LMFDB - Embedded newform 525.2.bs.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(2,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 3, 20]))

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

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

chi := DirichletCharacter("525.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bs (of order $60$, degree $16$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$1216$
Relative dimension:	$76$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			2.2
Character	$\chi$	$=$	525.2
Dual form			525.2.bs.a.263.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.10462 - 1.70428i) q^{2} +(0.495015 - 1.65981i) q^{3} +(1.10900 + 5.21743i) q^{4} +(0.865799 - 2.06165i) q^{5} +(-3.87060 + 2.64961i) q^{6} +(-2.02686 - 1.70054i) q^{7} +(4.09903 - 8.04480i) q^{8} +(-2.50992 - 1.64326i) q^{9} +O(q^{10})$	\(q+(-2.10462 - 1.70428i) q^{2} +(0.495015 - 1.65981i) q^{3} +(1.10900 + 5.21743i) q^{4} +(0.865799 - 2.06165i) q^{5} +(-3.87060 + 2.64961i) q^{6} +(-2.02686 - 1.70054i) q^{7} +(4.09903 - 8.04480i) q^{8} +(-2.50992 - 1.64326i) q^{9} +(-5.33581 + 2.86341i) q^{10} +(0.904477 - 2.03149i) q^{11} +(9.20890 + 0.741980i) q^{12} +(6.37405 - 1.00955i) q^{13} +(1.36755 + 7.03333i) q^{14} +(-2.99336 - 2.45761i) q^{15} +(-12.5918 + 5.60624i) q^{16} +(-0.0812255 - 1.54988i) q^{17} +(2.48184 + 7.73604i) q^{18} +(0.362533 - 1.70558i) q^{19} +(11.7167 + 2.23088i) q^{20} +(-3.82590 + 2.52240i) q^{21} +(-5.36581 + 2.73402i) q^{22} +(-0.543993 + 0.671775i) q^{23} +(-11.3237 - 10.7859i) q^{24} +(-3.50078 - 3.56995i) q^{25} +(-15.1355 - 8.73848i) q^{26} +(-3.96994 + 3.35255i) q^{27} +(6.62467 - 12.4609i) q^{28} +(-1.29430 + 3.98344i) q^{29} +(2.11140 + 10.2738i) q^{30} +(3.59467 - 3.99228i) q^{31} +(18.6131 + 4.98736i) q^{32} +(-2.92415 - 2.50687i) q^{33} +(-2.47048 + 3.40032i) q^{34} +(-5.26077 + 2.70634i) q^{35} +(5.79008 - 14.9177i) q^{36} +(-4.97666 - 1.91036i) q^{37} +(-3.66979 + 2.97174i) q^{38} +(1.47959 - 11.0794i) q^{39} +(-13.0366 - 15.4159i) q^{40} +(-5.97073 + 8.21801i) q^{41} +(12.3509 + 1.21172i) q^{42} +(-0.908010 + 0.908010i) q^{43} +(11.6022 + 2.46613i) q^{44} +(-5.56091 + 3.75184i) q^{45} +(2.28979 - 0.486710i) q^{46} +(6.80191 + 0.356473i) q^{47} +(3.07214 + 23.6752i) q^{48} +(1.21632 + 6.89352i) q^{49} +(1.28360 + 13.4797i) q^{50} +(-2.61270 - 0.632392i) q^{51} +(12.3361 + 32.1366i) q^{52} +(2.19823 + 1.42755i) q^{53} +(14.0689 - 0.289920i) q^{54} +(-3.40512 - 3.62357i) q^{55} +(-21.9887 + 9.33511i) q^{56} +(-2.65148 - 1.44602i) q^{57} +(9.51291 - 6.17776i) q^{58} +(0.403491 - 3.83896i) q^{59} +(9.50276 - 18.3431i) q^{60} +(1.46088 + 13.8993i) q^{61} +(-14.3694 + 2.27589i) q^{62} +(2.29283 + 7.59888i) q^{63} +(-14.4701 - 19.9164i) q^{64} +(3.43731 - 14.0151i) q^{65} +(1.88179 + 10.2596i) q^{66} +(-5.14069 + 0.269412i) q^{67} +(7.99629 - 2.14260i) q^{68} +(0.845733 + 1.23546i) q^{69} +(15.6843 + 3.27003i) q^{70} +(7.18159 + 2.33344i) q^{71} +(-23.5079 + 13.4560i) q^{72} +(0.483739 - 0.185690i) q^{73} +(7.21816 + 12.5022i) q^{74} +(-7.65836 + 4.04345i) q^{75} +9.30081 q^{76} +(-5.28788 + 2.57944i) q^{77} +(-21.9965 + 20.7963i) q^{78} +(1.95507 - 1.76035i) q^{79} +(0.656107 + 30.8138i) q^{80} +(3.59941 + 8.24890i) q^{81} +(26.5719 - 7.11992i) q^{82} +(0.890858 - 1.74841i) q^{83} +(-17.4034 - 17.1640i) q^{84} +(-3.26562 - 1.17442i) q^{85} +(3.45852 - 0.363505i) q^{86} +(5.97104 + 4.12015i) q^{87} +(-12.6354 - 15.6035i) q^{88} +(-0.327797 - 3.11878i) q^{89} +(18.0978 + 1.58118i) q^{90} +(-14.6361 - 8.79312i) q^{91} +(-4.10823 - 2.09325i) q^{92} +(-4.84701 - 7.94270i) q^{93} +(-13.7079 - 12.3426i) q^{94} +(-3.20243 - 2.22411i) q^{95} +(17.4918 - 28.4253i) q^{96} +(9.71444 - 4.94976i) q^{97} +(9.18863 - 16.5812i) q^{98} +(-5.60842 + 3.61259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1216 q - 8 q^{3} - 20 q^{4} - 24 q^{6} - 28 q^{7} - 10 q^{9}+O(q^{10}) $ 1216 * q - 8 * q^3 - 20 * q^4 - 24 * q^6 - 28 * q^7 - 10 * q^9	$ 1216 q - 8 q^{3} - 20 q^{4} - 24 q^{6} - 28 q^{7} - 10 q^{9} - 12 q^{10} - 64 q^{13} - 44 q^{15} - 140 q^{16} - 24 q^{18} - 20 q^{19} - 12 q^{21} + 8 q^{22} - 24 q^{25} - 80 q^{27} - 40 q^{28} - 50 q^{30} - 12 q^{31} - 6 q^{33} - 80 q^{34} + 8 q^{36} - 24 q^{37} - 50 q^{39} - 4 q^{40} - 34 q^{42} - 96 q^{43} + 30 q^{45} - 12 q^{46} - 44 q^{48} - 16 q^{51} - 136 q^{52} - 10 q^{54} - 40 q^{55} - 112 q^{57} - 76 q^{58} - 60 q^{60} - 12 q^{61} - 14 q^{63} - 80 q^{64} - 30 q^{66} - 32 q^{67} + 100 q^{69} - 100 q^{70} + 24 q^{72} - 72 q^{73} - 96 q^{75} - 64 q^{76} + 20 q^{78} - 20 q^{79} - 6 q^{81} - 204 q^{82} + 100 q^{84} - 56 q^{85} + 36 q^{87} - 140 q^{88} + 164 q^{90} - 24 q^{91} + 34 q^{93} - 20 q^{94} - 30 q^{96} - 240 q^{97}+O(q^{100}) $ 1216 * q - 8 * q^3 - 20 * q^4 - 24 * q^6 - 28 * q^7 - 10 * q^9 - 12 * q^10 - 64 * q^13 - 44 * q^15 - 140 * q^16 - 24 * q^18 - 20 * q^19 - 12 * q^21 + 8 * q^22 - 24 * q^25 - 80 * q^27 - 40 * q^28 - 50 * q^30 - 12 * q^31 - 6 * q^33 - 80 * q^34 + 8 * q^36 - 24 * q^37 - 50 * q^39 - 4 * q^40 - 34 * q^42 - 96 * q^43 + 30 * q^45 - 12 * q^46 - 44 * q^48 - 16 * q^51 - 136 * q^52 - 10 * q^54 - 40 * q^55 - 112 * q^57 - 76 * q^58 - 60 * q^60 - 12 * q^61 - 14 * q^63 - 80 * q^64 - 30 * q^66 - 32 * q^67 + 100 * q^69 - 100 * q^70 + 24 * q^72 - 72 * q^73 - 96 * q^75 - 64 * q^76 + 20 * q^78 - 20 * q^79 - 6 * q^81 - 204 * q^82 + 100 * q^84 - 56 * q^85 + 36 * q^87 - 140 * q^88 + 164 * q^90 - 24 * q^91 + 34 * q^93 - 20 * q^94 - 30 * q^96 - 240 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{20}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.10462	−	1.70428i	−1.48819	−	1.20511i	−0.925674	−	0.378323i	$-0.876501\pi$
$2$	−2.10462	−	1.70428i	−1.48819	−	1.20511i	−0.562514	−	0.826788i	$-0.690166\pi$
$3$	0.495015	−	1.65981i	0.285797	−	0.958290i
$3$	0.495015	−	1.65981i	0.285797	−	0.958290i
$4$	1.10900	+	5.21743i	0.554499	+	2.60871i
$5$	0.865799	−	2.06165i	0.387197	−	0.921997i
$5$	0.865799	−	2.06165i	0.387197	−	0.921997i
$6$	−3.87060	+	2.64961i	−1.58017	+	1.08170i
$7$	−2.02686	−	1.70054i	−0.766081	−	0.642744i
$7$	−2.02686	−	1.70054i	−0.766081	−	0.642744i
$8$	4.09903	−	8.04480i	1.44923	−	2.84427i
$9$	−2.50992	−	1.64326i	−0.836640	−	0.547753i
$10$	−5.33581	+	2.86341i	−1.68733	+	0.905489i
$11$	0.904477	−	2.03149i	0.272710	−	0.612517i	−0.724326	−	0.689458i	$-0.757849\pi$
$11$	0.904477	−	2.03149i	0.272710	−	0.612517i	0.997036	+	0.0769413i	$0.0245154\pi$
$12$	9.20890	+	0.741980i	2.65838	+	0.214191i
$13$	6.37405	−	1.00955i	1.76784	−	0.279999i	0.814123	−	0.580692i	$-0.197218\pi$
$13$	6.37405	−	1.00955i	1.76784	−	0.279999i	0.953721	+	0.300693i	$0.0972179\pi$
$14$	1.36755	+	7.03333i	0.365494	+	1.87974i
$15$	−2.99336	−	2.45761i	−0.772881	−	0.634551i
$16$	−12.5918	+	5.60624i	−3.14796	+	1.40156i
$17$	−0.0812255	−	1.54988i	−0.0197001	−	0.375900i	−0.990633	−	0.136549i	$-0.956399\pi$
$17$	−0.0812255	−	1.54988i	−0.0197001	−	0.375900i	0.970933	−	0.239351i	$-0.0769345\pi$
$18$	2.48184	+	7.73604i	0.584975	+	1.82340i
$19$	0.362533	−	1.70558i	0.0831708	−	0.391288i	−0.916797	−	0.399354i	$-0.869234\pi$
$19$	0.362533	−	1.70558i	0.0831708	−	0.391288i	0.999967	+	0.00806658i	$0.00256770\pi$
$20$	11.7167	+	2.23088i	2.61993	+	0.498840i
$21$	−3.82590	+	2.52240i	−0.834879	+	0.550434i
$22$	−5.36581	+	2.73402i	−1.14399	+	0.582894i
$23$	−0.543993	+	0.671775i	−0.113430	+	0.140075i	−0.830699	−	0.556722i	$-0.812059\pi$
$23$	−0.543993	+	0.671775i	−0.113430	+	0.140075i	0.717268	+	0.696797i	$0.245392\pi$
$24$	−11.3237	−	10.7859i	−2.31145	−	2.20166i
$25$	−3.50078	−	3.56995i	−0.700157	−	0.713989i
$26$	−15.1355	−	8.73848i	−2.96831	−	1.71376i
$27$	−3.96994	+	3.35255i	−0.764015	+	0.645198i
$28$	6.62467	−	12.4609i	1.25194	−	2.35489i
$29$	−1.29430	+	3.98344i	−0.240345	+	0.739706i	0.756022	+	0.654546i	$0.227140\pi$
$29$	−1.29430	+	3.98344i	−0.240345	+	0.739706i	−0.996367	+	0.0851601i	$0.972860\pi$
$30$	2.11140	+	10.2738i	0.385488	+	1.87574i
$31$	3.59467	−	3.99228i	0.645622	−	0.717035i	−0.328134	−	0.944631i	$-0.606420\pi$
$31$	3.59467	−	3.99228i	0.645622	−	0.717035i	0.973756	+	0.227596i	$0.0730864\pi$
$32$	18.6131	+	4.98736i	3.29036	+	0.881650i
$33$	−2.92415	−	2.50687i	−0.509029	−	0.436391i
$34$	−2.47048	+	3.40032i	−0.423684	+	0.583151i
$35$	−5.26077	+	2.70634i	−0.889232	+	0.457456i
$36$	5.79008	−	14.9177i	0.965014	−	2.48628i
$37$	−4.97666	−	1.91036i	−0.818158	−	0.314061i	−0.0869469	−	0.996213i	$-0.527711\pi$
$37$	−4.97666	−	1.91036i	−0.818158	−	0.314061i	−0.731211	+	0.682152i	$0.761044\pi$
$38$	−3.66979	+	2.97174i	−0.595319	+	0.482080i
$39$	1.47959	−	11.0794i	0.236924	−	1.77413i
$40$	−13.0366	−	15.4159i	−2.06127	−	2.43747i
$41$	−5.97073	+	8.21801i	−0.932472	+	1.28344i	0.0264161	+	0.999651i	$0.491591\pi$
$41$	−5.97073	+	8.21801i	−0.932472	+	1.28344i	−0.958888	+	0.283786i	$0.908409\pi$
$42$	12.3509	+	1.21172i	1.90579	+	0.186973i
$43$	−0.908010	+	0.908010i	−0.138470	+	0.138470i	−0.772944	−	0.634474i	$-0.781217\pi$
$43$	−0.908010	+	0.908010i	−0.138470	+	0.138470i	0.634474	+	0.772944i	$0.281217\pi$
$44$	11.6022	+	2.46613i	1.74910	+	0.371782i
$45$	−5.56091	+	3.75184i	−0.828971	+	0.559292i
$46$	2.28979	−	0.486710i	0.337611	−	0.0717615i
$47$	6.80191	+	0.356473i	0.992160	+	0.0519969i	0.541502	−	0.840700i	$-0.317856\pi$
$47$	6.80191	+	0.356473i	0.992160	+	0.0519969i	0.450658	+	0.892697i	$0.351189\pi$
$48$	3.07214	+	23.6752i	0.443426	+	3.41722i
$49$	1.21632	+	6.89352i	0.173760	+	0.984788i
$50$	1.28360	+	13.4797i	0.181529	+	1.90632i
$51$	−2.61270	−	0.632392i	−0.365851	−	0.0885526i
$52$	12.3361	+	32.1366i	1.71071	+	4.45654i
$53$	2.19823	+	1.42755i	0.301950	+	0.196089i	0.686717	−	0.726925i	$-0.259051\pi$
$53$	2.19823	+	1.42755i	0.301950	+	0.196089i	−0.384766	+	0.923014i	$0.625718\pi$
$54$	14.0689	−	0.289920i	1.91453	−	0.0394532i
$55$	−3.40512	−	3.62357i	−0.459146	−	0.488603i
$56$	−21.9887	+	9.33511i	−2.93836	+	1.24746i
$57$	−2.65148	−	1.44602i	−0.351197	−	0.191531i
$58$	9.51291	−	6.17776i	1.24911	−	0.811179i
$59$	0.403491	−	3.83896i	0.0525300	−	0.499790i	−0.936349	−	0.351070i	$-0.885818\pi$
$59$	0.403491	−	3.83896i	0.0525300	−	0.499790i	0.988879	−	0.148720i	$-0.0475153\pi$
$60$	9.50276	−	18.3431i	1.22680	−	2.36808i
$61$	1.46088	+	13.8993i	0.187046	+	1.77962i	0.537718	+	0.843125i	$0.319286\pi$
$61$	1.46088	+	13.8993i	0.187046	+	1.77962i	−0.350672	+	0.936498i	$0.614047\pi$
$62$	−14.3694	+	2.27589i	−1.82491	+	0.289038i
$63$	2.29283	+	7.59888i	0.288869	+	0.957369i
$64$	−14.4701	−	19.9164i	−1.80876	−	2.48954i
$65$	3.43731	−	14.0151i	0.426346	−	1.73836i
$66$	1.88179	+	10.2596i	0.231632	+	1.26287i
$67$	−5.14069	+	0.269412i	−0.628035	+	0.0329139i	−0.363699	−	0.931517i	$-0.618486\pi$
$67$	−5.14069	+	0.269412i	−0.628035	+	0.0329139i	−0.264336	+	0.964431i	$0.585153\pi$
$68$	7.99629	−	2.14260i	0.969692	−	0.259828i
$69$	0.845733	+	1.23546i	0.101814	+	0.148732i
$70$	15.6843	+	3.27003i	1.87463	+	0.390844i
$71$	7.18159	+	2.33344i	0.852298	+	0.276928i	0.702408	−	0.711774i	$-0.252108\pi$
$71$	7.18159	+	2.33344i	0.852298	+	0.276928i	0.149890	+	0.988703i	$0.452108\pi$
$72$	−23.5079	+	13.4560i	−2.77044	+	1.58581i
$73$	0.483739	−	0.185690i	0.0566174	−	0.0217334i	−0.329894	−	0.944018i	$-0.607013\pi$
$73$	0.483739	−	0.185690i	0.0566174	−	0.0217334i	0.386512	+	0.922284i	$0.373680\pi$
$74$	7.21816	+	12.5022i	0.839094	+	1.45335i
$75$	−7.65836	+	4.04345i	−0.884311	+	0.466898i
$76$	9.30081			1.06688
$77$	−5.28788	+	2.57944i	−0.602610	+	0.293955i
$78$	−21.9965	+	20.7963i	−2.49061	+	2.35472i
$79$	1.95507	−	1.76035i	0.219963	−	0.198055i	−0.551781	−	0.833989i	$-0.686052\pi$
$79$	1.95507	−	1.76035i	0.219963	−	0.198055i	0.771744	+	0.635934i	$0.219385\pi$
$80$	0.656107	+	30.8138i	0.0733550	+	3.44509i
$81$	3.59941	+	8.24890i	0.399934	+	0.916544i
$82$	26.5719	−	7.11992i	2.93438	−	0.786264i
$83$	0.890858	−	1.74841i	0.0977844	−	0.191913i	−0.836932	−	0.547306i	$-0.815653\pi$
$83$	0.890858	−	1.74841i	0.0977844	−	0.191913i	0.934717	+	0.355394i	$0.115653\pi$
$84$	−17.4034	−	17.1640i	−1.89886	−	1.87275i
$85$	−3.26562	−	1.17442i	−0.354206	−	0.127384i
$86$	3.45852	−	0.363505i	0.372942	−	0.0391978i
$87$	5.97104	+	4.12015i	0.640163	+	0.441726i
$88$	−12.6354	−	15.6035i	−1.34694	−	1.66334i
$89$	−0.327797	−	3.11878i	−0.0347464	−	0.330590i	−0.998062	−	0.0622204i	$-0.980182\pi$
$89$	−0.327797	−	3.11878i	−0.0347464	−	0.330590i	0.963316	−	0.268370i	$-0.0864849\pi$
$90$	18.0978	+	1.58118i	1.90767	+	0.166671i
$91$	−14.6361	−	8.79312i	−1.53428	−	0.921770i
$92$	−4.10823	−	2.09325i	−0.428312	−	0.218236i
$93$	−4.84701	−	7.94270i	−0.502611	−	0.823619i
$94$	−13.7079	−	12.3426i	−1.41386	−	1.27304i
$95$	−3.20243	−	2.22411i	−0.328563	−	0.228189i
$96$	17.4918	−	28.4253i	1.78525	−	2.90115i
$97$	9.71444	−	4.94976i	0.986352	−	0.502572i	0.115072	−	0.993357i	$-0.463290\pi$
$97$	9.71444	−	4.94976i	0.986352	−	0.502572i	0.871280	+	0.490786i	$0.163290\pi$
$98$	9.18863	−	16.5812i	0.928191	−	1.67495i
$99$	−5.60842	+	3.61259i	−0.563668	+	0.363079i
$100$	14.7436	−	22.2242i	1.47436	−	2.22242i
$101$	4.12754	−	2.38303i	0.410705	−	0.237121i	−0.280387	−	0.959887i	$-0.590463\pi$
$101$	4.12754	−	2.38303i	0.410705	−	0.237121i	0.691093	+	0.722766i	$0.257130\pi$
$102$	4.42096	+	5.78373i	0.437740	+	0.572674i
$103$	−8.55332	−	0.448260i	−0.842783	−	0.0441684i	−0.373943	−	0.927452i	$-0.621995\pi$
$103$	−8.55332	−	0.448260i	−0.842783	−	0.0441684i	−0.468840	+	0.883283i	$0.655328\pi$
$104$	18.0058	−	55.4162i	1.76561	−	5.43400i
$105$	1.88785	+	10.0715i	0.184235	+	0.982882i
$106$	−2.19348	−	6.75085i	−0.213050	−	0.655701i
$107$	−4.96888	−	18.5441i	−0.480360	−	1.79273i	−0.600102	−	0.799923i	$-0.704873\pi$
$107$	−4.96888	−	18.5441i	−0.480360	−	1.79273i	0.119742	−	0.992805i	$-0.461793\pi$
$108$	−21.8943	−	16.9949i	−2.10678	−	1.63534i
$109$	0.0512058	+	0.00538195i	0.00490463	+	0.000515497i	0.106980	−	0.994261i	$-0.465882\pi$
$109$	0.0512058	+	0.00538195i	0.00490463	+	0.000515497i	−0.102076	+	0.994777i	$0.532548\pi$
$110$	0.990867	+	13.4295i	0.0944754	+	1.28045i
$111$	−5.63435	+	7.31464i	−0.534789	+	0.694275i
$112$	35.0555	+	10.0499i	3.31243	+	0.949622i
$113$	0.308283	+	1.94642i	0.0290008	+	0.183104i	0.997936	−	0.0642089i	$-0.0204524\pi$
$113$	0.308283	+	1.94642i	0.0290008	+	0.183104i	−0.968936	+	0.247313i	$0.920452\pi$
$114$	3.11591	+	7.56220i	0.291832	+	0.708265i
$115$	0.913976	+	1.70314i	0.0852287	+	0.158819i
$116$	−22.2187	−	2.33528i	−2.06295	−	0.216825i
$117$	−17.6573	−	7.94032i	−1.63242	−	0.734083i
$118$	−7.39187	+	7.39187i	−0.680477	+	0.680477i
$119$	−2.47099	+	3.27951i	−0.226516	+	0.300632i
$120$	−32.0408	+	14.0071i	−2.92491	+	1.27867i
$121$	4.05157	+	4.49973i	0.368325	+	0.409066i
$122$	20.6138	−	31.7424i	1.86628	−	2.87382i
$123$	10.6847	+	13.9783i	0.963408	+	1.26038i
$124$	24.8159	+	14.3275i	2.22854	+	1.28665i
$125$	−10.3909	+	4.12653i	−0.929394	+	0.369088i
$126$	8.12512	−	19.9003i	0.723843	−	1.77286i
$127$	−15.3513	−	2.43141i	−1.36221	−	0.215753i	−0.567817	−	0.823155i	$-0.692212\pi$
$127$	−15.3513	−	2.43141i	−1.36221	−	0.215753i	−0.794395	+	0.607402i	$0.792212\pi$
$128$	−1.47218	+	28.0908i	−0.130123	+	2.48290i
$129$	1.05764	+	1.95660i	0.0931204	+	0.172269i
$130$	−31.1200	+	23.6383i	−2.72940	+	2.07322i
$131$	0.569884	−	2.68109i	0.0497910	−	0.234248i	−0.946215	−	0.323540i	$-0.895127\pi$
$131$	0.569884	−	2.68109i	0.0497910	−	0.234248i	0.996006	+	0.0892917i	$0.0284603\pi$
$132$	9.83656	−	18.0367i	0.856162	−	1.56989i
$133$	−3.63522	+	2.84048i	−0.315213	+	0.246300i
$134$	11.2783	+	8.19418i	0.974299	+	0.707870i
$135$	3.47460	+	11.0873i	0.299046	+	0.954239i
$136$	−12.8014	−	5.69954i	−1.09771	−	0.488732i
$137$	3.69595	+	4.56412i	0.315767	+	0.389939i	0.910175	−	0.414224i	$-0.135947\pi$
$137$	3.69595	+	4.56412i	0.315767	+	0.389939i	−0.594408	+	0.804163i	$0.702614\pi$
$138$	0.325635	−	4.04154i	0.0277199	−	0.344039i
$139$	2.51449	+	3.46090i	0.213276	+	0.293550i	0.902230	−	0.431256i	$-0.141929\pi$
$139$	2.51449	+	3.46090i	0.213276	+	0.293550i	−0.688953	+	0.724806i	$0.741929\pi$
$140$	−19.9543	−	24.4464i	−1.68645	−	2.06609i
$141$	3.95872	−	11.1134i	0.333384	−	0.935917i
$142$	−11.1376	−	17.1505i	−0.934650	−	1.43923i
$143$	3.71429	−	13.8619i	0.310605	−	1.15919i
$144$	40.8170	+	6.62039i	3.40141	+	0.551699i
$145$	7.09185	+	6.11724i	0.588946	+	0.508009i
$146$	−1.33455	−	0.433623i	−0.110448	−	0.0358869i
$147$	12.0440	+	1.39354i	0.993373	+	0.114937i
$148$	4.44806	−	28.0839i	0.365628	−	2.30849i
$149$	6.03041	−	10.4450i	0.494031	−	0.855686i	−0.505946	−	0.862565i	$-0.668856\pi$
$149$	6.03041	−	10.4450i	0.494031	−	0.855686i	0.999976	+	0.00687909i	$0.00218970\pi$
$150$	23.0091	+	4.54211i	1.87868	+	0.370862i
$151$	−0.544170	−	0.942530i	−0.0442839	−	0.0767020i	0.843034	−	0.537860i	$-0.180767\pi$
$151$	−0.544170	−	0.942530i	−0.0442839	−	0.0767020i	−0.887318	+	0.461158i	$0.847434\pi$
$152$	−12.2350	−	9.90774i	−0.992393	−	0.803624i
$153$	−2.34298	+	4.02354i	−0.189418	+	0.325284i
$154$	15.5250	+	3.58331i	1.25104	+	0.288752i
$155$	−5.11842	−	10.8675i	−0.411122	−	0.872895i
$156$	59.4471	−	4.56743i	4.75958	−	0.365687i
$157$	1.61941	−	6.04373i	0.129243	−	0.482342i	−0.870712	−	0.491793i	$-0.836342\pi$
$157$	1.61941	−	6.04373i	0.129243	−	0.482342i	0.999955	+	0.00945092i	$0.00300837\pi$
$158$	−7.11482	+	0.372872i	−0.566025	+	0.0296641i
$159$	3.45761	−	2.94198i	0.274206	−	0.233314i
$160$	26.3974	−	34.0556i	2.08690	−	2.69233i
$161$	2.24498	−	0.436512i	0.176929	−	0.0344019i
$162$	6.48310	−	23.4952i	0.509360	−	1.84595i
$163$	−0.105921	+	0.275935i	−0.00829640	+	0.0216129i	−0.937666	−	0.347538i	$-0.887018\pi$
$163$	−0.105921	+	0.275935i	−0.00829640	+	0.0216129i	0.929370	+	0.369150i	$0.120351\pi$
$164$	−49.4984	−	22.0381i	−3.86518	−	1.72089i
$165$	−7.70002	+	3.85812i	−0.599446	+	0.300354i
$166$	−4.85470	+	2.16145i	−0.376797	+	0.167761i
$167$	13.8423	+	7.05298i	1.07115	+	0.545776i	0.898394	−	0.439190i	$-0.144734\pi$
$167$	13.8423	+	7.05298i	1.07115	+	0.545776i	0.172751	+	0.984966i	$0.444734\pi$
$168$	4.60977	+	41.1180i	0.355651	+	3.17232i
$169$	27.2456	−	8.85264i	2.09582	−	0.680972i
$170$	4.87133	+	8.03725i	0.373614	+	0.616429i
$171$	−3.71264	+	3.68514i	−0.283913	+	0.281810i
$172$	−5.74446	−	3.73050i	−0.438011	−	0.284448i
$173$	−13.8969	+	17.1613i	−1.05656	+	1.30475i	−0.105949	+	0.994372i	$0.533788\pi$
$173$	−13.8969	+	17.1613i	−1.05656	+	1.30475i	−0.950614	+	0.310375i	$0.899545\pi$
$174$	−5.54485	−	18.8477i	−0.420354	−	1.42884i
$175$	1.02476	+	13.1890i	0.0774644	+	0.996995i
$176$			30.6509i			2.31040i
$177$	−6.17220	−	2.57006i	−0.463931	−	0.193177i
$178$	−4.62540	+	7.12249i	−0.346688	+	0.533853i
$179$	20.8384	−	4.42935i	1.55754	−	0.331065i	0.652966	−	0.757387i	$-0.273524\pi$
$179$	20.8384	−	4.42935i	1.55754	−	0.331065i	0.904571	+	0.426322i	$0.140191\pi$
$180$	−25.7420	−	24.8528i	−1.91870	−	1.85242i
$181$	−5.23613	−	16.1152i	−0.389199	−	1.19783i	−0.933388	−	0.358868i	$-0.883163\pi$
$181$	−5.23613	−	16.1152i	−0.389199	−	1.19783i	0.544189	−	0.838962i	$-0.316837\pi$
$182$	15.8174	+	43.4502i	1.17246	+	3.22074i
$183$	23.7933	+	4.45559i	1.75885	+	0.329366i
$184$	3.17445	+	7.12994i	0.234024	+	0.525626i
$185$	−8.24728	+	8.60613i	−0.606352	+	0.632735i
$186$	−3.33552	+	24.9770i	−0.244572	+	1.83140i
$187$	−3.22202	−	1.23682i	−0.235617	−	0.0904451i
$188$	5.68343	+	35.8838i	0.414507	+	2.61709i
$189$	13.7477	−	0.0440980i	0.999995	−	0.00320766i
$190$	2.94938	+	10.1387i	0.213970	+	0.735542i
$191$	−4.01330	−	9.01401i	−0.290392	−	0.652231i	0.708159	−	0.706053i	$-0.249526\pi$
$191$	−4.01330	−	9.01401i	−0.290392	−	0.652231i	−0.998551	+	0.0538225i	$0.982859\pi$
$192$	−40.2202	+	14.1587i	−2.90264	+	1.02181i
$193$	12.5891	+	3.37323i	0.906182	+	0.242811i	0.681669	−	0.731661i	$-0.261254\pi$
$193$	12.5891	+	3.37323i	0.906182	+	0.242811i	0.224513	+	0.974471i	$0.427921\pi$
$194$	−28.8810	−	6.13884i	−2.07353	−	0.440743i
$195$	−21.5609	−	12.6430i	−1.54401	−	0.905382i
$196$	−34.6175	+	13.9910i	−2.47268	+	0.999354i
$197$	−11.8106	−	23.1797i	−0.841474	−	1.65149i	−0.755463	−	0.655191i	$-0.772588\pi$
$197$	−11.8106	−	23.1797i	−0.841474	−	1.65149i	−0.0860104	−	0.996294i	$-0.527412\pi$
$198$	17.9604	+	1.95524i	1.27639	+	0.138953i
$199$	1.25743	−	0.725980i	0.0891371	−	0.0514633i	−0.454769	−	0.890609i	$-0.650278\pi$
$199$	1.25743	−	0.725980i	0.0891371	−	0.0514633i	0.543906	+	0.839146i	$0.316945\pi$
$200$	−43.0693	+	13.5298i	−3.04546	+	0.956701i
$201$	−2.09754	+	8.66592i	−0.147949	+	0.611247i
$202$	−12.7482	−	2.01912i	−0.896964	−	0.142065i
$203$	9.39736	−	5.87286i	0.659565	−	0.412194i
$204$	0.401979	−	14.3329i	0.0281441	−	1.00350i
$205$	11.7732	+	19.4247i	0.822275	+	1.35668i
$206$	17.2375	+	15.5207i	1.20099	+	1.08138i
$207$	2.46928	−	0.792182i	0.171627	−	0.0550605i
$208$	−74.6012	+	48.4466i	−5.17266	+	3.35916i
$209$	−3.13697	−	2.27914i	−0.216989	−	0.157652i
$210$	13.1916	−	24.4142i	0.910305	−	1.68474i
$211$	−3.93356	+	2.85790i	−0.270797	+	0.196746i	−0.714893	−	0.699233i	$-0.753525\pi$
$211$	−3.93356	+	2.85790i	−0.270797	+	0.196746i	0.444096	+	0.895979i	$0.353525\pi$
$212$	−5.01030	+	13.0523i	−0.344109	+	0.896433i
$213$	7.42805	−	10.7650i	0.508962	−	0.737603i
$214$	−21.1469	+	47.4966i	−1.44557	+	3.24680i
$215$	1.08584	+	2.65815i	0.0740539	+	0.181284i
$216$	10.6977	+	45.6796i	0.727885	+	3.10810i
$217$	−14.0749	+	1.97892i	−0.955469	+	0.134338i
$218$	−0.0985962	−	0.0985962i	−0.00667778	−	0.00667778i
$219$	−0.0687517	−	0.894833i	−0.00464581	−	0.0604672i
$220$	15.1295	−	21.7845i	1.02003	−	1.46871i
$221$	−2.08241	−	9.79699i	−0.140078	−	0.659017i
$222$	24.3244	−	5.79197i	1.63254	−	0.388731i
$223$	4.10344	−	25.9081i	0.274787	−	1.73493i	−0.334865	−	0.942266i	$-0.608691\pi$
$223$	4.10344	−	25.9081i	0.274787	−	1.73493i	0.609652	−	0.792669i	$-0.291309\pi$
$224$	−29.2449	−	41.7610i	−1.95401	−	2.79028i
$225$	2.92035	+	14.7130i	0.194690	+	0.980865i
$226$	2.66844	−	4.62187i	0.177502	−	0.307442i
$227$	−10.6553	+	4.09020i	−0.707219	+	0.271476i	−0.685276	−	0.728283i	$-0.740319\pi$
$227$	−10.6553	+	4.09020i	−0.707219	+	0.271476i	−0.0219429	+	0.999759i	$0.506985\pi$
$228$	4.60404	−	15.4376i	0.304910	−	1.02238i
$229$	−4.07924	+	3.67296i	−0.269564	+	0.242716i	−0.792815	−	0.609462i	$-0.791385\pi$
$229$	−4.07924	+	3.67296i	−0.269564	+	0.242716i	0.523252	+	0.852178i	$0.324719\pi$
$230$	0.979074	−	5.14214i	0.0645582	−	0.339063i
$231$	1.66380	+	10.0537i	0.109470	+	0.661486i
$232$	26.7406	+	26.7406i	1.75561	+	1.75561i
$233$	12.0245	+	18.5161i	0.787751	+	1.21303i	0.973106	+	0.230359i	$0.0739899\pi$
$233$	12.0245	+	18.5161i	0.787751	+	1.21303i	−0.185355	+	0.982672i	$0.559343\pi$
$234$	23.6293	+	46.8044i	1.54470	+	3.05970i
$235$	6.62401	−	13.7145i	0.432102	−	0.894636i
$236$	20.4770	−	2.15222i	1.33294	−	0.140097i
$237$	−1.95406	−	4.11644i	−0.126930	−	0.267392i
$238$	10.7897	−	2.69082i	0.699393	−	0.174420i
$239$	−11.1597	+	8.10797i	−0.721859	+	0.524461i	−0.886977	−	0.461813i	$-0.847199\pi$
$239$	−11.1597	+	8.10797i	−0.721859	+	0.524461i	0.165119	+	0.986274i	$0.447199\pi$
$240$	51.4697	+	14.1643i	3.32236	+	0.914299i
$241$	−1.35458	+	12.8879i	−0.0872560	+	0.830186i	0.860126	+	0.510081i	$0.170385\pi$
$241$	−1.35458	+	12.8879i	−0.0872560	+	0.830186i	−0.947382	+	0.320104i	$0.896282\pi$
$242$	−0.858189	−	16.3752i	−0.0551665	−	1.05264i
$243$	15.4733	−	1.89100i	0.992615	−	0.121307i
$244$	−70.8985	+	23.0363i	−4.53881	+	1.47475i
$245$	15.2651	+	3.46078i	0.975251	+	0.221101i
$246$	1.33579	−	47.6287i	0.0851667	−	3.03670i
$247$	0.588931	−	11.2375i	0.0374728	−	0.715023i
$248$	−17.3825	−	45.2829i	−1.10379	−	2.87547i
$249$	−2.46103	−	2.34414i	−0.155962	−	0.148554i
$250$	28.9017	+	9.02437i	1.82791	+	0.570751i
$251$		−	13.9705i		−	0.881809i	−0.897554	−	0.440905i	$-0.854658\pi$
$251$		−	13.9705i		−	0.881809i	0.897554	−	0.440905i	$-0.145342\pi$
$252$	−37.1039	+	20.3898i	−2.33732	+	1.28444i
$253$	0.872675	+	1.71272i	0.0548646	+	0.107678i
$254$	28.1648	+	31.2802i	1.76722	+	1.96270i
$255$	−3.56585	+	4.83895i	−0.223302	+	0.303027i
$256$	18.0279	−	20.0220i	1.12674	−	1.25137i
$257$	−1.69836	−	6.33835i	−0.105941	−	0.395376i	0.892510	−	0.451028i	$-0.148943\pi$
$257$	−1.69836	−	6.33835i	−0.105941	−	0.395376i	−0.998450	+	0.0556528i	$0.982276\pi$
$258$	1.10867	−	5.92042i	0.0690228	−	0.368589i
$259$	6.83834	+	12.3350i	0.424914	+	0.766462i
$260$	76.9349	+	2.39117i	4.77130	+	0.148294i
$261$	9.79440	−	7.87125i	0.606258	−	0.487218i
$262$	−5.76873	+	4.67143i	−0.356394	+	0.288602i
$263$	6.20179	−	5.02211i	0.382419	−	0.309677i	−0.418765	−	0.908094i	$-0.637537\pi$
$263$	6.20179	−	5.02211i	0.382419	−	0.309677i	0.801184	+	0.598418i	$0.204204\pi$
$264$	−32.1535	+	13.2484i	−1.97891	+	0.815386i
$265$	4.84633	−	3.29601i	0.297708	−	0.202472i
$266$	12.4917	+	0.217335i	0.765916	+	0.0133257i
$267$	−5.33884	−	0.999762i	−0.326732	−	0.0611845i
$268$	−7.10666	−	26.5224i	−0.434108	−	1.62011i
$269$	3.69287	−	4.10135i	0.225158	−	0.250064i	−0.619972	−	0.784624i	$-0.712856\pi$
$269$	3.69287	−	4.10135i	0.225158	−	0.250064i	0.845130	+	0.534560i	$0.179523\pi$
$270$	11.5831	−	29.2561i	0.704926	−	1.78047i
$271$	−13.1626	−	14.6186i	−0.799572	−	0.888015i	0.196135	−	0.980577i	$-0.437161\pi$
$271$	−13.1626	−	14.6186i	−0.799572	−	0.888015i	−0.995707	+	0.0925623i	$0.970494\pi$
$272$	9.71175	+	19.0604i	0.588861	+	1.15571i
$273$	−21.8400	+	19.9404i	−1.32182	+	1.20685i
$274$		−	15.9047i		−	0.960836i
$275$	−10.4187	+	3.88287i	−0.628270	+	0.234146i
$276$	−5.50802	+	5.78268i	−0.331544	+	0.348076i
$277$	2.95131	+	7.68843i	0.177327	+	0.461953i	0.993220	−	0.116250i	$-0.0370874\pi$
$277$	2.95131	+	7.68843i	0.177327	+	0.461953i	−0.815893	+	0.578203i	$0.803754\pi$
$278$	0.606320	−	11.5693i	0.0363646	−	0.693879i
$279$	−15.5827	+	4.11335i	−0.932911	+	0.246260i
$280$	0.207936	+	53.4152i	0.0124266	+	3.19217i
$281$	4.48287	−	1.45657i	0.267425	−	0.0868918i	−0.172235	−	0.985056i	$-0.555099\pi$
$281$	4.48287	−	1.45657i	0.267425	−	0.0868918i	0.439660	+	0.898164i	$0.355099\pi$
$282$	−27.2720	+	16.6426i	−1.62402	+	0.991055i
$283$	−0.366891	−	7.00069i	−0.0218094	−	0.416148i	−0.987617	−	0.156887i	$-0.949854\pi$
$283$	−0.366891	−	7.00069i	−0.0218094	−	0.416148i	0.965807	−	0.259261i	$-0.0834791\pi$
$284$	−4.21018	+	40.0572i	−0.249828	+	2.37696i
$285$	−5.27684	+	4.21445i	−0.312573	+	0.249643i
$286$	−31.4418	+	22.8438i	−1.85919	+	1.35078i
$287$	26.0769	−	6.50327i	1.53927	−	0.383876i
$288$	−38.5219	−	43.1040i	−2.26992	−	2.53993i
$289$	14.5114	−	1.52521i	0.853609	−	0.0897179i
$290$	−4.50009	−	24.9610i	−0.264254	−	1.46576i
$291$	−3.40685	−	18.5743i	−0.199713	−	1.08884i
$292$	1.50529	+	2.31794i	0.0880905	+	0.135647i
$293$	11.4731	+	11.4731i	0.670263	+	0.670263i	0.957777	−	0.287513i	$-0.0928286\pi$
$293$	11.4731	+	11.4731i	0.670263	+	0.670263i	−0.287513	+	0.957777i	$0.592829\pi$
$294$	−22.9730	−	23.4593i	−1.33981	−	1.36817i
$295$	−7.56524	−	4.15562i	−0.440465	−	0.241950i
$296$	−35.7679	+	32.2056i	−2.07897	+	1.87191i
$297$	3.21994	+	11.0972i	0.186840	+	0.643924i
$298$	−30.4929	+	11.7051i	−1.76641	+	0.678060i
$299$	−2.78925	+	4.83112i	−0.161306	+	0.279391i
$300$	−29.5895	−	35.4728i	−1.70835	−	2.04802i
$301$	3.38452	−	0.296300i	0.195080	−	0.0170785i
$302$	−0.461070	+	2.91108i	−0.0265316	+	0.167514i
$303$	−1.91219	−	8.03055i	−0.109852	−	0.461343i
$304$	4.99696	+	23.5088i	0.286595	+	1.34832i
$305$	29.9203	+	9.02219i	1.71323	+	0.516609i
$306$	11.7883	−	4.47491i	0.673893	−	0.255813i
$307$	−4.79490	−	4.79490i	−0.273659	−	0.273659i	0.556912	−	0.830571i	$-0.311986\pi$
$307$	−4.79490	−	4.79490i	−0.273659	−	0.273659i	−0.830571	+	0.556912i	$0.811986\pi$
$308$	−19.3223	−	24.7285i	−1.10099	−	1.40904i
$309$	−4.97804	+	13.9750i	−0.283191	+	0.795008i
$310$	−7.74892	+	31.5951i	−0.440109	+	1.79448i
$311$	1.28826	−	2.89348i	0.0730506	−	0.164074i	−0.873329	−	0.487130i	$-0.838044\pi$
$311$	1.28826	−	2.89348i	0.0730506	−	0.164074i	0.946380	+	0.323056i	$0.104710\pi$
$312$	−83.0670	−	57.3180i	−4.70274	−	3.24499i
$313$	10.0428	−	26.1625i	0.567655	−	1.47879i	−0.286143	−	0.958187i	$-0.592373\pi$
$313$	10.0428	−	26.1625i	0.567655	−	1.47879i	0.853798	−	0.520605i	$-0.174293\pi$
$314$	−13.7085	+	9.95979i	−0.773614	+	0.562063i
$315$	17.6513	+	1.85209i	0.994540	+	0.104354i
$316$	11.3527	+	8.24822i	0.638639	+	0.463999i
$317$	25.5982	−	16.6237i	1.43774	−	0.933680i	0.438349	−	0.898805i	$-0.355563\pi$
$317$	25.5982	−	16.6237i	1.43774	−	0.933680i	0.999392	−	0.0348747i	$-0.0111032\pi$
$318$	−12.2909	+	0.298991i	−0.689240	+	0.0167666i
$319$	6.92165	+	6.23228i	0.387538	+	0.348941i
$320$	−53.5887	+	12.5887i	−2.99570	+	0.703727i
$321$	−33.2394	−	0.932226i	−1.85524	−	0.0520318i
$322$	−5.46876	−	2.90739i	−0.304762	−	0.162023i
$323$	−2.67289	−	0.423344i	−0.148723	−	0.0235555i
$324$	−39.0463	+	27.9277i	−2.16924	+	1.55154i
$325$	−25.9182	−	19.2208i	−1.43768	−	1.06618i
$326$	0.693195	−	0.400216i	0.0383925	−	0.0221659i
$327$	0.0342806	−	0.0823277i	0.00189572	−	0.00455273i
$328$	41.6380	+	81.7192i	2.29907	+	4.51219i
$329$	−13.1803	−	12.2894i	−0.726654	−	0.677539i
$330$	22.7809	+	5.00316i	1.25405	+	0.275415i
$331$	13.0150	+	2.76643i	0.715370	+	0.152057i	0.551197	−	0.834375i	$-0.314171\pi$
$331$	13.0150	+	2.76643i	0.715370	+	0.152057i	0.164173	+	0.986432i	$0.447505\pi$
$332$	10.1102	+	2.70901i	0.554867	+	0.148676i
$333$	9.35180	+	12.9728i	0.512476	+	0.710904i
$334$	−17.1123	−	38.4349i	−0.936345	−	2.10307i
$335$	−3.89537	+	10.8315i	−0.212827	+	0.591791i
$336$	34.0338	−	53.2106i	1.85670	−	2.90287i
$337$	2.16485	+	13.6683i	0.117927	+	0.744560i	0.973805	+	0.227383i	$0.0730170\pi$
$337$	2.16485	+	13.6683i	0.117927	+	0.744560i	−0.855879	+	0.517177i	$0.826983\pi$
$338$	−72.4290	−	27.8029i	−3.93962	−	1.51228i
$339$	3.38329	+	0.451817i	0.183755	+	0.0245394i
$340$	2.50589	−	18.3406i	0.135901	−	0.994658i
$341$	−4.85898	−	10.9135i	−0.263129	−	0.590997i
$342$	14.0942	−	1.42841i	0.762128	−	0.0772398i
$343$	9.25740	−	16.0406i	0.499853	−	0.866110i
$344$	3.58280	+	11.0267i	0.193172	+	0.594521i
$345$	3.27932	−	0.673942i	0.176553	−	0.0362838i
$346$	58.4953	−	12.4336i	3.14473	−	0.668433i
$347$	−15.3245	+	23.5977i	−0.822663	+	1.26679i	0.138376	+	0.990380i	$0.455812\pi$
$347$	−15.3245	+	23.5977i	−0.822663	+	1.26679i	−0.961040	+	0.276411i	$0.910855\pi$
$348$	−14.8747	+	35.7227i	−0.797367	+	1.91494i
$349$			28.2123i			1.51017i	0.655626	+	0.755086i	$0.272405\pi$
$349$			28.2123i			1.51017i	−0.655626	+	0.755086i	$0.727595\pi$
$350$	20.3211	−	29.5043i	1.08621	−	1.57707i
$351$	−21.9200	+	25.3772i	−1.17001	+	1.35453i
$352$	26.9669	−	33.3013i	1.43734	−	1.77497i
$353$	−4.75765	−	3.08965i	−0.253224	−	0.164446i	0.411785	−	0.911281i	$-0.364906\pi$
$353$	−4.75765	−	3.08965i	−0.253224	−	0.164446i	−0.665009	+	0.746836i	$0.731572\pi$
$354$	8.61000	+	15.9282i	0.457616	+	0.846572i
$355$	11.0285	−	12.7856i	0.585334	−	0.678590i
$356$	15.9085	−	5.16898i	0.843148	−	0.273955i
$357$	4.22017	+	5.72478i	0.223355	+	0.302987i
$358$	−51.4057	−	26.1925i	−2.71688	−	1.38432i
$359$	9.43969	−	4.20282i	0.498208	−	0.221816i	−0.142219	−	0.989835i	$-0.545424\pi$
$359$	9.43969	−	4.20282i	0.498208	−	0.221816i	0.640427	+	0.768019i	$0.278757\pi$
$360$	7.38849	+	60.1153i	0.389408	+	3.16835i
$361$	14.5798	+	6.49134i	0.767357	+	0.341649i
$362$	−16.4448	+	42.8401i	−0.864318	+	2.25162i
$363$	9.47426	−	4.49740i	0.497270	−	0.236052i
$364$	29.6461	−	86.1143i	1.55388	−	4.51362i
$365$	0.0359934	−	1.15807i	0.00188398	−	0.0606162i
$366$	−42.4822	−	49.9279i	−2.22058	−	2.60977i
$367$	15.9057	−	0.833584i	0.830272	−	0.0435127i	0.367536	−	0.930009i	$-0.380201\pi$
$367$	15.9057	−	0.833584i	0.830272	−	0.0435127i	0.462735	+	0.886496i	$0.346868\pi$
$368$	3.08373	−	11.5086i	0.160750	−	0.599929i
$369$	28.4904	−	10.8151i	1.48315	−	0.563011i
$370$	32.0246	−	4.05689i	1.66488	−	0.210908i
$371$	−2.02790	−	6.63162i	−0.105283	−	0.344297i
$372$	36.0651	−	34.0974i	1.86989	−	1.76787i
$373$	−14.7497	−	11.9441i	−0.763711	−	0.618441i	0.166256	−	0.986083i	$-0.446832\pi$
$373$	−14.7497	−	11.9441i	−0.763711	−	0.618441i	−0.929968	+	0.367641i	$0.880165\pi$
$374$	4.67322	+	8.09426i	0.241647	+	0.418544i
$375$	1.70557	+	19.2897i	0.0880754	+	0.996114i
$376$	30.7490	−	53.2588i	1.58576	−	2.74661i
$377$	−4.22844	+	26.6973i	−0.217776	+	1.37498i
$378$	−29.0087	−	23.3371i	−1.49205	−	1.20033i
$379$	16.8001	+	5.45868i	0.862963	+	0.280394i	0.706866	−	0.707348i	$-0.250109\pi$
$379$	16.8001	+	5.45868i	0.862963	+	0.280394i	0.156098	+	0.987742i	$0.450109\pi$
$380$	8.05263	−	19.1750i	0.413091	−	0.983656i
$381$	−11.6348	+	24.2767i	−0.596070	+	1.24373i
$382$	−6.91599	+	25.8108i	−0.353853	+	1.32060i
$383$	3.16680	+	4.87644i	0.161816	+	0.249174i	0.910273	−	0.414009i	$-0.135872\pi$
$383$	3.16680	+	4.87644i	0.161816	+	0.249174i	−0.748457	+	0.663183i	$0.769205\pi$
$384$	45.8966	+	16.3489i	2.34215	+	0.834302i
$385$	0.739660	+	13.1350i	0.0376966	+	0.669422i
$386$	−20.7462	−	28.5547i	−1.05595	−	1.45340i
$387$	3.77113	−	0.786939i	0.191697	−	0.0400024i
$388$	36.5983	+	45.1951i	1.85800	+	2.29444i
$389$	−21.6714	−	9.64875i	−1.09879	−	0.489211i	−0.224427	−	0.974491i	$-0.572051\pi$
$389$	−21.6714	−	9.64875i	−1.09879	−	0.489211i	−0.874359	+	0.485280i	$0.838718\pi$
$390$	23.8302	+	63.3544i	1.20669	+	3.20808i
$391$	1.08535	+	0.788556i	0.0548887	+	0.0398790i
$392$	60.4427	+	18.4717i	3.05282	+	0.932961i
$393$	−4.16800	−	2.27308i	−0.210248	−	0.114662i
$394$	−14.6479	+	68.9130i	−0.737952	+	3.47179i
$395$	−1.93653	−	5.55478i	−0.0974375	−	0.279491i
$396$	−25.0681	−	25.2552i	−1.25972	−	1.26912i
$397$	−1.43442	+	27.3703i	−0.0719913	+	1.37368i	0.688928	+	0.724830i	$0.258081\pi$
$397$	−1.43442	+	27.3703i	−0.0719913	+	1.37368i	−0.760920	+	0.648846i	$0.775252\pi$
$398$	−3.88369	−	0.615116i	−0.194672	−	0.0308330i
$399$	2.91516	+	7.43984i	0.145940	+	0.372458i
$400$	64.0952	+	25.3259i	3.20476	+	1.26629i
$401$	14.7886	+	8.53821i	0.738508	+	0.426378i	0.821527	−	0.570170i	$-0.193123\pi$
$401$	14.7886	+	8.53821i	0.738508	+	0.426378i	−0.0830186	+	0.996548i	$0.526456\pi$
$402$	19.1837	−	14.6636i	0.956796	−	0.731354i
$403$	18.8822	−	29.0760i	0.940589	−	1.44838i
$404$	17.0108	+	18.8924i	0.846316	+	0.939930i
$405$	20.1227	−	0.278822i	0.999904	−	0.0138548i
$406$	−29.7869	−	3.65565i	−1.47830	−	0.181427i
$407$	−8.38215	+	8.38215i	−0.415488	+	0.415488i
$408$	−15.7970	+	18.4265i	−0.782069	+	0.912246i
$409$	5.44895	+	0.572707i	0.269433	+	0.0283186i	0.238282	−	0.971196i	$-0.423416\pi$
$409$	5.44895	+	0.572707i	0.269433	+	0.0283186i	0.0311515	+	0.999515i	$0.490083\pi$
$410$	8.32716	−	60.9463i	0.411249	−	3.00993i
$411$	9.40511	−	3.87526i	0.463920	−	0.191153i
$412$	−7.14685	−	45.1234i	−0.352100	−	2.22307i
$413$	−7.34613	+	7.09488i	−0.361479	+	0.349116i
$414$	−6.54699	−	2.54111i	−0.321767	−	0.124889i
$415$	−2.83330	−	3.35040i	−0.139081	−	0.164465i
$416$	123.676	+	12.9989i	6.06371	+	0.637321i
$417$	6.98914	−	2.46037i	0.342260	−	0.120485i
$418$	2.71781	+	10.1430i	0.132932	+	0.496111i
$419$	−5.38539	−	16.5745i	−0.263094	−	0.809719i	−0.992126	−	0.125240i	$-0.960030\pi$
$419$	−5.38539	−	16.5745i	−0.263094	−	0.809719i	0.729033	−	0.684479i	$-0.239970\pi$
$420$	−50.4539	+	21.0191i	−2.46190	+	1.02562i
$421$	−6.80297	+	20.9374i	−0.331556	+	1.02043i	0.636837	+	0.770998i	$0.280242\pi$
$421$	−6.80297	+	20.9374i	−0.331556	+	1.02043i	−0.968394	+	0.249427i	$0.919758\pi$
$422$	13.1493	+	0.689125i	0.640098	+	0.0335461i
$423$	−16.4865	−	12.0720i	−0.801600	−	0.586961i
$424$	20.4950	−	11.8328i	0.995323	−	0.574650i
$425$	−5.24862	+	5.71575i	−0.254595	+	0.277255i
$426$	−33.9797	+	9.99660i	−1.64632	+	0.484337i
$427$	20.6753	−	30.6562i	1.00055	−	1.48356i
$428$	91.2422	−	46.4902i	4.41036	−	2.24719i
$429$	−21.1695	−	13.0269i	−1.02207	−	0.628943i
$430$	2.24496	−	7.44497i	0.108262	−	0.359029i
$431$	20.3783	+	18.3487i	0.981590	+	0.883828i	0.993237	−	0.116105i	$-0.0370408\pi$
$431$	20.3783	+	18.3487i	0.981590	+	0.883828i	−0.0116471	+	0.999932i	$0.503707\pi$
$432$	31.1936	−	64.4711i	1.50080	−	3.10187i
$433$	7.56699	+	3.85557i	0.363646	+	0.185287i	0.626260	−	0.779614i	$-0.284585\pi$
$433$	7.56699	+	3.85557i	0.363646	+	0.185287i	−0.262614	+	0.964901i	$0.584585\pi$
$434$	32.9950	+	19.8228i	1.58381	+	0.951526i
$435$	13.6640	−	8.74297i	0.655139	−	0.419193i
$436$	0.0287073	+	0.273131i	0.00137483	+	0.0130806i
$437$	0.948553	+	1.17137i	0.0453755	+	0.0560340i
$438$	−1.38035	+	2.00045i	−0.0659559	+	0.0955853i
$439$	−2.99781	+	0.315083i	−0.143078	+	0.0150381i	−0.175797	−	0.984427i	$-0.556250\pi$
$439$	−2.99781	+	0.315083i	−0.143078	+	0.0150381i	0.0327188	+	0.999465i	$0.489583\pi$
$440$	−43.1086	+	12.5404i	−2.05512	+	0.597838i
$441$	8.27496	−	19.3009i	0.394046	−	0.919091i
$442$	−12.3142	+	24.1679i	−0.585725	+	1.14955i
$443$	21.1423	−	5.66506i	1.00450	−	0.269155i	0.281171	−	0.959658i	$-0.409277\pi$
$443$	21.1423	−	5.66506i	1.00450	−	0.269155i	0.723330	+	0.690502i	$0.242610\pi$
$444$	−44.4121	−	21.2849i	−2.10770	−	1.01014i
$445$	−6.71363	−	2.02444i	−0.318257	−	0.0959674i
$446$	−52.7909	+	47.5332i	−2.49972	+	2.25076i
$447$	−14.3515	−	15.1797i	−0.678803	−	0.717977i
$448$	−4.53977	+	64.9746i	−0.214484	+	3.06976i
$449$	−18.8516			−0.889661			−0.444831	−	0.895615i	$-0.646736\pi$
$449$	−18.8516			−0.889661			−0.444831	+	0.895615i	$0.646736\pi$
$450$	18.9289	−	35.9423i	0.892315	−	1.69433i
$451$	11.2944	+	19.5625i	0.531832	+	0.921161i
$452$	−9.81344	+	3.76703i	−0.461585	+	0.177186i
$453$	−1.83379	+	0.436651i	−0.0861590	+	0.0205157i
$454$	29.3962	+	9.55142i	1.37963	+	0.448270i
$455$	−30.8002	+	22.5614i	−1.44394	+	1.05769i
$456$	−22.5015	+	15.4033i	−1.05373	+	0.721327i
$457$	−24.5545	+	6.57936i	−1.14861	+	0.307770i	−0.782409	−	0.622765i	$-0.786009\pi$
$457$	−24.5545	+	6.57936i	−1.14861	+	0.307770i	−0.366203	+	0.930535i	$0.619343\pi$
$458$	14.8450	−	0.777994i	0.693661	−	0.0363533i
$459$	5.51849	+	5.88060i	0.257581	+	0.274483i
$460$	−7.87244	+	6.65739i	−0.367054	+	0.310402i
$461$	3.05987	+	4.21154i	0.142512	+	0.196151i	0.874306	−	0.485375i	$-0.161317\pi$
$461$	3.05987	+	4.21154i	0.142512	+	0.196151i	−0.731794	+	0.681526i	$0.761317\pi$
$462$	13.6327	−	23.9948i	0.634252	−	1.11634i
$463$	1.79781	−	0.284745i	0.0835513	−	0.0132332i	−0.114519	−	0.993421i	$-0.536533\pi$
$463$	1.79781	−	0.284745i	0.0835513	−	0.0132332i	0.198070	+	0.980188i	$0.436533\pi$
$464$	−6.03455	−	57.4149i	−0.280147	−	2.66542i
$465$	−20.5716	+	3.11605i	−0.953984	+	0.144503i
$466$	6.24975	−	59.4624i	0.289514	−	2.75454i
$467$	−32.9922	+	21.4254i	−1.52670	+	0.991448i	−0.537760	+	0.843098i	$0.680730\pi$
$467$	−32.9922	+	21.4254i	−1.52670	+	0.991448i	−0.988935	+	0.148350i	$0.952604\pi$
$468$	21.8461	−	100.932i	1.00984	−	4.66557i
$469$	10.8776	+	8.19589i	0.502281	+	0.378451i
$470$	−37.3144	+	17.5746i	−1.72118	+	0.810654i
$471$	−9.22979	−	5.67965i	−0.425286	−	0.261704i
$472$	−29.2297	−	18.9820i	−1.34541	−	0.873718i
$473$	1.02334	+	2.66589i	0.0470531	+	0.122578i
$474$	−2.90304	+	11.9938i	−0.133341	+	0.550894i
$475$	−7.35799	+	4.67666i	−0.337608	+	0.214580i
$476$	−19.8509	−	9.25527i	−0.909866	−	0.424215i
$477$	−3.17156	−	7.19529i	−0.145216	−	0.329450i
$478$	37.3051	+	1.95508i	1.70629	+	0.0894231i
$479$	−9.18310	+	1.95193i	−0.419587	+	0.0891859i	−0.412867	−	0.910792i	$-0.635472\pi$
$479$	−9.18310	+	1.95193i	−0.419587	+	0.0891859i	−0.00672010	+	0.999977i	$0.502139\pi$
$480$	−43.4586	−	60.6726i	−1.98361	−	2.76931i
$481$	−33.6501	−	7.15255i	−1.53431	−	0.326128i
$482$	24.8156	−	24.8156i	1.13032	−	1.13032i
$483$	0.386772	−	3.94231i	0.0175987	−	0.179381i
$484$	−18.9838	+	26.1290i	−0.862900	+	1.18768i
$485$	−1.79390	−	24.3133i	−0.0814567	−	1.10401i
$486$	−35.7882	−	22.3911i	−1.62339	−	1.01568i
$487$	−5.81716	+	4.71064i	−0.263601	+	0.213460i	−0.752004	−	0.659158i	$-0.770913\pi$
$487$	−5.81716	+	4.71064i	−0.263601	+	0.213460i	0.488404	+	0.872618i	$0.337579\pi$
$488$	117.805	+	45.2212i	5.33279	+	2.04707i
$489$	0.405566	+	0.312401i	0.0183403	+	0.0141273i
$490$	−26.2290	−	33.2997i	−1.18491	−	1.50433i
$491$	2.56952	−	3.53665i	0.115961	−	0.159607i	−0.747091	−	0.664722i	$-0.768550\pi$
$491$	2.56952	−	3.53665i	0.115961	−	0.159607i	0.863052	+	0.505115i	$0.168550\pi$
$492$	−61.0814	+	71.2486i	−2.75376	+	3.21214i
$493$	6.27896	+	1.68244i	0.282790	+	0.0757734i
$494$	−20.3913	+	22.6469i	−0.917449	+	1.01893i
$495$	2.59211	+	14.6904i	0.116507	+	0.660283i
$496$	−22.8817	+	70.4227i	−1.02742	+	3.16207i
$497$	−10.5880	−	16.9421i	−0.474935	−	0.759959i
$498$	1.18444	+	9.12781i	0.0530762	+	0.409027i
$499$	−7.58936	−	4.38172i	−0.339747	−	0.196153i	0.320413	−	0.947278i	$-0.396178\pi$
$499$	−7.58936	−	4.38172i	−0.339747	−	0.196153i	−0.660160	+	0.751125i	$0.729512\pi$
$500$	−33.0534	−	49.6377i	−1.47819	−	2.21987i
$501$	18.5587	−	19.4841i	0.829142	−	0.870487i
$502$	−23.8097	+	29.4025i	−1.06268	+	1.31230i
$503$	3.34021	−	1.70192i	0.148932	−	0.0758849i	−0.377936	−	0.925832i	$-0.623366\pi$
$503$	3.34021	−	1.70192i	0.148932	−	0.0758849i	0.526868	+	0.849947i	$0.323366\pi$
$504$	70.5298	+	12.7027i	3.14165	+	0.565822i
$505$	−1.33936	−	10.5728i	−0.0596008	−	0.470482i
$506$	1.08232	−	5.09190i	0.0481149	−	0.226363i
$507$	−1.20669	−	49.6047i	−0.0535911	−	2.20302i
$508$	−4.33889	−	82.7910i	−0.192507	−	3.67325i
$509$	−4.34275	+	1.93352i	−0.192489	+	0.0857016i	−0.500718	−	0.865611i	$-0.666930\pi$
$509$	−4.34275	+	1.93352i	−0.192489	+	0.0857016i	0.308229	+	0.951312i	$0.400264\pi$
$510$	15.7517	−	4.10691i	0.697496	−	0.181857i
$511$	−1.29624	−	0.446251i	−0.0573425	−	0.0197410i
$512$	−16.4987	+	2.61313i	−0.729145	+	0.115485i
$513$	4.27882	+	7.98647i	0.188914	+	0.352611i
$514$	−7.22797	+	16.2343i	−0.318812	+	0.716063i
$515$	−8.32961	+	17.2458i	−0.367046	+	0.759942i
$516$	−9.03550	+	7.68805i	−0.397766	+	0.338448i
$517$	6.87634	−	13.4956i	0.302421	−	0.593535i
$518$	6.63034	−	37.6150i	0.291320	−	1.65271i
$519$	21.6052	+	31.5613i	0.948363	+	1.38539i
$520$	−98.6592	−	85.1009i	−4.32649	−	3.73192i
$521$	−2.58651	−	12.1686i	−0.113317	−	0.533114i	−0.997785	−	0.0665145i	$-0.978812\pi$
$521$	−2.58651	−	12.1686i	−0.113317	−	0.533114i	0.884468	−	0.466600i	$-0.154521\pi$
$522$	−34.0283	−	0.126487i	−1.48938	−	0.00553620i
$523$	24.3857	+	19.7472i	1.06631	+	0.863484i	0.991025	−	0.133677i	$-0.0426786\pi$
$523$	24.3857	+	19.7472i	1.06631	+	0.863484i	0.0752894	+	0.997162i	$0.476012\pi$
$524$	14.6204			0.638696
$525$	22.3985	+	4.82785i	0.977550	+	0.210705i
$526$	−21.6115			−0.942306
$527$	−6.47952	−	5.24701i	−0.282252	−	0.228563i
$528$	50.8745	+	15.1726i	2.21403	+	0.660304i
$529$	4.62662	+	21.7665i	0.201157	+	0.946370i
$530$	−15.8170	−	1.32269i	−0.687046	−	0.0574539i
$531$	−7.32113	+	8.97244i	−0.317710	+	0.389371i
$532$	−18.8514	−	15.8164i	−0.817313	−	0.685728i
$533$	−29.7613	+	58.4098i	−1.28910	+	2.53001i
$534$	9.53232	+	11.2030i	0.412504	+	0.484802i
$535$	−42.5335	−	5.81140i	−1.83888	−	0.251249i
$536$	−18.9045	+	42.4601i	−0.816549	+	1.83400i
$537$	2.96347	−	36.7804i	0.127883	−	1.58719i
$538$	−14.7619	+	2.33806i	−0.636432	+	0.100801i
$539$	15.1042	+	3.76409i	0.650585	+	0.162131i
$540$	−53.9936	+	30.4242i	−2.32352	+	1.30925i
$541$	7.04602	−	3.13709i	0.302932	−	0.134874i	−0.249641	−	0.968338i	$-0.580313\pi$
$541$	7.04602	−	3.13709i	0.302932	−	0.134874i	0.552573	+	0.833464i	$0.313646\pi$
$542$	2.78806	+	53.1993i	0.119757	+	2.28511i
$543$	−29.3400	+	0.713731i	−1.25910	+	0.0306291i
$544$	6.21793	−	29.2531i	0.266592	−	1.25422i
$545$	0.0554296	−	0.100909i	0.00237434	−	0.00432245i
$546$	79.9488	−	4.74530i	3.42149	−	0.203080i
$547$	11.6939	−	5.95832i	0.499994	−	0.254759i	−0.185758	−	0.982596i	$-0.559474\pi$
$547$	11.6939	−	5.95832i	0.499994	−	0.254759i	0.685751	+	0.727836i	$0.259474\pi$
$548$	−19.7142	+	24.3450i	−0.842148	+	1.03997i
$549$	19.1735	−	37.2867i	0.818303	−	1.59136i
$550$	28.5448	+	9.58444i	1.21716	+	0.408682i
$551$	6.32486	+	3.65166i	0.269448	+	0.155566i
$552$	13.4057	−	1.73956i	0.570586	−	0.0740405i
$553$	−6.95621	+	0.243311i	−0.295808	+	0.0103466i
$554$	6.89189	−	21.2111i	0.292808	−	0.901172i
$555$	10.2020	+	17.9490i	0.433051	+	0.761895i
$556$	−15.2684	+	16.9573i	−0.647526	+	0.719150i
$557$	32.3173	+	8.65938i	1.36933	+	0.366910i	0.867232	−	0.497903i	$-0.165897\pi$
$557$	32.3173	+	8.65938i	1.36933	+	0.366910i	0.502094	+	0.864813i	$0.332563\pi$
$558$	39.8059	+	17.9003i	1.68512	+	0.757780i
$559$	−4.87102	+	6.70439i	−0.206022	+	0.283565i
$560$	51.0703	−	63.5709i	2.15811	−	2.68636i
$561$	−3.64783	+	4.73569i	−0.154011	+	0.199941i
$562$	−11.9171	−	4.57455i	−0.502693	−	0.192966i
$563$	−22.3877	+	18.1292i	−0.943527	+	0.764053i	−0.971863	−	0.235545i	$-0.924312\pi$
$563$	−22.3877	+	18.1292i	−0.943527	+	0.764053i	0.0283364	+	0.999598i	$0.490979\pi$
$564$	62.3736	+	8.32960i	2.62640	+	0.350739i
$565$	4.27975	+	1.04964i	0.180050	+	0.0441587i
$566$	−11.1590	+	15.3591i	−0.469048	+	0.645589i
$567$	6.73210	−	22.8403i	0.282722	−	0.959202i
$568$	48.2096	−	48.2096i	2.02283	−	2.02283i
$569$	−29.3522	−	6.23900i	−1.23051	−	0.261552i	−0.453622	−	0.891194i	$-0.649868\pi$
$569$	−29.3522	−	6.23900i	−1.23051	−	0.261552i	−0.776885	+	0.629642i	$0.783202\pi$
$570$	18.2883	+	0.123431i	0.766014	+	0.00516996i
$571$	32.3807	−	6.88272i	1.35509	−	0.288033i	0.527589	−	0.849500i	$-0.323096\pi$
$571$	32.3807	−	6.88272i	1.35509	−	0.288033i	0.827499	+	0.561467i	$0.189763\pi$
$572$	76.4428	+	4.00620i	3.19623	+	0.167507i
$573$	−16.9482	+	2.19923i	−0.708020	+	0.0918742i
$574$	−65.9652	−	30.7555i	−2.75334	−	1.28371i
$575$	4.30260	−	0.409715i	0.179431	−	0.0170863i
$576$	3.59104	+	73.7666i	0.149627	+	3.07361i
$577$	−7.28353	−	18.9742i	−0.303217	−	0.789908i	−0.997530	−	0.0702351i	$-0.977625\pi$
$577$	−7.28353	−	18.9742i	−0.303217	−	0.789908i	0.694313	−	0.719673i	$-0.255708\pi$
$578$	−33.1402	−	21.5215i	−1.37845	−	0.895176i
$579$	11.8307	−	19.2256i	0.491667	−	0.798990i
$580$	−24.0514	+	43.7852i	−0.998682	+	1.81808i
$581$	−4.77888	+	2.02883i	−0.198261	+	0.0841703i
$582$	−24.4858	+	44.8980i	−1.01497	+	1.86108i
$583$	4.88830	−	3.17450i	0.202453	−	0.131474i
$584$	0.489022	−	4.65273i	0.0202359	−	0.192532i
$585$	−31.6578	+	29.5285i	−1.30889	+	1.22085i
$586$	−4.59303	−	43.6997i	−0.189736	−	1.80522i
$587$	−40.2198	+	6.37019i	−1.66005	+	0.262926i	−0.914813	−	0.403877i	$-0.867662\pi$
$587$	−40.2198	+	6.37019i	−1.66005	+	0.262926i	−0.745234	+	0.666803i	$0.767662\pi$
$588$	6.08610	+	64.3842i	0.250987	+	2.65516i
$589$	−5.50599	−	7.57834i	−0.226870	−	0.312260i
$590$	8.83956	+	21.6393i	0.363919	+	0.890876i
$591$	−44.3203	+	8.12911i	−1.82309	+	0.334387i
$592$	73.3751	−	3.84543i	3.01570	−	0.158046i
$593$	−25.3699	+	6.79784i	−1.04182	+	0.279154i	−0.738866	−	0.673853i	$-0.764638\pi$
$593$	−25.3699	+	6.79784i	−1.04182	+	0.279154i	−0.302950	+	0.953006i	$0.597972\pi$
$594$	12.1360	−	28.8430i	0.497947	−	1.18344i
$595$	4.62180	+	7.93371i	0.189475	+	0.325251i
$596$	61.1837	+	19.8798i	2.50618	+	0.814308i
$597$	−0.582538	−	2.44647i	−0.0238417	−	0.100127i
$598$	14.1039	−	5.41398i	0.576751	−	0.221394i
$599$	−21.3319	−	36.9480i	−0.871599	−	1.50965i	−0.860342	−	0.509717i	$-0.829750\pi$
$599$	−21.3319	−	36.9480i	−0.871599	−	1.50965i	−0.0112564	−	0.999937i	$-0.503583\pi$
$600$	1.13691	+	78.1842i	0.0464140	+	3.19186i
$601$	10.9629			0.447186			0.223593	−	0.974683i	$-0.428221\pi$
$601$	10.9629			0.447186			0.223593	+	0.974683i	$0.428221\pi$
$602$	−7.62809	−	5.14458i	−0.310898	−	0.209678i
$603$	13.3454	+	7.77128i	0.543468	+	0.316471i
$604$	4.31410	−	3.88443i	0.175538	−	0.158055i
$605$	12.7847	−	4.45705i	0.519772	−	0.181205i
$606$	−9.66193	+	20.1601i	−0.392489	+	0.818950i
$607$	−23.6767	+	6.34415i	−0.961007	+	0.257501i	−0.705027	−	0.709181i	$-0.749065\pi$
$607$	−23.6767	+	6.34415i	−0.961007	+	0.257501i	−0.255980	+	0.966682i	$0.582398\pi$
$608$	15.2542	−	29.9381i	0.618640	−	1.21415i
$609$	−5.09599	−	18.5050i	−0.206500	−	0.749859i
$610$	−47.5943	−	69.9809i	−1.92704	−	2.83344i
$611$	43.7156	−	4.59469i	1.76854	−	0.185881i
$612$	−23.5909	−	7.76221i	−0.953605	−	0.313769i
$613$	−20.5923	−	25.4293i	−0.831714	−	1.02708i	−0.999151	−	0.0411982i	$-0.986882\pi$
$613$	−20.5923	−	25.4293i	−0.831714	−	1.02708i	0.167437	−	0.985883i	$-0.446451\pi$
$614$	1.91955	+	18.2633i	0.0774667	+	0.737046i
$615$	38.0691	−	9.92571i	1.53510	−	0.400243i
$616$	−0.924082	+	53.1131i	−0.0372323	+	2.13999i
$617$	13.8157	+	7.03943i	0.556197	+	0.283397i	0.709409	−	0.704797i	$-0.248962\pi$
$617$	13.8157	+	7.03943i	0.556197	+	0.283397i	−0.153212	+	0.988193i	$0.548962\pi$
$618$	34.2942	−	20.9279i	1.37951	−	0.841844i
$619$	−4.23697	−	3.81498i	−0.170298	−	0.153337i	0.579575	−	0.814919i	$-0.303219\pi$
$619$	−4.23697	−	3.81498i	−0.170298	−	0.153337i	−0.749873	+	0.661582i	$0.769885\pi$
$620$	51.0239	−	38.7570i	2.04917	−	1.55652i
$621$	−0.0925401	−	4.49067i	−0.00371351	−	0.180204i
$622$	−7.64261	+	3.89410i	−0.306441	+	0.156139i
$623$	−4.63922	+	6.87876i	−0.185866	+	0.275592i
$624$	43.4833	+	147.805i	1.74072	+	5.91695i
$625$	−0.489021	+	24.9952i	−0.0195608	+	0.999809i
$626$	−65.7246	+	37.9461i	−2.62688	+	1.51663i
$627$	−5.33578	+	4.07856i	−0.213091	+	0.162882i
$628$	33.3286	+	1.74668i	1.32996	+	0.0697001i
$629$	−2.55659	+	7.86837i	−0.101938	+	0.313732i
$630$	−33.9928	−	33.9808i	−1.35430	−	1.35383i
$631$	−2.99758	−	9.22560i	−0.119332	−	0.367265i	0.873494	−	0.486835i	$-0.161849\pi$
$631$	−2.99758	−	9.22560i	−0.119332	−	0.367265i	−0.992826	+	0.119569i	$0.961849\pi$
$632$	−6.14780	−	22.9439i	−0.244546	−	0.912660i
$633$	2.79639	+	7.94365i	0.111147	+	0.315732i
$634$	−82.2059	−	8.64019i	−3.26482	−	0.343146i
$635$	−18.3039	+	29.5439i	−0.726368	+	1.17242i
$636$	19.1841	+	14.7772i	0.760698	+	0.585954i
$637$	14.7122	+	42.7117i	0.582920	+	1.69230i
$638$	−3.94583	−	24.9130i	−0.156217	−	0.986315i
$639$	−14.1908	−	17.6579i	−0.561378	−	0.698538i
$640$	56.6388	+	27.3561i	2.23885	+	1.08135i
$641$	−33.6933	−	3.54131i	−1.33081	−	0.139873i	−0.587717	−	0.809066i	$-0.699973\pi$
$641$	−33.6933	−	3.54131i	−1.33081	−	0.139873i	−0.743089	+	0.669193i	$0.766640\pi$
$642$	68.3673	+	58.6113i	2.69824	+	2.31320i
$643$	−14.7325	+	14.7325i	−0.580994	+	0.580994i	−0.935176	−	0.354182i	$-0.884759\pi$
$643$	−14.7325	+	14.7325i	−0.580994	+	0.580994i	0.354182	+	0.935176i	$0.384759\pi$
$644$	4.76715	+	11.2289i	0.187852	+	0.442482i
$645$	4.94953	−	0.486466i	0.194888	−	0.0191546i
$646$	4.90390	+	5.44634i	0.192941	+	0.214283i
$647$	7.96484	−	12.2648i	0.313130	−	0.482178i	−0.646706	−	0.762739i	$-0.723854\pi$
$647$	7.96484	−	12.2648i	0.313130	−	0.482178i	0.959836	+	0.280561i	$0.0905205\pi$
$648$	81.1148	+	4.85597i	3.18649	+	0.190761i
$649$	−7.43385	−	4.29194i	−0.291804	−	0.168473i
$650$	21.7902	+	84.6244i	0.854682	+	3.31924i
$651$	−3.68268	+	24.3413i	−0.144336	+	0.954010i
$652$	−1.55714	−	0.246626i	−0.0609822	−	0.00965862i
$653$	−1.41343	+	26.9699i	−0.0553118	+	1.05541i	0.820157	+	0.572138i	$0.193886\pi$
$653$	−1.41343	+	26.9699i	−0.0553118	+	1.05541i	−0.875469	+	0.483274i	$0.839447\pi$
$654$	−0.212457	+	0.114844i	−0.00830774	+	0.00449076i
$655$	−5.03407	−	3.49619i	−0.196697	−	0.136607i
$656$	29.1103	−	136.953i	1.13656	−	5.34712i
$657$	−1.51928	−	0.328841i	−0.0592729	−	0.0128293i
$658$	6.79479	+	48.3275i	0.264888	+	1.88400i
$659$	21.9280	+	15.9316i	0.854194	+	0.620609i	0.926299	−	0.376788i	$-0.122972\pi$
$659$	21.9280	+	15.9316i	0.854194	+	0.620609i	−0.0721049	+	0.997397i	$0.522972\pi$
$660$	−28.6688	−	35.8956i	−1.11593	−	1.39724i
$661$	38.6512	+	17.2086i	1.50336	+	0.669338i	0.982831	−	0.184507i	$-0.0590690\pi$
$661$	38.6512	+	17.2086i	1.50336	+	0.669338i	0.520527	+	0.853845i	$0.325736\pi$
$662$	−22.6768	−	28.0035i	−0.881360	−	1.08839i
$663$	−17.2919	−	1.39325i	−0.671563	−	0.0541092i
$664$	−10.4139	−	14.3335i	−0.404139	−	0.556250i
$665$	2.70869	+	9.95382i	0.105039	+	0.385993i
$666$	2.42736	−	43.2409i	0.0940584	−	1.67555i
$667$	−1.97189	−	3.03644i	−0.0763518	−	0.117571i
$668$	−21.4474	+	80.0427i	−0.829824	+	3.09695i
$669$	−40.9712	−	19.6358i	−1.58404	−	0.759164i
$670$	26.6583	−	16.1574i	1.02990	−	0.624216i
$671$	29.5576	+	9.60384i	1.14106	+	0.370752i
$672$	−83.7919	+	27.8686i	−3.23234	+	1.07505i
$673$	0.266007	−	1.67950i	0.0102538	−	0.0647400i	−0.982031	−	0.188720i	$-0.939566\pi$
$673$	0.266007	−	1.67950i	0.0102538	−	0.0647400i	0.992285	+	0.123980i	$0.0395660\pi$
$674$	18.7385	−	32.4560i	0.721780	−	1.25016i
$675$	25.8663	+	2.43592i	0.995595	+	0.0937586i
$676$	76.4034	+	132.335i	2.93859	+	5.08979i
$677$	−27.4041	−	22.1914i	−1.05322	−	0.852884i	−0.0638037	−	0.997962i	$-0.520323\pi$
$677$	−27.4041	−	22.1914i	−1.05322	−	0.852884i	−0.989420	+	0.145079i	$0.953656\pi$
$678$	−6.35050	−	6.71699i	−0.243890	−	0.257964i
$679$	−28.1071	−	6.48735i	−1.07865	−	0.248962i
$680$	−22.8339	+	21.4573i	−0.875639	+	0.822849i
$681$	1.51440	+	19.7105i	0.0580318	+	0.755308i
$682$	−8.37334	+	31.2497i	−0.320632	+	1.19661i
$683$	34.2626	−	1.79563i	1.31102	−	0.0687077i	0.616028	−	0.787724i	$-0.288741\pi$
$683$	34.2626	−	1.79563i	1.31102	−	0.0687077i	0.694993	+	0.719016i	$0.255407\pi$
$684$	−23.3443	−	15.2836i	−0.892591	−	0.584384i
$685$	12.6096	−	3.66814i	0.481787	−	0.140152i
$686$	−46.8210	+	17.9820i	−1.78763	+	0.686557i
$687$	4.07713	+	8.58892i	0.155552	+	0.327688i
$688$	6.34298	−	16.5240i	0.241824	−	0.629973i
$689$	15.4528	+	6.88004i	0.588706	+	0.262109i
$690$	−8.05030	−	4.17051i	−0.306470	−	0.158769i
$691$	15.9058	−	7.08171i	0.605084	−	0.269401i	−0.0812424	−	0.996694i	$-0.525889\pi$
$691$	15.9058	−	7.08171i	0.605084	−	0.269401i	0.686326	+	0.727294i	$0.259222\pi$
$692$	−104.949	−	53.4743i	−3.98957	−	2.03279i
$693$	17.5108	+	2.21515i	0.665182	+	0.0841467i
$694$	72.4694	−	23.5467i	2.75090	−	0.893822i
$695$	9.31220	−	2.18755i	0.353232	−	0.0829786i
$696$	57.6212	−	31.1473i	2.18413	−	1.18063i
$697$	13.2219	+	8.58638i	0.500814	+	0.325232i
$698$	48.0818	−	59.3761i	1.81992	−	2.24742i
$699$	36.6855	−	10.7926i	1.38757	−	0.408214i
$700$	−67.6762	+	19.9732i	−2.55792	+	0.754916i
$701$		−	47.9435i		−	1.81080i	−0.424559	−	0.905400i	$-0.639571\pi$
$701$		−	47.9435i		−	1.81080i	0.424559	−	0.905400i	$-0.360429\pi$
$702$	89.3832	−	16.0512i	3.37355	−	0.605815i
$703$	−5.06248	+	7.79554i	−0.190935	+	0.294014i
$704$	−53.5477	+	11.3819i	−2.01816	+	0.428972i
$705$	−19.4845	−	17.7835i	−0.733827	−	0.669764i
$706$	4.74737	+	14.6109i	0.178670	+	0.549889i
$707$	−12.4184	−	2.18897i	−0.467042	−	0.0823247i
$708$	6.56414	−	35.0532i	0.246695	−	1.31738i
$709$	−10.4953	−	23.5727i	−0.394158	−	0.885293i	−0.996222	−	0.0868453i	$-0.972321\pi$
$709$	−10.4953	−	23.5727i	−0.394158	−	0.885293i	0.602064	−	0.798448i	$-0.294345\pi$
$710$	−45.0012	+	8.11304i	−1.68886	+	0.304477i
$711$	−7.79979	+	1.20566i	−0.292515	+	0.0452159i
$712$	−26.4336	−	10.1469i	−0.990642	−	0.380272i
$713$	0.726444	+	4.58658i	0.0272055	+	0.171769i
$714$	0.874811	−	19.2408i	0.0327390	−	0.720070i
$715$	−25.3626	−	19.6592i	−0.948507	−	0.735213i
$716$	46.2196	+	103.811i	1.72731	+	3.87960i
$717$	7.93347	+	22.5365i	0.296281	+	0.841639i
$718$	−27.0297	−	7.24259i	−1.00874	−	0.270291i
$719$	36.0695	+	7.66680i	1.34516	+	0.285924i	0.823543	−	0.567253i	$-0.191994\pi$
$719$	36.0695	+	7.66680i	1.34516	+	0.285924i	0.521621	+	0.853177i	$0.325327\pi$
$720$	48.9882	−	78.4183i	1.82568	−	2.92248i
$721$	16.5741	+	15.4538i	0.617251	+	0.575531i
$722$	−19.6217	−	38.5098i	−0.730246	−	1.43319i
$723$	20.7210	+	8.62806i	0.770621	+	0.320881i
$724$	78.2729	−	45.1909i	2.90899	−	1.67950i
$725$	18.7517	−	9.32459i	0.696421	−	0.346306i
$726$	−27.6045	−	6.68155i	−1.02450	−	0.247975i
$727$	13.0860	+	2.07262i	0.485332	+	0.0768691i	0.394306	−	0.918979i	$-0.370985\pi$
$727$	13.0860	+	2.07262i	0.485332	+	0.0768691i	0.0910267	+	0.995848i	$0.470985\pi$
$728$	−130.733	+	81.7012i	−4.84528	+	3.02805i
$729$	4.52084	−	26.6188i	0.167439	−	0.985883i
$730$	−2.04943	+	2.37595i	−0.0758529	+	0.0879378i
$731$	1.48106	+	1.33355i	0.0547789	+	0.0493231i
$732$	3.14005	+	129.081i	0.116060	+	4.77098i
$733$	−22.5942	+	14.6728i	−0.834536	+	0.541954i	−0.889712	−	0.456523i	$-0.849095\pi$
$733$	−22.5942	+	14.6728i	−0.834536	+	0.541954i	0.0551759	+	0.998477i	$0.482428\pi$
$734$	−34.8961	−	25.3535i	−1.28804	−	0.935815i
$735$	13.3007	−	23.6240i	0.490603	−	0.871383i
$736$	−13.4758	+	9.79073i	−0.496724	+	0.360891i
$737$	−4.10233	+	10.6869i	−0.151111	+	0.393658i
$738$	−78.3933	−	25.7941i	−2.88570	−	0.949493i
$739$	−0.245822	+	0.552125i	−0.00904271	+	0.0203103i	−0.918010	−	0.396556i	$-0.870205\pi$
$739$	−0.245822	+	0.552125i	−0.00904271	+	0.0203103i	0.908968	+	0.416867i	$0.136872\pi$
$740$	−54.0481	−	33.4854i	−1.98685	−	1.23095i
$741$	−18.3605	−	6.54023i	−0.674490	−	0.240261i
$742$	−7.03422	+	17.4131i	−0.258234	+	0.639256i
$743$	−19.2061	−	19.2061i	−0.704602	−	0.704602i	0.260793	−	0.965395i	$-0.416016\pi$
$743$	−19.2061	−	19.2061i	−0.704602	−	0.704602i	−0.965395	+	0.260793i	$0.916016\pi$
$744$	−83.7655	+	6.43586i	−3.07099	+	0.235950i
$745$	−16.3127	−	21.4758i	−0.597653	−	0.786814i
$746$	10.6864	+	50.2754i	0.391256	+	1.84071i
$747$	−5.10907	+	2.92445i	−0.186931	+	0.107000i
$748$	2.87979	−	18.1823i	0.105296	−	0.664810i
$749$	−21.4638	+	46.0361i	−0.784271	+	1.68212i
$750$	29.2855	−	43.5041i	1.06935	−	1.58855i
$751$	10.1333	−	17.5514i	0.369770	−	0.640461i	−0.619759	−	0.784792i	$-0.712770\pi$
$751$	10.1333	−	17.5514i	0.369770	−	0.640461i	0.989529	+	0.144331i	$0.0461031\pi$
$752$	−87.6469	+	33.6445i	−3.19615	+	1.22689i
$753$	−23.1883	−	6.91560i	−0.845029	−	0.252018i
$754$	54.3990	−	48.9811i	1.98110	−	1.78379i
$755$	−2.41431	+	0.305845i	−0.0878656	+	0.0111308i
$756$	15.4762	+	71.6785i	0.562864	+	2.60692i
$757$	9.17052	+	9.17052i	0.333308	+	0.333308i	0.853841	−	0.520533i	$-0.174267\pi$
$757$	9.17052	+	9.17052i	0.333308	+	0.333308i	−0.520533	+	0.853841i	$0.674267\pi$
$758$	−26.0546	−	40.1206i	−0.946346	−	1.45724i
$759$	3.27477	−	0.600650i	0.118867	−	0.0218022i
$760$	−31.0194	+	16.6462i	−1.12519	+	0.603823i
$761$	49.1526	−	5.16615i	1.78178	−	0.187273i	0.844432	−	0.535663i	$-0.179938\pi$
$761$	49.1526	−	5.16615i	1.78178	−	0.187273i	0.937350	+	0.348390i	$0.113271\pi$
$762$	65.8612	−	31.2640i	2.38590	−	1.13258i
$763$	−0.0946348	−	0.0979861i	−0.00342601	−	0.00354733i
$764$	42.5792	−	30.9356i	1.54046	−	1.11921i
$765$	6.26657	+	8.31397i	0.226568	+	0.300592i
$766$	1.64595	−	15.6601i	0.0594705	−	0.565824i
$767$	−1.30375	−	24.8771i	−0.0470758	−	0.898259i
$768$	−24.3085	−	39.8339i	−0.877159	−	1.43738i
$769$	−21.8636	+	7.10392i	−0.788422	+	0.256174i	−0.675432	−	0.737422i	$-0.736043\pi$
$769$	−21.8636	+	7.10392i	−0.788422	+	0.256174i	−0.112990	+	0.993596i	$0.536043\pi$
$770$	20.8291	−	28.9048i	0.750629	−	1.04165i
$771$	−11.3612	−	0.318633i	−0.409162	−	0.0114753i
$772$	−3.63833	+	69.4235i	−0.130946	+	2.49861i
$773$	12.2901	+	32.0168i	0.442045	+	1.15157i	0.955901	+	0.293690i	$0.0948832\pi$
$773$	12.2901	+	32.0168i	0.442045	+	1.15157i	−0.513856	+	0.857876i	$0.671783\pi$
$774$	−9.27795	−	4.77087i	−0.333489	−	0.171485i
$775$	−26.8364	+	1.14335i	−0.963992	+	0.0410705i
$776$		−	98.4399i		−	3.53379i
$777$	23.8589	−	5.24430i	0.855932	−	0.188138i
$778$	29.1658	+	57.2412i	1.04565	+	2.05220i
$779$	11.8519	+	13.1629i	0.424639	+	0.471609i
$780$	42.0528	−	126.513i	1.50573	−	4.52991i
$781$	11.2359	−	12.4788i	0.402053	−	0.446525i
$782$	−0.940330	−	3.50936i	−0.0336261	−	0.125494i
$783$	−8.21639	−	20.1532i	−0.293630	−	0.720217i
$784$	−53.9624	−	79.9830i	−1.92723	−	2.85653i
$785$	−11.0580	−	8.57131i	−0.394675	−	0.305923i
$786$	4.89806	+	11.8874i	0.174708	+	0.424010i
$787$	−12.6518	+	10.2452i	−0.450987	+	0.365202i	−0.827740	−	0.561111i	$-0.810374\pi$
$787$	−12.6518	+	10.2452i	−0.450987	+	0.365202i	0.376753	+	0.926314i	$0.377041\pi$
$788$	107.840	−	87.3275i	3.84166	−	3.11091i
$789$	−5.26576	−	12.7798i	−0.187466	−	0.454973i
$790$	−5.39127	+	14.9911i	−0.191813	+	0.533359i
$791$	2.68513	−	4.46937i	0.0954721	−	0.158913i
$792$	6.07343	+	59.9268i	0.215810	+	2.12940i
$793$	23.3437	+	87.1200i	0.828961	+	3.09372i
$794$	49.6656	−	55.1593i	1.76257	−	1.95753i
$795$	−3.07174	−	9.67554i	−0.108943	−	0.343156i
$796$	5.18224	+	5.75546i	0.183680	+	0.203997i
$797$	7.72756	+	15.1662i	0.273724	+	0.537214i	0.986417	−	0.164263i	$-0.0525244\pi$
$797$	7.72756	+	15.1662i	0.273724	+	0.537214i	−0.712692	+	0.701477i	$0.752524\pi$
$798$	6.54432	−	20.6263i	0.231666	−	0.730161i
$799$		−	10.5711i		−	0.373977i
$800$	−47.3558	−	83.9074i	−1.67428	−	2.96657i
$801$	−4.30222	+	8.36655i	−0.152011	+	0.295617i
$802$	−16.5728	−	43.1736i	−0.585206	−	1.52451i
$803$	0.0603037	−	1.15066i	0.00212807	−	0.0406060i
$804$	−47.5400	−	1.33330i	−1.67661	−	0.0470218i
$805$	1.04377	−	5.00629i	0.0367880	−	0.176448i
$806$	−89.2936	+	29.0132i	−3.14523	+	1.02195i
$807$	−4.97942	−	8.15968i	−0.175284	−	0.287234i
$808$	−2.25214	−	42.9733i	−0.0792299	−	1.51180i
$809$	−3.48401	+	33.1482i	−0.122491	+	1.16543i	0.744681	+	0.667420i	$0.232602\pi$
$809$	−3.48401	+	33.1482i	−0.122491	+	1.16543i	−0.867173	+	0.498008i	$0.834065\pi$
$810$	−42.8257	−	33.7079i	−1.50474	−	1.18438i
$811$	9.31579	−	6.76832i	0.327122	−	0.237668i	−0.412087	−	0.911145i	$-0.635200\pi$
$811$	9.31579	−	6.76832i	0.327122	−	0.237668i	0.739208	+	0.673477i	$0.235200\pi$
$812$	41.0629	+	42.5171i	1.44103	+	1.49206i
$813$	−30.7797	+	14.6110i	−1.07949	+	0.512430i
$814$	31.9267	−	3.35564i	1.11903	−	0.117615i
$815$	0.477173	+	0.457277i	0.0167147	+	0.0160177i
$816$	36.4440	−	6.68447i	1.27580	−	0.234003i
$817$	1.21950	+	1.87787i	0.0426650	+	0.0656984i
$818$	−10.4919	−	10.4919i	−0.366840	−	0.366840i
$819$	22.2861	+	46.1209i	0.778738	+	1.61160i
$820$	−88.2905	+	82.9677i	−3.08324	+	2.89736i
$821$	−28.4280	+	25.5967i	−0.992146	+	0.893332i	−0.994295	−	0.106666i	$-0.965983\pi$
$821$	−28.4280	+	25.5967i	−0.992146	+	0.893332i	0.00214927	+	0.999998i	$0.499316\pi$
$822$	−26.3987	−	7.87305i	−0.920760	−	0.274604i
$823$	21.2281	−	8.14870i	0.739964	−	0.284046i	0.0409578	−	0.999161i	$-0.486959\pi$
$823$	21.2281	−	8.14870i	0.739964	−	0.284046i	0.699007	+	0.715115i	$0.253626\pi$
$824$	−38.6665	+	66.9723i	−1.34701	+	2.33309i
$825$	1.28741	+	19.2151i	0.0448220	+	0.668983i
$826$	27.5525	−	2.41210i	0.958673	−	0.0839277i
$827$	−5.82979	+	36.8079i	−0.202722	+	1.27993i	0.650949	+	0.759121i	$0.274371\pi$
$827$	−5.82979	+	36.8079i	−0.202722	+	1.27993i	−0.853671	+	0.520813i	$0.825629\pi$
$828$	6.87158	+	12.0048i	0.238804	+	0.417194i
$829$	−4.02066	−	18.9157i	−0.139643	−	0.656970i	−0.991163	−	0.132648i	$-0.957652\pi$
$829$	−4.02066	−	18.9157i	−0.139643	−	0.656970i	0.851520	−	0.524322i	$-0.175681\pi$
$830$	0.252958	+	11.8801i	0.00878029	+	0.412363i
$831$	14.2223	−	1.09272i	0.493365	−	0.0379062i
$832$	−112.340	−	112.340i	−3.89468	−	3.89468i
$833$	10.5853	−	2.44507i	0.366759	−	0.0847167i
$834$	−18.9026	−	6.73333i	−0.654544	−	0.233156i
$835$	26.5254	−	22.4314i	0.917948	−	0.776270i
$836$	8.41237	−	18.8945i	0.290948	−	0.653479i
$837$	−0.886293	+	27.9004i	−0.0306348	+	0.964380i
$838$	−16.9135	+	44.0613i	−0.584268	+	1.52207i
$839$	−4.02561	+	2.92478i	−0.138979	+	0.100974i	−0.655103	−	0.755540i	$-0.727375\pi$
$839$	−4.02561	+	2.92478i	−0.138979	+	0.100974i	0.516123	+	0.856514i	$0.327375\pi$
$840$	88.7619	+	26.0962i	3.06258	+	0.900404i
$841$	9.26891	+	6.73426i	0.319618	+	0.232216i
$842$	50.0009	−	32.4710i	1.72314	−	1.11902i
$843$	−0.198543	−	8.16172i	−0.00683820	−	0.281105i
$844$	−19.2732	−	17.3537i	−0.663410	−	0.597337i
$845$	5.33821	−	63.8355i	0.183640	−	2.19601i
$846$	14.1236	+	53.5046i	0.485578	+	1.83952i
$847$	−0.559996	−	16.0102i	−0.0192417	−	0.550116i
$848$	−35.6829	−	5.65162i	−1.22536	−	0.194077i
$849$	−11.8014	−	2.85648i	−0.405024	−	0.0980341i
$850$	20.7876	−	3.08432i	0.713008	−	0.105791i
$851$	3.99060	−	2.30397i	0.136796	−	0.0789792i
$852$	64.4031	+	26.8170i	2.20642	+	0.918735i
$853$	−20.8544	−	40.9290i	−0.714040	−	1.40138i	−0.907406	−	0.420255i	$-0.861941\pi$
$853$	−20.8544	−	40.9290i	−0.714040	−	1.40138i	0.193366	−	0.981127i	$-0.438059\pi$
$854$	−95.7605	+	29.2829i	−3.27686	+	1.00204i
$855$	4.38307	+	10.8448i	0.149898	+	0.370883i
$856$	−169.551	−	36.0393i	−5.79515	−	1.23180i
$857$	−27.3619	−	7.33160i	−0.934665	−	0.250443i	−0.240822	−	0.970569i	$-0.577417\pi$
$857$	−27.3619	−	7.33160i	−0.934665	−	0.250443i	−0.693843	+	0.720126i	$0.744084\pi$
$858$	22.3522	+	63.4954i	0.763091	+	2.16770i
$859$	9.69679	+	21.7793i	0.330850	+	0.743101i	1.00000		2.59609e-5i	$-8.26362e-6\pi$
$859$	9.69679	+	21.7793i	0.330850	+	0.743101i	−0.669150	+	0.743127i	$0.733342\pi$
$860$	−12.6645	+	8.61320i	−0.431857	+	0.293708i
$861$	2.11427	−	46.5018i	0.0720542	−	1.58478i
$862$	−11.6171	−	73.3475i	−0.395680	−	2.49823i
$863$	−24.9636	−	9.58264i	−0.849772	−	0.326197i	−0.105783	−	0.994389i	$-0.533735\pi$
$863$	−24.9636	−	9.58264i	−0.849772	−	0.326197i	−0.743989	+	0.668192i	$0.767068\pi$
$864$	−90.6132	+	42.6018i	−3.08272	+	1.44934i
$865$	23.3485	+	43.5087i	0.793874	+	1.47934i
$866$	−9.35461	−	21.0108i	−0.317882	−	0.713976i
$867$	4.65179	−	24.8411i	0.157983	−	0.843646i
$868$	−25.9339	−	71.2404i	−0.880255	−	2.41806i
$869$	−1.80782	−	5.56391i	−0.0613262	−	0.188743i
$870$	−43.6580	−	4.88676i	−1.48014	−	0.165677i
$871$	−32.4950	+	6.90703i	−1.10105	+	0.234036i
$872$	0.253191	−	0.389880i	0.00857413	−	0.0132030i
$873$	−32.5162	−	3.53984i	−1.10051	−	0.119805i
$874$		−	4.08188i		−	0.138072i
$875$	28.0783	+	9.30634i	0.949220	+	0.314612i
$876$	4.59248	−	1.35108i	0.155166	−	0.0456486i
$877$	7.61536	−	9.40418i	0.257152	−	0.317557i	−0.632177	−	0.774824i	$-0.717838\pi$
$877$	7.61536	−	9.40418i	0.257152	−	0.317557i	0.889329	+	0.457267i	$0.151172\pi$
$878$	6.84623	+	4.44599i	0.231049	+	0.150045i
$879$	24.7224	−	13.3637i	0.833866	−	0.450748i
$880$	63.1913	+	26.5375i	2.13018	+	0.894578i
$881$	15.7575	−	5.11991i	0.530882	−	0.172494i	−0.0312961	−	0.999510i	$-0.509963\pi$
$881$	15.7575	−	5.11991i	0.530882	−	0.172494i	0.562178	+	0.827016i	$0.309963\pi$
$882$	−50.3098	+	26.5181i	−1.69402	+	0.892911i
$883$	19.7421	+	10.0591i	0.664375	+	0.338516i	0.753446	−	0.657509i	$-0.228390\pi$
$883$	19.7421	+	10.0591i	0.664375	+	0.338516i	−0.0890714	+	0.996025i	$0.528390\pi$
$884$	48.8057	−	21.7297i	1.64151	−	0.730849i
$885$	−10.6424	+	10.4997i	−0.357742	+	0.352945i
$886$	−54.1513	−	24.1097i	−1.81925	−	0.809982i
$887$	−7.05319	+	18.3742i	−0.236823	+	0.616945i	−0.999557	−	0.0297675i	$-0.990523\pi$
$887$	−7.05319	+	18.3742i	−0.236823	+	0.616945i	0.762734	+	0.646713i	$0.223857\pi$
$888$	35.7494	+	75.3101i	1.19967	+	2.52724i
$889$	26.9803	+	31.0337i	0.904890	+	1.04084i
$890$	10.6794	+	15.7026i	0.357974	+	0.526352i
$891$	20.0131	+	0.148784i	0.670465	+	0.00498447i
$892$	139.724	−	7.32265i	4.67832	−	0.245180i
$893$	3.07391	−	11.4720i	0.102864	−	0.383895i
$894$	4.33383	+	56.4066i	0.144945	+	1.88652i
$895$	8.91014	−	46.7964i	0.297833	−	1.56423i
$896$	50.7535	−	54.4327i	1.69556	−	1.81847i
$897$	6.63801	+	7.02109i	0.221637	+	0.234427i
$898$	39.6753	+	32.1284i	1.32398	+	1.07214i
$899$	11.2504	+	19.4863i	0.375223	+	0.649906i
$900$	−73.5252	+	31.5534i	−2.45084	+	1.05178i
$901$	2.03397	−	3.52294i	0.0677613	−	0.117366i
$902$	9.56964	−	60.4203i	0.318634	−	2.01178i
$903$	1.18359	−	5.76432i	0.0393872	−	0.191825i
$904$	16.9222	+	5.49837i	0.562826	+	0.182873i
$905$	−37.7572	−	3.15743i	−1.25509	−	0.104956i
$906$	4.60360	+	2.20632i	0.152944	+	0.0733000i
$907$	10.1947	−	38.0470i	0.338508	−	1.26333i	−0.561508	−	0.827471i	$-0.689779\pi$
$907$	10.1947	−	38.0470i	0.338508	−	1.26333i	0.900016	−	0.435857i	$-0.143555\pi$
$908$	−33.1571	−	51.0574i	−1.10036	−	1.69440i
$909$	−14.2757	−	0.801380i	−0.473496	−	0.0265801i
$910$	103.274	+	5.00930i	3.42349	+	0.166057i
$911$	−0.0949069	−	0.130628i	−0.00314440	−	0.00432790i	0.807442	−	0.589947i	$-0.200851\pi$
$911$	−0.0949069	−	0.130628i	−0.00314440	−	0.00432790i	−0.810586	+	0.585619i	$0.800851\pi$
$912$	41.4937	+	3.34323i	1.37399	+	0.110706i
$913$	−2.74611	−	3.39116i	−0.0908829	−	0.112231i
$914$	62.8909	+	28.0008i	2.08025	+	0.926186i
$915$	29.7861	−	45.1958i	0.984697	−	1.49413i
$916$	−23.6873	−	17.2098i	−0.782650	−	0.568629i
$917$	−5.71439	+	4.46509i	−0.188706	+	0.147450i
$918$	−1.59209	−	21.7815i	−0.0525469	−	0.718896i
$919$	10.0225	−	47.1519i	0.330610	−	1.55540i	−0.427954	−	0.903800i	$-0.640766\pi$
$919$	10.0225	−	47.1519i	0.330610	−	1.55540i	0.758564	−	0.651598i	$-0.225901\pi$
$920$	17.4479	−	0.371511i	0.575239	−	0.0122484i
$921$	−10.3321	+	5.58506i	−0.340456	+	0.184034i
$922$	0.737826	−	14.0786i	0.0242990	−	0.463653i
$923$	48.1315	+	7.62329i	1.58427	+	0.250924i
$924$	−50.6094	+	19.8303i	−1.66493	+	0.652369i
$925$	10.6023	+	24.4542i	0.348602	+	0.804048i
$926$	−4.26898	−	2.46470i	−0.140288	−	0.0809950i
$927$	20.7315	+	15.1804i	0.680913	+	0.498590i
$928$	−43.9577	+	67.6890i	−1.44298	+	2.22200i
$929$	−20.9585	−	23.2768i	−0.687627	−	0.763687i	0.293729	−	0.955889i	$-0.405104\pi$
$929$	−20.9585	−	23.2768i	−0.687627	−	0.763687i	−0.981355	+	0.192202i	$0.938437\pi$
$930$	48.6059	+	28.5017i	1.59385	+	0.934609i
$931$	12.1984	+	0.424594i	0.399787	+	0.0139155i
$932$	−83.2713	+	83.2713i	−2.72764	+	2.72764i
$933$	−4.16491	−	3.57058i	−0.136353	−	0.116896i
$934$	105.951	+	11.1359i	3.46681	+	0.364377i
$935$	−5.33950	+	5.57184i	−0.174620	+	0.182218i
$936$	−136.256	+	109.502i	−4.45367	+	3.57919i
$937$	6.58020	+	41.5458i	0.214966	+	1.35724i	0.825120	+	0.564958i	$0.191108\pi$
$937$	6.58020	+	41.5458i	0.214966	+	1.35724i	−0.610154	+	0.792283i	$0.708892\pi$
$938$	−8.92504	−	35.7877i	−0.291413	−	1.16851i
$939$	−38.4533	−	29.6200i	−1.25488	−	0.966612i
$940$	78.9005	+	19.3509i	2.57345	+	0.631157i
$941$	4.82738	+	0.507378i	0.157368	+	0.0165401i	0.182885	−	0.983134i	$-0.441456\pi$
$941$	4.82738	+	0.507378i	0.157368	+	0.0165401i	−0.0255167	+	0.999674i	$0.508123\pi$
$942$	9.74543	+	27.6837i	0.317523	+	0.901982i
$943$	−2.27262	−	8.48153i	−0.0740066	−	0.276197i
$944$	16.4414	+	50.6016i	0.535123	+	1.64694i
$945$	11.8118	−	28.3810i	0.384238	−	0.923234i
$946$	2.38970	−	7.35473i	0.0776957	−	0.239123i
$947$	22.4549	+	1.17681i	0.729688	+	0.0382413i	0.413562	−	0.910476i	$-0.364285\pi$
$947$	22.4549	+	1.17681i	0.729688	+	0.0382413i	0.316126	+	0.948717i	$0.397618\pi$
$948$	19.3102	−	14.7603i	0.627166	−	0.479392i
$949$	2.89592	−	1.67196i	0.0940054	−	0.0542740i
$950$	23.4561	+	2.69754i	0.761016	+	0.0875197i
$951$	−14.9206	−	50.7171i	−0.483834	−	1.64462i
$952$	16.2543	+	33.3215i	0.526805	+	1.07995i
$953$	−10.0856	+	5.13890i	−0.326706	+	0.166465i	−0.609649	−	0.792672i	$-0.708689\pi$
$953$	−10.0856	+	5.13890i	−0.326706	+	0.166465i	0.282942	+	0.959137i	$0.408689\pi$
$954$	−5.58792	+	20.5486i	−0.180916	+	0.665284i
$955$	−22.0584	+	0.469682i	−0.713794	+	0.0151986i
$956$	−54.6788	−	49.2330i	−1.76844	−	1.59231i
$957$	13.7707	−	8.40353i	0.445143	−	0.271648i
$958$	22.6535	+	11.5426i	0.731903	+	0.372923i
$959$	0.270300	−	15.5360i	0.00872845	−	0.501682i
$960$	−5.63246	+	95.1785i	−0.181787	+	3.07187i
$961$	0.223693	+	2.12829i	0.00721589	+	0.0686546i
$962$	58.6305	+	72.4027i	1.89032	+	2.33436i
$963$	−18.0013	+	54.7095i	−0.580083	+	1.76299i
$964$	−68.7442	+	7.22530i	−2.21410	+	0.232711i
$965$	17.8540	−	23.0337i	0.574742	−	0.741481i
$966$	−7.53283	+	7.63788i	−0.242365	+	0.245745i
$967$	−22.6619	+	44.4765i	−0.728758	+	1.43027i	0.167106	+	0.985939i	$0.446558\pi$
$967$	−22.6619	+	44.4765i	−0.728758	+	1.43027i	−0.895864	+	0.444329i	$0.853442\pi$
$968$	52.8069	−	14.1496i	1.69728	−	0.454784i
$969$	−2.02579	+	4.22692i	−0.0650777	+	0.135788i
$970$	−37.6612	+	54.2274i	−1.20923	+	1.74114i
$971$	−11.9768	+	10.7839i	−0.384353	+	0.346073i	−0.838546	−	0.544830i	$-0.816594\pi$
$971$	−11.9768	+	10.7839i	−0.384353	+	0.346073i	0.454194	+	0.890903i	$0.349927\pi$
$972$	27.0260	+	78.6339i	0.866861	+	2.52218i
$973$	0.788883	−	11.2908i	0.0252904	−	0.361965i
$974$	20.2712			0.649530
$975$	−44.7327	+	33.5047i	−1.43259	+	1.07301i
$976$	−96.3179	−	166.827i	−3.08306	−	5.34002i
$977$	35.1253	−	13.4833i	1.12376	−	0.431370i	0.275683	−	0.961249i	$-0.411096\pi$
$977$	35.1253	−	13.4833i	1.12376	−	0.431370i	0.848073	+	0.529879i	$0.177763\pi$
$978$	−0.321140	−	1.34868i	−0.0102689	−	0.0431261i
$979$	−6.63225	−	2.15495i	−0.211968	−	0.0688725i
$980$	−1.12740	+	83.4825i	−0.0360135	+	2.66675i
$981$	−0.119679	−	0.0976526i	−0.00382104	−	0.00311781i
$982$	−11.4353	+	3.06408i	−0.364915	+	0.0977788i
$983$	43.2105	−	2.26456i	1.37820	−	0.0722284i	0.651221	−	0.758888i	$-0.274257\pi$
$983$	43.2105	−	2.26456i	1.37820	−	0.0722284i	0.726979	+	0.686660i	$0.240924\pi$
$984$	156.250	−	28.6589i	4.98105	−	0.913612i
$985$	−58.0140	+	4.28043i	−1.84848	+	0.136386i
$986$	−10.3474	−	14.2420i	−0.329530	−	0.453559i
$987$	−26.9226	+	15.7933i	−0.856954	+	0.502707i
$988$	59.2839	−	9.38964i	1.88607	−	0.298724i
$989$	−0.116028	−	1.10393i	−0.00368947	−	0.0351029i
$990$	19.5812	−	35.3353i	0.622330	−	1.12303i
$991$	−2.02404	+	19.2575i	−0.0642957	+	0.611733i	0.914171	+	0.405329i	$0.132843\pi$
$991$	−2.02404	+	19.2575i	−0.0642957	+	0.611733i	−0.978467	+	0.206404i	$0.933824\pi$
$992$	86.8189	−	56.3808i	2.75650	−	1.79009i
$993$	11.0344	−	20.2330i	0.350165	−	0.642075i
$994$	−6.59063	+	53.7016i	−0.209042	+	1.70331i
$995$	−0.408030	−	3.22094i	−0.0129354	−	0.102111i
$996$	9.50110	−	15.4399i	0.301054	−	0.489232i
$997$	−25.3409	−	16.4566i	−0.802556	−	0.521186i	0.0769722	−	0.997033i	$-0.475475\pi$
$997$	−25.3409	−	16.4566i	−0.802556	−	0.521186i	−0.879528	+	0.475848i	$0.842141\pi$
$998$	8.50499	+	22.1563i	0.269221	+	0.701344i
$999$	26.1616	−	9.10047i	0.827717	−	0.287926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bs.a.2.2	✓	1216
3.2	odd	2	inner	525.2.bs.a.2.75	yes	1216
7.4	even	3	inner	525.2.bs.a.452.75	yes	1216
21.11	odd	6	inner	525.2.bs.a.452.2	yes	1216
25.13	odd	20	inner	525.2.bs.a.338.2	yes	1216
75.38	even	20	inner	525.2.bs.a.338.75	yes	1216
175.88	odd	60	inner	525.2.bs.a.263.75	yes	1216
525.263	even	60	inner	525.2.bs.a.263.2	yes	1216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bs.a.2.2	✓	1216	1.1	even	1	trivial
525.2.bs.a.2.75	yes	1216	3.2	odd	2	inner
525.2.bs.a.263.2	yes	1216	525.263	even	60	inner
525.2.bs.a.263.75	yes	1216	175.88	odd	60	inner
525.2.bs.a.338.2	yes	1216	25.13	odd	20	inner
525.2.bs.a.338.75	yes	1216	75.38	even	20	inner
525.2.bs.a.452.2	yes	1216	21.11	odd	6	inner
525.2.bs.a.452.75	yes	1216	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.10462 - 1.70428i) q^{2} +(0.495015 - 1.65981i) q^{3} +(1.10900 + 5.21743i) q^{4} +(0.865799 - 2.06165i) q^{5} +(-3.87060 + 2.64961i) q^{6} +(-2.02686 - 1.70054i) q^{7} +(4.09903 - 8.04480i) q^{8} +(-2.50992 - 1.64326i) q^{9} +O(q^{10})\)	\(q+(-2.10462 - 1.70428i) q^{2} +(0.495015 - 1.65981i) q^{3} +(1.10900 + 5.21743i) q^{4} +(0.865799 - 2.06165i) q^{5} +(-3.87060 + 2.64961i) q^{6} +(-2.02686 - 1.70054i) q^{7} +(4.09903 - 8.04480i) q^{8} +(-2.50992 - 1.64326i) q^{9} +(-5.33581 + 2.86341i) q^{10} +(0.904477 - 2.03149i) q^{11} +(9.20890 + 0.741980i) q^{12} +(6.37405 - 1.00955i) q^{13} +(1.36755 + 7.03333i) q^{14} +(-2.99336 - 2.45761i) q^{15} +(-12.5918 + 5.60624i) q^{16} +(-0.0812255 - 1.54988i) q^{17} +(2.48184 + 7.73604i) q^{18} +(0.362533 - 1.70558i) q^{19} +(11.7167 + 2.23088i) q^{20} +(-3.82590 + 2.52240i) q^{21} +(-5.36581 + 2.73402i) q^{22} +(-0.543993 + 0.671775i) q^{23} +(-11.3237 - 10.7859i) q^{24} +(-3.50078 - 3.56995i) q^{25} +(-15.1355 - 8.73848i) q^{26} +(-3.96994 + 3.35255i) q^{27} +(6.62467 - 12.4609i) q^{28} +(-1.29430 + 3.98344i) q^{29} +(2.11140 + 10.2738i) q^{30} +(3.59467 - 3.99228i) q^{31} +(18.6131 + 4.98736i) q^{32} +(-2.92415 - 2.50687i) q^{33} +(-2.47048 + 3.40032i) q^{34} +(-5.26077 + 2.70634i) q^{35} +(5.79008 - 14.9177i) q^{36} +(-4.97666 - 1.91036i) q^{37} +(-3.66979 + 2.97174i) q^{38} +(1.47959 - 11.0794i) q^{39} +(-13.0366 - 15.4159i) q^{40} +(-5.97073 + 8.21801i) q^{41} +(12.3509 + 1.21172i) q^{42} +(-0.908010 + 0.908010i) q^{43} +(11.6022 + 2.46613i) q^{44} +(-5.56091 + 3.75184i) q^{45} +(2.28979 - 0.486710i) q^{46} +(6.80191 + 0.356473i) q^{47} +(3.07214 + 23.6752i) q^{48} +(1.21632 + 6.89352i) q^{49} +(1.28360 + 13.4797i) q^{50} +(-2.61270 - 0.632392i) q^{51} +(12.3361 + 32.1366i) q^{52} +(2.19823 + 1.42755i) q^{53} +(14.0689 - 0.289920i) q^{54} +(-3.40512 - 3.62357i) q^{55} +(-21.9887 + 9.33511i) q^{56} +(-2.65148 - 1.44602i) q^{57} +(9.51291 - 6.17776i) q^{58} +(0.403491 - 3.83896i) q^{59} +(9.50276 - 18.3431i) q^{60} +(1.46088 + 13.8993i) q^{61} +(-14.3694 + 2.27589i) q^{62} +(2.29283 + 7.59888i) q^{63} +(-14.4701 - 19.9164i) q^{64} +(3.43731 - 14.0151i) q^{65} +(1.88179 + 10.2596i) q^{66} +(-5.14069 + 0.269412i) q^{67} +(7.99629 - 2.14260i) q^{68} +(0.845733 + 1.23546i) q^{69} +(15.6843 + 3.27003i) q^{70} +(7.18159 + 2.33344i) q^{71} +(-23.5079 + 13.4560i) q^{72} +(0.483739 - 0.185690i) q^{73} +(7.21816 + 12.5022i) q^{74} +(-7.65836 + 4.04345i) q^{75} +9.30081 q^{76} +(-5.28788 + 2.57944i) q^{77} +(-21.9965 + 20.7963i) q^{78} +(1.95507 - 1.76035i) q^{79} +(0.656107 + 30.8138i) q^{80} +(3.59941 + 8.24890i) q^{81} +(26.5719 - 7.11992i) q^{82} +(0.890858 - 1.74841i) q^{83} +(-17.4034 - 17.1640i) q^{84} +(-3.26562 - 1.17442i) q^{85} +(3.45852 - 0.363505i) q^{86} +(5.97104 + 4.12015i) q^{87} +(-12.6354 - 15.6035i) q^{88} +(-0.327797 - 3.11878i) q^{89} +(18.0978 + 1.58118i) q^{90} +(-14.6361 - 8.79312i) q^{91} +(-4.10823 - 2.09325i) q^{92} +(-4.84701 - 7.94270i) q^{93} +(-13.7079 - 12.3426i) q^{94} +(-3.20243 - 2.22411i) q^{95} +(17.4918 - 28.4253i) q^{96} +(9.71444 - 4.94976i) q^{97} +(9.18863 - 16.5812i) q^{98} +(-5.60842 + 3.61259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1216 q - 8 q^{3} - 20 q^{4} - 24 q^{6} - 28 q^{7} - 10 q^{9}+O(q^{10}) \) 1216 * q - 8 * q^3 - 20 * q^4 - 24 * q^6 - 28 * q^7 - 10 * q^9	\( 1216 q - 8 q^{3} - 20 q^{4} - 24 q^{6} - 28 q^{7} - 10 q^{9} - 12 q^{10} - 64 q^{13} - 44 q^{15} - 140 q^{16} - 24 q^{18} - 20 q^{19} - 12 q^{21} + 8 q^{22} - 24 q^{25} - 80 q^{27} - 40 q^{28} - 50 q^{30} - 12 q^{31} - 6 q^{33} - 80 q^{34} + 8 q^{36} - 24 q^{37} - 50 q^{39} - 4 q^{40} - 34 q^{42} - 96 q^{43} + 30 q^{45} - 12 q^{46} - 44 q^{48} - 16 q^{51} - 136 q^{52} - 10 q^{54} - 40 q^{55} - 112 q^{57} - 76 q^{58} - 60 q^{60} - 12 q^{61} - 14 q^{63} - 80 q^{64} - 30 q^{66} - 32 q^{67} + 100 q^{69} - 100 q^{70} + 24 q^{72} - 72 q^{73} - 96 q^{75} - 64 q^{76} + 20 q^{78} - 20 q^{79} - 6 q^{81} - 204 q^{82} + 100 q^{84} - 56 q^{85} + 36 q^{87} - 140 q^{88} + 164 q^{90} - 24 q^{91} + 34 q^{93} - 20 q^{94} - 30 q^{96} - 240 q^{97}+O(q^{100}) \) 1216 * q - 8 * q^3 - 20 * q^4 - 24 * q^6 - 28 * q^7 - 10 * q^9 - 12 * q^10 - 64 * q^13 - 44 * q^15 - 140 * q^16 - 24 * q^18 - 20 * q^19 - 12 * q^21 + 8 * q^22 - 24 * q^25 - 80 * q^27 - 40 * q^28 - 50 * q^30 - 12 * q^31 - 6 * q^33 - 80 * q^34 + 8 * q^36 - 24 * q^37 - 50 * q^39 - 4 * q^40 - 34 * q^42 - 96 * q^43 + 30 * q^45 - 12 * q^46 - 44 * q^48 - 16 * q^51 - 136 * q^52 - 10 * q^54 - 40 * q^55 - 112 * q^57 - 76 * q^58 - 60 * q^60 - 12 * q^61 - 14 * q^63 - 80 * q^64 - 30 * q^66 - 32 * q^67 + 100 * q^69 - 100 * q^70 + 24 * q^72 - 72 * q^73 - 96 * q^75 - 64 * q^76 + 20 * q^78 - 20 * q^79 - 6 * q^81 - 204 * q^82 + 100 * q^84 - 56 * q^85 + 36 * q^87 - 140 * q^88 + 164 * q^90 - 24 * q^91 + 34 * q^93 - 20 * q^94 - 30 * q^96 - 240 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more