LMFDB - Embedded newform 750.2.o.b.469.4

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			469.4
Character	$\chi$	$=$	750.469
Dual form			750.2.o.b.379.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.998027 + 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-0.667283 + 2.13418i) q^{5} +(0.876307 - 0.481754i) q^{6} +(-0.730561 - 1.00553i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})$	\(q+(-0.998027 + 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-0.667283 + 2.13418i) q^{5} +(0.876307 - 0.481754i) q^{6} +(-0.730561 - 1.00553i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(0.531960 - 2.17187i) q^{10} +(-0.175185 - 2.78448i) q^{11} +(-0.844328 + 0.535827i) q^{12} +(4.50562 + 3.72737i) q^{13} +(0.792257 + 0.957674i) q^{14} +(-0.304914 - 2.21518i) q^{15} +(0.968583 - 0.248690i) q^{16} +(-0.848009 + 6.71268i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(0.281773 - 0.598798i) q^{19} +(-0.394538 + 2.20099i) q^{20} +(1.08917 + 0.598774i) q^{21} +(0.349678 + 2.76799i) q^{22} +(-0.207200 - 0.523328i) q^{23} +(0.809017 - 0.587785i) q^{24} +(-4.10947 - 2.84821i) q^{25} +(-4.73077 - 3.43711i) q^{26} +(-0.248690 + 0.968583i) q^{27} +(-0.850827 - 0.906038i) q^{28} +(-4.94145 + 4.64033i) q^{29} +(0.443405 + 2.19166i) q^{30} +(0.951784 + 0.120238i) q^{31} +(-0.951057 + 0.309017i) q^{32} +(1.34409 + 2.44488i) q^{33} +(0.424843 - 6.75268i) q^{34} +(2.63348 - 0.888176i) q^{35} +(0.535827 - 0.844328i) q^{36} +(0.819450 + 3.19155i) q^{37} +(-0.243618 + 0.615310i) q^{38} +(-5.66385 - 1.45423i) q^{39} +(0.255558 - 2.22142i) q^{40} +(-10.5231 - 4.16638i) q^{41} +(-1.12461 - 0.529203i) q^{42} +(-6.65187 - 2.16132i) q^{43} +(-0.522791 - 2.74057i) q^{44} +(1.21907 + 1.87453i) q^{45} +(0.239651 + 0.509285i) q^{46} +(-2.11530 - 0.403516i) q^{47} +(-0.770513 + 0.637424i) q^{48} +(1.68575 - 5.18819i) q^{49} +(4.28020 + 2.58455i) q^{50} +(-2.09082 - 6.43488i) q^{51} +(4.93726 + 3.13328i) q^{52} +(-1.85004 + 3.36521i) q^{53} +(0.187381 - 0.982287i) q^{54} +(6.05948 + 1.48416i) q^{55} +(0.906038 + 0.850827i) q^{56} +0.661782i q^{57} +(4.64033 - 4.94145i) q^{58} +(3.89693 + 6.14057i) q^{59} +(-0.580146 - 2.15950i) q^{60} +(-10.4611 + 4.14184i) q^{61} +(-0.957456 - 0.0602380i) q^{62} +(-1.24045 - 0.0780426i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-10.9614 + 7.12860i) q^{65} +(-1.49495 - 2.35566i) q^{66} +(-7.54035 + 8.02966i) q^{67} +6.76603i q^{68} +(0.410302 + 0.385300i) q^{69} +(-2.57251 + 1.05178i) q^{70} +(-2.21060 + 11.5884i) q^{71} +(-0.481754 + 0.876307i) q^{72} +(6.33052 + 4.01747i) q^{73} +(-1.01823 - 3.13380i) q^{74} +(4.93106 + 0.827410i) q^{75} +(0.204502 - 0.629392i) q^{76} +(-2.67190 + 2.21039i) q^{77} +(5.74398 + 1.09572i) q^{78} +(-3.38620 - 7.19604i) q^{79} +(-0.115570 + 2.23308i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(10.7639 + 3.49741i) q^{82} +(3.34978 + 1.57629i) q^{83} +(1.15562 + 0.457544i) q^{84} +(-13.7602 - 6.28906i) q^{85} +(6.77446 + 1.73938i) q^{86} +(2.49540 - 6.30266i) q^{87} +(0.693841 + 2.70233i) q^{88} +(0.422832 - 0.666276i) q^{89} +(-1.33437 - 1.79428i) q^{90} +(0.456359 - 7.25362i) q^{91} +(-0.271157 - 0.493232i) q^{92} +(-0.912395 + 0.296455i) q^{93} +(2.13647 + 0.269898i) q^{94} +(1.08992 + 1.00092i) q^{95} +(0.728969 - 0.684547i) q^{96} +(-9.86922 - 10.5097i) q^{97} +(-1.35665 + 5.28380i) q^{98} +(-2.25715 - 1.63991i) 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 $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{49}{50}\right)$	$1$

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 $

$2$	−0.998027	+	0.0627905i	−0.705711	+	0.0443996i
$2$	−0.998027	+	0.0627905i	−0.705711	+	0.0443996i
$3$	−0.904827	+	0.425779i	−0.522402	+	0.245824i
$3$	−0.904827	+	0.425779i	−0.522402	+	0.245824i
$4$	0.992115	−	0.125333i	0.496057	−	0.0626666i
$5$	−0.667283	+	2.13418i	−0.298418	+	0.954435i
$5$	−0.667283	+	2.13418i	−0.298418	+	0.954435i
$6$	0.876307	−	0.481754i	0.357751	−	0.196675i
$7$	−0.730561	−	1.00553i	−0.276126	−	0.380055i	0.648320	−	0.761368i	$-0.275472\pi$
$7$	−0.730561	−	1.00553i	−0.276126	−	0.380055i	−0.924446	+	0.381313i	$0.875472\pi$
$8$	−0.982287	+	0.187381i	−0.347291	+	0.0662493i
$9$	0.637424	−	0.770513i	0.212475	−	0.256838i
$10$	0.531960	−	2.17187i	0.168221	−	0.686806i
$11$	−0.175185	−	2.78448i	−0.0528201	−	0.839552i	−0.931863	−	0.362810i	$-0.881817\pi$
$11$	−0.175185	−	2.78448i	−0.0528201	−	0.839552i	0.879043	−	0.476742i	$-0.158183\pi$
$12$	−0.844328	+	0.535827i	−0.243736	+	0.154680i
$13$	4.50562	+	3.72737i	1.24963	+	1.03379i	0.997819	+	0.0660125i	$0.0210277\pi$
$13$	4.50562	+	3.72737i	1.24963	+	1.03379i	0.251816	+	0.967775i	$0.418972\pi$
$14$	0.792257	+	0.957674i	0.211740	+	0.255949i
$15$	−0.304914	−	2.21518i	−0.0787286	−	0.571957i
$16$	0.968583	−	0.248690i	0.242146	−	0.0621725i
$17$	−0.848009	+	6.71268i	−0.205672	+	1.62806i	0.464300	+	0.885678i	$0.346306\pi$
$17$	−0.848009	+	6.71268i	−0.205672	+	1.62806i	−0.669972	+	0.742386i	$0.733694\pi$
$18$	−0.587785	+	0.809017i	−0.138542	+	0.190687i
$19$	0.281773	−	0.598798i	0.0646432	−	0.137374i	−0.869895	−	0.493238i	$-0.835813\pi$
$19$	0.281773	−	0.598798i	0.0646432	−	0.137374i	0.934538	+	0.355864i	$0.115813\pi$
$20$	−0.394538	+	2.20099i	−0.0882213	+	0.492155i
$21$	1.08917	+	0.598774i	0.237675	+	0.130663i
$22$	0.349678	+	2.76799i	0.0745516	+	0.590136i
$23$	−0.207200	−	0.523328i	−0.0432042	−	0.109121i	0.906572	−	0.422051i	$-0.138690\pi$
$23$	−0.207200	−	0.523328i	−0.0432042	−	0.109121i	−0.949776	+	0.312929i	$0.898690\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	−4.10947	−	2.84821i	−0.821893	−	0.569642i
$26$	−4.73077	−	3.43711i	−0.927781	−	0.674073i
$27$	−0.248690	+	0.968583i	−0.0478604	+	0.186404i
$28$	−0.850827	−	0.906038i	−0.160791	−	0.171225i
$29$	−4.94145	+	4.64033i	−0.917604	+	0.861687i	−0.990759	−	0.135633i	$-0.956693\pi$
$29$	−4.94145	+	4.64033i	−0.917604	+	0.861687i	0.0731553	+	0.997321i	$0.476693\pi$
$30$	0.443405	+	2.19166i	0.0809543	+	0.400141i
$31$	0.951784	+	0.120238i	0.170945	+	0.0215954i	0.210340	−	0.977628i	$-0.432543\pi$
$31$	0.951784	+	0.120238i	0.170945	+	0.0215954i	−0.0393945	+	0.999224i	$0.512543\pi$
$32$	−0.951057	+	0.309017i	−0.168125	+	0.0546270i
$33$	1.34409	+	2.44488i	0.233975	+	0.425599i
$34$	0.424843	−	6.75268i	0.0728599	−	1.15808i
$35$	2.63348	−	0.888176i	0.445139	−	0.150129i
$36$	0.535827	−	0.844328i	0.0893045	−	0.140721i
$37$	0.819450	+	3.19155i	0.134717	+	0.524687i	0.999737	+	0.0229495i	$0.00730570\pi$
$37$	0.819450	+	3.19155i	0.134717	+	0.524687i	−0.865020	+	0.501738i	$0.832694\pi$
$38$	−0.243618	+	0.615310i	−0.0395201	+	0.0998164i
$39$	−5.66385	−	1.45423i	−0.906941	−	0.232863i
$40$	0.255558	−	2.22142i	0.0404073	−	0.351237i
$41$	−10.5231	−	4.16638i	−1.64343	−	0.650680i	−0.649466	−	0.760391i	$-0.725008\pi$
$41$	−10.5231	−	4.16638i	−1.64343	−	0.650680i	−0.993964	+	0.109711i	$0.965008\pi$
$42$	−1.12461	−	0.529203i	−0.173532	−	0.0816578i
$43$	−6.65187	−	2.16132i	−1.01440	−	0.329599i	−0.245795	−	0.969322i	$-0.579049\pi$
$43$	−6.65187	−	2.16132i	−1.01440	−	0.329599i	−0.768606	+	0.639723i	$0.779049\pi$
$44$	−0.522791	−	2.74057i	−0.0788137	−	0.413156i
$45$	1.21907	+	1.87453i	0.181729	+	0.279438i
$46$	0.239651	+	0.509285i	0.0353347	+	0.0750900i
$47$	−2.11530	−	0.403516i	−0.308549	−	0.0588588i	0.0307815	−	0.999526i	$-0.490200\pi$
$47$	−2.11530	−	0.403516i	−0.308549	−	0.0588588i	−0.339330	+	0.940667i	$0.610200\pi$
$48$	−0.770513	+	0.637424i	−0.111214	+	0.0920042i
$49$	1.68575	−	5.18819i	0.240821	−	0.741170i
$50$	4.28020	+	2.58455i	0.605311	+	0.365511i
$51$	−2.09082	−	6.43488i	−0.292773	−	0.901063i
$52$	4.93726	+	3.13328i	0.684674	+	0.434508i
$53$	−1.85004	+	3.36521i	−0.254122	+	0.462246i	−0.972339	−	0.233572i	$-0.924958\pi$
$53$	−1.85004	+	3.36521i	−0.254122	+	0.462246i	0.718217	+	0.695819i	$0.244958\pi$
$54$	0.187381	−	0.982287i	0.0254994	−	0.133672i
$55$	6.05948	+	1.48416i	0.817061	+	0.200124i
$56$	0.906038	+	0.850827i	0.121074	+	0.113697i
$57$			0.661782i			0.0876552i
$58$	4.64033	−	4.94145i	0.609305	−	0.648844i
$59$	3.89693	+	6.14057i	0.507337	+	0.799435i	0.997386	−	0.0722602i	$-0.0230212\pi$
$59$	3.89693	+	6.14057i	0.507337	+	0.799435i	−0.490049	+	0.871695i	$0.663021\pi$
$60$	−0.580146	−	2.15950i	−0.0748965	−	0.278790i
$61$	−10.4611	+	4.14184i	−1.33940	+	0.530308i	−0.925063	−	0.379813i	$-0.875988\pi$
$61$	−10.4611	+	4.14184i	−1.33940	+	0.530308i	−0.414342	+	0.910121i	$0.635988\pi$
$62$	−0.957456	−	0.0602380i	−0.121597	−	0.00765024i
$63$	−1.24045	−	0.0780426i	−0.156282	−	0.00983245i
$64$	0.929776	−	0.368125i	0.116222	−	0.0460156i
$65$	−10.9614	+	7.12860i	−1.35960	+	0.884194i
$66$	−1.49495	−	2.35566i	−0.184015	−	0.289962i
$67$	−7.54035	+	8.02966i	−0.921201	+	0.980979i	−0.999873	−	0.0159213i	$-0.994932\pi$
$67$	−7.54035	+	8.02966i	−0.921201	+	0.980979i	0.0786724	+	0.996901i	$0.474932\pi$
$68$			6.76603i			0.820502i
$69$	0.410302	+	0.385300i	0.0493946	+	0.0463846i
$70$	−2.57251	+	1.05178i	−0.307474	+	0.125712i
$71$	−2.21060	+	11.5884i	−0.262350	+	1.37528i	0.570278	+	0.821452i	$0.306835\pi$
$71$	−2.21060	+	11.5884i	−0.262350	+	1.37528i	−0.832628	+	0.553833i	$0.813165\pi$
$72$	−0.481754	+	0.876307i	−0.0567752	+	0.103274i
$73$	6.33052	+	4.01747i	0.740931	+	0.470209i	0.851959	−	0.523608i	$-0.175414\pi$
$73$	6.33052	+	4.01747i	0.740931	+	0.470209i	−0.111028	+	0.993817i	$0.535414\pi$
$74$	−1.01823	−	3.13380i	−0.118367	−	0.364296i
$75$	4.93106	+	0.827410i	0.569390	+	0.0955411i
$76$	0.204502	−	0.629392i	0.0234580	−	0.0721962i
$77$	−2.67190	+	2.21039i	−0.304491	+	0.251897i
$78$	5.74398	+	1.09572i	0.650378	+	0.124066i
$79$	−3.38620	−	7.19604i	−0.380977	−	0.809618i	−0.999712	−	0.0240173i	$-0.992354\pi$
$79$	−3.38620	−	7.19604i	−0.380977	−	0.809618i	0.618734	−	0.785600i	$-0.287646\pi$
$80$	−0.115570	+	2.23308i	−0.0129211	+	0.249666i
$81$	−0.187381	−	0.982287i	−0.0208201	−	0.109143i
$82$	10.7639	+	3.49741i	1.18868	+	0.386225i
$83$	3.34978	+	1.57629i	0.367686	+	0.173020i	0.600741	−	0.799444i	$-0.294872\pi$
$83$	3.34978	+	1.57629i	0.367686	+	0.173020i	−0.233055	+	0.972464i	$0.574872\pi$
$84$	1.15562	+	0.457544i	0.126089	+	0.0499221i
$85$	−13.7602	−	6.28906i	−1.49251	−	0.682145i
$86$	6.77446	+	1.73938i	0.730508	+	0.187563i
$87$	2.49540	−	6.30266i	0.267535	−	0.675716i
$88$	0.693841	+	2.70233i	0.0739637	+	0.288070i
$89$	0.422832	−	0.666276i	0.0448201	−	0.0706251i	−0.821179	−	0.570671i	$-0.806683\pi$
$89$	0.422832	−	0.666276i	0.0448201	−	0.0706251i	0.865999	+	0.500045i	$0.166683\pi$
$90$	−1.33437	−	1.79428i	−0.140655	−	0.189134i
$91$	0.456359	−	7.25362i	0.0478394	−	0.760386i
$92$	−0.271157	−	0.493232i	−0.0282700	−	0.0514230i
$93$	−0.912395	+	0.296455i	−0.0946110	+	0.0307410i
$94$	2.13647	+	0.269898i	0.220360	+	0.0278379i
$95$	1.08992	+	1.00092i	0.111824	+	0.102693i
$96$	0.728969	−	0.684547i	0.0744000	−	0.0698663i
$97$	−9.86922	−	10.5097i	−1.00207	−	1.06709i	−0.997746	−	0.0671031i	$-0.978624\pi$
$97$	−9.86922	−	10.5097i	−1.00207	−	1.06709i	−0.00432171	−	0.999991i	$-0.501376\pi$
$98$	−1.35665	+	5.28380i	−0.137042	+	0.533745i
$99$	−2.25715	−	1.63991i	−0.226852	−	0.164817i
$100$	−4.43404	−	2.31070i	−0.443404	−	0.231070i
$101$	−3.14363	+	2.28398i	−0.312803	+	0.227264i	−0.733098	−	0.680123i	$-0.761926\pi$
$101$	−3.14363	+	2.28398i	−0.312803	+	0.227264i	0.420295	+	0.907387i	$0.361926\pi$
$102$	2.49074	+	6.29090i	0.246620	+	0.622892i
$103$	1.34934	+	10.6811i	0.132954	+	1.05244i	0.907538	+	0.419969i	$0.137959\pi$
$103$	1.34934	+	10.6811i	0.132954	+	1.05244i	−0.774584	+	0.632470i	$0.782041\pi$
$104$	−5.12425	−	2.81708i	−0.502475	−	0.276238i
$105$	−2.00467	+	1.92493i	−0.195636	+	0.187854i
$106$	1.63508	−	3.47473i	0.158813	−	0.337496i
$107$	−8.00332	+	11.0156i	−0.773710	+	1.06492i	0.222238	+	0.974992i	$0.428664\pi$
$107$	−8.00332	+	11.0156i	−0.773710	+	1.06492i	−0.995948	+	0.0899280i	$0.971336\pi$
$108$	−0.125333	+	0.992115i	−0.0120602	+	0.0954663i
$109$	10.2189	−	2.62377i	0.978794	−	0.251312i	0.274787	−	0.961505i	$-0.411393\pi$
$109$	10.2189	−	2.62377i	0.978794	−	0.251312i	0.704007	+	0.710193i	$0.251393\pi$
$110$	−6.14072	−	1.10075i	−0.585495	−	0.104953i
$111$	−2.10036	−	2.53889i	−0.199357	−	0.240981i
$112$	−0.957674	−	0.792257i	−0.0904917	−	0.0748613i
$113$	5.77556	−	3.66528i	0.543319	−	0.344801i	−0.235675	−	0.971832i	$-0.575730\pi$
$113$	5.77556	−	3.66528i	0.543319	−	0.344801i	0.778994	+	0.627031i	$0.215730\pi$
$114$	−0.0415536	−	0.660476i	−0.00389186	−	0.0618593i
$115$	1.25514	−	0.0929949i	0.117042	−	0.00867182i
$116$	−4.32090	+	5.22307i	−0.401185	+	0.484949i
$117$	5.74398	−	1.09572i	0.531031	−	0.101300i
$118$	−4.27481	−	5.88377i	−0.393528	−	0.541645i
$119$	7.36933	−	4.05132i	0.675545	−	0.371384i
$120$	0.714597	+	2.11881i	0.0652335	+	0.193420i
$121$	3.19062	−	0.403070i	0.290057	−	0.0366427i
$122$	10.1804	−	4.79052i	0.921688	−	0.433713i
$123$	11.2955	−	0.710655i	1.01848	−	0.0640776i
$124$	0.959349			0.0861521
$125$	8.82077	−	6.86979i	0.788954	−	0.614452i
$126$	1.24290			0.110727
$127$	−10.9166	+	0.686816i	−0.968694	+	0.0609450i	−0.539247	−	0.842147i	$-0.681291\pi$
$127$	−10.9166	+	0.686816i	−0.968694	+	0.0609450i	−0.429446	+	0.903092i	$0.641291\pi$
$128$	−0.904827	+	0.425779i	−0.0799762	+	0.0376339i
$129$	6.93904	−	0.876605i	0.610948	−	0.0771807i
$130$	10.4922	−	7.80281i	0.920225	−	0.684352i
$131$	11.4139	−	6.27484i	0.997237	−	0.548235i	0.102454	−	0.994738i	$-0.467331\pi$
$131$	11.4139	−	6.27484i	0.997237	−	0.548235i	0.894783	+	0.446502i	$0.147331\pi$
$132$	1.63991	+	2.25715i	0.142736	+	0.196459i
$133$	−0.807963	+	0.154127i	−0.0700593	+	0.0133645i
$134$	7.02129	−	8.48728i	0.606547	−	0.733189i
$135$	−1.90119	−	1.17707i	−0.163628	−	0.101306i
$136$	−0.424843	−	6.75268i	−0.0364300	−	0.579038i
$137$	−16.2243	+	10.2962i	−1.38613	+	0.879666i	−0.999101	−	0.0424013i	$-0.986499\pi$
$137$	−16.2243	+	10.2962i	−1.38613	+	0.879666i	−0.387031	+	0.922067i	$0.626499\pi$
$138$	−0.433686	−	0.358776i	−0.0369178	−	0.0305411i
$139$	6.29192	+	7.60562i	0.533673	+	0.645100i	0.966588	−	0.256335i	$-0.0825149\pi$
$139$	6.29192	+	7.60562i	0.533673	+	0.645100i	−0.432915	+	0.901435i	$0.642515\pi$
$140$	2.50139	−	1.21123i	0.211406	−	0.102368i
$141$	2.08579	−	0.535540i	0.175655	−	0.0451006i
$142$	1.47860	−	11.7043i	0.124081	−	0.982203i
$143$	9.58948	−	13.1988i	0.801913	−	1.10374i
$144$	0.425779	−	0.904827i	0.0354816	−	0.0754023i
$145$	−6.60596	−	13.6424i	−0.548595	−	1.13294i
$146$	−6.57029	−	3.61205i	−0.543761	−	0.298935i
$147$	0.683716	+	5.41217i	0.0563920	+	0.446388i
$148$	1.21300	+	3.06368i	0.0997076	+	0.251833i
$149$	7.24542	−	5.26411i	0.593568	−	0.431253i	−0.250022	−	0.968240i	$-0.580438\pi$
$149$	7.24542	−	5.26411i	0.593568	−	0.431253i	0.843590	+	0.536988i	$0.180438\pi$
$150$	−4.97329	−	0.516154i	−0.406067	−	0.0421438i
$151$	16.2610	+	11.8143i	1.32330	+	0.961436i	0.999885	+	0.0151793i	$0.00483189\pi$
$151$	16.2610	+	11.8143i	1.32330	+	0.961436i	0.323418	+	0.946256i	$0.395168\pi$
$152$	−0.164579	+	0.640991i	−0.0133491	+	0.0519912i
$153$	4.63167	+	4.93222i	0.374448	+	0.398747i
$154$	2.52783	−	2.37379i	0.203699	−	0.191286i
$155$	−0.891720	+	1.95105i	−0.0716247	+	0.156712i
$156$	−5.80145	−	0.732893i	−0.464488	−	0.0586784i
$157$	0.0511636	−	0.0166241i	0.00408330	−	0.00132674i	−0.306975	−	0.951718i	$-0.599317\pi$
$157$	0.0511636	−	0.0166241i	0.00408330	−	0.00132674i	0.311058	+	0.950391i	$0.399317\pi$
$158$	3.83136	+	6.96922i	0.304807	+	0.554441i
$159$	0.241129	−	3.83264i	0.0191228	−	0.303948i
$160$	−0.0248743	−	2.23593i	−0.00196649	−	0.176766i
$161$	−0.374850	+	0.590669i	−0.0295423	+	0.0465512i
$162$	0.248690	+	0.968583i	0.0195389	+	0.0760991i
$163$	6.27111	−	15.8390i	0.491191	−	1.24061i	−0.447014	−	0.894527i	$-0.647512\pi$
$163$	6.27111	−	15.8390i	0.491191	−	1.24061i	0.938205	−	0.346080i	$-0.112488\pi$
$164$	−10.9623	−	2.81464i	−0.856011	−	0.219786i
$165$	−6.11471	+	1.23709i	−0.476030	+	0.0963076i
$166$	−3.44214	−	1.36284i	−0.267162	−	0.105777i
$167$	−3.39147	−	1.59591i	−0.262440	−	0.123495i	0.290058	−	0.957009i	$-0.406325\pi$
$167$	−3.39147	−	1.59591i	−0.262440	−	0.123495i	−0.552498	+	0.833514i	$0.686325\pi$
$168$	−1.18207	−	0.384079i	−0.0911989	−	0.0296323i
$169$	3.97135	+	20.8185i	0.305488	+	1.60143i
$170$	14.1280	+	5.41264i	1.08356	+	0.415131i
$171$	−0.281773	−	0.598798i	−0.0215477	−	0.0457913i
$172$	−6.87031	−	1.31058i	−0.523856	−	0.0999308i
$173$	13.1718	−	10.8967i	1.00143	−	0.828458i	0.0162343	−	0.999868i	$-0.494832\pi$
$173$	13.1718	−	10.8967i	1.00143	−	0.828458i	0.985200	+	0.171410i	$0.0548322\pi$
$174$	−2.09473	+	6.44691i	−0.158801	+	0.488739i
$175$	0.138254	+	6.21298i	0.0104510	+	0.469657i
$176$	−0.862153	−	2.65343i	−0.0649872	−	0.200010i
$177$	−6.14057	−	3.89693i	−0.461554	−	0.292911i
$178$	−0.380161	+	0.691511i	−0.0284943	+	0.0518309i
$179$	3.23573	−	16.9623i	0.241849	−	1.26782i	−0.629440	−	0.777049i	$-0.716716\pi$
$179$	3.23573	−	16.9623i	0.241849	−	1.26782i	0.871289	−	0.490770i	$-0.163284\pi$
$180$	1.44440	+	1.70696i	0.107659	+	0.127229i
$181$	10.6798	+	10.0290i	0.793825	+	0.745451i	0.971090	−	0.238712i	$-0.0767251\pi$
$181$	10.6798	+	10.0290i	0.793825	+	0.745451i	−0.177265	+	0.984163i	$0.556725\pi$
$182$			7.26796i			0.538737i
$183$	7.70197	−	8.20176i	0.569346	−	0.606292i
$184$	0.301592	+	0.475233i	0.0222337	+	0.0350346i
$185$	−7.35815	−	0.380811i	−0.540982	−	0.0279978i
$186$	0.891980	−	0.353160i	0.0654032	−	0.0258949i
$187$	18.8399	+	1.18530i	1.37771	+	0.0866781i
$188$	−2.14920	−	0.135216i	−0.156746	−	0.00986164i
$189$	1.15562	−	0.457544i	0.0840592	−	0.0332814i
$190$	−1.15062	−	0.930512i	−0.0834748	−	0.0675064i
$191$	−8.92200	−	14.0588i	−0.645573	−	1.01726i	−0.996719	−	0.0809398i	$-0.974208\pi$
$191$	−8.92200	−	14.0588i	−0.645573	−	1.01726i	0.351146	−	0.936321i	$-0.385792\pi$
$192$	−0.684547	+	0.728969i	−0.0494029	+	0.0526088i
$193$			23.8965i			1.72011i	0.510204	+	0.860053i	$0.329570\pi$
$193$			23.8965i			1.72011i	−0.510204	+	0.860053i	$0.670430\pi$
$194$	10.5097	+	9.86922i	0.754549	+	0.708569i
$195$	6.88298	−	11.1173i	0.492900	−	0.796126i
$196$	1.02220	−	5.35856i	0.0730143	−	0.382754i
$197$	−1.55920	+	2.83617i	−0.111088	+	0.202069i	−0.926007	−	0.377507i	$-0.876782\pi$
$197$	−1.55920	+	2.83617i	−0.111088	+	0.202069i	0.814919	+	0.579575i	$0.196782\pi$
$198$	2.35566	+	1.49495i	0.167410	+	0.106241i
$199$	7.93064	+	24.4080i	0.562188	+	1.73024i	0.676161	+	0.736753i	$0.263642\pi$
$199$	7.93064	+	24.4080i	0.562188	+	1.73024i	−0.113973	+	0.993484i	$0.536358\pi$
$200$	4.57038	+	2.02772i	0.323174	+	0.143382i
$201$	3.40385	−	10.4760i	0.240089	−	0.738919i
$202$	2.99401	−	2.47686i	0.210658	−	0.174271i
$203$	8.27602	+	1.57874i	0.580863	+	0.110806i
$204$	−2.88084	−	6.12209i	−0.201699	−	0.428632i
$205$	15.9137	−	19.6780i	1.11146	−	1.37437i
$206$	−2.01734	−	10.5753i	−0.140555	−	0.736815i
$207$	−0.535305	−	0.173931i	−0.0372063	−	0.0120891i
$208$	5.29103	+	2.48977i	0.366867	+	0.172634i
$209$	−1.71670	−	0.679691i	−0.118747	−	0.0470152i
$210$	1.87985	−	2.04700i	0.129722	−	0.141257i
$211$	−13.8125	−	3.54646i	−0.950894	−	0.244148i	−0.258780	−	0.965936i	$-0.583321\pi$
$211$	−13.8125	−	3.54646i	−0.950894	−	0.244148i	−0.692114	+	0.721788i	$0.743321\pi$
$212$	−1.41368	+	3.57054i	−0.0970917	+	0.245226i
$213$	−2.93387	−	11.4267i	−0.201026	−	0.782944i
$214$	7.29585	−	11.4964i	0.498734	−	0.785879i
$215$	9.05134	−	12.7541i	0.617296	−	0.869822i
$216$	0.0627905	−	0.998027i	0.00427235	−	0.0679071i
$217$	−0.574433	−	1.04489i	−0.0389951	−	0.0709317i
$218$	−10.0340	+	3.26024i	−0.679588	+	0.220812i
$219$	−7.43858	−	0.939711i	−0.502653	−	0.0634998i
$220$	6.19772	+	0.713003i	0.417850	+	0.0480707i
$221$	−28.8415	+	27.0839i	−1.94009	+	1.82186i
$222$	2.25563	+	2.40200i	0.151388	+	0.161212i
$223$	1.79784	−	7.00211i	0.120392	−	0.468896i	−0.879585	−	0.475743i	$-0.842179\pi$
$223$	1.79784	−	7.00211i	0.120392	−	0.468896i	0.999977	+	0.00684676i	$0.00217941\pi$
$224$	1.00553	+	0.730561i	0.0671849	+	0.0488127i
$225$	−4.81405	+	1.35088i	−0.320937	+	0.0900588i
$226$	−5.53402	+	4.02070i	−0.368117	+	0.267453i
$227$	−3.82719	−	9.66639i	−0.254020	−	0.641581i	0.745674	−	0.666311i	$-0.232127\pi$
$227$	−3.82719	−	9.66639i	−0.254020	−	0.641581i	−0.999694	+	0.0247297i	$0.992127\pi$
$228$	0.0829433	+	0.656564i	0.00549305	+	0.0434820i
$229$	6.48993	+	3.56787i	0.428866	+	0.235771i	0.681541	−	0.731780i	$-0.261310\pi$
$229$	6.48993	+	3.56787i	0.428866	+	0.235771i	−0.252674	+	0.967551i	$0.581310\pi$
$230$	−1.24682	+	0.171622i	−0.0822130	+	0.0113164i
$231$	1.47647	−	3.13766i	0.0971445	−	0.206443i
$232$	3.98441	−	5.48407i	0.261589	−	0.360047i
$233$	−0.0520108	+	0.411708i	−0.00340734	+	0.0269719i	−0.993727	−	0.111836i	$-0.964327\pi$
$233$	−0.0520108	+	0.411708i	−0.00340734	+	0.0269719i	0.990319	+	0.138808i	$0.0443270\pi$
$234$	−5.66385	+	1.45423i	−0.370257	+	0.0950659i
$235$	2.27268	−	4.24518i	0.148253	−	0.276925i
$236$	4.63582	+	5.60374i	0.301766	+	0.364772i
$237$	6.12785	+	5.06940i	0.398046	+	0.329293i
$238$	−7.10040	+	4.50605i	−0.460251	+	0.292084i
$239$	−1.07242	−	17.0456i	−0.0693689	−	1.10259i	−0.866630	−	0.498952i	$-0.833718\pi$
$239$	−1.07242	−	17.0456i	−0.0693689	−	1.10259i	0.797261	−	0.603635i	$-0.206282\pi$
$240$	−0.846228	−	2.06976i	−0.0546238	−	0.133602i
$241$	−5.80952	+	7.02251i	−0.374224	+	0.452359i	−0.923681	−	0.383163i	$-0.874835\pi$
$241$	−5.80952	+	7.02251i	−0.374224	+	0.452359i	0.549456	+	0.835522i	$0.314835\pi$
$242$	−3.15902	+	0.602615i	−0.203069	+	0.0387376i
$243$	0.587785	+	0.809017i	0.0377064	+	0.0518985i
$244$	−9.85949	+	5.42030i	−0.631189	+	0.346999i
$245$	9.94768	+	7.05968i	0.635534	+	0.451027i
$246$	−11.2286	+	1.41850i	−0.715911	+	0.0904405i
$247$	3.50151	−	1.64769i	0.222796	−	0.104840i
$248$	−0.957456	+	0.0602380i	−0.0607985	+	0.00382512i
$249$	−3.70212			−0.234612
$250$	−8.37201	+	7.41009i	−0.529492	+	0.468655i
$251$	24.3979			1.53998			0.769990	−	0.638055i	$-0.220261\pi$
$251$	24.3979			1.53998			0.769990	+	0.638055i	$0.220261\pi$
$252$	−1.24045	+	0.0780426i	−0.0781411	+	0.00491622i
$253$	−1.42090	+	0.668624i	−0.0893311	+	0.0420360i
$254$	10.8520	−	1.37092i	0.680912	−	0.0860192i
$255$	15.1284	−	0.168300i	0.947375	−	0.0105394i
$256$	0.876307	−	0.481754i	0.0547692	−	0.0301096i
$257$	0.800598	+	1.10193i	0.0499399	+	0.0687364i	0.833257	−	0.552886i	$-0.186474\pi$
$257$	0.800598	+	1.10193i	0.0499399	+	0.0687364i	−0.783317	+	0.621623i	$0.786474\pi$
$258$	−6.87031	+	1.31058i	−0.427727	+	0.0815932i
$259$	2.61054	−	3.15560i	0.162211	−	0.196080i
$260$	−9.98154	+	8.44622i	−0.619029	+	0.523812i
$261$	0.425637	+	6.76531i	0.0263463	+	0.418762i
$262$	−10.9974	+	6.97914i	−0.679420	+	0.431173i
$263$	6.27445	+	5.19067i	0.386899	+	0.320071i	0.810457	−	0.585798i	$-0.199219\pi$
$263$	6.27445	+	5.19067i	0.386899	+	0.320071i	−0.423558	+	0.905869i	$0.639219\pi$
$264$	−1.77840	−	2.14972i	−0.109453	−	0.132306i
$265$	−5.94746	−	6.19386i	−0.365350	−	0.380486i
$266$	0.796691	−	0.204555i	0.0488482	−	0.0125421i
$267$	−0.0989029	+	0.782897i	−0.00605276	+	0.0479125i
$268$	−6.47451	+	8.91140i	−0.395494	+	0.544351i
$269$	1.06363	−	2.26033i	0.0648506	−	0.137815i	−0.869774	−	0.493450i	$-0.835736\pi$
$269$	1.06363	−	2.26033i	0.0648506	−	0.137815i	0.934625	+	0.355636i	$0.115736\pi$
$270$	1.97134	+	1.05537i	0.119972	+	0.0642278i
$271$	−13.9694	−	7.67975i	−0.848581	−	0.466511i	−0.00277145	−	0.999996i	$-0.500882\pi$
$271$	−13.9694	−	7.67975i	−0.848581	−	0.466511i	−0.845810	+	0.533485i	$0.820882\pi$
$272$	0.848009	+	6.71268i	0.0514181	+	0.407016i
$273$	2.67551	+	6.75758i	0.161929	+	0.408987i
$274$	15.5457	−	11.2946i	0.939152	−	0.682334i
$275$	−7.21086	+	11.9417i	−0.434831	+	0.720111i
$276$	0.455358	+	0.330837i	0.0274093	+	0.0199140i
$277$	−0.472245	+	1.83927i	−0.0283744	+	0.110511i	−0.981193	−	0.193029i	$-0.938169\pi$
$277$	−0.472245	+	1.83927i	−0.0283744	+	0.110511i	0.952819	+	0.303540i	$0.0981688\pi$
$278$	−6.75706	−	7.19554i	−0.405262	−	0.431560i
$279$	0.699335	−	0.656720i	0.0418681	−	0.0393168i
$280$	−2.42040	+	1.36591i	−0.144647	+	0.0816286i
$281$	−13.7474	−	1.73670i	−0.820099	−	0.103603i	−0.295922	−	0.955212i	$-0.595627\pi$
$281$	−13.7474	−	1.73670i	−0.820099	−	0.103603i	−0.524177	+	0.851609i	$0.675627\pi$
$282$	−2.04805	+	0.665452i	−0.121960	+	0.0396271i
$283$	−0.0334523	−	0.0608495i	−0.00198853	−	0.00361713i	0.875311	−	0.483561i	$-0.160657\pi$
$283$	−0.0334523	−	0.0608495i	−0.00198853	−	0.00361713i	−0.877299	+	0.479944i	$0.840657\pi$
$284$	−0.740760	+	11.7740i	−0.0439560	+	0.698661i
$285$	−1.41236	−	0.441596i	−0.0836612	−	0.0261579i
$286$	−8.74180	+	13.7749i	−0.516914	+	0.814525i
$287$	3.49833	+	13.6251i	0.206500	+	0.804263i
$288$	−0.368125	+	0.929776i	−0.0216919	+	0.0547876i
$289$	−27.8750	−	7.15709i	−1.63971	−	0.421005i
$290$	7.44953	+	13.2007i	0.437452	+	0.775169i
$291$	13.4047	+	5.30731i	0.785799	+	0.311120i
$292$	6.78412	+	3.19237i	0.397011	+	0.186819i
$293$	24.0507	+	7.81454i	1.40506	+	0.456530i	0.910822	−	0.412799i	$-0.135449\pi$
$293$	24.0507	+	7.81454i	1.40506	+	0.456530i	0.494233	+	0.869329i	$0.335449\pi$
$294$	−1.02220	−	5.35856i	−0.0596159	−	0.312518i
$295$	−15.7055	+	4.21925i	−0.914407	+	0.245654i
$296$	−1.40297	−	2.98147i	−0.0815461	−	0.173294i
$297$	2.74057	+	0.522791i	0.159024	+	0.0303354i
$298$	−6.90059	+	5.70867i	−0.399741	+	0.330694i
$299$	1.01707	−	3.13023i	0.0588189	−	0.181026i
$300$	4.99588	+	0.202860i	0.288437	+	0.0117121i
$301$	2.68632	+	8.26764i	0.154837	+	0.476539i
$302$	−16.9708	−	10.7700i	−0.976557	−	0.619742i
$303$	1.87197	−	3.40510i	0.107542	−	0.195618i
$304$	0.124006	−	0.650060i	0.00711221	−	0.0372835i
$305$	−1.85893	−	25.0896i	−0.106442	−	1.43663i
$306$	−4.93222	−	4.63167i	−0.281957	−	0.264775i
$307$		−	12.4165i		−	0.708644i	−0.935123	−	0.354322i	$-0.884712\pi$
$307$		−	12.4165i		−	0.708644i	0.935123	−	0.354322i	$-0.115288\pi$
$308$	−2.37379	+	2.52783i	−0.135259	+	0.144037i
$309$	−5.76870	−	9.09002i	−0.328170	−	0.517113i
$310$	0.767453	−	2.00319i	0.0435884	−	0.113774i
$311$	−23.2427	+	9.20242i	−1.31797	+	0.521821i	−0.918680	−	0.395003i	$-0.870743\pi$
$311$	−23.2427	+	9.20242i	−1.31797	+	0.521821i	−0.399290	+	0.916825i	$0.630743\pi$
$312$	5.83602	+	0.367171i	0.330400	+	0.0207870i
$313$	−14.8133	−	0.931971i	−0.837295	−	0.0526781i	−0.361648	−	0.932315i	$-0.617786\pi$
$313$	−14.8133	−	0.931971i	−0.837295	−	0.0526781i	−0.475647	+	0.879636i	$0.657786\pi$
$314$	−0.0500188	+	0.0198039i	−0.00282273	+	0.00111760i
$315$	0.994290	−	2.59527i	0.0560219	−	0.146227i
$316$	−4.26140	−	6.71489i	−0.239722	−	0.377742i
$317$	8.90185	−	9.47951i	0.499978	−	0.532422i	−0.428632	−	0.903479i	$-0.641004\pi$
$317$	8.90185	−	9.47951i	0.499978	−	0.532422i	0.928610	+	0.371057i	$0.121004\pi$
$318$			3.84021i			0.215349i
$319$	13.7866	+	12.9464i	0.771899	+	0.724862i
$320$	0.165220	+	2.22996i	0.00923610	+	0.124658i
$321$	2.55139	−	13.3749i	0.142405	−	0.746513i
$322$	0.337022	−	0.613041i	0.0187815	−	0.0341634i
$323$	3.78060	+	2.39924i	0.210358	+	0.133497i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	−7.89936	−	28.1505i	−0.438178	−	1.56151i
$326$	−5.26420	+	16.2015i	−0.291557	+	0.897320i
$327$	−8.12920	+	6.72506i	−0.449546	+	0.371897i
$328$	11.1174	+	2.12076i	0.613855	+	0.117099i
$329$	1.13961	+	2.42180i	0.0628288	+	0.133518i
$330$	6.02497	−	1.61860i	0.331663	−	0.0891009i
$331$	2.32142	+	12.1693i	0.127597	+	0.668887i	0.987398	+	0.158257i	$0.0505876\pi$
$331$	2.32142	+	12.1693i	0.127597	+	0.668887i	−0.859801	+	0.510630i	$0.829412\pi$
$332$	3.52093	+	1.14402i	0.193236	+	0.0627862i
$333$	2.98147	+	1.40297i	0.163383	+	0.0768824i
$334$	3.48499	+	1.37980i	0.190690	+	0.0754995i
$335$	−12.1052	−	21.4505i	−0.661378	−	1.17197i
$336$	1.20386	+	0.309098i	0.0656758	+	0.0168627i
$337$	−6.92142	+	17.4815i	−0.377034	+	0.952279i	0.610092	+	0.792331i	$0.291133\pi$
$337$	−6.92142	+	17.4815i	−0.377034	+	0.952279i	−0.987125	+	0.159948i	$0.948867\pi$
$338$	−5.27072	−	20.5281i	−0.286689	−	1.11658i
$339$	−3.66528	+	5.77556i	−0.199071	+	0.313685i
$340$	−14.4399	−	4.51486i	−0.783116	−	0.244853i
$341$	0.168063	−	2.67129i	0.00910113	−	0.144658i
$342$	0.318816	+	0.579924i	0.0172396	+	0.0313587i
$343$	−14.7229	+	4.78377i	−0.794964	+	0.258299i
$344$	6.93904	+	0.876605i	0.374128	+	0.0472634i
$345$	−1.09609	+	0.618556i	−0.0590114	+	0.0333019i
$346$	−12.4616	+	11.7022i	−0.669940	+	0.629116i
$347$	−6.61685	−	7.04623i	−0.355211	−	0.378261i	0.526401	−	0.850237i	$-0.323541\pi$
$347$	−6.61685	−	7.04623i	−0.355211	−	0.378261i	−0.881612	+	0.471975i	$0.843541\pi$
$348$	1.68579	−	6.56572i	0.0903678	−	0.351959i
$349$	8.75935	+	6.36404i	0.468877	+	0.340659i	0.797003	−	0.603975i	$-0.206417\pi$
$349$	8.75935	+	6.36404i	0.468877	+	0.340659i	−0.328126	+	0.944634i	$0.606417\pi$
$350$	−0.528098	−	6.19204i	−0.0282280	−	0.330979i
$351$	−4.73077	+	3.43711i	−0.252510	+	0.183459i
$352$	1.02706	+	2.59406i	0.0547426	+	0.138264i
$353$	0.482755	+	3.82140i	0.0256944	+	0.203393i	0.999736	−	0.0229768i	$-0.00731438\pi$
$353$	0.482755	+	3.82140i	0.0256944	+	0.203393i	−0.974042	+	0.226369i	$0.927314\pi$
$354$	6.37315	+	3.50367i	0.338729	+	0.186218i
$355$	−23.2566	−	12.4505i	−1.23433	−	0.660806i
$356$	0.335991	−	0.714017i	0.0178075	−	0.0378428i
$357$	−4.94300	+	6.80345i	−0.261611	+	0.360077i
$358$	−2.16427	+	17.1320i	−0.114385	+	0.905453i
$359$	10.5950	−	2.72034i	0.559183	−	0.143574i	0.0414881	−	0.999139i	$-0.486790\pi$
$359$	10.5950	−	2.72034i	0.559183	−	0.143574i	0.517695	+	0.855565i	$0.326790\pi$
$360$	−1.54873	−	1.61289i	−0.0816253	−	0.0850070i
$361$	11.8319	+	14.3023i	0.622731	+	0.752753i
$362$	−11.2885	−	9.33864i	−0.593309	−	0.490828i
$363$	−2.71535	+	1.72321i	−0.142519	+	0.0904451i
$364$	−0.456359	−	7.25362i	−0.0239197	−	0.380193i
$365$	−12.7983	+	10.8297i	−0.669892	+	0.566852i
$366$	−7.17177	+	8.66919i	−0.374875	+	0.453146i
$367$	18.2744	−	3.48603i	0.953916	−	0.181969i	0.313149	−	0.949704i	$-0.398616\pi$
$367$	18.2744	−	3.48603i	0.953916	−	0.181969i	0.640768	+	0.767735i	$0.278616\pi$
$368$	−0.330837	−	0.455358i	−0.0172461	−	0.0237372i
$369$	−9.91792	+	5.45242i	−0.516306	+	0.283842i
$370$	7.36754	−	0.0819626i	0.383020	−	0.00426103i
$371$	4.73538	−	0.598218i	0.245849	−	0.0310579i
$372$	−0.868045	+	0.408471i	−0.0450060	+	0.0211782i
$373$	−10.7596	+	0.676935i	−0.557110	+	0.0350504i	−0.338850	−	0.940840i	$-0.610038\pi$
$373$	−10.7596	+	0.676935i	−0.557110	+	0.0350504i	−0.218260	+	0.975891i	$0.570038\pi$
$374$	−18.8771			−0.976113
$375$	−5.05626	+	9.97167i	−0.261104	+	0.514935i
$376$	2.15345			0.111056
$377$	−39.5605	+	2.48894i	−2.03747	+	0.128187i
$378$	−1.12461	+	0.529203i	−0.0578439	+	0.0272193i
$379$	−7.60077	+	0.960200i	−0.390425	+	0.0493222i	−0.318096	−	0.948059i	$-0.603043\pi$
$379$	−7.60077	+	0.960200i	−0.390425	+	0.0493222i	−0.0723296	+	0.997381i	$0.523043\pi$
$380$	1.20678	+	0.856427i	0.0619064	+	0.0439338i
$381$	9.58523	−	5.26952i	0.491066	−	0.269966i
$382$	9.78715	+	13.4709i	0.500754	+	0.689229i
$383$	33.0207	−	6.29904i	1.68728	−	0.321866i	0.747659	−	0.664083i	$-0.231178\pi$
$383$	33.0207	−	6.29904i	1.68728	−	0.321866i	0.939621	+	0.342217i	$0.111178\pi$
$384$	0.637424	−	0.770513i	0.0325284	−	0.0393201i
$385$	−2.93445	−	7.17727i	−0.149554	−	0.365787i
$386$	−1.50047	−	23.8493i	−0.0763721	−	1.21390i
$387$	−5.90539	+	3.74768i	−0.300188	+	0.190505i
$388$	−11.1086	−	9.18984i	−0.563954	−	0.466544i
$389$	−0.665699	−	0.804691i	−0.0337523	−	0.0407995i	0.753367	−	0.657600i	$-0.228428\pi$
$389$	−0.665699	−	0.804691i	−0.0337523	−	0.0407995i	−0.787119	+	0.616801i	$0.788428\pi$
$390$	−6.17134	+	11.5275i	−0.312498	+	0.583720i
$391$	3.68864	−	0.947082i	0.186543	−	0.0478960i
$392$	−0.683716	+	5.41217i	−0.0345329	+	0.273356i
$393$	−7.65590	+	10.5374i	−0.386189	+	0.531544i
$394$	1.37804	−	2.92848i	0.0694245	−	0.147535i
$395$	17.6172	−	2.42497i	0.886418	−	0.122013i
$396$	−2.44488	−	1.34409i	−0.122860	−	0.0675428i
$397$	−4.06903	−	32.2097i	−0.204219	−	1.61656i	−0.677416	−	0.735600i	$-0.736900\pi$
$397$	−4.06903	−	32.2097i	−0.204219	−	1.61656i	0.473198	−	0.880956i	$-0.343100\pi$
$398$	−9.44758	−	23.8619i	−0.473564	−	1.19609i
$399$	0.665442	−	0.483472i	0.0333138	−	0.0242039i
$400$	−4.68868	−	1.73674i	−0.234434	−	0.0868372i
$401$	−14.2170	−	10.3292i	−0.709961	−	0.515817i	0.173200	−	0.984887i	$-0.444589\pi$
$401$	−14.2170	−	10.3292i	−0.709961	−	0.515817i	−0.883161	+	0.469070i	$0.844589\pi$
$402$	−2.73934	+	10.6690i	−0.136626	+	0.532123i
$403$	3.84021	+	4.08940i	0.191294	+	0.203708i
$404$	−2.83258	+	2.65997i	−0.140926	+	0.132338i
$405$	2.22142	+	0.255558i	0.110383	+	0.0126988i
$406$	−8.35882	−	1.05596i	−0.414841	−	0.0524066i
$407$	8.74324	−	2.84085i	0.433386	−	0.140816i
$408$	3.25956	+	5.92912i	0.161372	+	0.293535i
$409$	−1.57362	+	25.0120i	−0.0778107	+	1.23677i	0.744459	+	0.667668i	$0.232707\pi$
$409$	−1.57362	+	25.0120i	−0.0778107	+	1.23677i	−0.822270	+	0.569098i	$0.807293\pi$
$410$	−14.6467	+	20.6384i	−0.723349	+	1.01926i
$411$	10.2962	−	16.2243i	0.507875	−	0.800283i
$412$	2.67739	+	10.4278i	0.131906	+	0.513739i
$413$	3.32759	−	8.40454i	0.163740	−	0.413560i
$414$	0.545170	+	0.139976i	0.0267937	+	0.00687944i
$415$	−5.59933	+	6.09721i	−0.274860	+	0.299300i
$416$	−5.43692	−	2.15263i	−0.266567	−	0.105541i
$417$	−8.93141	−	4.20280i	−0.437373	−	0.205812i
$418$	1.75599	+	0.570557i	0.0858885	+	0.0279069i
$419$	6.00647	+	31.4870i	0.293435	+	1.53824i	0.757735	+	0.652563i	$0.226306\pi$
$419$	6.00647	+	31.4870i	0.293435	+	1.53824i	−0.464299	+	0.885678i	$0.653694\pi$
$420$	−1.74761	+	2.16100i	−0.0852746	+	0.105446i
$421$	3.91501	+	8.31981i	0.190806	+	0.405483i	0.977224	−	0.212212i	$-0.0680667\pi$
$421$	3.91501	+	8.31981i	0.190806	+	0.405483i	−0.786418	+	0.617695i	$0.788067\pi$
$422$	14.0080	+	2.67216i	0.681897	+	0.130079i
$423$	−1.65926	+	1.37266i	−0.0806760	+	0.0667410i
$424$	1.18669	−	3.65226i	0.0576308	−	0.177369i
$425$	22.6040	−	25.1702i	1.09645	−	1.22094i
$426$	3.64557	+	11.2199i	0.176629	+	0.543607i
$427$	11.8072	+	7.49308i	0.571391	+	0.362616i
$428$	−6.55959	+	11.9318i	−0.317070	+	0.576747i
$429$	−3.05705	+	16.0256i	−0.147596	+	0.773724i
$430$	−8.23265	+	13.2973i	−0.397013	+	0.641251i
$431$	10.7793	+	10.1224i	0.519221	+	0.487581i	0.899275	−	0.437383i	$-0.144095\pi$
$431$	10.7793	+	10.1224i	0.519221	+	0.487581i	−0.380054	+	0.924964i	$0.624095\pi$
$432$			1.00000i			0.0481125i
$433$	−11.2192	+	11.9473i	−0.539162	+	0.574149i	−0.939643	−	0.342156i	$-0.888843\pi$
$433$	−11.2192	+	11.9473i	−0.539162	+	0.574149i	0.400481	+	0.916305i	$0.368843\pi$
$434$	0.638909	+	1.00676i	0.0306686	+	0.0483260i
$435$	11.7859	+	9.53130i	0.565090	+	0.456991i
$436$	9.80948	−	3.88385i	0.469789	−	0.186003i
$437$	−0.371751	−	0.0233886i	−0.0177833	−	0.00111883i
$438$	7.48291	+	0.470785i	0.357547	+	0.0224950i
$439$	−26.1416	+	10.3502i	−1.24767	+	0.493989i	−0.896801	−	0.442435i	$-0.854115\pi$
$439$	−26.1416	+	10.3502i	−1.24767	+	0.493989i	−0.350872	+	0.936423i	$0.614115\pi$
$440$	−6.23026	−	0.322438i	−0.297016	−	0.0153716i
$441$	−2.92304	−	4.60597i	−0.139192	−	0.219332i
$442$	27.0839	−	28.8415i	1.28825	−	1.37185i
$443$		−	5.79402i		−	0.275282i	−0.990482	−	0.137641i	$-0.956048\pi$
$443$		−	5.79402i		−	0.275282i	0.990482	−	0.137641i	$-0.0439521\pi$
$444$	−2.40200	−	2.25563i	−0.113994	−	0.107047i
$445$	1.13981	+	1.34699i	0.0540320	+	0.0638537i
$446$	−1.35462	+	7.10118i	−0.0641432	+	0.336250i
$447$	−4.31451	+	7.84806i	−0.204069	+	0.371201i
$448$	−1.04942	−	0.665982i	−0.0495804	−	0.0314647i
$449$	11.2680	+	34.6793i	0.531769	+	1.63662i	0.750528	+	0.660838i	$0.229799\pi$
$449$	11.2680	+	34.6793i	0.531769	+	1.63662i	−0.218759	+	0.975779i	$0.570201\pi$
$450$	4.71973	−	1.65049i	0.222490	−	0.0778050i
$451$	−9.75773	+	30.0312i	−0.459473	+	1.41411i
$452$	5.27063	−	4.36025i	0.247910	−	0.205089i
$453$	−19.7437	−	3.76631i	−0.927640	−	0.176957i
$454$	4.42660	+	9.40700i	0.207751	+	0.441493i
$455$	15.1760	+	5.81417i	0.711463	+	0.272572i
$456$	−0.124006	−	0.650060i	−0.00580710	−	0.0304419i
$457$	29.9211	+	9.72195i	1.39965	+	0.454774i	0.909078	−	0.416627i	$-0.136788\pi$
$457$	29.9211	+	9.72195i	1.39965	+	0.454774i	0.490572	+	0.871401i	$0.336788\pi$
$458$	−6.70115	−	3.15332i	−0.313124	−	0.147345i
$459$	−6.29090	−	2.49074i	−0.293634	−	0.116258i
$460$	1.23359	−	0.249572i	0.0575162	−	0.0116364i
$461$	37.6956	+	9.67860i	1.75566	+	0.450777i	0.982934	−	0.183961i	$-0.0588919\pi$
$461$	37.6956	+	9.67860i	1.75566	+	0.450777i	0.772728	+	0.634738i	$0.218892\pi$
$462$	−1.27654	+	3.22417i	−0.0593900	+	0.150002i
$463$	0.488168	+	1.90129i	0.0226871	+	0.0883604i	0.978919	−	0.204251i	$-0.0654758\pi$
$463$	0.488168	+	1.90129i	0.0226871	+	0.0883604i	−0.956231	+	0.292611i	$0.905476\pi$
$464$	−3.63220	+	5.72343i	−0.168621	+	0.265704i
$465$	−0.0238632	−	2.14504i	−0.00110663	−	0.0994737i
$466$	0.0260568	−	0.414161i	0.00120706	−	0.0191856i
$467$	−0.679842	−	1.23663i	−0.0314593	−	0.0572243i	0.860110	−	0.510109i	$-0.170395\pi$
$467$	−0.679842	−	1.23663i	−0.0314593	−	0.0572243i	−0.891569	+	0.452885i	$0.850395\pi$
$468$	5.56136	−	1.80700i	0.257074	−	0.0835284i
$469$	13.5828	+	1.71590i	0.627194	+	0.0792330i
$470$	−2.00164	+	4.37951i	−0.0923288	+	0.202012i
$471$	−0.0392160	+	0.0368263i	−0.00180698	+	0.00169687i
$472$	−4.97853	−	5.30160i	−0.229155	−	0.244026i
$473$	−4.85286	+	18.9006i	−0.223135	+	0.869052i
$474$	−6.43407	−	4.67462i	−0.295526	−	0.214713i
$475$	−2.86344	+	1.65819i	−0.131384	+	0.0760831i
$476$	6.80345	−	4.94300i	0.311836	−	0.226562i
$477$	1.41368	+	3.57054i	0.0647278	+	0.163484i
$478$	2.14060	+	16.9446i	0.0979089	+	0.775029i
$479$	−33.0436	−	18.1659i	−1.50980	−	0.830021i	−0.510252	−	0.860025i	$-0.670448\pi$
$479$	−33.0436	−	18.1659i	−1.50980	−	0.830021i	−0.999550	+	0.0300039i	$0.990448\pi$
$480$	0.974519	+	2.01254i	0.0444805	+	0.0918594i
$481$	−8.20396	+	17.4343i	−0.374068	+	0.794936i
$482$	5.35711	−	7.37343i	0.244010	−	0.335851i
$483$	0.0876798	−	0.694057i	0.00398957	−	0.0315807i
$484$	3.11495	−	0.799783i	0.141589	−	0.0363538i
$485$	29.0151	−	14.0498i	1.31751	−	0.637969i
$486$	−0.637424	−	0.770513i	−0.0289141	−	0.0349512i
$487$	−29.7640	−	24.6229i	−1.34873	−	1.11577i	−0.982707	−	0.185165i	$-0.940718\pi$
$487$	−29.7640	−	24.6229i	−1.34873	−	1.11577i	−0.366027	−	0.930604i	$-0.619282\pi$
$488$	9.49969	−	6.02869i	0.430031	−	0.272906i
$489$	1.06965	+	17.0017i	0.0483715	+	0.768842i
$490$	−10.3713	−	6.42113i	−0.468529	−	0.290077i
$491$	20.2463	−	24.4735i	0.913701	−	1.10447i	−0.0804804	−	0.996756i	$-0.525645\pi$
$491$	20.2463	−	24.4735i	0.913701	−	1.10447i	0.994181	−	0.107719i	$-0.0343545\pi$
$492$	11.1174	−	2.12076i	0.501211	−	0.0956111i
$493$	−26.9586	−	37.1054i	−1.21416	−	1.67114i
$494$	−3.39114	+	1.86430i	−0.152575	+	0.0838786i
$495$	5.00603	−	3.72287i	0.225004	−	0.167331i
$496$	0.951784	−	0.120238i	0.0427364	−	0.00539886i
$497$	13.2674	−	6.24318i	0.595125	−	0.280045i
$498$	3.69482	−	0.232458i	0.165569	−	0.0104167i
$499$	15.7285			0.704105			0.352053	−	0.935980i	$-0.385484\pi$
$499$	15.7285			0.704105			0.352053	+	0.935980i	$0.385484\pi$
$500$	7.89021	−	7.92115i	0.352861	−	0.354245i
$501$	3.74820			0.167457
$502$	−24.3497	+	1.53196i	−1.08678	+	0.0683745i
$503$	4.67022	−	2.19764i	0.208235	−	0.0979878i	−0.318834	−	0.947811i	$-0.603291\pi$
$503$	4.67022	−	2.19764i	0.208235	−	0.0979878i	0.527068	+	0.849823i	$0.323291\pi$
$504$	1.23310	−	0.155777i	0.0549268	−	0.00693887i
$505$	−2.77674	−	8.23314i	−0.123563	−	0.366370i
$506$	1.37611	−	0.756523i	0.0611756	−	0.0336316i
$507$	−12.4575	−	17.1463i	−0.553256	−	0.761492i
$508$	−10.7445	+	2.04962i	−0.476708	+	0.0909370i
$509$	25.2284	−	30.4959i	1.11823	−	1.35171i	0.189096	−	0.981959i	$-0.439444\pi$
$509$	25.2284	−	30.4959i	1.11823	−	1.35171i	0.929133	−	0.369747i	$-0.120556\pi$
$510$	−15.0879	+	1.11789i	−0.668106	+	0.0495008i
$511$	−0.585140	−	9.30054i	−0.0258851	−	0.411432i
$512$	−0.844328	+	0.535827i	−0.0373144	+	0.0236804i
$513$	0.509912	+	0.421836i	0.0225132	+	0.0186245i
$514$	−0.868208	−	1.04948i	−0.0382950	−	0.0462907i
$515$	−23.6958	−	4.24759i	−1.04416	−	0.187171i
$516$	6.77446	−	1.73938i	0.298229	−	0.0765721i
$517$	−0.753013	+	5.96071i	−0.0331175	+	0.262152i
$518$	−2.40725	+	3.31329i	−0.105768	+	0.145578i
$519$	−7.27863	+	15.4679i	−0.319497	+	0.678965i
$520$	9.43150	−	9.05630i	0.413599	−	0.397145i
$521$	−8.02333	−	4.41086i	−0.351508	−	0.193243i	0.296211	−	0.955123i	$-0.404277\pi$
$521$	−8.02333	−	4.41086i	−0.351508	−	0.193243i	−0.647719	+	0.761879i	$0.724277\pi$
$522$	−0.849594	−	6.72523i	−0.0371857	−	0.294355i
$523$	0.537720	+	1.35812i	0.0235128	+	0.0593866i	0.941059	−	0.338243i	$-0.109833\pi$
$523$	0.537720	+	1.35812i	0.0235128	+	0.0593866i	−0.917546	+	0.397630i	$0.869833\pi$
$524$	10.5374	−	7.65590i	0.460330	−	0.334450i
$525$	−2.77046	−	5.56281i	−0.120913	−	0.242781i
$526$	−6.58799	−	4.78646i	−0.287250	−	0.208699i
$527$	−1.61424	+	6.28706i	−0.0703175	+	0.273869i
$528$	1.90988	+	2.03381i	0.0831167	+	0.0885103i
$529$	16.5353	−	15.5277i	0.718928	−	0.675118i
$530$	6.32464	+	5.80820i	0.274725	+	0.252292i
$531$	7.21539	+	0.911515i	0.313121	+	0.0395564i
$532$	−0.782275	+	0.254176i	−0.0339159	+	0.0110199i
$533$	−31.8834	−	57.9956i	−1.38102	−	2.51207i
$534$	0.0495492	−	0.787563i	0.00214421	−	0.0340812i
$535$	−18.1689	−	24.4311i	−0.785508	−	1.05625i
$536$	5.90218	−	9.30036i	0.254936	−	0.401714i
$537$	4.29441	+	16.7256i	0.185317	+	0.721764i
$538$	−0.919603	+	2.32265i	−0.0396469	+	0.100137i
$539$	−14.7417	−	3.78503i	−0.634971	−	0.163033i
$540$	−2.03372	−	0.929506i	−0.0875174	−	0.0399996i
$541$	15.5107	+	6.14111i	0.666856	+	0.264027i	0.677067	−	0.735921i	$-0.263251\pi$
$541$	15.5107	+	6.14111i	0.666856	+	0.264027i	−0.0102117	+	0.999948i	$0.503251\pi$
$542$	14.4241	+	6.78745i	0.619566	+	0.291546i
$543$	−13.9335	−	4.52728i	−0.597946	−	0.194284i
$544$	−1.26783	−	6.64619i	−0.0543577	−	0.284953i
$545$	−1.21931	+	23.5598i	−0.0522293	+	1.00919i
$546$	−3.09455	−	6.57624i	−0.132434	−	0.281437i
$547$	10.5617	+	2.01474i	0.451584	+	0.0861442i	0.408156	−	0.912912i	$-0.366172\pi$
$547$	10.5617	+	2.01474i	0.451584	+	0.0861442i	0.0434280	+	0.999057i	$0.486172\pi$
$548$	−14.8059	+	12.2485i	−0.632475	+	0.523229i
$549$	−3.47681	+	10.7005i	−0.148387	+	0.456687i
$550$	6.44681	−	12.3709i	0.274893	−	0.527497i
$551$	1.38625	+	4.26645i	0.0590564	+	0.181757i
$552$	−0.475233	−	0.301592i	−0.0202273	−	0.0128366i
$553$	−4.76201	+	8.66207i	−0.202501	+	0.368349i
$554$	0.355824	−	1.86530i	0.0151175	−	0.0792488i
$555$	6.81999	−	2.78838i	0.289493	−	0.118360i
$556$	7.19554	+	6.75706i	0.305159	+	0.286563i
$557$			40.7904i			1.72834i	0.503197	+	0.864172i	$0.332157\pi$
$557$			40.7904i			1.72834i	−0.503197	+	0.864172i	$0.667843\pi$
$558$	−0.656720	+	0.699335i	−0.0278012	+	0.0296052i
$559$	−21.9148	−	34.5321i	−0.926895	−	1.46055i
$560$	2.32986	−	1.51519i	0.0984546	−	0.0640285i
$561$	−17.5515	+	6.94913i	−0.741025	+	0.293393i
$562$	13.8293	+	0.870065i	0.583353	+	0.0367015i
$563$	−27.8177	−	1.75014i	−1.17238	−	0.0737596i	−0.535369	−	0.844618i	$-0.679827\pi$
$563$	−27.8177	−	1.75014i	−1.17238	−	0.0737596i	−0.637006	+	0.770859i	$0.719827\pi$
$564$	2.00222	−	0.792737i	0.0843089	−	0.0333802i
$565$	3.96844	+	14.7719i	0.166954	+	0.621457i
$566$	0.0372071	+	0.0586289i	0.00156393	+	0.00246436i
$567$	−0.850827	+	0.906038i	−0.0357314	+	0.0380500i
$568$		−	11.7973i		−	0.495005i
$569$	11.9861	+	11.2557i	0.502484	+	0.471864i	0.893847	−	0.448372i	$-0.147996\pi$
$569$	11.9861	+	11.2557i	0.502484	+	0.471864i	−0.391362	+	0.920237i	$0.627996\pi$
$570$	1.43730	+	0.352042i	0.0602021	+	0.0147454i
$571$	−5.21474	+	27.3366i	−0.218230	+	1.14400i	0.689448	+	0.724335i	$0.257853\pi$
$571$	−5.21474	+	27.3366i	−0.218230	+	1.14400i	−0.907678	+	0.419667i	$0.862147\pi$
$572$	7.85962	−	14.2966i	0.328627	−	0.597771i
$573$	14.0588	+	8.92200i	0.587316	+	0.372722i
$574$	−4.34695	−	13.3785i	−0.181438	−	0.558409i
$575$	−0.639065	+	2.74075i	−0.0266508	+	0.114297i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	9.54242	−	7.89418i	0.397256	−	0.328639i	−0.417252	−	0.908791i	$-0.637007\pi$
$577$	9.54242	−	7.89418i	0.397256	−	0.328639i	0.814508	+	0.580152i	$0.197007\pi$
$578$	28.2694	+	5.39268i	1.17585	+	0.224306i
$579$	−10.1746	−	21.6222i	−0.422843	−	0.898587i
$580$	−8.26371	−	12.7068i	−0.343132	−	0.527623i
$581$	−0.862213	−	4.51988i	−0.0357706	−	0.187516i
$582$	−13.7115	−	4.45515i	−0.568361	−	0.184672i
$583$	9.69444	+	4.56186i	0.401503	+	0.188933i
$584$	−6.97119	−	2.76009i	−0.288470	−	0.114213i
$585$	−1.49439	+	12.9899i	−0.0617855	+	0.537065i
$586$	−24.4939	−	6.28896i	−1.01183	−	0.259795i
$587$	2.88233	−	7.27993i	0.118966	−	0.300475i	−0.858075	−	0.513524i	$-0.828340\pi$
$587$	2.88233	−	7.27993i	0.118966	−	0.300475i	0.977041	+	0.213050i	$0.0683396\pi$
$588$	1.35665	+	5.28380i	0.0559473	+	0.217900i
$589$	0.340186	−	0.536047i	0.0140171	−	0.0220874i
$590$	15.4095	−	5.19708i	0.634400	−	0.213960i
$591$	0.203222	−	3.23012i	0.00835943	−	0.132869i
$592$	1.58741	+	2.88749i	0.0652422	+	0.118675i
$593$	−31.1582	+	10.1239i	−1.27952	+	0.415740i	−0.868409	−	0.495848i	$-0.834857\pi$
$593$	−31.1582	+	10.1239i	−1.27952	+	0.415740i	−0.411106	+	0.911588i	$0.634857\pi$
$594$	−2.76799	−	0.349678i	−0.113572	−	0.0143475i
$595$	3.72883	+	18.4309i	0.152867	+	0.755592i
$596$	6.52852	−	6.13069i	0.267419	−	0.251123i
$597$	−17.5683	−	18.7083i	−0.719022	−	0.765680i
$598$	−0.818518	+	3.18792i	−0.0334717	+	0.130364i
$599$	−2.75499	−	2.00161i	−0.112566	−	0.0817837i	0.530078	−	0.847949i	$-0.322163\pi$
$599$	−2.75499	−	2.00161i	−0.112566	−	0.0817837i	−0.642644	+	0.766165i	$0.722163\pi$
$600$	−4.99876	+	0.111234i	−0.204074	+	0.00454113i
$601$	15.1828	−	11.0310i	0.619320	−	0.449963i	−0.233364	−	0.972390i	$-0.574973\pi$
$601$	15.1828	−	11.0310i	0.619320	−	0.449963i	0.852684	+	0.522427i	$0.174973\pi$
$602$	−3.20015	−	8.08265i	−0.130428	−	0.329424i
$603$	1.38056	+	10.9282i	0.0562207	+	0.445032i
$604$	17.6135	+	9.68311i	0.716684	+	0.394000i
$605$	−1.26883	+	7.07834i	−0.0515851	+	0.287775i
$606$	−1.65447	+	3.51592i	−0.0672081	+	0.142825i
$607$	−3.09935	+	4.26589i	−0.125799	+	0.173147i	−0.867271	−	0.497836i	$-0.834128\pi$
$607$	−3.09935	+	4.26589i	−0.125799	+	0.173147i	0.741472	+	0.670984i	$0.234128\pi$
$608$	−0.0829433	+	0.656564i	−0.00336380	+	0.0266272i
$609$	−8.16056	+	2.09528i	−0.330683	+	0.0849049i
$610$	3.43065	+	24.9234i	0.138903	+	1.00912i
$611$	−8.02670	−	9.70262i	−0.324726	−	0.392526i
$612$	5.21332	+	4.31283i	0.210736	+	0.174336i
$613$	−13.7716	+	8.73974i	−0.556231	+	0.352995i	−0.784039	−	0.620711i	$-0.786844\pi$
$613$	−13.7716	+	8.73974i	−0.556231	+	0.352995i	0.227808	+	0.973706i	$0.426844\pi$
$614$	0.779635	+	12.3920i	0.0314635	+	0.500098i
$615$	−6.02065	+	24.5809i	−0.242776	+	0.991199i
$616$	2.21039	−	2.67190i	0.0890590	−	0.107654i
$617$	32.6991	−	6.23768i	1.31642	−	0.251120i	0.519116	−	0.854704i	$-0.326261\pi$
$617$	32.6991	−	6.23768i	1.31642	−	0.251120i	0.797299	+	0.603584i	$0.206261\pi$
$618$	6.32809	+	8.70987i	0.254553	+	0.350362i
$619$	12.0712	−	6.63620i	0.485182	−	0.266731i	−0.220335	−	0.975424i	$-0.570715\pi$
$619$	12.0712	−	6.63620i	0.485182	−	0.266731i	0.705517	+	0.708693i	$0.250715\pi$
$620$	−0.640158	+	2.04743i	−0.0257093	+	0.0822266i
$621$	0.558415	−	0.0705442i	0.0224084	−	0.00283084i
$622$	22.6190	−	10.6437i	0.906938	−	0.426773i
$623$	−0.978865	+	0.0615850i	−0.0392174	+	0.00246735i
$624$	−5.84756			−0.234090
$625$	8.77542	+	23.4092i	0.351017	+	0.936369i
$626$	14.8426			0.593228
$627$	1.84272	−	0.115934i	0.0735911	−	0.00462996i
$628$	0.0486766	−	0.0229055i	0.00194241	−	0.000914028i
$629$	−22.1187	+	2.79425i	−0.881932	+	0.111414i
$630$	−0.829370	+	2.65258i	−0.0330429	+	0.105681i
$631$	32.0813	−	17.6368i	1.27713	−	0.702111i	0.308648	−	0.951176i	$-0.400123\pi$
$631$	32.0813	−	17.6368i	1.27713	−	0.702111i	0.968487	+	0.249065i	$0.0801234\pi$
$632$	4.67462	+	6.43407i	0.185946	+	0.255933i
$633$	14.0080	−	2.67216i	0.556767	−	0.106209i
$634$	−8.28906	+	10.0198i	−0.329201	+	0.397935i
$635$	5.81869	−	23.7564i	0.230908	−	0.942743i
$636$	−0.241129	−	3.83264i	−0.00956139	−	0.151974i
$637$	26.9337	−	17.0926i	1.06715	−	0.677234i
$638$	−14.5723	−	12.0552i	−0.576922	−	0.477271i
$639$	7.51989	+	9.08999i	0.297482	+	0.359594i
$640$	−0.304914	−	2.21518i	−0.0120528	−	0.0875627i
$641$	−7.92564	+	2.03496i	−0.313044	+	0.0803760i	−0.401943	−	0.915665i	$-0.631665\pi$
$641$	−7.92564	+	2.03496i	−0.313044	+	0.0803760i	0.0888993	+	0.996041i	$0.471665\pi$
$642$	−1.70654	+	13.5087i	−0.0673519	+	0.533146i
$643$	−15.3450	+	21.1205i	−0.605146	+	0.832913i	−0.996167	−	0.0874693i	$-0.972122\pi$
$643$	−15.3450	+	21.1205i	−0.605146	+	0.832913i	0.391021	+	0.920382i	$0.372122\pi$
$644$	−0.297864	+	0.632993i	−0.0117375	+	0.0249434i
$645$	−2.75947	+	15.3941i	−0.108654	+	0.606143i
$646$	−3.92378	−	2.15712i	−0.154379	−	0.0848707i
$647$	−3.32928	−	26.3540i	−0.130888	−	1.03608i	−0.911568	−	0.411150i	$-0.865127\pi$
$647$	−3.32928	−	26.3540i	−0.130888	−	1.03608i	0.780680	−	0.624931i	$-0.214873\pi$
$648$	0.368125	+	0.929776i	0.0144613	+	0.0365251i
$649$	16.4156	−	11.9266i	0.644369	−	0.468162i
$650$	9.65135	+	27.5989i	0.378557	+	1.08252i
$651$	0.964655	+	0.700863i	0.0378078	+	0.0274690i
$652$	4.23651	−	16.5001i	0.165914	−	0.646194i
$653$	−3.98721	−	4.24595i	−0.156032	−	0.166157i	0.646203	−	0.763165i	$-0.276356\pi$
$653$	−3.98721	−	4.24595i	−0.156032	−	0.166157i	−0.802235	+	0.597009i	$0.796356\pi$
$654$	7.69089	−	7.22222i	0.300738	−	0.282411i
$655$	5.77535	+	28.5464i	0.225662	+	1.11540i
$656$	−11.2286	−	1.41850i	−0.438404	−	0.0553833i
$657$	7.13074	−	2.31692i	0.278197	−	0.0903916i
$658$	−1.28943	−	2.34546i	−0.0502671	−	0.0914356i
$659$	2.99342	−	47.5791i	0.116607	−	1.85342i	−0.312195	−	0.950018i	$-0.601064\pi$
$659$	2.99342	−	47.5791i	0.116607	−	1.85342i	0.428802	−	0.903399i	$-0.358936\pi$
$660$	−5.91144	+	1.99372i	−0.230103	+	0.0776053i
$661$	4.96800	−	7.82832i	0.193233	−	0.304486i	−0.733872	−	0.679287i	$-0.762289\pi$
$661$	4.96800	−	7.82832i	0.193233	−	0.304486i	0.927105	+	0.374801i	$0.122289\pi$
$662$	−3.08096	−	11.9996i	−0.119745	−	0.466376i
$663$	14.5648	−	36.7864i	0.565648	−	1.42866i
$664$	−3.58581	−	0.920680i	−0.139156	−	0.0357293i
$665$	0.210205	−	1.82719i	0.00815139	−	0.0708552i
$666$	−3.06368	−	1.21300i	−0.118715	−	0.0470026i
$667$	3.45228	+	1.62452i	0.133673	+	0.0629017i
$668$	−3.56475	−	1.15826i	−0.137924	−	0.0448143i
$669$	1.35462	+	7.10118i	0.0523727	+	0.274547i
$670$	13.4282	+	20.6481i	0.518777	+	0.797707i
$671$	13.3655	+	28.4031i	0.515969	+	1.09649i
$672$	−1.22089	−	0.232897i	−0.0470968	−	0.00898420i
$673$	−0.803756	+	0.664925i	−0.0309825	+	0.0256310i	−0.652786	−	0.757542i	$-0.726400\pi$
$673$	−0.803756	+	0.664925i	−0.0309825	+	0.0256310i	0.621804	+	0.783173i	$0.286400\pi$
$674$	5.81009	−	17.8816i	0.223796	−	0.688774i
$675$	3.78071	−	3.27204i	0.145520	−	0.125941i
$676$	6.54929	+	20.1566i	0.251896	+	0.775255i
$677$	4.47610	+	2.84062i	0.172031	+	0.109174i	0.619054	−	0.785348i	$-0.287516\pi$
$677$	4.47610	+	2.84062i	0.172031	+	0.109174i	−0.447024	+	0.894522i	$0.647516\pi$
$678$	3.29540	−	5.99430i	0.126559	−	0.230210i
$679$	−3.35771	+	17.6018i	−0.128857	+	0.675493i
$680$	14.6949	+	3.59926i	0.563525	+	0.138025i
$681$	7.57870	+	7.11687i	0.290416	+	0.272719i
$682$			2.67657i			0.102491i
$683$	34.9011	−	37.1659i	1.33545	−	1.42211i	0.507120	−	0.861875i	$-0.330710\pi$
$683$	34.9011	−	37.1659i	1.33545	−	1.42211i	0.828332	−	0.560237i	$-0.189290\pi$
$684$	−0.354601	−	0.558761i	−0.0135585	−	0.0213648i
$685$	−11.1478	−	41.4960i	−0.425937	−	1.58548i
$686$	14.3935	−	5.69879i	0.549547	−	0.217581i
$687$	−7.39138	−	0.465026i	−0.281999	−	0.0177419i
$688$	−6.98039	−	0.439169i	−0.266125	−	0.0167432i
$689$	−20.8789	+	8.26656i	−0.795425	+	0.314931i
$690$	1.05509	−	0.686159i	0.0401664	−	0.0261216i
$691$	−12.0258	−	18.9496i	−0.457483	−	0.720877i	0.534786	−	0.844988i	$-0.320392\pi$
$691$	−12.0258	−	18.9496i	−0.457483	−	0.720877i	−0.992268	+	0.124111i	$0.960392\pi$
$692$	11.7022	−	12.4616i	0.444852	−	0.473719i
$693$			3.46768i			0.131726i
$694$	7.04623	+	6.61685i	0.267471	+	0.251172i
$695$	−20.4303	+	8.35299i	−0.774964	+	0.316847i
$696$	−1.27020	+	6.65861i	−0.0481468	+	0.252394i
$697$	36.8913	−	67.1050i	1.39736	−	2.54178i
$698$	−9.14166	−	5.80148i	−0.346017	−	0.219589i
$699$	−0.128236	−	0.394669i	−0.00485032	−	0.0149278i
$700$	0.915857	+	6.14667i	0.0346161	+	0.232322i
$701$	3.06689	−	9.43893i	0.115835	−	0.356503i	−0.876285	−	0.481793i	$-0.839986\pi$
$701$	3.06689	−	9.43893i	0.115835	−	0.356503i	0.992120	+	0.125289i	$0.0399859\pi$
$702$	4.50562	−	3.72737i	0.170054	−	0.140681i
$703$	2.14199	+	0.408607i	0.0807868	+	0.0154109i
$704$	−1.18792	−	2.52445i	−0.0447713	−	0.0951439i
$705$	−0.248874	+	4.80882i	−0.00937313	+	0.181111i
$706$	−0.721750	−	3.78355i	−0.0271634	−	0.142396i
$707$	4.59322	+	1.49243i	0.172746	+	0.0561286i
$708$	−6.58057	−	3.09658i	−0.247313	−	0.116377i
$709$	−0.323928	−	0.128252i	−0.0121654	−	0.00481661i	0.362034	−	0.932165i	$-0.382082\pi$
$709$	−0.323928	−	0.128252i	−0.0121654	−	0.00481661i	−0.374199	+	0.927348i	$0.622082\pi$
$710$	23.9925	+	10.9657i	0.900421	+	0.411534i
$711$	−7.70309	−	1.97782i	−0.288888	−	0.0741739i
$712$	−0.290494	+	0.733705i	−0.0108867	+	0.0274968i
$713$	−0.134286	−	0.523009i	−0.00502904	−	0.0195868i
$714$	4.50605	−	7.10040i	0.168635	−	0.265726i
$715$	21.7697	+	29.2730i	0.814141	+	1.09475i
$716$	1.08427	−	17.2341i	0.0405213	−	0.644067i
$717$	8.22801	+	14.9667i	0.307281	+	0.558942i
$718$	−10.4033	+	3.38023i	−0.388247	+	0.126149i
$719$	−37.6694	−	4.75876i	−1.40483	−	0.177472i	−0.613904	−	0.789380i	$-0.710402\pi$
$719$	−37.6694	−	4.75876i	−1.40483	−	0.177472i	−0.790928	+	0.611909i	$0.790402\pi$
$720$	1.64695	+	1.51247i	0.0613782	+	0.0563663i
$721$	9.75440	−	9.15999i	0.363273	−	0.341136i
$722$	−12.7066	−	13.5311i	−0.472890	−	0.503577i
$723$	2.26658	−	8.82773i	0.0842949	−	0.328307i
$724$	11.8526	+	8.61140i	0.440498	+	0.320040i
$725$	33.5233	−	4.99500i	1.24503	−	0.185510i
$726$	2.60179	−	1.89031i	0.0965613	−	0.0701559i
$727$	0.337362	+	0.852078i	0.0125121	+	0.0316018i	0.935898	−	0.352270i	$-0.114590\pi$
$727$	0.337362	+	0.852078i	0.0125121	+	0.0316018i	−0.923386	+	0.383872i	$0.874590\pi$
$728$	0.910917	+	7.21065i	0.0337608	+	0.267244i
$729$	−0.876307	−	0.481754i	−0.0324558	−	0.0178427i
$730$	12.0930	−	11.6119i	0.447582	−	0.429777i
$731$	20.1491	−	42.8191i	0.745242	−	1.58372i
$732$	6.61328	−	9.10240i	0.244434	−	0.336434i
$733$	3.08493	−	24.4197i	0.113944	−	0.901962i	−0.826718	−	0.562617i	$-0.809795\pi$
$733$	3.08493	−	24.4197i	0.113944	−	0.901962i	0.940662	−	0.339345i	$-0.110205\pi$
$734$	−18.0195	+	4.62661i	−0.665110	+	0.170771i
$735$	−12.0068	−	2.15228i	−0.442877	−	0.0793879i
$736$	0.358776	+	0.433686i	0.0132247	+	0.0159859i
$737$	23.6794	+	19.5893i	0.872241	+	0.721581i
$738$	9.55599	−	6.06441i	0.351761	−	0.223234i
$739$	2.84740	+	45.2581i	0.104743	+	1.66485i	0.602942	+	0.797785i	$0.293995\pi$
$739$	2.84740	+	45.2581i	0.104743	+	1.66485i	−0.498199	+	0.867063i	$0.666005\pi$
$740$	−7.34786	+	0.544412i	−0.270113	+	0.0200130i
$741$	−2.46671	+	2.98174i	−0.0906169	+	0.109537i
$742$	−4.68848	+	0.894375i	−0.172119	+	0.0328335i
$743$	16.2566	+	22.3752i	0.596396	+	0.820868i	0.995372	−	0.0960929i	$-0.0306346\pi$
$743$	16.2566	+	22.3752i	0.596396	+	0.820868i	−0.398977	+	0.916961i	$0.630635\pi$
$744$	0.840684	−	0.462170i	0.0308210	−	0.0169440i
$745$	6.39982	+	18.9757i	0.234471	+	0.695216i
$746$	10.6958	−	1.35120i	0.391602	−	0.0494709i
$747$	3.34978	−	1.57629i	0.122562	−	0.0576733i
$748$	18.8399	−	1.18530i	0.688854	−	0.0433390i
$749$	16.9235			0.618370
$750$	4.42016	−	10.2695i	0.161401	−	0.374988i
$751$	49.9842			1.82395			0.911975	−	0.410245i	$-0.134557\pi$
$751$	49.9842			1.82395			0.911975	+	0.410245i	$0.134557\pi$
$752$	−2.14920	+	0.135216i	−0.0783732	+	0.00493082i
$753$	−22.0759	+	10.3881i	−0.804489	+	0.378564i
$754$	39.3262	−	4.96805i	1.43218	−	0.180926i
$755$	−36.0646	+	26.8205i	−1.31253	+	0.976097i
$756$	1.08917	−	0.598774i	0.0396126	−	0.0217772i
$757$	−20.6278	−	28.3917i	−0.749730	−	1.03192i	−0.997999	−	0.0632243i	$-0.979862\pi$
$757$	−20.6278	−	28.3917i	−0.749730	−	1.03192i	0.248269	−	0.968691i	$-0.420138\pi$
$758$	7.52548	−	1.43556i	0.273338	−	0.0521420i
$759$	1.00098	−	1.20998i	0.0363333	−	0.0439194i
$760$	−1.25817	−	0.778963i	−0.0456387	−	0.0282560i
$761$	1.73498	+	27.5767i	0.0628929	+	0.999653i	0.895293	+	0.445478i	$0.146966\pi$
$761$	1.73498	+	27.5767i	0.0628929	+	0.999653i	−0.832400	+	0.554175i	$0.813034\pi$
$762$	−9.23543	+	5.86099i	−0.334565	+	0.212321i
$763$	−10.1038	−	8.35861i	−0.365783	−	0.302602i
$764$	−10.6137	−	12.8297i	−0.383990	−	0.464164i
$765$	−13.6169	+	6.59363i	−0.492320	+	0.238393i
$766$	−32.5600	+	8.36000i	−1.17644	+	0.302059i
$767$	−5.33014	+	42.1924i	−0.192460	+	1.52348i
$768$	−0.587785	+	0.809017i	−0.0212099	+	0.0291929i
$769$	9.88665	−	21.0102i	0.356522	−	0.757647i	−0.643448	−	0.765490i	$-0.722497\pi$
$769$	9.88665	−	21.0102i	0.356522	−	0.757647i	0.999969	+	0.00784302i	$0.00249654\pi$
$770$	3.37933	+	6.97885i	0.121782	+	0.251500i
$771$	−1.19358	−	0.656176i	−0.0429857	−	0.0236316i
$772$	2.99502	+	23.7081i	0.107793	+	0.853272i
$773$	12.1700	+	30.7380i	0.437726	+	1.10557i	0.966468	+	0.256787i	$0.0826639\pi$
$773$	12.1700	+	30.7380i	0.437726	+	1.10557i	−0.528742	+	0.848783i	$0.677336\pi$
$774$	5.65842	−	4.11108i	0.203388	−	0.147770i
$775$	−3.56886	−	3.20499i	−0.128197	−	0.115127i
$776$	11.6637	+	8.47419i	0.418703	+	0.304206i
$777$	−1.01850	+	3.96679i	−0.0365384	+	0.142308i
$778$	0.714912	+	0.761304i	0.0256308	+	0.0272941i
$779$	−5.45995	+	5.12723i	−0.195623	+	0.183702i
$780$	5.43534	−	11.8923i	0.194616	−	0.425813i
$781$	32.6548	+	4.12526i	1.16848	+	0.147613i
$782$	−3.62189	+	1.17682i	−0.129519	+	0.0420832i
$783$	−3.26566	−	5.94021i	−0.116705	−	0.212286i
$784$	0.342534	−	5.44442i	0.0122334	−	0.194444i
$785$	0.00133815	+	0.120285i	4.77608e−5	+	0.00429317i
$786$	6.97914	−	10.9974i	0.248938	−	0.392263i
$787$	3.69709	+	14.3992i	0.131787	+	0.513277i	0.999858	+	0.0168369i	$0.00535960\pi$
$787$	3.69709	+	14.3992i	0.131787	+	0.513277i	−0.868071	+	0.496440i	$0.834640\pi$
$788$	−1.19144	+	3.00923i	−0.0424432	+	0.107199i
$789$	−7.88737	−	2.02513i	−0.280798	−	0.0720966i
$790$	−17.4302	+	3.52638i	−0.620138	+	0.125463i
$791$	−7.90495	−	3.12979i	−0.281068	−	0.111283i
$792$	2.52445	+	1.18792i	0.0897026	+	0.0422108i
$793$	−62.5719	−	20.3308i	−2.22199	−	0.721969i
$794$	6.08346	+	31.8906i	0.215894	+	1.13175i
$795$	8.01864	+	3.07207i	0.284392	+	0.108955i
$796$	10.9272	+	23.2216i	0.387306	+	0.823066i
$797$	−18.7374	−	3.57434i	−0.663712	−	0.126610i	−0.155492	−	0.987837i	$-0.549696\pi$
$797$	−18.7374	−	3.57434i	−0.663712	−	0.126610i	−0.508220	+	0.861227i	$0.669696\pi$
$798$	−0.633772	+	0.524302i	−0.0224353	+	0.0185601i
$799$	4.50247	−	13.8572i	0.159286	−	0.490231i
$800$	4.78848	+	1.43891i	0.169298	+	0.0508732i
$801$	−0.243851	−	0.750498i	−0.00861607	−	0.0265175i
$802$	14.8375	+	9.41615i	0.523930	+	0.332496i
$803$	10.0776	−	18.3310i	0.355629	−	0.646887i
$804$	2.06402	−	10.8200i	0.0727925	−	0.381592i
$805$	−1.01046	−	1.19414i	−0.0356142	−	0.0420880i
$806$	−4.08940	−	3.84021i	−0.144043	−	0.135265i
$807$			2.49808i			0.0879365i
$808$	2.65997	−	2.83258i	0.0935774	−	0.0996499i
$809$	1.77730	+	2.80057i	0.0624864	+	0.0984628i	0.874135	−	0.485684i	$-0.161429\pi$
$809$	1.77730	+	2.80057i	0.0624864	+	0.0984628i	−0.811648	+	0.584147i	$0.801429\pi$
$810$	−2.23308	−	0.115570i	−0.0784624	−	0.00406071i
$811$	25.4429	−	10.0735i	0.893419	−	0.353730i	0.123856	−	0.992300i	$-0.460474\pi$
$811$	25.4429	−	10.0735i	0.893419	−	0.353730i	0.769563	+	0.638570i	$0.220474\pi$
$812$	8.40863	+	0.529026i	0.295085	+	0.0185652i
$813$	15.9098	+	1.00096i	0.557980	+	0.0351051i
$814$	−8.54761	+	3.38424i	−0.299594	+	0.118618i
$815$	29.6187	+	23.9528i	1.03750	+	0.839030i
$816$	−3.62542	−	5.71275i	−0.126915	−	0.199986i
$817$	−3.16852	+	3.37413i	−0.110852	+	0.118046i
$818$		−	25.0615i		−	0.876255i
$819$	−5.29811	−	4.97526i	−0.185131	−	0.173850i
$820$	13.3219	−	21.5174i	0.465221	−	0.751419i
$821$	−4.64084	+	24.3281i	−0.161966	+	0.849058i	0.804829	+	0.593507i	$0.202257\pi$
$821$	−4.64084	+	24.3281i	−0.161966	+	0.849058i	−0.966796	+	0.255551i	$0.917743\pi$
$822$	−9.25718	+	16.8387i	−0.322881	+	0.587319i
$823$	1.29443	+	0.821470i	0.0451210	+	0.0286346i	0.558196	−	0.829709i	$-0.311494\pi$
$823$	1.29443	+	0.821470i	0.0451210	+	0.0286346i	−0.513075	+	0.858344i	$0.671494\pi$
$824$	−3.32687	−	10.2391i	−0.115897	−	0.356695i
$825$	1.44006	−	13.8754i	0.0501365	−	0.483079i
$826$	−2.79330	+	8.59690i	−0.0971914	+	0.299124i
$827$	−37.3716	+	30.9164i	−1.29954	+	1.07507i	−0.307182	+	0.951651i	$0.599386\pi$
$827$	−37.3716	+	30.9164i	−1.29954	+	1.07507i	−0.992355	+	0.123419i	$0.960614\pi$
$828$	−0.552884	−	0.105468i	−0.0192140	−	0.00366527i
$829$	3.76856	+	8.00859i	0.130887	+	0.278150i	0.959519	−	0.281645i	$-0.0908800\pi$
$829$	3.76856	+	8.00859i	0.130887	+	0.278150i	−0.828631	+	0.559795i	$0.810880\pi$
$830$	5.20544	−	6.43676i	0.180683	−	0.223423i
$831$	−0.355824	−	1.86530i	−0.0123434	−	0.0647064i
$832$	5.56136	+	1.80700i	0.192805	+	0.0626463i
$833$	33.3971	+	15.7155i	1.15714	+	0.544510i
$834$	9.17768	+	3.63370i	0.317797	+	0.125825i
$835$	5.66903	−	6.17310i	0.196185	−	0.213629i
$836$	−1.78836	−	0.459172i	−0.0618516	−	0.0158808i
$837$	−0.353160	+	0.891980i	−0.0122070	+	0.0308313i
$838$	−7.97170	−	31.0477i	−0.275378	−	1.07253i
$839$	−19.1796	+	30.2222i	−0.662153	+	1.04339i	0.332795	+	0.942999i	$0.392008\pi$
$839$	−19.1796	+	30.2222i	−0.662153	+	1.04339i	−0.994948	+	0.100388i	$0.967992\pi$
$840$	1.60847	−	2.26647i	0.0554975	−	0.0782006i
$841$	1.06433	−	16.9171i	0.0367012	−	0.583348i
$842$	−4.42969	−	8.05757i	−0.152657	−	0.277682i
$843$	13.1784	−	4.28193i	0.453889	−	0.147478i
$844$	−14.1481	−	1.78732i	−0.486998	−	0.0615222i
$845$	−47.0806	−	5.41628i	−1.61962	−	0.186326i
$846$	1.56980	−	1.47414i	0.0539707	−	0.0506818i
$847$	−2.73624	−	2.91380i	−0.0940185	−	0.100120i
$848$	−0.955022	+	3.71957i	−0.0327956	+	0.127730i
$849$	0.0561770	+	0.0408150i	0.00192799	+	0.00140077i
$850$	−20.9789	+	26.5399i	−0.719571	+	0.910310i
$851$	1.50044	−	1.09013i	0.0514343	−	0.0373692i
$852$	−4.34288	−	10.9689i	−0.148785	−	0.375787i
$853$	−0.242022	−	1.91580i	−0.00828666	−	0.0655957i	0.987429	−	0.158063i	$-0.0505248\pi$
$853$	−0.242022	−	1.91580i	−0.00828666	−	0.0655957i	−0.995716	+	0.0924669i	$0.970525\pi$
$854$	−12.2544	−	6.73691i	−0.419337	−	0.230532i
$855$	1.46597	−	0.201787i	0.0501350	−	0.00690097i
$856$	5.79744	−	12.3202i	0.198152	−	0.421095i
$857$	−0.961841	+	1.32386i	−0.0328559	+	0.0452222i	−0.825129	−	0.564945i	$-0.808898\pi$
$857$	−0.961841	+	1.32386i	−0.0328559	+	0.0452222i	0.792273	+	0.610167i	$0.208898\pi$
$858$	2.04476	−	16.1860i	0.0698070	−	0.552579i
$859$	−44.0426	+	11.3082i	−1.50271	+	0.385831i	−0.908297	−	0.418326i	$-0.862617\pi$
$859$	−44.0426	+	11.3082i	−1.50271	+	0.385831i	−0.594416	+	0.804158i	$0.702617\pi$
$860$	7.38146	−	13.7880i	0.251706	−	0.470165i
$861$	−8.96666	−	10.8388i	−0.305583	−	0.369386i
$862$	−11.3936	−	9.42563i	−0.388069	−	0.321038i
$863$	20.6732	−	13.1196i	0.703724	−	0.446597i	−0.135220	−	0.990816i	$-0.543174\pi$
$863$	20.6732	−	13.1196i	0.703724	−	0.446597i	0.838943	+	0.544219i	$0.183174\pi$
$864$	−0.0627905	−	0.998027i	−0.00213618	−	0.0339536i
$865$	14.4661	+	35.3822i	0.491864	+	1.20303i
$866$	10.4469	−	12.6282i	0.355001	−	0.429122i
$867$	28.2694	−	5.39268i	0.960080	−	0.183145i
$868$	−0.700863	−	0.964655i	−0.0237888	−	0.0327425i
$869$	−19.4440	+	10.6894i	−0.659593	+	0.362614i
$870$	−12.3611	−	8.77245i	−0.419081	−	0.297414i
$871$	−63.9035	+	8.07289i	−2.16529	+	0.273540i
$872$	−9.54626	+	4.49213i	−0.323277	+	0.152123i
$873$	−14.3887	+	0.905261i	−0.486984	+	0.0306384i
$874$	0.372486			0.0125995
$875$	−13.3519	−	3.85076i	−0.451376	−	0.130180i
$876$	−7.49770			−0.253324
$877$	−28.7757	+	1.81041i	−0.971686	+	0.0611333i	−0.540691	−	0.841221i	$-0.681837\pi$
$877$	−28.7757	+	1.81041i	−0.971686	+	0.0611333i	−0.430995	+	0.902354i	$0.641837\pi$
$878$	25.4402	−	11.9712i	0.858564	−	0.404010i
$879$	−25.0890	+	3.16947i	−0.846230	+	0.106904i
$880$	6.23821	−	0.0693990i	0.210290	−	0.00233944i
$881$	−11.0656	+	6.08338i	−0.372811	+	0.204954i	−0.657133	−	0.753774i	$-0.728231\pi$
$881$	−11.0656	+	6.08338i	−0.372811	+	0.204954i	0.284323	+	0.958729i	$0.408231\pi$
$882$	3.20648	+	4.41334i	0.107968	+	0.148605i
$883$	15.5716	−	2.97045i	0.524027	−	0.0999636i	0.0814214	−	0.996680i	$-0.474054\pi$
$883$	15.5716	−	2.97045i	0.524027	−	0.0999636i	0.442606	+	0.896716i	$0.354054\pi$
$884$	−25.2195	+	30.4852i	−0.848225	+	1.02533i
$885$	12.4143	−	10.5047i	0.417301	−	0.353113i
$886$	0.363810	+	5.78259i	0.0122224	+	0.194270i
$887$	38.9878	−	24.7424i	1.30908	−	0.830768i	0.316064	−	0.948738i	$-0.397638\pi$
$887$	38.9878	−	24.7424i	1.30908	−	0.830768i	0.993017	+	0.117969i	$0.0376385\pi$
$888$	2.53889	+	2.10036i	0.0851997	+	0.0704833i
$889$	8.66587	+	10.4752i	0.290644	+	0.351328i
$890$	−1.22214	−	1.27277i	−0.0409661	−	0.0426633i
$891$	−2.70233	+	0.693841i	−0.0905315	+	0.0232445i
$892$	0.906062	−	7.17222i	0.0303372	−	0.240144i
$893$	−0.837660	+	1.15294i	−0.0280312	+	0.0385817i
$894$	3.81321	−	8.10348i	0.127533	−	0.271021i
$895$	34.0414	+	18.2243i	1.13788	+	0.609170i
$896$	1.08917	+	0.598774i	0.0363865	+	0.0200036i
$897$	0.412512	+	3.26537i	0.0137734	+	0.109027i
$898$	−13.4233	−	33.9033i	−0.447941	−	1.13137i
$899$	−5.26114	+	3.82244i	−0.175469	+	0.127486i
$900$	−4.60678	+	1.94359i	−0.153559	+	0.0647863i
$901$	−21.0207	−	15.2724i	−0.700301	−	0.508798i
$902$	7.85280	−	30.5846i	0.261470	−	1.01836i
$903$	−5.95084	−	6.33701i	−0.198032	−	0.210882i
$904$	−4.98645	+	4.68259i	−0.165847	+	0.155741i
$905$	−28.5302	+	16.1005i	−0.948377	+	0.535198i
$906$	19.9412	+	2.51916i	0.662503	+	0.0836936i
$907$	−42.8438	+	13.9208i	−1.42260	+	0.462232i	−0.916429	−	0.400198i	$-0.868941\pi$
$907$	−42.8438	+	13.9208i	−1.42260	+	0.462232i	−0.506176	+	0.862430i	$0.668941\pi$
$908$	−5.00854	−	9.11049i	−0.166214	−	0.302342i
$909$	−0.243988	+	3.87807i	−0.00809255	+	0.128627i
$910$	−15.5111	−	4.84979i	−0.514189	−	0.160769i
$911$	17.3910	−	27.4038i	0.576188	−	0.907928i	−0.423809	−	0.905751i	$-0.639307\pi$
$911$	17.3910	−	27.4038i	0.576188	−	0.907928i	0.999998	−	0.00217617i	$-0.000692698\pi$
$912$	0.164579	+	0.640991i	0.00544974	+	0.0212253i
$913$	3.80231	−	9.60353i	0.125838	−	0.317831i
$914$	−30.4725	−	7.82401i	−1.00794	−	0.258795i
$915$	12.3647	+	21.9103i	0.408763	+	0.724332i
$916$	6.88592	+	2.72633i	0.227517	+	0.0900805i
$917$	−14.6481	−	6.89287i	−0.483723	−	0.227623i
$918$	6.43488	+	2.09082i	0.212383	+	0.0690073i
$919$	−7.20880	−	37.7898i	−0.237796	−	1.24657i	−0.878110	−	0.478458i	$-0.841196\pi$
$919$	−7.20880	−	37.7898i	−0.237796	−	1.24657i	0.640314	−	0.768113i	$-0.278804\pi$
$920$	−1.21548	+	0.326537i	−0.0400732	+	0.0107656i
$921$	5.28667	+	11.2347i	0.174202	+	0.370197i
$922$	−38.2290	−	7.29257i	−1.25900	−	0.240168i
$923$	−53.1543	+	43.9730i	−1.74959	+	1.44739i
$924$	1.07157	−	3.29796i	0.0352522	−	0.108495i
$925$	5.72269	−	15.4495i	0.188161	−	0.507977i
$926$	−0.606588	−	1.86689i	−0.0199337	−	0.0613497i
$927$	9.09002	+	5.76870i	0.298556	+	0.189469i
$928$	3.26566	−	5.94021i	0.107200	−	0.194997i
$929$	4.01949	−	21.0709i	0.131875	−	0.691315i	−0.853524	−	0.521054i	$-0.825539\pi$
$929$	4.01949	−	21.0709i	0.131875	−	0.691315i	0.985399	−	0.170261i	$-0.0544610\pi$
$930$	0.158504	+	2.13931i	0.00519755	+	0.0701506i
$931$	−2.63168	−	2.47132i	−0.0862499	−	0.0809941i
$932$			0.414980i			0.0135931i
$933$	17.1124	−	18.2228i	0.560234	−	0.596589i
$934$	0.756149	+	1.19150i	0.0247420	+	0.0389871i
$935$	−15.1012	+	39.4168i	−0.493862	+	1.28907i
$936$	−5.43692	+	2.15263i	−0.177711	+	0.0703609i
$937$	10.7744	+	0.677866i	0.351983	+	0.0221449i	0.237798	−	0.971315i	$-0.423574\pi$
$937$	10.7744	+	0.677866i	0.351983	+	0.0221449i	0.114185	+	0.993459i	$0.463574\pi$
$938$	−13.6637	−	0.859647i	−0.446136	−	0.0280685i
$939$	13.8003	−	5.46391i	0.450354	−	0.178308i
$940$	1.72270	−	4.49655i	0.0561883	−	0.146661i
$941$	3.08863	+	4.86690i	0.100687	+	0.158657i	0.890936	−	0.454128i	$-0.150049\pi$
$941$	3.08863	+	4.86690i	0.100687	+	0.158657i	−0.790250	+	0.612785i	$0.790049\pi$
$942$	0.0368263	−	0.0392160i	0.00119987	−	0.00127773i
$943$			6.37030i			0.207445i
$944$	5.30160	+	4.97853i	0.172552	+	0.162037i
$945$	0.205353	+	2.77162i	0.00668014	+	0.0901609i
$946$	3.65650	−	19.1680i	0.118883	−	0.623207i
$947$	−18.5021	+	33.6552i	−0.601238	+	1.09365i	0.384142	+	0.923274i	$0.374497\pi$
$947$	−18.5021	+	33.6552i	−0.601238	+	1.09365i	−0.985380	+	0.170374i	$0.945503\pi$
$948$	6.71489	+	4.26140i	0.218090	+	0.138404i
$949$	13.5483	+	41.6974i	0.439797	+	1.35356i
$950$	2.75367	−	1.83472i	0.0893409	−	0.0595261i
$951$	−4.01846	+	12.3675i	−0.130307	+	0.401045i
$952$	−6.47965	+	5.36044i	−0.210007	+	0.173733i
$953$	33.3832	+	6.36818i	1.08139	+	0.206286i	0.697133	−	0.716942i	$-0.254459\pi$
$953$	33.3832	+	6.36818i	1.08139	+	0.206286i	0.384254	+	0.923227i	$0.374459\pi$
$954$	−1.63508	−	3.47473i	−0.0529378	−	0.112499i
$955$	35.9576	−	9.65995i	1.16356	−	0.312589i
$956$	−3.20034	−	16.7768i	−0.103506	−	0.542599i
$957$	−17.9868	−	5.84426i	−0.581430	−	0.188918i
$958$	34.1191	+	16.0552i	1.10234	+	0.518721i
$959$	22.2060	+	8.79197i	0.717068	+	0.283907i
$960$	−1.09896	−	1.94738i	−0.0354689	−	0.0628513i
$961$	−29.1346	−	7.48050i	−0.939827	−	0.241307i
$962$	7.09306	−	17.9150i	0.228689	−	0.577604i
$963$	3.38618	+	13.1883i	0.109118	+	0.424987i
$964$	−4.88356	+	7.69526i	−0.157289	+	0.247848i
$965$	−50.9995	−	15.9457i	−1.64173	−	0.513311i
$966$	−0.0439266	+	0.698193i	−0.00141331	+	0.0224640i
$967$	−23.5282	−	42.7976i	−0.756616	−	1.37628i	−0.920874	−	0.389861i	$-0.872523\pi$
$967$	−23.5282	−	42.7976i	−0.756616	−	1.37628i	0.164258	−	0.986417i	$-0.447477\pi$
$968$	−3.05858	+	0.993794i	−0.0983066	+	0.0319417i
$969$	−4.44233	−	0.561197i	−0.142708	−	0.0180282i
$970$	−28.0756	+	15.8439i	−0.901454	+	0.508719i
$971$	7.56874	−	7.10752i	0.242892	−	0.228091i	−0.553534	−	0.832827i	$-0.686721\pi$
$971$	7.56874	−	7.10752i	0.242892	−	0.228091i	0.796426	+	0.604735i	$0.206721\pi$
$972$	0.684547	+	0.728969i	0.0219569	+	0.0233817i
$973$	3.05106	−	11.8831i	0.0978124	−	0.380954i
$974$	31.2513	+	22.7054i	1.00136	+	0.727528i
$975$	19.1334	+	22.1079i	0.612760	+	0.708020i
$976$	−9.10240	+	6.61328i	−0.291361	+	0.211686i
$977$	−9.19858	−	23.2330i	−0.294289	−	0.743288i	−0.999415	−	0.0342063i	$-0.989110\pi$
$977$	−9.19858	−	23.2330i	−0.294289	−	0.743288i	0.705126	−	0.709082i	$-0.250890\pi$
$978$	−2.13509	−	16.9010i	−0.0682726	−	0.540433i
$979$	−1.92931	−	1.06064i	−0.0616609	−	0.0338983i
$980$	10.7540	+	5.75724i	0.343526	+	0.183908i
$981$	4.49213	−	9.54626i	0.143423	−	0.304789i
$982$	−18.6696	+	25.6965i	−0.595771	+	0.820008i
$983$	1.23831	−	9.80221i	0.0394959	−	0.312642i	−0.959974	−	0.280089i	$-0.909636\pi$
$983$	1.23831	−	9.80221i	0.0394959	−	0.312642i	0.999470	−	0.0325532i	$-0.0103639\pi$
$984$	−10.9623	+	2.81464i	−0.349465	+	0.0897274i
$985$	−5.01248	−	5.22014i	−0.159711	−	0.166328i
$986$	29.2353	+	35.3394i	0.931042	+	1.12544i
$987$	−2.06230	−	1.70608i	−0.0656438	−	0.0543052i
$988$	3.26739	−	2.07355i	0.103949	−	0.0659684i
$989$	0.247188	+	3.92894i	0.00786011	+	0.124933i
$990$	−4.76239	+	4.02986i	−0.151359	+	0.128077i
$991$	10.5005	−	12.6929i	0.333559	−	0.403204i	−0.576892	−	0.816821i	$-0.695735\pi$
$991$	10.5005	−	12.6929i	0.333559	−	0.403204i	0.910451	+	0.413617i	$0.135735\pi$
$992$	−0.942356	+	0.179764i	−0.0299198	+	0.00570751i
$993$	−7.28194	−	10.0227i	−0.231085	−	0.318062i
$994$	−12.8492	+	7.06393i	−0.407553	+	0.224054i
$995$	−57.3831	+	0.638377i	−1.81917	+	0.0202379i
$996$	−3.67293	+	0.463999i	−0.116381	+	0.0147024i
$997$	14.0773	−	6.62429i	0.445834	−	0.209793i	−0.189739	−	0.981835i	$-0.560764\pi$
$997$	14.0773	−	6.62429i	0.445834	−	0.209793i	0.635573	+	0.772041i	$0.280764\pi$
$998$	−15.6975	+	0.987602i	−0.496895	+	0.0312620i
$999$	−3.29507			−0.104251

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.b.469.4	yes	280
125.4	even	50	inner	750.2.o.b.379.4	✓	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.b.379.4	✓	280	125.4	even	50	inner
750.2.o.b.469.4	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)

\(f(q)\)	\(=\)	\(q+(-0.998027 + 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-0.667283 + 2.13418i) q^{5} +(0.876307 - 0.481754i) q^{6} +(-0.730561 - 1.00553i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})\)	\(q+(-0.998027 + 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-0.667283 + 2.13418i) q^{5} +(0.876307 - 0.481754i) q^{6} +(-0.730561 - 1.00553i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(0.531960 - 2.17187i) q^{10} +(-0.175185 - 2.78448i) q^{11} +(-0.844328 + 0.535827i) q^{12} +(4.50562 + 3.72737i) q^{13} +(0.792257 + 0.957674i) q^{14} +(-0.304914 - 2.21518i) q^{15} +(0.968583 - 0.248690i) q^{16} +(-0.848009 + 6.71268i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(0.281773 - 0.598798i) q^{19} +(-0.394538 + 2.20099i) q^{20} +(1.08917 + 0.598774i) q^{21} +(0.349678 + 2.76799i) q^{22} +(-0.207200 - 0.523328i) q^{23} +(0.809017 - 0.587785i) q^{24} +(-4.10947 - 2.84821i) q^{25} +(-4.73077 - 3.43711i) q^{26} +(-0.248690 + 0.968583i) q^{27} +(-0.850827 - 0.906038i) q^{28} +(-4.94145 + 4.64033i) q^{29} +(0.443405 + 2.19166i) q^{30} +(0.951784 + 0.120238i) q^{31} +(-0.951057 + 0.309017i) q^{32} +(1.34409 + 2.44488i) q^{33} +(0.424843 - 6.75268i) q^{34} +(2.63348 - 0.888176i) q^{35} +(0.535827 - 0.844328i) q^{36} +(0.819450 + 3.19155i) q^{37} +(-0.243618 + 0.615310i) q^{38} +(-5.66385 - 1.45423i) q^{39} +(0.255558 - 2.22142i) q^{40} +(-10.5231 - 4.16638i) q^{41} +(-1.12461 - 0.529203i) q^{42} +(-6.65187 - 2.16132i) q^{43} +(-0.522791 - 2.74057i) q^{44} +(1.21907 + 1.87453i) q^{45} +(0.239651 + 0.509285i) q^{46} +(-2.11530 - 0.403516i) q^{47} +(-0.770513 + 0.637424i) q^{48} +(1.68575 - 5.18819i) q^{49} +(4.28020 + 2.58455i) q^{50} +(-2.09082 - 6.43488i) q^{51} +(4.93726 + 3.13328i) q^{52} +(-1.85004 + 3.36521i) q^{53} +(0.187381 - 0.982287i) q^{54} +(6.05948 + 1.48416i) q^{55} +(0.906038 + 0.850827i) q^{56} +0.661782i q^{57} +(4.64033 - 4.94145i) q^{58} +(3.89693 + 6.14057i) q^{59} +(-0.580146 - 2.15950i) q^{60} +(-10.4611 + 4.14184i) q^{61} +(-0.957456 - 0.0602380i) q^{62} +(-1.24045 - 0.0780426i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-10.9614 + 7.12860i) q^{65} +(-1.49495 - 2.35566i) q^{66} +(-7.54035 + 8.02966i) q^{67} +6.76603i q^{68} +(0.410302 + 0.385300i) q^{69} +(-2.57251 + 1.05178i) q^{70} +(-2.21060 + 11.5884i) q^{71} +(-0.481754 + 0.876307i) q^{72} +(6.33052 + 4.01747i) q^{73} +(-1.01823 - 3.13380i) q^{74} +(4.93106 + 0.827410i) q^{75} +(0.204502 - 0.629392i) q^{76} +(-2.67190 + 2.21039i) q^{77} +(5.74398 + 1.09572i) q^{78} +(-3.38620 - 7.19604i) q^{79} +(-0.115570 + 2.23308i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(10.7639 + 3.49741i) q^{82} +(3.34978 + 1.57629i) q^{83} +(1.15562 + 0.457544i) q^{84} +(-13.7602 - 6.28906i) q^{85} +(6.77446 + 1.73938i) q^{86} +(2.49540 - 6.30266i) q^{87} +(0.693841 + 2.70233i) q^{88} +(0.422832 - 0.666276i) q^{89} +(-1.33437 - 1.79428i) q^{90} +(0.456359 - 7.25362i) q^{91} +(-0.271157 - 0.493232i) q^{92} +(-0.912395 + 0.296455i) q^{93} +(2.13647 + 0.269898i) q^{94} +(1.08992 + 1.00092i) q^{95} +(0.728969 - 0.684547i) q^{96} +(-9.86922 - 10.5097i) q^{97} +(-1.35665 + 5.28380i) q^{98} +(-2.25715 - 1.63991i) 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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