LMFDB - Embedded newform 552.2.bb.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	552.13
Dual form			552.2.bb.a.85.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28649 + 0.587327i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(1.31009 - 1.51118i) q^{4} +(2.37560 + 1.08490i) q^{5} +(0.201436 - 1.39979i) q^{6} +(1.76843 + 0.519257i) q^{7} +(-0.797864 + 2.71356i) q^{8} +(-0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-1.28649 + 0.587327i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(1.31009 - 1.51118i) q^{4} +(2.37560 + 1.08490i) q^{5} +(0.201436 - 1.39979i) q^{6} +(1.76843 + 0.519257i) q^{7} +(-0.797864 + 2.71356i) q^{8} +(-0.415415 - 0.909632i) q^{9} +(-3.69337 - 0.000455346i) q^{10} +(3.66757 + 3.17797i) q^{11} +(0.562992 + 1.91912i) q^{12} +(-0.735357 - 2.50439i) q^{13} +(-2.58003 + 0.370628i) q^{14} +(-2.19702 + 1.41194i) q^{15} +(-0.567307 - 3.95957i) q^{16} +(-0.317717 - 2.20977i) q^{17} +(1.06868 + 0.926245i) q^{18} +(1.84049 + 0.264623i) q^{19} +(4.75173 - 2.16863i) q^{20} +(-1.39291 + 1.20696i) q^{21} +(-6.58478 - 1.93435i) q^{22} +(4.13830 - 2.42373i) q^{23} +(-1.85144 - 2.13827i) q^{24} +(1.19216 + 1.37583i) q^{25} +(2.41692 + 2.78997i) q^{26} +(0.989821 + 0.142315i) q^{27} +(3.10149 - 1.99213i) q^{28} +(1.40144 - 0.201497i) q^{29} +(1.99717 - 3.10681i) q^{30} +(0.445741 - 0.286460i) q^{31} +(3.05539 + 4.76073i) q^{32} +(-4.65631 + 1.36722i) q^{33} +(1.70660 + 2.65623i) q^{34} +(3.63773 + 3.15211i) q^{35} +(-1.91885 - 0.563938i) q^{36} +(-6.09278 + 2.78248i) q^{37} +(-2.52319 + 0.740537i) q^{38} +(2.50439 + 0.735357i) q^{39} +(-4.83935 + 5.58073i) q^{40} +(-1.56265 + 3.42173i) q^{41} +(1.08308 - 2.37084i) q^{42} +(-0.469155 + 0.730019i) q^{43} +(9.60732 - 1.37891i) q^{44} -2.61160i q^{45} +(-3.90034 + 5.54863i) q^{46} +2.04867 q^{47} +(3.63771 + 1.66345i) q^{48} +(-3.03107 - 1.94795i) q^{49} +(-2.34176 - 1.06979i) q^{50} +(2.03075 + 0.927411i) q^{51} +(-4.74797 - 2.16974i) q^{52} +(-3.30615 + 11.2597i) q^{53} +(-1.35698 + 0.398263i) q^{54} +(5.26490 + 11.5285i) q^{55} +(-2.82000 + 4.38444i) q^{56} +(-1.21766 + 1.40526i) q^{57} +(-1.68459 + 1.08233i) q^{58} +(0.962583 + 3.27826i) q^{59} +(-0.744615 + 5.16986i) q^{60} +(1.27324 + 1.98120i) q^{61} +(-0.405194 + 0.630323i) q^{62} +(-0.262298 - 1.82432i) q^{63} +(-6.72683 - 4.33010i) q^{64} +(0.970105 - 6.74723i) q^{65} +(5.18728 - 4.49368i) q^{66} +(-3.55986 + 3.08463i) q^{67} +(-3.75559 - 2.41488i) q^{68} +(-0.198359 + 4.79173i) q^{69} +(-6.53121 - 1.91861i) q^{70} +(7.67205 + 8.85401i) q^{71} +(2.79979 - 0.401492i) q^{72} +(0.985217 - 6.85234i) q^{73} +(6.20406 - 7.15808i) q^{74} +(-1.80195 + 0.259081i) q^{75} +(2.81111 - 2.43463i) q^{76} +(4.83564 + 7.52441i) q^{77} +(-3.65376 + 0.524872i) q^{78} +(9.58201 - 2.81353i) q^{79} +(2.94804 - 10.0218i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(0.000655866 - 5.31980i) q^{82} +(-12.8319 + 5.86015i) q^{83} +(-0.000908918 + 3.68617i) q^{84} +(1.64261 - 5.59422i) q^{85} +(0.174801 - 1.21471i) q^{86} +(-0.588168 + 1.28791i) q^{87} +(-11.5498 + 7.41658i) q^{88} +(-6.64268 - 4.26899i) q^{89} +(1.53387 + 3.35979i) q^{90} -4.81068i q^{91} +(1.75887 - 9.42902i) q^{92} +0.529853i q^{93} +(-2.63558 + 1.20324i) q^{94} +(4.08518 + 2.62539i) q^{95} +(-5.65685 - 0.00348710i) q^{96} +(4.94567 - 10.8295i) q^{97} +(5.04351 + 0.725782i) q^{98} +(1.36722 - 4.65631i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.28649	+	0.587327i	−0.909683	+	0.415303i
$2$	−1.28649	+	0.587327i	−0.909683	+	0.415303i
$3$	−0.540641	+	0.841254i	−0.312139	+	0.485698i
$3$	−0.540641	+	0.841254i	−0.312139	+	0.485698i
$4$	1.31009	−	1.51118i	0.655047	−	0.755588i
$5$	2.37560	+	1.08490i	1.06240	+	0.485182i	0.868423	−	0.495824i	$-0.165134\pi$
$5$	2.37560	+	1.08490i	1.06240	+	0.485182i	0.193977	+	0.981006i	$0.437861\pi$
$6$	0.201436	−	1.39979i	0.0822360	−	0.571464i
$7$	1.76843	+	0.519257i	0.668403	+	0.196261i	0.598292	−	0.801278i	$-0.295846\pi$
$7$	1.76843	+	0.519257i	0.668403	+	0.196261i	0.0701110	+	0.997539i	$0.477665\pi$
$8$	−0.797864	+	2.71356i	−0.282087	+	0.959389i
$9$	−0.415415	−	0.909632i	−0.138472	−	0.303211i
$10$	−3.69337		0.000455346i	−1.16795		0.000143993i
$11$	3.66757	+	3.17797i	1.10581	+	0.958193i	0.999347	−	0.0361238i	$-0.0115011\pi$
$11$	3.66757	+	3.17797i	1.10581	+	0.958193i	0.106466	+	0.994316i	$0.466047\pi$
$12$	0.562992	+	1.91912i	0.162522	+	0.554004i
$13$	−0.735357	−	2.50439i	−0.203951	−	0.694594i	−0.996409	−	0.0846677i	$-0.973017\pi$
$13$	−0.735357	−	2.50439i	−0.203951	−	0.694594i	0.792458	−	0.609926i	$-0.208801\pi$
$14$	−2.58003	+	0.370628i	−0.689542	+	0.0990544i
$15$	−2.19702	+	1.41194i	−0.567269	+	0.364561i
$16$	−0.567307	−	3.95957i	−0.141827	−	0.989892i
$17$	−0.317717	−	2.20977i	−0.0770577	−	0.535948i	−0.991386	−	0.130974i	$-0.958190\pi$
$17$	−0.317717	−	2.20977i	−0.0770577	−	0.535948i	0.914328	−	0.404974i	$-0.132719\pi$
$18$	1.06868	+	0.926245i	0.251890	+	0.218318i
$19$	1.84049	+	0.264623i	0.422238	+	0.0607087i	0.350159	−	0.936690i	$-0.386128\pi$
$19$	1.84049	+	0.264623i	0.422238	+	0.0607087i	0.0720790	+	0.997399i	$0.477037\pi$
$20$	4.75173	−	2.16863i	1.06252	−	0.484920i
$21$	−1.39291	+	1.20696i	−0.303958	+	0.263381i
$22$	−6.58478	−	1.93435i	−1.40388	−	0.412404i
$23$	4.13830	−	2.42373i	0.862895	−	0.505383i
$23$	4.13830	−	2.42373i	0.862895	−	0.505383i
$24$	−1.85144	−	2.13827i	−0.377923	−	0.436472i
$25$	1.19216	+	1.37583i	0.238432	+	0.275165i
$26$	2.41692	+	2.78997i	0.473998	+	0.547159i
$27$	0.989821	+	0.142315i	0.190491	+	0.0273885i
$28$	3.10149	−	1.99213i	0.586127	−	0.376477i
$29$	1.40144	−	0.201497i	0.260242	−	0.0374171i	−0.0109589	−	0.999940i	$-0.503488\pi$
$29$	1.40144	−	0.201497i	0.260242	−	0.0374171i	0.271201	+	0.962523i	$0.412579\pi$
$30$	1.99717	−	3.10681i	0.364631	−	0.567224i
$31$	0.445741	−	0.286460i	0.0800574	−	0.0514498i	−0.500000	−	0.866026i	$-0.666667\pi$
$31$	0.445741	−	0.286460i	0.0800574	−	0.0514498i	0.580057	+	0.814576i	$0.303030\pi$
$32$	3.05539	+	4.76073i	0.540122	+	0.841587i
$33$	−4.65631	+	1.36722i	−0.810560	+	0.238002i
$34$	1.70660	+	2.65623i	0.292679	+	0.455541i
$35$	3.63773	+	3.15211i	0.614889	+	0.532804i
$36$	−1.91885	−	0.563938i	−0.319808	−	0.0939897i
$37$	−6.09278	+	2.78248i	−1.00165	+	0.457437i	−0.847605	−	0.530627i	$-0.821956\pi$
$37$	−6.09278	+	2.78248i	−1.00165	+	0.457437i	−0.154042	+	0.988064i	$0.549229\pi$
$38$	−2.52319	+	0.740537i	−0.409315	+	0.120131i
$39$	2.50439	+	0.735357i	0.401024	+	0.117751i
$40$	−4.83935	+	5.58073i	−0.765168	+	0.882391i
$41$	−1.56265	+	3.42173i	−0.244045	+	0.534385i	−0.991527	−	0.129897i	$-0.958535\pi$
$41$	−1.56265	+	3.42173i	−0.244045	+	0.534385i	0.747482	+	0.664282i	$0.231263\pi$
$42$	1.08308	−	2.37084i	0.167123	−	0.365828i
$43$	−0.469155	+	0.730019i	−0.0715454	+	0.111327i	−0.875183	−	0.483793i	$-0.839259\pi$
$43$	−0.469155	+	0.730019i	−0.0715454	+	0.111327i	0.803637	+	0.595119i	$0.202895\pi$
$44$	9.60732	−	1.37891i	1.44836	−	0.207878i
$45$		−	2.61160i		−	0.389315i
$46$	−3.90034	+	5.54863i	−0.575074	+	0.818101i
$47$	2.04867			0.298829			0.149414	−	0.988775i	$-0.452261\pi$
$47$	2.04867			0.298829			0.149414	+	0.988775i	$0.452261\pi$
$48$	3.63771	+	1.66345i	0.525058	+	0.240099i
$49$	−3.03107	−	1.94795i	−0.433010	−	0.278278i
$50$	−2.34176	−	1.06979i	−0.331175	−	0.151292i
$51$	2.03075	+	0.927411i	0.284362	+	0.129864i
$52$	−4.74797	−	2.16974i	−0.658425	−	0.300889i
$53$	−3.30615	+	11.2597i	−0.454134	+	1.54664i	0.340915	+	0.940094i	$0.389263\pi$
$53$	−3.30615	+	11.2597i	−0.454134	+	1.54664i	−0.795049	+	0.606545i	$0.792555\pi$
$54$	−1.35698	+	0.398263i	−0.184661	+	0.0541967i
$55$	5.26490	+	11.5285i	0.709918	+	1.55450i
$56$	−2.82000	+	4.38444i	−0.376838	+	0.585895i
$57$	−1.21766	+	1.40526i	−0.161283	+	0.186131i
$58$	−1.68459	+	1.08233i	−0.221198	+	0.142117i
$59$	0.962583	+	3.27826i	0.125318	+	0.426793i	0.998121	−	0.0612799i	$-0.0195182\pi$
$59$	0.962583	+	3.27826i	0.125318	+	0.426793i	−0.872803	+	0.488073i	$0.837700\pi$
$60$	−0.744615	+	5.16986i	−0.0961294	+	0.667426i
$61$	1.27324	+	1.98120i	0.163021	+	0.253666i	0.913148	−	0.407628i	$-0.133644\pi$
$61$	1.27324	+	1.98120i	0.163021	+	0.253666i	−0.750127	+	0.661294i	$0.770008\pi$
$62$	−0.405194	+	0.630323i	−0.0514596	+	0.0800511i
$63$	−0.262298	−	1.82432i	−0.0330465	−	0.229843i
$64$	−6.72683	−	4.33010i	−0.840853	−	0.541263i
$65$	0.970105	−	6.74723i	0.120327	−	0.836890i
$66$	5.18728	−	4.49368i	0.638510	−	0.553134i
$67$	−3.55986	+	3.08463i	−0.434906	+	0.376848i	−0.844620	−	0.535366i	$-0.820174\pi$
$67$	−3.55986	+	3.08463i	−0.434906	+	0.376848i	0.409714	+	0.912214i	$0.365628\pi$
$68$	−3.75559	−	2.41488i	−0.455432	−	0.292847i
$69$	−0.198359	+	4.79173i	−0.0238796	+	0.576856i
$70$	−6.53121	−	1.91861i	−0.780629	−	0.229318i
$71$	7.67205	+	8.85401i	0.910504	+	1.05078i	0.998505	+	0.0546575i	$0.0174067\pi$
$71$	7.67205	+	8.85401i	0.910504	+	1.05078i	−0.0880009	+	0.996120i	$0.528048\pi$
$72$	2.79979	−	0.401492i	0.329958	−	0.0473162i
$73$	0.985217	−	6.85234i	0.115311	−	0.802005i	−0.847299	−	0.531116i	$-0.821773\pi$
$73$	0.985217	−	6.85234i	0.115311	−	0.802005i	0.962610	−	0.270890i	$-0.0873179\pi$
$74$	6.20406	−	7.15808i	0.721207	−	0.832110i
$75$	−1.80195	+	0.259081i	−0.208071	+	0.0299161i
$76$	2.81111	−	2.43463i	0.322457	−	0.279271i
$77$	4.83564	+	7.52441i	0.551073	+	0.857486i
$78$	−3.65376	+	0.524872i	−0.413707	+	0.0594301i
$79$	9.58201	−	2.81353i	1.07806	−	0.316547i	0.305958	−	0.952045i	$-0.401023\pi$
$79$	9.58201	−	2.81353i	1.07806	−	0.316547i	0.772103	+	0.635498i	$0.219205\pi$
$80$	2.94804	−	10.0218i	0.329601	−	1.12047i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	0.000655866	−	5.31980i	7.24282e−5	−	0.587474i
$83$	−12.8319	+	5.86015i	−1.40849	+	0.643235i	−0.967173	−	0.254118i	$-0.918215\pi$
$83$	−12.8319	+	5.86015i	−1.40849	+	0.643235i	−0.441314	+	0.897353i	$0.645488\pi$
$84$	−0.000908918		3.68617i	−9.91711e−5		0.402194i
$85$	1.64261	−	5.59422i	0.178166	−	0.606778i
$86$	0.174801	−	1.21471i	0.0188493	−	0.130985i
$87$	−0.588168	+	1.28791i	−0.0630582	+	0.138078i
$88$	−11.5498	+	7.41658i	−1.23122	+	0.790611i
$89$	−6.64268	−	4.26899i	−0.704123	−	0.452512i	0.138959	−	0.990298i	$-0.455624\pi$
$89$	−6.64268	−	4.26899i	−0.704123	−	0.452512i	−0.843081	+	0.537786i	$0.819261\pi$
$90$	1.53387	+	3.35979i	0.161684	+	0.354153i
$91$		−	4.81068i		−	0.504296i
$92$	1.75887	−	9.42902i	0.183375	−	0.983043i
$93$			0.529853i			0.0549432i
$94$	−2.63558	+	1.20324i	−0.271839	+	0.124104i
$95$	4.08518	+	2.62539i	0.419131	+	0.269359i
$96$	−5.65685	−	0.00348710i	−0.577350	−	0.000355901i
$97$	4.94567	−	10.8295i	0.502157	−	1.09957i	−0.473606	−	0.880737i	$-0.657048\pi$
$97$	4.94567	−	10.8295i	0.502157	−	1.09957i	0.975762	−	0.218833i	$-0.0702249\pi$
$98$	5.04351	+	0.725782i	0.509472	+	0.0733151i
$99$	1.36722	−	4.65631i	0.137410	−	0.467977i
$100$	3.64096		0.000897770i	0.364096		8.97770e-5i
$101$	11.2923	−	5.15701i	1.12362	−	0.513141i	0.235099	−	0.971971i	$-0.424459\pi$
$101$	11.2923	−	5.15701i	1.12362	−	0.513141i	0.888524	+	0.458830i	$0.151731\pi$
$102$	−3.15722		0.000389246i	−0.312612		3.85411e-5i
$103$	−7.80713	+	9.00991i	−0.769260	+	0.887773i	−0.996285	−	0.0861160i	$-0.972554\pi$
$103$	−7.80713	+	9.00991i	−0.769260	+	0.887773i	0.227026	+	0.973889i	$0.427100\pi$
$104$	7.38254	+	0.00273053i	0.723918	+	0.000267750i
$105$	−4.61843	+	1.35609i	−0.450713	+	0.132341i
$106$	−2.35981	−	16.4272i	−0.229205	−	1.59555i
$107$	−8.71496	−	13.5607i	−0.842507	−	1.31097i	−0.948557	−	0.316606i	$-0.897457\pi$
$107$	−8.71496	−	13.5607i	−0.842507	−	1.31097i	0.106050	−	0.994361i	$-0.466180\pi$
$108$	1.51182	−	1.30935i	0.145475	−	0.125992i
$109$	4.80826	−	0.691323i	0.460548	−	0.0662168i	0.0918638	−	0.995772i	$-0.470718\pi$
$109$	4.80826	−	0.691323i	0.460548	−	0.0662168i	0.368684	+	0.929555i	$0.379808\pi$
$110$	−13.5442	−	11.7391i	−1.29139	−	1.11928i
$111$	0.953236	−	6.62990i	0.0904771	−	0.629282i
$112$	1.05279	−	7.29678i	0.0994795	−	0.689481i
$113$	−11.6861	−	13.4864i	−1.09933	−	1.26870i	−0.960470	−	0.278384i	$-0.910201\pi$
$113$	−11.6861	−	13.4864i	−1.09933	−	1.26870i	−0.138862	−	0.990312i	$-0.544344\pi$
$114$	0.741160	−	2.52301i	0.0694159	−	0.236301i
$115$	12.4604	−	1.26818i	1.16194	−	0.118258i
$116$	1.53153	−	2.38181i	0.142199	−	0.221145i
$117$	−1.97260	+	1.70927i	−0.182367	+	0.158022i
$118$	−3.16376	−	3.65208i	−0.291248	−	0.336202i
$119$	0.585579	−	4.07279i	0.0536800	−	0.373352i
$120$	−2.07846	−	7.08829i	−0.189737	−	0.647069i
$121$	1.78612	+	12.4228i	0.162375	+	1.12934i
$122$	−2.80161	−	1.80097i	−0.253646	−	0.163053i
$123$	−2.03371	−	3.16452i	−0.183374	−	0.285335i
$124$	0.151071	−	1.04888i	0.0135665	−	0.0941924i
$125$	−2.33941	−	7.96730i	−0.209243	−	0.712617i
$126$	1.40892	+	2.19291i	0.125516	+	0.195360i
$127$	−4.31607	+	4.98101i	−0.382989	+	0.441993i	−0.914210	−	0.405240i	$-0.867188\pi$
$127$	−4.31607	+	4.98101i	−0.382989	+	0.441993i	0.531221	+	0.847233i	$0.321733\pi$
$128$	11.1972	+	1.61977i	0.989698	+	0.143169i
$129$	−0.360487	−	0.789356i	−0.0317391	−	0.0694989i
$130$	2.71480	+	9.24998i	0.238104	+	0.811277i
$131$	−2.85266	+	9.71528i	−0.249238	+	0.848828i	0.735904	+	0.677086i	$0.236758\pi$
$131$	−2.85266	+	9.71528i	−0.249238	+	0.848828i	−0.985142	+	0.171741i	$0.945061\pi$
$132$	−4.03410	+	8.82769i	−0.351123	+	0.768352i
$133$	3.11737	+	1.42366i	0.270310	+	0.123447i
$134$	2.76802	−	6.05914i	0.239120	−	0.523430i
$135$	2.19702	+	1.41194i	0.189090	+	0.121520i
$136$	6.24984	+	0.900951i	0.535919	+	0.0772559i
$137$	8.67507			0.741161			0.370581	−	0.928800i	$-0.379159\pi$
$137$	8.67507			0.741161			0.370581	+	0.928800i	$0.379159\pi$
$138$	−2.55912	−	6.28099i	−0.217847	−	0.534674i
$139$		−	17.3825i		−	1.47436i	−0.675696	−	0.737181i	$-0.736157\pi$
$139$		−	17.3825i		−	1.47436i	0.675696	−	0.737181i	$-0.263843\pi$
$140$	9.52917	−	1.36769i	0.805362	−	0.115591i
$141$	−1.10759	+	1.72345i	−0.0932761	+	0.145140i
$142$	−15.0702	−	6.88457i	−1.26466	−	0.577740i
$143$	5.26191	−	11.5220i	0.440023	−	0.963516i
$144$	−3.36608	+	2.16090i	−0.280507	+	0.180075i
$145$	3.54787	+	1.04175i	0.294635	+	0.0865126i
$146$	2.75709	+	9.39408i	0.228179	+	0.777460i
$147$	3.27744	−	1.49676i	0.270319	−	0.123450i
$148$	−3.77730	+	12.8526i	−0.310492	+	1.05648i
$149$	8.88083	+	7.69529i	0.727546	+	0.630422i	0.937781	−	0.347229i	$-0.112877\pi$
$149$	8.88083	+	7.69529i	0.727546	+	0.630422i	−0.210234	+	0.977651i	$0.567423\pi$
$150$	2.16602	−	1.39164i	0.176855	−	0.113627i
$151$	9.18412	−	2.69670i	0.747393	−	0.219454i	0.114210	−	0.993457i	$-0.463566\pi$
$151$	9.18412	−	2.69670i	0.747393	−	0.219454i	0.633183	+	0.774002i	$0.281748\pi$
$152$	−2.18653	+	4.78316i	−0.177351	+	0.387965i
$153$	−1.87809	+	1.20698i	−0.151835	+	0.0975783i
$154$	−10.6403	−	6.83995i	−0.857418	−	0.551179i
$155$	1.36968	−	0.196931i	0.110015	−	0.0158178i
$156$	4.39225	−	2.82120i	0.351661	−	0.225876i
$157$	−21.5541	−	3.09902i	−1.72021	−	0.247328i	−0.789672	−	0.613530i	$-0.789749\pi$
$157$	−21.5541	−	3.09902i	−1.72021	−	0.247328i	−0.930536	+	0.366201i	$0.880658\pi$
$158$	−10.6747	+	9.24734i	−0.849231	+	0.735679i
$159$	−7.68483	−	8.86876i	−0.609446	−	0.703339i
$160$	2.09347	+	14.6244i	0.165503	+	1.15616i
$161$	8.57682	−	2.13735i	0.675948	−	0.168447i
$162$	0.398597	−	1.35688i	0.0313168	−	0.106606i
$163$	6.42240	−	5.56505i	0.503042	−	0.435888i	−0.366009	−	0.930611i	$-0.619276\pi$
$163$	6.42240	−	5.56505i	0.503042	−	0.435888i	0.869051	+	0.494723i	$0.164731\pi$
$164$	3.12362	+	6.84424i	0.243914	+	0.534445i
$165$	−12.5448	−	1.80367i	−0.976613	−	0.140416i
$166$	13.0663	−	15.0755i	1.01414	−	1.17009i
$167$	1.95777	+	13.6166i	0.151497	+	1.05368i	0.913712	+	0.406361i	$0.133203\pi$
$167$	1.95777	+	13.6166i	0.151497	+	1.05368i	−0.762215	+	0.647323i	$0.775888\pi$
$168$	−2.16382	−	4.74274i	−0.166942	−	0.365910i
$169$	5.20505	−	3.34508i	0.400389	−	0.257314i
$170$	1.17244	+	8.16163i	0.0899220	+	0.625969i
$171$	−0.523859	−	1.78410i	−0.0400605	−	0.136434i
$172$	0.488550	+	1.66537i	0.0372516	+	0.126983i
$173$	−10.1829	−	8.82351i	−0.774190	−	0.670839i	0.175343	−	0.984507i	$-0.443897\pi$
$173$	−10.1829	−	8.82351i	−0.774190	−	0.670839i	−0.949533	+	0.313668i	$0.898442\pi$
$174$	0.000246862	−	2.00232i	1.87145e−5	−	0.151796i
$175$	1.39384	+	3.05209i	0.105364	+	0.230716i
$176$	10.5027	−	16.3249i	0.791673	−	1.23053i
$177$	−3.27826	−	0.962583i	−0.246409	−	0.0723522i
$178$	11.0530	+	1.59057i	0.828458	+	0.119219i
$179$	−23.5580	−	10.7586i	−1.76081	−	0.804133i	−0.984864	−	0.173328i	$-0.944548\pi$
$179$	−23.5580	−	10.7586i	−1.76081	−	0.804133i	−0.775941	−	0.630805i	$-0.782725\pi$
$180$	−3.94659	−	3.42145i	−0.294162	−	0.255020i
$181$	−0.832132	+	1.29482i	−0.0618519	+	0.0962434i	−0.870802	−	0.491634i	$-0.836400\pi$
$181$	−0.832132	+	1.29482i	−0.0618519	+	0.0962434i	0.808950	+	0.587877i	$0.200036\pi$
$182$	2.82544	+	6.18887i	0.209436	+	0.458750i
$183$	−2.35505			−0.174090
$184$	3.27515	+	13.1633i	0.241447	+	0.970414i
$185$	−17.4927			−1.28609
$186$	−0.311197	−	0.681649i	−0.0228181	−	0.0499809i
$187$	5.85732	−	9.11417i	0.428330	−	0.666494i
$188$	2.68394	−	3.09589i	0.195747	−	0.225791i
$189$	1.67653	+	0.765645i	0.121950	+	0.0556925i
$190$	−6.79750	−	0.978188i	−0.493142	−	0.0709652i
$191$	−23.4228	−	6.87754i	−1.69481	−	0.497641i	−0.715264	−	0.698855i	$-0.753693\pi$
$191$	−23.4228	−	6.87754i	−1.69481	−	0.497641i	−0.979547	+	0.201213i	$0.935512\pi$
$192$	7.27951	−	3.31794i	0.525354	−	0.239451i
$193$	−0.511863	−	1.12082i	−0.0368447	−	0.0806786i	0.890315	−	0.455346i	$-0.150484\pi$
$193$	−0.511863	−	1.12082i	−0.0368447	−	0.0806786i	−0.927159	+	0.374667i	$0.877757\pi$
$194$	−0.00207576	+	16.8367i	−0.000149031	+	1.20881i
$195$	5.15165	+	4.46393i	0.368917	+	0.319669i
$196$	−6.91468	+	2.02848i	−0.493906	+	0.144892i
$197$	−0.833382	−	2.83824i	−0.0593760	−	0.202216i	0.924463	−	0.381272i	$-0.124514\pi$
$197$	−0.833382	−	2.83824i	−0.0593760	−	0.202216i	−0.983839	+	0.179056i	$0.942696\pi$
$198$	0.975872	+	6.79328i	0.0693522	+	0.482778i
$199$	7.26635	−	4.66980i	0.515098	−	0.331033i	−0.257132	−	0.966376i	$-0.582778\pi$
$199$	7.26635	−	4.66980i	0.515098	−	0.331033i	0.772230	+	0.635343i	$0.219141\pi$
$200$	−4.68457	+	2.13728i	−0.331249	+	0.151128i
$201$	−0.670355	−	4.66242i	−0.0472832	−	0.328862i
$202$	−11.4985	+	13.2667i	−0.809032	+	0.933440i
$203$	2.58298	+	0.371377i	0.181290	+	0.0260655i
$204$	4.06195	−	1.85382i	0.284394	−	0.129793i
$205$	−7.42447	+	6.43334i	−0.518548	+	0.449324i
$206$	4.75200	−	16.1765i	0.331088	−	1.12707i
$207$	−3.92382	−	2.75747i	−0.272724	−	0.191658i
$208$	−9.49914	+	4.33245i	−0.658647	+	0.300402i
$209$	5.90917	+	6.81955i	0.408746	+	0.471718i
$210$	5.14508	−	4.45713i	0.355044	−	0.307571i
$211$	26.3552	+	3.78931i	1.81437	+	0.260867i	0.964111	−	0.265501i	$-0.0855373\pi$
$211$	26.3552	+	3.78931i	1.81437	+	0.260867i	0.850257	+	0.526368i	$0.176446\pi$
$212$	12.6840	+	19.7474i	0.871143	+	1.35626i
$213$	−11.5963	+	1.66729i	−0.794565	+	0.114241i
$214$	19.1763	+	12.3272i	1.31086	+	0.842669i
$215$	−1.90652	+	1.22525i	−0.130024	+	0.0835611i
$216$	−1.17592	+	2.57239i	−0.0800114	+	0.175029i
$217$	0.937006	−	0.275130i	0.0636081	−	0.0186770i
$218$	−5.77973	+	3.71340i	−0.391452	+	0.251503i
$219$	5.23190	+	4.53347i	0.353539	+	0.306344i
$220$	24.3191	+	7.14725i	1.63960	+	0.481868i
$221$	−5.30050	+	2.42066i	−0.356550	+	0.162831i
$222$	2.66759	+	9.08914i	0.179037	+	0.610023i
$223$	2.91073	+	0.854668i	0.194917	+	0.0572328i	0.377734	−	0.925914i	$-0.376703\pi$
$223$	2.91073	+	0.854668i	0.194917	+	0.0572328i	−0.182817	+	0.983147i	$0.558522\pi$
$224$	2.93119	+	10.0055i	0.195849	+	0.668523i
$225$	0.756254	−	1.65597i	0.0504170	−	0.110398i
$226$	22.9549	+	10.4866i	1.52694	+	0.697556i
$227$	−5.86057	+	9.11922i	−0.388979	+	0.605264i	−0.979424	−	0.201815i	$-0.935316\pi$
$227$	−5.86057	+	9.11922i	−0.388979	+	0.605264i	0.590444	+	0.807078i	$0.298953\pi$
$228$	0.528338	+	3.68112i	0.0349901	+	0.243788i
$229$		−	15.9631i		−	1.05487i	−0.849595	−	0.527435i	$-0.823154\pi$
$229$		−	15.9631i		−	1.05487i	0.849595	−	0.527435i	$-0.176846\pi$
$230$	−15.2854	+	8.94985i	−1.00789	+	0.590136i
$231$	−8.94428			−0.588491
$232$	−0.571386	+	3.96367i	−0.0375134	+	0.260228i
$233$	−22.0074	−	14.1433i	−1.44175	−	0.926556i	−0.999561	−	0.0296343i	$-0.990566\pi$
$233$	−22.0074	−	14.1433i	−1.44175	−	0.926556i	−0.442189	−	0.896922i	$-0.645798\pi$
$234$	1.53382	−	3.35751i	0.100269	−	0.219487i
$235$	4.86681	+	2.22260i	0.317476	+	0.144986i
$236$	6.21510	+	2.84019i	0.404569	+	0.184881i
$237$	−2.81353	+	9.58201i	−0.182759	+	0.622419i
$238$	1.63872	+	5.58352i	0.106223	+	0.361926i
$239$	8.39636	+	18.3855i	0.543115	+	1.18926i	0.959924	+	0.280262i	$0.0904213\pi$
$239$	8.39636	+	18.3855i	0.543115	+	1.18926i	−0.416808	+	0.908994i	$0.636851\pi$
$240$	6.83706	+	7.89825i	0.441330	+	0.509830i
$241$	−9.61813	+	11.0999i	−0.619558	+	0.715008i	−0.975623	−	0.219453i	$-0.929573\pi$
$241$	−9.61813	+	11.0999i	−0.619558	+	0.715008i	0.356065	+	0.934461i	$0.384118\pi$
$242$	−9.59405	−	14.9327i	−0.616729	−	0.959909i
$243$	−0.281733	−	0.959493i	−0.0180732	−	0.0615515i
$244$	4.66200	+	0.671467i	0.298454	+	0.0429863i
$245$	−5.08727	−	7.91595i	−0.325014	−	0.505732i
$246$	4.47495	+	2.87665i	0.285312	+	0.183409i
$247$	−0.690699	−	4.80391i	−0.0439481	−	0.305666i
$248$	0.421687	+	1.43810i	0.0267771	+	0.0913195i
$249$	2.00760	−	13.9631i	0.127226	−	0.884878i
$250$	7.68903	+	8.87582i	0.486297	+	0.561356i
$251$	−5.23567	+	4.53673i	−0.330472	+	0.286356i	−0.804253	−	0.594287i	$-0.797434\pi$
$251$	−5.23567	+	4.53673i	−0.330472	+	0.286356i	0.473781	+	0.880643i	$0.342889\pi$
$252$	−3.10051	−	1.99366i	−0.195314	−	0.125589i
$253$	22.8800	+	4.26216i	1.43846	+	0.267960i
$254$	2.62708	−	8.94295i	0.164838	−	0.561131i
$255$	3.81809	+	4.40631i	0.239098	+	0.275934i
$256$	−15.3563	+	4.49258i	−0.959770	+	0.280786i
$257$	−2.86044	+	19.8948i	−0.178429	+	1.24100i	0.681969	+	0.731381i	$0.261124\pi$
$257$	−2.86044	+	19.8948i	−0.178429	+	1.24100i	−0.860398	+	0.509622i	$0.829785\pi$
$258$	0.927371	+	0.803772i	0.0577356	+	0.0500407i
$259$	−12.2195	+	1.75689i	−0.759281	+	0.109168i
$260$	−8.92532	−	10.3055i	−0.553525	−	0.639120i
$261$	−0.765469	−	1.19109i	−0.0473814	−	0.0737268i
$262$	−2.03613	−	14.1740i	−0.125793	−	0.875674i
$263$	−9.32323	+	2.73755i	−0.574895	+	0.168804i	−0.556240	−	0.831022i	$-0.687757\pi$
$263$	−9.32323	+	2.73755i	−0.574895	+	0.168804i	−0.0186547	+	0.999826i	$0.505938\pi$
$264$	0.00507675	−	13.7260i	0.000312452	−	0.844779i
$265$	−20.0697	+	23.1617i	−1.23287	+	1.42281i
$266$	−4.84661		0.000597527i	−0.297164		3.66367e-5i
$267$	7.18261	−	3.28019i	0.439568	−	0.200744i
$268$	−0.00232292	+	9.42073i	−0.000141895	+	0.575463i
$269$	6.63849	−	22.6086i	0.404756	−	1.37847i	−0.465140	−	0.885237i	$-0.653996\pi$
$269$	6.63849	−	22.6086i	0.404756	−	1.37847i	0.869896	−	0.493235i	$-0.164186\pi$
$270$	−3.65571	−	0.526072i	−0.222479	−	0.0320157i
$271$	10.8107	−	23.6720i	0.656700	−	1.43797i	−0.228865	−	0.973458i	$-0.573501\pi$
$271$	10.8107	−	23.6720i	0.656700	−	1.43797i	0.885565	−	0.464515i	$-0.153771\pi$
$272$	−8.56949	+	2.51164i	−0.519601	+	0.152290i
$273$	4.04700	+	2.60085i	0.244936	+	0.157411i
$274$	−11.1604	+	5.09510i	−0.674222	+	0.307806i
$275$			8.83458i			0.532745i
$276$	6.98128	+	6.57737i	0.420223	+	0.395911i
$277$			5.40470i			0.324737i	0.986730	+	0.162369i	$0.0519134\pi$
$277$			5.40470i			0.324737i	−0.986730	+	0.162369i	$0.948087\pi$
$278$	10.2092	+	22.3623i	0.612306	+	1.34120i
$279$	−0.445741	−	0.286460i	−0.0266858	−	0.0171499i
$280$	−11.4559	+	7.35625i	−0.684619	+	0.439620i
$281$	−0.436338	+	0.955446i	−0.0260297	+	0.0569972i	−0.922200	−	0.386713i	$-0.873611\pi$
$281$	−0.436338	+	0.955446i	−0.0260297	+	0.0569972i	0.896171	+	0.443710i	$0.146338\pi$
$282$	0.412675	−	2.86771i	0.0245745	−	0.170770i
$283$	7.33493	−	24.9805i	0.436017	−	1.48494i	−0.389748	−	0.920921i	$-0.627438\pi$
$283$	7.33493	−	24.9805i	0.436017	−	1.48494i	0.825765	−	0.564015i	$-0.190744\pi$
$284$	23.4311	+	0.00577752i	1.39038	+	0.000342833i
$285$	−4.41724	+	2.01728i	−0.261654	+	0.119494i
$286$	−0.00220849	+	17.9133i	−0.000130591	+	1.05924i
$287$	−4.54020	+	5.23967i	−0.267999	+	0.309288i
$288$	3.06126	−	4.75696i	0.180386	−	0.280307i
$289$	11.5292	−	3.38529i	0.678191	−	0.199135i
$290$	−5.17614	+	0.743565i	−0.303953	+	0.0436636i
$291$	6.43653	+	10.0154i	0.377316	+	0.587115i
$292$	−9.06436	−	10.4660i	−0.530452	−	0.612479i
$293$	33.7146	−	4.84743i	1.96963	−	0.283190i	0.970520	−	0.241020i	$-0.0774821\pi$
$293$	33.7146	−	4.84743i	1.96963	−	0.283190i	0.999110	−	0.0421698i	$-0.0134270\pi$
$294$	−3.33729	+	3.85048i	−0.194635	+	0.224565i
$295$	−1.26987	+	8.83213i	−0.0739346	+	0.514227i
$296$	−2.68922	−	18.7532i	−0.156308	−	1.09001i
$297$	3.17797	+	3.66757i	0.184404	+	0.212814i
$298$	−15.9447	−	4.68393i	−0.923653	−	0.271333i
$299$	−9.11311	−	8.58163i	−0.527025	−	0.496288i
$300$	−1.96921	+	3.06248i	−0.113692	+	0.176813i
$301$	−1.20873	+	1.04737i	−0.0696702	+	0.0603696i
$302$	−10.2314	+	8.86335i	−0.588751	+	0.510029i
$303$	−1.76671	+	12.2877i	−0.101495	+	0.705913i
$304$	0.00366789	−	7.43768i	0.000210368	−	0.426580i
$305$	0.875302	+	6.08786i	0.0501197	+	0.348590i
$306$	1.70725	−	2.65581i	0.0975970	−	0.151823i
$307$	−6.75808	−	10.5158i	−0.385704	−	0.600167i	0.593060	−	0.805158i	$-0.297920\pi$
$307$	−6.75808	−	10.5158i	−0.385704	−	0.600167i	−0.978764	+	0.204991i	$0.934283\pi$
$308$	17.7059	+	2.55017i	1.00888	+	0.145310i
$309$	−3.35876	−	11.4389i	−0.191073	−	0.650736i
$310$	−1.64641	+	1.05780i	−0.0935101	+	0.0600790i
$311$	−9.20654	+	10.6249i	−0.522055	+	0.602483i	−0.954144	−	0.299347i	$-0.903231\pi$
$311$	−9.20654	+	10.6249i	−0.522055	+	0.602483i	0.432089	+	0.901831i	$0.357777\pi$
$312$	−3.99360	+	6.20911i	−0.226093	+	0.351522i
$313$	9.81781	+	21.4980i	0.554935	+	1.21514i	0.954439	+	0.298407i	$0.0964553\pi$
$313$	9.81781	+	21.4980i	0.554935	+	1.21514i	−0.399503	+	0.916732i	$0.630817\pi$
$314$	29.5492	−	8.67248i	1.66756	−	0.489416i
$315$	1.35609	−	4.61843i	0.0764072	−	0.260219i
$316$	8.30159	−	18.1661i	0.467001	−	1.02192i
$317$	13.1275	+	5.99514i	0.737315	+	0.336720i	0.748426	−	0.663218i	$-0.230810\pi$
$317$	13.1275	+	5.99514i	0.737315	+	0.336720i	−0.0111116	+	0.999938i	$0.503537\pi$
$318$	15.0953	+	6.89604i	0.846502	+	0.386710i
$319$	5.78024	+	3.71474i	0.323631	+	0.207985i
$320$	−11.2825	−	17.5845i	−0.630712	−	0.983005i
$321$	16.1197			0.899713
$322$	−9.77864	+	7.78708i	−0.544942	+	0.433957i
$323$		−	4.15114i		−	0.230976i
$324$	0.284142	+	1.97971i	0.0157856	+	0.109984i
$325$	2.56895	−	3.99736i	0.142500	−	0.221734i
$326$	−4.99383	+	10.9314i	−0.276583	+	0.605435i
$327$	−2.01796	+	4.41872i	−0.111594	+	0.244356i
$328$	−8.03830	−	6.97043i	−0.443841	−	0.384878i
$329$	3.62292	+	1.06378i	0.199738	+	0.0586483i
$330$	17.1981	−	5.04751i	0.946724	−	0.277856i
$331$	−29.9583	+	13.6815i	−1.64666	+	0.752004i	−0.999942	−	0.0107259i	$-0.996586\pi$
$331$	−29.9583	+	13.6815i	−1.64666	+	0.752004i	−0.646717	+	0.762730i	$0.723858\pi$
$332$	−7.95533	+	27.0687i	−0.436605	+	1.48559i
$333$	5.06207	+	4.38631i	0.277400	+	0.240368i
$334$	−10.5160	−	16.3677i	−0.575413	−	0.895602i
$335$	−11.8033	+	3.46577i	−0.644884	+	0.189355i
$336$	5.56926	+	4.83060i	0.303828	+	0.263531i
$337$	−11.2877	+	7.25414i	−0.614878	+	0.395158i	−0.810683	−	0.585485i	$-0.800904\pi$
$337$	−11.2877	+	7.25414i	−0.614878	+	0.395158i	0.195806	+	0.980643i	$0.437268\pi$
$338$	−4.73157	+	7.36047i	−0.257363	+	0.400357i
$339$	17.6635	−	2.53962i	0.959347	−	0.137933i
$340$	−6.30187	−	9.81123i	−0.341767	−	0.532088i
$341$	2.54514	+	0.365937i	0.137827	+	0.0198166i
$342$	1.72179	+	1.98754i	0.0931036	+	0.107474i
$343$	−12.7975	−	14.7691i	−0.690999	−	0.797456i
$344$	−1.60663	−	1.85553i	−0.0866236	−	0.100044i
$345$	−5.66977	+	11.1680i	−0.305250	+	0.601266i
$346$	18.2824	+	5.37065i	0.982869	+	0.288728i
$347$	9.24581	−	8.01154i	0.496341	−	0.430082i	−0.370376	−	0.928882i	$-0.620771\pi$
$347$	9.24581	−	8.01154i	0.496341	−	0.430082i	0.866717	+	0.498800i	$0.166226\pi$
$348$	1.17570	+	2.57611i	0.0630241	+	0.138094i
$349$	1.85621	+	0.266883i	0.0993606	+	0.0142859i	0.191816	−	0.981431i	$-0.438562\pi$
$349$	1.85621	+	0.266883i	0.0993606	+	0.0142859i	−0.0924552	+	0.995717i	$0.529471\pi$
$350$	−3.58573	−	3.10783i	−0.191665	−	0.166120i
$351$	−0.371459	−	2.58356i	−0.0198270	−	0.137900i
$352$	−3.92359	+	27.1702i	−0.209128	+	1.44818i
$353$	31.1623	−	20.0268i	1.65860	−	1.06592i	0.738490	−	0.674264i	$-0.235539\pi$
$353$	31.1623	−	20.0268i	1.65860	−	1.06592i	0.920112	−	0.391655i	$-0.128097\pi$
$354$	4.78279	−	0.687059i	0.254202	−	0.0365168i
$355$	8.61999	+	29.3570i	0.457501	+	1.55811i
$356$	−15.1537	+	4.44548i	−0.803146	+	0.235610i
$357$	3.10966	+	2.69454i	0.164581	+	0.142610i
$358$	36.6258	+	0.00451551i	1.93573	+	0.000238652i
$359$	−1.19107	−	2.60807i	−0.0628622	−	0.137649i	0.875593	−	0.483049i	$-0.160471\pi$
$359$	−1.19107	−	2.60807i	−0.0628622	−	0.137649i	−0.938456	+	0.345400i	$0.887743\pi$
$360$	7.08675	+	2.08370i	0.373504	+	0.109821i
$361$	−14.9130	−	4.37885i	−0.784894	−	0.230466i
$362$	0.310042	−	2.15450i	0.0162954	−	0.113238i
$363$	−11.4163	−	5.21367i	−0.599203	−	0.273647i
$364$	−7.26978	−	6.30244i	−0.381040	−	0.330338i
$365$	9.77458	−	15.2095i	0.511625	−	0.796104i
$366$	3.02974	−	1.38319i	0.158367	−	0.0723003i
$367$	21.4917			1.12186			0.560929	−	0.827864i	$-0.310444\pi$
$367$	21.4917			1.12186			0.560929	+	0.827864i	$0.310444\pi$
$368$	−11.9446	−	15.0109i	−0.622656	−	0.782496i
$369$	3.76167			0.195825
$370$	22.5042	−	10.2740i	1.16994	−	0.534117i
$371$	−11.6934	+	18.1952i	−0.607089	+	0.944649i
$372$	0.800701	+	0.694157i	0.0415144	+	0.0359904i
$373$	−15.9124	−	7.26694i	−0.823912	−	0.376268i	−0.0415840	−	0.999135i	$-0.513240\pi$
$373$	−15.9124	−	7.26694i	−0.823912	−	0.376268i	−0.782328	+	0.622867i	$0.785968\pi$
$374$	−2.18237	+	15.1654i	−0.112848	+	0.784185i
$375$	7.96730	+	2.33941i	0.411429	+	0.120807i
$376$	−1.63456	+	5.55918i	−0.0842958	+	0.286693i
$377$	−1.53519	−	3.36160i	−0.0790663	−	0.173131i
$378$	−2.60652		0.000321351i	−0.134065		1.65285e-5i
$379$	3.17370	+	2.75002i	0.163022	+	0.141259i	0.732552	−	0.680711i	$-0.238329\pi$
$379$	3.17370	+	2.75002i	0.163022	+	0.141259i	−0.569530	+	0.821971i	$0.692875\pi$
$380$	9.31940	−	2.73393i	0.478075	−	0.140248i
$381$	−1.85685	−	6.32385i	−0.0951293	−	0.323981i
$382$	34.1724	−	4.90895i	1.74841	−	0.251164i
$383$	−4.02529	+	2.58690i	−0.205683	+	0.132184i	−0.639427	−	0.768852i	$-0.720828\pi$
$383$	−4.02529	+	2.58690i	−0.205683	+	0.132184i	0.433745	+	0.901036i	$0.357192\pi$
$384$	−7.41628	+	8.54393i	−0.378460	+	0.436006i
$385$	3.32432	+	23.1212i	0.169423	+	1.17836i
$386$	1.31679	+	1.14129i	0.0670230	+	0.0580903i
$387$	0.858942	+	0.123497i	0.0436625	+	0.00627772i
$388$	−9.88600	−	21.6614i	−0.501885	−	1.09969i
$389$	3.82435	−	3.31382i	0.193902	−	0.168017i	−0.552499	−	0.833514i	$-0.686326\pi$
$389$	3.82435	−	3.31382i	0.193902	−	0.168017i	0.746401	+	0.665497i	$0.231780\pi$
$390$	−9.24931	−	2.71708i	−0.468357	−	0.137585i
$391$	−6.67070	−	8.37463i	−0.337352	−	0.423523i
$392$	7.70426	−	6.67079i	0.389124	−	0.336926i
$393$	−6.63074	−	7.65229i	−0.334477	−	0.386007i
$394$	2.73911	+	3.16189i	0.137994	+	0.159294i
$395$	25.8154	+	3.71170i	1.29891	+	0.186756i
$396$	−5.24532	−	8.16631i	−0.263587	−	0.410373i
$397$	−5.99768	+	0.862337i	−0.301015	+	0.0432794i	−0.291168	−	0.956672i	$-0.594044\pi$
$397$	−5.99768	+	0.862337i	−0.301015	+	0.0432794i	−0.00984753	+	0.999952i	$0.503135\pi$
$398$	−6.60536	+	10.2754i	−0.331097	+	0.515057i
$399$	−2.88303	+	1.85281i	−0.144332	+	0.0927567i
$400$	4.77135	−	5.50095i	0.238568	−	0.275048i
$401$	−26.5150	+	7.78550i	−1.32409	+	0.388789i	−0.865969	−	0.500098i	$-0.833297\pi$
$401$	−26.5150	+	7.78550i	−1.32409	+	0.388789i	−0.458126	+	0.888887i	$0.651479\pi$
$402$	3.60077	+	5.60443i	0.179590	+	0.279523i
$403$	−1.04519	−	0.905660i	−0.0520645	−	0.0451142i
$404$	7.00079	−	23.8208i	0.348302	−	1.18513i
$405$	−2.37560	+	1.08490i	−0.118044	+	0.0539091i
$406$	−3.54109	+	1.03928i	−0.175741	+	0.0515788i
$407$	−31.1883	−	9.15772i	−1.54595	−	0.453931i
$408$	−4.13685	+	4.77061i	−0.204804	+	0.236180i
$409$	13.7237	−	30.0506i	0.678592	−	1.48591i	−0.185536	−	0.982637i	$-0.559402\pi$
$409$	13.7237	−	30.0506i	0.678592	−	1.48591i	0.864128	−	0.503272i	$-0.167870\pi$
$410$	5.77301	−	12.6370i	0.285109	−	0.624097i
$411$	−4.69010	+	7.29793i	−0.231345	+	0.359980i
$412$	3.38748	+	23.6018i	0.166889	+	1.16278i
$413$			6.29719i			0.309864i
$414$	6.66748	+	1.24289i	0.327689	+	0.0610847i
$415$	−36.8412			−1.80846
$416$	9.67595	−	11.1527i	0.474403	−	0.546808i
$417$	14.6231	+	9.39767i	0.716094	+	0.460206i
$418$	−11.6074	−	5.30264i	−0.567735	−	0.259360i
$419$	−25.0576	−	11.4434i	−1.22414	−	0.559047i	−0.304766	−	0.952427i	$-0.598578\pi$
$419$	−25.0576	−	11.4434i	−1.22414	−	0.559047i	−0.919376	+	0.393381i	$0.871305\pi$
$420$	−4.00128	+	8.75588i	−0.195243	+	0.427243i
$421$	−8.96532	+	30.5331i	−0.436943	+	1.48809i	0.387353	+	0.921932i	$0.373390\pi$
$421$	−8.96532	+	30.5331i	−0.436943	+	1.48809i	−0.824296	+	0.566160i	$0.808429\pi$
$422$	−36.1312	+	10.6042i	−1.75884	+	0.516206i
$423$	−0.851046	−	1.86353i	−0.0413793	−	0.0906080i
$424$	−27.9160	−	17.9551i	−1.35572	−	0.871979i
$425$	2.66149	−	3.07152i	0.129101	−	0.148991i
$426$	13.9392	−	8.95577i	0.675357	−	0.433908i
$427$	1.22288	+	4.16474i	0.0591792	+	0.201546i
$428$	−31.9101	−	4.59601i	−1.54243	−	0.222156i
$429$	6.84810	+	10.6558i	0.330629	+	0.514469i
$430$	1.73309	−	2.69601i	0.0835771	−	0.130013i
$431$	−3.79483	−	26.3936i	−0.182790	−	1.27134i	−0.850126	−	0.526579i	$-0.823475\pi$
$431$	−3.79483	−	26.3936i	−0.182790	−	1.27134i	0.667336	−	0.744757i	$-0.267435\pi$
$432$	0.00197260	−	4.00000i	9.49069e−5	−	0.192450i
$433$	1.61112	−	11.2056i	0.0774255	−	0.538506i	−0.913784	−	0.406201i	$-0.866853\pi$
$433$	1.61112	−	11.2056i	0.0774255	−	0.538506i	0.991209	−	0.132305i	$-0.0422377\pi$
$434$	−1.04385	+	0.904280i	−0.0501066	+	0.0434068i
$435$	−2.79450	+	2.42145i	−0.133986	+	0.116100i
$436$	5.25456	−	8.17183i	0.251648	−	0.391359i
$437$	8.25789	−	3.36578i	0.395028	−	0.161007i
$438$	−9.39340	−	2.75941i	−0.448834	−	0.131850i
$439$	−2.24901	−	2.59550i	−0.107340	−	0.123876i	0.699537	−	0.714596i	$-0.253389\pi$
$439$	−2.24901	−	2.59550i	−0.107340	−	0.123876i	−0.806877	+	0.590719i	$0.798844\pi$
$440$	−35.4840	+	5.08843i	−1.69163	+	0.242582i
$441$	−0.512766	+	3.56636i	−0.0244174	+	0.169827i
$442$	5.39730	−	6.22727i	0.256724	−	0.296201i
$443$	7.73978	−	1.11281i	0.367728	−	0.0528713i	0.0440259	−	0.999030i	$-0.485982\pi$
$443$	7.73978	−	1.11281i	0.367728	−	0.0528713i	0.323702	+	0.946159i	$0.395072\pi$
$444$	−8.77012	−	10.1263i	−0.416211	−	0.480573i
$445$	−11.1489	−	17.3481i	−0.528509	−	0.822377i
$446$	−4.24658	+	0.610032i	−0.201082	+	0.0288859i
$447$	−11.2750	+	3.31065i	−0.533291	+	0.156588i
$448$	−9.64747	−	11.1504i	−0.455800	−	0.526808i
$449$	16.4297	−	18.9608i	0.775363	−	0.894817i	−0.221402	−	0.975183i	$-0.571063\pi$
$449$	16.4297	−	18.9608i	0.775363	−	0.894817i	0.996765	+	0.0803657i	$0.0256088\pi$
$450$	−0.000317410		2.57455i	−1.49628e−5		0.121365i
$451$	−16.6053	+	7.58338i	−0.781912	+	0.357087i
$452$	−35.6902	−	0.00880032i	−1.67873	−	0.000413932i
$453$	−2.69670	+	9.18412i	−0.126702	+	0.431508i
$454$	2.18357	−	15.1738i	0.102480	−	0.712143i
$455$	5.21910	−	11.4282i	0.244675	−	0.535764i
$456$	−2.84172	−	4.42540i	−0.133076	−	0.207238i
$457$	6.94514	+	4.46337i	0.324880	+	0.208788i	0.692906	−	0.721028i	$-0.256330\pi$
$457$	6.94514	+	4.46337i	0.324880	+	0.208788i	−0.368026	+	0.929815i	$0.619966\pi$
$458$	9.37555	+	20.5363i	0.438091	+	0.959598i
$459$		−	2.23249i		−	0.104204i
$460$	14.4079	−	20.4914i	0.671773	−	0.955415i
$461$		−	5.22218i		−	0.243221i	−0.992578	−	0.121611i	$-0.961194\pi$
$461$		−	5.22218i		−	0.243221i	0.992578	−	0.121611i	$-0.0388059\pi$
$462$	11.5067	−	5.25322i	0.535340	−	0.244402i
$463$	1.83891	+	1.18180i	0.0854615	+	0.0549228i	0.582674	−	0.812706i	$-0.302007\pi$
$463$	1.83891	+	1.18180i	0.0854615	+	0.0549228i	−0.497212	+	0.867629i	$0.665643\pi$
$464$	−1.59289	−	5.43480i	−0.0739481	−	0.252304i
$465$	−0.574837	+	1.25872i	−0.0266574	+	0.0583717i
$466$	36.6189	+	5.26961i	1.69634	+	0.244110i
$467$	−4.80858	+	16.3765i	−0.222515	+	0.757815i	0.770250	+	0.637742i	$0.220131\pi$
$467$	−4.80858	+	16.3765i	−0.222515	+	0.757815i	−0.992765	+	0.120073i	$0.961687\pi$
$468$	−0.00128718	+	5.22025i	−5.95001e−5	+	0.241306i
$469$	−7.89707	+	3.60647i	−0.364653	+	0.166531i
$470$	−7.56647		0.000932853i	−0.349015		4.30293e-5i
$471$	14.2601	−	16.4570i	0.657071	−	0.758300i
$472$	−9.66376	−	0.00357427i	−0.444811	−	0.000164519i
$473$	−4.04063	+	1.18644i	−0.185788	+	0.0545524i
$474$	−2.00820	−	13.9796i	−0.0922398	−	0.642104i
$475$	1.83009	+	2.84767i	0.0839702	+	0.130660i
$476$	−5.38754	−	6.22066i	−0.246938	−	0.285123i
$477$	11.6156	−	1.67007i	0.531842	−	0.0764674i
$478$	−21.6001	−	18.7212i	−0.987964	−	0.856289i
$479$	1.52925	−	10.6361i	0.0698730	−	0.485977i	−0.924596	−	0.380949i	$-0.875597\pi$
$479$	1.52925	−	10.6361i	0.0698730	−	0.485977i	0.994469	−	0.105029i	$-0.0334935\pi$
$480$	−13.4346	−	6.14540i	−0.613204	−	0.280498i
$481$	11.4488	+	13.2126i	0.522020	+	0.602444i
$482$	5.85431	−	19.9289i	0.266657	−	0.907735i
$483$	−2.83892	+	8.37082i	−0.129175	+	0.380886i
$484$	21.1130	+	13.5758i	0.959681	+	0.617084i
$485$	23.4979	−	20.3610i	1.06698	−	0.924546i
$486$	0.925981	+	1.06891i	0.0420034	+	0.0484865i
$487$	2.69121	−	18.7178i	0.121951	−	0.848185i	−0.833392	−	0.552683i	$-0.813604\pi$
$487$	2.69121	−	18.7178i	0.121951	−	0.848185i	0.955342	−	0.295502i	$-0.0954869\pi$
$488$	−6.39196	+	1.87428i	−0.289351	+	0.0848448i
$489$	1.20940	+	8.41156i	0.0546910	+	0.380384i
$490$	11.1940	+	7.19587i	0.505692	+	0.325076i
$491$	−10.9268	−	17.0024i	−0.493119	−	0.767308i	0.502117	−	0.864799i	$-0.332555\pi$
$491$	−10.9268	−	17.0024i	−0.493119	−	0.767308i	−0.995236	+	0.0974913i	$0.968918\pi$
$492$	−7.44649	−	1.07252i	−0.335714	−	0.0483529i
$493$	−0.890525	−	3.03285i	−0.0401072	−	0.136593i
$494$	3.71004	+	5.77450i	0.166923	+	0.259807i
$495$	8.29959	−	9.57824i	0.373039	−	0.430510i
$496$	−1.38713	−	1.60243i	−0.0622840	−	0.0719512i
$497$	8.96994	+	19.6414i	0.402357	+	0.881039i
$498$	5.61819	+	19.1425i	0.251757	+	0.857796i
$499$	−8.56623	+	29.1739i	−0.383477	+	1.30600i	0.511266	+	0.859422i	$0.329177\pi$
$499$	−8.56623	+	29.1739i	−0.383477	+	1.30600i	−0.894743	+	0.446581i	$0.852642\pi$
$500$	−15.1048	−	6.90265i	−0.675509	−	0.308696i
$501$	−12.5135	−	5.71471i	−0.559061	−	0.255314i
$502$	4.07107	−	8.91149i	0.181701	−	0.397739i
$503$	26.9415	+	17.3142i	1.20126	+	0.772003i	0.979174	−	0.203024i	$-0.0650769\pi$
$503$	26.9415	+	17.3142i	1.20126	+	0.772003i	0.222087	+	0.975027i	$0.428713\pi$
$504$	5.15970	+	0.743800i	0.229831	+	0.0331315i
$505$	32.4207			1.44270
$506$	−31.9381	+	7.95484i	−1.41982	+	0.353636i
$507$			6.18726i			0.274786i
$508$	1.87273	+	13.0479i	0.0830888	+	0.578909i
$509$	−11.8980	+	18.5136i	−0.527368	+	0.820601i	−0.998096	−	0.0616775i	$-0.980355\pi$
$509$	−11.8980	+	18.5136i	−0.527368	+	0.820601i	0.470728	+	0.882278i	$0.343991\pi$
$510$	−7.49987	−	3.42619i	−0.332100	−	0.151714i
$511$	5.30041	−	11.6063i	0.234476	−	0.513432i
$512$	17.1171	−	14.7988i	0.756476	−	0.654022i
$513$	1.78410	+	0.523859i	0.0787699	+	0.0231289i
$514$	−8.00483	−	27.2744i	−0.353078	−	1.20302i
$515$	−28.3215	+	12.9340i	−1.24799	+	0.569939i
$516$	−1.66513	−	0.489371i	−0.0733031	−	0.0215434i
$517$	7.51362	+	6.51059i	0.330449	+	0.286335i
$518$	14.6883	−	9.43704i	0.645367	−	0.414640i
$519$	12.9281	−	3.79603i	0.567480	−	0.166627i
$520$	17.5350	+	8.01581i	0.768961	+	0.351516i
$521$	12.3936	−	7.96489i	0.542974	−	0.348948i	−0.240227	−	0.970717i	$-0.577222\pi$
$521$	12.3936	−	7.96489i	0.542974	−	0.348948i	0.783201	+	0.621769i	$0.213586\pi$
$522$	1.68433	+	1.08274i	0.0737210	+	0.0473905i
$523$	22.6053	−	3.25016i	0.988463	−	0.142119i	0.370927	−	0.928662i	$-0.379040\pi$
$523$	22.6053	−	3.25016i	0.988463	−	0.142119i	0.617536	+	0.786543i	$0.288131\pi$
$524$	10.9442	+	17.0388i	0.478101	+	0.744343i
$525$	−3.32115	−	0.477509i	−0.144947	−	0.0208402i
$526$	10.3864	−	8.99760i	0.452867	−	0.392314i
$527$	−0.774630	−	0.893971i	−0.0337434	−	0.0389420i
$528$	8.05514	+	17.6613i	0.350555	+	0.768611i
$529$	11.2510	−	20.0603i	0.489175	−	0.872185i
$530$	12.2159	−	41.5847i	0.530626	−	1.80632i
$531$	2.58214	−	2.23743i	0.112055	−	0.0970964i
$532$	6.23544	−	2.84577i	0.270341	−	0.123380i
$533$	9.71848	+	1.39731i	0.420954	+	0.0605240i
$534$	−7.31378	+	8.43846i	−0.316498	+	0.365168i
$535$	−5.99120	−	41.6697i	−0.259022	−	1.80154i
$536$	−5.53006	−	12.1210i	−0.238862	−	0.523548i
$537$	21.7871	−	14.0017i	0.940182	−	0.604218i
$538$	4.73833	+	32.9847i	0.204284	+	1.42207i
$539$	−4.92613	−	16.7769i	−0.212184	−	0.722631i
$540$	5.01200	−	1.47031i	0.215682	−	0.0632722i
$541$	31.9033	+	27.6444i	1.37163	+	1.18853i	0.960942	+	0.276750i	$0.0892572\pi$
$541$	31.9033	+	27.6444i	1.37163	+	1.18853i	0.410689	+	0.911775i	$0.365288\pi$
$542$	−0.00453737	+	36.8031i	−0.000194897	+	1.58083i
$543$	−0.639389	−	1.40007i	−0.0274388	−	0.0600826i
$544$	9.54937	−	8.26428i	0.409426	−	0.354328i
$545$	12.1725	+	3.57417i	0.521413	+	0.153101i
$546$	−6.73396	−	0.969045i	−0.288187	−	0.0414713i
$547$	−18.4816	−	8.44026i	−0.790216	−	0.360880i	−0.0209275	−	0.999781i	$-0.506662\pi$
$547$	−18.4816	−	8.44026i	−0.790216	−	0.360880i	−0.769289	+	0.638901i	$0.779389\pi$
$548$	11.3652	−	13.1096i	0.485495	−	0.560013i
$549$	1.27324	−	1.98120i	0.0543404	−	0.0845554i
$550$	−5.18879	−	11.3656i	−0.221251	−	0.484629i
$551$	2.63267			0.112155
$552$	−12.8444	−	4.36140i	−0.546693	−	0.185634i
$553$	18.4060			0.782704
$554$	−3.17433	−	6.95308i	−0.134864	−	0.295408i
$555$	9.45728	−	14.7158i	0.401439	−	0.624652i
$556$	−26.2680	−	22.7727i	−1.11401	−	0.965776i
$557$	−23.3541	−	10.6655i	−0.989544	−	0.451910i	−0.146183	−	0.989258i	$-0.546699\pi$
$557$	−23.3541	−	10.6655i	−0.989544	−	0.451910i	−0.843361	+	0.537348i	$0.819426\pi$
$558$	0.741685	+	0.106732i	0.0313980	+	0.00451831i
$559$	2.17325	+	0.638124i	0.0919187	+	0.0269898i
$560$	10.4173	−	16.1921i	0.440211	−	0.684239i
$561$	4.50062	+	9.85499i	0.190016	+	0.416078i
$562$	0.000183137	−	1.48544i	7.72515e−6	−	0.0626596i
$563$	32.1348	+	27.8450i	1.35432	+	1.17353i	0.967938	+	0.251188i	$0.0808213\pi$
$563$	32.1348	+	27.8450i	1.35432	+	1.17353i	0.386383	+	0.922338i	$0.373724\pi$
$564$	1.15338	+	3.93165i	0.0485662	+	0.165552i
$565$	−13.1300	−	44.7165i	−0.552382	−	1.88124i
$566$	5.23542	+	36.4451i	0.220061	+	1.53190i
$567$	−1.55050	+	0.996447i	−0.0651150	+	0.0418468i
$568$	−30.1471	+	13.7543i	−1.26495	+	0.577116i
$569$	2.99106	+	20.8033i	0.125392	+	0.872120i	0.951289	+	0.308300i	$0.0997599\pi$
$569$	2.99106	+	20.8033i	0.125392	+	0.872120i	−0.825897	+	0.563820i	$0.809331\pi$
$570$	4.49791	−	5.18957i	0.188397	−	0.217367i
$571$	−8.17895	−	1.17596i	−0.342278	−	0.0492122i	−0.0309677	−	0.999520i	$-0.509859\pi$
$571$	−8.17895	−	1.17596i	−0.342278	−	0.0492122i	−0.311311	+	0.950308i	$0.600768\pi$
$572$	−10.5181	−	23.0465i	−0.439785	−	0.963624i
$573$	18.4491	−	15.9862i	0.770720	−	0.667833i
$574$	2.76350	−	9.40734i	0.115346	−	0.392655i
$575$	8.26815	+	2.80410i	0.344806	+	0.116939i
$576$	−1.14438	+	7.91773i	−0.0476823	+	0.329905i
$577$	−18.5159	−	21.3685i	−0.770827	−	0.889582i	0.225584	−	0.974224i	$-0.427571\pi$
$577$	−18.5159	−	21.3685i	−0.770827	−	0.889582i	−0.996411	+	0.0846418i	$0.973025\pi$
$578$	−12.8439	+	11.1266i	−0.534237	+	0.462804i
$579$	1.21963	+	0.175356i	0.0506861	+	0.00728756i
$580$	6.22232	−	3.99667i	0.258368	−	0.165953i
$581$	−25.7353	+	3.70017i	−1.06768	+	0.153509i
$582$	−14.1628	−	9.10437i	−0.587069	−	0.377388i
$583$	−47.9085	+	30.7889i	−1.98417	+	1.27515i
$584$	17.8082	+	8.14068i	0.736907	+	0.336864i
$585$	−6.54049	+	1.92046i	−0.270416	+	0.0794013i
$586$	−40.5264	+	26.0377i	−1.67413	+	1.07561i
$587$	−26.0822	−	22.6004i	−1.07653	−	0.932817i	−0.0785840	−	0.996907i	$-0.525040\pi$
$587$	−26.0822	−	22.6004i	−1.07653	−	0.932817i	−0.997944	+	0.0640906i	$0.979585\pi$
$588$	2.03189	−	6.91368i	0.0837938	−	0.285115i
$589$	0.896187	−	0.409275i	0.0369267	−	0.0168639i
$590$	−3.55368	−	12.1082i	−0.146303	−	0.498489i
$591$	2.83824	+	0.833382i	0.116750	+	0.0342807i
$592$	14.4739	+	22.5463i	0.594874	+	0.926646i
$593$	−13.5332	+	29.6335i	−0.555740	+	1.21690i	0.398309	+	0.917251i	$0.369597\pi$
$593$	−13.5332	+	29.6335i	−0.555740	+	1.21690i	−0.954049	+	0.299650i	$0.903130\pi$
$594$	−6.24247	−	2.85177i	−0.256132	−	0.117010i
$595$	5.80967	−	9.04003i	0.238173	−	0.370605i
$596$	23.2637	−	3.33895i	0.952917	−	0.136769i
$597$			8.63753i			0.353511i
$598$	16.7641	+	5.68777i	0.685536	+	0.232590i
$599$	26.5132			1.08330			0.541649	−	0.840604i	$-0.317800\pi$
$599$	26.5132			1.08330			0.541649	+	0.840604i	$0.317800\pi$
$600$	0.734677	−	5.09641i	0.0299931	−	0.208060i
$601$	−9.52709	−	6.12269i	−0.388618	−	0.249750i	0.331713	−	0.943380i	$-0.392374\pi$
$601$	−9.52709	−	6.12269i	−0.388618	−	0.249750i	−0.720331	+	0.693631i	$0.756010\pi$
$602$	0.939868	−	2.05735i	0.0383062	−	0.0838514i
$603$	4.28470	+	1.95676i	0.174487	+	0.0796853i
$604$	7.95687	−	17.4118i	0.323761	−	0.708474i
$605$	−9.23434	+	31.4493i	−0.375429	+	1.27860i
$606$	−4.94408	−	16.8457i	−0.200839	−	0.684308i
$607$	10.8811	+	23.8262i	0.441649	+	0.967076i	0.991293	+	0.131677i	$0.0420361\pi$
$607$	10.8811	+	23.8262i	0.441649	+	0.967076i	−0.549644	+	0.835399i	$0.685237\pi$
$608$	4.36363	+	9.57062i	0.176969	+	0.388140i
$609$	−1.70889	+	1.97216i	−0.0692476	+	0.0799160i
$610$	−4.70163	−	7.31786i	−0.190363	−	0.296292i
$611$	−1.50650	−	5.13067i	−0.0609465	−	0.207565i
$612$	−0.636524	+	4.41938i	−0.0257299	+	0.178643i
$613$	12.5472	+	19.5239i	0.506778	+	0.788561i	0.996524	−	0.0833034i	$-0.0265471\pi$
$613$	12.5472	+	19.5239i	0.506778	+	0.788561i	−0.489747	+	0.871865i	$0.662911\pi$
$614$	14.8704	+	9.55920i	0.600119	+	0.385778i
$615$	−1.39810	−	9.72399i	−0.0563768	−	0.392109i
$616$	−24.2761	+	7.11836i	−0.978113	+	0.286807i
$617$	−0.588568	+	4.09358i	−0.0236949	+	0.164801i	−0.998233	−	0.0594201i	$-0.981075\pi$
$617$	−0.588568	+	4.09358i	−0.0236949	+	0.164801i	0.974538	+	0.224222i	$0.0719839\pi$
$618$	11.0394	+	12.7433i	0.444069	+	0.512611i
$619$	8.50677	−	7.37116i	0.341916	−	0.296272i	−0.466928	−	0.884295i	$-0.654639\pi$
$619$	8.50677	−	7.37116i	0.341916	−	0.296272i	0.808844	+	0.588024i	$0.200094\pi$
$620$	1.49682	−	2.32783i	0.0601136	−	0.0934878i
$621$	4.44111	−	1.81012i	0.178216	−	0.0726377i
$622$	5.60379	−	19.0761i	0.224691	−	0.764880i
$623$	−9.53039	−	10.9987i	−0.381827	−	0.440652i
$624$	1.49093	−	10.3335i	0.0596851	−	0.413671i
$625$	4.38162	−	30.4749i	0.175265	−	1.21899i
$626$	−25.2568	−	21.8906i	−1.00947	−	0.874925i
$627$	−8.93171	+	1.28419i	−0.356698	+	0.0512854i
$628$	−32.9211	+	28.5121i	−1.31370	+	1.13776i
$629$	8.08442	+	12.5796i	0.322347	+	0.501582i
$630$	0.967933	+	6.73802i	0.0385634	+	0.268449i
$631$	−29.7434	+	8.73345i	−1.18407	+	0.347673i	−0.813740	−	0.581228i	$-0.802572\pi$
$631$	−29.7434	+	8.73345i	−1.18407	+	0.347673i	−0.370326	+	0.928902i	$0.620754\pi$
$632$	−0.0104472	+	28.2462i	−0.000415568	+	1.12357i
$633$	−17.4365	+	20.1228i	−0.693038	+	0.799808i
$634$	−20.4095	−	0.00251624i	−0.810564	−	9.99325e-5i
$635$	−15.6572	+	7.15038i	−0.621335	+	0.283754i
$636$	−23.4701	−	0.00578715i	−0.930650	−	0.000229475i
$637$	−2.64952	+	9.02343i	−0.104978	+	0.357521i
$638$	−9.61797	−	1.38407i	−0.380779	−	0.0547957i
$639$	4.86681	−	10.6568i	0.192528	−	0.421578i
$640$	24.8427	+	15.9957i	0.981993	+	0.632287i
$641$	38.8596	+	24.9736i	1.53486	+	0.986397i	0.988899	+	0.148588i	$0.0474729\pi$
$641$	38.8596	+	24.9736i	1.53486	+	0.986397i	0.545964	+	0.837809i	$0.316163\pi$
$642$	−20.7378	+	9.46752i	−0.818454	+	0.373653i
$643$			28.9678i			1.14238i	0.820818	+	0.571189i	$0.193518\pi$
$643$			28.9678i			1.14238i	−0.820818	+	0.571189i	$0.806482\pi$
$644$	8.00652	−	15.7612i	0.315501	−	0.621079i
$645$		−	2.26629i		−	0.0892349i
$646$	2.43808	+	5.34039i	0.0959249	+	0.210115i
$647$	23.3498	+	15.0060i	0.917976	+	0.589948i	0.912070	−	0.410035i	$-0.134484\pi$
$647$	23.3498	+	15.0060i	0.917976	+	0.589948i	0.00590657	+	0.999983i	$0.498120\pi$
$648$	−1.52828	−	2.37999i	−0.0600366	−	0.0934948i
$649$	−6.88785	+	15.0823i	−0.270372	+	0.592032i
$650$	−0.957159	+	6.65137i	−0.0375429	+	0.260888i
$651$	−0.275130	+	0.937006i	−0.0107832	+	0.0367242i
$652$	0.00419082	−	16.9961i	0.000164125	−	0.665619i
$653$	−19.8169	+	9.05009i	−0.775497	+	0.354157i	−0.763531	−	0.645771i	$-0.776536\pi$
$653$	−19.8169	+	9.05009i	−0.775497	+	0.354157i	−0.0119655	+	0.999928i	$0.503809\pi$
$654$	0.000846965	−	6.86983i	3.31190e−5	−	0.268632i
$655$	−17.3169	+	19.9847i	−0.676627	+	0.780869i
$656$	14.4351	+	4.24626i	0.563595	+	0.165788i
$657$	−6.64238	+	1.95038i	−0.259144	+	0.0760915i
$658$	−5.28562	+	0.759292i	−0.206055	+	0.0296003i
$659$	10.9176	+	16.9882i	0.425291	+	0.661766i	0.986095	−	0.166183i	$-0.0531442\pi$
$659$	10.9176	+	16.9882i	0.425291	+	0.661766i	−0.560804	+	0.827949i	$0.689508\pi$
$660$	−19.1606	+	16.5945i	−0.745824	+	0.645938i
$661$	−40.4903	+	5.82162i	−1.57489	+	0.226435i	−0.873673	−	0.486514i	$-0.838268\pi$
$661$	−40.4903	+	5.82162i	−1.57489	+	0.226435i	−0.701216	+	0.712949i	$0.747359\pi$
$662$	30.5055	−	35.1964i	1.18563	−	1.36795i
$663$	0.829280	−	5.76777i	0.0322066	−	0.224002i
$664$	−5.66373	−	39.4958i	−0.219796	−	1.53274i
$665$	5.86110	+	6.76407i	0.227284	+	0.262299i
$666$	−9.08848	−	2.66984i	−0.352171	−	0.103454i
$667$	5.31122	−	4.23058i	0.205651	−	0.163809i
$668$	23.1420	+	14.8805i	0.895389	+	0.575744i
$669$	−2.29265	+	1.98659i	−0.0886390	+	0.0768062i
$670$	13.1493	−	11.3911i	0.508000	−	0.440075i
$671$	−1.62649	+	11.3125i	−0.0627899	+	0.436713i
$672$	−10.0019	−	2.94353i	−0.385832	−	0.113549i
$673$	−3.05352	−	21.2377i	−0.117704	−	0.818653i	−0.960073	−	0.279750i	$-0.909748\pi$
$673$	−3.05352	−	21.2377i	−0.117704	−	0.818653i	0.842368	−	0.538902i	$-0.181161\pi$
$674$	10.2609	−	15.9619i	0.395234	−	0.614829i
$675$	0.984225	+	1.53148i	0.0378828	+	0.0589469i
$676$	1.76410	−	12.2481i	0.0678499	−	0.471082i
$677$	0.992982	+	3.38178i	0.0381634	+	0.129973i	0.976371	−	0.216099i	$-0.0693335\pi$
$677$	0.992982	+	3.38178i	0.0381634	+	0.129973i	−0.938208	+	0.346072i	$0.887515\pi$
$678$	−21.2322	+	13.6414i	−0.815418	+	0.523895i
$679$	14.3694	−	16.5831i	0.551445	−	0.636402i
$680$	13.8697	+	8.92075i	0.531878	+	0.342095i
$681$	−4.50311	−	9.86044i	−0.172560	−	0.377853i
$682$	−3.48922	+	1.02406i	−0.133609	+	0.0392133i
$683$	−3.65308	+	12.4412i	−0.139781	+	0.476051i	−0.999391	−	0.0349004i	$-0.988889\pi$
$683$	−3.65308	+	12.4412i	−0.139781	+	0.476051i	0.859610	+	0.510951i	$0.170707\pi$
$684$	−3.38239	−	1.54570i	−0.129329	−	0.0591011i
$685$	20.6085	+	9.41158i	0.787410	+	0.359598i
$686$	25.1381	+	11.4839i	0.959776	+	0.438458i
$687$	13.4290	+	8.63030i	0.512349	+	0.329266i
$688$	3.15671	+	1.44350i	0.120349	+	0.0550331i
$689$	30.6299			1.16691
$690$	0.734794	−	17.6975i	0.0279731	−	0.673733i
$691$			31.3390i			1.19219i	0.802914	+	0.596095i	$0.203282\pi$
$691$			31.3390i			1.19219i	−0.802914	+	0.596095i	$0.796718\pi$
$692$	−26.6744	+	3.82849i	−1.01401	+	0.145537i
$693$	4.83564	−	7.52441i	0.183691	−	0.285829i
$694$	−7.18922	+	15.7371i	−0.272899	+	0.597370i
$695$	18.8582	−	41.2938i	0.715333	−	1.56636i
$696$	−3.02554	−	2.62360i	−0.114683	−	0.0994474i
$697$	8.05772	+	2.36596i	0.305208	+	0.0896172i
$698$	−2.54474	+	0.746861i	−0.0963197	+	0.0282691i
$699$	23.7961	−	10.8673i	0.900053	−	0.411040i
$700$	6.43830	+	1.89218i	0.243345	+	0.0715177i
$701$	7.65820	+	6.63587i	0.289246	+	0.250633i	0.787382	−	0.616466i	$-0.211436\pi$
$701$	7.65820	+	6.63587i	0.289246	+	0.250633i	−0.498135	+	0.867099i	$0.665982\pi$
$702$	1.99527	+	3.10554i	0.0753066	+	0.117211i
$703$	−11.9500	+	3.50885i	−0.450704	+	0.132339i
$704$	−10.9102	−	37.2586i	−0.411193	−	1.40424i
$705$	−4.50096	+	2.89259i	−0.169516	+	0.108941i
$706$	−28.3276	+	44.0667i	−1.06612	+	1.65847i
$707$	22.6474	−	3.25620i	0.851742	−	0.122462i
$708$	−5.74946	+	3.69295i	−0.216078	+	0.138790i
$709$	−19.7779	−	2.84364i	−0.742776	−	0.106795i	−0.239471	−	0.970904i	$-0.576974\pi$
$709$	−19.7779	−	2.84364i	−0.742776	−	0.106795i	−0.503306	+	0.864109i	$0.667883\pi$
$710$	−28.3316	−	32.7046i	−1.06327	−	1.22738i
$711$	−6.53979	−	7.54732i	−0.245261	−	0.283047i
$712$	16.8841	−	14.6192i	0.632759	−	0.547879i
$713$	1.15031	−	2.26581i	0.0430793	−	0.0848554i
$714$	−5.58312	−	1.64010i	−0.208943	−	0.0613791i
$715$	25.0004	−	21.6629i	0.934961	−	0.810148i
$716$	−47.1213	+	21.5055i	−1.76100	+	0.803699i
$717$	−20.0062	−	2.87646i	−0.747147	−	0.107424i
$718$	3.06409	+	2.65571i	0.114351	+	0.0991101i
$719$	5.93536	+	41.2813i	0.221352	+	1.53953i	0.732934	+	0.680300i	$0.238150\pi$
$719$	5.93536	+	41.2813i	0.221352	+	1.53953i	−0.511582	+	0.859234i	$0.670941\pi$
$720$	−10.3408	+	1.48158i	−0.385380	+	0.0552153i
$721$	−18.4848	+	11.8795i	−0.688410	+	0.442414i
$722$	21.7572	−	3.12547i	0.809717	−	0.116318i
$723$	−4.13789	−	14.0924i	−0.153890	−	0.524100i
$724$	0.866534	+	2.95384i	0.0322045	+	0.109778i
$725$	1.94797	+	1.68793i	0.0723458	+	0.0626880i
$726$	17.7491	+	0.00218825i	0.658731	+	8.12134e-5i
$727$	−1.62780	−	3.56439i	−0.0603718	−	0.132196i	0.877041	−	0.480415i	$-0.159514\pi$
$727$	−1.62780	−	3.56439i	−0.0603718	−	0.132196i	−0.937413	+	0.348219i	$0.886787\pi$
$728$	13.0541	+	3.83827i	0.483816	+	0.142256i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	−3.64189	+	25.3077i	−0.134792	+	0.936682i
$731$	1.76223	+	0.804784i	0.0651785	+	0.0297660i
$732$	−3.08534	+	3.55890i	−0.114037	+	0.131541i
$733$	5.13833	−	7.99540i	0.189789	−	0.295317i	−0.733299	−	0.679906i	$-0.762021\pi$
$733$	5.13833	−	7.99540i	0.189789	−	0.295317i	0.923088	+	0.384589i	$0.125657\pi$
$734$	−27.6488	+	12.6227i	−1.02054	+	0.465911i
$735$	9.40971			0.347082
$736$	24.1829	+	12.2959i	0.891393	+	0.453232i
$737$	−22.8589			−0.842018
$738$	−4.83933	+	2.20933i	−0.178138	+	0.0813265i
$739$	10.8062	−	16.8148i	0.397512	−	0.618541i	−0.583586	−	0.812051i	$-0.698351\pi$
$739$	10.8062	−	16.8148i	0.397512	−	0.618541i	0.981098	+	0.193510i	$0.0619873\pi$
$740$	−22.9171	+	26.4346i	−0.842450	+	0.971755i
$741$	4.41473	+	2.01614i	0.162179	+	0.0740647i
$742$	4.35680	−	30.2757i	0.159943	−	1.11146i
$743$	−10.2560	−	3.01142i	−0.376255	−	0.110478i	0.0881368	−	0.996108i	$-0.471909\pi$
$743$	−10.2560	−	3.01142i	−0.376255	−	0.110478i	−0.464391	+	0.885630i	$0.653727\pi$
$744$	−1.43779	−	0.422751i	−0.0527119	−	0.0154988i
$745$	12.7487	+	27.9157i	0.467076	+	1.02275i
$746$	24.7391	+	0.00305003i	0.905764	+	0.000111669i
$747$	10.6612	+	9.23794i	0.390071	+	0.337999i
$748$	−6.09948	−	20.7919i	−0.223019	−	0.760226i
$749$	−8.37026	−	28.5065i	−0.305843	−	1.04160i
$750$	−11.6238	+	1.66979i	−0.424442	+	0.0609721i
$751$	−10.0792	+	6.47750i	−0.367795	+	0.236367i	−0.711463	−	0.702724i	$-0.751967\pi$
$751$	−10.0792	+	6.47750i	−0.367795	+	0.236367i	0.343668	+	0.939091i	$0.388331\pi$
$752$	−1.16222	−	8.11183i	−0.0423819	−	0.295808i
$753$	−0.985926	−	6.85727i	−0.0359291	−	0.249893i
$754$	3.94936	+	3.42299i	0.143827	+	0.124658i
$755$	24.7434	+	3.55757i	0.900506	+	0.129473i
$756$	3.35344	−	1.53046i	0.121963	−	0.0556624i
$757$	−11.6174	+	10.0665i	−0.422241	+	0.365874i	−0.839910	−	0.542725i	$-0.817392\pi$
$757$	−11.6174	+	10.0665i	−0.422241	+	0.365874i	0.417670	+	0.908599i	$0.362847\pi$
$758$	−5.69808	−	1.67387i	−0.206964	−	0.0607977i
$759$	−15.9554	+	16.9436i	−0.579146	+	0.615014i
$760$	−10.3836	+	8.99070i	−0.376652	+	0.326127i
$761$	27.4361	+	31.6629i	0.994556	+	1.14778i	0.989018	+	0.147795i	$0.0472175\pi$
$761$	27.4361	+	31.6629i	0.994556	+	1.14778i	0.00553843	+	0.999985i	$0.498237\pi$
$762$	6.10298	+	7.04497i	0.221088	+	0.255212i
$763$	8.86203	+	1.27417i	0.320827	+	0.0461280i
$764$	−41.0792	+	26.3857i	−1.48619	+	0.954601i
$765$	−5.77105	+	0.829751i	−0.208653	+	0.0299997i
$766$	3.65912	−	5.69217i	0.132210	−	0.205666i
$767$	7.50221	−	4.82138i	0.270889	−	0.174090i
$768$	4.52286	−	15.3474i	0.163205	−	0.553803i
$769$	−14.3676	+	4.21871i	−0.518110	+	0.152131i	−0.530325	−	0.847795i	$-0.677930\pi$
$769$	−14.3676	+	4.21871i	−0.518110	+	0.152131i	0.0122150	+	0.999925i	$0.496112\pi$
$770$	−17.8564	−	27.7926i	−0.643499	−	1.00158i
$771$	−15.1901	−	13.1623i	−0.547058	−	0.474028i
$772$	−2.36435	−	0.694869i	−0.0850948	−	0.0250089i
$773$	19.9535	−	9.11245i	0.717677	−	0.327752i	−0.0228868	−	0.999738i	$-0.507286\pi$
$773$	19.9535	−	9.11245i	0.717677	−	0.327752i	0.740564	+	0.671986i	$0.234558\pi$
$774$	−1.17755	+	0.345602i	−0.0423262	+	0.0124224i
$775$	0.925514	+	0.271755i	0.0332454	+	0.00976174i
$776$	25.4406	+	22.0608i	0.913263	+	0.791938i
$777$	5.12835	−	11.2295i	0.183979	−	0.402857i
$778$	−2.97368	+	6.50932i	−0.106612	+	0.233370i
$779$	−3.78152	+	5.88416i	−0.135487	+	0.210822i
$780$	13.4949	−	1.93688i	0.483196	−	0.0693515i
$781$			56.8542i			2.03440i
$782$	13.5004	+	6.85596i	0.482774	+	0.245169i
$783$	1.41586			0.0505986
$784$	−5.99349	+	13.1068i	−0.214053	+	0.468100i
$785$	−47.8419	−	30.7461i	−1.70755	−	1.09738i
$786$	13.0248	+	5.95015i	0.464578	+	0.212235i
$787$	31.3360	+	14.3107i	1.11701	+	0.510121i	0.886397	−	0.462925i	$-0.153200\pi$
$787$	31.3360	+	14.3107i	1.11701	+	0.510121i	0.230612	+	0.973046i	$0.425927\pi$
$788$	−5.38089	−	2.45897i	−0.191686	−	0.0875972i
$789$	2.73755	−	9.32323i	0.0974592	−	0.331916i
$790$	−35.3912	+	10.3870i	−1.25916	+	0.369554i
$791$	−13.6630	−	29.9178i	−0.485801	−	1.06376i
$792$	11.5443	+	7.42513i	0.410210	+	0.263840i
$793$	4.02541	−	4.64557i	0.142947	−	0.164969i
$794$	7.20946	−	4.63198i	0.255854	−	0.164383i
$795$	−8.63435	−	29.4059i	−0.306229	−	1.04292i
$796$	2.46271	−	17.0986i	0.0872886	−	0.606044i
$797$	−4.07432	−	6.33976i	−0.144320	−	0.224566i	0.761567	−	0.648087i	$-0.224430\pi$
$797$	−4.07432	−	6.33976i	−0.144320	−	0.224566i	−0.905886	+	0.423521i	$0.860794\pi$
$798$	2.62078	−	4.07690i	0.0927744	−	0.144321i
$799$	−0.650896	−	4.52708i	−0.0230270	−	0.160157i
$800$	−2.90742	+	9.87924i	−0.102793	+	0.349284i
$801$	−1.12374	+	7.81580i	−0.0397055	+	0.276158i
$802$	29.5385	−	25.5889i	1.04304	−	0.903575i
$803$	25.3898	−	22.0004i	0.895988	−	0.776378i
$804$	−7.92397	−	5.09519i	−0.279457	−	0.179693i
$805$	22.6939	+	4.22749i	0.799855	+	0.148999i
$806$	1.87654	+	0.551253i	0.0660983	+	0.0194171i
$807$	15.4305	+	17.8078i	0.543181	+	0.626864i
$808$	4.98416	+	34.7568i	0.175342	+	1.22274i
$809$	3.39877	−	23.6390i	0.119495	−	0.831103i	−0.838620	−	0.544717i	$-0.816637\pi$
$809$	3.39877	−	23.6390i	0.119495	−	0.831103i	0.958114	−	0.286386i	$-0.0924538\pi$
$810$	2.41898	−	2.79096i	0.0849945	−	0.0980644i
$811$	5.75532	−	0.827490i	0.202097	−	0.0290571i	−0.0405230	−	0.999179i	$-0.512902\pi$
$811$	5.75532	−	0.827490i	0.202097	−	0.0290571i	0.242620	+	0.970122i	$0.421993\pi$
$812$	3.94516	−	3.41680i	0.138448	−	0.119906i
$813$	14.0695	+	21.8926i	0.493439	+	0.767806i
$814$	45.5019	−	6.53646i	1.59484	−	0.229103i
$815$	21.2946	−	6.25265i	0.745916	−	0.219021i
$816$	2.52009	−	8.56700i	0.0882208	−	0.299905i
$817$	−1.05666	+	1.21945i	−0.0369677	+	0.0426630i
$818$	−0.00576000	+	46.7200i	−0.000201394	+	1.63353i
$819$	−4.37595	+	1.99843i	−0.152908	+	0.0698307i
$820$	−0.00484470	+	19.6480i	−0.000169184	+	0.686137i
$821$	−5.87424	+	20.0058i	−0.205012	+	0.698208i	0.791224	+	0.611527i	$0.209444\pi$
$821$	−5.87424	+	20.0058i	−0.205012	+	0.698208i	−0.996236	+	0.0866814i	$0.972374\pi$
$822$	1.74747	−	12.1433i	0.0609501	−	0.423547i
$823$	−3.25128	+	7.11932i	−0.113333	+	0.248164i	−0.957796	−	0.287450i	$-0.907192\pi$
$823$	−3.25128	+	7.11932i	−0.113333	+	0.248164i	0.844463	+	0.535614i	$0.179920\pi$
$824$	−18.2199	−	28.3738i	−0.634721	−	0.988448i
$825$	−7.43212	−	4.77633i	−0.258753	−	0.166291i
$826$	−3.69851	−	8.10125i	−0.128688	−	0.281878i
$827$		−	15.5514i		−	0.540776i	−0.962751	−	0.270388i	$-0.912848\pi$
$827$		−	15.5514i		−	0.540776i	0.962751	−	0.270388i	$-0.0871520\pi$
$828$	−9.30760	+	2.31703i	−0.323461	+	0.0805223i
$829$		−	28.7722i		−	0.999301i	−0.866227	−	0.499650i	$-0.833462\pi$
$829$		−	28.7722i		−	0.999301i	0.866227	−	0.499650i	$-0.166538\pi$
$830$	47.3957	−	21.6378i	1.64513	−	0.751060i
$831$	−4.54673	−	2.92200i	−0.157724	−	0.101363i
$832$	−5.89767	+	20.0308i	−0.204465	+	0.694443i
$833$	−3.34150	+	7.31686i	−0.115776	+	0.253514i
$834$	−24.3319	−	3.50146i	−0.842544	−	0.121246i
$835$	−10.1218	+	34.4716i	−0.350278	+	1.19294i
$836$	18.0471	+	0.00444997i	0.624172	+	0.000153905i
$837$	0.481971	−	0.220109i	0.0166594	−	0.00760808i
$838$	38.9572	+	0.00480294i	1.34575	+	0.000165915i
$839$	−10.3234	+	11.9139i	−0.356404	+	0.411312i	−0.905432	−	0.424492i	$-0.860453\pi$
$839$	−10.3234	+	11.9139i	−0.356404	+	0.411312i	0.549027	+	0.835804i	$0.314998\pi$
$840$	0.00503545	−	13.6144i	0.000173740	−	0.469741i
$841$	−25.9019	+	7.60547i	−0.893167	+	0.262258i
$842$	−6.39914	−	44.5460i	−0.220529	−	1.53516i
$843$	−0.567871	−	0.883624i	−0.0195585	−	0.0304336i
$844$	40.2541	−	34.8630i	1.38560	−	1.20003i
$845$	15.9942	−	2.29962i	0.550217	−	0.0791093i
$846$	2.18936	+	1.89757i	0.0752718	+	0.0652397i
$847$	−3.29198	+	22.8962i	−0.113114	+	0.786723i
$848$	46.4591	+	6.70320i	1.59541	+	0.230189i
$849$	17.0494	+	19.6760i	0.585133	+	0.675279i
$850$	−1.61998	+	5.51464i	−0.0555649	+	0.189150i
$851$	−18.4698	+	26.2820i	−0.633136	+	0.900936i
$852$	−12.6727	+	19.7083i	−0.434158	+	0.675197i
$853$	21.3236	−	18.4770i	0.730108	−	0.632642i	−0.208343	−	0.978056i	$-0.566807\pi$
$853$	21.3236	−	18.4770i	0.730108	−	0.632642i	0.938450	+	0.345414i	$0.112261\pi$
$854$	−4.01928	−	4.63965i	−0.137537	−	0.158766i
$855$	0.691091	−	4.80664i	0.0236348	−	0.164384i
$856$	43.7512	−	12.8290i	1.49539	−	0.438484i
$857$	−7.12206	−	49.5350i	−0.243285	−	1.69208i	−0.635413	−	0.772172i	$-0.719170\pi$
$857$	−7.12206	−	49.5350i	−0.243285	−	1.69208i	0.392128	−	0.919910i	$-0.371739\pi$
$858$	−15.0685	−	9.68653i	−0.514429	−	0.330693i
$859$	1.73528	+	2.70015i	0.0592070	+	0.0921279i	0.869595	−	0.493766i	$-0.164380\pi$
$859$	1.73528	+	2.70015i	0.0592070	+	0.0921279i	−0.810388	+	0.585894i	$0.800744\pi$
$860$	−0.646158	+	4.48628i	−0.0220338	+	0.152981i
$861$	−1.95327	−	6.65223i	−0.0665673	−	0.226707i
$862$	20.3837	+	31.7262i	0.694271	+	1.08060i
$863$	−0.498304	+	0.575073i	−0.0169625	+	0.0195757i	−0.764167	−	0.645018i	$-0.776850\pi$
$863$	−0.498304	+	0.575073i	−0.0169625	+	0.0195757i	0.747205	+	0.664594i	$0.231395\pi$
$864$	2.34677	+	5.14710i	0.0798387	+	0.175108i
$865$	−14.6178	−	32.0085i	−0.497020	−	1.08832i
$866$	4.50866	+	15.3621i	0.153210	+	0.522025i
$867$	−3.38529	+	11.5292i	−0.114971	+	0.391554i
$868$	0.811797	−	1.77643i	0.0275542	−	0.0602959i
$869$	44.0840	+	20.1325i	1.49545	+	0.682948i
$870$	2.17291	−	4.75645i	0.0736684	−	0.161259i
$871$	10.3429	+	6.64698i	0.350456	+	0.225224i
$872$	−1.96039	+	13.5991i	−0.0663871	+	0.460523i
$873$	−11.9054			−0.402936
$874$	−8.64685	+	9.18010i	−0.292484	+	0.310522i
$875$		−	15.3043i		−	0.517381i
$876$	13.7052	−	1.96706i	0.463054	−	0.0664607i
$877$	−8.45381	+	13.1544i	−0.285465	+	0.444192i	−0.954139	−	0.299363i	$-0.903226\pi$
$877$	−8.45381	+	13.1544i	−0.285465	+	0.444192i	0.668674	+	0.743555i	$0.266862\pi$
$878$	4.41773	+	2.01817i	0.149091	+	0.0681099i
$879$	−14.1496	+	30.9833i	−0.477254	+	1.04504i
$880$	42.6611	−	27.3869i	1.43811	−	0.923212i
$881$	−6.60681	−	1.93993i	−0.222589	−	0.0653580i	0.168536	−	0.985695i	$-0.446096\pi$
$881$	−6.60681	−	1.93993i	−0.222589	−	0.0653580i	−0.391125	+	0.920337i	$0.627914\pi$
$882$	−1.43496	−	4.88924i	−0.0483175	−	0.164629i
$883$	−42.2286	+	19.2851i	−1.42110	+	0.648997i	−0.969918	−	0.243433i	$-0.921726\pi$
$883$	−42.2286	+	19.2851i	−1.42110	+	0.648997i	−0.451187	+	0.892430i	$0.648999\pi$
$884$	−3.28611	+	11.1813i	−0.110524	+	0.376067i
$885$	−6.74352	−	5.84329i	−0.226681	−	0.196420i
$886$	−9.30353	+	5.97740i	−0.312558	+	0.200815i
$887$	−36.7135	+	10.7801i	−1.23272	+	0.361959i	−0.832276	−	0.554362i	$-0.812962\pi$
$887$	−36.7135	+	10.7801i	−1.23272	+	0.361959i	−0.400444	+	0.916321i	$0.631144\pi$
$888$	17.2301	+	7.87642i	0.578204	+	0.264315i
$889$	−10.2191	+	6.56741i	−0.342737	+	0.220264i
$890$	24.5319	+	15.7700i	0.822311	+	0.528611i
$891$	−4.80349	+	0.690638i	−0.160923	+	0.0231372i
$892$	5.10488	−	3.27893i	0.170924	−	0.109787i
$893$	3.77056	+	0.542124i	0.126177	+	0.0181415i
$894$	12.5607	−	10.8812i	0.420094	−	0.363923i
$895$	−44.2923	−	51.1161i	−1.48053	−	1.70862i
$896$	18.9603	+	8.67865i	0.633418	+	0.289933i
$897$	12.1462	−	3.02686i	0.405551	−	0.101064i
$898$	−10.0003	+	34.0424i	−0.333715	+	1.13601i
$899$	0.566960	−	0.491274i	0.0189092	−	0.0163849i
$900$	−1.51169	−	3.31230i	−0.0503897	−	0.110410i
$901$	25.9318	+	3.72843i	0.863912	+	0.124212i
$902$	16.9085	−	19.5086i	0.562993	−	0.649567i
$903$	−0.227616	−	1.58310i	−0.00757458	−	0.0526824i
$904$	45.9201	−	20.9505i	1.52728	−	0.696803i
$905$	−3.38156	+	2.17320i	−0.112407	+	0.0722396i
$906$	−1.92481	−	13.3991i	−0.0639476	−	0.445155i
$907$	1.32242	+	4.50376i	0.0439104	+	0.149545i	0.978530	−	0.206103i	$-0.0660783\pi$
$907$	1.32242	+	4.50376i	0.0439104	+	0.149545i	−0.934620	+	0.355648i	$0.884260\pi$
$908$	6.10285	+	20.8034i	0.202530	+	0.690384i
$909$	−9.38196	−	8.12951i	−0.311180	−	0.269639i
$910$	−0.00219053	+	17.7676i	−7.26152e−5	+	0.588990i
$911$	−6.96032	−	15.2410i	−0.230606	−	0.504956i	0.758588	−	0.651571i	$-0.225890\pi$
$911$	−6.96032	−	15.2410i	−0.230606	−	0.504956i	−0.989194	+	0.146615i	$0.953162\pi$
$912$	6.25499	+	4.02420i	0.207123	+	0.133254i
$913$	−65.6853	−	19.2870i	−2.17387	−	0.638305i
$914$	−11.5563	−	1.66300i	−0.382248	−	0.0550071i
$915$	−5.59466	−	2.55500i	−0.184954	−	0.0844655i
$916$	−24.1230	−	20.9132i	−0.797048	−	0.690990i
$917$	−10.0894	+	15.6995i	−0.333183	+	0.518443i
$918$	1.31120	+	2.87207i	0.0432762	+	0.0947925i
$919$	0.481424			0.0158807			0.00794036	−	0.999968i	$-0.497472\pi$
$919$	0.481424			0.0158807			0.00794036	+	0.999968i	$0.497472\pi$
$920$	−6.50046	+	34.8240i	−0.214314	+	1.14811i
$921$	12.5001			0.411893
$922$	3.06713	+	6.71826i	0.101010	+	0.221254i
$923$	16.5323	−	25.7247i	0.544166	−	0.846738i
$924$	−11.7179	+	13.5164i	−0.385489	+	0.444656i
$925$	−11.0918	−	5.06545i	−0.364696	−	0.166551i
$926$	−3.05984	−	0.440323i	−0.100552	−	0.0144699i
$927$	11.4389	+	3.35876i	0.375703	+	0.110316i
$928$	5.24124	+	6.05625i	0.172052	+	0.198806i
$929$	−10.5387	−	23.0766i	−0.345765	−	0.757119i	−1.00000		0.000827766i	$-0.999737\pi$
$929$	−10.5387	−	23.0766i	−0.345765	−	0.757119i	0.654235	−	0.756291i	$-0.272991\pi$
$930$	0.000241267	−	1.95694i	7.91145e−6	−	0.0641706i
$931$	−5.06319	−	4.38728i	−0.165939	−	0.143787i
$932$	−50.2047	+	14.7280i	−1.64451	+	0.482431i
$933$	−3.96081	−	13.4893i	−0.129671	−	0.441620i
$934$	−3.43220	−	23.8924i	−0.112305	−	0.781783i
$935$	23.8026	−	15.2970i	0.778429	−	0.500266i
$936$	−3.06434	−	6.71653i	−0.100161	−	0.219537i
$937$	6.27180	+	43.6213i	0.204891	+	1.42505i	0.789509	+	0.613739i	$0.210335\pi$
$937$	6.27180	+	43.6213i	0.204891	+	1.42505i	−0.584618	+	0.811308i	$0.698756\pi$
$938$	8.04129	−	9.27783i	0.262557	−	0.302932i
$939$	−23.3932	−	3.36343i	−0.763407	−	0.109761i
$940$	9.73471	−	4.44279i	0.317511	−	0.144908i
$941$	13.1646	−	11.4072i	0.429153	−	0.371864i	−0.413334	−	0.910579i	$-0.635636\pi$
$941$	13.1646	−	11.4072i	0.429153	−	0.371864i	0.842488	+	0.538716i	$0.181090\pi$
$942$	−8.67977	+	29.5471i	−0.282802	+	0.962696i
$943$	1.82664	+	17.9476i	0.0594837	+	0.584454i
$944$	12.4344	−	5.67119i	0.404705	−	0.184582i
$945$	3.15211	+	3.63773i	0.102538	+	0.118335i
$946$	4.50139	−	3.89950i	0.146353	−	0.126784i
$947$	30.0813	+	4.32503i	0.977510	+	0.140545i	0.612510	−	0.790463i	$-0.290160\pi$
$947$	30.0813	+	4.32503i	0.977510	+	0.140545i	0.365000	+	0.931008i	$0.381069\pi$
$948$	10.7941	+	16.8051i	0.350577	+	0.545804i
$949$	−17.8854	+	2.57154i	−0.580586	+	0.0834757i
$950$	−4.02690	−	2.58863i	−0.130650	−	0.0839863i
$951$	−12.1407	+	7.80235i	−0.393689	+	0.253009i
$952$	10.5846	+	4.83854i	0.343048	+	0.156818i
$953$	−15.4402	+	4.53365i	−0.500157	+	0.146859i	−0.522074	−	0.852900i	$-0.674841\pi$
$953$	−15.4402	+	4.53365i	−0.500157	+	0.146859i	0.0219166	+	0.999760i	$0.493023\pi$
$954$	−13.9624	+	8.97068i	−0.452051	+	0.290437i
$955$	−48.1816	−	41.7496i	−1.55912	−	1.35099i
$956$	38.7837	+	11.3983i	1.25435	+	0.368648i
$957$	−6.25007	+	2.85431i	−0.202036	+	0.0922668i
$958$	4.27954	+	14.5814i	0.138266	+	0.471104i
$959$	15.3412	+	4.50459i	0.495394	+	0.145461i
$960$	20.8928	+	0.0154550i	0.674313	+	0.000498807i
$961$	−12.7612	+	27.9432i	−0.411653	+	0.901394i
$962$	−22.4889	−	10.2737i	−0.725070	−	0.331236i
$963$	−8.71496	+	13.5607i	−0.280836	+	0.436989i
$964$	4.17327	+	29.0766i	0.134412	+	0.936495i
$965$		−	3.21795i		−	0.103589i
$966$	−1.26418	−	12.4363i	−0.0406742	−	0.400132i
$967$	7.03317			0.226171			0.113086	−	0.993585i	$-0.463927\pi$
$967$	7.03317			0.226171			0.113086	+	0.993585i	$0.463927\pi$
$968$	−35.1350	−	5.06492i	−1.12928	−	0.162793i
$969$	3.49216	+	2.24428i	0.112184	+	0.0720965i
$970$	−18.2711	+	39.9951i	−0.586650	+	1.28416i
$971$	−48.8709	−	22.3186i	−1.56834	−	0.716238i	−0.573647	−	0.819103i	$-0.694472\pi$
$971$	−48.8709	−	22.3186i	−1.56834	−	0.716238i	−0.994695	+	0.102865i	$0.967199\pi$
$972$	−1.81906	−	0.831279i	−0.0583463	−	0.0266633i
$973$	9.02597	−	30.7396i	0.289359	−	0.985467i
$974$	7.53126	+	25.6608i	0.241317	+	0.822226i
$975$	1.97392	+	4.32227i	0.0632159	+	0.138424i
$976$	7.12236	−	6.16541i	0.227981	−	0.197350i
$977$	22.3454	−	25.7879i	0.714891	−	0.825028i	−0.275792	−	0.961217i	$-0.588940\pi$
$977$	22.3454	−	25.7879i	0.714891	−	0.825028i	0.990683	+	0.136189i	$0.0434855\pi$
$978$	−6.49621	−	10.1110i	−0.207726	−	0.323316i
$979$	−10.7958	−	36.7670i	−0.345034	−	1.17508i
$980$	−18.6272	−	2.68288i	−0.595024	−	0.0857013i
$981$	−2.62627	−	4.08656i	−0.0838504	−	0.130474i
$982$	24.0431	+	15.4558i	0.767247	+	0.493214i
$983$	−6.37123	−	44.3129i	−0.203211	−	1.41336i	−0.794678	−	0.607032i	$-0.792360\pi$
$983$	−6.37123	−	44.3129i	−0.203211	−	1.41336i	0.591467	−	0.806329i	$-0.298549\pi$
$984$	10.2097	−	2.99375i	0.325474	−	0.0954371i
$985$	1.09942	−	7.64665i	0.0350305	−	0.243643i
$986$	2.92692	+	3.37869i	0.0932122	+	0.107599i
$987$	−2.85361	+	2.47267i	−0.0908313	+	0.0787058i
$988$	−8.16444	−	5.24981i	−0.259745	−	0.167019i
$989$	−0.172131	+	4.15814i	−0.00547344	+	0.132221i
$990$	−5.05175	+	17.1968i	−0.160555	+	0.546552i
$991$	26.1358	+	30.1623i	0.830230	+	0.958137i	0.999624	−	0.0274117i	$-0.00872652\pi$
$991$	26.1358	+	30.1623i	0.830230	+	0.958137i	−0.169394	+	0.985548i	$0.554181\pi$
$992$	2.72567	+	1.24680i	0.0865402	+	0.0395861i
$993$	4.68708	−	32.5993i	0.148740	−	1.03451i
$994$	−23.0757	−	20.0002i	−0.731915	−	0.634366i
$995$	22.3282	−	3.21031i	0.707852	−	0.101774i
$996$	−18.4706	−	21.3269i	−0.585264	−	0.675768i
$997$	−21.6014	−	33.6125i	−0.684124	−	1.06452i	−0.993528	−	0.113587i	$-0.963766\pi$
$997$	−21.6014	−	33.6125i	−0.684124	−	1.06452i	0.309404	−	0.950931i	$-0.399870\pi$
$998$	−6.11428	−	42.5630i	−0.193544	−	1.34731i
$999$	−6.42676	+	1.88707i	−0.203334	+	0.0597041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.13.8	✓	480
8.5	even	2	inner	552.2.bb.a.13.33	yes	480
23.16	even	11	inner	552.2.bb.a.85.33	yes	480
184.85	even	22	inner	552.2.bb.a.85.8	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.13.8	✓	480	1.1	even	1	trivial
552.2.bb.a.13.33	yes	480	8.5	even	2	inner
552.2.bb.a.85.8	yes	480	184.85	even	22	inner
552.2.bb.a.85.33	yes	480	23.16	even	11	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28649 + 0.587327i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(1.31009 - 1.51118i) q^{4} +(2.37560 + 1.08490i) q^{5} +(0.201436 - 1.39979i) q^{6} +(1.76843 + 0.519257i) q^{7} +(-0.797864 + 2.71356i) q^{8} +(-0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-1.28649 + 0.587327i) q^{2} +(-0.540641 + 0.841254i) q^{3} +(1.31009 - 1.51118i) q^{4} +(2.37560 + 1.08490i) q^{5} +(0.201436 - 1.39979i) q^{6} +(1.76843 + 0.519257i) q^{7} +(-0.797864 + 2.71356i) q^{8} +(-0.415415 - 0.909632i) q^{9} +(-3.69337 - 0.000455346i) q^{10} +(3.66757 + 3.17797i) q^{11} +(0.562992 + 1.91912i) q^{12} +(-0.735357 - 2.50439i) q^{13} +(-2.58003 + 0.370628i) q^{14} +(-2.19702 + 1.41194i) q^{15} +(-0.567307 - 3.95957i) q^{16} +(-0.317717 - 2.20977i) q^{17} +(1.06868 + 0.926245i) q^{18} +(1.84049 + 0.264623i) q^{19} +(4.75173 - 2.16863i) q^{20} +(-1.39291 + 1.20696i) q^{21} +(-6.58478 - 1.93435i) q^{22} +(4.13830 - 2.42373i) q^{23} +(-1.85144 - 2.13827i) q^{24} +(1.19216 + 1.37583i) q^{25} +(2.41692 + 2.78997i) q^{26} +(0.989821 + 0.142315i) q^{27} +(3.10149 - 1.99213i) q^{28} +(1.40144 - 0.201497i) q^{29} +(1.99717 - 3.10681i) q^{30} +(0.445741 - 0.286460i) q^{31} +(3.05539 + 4.76073i) q^{32} +(-4.65631 + 1.36722i) q^{33} +(1.70660 + 2.65623i) q^{34} +(3.63773 + 3.15211i) q^{35} +(-1.91885 - 0.563938i) q^{36} +(-6.09278 + 2.78248i) q^{37} +(-2.52319 + 0.740537i) q^{38} +(2.50439 + 0.735357i) q^{39} +(-4.83935 + 5.58073i) q^{40} +(-1.56265 + 3.42173i) q^{41} +(1.08308 - 2.37084i) q^{42} +(-0.469155 + 0.730019i) q^{43} +(9.60732 - 1.37891i) q^{44} -2.61160i q^{45} +(-3.90034 + 5.54863i) q^{46} +2.04867 q^{47} +(3.63771 + 1.66345i) q^{48} +(-3.03107 - 1.94795i) q^{49} +(-2.34176 - 1.06979i) q^{50} +(2.03075 + 0.927411i) q^{51} +(-4.74797 - 2.16974i) q^{52} +(-3.30615 + 11.2597i) q^{53} +(-1.35698 + 0.398263i) q^{54} +(5.26490 + 11.5285i) q^{55} +(-2.82000 + 4.38444i) q^{56} +(-1.21766 + 1.40526i) q^{57} +(-1.68459 + 1.08233i) q^{58} +(0.962583 + 3.27826i) q^{59} +(-0.744615 + 5.16986i) q^{60} +(1.27324 + 1.98120i) q^{61} +(-0.405194 + 0.630323i) q^{62} +(-0.262298 - 1.82432i) q^{63} +(-6.72683 - 4.33010i) q^{64} +(0.970105 - 6.74723i) q^{65} +(5.18728 - 4.49368i) q^{66} +(-3.55986 + 3.08463i) q^{67} +(-3.75559 - 2.41488i) q^{68} +(-0.198359 + 4.79173i) q^{69} +(-6.53121 - 1.91861i) q^{70} +(7.67205 + 8.85401i) q^{71} +(2.79979 - 0.401492i) q^{72} +(0.985217 - 6.85234i) q^{73} +(6.20406 - 7.15808i) q^{74} +(-1.80195 + 0.259081i) q^{75} +(2.81111 - 2.43463i) q^{76} +(4.83564 + 7.52441i) q^{77} +(-3.65376 + 0.524872i) q^{78} +(9.58201 - 2.81353i) q^{79} +(2.94804 - 10.0218i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(0.000655866 - 5.31980i) q^{82} +(-12.8319 + 5.86015i) q^{83} +(-0.000908918 + 3.68617i) q^{84} +(1.64261 - 5.59422i) q^{85} +(0.174801 - 1.21471i) q^{86} +(-0.588168 + 1.28791i) q^{87} +(-11.5498 + 7.41658i) q^{88} +(-6.64268 - 4.26899i) q^{89} +(1.53387 + 3.35979i) q^{90} -4.81068i q^{91} +(1.75887 - 9.42902i) q^{92} +0.529853i q^{93} +(-2.63558 + 1.20324i) q^{94} +(4.08518 + 2.62539i) q^{95} +(-5.65685 - 0.00348710i) q^{96} +(4.94567 - 10.8295i) q^{97} +(5.04351 + 0.725782i) q^{98} +(1.36722 - 4.65631i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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