LMFDB - Embedded newform 56.2.p.a.37.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [56,2,Mod(37,56)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("56.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(56, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	56.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.447162251319$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.951588245534976.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 2 x^{10} - 9 x^{9} + 8 x^{8} - 13 x^{7} + 35 x^{6} - 26 x^{5} + 32 x^{4} - 72 x^{3} + \cdots + 64 $ x^12 - x^11 + 2x^10 - 9x^9 + 8x^8 - 13x^7 + 35x^6 - 26x^5 + 32x^4 - 72x^3 + 32x^2 - 32x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.4
Root			$1.41417 - 0.0105323i$ of defining polynomial
Character	$\chi$	$=$	56.37
Dual form			56.2.p.a.53.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.242117 + 1.39333i) q^{2} +(-2.13038 + 1.22998i) q^{3} +(-1.88276 - 0.674701i) q^{4} +(1.28690 + 0.742990i) q^{5} +(-1.19797 - 3.26613i) q^{6} +(0.129755 + 2.64257i) q^{7} +(1.39593 - 2.45995i) q^{8} +(1.52569 - 2.64257i) q^{9} +(-1.34681 + 1.61319i) q^{10} +(4.37021 - 2.52314i) q^{11} +(4.84086 - 0.878379i) q^{12} +2.58633i q^{13} +(-3.71339 - 0.459019i) q^{14} -3.65544 q^{15} +(3.08956 + 2.54060i) q^{16} +(-0.629755 - 1.09077i) q^{17} +(3.31258 + 2.76560i) q^{18} +(-2.68324 - 1.54917i) q^{19} +(-1.92162 - 2.26714i) q^{20} +(-3.52673 - 5.47008i) q^{21} +(2.45748 + 6.70006i) q^{22} +(0.697966 - 1.20891i) q^{23} +(0.0518180 + 6.95761i) q^{24} +(-1.39593 - 2.41782i) q^{25} +(-3.60362 - 0.626196i) q^{26} +0.126378i q^{27} +(1.53864 - 5.06286i) q^{28} -0.638384i q^{29} +(0.885046 - 5.09325i) q^{30} +(1.82772 + 3.16571i) q^{31} +(-4.28794 + 3.68966i) q^{32} +(-6.20682 + 10.7505i) q^{33} +(1.67228 - 0.613365i) q^{34} +(-1.79642 + 3.49712i) q^{35} +(-4.65544 + 3.94593i) q^{36} +(5.21370 + 3.01013i) q^{37} +(2.80817 - 3.36357i) q^{38} +(-3.18113 - 5.50988i) q^{39} +(3.62414 - 2.12854i) q^{40} +6.36226 q^{41} +(8.47554 - 3.58950i) q^{42} +1.02401i q^{43} +(-9.93042 + 1.80188i) q^{44} +(3.92680 - 2.26714i) q^{45} +(1.51543 + 1.26520i) q^{46} +(5.48316 - 9.49712i) q^{47} +(-9.70682 - 1.61236i) q^{48} +(-6.96633 + 0.685774i) q^{49} +(3.70682 - 1.35960i) q^{50} +(2.68324 + 1.54917i) q^{51} +(1.74500 - 4.86944i) q^{52} +(-4.99481 + 2.88375i) q^{53} +(-0.176087 - 0.0305984i) q^{54} +7.49868 q^{55} +(6.68172 + 3.36965i) q^{56} +7.62177 q^{57} +(0.889482 + 0.154564i) q^{58} +(3.01720 - 1.74198i) q^{59} +(6.88231 + 2.46633i) q^{60} +(-11.1614 - 6.44406i) q^{61} +(-4.85341 + 1.78015i) q^{62} +(7.18113 + 3.68884i) q^{63} +(-4.10275 - 6.86786i) q^{64} +(-1.92162 + 3.32834i) q^{65} +(-13.4763 - 11.2511i) q^{66} +(-0.443410 + 0.256003i) q^{67} +(0.449735 + 2.47855i) q^{68} +3.43393i q^{69} +(-4.43771 - 3.34973i) q^{70} -7.41363 q^{71} +(-4.37084 - 7.44196i) q^{72} +(-4.94731 - 8.56899i) q^{73} +(-5.45644 + 6.53562i) q^{74} +(5.94774 + 3.43393i) q^{75} +(4.00667 + 4.72709i) q^{76} +(7.23463 + 11.2212i) q^{77} +(8.44731 - 3.09834i) q^{78} +(-4.35341 + 7.54032i) q^{79} +(2.08830 + 5.56500i) q^{80} +(4.42162 + 7.65847i) q^{81} +(-1.54041 + 8.86475i) q^{82} +2.97196i q^{83} +(2.94930 + 12.6783i) q^{84} -1.87161i q^{85} +(-1.42679 - 0.247931i) q^{86} +(0.785198 + 1.36000i) q^{87} +(-0.106298 - 14.2727i) q^{88} +(1.29186 - 2.23757i) q^{89} +(2.20814 + 6.02026i) q^{90} +(-6.83456 + 0.335590i) q^{91} +(-2.12976 + 1.80517i) q^{92} +(-7.78749 - 4.49611i) q^{93} +(11.9051 + 9.93929i) q^{94} +(-2.30203 - 3.98724i) q^{95} +(4.59674 - 13.1345i) q^{96} -1.57040 q^{97} +(0.731157 - 9.87246i) q^{98} -15.3981i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 8 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{10} - 2 q^{12} - 16 q^{14} - 20 q^{15} + 8 q^{16} - 2 q^{17} + 6 q^{18} + 8 q^{20} + 12 q^{22} + 2 q^{23} + 18 q^{24} - 4 q^{25} - 2 q^{26} + 26 q^{28}+ \cdots + 52 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 - 8 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^10 - 2 * q^12 - 16 * q^14 - 20 * q^15 + 8 * q^16 - 2 * q^17 + 6 * q^18 + 8 * q^20 + 12 * q^22 + 2 * q^23 + 18 * q^24 - 4 * q^25 - 2 * q^26 + 26 * q^28 + 14 * q^30 + 10 * q^31 - 12 * q^32 - 14 * q^33 + 32 * q^34 - 32 * q^36 + 18 * q^38 + 4 * q^39 + 10 * q^40 - 8 * q^41 + 22 * q^42 - 30 * q^44 - 4 * q^46 + 30 * q^47 - 56 * q^48 - 12 * q^49 - 16 * q^50 - 32 * q^52 + 2 * q^54 + 4 * q^55 - 40 * q^56 - 4 * q^57 - 22 * q^58 + 6 * q^60 - 28 * q^62 + 44 * q^63 + 24 * q^64 + 8 * q^65 - 38 * q^66 + 4 * q^68 - 48 * q^70 + 32 * q^71 + 20 * q^72 - 10 * q^73 + 18 * q^74 + 52 * q^76 + 52 * q^78 - 22 * q^79 + 36 * q^80 + 22 * q^81 - 26 * q^82 + 56 * q^84 + 40 * q^86 - 20 * q^87 - 14 * q^88 - 10 * q^89 + 52 * q^90 - 20 * q^92 + 42 * q^94 - 34 * q^95 + 16 * q^96 + 40 * q^97 + 52 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.242117	+	1.39333i	−0.171203	+	0.985236i
$2$	−0.242117	+	1.39333i	−0.171203	+	0.985236i
$3$	−2.13038	+	1.22998i	−1.22998	+	0.710128i	−0.967025	−	0.254681i	$-0.918029\pi$
$3$	−2.13038	+	1.22998i	−1.22998	+	0.710128i	−0.262952	+	0.964809i	$0.584696\pi$
$4$	−1.88276	−	0.674701i	−0.941379	−	0.337350i
$5$	1.28690	+	0.742990i	0.575518	+	0.332275i	0.759350	−	0.650682i	$-0.225517\pi$
$5$	1.28690	+	0.742990i	0.575518	+	0.332275i	−0.183832	+	0.982958i	$0.558850\pi$
$6$	−1.19797	−	3.26613i	−0.489068	−	1.33339i
$7$	0.129755	+	2.64257i	0.0490429	+	0.998797i
$7$	0.129755	+	2.64257i	0.0490429	+	0.998797i
$8$	1.39593	−	2.45995i	0.493536	−	0.869725i
$9$	1.52569	−	2.64257i	0.508562	−	0.880856i
$10$	−1.34681	+	1.61319i	−0.425900	+	0.510134i
$11$	4.37021	−	2.52314i	1.31767	−	0.760756i	0.334315	−	0.942461i	$-0.391495\pi$
$11$	4.37021	−	2.52314i	1.31767	−	0.760756i	0.983353	+	0.181705i	$0.0581616\pi$
$12$	4.84086	−	0.878379i	1.39744	−	0.253566i
$13$			2.58633i			0.717320i	0.933468	+	0.358660i	$0.116766\pi$
$13$			2.58633i			0.717320i	−0.933468	+	0.358660i	$0.883234\pi$
$14$	−3.71339	−	0.459019i	−0.992447	−	0.122678i
$15$	−3.65544			−0.943831
$16$	3.08956	+	2.54060i	0.772389	+	0.635149i
$17$	−0.629755	−	1.09077i	−0.152738	−	0.264550i	0.779495	−	0.626408i	$-0.215476\pi$
$17$	−0.629755	−	1.09077i	−0.152738	−	0.264550i	−0.932233	+	0.361858i	$0.882142\pi$
$18$	3.31258	+	2.76560i	0.780783	+	0.651859i
$19$	−2.68324	−	1.54917i	−0.615577	−	0.355404i	0.159568	−	0.987187i	$-0.448990\pi$
$19$	−2.68324	−	1.54917i	−0.615577	−	0.355404i	−0.775145	+	0.631783i	$0.782323\pi$
$20$	−1.92162	−	2.26714i	−0.429687	−	0.506948i
$21$	−3.52673	−	5.47008i	−0.769595	−	1.19367i
$22$	2.45748	+	6.70006i	0.523936	+	1.42846i
$23$	0.697966	−	1.20891i	0.145536	−	0.252076i	−0.784037	−	0.620714i	$-0.786843\pi$
$23$	0.697966	−	1.20891i	0.145536	−	0.252076i	0.929573	+	0.368639i	$0.120176\pi$
$24$	0.0518180	+	6.95761i	0.0105773	+	1.42022i
$25$	−1.39593	−	2.41782i	−0.279186	−	0.483565i
$26$	−3.60362	−	0.626196i	−0.706729	−	0.122807i
$27$			0.126378i			0.0243215i
$28$	1.53864	−	5.06286i	0.290776	−	0.956791i
$29$		−	0.638384i		−	0.118545i	−0.998242	−	0.0592725i	$-0.981122\pi$
$29$		−	0.638384i		−	0.118545i	0.998242	−	0.0592725i	$-0.0188781\pi$
$30$	0.885046	−	5.09325i	0.161587	−	0.929896i
$31$	1.82772	+	3.16571i	0.328268	+	0.568578i	0.982168	−	0.188003i	$-0.0602016\pi$
$31$	1.82772	+	3.16571i	0.328268	+	0.568578i	−0.653900	+	0.756581i	$0.726868\pi$
$32$	−4.28794	+	3.68966i	−0.758007	+	0.652246i
$33$	−6.20682	+	10.7505i	−1.08047	+	1.87143i
$34$	1.67228	−	0.613365i	0.286793	−	0.105191i
$35$	−1.79642	+	3.49712i	−0.303650	+	0.591121i
$36$	−4.65544	+	3.94593i	−0.775907	+	0.657656i
$37$	5.21370	+	3.01013i	0.857127	+	0.494862i	0.863049	−	0.505120i	$-0.168552\pi$
$37$	5.21370	+	3.01013i	0.857127	+	0.494862i	−0.00592229	+	0.999982i	$0.501885\pi$
$38$	2.80817	−	3.36357i	0.455545	−	0.545643i
$39$	−3.18113	−	5.50988i	−0.509388	−	0.882287i
$40$	3.62414	−	2.12854i	0.573027	−	0.336552i
$41$	6.36226			0.993618			0.496809	−	0.867860i	$-0.334505\pi$
$41$	6.36226			0.993618			0.496809	+	0.867860i	$0.334505\pi$
$42$	8.47554	−	3.58950i	1.30780	−	0.553872i
$43$			1.02401i			0.156160i	0.996947	+	0.0780801i	$0.0248790\pi$
$43$			1.02401i			0.156160i	−0.996947	+	0.0780801i	$0.975121\pi$
$44$	−9.93042	+	1.80188i	−1.49707	+	0.271644i
$45$	3.92680	−	2.26714i	0.585373	−	0.337965i
$46$	1.51543	+	1.26520i	0.223438	+	0.186543i
$47$	5.48316	−	9.49712i	0.799802	−	1.38530i	−0.119943	−	0.992781i	$-0.538271\pi$
$47$	5.48316	−	9.49712i	0.799802	−	1.38530i	0.919745	−	0.392516i	$-0.128395\pi$
$48$	−9.70682	−	1.61236i	−1.40106	−	0.232724i
$49$	−6.96633	+	0.685774i	−0.995190	+	0.0979677i
$50$	3.70682	−	1.35960i	0.524223	−	0.192277i
$51$	2.68324	+	1.54917i	0.375729	+	0.216927i
$52$	1.74500	−	4.86944i	0.241988	−	0.675270i
$53$	−4.99481	+	2.88375i	−0.686089	+	0.396114i	−0.802145	−	0.597129i	$-0.796308\pi$
$53$	−4.99481	+	2.88375i	−0.686089	+	0.396114i	0.116056	+	0.993243i	$0.462975\pi$
$54$	−0.176087	−	0.0305984i	−0.0239624	−	0.00416391i
$55$	7.49868			1.01112
$56$	6.68172	+	3.36965i	0.892883	+	0.450289i
$57$	7.62177			1.00953
$58$	0.889482	+	0.154564i	0.116795	+	0.0202952i
$59$	3.01720	−	1.74198i	0.392806	−	0.226787i	−0.290569	−	0.956854i	$-0.593845\pi$
$59$	3.01720	−	1.74198i	0.392806	−	0.226787i	0.683375	+	0.730067i	$0.260511\pi$
$60$	6.88231	+	2.46633i	0.888503	+	0.318402i
$61$	−11.1614	−	6.44406i	−1.42908	−	0.825077i	−0.432028	−	0.901860i	$-0.642202\pi$
$61$	−11.1614	−	6.44406i	−1.42908	−	0.825077i	−0.997048	+	0.0767831i	$0.975535\pi$
$62$	−4.85341	+	1.78015i	−0.616383	+	0.226080i
$63$	7.18113	+	3.68884i	0.904737	+	0.464751i
$64$	−4.10275	−	6.86786i	−0.512844	−	0.858482i
$65$	−1.92162	+	3.32834i	−0.238348	+	0.412830i
$66$	−13.4763	−	11.2511i	−1.65882	−	1.38491i
$67$	−0.443410	+	0.256003i	−0.0541711	+	0.0312757i	−0.526841	−	0.849964i	$-0.676624\pi$
$67$	−0.443410	+	0.256003i	−0.0541711	+	0.0312757i	0.472670	+	0.881240i	$0.343290\pi$
$68$	0.449735	+	2.47855i	0.0545384	+	0.300568i
$69$			3.43393i			0.413396i
$70$	−4.43771	−	3.34973i	−0.530408	−	0.400369i
$71$	−7.41363			−0.879836			−0.439918	−	0.898038i	$-0.644993\pi$
$71$	−7.41363			−0.879836			−0.439918	+	0.898038i	$0.644993\pi$
$72$	−4.37084	−	7.44196i	−0.515108	−	0.877044i
$73$	−4.94731	−	8.56899i	−0.579038	−	1.00292i	−0.995590	−	0.0938118i	$-0.970095\pi$
$73$	−4.94731	−	8.56899i	−0.579038	−	1.00292i	0.416552	−	0.909112i	$-0.363239\pi$
$74$	−5.45644	+	6.53562i	−0.634299	+	0.759750i
$75$	5.94774	+	3.43393i	0.686786	+	0.396516i
$76$	4.00667	+	4.72709i	0.459596	+	0.542235i
$77$	7.23463	+	11.2212i	0.824463	+	1.27877i
$78$	8.44731	−	3.09834i	0.956469	−	0.350818i
$79$	−4.35341	+	7.54032i	−0.489797	+	0.848353i	−0.999931	−	0.0117420i	$-0.996262\pi$
$79$	−4.35341	+	7.54032i	−0.489797	+	0.848353i	0.510134	+	0.860095i	$0.329596\pi$
$80$	2.08830	+	5.56500i	0.233479	+	0.622185i
$81$	4.42162	+	7.65847i	0.491291	+	0.850941i
$82$	−1.54041	+	8.86475i	−0.170110	+	0.978948i
$83$			2.97196i			0.326215i	0.986608	+	0.163107i	$0.0521517\pi$
$83$			2.97196i			0.326215i	−0.986608	+	0.163107i	$0.947848\pi$
$84$	2.94930	+	12.6783i	0.321795	+	1.38332i
$85$		−	1.87161i		−	0.203004i
$86$	−1.42679	−	0.247931i	−0.153855	−	0.0267351i
$87$	0.785198	+	1.36000i	0.0841820	+	0.145808i
$88$	−0.106298	−	14.2727i	−0.0113314	−	1.52147i
$89$	1.29186	−	2.23757i	0.136937	−	0.237182i	−0.789399	−	0.613881i	$-0.789607\pi$
$89$	1.29186	−	2.23757i	0.136937	−	0.237182i	0.926336	+	0.376699i	$0.122941\pi$
$90$	2.20814	+	6.02026i	0.232758	+	0.634591i
$91$	−6.83456	+	0.335590i	−0.716456	+	0.0351794i
$92$	−2.12976	+	1.80517i	−0.222042	+	0.188202i
$93$	−7.78749	−	4.49611i	−0.807525	−	0.466225i
$94$	11.9051	+	9.93929i	1.22792	+	1.02516i
$95$	−2.30203	−	3.98724i	−0.236184	−	0.409082i
$96$	4.59674	−	13.1345i	0.469153	−	1.34053i
$97$	−1.57040			−0.159449			−0.0797247	−	0.996817i	$-0.525404\pi$
$97$	−1.57040			−0.159449			−0.0797247	+	0.996817i	$0.525404\pi$
$98$	0.731157	−	9.87246i	0.0738580	−	0.997269i
$99$		−	15.3981i		−	1.54757i
$100$	0.996894	+	5.49402i	0.0996894	+	0.549402i
$101$	0.181183	−	0.104606i	0.0180284	−	0.0104087i	−0.490959	−	0.871183i	$-0.663353\pi$
$101$	0.181183	−	0.104606i	0.0180284	−	0.0104087i	0.508987	+	0.860774i	$0.330020\pi$
$102$	−2.80817	+	3.36357i	−0.278050	+	0.333043i
$103$	−3.43846	+	5.95558i	−0.338801	+	0.586821i	−0.984207	−	0.177019i	$-0.943355\pi$
$103$	−3.43846	+	5.95558i	−0.338801	+	0.586821i	0.645406	+	0.763839i	$0.276688\pi$
$104$	6.36226	+	3.61034i	0.623871	+	0.354023i
$105$	−0.474313	−	9.65975i	−0.0462882	−	0.942695i
$106$	−2.80870	−	7.65764i	−0.272805	−	0.743776i
$107$	−11.2048	−	6.46908i	−1.08321	−	0.625389i	−0.151447	−	0.988465i	$-0.548393\pi$
$107$	−11.2048	−	6.46908i	−1.08321	−	0.625389i	−0.931759	+	0.363076i	$0.881726\pi$
$108$	0.0852675	−	0.237940i	0.00820487	−	0.0228958i
$109$	16.6430	−	9.60883i	1.59411	−	0.920359i	0.601517	−	0.798860i	$-0.294563\pi$
$109$	16.6430	−	9.60883i	1.59411	−	0.920359i	0.992591	−	0.121500i	$-0.0387703\pi$
$110$	−1.81556	+	10.4482i	−0.173107	+	0.996193i
$111$	−14.8096			−1.40566
$112$	−6.31281	+	8.49402i	−0.596505	+	0.802610i
$113$	−1.05137			−0.0989050			−0.0494525	−	0.998776i	$-0.515748\pi$
$113$	−1.05137			−0.0989050			−0.0494525	+	0.998776i	$0.515748\pi$
$114$	−1.84536	+	10.6197i	−0.172834	+	0.994623i
$115$	1.79642	−	1.03716i	0.167517	−	0.0967160i
$116$	−0.430718	+	1.20192i	−0.0399912	+	0.111596i
$117$	6.83456	+	3.94593i	0.631855	+	0.364802i
$118$	1.69665	+	4.62573i	0.156189	+	0.425833i
$119$	2.80071	−	1.80570i	0.256741	−	0.165529i
$120$	−5.10275	+	8.99222i	−0.465815	+	0.820874i
$121$	7.23250	−	12.5271i	0.657500	−	1.13882i
$122$	11.6811	−	13.9914i	1.05756	−	1.26672i
$123$	−13.5540	+	7.82543i	−1.22213	+	0.705595i
$124$	−1.30525	−	7.19342i	−0.117215	−	0.645989i
$125$		−	11.5786i		−	1.03562i
$126$	−6.87847	+	9.11258i	−0.612783	+	0.811813i
$127$	−7.20814			−0.639619			−0.319809	−	0.947482i	$-0.603619\pi$
$127$	−7.20814			−0.639619			−0.319809	+	0.947482i	$0.603619\pi$
$128$	10.5626	−	4.05367i	0.933608	−	0.358297i
$129$	−1.25951	−	2.18154i	−0.110894	−	0.192074i
$130$	−4.17223	−	3.48331i	−0.365929	−	0.305506i
$131$	12.7767	+	7.37662i	1.11630	+	0.644498i	0.940455	−	0.339919i	$-0.110400\pi$
$131$	12.7767	+	7.37662i	1.11630	+	0.644498i	0.175849	+	0.984417i	$0.443733\pi$
$132$	18.9393	−	16.0529i	1.64846	−	1.39722i
$133$	3.74562	−	7.29165i	0.324786	−	0.632267i
$134$	−0.249340	−	0.679801i	−0.0215397	−	0.0587258i
$135$	−0.0938978	+	0.162636i	−0.00808144	+	0.0139975i
$136$	−3.56233	+	0.0265311i	−0.305468	+	0.00227502i
$137$	4.68113	+	8.10795i	0.399936	+	0.692709i	0.993718	−	0.111917i	$-0.0356991\pi$
$137$	4.68113	+	8.10795i	0.399936	+	0.692709i	−0.593782	+	0.804626i	$0.702366\pi$
$138$	−4.78461	−	0.831414i	−0.407293	−	0.0707746i
$139$			1.69519i			0.143784i	0.997412	+	0.0718921i	$0.0229037\pi$
$139$			1.69519i			0.143784i	−0.997412	+	0.0718921i	$0.977096\pi$
$140$	5.74173	−	5.37218i	0.485265	−	0.454032i
$141$			26.9767i			2.27184i
$142$	1.79497	−	10.3297i	0.150630	−	0.866846i
$143$	6.52569	+	11.3028i	0.545705	+	0.945189i
$144$	11.4274	−	4.28821i	0.952283	−	0.357351i
$145$	0.474313	−	0.821534i	0.0393895	−	0.0682247i
$146$	13.1373	−	4.81855i	1.08725	−	0.398786i
$147$	13.9975	−	10.0294i	1.15449	−	0.827210i
$148$	−7.78520	−	9.18503i	−0.639939	−	0.755005i
$149$	−3.19276	−	1.84334i	−0.261561	−	0.151012i	0.363485	−	0.931600i	$-0.381587\pi$
$149$	−3.19276	−	1.84334i	−0.261561	−	0.151012i	−0.625047	+	0.780587i	$0.714920\pi$
$150$	−6.22466	+	7.45577i	−0.508241	+	0.608761i
$151$	7.13861	+	12.3644i	0.580932	+	1.00620i	0.995369	+	0.0961252i	$0.0306449\pi$
$151$	7.13861	+	12.3644i	0.580932	+	1.00620i	−0.414438	+	0.910078i	$0.636022\pi$
$152$	−7.55650	+	4.43811i	−0.612913	+	0.359978i
$153$	−3.84324			−0.310707
$154$	−17.3865	+	7.36342i	−1.40104	+	0.593361i
$155$			5.43191i			0.436302i
$156$	2.27178	+	12.5201i	0.181888	+	1.00241i
$157$	−11.1614	+	6.44406i	−0.890780	+	0.514292i	−0.874197	−	0.485571i	$-0.838612\pi$
$157$	−11.1614	+	6.44406i	−0.890780	+	0.514292i	−0.0165822	+	0.999863i	$0.505279\pi$
$158$	−9.45215	−	7.89139i	−0.751973	−	0.627806i
$159$	7.09390	−	12.2870i	0.562583	−	0.974422i
$160$	−8.25951	+	1.56232i	−0.652972	+	0.123512i
$161$	3.28520	+	1.68756i	0.258910	+	0.132998i
$162$	−11.7414	+	4.30654i	−0.922488	+	0.338354i
$163$	2.79831	+	1.61560i	0.219180	+	0.126544i	0.605571	−	0.795791i	$-0.292945\pi$
$163$	2.79831	+	1.61560i	0.219180	+	0.126544i	−0.386390	+	0.922335i	$0.626278\pi$
$164$	−11.9786	−	4.29262i	−0.935371	−	0.335197i
$165$	−15.9751	+	9.22320i	−1.24366	+	0.718026i
$166$	−4.14093	−	0.719563i	−0.321399	−	0.0558489i
$167$	−14.0487			−1.08712			−0.543562	−	0.839369i	$-0.682925\pi$
$167$	−14.0487			−1.08712			−0.543562	+	0.839369i	$0.682925\pi$
$168$	−18.3792	+	1.03972i	−1.41799	+	0.0802160i
$169$	6.31088			0.485453
$170$	2.60777	+	0.453149i	0.200007	+	0.0347549i
$171$	−8.18757	+	4.72709i	−0.626119	+	0.361490i
$172$	0.690901	−	1.92797i	0.0526807	−	0.147006i
$173$	−5.66273	−	3.26938i	−0.430529	−	0.248566i	0.269043	−	0.963128i	$-0.413293\pi$
$173$	−5.66273	−	3.26938i	−0.430529	−	0.248566i	−0.699572	+	0.714562i	$0.746626\pi$
$174$	−2.08505	+	0.764762i	−0.158067	+	0.0579765i
$175$	6.20814	−	4.00257i	0.469291	−	0.302566i
$176$	19.9123	+	3.30755i	1.50095	+	0.249316i
$177$	−4.28520	+	7.42218i	−0.322095	+	0.557885i
$178$	2.80490	+	2.34175i	0.210236	+	0.175522i
$179$	−0.109447	+	0.0631891i	−0.00818044	+	0.00472298i	−0.504085	−	0.863654i	$-0.668170\pi$
$179$	−0.109447	+	0.0631891i	−0.00818044	+	0.00472298i	0.495904	+	0.868377i	$0.334837\pi$
$180$	−8.92286	+	1.61906i	−0.665071	+	0.120678i
$181$			2.71920i			0.202117i	0.994880	+	0.101058i	$0.0322229\pi$
$181$			2.71920i			0.202117i	−0.994880	+	0.101058i	$0.967777\pi$
$182$	1.18718	−	9.60407i	0.0879994	−	0.711901i
$183$	31.7042			2.34364
$184$	−1.99956	−	3.40452i	−0.147409	−	0.250985i
$185$	4.47299	+	7.74745i	0.328861	+	0.569604i
$186$	8.15007	−	9.76199i	0.597592	−	0.715784i
$187$	−5.50433	−	3.17793i	−0.402516	−	0.232393i
$188$	−16.7312	+	14.1813i	−1.22025	+	1.03428i
$189$	−0.333963	+	0.0163982i	−0.0242922	+	0.00119280i
$190$	6.11292	−	2.24212i	0.443478	−	0.162661i
$191$	1.22365	−	2.11943i	0.0885404	−	0.153357i	−0.818354	−	0.574715i	$-0.805113\pi$
$191$	1.22365	−	2.11943i	0.0885404	−	0.153357i	0.906894	+	0.421358i	$0.138446\pi$
$192$	17.1877	+	9.58488i	1.24042	+	0.691729i
$193$	−1.97431	−	3.41961i	−0.142114	−	0.246149i	0.786178	−	0.618000i	$-0.212057\pi$
$193$	−1.97431	−	3.41961i	−0.142114	−	0.246149i	−0.928293	+	0.371851i	$0.878723\pi$
$194$	0.380220	−	2.18808i	0.0272982	−	0.157095i
$195$		−	9.45419i		−	0.677029i
$196$	13.5786	+	3.40904i	0.969900	+	0.243503i
$197$		−	19.5468i		−	1.39265i	−0.717727	−	0.696325i	$-0.754817\pi$
$197$		−	19.5468i		−	1.39265i	0.717727	−	0.696325i	$-0.245183\pi$
$198$	21.4547	+	3.72815i	1.52472	+	0.264948i
$199$	−10.3981	−	18.0101i	−0.737103	−	1.27670i	−0.953795	−	0.300460i	$-0.902860\pi$
$199$	−10.3981	−	18.0101i	−0.737103	−	1.27670i	0.216692	−	0.976240i	$-0.430473\pi$
$200$	−7.89636	+	0.0588095i	−0.558357	+	0.00415846i
$201$	0.629755	−	1.09077i	0.0444195	−	0.0769369i
$202$	0.101884	+	0.277775i	0.00716850	+	0.0195442i
$203$	1.68697	−	0.0828337i	0.118402	−	0.00581378i
$204$	−4.00667	−	4.72709i	−0.280523	−	0.330963i
$205$	8.18757	+	4.72709i	0.571845	+	0.330155i
$206$	−7.46560	−	6.23287i	−0.520153	−	0.434264i
$207$	−2.12976	−	3.68884i	−0.148028	−	0.256392i
$208$	−6.57083	+	7.99062i	−0.455605	+	0.554050i
$209$	−15.6351			−1.08150
$210$	13.5741	+	1.67792i	0.936702	+	0.115787i
$211$			17.2132i			1.18500i	0.805569	+	0.592502i	$0.201860\pi$
$211$			17.2132i			1.18500i	−0.805569	+	0.592502i	$0.798140\pi$
$212$	11.3497	−	2.05941i	0.779499	−	0.141441i
$213$	15.7939	−	9.11860i	1.08218	−	0.624796i
$214$	11.7265	−	14.0457i	0.801604	−	0.960145i
$215$	−0.760830	+	1.31780i	−0.0518882	+	0.0898730i
$216$	0.310885	+	0.176415i	0.0211530	+	0.0120036i
$217$	−8.12844	+	5.24064i	−0.551794	+	0.355758i
$218$	9.35875	+	25.5157i	0.633855	+	1.72814i
$219$	21.0793	+	12.1701i	1.42441	+	0.822382i
$220$	−14.1182	−	5.05936i	−0.951849	−	0.341102i
$221$	2.82109	−	1.62876i	0.189767	−	0.109562i
$222$	3.58565	−	20.6347i	0.240653	−	1.38491i
$223$	17.5164			1.17298			0.586492	−	0.809955i	$-0.300509\pi$
$223$	17.5164			1.17298			0.586492	+	0.809955i	$0.300509\pi$
$224$	−10.3066	−	10.8524i	−0.688636	−	0.725107i
$225$	−8.51902			−0.567935
$226$	0.254556	−	1.46492i	0.0169328	−	0.0974447i
$227$	−11.4237	+	6.59546i	−0.758215	+	0.437756i	−0.828655	−	0.559760i	$-0.810893\pi$
$227$	−11.4237	+	6.59546i	−0.758215	+	0.437756i	0.0704394	+	0.997516i	$0.477560\pi$
$228$	−14.3500	−	5.14241i	−0.950349	−	0.340565i
$229$	14.8693	+	8.58482i	0.982594	+	0.567301i	0.903052	−	0.429531i	$-0.141321\pi$
$229$	14.8693	+	8.58482i	0.982594	+	0.567301i	0.0795417	+	0.996832i	$0.474654\pi$
$230$	1.01017	+	2.75413i	0.0666087	+	0.181602i
$231$	−29.2143	−	15.0070i	−1.92216	−	0.987388i
$232$	−1.57040	−	0.891141i	−0.103102	−	0.0585062i
$233$	−12.4393	+	21.5455i	−0.814927	+	1.41149i	0.0944534	+	0.995529i	$0.469890\pi$
$233$	−12.4393	+	21.5455i	−0.814927	+	1.41149i	−0.909380	+	0.415966i	$0.863444\pi$
$234$	−7.15277	+	8.56744i	−0.467591	+	0.560071i
$235$	14.1125	−	8.14787i	0.920600	−	0.531508i
$236$	−6.85598	+	1.24402i	−0.446286	+	0.0809791i
$237$		−	21.4184i		−	1.39127i
$238$	1.83785	+	4.33952i	0.119130	+	0.281289i
$239$	−13.3242			−0.861872			−0.430936	−	0.902383i	$-0.641817\pi$
$239$	−13.3242			−0.861872			−0.430936	+	0.902383i	$0.641817\pi$
$240$	−11.2937	−	9.28701i	−0.729005	−	0.599474i
$241$	11.1218	+	19.2635i	0.716416	+	1.24087i	0.962411	+	0.271598i	$0.0875521\pi$
$241$	11.1218	+	19.2635i	0.716416	+	1.24087i	−0.245995	+	0.969271i	$0.579115\pi$
$242$	15.7033	+	13.1103i	1.00944	+	0.842763i
$243$	−19.1678	−	11.0665i	−1.22962	−	0.709919i
$244$	16.6665	+	19.6632i	1.06696	+	1.25881i
$245$	−9.47446	−	4.29339i	−0.605301	−	0.274295i
$246$	−7.62177	−	20.7800i	−0.485946	−	1.32488i
$247$	4.00667	−	6.93975i	0.254938	−	0.441566i
$248$	10.3389	−	0.0770004i	0.656519	−	0.00488953i
$249$	−3.65544	−	6.33141i	−0.231654	−	0.401237i
$250$	16.1328	+	2.80337i	1.02033	+	0.177301i
$251$		−	27.4386i		−	1.73191i	−0.500121	−	0.865955i	$-0.666711\pi$
$251$		−	27.4386i		−	1.73191i	0.500121	−	0.865955i	$-0.333289\pi$
$252$	−11.0315	−	11.7903i	−0.694917	−	0.742720i
$253$		−	7.04427i		−	0.442870i
$254$	1.74522	−	10.0433i	0.109505	−	0.630175i
$255$	2.30203	+	3.98724i	0.144159	+	0.249691i
$256$	3.09074	+	15.6986i	0.193171	+	0.981165i
$257$	12.0948	−	20.9487i	0.754451	−	1.30675i	−0.191196	−	0.981552i	$-0.561237\pi$
$257$	12.0948	−	20.9487i	0.754451	−	1.30675i	0.945647	−	0.325195i	$-0.105430\pi$
$258$	3.34456	−	1.22673i	0.208223	−	0.0763729i
$259$	−7.27797	+	14.1681i	−0.452231	+	0.880365i
$260$	5.86358	−	4.96995i	0.363644	−	0.308223i
$261$	−1.68697	−	0.973974i	−0.104421	−	0.0602875i
$262$	−13.3715	+	16.0162i	−0.826097	+	0.989482i
$263$	5.43846	+	9.41968i	0.335350	+	0.580842i	0.983552	−	0.180626i	$-0.0578123\pi$
$263$	5.43846	+	9.41968i	0.335350	+	0.580842i	−0.648202	+	0.761468i	$0.724479\pi$
$264$	17.7815	+	30.2755i	1.09438	+	1.86333i
$265$	−8.57040			−0.526475
$266$	9.25283	+	6.98433i	0.567327	+	0.428237i
$267$			6.35585i			0.388972i
$268$	1.00756	−	0.182822i	0.0615465	−	0.0111677i
$269$	−20.7887	+	12.0024i	−1.26751	+	0.731796i	−0.974516	−	0.224319i	$-0.927984\pi$
$269$	−20.7887	+	12.0024i	−1.26751	+	0.731796i	−0.292992	+	0.956115i	$0.594651\pi$
$270$	−0.203872	−	0.170208i	−0.0124072	−	0.0103585i
$271$	−3.11160	+	5.38945i	−0.189016	+	0.327386i	−0.944922	−	0.327294i	$-0.893863\pi$
$271$	−3.11160	+	5.38945i	−0.189016	+	0.327386i	0.755906	+	0.654680i	$0.227197\pi$
$272$	0.825537	−	4.96995i	0.0500555	−	0.301347i
$273$	14.1475	−	9.12129i	0.856243	−	0.552045i
$274$	−12.4305	+	4.55930i	−0.750952	+	0.275437i
$275$	−12.2010	−	7.04427i	−0.735750	−	0.424786i
$276$	2.31687	−	6.46526i	0.139459	−	0.389163i
$277$	−24.2493	+	14.0003i	−1.45700	+	0.841199i	−0.998863	−	0.0476832i	$-0.984816\pi$
$277$	−24.2493	+	14.0003i	−1.45700	+	0.841199i	−0.458136	+	0.888882i	$0.651483\pi$
$278$	−2.36197	−	0.410435i	−0.141661	−	0.0246163i
$279$	11.1541			0.667780
$280$	6.09507	+	9.30085i	0.364250	+	0.555832i
$281$	−16.7112			−0.996906			−0.498453	−	0.866917i	$-0.666098\pi$
$281$	−16.7112			−0.996906			−0.498453	+	0.866917i	$0.666098\pi$
$282$	−37.5875	−	6.53152i	−2.23830	−	0.388946i
$283$	24.1193	−	13.9253i	1.43374	−	0.827772i	0.436339	−	0.899782i	$-0.356275\pi$
$283$	24.1193	−	13.9253i	1.43374	−	0.827772i	0.997404	+	0.0720102i	$0.0229414\pi$
$284$	13.9581	+	5.00198i	0.828260	+	0.296813i
$285$	9.80843	+	5.66290i	0.581001	+	0.335441i
$286$	−17.3286	+	6.35585i	−1.02466	+	0.375829i
$287$	0.825537	+	16.8127i	0.0487299	+	0.992422i
$288$	3.20814	+	16.9604i	0.189041	+	0.999403i
$289$	7.70682	−	13.3486i	0.453342	−	0.785212i
$290$	1.02983	+	0.859784i	0.0604738	+	0.0504882i
$291$	3.34554	−	1.93155i	0.196119	−	0.113229i
$292$	3.53308	+	19.4713i	0.206758	+	1.13947i
$293$			20.1851i			1.17923i	0.807685	+	0.589614i	$0.200720\pi$
$293$			20.1851i			1.17923i	−0.807685	+	0.589614i	$0.799280\pi$
$294$	10.5853	+	21.9314i	0.617344	+	1.27907i
$295$	5.17710			0.301423
$296$	14.6828	−	8.62352i	0.853418	−	0.501232i
$297$	0.318870	+	0.552300i	0.0185027	+	0.0320477i
$298$	3.34141	−	4.00228i	0.193563	−	0.231846i
$299$	3.12665	+	1.80517i	0.180819	+	0.104396i
$300$	−8.88128	−	10.4782i	−0.512761	−	0.604959i
$301$	−2.70602	+	0.132871i	−0.155972	+	0.00765855i
$302$	−18.9562	+	6.95282i	−1.09080	+	0.400090i
$303$	−0.257326	+	0.445702i	−0.0147830	+	0.0256049i
$304$	−4.35421	−	11.6033i	−0.249731	−	0.665494i
$305$	−9.57574	−	16.5857i	−0.548305	−	0.949693i
$306$	0.930515	−	5.35491i	0.0531940	−	0.306120i
$307$			17.8844i			1.02071i	0.859962	+	0.510357i	$0.170487\pi$
$307$			17.8844i			1.02071i	−0.859962	+	0.510357i	$0.829513\pi$
$308$	−6.05012	−	26.0080i	−0.344738	−	1.48194i
$309$		−	16.9169i		−	0.962368i
$310$	−7.56847	−	1.31516i	−0.429860	−	0.0746961i
$311$	0.715667	+	1.23957i	0.0405818	+	0.0702897i	0.885603	−	0.464443i	$-0.153746\pi$
$311$	0.715667	+	1.23957i	0.0405818	+	0.0702897i	−0.845021	+	0.534733i	$0.820412\pi$
$312$	−17.9947	+	0.134018i	−1.01875	+	0.00758730i
$313$	−2.42829	+	4.20591i	−0.137255	+	0.237732i	−0.926457	−	0.376402i	$-0.877161\pi$
$313$	−2.42829	+	4.20591i	−0.137255	+	0.237732i	0.789202	+	0.614134i	$0.210495\pi$
$314$	−6.27635	−	17.1118i	−0.354195	−	0.965676i
$315$	6.50060	+	10.0827i	0.366267	+	0.568094i
$316$	13.2839	−	11.2594i	0.747277	−	0.633389i
$317$	9.78002	+	5.64650i	0.549301	+	0.317139i	0.748840	−	0.662751i	$-0.230611\pi$
$317$	9.78002	+	5.64650i	0.549301	+	0.317139i	−0.199539	+	0.979890i	$0.563944\pi$
$318$	15.4023	+	12.8591i	0.863719	+	0.721100i
$319$	−1.61073	−	2.78987i	−0.0901838	−	0.156203i
$320$	−0.177064	−	11.8865i	−0.00989815	−	0.664477i
$321$	31.8273			1.77642
$322$	−3.14674	+	4.16879i	−0.175361	+	0.232318i
$323$			3.90239i			0.217135i
$324$	−3.15767	−	17.4023i	−0.175426	−	0.966795i
$325$	6.25330	−	3.61034i	0.346871	−	0.200266i
$326$	−2.92860	+	3.50781i	−0.162200	+	0.194280i
$327$	−23.6373	+	40.9410i	−1.30714	+	2.26404i
$328$	8.88128	−	15.6509i	0.490387	−	0.864174i
$329$	25.8082	+	13.2573i	1.42285	+	0.730900i
$330$	−8.98316	−	24.4917i	−0.494507	−	1.34822i
$331$	−20.6415	−	11.9174i	−1.13456	−	0.655039i	−0.189483	−	0.981884i	$-0.560681\pi$
$331$	−20.6415	−	11.9174i	−1.13456	−	0.655039i	−0.945078	+	0.326845i	$0.894014\pi$
$332$	2.00518	−	5.59548i	0.110049	−	0.307092i
$333$	15.9089	−	9.18503i	0.871805	−	0.503337i
$334$	3.40144	−	19.5746i	0.186119	−	1.07107i
$335$	−0.760830			−0.0415686
$336$	3.00125	−	25.8601i	0.163732	−	1.41079i
$337$	16.4650			0.896906			0.448453	−	0.893806i	$-0.351975\pi$
$337$	16.4650			0.896906			0.448453	+	0.893806i	$0.351975\pi$
$338$	−1.52797	+	8.79317i	−0.0831109	+	0.478285i
$339$	2.23983	−	1.29317i	0.121651	−	0.0702351i
$340$	−1.26277	+	3.52378i	−0.0684836	+	0.191104i
$341$	15.9751	+	9.22320i	0.865098	+	0.499465i
$342$	−4.60407	−	12.5525i	−0.248959	−	0.678763i
$343$	−2.71612	−	18.3200i	−0.146657	−	0.989187i
$344$	2.51902	+	1.42945i	0.135817	+	0.0770708i
$345$	−2.55137	+	4.41911i	−0.137361	+	0.237917i
$346$	5.92638	−	7.09850i	0.318604	−	0.381618i
$347$	2.78706	−	1.60911i	0.149617	−	0.0863817i	−0.423322	−	0.905979i	$-0.639136\pi$
$347$	2.78706	−	1.60911i	0.149617	−	0.0863817i	0.572940	+	0.819597i	$0.305803\pi$
$348$	−0.560743	−	3.09033i	−0.0300590	−	0.165659i
$349$			22.8716i			1.22429i	0.790747	+	0.612143i	$0.209692\pi$
$349$			22.8716i			1.22429i	−0.790747	+	0.612143i	$0.790308\pi$
$350$	4.07382	+	9.61910i	0.217755	+	0.514162i
$351$	−0.326856			−0.0174463
$352$	−9.42964	+	26.9437i	−0.502601	+	1.43610i
$353$	−11.6608	−	20.1971i	−0.620641	−	1.07498i	−0.989367	−	0.145444i	$-0.953539\pi$
$353$	−11.6608	−	20.1971i	−0.620641	−	1.07498i	0.368725	−	0.929538i	$-0.379794\pi$
$354$	−9.30405	−	7.76775i	−0.494505	−	0.412851i
$355$	−9.54058	−	5.50826i	−0.506361	−	0.292348i
$356$	−3.94196	+	3.34119i	−0.208923	+	0.177083i
$357$	−3.74562	+	7.29165i	−0.198239	+	0.385915i
$358$	−0.0615446	−	0.167795i	−0.00325273	−	0.00886825i
$359$	2.55488	−	4.42518i	0.134841	−	0.233552i	−0.790696	−	0.612210i	$-0.790281\pi$
$359$	2.55488	−	4.42518i	0.134841	−	0.233552i	0.925537	+	0.378658i	$0.123614\pi$
$360$	−0.0955128	−	12.8245i	−0.00503397	−	0.675912i
$361$	−4.70015	−	8.14090i	−0.247376	−	0.428468i
$362$	−3.78876	−	0.658366i	−0.199133	−	0.0346030i
$363$			35.5833i			1.86764i
$364$	13.0942	+	3.97945i	0.686325	+	0.208580i
$365$		−	14.7032i		−	0.769600i
$366$	−7.67613	+	44.1745i	−0.401238	+	2.30904i
$367$	−14.0779	−	24.3837i	−0.734862	−	1.27282i	−0.954784	−	0.297301i	$-0.903914\pi$
$367$	−14.0779	−	24.3837i	−0.734862	−	1.27282i	0.219922	−	0.975517i	$-0.429420\pi$
$368$	5.22777	−	1.96176i	0.272516	−	0.102264i
$369$	9.70682	−	16.8127i	0.505317	−	0.875234i
$370$	−11.8778	+	4.35658i	−0.617496	+	0.226488i
$371$	−8.26861	−	12.8249i	−0.429285	−	0.665837i
$372$	11.6284	+	13.7193i	0.602906	+	0.711313i
$373$	−6.10052	−	3.52214i	−0.315873	−	0.182369i	0.333679	−	0.942687i	$-0.391710\pi$
$373$	−6.10052	−	3.52214i	−0.315873	−	0.182369i	−0.649551	+	0.760318i	$0.725043\pi$
$374$	5.76060	−	6.89994i	0.297874	−	0.356787i
$375$	14.2414	+	24.6667i	0.735420	+	1.27379i
$376$	−15.7084	−	26.7457i	−0.810096	−	1.37930i
$377$	1.65107			0.0850346
$378$	0.0580101	−	0.469292i	0.00298372	−	0.0241378i
$379$		−	13.1974i		−	0.677905i	−0.940803	−	0.338953i	$-0.889927\pi$
$379$		−	13.1974i		−	0.677905i	0.940803	−	0.338953i	$-0.110073\pi$
$380$	1.64398	+	9.06019i	0.0843344	+	0.464778i
$381$	15.3561	−	8.86584i	0.786716	−	0.454211i
$382$	2.65680	+	2.21811i	0.135934	+	0.113488i
$383$	2.46546	−	4.27031i	0.125979	−	0.218202i	−0.796136	−	0.605118i	$-0.793126\pi$
$383$	2.46546	−	4.27031i	0.125979	−	0.218202i	0.922115	+	0.386915i	$0.126459\pi$
$384$	−17.5164	+	21.6276i	−0.893879	+	1.10368i
$385$	0.972993	+	19.8158i	0.0495883	+	1.00991i
$386$	5.24267	−	1.92293i	0.266845	−	0.0978746i
$387$	2.70602	+	1.56232i	0.137555	+	0.0794172i
$388$	2.95667	+	1.05955i	0.150102	+	0.0537903i
$389$	19.8735	−	11.4739i	1.00762	−	0.581752i	0.0971291	−	0.995272i	$-0.469034\pi$
$389$	19.8735	−	11.4739i	1.00762	−	0.581752i	0.910495	+	0.413520i	$0.135701\pi$
$390$	13.1728	+	2.28902i	0.667033	+	0.115909i
$391$	−1.75819			−0.0889155
$392$	−8.03755	+	18.0941i	−0.405957	+	0.913892i
$393$	−36.2923			−1.83070
$394$	27.2352	+	4.73261i	1.37209	+	0.238426i
$395$	−11.2048	+	6.46908i	−0.563773	+	0.325495i
$396$	−10.3891	+	28.9909i	−0.522073	+	1.45685i
$397$	−25.9079	−	14.9579i	−1.30028	−	0.750716i	−0.319827	−	0.947476i	$-0.603625\pi$
$397$	−25.9079	−	14.9579i	−1.30028	−	0.750716i	−0.980452	+	0.196760i	$0.936958\pi$
$398$	27.6116	−	10.1275i	1.38404	−	0.507646i
$399$	0.988965	+	20.1410i	0.0495102	+	1.00831i
$400$	1.82991	−	11.0165i	0.0914953	−	0.550826i
$401$	7.83525	−	13.5711i	0.391274	−	0.677706i	−0.601344	−	0.798990i	$-0.705368\pi$
$401$	7.83525	−	13.5711i	0.391274	−	0.677706i	0.992618	+	0.121284i	$0.0387012\pi$
$402$	1.36733	+	1.14155i	0.0681962	+	0.0569355i
$403$	−8.18757	+	4.72709i	−0.407852	+	0.235473i
$404$	−0.411701	+	0.0747036i	−0.0204829	+	0.00371664i
$405$			13.1409i			0.652975i
$406$	−0.293030	+	2.37057i	−0.0145429	+	0.117650i
$407$	30.3800			1.50588
$408$	7.55650	−	4.43811i	0.374103	−	0.219719i
$409$	13.0434	+	22.5918i	0.644954	+	1.11709i	0.984312	+	0.176436i	$0.0564568\pi$
$409$	13.0434	+	22.5918i	0.644954	+	1.11709i	−0.339358	+	0.940657i	$0.610210\pi$
$410$	−8.56877	+	10.2635i	−0.423182	+	0.506878i
$411$	−19.9452	−	11.5154i	−0.983824	−	0.568011i
$412$	10.4920	−	8.89299i	0.516904	−	0.438126i
$413$	4.99481	+	7.74713i	0.245778	+	0.381211i
$414$	5.65544	−	2.07433i	0.277950	−	0.101948i
$415$	−2.20814	+	3.82460i	−0.108393	+	0.187742i
$416$	−9.54269	−	11.0900i	−0.467869	−	0.543733i
$417$	−2.08505	−	3.61141i	−0.102105	−	0.176851i
$418$	3.78553	−	21.7849i	0.185156	−	1.06554i
$419$			0.252757i			0.0123480i	0.999981	+	0.00617398i	$0.00196525\pi$
$419$			0.252757i			0.0123480i	−0.999981	+	0.00617398i	$0.998035\pi$
$420$	−5.62443	+	18.5070i	−0.274444	+	0.903049i
$421$			18.3701i			0.895302i	0.894208	+	0.447651i	$0.147739\pi$
$421$			18.3701i			0.895302i	−0.894208	+	0.447651i	$0.852261\pi$
$422$	−23.9837	−	4.16761i	−1.16751	−	0.202876i
$423$	−16.7312	−	28.9793i	−0.813498	−	1.40902i
$424$	0.121490	+	16.3125i	0.00590009	+	0.792206i
$425$	−1.75819	+	3.04528i	−0.0852848	+	0.147718i
$426$	8.88128	+	24.2139i	0.430299	+	1.17317i
$427$	15.5806	−	30.3310i	0.753998	−	1.46782i
$428$	16.7312	+	19.7396i	0.808732	+	0.954148i
$429$	−27.8044	−	16.0529i	−1.34241	−	0.775041i
$430$	−1.65192	−	1.37915i	−0.0796627	−	0.0665086i
$431$	−13.7223	−	23.7678i	−0.660982	−	1.14485i	−0.980358	−	0.197226i	$-0.936807\pi$
$431$	−13.7223	−	23.7678i	−0.660982	−	1.14485i	0.319377	−	0.947628i	$-0.396527\pi$
$432$	−0.321076	+	0.390453i	−0.0154478	+	0.0187857i
$433$	−7.26215			−0.348997			−0.174498	−	0.984657i	$-0.555830\pi$
$433$	−7.26215			−0.348997			−0.174498	+	0.984657i	$0.555830\pi$
$434$	−5.33393	−	12.5945i	−0.256037	−	0.604554i
$435$			2.33358i			0.111886i
$436$	−37.8178	+	6.86207i	−1.81114	+	0.328634i
$437$	−3.74562	+	2.16253i	−0.179177	+	0.103448i
$438$	−22.0607	+	26.4239i	−1.05410	+	1.26258i
$439$	−15.0022	+	25.9845i	−0.716015	+	1.24017i	0.246551	+	0.969130i	$0.420703\pi$
$439$	−15.0022	+	25.9845i	−0.716015	+	1.24017i	−0.962567	+	0.271045i	$0.912631\pi$
$440$	10.4676	−	18.4464i	0.499025	−	0.879398i
$441$	−8.81623	+	19.4553i	−0.419821	+	0.926441i
$442$	1.58637	+	4.32507i	0.0754558	+	0.205723i
$443$	30.3838	+	17.5421i	1.44358	+	0.833451i	0.998086	−	0.0618342i	$-0.0196950\pi$
$443$	30.3838	+	17.5421i	1.44358	+	0.833451i	0.445493	+	0.895285i	$0.353028\pi$
$444$	27.8828	+	9.99202i	1.32326	+	0.474200i
$445$	3.32499	−	1.91968i	0.157620	−	0.0910017i
$446$	−4.24102	+	24.4062i	−0.200818	+	1.15567i
$447$	9.06908			0.428953
$448$	17.6164	−	11.7329i	0.832298	−	0.554329i
$449$	−21.0107			−0.991556			−0.495778	−	0.868449i	$-0.665117\pi$
$449$	−21.0107			−0.991556			−0.495778	+	0.868449i	$0.665117\pi$
$450$	2.06260	−	11.8698i	0.0972320	−	0.559550i
$451$	27.8044	−	16.0529i	1.30926	−	0.755901i
$452$	1.97948	+	0.709363i	0.0931071	+	0.0333656i
$453$	−30.4159	−	17.5606i	−1.42906	−	0.825071i
$454$	−6.42380	−	17.5139i	−0.301484	−	0.821966i
$455$	−9.04471	−	4.64614i	−0.424022	−	0.217814i
$456$	10.6395	−	18.7492i	0.498239	−	0.878012i
$457$	−6.68780	+	11.5836i	−0.312842	+	0.541858i	−0.978976	−	0.203974i	$-0.934614\pi$
$457$	−6.68780	+	11.5836i	−0.312842	+	0.541858i	0.666135	+	0.745832i	$0.267948\pi$
$458$	−15.5616	+	18.6394i	−0.727148	+	0.870963i
$459$	0.137849	−	0.0795874i	0.00643426	−	0.00371482i
$460$	−4.08200	+	0.740682i	−0.190324	+	0.0345345i
$461$		−	2.68641i		−	0.125118i	−0.998041	−	0.0625592i	$-0.980074\pi$
$461$		−	2.68641i		−	0.125118i	0.998041	−	0.0625592i	$-0.0199262\pi$
$462$	27.9831	−	37.0719i	1.30189	−	1.72474i
$463$	−21.0380			−0.977721			−0.488860	−	0.872362i	$-0.662587\pi$
$463$	−21.0380			−0.977721			−0.488860	+	0.872362i	$0.662587\pi$
$464$	1.62188	−	1.97232i	0.0752937	−	0.0915629i
$465$	−6.68113	−	11.5721i	−0.309830	−	0.536641i
$466$	−27.0083	−	22.5487i	−1.25114	−	1.04455i
$467$	21.3849	+	12.3466i	0.989574	+	0.571331i	0.905147	−	0.425099i	$-0.139761\pi$
$467$	21.3849	+	12.3466i	0.989574	+	0.571331i	0.0844270	+	0.996430i	$0.473094\pi$
$468$	−10.2055	−	12.0405i	−0.471749	−	0.556573i
$469$	−0.734040	−	1.13852i	−0.0338948	−	0.0525721i
$470$	7.93582	+	21.6362i	0.366052	+	0.998004i
$471$	15.8521	−	27.4566i	0.730426	−	1.26513i
$472$	−0.0733884	−	9.85387i	−0.00337797	−	0.453561i
$473$	2.58373	+	4.47515i	0.118800	+	0.205767i
$474$	29.8429	+	5.18576i	1.37073	+	0.238190i
$475$			8.65014i			0.396896i
$476$	−6.49138	+	1.51006i	−0.297532	+	0.0692135i
$477$			17.5988i			0.805794i
$478$	3.22602	−	18.5651i	0.147555	−	0.849147i
$479$	20.4562	+	35.4311i	0.934666	+	1.61889i	0.775229	+	0.631680i	$0.217634\pi$
$479$	20.4562	+	35.4311i	0.934666	+	1.61889i	0.159437	+	0.987208i	$0.449032\pi$
$480$	15.6743	−	13.4874i	0.715431	−	0.615610i
$481$	−7.78520	+	13.4844i	−0.354974	+	0.614834i
$482$	−29.5332	+	10.8323i	−1.34520	+	0.493399i
$483$	−9.07439	+	0.445570i	−0.412899	+	0.0202741i
$484$	−22.0691	+	18.7057i	−1.00314	+	0.850257i
$485$	−2.02094	−	1.16679i	−0.0917660	−	0.0529811i
$486$	20.0603	−	24.0278i	0.909952	−	1.08992i
$487$	−8.76704	−	15.1850i	−0.397273	−	0.688096i	0.596116	−	0.802898i	$-0.296710\pi$
$487$	−8.76704	−	15.1850i	−0.397273	−	0.688096i	−0.993388	+	0.114802i	$0.963377\pi$
$488$	−31.4327	+	18.4612i	−1.42289	+	0.835697i
$489$	−7.94863			−0.359449
$490$	8.27606	−	12.1616i	0.373874	−	0.549404i
$491$		−	15.7509i		−	0.710830i	−0.934709	−	0.355415i	$-0.884340\pi$
$491$		−	15.7509i		−	0.710830i	0.934709	−	0.355415i	$-0.115660\pi$
$492$	30.7988	−	5.58847i	1.38852	−	0.251948i
$493$	−0.696329	+	0.402026i	−0.0313611	+	0.0181063i
$494$	8.69930	+	7.26286i	0.391400	+	0.326771i
$495$	11.4406	−	19.8158i	0.514219	−	0.890653i
$496$	−2.39593	+	14.4241i	−0.107581	+	0.647663i
$497$	−0.961958	−	19.5910i	−0.0431497	−	0.878778i
$498$	9.70682	−	3.56031i	0.434973	−	0.159541i
$499$	8.82147	+	5.09308i	0.394903	+	0.227997i	0.684282	−	0.729217i	$-0.260116\pi$
$499$	8.82147	+	5.09308i	0.394903	+	0.227997i	−0.289379	+	0.957215i	$0.593449\pi$
$500$	−7.81206	+	21.7996i	−0.349366	+	0.974909i
$501$	29.9292	−	17.2796i	1.33714	−	0.771997i
$502$	38.2312	+	6.64337i	1.70634	+	0.296508i
$503$	27.1001			1.20833			0.604167	−	0.796858i	$-0.293506\pi$
$503$	27.1001			1.20833			0.604167	+	0.796858i	$0.293506\pi$
$504$	19.0988	−	12.5159i	0.850726	−	0.557501i
$505$	0.310885			0.0138342
$506$	9.81502	+	1.70554i	0.436331	+	0.0758205i
$507$	−13.4446	+	7.76224i	−0.597096	+	0.344733i
$508$	13.5712	+	4.86333i	0.602124	+	0.215776i
$509$	19.4357	+	11.2212i	0.861471	+	0.497371i	0.864505	−	0.502625i	$-0.167632\pi$
$509$	19.4357	+	11.2212i	0.861471	+	0.497371i	−0.00303361	+	0.999995i	$0.500966\pi$
$510$	−6.11292	+	2.24212i	−0.270685	+	0.0992828i
$511$	22.0022	−	14.1855i	0.973319	−	0.627528i
$512$	−22.6218	+	0.505513i	−0.999750	+	0.0223407i
$513$	0.195781	−	0.339103i	0.00864396	−	0.0149718i
$514$	26.2602	+	21.9241i	1.15829	+	0.967030i
$515$	−8.84987	+	5.10948i	−0.389972	+	0.225150i
$516$	0.899470	+	4.95710i	0.0395970	+	0.218224i
$517$		−	55.3392i		−	2.43382i
$518$	−17.9788	−	13.5710i	−0.789944	−	0.596275i
$519$	16.0850			0.706055
$520$	5.50512	+	9.37323i	0.241415	+	0.411043i
$521$	5.13510	+	8.89426i	0.224973	+	0.389664i	0.956311	−	0.292350i	$-0.0944373\pi$
$521$	5.13510	+	8.89426i	0.224973	+	0.389664i	−0.731338	+	0.682015i	$0.761104\pi$
$522$	1.76552	−	2.11470i	0.0772746	−	0.0925579i
$523$	15.4655	+	8.92903i	0.676261	+	0.390439i	0.798445	−	0.602068i	$-0.205656\pi$
$523$	15.4655	+	8.92903i	0.676261	+	0.390439i	−0.122184	+	0.992507i	$0.538990\pi$
$524$	−19.0784	−	22.5088i	−0.833443	−	0.983302i
$525$	−8.30264	+	16.1629i	−0.362357	+	0.705406i
$526$	−14.4415	+	5.29692i	−0.629680	+	0.230956i
$527$	2.30203	−	3.98724i	0.100278	−	0.173687i
$528$	−46.4891	+	17.4453i	−2.02318	+	0.759211i
$529$	10.5257	+	18.2310i	0.457639	+	0.792653i
$530$	2.07504	−	11.9414i	0.0901341	−	0.518702i
$531$		−	10.6309i		−	0.461341i
$532$	−11.9718	+	11.2013i	−0.519043	+	0.485636i
$533$			16.4549i			0.712742i
$534$	−8.85582	−	1.53886i	−0.383229	−	0.0665931i
$535$	−9.61292	−	16.6501i	−0.415603	−	0.719845i
$536$	0.0107852	+	1.44813i	0.000465850	+	0.0625497i
$537$	0.155442	−	0.269234i	0.00670783	−	0.0116183i
$538$	−11.6900	−	31.8716i	−0.503991	−	1.37408i
$539$	−28.7140	+	20.5740i	−1.23680	+	0.886186i
$540$	0.286517	−	0.242851i	0.0123297	−	0.0104506i
$541$	19.9303	+	11.5067i	0.856869	+	0.494714i	0.862963	−	0.505268i	$-0.168606\pi$
$541$	19.9303	+	11.5067i	0.856869	+	0.494714i	−0.00609356	+	0.999981i	$0.501940\pi$
$542$	−6.75593	−	5.64038i	−0.290192	−	0.242275i
$543$	−3.34456	−	5.79294i	−0.143529	−	0.248599i
$544$	6.72492	+	2.35356i	0.288328	+	0.100908i
$545$	28.5571			1.22325
$546$	9.28365	+	21.9206i	0.397304	+	0.938113i
$547$		−	9.10136i		−	0.389146i	−0.980888	−	0.194573i	$-0.937668\pi$
$547$		−	9.10136i		−	0.389146i	0.980888	−	0.194573i	$-0.0623321\pi$
$548$	−3.34299	−	18.4237i	−0.142806	−	0.787021i
$549$	−34.0577	+	19.6632i	−1.45355	+	0.839206i
$550$	12.7691	−	15.2946i	0.544477	−	0.652163i
$551$	−0.988965	+	1.71294i	−0.0421313	+	0.0729736i
$552$	8.44731	+	4.79353i	0.359541	+	0.204026i
$553$	−20.4907	−	10.5258i	−0.871353	−	0.447602i
$554$	−13.6360	−	37.1771i	−0.579337	−	1.57950i
$555$	−19.0584	−	11.0034i	−0.808983	−	0.467067i
$556$	1.14375	−	3.19164i	0.0485057	−	0.135356i
$557$	−15.0016	+	8.66116i	−0.635637	+	0.366985i	−0.782932	−	0.622107i	$-0.786277\pi$
$557$	−15.0016	+	8.66116i	−0.635637	+	0.366985i	0.147295	+	0.989093i	$0.452943\pi$
$558$	−2.70061	+	15.5414i	−0.114326	+	0.657921i
$559$	−2.64843			−0.112017
$560$	−14.4349	+	6.24057i	−0.609986	+	0.263712i
$561$	15.6351			0.660115
$562$	4.04607	−	23.2843i	0.170673	−	0.982187i
$563$	6.91560	−	3.99272i	0.291458	−	0.168273i	−0.347141	−	0.937813i	$-0.612848\pi$
$563$	6.91560	−	3.99272i	0.291458	−	0.168273i	0.638599	+	0.769540i	$0.279514\pi$
$564$	18.2012	−	50.7905i	0.766408	−	2.13867i
$565$	−1.35301	−	0.781160i	−0.0569215	−	0.0328637i
$566$	13.5629	+	36.9778i	0.570090	+	1.55429i
$567$	−19.6643	+	12.6782i	−0.825823	+	0.532432i
$568$	−10.3489	+	18.2372i	−0.434231	+	0.765216i
$569$	−5.98535	+	10.3669i	−0.250919	+	0.434604i	−0.963779	−	0.266702i	$-0.914066\pi$
$569$	−5.98535	+	10.3669i	−0.250919	+	0.434604i	0.712860	+	0.701306i	$0.247399\pi$
$570$	−10.2651	+	12.2953i	−0.429958	+	0.514995i
$571$	−36.9016	+	21.3051i	−1.54428	+	0.891592i	−0.545722	+	0.837966i	$0.683745\pi$
$571$	−36.9016	+	21.3051i	−1.54428	+	0.891592i	−0.998561	+	0.0536265i	$0.982922\pi$
$572$	−4.66027	−	25.6834i	−0.194856	−	1.07388i
$573$			6.02026i			0.251500i
$574$	−23.6256	−	2.92040i	−0.986113	−	0.121895i
$575$	−3.89725			−0.162527
$576$	−24.4083	+	0.363590i	−1.01701	+	0.0151496i
$577$	14.9650	+	25.9202i	0.623001	+	1.07907i	0.988924	+	0.148425i	$0.0474203\pi$
$577$	14.9650	+	25.9202i	0.623001	+	1.07907i	−0.365922	+	0.930645i	$0.619246\pi$
$578$	16.7331	+	13.9701i	0.696005	+	0.581079i
$579$	8.41208	+	4.85672i	0.349594	+	0.201838i
$580$	−1.44731	+	1.22673i	−0.0600961	+	0.0509372i
$581$	−7.85360	+	0.385627i	−0.325822	+	0.0159985i
$582$	1.88128	+	5.12912i	0.0779816	+	0.212609i
$583$	−14.5522	+	25.2052i	−0.602692	+	1.04389i
$584$	−27.9854	+	0.208426i	−1.15804	+	0.00862473i
$585$	5.86358	+	10.1560i	0.242429	+	0.419900i
$586$	−28.1246	−	4.88717i	−1.16182	−	0.201887i
$587$			19.4269i			0.801833i	0.916115	+	0.400916i	$0.131308\pi$
$587$			19.4269i			0.801833i	−0.916115	+	0.400916i	$0.868692\pi$
$588$	−33.1207	+	9.43881i	−1.36587	+	0.389250i
$589$		−	11.3258i		−	0.466671i
$590$	−1.25347	+	7.21343i	−0.0516044	+	0.296972i
$591$	24.0421	+	41.6421i	0.988959	+	1.71293i
$592$	8.46050	+	22.5459i	0.347724	+	0.926630i
$593$	9.07706	−	15.7219i	0.372750	−	0.645622i	−0.617237	−	0.786777i	$-0.711748\pi$
$593$	9.07706	−	15.7219i	0.372750	−	0.645622i	0.989988	+	0.141155i	$0.0450815\pi$
$594$	−0.846742	+	0.310572i	−0.0347423	+	0.0127429i
$595$	4.94585	−	0.242851i	0.202760	−	0.00995592i
$596$	4.76750	+	5.62473i	0.195284	+	0.230398i
$597$	44.3039	+	25.5789i	1.81324	+	1.04687i
$598$	−3.27222	+	3.91940i	−0.133811	+	0.160276i
$599$	−5.59258	−	9.68663i	−0.228507	−	0.395785i	0.728859	−	0.684664i	$-0.240051\pi$
$599$	−5.59258	−	9.68663i	−0.228507	−	0.395785i	−0.957366	+	0.288879i	$0.906718\pi$
$600$	16.7499	−	9.83763i	0.683814	−	0.401620i
$601$	−4.21883			−0.172090			−0.0860448	−	0.996291i	$-0.527423\pi$
$601$	−4.21883			−0.172090			−0.0860448	+	0.996291i	$0.527423\pi$
$602$	0.470041	−	3.80256i	0.0191574	−	0.154981i
$603$			1.56232i			0.0636226i
$604$	−5.09798	−	28.0957i	−0.207434	−	1.14320i
$605$	18.6150	−	10.7474i	0.756806	−	0.436942i
$606$	−0.558708	−	0.466453i	−0.0226960	−	0.0189484i
$607$	13.6196	−	23.5898i	0.552802	−	0.957481i	−0.445269	−	0.895397i	$-0.646892\pi$
$607$	13.6196	−	23.5898i	0.552802	−	0.957481i	0.998071	−	0.0620841i	$-0.0197747\pi$
$608$	17.2215	−	3.25751i	0.698423	−	0.132110i
$609$	−3.49201	+	2.25141i	−0.141504	+	0.0912315i
$610$	25.4278	−	9.32653i	1.02954	−	0.377620i
$611$	24.5627	+	14.1813i	0.993701	+	0.573713i
$612$	7.23589	+	2.59304i	0.292493	+	0.104817i
$613$	3.20401	−	1.84984i	0.129409	−	0.0747141i	−0.433898	−	0.900962i	$-0.642862\pi$
$613$	3.20401	−	1.84984i	0.129409	−	0.0747141i	0.563307	+	0.826248i	$0.309529\pi$
$614$	−24.9189	−	4.33012i	−1.00564	−	0.174749i
$615$	−23.2569			−0.937808
$616$	37.7027	−	2.13285i	1.51908	−	0.0859351i
$617$	26.0487			1.04868			0.524341	−	0.851508i	$-0.324312\pi$
$617$	26.0487			1.04868			0.524341	+	0.851508i	$0.324312\pi$
$618$	23.5709	+	4.09587i	0.948159	+	0.164760i
$619$	−27.7816	+	16.0397i	−1.11664	+	0.644692i	−0.940541	−	0.339681i	$-0.889681\pi$
$619$	−27.7816	+	16.0397i	−1.11664	+	0.644692i	−0.176098	+	0.984373i	$0.556348\pi$
$620$	3.66492	−	10.2270i	0.147187	−	0.410725i
$621$	0.152780	+	0.0882077i	0.00613086	+	0.00353965i
$622$	−1.90041	+	0.697042i	−0.0761996	+	0.0279488i
$623$	6.08057	+	3.12350i	0.243613	+	0.125140i
$624$	4.17009	−	25.1051i	0.166937	−	1.00501i
$625$	1.62309	−	2.81127i	0.0649236	−	0.112451i
$626$	−5.27231	−	4.40174i	−0.210724	−	0.175929i
$627$	33.3088	−	19.2308i	1.33022	−	0.768005i
$628$	25.3621	−	4.60198i	1.01206	−	0.183639i
$629$		−	7.58258i		−	0.302337i
$630$	−15.6224	+	6.61631i	−0.622412	+	0.263600i
$631$	11.7538			0.467912			0.233956	−	0.972247i	$-0.424833\pi$
$631$	11.7538			0.467912			0.233956	+	0.972247i	$0.424833\pi$
$632$	12.4718	+	21.2350i	0.496101	+	0.844682i
$633$	−21.1718	−	36.6707i	−0.841504	−	1.45753i
$634$	−10.2354	+	12.2597i	−0.406499	+	0.486896i
$635$	−9.27612	−	5.35557i	−0.368112	−	0.212529i
$636$	−21.6461	+	18.3472i	−0.858325	+	0.727513i
$637$	−1.77364	−	18.0172i	−0.0702742	−	0.713869i
$638$	4.27721	−	1.56881i	0.169336	−	0.0621099i
$639$	−11.3109	+	19.5910i	−0.447452	+	0.775009i
$640$	16.6048	+	2.63122i	0.656361	+	0.104008i
$641$	−20.9136	−	36.2235i	−0.826039	−	1.43074i	−0.901123	−	0.433564i	$-0.857256\pi$
$641$	−20.9136	−	36.2235i	−0.826039	−	1.43074i	0.0750839	−	0.997177i	$-0.476078\pi$
$642$	−7.70593	+	44.3460i	−0.304129	+	1.75020i
$643$		−	42.9368i		−	1.69326i	−0.532180	−	0.846631i	$-0.678627\pi$
$643$		−	42.9368i		−	1.69326i	0.532180	−	0.846631i	$-0.321373\pi$
$644$	−5.04664	−	5.39379i	−0.198865	−	0.212545i
$645$		−	3.74321i		−	0.147389i
$646$	−5.43733	−	0.944836i	−0.213929	−	0.0371741i
$647$	4.55891	+	7.89626i	0.179229	+	0.310434i	0.941617	−	0.336687i	$-0.109306\pi$
$647$	4.55891	+	7.89626i	0.179229	+	0.310434i	−0.762388	+	0.647121i	$0.775973\pi$
$648$	25.0118	−	0.186279i	0.982555	−	0.00731774i
$649$	8.79054	−	15.2257i	0.345059	−	0.597660i
$650$	3.51638	+	9.58706i	0.137924	+	0.376035i
$651$	10.8708	−	21.1624i	0.426061	−	0.829419i
$652$	−4.17849	−	4.92981i	−0.163642	−	0.193066i
$653$	−18.8716	−	10.8955i	−0.738502	−	0.426374i	0.0830227	−	0.996548i	$-0.473543\pi$
$653$	−18.8716	−	10.8955i	−0.738502	−	0.426374i	−0.821524	+	0.570174i	$0.806876\pi$
$654$	−51.3215	−	42.8472i	−2.00683	−	1.67546i
$655$	10.9615	+	18.9859i	0.428301	+	0.741840i
$656$	19.6566	+	16.1639i	0.767460	+	0.631096i
$657$	−30.1922			−1.17791
$658$	−24.7205	+	32.7497i	−0.963706	+	1.27672i
$659$		−	0.152682i		−	0.00594765i	−0.999996	−	0.00297383i	$-0.999053\pi$
$659$		−	0.152682i		−	0.00594765i	0.999996	−	0.00297383i	$-0.000946600\pi$
$660$	36.3001	−	6.58668i	1.41298	−	0.256386i
$661$	−24.6004	+	14.2031i	−0.956845	+	0.552435i	−0.895201	−	0.445663i	$-0.852968\pi$
$661$	−24.6004	+	14.2031i	−0.956845	+	0.552435i	−0.0616446	+	0.998098i	$0.519635\pi$
$662$	21.6026	−	25.8751i	0.839608	−	1.00567i
$663$	−4.00667	+	6.93975i	−0.155606	+	0.269518i
$664$	7.31088	+	4.14865i	0.283717	+	0.160999i
$665$	10.2379	−	6.60065i	0.397007	−	0.255962i
$666$	8.94599	+	24.3903i	0.346650	+	0.945106i
$667$	−0.771750	−	0.445570i	−0.0298823	−	0.0172525i
$668$	26.4504	+	9.47869i	1.02340	+	0.366742i
$669$	−37.3166	+	21.5447i	−1.44274	+	0.832968i
$670$	0.184210	−	1.06009i	0.00711666	−	0.0409549i
$671$	−65.0371			−2.51073
$672$	35.3051	+	10.4429i	1.36193	+	0.402845i
$673$	26.2542			1.01203			0.506013	−	0.862526i	$-0.331119\pi$
$673$	26.2542			1.01203			0.506013	+	0.862526i	$0.331119\pi$
$674$	−3.98646	+	22.9413i	−0.153553	+	0.883664i
$675$	0.305561	−	0.176415i	0.0117610	−	0.00679023i
$676$	−11.8819	−	4.25796i	−0.456995	−	0.163768i
$677$	−4.00416	−	2.31180i	−0.153892	−	0.0888498i	0.421076	−	0.907025i	$-0.361652\pi$
$677$	−4.00416	−	2.31180i	−0.153892	−	0.0888498i	−0.574969	+	0.818175i	$0.694986\pi$
$678$	1.25951	+	3.43393i	0.0483712	+	0.131879i
$679$	−0.203767	−	4.14988i	−0.00781986	−	0.159258i
$680$	−4.60407	−	2.61264i	−0.176558	−	0.100190i
$681$	16.2245	−	28.1017i	0.621725	−	1.07686i
$682$	−16.7188	+	20.0255i	−0.640198	+	0.766816i
$683$	16.8469	−	9.72659i	0.644631	−	0.372178i	−0.141765	−	0.989900i	$-0.545278\pi$
$683$	16.8469	−	9.72659i	0.644631	−	0.372178i	0.786396	+	0.617723i	$0.211945\pi$
$684$	18.6046	−	3.37582i	0.711364	−	0.129078i
$685$			13.9121i			0.531555i
$686$	26.1835	+	0.651128i	0.999691	+	0.0248602i
$687$	−42.2365			−1.61142
$688$	−2.60160	+	3.16374i	−0.0991851	+	0.120617i
$689$	−7.45834	−	12.9182i	−0.284140	−	0.492145i
$690$	−5.53956	−	4.62486i	−0.210888	−	0.176065i
$691$	15.0449	+	8.68618i	0.572335	+	0.330438i	0.758081	−	0.652160i	$-0.226137\pi$
$691$	15.0449	+	8.68618i	0.572335	+	0.330438i	−0.185746	+	0.982598i	$0.559470\pi$
$692$	8.45570	+	9.97610i	0.321438	+	0.379234i
$693$	40.6905	−	1.99799i	1.54571	−	0.0758972i
$694$	1.56723	+	4.27290i	0.0594914	+	0.162197i
$695$	−1.25951	+	2.18154i	−0.0477760	+	0.0827504i
$696$	4.44163	−	0.0330798i	0.168359	−	0.00125388i
$697$	−4.00667	−	6.93975i	−0.151763	−	0.262862i
$698$	−31.8677	−	5.53760i	−1.20621	−	0.209601i
$699$		−	61.2003i		−	2.31481i
$700$	−14.3890	+	3.34724i	−0.543851	+	0.126514i
$701$		−	25.1180i		−	0.948695i	−0.880338	−	0.474348i	$-0.842684\pi$
$701$		−	25.1180i		−	0.948695i	0.880338	−	0.474348i	$-0.157316\pi$
$702$	0.0791376	−	0.455420i	0.00298686	−	0.0171887i
$703$	−9.32640	−	16.1538i	−0.351752	−	0.609252i
$704$	−35.2585	−	19.6622i	−1.32885	−	0.741046i
$705$	−20.0434	+	34.7162i	−0.754878	+	1.30749i
$706$	30.9646	−	11.3573i	1.16537	−	0.427438i
$707$	0.299938	+	0.465215i	0.0112803	+	0.0174962i
$708$	13.0757	−	11.0829i	0.491416	−	0.416523i
$709$	−17.4147	−	10.0544i	−0.654024	−	0.377601i	0.135972	−	0.990713i	$-0.456584\pi$
$709$	−17.4147	−	10.0544i	−0.654024	−	0.377601i	−0.789996	+	0.613112i	$0.789918\pi$
$710$	9.98478	−	11.9596i	0.374722	−	0.448834i
$711$	13.2839	+	23.0084i	0.498184	+	0.862881i
$712$	−3.70097	−	6.30143i	−0.138700	−	0.236156i
$713$	5.10275			0.191099
$714$	−9.25283	−	6.98433i	−0.346278	−	0.261382i
$715$			19.3941i			0.725297i
$716$	0.248696	−	0.0451260i	0.00929419	−	0.00168644i
$717$	28.3857	−	16.3885i	1.06008	−	0.612039i
$718$	5.54717	+	4.63121i	0.207019	+	0.172835i
$719$	19.1966	−	33.2496i	0.715914	−	1.24000i	−0.246692	−	0.969094i	$-0.579344\pi$
$719$	19.1966	−	33.2496i	0.715914	−	1.24000i	0.962606	−	0.270906i	$-0.0873231\pi$
$720$	17.8920	+	2.97196i	0.666794	+	0.110758i
$721$	−16.1842	−	8.31358i	−0.602730	−	0.309614i
$722$	12.4810	−	4.57783i	0.464494	−	0.170369i
$723$	−47.3873	−	27.3590i	−1.76235	−	1.01749i
$724$	1.83465	−	5.11960i	0.0681842	−	0.190269i
$725$	−1.54350	+	0.891141i	−0.0573242	+	0.0330961i
$726$	−49.5794	−	8.61532i	−1.84006	−	0.319745i
$727$	14.8679			0.551422			0.275711	−	0.961241i	$-0.411087\pi$
$727$	14.8679			0.551422			0.275711	+	0.961241i	$0.411087\pi$
$728$	−8.71504	+	17.2812i	−0.323001	+	0.640482i
$729$	27.9167			1.03395
$730$	20.4865	+	3.55990i	0.758238	+	0.131758i
$731$	1.11696	−	0.644877i	0.0413122	−	0.0238516i
$732$	−59.6913	−	21.3908i	−2.20625	−	0.790628i
$733$	36.4503	+	21.0446i	1.34632	+	0.777300i	0.987727	−	0.156192i	$-0.0499219\pi$
$733$	36.4503	+	21.0446i	1.34632	+	0.777300i	0.358597	+	0.933492i	$0.383255\pi$
$734$	37.3831	−	13.7115i	1.37984	−	0.506102i
$735$	25.4650	−	2.50681i	0.939291	−	0.0924650i
$736$	1.46765	+	7.75900i	0.0540982	+	0.286000i
$737$	−1.29186	+	2.23757i	−0.0475864	+	0.0824221i
$738$	21.0755	+	17.5955i	0.775800	+	0.647699i
$739$	−10.9859	+	6.34270i	−0.404122	+	0.233320i	−0.688261	−	0.725463i	$-0.741626\pi$
$739$	−10.9859	+	6.34270i	−0.404122	+	0.233320i	0.284139	+	0.958783i	$0.408292\pi$
$740$	−3.19435	−	17.6045i	−0.117427	−	0.647155i
$741$			19.7124i			0.724154i
$742$	19.8714	−	8.41580i	0.729501	−	0.308954i
$743$	−25.7219			−0.943644			−0.471822	−	0.881694i	$-0.656404\pi$
$743$	−25.7219			−0.943644			−0.471822	+	0.881694i	$0.656404\pi$
$744$	−21.9310	+	12.8806i	−0.804031	+	0.472226i
$745$	−2.73917	−	4.74438i	−0.100355	−	0.173821i
$746$	6.38455	−	7.64729i	0.233755	−	0.279987i
$747$	7.85360	+	4.53428i	0.287348	+	0.165901i
$748$	8.21917	+	9.69704i	0.300523	+	0.354559i
$749$	15.6411	−	30.4488i	0.571513	−	1.11257i
$750$	−37.8171	+	13.8707i	−1.38089	+	0.506487i
$751$	−17.9305	+	31.0565i	−0.654292	+	1.13327i	0.327779	+	0.944755i	$0.393700\pi$
$751$	−17.9305	+	31.0565i	−0.654292	+	1.13327i	−0.982071	+	0.188513i	$0.939633\pi$
$752$	41.0689	−	15.4114i	1.49763	−	0.561995i
$753$	33.7489	+	58.4548i	1.22988	+	2.13021i
$754$	−0.399754	+	2.30050i	−0.0145582	+	0.0837791i
$755$			21.2157i			0.772117i
$756$	0.639836	+	0.194451i	0.0232706	+	0.00707212i
$757$			30.7289i			1.11686i	0.829551	+	0.558431i	$0.188597\pi$
$757$			30.7289i			1.11686i	−0.829551	+	0.558431i	$0.811403\pi$
$758$	18.3884	+	3.19532i	0.667896	+	0.116059i
$759$	8.66429	+	15.0070i	0.314494	+	0.544719i
$760$	−13.0219	+	0.0969829i	−0.472354	+	0.00351794i
$761$	−22.5624	+	39.0792i	−0.817887	+	1.41662i	0.0893497	+	0.996000i	$0.471521\pi$
$761$	−22.5624	+	39.0792i	−0.817887	+	1.41662i	−0.907236	+	0.420621i	$0.861812\pi$
$762$	8.63510	+	23.5427i	0.312817	+	0.852863i
$763$	27.5515	+	42.7334i	0.997431	+	1.54705i
$764$	−3.73382	+	3.16477i	−0.135085	+	0.114497i
$765$	−4.94585	−	2.85549i	−0.178818	−	0.103240i
$766$	5.35303	+	4.46913i	0.193413	+	0.161476i
$767$	4.50535	+	7.80349i	0.162679	+	0.281768i
$768$	−25.8934	−	29.6426i	−0.934348	−	1.06963i
$769$	−28.0168			−1.01031			−0.505156	−	0.863028i	$-0.668565\pi$
$769$	−28.0168			−1.01031			−0.505156	+	0.863028i	$0.668565\pi$
$770$	−27.8456	−	3.44204i	−1.00348	−	0.124042i
$771$			59.5051i			2.14302i
$772$	1.40994	+	7.77037i	0.0507449	+	0.279662i
$773$	29.9953	−	17.3178i	1.07886	−	0.622878i	0.148268	−	0.988947i	$-0.452630\pi$
$773$	29.9953	−	17.3178i	1.07886	−	0.622878i	0.930588	+	0.366069i	$0.119297\pi$
$774$	−2.83201	+	3.39212i	−0.101794	+	0.121927i
$775$	5.10275	−	8.83822i	0.183296	−	0.317478i
$776$	−2.19216	+	3.86310i	−0.0786941	+	0.138677i
$777$	−1.92162	−	39.1353i	−0.0689377	−	1.40397i
$778$	11.1753	+	30.4684i	0.400655	+	1.09235i
$779$	−17.0715	−	9.85621i	−0.611649	−	0.353136i
$780$	−6.37875	+	17.8000i	−0.228396	+	0.637341i
$781$	−32.3992	+	18.7057i	−1.15933	+	0.669341i
$782$	0.425689	−	2.44975i	0.0152226	−	0.0876028i
$783$	0.0806779			0.00288319
$784$	−23.2651	−	15.5799i	−0.830898	−	0.556425i
$785$	−19.1515			−0.683546
$786$	8.78699	−	50.5673i	0.313422	−	1.80367i
$787$	−29.6763	+	17.1336i	−1.05784	+	0.610747i	−0.924835	−	0.380368i	$-0.875797\pi$
$787$	−29.6763	+	17.1336i	−1.05784	+	0.610747i	−0.133009	+	0.991115i	$0.542464\pi$
$788$	−13.1882	+	36.8018i	−0.469811	+	1.31101i
$789$	−23.1720	−	13.3784i	−0.824944	−	0.476282i
$790$	−6.30071	−	17.1783i	−0.224169	−	0.611175i
$791$	−0.136421	−	2.77833i	−0.00485058	−	0.0987860i
$792$	−37.8786	−	21.4947i	−1.34596	−	0.763781i
$793$	16.6665	−	28.8672i	0.591844	−	1.02510i
$794$	27.1141	−	32.4767i	0.962244	−	1.15256i
$795$	18.2582	−	10.5414i	0.647552	−	0.373865i
$796$	7.42574	+	40.9242i	0.263198	+	1.45052i
$797$			20.5838i			0.729114i	0.931181	+	0.364557i	$0.118780\pi$
$797$			20.5838i			0.729114i	−0.931181	+	0.364557i	$0.881220\pi$
$798$	−28.3026	−	3.49854i	−1.00190	−	0.123847i
$799$	−13.8122			−0.488641
$800$	14.9066	+	5.21696i	0.527029	+	0.184447i
$801$	−3.94196	−	6.82767i	−0.139282	−	0.241244i
$802$	17.0120	+	14.2029i	0.600713	+	0.501522i
$803$	−43.2416	−	24.9655i	−1.52596	−	0.881014i
$804$	−1.92162	+	1.62876i	−0.0677703	+	0.0574418i
$805$	2.97387	+	4.61258i	0.104815	+	0.162572i
$806$	−4.60407	−	12.5525i	−0.162171	−	0.442144i
$807$	29.5252	−	51.1392i	1.03934	−	1.80019i
$808$	−0.00440697	−	0.591724i	−0.000155037	−	0.0208168i
$809$	23.4504	+	40.6172i	0.824471	+	1.42802i	0.902323	+	0.431060i	$0.141860\pi$
$809$	23.4504	+	40.6172i	0.824471	+	1.42802i	−0.0778526	+	0.996965i	$0.524806\pi$
$810$	−18.3096	−	3.18163i	−0.643335	−	0.111791i
$811$			22.2462i			0.781168i	0.920567	+	0.390584i	$0.127727\pi$
$811$			22.2462i			0.781168i	−0.920567	+	0.390584i	$0.872273\pi$
$812$	−3.23205	−	0.982246i	−0.113423	−	0.0344701i
$813$		−	15.3088i		−	0.536902i
$814$	−7.35552	+	42.3294i	−0.257811	+	1.48365i
$815$	2.40076	+	4.15823i	0.0840948	+	0.145656i
$816$	4.35421	+	11.6033i	0.152428	+	0.406196i
$817$	1.58637	−	2.74767i	0.0554999	−	0.0961287i
$818$	−34.6360	+	12.7039i	−1.21102	+	0.444182i
$819$	−9.54058	+	18.5728i	−0.333375	+	0.648986i
$820$	−12.2258	−	14.4241i	−0.426945	−	0.503713i
$821$	−28.4062	−	16.4003i	−0.991384	−	0.572376i	−0.0856966	−	0.996321i	$-0.527312\pi$
$821$	−28.4062	−	16.4003i	−0.991384	−	0.572376i	−0.905688	+	0.423945i	$0.860645\pi$
$822$	20.8738	−	25.0022i	0.728058	−	0.872053i
$823$	6.88576	+	11.9265i	0.240023	+	0.415731i	0.960720	−	0.277518i	$-0.0895118\pi$
$823$	6.88576	+	11.9265i	0.240023	+	0.415731i	−0.720698	+	0.693249i	$0.756178\pi$
$824$	9.85060	+	16.7720i	0.343162	+	0.584281i
$825$	34.6572			1.20661
$826$	−12.0037	+	5.08372i	−0.417661	+	0.176885i
$827$		−	22.0460i		−	0.766615i	−0.923621	−	0.383307i	$-0.874785\pi$
$827$		−	22.0460i		−	0.766615i	0.923621	−	0.383307i	$-0.125215\pi$
$828$	1.52095	+	8.38215i	0.0528566	+	0.291300i
$829$	4.74751	−	2.74098i	0.164888	−	0.0951980i	−0.415285	−	0.909691i	$-0.636318\pi$
$829$	4.74751	−	2.74098i	0.164888	−	0.0951980i	0.580173	+	0.814493i	$0.302985\pi$
$830$	−4.79432	−	4.00267i	−0.166413	−	0.138935i
$831$	34.4402	−	59.6522i	1.19472	−	2.06931i
$832$	17.7626	−	10.6111i	0.615806	−	0.367873i
$833$	5.13510	+	7.16678i	0.177921	+	0.248314i
$834$	5.53672	−	2.03078i	0.191721	−	0.0703202i
$835$	−18.0793	−	10.4381i	−0.625659	−	0.361224i
$836$	29.4371	+	10.5490i	1.01810	+	0.364845i
$837$	−0.400076	+	0.230984i	−0.0138287	+	0.00798398i
$838$	−0.352174	−	0.0611968i	−0.0121657	−	0.00211401i
$839$	28.7512			0.992601			0.496301	−	0.868151i	$-0.334691\pi$
$839$	28.7512			0.992601			0.496301	+	0.868151i	$0.334691\pi$
$840$	−24.4247	−	12.3176i	−0.842731	−	0.424997i
$841$	28.5925			0.985947
$842$	−25.5956	−	4.44771i	−0.882084	−	0.153278i
$843$	35.6012	−	20.5544i	1.22617	−	0.707930i
$844$	11.6137	−	32.4083i	0.399762	−	1.11554i
$845$	8.12145	+	4.68892i	0.279387	+	0.161304i
$846$	44.4287	−	16.2957i	1.52749	−	0.560259i
$847$	34.0421	+	17.4869i	1.16970	+	0.600858i
$848$	−22.7582	−	3.78027i	−0.781519	−	0.129815i
$849$	−34.2556	+	59.3324i	−1.17565	+	2.03628i
$850$	−3.81740	−	3.18706i	−0.130936	−	0.109315i
$851$	7.27797	−	4.20194i	0.249486	−	0.144041i
$852$	−35.8884	+	6.51198i	−1.22952	+	0.223097i
$853$		−	21.7605i		−	0.745064i	−0.928019	−	0.372532i	$-0.878490\pi$
$853$		−	21.7605i		−	0.745064i	0.928019	−	0.372532i	$-0.121510\pi$
$854$	38.4889	+	29.0526i	1.31706	+	0.994161i
$855$	−14.0487			−0.480457
$856$	−31.5547	+	18.5328i	−1.07852	+	0.633439i
$857$	−5.89593	−	10.2121i	−0.201401	−	0.348837i	0.747579	−	0.664173i	$-0.231216\pi$
$857$	−5.89593	−	10.2121i	−0.201401	−	0.348837i	−0.948980	+	0.315336i	$0.897883\pi$
$858$	29.0990	−	34.8542i	0.993422	−	1.18990i
$859$	4.15132	+	2.39676i	0.141641	+	0.0817766i	0.569146	−	0.822237i	$-0.307274\pi$
$859$	4.15132	+	2.39676i	0.141641	+	0.0817766i	−0.427505	+	0.904013i	$0.640607\pi$
$860$	2.32158	−	1.96776i	0.0791651	−	0.0671000i
$861$	−22.4379	−	34.8021i	−0.764683	−	1.18605i
$862$	36.4389	−	13.3652i	1.24111	−	0.455220i
$863$	0.0628642	−	0.108884i	0.00213992	−	0.00370646i	−0.864953	−	0.501852i	$-0.832652\pi$
$863$	0.0628642	−	0.108884i	0.00213992	−	0.00370646i	0.867093	+	0.498146i	$0.165986\pi$
$864$	−0.466293	−	0.541902i	−0.0158636	−	0.0184359i
$865$	−4.85823	−	8.41471i	−0.165185	−	0.286109i
$866$	1.75829	−	10.1186i	0.0597492	−	0.343844i
$867$			37.9168i			1.28772i
$868$	18.8397	−	4.38260i	0.639463	−	0.148755i
$869$			43.9371i			1.49046i
$870$	−3.25145	−	0.564999i	−0.110234	−	0.0191553i
$871$	−0.662108	−	1.14681i	−0.0224347	−	0.0388580i
$872$	−0.404812	−	54.3543i	−0.0137087	−	1.84067i
$873$	−2.39593	+	4.14988i	−0.0810900	+	0.140452i
$874$	−2.10625	−	5.74249i	−0.0712451	−	0.194242i
$875$	30.5971	−	1.50238i	1.03437	−	0.0507897i
$876$	−31.4760	−	37.1357i	−1.06348	−	1.25470i
$877$	25.9534	+	14.9842i	0.876385	+	0.505981i	0.869465	−	0.493995i	$-0.164464\pi$
$877$	25.9534	+	14.9842i	0.876385	+	0.505981i	0.00692013	+	0.999976i	$0.497797\pi$
$878$	−32.5729	−	27.1944i	−1.09928	−	0.917765i
$879$	−24.8273	−	43.0021i	−0.837403	−	1.45042i
$880$	23.1676	+	19.0511i	0.780980	+	0.642213i
$881$	−30.2728			−1.01992			−0.509959	−	0.860199i	$-0.670339\pi$
$881$	−30.2728			−1.01992			−0.509959	+	0.860199i	$0.670339\pi$
$882$	−24.9731	−	16.9944i	−0.840889	−	0.572232i
$883$		−	43.3423i		−	1.45858i	−0.684203	−	0.729291i	$-0.739850\pi$
$883$		−	43.3423i		−	1.45858i	0.684203	−	0.729291i	$-0.260150\pi$
$884$	−6.41035	+	1.16316i	−0.215603	+	0.0391214i
$885$	−11.0292	+	6.36772i	−0.370743	+	0.214048i
$886$	−31.7985	+	38.0876i	−1.06829	+	1.27958i
$887$	−7.56821	+	13.1085i	−0.254116	+	0.440141i	−0.964655	−	0.263516i	$-0.915118\pi$
$887$	−7.56821	+	13.1085i	−0.254116	+	0.440141i	0.710539	+	0.703658i	$0.248451\pi$
$888$	−20.6731	+	36.4309i	−0.693745	+	1.22254i
$889$	−0.935294	−	19.0480i	−0.0313687	−	0.638849i
$890$	1.86972	+	5.09761i	0.0626732	+	0.170872i
$891$	38.6468	+	22.3128i	1.29472	+	0.747505i
$892$	−32.9791	−	11.8183i	−1.10422	−	0.395706i
$893$	−29.4253	+	16.9887i	−0.984680	+	0.568505i
$894$	−2.19578	+	12.6362i	−0.0734379	+	0.422619i
$895$	−0.187796			−0.00627731
$896$	12.0826	+	27.3863i	0.403653	+	0.914912i
$897$	−8.88128			−0.296537
$898$	5.08705	−	29.2749i	0.169757	−	0.976916i
$899$	2.02094	−	1.16679i	0.0674020	−	0.0389146i
$900$	16.0393	+	5.74779i	0.534642	+	0.191593i
$901$	6.29101	+	3.63212i	0.209584	+	0.121003i
$902$	15.6351	+	42.6275i	0.520592	+	1.41934i
$903$	5.60143	−	3.61141i	0.186404	−	0.120180i
$904$	−1.46765	+	2.58633i	−0.0488132	+	0.0860201i
$905$	−2.02034	+	3.49933i	−0.0671584	+	0.116322i
$906$	31.8321	−	38.1278i	1.05755	−	1.26671i
$907$	27.4761	−	15.8633i	0.912328	−	0.526733i	0.0311488	−	0.999515i	$-0.490083\pi$
$907$	27.4761	−	15.8633i	0.912328	−	0.526733i	0.881180	+	0.472782i	$0.156750\pi$
$908$	25.9580	−	4.71009i	0.861445	−	0.156310i
$909$		−	0.638384i		−	0.0211739i
$910$	8.66350	−	11.4774i	0.287192	−	0.380472i
$911$	29.4757			0.976574			0.488287	−	0.872683i	$-0.337622\pi$
$911$	29.4757			0.976574			0.488287	+	0.872683i	$0.337622\pi$
$912$	23.5479	+	19.3638i	0.779749	+	0.641201i
$913$	7.49868	+	12.9881i	0.248170	+	0.429843i
$914$	−14.5206	−	12.1229i	−0.480299	−	0.400991i
$915$	40.8000	+	23.5559i	1.34881	+	0.778734i
$916$	−22.2032	−	26.1955i	−0.733614	−	0.865524i
$917$	−17.8354	+	34.7204i	−0.588976	+	1.14657i
$918$	0.0775161	+	0.211340i	0.00255841	+	0.00697525i
$919$	−8.85875	+	15.3438i	−0.292223	+	0.506146i	−0.974335	−	0.225102i	$-0.927728\pi$
$919$	−8.85875	+	15.3438i	−0.292223	+	0.506146i	0.682112	+	0.731248i	$0.261062\pi$
$920$	−0.0436949	−	5.86692i	−0.00144058	−	0.193427i
$921$	−21.9974	−	38.1005i	−0.724838	−	1.25546i
$922$	3.74306	+	0.650426i	0.123271	+	0.0214206i
$923$		−	19.1741i		−	0.631124i
$924$	44.8783	+	47.9655i	1.47639	+	1.57795i
$925$		−	16.8077i		−	0.552635i
$926$	5.09368	−	29.3130i	0.167389	−	0.963285i
$927$	10.4920	+	18.1727i	0.344603	+	0.596870i
$928$	2.35542	+	2.73735i	0.0773205	+	0.0898579i
$929$	−26.6338	+	46.1311i	−0.873826	+	1.51351i	−0.0158180	+	0.999875i	$0.505035\pi$
$929$	−26.6338	+	46.1311i	−0.873826	+	1.51351i	−0.858008	+	0.513636i	$0.828298\pi$
$930$	17.7414	−	6.50725i	0.581762	−	0.213381i
$931$	19.7547	+	8.95192i	0.647434	+	0.293387i
$932$	37.9570	−	32.1722i	1.24332	−	1.05384i
$933$	−3.04929	−	1.76051i	−0.0998293	−	0.0576365i
$934$	−22.3805	+	26.8069i	−0.732313	+	0.877150i
$935$	−4.72233	−	8.17932i	−0.154437	−	0.267492i
$936$	19.2474	−	11.3044i	0.629121	−	0.369497i
$937$	−38.2055			−1.24812			−0.624060	−	0.781377i	$-0.714518\pi$
$937$	−38.2055			−1.24812			−0.624060	+	0.781377i	$0.714518\pi$
$938$	1.76407	−	0.747106i	0.0575988	−	0.0243939i
$939$		−	11.9469i		−	0.389874i
$940$	−32.0679	+	5.81874i	−1.04594	+	0.189786i
$941$	−8.31195	+	4.79890i	−0.270962	+	0.156440i	−0.629325	−	0.777143i	$-0.716668\pi$
$941$	−8.31195	+	4.79890i	−0.270962	+	0.156440i	0.358363	+	0.933582i	$0.383335\pi$
$942$	34.4182	+	28.7350i	1.12140	+	0.936236i
$943$	4.44064	−	7.69141i	0.144607	−	0.250467i
$944$	13.7475	+	2.28354i	0.447443	+	0.0743229i
$945$	−0.441960	−	0.227028i	−0.0143769	−	0.00738523i
$946$	−6.86094	+	2.51648i	−0.223068	+	0.0818179i
$947$	−14.3314	−	8.27425i	−0.465709	−	0.268877i	0.248733	−	0.968572i	$-0.419986\pi$
$947$	−14.3314	−	8.27425i	−0.465709	−	0.268877i	−0.714442	+	0.699695i	$0.753319\pi$
$948$	−14.4510	+	40.3256i	−0.469346	+	1.30972i
$949$	22.1622	−	12.7954i	0.719417	−	0.415356i
$950$	−12.0525	−	2.09435i	−0.391036	−	0.0679496i
$951$	−27.7803			−0.900837
$952$	−0.532342	−	9.41027i	−0.0172533	−	0.304989i
$953$	6.08942			0.197256			0.0986278	−	0.995124i	$-0.468555\pi$
$953$	6.08942			0.197256			0.0986278	+	0.995124i	$0.468555\pi$
$954$	−24.5210	−	4.26098i	−0.793897	−	0.137954i
$955$	3.14943	−	1.81832i	0.101913	−	0.0588396i
$956$	25.0863	+	8.98986i	0.811348	+	0.290753i
$957$	6.86296	+	3.96233i	0.221848	+	0.128084i
$958$	−54.3201	+	19.9238i	−1.75500	+	0.643708i
$959$	−20.8184	+	13.4223i	−0.672262	+	0.433427i
$960$	14.9974	+	25.1051i	0.484038	+	0.810262i
$961$	8.81887	−	15.2747i	0.284480	−	0.492733i
$962$	−16.9033	−	14.1122i	−0.544984	−	0.454995i
$963$	−34.1899	+	19.7396i	−1.10176	+	0.636099i
$964$	−7.94253	−	43.7723i	−0.255812	−	1.40981i
$965$		−	5.86758i		−	0.188884i
$966$	1.57624	−	12.7515i	0.0507147	−	0.410274i
$967$	21.5430			0.692778			0.346389	−	0.938091i	$-0.387408\pi$
$967$	21.5430			0.692778			0.346389	+	0.938091i	$0.387408\pi$
$968$	−20.7199	−	35.2786i	−0.665963	−	1.13390i
$969$	−4.79985	−	8.31358i	−0.154193	−	0.267071i
$970$	2.11503	−	2.53334i	0.0679095	−	0.0813406i
$971$	2.27385	+	1.31281i	0.0729715	+	0.0421301i	0.536042	−	0.844191i	$-0.319919\pi$
$971$	2.27385	+	1.31281i	0.0729715	+	0.0421301i	−0.463070	+	0.886322i	$0.653252\pi$
$972$	28.6218	+	33.7682i	0.918044	+	1.08311i
$973$	−4.47966	+	0.219960i	−0.143611	+	0.00705160i
$974$	23.2804	−	8.53887i	0.745951	−	0.273603i
$975$	−8.88128	+	15.3828i	−0.284429	+	0.492645i
$976$	−18.1122	−	48.2660i	−0.579756	−	1.54496i
$977$	17.2338	+	29.8499i	0.551359	+	0.954982i	0.998177	+	0.0603567i	$0.0192238\pi$
$977$	17.2338	+	29.8499i	0.551359	+	0.954982i	−0.446818	+	0.894625i	$0.647443\pi$
$978$	1.92450	−	11.0751i	0.0615387	−	0.354142i
$979$		−	13.0382i		−	0.416704i
$980$	14.9414	+	14.4758i	0.477285	+	0.462414i
$981$		−	58.6403i		−	1.87224i
$982$	21.9463	+	3.81358i	0.700335	+	0.121696i
$983$	−26.2210	−	45.4161i	−0.836320	−	1.44855i	−0.892951	−	0.450154i	$-0.851369\pi$
$983$	−26.2210	−	45.4161i	−0.836320	−	1.44855i	0.0566303	−	0.998395i	$-0.481964\pi$
$984$	0.329679	+	44.2661i	0.0105098	+	1.41115i
$985$	14.5230	−	25.1547i	0.462743	−	0.801494i
$986$	−0.391563	−	1.06756i	−0.0124699	−	0.0339979i
$987$	−71.2877	+	3.50036i	−2.26911	+	0.111418i
$988$	−12.2258	+	10.3626i	−0.388956	+	0.329677i
$989$	1.23794	+	0.714725i	0.0393642	+	0.0227269i
$990$	24.8400	+	20.7384i	0.789467	+	0.659109i
$991$	8.08057	+	13.9960i	0.256688	+	0.444596i	0.965353	−	0.260949i	$-0.0840355\pi$
$991$	8.08057	+	13.9960i	0.256688	+	0.444596i	−0.708665	+	0.705545i	$0.750702\pi$
$992$	−19.5175	−	6.83067i	−0.619682	−	0.216874i
$993$	58.6325			1.86064
$994$	27.5297	+	3.40300i	0.873191	+	0.107937i
$995$		−	30.9028i		−	0.979684i
$996$	2.61051	+	14.3868i	0.0827171	+	0.455865i
$997$	34.0954	−	19.6850i	1.07981	−	0.623430i	0.148967	−	0.988842i	$-0.452405\pi$
$997$	34.0954	−	19.6850i	1.07981	−	0.623430i	0.930846	+	0.365412i	$0.119072\pi$
$998$	−9.23219	+	11.0581i	−0.292240	+	0.350039i
$999$	−0.380415	+	0.658898i	−0.0120358	+	0.0208466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.2.p.a.37.4	yes	12
3.2	odd	2		504.2.cj.c.37.3		12
4.3	odd	2		224.2.t.a.177.6		12
7.2	even	3		392.2.b.e.197.5		6
7.3	odd	6		392.2.p.g.165.2		12
7.4	even	3	inner	56.2.p.a.53.2	yes	12
7.5	odd	6		392.2.b.f.197.5		6
7.6	odd	2		392.2.p.g.373.4		12
8.3	odd	2		224.2.t.a.177.1		12
8.5	even	2	inner	56.2.p.a.37.2	✓	12
12.11	even	2		2016.2.cr.c.1297.2		12
21.11	odd	6		504.2.cj.c.109.5		12
24.5	odd	2		504.2.cj.c.37.5		12
24.11	even	2		2016.2.cr.c.1297.5		12
28.3	even	6		1568.2.t.g.753.6		12
28.11	odd	6		224.2.t.a.81.1		12
28.19	even	6		1568.2.b.e.785.1		6
28.23	odd	6		1568.2.b.f.785.6		6
28.27	even	2		1568.2.t.g.177.1		12
56.3	even	6		1568.2.t.g.753.1		12
56.5	odd	6		392.2.b.f.197.6		6
56.11	odd	6		224.2.t.a.81.6		12
56.13	odd	2		392.2.p.g.373.2		12
56.19	even	6		1568.2.b.e.785.6		6
56.27	even	2		1568.2.t.g.177.6		12
56.37	even	6		392.2.b.e.197.6		6
56.45	odd	6		392.2.p.g.165.4		12
56.51	odd	6		1568.2.b.f.785.1		6
56.53	even	6	inner	56.2.p.a.53.4	yes	12
84.11	even	6		2016.2.cr.c.1873.5		12
168.11	even	6		2016.2.cr.c.1873.2		12
168.53	odd	6		504.2.cj.c.109.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.2	✓	12	8.5	even	2	inner
56.2.p.a.37.4	yes	12	1.1	even	1	trivial
56.2.p.a.53.2	yes	12	7.4	even	3	inner
56.2.p.a.53.4	yes	12	56.53	even	6	inner
224.2.t.a.81.1		12	28.11	odd	6
224.2.t.a.81.6		12	56.11	odd	6
224.2.t.a.177.1		12	8.3	odd	2
224.2.t.a.177.6		12	4.3	odd	2
392.2.b.e.197.5		6	7.2	even	3
392.2.b.e.197.6		6	56.37	even	6
392.2.b.f.197.5		6	7.5	odd	6
392.2.b.f.197.6		6	56.5	odd	6
392.2.p.g.165.2		12	7.3	odd	6
392.2.p.g.165.4		12	56.45	odd	6
392.2.p.g.373.2		12	56.13	odd	2
392.2.p.g.373.4		12	7.6	odd	2
504.2.cj.c.37.3		12	3.2	odd	2
504.2.cj.c.37.5		12	24.5	odd	2
504.2.cj.c.109.3		12	168.53	odd	6
504.2.cj.c.109.5		12	21.11	odd	6
1568.2.b.e.785.1		6	28.19	even	6
1568.2.b.e.785.6		6	56.19	even	6
1568.2.b.f.785.1		6	56.51	odd	6
1568.2.b.f.785.6		6	28.23	odd	6
1568.2.t.g.177.1		12	28.27	even	2
1568.2.t.g.177.6		12	56.27	even	2
1568.2.t.g.753.1		12	56.3	even	6
1568.2.t.g.753.6		12	28.3	even	6
2016.2.cr.c.1297.2		12	12.11	even	2
2016.2.cr.c.1297.5		12	24.11	even	2
2016.2.cr.c.1873.2		12	168.11	even	6
2016.2.cr.c.1873.5		12	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	56.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.242117 + 1.39333i) q^{2} +(-2.13038 + 1.22998i) q^{3} +(-1.88276 - 0.674701i) q^{4} +(1.28690 + 0.742990i) q^{5} +(-1.19797 - 3.26613i) q^{6} +(0.129755 + 2.64257i) q^{7} +(1.39593 - 2.45995i) q^{8} +(1.52569 - 2.64257i) q^{9} +(-1.34681 + 1.61319i) q^{10} +(4.37021 - 2.52314i) q^{11} +(4.84086 - 0.878379i) q^{12} +2.58633i q^{13} +(-3.71339 - 0.459019i) q^{14} -3.65544 q^{15} +(3.08956 + 2.54060i) q^{16} +(-0.629755 - 1.09077i) q^{17} +(3.31258 + 2.76560i) q^{18} +(-2.68324 - 1.54917i) q^{19} +(-1.92162 - 2.26714i) q^{20} +(-3.52673 - 5.47008i) q^{21} +(2.45748 + 6.70006i) q^{22} +(0.697966 - 1.20891i) q^{23} +(0.0518180 + 6.95761i) q^{24} +(-1.39593 - 2.41782i) q^{25} +(-3.60362 - 0.626196i) q^{26} +0.126378i q^{27} +(1.53864 - 5.06286i) q^{28} -0.638384i q^{29} +(0.885046 - 5.09325i) q^{30} +(1.82772 + 3.16571i) q^{31} +(-4.28794 + 3.68966i) q^{32} +(-6.20682 + 10.7505i) q^{33} +(1.67228 - 0.613365i) q^{34} +(-1.79642 + 3.49712i) q^{35} +(-4.65544 + 3.94593i) q^{36} +(5.21370 + 3.01013i) q^{37} +(2.80817 - 3.36357i) q^{38} +(-3.18113 - 5.50988i) q^{39} +(3.62414 - 2.12854i) q^{40} +6.36226 q^{41} +(8.47554 - 3.58950i) q^{42} +1.02401i q^{43} +(-9.93042 + 1.80188i) q^{44} +(3.92680 - 2.26714i) q^{45} +(1.51543 + 1.26520i) q^{46} +(5.48316 - 9.49712i) q^{47} +(-9.70682 - 1.61236i) q^{48} +(-6.96633 + 0.685774i) q^{49} +(3.70682 - 1.35960i) q^{50} +(2.68324 + 1.54917i) q^{51} +(1.74500 - 4.86944i) q^{52} +(-4.99481 + 2.88375i) q^{53} +(-0.176087 - 0.0305984i) q^{54} +7.49868 q^{55} +(6.68172 + 3.36965i) q^{56} +7.62177 q^{57} +(0.889482 + 0.154564i) q^{58} +(3.01720 - 1.74198i) q^{59} +(6.88231 + 2.46633i) q^{60} +(-11.1614 - 6.44406i) q^{61} +(-4.85341 + 1.78015i) q^{62} +(7.18113 + 3.68884i) q^{63} +(-4.10275 - 6.86786i) q^{64} +(-1.92162 + 3.32834i) q^{65} +(-13.4763 - 11.2511i) q^{66} +(-0.443410 + 0.256003i) q^{67} +(0.449735 + 2.47855i) q^{68} +3.43393i q^{69} +(-4.43771 - 3.34973i) q^{70} -7.41363 q^{71} +(-4.37084 - 7.44196i) q^{72} +(-4.94731 - 8.56899i) q^{73} +(-5.45644 + 6.53562i) q^{74} +(5.94774 + 3.43393i) q^{75} +(4.00667 + 4.72709i) q^{76} +(7.23463 + 11.2212i) q^{77} +(8.44731 - 3.09834i) q^{78} +(-4.35341 + 7.54032i) q^{79} +(2.08830 + 5.56500i) q^{80} +(4.42162 + 7.65847i) q^{81} +(-1.54041 + 8.86475i) q^{82} +2.97196i q^{83} +(2.94930 + 12.6783i) q^{84} -1.87161i q^{85} +(-1.42679 - 0.247931i) q^{86} +(0.785198 + 1.36000i) q^{87} +(-0.106298 - 14.2727i) q^{88} +(1.29186 - 2.23757i) q^{89} +(2.20814 + 6.02026i) q^{90} +(-6.83456 + 0.335590i) q^{91} +(-2.12976 + 1.80517i) q^{92} +(-7.78749 - 4.49611i) q^{93} +(11.9051 + 9.93929i) q^{94} +(-2.30203 - 3.98724i) q^{95} +(4.59674 - 13.1345i) q^{96} -1.57040 q^{97} +(0.731157 - 9.87246i) q^{98} -15.3981i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 8 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{10} - 2 q^{12} - 16 q^{14} - 20 q^{15} + 8 q^{16} - 2 q^{17} + 6 q^{18} + 8 q^{20} + 12 q^{22} + 2 q^{23} + 18 q^{24} - 4 q^{25} - 2 q^{26} + 26 q^{28}+ \cdots + 52 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 - 8 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^10 - 2 * q^12 - 16 * q^14 - 20 * q^15 + 8 * q^16 - 2 * q^17 + 6 * q^18 + 8 * q^20 + 12 * q^22 + 2 * q^23 + 18 * q^24 - 4 * q^25 - 2 * q^26 + 26 * q^28 + 14 * q^30 + 10 * q^31 - 12 * q^32 - 14 * q^33 + 32 * q^34 - 32 * q^36 + 18 * q^38 + 4 * q^39 + 10 * q^40 - 8 * q^41 + 22 * q^42 - 30 * q^44 - 4 * q^46 + 30 * q^47 - 56 * q^48 - 12 * q^49 - 16 * q^50 - 32 * q^52 + 2 * q^54 + 4 * q^55 - 40 * q^56 - 4 * q^57 - 22 * q^58 + 6 * q^60 - 28 * q^62 + 44 * q^63 + 24 * q^64 + 8 * q^65 - 38 * q^66 + 4 * q^68 - 48 * q^70 + 32 * q^71 + 20 * q^72 - 10 * q^73 + 18 * q^74 + 52 * q^76 + 52 * q^78 - 22 * q^79 + 36 * q^80 + 22 * q^81 - 26 * q^82 + 56 * q^84 + 40 * q^86 - 20 * q^87 - 14 * q^88 - 10 * q^89 + 52 * q^90 - 20 * q^92 + 42 * q^94 - 34 * q^95 + 16 * q^96 + 40 * q^97 + 52 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more