LMFDB - Embedded newform 750.2.o.b.229.6

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			229.6
Character	$\chi$	$=$	750.229
Dual form			750.2.o.b.619.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.248690 - 0.968583i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(1.73094 + 1.41557i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(2.54786 - 3.50683i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})$	\(q+(-0.248690 - 0.968583i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(1.73094 + 1.41557i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(2.54786 - 3.50683i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(0.940628 - 2.02860i) q^{10} +(-5.83577 + 1.49837i) q^{11} +(-0.770513 + 0.637424i) q^{12} +(-1.91533 - 4.83758i) q^{13} +(-4.03028 - 1.59570i) q^{14} +(1.96553 + 1.06615i) q^{15} +(0.535827 - 0.844328i) q^{16} +(1.66539 - 3.02933i) q^{17} +(-0.587785 - 0.809017i) q^{18} +(0.571804 - 2.99750i) q^{19} +(-2.19879 - 0.406584i) q^{20} +(1.84562 - 3.92213i) q^{21} +(2.90259 + 5.27980i) q^{22} +(9.04165 + 0.568852i) q^{23} +(0.809017 + 0.587785i) q^{24} +(0.992331 + 4.90054i) q^{25} +(-4.20928 + 3.05822i) q^{26} +(0.844328 - 0.535827i) q^{27} +(-0.543279 + 4.30050i) q^{28} +(1.72591 + 0.218034i) q^{29} +(0.543845 - 2.16892i) q^{30} +(-0.253990 - 0.139632i) q^{31} +(-0.951057 - 0.309017i) q^{32} +(-5.45164 + 2.56535i) q^{33} +(-3.34832 - 0.859703i) q^{34} +(9.37436 - 2.46345i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(3.11611 + 1.97754i) q^{37} +(-3.04553 + 0.191608i) q^{38} +(-2.78788 - 4.39300i) q^{39} +(0.153007 + 2.23083i) q^{40} +(0.514850 + 8.18331i) q^{41} +(-4.25790 - 0.812237i) q^{42} +(-5.88894 + 1.91343i) q^{43} +(4.39208 - 4.12444i) q^{44} +(2.13050 + 0.678960i) q^{45} +(-1.69759 - 8.89906i) q^{46} +(7.85906 - 8.36905i) q^{47} +(0.368125 - 0.929776i) q^{48} +(-3.64313 - 11.2124i) q^{49} +(4.49980 - 2.17987i) q^{50} +(1.06825 - 3.28773i) q^{51} +(4.00894 + 3.31649i) q^{52} +(-3.00690 - 1.41494i) q^{53} +(-0.728969 - 0.684547i) q^{54} +(-12.2224 - 5.66734i) q^{55} +(4.30050 - 0.543279i) q^{56} -3.05155i q^{57} +(-0.218034 - 1.72591i) q^{58} +(2.99047 + 3.61486i) q^{59} +(-2.23603 + 0.0126306i) q^{60} +(-0.504929 + 8.02561i) q^{61} +(-0.0720807 + 0.280736i) q^{62} +(1.07799 - 4.19850i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(3.53259 - 11.0849i) q^{65} +(3.84052 + 4.64239i) q^{66} +(0.471734 + 3.73416i) q^{67} +3.45693i q^{68} +(8.98809 - 1.13546i) q^{69} +(-4.71736 - 8.46721i) q^{70} +(-2.81024 - 2.63899i) q^{71} +(0.904827 + 0.425779i) q^{72} +(-4.12486 - 3.41238i) q^{73} +(1.14047 - 3.51001i) q^{74} +(1.89302 + 4.62779i) q^{75} +(0.942981 + 2.90220i) q^{76} +(-9.61419 + 24.2827i) q^{77} +(-3.56167 + 3.79279i) q^{78} +(-0.974780 - 5.10998i) q^{79} +(2.12269 - 0.702984i) q^{80} +(0.728969 - 0.684547i) q^{81} +(7.79817 - 2.53378i) q^{82} +(-12.1116 - 2.31041i) q^{83} +(0.272177 + 4.32612i) q^{84} +(7.17092 - 2.88613i) q^{85} +(3.31784 + 5.22808i) q^{86} +(1.73620 - 0.109232i) q^{87} +(-5.08713 - 3.22839i) q^{88} +(-11.4314 + 13.8182i) q^{89} +(0.127796 - 2.23241i) q^{90} +(-21.8446 - 5.60873i) q^{91} +(-8.19731 + 3.85736i) q^{92} +(-0.275656 - 0.0895660i) q^{93} +(-10.0606 - 5.53086i) q^{94} +(5.23293 - 4.37908i) q^{95} +(-0.992115 - 0.125333i) q^{96} +(-1.81214 + 14.3445i) q^{97} +(-9.95414 + 6.31709i) q^{98} +(-4.87438 + 3.54144i) 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 $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{21}{50}\right)$	$1$

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 $

$2$	−0.248690	−	0.968583i	−0.175850	−	0.684892i
$2$	−0.248690	−	0.968583i	−0.175850	−	0.684892i
$3$	0.982287	−	0.187381i	0.567124	−	0.108185i
$3$	0.982287	−	0.187381i	0.567124	−	0.108185i
$4$	−0.876307	+	0.481754i	−0.438153	+	0.240877i
$5$	1.73094	+	1.41557i	0.774101	+	0.633062i
$5$	1.73094	+	1.41557i	0.774101	+	0.633062i
$6$	−0.425779	−	0.904827i	−0.173824	−	0.369394i
$7$	2.54786	−	3.50683i	0.963000	−	1.32546i	0.0174958	−	0.999847i	$-0.494431\pi$
$7$	2.54786	−	3.50683i	0.963000	−	1.32546i	0.945504	−	0.325609i	$-0.105569\pi$
$8$	0.684547	+	0.728969i	0.242024	+	0.257729i
$9$	0.929776	−	0.368125i	0.309925	−	0.122708i
$10$	0.940628	−	2.02860i	0.297453	−	0.641500i
$11$	−5.83577	+	1.49837i	−1.75955	+	0.451776i	−0.983801	−	0.179264i	$-0.942628\pi$
$11$	−5.83577	+	1.49837i	−1.75955	+	0.451776i	−0.775750	+	0.631040i	$0.782628\pi$
$12$	−0.770513	+	0.637424i	−0.222428	+	0.184008i
$13$	−1.91533	−	4.83758i	−0.531218	−	1.34170i	−0.909381	−	0.415965i	$-0.863444\pi$
$13$	−1.91533	−	4.83758i	−0.531218	−	1.34170i	0.378162	−	0.925739i	$-0.376556\pi$
$14$	−4.03028	−	1.59570i	−1.07714	−	0.426469i
$15$	1.96553	+	1.06615i	0.507499	+	0.275278i
$16$	0.535827	−	0.844328i	0.133957	−	0.211082i
$17$	1.66539	−	3.02933i	0.403916	−	0.734720i	−0.593630	−	0.804738i	$-0.702306\pi$
$17$	1.66539	−	3.02933i	0.403916	−	0.734720i	0.997546	+	0.0700179i	$0.0223056\pi$
$18$	−0.587785	−	0.809017i	−0.138542	−	0.190687i
$19$	0.571804	−	2.99750i	0.131181	−	0.687674i	−0.854553	−	0.519364i	$-0.826169\pi$
$19$	0.571804	−	2.99750i	0.131181	−	0.687674i	0.985734	−	0.168310i	$-0.0538310\pi$
$20$	−2.19879	−	0.406584i	−0.491665	−	0.0909149i
$21$	1.84562	−	3.92213i	0.402746	−	0.855880i
$22$	2.90259	+	5.27980i	0.618835	+	1.12566i
$23$	9.04165	+	0.568852i	1.88531	+	0.118614i	0.963281	−	0.268496i	$-0.0865265\pi$
$23$	9.04165	+	0.568852i	1.88531	+	0.118614i	0.922034	+	0.387110i	$0.126526\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	0.992331	+	4.90054i	0.198466	+	0.980108i
$26$	−4.20928	+	3.05822i	−0.825507	+	0.599766i
$27$	0.844328	−	0.535827i	0.162491	−	0.103120i
$28$	−0.543279	+	4.30050i	−0.102670	+	0.812718i
$29$	1.72591	+	0.218034i	0.320494	+	0.0404878i	0.283935	−	0.958844i	$-0.408360\pi$
$29$	1.72591	+	0.218034i	0.320494	+	0.0404878i	0.0365595	+	0.999331i	$0.488360\pi$
$30$	0.543845	−	2.16892i	0.0992920	−	0.395990i
$31$	−0.253990	−	0.139632i	−0.0456180	−	0.0250787i	0.458781	−	0.888549i	$-0.348286\pi$
$31$	−0.253990	−	0.139632i	−0.0456180	−	0.0250787i	−0.504399	+	0.863470i	$0.668286\pi$
$32$	−0.951057	−	0.309017i	−0.168125	−	0.0546270i
$33$	−5.45164	+	2.56535i	−0.949008	+	0.446569i
$34$	−3.34832	−	0.859703i	−0.574233	−	0.147438i
$35$	9.37436	−	2.46345i	1.58456	−	0.416399i
$36$	−0.637424	+	0.770513i	−0.106237	+	0.128419i
$37$	3.11611	+	1.97754i	0.512285	+	0.325106i	0.766718	−	0.641984i	$-0.221889\pi$
$37$	3.11611	+	1.97754i	0.512285	+	0.325106i	−0.254432	+	0.967091i	$0.581889\pi$
$38$	−3.04553	+	0.191608i	−0.494050	+	0.0310830i
$39$	−2.78788	−	4.39300i	−0.446418	−	0.703443i
$40$	0.153007	+	2.23083i	0.0241926	+	0.352725i
$41$	0.514850	+	8.18331i	0.0804061	+	1.27802i	0.806835	+	0.590776i	$0.201178\pi$
$41$	0.514850	+	8.18331i	0.0804061	+	1.27802i	−0.726429	+	0.687241i	$0.758822\pi$
$42$	−4.25790	−	0.812237i	−0.657008	−	0.125331i
$43$	−5.88894	+	1.91343i	−0.898055	+	0.291796i	−0.721434	−	0.692483i	$-0.756517\pi$
$43$	−5.88894	+	1.91343i	−0.898055	+	0.291796i	−0.176621	+	0.984279i	$0.556517\pi$
$44$	4.39208	−	4.12444i	0.662131	−	0.621782i
$45$	2.13050	+	0.678960i	0.317596	+	0.101213i
$46$	−1.69759	−	8.89906i	−0.250295	−	1.31209i
$47$	7.85906	−	8.36905i	1.14636	−	1.22075i	0.174638	−	0.984633i	$-0.444124\pi$
$47$	7.85906	−	8.36905i	1.14636	−	1.22075i	0.971724	−	0.236119i	$-0.0758755\pi$
$48$	0.368125	−	0.929776i	0.0531342	−	0.134202i
$49$	−3.64313	−	11.2124i	−0.520448	−	1.60177i
$50$	4.49980	−	2.17987i	0.636367	−	0.308280i
$51$	1.06825	−	3.28773i	0.149585	−	0.460375i
$52$	4.00894	+	3.31649i	0.555940	+	0.459914i
$53$	−3.00690	−	1.41494i	−0.413029	−	0.194357i	0.208027	−	0.978123i	$-0.433296\pi$
$53$	−3.00690	−	1.41494i	−0.413029	−	0.194357i	−0.621056	+	0.783766i	$0.713296\pi$
$54$	−0.728969	−	0.684547i	−0.0992001	−	0.0931551i
$55$	−12.2224	−	5.66734i	−1.64807	−	0.764184i
$56$	4.30050	−	0.543279i	0.574678	−	0.0725987i
$57$		−	3.05155i		−	0.404188i
$58$	−0.218034	−	1.72591i	−0.0286292	−	0.226623i
$59$	2.99047	+	3.61486i	0.389327	+	0.470615i	0.928367	−	0.371665i	$-0.121213\pi$
$59$	2.99047	+	3.61486i	0.389327	+	0.470615i	−0.539040	+	0.842280i	$0.681213\pi$
$60$	−2.23603	+	0.0126306i	−0.288671	+	0.00163060i
$61$	−0.504929	+	8.02561i	−0.0646495	+	1.02757i	0.823292	+	0.567618i	$0.192135\pi$
$61$	−0.504929	+	8.02561i	−0.0646495	+	1.02757i	−0.887942	+	0.459956i	$0.847865\pi$
$62$	−0.0720807	+	0.280736i	−0.00915426	+	0.0356535i
$63$	1.07799	−	4.19850i	0.135814	−	0.528961i
$64$	−0.0627905	+	0.998027i	−0.00784881	+	0.124753i
$65$	3.53259	−	11.0849i	0.438164	−	1.37491i
$66$	3.84052	+	4.64239i	0.472735	+	0.571438i
$67$	0.471734	+	3.73416i	0.0576314	+	0.456200i	0.994353	+	0.106124i	$0.0338441\pi$
$67$	0.471734	+	3.73416i	0.0576314	+	0.456200i	−0.936721	+	0.350076i	$0.886156\pi$
$68$			3.45693i			0.419214i
$69$	8.98809	−	1.13546i	1.08204	−	0.136693i
$70$	−4.71736	−	8.46721i	−0.563833	−	1.01202i
$71$	−2.81024	−	2.63899i	−0.333514	−	0.313191i	0.499638	−	0.866234i	$-0.333466\pi$
$71$	−2.81024	−	2.63899i	−0.333514	−	0.313191i	−0.833152	+	0.553044i	$0.813466\pi$
$72$	0.904827	+	0.425779i	0.106635	+	0.0501786i
$73$	−4.12486	−	3.41238i	−0.482778	−	0.399389i	0.363947	−	0.931420i	$-0.381429\pi$
$73$	−4.12486	−	3.41238i	−0.482778	−	0.399389i	−0.846725	+	0.532031i	$0.821429\pi$
$74$	1.14047	−	3.51001i	0.132577	−	0.408030i
$75$	1.89302	+	4.62779i	0.218588	+	0.534371i
$76$	0.942981	+	2.90220i	0.108167	+	0.332905i
$77$	−9.61419	+	24.2827i	−1.09564	+	2.76727i
$78$	−3.56167	+	3.79279i	−0.403279	+	0.429449i
$79$	−0.974780	−	5.10998i	−0.109671	−	0.574917i	−0.994120	−	0.108281i	$-0.965466\pi$
$79$	−0.974780	−	5.10998i	−0.109671	−	0.574917i	0.884449	−	0.466637i	$-0.154534\pi$
$80$	2.12269	−	0.702984i	0.237324	−	0.0785960i
$81$	0.728969	−	0.684547i	0.0809965	−	0.0760608i
$82$	7.79817	−	2.53378i	0.861164	−	0.279809i
$83$	−12.1116	−	2.31041i	−1.32942	−	0.253600i	−0.526747	−	0.850022i	$-0.676588\pi$
$83$	−12.1116	−	2.31041i	−1.32942	−	0.253600i	−0.802671	+	0.596422i	$0.796588\pi$
$84$	0.272177	+	4.32612i	0.0296969	+	0.472019i
$85$	7.17092	−	2.88613i	0.777795	−	0.313044i
$86$	3.31784	+	5.22808i	0.357772	+	0.563758i
$87$	1.73620	−	0.109232i	0.186140	−	0.0117109i
$88$	−5.08713	−	3.22839i	−0.542289	−	0.344147i
$89$	−11.4314	+	13.8182i	−1.21173	+	1.46473i	−0.366422	+	0.930449i	$0.619417\pi$
$89$	−11.4314	+	13.8182i	−1.21173	+	1.46473i	−0.845307	+	0.534280i	$0.820583\pi$
$90$	0.127796	−	2.23241i	0.0134709	−	0.235317i
$91$	−21.8446	−	5.60873i	−2.28993	−	0.587955i
$92$	−8.19731	+	3.85736i	−0.854628	+	0.402158i
$93$	−0.275656	−	0.0895660i	−0.0285842	−	0.00928757i
$94$	−10.0606	−	5.53086i	−1.03767	−	0.570464i
$95$	5.23293	−	4.37908i	0.536887	−	0.449284i
$96$	−0.992115	−	0.125333i	−0.101257	−	0.0127918i
$97$	−1.81214	+	14.3445i	−0.183995	+	1.45647i	0.581774	+	0.813350i	$0.302359\pi$
$97$	−1.81214	+	14.3445i	−0.183995	+	1.45647i	−0.765769	+	0.643116i	$0.777641\pi$
$98$	−9.95414	+	6.31709i	−1.00552	+	0.638122i
$99$	−4.87438	+	3.54144i	−0.489893	+	0.355928i
$100$	−3.23044	−	3.81632i	−0.323044	−	0.381632i
$101$	13.8766	+	10.0819i	1.38077	+	1.00319i	0.996807	+	0.0798447i	$0.0254424\pi$
$101$	13.8766	+	10.0819i	1.38077	+	1.00319i	0.383967	+	0.923347i	$0.374558\pi$
$102$	−3.45011	−	0.217062i	−0.341612	−	0.0214924i
$103$	−4.32188	−	7.86147i	−0.425847	−	0.774613i	0.573147	−	0.819453i	$-0.305722\pi$
$103$	−4.32188	−	7.86147i	−0.425847	−	0.774613i	−0.998994	+	0.0448393i	$0.985722\pi$
$104$	2.21531	−	4.70777i	0.217229	−	0.461635i
$105$	8.74670	−	4.17640i	0.853591	−	0.407574i
$106$	−0.622700	+	3.26431i	−0.0604820	+	0.317058i
$107$	3.41641	+	4.70229i	0.330277	+	0.454588i	0.941570	−	0.336817i	$-0.109350\pi$
$107$	3.41641	+	4.70229i	0.330277	+	0.454588i	−0.611293	+	0.791404i	$0.709350\pi$
$108$	−0.481754	+	0.876307i	−0.0463568	+	0.0843226i
$109$	3.46856	−	5.46558i	0.332228	−	0.523507i	−0.636616	−	0.771181i	$-0.719666\pi$
$109$	3.46856	−	5.46558i	0.332228	−	0.523507i	0.968843	+	0.247674i	$0.0796662\pi$
$110$	−2.44969	+	13.2479i	−0.233569	+	1.26313i
$111$	3.43147	+	1.35862i	0.325701	+	0.128954i
$112$	−1.59570	−	4.03028i	−0.150780	−	0.380826i
$113$	1.85113	−	1.53139i	0.174140	−	0.144061i	−0.546271	−	0.837608i	$-0.683953\pi$
$113$	1.85113	−	1.53139i	0.174140	−	0.144061i	0.720411	+	0.693547i	$0.243953\pi$
$114$	−2.95568	+	0.758890i	−0.276825	+	0.0710766i
$115$	14.8453	+	13.7837i	1.38433	+	1.28534i
$116$	−1.61747	+	0.640401i	−0.150178	+	0.0594597i
$117$	−3.56167	−	3.79279i	−0.329276	−	0.350643i
$118$	2.75759	−	3.79550i	0.253857	−	0.349404i
$119$	−6.38016	−	13.5585i	−0.584868	−	1.24291i
$120$	0.568312	+	2.16264i	0.0518796	+	0.197421i
$121$	22.1717	−	12.1890i	2.01561	−	1.10809i
$122$	7.89904	−	1.50682i	0.715146	−	0.136421i
$123$	2.03913	+	7.94188i	0.183862	+	0.716096i
$124$	0.289842			0.0260286
$125$	−5.21938	+	9.88727i	−0.466836	+	0.884344i
$126$	−4.33468			−0.386164
$127$	2.15475	+	8.39220i	0.191203	+	0.744687i	0.989757	+	0.142763i	$0.0455988\pi$
$127$	2.15475	+	8.39220i	0.191203	+	0.744687i	−0.798554	+	0.601924i	$0.794401\pi$
$128$	0.982287	−	0.187381i	0.0868227	−	0.0165623i
$129$	−5.42609	+	2.98302i	−0.477740	+	0.262640i
$130$	−11.6151	−	0.664916i	−1.01872	−	0.0583170i
$131$	1.13556	+	2.41320i	0.0992147	+	0.210842i	0.948272	−	0.317459i	$-0.102829\pi$
$131$	1.13556	+	2.41320i	0.0992147	+	0.210842i	−0.849057	+	0.528301i	$0.822829\pi$
$132$	3.54144	−	4.87438i	0.308243	−	0.424260i
$133$	−9.05484	−	9.64242i	−0.785154	−	0.836104i
$134$	3.49953	−	1.38556i	0.302313	−	0.119694i
$135$	2.21998	+	0.267718i	0.191066	+	0.0230415i
$136$	3.34832	−	0.859703i	0.287116	−	0.0737189i
$137$	−14.7300	+	12.1857i	−1.25847	+	1.04110i	−0.261352	+	0.965244i	$0.584168\pi$
$137$	−14.7300	+	12.1857i	−1.25847	+	1.04110i	−0.997119	+	0.0758538i	$0.975832\pi$
$138$	−3.33503	−	8.42334i	−0.283897	−	0.717042i
$139$	−2.20168	−	0.871707i	−0.186744	−	0.0739372i	0.272892	−	0.962045i	$-0.412020\pi$
$139$	−2.20168	−	0.871707i	−0.186744	−	0.0739372i	−0.459636	+	0.888108i	$0.652020\pi$
$140$	−7.02803	+	6.67487i	−0.593977	+	0.564129i
$141$	6.15165	−	9.69345i	0.518063	−	0.816336i
$142$	−1.85720	+	3.37824i	−0.155853	+	0.283496i
$143$	18.4259	+	25.3611i	1.54086	+	2.12081i
$144$	0.187381	−	0.982287i	0.0156151	−	0.0818573i
$145$	2.67882	+	2.82055i	0.222464	+	0.234234i
$146$	−2.27936	+	4.84390i	−0.188642	+	0.400884i
$147$	−5.67960	−	10.3312i	−0.468445	−	0.852099i
$148$	−3.68336	−	0.231737i	−0.302770	−	0.0190487i
$149$	−6.08740	−	4.42276i	−0.498699	−	0.362326i	0.309821	−	0.950795i	$-0.399731\pi$
$149$	−6.08740	−	4.42276i	−0.498699	−	0.362326i	−0.808520	+	0.588469i	$0.799731\pi$
$150$	4.01163	−	2.98444i	0.327548	−	0.243678i
$151$	10.4965	−	7.62616i	0.854194	−	0.620608i	−0.0721055	−	0.997397i	$-0.522972\pi$
$151$	10.4965	−	7.62616i	0.854194	−	0.620608i	0.926299	+	0.376789i	$0.122972\pi$
$152$	2.57651	−	1.63510i	0.208983	−	0.132624i
$153$	0.433268	−	3.42967i	0.0350276	−	0.277272i
$154$	25.9107	+	3.27329i	2.08795	+	0.263769i
$155$	−0.241984	−	0.601236i	−0.0194366	−	0.0482925i
$156$	4.55938	+	2.50654i	0.365043	+	0.200684i
$157$	4.88983	+	1.58880i	0.390251	+	0.126800i	0.497569	−	0.867425i	$-0.334226\pi$
$157$	4.88983	+	1.58880i	0.390251	+	0.126800i	−0.107318	+	0.994225i	$0.534226\pi$
$158$	−4.70702	+	2.21496i	−0.374470	+	0.176212i
$159$	−3.21877	−	0.826439i	−0.255265	−	0.0655409i
$160$	−1.20879	−	1.88118i	−0.0955633	−	0.148720i
$161$	25.0317	−	30.2582i	1.97278	−	2.38468i
$162$	−0.844328	−	0.535827i	−0.0663367	−	0.0420985i
$163$	0.424372	−	0.0266992i	0.0332393	−	0.00209124i	−0.0461621	−	0.998934i	$-0.514699\pi$
$163$	0.424372	−	0.0266992i	0.0332393	−	0.00209124i	0.0794015	+	0.996843i	$0.474699\pi$
$164$	−4.39350	−	6.92305i	−0.343075	−	0.540600i
$165$	−13.0679	−	3.27670i	−1.01733	−	0.255091i
$166$	0.774205	+	12.3056i	0.0600900	+	0.955102i
$167$	19.1915	+	3.66097i	1.48508	+	0.283294i	0.865210	−	0.501410i	$-0.167185\pi$
$167$	19.1915	+	3.66097i	1.48508	+	0.283294i	0.619871	+	0.784704i	$0.287185\pi$
$168$	4.12252	−	1.33949i	0.318060	−	0.103344i
$169$	−10.2571	+	9.63207i	−0.789009	+	0.740928i
$170$	−4.57879	−	6.22788i	−0.351177	−	0.477656i
$171$	−0.571804	−	2.99750i	−0.0437269	−	0.229225i
$172$	4.23871	−	4.51377i	0.323199	−	0.344172i
$173$	−5.79524	+	14.6371i	−0.440604	+	1.11284i	0.524602	+	0.851347i	$0.324214\pi$
$173$	−5.79524	+	14.6371i	−0.440604	+	1.11284i	−0.965206	+	0.261490i	$0.915786\pi$
$174$	−0.537575	−	1.65449i	−0.0407535	−	0.125426i
$175$	19.7137	+	9.00595i	1.49021	+	0.680786i
$176$	−1.86185	+	5.73017i	−0.140342	+	0.431928i
$177$	3.61486	+	2.99047i	0.271710	+	0.224778i
$178$	16.2270	+	7.63584i	1.21626	+	0.572330i
$179$	2.66898	+	2.50634i	0.199489	+	0.187333i	0.777853	−	0.628446i	$-0.216309\pi$
$179$	2.66898	+	2.50634i	0.199489	+	0.187333i	−0.578364	+	0.815779i	$0.696309\pi$
$180$	−2.19406	+	0.431398i	−0.163536	+	0.0321545i
$181$	−19.3168	+	2.44028i	−1.43581	+	0.181385i	−0.804410	−	0.594074i	$-0.797518\pi$
$181$	−19.3168	+	2.44028i	−1.43581	+	0.181385i	−0.631398	+	0.775459i	$0.717518\pi$
$182$			22.5531i			1.67175i
$183$	1.00786	+	7.97807i	0.0745035	+	0.589756i
$184$	5.77476	+	6.98049i	0.425721	+	0.514608i
$185$	2.59446	+	7.83408i	0.190749	+	0.575973i
$186$	−0.0181993	+	0.289270i	−0.00133444	+	0.0212103i
$187$	−5.17976	+	20.1738i	−0.378782	+	1.47526i
$188$	−2.85513	+	11.1200i	−0.208232	+	0.811009i
$189$	0.272177	−	4.32612i	0.0197979	−	0.314679i
$190$	−5.54287	−	3.97949i	−0.402122	−	0.288703i
$191$	−3.61282	−	4.36715i	−0.261414	−	0.315996i	0.623433	−	0.781877i	$-0.285737\pi$
$191$	−3.61282	−	4.36715i	−0.261414	−	0.315996i	−0.884847	+	0.465881i	$0.845737\pi$
$192$	0.125333	+	0.992115i	0.00904515	+	0.0715997i
$193$			2.44728i			0.176159i	0.996113	+	0.0880796i	$0.0280730\pi$
$193$			2.44728i			0.176159i	−0.996113	+	0.0880796i	$0.971927\pi$
$194$	14.3445	−	1.81214i	1.02988	−	0.130104i
$195$	1.39293	−	11.5505i	0.0997494	−	0.827146i
$196$	8.59412	+	8.07042i	0.613866	+	0.576458i
$197$	−12.4607	−	5.86358i	−0.887790	−	0.417762i	−0.0728741	−	0.997341i	$-0.523217\pi$
$197$	−12.4607	−	5.86358i	−0.887790	−	0.417762i	−0.814916	+	0.579579i	$0.803217\pi$
$198$	4.64239	+	3.84052i	0.329920	+	0.272934i
$199$	0.101959	−	0.313798i	0.00722769	−	0.0222446i	−0.947378	−	0.320118i	$-0.896277\pi$
$199$	0.101959	−	0.313798i	0.00722769	−	0.0222446i	0.954605	+	0.297874i	$0.0962774\pi$
$200$	−2.89304	+	4.07803i	−0.204569	+	0.288360i
$201$	1.16309	+	3.57962i	0.0820380	+	0.252487i
$202$	6.31423	−	15.9479i	0.444268	−	1.12209i
$203$	5.16199	−	5.49696i	0.362301	−	0.385811i
$204$	0.647764	+	3.39570i	0.0453525	+	0.237746i
$205$	−10.6929	+	14.8936i	−0.746821	+	1.04022i
$206$	−6.53968	+	6.14116i	−0.455641	+	0.427875i
$207$	8.61612	−	2.79955i	0.598862	−	0.194582i
$208$	−5.11079	−	0.974936i	−0.354370	−	0.0675997i
$209$	1.15445	+	18.3495i	0.0798551	+	1.26926i
$210$	−6.22040	−	7.43328i	−0.429249	−	0.512945i
$211$	2.61290	+	4.11727i	0.179879	+	0.283444i	0.922288	−	0.386502i	$-0.126317\pi$
$211$	2.61290	+	4.11727i	0.179879	+	0.283444i	−0.742409	+	0.669947i	$0.766317\pi$
$212$	3.31661	−	0.208664i	0.227786	−	0.0143311i
$213$	−3.25496	−	2.06566i	−0.223026	−	0.141537i
$214$	3.70493	−	4.47849i	0.253264	−	0.306144i
$215$	−12.9020	−	5.02415i	−0.879910	−	0.342644i
$216$	0.968583	+	0.248690i	0.0659037	+	0.0169212i
$217$	−1.13680	+	0.534937i	−0.0771709	+	0.0363139i
$218$	−6.15646	−	2.00036i	−0.416968	−	0.135481i
$219$	−4.69122	−	2.57902i	−0.317003	−	0.174274i
$220$	13.4409	−	0.921878i	0.906183	−	0.0621530i
$221$	−17.8444	−	2.25427i	−1.20034	−	0.151639i
$222$	0.462560	−	3.66154i	0.0310450	−	0.245746i
$223$	−1.77687	+	1.12763i	−0.118988	+	0.0755120i	−0.593989	−	0.804473i	$-0.702448\pi$
$223$	−1.77687	+	1.12763i	−0.118988	+	0.0755120i	0.475001	+	0.879985i	$0.342448\pi$
$224$	−3.50683	+	2.54786i	−0.234310	+	0.170236i
$225$	2.72665	+	4.19110i	0.181777	+	0.279407i
$226$	−1.94363	−	1.41213i	−0.129289	−	0.0939337i
$227$	−21.4627	−	1.35032i	−1.42453	−	0.0896237i	−0.668280	−	0.743909i	$-0.732969\pi$
$227$	−21.4627	−	1.35032i	−1.42453	−	0.0896237i	−0.756247	+	0.654286i	$0.772969\pi$
$228$	1.47010	+	2.67409i	0.0973595	+	0.177096i
$229$	−1.31120	+	2.78645i	−0.0866468	+	0.184134i	−0.943454	−	0.331503i	$-0.892444\pi$
$229$	−1.31120	+	2.78645i	−0.0866468	+	0.184134i	0.856807	+	0.515636i	$0.172444\pi$
$230$	9.65880	−	17.8068i	0.636883	−	1.17415i
$231$	−4.89378	+	25.6541i	−0.321987	+	1.68792i
$232$	1.02253	+	1.40739i	0.0671323	+	0.0923997i
$233$	7.89224	−	14.3559i	0.517038	−	0.940488i	−0.480929	−	0.876759i	$-0.659701\pi$
$233$	7.89224	−	14.3559i	0.517038	−	0.940488i	0.997967	−	0.0637290i	$-0.0202993\pi$
$234$	−2.78788	+	4.39300i	−0.182250	+	0.287179i
$235$	25.4506	−	3.36131i	1.66021	−	0.219268i
$236$	−4.36205	−	1.72706i	−0.283945	−	0.112422i
$237$	−1.91503	−	4.83681i	−0.124394	−	0.314185i
$238$	−11.5459	+	9.55159i	−0.748409	+	0.619137i
$239$	−0.460945	+	0.118350i	−0.0298160	+	0.00765546i	−0.263568	−	0.964641i	$-0.584899\pi$
$239$	−0.460945	+	0.118350i	−0.0298160	+	0.00765546i	0.233752	+	0.972296i	$0.424899\pi$
$240$	1.95337	−	1.08829i	0.126089	−	0.0702485i
$241$	−5.86045	+	2.32031i	−0.377505	+	0.149465i	−0.549211	−	0.835683i	$-0.685072\pi$
$241$	−5.86045	+	2.32031i	−0.377505	+	0.149465i	0.171707	+	0.985148i	$0.445072\pi$
$242$	−17.3200	−	18.4439i	−1.11337	−	1.18562i
$243$	0.587785	−	0.809017i	0.0377064	−	0.0518985i
$244$	−3.42390	−	7.27615i	−0.219192	−	0.465808i
$245$	9.56588	−	24.5652i	0.611142	−	1.56941i
$246$	7.18526	−	3.95013i	0.458116	−	0.251851i
$247$	−15.5959	+	2.97507i	−0.992340	+	0.189299i
$248$	−0.0720807	−	0.280736i	−0.00457713	−	0.0178267i
$249$	−12.3300			−0.781380
$250$	10.8746	+	2.59654i	0.687773	+	0.164220i
$251$	9.13350			0.576502			0.288251	−	0.957555i	$-0.406926\pi$
$251$	9.13350			0.576502			0.288251	+	0.957555i	$0.406926\pi$
$252$	1.07799	+	4.19850i	0.0679070	+	0.264480i
$253$	−53.6174	+	10.2281i	−3.37089	+	0.643032i
$254$	7.59268	−	4.17411i	0.476407	−	0.261907i
$255$	6.50309	−	4.17870i	0.407240	−	0.261680i
$256$	−0.425779	−	0.904827i	−0.0266112	−	0.0565517i
$257$	4.23974	−	5.83550i	0.264468	−	0.364008i	−0.656045	−	0.754722i	$-0.727772\pi$
$257$	4.23974	−	5.83550i	0.264468	−	0.364008i	0.920512	+	0.390714i	$0.127772\pi$
$258$	4.23871	+	4.51377i	0.263891	+	0.281015i
$259$	14.8743	−	5.88916i	0.924245	−	0.365934i
$260$	2.24454	+	11.4156i	0.139201	+	0.707965i
$261$	1.68498	−	0.432629i	0.104297	−	0.0267790i
$262$	2.05498	−	1.70003i	0.126957	−	0.105028i
$263$	6.59860	+	16.6662i	0.406887	+	1.02768i	0.978333	+	0.207039i	$0.0663828\pi$
$263$	6.59860	+	16.6662i	0.406887	+	1.02768i	−0.571446	+	0.820640i	$0.693617\pi$
$264$	−5.60196	−	2.21797i	−0.344777	−	0.136507i
$265$	−3.20183	−	6.70565i	−0.196687	−	0.411925i
$266$	−7.08764	+	11.1683i	−0.434571	+	0.684775i
$267$	−8.63967	+	15.7155i	−0.528739	+	0.961773i
$268$	−2.21233	−	3.04501i	−0.135139	−	0.186003i
$269$	−2.40493	+	12.6071i	−0.146631	+	0.768668i	0.830662	+	0.556777i	$0.187962\pi$
$269$	−2.40493	+	12.6071i	−0.146631	+	0.768668i	−0.977293	+	0.211891i	$0.932038\pi$
$270$	−0.292780	−	2.21682i	−0.0178180	−	0.134911i
$271$	9.60352	−	20.4085i	0.583372	−	1.23973i	−0.367465	−	0.930037i	$-0.619774\pi$
$271$	9.60352	−	20.4085i	0.583372	−	1.23973i	0.950837	−	0.309691i	$-0.100226\pi$
$272$	−1.66539	−	3.02933i	−0.100979	−	0.183680i
$273$	−22.5086	−	1.41612i	−1.36228	−	0.0857076i
$274$	15.4661	+	11.2368i	0.934341	+	0.678839i
$275$	−13.1338	−	27.1115i	−0.792001	−	1.63489i
$276$	−7.32931	+	5.32506i	−0.441173	+	0.320531i
$277$	8.02258	−	5.09128i	0.482030	−	0.305906i	−0.272518	−	0.962151i	$-0.587856\pi$
$277$	8.02258	−	5.09128i	0.482030	−	0.305906i	0.754548	+	0.656245i	$0.227856\pi$
$278$	−0.296785	+	2.34930i	−0.0178000	+	0.140901i
$279$	−0.287556	−	0.0363268i	−0.0172155	−	0.00217483i
$280$	8.21297	+	5.14726i	0.490819	+	0.307608i
$281$	8.67687	+	4.77015i	0.517619	+	0.284563i	0.719073	−	0.694935i	$-0.244567\pi$
$281$	8.67687	+	4.77015i	0.517619	+	0.284563i	−0.201454	+	0.979498i	$0.564567\pi$
$282$	−10.9188	−	3.54772i	−0.650203	−	0.211264i
$283$	16.5371	−	7.78176i	0.983027	−	0.462577i	0.134031	−	0.990977i	$-0.457208\pi$
$283$	16.5371	−	7.78176i	0.983027	−	0.462577i	0.848996	+	0.528400i	$0.177208\pi$
$284$	3.73398	+	0.958722i	0.221571	+	0.0568897i
$285$	4.31968	−	5.28206i	0.255876	−	0.312882i
$286$	19.9820	−	24.1541i	1.18156	−	1.42826i
$287$	30.0092	+	19.0444i	1.77139	+	1.12416i
$288$	−0.998027	+	0.0627905i	−0.0588093	+	0.00369997i
$289$	2.70573	+	4.26356i	0.159161	+	0.250797i
$290$	2.06574	−	3.29610i	0.121305	−	0.193554i
$291$	0.907859	+	14.4300i	0.0532197	+	0.845902i
$292$	5.25857	+	1.00313i	0.307735	+	0.0587035i
$293$	23.0455	−	7.48794i	1.34633	−	0.437450i	0.454875	−	0.890555i	$-0.349684\pi$
$293$	23.0455	−	7.48794i	1.34633	−	0.437450i	0.891457	+	0.453105i	$0.149684\pi$
$294$	−8.59412	+	8.07042i	−0.501219	+	0.470676i
$295$	0.0592563	+	10.4903i	0.00345004	+	0.610771i
$296$	0.691557	+	3.62527i	0.0401959	+	0.210714i
$297$	−4.12444	+	4.39208i	−0.239324	+	0.254854i
$298$	−2.76993	+	6.99605i	−0.160458	+	0.405270i
$299$	−14.5659	−	44.8293i	−0.842369	−	2.59254i
$300$	−3.88833	−	3.14339i	−0.224493	−	0.181484i
$301$	−8.29411	+	25.5266i	−0.478065	+	1.47133i
$302$	−9.99694	−	8.27019i	−0.575259	−	0.475896i
$303$	15.5200	+	7.30315i	0.891600	+	0.419555i
$304$	−2.22449	−	2.08893i	−0.127583	−	0.119808i
$305$	−12.2348	+	13.1771i	−0.700563	+	0.754520i
$306$	−3.42967	+	0.433268i	−0.196061	+	0.0247683i
$307$		−	1.51141i		−	0.0862608i	−0.999069	−	0.0431304i	$-0.986267\pi$
$307$		−	1.51141i		−	0.0862608i	0.999069	−	0.0431304i	$-0.0137331\pi$
$308$	−3.27329	−	25.9107i	−0.186513	−	1.47640i
$309$	−5.71842	−	6.91238i	−0.325309	−	0.393231i
$310$	−0.522169	+	0.383903i	−0.0296572	+	0.0218042i
$311$	−1.99694	+	31.7405i	−0.113236	+	1.79984i	0.374894	+	0.927068i	$0.377679\pi$
$311$	−1.99694	+	31.7405i	−0.113236	+	1.79984i	−0.488130	+	0.872771i	$0.662321\pi$
$312$	1.29392	−	5.03949i	0.0732539	−	0.285305i
$313$	−7.28248	+	28.3634i	−0.411630	+	1.60319i	0.337872	+	0.941192i	$0.390293\pi$
$313$	−7.28248	+	28.3634i	−0.411630	+	1.60319i	−0.749502	+	0.662002i	$0.769707\pi$
$314$	0.322836	−	5.13133i	0.0182187	−	0.289578i
$315$	7.80920	−	5.74139i	0.439998	−	0.323491i
$316$	3.31596	+	4.00830i	0.186537	+	0.225485i
$317$	2.81156	+	22.2558i	0.157913	+	1.25001i	0.849450	+	0.527670i	$0.176934\pi$
$317$	2.81156	+	22.2558i	0.157913	+	1.25001i	−0.691537	+	0.722341i	$0.743066\pi$
$318$			3.32317i			0.186354i
$319$	−10.3987	+	1.31366i	−0.582217	+	0.0735511i
$320$	−1.52146	+	1.63864i	−0.0850523	+	0.0916030i
$321$	4.23702	+	3.97883i	0.236487	+	0.222077i
$322$	−35.5327	−	16.7204i	−1.98016	−	0.931792i
$323$	−8.12814	−	6.72418i	−0.452262	−	0.374144i
$324$	−0.309017	+	0.951057i	−0.0171676	+	0.0528365i
$325$	21.8061	−	14.1867i	1.20959	−	0.786934i
$326$	−0.131397	−	0.404399i	−0.00727742	−	0.0223976i
$327$	2.38298	−	6.01871i	0.131779	−	0.332835i
$328$	−5.61293	+	5.97717i	−0.309922	+	0.330034i
$329$	−9.32503	−	48.8835i	−0.514106	−	2.69504i
$330$	0.0760999	+	13.4722i	0.00418916	+	0.741622i
$331$	14.9340	−	14.0239i	0.820846	−	0.770825i	−0.155317	−	0.987865i	$-0.549640\pi$
$331$	14.9340	−	14.0239i	0.820846	−	0.770825i	0.976163	+	0.217039i	$0.0696400\pi$
$332$	11.7265	−	3.81017i	0.643575	−	0.209110i
$333$	3.62527	+	0.691557i	0.198663	+	0.0378971i
$334$	−1.22677	−	19.4990i	−0.0671260	−	1.06694i
$335$	−4.46941	+	7.13138i	−0.244190	+	0.389629i
$336$	−2.32264	−	3.65989i	−0.126710	−	0.199663i
$337$	0.708041	−	0.0445461i	0.0385694	−	0.00242658i	−0.0434941	−	0.999054i	$-0.513849\pi$
$337$	0.708041	−	0.0445461i	0.0385694	−	0.00242658i	0.0820635	+	0.996627i	$0.473849\pi$
$338$	11.8803	+	7.53947i	0.646203	+	0.410093i
$339$	1.53139	−	1.85113i	0.0831736	−	0.100540i
$340$	−4.89352	+	5.98375i	−0.265388	+	0.324514i
$341$	1.69145	+	0.434291i	0.0915972	+	0.0235182i
$342$	−2.76113	+	1.29929i	−0.149305	+	0.0702574i
$343$	−19.7445	−	6.41538i	−1.06610	−	0.346398i
$344$	−5.42609	−	2.98302i	−0.292555	−	0.160834i
$345$	17.1652	+	10.7578i	0.924143	+	0.579183i
$346$	15.6185	+	1.97307i	0.839654	+	0.106073i
$347$	1.20614	−	9.54760i	0.0647491	−	0.512542i	−0.926070	−	0.377351i	$-0.876835\pi$
$347$	1.20614	−	9.54760i	0.0647491	−	0.512542i	0.990820	−	0.135191i	$-0.0431649\pi$
$348$	−1.46882	+	0.932141i	−0.0787369	+	0.0499680i
$349$	−8.04682	+	5.84636i	−0.430737	+	0.312948i	−0.781943	−	0.623349i	$-0.785771\pi$
$349$	−8.04682	+	5.84636i	−0.430737	+	0.312948i	0.351207	+	0.936298i	$0.385771\pi$
$350$	3.82042	−	21.3340i	0.204210	−	1.14035i
$351$	−4.20928	−	3.05822i	−0.224675	−	0.163236i
$352$	6.01317	+	0.378317i	0.320503	+	0.0201643i
$353$	−14.2910	−	25.9952i	−0.760633	−	1.38359i	−0.918215	−	0.396081i	$-0.870370\pi$
$353$	−14.2910	−	25.9952i	−0.760633	−	1.38359i	0.157582	−	0.987506i	$-0.449630\pi$
$354$	1.99754	−	4.24500i	0.106168	−	0.225619i
$355$	−1.12869	−	8.54603i	−0.0599049	−	0.453576i
$356$	3.36046	−	17.6161i	0.178104	−	0.933653i
$357$	−8.80777	−	12.1229i	−0.466157	−	0.641609i
$358$	1.76385	−	3.20843i	0.0932225	−	0.169571i
$359$	0.648702	−	1.02219i	0.0342372	−	0.0539492i	−0.826778	−	0.562528i	$-0.809829\pi$
$359$	0.648702	−	1.02219i	0.0342372	−	0.0539492i	0.861016	+	0.508579i	$0.169829\pi$
$360$	0.963485	+	2.01784i	0.0507801	+	0.106350i
$361$	9.00771	+	3.56640i	0.474090	+	0.187705i
$362$	7.16751	+	18.1031i	0.376716	+	0.951476i
$363$	19.4950	−	16.1277i	1.02322	−	0.846484i
$364$	21.8446	−	5.60873i	1.14497	−	0.293977i
$365$	−2.30944	−	11.7457i	−0.120882	−	0.614796i
$366$	7.47678	−	2.96027i	0.390818	−	0.154736i
$367$	−25.4716	−	27.1245i	−1.32961	−	1.41589i	−0.838614	−	0.544726i	$-0.816634\pi$
$367$	−25.4716	−	27.1245i	−1.32961	−	1.41589i	−0.490994	−	0.871163i	$-0.663366\pi$
$368$	5.32506	−	7.32931i	0.277588	−	0.382067i
$369$	3.49117	+	7.41912i	0.181743	+	0.386224i
$370$	6.94275	−	4.46121i	0.360936	−	0.231927i
$371$	−12.6231	+	6.93960i	−0.655358	+	0.360286i
$372$	0.284708	−	0.0543109i	0.0147614	−	0.00281589i
$373$	0.405023	+	1.57746i	0.0209713	+	0.0816778i	0.978207	−	0.207630i	$-0.0665749\pi$
$373$	0.405023	+	1.57746i	0.0209713	+	0.0816778i	−0.957236	+	0.289308i	$0.906575\pi$
$374$	20.8282			1.07700
$375$	−3.27424	+	10.6902i	−0.169081	+	0.552037i
$376$	11.4807			0.592071
$377$	−2.25095	−	8.76685i	−0.115930	−	0.451516i
$378$	−4.25790	+	0.812237i	−0.219003	+	0.0417770i
$379$	−12.4055	+	6.81997i	−0.637227	+	0.350318i	−0.767396	−	0.641173i	$-0.778448\pi$
$379$	−12.4055	+	6.81997i	−0.637227	+	0.350318i	0.130169	+	0.991492i	$0.458448\pi$
$380$	−2.47601	+	6.35839i	−0.127017	+	0.326179i
$381$	3.68912	+	7.83979i	0.189000	+	0.401645i
$382$	−3.33147	+	4.58538i	−0.170453	+	0.234608i
$383$	8.78443	+	9.35446i	0.448863	+	0.477991i	0.913109	−	0.407716i	$-0.133675\pi$
$383$	8.78443	+	9.35446i	0.448863	+	0.477991i	−0.464246	+	0.885706i	$0.653675\pi$
$384$	0.929776	−	0.368125i	0.0474475	−	0.0187858i
$385$	−51.0154	+	28.4224i	−2.59999	+	1.44854i
$386$	2.37040	−	0.608614i	0.120650	−	0.0309777i
$387$	−4.77102	+	3.94693i	−0.242524	+	0.200634i
$388$	−5.32254	−	13.4432i	−0.270211	−	0.682476i
$389$	−15.0137	−	5.94435i	−0.761225	−	0.301390i	−0.0447456	−	0.998998i	$-0.514248\pi$
$389$	−15.0137	−	5.94435i	−0.761225	−	0.301390i	−0.716480	+	0.697608i	$0.754248\pi$
$390$	−11.5340	+	1.52332i	−0.584047	+	0.0771364i
$391$	16.7811	−	26.4428i	0.848657	−	1.33727i
$392$	5.67960	−	10.3312i	0.286863	−	0.521802i
$393$	1.56764	+	2.15767i	0.0790769	+	0.108840i
$394$	−2.58050	+	13.5275i	−0.130004	+	0.681504i
$395$	5.54623	−	10.2250i	0.279061	−	0.514473i
$396$	2.56535	−	5.45164i	0.128913	−	0.273955i
$397$	5.25566	+	9.56001i	0.263774	+	0.479803i	0.974716	−	0.223448i	$-0.0717312\pi$
$397$	5.25566	+	9.56001i	0.263774	+	0.479803i	−0.710942	+	0.703251i	$0.751731\pi$
$398$	−0.329296	−	0.0207175i	−0.0165061	−	0.00103848i
$399$	−10.7013	−	7.77492i	−0.535733	−	0.389233i
$400$	4.66938	+	1.78799i	0.233469	+	0.0893994i
$401$	−13.1818	+	9.57715i	−0.658269	+	0.478260i	−0.866078	−	0.499909i	$-0.833367\pi$
$401$	−13.1818	+	9.57715i	−0.658269	+	0.478260i	0.207809	+	0.978169i	$0.433367\pi$
$402$	3.17791	−	2.01676i	0.158500	−	0.100587i
$403$	−0.189007	+	1.49614i	−0.00941509	+	0.0745281i
$404$	−17.0172	−	2.14977i	−0.846637	−	0.106955i
$405$	2.23083	−	0.153007i	0.110851	−	0.00760299i
$406$	−6.60800	−	3.63278i	−0.327949	−	0.180292i
$407$	−21.1480	−	6.87140i	−1.04827	−	0.340603i
$408$	3.12792	−	1.47189i	0.154855	−	0.0728693i
$409$	14.1756	+	3.63968i	0.700940	+	0.179971i	0.582309	−	0.812968i	$-0.302149\pi$
$409$	14.1756	+	3.63968i	0.700940	+	0.179971i	0.118631	+	0.992938i	$0.462149\pi$
$410$	17.0849	+	6.65302i	0.843765	+	0.328569i
$411$	−12.1857	+	14.7300i	−0.601078	+	0.726578i
$412$	7.57458	+	4.80697i	0.373173	+	0.236823i
$413$	20.2960	−	1.27692i	0.998701	−	0.0628329i
$414$	−4.85434	−	7.64921i	−0.238578	−	0.375938i
$415$	−17.6939	−	21.1439i	−0.868559	−	1.03791i
$416$	0.326696	+	5.19269i	0.0160176	+	0.254592i
$417$	−2.32602	−	0.443713i	−0.113906	−	0.0217287i
$418$	17.4859	−	5.68152i	0.855264	−	0.277892i
$419$	−3.89392	+	3.65663i	−0.190230	+	0.178638i	−0.773810	−	0.633418i	$-0.781652\pi$
$419$	−3.89392	+	3.65663i	−0.190230	+	0.178638i	0.583580	+	0.812056i	$0.301652\pi$
$420$	−5.65280	+	7.87356i	−0.275829	+	0.384190i
$421$	−5.47150	−	28.6826i	−0.266665	−	1.39790i	−0.823516	−	0.567293i	$-0.807991\pi$
$421$	−5.47150	−	28.6826i	−0.266665	−	1.39790i	0.556852	−	0.830612i	$-0.312009\pi$
$422$	3.33811	−	3.55473i	0.162497	−	0.173042i
$423$	4.22632	−	10.6745i	0.205491	−	0.519010i
$424$	−1.02692	−	3.16052i	−0.0498715	−	0.153489i
$425$	16.4980	+	5.15520i	0.800269	+	0.250064i
$426$	−1.19129	+	3.66641i	−0.0577181	+	0.177638i
$427$	26.8580	+	22.2188i	1.29975	+	1.07524i
$428$	−5.25917	−	2.47478i	−0.254212	−	0.119623i
$429$	22.8518	+	21.4592i	1.10329	+	1.03606i
$430$	−1.65771	+	13.7461i	−0.0799419	+	0.662897i
$431$	7.98747	−	1.00905i	0.384743	−	0.0486043i	0.0694168	−	0.997588i	$-0.477886\pi$
$431$	7.98747	−	1.00905i	0.384743	−	0.0486043i	0.315326	+	0.948983i	$0.397886\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−3.33039	−	26.3628i	−0.160048	−	1.26691i	−0.843584	−	0.536997i	$-0.819559\pi$
$433$	−3.33039	−	26.3628i	−0.160048	−	1.26691i	0.683536	−	0.729917i	$-0.260441\pi$
$434$	0.800841	+	0.968050i	0.0384416	+	0.0464679i
$435$	3.15989	+	2.26863i	0.151505	+	0.108773i
$436$	−0.406461	+	6.46051i	−0.0194660	+	0.309402i
$437$	6.87518	−	26.7771i	0.328885	−	1.28092i
$438$	−1.33134	+	5.18521i	−0.0636136	+	0.247759i
$439$	1.70076	−	27.0327i	0.0811726	−	1.29020i	−0.720927	−	0.693011i	$-0.756284\pi$
$439$	1.70076	−	27.0327i	0.0811726	−	1.29020i	0.802099	−	0.597191i	$-0.203716\pi$
$440$	−4.23552	−	12.7893i	−0.201921	−	0.609708i
$441$	−7.51486	−	9.08391i	−0.357851	−	0.432567i
$442$	2.25427	+	17.8444i	0.107225	+	0.848772i
$443$		−	20.1532i		−	0.957506i	−0.877950	−	0.478753i	$-0.841089\pi$
$443$		−	20.1532i		−	0.957506i	0.877950	−	0.478753i	$-0.158911\pi$
$444$	−3.66154	+	0.462560i	−0.173769	+	0.0219521i
$445$	−39.3478	+	7.73659i	−1.86526	+	0.366750i
$446$	1.53410	+	1.44061i	0.0726416	+	0.0682150i
$447$	−6.80832	−	3.20375i	−0.322022	−	0.151532i
$448$	3.33993	+	2.76303i	0.157797	+	0.130541i
$449$	−6.15456	+	18.9418i	−0.290452	+	0.893918i	0.694260	+	0.719725i	$0.255732\pi$
$449$	−6.15456	+	18.9418i	−0.290452	+	0.893918i	−0.984711	+	0.174194i	$0.944268\pi$
$450$	3.38134	−	3.68328i	0.159398	−	0.173631i
$451$	−15.2662	−	46.9845i	−0.718856	−	2.21241i
$452$	−0.884406	+	2.23375i	−0.0415989	+	0.105067i
$453$	8.88159	−	9.45793i	0.417293	−	0.444372i
$454$	4.02966	+	21.1242i	0.189121	+	0.991408i
$455$	−29.8722	−	40.6309i	−1.40043	−	1.90481i
$456$	2.22449	−	2.08893i	0.104171	−	0.0978231i
$457$	−3.68748	+	1.19813i	−0.172493	+	0.0560463i	−0.393990	−	0.919115i	$-0.628906\pi$
$457$	−3.68748	+	1.19813i	−0.172493	+	0.0560463i	0.221497	+	0.975161i	$0.428906\pi$
$458$	3.02499	+	0.577048i	0.141349	+	0.0269637i
$459$	−0.217062	−	3.45011i	−0.0101316	−	0.161037i
$460$	−19.6494	−	4.92698i	−0.916159	−	0.229722i
$461$	−12.5464	−	19.7700i	−0.584344	−	0.920779i	−0.999937	−	0.0112284i	$-0.996426\pi$
$461$	−12.5464	−	19.7700i	−0.584344	−	0.920779i	0.415593	−	0.909551i	$-0.363574\pi$
$462$	26.0652	−	1.63988i	1.21266	−	0.0762941i
$463$	0.624865	+	0.396551i	0.0290399	+	0.0184293i	0.550268	−	0.834988i	$-0.314526\pi$
$463$	0.624865	+	0.396551i	0.0290399	+	0.0184293i	−0.521228	+	0.853418i	$0.674526\pi$
$464$	1.10888	−	1.34041i	0.0514786	−	0.0622269i
$465$	−0.350358	−	0.545244i	−0.0162475	−	0.0252851i
$466$	−15.8676	−	4.07412i	−0.735054	−	0.188730i
$467$	−7.51951	+	3.53841i	−0.347962	+	0.163738i	−0.591815	−	0.806074i	$-0.701588\pi$
$467$	−7.51951	+	3.53841i	−0.347962	+	0.163738i	0.243853	+	0.969812i	$0.421588\pi$
$468$	4.94830	+	1.60780i	0.228735	+	0.0743206i
$469$	14.2970	+	7.85982i	0.660172	+	0.362933i
$470$	−9.58501	−	23.8151i	−0.442124	−	1.09851i
$471$	5.10093	+	0.644397i	0.235038	+	0.0296923i
$472$	−0.588001	+	4.65451i	−0.0270649	+	0.214241i
$473$	31.4995	−	19.9902i	1.44835	−	0.919149i
$474$	−4.20860	+	3.05773i	−0.193308	+	0.140446i
$475$	15.2568	−	0.172366i	0.700029	−	0.00790870i
$476$	12.1229	+	8.80777i	0.555650	+	0.403703i
$477$	−3.31661	−	0.208664i	−0.151857	−	0.00955406i
$478$	0.229265	+	0.417031i	0.0104863	+	0.0190745i
$479$	−10.5249	+	22.3665i	−0.480895	+	1.02195i	0.506289	+	0.862364i	$0.331017\pi$
$479$	−10.5249	+	22.3665i	−0.480895	+	1.02195i	−0.987183	+	0.159589i	$0.948983\pi$
$480$	−1.53988	−	1.62135i	−0.0702854	−	0.0740042i
$481$	3.59814	−	18.8621i	0.164061	−	0.860038i
$482$	3.70485	+	5.09929i	0.168751	+	0.232266i
$483$	18.9185	−	34.4127i	0.860823	−	1.56583i
$484$	−13.5571	+	21.3626i	−0.616233	+	0.971028i
$485$	−23.4424	+	22.2644i	−1.06446	+	1.01097i
$486$	−0.929776	−	0.368125i	−0.0421755	−	0.0166985i
$487$	6.42712	+	16.2330i	0.291241	+	0.735590i	0.999559	+	0.0296966i	$0.00945411\pi$
$487$	6.42712	+	16.2330i	0.291241	+	0.735590i	−0.708318	+	0.705893i	$0.750546\pi$
$488$	−6.19607	+	5.12583i	−0.280483	+	0.232036i
$489$	0.411852	−	0.105746i	0.0186246	−	0.00478198i
$490$	−26.1723	−	3.15624i	−1.18235	−	0.142585i
$491$	13.7255	−	5.43432i	0.619424	−	0.245248i	−0.0373887	−	0.999301i	$-0.511904\pi$
$491$	13.7255	−	5.43432i	0.619424	−	0.245248i	0.656813	+	0.754053i	$0.271904\pi$
$492$	−5.61293	−	5.97717i	−0.253051	−	0.269472i
$493$	3.53481	−	4.86525i	0.159200	−	0.219120i
$494$	6.76013	+	14.3660i	0.304153	+	0.646357i
$495$	−13.4504	−	0.769978i	−0.604551	−	0.0346080i
$496$	−0.253990	+	0.139632i	−0.0114045	+	0.00626968i
$497$	−16.4146	+	3.13125i	−0.736295	+	0.140456i
$498$	3.06634	+	11.9426i	0.137406	+	0.535161i
$499$	−23.9392			−1.07167			−0.535833	−	0.844324i	$-0.680002\pi$
$499$	−23.9392			−1.07167			−0.535833	+	0.844324i	$0.680002\pi$
$500$	−0.189450	−	11.1787i	−0.00847248	−	0.499928i
$501$	19.5375			0.872873
$502$	−2.27141	−	8.84656i	−0.101378	−	0.394841i
$503$	−27.4569	+	5.23768i	−1.22424	+	0.233537i	−0.758671	−	0.651474i	$-0.774151\pi$
$503$	−27.4569	+	5.23768i	−1.22424	+	0.233537i	−0.465571	+	0.885010i	$0.654151\pi$
$504$	3.79851	−	2.08825i	0.169199	−	0.0930179i
$505$	9.74794	+	37.0946i	0.433778	+	1.65069i
$506$	23.2408	+	49.3893i	1.03318	+	2.19562i
$507$	−8.27056	+	11.3834i	−0.367308	+	0.505557i
$508$	−5.93119	−	6.31608i	−0.263154	−	0.280231i
$509$	−24.0769	+	9.53273i	−1.06719	+	0.422531i	−0.835063	−	0.550154i	$-0.814569\pi$
$509$	−24.0769	+	9.53273i	−1.06719	+	0.422531i	−0.232128	+	0.972685i	$0.574569\pi$
$510$	−5.66467	−	5.25959i	−0.250836	−	0.232898i
$511$	−22.4762	+	5.77091i	−0.994289	+	0.255290i
$512$	−0.770513	+	0.637424i	−0.0340522	+	0.0281704i
$513$	−1.12335	−	2.83726i	−0.0495972	−	0.125268i
$514$	−6.70655	−	2.65531i	−0.295813	−	0.117121i
$515$	3.64752	−	19.7257i	0.160729	−	0.869217i
$516$	3.31784	−	5.22808i	0.146060	−	0.230153i
$517$	−33.3237	+	60.6157i	−1.46558	+	2.66587i
$518$	−9.40323	−	12.9424i	−0.413154	−	0.568658i
$519$	−2.94987	+	15.4638i	−0.129485	+	0.678783i
$520$	10.4988	−	5.01297i	0.460401	−	0.219833i
$521$	4.08533	−	8.68177i	0.178982	−	0.380355i	−0.795125	−	0.606446i	$-0.792595\pi$
$521$	4.08533	−	8.68177i	0.178982	−	0.380355i	0.974106	+	0.226091i	$0.0725946\pi$
$522$	−0.838073	−	1.52445i	−0.0366815	−	0.0667234i
$523$	30.5294	+	1.92075i	1.33496	+	0.0839885i	0.714161	−	0.699982i	$-0.246808\pi$
$523$	30.5294	+	1.92075i	1.33496	+	0.0839885i	0.620799	+	0.783970i	$0.286808\pi$
$524$	−2.15767	−	1.56764i	−0.0942582	−	0.0684826i
$525$	21.0520	+	5.15246i	0.918786	+	0.224872i
$526$	14.5016	−	10.5360i	0.632298	−	0.459391i
$527$	−0.845985	+	0.536878i	−0.0368517	+	0.0233868i
$528$	−0.755140	+	5.97755i	−0.0328633	+	0.260139i
$529$	58.6092	+	7.40407i	2.54823	+	0.321916i
$530$	−5.69871	+	4.76886i	−0.247536	+	0.207146i
$531$	4.11119	+	2.26015i	0.178411	+	0.0980820i
$532$	12.5801	+	4.08752i	0.545416	+	0.177216i
$533$	38.6013	−	18.1644i	1.67201	−	0.786787i
$534$	17.3704	+	4.45995i	0.751689	+	0.193001i
$535$	−0.742795	+	12.9756i	−0.0321138	+	0.560983i
$536$	−2.39916	+	2.90008i	−0.103628	+	0.125265i
$537$	3.09135	+	1.96183i	0.133402	+	0.0846592i
$538$	12.8091	−	0.805880i	0.552239	−	0.0347440i
$539$	38.0608	+	59.9743i	1.63940	+	2.58328i
$540$	−2.07436	+	0.834882i	−0.0892663	+	0.0359276i
$541$	0.318361	+	5.06021i	0.0136874	+	0.217555i	0.998925	+	0.0463613i	$0.0147625\pi$
$541$	0.318361	+	5.06021i	0.0136874	+	0.217555i	−0.985237	+	0.171194i	$0.945237\pi$
$542$	−22.1556	−	4.22641i	−0.951666	−	0.181540i
$543$	−18.5174	+	6.01667i	−0.794658	+	0.258200i
$544$	−2.51999	+	2.36643i	−0.108044	+	0.101460i
$545$	13.7408	−	4.55062i	0.588590	−	0.194927i
$546$	4.22603	+	22.1536i	0.180858	+	0.948088i
$547$	29.2801	−	31.1801i	1.25193	−	1.33317i	0.330900	−	0.943666i	$-0.392648\pi$
$547$	29.2801	−	31.1801i	1.25193	−	1.33317i	0.921026	−	0.389501i	$-0.127352\pi$
$548$	7.03749	−	17.7747i	0.300627	−	0.759297i
$549$	2.48495	+	7.64790i	0.106055	+	0.326405i
$550$	−22.9935	+	19.4636i	−0.980447	+	0.829930i
$551$	1.64044	−	5.04875i	0.0698850	−	0.215084i
$552$	6.98049	+	5.77476i	0.297109	+	0.245790i
$553$	−20.4034	−	9.60112i	−0.867641	−	0.408281i
$554$	−6.92647	−	6.50439i	−0.294277	−	0.276345i
$555$	4.01647	+	7.20917i	0.170490	+	0.306012i
$556$	2.34930	−	0.296785i	0.0996323	−	0.0125865i
$557$			0.369481i			0.0156554i	0.999969	+	0.00782772i	$0.00249166\pi$
$557$			0.369481i			0.0156554i	−0.999969	+	0.00782772i	$0.997508\pi$
$558$	0.0363268	+	0.287556i	0.00153784	+	0.0121732i
$559$	20.5357	+	24.8234i	0.868567	+	1.04992i
$560$	2.94307	−	9.23501i	0.124367	−	0.390251i
$561$	−1.30781	+	20.7871i	−0.0552159	+	0.877632i
$562$	2.46244	−	9.59056i	0.103872	−	0.404553i
$563$	−0.999260	+	3.89186i	−0.0421138	+	0.164022i	−0.986162	−	0.165786i	$-0.946984\pi$
$563$	−0.999260	+	3.89186i	−0.0421138	+	0.164022i	0.944048	+	0.329808i	$0.106984\pi$
$564$	−0.720878	+	11.4580i	−0.0303544	+	0.482470i
$565$	5.37199	−	0.0303445i	0.226001	−	0.00127660i
$566$	−11.6499	−	14.0823i	−0.489681	−	0.591923i
$567$	−0.543279	−	4.30050i	−0.0228156	−	0.180604i
$568$		−	3.85509i		−	0.161756i
$569$	−1.03810	+	0.131143i	−0.0435196	+	0.00549780i	−0.147063	−	0.989127i	$-0.546982\pi$
$569$	−1.03810	+	0.131143i	−0.0435196	+	0.00549780i	0.103543	+	0.994625i	$0.466982\pi$
$570$	−6.19038	−	2.87037i	−0.259286	−	0.120227i
$571$	12.5147	+	11.7521i	0.523724	+	0.491810i	0.900717	−	0.434406i	$-0.143042\pi$
$571$	12.5147	+	11.7521i	0.523724	+	0.491810i	−0.376993	+	0.926216i	$0.623042\pi$
$572$	−28.3646	−	13.3474i	−1.18598	−	0.558082i
$573$	−4.36715	−	3.61282i	−0.182440	−	0.150928i
$574$	10.9831	−	33.8026i	0.458427	−	1.41089i
$575$	6.18463	+	44.8735i	0.257917	+	1.87135i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	14.7449	−	37.2413i	0.613838	−	1.55038i	−0.206469	−	0.978453i	$-0.566197\pi$
$577$	14.7449	−	37.2413i	0.613838	−	1.55038i	0.820307	−	0.571924i	$-0.193803\pi$
$578$	3.45672	−	3.68103i	0.143781	−	0.153111i
$579$	0.458575	+	2.40393i	0.0190577	+	0.0999041i
$580$	−3.70628	−	1.18114i	−0.153895	−	0.0490441i
$581$	−38.9608	+	36.5866i	−1.61636	+	1.51787i
$582$	13.7509	−	4.46794i	0.569993	−	0.185202i
$583$	19.6677	+	3.75181i	0.814551	+	0.155384i
$584$	−0.336142	−	5.34283i	−0.0139097	−	0.221088i
$585$	−0.796090	−	11.6069i	−0.0329143	−	0.479886i
$586$	−12.9839	−	20.4593i	−0.536359	−	0.845166i
$587$	4.94527	−	0.311130i	0.204113	−	0.0128417i	0.0395952	−	0.999216i	$-0.487393\pi$
$587$	4.94527	−	0.311130i	0.204113	−	0.0128417i	0.164518	+	0.986374i	$0.447393\pi$
$588$	9.95414	+	6.31709i	0.410502	+	0.260512i
$589$	−0.563781	+	0.681494i	−0.0232302	+	0.0280805i
$590$	10.1460	−	2.66624i	0.417706	−	0.109767i
$591$	−13.3387	−	3.42481i	−0.548683	−	0.140878i
$592$	3.33939	−	1.57140i	0.137248	−	0.0645841i
$593$	20.9773	+	6.81595i	0.861436	+	0.279898i	0.706228	−	0.707984i	$-0.250395\pi$
$593$	20.9773	+	6.81595i	0.861436	+	0.279898i	0.155208	+	0.987882i	$0.450395\pi$
$594$	5.27980	+	2.90259i	0.216633	+	0.119095i
$595$	8.14934	−	32.5006i	0.334090	−	1.33240i
$596$	7.46511	+	0.943063i	0.305783	+	0.0386293i
$597$	0.0413533	−	0.327345i	0.00169248	−	0.0133973i
$598$	−39.7985	+	25.2569i	−1.62748	+	1.03283i
$599$	17.9182	−	13.0183i	0.732119	−	0.531915i	−0.158114	−	0.987421i	$-0.550541\pi$
$599$	17.9182	−	13.0183i	0.732119	−	0.531915i	0.890233	+	0.455506i	$0.150541\pi$
$600$	−2.07765	+	4.54790i	−0.0848198	+	0.185667i
$601$	15.3098	+	11.1233i	0.624502	+	0.453727i	0.854491	−	0.519466i	$-0.173869\pi$
$601$	15.3098	+	11.1233i	0.624502	+	0.453727i	−0.229989	+	0.973193i	$0.573869\pi$
$602$	26.7873	+	1.68532i	1.09177	+	0.0686884i
$603$	1.81324	+	3.29827i	0.0738409	+	0.134316i
$604$	−5.52423	+	11.7396i	−0.224778	+	0.477677i
$605$	55.6324	+	10.2871i	2.26178	+	0.418231i
$606$	3.21405	−	16.8486i	0.130562	−	0.684428i
$607$	3.59550	+	4.94878i	0.145937	+	0.200865i	0.875727	−	0.482806i	$-0.160382\pi$
$607$	3.59550	+	4.94878i	0.145937	+	0.200865i	−0.729791	+	0.683671i	$0.760382\pi$
$608$	−1.47010	+	2.67409i	−0.0596203	+	0.108449i
$609$	4.04053	−	6.36685i	0.163730	−	0.257998i
$610$	15.8058	+	8.57341i	0.639959	+	0.347127i
$611$	−55.5387	−	21.9893i	−2.24686	−	0.889593i
$612$	1.27258	+	3.21417i	0.0514410	+	0.129925i
$613$	6.20561	−	5.13372i	0.250642	−	0.207349i	−0.503615	−	0.863928i	$-0.667997\pi$
$613$	6.20561	−	5.13372i	0.250642	−	0.207349i	0.754257	+	0.656579i	$0.227997\pi$
$614$	−1.46393	+	0.375873i	−0.0590793	+	0.0151690i
$615$	−7.71266	+	16.6335i	−0.311005	+	0.670727i
$616$	−24.2827	+	9.61419i	−0.978377	+	0.387367i
$617$	9.94594	+	10.5914i	0.400409	+	0.426392i	0.897300	−	0.441421i	$-0.145525\pi$
$617$	9.94594	+	10.5914i	0.400409	+	0.426392i	−0.496892	+	0.867813i	$0.665525\pi$
$618$	−5.27310	+	7.25780i	−0.212115	+	0.291952i
$619$	3.02976	+	6.43857i	0.121776	+	0.258788i	0.956416	−	0.292009i	$-0.0943238\pi$
$619$	3.02976	+	6.43857i	0.121776	+	0.258788i	−0.834639	+	0.550797i	$0.814324\pi$
$620$	0.501700	+	0.410291i	0.0201487	+	0.0164777i
$621$	7.93893	−	4.36446i	0.318578	−	0.175140i
$622$	31.2399	−	5.95934i	1.25261	−	0.238948i
$623$	19.3325	+	75.2949i	0.774539	+	3.01663i
$624$	−5.20295			−0.208285
$625$	−23.0306	+	9.72591i	−0.921222	+	0.389037i
$626$	29.2834			1.17040
$627$	4.57236	+	17.8082i	0.182602	+	0.711189i
$628$	−5.05040	+	0.963416i	−0.201533	+	0.0384445i
$629$	11.1802	−	6.14635i	0.445782	−	0.245071i
$630$	−7.50308	−	6.13603i	−0.298930	−	0.244465i
$631$	−1.75187	−	3.72291i	−0.0697408	−	0.148207i	0.866917	−	0.498452i	$-0.166098\pi$
$631$	−1.75187	−	3.72291i	−0.0697408	−	0.148207i	−0.936658	+	0.350246i	$0.886098\pi$
$632$	3.05773	−	4.20860i	0.121630	−	0.167409i
$633$	3.33811	+	3.55473i	0.132678	+	0.141288i
$634$	20.8574	−	8.25803i	0.828353	−	0.327968i
$635$	−8.14998	+	17.5766i	−0.323422	+	0.697507i
$636$	3.21877	−	0.826439i	0.127632	−	0.0327705i
$637$	−47.2631	+	39.0995i	−1.87263	+	1.54918i
$638$	3.85845	+	9.74534i	0.152758	+	0.385822i
$639$	−3.58437	−	1.41915i	−0.141796	−	0.0561408i
$640$	1.96553	+	1.06615i	0.0776946	+	0.0421432i
$641$	9.90721	−	15.6113i	0.391311	−	0.616608i	−0.590371	−	0.807132i	$-0.701019\pi$
$641$	9.90721	−	15.6113i	0.391311	−	0.616608i	0.981683	+	0.190524i	$0.0610187\pi$
$642$	2.80012	−	5.09340i	0.110512	−	0.201021i
$643$	4.28414	+	5.89661i	0.168950	+	0.232540i	0.885093	−	0.465413i	$-0.154094\pi$
$643$	4.28414	+	5.89661i	0.168950	+	0.232540i	−0.716143	+	0.697953i	$0.754094\pi$
$644$	−7.35849	+	38.5745i	−0.289965	+	1.52005i
$645$	−13.6149	−	2.51757i	−0.536087	−	0.0991291i
$646$	−4.49154	+	9.54502i	−0.176717	+	0.375544i
$647$	−17.7094	−	32.2133i	−0.696229	−	1.26644i	−0.953877	−	0.300198i	$-0.902947\pi$
$647$	−17.7094	−	32.2133i	−0.696229	−	1.26644i	0.257648	−	0.966239i	$-0.417053\pi$
$648$	0.998027	+	0.0627905i	0.0392062	+	0.00246664i
$649$	−22.8681	−	16.6147i	−0.897653	−	0.652183i
$650$	−19.1639	−	17.5930i	−0.751671	−	0.690053i
$651$	−1.01643	+	0.738476i	−0.0398368	+	0.0289432i
$652$	−0.359017	+	0.227839i	−0.0140602	+	0.00892287i
$653$	−3.40603	+	26.9615i	−0.133288	+	1.05508i	0.773588	+	0.633689i	$0.218460\pi$
$653$	−3.40603	+	26.9615i	−0.133288	+	1.05508i	−0.906877	+	0.421396i	$0.861540\pi$
$654$	−6.42224	−	0.811318i	−0.251130	−	0.0317250i
$655$	−1.45045	+	5.78458i	−0.0566737	+	0.226022i
$656$	7.18526	+	3.95013i	0.280537	+	0.154227i
$657$	−5.09138	−	1.65429i	−0.198634	−	0.0645400i
$658$	−45.0287	+	21.1889i	−1.75540	+	0.826030i
$659$	−21.5587	−	5.53533i	−0.839807	−	0.215626i	−0.195798	−	0.980644i	$-0.562730\pi$
$659$	−21.5587	−	5.53533i	−0.839807	−	0.215626i	−0.644008	+	0.765019i	$0.722730\pi$
$660$	13.0300	−	3.42412i	0.507194	−	0.133284i
$661$	−23.0485	+	27.8608i	−0.896481	+	1.08366i	0.0995832	+	0.995029i	$0.468249\pi$
$661$	−23.0485	+	27.8608i	−0.896481	+	1.08366i	−0.996065	+	0.0886306i	$0.971751\pi$
$662$	−17.2973	−	10.9772i	−0.672278	−	0.426641i
$663$	−17.9507	+	1.12937i	−0.697149	+	0.0438609i
$664$	−6.60673	−	10.4105i	−0.256391	−	0.404007i
$665$	−2.02390	−	29.5082i	−0.0784836	−	1.14428i
$666$	−0.231737	−	3.68336i	−0.00897963	−	0.142727i
$667$	15.4811	+	2.95317i	0.599430	+	0.114347i
$668$	−18.5813	+	6.03743i	−0.718932	+	0.233595i
$669$	−1.53410	+	1.44061i	−0.0593116	+	0.0556973i
$670$	8.01884	+	2.55549i	0.309795	+	0.0987273i
$671$	−9.07870	−	47.5922i	−0.350479	−	1.83728i
$672$	−2.96729	+	3.15984i	−0.114466	+	0.121894i
$673$	3.20258	−	8.08881i	0.123451	−	0.311801i	−0.854888	−	0.518813i	$-0.826374\pi$
$673$	3.20258	−	8.08881i	0.123451	−	0.311801i	0.978338	+	0.207012i	$0.0663741\pi$
$674$	−0.219229	−	0.674718i	−0.00844439	−	0.0259892i
$675$	3.46369	+	3.60594i	0.133318	+	0.138793i
$676$	4.34809	−	13.3820i	0.167234	−	0.514694i
$677$	−2.02219	−	1.67290i	−0.0777192	−	0.0642949i	0.597753	−	0.801680i	$-0.296060\pi$
$677$	−2.02219	−	1.67290i	−0.0777192	−	0.0642949i	−0.675472	+	0.737385i	$0.736060\pi$
$678$	−2.17381	−	1.02292i	−0.0834848	−	0.0392850i
$679$	45.6867	+	42.9027i	1.75330	+	1.64645i
$680$	7.01273	+	3.25168i	0.268926	+	0.124696i
$681$	−21.3355	+	2.69531i	−0.817580	+	0.103284i
$682$		−	1.74631i		−	0.0668698i
$683$	−4.73447	−	37.4772i	−0.181159	−	1.43402i	−0.776281	−	0.630388i	$-0.782896\pi$
$683$	−4.73447	−	37.4772i	−0.181159	−	1.43402i	0.595121	−	0.803636i	$-0.297104\pi$
$684$	1.94513	+	2.35126i	0.0743740	+	0.0899027i
$685$	−42.7466	+	0.241461i	−1.63326	+	0.00922573i
$686$	−1.30357	+	20.7196i	−0.0497705	+	0.791080i
$687$	−0.765851	+	2.98279i	−0.0292190	+	0.113801i
$688$	−1.53989	+	5.99746i	−0.0587076	+	0.228651i
$689$	−1.08567	+	17.2562i	−0.0413606	+	0.657409i
$690$	6.15105	−	19.3013i	0.234167	−	0.734788i
$691$	18.7641	+	22.6819i	0.713821	+	0.862862i	0.995313	−	0.0967017i	$-0.0308293\pi$
$691$	18.7641	+	22.6819i	0.713821	+	0.862862i	−0.281492	+	0.959564i	$0.590829\pi$
$692$	−1.97307	−	15.6185i	−0.0750049	−	0.593725i
$693$			26.1167i			0.992091i
$694$	−9.54760	+	1.20614i	−0.362422	+	0.0457846i
$695$	−2.57702	−	4.62551i	−0.0977521	−	0.175455i
$696$	1.26814	+	1.19086i	0.0480686	+	0.0451394i
$697$	25.6474	+	12.0687i	0.971463	+	0.457136i
$698$	7.66385	+	6.34009i	0.290081	+	0.239976i
$699$	5.06241	−	15.5805i	0.191478	−	0.589309i
$700$	−21.6139	+	1.60516i	−0.816927	+	0.0606692i
$701$	−4.29138	−	13.2075i	−0.162083	−	0.498840i	0.836726	−	0.547621i	$-0.184466\pi$
$701$	−4.29138	−	13.2075i	−0.162083	−	0.498840i	−0.998810	+	0.0487807i	$0.984466\pi$
$702$	−1.91533	+	4.83758i	−0.0722896	+	0.182583i
$703$	7.70949	−	8.20977i	0.290769	−	0.309637i
$704$	−1.12898	−	5.91834i	−0.0425502	−	0.223056i
$705$	24.3699	−	8.07074i	0.917824	−	0.303961i
$706$	−21.6245	+	20.3068i	−0.813850	+	0.764256i
$707$	70.7113	−	22.9755i	2.65937	−	0.864083i
$708$	−4.60840	−	0.879099i	−0.173194	−	0.0330386i
$709$	−1.13326	−	18.0126i	−0.0425604	−	0.676478i	−0.960243	−	0.279164i	$-0.909943\pi$
$709$	−1.13326	−	18.0126i	−0.0425604	−	0.676478i	0.917683	−	0.397313i	$-0.130057\pi$
$710$	−7.99685	+	3.21855i	−0.300116	+	0.120790i
$711$	−2.78744	−	4.39230i	−0.104537	−	0.164724i
$712$	−17.8984	+	1.12607i	−0.670771	+	0.0422013i
$713$	−2.21706	−	1.40699i	−0.0830296	−	0.0526922i
$714$	−9.55159	+	11.5459i	−0.357459	+	0.432094i
$715$	−4.00616	+	69.9819i	−0.149822	+	2.61717i
$716$	−3.54629	−	0.910532i	−0.132531	−	0.0340282i
$717$	−0.430603	+	0.202627i	−0.0160812	+	0.00756723i
$718$	−1.15140	−	0.374113i	−0.0429700	−	0.0139618i
$719$	−35.6228	−	19.5838i	−1.32851	−	0.730353i	−0.350036	−	0.936736i	$-0.613831\pi$
$719$	−35.6228	−	19.5838i	−1.32851	−	0.730353i	−0.978471	+	0.206384i	$0.933831\pi$
$720$	1.71484	−	1.43503i	0.0639084	−	0.0534805i
$721$	−38.5803	−	4.87383i	−1.43681	−	0.181511i
$722$	1.21423	−	9.61164i	0.0451891	−	0.357708i
$723$	−5.32186	+	3.37735i	−0.197922	+	0.125605i
$724$	15.7518	−	11.4444i	0.585413	−	0.425327i
$725$	0.644195	+	8.67426i	0.0239248	+	0.322154i
$726$	−20.4692	−	14.8718i	−0.759684	−	0.551943i
$727$	35.1383	+	2.21071i	1.30321	+	0.0819908i	0.699164	−	0.714961i	$-0.253556\pi$
$727$	35.1383	+	2.21071i	1.30321	+	0.0819908i	0.604043	+	0.796952i	$0.293556\pi$
$728$	−10.8650	−	19.7634i	−0.402685	−	0.732482i
$729$	0.425779	−	0.904827i	0.0157696	−	0.0335121i
$730$	−10.8023	+	5.15791i	−0.399812	+	0.190903i
$731$	−4.01095	+	21.0261i	−0.148350	+	0.777680i
$732$	−4.72666	−	6.50569i	−0.174703	−	0.240457i
$733$	−4.36462	+	7.93921i	−0.161211	+	0.293241i	−0.944559	−	0.328342i	$-0.893510\pi$
$733$	−4.36462	+	7.93921i	−0.161211	+	0.293241i	0.783348	+	0.621583i	$0.213510\pi$
$734$	−19.9378	+	31.4170i	−0.735919	+	1.15962i
$735$	4.79339	−	25.9225i	0.176807	−	0.956166i
$736$	−8.42334	−	3.33503i	−0.310488	−	0.122931i
$737$	−8.34808	−	21.0848i	−0.307506	−	0.776670i
$738$	6.31781	−	5.22655i	0.232562	−	0.192392i
$739$	−23.9256	+	6.14306i	−0.880119	+	0.225976i	−0.661600	−	0.749857i	$-0.730122\pi$
$739$	−23.9256	+	6.14306i	−0.880119	+	0.225976i	−0.218518	+	0.975833i	$0.570122\pi$
$740$	−6.04764	−	5.61517i	−0.222316	−	0.206418i
$741$	−14.7621	+	5.84474i	−0.542300	+	0.214712i
$742$	9.86082	+	10.5007i	0.362002	+	0.385493i
$743$	11.9912	−	16.5045i	0.439914	−	0.605490i	−0.530279	−	0.847823i	$-0.677913\pi$
$743$	11.9912	−	16.5045i	0.439914	−	0.605490i	0.970193	+	0.242334i	$0.0779128\pi$
$744$	−0.123409	−	0.262257i	−0.00452438	−	0.00961480i
$745$	−4.27623	−	16.2727i	−0.156669	−	0.596185i
$746$	1.42718	−	0.784597i	0.0522527	−	0.0287261i
$747$	−12.1116	+	2.31041i	−0.443139	+	0.0845333i
$748$	−5.17976	−	20.1738i	−0.189391	−	0.737629i
$749$	25.1947			0.920593
$750$	11.1686	+	0.512842i	0.407819	+	0.0187263i
$751$	9.27202			0.338341			0.169170	−	0.985587i	$-0.445891\pi$
$751$	9.27202			0.338341			0.169170	+	0.985587i	$0.445891\pi$
$752$	−2.85513	−	11.1200i	−0.104116	−	0.405504i
$753$	8.97172	−	1.71145i	0.326948	−	0.0623686i
$754$	−7.93164	+	4.36046i	−0.288853	+	0.158798i
$755$	28.9642	+	1.65808i	1.05412	+	0.0603436i
$756$	1.84562	+	3.92213i	0.0671244	+	0.142647i
$757$	−9.95566	+	13.7028i	−0.361845	+	0.498036i	−0.950662	−	0.310230i	$-0.899594\pi$
$757$	−9.95566	+	13.7028i	−0.361845	+	0.498036i	0.588817	+	0.808266i	$0.299594\pi$
$758$	9.69083	+	10.3197i	0.351987	+	0.374828i
$759$	−50.7511	+	20.0938i	−1.84215	+	0.729358i
$760$	6.77439	+	0.816956i	0.245733	+	0.0296341i
$761$	−22.9268	+	5.88660i	−0.831096	+	0.213389i	−0.640187	−	0.768219i	$-0.721143\pi$
$761$	−22.9268	+	5.88660i	−0.831096	+	0.213389i	−0.190908	+	0.981608i	$0.561143\pi$
$762$	6.67604	−	5.52290i	0.241847	−	0.200074i
$763$	−10.3294	−	26.0892i	−0.373950	−	0.944491i
$764$	5.26983	+	2.08647i	0.190656	+	0.0754859i
$765$	5.60490	−	5.32324i	0.202645	−	0.192462i
$766$	6.87598	−	10.8348i	0.248439	−	0.391478i
$767$	11.7594	−	21.3903i	0.424609	−	0.772360i
$768$	−0.587785	−	0.809017i	−0.0212099	−	0.0291929i
$769$	8.34598	−	43.7511i	0.300964	−	1.57771i	−0.434838	−	0.900509i	$-0.643194\pi$
$769$	8.34598	−	43.7511i	0.300964	−	1.57771i	0.735801	−	0.677197i	$-0.236806\pi$
$770$	40.2165	+	42.3443i	1.44930	+	1.52598i
$771$	3.07118	−	6.52658i	0.110606	−	0.235049i
$772$	−1.17899	−	2.14457i	−0.0424327	−	0.0771848i
$773$	24.2389	+	1.52498i	0.871812	+	0.0548498i	0.492391	−	0.870374i	$-0.336123\pi$
$773$	24.2389	+	1.52498i	0.871812	+	0.0548498i	0.379421	+	0.925224i	$0.376123\pi$
$774$	5.00943	+	3.63956i	0.180060	+	0.130821i
$775$	0.432231	−	1.38325i	0.0155262	−	0.0496878i
$776$	−11.6972	+	8.49852i	−0.419905	+	0.305079i
$777$	13.5073	−	8.57201i	0.484573	−	0.307519i
$778$	−2.02384	+	16.0203i	−0.0725581	+	0.574356i
$779$	24.8239	+	3.13598i	0.889407	+	0.112358i
$780$	4.34385	+	10.7928i	0.155535	+	0.386444i
$781$	20.3541	+	11.1898i	0.728327	+	0.400401i
$782$	−29.7853	−	9.67784i	−1.06512	−	0.346079i
$783$	1.57406	−	0.740699i	0.0562525	−	0.0264704i
$784$	−11.4190	−	2.93191i	−0.407823	−	0.104711i
$785$	6.21496	+	9.67202i	0.221822	+	0.345209i
$786$	1.70003	−	2.05498i	0.0606379	−	0.0732986i
$787$	−13.7316	−	8.71431i	−0.489477	−	0.310632i	0.268084	−	0.963395i	$-0.413609\pi$
$787$	−13.7316	−	8.71431i	−0.489477	−	0.310632i	−0.757561	+	0.652764i	$0.773609\pi$
$788$	13.7442	−	0.864713i	0.489618	−	0.0308041i
$789$	9.60465	+	15.1345i	0.341934	+	0.538803i
$790$	−11.2830	−	2.82915i	−0.401431	−	0.100657i
$791$	−0.653894	−	10.3934i	−0.0232498	−	0.369545i
$792$	−5.91834	−	1.12898i	−0.210299	−	0.0401167i
$793$	39.7917	−	12.9291i	1.41304	−	0.459126i
$794$	7.95263	−	7.46802i	0.282228	−	0.265030i
$795$	−4.40163	−	5.98691i	−0.156110	−	0.212334i
$796$	0.0618259	+	0.324103i	0.00219136	+	0.0114875i
$797$	3.80980	−	4.05702i	0.134950	−	0.143707i	−0.657944	−	0.753067i	$-0.728574\pi$
$797$	3.80980	−	4.05702i	0.134950	−	0.143707i	0.792894	+	0.609360i	$0.208574\pi$
$798$	−4.86936	+	12.2986i	−0.172374	+	0.435366i
$799$	−12.2642	−	37.7454i	−0.433877	−	1.33534i
$800$	0.570587	−	4.96734i	0.0201733	−	0.175622i
$801$	−5.54185	+	17.0561i	−0.195812	+	0.602646i
$802$	12.5545	+	10.3859i	0.443313	+	0.366741i
$803$	29.1848	+	13.7333i	1.02991	+	0.484638i
$804$	−2.74372	−	2.57652i	−0.0967635	−	0.0908669i
$805$	86.1610	−	16.9410i	3.03678	−	0.597093i
$806$	1.49614	−	0.189007i	0.0526993	−	0.00665748i
$807$			12.8344i			0.451793i
$808$	2.14977	+	17.0172i	0.0756287	+	0.598662i
$809$	−15.3114	−	18.5083i	−0.538321	−	0.650718i	0.429290	−	0.903167i	$-0.358764\pi$
$809$	−15.3114	−	18.5083i	−0.538321	−	0.650718i	−0.967610	+	0.252449i	$0.918764\pi$
$810$	−0.702984	−	2.12269i	−0.0247004	−	0.0745837i
$811$	−2.98368	+	47.4243i	−0.104771	+	1.66529i	0.497848	+	0.867264i	$0.334124\pi$
$811$	−2.98368	+	47.4243i	−0.104771	+	1.66529i	−0.602620	+	0.798029i	$0.705876\pi$
$812$	−1.87530	+	7.30383i	−0.0658103	+	0.256314i
$813$	5.60924	−	21.8465i	0.196725	−	0.766192i
$814$	−1.39623	+	22.1924i	−0.0489378	+	0.777845i
$815$	0.772358	+	0.554512i	0.0270545	+	0.0194237i
$816$	−2.20353	−	2.66361i	−0.0771390	−	0.0932450i
$817$	2.36820	+	18.7462i	0.0828527	+	0.655847i
$818$		−	14.6354i		−	0.511716i
$819$	−22.3753	+	2.82666i	−0.781856	+	0.0987713i
$820$	2.19515	−	18.2027i	0.0766580	−	0.635667i
$821$	−15.2207	−	14.2932i	−0.531208	−	0.498837i	0.371887	−	0.928278i	$-0.378711\pi$
$821$	−15.2207	−	14.2932i	−0.531208	−	0.498837i	−0.903095	+	0.429441i	$0.858711\pi$
$822$	17.2977	+	8.13969i	0.603327	+	0.283904i
$823$	4.09153	+	3.38481i	0.142622	+	0.117987i	0.705999	−	0.708213i	$-0.250498\pi$
$823$	4.09153	+	3.38481i	0.142622	+	0.117987i	−0.563377	+	0.826200i	$0.690498\pi$
$824$	2.77223	−	8.53206i	0.0965753	−	0.297228i
$825$	−17.9814	−	24.1703i	−0.626032	−	0.841501i
$826$	−6.28421	−	19.3408i	−0.218656	−	0.672953i
$827$	14.3762	−	36.3101i	0.499909	−	1.26263i	−0.432635	−	0.901569i	$-0.642416\pi$
$827$	14.3762	−	36.3101i	0.499909	−	1.26263i	0.932544	−	0.361057i	$-0.117584\pi$
$828$	−6.20167	+	6.60411i	−0.215523	+	0.229509i
$829$	0.976414	+	5.11854i	0.0339123	+	0.177774i	0.995213	−	0.0977254i	$-0.0311567\pi$
$829$	0.976414	+	5.11854i	0.0339123	+	0.177774i	−0.961301	+	0.275500i	$0.911157\pi$
$830$	−16.0794	+	22.3963i	−0.558123	+	0.777387i
$831$	6.92647	−	6.50439i	0.240277	−	0.225635i
$832$	4.94830	−	1.60780i	0.171552	−	0.0557405i
$833$	−40.0333	−	7.63676i	−1.38707	−	0.264598i
$834$	0.148686	+	2.36330i	0.00514857	+	0.0818342i
$835$	28.0370	+	33.5038i	0.970260	+	1.15945i
$836$	−9.85159	−	15.5236i	−0.340724	−	0.536896i
$837$	−0.289270	+	0.0181993i	−0.00999863	+	0.000629060i
$838$	4.51013	+	2.86222i	0.155800	+	0.0988736i
$839$	−15.3127	+	18.5099i	−0.528654	+	0.639032i	−0.965469	−	0.260519i	$-0.916106\pi$
$839$	−15.3127	+	18.5099i	−0.528654	+	0.639032i	0.436815	+	0.899551i	$0.356106\pi$
$840$	9.03199	+	3.51713i	0.311633	+	0.121353i
$841$	−25.1577	−	6.45939i	−0.867506	−	0.222738i
$842$	−26.4208	+	12.4327i	−0.910520	+	0.428458i
$843$	9.41702	+	3.05978i	0.324339	+	0.105384i
$844$	−4.27321	−	2.34922i	−0.147090	−	0.0808634i
$845$	−31.3893	+	2.15292i	−1.07983	+	0.0740628i
$846$	−11.3901	−	1.43891i	−0.391601	−	0.0494708i
$847$	13.7457	−	108.808i	0.472307	−	3.73870i
$848$	−2.80585	+	1.78064i	−0.0963532	+	0.0611476i
$849$	14.7860	−	10.7427i	0.507454	−	0.368687i
$850$	0.890364	−	17.2617i	0.0305392	−	0.592071i
$851$	27.0499	+	19.6529i	0.927257	+	0.673692i
$852$	3.84748	+	0.242063i	0.131813	+	0.00829295i
$853$	−22.2870	−	40.5399i	−0.763093	−	1.38806i	−0.916556	−	0.399906i	$-0.869043\pi$
$853$	−22.2870	−	40.5399i	−0.763093	−	1.38806i	0.153463	−	0.988154i	$-0.450957\pi$
$854$	14.8415	−	31.5398i	0.507865	−	1.07927i
$855$	3.25341	−	5.99793i	0.111264	−	0.205125i
$856$	−1.08913	+	5.70940i	−0.0372256	+	0.195143i
$857$	15.5305	+	21.3759i	0.530512	+	0.730188i	0.987208	−	0.159435i	$-0.0509673\pi$
$857$	15.5305	+	21.3759i	0.530512	+	0.730188i	−0.456696	+	0.889623i	$0.650967\pi$
$858$	15.1021	−	27.4705i	0.515576	−	0.937829i
$859$	−11.6075	+	18.2905i	−0.396043	+	0.624064i	−0.982576	−	0.185861i	$-0.940492\pi$
$859$	−11.6075	+	18.2905i	−0.396043	+	0.624064i	0.586533	+	0.809925i	$0.300492\pi$
$860$	13.7265	−	1.81289i	0.468071	−	0.0618192i
$861$	33.0462	+	13.0839i	1.12621	+	0.445899i
$862$	−2.96375	−	7.48558i	−0.100946	−	0.254960i
$863$	−17.5253	+	14.4982i	−0.596570	+	0.493525i	−0.886007	−	0.463672i	$-0.846532\pi$
$863$	−17.5253	+	14.4982i	−0.596570	+	0.493525i	0.289438	+	0.957197i	$0.406532\pi$
$864$	−0.968583	+	0.248690i	−0.0329519	+	0.00846060i
$865$	−30.7510	+	17.1324i	−1.04557	+	0.582520i
$866$	−24.7063	+	9.78192i	−0.839554	+	0.332403i
$867$	3.45672	+	3.68103i	0.117396	+	0.125014i
$868$	0.738476	−	1.01643i	0.0250655	−	0.0344997i
$869$	13.3452	+	28.3601i	0.452706	+	0.962050i
$870$	1.41153	−	3.62480i	0.0478553	−	0.122892i
$871$	17.1608	−	9.43421i	0.581470	−	0.319666i
$872$	6.35863	−	1.21297i	0.215330	−	0.0410764i
$873$	3.59569	+	14.0043i	0.121696	+	0.473974i
$874$	−27.6456			−0.935127
$875$	21.3747	+	43.4948i	0.722597	+	1.47039i
$876$	5.35339			0.180874
$877$	11.0239	+	42.9351i	0.372249	+	1.44981i	0.828513	+	0.559970i	$0.189187\pi$
$877$	11.0239	+	42.9351i	0.372249	+	1.44981i	−0.456264	+	0.889845i	$0.650813\pi$
$878$	−26.6064	+	5.07545i	−0.897923	+	0.171288i
$879$	21.2342	−	11.6736i	0.716212	−	0.393741i
$880$	−11.3342	+	7.28303i	−0.382076	+	0.245511i
$881$	−19.8477	−	42.1786i	−0.668687	−	1.42103i	−0.894592	−	0.446884i	$-0.852534\pi$
$881$	−19.8477	−	42.1786i	−0.668687	−	1.42103i	0.225905	−	0.974149i	$-0.427466\pi$
$882$	−6.92965	+	9.53785i	−0.233333	+	0.321156i
$883$	−23.6947	−	25.2323i	−0.797389	−	0.849133i	0.193875	−	0.981026i	$-0.437894\pi$
$883$	−23.6947	−	25.2323i	−0.797389	−	0.849133i	−0.991264	+	0.131893i	$0.957894\pi$
$884$	16.7232	−	6.62118i	0.562461	−	0.222694i
$885$	2.02390	+	10.2934i	0.0680327	+	0.346010i
$886$	−19.5200	+	5.01189i	−0.655788	+	0.168378i
$887$	−42.5863	+	35.2304i	−1.42991	+	1.18292i	−0.477291	+	0.878745i	$0.658381\pi$
$887$	−42.5863	+	35.2304i	−1.42991	+	1.18292i	−0.952616	+	0.304176i	$0.901619\pi$
$888$	1.35862	+	3.43147i	0.0455921	+	0.115153i
$889$	34.9200	+	13.8258i	1.17118	+	0.463702i
$890$	17.2789	+	36.1876i	0.579191	+	1.21301i
$891$	−3.22839	+	5.08713i	−0.108155	+	0.170425i
$892$	1.01384	−	1.84417i	0.0339458	−	0.0617472i
$893$	−20.5924	−	28.3430i	−0.689098	−	0.948462i
$894$	−1.40994	+	7.39116i	−0.0471554	+	0.247197i
$895$	1.07196	+	8.11647i	0.0358317	+	0.271304i
$896$	1.84562	−	3.92213i	0.0616577	−	0.131029i
$897$	−22.7081	−	41.3059i	−0.758201	−	1.37916i
$898$	19.8773	+	1.25057i	0.663313	+	0.0417321i
$899$	−0.407921	−	0.296372i	−0.0136049	−	0.00988455i
$900$	−4.40847	−	2.35912i	−0.146949	−	0.0786372i
$901$	−9.29396	+	6.75246i	−0.309627	+	0.224957i
$902$	−41.7118	+	26.4711i	−1.38885	+	0.881392i
$903$	−3.36398	+	26.6287i	−0.111946	+	0.886146i
$904$	2.38352	+	0.301109i	0.0792747	+	0.0100147i
$905$	−36.8907	−	23.1203i	−1.22629	−	0.768545i
$906$	−11.3695	−	6.25046i	−0.377728	−	0.207658i
$907$	−32.3126	−	10.4990i	−1.07292	−	0.348614i	−0.281298	−	0.959621i	$-0.590765\pi$
$907$	−32.3126	−	10.4990i	−1.07292	−	0.348614i	−0.791625	+	0.611007i	$0.790765\pi$
$908$	19.4584	−	9.15643i	0.645750	−	0.303867i
$909$	16.6136	+	4.26564i	0.551037	+	0.141482i
$910$	−31.9255	+	39.0382i	−1.05832	+	1.29410i
$911$	15.8850	−	19.2016i	0.526293	−	0.636179i	−0.438644	−	0.898661i	$-0.644541\pi$
$911$	15.8850	−	19.2016i	0.526293	−	0.636179i	0.964937	+	0.262482i	$0.0845410\pi$
$912$	−2.57651	−	1.63510i	−0.0853168	−	0.0541437i
$913$	74.1422	−	4.66463i	2.45375	−	0.154377i
$914$	2.07753	+	3.27366i	0.0687186	+	0.108283i
$915$	−9.54895	+	15.2363i	−0.315679	+	0.503696i
$916$	−0.193366	−	3.07346i	−0.00638899	−	0.101550i
$917$	11.3559	+	2.16626i	0.375006	+	0.0715361i
$918$	−3.28773	+	1.06825i	−0.108511	+	0.0352575i
$919$	12.2245	−	11.4796i	0.403249	−	0.378676i	−0.456217	−	0.889868i	$-0.650796\pi$
$919$	12.2245	−	11.4796i	0.403249	−	0.378676i	0.859466	+	0.511192i	$0.170796\pi$
$920$	0.114427	+	20.2574i	0.00377255	+	0.667867i
$921$	−0.283210	−	1.48464i	−0.00933210	−	0.0489206i
$922$	−16.0287	+	17.0688i	−0.527877	+	0.562132i
$923$	−7.38379	+	18.6493i	−0.243040	+	0.613850i
$924$	−8.07050	−	24.8384i	−0.265500	−	0.817125i
$925$	−6.59882	+	17.2330i	−0.216968	+	0.566617i
$926$	0.228695	−	0.703852i	0.00751539	−	0.0231300i
$927$	−6.91238	−	5.71842i	−0.227032	−	0.187817i
$928$	−1.57406	−	0.740699i	−0.0516712	−	0.0243146i
$929$	−12.6411	−	11.8708i	−0.414742	−	0.389469i	0.448894	−	0.893585i	$-0.351818\pi$
$929$	−12.6411	−	11.8708i	−0.414742	−	0.389469i	−0.863636	+	0.504116i	$0.831818\pi$
$930$	−0.440983	+	0.474947i	−0.0144604	+	0.0155741i
$931$	−35.6924	+	4.50899i	−1.16977	+	0.147776i
$932$			16.3823i			0.536621i
$933$	3.98601	+	31.5525i	0.130496	+	1.03298i
$934$	5.29728	+	6.40331i	0.173332	+	0.209523i
$935$	−37.5233	+	27.5875i	−1.22714	+	0.902207i
$936$	0.326696	−	5.19269i	0.0106784	−	0.169728i
$937$	5.57155	−	21.6998i	0.182015	−	0.708900i	−0.810391	−	0.585890i	$-0.800745\pi$
$937$	5.57155	−	21.6998i	0.182015	−	0.708900i	0.992405	−	0.123011i	$-0.0392549\pi$
$938$	4.05738	−	15.8024i	0.132478	−	0.515968i
$939$	−1.83872	+	29.2256i	−0.0600043	+	0.953742i
$940$	−20.6832	+	15.2064i	−0.674611	+	0.495979i
$941$	−23.4930	−	28.3982i	−0.765850	−	0.925753i	0.233059	−	0.972463i	$-0.425127\pi$
$941$	−23.4930	−	28.3982i	−0.765850	−	0.925753i	−0.998909	+	0.0467094i	$0.985127\pi$
$942$	−0.644397	−	5.10093i	−0.0209956	−	0.166197i
$943$			74.2835i			2.41900i
$944$	4.65451	−	0.588001i	0.151491	−	0.0191378i
$945$	6.59505	−	7.10299i	0.214537	−	0.231060i
$946$	−27.1957	−	25.5385i	−0.884210	−	0.830328i
$947$	28.2268	+	13.2825i	0.917247	+	0.431624i	0.825656	−	0.564173i	$-0.190805\pi$
$947$	28.2268	+	13.2825i	0.917247	+	0.431624i	0.0915904	+	0.995797i	$0.470805\pi$
$948$	4.00830	+	3.31596i	0.130184	+	0.107697i
$949$	−8.60719	+	26.4902i	−0.279401	+	0.859909i
$950$	−3.96116	−	14.7346i	−0.128517	−	0.478053i
$951$	6.93209	+	21.3348i	0.224788	+	0.691827i
$952$	5.51622	−	13.9324i	0.178782	−	0.451551i
$953$	−28.9771	+	30.8575i	−0.938661	+	0.999572i	0.0613380	+	0.998117i	$0.480463\pi$
$953$	−28.9771	+	30.8575i	−0.938661	+	0.999572i	−0.999999	+	0.00145530i	$0.999537\pi$
$954$	0.622700	+	3.26431i	0.0201607	+	0.105686i
$955$	−0.0715881	−	12.6735i	−0.00231654	−	0.410104i
$956$	0.346913	−	0.325773i	0.0112200	−	0.0105363i
$957$	−9.96838	+	3.23892i	−0.322232	+	0.104700i
$958$	24.2813	+	4.63190i	0.784493	+	0.149650i
$959$	5.20324	+	82.7032i	0.168021	+	2.67062i
$960$	−1.18746	+	1.89471i	−0.0383252	+	0.0611516i
$961$	−16.5656	−	26.1032i	−0.534375	−	0.842040i
$962$	−19.1643	+	1.20572i	−0.617883	+	0.0388739i
$963$	4.90753	+	3.11441i	0.158143	+	0.100361i
$964$	4.01773	−	4.85660i	0.129402	−	0.156421i
$965$	−3.46430	+	4.23611i	−0.111520	+	0.136365i
$966$	−38.0364	−	9.76608i	−1.22380	−	0.314219i
$967$	20.1294	−	9.47219i	0.647319	−	0.304605i	−0.0739482	−	0.997262i	$-0.523560\pi$
$967$	20.1294	−	9.47219i	0.647319	−	0.304605i	0.721267	+	0.692657i	$0.243560\pi$
$968$	24.0630	+	7.81854i	0.773414	+	0.251297i
$969$	−9.24416	−	5.08202i	−0.296965	−	0.163258i
$970$	27.3948	+	17.1690i	0.879593	+	0.551262i
$971$	−34.2016	−	4.32067i	−1.09758	−	0.138657i	−0.444378	−	0.895839i	$-0.646575\pi$
$971$	−34.2016	−	4.32067i	−1.09758	−	0.138657i	−0.653204	+	0.757182i	$0.726575\pi$
$972$	−0.125333	+	0.992115i	−0.00402007	+	0.0318221i
$973$	−8.66650	+	5.49993i	−0.277835	+	0.176320i
$974$	14.1247	−	10.2622i	0.452585	−	0.328822i
$975$	18.7616	−	18.0214i	0.600851	−	0.577148i
$976$	6.50569	+	4.72666i	0.208242	+	0.151297i
$977$	44.8172	+	2.81966i	1.43383	+	0.0902089i	0.760598	−	0.649223i	$-0.224906\pi$
$977$	44.8172	+	2.81966i	1.43383	+	0.0902089i	0.673232	+	0.739432i	$0.264906\pi$
$978$	−0.204847	−	0.372615i	−0.00655028	−	0.0119149i
$979$	46.0064	−	97.7685i	1.47037	−	3.12470i
$980$	3.45171	+	26.1350i	0.110261	+	0.834852i
$981$	1.21297	−	6.35863i	0.0387272	−	0.203015i
$982$	−8.67699	−	11.9429i	−0.276894	−	0.381112i
$983$	−22.4824	+	40.8953i	−0.717076	+	1.30436i	0.226763	+	0.973950i	$0.427186\pi$
$983$	−22.4824	+	40.8953i	−0.717076	+	1.30436i	−0.943839	+	0.330406i	$0.892814\pi$
$984$	−4.39350	+	6.92305i	−0.140060	+	0.220699i
$985$	−13.2685	−	27.7885i	−0.422771	−	0.885417i
$986$	−5.59147	−	2.21382i	−0.178069	−	0.0705024i
$987$	−18.3197	−	46.2703i	−0.583123	−	1.47280i
$988$	12.2335	−	10.1204i	0.389199	−	0.321974i
$989$	−54.3342	+	13.9507i	−1.72773	+	0.443605i
$990$	2.59920	+	13.2193i	0.0826079	+	0.420138i
$991$	4.30348	−	1.70387i	0.136705	−	0.0541252i	−0.298776	−	0.954323i	$-0.596578\pi$
$991$	4.30348	−	1.70387i	0.136705	−	0.0541252i	0.435481	+	0.900198i	$0.356578\pi$
$992$	0.198410	+	0.211286i	0.00629954	+	0.00670832i
$993$	12.0416	−	16.5739i	0.382130	−	0.525956i
$994$	7.11502	+	15.1202i	0.225675	+	0.479583i
$995$	0.620688	−	0.398837i	0.0196771	−	0.0126440i
$996$	10.8048	−	5.94001i	0.342364	−	0.188216i
$997$	9.57575	−	1.82667i	0.303267	−	0.0578513i	−0.0335018	−	0.999439i	$-0.510666\pi$
$997$	9.57575	−	1.82667i	0.303267	−	0.0578513i	0.336769	+	0.941587i	$0.390666\pi$
$998$	5.95344	+	23.1871i	0.188453	+	0.733975i
$999$	3.69064			0.116767

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.b.229.6	✓	280
125.119	even	50	inner	750.2.o.b.619.6	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.b.229.6	✓	280	1.1	even	1	trivial
750.2.o.b.619.6	yes	280	125.119	even	50	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.248690 - 0.968583i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(1.73094 + 1.41557i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(2.54786 - 3.50683i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})\)	\(q+(-0.248690 - 0.968583i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(1.73094 + 1.41557i) q^{5} +(-0.425779 - 0.904827i) q^{6} +(2.54786 - 3.50683i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(0.940628 - 2.02860i) q^{10} +(-5.83577 + 1.49837i) q^{11} +(-0.770513 + 0.637424i) q^{12} +(-1.91533 - 4.83758i) q^{13} +(-4.03028 - 1.59570i) q^{14} +(1.96553 + 1.06615i) q^{15} +(0.535827 - 0.844328i) q^{16} +(1.66539 - 3.02933i) q^{17} +(-0.587785 - 0.809017i) q^{18} +(0.571804 - 2.99750i) q^{19} +(-2.19879 - 0.406584i) q^{20} +(1.84562 - 3.92213i) q^{21} +(2.90259 + 5.27980i) q^{22} +(9.04165 + 0.568852i) q^{23} +(0.809017 + 0.587785i) q^{24} +(0.992331 + 4.90054i) q^{25} +(-4.20928 + 3.05822i) q^{26} +(0.844328 - 0.535827i) q^{27} +(-0.543279 + 4.30050i) q^{28} +(1.72591 + 0.218034i) q^{29} +(0.543845 - 2.16892i) q^{30} +(-0.253990 - 0.139632i) q^{31} +(-0.951057 - 0.309017i) q^{32} +(-5.45164 + 2.56535i) q^{33} +(-3.34832 - 0.859703i) q^{34} +(9.37436 - 2.46345i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(3.11611 + 1.97754i) q^{37} +(-3.04553 + 0.191608i) q^{38} +(-2.78788 - 4.39300i) q^{39} +(0.153007 + 2.23083i) q^{40} +(0.514850 + 8.18331i) q^{41} +(-4.25790 - 0.812237i) q^{42} +(-5.88894 + 1.91343i) q^{43} +(4.39208 - 4.12444i) q^{44} +(2.13050 + 0.678960i) q^{45} +(-1.69759 - 8.89906i) q^{46} +(7.85906 - 8.36905i) q^{47} +(0.368125 - 0.929776i) q^{48} +(-3.64313 - 11.2124i) q^{49} +(4.49980 - 2.17987i) q^{50} +(1.06825 - 3.28773i) q^{51} +(4.00894 + 3.31649i) q^{52} +(-3.00690 - 1.41494i) q^{53} +(-0.728969 - 0.684547i) q^{54} +(-12.2224 - 5.66734i) q^{55} +(4.30050 - 0.543279i) q^{56} -3.05155i q^{57} +(-0.218034 - 1.72591i) q^{58} +(2.99047 + 3.61486i) q^{59} +(-2.23603 + 0.0126306i) q^{60} +(-0.504929 + 8.02561i) q^{61} +(-0.0720807 + 0.280736i) q^{62} +(1.07799 - 4.19850i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(3.53259 - 11.0849i) q^{65} +(3.84052 + 4.64239i) q^{66} +(0.471734 + 3.73416i) q^{67} +3.45693i q^{68} +(8.98809 - 1.13546i) q^{69} +(-4.71736 - 8.46721i) q^{70} +(-2.81024 - 2.63899i) q^{71} +(0.904827 + 0.425779i) q^{72} +(-4.12486 - 3.41238i) q^{73} +(1.14047 - 3.51001i) q^{74} +(1.89302 + 4.62779i) q^{75} +(0.942981 + 2.90220i) q^{76} +(-9.61419 + 24.2827i) q^{77} +(-3.56167 + 3.79279i) q^{78} +(-0.974780 - 5.10998i) q^{79} +(2.12269 - 0.702984i) q^{80} +(0.728969 - 0.684547i) q^{81} +(7.79817 - 2.53378i) q^{82} +(-12.1116 - 2.31041i) q^{83} +(0.272177 + 4.32612i) q^{84} +(7.17092 - 2.88613i) q^{85} +(3.31784 + 5.22808i) q^{86} +(1.73620 - 0.109232i) q^{87} +(-5.08713 - 3.22839i) q^{88} +(-11.4314 + 13.8182i) q^{89} +(0.127796 - 2.23241i) q^{90} +(-21.8446 - 5.60873i) q^{91} +(-8.19731 + 3.85736i) q^{92} +(-0.275656 - 0.0895660i) q^{93} +(-10.0606 - 5.53086i) q^{94} +(5.23293 - 4.37908i) q^{95} +(-0.992115 - 0.125333i) q^{96} +(-1.81214 + 14.3445i) q^{97} +(-9.95414 + 6.31709i) q^{98} +(-4.87438 + 3.54144i) 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

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