LMFDB - Embedded newform 945.2.cx.a.236.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(236,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 0, 15]))

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

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

chi := DirichletCharacter("945.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cx (of order $18$, degree $6$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$48$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			236.12
Character	$\chi$	$=$	945.236
Dual form			945.2.cx.a.941.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68254 - 0.296677i) q^{2} +(1.27794 - 1.16914i) q^{3} +(0.863525 + 0.314298i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-2.49703 + 1.58798i) q^{6} +(1.93664 - 1.80262i) q^{7} +(1.59953 + 0.923487i) q^{8} +(0.266241 - 2.98816i) q^{9} +O(q^{10})$	\(q+(-1.68254 - 0.296677i) q^{2} +(1.27794 - 1.16914i) q^{3} +(0.863525 + 0.314298i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-2.49703 + 1.58798i) q^{6} +(1.93664 - 1.80262i) q^{7} +(1.59953 + 0.923487i) q^{8} +(0.266241 - 2.98816i) q^{9} +(-1.47960 - 0.854246i) q^{10} +(-0.796021 - 2.18705i) q^{11} +(1.47099 - 0.607927i) q^{12} +(-0.125567 + 0.344992i) q^{13} +(-3.79326 + 2.45842i) q^{14} +(1.60074 - 0.661549i) q^{15} +(-3.82519 - 3.20971i) q^{16} +(0.397157 - 0.687896i) q^{17} +(-1.33448 + 4.94870i) q^{18} +(3.17759 - 1.83459i) q^{19} +(0.703952 + 0.590686i) q^{20} +(0.367391 - 4.56782i) q^{21} +(0.690488 + 3.91595i) q^{22} +(-4.34813 + 0.766692i) q^{23} +(3.12378 - 0.689907i) q^{24} +(0.766044 + 0.642788i) q^{25} +(0.313622 - 0.543209i) q^{26} +(-3.15333 - 4.12995i) q^{27} +(2.23889 - 0.947927i) q^{28} +(2.15369 + 5.91721i) q^{29} +(-2.88956 + 0.638179i) q^{30} +(1.47505 - 4.05268i) q^{31} +(3.10935 + 3.70558i) q^{32} +(-3.57422 - 1.86425i) q^{33} +(-0.872313 + 1.03958i) q^{34} +(2.43638 - 1.03154i) q^{35} +(1.16908 - 2.49668i) q^{36} +1.72724 q^{37} +(-5.89070 + 2.14404i) q^{38} +(0.242877 + 0.587683i) q^{39} +(1.18721 + 1.41486i) q^{40} +(7.06368 + 2.57097i) q^{41} +(-1.97331 + 7.57653i) q^{42} +(0.892453 - 5.06135i) q^{43} -2.13876i q^{44} +(1.27220 - 2.71689i) q^{45} +7.54334 q^{46} +(-4.14338 + 1.50807i) q^{47} +(-8.64094 + 0.370357i) q^{48} +(0.501127 - 6.98204i) q^{49} +(-1.09820 - 1.30878i) q^{50} +(-0.296703 - 1.34342i) q^{51} +(-0.216861 + 0.258444i) q^{52} +(8.76726 - 5.06178i) q^{53} +(4.08033 + 7.88431i) q^{54} -2.32741i q^{55} +(4.76240 - 1.09488i) q^{56} +(1.91588 - 6.05952i) q^{57} +(-1.86816 - 10.5949i) q^{58} +(-11.3111 + 9.49117i) q^{59} +(1.59020 - 0.0681571i) q^{60} +(-1.50223 - 4.12733i) q^{61} +(-3.68416 + 6.38116i) q^{62} +(-4.87091 - 6.26692i) q^{63} +(0.861198 + 1.49164i) q^{64} +(-0.235989 + 0.281240i) q^{65} +(5.46068 + 4.19706i) q^{66} +(-0.906274 - 5.13973i) q^{67} +(0.559159 - 0.469190i) q^{68} +(-4.66026 + 6.06334i) q^{69} +(-4.40532 + 1.01279i) q^{70} +(-4.43183 + 2.55872i) q^{71} +(3.18539 - 4.53378i) q^{72} -5.68569i q^{73} +(-2.90615 - 0.512433i) q^{74} +(1.73046 - 0.0741689i) q^{75} +(3.32054 - 0.585501i) q^{76} +(-5.48402 - 2.80060i) q^{77} +(-0.234297 - 1.06085i) q^{78} +(-1.10436 + 6.26315i) q^{79} +(-2.49672 - 4.32444i) q^{80} +(-8.85823 - 1.59114i) q^{81} +(-11.1222 - 6.42138i) q^{82} +(-5.45229 + 1.98447i) q^{83} +(1.75291 - 3.82896i) q^{84} +(0.608479 - 0.510575i) q^{85} +(-3.00317 + 8.25114i) q^{86} +(9.67030 + 5.04386i) q^{87} +(0.746456 - 4.23336i) q^{88} +(6.62626 + 11.4770i) q^{89} +(-2.94656 + 4.19384i) q^{90} +(0.378712 + 0.894474i) q^{91} +(-3.99569 - 0.704548i) q^{92} +(-2.85311 - 6.90360i) q^{93} +(7.41879 - 1.30813i) q^{94} +(3.61343 - 0.637145i) q^{95} +(8.30587 + 1.10024i) q^{96} +(-11.4610 - 2.02088i) q^{97} +(-2.91457 + 11.5989i) q^{98} +(-6.74719 + 1.79636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 6 q^{3} - 12 q^{6} + 6 q^{9}+O(q^{10}) $ 288 * q - 6 * q^3 - 12 * q^6 + 6 * q^9	$ 288 q - 6 q^{3} - 12 q^{6} + 6 q^{9} - 6 q^{11} - 42 q^{12} + 3 q^{13} + 42 q^{14} - 9 q^{23} - 24 q^{27} - 36 q^{29} + 12 q^{31} + 60 q^{33} + 60 q^{34} + 42 q^{36} + 42 q^{39} - 54 q^{41} + 63 q^{42} + 45 q^{43} + 30 q^{45} - 63 q^{47} + 18 q^{49} + 72 q^{51} + 102 q^{52} - 123 q^{54} - 27 q^{56} - 12 q^{57} + 48 q^{61} - 99 q^{62} - 66 q^{63} + 144 q^{64} + 3 q^{65} - 18 q^{66} + 54 q^{67} - 117 q^{68} + 198 q^{69} - 21 q^{70} - 36 q^{71} - 237 q^{72} + 6 q^{74} - 108 q^{76} + 27 q^{77} - 48 q^{78} + 9 q^{79} + 144 q^{80} + 6 q^{81} - 18 q^{83} + 69 q^{84} - 18 q^{85} - 3 q^{86} - 30 q^{90} + 18 q^{91} - 96 q^{92} + 12 q^{93} - 174 q^{94} - 60 q^{96} - 45 q^{97} - 234 q^{99}+O(q^{100}) $ 288 * q - 6 * q^3 - 12 * q^6 + 6 * q^9 - 6 * q^11 - 42 * q^12 + 3 * q^13 + 42 * q^14 - 9 * q^23 - 24 * q^27 - 36 * q^29 + 12 * q^31 + 60 * q^33 + 60 * q^34 + 42 * q^36 + 42 * q^39 - 54 * q^41 + 63 * q^42 + 45 * q^43 + 30 * q^45 - 63 * q^47 + 18 * q^49 + 72 * q^51 + 102 * q^52 - 123 * q^54 - 27 * q^56 - 12 * q^57 + 48 * q^61 - 99 * q^62 - 66 * q^63 + 144 * q^64 + 3 * q^65 - 18 * q^66 + 54 * q^67 - 117 * q^68 + 198 * q^69 - 21 * q^70 - 36 * q^71 - 237 * q^72 + 6 * q^74 - 108 * q^76 + 27 * q^77 - 48 * q^78 + 9 * q^79 + 144 * q^80 + 6 * q^81 - 18 * q^83 + 69 * q^84 - 18 * q^85 - 3 * q^86 - 30 * q^90 + 18 * q^91 - 96 * q^92 + 12 * q^93 - 174 * q^94 - 60 * q^96 - 45 * q^97 - 234 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.68254	−	0.296677i	−1.18973	−	0.209782i	−0.456477	−	0.889735i	$-0.650889\pi$
$2$	−1.68254	−	0.296677i	−1.18973	−	0.209782i	−0.733256	+	0.679953i	$0.762000\pi$
$3$	1.27794	−	1.16914i	0.737817	−	0.675001i
$3$	1.27794	−	1.16914i	0.737817	−	0.675001i
$4$	0.863525	+	0.314298i	0.431763	+	0.157149i
$5$	0.939693	+	0.342020i	0.420243	+	0.152956i
$5$	0.939693	+	0.342020i	0.420243	+	0.152956i
$6$	−2.49703	+	1.58798i	−1.01941	+	0.648290i
$7$	1.93664	−	1.80262i	0.731980	−	0.681326i
$7$	1.93664	−	1.80262i	0.731980	−	0.681326i
$8$	1.59953	+	0.923487i	0.565518	+	0.326502i
$9$	0.266241	−	2.98816i	0.0887469	−	0.996054i
$10$	−1.47960	−	0.854246i	−0.467890	−	0.270136i
$11$	−0.796021	−	2.18705i	−0.240009	−	0.659420i	−0.999955	−	0.00943430i	$-0.996997\pi$
$11$	−0.796021	−	2.18705i	−0.240009	−	0.659420i	0.759946	−	0.649986i	$-0.225225\pi$
$12$	1.47099	−	0.607927i	0.424637	−	0.175493i
$13$	−0.125567	+	0.344992i	−0.0348260	+	0.0956837i	−0.955887	−	0.293735i	$-0.905102\pi$
$13$	−0.125567	+	0.344992i	−0.0348260	+	0.0956837i	0.921061	+	0.389418i	$0.127324\pi$
$14$	−3.79326	+	2.45842i	−1.01379	+	0.657040i
$15$	1.60074	−	0.661549i	0.413308	−	0.170811i
$16$	−3.82519	−	3.20971i	−0.956297	−	0.802429i
$17$	0.397157	−	0.687896i	0.0963246	−	0.166839i	−0.813836	−	0.581095i	$-0.802625\pi$
$17$	0.397157	−	0.687896i	0.0963246	−	0.166839i	0.910161	+	0.414255i	$0.135958\pi$
$18$	−1.33448	+	4.94870i	−0.314539	+	1.16642i
$19$	3.17759	−	1.83459i	0.728990	−	0.420883i	−0.0890624	−	0.996026i	$-0.528387\pi$
$19$	3.17759	−	1.83459i	0.728990	−	0.420883i	0.818053	+	0.575143i	$0.195054\pi$
$20$	0.703952	+	0.590686i	0.157409	+	0.132081i
$21$	0.367391	−	4.56782i	0.0801712	−	0.996781i
$22$	0.690488	+	3.91595i	0.147213	+	0.834884i
$23$	−4.34813	+	0.766692i	−0.906647	+	0.159866i	−0.607481	−	0.794335i	$-0.707820\pi$
$23$	−4.34813	+	0.766692i	−0.906647	+	0.159866i	−0.299167	+	0.954201i	$0.596709\pi$
$24$	3.12378	−	0.689907i	0.637638	−	0.140827i
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$	0.313622	−	0.543209i	0.0615063	−	0.106532i
$27$	−3.15333	−	4.12995i	−0.606859	−	0.794810i
$28$	2.23889	−	0.947927i	0.423111	−	0.179141i
$29$	2.15369	+	5.91721i	0.399930	+	1.09880i	0.962318	+	0.271925i	$0.0876604\pi$
$29$	2.15369	+	5.91721i	0.399930	+	1.09880i	−0.562388	+	0.826873i	$0.690117\pi$
$30$	−2.88956	+	0.638179i	−0.527559	+	0.116515i
$31$	1.47505	−	4.05268i	0.264927	−	0.727882i	−0.733890	−	0.679268i	$-0.762297\pi$
$31$	1.47505	−	4.05268i	0.264927	−	0.727882i	0.998818	−	0.0486140i	$-0.0154804\pi$
$32$	3.10935	+	3.70558i	0.549660	+	0.655060i
$33$	−3.57422	−	1.86425i	−0.622192	−	0.324525i
$34$	−0.872313	+	1.03958i	−0.149600	+	0.178287i
$35$	2.43638	−	1.03154i	0.411823	−	0.174362i
$36$	1.16908	−	2.49668i	0.194846	−	0.416113i
$37$	1.72724			0.283957			0.141979	−	0.989870i	$-0.454654\pi$
$37$	1.72724			0.283957			0.141979	+	0.989870i	$0.454654\pi$
$38$	−5.89070	+	2.14404i	−0.955597	+	0.347809i
$39$	0.242877	+	0.587683i	0.0388914	+	0.0941046i
$40$	1.18721	+	1.41486i	0.187715	+	0.223710i
$41$	7.06368	+	2.57097i	1.10316	+	0.401518i	0.828481	−	0.560017i	$-0.189206\pi$
$41$	7.06368	+	2.57097i	1.10316	+	0.401518i	0.274681	+	0.961535i	$0.411428\pi$
$42$	−1.97331	+	7.57653i	−0.304489	+	1.16908i
$43$	0.892453	−	5.06135i	0.136098	−	0.771849i	−0.837991	−	0.545684i	$-0.816270\pi$
$43$	0.892453	−	5.06135i	0.136098	−	0.771849i	0.974089	−	0.226165i	$-0.0726189\pi$
$44$		−	2.13876i		−	0.322430i
$45$	1.27220	−	2.71689i	0.189648	−	0.405011i
$46$	7.54334			1.11220
$47$	−4.14338	+	1.50807i	−0.604374	+	0.219974i	−0.626040	−	0.779791i	$-0.715325\pi$
$47$	−4.14338	+	1.50807i	−0.604374	+	0.219974i	0.0216660	+	0.999765i	$0.493103\pi$
$48$	−8.64094	+	0.370357i	−1.24721	+	0.0534565i
$49$	0.501127	−	6.98204i	0.0715895	−	0.997434i
$50$	−1.09820	−	1.30878i	−0.155309	−	0.185090i
$51$	−0.296703	−	1.34342i	−0.0415467	−	0.188116i
$52$	−0.216861	+	0.258444i	−0.0300731	+	0.0358398i
$53$	8.76726	−	5.06178i	1.20428	−	0.695289i	0.242772	−	0.970083i	$-0.421943\pi$
$53$	8.76726	−	5.06178i	1.20428	−	0.695289i	0.961503	+	0.274795i	$0.0886098\pi$
$54$	4.08033	+	7.88431i	0.555263	+	1.07292i
$55$		−	2.32741i		−	0.313828i
$56$	4.76240	−	1.09488i	0.636402	−	0.146309i
$57$	1.91588	−	6.05952i	0.253765	−	0.802604i
$58$	−1.86816	−	10.5949i	−0.245302	−	1.39117i
$59$	−11.3111	+	9.49117i	−1.47258	+	1.23564i	−0.558890	+	0.829242i	$0.688773\pi$
$59$	−11.3111	+	9.49117i	−1.47258	+	1.23564i	−0.913694	+	0.406403i	$0.866783\pi$
$60$	1.59020	−	0.0681571i	0.205294	−	0.00879905i
$61$	−1.50223	−	4.12733i	−0.192340	−	0.528451i	0.805610	−	0.592446i	$-0.201838\pi$
$61$	−1.50223	−	4.12733i	−0.192340	−	0.528451i	−0.997950	+	0.0639957i	$0.979616\pi$
$62$	−3.68416	+	6.38116i	−0.467889	+	0.810408i
$63$	−4.87091	−	6.26692i	−0.613677	−	0.789557i
$64$	0.861198	+	1.49164i	0.107650	+	0.186455i
$65$	−0.235989	+	0.281240i	−0.0292708	+	0.0348836i
$66$	5.46068	+	4.19706i	0.672163	+	0.516622i
$67$	−0.906274	−	5.13973i	−0.110719	−	0.627918i	−0.988781	−	0.149372i	$-0.952275\pi$
$67$	−0.906274	−	5.13973i	−0.110719	−	0.627918i	0.878062	−	0.478547i	$-0.158836\pi$
$68$	0.559159	−	0.469190i	0.0678080	−	0.0568976i
$69$	−4.66026	+	6.06334i	−0.561029	+	0.729940i
$70$	−4.40532	+	1.01279i	−0.526537	+	0.121051i
$71$	−4.43183	+	2.55872i	−0.525962	+	0.303664i	−0.739371	−	0.673299i	$-0.764877\pi$
$71$	−4.43183	+	2.55872i	−0.525962	+	0.303664i	0.213409	+	0.976963i	$0.431543\pi$
$72$	3.18539	−	4.53378i	0.375402	−	0.534311i
$73$		−	5.68569i		−	0.665460i	−0.943022	−	0.332730i	$-0.892030\pi$
$73$		−	5.68569i		−	0.665460i	0.943022	−	0.332730i	$-0.107970\pi$
$74$	−2.90615	−	0.512433i	−0.337833	−	0.0595691i
$75$	1.73046	−	0.0741689i	0.199817	−	0.00856429i
$76$	3.32054	−	0.585501i	0.380892	−	0.0671615i
$77$	−5.48402	−	2.80060i	−0.624962	−	0.319158i
$78$	−0.234297	−	1.06085i	−0.0265289	−	0.120118i
$79$	−1.10436	+	6.26315i	−0.124250	+	0.704659i	0.857500	+	0.514484i	$0.172017\pi$
$79$	−1.10436	+	6.26315i	−0.124250	+	0.704659i	−0.981750	+	0.190175i	$0.939095\pi$
$80$	−2.49672	−	4.32444i	−0.279141	−	0.483487i
$81$	−8.85823	−	1.59114i	−0.984248	−	0.176793i
$82$	−11.1222	−	6.42138i	−1.22824	−	0.709123i
$83$	−5.45229	+	1.98447i	−0.598467	+	0.217824i	−0.623449	−	0.781864i	$-0.714269\pi$
$83$	−5.45229	+	1.98447i	−0.598467	+	0.217824i	0.0249825	+	0.999688i	$0.492047\pi$
$84$	1.75291	−	3.82896i	0.191258	−	0.417774i
$85$	0.608479	−	0.510575i	0.0659989	−	0.0553796i
$86$	−3.00317	+	8.25114i	−0.323840	+	0.889743i
$87$	9.67030	+	5.04386i	1.03677	+	0.540759i
$88$	0.746456	−	4.23336i	0.0795724	−	0.451278i
$89$	6.62626	+	11.4770i	0.702382	+	1.21656i	0.967628	+	0.252380i	$0.0812134\pi$
$89$	6.62626	+	11.4770i	0.702382	+	1.21656i	−0.265246	+	0.964181i	$0.585453\pi$
$90$	−2.94656	+	4.19384i	−0.310594	+	0.442070i
$91$	0.378712	+	0.894474i	0.0396998	+	0.0937664i
$92$	−3.99569	−	0.704548i	−0.416579	−	0.0734542i
$93$	−2.85311	−	6.90360i	−0.295853	−	0.715870i
$94$	7.41879	−	1.30813i	0.765190	−	0.134924i
$95$	3.61343	−	0.637145i	0.370730	−	0.0653697i
$96$	8.30587	+	1.10024i	0.847714	+	0.112293i
$97$	−11.4610	−	2.02088i	−1.16369	−	0.205189i	−0.441743	−	0.897141i	$-0.645640\pi$
$97$	−11.4610	−	2.02088i	−1.16369	−	0.205189i	−0.721943	+	0.691952i	$0.756751\pi$
$98$	−2.91457	+	11.5989i	−0.294416	+	1.17166i
$99$	−6.74719	+	1.79636i	−0.678119	+	0.180541i
$100$	0.459472	+	0.795829i	0.0459472	+	0.0795829i
$101$	2.62647	−	14.8954i	0.261343	−	1.48215i	−0.517906	−	0.855437i	$-0.673288\pi$
$101$	2.62647	−	14.8954i	0.261343	−	1.48215i	0.779250	−	0.626714i	$-0.215600\pi$
$102$	0.100653	+	2.34837i	0.00996613	+	0.232523i
$103$	5.07140	−	13.9336i	0.499700	−	1.37291i	−0.391866	−	0.920022i	$-0.628170\pi$
$103$	5.07140	−	13.9336i	0.499700	−	1.37291i	0.891566	−	0.452891i	$-0.149607\pi$
$104$	−0.519444	+	0.435865i	−0.0509356	+	0.0427401i
$105$	1.90752	−	4.16670i	0.186155	−	0.406628i
$106$	−16.2529	+	5.91559i	−1.57862	+	0.574572i
$107$	−0.256645	−	0.148174i	−0.0248108	−	0.0143245i	0.487543	−	0.873099i	$-0.337893\pi$
$107$	−0.256645	−	0.148174i	−0.0248108	−	0.0143245i	−0.512354	+	0.858774i	$0.671226\pi$
$108$	−1.42495	−	4.55740i	−0.137116	−	0.438536i
$109$	4.46692	+	7.73694i	0.427854	+	0.741064i	0.996682	−	0.0813918i	$-0.0259365\pi$
$109$	4.46692	+	7.73694i	0.427854	+	0.741064i	−0.568828	+	0.822456i	$0.692603\pi$
$110$	−0.690488	+	3.91595i	−0.0658354	+	0.373371i
$111$	2.20731	−	2.01938i	0.209508	−	0.191671i
$112$	−13.1939	+	0.679307i	−1.24671	+	0.0641885i
$113$	−16.2107	+	2.85838i	−1.52497	+	0.268894i	−0.872385	−	0.488820i	$-0.837428\pi$
$113$	−16.2107	+	2.85838i	−1.52497	+	0.268894i	−0.652587	+	0.757713i	$0.726317\pi$
$114$	−5.02126	+	9.62697i	−0.470284	+	0.901648i
$115$	−4.34813	−	0.766692i	−0.405465	−	0.0714944i
$116$			5.78656i			0.537269i
$117$	0.997462	+	0.467065i	0.0922154	+	0.0431802i
$118$	21.8472	−	12.6135i	2.01120	−	1.16117i
$119$	−0.470866	−	2.04813i	−0.0431642	−	0.187751i
$120$	3.17135	+	0.420093i	0.289503	+	0.0383491i
$121$	4.27695	−	3.58879i	0.388814	−	0.326253i
$122$	1.30307	+	7.39006i	0.117974	+	0.669065i
$123$	12.0327	−	4.97287i	1.08496	−	0.448389i
$124$	2.54749	−	3.03598i	0.228772	−	0.272639i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	6.33623	+	11.9894i	0.564476	+	1.06810i
$127$	−5.63666	+	9.76299i	−0.500173	+	0.866325i	0.499827	+	0.866125i	$0.333397\pi$
$127$	−5.63666	+	9.76299i	−0.500173	+	0.866325i	−1.00000		0.000199740i	$0.999936\pi$
$128$	−4.31536	−	11.8564i	−0.381428	−	1.04796i
$129$	−4.77691	−	7.51148i	−0.420584	−	0.661349i
$130$	0.480497	−	0.403185i	0.0421424	−	0.0353616i
$131$	−2.92281	−	16.5761i	−0.255367	−	1.44826i	−0.795129	−	0.606440i	$-0.792597\pi$
$131$	−2.92281	−	16.5761i	−0.255367	−	1.44826i	0.539762	−	0.841818i	$-0.318514\pi$
$132$	−2.50050	−	2.73320i	−0.217641	−	0.237894i
$133$	2.84679	−	9.28092i	0.246848	−	0.804758i
$134$			8.91666i			0.770282i
$135$	−1.55063	−	4.95939i	−0.133457	−	0.426836i
$136$	1.27053	−	0.733538i	0.108947	−	0.0629004i
$137$	12.4210	−	14.8028i	1.06120	−	1.26469i	0.0982083	−	0.995166i	$-0.468689\pi$
$137$	12.4210	−	14.8028i	1.06120	−	1.26469i	0.962993	−	0.269525i	$-0.0868667\pi$
$138$	9.63991	−	8.81919i	0.820603	−	0.750740i
$139$	−0.972372	−	1.15883i	−0.0824755	−	0.0982905i	0.723229	−	0.690609i	$-0.242657\pi$
$139$	−0.972372	−	1.15883i	−0.0824755	−	0.0982905i	−0.805704	+	0.592318i	$0.798213\pi$
$140$	2.42808	−	0.125013i	0.205210	−	0.0105656i
$141$	−3.53184	+	6.77138i	−0.297434	+	0.570253i
$142$	8.21583	−	2.99032i	0.689457	−	0.250942i
$143$	0.854469			0.0714543
$144$	−10.6096	+	10.5757i	−0.884131	+	0.881311i
$145$			6.29696i			0.522934i
$146$	−1.68681	+	9.56638i	−0.139601	+	0.791719i
$147$	−7.52255	−	9.50848i	−0.620449	−	0.784247i
$148$	1.49152	+	0.542869i	0.122602	+	0.0446235i
$149$	0.173688	+	0.206994i	0.0142291	+	0.0169576i	0.773112	−	0.634269i	$-0.218699\pi$
$149$	0.173688	+	0.206994i	0.0142291	+	0.0169576i	−0.758883	+	0.651227i	$0.774255\pi$
$150$	−2.93357	−	0.388596i	−0.239525	−	0.0317287i
$151$	−5.41629	+	1.97137i	−0.440772	+	0.160428i	−0.552867	−	0.833270i	$-0.686466\pi$
$151$	−5.41629	+	1.97137i	−0.440772	+	0.160428i	0.112095	+	0.993697i	$0.464244\pi$
$152$	6.77686			0.549676
$153$	−1.94980	−	1.36991i	−0.157632	−	0.110751i
$154$	8.39619	+	6.33909i	0.676585	+	0.510818i
$155$	2.77219	−	3.30377i	0.222668	−	0.265365i
$156$	0.0250227	+	0.583815i	0.00200342	+	0.0467426i
$157$	1.68338	+	2.00617i	0.134348	+	0.160110i	0.829024	−	0.559213i	$-0.188897\pi$
$157$	1.68338	+	2.00617i	0.134348	+	0.160110i	−0.694676	+	0.719323i	$0.744452\pi$
$158$	3.71626	−	10.2103i	0.295650	−	0.812290i
$159$	5.28608	−	16.7187i	0.419214	−	1.32588i
$160$	1.65445	+	4.54556i	0.130796	+	0.359358i
$161$	−7.03869	+	9.32282i	−0.554727	+	0.734741i
$162$	14.4322	+	5.30518i	1.13390	+	0.416814i
$163$	0.350941	−	0.607848i	0.0274878	−	0.0476103i	−0.851954	−	0.523616i	$-0.824583\pi$
$163$	0.350941	−	0.607848i	0.0274878	−	0.0476103i	0.879442	+	0.476006i	$0.157916\pi$
$164$	5.29162	+	4.44020i	0.413206	+	0.346721i
$165$	−2.72106	−	2.97428i	−0.211834	−	0.231547i
$166$	9.76242	−	1.72138i	0.757711	−	0.133605i
$167$	1.42117	+	8.05984i	0.109973	+	0.623689i	0.989117	+	0.147132i	$0.0470042\pi$
$167$	1.42117	+	8.05984i	0.109973	+	0.623689i	−0.879144	+	0.476557i	$0.841885\pi$
$168$	4.80598	−	6.96708i	0.370789	−	0.537522i
$169$	9.85533	+	8.26960i	0.758102	+	0.636123i
$170$	−1.17526	+	0.678539i	−0.0901386	+	0.0520416i
$171$	−4.63603	−	9.98361i	−0.354526	−	0.763466i
$172$	2.36143	−	4.09011i	0.180057	−	0.311868i
$173$	7.87888	+	6.61116i	0.599020	+	0.502637i	0.891130	−	0.453747i	$-0.149913\pi$
$173$	7.87888	+	6.61116i	0.599020	+	0.502637i	−0.292110	+	0.956385i	$0.594357\pi$
$174$	−14.7742	−	11.3554i	−1.12003	−	0.860853i
$175$	2.64225	−	0.136040i	0.199735	−	0.0102837i
$176$	−3.97488	+	10.9209i	−0.299618	+	0.823192i
$177$	−3.35844	+	25.3534i	−0.252436	+	1.90568i
$178$	−7.74395	−	21.2763i	−0.580434	−	1.59473i
$179$	1.71998	+	0.993029i	0.128557	+	0.0742225i	0.562899	−	0.826525i	$-0.309686\pi$
$179$	1.71998	+	0.993029i	0.128557	+	0.0742225i	−0.434342	+	0.900748i	$0.643019\pi$
$180$	1.95249	−	1.94626i	0.145530	−	0.145066i
$181$	7.53475	+	4.35019i	0.560053	+	0.323347i	0.753167	−	0.657829i	$-0.228525\pi$
$181$	7.53475	+	4.35019i	0.560053	+	0.323347i	−0.193114	+	0.981176i	$0.561859\pi$
$182$	−0.371828	−	1.61734i	−0.0275617	−	0.119885i
$183$	−6.74516	−	3.51816i	−0.498617	−	0.260070i
$184$	−7.66298	−	2.78910i	−0.564922	−	0.205615i
$185$	1.62308	+	0.590752i	0.119331	+	0.0434330i
$186$	2.75232	+	12.4620i	0.201810	+	0.913758i
$187$	−1.82061	−	0.321022i	−0.133136	−	0.0234755i
$188$	−4.05189			−0.295515
$189$	−13.5516	−	2.31396i	−0.985733	−	0.168316i
$190$	−6.26875			−0.454783
$191$	7.31775	+	1.29032i	0.529494	+	0.0933640i	0.432003	−	0.901872i	$-0.357807\pi$
$191$	7.31775	+	1.29032i	0.529494	+	0.0933640i	0.0974911	+	0.995236i	$0.468918\pi$
$192$	2.84448	+	0.899361i	0.205283	+	0.0649058i
$193$	7.30217	+	2.65777i	0.525621	+	0.191311i	0.591182	−	0.806538i	$-0.298661\pi$
$193$	7.30217	+	2.65777i	0.525621	+	0.191311i	−0.0655608	+	0.997849i	$0.520884\pi$
$194$	18.6840	+	6.80041i	1.34143	+	0.488241i
$195$	0.0272299	+	0.635310i	0.00194997	+	0.0454955i
$196$	2.62717	−	5.87167i	0.187655	−	0.419405i
$197$	6.05198	+	3.49411i	0.431186	+	0.248945i	0.699852	−	0.714288i	$-0.253249\pi$
$197$	6.05198	+	3.49411i	0.431186	+	0.248945i	−0.268666	+	0.963233i	$0.586583\pi$
$198$	11.8853	−	1.02070i	0.844654	−	0.0725383i
$199$	11.0378	+	6.37270i	0.782452	+	0.451749i	0.837299	−	0.546746i	$-0.184134\pi$
$199$	11.0378	+	6.37270i	0.782452	+	0.451749i	−0.0548465	+	0.998495i	$0.517467\pi$
$200$	0.631702	+	1.73559i	0.0446681	+	0.122725i
$201$	−7.16721	−	5.50869i	−0.505536	−	0.388553i
$202$	−8.83825	+	24.2829i	−0.621857	+	1.70854i
$203$	14.8374	+	7.57721i	1.04138	+	0.531816i
$204$	0.166022	−	1.25333i	0.0116239	−	0.0877505i
$205$	5.75837	+	4.83184i	0.402182	+	0.337471i
$206$	−12.6666	+	21.9391i	−0.882522	+	1.52857i
$207$	1.13335	+	13.1970i	0.0787734	+	0.917257i
$208$	1.58764	−	0.916627i	0.110083	−	0.0635566i
$209$	−6.54176	−	5.48919i	−0.452503	−	0.379695i
$210$	−4.44564	+	6.44470i	−0.306778	+	0.444727i
$211$	4.72494	+	26.7965i	0.325278	+	1.84474i	0.507714	+	0.861526i	$0.330491\pi$
$211$	4.72494	+	26.7965i	0.325278	+	1.84474i	−0.182436	+	0.983218i	$0.558398\pi$
$212$	9.16165	−	1.61545i	0.629225	−	0.110949i
$213$	−2.67211	+	8.45130i	−0.183090	+	0.579074i
$214$	0.387855	+	0.325449i	0.0265132	+	0.0222472i
$215$	2.56972	−	4.45088i	0.175253	−	0.303547i
$216$	−1.22988	−	9.51803i	−0.0836826	−	0.647620i
$217$	−4.44879	−	10.5075i	−0.302003	−	0.713297i
$218$	−5.22039	−	14.3429i	−0.353570	−	0.971424i
$219$	−6.64735	−	7.26595i	−0.449186	−	0.490987i
$220$	0.731499	−	2.00978i	0.0493177	−	0.135499i
$221$	0.187449	+	0.223393i	0.0126092	+	0.0150270i
$222$	−4.31298	+	2.74283i	−0.289468	+	0.184087i
$223$	−4.89737	+	5.83646i	−0.327952	+	0.390838i	−0.904675	−	0.426101i	$-0.859887\pi$
$223$	−4.89737	+	5.83646i	−0.327952	+	0.390838i	0.576723	+	0.816940i	$0.304331\pi$
$224$	12.7014	+	1.57139i	0.848649	+	0.104993i
$225$	2.12471	−	2.11793i	0.141647	−	0.141195i
$226$	28.1231			1.87072
$227$	−25.4837	+	9.27530i	−1.69141	+	0.615624i	−0.994802	−	0.101827i	$-0.967531\pi$
$227$	−25.4837	+	9.27530i	−1.69141	+	0.615624i	−0.696610	+	0.717450i	$0.745309\pi$
$228$	3.55891	−	4.63040i	0.235694	−	0.306655i
$229$	14.5634	+	17.3560i	0.962376	+	1.14691i	0.989096	+	0.147272i	$0.0470492\pi$
$229$	14.5634	+	17.3560i	0.962376	+	1.14691i	−0.0267203	+	0.999643i	$0.508506\pi$
$230$	7.08842	+	2.57997i	0.467397	+	0.170118i
$231$	−10.2825	+	2.83258i	−0.676540	+	0.186370i
$232$	−2.01959	+	11.4536i	−0.132592	+	0.751968i
$233$		−	1.01803i		−	0.0666932i	−0.999444	−	0.0333466i	$-0.989383\pi$
$233$		−	1.01803i		−	0.0666932i	0.999444	−	0.0333466i	$-0.0106165\pi$
$234$	−1.53970	−	1.08178i	−0.100653	−	0.0707180i
$235$	−4.40929			−0.287630
$236$	−12.7505	+	4.64080i	−0.829987	+	0.302091i
$237$	5.91117	+	9.29505i	0.383972	+	0.603778i
$238$	0.184617	+	3.58574i	0.0119670	+	0.232429i
$239$	4.02554	+	4.79746i	0.260391	+	0.310322i	0.880362	−	0.474303i	$-0.157300\pi$
$239$	4.02554	+	4.79746i	0.260391	+	0.310322i	−0.619971	+	0.784625i	$0.712856\pi$
$240$	−8.24650	−	2.60735i	−0.532309	−	0.168304i
$241$	0.806734	−	0.961428i	0.0519663	−	0.0619310i	−0.739435	−	0.673228i	$-0.764907\pi$
$241$	0.806734	−	0.961428i	0.0519663	−	0.0619310i	0.791401	+	0.611297i	$0.209352\pi$
$242$	−8.26083	+	4.76939i	−0.531026	+	0.306588i
$243$	−13.1805	+	8.32310i	−0.845530	+	0.533927i
$244$		−	4.03620i		−	0.258391i
$245$	2.85890	−	6.38958i	0.182649	−	0.408215i
$246$	−21.7209	+	4.79720i	−1.38487	+	0.305859i
$247$	0.233917	+	1.32661i	0.0148838	+	0.0844101i
$248$	6.10198	−	5.12017i	0.387476	−	0.325131i
$249$	−4.64756	+	8.91050i	−0.294527	+	0.564680i
$250$	−0.584339	−	1.60546i	−0.0369568	−	0.101538i
$251$	0.0269369	−	0.0466561i	0.00170024	−	0.00294491i	−0.865174	−	0.501472i	$-0.832792\pi$
$251$	0.0269369	−	0.0466561i	0.00170024	−	0.00294491i	0.866874	+	0.498527i	$0.166125\pi$
$252$	−2.23648	−	6.94256i	−0.140885	−	0.437340i
$253$	5.13800	+	8.89927i	0.323023	+	0.559492i
$254$	12.3803	−	14.7543i	0.776811	−	0.925768i
$255$	0.180666	−	1.36388i	0.0113138	−	0.0854093i
$256$	3.14507	+	17.8366i	0.196567	+	1.11478i
$257$	16.9691	−	14.2388i	1.05850	−	0.888189i	0.0645406	−	0.997915i	$-0.479442\pi$
$257$	16.9691	−	14.2388i	1.05850	−	0.888189i	0.993962	+	0.109726i	$0.0349974\pi$
$258$	5.80885	+	14.0555i	0.361643	+	0.875060i
$259$	3.34504	−	3.11356i	0.207851	−	0.193467i
$260$	−0.292175	+	0.168688i	−0.0181199	+	0.0104616i
$261$	18.2550	−	4.86017i	1.12996	−	0.300837i
$262$			28.7570i			1.77661i
$263$	−20.5395	−	3.62167i	−1.26652	−	0.223321i	−0.500272	−	0.865868i	$-0.666767\pi$
$263$	−20.5395	−	3.62167i	−1.26652	−	0.223321i	−0.766247	+	0.642547i	$0.777878\pi$
$264$	−3.99545	−	6.28267i	−0.245903	−	0.386672i
$265$	9.96976	−	1.75794i	0.612437	−	0.107989i
$266$	−7.54326	+	14.7709i	−0.462507	+	0.905662i
$267$	21.8861	+	6.91989i	1.33941	+	0.423490i
$268$	0.832815	−	4.72313i	0.0508723	−	0.288511i
$269$	15.9298	+	27.5913i	0.971260	+	1.68227i	0.691762	+	0.722125i	$0.256835\pi$
$269$	15.9298	+	27.5913i	0.971260	+	1.68227i	0.279498	+	0.960146i	$0.409832\pi$
$270$	1.13766	+	8.80439i	0.0692361	+	0.535818i
$271$	12.5998	+	7.27451i	0.765385	+	0.441895i	0.831226	−	0.555935i	$-0.187640\pi$
$271$	12.5998	+	7.27451i	0.765385	+	0.441895i	−0.0658410	+	0.997830i	$0.520973\pi$
$272$	−3.72715	+	1.35657i	−0.225992	+	0.0822542i
$273$	1.52973	+	0.700315i	0.0925836	+	0.0423850i
$274$	−25.2905	+	21.2213i	−1.52786	+	1.28202i
$275$	0.796021	−	2.18705i	0.0480019	−	0.131884i
$276$	−5.92995	+	3.77114i	−0.356941	+	0.226996i
$277$	−1.60360	+	9.09448i	−0.0963512	+	0.546435i	0.897974	+	0.440049i	$0.145039\pi$
$277$	−1.60360	+	9.09448i	−0.0963512	+	0.546435i	−0.994325	+	0.106386i	$0.966072\pi$
$278$	1.29225	+	2.23825i	0.0775042	+	0.134241i
$279$	−11.7173	−	5.48669i	−0.701498	−	0.328479i
$280$	4.84966	+	0.599987i	0.289823	+	0.0358561i
$281$	19.8785	+	3.50512i	1.18585	+	0.209098i	0.731574	−	0.681762i	$-0.238786\pi$
$281$	19.8785	+	3.50512i	1.18585	+	0.209098i	0.454279	+	0.890860i	$0.349897\pi$
$282$	7.95135	−	10.3453i	0.473496	−	0.616053i
$283$	15.1491	−	2.67119i	0.900518	−	0.158786i	0.295823	−	0.955243i	$-0.404406\pi$
$283$	15.1491	−	2.67119i	0.900518	−	0.158786i	0.604695	+	0.796457i	$0.293295\pi$
$284$	−4.63120	+	0.816606i	−0.274811	+	0.0484566i
$285$	3.87282	−	5.03882i	0.229406	−	0.298474i
$286$	−1.43768	−	0.253501i	−0.0850115	−	0.0149898i
$287$	18.3143	−	7.75410i	1.08106	−	0.457710i
$288$	11.9007	−	8.30466i	0.701255	−	0.489357i
$289$	8.18453	+	14.1760i	0.481443	+	0.833884i
$290$	1.86816	−	10.5949i	0.109702	−	0.622152i
$291$	−17.0091	+	10.8169i	−0.997091	+	0.634098i
$292$	1.78700	−	4.90974i	0.104576	−	0.287321i
$293$	−18.9587	+	15.9083i	−1.10758	+	0.929371i	−0.997911	−	0.0645972i	$-0.979424\pi$
$293$	−18.9587	+	15.9083i	−1.10758	+	0.929371i	−0.109670	+	0.993968i	$0.534979\pi$
$294$	9.83601	+	18.2301i	0.573648	+	1.06320i
$295$	−13.8752	+	5.05015i	−0.807843	+	0.294031i
$296$	2.76277	+	1.59509i	0.160583	+	0.0927126i
$297$	−6.52229	+	10.1840i	−0.378462	+	0.590937i
$298$	−0.230827	−	0.399804i	−0.0133714	−	0.0231600i
$299$	0.281478	−	1.59634i	0.0162783	−	0.0923188i
$300$	1.51761	+	0.479833i	0.0876192	+	0.0277032i
$301$	−7.39534	−	11.4108i	−0.426260	−	0.657705i
$302$	9.69797	−	1.71001i	0.558055	−	0.0984002i
$303$	−14.0583	−	22.1061i	−0.807630	−	1.26996i
$304$	−18.0434	−	3.18154i	−1.03486	−	0.182474i
$305$		−	4.39222i		−	0.251498i
$306$	2.87419	+	2.88339i	0.164307	+	0.164833i
$307$	24.2225	−	13.9849i	1.38245	−	0.798159i	0.390002	−	0.920814i	$-0.372474\pi$
$307$	24.2225	−	13.9849i	1.38245	−	0.798159i	0.992449	+	0.122655i	$0.0391408\pi$
$308$	−3.85537	−	4.14200i	−0.219680	−	0.236013i
$309$	−9.80930	−	23.7353i	−0.558031	−	1.35026i
$310$	−5.64447	+	4.73627i	−0.320584	+	0.269002i
$311$	1.30792	+	7.41758i	0.0741653	+	0.420612i	0.999173	+	0.0406636i	$0.0129472\pi$
$311$	1.30792	+	7.41758i	0.0741653	+	0.420612i	−0.925008	+	0.379949i	$0.875942\pi$
$312$	−0.154230	+	1.16431i	−0.00873157	+	0.0659160i
$313$	−10.1076	+	12.0458i	−0.571317	+	0.680869i	−0.971901	−	0.235391i	$-0.924363\pi$
$313$	−10.1076	+	12.0458i	−0.571317	+	0.680869i	0.400584	+	0.916260i	$0.368807\pi$
$314$	−2.23716	−	3.87487i	−0.126250	−	0.218672i
$315$	−2.43374	−	7.55492i	−0.137126	−	0.425672i
$316$	−2.92214	+	5.06129i	−0.164383	+	0.284720i
$317$	−2.13506	−	5.86602i	−0.119917	−	0.329469i	0.865182	−	0.501458i	$-0.167203\pi$
$317$	−2.13506	−	5.86602i	−0.119917	−	0.329469i	−0.985099	+	0.171989i	$0.944981\pi$
$318$	−13.8541	+	26.5616i	−0.776899	+	1.48950i
$319$	11.2269	−	9.42045i	0.628583	−	0.527444i
$320$	0.299091	+	1.69623i	0.0167197	+	0.0948221i
$321$	−0.501212	+	0.110696i	−0.0279749	+	0.00617845i
$322$	14.6087	−	13.5978i	0.814112	−	0.757774i
$323$		−	2.91447i		−	0.162166i
$324$	−7.14922	−	4.15811i	−0.397179	−	0.231006i
$325$	−0.317947	+	0.183567i	−0.0176365	+	0.0101824i
$326$	−0.770805	+	0.918609i	−0.0426909	+	0.0508771i
$327$	14.7540	+	4.66487i	0.815897	+	0.257968i
$328$	8.92429	+	10.6356i	0.492762	+	0.587250i
$329$	−5.30575	+	10.3895i	−0.292515	+	0.572792i
$330$	3.69588	+	5.81161i	0.203452	+	0.319919i
$331$	−11.9668	+	4.35556i	−0.657754	+	0.239403i	−0.649266	−	0.760561i	$-0.724924\pi$
$331$	−11.9668	+	4.35556i	−0.657754	+	0.239403i	−0.00848777	+	0.999964i	$0.502702\pi$
$332$	−5.33191			−0.292626
$333$	0.459863	−	5.16129i	0.0252003	−	0.282837i
$334$		−	13.9826i		−	0.765094i
$335$	0.906274	−	5.13973i	0.0495150	−	0.280814i
$336$	−16.0668	+	16.2936i	−0.876513	+	0.888887i
$337$	−0.0814021	−	0.0296279i	−0.00443426	−	0.00161394i	0.339802	−	0.940497i	$-0.389640\pi$
$337$	−0.0814021	−	0.0296279i	−0.00443426	−	0.00161394i	−0.344236	+	0.938883i	$0.611862\pi$
$338$	−14.1285	−	16.8377i	−0.768491	−	0.915852i
$339$	−17.3744	+	22.6053i	−0.943646	+	1.22775i
$340$	0.685910	−	0.249651i	0.0371987	−	0.0135392i
$341$	−10.0376			−0.543565
$342$	4.83839	+	18.1732i	0.261630	+	0.982694i
$343$	−11.6155	−	14.4250i	−0.627176	−	0.778878i
$344$	6.10160	−	7.27160i	0.328976	−	0.392058i
$345$	−6.45300	+	4.10377i	−0.347418	+	0.220940i
$346$	−11.2951	−	13.4610i	−0.607229	−	0.723668i
$347$	10.5894	−	29.0942i	0.568469	−	1.56186i	−0.238425	−	0.971161i	$-0.576631\pi$
$347$	10.5894	−	29.0942i	0.568469	−	1.56186i	0.806894	−	0.590696i	$-0.201147\pi$
$348$	6.76528	+	7.39486i	0.362657	+	0.396406i
$349$	−5.67563	−	15.5937i	−0.303809	−	0.834709i	−0.993829	−	0.110919i	$-0.964621\pi$
$349$	−5.67563	−	15.5937i	−0.303809	−	0.834709i	0.690020	−	0.723790i	$-0.257602\pi$
$350$	−4.48604	−	0.555001i	−0.239789	−	0.0296661i
$351$	1.82076	−	0.569289i	0.0971848	−	0.0303864i
$352$	5.62917	−	9.75002i	0.300036	−	0.519678i
$353$	−1.72841	−	1.45031i	−0.0919941	−	0.0771922i	0.595631	−	0.803258i	$-0.296902\pi$
$353$	−1.72841	−	1.45031i	−0.0919941	−	0.0771922i	−0.687625	+	0.726066i	$0.741347\pi$
$354$	13.1724	−	41.6616i	0.700107	−	2.21429i
$355$	−5.03970	+	0.888634i	−0.267479	+	0.0471638i
$356$	2.11474	+	11.9933i	0.112081	+	0.635644i
$357$	−2.99627	−	2.06687i	−0.158580	−	0.109390i
$358$	−2.59931	−	2.18108i	−0.137378	−	0.115274i
$359$	3.00381	−	1.73425i	0.158535	−	0.0915301i	−0.418634	−	0.908155i	$-0.637491\pi$
$359$	3.00381	−	1.73425i	0.158535	−	0.0915301i	0.577169	+	0.816625i	$0.304158\pi$
$360$	4.54393	−	3.17089i	0.239486	−	0.167121i
$361$	−2.76859	+	4.79535i	−0.145715	+	0.252387i
$362$	−11.3869	−	9.55473i	−0.598481	−	0.502186i
$363$	1.26989	−	9.58658i	0.0666518	−	0.503165i
$364$	0.0458966	+	0.891430i	0.00240563	+	0.0467236i
$365$	1.94462	−	5.34280i	0.101786	−	0.279655i
$366$	10.3052	+	7.92056i	0.538663	+	0.414014i
$367$	−0.567744	−	1.55986i	−0.0296360	−	0.0814243i	0.923992	−	0.382411i	$-0.124906\pi$
$367$	−0.567744	−	1.55986i	−0.0296360	−	0.0814243i	−0.953628	+	0.300987i	$0.902684\pi$
$368$	19.0933	+	11.0235i	0.995306	+	0.574640i
$369$	9.56312	−	20.4229i	0.497836	−	1.06318i
$370$	−2.55563	−	1.47549i	−0.132861	−	0.0767071i
$371$	7.85454	−	25.6069i	0.407787	−	1.32944i
$372$	−0.293946	−	6.85816i	−0.0152404	−	0.355579i
$373$	−29.5101	−	10.7408i	−1.52798	−	0.556138i	−0.564852	−	0.825192i	$-0.691067\pi$
$373$	−29.5101	−	10.7408i	−1.52798	−	0.556138i	−0.963125	+	0.269054i	$0.913289\pi$
$374$	2.96800	+	1.08026i	0.153471	+	0.0558591i
$375$	1.65147	+	0.522157i	0.0852815	+	0.0269641i
$376$	−8.02012	−	1.41416i	−0.413606	−	0.0729299i
$377$	−2.31182			−0.119065
$378$	22.1145	+	7.91377i	1.13745	+	0.407040i
$379$	−15.0906			−0.775151			−0.387575	−	0.921838i	$-0.626687\pi$
$379$	−15.0906			−0.775151			−0.387575	+	0.921838i	$0.626687\pi$
$380$	3.32054	+	0.585501i	0.170340	+	0.0300356i
$381$	4.21097	+	19.0665i	0.215734	+	0.976806i
$382$	−11.9296	−	4.34201i	−0.610370	−	0.222156i
$383$	35.1641	+	12.7987i	1.79680	+	0.653983i	0.998673	+	0.0514963i	$0.0163990\pi$
$383$	35.1641	+	12.7987i	1.79680	+	0.653983i	0.798129	+	0.602486i	$0.205823\pi$
$384$	−19.3765	−	10.1064i	−0.988800	−	0.515741i
$385$	−4.19543	−	4.50735i	−0.213819	−	0.229716i
$386$	−11.4977	−	6.63818i	−0.585215	−	0.337874i
$387$	−14.8865	−	4.01433i	−0.756725	−	0.204060i
$388$	−9.26169	−	5.34724i	−0.470191	−	0.271465i
$389$	−4.70823	−	12.9358i	−0.238717	−	0.655869i	−0.999972	−	0.00741731i	$-0.997639\pi$
$389$	−4.70823	−	12.9358i	−0.238717	−	0.655869i	0.761256	−	0.648452i	$-0.224583\pi$
$390$	0.142666	−	1.07701i	0.00722419	−	0.0545365i
$391$	−1.19948	+	3.29555i	−0.0606605	+	0.166663i
$392$	7.24939	−	10.7052i	0.366149	−	0.540693i
$393$	−23.1148	−	17.7660i	−1.16599	−	0.896176i
$394$	−9.14606	−	7.67445i	−0.460772	−	0.386633i
$395$	−3.17988	+	5.50772i	−0.159997	+	0.277123i
$396$	−6.39097	−	0.569425i	−0.321158	−	0.0286147i
$397$	−1.69876	+	0.980782i	−0.0852585	+	0.0492240i	−0.542023	−	0.840364i	$-0.682341\pi$
$397$	−1.69876	+	0.980782i	−0.0852585	+	0.0492240i	0.456765	+	0.889588i	$0.349008\pi$
$398$	−16.6809	−	13.9970i	−0.836140	−	0.701605i
$399$	−7.21265	−	15.1887i	−0.361084	−	0.760386i
$400$	−0.867100	−	4.91757i	−0.0433550	−	0.245878i
$401$	28.9380	−	5.10255i	1.44510	−	0.254809i	0.604557	−	0.796562i	$-0.293350\pi$
$401$	28.9380	−	5.10255i	1.44510	−	0.254809i	0.840538	+	0.541752i	$0.182239\pi$
$402$	10.4248	+	11.3949i	0.519941	+	0.568327i
$403$	1.21292	+	1.01776i	0.0604201	+	0.0506984i
$404$	6.94962	−	12.0371i	0.345756	−	0.598868i
$405$	−7.77981	−	4.52488i	−0.386582	−	0.224843i
$406$	−22.7165	−	17.1508i	−1.12740	−	0.851182i
$407$	−1.37492	−	3.77757i	−0.0681524	−	0.187247i
$408$	0.766044	−	2.42283i	0.0379248	−	0.119948i
$409$	4.02042	−	11.0460i	0.198797	−	0.546190i	−0.799735	−	0.600353i	$-0.795027\pi$
$409$	4.02042	−	11.0460i	0.198797	−	0.546190i	0.998532	+	0.0541629i	$0.0172490\pi$
$410$	−8.25517	−	9.83812i	−0.407694	−	0.485870i
$411$	−1.43322	−	33.4390i	−0.0706955	−	1.64942i
$412$	8.75856	−	10.4380i	0.431503	−	0.514246i
$413$	−4.79660	+	38.7706i	−0.236025	+	1.90778i
$414$	2.00834	−	22.5407i	0.0987048	−	1.10782i
$415$	−5.80221			−0.284819
$416$	−1.66883	+	0.607403i	−0.0818210	+	0.0297804i
$417$	−2.59746	−	0.344072i	−0.127198	−	0.0168493i
$418$	9.37824	+	11.1765i	0.458705	+	0.546663i
$419$	17.6521	+	6.42483i	0.862360	+	0.313874i	0.735069	−	0.677992i	$-0.237150\pi$
$419$	17.6521	+	6.42483i	0.862360	+	0.313874i	0.127291	+	0.991865i	$0.459372\pi$
$420$	2.95678	−	2.99852i	0.144276	−	0.146313i
$421$	−3.75386	+	21.2892i	−0.182952	+	1.03757i	0.745607	+	0.666386i	$0.232160\pi$
$421$	−3.75386	+	21.2892i	−0.182952	+	1.03757i	−0.928559	+	0.371185i	$0.878951\pi$
$422$		−	46.4878i		−	2.26299i
$423$	3.40321	+	12.7826i	0.165470	+	0.621511i
$424$	18.6979			0.908053
$425$	0.746410	−	0.271671i	0.0362062	−	0.0131780i
$426$	7.00322	−	13.4269i	0.339307	−	0.650534i
$427$	−10.3493	−	5.28520i	−0.500837	−	0.255769i
$428$	−0.175049	−	0.208615i	−0.00846130	−	0.0100838i
$429$	1.09196	−	0.998991i	0.0527202	−	0.0482318i
$430$	−5.64411	+	6.72639i	−0.272183	+	0.324375i
$431$	−6.36866	+	3.67695i	−0.306767	+	0.177112i	−0.645479	−	0.763778i	$-0.723342\pi$
$431$	−6.36866	+	3.67695i	−0.306767	+	0.177112i	0.338712	+	0.940890i	$0.390009\pi$
$432$	−1.19388	+	25.9191i	−0.0574407	+	1.24704i
$433$			31.7845i			1.52747i	0.645532	+	0.763733i	$0.276636\pi$
$433$			31.7845i			1.52747i	−0.645532	+	0.763733i	$0.723364\pi$
$434$	4.36791	+	18.9991i	0.209667	+	0.911988i
$435$	7.36201	+	8.04712i	0.352981	+	0.385830i
$436$	1.42560	+	8.08499i	0.0682739	+	0.387201i
$437$	−12.4100	+	10.4132i	−0.593652	+	0.498133i
$438$	9.02876	+	14.1973i	0.431411	+	0.678375i
$439$	3.26289	+	8.96472i	0.155729	+	0.427863i	0.992881	−	0.119108i	$-0.0380033\pi$
$439$	3.26289	+	8.96472i	0.155729	+	0.427863i	−0.837152	+	0.546970i	$0.815781\pi$
$440$	2.14933	−	3.72275i	0.102465	−	0.177475i
$441$	−20.7300	−	3.35635i	−0.987145	−	0.159826i
$442$	−0.249114	−	0.431478i	−0.0118492	−	0.0205233i
$443$	−7.91141	+	9.42845i	−0.375882	+	0.447959i	−0.920510	−	0.390719i	$-0.872226\pi$
$443$	−7.91141	+	9.42845i	−0.375882	+	0.447959i	0.544628	+	0.838678i	$0.316671\pi$
$444$	2.54075	−	1.05004i	0.120579	−	0.0498326i
$445$	2.30127	+	13.0512i	0.109091	+	0.618685i
$446$	9.97154	−	8.36712i	0.472166	−	0.396194i
$447$	0.463966	+	0.0614594i	0.0219449	+	0.00290693i
$448$	4.35668	+	1.33635i	0.205834	+	0.0631366i
$449$	17.9323	−	10.3532i	0.846277	−	0.488598i	−0.0131159	−	0.999914i	$-0.504175\pi$
$449$	17.9323	−	10.3532i	0.846277	−	0.488598i	0.859393	+	0.511316i	$0.170842\pi$
$450$	−4.20323	+	2.93314i	−0.198142	+	0.138270i
$451$		−	17.4952i		−	0.823816i
$452$	−14.8967	−	2.62669i	−0.700683	−	0.123549i
$453$	−4.61688	+	8.85167i	−0.216920	+	0.415888i
$454$	45.6290	−	8.04562i	2.14147	−	0.377600i
$455$	0.0499449	+	0.970058i	0.00234145	+	0.0454770i
$456$	8.66040	−	7.92308i	0.405560	−	0.371032i
$457$	−3.47863	+	19.7283i	−0.162723	+	0.922850i	0.788658	+	0.614833i	$0.210776\pi$
$457$	−3.47863	+	19.7283i	−0.162723	+	0.922850i	−0.951381	+	0.308017i	$0.900335\pi$
$458$	−19.3543	−	33.5227i	−0.904368	−	1.56641i
$459$	−4.09334	+	0.528924i	−0.191061	+	0.0246881i
$460$	−3.51375	−	2.02866i	−0.163829	−	0.0945870i
$461$	10.2457	−	3.72912i	0.477189	−	0.173682i	−0.0922174	−	0.995739i	$-0.529395\pi$
$461$	10.2457	−	3.72912i	0.477189	−	0.173682i	0.569406	+	0.822056i	$0.307173\pi$
$462$	18.1411	−	1.71534i	0.843998	−	0.0798050i
$463$	27.8102	−	23.3355i	1.29245	−	1.08449i	0.301050	−	0.953608i	$-0.402663\pi$
$463$	27.8102	−	23.3355i	1.29245	−	1.08449i	0.991398	−	0.130884i	$-0.0417815\pi$
$464$	10.7543	−	29.5472i	0.499256	−	1.37169i
$465$	−0.319873	−	7.46308i	−0.0148338	−	0.346092i
$466$	−0.302025	+	1.71287i	−0.0139910	+	0.0793470i
$467$	−4.80062	−	8.31491i	−0.222146	−	0.384768i	0.733313	−	0.679891i	$-0.237973\pi$
$467$	−4.80062	−	8.31491i	−0.222146	−	0.384768i	−0.955459	+	0.295123i	$0.904640\pi$
$468$	0.714536	+	0.716823i	0.0330295	+	0.0331352i
$469$	−11.0201	−	8.32013i	−0.508861	−	0.384188i
$470$	7.41879	+	1.30813i	0.342203	+	0.0603396i
$471$	4.49673	+	0.595660i	0.207198	+	0.0274466i
$472$	−26.8574	+	4.73569i	−1.23621	+	0.217978i
$473$	−11.7798	+	2.07710i	−0.541638	+	0.0955054i
$474$	−7.18813	−	17.3930i	−0.330162	−	0.798885i
$475$	3.61343	+	0.637145i	0.165795	+	0.0292342i
$476$	0.237117	−	1.91660i	0.0108682	−	0.0878473i
$477$	−12.7912	−	27.5456i	−0.585670	−	1.26123i
$478$	−5.34983	−	9.26618i	−0.244696	−	0.423825i
$479$	2.77329	−	15.7281i	0.126715	−	0.718635i	−0.853560	−	0.520995i	$-0.825561\pi$
$479$	2.77329	−	15.7281i	0.126715	−	0.718635i	0.980275	−	0.197640i	$-0.0633278\pi$
$480$	7.42866	+	3.87466i	0.339070	+	0.176853i
$481$	−0.216885	+	0.595886i	−0.00988909	+	0.0271701i
$482$	−1.64259	+	1.37830i	−0.0748180	+	0.0627798i
$483$	1.90465	+	20.1432i	0.0866648	+	0.916546i
$484$	4.82120	−	1.75477i	0.219146	−	0.0797625i
$485$	−10.0786	−	5.81889i	−0.457647	−	0.264222i
$486$	24.6460	−	10.0936i	1.11796	−	0.457854i
$487$	3.75660	+	6.50663i	0.170228	+	0.294844i	0.938500	−	0.345281i	$-0.112216\pi$
$487$	3.75660	+	6.50663i	0.170228	+	0.294844i	−0.768272	+	0.640124i	$0.778883\pi$
$488$	1.40869	−	7.98906i	0.0637683	−	0.361648i
$489$	−0.262177	−	1.18709i	−0.0118560	−	0.0536820i
$490$	−6.70584	+	9.90252i	−0.302939	+	0.447350i
$491$	−19.1944	+	3.38449i	−0.866231	+	0.152740i	−0.589069	−	0.808083i	$-0.700505\pi$
$491$	−19.1944	+	3.38449i	−0.866231	+	0.152740i	−0.277163	+	0.960823i	$0.589394\pi$
$492$	11.9535	−	0.512338i	0.538908	−	0.0230980i
$493$	4.92578	+	0.868547i	0.221846	+	0.0391174i
$494$		−	2.30147i		−	0.103548i
$495$	−6.95468	−	0.619651i	−0.312590	−	0.0278513i
$496$	−18.6503	+	10.7678i	−0.837423	+	0.483486i
$497$	−3.97046	+	12.9442i	−0.178099	+	0.580628i
$498$	10.4632	−	13.6134i	0.468868	−	0.610032i
$499$	−11.3994	+	9.56524i	−0.510308	+	0.428199i	−0.861237	−	0.508203i	$-0.830310\pi$
$499$	−11.3994	+	9.56524i	−0.510308	+	0.428199i	0.350930	+	0.936402i	$0.385866\pi$
$500$	0.159573	+	0.904984i	0.00713632	+	0.0404721i
$501$	11.2392	+	8.63842i	0.502131	+	0.385936i
$502$	−0.0591641	+	0.0705090i	−0.00264062	+	0.00314697i
$503$	−0.549784	−	0.952253i	−0.0245136	−	0.0424589i	0.853508	−	0.521079i	$-0.174470\pi$
$503$	−0.549784	−	0.952253i	−0.0245136	−	0.0424589i	−0.878022	+	0.478620i	$0.841137\pi$
$504$	−2.00373	−	14.5223i	−0.0892532	−	0.646876i
$505$	7.56261	−	13.0988i	0.336532	−	0.582890i
$506$	−6.00466	−	16.4977i	−0.266940	−	0.733411i
$507$	22.2628	−	0.954199i	0.988724	−	0.0423775i
$508$	−7.93589	+	6.65900i	−0.352098	+	0.295445i
$509$	5.09211	+	28.8788i	0.225704	+	1.28003i	0.861335	+	0.508037i	$0.169629\pi$
$509$	5.09211	+	28.8788i	0.225704	+	1.28003i	−0.635632	+	0.771993i	$0.719260\pi$
$510$	−0.708608	+	2.24117i	−0.0313777	+	0.0992408i
$511$	−10.2491	−	11.0111i	−0.453395	−	0.487103i
$512$		−	5.70918i		−	0.252312i
$513$	−17.5968	−	7.33826i	−0.776916	−	0.323992i
$514$	−32.7754	+	18.9229i	−1.44566	+	0.834653i
$515$	9.53111	−	11.3587i	0.419991	−	0.500526i
$516$	−1.76415	−	7.98773i	−0.0776622	−	0.351640i
$517$	6.59643	+	7.86132i	0.290111	+	0.345740i
$518$	−6.55188	+	4.24629i	−0.287873	+	0.186571i
$519$	17.7981	−	0.762838i	0.781248	−	0.0334849i
$520$	−0.637192	+	0.231919i	−0.0279427	+	0.0101703i
$521$	−19.2621			−0.843886			−0.421943	−	0.906622i	$-0.638652\pi$
$521$	−19.2621			−0.843886			−0.421943	+	0.906622i	$0.638652\pi$
$522$	−32.1566	+	2.76158i	−1.40746	+	0.120871i
$523$			31.2187i			1.36510i	0.730839	+	0.682550i	$0.239129\pi$
$523$			31.2187i			1.36510i	−0.730839	+	0.682550i	$0.760871\pi$
$524$	2.68590	−	15.2325i	0.117334	−	0.665434i
$525$	3.21758	−	3.26300i	0.140427	−	0.142409i
$526$	33.4840	+	12.1872i	1.45997	+	0.531386i
$527$	−2.20199	−	2.62423i	−0.0959202	−	0.114313i
$528$	7.68836	+	18.6034i	0.334593	+	0.809607i
$529$	−3.29453	+	1.19911i	−0.143241	+	0.0521353i
$530$	−17.2960			−0.751291
$531$	25.3497	+	36.3264i	1.10008	+	1.57643i
$532$	5.37525	−	7.11957i	0.233046	−	0.308673i
$533$	−1.77393	+	2.11409i	−0.0768374	+	0.0915713i
$534$	−34.7712	−	18.1361i	−1.50470	−	0.784824i
$535$	−0.190489	−	0.227016i	−0.00823555	−	0.00981475i
$536$	3.29687	−	9.05807i	0.142403	−	0.391249i
$537$	3.35901	−	0.741860i	0.144952	−	0.0320136i
$538$	−18.6169	−	51.1494i	−0.802630	−	2.20521i
$539$	−15.6690	+	4.46186i	−0.674911	+	0.192186i
$540$	0.219711	−	4.76992i	0.00945486	−	0.205265i
$541$	16.6718	−	28.8764i	0.716775	−	1.24149i	−0.245495	−	0.969398i	$-0.578951\pi$
$541$	16.6718	−	28.8764i	0.716775	−	1.24149i	0.962271	−	0.272094i	$-0.0877160\pi$
$542$	−19.0415	−	15.9777i	−0.817902	−	0.686301i
$543$	14.7149	−	3.24988i	0.631476	−	0.139466i
$544$	3.78395	−	0.667212i	0.162235	−	0.0286065i
$545$	1.55135	+	8.79812i	0.0664524	+	0.376870i
$546$	−2.36606	−	1.63214i	−0.101258	−	0.0698492i
$547$	14.1879	+	11.9051i	0.606631	+	0.509024i	0.893569	−	0.448925i	$-0.148193\pi$
$547$	14.1879	+	11.9051i	0.606631	+	0.509024i	−0.286939	+	0.957949i	$0.592638\pi$
$548$	15.3784	−	8.87871i	0.656932	−	0.379280i
$549$	−12.7331	+	3.39003i	−0.543435	+	0.144683i
$550$	−1.98818	+	3.44363i	−0.0847763	+	0.146837i
$551$	17.6992	+	14.8514i	0.754010	+	0.632690i
$552$	−13.0536	+	5.39478i	−0.555599	+	0.229617i
$553$	9.15132	+	14.1202i	0.389154	+	0.600451i
$554$	5.39624	−	14.8260i	0.229264	−	0.629898i
$555$	2.76486	−	1.14266i	0.117362	−	0.0485031i
$556$	−0.475451	−	1.30629i	−0.0201636	−	0.0553991i
$557$	−29.9769	−	17.3072i	−1.27016	−	0.733328i	−0.295144	−	0.955453i	$-0.595367\pi$
$557$	−29.9769	−	17.3072i	−1.27016	−	0.733328i	−0.975018	+	0.222125i	$0.928701\pi$
$558$	18.0871	+	12.7078i	0.765687	+	0.537964i
$559$	1.63407	+	0.943428i	0.0691136	+	0.0399028i
$560$	−12.6305	−	3.87424i	−0.533738	−	0.163716i
$561$	−2.70194	+	1.71829i	−0.114076	+	0.0725463i
$562$	−32.4064	−	11.7950i	−1.36698	−	0.497541i
$563$	−25.5096	−	9.28473i	−1.07510	−	0.391305i	−0.257019	−	0.966406i	$-0.582740\pi$
$563$	−25.5096	−	9.28473i	−1.07510	−	0.391305i	−0.818082	+	0.575102i	$0.804962\pi$
$564$	−5.17806	+	4.73721i	−0.218036	+	0.199473i
$565$	−16.2107	−	2.85838i	−0.681988	−	0.120253i
$566$	−26.2813			−1.10469
$567$	−20.0234	+	12.8866i	−0.840904	+	0.541185i
$568$	−9.45178			−0.396588
$569$	44.9441	+	7.92485i	1.88415	+	0.332227i	0.992673	−	0.120831i	$-0.0385560\pi$
$569$	44.9441	+	7.92485i	1.88415	+	0.332227i	0.891481	+	0.453058i	$0.149667\pi$
$570$	−8.01106	+	7.32902i	−0.335546	+	0.306979i
$571$	−7.41868	−	2.70018i	−0.310462	−	0.112999i	0.182090	−	0.983282i	$-0.441714\pi$
$571$	−7.41868	−	2.70018i	−0.310462	−	0.112999i	−0.492552	+	0.870283i	$0.663936\pi$
$572$	0.737856	+	0.268558i	0.0308513	+	0.0112290i
$573$	10.8602	−	6.90650i	0.453690	−	0.288523i
$574$	−33.1149	+	7.61313i	−1.38219	+	0.317766i
$575$	−3.82368	−	2.20760i	−0.159458	−	0.0920634i
$576$	4.68654	−	2.17626i	0.195273	−	0.0906777i
$577$	−23.4228	−	13.5232i	−0.975104	−	0.562977i	−0.0743157	−	0.997235i	$-0.523677\pi$
$577$	−23.4228	−	13.5232i	−0.975104	−	0.562977i	−0.900788	+	0.434258i	$0.857011\pi$
$578$	−9.56508	−	26.2798i	−0.397855	−	1.09310i
$579$	12.4390	−	5.14077i	0.516947	−	0.213643i
$580$	−1.97912	+	5.43759i	−0.0821785	+	0.225784i
$581$	−6.98186	+	13.6716i	−0.289656	+	0.567194i
$582$	31.8275	−	13.1536i	1.31929	−	0.545235i
$583$	−18.0493	−	15.1451i	−0.747525	−	0.627248i
$584$	5.25066	−	9.09441i	0.217274	−	0.376329i
$585$	0.777562	+	0.780050i	0.0321482	+	0.0322511i
$586$	36.6184	−	21.1416i	1.51269	−	0.873352i
$587$	20.8187	+	17.4689i	0.859279	+	0.721021i	0.961813	−	0.273709i	$-0.0882505\pi$
$587$	20.8187	+	17.4689i	0.859279	+	0.721021i	−0.102534	+	0.994730i	$0.532695\pi$
$588$	−3.50742	−	10.5751i	−0.144643	−	0.436111i
$589$	−2.74786	−	15.5839i	−0.113223	−	0.642122i
$590$	24.8437	−	4.38062i	1.02280	−	0.180347i
$591$	11.8191	−	2.61034i	0.486175	−	0.107375i
$592$	−6.60703	−	5.54396i	−0.271547	−	0.227855i
$593$	−9.98762	+	17.2991i	−0.410143	+	0.710388i	−0.994905	−	0.100817i	$-0.967854\pi$
$593$	−9.98762	+	17.2991i	−0.410143	+	0.710388i	0.584762	+	0.811205i	$0.301188\pi$
$594$	13.9954	−	15.2000i	0.574236	−	0.623662i
$595$	0.258032	−	2.08565i	0.0105783	−	0.0855035i
$596$	0.0849267	+	0.233334i	0.00347873	+	0.00955774i
$597$	21.5562	−	4.76084i	0.882237	−	0.194848i
$598$	−0.947194	+	2.60239i	−0.0387337	+	0.106420i
$599$	−22.1786	−	26.4314i	−0.906193	−	1.07996i	−0.996462	−	0.0840408i	$-0.973217\pi$
$599$	−22.1786	−	26.4314i	−0.906193	−	1.07996i	0.0902698	−	0.995917i	$-0.471227\pi$
$600$	2.83641	+	1.47942i	0.115796	+	0.0603972i
$601$	−15.4150	+	18.3709i	−0.628790	+	0.749363i	−0.982555	−	0.185971i	$-0.940457\pi$
$601$	−15.4150	+	18.3709i	−0.628790	+	0.749363i	0.353765	+	0.935334i	$0.384901\pi$
$602$	9.05762	+	21.3930i	0.369161	+	0.871915i
$603$	−15.5996	+	1.33969i	−0.635267	+	0.0545563i
$604$	−5.29670			−0.215520
$605$	5.24646	−	1.90955i	0.213299	−	0.0776344i
$606$	17.0953	+	41.3651i	0.694449	+	1.68034i
$607$	−6.71515	−	8.00280i	−0.272560	−	0.324824i	0.612350	−	0.790587i	$-0.290224\pi$
$607$	−6.71515	−	8.00280i	−0.272560	−	0.324824i	−0.884909	+	0.465763i	$0.845780\pi$
$608$	16.6784	+	6.07046i	0.676400	+	0.246190i
$609$	27.8200	−	7.66375i	1.12732	−	0.310551i
$610$	−1.30307	+	7.39006i	−0.0527596	+	0.299215i
$611$		−	1.61880i		−	0.0654895i
$612$	−1.25315	−	1.79578i	−0.0506554	−	0.0725899i
$613$	40.5739			1.63877			0.819383	−	0.573247i	$-0.194316\pi$
$613$	40.5739			1.63877			0.819383	+	0.573247i	$0.194316\pi$
$614$	−44.9042	+	16.3438i	−1.81219	+	0.659582i
$615$	13.0079	−	0.557529i	0.524529	−	0.0224817i
$616$	−6.18552	−	9.54406i	−0.249222	−	0.384541i
$617$	−24.2637	−	28.9164i	−0.976820	−	1.16413i	−0.986431	−	0.164175i	$-0.947504\pi$
$617$	−24.2637	−	28.9164i	−0.976820	−	1.16413i	0.00961149	−	0.999954i	$-0.496941\pi$
$618$	9.46278	+	42.8458i	0.380649	+	1.72351i
$619$	9.00253	−	10.7288i	0.361842	−	0.431227i	−0.554154	−	0.832414i	$-0.686958\pi$
$619$	9.00253	−	10.7288i	0.361842	−	0.431227i	0.915996	+	0.401188i	$0.131402\pi$
$620$	3.43223	−	1.98160i	0.137842	−	0.0795829i
$621$	16.8775	+	15.5399i	0.677270	+	0.623596i
$622$		−	12.8684i		−	0.515975i
$623$	33.5213	+	10.2822i	1.34300	+	0.411947i
$624$	0.957246	−	3.02756i	0.0383205	−	0.121200i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	20.5802	−	17.2688i	0.822549	−	0.690200i
$627$	−14.7776	+	0.633378i	−0.590159	+	0.0252947i
$628$	0.823104	+	2.26146i	0.0328454	+	0.0902420i
$629$	0.685986	−	1.18816i	0.0273521	−	0.0473752i
$630$	1.85349	+	13.4335i	0.0738450	+	0.535202i
$631$	−17.6329	−	30.5410i	−0.701954	−	1.21582i	−0.967780	−	0.251798i	$-0.918978\pi$
$631$	−17.6329	−	30.5410i	−0.701954	−	1.21582i	0.265826	−	0.964021i	$-0.414355\pi$
$632$	−7.55039	+	8.99821i	−0.300338	+	0.357929i
$633$	37.3669	+	28.7201i	1.48520	+	1.14152i
$634$	1.85200	+	10.5032i	0.0735523	+	0.417136i
$635$	−8.63587	+	7.24635i	−0.342704	+	0.287563i
$636$	9.81933	−	12.7757i	0.389362	−	0.506588i
$637$	2.34583	+	1.04960i	0.0929450	+	0.0415866i
$638$	−21.6844	+	12.5195i	−0.858494	+	0.495652i
$639$	6.46594	+	13.9243i	0.255789	+	0.550836i
$640$		−	12.6173i		−	0.498741i
$641$	−30.4919	−	5.37655i	−1.20436	−	0.212361i	−0.464777	−	0.885428i	$-0.653865\pi$
$641$	−30.4919	−	5.37655i	−1.20436	−	0.212361i	−0.739581	+	0.673067i	$0.764976\pi$
$642$	0.876147	−	0.0375523i	0.0345788	−	0.00148207i
$643$	24.4271	−	4.30715i	0.963310	−	0.169857i	0.330193	−	0.943914i	$-0.392886\pi$
$643$	24.4271	−	4.30715i	0.963310	−	0.169857i	0.633117	+	0.774056i	$0.281775\pi$
$644$	−9.00823	+	5.83825i	−0.354974	+	0.230059i
$645$	−1.91975	−	8.69229i	−0.0755901	−	0.342258i
$646$	−0.864655	+	4.90370i	−0.0340194	+	0.192934i
$647$	23.0431	+	39.9118i	0.905918	+	1.56910i	0.819680	+	0.572821i	$0.194151\pi$
$647$	23.0431	+	39.9118i	0.905918	+	1.56910i	0.0862378	+	0.996275i	$0.472516\pi$
$648$	−12.6996	−	10.7255i	−0.498887	−	0.421339i
$649$	29.7616	+	17.1828i	1.16824	+	0.674486i
$650$	0.589417	−	0.214530i	0.0231188	−	0.00841456i
$651$	−17.9700	−	8.22670i	−0.704299	−	0.322430i
$652$	0.494091	−	0.414592i	0.0193501	−	0.0162367i
$653$	−4.87423	+	13.3918i	−0.190744	+	0.524064i	−0.997792	−	0.0664222i	$-0.978842\pi$
$653$	−4.87423	+	13.3918i	−0.190744	+	0.524064i	0.807048	+	0.590486i	$0.201064\pi$
$654$	−23.4401	−	12.2260i	−0.916582	−	0.478073i
$655$	2.92281	−	16.5761i	0.114204	−	0.647681i
$656$	−18.7678	−	32.5069i	−0.732761	−	1.26918i
$657$	−16.9898	−	1.51376i	−0.662834	−	0.0590575i
$658$	12.0094	−	15.9066i	0.468176	−	0.620105i
$659$	−16.9284	−	2.98494i	−0.659438	−	0.116277i	−0.166093	−	0.986110i	$-0.553115\pi$
$659$	−16.9284	−	2.98494i	−0.659438	−	0.116277i	−0.493345	+	0.869833i	$0.664226\pi$
$660$	−1.41489	−	3.42359i	−0.0550747	−	0.133263i
$661$	34.7685	−	6.13063i	1.35234	−	0.238454i	0.549921	−	0.835216i	$-0.314658\pi$
$661$	34.7685	−	6.13063i	1.35234	−	0.238454i	0.802418	+	0.596762i	$0.203547\pi$
$662$	21.4267	−	3.77811i	0.832774	−	0.146841i
$663$	0.500725	+	0.0663285i	0.0194465	+	0.00257599i
$664$	−10.5537	−	1.86091i	−0.409564	−	0.0722172i
$665$	5.84937	−	7.74755i	0.226829	−	0.300437i
$666$	−2.30497	+	8.54762i	−0.0893157	+	0.331213i
$667$	−13.9012	−	24.0776i	−0.538256	−	0.932287i
$668$	−1.30597	+	7.40654i	−0.0505296	+	0.286568i
$669$	0.565090	+	13.1843i	0.0218476	+	0.509735i
$670$	−3.04968	+	8.37892i	−0.117819	+	0.323706i
$671$	−7.83088	+	6.57089i	−0.302308	+	0.253666i
$672$	18.0688	−	12.8416i	0.697018	−	0.495374i
$673$	12.5825	−	4.57967i	0.485021	−	0.176533i	−0.0879238	−	0.996127i	$-0.528023\pi$
$673$	12.5825	−	4.57967i	0.485021	−	0.176533i	0.572945	+	0.819594i	$0.305801\pi$
$674$	0.128172	+	0.0740002i	0.00493700	+	0.00285038i
$675$	0.239091	−	5.19065i	0.00920261	−	0.199788i
$676$	5.91121	+	10.2385i	0.227354	+	0.393789i
$677$	−4.21464	+	23.9024i	−0.161982	+	0.918644i	0.790140	+	0.612926i	$0.210008\pi$
$677$	−4.21464	+	23.9024i	−0.161982	+	0.918644i	−0.952122	+	0.305718i	$0.901104\pi$
$678$	35.9395	−	32.8797i	1.38025	−	1.26274i
$679$	−25.8386	+	16.7461i	−0.991596	+	0.642656i
$680$	1.44479	−	0.254755i	0.0554051	−	0.00976941i
$681$	−21.7224	+	41.6471i	−0.832405	+	1.59592i
$682$	16.8886	+	2.97791i	0.646697	+	0.114030i
$683$		−	18.0779i		−	0.691731i	−0.938284	−	0.345865i	$-0.887585\pi$
$683$		−	18.0779i		−	0.691731i	0.938284	−	0.345865i	$-0.112415\pi$
$684$	−0.865508	−	10.0782i	−0.0330935	−	0.385350i
$685$	16.7348	−	9.66186i	0.639405	−	0.369161i
$686$	15.2639	+	27.7166i	0.582777	+	1.05823i
$687$	38.9026	+	5.15323i	1.48423	+	0.196608i
$688$	−19.6593	+	16.4961i	−0.749504	+	0.628908i
$689$	0.645397	+	3.66023i	0.0245877	+	0.139444i
$690$	12.0749	−	4.99029i	0.459683	−	0.189977i
$691$	−27.0462	+	32.2324i	−1.02888	+	1.22618i	−0.0551535	+	0.998478i	$0.517565\pi$
$691$	−27.0462	+	32.2324i	−1.02888	+	1.22618i	−0.973731	+	0.227699i	$0.926880\pi$
$692$	4.72574	+	8.18522i	0.179646	+	0.311155i
$693$	−9.82872	+	15.6415i	−0.373362	+	0.594172i
$694$	−26.4486	+	45.8104i	−1.00398	+	1.73894i
$695$	−0.517388	−	1.42151i	−0.0196257	−	0.0539210i
$696$	10.8100	+	16.9982i	0.409751	+	0.644315i
$697$	4.57395	−	3.83800i	0.173251	−	0.145375i
$698$	4.92317	+	27.9207i	0.186345	+	1.05681i
$699$	−1.19021	−	1.30097i	−0.0450180	−	0.0492073i
$700$	2.32441	+	0.712979i	0.0878544	+	0.0269481i
$701$		−	4.23632i		−	0.160003i	−0.996795	−	0.0800017i	$-0.974507\pi$
$701$		−	4.23632i		−	0.160003i	0.996795	−	0.0800017i	$-0.0254926\pi$
$702$	−3.23238	+	0.417674i	−0.121998	+	0.0157641i
$703$	5.48848	−	3.16878i	0.207002	−	0.119513i
$704$	2.57676	−	3.07086i	0.0971152	−	0.115737i
$705$	−5.63479	+	5.15506i	−0.212218	+	0.194151i
$706$	2.47784	+	2.95298i	0.0932549	+	0.111137i
$707$	−21.7643	−	33.5816i	−0.818530	−	1.26296i
$708$	−10.8686	+	20.8377i	−0.408467	+	0.783130i
$709$	−5.09275	+	1.85361i	−0.191262	+	0.0696138i	−0.435876	−	0.900007i	$-0.643561\pi$
$709$	−5.09275	+	1.85361i	−0.191262	+	0.0696138i	0.244613	+	0.969621i	$0.421339\pi$
$710$	8.74311			0.328123
$711$	18.4213	+	4.96752i	0.690852	+	0.186296i
$712$			24.4770i			0.917316i
$713$	−3.30656	+	18.7525i	−0.123832	+	0.702285i
$714$	4.42815	+	4.36651i	0.165719	+	0.163412i
$715$	0.802939	+	0.292246i	0.0300282	+	0.0109294i
$716$	1.17314	+	1.39809i	0.0438422	+	0.0522491i
$717$	10.7533	+	1.42443i	0.401588	+	0.0531964i
$718$	−5.56852	+	2.02678i	−0.207815	+	0.0756386i
$719$	−22.1763			−0.827035			−0.413518	−	0.910496i	$-0.635700\pi$
$719$	−22.1763			−0.827035			−0.413518	+	0.910496i	$0.635700\pi$
$720$	−13.5868	+	6.30925i	−0.506352	+	0.235132i
$721$	−15.2954	−	36.1260i	−0.569632	−	1.34540i
$722$	6.08093	−	7.24696i	0.226309	−	0.269704i
$723$	−0.0930861	−	2.17182i	−0.00346191	−	0.0807710i
$724$	5.13919	+	6.12465i	0.190997	+	0.227621i
$725$	−2.15369	+	5.91721i	−0.0799860	+	0.219760i
$726$	−4.98074	+	15.7530i	−0.184853	+	0.584649i
$727$	10.8962	+	29.9369i	0.404116	+	1.11030i	0.960234	+	0.279196i	$0.0900680\pi$
$727$	10.8962	+	29.9369i	0.404116	+	1.11030i	−0.556118	+	0.831103i	$0.687710\pi$
$728$	−0.220275	+	1.78047i	−0.00816394	+	0.0659887i
$729$	−7.11301	+	26.0462i	−0.263445	+	0.964674i
$730$	−4.85698	+	8.41253i	−0.179765	+	0.311362i
$731$	−3.12724	−	2.62406i	−0.115665	−	0.0970545i
$732$	−4.71887	−	5.15801i	−0.174414	−	0.190645i
$733$	−16.9670	+	2.99173i	−0.626689	+	0.110502i	−0.477968	−	0.878377i	$-0.658627\pi$
$733$	−16.9670	+	2.99173i	−0.626689	+	0.110502i	−0.148721	+	0.988879i	$0.547516\pi$
$734$	0.492475	+	2.79296i	0.0181776	+	0.103090i
$735$	−3.81679	−	11.5079i	−0.140784	−	0.424476i
$736$	−16.3609	−	13.7284i	−0.603070	−	0.506036i
$737$	−10.5194	+	6.07340i	−0.387489	+	0.223717i
$738$	−22.1493	+	31.5252i	−0.815327	+	1.16046i
$739$	−8.89438	+	15.4055i	−0.327185	+	0.566701i	−0.981952	−	0.189130i	$-0.939433\pi$
$739$	−8.89438	+	15.4055i	−0.327185	+	0.566701i	0.654767	+	0.755831i	$0.272767\pi$
$740$	1.21590	+	1.02026i	0.0446973	+	0.0375055i
$741$	1.84992	+	1.42184i	0.0679584	+	0.0522326i
$742$	−20.8125	+	40.7542i	−0.764051	+	1.49613i
$743$	−6.49400	+	17.8421i	−0.238242	+	0.654564i	0.761736	+	0.647887i	$0.224347\pi$
$743$	−6.49400	+	17.8421i	−0.238242	+	0.654564i	−0.999978	+	0.00667613i	$0.997875\pi$
$744$	1.81176	−	13.6773i	0.0664225	−	0.501434i
$745$	0.0924176	+	0.253915i	0.00338592	+	0.00930274i
$746$	46.4653	+	26.8268i	1.70122	+	0.982198i
$747$	4.47830	+	16.8207i	0.163853	+	0.615437i
$748$	−1.47124	−	0.849423i	−0.0537940	−	0.0310580i
$749$	−0.764130	+	0.175674i	−0.0279207	+	0.00641898i
$750$	−2.62375	−	1.36850i	−0.0958056	−	0.0499706i
$751$	11.8513	+	4.31353i	0.432461	+	0.157403i	0.549073	−	0.835775i	$-0.314981\pi$
$751$	11.8513	+	4.31353i	0.432461	+	0.157403i	−0.116612	+	0.993178i	$0.537203\pi$
$752$	20.6897	+	7.53042i	0.754474	+	0.274606i
$753$	−0.0201237	−	0.0911164i	−0.000733348	−	0.00332047i
$754$	3.88973	+	0.685864i	0.141656	+	0.0249777i
$755$	−5.76390			−0.209770
$756$	−10.9749	−	6.25740i	−0.399152	−	0.227579i
$757$	35.0928			1.27547			0.637735	−	0.770256i	$-0.279872\pi$
$757$	35.0928			1.27547			0.637735	+	0.770256i	$0.279872\pi$
$758$	25.3904	+	4.47702i	0.922222	+	0.162613i
$759$	16.9705	+	5.36568i	0.615990	+	0.194762i
$760$	6.36817	+	2.31782i	0.230998	+	0.0840763i
$761$	7.00035	+	2.54792i	0.253762	+	0.0923620i	0.465769	−	0.884906i	$-0.345778\pi$
$761$	7.00035	+	2.54792i	0.253762	+	0.0923620i	−0.212007	+	0.977268i	$0.568000\pi$
$762$	−1.42852	−	33.3294i	−0.0517499	−	1.20740i
$763$	22.5976	+	6.93148i	0.818087	+	0.250936i
$764$	5.91352	+	3.41417i	0.213944	+	0.123520i
$765$	−1.36368	−	1.95417i	−0.0493039	−	0.0706532i
$766$	−55.3678	−	31.9666i	−2.00052	−	1.15500i
$767$	−1.85408	−	5.09403i	−0.0669468	−	0.183935i
$768$	24.8726	+	19.1170i	0.897511	+	0.689824i
$769$	−13.8610	+	38.0827i	−0.499839	+	1.37330i	0.391591	+	0.920139i	$0.371925\pi$
$769$	−13.8610	+	38.0827i	−0.499839	+	1.37330i	−0.891430	+	0.453157i	$0.850298\pi$
$770$	5.72175	+	8.82846i	0.206197	+	0.318156i
$771$	5.03836	−	38.0354i	0.181452	−	1.36981i
$772$	5.47028	+	4.59011i	0.196880	+	0.165202i
$773$	−11.5299	+	19.9703i	−0.414700	+	0.718282i	−0.995397	−	0.0958382i	$-0.969447\pi$
$773$	−11.5299	+	19.9703i	−0.414700	+	0.718282i	0.580697	+	0.814120i	$0.302780\pi$
$774$	23.8562	+	11.1707i	0.857493	+	0.401524i
$775$	3.73497	−	2.15638i	0.134164	−	0.0774596i
$776$	−16.4659	−	13.8165i	−0.591091	−	0.495984i
$777$	0.634573	−	7.88975i	0.0227652	−	0.283043i
$778$	4.08403	+	23.1617i	0.146420	+	0.830388i
$779$	27.1622	−	4.78943i	0.973186	−	0.171599i
$780$	−0.176163	+	0.557165i	−0.00630764	+	0.0199497i
$781$	9.12388	+	7.65585i	0.326478	+	0.273948i
$782$	2.99589	−	5.18903i	0.107133	−	0.185559i
$783$	17.6465	−	27.5536i	0.630635	−	0.984684i
$784$	−24.3273	+	25.0991i	−0.868831	+	0.896398i
$785$	0.895706	+	2.46093i	0.0319691	+	0.0878344i
$786$	33.6208	+	36.7496i	1.19921	+	1.31081i
$787$	−3.43325	+	9.43278i	−0.122382	+	0.336242i	−0.985722	−	0.168381i	$-0.946146\pi$
$787$	−3.43325	+	9.43278i	−0.122382	+	0.336242i	0.863340	+	0.504623i	$0.168368\pi$
$788$	4.12785	+	4.91938i	0.147049	+	0.175246i
$789$	−30.4824	+	19.3852i	−1.08520	+	0.690132i
$790$	6.98428	−	8.32354i	0.248489	−	0.296138i
$791$	−26.2416	+	34.7573i	−0.933045	+	1.23583i
$792$	−12.4512	−	3.35762i	−0.442435	−	0.119308i
$793$	1.61253			0.0572625
$794$	3.14921	−	1.14622i	0.111761	−	0.0406777i
$795$	10.6854	−	13.9025i	0.378974	−	0.493072i
$796$	7.52854	+	8.97216i	0.266842	+	0.318010i
$797$	−16.2376	−	5.91001i	−0.575166	−	0.209343i	0.0380266	−	0.999277i	$-0.487893\pi$
$797$	−16.2376	−	5.91001i	−0.575166	−	0.209343i	−0.613193	+	0.789933i	$0.710115\pi$
$798$	7.62940	+	27.6954i	0.270078	+	0.980405i
$799$	−0.608178	+	3.44915i	−0.0215158	+	0.122022i
$800$			4.83729i			0.171024i
$801$	36.0594	−	16.7447i	1.27409	−	0.591644i
$802$	−50.2031			−1.77273
$803$	−12.4349	+	4.52593i	−0.438818	+	0.159717i
$804$	−4.45770	−	7.00953i	−0.157211	−	0.247207i
$805$	−9.80280	+	6.35321i	−0.345503	+	0.223921i
$806$	−1.73884	−	2.07227i	−0.0612481	−	0.0729926i
$807$	52.6153	+	16.6358i	1.85215	+	0.585607i
$808$	17.9568	−	21.4001i	0.631720	−	0.752854i
$809$	−25.8312	+	14.9137i	−0.908177	+	0.524336i	−0.879844	−	0.475262i	$-0.842353\pi$
$809$	−25.8312	+	14.9137i	−0.908177	+	0.524336i	−0.0283327	+	0.999599i	$0.509020\pi$
$810$	11.7474	+	9.92136i	0.412761	+	0.348601i
$811$		−	22.1110i		−	0.776422i	−0.921571	−	0.388211i	$-0.873093\pi$
$811$		−	22.1110i		−	0.776422i	0.921571	−	0.388211i	$-0.126907\pi$
$812$	10.4310	+	11.2065i	0.366055	+	0.393270i
$813$	24.6067	−	5.43455i	0.862993	−	0.190598i
$814$	1.19264	+	6.76380i	0.0418020	+	0.237071i
$815$	0.537673	−	0.451161i	0.0188339	−	0.0158035i
$816$	−3.17704	+	6.09116i	−0.111219	+	0.213233i
$817$	−6.44963	−	17.7202i	−0.225644	−	0.619952i
$818$	−10.0416	+	17.3925i	−0.351096	+	0.608116i
$819$	2.77366	−	0.893508i	0.0969196	−	0.0312217i
$820$	3.45386	+	5.98226i	0.120614	+	0.208910i
$821$	−1.20666	+	1.43805i	−0.0421128	+	0.0501881i	−0.786690	−	0.617349i	$-0.788207\pi$
$821$	−1.20666	+	1.43805i	−0.0421128	+	0.0501881i	0.744577	+	0.667537i	$0.232651\pi$
$822$	−7.50911	+	56.6875i	−0.261910	+	1.97720i
$823$	−7.64600	−	43.3626i	−0.266523	−	1.51153i	−0.764664	−	0.644430i	$-0.777095\pi$
$823$	−7.64600	−	43.3626i	−0.266523	−	1.51153i	0.498141	−	0.867096i	$-0.334016\pi$
$824$	20.9793	−	17.6037i	0.730848	−	0.613255i
$825$	−1.53970	−	3.72557i	−0.0536053	−	0.129708i
$826$	19.5728	−	63.8099i	0.681024	−	2.22023i
$827$	24.5518	−	14.1750i	0.853751	−	0.492913i	−0.00816357	−	0.999967i	$-0.502599\pi$
$827$	24.5518	−	14.1750i	0.853751	−	0.492913i	0.861915	+	0.507053i	$0.169265\pi$
$828$	−3.16912	+	11.7522i	−0.110134	+	0.408417i
$829$			12.0627i			0.418956i	0.977813	+	0.209478i	$0.0671765\pi$
$829$			12.0627i			0.418956i	−0.977813	+	0.209478i	$0.932823\pi$
$830$	9.76242	+	1.72138i	0.338859	+	0.0597499i
$831$	8.58339	+	13.4970i	0.297754	+	0.468206i
$832$	−0.622742	+	0.109806i	−0.0215897	+	0.00380684i
$833$	−4.60389	−	3.11769i	−0.159515	−	0.108021i
$834$	4.26824	+	1.34952i	0.147797	+	0.0467300i
$835$	−1.42117	+	8.05984i	−0.0491815	+	0.278922i
$836$	−3.92374	−	6.79612i	−0.135705	−	0.235049i
$837$	−21.3887	+	6.68753i	−0.739301	+	0.231155i
$838$	−27.7942	−	16.0470i	−0.960133	−	0.554333i
$839$	20.7910	−	7.56730i	0.717785	−	0.261252i	0.0427997	−	0.999084i	$-0.486372\pi$
$839$	20.7910	−	7.56730i	0.717785	−	0.261252i	0.674985	+	0.737831i	$0.264150\pi$
$840$	6.89902	−	4.90317i	0.238039	−	0.169175i
$841$	−8.15973	+	6.84682i	−0.281370	+	0.236097i
$842$	12.6320	−	34.7061i	0.435327	−	1.19605i
$843$	29.5014	−	18.7614i	1.01608	−	0.646176i
$844$	−4.34196	+	24.6245i	−0.149456	+	0.847609i
$845$	6.43261	+	11.1416i	0.221288	+	0.383283i
$846$	−1.93373	−	22.5168i	−0.0664830	−	0.774144i
$847$	1.81368	−	14.6599i	0.0623189	−	0.503720i
$848$	−49.7833	−	8.77814i	−1.70956	−	0.301442i
$849$	16.2365	−	21.1249i	0.557237	−	0.725005i
$850$	−1.33646	+	0.235654i	−0.0458402	+	0.00808287i
$851$	−7.51028	+	1.32426i	−0.257449	+	0.0453952i
$852$	−4.96366	+	6.45808i	−0.170052	+	0.221250i
$853$	11.0308	+	1.94503i	0.377689	+	0.0665967i	0.359270	−	0.933234i	$-0.383026\pi$
$853$	11.0308	+	1.94503i	0.377689	+	0.0665967i	0.0184187	+	0.999830i	$0.494137\pi$
$854$	15.8450	+	11.9629i	0.542206	+	0.409363i
$855$	−0.941850	−	10.9671i	−0.0322106	−	0.375068i
$856$	−0.273674	−	0.474017i	−0.00935397	−	0.0162016i
$857$	−8.17972	+	46.3895i	−0.279414	+	1.58464i	0.445168	+	0.895447i	$0.353144\pi$
$857$	−8.17972	+	46.3895i	−0.279414	+	1.58464i	−0.724582	+	0.689188i	$0.757967\pi$
$858$	−2.13363	+	1.35688i	−0.0728411	+	0.0463231i
$859$	−0.623218	+	1.71228i	−0.0212639	+	0.0584221i	−0.949870	−	0.312644i	$-0.898785\pi$
$859$	−0.623218	+	1.71228i	−0.0212639	+	0.0584221i	0.928607	+	0.371066i	$0.121008\pi$
$860$	3.61792	−	3.03579i	0.123370	−	0.103520i
$861$	14.3389	−	31.3211i	0.488667	−	1.06742i
$862$	11.8064	−	4.29716i	0.402126	−	0.146362i
$863$	−0.101172	−	0.0584117i	−0.00344393	−	0.00198836i	0.498277	−	0.867018i	$-0.333966\pi$
$863$	−0.101172	−	0.0584117i	−0.00344393	−	0.00198836i	−0.501721	+	0.865030i	$0.667300\pi$
$864$	5.49905	−	24.5264i	0.187082	−	0.834404i
$865$	5.14257	+	8.90720i	0.174853	+	0.302854i
$866$	9.42972	−	53.4786i	0.320435	−	1.81728i
$867$	27.0330	+	8.54722i	0.918089	+	0.290279i
$868$	−0.539154	−	10.4718i	−0.0183001	−	0.355435i
$869$	14.5769	−	2.57030i	0.494488	−	0.0871915i
$870$	−9.99946	−	15.7237i	−0.339013	−	0.533083i
$871$	1.88697	+	0.332723i	0.0639374	+	0.0112739i
$872$			16.5006i			0.558780i
$873$	−9.09010	+	33.7092i	−0.307653	+	1.14089i
$874$	23.9697	−	13.8389i	0.810787	−	0.468108i
$875$	2.52943	+	0.775867i	0.0855104	+	0.0262291i
$876$	−3.45648	−	8.36358i	−0.116784	−	0.282579i
$877$	−39.2298	+	32.9177i	−1.32470	+	1.11155i	−0.339411	+	0.940638i	$0.610228\pi$
$877$	−39.2298	+	32.9177i	−1.32470	+	1.11155i	−0.985286	+	0.170915i	$0.945328\pi$
$878$	−2.83031	−	16.0515i	−0.0955183	−	0.541711i
$879$	−5.62912	+	42.4951i	−0.189865	+	1.43332i
$880$	−7.47032	+	8.90278i	−0.251825	+	0.300113i
$881$	−15.7890	−	27.3473i	−0.531945	−	0.921355i	−0.999305	−	0.0372882i	$-0.988128\pi$
$881$	−15.7890	−	27.3473i	−0.531945	−	0.921355i	0.467360	−	0.884067i	$-0.345205\pi$
$882$	33.8833	+	11.7973i	1.14091	+	0.397236i
$883$	−0.764928	+	1.32489i	−0.0257419	+	0.0445862i	−0.878609	−	0.477541i	$-0.841528\pi$
$883$	−0.764928	+	1.32489i	−0.0257419	+	0.0445862i	0.852867	+	0.522127i	$0.174861\pi$
$884$	0.0916551	+	0.251820i	0.00308269	+	0.00846963i
$885$	−11.8273	+	22.6757i	−0.397569	+	0.762236i
$886$	16.1084	−	13.5166i	0.541173	−	0.454098i
$887$	−4.41882	−	25.0604i	−0.148370	−	0.841445i	−0.964600	−	0.263719i	$-0.915051\pi$
$887$	−4.41882	−	25.0604i	−0.148370	−	0.841445i	0.816230	−	0.577727i	$-0.196060\pi$
$888$	5.39552	−	1.19164i	0.181062	−	0.0399888i
$889$	6.68278	+	29.0681i	0.224133	+	0.974913i
$890$		−	22.6418i		−	0.758955i
$891$	3.57143	+	20.6400i	0.119648	+	0.691465i
$892$	−6.06339	+	3.50070i	−0.203017	+	0.117212i
$893$	−10.3993	+	12.3934i	−0.347999	+	0.414729i
$894$	−0.762407	−	0.241056i	−0.0254987	−	0.00806210i
$895$	1.27661	+	1.52141i	0.0426725	+	0.0508551i
$896$	−29.7298	−	15.1825i	−0.993202	−	0.507212i
$897$	−1.50663	−	2.36911i	−0.0503049	−	0.0791022i
$898$	−33.2433	+	12.0996i	−1.10934	+	0.403768i
$899$	27.1573			0.905748
$900$	2.50040	−	1.16110i	0.0833466	−	0.0387032i
$901$		−	8.04128i		−	0.267894i
$902$	−5.19041	+	29.4363i	−0.172822	+	0.980120i
$903$	−22.7915	−	5.93606i	−0.758454	−	0.197540i
$904$	−28.5691	−	10.3983i	−0.950194	−	0.345842i
$905$	5.59249	+	6.66488i	0.185901	+	0.221548i
$906$	10.3941	−	13.5235i	0.345322	−	0.449289i
$907$	2.42806	−	0.883742i	0.0806224	−	0.0293442i	−0.301394	−	0.953500i	$-0.597452\pi$
$907$	2.42806	−	0.883742i	0.0806224	−	0.0293442i	0.382017	+	0.924156i	$0.375230\pi$
$908$	−24.9210			−0.827033
$909$	−43.8107	−	11.8141i	−1.45311	−	0.391848i
$910$	0.203759	−	1.64698i	0.00675456	−	0.0545967i
$911$	−4.17103	+	4.97084i	−0.138192	+	0.164691i	−0.830702	−	0.556717i	$-0.812061\pi$
$911$	−4.17103	+	4.97084i	−0.138192	+	0.164691i	0.692510	+	0.721409i	$0.256505\pi$
$912$	−26.7780	+	17.0294i	−0.886707	+	0.563899i
$913$	8.68028	+	10.3448i	0.287275	+	0.342361i
$914$	11.7058	−	32.1615i	0.387194	−	1.06381i
$915$	−5.13510	−	5.61297i	−0.169761	−	0.185559i
$916$	7.12092	+	19.5646i	0.235282	+	0.646431i
$917$	−35.5408	−	26.8331i	−1.17366	−	0.886108i
$918$	7.04412	+	0.324465i	0.232490	+	0.0107089i
$919$	14.5225	−	25.1538i	0.479054	−	0.829746i	−0.520657	−	0.853766i	$-0.674313\pi$
$919$	14.5225	−	25.1538i	0.479054	−	0.829746i	0.999711	+	0.0240196i	$0.00764643\pi$
$920$	−6.24692	−	5.24178i	−0.205955	−	0.172817i
$921$	14.6046	−	46.1912i	0.481238	−	1.52205i
$922$	−18.3451	+	3.23473i	−0.604162	+	0.106530i
$923$	−0.326247	−	1.85024i	−0.0107386	−	0.0609014i
$924$	−9.76949	−	0.785761i	−0.321392	−	0.0258496i
$925$	1.32315	+	1.11025i	0.0435048	+	0.0365048i
$926$	−53.7147	+	31.0122i	−1.76517	+	1.01912i
$927$	−40.2855	−	18.8638i	−1.32315	−	0.619570i
$928$	−15.2301	+	26.3793i	−0.499953	+	0.865944i
$929$	−7.35368	−	6.17047i	−0.241267	−	0.202447i	0.514134	−	0.857710i	$-0.328113\pi$
$929$	−7.35368	−	6.17047i	−0.241267	−	0.202447i	−0.755401	+	0.655263i	$0.772558\pi$
$930$	−1.67592	+	12.6518i	−0.0549557	+	0.414869i
$931$	−11.2168	−	23.1055i	−0.367615	−	0.757251i
$932$	0.319963	−	0.879092i	0.0104807	−	0.0287956i
$933$	10.3436	+	7.95005i	0.338634	+	0.260273i
$934$	5.61037	+	15.4144i	0.183577	+	0.504374i
$935$	−1.60102	−	0.924346i	−0.0523588	−	0.0302294i
$936$	1.16414	+	1.66823i	0.0380511	+	0.0545277i
$937$	2.44906	+	1.41397i	0.0800074	+	0.0461923i	0.539470	−	0.842005i	$-0.318625\pi$
$937$	2.44906	+	1.41397i	0.0800074	+	0.0461923i	−0.459463	+	0.888197i	$0.651958\pi$
$938$	16.0733	+	17.2683i	0.524813	+	0.563831i
$939$	1.16628	+	27.2110i	0.0380602	+	0.887996i
$940$	−3.80753	−	1.38583i	−0.124188	−	0.0452008i
$941$	16.6092	+	6.04525i	0.541444	+	0.197070i	0.598241	−	0.801316i	$-0.295866\pi$
$941$	16.6092	+	6.04525i	0.541444	+	0.197070i	−0.0567967	+	0.998386i	$0.518089\pi$
$942$	−7.38919	−	2.33629i	−0.240753	−	0.0761206i
$943$	−32.6849	−	5.76324i	−1.06437	−	0.187677i
$944$	73.7312			2.39975
$945$	−11.9429	−	6.80933i	−0.388503	−	0.221508i
$946$	20.4362			0.664440
$947$	50.4199	+	8.89039i	1.63843	+	0.288899i	0.915588	−	0.402118i	$-0.131726\pi$
$947$	50.4199	+	8.89039i	1.63843	+	0.288899i	0.722839	+	0.691017i	$0.242837\pi$
$948$	2.18303	+	9.88438i	0.0709016	+	0.321030i
$949$	1.96152	+	0.713935i	0.0636736	+	0.0231753i
$950$	−5.89070	−	2.14404i	−0.191119	−	0.0695618i
$951$	−9.58665	−	5.00023i	−0.310868	−	0.162144i
$952$	1.13826	−	3.71087i	0.0368911	−	0.120270i
$953$	−14.7483	−	8.51491i	−0.477743	−	0.275825i	0.241732	−	0.970343i	$-0.422284\pi$
$953$	−14.7483	−	8.51491i	−0.477743	−	0.275825i	−0.719475	+	0.694518i	$0.755618\pi$
$954$	13.3495	+	50.1414i	0.432207	+	1.62339i
$955$	6.43512	+	3.71532i	0.208236	+	0.120225i
$956$	1.96833	+	5.40794i	0.0636604	+	0.174905i
$957$	3.33341	−	25.1645i	0.107754	−	0.813451i
$958$	−9.33232	+	25.6403i	−0.301513	+	0.828401i
$959$	−2.62880	−	51.0581i	−0.0848885	−	1.64875i
$960$	2.36534	+	1.81799i	0.0763411	+	0.0586755i
$961$	9.49898	+	7.97059i	0.306419	+	0.257116i
$962$	0.541702	−	0.938255i	0.0174652	−	0.0302506i
$963$	−0.511098	+	0.727447i	−0.0164699	+	0.0234417i
$964$	0.998810	−	0.576663i	0.0321695	−	0.0185731i
$965$	5.95278	+	4.99498i	0.191627	+	0.160794i
$966$	2.77135	−	34.4567i	0.0891668	−	1.10862i
$967$	−7.14214	−	40.5051i	−0.229676	−	1.30256i	−0.853542	−	0.521024i	$-0.825550\pi$
$967$	−7.14214	−	40.5051i	−0.229676	−	1.30256i	0.623866	−	0.781531i	$-0.285561\pi$
$968$	10.1553	−	1.79065i	0.326404	−	0.0575538i
$969$	−3.40741	−	3.72451i	−0.109462	−	0.119648i
$970$	15.2313	+	12.7806i	0.489048	+	0.410360i
$971$	13.9811	−	24.2160i	0.448675	−	0.777127i	−0.549625	−	0.835411i	$-0.685230\pi$
$971$	13.9811	−	24.2160i	0.448675	−	0.777127i	0.998300	+	0.0582838i	$0.0185628\pi$
$972$	−13.9976	+	3.04461i	−0.448975	+	0.0976558i
$973$	−3.97206	−	0.491412i	−0.127338	−	0.0157540i
$974$	−4.39026	−	12.0621i	−0.140673	−	0.386496i
$975$	−0.191701	+	0.606309i	−0.00613935	+	0.0194174i
$976$	−7.50126	+	20.6095i	−0.240110	+	0.659695i
$977$	−4.43115	−	5.28084i	−0.141765	−	0.168949i	0.690490	−	0.723342i	$-0.257395\pi$
$977$	−4.43115	−	5.28084i	−0.141765	−	0.168949i	−0.832255	+	0.554393i	$0.812950\pi$
$978$	0.0889404	+	2.07510i	0.00284400	+	0.0663544i
$979$	19.8262	−	23.6279i	0.633647	−	0.755151i
$980$	4.47696	−	4.61901i	0.143011	−	0.147549i
$981$	24.3085	−	11.2880i	0.776111	−	0.360398i
$982$	33.2994			1.06263
$983$	11.1342	−	4.05250i	0.355125	−	0.129255i	−0.158296	−	0.987392i	$-0.550600\pi$
$983$	11.1342	−	4.05250i	0.355125	−	0.129255i	0.513421	+	0.858137i	$0.328378\pi$
$984$	23.8391	+	3.15785i	0.759962	+	0.100669i
$985$	4.49195	+	5.35329i	0.143125	+	0.170570i
$986$	−8.03012	−	2.92272i	−0.255731	−	0.0930785i
$987$	5.36634	+	19.4803i	0.170813	+	0.620064i
$988$	−0.214957	+	1.21908i	−0.00683869	+	0.0387841i
$989$			22.6916i			0.721552i
$990$	11.5177	+	3.10588i	0.366055	+	0.0987112i
$991$	7.81387			0.248216			0.124108	−	0.992269i	$-0.460393\pi$
$991$	7.81387			0.248216			0.124108	+	0.992269i	$0.460393\pi$
$992$	19.6040	−	7.13525i	0.622426	−	0.226545i
$993$	−10.2006	+	19.5569i	−0.323705	+	0.620620i
$994$	10.5207	−	20.6012i	0.333696	−	0.653430i
$995$	8.19259	+	9.76355i	0.259723	+	0.309525i
$996$	−6.81384	+	6.23373i	−0.215905	+	0.197523i
$997$	33.2500	−	39.6258i	1.05304	−	1.25496i	0.0870972	−	0.996200i	$-0.472241\pi$
$997$	33.2500	−	39.6258i	1.05304	−	1.25496i	0.965941	−	0.258762i	$-0.0833146\pi$
$998$	22.0177	−	12.7119i	0.696958	−	0.402389i
$999$	−5.44657	−	7.13343i	−0.172322	−	0.225692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cx.a.236.12	✓	288
7.3	odd	6		945.2.de.a.101.37	yes	288
27.23	odd	18		945.2.de.a.131.37	yes	288
189.185	even	18	inner	945.2.cx.a.941.12	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cx.a.236.12	✓	288	1.1	even	1	trivial
945.2.cx.a.941.12	yes	288	189.185	even	18	inner
945.2.de.a.101.37	yes	288	7.3	odd	6
945.2.de.a.131.37	yes	288	27.23	odd	18

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cx (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68254 - 0.296677i) q^{2} +(1.27794 - 1.16914i) q^{3} +(0.863525 + 0.314298i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-2.49703 + 1.58798i) q^{6} +(1.93664 - 1.80262i) q^{7} +(1.59953 + 0.923487i) q^{8} +(0.266241 - 2.98816i) q^{9} +O(q^{10})\)	\(q+(-1.68254 - 0.296677i) q^{2} +(1.27794 - 1.16914i) q^{3} +(0.863525 + 0.314298i) q^{4} +(0.939693 + 0.342020i) q^{5} +(-2.49703 + 1.58798i) q^{6} +(1.93664 - 1.80262i) q^{7} +(1.59953 + 0.923487i) q^{8} +(0.266241 - 2.98816i) q^{9} +(-1.47960 - 0.854246i) q^{10} +(-0.796021 - 2.18705i) q^{11} +(1.47099 - 0.607927i) q^{12} +(-0.125567 + 0.344992i) q^{13} +(-3.79326 + 2.45842i) q^{14} +(1.60074 - 0.661549i) q^{15} +(-3.82519 - 3.20971i) q^{16} +(0.397157 - 0.687896i) q^{17} +(-1.33448 + 4.94870i) q^{18} +(3.17759 - 1.83459i) q^{19} +(0.703952 + 0.590686i) q^{20} +(0.367391 - 4.56782i) q^{21} +(0.690488 + 3.91595i) q^{22} +(-4.34813 + 0.766692i) q^{23} +(3.12378 - 0.689907i) q^{24} +(0.766044 + 0.642788i) q^{25} +(0.313622 - 0.543209i) q^{26} +(-3.15333 - 4.12995i) q^{27} +(2.23889 - 0.947927i) q^{28} +(2.15369 + 5.91721i) q^{29} +(-2.88956 + 0.638179i) q^{30} +(1.47505 - 4.05268i) q^{31} +(3.10935 + 3.70558i) q^{32} +(-3.57422 - 1.86425i) q^{33} +(-0.872313 + 1.03958i) q^{34} +(2.43638 - 1.03154i) q^{35} +(1.16908 - 2.49668i) q^{36} +1.72724 q^{37} +(-5.89070 + 2.14404i) q^{38} +(0.242877 + 0.587683i) q^{39} +(1.18721 + 1.41486i) q^{40} +(7.06368 + 2.57097i) q^{41} +(-1.97331 + 7.57653i) q^{42} +(0.892453 - 5.06135i) q^{43} -2.13876i q^{44} +(1.27220 - 2.71689i) q^{45} +7.54334 q^{46} +(-4.14338 + 1.50807i) q^{47} +(-8.64094 + 0.370357i) q^{48} +(0.501127 - 6.98204i) q^{49} +(-1.09820 - 1.30878i) q^{50} +(-0.296703 - 1.34342i) q^{51} +(-0.216861 + 0.258444i) q^{52} +(8.76726 - 5.06178i) q^{53} +(4.08033 + 7.88431i) q^{54} -2.32741i q^{55} +(4.76240 - 1.09488i) q^{56} +(1.91588 - 6.05952i) q^{57} +(-1.86816 - 10.5949i) q^{58} +(-11.3111 + 9.49117i) q^{59} +(1.59020 - 0.0681571i) q^{60} +(-1.50223 - 4.12733i) q^{61} +(-3.68416 + 6.38116i) q^{62} +(-4.87091 - 6.26692i) q^{63} +(0.861198 + 1.49164i) q^{64} +(-0.235989 + 0.281240i) q^{65} +(5.46068 + 4.19706i) q^{66} +(-0.906274 - 5.13973i) q^{67} +(0.559159 - 0.469190i) q^{68} +(-4.66026 + 6.06334i) q^{69} +(-4.40532 + 1.01279i) q^{70} +(-4.43183 + 2.55872i) q^{71} +(3.18539 - 4.53378i) q^{72} -5.68569i q^{73} +(-2.90615 - 0.512433i) q^{74} +(1.73046 - 0.0741689i) q^{75} +(3.32054 - 0.585501i) q^{76} +(-5.48402 - 2.80060i) q^{77} +(-0.234297 - 1.06085i) q^{78} +(-1.10436 + 6.26315i) q^{79} +(-2.49672 - 4.32444i) q^{80} +(-8.85823 - 1.59114i) q^{81} +(-11.1222 - 6.42138i) q^{82} +(-5.45229 + 1.98447i) q^{83} +(1.75291 - 3.82896i) q^{84} +(0.608479 - 0.510575i) q^{85} +(-3.00317 + 8.25114i) q^{86} +(9.67030 + 5.04386i) q^{87} +(0.746456 - 4.23336i) q^{88} +(6.62626 + 11.4770i) q^{89} +(-2.94656 + 4.19384i) q^{90} +(0.378712 + 0.894474i) q^{91} +(-3.99569 - 0.704548i) q^{92} +(-2.85311 - 6.90360i) q^{93} +(7.41879 - 1.30813i) q^{94} +(3.61343 - 0.637145i) q^{95} +(8.30587 + 1.10024i) q^{96} +(-11.4610 - 2.02088i) q^{97} +(-2.91457 + 11.5989i) q^{98} +(-6.74719 + 1.79636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 6 q^{3} - 12 q^{6} + 6 q^{9}+O(q^{10}) \) 288 * q - 6 * q^3 - 12 * q^6 + 6 * q^9	\( 288 q - 6 q^{3} - 12 q^{6} + 6 q^{9} - 6 q^{11} - 42 q^{12} + 3 q^{13} + 42 q^{14} - 9 q^{23} - 24 q^{27} - 36 q^{29} + 12 q^{31} + 60 q^{33} + 60 q^{34} + 42 q^{36} + 42 q^{39} - 54 q^{41} + 63 q^{42} + 45 q^{43} + 30 q^{45} - 63 q^{47} + 18 q^{49} + 72 q^{51} + 102 q^{52} - 123 q^{54} - 27 q^{56} - 12 q^{57} + 48 q^{61} - 99 q^{62} - 66 q^{63} + 144 q^{64} + 3 q^{65} - 18 q^{66} + 54 q^{67} - 117 q^{68} + 198 q^{69} - 21 q^{70} - 36 q^{71} - 237 q^{72} + 6 q^{74} - 108 q^{76} + 27 q^{77} - 48 q^{78} + 9 q^{79} + 144 q^{80} + 6 q^{81} - 18 q^{83} + 69 q^{84} - 18 q^{85} - 3 q^{86} - 30 q^{90} + 18 q^{91} - 96 q^{92} + 12 q^{93} - 174 q^{94} - 60 q^{96} - 45 q^{97} - 234 q^{99}+O(q^{100}) \) 288 * q - 6 * q^3 - 12 * q^6 + 6 * q^9 - 6 * q^11 - 42 * q^12 + 3 * q^13 + 42 * q^14 - 9 * q^23 - 24 * q^27 - 36 * q^29 + 12 * q^31 + 60 * q^33 + 60 * q^34 + 42 * q^36 + 42 * q^39 - 54 * q^41 + 63 * q^42 + 45 * q^43 + 30 * q^45 - 63 * q^47 + 18 * q^49 + 72 * q^51 + 102 * q^52 - 123 * q^54 - 27 * q^56 - 12 * q^57 + 48 * q^61 - 99 * q^62 - 66 * q^63 + 144 * q^64 + 3 * q^65 - 18 * q^66 + 54 * q^67 - 117 * q^68 + 198 * q^69 - 21 * q^70 - 36 * q^71 - 237 * q^72 + 6 * q^74 - 108 * q^76 + 27 * q^77 - 48 * q^78 + 9 * q^79 + 144 * q^80 + 6 * q^81 - 18 * q^83 + 69 * q^84 - 18 * q^85 - 3 * q^86 - 30 * q^90 + 18 * q^91 - 96 * q^92 + 12 * q^93 - 174 * q^94 - 60 * q^96 - 45 * q^97 - 234 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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