LMFDB - Embedded newform 432.2.bg.a.157.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(13,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 16]))

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

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

chi := DirichletCharacter("432.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.bg (of order $36$, degree $12$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$70$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			157.10
Character	$\chi$	$=$	432.157
Dual form			432.2.bg.a.421.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28839 + 0.583148i) q^{2} +(-1.53223 - 0.807632i) q^{3} +(1.31988 - 1.50264i) q^{4} +(-1.86400 + 3.99736i) q^{5} +(2.44507 + 0.147023i) q^{6} +(-4.16246 + 0.733954i) q^{7} +(-0.824247 + 2.70566i) q^{8} +(1.69546 + 2.47496i) q^{9} +O(q^{10})$	\(q+(-1.28839 + 0.583148i) q^{2} +(-1.53223 - 0.807632i) q^{3} +(1.31988 - 1.50264i) q^{4} +(-1.86400 + 3.99736i) q^{5} +(2.44507 + 0.147023i) q^{6} +(-4.16246 + 0.733954i) q^{7} +(-0.824247 + 2.70566i) q^{8} +(1.69546 + 2.47496i) q^{9} +(0.0704963 - 6.23714i) q^{10} +(2.99267 - 1.39551i) q^{11} +(-3.23593 + 1.23642i) q^{12} +(0.0873603 + 0.998533i) q^{13} +(4.93485 - 3.37295i) q^{14} +(6.08448 - 4.61946i) q^{15} +(-0.515856 - 3.96660i) q^{16} +(-0.452610 + 0.783943i) q^{17} +(-3.62768 - 2.19999i) q^{18} +(0.774835 - 2.89172i) q^{19} +(3.54635 + 8.07695i) q^{20} +(6.97061 + 2.23715i) q^{21} +(-3.04193 + 3.54312i) q^{22} +(-5.56054 - 0.980473i) q^{23} +(3.44812 - 3.48001i) q^{24} +(-9.29048 - 11.0720i) q^{25} +(-0.694847 - 1.23555i) q^{26} +(-0.598986 - 5.16151i) q^{27} +(-4.39106 + 7.22341i) q^{28} +(1.30091 + 0.113815i) q^{29} +(-5.14533 + 9.49980i) q^{30} +(-0.401367 + 2.27627i) q^{31} +(2.97774 + 4.80969i) q^{32} +(-5.71252 - 0.278740i) q^{33} +(0.125981 - 1.27396i) q^{34} +(4.82495 - 18.0070i) q^{35} +(5.95677 + 0.718965i) q^{36} +(-1.69520 - 6.32657i) q^{37} +(0.688018 + 4.17750i) q^{38} +(0.672591 - 1.60054i) q^{39} +(-9.27913 - 8.33818i) q^{40} +(-1.91685 + 2.28442i) q^{41} +(-10.2854 + 1.18259i) q^{42} +(4.34474 - 2.02599i) q^{43} +(1.85301 - 6.33881i) q^{44} +(-13.0536 + 2.16406i) q^{45} +(7.73588 - 1.97939i) q^{46} +(0.000105566 + 0.000598694i) q^{47} +(-2.41314 + 6.49436i) q^{48} +(10.2095 - 3.71596i) q^{49} +(18.4263 + 8.84723i) q^{50} +(1.32664 - 0.835640i) q^{51} +(1.61574 + 1.18667i) q^{52} +(7.06619 - 7.06619i) q^{53} +(3.78165 + 6.30072i) q^{54} +14.5640i q^{55} +(1.44506 - 11.8672i) q^{56} +(-3.52267 + 3.80501i) q^{57} +(-1.74244 + 0.611986i) q^{58} +(0.870989 - 1.86784i) q^{59} +(1.08937 - 15.2399i) q^{60} +(-2.76945 + 3.95519i) q^{61} +(-0.810286 - 3.16677i) q^{62} +(-8.87379 - 9.05751i) q^{63} +(-6.64123 - 4.46027i) q^{64} +(-4.15434 - 1.51206i) q^{65} +(7.52248 - 2.97212i) q^{66} +(0.238984 + 2.73160i) q^{67} +(0.580596 + 1.71482i) q^{68} +(7.72816 + 5.99318i) q^{69} +(4.28433 + 26.0136i) q^{70} +(-10.1053 - 5.83431i) q^{71} +(-8.09388 + 2.54738i) q^{72} +(12.0451 - 6.95424i) q^{73} +(5.87340 + 7.16251i) q^{74} +(5.29309 + 24.4681i) q^{75} +(-3.32254 - 4.98102i) q^{76} +(-11.4326 + 8.00522i) q^{77} +(0.0667949 + 2.45433i) q^{78} +(3.27900 - 2.75141i) q^{79} +(16.8175 + 5.33168i) q^{80} +(-3.25082 + 8.39239i) q^{81} +(1.13749 - 4.06102i) q^{82} +(8.76070 + 0.766462i) q^{83} +(12.5620 - 7.52157i) q^{84} +(-2.29004 - 3.27052i) q^{85} +(-4.41625 + 5.14388i) q^{86} +(-1.90137 - 1.22505i) q^{87} +(1.30907 + 9.24741i) q^{88} +(-10.8363 + 6.25635i) q^{89} +(15.5562 - 10.4004i) q^{90} +(-1.09651 - 4.09223i) q^{91} +(-8.81252 + 7.06138i) q^{92} +(2.45337 - 3.16361i) q^{93} +(-0.000485137 - 0.000709788i) q^{94} +(10.1150 + 8.48748i) q^{95} +(-0.678124 - 9.77446i) q^{96} +(1.57361 + 0.572747i) q^{97} +(-10.9869 + 10.7413i) q^{98} +(8.52778 + 5.04071i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8}+O(q^{10}) $ 840 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 6 * q^8	\( 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 30 q^{12} - 12 q^{13} - 12 q^{14} - 24 q^{15} - 12 q^{16} - 12 q^{17} - 12 q^{18} - 6 q^{19} - 54 q^{20} - 12 q^{21} - 12 q^{22} + 18 q^{24} - 24 q^{26} - 12 q^{27} - 24 q^{28} - 12 q^{29} - 12 q^{30} - 24 q^{31} - 12 q^{32} - 24 q^{33} - 6 q^{35} - 12 q^{36} - 6 q^{37} - 12 q^{38} - 12 q^{40} - 72 q^{42} - 12 q^{43} - 6 q^{44} - 12 q^{45} - 6 q^{46} - 24 q^{47} - 12 q^{48} - 24 q^{49} - 168 q^{50} + 6 q^{51} - 12 q^{52} - 24 q^{53} + 156 q^{54} - 54 q^{56} + 42 q^{58} - 48 q^{59} - 72 q^{60} - 12 q^{61} + 60 q^{62} - 24 q^{63} - 6 q^{64} - 24 q^{65} - 198 q^{66} - 12 q^{67} - 66 q^{68} - 12 q^{69} - 54 q^{70} - 144 q^{72} - 96 q^{74} - 96 q^{75} - 12 q^{76} - 12 q^{77} - 90 q^{78} - 24 q^{79} - 204 q^{80} - 24 q^{81} - 24 q^{82} + 48 q^{83} + 36 q^{84} + 18 q^{85} - 72 q^{86} - 12 q^{88} - 66 q^{90} - 6 q^{91} + 102 q^{92} - 12 q^{93} - 12 q^{94} - 24 q^{95} - 120 q^{96} - 24 q^{97} - 6 q^{98} - 12 q^{99}+O(q^{100}) \) 840 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 6 * q^8 - 6 * q^10 - 12 * q^11 - 30 * q^12 - 12 * q^13 - 12 * q^14 - 24 * q^15 - 12 * q^16 - 12 * q^17 - 12 * q^18 - 6 * q^19 - 54 * q^20 - 12 * q^21 - 12 * q^22 + 18 * q^24 - 24 * q^26 - 12 * q^27 - 24 * q^28 - 12 * q^29 - 12 * q^30 - 24 * q^31 - 12 * q^32 - 24 * q^33 - 6 * q^35 - 12 * q^36 - 6 * q^37 - 12 * q^38 - 12 * q^40 - 72 * q^42 - 12 * q^43 - 6 * q^44 - 12 * q^45 - 6 * q^46 - 24 * q^47 - 12 * q^48 - 24 * q^49 - 168 * q^50 + 6 * q^51 - 12 * q^52 - 24 * q^53 + 156 * q^54 - 54 * q^56 + 42 * q^58 - 48 * q^59 - 72 * q^60 - 12 * q^61 + 60 * q^62 - 24 * q^63 - 6 * q^64 - 24 * q^65 - 198 * q^66 - 12 * q^67 - 66 * q^68 - 12 * q^69 - 54 * q^70 - 144 * q^72 - 96 * q^74 - 96 * q^75 - 12 * q^76 - 12 * q^77 - 90 * q^78 - 24 * q^79 - 204 * q^80 - 24 * q^81 - 24 * q^82 + 48 * q^83 + 36 * q^84 + 18 * q^85 - 72 * q^86 - 12 * q^88 - 66 * q^90 - 6 * q^91 + 102 * q^92 - 12 * q^93 - 12 * q^94 - 24 * q^95 - 120 * q^96 - 24 * q^97 - 6 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−1.28839	+	0.583148i	−0.911026	+	0.412348i
$2$	−1.28839	+	0.583148i	−0.911026	+	0.412348i
$3$	−1.53223	−	0.807632i	−0.884634	−	0.466286i
$3$	−1.53223	−	0.807632i	−0.884634	−	0.466286i
$4$	1.31988	−	1.50264i	0.659938	−	0.751320i
$5$	−1.86400	+	3.99736i	−0.833607	+	1.78768i	−0.266977	+	0.963703i	$0.586025\pi$
$5$	−1.86400	+	3.99736i	−0.833607	+	1.78768i	−0.566629	+	0.823973i	$0.691753\pi$
$6$	2.44507	+	0.147023i	0.998197	+	0.0600220i
$7$	−4.16246	+	0.733954i	−1.57326	+	0.277408i	−0.891105	−	0.453797i	$-0.850069\pi$
$7$	−4.16246	+	0.733954i	−1.57326	+	0.277408i	−0.682157	+	0.731206i	$0.738958\pi$
$8$	−0.824247	+	2.70566i	−0.291415	+	0.956597i
$9$	1.69546	+	2.47496i	0.565154	+	0.824985i
$10$	0.0704963	−	6.23714i	0.0222929	−	1.97236i
$11$	2.99267	−	1.39551i	0.902325	−	0.420761i	0.0846297	−	0.996412i	$-0.473029\pi$
$11$	2.99267	−	1.39551i	0.902325	−	0.420761i	0.817695	+	0.575651i	$0.195251\pi$
$12$	−3.23593	+	1.23642i	−0.934134	+	0.356923i
$13$	0.0873603	+	0.998533i	0.0242294	+	0.276943i	0.998639	+	0.0521619i	$0.0166112\pi$
$13$	0.0873603	+	0.998533i	0.0242294	+	0.276943i	−0.974409	+	0.224781i	$0.927833\pi$
$14$	4.93485	−	3.37295i	1.31889	−	0.901458i
$15$	6.08448	−	4.61946i	1.57101	−	1.19274i
$16$	−0.515856	−	3.96660i	−0.128964	−	0.991649i
$17$	−0.452610	+	0.783943i	−0.109774	+	0.190134i	−0.915679	−	0.401911i	$-0.868346\pi$
$17$	−0.452610	+	0.783943i	−0.109774	+	0.190134i	0.805905	+	0.592045i	$0.201679\pi$
$18$	−3.62768	−	2.19999i	−0.855051	−	0.518543i
$19$	0.774835	−	2.89172i	0.177759	−	0.663407i	−0.818306	−	0.574783i	$-0.805086\pi$
$19$	0.774835	−	2.89172i	0.177759	−	0.663407i	0.996065	−	0.0886239i	$-0.0282469\pi$
$20$	3.54635	+	8.07695i	0.792988	+	1.80606i
$21$	6.97061	+	2.23715i	1.52111	+	0.488186i
$22$	−3.04193	+	3.54312i	−0.648542	+	0.755396i
$23$	−5.56054	−	0.980473i	−1.15945	−	0.204443i	−0.439353	−	0.898314i	$-0.644792\pi$
$23$	−5.56054	−	0.980473i	−1.15945	−	0.204443i	−0.720099	+	0.693872i	$0.755904\pi$
$24$	3.44812	−	3.48001i	0.703844	−	0.710355i
$25$	−9.29048	−	11.0720i	−1.85810	−	2.21439i
$26$	−0.694847	−	1.23555i	−0.136271	−	0.242312i
$27$	−0.598986	−	5.16151i	−0.115275	−	0.993334i
$28$	−4.39106	+	7.22341i	−0.829832	+	1.36510i
$29$	1.30091	+	0.113815i	0.241573	+	0.0211349i	0.207299	−	0.978278i	$-0.433533\pi$
$29$	1.30091	+	0.113815i	0.241573	+	0.0211349i	0.0342737	+	0.999412i	$0.489088\pi$
$30$	−5.14533	+	9.49980i	−0.939404	+	1.73442i
$31$	−0.401367	+	2.27627i	−0.0720877	+	0.408830i	0.927315	+	0.374281i	$0.122110\pi$
$31$	−0.401367	+	2.27627i	−0.0720877	+	0.408830i	−0.999403	+	0.0345486i	$0.989001\pi$
$32$	2.97774	+	4.80969i	0.526394	+	0.850241i
$33$	−5.71252	−	0.278740i	−0.994422	−	0.0485224i
$34$	0.125981	−	1.27396i	0.0216055	−	0.218482i
$35$	4.82495	−	18.0070i	0.815565	−	3.04373i
$36$	5.95677	+	0.718965i	0.992795	+	0.119828i
$37$	−1.69520	−	6.32657i	−0.278689	−	1.04008i	−0.953329	−	0.301934i	$-0.902368\pi$
$37$	−1.69520	−	6.32657i	−0.278689	−	1.04008i	0.674640	−	0.738147i	$-0.264299\pi$
$38$	0.688018	+	4.17750i	0.111611	+	0.677680i
$39$	0.672591	−	1.60054i	0.107701	−	0.256291i
$40$	−9.27913	−	8.33818i	−1.46716	−	1.31838i
$41$	−1.91685	+	2.28442i	−0.299362	+	0.356766i	−0.894667	−	0.446734i	$-0.852587\pi$
$41$	−1.91685	+	2.28442i	−0.299362	+	0.356766i	0.595305	+	0.803500i	$0.297031\pi$
$42$	−10.2854	+	1.18259i	−1.58708	+	0.182478i
$43$	4.34474	−	2.02599i	0.662567	−	0.308960i	−0.0620891	−	0.998071i	$-0.519776\pi$
$43$	4.34474	−	2.02599i	0.662567	−	0.308960i	0.724656	+	0.689110i	$0.241999\pi$
$44$	1.85301	−	6.33881i	0.279352	−	0.955611i
$45$	−13.0536	+	2.16406i	−1.94592	+	0.322599i
$46$	7.73588	−	1.97939i	1.14059	−	0.291845i
$47$	0.000105566	0	0.000598694i	1.53984e−5	0	8.73285e-5i	0.984815	−	0.173605i	$-0.0555414\pi$
$47$	0.000105566	0	0.000598694i	1.53984e−5	0	8.73285e-5i	−0.984800	+	0.173692i	$0.944430\pi$
$48$	−2.41314	+	6.49436i	−0.348307	+	0.937381i
$49$	10.2095	−	3.71596i	1.45850	−	0.530852i
$50$	18.4263	+	8.84723i	2.60588	+	1.25119i
$51$	1.32664	−	0.835640i	0.185767	−	0.117013i
$52$	1.61574	+	1.18667i	0.224063	+	0.164561i
$53$	7.06619	−	7.06619i	0.970616	−	0.970616i	−0.0289640	−	0.999580i	$-0.509221\pi$
$53$	7.06619	−	7.06619i	0.970616	−	0.970616i	0.999580	+	0.0289640i	$0.00922081\pi$
$54$	3.78165	+	6.30072i	0.514618	+	0.857420i
$55$			14.5640i			1.96381i
$56$	1.44506	−	11.8672i	0.193104	−	1.58582i
$57$	−3.52267	+	3.80501i	−0.466590	+	0.503985i
$58$	−1.74244	+	0.611986i	−0.228794	+	0.0803577i
$59$	0.870989	−	1.86784i	0.113393	−	0.243172i	−0.841418	−	0.540384i	$-0.818279\pi$
$59$	0.870989	−	1.86784i	0.113393	−	0.243172i	0.954812	+	0.297212i	$0.0960567\pi$
$60$	1.08937	−	15.2399i	0.140637	−	1.96746i
$61$	−2.76945	+	3.95519i	−0.354592	+	0.506410i	−0.956332	−	0.292282i	$-0.905585\pi$
$61$	−2.76945	+	3.95519i	−0.354592	+	0.506410i	0.601740	+	0.798692i	$0.294474\pi$
$62$	−0.810286	−	3.16677i	−0.102906	−	0.402180i
$63$	−8.87379	−	9.05751i	−1.11799	−	1.14114i
$64$	−6.64123	−	4.46027i	−0.830154	−	0.557534i
$65$	−4.15434	−	1.51206i	−0.515282	−	0.187547i
$66$	7.52248	−	2.97212i	0.925953	−	0.365843i
$67$	0.238984	+	2.73160i	0.0291965	+	0.333718i	0.996719	+	0.0809343i	$0.0257904\pi$
$67$	0.238984	+	2.73160i	0.0291965	+	0.333718i	−0.967523	+	0.252783i	$0.918654\pi$
$68$	0.580596	+	1.71482i	0.0704076	+	0.207952i
$69$	7.72816	+	5.99318i	0.930362	+	0.721494i
$70$	4.28433	+	26.0136i	0.512076	+	3.10922i
$71$	−10.1053	−	5.83431i	−1.19928	−	0.692405i	−0.238886	−	0.971048i	$-0.576782\pi$
$71$	−10.1053	−	5.83431i	−1.19928	−	0.692405i	−0.960395	+	0.278642i	$0.910116\pi$
$72$	−8.09388	+	2.54738i	−0.953873	+	0.300211i
$73$	12.0451	−	6.95424i	1.40977	−	0.813932i	0.414406	−	0.910092i	$-0.363989\pi$
$73$	12.0451	−	6.95424i	1.40977	−	0.813932i	0.995366	+	0.0961601i	$0.0306561\pi$
$74$	5.87340	+	7.16251i	0.682769	+	0.832624i
$75$	5.29309	+	24.4681i	0.611193	+	2.82533i
$76$	−3.32254	−	4.98102i	−0.381121	−	0.571362i
$77$	−11.4326	+	8.00522i	−1.30287	+	0.912280i
$78$	0.0667949	+	2.45433i	0.00756303	+	0.277898i
$79$	3.27900	−	2.75141i	0.368916	−	0.309558i	−0.439416	−	0.898284i	$-0.644815\pi$
$79$	3.27900	−	2.75141i	0.368916	−	0.309558i	0.808333	+	0.588726i	$0.200370\pi$
$80$	16.8175	+	5.33168i	1.88025	+	0.596100i
$81$	−3.25082	+	8.39239i	−0.361202	+	0.932488i
$82$	1.13749	−	4.06102i	0.125615	−	0.448465i
$83$	8.76070	+	0.766462i	0.961612	+	0.0841302i	0.557139	−	0.830420i	$-0.311899\pi$
$83$	8.76070	+	0.766462i	0.961612	+	0.0841302i	0.404474	+	0.914550i	$0.367455\pi$
$84$	12.5620	−	7.52157i	1.37062	−	0.820670i
$85$	−2.29004	−	3.27052i	−0.248390	−	0.354737i
$86$	−4.41625	+	5.14388i	−0.476217	+	0.554679i
$87$	−1.90137	−	1.22505i	−0.203849	−	0.131339i
$88$	1.30907	+	9.24741i	0.139547	+	0.985777i
$89$	−10.8363	+	6.25635i	−1.14865	+	0.663172i	−0.948557	−	0.316605i	$-0.897457\pi$
$89$	−10.8363	+	6.25635i	−1.14865	+	0.663172i	−0.200090	+	0.979777i	$0.564124\pi$
$90$	15.5562	−	10.4004i	1.63976	−	1.09629i
$91$	−1.09651	−	4.09223i	−0.114946	−	0.428983i
$92$	−8.81252	+	7.06138i	−0.918768	+	0.736200i
$93$	2.45337	−	3.16361i	0.254403	−	0.328051i
$94$	−0.000485137	0	0.000709788i	−5.00381e−5	0	7.32090e-5i
$95$	10.1150	+	8.48748i	1.03778	+	0.870797i
$96$	−0.678124	−	9.77446i	−0.0692107	−	0.997602i
$97$	1.57361	+	0.572747i	0.159776	+	0.0581537i	0.420670	−	0.907214i	$-0.361795\pi$
$97$	1.57361	+	0.572747i	0.159776	+	0.0581537i	−0.260894	+	0.965367i	$0.584017\pi$
$98$	−10.9869	+	10.7413i	−1.10984	+	1.08503i
$99$	8.52778	+	5.04071i	0.857074	+	0.506610i
$100$	−28.8995	−	0.653366i	−2.88995	−	0.0653366i
$101$	−5.89588	−	4.12834i	−0.586662	−	0.410785i	0.242210	−	0.970224i	$-0.422128\pi$
$101$	−5.89588	−	4.12834i	−0.586662	−	0.410785i	−0.828872	+	0.559439i	$0.811017\pi$
$102$	−1.22192	+	1.85025i	−0.120988	+	0.183202i
$103$	1.97018	+	5.41302i	0.194128	+	0.533361i	0.998121	−	0.0612774i	$-0.0195174\pi$
$103$	1.97018	+	5.41302i	0.194128	+	0.533361i	−0.803993	+	0.594638i	$0.797295\pi$
$104$	−2.77370	−	0.586670i	−0.271984	−	0.0575277i
$105$	−21.9359	+	23.6940i	−2.14073	+	2.31230i
$106$	−4.98334	+	13.2246i	−0.484025	+	1.28449i
$107$	−5.92302	+	5.92302i	−0.572600	+	0.572600i	−0.932854	−	0.360254i	$-0.882690\pi$
$107$	−5.92302	+	5.92302i	−0.572600	+	0.572600i	0.360254	+	0.932854i	$0.382690\pi$
$108$	−8.54648	−	5.91250i	−0.822386	−	0.568930i
$109$	−4.12853	−	4.12853i	−0.395441	−	0.395441i	0.481180	−	0.876622i	$-0.340208\pi$
$109$	−4.12853	−	4.12853i	−0.395441	−	0.395441i	−0.876622	+	0.481180i	$0.840208\pi$
$110$	−8.49299	−	18.7641i	−0.809775	−	1.78909i
$111$	−2.51210	+	11.0629i	−0.238438	+	1.05004i
$112$	5.05853	+	16.1322i	0.477986	+	1.52435i
$113$	−17.1220	+	6.23190i	−1.61070	+	0.586247i	−0.981579	−	0.191058i	$-0.938808\pi$
$113$	−17.1220	+	6.23190i	−1.61070	+	0.586247i	−0.629123	+	0.777306i	$0.716586\pi$
$114$	2.31968	−	6.95656i	0.217258	−	0.651541i
$115$	14.2842	−	20.3999i	1.33200	−	1.90230i
$116$	1.88806	−	1.80458i	0.175302	−	0.167551i
$117$	−2.32321	+	1.90919i	−0.214781	+	0.176504i
$118$	−0.0329407	+	2.91442i	−0.00303244	+	0.268294i
$119$	1.30859	−	3.59532i	0.119958	−	0.329583i
$120$	7.48359	+	20.2701i	0.683155	+	1.85040i
$121$	−0.0620089	+	0.0738993i	−0.00563717	+	0.00671812i
$122$	1.26166	−	6.71081i	0.114225	−	0.607568i
$123$	4.78203	−	1.95214i	0.431181	−	0.176019i
$124$	2.89066	+	3.60750i	0.259588	+	0.323963i
$125$	40.2746	−	10.7915i	3.60227	−	0.965224i
$126$	16.7147	+	6.49483i	1.48907	+	0.578606i
$127$	−9.52841	−	16.5037i	−0.845509	−	1.46447i	−0.885178	−	0.465252i	$-0.845964\pi$
$127$	−9.52841	−	16.5037i	−0.845509	−	1.46447i	0.0396688	−	0.999213i	$-0.487370\pi$
$128$	11.1575	+	1.87372i	0.986190	+	0.165615i
$129$	−8.29340	−	0.404673i	−0.730193	−	0.0356294i
$130$	6.23414	−	0.474485i	0.546771	−	0.0416151i
$131$	−6.49449	+	4.54749i	−0.567426	+	0.397316i	−0.821788	−	0.569793i	$-0.807023\pi$
$131$	−6.49449	+	4.54749i	−0.567426	+	0.397316i	0.254362	+	0.967109i	$0.418134\pi$
$132$	−7.95866	+	8.21596i	−0.692713	+	0.715108i
$133$	−1.10283	+	12.6054i	−0.0956273	+	1.09302i
$134$	−1.90083	−	3.37999i	−0.164207	−	0.291986i
$135$	21.7490	+	7.22670i	1.87185	+	0.621976i
$136$	−1.74802	−	1.87077i	−0.149892	−	0.160417i
$137$	1.85218	+	2.20734i	0.158242	+	0.188586i	0.839340	−	0.543607i	$-0.182942\pi$
$137$	1.85218	+	2.20734i	0.158242	+	0.188586i	−0.681098	+	0.732192i	$0.738497\pi$
$138$	−13.4518	−	3.21486i	−1.14509	−	0.273667i
$139$	−7.84194	−	11.1994i	−0.665145	−	0.949925i	−0.999971	−	0.00764498i	$-0.997567\pi$
$139$	−7.84194	−	11.1994i	−0.665145	−	0.949925i	0.334826	−	0.942280i	$-0.391322\pi$
$140$	−20.6896	−	31.0171i	−1.74859	−	2.62142i
$141$	0.000321773	−	0.00100260i	2.70982e−5	−	8.44338e-5i
$142$	16.4218	+	1.62394i	1.37809	+	0.136278i
$143$	1.65490	+	2.86637i	0.138390	+	0.239698i
$144$	8.94254	−	8.00194i	0.745212	−	0.666828i
$145$	−2.87986	+	4.98806i	−0.239159	+	0.414236i
$146$	−11.4634	+	15.9838i	−0.948716	+	1.32283i
$147$	−18.6445	−	2.55182i	−1.53777	−	0.210471i
$148$	−11.7440	−	5.80301i	−0.965351	−	0.477004i
$149$	−5.57072	+	0.487375i	−0.456371	+	0.0399273i	−0.313024	−	0.949745i	$-0.601342\pi$
$149$	−5.57072	+	0.487375i	−0.456371	+	0.0399273i	−0.143347	+	0.989672i	$0.545787\pi$
$150$	−21.0881	−	28.4377i	−1.72183	−	2.32193i
$151$	0.537879	−	1.47781i	0.0437720	−	0.120262i	−0.915881	−	0.401450i	$-0.868506\pi$
$151$	0.537879	−	1.47781i	0.0437720	−	0.120262i	0.959653	+	0.281188i	$0.0907284\pi$
$152$	7.18538	+	4.47994i	0.582811	+	0.363371i
$153$	−2.70761	+	0.208956i	−0.218897	+	0.0168931i
$154$	10.0614	−	16.9807i	0.810772	−	1.36835i
$155$	−8.35092	−	5.84738i	−0.670762	−	0.469672i
$156$	−1.51730	−	3.12317i	−0.121481	−	0.250054i
$157$	3.76646	+	1.75633i	0.300596	+	0.140170i	0.567065	−	0.823673i	$-0.308079\pi$
$157$	3.76646	+	1.75633i	0.300596	+	0.140170i	−0.266468	+	0.963844i	$0.585857\pi$
$158$	−2.62014	+	5.45702i	−0.208447	+	0.434137i
$159$	−16.5339	+	5.12016i	−1.31123	+	0.406055i
$160$	−24.7766	+	2.93783i	−1.95876	+	0.232256i
$161$	23.8651			1.88084
$162$	−0.705703	−	12.7083i	−0.0554452	−	0.998462i
$163$	5.55978	+	5.55978i	0.435476	+	0.435476i	0.890486	−	0.455010i	$-0.150364\pi$
$163$	5.55978	+	5.55978i	0.435476	+	0.435476i	−0.455010	+	0.890486i	$0.650364\pi$
$164$	0.902648	+	5.89549i	0.0704850	+	0.460360i
$165$	11.7624	−	22.3155i	0.915699	−	1.73726i
$166$	−11.7341	+	4.12129i	−0.910745	+	0.319874i
$167$	−1.24242	−	3.41352i	−0.0961412	−	0.264146i	0.882294	−	0.470698i	$-0.155998\pi$
$167$	−1.24242	−	3.41352i	−0.0961412	−	0.264146i	−0.978436	+	0.206552i	$0.933776\pi$
$168$	−11.7985	+	17.0162i	−0.910272	+	1.31283i
$169$	11.8131	−	2.08296i	0.908697	−	0.160228i
$170$	4.85765	+	2.87825i	0.372565	+	0.220752i
$171$	8.47059	−	2.98513i	0.647763	−	0.228278i
$172$	2.69019	−	9.20264i	0.205125	−	0.701695i
$173$	−1.61288	−	3.45882i	−0.122625	−	0.262969i	0.835407	−	0.549632i	$-0.185232\pi$
$173$	−1.61288	−	3.45882i	−0.122625	−	0.262969i	−0.958032	+	0.286662i	$0.907454\pi$
$174$	3.16409	+	0.469550i	0.239869	+	0.0355965i
$175$	46.7976	+	39.2678i	3.53756	+	2.96837i
$176$	−7.07920	−	11.1508i	−0.533615	−	0.840527i
$177$	−2.84308	+	2.15853i	−0.213699	+	0.162245i
$178$	10.3130	−	14.3798i	0.772991	−	1.07781i
$179$	−5.94637	+	1.59333i	−0.444453	+	0.119091i	−0.474103	−	0.880470i	$-0.657227\pi$
$179$	−5.94637	+	1.59333i	−0.444453	+	0.119091i	0.0296498	+	0.999560i	$0.490561\pi$
$180$	−13.9774	+	22.4712i	−1.04181	+	1.67491i
$181$	9.28090	+	2.48681i	0.689844	+	0.184843i	0.586677	−	0.809821i	$-0.300436\pi$
$181$	9.28090	+	2.48681i	0.689844	+	0.184843i	0.103167	+	0.994664i	$0.467102\pi$
$182$	3.79911	+	4.63295i	0.281609	+	0.343417i
$183$	7.43778	−	3.82356i	0.549816	−	0.282646i
$184$	7.23608	−	14.2368i	0.533451	−	1.04955i
$185$	28.4494	+	5.01640i	2.09164	+	0.368813i
$186$	−1.31604	+	5.50663i	−0.0964965	+	0.403766i
$187$	−0.260515	+	2.97770i	−0.0190508	+	0.217751i
$188$	0.00103896		0.000631574i	7.57736e−5		4.60623e-5i
$189$	6.28157	+	21.0450i	0.456917	+	1.53080i
$190$	−17.9815	−	5.03661i	−1.30451	−	0.365394i
$191$	−8.82771	+	7.40733i	−0.638751	+	0.535976i	−0.903634	−	0.428305i	$-0.859111\pi$
$191$	−8.82771	+	7.40733i	−0.638751	+	0.535976i	0.264884	+	0.964280i	$0.414666\pi$
$192$	6.57365	+	12.1978i	0.474412	+	0.880303i
$193$	1.77251	−	10.0524i	0.127588	−	0.723589i	−0.852148	−	0.523300i	$-0.824701\pi$
$193$	1.77251	−	10.0524i	0.127588	−	0.723589i	0.979737	−	0.200289i	$-0.0641882\pi$
$194$	−2.36141	+	0.179729i	−0.169540	+	0.0129038i
$195$	5.14422	+	5.67199i	0.368385	+	0.406180i
$196$	7.89155	−	20.2459i	0.563682	−	1.44613i
$197$	2.58673	+	0.693113i	0.184297	+	0.0493823i	0.349787	−	0.936829i	$-0.386254\pi$
$197$	2.58673	+	0.693113i	0.184297	+	0.0493823i	−0.165490	+	0.986211i	$0.552921\pi$
$198$	−13.9266	−	1.52141i	−0.989717	−	0.108122i
$199$	−13.6546	−	7.88348i	−0.967949	−	0.558845i	−0.0693383	−	0.997593i	$-0.522089\pi$
$199$	−13.6546	−	7.88348i	−0.967949	−	0.558845i	−0.898610	+	0.438748i	$0.855422\pi$
$200$	37.6147	−	16.0109i	2.65976	−	1.13214i
$201$	1.83995	−	4.37845i	0.129780	−	0.308832i
$202$	10.0036	+	1.88072i	0.703850	+	0.132327i
$203$	−5.49852	+	0.481058i	−0.385920	+	0.0337637i
$204$	0.495334	−	3.09640i	0.0346803	−	0.216792i
$205$	−5.55863	−	11.9205i	−0.388231	−	0.832565i
$206$	−5.69495	−	5.82516i	−0.396786	−	0.405858i
$207$	−7.00105	−	15.4244i	−0.486607	−	1.07207i
$208$	3.91571	−	0.861622i	0.271506	−	0.0597427i
$209$	−1.71659	−	9.73527i	−0.118739	−	0.673403i
$210$	14.4448	−	43.3189i	0.996786	−	2.98929i
$211$	−16.2520	−	7.57844i	−1.11883	−	0.521721i	−0.226915	−	0.973915i	$-0.572864\pi$
$211$	−16.2520	−	7.57844i	−1.11883	−	0.521721i	−0.891920	+	0.452193i	$0.850642\pi$
$212$	−1.29145	−	19.9444i	−0.0886971	−	1.36979i
$213$	10.7717	+	17.1009i	0.738065	+	1.17173i
$214$	4.17714	−	11.0851i	0.285543	−	0.757765i
$215$			21.1440i			1.44201i
$216$	14.4590	+	2.63371i	0.983812	+	0.179201i
$217$		−	9.76945i		−	0.663194i
$218$	7.72669	+	2.91159i	0.523317	+	0.197198i
$219$	−24.0723	+	0.927498i	−1.62666	+	0.0626745i
$220$	21.8845	+	19.2227i	1.47545	+	1.29599i
$221$	−0.822333	−	0.383460i	−0.0553161	−	0.0257943i
$222$	−3.21473	−	15.7182i	−0.215759	−	1.05493i
$223$	2.64525	+	15.0020i	0.177139	+	1.00461i	0.935646	+	0.352940i	$0.114818\pi$
$223$	2.64525	+	15.0020i	0.177139	+	1.00461i	−0.758507	+	0.651665i	$0.774071\pi$
$224$	−15.9248	−	17.8346i	−1.06402	−	1.19162i
$225$	11.6510	−	41.7656i	0.776731	−	2.78438i
$226$	18.4256	−	18.0137i	1.22565	−	1.19826i
$227$	−5.25802	−	11.2759i	−0.348987	−	0.748405i	0.650955	−	0.759116i	$-0.274368\pi$
$227$	−5.25802	−	11.2759i	−0.348987	−	0.748405i	−0.999943	+	0.0107105i	$0.996591\pi$
$228$	1.06806	+	10.3154i	0.0707343	+	0.683157i
$229$	22.6088	−	1.97802i	1.49403	−	0.130711i	0.689356	−	0.724423i	$-0.257894\pi$
$229$	22.6088	−	1.97802i	1.49403	−	0.130711i	0.804677	+	0.593712i	$0.202338\pi$
$230$	−6.50734	+	34.6127i	−0.429081	+	2.28229i
$231$	23.9827	−	3.03248i	1.57795	−	0.199523i
$232$	−1.38022	+	3.42601i	−0.0906156	+	0.224929i
$233$	−22.8629	−	13.1999i	−1.49780	−	0.864756i	−0.497804	−	0.867289i	$-0.665860\pi$
$233$	−22.8629	−	13.1999i	−1.49780	−	0.864756i	−0.999997	+	0.00253368i	$0.999194\pi$
$234$	1.87985	−	3.81455i	0.122890	−	0.249365i
$235$	−0.00258997		0.000693981i	−0.000168951		4.52703e-5i
$236$	−1.65710	−	3.77410i	−0.107868	−	0.245673i
$237$	−7.24631	+	1.56757i	−0.470698	+	0.101824i
$238$	0.410638	+	5.39527i	0.0266177	+	0.349723i
$239$	4.36531	−	24.7569i	0.282368	−	1.60139i	−0.432168	−	0.901793i	$-0.642251\pi$
$239$	4.36531	−	24.7569i	0.282368	−	1.60139i	0.714536	−	0.699598i	$-0.246638\pi$
$240$	−21.4622	−	21.7517i	−1.38538	−	1.40407i
$241$	−19.2277	+	16.1340i	−1.23857	+	1.03928i	−0.240932	+	0.970542i	$0.577453\pi$
$241$	−19.2277	+	16.1340i	−1.23857	+	1.03928i	−0.997635	+	0.0687391i	$0.978102\pi$
$242$	0.0367971	−	0.131371i	0.00236541	−	0.00844486i
$243$	11.7590	−	10.2336i	0.754338	−	0.656487i
$244$	2.28789	+	9.38185i	0.146467	+	0.600611i
$245$	−4.17651	+	47.7378i	−0.266828	+	3.04985i
$246$	−5.02271	+	5.30374i	−0.320236	+	0.338154i
$247$	2.95517	+	0.521076i	0.188033	+	0.0331553i
$248$	−5.82799	−	2.96217i	−0.370078	−	0.188098i
$249$	−12.8044	−	8.24982i	−0.811446	−	0.522811i
$250$	−45.5961	+	37.3897i	−2.88375	+	2.36473i
$251$	−18.3558	−	4.91842i	−1.15861	−	0.310448i	−0.372198	−	0.928153i	$-0.621396\pi$
$251$	−18.3558	−	4.91842i	−1.15861	−	0.310448i	−0.786409	+	0.617706i	$0.788062\pi$
$252$	−25.3225	+	1.37933i	−1.59517	+	0.0868896i
$253$	−18.0091	+	4.82553i	−1.13222	+	0.303379i
$254$	21.9004	+	15.7066i	1.37415	+	0.985522i
$255$	0.867497	+	6.86069i	0.0543248	+	0.429633i
$256$	−15.4678	+	4.09238i	−0.966737	+	0.255774i
$257$	−7.41624	−	6.22297i	−0.462613	−	0.388178i	0.381479	−	0.924378i	$-0.375415\pi$
$257$	−7.41624	−	6.22297i	−0.462613	−	0.388178i	−0.844091	+	0.536200i	$0.819859\pi$
$258$	10.9211	−	4.31491i	0.679917	−	0.268635i
$259$	11.6996	+	25.0899i	0.726978	+	1.55901i
$260$	−7.75529	+	4.24675i	−0.480963	+	0.263372i
$261$	1.92396	+	3.41266i	0.119090	+	0.211239i
$262$	5.71554	−	9.64617i	0.353108	−	0.595942i
$263$	−20.3755	+	3.59275i	−1.25641	+	0.221539i	−0.761935	−	0.647654i	$-0.775750\pi$
$263$	−20.3755	+	3.59275i	−1.25641	+	0.221539i	−0.494474	+	0.869192i	$0.664639\pi$
$264$	5.46270	−	15.2264i	0.336206	−	0.937121i
$265$	15.0748	+	41.4176i	0.926035	+	2.54426i
$266$	−5.92994	−	16.8837i	−0.363588	−	1.03521i
$267$	21.6566	−	0.834420i	1.32536	−	0.0510657i
$268$	4.42004	+	3.24626i	0.269997	+	0.198297i
$269$	−4.15953	−	4.15953i	−0.253611	−	0.253611i	0.568838	−	0.822449i	$-0.307393\pi$
$269$	−4.15953	−	4.15953i	−0.253611	−	0.253611i	−0.822449	+	0.568838i	$0.807393\pi$
$270$	−32.2353	+	3.37209i	−1.96178	+	0.205219i
$271$	−19.5649			−1.18848			−0.594242	−	0.804286i	$-0.702548\pi$
$271$	−19.5649			−1.18848			−0.594242	+	0.804286i	$0.702548\pi$
$272$	3.34307	+	1.39092i	0.202703	+	0.0843368i
$273$	−1.62491	+	7.15582i	−0.0983440	+	0.433090i
$274$	−3.67353	−	1.76381i	−0.221926	−	0.106556i
$275$	−43.2544	−	20.1698i	−2.60834	−	1.21629i
$276$	19.2058	−	3.70240i	1.15605	−	0.222859i
$277$	−9.44635	−	6.61441i	−0.567576	−	0.397421i	0.254268	−	0.967134i	$-0.418166\pi$
$277$	−9.44635	−	6.61441i	−0.567576	−	0.397421i	−0.821844	+	0.569713i	$0.807054\pi$
$278$	16.6344	+	9.85620i	0.997664	+	0.591135i
$279$	−6.31416	+	2.86596i	−0.378019	+	0.171580i
$280$	44.7438	+	27.8969i	2.67395	+	1.66716i
$281$	6.13926	−	16.8675i	0.366238	−	1.00623i	−0.610542	−	0.791984i	$-0.709048\pi$
$281$	6.13926	−	16.8675i	0.366238	−	1.00623i	0.976780	−	0.214246i	$-0.0687294\pi$
$282$	0.000170094		0.00147937i	1.01290e−5		8.80953e-5i
$283$	−25.2440	+	2.20856i	−1.50060	+	0.131285i	−0.807634	−	0.589685i	$-0.799252\pi$
$283$	−25.2440	+	2.20856i	−1.50060	+	0.131285i	−0.692966	+	0.720970i	$0.743697\pi$
$284$	−22.1046	+	7.48410i	−1.31167	+	0.444100i
$285$	−8.64373	−	21.1740i	−0.512010	−	1.25424i
$286$	−3.80367	−	2.72794i	−0.224916	−	0.161306i
$287$	6.30217	−	10.9157i	0.372005	−	0.644332i
$288$	−6.85513	+	15.5244i	−0.403942	+	0.914785i
$289$	8.09029	+	14.0128i	0.475899	+	0.824282i
$290$	0.801588	−	8.10593i	0.0470709	−	0.475996i
$291$	−1.94857	−	2.14848i	−0.114227	−	0.125946i
$292$	5.44831	−	27.2782i	0.318838	−	1.59633i
$293$	3.09371	+	4.41827i	0.180736	+	0.258118i	0.899290	−	0.437354i	$-0.144084\pi$
$293$	3.09371	+	4.41827i	0.180736	+	0.258118i	−0.718553	+	0.695472i	$0.755195\pi$
$294$	25.5094	−	7.58477i	1.48774	−	0.442353i
$295$	5.84292	+	6.96332i	0.340188	+	0.405420i
$296$	18.5148	+	0.628015i	1.07615	+	0.0365026i
$297$	−8.99549	−	14.6108i	−0.521972	−	0.847807i
$298$	6.89303	−	3.87649i	0.399302	−	0.224559i
$299$	0.493264	−	5.63803i	0.0285262	−	0.326056i
$300$	43.7530	+	24.3412i	2.52608	+	1.40534i
$301$	−16.5978	+	11.6219i	−0.956683	+	0.669877i
$302$	0.168787	+	2.21765i	0.00971261	+	0.127612i
$303$	5.69967	+	11.0873i	0.327437	+	0.636946i
$304$	−11.8700	−	1.58175i	−0.680792	−	0.0907194i
$305$	−10.6481	−	18.4430i	−0.609706	−	1.05604i
$306$	3.36659	−	1.84815i	0.192455	−	0.105652i
$307$	−18.3389	+	4.91388i	−1.04665	+	0.280450i	−0.740868	−	0.671650i	$-0.765586\pi$
$307$	−18.3389	+	4.91388i	−1.04665	+	0.280450i	−0.305785	+	0.952100i	$0.598919\pi$
$308$	−3.06070	+	27.7450i	−0.174399	+	1.58092i
$309$	1.35296	−	9.88518i	0.0769672	−	0.562348i
$310$	14.1691	+	2.66385i	0.804750	+	0.151297i
$311$	2.21090	−	2.63485i	0.125369	−	0.149409i	−0.699709	−	0.714428i	$-0.746687\pi$
$311$	2.21090	−	2.63485i	0.125369	−	0.149409i	0.825078	+	0.565019i	$0.191131\pi$
$312$	3.77614	+	3.13904i	0.213782	+	0.177713i
$313$	1.65433	−	4.54522i	0.0935081	−	0.256911i	−0.884117	−	0.467265i	$-0.845239\pi$
$313$	1.65433	−	4.54522i	0.0935081	−	0.256911i	0.977625	+	0.210354i	$0.0674616\pi$
$314$	−5.87686	−	0.0664242i	−0.331650	−	0.00374854i
$315$	52.7469	−	18.5886i	2.97195	−	1.04735i
$316$	0.193497	−	8.55868i	0.0108850	−	0.481463i
$317$	5.28986	−	7.55471i	0.297108	−	0.424315i	−0.642647	−	0.766162i	$-0.722164\pi$
$317$	5.28986	−	7.55471i	0.297108	−	0.424315i	0.939755	+	0.341848i	$0.111053\pi$
$318$	18.3163	−	16.2385i	1.02712	−	0.910608i
$319$	4.05203	−	1.47482i	0.226870	−	0.0825739i
$320$	30.2086	−	18.2335i	1.68871	−	1.01928i
$321$	13.8591	−	4.29182i	0.773537	−	0.239546i
$322$	−30.7475	+	13.9169i	−1.71349	+	0.775559i
$323$	1.91625	+	1.91625i	0.106623	+	0.106623i
$324$	8.32007	+	15.9617i	0.462226	+	0.886762i
$325$	10.2441	−	10.2441i	0.568240	−	0.568240i
$326$	−10.4053	−	3.92097i	−0.576298	−	0.217162i
$327$	2.99153	+	9.66019i	0.165432	+	0.534210i
$328$	−4.60090	−	7.06928i	−0.254042	−	0.390336i
$329$	−0.000878827	−	0.00241456i	−4.84513e−5	−	0.000133119i
$330$	−2.14125	+	35.6101i	−0.117872	+	1.96027i
$331$	16.7515	+	11.7295i	0.920747	+	0.644714i	0.934795	−	0.355187i	$-0.115583\pi$
$331$	16.7515	+	11.7295i	0.920747	+	0.644714i	−0.0140481	+	0.999901i	$0.504472\pi$
$332$	12.7148	−	12.1526i	0.697813	−	0.666958i
$333$	12.7838	−	14.9220i	0.700550	−	0.817720i
$334$	3.59130	+	3.67341i	0.196507	+	0.201000i
$335$	−11.3646	−	4.13639i	−0.620917	−	0.225995i
$336$	5.27803	−	28.8037i	0.287940	−	1.57137i
$337$	−14.9135	−	12.5139i	−0.812390	−	0.681676i	0.138787	−	0.990322i	$-0.455680\pi$
$337$	−14.9135	−	12.5139i	−0.812390	−	0.681676i	−0.951177	+	0.308646i	$0.900124\pi$
$338$	−14.0051	+	9.57243i	−0.761777	+	0.520671i
$339$	31.2679	+	4.27956i	1.69824	+	0.232434i
$340$	−7.93698	−	0.875569i	−0.430443	−	0.0474844i
$341$	1.97538	+	7.37223i	0.106973	+	0.399229i
$342$	−9.17262	+	8.78561i	−0.495999	+	0.475071i
$343$	−14.1466	+	8.16752i	−0.763842	+	0.441005i
$344$	1.90050	+	13.4253i	0.102468	+	0.723845i
$345$	−38.3622	+	19.7210i	−2.06535	+	1.06174i
$346$	4.09501	+	3.51575i	0.220149	+	0.189008i
$347$	17.2698	+	24.6639i	0.927093	+	1.32403i	0.945987	+	0.324205i	$0.105097\pi$
$347$	17.2698	+	24.6639i	0.927093	+	1.32403i	−0.0188938	+	0.999821i	$0.506014\pi$
$348$	−4.35038	+	1.24017i	−0.233205	+	0.0664801i
$349$	17.0136	+	1.48849i	0.910715	+	0.0796773i	0.532875	−	0.846194i	$-0.321111\pi$
$349$	17.0136	+	1.48849i	0.910715	+	0.0796773i	0.377840	+	0.925871i	$0.376667\pi$
$350$	−83.1923	−	23.3022i	−4.44681	−	1.24555i
$351$	5.10161	−	1.04902i	0.272304	−	0.0559925i
$352$	15.6233	+	10.2384i	0.832727	+	0.545707i
$353$	3.73426	−	3.13342i	0.198755	−	0.166775i	−0.537978	−	0.842959i	$-0.680812\pi$
$353$	3.73426	−	3.13342i	0.198755	−	0.166775i	0.736733	+	0.676184i	$0.236367\pi$
$354$	2.40425	−	4.43896i	0.127784	−	0.235928i
$355$	42.1582	−	29.5195i	2.23752	−	1.56673i
$356$	−4.90155	+	24.5407i	−0.259782	+	1.30065i
$357$	−4.90876	+	4.45201i	−0.259799	+	0.235625i
$358$	6.73208	−	5.52044i	0.355801	−	0.291764i
$359$	11.3800	−	6.57025i	0.600614	−	0.346765i	−0.168669	−	0.985673i	$-0.553947\pi$
$359$	11.3800	−	6.57025i	0.600614	−	0.346765i	0.769283	+	0.638908i	$0.220614\pi$
$360$	4.90421	−	37.1025i	0.258475	−	1.95547i
$361$	8.69278	+	5.01878i	0.457515	+	0.264146i
$362$	−13.4076	+	2.20817i	−0.704686	+	0.116059i
$363$	0.154695	−	0.0631505i	0.00811940	−	0.00331454i
$364$	−7.59641	−	3.75358i	−0.398160	−	0.196741i
$365$	5.34655	+	61.1113i	0.279851	+	3.19871i
$366$	−7.35302	+	9.26355i	−0.384349	+	0.484214i
$367$	−8.19558	−	2.98295i	−0.427806	−	0.155708i	0.119139	−	0.992878i	$-0.461987\pi$
$367$	−8.19558	−	2.98295i	−0.427806	−	0.155708i	−0.546944	+	0.837169i	$0.684209\pi$
$368$	−1.02070	+	22.5622i	−0.0532079	+	1.17614i
$369$	−8.90378	−	0.870986i	−0.463512	−	0.0453417i
$370$	−39.5792	+	10.1272i	−2.05762	+	0.526487i
$371$	−24.2265	+	34.5990i	−1.25778	+	1.79629i
$372$	−1.51562	−	7.86211i	−0.0785812	−	0.407631i
$373$	12.0755	−	25.8961i	0.625248	−	1.34085i	−0.297233	−	0.954805i	$-0.596064\pi$
$373$	12.0755	−	25.8961i	0.625248	−	1.34085i	0.922481	−	0.386043i	$-0.126158\pi$
$374$	−1.40080	−	3.98835i	−0.0724336	−	0.206233i
$375$	−70.4255	−	15.9919i	−3.63676	−	0.825818i
$376$	−0.00170688		0.000207846i	−8.80254e−5		1.07188e-5i
$377$			1.30894i			0.0674140i
$378$	−20.3654	−	23.4509i	−1.04748	−	1.20619i
$379$	−4.95858	+	4.95858i	−0.254705	+	0.254705i	−0.822897	−	0.568191i	$-0.807643\pi$
$379$	−4.95858	+	4.95858i	−0.254705	+	0.254705i	0.568191	+	0.822897i	$0.307643\pi$
$380$	26.1041	−	3.99676i	1.33911	−	0.205030i
$381$	1.27082	+	32.9829i	0.0651060	+	1.68976i
$382$	7.05392	−	14.6914i	0.360910	−	0.751676i
$383$	31.9993	−	11.6468i	1.63509	−	0.595123i	0.648917	−	0.760859i	$-0.275222\pi$
$383$	31.9993	−	11.6468i	1.63509	−	0.595123i	0.986170	+	0.165737i	$0.0530001\pi$
$384$	−15.5825	−	11.8821i	−0.795193	−	0.606356i
$385$	−10.6893	−	60.6222i	−0.544778	−	3.08959i
$386$	3.57837	+	13.9850i	0.182134	+	0.711820i
$387$	12.3806	+	7.31807i	0.629340	+	0.371998i
$388$	2.93760	−	1.60862i	0.149134	−	0.0816651i
$389$	17.6795	−	8.24409i	0.896386	−	0.417992i	0.0808693	−	0.996725i	$-0.474230\pi$
$389$	17.6795	−	8.24409i	0.896386	−	0.417992i	0.815517	+	0.578733i	$0.196453\pi$
$390$	−9.93536	−	4.30787i	−0.503096	−	0.218138i
$391$	3.28539	−	3.91537i	0.166149	−	0.198009i
$392$	1.63898	+	30.6864i	0.0827810	+	1.54990i
$393$	13.6238	−	1.72265i	0.687227	−	0.0868961i
$394$	−3.73690	+	0.615452i	−0.188262	+	0.0310060i
$395$	4.88632	+	18.2360i	0.245857	+	0.917552i
$396$	18.8300	−	6.16108i	0.946242	−	0.309606i
$397$	−2.45176	+	9.15009i	−0.123050	+	0.459230i	−0.999763	−	0.0217849i	$-0.993065\pi$
$397$	−2.45176	+	9.15009i	−0.123050	+	0.459230i	0.876712	+	0.481015i	$0.159732\pi$
$398$	22.1896	+	2.19431i	1.11227	+	0.109991i
$399$	11.8703	−	18.4237i	0.594258	−	0.922337i
$400$	−39.1255	+	42.5631i	−1.95627	+	2.12816i
$401$	1.63450	−	9.26972i	0.0816231	−	0.462908i	−0.916411	−	0.400238i	$-0.868927\pi$
$401$	1.63450	−	9.26972i	0.0816231	−	0.462908i	0.998034	−	0.0626696i	$-0.0199614\pi$
$402$	0.182725	+	6.71409i	0.00911348	+	0.334868i
$403$	−2.30799	−	0.201923i	−0.114969	−	0.0100585i
$404$	−13.9852	+	3.41049i	−0.695791	+	0.169678i
$405$	−27.4879	−	28.6381i	−1.36589	−	1.42304i
$406$	6.80368	−	3.82624i	0.337661	−	0.189893i
$407$	−13.9019	−	16.5677i	−0.689094	−	0.821230i
$408$	1.16748	+	4.27821i	0.0577989	+	0.211803i
$409$	10.2134	+	1.80089i	0.505019	+	0.0890485i	0.420353	−	0.907361i	$-0.361906\pi$
$409$	10.2134	+	1.80089i	0.505019	+	0.0890485i	0.0846665	+	0.996409i	$0.473018\pi$
$410$	14.1131	+	12.1167i	0.696996	+	0.598402i
$411$	−1.05525	−	4.87803i	−0.0520515	−	0.240616i
$412$	10.7342	+	4.18405i	0.528837	+	0.206133i
$413$	−2.25455	+	8.41408i	−0.110939	+	0.414030i
$414$	18.0148	+	15.7900i	0.885379	+	0.776035i
$415$	−19.3938	+	33.5910i	−0.952004	+	1.64892i
$416$	−4.54249	+	3.39354i	−0.222714	+	0.166382i
$417$	2.97063	+	23.4935i	0.145472	+	1.15048i
$418$	7.88874	+	11.5418i	0.385851	+	0.564526i
$419$	0.998591	+	11.4139i	0.0487843	+	0.557608i	0.980777	+	0.195131i	$0.0625132\pi$
$419$	0.998591	+	11.4139i	0.0487843	+	0.557608i	−0.931993	+	0.362477i	$0.881931\pi$
$420$	6.65091	+	64.2350i	0.324531	+	3.13435i
$421$	−18.6595	+	8.70109i	−0.909410	+	0.424065i	−0.820285	−	0.571955i	$-0.806185\pi$
$421$	−18.6595	+	8.70109i	−0.909410	+	0.424065i	−0.0891255	+	0.996020i	$0.528407\pi$
$422$	25.3582	+	0.286616i	1.23442	+	0.0139522i
$423$	−0.00130276	+	0.00127633i	−6.33423e−5	+	6.20575e-5i
$424$	13.2945	+	24.9430i	0.645636	+	1.21134i
$425$	12.8847	−	2.27193i	0.625002	−	0.110205i
$426$	−23.8505	−	15.7510i	−1.15556	−	0.763140i
$427$	8.62481	−	18.4960i	0.417384	−	0.895082i
$428$	1.08252	+	16.7178i	0.0523255	+	0.808087i
$429$	−0.220717	−	5.72849i	−0.0106563	−	0.276574i
$430$	−12.3301	−	27.2416i	−0.594609	−	1.31371i
$431$	3.49281			0.168243			0.0841215	−	0.996456i	$-0.473192\pi$
$431$	3.49281			0.168243			0.0841215	+	0.996456i	$0.473192\pi$
$432$	−20.1647	+	5.03853i	−0.970172	+	0.242417i
$433$	−7.29446			−0.350549			−0.175275	−	0.984520i	$-0.556081\pi$
$433$	−7.29446			−0.350549			−0.175275	+	0.984520i	$0.556081\pi$
$434$	5.69704	+	12.5868i	0.273467	+	0.604187i
$435$	8.44112	−	5.31699i	0.404721	−	0.254930i
$436$	−11.6528	+	0.754549i	−0.558070	+	0.0361363i
$437$	−7.14376	+	15.3198i	−0.341732	+	0.732847i
$438$	30.4736	−	15.2327i	1.45608	−	0.727847i
$439$	−17.2604	+	3.04348i	−0.823795	+	0.145257i	−0.569628	−	0.821903i	$-0.692913\pi$
$439$	−17.2604	+	3.04348i	−0.823795	+	0.145257i	−0.254167	+	0.967160i	$0.581801\pi$
$440$	−39.4054	−	12.0044i	−1.87858	−	0.572285i
$441$	26.5067	+	18.9679i	1.26222	+	0.903231i
$442$	1.28310	+	0.0145024i	0.0610307	+	0.000689810i
$443$	−0.936058	+	0.436491i	−0.0444734	+	0.0207383i	−0.444728	−	0.895666i	$-0.646700\pi$
$443$	−0.936058	+	0.436491i	−0.0444734	+	0.0207383i	0.400254	+	0.916404i	$0.368922\pi$
$444$	13.3078	+	18.3764i	0.631562	+	0.872104i
$445$	−4.81000	−	54.9786i	−0.228016	−	2.60623i
$446$	−12.1565	−	17.7857i	−0.575625	−	0.842179i
$447$	8.92925	+	3.75232i	0.422339	+	0.177479i
$448$	30.9175	+	13.6913i	1.46071	+	0.646855i
$449$	0.420090	−	0.727618i	0.0198253	−	0.0343384i	−0.855943	−	0.517071i	$-0.827022\pi$
$449$	0.420090	−	0.727618i	0.0198253	−	0.0343384i	0.875768	+	0.482733i	$0.160356\pi$
$450$	9.34462	+	60.6045i	0.440510	+	2.85692i
$451$	−2.54860	+	9.51149i	−0.120009	+	0.447879i
$452$	−13.2346	+	33.9535i	−0.622503	+	1.59704i
$453$	−2.01768	+	1.82994i	−0.0947989	+	0.0859780i
$454$	13.3499	+	11.4615i	0.626540	+	0.537913i
$455$	18.4020	+	3.24478i	0.862701	+	0.152117i
$456$	−7.39152	−	12.6674i	−0.346140	−	0.593207i
$457$	−4.70555	−	5.60785i	−0.220116	−	0.262324i	0.644674	−	0.764458i	$-0.276993\pi$
$457$	−4.70555	−	5.60785i	−0.220116	−	0.262324i	−0.864790	+	0.502133i	$0.832549\pi$
$458$	−27.9754	+	15.7327i	−1.30720	+	0.735143i
$459$	4.31744	+	1.86658i	0.201521	+	0.0871245i
$460$	−11.8004	−	48.3893i	−0.550196	−	2.25616i
$461$	−10.8422	−	0.948574i	−0.504974	−	0.0441795i	−0.168177	−	0.985757i	$-0.553788\pi$
$461$	−10.8422	−	0.948574i	−0.504974	−	0.0441795i	−0.336797	+	0.941577i	$0.609344\pi$
$462$	−29.1306	+	17.8925i	−1.35528	+	0.832434i
$463$	0.612243	−	3.47220i	0.0284533	−	0.161367i	−0.967270	−	0.253748i	$-0.918337\pi$
$463$	0.612243	−	3.47220i	0.0284533	−	0.161367i	0.995724	+	0.0923810i	$0.0294478\pi$
$464$	−0.219624	−	5.21890i	−0.0101958	−	0.242281i
$465$	8.07301	+	15.7040i	0.374377	+	0.728255i
$466$	37.1538	+	3.67411i	1.72112	+	0.170200i
$467$	−1.70567	+	6.36565i	−0.0789290	+	0.294567i	−0.994095	−	0.108509i	$-0.965392\pi$
$467$	−1.70567	+	6.36565i	−0.0789290	+	0.294567i	0.915166	+	0.403076i	$0.132059\pi$
$468$	−0.197525	+	6.01084i	−0.00913060	+	0.277851i
$469$	−2.99963	−	11.1948i	−0.138510	−	0.516926i
$470$	0.00374158		0.000616223i	0.000172586		2.84243e-5i
$471$	−4.35262	−	5.73302i	−0.200558	−	0.264164i
$472$	4.33584	+	3.89617i	0.199573	+	0.179336i
$473$	10.1751	−	12.1262i	0.467853	−	0.557565i
$474$	8.42192	−	6.24531i	0.386832	−	0.286856i
$475$	−39.2157	+	18.2866i	−1.79934	+	0.839045i
$476$	−3.67530	−	6.71172i	−0.168457	−	0.307631i
$477$	29.4690	+	5.50806i	1.34929	+	0.252197i
$478$	8.81275	+	34.4421i	0.403086	+	1.57534i
$479$	−3.38253	−	19.1833i	−0.154552	−	0.876505i	−0.959195	−	0.282747i	$-0.908754\pi$
$479$	−3.38253	−	19.1833i	−0.154552	−	0.876505i	0.804643	−	0.593759i	$-0.202357\pi$
$480$	40.3361	+	15.5089i	1.84108	+	0.707882i
$481$	6.16919	−	2.24540i	0.281291	−	0.102382i
$482$	15.3642	−	31.9994i	0.699821	−	1.45753i
$483$	−36.5669	−	19.2742i	−1.66385	−	0.877008i
$484$	0.0292001	+	0.190715i	0.00132728	+	0.00866886i
$485$	−5.22269	+	5.22269i	−0.237150	+	0.237150i
$486$	−9.18236	+	20.0421i	−0.416520	+	0.909126i
$487$			18.5759i			0.841757i	0.907117	+	0.420878i	$0.138278\pi$
$487$			18.5759i			0.841757i	−0.907117	+	0.420878i	$0.861722\pi$
$488$	−8.41870	−	10.7533i	−0.381097	−	0.486777i
$489$	−4.02861	−	13.0091i	−0.182180	−	0.588293i
$490$	−22.4572	−	63.9402i	−1.01451	−	2.88852i
$491$	−4.89539	+	10.4982i	−0.220926	+	0.473777i	−0.985264	−	0.171038i	$-0.945288\pi$
$491$	−4.89539	+	10.4982i	−0.220926	+	0.473777i	0.764338	+	0.644815i	$0.223066\pi$
$492$	3.37832	−	9.76225i	0.152306	−	0.440116i
$493$	−0.678029	+	0.968325i	−0.0305369	+	0.0436112i
$494$	−4.11127	+	1.05196i	−0.184975	+	0.0473297i
$495$	−36.0453	+	24.6928i	−1.62012	+	1.10986i
$496$	9.23608	+	0.417837i	0.414712	+	0.0187614i
$497$	46.3451	+	16.8682i	2.07886	+	0.756644i
$498$	21.3079	+	3.16208i	0.954829	+	0.141696i
$499$	2.88018	+	32.9206i	0.128934	+	1.47373i	0.734867	+	0.678211i	$0.237245\pi$
$499$	2.88018	+	32.9206i	0.128934	+	1.47373i	−0.605932	+	0.795516i	$0.707200\pi$
$500$	36.9416	−	74.7617i	1.65208	−	3.34344i
$501$	−0.853192	+	6.23371i	−0.0381178	+	0.278502i
$502$	26.5175	−	4.36733i	1.18353	−	0.194923i
$503$	21.5427	+	12.4377i	0.960540	+	0.554568i	0.896339	−	0.443369i	$-0.146217\pi$
$503$	21.5427	+	12.4377i	0.960540	+	0.554568i	0.0642008	+	0.997937i	$0.479550\pi$
$504$	31.8208	−	16.5439i	1.41741	−	0.736923i
$505$	27.4924	−	15.8727i	1.22340	−	0.706327i
$506$	20.3887	−	16.7191i	0.906388	−	0.743256i
$507$	−19.7826	−	6.34903i	−0.878576	−	0.281970i
$508$	−37.3754	−	7.46504i	−1.65827	−	0.331208i
$509$	20.6242	−	14.4412i	0.914150	−	0.640095i	−0.0189079	−	0.999821i	$-0.506019\pi$
$509$	20.6242	−	14.4412i	0.914150	−	0.640095i	0.933058	+	0.359727i	$0.117130\pi$
$510$	−5.11847	−	8.33334i	−0.226650	−	0.369007i
$511$	−45.0331	+	37.7873i	−1.99215	+	1.67161i
$512$	17.5420	−	14.2926i	0.775255	−	0.631649i
$513$	−15.3898	−	2.26722i	−0.679476	−	0.100100i
$514$	13.1839	+	3.69281i	0.581517	+	0.162883i
$515$	−25.3102	−	2.21436i	−1.11530	−	0.0975763i
$516$	−11.5543	+	11.9279i	−0.508651	+	0.525096i
$517$	0.00115141	+	0.00164438i	5.06387e−5	+	7.23196e-5i
$518$	−29.7047	−	25.5028i	−1.30515	−	1.12053i
$519$	−0.322157	+	6.60232i	−0.0141411	+	0.289810i
$520$	7.51532	−	9.99394i	0.329568	−	0.438263i
$521$	4.38810	−	2.53347i	0.192246	−	0.110993i	−0.400788	−	0.916171i	$-0.631263\pi$
$521$	4.38810	−	2.53347i	0.192246	−	0.110993i	0.593034	+	0.805178i	$0.297930\pi$
$522$	−4.46889	−	3.27487i	−0.195598	−	0.143337i
$523$	−1.56140	−	5.82722i	−0.0682752	−	0.254806i	0.923349	−	0.383961i	$-0.125440\pi$
$523$	−1.56140	−	5.82722i	−0.0682752	−	0.254806i	−0.991624	+	0.129155i	$0.958774\pi$
$524$	−1.73868	+	15.7610i	−0.0759544	+	0.688523i
$525$	−39.9907	−	97.9625i	−1.74534	−	4.27544i
$526$	24.1564	−	16.5108i	1.05327	−	0.719906i
$527$	−1.60280	−	1.34491i	−0.0698191	−	0.0585852i
$528$	1.84119	+	22.8031i	0.0801274	+	0.992376i
$529$	8.34531	+	3.03745i	0.362840	+	0.132063i
$530$	−43.5747	−	44.5710i	−1.89276	−	1.93604i
$531$	6.09956	−	1.01120i	0.264698	−	0.0438822i
$532$	17.4858	+	18.2947i	0.758103	+	0.793175i
$533$	−2.44852	−	1.71447i	−0.106057	−	0.0742621i
$534$	−27.4154	+	13.7041i	−1.18638	+	0.593032i
$535$	−12.6360	−	34.7170i	−0.546300	−	1.50095i
$536$	−7.58776	−	1.60490i	−0.327741	−	0.0693211i
$537$	10.3980	+	2.36114i	0.448708	+	0.101891i
$538$	7.78471	+	2.93346i	0.335623	+	0.126470i
$539$	25.3681	−	25.3681i	1.09268	−	1.09268i
$540$	39.5651	−	23.1425i	1.70261	−	0.995895i
$541$	19.1672	+	19.1672i	0.824064	+	0.824064i	0.986688	−	0.162624i	$-0.0519958\pi$
$541$	19.1672	+	19.1672i	0.824064	+	0.824064i	−0.162624	+	0.986688i	$0.551996\pi$
$542$	25.2072	−	11.4093i	1.08274	−	0.490069i
$543$	−12.2121	−	11.3059i	−0.524069	−	0.485183i
$544$	−5.11827	+	0.157465i	−0.219444	+	0.00675124i
$545$	24.1988	−	8.80765i	1.03656	−	0.377278i
$546$	−2.07940	−	10.1670i	−0.0889899	−	0.435108i
$547$	10.9349	−	15.6167i	0.467544	−	0.667722i	−0.514257	−	0.857636i	$-0.671932\pi$
$547$	10.9349	−	15.6167i	0.467544	−	0.667722i	0.981801	+	0.189914i	$0.0608210\pi$
$548$	5.76148	+	0.130257i	0.246118	+	0.00556430i
$549$	−14.4844	−	0.148402i	−0.618180	−	0.00633366i
$550$	67.4903	+	0.762821i	2.87780	+	0.0325268i
$551$	1.33711	−	3.67368i	0.0569629	−	0.156504i
$552$	−22.5854	+	15.9700i	−0.961300	+	0.679727i
$553$	−11.6293	+	13.8593i	−0.494528	+	0.589356i
$554$	16.0277	+	3.01328i	0.680953	+	0.128022i
$555$	−39.5397	−	30.6630i	−1.67837	−	1.30157i
$556$	−27.1791	−	2.99827i	−1.15265	−	0.127155i
$557$	43.3047	−	11.6035i	1.83488	−	0.491654i	0.836468	−	0.548016i	$-0.184617\pi$
$557$	43.3047	−	11.6035i	1.83488	−	0.491654i	0.998410	+	0.0563617i	$0.0179500\pi$
$558$	6.46380	−	7.37455i	0.273634	−	0.312190i
$559$	2.40257	+	4.16138i	0.101618	+	0.176008i
$560$	−73.9153	−	9.84964i	−3.12349	−	0.416223i
$561$	2.80406	−	4.35213i	0.118387	−	0.183747i
$562$	1.92651	+	25.3119i	0.0812649	+	1.06772i
$563$	−18.1708	+	12.7233i	−0.765807	+	0.536224i	−0.889960	−	0.456039i	$-0.849268\pi$
$563$	−18.1708	+	12.7233i	−0.765807	+	0.536224i	0.124152	+	0.992263i	$0.460379\pi$
$564$	−0.00108184	−	0.00180681i	−4.55537e−5	−	7.60804e-5i
$565$	7.00426	−	80.0591i	0.294672	−	3.36811i
$566$	31.2361	−	17.5665i	1.31295	−	0.738374i
$567$	7.37176	−	37.3189i	0.309585	−	1.56725i
$568$	24.1150	−	22.5327i	1.01184	−	0.945451i
$569$	−1.83342	−	2.18498i	−0.0768609	−	0.0915993i	0.726244	−	0.687437i	$-0.241264\pi$
$569$	−1.83342	−	2.18498i	−0.0768609	−	0.0915993i	−0.803105	+	0.595838i	$0.796820\pi$
$570$	23.4840	+	22.2396i	0.983637	+	0.931516i
$571$	−6.73034	−	9.61193i	−0.281656	−	0.402247i	0.653250	−	0.757143i	$-0.273405\pi$
$571$	−6.73034	−	9.61193i	−0.281656	−	0.402247i	−0.934906	+	0.354896i	$0.884516\pi$
$572$	6.49139	+	1.29653i	0.271419	+	0.0542108i
$573$	19.5085	−	4.22020i	0.814979	−	0.176301i
$574$	−1.75416	+	17.7387i	−0.0732174	+	0.740399i
$575$	40.8043	+	70.6751i	1.70166	+	2.94736i
$576$	−0.220989	−	23.9990i	−0.00920787	−	0.999958i
$577$	−20.9304	+	36.2526i	−0.871346	+	1.50921i	−0.0107402	+	0.999942i	$0.503419\pi$
$577$	−20.9304	+	36.2526i	−0.871346	+	1.50921i	−0.860605	+	0.509272i	$0.829915\pi$
$578$	−18.5950	−	13.3360i	−0.773448	−	0.554706i
$579$	−10.8346	+	13.9711i	−0.450269	+	0.580619i
$580$	3.69420	+	10.9110i	0.153393	+	0.453055i
$581$	−37.0286	+	3.23958i	−1.53621	+	0.134401i
$582$	3.76339	+	1.63177i	0.155997	+	0.0676389i
$583$	11.2859	−	31.0077i	0.467414	−	1.28421i
$584$	8.88770	+	38.3220i	0.367776	+	1.58578i
$585$	−3.30125	−	12.8454i	−0.136490	−	0.531094i
$586$	−6.56239	−	3.88835i	−0.271090	−	0.160626i
$587$	−2.90678	−	2.03535i	−0.119976	−	0.0840078i	0.512049	−	0.858956i	$-0.328887\pi$
$587$	−2.90678	−	2.03535i	−0.119976	−	0.0840078i	−0.632024	+	0.774949i	$0.717776\pi$
$588$	−28.4429	+	24.6479i	−1.17296	+	1.01646i
$589$	6.27134	+	2.92437i	0.258406	+	0.120497i
$590$	−11.5886	−	5.56415i	−0.477094	−	0.229073i
$591$	−3.40369	−	3.15114i	−0.140009	−	0.129620i
$592$	−24.2205	+	9.98777i	−0.995455	+	0.410495i
$593$	−20.4054			−0.837948			−0.418974	−	0.907998i	$-0.637610\pi$
$593$	−20.4054			−0.837948			−0.418974	+	0.907998i	$0.637610\pi$
$594$	20.1100	+	13.5787i	0.825121	+	0.557140i
$595$	11.9326	+	11.9326i	0.489189	+	0.489189i
$596$	−6.62031	+	9.01407i	−0.271179	+	0.369231i
$597$	14.5550	+	23.1072i	0.595698	+	0.945715i
$598$	2.65230	+	7.55161i	0.108460	+	0.308808i
$599$	−16.0679	−	44.1462i	−0.656517	−	1.80377i	−0.592133	−	0.805841i	$-0.701714\pi$
$599$	−16.0679	−	44.1462i	−0.656517	−	1.80377i	−0.0643844	−	0.997925i	$-0.520508\pi$
$600$	−70.5652	−	5.84642i	−2.88081	−	0.238679i
$601$	3.68649	−	0.650027i	0.150375	−	0.0265152i	−0.0979538	−	0.995191i	$-0.531230\pi$
$601$	3.68649	−	0.650027i	0.150375	−	0.0265152i	0.248329	+	0.968676i	$0.420119\pi$
$602$	14.6071	−	24.6525i	0.595341	−	1.00476i
$603$	−6.35539	+	5.22279i	−0.258812	+	0.212689i
$604$	−1.51068	−	2.75876i	−0.0614688	−	0.112253i
$605$	−0.179818	−	0.385621i	−0.00731063	−	0.0156777i
$606$	−13.8089	−	10.9609i	−0.560948	−	0.445257i
$607$	−18.0676	−	15.1605i	−0.733341	−	0.615346i	0.197700	−	0.980263i	$-0.436653\pi$
$607$	−18.0676	−	15.1605i	−0.733341	−	0.615346i	−0.931040	+	0.364917i	$0.881097\pi$
$608$	16.2155	−	4.88408i	0.657627	−	0.198075i
$609$	8.81352	+	3.70369i	0.357142	+	0.150081i
$610$	24.4738	+	17.5523i	0.990916	+	0.710671i
$611$	−0.000588593	0	0.000157713i	−2.38119e−5	0	6.38039e-6i
$612$	−3.25972	+	4.34436i	−0.131766	+	0.175610i
$613$	−21.7665	−	5.83231i	−0.879140	−	0.235565i	−0.209104	−	0.977893i	$-0.567055\pi$
$613$	−21.7665	−	5.83231i	−0.879140	−	0.235565i	−0.670036	+	0.742329i	$0.733721\pi$
$614$	20.7620	−	17.0252i	0.837886	−	0.687083i
$615$	−1.11029	+	22.7543i	−0.0447710	+	0.917542i
$616$	−12.2361	−	37.5312i	−0.493007	−	1.51217i
$617$	−42.2907	−	7.45700i	−1.70256	−	0.300207i	−0.763973	−	0.645248i	$-0.776754\pi$
$617$	−42.2907	−	7.45700i	−1.70256	−	0.300207i	−0.938588	+	0.345041i	$0.887865\pi$
$618$	4.02139	+	13.5249i	0.161764	+	0.544051i
$619$	−0.266283	+	3.04362i	−0.0107028	+	0.122334i	−0.999666	−	0.0258245i	$-0.991779\pi$
$619$	−0.266283	+	3.04362i	−0.0107028	+	0.122334i	0.988964	+	0.148158i	$0.0473344\pi$
$620$	−19.8087	+	4.83062i	−0.795536	+	0.194002i
$621$	−1.73004	+	29.2881i	−0.0694241	+	1.17529i
$622$	−1.31199	+	4.68399i	−0.0526059	+	0.187811i
$623$	40.5139	−	33.9952i	1.62315	−	1.36199i
$624$	−6.69565	−	1.84225i	−0.268040	−	0.0737490i
$625$	−19.3851	+	109.938i	−0.775404	+	4.39753i
$626$	0.519130	+	6.82072i	0.0207486	+	0.272611i
$627$	−5.23230	+	16.3031i	−0.208958	+	0.651081i
$628$	7.61040	−	3.34150i	0.303688	−	0.133340i
$629$	5.72693	+	1.53453i	0.228348	+	0.0611856i
$630$	−57.1185	+	54.7085i	−2.27566	+	2.17964i
$631$	26.9208	+	15.5427i	1.07170	+	0.618746i	0.928645	−	0.370969i	$-0.120974\pi$
$631$	26.9208	+	15.5427i	1.07170	+	0.618746i	0.143054	+	0.989715i	$0.454308\pi$
$632$	4.74168	+	11.1397i	0.188614	+	0.443114i
$633$	18.7813	+	24.7376i	0.746488	+	0.983230i
$634$	−2.40987	+	12.8182i	−0.0957081	+	0.509074i
$635$	83.7322	−	7.32562i	3.32281	−	0.290708i
$636$	−14.1290	+	31.6025i	−0.560250	+	1.25312i
$637$	4.60242	+	9.86992i	0.182355	+	0.391061i
$638$	−4.36054	+	4.26307i	−0.172635	+	0.168776i
$639$	−2.69353	−	34.9021i	−0.106554	−	1.38070i
$640$	−28.2875	+	41.1079i	−1.11816	+	1.62493i
$641$	5.39630	+	30.6039i	0.213141	+	1.20878i	0.884103	+	0.467292i	$0.154770\pi$
$641$	5.39630	+	30.6039i	0.213141	+	1.20878i	−0.670962	+	0.741492i	$0.734119\pi$
$642$	−15.3531	+	13.6114i	−0.605937	+	0.537199i
$643$	15.4691	+	7.21336i	0.610041	+	0.284467i	0.702985	−	0.711204i	$-0.251850\pi$
$643$	15.4691	+	7.21336i	0.610041	+	0.284467i	−0.0929439	+	0.995671i	$0.529628\pi$
$644$	31.4990	−	35.8607i	1.24123	−	1.41311i
$645$	17.0765	−	32.3974i	0.672388	−	1.27565i
$646$	−3.58632	−	1.35141i	−0.141102	−	0.0531705i
$647$			47.0326i			1.84904i	0.381129	+	0.924522i	$0.375535\pi$
$647$			47.0326i			1.84904i	−0.381129	+	0.924522i	$0.624465\pi$
$648$	−20.0275	−	15.7130i	−0.786755	−	0.617266i
$649$		−	6.80531i		−	0.267132i
$650$	−7.22452	+	19.1722i	−0.283369	+	0.751995i
$651$	−7.89012	+	14.9691i	−0.309238	+	0.586683i
$652$	15.6926	−	1.01613i	0.614569	−	0.0397948i
$653$	−18.4253	−	8.59187i	−0.721039	−	0.336226i	0.0272230	−	0.999629i	$-0.491334\pi$
$653$	−18.4253	−	8.59187i	−0.721039	−	0.336226i	−0.748262	+	0.663403i	$0.769111\pi$
$654$	−9.48757	−	10.7015i	−0.370993	−	0.418464i
$655$	−6.07224	−	34.4374i	−0.237262	−	1.34558i
$656$	10.0502	+	6.42495i	0.392394	+	0.250852i
$657$	37.6334	+	18.0204i	1.46822	+	0.703044i
$658$	0.00254031	+	0.00259840i	9.90318e−5	+	0.000101296i
$659$	−16.1618	−	34.6591i	−0.629574	−	1.35013i	−0.919505	−	0.393079i	$-0.871410\pi$
$659$	−16.1618	−	34.6591i	−0.629574	−	1.35013i	0.289931	−	0.957048i	$-0.406368\pi$
$660$	−18.0072	−	47.1282i	−0.700931	−	1.83446i
$661$	−43.2407	+	3.78307i	−1.68187	+	0.147145i	−0.887660	−	0.460499i	$-0.847670\pi$
$661$	−43.2407	+	3.78307i	−1.68187	+	0.147145i	−0.794210	+	0.607644i	$0.792115\pi$
$662$	−28.4225	−	5.34355i	−1.10467	−	0.207683i
$663$	0.950309	+	1.25169i	0.0369069	+	0.0486117i
$664$	−9.29477	+	23.0718i	−0.360707	+	0.895358i
$665$	−48.3326	−	27.9048i	−1.87426	−	1.08210i
$666$	−7.76877	+	26.6802i	−0.301034	+	1.03384i
$667$	−7.12216	−	1.90838i	−0.275771	−	0.0738927i
$668$	−6.76912	−	2.63851i	−0.261905	−	0.102087i
$669$	8.06292	−	25.1228i	0.311731	−	0.971305i
$670$	17.0542	−	1.29801i	0.658861	−	0.0501464i
$671$	−2.76858	+	15.7014i	−0.106880	+	0.606145i
$672$	9.99667	+	40.1881i	0.385630	+	1.55029i
$673$	33.8459	−	28.4001i	1.30466	−	1.09474i	0.315344	−	0.948977i	$-0.397880\pi$
$673$	33.8459	−	28.4001i	1.30466	−	1.09474i	0.989319	−	0.145765i	$-0.0465643\pi$
$674$	26.5118	+	7.42596i	1.02120	+	0.286037i
$675$	−51.5832	+	54.5849i	−1.98544	+	2.10097i
$676$	12.4618	−	20.5000i	0.479301	−	0.788463i
$677$	−1.29713	+	14.8263i	−0.0498529	+	0.569822i	0.929657	+	0.368426i	$0.120103\pi$
$677$	−1.29713	+	14.8263i	−0.0498529	+	0.569822i	−0.979510	+	0.201396i	$0.935452\pi$
$678$	−42.7808	+	12.7201i	−1.64299	+	0.488513i
$679$	−6.97046	−	1.22908i	−0.267502	−	0.0471678i
$680$	10.7365	−	3.50037i	0.411725	−	0.134233i
$681$	−1.05024	+	21.5238i	−0.0402454	+	0.824793i
$682$	−6.84416	−	8.34634i	−0.262077	−	0.319598i
$683$	−25.2686	−	6.77071i	−0.966878	−	0.259074i	−0.259369	−	0.965778i	$-0.583515\pi$
$683$	−25.2686	−	6.77071i	−0.966878	−	0.259074i	−0.707509	+	0.706704i	$0.750181\pi$
$684$	6.69456	−	16.6683i	0.255973	−	0.637326i
$685$	−12.2760	+	3.28935i	−0.469042	+	0.125679i
$686$	13.4633	−	18.7725i	0.514033	−	0.716736i
$687$	−36.2394	−	15.2288i	−1.38262	−	0.581016i
$688$	−10.2775	−	16.1887i	−0.391827	−	0.617190i
$689$	7.67313	+	6.43852i	0.292323	+	0.245288i
$690$	37.9251	−	47.7791i	1.44378	−	1.81892i
$691$	−8.58920	−	18.4196i	−0.326748	−	0.700714i	0.672475	−	0.740120i	$-0.265231\pi$
$691$	−8.58920	−	18.4196i	−0.326748	−	0.700714i	−0.999223	+	0.0394057i	$0.987454\pi$
$692$	−7.32616	−	2.14164i	−0.278499	−	0.0814131i
$693$	−39.1962	−	14.7227i	−1.48894	−	0.559271i
$694$	−36.6329	−	21.7057i	−1.39057	−	0.823938i
$695$	59.3857	−	10.4713i	2.25263	−	0.397199i
$696$	4.88177	−	4.13474i	0.185043	−	0.156727i
$697$	−0.923266	−	2.53665i	−0.0349712	−	0.0960825i
$698$	−22.7880	+	8.00368i	−0.862540	+	0.302944i
$699$	24.3706	+	38.6902i	0.921782	+	1.46340i
$700$	120.772	−	18.4913i	4.56477	−	0.698904i
$701$	−29.5458	−	29.5458i	−1.11593	−	1.11593i	−0.992333	−	0.123596i	$-0.960557\pi$
$701$	−29.5458	−	29.5458i	−1.11593	−	1.11593i	−0.123596	−	0.992333i	$-0.539443\pi$
$702$	−5.96111	+	4.32654i	−0.224988	+	0.163295i
$703$	−19.6082			−0.739537
$704$	−26.0994	−	4.08024i	−0.983657	−	0.153780i
$705$	0.00340795	+	0.00315508i	0.000128351	+	0.000118827i
$706$	−2.98392	+	6.21468i	−0.112301	+	0.233893i
$707$	27.5713	+	12.8567i	1.03693	+	0.483527i
$708$	−0.509029	+	7.12112i	−0.0191305	+	0.267628i
$709$	3.99286	+	2.79583i	0.149955	+	0.105000i	0.646146	−	0.763214i	$-0.276380\pi$
$709$	3.99286	+	2.79583i	0.149955	+	0.105000i	−0.496191	+	0.868213i	$0.665269\pi$
$710$	−37.1018	+	62.6170i	−1.39240	+	2.34997i
$711$	12.3690	+	3.45047i	0.463875	+	0.129403i
$712$	−7.99579	−	34.4762i	−0.299655	−	1.29205i
$713$	4.46363	−	12.2637i	0.167164	−	0.459280i
$714$	3.72820	−	8.59844i	0.139524	−	0.321789i
$715$	−14.5427	+	1.27232i	−0.543865	+	0.0475820i
$716$	−5.45428	+	11.0383i	−0.203836	+	0.412519i
$717$	−26.6831	+	34.4077i	−0.996500	+	1.28498i
$718$	−10.8304	+	15.1013i	−0.404187	+	0.563574i
$719$	7.91535	−	13.7098i	0.295193	−	0.511289i	−0.679837	−	0.733363i	$-0.737950\pi$
$719$	7.91535	−	13.7098i	0.295193	−	0.511289i	0.975030	+	0.222075i	$0.0712829\pi$
$720$	15.3177	+	50.6622i	0.570859	+	1.88807i
$721$	−12.1737	−	21.0855i	−0.453372	−	0.785264i
$722$	−14.1264	−	1.39694i	−0.525728	−	0.0519888i
$723$	42.4916	−	9.19206i	1.58028	−	0.341856i
$724$	15.9864	−	10.6636i	0.594130	−	0.396309i
$725$	−10.8259	−	15.4610i	−0.402065	−	0.574208i
$726$	−0.162481	+	0.171573i	−0.00603024	+	0.00636765i
$727$	17.5196	+	20.8791i	0.649767	+	0.774362i	0.985879	−	0.167460i	$-0.0535566\pi$
$727$	17.5196	+	20.8791i	0.649767	+	0.774362i	−0.336112	+	0.941822i	$0.609112\pi$
$728$	11.9760	+	0.406221i	0.443860	+	0.0150556i
$729$	−26.2824	+	6.18335i	−0.973423	+	0.229013i
$730$	−42.5254	−	75.6172i	−1.57394	−	2.79872i
$731$	−0.378215	+	4.32301i	−0.0139888	+	0.159892i
$732$	4.07150	−	16.2229i	0.150487	−	0.599617i
$733$	−0.904603	+	0.633410i	−0.0334123	+	0.0233955i	−0.590163	−	0.807284i	$-0.700937\pi$
$733$	−0.904603	+	0.633410i	−0.0334123	+	0.0233955i	0.556751	+	0.830679i	$0.312048\pi$
$734$	12.2986	−	0.936053i	0.453948	−	0.0345503i
$735$	44.9539	−	69.7722i	1.65815	−	2.57359i
$736$	−11.8420	−	29.6640i	−0.436504	−	1.09343i
$737$	4.52716	+	7.84127i	0.166760	+	0.288837i
$738$	11.9794	−	4.07006i	0.440969	−	0.149821i
$739$	−9.86973	+	2.64459i	−0.363064	+	0.0972827i	−0.435739	−	0.900073i	$-0.643513\pi$
$739$	−9.86973	+	2.64459i	−0.363064	+	0.0972827i	0.0726752	+	0.997356i	$0.476846\pi$
$740$	45.0876	−	36.1283i	1.65745	−	1.32810i
$741$	−4.10717	−	3.18510i	−0.150881	−	0.117008i
$742$	11.0367	−	58.7045i	0.405170	−	2.15511i
$743$	−21.9584	+	26.1689i	−0.805574	+	0.960045i	−0.999781	−	0.0209150i	$-0.993342\pi$
$743$	−21.9584	+	26.1689i	−0.805574	+	0.960045i	0.194207	+	0.980960i	$0.437786\pi$
$744$	6.53748	+	9.24560i	0.239676	+	0.338960i
$745$	8.43562	−	23.1767i	0.309057	−	0.849128i
$746$	−0.456695	+	40.4060i	−0.0167208	+	1.47937i
$747$	12.9565	+	22.9819i	0.474053	+	0.840862i
$748$	4.13057	+	4.32166i	0.151029	+	0.158016i
$749$	20.3071	−	29.0016i	0.742006	−	1.05969i
$750$	100.061	−	20.4648i	3.65371	−	0.747269i
$751$	30.6601	−	11.1594i	1.11880	−	0.407211i	0.284587	−	0.958650i	$-0.408143\pi$
$751$	30.6601	−	11.1594i	1.11880	−	0.407211i	0.834215	+	0.551439i	$0.185921\pi$
$752$	0.00232032		0.000727577i	8.46134e−5		2.65320e-5i
$753$	24.1530	+	22.3609i	0.880185	+	0.814875i
$754$	−0.763309	−	1.68642i	−0.0277981	−	0.0614160i
$755$	4.90474	+	4.90474i	0.178502	+	0.178502i
$756$	39.9139	+	18.3378i	1.45165	+	0.666939i
$757$	−24.7189	+	24.7189i	−0.898424	+	0.898424i	−0.995297	−	0.0968731i	$-0.969116\pi$
$757$	−24.7189	+	24.7189i	−0.898424	+	0.898424i	0.0968731	+	0.995297i	$0.469116\pi$
$758$	3.49698	−	9.28016i	0.127016	−	0.337070i
$759$	31.4914	+	7.15091i	1.14306	+	0.259562i
$760$	−31.3015	+	20.3720i	−1.13542	+	0.738969i
$761$	0.459058	+	1.26125i	0.0166408	+	0.0457203i	0.947735	−	0.319059i	$-0.103367\pi$
$761$	0.459058	+	1.26125i	0.0166408	+	0.0457203i	−0.931094	+	0.364779i	$0.881145\pi$
$762$	−20.8712	−	41.7536i	−0.756085	−	1.51257i
$763$	20.2150	+	14.1547i	0.731832	+	0.512434i
$764$	−0.520931	+	23.0416i	−0.0188466	+	0.833617i
$765$	4.21171	−	11.2128i	0.152275	−	0.405399i
$766$	−34.4356	+	33.6659i	−1.24421	+	1.21640i
$767$	1.94119	+	0.706536i	0.0700924	+	0.0255115i
$768$	27.0054	+	6.22180i	0.974472	+	0.224510i
$769$	10.8465	+	9.10131i	0.391135	+	0.328201i	0.817055	−	0.576559i	$-0.195605\pi$
$769$	10.8465	+	9.10131i	0.391135	+	0.328201i	−0.425920	+	0.904761i	$0.640049\pi$
$770$	49.1237	+	71.8713i	1.77030	+	2.59006i
$771$	6.33753	+	15.5246i	0.228241	+	0.559105i
$772$	−12.7657	−	15.9314i	−0.459447	−	0.573384i
$773$	7.05364	+	26.3245i	0.253702	+	0.946828i	0.968808	+	0.247812i	$0.0797116\pi$
$773$	7.05364	+	26.3245i	0.253702	+	0.946828i	−0.715106	+	0.699016i	$0.753622\pi$
$774$	−20.2185	−	2.20878i	−0.726738	−	0.0793929i
$775$	28.9316	−	16.7037i	1.03925	−	0.600014i
$776$	−2.84671	+	3.78558i	−0.102191	+	0.135894i
$777$	2.33689	−	47.8925i	0.0838355	−	1.71813i
$778$	−17.9705	+	20.9313i	−0.644273	+	0.750425i
$779$	5.12066	+	7.31306i	0.183467	+	0.262017i
$780$	15.3127	−	0.243587i	0.548283	−	0.00872183i
$781$	−38.3837	−	3.35814i	−1.37348	−	0.120164i
$782$	−1.94960	+	6.96038i	−0.0697177	+	0.248903i
$783$	−0.191770	−	6.78284i	−0.00685330	−	0.242399i
$784$	−20.0064	−	38.5802i	−0.714513	−	1.37786i
$785$	−14.0414	+	11.7821i	−0.501158	+	0.420522i
$786$	−16.5481	+	10.1641i	−0.590251	+	0.362542i
$787$	2.33353	−	1.63395i	0.0831813	−	0.0582442i	−0.531246	−	0.847218i	$-0.678276\pi$
$787$	2.33353	−	1.63395i	0.0831813	−	0.0582442i	0.614427	+	0.788973i	$0.289387\pi$
$788$	4.45567	−	2.97211i	0.158727	−	0.105877i
$789$	34.1216	+	10.9510i	1.21476	+	0.389866i
$790$	−16.9298	−	20.6455i	−0.602334	−	0.734535i
$791$	66.6957	−	38.5068i	2.37142	−	1.36914i
$792$	−20.6675	+	18.9185i	−0.734386	+	0.672240i
$793$	−4.19133	−	2.41986i	−0.148838	−	0.0859319i
$794$	−2.17705	−	13.2186i	−0.0772606	−	0.469110i
$795$	10.3521	−	75.6361i	0.367152	−	2.68254i
$796$	−29.8684	+	10.1127i	−1.05866	+	0.358436i
$797$	−0.119757	−	1.36882i	−0.00424199	−	0.0484862i	0.993779	−	0.111373i	$-0.0355248\pi$
$797$	−0.119757	−	1.36882i	−0.00424199	−	0.0484862i	−0.998021	+	0.0628868i	$0.979969\pi$
$798$	−4.54978	+	30.6589i	−0.161060	+	1.08531i
$799$	−0.000517122	0	0.000188217i	−1.82945e−5	0	6.65864e-6i
$800$	25.5881	−	77.6537i	0.904675	−	2.74547i
$801$	−33.8568	−	16.2120i	−1.19627	−	0.572823i
$802$	3.29975	+	12.8961i	0.116518	+	0.455378i
$803$	26.3423	−	37.6208i	0.929601	−	1.32761i
$804$	−4.15073	−	8.54378i	−0.146385	−	0.301316i
$805$	−44.4846	+	95.3976i	−1.56788	+	3.36232i
$806$	3.09133	−	1.08575i	0.108888	−	0.0382438i
$807$	3.01399	+	9.73274i	0.106098	+	0.342609i
$808$	16.0295	−	12.5495i	0.563917	−	0.441489i
$809$		−	29.8488i		−	1.04943i	−0.851279	−	0.524714i	$-0.824172\pi$
$809$		−	29.8488i		−	1.04943i	0.851279	−	0.524714i	$-0.175828\pi$
$810$	52.1153	+	20.8674i	1.83115	+	0.733206i
$811$	26.2921	−	26.2921i	0.923242	−	0.923242i	−0.0740151	−	0.997257i	$-0.523581\pi$
$811$	26.2921	−	26.2921i	0.923242	−	0.923242i	0.997257	+	0.0740151i	$0.0235813\pi$
$812$	−6.53450	+	8.89723i	−0.229316	+	0.312232i
$813$	29.9780	+	15.8013i	1.05137	+	0.554174i
$814$	27.5725	+	13.2387i	0.966415	+	0.464015i
$815$	−32.5879	+	11.8610i	−1.14150	+	0.415474i
$816$	−3.99900	−	4.83118i	−0.139993	−	0.169125i
$817$	−2.49214	−	14.1336i	−0.0871888	−	0.494472i
$818$	−14.2090	+	3.63567i	−0.496805	+	0.127118i
$819$	8.26901	−	9.65204i	0.288942	−	0.337270i
$820$	−25.2489	−	7.38098i	−0.881731	−	0.257755i
$821$	−8.85778	+	4.13045i	−0.309139	+	0.144154i	−0.570996	−	0.820953i	$-0.693443\pi$
$821$	−8.85778	+	4.13045i	−0.309139	+	0.144154i	0.261857	+	0.965107i	$0.415665\pi$
$822$	4.20418	+	5.66942i	0.146638	+	0.197744i
$823$	6.14194	−	7.31968i	0.214095	−	0.255148i	−0.648300	−	0.761385i	$-0.724520\pi$
$823$	6.14194	−	7.31968i	0.214095	−	0.255148i	0.862394	+	0.506237i	$0.168964\pi$
$824$	−16.2697	+	0.868976i	−0.566783	+	0.0302722i
$825$	49.9859	+	65.8385i	1.74028	+	2.29220i
$826$	−2.00193	−	12.1553i	−0.0696562	−	0.422938i
$827$	3.12473	+	11.6616i	0.108657	+	0.405515i	0.998734	−	0.0502951i	$-0.0160162\pi$
$827$	3.12473	+	11.6616i	0.108657	+	0.405515i	−0.890077	+	0.455810i	$0.849350\pi$
$828$	−32.4179	−	9.83828i	−1.12660	−	0.341904i
$829$	7.35340	−	27.4433i	0.255394	−	0.953144i	−0.712477	−	0.701696i	$-0.752427\pi$
$829$	7.35340	−	27.4433i	0.255394	−	0.953144i	0.967871	−	0.251448i	$-0.0809068\pi$
$830$	5.39813	−	54.5877i	0.187372	−	1.89477i
$831$	9.13198	+	17.7640i	0.316785	+	0.616225i
$832$	3.87355	−	7.02114i	0.134291	−	0.243414i
$833$	−1.70783	+	9.68557i	−0.0591727	+	0.335585i
$834$	−17.5275	−	28.5364i	−0.606929	−	0.988135i
$835$	15.9609	+	1.39640i	0.552351	+	0.0483244i
$836$	−16.8943	−	10.2699i	−0.584302	−	0.355193i
$837$	11.9894	+	0.708210i	0.414414	+	0.0244793i
$838$	−7.94259	−	14.1232i	−0.274372	−	0.487879i
$839$	−18.4173	−	21.9488i	−0.635834	−	0.757758i	0.347872	−	0.937542i	$-0.386904\pi$
$839$	−18.4173	−	21.9488i	−0.635834	−	0.757758i	−0.983706	+	0.179784i	$0.942460\pi$
$840$	−46.0275	−	78.8810i	−1.58810	−	2.72165i
$841$	−26.8800	−	4.73967i	−0.926897	−	0.163437i
$842$	18.9667	−	22.0916i	0.653634	−	0.761328i
$843$	−23.0295	+	20.8866i	−0.793178	+	0.719373i
$844$	−32.8383	+	14.4183i	−1.13034	+	0.496300i
$845$	−13.6932	+	51.1038i	−0.471061	+	1.75802i
$846$	0.000934163	−	0.00240411i	3.21172e−5	−	8.26551e-5i
$847$	0.203871	−	0.353115i	0.00700508	−	0.0121332i
$848$	−31.6739	−	24.3836i	−1.08769	−	0.837337i
$849$	40.4633	+	17.0038i	1.38870	+	0.583570i
$850$	−15.2757	+	10.4408i	−0.523951	+	0.358118i
$851$	3.22319	+	36.8412i	0.110489	+	1.26290i
$852$	39.9138	+	6.38504i	1.36742	+	0.218748i
$853$	−36.5218	+	17.0304i	−1.25048	+	0.583109i	−0.931186	−	0.364545i	$-0.881224\pi$
$853$	−36.5218	+	17.0304i	−1.25048	+	0.583109i	−0.319297	+	0.947655i	$0.603447\pi$
$854$	−0.326189	+	28.8595i	−0.0111620	+	0.987551i
$855$	−3.85657	+	39.4243i	−0.131892	+	1.34828i
$856$	−11.1437	−	20.9077i	−0.380883	−	0.714612i
$857$	26.5633	−	4.68382i	0.907384	−	0.159996i	0.299569	−	0.954075i	$-0.403157\pi$
$857$	26.5633	−	4.68382i	0.907384	−	0.159996i	0.607815	+	0.794079i	$0.292046\pi$
$858$	3.62493	+	7.25180i	0.123753	+	0.247572i
$859$	−1.56504	+	3.35624i	−0.0533985	+	0.114513i	−0.931197	−	0.364517i	$-0.881234\pi$
$859$	−1.56504	+	3.35624i	−0.0533985	+	0.114513i	0.877798	+	0.479031i	$0.159012\pi$
$860$	31.7718	+	27.9074i	1.08341	+	0.951635i
$861$	−18.4722	+	11.6355i	−0.629531	+	0.396537i
$862$	−4.50009	+	2.03683i	−0.153274	+	0.0693747i
$863$	−37.2537			−1.26813			−0.634065	−	0.773280i	$-0.718615\pi$
$863$	−37.2537			−1.26813			−0.634065	+	0.773280i	$0.718615\pi$
$864$	23.0416	−	18.2506i	0.783892	−	0.620897i
$865$	16.8326			0.572325
$866$	9.39808	−	4.25375i	0.319360	−	0.144548i
$867$	−1.07901	−	28.0048i	−0.0366453	−	0.951093i
$868$	−14.6800	−	12.8945i	−0.498271	−	0.437667i
$869$	5.97337	−	12.8099i	0.202633	−	0.434547i
$870$	−7.77482	+	11.7728i	−0.263591	+	0.399134i
$871$	−2.70671	+	0.477266i	−0.0917134	+	0.0161715i
$872$	14.5733	−	7.76749i	0.493516	−	0.263040i
$873$	1.25047	+	4.86569i	0.0423221	+	0.164679i
$874$	0.270176	−	23.9037i	0.00913884	−	0.808556i
$875$	−159.721	+	74.4790i	−5.39955	+	2.51785i
$876$	−30.3788	+	37.3962i	−1.02640	+	1.26350i
$877$	4.70225	+	53.7470i	0.158784	+	1.81491i	0.490405	+	0.871495i	$0.336849\pi$
$877$	4.70225	+	53.7470i	0.158784	+	1.81491i	−0.331621	+	0.943413i	$0.607595\pi$
$878$	20.4633	−	13.9866i	0.690602	−	0.472024i
$879$	−1.17194	−	9.26838i	−0.0395284	−	0.312615i
$880$	57.7696	−	7.51294i	1.94741	−	0.253261i
$881$	−22.7564	+	39.4152i	−0.766682	+	1.32793i	0.172671	+	0.984979i	$0.444760\pi$
$881$	−22.7564	+	39.4152i	−0.766682	+	1.32793i	−0.939353	+	0.342952i	$0.888573\pi$
$882$	−45.2120	−	8.98057i	−1.52237	−	0.302391i
$883$	2.84723	−	10.6260i	0.0958169	−	0.357593i	−0.901325	−	0.433143i	$-0.857404\pi$
$883$	2.84723	−	10.6260i	0.0958169	−	0.357593i	0.997142	+	0.0755496i	$0.0240711\pi$
$884$	−1.66158	+	0.729551i	−0.0558850	+	0.0245374i
$885$	−3.32890	−	15.3883i	−0.111900	−	0.517273i
$886$	0.951464	−	1.10823i	0.0319651	−	0.0372317i
$887$	−4.50964	−	0.795171i	−0.151419	−	0.0266992i	0.0974249	−	0.995243i	$-0.468939\pi$
$887$	−4.50964	−	0.795171i	−0.151419	−	0.0266992i	−0.248844	+	0.968544i	$0.580051\pi$
$888$	−27.8618	−	15.9154i	−0.934980	−	0.534087i
$889$	51.7745	+	61.7025i	1.73646	+	2.06944i
$890$	38.2578	+	68.0287i	1.28240	+	2.28033i
$891$	1.98300	+	29.6522i	0.0664330	+	0.993387i
$892$	26.0339	+	15.8259i	0.871681	+	0.529889i
$893$	0.00181305		0.000158622i	6.06715e−5		5.30807e-6i
$894$	−13.6925	+	0.372642i	−0.457945	+	0.0124630i
$895$	4.71495	−	26.7398i	0.157603	−	0.893812i
$896$	−47.8177	+	0.389776i	−1.59748	+	0.0130215i
$897$	−5.30925	+	8.24039i	−0.177271	+	0.275139i
$898$	−0.116929	+	1.18243i	−0.00390198	+	0.0394581i
$899$	−0.781215	+	2.91554i	−0.0260550	+	0.0972386i
$900$	−47.3809	−	72.6326i	−1.57936	−	2.42109i
$901$	2.34127	+	8.73772i	0.0779989	+	0.291096i
$902$	−2.26304	−	13.7407i	−0.0753509	−	0.457515i
$903$	34.8180	−	4.40254i	1.15867	−	0.146507i
$904$	−2.74867	−	51.4630i	−0.0914193	−	1.71163i
$905$	−27.2403	+	32.4637i	−0.905498	+	1.07913i
$906$	1.53243	−	3.53427i	0.0509114	−	0.117418i
$907$	23.0228	−	10.7357i	0.764460	−	0.356474i	−0.000964057	−	1.00000i	$-0.500307\pi$
$907$	23.0228	−	10.7357i	0.764460	−	0.356474i	0.765424	+	0.643526i	$0.222529\pi$
$908$	−23.8835	−	6.98182i	−0.792602	−	0.231700i
$909$	0.221219	−	21.5915i	0.00733736	−	0.716144i
$910$	−25.6011	+	6.55060i	−0.848669	+	0.217150i
$911$	3.95775	+	22.4455i	0.131126	+	0.743652i	0.977479	+	0.211031i	$0.0676820\pi$
$911$	3.95775	+	22.4455i	0.131126	+	0.743652i	−0.846353	+	0.532622i	$0.821207\pi$
$912$	16.9101	+	12.0102i	0.559950	+	0.397697i
$913$	27.2875	−	9.93185i	0.903085	−	0.328696i
$914$	9.33277	+	4.48105i	0.308701	+	0.148220i
$915$	1.42015	+	36.8586i	0.0469487	+	1.21851i
$916$	26.8686	−	36.5837i	0.887763	−	1.20876i
$917$	23.6954	−	23.6954i	0.782491	−	0.782491i
$918$	−6.65102	+	0.112833i	−0.219516	+	0.00372403i
$919$			18.2674i			0.602585i	0.953532	+	0.301293i	$0.0974181\pi$
$919$			18.2674i			0.602585i	−0.953532	+	0.301293i	$0.902582\pi$
$920$	43.4216	+	55.4627i	1.43157	+	1.82855i
$921$	32.0680	+	7.28184i	1.05668	+	0.239945i
$922$	14.5222	−	5.10051i	0.478262	−	0.167976i
$923$	4.94295	−	10.6002i	0.162699	−	0.348909i
$924$	27.0975	−	40.0399i	0.891441	−	1.31722i
$925$	−54.2983	+	77.5460i	−1.78532	+	2.54970i
$926$	1.23600	+	4.83056i	0.0406176	+	0.158742i
$927$	−10.0566	+	14.0537i	−0.330303	+	0.461584i
$928$	3.32635	+	6.59588i	0.109193	+	0.216520i
$929$	−13.9675	−	5.08376i	−0.458259	−	0.166793i	0.102567	−	0.994726i	$-0.467294\pi$
$929$	−13.9675	−	5.08376i	−0.458259	−	0.166793i	−0.560826	+	0.827933i	$0.689516\pi$
$930$	−19.5589	−	15.5250i	−0.641362	−	0.509086i
$931$	−2.83484	−	32.4024i	−0.0929082	−	1.06195i
$932$	−50.0110	+	16.9325i	−1.63816	+	0.554643i
$933$	−5.51560	+	2.25160i	−0.180573	+	0.0737142i
$934$	−1.51456	−	9.19607i	−0.0495578	−	0.300905i
$935$	−11.4174	−	6.59182i	−0.373388	−	0.215576i
$936$	−3.25072	−	7.85946i	−0.106253	−	0.256895i
$937$	35.4539	−	20.4693i	1.15823	−	0.668703i	0.207348	−	0.978267i	$-0.433517\pi$
$937$	35.4539	−	20.4693i	1.15823	−	0.668703i	0.950878	+	0.309565i	$0.100183\pi$
$938$	10.3929	+	12.6739i	0.339339	+	0.413819i
$939$	−6.20568	+	5.62825i	−0.202515	+	0.183671i
$940$	−0.00446125	+	0.00297583i	−0.000145510	+	9.70608e-5i
$941$	−17.0423	+	11.9331i	−0.555563	+	0.389009i	−0.817372	−	0.576111i	$-0.804570\pi$
$941$	−17.0423	+	11.9331i	−0.555563	+	0.389009i	0.261809	+	0.965120i	$0.415681\pi$
$942$	8.95106	+	4.84811i	0.291641	+	0.157960i
$943$	12.8985	−	10.8232i	0.420034	−	0.352451i
$944$	−7.85828	−	2.49133i	−0.255765	−	0.0810857i
$945$	−95.8332	−	14.1181i	−3.11745	−	0.459263i
$946$	−6.03808	+	21.5569i	−0.196315	+	0.700874i
$947$	49.1301	+	4.29832i	1.59651	+	0.139677i	0.850398	−	0.526140i	$-0.176361\pi$
$947$	49.1301	+	4.29832i	1.59651	+	0.139677i	0.746115	+	0.665817i	$0.231917\pi$
$948$	−7.20874	+	12.9576i	−0.234129	+	0.420843i
$949$	7.99630	+	11.4199i	0.259571	+	0.370706i
$950$	39.8611	−	46.4287i	1.29327	−	1.50635i
$951$	−14.2067	+	7.30330i	−0.460684	+	0.236826i
$952$	8.64914	+	6.50404i	0.280320	+	0.210797i
$953$	45.1167	−	26.0482i	1.46147	−	0.843783i	0.462395	−	0.886674i	$-0.346990\pi$
$953$	45.1167	−	26.0482i	1.46147	−	0.843783i	0.999080	+	0.0428912i	$0.0136569\pi$
$954$	−41.1794	+	10.0883i	−1.33323	+	0.326621i
$955$	−13.1549	−	49.0948i	−0.425683	−	1.58867i
$956$	−31.4391	−	39.2355i	−1.01681	−	1.26897i
$957$	−7.39975	−	1.01279i	−0.239200	−	0.0327387i
$958$	15.5447	+	22.7429i	0.502226	+	0.734790i
$959$	−9.32970	−	7.82855i	−0.301272	−	0.252797i
$960$	−61.0125	+	3.54049i	−1.96917	+	0.114269i
$961$	24.1102	+	8.77539i	0.777748	+	0.283077i
$962$	−6.63890	+	6.49050i	−0.214047	+	0.209262i
$963$	−24.7015	−	4.61696i	−0.795994	−	0.148780i
$964$	−1.13464	+	50.1872i	−0.0365444	+	1.61642i
$965$	36.8792	+	25.8231i	1.18718	+	0.831276i
$966$	58.3520	+	3.50873i	1.87744	+	0.112891i
$967$	−2.04115	−	5.60802i	−0.0656390	−	0.180342i	0.902537	−	0.430613i	$-0.141703\pi$
$967$	−2.04115	−	5.60802i	−0.0656390	−	0.180342i	−0.968176	+	0.250271i	$0.919480\pi$
$968$	−0.148836	−	0.228686i	−0.00478377	−	0.00735026i
$969$	−1.38851	−	4.48376i	−0.0446054	−	0.144039i
$970$	3.68324	−	9.77445i	0.118262	−	0.313839i
$971$	20.7497	−	20.7497i	0.665891	−	0.665891i	−0.290871	−	0.956762i	$-0.593945\pi$
$971$	20.7497	−	20.7497i	0.665891	−	0.665891i	0.956762	+	0.290871i	$0.0939451\pi$
$972$	0.142927	−	31.1766i	0.00458437	−	0.999989i
$973$	40.8616	+	40.8616i	1.30996	+	1.30996i
$974$	−10.8325	−	23.9330i	−0.347097	−	0.766862i
$975$	−23.9698	+	7.42287i	−0.767647	+	0.237722i
$976$	17.1173	+	8.94500i	0.547911	+	0.286322i
$977$	−23.0737	+	8.39815i	−0.738194	+	0.268681i	−0.683629	−	0.729829i	$-0.739599\pi$
$977$	−23.0737	+	8.39815i	−0.738194	+	0.268681i	−0.0545651	+	0.998510i	$0.517377\pi$
$978$	12.7767	+	14.4115i	0.408552	+	0.460829i
$979$	−23.6988	+	33.8454i	−0.757417	+	1.08170i
$980$	66.2202	+	69.2837i	2.11533	+	2.21319i
$981$	3.21817	−	17.2177i	0.102748	−	0.549719i
$982$	0.185143	−	16.3805i	0.00590816	−	0.522722i
$983$	−20.2622	+	55.6700i	−0.646264	+	1.77560i	−0.0151762	+	0.999885i	$0.504831\pi$
$983$	−20.2622	+	55.6700i	−0.646264	+	1.77560i	−0.631088	+	0.775711i	$0.717391\pi$
$984$	1.34027	+	14.5476i	0.0427262	+	0.463761i
$985$	−7.59230	+	9.04815i	−0.241911	+	0.288298i
$986$	0.308885	−	1.64297i	0.00983691	−	0.0523228i
$987$	−0.000603507		0.00440943i	−1.92099e−5		0.000140354i
$988$	4.68345	−	3.75280i	0.149000	−	0.119393i
$989$	−26.1455	+	7.00567i	−0.831380	+	0.222767i
$990$	32.0408	−	52.8336i	1.01832	−	1.67916i
$991$	11.0885	+	19.2059i	0.352239	+	0.610096i	0.986641	−	0.162907i	$-0.0520871\pi$
$991$	11.0885	+	19.2059i	0.352239	+	0.610096i	−0.634402	+	0.773003i	$0.718754\pi$
$992$	−12.1433	+	4.84767i	−0.385550	+	0.153914i
$993$	−16.1941	−	31.5014i	−0.513903	−	0.999668i
$994$	−69.5471	+	5.29328i	−2.20590	+	0.167893i
$995$	56.9653	−	39.8876i	1.80592	−	1.26452i
$996$	−29.2967	+	8.35167i	−0.928302	+	0.264633i
$997$	1.56384	−	17.8748i	0.0495273	−	0.566100i	−0.930373	−	0.366614i	$-0.880517\pi$
$997$	1.56384	−	17.8748i	0.0495273	−	0.566100i	0.979901	−	0.199486i	$-0.0639273\pi$
$998$	−22.9084	−	40.7348i	−0.725152	−	1.28944i
$999$	−31.6393	+	12.5393i	−1.00102	+	0.396726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.bg.a.157.10	✓	840
16.5	even	4	inner	432.2.bg.a.373.24	yes	840
27.16	even	9	inner	432.2.bg.a.205.24	yes	840
432.421	even	36	inner	432.2.bg.a.421.10	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.bg.a.157.10	✓	840	1.1	even	1	trivial
432.2.bg.a.205.24	yes	840	27.16	even	9	inner
432.2.bg.a.373.24	yes	840	16.5	even	4	inner
432.2.bg.a.421.10	yes	840	432.421	even	36	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.bg (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28839 + 0.583148i) q^{2} +(-1.53223 - 0.807632i) q^{3} +(1.31988 - 1.50264i) q^{4} +(-1.86400 + 3.99736i) q^{5} +(2.44507 + 0.147023i) q^{6} +(-4.16246 + 0.733954i) q^{7} +(-0.824247 + 2.70566i) q^{8} +(1.69546 + 2.47496i) q^{9} +O(q^{10})\)	\(q+(-1.28839 + 0.583148i) q^{2} +(-1.53223 - 0.807632i) q^{3} +(1.31988 - 1.50264i) q^{4} +(-1.86400 + 3.99736i) q^{5} +(2.44507 + 0.147023i) q^{6} +(-4.16246 + 0.733954i) q^{7} +(-0.824247 + 2.70566i) q^{8} +(1.69546 + 2.47496i) q^{9} +(0.0704963 - 6.23714i) q^{10} +(2.99267 - 1.39551i) q^{11} +(-3.23593 + 1.23642i) q^{12} +(0.0873603 + 0.998533i) q^{13} +(4.93485 - 3.37295i) q^{14} +(6.08448 - 4.61946i) q^{15} +(-0.515856 - 3.96660i) q^{16} +(-0.452610 + 0.783943i) q^{17} +(-3.62768 - 2.19999i) q^{18} +(0.774835 - 2.89172i) q^{19} +(3.54635 + 8.07695i) q^{20} +(6.97061 + 2.23715i) q^{21} +(-3.04193 + 3.54312i) q^{22} +(-5.56054 - 0.980473i) q^{23} +(3.44812 - 3.48001i) q^{24} +(-9.29048 - 11.0720i) q^{25} +(-0.694847 - 1.23555i) q^{26} +(-0.598986 - 5.16151i) q^{27} +(-4.39106 + 7.22341i) q^{28} +(1.30091 + 0.113815i) q^{29} +(-5.14533 + 9.49980i) q^{30} +(-0.401367 + 2.27627i) q^{31} +(2.97774 + 4.80969i) q^{32} +(-5.71252 - 0.278740i) q^{33} +(0.125981 - 1.27396i) q^{34} +(4.82495 - 18.0070i) q^{35} +(5.95677 + 0.718965i) q^{36} +(-1.69520 - 6.32657i) q^{37} +(0.688018 + 4.17750i) q^{38} +(0.672591 - 1.60054i) q^{39} +(-9.27913 - 8.33818i) q^{40} +(-1.91685 + 2.28442i) q^{41} +(-10.2854 + 1.18259i) q^{42} +(4.34474 - 2.02599i) q^{43} +(1.85301 - 6.33881i) q^{44} +(-13.0536 + 2.16406i) q^{45} +(7.73588 - 1.97939i) q^{46} +(0.000105566 + 0.000598694i) q^{47} +(-2.41314 + 6.49436i) q^{48} +(10.2095 - 3.71596i) q^{49} +(18.4263 + 8.84723i) q^{50} +(1.32664 - 0.835640i) q^{51} +(1.61574 + 1.18667i) q^{52} +(7.06619 - 7.06619i) q^{53} +(3.78165 + 6.30072i) q^{54} +14.5640i q^{55} +(1.44506 - 11.8672i) q^{56} +(-3.52267 + 3.80501i) q^{57} +(-1.74244 + 0.611986i) q^{58} +(0.870989 - 1.86784i) q^{59} +(1.08937 - 15.2399i) q^{60} +(-2.76945 + 3.95519i) q^{61} +(-0.810286 - 3.16677i) q^{62} +(-8.87379 - 9.05751i) q^{63} +(-6.64123 - 4.46027i) q^{64} +(-4.15434 - 1.51206i) q^{65} +(7.52248 - 2.97212i) q^{66} +(0.238984 + 2.73160i) q^{67} +(0.580596 + 1.71482i) q^{68} +(7.72816 + 5.99318i) q^{69} +(4.28433 + 26.0136i) q^{70} +(-10.1053 - 5.83431i) q^{71} +(-8.09388 + 2.54738i) q^{72} +(12.0451 - 6.95424i) q^{73} +(5.87340 + 7.16251i) q^{74} +(5.29309 + 24.4681i) q^{75} +(-3.32254 - 4.98102i) q^{76} +(-11.4326 + 8.00522i) q^{77} +(0.0667949 + 2.45433i) q^{78} +(3.27900 - 2.75141i) q^{79} +(16.8175 + 5.33168i) q^{80} +(-3.25082 + 8.39239i) q^{81} +(1.13749 - 4.06102i) q^{82} +(8.76070 + 0.766462i) q^{83} +(12.5620 - 7.52157i) q^{84} +(-2.29004 - 3.27052i) q^{85} +(-4.41625 + 5.14388i) q^{86} +(-1.90137 - 1.22505i) q^{87} +(1.30907 + 9.24741i) q^{88} +(-10.8363 + 6.25635i) q^{89} +(15.5562 - 10.4004i) q^{90} +(-1.09651 - 4.09223i) q^{91} +(-8.81252 + 7.06138i) q^{92} +(2.45337 - 3.16361i) q^{93} +(-0.000485137 - 0.000709788i) q^{94} +(10.1150 + 8.48748i) q^{95} +(-0.678124 - 9.77446i) q^{96} +(1.57361 + 0.572747i) q^{97} +(-10.9869 + 10.7413i) q^{98} +(8.52778 + 5.04071i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8}+O(q^{10}) \) 840 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 6 * q^8	\( 840 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8} - 6 q^{10} - 12 q^{11} - 30 q^{12} - 12 q^{13} - 12 q^{14} - 24 q^{15} - 12 q^{16} - 12 q^{17} - 12 q^{18} - 6 q^{19} - 54 q^{20} - 12 q^{21} - 12 q^{22} + 18 q^{24} - 24 q^{26} - 12 q^{27} - 24 q^{28} - 12 q^{29} - 12 q^{30} - 24 q^{31} - 12 q^{32} - 24 q^{33} - 6 q^{35} - 12 q^{36} - 6 q^{37} - 12 q^{38} - 12 q^{40} - 72 q^{42} - 12 q^{43} - 6 q^{44} - 12 q^{45} - 6 q^{46} - 24 q^{47} - 12 q^{48} - 24 q^{49} - 168 q^{50} + 6 q^{51} - 12 q^{52} - 24 q^{53} + 156 q^{54} - 54 q^{56} + 42 q^{58} - 48 q^{59} - 72 q^{60} - 12 q^{61} + 60 q^{62} - 24 q^{63} - 6 q^{64} - 24 q^{65} - 198 q^{66} - 12 q^{67} - 66 q^{68} - 12 q^{69} - 54 q^{70} - 144 q^{72} - 96 q^{74} - 96 q^{75} - 12 q^{76} - 12 q^{77} - 90 q^{78} - 24 q^{79} - 204 q^{80} - 24 q^{81} - 24 q^{82} + 48 q^{83} + 36 q^{84} + 18 q^{85} - 72 q^{86} - 12 q^{88} - 66 q^{90} - 6 q^{91} + 102 q^{92} - 12 q^{93} - 12 q^{94} - 24 q^{95} - 120 q^{96} - 24 q^{97} - 6 q^{98} - 12 q^{99}+O(q^{100}) \) 840 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 6 * q^8 - 6 * q^10 - 12 * q^11 - 30 * q^12 - 12 * q^13 - 12 * q^14 - 24 * q^15 - 12 * q^16 - 12 * q^17 - 12 * q^18 - 6 * q^19 - 54 * q^20 - 12 * q^21 - 12 * q^22 + 18 * q^24 - 24 * q^26 - 12 * q^27 - 24 * q^28 - 12 * q^29 - 12 * q^30 - 24 * q^31 - 12 * q^32 - 24 * q^33 - 6 * q^35 - 12 * q^36 - 6 * q^37 - 12 * q^38 - 12 * q^40 - 72 * q^42 - 12 * q^43 - 6 * q^44 - 12 * q^45 - 6 * q^46 - 24 * q^47 - 12 * q^48 - 24 * q^49 - 168 * q^50 + 6 * q^51 - 12 * q^52 - 24 * q^53 + 156 * q^54 - 54 * q^56 + 42 * q^58 - 48 * q^59 - 72 * q^60 - 12 * q^61 + 60 * q^62 - 24 * q^63 - 6 * q^64 - 24 * q^65 - 198 * q^66 - 12 * q^67 - 66 * q^68 - 12 * q^69 - 54 * q^70 - 144 * q^72 - 96 * q^74 - 96 * q^75 - 12 * q^76 - 12 * q^77 - 90 * q^78 - 24 * q^79 - 204 * q^80 - 24 * q^81 - 24 * q^82 + 48 * q^83 + 36 * q^84 + 18 * q^85 - 72 * q^86 - 12 * q^88 - 66 * q^90 - 6 * q^91 + 102 * q^92 - 12 * q^93 - 12 * q^94 - 24 * q^95 - 120 * q^96 - 24 * q^97 - 6 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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