	−0.927639	−	0.373478i	$-0.878165\pi$
$23$	−3.77557	−	6.53948i	−0.787261	−	1.36358i	0.140378	−	0.990098i	$-0.455168\pi$
$24$	−1.74686	−	0.565401i	−0.356575	−	0.115412i
$25$			4.99767i			0.999534i
$26$	6.12107	−	2.66246i	1.20044	−	0.522152i
$27$	−0.795414	+	5.13491i	−0.153077	+	0.988214i
$28$	−0.369439	+	1.37877i	−0.0698175	+	0.260562i
$29$	−4.84979	+	2.80003i	−0.900584	+	0.519952i	−0.877390	−	0.479779i	$-0.840717\pi$
$29$	−4.84979	+	2.80003i	−0.900584	+	0.519952i	−0.0231944	+	0.999731i	$0.507384\pi$
$30$	0.0841837	−	0.129954i	0.0153698	−	0.0237262i
$31$	−7.53697	−	7.53697i	−1.35368	−	1.35368i	−0.881505	−	0.472175i	$-0.843469\pi$
$31$	−7.53697	−	7.53697i	−1.35368	−	1.35368i	−0.472175	−	0.881505i	$-0.656531\pi$
$32$	1.75953	+	6.56667i	0.311044	+	1.16083i
$33$	0.830442	+	3.88528i	0.144561	+	0.676340i
$34$	3.53524	−	3.53524i	0.606289	−	0.606289i
$35$	0.0418182	+	0.0241437i	0.00706856	+	0.00408104i
$36$	3.90804	−	1.75059i	0.651340	−	0.291765i
$37$	−7.04136	−	1.88673i	−1.15759	−	0.310176i	−0.371588	−	0.928398i	$-0.621187\pi$
$37$	−7.04136	−	1.88673i	−1.15759	−	0.310176i	−0.786004	+	0.618222i	$0.787853\pi$
$38$	6.85939			1.11274
$39$	2.58258	−	5.68597i	0.413544	−	0.910484i
$40$	0.0511877			0.00809348
$41$	−1.06090	−	0.284266i	−0.165684	−	0.0443949i	0.175023	−	0.984564i	$-0.444000\pi$
$41$	−1.06090	−	0.284266i	−0.165684	−	0.0443949i	−0.340707	+	0.940169i	$0.610667\pi$
$42$	1.45900	+	2.85544i	0.225128	+	0.440604i
$43$	7.18359	+	4.14745i	1.09549	+	0.632480i	0.935032	−	0.354563i	$-0.115370\pi$
$43$	7.18359	+	4.14745i	1.09549	+	0.632480i	0.160455	+	0.987043i	$0.448704\pi$
$44$	2.31523	−	2.31523i	0.349034	−	0.349034i
$45$	−0.0229855	−	0.143027i	−0.00342648	−	0.0213212i
$46$	3.61819	+	13.5033i	0.533473	+	1.99095i
$47$	−0.532347	−	0.532347i	−0.0776508	−	0.0776508i	0.667215	−	0.744865i	$-0.267486\pi$
$47$	−0.532347	−	0.532347i	−0.0776508	−	0.0776508i	−0.744865	+	0.667215i	$0.767486\pi$
$48$	7.00289	+	4.53646i	1.01078	+	0.654781i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	2.39467	−	8.93704i	0.338658	−	1.26389i
$51$	0.239510	−	4.67135i	0.0335381	−	0.654119i
$52$	−5.08995	+	0.761372i	−0.705849	+	0.105583i
$53$			1.25773i			0.172763i	0.996262	+	0.0863814i	$0.0275304\pi$
$53$			1.25773i			0.172763i	−0.996262	+	0.0863814i	$0.972470\pi$
$54$	3.88283	−	8.80134i	0.528386	−	1.19771i
$55$	−0.0553817	−	0.0959239i	−0.00746767	−	0.0129344i
$56$	−0.530030	+	0.918039i	−0.0708283	+	0.122678i
$57$	4.76424	−	4.29952i	0.631039	−	0.569485i
$58$	10.0143	−	2.68331i	1.31494	−	0.352336i
$59$	−0.918551	+	0.246125i	−0.119585	+	0.0320428i	−0.318115	−	0.948052i	$-0.603050\pi$
$59$	−0.918551	+	0.246125i	−0.119585	+	0.0320428i	0.198530	+	0.980095i	$0.436383\pi$
$60$	−0.0886283	+	0.0799832i	−0.0114419	+	0.0103258i
$61$	−0.722037	+	1.25060i	−0.0924474	+	0.160124i	−0.908540	−	0.417797i	$-0.862802\pi$
$61$	−0.722037	+	1.25060i	−0.0924474	+	0.160124i	0.816093	+	0.577921i	$0.196136\pi$
$62$	9.86653	+	17.0893i	1.25305	+	2.17035i
$63$	2.80317	+	1.06876i	0.353166	+	0.134651i
$64$		−	2.95124i		−	0.368905i
$65$	−0.0196866	+	0.172986i	−0.00244182	+	0.0214563i
$66$	0.376631	−	7.34573i	0.0463601	−	0.904197i
$67$	2.72551	−	10.1717i	0.332974	−	1.24267i	−0.573076	−	0.819502i	$-0.694250\pi$
$67$	2.72551	−	10.1717i	0.332974	−	1.24267i	0.906049	−	0.423172i	$-0.139083\pi$
$68$	−3.33833	+	1.92739i	−0.404832	+	0.233730i
$69$	10.9770	+	7.11088i	1.32148	+	0.856050i
$70$	−0.0632124	−	0.0632124i	−0.00755533	−	0.00755533i
$71$	−2.64960	−	9.88844i	−0.314450	−	1.17354i	−0.924501	−	0.381180i	$-0.875518\pi$
$71$	−2.64960	−	9.88844i	−0.314450	−	1.17354i	0.610051	−	0.792362i	$-0.291149\pi$
$72$	3.13989	−	0.504604i	0.370040	−	0.0594682i
$73$	3.34308	−	3.34308i	0.391278	−	0.391278i	−0.483865	−	0.875143i	$-0.660767\pi$
$73$	3.34308	−	3.34308i	0.391278	−	0.391278i	0.875143	+	0.483865i	$0.160767\pi$
$74$	11.6876	+	6.74785i	1.35866	+	0.784421i
$75$	−3.93857	−	7.70829i	−0.454787	−	0.890076i
$76$	−5.10850	−	1.36882i	−0.585985	−	0.157014i
$77$	2.29383			0.261407
$78$	−7.34277	+	8.93043i	−0.831404	+	1.01117i
$79$	−2.36122			−0.265658			−0.132829	−	0.991139i	$-0.542406\pi$
$79$	−2.36122			−0.265658			−0.132829	+	0.991139i	$0.542406\pi$
$80$	−0.224690	−	0.0602056i	−0.0251211	−	0.00673119i
$81$	−2.81990	−	8.54682i	−0.313323	−	0.949647i
$82$	1.76093	+	1.01667i	0.194462	+	0.112273i
$83$	−8.80818	+	8.80818i	−0.966824	+	0.966824i	−0.999467	−	0.0326432i	$-0.989608\pi$
$83$	−8.80818	+	8.80818i	−0.966824	+	0.966824i	0.0326432	+	0.999467i	$0.489608\pi$
$84$	−0.516767	−	2.41773i	−0.0563839	−	0.263796i
$85$	0.0337507	+	0.125959i	0.00366077	+	0.0136622i
$86$	−10.8587	−	10.8587i	−1.17093	−	1.17093i
$87$	5.27356	−	8.14074i	0.565385	−	0.872779i
$88$	2.10583	−	1.21580i	0.224482	−	0.129605i
$89$	−1.21816	+	4.54622i	−0.129124	+	0.481899i	−0.999953	−	0.00968794i	$-0.996916\pi$
$89$	−1.21816	+	4.54622i	−0.129124	+	0.481899i	0.870829	+	0.491587i	$0.163583\pi$
$90$	−0.0274290	+	0.266781i	−0.00289127	+	0.0281212i
$91$	−2.89862	−	2.14429i	−0.303858	−	0.224783i
$92$		−	10.7785i		−	1.12374i
$93$	17.5646	+	5.68510i	1.82136	+	0.589517i
$94$	0.696888	+	1.20704i	0.0718785	+	0.124497i
$95$	−0.0894555	+	0.154942i	−0.00917794	+	0.0158967i
$96$	−7.88894	−	8.74162i	−0.805161	−	0.892188i
$97$	−7.22276	+	1.93533i	−0.733361	+	0.196503i	−0.606125	−	0.795369i	$-0.707277\pi$
$97$	−7.22276	+	1.93533i	−0.733361	+	0.196503i	−0.127235	+	0.991873i	$0.540610\pi$
$98$	1.78824	−	0.479158i	0.180640	−	0.0484023i
$99$	−4.34277	−	5.33811i	−0.436465	−	0.536500i
$100$	−3.56685	+	6.17796i	−0.356685	+	0.617796i
$101$	7.83363	+	13.5682i	0.779475	+	1.35009i	0.932244	+	0.361829i	$0.117848\pi$
$101$	7.83363	+	13.5682i	0.779475	+	1.35009i	−0.152769	+	0.988262i	$0.548819\pi$
$102$	−2.66662	+	8.23874i	−0.264034	+	0.815757i
$103$			11.1455i			1.09820i	0.835758	+	0.549099i	$0.185029\pi$
$103$			11.1455i			1.09820i	−0.835758	+	0.549099i	$0.814971\pi$
$104$	−3.79759	−	0.432182i	−0.372384	−	0.0423790i
$105$	−0.0835267	−	0.00428259i	−0.00815137	−	0.000417938i
$106$	0.602652	−	2.24913i	0.0585348	−	0.218455i
$107$	−17.4195	+	10.0572i	−1.68401	+	0.972262i	−0.725057	+	0.688689i	$0.758186\pi$
$107$	−17.4195	+	10.0572i	−1.68401	+	0.972262i	−0.958951	+	0.283573i	$0.908480\pi$
$108$	−4.64806	+	5.77993i	−0.447260	+	0.556174i
$109$	4.18101	+	4.18101i	0.400468	+	0.400468i	0.878398	−	0.477930i	$-0.158613\pi$
$109$	4.18101	+	4.18101i	0.400468	+	0.400468i	−0.477930	+	0.878398i	$0.658613\pi$
$110$	0.0530732	+	0.198072i	0.00506033	+	0.0188854i
$111$	12.3473	−	2.63912i	1.17196	−	0.250495i
$112$	3.40636	−	3.40636i	0.321871	−	0.321871i
$113$	−2.07394	−	1.19739i	−0.195100	−	0.112641i	0.399268	−	0.916834i	$-0.369264\pi$
$113$	−2.07394	−	1.19739i	−0.195100	−	0.112641i	−0.594368	+	0.804193i	$0.702598\pi$
$114$	−10.5798	+	5.40576i	−0.990885	+	0.506296i
$115$	−0.352201	−	0.0943720i	−0.0328429	−	0.00880024i
$116$	−7.99355			−0.742182
$117$	0.497694	+	10.8052i	0.0460119	+	0.998941i
$118$	1.76053			0.162069
$119$	−2.60853	−	0.698953i	−0.239123	−	0.0640729i
$120$	−0.0789507	+	0.0403401i	−0.00720718	+	0.00368253i
$121$	4.96954	+	2.86917i	0.451776	+	0.260833i
$122$	1.89041	−	1.89041i	0.171150	−	0.171150i
$123$	1.86033	−	0.397627i	0.167740	−	0.0358529i
$124$	−3.93781	−	14.6961i	−0.353626	−	1.31975i
$125$	0.341364	+	0.341364i	0.0305326	+	0.0305326i
$126$	−4.50064	−	3.25436i	−0.400949	−	0.289921i
$127$	−4.74020	+	2.73675i	−0.420625	+	0.242848i	−0.695344	−	0.718677i	$-0.744748\pi$
$127$	−4.74020	+	2.73675i	−0.420625	+	0.242848i	0.274720	+	0.961524i	$0.411415\pi$
$128$	2.10496	−	7.85580i	0.186054	−	0.694362i
$129$	−14.3483	−	0.735669i	−1.26330	−	0.0647721i
$130$	0.118092	−	0.299909i	0.0103574	−	0.0263037i
$131$		−	8.74576i		−	0.764120i	−0.924137	−	0.382060i	$-0.875215\pi$
$131$		−	8.74576i		−	0.764120i	0.924137	−	0.382060i	$-0.124785\pi$
$132$	−1.74636	+	5.39554i	−0.152002	+	0.469622i
$133$	−1.85256	−	3.20873i	−0.160637	−	0.278232i
$134$	−9.74773	+	16.8836i	−0.842076	+	1.45852i
$135$	0.148170	+	0.202487i	0.0127524	+	0.0174273i
$136$	−2.76520	+	0.740932i	−0.237114	+	0.0635344i
$137$	−0.383938	+	0.102876i	−0.0328020	+	0.00878928i	−0.275183	−	0.961392i	$-0.588738\pi$
$137$	−0.383938	+	0.102876i	−0.0328020	+	0.00878928i	0.242381	+	0.970181i	$0.422072\pi$
$138$	−16.2223	−	17.9757i	−1.38093	−	1.53019i
$139$	0.196318	−	0.340034i	0.0166515	−	0.0288413i	−0.857580	−	0.514351i	$-0.828033\pi$
$139$	0.196318	−	0.340034i	0.0166515	−	0.0288413i	0.874231	+	0.485510i	$0.161366\pi$
$140$	0.0344629	+	0.0596915i	0.00291265	+	0.00504485i
$141$	1.24061	+	0.401547i	0.104479	+	0.0338163i
$142$			18.9525i			1.59046i
$143$	3.29885	+	7.58415i	0.275864	+	0.634218i
$144$	−14.3762	−	1.47808i	−1.19802	−	0.123173i
$145$	−0.0699880	+	0.261199i	−0.00581219	+	0.0216914i
$146$	−7.58010	+	4.37637i	−0.627333	+	0.362191i
$147$	0.941697	−	1.45369i	0.0776698	−	0.119898i
$148$	−7.35774	−	7.35774i	−0.604803	−	0.604803i
$149$	−2.58915	−	9.66282i	−0.212111	−	0.791609i	−0.987164	−	0.159713i	$-0.948943\pi$
$149$	−2.58915	−	9.66282i	−0.212111	−	0.791609i	0.775052	−	0.631897i	$-0.217723\pi$
$150$	3.34963	+	15.6715i	0.273497	+	1.27957i
$151$	7.40910	−	7.40910i	0.602944	−	0.602944i	−0.338149	−	0.941093i	$-0.609801\pi$
$151$	7.40910	−	7.40910i	0.602944	−	0.602944i	0.941093	+	0.338149i	$0.109801\pi$
$152$	−3.40145	−	1.96383i	−0.275894	−	0.159287i
$153$	3.31199	+	7.39373i	0.267759	+	0.597748i
$154$	−4.10193	−	1.09911i	−0.330543	−	0.0885687i
$155$	−0.514691			−0.0413410
$156$	7.25060	−	5.18562i	0.580512	−	0.415182i
$157$	9.51601			0.759460			0.379730	−	0.925097i	$-0.376017\pi$
$157$	9.51601			0.759460			0.379730	+	0.925097i	$0.376017\pi$
$158$	4.22244	+	1.13140i	0.335919	+	0.0900092i
$159$	−0.991196	−	1.93990i	−0.0786069	−	0.153844i
$160$	0.284293	+	0.164137i	0.0224753	+	0.0129761i
$161$	5.33946	−	5.33946i	0.420809	−	0.420809i
$162$	0.947394	+	16.6350i	0.0744343	+	1.30697i
$163$	2.76073	+	10.3032i	0.216237	+	0.807009i	0.985727	+	0.168350i	$0.0538439\pi$
$163$	2.76073	+	10.3032i	0.216237	+	0.807009i	−0.769490	+	0.638659i	$0.779489\pi$
$164$	−1.10856	−	1.10856i	−0.0865643	−	0.0865643i
$165$	0.161015	+	0.104306i	0.0125350	+	0.00812017i
$166$	19.9717	−	11.5307i	1.55010	−	0.894953i
$167$	5.92244	−	22.1028i	0.458292	−	1.71037i	−0.219933	−	0.975515i	$-0.570584\pi$
$167$	5.92244	−	22.1028i	0.458292	−	1.71037i	0.678225	−	0.734854i	$-0.262749\pi$
$168$	0.0940161	−	1.83367i	0.00725350	−	0.141471i
$169$	2.92108	−	12.6676i	0.224699	−	0.974428i
$170$		−	0.241418i		−	0.0185159i
$171$	−3.95987	+	10.3861i	−0.302819	+	0.794244i
$172$	5.92009	+	10.2539i	0.451402	+	0.781852i
$173$	1.89072	−	3.27482i	0.143749	−	0.248980i	−0.785157	−	0.619297i	$-0.787418\pi$
$173$	1.89072	−	3.27482i	0.143749	−	0.248980i	0.928905	+	0.370317i	$0.120751\pi$
$174$	−13.3311	+	12.0307i	−1.01063	+	0.912048i
$175$	−4.82738	+	1.29349i	−0.364915	+	0.0977788i
$176$	−10.6736	+	2.85999i	−0.804554	+	0.215580i
$177$	1.22279	−	1.10351i	0.0919102	−	0.0829450i
$178$	4.35672	−	7.54606i	0.326550	−	0.565601i
$179$	7.88772	+	13.6619i	0.589556	+	1.02114i	0.994291	+	0.106707i	$0.0340307\pi$
$179$	7.88772	+	13.6619i	0.589556	+	1.02114i	−0.404734	+	0.914434i	$0.632636\pi$
$180$	0.0736649	−	0.193211i	0.00549065	−	0.0144011i
$181$		−	6.35523i		−	0.472380i	−0.971707	−	0.236190i	$-0.924101\pi$
$181$		−	6.35523i		−	0.472380i	0.971707	−	0.236190i	$-0.0758988\pi$
$182$	4.15599	+	5.22341i	0.308063	+	0.387185i
$183$	0.128074	−	2.49793i	0.00946750	−	0.184652i
$184$	2.07176	−	7.73191i	0.152732	−	0.570004i
$185$	−0.304844	+	0.176002i	−0.0224126	+	0.0129399i
$186$	−28.6857	−	18.5826i	−2.10334	−	1.36254i
$187$	4.38024	+	4.38024i	0.320315	+	0.320315i
$188$	−0.278133	−	1.03801i	−0.0202850	−	0.0757045i
$189$	−5.16581	+	0.560702i	−0.375758	+	0.0407851i
$190$	0.234210	−	0.234210i	0.0169914	−	0.0169914i
$191$	−11.1403	−	6.43184i	−0.806082	−	0.465392i	0.0395112	−	0.999219i	$-0.487420\pi$
$191$	−11.1403	−	6.43184i	−0.806082	−	0.465392i	−0.845594	+	0.533827i	$0.820753\pi$
$192$	2.32582	+	4.55192i	0.167851	+	0.328507i
$193$	−11.8737	−	3.18156i	−0.854691	−	0.229014i	−0.195235	−	0.980757i	$-0.562547\pi$
$193$	−11.8737	−	3.18156i	−0.854691	−	0.229014i	−0.659456	+	0.751743i	$0.729213\pi$
$194$	13.8434			0.993897
$195$	−0.105963	−	0.282325i	−0.00758819	−	0.0202177i
$196$	−1.42740			−0.101957
$197$	21.0102	+	5.62966i	1.49691	+	0.401097i	0.912065	−	0.410045i	$-0.134487\pi$
$197$	21.0102	+	5.62966i	1.49691	+	0.401097i	0.584849	+	0.811142i	$0.301154\pi$
$198$	5.20813	+	11.6267i	0.370126	+	0.826274i
$199$	14.8170	+	8.55462i	1.05035	+	0.606421i	0.922748	−	0.385404i	$-0.125938\pi$
$199$	14.8170	+	8.55462i	1.05035	+	0.606421i	0.127604	+	0.991825i	$0.459271\pi$
$200$	−3.74613	+	3.74613i	−0.264892	+	0.264892i
$201$	3.81240	+	17.8366i	0.268906	+	1.25809i
$202$	−7.50710	−	28.0169i	−0.528197	−	1.97126i
$203$	−3.95984	−	3.95984i	−0.277926	−	0.277926i
$204$	3.63003	−	5.60363i	0.254153	−	0.392333i
$205$	−0.0459298	+	0.0265176i	−0.00320787	+	0.00185207i
$206$	5.34045	−	19.9308i	0.372087	−	1.38865i
$207$	−22.5346	−	2.31689i	−1.56626	−	0.161035i
$208$	16.1614	+	6.36371i	1.12059	+	0.441244i
$209$			8.49893i			0.587884i
$210$	0.147314	+	0.0476808i	0.0101656	+	0.00329029i
$211$	−5.21930	−	9.04009i	−0.359311	−	0.622346i	0.628535	−	0.777782i	$-0.283655\pi$
$211$	−5.21930	−	9.04009i	−0.359311	−	0.622346i	−0.987846	+	0.155436i	$0.950322\pi$
$212$	−0.897646	+	1.55477i	−0.0616506	+	0.106782i
$213$	11.8796	+	13.1636i	0.813976	+	0.901955i
$214$	35.9693	−	9.63794i	2.45881	−	0.658836i
$215$	0.386892	−	0.103667i	0.0263858	−	0.00707005i
$216$	−4.44523	+	3.25278i	−0.302460	+	0.221324i
$217$	5.32944	−	9.23087i	0.361786	−	0.626632i
$218$	−5.47329	−	9.48002i	−0.370698	−	0.642068i
$219$	−2.52167	+	7.79090i	−0.170398	+	0.526461i
$220$		−	0.158104i		−	0.0106594i
$221$	−1.44046	−	9.62982i	−0.0968959	−	0.647772i
$222$	−23.3446	−	1.19692i	−1.56678	−	0.0803323i
$223$	−3.05008	+	11.3830i	−0.204248	+	0.762265i	0.785429	+	0.618952i	$0.212442\pi$
$223$	−3.05008	+	11.3830i	−0.204248	+	0.762265i	−0.989677	+	0.143313i	$0.954224\pi$
$224$	−5.88751	+	3.39916i	−0.393376	+	0.227116i
$225$	12.1495	+	8.78517i	0.809969	+	0.585678i
$226$	3.13498	+	3.13498i	0.208536	+	0.208536i
$227$	2.09816	+	7.83043i	0.139260	+	0.519724i	0.999944	+	0.0105849i	$0.00336934\pi$
$227$	2.09816	+	7.83043i	0.139260	+	0.519724i	−0.860684	+	0.509139i	$0.829964\pi$
$228$	8.95798	−	1.91468i	0.593256	−	0.126803i
$229$	−14.2165	+	14.2165i	−0.939453	+	0.939453i	−0.998269	−	0.0588156i	$-0.981268\pi$
$229$	−14.2165	+	14.2165i	−0.939453	+	0.939453i	0.0588156	+	0.998269i	$0.481268\pi$
$230$	0.584602	+	0.337520i	0.0385475	+	0.0222554i
$231$	−3.53796	+	1.80773i	−0.232780	+	0.118940i
$232$	−5.73412	−	1.53645i	−0.376464	−	0.100873i
$233$	13.8572			0.907817			0.453909	−	0.891048i	$-0.350029\pi$
$233$	13.8572			0.907817			0.453909	+	0.891048i	$0.350029\pi$
$234$	4.28740	−	19.5608i	0.280276	−	1.27873i
$235$	−0.0363534			−0.00237143
$236$	−1.31114	−	0.351320i	−0.0853482	−	0.0228690i
$237$	3.64189	−	1.86084i	0.236566	−	0.120874i
$238$	4.32977	+	2.49979i	0.280657	+	0.162038i
$239$	10.5059	−	10.5059i	0.679568	−	0.679568i	−0.280335	−	0.959902i	$-0.590445\pi$
$239$	10.5059	−	10.5059i	0.679568	−	0.679568i	0.959902	+	0.280335i	$0.0904454\pi$
$240$	0.394004	−	0.0842147i	0.0254329	−	0.00543604i
$241$	−3.96011	−	14.7793i	−0.255093	−	0.952022i	−0.968038	−	0.250802i	$-0.919306\pi$
$241$	−3.96011	−	14.7793i	−0.255093	−	0.952022i	0.712945	−	0.701220i	$-0.247361\pi$
$242$	−7.51196	−	7.51196i	−0.482887	−	0.482887i
$243$	11.0850	+	10.9601i	0.711100	+	0.703091i
$244$	−1.78512	+	1.03064i	−0.114281	+	0.0659799i
$245$	−0.0124977	+	0.0466421i	−0.000798450	+	0.00297986i
$246$	−3.51724	−	0.180336i	−0.224251	−	0.0114978i
$247$	7.94485	−	10.7398i	0.505519	−	0.683355i
$248$		−	11.2991i		−	0.717491i
$249$	6.64397	−	20.5271i	0.421044	−	1.30085i
$250$	−0.446875	−	0.774010i	−0.0282629	−	0.0489527i
$251$	10.5330	−	18.2437i	0.664836	−	1.15153i	−0.314494	−	0.949259i	$-0.601835\pi$
$251$	10.5330	−	18.2437i	0.664836	−	1.15153i	0.979330	−	0.202270i	$-0.0648318\pi$
$252$	2.70242	+	3.32179i	0.170236	+	0.209253i
$253$	−16.7309	+	4.48302i	−1.05186	+	0.281845i
$254$	9.78796	−	2.62268i	0.614151	−	0.164561i
$255$	−0.151322	−	0.167678i	−0.00947618	−	0.0105004i
$256$	−10.4796	+	18.1512i	−0.654974	+	1.13445i
$257$	9.39894	+	16.2794i	0.586290	+	1.01548i	0.994713	+	0.102691i	$0.0327454\pi$
$257$	9.39894	+	16.2794i	0.586290	+	1.01548i	−0.408423	+	0.912793i	$0.633921\pi$
$258$	25.3058	+	8.19068i	1.57547	+	0.509929i
$259$		−	7.28975i		−	0.452963i
$260$	−0.147797	+	0.199790i	−0.00916596	+	0.0123904i
$261$	−1.71824	+	16.7121i	−0.106357	+	1.03445i
$262$	−4.19060	+	15.6395i	−0.258896	+	0.966214i
$263$	6.34138	−	3.66120i	0.391026	−	0.225759i	−0.291578	−	0.956547i	$-0.594180\pi$
$263$	6.34138	−	3.66120i	0.391026	−	0.225759i	0.682605	+	0.730788i	$0.260847\pi$
$264$	−2.28983	+	3.53479i	−0.140929	+	0.217551i
$265$	0.0429445	+	0.0429445i	0.00263806	+	0.00263806i
$266$	1.77534	+	6.62566i	0.108853	+	0.406245i
$267$	−1.70394	−	7.97200i	−0.104279	−	0.487878i
$268$	10.6288	−	10.6288i	0.649255	−	0.649255i
$269$	19.7713	+	11.4150i	1.20548	+	0.695983i	0.961768	−	0.273865i	$-0.0883020\pi$
$269$	19.7713	+	11.4150i	1.20548	+	0.695983i	0.243710	+	0.969848i	$0.421635\pi$
$270$	−0.167940	−	0.433093i	−0.0102205	−	0.0263572i
$271$	22.4615	+	6.01854i	1.36444	+	0.365600i	0.865445	−	0.501005i	$-0.167036\pi$
$271$	22.4615	+	6.01854i	1.36444	+	0.365600i	0.498995	+	0.866605i	$0.333703\pi$
$272$	13.0094			0.788811
$273$	6.16065	+	1.02295i	0.372859	+	0.0619116i
$274$	0.735868			0.0444554
$275$	11.0732	+	2.96705i	0.667739	+	0.178920i
$276$	8.49437	+	16.6246i	0.511301	+	1.00068i
$277$	−23.9869	−	13.8489i	−1.44124	−	0.832098i	−0.443303	−	0.896372i	$-0.646194\pi$
$277$	−23.9869	−	13.8489i	−1.44124	−	0.832098i	−0.997932	+	0.0642738i	$0.979527\pi$
$278$	−0.513995	+	0.513995i	−0.0308274	+	0.0308274i
$279$	−31.5716	+	5.07378i	−1.89014	+	0.303759i
$280$	0.0132483	+	0.0494435i	0.000791740	+	0.00295481i
$281$	11.6304	+	11.6304i	0.693810	+	0.693810i	0.963068	−	0.269258i	$-0.0867786\pi$
$281$	11.6304	+	11.6304i	0.693810	+	0.693810i	−0.269258	+	0.963068i	$0.586779\pi$
$282$	−2.02611	−	1.31251i	−0.120653	−	0.0781590i
$283$	−27.0500	+	15.6173i	−1.60796	+	0.928354i	−0.618130	+	0.786076i	$0.712109\pi$
$283$	−27.0500	+	15.6173i	−1.60796	+	0.928354i	−0.989827	+	0.142278i	$0.954557\pi$
$284$	3.78205	−	14.1148i	0.224423	−	0.837560i
$285$	0.0158675	−	0.309477i	0.000939910	−	0.0183318i
$286$	−2.26514	−	15.1430i	−0.133940	−	0.895422i
$287$		−	1.09832i		−	0.0648318i
$288$	19.0568	+	7.26574i	1.12293	+	0.428138i
$289$	4.85353	+	8.40655i	0.285501	+	0.494503i
$290$	0.250311	−	0.433551i	0.0146988	−	0.0254590i
$291$	9.61502	−	8.67714i	0.563643	−	0.508663i
$292$	6.51857	−	1.74665i	0.381470	−	0.102215i
$293$	−16.3834	+	4.38992i	−0.957129	+	0.256462i	−0.703385	−	0.710809i	$-0.748329\pi$
$293$	−16.3834	+	4.38992i	−0.957129	+	0.256462i	−0.253744	+	0.967271i	$0.581662\pi$
$294$	−2.38053	+	2.14832i	−0.138835	+	0.125293i
$295$	−0.0229596	+	0.0397672i	−0.00133676	+	0.00231533i
$296$	−3.86379	−	6.69227i	−0.224578	−	0.388981i
$297$	10.9051	+	4.81091i	0.632775	+	0.279157i
$298$			18.5201i			1.07284i
$299$	25.3329	+	9.97509i	1.46504	+	0.576874i
$300$	0.632683	−	12.3397i	0.0365280	−	0.712434i
$301$	−2.14688	+	8.01226i	−0.123744	+	0.461819i
$302$	−16.7994	+	9.69913i	−0.966696	+	0.558122i
$303$	−22.7753	−	14.7538i	−1.30841	−	0.847584i
$304$	12.6210	+	12.6210i	0.723864	+	0.723864i
$305$	0.0180476	+	0.0673547i	0.00103340	+	0.00385672i
$306$	−2.37988	−	14.8088i	−0.136048	−	0.846560i
$307$	−1.27928	+	1.27928i	−0.0730123	+	0.0730123i	−0.742670	−	0.669658i	$-0.766441\pi$
$307$	−1.27928	+	1.27928i	−0.0730123	+	0.0730123i	0.669658	+	0.742670i	$0.266441\pi$
$308$	2.83556	+	1.63711i	0.161571	+	0.0932832i
$309$	−8.78356	−	17.1905i	−0.499679	−	0.977936i
$310$	0.920392	+	0.246618i	0.0522747	+	0.0140070i
$311$	−14.2101			−0.805781			−0.402891	−	0.915248i	$-0.631994\pi$
$311$	−14.2101			−0.805781			−0.402891	+	0.915248i	$0.631994\pi$
$312$	6.19791	−	2.32622i	0.350888	−	0.131697i
$313$	−6.84212			−0.386740			−0.193370	−	0.981126i	$-0.561942\pi$
$313$	−6.84212			−0.386740			−0.193370	+	0.981126i	$0.561942\pi$
$314$	−17.0169	−	4.55967i	−0.960321	−	0.257317i
$315$	0.132205	−	0.0592205i	0.00744889	−	0.00333670i
$316$	−2.91887	−	1.68521i	−0.164199	−	0.0948004i
$317$	−15.5600	+	15.5600i	−0.873939	+	0.873939i	−0.992899	−	0.118960i	$-0.962044\pi$
$317$	−15.5600	+	15.5600i	−0.873939	+	0.873939i	0.118960	+	0.992899i	$0.462044\pi$
$318$	0.842982	+	3.94395i	0.0472721	+	0.221165i
$319$	3.32469	+	12.4079i	0.186147	+	0.694709i
$320$	−0.100768	−	0.100768i	−0.00563312	−	0.00563312i
$321$	18.9416	−	29.2399i	1.05722	−	1.63201i
$322$	−12.1067	+	6.98981i	−0.674680	+	0.389527i
$323$	2.58971	−	9.66492i	0.144095	−	0.537770i
$324$	2.61401	−	12.5779i	0.145223	−	0.698771i
$325$	−11.2191	−	14.1006i	−0.622326	−	0.782163i
$326$		−	19.7474i		−	1.09371i
$327$	−9.74367	−	3.15371i	−0.538826	−	0.174401i
$328$	−0.582143	−	1.00830i	−0.0321435	−	0.0556741i
$329$	0.376426	−	0.651990i	0.0207531	−	0.0359453i
$330$	−0.237956	−	0.263675i	−0.0130990	−	0.0145149i
$331$	−5.28657	+	1.41653i	−0.290576	+	0.0778597i	−0.401163	−	0.916007i	$-0.631394\pi$
$331$	−5.28657	+	1.41653i	−0.290576	+	0.0778597i	0.110586	+	0.993867i	$0.464727\pi$
$332$	−17.1748	+	4.60198i	−0.942591	+	0.252566i
$333$	−16.9644	+	13.8012i	−0.929642	+	0.756302i
$334$	−21.1815	+	36.6875i	−1.15900	+	2.00745i
$335$	−0.254247	−	0.440368i	−0.0138910	−	0.0240599i
$336$	−2.56940	+	7.93839i	−0.140172	+	0.433075i
$337$		−	9.64140i		−	0.525200i	−0.964905	−	0.262600i	$-0.915420\pi$
$337$		−	9.64140i		−	0.525200i	0.964905	−	0.262600i	$-0.0845800\pi$
$338$	−11.2934	+	21.2530i	−0.614278	+	1.15601i
$339$	4.14245	+	0.212392i	0.224987	+	0.0115355i
$340$	−0.0481759	+	0.179795i	−0.00261270	+	0.00975074i
$341$	−21.1741	+	12.2249i	−1.14664	+	0.662013i
$342$	12.0578	−	16.6754i	0.652011	−	0.901705i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	2.27582	+	8.49348i	0.122704	+	0.457938i
$345$	0.617600	−	0.132006i	0.0332505	−	0.00710698i
$346$	−4.95022	+	4.95022i	−0.266126	+	0.266126i
$347$	−12.9014	−	7.44865i	−0.692585	−	0.399864i	0.111994	−	0.993709i	$-0.464276\pi$
$347$	−12.9014	−	7.44865i	−0.692585	−	0.399864i	−0.804580	+	0.593844i	$0.797609\pi$
$348$	12.3291	−	6.29957i	0.660907	−	0.337693i
$349$	−10.9754	−	2.94085i	−0.587500	−	0.157420i	−0.0471898	−	0.998886i	$-0.515027\pi$
$349$	−10.9754	−	2.94085i	−0.587500	−	0.157420i	−0.540311	+	0.841466i	$0.681693\pi$
$350$	9.25231			0.494557
$351$	−9.28302	−	16.2735i	−0.495491	−	0.868613i
$352$	15.5942			0.831174
$353$	−19.2775	−	5.16538i	−1.02604	−	0.274926i	−0.293721	−	0.955891i	$-0.594894\pi$
$353$	−19.2775	−	5.16538i	−1.02604	−	0.274926i	−0.732315	+	0.680966i	$0.761560\pi$
$354$	−2.71539	+	1.38744i	−0.144322	+	0.0737415i
$355$	−0.428104	−	0.247166i	−0.0227214	−	0.0131182i
$356$	−4.75050	+	4.75050i	−0.251776	+	0.251776i
$357$	4.57416	−	0.977685i	0.242090	−	0.0517446i
$358$	−7.55893	−	28.2103i	−0.399502	−	1.49096i
$359$	11.2418	+	11.2418i	0.593318	+	0.593318i	0.938526	−	0.345208i	$-0.112192\pi$
$359$	11.2418	+	11.2418i	0.593318	+	0.593318i	−0.345208	+	0.938526i	$0.612192\pi$
$360$	0.0899804	−	0.124439i	0.00474238	−	0.00655852i
$361$	−4.56574	+	2.63603i	−0.240302	+	0.138738i
$362$	−3.04516	+	11.3647i	−0.160050	+	0.597315i
$363$	−9.92604	−	0.508929i	−0.520982	−	0.0267118i
$364$	−2.05281	−	4.71946i	−0.107596	−	0.247367i
$365$		−	0.228295i		−	0.0119495i
$366$	−1.42593	+	4.40553i	−0.0745346	+	0.230281i
$367$	−10.2973	−	17.8354i	−0.537512	−	0.930999i	−0.999037	−	0.0438714i	$-0.986031\pi$
$367$	−10.2973	−	17.8354i	−0.537512	−	0.930999i	0.461525	−	0.887127i	$-0.347303\pi$
$368$	−18.1881	+	31.5028i	−0.948123	+	1.64220i
$369$	−2.55596	+	2.07938i	−0.133058	+	0.108248i
$370$	0.629468	−	0.168665i	0.0327245	−	0.00876850i
$371$	−1.21488	+	0.325525i	−0.0630732	+	0.0169004i
$372$	17.6553	+	19.5636i	0.915387	+	1.01433i
$373$	7.14319	−	12.3724i	0.369860	−	0.640617i	−0.619683	−	0.784852i	$-0.712739\pi$
$373$	7.14319	−	12.3724i	0.369860	−	0.640617i	0.989543	+	0.144235i	$0.0460722\pi$
$374$	−5.73411	−	9.93177i	−0.296504	−	0.513560i
$375$	−0.795536	−	0.257489i	−0.0410813	−	0.0132967i
$376$		−	0.798069i		−	0.0411573i
$377$	7.39770	−	18.7873i	0.381001	−	0.967595i
$378$	9.50639	+	1.47257i	0.488956	+	0.0757408i
$379$	−7.44584	+	27.7882i	−0.382467	+	1.42739i	0.459654	+	0.888098i	$0.347973\pi$
$379$	−7.44584	+	27.7882i	−0.382467	+	1.42739i	−0.842121	+	0.539288i	$0.818693\pi$
$380$	−0.221164	+	0.127689i	−0.0113455	+	0.00655032i
$381$	5.15438	−	7.95677i	0.264067	−	0.407638i
$382$	16.8397	+	16.8397i	0.861592	+	0.861592i
$383$	−7.46822	−	27.8718i	−0.381608	−	1.42418i	−0.843445	−	0.537216i	$-0.819476\pi$
$383$	−7.46822	−	27.8718i	−0.381608	−	1.42418i	0.461837	−	0.886965i	$-0.347191\pi$
$384$	2.94438	+	13.7755i	0.150255	+	0.702977i
$385$	0.0783216	−	0.0783216i	0.00399164	−	0.00399164i
$386$	19.7087	+	11.3788i	1.00314	+	0.579166i
$387$	22.7103	−	10.1730i	1.15443	−	0.517122i
$388$	−10.3098	−	2.76250i	−0.523401	−	0.140245i
$389$	30.8783			1.56559			0.782797	−	0.622278i	$-0.213793\pi$
$389$	30.8783			1.56559			0.782797	+	0.622278i	$0.213793\pi$
$390$	0.0542098	+	0.555639i	0.00274502	+	0.0281359i
$391$	20.3922			1.03128
$392$	−1.02394	−	0.274364i	−0.0517168	−	0.0138575i
$393$	6.89237	+	13.4893i	0.347674	+	0.680443i
$394$	−34.8738	−	20.1344i	−1.75692	−	1.01436i
$395$	−0.0806225	+	0.0806225i	−0.00405656	+	0.00405656i
$396$	−1.55858	−	9.69824i	−0.0783216	−	0.487355i
$397$	−0.971565	−	3.62593i	−0.0487615	−	0.181980i	0.937250	−	0.348658i	$-0.113363\pi$
$397$	−0.971565	−	3.62593i	−0.0487615	−	0.181980i	−0.986011	+	0.166678i	$0.946696\pi$
$398$	−22.3974	−	22.3974i	−1.12268	−	1.12268i
$399$	5.38609	+	3.48910i	0.269642	+	0.174674i
$400$	20.8499	−	12.0377i	1.04250	−	0.601885i
$401$	0.0231409	−	0.0863631i	0.00115560	−	0.00431277i	−0.965346	−	0.260975i	$-0.915956\pi$
$401$	0.0231409	−	0.0863631i	0.00115560	−	0.00431277i	0.966501	+	0.256662i	$0.0826227\pi$
$402$	1.72904	−	33.7228i	0.0862367	−	1.68194i
$403$	38.1847	+	4.34558i	1.90211	+	0.216469i
$404$			22.3635i			1.11263i
$405$	−0.388110	−	0.195542i	−0.0192853	−	0.00971657i
$406$	5.18377	+	8.97854i	0.257266	+	0.445598i
$407$	−8.36073	+	14.4812i	−0.414426	+	0.717807i
$408$	3.68106	−	3.32200i	0.182240	−	0.164463i
$409$	−8.14317	+	2.18196i	−0.402654	+	0.107891i	−0.454462	−	0.890766i	$-0.650168\pi$
$409$	−8.14317	+	2.18196i	−0.402654	+	0.107891i	0.0518077	+	0.998657i	$0.483502\pi$
$410$	0.0948397	−	0.0254122i	0.00468380	−	0.00125502i
$411$	0.511102	−	0.461248i	0.0252108	−	0.0227517i
$412$	−7.95456	+	13.7777i	−0.391893	+	0.678779i
$413$	−0.475477	−	0.823550i	−0.0233967	−	0.0405243i
$414$	39.1872	+	14.9408i	1.92595	+	0.734300i
$415$			0.601500i			0.0295265i
$416$	−19.7058	−	14.5775i	−0.966155	−	0.714723i
$417$	−0.0348227	+	0.679175i	−0.00170528	+	0.0332593i
$418$	4.07233	−	15.1982i	0.199184	−	0.743366i
$419$	0.412833	−	0.238349i	0.0201682	−	0.0116441i	−0.489882	−	0.871789i	$-0.662960\pi$
$419$	0.412833	−	0.238349i	0.0201682	−	0.0116441i	0.510050	+	0.860145i	$0.329627\pi$
$420$	−0.100197	−	0.0649072i	−0.00488909	−	0.00316715i
$421$	2.46899	+	2.46899i	0.120331	+	0.120331i	0.764708	−	0.644377i	$-0.222883\pi$
$421$	2.46899	+	2.46899i	0.120331	+	0.120331i	−0.644377	+	0.764708i	$0.722883\pi$
$422$	5.00174	+	18.6668i	0.243481	+	0.908683i
$423$	−2.22995	+	0.358369i	−0.108424	+	0.0174245i
$424$	−0.942765	+	0.942765i	−0.0457847	+	0.0457847i
$425$	−11.6883	−	6.74822i	−0.566964	−	0.327337i
$426$	−14.9361	−	29.2319i	−0.723658	−	1.41629i
$427$	−1.39487	−	0.373754i	−0.0675024	−	0.0180872i
$428$	−28.7113			−1.38781
$429$	−11.0650	−	9.09785i	−0.534223	−	0.439248i
$430$	−0.741529			−0.0357597
$431$	−26.0902	−	6.99084i	−1.25672	−	0.336737i	−0.431791	−	0.901974i	$-0.642118\pi$
$431$	−26.0902	−	6.99084i	−1.25672	−	0.336737i	−0.824929	+	0.565237i	$0.808785\pi$
$432$	23.3384	−	9.04986i	1.12287	−	0.435412i
$433$	17.6495	+	10.1899i	0.848179	+	0.489697i	0.860036	−	0.510233i	$-0.170441\pi$
$433$	17.6495	+	10.1899i	0.848179	+	0.489697i	−0.0118568	+	0.999930i	$0.503774\pi$
$434$	−13.9534	+	13.9534i	−0.669784	+	0.669784i
$435$	−0.0978982	−	0.458023i	−0.00469386	−	0.0219605i
$436$	2.18444	+	8.15242i	0.104615	+	0.390430i
$437$	19.7834	+	19.7834i	0.946367	+	0.946367i
$438$	8.24243	−	12.7238i	0.393838	−	0.607964i
$439$	9.84557	−	5.68434i	0.469904	−	0.271299i	−0.246296	−	0.969195i	$-0.579213\pi$
$439$	9.84557	−	5.68434i	0.469904	−	0.271299i	0.716199	+	0.697896i	$0.245880\pi$
$440$	0.0303895	−	0.113415i	0.00144876	−	0.00540685i
$441$	−0.306826	+	2.98427i	−0.0146108	+	0.142108i
$442$	−2.03831	+	17.9107i	−0.0969526	+	0.851923i
$443$			11.4779i			0.545330i	0.962109	+	0.272665i	$0.0879050\pi$
$443$			11.4779i			0.545330i	−0.962109	+	0.272665i	$0.912095\pi$
$444$	17.1469	+	5.54991i	0.813757	+	0.263387i
$445$	0.113635	+	0.196821i	0.00538681	+	0.00933022i
$446$	10.9086	−	18.8942i	0.516535	−	0.894665i
$447$	11.6085	+	12.8633i	0.549065	+	0.608411i
$448$	2.85068	−	0.763837i	0.134682	−	0.0360879i
$449$	−21.0864	+	5.65010i	−0.995131	+	0.266645i	−0.719404	−	0.694591i	$-0.755585\pi$
$449$	−21.0864	+	5.65010i	−0.995131	+	0.266645i	−0.275727	+	0.961236i	$0.588918\pi$
$450$	−17.5168	−	21.5316i	−0.825751	−	1.01501i
$451$	−1.25968	+	2.18183i	−0.0593161	+	0.102738i
$452$	−1.70916	−	2.96036i	−0.0803923	−	0.139244i
$453$	−5.58864	+	17.2666i	−0.262577	+	0.811255i
$454$		−	15.0081i		−	0.704363i
$455$	−0.172187	+	0.0257564i	−0.00807226	+	0.00120748i
$456$	6.79397	+	0.348341i	0.318157	+	0.0163126i
$457$	4.38993	−	16.3834i	0.205352	−	0.766384i	−0.783990	−	0.620774i	$-0.786819\pi$
$457$	4.38993	−	16.3834i	0.205352	−	0.766384i	0.989342	−	0.145611i	$-0.0465147\pi$
$458$	32.2345	−	18.6106i	1.50622	−	0.869617i
$459$	−10.9352	−	8.79380i	−0.510412	−	0.410459i
$460$	−0.368027	−	0.368027i	−0.0171593	−	0.0171593i
$461$	−9.27056	−	34.5982i	−0.431773	−	1.61140i	−0.748672	−	0.662940i	$-0.769308\pi$
$461$	−9.27056	−	34.5982i	−0.431773	−	1.61140i	0.316899	−	0.948459i	$-0.397358\pi$
$462$	7.19291	−	1.53742i	0.334644	−	0.0715271i
$463$	−22.6918	+	22.6918i	−1.05458	+	1.05458i	−0.0561566	+	0.998422i	$0.517885\pi$
$463$	−22.6918	+	22.6918i	−1.05458	+	1.05458i	−0.998422	+	0.0561566i	$0.982115\pi$
$464$	23.3630	+	13.4887i	1.08460	+	0.626195i
$465$	0.793847	−	0.405619i	0.0368138	−	0.0188101i
$466$	−24.7801	−	6.63980i	−1.14792	−	0.307583i
$467$	−27.9767			−1.29461			−0.647303	−	0.762233i	$-0.724103\pi$
$467$	−27.9767			−1.29461			−0.647303	+	0.762233i	$0.724103\pi$
$468$	−7.09646	+	13.7123i	−0.328034	+	0.633849i
$469$	10.5305			0.486256
$470$	0.0650086	+	0.0174190i	0.00299862	+	0.000803479i
$471$	−14.6773	+	7.49940i	−0.676293	+	0.345554i
$472$	−0.873013	−	0.504034i	−0.0401837	−	0.0232001i
$473$	13.4542	−	13.4542i	0.618625	−	0.618625i
$474$	−7.40422	+	1.58258i	−0.340087	+	0.0726905i
$475$	−4.79255	−	17.8860i	−0.219897	−	0.820667i
$476$	−2.72574	−	2.72574i	−0.124934	−	0.124934i
$477$	3.05760	+	2.21091i	0.139998	+	0.101231i
$478$	−23.8210	+	13.7531i	−1.08955	+	0.629050i
$479$	−5.20248	+	19.4159i	−0.237707	+	0.887136i	0.739202	+	0.673484i	$0.235203\pi$
$479$	−5.20248	+	19.4159i	−0.237707	+	0.887136i	−0.976910	+	0.213653i	$0.931464\pi$
$480$	−0.567840	−	0.0291144i	−0.0259183	−	0.00132888i
$481$	24.1022	−	10.4837i	1.09897	−	0.478014i
$482$			28.3266i			1.29024i
$483$	−4.02753	+	12.4434i	−0.183259	+	0.566194i
$484$	4.09546	+	7.09354i	0.186157	+	0.322434i
$485$	−0.180536	+	0.312698i	−0.00819772	+	0.0141989i
$486$	−14.5710	−	24.9108i	−0.660952	−	1.12998i
$487$	30.0274	−	8.04581i	1.36067	−	0.364590i	0.496608	−	0.867975i	$-0.334579\pi$
$487$	30.0274	−	8.04581i	1.36067	−	0.364590i	0.864062	+	0.503385i	$0.167912\pi$
$488$	−1.47864	+	0.396202i	−0.0669351	+	0.0179352i
$489$	−12.3779	−	13.7157i	−0.559746	−	0.620247i
$490$	0.0446979	−	0.0774191i	0.00201925	−	0.00349744i
$491$	14.8395	+	25.7028i	0.669698	+	1.15995i	0.977989	+	0.208659i	$0.0669097\pi$
$491$	14.8395	+	25.7028i	0.669698	+	1.15995i	−0.308291	+	0.951292i	$0.599757\pi$
$492$	2.58346	+	0.836185i	0.116472	+	0.0376981i
$493$		−	15.1232i		−	0.681116i
$494$	−19.3534	+	15.3985i	−0.870749	+	0.692810i
$495$	−0.330548	−	0.0339851i	−0.0148570	−	0.00152752i
$496$	−13.2897	+	49.5977i	−0.596724	+	2.22700i
$497$	8.86573	−	5.11863i	0.397683	−	0.229602i
$498$	−21.7168	+	33.5239i	−0.973151	+	1.50224i
$499$	23.9310	+	23.9310i	1.07130	+	1.07130i	0.997255	+	0.0740423i	$0.0235900\pi$
$499$	23.9310	+	23.9310i	1.07130	+	1.07130i	0.0740423	+	0.997255i	$0.476410\pi$
$500$	0.178351	+	0.665617i	0.00797612	+	0.0297673i
$501$	8.28422	+	38.7583i	0.370112	+	1.73159i
$502$	−27.5771	+	27.5771i	−1.23083	+	1.23083i
$503$	−12.5134	−	7.22462i	−0.557946	−	0.322130i	0.194375	−	0.980927i	$-0.437732\pi$
$503$	−12.5134	−	7.22462i	−0.557946	−	0.322130i	−0.752320	+	0.658797i	$0.771065\pi$
$504$	1.30007	+	2.90230i	0.0579099	+	0.129279i
$505$	0.730754	+	0.195805i	0.0325181	+	0.00871321i
$506$	32.0669			1.42555
$507$	5.47768	+	21.8402i	0.243272	+	0.969958i
$508$	−7.81291			−0.346642
$509$	−21.2723	−	5.69990i	−0.942878	−	0.252643i	−0.245541	−	0.969386i	$-0.578965\pi$
$509$	−21.2723	−	5.69990i	−0.942878	−	0.252643i	−0.697338	+	0.716743i	$0.745632\pi$
$510$	0.190257	+	0.372357i	0.00842471	+	0.0164882i
$511$	4.09442	+	2.36391i	0.181126	+	0.104573i
$512$	15.9356	−	15.9356i	0.704262	−	0.704262i
$513$	−2.07747	−	19.1400i	−0.0917226	−	0.845050i
$514$	−9.00716	−	33.6152i	−0.397289	−	1.48270i
$515$	0.380556	+	0.380556i	0.0167693	+	0.0167693i
$516$	−17.2119	−	11.1499i	−0.757712	−	0.490845i
$517$	−1.49556	+	0.863459i	−0.0657744	+	0.0379749i
$518$	−3.49294	+	13.0358i	−0.153471	+	0.572762i
$519$	−0.335373	+	6.54105i	−0.0147213	+	0.287120i
$520$	−0.144423	+	0.114910i	−0.00633337	+	0.00503913i
$521$		−	28.0902i		−	1.23065i	−0.788272	−	0.615326i	$-0.789024\pi$
$521$		−	28.0902i		−	1.23065i	0.788272	−	0.615326i	$-0.210976\pi$
$522$	11.0804	−	29.0619i	0.484974	−	1.27201i
$523$	−21.3032	−	36.8983i	−0.931525	−	1.61345i	−0.780716	−	0.624886i	$-0.785145\pi$
$523$	−21.3032	−	36.8983i	−0.931525	−	1.61345i	−0.150809	−	0.988563i	$-0.548188\pi$
$524$	6.24187	−	10.8112i	0.272677	−	0.472291i
$525$	6.42626	−	5.79942i	0.280465	−	0.253107i
$526$	−13.0942	+	3.50859i	−0.570935	+	0.152982i
$527$	27.8040	−	7.45006i	1.21116	−	0.324530i
$528$	14.2088	−	12.8229i	0.618360	−	0.558043i
$529$	−17.0099	+	29.4619i	−0.739559	+	1.28095i
$530$	−0.0562180	−	0.0973724i	−0.00244195	−	0.00422959i
$531$	−1.01634	+	2.66569i	−0.0441053	+	0.115681i
$532$		−	5.28871i		−	0.229295i
$533$	3.63140	−	1.57954i	0.157293	−	0.0684173i
$534$	−0.772789	+	15.0723i	−0.0334419	+	0.652243i
$535$	−0.251383	+	0.938174i	−0.0108682	+	0.0405608i
$536$	9.66746	−	5.58151i	0.417571	−	0.241084i
$537$	−22.9326	−	14.8557i	−0.989614	−	0.641070i
$538$	−29.8863	−	29.8863i	−1.28849	−	1.28849i
$539$	0.593688	+	2.21567i	0.0255719	+	0.0954358i
$540$	0.0386468	+	0.356058i	0.00166310	+	0.0153223i
$541$	−28.1310	+	28.1310i	−1.20945	+	1.20945i	−0.238240	+	0.971206i	$0.576570\pi$
$541$	−28.1310	+	28.1310i	−1.20945	+	1.20945i	−0.971206	+	0.238240i	$0.923430\pi$
$542$	−37.2828	−	21.5252i	−1.60143	−	0.924588i
$543$	5.00844	+	9.80216i	0.214933	+	0.420651i
$544$	−17.7336	−	4.75170i	−0.760321	−	0.203727i
$545$	0.285516			0.0122302
$546$	−10.5266	−	4.78120i	−0.450496	−	0.204617i
$547$	21.8751			0.935313			0.467657	−	0.883910i	$-0.345098\pi$
$547$	21.8751			0.935313			0.467657	+	0.883910i	$0.345098\pi$
$548$	−0.548035	−	0.146845i	−0.0234109	−	0.00627293i
$549$	1.77103	+	3.95368i	0.0755859	+	0.168739i
$550$	−18.3799	−	10.6116i	−0.783720	−	0.452481i
$551$	14.6717	−	14.6717i	0.625035	−	0.625035i
$552$	2.89795	+	13.5582i	0.123345	+	0.577077i
$553$	−0.611129	−	2.28076i	−0.0259878	−	0.0969880i
$554$	36.2587	+	36.2587i	1.54048	+	1.54048i
$555$	0.331481	−	0.511703i	0.0140706	−	0.0217206i
$556$	0.485365	−	0.280226i	0.0205841	−	0.0118842i
$557$	0.346185	−	1.29198i	0.0146683	−	0.0547429i	−0.958204	−	0.286087i	$-0.907646\pi$
$557$	0.346185	−	1.29198i	0.0146683	−	0.0547429i	0.972872	+	0.231344i	$0.0743122\pi$
$558$	58.8888	+	6.05461i	2.49296	+	0.256312i
$559$	−29.5786	+	4.42447i	−1.25104	+	0.187135i
$560$		−	0.232617i		−	0.00982984i
$561$	−10.2080	−	3.30400i	−0.430981	−	0.139495i
$562$	−15.2251	−	26.3707i	−0.642233	−	1.11238i
$563$	−22.2621	+	38.5591i	−0.938235	+	1.62507i	−0.169474	+	0.985535i	$0.554207\pi$
$563$	−22.2621	+	38.5591i	−0.938235	+	1.62507i	−0.768761	+	0.639536i	$0.779127\pi$
$564$	1.24702	+	1.38181i	0.0525091	+	0.0581846i
$565$	−0.111698	+	0.0299294i	−0.00469916	+	0.00125914i
$566$	55.8552	−	14.9663i	2.34777	−	0.629082i
$567$	7.52575	−	4.93590i	0.316052	−	0.207288i
$568$	5.42606	−	9.39821i	0.227672	−	0.394340i
$569$	8.79358	+	15.2309i	0.368646	+	0.638514i	0.989354	−	0.145528i	$-0.0464881\pi$
$569$	8.79358	+	15.2309i	0.368646	+	0.638514i	−0.620708	+	0.784042i	$0.713155\pi$
$570$	−0.176663	+	0.545816i	−0.00739961	+	0.0228617i
$571$			21.0046i			0.879014i	0.898239	+	0.439507i	$0.144847\pi$
$571$			21.0046i			0.879014i	−0.898239	+	0.439507i	$0.855153\pi$
$572$	−1.33489	+	11.7297i	−0.0558145	+	0.490443i
$573$	22.2513	+	1.14087i	0.929563	+	0.0476606i
$574$	−0.526269	+	1.96406i	−0.0219660	+	0.0819784i
$575$	32.6821	−	18.8690i	1.36294	−	0.786894i
$576$	−7.17458	−	5.18784i	−0.298941	−	0.216160i
$577$	−3.30381	−	3.30381i	−0.137539	−	0.137539i	0.634985	−	0.772524i	$-0.281006\pi$
$577$	−3.30381	−	3.30381i	−0.137539	−	0.137539i	−0.772524	+	0.634985i	$0.781006\pi$
$578$	−4.65121	−	17.3586i	−0.193465	−	0.722021i
$579$	20.8211	−	4.45032i	0.865296	−	0.184949i
$580$	−0.272935	+	0.272935i	−0.0113330	+	0.0113330i
$581$	−10.7878	−	6.22833i	−0.447552	−	0.258395i
$582$	−21.3517	+	10.9097i	−0.885057	+	0.452223i
$583$	2.78672	+	0.746700i	0.115414	+	0.0309251i
$584$	5.01178			0.207389
$585$	0.385931	+	0.351944i	0.0159563	+	0.0145511i
$586$	31.4010			1.29716
$587$	16.7659	+	4.49242i	0.692004	+	0.185422i	0.587647	−	0.809118i	$-0.300055\pi$
$587$	16.7659	+	4.49242i	0.692004	+	0.185422i	0.104358	+	0.994540i	$0.466721\pi$
$588$	2.20160	−	1.12491i	0.0907923	−	0.0463906i
$589$	34.2015	+	19.7462i	1.40925	+	0.813630i
$590$	0.0601121	−	0.0601121i	0.00247478	−	0.00247478i
$591$	−36.8423	+	7.87469i	−1.51549	+	0.323922i
$592$	9.08897	+	33.9205i	0.373554	+	1.39412i
$593$	2.18756	+	2.18756i	0.0898325	+	0.0898325i	0.750595	−	0.660763i	$-0.229767\pi$
$593$	2.18756	+	2.18756i	0.0898325	+	0.0898325i	−0.660763	+	0.750595i	$0.729767\pi$
$594$	−17.1957	−	13.8283i	−0.705548	−	0.567383i
$595$	−0.112932	+	0.0652013i	−0.00462976	+	0.00267299i
$596$	3.69576	−	13.7928i	0.151384	−	0.564973i
$597$	−29.5952	−	1.51741i	−1.21125	−	0.0621033i
$598$	−40.5217	−	29.9763i	−1.65705	−	1.22582i
$599$		−	13.8916i		−	0.567596i	−0.958884	−	0.283798i	$-0.908405\pi$
$599$		−	13.8916i		−	0.567596i	0.958884	−	0.283798i	$-0.0915946\pi$
$600$	2.82569	−	8.73021i	0.115358	−	0.356409i
$601$	20.9959	+	36.3660i	0.856441	+	1.48340i	0.875302	+	0.483577i	$0.160663\pi$
$601$	20.9959	+	36.3660i	0.856441	+	1.48340i	−0.0188614	+	0.999822i	$0.506004\pi$
$602$	7.67828	−	13.2992i	0.312943	−	0.542033i
$603$	−19.9368	−	24.5062i	−0.811890	−	0.997970i
$604$	14.4468	−	3.87100i	0.587831	−	0.157509i
$605$	0.267648	−	0.0717160i	0.0108814	−	0.00291567i
$606$	33.6584	+	37.2964i	1.36728	+	1.51506i
$607$	−5.33586	+	9.24198i	−0.216576	+	0.375120i	−0.953759	−	0.300573i	$-0.902822\pi$
$607$	−5.33586	+	9.24198i	−0.216576	+	0.375120i	0.737183	+	0.675693i	$0.236156\pi$
$608$	−12.5943	−	21.8140i	−0.510766	−	0.884673i
$609$	9.22824	+	2.98689i	0.373947	+	0.121035i
$610$		−	0.129094i		−	0.00522687i
$611$	2.69704	+	0.306935i	0.109111	+	0.0124173i
$612$	−1.18274	+	11.5037i	−0.0478096	+	0.465008i
$613$	7.05964	−	26.3469i	0.285136	−	1.06414i	−0.663603	−	0.748085i	$-0.730974\pi$
$613$	7.05964	−	26.3469i	0.285136	−	1.06414i	0.948740	−	0.316059i	$-0.102360\pi$
$614$	2.90064	−	1.67468i	0.117060	−	0.0675848i
$615$	0.0499430	−	0.0770965i	0.00201390	−	0.00310883i
$616$	1.71940	+	1.71940i	0.0692767	+	0.0692767i
$617$	0.379408	+	1.41597i	0.0152744	+	0.0570048i	0.973142	−	0.230204i	$-0.0739393\pi$
$617$	0.379408	+	1.41597i	0.0152744	+	0.0570048i	−0.957868	+	0.287209i	$0.907273\pi$
$618$	7.47015	+	34.9496i	0.300493	+	1.40588i
$619$	18.8189	−	18.8189i	0.756397	−	0.756397i	−0.219268	−	0.975665i	$-0.570367\pi$
$619$	18.8189	−	18.8189i	0.756397	−	0.756397i	0.975665	+	0.219268i	$0.0703668\pi$
$620$	−0.636244	−	0.367336i	−0.0255522	−	0.0147526i
$621$	36.5828	−	14.1856i	1.46802	−	0.569250i
$622$	25.4111	+	6.80889i	1.01889	+	0.273012i
$623$	−4.70660			−0.188566
$624$	−29.9420	+	2.92124i	−1.19864	+	0.116943i
$625$	−24.9650			−0.998601
$626$	12.2354	+	3.27846i	0.489024	+	0.131034i
$627$	−6.69786	−	13.1086i	−0.267487	−	0.523505i
$628$	11.7634	+	6.79160i	0.469410	+	0.271014i
$629$	13.9203	−	13.9203i	0.555039	−	0.555039i
$630$	−0.264790	+	0.0425537i	−0.0105495	+	0.00169538i
$631$	−1.00783	−	3.76129i	−0.0401213	−	0.149735i	0.942959	−	0.332908i	$-0.108030\pi$
$631$	−1.00783	−	3.76129i	−0.0401213	−	0.149735i	−0.983081	+	0.183173i	$0.941363\pi$
$632$	−1.76991	−	1.76991i	−0.0704034	−	0.0704034i
$633$	15.1745	+	9.82999i	0.603131	+	0.390707i
$634$	35.2808	−	20.3694i	1.40118	−	0.808972i
$635$	−0.0684064	+	0.255296i	−0.00271462	+	0.0101311i
$636$	0.159223	−	3.10546i	0.00631361	−	0.123139i
$637$	1.32100	−	3.35484i	0.0523401	−	0.132924i
$638$		−	23.7814i		−	0.941514i
$639$	−28.6968	−	10.9411i	−1.13523	−	0.432825i
$640$	−0.196359	−	0.340104i	−0.00776178	−	0.0134438i
$641$	12.7341	−	22.0562i	0.502968	−	0.871167i	−0.497026	−	0.867736i	$-0.665575\pi$
$641$	12.7341	−	22.0562i	0.502968	−	0.871167i	0.999994	−	0.00343095i	$-0.00109211\pi$
$642$	−47.8827	+	43.2121i	−1.88978	+	1.70544i
$643$	14.7689	−	3.95732i	0.582429	−	0.156061i	0.0444382	−	0.999012i	$-0.485850\pi$
$643$	14.7689	−	3.95732i	0.582429	−	0.156061i	0.537991	+	0.842951i	$0.319184\pi$
$644$	10.4113	−	2.78969i	0.410261	−	0.109929i
$645$	−0.515034	+	0.464797i	−0.0202795	+	0.0183013i
$646$	−9.26205	+	16.0423i	−0.364410	+	0.631177i
$647$	−17.9317	−	31.0587i	−0.704970	−	1.22104i	−0.966703	−	0.255903i	$-0.917627\pi$
$647$	−17.9317	−	31.0587i	−0.704970	−	1.22104i	0.261733	−	0.965140i	$-0.415706\pi$
$648$	4.29276	−	8.52022i	0.168635	−	0.334706i
$649$			2.18133i			0.0856247i
$650$	13.3061	+	30.5911i	0.521908	+	1.19988i
$651$	−0.945330	+	18.4375i	−0.0370504	+	0.722623i
$652$	−3.94068	+	14.7068i	−0.154329	+	0.575964i
$653$	22.3150	−	12.8836i	0.873255	−	0.504174i	0.00482650	−	0.999988i	$-0.498464\pi$
$653$	22.3150	−	12.8836i	0.873255	−	0.504174i	0.868429	+	0.495814i	$0.165130\pi$
$654$	15.9129	+	10.3084i	0.622244	+	0.403089i
$655$	−0.298619	−	0.298619i	−0.0116680	−	0.0116680i
$656$	1.36940	+	5.11068i	0.0534662	+	0.199539i
$657$	−2.25051	−	14.0038i	−0.0878009	−	0.546340i
$658$	−0.985548	+	0.985548i	−0.0384207	+	0.0384207i
$659$	−11.0070	−	6.35487i	−0.428770	−	0.247550i	0.270053	−	0.962846i	$-0.412959\pi$
$659$	−11.0070	−	6.35487i	−0.428770	−	0.247550i	−0.698822	+	0.715295i	$0.746292\pi$
$660$	0.124599	+	0.243856i	0.00485001	+	0.00949209i
$661$	8.87087	+	2.37694i	0.345037	+	0.0924524i	0.427176	−	0.904169i	$-0.359508\pi$
$661$	8.87087	+	2.37694i	0.345037	+	0.0924524i	−0.0821390	+	0.996621i	$0.526175\pi$
$662$	10.1324			0.393808
$663$	9.81082	+	13.7176i	0.381021	+	0.532748i
$664$	−13.2048			−0.512446
$665$	−0.172815	−	0.0463056i	−0.00670147	−	0.00179565i
$666$	36.9494	−	16.5513i	1.43176	−	0.641351i
$667$	36.6215	+	21.1434i	1.41799	+	0.818676i
$668$	23.0960	−	23.0960i	0.893610	−	0.893610i
$669$	−4.26640	−	19.9606i	−0.164949	−	0.771723i
$670$	0.243649	+	0.909310i	0.00941298	+	0.0351297i
$671$	2.34227	+	2.34227i	0.0904222	+	0.0904222i
$672$	6.40195	−	9.88263i	0.246961	−	0.381231i
$673$	0.687055	−	0.396671i	0.0264840	−	0.0152906i	−0.486700	−	0.873569i	$-0.661799\pi$
$673$	0.687055	−	0.396671i	0.0264840	−	0.0152906i	0.513184	+	0.858279i	$0.328466\pi$
$674$	−4.61975	+	17.2412i	−0.177946	+	0.664105i
$675$	−25.6626	−	3.97521i	−0.987753	−	0.153006i
$676$	12.6518	−	13.5745i	0.486608	−	0.522095i
$677$			36.8647i			1.41682i	0.705799	+	0.708412i	$0.250588\pi$
$677$			36.8647i			1.41682i	−0.705799	+	0.708412i	$0.749412\pi$
$678$	−7.30593	−	2.36470i	−0.280583	−	0.0908156i
$679$	−3.73878	−	6.47575i	−0.143481	−	0.248517i
$680$	−0.0691173	+	0.119715i	−0.00265053	+	0.00459085i
$681$	−9.40717	−	10.4240i	−0.360483	−	0.399447i
$682$	43.7220	−	11.7153i	1.67420	−	0.448601i
$683$	−28.0320	+	7.51115i	−1.07261	+	0.287406i	−0.751567	−	0.659657i	$-0.770702\pi$
$683$	−28.0320	+	7.51115i	−1.07261	+	0.287406i	−0.321048	+	0.947063i	$0.604035\pi$
$684$	−12.3076	+	10.0128i	−0.470595	+	0.382848i
$685$	−0.00959670	+	0.0166220i	−0.000366671	+	0.000635093i
$686$	0.925663	+	1.60329i	0.0353420	+	0.0612141i
$687$	10.7234	−	33.1310i	0.409125	−	1.26403i
$688$		−	39.9592i		−	1.52343i
$689$	−2.82345	−	3.54862i	−0.107565	−	0.135192i
$690$	−1.16767	−	0.0598689i	−0.0444525	−	0.00227917i
$691$	9.85581	−	36.7824i	0.374933	−	1.39927i	−0.478510	−	0.878082i	$-0.658823\pi$
$691$	9.85581	−	36.7824i	0.374933	−	1.39927i	0.853443	−	0.521186i	$-0.174510\pi$
$692$	4.67450	−	2.69882i	0.177698	−	0.102594i
$693$	4.03222	−	5.57640i	0.153171	−	0.211830i
$694$	19.5018	+	19.5018i	0.740279	+	0.740279i
$695$	−0.00490707	−	0.0183134i	−0.000186136	−	0.000694668i
$696$	10.0550	−	2.14917i	0.381135	−	0.0814641i
$697$	2.09732	−	2.09732i	0.0794418	−	0.0794418i
$698$	18.2176	+	10.5179i	0.689545	+	0.398109i
$699$	−21.3731	+	10.9206i	−0.808404	+	0.413056i
$700$	−6.89062	−	1.84634i	−0.260441	−	0.0697849i
$701$	−36.5687			−1.38118			−0.690591	−	0.723246i	$-0.742649\pi$
$701$	−36.5687			−1.38118			−0.690591	+	0.723246i	$0.742649\pi$
$702$	8.80272	+	33.5489i	0.332237	+	1.26622i
$703$	27.0094			1.01868
$704$	−6.53898	−	1.75211i	−0.246447	−	0.0660353i
$705$	0.0560706	−	0.0286494i	0.00211174	−	0.00107900i
$706$	31.9978	+	18.4739i	1.20425	+	0.695275i
$707$	−11.0784	+	11.0784i	−0.416647	+	0.416647i
$708$	2.29915	−	0.491421i	0.0864072	−	0.0184687i
$709$	5.14557	+	19.2035i	0.193246	+	0.721204i	0.992714	+	0.120495i	$0.0384483\pi$
$709$	5.14557	+	19.2035i	0.193246	+	0.721204i	−0.799468	+	0.600709i	$0.794885\pi$
$710$	0.647122	+	0.647122i	0.0242861	+	0.0242861i
$711$	−4.15068	+	5.74022i	−0.155663	+	0.215275i
$712$	−4.32084	+	2.49464i	−0.161930	+	0.0934905i
$713$	−20.8315	+	77.7442i	−0.780146	+	2.91154i
$714$	−8.64818	−	0.443410i	−0.323650	−	0.0165942i
$715$	0.371593	+	0.146319i	0.0138968	+	0.00547202i
$716$			22.5179i			0.841535i
$717$	−7.92452	+	24.4835i	−0.295947	+	0.914352i
$718$	−14.7164	−	25.4896i	−0.549212	−	0.951264i
$719$	21.4272	−	37.1130i	0.799100	−	1.38408i	−0.121102	−	0.992640i	$-0.538643\pi$
$719$	21.4272	−	37.1130i	0.799100	−	1.38408i	0.920203	−	0.391443i	$-0.128024\pi$
$720$	−0.541335	+	0.440398i	−0.0201744	+	0.0164127i
$721$	−10.7657	+	2.88466i	−0.400936	+	0.107431i
$722$	9.42772	−	2.52615i	0.350864	−	0.0940136i
$723$	17.7553	+	19.6744i	0.660328	+	0.731700i
$724$	4.53574	−	7.85613i	0.168569	−	0.291971i
$725$	−13.9936	−	24.2377i	−0.519710	−	0.900164i
$726$	17.5063	+	5.66623i	0.649720	+	0.210294i
$727$		−	32.7597i		−	1.21499i	−0.794323	−	0.607496i	$-0.792174\pi$
$727$		−	32.7597i		−	1.21499i	0.794323	−	0.607496i	$-0.207826\pi$
$728$	−0.565432	−	3.78005i	−0.0209563	−	0.140098i
$729$	−25.7346	−	8.16876i	−0.953135	−	0.302547i
$730$	−0.109389	+	0.408246i	−0.00404868	+	0.0151099i
$731$	−19.3996	+	11.2004i	−0.717521	+	0.414261i
$732$	1.94110	−	2.99645i	0.0717450	−	0.110752i
$733$	−16.9174	−	16.9174i	−0.624858	−	0.624858i	0.321911	−	0.946770i	$-0.395675\pi$
$733$	−16.9174	−	16.9174i	−0.624858	−	0.624858i	−0.946770	+	0.321911i	$0.895675\pi$
$734$	9.86803	+	36.8280i	0.364236	+	1.35935i
$735$	−0.0174816	−	0.0817890i	−0.000644820	−	0.00301683i
$736$	36.2993	−	36.2993i	1.33801	−	1.33801i
$737$	−20.9191	−	12.0777i	−0.770566	−	0.444886i
$738$	5.56703	−	2.49373i	0.204925	−	0.0917954i
$739$	−8.05874	−	2.15933i	−0.296445	−	0.0794323i	0.107531	−	0.994202i	$-0.465706\pi$
$739$	−8.05874	−	2.15933i	−0.296445	−	0.0794323i	−0.403976	+	0.914769i	$0.632372\pi$
$740$	−0.502451			−0.0184705
$741$	−3.79014	+	22.8260i	−0.139234	+	0.838533i
$742$	2.32847			0.0854808
$743$	17.8064	+	4.77121i	0.653254	+	0.175039i	0.570200	−	0.821506i	$-0.306866\pi$
$743$	17.8064	+	4.77121i	0.653254	+	0.175039i	0.0830542	+	0.996545i	$0.473533\pi$
$744$	8.90459	+	17.4274i	0.326458	+	0.638920i
$745$	−0.418336	−	0.241527i	−0.0153267	−	0.00884885i
$746$	−18.7021	+	18.7021i	−0.684731	+	0.684731i
$747$	5.92955	+	36.8965i	0.216951	+	1.34997i
$748$	2.28853	+	8.54091i	0.0836770	+	0.312287i
$749$	−14.2230	−	14.2230i	−0.519696	−	0.519696i
$750$	1.29923	+	0.841641i	0.0474413	+	0.0307324i
$751$	−8.19388	+	4.73074i	−0.298999	+	0.172627i	−0.641993	−	0.766710i	$-0.721892\pi$
$751$	−8.19388	+	4.73074i	−0.298999	+	0.172627i	0.342994	+	0.939338i	$0.388559\pi$
$752$	−0.938668	+	3.50316i	−0.0342297	+	0.127747i
$753$	−1.86833	+	36.4394i	−0.0680856	+	1.32793i
$754$	−22.2310	+	30.0516i	−0.809604	+	1.09441i
$755$		−	0.505958i		−	0.0184137i
$756$	−6.78599	−	2.99373i	−0.246804	−	0.108881i
$757$	−10.9869	−	19.0299i	−0.399326	−	0.691653i	0.594317	−	0.804231i	$-0.297422\pi$
$757$	−10.9869	−	19.0299i	−0.399326	−	0.691653i	−0.993643	+	0.112578i	$0.964089\pi$
$758$	26.6299	−	46.1244i	0.967243	−	1.67531i
$759$	22.2723	−	20.0998i	0.808433	−	0.729576i
$760$	−0.183194	+	0.0490867i	−0.00664515	+	0.00178056i
$761$	−6.70942	+	1.79778i	−0.243216	+	0.0651696i	−0.378368	−	0.925655i	$-0.623515\pi$
$761$	−6.70942	+	1.79778i	−0.243216	+	0.0651696i	0.135151	+	0.990825i	$0.456848\pi$
$762$	−13.0298	+	11.7589i	−0.472021	+	0.425979i
$763$	−2.95642	+	5.12067i	−0.107030	+	0.185381i
$764$	−9.18084	−	15.9017i	−0.332151	−	0.575303i
$765$	0.365541	+	0.139369i	0.0132161	+	0.00503888i
$766$			53.4199i			1.93014i
$767$	2.03912	−	2.75646i	0.0736284	−	0.0995300i
$768$	1.85885	−	36.2547i	0.0670756	−	1.30823i
$769$	4.92567	−	18.3829i	0.177624	−	0.662903i	−0.818466	−	0.574556i	$-0.805175\pi$
$769$	4.92567	−	18.3829i	0.177624	−	0.662903i	0.996090	−	0.0883470i	$-0.0281584\pi$
$770$	−0.177586	+	0.102530i	−0.00639977	+	0.00369491i
$771$	−27.3263	−	17.7019i	−0.984131	−	0.637518i
$772$	−12.4073	−	12.4073i	−0.446547	−	0.446547i
$773$	−2.02825	−	7.56954i	−0.0729511	−	0.272257i	0.919810	−	0.392365i	$-0.128343\pi$
$773$	−2.02825	−	7.56954i	−0.0729511	−	0.272257i	−0.992761	+	0.120107i	$0.961676\pi$
$774$	−45.4860	+	7.30994i	−1.63496	+	0.262750i
$775$	37.6673	−	37.6673i	1.35305	−	1.35305i
$776$	−6.86469	−	3.96333i	−0.246428	−	0.142275i
$777$	5.74492	+	11.2435i	0.206098	+	0.403360i
$778$	−55.2179	−	14.7956i	−1.97966	−	0.530448i
$779$	4.06941			0.145802
$780$	0.0705074	−	0.424627i	0.00252457	−	0.0152041i
$781$	−23.4826			−0.840273
$782$	−36.4662	−	9.77109i	−1.30403	−	0.349413i
$783$	−10.5203	−	27.1304i	−0.375965	−	0.969563i
$784$	4.17193	+	2.40866i	0.148997	+	0.0860237i
$785$	0.324918	−	0.324918i	0.0115968	−	0.0115968i
$786$	−5.86175	−	27.4246i	−0.209082	−	0.978203i
$787$	8.35933	+	31.1974i	0.297978	+	1.11207i	0.938823	+	0.344399i	$0.111917\pi$
$787$	8.35933	+	31.1974i	0.297978	+	1.11207i	−0.640846	+	0.767670i	$0.721416\pi$
$788$	21.9542	+	21.9542i	0.782087	+	0.782087i
$789$	−6.89548	+	10.6445i	−0.245485	+	0.378953i
$790$	0.182803	−	0.105542i	0.00650386	−	0.00375500i
$791$	0.619816	−	2.31318i	0.0220381	−	0.0822474i
$792$	0.746078	−	7.25655i	0.0265107	−	0.257850i
$793$	−0.770264	−	5.14939i	−0.0273529	−	0.182860i
$794$			6.94958i			0.246631i
$795$	−0.100080	−	0.0323928i	−0.00354949	−	0.00114885i
$796$	12.2109	+	21.1499i	0.432804	+	0.749638i
$797$	4.26540	−	7.38790i	0.151088	−	0.261693i	−0.780539	−	0.625106i	$-0.785056\pi$
$797$	4.26540	−	7.38790i	0.151088	−	0.261693i	0.931628	+	0.363414i	$0.118389\pi$
$798$	−7.95981	−	8.82015i	−0.281774	−	0.312230i
$799$	1.96384	−	0.526208i	0.0694756	−	0.0186159i
$800$	−32.8180	+	8.79356i	−1.16029	+	0.310899i
$801$	8.91070	+	10.9530i	0.314844	+	0.387004i
$802$	−0.0827632	+	0.143350i	−0.00292247	+	0.00506187i
$803$	−5.42242	−	9.39191i	−0.191353	−	0.331433i
$804$	−8.01723	+	24.7699i	−0.282746	+	0.873567i
$805$		−	0.364626i		−	0.0128514i
$806$	−66.2013	−	26.0675i	−2.33184	−	0.918187i
$807$	−39.4908	−	2.02477i	−1.39014	−	0.0712754i
$808$	−4.29853	+	16.0423i	−0.151222	+	0.564367i
$809$	−33.9116	+	19.5789i	−1.19227	+	0.688356i	−0.958820	−	0.284014i	$-0.908334\pi$
$809$	−33.9116	+	19.5789i	−1.19227	+	0.688356i	−0.233447	+	0.972369i	$0.575001\pi$
$810$	0.600339	+	0.535643i	0.0210938	+	0.0188206i
$811$	−0.668981	−	0.668981i	−0.0234911	−	0.0234911i	0.695264	−	0.718755i	$-0.255288\pi$
$811$	−0.668981	−	0.668981i	−0.0234911	−	0.0234911i	−0.718755	+	0.695264i	$0.755288\pi$
$812$	−2.06888	−	7.72118i	−0.0726036	−	0.270960i
$813$	−39.3872	+	8.41865i	−1.38137	+	0.295255i
$814$	21.8898	−	21.8898i	0.767237	−	0.767237i
$815$	0.446060	+	0.257533i	0.0156248	+	0.00902099i
$816$	−20.0654	+	10.2525i	−0.702430	+	0.358909i
$817$	−29.6864	−	7.95445i	−1.03860	−	0.278291i
$818$	15.6075			0.545702
$819$	−10.3082	+	3.27733i	−0.360198	+	0.114519i
$820$	−0.0757026			−0.00264365
$821$	−16.8910	−	4.52594i	−0.589501	−	0.157956i	−0.0482757	−	0.998834i	$-0.515373\pi$
$821$	−16.8910	−	4.52594i	−0.589501	−	0.157956i	−0.541225	+	0.840878i	$0.682039\pi$
$822$	−1.13499	+	0.579924i	−0.0395872	+	0.0202272i
$823$	−44.6671	−	25.7886i	−1.55700	−	0.898933i	−0.997542	−	0.0700734i	$-0.977677\pi$
$823$	−44.6671	−	25.7886i	−1.55700	−	0.898933i	−0.559456	−	0.828860i	$-0.688990\pi$
$824$	−8.35439	+	8.35439i	−0.291039	+	0.291039i
$825$	−19.4173	+	4.15027i	−0.676024	+	0.144494i
$826$	0.455657	+	1.70054i	0.0158544	+	0.0591692i
$827$	28.6964	+	28.6964i	0.997873	+	0.997873i	0.999998	−	0.00212456i	$-0.000676269\pi$
$827$	28.6964	+	28.6964i	0.997873	+	0.997873i	−0.00212456	+	0.999998i	$0.500676\pi$
$828$	−26.2030	−	18.9471i	−0.910618	−	0.658456i
$829$	−18.0629	+	10.4286i	−0.627351	+	0.362201i	−0.779725	−	0.626122i	$-0.784641\pi$
$829$	−18.0629	+	10.4286i	−0.627351	+	0.362201i	0.152374	+	0.988323i	$0.451308\pi$
$830$	0.288214	−	1.07563i	0.0100040	−	0.0373356i
$831$	47.9110	+	2.45649i	1.66201	+	0.0852148i
$832$	6.62516	+	8.32675i	0.229686	+	0.288678i
$833$		−	2.70055i		−	0.0935684i
$834$	0.387704	−	1.19784i	0.0134251	−	0.0414779i
$835$	−0.552470	−	0.956906i	−0.0191190	−	0.0331151i
$836$	−6.06571	+	10.5061i	−0.209787	+	0.363362i
$837$	44.6967	−	32.7067i	1.54494	−	1.13051i
$838$	−0.852453	+	0.228414i	−0.0294475	+	0.00789044i
$839$	−31.3858	+	8.40981i	−1.08356	+	0.290339i	−0.756053	−	0.654510i	$-0.772875\pi$
$839$	−31.3858	+	8.40981i	−1.08356	+	0.290339i	−0.327506	+	0.944849i	$0.606208\pi$
$840$	−0.0593995	−	0.0658197i	−0.00204948	−	0.00227100i
$841$	1.18033	−	2.04440i	0.0407011	−	0.0704964i
$842$	−3.23211	−	5.59818i	−0.111386	−	0.192926i
$843$	−27.1041	−	8.77273i	−0.933515	−	0.302149i
$844$		−	14.9001i		−	0.512883i
$845$	−0.332788	−	0.532265i	−0.0114483	−	0.0183105i
$846$	4.15940	+	0.427646i	0.143003	+	0.0147028i
$847$	−1.48519	+	5.54280i	−0.0510317	+	0.190453i
$848$	5.24716	−	3.02945i	0.180188	−	0.104032i
$849$	29.4136	−	45.4054i	1.00947	−	1.55831i
$850$	17.6680	+	17.6680i	0.606006	+	0.606006i
$851$	14.2469	+	53.1703i	0.488378	+	1.82265i
$852$	5.29028	+	24.7509i	0.181242	+	0.847952i
$853$	0.703546	−	0.703546i	0.0240889	−	0.0240889i	−0.694960	−	0.719049i	$-0.744578\pi$
$853$	0.703546	−	0.703546i	0.0240889	−	0.0240889i	0.719049	+	0.694960i	$0.244578\pi$
$854$	2.31528	+	1.33673i	0.0792271	+	0.0457418i
$855$	0.219419	+	0.489834i	0.00750398	+	0.0167520i
$856$	−20.5958	−	5.51864i	−0.703952	−	0.188623i
$857$	−11.3057			−0.386195			−0.193098	−	0.981180i	$-0.561853\pi$
$857$	−11.3057			−0.386195			−0.193098	+	0.981180i	$0.561853\pi$
$858$	15.4276	+	21.5710i	0.526689	+	0.736423i
$859$	−36.1854			−1.23463			−0.617316	−	0.786716i	$-0.711780\pi$
$859$	−36.1854			−1.23463			−0.617316	+	0.786716i	$0.711780\pi$
$860$	0.552251	+	0.147975i	0.0188316	+	0.00504591i
$861$	0.865566	+	1.69402i	0.0294984	+	0.0577322i
$862$	43.3059	+	25.0027i	1.47500	+	0.851594i
$863$	−24.0483	+	24.0483i	−0.818613	+	0.818613i	−0.985907	−	0.167294i	$-0.946497\pi$
$863$	−24.0483	+	24.0483i	−0.818613	+	0.818613i	0.167294	+	0.985907i	$0.446497\pi$
$864$	−35.1188	+	3.81183i	−1.19477	+	0.129681i
$865$	−0.0472594	−	0.176374i	−0.00160687	−	0.00599691i
$866$	−26.6789	−	26.6789i	−0.906587	−	0.906587i
$867$	−14.1110	−	9.14110i	−0.479235	−	0.310448i
$868$	13.1762	−	7.60727i	0.447229	−	0.258208i
$869$	−1.40183	+	5.23169i	−0.0475537	+	0.177473i
$870$	−0.0443998	+	0.865965i	−0.00150530	+	0.0293590i
$871$	15.1444	+	34.8174i	0.513148	+	1.17974i
$872$			6.26797i			0.212260i
$873$	−7.99169	+	20.9609i	−0.270478	+	0.709417i
$874$	−25.8981	−	44.8568i	−0.876016	−	1.51730i
$875$	−0.241381	+	0.418084i	−0.00816017	+	0.0141338i
$876$	−8.67759	+	7.83115i	−0.293189	+	0.264590i
$877$	41.0327	−	10.9947i	1.38557	−	0.371264i	0.512432	−	0.858728i	$-0.328745\pi$
$877$	41.0327	−	10.9947i	1.38557	−	0.371264i	0.873143	+	0.487464i	$0.162078\pi$
$878$	−20.3300	+	5.44740i	−0.686103	+	0.183841i
$879$	21.8098	−	19.6824i	0.735625	−	0.663870i
$880$	−0.266792	+	0.462097i	−0.00899355	+	0.0155773i
$881$	−3.63245	−	6.29159i	−0.122380	−	0.211969i	0.798326	−	0.602226i	$-0.205719\pi$
$881$	−3.63245	−	6.29159i	−0.122380	−	0.211969i	−0.920706	+	0.390257i	$0.872386\pi$
$882$	1.97862	−	5.18958i	0.0666235	−	0.174742i
$883$		−	5.42330i		−	0.182509i	−0.995828	−	0.0912543i	$-0.970912\pi$
$883$		−	5.42330i		−	0.182509i	0.995828	−	0.0912543i	$-0.0290876\pi$
$884$	5.09217	−	12.9321i	0.171268	−	0.434955i
$885$	0.00407254	−	0.0794300i	0.000136897	−	0.00267001i
$886$	5.49971	−	20.5252i	0.184766	−	0.689558i
$887$	10.5402	−	6.08536i	0.353904	−	0.204327i	−0.312499	−	0.949918i	$-0.601166\pi$
$887$	10.5402	−	6.08536i	0.353904	−	0.204327i	0.666403	+	0.745591i	$0.267833\pi$
$888$	11.2335	+	7.27703i	0.376971	+	0.244201i
$889$	−3.87035	−	3.87035i	−0.129808	−	0.129808i
$890$	−0.108898	−	0.406413i	−0.00365027	−	0.0136230i
$891$	−20.6111	+	1.17384i	−0.690498	+	0.0393252i
$892$	−11.8945	+	11.8945i	−0.398258	+	0.398258i
$893$	2.41570	+	1.39471i	0.0808384	+	0.0466721i
$894$	−14.5953	−	28.5650i	−0.488141	−	0.955355i
$895$	0.735800	+	0.197157i	0.0245951	+	0.00659024i
$896$	8.13293			0.271702
$897$	−46.9340	+	4.57903i	−1.56708	+	0.152889i
$898$	40.4150			1.34867
$899$	57.6565	+	15.4490i	1.92295	+	0.515253i
$900$	8.74887	+	19.5311i	0.291629	+	0.651036i
$901$	−2.94151	−	1.69828i	−0.0979959	−	0.0565780i
$902$	3.29806	−	3.29806i	0.109813	−	0.109813i
$903$	−3.00302	−	14.0498i	−0.0999343	−	0.467549i
$904$	−0.657042	−	2.45212i	−0.0218529	−	0.0815562i
$905$	−0.216996	−	0.216996i	−0.00721318	−	0.00721318i
$906$	18.2673	−	28.1990i	0.606890	−	0.936850i
$907$	13.5623	−	7.83019i	0.450328	−	0.259997i	−0.257641	−	0.966241i	$-0.582945\pi$
$907$	13.5623	−	7.83019i	0.450328	−	0.259997i	0.707969	+	0.706244i	$0.249612\pi$
$908$	−2.99492	+	11.1772i	−0.0993898	+	0.370928i
$909$	46.7553	+	4.80712i	1.55078	+	0.159442i
$910$	0.320254	+	0.0364463i	0.0106163	+	0.00120818i
$911$			35.0438i			1.16105i	0.814241	+	0.580527i	$0.197153\pi$
$911$			35.0438i			1.16105i	−0.814241	+	0.580527i	$0.802847\pi$
$912$	−29.4127	−	9.51995i	−0.973952	−	0.315237i
$913$	14.2867	+	24.7454i	0.472822	+	0.818952i
$914$	−15.7005	+	27.1941i	−0.519326	+	0.899500i
$915$	−0.0809173	−	0.0896633i	−0.00267504	−	0.00296418i
$916$	−27.7204	+	7.42765i	−0.915906	+	0.245416i
$917$	8.44775	−	2.26357i	0.278969	−	0.0747496i
$918$	15.3412	+	20.9651i	0.506334	+	0.691953i
$919$	2.26637	−	3.92547i	0.0747607	−	0.129489i	−0.826221	−	0.563345i	$-0.809514\pi$
$919$	2.26637	−	3.92547i	0.0747607	−	0.129489i	0.900982	+	0.433856i	$0.142847\pi$
$920$	−0.193263	−	0.334741i	−0.00637168	−	0.0110361i
$921$	0.964954	−	2.98131i	0.0317963	−	0.0982374i
$922$			66.3121i			2.18387i
$923$	29.6740	+	21.9517i	0.976732	+	0.722548i
$924$	−5.66369	−	0.290389i	−0.186322	−	0.00955310i
$925$	9.42923	−	35.1904i	0.310031	−	1.15705i
$926$	51.4515	−	29.7055i	1.69080	−	0.976184i
$927$	27.0951	+	19.5921i	0.889920	+	0.643490i
$928$	−26.9202	−	26.9202i	−0.883700	−	0.883700i
$929$	−11.8226	−	44.1225i	−0.387886	−	1.44761i	−0.833567	−	0.552419i	$-0.813705\pi$
$929$	−11.8226	−	44.1225i	−0.387886	−	1.44761i	0.445680	−	0.895192i	$-0.352962\pi$
$930$	−1.61395	+	0.344966i	−0.0529234	+	0.0113119i
$931$	2.61992	−	2.61992i	0.0858643	−	0.0858643i
$932$	17.1299	+	9.88993i	0.561107	+	0.323956i
$933$	21.9173	−	11.1987i	0.717541	−	0.366630i
$934$	50.0291	+	13.4052i	1.63700	+	0.438633i
$935$	0.299122			0.00978233
$936$	−7.72626	+	8.47238i	−0.252541	+	0.276928i
$937$	−0.124691			−0.00407347			−0.00203674	−	0.999998i	$-0.500648\pi$
$937$	−0.124691			−0.00407347			−0.00203674	+	0.999998i	$0.500648\pi$
$938$	−18.8312	−	5.04580i	−0.614860	−	0.164751i
$939$	10.5531	−	5.39215i	0.344388	−	0.175966i
$940$	−0.0449389	−	0.0259455i	−0.00146574	−	0.000846248i
$941$	−14.4066	+	14.4066i	−0.469642	+	0.469642i	−0.901798	−	0.432157i	$-0.857753\pi$
$941$	−14.4066	+	14.4066i	−0.469642	+	0.469642i	0.432157	+	0.901798i	$0.357753\pi$
$942$	29.8399	−	6.37800i	0.972237	−	0.207807i
$943$	2.14653	+	8.01097i	0.0699008	+	0.260873i
$944$	3.23930	+	3.23930i	0.105430	+	0.105430i
$945$	−0.157239	+	0.195528i	−0.00511498	+	0.00636054i
$946$	−30.5061	+	17.6127i	−0.991838	+	0.572638i
$947$	−2.80946	+	10.4851i	−0.0912953	+	0.340719i	−0.996432	−	0.0844025i	$-0.973102\pi$
$947$	−2.80946	+	10.4851i	−0.0912953	+	0.340719i	0.905136	+	0.425121i	$0.139769\pi$
$948$	5.83008	+	0.298920i	0.189352	+	0.00970847i
$949$	−1.92751	+	16.9371i	−0.0625698	+	0.549801i
$950$			34.2809i			1.11222i
$951$	11.7369	−	36.2620i	0.380594	−	1.17588i
$952$	−1.43137	−	2.47921i	−0.0463910	−	0.0803516i
$953$	−0.979898	+	1.69723i	−0.0317420	+	0.0549788i	−0.881460	−	0.472259i	$-0.843439\pi$
$953$	−0.979898	+	1.69723i	−0.0317420	+	0.0549788i	0.849718	+	0.527237i	$0.176772\pi$
$954$	−4.40835	−	5.41871i	−0.142726	−	0.175437i
$955$	−0.599990	+	0.160767i	−0.0194152	+	0.00520229i
$956$	20.4851	−	5.48896i	0.662535	−	0.177526i
$957$	−14.9064	−	16.5175i	−0.481854	−	0.533936i
$958$	18.6066	−	32.2276i	0.601152	−	1.04123i
$959$	−0.198741	−	0.344229i	−0.00641768	−	0.0111157i
$960$	0.234836	+	0.0760090i	0.00757931	+	0.00245318i
$961$			82.6118i			2.66490i
$962$	−48.1240	+	7.19855i	−1.55158	+	0.232091i
$963$	−6.17159	+	60.0265i	−0.198877	+	1.93433i
$964$	5.65269	−	21.0961i	0.182061	−	0.679460i
$965$	−0.514054	+	0.296789i	−0.0165480	+	0.00955399i
$966$	13.1646	−	20.3220i	0.423563	−	0.653849i
$967$	−20.7609	−	20.7609i	−0.667626	−	0.667626i	0.289540	−	0.957166i	$-0.406498\pi$
$967$	−20.7609	−	20.7609i	−0.667626	−	0.667626i	−0.957166	+	0.289540i	$0.906498\pi$
$968$	1.57439	+	5.87570i	0.0506028	+	0.188852i
$969$	3.62244	+	16.9478i	0.116370	+	0.544443i
$970$	0.472674	−	0.472674i	0.0151767	−	0.0151767i
$971$	−17.8203	−	10.2885i	−0.571880	−	0.330175i	0.186020	−	0.982546i	$-0.440441\pi$
$971$	−17.8203	−	10.2885i	−0.571880	−	0.330175i	−0.757900	+	0.652371i	$0.773774\pi$
$972$	5.88062	+	21.4599i	0.188621	+	0.688326i
$973$	0.379258	+	0.101622i	0.0121585	+	0.00325785i
$974$	−57.5514			−1.84407
$975$	28.4166	+	12.9069i	0.910059	+	0.413351i
$976$	6.95657			0.222674
$977$	44.6170	+	11.9551i	1.42742	+	0.382477i	0.888112	−	0.459628i	$-0.152017\pi$
$977$	44.6170	+	11.9551i	1.42742	+	0.382477i	0.539313	+	0.842105i	$0.318684\pi$
$978$	15.5626	+	30.4580i	0.497637	+	0.973940i
$979$	9.34974	+	5.39807i	0.298819	+	0.172523i
$980$	−0.0487379	+	0.0487379i	−0.00155687	+	0.00155687i
$981$	17.5138	−	2.81460i	0.559172	−	0.0898631i
$982$	−14.2209	−	53.0733i	−0.453809	−	1.69364i
$983$	10.5137	+	10.5137i	0.335336	+	0.335336i	0.854608	−	0.519273i	$-0.173797\pi$
$983$	10.5137	+	10.5137i	0.335336	+	0.335336i	−0.519273	+	0.854608i	$0.673797\pi$
$984$	1.69251	+	1.09640i	0.0539552	+	0.0349521i
$985$	0.909602	−	0.525159i	0.0289823	−	0.0167330i
$986$	−7.24641	+	27.0440i	−0.230773	+	0.861256i
$987$	−0.0667700	+	1.30227i	−0.00212531	+	0.0414517i
$988$	17.4862	−	7.60590i	0.556309	−	0.241976i
$989$		−	62.6359i		−	1.99171i
$990$	0.574815	+	0.219158i	0.0182688	+	0.00696531i
$991$	14.2342	+	24.6543i	0.452163	+	0.783170i	0.998520	−	0.0543827i	$-0.0173191\pi$
$991$	14.2342	+	24.6543i	0.452163	+	0.783170i	−0.546357	+	0.837552i	$0.683986\pi$
$992$	36.2312	−	62.7543i	1.15034	−	1.99245i
$993$	7.03754	−	6.35108i	0.223330	−	0.201545i
$994$	−18.3067	+	4.90527i	−0.580654	+	0.155586i
$995$	0.798011	−	0.213826i	0.0252987	−	0.00677876i
$996$	22.8633	−	20.6332i	0.724452	−	0.653787i
$997$	8.16900	−	14.1491i	0.258715	−	0.448107i	−0.707183	−	0.707030i	$-0.750034\pi$
$997$	8.16900	−	14.1491i	0.258715	−	0.448107i	0.965898	+	0.258923i	$0.0833677\pi$
$998$	−31.3277	−	54.2611i	−0.991660	−	1.71761i
$999$	15.2890	−	34.6560i	0.483721	−	1.09647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cc.a.50.7	✓	112
3.2	odd	2	inner	273.2.cc.a.50.22	yes	112
13.6	odd	12	inner	273.2.cc.a.71.22	yes	112
39.32	even	12	inner	273.2.cc.a.71.7	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cc.a.50.7	✓	112	1.1	even	1	trivial
273.2.cc.a.50.22	yes	112	3.2	odd	2	inner
273.2.cc.a.71.7	yes	112	39.32	even	12	inner
273.2.cc.a.71.22	yes	112	13.6	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.78824 - 0.479158i) q^{2} +(-1.54238 + 0.788082i) q^{3} +(1.23617 + 0.713702i) q^{4} +(0.0341444 - 0.0341444i) q^{5} +(3.13576 - 0.670240i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.749576 + 0.749576i) q^{8} +(1.75785 - 2.43104i) q^{9} +O(q^{10})\)	\(q+(-1.78824 - 0.479158i) q^{2} +(-1.54238 + 0.788082i) q^{3} +(1.23617 + 0.713702i) q^{4} +(0.0341444 - 0.0341444i) q^{5} +(3.13576 - 0.670240i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.749576 + 0.749576i) q^{8} +(1.75785 - 2.43104i) q^{9} +(-0.0774191 + 0.0446979i) q^{10} +(0.593688 - 2.21567i) q^{11} +(-2.46909 - 0.126596i) q^{12} +(-2.82144 + 2.24487i) q^{13} -1.85133i q^{14} +(-0.0257549 + 0.0795721i) q^{15} +(-2.40866 - 4.17193i) q^{16} +(-1.35027 + 2.33874i) q^{17} +(-4.30832 + 3.50500i) q^{18} +(-3.57887 + 0.958956i) q^{19} +(0.0665772 - 0.0178393i) q^{20} +(-1.16043 - 1.28585i) q^{21} +(-2.12332 + 3.67769i) q^{22} +(-3.77557 - 6.53948i) q^{23} +(-1.74686 - 0.565401i) q^{24} +4.99767i q^{25} +(6.12107 - 2.66246i) q^{26} +(-0.795414 + 5.13491i) q^{27} +(-0.369439 + 1.37877i) q^{28} +(-4.84979 + 2.80003i) q^{29} +(0.0841837 - 0.129954i) q^{30} +(-7.53697 - 7.53697i) q^{31} +(1.75953 + 6.56667i) q^{32} +(0.830442 + 3.88528i) q^{33} +(3.53524 - 3.53524i) q^{34} +(0.0418182 + 0.0241437i) q^{35} +(3.90804 - 1.75059i) q^{36} +(-7.04136 - 1.88673i) q^{37} +6.85939 q^{38} +(2.58258 - 5.68597i) q^{39} +0.0511877 q^{40} +(-1.06090 - 0.284266i) q^{41} +(1.45900 + 2.85544i) q^{42} +(7.18359 + 4.14745i) q^{43} +(2.31523 - 2.31523i) q^{44} +(-0.0229855 - 0.143027i) q^{45} +(3.61819 + 13.5033i) q^{46} +(-0.532347 - 0.532347i) q^{47} +(7.00289 + 4.53646i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(2.39467 - 8.93704i) q^{50} +(0.239510 - 4.67135i) q^{51} +(-5.08995 + 0.761372i) q^{52} +1.25773i q^{53} +(3.88283 - 8.80134i) q^{54} +(-0.0553817 - 0.0959239i) q^{55} +(-0.530030 + 0.918039i) q^{56} +(4.76424 - 4.29952i) q^{57} +(10.0143 - 2.68331i) q^{58} +(-0.918551 + 0.246125i) q^{59} +(-0.0886283 + 0.0799832i) q^{60} +(-0.722037 + 1.25060i) q^{61} +(9.86653 + 17.0893i) q^{62} +(2.80317 + 1.06876i) q^{63} -2.95124i q^{64} +(-0.0196866 + 0.172986i) q^{65} +(0.376631 - 7.34573i) q^{66} +(2.72551 - 10.1717i) q^{67} +(-3.33833 + 1.92739i) q^{68} +(10.9770 + 7.11088i) q^{69} +(-0.0632124 - 0.0632124i) q^{70} +(-2.64960 - 9.88844i) q^{71} +(3.13989 - 0.504604i) q^{72} +(3.34308 - 3.34308i) q^{73} +(11.6876 + 6.74785i) q^{74} +(-3.93857 - 7.70829i) q^{75} +(-5.10850 - 1.36882i) q^{76} +2.29383 q^{77} +(-7.34277 + 8.93043i) q^{78} -2.36122 q^{79} +(-0.224690 - 0.0602056i) q^{80} +(-2.81990 - 8.54682i) q^{81} +(1.76093 + 1.01667i) q^{82} +(-8.80818 + 8.80818i) q^{83} +(-0.516767 - 2.41773i) q^{84} +(0.0337507 + 0.125959i) q^{85} +(-10.8587 - 10.8587i) q^{86} +(5.27356 - 8.14074i) q^{87} +(2.10583 - 1.21580i) q^{88} +(-1.21816 + 4.54622i) q^{89} +(-0.0274290 + 0.266781i) q^{90} +(-2.89862 - 2.14429i) q^{91} -10.7785i q^{92} +(17.5646 + 5.68510i) q^{93} +(0.696888 + 1.20704i) q^{94} +(-0.0894555 + 0.154942i) q^{95} +(-7.88894 - 8.74162i) q^{96} +(-7.22276 + 1.93533i) q^{97} +(1.78824 - 0.479158i) q^{98} +(-4.34277 - 5.33811i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{6}+O(q^{10}) \) 112 * q - 12 * q^6	\( 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) \) 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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