LMFDB - Embedded newform 525.2.n.d.316.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			316.4
Character	$\chi$	$=$	525.316
Dual form			525.2.n.d.211.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0219060 + 0.0159156i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.617807 - 1.90142i) q^{4} +(1.28481 - 1.83010i) q^{5} +(-0.00836734 + 0.0257520i) q^{6} -1.00000 q^{7} +(0.0334632 - 0.102989i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.0219060 + 0.0159156i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.617807 - 1.90142i) q^{4} +(1.28481 - 1.83010i) q^{5} +(-0.00836734 + 0.0257520i) q^{6} -1.00000 q^{7} +(0.0334632 - 0.102989i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.0572722 - 0.0196417i) q^{10} +(0.317060 + 0.230357i) q^{11} +(1.61744 - 1.17514i) q^{12} +(1.51932 - 1.10385i) q^{13} +(-0.0219060 - 0.0159156i) q^{14} +(2.13756 + 0.656392i) q^{15} +(-3.23251 + 2.34856i) q^{16} +(1.52161 - 4.68303i) q^{17} -0.0270773 q^{18} +(1.50087 - 4.61920i) q^{19} +(-4.27355 - 1.31230i) q^{20} +(-0.309017 - 0.951057i) q^{21} +(0.00327922 + 0.0100924i) q^{22} +(-4.24583 - 3.08477i) q^{23} +0.108289 q^{24} +(-1.69854 - 4.70265i) q^{25} +0.0508506 q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.617807 + 1.90142i) q^{28} +(0.115006 + 0.353953i) q^{29} +(0.0363784 + 0.0483995i) q^{30} +(-1.91585 + 5.89638i) q^{31} -0.324769 q^{32} +(-0.121106 + 0.372726i) q^{33} +(0.107866 - 0.0783691i) q^{34} +(-1.28481 + 1.83010i) q^{35} +(1.61744 + 1.17514i) q^{36} +(8.63276 - 6.27207i) q^{37} +(0.106396 - 0.0773009i) q^{38} +(1.51932 + 1.10385i) q^{39} +(-0.145487 - 0.193562i) q^{40} +(-3.04888 + 2.21514i) q^{41} +(0.00836734 - 0.0257520i) q^{42} +5.80040 q^{43} +(0.242123 - 0.745179i) q^{44} +(0.0362758 + 2.23577i) q^{45} +(-0.0439129 - 0.135150i) q^{46} +(-1.04383 - 3.21258i) q^{47} +(-3.23251 - 2.34856i) q^{48} +1.00000 q^{49} +(0.0376375 - 0.130050i) q^{50} +4.92403 q^{51} +(-3.03752 - 2.20689i) q^{52} +(0.290112 + 0.892873i) q^{53} +(-0.00836734 - 0.0257520i) q^{54} +(0.828938 - 0.284287i) q^{55} +(-0.0334632 + 0.102989i) q^{56} +4.85692 q^{57} +(-0.00311405 + 0.00958407i) q^{58} +(-3.45290 + 2.50868i) q^{59} +(-0.0725251 - 4.46991i) q^{60} +(7.89510 + 5.73612i) q^{61} +(-0.135813 + 0.0986741i) q^{62} +(0.809017 - 0.587785i) q^{63} +(6.45790 + 4.69194i) q^{64} +(-0.0681252 - 4.19873i) q^{65} +(-0.00858512 + 0.00623746i) q^{66} +(1.71662 - 5.28320i) q^{67} -9.84445 q^{68} +(1.62176 - 4.99127i) q^{69} +(-0.0572722 + 0.0196417i) q^{70} +(3.02308 + 9.30410i) q^{71} +(0.0334632 + 0.102989i) q^{72} +(5.29237 + 3.84513i) q^{73} +0.288933 q^{74} +(3.94761 - 3.06861i) q^{75} -9.71028 q^{76} +(-0.317060 - 0.230357i) q^{77} +(0.0157137 + 0.0483618i) q^{78} +(3.63971 + 11.2019i) q^{79} +(0.144944 + 8.93326i) q^{80} +(0.309017 - 0.951057i) q^{81} -0.102044 q^{82} +(-3.09278 + 9.51860i) q^{83} +(-1.61744 + 1.17514i) q^{84} +(-6.61545 - 8.80149i) q^{85} +(0.127064 + 0.0923171i) q^{86} +(-0.301090 + 0.218755i) q^{87} +(0.0343342 - 0.0249452i) q^{88} +(-8.64480 - 6.28082i) q^{89} +(-0.0347891 + 0.0495542i) q^{90} +(-1.51932 + 1.10385i) q^{91} +(-3.24233 + 9.97887i) q^{92} -6.19982 q^{93} +(0.0282641 - 0.0869879i) q^{94} +(-6.52528 - 8.68153i) q^{95} +(-0.100359 - 0.308873i) q^{96} +(3.84016 + 11.8188i) q^{97} +(0.0219060 + 0.0159156i) q^{98} -0.391908 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9}+O(q^{10}) $ 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9} + 8 q^{10} + 2 q^{11} - 5 q^{12} + 12 q^{13} - q^{14} - 8 q^{15} - 17 q^{16} + 12 q^{17} - 4 q^{18} - 13 q^{19} - 27 q^{20} + 8 q^{21} - 21 q^{22} - 12 q^{23} - 18 q^{24} + 11 q^{25} - 2 q^{26} - 8 q^{27} + 15 q^{28} + 21 q^{29} - 12 q^{30} + 3 q^{31} - 50 q^{32} - 13 q^{33} - 41 q^{34} + 3 q^{35} - 5 q^{36} - 22 q^{37} + 44 q^{38} + 12 q^{39} - 39 q^{40} - 3 q^{41} - q^{42} + 24 q^{43} - 43 q^{44} + 2 q^{45} + 10 q^{46} + 8 q^{47} - 17 q^{48} + 32 q^{49} + 19 q^{50} - 8 q^{51} + 53 q^{52} + 18 q^{53} + q^{54} + 23 q^{55} + 3 q^{56} + 42 q^{57} - 32 q^{58} + 28 q^{59} + 73 q^{60} + 36 q^{61} + 10 q^{62} + 8 q^{63} + 9 q^{64} - 34 q^{65} + 4 q^{66} - 22 q^{67} - 78 q^{68} - 2 q^{69} - 8 q^{70} - 40 q^{71} - 3 q^{72} - 10 q^{73} - 34 q^{74} + 6 q^{75} + 132 q^{76} - 2 q^{77} + 28 q^{78} + 18 q^{79} + 148 q^{80} - 8 q^{81} + 102 q^{82} + 16 q^{83} + 5 q^{84} + 18 q^{85} + 16 q^{86} - 34 q^{87} + 13 q^{88} - 17 q^{89} - 2 q^{90} - 12 q^{91} - 106 q^{92} + 18 q^{93} - 20 q^{94} - 92 q^{95} - 15 q^{96} + 30 q^{97} + q^{98} + 22 q^{99}+O(q^{100}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9 + 8 * q^10 + 2 * q^11 - 5 * q^12 + 12 * q^13 - q^14 - 8 * q^15 - 17 * q^16 + 12 * q^17 - 4 * q^18 - 13 * q^19 - 27 * q^20 + 8 * q^21 - 21 * q^22 - 12 * q^23 - 18 * q^24 + 11 * q^25 - 2 * q^26 - 8 * q^27 + 15 * q^28 + 21 * q^29 - 12 * q^30 + 3 * q^31 - 50 * q^32 - 13 * q^33 - 41 * q^34 + 3 * q^35 - 5 * q^36 - 22 * q^37 + 44 * q^38 + 12 * q^39 - 39 * q^40 - 3 * q^41 - q^42 + 24 * q^43 - 43 * q^44 + 2 * q^45 + 10 * q^46 + 8 * q^47 - 17 * q^48 + 32 * q^49 + 19 * q^50 - 8 * q^51 + 53 * q^52 + 18 * q^53 + q^54 + 23 * q^55 + 3 * q^56 + 42 * q^57 - 32 * q^58 + 28 * q^59 + 73 * q^60 + 36 * q^61 + 10 * q^62 + 8 * q^63 + 9 * q^64 - 34 * q^65 + 4 * q^66 - 22 * q^67 - 78 * q^68 - 2 * q^69 - 8 * q^70 - 40 * q^71 - 3 * q^72 - 10 * q^73 - 34 * q^74 + 6 * q^75 + 132 * q^76 - 2 * q^77 + 28 * q^78 + 18 * q^79 + 148 * q^80 - 8 * q^81 + 102 * q^82 + 16 * q^83 + 5 * q^84 + 18 * q^85 + 16 * q^86 - 34 * q^87 + 13 * q^88 - 17 * q^89 - 2 * q^90 - 12 * q^91 - 106 * q^92 + 18 * q^93 - 20 * q^94 - 92 * q^95 - 15 * q^96 + 30 * q^97 + q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.0219060	+	0.0159156i	0.0154899	+	0.0112540i	0.595503	−	0.803353i	$-0.296953\pi$
$2$	0.0219060	+	0.0159156i	0.0154899	+	0.0112540i	−0.580013	+	0.814607i	$0.696953\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.617807	−	1.90142i	−0.308904	−	0.950708i
$5$	1.28481	−	1.83010i	0.574583	−	0.818446i
$5$	1.28481	−	1.83010i	0.574583	−	0.818446i
$6$	−0.00836734	+	0.0257520i	−0.00341595	+	0.0105132i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	0.0334632	−	0.102989i	0.0118310	−	0.0364122i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	0.0572722	−	0.0196417i	0.0181111	−	0.00621124i
$11$	0.317060	+	0.230357i	0.0955971	+	0.0694554i	0.634557	−	0.772876i	$-0.281183\pi$
$11$	0.317060	+	0.230357i	0.0955971	+	0.0694554i	−0.538960	+	0.842331i	$0.681183\pi$
$12$	1.61744	−	1.17514i	0.466915	−	0.339234i
$13$	1.51932	−	1.10385i	0.421383	−	0.306152i	−0.356811	−	0.934176i	$-0.616136\pi$
$13$	1.51932	−	1.10385i	0.421383	−	0.306152i	0.778194	+	0.628024i	$0.216136\pi$
$14$	−0.0219060	−	0.0159156i	−0.00585462	−	0.00425363i
$15$	2.13756	+	0.656392i	0.551915	+	0.169480i
$16$	−3.23251	+	2.34856i	−0.808127	+	0.587139i
$17$	1.52161	−	4.68303i	0.369044	−	1.13580i	−0.578365	−	0.815778i	$-0.696309\pi$
$17$	1.52161	−	4.68303i	0.369044	−	1.13580i	0.947409	−	0.320024i	$-0.103691\pi$
$18$	−0.0270773			−0.00638218
$19$	1.50087	−	4.61920i	0.344323	−	1.05972i	−0.617622	−	0.786475i	$-0.711904\pi$
$19$	1.50087	−	4.61920i	0.344323	−	1.05972i	0.961945	−	0.273243i	$-0.0880962\pi$
$20$	−4.27355	−	1.31230i	−0.955594	−	0.293440i
$21$	−0.309017	−	0.951057i	−0.0674330	−	0.207538i
$22$	0.00327922	+	0.0100924i	0.000699133	+	0.00215171i
$23$	−4.24583	−	3.08477i	−0.885316	−	0.643220i	0.0493367	−	0.998782i	$-0.484289\pi$
$23$	−4.24583	−	3.08477i	−0.885316	−	0.643220i	−0.934652	+	0.355563i	$0.884289\pi$
$24$	0.108289			0.0221045
$25$	−1.69854	−	4.70265i	−0.339708	−	0.940531i
$26$	0.0508506			0.00997261
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.617807	+	1.90142i	0.116755	+	0.359334i
$29$	0.115006	+	0.353953i	0.0213561	+	0.0657273i	0.961167	−	0.275969i	$-0.0889986\pi$
$29$	0.115006	+	0.353953i	0.0213561	+	0.0657273i	−0.939810	+	0.341696i	$0.888999\pi$
$30$	0.0363784	+	0.0483995i	0.00664176	+	0.00883649i
$31$	−1.91585	+	5.89638i	−0.344097	+	1.05902i	0.617969	+	0.786203i	$0.287956\pi$
$31$	−1.91585	+	5.89638i	−0.344097	+	1.05902i	−0.962066	+	0.272819i	$0.912044\pi$
$32$	−0.324769			−0.0574115
$33$	−0.121106	+	0.372726i	−0.0210819	+	0.0648833i
$34$	0.107866	−	0.0783691i	0.0184988	−	0.0134402i
$35$	−1.28481	+	1.83010i	−0.217172	+	0.309344i
$36$	1.61744	+	1.17514i	0.269573	+	0.195857i
$37$	8.63276	−	6.27207i	1.41922	−	1.03112i	0.427318	−	0.904102i	$-0.359459\pi$
$37$	8.63276	−	6.27207i	1.41922	−	1.03112i	0.991900	−	0.127021i	$-0.0405414\pi$
$38$	0.106396	−	0.0773009i	0.0172596	−	0.0125399i
$39$	1.51932	+	1.10385i	0.243285	+	0.176757i
$40$	−0.145487	−	0.193562i	−0.0230035	−	0.0306049i
$41$	−3.04888	+	2.21514i	−0.476155	+	0.345947i	−0.799835	−	0.600220i	$-0.795080\pi$
$41$	−3.04888	+	2.21514i	−0.476155	+	0.345947i	0.323680	+	0.946166i	$0.395080\pi$
$42$	0.00836734	−	0.0257520i	0.00129111	−	0.00397362i
$43$	5.80040			0.884553			0.442277	−	0.896879i	$-0.354171\pi$
$43$	5.80040			0.884553			0.442277	+	0.896879i	$0.354171\pi$
$44$	0.242123	−	0.745179i	0.0365015	−	0.112340i
$45$	0.0362758	+	2.23577i	0.00540768	+	0.333289i
$46$	−0.0439129	−	0.135150i	−0.00647460	−	0.0199268i
$47$	−1.04383	−	3.21258i	−0.152258	−	0.468602i	0.845615	−	0.533794i	$-0.179234\pi$
$47$	−1.04383	−	3.21258i	−0.152258	−	0.468602i	−0.997873	+	0.0651914i	$0.979234\pi$
$48$	−3.23251	−	2.34856i	−0.466573	−	0.338985i
$49$	1.00000			0.142857
$50$	0.0376375	−	0.130050i	0.00532274	−	0.0183918i
$51$	4.92403			0.689502
$52$	−3.03752	−	2.20689i	−0.421228	−	0.306040i
$53$	0.290112	+	0.892873i	0.0398499	+	0.122646i	0.969002	−	0.247051i	$-0.0794616\pi$
$53$	0.290112	+	0.892873i	0.0398499	+	0.122646i	−0.929152	+	0.369697i	$0.879462\pi$
$54$	−0.00836734	−	0.0257520i	−0.00113865	−	0.00350441i
$55$	0.828938	−	0.284287i	0.111774	−	0.0383332i
$56$	−0.0334632	+	0.102989i	−0.00447171	+	0.0137625i
$57$	4.85692			0.643315
$58$	−0.00311405	+	0.00958407i	−0.000408895	+	0.00125845i
$59$	−3.45290	+	2.50868i	−0.449529	+	0.326602i	−0.789410	−	0.613867i	$-0.789613\pi$
$59$	−3.45290	+	2.50868i	−0.449529	+	0.326602i	0.339881	+	0.940469i	$0.389613\pi$
$60$	−0.0725251	−	4.46991i	−0.00936295	−	0.577063i
$61$	7.89510	+	5.73612i	1.01086	+	0.734436i	0.964390	−	0.264484i	$-0.0852016\pi$
$61$	7.89510	+	5.73612i	1.01086	+	0.734436i	0.0464737	+	0.998920i	$0.485202\pi$
$62$	−0.135813	+	0.0986741i	−0.0172483	+	0.0125316i
$63$	0.809017	−	0.587785i	0.101927	−	0.0740540i
$64$	6.45790	+	4.69194i	0.807238	+	0.586493i
$65$	−0.0681252	−	4.19873i	−0.00844990	−	0.520789i
$66$	−0.00858512	+	0.00623746i	−0.00105676	+	0.000767778i
$67$	1.71662	−	5.28320i	0.209718	−	0.645446i	−0.789769	−	0.613405i	$-0.789799\pi$
$67$	1.71662	−	5.28320i	0.209718	−	0.645446i	0.999487	−	0.0320407i	$-0.0102006\pi$
$68$	−9.84445			−1.19382
$69$	1.62176	−	4.99127i	0.195237	−	0.600878i
$70$	−0.0572722	+	0.0196417i	−0.00684533	+	0.00234763i
$71$	3.02308	+	9.30410i	0.358774	+	1.10419i	0.953789	+	0.300478i	$0.0971462\pi$
$71$	3.02308	+	9.30410i	0.358774	+	1.10419i	−0.595015	+	0.803715i	$0.702854\pi$
$72$	0.0334632	+	0.102989i	0.00394368	+	0.0121374i
$73$	5.29237	+	3.84513i	0.619425	+	0.450038i	0.852720	−	0.522367i	$-0.174951\pi$
$73$	5.29237	+	3.84513i	0.619425	+	0.450038i	−0.233296	+	0.972406i	$0.574951\pi$
$74$	0.288933			0.0335878
$75$	3.94761	−	3.06861i	0.455831	−	0.354332i
$76$	−9.71028			−1.11384
$77$	−0.317060	−	0.230357i	−0.0361323	−	0.0262517i
$78$	0.0157137	+	0.0483618i	0.00177922	+	0.00547589i
$79$	3.63971	+	11.2019i	0.409499	+	1.26031i	0.917079	+	0.398705i	$0.130540\pi$
$79$	3.63971	+	11.2019i	0.409499	+	1.26031i	−0.507580	+	0.861605i	$0.669460\pi$
$80$	0.144944	+	8.93326i	0.0162052	+	0.998769i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−0.102044			−0.0112689
$83$	−3.09278	+	9.51860i	−0.339477	+	1.04480i	0.624998	+	0.780626i	$0.285100\pi$
$83$	−3.09278	+	9.51860i	−0.339477	+	1.04480i	−0.964475	+	0.264176i	$0.914900\pi$
$84$	−1.61744	+	1.17514i	−0.176477	+	0.128218i
$85$	−6.61545	−	8.80149i	−0.717546	−	0.954656i
$86$	0.127064	+	0.0923171i	0.0137016	+	0.00995481i
$87$	−0.301090	+	0.218755i	−0.0322802	+	0.0234530i
$88$	0.0343342	−	0.0249452i	0.00366004	−	0.00265917i
$89$	−8.64480	−	6.28082i	−0.916347	−	0.665765i	0.0262648	−	0.999655i	$-0.491639\pi$
$89$	−8.64480	−	6.28082i	−0.916347	−	0.665765i	−0.942612	+	0.333890i	$0.891639\pi$
$90$	−0.0347891	+	0.0495542i	−0.00366709	+	0.00522347i
$91$	−1.51932	+	1.10385i	−0.159268	+	0.115715i
$92$	−3.24233	+	9.97887i	−0.338037	+	1.04037i
$93$	−6.19982			−0.642892
$94$	0.0282641	−	0.0869879i	0.00291522	−	0.00897211i
$95$	−6.52528	−	8.68153i	−0.669480	−	0.890706i
$96$	−0.100359	−	0.308873i	−0.0102428	−	0.0315243i
$97$	3.84016	+	11.8188i	0.389910	+	1.20002i	0.932856	+	0.360251i	$0.117309\pi$
$97$	3.84016	+	11.8188i	0.389910	+	1.20002i	−0.542946	+	0.839768i	$0.682691\pi$
$98$	0.0219060	+	0.0159156i	0.00221284	+	0.00160772i
$99$	−0.391908			−0.0393882
$100$	−7.89233	+	6.13497i	−0.789233	+	0.613497i
$101$	2.14877			0.213810			0.106905	−	0.994269i	$-0.465906\pi$
$101$	2.14877			0.213810			0.106905	+	0.994269i	$0.465906\pi$
$102$	0.107866	+	0.0783691i	0.0106803	+	0.00775969i
$103$	−0.219426	−	0.675325i	−0.0216207	−	0.0665417i	0.939664	−	0.342099i	$-0.111138\pi$
$103$	−0.219426	−	0.675325i	−0.0216207	−	0.0665417i	−0.961285	+	0.275557i	$0.911138\pi$
$104$	−0.0628432	−	0.193412i	−0.00616228	−	0.0189656i
$105$	−2.13756	−	0.656392i	−0.208604	−	0.0640573i
$106$	−0.00785544	+	0.0241766i	−0.000762988	+	0.00234824i
$107$	−3.30885			−0.319879			−0.159939	−	0.987127i	$-0.551130\pi$
$107$	−3.30885			−0.319879			−0.159939	+	0.987127i	$0.551130\pi$
$108$	−0.617807	+	1.90142i	−0.0594485	+	0.182964i
$109$	7.44542	−	5.40942i	0.713142	−	0.518128i	−0.171044	−	0.985263i	$-0.554714\pi$
$109$	7.44542	−	5.40942i	0.713142	−	0.518128i	0.884186	+	0.467135i	$0.154714\pi$
$110$	0.0226833	+	0.00696549i	0.00216277	+	0.000664134i
$111$	8.63276	+	6.27207i	0.819386	+	0.595319i
$112$	3.23251	−	2.34856i	0.305443	−	0.221918i
$113$	−15.3374	+	11.1433i	−1.44282	+	1.04827i	−0.455378	+	0.890298i	$0.650496\pi$
$113$	−15.3374	+	11.1433i	−1.44282	+	1.04827i	−0.987443	+	0.157973i	$0.949504\pi$
$114$	0.106396	+	0.0773009i	0.00996486	+	0.00723989i
$115$	−11.1005	+	3.80695i	−1.03513	+	0.355000i
$116$	0.601959	−	0.437349i	0.0558905	−	0.0406068i
$117$	−0.580327	+	1.78606i	−0.0536513	+	0.165122i
$118$	−0.115566			−0.0106387
$119$	−1.52161	+	4.68303i	−0.139486	+	0.429293i
$120$	0.139131	−	0.198180i	0.0127008	−	0.0180913i
$121$	−3.35172	−	10.3155i	−0.304702	−	0.937777i
$122$	0.0816559	+	0.251311i	0.00739277	+	0.0227526i
$123$	−3.04888	−	2.21514i	−0.274908	−	0.199732i
$124$	12.3951			1.11311
$125$	−10.7886	−	2.93350i	−0.964965	−	0.262380i
$126$	0.0270773			0.00241224
$127$	−5.71440	−	4.15176i	−0.507071	−	0.368409i	0.304640	−	0.952467i	$-0.401464\pi$
$127$	−5.71440	−	4.15176i	−0.507071	−	0.368409i	−0.811711	+	0.584059i	$0.801464\pi$
$128$	0.267510	+	0.823310i	0.0236447	+	0.0727710i
$129$	1.79242	+	5.51651i	0.157814	+	0.485702i
$130$	0.0653331	−	0.0930617i	0.00573010	−	0.00816205i
$131$	−2.71809	+	8.36544i	−0.237481	+	0.730891i	0.759302	+	0.650739i	$0.225541\pi$
$131$	−2.71809	+	8.36544i	−0.237481	+	0.730891i	−0.996783	+	0.0801526i	$0.974459\pi$
$132$	0.783528			0.0681973
$133$	−1.50087	+	4.61920i	−0.130142	+	0.400536i
$134$	0.121690	−	0.0884127i	0.0105124	−	0.00763769i
$135$	−2.11514	+	0.725392i	−0.182042	+	0.0624318i
$136$	−0.431384	−	0.313419i	−0.0369909	−	0.0268754i
$137$	17.5943	−	12.7830i	1.50318	−	1.09212i	0.534087	−	0.845430i	$-0.320656\pi$
$137$	17.5943	−	12.7830i	1.50318	−	1.09212i	0.969093	−	0.246694i	$-0.0793443\pi$
$138$	0.114965	−	0.0835273i	0.00978651	−	0.00711031i
$139$	12.0627	+	8.76409i	1.02315	+	0.743360i	0.966926	−	0.255058i	$-0.0820946\pi$
$139$	12.0627	+	8.76409i	1.02315	+	0.743360i	0.0562219	+	0.998418i	$0.482095\pi$
$140$	4.27355	+	1.31230i	0.361181	+	0.110910i
$141$	2.73278	−	1.98548i	0.230142	−	0.167208i
$142$	−0.0818569	+	0.251930i	−0.00686928	+	0.0211415i
$143$	0.735994			0.0615469
$144$	1.23471	−	3.80004i	0.102892	−	0.316670i
$145$	0.795530	+	0.244288i	0.0660651	+	0.0202870i
$146$	0.0547368	+	0.168463i	0.00453005	+	0.0139421i
$147$	0.309017	+	0.951057i	0.0254873	+	0.0784418i
$148$	−17.2592	−	12.5395i	−1.41870	−	1.03074i
$149$	23.1471			1.89628			0.948142	−	0.317849i	$-0.102960\pi$
$149$	23.1471			1.89628			0.948142	+	0.317849i	$0.102960\pi$
$150$	0.135315	−	0.00439218i	0.0110484	−	0.000358620i
$151$	−13.3998			−1.09046			−0.545232	−	0.838285i	$-0.683558\pi$
$151$	−13.3998			−1.09046			−0.545232	+	0.838285i	$0.683558\pi$
$152$	−0.425504	−	0.309147i	−0.0345130	−	0.0250751i
$153$	1.52161	+	4.68303i	0.123015	+	0.378601i
$154$	−0.00327922	−	0.0100924i	−0.000264247	−	0.000813270i
$155$	8.32948	+	11.0819i	0.669040	+	0.890121i
$156$	1.16023	−	3.57082i	0.0928927	−	0.285894i
$157$	2.38422			0.190282			0.0951409	−	0.995464i	$-0.469670\pi$
$157$	2.38422			0.190282			0.0951409	+	0.995464i	$0.469670\pi$
$158$	−0.0985535	+	0.303316i	−0.00784049	+	0.0241306i
$159$	−0.759523	+	0.551826i	−0.0602341	+	0.0437626i
$160$	−0.417265	+	0.594359i	−0.0329877	+	0.0469882i
$161$	4.24583	+	3.08477i	0.334618	+	0.243114i
$162$	0.0219060	−	0.0159156i	0.00172110	−	0.00125045i
$163$	5.92012	−	4.30122i	0.463699	−	0.336897i	−0.331281	−	0.943532i	$-0.607481\pi$
$163$	5.92012	−	4.30122i	0.463699	−	0.336897i	0.794981	+	0.606635i	$0.207481\pi$
$164$	6.09552	+	4.42865i	0.475980	+	0.345820i
$165$	0.526529	+	0.700518i	0.0409902	+	0.0545352i
$166$	−0.219245	+	0.159291i	−0.0170167	+	0.0123634i
$167$	−3.42802	+	10.5504i	−0.265268	+	0.816411i	0.726364	+	0.687311i	$0.241209\pi$
$167$	−3.42802	+	10.5504i	−0.265268	+	0.816411i	−0.991632	+	0.129100i	$0.958791\pi$
$168$	−0.108289			−0.00835470
$169$	−2.92738	+	9.00955i	−0.225183	+	0.693042i
$170$	−0.00483664	−	0.298094i	−0.000370953	−	0.0228628i
$171$	1.50087	+	4.61920i	0.114774	+	0.353239i
$172$	−3.58353	−	11.0290i	−0.273242	−	0.840952i
$173$	−15.6196	−	11.3483i	−1.18754	−	0.862798i	−0.194537	−	0.980895i	$-0.562320\pi$
$173$	−15.6196	−	11.3483i	−1.18754	−	0.862798i	−0.993002	+	0.118097i	$0.962320\pi$
$174$	−0.0100773			−0.000763958
$175$	1.69854	+	4.70265i	0.128398	+	0.355487i
$176$	−1.56591			−0.118035
$177$	−3.45290	−	2.50868i	−0.259536	−	0.188564i
$178$	−0.0894098	−	0.275175i	−0.00670155	−	0.0206252i
$179$	3.26801	+	10.0579i	0.244262	+	0.751762i	0.995757	+	0.0920230i	$0.0293333\pi$
$179$	3.26801	+	10.0579i	0.244262	+	0.751762i	−0.751494	+	0.659739i	$0.770667\pi$
$180$	4.22872	−	1.45025i	0.315190	−	0.108095i
$181$	−3.70651	+	11.4075i	−0.275503	+	0.847910i	0.713583	+	0.700570i	$0.247071\pi$
$181$	−3.70651	+	11.4075i	−0.275503	+	0.847910i	−0.989086	+	0.147340i	$0.952929\pi$
$182$	−0.0508506			−0.00376929
$183$	−3.01566	+	9.28124i	−0.222924	+	0.686089i
$184$	−0.459777	+	0.334048i	−0.0338952	+	0.0246263i
$185$	−0.387088	−	23.8572i	−0.0284593	−	1.75402i
$186$	−0.135813	−	0.0986741i	−0.00995831	−	0.00723513i
$187$	1.56121	−	1.13429i	0.114167	−	0.0829473i
$188$	−5.46356	+	3.96951i	−0.398471	+	0.289506i
$189$	0.809017	+	0.587785i	0.0588473	+	0.0427551i
$190$	−0.00477071	−	0.294031i	−0.000346104	−	0.0213313i
$191$	15.7893	−	11.4716i	1.14247	−	0.830056i	0.155011	−	0.987913i	$-0.450459\pi$
$191$	15.7893	−	11.4716i	1.14247	−	0.830056i	0.987462	+	0.157857i	$0.0504585\pi$
$192$	−2.46670	+	7.59172i	−0.178019	+	0.547885i
$193$	23.8232			1.71483			0.857417	−	0.514622i	$-0.172068\pi$
$193$	23.8232			1.71483			0.857417	+	0.514622i	$0.172068\pi$
$194$	−0.103981	+	0.320021i	−0.00746542	+	0.0229762i
$195$	3.97218	−	1.36227i	0.284454	−	0.0975543i
$196$	−0.617807	−	1.90142i	−0.0441291	−	0.135815i
$197$	−3.28898	−	10.1224i	−0.234330	−	0.721193i	−0.997210	−	0.0746529i	$-0.976215\pi$
$197$	−3.28898	−	10.1224i	−0.234330	−	0.721193i	0.762880	−	0.646541i	$-0.223785\pi$
$198$	−0.00858512	−	0.00623746i	−0.000610118	−	0.000443277i
$199$	6.57285			0.465937			0.232969	−	0.972484i	$-0.425156\pi$
$199$	6.57285			0.465937			0.232969	+	0.972484i	$0.425156\pi$
$200$	−0.541161	+	0.0175655i	−0.0382659	+	0.00124207i
$201$	5.55509			0.391826
$202$	0.0470708	+	0.0341990i	0.00331189	+	0.00240623i
$203$	−0.115006	−	0.353953i	−0.00807185	−	0.0248426i
$204$	−3.04210	−	9.36263i	−0.212990	−	0.655515i
$205$	0.136710	+	8.42578i	0.00954823	+	0.588482i
$206$	0.00594147	−	0.0182860i	0.000413962	−	0.00127404i
$207$	5.24813			0.364770
$208$	−2.31876	+	7.13640i	−0.160777	+	0.494820i
$209$	1.53993	−	1.11883i	0.106519	−	0.0773909i
$210$	−0.0363784	−	0.0483995i	−0.00251035	−	0.00333988i
$211$	2.80181	+	2.03563i	0.192884	+	0.140139i	0.680036	−	0.733179i	$-0.261964\pi$
$211$	2.80181	+	2.03563i	0.192884	+	0.140139i	−0.487152	+	0.873317i	$0.661964\pi$
$212$	1.51849	−	1.10325i	0.104290	−	0.0757713i
$213$	−7.91454	+	5.75025i	−0.542295	+	0.394000i
$214$	−0.0724836	−	0.0526624i	−0.00495488	−	0.00359993i
$215$	7.45240	−	10.6153i	0.508249	−	0.723959i
$216$	−0.0876079	+	0.0636508i	−0.00596096	+	0.00433089i
$217$	1.91585	−	5.89638i	0.130056	−	0.400272i
$218$	0.249194			0.0168775
$219$	−2.02150	+	6.22155i	−0.136601	+	0.420413i
$220$	−1.05267	−	1.40052i	−0.0709711	−	0.0944232i
$221$	−2.85755	−	8.79463i	−0.192220	−	0.591591i
$222$	0.0892853	+	0.274792i	0.00599243	+	0.0184428i
$223$	1.73095	+	1.25761i	0.115913	+	0.0842158i	0.644232	−	0.764830i	$-0.277177\pi$
$223$	1.73095	+	1.25761i	0.115913	+	0.0842158i	−0.528319	+	0.849046i	$0.677177\pi$
$224$	0.324769			0.0216995
$225$	4.13830	+	2.80615i	0.275887	+	0.187077i
$226$	−0.513333			−0.0341464
$227$	1.73665	+	1.26175i	0.115266	+	0.0837454i	0.643925	−	0.765089i	$-0.277305\pi$
$227$	1.73665	+	1.26175i	0.115266	+	0.0837454i	−0.528659	+	0.848834i	$0.677305\pi$
$228$	−3.00064	−	9.23502i	−0.198722	−	0.611604i
$229$	−0.256184	−	0.788454i	−0.0169291	−	0.0521025i	0.942235	−	0.334952i	$-0.108720\pi$
$229$	−0.256184	−	0.788454i	−0.0169291	−	0.0521025i	−0.959164	+	0.282850i	$0.908720\pi$
$230$	−0.303758	−	0.0932766i	−0.0200292	−	0.00615048i
$231$	0.121106	−	0.372726i	0.00796820	−	0.0245236i
$232$	0.0403018			0.00264594
$233$	0.815604	−	2.51017i	0.0534320	−	0.164447i	−0.920780	−	0.390083i	$-0.872446\pi$
$233$	0.815604	−	2.51017i	0.0534320	−	0.164447i	0.974212	+	0.225637i	$0.0724462\pi$
$234$	−0.0411390	+	0.0298892i	−0.00268934	+	0.00195392i
$235$	−7.22046	−	2.21723i	−0.471011	−	0.144636i
$236$	6.90326	+	5.01552i	0.449364	+	0.326482i
$237$	−9.52889	+	6.92314i	−0.618968	+	0.449706i
$238$	−0.107866	+	0.0783691i	−0.00699190	+	0.00507991i
$239$	−17.2640	−	12.5430i	−1.11672	−	0.811342i	−0.133008	−	0.991115i	$-0.542464\pi$
$239$	−17.2640	−	12.5430i	−1.11672	−	0.811342i	−0.983708	+	0.179773i	$0.942464\pi$
$240$	−8.45125	+	2.89838i	−0.545526	+	0.187090i
$241$	−21.0874	+	15.3209i	−1.35836	+	0.986905i	−0.359810	+	0.933026i	$0.617159\pi$
$241$	−21.0874	+	15.3209i	−1.35836	+	0.986905i	−0.998547	+	0.0538790i	$0.982841\pi$
$242$	0.0907556	−	0.279317i	0.00583399	−	0.0179552i
$243$	1.00000			0.0641500
$244$	6.02911	−	18.5557i	0.385974	−	1.18791i
$245$	1.28481	−	1.83010i	0.0820833	−	0.116921i
$246$	−0.0315333	−	0.0970496i	−0.00201049	−	0.00618766i
$247$	−2.81860	−	8.67476i	−0.179343	−	0.551962i
$248$	0.543153	+	0.394624i	0.0344903	+	0.0250586i
$249$	−10.0084			−0.634260
$250$	−0.189647	−	0.235969i	−0.0119943	−	0.0149240i
$251$	11.4251			0.721143			0.360571	−	0.932732i	$-0.382582\pi$
$251$	11.4251			0.721143			0.360571	+	0.932732i	$0.382582\pi$
$252$	−1.61744	−	1.17514i	−0.101889	−	0.0740268i
$253$	−0.635580	−	1.95612i	−0.0399586	−	0.122980i
$254$	−0.0591018	−	0.181897i	−0.00370838	−	0.0114132i
$255$	6.32643	−	9.01148i	0.396176	−	0.564321i
$256$	4.92616	−	15.1612i	0.307885	−	0.947572i
$257$	−19.9358			−1.24356			−0.621782	−	0.783190i	$-0.713591\pi$
$257$	−19.9358			−1.24356			−0.621782	+	0.783190i	$0.713591\pi$
$258$	−0.0485340	+	0.149372i	−0.00302159	+	0.00929950i
$259$	−8.63276	+	6.27207i	−0.536414	+	0.389728i
$260$	−7.94145	+	2.72354i	−0.492508	+	0.168907i
$261$	−0.301090	−	0.218755i	−0.0186370	−	0.0135406i
$262$	−0.192684	+	0.139993i	−0.0119040	+	0.00864879i
$263$	11.8520	−	8.61099i	0.730826	−	0.530976i	−0.158999	−	0.987279i	$-0.550827\pi$
$263$	11.8520	−	8.61099i	0.730826	−	0.530976i	0.889825	+	0.456303i	$0.150827\pi$
$264$	0.0343342	+	0.0249452i	0.00211312	+	0.00153527i
$265$	2.00679	+	0.616235i	0.123276	+	0.0378550i
$266$	−0.106396	+	0.0773009i	−0.00652353	+	0.00473962i
$267$	3.30202	−	10.1626i	0.202080	−	0.621940i
$268$	−11.1061			−0.678413
$269$	3.42350	−	10.5364i	0.208734	−	0.642418i	−0.790805	−	0.612068i	$-0.790338\pi$
$269$	3.42350	−	10.5364i	0.208734	−	0.642418i	0.999539	−	0.0303499i	$-0.00966216\pi$
$270$	−0.0578792	−	0.0177733i	−0.00352242	−	0.00108165i
$271$	−2.70282	−	8.31841i	−0.164184	−	0.505308i	0.834791	−	0.550567i	$-0.185589\pi$
$271$	−2.70282	−	8.31841i	−0.164184	−	0.505308i	−0.998975	+	0.0452596i	$0.985589\pi$
$272$	6.07974	+	18.7115i	0.368639	+	1.13455i
$273$	−1.51932	−	1.10385i	−0.0919532	−	0.0668079i
$274$	0.588869			0.0355749
$275$	0.544752	−	1.88229i	0.0328498	−	0.113507i
$276$	−10.4924			−0.631569
$277$	−18.8021	−	13.6605i	−1.12971	−	0.820780i	−0.144054	−	0.989570i	$-0.546014\pi$
$277$	−18.8021	−	13.6605i	−1.12971	−	0.820780i	−0.985652	+	0.168790i	$0.946014\pi$
$278$	0.124760	+	0.383972i	0.00748261	+	0.0230291i
$279$	−1.91585	−	5.89638i	−0.114699	−	0.353007i
$280$	0.145487	+	0.193562i	0.00869451	+	0.0115676i
$281$	1.35457	−	4.16893i	0.0808067	−	0.248697i	−0.902489	−	0.430713i	$-0.858262\pi$
$281$	1.35457	−	4.16893i	0.0808067	−	0.248697i	0.983296	+	0.182016i	$0.0582621\pi$
$282$	0.0914644			0.00544663
$283$	−0.0174480	+	0.0536994i	−0.00103718	+	0.00319210i	−0.951574	−	0.307421i	$-0.900534\pi$
$283$	−0.0174480	+	0.0536994i	−0.00103718	+	0.00319210i	0.950537	+	0.310613i	$0.100534\pi$
$284$	15.8233	−	11.4963i	0.938938	−	0.682179i
$285$	6.24020	−	8.88865i	0.369638	−	0.526518i
$286$	0.0161227	+	0.0117138i	0.000953353	+	0.000692652i
$287$	3.04888	−	2.21514i	0.179970	−	0.130756i
$288$	0.262743	−	0.190894i	0.0154823	−	0.0112485i
$289$	−5.86220	−	4.25914i	−0.344836	−	0.250538i
$290$	0.0135389	+	0.0180127i	0.000795030	+	0.00105774i
$291$	−10.0537	+	7.30443i	−0.589357	+	0.428193i
$292$	4.04153	−	12.4385i	0.236512	−	0.727910i
$293$	32.1972			1.88098			0.940489	−	0.339823i	$-0.110367\pi$
$293$	32.1972			1.88098			0.940489	+	0.339823i	$0.110367\pi$
$294$	−0.00836734	+	0.0257520i	−0.000487993	+	0.00150189i
$295$	0.154826	+	9.54232i	0.00901431	+	0.555575i
$296$	−0.357076	−	1.09897i	−0.0207546	−	0.0638761i
$297$	−0.121106	−	0.372726i	−0.00702729	−	0.0216278i
$298$	0.507060	+	0.368400i	0.0293732	+	0.0213409i
$299$	−9.85587			−0.569980
$300$	−8.27357	−	5.61024i	−0.477675	−	0.323907i
$301$	−5.80040			−0.334330
$302$	−0.293537	−	0.213267i	−0.0168911	−	0.0122721i
$303$	0.664005	+	2.04360i	0.0381461	+	0.117402i
$304$	5.99688	+	18.4565i	0.343945	+	1.05855i
$305$	20.6414	−	7.07902i	1.18192	−	0.405343i
$306$	−0.0412010	+	0.126804i	−0.00235531	+	0.00724889i
$307$	10.3879			0.592868			0.296434	−	0.955053i	$-0.404202\pi$
$307$	10.3879			0.592868			0.296434	+	0.955053i	$0.404202\pi$
$308$	−0.242123	+	0.745179i	−0.0137963	+	0.0424605i
$309$	0.574466	−	0.417374i	0.0326802	−	0.0237436i
$310$	0.00608978	+	0.375329i	0.000345876	+	0.0213173i
$311$	−5.85758	−	4.25578i	−0.332153	−	0.241323i	0.409191	−	0.912449i	$-0.365811\pi$
$311$	−5.85758	−	4.25578i	−0.332153	−	0.241323i	−0.741344	+	0.671126i	$0.765811\pi$
$312$	0.164526	−	0.119535i	0.00931443	−	0.00676733i
$313$	7.41128	−	5.38461i	0.418910	−	0.304356i	−0.358289	−	0.933611i	$-0.616640\pi$
$313$	7.41128	−	5.38461i	0.418910	−	0.304356i	0.777199	+	0.629255i	$0.216640\pi$
$314$	0.0522288	+	0.0379464i	0.00294744	+	0.00214144i
$315$	−0.0362758	−	2.23577i	−0.00204391	−	0.125972i
$316$	19.0508	−	13.8412i	1.07169	−	0.778629i
$317$	4.74778	−	14.6122i	0.266662	−	0.820701i	−0.724644	−	0.689123i	$-0.757996\pi$
$317$	4.74778	−	14.6122i	0.266662	−	0.820701i	0.991306	−	0.131577i	$-0.0420041\pi$
$318$	−0.0254208			−0.00142552
$319$	−0.0450718	+	0.138717i	−0.00252354	+	0.00776664i
$320$	16.8839	−	5.79038i	0.943838	−	0.323692i
$321$	−1.02249	−	3.14690i	−0.0570699	−	0.175643i
$322$	0.0439129	+	0.135150i	0.00244717	+	0.00753161i
$323$	−19.3481	−	14.0572i	−1.07656	−	0.782166i
$324$	−1.99927			−0.111070
$325$	−7.77164	−	5.26989i	−0.431093	−	0.292321i
$326$	0.198143			0.0109741
$327$	7.44542	+	5.40942i	0.411733	+	0.299141i
$328$	0.126110	+	0.388127i	0.00696327	+	0.0214307i
$329$	1.04383	+	3.21258i	0.0575482	+	0.177115i
$330$	0.000384952		0.0237256i	2.11909e−5		0.00130605i
$331$	2.62000	−	8.06354i	0.144008	−	0.443212i	−0.852874	−	0.522117i	$-0.825142\pi$
$331$	2.62000	−	8.06354i	0.144008	−	0.443212i	0.996882	+	0.0789048i	$0.0251423\pi$
$332$	20.0096			1.09817
$333$	−3.29742	+	10.1484i	−0.180698	+	0.556130i
$334$	−0.243010	+	0.176557i	−0.0132969	+	0.00966076i
$335$	−7.46327	−	9.92947i	−0.407762	−	0.542505i
$336$	3.23251	+	2.34856i	0.176348	+	0.128124i
$337$	−4.53277	+	3.29325i	−0.246916	+	0.179395i	−0.704359	−	0.709844i	$-0.748765\pi$
$337$	−4.53277	+	3.29325i	−0.246916	+	0.179395i	0.457443	+	0.889239i	$0.348765\pi$
$338$	−0.207520	+	0.150772i	−0.0112876	+	0.00820091i
$339$	−15.3374	−	11.1433i	−0.833014	−	0.605220i
$340$	−12.6482	+	18.0163i	−0.685946	+	0.977073i
$341$	−1.96571	+	1.42818i	−0.106449	+	0.0773400i
$342$	−0.0406395	+	0.125075i	−0.00219753	+	0.00676331i
$343$	−1.00000			−0.0539949
$344$	0.194100	−	0.597379i	0.0104652	−	0.0322085i
$345$	−7.05087	−	9.38080i	−0.379606	−	0.505045i
$346$	−0.161548	−	0.497193i	−0.00868486	−	0.0267292i
$347$	5.10995	+	15.7268i	0.274317	+	0.844260i	0.989399	+	0.145220i	$0.0463890\pi$
$347$	5.10995	+	15.7268i	0.274317	+	0.844260i	−0.715083	+	0.699040i	$0.753611\pi$
$348$	0.601959	+	0.437349i	0.0322684	+	0.0234444i
$349$	1.03051			0.0551620			0.0275810	−	0.999620i	$-0.491220\pi$
$349$	1.03051			0.0551620			0.0275810	+	0.999620i	$0.491220\pi$
$350$	−0.0376375	+	0.130050i	−0.00201181	+	0.00695144i
$351$	−1.87798			−0.100239
$352$	−0.102971	−	0.0748129i	−0.00548838	−	0.00398754i
$353$	11.0618	+	34.0448i	0.588762	+	1.81202i	0.583608	+	0.812036i	$0.301641\pi$
$353$	11.0618	+	34.0448i	0.588762	+	1.81202i	0.00515429	+	0.999987i	$0.498359\pi$
$354$	−0.0357120	−	0.109910i	−0.00189807	−	0.00584166i
$355$	20.9115	+	6.42142i	1.10987	+	0.340813i
$356$	−6.60162	+	20.3177i	−0.349885	+	1.07684i
$357$	−4.92403			−0.260607
$358$	−0.0884888	+	0.272340i	−0.00467678	+	0.0143936i
$359$	−19.1959	+	13.9466i	−1.01312	+	0.736076i	−0.964862	−	0.262759i	$-0.915368\pi$
$359$	−19.1959	+	13.9466i	−1.01312	+	0.736076i	−0.0482602	+	0.998835i	$0.515368\pi$
$360$	0.231475	+	0.0710802i	0.0121998	+	0.00374625i
$361$	−3.71311	−	2.69773i	−0.195427	−	0.141986i
$362$	−0.262752	+	0.190900i	−0.0138099	+	0.0100335i
$363$	8.77493	−	6.37536i	0.460564	−	0.334620i
$364$	3.03752	+	2.20689i	0.159209	+	0.115672i
$365$	13.8366	−	4.74532i	0.724243	−	0.248381i
$366$	−0.213778	+	0.155319i	−0.0111743	+	0.00811864i
$367$	4.11620	−	12.6684i	0.214864	−	0.661283i	−0.784299	−	0.620383i	$-0.786977\pi$
$367$	4.11620	−	12.6684i	0.214864	−	0.661283i	0.999163	−	0.0409004i	$-0.0130226\pi$
$368$	20.9694			1.09311
$369$	1.16457	−	3.58417i	0.0606250	−	0.186584i
$370$	0.371223	−	0.528777i	0.0192990	−	0.0274898i
$371$	−0.290112	−	0.892873i	−0.0150619	−	0.0463556i
$372$	3.83030	+	11.7884i	0.198592	+	0.611202i
$373$	−11.7388	−	8.52876i	−0.607813	−	0.441602i	0.240830	−	0.970567i	$-0.422580\pi$
$373$	−11.7388	−	8.52876i	−0.607813	−	0.441602i	−0.848644	+	0.528965i	$0.822580\pi$
$374$	0.0522528			0.00270193
$375$	−0.543947	−	11.1671i	−0.0280893	−	0.576667i
$376$	−0.365791			−0.0188642
$377$	0.565441	+	0.410817i	0.0291217	+	0.0211581i
$378$	0.00836734	+	0.0257520i	0.000430370	+	0.00132454i
$379$	10.6450	+	32.7619i	0.546796	+	1.68286i	0.716681	+	0.697401i	$0.245660\pi$
$379$	10.6450	+	32.7619i	0.546796	+	1.68286i	−0.169886	+	0.985464i	$0.554340\pi$
$380$	−12.4758	+	17.7708i	−0.639997	+	0.911622i
$381$	2.18271	−	6.71768i	0.111823	−	0.344157i
$382$	0.528458			0.0270383
$383$	−3.49958	+	10.7706i	−0.178820	+	0.550353i	−0.999787	−	0.0206232i	$-0.993435\pi$
$383$	−3.49958	+	10.7706i	−0.178820	+	0.550353i	0.820967	+	0.570976i	$0.193435\pi$
$384$	−0.700349	+	0.508833i	−0.0357395	+	0.0259663i
$385$	−0.828938	+	0.284287i	−0.0422466	+	0.0144886i
$386$	0.521872	+	0.379162i	0.0265626	+	0.0192988i
$387$	−4.69263	+	3.40939i	−0.238540	+	0.173309i
$388$	20.1000	−	14.6035i	1.02042	−	0.741380i
$389$	−24.8926	−	18.0855i	−1.26210	−	0.916973i	−0.263246	−	0.964729i	$-0.584793\pi$
$389$	−24.8926	−	18.0855i	−1.26210	−	0.916973i	−0.998859	+	0.0477558i	$0.984793\pi$
$390$	0.108696	+	0.0333779i	0.00550403	+	0.00169015i
$391$	−20.9066	+	15.1895i	−1.05729	+	0.768167i
$392$	0.0334632	−	0.102989i	0.00169015	−	0.00520174i
$393$	−8.79594			−0.443696
$394$	0.0890566	−	0.274088i	0.00448661	−	0.0138084i
$395$	25.1769	+	7.73121i	1.26679	+	0.388999i
$396$	0.242123	+	0.745179i	0.0121672	+	0.0374467i
$397$	−7.97961	−	24.5587i	−0.400485	−	1.23257i	−0.924607	−	0.380923i	$-0.875606\pi$
$397$	−7.97961	−	24.5587i	−0.400485	−	1.23257i	0.524121	−	0.851644i	$-0.324394\pi$
$398$	0.143985	+	0.104611i	0.00721731	+	0.00524368i
$399$	−4.85692			−0.243150
$400$	16.5350	+	11.2123i	0.826750	+	0.560613i
$401$	27.3405			1.36532			0.682661	−	0.730735i	$-0.260823\pi$
$401$	27.3405			1.36532			0.682661	+	0.730735i	$0.260823\pi$
$402$	0.121690	+	0.0884127i	0.00606933	+	0.00440962i
$403$	3.59793	+	11.0733i	0.179225	+	0.551599i
$404$	−1.32752	−	4.08570i	−0.0660468	−	0.203271i
$405$	−1.34350	−	1.78746i	−0.0667592	−	0.0888194i
$406$	0.00311405	−	0.00958407i	0.000154548	−	0.000475650i
$407$	4.18192			0.207290
$408$	0.164774	−	0.507122i	0.00815753	−	0.0251063i
$409$	−23.0435	+	16.7421i	−1.13943	+	0.827844i	−0.987040	−	0.160477i	$-0.948697\pi$
$409$	−23.0435	+	16.7421i	−1.13943	+	0.827844i	−0.152389	+	0.988321i	$0.548697\pi$
$410$	−0.131107	+	0.186751i	−0.00647490	+	0.00922297i
$411$	17.5943	+	12.7830i	0.867861	+	0.630538i
$412$	−1.14851	+	0.834441i	−0.0565830	+	0.0411100i
$413$	3.45290	−	2.50868i	0.169906	−	0.123444i
$414$	0.114965	+	0.0835273i	0.00565024	+	0.00410514i
$415$	13.4464	+	17.8897i	0.660057	+	0.878169i
$416$	−0.493426	+	0.358495i	−0.0241922	+	0.0175767i
$417$	−4.60755	+	14.1806i	−0.225633	+	0.694427i
$418$	0.0515406			0.00252093
$419$	3.93404	−	12.1077i	0.192190	−	0.591501i	−0.807808	−	0.589446i	$-0.799346\pi$
$419$	3.93404	−	12.1077i	0.192190	−	0.591501i	0.999998	−	0.00205465i	$-0.000654014\pi$
$420$	0.0725251	+	4.46991i	0.00353886	+	0.218109i
$421$	4.54328	+	13.9828i	0.221426	+	0.681478i	0.998635	+	0.0522358i	$0.0166347\pi$
$421$	4.54328	+	13.9828i	0.221426	+	0.681478i	−0.777209	+	0.629242i	$0.783365\pi$
$422$	0.0289780	+	0.0891851i	0.00141063	+	0.00434146i
$423$	2.73278	+	1.98548i	0.132872	+	0.0965374i
$424$	0.101664			0.00493726
$425$	−24.6072	+	0.798723i	−1.19362	+	0.0387437i
$426$	−0.264895			−0.0128342
$427$	−7.89510	−	5.73612i	−0.382071	−	0.277591i
$428$	2.04423	+	6.29150i	0.0988117	+	0.304111i
$429$	0.227435	+	0.699972i	0.0109806	+	0.0337950i
$430$	0.332202	−	0.113930i	0.0160202	−	0.00549417i
$431$	−5.44966	+	16.7723i	−0.262501	+	0.807895i	0.729758	+	0.683706i	$0.239633\pi$
$431$	−5.44966	+	16.7723i	−0.262501	+	0.807895i	−0.992259	+	0.124189i	$0.960367\pi$
$432$	3.99560			0.192238
$433$	0.625804	−	1.92603i	0.0300742	−	0.0925589i	−0.934893	−	0.354930i	$-0.884505\pi$
$433$	0.625804	−	1.92603i	0.0300742	−	0.0925589i	0.964967	+	0.262371i	$0.0845046\pi$
$434$	0.135813	−	0.0986741i	0.00651924	−	0.00473651i
$435$	0.0135007	+	0.832083i	0.000647309	+	0.0398953i
$436$	−14.8854	−	10.8149i	−0.712881	−	0.517938i
$437$	−20.6216	+	14.9825i	−0.986466	+	0.716710i
$438$	−0.143303	+	0.104116i	−0.00684728	+	0.00497484i
$439$	−28.3924	−	20.6283i	−1.35509	−	0.984533i	−0.998740	−	0.0501820i	$-0.984020\pi$
$439$	−28.3924	−	20.6283i	−1.35509	−	0.984533i	−0.356354	−	0.934351i	$-0.615980\pi$
$440$	−0.00153952	−	0.0948849i	−7.33940e−5	−	0.00452346i
$441$	−0.809017	+	0.587785i	−0.0385246	+	0.0279898i
$442$	0.0773747	−	0.238135i	0.00368034	−	0.0113269i
$443$	14.2724			0.678100			0.339050	−	0.940768i	$-0.389894\pi$
$443$	14.2724			0.678100			0.339050	+	0.940768i	$0.389894\pi$
$444$	6.59243	−	20.2894i	0.312863	−	0.962893i
$445$	−22.6014	+	7.75123i	−1.07141	+	0.367443i
$446$	0.0179025	+	0.0550983i	0.000847710	+	0.00260898i
$447$	7.15284	+	22.0142i	0.338318	+	1.04124i
$448$	−6.45790	−	4.69194i	−0.305107	−	0.221673i
$449$	12.7550			0.601948			0.300974	−	0.953632i	$-0.402688\pi$
$449$	12.7550			0.601948			0.300974	+	0.953632i	$0.402688\pi$
$450$	0.0459919	+	0.127335i	0.00216808	+	0.00600263i
$451$	−1.47695			−0.0695469
$452$	30.6636	+	22.2784i	1.44229	+	1.04789i
$453$	−4.14078	−	12.7440i	−0.194551	−	0.598766i
$454$	0.0179615	+	0.0552798i	0.000842975	+	0.00259441i
$455$	0.0681252	+	4.19873i	0.00319376	+	0.196840i
$456$	0.162528	−	0.500210i	0.00761108	−	0.0234245i
$457$	−15.1478			−0.708584			−0.354292	−	0.935135i	$-0.615278\pi$
$457$	−15.1478			−0.708584			−0.354292	+	0.935135i	$0.615278\pi$
$458$	0.00693677	−	0.0213492i	0.000324134	−	0.000997582i
$459$	−3.98362	+	2.89427i	−0.185940	+	0.135093i
$460$	14.0966	+	18.7547i	0.657256	+	0.874444i
$461$	−24.9039	−	18.0937i	−1.15989	−	0.842708i	−0.170124	−	0.985423i	$-0.554417\pi$
$461$	−24.9039	−	18.0937i	−1.15989	−	0.842708i	−0.989764	+	0.142715i	$0.954417\pi$
$462$	0.00858512	−	0.00623746i	0.000399416	−	0.000290193i
$463$	34.0821	−	24.7621i	1.58393	−	1.15079i	0.671921	−	0.740623i	$-0.265469\pi$
$463$	34.0821	−	24.7621i	1.58393	−	1.15079i	0.912009	−	0.410170i	$-0.134531\pi$
$464$	−1.20304	−	0.874057i	−0.0558495	−	0.0405771i
$465$	−7.96558	+	11.3463i	−0.369395	+	0.526172i
$466$	0.0578175	−	0.0420069i	0.00267835	−	0.00194593i
$467$	−8.81612	+	27.1332i	−0.407961	+	1.25558i	0.510436	+	0.859916i	$0.329484\pi$
$467$	−8.81612	+	27.1332i	−0.407961	+	1.25558i	−0.918397	+	0.395660i	$0.870516\pi$
$468$	3.75458			0.173556
$469$	−1.71662	+	5.28320i	−0.0792660	+	0.243956i
$470$	−0.122883	−	0.163489i	−0.00566816	−	0.00754117i
$471$	0.736766	+	2.26753i	0.0339484	+	0.104482i
$472$	0.142822	+	0.439560i	0.00657390	+	0.0202324i
$473$	1.83908	+	1.33617i	0.0845608	+	0.0614370i
$474$	−0.318926			−0.0146487
$475$	−24.2718	+	0.787836i	−1.11367	+	0.0361484i
$476$	9.84445			0.451220
$477$	−0.759523	−	0.551826i	−0.0347762	−	0.0252664i
$478$	−0.178555	−	0.549535i	−0.00816691	−	0.0251352i
$479$	−9.74991	−	30.0071i	−0.445485	−	1.37106i	−0.881951	−	0.471340i	$-0.843770\pi$
$479$	−9.74991	−	30.0071i	−0.445485	−	1.37106i	0.436467	−	0.899720i	$-0.356230\pi$
$480$	−0.694211	−	0.213175i	−0.0316863	−	0.00973008i
$481$	6.19249	−	19.0585i	0.282353	−	0.868994i
$482$	−0.705781			−0.0321475
$483$	−1.62176	+	4.99127i	−0.0737927	+	0.227111i
$484$	−17.5434	+	12.7460i	−0.797428	+	0.579366i
$485$	26.5635	+	8.15700i	1.20619	+	0.370390i
$486$	0.0219060	+	0.0159156i	0.000993676	+	0.000721948i
$487$	−10.9675	+	7.96833i	−0.496983	+	0.361080i	−0.807864	−	0.589370i	$-0.799376\pi$
$487$	−10.9675	+	7.96833i	−0.496983	+	0.361080i	0.310880	+	0.950449i	$0.399376\pi$
$488$	0.854955	−	0.621161i	0.0387020	−	0.0281186i
$489$	5.92012	+	4.30122i	0.267717	+	0.194508i
$490$	0.0572722	−	0.0196417i	0.00258729	−	0.000887320i
$491$	2.37043	−	1.72222i	0.106976	−	0.0777226i	−0.533011	−	0.846108i	$-0.678940\pi$
$491$	2.37043	−	1.72222i	0.106976	−	0.0777226i	0.639987	+	0.768386i	$0.278940\pi$
$492$	−2.32828	+	7.16571i	−0.104967	+	0.323055i
$493$	1.83257			0.0825346
$494$	0.0763201	−	0.234889i	0.00343380	−	0.0105682i
$495$	−0.503526	+	0.717231i	−0.0226318	+	0.0322371i
$496$	−7.65497	−	23.5596i	−0.343719	−	1.05786i
$497$	−3.02308	−	9.30410i	−0.135604	−	0.417346i
$498$	−0.219245	−	0.159291i	−0.00982460	−	0.00713799i
$499$	−14.2029			−0.635807			−0.317903	−	0.948123i	$-0.602979\pi$
$499$	−14.2029			−0.635807			−0.317903	+	0.948123i	$0.602979\pi$
$500$	1.08749	+	22.3260i	0.0486342	+	0.998450i
$501$	−11.0933			−0.495612
$502$	0.250277	+	0.181837i	0.0111704	+	0.00811578i
$503$	−7.59086	−	23.3623i	−0.338460	−	1.04167i	−0.964993	−	0.262277i	$-0.915527\pi$
$503$	−7.59086	−	23.3623i	−0.338460	−	1.04167i	0.626533	−	0.779395i	$-0.284473\pi$
$504$	−0.0334632	−	0.102989i	−0.00149057	−	0.00458751i
$505$	2.76075	−	3.93246i	0.122852	−	0.174992i
$506$	0.0172098	−	0.0529663i	0.000765069	−	0.00235464i
$507$	−9.47320			−0.420719
$508$	−4.36381	+	13.4304i	−0.193613	+	0.595879i
$509$	−19.5023	+	14.1692i	−0.864424	+	0.628041i	−0.929085	−	0.369866i	$-0.879403\pi$
$509$	−19.5023	+	14.1692i	−0.864424	+	0.628041i	0.0646608	+	0.997907i	$0.479403\pi$
$510$	0.282010	−	0.0967161i	0.0124876	−	0.00428266i
$511$	−5.29237	−	3.84513i	−0.234121	−	0.170099i
$512$	1.74991	−	1.27138i	0.0773358	−	0.0561878i
$513$	−3.92933	+	2.85482i	−0.173484	+	0.126044i
$514$	−0.436714	−	0.317291i	−0.0192626	−	0.0139951i
$515$	−1.51783	−	0.466090i	−0.0668837	−	0.0205384i
$516$	9.38181	−	6.81628i	0.413011	−	0.300070i
$517$	0.409085	−	1.25903i	0.0179915	−	0.0553722i
$518$	−0.288933			−0.0126950
$519$	5.96617	−	18.3620i	0.261886	−	0.806002i
$520$	−0.434704	−	0.133487i	−0.0190630	−	0.00585379i
$521$	6.83920	+	21.0489i	0.299631	+	0.922169i	0.981627	+	0.190812i	$0.0611122\pi$
$521$	6.83920	+	21.0489i	0.299631	+	0.922169i	−0.681996	+	0.731356i	$0.738888\pi$
$522$	−0.00311405	−	0.00958407i	−0.000136298	−	0.000419484i
$523$	9.55761	+	6.94401i	0.417925	+	0.303640i	0.776802	−	0.629744i	$-0.216840\pi$
$523$	9.55761	+	6.94401i	0.417925	+	0.303640i	−0.358877	+	0.933385i	$0.616840\pi$
$524$	17.5854			0.768223
$525$	−3.94761	+	3.06861i	−0.172288	+	0.133925i
$526$	0.396679			0.0172960
$527$	24.6978	+	17.9440i	1.07585	+	0.781652i
$528$	−0.483892	−	1.48927i	−0.0210587	−	0.0648120i
$529$	1.40382	+	4.32051i	0.0610356	+	0.187848i
$530$	0.0341528	+	0.0454385i	0.00148350	+	0.00197372i
$531$	1.31889	−	4.05913i	0.0572349	−	0.176151i
$532$	9.71028			0.420994
$533$	−2.18703	+	6.73099i	−0.0947309	+	0.291552i
$534$	0.234078	−	0.170067i	0.0101295	−	0.00735954i
$535$	−4.25123	+	6.05553i	−0.183797	+	0.261803i
$536$	−0.486669	−	0.353586i	−0.0210209	−	0.0152726i
$537$	−8.55576	+	6.21612i	−0.369208	+	0.268245i
$538$	0.242689	−	0.176324i	0.0104631	−	0.00760187i
$539$	0.317060	+	0.230357i	0.0136567	+	0.00992220i
$540$	2.68602	+	3.57360i	0.115588	+	0.153783i
$541$	7.51062	−	5.45678i	0.322907	−	0.234605i	−0.414508	−	0.910046i	$-0.636046\pi$
$541$	7.51062	−	5.45678i	0.322907	−	0.234605i	0.737415	+	0.675440i	$0.236046\pi$
$542$	0.0731849	−	0.225240i	0.00314356	−	0.00967489i
$543$	−11.9945			−0.514734
$544$	−0.494171	+	1.52090i	−0.0211874	+	0.0652081i
$545$	−0.333848	−	20.5759i	−0.0143005	−	0.881376i
$546$	−0.0157137	−	0.0483618i	−0.000672484	−	0.00206969i
$547$	−0.440410	−	1.35544i	−0.0188306	−	0.0579546i	0.941200	−	0.337851i	$-0.109700\pi$
$547$	−0.440410	−	1.35544i	−0.0188306	−	0.0579546i	−0.960030	+	0.279896i	$0.909700\pi$
$548$	−35.1756	−	25.5566i	−1.50263	−	1.09172i
$549$	−9.75888			−0.416499
$550$	0.0418912	−	0.0325634i	0.00178625	−	0.00138851i
$551$	1.80759			0.0770058
$552$	−0.459777	−	0.334048i	−0.0195694	−	0.0142180i
$553$	−3.63971	−	11.2019i	−0.154776	−	0.476352i
$554$	−0.194462	−	0.598493i	−0.00826191	−	0.0254275i
$555$	22.5700	−	7.74043i	0.958042	−	0.328563i
$556$	9.21173	−	28.3508i	0.390664	−	1.20234i
$557$	−35.3089			−1.49609			−0.748043	−	0.663650i	$-0.769007\pi$
$557$	−35.3089			−1.49609			−0.748043	+	0.663650i	$0.769007\pi$
$558$	0.0518760	−	0.159658i	0.00219609	−	0.00675886i
$559$	8.81265	−	6.40276i	0.372735	−	0.270808i
$560$	−0.144944	−	8.93326i	−0.00612499	−	0.377499i
$561$	1.56121	+	1.13429i	0.0659145	+	0.0478897i
$562$	0.0960242	−	0.0697657i	0.00405054	−	0.00294289i
$563$	15.6474	−	11.3685i	0.659461	−	0.479126i	−0.207020	−	0.978337i	$-0.566377\pi$
$563$	15.6474	−	11.3685i	0.659461	−	0.479126i	0.866481	+	0.499211i	$0.166377\pi$
$564$	−5.46356	−	3.96951i	−0.230057	−	0.167146i
$565$	0.687720	+	42.3860i	0.0289326	+	1.78319i
$566$	−0.00123688		0.000898643i	−5.19897e−5		3.77728e-5i
$567$	−0.309017	+	0.951057i	−0.0129775	+	0.0399406i
$568$	1.05938			0.0444508
$569$	−8.36708	+	25.7512i	−0.350766	+	1.07955i	0.607658	+	0.794199i	$0.292109\pi$
$569$	−8.36708	+	25.7512i	−0.350766	+	1.07955i	−0.958424	+	0.285348i	$0.907891\pi$
$570$	0.278166	−	0.0953979i	0.0116511	−	0.00399578i
$571$	6.17195	+	18.9953i	0.258288	+	0.794929i	0.993164	+	0.116728i	$0.0372404\pi$
$571$	6.17195	+	18.9953i	0.258288	+	0.794929i	−0.734876	+	0.678202i	$0.762760\pi$
$572$	−0.454702	−	1.39943i	−0.0190121	−	0.0585131i
$573$	15.7893	+	11.4716i	0.659607	+	0.479233i
$574$	0.102044			0.00425923
$575$	−7.29491	+	25.2063i	−0.304219	+	1.05117i
$576$	−7.98241			−0.332600
$577$	6.65841	+	4.83762i	0.277193	+	0.201393i	0.717692	−	0.696360i	$-0.245198\pi$
$577$	6.65841	+	4.83762i	0.277193	+	0.201393i	−0.440499	+	0.897753i	$0.645198\pi$
$578$	−0.0606305	−	0.186601i	−0.00252189	−	0.00776159i
$579$	7.36179	+	22.6573i	0.305945	+	0.941603i
$580$	−0.0269915	−	1.66356i	−0.00112076	−	0.0690754i
$581$	3.09278	−	9.51860i	0.128310	−	0.394898i
$582$	−0.336490			−0.0139480
$583$	−0.113697	+	0.349924i	−0.00470885	+	0.0144924i
$584$	0.573107	−	0.416386i	0.0237153	−	0.0172302i
$585$	2.52307	+	3.35680i	0.104316	+	0.138787i
$586$	0.705311	+	0.512438i	0.0291361	+	0.0211686i
$587$	−27.5996	+	20.0523i	−1.13916	+	0.827645i	−0.987001	−	0.160711i	$-0.948621\pi$
$587$	−27.5996	+	20.0523i	−1.13916	+	0.827645i	−0.152155	+	0.988357i	$0.548621\pi$
$588$	1.61744	−	1.17514i	0.0667021	−	0.0484619i
$589$	24.3611	+	17.6994i	1.00378	+	0.729291i
$590$	−0.148480	+	0.211498i	−0.00611284	+	0.00870724i
$591$	8.61065	−	6.25601i	0.354195	−	0.257338i
$592$	−13.1752	+	40.5491i	−0.541497	+	1.66656i
$593$	−17.8935			−0.734797			−0.367399	−	0.930064i	$-0.619752\pi$
$593$	−17.8935			−0.734797			−0.367399	+	0.930064i	$0.619752\pi$
$594$	0.00327922	−	0.0100924i	0.000134548	−	0.000414097i
$595$	6.61545	+	8.80149i	0.271207	+	0.360826i
$596$	−14.3004	−	44.0122i	−0.585769	−	1.80281i
$597$	2.03112	+	6.25116i	0.0831283	+	0.255843i
$598$	−0.215903	−	0.156862i	−0.00882891	−	0.00641458i
$599$	27.8051			1.13609			0.568043	−	0.822999i	$-0.307701\pi$
$599$	27.8051			1.13609			0.568043	+	0.822999i	$0.307701\pi$
$600$	−0.183934	−	0.509247i	−0.00750907	−	0.0207899i
$601$	−43.6661			−1.78118			−0.890588	−	0.454811i	$-0.849707\pi$
$601$	−43.6661			−1.78118			−0.890588	+	0.454811i	$0.849707\pi$
$602$	−0.127064	−	0.0923171i	−0.00517872	−	0.00376256i
$603$	1.71662	+	5.28320i	0.0699060	+	0.215149i
$604$	8.27853	+	25.4787i	0.336848	+	1.03671i
$605$	−23.1848	−	7.11949i	−0.942597	−	0.289449i
$606$	−0.0179795	+	0.0553351i	−0.000730365	+	0.00224783i
$607$	16.9820			0.689278			0.344639	−	0.938735i	$-0.388001\pi$
$607$	16.9820			0.689278			0.344639	+	0.938735i	$0.388001\pi$
$608$	−0.487436	+	1.50017i	−0.0197681	+	0.0608400i
$609$	0.301090	−	0.218755i	0.0122008	−	0.00886439i
$610$	0.564836	+	0.173448i	0.0228696	+	0.00702268i
$611$	−5.13210	−	3.72869i	−0.207623	−	0.150847i
$612$	7.96433	−	5.78642i	0.321939	−	0.233902i
$613$	29.1327	−	21.1661i	1.17666	−	0.854892i	0.184867	−	0.982764i	$-0.440815\pi$
$613$	29.1327	−	21.1661i	1.17666	−	0.854892i	0.991791	+	0.127872i	$0.0408147\pi$
$614$	0.227557	+	0.165330i	0.00918345	+	0.00667217i
$615$	−7.97115	+	2.73373i	−0.321428	+	0.110235i
$616$	−0.0343342	+	0.0249452i	−0.00138336	+	0.00100507i
$617$	5.34695	−	16.4562i	0.215260	−	0.662502i	−0.783875	−	0.620919i	$-0.786760\pi$
$617$	5.34695	−	16.4562i	0.215260	−	0.662502i	0.999135	−	0.0415834i	$-0.0132402\pi$
$618$	0.0192270			0.000773423
$619$	0.629557	−	1.93758i	0.0253040	−	0.0778778i	−0.937607	−	0.347697i	$-0.886964\pi$
$619$	0.629557	−	1.93758i	0.0253040	−	0.0778778i	0.962911	+	0.269819i	$0.0869639\pi$
$620$	15.9253	−	22.6843i	0.639576	−	0.911023i
$621$	1.62176	+	4.99127i	0.0650790	+	0.200293i
$622$	−0.0605826	−	0.186454i	−0.00242914	−	0.00747613i
$623$	8.64480	+	6.28082i	0.346347	+	0.251636i
$624$	−7.50365			−0.300387
$625$	−19.2299	+	15.9753i	−0.769196	+	0.639012i
$626$	0.248051			0.00991411
$627$	1.53993	+	1.11883i	0.0614990	+	0.0446817i
$628$	−1.47299	−	4.53340i	−0.0587788	−	0.180902i
$629$	−16.2366	−	49.9712i	−0.647396	−	1.99248i
$630$	0.0347891	−	0.0495542i	0.00138603	−	0.00197429i
$631$	−1.41689	+	4.36073i	−0.0564053	+	0.173598i	−0.975290	−	0.220928i	$-0.929091\pi$
$631$	−1.41689	+	4.36073i	−0.0564053	+	0.173598i	0.918885	+	0.394526i	$0.129091\pi$
$632$	1.27547			0.0507354
$633$	−1.07020	+	3.29372i	−0.0425365	+	0.130914i
$634$	0.336566	−	0.244530i	0.0133668	−	0.00971152i
$635$	−14.9400	+	5.12373i	−0.592877	+	0.203329i
$636$	1.51849	+	1.10325i	0.0602120	+	0.0437466i
$637$	1.51932	−	1.10385i	0.0601975	−	0.0437360i
$638$	−0.00319510	+	0.00232138i	−0.000126495	+	9.19043e-5i
$639$	−7.91454	−	5.75025i	−0.313094	−	0.227476i
$640$	1.85044	+	0.568225i	0.0731450	+	0.0224611i
$641$	−0.291808	+	0.212011i	−0.0115257	+	0.00837393i	−0.593533	−	0.804810i	$-0.702267\pi$
$641$	−0.291808	+	0.212011i	−0.0115257	+	0.00837393i	0.582007	+	0.813183i	$0.302267\pi$
$642$	0.0276863	−	0.0852096i	0.00109269	−	0.00336295i
$643$	49.9164			1.96851			0.984255	−	0.176756i	$-0.0565603\pi$
$643$	49.9164			1.96851			0.984255	+	0.176756i	$0.0565603\pi$
$644$	3.24233	−	9.97887i	0.127766	−	0.393223i
$645$	12.3987	+	3.80734i	0.488198	+	0.149914i
$646$	−0.200110	−	0.615876i	−0.00787323	−	0.0242313i
$647$	1.24233	+	3.82350i	0.0488410	+	0.150317i	0.972503	−	0.232892i	$-0.0748188\pi$
$647$	1.24233	+	3.82350i	0.0488410	+	0.150317i	−0.923662	+	0.383209i	$0.874819\pi$
$648$	−0.0876079	−	0.0636508i	−0.00344156	−	0.00250044i
$649$	−1.67267			−0.0656580
$650$	−0.0863718	−	0.239133i	−0.00338778	−	0.00937955i
$651$	6.19982			0.242990
$652$	−11.8359	−	8.59928i	−0.463529	−	0.336774i
$653$	2.32018	+	7.14078i	0.0907957	+	0.279440i	0.986135	−	0.165944i	$-0.0530671\pi$
$653$	2.32018	+	7.14078i	0.0907957	+	0.279440i	−0.895340	+	0.445384i	$0.853067\pi$
$654$	0.0770051	+	0.236997i	0.00301114	+	0.00926732i
$655$	11.8174	+	15.7224i	0.461743	+	0.614323i
$656$	4.65315	−	14.3209i	0.181675	−	0.559138i
$657$	−6.54172			−0.255217
$658$	−0.0282641	+	0.0869879i	−0.00110185	+	0.00339114i
$659$	−27.7548	+	20.1651i	−1.08117	+	0.785519i	−0.977887	−	0.209133i	$-0.932936\pi$
$659$	−27.7548	+	20.1651i	−1.08117	+	0.785519i	−0.103287	+	0.994652i	$0.532936\pi$
$660$	1.00668	−	1.43394i	0.0391850	−	0.0558159i
$661$	10.3546	+	7.52309i	0.402749	+	0.292614i	0.770660	−	0.637247i	$-0.219927\pi$
$661$	10.3546	+	7.52309i	0.402749	+	0.292614i	−0.367911	+	0.929861i	$0.619927\pi$
$662$	0.185730	−	0.134941i	0.00721861	−	0.00524463i
$663$	7.48116	−	5.43538i	0.290544	−	0.211093i
$664$	0.876819	+	0.637046i	0.0340272	+	0.0247222i
$665$	6.52528	+	8.68153i	0.253040	+	0.336655i
$666$	−0.233752	+	0.169831i	−0.00905770	+	0.00658080i
$667$	0.603567	−	1.85759i	0.0233702	−	0.0719261i
$668$	22.1785			0.858110
$669$	−0.661164	+	2.03485i	−0.0255621	+	0.0786720i
$670$	−0.00545649	−	0.336298i	−0.000210803	−	0.0129923i
$671$	1.18186	+	3.63739i	0.0456252	+	0.140420i
$672$	0.100359	+	0.308873i	0.00387143	+	0.0119150i
$673$	−9.19109	−	6.67772i	−0.354291	−	0.257407i	0.396376	−	0.918088i	$-0.370268\pi$
$673$	−9.19109	−	6.67772i	−0.354291	−	0.257407i	−0.750667	+	0.660681i	$0.770268\pi$
$674$	−0.151709			−0.00584361
$675$	−1.39000	+	4.80290i	−0.0535012	+	0.184864i
$676$	18.9394			0.728440
$677$	−9.66941	−	7.02523i	−0.371625	−	0.270002i	0.386259	−	0.922390i	$-0.373767\pi$
$677$	−9.66941	−	7.02523i	−0.371625	−	0.270002i	−0.757885	+	0.652389i	$0.773767\pi$
$678$	−0.158629	−	0.488209i	−0.00609210	−	0.0187496i
$679$	−3.84016	−	11.8188i	−0.147372	−	0.453564i
$680$	−1.12783	+	0.386794i	−0.0432504	+	0.0148329i
$681$	−0.663342	+	2.04156i	−0.0254193	+	0.0782327i
$682$	−0.0657912			−0.00251928
$683$	−3.20580	+	9.86643i	−0.122666	+	0.377528i	−0.993469	−	0.114105i	$-0.963600\pi$
$683$	−3.20580	+	9.86643i	−0.122666	+	0.377528i	0.870802	+	0.491633i	$0.163600\pi$
$684$	7.85578	−	5.70756i	0.300373	−	0.218234i
$685$	−0.788917	−	48.6230i	−0.0301430	−	1.85779i
$686$	−0.0219060	−	0.0159156i	−0.000836374	−	0.000607662i
$687$	0.670699	−	0.487291i	0.0255888	−	0.0185913i
$688$	−18.7499	+	13.6226i	−0.714832	+	0.519356i
$689$	1.42637	+	1.03632i	0.0543403	+	0.0394805i
$690$	−0.00515498	−	0.317715i	−0.000196247	−	0.0120952i
$691$	−17.0059	+	12.3555i	−0.646936	+	0.470026i	−0.862226	−	0.506524i	$-0.830930\pi$
$691$	−17.0059	+	12.3555i	−0.646936	+	0.470026i	0.215290	+	0.976550i	$0.430930\pi$
$692$	−11.9280	+	36.7105i	−0.453433	+	1.39552i
$693$	0.391908			0.0148873
$694$	−0.138364	+	0.425840i	−0.00525221	+	0.0161647i
$695$	31.5375	−	10.8159i	1.19628	−	0.410269i
$696$	0.0124539	+	0.0383293i	0.000472065	+	0.00145287i
$697$	5.73437	+	17.6486i	0.217205	+	0.668487i
$698$	0.0225744	+	0.0164012i	0.000854452	+	0.000620796i
$699$	2.63935			0.0998294
$700$	7.89233	−	6.13497i	0.298302	−	0.231880i
$701$	25.9514			0.980172			0.490086	−	0.871674i	$-0.336965\pi$
$701$	25.9514			0.980172			0.490086	+	0.871674i	$0.336965\pi$
$702$	−0.0411390	−	0.0298892i	−0.00155269	−	0.00112810i
$703$	−16.0153	−	49.2901i	−0.604029	−	1.85901i
$704$	0.966718	+	2.97525i	0.0364346	+	0.112134i
$705$	−0.122536	−	7.55223i	−0.00461498	−	0.284433i
$706$	−0.299524	+	0.921841i	−0.0112727	+	0.0346939i
$707$	−2.14877			−0.0808127
$708$	−2.63681	+	8.11527i	−0.0990975	+	0.304991i
$709$	10.6626	−	7.74686i	0.400444	−	0.290940i	−0.369278	−	0.929319i	$-0.620395\pi$
$709$	10.6626	−	7.74686i	0.400444	−	0.290940i	0.769722	+	0.638379i	$0.220395\pi$
$710$	0.355886	+	0.473487i	0.0133562	+	0.0177697i
$711$	−9.52889	−	6.92314i	−0.357361	−	0.259638i
$712$	−0.936140	+	0.680145i	−0.0350833	+	0.0254895i
$713$	26.3234	−	19.1250i	0.985818	−	0.716238i
$714$	−0.107866	−	0.0783691i	−0.00403677	−	0.00293289i
$715$	0.945610	−	1.34694i	0.0353638	−	0.0503728i
$716$	17.1052	−	12.4277i	0.639253	−	0.464444i
$717$	6.59427	−	20.2951i	0.246267	−	0.757933i
$718$	−0.642475			−0.0239770
$719$	−15.3132	+	47.1291i	−0.571085	+	1.75762i	0.0780542	+	0.996949i	$0.475129\pi$
$719$	−15.3132	+	47.1291i	−0.571085	+	1.75762i	−0.649139	+	0.760670i	$0.724871\pi$
$720$	−5.36810	−	7.14196i	−0.200057	−	0.266165i
$721$	0.219426	+	0.675325i	0.00817186	+	0.0251504i
$722$	−0.0384032	−	0.118193i	−0.00142922	−	0.00439868i
$723$	−21.0874	−	15.3209i	−0.784248	−	0.569790i
$724$	23.9802			0.891219
$725$	1.46917	−	1.14204i	0.0545637	−	0.0424142i
$726$	0.293691			0.0108999
$727$	35.6520	+	25.9027i	1.32226	+	0.960677i	0.999901	+	0.0140591i	$0.00447529\pi$
$727$	35.6520	+	25.9027i	1.32226	+	0.960677i	0.322357	+	0.946618i	$0.395525\pi$
$728$	0.0628432	+	0.193412i	0.00232912	+	0.00716831i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	0.378630	+	0.116268i	0.0140137	+	0.00430327i
$731$	8.82595	−	27.1635i	0.326439	−	1.00468i
$732$	19.5106			0.721133
$733$	−10.8768	+	33.4754i	−0.401744	+	1.23644i	0.521839	+	0.853044i	$0.325246\pi$
$733$	−10.8768	+	33.4754i	−0.401744	+	1.23644i	−0.923583	+	0.383398i	$0.874754\pi$
$734$	0.291794	−	0.212001i	0.0107703	−	0.00782510i
$735$	2.13756	+	0.656392i	0.0788450	+	0.0242114i
$736$	1.37891	+	1.00184i	0.0508273	+	0.0369282i
$737$	1.76129	−	1.27966i	0.0648781	−	0.0471367i
$738$	0.0825553	−	0.0599799i	0.00303890	−	0.00220789i
$739$	−32.6234	−	23.7023i	−1.20007	−	0.871903i	−0.205779	−	0.978598i	$-0.565973\pi$
$739$	−32.6234	−	23.7023i	−1.20007	−	0.871903i	−0.994292	+	0.106696i	$0.965973\pi$
$740$	−45.1234	+	15.4752i	−1.65877	+	0.568879i
$741$	7.37920	−	5.36130i	0.271082	−	0.196952i
$742$	0.00785544	−	0.0241766i	0.000288382	−	0.000887550i
$743$	−1.01949			−0.0374013			−0.0187007	−	0.999825i	$-0.505953\pi$
$743$	−1.01949			−0.0374013			−0.0187007	+	0.999825i	$0.505953\pi$
$744$	−0.207466	+	0.638515i	−0.00760608	+	0.0234091i
$745$	29.7395	−	42.3615i	1.08957	−	1.55201i
$746$	−0.121410	−	0.373662i	−0.00444514	−	0.0136807i
$747$	−3.09278	−	9.51860i	−0.113159	−	0.348267i
$748$	−3.12128	−	2.26774i	−0.114125	−	0.0829169i
$749$	3.30885			0.120903
$750$	0.165816	−	0.253284i	0.00605473	−	0.00924861i
$751$	51.7440			1.88817			0.944083	−	0.329707i	$-0.106950\pi$
$751$	51.7440			1.88817			0.944083	+	0.329707i	$0.106950\pi$
$752$	10.9191	+	7.93319i	0.398179	+	0.289294i
$753$	3.53054	+	10.8659i	0.128660	+	0.395974i
$754$	0.00584813	+	0.0179987i	0.000212976	+	0.000655473i
$755$	−17.2162	+	24.5231i	−0.626562	+	0.892486i
$756$	0.617807	−	1.90142i	0.0224694	−	0.0691538i
$757$	−6.66352			−0.242190			−0.121095	−	0.992641i	$-0.538641\pi$
$757$	−6.66352			−0.242190			−0.121095	+	0.992641i	$0.538641\pi$
$758$	−0.288237	+	0.887103i	−0.0104692	+	0.0322210i
$759$	1.66397	−	1.20895i	0.0603983	−	0.0438819i
$760$	−1.11246	+	0.381522i	−0.0403532	+	0.0138392i
$761$	−32.1514	−	23.3594i	−1.16549	−	0.846777i	−0.175026	−	0.984564i	$-0.556001\pi$
$761$	−32.1514	−	23.3594i	−1.16549	−	0.846777i	−0.990462	+	0.137787i	$0.956001\pi$
$762$	0.154730	−	0.112418i	0.00560529	−	0.00407248i
$763$	−7.44542	+	5.40942i	−0.269542	+	0.195834i
$764$	−31.5670	−	22.9348i	−1.14205	−	0.829751i
$765$	10.5254	+	3.23209i	0.380547	+	0.116857i
$766$	−0.248083	+	0.180243i	−0.00896360	+	0.00651244i
$767$	−2.47685	+	7.62295i	−0.0894337	+	0.275249i
$768$	15.9414			0.575235
$769$	11.3052	−	34.7938i	0.407676	−	1.25470i	−0.510965	−	0.859602i	$-0.670712\pi$
$769$	11.3052	−	34.7938i	0.407676	−	1.25470i	0.918640	−	0.395095i	$-0.129288\pi$
$770$	−0.0226833	−	0.00696549i	−0.000817450	−	0.000251019i
$771$	−6.16051	−	18.9601i	−0.221865	−	0.682832i
$772$	−14.7182	−	45.2979i	−0.529719	−	1.63031i
$773$	−32.1908	−	23.3880i	−1.15782	−	0.841207i	−0.168321	−	0.985732i	$-0.553835\pi$
$773$	−32.1908	−	23.3880i	−1.15782	−	0.841207i	−0.989501	+	0.144525i	$0.953835\pi$
$774$	−0.157059			−0.00564538
$775$	30.9828	−	1.00567i	1.11293	−	0.0361247i
$776$	1.34571			0.0483083
$777$	−8.63276	−	6.27207i	−0.309699	−	0.225009i
$778$	−0.257454	−	0.792363i	−0.00923018	−	0.0284076i
$779$	5.65621	+	17.4080i	0.202655	+	0.623707i
$780$	−5.04429	−	6.71115i	−0.180614	−	0.240298i
$781$	−1.18477	+	3.64635i	−0.0423944	+	0.130476i
$782$	−0.699730			−0.0250223
$783$	0.115006	−	0.353953i	0.00410998	−	0.0126492i
$784$	−3.23251	+	2.34856i	−0.115447	+	0.0838770i
$785$	3.06327	−	4.36337i	0.109333	−	0.155735i
$786$	−0.192684	−	0.139993i	−0.00687280	−	0.00499338i
$787$	−37.8574	+	27.5050i	−1.34947	+	0.980447i	−0.350432	+	0.936588i	$0.613965\pi$
$787$	−37.8574	+	27.5050i	−1.34947	+	0.980447i	−0.999038	+	0.0438593i	$0.986035\pi$
$788$	−17.2150	+	12.5074i	−0.613259	+	0.445559i
$789$	11.8520	+	8.61099i	0.421943	+	0.306559i
$790$	0.428478	+	0.570066i	0.0152445	+	0.0202820i
$791$	15.3374	−	11.1433i	0.545335	−	0.396209i
$792$	−0.0131145	+	0.0403623i	−0.000466003	+	0.00143421i
$793$	18.3270			0.650809
$794$	0.216066	−	0.664984i	0.00766791	−	0.0235994i
$795$	0.0340566	+	2.09899i	0.00120786	+	0.0744436i
$796$	−4.06076	−	12.4977i	−0.143930	−	0.442970i
$797$	−8.14723	−	25.0746i	−0.288590	−	0.888188i	−0.985300	−	0.170835i	$-0.945353\pi$
$797$	−8.14723	−	25.0746i	−0.288590	−	0.888188i	0.696710	−	0.717353i	$-0.254647\pi$
$798$	−0.106396	−	0.0773009i	−0.00376636	−	0.00273642i
$799$	−16.6329			−0.588430
$800$	0.551633	+	1.52727i	0.0195032	+	0.0539973i
$801$	10.6856			0.377556
$802$	0.598922	+	0.435142i	0.0211487	+	0.0153654i
$803$	0.792243	+	2.43827i	0.0279576	+	0.0860448i
$804$	−3.43197	−	10.5625i	−0.121036	−	0.372512i
$805$	11.1005	−	3.80695i	0.391242	−	0.134177i
$806$	−0.0974221	+	0.299834i	−0.00343155	+	0.0105612i
$807$	11.0787			0.389988
$808$	0.0719046	−	0.221300i	0.00252960	−	0.00778530i
$809$	21.6482	−	15.7283i	0.761110	−	0.552979i	−0.138140	−	0.990413i	$-0.544113\pi$
$809$	21.6482	−	15.7283i	0.761110	−	0.552979i	0.899251	+	0.437434i	$0.144113\pi$
$810$	−0.000982251	−	0.0605387i	−3.45128e−5	−	0.00212711i
$811$	−43.0732	−	31.2945i	−1.51250	−	1.09890i	−0.965051	−	0.262064i	$-0.915597\pi$
$811$	−43.0732	−	31.2945i	−1.51250	−	1.09890i	−0.547454	−	0.836836i	$-0.684403\pi$
$812$	−0.601959	+	0.437349i	−0.0211246	+	0.0153479i
$813$	7.07606	−	5.14106i	0.248168	−	0.180305i
$814$	0.0916091	+	0.0665579i	0.00321090	+	0.00233285i
$815$	−0.265455	−	16.3606i	−0.00929847	−	0.573089i
$816$	−15.9170	+	11.5644i	−0.557206	+	0.404834i
$817$	8.70565	−	26.7932i	0.304572	−	0.937377i
$818$	−0.771252			−0.0269662
$819$	0.580327	−	1.78606i	0.0202783	−	0.0624101i
$820$	15.9364	−	5.46545i	0.556525	−	0.190862i
$821$	5.87420	+	18.0789i	0.205011	+	0.630959i	0.999713	+	0.0239594i	$0.00762724\pi$
$821$	5.87420	+	18.0789i	0.205011	+	0.630959i	−0.794702	+	0.607000i	$0.792373\pi$
$822$	0.181971	+	0.560048i	0.00634695	+	0.0195339i
$823$	23.6348	+	17.1717i	0.823857	+	0.598567i	0.917815	−	0.397009i	$-0.129952\pi$
$823$	23.6348	+	17.1717i	0.823857	+	0.598567i	−0.0939576	+	0.995576i	$0.529952\pi$
$824$	−0.0768939			−0.00267873
$825$	1.95851	−	0.0635710i	0.0681864	−	0.00221326i
$826$	0.115566			0.00402107
$827$	−34.5958	−	25.1353i	−1.20301	−	0.874040i	−0.208435	−	0.978036i	$-0.566837\pi$
$827$	−34.5958	−	25.1353i	−1.20301	−	0.874040i	−0.994578	+	0.103996i	$0.966837\pi$
$828$	−3.24233	−	9.97887i	−0.112679	−	0.346790i
$829$	−2.61664	−	8.05318i	−0.0908795	−	0.279698i	0.895278	−	0.445507i	$-0.146977\pi$
$829$	−2.61664	−	8.05318i	−0.0908795	−	0.279698i	−0.986158	+	0.165809i	$0.946977\pi$
$830$	0.00983081	+	0.605898i	0.000341232	+	0.0210310i
$831$	7.18175	−	22.1032i	0.249132	−	0.766750i
$832$	14.9908			0.519712
$833$	1.52161	−	4.68303i	0.0527206	−	0.162257i
$834$	−0.326626	+	0.237308i	−0.0113101	+	0.00821729i
$835$	14.9039	+	19.8288i	0.515770	+	0.686203i
$836$	−3.07874	−	2.23683i	−0.106480	−	0.0773625i
$837$	5.01576	−	3.64416i	0.173370	−	0.125961i
$838$	0.278881	−	0.202619i	0.00963378	−	0.00699935i
$839$	−17.0929	−	12.4187i	−0.590113	−	0.428742i	0.252243	−	0.967664i	$-0.418832\pi$
$839$	−17.0929	−	12.4187i	−0.590113	−	0.428742i	−0.842356	+	0.538922i	$0.818832\pi$
$840$	−0.139131	+	0.198180i	−0.00480047	+	0.00683787i
$841$	23.3494	−	16.9644i	0.805153	−	0.584978i
$842$	−0.123020	+	0.378615i	−0.00423953	+	0.0130479i
$843$	4.38347			0.150975
$844$	2.13961	−	6.58503i	0.0736483	−	0.226666i
$845$	12.7273	+	16.9329i	0.437831	+	0.582510i
$846$	0.0282641	+	0.0869879i	0.000971739	+	0.00299070i
$847$	3.35172	+	10.3155i	0.115167	+	0.354446i
$848$	−3.03475	−	2.20488i	−0.104214	−	0.0757157i
$849$	−0.0564629			−0.00193780
$850$	−0.551757	−	0.374142i	−0.0189251	−	0.0128330i
$851$	−56.0011			−1.91969
$852$	15.8233	+	11.4963i	0.542096	+	0.393856i
$853$	10.2444	+	31.5289i	0.350760	+	1.07953i	0.958427	+	0.285337i	$0.0921056\pi$
$853$	10.2444	+	31.5289i	0.350760	+	1.07953i	−0.607667	+	0.794192i	$0.707894\pi$
$854$	−0.0816559	−	0.251311i	−0.00279421	−	0.00859968i
$855$	10.3819	+	3.18804i	0.355055	+	0.109029i
$856$	−0.110725	+	0.340776i	−0.00378450	+	0.0116475i
$857$	−23.5662			−0.805006			−0.402503	−	0.915419i	$-0.631860\pi$
$857$	−23.5662			−0.805006			−0.402503	+	0.915419i	$0.631860\pi$
$858$	−0.00615831	+	0.0189533i	−0.000210241	+	0.000647056i
$859$	−0.651091	+	0.473046i	−0.0222150	+	0.0161401i	−0.598837	−	0.800871i	$-0.704370\pi$
$859$	−0.651091	+	0.473046i	−0.0222150	+	0.0161401i	0.576622	+	0.817011i	$0.304370\pi$
$860$	−24.7883	−	7.61188i	−0.845274	−	0.259563i
$861$	3.04888	+	2.21514i	0.103905	+	0.0754917i
$862$	−0.386322	+	0.280680i	−0.0131582	+	0.00955999i
$863$	−10.2881	+	7.47476i	−0.350212	+	0.254444i	−0.748958	−	0.662618i	$-0.769445\pi$
$863$	−10.2881	+	7.47476i	−0.350212	+	0.254444i	0.398746	+	0.917061i	$0.369445\pi$
$864$	0.262743	+	0.190894i	0.00893871	+	0.00649435i
$865$	−40.8368	+	14.0051i	−1.38849	+	0.476188i
$866$	0.0443628	−	0.0322314i	0.00150751	−	0.00109527i
$867$	2.23916	−	6.89143i	0.0760460	−	0.234045i
$868$	−12.3951			−0.420717
$869$	−1.42643	+	4.39010i	−0.0483883	+	0.148924i
$870$	−0.0129474	+	0.0184425i	−0.000438957	+	0.000625258i
$871$	−3.22377	−	9.92174i	−0.109233	−	0.336185i
$872$	−0.307964	−	0.947815i	−0.0104290	−	0.0320971i
$873$	−10.0537	−	7.30443i	−0.340266	−	0.247217i
$874$	−0.690193			−0.0233461
$875$	10.7886	+	2.93350i	0.364722	+	0.0991704i
$876$	13.0787			0.441887
$877$	−6.97254	−	5.06585i	−0.235446	−	0.171062i	0.463806	−	0.885937i	$-0.346483\pi$
$877$	−6.97254	−	5.06585i	−0.235446	−	0.171062i	−0.699252	+	0.714875i	$0.746483\pi$
$878$	−0.293651	−	0.903765i	−0.00991024	−	0.0305006i
$879$	9.94947	+	30.6213i	0.335587	+	1.03283i
$880$	−2.01189	+	2.86577i	−0.0678207	+	0.0966050i
$881$	−2.72474	+	8.38589i	−0.0917988	+	0.282528i	−0.986406	−	0.164325i	$-0.947455\pi$
$881$	−2.72474	+	8.38589i	−0.0917988	+	0.282528i	0.894607	+	0.446853i	$0.147455\pi$
$882$	−0.0270773			−0.000911740
$883$	7.24984	−	22.3127i	0.243977	−	0.750883i	−0.751826	−	0.659361i	$-0.770827\pi$
$883$	7.24984	−	22.3127i	0.243977	−	0.750883i	0.995803	−	0.0915219i	$-0.0291732\pi$
$884$	−14.9568	+	10.8668i	−0.503053	+	0.365489i
$885$	−9.02744	+	3.09599i	−0.303454	+	0.104070i
$886$	0.312650	+	0.227154i	0.0105037	+	0.00763137i
$887$	15.2068	−	11.0484i	0.510596	−	0.370970i	−0.302454	−	0.953164i	$-0.597806\pi$
$887$	15.2068	−	11.0484i	0.510596	−	0.370970i	0.813050	+	0.582195i	$0.197806\pi$
$888$	0.934836	−	0.679198i	0.0313710	−	0.0227924i
$889$	5.71440	+	4.15176i	0.191655	+	0.139245i
$890$	−0.618472	−	0.189918i	−0.0207312	−	0.00636606i
$891$	0.317060	−	0.230357i	0.0106219	−	0.00771727i
$892$	1.32184	−	4.06822i	0.0442586	−	0.136214i
$893$	−16.4062			−0.549013
$894$	−0.193680	+	0.596084i	−0.00647761	+	0.0199360i
$895$	22.6057	+	6.94167i	0.755626	+	0.232034i
$896$	−0.267510	−	0.823310i	−0.00893687	−	0.0275049i
$897$	−3.04563	−	9.37349i	−0.101691	−	0.312972i
$898$	0.279412	+	0.203005i	0.00932409	+	0.00677435i
$899$	−2.30737			−0.0769552
$900$	2.77898	−	9.60229i	0.0926328	−	0.320076i
$901$	4.62279			0.154007
$902$	−0.0323541	−	0.0235066i	−0.00107727	−	0.000782684i
$903$	−1.79242	−	5.51651i	−0.0596481	−	0.183578i
$904$	0.634398	+	1.95248i	0.0210998	+	0.0649384i
$905$	16.1147	+	21.4397i	0.535670	+	0.712679i
$906$	0.112121	−	0.345073i	0.00372497	−	0.0114643i
$907$	−49.3383			−1.63825			−0.819126	−	0.573613i	$-0.805541\pi$
$907$	−49.3383			−1.63825			−0.819126	+	0.573613i	$0.805541\pi$
$908$	1.32620	−	4.08162i	0.0440114	−	0.135453i
$909$	−1.73839	+	1.26301i	−0.0576587	+	0.0418915i
$910$	−0.0653331	+	0.0930617i	−0.00216577	+	0.00308496i
$911$	−23.5434	−	17.1053i	−0.780028	−	0.566723i	0.124960	−	0.992162i	$-0.460120\pi$
$911$	−23.5434	−	17.1053i	−0.780028	−	0.566723i	−0.904987	+	0.425439i	$0.860120\pi$
$912$	−15.7000	+	11.4067i	−0.519880	+	0.377715i
$913$	−3.17328	+	2.30552i	−0.105020	+	0.0763016i
$914$	−0.331827	−	0.241087i	−0.0109759	−	0.00797444i
$915$	13.1111	+	17.4436i	0.433439	+	0.576667i
$916$	−1.34091	+	0.974225i	−0.0443048	+	0.0321893i
$917$	2.71809	−	8.36544i	0.0897594	−	0.276251i
$918$	−0.133329			−0.00440053
$919$	11.8551	−	36.4862i	0.391063	−	1.20357i	−0.540922	−	0.841073i	$-0.681925\pi$
$919$	11.8551	−	36.4862i	0.391063	−	1.20357i	0.931985	−	0.362496i	$-0.118075\pi$
$920$	0.0206161	+	1.27063i	0.000679694	+	0.0418913i
$921$	3.21004	+	9.87947i	0.105774	+	0.325540i
$922$	−0.257571	−	0.792721i	−0.00848264	−	0.0261069i
$923$	14.8633	+	10.7988i	0.489232	+	0.355448i
$924$	−0.783528			−0.0257762
$925$	−44.1585	−	29.9435i	−1.45192	−	0.984537i
$926$	1.14071			0.0374860
$927$	0.574466	+	0.417374i	0.0188679	+	0.0137084i
$928$	−0.0373504	−	0.114953i	−0.00122609	−	0.00377351i
$929$	14.3158	+	44.0594i	0.469685	+	1.44554i	0.852994	+	0.521921i	$0.174785\pi$
$929$	14.3158	+	44.0594i	0.469685	+	1.44554i	−0.383309	+	0.923620i	$0.625215\pi$
$930$	−0.355077	+	0.121775i	−0.0116434	+	0.00399315i
$931$	1.50087	−	4.61920i	0.0491890	−	0.151388i
$932$	−5.27676			−0.172846
$933$	2.23740	−	6.88600i	0.0732491	−	0.225438i
$934$	−0.624968	+	0.454066i	−0.0204496	+	0.0148575i
$935$	−0.0700038	−	4.31452i	−0.00228937	−	0.141100i
$936$	0.164526	+	0.119535i	0.00537769	+	0.00390712i
$937$	22.1665	−	16.1049i	0.724148	−	0.526125i	−0.163558	−	0.986534i	$-0.552297\pi$
$937$	22.1665	−	16.1049i	0.724148	−	0.526125i	0.887707	+	0.460409i	$0.152297\pi$
$938$	−0.121690	+	0.0884127i	−0.00397331	+	0.00288678i
$939$	7.41128	+	5.38461i	0.241858	+	0.175720i
$940$	0.244983	+	15.0989i	0.00799045	+	0.492472i
$941$	−15.3570	+	11.1575i	−0.500623	+	0.363724i	−0.809255	−	0.587458i	$-0.800129\pi$
$941$	−15.3570	+	11.1575i	−0.500623	+	0.363724i	0.308632	+	0.951182i	$0.400129\pi$
$942$	−0.0199496	+	0.0613986i	−0.000649994	+	0.00200047i
$943$	19.7782			0.644067
$944$	5.26976	−	16.2186i	0.171516	−	0.527872i
$945$	2.11514	−	0.725392i	0.0688054	−	0.0235970i
$946$	0.0190208	+	0.0585401i	0.000618420	+	0.00190330i
$947$	−4.07732	−	12.5487i	−0.132495	−	0.407778i	0.862697	−	0.505721i	$-0.168774\pi$
$947$	−4.07732	−	12.5487i	−0.132495	−	0.407778i	−0.995192	+	0.0979434i	$0.968774\pi$
$948$	19.0508	+	13.8412i	0.618741	+	0.449541i
$949$	12.2852			0.398795
$950$	−0.544237	−	0.369043i	−0.0176574	−	0.0119733i
$951$	15.3641			0.498216
$952$	0.431384	+	0.313419i	0.0139812	+	0.0101580i
$953$	0.513554	+	1.58056i	0.0166357	+	0.0511993i	0.959030	−	0.283305i	$-0.0914310\pi$
$953$	0.513554	+	1.58056i	0.0166357	+	0.0511993i	−0.942394	+	0.334505i	$0.891431\pi$
$954$	−0.00785544	−	0.0241766i	−0.000254329	−	0.000782745i
$955$	−0.707983	−	43.6348i	−0.0229098	−	1.41199i
$956$	−13.1837	+	40.5753i	−0.426391	+	1.31230i
$957$	−0.145855			−0.00471483
$958$	0.264001	−	0.812511i	0.00852948	−	0.0262511i
$959$	−17.5943	+	12.7830i	−0.568149	+	0.412784i
$960$	10.7244	+	14.2682i	0.346128	+	0.460504i
$961$	−6.01730	−	4.37183i	−0.194107	−	0.141027i
$962$	0.438981	−	0.318938i	0.0141533	−	0.0102830i
$963$	2.67692	−	1.94489i	0.0862624	−	0.0626733i
$964$	42.1593	+	30.6305i	1.35786	+	0.986543i
$965$	30.6083	−	43.5989i	0.985315	−	1.40350i
$966$	−0.114965	+	0.0835273i	−0.00369895	+	0.00268745i
$967$	15.9980	−	49.2367i	0.514460	−	1.58334i	−0.269803	−	0.962916i	$-0.586958\pi$
$967$	15.9980	−	49.2367i	0.514460	−	1.58334i	0.784262	−	0.620429i	$-0.213042\pi$
$968$	−1.17455			−0.0377515
$969$	7.39033	−	22.7451i	0.237412	−	0.730678i
$970$	0.452076	+	0.601462i	0.0145153	+	0.0193118i
$971$	12.0597	+	37.1159i	0.387013	+	1.19110i	0.935009	+	0.354623i	$0.115391\pi$
$971$	12.0597	+	37.1159i	0.387013	+	1.19110i	−0.547996	+	0.836481i	$0.684609\pi$
$972$	−0.617807	−	1.90142i	−0.0198162	−	0.0609879i
$973$	−12.0627	−	8.76409i	−0.386713	−	0.280964i
$974$	−0.367074			−0.0117618
$975$	2.61039	−	9.01975i	0.0835995	−	0.288863i
$976$	−38.9926			−1.24812
$977$	38.9657	+	28.3103i	1.24662	+	0.905726i	0.998021	−	0.0628794i	$-0.0200284\pi$
$977$	38.9657	+	28.3103i	1.24662	+	0.905726i	0.248604	+	0.968605i	$0.420028\pi$
$978$	0.0612294	+	0.188445i	0.00195790	+	0.00602580i
$979$	−1.29409	−	3.98279i	−0.0413592	−	0.127291i
$980$	−4.27355	−	1.31230i	−0.136513	−	0.0419200i
$981$	−2.84390	+	8.75262i	−0.0907987	+	0.279450i
$982$	0.0793368			0.00253174
$983$	−18.1055	+	55.7229i	−0.577475	+	1.77729i	0.0501171	+	0.998743i	$0.484041\pi$
$983$	−18.1055	+	55.7229i	−0.577475	+	1.77729i	−0.627592	+	0.778542i	$0.715959\pi$
$984$	−0.330161	+	0.239876i	−0.0105251	+	0.00764696i
$985$	−22.7508	−	6.98621i	−0.724900	−	0.222599i
$986$	0.0401442	+	0.0291664i	0.00127845	+	0.000928848i
$987$	−2.73278	+	1.98548i	−0.0869854	+	0.0631986i
$988$	−14.7530	+	10.7187i	−0.469355	+	0.341006i
$989$	−24.6275	−	17.8929i	−0.783109	−	0.568962i
$990$	−0.0224454	+	0.00769771i	−0.000713362	+	0.000244649i
$991$	−5.61854	+	4.08211i	−0.178479	+	0.129673i	−0.673438	−	0.739244i	$-0.735183\pi$
$991$	−5.61854	+	4.08211i	−0.178479	+	0.129673i	0.494959	+	0.868916i	$0.335183\pi$
$992$	0.622208	−	1.91496i	0.0197551	−	0.0608000i
$993$	8.47851			0.269057
$994$	0.0818569	−	0.251930i	0.00259634	−	0.00799072i
$995$	8.44485	−	12.0290i	0.267720	−	0.381345i
$996$	6.18329	+	19.0302i	0.195925	+	0.602996i
$997$	13.9268	+	42.8624i	0.441067	+	1.35747i	0.886739	+	0.462269i	$0.152965\pi$
$997$	13.9268	+	42.8624i	0.441067	+	1.35747i	−0.445672	+	0.895196i	$0.647035\pi$
$998$	−0.311127	−	0.226047i	−0.00984857	−	0.00715540i
$999$	−10.6707			−0.337606

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.d.316.4	yes	32
25.11	even	5	inner	525.2.n.d.211.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.d.211.4	✓	32	25.11	even	5	inner
525.2.n.d.316.4	yes	32	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0219060 + 0.0159156i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.617807 - 1.90142i) q^{4} +(1.28481 - 1.83010i) q^{5} +(-0.00836734 + 0.0257520i) q^{6} -1.00000 q^{7} +(0.0334632 - 0.102989i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.0219060 + 0.0159156i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.617807 - 1.90142i) q^{4} +(1.28481 - 1.83010i) q^{5} +(-0.00836734 + 0.0257520i) q^{6} -1.00000 q^{7} +(0.0334632 - 0.102989i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.0572722 - 0.0196417i) q^{10} +(0.317060 + 0.230357i) q^{11} +(1.61744 - 1.17514i) q^{12} +(1.51932 - 1.10385i) q^{13} +(-0.0219060 - 0.0159156i) q^{14} +(2.13756 + 0.656392i) q^{15} +(-3.23251 + 2.34856i) q^{16} +(1.52161 - 4.68303i) q^{17} -0.0270773 q^{18} +(1.50087 - 4.61920i) q^{19} +(-4.27355 - 1.31230i) q^{20} +(-0.309017 - 0.951057i) q^{21} +(0.00327922 + 0.0100924i) q^{22} +(-4.24583 - 3.08477i) q^{23} +0.108289 q^{24} +(-1.69854 - 4.70265i) q^{25} +0.0508506 q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.617807 + 1.90142i) q^{28} +(0.115006 + 0.353953i) q^{29} +(0.0363784 + 0.0483995i) q^{30} +(-1.91585 + 5.89638i) q^{31} -0.324769 q^{32} +(-0.121106 + 0.372726i) q^{33} +(0.107866 - 0.0783691i) q^{34} +(-1.28481 + 1.83010i) q^{35} +(1.61744 + 1.17514i) q^{36} +(8.63276 - 6.27207i) q^{37} +(0.106396 - 0.0773009i) q^{38} +(1.51932 + 1.10385i) q^{39} +(-0.145487 - 0.193562i) q^{40} +(-3.04888 + 2.21514i) q^{41} +(0.00836734 - 0.0257520i) q^{42} +5.80040 q^{43} +(0.242123 - 0.745179i) q^{44} +(0.0362758 + 2.23577i) q^{45} +(-0.0439129 - 0.135150i) q^{46} +(-1.04383 - 3.21258i) q^{47} +(-3.23251 - 2.34856i) q^{48} +1.00000 q^{49} +(0.0376375 - 0.130050i) q^{50} +4.92403 q^{51} +(-3.03752 - 2.20689i) q^{52} +(0.290112 + 0.892873i) q^{53} +(-0.00836734 - 0.0257520i) q^{54} +(0.828938 - 0.284287i) q^{55} +(-0.0334632 + 0.102989i) q^{56} +4.85692 q^{57} +(-0.00311405 + 0.00958407i) q^{58} +(-3.45290 + 2.50868i) q^{59} +(-0.0725251 - 4.46991i) q^{60} +(7.89510 + 5.73612i) q^{61} +(-0.135813 + 0.0986741i) q^{62} +(0.809017 - 0.587785i) q^{63} +(6.45790 + 4.69194i) q^{64} +(-0.0681252 - 4.19873i) q^{65} +(-0.00858512 + 0.00623746i) q^{66} +(1.71662 - 5.28320i) q^{67} -9.84445 q^{68} +(1.62176 - 4.99127i) q^{69} +(-0.0572722 + 0.0196417i) q^{70} +(3.02308 + 9.30410i) q^{71} +(0.0334632 + 0.102989i) q^{72} +(5.29237 + 3.84513i) q^{73} +0.288933 q^{74} +(3.94761 - 3.06861i) q^{75} -9.71028 q^{76} +(-0.317060 - 0.230357i) q^{77} +(0.0157137 + 0.0483618i) q^{78} +(3.63971 + 11.2019i) q^{79} +(0.144944 + 8.93326i) q^{80} +(0.309017 - 0.951057i) q^{81} -0.102044 q^{82} +(-3.09278 + 9.51860i) q^{83} +(-1.61744 + 1.17514i) q^{84} +(-6.61545 - 8.80149i) q^{85} +(0.127064 + 0.0923171i) q^{86} +(-0.301090 + 0.218755i) q^{87} +(0.0343342 - 0.0249452i) q^{88} +(-8.64480 - 6.28082i) q^{89} +(-0.0347891 + 0.0495542i) q^{90} +(-1.51932 + 1.10385i) q^{91} +(-3.24233 + 9.97887i) q^{92} -6.19982 q^{93} +(0.0282641 - 0.0869879i) q^{94} +(-6.52528 - 8.68153i) q^{95} +(-0.100359 - 0.308873i) q^{96} +(3.84016 + 11.8188i) q^{97} +(0.0219060 + 0.0159156i) q^{98} -0.391908 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9}+O(q^{10}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9} + 8 q^{10} + 2 q^{11} - 5 q^{12} + 12 q^{13} - q^{14} - 8 q^{15} - 17 q^{16} + 12 q^{17} - 4 q^{18} - 13 q^{19} - 27 q^{20} + 8 q^{21} - 21 q^{22} - 12 q^{23} - 18 q^{24} + 11 q^{25} - 2 q^{26} - 8 q^{27} + 15 q^{28} + 21 q^{29} - 12 q^{30} + 3 q^{31} - 50 q^{32} - 13 q^{33} - 41 q^{34} + 3 q^{35} - 5 q^{36} - 22 q^{37} + 44 q^{38} + 12 q^{39} - 39 q^{40} - 3 q^{41} - q^{42} + 24 q^{43} - 43 q^{44} + 2 q^{45} + 10 q^{46} + 8 q^{47} - 17 q^{48} + 32 q^{49} + 19 q^{50} - 8 q^{51} + 53 q^{52} + 18 q^{53} + q^{54} + 23 q^{55} + 3 q^{56} + 42 q^{57} - 32 q^{58} + 28 q^{59} + 73 q^{60} + 36 q^{61} + 10 q^{62} + 8 q^{63} + 9 q^{64} - 34 q^{65} + 4 q^{66} - 22 q^{67} - 78 q^{68} - 2 q^{69} - 8 q^{70} - 40 q^{71} - 3 q^{72} - 10 q^{73} - 34 q^{74} + 6 q^{75} + 132 q^{76} - 2 q^{77} + 28 q^{78} + 18 q^{79} + 148 q^{80} - 8 q^{81} + 102 q^{82} + 16 q^{83} + 5 q^{84} + 18 q^{85} + 16 q^{86} - 34 q^{87} + 13 q^{88} - 17 q^{89} - 2 q^{90} - 12 q^{91} - 106 q^{92} + 18 q^{93} - 20 q^{94} - 92 q^{95} - 15 q^{96} + 30 q^{97} + q^{98} + 22 q^{99}+O(q^{100}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9 + 8 * q^10 + 2 * q^11 - 5 * q^12 + 12 * q^13 - q^14 - 8 * q^15 - 17 * q^16 + 12 * q^17 - 4 * q^18 - 13 * q^19 - 27 * q^20 + 8 * q^21 - 21 * q^22 - 12 * q^23 - 18 * q^24 + 11 * q^25 - 2 * q^26 - 8 * q^27 + 15 * q^28 + 21 * q^29 - 12 * q^30 + 3 * q^31 - 50 * q^32 - 13 * q^33 - 41 * q^34 + 3 * q^35 - 5 * q^36 - 22 * q^37 + 44 * q^38 + 12 * q^39 - 39 * q^40 - 3 * q^41 - q^42 + 24 * q^43 - 43 * q^44 + 2 * q^45 + 10 * q^46 + 8 * q^47 - 17 * q^48 + 32 * q^49 + 19 * q^50 - 8 * q^51 + 53 * q^52 + 18 * q^53 + q^54 + 23 * q^55 + 3 * q^56 + 42 * q^57 - 32 * q^58 + 28 * q^59 + 73 * q^60 + 36 * q^61 + 10 * q^62 + 8 * q^63 + 9 * q^64 - 34 * q^65 + 4 * q^66 - 22 * q^67 - 78 * q^68 - 2 * q^69 - 8 * q^70 - 40 * q^71 - 3 * q^72 - 10 * q^73 - 34 * q^74 + 6 * q^75 + 132 * q^76 - 2 * q^77 + 28 * q^78 + 18 * q^79 + 148 * q^80 - 8 * q^81 + 102 * q^82 + 16 * q^83 + 5 * q^84 + 18 * q^85 + 16 * q^86 - 34 * q^87 + 13 * q^88 - 17 * q^89 - 2 * q^90 - 12 * q^91 - 106 * q^92 + 18 * q^93 - 20 * q^94 - 92 * q^95 - 15 * q^96 + 30 * q^97 + q^98 + 22 * q^99

Introduction

L-functions

Modular forms

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