LMFDB - Embedded newform 804.2.w.a.59.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(59,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 12]))

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

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

chi := DirichletCharacter("804.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.w (of order $22$, degree $10$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$1320$
Relative dimension:	$132$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			59.2
Character	$\chi$	$=$	804.59
Dual form			804.2.w.a.695.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41300 + 0.0585241i) q^{2} +(-1.35142 + 1.08336i) q^{3} +(1.99315 - 0.165389i) q^{4} +(-0.520814 + 0.810403i) q^{5} +(1.84615 - 1.60988i) q^{6} +(-3.60615 - 0.518486i) q^{7} +(-2.80665 + 0.350343i) q^{8} +(0.652653 - 2.92815i) q^{9} +O(q^{10})$	\(q+(-1.41300 + 0.0585241i) q^{2} +(-1.35142 + 1.08336i) q^{3} +(1.99315 - 0.165389i) q^{4} +(-0.520814 + 0.810403i) q^{5} +(1.84615 - 1.60988i) q^{6} +(-3.60615 - 0.518486i) q^{7} +(-2.80665 + 0.350343i) q^{8} +(0.652653 - 2.92815i) q^{9} +(0.688484 - 1.17558i) q^{10} +(-4.43187 - 2.84819i) q^{11} +(-2.51440 + 2.38281i) q^{12} +(0.999681 + 2.18900i) q^{13} +(5.12584 + 0.521575i) q^{14} +(-0.174123 - 1.65942i) q^{15} +(3.94529 - 0.659291i) q^{16} +(-0.180888 - 0.616047i) q^{17} +(-0.750833 + 4.17567i) q^{18} +(8.00295 - 1.15065i) q^{19} +(-0.904029 + 1.70139i) q^{20} +(5.43512 - 3.20607i) q^{21} +(6.42893 + 3.76513i) q^{22} +(-2.25692 - 2.60462i) q^{23} +(3.41340 - 3.51407i) q^{24} +(1.69157 + 3.70402i) q^{25} +(-1.54066 - 3.03455i) q^{26} +(2.29024 + 4.66421i) q^{27} +(-7.27335 - 0.437001i) q^{28} -2.50262i q^{29} +(0.343152 + 2.33458i) q^{30} +(-3.31716 - 1.51490i) q^{31} +(-5.53612 + 1.16247i) q^{32} +(9.07492 - 0.952229i) q^{33} +(0.291648 + 0.859889i) q^{34} +(2.29832 - 2.65240i) q^{35} +(0.816551 - 5.94418i) q^{36} -4.37584 q^{37} +(-11.2408 + 2.09424i) q^{38} +(-3.72246 - 1.87523i) q^{39} +(1.17782 - 2.45698i) q^{40} +(3.08483 + 10.5060i) q^{41} +(-7.49220 + 4.84827i) q^{42} +(-0.150849 - 0.513743i) q^{43} +(-9.30444 - 4.94388i) q^{44} +(2.03307 + 2.05393i) q^{45} +(3.34146 + 3.54825i) q^{46} +(6.29056 + 7.25969i) q^{47} +(-4.61748 + 5.16516i) q^{48} +(6.01902 + 1.76734i) q^{49} +(-2.60697 - 5.13479i) q^{50} +(0.911856 + 0.636569i) q^{51} +(2.35455 + 4.19766i) q^{52} +(2.43019 - 8.27646i) q^{53} +(-3.50908 - 6.45650i) q^{54} +(4.61636 - 2.10822i) q^{55} +(10.3028 + 0.191818i) q^{56} +(-9.56874 + 10.2251i) q^{57} +(0.146463 + 3.53620i) q^{58} +(-0.741986 + 1.62472i) q^{59} +(-0.621503 - 3.27868i) q^{60} +(8.24157 - 5.29653i) q^{61} +(4.77581 + 1.94642i) q^{62} +(-3.87177 + 10.2209i) q^{63} +(7.75452 - 1.96658i) q^{64} +(-2.29462 - 0.329916i) q^{65} +(-12.7672 + 1.87660i) q^{66} +(2.21072 + 7.88116i) q^{67} +(-0.462424 - 1.19796i) q^{68} +(5.87178 + 1.07487i) q^{69} +(-3.09230 + 3.88235i) q^{70} +(6.96960 + 2.04646i) q^{71} +(-0.805911 + 8.44692i) q^{72} +(4.61078 - 2.96317i) q^{73} +(6.18307 - 0.256092i) q^{74} +(-6.29881 - 3.17309i) q^{75} +(15.7608 - 3.61702i) q^{76} +(14.5052 + 12.5689i) q^{77} +(5.36959 + 2.43185i) q^{78} +(-2.49436 + 1.13914i) q^{79} +(-1.52047 + 3.54064i) q^{80} +(-8.14809 - 3.82213i) q^{81} +(-4.97372 - 14.6644i) q^{82} +(1.34330 + 0.863286i) q^{83} +(10.3027 - 7.28910i) q^{84} +(0.593455 + 0.174254i) q^{85} +(0.243216 + 0.717092i) q^{86} +(2.71124 + 3.38208i) q^{87} +(13.4365 + 6.44118i) q^{88} +(-4.30701 - 3.73205i) q^{89} +(-2.99293 - 2.78323i) q^{90} +(-2.47003 - 8.41216i) q^{91} +(-4.92915 - 4.81813i) q^{92} +(6.12405 - 1.54643i) q^{93} +(-9.31344 - 9.88981i) q^{94} +(-3.23556 + 7.08488i) q^{95} +(6.22223 - 7.56861i) q^{96} +1.97841 q^{97} +(-8.60833 - 2.14500i) q^{98} +(-11.2324 + 11.1183i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1320 q - 18 q^{4} - 5 q^{6} - 22 q^{9}+O(q^{10}) $ 1320 * q - 18 * q^4 - 5 * q^6 - 22 * q^9	$ 1320 q - 18 q^{4} - 5 q^{6} - 22 q^{9} - 26 q^{10} - 15 q^{12} - 44 q^{13} - 34 q^{16} - 13 q^{18} - 66 q^{21} + 74 q^{22} + 13 q^{24} + 80 q^{25} - 110 q^{28} - 36 q^{30} - 22 q^{33} - 54 q^{34} - 37 q^{36} - 72 q^{37} - 22 q^{40} + q^{42} - 154 q^{45} - 82 q^{46} + 11 q^{48} + 96 q^{49} - 14 q^{52} - 138 q^{54} - 6 q^{57} + 74 q^{58} + 3 q^{60} - 28 q^{61} - 6 q^{64} - 4 q^{66} - 38 q^{69} - 18 q^{70} - 145 q^{72} + 96 q^{73} + 14 q^{76} - 51 q^{78} - 38 q^{81} - 74 q^{82} - 41 q^{84} - 76 q^{85} + 6 q^{88} - 5 q^{90} + 78 q^{93} - 22 q^{94} + 184 q^{96} - 128 q^{97}+O(q^{100}) $ 1320 * q - 18 * q^4 - 5 * q^6 - 22 * q^9 - 26 * q^10 - 15 * q^12 - 44 * q^13 - 34 * q^16 - 13 * q^18 - 66 * q^21 + 74 * q^22 + 13 * q^24 + 80 * q^25 - 110 * q^28 - 36 * q^30 - 22 * q^33 - 54 * q^34 - 37 * q^36 - 72 * q^37 - 22 * q^40 + q^42 - 154 * q^45 - 82 * q^46 + 11 * q^48 + 96 * q^49 - 14 * q^52 - 138 * q^54 - 6 * q^57 + 74 * q^58 + 3 * q^60 - 28 * q^61 - 6 * q^64 - 4 * q^66 - 38 * q^69 - 18 * q^70 - 145 * q^72 + 96 * q^73 + 14 * q^76 - 51 * q^78 - 38 * q^81 - 74 * q^82 - 41 * q^84 - 76 * q^85 + 6 * q^88 - 5 * q^90 + 78 * q^93 - 22 * q^94 + 184 * q^96 - 128 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{6}{11}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.41300	+	0.0585241i	−0.999143	+	0.0413828i
$2$	−1.41300	+	0.0585241i	−0.999143	+	0.0413828i
$3$	−1.35142	+	1.08336i	−0.780241	+	0.625479i
$3$	−1.35142	+	1.08336i	−0.780241	+	0.625479i
$4$	1.99315	−	0.165389i	0.996575	−	0.0826947i
$5$	−0.520814	+	0.810403i	−0.232915	+	0.362423i	−0.937962	−	0.346737i	$-0.887290\pi$
$5$	−0.520814	+	0.810403i	−0.232915	+	0.362423i	0.705047	+	0.709161i	$0.250926\pi$
$6$	1.84615	−	1.60988i	0.753688	−	0.657232i
$7$	−3.60615	−	0.518486i	−1.36300	−	0.195969i	−0.578287	−	0.815834i	$-0.696279\pi$
$7$	−3.60615	−	0.518486i	−1.36300	−	0.195969i	−0.784709	+	0.619864i	$0.787188\pi$
$8$	−2.80665	+	0.350343i	−0.992299	+	0.123865i
$9$	0.652653	−	2.92815i	0.217551	−	0.976049i
$10$	0.688484	−	1.17558i	0.217718	−	0.371751i
$11$	−4.43187	−	2.84819i	−1.33626	−	0.858761i	−0.339610	−	0.940566i	$-0.610295\pi$
$11$	−4.43187	−	2.84819i	−1.33626	−	0.858761i	−0.996648	+	0.0818048i	$0.973932\pi$
$12$	−2.51440	+	2.38281i	−0.725844	+	0.687859i
$13$	0.999681	+	2.18900i	0.277261	+	0.607118i	0.996117	−	0.0880418i	$-0.0280609\pi$
$13$	0.999681	+	2.18900i	0.277261	+	0.607118i	−0.718855	+	0.695160i	$0.755334\pi$
$14$	5.12584	+	0.521575i	1.36994	+	0.139397i
$15$	−0.174123	−	1.65942i	−0.0449583	−	0.428461i
$16$	3.94529	−	0.659291i	0.986323	−	0.164823i
$17$	−0.180888	−	0.616047i	−0.0438717	−	0.149413i	0.934644	−	0.355584i	$-0.115718\pi$
$17$	−0.180888	−	0.616047i	−0.0438717	−	0.149413i	−0.978516	+	0.206171i	$0.933900\pi$
$18$	−0.750833	+	4.17567i	−0.176973	+	0.984216i
$19$	8.00295	−	1.15065i	1.83600	−	0.263977i	0.864779	−	0.502152i	$-0.167458\pi$
$19$	8.00295	−	1.15065i	1.83600	−	0.263977i	0.971222	+	0.238175i	$0.0765491\pi$
$20$	−0.904029	+	1.70139i	−0.202147	+	0.380443i
$21$	5.43512	−	3.20607i	1.18604	−	0.699623i
$22$	6.42893	+	3.76513i	1.37065	+	0.802728i
$23$	−2.25692	−	2.60462i	−0.470600	−	0.543101i	0.469979	−	0.882678i	$-0.344262\pi$
$23$	−2.25692	−	2.60462i	−0.470600	−	0.543101i	−0.940578	+	0.339577i	$0.889716\pi$
$24$	3.41340	−	3.51407i	0.696757	−	0.717307i
$25$	1.69157	+	3.70402i	0.338314	+	0.740804i
$26$	−1.54066	−	3.03455i	−0.302148	−	0.595124i
$27$	2.29024	+	4.66421i	0.440756	+	0.897627i
$28$	−7.27335	−	0.437001i	−1.37453	−	0.0825855i
$29$		−	2.50262i		−	0.464724i	−0.972629	−	0.232362i	$-0.925355\pi$
$29$		−	2.50262i		−	0.464724i	0.972629	−	0.232362i	$-0.0746454\pi$
$30$	0.343152	+	2.33458i	0.0626507	+	0.426233i
$31$	−3.31716	−	1.51490i	−0.595779	−	0.272083i	0.0946180	−	0.995514i	$-0.469837\pi$
$31$	−3.31716	−	1.51490i	−0.595779	−	0.272083i	−0.690397	+	0.723430i	$0.742564\pi$
$32$	−5.53612	+	1.16247i	−0.978657	+	0.205498i
$33$	9.07492	−	0.952229i	1.57974	−	0.165762i
$34$	0.291648	+	0.859889i	0.0500173	+	0.147470i
$35$	2.29832	−	2.65240i	0.388486	−	0.448337i
$36$	0.816551	−	5.94418i	0.136092	−	0.990696i
$37$	−4.37584			−0.719384			−0.359692	−	0.933071i	$-0.617118\pi$
$37$	−4.37584			−0.719384			−0.359692	+	0.933071i	$0.617118\pi$
$38$	−11.2408	+	2.09424i	−1.82350	+	0.339730i
$39$	−3.72246	−	1.87523i	−0.596070	−	0.300277i
$40$	1.17782	−	2.45698i	0.186230	−	0.388482i
$41$	3.08483	+	10.5060i	0.481769	+	1.64076i	0.738486	+	0.674268i	$0.235541\pi$
$41$	3.08483	+	10.5060i	0.481769	+	1.64076i	−0.256717	+	0.966487i	$0.582641\pi$
$42$	−7.49220	+	4.84827i	−1.15607	+	0.748105i
$43$	−0.150849	−	0.513743i	−0.0230042	−	0.0783451i	0.947191	−	0.320670i	$-0.103908\pi$
$43$	−0.150849	−	0.513743i	−0.0230042	−	0.0783451i	−0.970195	+	0.242325i	$0.922090\pi$
$44$	−9.30444	−	4.94388i	−1.40270	−	0.745319i
$45$	2.03307	+	2.05393i	0.303072	+	0.306182i
$46$	3.34146	+	3.54825i	0.492672	+	0.523161i
$47$	6.29056	+	7.25969i	0.917572	+	1.05893i	0.998065	+	0.0621793i	$0.0198051\pi$
$47$	6.29056	+	7.25969i	0.917572	+	1.05893i	−0.0804931	+	0.996755i	$0.525649\pi$
$48$	−4.61748	+	5.16516i	−0.666476	+	0.745526i
$49$	6.01902	+	1.76734i	0.859861	+	0.252478i
$50$	−2.60697	−	5.13479i	−0.368681	−	0.726169i
$51$	0.911856	+	0.636569i	0.127685	+	0.0891375i
$52$	2.35455	+	4.19766i	0.326517	+	0.582111i
$53$	2.43019	−	8.27646i	0.333812	−	1.13686i	−0.606085	−	0.795400i	$-0.707261\pi$
$53$	2.43019	−	8.27646i	0.333812	−	1.13686i	0.939897	−	0.341459i	$-0.110921\pi$
$54$	−3.50908	−	6.45650i	−0.477525	−	0.878618i
$55$	4.61636	−	2.10822i	0.622470	−	0.284273i
$56$	10.3028	+	0.191818i	1.37677	+	0.0256328i
$57$	−9.56874	+	10.2251i	−1.26741	+	1.35435i
$58$	0.146463	+	3.53620i	0.0192316	+	0.464326i
$59$	−0.741986	+	1.62472i	−0.0965983	+	0.211521i	−0.951762	−	0.306837i	$-0.900729\pi$
$59$	−0.741986	+	1.62472i	−0.0965983	+	0.211521i	0.855164	+	0.518358i	$0.173457\pi$
$60$	−0.621503	−	3.27868i	−0.0802357	−	0.423276i
$61$	8.24157	−	5.29653i	1.05522	−	0.678151i	0.106518	−	0.994311i	$-0.466030\pi$
$61$	8.24157	−	5.29653i	1.05522	−	0.678151i	0.948706	+	0.316159i	$0.102393\pi$
$62$	4.77581	+	1.94642i	0.606529	+	0.247195i
$63$	−3.87177	+	10.2209i	−0.487797	+	1.28772i
$64$	7.75452	−	1.96658i	0.969315	−	0.245822i
$65$	−2.29462	−	0.329916i	−0.284612	−	0.0409210i
$66$	−12.7672	+	1.87660i	−1.57153	+	0.230994i
$67$	2.21072	+	7.88116i	0.270082	+	0.962837i
$67$	2.21072	+	7.88116i	0.270082	+	0.962837i
$68$	−0.462424	−	1.19796i	−0.0560771	−	0.145274i
$69$	5.87178	+	1.07487i	0.706880	+	0.129399i
$70$	−3.09230	+	3.88235i	−0.369600	+	0.464030i
$71$	6.96960	+	2.04646i	0.827140	+	0.242870i	0.667788	−	0.744352i	$-0.267241\pi$
$71$	6.96960	+	2.04646i	0.827140	+	0.242870i	0.159352	+	0.987222i	$0.449060\pi$
$72$	−0.805911	+	8.44692i	−0.0949775	+	0.995479i
$73$	4.61078	−	2.96317i	0.539651	−	0.346812i	−0.242252	−	0.970213i	$-0.577886\pi$
$73$	4.61078	−	2.96317i	0.539651	−	0.346812i	0.781902	+	0.623401i	$0.214250\pi$
$74$	6.18307	−	0.256092i	0.718767	−	0.0297701i
$75$	−6.29881	−	3.17309i	−0.727324	−	0.366397i
$76$	15.7608	−	3.61702i	1.80788	−	0.414901i
$77$	14.5052	+	12.5689i	1.65302	+	1.43235i
$78$	5.36959	+	2.43185i	0.607986	+	0.275353i
$79$	−2.49436	+	1.13914i	−0.280638	+	0.128163i	−0.550761	−	0.834663i	$-0.685663\pi$
$79$	−2.49436	+	1.13914i	−0.280638	+	0.128163i	0.270124	+	0.962826i	$0.412935\pi$
$80$	−1.52047	+	3.54064i	−0.169994	+	0.395856i
$81$	−8.14809	−	3.82213i	−0.905343	−	0.424681i
$82$	−4.97372	−	14.6644i	−0.549255	−	1.61941i
$83$	1.34330	+	0.863286i	0.147446	+	0.0947579i	0.612284	−	0.790638i	$-0.290251\pi$
$83$	1.34330	+	0.863286i	0.147446	+	0.0947579i	−0.464838	+	0.885396i	$0.653887\pi$
$84$	10.3027	−	7.28910i	1.12412	−	0.795305i
$85$	0.593455	+	0.174254i	0.0643692	+	0.0189005i
$86$	0.243216	+	0.717092i	0.0262266	+	0.0773260i
$87$	2.71124	+	3.38208i	0.290675	+	0.362597i
$88$	13.4365	+	6.44118i	1.43234	+	0.686633i
$89$	−4.30701	−	3.73205i	−0.456542	−	0.395596i	0.396003	−	0.918249i	$-0.370397\pi$
$89$	−4.30701	−	3.73205i	−0.456542	−	0.395596i	−0.852546	+	0.522653i	$0.824942\pi$
$90$	−2.99293	−	2.78323i	−0.315483	−	0.293378i
$91$	−2.47003	−	8.41216i	−0.258930	−	0.881834i
$92$	−4.92915	−	4.81813i	−0.513899	−	0.502325i
$93$	6.12405	−	1.54643i	0.635034	−	0.160357i
$94$	−9.31344	−	9.88981i	−0.960608	−	1.02006i
$95$	−3.23556	+	7.08488i	−0.331961	+	0.726894i
$96$	6.22223	−	7.56861i	0.635053	−	0.772468i
$97$	1.97841			0.200877			0.100439	−	0.994943i	$-0.467975\pi$
$97$	1.97841			0.200877			0.100439	+	0.994943i	$0.467975\pi$
$98$	−8.60833	−	2.14500i	−0.869572	−	0.216678i
$99$	−11.2324	+	11.1183i	−1.12890	+	1.11743i
$100$	3.98416	+	7.10290i	0.398416	+	0.710290i
$101$	16.9093	−	2.43119i	1.68254	−	0.241913i	0.766282	−	0.642504i	$-0.222105\pi$
$101$	16.9093	−	2.43119i	1.68254	−	0.241913i	0.916257	+	0.400592i	$0.131195\pi$
$102$	−1.32571	−	0.846108i	−0.131265	−	0.0837772i
$103$	9.61035	+	4.38890i	0.946936	+	0.432451i	0.828174	−	0.560472i	$-0.189380\pi$
$103$	9.61035	+	4.38890i	0.946936	+	0.432451i	0.118762	+	0.992923i	$0.462107\pi$
$104$	−3.57265	−	5.79350i	−0.350327	−	0.568100i
$105$	−0.232475	+	6.07440i	−0.0226872	+	0.592801i
$106$	−2.94949	+	11.8369i	−0.286480	+	1.14970i
$107$	−1.49522	+	0.960917i	−0.144548	+	0.0928953i	−0.610916	−	0.791695i	$-0.709199\pi$
$107$	−1.49522	+	0.960917i	−0.144548	+	0.0928953i	0.466368	+	0.884591i	$0.345562\pi$
$108$	5.33620	+	8.91768i	0.513476	+	0.858104i
$109$	−3.79151	−	8.30225i	−0.363161	−	0.795211i	−0.999713	−	0.0239773i	$-0.992367\pi$
$109$	−3.79151	−	8.30225i	−0.363161	−	0.795211i	0.636552	−	0.771234i	$-0.280360\pi$
$110$	−6.39955	+	3.24909i	−0.610173	+	0.309789i
$111$	5.91358	−	4.74062i	0.561292	−	0.449960i
$112$	−14.5691	+	0.331924i	−1.37665	+	0.0313639i
$113$	6.75946	+	10.5179i	0.635877	+	0.989443i	0.998348	+	0.0574487i	$0.0182966\pi$
$113$	6.75946	+	10.5179i	0.635877	+	0.989443i	−0.362472	+	0.931995i	$0.618067\pi$
$114$	12.9222	−	15.0081i	1.21028	−	1.40564i
$115$	3.28623	−	0.472488i	0.306442	−	0.0440597i
$116$	−0.413906	−	4.98809i	−0.0384302	−	0.463132i
$117$	7.06214	−	1.49856i	0.652895	−	0.138542i
$118$	0.953342	−	2.33916i	0.0877622	−	0.215337i
$119$	0.332896	+	2.31534i	0.0305165	+	0.212247i
$120$	1.07007	+	4.59641i	0.0976833	+	0.419593i
$121$	6.95972	+	15.2397i	0.632701	+	1.38542i
$122$	−11.3354	+	7.96634i	−1.02626	+	0.721239i
$123$	−15.5506	−	10.8559i	−1.40215	−	0.978847i
$124$	−6.86214	−	2.47079i	−0.616239	−	0.221884i
$125$	−8.65035	−	1.24373i	−0.773711	−	0.111243i
$126$	4.87264	−	14.6688i	0.434090	−	1.30680i
$127$	−4.66457	−	0.670664i	−0.413914	−	0.0595118i	−0.0677877	−	0.997700i	$-0.521594\pi$
$127$	−4.66457	−	0.670664i	−0.413914	−	0.0595118i	−0.346126	+	0.938188i	$0.612503\pi$
$128$	−10.8421	+	3.23260i	−0.958312	+	0.285724i
$129$	0.760429	+	0.530857i	0.0669520	+	0.0467394i
$130$	3.26160	+	0.331882i	0.286062	+	0.0291079i
$131$	12.3261	+	14.2251i	1.07694	+	1.24285i	0.968571	+	0.248739i	$0.0800161\pi$
$131$	12.3261	+	14.2251i	1.07694	+	1.24285i	0.108365	+	0.994111i	$0.465438\pi$
$132$	17.9302	−	3.39883i	1.56062	−	0.295830i
$133$	−29.4564			−2.55419
$134$	−3.58499	−	11.0067i	−0.309696	−	0.950836i
$135$	−4.97267	−	0.573170i	−0.427980	−	0.0493306i
$136$	0.723515	+	1.66565i	0.0620409	+	0.142829i
$137$	16.0810	−	13.9343i	1.37389	−	1.19049i	0.413949	−	0.910300i	$-0.364149\pi$
$137$	16.0810	−	13.9343i	1.37389	−	1.19049i	0.959946	−	0.280186i	$-0.0903961\pi$
$138$	−8.35975	−	1.17515i	−0.711629	−	0.100036i
$139$	8.33741	−	12.9733i	0.707170	−	1.10038i	−0.282811	−	0.959176i	$-0.591267\pi$
$139$	8.33741	−	12.9733i	0.707170	−	1.10038i	0.989981	−	0.141202i	$-0.0450966\pi$
$140$	4.14221	−	5.66674i	0.350081	−	0.478927i
$141$	−16.3660	−	2.99591i	−1.37827	−	0.252301i
$142$	−9.96783	−	2.48376i	−0.836482	−	0.208433i
$143$	1.80422	−	12.5486i	0.150876	−	1.04937i
$144$	0.644405	−	11.9827i	0.0537005	−	0.998557i
$145$	2.02813	+	1.30340i	0.168427	+	0.108241i
$146$	−6.34162	+	4.45680i	−0.524836	+	0.368848i
$147$	−10.0489	+	4.13236i	−0.828818	+	0.340832i
$148$	−8.72170	+	0.723717i	−0.716920	+	0.0594892i
$149$	−12.0839	+	1.73741i	−0.989955	+	0.142334i	−0.618220	−	0.786005i	$-0.712146\pi$
$149$	−12.0839	+	1.73741i	−0.989955	+	0.142334i	−0.371735	+	0.928339i	$0.621237\pi$
$150$	9.08594	+	4.11495i	0.741864	+	0.335985i
$151$	3.65483	+	12.4472i	0.297426	+	1.01294i	0.963646	+	0.267184i	$0.0860930\pi$
$151$	3.65483	+	12.4472i	0.297426	+	1.01294i	−0.666220	+	0.745755i	$0.732089\pi$
$152$	−22.0583	+	6.03324i	−1.78917	+	0.489360i
$153$	−1.92193	+	0.127601i	−0.155379	+	0.0103159i
$154$	−21.2315	−	16.9109i	−1.71088	−	1.36272i
$155$	2.95530	−	1.89926i	0.237375	−	0.152552i
$156$	−7.72956	−	3.12196i	−0.618860	−	0.249956i
$157$	−7.34581	−	8.47751i	−0.586259	−	0.676579i	0.382679	−	0.923881i	$-0.375001\pi$
$157$	−7.34581	−	8.47751i	−0.586259	−	0.676579i	−0.968938	+	0.247302i	$0.920456\pi$
$158$	3.45787	−	1.75558i	0.275093	−	0.139667i
$159$	5.68221	+	13.8177i	0.450628	+	1.09582i
$160$	1.94122	−	5.09192i	0.153467	−	0.402552i
$161$	6.78832	+	10.5628i	0.534994	+	0.832467i
$162$	11.7370	+	4.92382i	0.922142	+	0.386852i
$163$		−	11.3900i		−	0.892134i	−0.895000	−	0.446067i	$-0.852824\pi$
$163$		−	11.3900i		−	0.892134i	0.895000	−	0.446067i	$-0.147176\pi$
$164$	7.88610	+	20.4298i	0.615801	+	1.59530i
$165$	−3.95466	+	7.85028i	−0.307870	+	0.611143i
$166$	−1.94861	−	1.14121i	−0.151241	−	0.0885750i
$167$	−1.57725	−	10.9700i	−0.122051	−	0.848884i	−0.955227	−	0.295875i	$-0.904389\pi$
$167$	−1.57725	−	10.9700i	−0.122051	−	0.848884i	0.833175	−	0.553009i	$-0.186520\pi$
$168$	−14.1312	+	10.9025i	−1.09025	+	0.841144i
$169$	4.72085	−	5.44815i	0.363142	−	0.419089i
$170$	−0.848751	−	0.211490i	−0.0650962	−	0.0162205i
$171$	1.85388	−	24.1848i	0.141769	−	1.84946i
$172$	−0.385631	−	0.999018i	−0.0294041	−	0.0761744i
$173$	−2.27513	−	1.03902i	−0.172975	−	0.0789952i	0.327045	−	0.945009i	$-0.393947\pi$
$173$	−2.27513	−	1.03902i	−0.172975	−	0.0789952i	−0.500021	+	0.866013i	$0.666674\pi$
$174$	−4.02892	−	4.62021i	−0.305432	−	0.350257i
$175$	−4.17957	−	14.2343i	−0.315946	−	1.07601i
$176$	−19.3628	−	8.31505i	−1.45953	−	0.626770i
$177$	−0.757430	−	2.99952i	−0.0569320	−	0.225457i
$178$	6.30423	+	5.02133i	0.472522	+	0.376364i
$179$	4.54891	−	5.24972i	0.340001	−	0.392382i	−0.559839	−	0.828601i	$-0.689137\pi$
$179$	4.54891	−	5.24972i	0.340001	−	0.392382i	0.899841	+	0.436219i	$0.143683\pi$
$180$	4.39191	+	3.75755i	0.327353	+	0.280071i
$181$	−11.1655	−	12.8857i	−0.829926	−	0.957785i	0.169690	−	0.985497i	$-0.445723\pi$
$181$	−11.1655	−	12.8857i	−0.829926	−	0.957785i	−0.999616	+	0.0277123i	$0.991178\pi$
$182$	3.98248	+	11.7418i	0.295201	+	0.870363i
$183$	−5.39973	+	16.0864i	−0.399159	+	1.18914i
$184$	7.24688	+	6.51955i	0.534247	+	0.480628i
$185$	2.27900	−	3.54619i	0.167555	−	0.260721i
$186$	−8.56279	+	2.54351i	−0.627854	+	0.186499i
$187$	−0.952947	+	3.24544i	−0.0696864	+	0.237330i
$188$	13.7387	+	13.4293i	1.00200	+	0.979429i
$189$	−5.84061	−	18.0073i	−0.424842	−	1.30984i
$190$	4.15721	−	10.2003i	0.301596	−	0.740009i
$191$	11.5241	−	13.2995i	0.833853	−	0.962318i	−0.165863	−	0.986149i	$-0.553041\pi$
$191$	11.5241	−	13.2995i	0.833853	−	0.962318i	0.999716	+	0.0238308i	$0.00758630\pi$
$192$	−8.34907	+	11.0586i	−0.602542	+	0.798087i
$193$	−1.98968	+	4.35680i	−0.143221	+	0.313609i	−0.967625	−	0.252392i	$-0.918783\pi$
$193$	−1.98968	+	4.35680i	−0.143221	+	0.313609i	0.824405	+	0.566001i	$0.191510\pi$
$194$	−2.79550	+	0.115785i	−0.200705	+	0.00831287i
$195$	3.45840	−	2.04005i	0.247661	−	0.146091i
$196$	12.2891	+	2.52710i	0.877794	+	0.180507i
$197$	2.68891	−	9.15757i	0.191577	−	0.652450i	−0.806544	−	0.591174i	$-0.798665\pi$
$197$	2.68891	−	9.15757i	0.191577	−	0.652450i	0.998121	−	0.0612764i	$-0.0195171\pi$
$198$	15.2207	−	16.3675i	1.08169	−	1.16319i
$199$	−9.25092	−	1.33008i	−0.655780	−	0.0942869i	−0.193610	−	0.981078i	$-0.562020\pi$
$199$	−9.25092	−	1.33008i	−0.655780	−	0.0942869i	−0.462170	+	0.886792i	$0.652929\pi$
$200$	−6.04531	−	9.80325i	−0.427468	−	0.693194i
$201$	−11.5258	−	8.25572i	−0.812964	−	0.582314i
$202$	−23.7506	+	4.42488i	−1.67109	+	0.311333i
$203$	−1.29757	+	9.02480i	−0.0910716	+	0.633417i
$204$	1.92275	+	1.11797i	0.134619	+	0.0782733i
$205$	−10.1207	−	2.97170i	−0.706859	−	0.207553i
$206$	−13.8363	−	5.63909i	−0.964021	−	0.392894i
$207$	−9.09970	+	4.90867i	−0.632473	+	0.341176i
$208$	5.38722	+	7.97715i	0.373536	+	0.553116i
$209$	−38.7453	−	17.6944i	−2.68007	−	1.22395i
$210$	−0.0270117	−	8.59675i	−0.00186399	−	0.593232i
$211$	−3.63365	−	3.14858i	−0.250151	−	0.216757i	0.520755	−	0.853706i	$-0.325651\pi$
$211$	−3.63365	−	3.14858i	−0.250151	−	0.216757i	−0.770906	+	0.636949i	$0.780196\pi$
$212$	3.47489	−	16.8981i	0.238656	−	1.16057i
$213$	−11.6359	+	4.78498i	−0.797278	+	0.327862i
$214$	2.05651	−	1.44528i	0.140580	−	0.0987976i
$215$	0.494903	+	0.145317i	0.0337521	+	0.00991051i
$216$	−8.06195	−	12.2884i	−0.548547	−	0.836120i
$217$	11.1767	+	7.18284i	0.758725	+	0.487603i
$218$	5.84329	+	11.5092i	0.395758	+	0.779502i
$219$	−3.02090	+	8.99962i	−0.204133	+	0.608138i
$220$	8.85242	−	4.96550i	0.596830	−	0.334774i
$221$	1.16769	−	1.01181i	0.0785476	−	0.0680619i
$222$	−8.07846	+	7.04459i	−0.542191	+	0.472802i
$223$	7.05263	+	6.11114i	0.472279	+	0.409232i	0.858213	−	0.513294i	$-0.171575\pi$
$223$	7.05263	+	6.11114i	0.472279	+	0.409232i	−0.385933	+	0.922527i	$0.626121\pi$
$224$	20.5668	−	1.32166i	1.37418	−	0.0883068i
$225$	11.9499	−	2.53572i	0.796662	−	0.169048i
$226$	−10.1667	−	14.4663i	−0.676278	−	0.962282i
$227$	15.7249	−	4.61725i	1.04370	−	0.306458i	0.285430	−	0.958399i	$-0.407864\pi$
$227$	15.7249	−	4.61725i	1.04370	−	0.306458i	0.758269	+	0.651942i	$0.226045\pi$
$228$	−17.3808	+	21.9627i	−1.15107	+	1.45452i
$229$	−9.26419	+	20.2858i	−0.612195	+	1.34052i	0.308867	+	0.951105i	$0.400050\pi$
$229$	−9.26419	+	20.2858i	−0.612195	+	1.34052i	−0.921062	+	0.389415i	$0.872677\pi$
$230$	−4.61579	+	0.859950i	−0.304356	+	0.0567034i
$231$	−33.2192	−	1.27134i	−2.18566	−	0.0836480i
$232$	0.876774	+	7.02396i	0.0575630	+	0.461145i
$233$	18.0096	+	15.6054i	1.17985	+	1.02235i	0.999247	+	0.0387898i	$0.0123503\pi$
$233$	18.0096	+	15.6054i	1.17985	+	1.02235i	0.180603	+	0.983556i	$0.442195\pi$
$234$	−9.89112	+	2.53077i	−0.646603	+	0.165442i
$235$	−9.15948	+	1.31693i	−0.597499	+	0.0859074i
$236$	−1.21018	+	3.36103i	−0.0787758	+	0.218784i
$237$	2.13682	−	4.24174i	0.138802	−	0.275531i
$238$	−0.605886	−	3.25210i	−0.0392738	−	0.210803i
$239$	25.6128			1.65675			0.828377	−	0.560171i	$-0.189265\pi$
$239$	25.6128			1.65675			0.828377	+	0.560171i	$0.189265\pi$
$240$	−1.78101	−	6.43211i	−0.114964	−	0.415191i
$241$	−14.5477	+	9.34923i	−0.937099	+	0.602237i	−0.917571	−	0.397572i	$-0.869853\pi$
$241$	−14.5477	+	9.34923i	−0.937099	+	0.602237i	−0.0195284	+	0.999809i	$0.506216\pi$
$242$	−10.7260	−	21.1263i	−0.689492	−	1.35805i
$243$	15.1522	−	3.66204i	0.972015	−	0.234920i
$244$	15.5507	−	11.9198i	0.995531	−	0.763090i
$245$	−4.56705	+	3.95738i	−0.291778	+	0.252827i
$246$	22.6084	+	14.4294i	1.44146	+	0.919984i
$247$	10.5192	+	16.3681i	0.669318	+	1.04148i
$248$	9.84082	+	3.08963i	0.624893	+	0.196192i
$249$	−2.75061	+	0.288620i	−0.174313	+	0.0182906i
$250$	12.2958	+	1.25114i	0.777652	+	0.0791293i
$251$	4.37120	−	1.28350i	0.275908	−	0.0810138i	−0.140852	−	0.990031i	$-0.544984\pi$
$251$	4.37120	−	1.28350i	0.275908	−	0.0810138i	0.416759	+	0.909017i	$0.363166\pi$
$252$	−6.02658	+	21.0122i	−0.379639	+	1.32364i
$253$	2.58391	+	17.9715i	0.162449	+	1.12986i
$254$	6.63030	+	0.674660i	0.416022	+	0.0423320i
$255$	−0.990785	+	0.407437i	−0.0620454	+	0.0255147i
$256$	15.1307	−	5.20220i	0.945667	−	0.325137i
$257$	−15.3382	+	23.8667i	−0.956770	+	1.48876i	−0.0864616	+	0.996255i	$0.527556\pi$
$257$	−15.3382	+	23.8667i	−0.956770	+	1.48876i	−0.870308	+	0.492508i	$0.836080\pi$
$258$	−1.10556	−	0.705599i	−0.0688289	−	0.0439287i
$259$	15.7799	+	2.26881i	0.980517	+	0.140977i
$260$	−4.62808	−	0.278067i	−0.287021	−	0.0172450i
$261$	−7.32803	−	1.63334i	−0.453594	−	0.101101i
$262$	−18.2493	−	19.3787i	−1.12745	−	1.19722i
$263$	−16.2139	−	10.4201i	−0.999794	−	0.642529i	−0.0650618	−	0.997881i	$-0.520724\pi$
$263$	−16.2139	−	10.4201i	−0.999794	−	0.642529i	−0.934732	+	0.355353i	$0.884361\pi$
$264$	−25.1365	+	5.85190i	−1.54704	+	0.360160i
$265$	5.44159	+	6.27993i	0.334274	+	0.385773i
$266$	41.6220	−	1.72391i	2.55201	−	0.105700i
$267$	9.86373	+	0.377497i	0.603650	+	0.0231024i
$268$	5.70976	+	15.3427i	0.348779	+	0.937205i
$269$		−	7.45833i		−	0.454742i	−0.973808	−	0.227371i	$-0.926987\pi$
$269$		−	7.45833i		−	0.454742i	0.973808	−	0.227371i	$-0.0730131\pi$
$270$	7.05994	+	0.518870i	0.429654	+	0.0315774i
$271$	8.62807	−	7.47627i	0.524118	−	0.454151i	−0.352172	−	0.935935i	$-0.614557\pi$
$271$	8.62807	−	7.47627i	0.524118	−	0.454151i	0.876290	+	0.481785i	$0.160011\pi$
$272$	−1.11981	−	2.31123i	−0.0678984	−	0.140139i
$273$	12.4515	+	8.69239i	0.753597	+	0.526087i
$274$	−21.9070	+	20.6303i	−1.32345	+	1.24632i
$275$	3.05294	−	21.2336i	0.184099	−	1.28044i
$276$	11.8811	+	1.17125i	0.715159	+	0.0705007i
$277$	0.191016	−	1.32854i	0.0114770	−	0.0798244i	−0.983278	−	0.182111i	$-0.941707\pi$
$277$	0.191016	−	1.32854i	0.0114770	−	0.0798244i	0.994755	+	0.102287i	$0.0326160\pi$
$278$	−11.0215	+	18.8192i	−0.661027	+	1.12870i
$279$	−6.60079	+	8.72443i	−0.395179	+	0.522318i
$280$	−5.52131	+	8.24954i	−0.329961	+	0.493004i
$281$	−21.6520	+	9.88816i	−1.29165	+	0.589878i	−0.938368	−	0.345638i	$-0.887663\pi$
$281$	−21.6520	+	9.88816i	−1.29165	+	0.589878i	−0.353285	+	0.935516i	$0.614935\pi$
$282$	23.3006	+	3.27542i	1.38753	+	0.195049i
$283$	−6.54844	+	0.941524i	−0.389264	+	0.0559678i	−0.334169	−	0.942513i	$-0.608455\pi$
$283$	−6.54844	+	0.941524i	−0.389264	+	0.0559678i	−0.0550957	+	0.998481i	$0.517546\pi$
$284$	14.2299	+	2.92620i	0.844391	+	0.173638i
$285$	−3.30291	−	13.0799i	−0.195647	−	0.774787i
$286$	−1.81497	+	17.8368i	−0.107321	+	1.05471i
$287$	−5.67715	−	39.4855i	−0.335112	−	2.33075i
$288$	−0.209270	+	16.9693i	−0.0123314	+	0.999924i
$289$	13.9545	−	8.96802i	0.820854	−	0.527531i
$290$	−2.94203	−	1.72301i	−0.172762	−	0.101179i
$291$	−2.67366	+	2.14334i	−0.156733	+	0.125645i
$292$	8.69990	−	6.66861i	0.509123	−	0.390251i
$293$	6.10119	−	2.78632i	0.356435	−	0.162779i	−0.229146	−	0.973392i	$-0.573593\pi$
$293$	6.10119	−	2.78632i	0.356435	−	0.162779i	0.585582	+	0.810613i	$0.300866\pi$
$294$	13.9572	−	6.42714i	0.814003	−	0.374838i
$295$	−0.930243	−	1.44749i	−0.0541608	−	0.0842759i
$296$	12.2814	−	1.53304i	0.713844	−	0.0891064i
$297$	3.13451	−	27.1942i	0.181883	−	1.57797i
$298$	16.9730	−	3.16216i	0.983217	−	0.183179i
$299$	3.44531	−	7.54417i	0.199247	−	0.436291i
$300$	−13.0793	−	5.28269i	−0.755132	−	0.304996i
$301$	0.277614	+	1.93085i	0.0160014	+	0.111292i
$302$	−5.89274	−	17.3740i	−0.339089	−	0.999763i
$303$	−20.2177	+	21.6044i	−1.16147	+	1.24114i
$304$	30.8154	−	9.81593i	1.76738	−	0.562982i
$305$			9.43750i			0.540390i
$306$	2.70823	−	0.292779i	0.154819	−	0.0167371i
$307$	7.66150	+	3.49889i	0.437265	+	0.199692i	0.621870	−	0.783121i	$-0.286373\pi$
$307$	7.66150	+	3.49889i	0.437265	+	0.199692i	−0.184605	+	0.982813i	$0.559101\pi$
$308$	30.9898	+	22.6526i	1.76581	+	1.29075i
$309$	−17.7424	+	4.48026i	−1.00933	+	0.254873i
$310$	−4.06469	+	2.85661i	−0.230859	+	0.162244i
$311$	−0.897268	+	0.263462i	−0.0508794	+	0.0149395i	−0.307073	−	0.951686i	$-0.599350\pi$
$311$	−0.897268	+	0.263462i	−0.0508794	+	0.0149395i	0.256194	+	0.966625i	$0.417531\pi$
$312$	11.1046	+	3.95896i	0.628674	+	0.224132i
$313$	16.0261	−	18.4951i	0.905849	−	1.04540i	−0.0929141	−	0.995674i	$-0.529618\pi$
$313$	16.0261	−	18.4951i	0.905849	−	1.04540i	0.998763	−	0.0497308i	$-0.0158363\pi$
$314$	10.8758	+	11.5488i	0.613756	+	0.651739i
$315$	−6.26661	−	8.46090i	−0.353083	−	0.476718i
$316$	−4.78323	+	2.68301i	−0.269078	+	0.150931i
$317$	−1.35455	+	4.61319i	−0.0760793	+	0.259102i	−0.988746	−	0.149601i	$-0.952201\pi$
$317$	−1.35455	+	4.61319i	−0.0760793	+	0.259102i	0.912667	+	0.408704i	$0.134019\pi$
$318$	−8.83764	−	19.1919i	−0.495590	−	1.07623i
$319$	−7.12793	+	11.0913i	−0.399087	+	0.620992i
$320$	−2.44495	+	7.30851i	−0.136677	+	0.408558i
$321$	0.979639	−	2.91846i	0.0546781	−	0.162893i
$322$	−10.2101	−	14.5280i	−0.568986	−	0.809615i
$323$	−2.15649	−	4.72205i	−0.119990	−	0.262742i
$324$	−16.8725	−	6.27047i	−0.937361	−	0.348359i
$325$	−6.41705	+	7.40568i	−0.355954	+	0.410793i
$326$	0.666589	+	16.0941i	0.0369190	+	0.891369i
$327$	14.1183	+	7.11222i	0.780741	+	0.393307i
$328$	−12.3387	−	28.4058i	−0.681291	−	1.56845i
$329$	−18.9206	−	29.4411i	−1.04313	−	1.62314i
$330$	5.12851	−	11.3239i	0.282315	−	0.623360i
$331$	3.30942	−	11.2708i	0.181902	−	0.619502i	−0.817169	−	0.576399i	$-0.804457\pi$
$331$	3.30942	−	11.2708i	0.181902	−	0.619502i	0.999071	−	0.0431029i	$-0.0137243\pi$
$332$	2.82017	+	1.49849i	0.154777	+	0.0822404i
$333$	−2.85591	+	12.8131i	−0.156503	+	0.702154i
$334$	2.87066	+	15.4083i	0.157076	+	0.843106i
$335$	−7.53829	−	2.31305i	−0.411861	−	0.126375i
$336$	19.3294	−	16.2322i	1.05450	−	0.885540i
$337$	3.78261	−	26.3086i	0.206052	−	1.43312i	−0.579826	−	0.814740i	$-0.696879\pi$
$337$	3.78261	−	26.3086i	0.206052	−	1.43312i	0.785878	−	0.618382i	$-0.212211\pi$
$338$	−6.35172	+	7.97454i	−0.345488	+	0.433758i
$339$	−20.5296	−	6.89116i	−1.11501	−	0.374276i
$340$	1.21166	+	0.249163i	0.0657117	+	0.0135128i
$341$	10.3865	+	16.1617i	0.562461	+	0.875206i
$342$	−1.20414	+	34.2816i	−0.0651124	+	1.85374i
$343$	2.40885	+	1.10008i	0.130066	+	0.0593990i
$344$	0.603364	+	1.38905i	0.0325312	+	0.0748923i
$345$	−3.92919	+	4.19870i	−0.211540	+	0.226051i
$346$	3.27558	+	1.33499i	0.176096	+	0.0717693i
$347$	0.0874751	+	0.191544i	0.00469591	+	0.0102826i	0.911965	−	0.410267i	$-0.134565\pi$
$347$	0.0874751	+	0.191544i	0.00469591	+	0.0102826i	−0.907270	+	0.420550i	$0.861837\pi$
$348$	5.96327	+	6.29258i	0.319665	+	0.337318i
$349$	7.93115	+	2.32880i	0.424545	+	0.124658i	0.487024	−	0.873389i	$-0.338082\pi$
$349$	7.93115	+	2.32880i	0.424545	+	0.124658i	−0.0624791	+	0.998046i	$0.519901\pi$
$350$	6.73879	+	19.8685i	0.360203	+	1.06202i
$351$	−7.92042	+	9.67603i	−0.422761	+	0.516468i
$352$	27.8463	+	10.6160i	1.48421	+	0.565834i
$353$	7.38114	−	25.1379i	0.392859	−	1.33795i	−0.491391	−	0.870939i	$-0.663511\pi$
$353$	7.38114	−	25.1379i	0.392859	−	1.33795i	0.884250	−	0.467015i	$-0.154670\pi$
$354$	1.24579	+	4.19399i	0.0662132	+	0.222908i
$355$	−5.28833	+	4.58236i	−0.280675	+	0.243206i
$356$	−9.20176	−	6.72620i	−0.487692	−	0.356488i
$357$	−2.95824	−	2.76835i	−0.156566	−	0.146516i
$358$	−6.12038	+	7.68408i	−0.323472	+	0.406116i
$359$	−31.3615	+	9.20857i	−1.65520	+	0.486010i	−0.970153	−	0.242493i	$-0.922035\pi$
$359$	−31.3615	+	9.20857i	−1.65520	+	0.486010i	−0.685043	+	0.728502i	$0.740217\pi$
$360$	−6.42568	−	5.05239i	−0.338663	−	0.266284i
$361$	44.4928	−	13.0643i	2.34173	−	0.687593i
$362$	16.5310	+	17.5540i	0.868850	+	0.922620i
$363$	−25.9155	−	13.0552i	−1.36021	−	0.685222i
$364$	−6.31443	−	16.3582i	−0.330966	−	0.857401i
$365$			5.27985i			0.276360i
$366$	6.68838	−	23.0462i	0.349607	−	1.20464i
$367$	−9.59260	−	8.31204i	−0.500730	−	0.433885i	0.367517	−	0.930017i	$-0.380208\pi$
$367$	−9.59260	−	8.31204i	−0.500730	−	0.433885i	−0.868247	+	0.496132i	$0.834753\pi$
$368$	−10.6214	−	8.78803i	−0.553679	−	0.458108i
$369$	32.7763	−	2.17608i	1.70627	−	0.113282i
$370$	−3.01269	+	5.14415i	−0.156622	+	0.267432i
$371$	−13.0548	+	28.5861i	−0.677774	+	1.48412i
$372$	11.9504	−	4.09512i	0.619598	−	0.212322i
$373$	16.9142			0.875786			0.437893	−	0.899027i	$-0.355725\pi$
$373$	16.9142			0.875786			0.437893	+	0.899027i	$0.355725\pi$
$374$	1.15658	−	4.64159i	0.0598053	−	0.240011i
$375$	13.0376	−	7.69066i	0.673261	−	0.397144i
$376$	−20.1987	−	18.1715i	−1.04167	−	0.937125i
$377$	5.47821	−	2.50182i	0.282142	−	0.128850i
$378$	9.30665	+	25.1025i	0.478683	+	1.29113i
$379$	−17.4074	+	15.0836i	−0.894157	+	0.774792i	−0.975063	−	0.221930i	$-0.928764\pi$
$379$	−17.4074	+	15.0836i	−0.894157	+	0.774792i	0.0809054	+	0.996722i	$0.474219\pi$
$380$	−5.27719	+	14.6564i	−0.270714	+	0.751856i
$381$	7.03035	−	4.14708i	0.360176	−	0.212461i
$382$	−15.5052	+	19.4667i	−0.793316	+	0.996001i
$383$	5.07477	+	35.2958i	0.259308	+	1.80353i	0.537780	+	0.843085i	$0.319263\pi$
$383$	5.07477	+	35.2958i	0.259308	+	1.80353i	−0.278471	+	0.960445i	$0.589828\pi$
$384$	11.1501	−	16.1145i	0.568999	−	0.822338i
$385$	−17.7404	+	5.20904i	−0.904133	+	0.265477i
$386$	2.55645	−	6.27261i	0.130120	−	0.319268i
$387$	−1.60277	+	0.106411i	−0.0814732	+	0.00540916i
$388$	3.94327	−	0.327208i	0.200189	−	0.0166115i
$389$	−18.7023	+	8.54106i	−0.948244	+	0.433049i	−0.828646	−	0.559774i	$-0.810888\pi$
$389$	−18.7023	+	8.54106i	−0.948244	+	0.433049i	−0.119599	+	0.992822i	$0.538161\pi$
$390$	−4.76733	+	3.08499i	−0.241403	+	0.156214i
$391$	−1.19632	+	1.86151i	−0.0605005	+	0.0941406i
$392$	−17.5124	−	2.85159i	−0.884512	−	0.144027i
$393$	−32.0686	−	5.87037i	−1.61765	−	0.296121i
$394$	−3.26349	+	13.0970i	−0.164412	+	0.659819i
$395$	0.375939	−	2.61472i	0.0189156	−	0.131561i
$396$	−20.5490	+	24.0181i	−1.03263	+	1.20696i
$397$	−1.78020	−	1.14407i	−0.0893459	−	0.0574191i	0.495205	−	0.868776i	$-0.335093\pi$
$397$	−1.78020	−	1.14407i	−0.0893459	−	0.0574191i	−0.584551	+	0.811357i	$0.698729\pi$
$398$	13.1494	+	1.33801i	0.659120	+	0.0670682i
$399$	39.8079	−	31.9120i	1.99289	−	1.59760i
$400$	9.11577	+	13.4982i	0.455788	+	0.674911i
$401$			7.76612i			0.387821i	0.981019	+	0.193911i	$0.0621172\pi$
$401$			7.76612i			0.387821i	−0.981019	+	0.193911i	$0.937883\pi$
$402$	16.7691	+	10.9908i	0.836365	+	0.548172i
$403$		−	8.77566i		−	0.437147i
$404$	33.3007	−	7.64235i	1.65677	−	0.380221i
$405$	7.34110	−	4.61261i	0.364782	−	0.229203i
$406$	1.30530	−	12.8280i	0.0647811	−	0.636643i
$407$	19.3931	+	12.4632i	0.961283	+	0.617779i
$408$	−2.78227	−	1.46716i	−0.137743	−	0.0726353i
$409$	−3.94205	+	27.4176i	−0.194922	+	1.35571i	0.623829	+	0.781561i	$0.285576\pi$
$409$	−3.94205	+	27.4176i	−0.194922	+	1.35571i	−0.818750	+	0.574150i	$0.805333\pi$
$410$	14.4745	+	3.60671i	0.714843	+	0.178123i
$411$	−6.63628	+	36.2526i	−0.327344	+	1.78821i
$412$	19.8807	+	7.15828i	0.979454	+	0.352663i
$413$	3.51811	−	5.47428i	0.173115	−	0.269372i
$414$	12.5706	−	7.46851i	0.617812	−	0.367057i
$415$	−1.39922	+	0.639002i	−0.0686849	+	0.0313674i
$416$	−8.07901	−	10.9564i	−0.396106	−	0.537184i
$417$	2.78743	+	26.5647i	0.136501	+	1.30088i
$418$	55.7827	+	22.7347i	2.72842	+	1.11199i
$419$	36.5661	−	10.7368i	1.78637	−	0.524526i	0.790273	−	0.612755i	$-0.209939\pi$
$419$	36.5661	−	10.7368i	1.78637	−	0.524526i	0.996100	+	0.0882286i	$0.0281206\pi$
$420$	0.541285	+	12.1456i	0.0264120	+	0.592647i
$421$	−3.72254	−	25.8909i	−0.181426	−	1.26184i	−0.853395	−	0.521265i	$-0.825460\pi$
$421$	−3.72254	−	25.8909i	−0.181426	−	1.26184i	0.671969	−	0.740579i	$-0.265449\pi$
$422$	5.31863	+	4.23629i	0.258907	+	0.206219i
$423$	25.3630	−	13.6816i	1.23319	−	0.665223i
$424$	−3.92108	+	24.0805i	−0.190424	+	1.16945i
$425$	1.97587	−	1.71210i	0.0958436	−	0.0830490i
$426$	16.1615	−	7.44217i	0.783028	−	0.360574i
$427$	−32.4665	+	14.8269i	−1.57116	+	0.717526i
$428$	−2.82126	+	2.16254i	−0.136371	+	0.104531i
$429$	11.1564	+	18.9130i	0.538638	+	0.913130i
$430$	−0.707803	−	0.176369i	−0.0341333	−	0.00850526i
$431$	11.7225			0.564653			0.282326	−	0.959318i	$-0.408894\pi$
$431$	11.7225			0.564653			0.282326	+	0.959318i	$0.408894\pi$
$432$	12.1107	+	16.8917i	0.582678	+	0.812703i
$433$	−6.60152	+	14.4553i	−0.317249	+	0.694678i	−0.999330	−	0.0365982i	$-0.988348\pi$
$433$	−6.60152	+	14.4553i	−0.317249	+	0.694678i	0.682081	+	0.731277i	$0.261075\pi$
$434$	−16.2131	−	9.49526i	−0.778253	−	0.455787i
$435$	−4.15290	+	0.435762i	−0.199116	+	0.0208932i
$436$	−8.93015	−	15.9206i	−0.427677	−	0.762456i
$437$	−21.0590	−	18.2477i	−1.00739	−	0.872907i
$438$	3.74184	−	12.8933i	0.178792	−	0.616064i
$439$			33.3389i			1.59118i	0.605837	+	0.795589i	$0.292839\pi$
$439$			33.3389i			1.59118i	−0.605837	+	0.795589i	$0.707161\pi$
$440$	−12.2179	+	7.53434i	−0.582465	+	0.359186i
$441$	9.10338	−	16.4711i	0.433494	−	0.784339i
$442$	−1.59074	+	1.49803i	−0.0756637	+	0.0712541i
$443$	26.4529	−	7.76728i	1.25682	−	0.369035i	0.415508	−	0.909590i	$-0.363604\pi$
$443$	26.4529	−	7.76728i	1.25682	−	0.369035i	0.841309	+	0.540555i	$0.181786\pi$
$444$	11.0026	−	10.4268i	0.522161	−	0.494834i
$445$	5.26761	−	1.54671i	0.249709	−	0.0733211i
$446$	−10.3230	−	8.22230i	−0.488810	−	0.389337i
$447$	14.4482	−	15.4392i	0.683376	−	0.730251i
$448$	−28.9836	+	3.07116i	−1.36935	+	0.145098i
$449$	−12.2561	+	10.6199i	−0.578400	+	0.501186i	−0.894217	−	0.447634i	$-0.852267\pi$
$449$	−12.2561	+	10.6199i	−0.578400	+	0.501186i	0.315817	+	0.948820i	$0.397721\pi$
$450$	−16.7369	+	4.28234i	−0.788984	+	0.201872i
$451$	16.2514	−	55.3472i	0.765249	−	2.60620i
$452$	15.2122	+	19.8459i	0.715520	+	0.933471i
$453$	−18.4240	−	12.8619i	−0.865636	−	0.604303i
$454$	−21.9491	+	7.44447i	−1.03012	+	0.349386i
$455$	8.10367	+	2.37945i	0.379906	+	0.111550i
$456$	23.2738	−	32.0506i	1.08989	−	1.50091i
$457$	9.65132	+	21.1334i	0.451470	+	0.988580i	0.989350	+	0.145559i	$0.0464981\pi$
$457$	9.65132	+	21.1334i	0.451470	+	0.988580i	−0.537880	+	0.843021i	$0.680775\pi$
$458$	11.9031	−	29.2060i	0.556196	−	1.36471i
$459$	2.45909	−	2.25459i	0.114781	−	0.105235i
$460$	6.47180	−	1.48525i	0.301749	−	0.0692500i
$461$	9.86659	+	4.50592i	0.459533	+	0.209862i	0.631711	−	0.775204i	$-0.282353\pi$
$461$	9.86659	+	4.50592i	0.459533	+	0.209862i	−0.172178	+	0.985066i	$0.555080\pi$
$462$	47.0132	−	0.147720i	2.18725	−	0.00687254i
$463$	−17.1212	−	26.6410i	−0.795688	−	1.23811i	−0.967472	−	0.252979i	$-0.918590\pi$
$463$	−17.1212	−	26.6410i	−0.795688	−	1.23811i	0.171784	−	0.985135i	$-0.445047\pi$
$464$	−1.64995	−	9.87355i	−0.0765972	−	0.458368i
$465$	−1.93626	+	5.76835i	−0.0897919	+	0.267501i
$466$	−26.3609	−	20.9965i	−1.22115	−	0.972645i
$467$	0.252935	−	1.75920i	0.0117044	−	0.0814060i	−0.983132	−	0.182897i	$-0.941452\pi$
$467$	0.252935	−	1.75920i	0.0117044	−	0.0814060i	0.994836	+	0.101491i	$0.0323615\pi$
$468$	13.8281	−	4.15485i	0.639203	−	0.192058i
$469$	−3.88591	−	29.5669i	−0.179435	−	1.36527i
$470$	12.8653	−	2.39688i	0.593432	−	0.110560i
$471$	19.1115	+	3.49848i	0.880610	+	0.161202i
$472$	1.51328	−	4.81997i	0.0696544	−	0.221857i
$473$	−0.794696	+	2.70649i	−0.0365402	+	0.124444i
$474$	−2.77109	+	6.11865i	−0.127280	+	0.281039i
$475$	17.7996	+	27.6967i	0.816700	+	1.27081i
$476$	1.04645	+	4.55977i	0.0479637	+	0.208997i
$477$	−22.6486	−	12.5176i	−1.03701	−	0.573142i
$478$	−36.1909	+	1.49897i	−1.65533	+	0.0685611i
$479$	−4.71978	+	5.44692i	−0.215652	+	0.248876i	−0.853261	−	0.521485i	$-0.825378\pi$
$479$	−4.71978	+	5.44692i	−0.215652	+	0.248876i	0.637608	+	0.770361i	$0.279924\pi$
$480$	2.89300	+	8.98435i	0.132047	+	0.410078i
$481$	−4.37444	−	9.57869i	−0.199457	−	0.436751i
$482$	20.0088	−	14.0619i	0.911374	−	0.640501i
$483$	−20.6172	−	6.92057i	−0.938116	−	0.314897i
$484$	16.3922	+	29.2238i	0.745101	+	1.32836i
$485$	−1.03039	+	1.60331i	−0.0467874	+	0.0728026i
$486$	−21.1958	+	6.06124i	−0.961460	+	0.274944i
$487$	−3.45153	+	11.7548i	−0.156404	+	0.532662i	−0.999991	−	0.00433053i	$-0.998622\pi$
$487$	−3.45153	+	11.7548i	−0.156404	+	0.532662i	0.843587	+	0.536993i	$0.180440\pi$
$488$	−21.2756	+	17.7529i	−0.963099	+	0.803634i
$489$	12.3395	+	15.3926i	0.558011	+	0.696079i
$490$	6.22166	−	5.85906i	0.281066	−	0.264685i
$491$	−8.91685	+	10.2906i	−0.402412	+	0.464408i	−0.920399	−	0.390981i	$-0.872136\pi$
$491$	−8.91685	+	10.2906i	−0.402412	+	0.464408i	0.517987	+	0.855388i	$0.326681\pi$
$492$	−32.7902	−	19.0656i	−1.47830	−	0.859544i
$493$	−1.54173	+	0.452692i	−0.0694360	+	0.0203882i
$494$	−15.8215	−	22.5126i	−0.711844	−	1.01289i
$495$	−3.16030	−	14.8933i	−0.142045	−	0.669405i
$496$	−14.0859	−	3.78973i	−0.632477	−	0.170164i
$497$	−24.0724	−	10.9935i	−1.07979	−	0.493125i
$498$	3.86972	−	0.568798i	0.173406	−	0.0254885i
$499$			10.2944i			0.460842i	0.973091	+	0.230421i	$0.0740103\pi$
$499$			10.2944i			0.460842i	−0.973091	+	0.230421i	$0.925990\pi$
$500$	−17.4472	−	1.04827i	−0.780260	−	0.0468801i
$501$	14.0160	+	13.1163i	0.626189	+	0.585993i
$502$	−6.10140	+	2.06941i	−0.272319	+	0.0923622i
$503$	2.30639	+	16.0413i	0.102837	+	0.715245i	0.974377	+	0.224921i	$0.0722124\pi$
$503$	2.30639	+	16.0413i	0.102837	+	0.715245i	−0.871540	+	0.490324i	$0.836879\pi$
$504$	7.28584	−	30.0430i	0.324537	−	1.33822i
$505$	−6.83636	+	14.9695i	−0.304214	+	0.666136i
$506$	−4.70283	−	25.2425i	−0.209066	−	1.12217i
$507$	−0.477514	+	12.4771i	−0.0212071	+	0.554128i
$508$	−9.40811	−	0.565264i	−0.417418	−	0.0250795i
$509$	−22.3628	−	34.7972i	−0.991215	−	1.54236i	−0.831745	−	0.555157i	$-0.812658\pi$
$509$	−22.3628	−	34.7972i	−0.991215	−	1.54236i	−0.159469	−	0.987203i	$-0.550978\pi$
$510$	1.37614	−	0.633694i	0.0609363	−	0.0280604i
$511$	−18.1635	+	8.29500i	−0.803506	+	0.366949i
$512$	−21.0752	+	8.23622i	−0.931402	+	0.363993i
$513$	23.6955	+	34.6921i	1.04618	+	1.53169i
$514$	20.2761	−	34.6213i	0.894341	−	1.52708i
$515$	−8.56198	+	5.50245i	−0.377286	+	0.242467i
$516$	1.60345	+	0.932311i	0.0705878	+	0.0410427i
$517$	−7.20195	−	50.0907i	−0.316742	−	2.20299i
$518$	−22.4298	−	2.28233i	−0.985511	−	0.100280i
$519$	4.20029	−	1.06065i	0.184372	−	0.0465572i
$520$	6.55576	+	0.122055i	0.287489	+	0.00535247i
$521$	10.2532	−	1.47418i	0.449199	−	0.0645850i	0.0859967	−	0.996295i	$-0.472593\pi$
$521$	10.2532	−	1.47418i	0.449199	−	0.0645850i	0.363202	+	0.931710i	$0.381683\pi$
$522$	10.4501	+	1.87905i	0.457389	+	0.0822437i
$523$	−13.3382	+	6.09136i	−0.583240	+	0.266357i	−0.685108	−	0.728441i	$-0.740245\pi$
$523$	−13.3382	+	6.09136i	−0.583240	+	0.266357i	0.101869	+	0.994798i	$0.467518\pi$
$524$	26.9204	+	26.3141i	1.17602	+	1.14954i
$525$	21.0692	+	14.7085i	0.919537	+	0.641931i
$526$	23.5202	+	13.7747i	1.02553	+	0.600604i
$527$	−0.333214	+	2.31755i	−0.0145150	+	0.100954i
$528$	35.1754	−	9.73984i	1.53081	−	0.423872i
$529$	1.58286	−	11.0091i	0.0688202	−	0.478655i
$530$	−8.05650	−	8.55509i	−0.349952	−	0.371609i
$531$	4.27317	+	3.23302i	0.185440	+	0.140301i
$532$	−58.7110	+	4.87178i	−2.54545	+	0.211218i
$533$	−19.9136	+	17.2553i	−0.862556	+	0.747409i
$534$	−13.9596	+	0.0438621i	−0.604089	+	0.00189810i
$535$		−	1.71219i		−	0.0740243i
$536$	−8.96581	−	21.3451i	−0.387264	−	0.921969i
$537$	−0.460122	+	12.0227i	−0.0198557	+	0.518817i
$538$	0.436492	+	10.5386i	0.0188185	+	0.454353i
$539$	−21.6418	−	24.9760i	−0.932178	−	1.07579i
$540$	−10.0061	−	0.319987i	−0.430593	−	0.0137701i
$541$	18.4203	+	11.8380i	0.791950	+	0.508955i	0.872980	−	0.487756i	$-0.162184\pi$
$541$	18.4203	+	11.8380i	0.791950	+	0.508955i	−0.0810297	+	0.996712i	$0.525821\pi$
$542$	−11.7539	+	11.0689i	−0.504875	+	0.475451i
$543$	29.0491	+	5.31764i	1.24662	+	0.228202i
$544$	1.71756	+	3.20023i	0.0736396	+	0.137209i
$545$	8.70284	+	1.25128i	0.372789	+	0.0535989i
$546$	−18.1027	−	11.5537i	−0.774722	−	0.494451i
$547$	0.403282	−	0.627520i	0.0172431	−	0.0268308i	−0.832525	−	0.553987i	$-0.813106\pi$
$547$	0.403282	−	0.627520i	0.0172431	−	0.0268308i	0.849768	+	0.527157i	$0.176742\pi$
$548$	29.7473	−	30.4327i	1.27074	−	1.30002i
$549$	−10.1301	−	27.5893i	−0.432344	−	1.17748i
$550$	−3.07113	+	30.1819i	−0.130953	+	1.28696i
$551$	−2.87964	−	20.0283i	−0.122677	−	0.853234i
$552$	−16.8566	−	0.959641i	−0.717464	−	0.0408451i
$553$	9.58566	−	2.81460i	0.407624	−	0.119689i
$554$	−0.192154	+	1.88841i	−0.00816382	+	0.0802309i
$555$	0.761933	+	7.26137i	0.0323423	+	0.308228i
$556$	14.4721	−	27.2366i	0.613752	−	1.15509i
$557$	12.7050	+	19.7693i	0.538327	+	0.837653i	0.998747	−	0.0500485i	$-0.0159376\pi$
$557$	12.7050	+	19.7693i	0.538327	+	0.837653i	−0.460420	+	0.887701i	$0.652301\pi$
$558$	8.81634	−	12.7139i	0.373226	−	0.538224i
$559$	0.973780	−	0.843785i	0.0411865	−	0.0356883i
$560$	7.31882	−	11.9797i	0.309277	−	0.506237i
$561$	−2.22816	−	5.41833i	−0.0940729	−	0.228762i
$562$	30.0157	−	15.2392i	1.26614	−	0.642825i
$563$	−24.4248	+	15.6968i	−1.02938	+	0.661543i	−0.942338	−	0.334661i	$-0.891378\pi$
$563$	−24.4248	+	15.6968i	−1.02938	+	0.661543i	−0.0870427	+	0.996205i	$0.527742\pi$
$564$	−33.1154	−	3.26454i	−1.39441	−	0.137462i
$565$	−12.0442			−0.506703
$566$	9.19786	−	1.71362i	0.386615	−	0.0720287i
$567$	27.4015	+	18.0078i	1.15075	+	0.756258i
$568$	−20.2782	−	3.30194i	−0.850853	−	0.138546i
$569$	12.7131	−	1.82786i	0.532960	−	0.0766281i	0.129420	−	0.991590i	$-0.458689\pi$
$569$	12.7131	−	1.82786i	0.532960	−	0.0766281i	0.403540	+	0.914962i	$0.367780\pi$
$570$	5.43251	+	18.2886i	0.227543	+	0.766027i
$571$	16.5382	+	14.3304i	0.692101	+	0.599709i	0.928227	−	0.372014i	$-0.121333\pi$
$571$	16.5382	+	14.3304i	0.692101	+	0.599709i	−0.236127	+	0.971722i	$0.575878\pi$
$572$	1.52067	−	25.3097i	0.0635824	−	1.05825i
$573$	−1.16566	+	30.4579i	−0.0486962	+	1.27240i
$574$	10.3327	+	55.4608i	0.431278	+	2.31489i
$575$	5.82984	−	12.7656i	0.243121	−	0.532361i
$576$	−0.697412	−	23.9899i	−0.0290588	−	0.999578i
$577$	−24.0885	+	7.07302i	−1.00282	+	0.294454i	−0.741611	−	0.670830i	$-0.765938\pi$
$577$	−24.0885	+	7.07302i	−1.00282	+	0.294454i	−0.261205	+	0.965283i	$0.584120\pi$
$578$	−19.1929	+	13.4885i	−0.798320	+	0.561048i
$579$	−2.03110	−	8.04340i	−0.0844096	−	0.334272i
$580$	4.25793	+	2.26244i	0.176801	+	0.0939426i
$581$	−4.39653	−	3.80962i	−0.182399	−	0.158050i
$582$	3.65245	−	3.18501i	0.151399	−	0.132023i
$583$	−34.3432	+	29.7585i	−1.42235	+	1.23247i
$584$	−11.9027	+	9.93191i	−0.492537	+	0.410985i
$585$	−2.46363	+	6.50365i	−0.101859	+	0.268893i
$586$	−8.45793	+	4.29414i	−0.349394	+	0.177389i
$587$	−7.67562	−	4.93282i	−0.316807	−	0.203599i	0.372567	−	0.928005i	$-0.378478\pi$
$587$	−7.67562	−	4.93282i	−0.316807	−	0.203599i	−0.689373	+	0.724406i	$0.742114\pi$
$588$	−19.3455	+	9.89840i	−0.797794	+	0.408203i
$589$	−28.2902	−	8.30674i	−1.16568	−	0.342273i
$590$	1.39915	+	1.99086i	0.0576020	+	0.0819624i
$591$	6.28714	+	15.2888i	0.258618	+	0.628895i
$592$	−17.2640	+	2.88495i	−0.709545	+	0.118571i
$593$	25.4235	+	22.0296i	1.04402	+	0.904647i	0.995555	−	0.0941781i	$-0.0300223\pi$
$593$	25.4235	+	22.0296i	1.04402	+	0.904647i	0.0484628	+	0.998825i	$0.484568\pi$
$594$	−2.83755	+	38.6089i	−0.116426	+	1.58414i
$595$	−2.04974	−	0.936084i	−0.0840311	−	0.0383757i
$596$	−23.7978	+	5.46147i	−0.974794	+	0.223711i
$597$	13.9428	−	8.22460i	0.570641	−	0.336610i
$598$	−4.42671	+	10.8616i	−0.181022	+	0.444162i
$599$	35.9716	+	10.5622i	1.46976	+	0.431560i	0.916021	−	0.401130i	$-0.131382\pi$
$599$	35.9716	+	10.5622i	1.46976	+	0.431560i	0.553739	+	0.832691i	$0.313201\pi$
$600$	18.7902	+	6.69900i	0.767107	+	0.273486i
$601$	−5.26100	+	36.5910i	−0.214601	+	1.49258i	0.542929	+	0.839779i	$0.317315\pi$
$601$	−5.26100	+	36.5910i	−0.214601	+	1.49258i	−0.757530	+	0.652801i	$0.773594\pi$
$602$	−0.505270	−	2.71204i	−0.0205933	−	0.110535i
$603$	24.5200	−	1.32965i	0.998533	−	0.0541473i
$604$	9.34326	+	24.2047i	0.380172	+	0.984874i
$605$	−15.9750	−	2.29685i	−0.649475	−	0.0933804i
$606$	27.3032	−	31.7104i	1.10912	−	1.28815i
$607$	8.28019	−	28.1997i	0.336083	−	1.14459i	−0.602091	−	0.798427i	$-0.705666\pi$
$607$	8.28019	−	28.1997i	0.336083	−	1.14459i	0.938174	−	0.346165i	$-0.112516\pi$
$608$	−42.9677	+	15.6734i	−1.74257	+	0.635639i
$609$	−8.02357	−	13.6020i	−0.325132	−	0.551181i
$610$	−0.552321	−	13.3352i	−0.0223628	−	0.539927i
$611$	−9.60288	+	21.0274i	−0.388491	+	0.850676i
$612$	−3.80960	+	0.572195i	−0.153994	+	0.0231296i
$613$	−8.14232	+	9.39674i	−0.328865	+	0.379531i	−0.895970	−	0.444115i	$-0.853518\pi$
$613$	−8.14232	+	9.39674i	−0.328865	+	0.379531i	0.567105	+	0.823646i	$0.308064\pi$
$614$	−11.0305	−	4.49556i	−0.445154	−	0.181426i
$615$	16.8967	−	6.94836i	0.681340	−	0.280185i
$616$	−45.1144	−	30.1945i	−1.81771	−	1.21657i
$617$	3.91447	−	13.3315i	0.157591	−	0.536705i	−0.842407	−	0.538842i	$-0.818862\pi$
$617$	3.91447	−	13.3315i	0.157591	−	0.536705i	0.999998	+	0.00213710i	$0.000680260\pi$
$618$	24.8078	−	7.36897i	0.997915	−	0.296423i
$619$	9.13954	−	14.2214i	0.367349	−	0.571606i	−0.607542	−	0.794287i	$-0.707844\pi$
$619$	9.13954	−	14.2214i	0.367349	−	0.571606i	0.974891	+	0.222681i	$0.0714808\pi$
$620$	5.57624	−	4.27428i	0.223947	−	0.171659i
$621$	6.97961	−	16.4919i	0.280082	−	0.661798i
$622$	1.25242	−	0.424784i	0.0502176	−	0.0170323i
$623$	13.5967	+	15.6914i	0.544741	+	0.628664i
$624$	−15.9225	−	4.94414i	−0.637411	−	0.197924i
$625$	−7.81981	+	9.02454i	−0.312792	+	0.360982i
$626$	−21.5625	+	27.0715i	−0.861811	+	1.08200i
$627$	71.5304	−	18.0627i	2.85665	−	0.721355i
$628$	−16.0434	−	15.6820i	−0.640201	−	0.625781i
$629$	0.791535	+	2.69572i	0.0315606	+	0.107485i
$630$	9.34989	+	11.5885i	0.372509	+	0.461698i
$631$	34.2457	+	15.6395i	1.36330	+	0.622598i	0.956718	−	0.291017i	$-0.0939935\pi$
$631$	34.2457	+	15.6395i	1.36330	+	0.622598i	0.406581	+	0.913615i	$0.366721\pi$
$632$	6.60170	−	4.07103i	0.262601	−	0.161937i
$633$	8.32163	+	0.318479i	0.330755	+	0.0126584i
$634$	1.64400	−	6.59772i	0.0652918	−	0.262029i
$635$	2.97288	−	3.43089i	0.117975	−	0.136151i
$636$	13.6108	+	26.6010i	0.539703	+	1.05480i
$637$	2.14839	+	14.9424i	0.0851224	+	0.592039i
$638$	9.42267	−	16.0891i	0.373047	−	0.636975i
$639$	10.5411	−	19.0724i	0.416998	−	0.754492i
$640$	3.02699	−	10.4700i	0.119652	−	0.413864i
$641$		−	7.68045i		−	0.303359i	−0.988430	−	0.151680i	$-0.951532\pi$
$641$		−	7.68045i		−	0.303359i	0.988430	−	0.151680i	$-0.0484682\pi$
$642$	−1.21343	+	4.18112i	−0.0478903	+	0.165016i
$643$	−12.7188	−	19.7909i	−0.501581	−	0.780476i	0.494476	−	0.869192i	$-0.335360\pi$
$643$	−12.7188	−	19.7909i	−0.501581	−	0.780476i	−0.996057	+	0.0887156i	$0.971724\pi$
$644$	15.2771	+	19.9306i	0.602003	+	0.785375i
$645$	−0.826250	+	0.339776i	−0.0325336	+	0.0133787i
$646$	3.32348	+	6.54606i	0.130760	+	0.257551i
$647$	−2.29696	−	2.65083i	−0.0903027	−	0.104215i	0.708800	−	0.705410i	$-0.249237\pi$
$647$	−2.29696	−	2.65083i	−0.0903027	−	0.104215i	−0.799102	+	0.601195i	$0.794692\pi$
$648$	24.2079	+	7.87274i	0.950974	+	0.309270i
$649$	7.91590	−	5.08724i	0.310726	−	0.199692i
$650$	8.63390	−	10.8398i	0.338649	−	0.425171i
$651$	−22.8860	+	2.40142i	−0.896974	+	0.0941192i
$652$	−1.88378	−	22.7020i	−0.0737747	−	0.889078i
$653$	1.33152	+	4.53473i	0.0521063	+	0.177458i	0.981435	−	0.191796i	$-0.0614313\pi$
$653$	1.33152	+	4.53473i	0.0521063	+	0.177458i	−0.929328	+	0.369254i	$0.879613\pi$
$654$	−20.3654	−	9.22332i	−0.796349	−	0.360660i
$655$	−17.9476	+	2.58048i	−0.701272	+	0.100828i
$656$	19.0970	+	39.4153i	0.745614	+	1.53891i
$657$	−5.66735	−	15.4350i	−0.221104	−	0.602175i
$658$	28.4579	+	40.4930i	1.10940	+	1.57858i
$659$	10.1046	+	6.49383i	0.393619	+	0.252964i	0.722447	−	0.691426i	$-0.243017\pi$
$659$	10.1046	+	6.49383i	0.393619	+	0.252964i	−0.328828	+	0.944390i	$0.606654\pi$
$660$	−6.58388	+	16.3008i	−0.256277	+	0.634509i
$661$	2.52870	−	17.5875i	0.0983549	−	0.684073i	−0.879670	−	0.475585i	$-0.842237\pi$
$661$	2.52870	−	17.5875i	0.0983549	−	0.684073i	0.978025	−	0.208488i	$-0.0668544\pi$
$662$	−4.01660	+	16.1194i	−0.156110	+	0.626499i
$663$	−0.481881	+	2.63241i	−0.0187147	+	0.102235i
$664$	−4.07261	−	1.95232i	−0.158048	−	0.0757648i
$665$	15.3413	−	23.8716i	0.594911	−	0.925699i
$666$	3.28553	−	18.2721i	0.127312	−	0.708029i
$667$	−6.51837	+	5.64820i	−0.252392	+	0.218699i
$668$	−4.95801	−	21.6040i	−0.191831	−	0.835884i
$669$	−16.1516	−	0.618142i	−0.624458	−	0.0238987i
$670$	10.7870	+	2.82717i	0.416738	+	0.109223i
$671$	−51.6111			−1.99242
$672$	−26.3625	+	24.0674i	−1.01695	+	0.928420i
$673$	20.3860	+	23.5267i	0.785824	+	0.906890i	0.997516	−	0.0704471i	$-0.0224426\pi$
$673$	20.3860	+	23.5267i	0.785824	+	0.906890i	−0.211691	+	0.977337i	$0.567897\pi$
$674$	−3.80515	+	37.3955i	−0.146569	+	1.44042i
$675$	−13.4022	+	16.3729i	−0.515852	+	0.630194i
$676$	8.50830	−	11.6398i	0.327242	−	0.447683i
$677$	11.8224	+	1.69980i	0.454372	+	0.0653288i	0.365701	−	0.930732i	$-0.380829\pi$
$677$	11.8224	+	1.69980i	0.454372	+	0.0653288i	0.0886702	+	0.996061i	$0.471738\pi$
$678$	29.4116	+	8.53574i	1.12955	+	0.327813i
$679$	−7.13445	−	1.02578i	−0.273795	−	0.0393658i
$680$	−1.72667	−	0.281157i	−0.0662146	−	0.0107819i
$681$	−16.2488	+	23.2756i	−0.622654	+	0.891923i
$682$	−15.6220	−	22.2287i	−0.598198	−	0.851180i
$683$	−13.5941	−	29.7668i	−0.520162	−	1.13900i	−0.969378	−	0.245573i	$-0.921024\pi$
$683$	−13.5941	−	29.7668i	−0.520162	−	1.13900i	0.449216	−	0.893423i	$-0.351703\pi$
$684$	−0.304851	−	48.5105i	−0.0116563	−	1.85485i
$685$	2.91716	+	20.2893i	0.111459	+	0.775213i
$686$	−3.46809	−	1.41345i	−0.132412	−	0.0539656i
$687$	−9.45703	−	37.4510i	−0.360808	−	1.42884i
$688$	−0.933848	−	1.92741i	−0.0356026	−	0.0734819i
$689$	20.5465	−	2.95415i	0.782761	−	0.112544i
$690$	5.30622	−	6.16273i	0.202004	−	0.234611i
$691$	14.1109	+	21.9570i	0.536804	+	0.835284i	0.998664	−	0.0516689i	$-0.0164540\pi$
$691$	14.1109	+	21.9570i	0.536804	+	0.835284i	−0.461860	+	0.886953i	$0.652818\pi$
$692$	−4.70653	−	1.69464i	−0.178915	−	0.0644205i
$693$	46.2703	−	34.2703i	1.75766	−	1.30182i
$694$	−0.134812	−	0.265532i	−0.00511741	−	0.0100795i
$695$	6.17132	+	13.5133i	0.234092	+	0.512589i
$696$	−8.79438	−	8.54243i	−0.333350	−	0.323800i
$697$	5.91415	−	3.80080i	0.224015	−	0.143965i
$698$	−11.3430	−	2.82643i	−0.429340	−	0.106982i
$699$	−41.2448	−	1.57849i	−1.56002	−	0.0597040i
$700$	−10.6847	−	27.6798i	−0.403844	−	1.04620i
$701$	0.333977	+	0.152522i	0.0126141	+	0.00576068i	0.421712	−	0.906730i	$-0.361429\pi$
$701$	0.333977	+	0.152522i	0.0126141	+	0.00576068i	−0.409098	+	0.912490i	$0.634157\pi$
$702$	10.6253	−	14.1358i	0.401026	−	0.533521i
$703$	−35.0196	+	5.03506i	−1.32079	+	0.189901i
$704$	−39.9682	−	13.3707i	−1.50636	−	0.503928i
$705$	10.9516	−	11.7028i	0.412460	−	0.440752i
$706$	−8.95840	+	35.9518i	−0.337154	+	1.35307i
$707$	−62.2380			−2.34070
$708$	−2.00576	−	5.85321i	−0.0753811	−	0.219977i
$709$	1.74583	−	3.82283i	0.0655659	−	0.143569i	−0.874012	−	0.485904i	$-0.838490\pi$
$709$	1.74583	−	3.82283i	0.0655659	−	0.143569i	0.939578	+	0.342335i	$0.111218\pi$
$710$	7.20424	−	6.78438i	0.270370	−	0.254613i
$711$	1.70761	+	8.04732i	0.0640402	+	0.301798i
$712$	13.3958	+	8.96560i	0.502027	+	0.336000i
$713$	3.54082	+	12.0589i	0.132605	+	0.451611i
$714$	4.34201	+	3.73855i	0.162496	+	0.139912i
$715$	9.22977	+	7.99764i	0.345174	+	0.299095i
$716$	8.19841	−	11.2158i	0.306389	−	0.419155i
$717$	−34.6136	+	27.7479i	−1.29267	+	1.03627i
$718$	43.7749	−	14.8471i	1.63367	−	0.554090i
$719$	−38.0007	−	11.1580i	−1.41719	−	0.416124i	−0.518637	−	0.854994i	$-0.673560\pi$
$719$	−38.0007	−	11.1580i	−1.41719	−	0.416124i	−0.898550	+	0.438871i	$0.855379\pi$
$720$	9.37519	+	6.76298i	0.349393	+	0.252041i
$721$	−32.3808	−	20.8098i	−1.20592	−	0.774999i
$722$	−62.1038	+	21.0637i	−2.31127	+	0.783911i
$723$	9.53139	−	28.3951i	0.354476	−	1.05603i
$724$	−24.3857	−	23.8364i	−0.906287	−	0.885874i
$725$	9.26974	−	4.23335i	0.344270	−	0.157223i
$726$	37.3827	+	16.9304i	1.38740	+	0.628345i
$727$	−7.07602	−	6.13140i	−0.262435	−	0.227401i	0.513697	−	0.857972i	$-0.328276\pi$
$727$	−7.07602	−	6.13140i	−0.262435	−	0.227401i	−0.776132	+	0.630570i	$0.782821\pi$
$728$	9.87965	+	22.7446i	0.366164	+	0.842971i
$729$	−16.5096	+	21.3643i	−0.611468	+	0.791269i
$730$	−0.308998	−	7.46044i	−0.0114365	−	0.276123i
$731$	−0.289203	+	0.185860i	−0.0106966	+	0.00687426i
$732$	−8.10194	+	32.9557i	−0.299456	+	1.21808i
$733$	−30.4377	−	8.93731i	−1.12424	−	0.330107i	−0.333800	−	0.942644i	$-0.608331\pi$
$733$	−30.4377	−	8.93731i	−1.12424	−	0.330107i	−0.790442	+	0.612537i	$0.790149\pi$
$734$	14.0408	+	11.1835i	0.518256	+	0.412792i
$735$	1.88472	−	10.2958i	0.0695190	−	0.379768i
$736$	15.5224	+	11.7959i	0.572162	+	0.434802i
$737$	12.6494	−	41.2248i	0.465947	−	1.51854i
$738$	−46.1856	+	4.99301i	−1.70012	+	0.183795i
$739$	−8.02086	−	1.15323i	−0.295052	−	0.0424221i	−0.00680076	−	0.999977i	$-0.502165\pi$
$739$	−8.02086	−	1.15323i	−0.295052	−	0.0424221i	−0.288251	+	0.957555i	$0.593074\pi$
$740$	3.95589	−	7.44502i	0.145421	−	0.273684i
$741$	−31.9484	−	10.7241i	−1.17365	−	0.393960i
$742$	16.7735	−	41.1563i	0.615776	−	1.51089i
$743$	−6.82389	+	4.38545i	−0.250344	+	0.160887i	−0.659795	−	0.751446i	$-0.729357\pi$
$743$	−6.82389	+	4.38545i	−0.250344	+	0.160887i	0.409450	+	0.912332i	$0.365720\pi$
$744$	−16.6462	+	6.48579i	−0.610281	+	0.237781i
$745$	4.88549	−	10.6977i	0.178990	−	0.391934i
$746$	−23.8999	+	0.989891i	−0.875036	+	0.0362425i
$747$	3.40454	−	3.36995i	0.124565	−	0.123300i
$748$	−1.36261	+	6.62626i	−0.0498218	+	0.242280i
$749$	5.89019	−	2.68996i	0.215223	−	0.0982890i
$750$	−17.9721	+	11.6299i	−0.656249	+	0.424665i
$751$	7.08716	−	24.1367i	0.258614	−	0.880759i	−0.723156	−	0.690685i	$-0.757309\pi$
$751$	7.08716	−	24.1367i	0.258614	−	0.880759i	0.981770	−	0.190074i	$-0.0608728\pi$
$752$	29.6043	+	24.4943i	1.07956	+	0.893215i
$753$	−4.51681	+	6.47013i	−0.164602	+	0.235785i
$754$	−7.59431	+	3.85568i	−0.276569	+	0.140416i
$755$	−11.9907	−	3.52080i	−0.436388	−	0.128135i
$756$	−14.6194	−	34.9252i	−0.531703	−	1.27022i
$757$	−9.31684	−	10.7522i	−0.338626	−	0.390796i	0.560740	−	0.827992i	$-0.310517\pi$
$757$	−9.31684	−	10.7522i	−0.338626	−	0.390796i	−0.899366	+	0.437196i	$0.855971\pi$
$758$	23.7139	−	22.3319i	0.861328	−	0.811131i
$759$	−22.9615	−	21.4876i	−0.833451	−	0.779952i
$760$	6.59893	−	21.0183i	0.239368	−	0.762414i
$761$	13.1262	+	44.7037i	0.475824	+	1.62051i	0.751834	+	0.659352i	$0.229169\pi$
$761$	13.1262	+	44.7037i	0.475824	+	1.62051i	−0.276011	+	0.961155i	$0.589012\pi$
$762$	−9.69120	+	6.27127i	−0.351075	+	0.227184i
$763$	9.36815	+	31.9050i	0.339150	+	1.15504i
$764$	20.7696	−	28.4139i	0.751419	−	1.02798i
$765$	0.897562	−	1.62400i	0.0324514	−	0.0587157i
$766$	−9.23631	−	49.5760i	−0.333721	−	1.79125i
$767$	−4.29826			−0.155201
$768$	−14.8120	+	23.4223i	−0.534481	+	0.845180i
$769$	−13.7460	+	15.8637i	−0.495693	+	0.572060i	−0.947378	−	0.320118i	$-0.896278\pi$
$769$	−13.7460	+	15.8637i	−0.495693	+	0.572060i	0.451685	+	0.892177i	$0.350823\pi$
$770$	24.7623	−	8.39862i	0.892372	−	0.302665i
$771$	−5.12798	−	48.8706i	−0.184680	−	1.76003i
$772$	−3.24517	+	9.01283i	−0.116796	+	0.324379i
$773$	−17.8551	−	8.15414i	−0.642202	−	0.293284i	0.0675707	−	0.997714i	$-0.478475\pi$
$773$	−17.8551	−	8.15414i	−0.642202	−	0.293284i	−0.709773	+	0.704431i	$0.751202\pi$
$774$	2.25848	−	0.244159i	0.0811796	−	0.00877611i
$775$		−	14.8494i		−	0.533406i
$776$	−5.55270	+	0.693123i	−0.199330	+	0.0248817i
$777$	−23.7832	+	14.0293i	−0.853217	+	0.503297i
$778$	25.9265	−	13.1631i	0.929511	−	0.471919i
$779$	36.7764	+	80.5291i	1.31765	+	2.88525i
$780$	6.55571	−	4.63810i	0.234732	−	0.166071i
$781$	−25.0597	−	28.9204i	−0.896705	−	1.03485i
$782$	1.58146	−	2.70033i	0.0565529	−	0.0965637i
$783$	11.6727	−	5.73158i	0.417149	−	0.204830i
$784$	24.9120	+	3.00440i	0.889714	+	0.107300i
$785$	10.6960	−	1.53785i	0.381757	−	0.0548883i
$786$	45.6565	+	6.41806i	1.62851	+	0.228925i
$787$	−10.5399	−	35.8957i	−0.375708	−	1.27954i	−0.902919	−	0.429810i	$-0.858580\pi$
$787$	−10.5399	−	35.8957i	−0.375708	−	1.27954i	0.527211	−	0.849734i	$-0.323238\pi$
$788$	3.84483	−	18.6971i	0.136966	−	0.666058i
$789$	33.2005	−	3.48372i	1.18197	−	0.124024i
$790$	−0.378179	+	3.71660i	−0.0134550	+	0.132231i
$791$	−18.9222	−	41.4339i	−0.672797	−	1.47322i
$792$	27.6301	−	35.1403i	0.981794	−	1.24866i
$793$	19.8330	+	12.7459i	0.704291	+	0.452620i
$794$	2.58239	+	1.51239i	0.0916456	+	0.0536726i
$795$	−14.1573	−	2.59159i	−0.502107	−	0.0919141i
$796$	−18.6584	−	1.12105i	−0.661331	−	0.0397345i
$797$	34.3902	+	4.94456i	1.21816	+	0.175145i	0.721262	−	0.692663i	$-0.243563\pi$
$797$	34.3902	+	4.94456i	1.21816	+	0.175145i	0.496900	+	0.867808i	$0.334472\pi$
$798$	−54.3810	+	47.4214i	−1.92507	+	1.67870i
$799$	3.33442	−	5.18847i	0.117963	−	0.183555i
$800$	−13.6706	−	18.5395i	−0.483328	−	0.655471i
$801$	−13.7390	+	10.1758i	−0.485443	+	0.359545i
$802$	−0.454505	−	10.9735i	−0.0160491	−	0.387489i
$803$	−28.8740			−1.01894
$804$	−24.3380	−	14.5487i	−0.858334	−	0.513092i
$805$	−12.0956			−0.426314
$806$	0.513587	+	12.4000i	0.0180903	+	0.436772i
$807$	8.08007	+	10.0793i	0.284432	+	0.354808i
$808$	−46.6067	+	12.7475i	−1.63962	+	0.448457i
$809$	26.8155	−	41.7258i	0.942783	−	1.46700i	0.0594627	−	0.998231i	$-0.481061\pi$
$809$	26.8155	−	41.7258i	0.942783	−	1.46700i	0.883321	−	0.468769i	$-0.155302\pi$
$810$	−10.1030	+	6.94726i	−0.354985	+	0.244102i
$811$	35.6158	+	5.12077i	1.25064	+	0.179815i	0.735638	−	0.677375i	$-0.236883\pi$
$811$	35.6158	+	5.12077i	1.25064	+	0.179815i	0.515001	+	0.857190i	$0.327792\pi$
$812$	−1.09365	+	18.2024i	−0.0383795	+	0.638779i
$813$	−3.56062	+	19.4509i	−0.124876	+	0.682172i
$814$	−28.1320	−	16.4756i	−0.986025	−	0.577469i
$815$	9.23049	+	5.93207i	0.323330	+	0.207792i
$816$	4.01722	+	1.91027i	0.140631	+	0.0668729i
$817$	−1.79837	−	3.93788i	−0.0629170	−	0.137769i
$818$	3.96554	−	38.9718i	0.138652	−	1.36262i
$819$	−26.2441	+	1.74240i	−0.917044	+	0.0608843i
$820$	−20.6635	−	4.24919i	−0.721601	−	0.148388i
$821$	14.3503	+	48.8726i	0.500828	+	1.70566i	0.690078	+	0.723735i	$0.257576\pi$
$821$	14.3503	+	48.8726i	0.500828	+	1.70566i	−0.189250	+	0.981929i	$0.560606\pi$
$822$	7.25543	−	51.6134i	0.253062	−	1.80022i
$823$	−19.7726	+	2.84288i	−0.689231	+	0.0990965i	−0.478026	−	0.878345i	$-0.658648\pi$
$823$	−19.7726	+	2.84288i	−0.689231	+	0.0990965i	−0.211205	+	0.977442i	$0.567739\pi$
$824$	−28.5105	−	8.95117i	−0.993209	−	0.311829i
$825$	18.8779	+	32.0029i	0.657245	+	1.11420i
$826$	−4.65071	+	7.94106i	−0.161819	+	0.276305i
$827$	−16.9104	−	19.5157i	−0.588033	−	0.678627i	0.381279	−	0.924460i	$-0.375484\pi$
$827$	−16.9104	−	19.5157i	−0.588033	−	0.678627i	−0.969312	+	0.245833i	$0.920938\pi$
$828$	−17.3252	+	11.2887i	−0.602093	+	0.392310i
$829$	−7.44733	−	16.3074i	−0.258656	−	0.566378i	0.735099	−	0.677960i	$-0.237136\pi$
$829$	−7.44733	−	16.3074i	−0.258656	−	0.566378i	−0.993755	+	0.111581i	$0.964408\pi$
$830$	1.93970	−	0.984799i	0.0673280	−	0.0341829i
$831$	1.18115	+	2.00235i	0.0409737	+	0.0694608i
$832$	12.0569	+	15.0087i	0.417997	+	0.520332i
$833$		−	4.02769i		−	0.139551i
$834$	−5.49332	−	37.3729i	−0.190218	−	1.29412i
$835$	9.71157	+	4.43513i	0.336083	+	0.153484i
$836$	−80.1516	−	28.8595i	−2.77210	−	0.998126i
$837$	−0.531295	−	18.9414i	−0.0183642	−	0.654710i
$838$	−51.0397	+	17.3111i	−1.76314	+	0.598002i
$839$	16.2173	−	18.7158i	0.559884	−	0.646140i	−0.403273	−	0.915080i	$-0.632128\pi$
$839$	16.2173	−	18.7158i	0.559884	−	0.646140i	0.963157	+	0.268939i	$0.0866731\pi$
$840$	−1.47565	−	17.1301i	−0.0509147	−	0.591046i
$841$	22.7369			0.784031
$842$	6.77520	+	36.3660i	0.233489	+	1.25325i
$843$	18.5485	−	36.8200i	0.638843	−	1.26815i
$844$	−7.76316	−	5.67462i	−0.267219	−	0.195328i
$845$	1.95651	+	6.66327i	0.0673060	+	0.229223i
$846$	−35.0372	+	20.8165i	−1.20461	+	0.715686i
$847$	−17.1962	−	58.5649i	−0.590869	−	2.01232i
$848$	4.13120	−	34.2553i	0.141866	−	1.17633i
$849$	7.82966	−	8.36672i	0.268713	−	0.287145i
$850$	−2.69170	+	2.53483i	−0.0923247	+	0.0869441i
$851$	9.87591	+	11.3974i	0.338542	+	0.390698i
$852$	−22.4007	+	11.4616i	−0.767435	+	0.392669i
$853$	16.1185	+	4.73281i	0.551886	+	0.162048i	0.545773	−	0.837933i	$-0.316236\pi$
$853$	16.1185	+	4.73281i	0.551886	+	0.162048i	0.00611279	+	0.999981i	$0.498054\pi$
$854$	45.0075	−	22.8506i	1.54012	−	0.781931i
$855$	18.6339	+	14.0982i	0.637265	+	0.482147i
$856$	3.85989	−	3.22079i	0.131928	−	0.110084i
$857$	7.22962	−	24.6218i	0.246959	−	0.841065i	−0.738947	−	0.673764i	$-0.764677\pi$
$857$	7.22962	−	24.6218i	0.246959	−	0.841065i	0.985906	−	0.167301i	$-0.0535053\pi$
$858$	−16.8710	−	26.0712i	−0.575965	−	0.890057i
$859$	38.1004	−	17.3999i	1.29997	−	0.593677i	0.359371	−	0.933195i	$-0.382991\pi$
$859$	38.1004	−	17.3999i	1.29997	−	0.593677i	0.940599	+	0.339518i	$0.110264\pi$
$860$	1.01045	+	0.207786i	0.0344560	+	0.00708544i
$861$	50.4493	+	47.2109i	1.71931	+	1.60894i
$862$	−16.5639	+	0.686048i	−0.564169	+	0.0233669i
$863$	−1.89386	+	4.14697i	−0.0644677	+	0.141165i	−0.939123	−	0.343580i	$-0.888360\pi$
$863$	−1.89386	+	4.14697i	−0.0644677	+	0.141165i	0.874656	+	0.484745i	$0.161088\pi$
$864$	−18.1011	−	23.1593i	−0.615810	−	0.787894i
$865$	2.02695	−	1.30264i	0.0689183	−	0.0442911i
$866$	8.48198	−	20.8117i	0.288229	−	0.707212i
$867$	−9.14275	+	27.2373i	−0.310504	+	0.925028i
$868$	23.4648	+	12.4680i	0.796448	+	0.423190i
$869$	14.2992	+	2.05591i	0.485066	+	0.0697419i
$870$	5.84255	−	0.858778i	0.198081	−	0.0291153i
$871$	−15.0418	+	12.7179i	−0.509672	+	0.430930i
$872$	13.5501	+	21.9731i	0.458863	+	0.744105i
$873$	1.29122	−	5.79308i	0.0437011	−	0.196066i
$874$	30.8243	+	24.5516i	1.04265	+	0.830471i
$875$	30.5496	+	8.97017i	1.03276	+	0.303247i
$876$	−4.53266	+	18.4372i	−0.153145	+	0.622935i
$877$	24.5218	−	15.7592i	0.828041	−	0.532150i	−0.0566139	−	0.998396i	$-0.518030\pi$
$877$	24.5218	−	15.7592i	0.828041	−	0.532150i	0.884655	+	0.466247i	$0.154394\pi$
$878$	−1.95113	−	47.1079i	−0.0658474	−	1.58982i
$879$	−5.22665	+	10.3753i	−0.176291	+	0.349949i
$880$	16.8230	−	11.3611i	0.567102	−	0.382982i
$881$	−8.99858	−	7.79731i	−0.303170	−	0.262698i	0.489968	−	0.871741i	$-0.337009\pi$
$881$	−8.99858	−	7.79731i	−0.303170	−	0.262698i	−0.793138	+	0.609042i	$0.791554\pi$
$882$	−11.8991	+	23.8065i	−0.400665	+	0.801606i
$883$	−12.1718	+	5.55869i	−0.409615	+	0.187065i	−0.609556	−	0.792743i	$-0.708652\pi$
$883$	−12.1718	+	5.55869i	−0.409615	+	0.187065i	0.199941	+	0.979808i	$0.435925\pi$
$884$	2.16005	−	2.20982i	0.0726502	−	0.0743242i
$885$	2.82530	+	0.948366i	0.0949713	+	0.0318790i
$886$	−36.9235	+	12.5233i	−1.24047	+	0.420729i
$887$	44.2760	+	28.4545i	1.48664	+	0.955407i	0.996485	+	0.0837740i	$0.0266974\pi$
$887$	44.2760	+	28.4545i	1.48664	+	0.955407i	0.490158	+	0.871633i	$0.336939\pi$
$888$	−14.9365	+	15.3770i	−0.501236	+	0.516019i
$889$	16.4734	+	4.83703i	0.552500	+	0.162229i
$890$	−7.35263	+	2.49379i	−0.246461	+	0.0835920i
$891$	25.2251	+	40.1465i	0.845073	+	1.34496i
$892$	15.0677	+	11.0140i	0.504503	+	0.368776i
$893$	58.6963	+	50.8607i	1.96420	+	1.70199i
$894$	−19.5118	+	22.6613i	−0.652571	+	0.757906i
$895$	1.88525	+	6.42058i	0.0630170	+	0.214616i
$896$	40.7741	−	6.03579i	1.36217	−	0.201642i
$897$	3.51702	+	13.9278i	0.117430	+	0.465037i
$898$	16.6963	−	15.7233i	0.557164	−	0.524693i
$899$	−3.79120	+	8.30158i	−0.126444	+	0.276873i
$900$	23.3986	−	7.03047i	0.779954	−	0.234349i
$901$	−5.53828			−0.184507
$902$	−19.7241	+	79.1568i	−0.656742	+	2.63563i
$903$	−2.46698	−	2.30862i	−0.0820958	−	0.0768261i
$904$	−22.6563	−	27.1520i	−0.753537	−	0.903061i
$905$	16.2577	−	2.33751i	0.540426	−	0.0777015i
$906$	26.7859	+	17.0956i	0.889902	+	0.567962i
$907$	15.9322	+	7.27600i	0.529020	+	0.241595i	0.661974	−	0.749527i	$-0.269719\pi$
$907$	15.9322	+	7.27600i	0.529020	+	0.241595i	−0.132954	+	0.991122i	$0.542446\pi$
$908$	30.5785	−	11.8036i	1.01478	−	0.391716i
$909$	3.91703	−	51.0996i	0.129920	−	1.69487i
$910$	−11.5898	−	2.88791i	−0.384197	−	0.0957333i
$911$	−15.6180	+	10.0371i	−0.517448	+	0.332544i	−0.773162	−	0.634209i	$-0.781326\pi$
$911$	−15.6180	+	10.0371i	−0.517448	+	0.332544i	0.255714	+	0.966753i	$0.417690\pi$
$912$	−31.0102	+	46.6496i	−1.02685	+	1.54472i
$913$	−3.49452	−	7.65194i	−0.115652	−	0.253242i
$914$	−14.8741	−	29.2968i	−0.491993	−	0.969050i
$915$	−10.2242	−	12.7540i	−0.338003	−	0.421634i
$916$	−15.1099	+	41.9647i	−0.499244	+	1.38655i
$917$	−37.0742	−	57.6886i	−1.22430	−	1.90505i
$918$	−3.34276	+	3.32966i	−0.110327	+	0.109895i
$919$	−7.30582	+	1.05042i	−0.240997	+	0.0346501i	−0.261755	−	0.965134i	$-0.584301\pi$
$919$	−7.30582	+	1.05042i	−0.240997	+	0.0346501i	0.0207579	+	0.999785i	$0.493392\pi$
$920$	−9.05774	+	2.47741i	−0.298625	+	0.0816779i
$921$	−14.1444	+	3.57172i	−0.466075	+	0.117692i
$922$	−14.2052	−	5.78944i	−0.467824	−	0.190665i
$923$	2.48769	+	17.3022i	0.0818832	+	0.569510i
$924$	−66.4212	+	2.96014i	−2.18510	+	0.0973813i
$925$	−7.40204	−	16.2082i	−0.243378	−	0.532922i
$926$	25.7514	+	36.6418i	0.846243	+	1.20413i
$927$	19.1236	−	25.2761i	0.628100	−	0.830176i
$928$	2.90923	+	13.8548i	0.0955001	+	0.454806i
$929$	16.4056	+	2.35877i	0.538250	+	0.0773886i	0.406078	−	0.913838i	$-0.366896\pi$
$929$	16.4056	+	2.35877i	0.538250	+	0.0773886i	0.132171	+	0.991227i	$0.457805\pi$
$930$	2.39835	−	8.26400i	0.0786450	−	0.270987i
$931$	50.2035	+	7.21818i	1.64535	+	0.236566i
$932$	38.4769	+	28.1254i	1.26035	+	0.921277i
$933$	0.927159	−	1.32811i	0.0303538	−	0.0434805i
$934$	−0.254442	+	2.50055i	−0.00832558	+	0.0818206i
$935$	−2.13381	−	2.46254i	−0.0697829	−	0.0805338i
$936$	−19.2959	+	6.68009i	−0.630707	+	0.218346i
$937$	6.17720			0.201800			0.100900	−	0.994897i	$-0.467828\pi$
$937$	6.17720			0.201800			0.100900	+	0.994897i	$0.467828\pi$
$938$	7.22117	+	41.5506i	0.235780	+	1.35668i
$939$	−1.62104	+	42.3567i	−0.0529006	+	1.38226i
$940$	−18.0384	+	4.13973i	−0.588348	+	0.135023i
$941$	−33.6706	+	29.1757i	−1.09763	+	0.951101i	−0.999030	−	0.0440257i	$-0.985982\pi$
$941$	−33.6706	+	29.1757i	−1.09763	+	0.951101i	−0.0985992	+	0.995127i	$0.531436\pi$
$942$	−27.2093	−	3.82488i	−0.886526	−	0.124621i
$943$	20.4018	−	31.7459i	0.664375	−	1.03379i
$944$	−1.85619	+	6.89919i	−0.0604137	+	0.224549i
$945$	17.6350	+	4.64520i	0.573667	+	0.151108i
$946$	0.964513	−	3.87078i	0.0313590	−	0.125850i
$947$	2.12469	−	14.7775i	0.0690431	−	0.480205i	−0.925737	−	0.378167i	$-0.876555\pi$
$947$	2.12469	−	14.7775i	0.0690431	−	0.480205i	0.994780	−	0.102038i	$-0.0325364\pi$
$948$	3.55747	−	8.80784i	0.115541	−	0.286065i
$949$	11.0957	+	7.13075i	0.360180	+	0.231474i
$950$	−26.7718	−	38.0938i	−0.868591	−	1.23592i
$951$	−3.16719	−	7.70181i	−0.102703	−	0.249748i
$952$	−1.74549	−	6.38172i	−0.0565715	−	0.206833i
$953$	0.981740	−	0.141153i	0.0318017	−	0.00457239i	−0.126396	−	0.991980i	$-0.540341\pi$
$953$	0.981740	−	0.141153i	0.0318017	−	0.00457239i	0.158197	+	0.987408i	$0.449432\pi$
$954$	32.7351	+	16.3619i	1.05984	+	0.529736i
$955$	4.77605	+	16.2657i	0.154549	+	0.526346i
$956$	51.0501	−	4.23608i	1.65108	−	0.137005i
$957$	−2.38306	−	22.7110i	−0.0770335	−	0.734144i
$958$	6.35028	−	7.97273i	0.205168	−	0.257587i
$959$	−65.2153	+	41.9113i	−2.10591	+	1.35339i
$960$	−4.61362	−	12.5256i	−0.148904	−	0.404262i
$961$	−11.5920	−	13.3779i	−0.373937	−	0.431546i
$962$	6.74168	+	13.2787i	0.217360	+	0.428123i
$963$	1.83785	+	5.00536i	0.0592238	+	0.161295i
$964$	−27.4495	+	21.0405i	−0.884088	+	0.677668i
$965$	−2.49451	−	3.88153i	−0.0803010	−	0.124951i
$966$	29.5372	+	8.57218i	0.950343	+	0.275805i
$967$		−	44.7912i		−	1.44039i	−0.693773	−	0.720194i	$-0.744053\pi$
$967$		−	44.7912i		−	1.44039i	0.693773	−	0.720194i	$-0.255947\pi$
$968$	−24.8726	−	40.3340i	−0.799434	−	1.29638i
$969$	8.03001	+	4.04520i	0.257961	+	0.129951i
$970$	1.36210	−	2.32578i	0.0437345	−	0.0746764i
$971$	−1.13042	−	7.86225i	−0.0362769	−	0.252312i	0.963611	−	0.267310i	$-0.0861348\pi$
$971$	−1.13042	−	7.86225i	−0.0362769	−	0.252312i	−0.999888	+	0.0149983i	$0.995226\pi$
$972$	29.5950	−	9.80501i	0.949259	−	0.314496i
$973$	−36.7924	+	42.4607i	−1.17951	+	1.36123i
$974$	4.18908	−	16.8116i	0.134227	−	0.538678i
$975$	0.649085	−	16.9601i	0.0207874	−	0.543159i
$976$	29.0234	−	26.3300i	0.929017	−	0.842802i
$977$	−5.20055	−	2.37501i	−0.166380	−	0.0759834i	0.330484	−	0.943812i	$-0.392788\pi$
$977$	−5.20055	−	2.37501i	−0.166380	−	0.0759834i	−0.496864	+	0.867828i	$0.665515\pi$
$978$	−18.3366	−	21.0277i	−0.586339	−	0.672391i
$979$	8.45854	+	28.8071i	0.270336	+	0.920680i
$980$	−8.44832	+	8.64298i	−0.269872	+	0.276090i
$981$	−26.7847	+	5.68361i	−0.855171	+	0.181464i
$982$	11.9973	−	15.0625i	0.382848	−	0.480663i
$983$	−27.5090	+	31.7471i	−0.877401	+	1.01258i	0.122397	+	0.992481i	$0.460942\pi$
$983$	−27.5090	+	31.7471i	−0.877401	+	1.01258i	−0.999798	+	0.0200939i	$0.993603\pi$
$984$	47.4484	+	25.0207i	1.51260	+	0.797631i
$985$	6.02090	+	6.94849i	0.191842	+	0.221397i
$986$	2.15197	−	0.729884i	0.0685328	−	0.0232442i
$987$	57.4650	+	19.2893i	1.82913	+	0.613984i
$988$	23.6734	+	30.8844i	0.753150	+	0.982563i
$989$	−0.997653	+	1.55238i	−0.0317235	+	0.0493628i
$990$	5.33713	+	20.8593i	0.169625	+	0.662953i
$991$	−15.0513	+	51.2600i	−0.478120	+	1.62833i	0.268644	+	0.963240i	$0.413425\pi$
$991$	−15.0513	+	51.2600i	−0.478120	+	1.62833i	−0.746764	+	0.665089i	$0.768394\pi$
$992$	20.1252	+	4.53054i	0.638977	+	0.143845i
$993$	7.73800	+	18.8169i	0.245558	+	0.597136i
$994$	34.6577	+	14.1250i	1.09927	+	0.448018i
$995$	5.89591	−	6.80424i	0.186913	−	0.215709i
$996$	−5.43464	+	1.03018i	−0.172203	+	0.0326427i
$997$	−8.68336	+	19.0139i	−0.275005	+	0.602176i	−0.995859	−	0.0909103i	$-0.971022\pi$
$997$	−8.68336	+	19.0139i	−0.275005	+	0.602176i	0.720854	+	0.693086i	$0.243750\pi$
$998$	−0.602472	−	14.5461i	−0.0190709	−	0.460447i
$999$	−10.0217	−	20.4098i	−0.317073	−	0.645738i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.w.a.59.2	✓	1320
3.2	odd	2	inner	804.2.w.a.59.131	yes	1320
4.3	odd	2	inner	804.2.w.a.59.14	yes	1320
12.11	even	2	inner	804.2.w.a.59.119	yes	1320
67.25	even	11	inner	804.2.w.a.695.119	yes	1320
201.92	odd	22	inner	804.2.w.a.695.14	yes	1320
268.159	odd	22	inner	804.2.w.a.695.131	yes	1320
804.695	even	22	inner	804.2.w.a.695.2	yes	1320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.w.a.59.2	✓	1320	1.1	even	1	trivial
804.2.w.a.59.14	yes	1320	4.3	odd	2	inner
804.2.w.a.59.119	yes	1320	12.11	even	2	inner
804.2.w.a.59.131	yes	1320	3.2	odd	2	inner
804.2.w.a.695.2	yes	1320	804.695	even	22	inner
804.2.w.a.695.14	yes	1320	201.92	odd	22	inner
804.2.w.a.695.119	yes	1320	67.25	even	11	inner
804.2.w.a.695.131	yes	1320	268.159	odd	22	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.w (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41300 + 0.0585241i) q^{2} +(-1.35142 + 1.08336i) q^{3} +(1.99315 - 0.165389i) q^{4} +(-0.520814 + 0.810403i) q^{5} +(1.84615 - 1.60988i) q^{6} +(-3.60615 - 0.518486i) q^{7} +(-2.80665 + 0.350343i) q^{8} +(0.652653 - 2.92815i) q^{9} +O(q^{10})\)	\(q+(-1.41300 + 0.0585241i) q^{2} +(-1.35142 + 1.08336i) q^{3} +(1.99315 - 0.165389i) q^{4} +(-0.520814 + 0.810403i) q^{5} +(1.84615 - 1.60988i) q^{6} +(-3.60615 - 0.518486i) q^{7} +(-2.80665 + 0.350343i) q^{8} +(0.652653 - 2.92815i) q^{9} +(0.688484 - 1.17558i) q^{10} +(-4.43187 - 2.84819i) q^{11} +(-2.51440 + 2.38281i) q^{12} +(0.999681 + 2.18900i) q^{13} +(5.12584 + 0.521575i) q^{14} +(-0.174123 - 1.65942i) q^{15} +(3.94529 - 0.659291i) q^{16} +(-0.180888 - 0.616047i) q^{17} +(-0.750833 + 4.17567i) q^{18} +(8.00295 - 1.15065i) q^{19} +(-0.904029 + 1.70139i) q^{20} +(5.43512 - 3.20607i) q^{21} +(6.42893 + 3.76513i) q^{22} +(-2.25692 - 2.60462i) q^{23} +(3.41340 - 3.51407i) q^{24} +(1.69157 + 3.70402i) q^{25} +(-1.54066 - 3.03455i) q^{26} +(2.29024 + 4.66421i) q^{27} +(-7.27335 - 0.437001i) q^{28} -2.50262i q^{29} +(0.343152 + 2.33458i) q^{30} +(-3.31716 - 1.51490i) q^{31} +(-5.53612 + 1.16247i) q^{32} +(9.07492 - 0.952229i) q^{33} +(0.291648 + 0.859889i) q^{34} +(2.29832 - 2.65240i) q^{35} +(0.816551 - 5.94418i) q^{36} -4.37584 q^{37} +(-11.2408 + 2.09424i) q^{38} +(-3.72246 - 1.87523i) q^{39} +(1.17782 - 2.45698i) q^{40} +(3.08483 + 10.5060i) q^{41} +(-7.49220 + 4.84827i) q^{42} +(-0.150849 - 0.513743i) q^{43} +(-9.30444 - 4.94388i) q^{44} +(2.03307 + 2.05393i) q^{45} +(3.34146 + 3.54825i) q^{46} +(6.29056 + 7.25969i) q^{47} +(-4.61748 + 5.16516i) q^{48} +(6.01902 + 1.76734i) q^{49} +(-2.60697 - 5.13479i) q^{50} +(0.911856 + 0.636569i) q^{51} +(2.35455 + 4.19766i) q^{52} +(2.43019 - 8.27646i) q^{53} +(-3.50908 - 6.45650i) q^{54} +(4.61636 - 2.10822i) q^{55} +(10.3028 + 0.191818i) q^{56} +(-9.56874 + 10.2251i) q^{57} +(0.146463 + 3.53620i) q^{58} +(-0.741986 + 1.62472i) q^{59} +(-0.621503 - 3.27868i) q^{60} +(8.24157 - 5.29653i) q^{61} +(4.77581 + 1.94642i) q^{62} +(-3.87177 + 10.2209i) q^{63} +(7.75452 - 1.96658i) q^{64} +(-2.29462 - 0.329916i) q^{65} +(-12.7672 + 1.87660i) q^{66} +(2.21072 + 7.88116i) q^{67} +(-0.462424 - 1.19796i) q^{68} +(5.87178 + 1.07487i) q^{69} +(-3.09230 + 3.88235i) q^{70} +(6.96960 + 2.04646i) q^{71} +(-0.805911 + 8.44692i) q^{72} +(4.61078 - 2.96317i) q^{73} +(6.18307 - 0.256092i) q^{74} +(-6.29881 - 3.17309i) q^{75} +(15.7608 - 3.61702i) q^{76} +(14.5052 + 12.5689i) q^{77} +(5.36959 + 2.43185i) q^{78} +(-2.49436 + 1.13914i) q^{79} +(-1.52047 + 3.54064i) q^{80} +(-8.14809 - 3.82213i) q^{81} +(-4.97372 - 14.6644i) q^{82} +(1.34330 + 0.863286i) q^{83} +(10.3027 - 7.28910i) q^{84} +(0.593455 + 0.174254i) q^{85} +(0.243216 + 0.717092i) q^{86} +(2.71124 + 3.38208i) q^{87} +(13.4365 + 6.44118i) q^{88} +(-4.30701 - 3.73205i) q^{89} +(-2.99293 - 2.78323i) q^{90} +(-2.47003 - 8.41216i) q^{91} +(-4.92915 - 4.81813i) q^{92} +(6.12405 - 1.54643i) q^{93} +(-9.31344 - 9.88981i) q^{94} +(-3.23556 + 7.08488i) q^{95} +(6.22223 - 7.56861i) q^{96} +1.97841 q^{97} +(-8.60833 - 2.14500i) q^{98} +(-11.2324 + 11.1183i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1320 q - 18 q^{4} - 5 q^{6} - 22 q^{9}+O(q^{10}) \) 1320 * q - 18 * q^4 - 5 * q^6 - 22 * q^9	\( 1320 q - 18 q^{4} - 5 q^{6} - 22 q^{9} - 26 q^{10} - 15 q^{12} - 44 q^{13} - 34 q^{16} - 13 q^{18} - 66 q^{21} + 74 q^{22} + 13 q^{24} + 80 q^{25} - 110 q^{28} - 36 q^{30} - 22 q^{33} - 54 q^{34} - 37 q^{36} - 72 q^{37} - 22 q^{40} + q^{42} - 154 q^{45} - 82 q^{46} + 11 q^{48} + 96 q^{49} - 14 q^{52} - 138 q^{54} - 6 q^{57} + 74 q^{58} + 3 q^{60} - 28 q^{61} - 6 q^{64} - 4 q^{66} - 38 q^{69} - 18 q^{70} - 145 q^{72} + 96 q^{73} + 14 q^{76} - 51 q^{78} - 38 q^{81} - 74 q^{82} - 41 q^{84} - 76 q^{85} + 6 q^{88} - 5 q^{90} + 78 q^{93} - 22 q^{94} + 184 q^{96} - 128 q^{97}+O(q^{100}) \) 1320 * q - 18 * q^4 - 5 * q^6 - 22 * q^9 - 26 * q^10 - 15 * q^12 - 44 * q^13 - 34 * q^16 - 13 * q^18 - 66 * q^21 + 74 * q^22 + 13 * q^24 + 80 * q^25 - 110 * q^28 - 36 * q^30 - 22 * q^33 - 54 * q^34 - 37 * q^36 - 72 * q^37 - 22 * q^40 + q^42 - 154 * q^45 - 82 * q^46 + 11 * q^48 + 96 * q^49 - 14 * q^52 - 138 * q^54 - 6 * q^57 + 74 * q^58 + 3 * q^60 - 28 * q^61 - 6 * q^64 - 4 * q^66 - 38 * q^69 - 18 * q^70 - 145 * q^72 + 96 * q^73 + 14 * q^76 - 51 * q^78 - 38 * q^81 - 74 * q^82 - 41 * q^84 - 76 * q^85 + 6 * q^88 - 5 * q^90 + 78 * q^93 - 22 * q^94 + 184 * q^96 - 128 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more