LMFDB - Embedded newform 380.3.b.a.191.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,3,Mod(191,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("380.191");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	380.b (of order $2$, degree $1$, 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:	$10.3542500457$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			191.7
Character	$\chi$	$=$	380.191
Dual form			380.3.b.a.191.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93566 - 0.503224i) q^{2} +0.768825i q^{3} +(3.49353 + 1.94814i) q^{4} +2.23607 q^{5} +(0.386891 - 1.48818i) q^{6} -10.1723i q^{7} +(-5.78193 - 5.52895i) q^{8} +8.40891 q^{9} +O(q^{10})$	\(q+(-1.93566 - 0.503224i) q^{2} +0.768825i q^{3} +(3.49353 + 1.94814i) q^{4} +2.23607 q^{5} +(0.386891 - 1.48818i) q^{6} -10.1723i q^{7} +(-5.78193 - 5.52895i) q^{8} +8.40891 q^{9} +(-4.32826 - 1.12524i) q^{10} -7.26771i q^{11} +(-1.49778 + 2.68592i) q^{12} -23.3429 q^{13} +(-5.11895 + 19.6901i) q^{14} +1.71915i q^{15} +(8.40953 + 13.6118i) q^{16} -3.05348 q^{17} +(-16.2768 - 4.23156i) q^{18} +4.35890i q^{19} +(7.81177 + 4.35617i) q^{20} +7.82073 q^{21} +(-3.65728 + 14.0678i) q^{22} -14.8204i q^{23} +(4.25080 - 4.44529i) q^{24} +5.00000 q^{25} +(45.1839 + 11.7467i) q^{26} +13.3844i q^{27} +(19.8171 - 35.5373i) q^{28} -39.7955 q^{29} +(0.865115 - 3.32767i) q^{30} -33.6100i q^{31} +(-9.42820 - 30.5796i) q^{32} +5.58760 q^{33} +(5.91049 + 1.53658i) q^{34} -22.7460i q^{35} +(29.3768 + 16.3817i) q^{36} +19.0059 q^{37} +(2.19350 - 8.43733i) q^{38} -17.9466i q^{39} +(-12.9288 - 12.3631i) q^{40} -1.45658 q^{41} +(-15.1382 - 3.93558i) q^{42} +51.7704i q^{43} +(14.1585 - 25.3900i) q^{44} +18.8029 q^{45} +(-7.45798 + 28.6872i) q^{46} -70.0968i q^{47} +(-10.4651 + 6.46546i) q^{48} -54.4759 q^{49} +(-9.67828 - 2.51612i) q^{50} -2.34759i q^{51} +(-81.5492 - 45.4752i) q^{52} -73.8899 q^{53} +(6.73535 - 25.9076i) q^{54} -16.2511i q^{55} +(-56.2422 + 58.8156i) q^{56} -3.35123 q^{57} +(77.0304 + 20.0260i) q^{58} -74.5950i q^{59} +(-3.34913 + 6.00589i) q^{60} +30.7747 q^{61} +(-16.9134 + 65.0575i) q^{62} -85.5380i q^{63} +(2.86139 + 63.9360i) q^{64} -52.1963 q^{65} +(-10.8157 - 2.81181i) q^{66} -121.999i q^{67} +(-10.6674 - 5.94860i) q^{68} +11.3943 q^{69} +(-11.4463 + 44.0284i) q^{70} -39.1862i q^{71} +(-48.6197 - 46.4924i) q^{72} +17.5212 q^{73} +(-36.7889 - 9.56423i) q^{74} +3.84413i q^{75} +(-8.49173 + 15.2280i) q^{76} -73.9294 q^{77} +(-9.03117 + 34.7385i) q^{78} +59.7663i q^{79} +(18.8043 + 30.4368i) q^{80} +65.3899 q^{81} +(2.81944 + 0.732987i) q^{82} -72.9967i q^{83} +(27.3220 + 15.2358i) q^{84} -6.82779 q^{85} +(26.0521 - 100.210i) q^{86} -30.5958i q^{87} +(-40.1828 + 42.0214i) q^{88} -2.69178 q^{89} +(-36.3959 - 9.46206i) q^{90} +237.451i q^{91} +(28.8722 - 51.7756i) q^{92} +25.8402 q^{93} +(-35.2744 + 135.683i) q^{94} +9.74679i q^{95} +(23.5103 - 7.24863i) q^{96} +144.741 q^{97} +(105.447 + 27.4136i) q^{98} -61.1135i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9}+O(q^{10}) $ 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9	$ 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9} - 80 q^{12} - 80 q^{14} + 4 q^{16} - 44 q^{18} - 40 q^{20} + 16 q^{21} + 160 q^{22} + 204 q^{24} + 360 q^{25} + 28 q^{26} + 20 q^{28} + 16 q^{29} + 40 q^{30} - 136 q^{32} - 96 q^{34} + 8 q^{36} - 192 q^{37} - 4 q^{42} - 40 q^{44} + 80 q^{45} - 232 q^{46} - 156 q^{48} - 504 q^{49} + 20 q^{50} + 228 q^{52} + 320 q^{53} + 92 q^{54} + 8 q^{56} + 380 q^{58} - 140 q^{60} - 168 q^{62} - 60 q^{64} - 40 q^{66} + 396 q^{68} - 48 q^{69} - 120 q^{70} - 284 q^{72} + 192 q^{74} - 640 q^{77} - 520 q^{78} + 120 q^{80} + 568 q^{81} - 240 q^{82} + 112 q^{84} + 688 q^{86} - 484 q^{88} + 240 q^{89} + 12 q^{92} + 512 q^{93} + 432 q^{94} + 300 q^{96} - 44 q^{98}+O(q^{100}) $ 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9 - 80 * q^12 - 80 * q^14 + 4 * q^16 - 44 * q^18 - 40 * q^20 + 16 * q^21 + 160 * q^22 + 204 * q^24 + 360 * q^25 + 28 * q^26 + 20 * q^28 + 16 * q^29 + 40 * q^30 - 136 * q^32 - 96 * q^34 + 8 * q^36 - 192 * q^37 - 4 * q^42 - 40 * q^44 + 80 * q^45 - 232 * q^46 - 156 * q^48 - 504 * q^49 + 20 * q^50 + 228 * q^52 + 320 * q^53 + 92 * q^54 + 8 * q^56 + 380 * q^58 - 140 * q^60 - 168 * q^62 - 60 * q^64 - 40 * q^66 + 396 * q^68 - 48 * q^69 - 120 * q^70 - 284 * q^72 + 192 * q^74 - 640 * q^77 - 520 * q^78 + 120 * q^80 + 568 * q^81 - 240 * q^82 + 112 * q^84 + 688 * q^86 - 484 * q^88 + 240 * q^89 + 12 * q^92 + 512 * q^93 + 432 * q^94 + 300 * q^96 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	−1.93566	−	0.503224i	−0.967828	−	0.251612i
$2$	−1.93566	−	0.503224i	−0.967828	−	0.251612i
$3$			0.768825i			0.256275i	0.991756	+	0.128138i	$0.0408999\pi$
$3$			0.768825i			0.256275i	−0.991756	+	0.128138i	$0.959100\pi$
$4$	3.49353	+	1.94814i	0.873383	+	0.487034i
$5$	2.23607			0.447214
$5$	2.23607			0.447214
$6$	0.386891	−	1.48818i	0.0644819	−	0.248030i
$7$		−	10.1723i		−	1.45319i	−0.687067	−	0.726594i	$-0.741102\pi$
$7$		−	10.1723i		−	1.45319i	0.687067	−	0.726594i	$-0.258898\pi$
$8$	−5.78193	−	5.52895i	−0.722741	−	0.691119i
$9$	8.40891			0.934323
$10$	−4.32826	−	1.12524i	−0.432826	−	0.112524i
$11$		−	7.26771i		−	0.660701i	−0.943858	−	0.330350i	$-0.892833\pi$
$11$		−	7.26771i		−	0.660701i	0.943858	−	0.330350i	$-0.107167\pi$
$12$	−1.49778	+	2.68592i	−0.124815	+	0.223826i
$13$	−23.3429			−1.79561			−0.897804	−	0.440394i	$-0.854839\pi$
$13$	−23.3429			−1.79561			−0.897804	+	0.440394i	$0.854839\pi$
$14$	−5.11895	+	19.6901i	−0.365639	+	1.40644i
$15$			1.71915i			0.114610i
$16$	8.40953	+	13.6118i	0.525595	+	0.850735i
$17$	−3.05348			−0.179617			−0.0898083	−	0.995959i	$-0.528625\pi$
$17$	−3.05348			−0.179617			−0.0898083	+	0.995959i	$0.528625\pi$
$18$	−16.2768	−	4.23156i	−0.904264	−	0.235087i
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	7.81177	+	4.35617i	0.390589	+	0.217808i
$21$	7.82073			0.372416
$22$	−3.65728	+	14.0678i	−0.166240	+	0.639445i
$23$		−	14.8204i		−	0.644366i	−0.946677	−	0.322183i	$-0.895583\pi$
$23$		−	14.8204i		−	0.644366i	0.946677	−	0.322183i	$-0.104417\pi$
$24$	4.25080	−	4.44529i	0.177117	−	0.185221i
$25$	5.00000			0.200000
$26$	45.1839	+	11.7467i	1.73784	+	0.451797i
$27$			13.3844i			0.495719i
$28$	19.8171	−	35.5373i	0.707752	−	1.26919i
$29$	−39.7955			−1.37226			−0.686129	−	0.727480i	$-0.740692\pi$
$29$	−39.7955			−1.37226			−0.686129	+	0.727480i	$0.740692\pi$
$30$	0.865115	−	3.32767i	0.0288372	−	0.110922i
$31$		−	33.6100i		−	1.08419i	−0.840316	−	0.542097i	$-0.817630\pi$
$31$		−	33.6100i		−	1.08419i	0.840316	−	0.542097i	$-0.182370\pi$
$32$	−9.42820	−	30.5796i	−0.294631	−	0.955611i
$33$	5.58760			0.169321
$34$	5.91049	+	1.53658i	0.173838	+	0.0451937i
$35$		−	22.7460i		−	0.649885i
$36$	29.3768	+	16.3817i	0.816022	+	0.455047i
$37$	19.0059			0.513674			0.256837	−	0.966455i	$-0.417320\pi$
$37$	19.0059			0.513674			0.256837	+	0.966455i	$0.417320\pi$
$38$	2.19350	−	8.43733i	0.0577237	−	0.222035i
$39$		−	17.9466i		−	0.460170i
$40$	−12.9288	−	12.3631i	−0.323220	−	0.309078i
$41$	−1.45658			−0.0355264			−0.0177632	−	0.999842i	$-0.505655\pi$
$41$	−1.45658			−0.0355264			−0.0177632	+	0.999842i	$0.505655\pi$
$42$	−15.1382	−	3.93558i	−0.360434	−	0.0937042i
$43$			51.7704i			1.20396i	0.798510	+	0.601982i	$0.205622\pi$
$43$			51.7704i			1.20396i	−0.798510	+	0.601982i	$0.794378\pi$
$44$	14.1585	−	25.3900i	0.321784	−	0.577045i
$45$	18.8029			0.417842
$46$	−7.45798	+	28.6872i	−0.162130	+	0.623635i
$47$		−	70.0968i		−	1.49142i	−0.666270	−	0.745710i	$-0.732110\pi$
$47$		−	70.0968i		−	1.49142i	0.666270	−	0.745710i	$-0.267890\pi$
$48$	−10.4651	+	6.46546i	−0.218022	+	0.134697i
$49$	−54.4759			−1.11175
$50$	−9.67828	−	2.51612i	−0.193566	−	0.0503224i
$51$		−	2.34759i		−	0.0460312i
$52$	−81.5492	−	45.4752i	−1.56825	−	0.874523i
$53$	−73.8899			−1.39415			−0.697075	−	0.716999i	$-0.745515\pi$
$53$	−73.8899			−1.39415			−0.697075	+	0.716999i	$0.745515\pi$
$54$	6.73535	−	25.9076i	0.124729	−	0.479771i
$55$		−	16.2511i		−	0.295474i
$56$	−56.2422	+	58.8156i	−1.00433	+	1.05028i
$57$	−3.35123			−0.0587935
$58$	77.0304	+	20.0260i	1.32811	+	0.345277i
$59$		−	74.5950i		−	1.26432i	−0.774837	−	0.632161i	$-0.782168\pi$
$59$		−	74.5950i		−	1.26432i	0.774837	−	0.632161i	$-0.217832\pi$
$60$	−3.34913	+	6.00589i	−0.0558188	+	0.100098i
$61$	30.7747			0.504503			0.252252	−	0.967662i	$-0.418829\pi$
$61$	30.7747			0.504503			0.252252	+	0.967662i	$0.418829\pi$
$62$	−16.9134	+	65.0575i	−0.272796	+	1.04931i
$63$		−	85.5380i		−	1.35775i
$64$	2.86139	+	63.9360i	0.0447092	+	0.999000i
$65$	−52.1963			−0.803021
$66$	−10.8157	−	2.81181i	−0.163874	−	0.0426032i
$67$		−	121.999i		−	1.82089i	−0.413635	−	0.910443i	$-0.635741\pi$
$67$		−	121.999i		−	1.82089i	0.413635	−	0.910443i	$-0.364259\pi$
$68$	−10.6674	−	5.94860i	−0.156874	−	0.0874794i
$69$	11.3943			0.165135
$70$	−11.4463	+	44.0284i	−0.163519	+	0.628977i
$71$		−	39.1862i		−	0.551918i	−0.961169	−	0.275959i	$-0.911005\pi$
$71$		−	39.1862i		−	0.551918i	0.961169	−	0.275959i	$-0.0889954\pi$
$72$	−48.6197	−	46.4924i	−0.675274	−	0.645728i
$73$	17.5212			0.240016			0.120008	−	0.992773i	$-0.461708\pi$
$73$	17.5212			0.240016			0.120008	+	0.992773i	$0.461708\pi$
$74$	−36.7889	−	9.56423i	−0.497148	−	0.129246i
$75$			3.84413i			0.0512550i
$76$	−8.49173	+	15.2280i	−0.111733	+	0.200368i
$77$	−73.9294			−0.960122
$78$	−9.03117	+	34.7385i	−0.115784	+	0.445365i
$79$			59.7663i			0.756536i	0.925696	+	0.378268i	$0.123480\pi$
$79$			59.7663i			0.756536i	−0.925696	+	0.378268i	$0.876520\pi$
$80$	18.8043	+	30.4368i	0.235053	+	0.380460i
$81$	65.3899			0.807283
$82$	2.81944	+	0.732987i	0.0343835	+	0.00893887i
$83$		−	72.9967i		−	0.879478i	−0.898126	−	0.439739i	$-0.855071\pi$
$83$		−	72.9967i		−	0.879478i	0.898126	−	0.439739i	$-0.144929\pi$
$84$	27.3220	+	15.2358i	0.325261	+	0.181379i
$85$	−6.82779			−0.0803270
$86$	26.0521	−	100.210i	0.302932	−	1.16523i
$87$		−	30.5958i		−	0.351676i
$88$	−40.1828	+	42.0214i	−0.456623	+	0.477516i
$89$	−2.69178			−0.0302447			−0.0151224	−	0.999886i	$-0.504814\pi$
$89$	−2.69178			−0.0302447			−0.0151224	+	0.999886i	$0.504814\pi$
$90$	−36.3959	−	9.46206i	−0.404399	−	0.105134i
$91$			237.451i			2.60936i
$92$	28.8722	−	51.7756i	0.313828	−	0.562778i
$93$	25.8402			0.277852
$94$	−35.2744	+	135.683i	−0.375259	+	1.44344i
$95$			9.74679i			0.102598i
$96$	23.5103	−	7.24863i	0.244899	−	0.0755066i
$97$	144.741			1.49217			0.746087	−	0.665848i	$-0.231930\pi$
$97$	144.741			1.49217			0.746087	+	0.665848i	$0.231930\pi$
$98$	105.447	+	27.4136i	1.07599	+	0.279730i
$99$		−	61.1135i		−	0.617308i
$100$	17.4677	+	9.74068i	0.174677	+	0.0974068i
$101$	−19.2912			−0.191002			−0.0955009	−	0.995429i	$-0.530445\pi$
$101$	−19.2912			−0.191002			−0.0955009	+	0.995429i	$0.530445\pi$
$102$	−1.18137	+	4.54413i	−0.0115820	+	0.0445503i
$103$			149.414i			1.45062i	0.688422	+	0.725310i	$0.258304\pi$
$103$			149.414i			1.45062i	−0.688422	+	0.725310i	$0.741696\pi$
$104$	134.967	+	129.062i	1.29776	+	1.24098i
$105$	17.4877			0.166549
$106$	143.025	+	37.1832i	1.34930	+	0.350785i
$107$			47.6401i			0.445235i	0.974906	+	0.222617i	$0.0714601\pi$
$107$			47.6401i			0.445235i	−0.974906	+	0.222617i	$0.928540\pi$
$108$	−26.0747	+	46.7588i	−0.241432	+	0.432952i
$109$	104.045			0.954541			0.477270	−	0.878757i	$-0.341626\pi$
$109$	104.045			0.954541			0.477270	+	0.878757i	$0.341626\pi$
$110$	−8.17793	+	31.4565i	−0.0743449	+	0.285968i
$111$			14.6122i			0.131642i
$112$	138.463	−	85.5443i	1.23628	−	0.763789i
$113$	122.367			1.08289			0.541446	−	0.840735i	$-0.317877\pi$
$113$	122.367			1.08289			0.541446	+	0.840735i	$0.317877\pi$
$114$	6.48683	+	1.68642i	0.0569020	+	0.0147932i
$115$		−	33.1394i		−	0.288169i
$116$	−139.027	−	77.5271i	−1.19851	−	0.668337i
$117$	−196.288			−1.67768
$118$	−37.5380	+	144.390i	−0.318119	+	1.22365i
$119$			31.0610i			0.261017i
$120$	9.50507	−	9.93998i	0.0792089	−	0.0828331i
$121$	68.1804			0.563475
$122$	−59.5692	−	15.4866i	−0.488272	−	0.126939i
$123$		−	1.11986i		−	0.00910453i
$124$	65.4769	−	117.418i	0.528040	−	0.946917i
$125$	11.1803			0.0894427
$126$	−43.0448	+	165.572i	−0.341625	+	1.31407i
$127$		−	204.225i		−	1.60807i	−0.594580	−	0.804037i	$-0.702682\pi$
$127$		−	204.225i		−	1.60807i	0.594580	−	0.804037i	$-0.297318\pi$
$128$	26.6355	−	125.198i	0.208089	−	0.978110i
$129$	−39.8024			−0.308546
$130$	101.034	+	26.2664i	0.777186	+	0.202050i
$131$			123.057i			0.939369i	0.882834	+	0.469685i	$0.155632\pi$
$131$			123.057i			0.939369i	−0.882834	+	0.469685i	$0.844368\pi$
$132$	19.5204	+	10.8854i	0.147882	+	0.0824652i
$133$	44.3401			0.333384
$134$	−61.3930	+	236.149i	−0.458156	+	1.76230i
$135$			29.9284i			0.221692i
$136$	17.6550	+	16.8826i	0.129816	+	0.124136i
$137$	−53.3238			−0.389225			−0.194612	−	0.980880i	$-0.562345\pi$
$137$	−53.3238			−0.389225			−0.194612	+	0.980880i	$0.562345\pi$
$138$	−22.0555	−	5.73388i	−0.159822	−	0.0415499i
$139$			6.07365i			0.0436953i	0.999761	+	0.0218477i	$0.00695488\pi$
$139$			6.07365i			0.0436953i	−0.999761	+	0.0218477i	$0.993045\pi$
$140$	44.3123	−	79.4638i	0.316516	−	0.567599i
$141$	53.8922			0.382214
$142$	−19.7194	+	75.8510i	−0.138869	+	0.534162i
$143$			169.649i			1.18636i
$144$	70.7149	+	114.460i	0.491076	+	0.794861i
$145$	−88.9854			−0.613693
$146$	−33.9149	−	8.81706i	−0.232294	−	0.0603908i
$147$		−	41.8825i		−	0.284915i
$148$	66.3978	+	37.0261i	0.448634	+	0.250177i
$149$	−203.115			−1.36319			−0.681594	−	0.731731i	$-0.738713\pi$
$149$	−203.115			−1.36319			−0.681594	+	0.731731i	$0.738713\pi$
$150$	1.93446	−	7.44091i	0.0128964	−	0.0496060i
$151$			49.7009i			0.329145i	0.986365	+	0.164572i	$0.0526244\pi$
$151$			49.7009i			0.329145i	−0.986365	+	0.164572i	$0.947376\pi$
$152$	24.1001	−	25.2028i	0.158554	−	0.165808i
$153$	−25.6764			−0.167820
$154$	143.102	+	37.2030i	0.929233	+	0.241578i
$155$		−	75.1543i		−	0.484866i
$156$	34.9625	−	62.6971i	0.224118	−	0.401904i
$157$	−82.2703			−0.524014			−0.262007	−	0.965066i	$-0.584384\pi$
$157$	−82.2703			−0.524014			−0.262007	+	0.965066i	$0.584384\pi$
$158$	30.0758	−	115.687i	0.190353	−	0.732196i
$159$		−	56.8084i		−	0.357286i
$160$	−21.0821	−	68.3780i	−0.131763	−	0.427362i
$161$	−150.758			−0.936384
$162$	−126.572	−	32.9058i	−0.781311	−	0.203122i
$163$			99.4889i			0.610361i	0.952295	+	0.305181i	$0.0987168\pi$
$163$			99.4889i			0.610361i	−0.952295	+	0.305181i	$0.901283\pi$
$164$	−5.08862	−	2.83762i	−0.0310282	−	0.0173026i
$165$	12.4942			0.0757227
$166$	−36.7337	+	141.297i	−0.221287	+	0.851184i
$167$			208.667i			1.24950i	0.780824	+	0.624751i	$0.214800\pi$
$167$			208.667i			1.24950i	−0.780824	+	0.624751i	$0.785200\pi$
$168$	−45.2189	−	43.2404i	−0.269160	−	0.257384i
$169$	375.892			2.22421
$170$	13.2163	+	3.43591i	0.0777427	+	0.0202112i
$171$			36.6536i			0.214348i
$172$	−100.856	+	180.862i	−0.586371	+	1.05152i
$173$	190.986			1.10397			0.551983	−	0.833855i	$-0.313871\pi$
$173$	190.986			1.10397			0.551983	+	0.833855i	$0.313871\pi$
$174$	−15.3965	+	59.2229i	−0.0884858	+	0.340362i
$175$		−	50.8616i		−	0.290637i
$176$	98.9263	−	61.1180i	0.562081	−	0.347261i
$177$	57.3505			0.324014
$178$	5.21037	+	1.35457i	0.0292717	+	0.00760994i
$179$		−	120.444i		−	0.672873i	−0.941706	−	0.336436i	$-0.890778\pi$
$179$		−	120.444i		−	0.672873i	0.941706	−	0.336436i	$-0.109222\pi$
$180$	65.6885	+	36.6306i	0.364936	+	0.203503i
$181$	183.384			1.01317			0.506586	−	0.862189i	$-0.330907\pi$
$181$	183.384			1.01317			0.506586	+	0.862189i	$0.330907\pi$
$182$	119.491	−	459.624i	0.656545	−	2.52541i
$183$			23.6604i			0.129292i
$184$	−81.9413	+	85.6905i	−0.445333	+	0.465710i
$185$	42.4985			0.229722
$186$	−50.0178	−	13.0034i	−0.268913	−	0.0699109i
$187$			22.1918i			0.118673i
$188$	136.558	−	244.885i	0.726373	−	1.30258i
$189$	136.150			0.720372
$190$	4.90482	−	18.8664i	0.0258148	−	0.0992971i
$191$		−	119.226i		−	0.624219i	−0.950046	−	0.312110i	$-0.898964\pi$
$191$		−	119.226i		−	0.624219i	0.950046	−	0.312110i	$-0.101036\pi$
$192$	−49.1556	+	2.19991i	−0.256019	+	0.0114579i
$193$	−144.316			−0.747753			−0.373877	−	0.927478i	$-0.621972\pi$
$193$	−144.316			−0.747753			−0.373877	+	0.927478i	$0.621972\pi$
$194$	−280.169	−	72.8371i	−1.44417	−	0.375449i
$195$		−	40.1299i		−	0.205794i
$196$	−190.313	−	106.127i	−0.970986	−	0.541462i
$197$	−341.794			−1.73499			−0.867496	−	0.497443i	$-0.834272\pi$
$197$	−341.794			−1.73499			−0.867496	+	0.497443i	$0.834272\pi$
$198$	−30.7538	+	118.295i	−0.155322	+	0.597448i
$199$			166.430i			0.836332i	0.908371	+	0.418166i	$0.137327\pi$
$199$			166.430i			0.836332i	−0.908371	+	0.418166i	$0.862673\pi$
$200$	−28.9096	−	27.6448i	−0.144548	−	0.138224i
$201$	93.7962			0.466648
$202$	37.3411	+	9.70778i	0.184857	+	0.0480583i
$203$			404.812i			1.99415i
$204$	4.57343	−	8.20139i	0.0224188	−	0.0402029i
$205$	−3.25702			−0.0158879
$206$	75.1886	−	289.214i	0.364993	−	1.40395i
$207$		−	124.623i		−	0.602046i
$208$	−196.303	−	317.738i	−0.943764	−	1.52759i
$209$	31.6792			0.151575
$210$	−33.8501	−	8.80022i	−0.161191	−	0.0419058i
$211$		−	167.202i		−	0.792428i	−0.918158	−	0.396214i	$-0.870324\pi$
$211$		−	167.202i		−	0.792428i	0.918158	−	0.396214i	$-0.129676\pi$
$212$	−258.137	−	143.948i	−1.21763	−	0.678998i
$213$	30.1273			0.141443
$214$	23.9736	−	92.2149i	0.112026	−	0.430911i
$215$			115.762i			0.538429i
$216$	74.0017	−	77.3877i	0.342601	−	0.358276i
$217$	−341.892			−1.57554
$218$	−201.395	−	52.3579i	−0.923831	−	0.240174i
$219$			13.4707i			0.0615101i
$220$	31.6593	−	56.7737i	0.143906	−	0.258062i
$221$	71.2772			0.322521
$222$	7.35322	−	28.2843i	0.0331226	−	0.127407i
$223$			434.169i			1.94695i	0.228803	+	0.973473i	$0.426519\pi$
$223$			434.169i			1.94695i	−0.228803	+	0.973473i	$0.573481\pi$
$224$	−311.065	+	95.9065i	−1.38868	+	0.428154i
$225$	42.0445			0.186865
$226$	−236.860	−	61.5779i	−1.04805	−	0.272469i
$227$		−	23.3196i		−	0.102729i	−0.998680	−	0.0513647i	$-0.983643\pi$
$227$		−	23.3196i		−	0.102729i	0.998680	−	0.0513647i	$-0.0163571\pi$
$228$	−11.7076	−	6.52866i	−0.0513493	−	0.0286345i
$229$	−9.46603			−0.0413364			−0.0206682	−	0.999786i	$-0.506579\pi$
$229$	−9.46603			−0.0413364			−0.0206682	+	0.999786i	$0.506579\pi$
$230$	−16.6766	+	64.1466i	−0.0725068	+	0.278898i
$231$		−	56.8388i		−	0.246055i
$232$	230.095	+	220.027i	0.991788	+	0.948394i
$233$	264.028			1.13317			0.566584	−	0.824004i	$-0.308264\pi$
$233$	264.028			1.13317			0.566584	+	0.824004i	$0.308264\pi$
$234$	379.947	+	98.7770i	1.62370	+	0.422124i
$235$		−	156.741i		−	0.666984i
$236$	145.321	−	260.600i	0.615768	−	1.10424i
$237$	−45.9498			−0.193881
$238$	15.6306	−	60.1234i	0.0656749	−	0.252619i
$239$		−	167.364i		−	0.700269i	−0.936699	−	0.350135i	$-0.886136\pi$
$239$		−	167.364i		−	0.700269i	0.936699	−	0.350135i	$-0.113864\pi$
$240$	−23.4006	+	14.4572i	−0.0975024	+	0.0602383i
$241$	−235.122			−0.975611			−0.487806	−	0.872952i	$-0.662203\pi$
$241$	−235.122			−0.975611			−0.487806	+	0.872952i	$0.662203\pi$
$242$	−131.974	−	34.3100i	−0.545347	−	0.141777i
$243$			170.733i			0.702605i
$244$	107.512	+	59.9533i	0.440624	+	0.245710i
$245$	−121.812			−0.497191
$246$	−0.563539	+	2.16766i	−0.00229081	+	0.00881162i
$247$		−	101.749i		−	0.411941i
$248$	−185.828	+	194.331i	−0.749307	+	0.783592i
$249$	56.1217			0.225388
$250$	−21.6413	−	5.62621i	−0.0865652	−	0.0225049i
$251$		−	1.00812i		−	0.00401641i	−0.999998	−	0.00200820i	$-0.999361\pi$
$251$		−	1.00812i		−	0.00401641i	0.999998	−	0.00200820i	$-0.000639232\pi$
$252$	166.640	−	298.830i	0.661269	−	1.18583i
$253$	−107.710			−0.425733
$254$	−102.771	+	395.310i	−0.404610	+	1.55634i
$255$		−	5.24938i		−	0.0205858i
$256$	−114.560	+	228.937i	−0.447499	+	0.894284i
$257$	269.225			1.04757			0.523783	−	0.851851i	$-0.324520\pi$
$257$	269.225			1.04757			0.523783	+	0.851851i	$0.324520\pi$
$258$	77.0438	+	20.0295i	0.298619	+	0.0776338i
$259$		−	193.334i		−	0.746464i
$260$	−182.350	−	101.686i	−0.701345	−	0.391099i
$261$	−334.637			−1.28213
$262$	61.9254	−	238.197i	0.236357	−	0.909148i
$263$		−	360.607i		−	1.37113i	−0.728012	−	0.685564i	$-0.759555\pi$
$263$		−	360.607i		−	1.37113i	0.728012	−	0.685564i	$-0.240445\pi$
$264$	−32.3071	−	30.8936i	−0.122375	−	0.117021i
$265$	−165.223			−0.623483
$266$	−85.8272	−	22.3130i	−0.322658	−	0.0838834i
$267$		−	2.06951i		−	0.00775097i
$268$	237.671	−	426.209i	0.886834	−	1.59033i
$269$	182.153			0.677147			0.338574	−	0.940940i	$-0.390056\pi$
$269$	182.153			0.677147			0.338574	+	0.940940i	$0.390056\pi$
$270$	15.0607	−	57.9312i	0.0557804	−	0.214560i
$271$			72.4803i			0.267455i	0.991018	+	0.133728i	$0.0426947\pi$
$271$			72.4803i			0.267455i	−0.991018	+	0.133728i	$0.957305\pi$
$272$	−25.6783	−	41.5632i	−0.0944057	−	0.152806i
$273$	−182.559			−0.668713
$274$	103.217	+	26.8338i	0.376703	+	0.0979336i
$275$		−	36.3385i		−	0.132140i
$276$	39.8064	+	22.1977i	0.144226	+	0.0804263i
$277$	345.509			1.24732			0.623662	−	0.781694i	$-0.285644\pi$
$277$	345.509			1.24732			0.623662	+	0.781694i	$0.285644\pi$
$278$	3.05640	−	11.7565i	0.0109943	−	0.0422896i
$279$		−	282.624i		−	1.01299i
$280$	−125.761	+	131.516i	−0.449148	+	0.469699i
$281$	−343.716			−1.22319			−0.611594	−	0.791172i	$-0.709471\pi$
$281$	−343.716			−1.22319			−0.611594	+	0.791172i	$0.709471\pi$
$282$	−104.317	−	27.1198i	−0.369917	−	0.0961696i
$283$			155.251i			0.548590i	0.961646	+	0.274295i	$0.0884445\pi$
$283$			155.251i			0.548590i	−0.961646	+	0.274295i	$0.911555\pi$
$284$	76.3400	−	136.898i	0.268803	−	0.482036i
$285$	−7.49358			−0.0262933
$286$	85.3717	−	328.383i	0.298502	−	1.14819i
$287$			14.8168i			0.0516265i
$288$	−79.2808	−	257.141i	−0.275281	−	0.892849i
$289$	−279.676			−0.967738
$290$	172.245	+	44.7796i	0.593949	+	0.154412i
$291$			111.281i			0.382407i
$292$	61.2107	+	34.1336i	0.209626	+	0.116896i
$293$	−34.6131			−0.118133			−0.0590667	−	0.998254i	$-0.518812\pi$
$293$	−34.6131			−0.118133			−0.0590667	+	0.998254i	$0.518812\pi$
$294$	−21.0762	+	81.0700i	−0.0716879	+	0.275748i
$295$		−	166.800i		−	0.565422i
$296$	−109.891	−	105.083i	−0.371253	−	0.355010i
$297$	97.2740			0.327522
$298$	393.161	+	102.212i	1.31933	+	0.342994i
$299$			345.952i			1.15703i
$300$	−7.48888	+	13.4296i	−0.0249629	+	0.0447653i
$301$	526.625			1.74958
$302$	25.0107	−	96.2038i	0.0828167	−	0.318556i
$303$		−	14.8315i		−	0.0489490i
$304$	−59.3323	+	36.6563i	−0.195172	+	0.120580i
$305$	68.8143			0.225621
$306$	49.7008	+	12.9210i	0.162421	+	0.0422255i
$307$			364.975i			1.18884i	0.804153	+	0.594422i	$0.202619\pi$
$307$			364.975i			1.18884i	−0.804153	+	0.594422i	$0.797381\pi$
$308$	−258.275	−	144.025i	−0.838554	−	0.467612i
$309$	−114.873			−0.371758
$310$	−37.8194	+	145.473i	−0.121998	+	0.469267i
$311$		−	122.875i		−	0.395096i	−0.980293	−	0.197548i	$-0.936702\pi$
$311$		−	122.875i		−	0.395096i	0.980293	−	0.197548i	$-0.0632978\pi$
$312$	−99.2260	+	103.766i	−0.318032	+	0.332584i
$313$	−168.459			−0.538206			−0.269103	−	0.963111i	$-0.586727\pi$
$313$	−168.459			−0.538206			−0.269103	+	0.963111i	$0.586727\pi$
$314$	159.247	+	41.4004i	0.507156	+	0.131848i
$315$		−	191.269i		−	0.607203i
$316$	−116.433	+	208.795i	−0.368459	+	0.660745i
$317$	617.139			1.94681			0.973406	−	0.229088i	$-0.0735743\pi$
$317$	617.139			1.94681			0.973406	+	0.229088i	$0.0735743\pi$
$318$	−28.5874	+	109.962i	−0.0898973	+	0.345791i
$319$			289.222i			0.906652i
$320$	6.39826	+	142.965i	0.0199946	+	0.446766i
$321$	−36.6269			−0.114103
$322$	291.815	+	75.8649i	0.906259	+	0.235605i
$323$		−	13.3098i		−	0.0412069i
$324$	228.442	+	127.388i	0.705067	+	0.393174i
$325$	−116.715			−0.359122
$326$	50.0652	−	192.576i	0.153574	−	0.590725i
$327$			79.9924i			0.244625i
$328$	8.42186	+	8.05338i	0.0256764	+	0.0245530i
$329$	−713.046			−2.16731
$330$	−24.1846	−	6.28740i	−0.0732866	−	0.0190527i
$331$			543.840i			1.64302i	0.570193	+	0.821511i	$0.306868\pi$
$331$			543.840i			1.64302i	−0.570193	+	0.821511i	$0.693132\pi$
$332$	142.208	−	255.016i	0.428336	−	0.768121i
$333$	159.819			0.479937
$334$	105.006	−	403.907i	0.314390	−	1.20930i
$335$		−	272.799i		−	0.814325i
$336$	65.7686	+	106.454i	0.195740	+	0.316827i
$337$	151.421			0.449319			0.224660	−	0.974437i	$-0.427873\pi$
$337$	151.421			0.449319			0.224660	+	0.974437i	$0.427873\pi$
$338$	−727.597	−	189.158i	−2.15265	−	0.559638i
$339$			94.0788i			0.277518i
$340$	−23.8531	−	13.3015i	−0.0701562	−	0.0391220i
$341$	−244.268			−0.716328
$342$	18.4450	−	70.9487i	0.0539326	−	0.207452i
$343$			55.7027i			0.162399i
$344$	286.236	−	299.333i	0.832082	−	0.870154i
$345$	25.4784			0.0738505
$346$	−369.683	−	96.1087i	−1.06845	−	0.277771i
$347$			473.494i			1.36454i	0.731103	+	0.682268i	$0.239006\pi$
$347$			473.494i			1.36454i	−0.731103	+	0.682268i	$0.760994\pi$
$348$	59.6048	−	106.887i	0.171278	−	0.307148i
$349$	146.856			0.420791			0.210396	−	0.977616i	$-0.432525\pi$
$349$	146.856			0.420791			0.210396	+	0.977616i	$0.432525\pi$
$350$	−25.5947	+	98.4505i	−0.0731278	+	0.281287i
$351$		−	312.431i		−	0.890117i
$352$	−222.243	+	68.5214i	−0.631373	+	0.194663i
$353$	459.486			1.30166			0.650830	−	0.759224i	$-0.274421\pi$
$353$	459.486			1.30166			0.650830	+	0.759224i	$0.274421\pi$
$354$	−111.011	−	28.8601i	−0.313590	−	0.0815258i
$355$		−	87.6230i		−	0.246825i
$356$	−9.40383	−	5.24396i	−0.0264152	−	0.0147302i
$357$	−23.8805			−0.0668920
$358$	−60.6104	+	233.139i	−0.169303	+	0.651225i
$359$		−	543.855i		−	1.51492i	−0.652883	−	0.757458i	$-0.726441\pi$
$359$		−	543.855i		−	1.51492i	0.652883	−	0.757458i	$-0.273559\pi$
$360$	−108.717	−	103.960i	−0.301992	−	0.288779i
$361$	−19.0000			−0.0526316
$362$	−354.969	−	92.2833i	−0.980577	−	0.254926i
$363$			52.4188i			0.144404i
$364$	−462.588	+	829.544i	−1.27085	+	2.27897i
$365$	39.1785			0.107338
$366$	11.9065	−	45.7983i	0.0325313	−	0.125132i
$367$			40.3733i			0.110009i	0.998486	+	0.0550045i	$0.0175173\pi$
$367$			40.3733i			0.110009i	−0.998486	+	0.0550045i	$0.982483\pi$
$368$	201.732	−	124.633i	0.548184	−	0.338676i
$369$	−12.2483			−0.0331931
$370$	−82.2626	−	21.3863i	−0.222331	−	0.0578007i
$371$			751.631i			2.02596i
$372$	90.2737	+	50.3403i	0.242671	+	0.135323i
$373$	498.004			1.33513			0.667566	−	0.744551i	$-0.267336\pi$
$373$	498.004			1.33513			0.667566	+	0.744551i	$0.267336\pi$
$374$	11.1674	−	42.9557i	0.0298595	−	0.114855i
$375$			8.59573i			0.0229219i
$376$	−387.562	+	405.294i	−1.03075	+	1.07791i
$377$	928.943			2.46404
$378$	−263.540	−	68.5141i	−0.697197	−	0.181254i
$379$		−	587.987i		−	1.55142i	−0.631092	−	0.775708i	$-0.717393\pi$
$379$		−	587.987i		−	1.55142i	0.631092	−	0.775708i	$-0.282607\pi$
$380$	−18.9881	+	34.0507i	−0.0499687	+	0.0896072i
$381$	157.014			0.412109
$382$	−59.9973	+	230.780i	−0.157061	+	0.604137i
$383$		−	328.505i		−	0.857717i	−0.903372	−	0.428858i	$-0.858916\pi$
$383$		−	328.505i		−	0.857717i	0.903372	−	0.428858i	$-0.141084\pi$
$384$	96.2554	+	20.4780i	0.250665	+	0.0533281i
$385$	−165.311			−0.429380
$386$	279.347	+	72.6234i	0.723697	+	0.188144i
$387$			435.333i			1.12489i
$388$	505.657	+	281.975i	1.30324	+	0.726740i
$389$	552.203			1.41954			0.709772	−	0.704431i	$-0.248798\pi$
$389$	552.203			1.41954			0.709772	+	0.704431i	$0.248798\pi$
$390$	−20.1943	+	77.6776i	−0.0517803	+	0.199173i
$391$			45.2539i			0.115739i
$392$	314.976	+	301.195i	0.803510	+	0.768354i
$393$	−94.6096			−0.240737
$394$	661.595	+	171.999i	1.67918	+	0.436545i
$395$			133.642i			0.338333i
$396$	119.057	−	213.502i	0.300650	−	0.539146i
$397$	−771.723			−1.94389			−0.971943	−	0.235216i	$-0.924420\pi$
$397$	−771.723			−1.94389			−0.971943	+	0.235216i	$0.924420\pi$
$398$	83.7516	−	322.151i	0.210431	−	0.809426i
$399$			34.0898i			0.0854380i
$400$	42.0476	+	68.0588i	0.105119	+	0.170147i
$401$	138.859			0.346281			0.173141	−	0.984897i	$-0.444608\pi$
$401$	138.859			0.346281			0.173141	+	0.984897i	$0.444608\pi$
$402$	−181.557	−	47.2005i	−0.451635	−	0.117414i
$403$			784.556i			1.94679i
$404$	−67.3943	−	37.5819i	−0.166818	−	0.0930244i
$405$	146.216			0.361028
$406$	203.711	−	783.577i	0.501752	−	1.92999i
$407$		−	138.129i		−	0.339384i
$408$	−12.9797	+	13.5736i	−0.0318131	+	0.0332687i
$409$	215.726			0.527448			0.263724	−	0.964598i	$-0.415049\pi$
$409$	215.726			0.527448			0.263724	+	0.964598i	$0.415049\pi$
$410$	6.30447	+	1.63901i	0.0153768	+	0.00399758i
$411$		−	40.9967i		−	0.0997487i
$412$	−291.079	+	521.982i	−0.706502	+	1.26695i
$413$	−758.804			−1.83730
$414$	−62.7135	+	241.228i	−0.151482	+	0.582677i
$415$		−	163.226i		−	0.393315i
$416$	220.082	+	713.816i	0.529042	+	1.71590i
$417$	−4.66957			−0.0111980
$418$	−61.3201	−	15.9417i	−0.146699	−	0.0381381i
$419$			462.357i			1.10348i	0.834017	+	0.551739i	$0.186036\pi$
$419$			462.357i			1.10348i	−0.834017	+	0.551739i	$0.813964\pi$
$420$	61.0938	+	34.0684i	0.145461	+	0.0811152i
$421$	240.916			0.572248			0.286124	−	0.958193i	$-0.407633\pi$
$421$	240.916			0.572248			0.286124	+	0.958193i	$0.407633\pi$
$422$	−84.1401	+	323.646i	−0.199384	+	0.766934i
$423$		−	589.437i		−	1.39347i
$424$	427.226	+	408.534i	1.00761	+	0.963523i
$425$	−15.2674			−0.0359233
$426$	−58.3161	−	15.1608i	−0.136892	−	0.0355887i
$427$		−	313.050i		−	0.733138i
$428$	−92.8095	+	166.432i	−0.216845	+	0.388860i
$429$	−130.431			−0.304035
$430$	58.2543	−	224.076i	0.135475	−	0.521107i
$431$		−	64.5817i		−	0.149841i	−0.997189	−	0.0749207i	$-0.976130\pi$
$431$		−	64.5817i		−	0.149841i	0.997189	−	0.0749207i	$-0.0238704\pi$
$432$	−182.185	+	112.557i	−0.421725	+	0.260548i
$433$	−415.575			−0.959759			−0.479879	−	0.877335i	$-0.659320\pi$
$433$	−415.575			−0.959759			−0.479879	+	0.877335i	$0.659320\pi$
$434$	661.785	+	172.048i	1.52485	+	0.396424i
$435$		−	68.4143i		−	0.157274i
$436$	363.484	+	202.694i	0.833680	+	0.464894i
$437$	64.6007			0.147828
$438$	6.77878	−	26.0747i	0.0154767	−	0.0595312i
$439$		−	538.530i		−	1.22672i	−0.789804	−	0.613360i	$-0.789818\pi$
$439$		−	538.530i		−	1.22672i	0.789804	−	0.613360i	$-0.210182\pi$
$440$	−89.8515	+	93.9626i	−0.204208	+	0.213551i
$441$	−458.083			−1.03874
$442$	−137.968	−	35.8684i	−0.312145	−	0.0811501i
$443$			511.391i			1.15438i	0.816609	+	0.577191i	$0.195851\pi$
$443$			511.391i			1.15438i	−0.816609	+	0.577191i	$0.804149\pi$
$444$	−28.4666	+	51.0483i	−0.0641140	+	0.114974i
$445$	−6.01901			−0.0135259
$446$	218.484	−	840.402i	0.489875	−	1.88431i
$447$		−	156.160i		−	0.349351i
$448$	650.377	−	29.1069i	1.45173	−	0.0649709i
$449$	−363.851			−0.810358			−0.405179	−	0.914237i	$-0.632791\pi$
$449$	−363.851			−0.810358			−0.405179	+	0.914237i	$0.632791\pi$
$450$	−81.3838	−	21.1578i	−0.180853	−	0.0470174i
$451$			10.5860i			0.0234723i
$452$	427.493	+	238.387i	0.945780	+	0.527406i
$453$	−38.2113			−0.0843516
$454$	−11.7350	+	45.1387i	−0.0258479	+	0.0994244i
$455$			530.957i			1.16694i
$456$	19.3766	+	18.5288i	0.0424925	+	0.0406333i
$457$	502.546			1.09966			0.549831	−	0.835276i	$-0.314692\pi$
$457$	502.546			1.09966			0.549831	+	0.835276i	$0.314692\pi$
$458$	18.3230	+	4.76353i	0.0400065	+	0.0104007i
$459$		−	40.8690i		−	0.0890393i
$460$	64.5602	−	115.774i	0.140348	−	0.251682i
$461$	695.837			1.50941			0.754704	−	0.656066i	$-0.227781\pi$
$461$	695.837			1.50941			0.754704	+	0.656066i	$0.227781\pi$
$462$	−28.6026	+	110.020i	−0.0619104	+	0.238139i
$463$		−	346.481i		−	0.748339i	−0.927360	−	0.374170i	$-0.877928\pi$
$463$		−	346.481i		−	0.748339i	0.927360	−	0.374170i	$-0.122072\pi$
$464$	−334.661	−	541.687i	−0.721253	−	1.16743i
$465$	57.7805			0.124259
$466$	−511.068	−	132.865i	−1.09671	−	0.285119i
$467$		−	523.604i		−	1.12121i	−0.828084	−	0.560604i	$-0.810569\pi$
$467$		−	523.604i		−	1.12121i	0.828084	−	0.560604i	$-0.189431\pi$
$468$	−685.740	−	382.397i	−1.46526	−	0.817087i
$469$	−1241.02			−2.64609
$470$	−78.8759	+	303.397i	−0.167821	+	0.645526i
$471$		−	63.2515i		−	0.134292i
$472$	−412.432	+	431.303i	−0.873797	+	0.913778i
$473$	376.252			0.795460
$474$	88.9431	+	23.1231i	0.187644	+	0.0487828i
$475$			21.7945i			0.0458831i
$476$	−60.5110	+	108.512i	−0.127124	+	0.227967i
$477$	−621.333			−1.30259
$478$	−84.2217	+	323.960i	−0.176196	+	0.677740i
$479$		−	481.716i		−	1.00567i	−0.864382	−	0.502836i	$-0.832290\pi$
$479$		−	481.716i		−	1.00567i	0.864382	−	0.502836i	$-0.167710\pi$
$480$	52.5707	−	16.2084i	0.109522	−	0.0337676i
$481$	−443.654			−0.922357
$482$	455.116	+	118.319i	0.944224	+	0.245475i
$483$		−	115.906i		−	0.239972i
$484$	238.190	+	132.825i	0.492129	+	0.274431i
$485$	323.651			0.667321
$486$	85.9169	−	330.481i	0.176784	−	0.680001i
$487$			506.422i			1.03988i	0.854202	+	0.519941i	$0.174046\pi$
$487$			506.422i			1.03988i	−0.854202	+	0.519941i	$0.825954\pi$
$488$	−177.937	−	170.152i	−0.364625	−	0.348672i
$489$	−76.4895			−0.156420
$490$	235.786	+	61.2986i	0.481196	+	0.125099i
$491$		−	364.498i		−	0.742359i	−0.928561	−	0.371180i	$-0.878953\pi$
$491$		−	364.498i		−	0.742359i	0.928561	−	0.371180i	$-0.121047\pi$
$492$	2.18164	−	3.91226i	0.00443422	−	0.00795174i
$493$	121.515			0.246480
$494$	−51.2027	+	196.952i	−0.103649	+	0.398688i
$495$		−	136.654i		−	0.276069i
$496$	457.491	−	282.644i	0.922362	−	0.569848i
$497$	−398.614			−0.802040
$498$	−108.632	−	28.2418i	−0.218137	−	0.0567104i
$499$		−	810.293i		−	1.62383i	−0.583773	−	0.811917i	$-0.698424\pi$
$499$		−	810.293i		−	1.62383i	0.583773	−	0.811917i	$-0.301576\pi$
$500$	39.0589	+	21.7808i	0.0781177	+	0.0435617i
$501$	−160.428			−0.320216
$502$	−0.507309	+	1.95137i	−0.00101058	+	0.00388719i
$503$			663.162i			1.31841i	0.751962	+	0.659207i	$0.229108\pi$
$503$			663.162i			1.31841i	−0.751962	+	0.659207i	$0.770892\pi$
$504$	−472.936	+	494.575i	−0.938364	+	0.981299i
$505$	−43.1364			−0.0854186
$506$	208.490	+	54.2024i	0.412036	+	0.107119i
$507$			288.995i			0.570010i
$508$	397.859	−	713.467i	0.783187	−	1.40446i
$509$	−650.672			−1.27833			−0.639167	−	0.769068i	$-0.720721\pi$
$509$	−650.672			−1.27833			−0.639167	+	0.769068i	$0.720721\pi$
$510$	−2.64161	+	10.1610i	−0.00517963	+	0.0199235i
$511$		−	178.231i		−	0.348788i
$512$	336.955	−	385.494i	0.658115	−	0.752918i
$513$	−58.3413			−0.113726
$514$	−521.127	−	135.480i	−1.01386	−	0.263580i
$515$			334.100i			0.648737i
$516$	−139.051	−	77.5405i	−0.269479	−	0.150272i
$517$	−509.443			−0.985383
$518$	−97.2903	+	374.228i	−0.187819	+	0.722449i
$519$			146.835i			0.282919i
$520$	301.796	+	288.591i	0.580376	+	0.554983i
$521$	−40.1628			−0.0770879			−0.0385440	−	0.999257i	$-0.512272\pi$
$521$	−40.1628			−0.0770879			−0.0385440	+	0.999257i	$0.512272\pi$
$522$	647.742	+	168.397i	1.24088	+	0.322600i
$523$		−	444.876i		−	0.850623i	−0.905047	−	0.425311i	$-0.860165\pi$
$523$		−	444.876i		−	0.850623i	0.905047	−	0.425311i	$-0.139835\pi$
$524$	−239.733	+	429.905i	−0.457505	+	0.820429i
$525$	39.1036			0.0744831
$526$	−181.466	+	698.011i	−0.344992	+	1.32702i
$527$			102.628i			0.194739i
$528$	46.9890	+	76.0570i	0.0889944	+	0.144047i
$529$	309.355			0.584793
$530$	319.815	+	83.1441i	0.603424	+	0.156876i
$531$		−	627.263i		−	1.18129i
$532$	154.903	+	86.3805i	0.291172	+	0.162369i
$533$	34.0009			0.0637915
$534$	−1.04143	+	4.00586i	−0.00195024	+	0.00750161i
$535$			106.527i			0.199115i
$536$	−674.528	+	705.391i	−1.25845	+	1.31603i
$537$	92.6005			0.172440
$538$	−352.585	−	91.6635i	−0.655362	−	0.170378i
$539$			395.915i			0.734536i
$540$	−58.3047	+	104.556i	−0.107972	+	0.193622i
$541$	281.421			0.520187			0.260094	−	0.965583i	$-0.416247\pi$
$541$	281.421			0.520187			0.260094	+	0.965583i	$0.416247\pi$
$542$	36.4738	−	140.297i	0.0672949	−	0.258851i
$543$			140.990i			0.259651i
$544$	28.7888	+	93.3741i	0.0529206	+	0.171644i
$545$	232.652			0.426884
$546$	353.371	+	91.8678i	0.647199	+	0.168256i
$547$		−	838.937i		−	1.53371i	−0.641823	−	0.766853i	$-0.721822\pi$
$547$		−	838.937i		−	1.53371i	0.641823	−	0.766853i	$-0.278178\pi$
$548$	−186.288	−	103.882i	−0.339942	−	0.189566i
$549$	258.782			0.471369
$550$	−18.2864	+	70.3389i	−0.0332480	+	0.127889i
$551$		−	173.465i		−	0.314818i
$552$	−65.8811	−	62.9986i	−0.119350	−	0.114128i
$553$	607.962			1.09939
$554$	−668.786	−	173.868i	−1.20720	−	0.313841i
$555$			32.6739i			0.0588720i
$556$	−11.8323	+	21.2185i	−0.0212811	+	0.0381627i
$557$	−49.6863			−0.0892033			−0.0446017	−	0.999005i	$-0.514202\pi$
$557$	−49.6863			−0.0892033			−0.0446017	+	0.999005i	$0.514202\pi$
$558$	−142.223	+	547.062i	−0.254880	+	0.980398i
$559$		−	1208.47i		−	2.16185i
$560$	309.613	−	191.283i	0.552880	−	0.341577i
$561$	−17.0616			−0.0304129
$562$	665.316	+	172.966i	1.18384	+	0.307769i
$563$			892.268i			1.58484i	0.609973	+	0.792422i	$0.291180\pi$
$563$			892.268i			1.58484i	−0.609973	+	0.792422i	$0.708820\pi$
$564$	188.274	+	104.989i	0.333819	+	0.186151i
$565$	273.621			0.484284
$566$	78.1260	−	300.513i	0.138032	−	0.530941i
$567$		−	665.166i		−	1.17313i
$568$	−216.659	+	226.572i	−0.381441	+	0.398894i
$569$	643.792			1.13145			0.565723	−	0.824596i	$-0.308597\pi$
$569$	643.792			1.13145			0.565723	+	0.824596i	$0.308597\pi$
$570$	14.5050	+	3.77095i	0.0254474	+	0.00661570i
$571$		−	705.256i		−	1.23512i	−0.786522	−	0.617562i	$-0.788120\pi$
$571$		−	705.256i		−	1.23512i	0.786522	−	0.617562i	$-0.211880\pi$
$572$	−330.500	+	592.676i	−0.577798	+	1.03615i
$573$	91.6639			0.159972
$574$	7.45617	−	28.6803i	0.0129898	−	0.0499656i
$575$		−	74.1021i		−	0.128873i
$576$	24.0612	+	537.632i	0.0417728	+	0.933389i
$577$	−347.095			−0.601551			−0.300776	−	0.953695i	$-0.597246\pi$
$577$	−347.095			−0.601551			−0.300776	+	0.953695i	$0.597246\pi$
$578$	541.357	+	140.740i	0.936604	+	0.243494i
$579$		−	110.954i		−	0.191631i
$580$	−310.873	−	173.356i	−0.535989	−	0.298889i
$581$	−742.545			−1.27805
$582$	55.9990	−	215.401i	0.0962182	−	0.370104i
$583$			537.010i			0.921116i
$584$	−101.306	−	96.8736i	−0.173469	−	0.165879i
$585$	−438.914			−0.750281
$586$	66.9991	+	17.4181i	0.114333	+	0.0297238i
$587$			467.392i			0.796238i	0.917334	+	0.398119i	$0.130337\pi$
$587$			467.392i			0.796238i	−0.917334	+	0.398119i	$0.869663\pi$
$588$	81.5928	−	146.318i	0.138763	−	0.248840i
$589$	146.503			0.248731
$590$	−83.9375	+	322.867i	−0.142267	+	0.547231i
$591$		−	262.780i		−	0.444635i
$592$	159.831	+	258.704i	0.269984	+	0.437000i
$593$	583.990			0.984806			0.492403	−	0.870367i	$-0.336119\pi$
$593$	583.990			0.984806			0.492403	+	0.870367i	$0.336119\pi$
$594$	−188.289	−	48.9506i	−0.316985	−	0.0824084i
$595$			69.4544i			0.116730i
$596$	−709.589	−	395.696i	−1.19058	−	0.663919i
$597$	−127.956			−0.214331
$598$	174.091	−	669.643i	0.291122	−	1.11981i
$599$		−	994.689i		−	1.66058i	−0.557329	−	0.830291i	$-0.688174\pi$
$599$		−	994.689i		−	1.66058i	0.557329	−	0.830291i	$-0.311826\pi$
$600$	21.2540	−	22.2265i	0.0354233	−	0.0370441i
$601$	384.834			0.640323			0.320162	−	0.947363i	$-0.396263\pi$
$601$	384.834			0.640323			0.320162	+	0.947363i	$0.396263\pi$
$602$	−1019.36	−	265.010i	−1.69330	−	0.440216i
$603$		−	1025.88i		−	1.70130i
$604$	−96.8241	+	173.632i	−0.160305	+	0.287469i
$605$	152.456			0.251993
$606$	−7.46359	+	28.7088i	−0.0123161	+	0.0473742i
$607$		−	155.269i		−	0.255797i	−0.991787	−	0.127898i	$-0.959177\pi$
$607$		−	155.269i		−	0.255797i	0.991787	−	0.127898i	$-0.0408231\pi$
$608$	133.293	−	41.0966i	0.219232	−	0.0675930i
$609$	−311.230			−0.511051
$610$	−133.201	−	34.6290i	−0.218362	−	0.0567688i
$611$			1636.26i			2.67801i
$612$	−89.7015	−	50.0212i	−0.146571	−	0.0817340i
$613$	971.134			1.58423			0.792116	−	0.610370i	$-0.208979\pi$
$613$	971.134			1.58423			0.792116	+	0.610370i	$0.208979\pi$
$614$	183.664	−	706.466i	0.299127	−	1.15060i
$615$		−	2.50408i		−	0.00407167i
$616$	427.454	+	408.752i	0.693920	+	0.663558i
$617$	−298.583			−0.483927			−0.241963	−	0.970285i	$-0.577791\pi$
$617$	−298.583			−0.483927			−0.241963	+	0.970285i	$0.577791\pi$
$618$	222.355	+	57.8069i	0.359798	+	0.0935387i
$619$			444.544i			0.718165i	0.933306	+	0.359082i	$0.116910\pi$
$619$			444.544i			0.718165i	−0.933306	+	0.359082i	$0.883090\pi$
$620$	146.411	−	262.554i	0.236147	−	0.423474i
$621$	198.362			0.319424
$622$	−61.8335	+	237.843i	−0.0994108	+	0.382385i
$623$			27.3816i			0.0439513i
$624$	244.285	−	150.923i	0.391482	−	0.241863i
$625$	25.0000			0.0400000
$626$	326.078	+	84.7724i	0.520891	+	0.135419i
$627$			24.3558i			0.0388449i
$628$	−287.414	−	160.274i	−0.457665	−	0.255213i
$629$	−58.0342			−0.0922643
$630$	−96.2510	+	370.231i	−0.152779	+	0.587668i
$631$			724.777i			1.14862i	0.818639	+	0.574308i	$0.194729\pi$
$631$			724.777i			1.14862i	−0.818639	+	0.574308i	$0.805271\pi$
$632$	330.445	−	345.565i	0.522856	−	0.546779i
$633$	128.549			0.203079
$634$	−1194.57	−	310.559i	−1.88418	−	0.489841i
$635$		−	456.662i		−	0.719152i
$636$	110.671	−	198.462i	0.174010	−	0.312047i
$637$	1271.63			1.99627
$638$	145.543	−	559.835i	0.228125	−	0.877484i
$639$		−	329.513i		−	0.515670i
$640$	59.5587	−	279.951i	0.0930604	−	0.437424i
$641$	−219.564			−0.342533			−0.171267	−	0.985225i	$-0.554786\pi$
$641$	−219.564			−0.342533			−0.171267	+	0.985225i	$0.554786\pi$
$642$	70.8971	+	18.4315i	0.110432	+	0.0287096i
$643$		−	1166.31i		−	1.81386i	−0.421286	−	0.906928i	$-0.638421\pi$
$643$		−	1166.31i		−	1.81386i	0.421286	−	0.906928i	$-0.361579\pi$
$644$	−526.677	−	293.697i	−0.817822	−	0.456051i
$645$	−89.0009			−0.137986
$646$	−6.69782	+	25.7632i	−0.0103681	+	0.0398812i
$647$			699.560i			1.08124i	0.841268	+	0.540618i	$0.181809\pi$
$647$			699.560i			1.08124i	−0.841268	+	0.540618i	$0.818191\pi$
$648$	−378.080	−	361.538i	−0.583456	−	0.557928i
$649$	−542.135			−0.835339
$650$	225.919	+	58.7336i	0.347568	+	0.0903593i
$651$		−	262.855i		−	0.403771i
$652$	−193.818	+	347.567i	−0.297267	+	0.533079i
$653$	−604.829			−0.926231			−0.463115	−	0.886298i	$-0.653268\pi$
$653$	−604.829			−0.926231			−0.463115	+	0.886298i	$0.653268\pi$
$654$	40.2541	−	154.838i	0.0615506	−	0.236755i
$655$			275.165i			0.420099i
$656$	−12.2492	−	19.8266i	−0.0186725	−	0.0302235i
$657$	147.334			0.224252
$658$	1380.21	+	358.822i	2.09759	+	0.545322i
$659$			142.674i			0.216501i	0.994124	+	0.108251i	$0.0345249\pi$
$659$			142.674i			0.216501i	−0.994124	+	0.108251i	$0.965475\pi$
$660$	43.6490	+	24.3405i	0.0661349	+	0.0368795i
$661$	443.497			0.670949			0.335474	−	0.942049i	$-0.391103\pi$
$661$	443.497			0.670949			0.335474	+	0.942049i	$0.391103\pi$
$662$	273.673	−	1052.69i	0.413404	−	1.59016i
$663$			54.7997i			0.0826541i
$664$	−403.595	+	422.062i	−0.607824	+	0.635635i
$665$	99.1474			0.149094
$666$	−309.355	−	80.4247i	−0.464497	−	0.120758i
$667$			589.786i			0.884236i
$668$	−406.512	+	728.984i	−0.608550	+	1.09129i
$669$	−333.800			−0.498954
$670$	−137.279	+	528.045i	−0.204894	+	0.788127i
$671$		−	223.662i		−	0.333326i
$672$	−73.7354	−	239.154i	−0.109725	−	0.355885i
$673$	−624.187			−0.927469			−0.463734	−	0.885974i	$-0.653491\pi$
$673$	−624.187			−0.927469			−0.463734	+	0.885974i	$0.653491\pi$
$674$	−293.098	−	76.1985i	−0.434864	−	0.113054i
$675$			66.9220i			0.0991438i
$676$	1313.19	+	732.288i	1.94259	+	1.08327i
$677$	−484.051			−0.714994			−0.357497	−	0.933914i	$-0.616370\pi$
$677$	−484.051			−0.714994			−0.357497	+	0.933914i	$0.616370\pi$
$678$	47.3427	−	182.104i	0.0698269	−	0.268590i
$679$		−	1472.35i		−	2.16841i
$680$	39.4778	+	37.7505i	0.0580556	+	0.0555155i
$681$	17.9287			0.0263270
$682$	472.819	+	122.921i	0.693282	+	0.180237i
$683$			206.065i			0.301705i	0.988556	+	0.150853i	$0.0482019\pi$
$683$			206.065i			0.301705i	−0.988556	+	0.150853i	$0.951798\pi$
$684$	−71.4062	+	128.050i	−0.104395	+	0.187208i
$685$	−119.236			−0.174067
$686$	28.0309	−	107.821i	0.0408614	−	0.157174i
$687$		−	7.27772i		−	0.0105935i
$688$	−704.686	+	435.365i	−1.02425	+	0.632798i
$689$	1724.81			2.50335
$690$	−49.3175	−	12.8214i	−0.0714746	−	0.0185817i
$691$			1311.52i			1.89800i	0.315281	+	0.948998i	$0.397901\pi$
$691$			1311.52i			1.89800i	−0.315281	+	0.948998i	$0.602099\pi$
$692$	667.216	+	372.067i	0.964185	+	0.537669i
$693$	−621.665			−0.897064
$694$	238.273	−	916.521i	0.343333	−	1.32064i
$695$			13.5811i			0.0195411i
$696$	−169.163	+	176.903i	−0.243050	+	0.254170i
$697$	4.44765			0.00638113
$698$	−284.263	−	73.9015i	−0.407254	−	0.105876i
$699$			202.992i			0.290403i
$700$	99.0853	−	177.686i	0.141550	−	0.253838i
$701$	−1067.67			−1.52307			−0.761535	−	0.648123i	$-0.775554\pi$
$701$	−1067.67			−1.52307			−0.761535	+	0.648123i	$0.775554\pi$
$702$	−157.223	+	604.759i	−0.223964	+	0.861480i
$703$			82.8449i			0.117845i
$704$	464.668	−	20.7957i	0.660040	−	0.0295394i
$705$	120.507			0.170931
$706$	−889.407	−	231.224i	−1.25978	−	0.327513i
$707$			196.236i			0.277561i
$708$	200.356	+	111.727i	0.282989	+	0.157806i
$709$	−855.718			−1.20694			−0.603468	−	0.797387i	$-0.706215\pi$
$709$	−855.718			−1.20694			−0.603468	+	0.797387i	$0.706215\pi$
$710$	−44.0940	+	169.608i	−0.0621042	+	0.238884i
$711$			502.569i			0.706849i
$712$	15.5637	+	14.8827i	0.0218591	+	0.0209027i
$713$	−498.114			−0.698618
$714$	46.2244	+	12.0172i	0.0647400	+	0.0168308i
$715$			379.348i			0.530556i
$716$	234.642	−	420.776i	0.327712	−	0.587675i
$717$	128.674			0.179462
$718$	−273.681	+	1052.72i	−0.381171	+	1.46618i
$719$		−	15.8060i		−	0.0219832i	−0.999940	−	0.0109916i	$-0.996501\pi$
$719$		−	15.8060i		−	0.0219832i	0.999940	−	0.0109916i	$-0.00349881\pi$
$720$	158.123	+	255.940i	0.219616	+	0.355473i
$721$	1519.88			2.10802
$722$	36.7775	+	9.56125i	0.0509383	+	0.0132427i
$723$		−	180.768i		−	0.250025i
$724$	640.658	+	357.257i	0.884887	+	0.493450i
$725$	−198.978			−0.274452
$726$	26.3784	−	101.465i	0.0363339	−	0.139759i
$727$		−	268.705i		−	0.369607i	−0.982775	−	0.184804i	$-0.940835\pi$
$727$		−	268.705i		−	0.369607i	0.982775	−	0.184804i	$-0.0591649\pi$
$728$	1312.86	−	1372.93i	1.80338	−	1.88589i
$729$	457.245			0.627223
$730$	−75.8361	−	19.7155i	−0.103885	−	0.0270076i
$731$		−	158.080i		−	0.216252i
$732$	−46.0936	+	82.6582i	−0.0629694	+	0.112921i
$733$	−1187.70			−1.62032			−0.810160	−	0.586208i	$-0.800620\pi$
$733$	−1187.70			−1.62032			−0.810160	+	0.586208i	$0.800620\pi$
$734$	20.3168	−	78.1488i	0.0276796	−	0.106470i
$735$		−	93.6520i		−	0.127418i
$736$	−453.202	+	139.730i	−0.615763	+	0.189850i
$737$	−886.656			−1.20306
$738$	23.7084	+	6.16362i	0.0321253	+	0.00835179i
$739$		−	63.8403i		−	0.0863875i	−0.999067	−	0.0431937i	$-0.986247\pi$
$739$		−	63.8403i		−	0.0863875i	0.999067	−	0.0431937i	$-0.0137533\pi$
$740$	148.470	+	82.7929i	0.200635	+	0.111882i
$741$	78.2275			0.105570
$742$	378.239	−	1454.90i	0.509756	−	1.96078i
$743$			62.9930i			0.0847820i	0.999101	+	0.0423910i	$0.0134975\pi$
$743$			62.9930i			0.0847820i	−0.999101	+	0.0423910i	$0.986502\pi$
$744$	−149.406	−	142.869i	−0.200815	−	0.192029i
$745$	−454.179			−0.609636
$746$	−963.964	−	250.607i	−1.29218	−	0.335935i
$747$		−	613.822i		−	0.821717i
$748$	−43.2327	+	77.5278i	−0.0577977	+	0.103647i
$749$	484.610			0.647009
$750$	4.32557	−	16.6384i	0.00576743	−	0.0221845i
$751$		−	777.359i		−	1.03510i	−0.855653	−	0.517549i	$-0.826844\pi$
$751$		−	777.359i		−	1.03510i	0.855653	−	0.517549i	$-0.173156\pi$
$752$	954.140	−	589.481i	1.26880	−	0.783884i
$753$	0.775067			0.00102931
$754$	−1798.11	−	467.466i	−2.38477	−	0.619982i
$755$			111.134i			0.147198i
$756$	475.646	+	265.239i	0.629161	+	0.350846i
$757$	320.752			0.423715			0.211858	−	0.977301i	$-0.432049\pi$
$757$	320.752			0.423715			0.211858	+	0.977301i	$0.432049\pi$
$758$	−295.889	+	1138.14i	−0.390355	+	1.50150i
$759$		−	82.8105i		−	0.109105i
$760$	53.8896	−	56.3553i	0.0709073	−	0.0741517i
$761$	−475.655			−0.625039			−0.312520	−	0.949911i	$-0.601173\pi$
$761$	−475.655			−0.625039			−0.312520	+	0.949911i	$0.601173\pi$
$762$	−303.924	−	79.0129i	−0.398851	−	0.103692i
$763$		−	1058.38i		−	1.38713i
$764$	232.268	−	416.519i	0.304016	−	0.545183i
$765$	−57.4143			−0.0750513
$766$	−165.312	+	635.874i	−0.215812	+	0.830122i
$767$			1741.27i			2.27023i
$768$	−176.012	−	88.0764i	−0.229183	−	0.114683i
$769$	315.501			0.410274			0.205137	−	0.978733i	$-0.434236\pi$
$769$	315.501			0.410274			0.205137	+	0.978733i	$0.434236\pi$
$770$	319.986	+	83.1885i	0.415566	+	0.108037i
$771$			206.987i			0.268465i
$772$	−504.174	−	281.148i	−0.653075	−	0.364181i
$773$	−33.5711			−0.0434296			−0.0217148	−	0.999764i	$-0.506913\pi$
$773$	−33.5711			−0.0434296			−0.0217148	+	0.999764i	$0.506913\pi$
$774$	219.070	−	842.655i	0.283036	−	1.08870i
$775$		−	168.050i		−	0.216839i
$776$	−836.882	−	800.266i	−1.07846	−	1.03127i
$777$	148.640			0.191300
$778$	−1068.88	−	277.882i	−1.37388	−	0.357174i
$779$		−	6.34910i		−	0.00815032i
$780$	78.1785	−	140.195i	0.100229	−	0.179737i
$781$	−284.794			−0.364653
$782$	22.7728	−	87.5959i	0.0291212	−	0.112015i
$783$		−	532.639i		−	0.680254i
$784$	−458.117	−	741.513i	−0.584333	−	0.945807i
$785$	−183.962			−0.234346
$786$	183.132	+	47.6098i	0.232992	+	0.0605723i
$787$			398.511i			0.506367i	0.967418	+	0.253184i	$0.0814777\pi$
$787$			398.511i			0.506367i	−0.967418	+	0.253184i	$0.918522\pi$
$788$	−1194.07	−	665.861i	−1.51531	−	0.845001i
$789$	277.244			0.351386
$790$	67.2516	−	258.684i	0.0851286	−	0.327448i
$791$		−	1244.75i		−	1.57365i
$792$	−337.894	+	353.354i	−0.426633	+	0.446154i
$793$	−718.371			−0.905890
$794$	1493.79	+	388.349i	1.88135	+	0.489105i
$795$		−	127.028i		−	0.159783i
$796$	−324.228	+	581.429i	−0.407322	+	0.730438i
$797$	−806.483			−1.01190			−0.505949	−	0.862563i	$-0.668858\pi$
$797$	−806.483			−1.01190			−0.505949	+	0.862563i	$0.668858\pi$
$798$	17.1548	−	65.9861i	0.0214972	−	0.0826893i
$799$			214.039i			0.267884i
$800$	−47.1410	−	152.898i	−0.0589262	−	0.191122i
$801$	−22.6349			−0.0282584
$802$	−268.783	−	69.8771i	−0.335141	−	0.0871285i
$803$		−	127.339i		−	0.158579i
$804$	327.680	+	182.728i	0.407562	+	0.227273i
$805$	−337.105			−0.418764
$806$	394.807	−	1518.63i	0.489835	−	1.88416i
$807$			140.043i			0.173536i
$808$	111.540	+	106.660i	0.138045	+	0.132005i
$809$	−1499.00			−1.85290			−0.926451	−	0.376415i	$-0.877157\pi$
$809$	−1499.00			−1.85290			−0.926451	+	0.376415i	$0.877157\pi$
$810$	−283.024	−	73.5795i	−0.349413	−	0.0908389i
$811$		−	582.111i		−	0.717770i	−0.933382	−	0.358885i	$-0.883157\pi$
$811$		−	582.111i		−	0.717770i	0.933382	−	0.358885i	$-0.116843\pi$
$812$	−788.630	+	1414.22i	−0.971219	+	1.74166i
$813$	−55.7247			−0.0685420
$814$	−69.5100	+	267.371i	−0.0853932	+	0.328466i
$815$			222.464i			0.272962i
$816$	31.9549	−	19.7422i	0.0391604	−	0.0241938i
$817$	−225.662			−0.276208
$818$	−417.572	−	108.559i	−0.510479	−	0.132712i
$819$			1996.71i			2.43798i
$820$	−11.3785	−	6.34512i	−0.0138762	−	0.00773795i
$821$	1099.23			1.33890			0.669448	−	0.742859i	$-0.266531\pi$
$821$	1099.23			1.33890			0.669448	+	0.742859i	$0.266531\pi$
$822$	−20.6305	+	79.3555i	−0.0250979	+	0.0965396i
$823$		−	1398.63i		−	1.69942i	−0.527247	−	0.849712i	$-0.676776\pi$
$823$		−	1398.63i		−	1.69942i	0.527247	−	0.849712i	$-0.323224\pi$
$824$	826.102	−	863.900i	1.00255	−	1.04842i
$825$	27.9380			0.0338642
$826$	1468.78	+	381.848i	1.77819	+	0.462286i
$827$		−	68.2056i		−	0.0824735i	−0.999149	−	0.0412368i	$-0.986870\pi$
$827$		−	68.2056i		−	0.0824735i	0.999149	−	0.0412368i	$-0.0131298\pi$
$828$	242.784	−	435.376i	0.293217	−	0.525816i
$829$	1247.87			1.50527			0.752637	−	0.658436i	$-0.228782\pi$
$829$	1247.87			1.50527			0.752637	+	0.658436i	$0.228782\pi$
$830$	−82.1390	+	315.949i	−0.0989626	+	0.380661i
$831$			265.636i			0.319658i
$832$	−66.7932	−	1492.45i	−0.0802803	−	1.79381i
$833$	166.341			0.199689
$834$	9.03869	+	2.34984i	0.0108378	+	0.00281755i
$835$			466.593i			0.558794i
$836$	110.672	+	61.7154i	0.132383	+	0.0738223i
$837$	449.850			0.537455
$838$	232.669	−	894.965i	0.277648	−	1.06798i
$839$			1209.94i			1.44212i	0.692871	+	0.721062i	$0.256346\pi$
$839$			1209.94i			1.44212i	−0.692871	+	0.721062i	$0.743654\pi$
$840$	−101.113	−	96.6885i	−0.120372	−	0.115105i
$841$	742.682			0.883094
$842$	−466.331	−	121.235i	−0.553837	−	0.143984i
$843$		−	264.257i		−	0.313473i
$844$	325.733	−	584.126i	0.385939	−	0.692093i
$845$	840.519			0.994697
$846$	−296.619	+	1140.95i	−0.350613	+	1.34864i
$847$		−	693.552i		−	0.818834i
$848$	−621.379	−	1005.77i	−0.732759	−	1.18605i
$849$	−119.361			−0.140590
$850$	29.5525	+	7.68292i	0.0347676	+	0.00903873i
$851$		−	281.676i		−	0.330994i
$852$	105.251	+	58.6921i	0.123534	+	0.0688875i
$853$	−642.132			−0.752792			−0.376396	−	0.926459i	$-0.622837\pi$
$853$	−642.132			−0.752792			−0.376396	+	0.926459i	$0.622837\pi$
$854$	−157.534	+	605.957i	−0.184466	+	0.709551i
$855$			81.9599i			0.0958595i
$856$	263.400	−	275.452i	0.307710	−	0.321789i
$857$	1094.07			1.27663			0.638316	−	0.769775i	$-0.279631\pi$
$857$	1094.07			1.27663			0.638316	+	0.769775i	$0.279631\pi$
$858$	252.469	+	65.6359i	0.294253	+	0.0764987i
$859$			711.854i			0.828701i	0.910117	+	0.414351i	$0.135991\pi$
$859$			711.854i			0.828701i	−0.910117	+	0.414351i	$0.864009\pi$
$860$	−225.521	+	404.419i	−0.262233	+	0.470255i
$861$	−11.3915			−0.0132306
$862$	−32.4990	+	125.008i	−0.0377019	+	0.145021i
$863$			220.489i			0.255491i	0.991807	+	0.127746i	$0.0407741\pi$
$863$			220.489i			0.255491i	−0.991807	+	0.127746i	$0.959226\pi$
$864$	409.289	−	126.191i	0.473714	−	0.146054i
$865$	427.058			0.493709
$866$	804.411	+	209.127i	0.928881	+	0.241487i
$867$		−	215.022i		−	0.248007i
$868$	−1194.41	−	666.052i	−1.37605	−	0.767341i
$869$	434.364			0.499844
$870$	−34.4277	+	132.426i	−0.0395720	+	0.152214i
$871$			2847.82i			3.26960i
$872$	−601.580	−	575.259i	−0.689886	−	0.659701i
$873$	1217.11			1.39417
$874$	−125.045	−	32.5086i	−0.143072	−	0.0371952i
$875$		−	113.730i		−	0.129977i
$876$	−26.2428	+	47.0603i	−0.0299575	+	0.0537218i
$877$	1459.48			1.66417			0.832087	−	0.554645i	$-0.187146\pi$
$877$	1459.48			1.66417			0.832087	+	0.554645i	$0.187146\pi$
$878$	−271.001	+	1042.41i	−0.308657	+	1.18725i
$879$		−	26.6114i		−	0.0302747i
$880$	221.206	−	136.664i	0.251370	−	0.155300i
$881$	−705.153			−0.800401			−0.400201	−	0.916428i	$-0.631060\pi$
$881$	−705.153			−0.800401			−0.400201	+	0.916428i	$0.631060\pi$
$882$	886.691	+	230.518i	1.00532	+	0.261359i
$883$			1139.40i			1.29037i	0.764024	+	0.645187i	$0.223221\pi$
$883$			1139.40i			1.29037i	−0.764024	+	0.645187i	$0.776779\pi$
$884$	249.009	+	138.858i	0.281684	+	0.157079i
$885$	128.240			0.144904
$886$	257.344	−	989.878i	0.290456	−	1.11724i
$887$		−	288.966i		−	0.325779i	−0.986644	−	0.162890i	$-0.947919\pi$
$887$		−	288.966i		−	0.325779i	0.986644	−	0.162890i	$-0.0520815\pi$
$888$	80.7903	−	84.4869i	0.0909801	−	0.0951429i
$889$	−2077.44			−2.33683
$890$	11.6507	+	3.02891i	0.0130907	+	0.00340327i
$891$		−	475.235i		−	0.533372i
$892$	−845.820	+	1516.78i	−0.948229	+	1.70043i
$893$	305.545			0.342155
$894$	−78.5834	+	302.272i	−0.0879009	+	0.338112i
$895$		−	269.321i		−	0.300918i
$896$	−1273.55	−	270.944i	−1.42138	−	0.302393i
$897$	−265.976			−0.296518
$898$	704.290	+	183.098i	0.784288	+	0.203896i
$899$			1337.53i			1.48780i
$900$	146.884	+	81.9085i	0.163204	+	0.0910095i
$901$	225.622			0.250412
$902$	5.32714	−	20.4909i	0.00590592	−	0.0227172i
$903$			404.883i			0.448375i
$904$	−707.517	−	676.561i	−0.782651	−	0.748408i
$905$	410.060			0.453104
$906$	73.9639	+	19.2288i	0.0816378	+	0.0212239i
$907$			1487.08i			1.63956i	0.572682	+	0.819778i	$0.305903\pi$
$907$			1487.08i			1.63956i	−0.572682	+	0.819778i	$0.694097\pi$
$908$	45.4297	−	81.4677i	0.0500327	−	0.0897221i
$909$	−162.218			−0.178457
$910$	267.190	−	1027.75i	0.293616	−	1.12940i
$911$		−	1338.49i		−	1.46925i	−0.678472	−	0.734626i	$-0.737358\pi$
$911$		−	1338.49i		−	1.46925i	0.678472	−	0.734626i	$-0.262642\pi$
$912$	−28.1823	−	45.6161i	−0.0309016	−	0.0500177i
$913$	−530.519			−0.581072
$914$	−972.756	−	252.893i	−1.06428	−	0.276688i
$915$			52.9062i			0.0578210i
$916$	−33.0699	−	18.4411i	−0.0361025	−	0.0201322i
$917$	1251.78			1.36508
$918$	−20.5663	+	79.1084i	−0.0224033	+	0.0861748i
$919$		−	640.851i		−	0.697336i	−0.937246	−	0.348668i	$-0.886634\pi$
$919$		−	640.851i		−	0.697336i	0.937246	−	0.348668i	$-0.113366\pi$
$920$	−183.226	+	191.610i	−0.199159	+	0.208272i
$921$	−280.602			−0.304671
$922$	−1346.90	−	350.162i	−1.46085	−	0.379785i
$923$			914.720i			0.991029i
$924$	110.730	−	198.568i	0.119837	−	0.214901i
$925$	95.0296			0.102735
$926$	−174.358	+	670.668i	−0.188291	+	0.724264i
$927$			1256.41i			1.35535i
$928$	375.200	+	1216.93i	0.404310	+	1.31135i
$929$	370.439			0.398751			0.199375	−	0.979923i	$-0.436109\pi$
$929$	370.439			0.398751			0.199375	+	0.979923i	$0.436109\pi$
$930$	−111.843	−	29.0765i	−0.120262	−	0.0312651i
$931$		−	237.455i		−	0.255054i
$932$	922.391	+	514.363i	0.989690	+	0.551892i
$933$	94.4692			0.101253
$934$	−263.490	+	1013.52i	−0.282109	+	1.08514i
$935$			49.6224i			0.0530721i
$936$	1134.93	+	1085.27i	1.21253	+	1.15948i
$937$	−1591.09			−1.69807			−0.849033	−	0.528339i	$-0.822815\pi$
$937$	−1591.09			−1.69807			−0.849033	+	0.528339i	$0.822815\pi$
$938$	2402.18	+	624.508i	2.56096	+	0.665787i
$939$		−	129.515i		−	0.137929i
$940$	305.353	−	547.580i	0.324844	−	0.582532i
$941$	−361.084			−0.383723			−0.191862	−	0.981422i	$-0.561452\pi$
$941$	−361.084			−0.383723			−0.191862	+	0.981422i	$0.561452\pi$
$942$	−31.8296	+	122.433i	−0.0337894	+	0.129971i
$943$			21.5872i			0.0228920i
$944$	1015.37	−	627.309i	1.07560	−	0.664522i
$945$	304.441			0.322160
$946$	−728.295	−	189.339i	−0.769868	−	0.200147i
$947$		−	14.6632i		−	0.0154838i	−0.999970	−	0.00774190i	$-0.997536\pi$
$947$		−	14.6632i		−	0.0154838i	0.999970	−	0.00774190i	$-0.00246435\pi$
$948$	−160.527	−	89.5166i	−0.169333	−	0.0944268i
$949$	−408.995			−0.430974
$950$	10.9675	−	42.1867i	0.0115447	−	0.0444070i
$951$			474.472i			0.498919i
$952$	171.735	−	179.592i	0.180393	−	0.188647i
$953$	696.208			0.730543			0.365272	−	0.930901i	$-0.380976\pi$
$953$	696.208			0.730543			0.365272	+	0.930901i	$0.380976\pi$
$954$	1202.69	+	312.670i	1.26068	+	0.327746i
$955$		−	266.597i		−	0.279159i
$956$	326.049	−	584.693i	0.341055	−	0.611603i
$957$	−222.361			−0.232352
$958$	−242.411	+	932.437i	−0.253039	+	0.973317i
$959$			542.427i			0.565617i
$960$	−109.915	+	4.91914i	−0.114495	+	0.00512411i
$961$	−168.634			−0.175477
$962$	858.761	+	223.257i	0.892683	+	0.232076i
$963$			400.601i			0.415993i
$964$	−821.407	−	458.050i	−0.852082	−	0.475156i
$965$	−322.701			−0.334405
$966$	−58.3269	+	224.355i	−0.0603798	+	0.232252i
$967$			29.4263i			0.0304305i	0.999884	+	0.0152152i	$0.00484335\pi$
$967$			29.4263i			0.0304305i	−0.999884	+	0.0152152i	$0.995157\pi$
$968$	−394.214	−	376.966i	−0.407246	−	0.389428i
$969$	10.2329			0.0105603
$970$	−626.476	−	162.869i	−0.645852	−	0.167906i
$971$		−	721.185i		−	0.742724i	−0.928488	−	0.371362i	$-0.878891\pi$
$971$		−	721.185i		−	0.742724i	0.928488	−	0.371362i	$-0.121109\pi$
$972$	−332.611	+	596.461i	−0.342193	+	0.613643i
$973$	61.7830			0.0634975
$974$	254.844	−	980.259i	0.261647	−	1.00643i
$975$		−	89.7331i		−	0.0920340i
$976$	258.801	+	418.898i	0.265165	+	0.429198i
$977$	586.000			0.599795			0.299898	−	0.953971i	$-0.403047\pi$
$977$	586.000			0.599795			0.299898	+	0.953971i	$0.403047\pi$
$978$	148.057	+	38.4914i	0.151388	+	0.0393572i
$979$			19.5631i			0.0199827i
$980$	−425.554	−	237.306i	−0.434238	−	0.242149i
$981$	874.904			0.891849
$982$	−183.424	+	705.543i	−0.186786	+	0.718476i
$983$			371.614i			0.378041i	0.981973	+	0.189020i	$0.0605312\pi$
$983$			371.614i			0.378041i	−0.981973	+	0.189020i	$0.939469\pi$
$984$	−6.19164	+	6.47494i	−0.00629232	+	0.00658022i
$985$	−764.274			−0.775912
$986$	−235.211	−	61.1492i	−0.238551	−	0.0620174i
$987$		−	548.208i		−	0.555428i
$988$	198.222	−	355.465i	0.200629	−	0.359782i
$989$	767.259			0.775793
$990$	−68.7675	+	264.515i	−0.0694621	+	0.267187i
$991$		−	586.679i		−	0.592007i	−0.955187	−	0.296004i	$-0.904346\pi$
$991$		−	586.679i		−	0.592007i	0.955187	−	0.296004i	$-0.0956540\pi$
$992$	−1027.78	+	316.882i	−1.03607	+	0.319437i
$993$	−418.118			−0.421065
$994$	771.580	+	200.592i	0.776237	+	0.201803i
$995$			372.149i			0.374019i
$996$	196.063	+	109.333i	0.196850	+	0.109772i
$997$	482.461			0.483913			0.241956	−	0.970287i	$-0.422211\pi$
$997$	482.461			0.483913			0.241956	+	0.970287i	$0.422211\pi$
$998$	−407.759	+	1568.45i	−0.408576	+	1.57159i
$999$			254.383i			0.254638i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.b.a.191.7	✓	72
4.3	odd	2	inner	380.3.b.a.191.8	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.b.a.191.7	✓	72	1.1	even	1	trivial
380.3.b.a.191.8	yes	72	4.3	odd	2	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.93566 - 0.503224i) q^{2} +0.768825i q^{3} +(3.49353 + 1.94814i) q^{4} +2.23607 q^{5} +(0.386891 - 1.48818i) q^{6} -10.1723i q^{7} +(-5.78193 - 5.52895i) q^{8} +8.40891 q^{9} +O(q^{10})\)	\(q+(-1.93566 - 0.503224i) q^{2} +0.768825i q^{3} +(3.49353 + 1.94814i) q^{4} +2.23607 q^{5} +(0.386891 - 1.48818i) q^{6} -10.1723i q^{7} +(-5.78193 - 5.52895i) q^{8} +8.40891 q^{9} +(-4.32826 - 1.12524i) q^{10} -7.26771i q^{11} +(-1.49778 + 2.68592i) q^{12} -23.3429 q^{13} +(-5.11895 + 19.6901i) q^{14} +1.71915i q^{15} +(8.40953 + 13.6118i) q^{16} -3.05348 q^{17} +(-16.2768 - 4.23156i) q^{18} +4.35890i q^{19} +(7.81177 + 4.35617i) q^{20} +7.82073 q^{21} +(-3.65728 + 14.0678i) q^{22} -14.8204i q^{23} +(4.25080 - 4.44529i) q^{24} +5.00000 q^{25} +(45.1839 + 11.7467i) q^{26} +13.3844i q^{27} +(19.8171 - 35.5373i) q^{28} -39.7955 q^{29} +(0.865115 - 3.32767i) q^{30} -33.6100i q^{31} +(-9.42820 - 30.5796i) q^{32} +5.58760 q^{33} +(5.91049 + 1.53658i) q^{34} -22.7460i q^{35} +(29.3768 + 16.3817i) q^{36} +19.0059 q^{37} +(2.19350 - 8.43733i) q^{38} -17.9466i q^{39} +(-12.9288 - 12.3631i) q^{40} -1.45658 q^{41} +(-15.1382 - 3.93558i) q^{42} +51.7704i q^{43} +(14.1585 - 25.3900i) q^{44} +18.8029 q^{45} +(-7.45798 + 28.6872i) q^{46} -70.0968i q^{47} +(-10.4651 + 6.46546i) q^{48} -54.4759 q^{49} +(-9.67828 - 2.51612i) q^{50} -2.34759i q^{51} +(-81.5492 - 45.4752i) q^{52} -73.8899 q^{53} +(6.73535 - 25.9076i) q^{54} -16.2511i q^{55} +(-56.2422 + 58.8156i) q^{56} -3.35123 q^{57} +(77.0304 + 20.0260i) q^{58} -74.5950i q^{59} +(-3.34913 + 6.00589i) q^{60} +30.7747 q^{61} +(-16.9134 + 65.0575i) q^{62} -85.5380i q^{63} +(2.86139 + 63.9360i) q^{64} -52.1963 q^{65} +(-10.8157 - 2.81181i) q^{66} -121.999i q^{67} +(-10.6674 - 5.94860i) q^{68} +11.3943 q^{69} +(-11.4463 + 44.0284i) q^{70} -39.1862i q^{71} +(-48.6197 - 46.4924i) q^{72} +17.5212 q^{73} +(-36.7889 - 9.56423i) q^{74} +3.84413i q^{75} +(-8.49173 + 15.2280i) q^{76} -73.9294 q^{77} +(-9.03117 + 34.7385i) q^{78} +59.7663i q^{79} +(18.8043 + 30.4368i) q^{80} +65.3899 q^{81} +(2.81944 + 0.732987i) q^{82} -72.9967i q^{83} +(27.3220 + 15.2358i) q^{84} -6.82779 q^{85} +(26.0521 - 100.210i) q^{86} -30.5958i q^{87} +(-40.1828 + 42.0214i) q^{88} -2.69178 q^{89} +(-36.3959 - 9.46206i) q^{90} +237.451i q^{91} +(28.8722 - 51.7756i) q^{92} +25.8402 q^{93} +(-35.2744 + 135.683i) q^{94} +9.74679i q^{95} +(23.5103 - 7.24863i) q^{96} +144.741 q^{97} +(105.447 + 27.4136i) q^{98} -61.1135i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9}+O(q^{10}) \) 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9	\( 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9} - 80 q^{12} - 80 q^{14} + 4 q^{16} - 44 q^{18} - 40 q^{20} + 16 q^{21} + 160 q^{22} + 204 q^{24} + 360 q^{25} + 28 q^{26} + 20 q^{28} + 16 q^{29} + 40 q^{30} - 136 q^{32} - 96 q^{34} + 8 q^{36} - 192 q^{37} - 4 q^{42} - 40 q^{44} + 80 q^{45} - 232 q^{46} - 156 q^{48} - 504 q^{49} + 20 q^{50} + 228 q^{52} + 320 q^{53} + 92 q^{54} + 8 q^{56} + 380 q^{58} - 140 q^{60} - 168 q^{62} - 60 q^{64} - 40 q^{66} + 396 q^{68} - 48 q^{69} - 120 q^{70} - 284 q^{72} + 192 q^{74} - 640 q^{77} - 520 q^{78} + 120 q^{80} + 568 q^{81} - 240 q^{82} + 112 q^{84} + 688 q^{86} - 484 q^{88} + 240 q^{89} + 12 q^{92} + 512 q^{93} + 432 q^{94} + 300 q^{96} - 44 q^{98}+O(q^{100}) \) 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9 - 80 * q^12 - 80 * q^14 + 4 * q^16 - 44 * q^18 - 40 * q^20 + 16 * q^21 + 160 * q^22 + 204 * q^24 + 360 * q^25 + 28 * q^26 + 20 * q^28 + 16 * q^29 + 40 * q^30 - 136 * q^32 - 96 * q^34 + 8 * q^36 - 192 * q^37 - 4 * q^42 - 40 * q^44 + 80 * q^45 - 232 * q^46 - 156 * q^48 - 504 * q^49 + 20 * q^50 + 228 * q^52 + 320 * q^53 + 92 * q^54 + 8 * q^56 + 380 * q^58 - 140 * q^60 - 168 * q^62 - 60 * q^64 - 40 * q^66 + 396 * q^68 - 48 * q^69 - 120 * q^70 - 284 * q^72 + 192 * q^74 - 640 * q^77 - 520 * q^78 + 120 * q^80 + 568 * q^81 - 240 * q^82 + 112 * q^84 + 688 * q^86 - 484 * q^88 + 240 * q^89 + 12 * q^92 + 512 * q^93 + 432 * q^94 + 300 * q^96 - 44 * q^98

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