LMFDB - Embedded newform 750.2.o.b.589.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(19,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("750.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, degree $20$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$14$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			589.11
Character	$\chi$	$=$	750.589
Dual form			750.2.o.b.559.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.481754 - 0.876307i) q^{2} +(0.368125 - 0.929776i) q^{3} +(-0.535827 - 0.844328i) q^{4} +(0.106899 - 2.23351i) q^{5} +(-0.637424 - 0.770513i) q^{6} +(4.43682 + 1.44161i) q^{7} +(-0.998027 + 0.0627905i) q^{8} +(-0.728969 - 0.684547i) q^{9} +O(q^{10})$	\(q+(0.481754 - 0.876307i) q^{2} +(0.368125 - 0.929776i) q^{3} +(-0.535827 - 0.844328i) q^{4} +(0.106899 - 2.23351i) q^{5} +(-0.637424 - 0.770513i) q^{6} +(4.43682 + 1.44161i) q^{7} +(-0.998027 + 0.0627905i) q^{8} +(-0.728969 - 0.684547i) q^{9} +(-1.90574 - 1.16968i) q^{10} +(2.85306 + 1.56848i) q^{11} +(-0.982287 + 0.187381i) q^{12} +(3.06009 - 3.25866i) q^{13} +(3.40075 - 3.19352i) q^{14} +(-2.03731 - 0.921602i) q^{15} +(-0.425779 + 0.904827i) q^{16} +(6.23095 + 3.95428i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(-6.63250 + 2.62599i) q^{19} +(-1.94310 + 1.10652i) q^{20} +(2.97368 - 3.59456i) q^{21} +(2.74894 - 1.74453i) q^{22} +(-0.877808 - 6.94857i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(-4.97715 - 0.477520i) q^{25} +(-1.38138 - 4.25145i) q^{26} +(-0.904827 + 0.425779i) q^{27} +(-1.16018 - 4.51859i) q^{28} +(-0.463526 + 0.119013i) q^{29} +(-1.78909 + 1.34133i) q^{30} +(-5.18422 + 8.16903i) q^{31} +(0.587785 + 0.809017i) q^{32} +(2.50862 - 2.07531i) q^{33} +(6.46695 - 3.55523i) q^{34} +(3.69415 - 9.75559i) q^{35} +(-0.187381 + 0.982287i) q^{36} +(-5.80726 - 2.73269i) q^{37} +(-0.894057 + 7.07719i) q^{38} +(-1.90333 - 4.04479i) q^{39} +(0.0335554 + 2.23582i) q^{40} +(2.10060 + 0.265368i) q^{41} +(-1.71736 - 4.33755i) q^{42} +(-4.36440 + 6.00707i) q^{43} +(-0.204432 - 3.24935i) q^{44} +(-1.60687 + 1.55498i) q^{45} +(-6.51196 - 2.57827i) q^{46} +(-6.74836 - 0.424571i) q^{47} +(0.684547 + 0.728969i) q^{48} +(11.9440 + 8.67786i) q^{49} +(-2.81621 + 4.13146i) q^{50} +(5.97036 - 4.33772i) q^{51} +(-4.39106 - 0.837639i) q^{52} +(-0.503706 - 0.416702i) q^{53} +(-0.0627905 + 0.998027i) q^{54} +(3.80821 - 6.20466i) q^{55} +(-4.51859 - 1.16018i) q^{56} +7.13344i q^{57} +(-0.119013 + 0.463526i) q^{58} +(-0.579463 - 3.03765i) q^{59} +(0.313513 + 2.21398i) q^{60} +(-10.7151 + 1.35363i) q^{61} +(4.66105 + 8.47843i) q^{62} +(-2.24745 - 4.08810i) q^{63} +(0.992115 - 0.125333i) q^{64} +(-6.95114 - 7.18309i) q^{65} +(-0.610071 - 3.19810i) q^{66} +(-0.0477502 + 0.185975i) q^{67} -7.37978i q^{68} +(-6.78376 - 1.74177i) q^{69} +(-6.76922 - 7.93700i) q^{70} +(0.304845 - 4.84537i) q^{71} +(0.770513 + 0.637424i) q^{72} +(8.30029 + 1.58337i) q^{73} +(-5.19234 + 3.77246i) q^{74} +(-2.27620 + 4.45185i) q^{75} +(5.77107 + 4.19293i) q^{76} +(10.3974 + 11.0721i) q^{77} +(-4.46142 - 0.280689i) q^{78} +(3.02396 + 1.19727i) q^{79} +(1.97543 + 1.04771i) q^{80} +(0.0627905 + 0.998027i) q^{81} +(1.24452 - 1.71293i) q^{82} +(1.82404 + 4.60700i) q^{83} +(-4.62837 - 0.584699i) q^{84} +(9.49801 - 13.4942i) q^{85} +(3.16148 + 6.71848i) q^{86} +(-0.0599796 + 0.474788i) q^{87} +(-2.94591 - 1.38624i) q^{88} +(1.30645 - 6.84866i) q^{89} +(0.588526 + 2.15723i) q^{90} +(18.2748 - 10.0467i) q^{91} +(-5.39652 + 4.46439i) q^{92} +(5.68693 + 7.82739i) q^{93} +(-3.62310 + 5.70910i) q^{94} +(5.15618 + 15.0945i) q^{95} +(0.968583 - 0.248690i) q^{96} +(3.57121 + 13.9089i) q^{97} +(13.3586 - 6.28606i) q^{98} +(-1.00609 - 3.09642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q+O(q^{10}) $ 280 * q	$ 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) $ 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{33}{50}\right)$	$1$

Coefficient data

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

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

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

$2$	0.481754	−	0.876307i	0.340651	−	0.619642i
$2$	0.481754	−	0.876307i	0.340651	−	0.619642i
$3$	0.368125	−	0.929776i	0.212537	−	0.536807i
$3$	0.368125	−	0.929776i	0.212537	−	0.536807i
$4$	−0.535827	−	0.844328i	−0.267913	−	0.422164i
$5$	0.106899	−	2.23351i	0.0478066	−	0.998857i
$5$	0.106899	−	2.23351i	0.0478066	−	0.998857i
$6$	−0.637424	−	0.770513i	−0.260227	−	0.314561i
$7$	4.43682	+	1.44161i	1.67696	+	0.544878i	0.984318	−	0.176402i	$-0.0564458\pi$
$7$	4.43682	+	1.44161i	1.67696	+	0.544878i	0.692644	+	0.721280i	$0.256446\pi$
$8$	−0.998027	+	0.0627905i	−0.352856	+	0.0221998i
$9$	−0.728969	−	0.684547i	−0.242990	−	0.228182i
$10$	−1.90574	−	1.16968i	−0.602649	−	0.369885i
$11$	2.85306	+	1.56848i	0.860229	+	0.472915i	0.849846	−	0.527031i	$-0.176695\pi$
$11$	2.85306	+	1.56848i	0.860229	+	0.472915i	0.0103828	+	0.999946i	$0.496695\pi$
$12$	−0.982287	+	0.187381i	−0.283562	+	0.0540923i
$13$	3.06009	−	3.25866i	0.848716	−	0.903791i	−0.147644	−	0.989041i	$-0.547169\pi$
$13$	3.06009	−	3.25866i	0.848716	−	0.903791i	0.996360	+	0.0852500i	$0.0271689\pi$
$14$	3.40075	−	3.19352i	0.908889	−	0.853503i
$15$	−2.03731	−	0.921602i	−0.526032	−	0.237957i
$16$	−0.425779	+	0.904827i	−0.106445	+	0.226207i
$17$	6.23095	+	3.95428i	1.51123	+	0.959054i	0.994704	+	0.102781i	$0.0327741\pi$
$17$	6.23095	+	3.95428i	1.51123	+	0.959054i	0.516523	+	0.856273i	$0.327226\pi$
$18$	−0.951057	+	0.309017i	−0.224166	+	0.0728360i
$19$	−6.63250	+	2.62599i	−1.52160	+	0.602444i	−0.972415	−	0.233257i	$-0.925062\pi$
$19$	−6.63250	+	2.62599i	−1.52160	+	0.602444i	−0.549185	+	0.835701i	$0.685062\pi$
$20$	−1.94310	+	1.10652i	−0.434489	+	0.247425i
$21$	2.97368	−	3.59456i	0.648910	−	0.784398i
$22$	2.74894	−	1.74453i	0.586076	−	0.371935i
$23$	−0.877808	−	6.94857i	−0.183036	−	1.44888i	−0.769368	−	0.638806i	$-0.779429\pi$
$23$	−0.877808	−	6.94857i	−0.183036	−	1.44888i	0.586332	−	0.810071i	$-0.300571\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	−4.97715	−	0.477520i	−0.995429	−	0.0955039i
$26$	−1.38138	−	4.25145i	−0.270911	−	0.833778i
$27$	−0.904827	+	0.425779i	−0.174134	+	0.0819413i
$28$	−1.16018	−	4.51859i	−0.219253	−	0.853933i
$29$	−0.463526	+	0.119013i	−0.0860747	+	0.0221002i	−0.291482	−	0.956576i	$-0.594148\pi$
$29$	−0.463526	+	0.119013i	−0.0860747	+	0.0221002i	0.205407	+	0.978677i	$0.434148\pi$
$30$	−1.78909	+	1.34133i	−0.326642	+	0.244892i
$31$	−5.18422	+	8.16903i	−0.931114	+	1.46720i	−0.0475609	+	0.998868i	$0.515145\pi$
$31$	−5.18422	+	8.16903i	−0.931114	+	1.46720i	−0.883553	+	0.468332i	$0.844855\pi$
$32$	0.587785	+	0.809017i	0.103907	+	0.143015i
$33$	2.50862	−	2.07531i	0.436694	−	0.361265i
$34$	6.46695	−	3.55523i	1.10907	−	0.609718i
$35$	3.69415	−	9.75559i	0.624425	−	1.64900i
$36$	−0.187381	+	0.982287i	−0.0312302	+	0.163715i
$37$	−5.80726	−	2.73269i	−0.954708	−	0.449251i	−0.115648	−	0.993290i	$-0.536894\pi$
$37$	−5.80726	−	2.73269i	−0.954708	−	0.449251i	−0.839060	+	0.544039i	$0.816894\pi$
$38$	−0.894057	+	7.07719i	−0.145035	+	1.14807i
$39$	−1.90333	−	4.04479i	−0.304778	−	0.647685i
$40$	0.0335554	+	2.23582i	0.00530557	+	0.353514i
$41$	2.10060	+	0.265368i	0.328059	+	0.0414435i	0.287638	−	0.957739i	$-0.407130\pi$
$41$	2.10060	+	0.265368i	0.328059	+	0.0414435i	0.0404213	+	0.999183i	$0.487130\pi$
$42$	−1.71736	−	4.33755i	−0.264994	−	0.669298i
$43$	−4.36440	+	6.00707i	−0.665564	+	0.916070i	−0.999650	−	0.0264724i	$-0.991573\pi$
$43$	−4.36440	+	6.00707i	−0.665564	+	0.916070i	0.334085	+	0.942543i	$0.391573\pi$
$44$	−0.204432	−	3.24935i	−0.0308192	−	0.489858i
$45$	−1.60687	+	1.55498i	−0.239538	+	0.231803i
$46$	−6.51196	−	2.57827i	−0.960137	−	0.380145i
$47$	−6.74836	−	0.424571i	−0.984350	−	0.0619301i	−0.437551	−	0.899194i	$-0.644154\pi$
$47$	−6.74836	−	0.424571i	−0.984350	−	0.0619301i	−0.546799	+	0.837264i	$0.684154\pi$
$48$	0.684547	+	0.728969i	0.0988059	+	0.105218i
$49$	11.9440	+	8.67786i	1.70629	+	1.23969i
$50$	−2.81621	+	4.13146i	−0.398272	+	0.584276i
$51$	5.97036	−	4.33772i	0.836018	−	0.607403i
$52$	−4.39106	−	0.837639i	−0.608930	−	0.116160i
$53$	−0.503706	−	0.416702i	−0.0691894	−	0.0572384i	0.602187	−	0.798355i	$-0.294296\pi$
$53$	−0.503706	−	0.416702i	−0.0691894	−	0.0572384i	−0.671376	+	0.741117i	$0.734296\pi$
$54$	−0.0627905	+	0.998027i	−0.00854471	+	0.135814i
$55$	3.80821	−	6.20466i	0.513499	−	0.836637i
$56$	−4.51859	−	1.16018i	−0.603822	−	0.155035i
$57$			7.13344i			0.944847i
$58$	−0.119013	+	0.463526i	−0.0156272	+	0.0608640i
$59$	−0.579463	−	3.03765i	−0.0754396	−	0.395468i	−0.999899	−	0.0141885i	$-0.995483\pi$
$59$	−0.579463	−	3.03765i	−0.0754396	−	0.395468i	0.924460	−	0.381280i	$-0.124517\pi$
$60$	0.313513	+	2.21398i	0.0404743	+	0.285824i
$61$	−10.7151	+	1.35363i	−1.37192	+	0.173314i	−0.776510	−	0.630105i	$-0.783012\pi$
$61$	−10.7151	+	1.35363i	−1.37192	+	0.173314i	−0.595414	+	0.803419i	$0.703012\pi$
$62$	4.66105	+	8.47843i	0.591954	+	1.07676i
$63$	−2.24745	−	4.08810i	−0.283153	−	0.515053i
$64$	0.992115	−	0.125333i	0.124014	−	0.0156667i
$65$	−6.95114	−	7.18309i	−0.862183	−	0.890953i
$66$	−0.610071	−	3.19810i	−0.0750945	−	0.393659i
$67$	−0.0477502	+	0.185975i	−0.00583361	+	0.0227204i	−0.971433	−	0.237313i	$-0.923733\pi$
$67$	−0.0477502	+	0.185975i	−0.00583361	+	0.0227204i	0.965600	+	0.260033i	$0.0837334\pi$
$68$		−	7.37978i		−	0.894929i
$69$	−6.78376	−	1.74177i	−0.816668	−	0.209685i
$70$	−6.76922	−	7.93700i	−0.809077	−	0.948653i
$71$	0.304845	−	4.84537i	0.0361784	−	0.575040i	−0.937625	−	0.347648i	$-0.886980\pi$
$71$	0.304845	−	4.84537i	0.0361784	−	0.575040i	0.973803	−	0.227391i	$-0.0730197\pi$
$72$	0.770513	+	0.637424i	0.0908059	+	0.0751211i
$73$	8.30029	+	1.58337i	0.971476	+	0.185319i	0.648606	−	0.761125i	$-0.275352\pi$
$73$	8.30029	+	1.58337i	0.971476	+	0.185319i	0.322870	+	0.946443i	$0.395352\pi$
$74$	−5.19234	+	3.77246i	−0.603598	+	0.438539i
$75$	−2.27620	+	4.45185i	−0.262832	+	0.514055i
$76$	5.77107	+	4.19293i	0.661987	+	0.480962i
$77$	10.3974	+	11.0721i	1.18489	+	1.26178i
$78$	−4.46142	−	0.280689i	−0.505156	−	0.0317817i
$79$	3.02396	+	1.19727i	0.340223	+	0.134704i	0.532022	−	0.846730i	$-0.321432\pi$
$79$	3.02396	+	1.19727i	0.340223	+	0.134704i	−0.191800	+	0.981434i	$0.561432\pi$
$80$	1.97543	+	1.04771i	0.220859	+	0.117137i
$81$	0.0627905	+	0.998027i	0.00697672	+	0.110892i
$82$	1.24452	−	1.71293i	0.137434	−	0.189162i
$83$	1.82404	+	4.60700i	0.200214	+	0.505683i	0.994845	−	0.101410i	$-0.0323354\pi$
$83$	1.82404	+	4.60700i	0.200214	+	0.505683i	−0.794630	+	0.607093i	$0.792335\pi$
$84$	−4.62837	−	0.584699i	−0.504996	−	0.0637959i
$85$	9.49801	−	13.4942i	1.03020	−	1.46365i
$86$	3.16148	+	6.71848i	0.340911	+	0.724472i
$87$	−0.0599796	+	0.474788i	−0.00643049	+	0.0509026i
$88$	−2.94591	−	1.38624i	−0.314035	−	0.147774i
$89$	1.30645	−	6.84866i	0.138484	−	0.725956i	−0.843521	−	0.537097i	$-0.819521\pi$
$89$	1.30645	−	6.84866i	0.138484	−	0.725956i	0.982004	−	0.188859i	$-0.0604790\pi$
$90$	0.588526	+	2.15723i	0.0620361	+	0.227392i
$91$	18.2748	−	10.0467i	1.91572	−	1.05318i
$92$	−5.39652	+	4.46439i	−0.562626	+	0.465444i
$93$	5.68693	+	7.82739i	0.589707	+	0.811662i
$94$	−3.62310	+	5.70910i	−0.373695	+	0.588848i
$95$	5.15618	+	15.0945i	0.529013	+	1.54866i
$96$	0.968583	−	0.248690i	0.0988556	−	0.0253818i
$97$	3.57121	+	13.9089i	0.362601	+	1.41224i	0.844286	+	0.535893i	$0.180025\pi$
$97$	3.57121	+	13.9089i	0.362601	+	1.41224i	−0.481685	+	0.876345i	$0.659975\pi$
$98$	13.3586	−	6.28606i	1.34942	−	0.634988i
$99$	−1.00609	−	3.09642i	−0.101116	−	0.311202i
$100$	2.26370	+	4.45821i	0.226370	+	0.445821i
$101$	3.45846	−	10.6440i	0.344130	−	1.05912i	−0.617919	−	0.786242i	$-0.712024\pi$
$101$	3.45846	−	10.6440i	0.344130	−	1.05912i	0.962048	−	0.272880i	$-0.0879761\pi$
$102$	−0.924931	−	7.32158i	−0.0915818	−	0.724945i
$103$	−1.96127	+	1.24466i	−0.193250	+	0.122640i	−0.628931	−	0.777461i	$-0.716507\pi$
$103$	−1.96127	+	1.24466i	−0.193250	+	0.122640i	0.435682	+	0.900101i	$0.356507\pi$
$104$	−2.84944	+	3.44438i	−0.279410	+	0.337749i
$105$	−7.71061	−	7.02600i	−0.752479	−	0.685668i
$106$	−0.607821	+	0.240653i	−0.0590368	+	0.0233743i
$107$	−3.64200	+	1.18336i	−0.352086	+	0.114400i	−0.479720	−	0.877422i	$-0.659262\pi$
$107$	−3.64200	+	1.18336i	−0.352086	+	0.114400i	0.127634	+	0.991821i	$0.459262\pi$
$108$	0.844328	+	0.535827i	0.0812455	+	0.0515600i
$109$	−0.475229	+	1.00991i	−0.0455187	+	0.0967322i	−0.926293	−	0.376804i	$-0.877023\pi$
$109$	−0.475229	+	1.00991i	−0.0455187	+	0.0967322i	0.880774	+	0.473537i	$0.157023\pi$
$110$	−3.60257	−	6.32628i	−0.343492	−	0.603187i
$111$	−4.67859	+	4.39348i	−0.444072	+	0.417011i
$112$	−3.19352	+	3.40075i	−0.301759	+	0.321341i
$113$	2.04823	−	0.390720i	0.192681	−	0.0367559i	−0.0901374	−	0.995929i	$-0.528731\pi$
$113$	2.04823	−	0.390720i	0.192681	−	0.0367559i	0.282818	+	0.959173i	$0.408731\pi$
$114$	6.25108	+	3.43656i	0.585467	+	0.321863i
$115$	−15.6135	+	1.21780i	−1.45597	+	0.113560i
$116$	0.348856	+	0.327598i	0.0323905	+	0.0304167i
$117$	−4.46142	+	0.280689i	−0.412458	+	0.0259497i
$118$	−2.94107	−	0.955612i	−0.270747	−	0.0879712i
$119$	21.9451	+	26.5271i	2.01170	+	2.43173i
$120$	2.09116	+	0.791860i	0.190896	+	0.0722866i
$121$	−0.214301	−	0.337684i	−0.0194819	−	0.0306985i
$122$	−3.97583	+	10.0418i	−0.359955	+	0.909142i
$123$	1.02002	−	1.85540i	0.0919719	−	0.167296i
$124$	9.67518			0.868857
$125$	−1.59860	+	11.0655i	−0.142983	+	0.989725i
$126$	−4.66515			−0.415605
$127$	−7.44940	+	13.5504i	−0.661028	+	1.20240i	0.307036	+	0.951698i	$0.400663\pi$
$127$	−7.44940	+	13.5504i	−0.661028	+	1.20240i	−0.968063	+	0.250707i	$0.919337\pi$
$128$	0.368125	−	0.929776i	0.0325379	−	0.0821814i
$129$	3.97860	+	6.26926i	0.350296	+	0.551978i
$130$	−9.64333	+	2.63085i	−0.845776	+	0.230741i
$131$	−1.66707	−	2.01514i	−0.145653	−	0.176064i	0.692642	−	0.721282i	$-0.256447\pi$
$131$	−1.66707	−	2.01514i	−0.145653	−	0.176064i	−0.838294	+	0.545218i	$0.816447\pi$
$132$	−3.09642	−	1.00609i	−0.269509	−	0.0875688i
$133$	−33.2129	+	2.08958i	−2.87992	+	0.181189i
$134$	0.139967	+	0.131438i	0.0120913	+	0.0113545i
$135$	0.854258	+	2.06646i	0.0735228	+	0.177852i
$136$	−6.46695	−	3.55523i	−0.554536	−	0.304859i
$137$	6.25720	−	1.19362i	0.534589	−	0.101978i	0.0869838	−	0.996210i	$-0.472277\pi$
$137$	6.25720	−	1.19362i	0.534589	−	0.101978i	0.447605	+	0.894232i	$0.352277\pi$
$138$	−4.79443	+	5.10555i	−0.408129	+	0.434613i
$139$	13.3600	−	12.5459i	1.13318	−	1.06413i	0.135879	−	0.990725i	$-0.456614\pi$
$139$	13.3600	−	12.5459i	1.13318	−	1.06413i	0.997302	−	0.0734032i	$-0.0233860\pi$
$140$	−10.2163	+	2.10824i	−0.863438	+	0.178178i
$141$	−2.87899	+	6.11817i	−0.242455	+	0.515243i
$142$	−4.09917	−	2.60141i	−0.343995	−	0.218306i
$143$	13.8418	−	4.49746i	1.15751	−	0.376096i
$144$	0.929776	−	0.368125i	0.0774814	−	0.0306770i
$145$	0.216267	+	1.04801i	0.0179600	+	0.0870328i
$146$	5.38621	−	6.51081i	0.445766	−	0.538838i
$147$	12.4654	−	7.91076i	1.02813	−	0.652469i
$148$	0.804400	+	6.36748i	0.0661213	+	0.523404i
$149$	3.26037	−	10.0344i	0.267100	−	0.822050i	−0.724102	−	0.689693i	$-0.757746\pi$
$149$	3.26037	−	10.0344i	0.267100	−	0.822050i	0.991202	−	0.132357i	$-0.0422545\pi$
$150$	2.80462	+	4.13934i	0.228996	+	0.337976i
$151$	−0.993815	−	3.05865i	−0.0808755	−	0.248909i	0.902441	−	0.430814i	$-0.141774\pi$
$151$	−0.993815	−	3.05865i	−0.0808755	−	0.248909i	−0.983316	+	0.181905i	$0.941774\pi$
$152$	6.45453	−	3.03727i	0.523531	−	0.246355i
$153$	−1.83528	−	7.14793i	−0.148373	−	0.577876i
$154$	14.7115	−	3.77727i	1.18549	−	0.304381i
$155$	17.6914	+	12.4523i	1.42101	+	1.00019i
$156$	−2.39527	+	3.77435i	−0.191775	+	0.302190i
$157$	−5.92531	−	8.15550i	−0.472892	−	0.650879i	0.504228	−	0.863571i	$-0.331777\pi$
$157$	−5.92531	−	8.15550i	−0.472892	−	0.650879i	−0.977119	+	0.212691i	$0.931777\pi$
$158$	2.50598	−	2.07313i	0.199365	−	0.164929i
$159$	−0.572866	+	0.314936i	−0.0454313	+	0.0249760i
$160$	1.86978	−	1.22634i	0.147819	−	0.0969508i
$161$	6.12245	−	32.0950i	0.482517	−	2.52944i
$162$	0.904827	+	0.425779i	0.0710899	+	0.0334524i
$163$	−1.89594	+	15.0079i	−0.148502	+	1.17551i	0.725020	+	0.688727i	$0.241830\pi$
$163$	−1.89594	+	15.0079i	−0.148502	+	1.17551i	−0.873522	+	0.486785i	$0.838170\pi$
$164$	−0.901503	−	1.91579i	−0.0703955	−	0.149598i
$165$	−4.36705	−	5.82487i	−0.339975	−	0.453466i
$166$	4.91588	+	0.621020i	0.381546	+	0.0482005i
$167$	2.14250	+	5.41135i	0.165792	+	0.418742i	0.988792	−	0.149298i	$-0.0477015\pi$
$167$	2.14250	+	5.41135i	0.165792	+	0.418742i	−0.823000	+	0.568041i	$0.807702\pi$
$168$	−2.74211	+	3.77419i	−0.211558	+	0.291185i
$169$	−0.438468	−	6.96925i	−0.0337283	−	0.536096i
$170$	−7.24935	−	14.8240i	−0.555999	−	1.13695i
$171$	6.63250	+	2.62599i	0.507200	+	0.200815i
$172$	7.41050	+	0.466229i	0.565045	+	0.0355496i
$173$	−8.83937	−	9.41297i	−0.672045	−	0.715655i	0.299080	−	0.954228i	$-0.403320\pi$
$173$	−8.83937	−	9.41297i	−0.672045	−	0.715655i	−0.971124	+	0.238573i	$0.923320\pi$
$174$	0.387164	+	0.281291i	0.0293508	+	0.0213246i
$175$	−21.3943	−	9.29378i	−1.61726	−	0.702544i
$176$	−2.63398	+	1.91370i	−0.198543	+	0.144250i
$177$	−3.03765	−	0.579463i	−0.228324	−	0.0435551i
$178$	−5.37214	−	4.44422i	−0.402659	−	0.333108i
$179$	−1.27861	+	20.3230i	−0.0955679	+	1.51901i	0.599681	+	0.800239i	$0.295294\pi$
$179$	−1.27861	+	20.3230i	−0.0955679	+	1.51901i	−0.695249	+	0.718769i	$0.744706\pi$
$180$	2.17392	+	0.523524i	0.162034	+	0.0390212i
$181$	−13.7191	−	3.52247i	−1.01973	−	0.261823i	−0.298422	−	0.954434i	$-0.596460\pi$
$181$	−13.7191	−	3.52247i	−1.01973	−	0.261823i	−0.721311	+	0.692611i	$0.756460\pi$
$182$		−	20.8543i		−	1.54583i
$183$	−2.68591	+	10.4609i	−0.198548	+	0.773294i
$184$	1.31238	+	6.87974i	0.0967499	+	0.507181i
$185$	−6.72428	+	12.6785i	−0.494379	+	0.932139i
$186$	9.59889	−	1.21262i	0.703825	−	0.0889137i
$187$	11.5750	+	21.0549i	0.846450	+	1.53969i
$188$	3.25748	+	5.92533i	0.237576	+	0.432149i
$189$	−4.62837	+	0.584699i	−0.336664	+	0.0425306i
$190$	15.7114	+	2.75343i	1.13982	+	0.199755i
$191$	3.18233	+	16.6824i	0.230265	+	1.20709i	0.890129	+	0.455708i	$0.150614\pi$
$191$	3.18233	+	16.6824i	0.230265	+	1.20709i	−0.659864	+	0.751385i	$0.729386\pi$
$192$	0.248690	−	0.968583i	0.0179476	−	0.0699015i
$193$		−	1.48503i		−	0.106895i	−0.998571	−	0.0534476i	$-0.982979\pi$
$193$		−	1.48503i		−	0.106895i	0.998571	−	0.0534476i	$-0.0170210\pi$
$194$	13.9089	+	3.57121i	0.998603	+	0.256398i
$195$	−9.23755	+	3.81874i	−0.661515	+	0.273465i
$196$	0.927018	−	14.7345i	0.0662155	−	1.05247i
$197$	7.70639	+	6.37528i	0.549057	+	0.454220i	0.870121	−	0.492838i	$-0.164040\pi$
$197$	7.70639	+	6.37528i	0.549057	+	0.454220i	−0.321064	+	0.947058i	$0.604040\pi$
$198$	−3.19810	−	0.610071i	−0.227279	−	0.0433559i
$199$	12.6727	−	9.20728i	0.898347	−	0.652687i	−0.0396942	−	0.999212i	$-0.512638\pi$
$199$	12.6727	−	9.20728i	0.898347	−	0.652687i	0.938041	+	0.346525i	$0.112638\pi$
$200$	4.99731	+	0.164060i	0.353363	+	0.0116008i
$201$	0.155337	+	0.112859i	0.0109566	+	0.00796045i
$202$	−7.66132	−	8.15848i	−0.539049	−	0.574028i
$203$	−2.22816	−	0.140184i	−0.156386	−	0.00983896i
$204$	−6.86154	−	2.71668i	−0.480404	−	0.190205i
$205$	0.817255	−	4.66336i	0.0570796	−	0.325703i
$206$	0.145855	+	2.31830i	0.0101622	+	0.161523i
$207$	−4.11673	+	5.66619i	−0.286132	+	0.393827i
$208$	1.64560	+	4.15632i	0.114102	+	0.288189i
$209$	−23.0417	−	2.91085i	−1.59383	−	0.201347i
$210$	−9.87155	+	3.37206i	−0.681202	+	0.232694i
$211$	7.08595	+	15.0584i	0.487817	+	1.03666i	0.985558	+	0.169338i	$0.0541631\pi$
$211$	7.08595	+	15.0584i	0.487817	+	1.03666i	−0.497741	+	0.867326i	$0.665837\pi$
$212$	−0.0819339	+	0.648573i	−0.00562724	+	0.0445442i
$213$	−4.39289	−	2.06714i	−0.300996	−	0.141638i
$214$	−0.717564	+	3.76160i	−0.0490516	+	0.257138i
$215$	12.9503	+	10.3901i	0.883205	+	0.708597i
$216$	0.876307	−	0.481754i	0.0596251	−	0.0327792i
$217$	−34.7780	+	28.7709i	−2.36089	+	1.95310i
$218$	0.656050	+	0.902976i	0.0444333	+	0.0611573i
$219$	4.52772	−	7.13454i	0.305955	−	0.482107i
$220$	−7.27931	+	0.109249i	−0.490771	+	0.00736555i
$221$	31.9529	−	8.20412i	2.14939	−	0.551869i
$222$	1.59611	+	6.21645i	0.107124	+	0.417221i
$223$	6.39896	−	3.01112i	0.428506	−	0.201640i	−0.199417	−	0.979915i	$-0.563905\pi$
$223$	6.39896	−	3.01112i	0.428506	−	0.201640i	0.627924	+	0.778275i	$0.283905\pi$
$224$	1.44161	+	4.43682i	0.0963217	+	0.296448i
$225$	3.30130	+	3.75519i	0.220087	+	0.250346i
$226$	0.644350	−	1.98311i	0.0428615	−	0.131914i
$227$	−0.892628	−	7.06587i	−0.0592458	−	0.468979i	−0.993628	−	0.112707i	$-0.964048\pi$
$227$	−0.892628	−	7.06587i	−0.0592458	−	0.468979i	0.934382	−	0.356271i	$-0.115952\pi$
$228$	6.02296	−	3.82229i	0.398880	−	0.253137i
$229$	11.9052	−	14.3909i	0.786718	−	0.950979i	−0.212942	−	0.977065i	$-0.568304\pi$
$229$	11.9052	−	14.3909i	0.786718	−	0.950979i	0.999660	+	0.0260860i	$0.00830438\pi$
$230$	−6.45471	+	14.2689i	−0.425611	+	0.940865i
$231$	14.1221	−	5.59133i	0.929164	−	0.367882i
$232$	0.455139	−	0.147884i	0.0298813	−	0.00970903i
$233$	−18.0200	−	11.4358i	−1.18053	−	0.749187i	−0.207133	−	0.978313i	$-0.566413\pi$
$233$	−18.0200	−	11.4358i	−1.18053	−	0.749187i	−0.973397	+	0.229126i	$0.926413\pi$
$234$	−1.90333	+	4.04479i	−0.124425	+	0.264416i
$235$	−1.66968	+	15.0272i	−0.108918	+	0.980264i
$236$	−2.25428	+	2.11691i	−0.146741	+	0.137799i
$237$	2.22639	−	2.37087i	0.144620	−	0.154004i
$238$	33.8180	−	6.45112i	2.19209	−	0.418164i
$239$	4.51567	+	2.48251i	0.292094	+	0.160580i	0.621063	−	0.783761i	$-0.286701\pi$
$239$	4.51567	+	2.48251i	0.292094	+	0.160580i	−0.328969	+	0.944341i	$0.606701\pi$
$240$	1.70134	−	1.45102i	0.109821	−	0.0936628i
$241$	3.76967	+	3.53995i	0.242826	+	0.228029i	0.796398	−	0.604772i	$-0.206736\pi$
$241$	3.76967	+	3.53995i	0.242826	+	0.228029i	−0.553573	+	0.832801i	$0.686736\pi$
$242$	−0.399155	+	0.0251127i	−0.0256586	+	0.00161431i
$243$	0.951057	+	0.309017i	0.0610103	+	0.0198234i
$244$	6.88433	+	8.32172i	0.440724	+	0.532744i
$245$	20.6589	−	25.7495i	1.31985	−	1.64508i
$246$	−1.13451	−	1.78770i	−0.0723335	−	0.113979i
$247$	−11.7388	+	29.6489i	−0.746923	+	1.88651i
$248$	4.66105	−	8.47843i	0.295977	−	0.538381i
$249$	4.95495			0.314007
$250$	8.92661	+	6.73169i	0.564568	+	0.425749i
$251$	−13.8010			−0.871114			−0.435557	−	0.900161i	$-0.643449\pi$
$251$	−13.8010			−0.871114			−0.435557	+	0.900161i	$0.643449\pi$
$252$	−2.24745	+	4.08810i	−0.141576	+	0.257526i
$253$	8.39426	−	21.2015i	0.527742	−	1.33293i
$254$	8.28554	+	13.0559i	0.519881	+	0.819201i
$255$	−9.05013	−	13.7986i	−0.566741	−	0.864100i
$256$	−0.637424	−	0.770513i	−0.0398390	−	0.0481571i
$257$	13.5865	+	4.41454i	0.847505	+	0.275371i	0.700401	−	0.713750i	$-0.253005\pi$
$257$	13.5865	+	4.41454i	0.847505	+	0.275371i	0.147105	+	0.989121i	$0.453005\pi$
$258$	7.41050	−	0.466229i	0.461358	−	0.0290262i
$259$	−21.8263	−	20.4963i	−1.35622	−	1.27358i
$260$	−2.34028	+	9.71794i	−0.145138	+	0.602681i
$261$	0.419366	+	0.230549i	0.0259581	+	0.0142706i
$262$	−2.56900	+	0.490063i	−0.158713	+	0.0302762i
$263$	−1.09839	+	1.16967i	−0.0677297	+	0.0721248i	−0.761941	−	0.647647i	$-0.775753\pi$
$263$	−1.09839	+	1.16967i	−0.0677297	+	0.0721248i	0.694211	+	0.719771i	$0.255753\pi$
$264$	−2.37336	+	2.22873i	−0.146070	+	0.137169i
$265$	−0.984554	+	1.08049i	−0.0604807	+	0.0663739i
$266$	−14.1693	+	30.1114i	−0.868777	+	1.84625i
$267$	−5.88678	−	3.73587i	−0.360265	−	0.228631i
$268$	0.182609	−	0.0593334i	0.0111546	−	0.00362436i
$269$	−20.5007	+	8.11681i	−1.24995	+	0.494890i	−0.897531	−	0.440952i	$-0.854641\pi$
$269$	−20.5007	+	8.11681i	−1.24995	+	0.494890i	−0.352420	+	0.935842i	$0.614641\pi$
$270$	2.22239	+	0.246931i	0.135250	+	0.0150278i
$271$	1.85392	−	2.24100i	0.112618	−	0.136131i	−0.711192	−	0.702998i	$-0.751844\pi$
$271$	1.85392	−	2.24100i	0.112618	−	0.136131i	0.823810	+	0.566866i	$0.191844\pi$
$272$	−6.23095	+	3.95428i	−0.377807	+	0.239764i
$273$	−2.61374	−	20.6899i	−0.158191	−	1.25221i
$274$	1.96845	−	6.05826i	0.118918	−	0.365993i
$275$	−13.4511	−	9.16895i	−0.811131	−	0.552908i
$276$	2.16429	+	6.66100i	0.130275	+	0.400945i
$277$	12.9117	−	6.07578i	0.775788	−	0.365058i	0.00322371	−	0.999995i	$-0.498974\pi$
$277$	12.9117	−	6.07578i	0.775788	−	0.365058i	0.772564	+	0.634937i	$0.218974\pi$
$278$	−4.55781	−	17.7515i	−0.273359	−	1.06466i
$279$	9.37122	−	2.40612i	0.561040	−	0.144051i
$280$	−3.07430	+	9.96830i	−0.183725	+	0.595720i
$281$	−10.3402	+	16.2936i	−0.616848	+	0.971996i	0.382008	+	0.924159i	$0.375233\pi$
$281$	−10.3402	+	16.2936i	−0.616848	+	0.971996i	−0.998855	+	0.0478370i	$0.984767\pi$
$282$	3.97443	+	5.47034i	0.236674	+	0.325754i
$283$	15.8854	−	13.1416i	0.944292	−	0.781186i	−0.0315868	−	0.999501i	$-0.510056\pi$
$283$	15.8854	−	13.1416i	0.944292	−	0.781186i	0.975878	+	0.218315i	$0.0700561\pi$
$284$	−4.25443	+	2.33889i	−0.252454	+	0.138788i
$285$	15.9326	+	0.762556i	0.943766	+	0.0451699i
$286$	2.72716	−	14.2963i	0.161261	−	0.845357i
$287$	8.93746	+	4.20565i	0.527561	+	0.248252i
$288$	0.125333	−	0.992115i	0.00738533	−	0.0584609i
$289$	15.9502	+	33.8958i	0.938244	+	1.99387i
$290$	1.02257	+	0.315368i	0.0600473	+	0.0185190i
$291$	14.2468	+	1.79980i	0.835165	+	0.105506i
$292$	−3.11064	−	7.85658i	−0.182036	−	0.459771i
$293$	−0.223690	+	0.307882i	−0.0130681	+	0.0179867i	−0.815501	−	0.578756i	$-0.803539\pi$
$293$	−0.223690	+	0.307882i	−0.0130681	+	0.0179867i	0.802433	+	0.596742i	$0.203539\pi$
$294$	−0.927018	−	14.7345i	−0.0540648	−	0.859335i
$295$	−6.84657	+	0.969515i	−0.398623	+	0.0564473i
$296$	5.96739	+	2.36266i	0.346847	+	0.137327i
$297$	−3.24935	−	0.204432i	−0.188546	−	0.0118623i
$298$	−7.22251	−	7.69119i	−0.418389	−	0.445539i
$299$	−25.3292	−	18.4027i	−1.46483	−	1.06426i
$300$	4.97846	−	0.463562i	0.287432	−	0.0267638i
$301$	−28.0239	+	20.3606i	−1.61527	+	1.17356i
$302$	−3.15909	−	0.602628i	−0.181785	−	0.0346773i
$303$	−8.62344	−	7.13393i	−0.495403	−	0.409833i
$304$	0.447912	−	7.11936i	0.0256895	−	0.408323i
$305$	1.87791	+	24.0769i	0.107529	+	1.37864i
$306$	−7.14793	−	1.83528i	−0.408620	−	0.104916i
$307$		−	8.61440i		−	0.491650i	−0.969314	−	0.245825i	$-0.920941\pi$
$307$		−	8.61440i		−	0.491650i	0.969314	−	0.245825i	$-0.0790589\pi$
$308$	3.77727	−	14.7115i	0.215230	−	0.838265i
$309$	0.435264	+	2.28173i	0.0247613	+	0.129803i
$310$	19.4349	−	9.50418i	1.10383	−	0.539801i
$311$	6.73822	−	0.851235i	0.382089	−	0.0482691i	0.0680570	−	0.997681i	$-0.478320\pi$
$311$	6.73822	−	0.851235i	0.382089	−	0.0482691i	0.314032	+	0.949412i	$0.398320\pi$
$312$	2.15355	+	3.91730i	0.121921	+	0.221773i
$313$	−8.22287	−	14.9573i	−0.464784	−	0.845439i	−1.00000		0.000723484i	$-0.999770\pi$
$313$	−8.22287	−	14.9573i	−0.464784	−	0.845439i	0.535216	−	0.844715i	$-0.320230\pi$
$314$	−10.0013	+	1.26345i	−0.564404	+	0.0713008i
$315$	−9.37108	+	4.58270i	−0.528000	+	0.258206i
$316$	−0.609431	−	3.19475i	−0.0342832	−	0.179719i
$317$	2.81473	−	10.9627i	0.158091	−	0.615725i	−0.839308	−	0.543656i	$-0.817040\pi$
$317$	2.81473	−	10.9627i	0.158091	−	0.615725i	0.997400	−	0.0720691i	$-0.0229602\pi$
$318$			0.653728i			0.0366593i
$319$	−1.50914	−	0.387480i	−0.0844954	−	0.0216947i
$320$	−0.173877	−	2.22930i	−0.00972003	−	0.124622i
$321$	−0.240452	+	3.82187i	−0.0134207	+	0.213316i
$322$	−25.1756	−	20.8270i	−1.40298	−	1.16065i
$323$	−51.7107	−	9.86434i	−2.87726	−	0.548867i
$324$	0.809017	−	0.587785i	0.0449454	−	0.0326547i
$325$	−16.7866	+	14.7576i	−0.931152	+	0.818604i
$326$	12.2382	+	8.89155i	0.677810	+	0.492458i
$327$	0.764050	+	0.813631i	0.0422521	+	0.0449939i
$328$	−2.11312	−	0.132946i	−0.116678	−	0.00734074i
$329$	−29.3292	−	11.6123i	−1.61697	−	0.640205i
$330$	−7.20822	+	1.02073i	−0.396799	+	0.0561892i
$331$	−1.94995	−	30.9936i	−0.107179	−	1.70356i	−0.573712	−	0.819057i	$-0.694497\pi$
$331$	−1.94995	−	30.9936i	−0.107179	−	1.70356i	0.466533	−	0.884504i	$-0.345503\pi$
$332$	2.91245	−	4.00864i	0.159841	−	0.220003i
$333$	2.36266	+	5.96739i	0.129473	+	0.327011i
$334$	5.77416	+	0.729446i	0.315948	+	0.0399135i
$335$	0.410272	+	0.126531i	0.0224156	+	0.00691313i
$336$	1.98633	+	4.22116i	0.108363	+	0.230283i
$337$	3.45417	−	27.3426i	0.188161	−	1.48944i	−0.561419	−	0.827531i	$-0.689745\pi$
$337$	3.45417	−	27.3426i	0.188161	−	1.48944i	0.749580	−	0.661914i	$-0.230255\pi$
$338$	−6.31844	−	2.97323i	−0.343678	−	0.161722i
$339$	0.390720	−	2.04823i	0.0212210	−	0.111244i
$340$	−16.4828	−	0.788890i	−0.893906	−	0.0427836i
$341$	−27.6038	+	15.1753i	−1.49483	+	0.821790i
$342$	5.49641	−	4.54702i	0.297212	−	0.245875i
$343$	21.2888	+	29.3015i	1.14949	+	1.58213i
$344$	3.97860	−	6.26926i	0.214512	−	0.338016i
$345$	−4.61544	+	14.9654i	−0.248487	+	0.805710i
$346$	−12.5070	+	3.21126i	−0.672383	+	0.172639i
$347$	−4.86357	−	18.9423i	−0.261090	−	1.01688i	−0.954950	−	0.296768i	$-0.904091\pi$
$347$	−4.86357	−	18.9423i	−0.261090	−	1.01688i	0.693860	−	0.720110i	$-0.255909\pi$
$348$	0.433015	−	0.203761i	0.0232120	−	0.0109228i
$349$	−5.25018	−	16.1584i	−0.281035	−	0.864938i	−0.987559	−	0.157249i	$-0.949738\pi$
$349$	−5.25018	−	16.1584i	−0.281035	−	0.864938i	0.706524	−	0.707690i	$-0.250262\pi$
$350$	−18.4510	+	14.2707i	−0.986247	+	0.762800i
$351$	−1.38138	+	4.25145i	−0.0737326	+	0.226926i
$352$	0.408057	+	3.23010i	0.0217495	+	0.172165i
$353$	−0.955452	+	0.606348i	−0.0508536	+	0.0322726i	−0.561011	−	0.827809i	$-0.689587\pi$
$353$	−0.955452	+	0.606348i	−0.0508536	+	0.0322726i	0.510157	+	0.860081i	$0.329587\pi$
$354$	−1.97119	+	2.38275i	−0.104767	+	0.126642i
$355$	−10.7896	−	1.19884i	−0.572653	−	0.0636278i
$356$	−6.48254	+	2.56662i	−0.343574	+	0.136031i
$357$	32.7428	−	10.6388i	1.73293	−	0.563063i
$358$	17.1932	+	10.9111i	0.908687	+	0.576670i
$359$	3.52230	−	7.48527i	0.185900	−	0.395057i	−0.790053	−	0.613038i	$-0.789947\pi$
$359$	3.52230	−	7.48527i	0.185900	−	0.395057i	0.975953	+	0.217981i	$0.0699471\pi$
$360$	1.50606	−	1.65281i	0.0793764	−	0.0871107i
$361$	23.2438	−	21.8274i	1.22336	−	1.14881i
$362$	−9.69599	+	10.3252i	−0.509610	+	0.542680i
$363$	−0.392860	+	0.0749420i	−0.0206198	+	0.00393344i
$364$	−18.2748	−	10.0467i	−0.957860	−	0.526588i
$365$	4.42376	−	18.3695i	0.231550	−	0.961505i
$366$	7.87303	+	7.39327i	0.411530	+	0.386452i
$367$	−8.48272	+	0.533687i	−0.442794	+	0.0278582i	−0.282623	−	0.959231i	$-0.591205\pi$
$367$	−8.48272	+	0.533687i	−0.442794	+	0.0278582i	−0.160171	+	0.987089i	$0.551205\pi$
$368$	6.66100	+	2.16429i	0.347229	+	0.112821i
$369$	−1.34962	−	1.63141i	−0.0702583	−	0.0849277i
$370$	7.87077	+	12.0004i	0.409182	+	0.623873i
$371$	−1.63413	−	2.57498i	−0.0848400	−	0.133686i
$372$	3.56167	−	8.99576i	0.184664	−	0.466408i
$373$	−2.31976	+	4.21962i	−0.120112	+	0.218484i	−0.929527	−	0.368754i	$-0.879785\pi$
$373$	−2.31976	+	4.21962i	−0.120112	+	0.218484i	0.809415	+	0.587237i	$0.199785\pi$
$374$	24.0269			1.24240
$375$	9.69993	+	5.55981i	0.500902	+	0.287107i
$376$	6.76171			0.348708
$377$	−1.03061	+	1.87467i	−0.0530790	+	0.0965503i
$378$	−1.71736	+	4.33755i	−0.0883313	+	0.223099i
$379$	10.5931	+	16.6921i	0.544133	+	0.857417i	0.999458	−	0.0329086i	$-0.0104770\pi$
$379$	10.5931	+	16.6921i	0.544133	+	0.857417i	−0.455325	+	0.890325i	$0.650477\pi$
$380$	9.98187	−	12.4415i	0.512059	−	0.638237i
$381$	9.85655	+	11.9145i	0.504966	+	0.610399i
$382$	16.1520	+	5.24809i	0.826406	+	0.268516i
$383$	−23.0533	+	1.45039i	−1.17797	+	0.0741116i	−0.639676	−	0.768645i	$-0.720931\pi$
$383$	−23.0533	+	1.45039i	−1.17797	+	0.0741116i	−0.538295	+	0.842757i	$0.680931\pi$
$384$	−0.728969	−	0.684547i	−0.0372000	−	0.0349331i
$385$	25.8411	−	22.0390i	1.31698	−	1.12321i
$386$	−1.30135	−	0.715421i	−0.0662368	−	0.0364140i
$387$	7.29363	−	1.39133i	0.370756	−	0.0707255i
$388$	9.83015	−	10.4680i	0.499050	−	0.531435i
$389$	−3.14276	+	2.95125i	−0.159344	+	0.149634i	−0.760118	−	0.649785i	$-0.774859\pi$
$389$	−3.14276	+	2.95125i	−0.159344	+	0.149634i	0.600774	+	0.799419i	$0.294859\pi$
$390$	−1.10384	+	9.93462i	−0.0558952	+	0.503059i
$391$	22.0070	−	46.7673i	1.11294	−	2.36512i
$392$	−12.4654	−	7.91076i	−0.629596	−	0.399554i
$393$	−2.48732	+	0.808179i	−0.125469	+	0.0407673i
$394$	9.29928	−	3.68184i	0.468491	−	0.185489i
$395$	2.99738	−	6.62607i	0.150815	−	0.333394i
$396$	−2.07531	+	2.50862i	−0.104288	+	0.126063i
$397$	12.8638	−	8.16364i	0.645617	−	0.409721i	−0.172310	−	0.985043i	$-0.555123\pi$
$397$	12.8638	−	8.16364i	0.645617	−	0.409721i	0.817927	+	0.575322i	$0.195123\pi$
$398$	−1.96327	−	15.5408i	−0.0984096	−	0.778992i
$399$	−10.2836	+	31.6498i	−0.514826	+	1.58447i
$400$	2.55124	−	4.30014i	0.127562	−	0.215007i
$401$	6.75702	+	20.7960i	0.337430	+	1.03850i	0.965513	+	0.260355i	$0.0838397\pi$
$401$	6.75702	+	20.7960i	0.337430	+	1.03850i	−0.628083	+	0.778146i	$0.716160\pi$
$402$	0.173733	−	0.0817526i	0.00866502	−	0.00407745i
$403$	10.7559	+	41.8916i	0.535791	+	2.08677i
$404$	−10.8402	+	2.78329i	−0.539320	+	0.138474i
$405$	2.23582	−	0.0335554i	0.111099	−	0.00166738i
$406$	−1.19627	+	1.88501i	−0.0593697	+	0.0935517i
$407$	−12.2823	−	16.9051i	−0.608809	−	0.837954i
$408$	−5.68621	+	4.70405i	−0.281510	+	0.232885i
$409$	−9.02707	+	4.96267i	−0.446360	+	0.245388i	−0.689048	−	0.724716i	$-0.741971\pi$
$409$	−9.02707	+	4.96267i	−0.446360	+	0.245388i	0.242688	+	0.970104i	$0.421971\pi$
$410$	−3.69282	−	2.96276i	−0.182375	−	0.146320i
$411$	1.19362	−	6.25720i	0.0588772	−	0.308645i
$412$	2.10180	+	0.989034i	0.103548	+	0.0487262i
$413$	1.80814	−	14.3129i	0.0889726	−	0.704291i
$414$	2.98207	+	6.33722i	0.146561	+	0.311457i
$415$	10.4848	−	3.58153i	0.514677	−	0.175810i
$416$	4.43499	+	0.560269i	0.217443	+	0.0274695i
$417$	−6.74672	−	17.0403i	−0.330389	−	0.834466i
$418$	−13.6512	+	18.7893i	−0.667703	+	0.919014i
$419$	0.532300	+	8.46066i	0.0260045	+	0.413330i	0.989397	+	0.145236i	$0.0463940\pi$
$419$	0.532300	+	8.46066i	0.0260045	+	0.413330i	−0.963393	+	0.268095i	$0.913606\pi$
$420$	−1.80070	+	10.2750i	−0.0878651	+	0.501369i
$421$	−5.09925	−	2.01893i	−0.248522	−	0.0983968i	0.240561	−	0.970634i	$-0.422669\pi$
$421$	−5.09925	−	2.01893i	−0.248522	−	0.0983968i	−0.489083	+	0.872237i	$0.662669\pi$
$422$	16.6095	+	1.04498i	0.808537	+	0.0508688i
$423$	4.62871	+	4.92907i	0.225055	+	0.239660i
$424$	0.528877	+	0.384252i	0.0256845	+	0.0186609i
$425$	−29.1241	−	22.6564i	−1.41273	−	1.09900i
$426$	−3.92774	+	2.85367i	−0.190299	+	0.138261i
$427$	−49.4923	−	9.44116i	−2.39510	−	0.456890i
$428$	2.95063	+	2.44097i	0.142624	+	0.117989i
$429$	0.913858	−	14.5254i	0.0441215	−	0.701291i
$430$	15.3438	−	6.34300i	0.739942	−	0.305886i
$431$	24.2524	+	6.22695i	1.16820	+	0.299942i	0.782480	−	0.622676i	$-0.213954\pi$
$431$	24.2524	+	6.22695i	1.16820	+	0.299942i	0.385716	+	0.922618i	$0.373954\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−5.49707	+	21.4097i	−0.264172	+	1.02888i	0.688586	+	0.725155i	$0.258232\pi$
$433$	−5.49707	+	21.4097i	−0.264172	+	1.02888i	−0.952758	+	0.303729i	$0.901768\pi$
$434$	8.45768	+	44.3367i	0.405982	+	2.12823i
$435$	1.05403	+	0.184719i	0.0505369	+	0.00885662i
$436$	1.10734	−	0.139889i	0.0530319	−	0.00669949i
$437$	24.0690	+	43.7813i	1.15137	+	2.09434i
$438$	−4.07080	−	7.40476i	−0.194510	−	0.353813i
$439$	12.5372	−	1.58382i	0.598368	−	0.0755915i	0.179686	−	0.983724i	$-0.442492\pi$
$439$	12.5372	−	1.58382i	0.598368	−	0.0755915i	0.418683	+	0.908133i	$0.362492\pi$
$440$	−3.41110	+	6.43154i	−0.162618	+	0.306612i
$441$	−2.76643	−	14.5021i	−0.131735	−	0.690579i
$442$	8.20412	−	31.9529i	0.390230	−	1.51985i
$443$			35.0784i			1.66662i	0.552804	+	0.833311i	$0.313558\pi$
$443$			35.0784i			1.66662i	−0.552804	+	0.833311i	$0.686442\pi$
$444$	6.21645	+	1.59611i	0.295020	+	0.0757482i
$445$	−15.1569	−	3.65009i	−0.718506	−	0.173031i
$446$	0.444056	−	7.05807i	0.0210267	−	0.334210i
$447$	−8.12952	−	6.72533i	−0.384513	−	0.318097i
$448$	4.58252	+	0.874163i	0.216504	+	0.0413003i
$449$	24.0464	−	17.4707i	1.13482	−	0.824493i	0.148429	−	0.988923i	$-0.452578\pi$
$449$	24.0464	−	17.4707i	1.13482	−	0.824493i	0.986389	+	0.164430i	$0.0525783\pi$
$450$	4.88111	−	1.08387i	0.230098	−	0.0510943i
$451$	5.57692	+	4.05187i	0.262607	+	0.190795i
$452$	−1.42739	−	1.52002i	−0.0671388	−	0.0714956i
$453$	−3.20971	−	0.201938i	−0.150805	−	0.00948785i
$454$	−6.62190	−	2.62180i	−0.310781	−	0.123047i
$455$	−20.4858	−	41.8910i	−0.960388	−	1.96388i
$456$	−0.447912	−	7.11936i	−0.0209754	−	0.333395i
$457$	−24.7771	+	34.1028i	−1.15903	+	1.59526i	−0.444260	+	0.895898i	$0.646533\pi$
$457$	−24.7771	+	34.1028i	−1.15903	+	1.59526i	−0.714765	+	0.699364i	$0.753467\pi$
$458$	−6.87548	−	17.3655i	−0.321270	−	0.811436i
$459$	−7.32158	−	0.924931i	−0.341742	−	0.0431721i
$460$	9.39438	+	12.5304i	0.438015	+	0.584234i
$461$	−10.3983	−	22.0976i	−0.484299	−	1.02919i	−0.986398	−	0.164378i	$-0.947438\pi$
$461$	−10.3983	−	22.0976i	−0.484299	−	1.02919i	0.502098	−	0.864811i	$-0.332562\pi$
$462$	1.90365	−	15.0689i	0.0885656	−	0.701069i
$463$	−16.0301	−	7.54321i	−0.744983	−	0.350563i	0.0155348	−	0.999879i	$-0.495055\pi$
$463$	−16.0301	−	7.54321i	−0.744983	−	0.350563i	−0.760518	+	0.649317i	$0.775055\pi$
$464$	0.0896734	−	0.470085i	0.00416298	−	0.0218231i
$465$	18.0905	−	11.8651i	0.838926	−	0.550230i
$466$	−18.7025	+	10.2818i	−0.866377	+	0.476295i
$467$	24.3594	−	20.1519i	1.12722	−	0.932518i	0.128970	−	0.991649i	$-0.458833\pi$
$467$	24.3594	−	20.1519i	1.12722	−	0.932518i	0.998250	+	0.0591310i	$0.0188330\pi$
$468$	2.62754	+	3.61650i	0.121458	+	0.167173i
$469$	−0.479962	+	0.756300i	−0.0221626	+	0.0349227i
$470$	12.3640	+	8.70254i	0.570310	+	0.401418i
$471$	−9.76404	+	2.50698i	−0.449903	+	0.115516i
$472$	0.769055	+	2.99527i	0.0353986	+	0.137868i
$473$	−21.8738	+	10.2930i	−1.00576	+	0.473275i
$474$	−1.00503	−	3.09317i	−0.0461627	−	0.142074i
$475$	34.2649	−	9.90280i	1.57218	−	0.454372i
$476$	10.6388	−	32.7428i	0.487627	−	1.50076i
$477$	0.0819339	+	0.648573i	0.00375149	+	0.0296961i
$478$	4.35088	−	2.76115i	0.199005	−	0.126292i
$479$	5.79785	−	7.00840i	0.264911	−	0.320222i	−0.621239	−	0.783621i	$-0.713370\pi$
$479$	5.79785	−	7.00840i	0.264911	−	0.320222i	0.886150	+	0.463399i	$0.153370\pi$
$480$	−0.451911	−	2.18993i	−0.0206268	−	0.0999560i
$481$	−26.6756	+	10.5616i	−1.21630	+	0.481569i
$482$	4.91814	−	1.59800i	0.224015	−	0.0727869i
$483$	−27.5874	−	17.5075i	−1.25527	−	0.796618i
$484$	−0.170288	+	0.361880i	−0.00774036	+	0.0164491i
$485$	31.4475	−	6.48948i	1.42796	−	0.294672i
$486$	0.728969	−	0.684547i	0.0330667	−	0.0310517i
$487$	−0.394307	+	0.419894i	−0.0178677	+	0.0190272i	−0.737840	−	0.674975i	$-0.764154\pi$
$487$	−0.394307	+	0.419894i	−0.0178677	+	0.0190272i	0.719973	+	0.694002i	$0.244154\pi$
$488$	10.6089	−	2.02376i	0.480244	−	0.0916114i
$489$	13.2561	+	7.28759i	0.599461	+	0.329556i
$490$	−12.6120	−	30.5085i	−0.569751	−	1.37823i
$491$	−16.6912	−	15.6741i	−0.753263	−	0.707361i	0.209470	−	0.977815i	$-0.432826\pi$
$491$	−16.6912	−	15.6741i	−0.753263	−	0.707361i	−0.962733	+	0.270454i	$0.912826\pi$
$492$	−2.11312	+	0.132946i	−0.0952669	+	0.00599369i
$493$	−3.35882	−	1.09135i	−0.151274	−	0.0491518i
$494$	20.3263	+	24.5702i	0.914522	+	1.10547i
$495$	−7.02345	+	1.91611i	−0.315680	+	0.0861226i
$496$	−5.18422	−	8.16903i	−0.232778	−	0.366800i
$497$	8.33768	−	21.0586i	0.373996	−	0.944607i
$498$	2.38707	−	4.34206i	0.106967	−	0.194572i
$499$	−26.1773			−1.17186			−0.585928	−	0.810363i	$-0.699270\pi$
$499$	−26.1773			−1.17186			−0.585928	+	0.810363i	$0.699270\pi$
$500$	10.1995	−	4.57943i	0.456133	−	0.204798i
$501$	5.82005			0.260021
$502$	−6.64870	+	12.0939i	−0.296746	+	0.539779i
$503$	4.82324	−	12.1821i	0.215058	−	0.543174i	−0.781698	−	0.623657i	$-0.785646\pi$
$503$	4.82324	−	12.1821i	0.215058	−	0.543174i	0.996756	+	0.0804829i	$0.0256462\pi$
$504$	2.49971	+	3.93892i	0.111346	+	0.175453i
$505$	−23.4039	−	8.86234i	−1.04146	−	0.394369i
$506$	−14.5350	−	17.5698i	−0.646161	−	0.781074i
$507$	−6.64126	−	2.15788i	−0.294949	−	0.0958346i
$508$	15.4326	−	0.970936i	0.684710	−	0.0430783i
$509$	−3.11630	−	2.92640i	−0.138127	−	0.129710i	0.612404	−	0.790545i	$-0.290203\pi$
$509$	−3.11630	−	2.92640i	−0.138127	−	0.129710i	−0.750532	+	0.660834i	$0.770203\pi$
$510$	−16.4517	+	1.28317i	−0.728494	+	0.0568199i
$511$	34.5443	+	18.9909i	1.52815	+	0.840108i
$512$	−0.982287	+	0.187381i	−0.0434114	+	0.00828116i
$513$	4.88317	−	5.20005i	0.215597	−	0.229588i
$514$	10.4139	−	9.77926i	0.459335	−	0.431345i
$515$	2.57031	+	4.51358i	0.113261	+	0.198892i
$516$	3.16148	−	6.71848i	0.139176	−	0.295765i
$517$	−18.5875	−	11.7960i	−0.817478	−	0.518788i
$518$	−28.4759	+	9.25239i	−1.25116	+	0.406527i
$519$	−12.0059	+	4.75349i	−0.527002	+	0.208655i
$520$	7.38846	+	6.73245i	0.324005	+	0.295237i
$521$	17.4588	−	21.1041i	0.764885	−	0.924587i	−0.233979	−	0.972242i	$-0.575175\pi$
$521$	17.4588	−	21.1041i	0.764885	−	0.924587i	0.998864	+	0.0476545i	$0.0151746\pi$
$522$	0.404063	−	0.256426i	0.0176853	−	0.0112235i
$523$	1.94514	+	15.3974i	0.0850550	+	0.673279i	0.975783	+	0.218742i	$0.0701954\pi$
$523$	1.94514	+	15.3974i	0.0850550	+	0.673279i	−0.890728	+	0.454537i	$0.849805\pi$
$524$	−0.808179	+	2.48732i	−0.0353055	+	0.108659i
$525$	−16.5169	+	16.4707i	−0.720857	+	0.718839i
$526$	0.495834	+	1.52602i	0.0216194	+	0.0665376i
$527$	−64.6052	+	30.4009i	−2.81425	+	1.32428i
$528$	0.809678	+	3.15349i	0.0352367	+	0.137238i
$529$	−25.2346	+	6.47915i	−1.09716	+	0.281702i
$530$	0.472527	+	1.38330i	0.0205252	+	0.0600867i
$531$	−1.65700	+	2.61102i	−0.0719078	+	0.113309i
$532$	19.5607	+	26.9229i	0.848062	+	1.16726i
$533$	7.29278	−	6.03311i	0.315885	−	0.261323i
$534$	−6.10974	+	3.35886i	−0.264394	+	0.145352i
$535$	2.25372	+	8.26096i	0.0974368	+	0.357152i
$536$	0.0359785	−	0.188606i	0.00155403	−	0.00814654i
$537$	18.4251	+	8.67020i	0.795102	+	0.374147i
$538$	−2.76348	+	21.8752i	−0.119142	+	0.943107i
$539$	20.4660	+	43.4924i	0.881532	+	1.87335i
$540$	1.28703	−	1.82854i	0.0553851	−	0.0786877i
$541$	4.02411	+	0.508364i	0.173010	+	0.0218563i	0.211361	−	0.977408i	$-0.432210\pi$
$541$	4.02411	+	0.508364i	0.173010	+	0.0218563i	−0.0383508	+	0.999264i	$0.512210\pi$
$542$	−1.07067	−	2.70421i	−0.0459894	−	0.116156i
$543$	−8.32545	+	11.4590i	−0.357279	+	0.491753i
$544$	0.463380	+	7.36521i	0.0198673	+	0.315781i
$545$	2.20485	+	1.16939i	0.0944455	+	0.0500911i
$546$	−19.3899	−	7.67700i	−0.829810	−	0.328545i
$547$	11.2702	+	0.709063i	0.481881	+	0.0303174i	0.301874	−	0.953348i	$-0.402388\pi$
$547$	11.2702	+	0.709063i	0.481881	+	0.0303174i	0.180007	+	0.983665i	$0.442388\pi$
$548$	−4.36058	−	4.64355i	−0.186275	−	0.198363i
$549$	8.73757	+	6.34822i	0.372910	+	0.270935i
$550$	−14.5149	+	7.37011i	−0.618918	+	0.314262i
$551$	2.76181	−	2.00657i	0.117657	−	0.0854829i
$552$	6.87974	+	1.31238i	0.292821	+	0.0558586i
$553$	11.6908	+	9.67147i	0.497143	+	0.411273i
$554$	0.896007	−	14.2416i	0.0380677	−	0.605069i
$555$	9.31276	+	10.9193i	0.395305	+	0.463500i
$556$	−17.7515	−	4.55781i	−0.752831	−	0.193294i
$557$		−	14.3166i		−	0.606615i	−0.952893	−	0.303307i	$-0.901909\pi$
$557$		−	14.3166i		−	0.606615i	0.952893	−	0.303307i	$-0.0980909\pi$
$558$	2.40612	−	9.37122i	0.101859	−	0.396715i
$559$	6.21960	+	32.6043i	0.263061	+	1.37901i
$560$	7.25423	+	7.49629i	0.306547	+	0.316776i
$561$	23.8374	−	3.01137i	1.00642	−	0.127140i
$562$	9.29676	+	16.9107i	0.392160	+	0.713337i
$563$	9.34010	+	16.9896i	0.393638	+	0.716025i	0.996657	−	0.0817018i	$-0.0260355\pi$
$563$	9.34010	+	16.9896i	0.393638	+	0.716025i	−0.603019	+	0.797727i	$0.706036\pi$
$564$	6.70839	−	0.847467i	0.282474	−	0.0356848i
$565$	−0.653725	−	4.61650i	−0.0275024	−	0.194218i
$566$	−3.86318	−	20.2515i	−0.162382	−	0.851235i
$567$	−1.16018	+	4.51859i	−0.0487228	+	0.189763i
$568$			4.85495i			0.203709i
$569$	−40.2206	−	10.3269i	−1.68613	−	0.432925i	−0.720631	−	0.693319i	$-0.756148\pi$
$569$	−40.2206	−	10.3269i	−1.68613	−	0.432925i	−0.965503	+	0.260393i	$0.916148\pi$
$570$	8.34383	−	13.5945i	0.349484	−	0.569410i
$571$	2.78925	−	44.3338i	0.116726	−	1.85531i	−0.309757	−	0.950816i	$-0.600248\pi$
$571$	2.78925	−	44.3338i	0.116726	−	1.85531i	0.426483	−	0.904495i	$-0.359752\pi$
$572$	−11.2141	−	9.27712i	−0.468886	−	0.387896i
$573$	16.6824	+	3.18233i	0.696916	+	0.132944i
$574$	7.99109	−	5.80587i	0.333542	−	0.242332i
$575$	1.05090	+	35.0032i	0.0438256	+	1.45973i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	1.06959	+	1.13899i	0.0445274	+	0.0474169i	0.750847	−	0.660477i	$-0.229646\pi$
$577$	1.06959	+	1.13899i	0.0445274	+	0.0474169i	−0.706319	+	0.707893i	$0.749646\pi$
$578$	37.3872	+	2.35220i	1.55510	+	0.0978387i
$579$	−1.38075	−	0.546678i	−0.0573820	−	0.0227192i
$580$	0.768985	−	0.744154i	0.0319304	−	0.0308993i
$581$	1.45144	+	23.0700i	0.0602159	+	0.957104i
$582$	8.44064	−	11.6175i	0.349876	−	0.481563i
$583$	−0.783513	−	1.97893i	−0.0324498	−	0.0819588i
$584$	−8.38333	−	1.05906i	−0.346905	−	0.0438243i
$585$	0.150001	+	9.99463i	0.00620176	+	0.413227i
$586$	0.162036	+	0.344344i	0.00669365	+	0.0142247i
$587$	2.32681	−	18.4186i	0.0960378	−	0.760218i	−0.868392	−	0.495878i	$-0.834846\pi$
$587$	2.32681	−	18.4186i	0.0960378	−	0.760218i	0.964430	−	0.264339i	$-0.0851538\pi$
$588$	−13.3586	−	6.28606i	−0.550897	−	0.259233i
$589$	12.9325	−	67.7948i	0.532876	−	2.79344i
$590$	−2.44877	+	6.46676i	−0.100814	+	0.266232i
$591$	8.76449	−	4.81832i	0.360523	−	0.198199i
$592$	4.94522	−	4.09104i	0.203247	−	0.168141i
$593$	−16.2975	−	22.4316i	−0.669258	−	0.921155i	0.330485	−	0.943811i	$-0.392788\pi$
$593$	−16.2975	−	22.4316i	−0.669258	−	0.921155i	−0.999743	+	0.0226563i	$0.992788\pi$
$594$	−1.74453	+	2.74894i	−0.0715789	+	0.112790i
$595$	61.5944	−	46.1789i	2.52512	−	1.89315i
$596$	−10.2193	+	2.62387i	−0.418599	+	0.107478i
$597$	−3.89557	−	15.1722i	−0.159435	−	0.620959i
$598$	−28.3289	+	13.3306i	−1.15845	+	0.545127i
$599$	−11.0492	−	34.0060i	−0.451459	−	1.38945i	−0.875243	−	0.483684i	$-0.839298\pi$
$599$	−11.0492	−	34.0060i	−0.451459	−	1.38945i	0.423784	−	0.905763i	$-0.360702\pi$
$600$	1.99217	−	4.58598i	0.0813300	−	0.187222i
$601$	−4.65851	+	14.3374i	−0.190025	+	0.584836i	−0.999999	−	0.00162988i	$-0.999481\pi$
$601$	−4.65851	+	14.3374i	−0.190025	+	0.584836i	0.809974	+	0.586466i	$0.199481\pi$
$602$	4.34148	+	34.3663i	0.176945	+	1.40067i
$603$	0.162117	−	0.102882i	0.00660191	−	0.00418970i
$604$	−2.04999	+	2.47801i	−0.0834129	+	0.100829i
$605$	−0.777129	+	0.442545i	−0.0315948	+	0.0179920i
$606$	−10.4059	+	4.11998i	−0.422710	+	0.167363i
$607$	14.8218	−	4.81590i	0.601599	−	0.195471i	0.00764529	−	0.999971i	$-0.497566\pi$
$607$	14.8218	−	4.81590i	0.601599	−	0.195471i	0.593953	+	0.804500i	$0.297566\pi$
$608$	−6.02296	−	3.82229i	−0.244263	−	0.155014i
$609$	−0.950578	+	2.02008i	−0.0385194	+	0.0818578i
$610$	22.0035	+	9.95352i	0.890894	+	0.403006i
$611$	−22.0341	+	20.6914i	−0.891405	+	0.837085i
$612$	−5.05180	+	5.37962i	−0.204207	+	0.217458i
$613$	1.29154	−	0.246374i	0.0521648	−	0.00995097i	−0.161233	−	0.986916i	$-0.551547\pi$
$613$	1.29154	−	0.246374i	0.0521648	−	0.00995097i	0.213398	+	0.976965i	$0.431547\pi$
$614$	−7.54886	−	4.15002i	−0.304647	−	0.167481i
$615$	−4.03503	−	2.47656i	−0.162708	−	0.0998646i
$616$	−11.0721	−	10.3974i	−0.446106	−	0.418922i
$617$	22.9451	−	1.44358i	0.923734	−	0.0581164i	0.406205	−	0.913782i	$-0.366852\pi$
$617$	22.9451	−	1.44358i	0.923734	−	0.0581164i	0.517529	+	0.855666i	$0.326852\pi$
$618$	2.20919	+	0.717809i	0.0888666	+	0.0288745i
$619$	30.5529	+	36.9321i	1.22802	+	1.48443i	0.820918	+	0.571046i	$0.193462\pi$
$619$	30.5529	+	36.9321i	1.22802	+	1.48443i	0.407107	+	0.913381i	$0.366538\pi$
$620$	1.03427	−	21.6096i	0.0415371	−	0.867863i
$621$	3.75282	+	5.91350i	0.150595	+	0.237301i
$622$	2.50022	−	6.31483i	0.100250	−	0.253202i
$623$	15.6696	−	28.5029i	0.627789	−	1.14194i
$624$	4.47024			0.178953
$625$	24.5439	+	4.75337i	0.981758	+	0.190135i
$626$	−17.0686			−0.682199
$627$	−11.1887	+	20.3521i	−0.446832	+	0.812784i
$628$	−3.71097	+	9.37284i	−0.148084	+	0.374017i
$629$	−25.3789	−	39.9908i	−1.01192	−	1.59454i
$630$	−0.498700	+	10.4197i	−0.0198687	+	0.415130i
$631$	25.6968	+	31.0621i	1.02297	+	1.23656i	0.971290	+	0.237899i	$0.0764589\pi$
$631$	25.6968	+	31.0621i	1.02297	+	1.23656i	0.0516840	+	0.998663i	$0.483541\pi$
$632$	−3.09317	−	1.00503i	−0.123040	−	0.0399781i
$633$	16.6095	−	1.04498i	0.660167	−	0.0415342i
$634$	−8.25065	−	7.74788i	−0.327675	−	0.307707i
$635$	29.4687	+	18.0868i	1.16943	+	0.717755i
$636$	0.572866	+	0.314936i	0.0227156	+	0.0124880i
$637$	64.8281	−	12.3666i	2.56858	−	0.489983i
$638$	−1.06658	+	1.13580i	−0.0422264	+	0.0449666i
$639$	−3.53911	+	3.32344i	−0.140005	+	0.131473i
$640$	−2.03731	−	0.921602i	−0.0805319	−	0.0364295i
$641$	−15.7166	+	33.3996i	−0.620770	+	1.31920i	0.309000	+	0.951062i	$0.400006\pi$
$641$	−15.7166	+	33.3996i	−0.620770	+	1.31920i	−0.929770	+	0.368141i	$0.879994\pi$
$642$	3.23330	+	2.05191i	0.127608	+	0.0809825i
$643$	−2.39253	+	0.777380i	−0.0943522	+	0.0306569i	−0.355813	−	0.934557i	$-0.615796\pi$
$643$	−2.39253	+	0.777380i	−0.0943522	+	0.0306569i	0.261460	+	0.965214i	$0.415796\pi$
$644$	−30.3793	+	12.0280i	−1.19711	+	0.473970i
$645$	14.4278	−	8.21606i	0.568093	−	0.323507i
$646$	−33.5560	+	40.5622i	−1.32024	+	1.59590i
$647$	−22.1036	+	14.0274i	−0.868981	+	0.551472i	−0.893925	−	0.448217i	$-0.852059\pi$
$647$	−22.1036	+	14.0274i	−0.868981	+	0.551472i	0.0249437	+	0.999689i	$0.492059\pi$
$648$	−0.125333	−	0.992115i	−0.00492355	−	0.0389739i
$649$	3.11125	−	9.57546i	0.122127	−	0.375870i
$650$	4.84518	+	21.8197i	0.190043	+	0.855840i
$651$	13.9479	+	42.9271i	0.546659	+	1.68244i
$652$	13.6875	−	6.44086i	0.536044	−	0.252243i
$653$	5.70755	+	22.2294i	0.223354	+	0.869905i	0.977107	+	0.212748i	$0.0682412\pi$
$653$	5.70755	+	22.2294i	0.223354	+	0.869905i	−0.753754	+	0.657157i	$0.771759\pi$
$654$	1.08107	−	0.277573i	0.0422733	−	0.0108540i
$655$	−4.67905	+	3.50800i	−0.182826	+	0.137069i
$656$	−1.13451	+	1.78770i	−0.0442950	+	0.0697978i
$657$	−4.96676	−	6.83616i	−0.193772	−	0.266704i
$658$	−24.3054	+	20.1072i	−0.947522	+	0.783858i
$659$	−28.5016	+	15.6689i	−1.11026	+	0.610373i	−0.927889	−	0.372856i	$-0.878379\pi$
$659$	−28.5016	+	15.6689i	−1.11026	+	0.610373i	−0.182375	+	0.983229i	$0.558379\pi$
$660$	−2.57812	+	6.80835i	−0.100353	+	0.265015i
$661$	−4.81686	+	25.2509i	−0.187354	+	0.982146i	0.757049	+	0.653358i	$0.226640\pi$
$661$	−4.81686	+	25.2509i	−0.187354	+	0.982146i	−0.944404	+	0.328788i	$0.893360\pi$
$662$	−28.0993	−	13.2225i	−1.09211	−	0.513908i
$663$	4.13466	−	32.7292i	0.160577	−	1.27110i
$664$	−2.10971	−	4.48337i	−0.0818728	−	0.173989i
$665$	1.11668	+	74.4048i	0.0433028	+	2.88529i
$666$	6.36748	+	0.804400i	0.246735	+	0.0311699i
$667$	1.23386	+	3.11637i	0.0477752	+	0.120666i
$668$	3.42094	−	4.70852i	0.132360	−	0.182178i
$669$	−0.444056	−	7.05807i	−0.0171682	−	0.272881i
$670$	0.308530	−	0.298567i	0.0119196	−	0.0115347i
$671$	−32.6938	−	12.9444i	−1.26213	−	0.499713i
$672$	4.65595	+	0.292927i	0.179607	+	0.0112999i
$673$	21.3538	+	22.7395i	0.823130	+	0.876544i	0.994071	−	0.108737i	$-0.0346806\pi$
$673$	21.3538	+	22.7395i	0.823130	+	0.876544i	−0.170941	+	0.985281i	$0.554681\pi$
$674$	−22.2964	−	16.1993i	−0.858826	−	0.623974i
$675$	4.70677	−	1.68709i	0.181164	−	0.0649362i
$676$	−5.64939	+	4.10452i	−0.217284	+	0.157866i
$677$	22.5451	+	4.30071i	0.866479	+	0.165290i	0.601411	−	0.798940i	$-0.294606\pi$
$677$	22.5451	+	4.30071i	0.866479	+	0.165290i	0.265068	+	0.964230i	$0.414606\pi$
$678$	−1.60664	−	1.32913i	−0.0617028	−	0.0510450i
$679$	−4.20646	+	66.8598i	−0.161429	+	2.56584i
$680$	−8.63196	+	14.0639i	−0.331021	+	0.539328i
$681$	−6.89828	−	1.77118i	−0.264343	−	0.0678717i
$682$			31.5002i			1.20620i
$683$	−3.93795	+	15.3373i	−0.150682	+	0.586866i	0.847725	+	0.530436i	$0.177972\pi$
$683$	−3.93795	+	15.3373i	−0.150682	+	0.586866i	−0.998407	+	0.0564301i	$0.982028\pi$
$684$	−1.33667	−	7.00708i	−0.0511090	−	0.267923i
$685$	−1.99709	−	14.1031i	−0.0763047	−	0.538853i
$686$	35.9330	−	4.53940i	1.37193	−	0.173315i
$687$	−8.99774	−	16.3668i	−0.343285	−	0.624434i
$688$	−3.57709	−	6.50671i	−0.136375	−	0.248066i
$689$	−2.89928	+	0.366264i	−0.110454	+	0.0139535i
$690$	10.8908	+	11.2542i	0.414605	+	0.428439i
$691$	2.90999	+	15.2547i	0.110701	+	0.580315i	0.993805	+	0.111138i	$0.0354495\pi$
$691$	2.90999	+	15.2547i	0.110701	+	0.580315i	−0.883104	+	0.469177i	$0.844550\pi$
$692$	−3.21126	+	12.5070i	−0.122074	+	0.475446i
$693$		−	15.1887i		−	0.576970i
$694$	−18.9423	−	4.86357i	−0.719041	−	0.184618i
$695$	−26.5932	−	31.1809i	−1.00874	−	1.18276i
$696$	0.0300491	−	0.477617i	0.00113901	−	0.0181040i
$697$	12.0394	+	9.95988i	0.456026	+	0.377257i
$698$	−16.6890	−	3.18359i	−0.631687	−	0.120501i
$699$	−17.2664	+	12.5448i	−0.653075	+	0.474487i
$700$	3.61665	+	23.0437i	0.136697	+	0.870969i
$701$	22.7904	+	16.5582i	0.860780	+	0.625393i	0.928097	−	0.372338i	$-0.121444\pi$
$701$	22.7904	+	16.5582i	0.860780	+	0.625393i	−0.0673169	+	0.997732i	$0.521444\pi$
$702$	3.06009	+	3.25866i	0.115496	+	0.122990i
$703$	45.6927	+	2.87474i	1.72333	+	0.108423i
$704$	3.02714	+	1.19853i	0.114090	+	0.0451713i
$705$	13.3573	+	7.08429i	0.503063	+	0.266810i
$706$	0.0710545	+	1.12938i	0.00267417	+	0.0425047i
$707$	30.6892	−	42.2400i	1.15418	−	1.58860i
$708$	1.13840	+	2.87526i	0.0427836	+	0.108059i
$709$	2.07588	+	0.262245i	0.0779613	+	0.00984880i	0.164217	−	0.986424i	$-0.447490\pi$
$709$	2.07588	+	0.262245i	0.0779613	+	0.00984880i	−0.0862558	+	0.996273i	$0.527490\pi$
$710$	−6.24848	+	8.87745i	−0.234501	+	0.333165i
$711$	−1.38479	−	2.94282i	−0.0519335	−	0.110364i
$712$	−0.873842	+	6.91717i	−0.0327486	+	0.259232i
$713$	61.3138	+	28.8521i	2.29622	+	1.08052i
$714$	6.45112	−	33.8180i	0.241427	−	1.26561i
$715$	−8.56546	−	31.3965i	−0.320330	−	1.17416i
$716$	17.8444	−	9.81002i	0.666875	−	0.366617i
$717$	3.97051	−	3.28469i	0.148281	−	0.122669i
$718$	−4.86251	−	6.69267i	−0.181467	−	0.249768i
$719$	24.1663	−	38.0800i	0.901252	−	1.42015i	−0.00619551	−	0.999981i	$-0.501972\pi$
$719$	24.1663	−	38.0800i	0.901252	−	1.42015i	0.907448	−	0.420165i	$-0.138028\pi$
$720$	−0.722818	−	2.11602i	−0.0269378	−	0.0788593i
$721$	−10.4961	+	2.69495i	−0.390897	+	0.100365i
$722$	−7.92970	−	30.8842i	−0.295113	−	1.14939i
$723$	4.67907	−	2.20181i	0.174017	−	0.0818860i
$724$	4.37695	+	13.4709i	0.162668	+	0.500641i
$725$	2.36387	−	0.371004i	0.0877919	−	0.0137787i
$726$	−0.123590	+	0.380369i	−0.00458684	+	0.0141168i
$727$	3.56573	+	28.2256i	0.132245	+	1.04683i	0.908932	+	0.416944i	$0.136899\pi$
$727$	3.56573	+	28.2256i	0.132245	+	1.04683i	−0.776687	+	0.629887i	$0.783101\pi$
$728$	−17.6079	+	11.1743i	−0.652592	+	0.414148i
$729$	0.637424	−	0.770513i	0.0236083	−	0.0285375i
$730$	−13.9662	−	12.7262i	−0.516912	−	0.471016i
$731$	−50.9480	+	20.1717i	−1.88438	+	0.746079i
$732$	10.2716	−	3.33745i	0.379650	−	0.123356i
$733$	−8.20368	−	5.20621i	−0.303010	−	0.192296i	0.375625	−	0.926772i	$-0.377428\pi$
$733$	−8.20368	−	5.20621i	−0.303010	−	0.192296i	−0.678635	+	0.734476i	$0.737428\pi$
$734$	−3.61891	+	7.69057i	−0.133576	+	0.283864i
$735$	−16.3362	−	28.6872i	−0.602571	−	1.05814i
$736$	5.10555	−	4.79443i	0.188193	−	0.176725i
$737$	−0.427932	+	0.455701i	−0.0157631	+	0.0167860i
$738$	−2.07980	+	0.396743i	−0.0765584	+	0.0146043i
$739$	47.0805	+	25.8827i	1.73189	+	0.952112i	0.939816	+	0.341682i	$0.110996\pi$
$739$	47.0805	+	25.8827i	1.73189	+	0.952112i	0.792070	+	0.610431i	$0.209004\pi$
$740$	14.3078	−	1.11596i	0.525966	−	0.0410235i
$741$	23.2455	+	21.8289i	0.853944	+	0.801906i
$742$	−3.04372	+	0.191495i	−0.111739	+	0.00703000i
$743$	−10.9046	−	3.54313i	−0.400052	−	0.129985i	0.102079	−	0.994776i	$-0.467451\pi$
$743$	−10.9046	−	3.54313i	−0.400052	−	0.129985i	−0.502131	+	0.864791i	$0.667451\pi$
$744$	−6.16719	−	7.45485i	−0.226100	−	0.273308i
$745$	−22.0634	−	8.35475i	−0.808341	−	0.306094i
$746$	2.58013	+	4.06563i	0.0944653	+	0.148853i
$747$	1.82404	−	4.60700i	0.0667381	−	0.168561i
$748$	11.5750	−	21.0549i	0.423225	−	0.769844i
$749$	−17.8649			−0.652769
$750$	9.54507	−	5.82165i	0.348537	−	0.212577i
$751$	31.5915			1.15279			0.576396	−	0.817171i	$-0.304459\pi$
$751$	31.5915			1.15279			0.576396	+	0.817171i	$0.304459\pi$
$752$	3.25748	−	5.92533i	0.118788	−	0.216074i
$753$	−5.08050	+	12.8319i	−0.185144	+	0.467620i
$754$	1.14628	+	1.80626i	0.0417452	+	0.0657800i
$755$	−6.93776	+	1.89273i	−0.252491	+	0.0688835i
$756$	2.97368	+	3.59456i	0.108152	+	0.130733i
$757$	−39.0245	−	12.6798i	−1.41837	−	0.460857i	−0.503286	−	0.864120i	$-0.667876\pi$
$757$	−39.0245	−	12.6798i	−1.41837	−	0.460857i	−0.915084	+	0.403263i	$0.867876\pi$
$758$	19.7307	−	1.24135i	0.716651	−	0.0450879i
$759$	−16.6225	−	15.6096i	−0.603358	−	0.566591i
$760$	−6.09379	−	14.7409i	−0.221045	−	0.534710i
$761$	4.34006	+	2.38597i	0.157327	+	0.0864913i	0.558472	−	0.829523i	$-0.311388\pi$
$761$	4.34006	+	2.38597i	0.157327	+	0.0864913i	−0.401145	+	0.916014i	$0.631388\pi$
$762$	15.1892	−	2.89749i	0.550247	−	0.104965i
$763$	−3.56441	+	3.79571i	−0.129040	+	0.137414i
$764$	12.3802	−	11.6258i	0.447900	−	0.420606i
$765$	−16.1612	+	3.33500i	−0.584308	+	0.120577i
$766$	−9.83504	+	20.9005i	−0.355354	+	0.755167i
$767$	−11.6719	−	7.40720i	−0.421447	−	0.267459i
$768$	−0.951057	+	0.309017i	−0.0343183	+	0.0111507i
$769$	23.7190	−	9.39102i	0.855329	−	0.338649i	0.100793	−	0.994907i	$-0.467862\pi$
$769$	23.7190	−	9.39102i	0.855329	−	0.338649i	0.754536	+	0.656259i	$0.227862\pi$
$770$	−6.86393	−	33.2621i	−0.247359	−	1.19868i
$771$	9.10607	−	11.0074i	0.327947	−	0.396420i
$772$	−1.25386	+	0.795721i	−0.0451273	+	0.0286386i
$773$	2.82969	+	22.3993i	0.101777	+	0.805647i	0.957544	+	0.288286i	$0.0930855\pi$
$773$	2.82969	+	22.3993i	0.101777	+	0.805647i	−0.855767	+	0.517361i	$0.826915\pi$
$774$	2.29450	−	7.06174i	0.0824740	−	0.253829i
$775$	29.7035	−	38.1829i	1.06698	−	1.37157i
$776$	−4.43751	−	13.6572i	−0.159297	−	0.490267i
$777$	−27.0918	+	12.7484i	−0.971912	+	0.457347i
$778$	1.07216	+	4.17580i	0.0384389	+	0.149710i
$779$	−14.6291	+	3.75612i	−0.524143	+	0.134577i
$780$	8.17399	+	5.75334i	0.292676	+	0.206003i
$781$	8.46961	−	13.3460i	0.303066	−	0.477556i
$782$	−30.3805	−	41.8152i	−1.08641	−	1.49531i
$783$	0.368738	−	0.305046i	0.0131776	−	0.0109015i
$784$	−12.9375	+	7.11244i	−0.462053	+	0.254016i
$785$	−18.8488	+	12.3624i	−0.672743	+	0.441235i
$786$	−0.490063	+	2.56900i	−0.0174800	+	0.0916332i
$787$	−18.6053	−	8.75500i	−0.663208	−	0.312082i	0.0645513	−	0.997914i	$-0.479438\pi$
$787$	−18.6053	−	8.75500i	−0.663208	−	0.312082i	−0.727760	+	0.685832i	$0.759438\pi$
$788$	1.25354	−	9.92276i	0.0446554	−	0.353484i
$789$	0.683185	+	1.45184i	0.0243220	+	0.0516869i
$790$	−4.36247	−	5.81876i	−0.155210	−	0.207022i
$791$	9.65089	+	1.21919i	0.343146	+	0.0433494i
$792$	1.19853	+	3.02714i	0.0425879	+	0.107565i
$793$	−28.3780	+	39.0590i	−1.00773	+	1.38703i
$794$	−0.956651	−	15.2055i	−0.0339503	−	0.539624i
$795$	0.642174	+	1.31317i	0.0227756	+	0.0465733i
$796$	−14.5644	−	5.76644i	−0.516220	−	0.204386i
$797$	27.0914	+	1.70445i	0.959628	+	0.0603747i	0.534872	−	0.844933i	$-0.320360\pi$
$797$	27.0914	+	1.70445i	0.959628	+	0.0603747i	0.424756	+	0.905308i	$0.360360\pi$
$798$	22.7808	+	24.2590i	0.806430	+	0.858761i
$799$	−40.3698	−	29.3304i	−1.42818	−	1.03764i
$800$	−2.53917	−	4.30727i	−0.0897733	−	0.152285i
$801$	−5.64059	+	4.09813i	−0.199300	+	0.144800i
$802$	21.4789	+	4.09731i	0.758445	+	0.144681i
$803$	21.1977	+	17.5363i	0.748051	+	0.618842i
$804$	0.0120562	−	0.191628i	0.000425190	−	0.00675820i
$805$	−71.0301	−	17.1055i	−2.50348	−	0.602889i
$806$	41.8916	+	10.7559i	1.47557	+	0.378861i
$807$			22.0491i			0.776164i
$808$	−2.78329	+	10.8402i	−0.0979158	+	0.381357i
$809$	−9.07346	−	47.5647i	−0.319006	−	1.67229i	−0.675014	−	0.737804i	$-0.735863\pi$
$809$	−9.07346	−	47.5647i	−0.319006	−	1.67229i	0.356009	−	0.934483i	$-0.384137\pi$
$810$	1.04771	−	1.97543i	0.0368127	−	0.0694094i
$811$	−30.9491	+	3.90978i	−1.08677	+	0.137291i	−0.648248	−	0.761429i	$-0.724498\pi$
$811$	−30.9491	+	3.90978i	−1.08677	+	0.137291i	−0.438522	+	0.898720i	$0.644498\pi$
$812$	1.07554	+	1.95641i	0.0377442	+	0.0686565i
$813$	−1.40116	−	2.54870i	−0.0491408	−	0.0893868i
$814$	−20.7311	+	2.61894i	−0.726624	+	0.0917939i
$815$	33.3177	+	5.83894i	1.16707	+	0.204529i
$816$	1.38283	+	7.24906i	0.0484088	+	0.253768i
$817$	13.1723	−	51.3028i	0.460841	−	1.79486i
$818$			10.3013i			0.360175i
$819$	−20.1992	−	5.18627i	−0.705816	−	0.181223i
$820$	−4.37531	+	1.80872i	−0.152792	+	0.0631633i
$821$	−0.891216	+	14.1655i	−0.0311036	+	0.494378i	0.951379	+	0.308023i	$0.0996674\pi$
$821$	−0.891216	+	14.1655i	−0.0311036	+	0.494378i	−0.982482	+	0.186355i	$0.940333\pi$
$822$	−4.90819	−	4.06041i	−0.171193	−	0.141623i
$823$	−11.7060	−	2.23305i	−0.408047	−	0.0778391i	−0.0207286	−	0.999785i	$-0.506599\pi$
$823$	−11.7060	−	2.23305i	−0.408047	−	0.0778391i	−0.387318	+	0.921946i	$0.626599\pi$
$824$	1.87925	−	1.36535i	0.0654667	−	0.0475644i
$825$	−13.4767	+	9.13119i	−0.469200	+	0.317907i
$826$	−11.6714	−	8.47976i	−0.406100	−	0.295049i
$827$	19.7113	+	20.9904i	0.685431	+	0.729909i	0.973749	−	0.227625i	$-0.0730961\pi$
$827$	19.7113	+	20.9904i	0.685431	+	0.729909i	−0.288318	+	0.957535i	$0.593096\pi$
$828$	6.98997	+	0.439772i	0.242918	+	0.0152831i
$829$	24.5056	+	9.70244i	0.851113	+	0.336980i	0.752859	−	0.658182i	$-0.228674\pi$
$829$	24.5056	+	9.70244i	0.851113	+	0.336980i	0.0982541	+	0.995161i	$0.468674\pi$
$830$	1.91256	−	10.9133i	0.0663858	−	0.378806i
$831$	−0.896007	−	14.2416i	−0.0310821	−	0.494036i
$832$	2.62754	−	3.61650i	0.0910936	−	0.125380i
$833$	40.1081	+	101.301i	1.38966	+	3.50989i
$834$	−18.1828	−	2.29702i	−0.629618	−	0.0795392i
$835$	12.3153	−	4.20684i	0.426190	−	0.145584i
$836$	9.88866	+	21.0145i	0.342006	+	0.726801i
$837$	1.21262	−	9.59889i	0.0419143	−	0.331786i
$838$	7.67057	+	3.60950i	0.264976	+	0.124688i
$839$	0.0841587	−	0.441175i	0.00290548	−	0.0152311i	−0.980805	−	0.194991i	$-0.937532\pi$
$839$	0.0841587	−	0.441175i	0.00290548	−	0.0152311i	0.983710	+	0.179760i	$0.0575322\pi$
$840$	8.13656	+	6.52799i	0.280738	+	0.225237i
$841$	−25.2122	+	13.8605i	−0.869386	+	0.477949i
$842$	−4.22579	+	3.49587i	−0.145630	+	0.120476i
$843$	11.3429	+	15.6122i	0.390671	+	0.537713i
$844$	8.91740	−	14.0516i	0.306950	−	0.483675i
$845$	−15.6128	+	0.234318i	−0.537096	+	0.00806080i
$846$	6.54927	−	1.68157i	0.225169	−	0.0578135i
$847$	−0.464006	−	1.80718i	−0.0159434	−	0.0620955i
$848$	0.591511	−	0.278344i	0.0203126	−	0.00955837i
$849$	−6.37091	−	19.6077i	−0.218649	−	0.672933i
$850$	−33.8846	+	14.6068i	−1.16223	+	0.501010i
$851$	−13.8906	+	42.7509i	−0.476164	+	1.46548i
$852$	0.608487	+	4.81667i	0.0208464	+	0.165016i
$853$	−0.757073	+	0.480453i	−0.0259217	+	0.0164504i	−0.548725	−	0.836003i	$-0.684886\pi$
$853$	−0.757073	+	0.480453i	−0.0259217	+	0.0164504i	0.522803	+	0.852454i	$0.324886\pi$
$854$	−32.1164	+	38.8221i	−1.09900	+	1.32846i
$855$	6.57419	−	14.5331i	0.224833	−	0.497020i
$856$	3.56051	−	1.40971i	0.121696	−	0.0481828i
$857$	30.5310	−	9.92013i	1.04292	−	0.338865i	0.263034	−	0.964787i	$-0.415277\pi$
$857$	30.5310	−	9.92013i	1.04292	−	0.338865i	0.779886	+	0.625922i	$0.215277\pi$
$858$	−12.2884	−	7.79847i	−0.419520	−	0.266235i
$859$	12.2650	−	26.0644i	0.418476	−	0.889306i	−0.578795	−	0.815473i	$-0.696477\pi$
$859$	12.2650	−	26.0644i	0.418476	−	0.889306i	0.997271	−	0.0738330i	$-0.0235232\pi$
$860$	1.83350	−	16.5016i	0.0625219	−	0.562700i
$861$	7.20041	−	6.76164i	0.245389	−	0.230436i
$862$	17.1404	−	18.2527i	0.583804	−	0.621688i
$863$	−15.5349	+	2.96344i	−0.528813	+	0.100877i	−0.444872	−	0.895594i	$-0.646751\pi$
$863$	−15.5349	+	2.96344i	−0.528813	+	0.100877i	−0.0839412	+	0.996471i	$0.526751\pi$
$864$	−0.876307	−	0.481754i	−0.0298126	−	0.0163896i
$865$	−21.9689	+	18.7366i	−0.746965	+	0.637063i
$866$	16.1132	+	15.1313i	0.547549	+	0.514183i
$867$	37.3872	−	2.35220i	1.26973	−	0.0798849i
$868$	42.9271	+	13.9479i	1.45704	+	0.473421i
$869$	6.74964	+	8.15891i	0.228966	+	0.276772i
$870$	0.669654	−	0.834666i	0.0227034	−	0.0282978i
$871$	0.459909	+	0.724701i	0.0155834	+	0.0245555i
$872$	0.410878	−	1.03776i	0.0139141	−	0.0351430i
$873$	6.91802	−	12.5838i	0.234140	−	0.425898i
$874$	49.9611			1.68996
$875$	−23.0448	+	46.7910i	−0.779056	+	1.58182i
$876$	−8.44996			−0.285498
$877$	−12.8659	+	23.4030i	−0.434451	+	0.790263i	−0.999392	−	0.0348681i	$-0.988899\pi$
$877$	−12.8659	+	23.4030i	−0.434451	+	0.790263i	0.564941	+	0.825131i	$0.308899\pi$
$878$	4.65194	−	11.7495i	0.156995	−	0.396525i
$879$	0.203916	+	0.321320i	0.00687792	+	0.0108379i
$880$	3.99269	+	6.08759i	0.134594	+	0.205212i
$881$	−9.58955	−	11.5918i	−0.323080	−	0.390537i	0.583820	−	0.811883i	$-0.301558\pi$
$881$	−9.58955	−	11.5918i	−0.323080	−	0.390537i	−0.906900	+	0.421347i	$0.861558\pi$
$882$	−14.0411	−	4.56222i	−0.472787	−	0.153618i
$883$	−44.4558	+	2.79692i	−1.49606	+	0.0941240i	−0.789596	−	0.613627i	$-0.789710\pi$
$883$	−44.4558	+	2.79692i	−1.49606	+	0.0941240i	−0.706462	+	0.707751i	$0.749710\pi$
$884$	−24.0482	−	22.5828i	−0.808829	−	0.759541i
$885$	−1.61896	+	6.72268i	−0.0544207	+	0.225980i
$886$	30.7394	+	16.8991i	1.03271	+	0.567737i
$887$	−3.09354	+	0.590125i	−0.103871	+	0.0198145i	−0.239055	−	0.971006i	$-0.576838\pi$
$887$	−3.09354	+	0.590125i	−0.103871	+	0.0198145i	0.135184	+	0.990821i	$0.456838\pi$
$888$	4.39348	−	4.67859i	0.147436	−	0.157003i
$889$	−52.5861	+	49.3817i	−1.76368	+	1.65621i
$890$	−10.5005	+	11.5236i	−0.351977	+	0.386273i
$891$	−1.38624	+	2.94591i	−0.0464408	+	0.0986917i
$892$	−5.97111	−	3.78938i	−0.199928	−	0.126878i
$893$	45.8735	−	14.9052i	1.53510	−	0.498783i
$894$	−9.80987	+	3.88400i	−0.328091	+	0.129901i
$895$	45.2549	+	5.02829i	1.51270	+	0.168077i
$896$	2.97368	−	3.59456i	0.0993437	−	0.120086i
$897$	−26.4347	+	16.7760i	−0.882631	+	0.560134i
$898$	−3.72527	−	29.4886i	−0.124314	−	0.984046i
$899$	1.43080	−	4.40355i	0.0477198	−	0.146867i
$900$	1.40169	−	4.79951i	0.0467229	−	0.159984i
$901$	−1.49081	−	4.58825i	−0.0496661	−	0.152857i
$902$	6.23738	−	2.93509i	0.207682	−	0.0977277i
$903$	8.61449	+	33.5512i	0.286672	+	1.11651i
$904$	−2.01965	+	0.518558i	−0.0671726	+	0.0172470i
$905$	−9.33403	+	30.2652i	−0.310274	+	1.00605i
$906$	−1.72325	+	2.71540i	−0.0572510	+	0.0902132i
$907$	7.67160	+	10.5591i	0.254731	+	0.350608i	0.917161	−	0.398516i	$-0.130475\pi$
$907$	7.67160	+	10.5591i	0.254731	+	0.350608i	−0.662430	+	0.749124i	$0.730475\pi$
$908$	−5.48762	+	4.53976i	−0.182113	+	0.150657i
$909$	−9.80746	+	5.39169i	−0.325293	+	0.178831i
$910$	−46.5784	−	2.22931i	−1.54406	−	0.0739008i
$911$	−1.54455	+	8.09681i	−0.0511732	+	0.268259i	−0.998673	−	0.0514965i	$-0.983601\pi$
$911$	−1.54455	+	8.09681i	−0.0511732	+	0.268259i	0.947500	+	0.319756i	$0.103601\pi$
$912$	−6.45453	−	3.03727i	−0.213731	−	0.100574i
$913$	−2.02190	+	16.0050i	−0.0669151	+	0.529688i
$914$	17.9480	+	38.1415i	0.593668	+	1.26161i
$915$	23.0775	+	7.11727i	0.762917	+	0.235290i
$916$	−18.5298	−	2.34086i	−0.612241	−	0.0773441i
$917$	−4.49144	−	11.3441i	−0.148321	−	0.374615i
$918$	−4.33772	+	5.97036i	−0.143166	+	0.197051i
$919$	1.89389	+	30.1026i	0.0624737	+	0.992992i	0.897002	+	0.442026i	$0.145740\pi$
$919$	1.89389	+	30.1026i	0.0624737	+	0.992992i	−0.834528	+	0.550965i	$0.814260\pi$
$920$	15.5063	−	2.19578i	0.511226	−	0.0723927i
$921$	−8.00947	−	3.17117i	−0.263921	−	0.104494i
$922$	−24.3737	−	1.53346i	−0.802706	−	0.0505020i
$923$	−14.8566	−	15.8206i	−0.489010	−	0.520743i
$924$	−12.2879	−	8.92768i	−0.404242	−	0.293699i
$925$	27.5987	+	16.3741i	0.907439	+	0.538376i
$926$	−14.3327	+	10.4133i	−0.471003	+	0.342204i
$927$	2.28173	+	0.435264i	0.0749420	+	0.0142960i
$928$	−0.368738	−	0.305046i	−0.0121044	−	0.0100136i
$929$	2.33914	−	37.1795i	0.0767446	−	1.21982i	−0.751607	−	0.659611i	$-0.770721\pi$
$929$	2.33914	−	37.1795i	0.0767446	−	1.21982i	0.828351	−	0.560209i	$-0.189279\pi$
$930$	−1.68229	−	21.5689i	−0.0551646	−	0.707271i
$931$	−102.007	−	26.1909i	−3.34314	−	0.858373i
$932$			21.3424i			0.699094i
$933$	1.68904	−	6.57839i	0.0552968	−	0.215367i
$934$	−5.92398	−	31.0546i	−0.193838	−	1.01614i
$935$	48.2637	−	23.6022i	1.57839	−	0.771875i
$936$	4.43499	−	0.560269i	0.144962	−	0.0183130i
$937$	23.6696	+	43.0549i	0.773252	+	1.40654i	0.909430	+	0.415856i	$0.136518\pi$
$937$	23.6696	+	43.0549i	0.773252	+	1.40654i	−0.136178	+	0.990684i	$0.543482\pi$
$938$	0.431527	+	0.784944i	0.0140899	+	0.0256293i
$939$	−16.9340	+	2.13926i	−0.552621	+	0.0698123i
$940$	13.5825	−	6.64220i	0.443013	−	0.216645i
$941$	−1.98446	−	10.4029i	−0.0646915	−	0.339125i	0.935196	−	0.354131i	$-0.115223\pi$
$941$	−1.98446	−	10.4029i	−0.0646915	−	0.339125i	−0.999887	+	0.0150060i	$0.995223\pi$
$942$	−2.50698	+	9.76404i	−0.0816818	+	0.318130i
$943$		−	14.8291i		−	0.482903i
$944$	2.99527	+	0.769055i	0.0974877	+	0.0250306i
$945$	0.811164	+	10.4000i	0.0263872	+	0.338312i
$946$	−1.51794	+	24.1269i	−0.0493524	+	0.784433i
$947$	39.4826	+	32.6628i	1.28301	+	1.06140i	0.994588	+	0.103896i	$0.0331308\pi$
$947$	39.4826	+	32.6628i	1.28301	+	1.06140i	0.288423	+	0.957503i	$0.406869\pi$
$948$	−3.19475	−	0.609431i	−0.103761	−	0.0197934i
$949$	30.5593	−	22.2026i	0.991996	−	0.720727i
$950$	7.82935	−	34.7973i	0.254018	−	1.12897i
$951$	−9.15666	−	6.65270i	−0.296925	−	0.215729i
$952$	−23.5674	−	25.0968i	−0.763825	−	0.813391i
$953$	1.54511	+	0.0972099i	0.0500509	+	0.00314894i	0.0877962	−	0.996138i	$-0.472018\pi$
$953$	1.54511	+	0.0972099i	0.0500509	+	0.00314894i	−0.0377453	+	0.999287i	$0.512018\pi$
$954$	0.607821	+	0.240653i	0.0196789	+	0.00779144i
$955$	37.6004	−	5.32444i	1.21672	−	0.172295i
$956$	−0.323564	−	5.14290i	−0.0104648	−	0.166333i
$957$	−0.915820	+	1.26052i	−0.0296043	+	0.0407468i
$958$	−3.34837	−	8.45702i	−0.108181	−	0.273234i
$959$	29.4828	+	3.72455i	0.952050	+	0.120272i
$960$	−2.13676	−	0.658992i	−0.0689635	−	0.0212689i
$961$	−26.6577	−	56.6504i	−0.859925	−	1.82743i
$962$	−3.59586	+	28.4642i	−0.115935	+	0.917721i
$963$	3.46497	+	1.63049i	0.111657	+	0.0525419i
$964$	0.968993	−	5.07964i	0.0312092	−	0.163604i
$965$	−3.31684	−	0.158749i	−0.106773	−	0.00511030i
$966$	−28.6322	+	15.7407i	−0.921227	+	0.506449i
$967$	−14.2638	+	11.8000i	−0.458692	+	0.379463i	−0.837878	−	0.545857i	$-0.816204\pi$
$967$	−14.2638	+	11.8000i	−0.458692	+	0.379463i	0.379186	+	0.925321i	$0.376204\pi$
$968$	0.235081	+	0.323562i	0.00755580	+	0.0103997i
$969$	−28.2076	+	44.4481i	−0.906159	+	1.42788i
$970$	9.46318	−	30.6840i	0.303844	−	0.985204i
$971$	20.7618	−	5.33072i	0.666277	−	0.171071i	0.0996214	−	0.995025i	$-0.468237\pi$
$971$	20.7618	−	5.33072i	0.666277	−	0.171071i	0.566656	+	0.823954i	$0.308237\pi$
$972$	−0.248690	−	0.968583i	−0.00797673	−	0.0310673i
$973$	77.3623	−	36.4040i	2.48012	−	1.16706i
$974$	0.177997	+	0.547819i	0.00570340	+	0.0175533i
$975$	7.54171	+	21.0404i	0.241528	+	0.673832i
$976$	3.33745	−	10.2716i	0.106829	−	0.328787i
$977$	−4.85148	−	38.4034i	−0.155213	−	1.22863i	−0.856648	−	0.515901i	$-0.827457\pi$
$977$	−4.85148	−	38.4034i	−0.155213	−	1.22863i	0.701436	−	0.712733i	$-0.252543\pi$
$978$	12.7723	−	8.10557i	0.408414	−	0.259187i
$979$	14.4694	−	17.4905i	0.462443	−	0.558997i
$980$	−32.8106	−	3.64561i	−1.04810	−	0.116455i
$981$	1.03776	−	0.410878i	0.0331331	−	0.0131183i
$982$	−21.7763	+	7.07556i	−0.694911	+	0.225790i
$983$	−45.5110	−	28.8822i	−1.45158	−	0.921198i	−0.999574	−	0.0291800i	$-0.990710\pi$
$983$	−45.5110	−	28.8822i	−1.45158	−	0.921198i	−0.452001	−	0.892018i	$-0.649290\pi$
$984$	−0.901503	+	1.91579i	−0.0287389	+	0.0610732i
$985$	15.0631	−	16.5308i	0.479949	−	0.526715i
$986$	−2.57448	+	2.41760i	−0.0819881	+	0.0769920i
$987$	−21.5936	+	22.9949i	−0.687333	+	0.731935i
$988$	31.3233	−	5.97525i	0.996528	−	0.190098i
$989$	45.5717	+	25.0532i	1.44909	+	0.796646i
$990$	−1.70447	+	7.07779i	−0.0541717	+	0.224947i
$991$	−5.13828	−	4.82517i	−0.163223	−	0.153277i	0.598632	−	0.801024i	$-0.295711\pi$
$991$	−5.13828	−	4.82517i	−0.163223	−	0.153277i	−0.761855	+	0.647748i	$0.775711\pi$
$992$	−9.65609	+	0.607510i	−0.306581	+	0.0192884i
$993$	−29.5349	−	9.59648i	−0.937262	−	0.304535i
$994$	−14.4371	−	17.4514i	−0.457916	−	0.553525i
$995$	−19.2099	−	29.2890i	−0.608994	−	0.928522i
$996$	−2.65499	−	4.18360i	−0.0841267	−	0.132563i
$997$	−0.273243	+	0.690132i	−0.00865368	+	0.0218567i	−0.934039	−	0.357171i	$-0.883741\pi$
$997$	−0.273243	+	0.690132i	−0.00865368	+	0.0218567i	0.925385	+	0.379027i	$0.123741\pi$
$998$	−12.6110	+	22.9393i	−0.399195	+	0.726132i
$999$	6.41809			0.203059

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.b.589.11	yes	280
125.59	even	50	inner	750.2.o.b.559.11	✓	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.b.559.11	✓	280	125.59	even	50	inner
750.2.o.b.589.11	yes	280	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.481754 - 0.876307i) q^{2} +(0.368125 - 0.929776i) q^{3} +(-0.535827 - 0.844328i) q^{4} +(0.106899 - 2.23351i) q^{5} +(-0.637424 - 0.770513i) q^{6} +(4.43682 + 1.44161i) q^{7} +(-0.998027 + 0.0627905i) q^{8} +(-0.728969 - 0.684547i) q^{9} +O(q^{10})\)	\(q+(0.481754 - 0.876307i) q^{2} +(0.368125 - 0.929776i) q^{3} +(-0.535827 - 0.844328i) q^{4} +(0.106899 - 2.23351i) q^{5} +(-0.637424 - 0.770513i) q^{6} +(4.43682 + 1.44161i) q^{7} +(-0.998027 + 0.0627905i) q^{8} +(-0.728969 - 0.684547i) q^{9} +(-1.90574 - 1.16968i) q^{10} +(2.85306 + 1.56848i) q^{11} +(-0.982287 + 0.187381i) q^{12} +(3.06009 - 3.25866i) q^{13} +(3.40075 - 3.19352i) q^{14} +(-2.03731 - 0.921602i) q^{15} +(-0.425779 + 0.904827i) q^{16} +(6.23095 + 3.95428i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(-6.63250 + 2.62599i) q^{19} +(-1.94310 + 1.10652i) q^{20} +(2.97368 - 3.59456i) q^{21} +(2.74894 - 1.74453i) q^{22} +(-0.877808 - 6.94857i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(-4.97715 - 0.477520i) q^{25} +(-1.38138 - 4.25145i) q^{26} +(-0.904827 + 0.425779i) q^{27} +(-1.16018 - 4.51859i) q^{28} +(-0.463526 + 0.119013i) q^{29} +(-1.78909 + 1.34133i) q^{30} +(-5.18422 + 8.16903i) q^{31} +(0.587785 + 0.809017i) q^{32} +(2.50862 - 2.07531i) q^{33} +(6.46695 - 3.55523i) q^{34} +(3.69415 - 9.75559i) q^{35} +(-0.187381 + 0.982287i) q^{36} +(-5.80726 - 2.73269i) q^{37} +(-0.894057 + 7.07719i) q^{38} +(-1.90333 - 4.04479i) q^{39} +(0.0335554 + 2.23582i) q^{40} +(2.10060 + 0.265368i) q^{41} +(-1.71736 - 4.33755i) q^{42} +(-4.36440 + 6.00707i) q^{43} +(-0.204432 - 3.24935i) q^{44} +(-1.60687 + 1.55498i) q^{45} +(-6.51196 - 2.57827i) q^{46} +(-6.74836 - 0.424571i) q^{47} +(0.684547 + 0.728969i) q^{48} +(11.9440 + 8.67786i) q^{49} +(-2.81621 + 4.13146i) q^{50} +(5.97036 - 4.33772i) q^{51} +(-4.39106 - 0.837639i) q^{52} +(-0.503706 - 0.416702i) q^{53} +(-0.0627905 + 0.998027i) q^{54} +(3.80821 - 6.20466i) q^{55} +(-4.51859 - 1.16018i) q^{56} +7.13344i q^{57} +(-0.119013 + 0.463526i) q^{58} +(-0.579463 - 3.03765i) q^{59} +(0.313513 + 2.21398i) q^{60} +(-10.7151 + 1.35363i) q^{61} +(4.66105 + 8.47843i) q^{62} +(-2.24745 - 4.08810i) q^{63} +(0.992115 - 0.125333i) q^{64} +(-6.95114 - 7.18309i) q^{65} +(-0.610071 - 3.19810i) q^{66} +(-0.0477502 + 0.185975i) q^{67} -7.37978i q^{68} +(-6.78376 - 1.74177i) q^{69} +(-6.76922 - 7.93700i) q^{70} +(0.304845 - 4.84537i) q^{71} +(0.770513 + 0.637424i) q^{72} +(8.30029 + 1.58337i) q^{73} +(-5.19234 + 3.77246i) q^{74} +(-2.27620 + 4.45185i) q^{75} +(5.77107 + 4.19293i) q^{76} +(10.3974 + 11.0721i) q^{77} +(-4.46142 - 0.280689i) q^{78} +(3.02396 + 1.19727i) q^{79} +(1.97543 + 1.04771i) q^{80} +(0.0627905 + 0.998027i) q^{81} +(1.24452 - 1.71293i) q^{82} +(1.82404 + 4.60700i) q^{83} +(-4.62837 - 0.584699i) q^{84} +(9.49801 - 13.4942i) q^{85} +(3.16148 + 6.71848i) q^{86} +(-0.0599796 + 0.474788i) q^{87} +(-2.94591 - 1.38624i) q^{88} +(1.30645 - 6.84866i) q^{89} +(0.588526 + 2.15723i) q^{90} +(18.2748 - 10.0467i) q^{91} +(-5.39652 + 4.46439i) q^{92} +(5.68693 + 7.82739i) q^{93} +(-3.62310 + 5.70910i) q^{94} +(5.15618 + 15.0945i) q^{95} +(0.968583 - 0.248690i) q^{96} +(3.57121 + 13.9089i) q^{97} +(13.3586 - 6.28606i) q^{98} +(-1.00609 - 3.09642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q+O(q^{10}) \) 280 * q	\( 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) \) 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more