LMFDB - Embedded newform 144.3.w.a.5.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(5,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("144.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.w (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.17
Character	$\chi$	$=$	144.5
Dual form			144.3.w.a.29.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.786053 + 1.83905i) q^{2} +(1.51963 - 2.58664i) q^{3} +(-2.76424 - 2.89119i) q^{4} +(1.99100 + 7.43050i) q^{5} +(3.56247 + 4.82792i) q^{6} +(-1.50577 + 0.869355i) q^{7} +(7.48989 - 2.81097i) q^{8} +(-4.38144 - 7.86149i) q^{9} +O(q^{10})$	\(q+(-0.786053 + 1.83905i) q^{2} +(1.51963 - 2.58664i) q^{3} +(-2.76424 - 2.89119i) q^{4} +(1.99100 + 7.43050i) q^{5} +(3.56247 + 4.82792i) q^{6} +(-1.50577 + 0.869355i) q^{7} +(7.48989 - 2.81097i) q^{8} +(-4.38144 - 7.86149i) q^{9} +(-15.2301 - 2.17922i) q^{10} +(15.2997 + 4.09955i) q^{11} +(-11.6791 + 2.75657i) q^{12} +(5.73919 + 21.4190i) q^{13} +(-0.415179 - 3.45255i) q^{14} +(22.2456 + 6.14163i) q^{15} +(-0.717932 + 15.9839i) q^{16} +1.12960i q^{17} +(17.9017 - 1.87816i) q^{18} +(12.2501 - 12.2501i) q^{19} +(15.9794 - 26.2961i) q^{20} +(-0.0395007 + 5.21598i) q^{21} +(-19.5657 + 24.9146i) q^{22} +(-6.80266 + 11.7825i) q^{23} +(4.11091 - 23.6453i) q^{24} +(-29.5977 + 17.0882i) q^{25} +(-43.9019 - 6.28174i) q^{26} +(-26.9930 - 0.613350i) q^{27} +(6.67578 + 1.95035i) q^{28} +(0.249824 - 0.932358i) q^{29} +(-28.7810 + 36.0833i) q^{30} +(1.87100 - 3.24066i) q^{31} +(-28.8309 - 13.8845i) q^{32} +(33.8540 - 33.3451i) q^{33} +(-2.07740 - 0.887925i) q^{34} +(-9.45773 - 9.45773i) q^{35} +(-10.6177 + 34.3986i) q^{36} +(-35.9564 - 35.9564i) q^{37} +(12.8994 + 32.1578i) q^{38} +(64.1247 + 17.7037i) q^{39} +(35.7992 + 50.0570i) q^{40} +(30.2406 - 52.3783i) q^{41} +(-9.56143 - 4.17268i) q^{42} +(4.42169 - 16.5020i) q^{43} +(-30.4396 - 55.5666i) q^{44} +(49.6914 - 48.2085i) q^{45} +(-16.3215 - 21.7722i) q^{46} +(11.2070 - 6.47034i) q^{47} +(40.2536 + 26.1467i) q^{48} +(-22.9884 + 39.8171i) q^{49} +(-8.16084 - 67.8640i) q^{50} +(2.92187 + 1.71658i) q^{51} +(46.0617 - 75.8003i) q^{52} +(38.2384 - 38.2384i) q^{53} +(22.3459 - 49.1595i) q^{54} +121.847i q^{55} +(-8.83431 + 10.7440i) q^{56} +(-13.0710 - 50.3022i) q^{57} +(1.51828 + 1.19232i) q^{58} +(5.85788 + 21.8619i) q^{59} +(-43.7357 - 81.2933i) q^{60} +(-95.2073 - 25.5107i) q^{61} +(4.48905 + 5.98819i) q^{62} +(13.4319 + 8.02855i) q^{63} +(48.1969 - 42.1077i) q^{64} +(-147.727 + 85.2902i) q^{65} +(34.7125 + 88.4705i) q^{66} +(-20.8577 - 77.8418i) q^{67} +(3.26589 - 3.12249i) q^{68} +(20.1397 + 35.5012i) q^{69} +(24.8276 - 9.95900i) q^{70} +96.9917 q^{71} +(-54.9149 - 46.5656i) q^{72} -19.4973i q^{73} +(94.3893 - 37.8621i) q^{74} +(-0.776435 + 102.526i) q^{75} +(-69.2795 - 1.55509i) q^{76} +(-26.6018 + 7.12794i) q^{77} +(-82.9634 + 104.013i) q^{78} +(-60.9180 - 105.513i) q^{79} +(-120.198 + 26.4893i) q^{80} +(-42.6060 + 68.8893i) q^{81} +(72.5558 + 96.7862i) q^{82} +(-21.7550 + 81.1908i) q^{83} +(15.1896 - 14.3040i) q^{84} +(-8.39350 + 2.24903i) q^{85} +(26.8724 + 21.1032i) q^{86} +(-2.03203 - 2.06305i) q^{87} +(126.117 - 12.3018i) q^{88} -62.3081 q^{89} +(49.5980 + 129.280i) q^{90} +(-27.2626 - 27.2626i) q^{91} +(52.8698 - 12.9021i) q^{92} +(-5.53920 - 9.76420i) q^{93} +(3.09005 + 25.6962i) q^{94} +(115.414 + 66.6344i) q^{95} +(-79.7266 + 53.4759i) q^{96} +(63.8929 + 110.666i) q^{97} +(-55.1558 - 73.5754i) q^{98} +(-34.8063 - 138.241i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6}+O(q^{10}) $ 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6	$ 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6} - 8 q^{10} - 6 q^{11} - 64 q^{12} - 2 q^{13} - 6 q^{14} - 8 q^{15} - 2 q^{16} + 54 q^{18} - 8 q^{19} + 120 q^{20} - 22 q^{21} - 2 q^{22} - 160 q^{24} + 44 q^{27} - 72 q^{28} - 6 q^{29} - 90 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 6 q^{34} - 202 q^{36} - 8 q^{37} - 6 q^{38} - 2 q^{40} + 44 q^{42} - 2 q^{43} + 46 q^{45} - 160 q^{46} - 12 q^{47} - 118 q^{48} + 472 q^{49} + 228 q^{50} - 48 q^{51} - 2 q^{52} + 206 q^{54} - 300 q^{56} - 92 q^{58} - 438 q^{59} - 90 q^{60} - 2 q^{61} - 204 q^{63} + 244 q^{64} - 12 q^{65} - 508 q^{66} - 2 q^{67} - 144 q^{68} + 14 q^{69} + 96 q^{70} + 6 q^{72} + 246 q^{74} + 152 q^{75} - 158 q^{76} - 6 q^{77} + 304 q^{78} - 4 q^{79} - 8 q^{81} - 388 q^{82} - 726 q^{83} + 542 q^{84} + 48 q^{85} + 894 q^{86} + 22 q^{88} - 528 q^{90} - 204 q^{91} - 348 q^{92} + 62 q^{93} - 18 q^{94} - 12 q^{95} + 262 q^{96} - 4 q^{97} + 286 q^{99}+O(q^{100}) $ 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6 - 8 * q^10 - 6 * q^11 - 64 * q^12 - 2 * q^13 - 6 * q^14 - 8 * q^15 - 2 * q^16 + 54 * q^18 - 8 * q^19 + 120 * q^20 - 22 * q^21 - 2 * q^22 - 160 * q^24 + 44 * q^27 - 72 * q^28 - 6 * q^29 - 90 * q^30 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 6 * q^34 - 202 * q^36 - 8 * q^37 - 6 * q^38 - 2 * q^40 + 44 * q^42 - 2 * q^43 + 46 * q^45 - 160 * q^46 - 12 * q^47 - 118 * q^48 + 472 * q^49 + 228 * q^50 - 48 * q^51 - 2 * q^52 + 206 * q^54 - 300 * q^56 - 92 * q^58 - 438 * q^59 - 90 * q^60 - 2 * q^61 - 204 * q^63 + 244 * q^64 - 12 * q^65 - 508 * q^66 - 2 * q^67 - 144 * q^68 + 14 * q^69 + 96 * q^70 + 6 * q^72 + 246 * q^74 + 152 * q^75 - 158 * q^76 - 6 * q^77 + 304 * q^78 - 4 * q^79 - 8 * q^81 - 388 * q^82 - 726 * q^83 + 542 * q^84 + 48 * q^85 + 894 * q^86 + 22 * q^88 - 528 * q^90 - 204 * q^91 - 348 * q^92 + 62 * q^93 - 18 * q^94 - 12 * q^95 + 262 * q^96 - 4 * q^97 + 286 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.786053	+	1.83905i	−0.393026	+	0.919527i
$2$	−0.786053	+	1.83905i	−0.393026	+	0.919527i
$3$	1.51963	−	2.58664i	0.506544	−	0.862214i
$3$	1.51963	−	2.58664i	0.506544	−	0.862214i
$4$	−2.76424	−	2.89119i	−0.691061	−	0.722797i
$5$	1.99100	+	7.43050i	0.398199	+	1.48610i	0.816262	+	0.577682i	$0.196043\pi$
$5$	1.99100	+	7.43050i	0.398199	+	1.48610i	−0.418062	+	0.908418i	$0.637291\pi$
$6$	3.56247	+	4.82792i	0.593744	+	0.804654i
$7$	−1.50577	+	0.869355i	−0.215110	+	0.124194i	−0.603684	−	0.797224i	$-0.706301\pi$
$7$	−1.50577	+	0.869355i	−0.215110	+	0.124194i	0.388574	+	0.921417i	$0.372968\pi$
$8$	7.48989	−	2.81097i	0.936236	−	0.351371i
$9$	−4.38144	−	7.86149i	−0.486827	−	0.873499i
$10$	−15.2301	−	2.17922i	−1.52301	−	0.217922i
$11$	15.2997	+	4.09955i	1.39089	+	0.372687i	0.875063	−	0.484009i	$-0.160820\pi$
$11$	15.2997	+	4.09955i	1.39089	+	0.372687i	0.515822	+	0.856696i	$0.327486\pi$
$12$	−11.6791	+	2.75657i	−0.973258	+	0.229714i
$13$	5.73919	+	21.4190i	0.441476	+	1.64761i	0.725076	+	0.688669i	$0.241805\pi$
$13$	5.73919	+	21.4190i	0.441476	+	1.64761i	−0.283599	+	0.958943i	$0.591528\pi$
$14$	−0.415179	−	3.45255i	−0.0296556	−	0.246611i
$15$	22.2456	+	6.14163i	1.48304	+	0.409442i
$16$	−0.717932	+	15.9839i	−0.0448707	+	0.998993i
$17$			1.12960i			0.0664471i	0.999448	+	0.0332235i	$0.0105773\pi$
$17$			1.12960i			0.0664471i	−0.999448	+	0.0332235i	$0.989423\pi$
$18$	17.9017	−	1.87816i	0.994541	−	0.104342i
$19$	12.2501	−	12.2501i	0.644741	−	0.644741i	−0.306976	−	0.951717i	$-0.599317\pi$
$19$	12.2501	−	12.2501i	0.644741	−	0.644741i	0.951717	+	0.306976i	$0.0993171\pi$
$20$	15.9794	−	26.2961i	0.798969	−	1.31480i
$21$	−0.0395007	+	5.21598i	−0.00188099	+	0.248380i
$22$	−19.5657	+	24.9146i	−0.889350	+	1.13248i
$23$	−6.80266	+	11.7825i	−0.295768	+	0.512285i	−0.975163	−	0.221488i	$-0.928909\pi$
$23$	−6.80266	+	11.7825i	−0.295768	+	0.512285i	0.679395	+	0.733772i	$0.262242\pi$
$24$	4.11091	−	23.6453i	0.171288	−	0.985221i
$25$	−29.5977	+	17.0882i	−1.18391	+	0.683529i
$26$	−43.9019	−	6.28174i	−1.68854	−	0.241606i
$27$	−26.9930	−	0.613350i	−0.999742	−	0.0227167i
$28$	6.67578	+	1.95035i	0.238421	+	0.0696553i
$29$	0.249824	−	0.932358i	0.00861464	−	0.0321503i	−0.961485	−	0.274858i	$-0.911369\pi$
$29$	0.249824	−	0.932358i	0.00861464	−	0.0321503i	0.970099	+	0.242708i	$0.0780357\pi$
$30$	−28.7810	+	36.0833i	−0.959368	+	1.20278i
$31$	1.87100	−	3.24066i	0.0603547	−	0.104537i	−0.834269	−	0.551357i	$-0.814110\pi$
$31$	1.87100	−	3.24066i	0.0603547	−	0.104537i	0.894624	+	0.446820i	$0.147443\pi$
$32$	−28.8309	−	13.8845i	−0.900966	−	0.433890i
$33$	33.8540	−	33.3451i	1.02588	−	1.01046i
$34$	−2.07740	−	0.887925i	−0.0610999	−	0.0261154i
$35$	−9.45773	−	9.45773i	−0.270221	−	0.270221i
$36$	−10.6177	+	34.3986i	−0.294936	+	0.955517i
$37$	−35.9564	−	35.9564i	−0.971794	−	0.971794i	0.0278191	−	0.999613i	$-0.491144\pi$
$37$	−35.9564	−	35.9564i	−0.971794	−	0.971794i	−0.999613	+	0.0278191i	$0.991144\pi$
$38$	12.8994	+	32.1578i	0.339457	+	0.846258i
$39$	64.1247	+	17.7037i	1.64422	+	0.453941i
$40$	35.7992	+	50.0570i	0.894981	+	1.25143i
$41$	30.2406	−	52.3783i	0.737576	−	1.27752i	−0.216008	−	0.976392i	$-0.569304\pi$
$41$	30.2406	−	52.3783i	0.737576	−	1.27752i	0.953584	−	0.301127i	$-0.0973629\pi$
$42$	−9.56143	−	4.17268i	−0.227653	−	0.0993496i
$43$	4.42169	−	16.5020i	0.102830	−	0.383767i	−0.895260	−	0.445544i	$-0.853010\pi$
$43$	4.42169	−	16.5020i	0.102830	−	0.383767i	0.998090	+	0.0617772i	$0.0196768\pi$
$44$	−30.4396	−	55.5666i	−0.691809	−	1.26288i
$45$	49.6914	−	48.2085i	1.10425	−	1.07130i
$46$	−16.3215	−	21.7722i	−0.354815	−	0.473308i
$47$	11.2070	−	6.47034i	0.238446	−	0.137667i	−0.376016	−	0.926613i	$-0.622706\pi$
$47$	11.2070	−	6.47034i	0.238446	−	0.137667i	0.614462	+	0.788946i	$0.289373\pi$
$48$	40.2536	+	26.1467i	0.838617	+	0.544722i
$49$	−22.9884	+	39.8171i	−0.469152	+	0.812595i
$50$	−8.16084	−	67.8640i	−0.163217	−	1.35728i
$51$	2.92187	+	1.71658i	0.0572916	+	0.0336583i
$52$	46.0617	−	75.8003i	0.885802	−	1.45770i
$53$	38.2384	−	38.2384i	0.721479	−	0.721479i	−0.247427	−	0.968906i	$-0.579585\pi$
$53$	38.2384	−	38.2384i	0.721479	−	0.721479i	0.968906	+	0.247427i	$0.0795852\pi$
$54$	22.3459	−	49.1595i	0.413814	−	0.910362i
$55$			121.847i			2.21540i
$56$	−8.83431	+	10.7440i	−0.157756	+	0.191858i
$57$	−13.0710	−	50.3022i	−0.229315	−	0.882495i
$58$	1.51828	+	1.19232i	0.0261773	+	0.0205573i
$59$	5.85788	+	21.8619i	0.0992861	+	0.370541i	0.997634	−	0.0687430i	$-0.0218989\pi$
$59$	5.85788	+	21.8619i	0.0992861	+	0.370541i	−0.898348	+	0.439284i	$0.855232\pi$
$60$	−43.7357	−	81.2933i	−0.728929	−	1.35489i
$61$	−95.2073	−	25.5107i	−1.56078	−	0.418209i	−0.627867	−	0.778321i	$-0.716072\pi$
$61$	−95.2073	−	25.5107i	−1.56078	−	0.418209i	−0.932909	+	0.360112i	$0.882738\pi$
$62$	4.48905	+	5.98819i	0.0724040	+	0.0965837i
$63$	13.4319	+	8.02855i	0.213204	+	0.127437i
$64$	48.1969	−	42.1077i	0.753077	−	0.657932i
$65$	−147.727	+	85.2902i	−2.27272	+	1.31216i
$66$	34.7125	+	88.4705i	0.525946	+	1.34046i
$67$	−20.8577	−	77.8418i	−0.311308	−	1.16182i	−0.927378	−	0.374127i	$-0.877943\pi$
$67$	−20.8577	−	77.8418i	−0.311308	−	1.16182i	0.616069	−	0.787692i	$-0.288724\pi$
$68$	3.26589	−	3.12249i	0.0480277	−	0.0459189i
$69$	20.1397	+	35.5012i	0.291880	+	0.514510i
$70$	24.8276	−	9.95900i	0.354679	−	0.142271i
$71$	96.9917			1.36608			0.683040	−	0.730381i	$-0.260657\pi$
$71$	96.9917			1.36608			0.683040	+	0.730381i	$0.260657\pi$
$72$	−54.9149	−	46.5656i	−0.762707	−	0.646745i
$73$		−	19.4973i		−	0.267087i	−0.991043	−	0.133543i	$-0.957364\pi$
$73$		−	19.4973i		−	0.267087i	0.991043	−	0.133543i	$-0.0426355\pi$
$74$	94.3893	−	37.8621i	1.27553	−	0.511650i
$75$	−0.776435	+	102.526i	−0.0103525	+	1.36702i
$76$	−69.2795	−	1.55509i	−0.911573	−	0.0204618i
$77$	−26.6018	+	7.12794i	−0.345478	+	0.0925706i
$78$	−82.9634	+	104.013i	−1.06363	+	1.33350i
$79$	−60.9180	−	105.513i	−0.771114	−	1.33561i	−0.936953	−	0.349456i	$-0.886366\pi$
$79$	−60.9180	−	105.513i	−0.771114	−	1.33561i	0.165838	−	0.986153i	$-0.446967\pi$
$80$	−120.198	+	26.4893i	−1.50247	+	0.331116i
$81$	−42.6060	+	68.8893i	−0.526000	+	0.850485i
$82$	72.5558	+	96.7862i	0.884826	+	1.18032i
$83$	−21.7550	+	81.1908i	−0.262109	+	0.978202i	0.701888	+	0.712287i	$0.252341\pi$
$83$	−21.7550	+	81.1908i	−0.262109	+	0.978202i	−0.963996	+	0.265915i	$0.914326\pi$
$84$	15.1896	−	14.3040i	0.180828	−	0.170286i
$85$	−8.39350	+	2.24903i	−0.0987470	+	0.0264592i
$86$	26.8724	+	21.1032i	0.312469	+	0.245386i
$87$	−2.03203	−	2.06305i	−0.0233567	−	0.0237132i
$88$	126.117	−	12.3018i	1.43315	−	0.139794i
$89$	−62.3081			−0.700091			−0.350045	−	0.936733i	$-0.613834\pi$
$89$	−62.3081			−0.700091			−0.350045	+	0.936733i	$0.613834\pi$
$90$	49.5980	+	129.280i	0.551089	+	1.43644i
$91$	−27.2626	−	27.2626i	−0.299589	−	0.299589i
$92$	52.8698	−	12.9021i	0.574671	−	0.140240i
$93$	−5.53920	−	9.76420i	−0.0595613	−	0.104991i
$94$	3.09005	+	25.6962i	0.0328728	+	0.273364i
$95$	115.414	+	66.6344i	1.21489	+	0.701415i
$96$	−79.7266	+	53.4759i	−0.830485	+	0.557041i
$97$	63.8929	+	110.666i	0.658690	+	1.14088i	0.980955	+	0.194235i	$0.0622224\pi$
$97$	63.8929	+	110.666i	0.658690	+	1.14088i	−0.322265	+	0.946649i	$0.604444\pi$
$98$	−55.1558	−	73.5754i	−0.562814	−	0.750769i
$99$	−34.8063	−	138.241i	−0.351579	−	1.39637i
$100$	131.220	+	38.3364i	1.31220	+	0.383364i
$101$	11.5405	+	3.09227i	0.114263	+	0.0306166i	0.315497	−	0.948926i	$-0.397829\pi$
$101$	11.5405	+	3.09227i	0.114263	+	0.0306166i	−0.201235	+	0.979543i	$0.564495\pi$
$102$	−5.45362	+	4.02416i	−0.0534669	+	0.0394526i
$103$	42.5462	+	24.5640i	0.413069	+	0.238486i	0.692108	−	0.721794i	$-0.256682\pi$
$103$	42.5462	+	24.5640i	0.413069	+	0.238486i	−0.279038	+	0.960280i	$0.590016\pi$
$104$	103.194	+	144.293i	0.992249	+	1.38743i
$105$	−38.8360	+	10.0915i	−0.369867	+	0.0961095i
$106$	40.2651	+	100.380i	0.379859	+	0.946980i
$107$	−30.8837	+	30.8837i	−0.288633	+	0.288633i	−0.836540	−	0.547906i	$-0.815425\pi$
$107$	−30.8837	+	30.8837i	−0.288633	+	0.288633i	0.547906	+	0.836540i	$0.315425\pi$
$108$	72.8420	+	79.7374i	0.674463	+	0.738309i
$109$	86.7267	−	86.7267i	0.795658	−	0.795658i	−0.186750	−	0.982408i	$-0.559795\pi$
$109$	86.7267	−	86.7267i	0.795658	−	0.795658i	0.982408	+	0.186750i	$0.0597954\pi$
$110$	−224.083	−	95.7781i	−2.03712	−	0.870710i
$111$	−147.647	+	38.3658i	−1.33015	+	0.345638i
$112$	−12.8146	−	24.6922i	−0.114416	−	0.220466i
$113$	−124.345	−	71.7904i	−1.10040	−	0.635314i	−0.164071	−	0.986449i	$-0.552462\pi$
$113$	−124.345	−	71.7904i	−1.10040	−	0.635314i	−0.936325	+	0.351135i	$0.885796\pi$
$114$	102.783	+	15.5020i	0.901605	+	0.135982i
$115$	−101.094	−	27.0882i	−0.879081	−	0.235549i
$116$	−3.38620	+	1.85497i	−0.0291913	+	0.0159911i
$117$	143.239	−	138.964i	1.22426	−	1.18773i
$118$	−44.8099	−	6.41166i	−0.379745	−	0.0543361i
$119$	−0.982024	−	1.70092i	−0.00825230	−	0.0142934i
$120$	183.881	−	16.5316i	1.53234	−	0.137763i
$121$	112.487	+	64.9442i	0.929641	+	0.536729i
$122$	121.754	−	155.039i	0.997980	−	1.27081i
$123$	−89.5293	−	157.817i	−0.727880	−	1.28307i
$124$	−14.5412	+	3.54857i	−0.117268	+	0.0286175i
$125$	−49.9154	−	49.9154i	−0.399323	−	0.399323i
$126$	−25.3231	+	18.3911i	−0.200977	+	0.145961i
$127$	−160.336			−1.26249			−0.631246	−	0.775583i	$-0.717456\pi$
$127$	−160.336			−1.26249			−0.631246	+	0.775583i	$0.717456\pi$
$128$	39.5529	+	121.736i	0.309007	+	0.951060i
$129$	−35.9654	−	36.5143i	−0.278801	−	0.283056i
$130$	−40.7321	−	338.720i	−0.313324	−	2.60554i
$131$	136.866	−	36.6731i	1.04478	−	0.279947i	0.304686	−	0.952453i	$-0.401449\pi$
$131$	136.866	−	36.6731i	1.04478	−	0.279947i	0.740092	+	0.672506i	$0.234782\pi$
$132$	−189.988	−	5.70435i	−1.43930	−	0.0432147i
$133$	−7.79611	+	29.0955i	−0.0586174	+	0.218763i
$134$	159.551	+	22.8294i	1.19068	+	0.170369i
$135$	−49.1856	−	201.793i	−0.364337	−	1.49476i
$136$	3.17527	+	8.46058i	0.0233475	+	0.0622102i
$137$	111.875	+	193.773i	0.816606	+	1.41440i	0.908169	+	0.418603i	$0.137480\pi$
$137$	111.875	+	193.773i	0.816606	+	1.41440i	−0.0915637	+	0.995799i	$0.529187\pi$
$138$	−81.1195	+	9.13222i	−0.587822	+	0.0661755i
$139$	119.668	−	32.0649i	0.860920	−	0.230683i	0.198763	−	0.980048i	$-0.436308\pi$
$139$	119.668	−	32.0649i	0.860920	−	0.230683i	0.662157	+	0.749365i	$0.269641\pi$
$140$	−1.20062	+	53.4875i	−0.00857584	+	0.382054i
$141$	0.293992	−	38.8209i	0.00208505	−	0.275326i
$142$	−76.2406	+	178.373i	−0.536906	+	1.25615i
$143$			351.233i			2.45617i
$144$	128.803	−	64.3884i	0.894463	−	0.447142i
$145$	7.42529			0.0512089
$146$	35.8566	+	15.3259i	0.245593	+	0.104972i
$147$	68.0588	+	119.970i	0.462985	+	0.816124i
$148$	−4.56450	+	203.349i	−0.0308412	+	1.37398i
$149$	25.1133	+	93.7241i	0.168546	+	0.629021i	0.997561	+	0.0697956i	$0.0222347\pi$
$149$	25.1133	+	93.7241i	0.168546	+	0.629021i	−0.829016	+	0.559225i	$0.811099\pi$
$150$	−187.941	−	82.0191i	−1.25294	−	0.546794i
$151$	−29.7196	+	17.1586i	−0.196818	+	0.113633i	−0.595171	−	0.803599i	$-0.702916\pi$
$151$	−29.7196	+	17.1586i	−0.196818	+	0.113633i	0.398352	+	0.917233i	$0.369582\pi$
$152$	57.3173	−	126.186i	0.377087	−	0.830174i
$153$	8.88034	−	4.94927i	0.0580414	−	0.0323482i
$154$	7.80177	−	54.5251i	0.0506609	−	0.354059i
$155$	27.8049	+	7.45029i	0.179386	+	0.0480664i
$156$	−126.071	−	234.334i	−0.808150	−	1.50214i
$157$	−7.06398	−	26.3631i	−0.0449935	−	0.167918i	0.939773	−	0.341798i	$-0.111036\pi$
$157$	−7.06398	−	26.3631i	−0.0449935	−	0.167918i	−0.984767	+	0.173881i	$0.944369\pi$
$158$	241.929	−	29.0927i	1.53120	−	0.184131i
$159$	−40.8008	−	157.017i	−0.256609	−	0.987530i
$160$	45.7665	−	241.872i	0.286041	−	1.51170i
$161$		−	23.6557i		−	0.146930i
$162$	−93.2005	−	132.505i	−0.575312	−	0.817934i
$163$	164.334	−	164.334i	1.00818	−	1.00818i	0.00821510	−	0.999966i	$-0.497385\pi$
$163$	164.334	−	164.334i	1.00818	−	1.00818i	0.999966	−	0.00821510i	$-0.00261498\pi$
$164$	−235.028	+	57.3549i	−1.43310	+	0.349725i
$165$	315.175	+	185.162i	1.91015	+	1.12220i
$166$	−132.214	−	103.829i	−0.796468	−	0.625475i
$167$	11.4120	−	19.7661i	0.0683353	−	0.118360i	−0.829833	−	0.558011i	$-0.811565\pi$
$167$	11.4120	−	19.7661i	0.0683353	−	0.118360i	0.898169	+	0.439651i	$0.144898\pi$
$168$	14.3661	+	39.1782i	0.0855125	+	0.233203i
$169$	−279.475	+	161.355i	−1.65370	+	0.954764i
$170$	2.46164	−	17.2040i	0.0144802	−	0.101200i
$171$	−149.977	−	42.6309i	−0.877058	−	0.249304i
$172$	−59.9330	+	32.8315i	−0.348448	+	0.190881i
$173$	−30.1316	+	112.453i	−0.174171	+	0.650015i	0.822520	+	0.568736i	$0.192567\pi$
$173$	−30.1316	+	112.453i	−0.174171	+	0.650015i	−0.996691	+	0.0812794i	$0.974099\pi$
$174$	5.39134	−	2.11536i	0.0309847	−	0.0121572i
$175$	29.7115	−	51.4618i	0.169780	−	0.294067i
$176$	−76.5109	+	241.606i	−0.434721	+	1.37276i
$177$	65.4508	+	18.0698i	0.369778	+	0.102089i
$178$	48.9774	−	114.588i	0.275154	−	0.643752i
$179$	−220.010	−	220.010i	−1.22911	−	1.22911i	−0.964302	−	0.264804i	$-0.914693\pi$
$179$	−220.010	−	220.010i	−1.22911	−	1.22911i	−0.264804	−	0.964302i	$-0.585307\pi$
$180$	−276.739	−	10.4071i	−1.53744	−	0.0578175i
$181$	27.4309	+	27.4309i	0.151552	+	0.151552i	0.778811	−	0.627259i	$-0.215823\pi$
$181$	27.4309	+	27.4309i	0.151552	+	0.151552i	−0.627259	+	0.778811i	$0.715823\pi$
$182$	71.5672	−	28.7075i	0.393226	−	0.157734i
$183$	−210.667	+	207.500i	−1.15119	+	1.13388i
$184$	−17.8308	+	107.372i	−0.0969067	+	0.583544i
$185$	195.585	−	338.763i	1.05722	−	1.83115i
$186$	22.3110	−	2.51171i	0.119952	−	0.0135038i
$187$	−4.63085	+	17.2826i	−0.0247639	+	0.0924202i
$188$	−49.6857	−	14.5158i	−0.264286	−	0.0772118i
$189$	41.1785	−	22.5430i	0.217875	−	0.119275i
$190$	−213.266	+	159.875i	−1.12245	+	0.841447i
$191$	189.546	−	109.435i	0.992390	−	0.572957i	0.0864021	−	0.996260i	$-0.472463\pi$
$191$	189.546	−	109.435i	0.992390	−	0.572957i	0.905988	+	0.423304i	$0.139130\pi$
$192$	−35.6758	−	188.656i	−0.185812	−	0.982585i
$193$	−16.5153	+	28.6054i	−0.0855716	+	0.148214i	−0.905635	−	0.424059i	$-0.860605\pi$
$193$	−16.5153	+	28.6054i	−0.0855716	+	0.148214i	0.820063	+	0.572273i	$0.193938\pi$
$194$	−253.744	+	30.5134i	−1.30796	+	0.157286i
$195$	−3.87531	+	511.726i	−0.0198734	+	2.62424i
$196$	178.664	−	43.6003i	0.911553	−	0.222451i
$197$	−73.3903	+	73.3903i	−0.372540	+	0.372540i	−0.868402	−	0.495862i	$-0.834852\pi$
$197$	−73.3903	+	73.3903i	−0.372540	+	0.372540i	0.495862	+	0.868402i	$0.334852\pi$
$198$	281.592	+	44.6538i	1.42218	+	0.225524i
$199$		−	304.640i		−	1.53085i	−0.643523	−	0.765427i	$-0.722528\pi$
$199$		−	304.640i		−	1.53085i	0.643523	−	0.765427i	$-0.277472\pi$
$200$	−173.649	+	211.187i	−0.868245	+	1.05594i
$201$	−233.045	−	64.3396i	−1.15943	−	0.320098i
$202$	−14.7583	+	18.7930i	−0.0730610	+	0.0930345i
$203$	0.434373	+	1.62110i	0.00213977	+	0.00798572i
$204$	−3.11382	−	13.1927i	−0.0152638	−	0.0646701i
$205$	449.406	+	120.418i	2.19222	+	0.587405i
$206$	−78.6181	+	58.9361i	−0.381641	+	0.286097i
$207$	122.434	+	1.85449i	0.591468	+	0.00895891i
$208$	−346.479	+	76.3572i	−1.66576	+	0.367102i
$209$	237.643	−	137.203i	1.13705	−	0.656475i
$210$	11.9684	−	79.3540i	0.0569922	−	0.377876i
$211$	−51.1274	−	190.810i	−0.242310	−	0.904314i	−0.974716	−	0.223446i	$-0.928269\pi$
$211$	−51.1274	−	190.810i	−0.242310	−	0.904314i	0.732406	−	0.680868i	$-0.238397\pi$
$212$	−216.255	−	4.85419i	−1.02007	−	0.0228971i
$213$	147.392	−	250.883i	0.691980	−	1.17785i
$214$	−32.5206	−	81.0731i	−0.151966	−	0.378846i
$215$	131.422			0.611263
$216$	−203.899	+	71.2826i	−0.943977	+	0.330012i
$217$			6.50624i			0.0299827i
$218$	91.3234	+	227.667i	0.418914	+	1.04434i
$219$	−50.4326	−	29.6288i	−0.230286	−	0.135291i
$220$	352.282	−	336.814i	1.60128	−	1.53097i
$221$	−24.1949	+	6.48299i	−0.109479	+	0.0293348i
$222$	45.5013	−	301.688i	0.204961	−	1.35895i
$223$	47.3041	+	81.9332i	0.212126	+	0.367413i	0.952380	−	0.304914i	$-0.0986279\pi$
$223$	47.3041	+	81.9332i	0.212126	+	0.367413i	−0.740254	+	0.672328i	$0.765295\pi$
$224$	55.4832	−	4.15748i	0.247693	−	0.0185602i
$225$	264.019	+	157.811i	1.17342	+	0.701381i
$226$	229.768	−	172.246i	1.01667	−	0.762148i
$227$	84.1564	−	314.076i	0.370733	−	1.38359i	−0.488747	−	0.872425i	$-0.662546\pi$
$227$	84.1564	−	314.076i	0.370733	−	1.38359i	0.859480	−	0.511169i	$-0.170787\pi$
$228$	−109.302	+	176.838i	−0.479394	+	0.775606i
$229$	−97.5906	+	26.1493i	−0.426160	+	0.114189i	−0.465523	−	0.885036i	$-0.654134\pi$
$229$	−97.5906	+	26.1493i	−0.426160	+	0.114189i	0.0393631	+	0.999225i	$0.487467\pi$
$230$	129.282	−	164.625i	0.562096	−	0.715762i
$231$	−21.9875	+	79.6412i	−0.0951842	+	0.344767i
$232$	−0.749667	−	7.68550i	−0.00323132	−	0.0331272i
$233$	61.4767			0.263848			0.131924	−	0.991260i	$-0.457884\pi$
$233$	61.4767			0.263848			0.131924	+	0.991260i	$0.457884\pi$
$234$	142.970	+	372.658i	0.610982	+	1.59255i
$235$	70.3909	+	70.3909i	0.299536	+	0.299536i
$236$	47.0143	−	77.3679i	0.199213	−	0.327830i
$237$	−365.498	−	2.76792i	−1.54218	−	0.0116790i
$238$	3.90000	−	0.468986i	0.0163865	−	0.00197053i
$239$	−158.478	−	91.4971i	−0.663087	−	0.382833i	0.130365	−	0.991466i	$-0.458385\pi$
$239$	−158.478	−	91.4971i	−0.663087	−	0.382833i	−0.793452	+	0.608633i	$0.791718\pi$
$240$	−114.138	+	351.162i	−0.475575	+	1.46318i
$241$	−8.63160	−	14.9504i	−0.0358158	−	0.0620347i	0.847562	−	0.530697i	$-0.178070\pi$
$241$	−8.63160	−	14.9504i	−0.0358158	−	0.0620347i	−0.883378	+	0.468662i	$0.844736\pi$
$242$	−207.856	+	155.819i	−0.858910	+	0.643882i
$243$	113.446	+	214.893i	0.466858	+	0.884332i
$244$	189.420	+	345.780i	0.776311	+	1.41713i
$245$	−341.631	−	91.5399i	−1.39441	−	0.373632i
$246$	360.609	−	40.5965i	1.46589	−	0.165026i
$247$	332.690	+	192.079i	1.34692	+	0.777646i
$248$	4.90417	−	29.5315i	0.0197749	−	0.119079i
$249$	176.952	+	179.653i	0.710651	+	0.721496i
$250$	131.033	−	52.5610i	0.524133	−	0.210244i
$251$	−53.7711	+	53.7711i	−0.214227	+	0.214227i	−0.806061	−	0.591833i	$-0.798404\pi$
$251$	−53.7711	+	53.7711i	−0.214227	+	0.214227i	0.591833	+	0.806061i	$0.298404\pi$
$252$	−13.9169	−	61.0269i	−0.0552257	−	0.242170i
$253$	−152.382	+	152.382i	−0.602301	+	0.602301i
$254$	126.033	−	294.868i	0.496193	−	1.16090i
$255$	−6.93758	+	25.1287i	−0.0272062	+	0.0985438i
$256$	−254.969	−	22.9507i	−0.995973	−	0.0896511i
$257$	−1.99425	−	1.15138i	−0.00775972	−	0.00448008i	0.496115	−	0.868257i	$-0.334759\pi$
$257$	−1.99425	−	1.15138i	−0.00775972	−	0.00448008i	−0.503875	+	0.863777i	$0.668093\pi$
$258$	95.4224	−	37.4402i	0.369854	−	0.145117i
$259$	85.4008	+	22.8831i	0.329733	+	0.0883517i
$260$	654.943	+	191.344i	2.51901	+	0.735937i
$261$	−8.42431	+	2.12108i	−0.0322770	+	0.00812673i
$262$	−40.1400	+	280.531i	−0.153206	+	1.07073i
$263$	−11.0389	−	19.1199i	−0.0419730	−	0.0726994i	0.844276	−	0.535909i	$-0.180031\pi$
$263$	−11.0389	−	19.1199i	−0.0419730	−	0.0726994i	−0.886249	+	0.463210i	$0.846698\pi$
$264$	159.831	−	344.914i	0.605421	−	1.30649i
$265$	360.263	+	207.998i	1.35948	+	0.784898i
$266$	−47.3800	−	37.2080i	−0.178120	−	0.139880i
$267$	−94.6853	+	161.169i	−0.354627	+	0.603628i
$268$	−167.400	+	275.477i	−0.624626	+	1.02790i
$269$	−233.470	−	233.470i	−0.867918	−	0.867918i	0.124324	−	0.992242i	$-0.460324\pi$
$269$	−233.470	−	233.470i	−0.867918	−	0.867918i	−0.992242	+	0.124324i	$0.960324\pi$
$270$	409.771	+	68.1650i	1.51767	+	0.252463i
$271$	−205.475			−0.758209			−0.379104	−	0.925354i	$-0.623768\pi$
$271$	−205.475			−0.758209			−0.379104	+	0.925354i	$0.623768\pi$
$272$	−18.0554	−	0.810976i	−0.0663801	−	0.00298153i
$273$	−111.948	+	29.0895i	−0.410065	+	0.106555i
$274$	−444.299	+	53.4282i	−1.62153	+	0.194994i
$275$	−522.891	+	140.108i	−1.90142	+	0.509484i
$276$	46.9695	−	156.362i	0.170180	−	0.566527i
$277$	−42.7341	+	159.486i	−0.154275	+	0.575761i	0.844892	+	0.534937i	$0.179665\pi$
$277$	−42.7341	+	159.486i	−0.154275	+	0.575761i	−0.999166	+	0.0408235i	$0.987002\pi$
$278$	−35.0961	+	245.280i	−0.126245	+	0.882304i
$279$	−33.6741	−	0.510058i	−0.120696	−	0.00182816i
$280$	−97.4227	−	44.2520i	−0.347938	−	0.158043i
$281$	−80.3152	−	139.110i	−0.285819	−	0.495054i	0.686988	−	0.726669i	$-0.258932\pi$
$281$	−80.3152	−	139.110i	−0.285819	−	0.495054i	−0.972808	+	0.231615i	$0.925599\pi$
$282$	71.1627	+	31.0560i	0.252350	+	0.110127i
$283$	−126.634	+	33.9316i	−0.447471	+	0.119900i	−0.475516	−	0.879707i	$-0.657739\pi$
$283$	−126.634	+	33.9316i	−0.447471	+	0.119900i	0.0280447	+	0.999607i	$0.491072\pi$
$284$	−268.109	−	280.421i	−0.944044	−	0.987399i
$285$	347.747	−	197.276i	1.22016	−	0.692195i
$286$	−645.936	−	276.087i	−2.25852	−	0.965340i
$287$			105.159i			0.366409i
$288$	17.1681	+	287.488i	0.0596113	+	0.998222i
$289$	287.724			0.995585
$290$	−5.83667	+	13.6555i	−0.0201264	+	0.0470879i
$291$	383.346	+	2.90309i	1.31734	+	0.00997626i
$292$	−56.3704	+	53.8953i	−0.193049	+	0.184573i
$293$	107.565	+	401.438i	0.367116	+	1.37010i	0.864529	+	0.502583i	$0.167617\pi$
$293$	107.565	+	401.438i	0.367116	+	1.37010i	−0.497413	+	0.867514i	$0.665717\pi$
$294$	−274.130	+	30.8608i	−0.932414	+	0.104969i
$295$	−150.782	+	87.0540i	−0.511125	+	0.295098i
$296$	−370.381	−	168.237i	−1.25129	−	0.568369i
$297$	−410.472	−	120.043i	−1.38206	−	0.404187i
$298$	−192.104	−	27.4874i	−0.644645	−	0.0922395i
$299$	−291.412	−	78.0835i	−0.974621	−	0.261149i
$300$	298.569	−	281.163i	0.995231	−	0.937210i
$301$	7.68805	+	28.6922i	0.0255417	+	0.0953229i
$302$	−8.19445	−	68.1435i	−0.0271340	−	0.225641i
$303$	25.5360	−	25.1521i	0.0842771	−	0.0830102i
$304$	187.009	+	204.599i	0.615162	+	0.673022i
$305$		−	758.230i		−	2.48600i
$306$	2.12157	+	20.2218i	0.00693323	+	0.0660843i
$307$	102.995	−	102.995i	0.335488	−	0.335488i	−0.519178	−	0.854666i	$-0.673762\pi$
$307$	102.995	−	102.995i	0.335488	−	0.335488i	0.854666	+	0.519178i	$0.173762\pi$
$308$	94.1421	+	57.2075i	0.305656	+	0.185739i
$309$	128.193	−	72.7234i	0.414864	−	0.235351i
$310$	−35.5576	+	45.2784i	−0.114702	+	0.146059i
$311$	−66.9346	+	115.934i	−0.215224	+	0.372778i	−0.953342	−	0.301893i	$-0.902381\pi$
$311$	−66.9346	+	115.934i	−0.215224	+	0.372778i	0.738118	+	0.674672i	$0.235715\pi$
$312$	530.051	−	47.6535i	1.69888	−	0.152735i
$313$	237.334	−	137.025i	0.758257	−	0.437780i	−0.0704129	−	0.997518i	$-0.522432\pi$
$313$	237.334	−	137.025i	0.758257	−	0.437780i	0.828669	+	0.559738i	$0.189098\pi$
$314$	54.0359	+	7.73176i	0.172089	+	0.0246235i
$315$	−32.9134	+	115.790i	−0.104487	+	0.367588i
$316$	−136.666	+	467.789i	−0.432488	+	1.48035i
$317$	−93.1714	+	347.720i	−0.293916	+	1.09691i	0.648158	+	0.761506i	$0.275539\pi$
$317$	−93.1714	+	347.720i	−0.293916	+	1.09691i	−0.942074	+	0.335404i	$0.891127\pi$
$318$	320.835	+	48.3891i	1.00891	+	0.152167i
$319$	7.64450	−	13.2407i	0.0239639	−	0.0415068i
$320$	408.841	+	274.291i	1.27763	+	0.857161i
$321$	32.9533	+	126.817i	0.102658	+	0.395069i
$322$	43.5041	+	18.5946i	0.135106	+	0.0577473i
$323$	13.8377	+	13.8377i	0.0428412	+	0.0428412i
$324$	316.945	−	67.2447i	0.978225	−	0.207545i
$325$	−535.879	−	535.879i	−1.64886	−	1.64886i
$326$	173.044	+	431.393i	0.530808	+	1.32329i
$327$	−92.5383	−	356.124i	−0.282992	−	1.08906i
$328$	79.2654	−	477.313i	0.241663	−	1.45522i
$329$	−11.2500	+	19.4857i	−0.0341947	+	0.0592269i
$330$	−588.268	+	434.076i	−1.78263	+	1.31538i
$331$	68.9272	−	257.240i	0.208239	−	0.777160i	−0.780198	−	0.625532i	$-0.784882\pi$
$331$	68.9272	−	257.240i	0.208239	−	0.777160i	0.988438	−	0.151628i	$-0.0484514\pi$
$332$	294.874	−	161.533i	0.888175	−	0.486546i
$333$	−125.130	+	440.211i	−0.375766	+	1.32196i
$334$	27.3806	+	36.5245i	0.0819778	+	0.109355i
$335$	536.877	−	309.966i	1.60262	−	0.925271i
$336$	−83.3433	−	4.37610i	−0.248046	−	0.0130241i
$337$	−55.4620	+	96.0630i	−0.164576	+	0.285053i	−0.936504	−	0.350656i	$-0.885959\pi$
$337$	−55.4620	+	96.0630i	−0.164576	+	0.285053i	0.771929	+	0.635709i	$0.219292\pi$
$338$	−77.0585	−	640.804i	−0.227984	−	1.89587i
$339$	−374.654	+	212.540i	−1.10517	+	0.626962i
$340$	29.7040	+	18.0503i	0.0873648	+	0.0530891i
$341$	41.9110	−	41.9110i	0.122906	−	0.122906i
$342$	196.290	−	242.306i	0.573948	−	0.708496i
$343$		−	165.137i		−	0.481450i
$344$	−13.2685	−	136.027i	−0.0385712	−	0.395428i
$345$	−223.694	+	220.331i	−0.648387	+	0.638640i
$346$	−183.121	−	143.807i	−0.529253	−	0.415628i
$347$	7.11585	+	26.5567i	0.0205068	+	0.0765323i	0.975421	−	0.220350i	$-0.0707199\pi$
$347$	7.11585	+	26.5567i	0.0205068	+	0.0765323i	−0.954914	+	0.296882i	$0.904053\pi$
$348$	−0.347620	+	11.5778i	−0.000998907	+	0.0332694i
$349$	−69.9110	−	18.7326i	−0.200318	−	0.0536750i	0.157265	−	0.987556i	$-0.449732\pi$
$349$	−69.9110	−	18.7326i	−0.200318	−	0.0536750i	−0.357583	+	0.933881i	$0.616399\pi$
$350$	71.2863	+	95.0927i	0.203675	+	0.271694i
$351$	−141.781	−	581.683i	−0.403934	−	1.65722i
$352$	−384.185	−	330.623i	−1.09143	−	0.939270i
$353$	−111.275	+	64.2444i	−0.315225	+	0.181995i	−0.649262	−	0.760565i	$-0.724922\pi$
$353$	−111.275	+	64.2444i	−0.315225	+	0.181995i	0.334037	+	0.942560i	$0.391589\pi$
$354$	−84.6791	+	106.164i	−0.239207	+	0.299898i
$355$	193.110	+	720.697i	0.543972	+	2.03013i
$356$	172.235	+	180.144i	0.483805	+	0.506023i
$357$	−5.89197	−	0.0446200i	−0.0165041	−	0.000124986i
$358$	577.550	−	231.671i	1.61327	−	0.647125i
$359$	4.76387			0.0132698			0.00663492	−	0.999978i	$-0.497888\pi$
$359$	4.76387			0.0132698			0.00663492	+	0.999978i	$0.497888\pi$
$360$	236.671	−	500.757i	0.657418	−	1.39099i
$361$			60.8707i			0.168617i
$362$	−72.0090	+	28.8848i	−0.198920	+	0.0797922i
$363$	338.925	−	192.271i	0.933679	−	0.529673i
$364$	−3.46086	+	154.182i	−0.00950787	+	0.423576i
$365$	144.875	−	38.8191i	0.396918	−	0.106354i
$366$	−216.009	−	550.535i	−0.590189	−	1.50419i
$367$	73.5089	+	127.321i	0.200297	+	0.346924i	0.948624	−	0.316406i	$-0.102476\pi$
$367$	73.5089	+	127.321i	0.200297	+	0.346924i	−0.748327	+	0.663330i	$0.769143\pi$
$368$	−183.447	−	117.192i	−0.498497	−	0.318456i
$369$	−544.268	−	8.24399i	−1.47498	−	0.0223414i
$370$	469.264	+	625.977i	1.26828	+	1.69183i
$371$	−24.3354	+	90.8209i	−0.0655940	+	0.244800i
$372$	−12.9184	+	43.0055i	−0.0347270	+	0.115606i
$373$	−621.849	+	166.624i	−1.66716	+	0.446713i	−0.964342	−	0.264660i	$-0.914740\pi$
$373$	−621.849	+	166.624i	−1.66716	+	0.446713i	−0.702815	+	0.711373i	$0.748074\pi$
$374$	−28.1435	−	22.1014i	−0.0752500	−	0.0590947i
$375$	−204.966	+	53.2602i	−0.546577	+	0.142027i
$376$	65.7510	−	79.9645i	0.174870	−	0.212672i
$377$	21.4039			0.0567743
$378$	9.08932	+	93.4494i	0.0240458	+	0.247221i
$379$	242.354	+	242.354i	0.639457	+	0.639457i	0.950422	−	0.310964i	$-0.100652\pi$
$379$	242.354	+	242.354i	0.639457	+	0.639457i	−0.310964	+	0.950422i	$0.600652\pi$
$380$	−126.380	−	517.878i	−0.332579	−	1.36284i
$381$	−243.652	+	414.733i	−0.639508	+	1.08854i
$382$	52.2628	+	434.608i	0.136814	+	1.13772i
$383$	183.167	+	105.751i	0.478242	+	0.276113i	0.719683	−	0.694302i	$-0.244287\pi$
$383$	183.167	+	105.751i	0.478242	+	0.276113i	−0.241442	+	0.970415i	$0.577620\pi$
$384$	374.992	+	82.6841i	0.976543	+	0.215323i
$385$	−105.928	−	183.473i	−0.275138	−	0.476554i
$386$	−39.6249	−	52.8579i	−0.102655	−	0.136938i
$387$	−149.104	+	37.5414i	−0.385280	+	0.0970061i
$388$	143.340	−	490.633i	0.369433	−	1.26452i
$389$	−243.202	−	65.1659i	−0.625199	−	0.167522i	−0.0677088	−	0.997705i	$-0.521569\pi$
$389$	−243.202	−	65.1659i	−0.625199	−	0.167522i	−0.557490	+	0.830184i	$0.688236\pi$
$390$	−938.047	−	409.371i	−2.40525	−	1.04967i
$391$	−13.3096	−	7.68428i	−0.0340398	−	0.0196529i
$392$	−60.2563	+	362.846i	−0.153715	+	0.925627i
$393$	113.126	−	409.753i	0.287851	−	1.04263i
$394$	−77.2802	−	192.658i	−0.196143	−	0.488978i
$395$	662.728	−	662.728i	1.67779	−	1.67779i
$396$	−303.467	+	482.762i	−0.766330	+	1.21910i
$397$	57.9316	−	57.9316i	0.145923	−	0.145923i	−0.630371	−	0.776294i	$-0.717097\pi$
$397$	57.9316	−	57.9316i	0.145923	−	0.145923i	0.776294	+	0.630371i	$0.217097\pi$
$398$	560.249	+	239.463i	1.40766	+	0.601666i
$399$	63.4124	+	64.3801i	0.158928	+	0.161354i
$400$	−251.887	−	485.354i	−0.629718	−	1.21339i
$401$	−243.809	−	140.763i	−0.608002	−	0.351030i	0.164181	−	0.986430i	$-0.447502\pi$
$401$	−243.809	−	140.763i	−0.608002	−	0.351030i	−0.772183	+	0.635400i	$0.780835\pi$
$402$	301.510	−	378.008i	0.750024	−	0.940318i
$403$	80.1495	+	21.4760i	0.198882	+	0.0532903i
$404$	−22.9605	−	41.9136i	−0.0568328	−	0.103747i
$405$	−596.710	−	179.426i	−1.47336	−	0.443026i
$406$	−3.32273	−	0.475436i	−0.00818407	−	0.00117102i
$407$	−402.718	−	697.528i	−0.989479	−	1.71383i
$408$	26.7097	+	4.64369i	0.0654650	+	0.0113816i
$409$	45.6115	+	26.3338i	0.111519	+	0.0643858i	0.554722	−	0.832036i	$-0.312825\pi$
$409$	45.6115	+	26.3338i	0.111519	+	0.0643858i	−0.443203	+	0.896421i	$0.646158\pi$
$410$	−574.712	+	731.827i	−1.40174	+	1.78494i
$411$	671.231	+	5.08324i	1.63316	+	0.0123680i
$412$	−46.5886	−	190.910i	−0.113079	−	0.463373i
$413$	−27.8264	−	27.8264i	−0.0673762	−	0.0673762i
$414$	−99.6499	+	223.705i	−0.240700	+	0.540350i
$415$	−646.603			−1.55808
$416$	131.925	−	697.214i	0.317128	−	1.67599i
$417$	98.9106	−	358.265i	0.237196	−	0.859148i
$418$	65.5243	+	544.887i	0.156757	+	1.30356i
$419$	−491.103	+	131.591i	−1.17208	+	0.314059i	−0.791782	−	0.610803i	$-0.790847\pi$
$419$	−491.103	+	131.591i	−1.17208	+	0.314059i	−0.380302	+	0.924862i	$0.624180\pi$
$420$	136.529	+	84.3869i	0.325068	+	0.200921i
$421$	159.121	−	593.849i	0.377961	−	1.41057i	−0.471010	−	0.882128i	$-0.656110\pi$
$421$	159.121	−	593.849i	0.377961	−	1.41057i	0.848971	−	0.528440i	$-0.177223\pi$
$422$	391.099	+	55.9607i	0.926775	+	0.132608i
$423$	−99.9691	−	59.7539i	−0.236333	−	0.141262i
$424$	178.915	−	393.888i	0.421968	−	0.928982i
$425$	−19.3029	−	33.4335i	−0.0454185	−	0.0786671i
$426$	345.530	+	468.268i	0.811102	+	1.09922i
$427$	165.538	−	44.3558i	0.387677	−	0.103878i
$428$	174.661	+	3.92055i	0.408086	+	0.00916017i
$429$	908.513	+	533.744i	2.11775	+	1.24416i
$430$	−103.304	+	241.692i	−0.240243	+	0.562073i
$431$			501.480i			1.16353i	0.813358	+	0.581763i	$0.197637\pi$
$431$			501.480i			1.16353i	−0.813358	+	0.581763i	$0.802363\pi$
$432$	29.1829	−	431.013i	0.0675530	−	0.997716i
$433$	527.222			1.21760			0.608802	−	0.793322i	$-0.291650\pi$
$433$	527.222			1.21760			0.608802	+	0.793322i	$0.291650\pi$
$434$	−11.9653	−	5.11425i	−0.0275699	−	0.0117840i
$435$	11.2837	−	19.2066i	0.0259395	−	0.0441530i
$436$	−490.477	−	11.0096i	−1.12495	−	0.0252513i
$437$	61.0041	+	227.670i	0.139598	+	0.520985i
$438$	94.1316	−	69.4586i	0.214912	−	0.158581i
$439$	−697.768	+	402.857i	−1.58945	+	0.917669i	−0.596051	+	0.802946i	$0.703264\pi$
$439$	−697.768	+	402.857i	−1.58945	+	0.917669i	−0.993398	+	0.114722i	$0.963402\pi$
$440$	342.508	+	912.620i	0.778426	+	2.07414i
$441$	413.744	+	6.26695i	0.938196	+	0.0142108i
$442$	7.09586	−	49.5916i	0.0160540	−	0.112198i
$443$	703.771	+	188.575i	1.58865	+	0.425677i	0.941590	−	0.336763i	$-0.109332\pi$
$443$	703.771	+	188.575i	1.58865	+	0.425677i	0.647059	+	0.762440i	$0.275999\pi$
$444$	519.054	+	320.822i	1.16904	+	0.722572i
$445$	−124.055	−	462.980i	−0.278776	−	1.04041i
$446$	−187.863	+	22.5911i	−0.421218	+	0.0506527i
$447$	280.594	+	77.4670i	0.627727	+	0.173304i
$448$	−35.9669	+	105.305i	−0.0802833	+	0.235055i
$449$			657.505i			1.46438i	0.681102	+	0.732189i	$0.261501\pi$
$449$			657.505i			1.46438i	−0.681102	+	0.732189i	$0.738499\pi$
$450$	−497.756	+	361.498i	−1.10612	+	0.803330i
$451$	677.401	−	677.401i	1.50200	−	1.50200i
$452$	136.159	+	557.950i	0.301237	+	1.23440i
$453$	−0.779633	+	102.949i	−0.00172104	+	0.227260i
$454$	511.451	+	401.648i	1.12654	+	0.884688i
$455$	148.295	−	256.854i	0.325923	−	0.564515i
$456$	−239.298	−	340.016i	−0.524776	−	0.745649i
$457$	−706.736	+	408.034i	−1.54647	+	0.892853i	−0.548060	+	0.836439i	$0.684633\pi$
$457$	−706.736	+	408.034i	−1.54647	+	0.892853i	−0.998407	+	0.0564143i	$0.982033\pi$
$458$	28.6213	−	200.029i	0.0624920	−	0.436745i
$459$	0.692840	−	30.4913i	0.00150946	−	0.0664299i
$460$	201.132	+	367.161i	0.437244	+	0.798176i
$461$	165.248	−	616.713i	0.358455	−	1.33777i	−0.517626	−	0.855607i	$-0.673184\pi$
$461$	165.248	−	616.713i	0.358455	−	1.33777i	0.876081	−	0.482164i	$-0.160149\pi$
$462$	−129.181	−	103.039i	−0.279613	−	0.223027i
$463$	−38.9927	+	67.5374i	−0.0842175	+	0.145869i	−0.905058	−	0.425289i	$-0.860172\pi$
$463$	−38.9927	+	67.5374i	−0.0842175	+	0.145869i	0.820840	+	0.571158i	$0.193506\pi$
$464$	14.7233	+	4.66253i	0.0317313	+	0.0100486i
$465$	61.5244	−	60.5996i	0.132311	−	0.130322i
$466$	−48.3239	+	113.059i	−0.103699	+	0.242616i
$467$	568.618	+	568.618i	1.21760	+	1.21760i	0.968471	+	0.249126i	$0.0801432\pi$
$467$	568.618	+	568.618i	1.21760	+	1.21760i	0.249126	+	0.968471i	$0.419857\pi$
$468$	−797.720	−	29.9993i	−1.70453	−	0.0641011i
$469$	99.0790	+	99.0790i	0.211256	+	0.211256i
$470$	−184.784	+	74.1217i	−0.393157	+	0.157706i
$471$	−78.9266	−	21.7902i	−0.167572	−	0.0462638i
$472$	105.328	+	147.277i	0.223153	+	0.312028i
$473$	135.302	−	234.349i	0.286050	−	0.495453i
$474$	292.391	−	669.994i	0.616858	−	1.41349i
$475$	−153.242	+	571.906i	−0.322614	+	1.20401i
$476$	−2.20311	+	7.54096i	−0.00462839	+	0.0158423i
$477$	−468.150	−	133.071i	−0.981446	−	0.278976i
$478$	292.840	−	219.527i	0.612636	−	0.459263i
$479$	−701.475	+	404.997i	−1.46446	+	0.845504i	−0.999213	−	0.0396781i	$-0.987367\pi$
$479$	−701.475	+	404.997i	−1.46446	+	0.845504i	−0.465244	+	0.885182i	$0.654033\pi$
$480$	−556.088	−	485.938i	−1.15852	−	1.01237i
$481$	563.788	−	976.509i	1.17212	−	2.03016i
$482$	34.2794	−	4.12220i	0.0711192	−	0.00855229i
$483$	−61.1889	−	35.9480i	−0.126685	−	0.0744264i
$484$	−123.174	−	504.741i	−0.254493	−	1.04285i
$485$	−695.092	+	695.092i	−1.43318	+	1.43318i
$486$	−484.374	+	39.7172i	−0.996655	+	0.0817226i
$487$			784.135i			1.61013i	0.593185	+	0.805066i	$0.297870\pi$
$487$			784.135i			1.61013i	−0.593185	+	0.805066i	$0.702130\pi$
$488$	−784.802	+	76.5519i	−1.60820	+	0.156869i
$489$	−175.346	−	674.799i	−0.358580	−	1.37996i
$490$	436.887	−	556.324i	0.891606	−	1.13535i
$491$	27.9001	+	104.125i	0.0568230	+	0.212066i	0.988500	−	0.151222i	$-0.0483208\pi$
$491$	27.9001	+	104.125i	0.0568230	+	0.212066i	−0.931677	+	0.363288i	$0.881654\pi$
$492$	−208.799	+	695.091i	−0.424388	+	1.41279i
$493$	1.05319	+	0.282202i	0.00213629	+	0.000572417i
$494$	−614.755	+	460.851i	−1.24444	+	0.932896i
$495$	957.898	−	533.865i	1.93515	−	1.07852i
$496$	50.4551	+	32.2323i	0.101724	+	0.0649846i
$497$	−146.047	+	84.3203i	−0.293857	+	0.169658i
$498$	−469.484	+	184.208i	−0.942740	+	0.369895i
$499$	12.8421	+	47.9274i	0.0257357	+	0.0960469i	0.977599	−	0.210475i	$-0.0675012\pi$
$499$	12.8421	+	47.9274i	0.0257357	+	0.0960469i	−0.951863	+	0.306522i	$0.900835\pi$
$500$	−6.33654	+	282.293i	−0.0126731	+	0.564586i
$501$	−33.7859	−	59.5560i	−0.0674370	−	0.118874i
$502$	−56.6211	−	141.155i	−0.112791	−	0.281185i
$503$	287.179			0.570933			0.285467	−	0.958389i	$-0.407851\pi$
$503$	287.179			0.570933			0.285467	+	0.958389i	$0.407851\pi$
$504$	123.171	+	22.3765i	0.244387	+	0.0443978i
$505$			91.9086i			0.181997i
$506$	−160.459	−	400.019i	−0.317112	−	0.790552i
$507$	−7.33146	+	968.103i	−0.0144605	+	1.90947i
$508$	443.209	+	463.563i	0.872458	+	0.912525i
$509$	455.382	−	122.019i	0.894661	−	0.239724i	0.217939	−	0.975962i	$-0.430067\pi$
$509$	455.382	−	122.019i	0.894661	−	0.239724i	0.676722	+	0.736239i	$0.263400\pi$
$510$	−40.7597	−	32.5111i	−0.0799210	−	0.0637472i
$511$	16.9501	+	29.3584i	0.0331705	+	0.0574529i
$512$	242.627	−	450.862i	0.473880	−	0.880589i
$513$	−338.181	+	323.153i	−0.659221	+	0.629929i
$514$	3.68504	−	2.76249i	0.00716933	−	0.00537449i
$515$	−97.8139	+	365.046i	−0.189930	+	0.708828i
$516$	−6.15259	+	204.917i	−0.0119236	+	0.397126i
$517$	197.989	−	53.0510i	0.382957	−	0.102613i
$518$	−109.213	+	139.069i	−0.210835	+	0.268474i
$519$	245.086	+	248.826i	0.472227	+	0.479434i
$520$	−866.711	+	1054.07i	−1.66675	+	2.02706i
$521$	588.551			1.12966			0.564828	−	0.825209i	$-0.308943\pi$
$521$	588.551			1.12966			0.564828	+	0.825209i	$0.308943\pi$
$522$	2.72118	−	17.1600i	0.00521298	−	0.0328736i
$523$	70.9014	+	70.9014i	0.135567	+	0.135567i	0.771634	−	0.636067i	$-0.219440\pi$
$523$	70.9014	+	70.9014i	0.135567	+	0.135567i	−0.636067	+	0.771634i	$0.719440\pi$
$524$	−484.359	−	294.332i	−0.924350	−	0.561701i
$525$	−87.9628	−	155.056i	−0.167548	−	0.295345i
$526$	43.8398	−	5.27186i	0.0833456	−	0.0100226i
$527$	3.66065	+	2.11348i	0.00694620	+	0.00401039i
$528$	508.680	+	565.059i	0.963409	+	1.07019i
$529$	171.948	+	297.822i	0.325043	+	0.562991i
$530$	−665.705	+	499.046i	−1.25605	+	0.941596i
$531$	146.201	−	141.838i	0.275332	−	0.267115i
$532$	105.671	−	57.8869i	0.198629	−	0.108810i
$533$	1295.44	+	347.113i	2.43048	+	0.651245i
$534$	−221.970	−	300.819i	−0.415675	−	0.563331i
$535$	−290.971	−	167.992i	−0.543871	−	0.314004i
$536$	−375.032	−	524.397i	−0.699687	−	0.978352i
$537$	−903.422	+	234.753i	−1.68235	+	0.437157i
$538$	612.883	−	245.844i	1.13919	−	0.456959i
$539$	−514.950	+	514.950i	−0.955380	+	0.955380i
$540$	−447.461	+	700.009i	−0.828631	+	1.29631i
$541$	51.7287	−	51.7287i	0.0956168	−	0.0956168i	−0.657680	−	0.753297i	$-0.728462\pi$
$541$	51.7287	−	51.7287i	0.0956168	−	0.0956168i	0.753297	+	0.657680i	$0.228462\pi$
$542$	161.514	−	377.879i	0.297996	−	0.697193i
$543$	112.639	−	29.2690i	0.207438	−	0.0539025i
$544$	15.6839	−	32.5674i	0.0288307	−	0.0598665i
$545$	817.096	+	471.750i	1.49926	+	0.865597i
$546$	34.4996	−	228.744i	0.0631861	−	0.418944i
$547$	−229.186	−	61.4101i	−0.418987	−	0.112267i	0.0431652	−	0.999068i	$-0.486256\pi$
$547$	−229.186	−	61.4101i	−0.418987	−	0.112267i	−0.462152	+	0.886801i	$0.652922\pi$
$548$	250.985	−	859.087i	0.458002	−	1.56768i
$549$	216.593	+	860.245i	0.394522	+	1.56693i
$550$	153.353	−	1071.76i	0.278824	−	1.94865i
$551$	−8.36109	−	14.4818i	−0.0151744	−	0.0262828i
$552$	250.637	+	209.288i	0.454052	+	0.379145i
$553$	183.457	+	105.919i	0.331748	+	0.191535i
$554$	−259.712	−	203.955i	−0.468794	−	0.368149i
$555$	−579.042	−	1020.70i	−1.04332	−	1.83910i
$556$	−423.497	−	257.347i	−0.761685	−	0.462854i
$557$	6.12472	+	6.12472i	0.0109959	+	0.0109959i	0.712583	−	0.701587i	$-0.247525\pi$
$557$	6.12472	+	6.12472i	0.0109959	+	0.0109959i	−0.701587	+	0.712583i	$0.747525\pi$
$558$	27.4076	−	61.5275i	0.0491176	−	0.110264i
$559$	378.832			0.677696
$560$	157.961	−	144.381i	0.282074	−	0.257824i
$561$	37.6667	+	38.2415i	0.0671420	+	0.0681667i
$562$	318.963	−	38.3562i	0.567550	−	0.0682495i
$563$	−948.708	+	254.206i	−1.68509	+	0.451520i	−0.969116	−	0.246604i	$-0.920685\pi$
$563$	−948.708	+	254.206i	−1.68509	+	0.451520i	−0.715978	+	0.698123i	$0.754019\pi$
$564$	−113.051	+	106.460i	−0.200445	+	0.188760i
$565$	285.869	−	1066.88i	0.505963	−	1.88828i
$566$	37.1393	−	259.559i	0.0656171	−	0.458586i
$567$	4.26547	−	140.771i	0.00752287	−	0.248273i
$568$	726.457	−	272.640i	1.27897	−	0.480001i
$569$	146.583	+	253.889i	0.257615	+	0.446202i	0.965603	−	0.260023i	$-0.0837300\pi$
$569$	146.583	+	253.889i	0.257615	+	0.446202i	−0.707988	+	0.706225i	$0.750397\pi$
$570$	89.4533	+	794.594i	0.156936	+	1.39402i
$571$	−96.1503	+	25.7634i	−0.168389	+	0.0451198i	−0.342029	−	0.939690i	$-0.611114\pi$
$571$	−96.1503	+	25.7634i	−0.168389	+	0.0451198i	0.173639	+	0.984809i	$0.444447\pi$
$572$	1015.48	−	970.892i	1.77531	−	1.69736i
$573$	4.97237	−	656.589i	0.00867778	−	1.14588i
$574$	−193.394	−	82.6608i	−0.336923	−	0.144008i
$575$		−	464.981i		−	0.808663i
$576$	−542.201	−	194.408i	−0.941321	−	0.337513i
$577$	−571.056			−0.989698			−0.494849	−	0.868979i	$-0.664777\pi$
$577$	−571.056			−0.989698			−0.494849	+	0.868979i	$0.664777\pi$
$578$	−226.166	+	529.140i	−0.391291	+	0.915467i
$579$	48.8947	+	86.1888i	0.0844467	+	0.148858i
$580$	−20.5253	−	21.4679i	−0.0353884	−	0.0370136i
$581$	−37.8257	−	141.167i	−0.0651044	−	0.242973i
$582$	−306.670	+	702.713i	−0.526924	+	1.20741i
$583$	741.798	−	428.277i	1.27238	−	0.734609i
$584$	−54.8063	−	146.033i	−0.0938464	−	0.250056i
$585$	1317.76	+	787.660i	2.25259	+	1.34643i
$586$	−822.819	−	117.734i	−1.40413	−	0.200911i
$587$	−589.978	−	158.084i	−1.00507	−	0.269309i	−0.281504	−	0.959560i	$-0.590833\pi$
$587$	−589.978	−	158.084i	−1.00507	−	0.269309i	−0.723569	+	0.690252i	$0.757500\pi$
$588$	158.726	−	528.398i	0.269942	−	0.898635i
$589$	−16.7785	−	62.6182i	−0.0284864	−	0.106313i
$590$	−41.5745	−	345.725i	−0.0704652	−	0.585975i
$591$	78.3083	+	301.361i	0.132501	+	0.509917i
$592$	600.537	−	548.908i	1.01442	−	0.927210i
$593$			54.2089i			0.0914147i	0.998955	+	0.0457074i	$0.0145542\pi$
$593$			54.2089i			0.0914147i	−0.998955	+	0.0457074i	$0.985446\pi$
$594$	543.419	−	660.520i	0.914847	−	1.11199i
$595$	10.6834	−	10.6834i	0.0179554	−	0.0179554i
$596$	201.555	−	331.683i	0.338179	−	0.556516i
$597$	−787.994	−	462.940i	−1.31992	−	0.775445i
$598$	372.665	−	474.544i	0.623185	−	0.793552i
$599$	−165.854	+	287.267i	−0.276885	+	0.479578i	−0.970609	−	0.240662i	$-0.922635\pi$
$599$	−165.854	+	287.267i	−0.276885	+	0.479578i	0.693724	+	0.720241i	$0.255969\pi$
$600$	282.383	+	770.094i	0.470638	+	1.28349i
$601$	173.739	−	100.308i	0.289083	−	0.166902i	−0.348445	−	0.937329i	$-0.613290\pi$
$601$	173.739	−	100.308i	0.289083	−	0.166902i	0.637528	+	0.770427i	$0.279957\pi$
$602$	−58.8097	−	8.41483i	−0.0976905	−	0.0139781i
$603$	−520.566	+	505.031i	−0.863294	+	0.837531i
$604$	131.761	+	38.4943i	0.218147	+	0.0637323i
$605$	−258.607	+	965.136i	−0.427450	+	1.59527i
$606$	26.1835	+	66.7329i	0.0432070	+	0.110120i
$607$	82.2140	−	142.399i	0.135443	−	0.234595i	−0.790323	−	0.612690i	$-0.790087\pi$
$607$	82.2140	−	142.399i	0.135443	−	0.234595i	0.925767	+	0.378095i	$0.123421\pi$
$608$	−523.267	+	183.095i	−0.860637	+	0.301143i
$609$	4.85329	+	1.33991i	0.00796928	+	0.00220018i
$610$	1394.43	+	596.009i	2.28595	+	0.977064i
$611$	202.907	+	202.907i	0.332090	+	0.332090i
$612$	−38.8567	−	11.9937i	−0.0634913	−	0.0195976i
$613$	281.900	+	281.900i	0.459870	+	0.459870i	0.898613	−	0.438743i	$-0.144576\pi$
$613$	281.900	+	281.900i	0.459870	+	0.459870i	−0.438743	+	0.898613i	$0.644576\pi$
$614$	108.454	+	270.373i	0.176635	+	0.440346i
$615$	994.410	−	979.461i	1.61693	−	1.59262i
$616$	−179.208	+	128.164i	−0.290923	+	0.208059i
$617$	76.6449	−	132.753i	0.124222	−	0.215159i	−0.797207	−	0.603707i	$-0.793690\pi$
$617$	76.6449	−	132.753i	0.124222	−	0.215159i	0.921429	+	0.388548i	$0.127023\pi$
$618$	32.9759	+	292.918i	0.0533591	+	0.473977i
$619$	261.930	−	977.536i	0.423150	−	1.57922i	−0.344779	−	0.938684i	$-0.612046\pi$
$619$	261.930	−	977.536i	0.423150	−	1.57922i	0.767930	−	0.640534i	$-0.221287\pi$
$620$	−55.3192	−	100.984i	−0.0892245	−	0.162877i
$621$	190.851	−	313.874i	0.307329	−	0.505434i
$622$	−160.595	−	214.227i	−0.258191	−	0.344416i
$623$	93.8215	−	54.1679i	0.150596	−	0.0869468i
$624$	−329.011	+	1012.25i	−0.527261	+	1.62220i
$625$	−155.691	+	269.664i	−0.249105	+	0.431463i
$626$	65.4392	+	544.180i	0.104535	+	0.869296i
$627$	6.23408	−	823.196i	0.00994271	−	1.31291i
$628$	−56.6942	+	93.2973i	−0.0902773	+	0.148563i
$629$	40.6163	−	40.6163i	0.0645728	−	0.0645728i
$630$	−187.073	−	151.547i	−0.296941	−	0.240550i
$631$		−	180.759i		−	0.286465i	−0.989689	−	0.143232i	$-0.954250\pi$
$631$		−	180.759i		−	0.286465i	0.989689	−	0.143232i	$-0.0457496\pi$
$632$	−752.863	−	619.043i	−1.19124	−	0.979499i
$633$	−571.253	−	157.713i	−0.902453	−	0.249151i
$634$	−566.239	−	444.674i	−0.893121	−	0.701378i
$635$	−319.230	−	1191.38i	−0.502724	−	1.87619i
$636$	−341.183	+	551.997i	−0.536452	+	0.867919i
$637$	−984.777	−	263.870i	−1.54596	−	0.414239i
$638$	18.3413	+	24.4665i	0.0287481	+	0.0383488i
$639$	−424.963	−	762.499i	−0.665044	−	1.19327i
$640$	−825.807	+	536.273i	−1.29032	+	0.837927i
$641$	−546.031	+	315.251i	−0.851843	+	0.491812i	−0.861272	−	0.508144i	$-0.830332\pi$
$641$	−546.031	+	315.251i	−0.851843	+	0.491812i	0.00942932	+	0.999956i	$0.496999\pi$
$642$	−259.127	−	39.0821i	−0.403624	−	0.0608755i
$643$	−202.558	−	755.957i	−0.315020	−	1.17567i	−0.923971	−	0.382463i	$-0.875076\pi$
$643$	−202.558	−	755.957i	−0.315020	−	1.17567i	0.608950	−	0.793208i	$-0.291591\pi$
$644$	−68.3931	+	65.3901i	−0.106200	+	0.101537i
$645$	199.713	−	339.941i	0.309632	−	0.527040i
$646$	−36.3254	+	14.5711i	−0.0562313	+	0.0225559i
$647$	141.404			0.218553			0.109277	−	0.994011i	$-0.465147\pi$
$647$	141.404			0.218553			0.109277	+	0.994011i	$0.465147\pi$
$648$	−125.469	+	635.737i	−0.193625	+	0.981076i
$649$			358.496i			0.552383i
$650$	1406.74	−	564.281i	2.16421	−	0.868125i
$651$	16.8293	+	9.88709i	0.0258515	+	0.0151875i
$652$	−929.377	−	20.8614i	−1.42542	−	0.0319960i
$653$	33.4525	−	8.96356i	0.0512289	−	0.0137267i	−0.233114	−	0.972450i	$-0.574891\pi$
$653$	33.4525	−	8.96356i	0.0512289	−	0.0137267i	0.284342	+	0.958723i	$0.408225\pi$
$654$	727.671	+	109.749i	1.11265	+	0.167812i
$655$	544.999	+	943.966i	0.832060	+	1.44117i
$656$	815.498	+	520.966i	1.24314	+	0.794156i
$657$	−153.278	+	85.4263i	−0.233300	+	0.130025i
$658$	−26.9920	−	36.0062i	−0.0410213	−	0.0547207i
$659$	315.298	−	1176.71i	0.478449	−	1.78560i	−0.129454	−	0.991585i	$-0.541323\pi$
$659$	315.298	−	1176.71i	0.478449	−	1.78560i	0.607904	−	0.794011i	$-0.292011\pi$
$660$	−335.879	−	1423.06i	−0.508908	−	2.15616i
$661$	312.659	−	83.7767i	0.473009	−	0.126742i	−0.0144365	−	0.999896i	$-0.504595\pi$
$661$	312.659	−	83.7767i	0.473009	−	0.126742i	0.487446	+	0.873153i	$0.337929\pi$
$662$	418.898	+	328.965i	0.632776	+	0.496926i
$663$	−19.9981	+	72.4352i	−0.0301630	+	0.109254i
$664$	65.2819	+	669.263i	0.0983161	+	1.00793i
$665$	−231.716			−0.348445
$666$	−711.214	−	576.150i	−1.06789	−	0.865090i
$667$	9.28608	+	9.28608i	0.0139222	+	0.0139222i
$668$	−88.6931	+	21.6442i	−0.132774	+	0.0324015i
$669$	283.817	+	2.14935i	0.424240	+	0.00321278i
$670$	148.031	+	1230.99i	0.220941	+	1.83731i
$671$	−1352.06	−	780.615i	−2.01500	−	1.16336i
$672$	73.5601	−	149.833i	0.109464	−	0.222966i
$673$	−578.141	−	1001.37i	−0.859051	−	1.48792i	−0.872835	−	0.488015i	$-0.837721\pi$
$673$	−578.141	−	1001.37i	−0.859051	−	1.48792i	0.0137844	−	0.999905i	$-0.495612\pi$
$674$	−133.069	−	177.508i	−0.197432	−	0.263365i
$675$	809.412	−	443.109i	1.19913	−	0.656458i
$676$	1239.04	+	361.991i	1.83291	+	0.535489i
$677$	288.831	+	77.3920i	0.426634	+	0.114316i	0.465745	−	0.884919i	$-0.345786\pi$
$677$	288.831	+	77.3920i	0.426634	+	0.114316i	−0.0391119	+	0.999235i	$0.512453\pi$
$678$	−96.3749	−	856.077i	−0.142146	−	1.26265i
$679$	−192.416	−	111.091i	−0.283381	−	0.163610i
$680$	−56.5444	+	40.4388i	−0.0831536	+	0.0594689i
$681$	−684.515	−	694.962i	−1.00516	−	1.02050i
$682$	44.1323	+	110.021i	0.0647102	+	0.161321i
$683$	−473.690	+	473.690i	−0.693542	+	0.693542i	−0.963010	−	0.269467i	$-0.913152\pi$
$683$	−473.690	+	473.690i	−0.693542	+	0.693542i	0.269467	+	0.963010i	$0.413152\pi$
$684$	291.319	+	551.454i	0.425904	+	0.806219i
$685$	−1217.09	+	1217.09i	−1.77677	+	1.77677i
$686$	303.697	+	129.807i	0.442706	+	0.189223i
$687$	−80.6628	+	292.169i	−0.117413	+	0.425283i
$688$	260.591	+	82.5231i	0.378767	+	0.119946i
$689$	1038.48	+	599.569i	1.50723	+	0.870202i
$690$	−229.366	−	584.576i	−0.332414	−	0.847212i
$691$	179.816	+	48.1817i	0.260226	+	0.0697275i	0.386573	−	0.922259i	$-0.373659\pi$
$691$	179.816	+	48.1817i	0.260226	+	0.0697275i	−0.126347	+	0.991986i	$0.540325\pi$
$692$	408.413	−	223.730i	0.590192	−	0.323309i
$693$	172.590	+	177.899i	0.249048	+	0.256709i
$694$	−54.4327	−	7.78854i	−0.0784333	−	0.0112227i
$695$	476.517	+	825.351i	0.685636	+	1.18756i
$696$	−21.0189	−	9.74002i	−0.0301995	−	0.0139943i
$697$	59.1665	+	34.1598i	0.0848874	+	0.0490097i
$698$	89.4039	−	113.845i	0.128086	−	0.163102i
$699$	93.4219	−	159.018i	0.133651	−	0.227494i
$700$	−230.915	+	56.3514i	−0.329879	+	0.0805020i
$701$	749.244	+	749.244i	1.06882	+	1.06882i	0.997450	+	0.0713720i	$0.0227377\pi$
$701$	749.244	+	749.244i	1.06882	+	1.06882i	0.0713720	+	0.997450i	$0.477262\pi$
$702$	1181.19	+	196.491i	1.68261	+	0.279901i
$703$	−880.937			−1.25311
$704$	910.023	−	446.650i	1.29265	−	0.634446i
$705$	289.044	−	75.1078i	0.409992	−	0.106536i
$706$	−30.6813	−	255.139i	−0.0434579	−	0.361387i
$707$	−20.0656	+	5.37657i	−0.0283814	+	0.00760477i
$708$	−128.679	−	239.180i	−0.181749	−	0.337825i
$709$	−203.623	+	759.932i	−0.287198	+	1.07184i	0.660021	+	0.751247i	$0.270547\pi$
$709$	−203.623	+	759.932i	−0.287198	+	1.07184i	−0.947218	+	0.320589i	$0.896119\pi$
$710$	−1477.20	−	211.366i	−2.08056	−	0.297698i
$711$	−562.582	+	941.206i	−0.791254	+	1.32378i
$712$	−466.681	+	175.146i	−0.655450	+	0.245991i
$713$	25.4555	+	44.0902i	0.0357019	+	0.0618376i
$714$	4.71346	−	10.8006i	0.00660149	−	0.0151269i
$715$	−2609.84	+	699.303i	−3.65012	+	0.978046i
$716$	−27.9293	+	1244.25i	−0.0390074	+	1.73778i
$717$	−477.498	+	270.883i	−0.665967	+	0.377801i
$718$	−3.74465	+	8.76102i	−0.00521539	+	0.0122020i
$719$		−	156.039i		−	0.217022i	−0.994095	−	0.108511i	$-0.965392\pi$
$719$		−	156.039i		−	0.217022i	0.994095	−	0.108511i	$-0.0346082\pi$
$720$	734.884	+	828.872i	1.02067	+	1.15121i
$721$	−85.4195			−0.118474
$722$	−111.944	−	47.8476i	−0.155048	−	0.0662709i
$723$	−51.7881	−	0.392193i	−0.0716295	−	0.000542452i
$724$	3.48223	−	155.133i	0.00480971	−	0.214273i
$725$	8.53811	+	31.8647i	0.0117767	+	0.0439513i
$726$	87.1842	+	774.438i	0.120088	+	1.06672i
$727$	−187.077	+	108.009i	−0.257327	+	0.148568i	−0.623115	−	0.782130i	$-0.714133\pi$
$727$	−187.077	+	108.009i	−0.257327	+	0.148568i	0.365787	+	0.930698i	$0.380800\pi$
$728$	−280.828	−	127.560i	−0.385753	−	0.175219i
$729$	728.248	+	33.1124i	0.998968	+	0.0454216i
$730$	−42.4889	+	296.947i	−0.0582039	+	0.406776i
$731$	18.6406	+	4.99474i	0.0255002	+	0.00683276i
$732$	1182.26	+	35.4971i	1.61511	+	0.0484932i
$733$	−145.404	−	542.654i	−0.198368	−	0.740320i	−0.991369	−	0.131100i	$-0.958149\pi$
$733$	−145.404	−	542.654i	−0.198368	−	0.740320i	0.793001	−	0.609220i	$-0.208517\pi$
$734$	−291.932	+	35.1057i	−0.397728	+	0.0478280i
$735$	−755.935	+	744.571i	−1.02848	+	1.01302i
$736$	359.722	−	245.250i	0.488752	−	0.333220i
$737$		−	1276.47i		−	1.73198i
$738$	442.985	−	994.459i	0.600251	−	1.34751i
$739$	−1018.28	+	1018.28i	−1.37791	+	1.37791i	−0.529773	+	0.848139i	$0.677723\pi$
$739$	−1018.28	+	1018.28i	−1.37791	+	1.37791i	−0.848139	+	0.529773i	$0.822277\pi$
$740$	−1520.07	+	370.950i	−2.05415	+	0.501284i
$741$	1002.40	−	568.661i	1.35277	−	0.767424i
$742$	−147.896	−	116.144i	−0.199320	−	0.156528i
$743$	220.697	−	382.258i	0.297035	−	0.514479i	−0.678422	−	0.734673i	$-0.737336\pi$
$743$	220.697	−	382.258i	0.297035	−	0.514479i	0.975456	+	0.220194i	$0.0706690\pi$
$744$	−68.9349	−	57.5623i	−0.0926544	−	0.0773687i
$745$	−646.417	+	373.209i	−0.867674	+	0.500952i
$746$	182.376	−	1274.59i	0.244472	−	1.70857i
$747$	733.599	−	184.706i	0.982060	−	0.247263i
$748$	62.7680	−	34.3846i	0.0839144	−	0.0459687i
$749$	19.6548	−	73.3527i	0.0262414	−	0.0979342i
$750$	63.1658	−	418.809i	0.0842210	−	0.558413i
$751$	−231.066	+	400.219i	−0.307678	+	0.532915i	−0.977854	−	0.209288i	$-0.932885\pi$
$751$	−231.066	+	400.219i	−0.307678	+	0.532915i	0.670176	+	0.742202i	$0.266219\pi$
$752$	95.3753	+	183.776i	0.126829	+	0.244383i
$753$	57.3743	+	220.799i	0.0761943	+	0.293226i
$754$	−16.8246	+	39.3630i	−0.0223138	+	0.0522055i
$755$	−186.669	−	186.669i	−0.247243	−	0.247243i
$756$	−179.003	−	56.7404i	−0.236777	−	0.0750535i
$757$	860.683	+	860.683i	1.13697	+	1.13697i	0.988991	+	0.147974i	$0.0472751\pi$
$757$	860.683	+	860.683i	1.13697	+	1.13697i	0.147974	+	0.988991i	$0.452725\pi$
$758$	−636.206	+	255.200i	−0.839322	+	0.336675i
$759$	162.593	+	625.723i	0.214220	+	0.824404i
$760$	1051.75	+	174.659i	1.38388	+	0.229815i
$761$	−494.494	+	856.489i	−0.649795	+	1.12548i	0.333377	+	0.942794i	$0.391812\pi$
$761$	−494.494	+	856.489i	−0.649795	+	1.12548i	−0.983172	+	0.182684i	$0.941521\pi$
$762$	−571.193	−	774.092i	−0.749597	−	1.01587i
$763$	−55.1939	+	205.987i	−0.0723381	+	0.269969i
$764$	−840.349	−	245.510i	−1.09993	−	0.321349i
$765$	54.4563	+	56.1314i	0.0711847	+	0.0733743i
$766$	−338.461	+	253.727i	−0.441855	+	0.331236i
$767$	−434.640	+	250.940i	−0.566675	+	0.327170i
$768$	−446.824	+	624.637i	−0.581803	+	0.813330i
$769$	−341.309	+	591.165i	−0.443835	+	0.768746i	−0.997970	−	0.0636814i	$-0.979716\pi$
$769$	−341.309	+	591.165i	−0.443835	+	0.768746i	0.554135	+	0.832427i	$0.313049\pi$
$770$	420.683	−	50.5883i	0.546341	−	0.0656991i
$771$	−6.00873	+	3.40873i	−0.00779343	+	0.00442119i
$772$	128.356	−	31.3233i	0.166264	−	0.0405742i
$773$	510.754	−	510.754i	0.660742	−	0.660742i	−0.294813	−	0.955555i	$-0.595257\pi$
$773$	510.754	−	510.754i	0.660742	−	0.660742i	0.955555	+	0.294813i	$0.0952574\pi$
$774$	48.1627	−	303.719i	0.0622257	−	0.392402i
$775$			127.888i			0.165017i
$776$	789.629	+	649.274i	1.01756	+	0.836693i
$777$	188.968	−	186.128i	0.243202	−	0.239546i
$778$	311.014	−	396.039i	0.399760	−	0.509047i
$779$	−271.188	−	1012.09i	−0.348124	−	1.29922i
$780$	1490.21	−	1403.33i	1.91053	−	1.79914i
$781$	1483.95	+	397.623i	1.90006	+	0.509120i
$782$	24.5938	−	18.4368i	0.0314499	−	0.0235764i
$783$	−7.31538	+	25.0139i	−0.00934276	+	0.0319463i
$784$	−619.929	−	396.031i	−0.790725	−	0.505141i
$785$	181.827	−	104.978i	0.231627	−	0.133730i
$786$	664.635	+	530.131i	0.845591	+	0.674467i
$787$	−1.84150	−	6.87257i	−0.00233990	−	0.00873262i	0.964746	−	0.263183i	$-0.0847722\pi$
$787$	−1.84150	−	6.87257i	−0.00233990	−	0.00873262i	−0.967086	+	0.254450i	$0.918106\pi$
$788$	415.054	+	9.31658i	0.526718	+	0.0118231i
$789$	−66.2315	−	0.501573i	−0.0839436	−	0.000635707i
$790$	697.854	+	1739.73i	0.883359	+	2.20219i
$791$	249.646			0.315608
$792$	−649.285	−	937.568i	−0.819804	−	1.18380i
$793$		−	2185.65i		−	2.75618i
$794$	61.0020	+	152.077i	0.0768287	+	0.191532i
$795$	1085.48	−	615.791i	1.36539	−	0.774580i
$796$	−880.771	+	842.098i	−1.10650	+	1.05791i
$797$	703.157	−	188.410i	0.882254	−	0.236399i	0.210875	−	0.977513i	$-0.432369\pi$
$797$	703.157	−	188.410i	0.882254	−	0.236399i	0.671380	+	0.741114i	$0.265702\pi$
$798$	−168.244	+	66.0126i	−0.210832	+	0.0827226i
$799$	7.30889	+	12.6594i	0.00914755	+	0.0158440i
$800$	1090.59	−	81.7202i	1.36324	−	0.102150i
$801$	272.999	+	489.834i	0.340823	+	0.611528i
$802$	450.517	−	337.730i	0.561742	−	0.421110i
$803$	79.9303	−	298.304i	0.0995396	−	0.371487i
$804$	458.175	+	851.627i	0.569869	+	1.05924i
$805$	175.774	−	47.0985i	0.218353	−	0.0585074i
$806$	−102.497	+	130.518i	−0.127168	+	0.161933i
$807$	−958.691	+	249.115i	−1.18797	+	0.308693i
$808$	95.1296	−	9.27922i	0.117735	−	0.0114842i
$809$	−977.087			−1.20777			−0.603886	−	0.797071i	$-0.706382\pi$
$809$	−977.087			−1.20777			−0.603886	+	0.797071i	$0.706382\pi$
$810$	799.019	−	956.345i	0.986443	−	1.18067i
$811$	481.721	+	481.721i	0.593984	+	0.593984i	0.938705	−	0.344721i	$-0.112027\pi$
$811$	481.721	+	481.721i	0.593984	+	0.593984i	−0.344721	+	0.938705i	$0.612027\pi$
$812$	3.48619	−	5.73697i	0.00429334	−	0.00706523i
$813$	−312.246	+	531.489i	−0.384066	+	0.653738i
$814$	1599.35	−	192.326i	1.96480	−	0.236273i
$815$	1548.27	+	893.893i	1.89972	+	1.09680i
$816$	−29.5353	+	45.4705i	−0.0361952	+	0.0557236i
$817$	−147.985	−	256.317i	−0.181132	−	0.313729i
$818$	−84.2823	+	63.1822i	−0.103035	+	0.0772399i
$819$	−94.8751	+	333.774i	−0.115843	+	0.407538i
$820$	−894.116	−	1632.18i	−1.09039	−	1.99046i
$821$	−443.063	−	118.718i	−0.539663	−	0.144602i	−0.0213163	−	0.999773i	$-0.506786\pi$
$821$	−443.063	−	118.718i	−0.539663	−	0.144602i	−0.518347	+	0.855170i	$0.673452\pi$
$822$	−536.971	+	1230.43i	−0.653249	+	1.49688i
$823$	113.938	+	65.7823i	0.138443	+	0.0799299i	0.567622	−	0.823290i	$-0.307864\pi$
$823$	113.938	+	65.7823i	0.138443	+	0.0799299i	−0.429179	+	0.903219i	$0.641197\pi$
$824$	387.715	+	64.3862i	0.470528	+	0.0781386i
$825$	−432.192	+	1565.44i	−0.523869	+	1.89751i
$826$	73.0473	−	29.3012i	0.0884349	−	0.0354736i
$827$	−173.569	+	173.569i	−0.209878	+	0.209878i	−0.804215	−	0.594338i	$-0.797414\pi$
$827$	−173.569	+	173.569i	−0.209878	+	0.209878i	0.594338	+	0.804215i	$0.297414\pi$
$828$	−333.075	−	359.105i	−0.402264	−	0.433702i
$829$	700.211	−	700.211i	0.844645	−	0.844645i	−0.144814	−	0.989459i	$-0.546258\pi$
$829$	700.211	−	700.211i	0.844645	−	0.844645i	0.989459	+	0.144814i	$0.0462583\pi$
$830$	508.264	−	1189.14i	0.612366	−	1.43270i
$831$	347.593	+	352.897i	0.418282	+	0.424666i
$832$	1178.51	+	790.665i	1.41648	+	0.950318i
$833$	−44.9774	−	25.9677i	−0.0539945	−	0.0311738i
$834$	581.120	+	463.517i	0.696786	+	0.555776i
$835$	169.594	+	45.4425i	0.203106	+	0.0544221i
$836$	−1053.58	−	307.808i	−1.26027	−	0.368191i
$837$	−52.4915	+	86.3276i	−0.0627139	+	0.103139i
$838$	144.031	−	1006.60i	0.171874	−	1.20120i
$839$	266.174	+	461.026i	0.317251	+	0.549495i	0.979913	−	0.199423i	$-0.0639068\pi$
$839$	266.174	+	461.026i	0.317251	+	0.549495i	−0.662662	+	0.748918i	$0.730574\pi$
$840$	−262.511	+	184.751i	−0.312513	+	0.219942i
$841$	727.520	+	420.034i	0.865066	+	0.499446i
$842$	967.043	+	759.430i	1.14851	+	0.901935i
$843$	−481.878	−	3.64927i	−0.571622	−	0.00432891i
$844$	−410.339	+	675.265i	−0.486184	+	0.800077i
$845$	−1755.38	−	1755.38i	−2.07738	−	2.07738i
$846$	188.472	−	136.879i	0.222780	−	0.161795i
$847$	−225.838			−0.266633
$848$	583.745	+	638.651i	0.688379	+	0.753126i
$849$	−104.669	+	379.121i	−0.123285	+	0.446550i
$850$	76.6592	−	9.21849i	0.0901872	−	0.0108453i
$851$	668.257	−	179.059i	0.785260	−	0.210410i
$852$	−1132.78	+	267.364i	−1.32955	+	0.313807i
$853$	−172.687	+	644.476i	−0.202447	+	0.755541i	0.787766	+	0.615974i	$0.211238\pi$
$853$	−172.687	+	644.476i	−0.202447	+	0.755541i	−0.990213	+	0.139566i	$0.955429\pi$
$854$	−48.5489	+	339.299i	−0.0568489	+	0.397306i
$855$	18.1654	−	1199.28i	0.0212461	−	1.40267i
$856$	−144.503	+	318.129i	−0.168812	+	0.371646i
$857$	19.2177	+	33.2860i	0.0224244	+	0.0388402i	0.877020	−	0.480454i	$-0.159528\pi$
$857$	19.2177	+	33.2860i	0.0224244	+	0.0388402i	−0.854595	+	0.519294i	$0.826195\pi$
$858$	−1695.72	+	1251.25i	−1.97637	+	1.45834i
$859$	511.428	−	137.037i	0.595376	−	0.159531i	0.0514670	−	0.998675i	$-0.483610\pi$
$859$	511.428	−	137.037i	0.595376	−	0.159531i	0.543909	+	0.839144i	$0.316944\pi$
$860$	−363.281	−	379.965i	−0.422420	−	0.441819i
$861$	272.010	+	159.803i	0.315923	+	0.185602i
$862$	−922.249	−	394.190i	−1.06989	−	0.457297i
$863$		−	508.342i		−	0.589040i	−0.955645	−	0.294520i	$-0.904840\pi$
$863$		−	508.342i		−	0.589040i	0.955645	−	0.294520i	$-0.0951598\pi$
$864$	769.717	+	392.468i	0.890877	+	0.454245i
$865$	−895.571			−1.03534
$866$	−414.425	+	969.591i	−0.478550	+	1.11962i
$867$	437.235	−	744.239i	0.504307	−	0.858407i
$868$	18.8108	−	17.9848i	0.0216714	−	0.0207198i
$869$	−499.473	−	1864.06i	−0.574768	−	2.14506i
$870$	26.4523	+	35.8487i	0.0304050	+	0.0412054i
$871$	1547.59	−	893.499i	1.77679	−	1.02583i
$872$	405.788	−	893.359i	0.465353	−	1.02449i
$873$	590.055	−	987.169i	0.675893	−	1.13078i
$874$	−466.651	−	66.7711i	−0.533925	−	0.0763971i
$875$	118.555	+	31.7668i	0.135492	+	0.0363049i
$876$	53.7457	+	227.711i	0.0613535	+	0.259944i
$877$	−327.951	−	1223.93i	−0.373946	−	1.39559i	−0.854879	−	0.518828i	$-0.826369\pi$
$877$	−327.951	−	1223.93i	−0.373946	−	1.39559i	0.480933	−	0.876757i	$-0.340298\pi$
$878$	−192.393	−	1599.90i	−0.219126	−	1.82221i
$879$	1201.84	+	331.806i	1.36728	+	0.377481i
$880$	−1947.59	−	87.4778i	−2.21317	−	0.0994066i
$881$		−	162.295i		−	0.184217i	−0.995749	−	0.0921086i	$-0.970639\pi$
$881$		−	162.295i		−	0.184217i	0.995749	−	0.0921086i	$-0.0293607\pi$
$882$	−336.750	+	755.972i	−0.381803	+	0.857112i
$883$	−1046.26	+	1046.26i	−1.18489	+	1.18489i	−0.206427	+	0.978462i	$0.566184\pi$
$883$	−1046.26	+	1046.26i	−1.18489	+	1.18489i	−0.978462	+	0.206427i	$0.933816\pi$
$884$	85.6240	+	52.0313i	0.0968597	+	0.0588589i
$885$	−3.95546	+	522.309i	−0.00446944	+	0.590180i
$886$	−900.001	+	1146.04i	−1.01580	+	1.29350i
$887$	−792.245	+	1372.21i	−0.893174	+	1.54702i	−0.0571260	+	0.998367i	$0.518194\pi$
$887$	−792.245	+	1372.21i	−0.893174	+	1.54702i	−0.836048	+	0.548656i	$0.815140\pi$
$888$	−998.013	+	702.386i	−1.12389	+	0.790975i
$889$	241.430	−	139.389i	0.271574	−	0.156793i
$890$	948.960	+	135.783i	1.06625	+	0.152565i
$891$	−934.276	+	879.322i	−1.04857	+	0.986894i
$892$	106.124	−	363.248i	0.118973	−	0.407229i
$893$	58.0240	−	216.548i	0.0649764	−	0.242495i
$894$	−363.028	+	455.134i	−0.406071	+	0.509099i
$895$	1196.75	−	2072.82i	1.33715	−	2.31601i
$896$	−165.389	−	148.920i	−0.184586	−	0.166205i
$897$	−644.813	+	635.120i	−0.718855	+	0.708049i
$898$	−1209.19	−	516.834i	−1.34653	−	0.575539i
$899$	−2.55403	−	2.55403i	−0.00284097	−	0.00284097i
$900$	−273.553	−	1199.56i	−0.303948	−	1.33284i
$901$	43.1941	+	43.1941i	0.0479402	+	0.0479402i
$902$	713.304	+	1778.25i	0.790803	+	1.97145i
$903$	85.8994	+	23.7153i	0.0951267	+	0.0262628i
$904$	−1133.13	−	188.174i	−1.25346	−	0.208157i
$905$	−149.210	+	258.440i	−0.164873	+	0.285569i
$906$	−188.715	−	82.3569i	−0.208295	−	0.0909016i
$907$	255.553	−	953.736i	0.281756	−	1.05153i	−0.669421	−	0.742883i	$-0.733458\pi$
$907$	255.553	−	953.736i	0.281756	−	1.05153i	0.951177	−	0.308645i	$-0.0998756\pi$
$908$	−1140.68	+	624.870i	−1.25626	+	0.688183i
$909$	−26.2542	−	104.274i	−0.0288825	−	0.114713i
$910$	355.802	+	474.624i	0.390991	+	0.521565i
$911$	−935.341	+	540.020i	−1.02672	+	0.592777i	−0.916043	−	0.401080i	$-0.868635\pi$
$911$	−935.341	+	540.020i	−1.02672	+	0.592777i	−0.110676	+	0.993857i	$0.535302\pi$
$912$	813.409	−	172.811i	0.891896	−	0.189486i
$913$	−665.692	+	1153.01i	−0.729126	+	1.26288i
$914$	−194.865	−	1620.46i	−0.213200	−	1.77293i
$915$	−1961.27	−	1152.23i	−2.14347	−	1.25927i
$916$	345.367	+	209.870i	0.377038	+	0.229115i
$917$	−174.206	+	174.206i	−0.189974	+	0.189974i
$918$	55.5306	+	25.2420i	0.0604908	+	0.0274967i
$919$			90.0207i			0.0979551i	0.998800	+	0.0489775i	$0.0155963\pi$
$919$			90.0207i			0.0979551i	−0.998800	+	0.0489775i	$0.984404\pi$
$920$	−833.330	+	81.2854i	−0.905793	+	0.0883537i
$921$	−109.897	−	422.925i	−0.119323	−	0.459202i
$922$	1004.27	+	788.668i	1.08924	+	0.855388i
$923$	556.654	+	2077.46i	0.603092	+	2.25077i
$924$	291.037	−	156.578i	0.314975	−	0.169456i
$925$	1678.66	+	449.794i	1.81476	+	0.486264i
$926$	−93.5546	−	124.798i	−0.101031	−	0.134771i
$927$	6.69648	−	442.102i	0.00722382	−	0.476917i
$928$	−20.1480	+	23.4120i	−0.0217112	+	0.0252285i
$929$	−454.545	+	262.432i	−0.489284	+	0.282488i	−0.724277	−	0.689509i	$-0.757827\pi$
$929$	−454.545	+	262.432i	−0.489284	+	0.282488i	0.234993	+	0.971997i	$0.424493\pi$
$930$	63.0845	+	160.781i	0.0678328	+	0.172883i
$931$	206.153	+	769.374i	0.221432	+	0.826395i
$932$	−169.936	−	177.741i	−0.182335	−	0.190709i
$933$	198.164	+	349.313i	0.212395	+	0.374397i
$934$	−1492.68	+	598.755i	−1.59816	+	0.641066i
$935$	−137.638			−0.147207
$936$	682.220	−	1443.47i	0.728868	−	1.54217i
$937$		−	700.426i		−	0.747520i	−0.927525	−	0.373760i	$-0.878068\pi$
$937$		−	700.426i		−	0.747520i	0.927525	−	0.373760i	$-0.121932\pi$
$938$	−260.093	+	104.330i	−0.277285	+	0.111226i
$939$	6.22598	−	822.127i	0.00663044	−	0.875534i
$940$	8.93581	−	398.091i	0.00950618	−	0.423501i
$941$	−538.990	+	144.422i	−0.572784	+	0.153477i	−0.533573	−	0.845754i	$-0.679151\pi$
$941$	−538.990	+	144.422i	−0.572784	+	0.153477i	−0.0392110	+	0.999231i	$0.512484\pi$
$942$	102.114	−	128.022i	0.108401	−	0.135904i
$943$	411.433	+	712.623i	0.436302	+	0.755698i
$944$	−353.644	+	77.9364i	−0.374623	+	0.0825597i
$945$	249.492	+	261.094i	0.264013	+	0.276290i
$946$	324.627	+	433.038i	0.343157	+	0.457756i
$947$	244.123	−	911.078i	0.257785	−	0.962068i	−0.708734	−	0.705476i	$-0.750733\pi$
$947$	244.123	−	911.078i	0.257785	−	0.962068i	0.966520	−	0.256593i	$-0.0825998\pi$
$948$	1002.32	+	1064.37i	1.05730	+	1.12276i
$949$	417.612	−	111.899i	0.440055	−	0.117912i
$950$	−931.311	−	731.369i	−0.980327	−	0.769862i
$951$	757.842	+	769.408i	0.796890	+	0.809051i
$952$	−12.1365	−	9.97924i	−0.0127484	−	0.0104824i
$953$	454.742			0.477169			0.238584	−	0.971122i	$-0.423317\pi$
$953$	454.742			0.477169			0.238584	+	0.971122i	$0.423317\pi$
$954$	612.716	−	756.352i	0.642260	−	0.792822i
$955$	1190.54	+	1190.54i	1.24664	+	1.24664i
$956$	173.535	+	711.109i	0.181522	+	0.743838i
$957$	−22.6320	−	39.8945i	−0.0236489	−	0.0416870i
$958$	−193.415	−	1608.40i	−0.201894	−	1.67891i
$959$	−336.915	−	194.518i	−0.351320	−	0.202834i
$960$	1330.78	−	640.704i	1.38623	−	0.667400i
$961$	473.499	+	820.124i	0.492715	+	0.853407i
$962$	1352.69	+	1804.42i	1.40612	+	1.87570i
$963$	378.107	+	107.477i	0.392635	+	0.111606i
$964$	−19.3645	+	66.2820i	−0.0200877	+	0.0687573i
$965$	−245.434	−	65.7639i	−0.254336	−	0.0681491i
$966$	114.208	−	84.2727i	0.118228	−	0.0872388i
$967$	148.487	+	85.7291i	0.153554	+	0.0886547i	0.574808	−	0.818288i	$-0.305077\pi$
$967$	148.487	+	85.7291i	0.153554	+	0.0886547i	−0.421254	+	0.906943i	$0.638410\pi$
$968$	1025.07	+	170.229i	1.05895	+	0.175856i
$969$	56.8214	−	14.7650i	0.0586392	−	0.0152373i
$970$	−731.933	−	1824.69i	−0.754570	−	1.88112i
$971$	840.268	−	840.268i	0.865364	−	0.865364i	−0.126591	−	0.991955i	$-0.540404\pi$
$971$	840.268	−	840.268i	0.865364	−	0.865364i	0.991955	+	0.126591i	$0.0404036\pi$
$972$	307.702	−	922.011i	0.316566	−	0.948571i
$973$	−152.316	+	152.316i	−0.156543	+	0.156543i
$974$	−1442.07	−	616.371i	−1.48056	−	0.632825i
$975$	−2200.47	+	571.789i	−2.25689	+	0.586450i
$976$	476.113	−	1503.47i	0.487821	−	1.54044i
$977$	−951.784	−	549.513i	−0.974191	−	0.562449i	−0.0736794	−	0.997282i	$-0.523474\pi$
$977$	−951.784	−	549.513i	−0.974191	−	0.562449i	−0.900511	+	0.434833i	$0.856807\pi$
$978$	1378.82	+	207.957i	1.40984	+	0.212635i
$979$	−953.297	−	255.435i	−0.973746	−	0.260914i
$980$	679.693	+	1240.76i	0.693564	+	1.26608i
$981$	−1061.79	−	301.813i	−1.08235	−	0.307659i
$982$	−213.422	−	30.5376i	−0.217334	−	0.0310974i
$983$	91.7915	+	158.988i	0.0933789	+	0.161737i	0.908931	−	0.416947i	$-0.136900\pi$
$983$	91.7915	+	158.988i	0.0933789	+	0.161737i	−0.815552	+	0.578684i	$0.803567\pi$
$984$	−1114.18	−	930.371i	−1.13230	−	0.945499i
$985$	−691.447	−	399.207i	−0.701977	−	0.405287i
$986$	−1.34685	+	1.71505i	−0.00136597	+	0.00173940i
$987$	33.3065	+	58.7109i	0.0337452	+	0.0594842i
$988$	−364.300	−	1492.82i	−0.368725	−	1.51095i
$989$	164.356	+	164.356i	0.166184	+	0.166184i
$990$	228.848	+	2181.27i	0.231160	+	2.20331i
$991$	14.9447			0.0150804			0.00754022	−	0.999972i	$-0.497600\pi$
$991$	14.9447			0.0150804			0.00754022	+	0.999972i	$0.497600\pi$
$992$	−98.9374	+	67.4533i	−0.0997353	+	0.0679973i
$993$	−560.644	−	569.200i	−0.564596	−	0.573212i
$994$	−40.2689	−	334.869i	−0.0405120	−	0.336890i
$995$	2263.63	−	606.537i	2.27500	−	0.609585i
$996$	30.2711	−	1008.20i	0.0303927	−	1.01225i
$997$	325.325	−	1214.13i	0.326304	−	1.21778i	−0.586691	−	0.809811i	$-0.699570\pi$
$997$	325.325	−	1214.13i	0.326304	−	1.21778i	0.912995	−	0.407971i	$-0.133764\pi$
$998$	−98.2357	−	14.0561i	−0.0984326	−	0.0140843i
$999$	948.518	+	992.625i	0.949467	+	0.993619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.w.a.5.17	✓	184
3.2	odd	2		432.3.x.a.341.30		184
9.2	odd	6	inner	144.3.w.a.101.2	yes	184
9.7	even	3		432.3.x.a.197.45		184
16.13	even	4	inner	144.3.w.a.77.2	yes	184
48.29	odd	4		432.3.x.a.125.45		184
144.29	odd	12	inner	144.3.w.a.29.17	yes	184
144.61	even	12		432.3.x.a.413.30		184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.17	✓	184	1.1	even	1	trivial
144.3.w.a.29.17	yes	184	144.29	odd	12	inner
144.3.w.a.77.2	yes	184	16.13	even	4	inner
144.3.w.a.101.2	yes	184	9.2	odd	6	inner
432.3.x.a.125.45		184	48.29	odd	4
432.3.x.a.197.45		184	9.7	even	3
432.3.x.a.341.30		184	3.2	odd	2
432.3.x.a.413.30		184	144.61	even	12

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.786053 + 1.83905i) q^{2} +(1.51963 - 2.58664i) q^{3} +(-2.76424 - 2.89119i) q^{4} +(1.99100 + 7.43050i) q^{5} +(3.56247 + 4.82792i) q^{6} +(-1.50577 + 0.869355i) q^{7} +(7.48989 - 2.81097i) q^{8} +(-4.38144 - 7.86149i) q^{9} +O(q^{10})\)	\(q+(-0.786053 + 1.83905i) q^{2} +(1.51963 - 2.58664i) q^{3} +(-2.76424 - 2.89119i) q^{4} +(1.99100 + 7.43050i) q^{5} +(3.56247 + 4.82792i) q^{6} +(-1.50577 + 0.869355i) q^{7} +(7.48989 - 2.81097i) q^{8} +(-4.38144 - 7.86149i) q^{9} +(-15.2301 - 2.17922i) q^{10} +(15.2997 + 4.09955i) q^{11} +(-11.6791 + 2.75657i) q^{12} +(5.73919 + 21.4190i) q^{13} +(-0.415179 - 3.45255i) q^{14} +(22.2456 + 6.14163i) q^{15} +(-0.717932 + 15.9839i) q^{16} +1.12960i q^{17} +(17.9017 - 1.87816i) q^{18} +(12.2501 - 12.2501i) q^{19} +(15.9794 - 26.2961i) q^{20} +(-0.0395007 + 5.21598i) q^{21} +(-19.5657 + 24.9146i) q^{22} +(-6.80266 + 11.7825i) q^{23} +(4.11091 - 23.6453i) q^{24} +(-29.5977 + 17.0882i) q^{25} +(-43.9019 - 6.28174i) q^{26} +(-26.9930 - 0.613350i) q^{27} +(6.67578 + 1.95035i) q^{28} +(0.249824 - 0.932358i) q^{29} +(-28.7810 + 36.0833i) q^{30} +(1.87100 - 3.24066i) q^{31} +(-28.8309 - 13.8845i) q^{32} +(33.8540 - 33.3451i) q^{33} +(-2.07740 - 0.887925i) q^{34} +(-9.45773 - 9.45773i) q^{35} +(-10.6177 + 34.3986i) q^{36} +(-35.9564 - 35.9564i) q^{37} +(12.8994 + 32.1578i) q^{38} +(64.1247 + 17.7037i) q^{39} +(35.7992 + 50.0570i) q^{40} +(30.2406 - 52.3783i) q^{41} +(-9.56143 - 4.17268i) q^{42} +(4.42169 - 16.5020i) q^{43} +(-30.4396 - 55.5666i) q^{44} +(49.6914 - 48.2085i) q^{45} +(-16.3215 - 21.7722i) q^{46} +(11.2070 - 6.47034i) q^{47} +(40.2536 + 26.1467i) q^{48} +(-22.9884 + 39.8171i) q^{49} +(-8.16084 - 67.8640i) q^{50} +(2.92187 + 1.71658i) q^{51} +(46.0617 - 75.8003i) q^{52} +(38.2384 - 38.2384i) q^{53} +(22.3459 - 49.1595i) q^{54} +121.847i q^{55} +(-8.83431 + 10.7440i) q^{56} +(-13.0710 - 50.3022i) q^{57} +(1.51828 + 1.19232i) q^{58} +(5.85788 + 21.8619i) q^{59} +(-43.7357 - 81.2933i) q^{60} +(-95.2073 - 25.5107i) q^{61} +(4.48905 + 5.98819i) q^{62} +(13.4319 + 8.02855i) q^{63} +(48.1969 - 42.1077i) q^{64} +(-147.727 + 85.2902i) q^{65} +(34.7125 + 88.4705i) q^{66} +(-20.8577 - 77.8418i) q^{67} +(3.26589 - 3.12249i) q^{68} +(20.1397 + 35.5012i) q^{69} +(24.8276 - 9.95900i) q^{70} +96.9917 q^{71} +(-54.9149 - 46.5656i) q^{72} -19.4973i q^{73} +(94.3893 - 37.8621i) q^{74} +(-0.776435 + 102.526i) q^{75} +(-69.2795 - 1.55509i) q^{76} +(-26.6018 + 7.12794i) q^{77} +(-82.9634 + 104.013i) q^{78} +(-60.9180 - 105.513i) q^{79} +(-120.198 + 26.4893i) q^{80} +(-42.6060 + 68.8893i) q^{81} +(72.5558 + 96.7862i) q^{82} +(-21.7550 + 81.1908i) q^{83} +(15.1896 - 14.3040i) q^{84} +(-8.39350 + 2.24903i) q^{85} +(26.8724 + 21.1032i) q^{86} +(-2.03203 - 2.06305i) q^{87} +(126.117 - 12.3018i) q^{88} -62.3081 q^{89} +(49.5980 + 129.280i) q^{90} +(-27.2626 - 27.2626i) q^{91} +(52.8698 - 12.9021i) q^{92} +(-5.53920 - 9.76420i) q^{93} +(3.09005 + 25.6962i) q^{94} +(115.414 + 66.6344i) q^{95} +(-79.7266 + 53.4759i) q^{96} +(63.8929 + 110.666i) q^{97} +(-55.1558 - 73.5754i) q^{98} +(-34.8063 - 138.241i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6}+O(q^{10}) \) 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6	\( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6} - 8 q^{10} - 6 q^{11} - 64 q^{12} - 2 q^{13} - 6 q^{14} - 8 q^{15} - 2 q^{16} + 54 q^{18} - 8 q^{19} + 120 q^{20} - 22 q^{21} - 2 q^{22} - 160 q^{24} + 44 q^{27} - 72 q^{28} - 6 q^{29} - 90 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 6 q^{34} - 202 q^{36} - 8 q^{37} - 6 q^{38} - 2 q^{40} + 44 q^{42} - 2 q^{43} + 46 q^{45} - 160 q^{46} - 12 q^{47} - 118 q^{48} + 472 q^{49} + 228 q^{50} - 48 q^{51} - 2 q^{52} + 206 q^{54} - 300 q^{56} - 92 q^{58} - 438 q^{59} - 90 q^{60} - 2 q^{61} - 204 q^{63} + 244 q^{64} - 12 q^{65} - 508 q^{66} - 2 q^{67} - 144 q^{68} + 14 q^{69} + 96 q^{70} + 6 q^{72} + 246 q^{74} + 152 q^{75} - 158 q^{76} - 6 q^{77} + 304 q^{78} - 4 q^{79} - 8 q^{81} - 388 q^{82} - 726 q^{83} + 542 q^{84} + 48 q^{85} + 894 q^{86} + 22 q^{88} - 528 q^{90} - 204 q^{91} - 348 q^{92} + 62 q^{93} - 18 q^{94} - 12 q^{95} + 262 q^{96} - 4 q^{97} + 286 q^{99}+O(q^{100}) \) 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6 - 8 * q^10 - 6 * q^11 - 64 * q^12 - 2 * q^13 - 6 * q^14 - 8 * q^15 - 2 * q^16 + 54 * q^18 - 8 * q^19 + 120 * q^20 - 22 * q^21 - 2 * q^22 - 160 * q^24 + 44 * q^27 - 72 * q^28 - 6 * q^29 - 90 * q^30 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 6 * q^34 - 202 * q^36 - 8 * q^37 - 6 * q^38 - 2 * q^40 + 44 * q^42 - 2 * q^43 + 46 * q^45 - 160 * q^46 - 12 * q^47 - 118 * q^48 + 472 * q^49 + 228 * q^50 - 48 * q^51 - 2 * q^52 + 206 * q^54 - 300 * q^56 - 92 * q^58 - 438 * q^59 - 90 * q^60 - 2 * q^61 - 204 * q^63 + 244 * q^64 - 12 * q^65 - 508 * q^66 - 2 * q^67 - 144 * q^68 + 14 * q^69 + 96 * q^70 + 6 * q^72 + 246 * q^74 + 152 * q^75 - 158 * q^76 - 6 * q^77 + 304 * q^78 - 4 * q^79 - 8 * q^81 - 388 * q^82 - 726 * q^83 + 542 * q^84 + 48 * q^85 + 894 * q^86 + 22 * q^88 - 528 * q^90 - 204 * q^91 - 348 * q^92 + 62 * q^93 - 18 * q^94 - 12 * q^95 + 262 * q^96 - 4 * q^97 + 286 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more