LMFDB - Embedded newform 93.2.m.b.82.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(7,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 28]))

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

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

chi := DirichletCharacter("93.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.m (of order $15$, degree $8$, 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:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			82.2
Character	$\chi$	$=$	93.82
Dual form			93.2.m.b.76.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0419030 - 0.128964i) q^{2} +(0.669131 + 0.743145i) q^{3} +(1.60316 - 1.16476i) q^{4} +(-1.42565 - 2.46931i) q^{5} +(0.0678004 - 0.117434i) q^{6} +(0.302129 + 2.87456i) q^{7} +(-0.436796 - 0.317351i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.0419030 - 0.128964i) q^{2} +(0.669131 + 0.743145i) q^{3} +(1.60316 - 1.16476i) q^{4} +(-1.42565 - 2.46931i) q^{5} +(0.0678004 - 0.117434i) q^{6} +(0.302129 + 2.87456i) q^{7} +(-0.436796 - 0.317351i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-0.258713 + 0.287329i) q^{10} +(2.12038 + 0.944052i) q^{11} +(1.93831 + 0.412000i) q^{12} +(-4.35949 + 0.926639i) q^{13} +(0.358055 - 0.159416i) q^{14} +(0.881103 - 2.71176i) q^{15} +(1.20208 - 3.69962i) q^{16} +(-4.65849 + 2.07410i) q^{17} +(0.132638 - 0.0281930i) q^{18} +(1.56263 + 0.332146i) q^{19} +(-5.16170 - 2.29814i) q^{20} +(-1.93405 + 2.14798i) q^{21} +(0.0328988 - 0.313011i) q^{22} +(-3.04646 - 2.21338i) q^{23} +(-0.0564360 - 0.536952i) q^{24} +(-1.56498 + 2.71063i) q^{25} +(0.302179 + 0.523389i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(3.83254 + 4.25647i) q^{28} +(2.34067 + 7.20384i) q^{29} -0.386640 q^{30} +(-5.50065 - 0.861888i) q^{31} -1.60731 q^{32} +(0.717241 + 2.20744i) q^{33} +(0.462688 + 0.513868i) q^{34} +(6.66745 - 4.84418i) q^{35} +(0.990806 + 1.71613i) q^{36} +(4.97994 - 8.62551i) q^{37} +(-0.0226437 - 0.215440i) q^{38} +(-3.60570 - 2.61969i) q^{39} +(-0.160916 + 1.53102i) q^{40} +(5.31571 - 5.90369i) q^{41} +(0.358055 + 0.159416i) q^{42} +(2.08154 + 0.442445i) q^{43} +(4.49889 - 0.956270i) q^{44} +(2.60480 - 1.15973i) q^{45} +(-0.157791 + 0.485630i) q^{46} +(0.405073 - 1.24669i) q^{47} +(3.55370 - 1.58221i) q^{48} +(-1.32480 + 0.281596i) q^{49} +(0.415151 + 0.0882430i) q^{50} +(-4.65849 - 2.07410i) q^{51} +(-5.90964 + 6.56332i) q^{52} +(-0.799791 + 7.60950i) q^{53} +(0.109703 + 0.0797042i) q^{54} +(-0.691770 - 6.58175i) q^{55} +(0.780277 - 1.35148i) q^{56} +(0.798768 + 1.38351i) q^{57} +(0.830956 - 0.603725i) q^{58} +(8.54193 + 9.48678i) q^{59} +(-1.74600 - 5.37365i) q^{60} +2.92690 q^{61} +(0.119341 + 0.745502i) q^{62} -2.89040 q^{63} +(-2.33681 - 7.19196i) q^{64} +(8.50328 + 9.44385i) q^{65} +(0.254626 - 0.184997i) q^{66} +(-0.599042 - 1.03757i) q^{67} +(-5.05247 + 8.75114i) q^{68} +(-0.393615 - 3.74500i) q^{69} +(-0.904111 - 0.656875i) q^{70} +(1.33823 - 12.7324i) q^{71} +(0.361270 - 0.401231i) q^{72} +(-1.18812 - 0.528985i) q^{73} +(-1.32105 - 0.280799i) q^{74} +(-3.06156 + 0.650756i) q^{75} +(2.89201 - 1.28760i) q^{76} +(-2.07311 + 6.38038i) q^{77} +(-0.186757 + 0.574778i) q^{78} +(-11.6986 + 5.20855i) q^{79} +(-10.8492 + 2.30608i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-0.984108 - 0.438153i) q^{82} +(8.80165 - 9.77522i) q^{83} +(-0.598702 + 5.69627i) q^{84} +(11.7630 + 8.54630i) q^{85} +(-0.0301632 - 0.286983i) q^{86} +(-3.78728 + 6.55977i) q^{87} +(-0.626576 - 1.08526i) q^{88} +(-2.52723 + 1.83614i) q^{89} +(-0.258713 - 0.287329i) q^{90} +(-3.98081 - 12.2517i) q^{91} -7.46201 q^{92} +(-3.04015 - 4.66450i) q^{93} -0.177752 q^{94} +(-1.40759 - 4.33212i) q^{95} +(-1.07550 - 1.19446i) q^{96} +(-14.8026 + 10.7547i) q^{97} +(0.0918289 + 0.159052i) q^{98} +(-1.16052 + 2.01008i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9 + 24 * q^10 - 22 * q^11 + 12 * q^12 - 8 * q^13 + 10 * q^14 - 8 * q^15 - 2 * q^16 - 17 * q^17 + 5 * q^19 - 22 * q^20 - 11 * q^21 - 37 * q^22 + 26 * q^23 + 26 * q^24 - 8 * q^25 + 4 * q^26 - 6 * q^27 - 36 * q^28 + 2 * q^29 + 42 * q^30 + 36 * q^32 + 14 * q^33 + 40 * q^34 + 9 * q^35 - 13 * q^36 - 13 * q^37 - q^38 - 19 * q^39 - 27 * q^40 + 36 * q^41 + 10 * q^42 - 11 * q^43 - 38 * q^44 - q^45 - 23 * q^46 - 13 * q^47 - 14 * q^48 - 22 * q^49 + 71 * q^50 - 17 * q^51 + 9 * q^52 - 20 * q^53 - 5 * q^54 + 26 * q^55 + 28 * q^56 - 15 * q^57 + 40 * q^58 - 16 * q^59 - 61 * q^60 + 70 * q^61 - 2 * q^62 + 12 * q^63 + 34 * q^64 + 94 * q^65 - 16 * q^66 + 4 * q^67 + 51 * q^68 - 13 * q^69 - 43 * q^70 - 5 * q^71 + q^72 - 12 * q^73 + 74 * q^74 - 8 * q^75 + 71 * q^76 + 25 * q^77 + 17 * q^78 - 29 * q^79 - 113 * q^80 + 3 * q^81 - 60 * q^82 - 11 * q^83 - 41 * q^84 + 16 * q^85 - 144 * q^86 + 14 * q^87 + 26 * q^88 - 27 * q^89 + 24 * q^90 - 81 * q^91 + 28 * q^92 - 36 * q^93 - 80 * q^94 - 56 * q^95 - 43 * q^96 - 21 * q^97 - 14 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{4}{15}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.0419030	−	0.128964i	−0.0296299	−	0.0911914i	0.935148	−	0.354257i	$-0.115266\pi$
$2$	−0.0419030	−	0.128964i	−0.0296299	−	0.0911914i	−0.964778	+	0.263066i	$0.915266\pi$
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$4$	1.60316	−	1.16476i	0.801579	−	0.582381i
$5$	−1.42565	−	2.46931i	−0.637572	−	1.10431i	−0.985964	−	0.166958i	$-0.946606\pi$
$5$	−1.42565	−	2.46931i	−0.637572	−	1.10431i	0.348392	−	0.937349i	$-0.386728\pi$
$6$	0.0678004	−	0.117434i	0.0276794	−	0.0479421i
$7$	0.302129	+	2.87456i	0.114194	+	1.08648i	0.890141	+	0.455685i	$0.150606\pi$
$7$	0.302129	+	2.87456i	0.114194	+	1.08648i	−0.775947	+	0.630798i	$0.782728\pi$
$8$	−0.436796	−	0.317351i	−0.154431	−	0.112201i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	−0.258713	+	0.287329i	−0.0818121	+	0.0908615i
$11$	2.12038	+	0.944052i	0.639317	+	0.284642i	0.700683	−	0.713473i	$-0.252879\pi$
$11$	2.12038	+	0.944052i	0.639317	+	0.284642i	−0.0613654	+	0.998115i	$0.519545\pi$
$12$	1.93831	+	0.412000i	0.559542	+	0.118934i
$13$	−4.35949	+	0.926639i	−1.20911	+	0.257003i	−0.767999	−	0.640451i	$-0.778747\pi$
$13$	−4.35949	+	0.926639i	−1.20911	+	0.257003i	−0.441107	+	0.897455i	$0.645414\pi$
$14$	0.358055	−	0.159416i	0.0956943	−	0.0426058i
$15$	0.881103	−	2.71176i	0.227500	−	0.700172i
$16$	1.20208	−	3.69962i	0.300520	−	0.924905i
$17$	−4.65849	+	2.07410i	−1.12985	+	0.503042i	−0.884569	−	0.466410i	$-0.845547\pi$
$17$	−4.65849	+	2.07410i	−1.12985	+	0.503042i	−0.245282	+	0.969452i	$0.578881\pi$
$18$	0.132638	−	0.0281930i	0.0312630	−	0.00664515i
$19$	1.56263	+	0.332146i	0.358491	+	0.0761996i	0.383636	−	0.923484i	$-0.374672\pi$
$19$	1.56263	+	0.332146i	0.358491	+	0.0761996i	−0.0251456	+	0.999684i	$0.508005\pi$
$20$	−5.16170	−	2.29814i	−1.15419	−	0.513879i
$21$	−1.93405	+	2.14798i	−0.422045	+	0.468729i
$22$	0.0328988	−	0.313011i	0.00701404	−	0.0667341i
$23$	−3.04646	−	2.21338i	−0.635230	−	0.461522i	0.222978	−	0.974823i	$-0.428422\pi$
$23$	−3.04646	−	2.21338i	−0.635230	−	0.461522i	−0.858208	+	0.513302i	$0.828422\pi$
$24$	−0.0564360	−	0.536952i	−0.0115199	−	0.109605i
$25$	−1.56498	+	2.71063i	−0.312996	+	0.542125i
$26$	0.302179	+	0.523389i	0.0592621	+	0.102645i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	3.83254	+	4.25647i	0.724283	+	0.804398i
$29$	2.34067	+	7.20384i	0.434652	+	1.33772i	0.893443	+	0.449176i	$0.148282\pi$
$29$	2.34067	+	7.20384i	0.434652	+	1.33772i	−0.458792	+	0.888544i	$0.651718\pi$
$30$	−0.386640			−0.0705904
$31$	−5.50065	−	0.861888i	−0.987946	−	0.154800i
$31$	−5.50065	−	0.861888i	−0.987946	−	0.154800i
$32$	−1.60731			−0.284135
$33$	0.717241	+	2.20744i	0.124856	+	0.384266i
$34$	0.462688	+	0.513868i	0.0793504	+	0.0881276i
$35$	6.66745	−	4.84418i	1.12700	−	0.818816i
$36$	0.990806	+	1.71613i	0.165134	+	0.286021i
$37$	4.97994	−	8.62551i	0.818697	−	1.41802i	−0.0879457	−	0.996125i	$-0.528030\pi$
$37$	4.97994	−	8.62551i	0.818697	−	1.41802i	0.906643	−	0.421899i	$-0.138636\pi$
$38$	−0.0226437	−	0.215440i	−0.00367329	−	0.0349490i
$39$	−3.60570	−	2.61969i	−0.577373	−	0.419486i
$40$	−0.160916	+	1.53102i	−0.0254431	+	0.242075i
$41$	5.31571	−	5.90369i	0.830174	−	0.922001i	−0.167787	−	0.985823i	$-0.553662\pi$
$41$	5.31571	−	5.90369i	0.830174	−	0.922001i	0.997961	+	0.0638217i	$0.0203289\pi$
$42$	0.358055	+	0.159416i	0.0552491	+	0.0245985i
$43$	2.08154	+	0.442445i	0.317432	+	0.0674722i	0.363872	−	0.931449i	$-0.381454\pi$
$43$	2.08154	+	0.442445i	0.317432	+	0.0674722i	−0.0464406	+	0.998921i	$0.514788\pi$
$44$	4.49889	−	0.956270i	0.678234	−	0.144163i
$45$	2.60480	−	1.15973i	0.388301	−	0.172883i
$46$	−0.157791	+	0.485630i	−0.0232650	+	0.0716023i
$47$	0.405073	−	1.24669i	0.0590860	−	0.181848i	−0.917157	−	0.398526i	$-0.869522\pi$
$47$	0.405073	−	1.24669i	0.0590860	−	0.181848i	0.976243	+	0.216678i	$0.0695220\pi$
$48$	3.55370	−	1.58221i	0.512933	−	0.228372i
$49$	−1.32480	+	0.281596i	−0.189258	+	0.0402279i
$50$	0.415151	+	0.0882430i	0.0587112	+	0.0124794i
$51$	−4.65849	−	2.07410i	−0.652320	−	0.290431i
$52$	−5.90964	+	6.56332i	−0.819520	+	0.910169i
$53$	−0.799791	+	7.60950i	−0.109860	+	1.04525i	0.791202	+	0.611555i	$0.209456\pi$
$53$	−0.799791	+	7.60950i	−0.109860	+	1.04525i	−0.901062	+	0.433690i	$0.857211\pi$
$54$	0.109703	+	0.0797042i	0.0149287	+	0.0108464i
$55$	−0.691770	−	6.58175i	−0.0932782	−	0.887483i
$56$	0.780277	−	1.35148i	0.104269	−	0.180599i
$57$	0.798768	+	1.38351i	0.105799	+	0.183250i
$58$	0.830956	−	0.603725i	0.109110	−	0.0792729i
$59$	8.54193	+	9.48678i	1.11206	+	1.23507i	0.969448	+	0.245295i	$0.0788849\pi$
$59$	8.54193	+	9.48678i	1.11206	+	1.23507i	0.142617	+	0.989778i	$0.454448\pi$
$60$	−1.74600	−	5.37365i	−0.225408	−	0.693735i
$61$	2.92690			0.374751			0.187375	−	0.982288i	$-0.440002\pi$
$61$	2.92690			0.374751			0.187375	+	0.982288i	$0.440002\pi$
$62$	0.119341	+	0.745502i	0.0151563	+	0.0946788i
$63$	−2.89040			−0.364156
$64$	−2.33681	−	7.19196i	−0.292101	−	0.898995i
$65$	8.50328	+	9.44385i	1.05470	+	1.17137i
$66$	0.254626	−	0.184997i	0.0313423	−	0.0227715i
$67$	−0.599042	−	1.03757i	−0.0731847	−	0.126760i	0.827111	−	0.562039i	$-0.189983\pi$
$67$	−0.599042	−	1.03757i	−0.0731847	−	0.126760i	−0.900295	+	0.435279i	$0.856650\pi$
$68$	−5.05247	+	8.75114i	−0.612703	+	1.06123i
$69$	−0.393615	−	3.74500i	−0.0473857	−	0.450845i
$70$	−0.904111	−	0.656875i	−0.108062	−	0.0785116i
$71$	1.33823	−	12.7324i	0.158818	−	1.51105i	−0.567315	−	0.823501i	$-0.692018\pi$
$71$	1.33823	−	12.7324i	0.158818	−	1.51105i	0.726134	−	0.687554i	$-0.241315\pi$
$72$	0.361270	−	0.401231i	0.0425761	−	0.0472856i
$73$	−1.18812	−	0.528985i	−0.139059	−	0.0619130i	0.336027	−	0.941852i	$-0.390917\pi$
$73$	−1.18812	−	0.528985i	−0.139059	−	0.0619130i	−0.475086	+	0.879939i	$0.657583\pi$
$74$	−1.32105	−	0.280799i	−0.153569	−	0.0326422i
$75$	−3.06156	+	0.650756i	−0.353519	+	0.0751428i
$76$	2.89201	−	1.28760i	0.331736	−	0.147698i
$77$	−2.07311	+	6.38038i	−0.236253	+	0.727112i
$78$	−0.186757	+	0.574778i	−0.0211460	+	0.0650808i
$79$	−11.6986	+	5.20855i	−1.31619	+	0.586008i	−0.940203	−	0.340615i	$-0.889365\pi$
$79$	−11.6986	+	5.20855i	−1.31619	+	0.586008i	−0.375992	+	0.926623i	$0.622698\pi$
$80$	−10.8492	+	2.30608i	−1.21298	+	0.257827i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−0.984108	−	0.438153i	−0.108677	−	0.0483859i
$83$	8.80165	−	9.77522i	0.966107	−	1.07297i	−0.0311917	−	0.999513i	$-0.509930\pi$
$83$	8.80165	−	9.77522i	0.966107	−	1.07297i	0.997298	−	0.0734568i	$-0.0234031\pi$
$84$	−0.598702	+	5.69627i	−0.0653238	+	0.621514i
$85$	11.7630	+	8.54630i	1.27587	+	0.926977i
$86$	−0.0301632	−	0.286983i	−0.00325258	−	0.0309462i
$87$	−3.78728	+	6.55977i	−0.406039	+	0.703281i
$88$	−0.626576	−	1.08526i	−0.0667933	−	0.115689i
$89$	−2.52723	+	1.83614i	−0.267886	+	0.194631i	−0.713616	−	0.700537i	$-0.752944\pi$
$89$	−2.52723	+	1.83614i	−0.267886	+	0.194631i	0.445730	+	0.895167i	$0.352944\pi$
$90$	−0.258713	−	0.287329i	−0.0272707	−	0.0302872i
$91$	−3.98081	−	12.2517i	−0.417302	−	1.28432i
$92$	−7.46201			−0.777969
$93$	−3.04015	−	4.66450i	−0.315248	−	0.483686i
$94$	−0.177752			−0.0183337
$95$	−1.40759	−	4.33212i	−0.144416	−	0.444467i
$96$	−1.07550	−	1.19446i	−0.109768	−	0.121909i
$97$	−14.8026	+	10.7547i	−1.50297	+	1.09197i	−0.533796	+	0.845614i	$0.679235\pi$
$97$	−14.8026	+	10.7547i	−1.50297	+	1.09197i	−0.969178	+	0.246361i	$0.920765\pi$
$98$	0.0918289	+	0.159052i	0.00927612	+	0.0160667i
$99$	−1.16052	+	2.01008i	−0.116637	+	0.202021i
$100$	0.648324	+	6.16839i	0.0648324	+	0.616839i
$101$	−12.0305	−	8.74069i	−1.19708	−	0.869731i	−0.203088	−	0.979161i	$-0.565098\pi$
$101$	−12.0305	−	8.74069i	−1.19708	−	0.869731i	−0.993995	+	0.109429i	$0.965098\pi$
$102$	−0.0722790	+	0.687689i	−0.00715669	+	0.0680914i
$103$	10.0543	−	11.1664i	0.990681	−	1.10026i	−0.00427953	−	0.999991i	$-0.501362\pi$
$103$	10.0543	−	11.1664i	0.990681	−	1.10026i	0.994960	−	0.100271i	$-0.0319711\pi$
$104$	2.19828	+	0.978737i	0.215559	+	0.0959731i
$105$	8.06132	+	1.71349i	0.786704	+	0.167219i
$106$	1.01487	−	0.215716i	0.0985724	−	0.0209522i
$107$	1.02531	−	0.456499i	0.0991208	−	0.0441314i	−0.356577	−	0.934266i	$-0.616056\pi$
$107$	1.02531	−	0.456499i	0.0991208	−	0.0441314i	0.455698	+	0.890134i	$0.349390\pi$
$108$	−0.612352	+	1.88463i	−0.0589236	+	0.181348i
$109$	0.936236	−	2.88144i	0.0896751	−	0.275992i	−0.896154	−	0.443743i	$-0.853650\pi$
$109$	0.936236	−	2.88144i	0.0896751	−	0.275992i	0.985829	+	0.167751i	$0.0536504\pi$
$110$	−0.819822	+	0.365008i	−0.0781669	+	0.0348022i
$111$	9.74223	−	2.07078i	0.924692	−	0.196549i
$112$	10.9980	+	2.33769i	1.03921	+	0.220891i
$113$	4.42231	+	1.96894i	0.416016	+	0.185222i	0.604061	−	0.796938i	$-0.293548\pi$
$113$	4.42231	+	1.96894i	0.416016	+	0.185222i	−0.188045	+	0.982160i	$0.560215\pi$
$114$	0.144952	−	0.160985i	0.0135760	−	0.0150777i
$115$	−1.12232	+	10.6781i	−0.104657	+	0.995742i
$116$	12.1432	+	8.82257i	1.12747	+	0.819155i
$117$	−0.465871	−	4.43247i	−0.0430698	−	0.409782i
$118$	0.865521	−	1.49913i	0.0796777	−	0.138006i
$119$	−7.36958	−	12.7645i	−0.675569	−	1.17012i
$120$	−1.24544	+	0.904866i	−0.113693	+	0.0826026i
$121$	−3.75568	−	4.17110i	−0.341425	−	0.379191i
$122$	−0.122646	−	0.377464i	−0.0111038	−	0.0341740i
$123$	7.94420			0.716304
$124$	−9.82231	+	5.02521i	−0.882069	+	0.451277i
$125$	−5.33206			−0.476914
$126$	0.121116	+	0.372757i	0.0107899	+	0.0332079i
$127$	8.18305	+	9.08819i	0.726128	+	0.806447i	0.987304	−	0.158844i	$-0.0507768\pi$
$127$	8.18305	+	9.08819i	0.726128	+	0.806447i	−0.261176	+	0.965291i	$0.584110\pi$
$128$	−3.43027	+	2.49223i	−0.303195	+	0.220284i
$129$	1.06402	+	1.84294i	0.0936818	+	0.162262i
$130$	0.861605	−	1.49234i	0.0755677	−	0.130887i
$131$	−0.528215	−	5.02563i	−0.0461503	−	0.439091i	−0.993062	−	0.117596i	$-0.962481\pi$
$131$	−0.528215	−	5.02563i	−0.0461503	−	0.439091i	0.946911	−	0.321495i	$-0.104185\pi$
$132$	3.72100	+	2.70346i	0.323871	+	0.235306i
$133$	−0.482661	+	4.59222i	−0.0418521	+	0.398196i
$134$	−0.108708	+	0.120732i	−0.00939092	+	0.0104297i
$135$	2.60480	+	1.15973i	0.224185	+	0.0998138i
$136$	2.69303	+	0.572421i	0.230925	+	0.0490847i
$137$	8.85459	−	1.88210i	0.756498	−	0.160799i	0.186512	−	0.982453i	$-0.440282\pi$
$137$	8.85459	−	1.88210i	0.756498	−	0.160799i	0.569987	+	0.821654i	$0.306948\pi$
$138$	−0.466476	+	0.207689i	−0.0397091	+	0.0176796i
$139$	−1.96644	+	6.05209i	−0.166791	+	0.513331i	−0.999164	−	0.0408854i	$-0.986982\pi$
$139$	−1.96644	+	6.05209i	−0.166791	+	0.513331i	0.832372	+	0.554217i	$0.186982\pi$
$140$	5.04665	−	15.5320i	0.426520	−	1.31269i
$141$	1.19752	−	0.533169i	0.100849	−	0.0449009i
$142$	−1.69809	+	0.360941i	−0.142501	+	0.0302895i
$143$	−10.1186	−	2.15077i	−0.846156	−	0.179856i
$144$	3.55370	+	1.58221i	0.296142	+	0.131851i
$145$	14.4515	−	16.0500i	1.20013	−	1.33288i
$146$	−0.0184343	+	0.175391i	−0.00152563	+	0.0145154i
$147$	−1.09573	−	0.796096i	−0.0903745	−	0.0656609i
$148$	−2.06304	−	19.6285i	−0.169581	−	1.61345i
$149$	−8.54406	+	14.7987i	−0.699956	+	1.21236i	0.268525	+	0.963273i	$0.413464\pi$
$149$	−8.54406	+	14.7987i	−0.699956	+	1.21236i	−0.968481	+	0.249087i	$0.919869\pi$
$150$	0.212213	+	0.367563i	0.0173271	+	0.0300114i
$151$	5.38274	−	3.91079i	0.438041	−	0.318255i	−0.346815	−	0.937934i	$-0.612737\pi$
$151$	5.38274	−	3.91079i	0.438041	−	0.318255i	0.784856	+	0.619678i	$0.212737\pi$
$152$	−0.577142	−	0.640981i	−0.0468124	−	0.0519904i
$153$	−1.57579	−	4.84978i	−0.127395	−	0.392081i
$154$	0.909709			0.0733065
$155$	5.71376	+	14.8115i	0.458940	+	1.18969i
$156$	−8.83182			−0.707111
$157$	3.94632	+	12.1455i	0.314951	+	0.969320i	0.975775	+	0.218778i	$0.0702071\pi$
$157$	3.94632	+	12.1455i	0.314951	+	0.969320i	−0.660824	+	0.750541i	$0.729793\pi$
$158$	1.16192	+	1.29044i	0.0924375	+	0.102662i
$159$	−6.19012	+	4.49739i	−0.490909	+	0.356666i
$160$	2.29147	+	3.96894i	0.181156	+	0.313772i
$161$	5.44208	−	9.42596i	0.428896	−	0.742870i
$162$	0.0141741	+	0.134858i	0.00111363	+	0.0105954i
$163$	8.09028	+	5.87793i	0.633679	+	0.460395i	0.857673	−	0.514196i	$-0.171909\pi$
$163$	8.09028	+	5.87793i	0.633679	+	0.460395i	−0.223994	+	0.974591i	$0.571909\pi$
$164$	1.64552	−	15.6561i	0.128494	−	1.22253i
$165$	4.42831	−	4.91813i	0.344743	−	0.382876i
$166$	−1.62947	−	0.725486i	−0.126471	−	0.0563086i
$167$	7.33967	+	1.56010i	0.567961	+	0.120724i	0.482937	−	0.875655i	$-0.339570\pi$
$167$	7.33967	+	1.56010i	0.567961	+	0.120724i	0.0850238	+	0.996379i	$0.472903\pi$
$168$	1.52645	−	0.324458i	0.117768	−	0.0250324i
$169$	6.27042	−	2.79177i	0.482340	−	0.214752i
$170$	0.609262	−	1.87512i	0.0467283	−	0.143815i
$171$	−0.493665	+	1.51935i	−0.0377515	+	0.116187i
$172$	3.85238	−	1.71519i	0.293741	−	0.130782i
$173$	−21.4528	+	4.55993i	−1.63102	+	0.346685i	−0.930315	−	0.366762i	$-0.880466\pi$
$173$	−21.4528	+	4.55993i	−1.63102	+	0.346685i	−0.700709	+	0.713447i	$0.747133\pi$
$174$	1.00467	+	0.213550i	0.0761640	+	0.0161892i
$175$	−8.26469	−	3.67968i	−0.624752	−	0.278158i
$176$	6.04150	−	6.70976i	0.455395	−	0.505767i
$177$	−1.33438	+	12.6958i	−0.100298	+	0.954274i
$178$	0.342695	+	0.248982i	0.0256860	+	0.0186620i
$179$	0.354858	+	3.37625i	0.0265233	+	0.252352i	0.999747	+	0.0224924i	$0.00716016\pi$
$179$	0.354858	+	3.37625i	0.0265233	+	0.252352i	−0.973224	+	0.229860i	$0.926173\pi$
$180$	2.82509	−	4.89321i	0.210570	−	0.364718i
$181$	3.08183	+	5.33789i	0.229071	+	0.396762i	0.957533	−	0.288324i	$-0.0930979\pi$
$181$	3.08183	+	5.33789i	0.229071	+	0.396762i	−0.728462	+	0.685086i	$0.759765\pi$
$182$	−1.41322	+	1.02676i	−0.104755	+	0.0761087i
$183$	1.95848	+	2.17511i	0.144775	+	0.160789i
$184$	0.628262	+	1.93359i	0.0463161	+	0.142546i
$185$	−28.3987			−2.08791
$186$	−0.474161	+	0.587526i	−0.0347672	+	0.0430795i
$187$	−11.8358			−0.865520
$188$	−0.802698	−	2.47045i	−0.0585428	−	0.180176i
$189$	−1.93405	−	2.14798i	−0.140682	−	0.156243i
$190$	−0.499706	+	0.363058i	−0.0362525	+	0.0263390i
$191$	4.15417	+	7.19523i	0.300585	+	0.520629i	0.976269	−	0.216563i	$-0.0694848\pi$
$191$	4.15417	+	7.19523i	0.300585	+	0.520629i	−0.675684	+	0.737192i	$0.736151\pi$
$192$	3.78104	−	6.54895i	0.272873	−	0.472630i
$193$	0.00315488	+	0.0300167i	0.000227093	+	0.00216065i	0.994635	−	0.103448i	$-0.0329876\pi$
$193$	0.00315488	+	0.0300167i	0.000227093	+	0.00216065i	−0.994408	+	0.105609i	$0.966321\pi$
$194$	2.00724	+	1.45835i	0.144112	+	0.104703i
$195$	−1.32834	+	12.6383i	−0.0951246	+	0.905050i
$196$	−1.79588	+	1.99452i	−0.128277	+	0.142466i
$197$	−3.57267	−	1.59065i	−0.254542	−	0.113329i	0.275499	−	0.961301i	$-0.411157\pi$
$197$	−3.57267	−	1.59065i	−0.254542	−	0.113329i	−0.530041	+	0.847972i	$0.677824\pi$
$198$	0.307857	+	0.0654371i	0.0218785	+	0.00465041i
$199$	−8.22112	+	1.74745i	−0.582780	+	0.123874i	−0.489862	−	0.871800i	$-0.662953\pi$
$199$	−8.22112	+	1.74745i	−0.582780	+	0.123874i	−0.0929181	+	0.995674i	$0.529619\pi$
$200$	1.54380	−	0.687343i	0.109163	−	0.0486025i
$201$	0.370229	−	1.13945i	0.0261139	−	0.0803703i
$202$	−0.623120	+	1.91777i	−0.0438426	+	0.134934i
$203$	−20.0007	+	8.90490i	−1.40378	+	0.625001i
$204$	−9.88413	+	2.10094i	−0.692028	+	0.147095i
$205$	−22.1564	−	4.70948i	−1.54747	−	0.328925i
$206$	−1.86137	−	0.828738i	−0.129688	−	0.0577409i
$207$	2.51970	−	2.79841i	0.175131	−	0.194503i
$208$	−1.81225	+	17.2424i	−0.125657	+	1.19554i
$209$	2.99979	+	2.17947i	0.207500	+	0.150757i
$210$	−0.116815	−	1.11142i	−0.00806100	−	0.0766953i
$211$	−4.87500	+	8.44375i	−0.335609	+	0.581292i	−0.983602	−	0.180355i	$-0.942275\pi$
$211$	−4.87500	+	8.44375i	−0.335609	+	0.581292i	0.647993	+	0.761647i	$0.275609\pi$
$212$	7.58107	+	13.1308i	0.520670	+	0.901827i
$213$	10.3574	−	7.52512i	0.709680	−	0.515613i
$214$	−0.101836	−	0.113100i	−0.00696134	−	0.00773135i
$215$	−1.87502	−	5.77073i	−0.127876	−	0.393560i
$216$	0.539910			0.0367362
$217$	0.815647	−	16.0724i	0.0553697	−	1.09106i
$218$	−0.410833			−0.0278251
$219$	−0.401895	−	1.23691i	−0.0271575	−	0.0835823i
$220$	−8.77519	−	9.74584i	−0.591623	−	0.657064i
$221$	18.3867	−	13.3587i	1.23683	−	0.898606i
$222$	−0.675284	−	1.16963i	−0.0453221	−	0.0785002i
$223$	2.16091	−	3.74280i	0.144705	−	0.250637i	−0.784558	−	0.620056i	$-0.787110\pi$
$223$	2.16091	−	3.74280i	0.144705	−	0.250637i	0.929263	+	0.369419i	$0.120443\pi$
$224$	−0.485614	−	4.62031i	−0.0324465	−	0.308708i
$225$	−2.53219	−	1.83975i	−0.168813	−	0.122650i
$226$	0.0686145	−	0.652823i	0.00456417	−	0.0434252i
$227$	4.24011	−	4.70912i	0.281426	−	0.312555i	−0.585814	−	0.810446i	$-0.699225\pi$
$227$	4.24011	−	4.70912i	0.281426	−	0.312555i	0.867240	+	0.497890i	$0.165892\pi$
$228$	2.89201	+	1.28760i	0.191528	+	0.0852737i
$229$	12.4380	+	2.64378i	0.821927	+	0.174706i	0.599634	−	0.800274i	$-0.295313\pi$
$229$	12.4380	+	2.64378i	0.821927	+	0.174706i	0.222292	+	0.974980i	$0.428646\pi$
$230$	1.42413	−	0.302707i	0.0939040	−	0.0199599i
$231$	−6.12873	+	2.72869i	−0.403241	+	0.179534i
$232$	1.26375	−	3.88943i	0.0829693	−	0.255353i
$233$	−2.53198	+	7.79264i	−0.165876	+	0.510513i	−0.999100	−	0.0424228i	$-0.986492\pi$
$233$	−2.53198	+	7.79264i	−0.165876	+	0.510513i	0.833224	+	0.552935i	$0.186492\pi$
$234$	−0.552108	+	0.245814i	−0.0360924	+	0.0160694i
$235$	−3.65595	+	0.777096i	−0.238488	+	0.0506921i
$236$	24.7439	+	5.25948i	1.61069	+	0.342363i
$237$	−11.6986	−	5.20855i	−0.759905	−	0.338332i
$238$	−1.33735	+	1.48528i	−0.0866878	+	0.0962765i
$239$	2.30632	−	21.9432i	0.149184	−	1.41939i	−0.622121	−	0.782921i	$-0.713729\pi$
$239$	2.30632	−	21.9432i	0.149184	−	1.41939i	0.771304	−	0.636467i	$-0.219605\pi$
$240$	−8.97331	−	6.51949i	−0.579225	−	0.420832i
$241$	1.55418	+	14.7870i	0.100113	+	0.952514i	0.923128	+	0.384494i	$0.125624\pi$
$241$	1.55418	+	14.7870i	0.100113	+	0.952514i	−0.823014	+	0.568020i	$0.807709\pi$
$242$	−0.380548	+	0.659129i	−0.0244626	+	0.0423704i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	4.69228	−	3.40914i	0.300392	−	0.218248i
$245$	2.58406	+	2.86989i	0.165089	+	0.183350i
$246$	−0.332885	−	1.02452i	−0.0212240	−	0.0653208i
$247$	−7.12003			−0.453037
$248$	2.12914	+	2.12211i	0.135201	+	0.134754i
$249$	13.1539			0.833592
$250$	0.223429	+	0.687644i	0.0141309	+	0.0434904i
$251$	13.4682	+	14.9579i	0.850102	+	0.944134i	0.999000	−	0.0447186i	$-0.0142391\pi$
$251$	13.4682	+	14.9579i	0.850102	+	0.944134i	−0.148898	+	0.988853i	$0.547572\pi$
$252$	−4.63376	+	3.36663i	−0.291900	+	0.212078i
$253$	−4.37009	−	7.56921i	−0.274745	−	0.475872i
$254$	0.829156	−	1.43614i	0.0520259	−	0.0901115i
$255$	1.51983	+	14.4602i	0.0951753	+	0.905532i
$256$	−11.7705	−	8.55180i	−0.735659	−	0.534488i
$257$	−0.275359	+	2.61987i	−0.0171764	+	0.163423i	−0.999748	−	0.0224636i	$-0.992849\pi$
$257$	−0.275359	+	2.61987i	−0.0171764	+	0.163423i	0.982571	+	0.185887i	$0.0595157\pi$
$258$	0.193087	−	0.214445i	0.0120211	−	0.0133508i
$259$	26.2992	+	11.7091i	1.63415	+	0.727570i
$260$	24.6320	+	5.23568i	1.52761	+	0.324703i
$261$	−7.40905	+	1.57484i	−0.458608	+	0.0974802i
$262$	−0.625991	+	0.278709i	−0.0386739	+	0.0172187i
$263$	−4.17559	+	12.8511i	−0.257478	+	0.792435i	0.735854	+	0.677140i	$0.236781\pi$
$263$	−4.17559	+	12.8511i	−0.257478	+	0.792435i	−0.993331	+	0.115294i	$0.963219\pi$
$264$	0.387246	−	1.19182i	0.0238333	−	0.0733514i
$265$	19.9304	−	8.87359i	1.22432	−	0.545100i
$266$	0.612456	−	0.130181i	0.0375521	−	0.00798194i
$267$	−3.05557	−	0.649481i	−0.186998	−	0.0397476i
$268$	−2.16888	−	0.965650i	−0.132486	−	0.0589864i
$269$	−13.2043	+	14.6649i	−0.805080	+	0.894132i	−0.996170	−	0.0874404i	$-0.972131\pi$
$269$	−13.2043	+	14.6649i	−0.805080	+	0.894132i	0.191090	+	0.981573i	$0.438798\pi$
$270$	0.0404149	−	0.384522i	0.00245957	−	0.0234012i
$271$	−15.0132	−	10.9078i	−0.911989	−	0.662599i	0.0295281	−	0.999564i	$-0.490600\pi$
$271$	−15.0132	−	10.9078i	−0.911989	−	0.662599i	−0.941517	+	0.336965i	$0.890600\pi$
$272$	2.07349	+	19.7279i	0.125724	+	1.19618i
$273$	6.44109	−	11.1563i	0.389832	−	0.675209i
$274$	−0.613757	−	1.06306i	−0.0370784	−	0.0642217i
$275$	−5.87732	+	4.27012i	−0.354416	+	0.257498i
$276$	−4.99306	−	5.54536i	−0.300547	−	0.333791i
$277$	−0.392658	−	1.20848i	−0.0235925	−	0.0726104i	0.938567	−	0.345097i	$-0.112154\pi$
$277$	−0.392658	−	1.20848i	−0.0235925	−	0.0726104i	−0.962160	+	0.272487i	$0.912154\pi$
$278$	0.862902			0.0517534
$279$	1.43214	−	5.38042i	0.0857400	−	0.322118i
$280$	−4.44962			−0.265916
$281$	−1.33603	−	4.11187i	−0.0797007	−	0.245293i	0.903265	−	0.429083i	$-0.141163\pi$
$281$	−1.33603	−	4.11187i	−0.0797007	−	0.245293i	−0.982966	+	0.183790i	$0.941163\pi$
$282$	−0.118939	−	0.132095i	−0.00708272	−	0.00786616i
$283$	4.94179	−	3.59042i	0.293759	−	0.213428i	−0.431138	−	0.902286i	$-0.641888\pi$
$283$	4.94179	−	3.59042i	0.293759	−	0.213428i	0.724896	+	0.688858i	$0.241888\pi$
$284$	−12.6848	−	21.9707i	−0.752704	−	1.30372i
$285$	2.27753	−	3.94480i	0.134909	−	0.233670i
$286$	0.146626	+	1.39505i	0.00867018	+	0.0824912i
$287$	18.5766	+	13.4967i	1.09654	+	0.796683i
$288$	0.168010	−	1.59850i	0.00990006	−	0.0941927i
$289$	6.02448	−	6.69086i	0.354381	−	0.393580i
$290$	−2.67544	−	1.19118i	−0.157107	−	0.0699486i
$291$	−17.8972	−	3.80416i	−1.04915	−	0.223004i
$292$	−2.52089	+	0.535831i	−0.147524	+	0.0313571i
$293$	28.3179	−	12.6080i	1.65435	−	0.736565i	0.654542	−	0.756026i	$-0.272862\pi$
$293$	28.3179	−	12.6080i	1.65435	−	0.736565i	0.999811	+	0.0194609i	$0.00619499\pi$
$294$	−0.0567534	+	0.174669i	−0.00330992	+	0.0101869i
$295$	11.2479	−	34.6175i	0.654879	−	2.01551i
$296$	−4.91253	+	2.18720i	−0.285535	+	0.127128i
$297$	−2.27032	+	0.482571i	−0.131737	+	0.0280016i
$298$	2.26653	+	0.481765i	0.131296	+	0.0279079i
$299$	15.3320	+	6.82625i	0.886673	+	0.394772i
$300$	−4.15020	+	4.60926i	−0.239612	+	0.266116i
$301$	−0.642943	+	6.11719i	−0.0370586	+	0.352589i
$302$	−0.729904	−	0.530306i	−0.0420012	−	0.0305157i
$303$	−1.55440	−	14.7891i	−0.0892977	−	0.849611i
$304$	3.10722	−	5.38186i	0.178211	−	0.308671i
$305$	−4.17274	−	7.22740i	−0.238931	−	0.413840i
$306$	−0.559417	+	0.406440i	−0.0319797	+	0.0232346i
$307$	7.46262	+	8.28808i	0.425914	+	0.473026i	0.917461	−	0.397825i	$-0.130235\pi$
$307$	7.46262	+	8.28808i	0.425914	+	0.473026i	−0.491547	+	0.870851i	$0.663568\pi$
$308$	4.10810	+	12.6434i	0.234081	+	0.720427i
$309$	15.0259			0.854795
$310$	1.67073	−	1.35752i	0.0948912	−	0.0771018i
$311$	−4.21465			−0.238991			−0.119495	−	0.992835i	$-0.538128\pi$
$311$	−4.21465			−0.238991			−0.119495	+	0.992835i	$0.538128\pi$
$312$	0.743593	+	2.28854i	0.0420976	+	0.129563i
$313$	−2.06933	−	2.29823i	−0.116966	−	0.129903i	0.681818	−	0.731522i	$-0.261190\pi$
$313$	−2.06933	−	2.29823i	−0.116966	−	0.129903i	−0.798784	+	0.601618i	$0.794523\pi$
$314$	1.40098	−	1.01787i	0.0790616	−	0.0574416i
$315$	4.12071	+	7.13728i	0.232176	+	0.402140i
$316$	−12.6880	+	21.9762i	−0.713754	+	1.23626i
$317$	−1.33895	−	12.7393i	−0.0752032	−	0.715510i	−0.965548	−	0.260224i	$-0.916204\pi$
$317$	−1.33895	−	12.7393i	−0.0752032	−	0.715510i	0.890345	−	0.455286i	$-0.150463\pi$
$318$	0.839386	+	0.609850i	0.0470704	+	0.0341987i
$319$	−1.83770	+	17.4846i	−0.102892	+	0.978948i
$320$	−14.4277	+	16.0235i	−0.806531	+	0.895743i
$321$	1.02531	+	0.456499i	0.0572274	+	0.0254793i
$322$	−1.44365	−	0.306857i	−0.0804514	−	0.0171005i
$323$	−7.96838	+	1.69373i	−0.443373	+	0.0942418i
$324$	−1.81029	+	0.805994i	−0.100572	+	0.0447775i
$325$	4.31075	−	13.2671i	0.239117	−	0.735928i
$326$	0.419035	−	1.28966i	0.0232082	−	0.0714275i
$327$	2.76779	−	1.23230i	0.153059	−	0.0681463i
$328$	−4.19542	+	0.891765i	−0.231654	+	0.0492395i
$329$	3.70607	+	0.787749i	0.204322	+	0.0434300i
$330$	−0.819822	−	0.365008i	−0.0451297	−	0.0200930i
$331$	−13.2216	+	14.6841i	−0.726724	+	0.807109i	−0.987388	−	0.158321i	$-0.949392\pi$
$331$	−13.2216	+	14.6841i	−0.726724	+	0.807109i	0.260663	+	0.965430i	$0.416059\pi$
$332$	2.72462	−	25.9231i	0.149533	−	1.42271i
$333$	8.05771	+	5.85427i	0.441560	+	0.320812i
$334$	−0.106358	−	1.01193i	−0.00581964	−	0.0553701i
$335$	−1.70805	+	2.95844i	−0.0933210	+	0.161637i
$336$	5.62184	+	9.73732i	0.306697	+	0.531214i
$337$	−21.1108	+	15.3379i	−1.14998	+	0.835510i	−0.988478	−	0.151363i	$-0.951634\pi$
$337$	−21.1108	+	15.3379i	−1.14998	+	0.835510i	−0.161502	+	0.986872i	$0.551634\pi$
$338$	−0.622787	−	0.691675i	−0.0338751	−	0.0376222i
$339$	1.49590	+	4.60389i	0.0812459	+	0.250049i
$340$	28.8123			1.56257
$341$	−10.8498	−	7.02043i	−0.587548	−	0.380177i
$342$	0.216627			0.0117138
$343$	5.04255	+	15.5194i	0.272272	+	0.837967i
$344$	−0.768798	−	0.853837i	−0.0414508	−	0.0460358i
$345$	−8.68639	+	6.31103i	−0.467659	+	0.339774i
$346$	1.48700	+	2.57556i	0.0799417	+	0.138463i
$347$	10.7205	−	18.5685i	0.575508	−	0.996810i	−0.420478	−	0.907303i	$-0.638138\pi$
$347$	10.7205	−	18.5685i	0.575508	−	0.996810i	0.995986	−	0.0895070i	$-0.0285291\pi$
$348$	1.56896	+	14.9276i	0.0841049	+	0.800205i
$349$	−14.8254	−	10.7713i	−0.793586	−	0.576574i	0.115440	−	0.993314i	$-0.463172\pi$
$349$	−14.8254	−	10.7713i	−0.793586	−	0.576574i	−0.909025	+	0.416741i	$0.863172\pi$
$350$	−0.128231	+	1.22004i	−0.00685424	+	0.0652138i
$351$	2.98224	−	3.31211i	0.159180	−	0.176787i
$352$	−3.40810	−	1.51738i	−0.181652	−	0.0808768i
$353$	−29.2145	−	6.20973i	−1.55493	−	0.330510i	−0.651298	−	0.758822i	$-0.725775\pi$
$353$	−29.2145	−	6.20973i	−1.55493	−	0.330510i	−0.903631	+	0.428312i	$0.859109\pi$
$354$	1.69321	−	0.359904i	0.0899933	−	0.0191287i
$355$	−33.3480	+	14.8475i	−1.76993	+	0.788022i
$356$	−1.91288	+	5.88725i	−0.101383	+	0.312024i
$357$	4.55465	−	14.0178i	0.241058	−	0.741900i
$358$	0.420545	−	0.187239i	0.0222265	−	0.00989586i
$359$	21.1988	−	4.50594i	1.11883	−	0.237814i	0.388861	−	0.921296i	$-0.372869\pi$
$359$	21.1988	−	4.50594i	1.11883	−	0.237814i	0.729967	+	0.683482i	$0.239535\pi$
$360$	−1.50581	−	0.320070i	−0.0793631	−	0.0168691i
$361$	−15.0259	−	6.68996i	−0.790836	−	0.352103i
$362$	0.559258	−	0.621119i	0.0293940	−	0.0326453i
$363$	0.586694	−	5.58202i	0.0307935	−	0.292980i
$364$	−20.6522	−	15.0047i	−1.08247	−	0.786458i
$365$	0.387622	+	3.68798i	0.0202891	+	0.193038i
$366$	0.198445	−	0.343716i	0.0103729	−	0.0179663i
$367$	−0.115879	−	0.200709i	−0.00604885	−	0.0104769i	0.862985	−	0.505229i	$-0.168592\pi$
$367$	−0.115879	−	0.200709i	−0.00604885	−	0.0104769i	−0.869034	+	0.494752i	$0.835259\pi$
$368$	−11.8508	+	8.61008i	−0.617763	+	0.448831i
$369$	5.31571	+	5.90369i	0.276725	+	0.307334i
$370$	1.18999	+	3.66241i	0.0618646	+	0.190400i
$371$	−22.1156			−1.14819
$372$	−10.3069	−	3.93688i	−0.534386	−	0.204117i
$373$	23.9527			1.24023			0.620113	−	0.784512i	$-0.287087\pi$
$373$	23.9527			1.24023			0.620113	+	0.784512i	$0.287087\pi$
$374$	0.495956	+	1.52639i	0.0256453	+	0.0789280i
$375$	−3.56784	−	3.96249i	−0.184243	−	0.204622i
$376$	−0.572572	+	0.415998i	−0.0295282	+	0.0214535i
$377$	−16.8795	−	29.2361i	−0.869338	−	1.50574i
$378$	−0.195970	+	0.339430i	−0.0100796	+	0.0174584i
$379$	0.0747404	+	0.711108i	0.00383916	+	0.0365271i	0.996274	−	0.0862473i	$-0.0274875\pi$
$379$	0.0747404	+	0.711108i	0.00383916	+	0.0365271i	−0.992435	+	0.122774i	$0.960821\pi$
$380$	−7.30249	−	5.30557i	−0.374610	−	0.272170i
$381$	−1.27832	+	12.1624i	−0.0654902	+	0.623098i
$382$	0.753854	−	0.837240i	0.0385705	−	0.0428369i
$383$	−21.9513	−	9.77334i	−1.12166	−	0.499394i	−0.239759	−	0.970833i	$-0.577068\pi$
$383$	−21.9513	−	9.77334i	−1.12166	−	0.499394i	−0.881899	+	0.471438i	$0.843735\pi$
$384$	−4.14739	−	0.881554i	−0.211645	−	0.0449866i
$385$	18.7107	−	3.97707i	0.953583	−	0.202690i
$386$	0.00373888	−	0.00166465i	0.000190304	−	8.47287e-5i
$387$	−0.657601	+	2.02389i	−0.0334277	+	0.102880i
$388$	−11.2042	+	34.4830i	−0.568807	+	1.75061i
$389$	−12.4167	+	5.52826i	−0.629551	+	0.280294i	−0.696605	−	0.717455i	$-0.745307\pi$
$389$	−12.4167	+	5.52826i	−0.629551	+	0.280294i	0.0670537	+	0.997749i	$0.478640\pi$
$390$	1.68555	−	0.358275i	0.0853513	−	0.0181420i
$391$	18.7827	+	3.99238i	0.949880	+	0.201903i
$392$	0.668034	+	0.297428i	0.0337408	+	0.0150224i
$393$	3.38132	−	3.75534i	0.170565	−	0.189432i
$394$	−0.0554318	+	0.527399i	−0.00279262	+	0.0265700i
$395$	29.5397	+	21.4618i	1.48630	+	1.07986i
$396$	0.480769	+	4.57421i	0.0241595	+	0.229863i
$397$	12.2500	−	21.2177i	0.614811	−	1.06488i	−0.375606	−	0.926779i	$-0.622565\pi$
$397$	12.2500	−	21.2177i	0.614811	−	1.06488i	0.990418	−	0.138105i	$-0.0441012\pi$
$398$	0.569848	+	0.987006i	0.0285639	+	0.0494741i
$399$	−3.73565	+	2.71411i	−0.187016	+	0.135875i
$400$	8.14706	+	9.04823i	0.407353	+	0.452411i
$401$	5.73814	+	17.6602i	0.286549	+	0.881908i	0.985930	+	0.167159i	$0.0534592\pi$
$401$	5.73814	+	17.6602i	0.286549	+	0.881908i	−0.699381	+	0.714749i	$0.746541\pi$
$402$	−0.162461			−0.00810283
$403$	24.7787	−	1.33972i	1.23431	−	0.0667363i
$404$	−29.4677			−1.46607
$405$	0.881103	+	2.71176i	0.0437824	+	0.134748i
$406$	1.98650	+	2.20623i	0.0985884	+	0.109493i
$407$	18.7023	−	13.5880i	0.927037	−	0.673532i
$408$	1.37660	+	2.38434i	0.0681517	+	0.118042i
$409$	1.88356	−	3.26242i	0.0931360	−	0.161316i	−0.815693	−	0.578485i	$-0.803644\pi$
$409$	1.88356	−	3.26242i	0.0931360	−	0.161316i	0.908829	+	0.417169i	$0.136978\pi$
$410$	0.321064	+	3.05472i	0.0158562	+	0.150862i
$411$	7.32355	+	5.32087i	0.361244	+	0.262459i
$412$	3.11239	−	29.6125i	0.153337	−	1.45890i
$413$	−24.6896	+	27.4206i	−1.21490	+	1.34928i
$414$	−0.466476	−	0.207689i	−0.0229261	−	0.0102073i
$415$	−36.6861	−	7.79788i	−1.80085	−	0.382783i
$416$	7.00705	−	1.48939i	0.343549	−	0.0730236i
$417$	−5.81339	+	2.58829i	−0.284683	+	0.126749i
$418$	0.155374	−	0.478191i	0.00759958	−	0.0233891i
$419$	−5.50499	+	16.9426i	−0.268936	+	0.827700i	0.721824	+	0.692076i	$0.243304\pi$
$419$	−5.50499	+	16.9426i	−0.268936	+	0.827700i	−0.990760	+	0.135624i	$0.956696\pi$
$420$	14.9194	−	6.64254i	0.727991	−	0.324123i
$421$	38.3719	−	8.15619i	1.87013	−	0.397508i	0.874040	−	0.485854i	$-0.161491\pi$
$421$	38.3719	−	8.15619i	1.87013	−	0.397508i	0.996090	+	0.0883451i	$0.0281578\pi$
$422$	1.29322	+	0.274882i	0.0629528	+	0.0133810i
$423$	1.19752	+	0.533169i	0.0582252	+	0.0259235i
$424$	2.76423	−	3.06999i	0.134243	−	0.149092i
$425$	1.66836	−	15.8734i	0.0809272	−	0.769971i
$426$	−1.40448	−	1.02041i	−0.0680472	−	0.0494392i
$427$	0.884300	+	8.41355i	0.0427943	+	0.407160i
$428$	1.11203	−	1.92609i	0.0537519	−	0.0931010i
$429$	−5.17231	−	8.95870i	−0.249721	−	0.432530i
$430$	−0.665648	+	0.483621i	−0.0321004	+	0.0233223i
$431$	2.51918	+	2.79783i	0.121345	+	0.134767i	0.800756	−	0.598991i	$-0.204431\pi$
$431$	2.51918	+	2.79783i	0.121345	+	0.134767i	−0.679411	+	0.733758i	$0.737765\pi$
$432$	1.20208	+	3.69962i	0.0578351	+	0.177998i
$433$	−5.67881			−0.272906			−0.136453	−	0.990647i	$-0.543570\pi$
$433$	−5.67881			−0.272906			−0.136453	+	0.990647i	$0.543570\pi$
$434$	−2.10694	+	0.568291i	−0.101136	+	0.0272788i
$435$	21.5974			1.03552
$436$	−1.85526	−	5.70989i	−0.0888507	−	0.273454i
$437$	−4.02530	−	4.47055i	−0.192556	−	0.213855i
$438$	−0.142676	+	0.103660i	−0.00681731	+	0.00495307i
$439$	15.3630	+	26.6096i	0.733238	+	1.27001i	0.955492	+	0.295017i	$0.0953252\pi$
$439$	15.3630	+	26.6096i	0.733238	+	1.27001i	−0.222254	+	0.974989i	$0.571341\pi$
$440$	−1.78656	+	3.09442i	−0.0851710	+	0.147521i
$441$	−0.141573	−	1.34698i	−0.00674159	−	0.0641419i
$442$	−2.49326	−	1.81146i	−0.118592	−	0.0861622i
$443$	3.62846	−	34.5225i	0.172393	−	1.64021i	−0.476387	−	0.879236i	$-0.658054\pi$
$443$	3.62846	−	34.5225i	0.172393	−	1.64021i	0.648780	−	0.760976i	$-0.275280\pi$
$444$	13.2064	−	14.6672i	0.626747	−	0.696073i
$445$	8.13695	+	3.62280i	0.385728	+	0.171737i
$446$	−0.573236	−	0.121845i	−0.0271435	−	0.00576953i
$447$	−16.7147	+	3.55282i	−0.790578	+	0.168043i
$448$	19.9677	−	8.89021i	0.943386	−	0.420023i
$449$	8.58529	−	26.4228i	0.405165	−	1.24697i	−0.515593	−	0.856834i	$-0.672428\pi$
$449$	8.58529	−	26.4228i	0.405165	−	1.24697i	0.920758	−	0.390135i	$-0.127572\pi$
$450$	−0.131155	+	0.403652i	−0.00618269	+	0.0190284i
$451$	16.8447	−	7.49974i	0.793185	−	0.353149i
$452$	9.38301	−	1.99442i	0.441339	−	0.0938096i
$453$	6.50804	+	1.38333i	0.305774	+	0.0649943i
$454$	−0.784981	−	0.349496i	−0.0368410	−	0.0164027i
$455$	−24.5779	+	27.2965i	−1.15223	+	1.27968i
$456$	0.0901584	−	0.857800i	0.00422205	−	0.0401702i
$457$	−17.8457	−	12.9657i	−0.834786	−	0.606508i	0.0861231	−	0.996285i	$-0.472552\pi$
$457$	−17.8457	−	12.9657i	−0.834786	−	0.606508i	−0.920909	+	0.389777i	$0.872552\pi$
$458$	−0.180237	−	1.71484i	−0.00842191	−	0.0801291i
$459$	2.54968	−	4.41617i	0.119009	−	0.206129i
$460$	10.6383	+	18.4260i	0.496011	+	0.859116i
$461$	19.5884	−	14.2318i	0.912324	−	0.662842i	−0.0292774	−	0.999571i	$-0.509321\pi$
$461$	19.5884	−	14.2318i	0.912324	−	0.662842i	0.941602	+	0.336729i	$0.109321\pi$
$462$	0.608714	+	0.676046i	0.0283200	+	0.0314525i
$463$	−7.90388	−	24.3256i	−0.367325	−	1.13051i	−0.948513	−	0.316739i	$-0.897412\pi$
$463$	−7.90388	−	24.3256i	−0.367325	−	1.13051i	0.581188	−	0.813769i	$-0.302588\pi$
$464$	29.4652			1.36789
$465$	−7.18387	+	14.1570i	−0.333144	+	0.656515i
$466$	1.11107			0.0514692
$467$	−4.54254	−	13.9805i	−0.210203	−	0.646940i	−0.999459	−	0.0328754i	$-0.989534\pi$
$467$	−4.54254	−	13.9805i	−0.210203	−	0.646940i	0.789256	−	0.614064i	$-0.210466\pi$
$468$	−5.90964	−	6.56332i	−0.273173	−	0.303390i
$469$	2.80158	−	2.03547i	0.129365	−	0.0939891i
$470$	0.253412	+	0.438923i	0.0116890	+	0.0202460i
$471$	−6.38529	+	11.0596i	−0.294219	+	0.509601i
$472$	−0.720446	−	6.85458i	−0.0331612	−	0.315508i
$473$	3.99595	+	2.90323i	0.183734	+	0.133491i
$474$	−0.181510	+	1.72695i	−0.00833703	+	0.0793215i
$475$	−3.34580	+	3.71589i	−0.153516	+	0.170497i
$476$	−26.6822	−	11.8797i	−1.22298	−	0.544505i
$477$	−7.48421	−	1.59082i	−0.342679	−	0.0728386i
$478$	−2.92653	+	0.622052i	−0.133856	+	0.0284520i
$479$	−16.8213	+	7.48932i	−0.768584	+	0.342196i	−0.753291	−	0.657687i	$-0.771535\pi$
$479$	−16.8213	+	7.48932i	−0.768584	+	0.342196i	−0.0152930	+	0.999883i	$0.504868\pi$
$480$	−1.41620	+	4.35863i	−0.0646406	+	0.198943i
$481$	−13.7173	+	42.2174i	−0.625454	+	1.92495i
$482$	1.84187	−	0.820052i	0.0838947	−	0.0373523i
$483$	10.6463	−	2.26294i	0.484424	−	0.102968i
$484$	−10.8793	−	2.31246i	−0.494513	−	0.105112i
$485$	47.6600	+	21.2196i	2.16413	+	0.963532i
$486$	−0.0907347	+	0.100771i	−0.00411581	+	0.00457107i
$487$	−1.59093	+	15.1367i	−0.0720919	+	0.685908i	0.897472	+	0.441071i	$0.145401\pi$
$487$	−1.59093	+	15.1367i	−0.0720919	+	0.685908i	−0.969564	+	0.244837i	$0.921265\pi$
$488$	−1.27846	−	0.928854i	−0.0578731	−	0.0420472i
$489$	1.04530	+	9.94535i	0.0472700	+	0.449744i
$490$	0.261832	−	0.453507i	0.0118284	−	0.0204874i
$491$	−2.34607	−	4.06351i	−0.105877	−	0.183384i	0.808219	−	0.588881i	$-0.200431\pi$
$491$	−2.34607	−	4.06351i	−0.105877	−	0.183384i	−0.914096	+	0.405498i	$0.867098\pi$
$492$	12.7358	−	9.25311i	0.574175	−	0.417162i
$493$	−25.8455	−	28.7043i	−1.16402	−	1.29278i
$494$	0.298350	+	0.918228i	0.0134234	+	0.0413130i
$495$	6.61800			0.297457
$496$	−9.80088	+	19.3143i	−0.440073	+	0.867236i
$497$	37.0043			1.65987
$498$	−0.551186	−	1.69638i	−0.0246992	−	0.0760164i
$499$	−2.46187	−	2.73419i	−0.110209	−	0.122399i	0.685516	−	0.728057i	$-0.259577\pi$
$499$	−2.46187	−	2.73419i	−0.110209	−	0.122399i	−0.795725	+	0.605658i	$0.792910\pi$
$500$	−8.54813	+	6.21058i	−0.382284	+	0.277746i
$501$	3.75182	+	6.49835i	0.167619	+	0.290325i
$502$	1.36468	−	2.36369i	0.0609084	−	0.105497i
$503$	−2.59303	−	24.6711i	−0.115618	−	1.10003i	−0.886397	−	0.462926i	$-0.846800\pi$
$503$	−2.59303	−	24.6711i	−0.115618	−	1.10003i	0.770779	−	0.637102i	$-0.219867\pi$
$504$	1.26252	+	0.917271i	0.0562369	+	0.0408585i
$505$	−4.43206	+	42.1683i	−0.197224	+	1.87646i
$506$	−0.793037	+	0.880756i	−0.0352548	+	0.0391544i
$507$	6.27042	+	2.79177i	0.278479	+	0.123987i
$508$	23.7043	+	5.03851i	1.05171	+	0.223548i
$509$	17.3759	−	3.69336i	0.770172	−	0.163705i	0.193965	−	0.981009i	$-0.437865\pi$
$509$	17.3759	−	3.69336i	0.770172	−	0.163705i	0.576208	+	0.817303i	$0.304532\pi$
$510$	1.80116	−	0.801928i	0.0797567	−	0.0355100i
$511$	1.16164	−	3.57515i	0.0513878	−	0.158155i
$512$	−3.23014	+	9.94136i	−0.142754	+	0.439350i
$513$	−1.45942	+	0.649776i	−0.0644350	+	0.0286883i
$514$	0.349407	−	0.0742688i	0.0154117	−	0.00327586i
$515$	−41.9073	−	8.90768i	−1.84666	−	0.392519i
$516$	3.85238	+	1.71519i	0.169592	+	0.0755070i
$517$	2.03585	−	2.26104i	0.0895364	−	0.0994403i
$518$	0.408045	−	3.88229i	0.0179285	−	0.170578i
$519$	−17.7434	−	12.8913i	−0.778848	−	0.565866i
$520$	−0.717186	−	6.82357i	−0.0314507	−	0.299233i
$521$	−9.02192	+	15.6264i	−0.395257	+	0.684606i	−0.993134	−	0.116982i	$-0.962678\pi$
$521$	−9.02192	+	15.6264i	−0.395257	+	0.684606i	0.597877	+	0.801588i	$0.296011\pi$
$522$	0.513559	+	0.889510i	0.0224779	+	0.0389328i
$523$	15.0982	−	10.9695i	0.660198	−	0.479662i	−0.206532	−	0.978440i	$-0.566218\pi$
$523$	15.0982	−	10.9695i	0.660198	−	0.479662i	0.866730	+	0.498778i	$0.166218\pi$
$524$	−6.70047	−	7.44163i	−0.292711	−	0.325089i
$525$	−2.79563	−	8.60405i	−0.122011	−	0.375512i
$526$	1.83230			0.0798922
$527$	27.4124	−	7.39377i	1.19410	−	0.322078i
$528$	9.02888			0.392931
$529$	−2.72555	−	8.38837i	−0.118502	−	0.364712i
$530$	−1.97952	−	2.19848i	−0.0859847	−	0.0954957i
$531$	−10.3277	+	7.50350i	−0.448183	+	0.325624i
$532$	4.57506	+	7.92424i	0.198354	+	0.343559i
$533$	−17.7032	+	30.6628i	−0.766810	+	1.32815i
$534$	0.0442776	+	0.421273i	0.00191608	+	0.0182303i
$535$	−2.58898	−	1.88100i	−0.111931	−	0.0813229i
$536$	−0.0676151	+	0.643314i	−0.00292053	+	0.0277869i
$537$	−2.27159	+	2.52286i	−0.0980265	+	0.108869i
$538$	2.44454	+	1.08838i	0.105392	+	0.0469233i
$539$	−3.07492	−	0.653595i	−0.132446	−	0.0281523i
$540$	5.52672	−	1.17474i	0.237832	−	0.0505528i
$541$	−16.9681	+	7.55470i	−0.729517	+	0.324802i	−0.737667	−	0.675165i	$-0.764072\pi$
$541$	−16.9681	+	7.55470i	−0.729517	+	0.324802i	0.00815000	+	0.999967i	$0.497406\pi$
$542$	−0.777609	+	2.39323i	−0.0334012	+	0.102798i
$543$	−1.90468	+	5.86200i	−0.0817375	+	0.251562i
$544$	7.48764	−	3.33371i	0.321030	−	0.142932i
$545$	−8.44990	+	1.79608i	−0.361954	+	0.0769357i
$546$	−1.70866	−	0.363187i	−0.0731239	−	0.0155430i
$547$	−1.44708	−	0.644281i	−0.0618727	−	0.0275475i	0.375567	−	0.926795i	$-0.377448\pi$
$547$	−1.44708	−	0.644281i	−0.0618727	−	0.0275475i	−0.437440	+	0.899248i	$0.644115\pi$
$548$	12.0031	−	13.3308i	0.512747	−	0.569463i
$549$	−0.305944	+	2.91086i	−0.0130574	+	0.124233i
$550$	0.796969	+	0.579032i	0.0339829	+	0.0246900i
$551$	1.26486	+	12.0343i	0.0538849	+	0.512681i
$552$	−1.01655	+	1.76072i	−0.0432672	+	0.0749410i
$553$	−18.5068	−	32.0547i	−0.786989	−	1.36310i
$554$	−0.139397	+	0.101278i	−0.00592239	+	0.00430287i
$555$	−19.0024	−	21.1043i	−0.806608	−	0.895829i
$556$	3.89673	+	11.9929i	0.165258	+	0.508612i
$557$	−16.2178			−0.687168			−0.343584	−	0.939122i	$-0.611641\pi$
$557$	−16.2178			−0.687168			−0.343584	+	0.939122i	$0.611641\pi$
$558$	−0.753892	+	0.0407610i	−0.0319148	+	0.00172555i
$559$	−9.48444			−0.401149
$560$	−9.90684	−	30.4901i	−0.418640	−	1.28844i
$561$	−7.91971	−	8.79572i	−0.334370	−	0.371356i
$562$	−0.474300	+	0.344599i	−0.0200071	+	0.0145360i
$563$	7.49747	+	12.9860i	0.315981	+	0.547295i	0.979645	−	0.200736i	$-0.0643332\pi$
$563$	7.49747	+	12.9860i	0.315981	+	0.547295i	−0.663665	+	0.748030i	$0.731000\pi$
$564$	1.29879	−	2.24958i	0.0546891	−	0.0947242i
$565$	−1.44277	−	13.7271i	−0.0606979	−	0.577502i
$566$	−0.670111	−	0.486864i	−0.0281669	−	0.0204644i
$567$	0.302129	−	2.87456i	0.0126882	−	0.120720i
$568$	−4.62516	+	5.13676i	−0.194068	+	0.215534i
$569$	1.38776	+	0.617871i	0.0581779	+	0.0259025i	0.435619	−	0.900131i	$-0.356529\pi$
$569$	1.38776	+	0.617871i	0.0581779	+	0.0259025i	−0.377441	+	0.926033i	$0.623196\pi$
$570$	−0.604173	−	0.128421i	−0.0253060	−	0.00537896i
$571$	−0.742389	+	0.157800i	−0.0310680	+	0.00660371i	−0.223419	−	0.974722i	$-0.571722\pi$
$571$	−0.742389	+	0.157800i	−0.0310680	+	0.00660371i	0.192351	+	0.981326i	$0.438389\pi$
$572$	−18.7268	+	8.33770i	−0.783006	+	0.348617i
$573$	−2.56742	+	7.90170i	−0.107255	+	0.330098i
$574$	0.962171	−	2.96126i	0.0401603	−	0.123601i
$575$	10.7673	−	4.79391i	0.449027	−	0.199920i
$576$	7.39682	−	1.57224i	0.308201	−	0.0655101i
$577$	−9.16738	−	1.94859i	−0.381643	−	0.0811207i	0.0130955	−	0.999914i	$-0.495831\pi$
$577$	−9.16738	−	1.94859i	−0.381643	−	0.0811207i	−0.394738	+	0.918794i	$0.629165\pi$
$578$	−1.11532	−	0.496574i	−0.0463914	−	0.0206548i
$579$	−0.0201957	+	0.0224296i	−0.000839306	+	0.000932144i
$580$	4.47358	−	42.5633i	0.185755	−	1.76734i
$581$	30.7587	+	22.3475i	1.27609	+	0.927132i
$582$	0.259344	+	2.46749i	0.0107502	+	0.102281i
$583$	−8.87962	+	15.3800i	−0.367756	+	0.636973i
$584$	0.351092	+	0.608110i	0.0145283	+	0.0251638i
$585$	−10.2810	+	7.46955i	−0.425065	+	0.308828i
$586$	−2.81258	−	3.12369i	−0.116187	−	0.129038i
$587$	7.71376	+	23.7405i	0.318381	+	0.979876i	0.974340	+	0.225080i	$0.0722642\pi$
$587$	7.71376	+	23.7405i	0.318381	+	0.979876i	−0.655959	+	0.754796i	$0.727736\pi$
$588$	−2.68390			−0.110682
$589$	−8.30918	−	3.17383i	−0.342374	−	0.130775i
$590$	−4.93573			−0.203201
$591$	−1.20849	−	3.71936i	−0.0497108	−	0.152994i
$592$	−25.9248	−	28.7924i	−1.06550	−	1.18336i
$593$	22.8195	−	16.5794i	0.937087	−	0.680833i	−0.0106310	−	0.999943i	$-0.503384\pi$
$593$	22.8195	−	16.5794i	0.937087	−	0.680833i	0.947718	+	0.319110i	$0.103384\pi$
$594$	0.157368	+	0.272569i	0.00645687	+	0.0111836i
$595$	−21.0130	+	36.3955i	−0.861447	+	1.49207i
$596$	3.53955	+	33.6765i	0.144985	+	1.37944i
$597$	−6.79962	−	4.94021i	−0.278290	−	0.202189i
$598$	0.237884	−	2.26332i	0.00972781	−	0.0925539i
$599$	−23.4254	+	26.0166i	−0.957137	+	1.06301i	0.0408232	+	0.999166i	$0.487002\pi$
$599$	−23.4254	+	26.0166i	−0.957137	+	1.06301i	−0.997960	+	0.0638417i	$0.979665\pi$
$600$	1.54380	+	0.687343i	0.0630253	+	0.0280607i
$601$	−24.3900	−	5.18425i	−0.994889	−	0.211470i	−0.318427	−	0.947948i	$-0.603154\pi$
$601$	−24.3900	−	5.18425i	−0.994889	−	0.211470i	−0.676462	+	0.736477i	$0.736488\pi$
$602$	0.815839	−	0.173412i	0.0332511	−	0.00706774i
$603$	1.09450	−	0.487305i	0.0445717	−	0.0198446i
$604$	4.07424	−	12.5392i	0.165778	−	0.510214i
$605$	−4.94543	+	15.2205i	−0.201060	+	0.618800i
$606$	−1.84213	+	0.820168i	−0.0748313	+	0.0333170i
$607$	23.0192	−	4.89288i	0.934320	−	0.198596i	0.284493	−	0.958678i	$-0.408175\pi$
$607$	23.0192	−	4.89288i	0.934320	−	0.198596i	0.649827	+	0.760082i	$0.274841\pi$
$608$	−2.51162	−	0.533861i	−0.101860	−	0.0216509i
$609$	−20.0007	−	8.90490i	−0.810470	−	0.360845i
$610$	−0.757225	+	0.840983i	−0.0306591	+	0.0340504i
$611$	−0.610685	+	5.81028i	−0.0247057	+	0.235059i
$612$	−8.17508	−	5.93954i	−0.330458	−	0.240092i
$613$	1.11265	+	10.5862i	0.0449397	+	0.427573i	0.993742	+	0.111701i	$0.0356300\pi$
$613$	1.11265	+	10.5862i	0.0449397	+	0.427573i	−0.948802	+	0.315871i	$0.897703\pi$
$614$	0.756159	−	1.30971i	0.0305161	−	0.0528554i
$615$	−11.3257	−	19.6167i	−0.456696	−	0.791020i
$616$	2.93035	−	2.12902i	0.118067	−	0.0857808i
$617$	−2.75203	−	3.05644i	−0.110792	−	0.123048i	0.685197	−	0.728357i	$-0.259716\pi$
$617$	−2.75203	−	3.05644i	−0.110792	−	0.123048i	−0.795990	+	0.605310i	$0.793049\pi$
$618$	−0.629631	−	1.93780i	−0.0253275	−	0.0779499i
$619$	27.4112			1.10175			0.550875	−	0.834588i	$-0.314294\pi$
$619$	27.4112			1.10175			0.550875	+	0.834588i	$0.314294\pi$
$620$	26.4120	+	17.0901i	1.06073	+	0.686354i
$621$	3.76563			0.151109
$622$	0.176606	+	0.543538i	0.00708126	+	0.0217939i
$623$	−6.04165	−	6.70994i	−0.242054	−	0.268828i
$624$	−14.0262	+	10.1906i	−0.561497	+	0.407952i
$625$	15.4266	+	26.7196i	0.617063	+	1.06878i
$626$	−0.209677	+	0.363172i	−0.00838039	+	0.0145153i
$627$	0.387586	+	3.68763i	0.0154787	+	0.147270i
$628$	20.4733	+	14.8747i	0.816972	+	0.593565i
$629$	−5.30889	+	50.5107i	−0.211679	+	2.01400i
$630$	0.747782	−	0.830496i	0.0297924	−	0.0330878i
$631$	−37.0395	−	16.4910i	−1.47452	−	0.656498i	−0.497077	−	0.867706i	$-0.665593\pi$
$631$	−37.0395	−	16.4910i	−1.47452	−	0.656498i	−0.977441	+	0.211209i	$0.932260\pi$
$632$	6.76284	+	1.43749i	0.269011	+	0.0571801i
$633$	−9.53694	+	2.02714i	−0.379059	+	0.0805716i
$634$	−1.58681	+	0.706491i	−0.0630201	+	0.0280583i
$635$	10.7753	−	33.1631i	0.427606	−	1.31604i
$636$	−4.68536	+	14.4200i	−0.185787	+	0.571792i
$637$	5.51453	−	2.45523i	0.218494	−	0.0972796i
$638$	2.33189	−	0.495658i	0.0923203	−	0.0196233i
$639$	12.5227	+	2.66179i	0.495392	+	0.105299i
$640$	11.0445	+	4.91731i	0.436571	+	0.194374i
$641$	24.9495	−	27.7092i	0.985446	−	1.09445i	−0.0100792	−	0.999949i	$-0.503208\pi$
$641$	24.9495	−	27.7092i	0.985446	−	1.09445i	0.995525	−	0.0944992i	$-0.0301250\pi$
$642$	0.0159083	−	0.151357i	0.000627850	−	0.00597360i
$643$	1.12432	+	0.816864i	0.0443387	+	0.0322140i	0.609734	−	0.792606i	$-0.291276\pi$
$643$	1.12432	+	0.816864i	0.0443387	+	0.0322140i	−0.565395	+	0.824820i	$0.691276\pi$
$644$	−2.25449	−	21.4500i	−0.0888393	−	0.845250i
$645$	3.03385	−	5.25479i	0.119458	−	0.206907i
$646$	0.552329	+	0.956662i	0.0217311	+	0.0376394i
$647$	18.6143	−	13.5241i	0.731804	−	0.531687i	−0.158329	−	0.987386i	$-0.550611\pi$
$647$	18.6143	−	13.5241i	0.731804	−	0.531687i	0.890134	+	0.455699i	$0.150611\pi$
$648$	0.361270	+	0.401231i	0.0141920	+	0.0157619i
$649$	9.15610	+	28.1796i	0.359408	+	1.10614i
$650$	−1.89161			−0.0741952
$651$	12.4899	−	10.1484i	0.489517	−	0.397746i
$652$	19.8164			0.776069
$653$	6.26973	+	19.2963i	0.245354	+	0.755121i	0.995578	+	0.0939377i	$0.0299454\pi$
$653$	6.26973	+	19.2963i	0.245354	+	0.755121i	−0.750224	+	0.661183i	$0.770055\pi$
$654$	−0.274901	−	0.305308i	−0.0107495	−	0.0119385i
$655$	−11.6568	+	8.46913i	−0.455467	+	0.330916i
$656$	−15.4515	−	26.7628i	−0.603280	−	1.04491i
$657$	0.650280	−	1.12632i	0.0253698	−	0.0439418i
$658$	−0.0537039	−	0.510958i	−0.00209360	−	0.0199192i
$659$	36.1389	+	26.2565i	1.40777	+	1.02281i	0.993642	+	0.112590i	$0.0359146\pi$
$659$	36.1389	+	26.2565i	1.40777	+	1.02281i	0.414131	+	0.910217i	$0.364085\pi$
$660$	1.37082	−	13.0425i	0.0533591	−	0.507678i
$661$	−11.4921	+	12.7633i	−0.446990	+	0.496433i	−0.923961	−	0.382486i	$-0.875068\pi$
$661$	−11.4921	+	12.7633i	−0.446990	+	0.496433i	0.476971	+	0.878919i	$0.341735\pi$
$662$	2.44774	+	1.08980i	0.0951341	+	0.0423564i
$663$	22.2306	+	4.72526i	0.863365	+	0.183514i
$664$	−6.94671	+	1.47657i	−0.269584	+	0.0573020i
$665$	12.0277	−	5.35507i	0.466414	−	0.207661i
$666$	0.417348	−	1.28447i	0.0161719	−	0.0497721i
$667$	8.81409	−	27.1270i	0.341283	−	1.05036i
$668$	13.5838	−	6.04789i	0.525573	−	0.234000i
$669$	4.22738	−	0.898556i	0.163440	−	0.0347402i
$670$	0.453105	+	0.0963104i	0.0175050	+	0.00372079i
$671$	6.20612	+	2.76314i	0.239585	+	0.106670i
$672$	3.10862	−	3.45247i	0.119918	−	0.133182i
$673$	1.15365	−	10.9762i	0.0444699	−	0.423103i	−0.949526	−	0.313688i	$-0.898435\pi$
$673$	1.15365	−	10.9762i	0.0444699	−	0.423103i	0.993996	−	0.109415i	$-0.0348979\pi$
$674$	2.86265	+	2.07983i	0.110265	+	0.0801122i
$675$	−0.327170	−	3.11281i	−0.0125928	−	0.119812i
$676$	6.80072	−	11.7792i	0.261566	−	0.453046i
$677$	2.06841	+	3.58259i	0.0794955	+	0.137690i	0.903032	−	0.429573i	$-0.141336\pi$
$677$	2.06841	+	3.58259i	0.0794955	+	0.137690i	−0.823537	+	0.567263i	$0.808002\pi$
$678$	0.531054	−	0.385833i	0.0203950	−	0.0148178i
$679$	−35.3874	−	39.3016i	−1.35804	−	1.50826i
$680$	−2.42585	−	7.46599i	−0.0930270	−	0.286308i
$681$	6.33675			0.242825
$682$	−0.450745	+	1.69341i	−0.0172599	+	0.0648439i
$683$	−17.8255			−0.682076			−0.341038	−	0.940050i	$-0.610778\pi$
$683$	−17.8255			−0.682076			−0.341038	+	0.940050i	$0.610778\pi$
$684$	0.978254	+	3.01076i	0.0374045	+	0.115119i
$685$	−17.2711	−	19.1815i	−0.659893	−	0.732886i
$686$	1.79014	−	1.30061i	0.0683480	−	0.0496577i
$687$	6.35794	+	11.0123i	0.242571	+	0.420145i
$688$	4.13905	−	7.16905i	0.157800	−	0.273318i
$689$	−3.56457	−	33.9147i	−0.135799	−	1.29205i
$690$	1.17788	+	0.855781i	0.0448412	+	0.0325790i
$691$	2.50175	−	23.8025i	0.0951710	−	0.905492i	−0.837906	−	0.545815i	$-0.816220\pi$
$691$	2.50175	−	23.8025i	0.0951710	−	0.905492i	0.933077	−	0.359677i	$-0.117113\pi$
$692$	−29.0809	+	32.2977i	−1.10549	+	1.22777i
$693$	−6.12873	−	2.72869i	−0.232811	−	0.103654i
$694$	−2.84389	−	0.604488i	−0.107953	−	0.0229460i
$695$	17.7479	−	3.77244i	0.673217	−	0.143097i
$696$	3.73602	−	1.66338i	0.141614	−	0.0630504i
$697$	−12.5184	+	38.5276i	−0.474167	+	1.45934i
$698$	−0.767880	+	2.36329i	−0.0290647	+	0.0894520i
$699$	−7.48528	+	3.33266i	−0.283119	+	0.126053i
$700$	−17.5356	+	3.72730i	−0.662782	+	0.140879i
$701$	−2.02875	−	0.431223i	−0.0766247	−	0.0162871i	0.169440	−	0.985541i	$-0.445804\pi$
$701$	−2.02875	−	0.431223i	−0.0766247	−	0.0162871i	−0.246064	+	0.969253i	$0.579138\pi$
$702$	−0.552108	−	0.245814i	−0.0208380	−	0.00927766i
$703$	10.6467	−	11.8244i	0.401548	−	0.445964i
$704$	1.83467	−	17.4557i	0.0691468	−	0.657887i
$705$	−3.02380	−	2.19692i	−0.113883	−	0.0827408i
$706$	0.423341	+	4.02782i	0.0159327	+	0.151589i
$707$	21.4909	−	37.2233i	0.808249	−	1.39993i
$708$	12.6484	+	21.9076i	0.475354	+	0.823338i
$709$	4.32511	−	3.14237i	0.162433	−	0.118014i	−0.503600	−	0.863937i	$-0.667991\pi$
$709$	4.32511	−	3.14237i	0.162433	−	0.118014i	0.666032	+	0.745923i	$0.267991\pi$
$710$	3.31217	+	3.67854i	0.124303	+	0.138053i
$711$	−3.95718	−	12.1790i	−0.148406	−	0.456746i
$712$	1.68659			0.0632075
$713$	14.8498	+	14.8007i	0.556130	+	0.554292i
$714$	−1.99864			−0.0747974
$715$	9.11467	+	28.0521i	0.340869	+	1.04909i
$716$	4.50142	+	4.99933i	0.168226	+	0.186834i
$717$	17.8502	−	12.9689i	0.666628	−	0.484334i
$718$	−1.46940	−	2.54507i	−0.0548374	−	0.0949811i
$719$	2.63238	−	4.55942i	0.0981712	−	0.170038i	−0.812756	−	0.582604i	$-0.802034\pi$
$719$	2.63238	−	4.55942i	0.0981712	−	0.170038i	0.910928	+	0.412566i	$0.135367\pi$
$720$	−1.15939	−	11.0309i	−0.0432079	−	0.411096i
$721$	35.1363	+	25.5281i	1.30855	+	0.950714i
$722$	−0.233135	+	2.21813i	−0.00867637	+	0.0825502i
$723$	−9.94893	+	11.0494i	−0.370005	+	0.410932i
$724$	11.1580	+	4.96788i	0.414685	+	0.184630i
$725$	−23.1900	−	4.92919i	−0.861256	−	0.183066i
$726$	−0.744465	+	0.158241i	−0.0276297	+	0.00587287i
$727$	31.6019	−	14.0701i	1.17205	−	0.521830i	0.274002	−	0.961729i	$-0.411652\pi$
$727$	31.6019	−	14.0701i	1.17205	−	0.521830i	0.898047	+	0.439899i	$0.144986\pi$
$728$	−2.14928	+	6.61480i	−0.0796576	+	0.245161i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	0.459374	−	0.204527i	0.0170022	−	0.00756987i
$731$	−10.6145	+	2.25618i	−0.392592	+	0.0834480i
$732$	5.67323	+	1.20588i	0.209689	+	0.0445707i
$733$	18.0636	+	8.04244i	0.667195	+	0.297054i	0.712246	−	0.701930i	$-0.247678\pi$
$733$	18.0636	+	8.04244i	0.667195	+	0.297054i	−0.0450506	+	0.998985i	$0.514345\pi$
$734$	−0.0210285	+	0.0233546i	−0.000776178	+	0.000862033i
$735$	−0.403669	+	3.84066i	−0.0148896	+	0.141665i
$736$	4.89660	+	3.55758i	0.180491	+	0.131134i
$737$	−0.290673	−	2.76557i	−0.0107071	−	0.101871i
$738$	0.538620	−	0.932917i	0.0198269	−	0.0343412i
$739$	−6.31596	−	10.9396i	−0.232336	−	0.402418i	0.726159	−	0.687527i	$-0.241304\pi$
$739$	−6.31596	−	10.9396i	−0.232336	−	0.402418i	−0.958495	+	0.285109i	$0.907970\pi$
$740$	−45.5276	+	33.0777i	−1.67363	+	1.21596i
$741$	−4.76423	−	5.29121i	−0.175018	−	0.194378i
$742$	0.926710	+	2.85212i	0.0340206	+	0.104705i
$743$	−11.5104			−0.422274			−0.211137	−	0.977456i	$-0.567717\pi$
$743$	−11.5104			−0.422274			−0.211137	+	0.977456i	$0.567717\pi$
$744$	−0.152358	+	3.00223i	−0.00558572	+	0.110067i
$745$	48.7235			1.78509
$746$	−1.00369	−	3.08904i	−0.0367477	−	0.113098i
$747$	8.80165	+	9.77522i	0.322036	+	0.357657i
$748$	−18.9747	+	13.7859i	−0.693783	+	0.504063i
$749$	1.62201	+	2.80941i	0.0592671	+	0.102654i
$750$	−0.361516	+	0.626164i	−0.0132007	+	0.0228643i
$751$	1.98266	+	18.8637i	0.0723483	+	0.688348i	0.969243	+	0.246104i	$0.0791506\pi$
$751$	1.98266	+	18.8637i	0.0723483	+	0.688348i	−0.896895	+	0.442243i	$0.854183\pi$
$752$	−4.12534	−	2.99724i	−0.150436	−	0.109298i
$753$	−2.10393	+	20.0176i	−0.0766715	+	0.729481i
$754$	−3.06311	+	3.40193i	−0.111552	+	0.123891i
$755$	−17.3309	−	7.71619i	−0.630734	−	0.280821i
$756$	−5.60249	−	1.19085i	−0.203760	−	0.0433106i
$757$	−35.7784	+	7.60494i	−1.30039	+	0.276406i	−0.805524	−	0.592563i	$-0.798116\pi$
$757$	−35.7784	+	7.60494i	−1.30039	+	0.276406i	−0.494865	+	0.868970i	$0.664783\pi$
$758$	0.0885755	−	0.0394363i	0.00321721	−	0.00143239i
$759$	2.70086	−	8.31240i	0.0980351	−	0.301721i
$760$	−0.759973	+	2.33896i	−0.0275671	+	0.0848429i
$761$	−10.7057	+	4.76647i	−0.388080	+	0.172784i	−0.591496	−	0.806308i	$-0.701462\pi$
$761$	−10.7057	+	4.76647i	−0.388080	+	0.172784i	0.203416	+	0.979092i	$0.434796\pi$
$762$	1.62207	−	0.344783i	0.0587616	−	0.0124902i
$763$	8.56574	+	1.82070i	0.310101	+	0.0659139i
$764$	15.0405	+	6.69647i	0.544147	+	0.242270i
$765$	−9.72905	+	10.8052i	−0.351755	+	0.390663i
$766$	−0.340586	+	3.24046i	−0.0123059	+	0.117082i
$767$	−46.0293	−	33.4422i	−1.66202	−	1.20753i
$768$	−1.52080	−	14.4695i	−0.0548773	−	0.522123i
$769$	10.0536	−	17.4134i	0.362544	−	0.627944i	−0.625835	−	0.779956i	$-0.715242\pi$
$769$	10.0536	−	17.4134i	0.362544	−	0.627944i	0.988379	+	0.152011i	$0.0485750\pi$
$770$	−1.29693	−	2.24635i	−0.0467382	−	0.0809529i
$771$	−2.13119	+	1.54840i	−0.0767531	+	0.0557644i
$772$	0.0400201	+	0.0444468i	0.00144036	+	0.00159968i
$773$	−6.08147	−	18.7168i	−0.218735	−	0.673197i	−0.998867	−	0.0475828i	$-0.984848\pi$
$773$	−6.08147	−	18.7168i	−0.218735	−	0.673197i	0.780132	−	0.625615i	$-0.215152\pi$
$774$	0.288564			0.0103722
$775$	10.9447	−	13.5614i	0.393144	−	0.487139i
$776$	9.87873			0.354626
$777$	8.89598	+	27.3790i	0.319142	+	0.982217i
$778$	1.23324	+	1.36966i	0.0442139	+	0.0491045i
$779$	10.2673	−	7.45966i	0.367866	−	0.267270i
$780$	12.5911	+	21.8085i	0.450834	+	0.780868i
$781$	14.8576	−	25.7341i	0.531645	−	0.920837i
$782$	−0.272176	−	2.58958i	−0.00973299	−	0.0926032i
$783$	−6.12795	−	4.45222i	−0.218995	−	0.159109i
$784$	−0.550722	+	5.23977i	−0.0196686	+	0.187135i
$785$	24.3650	−	27.0600i	0.869623	−	0.965814i
$786$	−0.625991	−	0.278709i	−0.0223284	−	0.00994123i
$787$	23.6172	+	5.01999i	0.841862	+	0.178943i	0.608607	−	0.793472i	$-0.291729\pi$
$787$	23.6172	+	5.01999i	0.841862	+	0.178943i	0.233256	+	0.972415i	$0.425062\pi$
$788$	−7.58029	+	1.61124i	−0.270036	+	0.0573980i
$789$	−12.3443	+	5.49602i	−0.439467	+	0.195663i
$790$	1.53000	−	4.70887i	0.0544351	−	0.167534i
$791$	−4.32373	+	13.3071i	−0.153734	+	0.473145i
$792$	1.14481	−	0.509703i	0.0406791	−	0.0181115i
$793$	−12.7598	+	2.71218i	−0.453113	+	0.0963122i
$794$	−3.24963	−	0.690730i	−0.115325	−	0.0245131i
$795$	19.9304	+	8.87359i	0.706859	+	0.314714i
$796$	−11.1444	+	12.3771i	−0.395002	+	0.438695i
$797$	1.31583	−	12.5193i	0.0466091	−	0.443455i	−0.946185	−	0.323625i	$-0.895098\pi$
$797$	1.31583	−	12.5193i	0.0466091	−	0.443455i	0.992794	−	0.119830i	$-0.0382350\pi$
$798$	0.506557	+	0.368035i	0.0179319	+	0.0130283i
$799$	0.698717	+	6.64785i	0.0247188	+	0.235184i
$800$	2.51541	−	4.35681i	0.0889331	−	0.154037i
$801$	−1.56191	−	2.70532i	−0.0551875	−	0.0955876i
$802$	2.03708	−	1.48003i	0.0719319	−	0.0522616i
$803$	−2.01987	−	2.24329i	−0.0712797	−	0.0791642i
$804$	−0.733649	−	2.25794i	−0.0258738	−	0.0796314i
$805$	−31.0341			−1.09381
$806$	−1.21108	−	3.13942i	−0.0426584	−	0.110581i
$807$	−19.7335			−0.694653
$808$	2.48102	+	7.63580i	0.0872821	+	0.268627i
$809$	−30.4981	−	33.8716i	−1.07226	−	1.19086i	−0.980793	−	0.195053i	$-0.937512\pi$
$809$	−30.4981	−	33.8716i	−1.07226	−	1.19086i	−0.0914639	−	0.995808i	$-0.529155\pi$
$810$	0.312798	−	0.227261i	0.0109906	−	0.00798514i
$811$	−20.6501	−	35.7670i	−0.725123	−	1.25595i	−0.958923	−	0.283665i	$-0.908450\pi$
$811$	−20.6501	−	35.7670i	−0.725123	−	1.25595i	0.233801	−	0.972285i	$-0.424884\pi$
$812$	−21.6922	+	37.5720i	−0.761248	+	1.31852i
$813$	−1.93977	−	18.4557i	−0.0680308	−	0.647270i
$814$	−2.53604	−	1.84254i	−0.0888883	−	0.0645811i
$815$	2.98047	−	28.3573i	0.104401	−	0.993312i
$816$	−13.2733	+	14.7414i	−0.464657	+	0.516054i
$817$	3.10571	+	1.38275i	0.108655	+	0.0483763i
$818$	−0.499662	−	0.106206i	−0.0174703	−	0.00371342i
$819$	12.6007	−	2.67835i	0.440303	−	0.0935893i
$820$	−41.0056	+	18.2569i	−1.43198	+	0.637558i
$821$	−8.85932	+	27.2662i	−0.309192	+	0.951596i	0.668887	+	0.743364i	$0.266771\pi$
$821$	−8.85932	+	27.2662i	−0.309192	+	0.951596i	−0.978079	+	0.208232i	$0.933229\pi$
$822$	0.379322	−	1.16743i	0.0132304	−	0.0407190i
$823$	−18.2065	+	8.10605i	−0.634639	+	0.282559i	−0.698731	−	0.715385i	$-0.746251\pi$
$823$	−18.2065	+	8.10605i	−0.634639	+	0.282559i	0.0640923	+	0.997944i	$0.479585\pi$
$824$	−7.93537	+	1.68671i	−0.276442	+	0.0587595i
$825$	−7.10601	−	1.51043i	−0.247400	−	0.0525864i
$826$	4.57083	+	2.03507i	0.159040	+	0.0708090i
$827$	−29.6528	+	32.9328i	−1.03113	+	1.14518i	−0.0418532	+	0.999124i	$0.513326\pi$
$827$	−29.6528	+	32.9328i	−1.03113	+	1.14518i	−0.989276	+	0.146061i	$0.953340\pi$
$828$	0.779993	−	7.42114i	0.0271066	−	0.257902i
$829$	−3.32349	−	2.41466i	−0.115430	−	0.0838645i	0.528573	−	0.848888i	$-0.322727\pi$
$829$	−3.32349	−	2.41466i	−0.115430	−	0.0838645i	−0.644002	+	0.765023i	$0.722727\pi$
$830$	0.531611	+	5.05795i	0.0184525	+	0.175564i
$831$	0.635334	−	1.10043i	0.0220395	−	0.0381735i
$832$	16.8516	+	29.1879i	0.584226	+	1.01191i
$833$	5.58753	−	4.05958i	0.193596	−	0.140656i
$834$	0.577394	+	0.641261i	0.0199935	+	0.0222050i
$835$	−6.61148	−	20.3480i	−0.228800	−	0.704173i
$836$	7.34771			0.254126
$837$	4.95672	−	2.53592i	0.171329	−	0.0876542i
$838$	2.41566			0.0834477
$839$	9.26313	+	28.5090i	0.319799	+	0.984240i	0.973734	+	0.227689i	$0.0731169\pi$
$839$	9.26313	+	28.5090i	0.319799	+	0.984240i	−0.653935	+	0.756551i	$0.726883\pi$
$840$	−2.97738	−	3.30671i	−0.102729	−	0.114092i
$841$	−22.9551	+	16.6779i	−0.791556	+	0.575099i
$842$	−2.65975	−	4.60682i	−0.0916610	−	0.158762i
$843$	2.16174	−	3.74424i	0.0744542	−	0.128958i
$844$	2.01957	+	19.2149i	0.0695163	+	0.661404i
$845$	−15.8332	−	11.5035i	−0.544678	−	0.395732i
$846$	0.0185801	−	0.176778i	0.000638797	−	0.00607775i
$847$	10.8554	−	12.0561i	0.372996	−	0.414254i
$848$	27.1909	+	12.1061i	0.933738	+	0.415727i
$849$	5.97490	+	1.27001i	0.205058	+	0.0435865i
$850$	−2.11700	+	0.449982i	−0.0726125	+	0.0154343i
$851$	−34.2627	+	15.2547i	−1.17451	+	0.522926i
$852$	7.83964	−	24.1279i	0.268582	−	0.826609i
$853$	−4.05120	+	12.4683i	−0.138711	+	0.426907i	−0.996149	−	0.0876798i	$-0.972055\pi$
$853$	−4.05120	+	12.4683i	−0.138711	+	0.426907i	0.857438	+	0.514587i	$0.172055\pi$
$854$	1.04799	−	0.466596i	0.0358615	−	0.0159666i
$855$	4.45553	−	0.947051i	0.152376	−	0.0323885i
$856$	−0.592724	−	0.125987i	−0.0202589	−	0.00430616i
$857$	−8.49218	−	3.78096i	−0.290087	−	0.129155i	0.256534	−	0.966535i	$-0.417420\pi$
$857$	−8.49218	−	3.78096i	−0.290087	−	0.129155i	−0.546621	+	0.837380i	$0.684086\pi$
$858$	−0.938615	+	1.04244i	−0.0320438	+	0.0355882i
$859$	4.83334	−	45.9861i	0.164911	−	1.56903i	−0.528783	−	0.848757i	$-0.677352\pi$
$859$	4.83334	−	45.9861i	0.164911	−	1.56903i	0.693695	−	0.720269i	$-0.255982\pi$
$860$	−9.72749	−	7.06743i	−0.331705	−	0.240997i
$861$	2.40017	+	22.8361i	0.0817976	+	0.778252i
$862$	0.255259	−	0.442121i	0.00869415	−	0.0150587i
$863$	23.1774	+	40.1445i	0.788968	+	1.36653i	0.926599	+	0.376050i	$0.122718\pi$
$863$	23.1774	+	40.1445i	0.788968	+	1.36653i	−0.137631	+	0.990484i	$0.543949\pi$
$864$	1.30034	−	0.944752i	0.0442385	−	0.0321411i
$865$	41.8441	+	46.4726i	1.42274	+	1.58011i
$866$	0.237959	+	0.732362i	0.00808617	+	0.0248867i
$867$	9.00344			0.305773
$868$	−17.4129	−	26.7166i	−0.591032	−	0.906820i
$869$	−29.7226			−1.00827
$870$	−0.904996	−	2.78529i	−0.0306822	−	0.0944303i
$871$	3.57297	+	3.96819i	0.121066	+	0.134457i
$872$	−1.32337	+	0.961486i	−0.0448150	+	0.0325600i
$873$	−9.14849	−	15.8457i	−0.309630	−	0.536294i
$874$	−0.407868	+	0.706449i	−0.0137964	+	0.0238960i
$875$	−1.61097	−	15.3273i	−0.0544607	−	0.518159i
$876$	−2.08500	−	1.51484i	−0.0704457	−	0.0511818i
$877$	−3.18593	+	30.3121i	−0.107581	+	1.02357i	0.798941	+	0.601410i	$0.205394\pi$
$877$	−3.18593	+	30.3121i	−0.107581	+	1.02357i	−0.906522	+	0.422158i	$0.861273\pi$
$878$	2.78792	−	3.09630i	0.0940878	−	0.104495i
$879$	28.3179	+	12.6080i	0.955141	+	0.425256i
$880$	−25.1815	−	5.35250i	−0.848870	−	0.180433i
$881$	26.1550	−	5.55941i	0.881183	−	0.187301i	0.254966	−	0.966950i	$-0.417936\pi$
$881$	26.1550	−	5.55941i	0.881183	−	0.187301i	0.626217	+	0.779649i	$0.284602\pi$
$882$	−0.167780	+	0.0747003i	−0.00564944	+	0.00251529i
$883$	4.67469	−	14.3872i	0.157316	−	0.484169i	−0.841072	−	0.540923i	$-0.818075\pi$
$883$	4.67469	−	14.3872i	0.157316	−	0.484169i	0.998388	+	0.0567542i	$0.0180751\pi$
$884$	13.9171	−	42.8324i	0.468082	−	1.44061i
$885$	33.2521	−	14.8048i	1.11776	−	0.497658i
$886$	−4.60420	+	0.978653i	−0.154681	+	0.0328785i
$887$	−4.71357	−	1.00190i	−0.158266	−	0.0336405i	0.128097	−	0.991762i	$-0.459113\pi$
$887$	−4.71357	−	1.00190i	−0.158266	−	0.0336405i	−0.286363	+	0.958121i	$0.592446\pi$
$888$	−4.91253	−	2.18720i	−0.164854	−	0.0733976i
$889$	−23.6523	+	26.2685i	−0.793271	+	0.881017i
$890$	0.126249	−	1.20118i	0.00423188	−	0.0402637i
$891$	−1.87776	−	1.36427i	−0.0629074	−	0.0457049i
$892$	−0.895199	−	8.51725i	−0.0299735	−	0.285179i
$893$	1.04706	−	1.81356i	0.0350385	−	0.0606885i
$894$	1.15858	+	2.00672i	0.0387488	+	0.0671148i
$895$	7.83108	−	5.68961i	0.261764	−	0.190183i
$896$	−8.20047	−	9.10754i	−0.273958	−	0.304262i
$897$	5.18622	+	15.9616i	0.173163	+	0.532941i
$898$	−3.76734			−0.125718
$899$	−6.66630	−	41.6432i	−0.222334	−	1.38888i
$900$	−6.20237			−0.206746
$901$	−12.0570	−	37.1076i	−0.401677	−	1.23624i
$902$	−1.67304	−	1.85810i	−0.0557061	−	0.0618679i
$903$	−4.97617	+	3.61540i	−0.165597	+	0.120313i
$904$	−1.30680	−	2.26345i	−0.0434636	−	0.0752812i
$905$	8.78726	−	15.2200i	0.292098	−	0.505929i
$906$	−0.0943067	−	0.897268i	−0.00313313	−	0.0298097i
$907$	7.39757	+	5.37465i	0.245632	+	0.178462i	0.703789	−	0.710409i	$-0.251490\pi$
$907$	7.39757	+	5.37465i	0.245632	+	0.178462i	−0.458157	+	0.888872i	$0.651490\pi$
$908$	1.31256	−	12.4882i	0.0435589	−	0.414435i
$909$	9.95034	−	11.0510i	0.330032	−	0.366538i
$910$	4.55015	+	2.02586i	0.150836	+	0.0671565i
$911$	−23.7488	−	5.04796i	−0.786833	−	0.167246i	−0.203063	−	0.979166i	$-0.565090\pi$
$911$	−23.7488	−	5.04796i	−0.786833	−	0.167246i	−0.583770	+	0.811919i	$0.698423\pi$
$912$	6.07863	−	1.29205i	0.201284	−	0.0427841i
$913$	27.8911	−	12.4179i	0.923062	−	0.410974i
$914$	−0.924316	+	2.84475i	−0.0305737	+	0.0940960i
$915$	2.57890	−	7.93703i	0.0852557	−	0.262390i
$916$	23.0195	−	10.2489i	0.760585	−	0.338634i
$917$	14.2869	−	3.03677i	0.471795	−	0.100283i
$918$	−0.676367	−	0.143766i	−0.0223234	−	0.00474499i
$919$	45.2613	+	20.1516i	1.49303	+	0.664741i	0.980962	−	0.194202i	$-0.0622117\pi$
$919$	45.2613	+	20.1516i	1.49303	+	0.664741i	0.512071	+	0.858943i	$0.328878\pi$
$920$	3.87895	−	4.30801i	0.127885	−	0.142031i
$921$	−1.16578	+	11.0916i	−0.0384136	+	0.365481i
$922$	−2.65621	−	1.92985i	−0.0874775	−	0.0635561i
$923$	5.96432	+	56.7467i	0.196318	+	1.86784i
$924$	−6.64705	+	11.5130i	−0.218672	+	0.378751i
$925$	15.5870	+	26.9975i	0.512498	+	0.887672i
$926$	−2.80594	+	2.03863i	−0.0922088	+	0.0669936i
$927$	10.0543	+	11.1664i	0.330227	+	0.366754i
$928$	−3.76218	−	11.5788i	−0.123500	−	0.380093i
$929$	10.1197			0.332016			0.166008	−	0.986124i	$-0.446912\pi$
$929$	10.1197			0.332016			0.166008	+	0.986124i	$0.446912\pi$
$930$	2.12677	+	0.333240i	0.0697395	+	0.0109274i
$931$	−2.16370			−0.0709124
$932$	5.01740	+	15.4420i	0.164351	+	0.505819i
$933$	−2.82015	−	3.13209i	−0.0923275	−	0.102540i
$934$	−1.61263	+	1.17165i	−0.0527670	+	0.0383375i
$935$	16.8738	+	29.2262i	0.551832	+	0.955800i
$936$	−1.20316	+	2.08393i	−0.0393265	+	0.0681154i
$937$	0.264076	+	2.51252i	0.00862700	+	0.0820804i	0.997988	−	0.0633992i	$-0.0201941\pi$
$937$	0.264076	+	2.51252i	0.00862700	+	0.0820804i	−0.989361	+	0.145480i	$0.953527\pi$
$938$	−0.379896	−	0.276011i	−0.0124041	−	0.00901207i
$939$	0.323261	−	3.07563i	0.0105492	−	0.100369i
$940$	−4.95593	+	5.50412i	−0.161645	+	0.179525i
$941$	25.5240	+	11.3640i	0.832058	+	0.370456i	0.778141	−	0.628089i	$-0.216163\pi$
$941$	25.5240	+	11.3640i	0.832058	+	0.370456i	0.0539168	+	0.998545i	$0.482829\pi$
$942$	1.69386	+	0.360041i	0.0551889	+	0.0117308i
$943$	−29.2612	+	6.21965i	−0.952875	+	0.202540i
$944$	45.3656	−	20.1981i	1.47652	−	0.657391i
$945$	−2.54674	+	7.83805i	−0.0828454	+	0.254972i
$946$	0.206970	−	0.636988i	0.00672918	−	0.0207103i
$947$	−38.0189	+	16.9271i	−1.23545	+	0.550057i	−0.917381	−	0.398011i	$-0.869700\pi$
$947$	−38.0189	+	16.9271i	−1.23545	+	0.550057i	−0.318067	+	0.948068i	$0.603034\pi$
$948$	−24.8214	+	5.27596i	−0.806162	+	0.171355i
$949$	5.66978	+	1.20515i	0.184049	+	0.0391208i
$950$	0.619415	+	0.275781i	0.0200965	+	0.00894753i
$951$	8.57121	−	9.51929i	0.277940	−	0.308684i
$952$	−0.831819	+	7.91423i	−0.0269594	+	0.256502i
$953$	−40.9997	−	29.7880i	−1.32811	−	0.964928i	−0.999793	−	0.0203608i	$-0.993518\pi$
$953$	−40.9997	−	29.7880i	−1.32811	−	0.964928i	−0.328317	−	0.944568i	$-0.606482\pi$
$954$	0.108452	+	1.03185i	0.00351127	+	0.0334075i
$955$	11.8448	−	20.5158i	0.383289	−	0.663876i
$956$	−21.8612	−	37.8648i	−0.707043	−	1.22463i
$957$	−14.2232	+	10.3338i	−0.459772	+	0.334044i
$958$	1.67071	+	1.85552i	0.0539783	+	0.0599490i
$959$	8.08544	+	24.8844i	0.261093	+	0.803560i
$960$	−21.5618			−0.695904
$961$	29.5143	+	9.48189i	0.952074	+	0.305867i
$962$	6.01933			0.194071
$963$	0.346824	+	1.06741i	0.0111762	+	0.0343969i
$964$	19.7149	+	21.8956i	0.634975	+	0.705211i
$965$	0.0696226	−	0.0505838i	0.00224123	−	0.00162835i
$966$	−0.737951	−	1.27817i	−0.0237432	−	0.0411244i
$967$	4.33039	−	7.50046i	0.139256	−	0.241199i	−0.787959	−	0.615728i	$-0.788862\pi$
$967$	4.33039	−	7.50046i	0.139256	−	0.241199i	0.927215	+	0.374529i	$0.122196\pi$
$968$	0.316762	+	3.01379i	0.0101811	+	0.0968669i
$969$	−6.59058	−	4.78833i	−0.211720	−	0.153823i
$970$	0.739470	−	7.03559i	0.0237430	−	0.225899i
$971$	31.2108	−	34.6631i	1.00160	−	1.11239i	0.00794063	−	0.999968i	$-0.497472\pi$
$971$	31.2108	−	34.6631i	1.00160	−	1.11239i	0.993661	−	0.112422i	$-0.0358609\pi$
$972$	−1.81029	−	0.805994i	−0.0580652	−	0.0258523i
$973$	−17.9912	−	3.82415i	−0.576772	−	0.122597i
$974$	2.01875	−	0.429099i	0.0646850	−	0.0137492i
$975$	12.7438	−	5.67393i	0.408130	−	0.181711i
$976$	3.51836	−	10.8284i	0.112620	−	0.346609i
$977$	−5.51018	+	16.9586i	−0.176286	+	0.542553i	−0.999690	−	0.0249029i	$-0.992072\pi$
$977$	−5.51018	+	16.9586i	−0.176286	+	0.542553i	0.823404	+	0.567456i	$0.192072\pi$
$978$	1.23879	−	0.551545i	0.0396122	−	0.0176365i
$979$	−7.09209	+	1.50747i	−0.226664	+	0.0481790i
$980$	7.48539	+	1.59107i	0.239112	+	0.0508248i
$981$	2.76779	+	1.23230i	0.0883687	+	0.0393443i
$982$	−0.425739	+	0.472831i	−0.0135859	+	0.0150887i
$983$	0.845237	−	8.04189i	0.0269589	−	0.256497i	−0.972739	−	0.231904i	$-0.925504\pi$
$983$	0.845237	−	8.04189i	0.0269589	−	0.256497i	0.999698	−	0.0245926i	$-0.00782885\pi$
$984$	−3.47000	−	2.52110i	−0.110619	−	0.0803697i
$985$	1.16558	+	11.0897i	0.0371384	+	0.353348i
$986$	−2.61882	+	4.53593i	−0.0834002	+	0.144453i
$987$	1.89443	+	3.28125i	0.0603004	+	0.104443i
$988$	−11.4145	+	8.29314i	−0.363145	+	0.263840i
$989$	−5.36202	−	5.95512i	−0.170502	−	0.189362i
$990$	−0.277314	−	0.853484i	−0.00881361	−	0.0271255i
$991$	54.7383			1.73882			0.869409	−	0.494093i	$-0.164500\pi$
$991$	54.7383			1.73882			0.869409	+	0.494093i	$0.164500\pi$
$992$	8.84124	+	1.38532i	0.280710	+	0.0439840i
$993$	−19.7594			−0.627044
$994$	−1.55059	−	4.77223i	−0.0491818	−	0.151366i
$995$	16.0355	+	17.8092i	0.508359	+	0.564590i
$996$	21.0877	−	15.3211i	0.668190	−	0.485468i
$997$	−21.3760	−	37.0244i	−0.676986	−	1.17257i	−0.975884	−	0.218289i	$-0.929952\pi$
$997$	−21.3760	−	37.0244i	−0.676986	−	1.17257i	0.298898	−	0.954285i	$-0.403381\pi$
$998$	−0.249452	+	0.432064i	−0.00789627	+	0.0136767i
$999$	1.04109	+	9.90532i	0.0329387	+	0.313390i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.m.b.82.2	yes	24
3.2	odd	2		279.2.y.d.82.2		24
31.13	odd	30		2883.2.a.s.1.6		12
31.14	even	15	inner	93.2.m.b.76.2	✓	24
31.18	even	15		2883.2.a.t.1.6		12
93.14	odd	30		279.2.y.d.262.2		24
93.44	even	30		8649.2.a.bl.1.7		12
93.80	odd	30		8649.2.a.bk.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.b.76.2	✓	24	31.14	even	15	inner
93.2.m.b.82.2	yes	24	1.1	even	1	trivial
279.2.y.d.82.2		24	3.2	odd	2
279.2.y.d.262.2		24	93.14	odd	30
2883.2.a.s.1.6		12	31.13	odd	30
2883.2.a.t.1.6		12	31.18	even	15
8649.2.a.bk.1.7		12	93.80	odd	30
8649.2.a.bl.1.7		12	93.44	even	30

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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0419030 - 0.128964i) q^{2} +(0.669131 + 0.743145i) q^{3} +(1.60316 - 1.16476i) q^{4} +(-1.42565 - 2.46931i) q^{5} +(0.0678004 - 0.117434i) q^{6} +(0.302129 + 2.87456i) q^{7} +(-0.436796 - 0.317351i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.0419030 - 0.128964i) q^{2} +(0.669131 + 0.743145i) q^{3} +(1.60316 - 1.16476i) q^{4} +(-1.42565 - 2.46931i) q^{5} +(0.0678004 - 0.117434i) q^{6} +(0.302129 + 2.87456i) q^{7} +(-0.436796 - 0.317351i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-0.258713 + 0.287329i) q^{10} +(2.12038 + 0.944052i) q^{11} +(1.93831 + 0.412000i) q^{12} +(-4.35949 + 0.926639i) q^{13} +(0.358055 - 0.159416i) q^{14} +(0.881103 - 2.71176i) q^{15} +(1.20208 - 3.69962i) q^{16} +(-4.65849 + 2.07410i) q^{17} +(0.132638 - 0.0281930i) q^{18} +(1.56263 + 0.332146i) q^{19} +(-5.16170 - 2.29814i) q^{20} +(-1.93405 + 2.14798i) q^{21} +(0.0328988 - 0.313011i) q^{22} +(-3.04646 - 2.21338i) q^{23} +(-0.0564360 - 0.536952i) q^{24} +(-1.56498 + 2.71063i) q^{25} +(0.302179 + 0.523389i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(3.83254 + 4.25647i) q^{28} +(2.34067 + 7.20384i) q^{29} -0.386640 q^{30} +(-5.50065 - 0.861888i) q^{31} -1.60731 q^{32} +(0.717241 + 2.20744i) q^{33} +(0.462688 + 0.513868i) q^{34} +(6.66745 - 4.84418i) q^{35} +(0.990806 + 1.71613i) q^{36} +(4.97994 - 8.62551i) q^{37} +(-0.0226437 - 0.215440i) q^{38} +(-3.60570 - 2.61969i) q^{39} +(-0.160916 + 1.53102i) q^{40} +(5.31571 - 5.90369i) q^{41} +(0.358055 + 0.159416i) q^{42} +(2.08154 + 0.442445i) q^{43} +(4.49889 - 0.956270i) q^{44} +(2.60480 - 1.15973i) q^{45} +(-0.157791 + 0.485630i) q^{46} +(0.405073 - 1.24669i) q^{47} +(3.55370 - 1.58221i) q^{48} +(-1.32480 + 0.281596i) q^{49} +(0.415151 + 0.0882430i) q^{50} +(-4.65849 - 2.07410i) q^{51} +(-5.90964 + 6.56332i) q^{52} +(-0.799791 + 7.60950i) q^{53} +(0.109703 + 0.0797042i) q^{54} +(-0.691770 - 6.58175i) q^{55} +(0.780277 - 1.35148i) q^{56} +(0.798768 + 1.38351i) q^{57} +(0.830956 - 0.603725i) q^{58} +(8.54193 + 9.48678i) q^{59} +(-1.74600 - 5.37365i) q^{60} +2.92690 q^{61} +(0.119341 + 0.745502i) q^{62} -2.89040 q^{63} +(-2.33681 - 7.19196i) q^{64} +(8.50328 + 9.44385i) q^{65} +(0.254626 - 0.184997i) q^{66} +(-0.599042 - 1.03757i) q^{67} +(-5.05247 + 8.75114i) q^{68} +(-0.393615 - 3.74500i) q^{69} +(-0.904111 - 0.656875i) q^{70} +(1.33823 - 12.7324i) q^{71} +(0.361270 - 0.401231i) q^{72} +(-1.18812 - 0.528985i) q^{73} +(-1.32105 - 0.280799i) q^{74} +(-3.06156 + 0.650756i) q^{75} +(2.89201 - 1.28760i) q^{76} +(-2.07311 + 6.38038i) q^{77} +(-0.186757 + 0.574778i) q^{78} +(-11.6986 + 5.20855i) q^{79} +(-10.8492 + 2.30608i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-0.984108 - 0.438153i) q^{82} +(8.80165 - 9.77522i) q^{83} +(-0.598702 + 5.69627i) q^{84} +(11.7630 + 8.54630i) q^{85} +(-0.0301632 - 0.286983i) q^{86} +(-3.78728 + 6.55977i) q^{87} +(-0.626576 - 1.08526i) q^{88} +(-2.52723 + 1.83614i) q^{89} +(-0.258713 - 0.287329i) q^{90} +(-3.98081 - 12.2517i) q^{91} -7.46201 q^{92} +(-3.04015 - 4.66450i) q^{93} -0.177752 q^{94} +(-1.40759 - 4.33212i) q^{95} +(-1.07550 - 1.19446i) q^{96} +(-14.8026 + 10.7547i) q^{97} +(0.0918289 + 0.159052i) q^{98} +(-1.16052 + 2.01008i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9 + 24 * q^10 - 22 * q^11 + 12 * q^12 - 8 * q^13 + 10 * q^14 - 8 * q^15 - 2 * q^16 - 17 * q^17 + 5 * q^19 - 22 * q^20 - 11 * q^21 - 37 * q^22 + 26 * q^23 + 26 * q^24 - 8 * q^25 + 4 * q^26 - 6 * q^27 - 36 * q^28 + 2 * q^29 + 42 * q^30 + 36 * q^32 + 14 * q^33 + 40 * q^34 + 9 * q^35 - 13 * q^36 - 13 * q^37 - q^38 - 19 * q^39 - 27 * q^40 + 36 * q^41 + 10 * q^42 - 11 * q^43 - 38 * q^44 - q^45 - 23 * q^46 - 13 * q^47 - 14 * q^48 - 22 * q^49 + 71 * q^50 - 17 * q^51 + 9 * q^52 - 20 * q^53 - 5 * q^54 + 26 * q^55 + 28 * q^56 - 15 * q^57 + 40 * q^58 - 16 * q^59 - 61 * q^60 + 70 * q^61 - 2 * q^62 + 12 * q^63 + 34 * q^64 + 94 * q^65 - 16 * q^66 + 4 * q^67 + 51 * q^68 - 13 * q^69 - 43 * q^70 - 5 * q^71 + q^72 - 12 * q^73 + 74 * q^74 - 8 * q^75 + 71 * q^76 + 25 * q^77 + 17 * q^78 - 29 * q^79 - 113 * q^80 + 3 * q^81 - 60 * q^82 - 11 * q^83 - 41 * q^84 + 16 * q^85 - 144 * q^86 + 14 * q^87 + 26 * q^88 - 27 * q^89 + 24 * q^90 - 81 * q^91 + 28 * q^92 - 36 * q^93 - 80 * q^94 - 56 * q^95 - 43 * q^96 - 21 * q^97 - 14 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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