LMFDB - Embedded newform 360.2.bo.a.43.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(43,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 8, 9]))

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

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

chi := DirichletCharacter("360.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bo (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$68$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			43.20
Character	$\chi$	$=$	360.43
Dual form			360.2.bo.a.67.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.771662 - 1.18513i) q^{2} +(1.04238 + 1.38327i) q^{3} +(-0.809074 + 1.82904i) q^{4} +(2.10881 + 0.743585i) q^{5} +(0.834993 - 2.30278i) q^{6} +(3.18343 - 0.852996i) q^{7} +(2.79199 - 0.452544i) q^{8} +(-0.826881 + 2.88379i) q^{9} +O(q^{10})$	\(q+(-0.771662 - 1.18513i) q^{2} +(1.04238 + 1.38327i) q^{3} +(-0.809074 + 1.82904i) q^{4} +(2.10881 + 0.743585i) q^{5} +(0.834993 - 2.30278i) q^{6} +(3.18343 - 0.852996i) q^{7} +(2.79199 - 0.452544i) q^{8} +(-0.826881 + 2.88379i) q^{9} +(-0.746043 - 3.07301i) q^{10} +(-2.78642 + 4.82621i) q^{11} +(-3.37343 + 0.787391i) q^{12} +(-4.01090 - 1.07472i) q^{13} +(-3.46744 - 3.11455i) q^{14} +(1.16960 + 3.69216i) q^{15} +(-2.69080 - 2.95966i) q^{16} +(-0.987358 + 0.987358i) q^{17} +(4.05575 - 1.24535i) q^{18} -5.43586i q^{19} +(-3.06623 + 3.25549i) q^{20} +(4.49827 + 3.51439i) q^{21} +(7.86987 - 0.421938i) q^{22} +(4.16761 + 1.11671i) q^{23} +(3.53631 + 3.39036i) q^{24} +(3.89416 + 3.13616i) q^{25} +(1.82138 + 5.58276i) q^{26} +(-4.85100 + 1.86221i) q^{27} +(-1.01546 + 6.51276i) q^{28} +(0.793492 - 1.37437i) q^{29} +(3.47315 - 4.23523i) q^{30} +(6.30787 - 3.64185i) q^{31} +(-1.43121 + 5.47281i) q^{32} +(-9.58048 + 1.17639i) q^{33} +(1.93206 + 0.408242i) q^{34} +(7.34752 + 0.568341i) q^{35} +(-4.60557 - 3.84561i) q^{36} +(-0.0362471 - 0.0362471i) q^{37} +(-6.44221 + 4.19465i) q^{38} +(-2.69426 - 6.66842i) q^{39} +(6.22428 + 1.12175i) q^{40} +(-2.56637 - 4.44508i) q^{41} +(0.693876 - 8.04297i) q^{42} +(5.06217 - 1.35641i) q^{43} +(-6.57294 - 9.00124i) q^{44} +(-3.88808 + 5.46652i) q^{45} +(-1.89254 - 5.80089i) q^{46} +(2.67633 - 0.717121i) q^{47} +(1.28918 - 6.80720i) q^{48} +(3.34442 - 1.93090i) q^{49} +(0.711786 - 7.03515i) q^{50} +(-2.39499 - 0.336581i) q^{51} +(5.21082 - 6.46657i) q^{52} +(-4.30974 + 4.30974i) q^{53} +(5.95030 + 4.31207i) q^{54} +(-9.46473 + 8.10563i) q^{55} +(8.50207 - 3.82220i) q^{56} +(7.51927 - 5.66624i) q^{57} +(-2.24112 + 0.120156i) q^{58} +(-4.53169 + 2.61637i) q^{59} +(-7.69941 - 0.847973i) q^{60} +(-8.26202 - 4.77008i) q^{61} +(-9.18361 - 4.66538i) q^{62} +(-0.172450 + 9.88567i) q^{63} +(7.59041 - 2.52699i) q^{64} +(-7.65907 - 5.24882i) q^{65} +(8.78707 + 10.4464i) q^{66} +(9.45870 + 2.53445i) q^{67} +(-1.00707 - 2.60477i) q^{68} +(2.79953 + 6.92897i) q^{69} +(-4.99624 - 9.14634i) q^{70} -15.3962i q^{71} +(-1.00360 + 8.42572i) q^{72} +(-1.45336 - 1.45336i) q^{73} +(-0.0149871 + 0.0709282i) q^{74} +(-0.278960 + 8.65576i) q^{75} +(9.94242 + 4.39801i) q^{76} +(-4.75361 + 17.7407i) q^{77} +(-5.82390 + 8.33882i) q^{78} +(5.36470 - 9.29194i) q^{79} +(-3.47362 - 8.24221i) q^{80} +(-7.63253 - 4.76911i) q^{81} +(-3.28763 + 6.47158i) q^{82} +(0.730632 - 0.195772i) q^{83} +(-10.0674 + 5.38412i) q^{84} +(-2.81633 + 1.34797i) q^{85} +(-5.51381 - 4.95266i) q^{86} +(2.72825 - 0.335001i) q^{87} +(-5.59557 + 14.7357i) q^{88} +5.95337i q^{89} +(9.47883 + 0.389585i) q^{90} -13.6851 q^{91} +(-5.41441 + 6.71923i) q^{92} +(11.6129 + 4.92930i) q^{93} +(-2.91511 - 2.61843i) q^{94} +(4.04202 - 11.4632i) q^{95} +(-9.06225 + 3.72501i) q^{96} +(-0.404188 - 1.50845i) q^{97} +(-4.86913 - 2.47357i) q^{98} +(-11.6138 - 12.0262i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.771662	−	1.18513i	−0.545648	−	0.838015i
$2$	−0.771662	−	1.18513i	−0.545648	−	0.838015i
$3$	1.04238	+	1.38327i	0.601819	+	0.798632i
$3$	1.04238	+	1.38327i	0.601819	+	0.798632i
$4$	−0.809074	+	1.82904i	−0.404537	+	0.914522i
$5$	2.10881	+	0.743585i	0.943089	+	0.332541i
$5$	2.10881	+	0.743585i	0.943089	+	0.332541i
$6$	0.834993	−	2.30278i	0.340884	−	0.940105i
$7$	3.18343	−	0.852996i	1.20322	−	0.322402i	0.399123	−	0.916898i	$-0.369315\pi$
$7$	3.18343	−	0.852996i	1.20322	−	0.322402i	0.804099	+	0.594495i	$0.202648\pi$
$8$	2.79199	−	0.452544i	0.987117	−	0.159998i
$9$	−0.826881	+	2.88379i	−0.275627	+	0.961265i
$10$	−0.746043	−	3.07301i	−0.235919	−	0.971773i
$11$	−2.78642	+	4.82621i	−0.840136	+	1.45516i	0.0496429	+	0.998767i	$0.484192\pi$
$11$	−2.78642	+	4.82621i	−0.840136	+	1.45516i	−0.889779	+	0.456392i	$0.849142\pi$
$12$	−3.37343	+	0.787391i	−0.973825	+	0.227300i
$13$	−4.01090	−	1.07472i	−1.11242	−	0.298073i	−0.344609	−	0.938746i	$-0.611988\pi$
$13$	−4.01090	−	1.07472i	−1.11242	−	0.298073i	−0.767813	+	0.640674i	$0.778655\pi$
$14$	−3.46744	−	3.11455i	−0.926713	−	0.832399i
$15$	1.16960	+	3.69216i	0.301991	+	0.953311i
$16$	−2.69080	−	2.95966i	−0.672699	−	0.739916i
$17$	−0.987358	+	0.987358i	−0.239469	+	0.239469i	−0.816630	−	0.577161i	$-0.804161\pi$
$17$	−0.987358	+	0.987358i	−0.239469	+	0.239469i	0.577161	+	0.816630i	$0.304161\pi$
$18$	4.05575	−	1.24535i	0.955949	−	0.293532i
$19$		−	5.43586i		−	1.24707i	−0.781795	−	0.623536i	$-0.785696\pi$
$19$		−	5.43586i		−	1.24707i	0.781795	−	0.623536i	$-0.214304\pi$
$20$	−3.06623	+	3.25549i	−0.685631	+	0.727949i
$21$	4.49827	+	3.51439i	0.981603	+	0.766904i
$22$	7.86987	−	0.421938i	1.67786	−	0.0899574i
$23$	4.16761	+	1.11671i	0.869006	+	0.232850i	0.665658	−	0.746257i	$-0.268151\pi$
$23$	4.16761	+	1.11671i	0.869006	+	0.232850i	0.203348	+	0.979106i	$0.434818\pi$
$24$	3.53631	+	3.39036i	0.721846	+	0.692054i
$25$	3.89416	+	3.13616i	0.778832	+	0.627232i
$26$	1.82138	+	5.58276i	0.357201	+	1.09487i
$27$	−4.85100	+	1.86221i	−0.933575	+	0.358383i
$28$	−1.01546	+	6.51276i	−0.191904	+	1.23080i
$29$	0.793492	−	1.37437i	0.147348	−	0.255214i	−0.782899	−	0.622149i	$-0.786260\pi$
$29$	0.793492	−	1.37437i	0.147348	−	0.255214i	0.930246	+	0.366935i	$0.119593\pi$
$30$	3.47315	−	4.23523i	0.634108	−	0.773244i
$31$	6.30787	−	3.64185i	1.13293	−	0.654095i	0.188257	−	0.982120i	$-0.439716\pi$
$31$	6.30787	−	3.64185i	1.13293	−	0.654095i	0.944669	+	0.328024i	$0.106383\pi$
$32$	−1.43121	+	5.47281i	−0.253004	+	0.967465i
$33$	−9.58048	+	1.17639i	−1.66775	+	0.204783i
$34$	1.93206	+	0.408242i	0.331345	+	0.0700130i
$35$	7.34752	+	0.568341i	1.24196	+	0.0960672i
$36$	−4.60557	−	3.84561i	−0.767596	−	0.640934i
$37$	−0.0362471	−	0.0362471i	−0.00595899	−	0.00595899i	0.704121	−	0.710080i	$-0.251341\pi$
$37$	−0.0362471	−	0.0362471i	−0.00595899	−	0.00595899i	−0.710080	+	0.704121i	$0.751341\pi$
$38$	−6.44221	+	4.19465i	−1.04506	+	0.680461i
$39$	−2.69426	−	6.66842i	−0.431427	−	1.06780i
$40$	6.22428	+	1.12175i	0.984145	+	0.177365i
$41$	−2.56637	−	4.44508i	−0.400799	−	0.694204i	0.593023	−	0.805185i	$-0.297934\pi$
$41$	−2.56637	−	4.44508i	−0.400799	−	0.694204i	−0.993823	+	0.110981i	$0.964601\pi$
$42$	0.693876	−	8.04297i	0.107067	−	1.24106i
$43$	5.06217	−	1.35641i	0.771974	−	0.206850i	0.148731	−	0.988878i	$-0.452481\pi$
$43$	5.06217	−	1.35641i	0.771974	−	0.206850i	0.623243	+	0.782028i	$0.285815\pi$
$44$	−6.57294	−	9.00124i	−0.990907	−	1.35699i
$45$	−3.88808	+	5.46652i	−0.579601	+	0.814900i
$46$	−1.89254	−	5.80089i	−0.279040	−	0.855294i
$47$	2.67633	−	0.717121i	0.390383	−	0.104603i	−0.0582880	−	0.998300i	$-0.518564\pi$
$47$	2.67633	−	0.717121i	0.390383	−	0.104603i	0.448671	+	0.893697i	$0.351897\pi$
$48$	1.28918	−	6.80720i	0.186077	−	0.982535i
$49$	3.34442	−	1.93090i	0.477774	−	0.275843i
$50$	0.711786	−	7.03515i	0.100662	−	0.994921i
$51$	−2.39499	−	0.336581i	−0.335365	−	0.0471307i
$52$	5.21082	−	6.46657i	0.722610	−	0.896753i
$53$	−4.30974	+	4.30974i	−0.591989	+	0.591989i	−0.938168	−	0.346179i	$-0.887479\pi$
$53$	−4.30974	+	4.30974i	−0.591989	+	0.591989i	0.346179	+	0.938168i	$0.387479\pi$
$54$	5.95030	+	4.31207i	0.809733	+	0.586799i
$55$	−9.46473	+	8.10563i	−1.27622	+	1.09296i
$56$	8.50207	−	3.82220i	1.13614	−	0.510762i
$57$	7.51927	−	5.66624i	0.995951	−	0.750511i
$58$	−2.24112	+	0.120156i	−0.294273	+	0.0157772i
$59$	−4.53169	+	2.61637i	−0.589975	+	0.340622i	−0.765088	−	0.643926i	$-0.777304\pi$
$59$	−4.53169	+	2.61637i	−0.589975	+	0.340622i	0.175112	+	0.984548i	$0.443971\pi$
$60$	−7.69941	−	0.847973i	−0.993990	−	0.109473i
$61$	−8.26202	−	4.77008i	−1.05784	−	0.610746i	−0.133008	−	0.991115i	$-0.542464\pi$
$61$	−8.26202	−	4.77008i	−1.05784	−	0.610746i	−0.924835	+	0.380369i	$0.875797\pi$
$62$	−9.18361	−	4.66538i	−1.16632	−	0.592503i
$63$	−0.172450	+	9.88567i	−0.0217266	+	1.24548i
$64$	7.59041	−	2.52699i	0.948801	−	0.315874i
$65$	−7.65907	−	5.24882i	−0.949991	−	0.651035i
$66$	8.78707	+	10.4464i	1.08161	+	1.28586i
$67$	9.45870	+	2.53445i	1.15556	+	0.309632i	0.785193	−	0.619252i	$-0.212564\pi$
$67$	9.45870	+	2.53445i	1.15556	+	0.309632i	0.370371	+	0.928884i	$0.379231\pi$
$68$	−1.00707	−	2.60477i	−0.122126	−	0.315874i
$69$	2.79953	+	6.92897i	0.337024	+	0.834150i
$70$	−4.99624	−	9.14634i	−0.597165	−	1.09320i
$71$		−	15.3962i		−	1.82719i	−0.406623	−	0.913596i	$-0.633294\pi$
$71$		−	15.3962i		−	1.82719i	0.406623	−	0.913596i	$-0.366706\pi$
$72$	−1.00360	+	8.42572i	−0.118275	+	0.992981i
$73$	−1.45336	−	1.45336i	−0.170103	−	0.170103i	0.616922	−	0.787024i	$-0.288379\pi$
$73$	−1.45336	−	1.45336i	−0.170103	−	0.170103i	−0.787024	+	0.616922i	$0.788379\pi$
$74$	−0.0149871	+	0.0709282i	−0.00174221	+	0.00824523i
$75$	−0.278960	+	8.65576i	−0.0322115	+	0.999481i
$76$	9.94242	+	4.39801i	1.14047	+	0.504487i
$77$	−4.75361	+	17.7407i	−0.541724	+	2.02174i
$78$	−5.82390	+	8.33882i	−0.659427	+	0.944186i
$79$	5.36470	−	9.29194i	0.603576	−	1.04542i	−0.388699	−	0.921365i	$-0.627075\pi$
$79$	5.36470	−	9.29194i	0.603576	−	1.04542i	0.992275	−	0.124060i	$-0.0395914\pi$
$80$	−3.47362	−	8.24221i	−0.388362	−	0.921507i
$81$	−7.63253	−	4.76911i	−0.848059	−	0.529901i
$82$	−3.28763	+	6.47158i	−0.363058	+	0.714667i
$83$	0.730632	−	0.195772i	0.0801973	−	0.0214888i	−0.218497	−	0.975838i	$-0.570115\pi$
$83$	0.730632	−	0.195772i	0.0801973	−	0.0214888i	0.298695	+	0.954349i	$0.403449\pi$
$84$	−10.0674	+	5.38412i	−1.09845	+	0.587456i
$85$	−2.81633	+	1.34797i	−0.305474	+	0.146207i
$86$	−5.51381	−	4.95266i	−0.594569	−	0.534059i
$87$	2.72825	−	0.335001i	0.292499	−	0.0359159i
$88$	−5.59557	+	14.7357i	−0.596490	+	1.57083i
$89$			5.95337i			0.631056i	0.948916	+	0.315528i	$0.102182\pi$
$89$			5.95337i			0.631056i	−0.948916	+	0.315528i	$0.897818\pi$
$90$	9.47883	+	0.389585i	0.999156	+	0.0410658i
$91$	−13.6851			−1.43459
$92$	−5.41441	+	6.71923i	−0.564491	+	0.700529i
$93$	11.6129	+	4.92930i	1.20420	+	0.511144i
$94$	−2.91511	−	2.61843i	−0.300670	−	0.270070i
$95$	4.04202	−	11.4632i	0.414703	−	1.17610i
$96$	−9.06225	+	3.72501i	−0.924912	+	0.380182i
$97$	−0.404188	−	1.50845i	−0.0410391	−	0.153160i	0.942366	−	0.334584i	$-0.108596\pi$
$97$	−0.404188	−	1.50845i	−0.0410391	−	0.153160i	−0.983405	+	0.181424i	$0.941929\pi$
$98$	−4.86913	−	2.47357i	−0.491857	−	0.249869i
$99$	−11.6138	−	12.0262i	−1.16723	−	1.20867i
$100$	−8.88684	+	4.58520i	−0.888684	+	0.458520i
$101$	1.96348	+	1.13362i	0.195374	+	0.112799i	0.594496	−	0.804099i	$-0.297352\pi$
$101$	1.96348	+	1.13362i	0.195374	+	0.112799i	−0.399122	+	0.916898i	$0.630685\pi$
$102$	1.44923	+	3.09810i	0.143495	+	0.306758i
$103$	−15.7894	−	4.23076i	−1.55578	−	0.416869i	−0.624453	−	0.781063i	$-0.714678\pi$
$103$	−15.7894	−	4.23076i	−1.55578	−	0.416869i	−0.931323	+	0.364194i	$0.881345\pi$
$104$	−11.6847	−	1.18549i	−1.14578	−	0.116247i
$105$	6.87275	+	10.7560i	0.670711	+	1.04968i
$106$	8.43328	+	1.78195i	0.819113	+	0.173078i
$107$	10.0440	−	10.0440i	0.970985	−	0.970985i	−0.0286053	−	0.999591i	$-0.509107\pi$
$107$	10.0440	−	10.0440i	0.970985	−	0.970985i	0.999591	+	0.0286053i	$0.00910660\pi$
$108$	0.518751	−	10.3793i	0.0499169	−	0.998753i
$109$	−1.63092			−0.156214			−0.0781070	−	0.996945i	$-0.524888\pi$
$109$	−1.63092			−0.156214			−0.0781070	+	0.996945i	$0.524888\pi$
$110$	16.9098	+	4.96214i	1.61229	+	0.473121i
$111$	0.0123563	−	0.0879230i	0.00117281	−	0.00834528i
$112$	−11.0905	−	7.12663i	−1.04796	−	0.673403i
$113$	−1.64128	+	6.12533i	−0.154398	+	0.576222i	0.844758	+	0.535149i	$0.179744\pi$
$113$	−1.64128	+	6.12533i	−0.154398	+	0.576222i	−0.999156	+	0.0410734i	$0.986922\pi$
$114$	−12.5176	−	4.53890i	−1.17238	−	0.425107i
$115$	7.95833	+	5.45390i	0.742118	+	0.508578i
$116$	1.87179	+	2.56330i	0.173791	+	0.237996i
$117$	6.41579	−	10.6779i	0.593140	−	0.987175i
$118$	6.59768	+	3.35169i	0.607365	+	0.308548i
$119$	−2.30097	+	3.98539i	−0.210929	+	0.365340i
$120$	4.93639	+	9.77917i	0.450628	+	0.892712i
$121$	−10.0282	−	17.3694i	−0.911658	−	1.57904i
$122$	0.722317	+	13.4725i	0.0653955	+	1.21974i
$123$	3.47362	−	8.18345i	0.313205	−	0.737877i
$124$	1.55756	+	14.4839i	0.139873	+	1.30069i
$125$	5.88005	+	9.50921i	0.525927	+	0.850530i
$126$	11.8489	−	7.42402i	1.05558	−	0.661385i
$127$	−3.00043	−	3.00043i	−0.266246	−	0.266246i	0.561340	−	0.827585i	$-0.310286\pi$
$127$	−3.00043	−	3.00043i	−0.266246	−	0.266246i	−0.827585	+	0.561340i	$0.810286\pi$
$128$	−8.85205	−	7.04565i	−0.782418	−	0.622753i
$129$	7.15299	+	5.58847i	0.629786	+	0.492037i
$130$	−0.310319	+	13.1273i	−0.0272167	+	1.15134i
$131$	−0.578309	−	1.00166i	−0.0505271	−	0.0875155i	0.839656	−	0.543119i	$-0.182757\pi$
$131$	−0.578309	−	1.00166i	−0.0505271	−	0.0875155i	−0.890183	+	0.455604i	$0.849423\pi$
$132$	5.59966	−	18.4749i	0.487388	−	1.60803i
$133$	−4.63677	−	17.3046i	−0.402059	−	1.50050i
$134$	−4.29526	−	13.1655i	−0.371054	−	1.13733i
$135$	−11.6145	+	0.319922i	−0.999621	+	0.0275345i
$136$	−2.30987	+	3.20351i	−0.198070	+	0.274699i
$137$	0.707270	+	2.63957i	0.0604262	+	0.225514i	0.989535	−	0.144293i	$-0.0460907\pi$
$137$	0.707270	+	2.63957i	0.0604262	+	0.225514i	−0.929109	+	0.369806i	$0.879424\pi$
$138$	6.05145	−	8.66463i	0.515134	−	0.737583i
$139$	−11.2157	+	6.47537i	−0.951301	+	0.549234i	−0.893485	−	0.449093i	$-0.851747\pi$
$139$	−11.2157	+	6.47537i	−0.951301	+	0.549234i	−0.0578162	+	0.998327i	$0.518414\pi$
$140$	−6.98421	+	12.9791i	−0.590273	+	1.09693i
$141$	3.78173	+	2.95458i	0.318479	+	0.248821i
$142$	−18.2465	+	11.8807i	−1.53121	+	0.997003i
$143$	16.3628	−	16.3628i	1.36833	−	1.36833i
$144$	10.7600	−	5.31241i	0.896669	−	0.442701i
$145$	2.69529	−	2.30825i	0.223831	−	0.191690i
$146$	−0.600919	+	2.84392i	−0.0497324	+	0.235365i
$147$	6.15712	+	2.61350i	0.507831	+	0.215558i
$148$	0.0956242	−	0.0369709i	0.00786026	−	0.00303899i
$149$	−0.976168	−	1.69077i	−0.0799708	−	0.138513i	0.823266	−	0.567655i	$-0.192149\pi$
$149$	−0.976168	−	1.69077i	−0.0799708	−	0.138513i	−0.903237	+	0.429142i	$0.858816\pi$
$150$	10.4735	−	6.34872i	0.855156	−	0.518371i
$151$	11.2225	+	6.47931i	0.913274	+	0.527279i	0.881483	−	0.472216i	$-0.156546\pi$
$151$	11.2225	+	6.47931i	0.913274	+	0.527279i	0.0317907	+	0.999495i	$0.489879\pi$
$152$	−2.45996	−	15.1769i	−0.199529	−	1.23101i
$153$	−2.03091	−	3.66376i	−0.164189	−	0.296198i
$154$	24.6932	−	8.05618i	1.98984	−	0.649185i
$155$	16.0101	−	2.98953i	1.28596	−	0.240125i
$156$	14.3767	+	0.467335i	1.15106	+	0.0374167i
$157$	−3.97857	+	14.8482i	−0.317525	+	1.18502i	0.604091	+	0.796915i	$0.293536\pi$
$157$	−3.97857	+	14.8482i	−0.317525	+	1.18502i	−0.921616	+	0.388103i	$0.873130\pi$
$158$	−15.1519	+	0.812359i	−1.20542	+	0.0646278i
$159$	−10.4539	−	1.46915i	−0.829052	−	0.116511i
$160$	−7.08764	+	10.4769i	−0.560327	+	0.828271i
$161$	14.2198			1.12068
$162$	0.237715	+	12.7257i	0.0186766	+	0.999826i
$163$	1.17090	+	1.17090i	0.0917118	+	0.0917118i	0.751474	−	0.659762i	$-0.229343\pi$
$163$	1.17090	+	1.17090i	0.0917118	+	0.0917118i	−0.659762	+	0.751474i	$0.729343\pi$
$164$	10.2066	−	1.09760i	0.797003	−	0.0857079i
$165$	−21.0781	−	4.64313i	−1.64093	−	0.361467i
$166$	−0.795817	−	0.714825i	−0.0617674	−	0.0554812i
$167$	−1.78504	+	6.66187i	−0.138131	+	0.515511i	0.861835	+	0.507189i	$0.169316\pi$
$167$	−1.78504	+	6.66187i	−0.138131	+	0.515511i	−0.999965	+	0.00832147i	$0.997351\pi$
$168$	14.1495	+	7.77649i	1.09166	+	0.599969i
$169$	3.67394	+	2.12115i	0.282610	+	0.163165i
$170$	3.77078	+	2.29755i	0.289205	+	0.176214i
$171$	15.6759	+	4.49481i	1.19877	+	0.343727i
$172$	−1.61475	+	10.3564i	−0.123124	+	0.789666i
$173$	−4.32279	−	16.1329i	−0.328655	−	1.22656i	−0.910586	−	0.413320i	$-0.864369\pi$
$173$	−4.32279	−	16.1329i	−0.328655	−	1.22656i	0.581930	−	0.813239i	$-0.302298\pi$
$174$	−2.50231	−	2.97482i	−0.189699	−	0.225521i
$175$	15.0719	+	6.66203i	1.13933	+	0.503602i
$176$	21.7817	−	4.73951i	1.64185	−	0.357254i
$177$	−8.34290	−	3.54130i	−0.627091	−	0.266180i
$178$	7.05553	−	4.59399i	0.528834	−	0.344334i
$179$			16.4461i			1.22924i	0.788824	+	0.614619i	$0.210690\pi$
$179$			16.4461i			1.22924i	−0.788824	+	0.614619i	$0.789310\pi$
$180$	−6.85275	−	11.5343i	−0.510774	−	0.859715i
$181$		−	21.3778i		−	1.58900i	−0.607266	−	0.794498i	$-0.707734\pi$
$181$		−	21.3778i		−	1.58900i	0.607266	−	0.794498i	$-0.292266\pi$
$182$	10.5603	+	16.2187i	0.782781	+	1.20221i
$183$	−2.01386	−	16.4009i	−0.148869	−	1.21239i
$184$	12.1413	+	1.23181i	0.895067	+	0.0908102i
$185$	−0.0494855	−	0.103391i	−0.00363824	−	0.00760147i
$186$	−3.11935	−	17.5665i	−0.228722	−	1.28804i
$187$	−2.01401	−	7.51639i	−0.147279	−	0.549653i
$188$	−0.853706	+	5.47533i	−0.0622629	+	0.399329i
$189$	−13.8543	+	10.0661i	−1.00775	+	0.732201i
$190$	−16.7045	+	4.05538i	−1.21187	+	0.294208i
$191$	−5.68097	−	3.27991i	−0.411061	−	0.237326i	0.280185	−	0.959946i	$-0.409604\pi$
$191$	−5.68097	−	3.27991i	−0.411061	−	0.237326i	−0.691245	+	0.722620i	$0.742938\pi$
$192$	11.4076	+	7.86550i	0.823274	+	0.567644i
$193$	−3.53323	+	13.1862i	−0.254327	+	0.949163i	0.714136	+	0.700007i	$0.246820\pi$
$193$	−3.53323	+	13.1862i	−0.254327	+	0.949163i	−0.968463	+	0.249156i	$0.919847\pi$
$194$	−1.47582	+	1.64303i	−0.105957	+	0.117963i
$195$	−0.723140	−	16.0658i	−0.0517851	−	1.15050i
$196$	0.825817	+	7.67933i	0.0589869	+	0.548523i
$197$	−4.49027	−	4.49027i	−0.319918	−	0.319918i	0.528817	−	0.848736i	$-0.322636\pi$
$197$	−4.49027	−	4.49027i	−0.319918	−	0.319918i	−0.848736	+	0.528817i	$0.822636\pi$
$198$	−5.29067	+	23.0440i	−0.375992	+	1.63766i
$199$	4.73952			0.335976			0.167988	−	0.985789i	$-0.446273\pi$
$199$	4.73952			0.335976			0.167988	+	0.985789i	$0.446273\pi$
$200$	12.2917	+	6.99385i	0.869155	+	0.494540i
$201$	6.35374	+	15.7258i	0.448158	+	1.10921i
$202$	−0.171660	−	3.20176i	−0.0120779	−	0.225275i
$203$	1.35369	−	5.05205i	0.0950105	−	0.354584i
$204$	2.55334	−	4.10822i	0.178770	−	0.287633i
$205$	−2.10669	−	11.2821i	−0.147137	−	0.787979i
$206$	7.17008	+	21.9772i	0.499563	+	1.53123i
$207$	−6.66647	+	11.0951i	−0.463352	+	0.771165i
$208$	7.61171	+	14.7627i	0.527777	+	1.02361i
$209$	26.2346	+	15.1466i	1.81469	+	1.04771i
$210$	7.44389	−	16.4451i	0.513677	−	1.13482i
$211$	−2.36287	−	4.09261i	−0.162667	−	0.281747i	0.773158	−	0.634214i	$-0.218676\pi$
$211$	−2.36287	−	4.09261i	−0.162667	−	0.281747i	−0.935824	+	0.352467i	$0.885343\pi$
$212$	−4.39580	−	11.3696i	−0.301905	−	0.780868i
$213$	21.2971	−	16.0487i	1.45925	−	1.09964i
$214$	−19.6539	−	4.15287i	−1.34352	−	0.283884i
$215$	11.6838	+	0.903756i	0.796826	+	0.0616357i
$216$	−12.7012	+	7.39456i	−0.864207	+	0.503136i
$217$	16.9741	−	16.9741i	1.15228	−	1.15228i
$218$	1.25852	+	1.93286i	0.0852378	+	0.130910i
$219$	0.495435	−	3.52534i	0.0334784	−	0.238220i
$220$	−7.16788	−	23.8695i	−0.483259	−	1.60928i
$221$	5.02132	−	2.89906i	0.337770	−	0.195012i
$222$	−0.113735	+	0.0532030i	−0.00763341	+	0.00357075i
$223$	5.29902	+	19.7762i	0.354849	+	1.32431i	0.880675	+	0.473722i	$0.157090\pi$
$223$	5.29902	+	19.7762i	0.354849	+	1.32431i	−0.525826	+	0.850592i	$0.676244\pi$
$224$	0.112152	+	18.6431i	0.00749346	+	1.24564i
$225$	−12.2641	+	8.63673i	−0.817603	+	0.575782i
$226$	8.52583	−	2.78155i	0.567130	−	0.185026i
$227$	1.15437	+	4.30818i	0.0766185	+	0.285944i	0.993595	−	0.112996i	$-0.0360448\pi$
$227$	1.15437	+	4.30818i	0.0766185	+	0.285944i	−0.916977	+	0.398940i	$0.869378\pi$
$228$	4.28014	+	18.3375i	0.283459	+	1.21443i
$229$	−0.169851	−	0.294191i	−0.0112241	−	0.0194407i	0.860359	−	0.509689i	$-0.170239\pi$
$229$	−0.169851	−	0.294191i	−0.0112241	−	0.0194407i	−0.871583	+	0.490248i	$0.836906\pi$
$230$	0.322443	−	13.6402i	0.0212613	−	0.899410i
$231$	−29.4953	+	11.9170i	−1.94065	+	0.784084i
$232$	1.59346	−	4.19631i	0.104616	−	0.275501i
$233$	−12.3777	−	12.3777i	−0.810892	−	0.810892i	0.173876	−	0.984768i	$-0.444371\pi$
$233$	−12.3777	−	12.3777i	−0.810892	−	0.810892i	−0.984768	+	0.173876i	$0.944371\pi$
$234$	−17.6056	+	0.636197i	−1.15091	+	0.0415895i
$235$	6.17712	+	0.477809i	0.402951	+	0.0311688i
$236$	−1.11898	−	10.4055i	−0.0728396	−	0.677340i
$237$	18.4453	−	2.26490i	1.19815	−	0.147121i
$238$	6.49878	−	0.348428i	0.421254	−	0.0225852i
$239$	−2.11283	−	3.65954i	−0.136668	−	0.236716i	0.789565	−	0.613666i	$-0.210306\pi$
$239$	−2.11283	−	3.65954i	−0.136668	−	0.236716i	−0.926233	+	0.376951i	$0.876973\pi$
$240$	7.78038	−	13.3965i	0.502221	−	0.864739i
$241$	11.9782	−	20.7469i	0.771587	−	1.33643i	−0.165107	−	0.986276i	$-0.552797\pi$
$241$	11.9782	−	20.7469i	0.771587	−	1.33643i	0.936693	−	0.350151i	$-0.113870\pi$
$242$	−12.8466	+	25.2881i	−0.825813	+	1.62558i
$243$	−1.35904	−	15.5291i	−0.0871823	−	0.996192i
$244$	15.4093	−	11.2522i	0.986477	−	0.720351i
$245$	8.48853	−	1.58504i	0.542312	−	0.101265i
$246$	−12.3789	+	2.19817i	−0.789251	+	0.140150i
$247$	−5.84200	+	21.8027i	−0.371718	+	1.38727i
$248$	15.9634	−	13.0226i	1.01368	−	0.826935i
$249$	1.03240	+	0.806593i	0.0654259	+	0.0511158i
$250$	6.73226	−	14.3065i	0.425785	−	0.904824i
$251$	−17.9319			−1.13185			−0.565925	−	0.824457i	$-0.691481\pi$
$251$	−17.9319			−1.13185			−0.565925	+	0.824457i	$0.691481\pi$
$252$	−17.9418	−	8.31366i	−1.13023	−	0.523711i
$253$	−17.0022	+	17.0022i	−1.06892	+	1.06892i
$254$	−1.24059	+	5.87123i	−0.0778414	+	0.368394i
$255$	−4.80030	−	2.49066i	−0.300606	−	0.155971i
$256$	−1.51922	+	15.9277i	−0.0949514	+	0.995482i
$257$	−9.08434	−	2.43414i	−0.566665	−	0.151838i	−0.0358986	−	0.999355i	$-0.511429\pi$
$257$	−9.08434	−	2.43414i	−0.566665	−	0.151838i	−0.530767	+	0.847518i	$0.678096\pi$
$258$	1.10338	−	12.7897i	0.0686933	−	0.796249i
$259$	−0.146309	−	0.0844714i	−0.00909118	−	0.00524880i
$260$	15.7971	−	9.76209i	0.979693	−	0.605419i
$261$	3.30727	+	3.42471i	0.204715	+	0.211984i
$262$	−0.740841	+	1.45832i	−0.0457693	+	0.0900951i
$263$	1.30694	+	4.87757i	0.0805894	+	0.300764i	0.994442	−	0.105281i	$-0.0335743\pi$
$263$	1.30694	+	4.87757i	0.0805894	+	0.300764i	−0.913853	+	0.406045i	$0.866908\pi$
$264$	−26.2162	+	7.62004i	−1.61350	+	0.468981i
$265$	−12.2931	+	5.88377i	−0.755159	+	0.361437i
$266$	−16.9303	+	18.8485i	−1.03806	+	1.15568i
$267$	−8.23513	+	6.20568i	−0.503982	+	0.379782i
$268$	−12.2884	+	15.2498i	−0.750634	+	0.931530i
$269$	−21.6071			−1.31741			−0.658705	−	0.752401i	$-0.728896\pi$
$269$	−21.6071			−1.31741			−0.658705	+	0.752401i	$0.728896\pi$
$270$	9.34166	+	13.5179i	0.568515	+	0.822673i
$271$			3.38395i			0.205561i	0.994704	+	0.102780i	$0.0327739\pi$
$271$			3.38395i			0.205561i	−0.994704	+	0.102780i	$0.967226\pi$
$272$	5.57903	+	0.265468i	0.338278	+	0.0160964i
$273$	−14.2651	−	18.9302i	−0.863364	−	1.14571i
$274$	2.58246	−	2.87506i	0.156012	−	0.173689i
$275$	−25.9865	+	10.0554i	−1.56705	+	0.606364i
$276$	−14.9384	−	0.485594i	−0.899187	−	0.0292294i
$277$	9.17830	−	2.45932i	0.551471	−	0.147766i	0.0276859	−	0.999617i	$-0.491186\pi$
$277$	9.17830	−	2.45932i	0.551471	−	0.147766i	0.523785	+	0.851851i	$0.324520\pi$
$278$	16.3289	+	8.29525i	0.979341	+	0.497516i
$279$	5.28648	+	21.2020i	0.316494	+	1.26933i
$280$	20.7714	−	1.73827i	1.24133	−	0.103882i
$281$	−11.0144	+	19.0775i	−0.657064	+	1.13807i	0.324308	+	0.945951i	$0.394869\pi$
$281$	−11.0144	+	19.0775i	−0.657064	+	1.13807i	−0.981372	+	0.192117i	$0.938465\pi$
$282$	0.583347	−	6.76179i	0.0347378	−	0.402659i
$283$	−5.40867	+	20.1854i	−0.321512	+	1.19990i	0.596260	+	0.802791i	$0.296653\pi$
$283$	−5.40867	+	20.1854i	−0.321512	+	1.19990i	−0.917772	+	0.397108i	$0.870014\pi$
$284$	28.1603	+	12.4567i	1.67101	+	0.739167i
$285$	20.0700	−	6.35780i	1.18885	−	0.376604i
$286$	−32.0187	−	6.76553i	−1.89331	−	0.400054i
$287$	−11.9615	−	11.9615i	−0.706063	−	0.706063i
$288$	−14.5990	−	8.65267i	−0.860255	−	0.509863i
$289$			15.0502i			0.885309i
$290$	−4.81544	−	1.41308i	−0.282772	−	0.0829786i
$291$	1.66528	−	2.13148i	0.0976204	−	0.124950i
$292$	3.83413	−	1.48238i	0.224375	−	0.0867497i
$293$	1.36685	+	0.366248i	0.0798525	+	0.0213964i	0.298524	−	0.954402i	$-0.403506\pi$
$293$	1.36685	+	0.366248i	0.0798525	+	0.0213964i	−0.218672	+	0.975799i	$0.570172\pi$
$294$	−1.65387	−	9.31374i	−0.0964557	−	0.543188i
$295$	−11.5020	+	2.14773i	−0.669670	+	0.125046i
$296$	−0.117605	−	0.0847982i	−0.00683565	−	0.00492879i
$297$	4.52946	−	28.6008i	0.262826	−	1.65959i
$298$	−1.25052	+	2.46159i	−0.0724404	+	0.142596i
$299$	−15.5157	−	8.95799i	−0.897296	−	0.518054i
$300$	−15.6061	−	7.51338i	−0.901016	−	0.433785i
$301$	14.9580	−	8.63603i	0.862167	−	0.497773i
$302$	−0.981140	−	18.3000i	−0.0564583	−	1.05305i
$303$	0.478598	+	3.89769i	0.0274947	+	0.223917i
$304$	−16.0883	+	14.6268i	−0.922728	+	0.838904i
$305$	−13.8761	−	16.2027i	−0.794541	−	0.927764i
$306$	−2.77487	+	5.23408i	−0.158629	+	0.299213i
$307$	−7.18520	+	7.18520i	−0.410081	+	0.410081i	−0.881767	−	0.471686i	$-0.843646\pi$
$307$	−7.18520	+	7.18520i	−0.410081	+	0.410081i	0.471686	+	0.881767i	$0.343646\pi$
$308$	−28.6025	−	23.0481i	−1.62978	−	1.31329i
$309$	−10.6063	−	26.2511i	−0.603371	−	1.49337i
$310$	−15.8974	−	16.6672i	−0.902911	−	0.946633i
$311$	−14.8762	+	8.58880i	−0.843554	+	0.487026i	−0.858471	−	0.512863i	$-0.828585\pi$
$311$	−14.8762	+	8.58880i	−0.843554	+	0.487026i	0.0149167	+	0.999889i	$0.495252\pi$
$312$	−10.5401	−	17.3989i	−0.596715	−	0.985018i
$313$	−0.757515	+	0.202976i	−0.0428173	+	0.0114729i	−0.280164	−	0.959952i	$-0.590389\pi$
$313$	−0.757515	+	0.202976i	−0.0428173	+	0.0114729i	0.237347	+	0.971425i	$0.423722\pi$
$314$	20.6672	−	6.74269i	1.16632	−	0.380512i
$315$	−7.71450	+	20.7188i	−0.434663	+	1.16737i
$316$	12.6549	+	17.3301i	0.711894	+	0.974896i
$317$	34.3839	−	9.21314i	1.93119	−	0.517462i	0.958841	−	0.283944i	$-0.0916431\pi$
$317$	34.3839	−	9.21314i	1.93119	−	0.517462i	0.972353	−	0.233517i	$-0.0750236\pi$
$318$	6.32578	+	13.5230i	0.354732	+	0.758332i
$319$	4.42200	+	7.65913i	0.247584	+	0.428829i
$320$	17.8858	+	0.315163i	0.999845	+	0.0176182i
$321$	24.3631	+	3.42388i	1.35982	+	0.191103i
$322$	−10.9729	−	16.8524i	−0.611496	−	0.939145i
$323$	5.36714	+	5.36714i	0.298635	+	0.298635i
$324$	14.8982	−	10.1017i	0.827678	−	0.561204i
$325$	−12.2486	−	16.7639i	−0.679430	−	0.929896i
$326$	0.484130	−	2.29120i	0.0268135	−	0.126898i
$327$	−1.70004	−	2.25601i	−0.0940126	−	0.124758i
$328$	−9.17686	−	11.2492i	−0.506707	−	0.621134i
$329$	7.90820	−	4.56580i	0.435993	−	0.251721i
$330$	10.7625	+	28.5633i	0.592456	+	1.57236i
$331$	−14.5958	+	25.2807i	−0.802259	+	1.38955i	0.115867	+	0.993265i	$0.463035\pi$
$331$	−14.5958	+	25.2807i	−0.802259	+	1.38955i	−0.918126	+	0.396288i	$0.870298\pi$
$332$	−0.233060	+	1.49475i	−0.0127908	+	0.0820352i
$333$	0.134501	−	0.0745572i	0.00737063	−	0.00408571i
$334$	9.27264	−	3.02520i	0.507376	−	0.165532i
$335$	18.0620	+	12.3780i	0.986833	+	0.676284i
$336$	−1.70250	−	22.7699i	−0.0928791	−	1.24220i
$337$	23.2191	+	6.22154i	1.26483	+	0.338909i	0.828046	−	0.560660i	$-0.189452\pi$
$337$	23.2191	+	6.22154i	1.26483	+	0.338909i	0.436779	+	0.899569i	$0.356119\pi$
$338$	−0.321198	−	5.99091i	−0.0174709	−	0.325862i
$339$	−10.1838	+	4.11460i	−0.553109	+	0.223474i
$340$	−0.186862	−	6.24180i	−0.0101340	−	0.338509i
$341$			40.5908i			2.19812i
$342$	−6.76955	−	22.0465i	−0.366056	−	1.19214i
$343$	−7.31335	+	7.31335i	−0.394884	+	0.394884i
$344$	13.5197	−	6.07792i	0.728933	−	0.327700i
$345$	0.751394	+	16.6936i	0.0404537	+	0.898752i
$346$	−15.7838	+	17.5722i	−0.848544	+	0.944687i
$347$	25.9636	+	6.95694i	1.39380	+	0.373468i	0.876115	−	0.482102i	$-0.160127\pi$
$347$	25.9636	+	6.95694i	1.39380	+	0.373468i	0.517686	+	0.855570i	$0.326793\pi$
$348$	−1.59462	+	5.26112i	−0.0854808	+	0.282026i
$349$	−1.09610	+	1.89850i	−0.0586729	+	0.101625i	−0.893870	−	0.448326i	$-0.852020\pi$
$349$	−1.09610	+	1.89850i	−0.0586729	+	0.101625i	0.835197	+	0.549951i	$0.185354\pi$
$350$	−3.73504	−	23.0030i	−0.199646	−	1.22956i
$351$	21.4582	−	2.25569i	1.14535	−	0.120400i
$352$	−22.4250	−	22.1568i	−1.19526	−	1.18096i
$353$	18.8297	−	5.04542i	1.00221	−	0.268540i	0.279837	−	0.960048i	$-0.409720\pi$
$353$	18.8297	−	5.04542i	1.00221	−	0.268540i	0.722370	+	0.691507i	$0.243053\pi$
$354$	2.24100	+	12.6201i	0.119108	+	0.670752i
$355$	11.4484	−	32.4677i	0.607617	−	1.72320i
$356$	−10.8890	−	4.81672i	−0.577114	−	0.255286i
$357$	−7.91137	+	0.971436i	−0.418714	+	0.0514139i
$358$	19.4908	−	12.6908i	1.03012	−	0.670731i
$359$	7.06936			0.373106			0.186553	−	0.982445i	$-0.440268\pi$
$359$	7.06936			0.373106			0.186553	+	0.982445i	$0.440268\pi$
$360$	−8.38165	+	17.0220i	−0.441752	+	0.897137i
$361$	−10.5485			−0.555186
$362$	−25.3355	+	16.4964i	−1.33160	+	0.867032i
$363$	13.5734	−	31.9773i	0.712417	−	1.67837i
$364$	11.0723	−	25.0307i	0.580345	−	1.31196i
$365$	−1.98416	−	4.14555i	−0.103856	−	0.216988i
$366$	−17.8832	+	15.0426i	−0.934768	+	0.786290i
$367$	27.2333	−	7.29715i	1.42157	−	0.380908i	0.535529	−	0.844517i	$-0.320112\pi$
$367$	27.2333	−	7.29715i	1.42157	−	0.380908i	0.886040	+	0.463609i	$0.153446\pi$
$368$	−7.90911	−	15.3396i	−0.412291	−	0.799629i
$369$	14.9408	−	3.72532i	0.777785	−	0.193932i
$370$	−0.0843460	+	0.138430i	−0.00438494	+	0.00719663i
$371$	−10.0436	+	17.3959i	−0.521435	+	0.903152i
$372$	−18.4116	+	17.2523i	−0.954596	+	0.894489i
$373$	26.4371	+	7.08380i	1.36886	+	0.366785i	0.867063	−	0.498199i	$-0.166005\pi$
$373$	26.4371	+	7.08380i	1.36886	+	0.366785i	0.501799	+	0.864984i	$0.332672\pi$
$374$	−7.35378	+	8.18698i	−0.380255	+	0.423339i
$375$	−7.02457	+	18.0459i	−0.362747	+	0.931888i
$376$	7.14776	−	3.21335i	0.368618	−	0.165716i
$377$	−4.65967	+	4.65967i	−0.239985	+	0.239985i
$378$	22.6205	+	8.65157i	1.16347	+	0.444989i
$379$		−	31.5024i		−	1.61817i	−0.587691	−	0.809085i	$-0.699963\pi$
$379$		−	31.5024i		−	1.61817i	0.587691	−	0.809085i	$-0.300037\pi$
$380$	17.6964	+	16.6676i	0.907805	+	0.855030i
$381$	1.02282	−	7.27801i	0.0524006	−	0.372864i
$382$	0.496666	+	9.26368i	0.0254116	+	0.473971i
$383$	−1.77519	−	0.475662i	−0.0907081	−	0.0243052i	0.213180	−	0.977013i	$-0.431618\pi$
$383$	−1.77519	−	0.475662i	−0.0907081	−	0.0243052i	−0.303888	+	0.952708i	$0.598285\pi$
$384$	0.518826	−	19.5890i	0.0264762	−	0.999649i
$385$	−23.2162	+	33.8771i	−1.18321	+	1.72653i
$386$	18.3538	−	5.98795i	0.934186	−	0.304778i
$387$	−0.274224	+	15.7199i	−0.0139396	+	0.799085i
$388$	3.08604	+	0.481171i	0.156670	+	0.0244278i
$389$	−14.6635	+	25.3979i	−0.743470	+	1.28773i	0.207437	+	0.978248i	$0.433488\pi$
$389$	−14.6635	+	25.3979i	−0.743470	+	1.28773i	−0.950906	+	0.309479i	$0.899846\pi$
$390$	−18.4821	+	13.2544i	−0.935879	+	0.671164i
$391$	−5.21751	+	3.01233i	−0.263861	+	0.152340i
$392$	8.46376	−	6.90455i	0.427484	−	0.348732i
$393$	0.782751	−	1.84407i	0.0394845	−	0.0930211i
$394$	−1.85659	+	8.78653i	−0.0935336	+	0.442659i
$395$	18.2225	−	15.6058i	0.916873	−	0.785214i
$396$	31.3928	−	11.5120i	1.57755	−	0.578501i
$397$	−8.60308	−	8.60308i	−0.431776	−	0.431776i	0.457456	−	0.889232i	$-0.348761\pi$
$397$	−8.60308	−	8.60308i	−0.431776	−	0.431776i	−0.889232	+	0.457456i	$0.848761\pi$
$398$	−3.65731	−	5.61695i	−0.183324	−	0.281552i
$399$	19.1037	−	24.4520i	0.956384	−	1.22413i
$400$	−1.19642	−	19.9642i	−0.0598208	−	0.998209i
$401$	−3.10810	−	5.38338i	−0.155211	−	0.268833i	0.777925	−	0.628357i	$-0.216272\pi$
$401$	−3.10810	−	5.38338i	−0.155211	−	0.268833i	−0.933136	+	0.359524i	$0.882939\pi$
$402$	13.7342	−	19.6650i	0.685000	−	0.980803i
$403$	−29.2141	+	7.82791i	−1.45526	+	0.389936i
$404$	−3.66204	+	2.67411i	−0.182193	+	0.133042i
$405$	−12.5493	−	15.7326i	−0.623581	−	0.781759i
$406$	−7.03193	+	2.29417i	−0.348989	+	0.113858i
$407$	0.275936	−	0.0739368i	0.0136776	−	0.00366491i
$408$	−6.83910	+	0.144107i	−0.338586	+	0.00713438i
$409$	−24.3306	+	14.0473i	−1.20307	+	0.694593i	−0.961237	−	0.275725i	$-0.911082\pi$
$409$	−24.3306	+	14.0473i	−1.20307	+	0.694593i	−0.241834	+	0.970318i	$0.577749\pi$
$410$	−11.7452	+	11.2027i	−0.580053	+	0.553262i
$411$	−2.91400	+	3.72979i	−0.143737	+	0.183977i
$412$	20.5130	−	25.4565i	1.01060	−	1.25415i
$413$	−12.1945	+	12.1945i	−0.600054	+	0.600054i
$414$	18.2935	−	0.661054i	0.899075	−	0.0324890i
$415$	1.68634	+	0.130441i	0.0827791	+	0.00640308i
$416$	11.6221	−	20.4127i	0.569822	−	1.00082i
$417$	−20.6482	−	8.76452i	−1.01115	−	0.429200i
$418$	−2.29359	−	42.7795i	−0.112183	−	2.09241i
$419$	31.4879	−	18.1796i	1.53828	−	0.888129i	0.539346	−	0.842085i	$-0.318672\pi$
$419$	31.4879	−	18.1796i	1.53828	−	0.888129i	0.998939	−	0.0460447i	$-0.0146617\pi$
$420$	−25.2338	+	3.86811i	−1.23128	+	0.188744i
$421$	18.4586	+	10.6571i	0.899616	+	0.519393i	0.877075	−	0.480353i	$-0.159491\pi$
$421$	18.4586	+	10.6571i	0.899616	+	0.519393i	0.0225401	+	0.999746i	$0.492825\pi$
$422$	−3.02694	+	5.95842i	−0.147349	+	0.290051i
$423$	−0.144980	+	8.31096i	−0.00704916	+	0.404093i
$424$	−10.0824	+	13.9831i	−0.489645	+	0.679080i
$425$	−6.94144	+	0.748418i	−0.336709	+	0.0363036i
$426$	−35.4540	−	12.8557i	−1.71775	−	0.622861i
$427$	−30.3704	−	8.13772i	−1.46973	−	0.393812i
$428$	10.2445	+	26.4971i	0.495187	+	1.28079i
$429$	39.6906	+	5.57793i	1.91628	+	0.269305i
$430$	−7.94485	−	14.5442i	−0.383135	−	0.701383i
$431$		−	9.04492i		−	0.435678i	−0.975985	−	0.217839i	$-0.930099\pi$
$431$		−	9.04492i		−	0.435678i	0.975985	−	0.217839i	$-0.0699008\pi$
$432$	18.5646	+	9.34649i	0.893188	+	0.449683i
$433$	−1.19181	−	1.19181i	−0.0572749	−	0.0572749i	0.677889	−	0.735164i	$-0.262895\pi$
$433$	−1.19181	−	1.19181i	−0.0572749	−	0.0572749i	−0.735164	+	0.677889i	$0.762895\pi$
$434$	−33.2149	−	7.01829i	−1.59437	−	0.336889i
$435$	6.00246	+	1.32223i	0.287796	+	0.0633961i
$436$	1.31954	−	2.98303i	0.0631944	−	0.142861i
$437$	6.07026	−	22.6545i	0.290380	−	1.08371i
$438$	−4.56030	+	2.13322i	−0.217900	+	0.101929i
$439$	−2.47200	+	4.28163i	−0.117982	+	0.204351i	−0.918968	−	0.394332i	$-0.870976\pi$
$439$	−2.47200	+	4.28163i	−0.117982	+	0.204351i	0.800986	+	0.598683i	$0.204309\pi$
$440$	−22.7573	+	26.9140i	−1.08491	+	1.28308i
$441$	2.80288	+	11.2412i	0.133471	+	0.535297i
$442$	−7.31053	−	3.71383i	−0.347726	−	0.176649i
$443$	0.763406	−	0.204554i	0.0362705	−	0.00971865i	−0.240638	−	0.970615i	$-0.577357\pi$
$443$	0.763406	−	0.204554i	0.0362705	−	0.00971865i	0.276909	+	0.960896i	$0.410690\pi$
$444$	0.150818	+	0.0937364i	0.00715749	+	0.00444853i
$445$	−4.42684	+	12.5545i	−0.209852	+	0.595142i
$446$	19.3484	−	21.5406i	0.916172	−	1.01998i
$447$	1.32126	−	3.11274i	0.0624934	−	0.147227i
$448$	22.0080	−	14.5191i	1.03978	−	0.685963i
$449$		−	13.8598i		−	0.654083i	−0.945010	−	0.327042i	$-0.893948\pi$
$449$		−	13.8598i		−	0.654083i	0.945010	−	0.327042i	$-0.106052\pi$
$450$	19.6994	+	7.86988i	0.928637	+	0.370990i
$451$	28.6039			1.34690
$452$	−9.87557	−	7.95781i	−0.464508	−	0.374304i
$453$	2.73547	+	22.2777i	0.128524	+	1.04670i
$454$	4.21498	−	4.69255i	0.197819	−	0.220232i
$455$	−28.8593	−	10.1761i	−1.35295	−	0.477061i
$456$	18.4295	−	19.2229i	0.863040	−	0.900193i
$457$	7.15851	+	26.7159i	0.334861	+	1.24972i	0.904020	+	0.427491i	$0.140602\pi$
$457$	7.15851	+	26.7159i	0.334861	+	1.24972i	−0.569159	+	0.822228i	$0.692731\pi$
$458$	−0.217587	+	0.428312i	−0.0101672	+	0.0200137i
$459$	2.95100	−	6.62834i	0.137741	−	0.309384i
$460$	−16.4143	+	10.1435i	−0.765320	+	0.472944i
$461$	−32.6998	−	18.8792i	−1.52298	−	0.879293i	−0.999631	−	0.0271753i	$-0.991349\pi$
$461$	−32.6998	−	18.8792i	−1.52298	−	0.879293i	−0.523350	−	0.852118i	$-0.675318\pi$
$462$	36.8837	+	25.7599i	1.71598	+	1.19846i
$463$	16.8142	+	4.50534i	0.781420	+	0.209381i	0.627411	−	0.778688i	$-0.284115\pi$
$463$	16.8142	+	4.50534i	0.781420	+	0.209381i	0.154010	+	0.988069i	$0.450781\pi$
$464$	−6.20280	+	1.34968i	−0.287958	+	0.0626572i
$465$	20.8240	+	19.0301i	0.965689	+	0.882500i
$466$	−5.11781	+	24.2207i	−0.237078	+	1.12200i
$467$	−5.73692	+	5.73692i	−0.265473	+	0.265473i	−0.827273	−	0.561800i	$-0.810109\pi$
$467$	−5.73692	+	5.73692i	−0.265473	+	0.265473i	0.561800	+	0.827273i	$0.310109\pi$
$468$	14.3395	+	20.3740i	0.662846	+	0.941789i
$469$	32.2729			1.49023
$470$	−4.20038	−	7.68940i	−0.193749	−	0.354686i
$471$	−24.6863	+	9.97408i	−1.13749	+	0.459581i
$472$	−11.4684	+	9.35567i	−0.527876	+	0.430629i
$473$	−7.55902	+	28.2106i	−0.347564	+	1.29713i
$474$	−16.9178	−	20.1124i	−0.777059	−	0.923794i
$475$	17.0477	−	21.1681i	0.782203	−	0.971259i
$476$	−5.42780	−	7.43305i	−0.248783	−	0.340693i
$477$	−8.86477	−	15.9921i	−0.405890	−	0.732226i
$478$	−2.70664	+	5.32791i	−0.123799	+	0.243693i
$479$	−19.1184	+	33.1140i	−0.873540	+	1.51302i	−0.0152307	+	0.999884i	$0.504848\pi$
$479$	−19.1184	+	33.1140i	−0.873540	+	1.51302i	−0.858310	+	0.513132i	$0.828485\pi$
$480$	−21.8804	+	1.11679i	−0.998700	+	0.0509742i
$481$	0.106428	+	0.184339i	0.00485270	+	0.00840513i
$482$	−33.8310	+	1.81383i	−1.54096	+	0.0826175i
$483$	14.8225	+	19.6699i	0.674446	+	0.895010i
$484$	39.8830	−	4.28892i	1.81286	−	0.194951i
$485$	0.269306	−	3.48158i	0.0122285	−	0.158091i
$486$	−17.3553	+	13.5939i	−0.787253	+	0.616630i
$487$	3.76347	+	3.76347i	0.170539	+	0.170539i	0.787216	−	0.616677i	$-0.211522\pi$
$487$	3.76347	+	3.76347i	0.170539	+	0.170539i	−0.616677	+	0.787216i	$0.711522\pi$
$488$	−25.2261	−	9.57908i	−1.14193	−	0.433625i
$489$	−0.399147	+	2.84019i	−0.0180501	+	0.128438i
$490$	−8.42876	−	8.83691i	−0.380773	−	0.399211i
$491$	−2.23612	−	3.87308i	−0.100915	−	0.174790i	0.811147	−	0.584842i	$-0.198844\pi$
$491$	−2.23612	−	3.87308i	−0.100915	−	0.174790i	−0.912062	+	0.410053i	$0.865510\pi$
$492$	12.1575	+	12.9744i	0.548101	+	0.584932i
$493$	0.573533	+	2.14045i	0.0258306	+	0.0964012i
$494$	30.3471	−	9.90074i	1.36538	−	0.445455i
$495$	−15.5488	−	33.9967i	−0.698865	−	1.52804i
$496$	−27.7518	−	8.86969i	−1.24609	−	0.398261i
$497$	−13.1329	−	49.0126i	−0.589091	−	2.19852i
$498$	0.159252	−	1.84595i	0.00713626	−	0.0827191i
$499$	−16.2174	+	9.36310i	−0.725989	+	0.419150i	−0.816953	−	0.576704i	$-0.804339\pi$
$499$	−16.2174	+	9.36310i	−0.725989	+	0.419150i	0.0909638	+	0.995854i	$0.471005\pi$
$500$	−22.1501	+	3.06120i	−0.990585	+	0.136901i
$501$	−11.0759	+	4.47501i	−0.494833	+	0.199929i
$502$	13.8373	+	21.2516i	0.617591	+	0.948506i
$503$	−16.0979	+	16.0979i	−0.717771	+	0.717771i	−0.968148	−	0.250377i	$-0.919445\pi$
$503$	−16.0979	+	16.0979i	−0.717771	+	0.717771i	0.250377	+	0.968148i	$0.419445\pi$
$504$	3.99222	+	27.6787i	0.177828	+	1.23291i
$505$	3.29767	+	3.85060i	0.146744	+	0.171349i
$506$	33.2697	+	7.02987i	1.47902	+	0.312516i
$507$	0.895519	+	7.29310i	0.0397714	+	0.323898i
$508$	7.91550	−	3.06035i	0.351193	−	0.135781i
$509$	12.6549	+	21.9189i	0.560919	+	0.971540i	0.997417	+	0.0718348i	$0.0228854\pi$
$509$	12.6549	+	21.9189i	0.560919	+	0.971540i	−0.436498	+	0.899705i	$0.643781\pi$
$510$	0.752446	+	7.61094i	0.0333189	+	0.337018i
$511$	−5.86636	−	3.38695i	−0.259513	−	0.149830i
$512$	20.0488	−	10.4903i	0.886038	−	0.463612i
$513$	10.1227	+	26.3693i	0.446929	+	1.16423i
$514$	4.12526	+	12.6445i	0.181958	+	0.557724i
$515$	−30.1509	−	20.6626i	−1.32861	−	0.910504i
$516$	−16.0089	+	8.56164i	−0.704751	+	0.376905i
$517$	−3.99639	+	14.9147i	−0.175761	+	0.655950i
$518$	0.0127912	+	0.238578i	0.000562014	+	0.0104825i
$519$	17.8101	−	22.7962i	0.781778	−	1.00064i
$520$	−23.7594	−	11.1886i	−1.04192	−	0.490651i
$521$	−7.50815			−0.328938			−0.164469	−	0.986382i	$-0.552591\pi$
$521$	−7.50815			−0.328938			−0.164469	+	0.986382i	$0.552591\pi$
$522$	1.50663	−	6.56227i	0.0659435	−	0.287223i
$523$	17.4800	+	17.4800i	0.764348	+	0.764348i	0.977105	−	0.212757i	$-0.0682444\pi$
$523$	17.4800	+	17.4800i	0.764348	+	0.764348i	−0.212757	+	0.977105i	$0.568244\pi$
$524$	2.29998	−	0.247334i	0.100475	−	0.0108048i
$525$	6.49528	+	27.7929i	0.283477	+	1.21298i
$526$	4.77204	−	5.31273i	0.208071	−	0.231646i
$527$	−2.63231	+	9.82393i	−0.114665	+	0.427937i
$528$	29.2608	+	25.1896i	1.27341	+	1.09624i
$529$	−3.79666	−	2.19200i	−0.165072	−	0.0953046i
$530$	16.4592	+	10.0287i	0.714940	+	0.435617i
$531$	−3.79791	−	15.2319i	−0.164815	−	0.661007i
$532$	35.4024	+	5.51990i	1.53489	+	0.239318i
$533$	5.51623	+	20.5869i	0.238935	+	0.891716i
$534$	13.7093	+	4.97102i	0.593259	+	0.215117i
$535$	28.6493	−	13.7123i	1.23862	−	0.592832i
$536$	27.5555	+	2.79568i	1.19022	+	0.120755i
$537$	−22.7494	+	17.1431i	−0.981710	+	0.739779i
$538$	16.6734	+	25.6073i	0.718842	+	1.10401i
$539$			21.5212i			0.926982i
$540$	8.81188	−	21.5023i	0.379203	−	0.925314i
$541$			10.9132i			0.469194i	0.972093	+	0.234597i	$0.0753771\pi$
$541$			10.9132i			0.469194i	−0.972093	+	0.234597i	$0.924623\pi$
$542$	4.01043	−	2.61127i	0.172263	−	0.112164i
$543$	29.5713	−	22.2838i	1.26902	−	0.956289i
$544$	−3.99051	−	6.81673i	−0.171092	−	0.292265i
$545$	−3.43931	−	1.21273i	−0.147324	−	0.0519477i
$546$	−11.4270	+	31.5138i	−0.489029	+	1.34867i
$547$	6.04285	+	22.5522i	0.258374	+	0.964264i	0.966182	+	0.257860i	$0.0830172\pi$
$547$	6.04285	+	22.5522i	0.258374	+	0.964264i	−0.707809	+	0.706404i	$0.750316\pi$
$548$	−5.40012	−	0.841980i	−0.230682	−	0.0359676i
$549$	20.5876	−	19.8817i	0.878659	−	0.848529i
$550$	31.9698	+	23.0381i	1.36320	+	0.982348i
$551$	−7.47087	−	4.31331i	−0.318270	−	0.183753i
$552$	10.9519	+	18.0787i	0.466144	+	0.769480i
$553$	9.15214	−	34.1563i	0.389189	−	1.45247i
$554$	−9.99717	−	8.97974i	−0.424739	−	0.381512i
$555$	0.0914353	−	0.176225i	0.00388121	−	0.00748033i
$556$	−2.76942	−	25.7530i	−0.117450	−	1.09217i
$557$	−14.6821	−	14.6821i	−0.622100	−	0.622100i	0.323968	−	0.946068i	$-0.394983\pi$
$557$	−14.6821	−	14.6821i	−0.622100	−	0.622100i	−0.946068	+	0.323968i	$0.894983\pi$
$558$	21.0477	−	22.6259i	0.891022	−	0.957832i
$559$	−21.7616			−0.920418
$560$	−18.0886	−	23.2755i	−0.764382	−	0.983568i
$561$	8.29784	−	10.6209i	0.350335	−	0.448414i
$562$	31.1087	−	1.66787i	1.31224	−	0.0703550i
$563$	9.86315	−	36.8098i	0.415682	−	1.55135i	−0.367783	−	0.929912i	$-0.619883\pi$
$563$	9.86315	−	36.8098i	0.415682	−	1.55135i	0.783465	−	0.621435i	$-0.213450\pi$
$564$	−8.46376	+	4.52647i	−0.356388	+	0.190599i
$565$	−8.01584	+	11.6967i	−0.337229	+	0.492085i
$566$	28.0961	−	9.16635i	1.18097	−	0.385290i
$567$	−28.3656	−	8.67159i	−1.19124	−	0.364172i
$568$	−6.96745	−	42.9860i	−0.292348	−	1.80365i
$569$	−13.1812	−	7.61018i	−0.552585	−	0.319035i	0.197579	−	0.980287i	$-0.436692\pi$
$569$	−13.1812	−	7.61018i	−0.552585	−	0.319035i	−0.750164	+	0.661252i	$0.770025\pi$
$570$	−23.0221	−	18.8796i	−0.964291	−	0.790778i
$571$	6.87056	+	11.9002i	0.287524	+	0.498006i	0.973218	−	0.229884i	$-0.0738346\pi$
$571$	6.87056	+	11.9002i	0.287524	+	0.498006i	−0.685694	+	0.727890i	$0.740501\pi$
$572$	16.6896	+	43.1671i	0.697826	+	1.80491i
$573$	−1.38473	−	11.2772i	−0.0578480	−	0.471114i
$574$	−4.94570	+	23.4061i	−0.206430	+	0.976953i
$575$	12.7272	+	17.4189i	0.530760	+	0.726419i
$576$	1.01097	+	23.9787i	0.0421236	+	0.999112i
$577$	1.48618	−	1.48618i	0.0618705	−	0.0618705i	−0.675495	−	0.737365i	$-0.736070\pi$
$577$	1.48618	−	1.48618i	0.0618705	−	0.0618705i	0.737365	+	0.675495i	$0.236070\pi$
$578$	17.8365	−	11.6137i	0.741902	−	0.483067i
$579$	−21.9231	+	8.85763i	−0.911091	+	0.368110i
$580$	2.04121	+	6.79734i	0.0847566	+	0.282244i
$581$	2.15892	−	1.24645i	0.0895671	−	0.0517116i
$582$	−3.81112	−	0.328790i	−0.157976	−	0.0136288i
$583$	−8.79101	−	32.8085i	−0.364086	−	1.35879i
$584$	−4.71547	−	3.40005i	−0.195127	−	0.140695i
$585$	21.4696	−	17.7470i	0.887661	−	0.733750i
$586$	−0.620699	−	1.90252i	−0.0256408	−	0.0785925i
$587$	−4.79318	−	17.8884i	−0.197836	−	0.738333i	−0.991515	−	0.129996i	$-0.958504\pi$
$587$	−4.79318	−	17.8884i	−0.197836	−	0.738333i	0.793679	−	0.608337i	$-0.208163\pi$
$588$	−9.76178	+	9.14712i	−0.402569	+	0.377221i
$589$	−19.7966	−	34.2887i	−0.815703	−	1.41284i
$590$	11.4210	+	11.9740i	0.470194	+	0.492962i
$591$	1.53069	−	10.8918i	0.0629641	−	0.448030i
$592$	−0.00974566	+	0.204813i	−0.000400544	+	0.00841776i
$593$	11.1532	+	11.1532i	0.458008	+	0.458008i	0.898001	−	0.439993i	$-0.145019\pi$
$593$	11.1532	+	11.1532i	0.458008	+	0.458008i	−0.439993	+	0.898001i	$0.645019\pi$
$594$	−37.3910	+	16.7022i	−1.53417	+	0.685299i
$595$	−7.81578	+	6.69347i	−0.320416	+	0.274406i
$596$	3.88229	−	0.417492i	0.159025	−	0.0171012i
$597$	4.94039	+	6.55604i	0.202197	+	0.268321i
$598$	1.35648	+	25.3007i	0.0554705	+	1.03462i
$599$	−13.3620	−	23.1436i	−0.545955	−	0.945622i	−0.998546	−	0.0539040i	$-0.982834\pi$
$599$	−13.3620	−	23.1436i	−0.545955	−	0.945622i	0.452591	−	0.891718i	$-0.350500\pi$
$600$	3.13826	+	24.2930i	0.128119	+	0.991759i
$601$	20.9122	−	36.2209i	0.853025	−	1.47748i	−0.0254402	−	0.999676i	$-0.508099\pi$
$601$	20.9122	−	36.2209i	0.853025	−	1.47748i	0.878465	−	0.477806i	$-0.158568\pi$
$602$	−21.7774	−	11.0632i	−0.887580	−	0.450900i
$603$	−15.1300	+	25.1812i	−0.616143	+	1.02546i
$604$	−20.9308	+	15.2842i	−0.851661	+	0.621905i
$605$	−8.23200	−	44.0856i	−0.334679	−	1.79234i
$606$	4.24996	−	3.57490i	0.172643	−	0.145221i
$607$	2.76832	−	10.3315i	0.112363	−	0.419343i	−0.886714	−	0.462319i	$-0.847017\pi$
$607$	2.76832	−	10.3315i	0.112363	−	0.419343i	0.999076	+	0.0429766i	$0.0136841\pi$
$608$	29.7494	+	7.77983i	1.20650	+	0.315514i
$609$	8.39942	−	3.39364i	0.340362	−	0.137517i
$610$	−8.49470	+	28.9480i	−0.343940	+	1.17207i
$611$	−11.5052			−0.465450
$612$	8.34434	−	0.750361i	0.337300	−	0.0303316i
$613$	7.46382	−	7.46382i	0.301461	−	0.301461i	−0.540124	−	0.841585i	$-0.681623\pi$
$613$	7.46382	−	7.46382i	0.301461	−	0.301461i	0.841585	+	0.540124i	$0.181623\pi$
$614$	14.0600	+	2.97086i	0.567414	+	0.119894i
$615$	13.4103	−	14.6744i	0.540755	−	0.591729i
$616$	−5.24357	+	51.6831i	−0.211270	+	2.08237i
$617$	−11.6023	−	3.10882i	−0.467090	−	0.125156i	0.0175948	−	0.999845i	$-0.494399\pi$
$617$	−11.6023	−	3.10882i	−0.467090	−	0.125156i	−0.484685	+	0.874689i	$0.661066\pi$
$618$	−22.9265	+	32.8268i	−0.922240	+	1.32049i
$619$	25.9649	+	14.9908i	1.04362	+	0.602533i	0.920856	−	0.389904i	$-0.127492\pi$
$619$	25.9649	+	14.9908i	1.04362	+	0.602533i	0.122761	+	0.992436i	$0.460825\pi$
$620$	−7.48540	+	31.7020i	−0.300621	+	1.27318i
$621$	−22.2966	+	2.34383i	−0.894732	+	0.0940545i
$622$	21.6583	+	11.0026i	0.868418	+	0.441166i
$623$	5.07820	+	18.9521i	0.203454	+	0.759300i
$624$	−12.4866	+	25.9175i	−0.499864	+	1.03753i
$625$	5.32899	+	24.4254i	0.213160	+	0.977017i
$626$	0.825099	+	0.741127i	0.0329776	+	0.0296214i
$627$	6.39467	+	52.0781i	0.255378	+	2.07980i
$628$	−23.9391	−	19.2903i	−0.955274	−	0.769767i
$629$	0.0715778			0.00285399
$630$	30.5075	−	6.84519i	1.21545	−	0.272719i
$631$		−	15.9716i		−	0.635821i	−0.948121	−	0.317910i	$-0.897019\pi$
$631$		−	15.9716i		−	0.635821i	0.948121	−	0.317910i	$-0.102981\pi$
$632$	10.7732	−	28.3707i	0.428534	−	1.12853i
$633$	3.19818	−	7.53455i	0.127116	−	0.299471i
$634$	−37.4516	−	33.6400i	−1.48739	−	1.33602i
$635$	−4.09627	−	8.55843i	−0.162555	−	0.339631i
$636$	11.1452	−	17.9321i	0.441934	−	0.711053i
$637$	−15.4893	+	4.15034i	−0.613708	+	0.164442i
$638$	5.66479	−	11.1509i	0.224271	−	0.441469i
$639$	44.3995	+	12.7308i	1.75642	+	0.503624i
$640$	−13.4283	−	21.4402i	−0.530799	−	0.847498i
$641$	1.24192	−	2.15107i	0.0490530	−	0.0849623i	−0.840456	−	0.541879i	$-0.817713\pi$
$641$	1.24192	−	2.15107i	0.0490530	−	0.0849623i	0.889509	+	0.456917i	$0.151046\pi$
$642$	−14.7424	−	31.5156i	−0.581835	−	1.24382i
$643$	−7.90851	+	29.5150i	−0.311881	+	1.16396i	0.614977	+	0.788545i	$0.289165\pi$
$643$	−7.90851	+	29.5150i	−0.311881	+	1.16396i	−0.926858	+	0.375411i	$0.877501\pi$
$644$	−11.5049	+	26.0087i	−0.453356	+	1.02488i
$645$	10.9288	+	17.1039i	0.430321	+	0.673465i
$646$	2.21915	−	10.5024i	0.0873111	−	0.413211i
$647$	10.3717	+	10.3717i	0.407755	+	0.407755i	0.880955	−	0.473200i	$-0.156901\pi$
$647$	10.3717	+	10.3717i	0.407755	+	0.407755i	−0.473200	+	0.880955i	$0.656901\pi$
$648$	−23.4682	−	9.86125i	−0.921917	−	0.387386i
$649$		−	29.1612i		−	1.14468i
$650$	−10.4157	+	27.4523i	−0.408537	+	1.07677i
$651$	41.1734	+	5.78632i	1.61371	+	0.226784i
$652$	−3.08896	+	1.19428i	−0.120973	+	0.0467716i
$653$	12.9803	+	3.47806i	0.507958	+	0.136107i	0.503691	−	0.863884i	$-0.331975\pi$
$653$	12.9803	+	3.47806i	0.507958	+	0.136107i	0.00426711	+	0.999991i	$0.498642\pi$
$654$	−1.36181	+	3.75565i	−0.0532509	+	0.146858i
$655$	−0.474724	−	2.54234i	−0.0185490	−	0.0993373i
$656$	−6.25036	+	19.5564i	−0.244036	+	0.763549i
$657$	5.39294	−	2.98943i	0.210399	−	0.116629i
$658$	−11.5135	−	5.84900i	−0.448844	−	0.228018i
$659$	−1.37779	−	0.795468i	−0.0536711	−	0.0309870i	0.472924	−	0.881103i	$-0.343198\pi$
$659$	−1.37779	−	0.795468i	−0.0536711	−	0.0309870i	−0.526595	+	0.850116i	$0.676532\pi$
$660$	25.5463	−	34.7962i	0.994387	−	1.35444i
$661$	−16.3747	+	9.45397i	−0.636904	+	0.367717i	−0.783421	−	0.621492i	$-0.786527\pi$
$661$	−16.3747	+	9.45397i	−0.636904	+	0.367717i	0.146517	+	0.989208i	$0.453194\pi$
$662$	41.2240	−	2.21020i	1.60222	−	0.0859017i
$663$	9.24432	+	3.92392i	0.359019	+	0.152392i
$664$	1.95132	−	0.877237i	0.0757259	−	0.0340434i
$665$	3.08942	−	39.9400i	0.119803	−	1.54881i
$666$	−0.192150	−	0.101869i	−0.00744565	−	0.00394734i
$667$	4.84173	−	4.84173i	0.187473	−	0.187473i
$668$	−10.7406	−	8.65487i	−0.415567	−	0.334867i
$669$	−21.8323	+	27.9444i	−0.844085	+	1.08039i
$670$	0.731809	−	30.9575i	0.0282723	−	1.19599i
$671$	46.0429	−	26.5829i	1.77746	−	1.02622i
$672$	−25.6716	+	19.5884i	−0.990302	+	0.755637i
$673$	8.03622	−	2.15330i	0.309774	−	0.0830036i	−0.100583	−	0.994929i	$-0.532071\pi$
$673$	8.03622	−	2.15330i	0.309774	−	0.0830036i	0.410357	+	0.911925i	$0.365404\pi$
$674$	−10.5440	−	32.3186i	−0.406138	−	1.24487i
$675$	−24.7308	−	7.96175i	−0.951887	−	0.306448i
$676$	−6.85216	+	5.00362i	−0.263545	+	0.192447i
$677$	−35.9145	+	9.62325i	−1.38030	+	0.369851i	−0.871232	−	0.490872i	$-0.836678\pi$
$677$	−35.9145	+	9.62325i	−1.38030	+	0.369851i	−0.509073	+	0.860723i	$0.670012\pi$
$678$	12.7348	+	8.89410i	0.489078	+	0.341576i
$679$	−2.57341	−	4.45727i	−0.0987582	−	0.171054i
$680$	−7.25316	+	5.03802i	−0.278146	+	0.193199i
$681$	−4.75609	+	6.08758i	−0.182254	+	0.233277i
$682$	48.1055	−	31.3224i	1.84205	−	1.19940i
$683$	−23.1330	−	23.1330i	−0.885159	−	0.885159i	0.108894	−	0.994053i	$-0.465269\pi$
$683$	−23.1330	−	23.1330i	−0.885159	−	0.885159i	−0.994053	+	0.108894i	$0.965269\pi$
$684$	−20.9042	+	25.0352i	−0.799291	+	0.957247i
$685$	−0.471246	+	6.09227i	−0.0180054	+	0.232774i
$686$	14.3107	+	3.02385i	0.546386	+	0.115451i
$687$	0.229896	−	0.541610i	0.00877109	−	0.0206637i
$688$	−17.6358	−	11.3325i	−0.672358	−	0.432048i
$689$	21.9177	−	12.6542i	0.834997	−	0.482086i
$690$	19.2043	−	13.7723i	0.731094	−	0.524302i
$691$	16.4432	−	28.4805i	0.625530	−	1.08345i	−0.362908	−	0.931825i	$-0.618216\pi$
$691$	16.4432	−	28.4805i	0.625530	−	1.08345i	0.988438	−	0.151625i	$-0.0484505\pi$
$692$	33.0052	+	5.14612i	1.25467	+	0.195626i
$693$	−47.2299	−	28.3779i	−1.79411	−	1.07799i
$694$	−11.7903	−	36.1387i	−0.447553	−	1.37181i
$695$	−28.4667	+	5.31552i	−1.07980	+	0.201629i
$696$	7.46563	−	2.16997i	0.282984	−	0.0822526i
$697$	6.92280	+	1.85496i	0.262220	+	0.0702616i
$698$	3.09580	−	0.165979i	0.117178	−	0.00628239i
$699$	4.21945	−	30.0241i	0.159594	−	1.13562i
$700$	−24.3794	+	22.1771i	−0.921456	+	0.838215i
$701$		−	25.4936i		−	0.962880i	−0.876479	−	0.481440i	$-0.840114\pi$
$701$		−	25.4936i		−	0.962880i	0.876479	−	0.481440i	$-0.159886\pi$
$702$	−19.2318	−	23.6901i	−0.725856	−	0.894127i
$703$	−0.197034	+	0.197034i	−0.00743129	+	0.00743129i
$704$	−8.95422	+	43.6742i	−0.337475	+	1.64603i
$705$	5.77797	+	9.04269i	0.217611	+	0.340567i
$706$	−20.5097	−	18.4224i	−0.771892	−	0.693335i
$707$	7.21757	+	1.93394i	0.271445	+	0.0727334i
$708$	13.2272	−	12.3943i	0.497109	−	0.465808i
$709$	−8.29947	+	14.3751i	−0.311693	+	0.539869i	−0.978729	−	0.205157i	$-0.934229\pi$
$709$	−8.29947	+	14.3751i	−0.311693	+	0.539869i	0.667036	+	0.745026i	$0.267563\pi$
$710$	−47.3127	+	11.4862i	−1.77562	+	0.431070i
$711$	22.3601	+	23.1540i	0.838568	+	0.868344i
$712$	2.69416	+	16.6217i	0.100968	+	0.622926i
$713$	30.3556	−	8.13376i	1.13683	−	0.304612i
$714$	7.25618	+	8.62639i	0.271556	+	0.322835i
$715$	46.6733	−	22.3390i	1.74548	−	0.835429i
$716$	−30.0806	−	13.3061i	−1.12417	−	0.497273i
$717$	2.85975	−	6.73726i	0.106799	−	0.251607i
$718$	−5.45516	−	8.37812i	−0.203585	−	0.312669i
$719$	−0.873650			−0.0325817			−0.0162908	−	0.999867i	$-0.505186\pi$
$719$	−0.873650			−0.0325817			−0.0162908	+	0.999867i	$0.505186\pi$
$720$	26.6411	−	3.20187i	0.992855	−	0.119327i
$721$	−53.8732			−2.00634
$722$	8.13991	+	12.5014i	0.302936	+	0.465254i
$723$	41.1845	−	5.05705i	1.53167	−	0.188074i
$724$	39.1008	+	17.2962i	1.45317	+	0.642808i
$725$	7.40023	−	2.86350i	0.274838	−	0.106348i
$726$	−48.3714	+	8.58947i	−1.79523	+	0.318785i
$727$	−22.0925	+	5.91967i	−0.819366	+	0.219549i	−0.644069	−	0.764967i	$-0.722755\pi$
$727$	−22.0925	+	5.91967i	−0.819366	+	0.219549i	−0.175297	+	0.984516i	$0.556089\pi$
$728$	−38.2087	+	6.19311i	−1.41611	+	0.229532i
$729$	20.0643	−	18.0672i	0.743123	−	0.669154i
$730$	−3.38192	+	5.55046i	−0.125171	+	0.205432i
$731$	−3.65892	+	6.33743i	−0.135330	+	0.234398i
$732$	31.6272	+	9.58608i	1.16898	+	0.354312i
$733$	−5.42394	−	1.45334i	−0.200338	−	0.0536803i	0.157255	−	0.987558i	$-0.449736\pi$
$733$	−5.42394	−	1.45334i	−0.200338	−	0.0536803i	−0.357592	+	0.933878i	$0.616402\pi$
$734$	−29.6630	−	26.6442i	−1.09488	−	0.983454i
$735$	11.0408	+	10.0897i	0.407247	+	0.372165i
$736$	−12.0762	+	21.2103i	−0.445136	+	0.781822i
$737$	−38.5877	+	38.5877i	−1.42139	+	1.42139i
$738$	−15.9442	−	14.8321i	−0.586915	−	0.545977i
$739$		−	5.52205i		−	0.203132i	−0.994829	−	0.101566i	$-0.967615\pi$
$739$		−	5.52205i		−	0.203132i	0.994829	−	0.101566i	$-0.0323853\pi$
$740$	0.229144	−	0.00685994i	0.00842351	−	0.000252176i
$741$	−36.2486	+	14.6456i	−1.33163	+	0.538020i
$742$	28.3667	−	1.52086i	1.04138	−	0.0558326i
$743$	−51.4104	−	13.7754i	−1.88606	−	0.505369i	−0.999048	−	0.0436318i	$-0.986107\pi$
$743$	−51.4104	−	13.7754i	−1.88606	−	0.505369i	−0.887017	−	0.461738i	$-0.847226\pi$
$744$	34.6537	+	8.50722i	1.27047	+	0.311890i
$745$	−0.801319	−	4.29138i	−0.0293581	−	0.157224i
$746$	−12.0053	−	36.7978i	−0.439545	−	1.34726i
$747$	−0.0395791	+	2.26887i	−0.00144812	+	0.0830137i
$748$	15.3773	+	2.39761i	0.562249	+	0.0876652i
$749$	23.4067	−	40.5416i	0.855263	−	1.48136i
$750$	26.8074	−	5.60032i	0.978868	−	0.204495i
$751$	6.65809	−	3.84405i	0.242957	−	0.140271i	−0.373578	−	0.927599i	$-0.621869\pi$
$751$	6.65809	−	3.84405i	0.242957	−	0.140271i	0.616535	+	0.787327i	$0.288536\pi$
$752$	−9.32390	−	5.99141i	−0.340008	−	0.218484i
$753$	−18.6918	−	24.8046i	−0.681169	−	0.903931i
$754$	9.11802	+	1.92663i	0.332059	+	0.0701638i
$755$	18.8482	+	22.0085i	0.685956	+	0.800972i
$756$	−7.20214	−	33.4844i	−0.261939	−	1.21782i
$757$	21.5137	+	21.5137i	0.781930	+	0.781930i	0.980156	−	0.198226i	$-0.0635181\pi$
$757$	21.5137	+	21.5137i	0.781930	+	0.781930i	−0.198226	+	0.980156i	$0.563518\pi$
$758$	−37.3345	+	24.3092i	−1.35605	+	0.882951i
$759$	−41.2413	−	5.79587i	−1.49697	−	0.210377i
$760$	6.09769	−	33.8343i	0.221186	−	1.22730i
$761$	22.3333	+	38.6825i	0.809582	+	1.40224i	0.913153	+	0.407616i	$0.133640\pi$
$761$	22.3333	+	38.6825i	0.809582	+	1.40224i	−0.103571	+	0.994622i	$0.533027\pi$
$762$	−9.41468	+	4.40399i	−0.341058	+	0.159540i
$763$	−5.19192	+	1.39117i	−0.187960	+	0.0503638i
$764$	10.5954	−	7.73705i	0.383329	−	0.279917i
$765$	−1.55848	−	9.23634i	−0.0563469	−	0.333940i
$766$	0.806128	+	2.47089i	0.0291266	+	0.0892768i
$767$	20.9880	−	5.62371i	0.757832	−	0.203060i
$768$	−23.6160	+	14.5013i	−0.852168	+	0.523269i
$769$	−11.6705	+	6.73797i	−0.420849	+	0.242977i	−0.695441	−	0.718584i	$-0.744791\pi$
$769$	−11.6705	+	6.73797i	−0.420849	+	0.242977i	0.274591	+	0.961561i	$0.411457\pi$
$770$	58.0638	+	1.37258i	2.09247	+	0.0494643i
$771$	−6.10227	−	15.1034i	−0.219768	−	0.543936i
$772$	−21.2595	−	17.1310i	−0.765145	−	0.616560i
$773$	−22.1936	+	22.1936i	−0.798250	+	0.798250i	−0.982819	−	0.184570i	$-0.940911\pi$
$773$	−22.1936	+	22.1936i	−0.798250	+	0.798250i	0.184570	+	0.982819i	$0.440911\pi$
$774$	18.8417	−	11.8054i	0.677251	−	0.424337i
$775$	35.9853	+	5.60054i	1.29263	+	0.201177i
$776$	−1.81113	−	4.02866i	−0.0650157	−	0.144621i
$777$	−0.0356626	−	0.290436i	−0.00127939	−	0.0104193i
$778$	41.4152	−	2.22045i	1.48481	−	0.0796068i
$779$	−24.1628	+	13.9504i	−0.865722	+	0.499825i
$780$	29.9702	+	11.6758i	1.07311	+	0.418061i
$781$	74.3054	+	42.9002i	2.65885	+	1.53509i
$782$	7.59616	+	3.85893i	0.271638	+	0.137995i
$783$	−1.28986	+	8.14471i	−0.0460959	+	0.291068i
$784$	−14.7140	−	4.70269i	−0.525499	−	0.167953i
$785$	−19.4310	+	28.3537i	−0.693522	+	1.01199i
$786$	−2.78949	+	0.495338i	−0.0994977	+	0.0176681i
$787$	−3.89728	−	1.04427i	−0.138923	−	0.0372243i	0.188687	−	0.982037i	$-0.439577\pi$
$787$	−3.89728	−	1.04427i	−0.138923	−	0.0372243i	−0.327611	+	0.944813i	$0.606243\pi$
$788$	11.8459	−	4.57993i	0.421991	−	0.163153i
$789$	−5.38467	+	6.89214i	−0.191699	+	0.245367i
$790$	−32.5566	−	9.55363i	−1.15831	−	0.339903i
$791$			20.8995i			0.743101i
$792$	−37.8679	−	28.3212i	−1.34558	−	1.00635i
$793$	28.0116	+	28.0116i	0.994722	+	0.994722i
$794$	−3.55711	+	16.8345i	−0.126237	+	0.597433i
$795$	−20.9529	−	10.8716i	−0.743125	−	0.385574i
$796$	−3.83462	+	8.66878i	−0.135915	+	0.307257i
$797$	−1.20714	+	4.50512i	−0.0427592	+	0.159580i	−0.984004	−	0.178145i	$-0.942990\pi$
$797$	−1.20714	+	4.50512i	−0.0427592	+	0.159580i	0.941245	+	0.337724i	$0.109657\pi$
$798$	−43.7204	−	3.77181i	−1.54769	−	0.133521i
$799$	−1.93444	+	3.35055i	−0.0684356	+	0.118534i
$800$	−22.7370	+	16.8235i	−0.803873	+	0.594801i
$801$	−17.1683	−	4.92273i	−0.606612	−	0.173936i
$802$	−3.98162	+	7.83766i	−0.140596	+	0.276757i
$803$	11.0639	−	2.96456i	0.390436	−	0.104617i
$804$	−33.9038	−	1.10209i	−1.19570	−	0.0388678i
$805$	29.9869	+	10.5736i	1.05690	+	0.372672i
$806$	31.8206	+	28.5821i	1.12083	+	1.00676i
$807$	−22.5229	−	29.8885i	−0.792843	−	1.05213i
$808$	5.99503	+	2.27649i	0.210905	+	0.0800865i
$809$			11.6221i			0.408612i	0.978907	+	0.204306i	$0.0654938\pi$
$809$			11.6221i			0.408612i	−0.978907	+	0.204306i	$0.934506\pi$
$810$	−8.96135	+	27.0129i	−0.314870	+	0.949135i
$811$	−11.3517			−0.398610			−0.199305	−	0.979937i	$-0.563869\pi$
$811$	−11.3517			−0.398610			−0.199305	+	0.979937i	$0.563869\pi$
$812$	8.14517	+	6.56344i	0.285840	+	0.230332i
$813$	−4.68093	+	3.52737i	−0.164167	+	0.123710i
$814$	−0.300554	−	0.269966i	−0.0105344	−	0.00946231i
$815$	1.59854	+	3.33986i	0.0559944	+	0.116990i
$816$	5.44826	+	7.99403i	0.190727	+	0.279847i
$817$	−7.37323	−	27.5173i	−0.257957	−	0.962707i
$818$	35.4229	+	17.9952i	1.23853	+	0.629188i
$819$	11.3160	−	39.4651i	0.395412	−	1.37902i
$820$	22.3400	+	5.27487i	0.780146	+	0.184206i
$821$	−12.3882	−	7.15236i	−0.432353	−	0.249619i	0.267996	−	0.963420i	$-0.413639\pi$
$821$	−12.3882	−	7.15236i	−0.432353	−	0.249619i	−0.700348	+	0.713801i	$0.746972\pi$
$822$	6.66891	+	0.575334i	0.232605	+	0.0200671i
$823$	−38.3503	−	10.2759i	−1.33681	−	0.358196i	−0.481558	−	0.876414i	$-0.659929\pi$
$823$	−38.3503	−	10.2759i	−1.33681	−	0.358196i	−0.855248	+	0.518218i	$0.826596\pi$
$824$	−45.9984	−	4.66683i	−1.60243	−	0.162577i
$825$	−40.9973	−	25.4649i	−1.42734	−	0.886573i
$826$	23.8622	+	5.04207i	0.830272	+	0.175436i
$827$	0.306651	−	0.306651i	0.0106633	−	0.0106633i	−0.701755	−	0.712418i	$-0.747600\pi$
$827$	0.306651	−	0.306651i	0.0106633	−	0.0106633i	0.712418	+	0.701755i	$0.247600\pi$
$828$	−14.8998	−	21.1701i	−0.517804	−	0.735710i
$829$	−38.6945			−1.34391			−0.671957	−	0.740590i	$-0.734546\pi$
$829$	−38.6945			−1.34391			−0.671957	+	0.740590i	$0.734546\pi$
$830$	−1.14669	−	2.09919i	−0.0398023	−	0.0728639i
$831$	12.9692	+	10.1325i	0.449897	+	0.351494i
$832$	−33.1601	+	1.97798i	−1.14962	+	0.0685740i
$833$	−1.39565	+	5.20863i	−0.0483563	+	0.180468i
$834$	5.54634	+	31.2341i	0.192054	+	1.08155i
$835$	−8.71798	+	12.7213i	−0.301698	+	0.440238i
$836$	−48.9295	+	35.7295i	−1.69226	+	1.23573i
$837$	−23.8175	+	29.4132i	−0.823255	+	1.01667i
$838$	−45.8432	−	23.2888i	−1.58363	−	0.804500i
$839$	15.0834	−	26.1251i	0.520735	−	0.901940i	−0.478974	−	0.877829i	$-0.658991\pi$
$839$	15.0834	−	26.1251i	0.520735	−	0.901940i	0.999709	−	0.0241109i	$-0.00767549\pi$
$840$	24.0562	+	26.9205i	0.830018	+	0.928846i
$841$	13.2407	+	22.9336i	0.456577	+	0.790815i
$842$	−1.61376	−	30.0995i	−0.0556139	−	1.03730i
$843$	−37.8706	+	4.65013i	−1.30433	+	0.160159i
$844$	9.39729	−	1.01056i	0.323468	−	0.0347850i
$845$	6.17038	+	7.20498i	0.212268	+	0.247859i
$846$	9.96146	−	6.24144i	0.342482	−	0.214585i
$847$	−46.7402	−	46.7402i	−1.60601	−	1.60601i
$848$	24.3520	+	1.15875i	0.836253	+	0.0397916i
$849$	−33.5598	+	13.5593i	−1.15177	+	0.465352i
$850$	6.24342	+	7.64900i	0.214148	+	0.262358i
$851$	−0.110586	−	0.191541i	−0.00379085	−	0.00656595i
$852$	12.1228	+	51.9380i	0.415321	+	1.77937i
$853$	−11.8908	−	44.3771i	−0.407133	−	1.51944i	−0.800087	−	0.599884i	$-0.795214\pi$
$853$	−11.8908	−	44.3771i	−0.407133	−	1.51944i	0.392954	−	0.919558i	$-0.371453\pi$
$854$	13.7914	+	42.2725i	0.471932	+	1.44653i
$855$	29.7152	+	21.1351i	1.01624	+	0.722804i
$856$	23.4973	−	32.5879i	0.803120	−	1.11383i
$857$	10.8028	+	40.3164i	0.369015	+	1.37718i	0.861895	+	0.507086i	$0.169277\pi$
$857$	10.8028	+	40.3164i	0.369015	+	1.37718i	−0.492880	+	0.870097i	$0.664056\pi$
$858$	−24.0171	−	51.3428i	−0.819931	−	1.75282i
$859$	14.6188	−	8.44015i	0.498786	−	0.287974i	−0.229426	−	0.973326i	$-0.573685\pi$
$859$	14.6188	−	8.44015i	0.498786	−	0.287974i	0.728212	+	0.685352i	$0.240352\pi$
$860$	−11.1060	+	20.6389i	−0.378713	+	0.703781i
$861$	4.07755	−	29.0144i	0.138962	−	0.988808i
$862$	−10.7194	+	6.97962i	−0.365105	+	0.237727i
$863$	19.8356	−	19.8356i	0.675212	−	0.675212i	−0.283701	−	0.958913i	$-0.591562\pi$
$863$	19.8356	−	19.8356i	0.675212	−	0.675212i	0.958913	+	0.283701i	$0.0915622\pi$
$864$	−3.24876	−	29.2138i	−0.110525	−	0.993873i
$865$	2.88022	−	37.2355i	0.0979305	−	1.26605i
$866$	−0.492778	+	2.33213i	−0.0167453	+	0.0792491i
$867$	−20.8186	+	15.6881i	−0.707036	+	0.532796i
$868$	17.3131	+	44.7798i	0.587645	+	1.51992i
$869$	29.8966	+	51.7824i	1.01417	+	1.75660i
$870$	−3.06485	−	8.13402i	−0.103908	−	0.275769i
$871$	−35.2140	−	20.3308i	−1.19318	−	0.688884i
$872$	−4.55352	+	0.738064i	−0.154202	+	0.0249940i
$873$	4.68428	+	0.0817144i	0.158539	+	0.00276561i
$874$	−31.5328	+	10.2876i	−1.06661	+	0.347983i
$875$	26.8300	+	25.2562i	0.907020	+	0.853816i
$876$	6.04716	+	3.75844i	0.204315	+	0.126986i
$877$	1.34481	−	5.01889i	0.0454109	−	0.169476i	−0.939496	−	0.342559i	$-0.888706\pi$
$877$	1.34481	−	5.01889i	0.0454109	−	0.169476i	0.984907	+	0.173083i	$0.0553730\pi$
$878$	6.98184	−	0.374326i	0.235626	−	0.0126329i
$879$	0.918164	+	2.27250i	0.0309689	+	0.0766496i
$880$	49.4576	+	6.20180i	1.66722	+	0.209063i
$881$	31.0131			1.04486			0.522429	−	0.852683i	$-0.325026\pi$
$881$	31.0131			1.04486			0.522429	+	0.852683i	$0.325026\pi$
$882$	11.1595	−	11.9962i	0.375759	−	0.403934i
$883$	−9.74947	−	9.74947i	−0.328096	−	0.328096i	0.523766	−	0.851862i	$-0.324527\pi$
$883$	−9.74947	−	9.74947i	−0.328096	−	0.328096i	−0.851862	+	0.523766i	$0.824527\pi$
$884$	1.23988	+	11.5298i	0.0417018	+	0.387788i
$885$	−14.9603	−	13.6716i	−0.502886	−	0.459565i
$886$	−0.831515	−	0.746890i	−0.0279353	−	0.0250923i
$887$	−1.42448	+	5.31623i	−0.0478293	+	0.178502i	−0.985708	−	0.168461i	$-0.946120\pi$
$887$	−1.42448	+	5.31623i	−0.0478293	+	0.178502i	0.937879	+	0.346963i	$0.112787\pi$
$888$	−0.00529036	−	0.251072i	−0.000177533	−	0.00842542i
$889$	−12.1110	−	6.99230i	−0.406191	−	0.234514i
$890$	18.2948	−	4.44147i	0.613243	−	0.148878i
$891$	44.2842	−	23.5475i	1.48358	−	0.788872i
$892$	−40.4589	−	6.30830i	−1.35466	−	0.211217i
$893$	−3.89817	−	14.5482i	−0.130447	−	0.486835i
$894$	−4.70857	+	0.836116i	−0.157478	+	0.0279639i
$895$	−12.2291	+	34.6817i	−0.408773	+	1.15928i
$896$	−34.1898	−	14.8785i	−1.14220	−	0.497057i
$897$	−3.78194	−	30.8001i	−0.126275	−	1.02838i
$898$	−16.4257	+	10.6951i	−0.548131	+	0.356899i
$899$		−	11.5591i		−	0.385518i
$900$	−5.87441	−	29.4192i	−0.195814	−	0.980641i
$901$		−	8.51052i		−	0.283526i
$902$	−22.0725	−	33.8993i	−0.734935	−	1.12872i
$903$	27.5380	+	11.6890i	0.916406	+	0.388986i
$904$	−1.81045	+	17.8446i	−0.0602146	+	0.593502i
$905$	15.8962	−	45.0816i	0.528407	−	1.49856i
$906$	24.2911	−	20.4327i	0.807018	−	0.678832i
$907$	−10.4178	−	38.8798i	−0.345918	−	1.29098i	−0.891536	−	0.452950i	$-0.850372\pi$
$907$	−10.4178	−	38.8798i	−0.345918	−	1.29098i	0.545618	−	0.838034i	$-0.316295\pi$
$908$	−8.81383	−	1.37424i	−0.292497	−	0.0456058i
$909$	−4.89269	+	4.72491i	−0.162280	+	0.156715i
$910$	10.2097	+	42.0546i	0.338448	+	1.39410i
$911$	24.3274	+	14.0455i	0.806004	+	0.465347i	0.845566	−	0.533870i	$-0.179263\pi$
$911$	24.3274	+	14.0455i	0.806004	+	0.465347i	−0.0395621	+	0.999217i	$0.512596\pi$
$912$	−37.0030	−	7.00781i	−1.22529	−	0.232052i
$913$	−1.09101	+	4.07169i	−0.0361070	+	0.134753i
$914$	26.1379	−	29.0994i	0.864566	−	0.962524i
$915$	7.94859	−	36.0838i	0.262772	−	1.19289i
$916$	0.675510	−	0.0726428i	0.0223195	−	0.00240019i
$917$	−2.69542	−	2.69542i	−0.0890105	−	0.0890105i
$918$	−10.1326	+	1.61752i	−0.334427	+	0.0533860i
$919$	27.3309			0.901563			0.450782	−	0.892634i	$-0.351145\pi$
$919$	27.3309			0.901563			0.450782	+	0.892634i	$0.351145\pi$
$920$	24.6877	+	11.6257i	0.813929	+	0.383289i
$921$	−17.4288	−	2.44936i	−0.574299	−	0.0807093i
$922$	2.85882	+	53.3219i	0.0941501	+	1.75606i
$923$	−16.5465	+	61.7525i	−0.544636	+	2.03261i
$924$	2.06708	−	63.5899i	0.0680020	−	2.09195i
$925$	−0.0274754	−	0.254829i	−0.000903384	−	0.00837873i
$926$	−7.63543	−	23.4036i	−0.250916	−	0.769090i
$927$	25.2566	−	42.0350i	0.829535	−	1.38061i
$928$	6.38601	+	6.30964i	0.209631	+	0.207124i
$929$	−13.2431	−	7.64592i	−0.434493	−	0.250855i	0.266766	−	0.963761i	$-0.414045\pi$
$929$	−13.2431	−	7.64592i	−0.434493	−	0.250855i	−0.701259	+	0.712907i	$0.747378\pi$
$930$	6.48411	−	39.3640i	0.212622	−	1.29080i
$931$	−10.4961	−	18.1798i	−0.343996	−	0.595818i
$932$	32.6539	−	12.6249i	1.06961	−	0.413542i
$933$	−27.3874	−	11.6251i	−0.896622	−	0.380588i
$934$	11.2260	+	2.37204i	0.367325	+	0.0776155i
$935$	1.34191	−	17.3482i	0.0438852	−	0.567348i
$936$	13.0806	−	32.7161i	0.427553	−	1.06936i
$937$	−27.1832	+	27.1832i	−0.888037	+	0.888037i	−0.994334	−	0.106297i	$-0.966100\pi$
$937$	−27.1832	+	27.1832i	−0.888037	+	0.888037i	0.106297	+	0.994334i	$0.466100\pi$
$938$	−24.9038	−	38.2477i	−0.813138	−	1.24883i
$939$	−1.07039	−	0.836271i	−0.0349309	−	0.0272907i
$940$	−5.87168	+	10.9116i	−0.191513	+	0.355898i
$941$	18.4039	−	10.6255i	0.599951	−	0.346382i	−0.169072	−	0.985604i	$-0.554077\pi$
$941$	18.4039	−	10.6255i	0.599951	−	0.346382i	0.769022	+	0.639222i	$0.220744\pi$
$942$	30.8701	+	21.5599i	1.00580	+	0.702461i
$943$	−5.73176	−	21.3912i	−0.186652	−	0.696594i
$944$	19.9374	+	6.37215i	0.648908	+	0.207396i
$945$	−36.7011	+	10.9256i	−1.19389	+	0.355410i
$946$	39.2663	−	12.8107i	1.27666	−	0.416510i
$947$	−7.43547	−	27.7496i	−0.241620	−	0.901739i	−0.975052	−	0.221976i	$-0.928749\pi$
$947$	−7.43547	−	27.7496i	−0.241620	−	0.901739i	0.733432	−	0.679763i	$-0.237917\pi$
$948$	−10.7810	+	35.5698i	−0.350152	+	1.15525i
$949$	4.26732	+	7.39121i	0.138523	+	0.239929i
$950$	−38.2421	−	3.86917i	−1.24074	−	0.125532i
$951$	48.5854	+	37.9587i	1.57549	+	1.23089i
$952$	−4.62071	+	12.1685i	−0.149758	+	0.394382i
$953$	36.7552	+	36.7552i	1.19062	+	1.19062i	0.976894	+	0.213723i	$0.0685590\pi$
$953$	36.7552	+	36.7552i	1.19062	+	1.19062i	0.213723	+	0.976894i	$0.431441\pi$
$954$	−12.1121	+	22.8464i	−0.392143	+	0.739679i
$955$	−9.54120	−	11.1410i	−0.308746	−	0.360514i
$956$	8.40289	−	0.903627i	0.271769	−	0.0292254i
$957$	−5.98524	+	14.1006i	−0.193475	+	0.455806i
$958$	53.9973	−	2.89503i	1.74458	−	0.0935342i
$959$	4.50309	+	7.79957i	0.145412	+	0.251861i
$960$	18.2078	+	25.0694i	0.587655	+	0.809111i
$961$	11.0261	−	19.0978i	0.355682	−	0.616058i
$962$	0.136339	−	0.268379i	0.00439575	−	0.00865287i
$963$	20.6595	+	37.2698i	0.665744	+	1.20100i
$964$	28.2557	+	38.6945i	0.910056	+	1.24627i
$965$	−17.2560	+	25.1799i	−0.555489	+	0.810570i
$966$	11.8734	−	32.7451i	0.382022	−	1.05356i
$967$	1.17441	−	4.38295i	0.0377664	−	0.140946i	−0.944468	−	0.328602i	$-0.893422\pi$
$967$	1.17441	−	4.38295i	0.0377664	−	0.140946i	0.982235	+	0.187656i	$0.0600891\pi$
$968$	−35.8591	−	43.9570i	−1.15256	−	1.41283i
$969$	−1.82960	+	13.0188i	−0.0587753	+	0.418224i
$970$	−4.33395	+	2.36744i	−0.139155	+	0.0760141i
$971$	−36.7257			−1.17858			−0.589292	−	0.807920i	$-0.700593\pi$
$971$	−36.7257			−1.17858			−0.589292	+	0.807920i	$0.700593\pi$
$972$	29.5030	+	10.0785i	0.946308	+	0.323267i
$973$	−30.1808	+	30.1808i	−0.967552	+	0.967552i
$974$	1.55608	−	7.36434i	0.0498600	−	0.235969i
$975$	10.4214	−	34.4175i	0.333751	−	1.10224i
$976$	8.11358	+	37.2881i	0.259710	+	1.19356i
$977$	15.7273	+	4.21411i	0.503160	+	0.134821i	0.501466	−	0.865177i	$-0.332794\pi$
$977$	15.7273	+	4.21411i	0.503160	+	0.134821i	0.00169379	+	0.999999i	$0.499461\pi$
$978$	3.67401	−	1.71863i	0.117482	−	0.0549556i
$979$	−28.7322	−	16.5886i	−0.918287	−	0.530173i
$980$	−3.96874	+	16.8083i	−0.126777	+	0.536922i
$981$	1.34858	−	4.70325i	0.0430568	−	0.150163i
$982$	−2.86458	+	5.63881i	−0.0914123	+	0.179942i
$983$	13.5121	+	50.4280i	0.430970	+	1.60840i	0.750530	+	0.660837i	$0.229799\pi$
$983$	13.5121	+	50.4280i	0.430970	+	1.60840i	−0.319559	+	0.947566i	$0.603535\pi$
$984$	5.99493	−	24.4201i	0.191111	−	0.778483i
$985$	−6.13023	−	12.8080i	−0.195325	−	0.408098i
$986$	2.09415	−	2.33142i	0.0666912	−	0.0742475i
$987$	14.5591	+	6.17988i	0.463421	+	0.196708i
$988$	−35.1514	−	28.3252i	−1.11831	−	0.901146i
$989$	22.6119			0.719015
$990$	−28.2922	+	44.6613i	−0.899185	+	1.41943i
$991$		−	11.3945i		−	0.361957i	−0.983487	−	0.180979i	$-0.942074\pi$
$991$		−	11.3945i		−	0.361957i	0.983487	−	0.180979i	$-0.0579265\pi$
$992$	10.9033	+	39.7340i	0.346180	+	1.26156i
$993$	−50.1845	+	6.16215i	−1.59256	+	0.195550i
$994$	−47.9523	+	53.3854i	−1.52095	+	1.69328i
$995$	9.99475	+	3.52424i	0.316855	+	0.111726i
$996$	−2.31059	+	1.23572i	−0.0732137	+	0.0391552i
$997$	−11.9289	+	3.19635i	−0.377794	+	0.101229i	−0.442718	−	0.896661i	$-0.645986\pi$
$997$	−11.9289	+	3.19635i	−0.377794	+	0.101229i	0.0649249	+	0.997890i	$0.479319\pi$
$998$	23.6108	+	11.9946i	0.747388	+	0.379681i
$999$	0.243335	+	0.108335i	0.00769876	+	0.00342756i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bo.a.43.20	✓	272
5.2	odd	4	inner	360.2.bo.a.187.57	yes	272
8.3	odd	2	inner	360.2.bo.a.43.36	yes	272
9.4	even	3	inner	360.2.bo.a.283.67	yes	272
40.27	even	4	inner	360.2.bo.a.187.67	yes	272
45.22	odd	12	inner	360.2.bo.a.67.36	yes	272
72.67	odd	6	inner	360.2.bo.a.283.57	yes	272
360.67	even	12	inner	360.2.bo.a.67.20	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bo.a.43.20	✓	272	1.1	even	1	trivial
360.2.bo.a.43.36	yes	272	8.3	odd	2	inner
360.2.bo.a.67.20	yes	272	360.67	even	12	inner
360.2.bo.a.67.36	yes	272	45.22	odd	12	inner
360.2.bo.a.187.57	yes	272	5.2	odd	4	inner
360.2.bo.a.187.67	yes	272	40.27	even	4	inner
360.2.bo.a.283.57	yes	272	72.67	odd	6	inner
360.2.bo.a.283.67	yes	272	9.4	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.771662 - 1.18513i) q^{2} +(1.04238 + 1.38327i) q^{3} +(-0.809074 + 1.82904i) q^{4} +(2.10881 + 0.743585i) q^{5} +(0.834993 - 2.30278i) q^{6} +(3.18343 - 0.852996i) q^{7} +(2.79199 - 0.452544i) q^{8} +(-0.826881 + 2.88379i) q^{9} +O(q^{10})\)	\(q+(-0.771662 - 1.18513i) q^{2} +(1.04238 + 1.38327i) q^{3} +(-0.809074 + 1.82904i) q^{4} +(2.10881 + 0.743585i) q^{5} +(0.834993 - 2.30278i) q^{6} +(3.18343 - 0.852996i) q^{7} +(2.79199 - 0.452544i) q^{8} +(-0.826881 + 2.88379i) q^{9} +(-0.746043 - 3.07301i) q^{10} +(-2.78642 + 4.82621i) q^{11} +(-3.37343 + 0.787391i) q^{12} +(-4.01090 - 1.07472i) q^{13} +(-3.46744 - 3.11455i) q^{14} +(1.16960 + 3.69216i) q^{15} +(-2.69080 - 2.95966i) q^{16} +(-0.987358 + 0.987358i) q^{17} +(4.05575 - 1.24535i) q^{18} -5.43586i q^{19} +(-3.06623 + 3.25549i) q^{20} +(4.49827 + 3.51439i) q^{21} +(7.86987 - 0.421938i) q^{22} +(4.16761 + 1.11671i) q^{23} +(3.53631 + 3.39036i) q^{24} +(3.89416 + 3.13616i) q^{25} +(1.82138 + 5.58276i) q^{26} +(-4.85100 + 1.86221i) q^{27} +(-1.01546 + 6.51276i) q^{28} +(0.793492 - 1.37437i) q^{29} +(3.47315 - 4.23523i) q^{30} +(6.30787 - 3.64185i) q^{31} +(-1.43121 + 5.47281i) q^{32} +(-9.58048 + 1.17639i) q^{33} +(1.93206 + 0.408242i) q^{34} +(7.34752 + 0.568341i) q^{35} +(-4.60557 - 3.84561i) q^{36} +(-0.0362471 - 0.0362471i) q^{37} +(-6.44221 + 4.19465i) q^{38} +(-2.69426 - 6.66842i) q^{39} +(6.22428 + 1.12175i) q^{40} +(-2.56637 - 4.44508i) q^{41} +(0.693876 - 8.04297i) q^{42} +(5.06217 - 1.35641i) q^{43} +(-6.57294 - 9.00124i) q^{44} +(-3.88808 + 5.46652i) q^{45} +(-1.89254 - 5.80089i) q^{46} +(2.67633 - 0.717121i) q^{47} +(1.28918 - 6.80720i) q^{48} +(3.34442 - 1.93090i) q^{49} +(0.711786 - 7.03515i) q^{50} +(-2.39499 - 0.336581i) q^{51} +(5.21082 - 6.46657i) q^{52} +(-4.30974 + 4.30974i) q^{53} +(5.95030 + 4.31207i) q^{54} +(-9.46473 + 8.10563i) q^{55} +(8.50207 - 3.82220i) q^{56} +(7.51927 - 5.66624i) q^{57} +(-2.24112 + 0.120156i) q^{58} +(-4.53169 + 2.61637i) q^{59} +(-7.69941 - 0.847973i) q^{60} +(-8.26202 - 4.77008i) q^{61} +(-9.18361 - 4.66538i) q^{62} +(-0.172450 + 9.88567i) q^{63} +(7.59041 - 2.52699i) q^{64} +(-7.65907 - 5.24882i) q^{65} +(8.78707 + 10.4464i) q^{66} +(9.45870 + 2.53445i) q^{67} +(-1.00707 - 2.60477i) q^{68} +(2.79953 + 6.92897i) q^{69} +(-4.99624 - 9.14634i) q^{70} -15.3962i q^{71} +(-1.00360 + 8.42572i) q^{72} +(-1.45336 - 1.45336i) q^{73} +(-0.0149871 + 0.0709282i) q^{74} +(-0.278960 + 8.65576i) q^{75} +(9.94242 + 4.39801i) q^{76} +(-4.75361 + 17.7407i) q^{77} +(-5.82390 + 8.33882i) q^{78} +(5.36470 - 9.29194i) q^{79} +(-3.47362 - 8.24221i) q^{80} +(-7.63253 - 4.76911i) q^{81} +(-3.28763 + 6.47158i) q^{82} +(0.730632 - 0.195772i) q^{83} +(-10.0674 + 5.38412i) q^{84} +(-2.81633 + 1.34797i) q^{85} +(-5.51381 - 4.95266i) q^{86} +(2.72825 - 0.335001i) q^{87} +(-5.59557 + 14.7357i) q^{88} +5.95337i q^{89} +(9.47883 + 0.389585i) q^{90} -13.6851 q^{91} +(-5.41441 + 6.71923i) q^{92} +(11.6129 + 4.92930i) q^{93} +(-2.91511 - 2.61843i) q^{94} +(4.04202 - 11.4632i) q^{95} +(-9.06225 + 3.72501i) q^{96} +(-0.404188 - 1.50845i) q^{97} +(-4.86913 - 2.47357i) q^{98} +(-11.6138 - 12.0262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Introduction

L-functions

Modular forms

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