LMFDB - Embedded newform 690.2.n.b.89.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(89,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 5]))

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

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

chi := DirichletCharacter("690.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.n (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			89.17
Character	$\chi$	$=$	690.89
Dual form			690.2.n.b.659.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(0.943600 - 1.45245i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.20932 + 0.344845i) q^{5} +(1.57196 + 0.727290i) q^{6} +(2.74772 - 1.76585i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-1.21924 - 2.74107i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(0.943600 - 1.45245i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.20932 + 0.344845i) q^{5} +(1.57196 + 0.727290i) q^{6} +(2.74772 - 1.76585i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-1.21924 - 2.74107i) q^{9} +(-0.655753 - 2.13775i) q^{10} +(-0.103499 + 0.719848i) q^{11} +(-0.496174 + 1.65946i) q^{12} +(0.797957 - 1.24165i) q^{13} +(2.13892 + 2.46844i) q^{14} +(-1.58384 + 3.53432i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-0.487896 + 1.66162i) q^{17} +(2.53965 - 1.59692i) q^{18} +(-1.66137 - 5.65810i) q^{19} +(2.02267 - 0.953313i) q^{20} +(0.0279304 - 5.65718i) q^{21} -0.727250 q^{22} +(-1.82495 - 4.43504i) q^{23} +(-1.71318 - 0.254958i) q^{24} +(4.76216 - 1.52374i) q^{25} +(1.34257 + 0.613130i) q^{26} +(-5.13175 - 0.815584i) q^{27} +(-2.13892 + 2.46844i) q^{28} +(1.91557 - 6.52384i) q^{29} +(-3.72375 - 1.06473i) q^{30} +(-1.61915 - 3.54544i) q^{31} +(0.654861 + 0.755750i) q^{32} +(0.947884 + 0.829575i) q^{33} +(-1.71414 - 0.246456i) q^{34} +(-5.46163 + 4.84886i) q^{35} +(1.94210 + 2.28654i) q^{36} +(7.28503 + 8.40738i) q^{37} +(5.36407 - 2.44969i) q^{38} +(-1.05048 - 2.33061i) q^{39} +(1.23147 + 1.86641i) q^{40} +(0.240142 + 0.208084i) q^{41} +(5.60358 - 0.777455i) q^{42} +(3.85328 - 8.43752i) q^{43} +(-0.103499 - 0.719848i) q^{44} +(3.63893 + 5.63544i) q^{45} +(4.13018 - 2.43755i) q^{46} -0.296017 q^{47} +(0.00855129 - 1.73203i) q^{48} +(1.52381 - 3.33668i) q^{49} +(2.18596 + 4.49684i) q^{50} +(1.95305 + 2.27655i) q^{51} +(-0.415822 + 1.41616i) q^{52} +(1.32976 + 2.06915i) q^{53} +(0.0769591 - 5.19558i) q^{54} +(-0.0195746 - 1.62606i) q^{55} +(-2.74772 - 1.76585i) q^{56} +(-9.78579 - 2.92592i) q^{57} +(6.73005 + 0.967635i) q^{58} +(-4.64023 + 7.22033i) q^{59} +(0.523950 - 3.83738i) q^{60} +(4.22497 - 1.92948i) q^{61} +(3.27893 - 2.10724i) q^{62} +(-8.19044 - 5.37868i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-1.33477 + 3.01836i) q^{65} +(-0.686233 + 1.05630i) q^{66} +(0.0578385 + 0.402276i) q^{67} -1.73177i q^{68} +(-8.16371 - 1.53424i) q^{69} +(-5.57677 - 4.71598i) q^{70} +(-7.98308 + 1.14779i) q^{71} +(-1.98687 + 2.24774i) q^{72} +(0.808166 + 2.75236i) q^{73} +(-7.28503 + 8.40738i) q^{74} +(2.28041 - 8.35462i) q^{75} +(3.18814 + 4.96084i) q^{76} +(0.986759 + 2.16070i) q^{77} +(2.15739 - 1.37147i) q^{78} +(-1.78670 + 2.78017i) q^{79} +(-1.67216 + 1.48455i) q^{80} +(-6.02691 + 6.68404i) q^{81} +(-0.171790 + 0.267311i) q^{82} +(11.9849 - 10.3850i) q^{83} +(1.56701 + 5.43590i) q^{84} +(0.504916 - 3.83929i) q^{85} +(8.90001 + 2.61328i) q^{86} +(-7.66804 - 8.93817i) q^{87} +(0.697792 - 0.204890i) q^{88} +(-3.56233 + 7.80041i) q^{89} +(-5.06021 + 4.40390i) q^{90} -4.82076i q^{91} +(3.00053 + 3.74124i) q^{92} +(-6.67742 - 0.993741i) q^{93} +(-0.0421276 - 0.293004i) q^{94} +(5.62165 + 11.9276i) q^{95} +(1.71562 - 0.238029i) q^{96} +(-8.74637 + 10.0938i) q^{97} +(3.51958 + 1.03344i) q^{98} +(2.09934 - 0.593970i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9}+O(q^{10}) $ 240 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 + 24 * q^8 - 6 * q^9	$ 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9} + 9 q^{12} + 11 q^{15} - 24 q^{16} + 6 q^{18} + 4 q^{23} + 2 q^{24} - 12 q^{25} - 2 q^{27} + 22 q^{30} + 28 q^{31} + 24 q^{32} + 36 q^{35} - 6 q^{36} - 4 q^{46} - 104 q^{47} + 9 q^{48} + 70 q^{49} - 54 q^{50} - 9 q^{54} - 26 q^{55} + 44 q^{57} - 11 q^{60} + 44 q^{61} - 28 q^{62} + 121 q^{63} - 24 q^{64} - 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} - 16 q^{72} - 102 q^{75} - 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} + 93 q^{87} + 4 q^{92} - 172 q^{93} + 16 q^{94} - 26 q^{95} + 2 q^{96} - 4 q^{98}+O(q^{100}) $ 240 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 + 24 * q^8 - 6 * q^9 + 9 * q^12 + 11 * q^15 - 24 * q^16 + 6 * q^18 + 4 * q^23 + 2 * q^24 - 12 * q^25 - 2 * q^27 + 22 * q^30 + 28 * q^31 + 24 * q^32 + 36 * q^35 - 6 * q^36 - 4 * q^46 - 104 * q^47 + 9 * q^48 + 70 * q^49 - 54 * q^50 - 9 * q^54 - 26 * q^55 + 44 * q^57 - 11 * q^60 + 44 * q^61 - 28 * q^62 + 121 * q^63 - 24 * q^64 - 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 - 16 * q^72 - 102 * q^75 - 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 + 93 * q^87 + 4 * q^92 - 172 * q^93 + 16 * q^94 - 26 * q^95 + 2 * q^96 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{22}\right)$

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 $

$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$3$	0.943600	−	1.45245i	0.544788	−	0.838574i
$3$	0.943600	−	1.45245i	0.544788	−	0.838574i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−2.20932	+	0.344845i	−0.988037	+	0.154219i
$5$	−2.20932	+	0.344845i	−0.988037	+	0.154219i
$6$	1.57196	+	0.727290i	0.641749	+	0.296915i
$7$	2.74772	−	1.76585i	1.03854	−	0.667429i	0.0939141	−	0.995580i	$-0.470062\pi$
$7$	2.74772	−	1.76585i	1.03854	−	0.667429i	0.944625	+	0.328152i	$0.106426\pi$
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$	−1.21924	−	2.74107i	−0.406413	−	0.913689i
$10$	−0.655753	−	2.13775i	−0.207367	−	0.676017i
$11$	−0.103499	+	0.719848i	−0.0312060	+	0.217042i	−0.999457	−	0.0329357i	$-0.989514\pi$
$11$	−0.103499	+	0.719848i	−0.0312060	+	0.217042i	0.968251	+	0.249978i	$0.0804234\pi$
$12$	−0.496174	+	1.65946i	−0.143233	+	0.479045i
$13$	0.797957	−	1.24165i	0.221313	−	0.344370i	−0.712787	−	0.701380i	$-0.752567\pi$
$13$	0.797957	−	1.24165i	0.221313	−	0.344370i	0.934101	+	0.357010i	$0.116204\pi$
$14$	2.13892	+	2.46844i	0.571650	+	0.659719i
$15$	−1.58384	+	3.53432i	−0.408946	+	0.912559i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−0.487896	+	1.66162i	−0.118332	+	0.403002i	−0.997262	−	0.0739488i	$-0.976440\pi$
$17$	−0.487896	+	1.66162i	−0.118332	+	0.403002i	0.878930	+	0.476951i	$0.158258\pi$
$18$	2.53965	−	1.59692i	0.598602	−	0.376399i
$19$	−1.66137	−	5.65810i	−0.381144	−	1.29806i	−0.897247	−	0.441530i	$-0.854436\pi$
$19$	−1.66137	−	5.65810i	−0.381144	−	1.29806i	0.516103	−	0.856527i	$-0.327382\pi$
$20$	2.02267	−	0.953313i	0.452283	−	0.213167i
$21$	0.0279304	−	5.65718i	0.00609491	−	1.23450i
$22$	−0.727250			−0.155050
$23$	−1.82495	−	4.43504i	−0.380529	−	0.924769i
$23$	−1.82495	−	4.43504i	−0.380529	−	0.924769i
$24$	−1.71318	−	0.254958i	−0.349702	−	0.0520430i
$25$	4.76216	−	1.52374i	0.952433	−	0.304748i
$26$	1.34257	+	0.613130i	0.263299	+	0.120245i
$27$	−5.13175	−	0.815584i	−0.987605	−	0.156959i
$28$	−2.13892	+	2.46844i	−0.404217	+	0.466492i
$29$	1.91557	−	6.52384i	0.355713	−	1.21145i	−0.566271	−	0.824219i	$-0.691615\pi$
$29$	1.91557	−	6.52384i	0.355713	−	1.21145i	0.921984	−	0.387228i	$-0.126567\pi$
$30$	−3.72375	−	1.06473i	−0.679861	−	0.194393i
$31$	−1.61915	−	3.54544i	−0.290808	−	0.636780i	0.706687	−	0.707527i	$-0.250189\pi$
$31$	−1.61915	−	3.54544i	−0.290808	−	0.636780i	−0.997494	+	0.0707465i	$0.977462\pi$
$32$	0.654861	+	0.755750i	0.115764	+	0.133599i
$33$	0.947884	+	0.829575i	0.165005	+	0.144411i
$34$	−1.71414	−	0.246456i	−0.293973	−	0.0422669i
$35$	−5.46163	+	4.84886i	−0.923184	+	0.819607i
$36$	1.94210	+	2.28654i	0.323683	+	0.381089i
$37$	7.28503	+	8.40738i	1.19765	+	1.38216i	0.904707	+	0.426035i	$0.140090\pi$
$37$	7.28503	+	8.40738i	1.19765	+	1.38216i	0.292945	+	0.956129i	$0.405365\pi$
$38$	5.36407	−	2.44969i	0.870167	−	0.397392i
$39$	−1.05048	−	2.33061i	−0.168211	−	0.373197i
$40$	1.23147	+	1.86641i	0.194712	+	0.295106i
$41$	0.240142	+	0.208084i	0.0375038	+	0.0324973i	0.673411	−	0.739268i	$-0.264828\pi$
$41$	0.240142	+	0.208084i	0.0375038	+	0.0324973i	−0.635907	+	0.771766i	$0.719374\pi$
$42$	5.60358	−	0.777455i	0.864651	−	0.119964i
$43$	3.85328	−	8.43752i	0.587620	−	1.28671i	−0.349249	−	0.937030i	$-0.613563\pi$
$43$	3.85328	−	8.43752i	0.587620	−	1.28671i	0.936870	−	0.349679i	$-0.113709\pi$
$44$	−0.103499	−	0.719848i	−0.0156030	−	0.108521i
$45$	3.63893	+	5.63544i	0.542459	+	0.840082i
$46$	4.13018	−	2.43755i	0.608961	−	0.359397i
$47$	−0.296017			−0.0431785			−0.0215892	−	0.999767i	$-0.506873\pi$
$47$	−0.296017			−0.0431785			−0.0215892	+	0.999767i	$0.506873\pi$
$48$	0.00855129	−	1.73203i	0.00123427	−	0.249997i
$49$	1.52381	−	3.33668i	0.217688	−	0.476669i
$50$	2.18596	+	4.49684i	0.309141	+	0.635949i
$51$	1.95305	+	2.27655i	0.273481	+	0.318781i
$52$	−0.415822	+	1.41616i	−0.0576642	+	0.196386i
$53$	1.32976	+	2.06915i	0.182656	+	0.284219i	0.920492	−	0.390762i	$-0.127788\pi$
$53$	1.32976	+	2.06915i	0.182656	+	0.284219i	−0.737835	+	0.674981i	$0.764152\pi$
$54$	0.0769591	−	5.19558i	0.0104728	−	0.707029i
$55$	−0.0195746	−	1.62606i	−0.00263944	−	0.219258i
$56$	−2.74772	−	1.76585i	−0.367179	−	0.235972i
$57$	−9.78579	−	2.92592i	−1.29616	−	0.387548i
$58$	6.73005	+	0.967635i	0.883699	+	0.127057i
$59$	−4.64023	+	7.22033i	−0.604106	+	0.940008i	0.395660	+	0.918397i	$0.370516\pi$
$59$	−4.64023	+	7.22033i	−0.604106	+	0.940008i	−0.999766	+	0.0216106i	$0.993121\pi$
$60$	0.523950	−	3.83738i	0.0676416	−	0.495403i
$61$	4.22497	−	1.92948i	0.540953	−	0.247045i	−0.126149	−	0.992011i	$-0.540262\pi$
$61$	4.22497	−	1.92948i	0.540953	−	0.247045i	0.667102	+	0.744966i	$0.267535\pi$
$62$	3.27893	−	2.10724i	0.416424	−	0.267619i
$63$	−8.19044	−	5.37868i	−1.03190	−	0.677651i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	−1.33477	+	3.01836i	−0.165557	+	0.374381i
$66$	−0.686233	+	1.05630i	−0.0844695	+	0.130021i
$67$	0.0578385	+	0.402276i	0.00706610	+	0.0491458i	0.993049	−	0.117698i	$-0.0375515\pi$
$67$	0.0578385	+	0.402276i	0.00706610	+	0.0491458i	−0.985983	+	0.166844i	$0.946642\pi$
$68$		−	1.73177i		−	0.210008i
$69$	−8.16371	−	1.53424i	−0.982795	−	0.184701i
$70$	−5.57677	−	4.71598i	−0.666552	−	0.563667i
$71$	−7.98308	+	1.14779i	−0.947417	+	0.136218i	−0.598667	−	0.800998i	$-0.704303\pi$
$71$	−7.98308	+	1.14779i	−0.947417	+	0.136218i	−0.348750	+	0.937216i	$0.613394\pi$
$72$	−1.98687	+	2.24774i	−0.234155	+	0.264899i
$73$	0.808166	+	2.75236i	0.0945887	+	0.322140i	0.993171	−	0.116665i	$-0.0372203\pi$
$73$	0.808166	+	2.75236i	0.0945887	+	0.322140i	−0.898583	+	0.438804i	$0.855402\pi$
$74$	−7.28503	+	8.40738i	−0.846868	+	0.977337i
$75$	2.28041	−	8.35462i	0.263319	−	0.964709i
$76$	3.18814	+	4.96084i	0.365705	+	0.569048i
$77$	0.986759	+	2.16070i	0.112452	+	0.246235i
$78$	2.15739	−	1.37147i	0.244276	−	0.155288i
$79$	−1.78670	+	2.78017i	−0.201020	+	0.312793i	−0.927098	−	0.374819i	$-0.877705\pi$
$79$	−1.78670	+	2.78017i	−0.201020	+	0.312793i	0.726078	+	0.687612i	$0.241341\pi$
$80$	−1.67216	+	1.48455i	−0.186953	+	0.165978i
$81$	−6.02691	+	6.68404i	−0.669657	+	0.742671i
$82$	−0.171790	+	0.267311i	−0.0189711	+	0.0295196i
$83$	11.9849	−	10.3850i	1.31552	−	1.13990i	0.335272	−	0.942122i	$-0.391172\pi$
$83$	11.9849	−	10.3850i	1.31552	−	1.13990i	0.980246	−	0.197781i	$-0.0633735\pi$
$84$	1.56701	+	5.43590i	0.170975	+	0.593105i
$85$	0.504916	−	3.83929i	0.0547658	−	0.416430i
$86$	8.90001	+	2.61328i	0.959713	+	0.281797i
$87$	−7.66804	−	8.93817i	−0.822100	−	0.958273i
$88$	0.697792	−	0.204890i	0.0743848	−	0.0218414i
$89$	−3.56233	+	7.80041i	−0.377606	+	0.826841i	0.621452	+	0.783452i	$0.286543\pi$
$89$	−3.56233	+	7.80041i	−0.377606	+	0.826841i	−0.999058	+	0.0433895i	$0.986184\pi$
$90$	−5.06021	+	4.40390i	−0.533393	+	0.464211i
$91$		−	4.82076i		−	0.505353i
$92$	3.00053	+	3.74124i	0.312826	+	0.390051i
$93$	−6.67742	−	0.993741i	−0.692416	−	0.103046i
$94$	−0.0421276	−	0.293004i	−0.00434513	−	0.0302210i
$95$	5.62165	+	11.9276i	0.576769	+	1.22375i
$96$	1.71562	−	0.238029i	0.175099	−	0.0242938i
$97$	−8.74637	+	10.0938i	−0.888059	+	1.02487i	0.111457	+	0.993769i	$0.464448\pi$
$97$	−8.74637	+	10.0938i	−0.888059	+	1.02487i	−0.999516	+	0.0311057i	$0.990097\pi$
$98$	3.51958	+	1.03344i	0.355532	+	0.104394i
$99$	2.09934	−	0.593970i	0.210992	−	0.0596963i
$100$	−4.13998	+	2.80368i	−0.413998	+	0.280368i
$101$	4.21978	−	3.65646i	0.419884	−	0.363831i	−0.419144	−	0.907920i	$-0.637670\pi$
$101$	4.21978	−	3.65646i	0.419884	−	0.363831i	0.839028	+	0.544088i	$0.183124\pi$
$102$	−1.97543	+	2.25715i	−0.195597	+	0.223492i
$103$	−2.60682	+	18.1308i	−0.256857	+	1.78648i	0.298030	+	0.954557i	$0.403671\pi$
$103$	−2.60682	+	18.1308i	−0.256857	+	1.78648i	−0.554887	+	0.831926i	$0.687239\pi$
$104$	−1.46092	−	0.210049i	−0.143255	−	0.0205970i
$105$	1.88914	+	12.5081i	0.184361	+	1.22067i
$106$	−1.85884	+	1.61069i	−0.180547	+	0.156444i
$107$	9.34180	−	4.26626i	0.903106	−	0.412435i	0.0909369	−	0.995857i	$-0.471014\pi$
$107$	9.34180	−	4.26626i	0.903106	−	0.412435i	0.812169	+	0.583422i	$0.198287\pi$
$108$	5.15365	−	0.663233i	0.495910	−	0.0638196i
$109$	−3.44409	+	11.7295i	−0.329884	+	1.12348i	0.612922	+	0.790143i	$0.289994\pi$
$109$	−3.44409	+	11.7295i	−0.329884	+	1.12348i	−0.942807	+	0.333340i	$0.891824\pi$
$110$	1.60673	−	0.250788i	0.153195	−	0.0239117i
$111$	19.0855	−	2.64797i	1.81151	−	0.251334i
$112$	1.35684	−	2.97106i	0.128209	−	0.280738i
$113$	9.35371	−	1.34486i	0.879923	−	0.126514i	0.312478	−	0.949925i	$-0.398841\pi$
$113$	9.35371	−	1.34486i	0.879923	−	0.126514i	0.567445	+	0.823411i	$0.307932\pi$
$114$	1.50348	−	10.1026i	0.140814	−	0.946194i
$115$	5.56130	+	9.16907i	0.518594	+	0.855021i
$116$			6.79926i			0.631295i
$117$	−4.37634	−	0.673392i	−0.404592	−	0.0622552i
$118$	−7.80722	−	3.56544i	−0.718712	−	0.328225i
$119$	1.59357	+	5.42721i	0.146083	+	0.497512i
$120$	3.87289	−	0.0274993i	0.353544	−	0.00251034i
$121$	10.0470	+	2.95005i	0.913359	+	0.268187i
$122$	2.51112	+	3.90738i	0.227346	+	0.353757i
$123$	0.528830	−	0.152447i	0.0476830	−	0.0137456i
$124$	2.55243	+	2.94566i	0.229215	+	0.264528i
$125$	−9.99568	+	5.00864i	−0.894041	+	0.447986i
$126$	4.15832	−	8.87254i	0.370452	−	0.790429i
$127$	−11.0052	−	1.58231i	−0.976553	−	0.140407i	−0.364482	−	0.931210i	$-0.618754\pi$
$127$	−11.0052	−	1.58231i	−0.976553	−	0.140407i	−0.612070	+	0.790803i	$0.709663\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$	−8.61914	−	13.5584i	−0.758873	−	1.19375i
$130$	−3.17759	−	0.891622i	−0.278693	−	0.0782004i
$131$	7.01612	+	10.9173i	0.613001	+	0.953848i	0.999502	+	0.0315591i	$0.0100472\pi$
$131$	7.01612	+	10.9173i	0.613001	+	0.953848i	−0.386501	+	0.922289i	$0.626316\pi$
$132$	−1.14321	−	0.528922i	−0.0995034	−	0.0460367i
$133$	−14.5563	−	12.6131i	−1.26219	−	1.09370i
$134$	−0.389950	+	0.114500i	−0.0336866	+	0.00989126i
$135$	11.6189	+	0.0322293i	0.999996	+	0.00277386i
$136$	1.71414	−	0.246456i	0.146986	−	0.0211335i
$137$		−	2.34987i		−	0.200763i	−0.994949	−	0.100382i	$-0.967994\pi$
$137$		−	2.34987i		−	0.200763i	0.994949	−	0.100382i	$-0.0320064\pi$
$138$	0.356805	−	8.29896i	0.0303732	−	0.706454i
$139$	0.917075			0.0777853			0.0388926	−	0.999243i	$-0.487617\pi$
$139$	0.917075			0.0777853			0.0388926	+	0.999243i	$0.487617\pi$
$140$	3.87432	−	6.19116i	0.327440	−	0.523249i
$141$	−0.279321	+	0.429950i	−0.0235231	+	0.0362084i
$142$	−2.27222	−	7.73848i	−0.190681	−	0.649398i
$143$	0.811209	+	0.702916i	0.0678367	+	0.0587808i
$144$	−2.50762	−	1.64676i	−0.208969	−	0.137230i
$145$	−1.98240	+	15.0738i	−0.164629	+	1.25181i
$146$	−2.60933	+	1.19164i	−0.215950	+	0.0986210i
$147$	−3.40851	−	5.36176i	−0.281129	−	0.442231i
$148$	−9.35857	−	6.01439i	−0.769270	−	0.494380i
$149$	1.45041	−	10.0879i	0.118823	−	0.826429i	−0.840033	−	0.542535i	$-0.817465\pi$
$149$	1.45041	−	10.0879i	0.118823	−	0.826429i	0.958856	−	0.283894i	$-0.0916264\pi$
$150$	8.59412	+	1.06822i	0.701707	+	0.0872194i
$151$	−17.7643	−	11.4164i	−1.44564	−	0.929054i	−0.999417	−	0.0341294i	$-0.989134\pi$
$151$	−17.7643	−	11.4164i	−1.44564	−	0.929054i	−0.446218	−	0.894924i	$-0.647229\pi$
$152$	−4.45663	+	3.86169i	−0.361480	+	0.313225i
$153$	5.14948	−	0.688557i	0.416310	−	0.0556665i
$154$	−1.99828	+	1.28422i	−0.161026	+	0.103485i
$155$	4.79984	+	7.27465i	0.385533	+	0.584314i
$156$	1.66454	+	1.94025i	0.133270	+	0.155344i
$157$	15.3988	−	4.52150i	1.22896	−	0.360855i	0.398103	−	0.917341i	$-0.369669\pi$
$157$	15.3988	−	4.52150i	1.22896	−	0.360855i	0.830857	+	0.556485i	$0.187851\pi$
$158$	−3.00614	−	1.37286i	−0.239156	−	0.109219i
$159$	4.26010	+	0.0210327i	0.337848	+	0.00166801i
$160$	−1.70741	−	1.44387i	−0.134983	−	0.114148i
$161$	−12.8461	−	8.96362i	−1.01241	−	0.706432i
$162$	−7.47372	−	5.01433i	−0.587191	−	0.393963i
$163$	14.5365	−	2.09003i	1.13859	−	0.163704i	0.452872	−	0.891575i	$-0.350399\pi$
$163$	14.5365	−	2.09003i	1.13859	−	0.163704i	0.685714	+	0.727871i	$0.259490\pi$
$164$	−0.289038	−	0.131999i	−0.0225701	−	0.0103074i
$165$	−2.38025	−	1.50592i	−0.185302	−	0.117236i
$166$	11.9849	+	10.3850i	0.930212	+	0.806033i
$167$	−4.12542	−	1.21133i	−0.319234	−	0.0937357i	0.118190	−	0.992991i	$-0.462291\pi$
$167$	−4.12542	−	1.21133i	−0.319234	−	0.0937357i	−0.437424	+	0.899255i	$0.644109\pi$
$168$	−5.15756	+	2.32467i	−0.397914	+	0.179352i
$169$	4.49545	+	9.84366i	0.345804	+	0.757204i
$170$	3.87207	−	0.0466122i	0.296974	−	0.00357499i
$171$	−13.4836	+	11.4525i	−1.03112	+	0.875794i
$172$	−1.32008	+	9.18133i	−0.100655	+	0.700070i
$173$	−2.27457	+	15.8200i	−0.172932	+	1.20277i	0.699716	+	0.714421i	$0.253310\pi$
$173$	−2.27457	+	15.8200i	−0.172932	+	1.20277i	−0.872648	+	0.488349i	$0.837599\pi$
$174$	7.75592	−	8.86202i	0.587975	−	0.671828i
$175$	10.3944	−	12.5961i	0.785741	−	0.952174i
$176$	0.302111	+	0.661530i	0.0227725	+	0.0498647i
$177$	6.10868	+	13.5528i	0.459156	+	1.01869i
$178$	−8.22798	−	2.41595i	−0.616713	−	0.181083i
$179$	13.3592	+	11.5758i	0.998511	+	0.865215i	0.990879	−	0.134756i	$-0.0430252\pi$
$179$	13.3592	+	11.5758i	0.998511	+	0.865215i	0.00763206	+	0.999971i	$0.497571\pi$
$180$	−5.07921	−	4.38196i	−0.378582	−	0.326612i
$181$	−18.4414	−	8.42192i	−1.37074	−	0.625997i	−0.412238	−	0.911076i	$-0.635253\pi$
$181$	−18.4414	−	8.42192i	−1.37074	−	0.625997i	−0.958504	+	0.285080i	$0.907980\pi$
$182$	4.77169	−	0.686066i	0.353701	−	0.0508546i
$183$	1.18420	−	7.95724i	0.0875389	−	0.588216i
$184$	−3.27614	+	3.50242i	−0.241520	+	0.258202i
$185$	−18.9942	−	16.0624i	−1.39648	−	1.18093i
$186$	0.0333301	−	6.75088i	0.00244388	−	0.494998i
$187$	−1.14562	−	0.523186i	−0.0837758	−	0.0382591i
$188$	0.284026	−	0.0833976i	0.0207147	−	0.00608239i
$189$	−15.5408	+	6.82090i	−1.13043	+	0.496147i
$190$	−11.0062	+	7.26191i	−0.798471	+	0.526834i
$191$	0.401041	−	0.257733i	0.0290183	−	0.0186489i	−0.526051	−	0.850453i	$-0.676328\pi$
$191$	0.401041	−	0.257733i	0.0290183	−	0.0186489i	0.555070	+	0.831804i	$0.312692\pi$
$192$	0.479764	+	1.66428i	0.0346240	+	0.120109i
$193$	−2.50162	+	2.16767i	−0.180070	+	0.156032i	−0.740232	−	0.672351i	$-0.765284\pi$
$193$	−2.50162	+	2.16767i	−0.180070	+	0.156032i	0.560162	+	0.828383i	$0.310739\pi$
$194$	−11.2358	−	7.22084i	−0.806687	−	0.518426i
$195$	3.12454	+	4.78681i	0.223753	+	0.342790i
$196$	−0.522035	+	3.63083i	−0.0372882	+	0.259345i
$197$	−2.16157	−	1.38916i	−0.154006	−	0.0989735i	0.461368	−	0.887209i	$-0.347359\pi$
$197$	−2.16157	−	1.38916i	−0.154006	−	0.0989735i	−0.615374	+	0.788235i	$0.710995\pi$
$198$	0.886692	+	1.99344i	0.0630145	+	0.141668i
$199$	8.19677	−	3.74334i	0.581053	−	0.265358i	−0.103130	−	0.994668i	$-0.532886\pi$
$199$	8.19677	−	3.74334i	0.581053	−	0.265358i	0.684184	+	0.729310i	$0.260159\pi$
$200$	−3.36432	−	3.69883i	−0.237893	−	0.261547i
$201$	0.638863	+	0.295580i	0.0450619	+	0.0208486i
$202$	4.21978	+	3.65646i	0.296903	+	0.257268i
$203$	−6.25667	−	21.3083i	−0.439132	−	1.49555i
$204$	−2.51531	−	1.63410i	−0.176107	−	0.114410i
$205$	−0.602306	−	0.376912i	−0.0420669	−	0.0263247i
$206$	−18.3173			−1.27622
$207$	−9.93168	+	10.4097i	−0.690299	+	0.723524i
$208$		−	1.47595i		−	0.102338i
$209$	4.24492	−	0.610327i	0.293627	−	0.0422172i
$210$	−12.1120	+	3.65001i	−0.835806	+	0.251874i
$211$	−15.4355	+	4.53227i	−1.06262	+	0.312014i	−0.765907	−	0.642951i	$-0.777710\pi$
$211$	−15.4355	+	4.53227i	−1.06262	+	0.312014i	−0.296716	+	0.954966i	$0.595892\pi$
$212$	−1.85884	−	1.61069i	−0.127666	−	0.110623i
$213$	−5.86572	+	12.6781i	−0.401912	+	0.868689i
$214$	5.55231	+	8.63957i	0.379548	+	0.590589i
$215$	−5.60350	+	19.9699i	−0.382155	+	1.36194i
$216$	1.38992	+	5.00681i	0.0945723	+	0.340670i
$217$	−10.7097	−	6.88270i	−0.727021	−	0.467228i
$218$	−12.1003	−	1.73975i	−0.819533	−	0.117831i
$219$	4.76026	+	1.42330i	0.321669	+	0.0961780i
$220$	0.476897	+	1.55468i	0.0321524	+	0.104817i
$221$	1.67382	+	1.93169i	0.112594	+	0.129940i
$222$	5.33716	+	18.5144i	0.358207	+	1.24260i
$223$	−1.88085	−	2.92665i	−0.125951	−	0.195983i	0.772551	−	0.634952i	$-0.218980\pi$
$223$	−1.88085	−	2.92665i	−0.125951	−	0.195983i	−0.898502	+	0.438969i	$0.855344\pi$
$224$	3.13391	+	0.920200i	0.209393	+	0.0614834i
$225$	−9.98290	−	11.1956i	−0.665527	−	0.746374i
$226$	2.66234	+	9.06711i	0.177097	+	0.603135i
$227$	18.4257	+	8.41476i	1.22296	+	0.558507i	0.919030	−	0.394188i	$-0.128974\pi$
$227$	18.4257	+	8.41476i	1.22296	+	0.558507i	0.303930	+	0.952695i	$0.401701\pi$
$228$	10.2137	+	0.0504267i	0.676420	+	0.00333959i
$229$			9.44144i			0.623908i	0.950097	+	0.311954i	$0.100983\pi$
$229$			9.44144i			0.623908i	−0.950097	+	0.311954i	$0.899017\pi$
$230$	−8.28429	+	6.80959i	−0.546250	+	0.449011i
$231$	4.06942	+	0.605616i	0.267748	+	0.0398466i
$232$	−6.73005	+	0.967635i	−0.441850	+	0.0635284i
$233$	4.97061	−	10.8841i	0.325636	−	0.713042i	−0.674035	−	0.738699i	$-0.735440\pi$
$233$	4.97061	−	10.8841i	0.325636	−	0.713042i	0.999671	+	0.0256568i	$0.00816769\pi$
$234$	0.0437208	−	4.42762i	0.00285812	−	0.289443i
$235$	0.653995	−	0.102080i	0.0426619	−	0.00665895i
$236$	2.41806	−	8.23516i	0.157402	−	0.536063i
$237$	2.35213	+	5.21847i	0.152787	+	0.338976i
$238$	−5.14518	+	2.34973i	−0.333513	+	0.152310i
$239$	15.5939	−	13.5122i	1.00869	−	0.874034i	0.0166366	−	0.999862i	$-0.494704\pi$
$239$	15.5939	−	13.5122i	1.00869	−	0.874034i	0.992052	+	0.125828i	$0.0401587\pi$
$240$	0.578389	+	3.82955i	0.0373348	+	0.247197i
$241$	−9.29277	−	1.33610i	−0.598600	−	0.0860657i	−0.163647	−	0.986519i	$-0.552326\pi$
$241$	−9.29277	−	1.33610i	−0.598600	−	0.0860657i	−0.434953	+	0.900453i	$0.643235\pi$
$242$	−1.49019	+	10.3645i	−0.0957933	+	0.666257i
$243$	4.02125	+	15.0609i	0.257964	+	0.966155i
$244$	−3.51024	+	3.04164i	−0.224720	+	0.194721i
$245$	−2.21595	+	7.89727i	−0.141572	+	0.504538i
$246$	0.226155	+	0.501752i	0.0144191	+	0.0319905i
$247$	−8.35105	−	2.45209i	−0.531365	−	0.156023i
$248$	−2.55243	+	2.94566i	−0.162079	+	0.187050i
$249$	−3.77475	−	27.2068i	−0.239215	−	1.72416i
$250$	−6.38019	−	9.18113i	−0.403519	−	0.580666i
$251$	3.51524	+	24.4491i	0.221880	+	1.54321i	0.730917	+	0.682466i	$0.239092\pi$
$251$	3.51524	+	24.4491i	0.221880	+	1.54321i	−0.509037	+	0.860745i	$0.669998\pi$
$252$	9.37402	+	2.85330i	0.590508	+	0.179741i
$253$	3.38143	−	0.854670i	0.212589	−	0.0537327i
$254$		−	11.1184i		−	0.697628i
$255$	−5.09996	−	4.35612i	−0.319372	−	0.272791i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−1.94338	+	0.570628i	−0.121225	+	0.0355948i	−0.341782	−	0.939779i	$-0.611031\pi$
$257$	−1.94338	+	0.570628i	−0.121225	+	0.0355948i	0.220557	+	0.975374i	$0.429212\pi$
$258$	12.1937	−	10.4610i	0.759148	−	0.651271i
$259$	34.8634	+	10.2368i	2.16630	+	0.636084i
$260$	0.430328	−	3.27214i	0.0266878	−	0.202930i
$261$	−20.2178	+	2.70341i	−1.25145	+	0.167337i
$262$	−9.80767	+	8.49840i	−0.605920	+	0.525033i
$263$	10.8582	−	16.8957i	0.669547	−	1.04184i	−0.325796	−	0.945440i	$-0.605632\pi$
$263$	10.8582	−	16.8957i	0.669547	−	1.04184i	0.995343	−	0.0963952i	$-0.0307312\pi$
$264$	0.360843	−	1.20684i	0.0222083	−	0.0742761i
$265$	−3.65139	−	4.11284i	−0.224303	−	0.252650i
$266$	10.4132	−	16.2032i	0.638472	−	0.993481i
$267$	7.96831	+	12.5346i	0.487653	+	0.767103i
$268$	−0.168830	−	0.369686i	−0.0103129	−	0.0225822i
$269$	−7.98286	−	12.4216i	−0.486723	−	0.757356i	0.507844	−	0.861449i	$-0.330443\pi$
$269$	−7.98286	−	12.4216i	−0.486723	−	0.757356i	−0.994568	+	0.104093i	$0.966806\pi$
$270$	1.62164	+	11.5052i	0.0986899	+	0.700186i
$271$	−5.87144	+	6.77600i	−0.356664	+	0.411613i	−0.905519	−	0.424305i	$-0.860518\pi$
$271$	−5.87144	+	6.77600i	−0.356664	+	0.411613i	0.548855	+	0.835918i	$0.315064\pi$
$272$	0.487896	+	1.66162i	0.0295830	+	0.100751i
$273$	−7.00193	−	4.54887i	−0.423776	−	0.275310i
$274$	2.32595	−	0.334422i	0.140516	−	0.0202032i
$275$	0.603986	+	3.58574i	0.0364217	+	0.216228i
$276$	8.26526	−	0.827892i	0.497510	−	0.0498332i
$277$		−	32.6649i		−	1.96264i	−0.192377	−	0.981321i	$-0.561620\pi$
$277$		−	32.6649i		−	1.96264i	0.192377	−	0.981321i	$-0.438380\pi$
$278$	0.130513	+	0.907741i	0.00782767	+	0.0544427i
$279$	−7.74417	+	8.76094i	−0.463631	+	0.524504i
$280$	6.67952	+	2.95379i	0.399178	+	0.176523i
$281$	3.24036	−	3.73957i	0.193304	−	0.223084i	−0.650821	−	0.759231i	$-0.725575\pi$
$281$	3.24036	−	3.73957i	0.193304	−	0.223084i	0.844125	+	0.536147i	$0.180121\pi$
$282$	−0.465326	−	0.215290i	−0.0277097	−	0.0128203i
$283$	7.79627	−	5.01036i	0.463440	−	0.297835i	−0.288007	−	0.957628i	$-0.592993\pi$
$283$	7.79627	−	5.01036i	0.463440	−	0.297835i	0.751447	+	0.659793i	$0.229356\pi$
$284$	7.33634	−	3.35039i	0.435332	−	0.198809i
$285$	22.6289	+	3.08971i	1.34042	+	0.183019i
$286$	−0.580315	+	0.902987i	−0.0343147	+	0.0533948i
$287$	1.02729	+	0.147702i	0.0606388	+	0.00871854i
$288$	1.27313	−	2.71646i	0.0750199	−	0.160069i
$289$	11.7784	+	7.56950i	0.692845	+	0.445265i
$290$	−15.2025	+	0.183009i	−0.892722	+	0.0107466i
$291$	6.40777	+	22.2282i	0.375630	+	1.30304i
$292$	−1.55086	−	2.41319i	−0.0907572	−	0.141221i
$293$	6.42750	−	21.8900i	0.375498	−	1.27883i	−0.527636	−	0.849471i	$-0.676921\pi$
$293$	6.42750	−	21.8900i	0.375498	−	1.27883i	0.903134	−	0.429359i	$-0.141260\pi$
$294$	4.82211	−	4.13687i	0.281231	−	0.241267i
$295$	7.76184	−	17.5522i	0.451912	−	1.02193i
$296$	4.62131	−	10.1192i	0.268608	−	0.588169i
$297$	1.11822	−	3.60967i	0.0648860	−	0.209454i
$298$	10.1916			0.590383
$299$	−6.96298	−	1.27302i	−0.402679	−	0.0736207i
$300$	0.165728	+	8.65867i	0.00956833	+	0.499908i
$301$	−4.31165	−	29.9882i	−0.248520	−	1.72849i
$302$	8.77208	−	19.2082i	0.504776	−	1.10531i
$303$	−1.32905	−	9.57926i	−0.0763521	−	0.550314i
$304$	−4.45663	−	3.86169i	−0.255605	−	0.221483i
$305$	−8.66894	+	5.71980i	−0.496382	+	0.327515i
$306$	1.41439	+	4.99907i	0.0808556	+	0.285778i
$307$	16.0568	−	7.33288i	0.916408	−	0.418509i	0.0993417	−	0.995053i	$-0.468326\pi$
$307$	16.0568	−	7.33288i	0.916408	−	0.418509i	0.817066	+	0.576544i	$0.195599\pi$
$308$	−1.55553	−	1.79518i	−0.0886344	−	0.102290i
$309$	23.8744	+	20.8945i	1.35817	+	1.18865i
$310$	−6.51752	+	5.78628i	−0.370170	+	0.328638i
$311$	−22.4582	−	3.22901i	−1.27349	−	0.183100i	−0.527786	−	0.849377i	$-0.676978\pi$
$311$	−22.4582	−	3.22901i	−1.27349	−	0.183100i	−0.745704	+	0.666277i	$0.767887\pi$
$312$	−1.68361	+	1.92372i	−0.0953159	+	0.108909i
$313$	6.80241	+	7.85039i	0.384495	+	0.443731i	0.914697	−	0.404141i	$-0.132429\pi$
$313$	6.80241	+	7.85039i	0.384495	+	0.443731i	−0.530202	+	0.847871i	$0.677884\pi$
$314$	6.66696	+	14.5986i	0.376238	+	0.823847i
$315$	19.9501	+	9.05879i	1.12406	+	0.510405i
$316$	0.931067	−	3.17092i	0.0523766	−	0.178378i
$317$	1.99686	−	2.30450i	0.112155	−	0.129434i	−0.696896	−	0.717172i	$-0.745436\pi$
$317$	1.99686	−	2.30450i	0.112155	−	0.129434i	0.809051	+	0.587738i	$0.199982\pi$
$318$	0.585456	+	4.21973i	0.0328308	+	0.236631i
$319$	4.49791	+	2.05413i	0.251835	+	0.115009i
$320$	1.18618	−	1.89552i	0.0663094	−	0.105963i
$321$	2.61838	−	17.5942i	0.146144	−	0.982011i
$322$	7.04420	−	13.9910i	0.392558	−	0.779686i
$323$	10.2122			0.568221
$324$	3.89967	−	8.11126i	0.216648	−	0.450626i
$325$	1.90806	−	7.12880i	0.105840	−	0.395435i
$326$	4.13752	+	14.0911i	0.229156	+	0.780433i
$327$	13.7867	+	16.0703i	0.762407	+	0.888692i
$328$	0.0895214	−	0.304882i	0.00494299	−	0.0168343i
$329$	−0.813370	+	0.522721i	−0.0448425	+	0.0288186i
$330$	1.15185	−	2.57034i	0.0634072	−	0.141493i
$331$	−20.2113	−	23.3251i	−1.11091	−	1.28206i	−0.955753	−	0.294172i	$-0.904956\pi$
$331$	−20.2113	−	23.3251i	−1.11091	−	1.28206i	−0.155160	−	0.987889i	$-0.549589\pi$
$332$	−8.57367	+	13.3409i	−0.470541	+	0.732176i
$333$	14.1630	−	30.2194i	0.776127	−	1.65601i
$334$	0.611894	−	4.25582i	0.0334814	−	0.232868i
$335$	−0.266506	−	0.868810i	−0.0145608	−	0.0474681i
$336$	−3.03501	−	4.77423i	−0.165573	−	0.260455i
$337$	6.43537	+	14.0915i	0.350557	+	0.767613i	0.999974	+	0.00718065i	$0.00228569\pi$
$337$	6.43537	+	14.0915i	0.350557	+	0.767613i	−0.649417	+	0.760432i	$0.724987\pi$
$338$	−9.10369	+	5.85059i	−0.495176	+	0.318230i
$339$	6.87281	−	14.8548i	0.373280	−	0.806804i
$340$	0.597191	+	3.82603i	0.0323872	+	0.207495i
$341$	2.71976	−	0.798593i	0.147283	−	0.0432463i
$342$	−13.2548	−	11.7165i	−0.716740	−	0.633557i
$343$	1.54874	+	10.7717i	0.0836240	+	0.581618i
$344$	−9.27575			−0.500115
$345$	18.5653	+	0.574408i	0.999522	+	0.0309251i
$346$	−15.9827			−0.859233
$347$	−3.43226	−	23.8719i	−0.184254	−	1.28151i	−0.846566	−	0.532284i	$-0.821334\pi$
$347$	−3.43226	−	23.8719i	−0.184254	−	1.28151i	0.662312	−	0.749228i	$-0.269575\pi$
$348$	9.87560	+	6.41578i	0.529388	+	0.343922i
$349$	−4.83714	+	1.42031i	−0.258926	+	0.0760276i	−0.408619	−	0.912705i	$-0.633990\pi$
$349$	−4.83714	+	1.42031i	−0.258926	+	0.0760276i	0.149693	+	0.988733i	$0.452171\pi$
$350$	13.9471	+	8.49597i	0.745506	+	0.454129i
$351$	−5.10758	+	5.72101i	−0.272622	+	0.305365i
$352$	−0.611802	+	0.393181i	−0.0326092	+	0.0209566i
$353$	6.56143	+	14.3675i	0.349230	+	0.764707i	0.999985	+	0.00541925i	$0.00172501\pi$
$353$	6.56143	+	14.3675i	0.349230	+	0.764707i	−0.650756	+	0.759287i	$0.725548\pi$
$354$	−12.5455	+	7.97527i	−0.666787	+	0.423881i
$355$	17.2413	−	5.28876i	0.915076	−	0.280698i
$356$	1.22040	−	8.48806i	0.0646810	−	0.449866i
$357$	9.38646	+	2.80653i	0.496784	+	0.148537i
$358$	−9.55675	+	14.8706i	−0.505090	+	0.785935i
$359$	1.03639	+	1.19605i	0.0546984	+	0.0631254i	0.782439	−	0.622727i	$-0.213975\pi$
$359$	1.03639	+	1.19605i	0.0546984	+	0.0631254i	−0.727741	+	0.685852i	$0.759430\pi$
$360$	3.61451	−	5.65113i	0.190502	−	0.297841i
$361$	−13.2701	+	8.52818i	−0.698427	+	0.448852i
$362$	5.71171	−	19.4523i	0.300201	−	1.02239i
$363$	13.7651	−	11.8091i	0.722481	−	0.619815i
$364$	1.35817	+	4.62549i	0.0711872	+	0.242441i
$365$	−2.73463	−	5.80215i	−0.143137	−	0.303698i
$366$	8.04477	+	0.0397183i	0.420507	+	0.00207611i
$367$	34.0866			1.77931			0.889653	−	0.456637i	$-0.150946\pi$
$367$	34.0866			1.77931			0.889653	+	0.456637i	$0.150946\pi$
$368$	−3.93301	−	2.74434i	−0.205022	−	0.143059i
$369$	0.277582	−	0.911949i	0.0144504	−	0.0474742i
$370$	13.1957	−	21.0868i	0.686012	−	1.09625i
$371$	7.30760	+	3.33727i	0.379392	+	0.173262i
$372$	6.68690	−	0.927759i	0.346700	−	0.0481021i
$373$	−7.49073	+	8.64477i	−0.387855	+	0.447609i	−0.915779	−	0.401683i	$-0.868425\pi$
$373$	−7.49073	+	8.64477i	−0.387855	+	0.447609i	0.527923	+	0.849292i	$0.322971\pi$
$374$	0.354822	−	1.20841i	0.0183474	−	0.0624856i
$375$	−2.15711	+	19.2444i	−0.111393	+	0.993776i
$376$	0.122970	+	0.269266i	0.00634168	+	0.0138863i
$377$	−6.57175	−	7.58421i	−0.338462	−	0.390607i
$378$	−8.96316	−	14.4119i	−0.461015	−	0.741267i
$379$	26.4513	+	3.80312i	1.35871	+	0.195353i	0.782858	−	0.622200i	$-0.213761\pi$
$379$	26.4513	+	3.80312i	1.35871	+	0.195353i	0.575853	+	0.817553i	$0.304670\pi$
$380$	−8.75433	−	9.86066i	−0.449088	−	0.505841i
$381$	−12.6827	+	14.4915i	−0.649755	+	0.742420i
$382$	0.312184	+	0.360280i	0.0159727	+	0.0184335i
$383$	11.7553	−	5.36847i	0.600668	−	0.274316i	−0.0917849	−	0.995779i	$-0.529257\pi$
$383$	11.7553	−	5.36847i	0.600668	−	0.274316i	0.692453	+	0.721463i	$0.256530\pi$
$384$	−1.57906	+	0.711733i	−0.0805812	+	0.0363205i
$385$	−2.92517	−	4.43340i	−0.149080	−	0.225947i
$386$	−2.50162	−	2.16767i	−0.127329	−	0.110331i
$387$	−27.8259	−	0.274768i	−1.41447	−	0.0139672i
$388$	5.54831	−	12.1491i	0.281673	−	0.616778i
$389$	3.82143	+	26.5786i	0.193754	+	1.34759i	0.821962	+	0.569543i	$0.192880\pi$
$389$	3.82143	+	26.5786i	0.193754	+	1.34759i	−0.628208	+	0.778046i	$0.716211\pi$
$390$	−4.29342	+	3.77397i	−0.217406	+	0.191102i
$391$	8.25973	−	0.868547i	0.417713	−	0.0439243i
$392$	−3.66817			−0.185271
$393$	22.4773	+	0.110974i	1.13383	+	0.00559788i
$394$	1.06740	−	2.33727i	0.0537746	−	0.117750i
$395$	2.98867	−	6.75840i	0.150376	−	0.340052i
$396$	−1.84696	+	1.16136i	−0.0928134	+	0.0583607i
$397$	−6.70727	+	22.8429i	−0.336628	+	1.14645i	0.601127	+	0.799154i	$0.294719\pi$
$397$	−6.70727	+	22.8429i	−0.336628	+	1.14645i	−0.937755	+	0.347297i	$0.887099\pi$
$398$	4.87176	+	7.58060i	0.244199	+	0.379981i
$399$	−32.0553	+	9.24063i	−1.60477	+	0.462610i
$400$	3.18239	−	3.85647i	0.159120	−	0.192824i
$401$	27.8844	+	17.9202i	1.39248	+	0.894893i	0.999694	−	0.0247360i	$-0.00787450\pi$
$401$	27.8844	+	17.9202i	1.39248	+	0.894893i	0.392787	+	0.919629i	$0.371511\pi$
$402$	−0.201651	+	0.674426i	−0.0100575	+	0.0336373i
$403$	−5.69419	−	0.818702i	−0.283648	−	0.0407824i
$404$	−3.01870	+	4.69720i	−0.150186	+	0.233694i
$405$	11.0104	−	16.8455i	0.547112	−	0.837060i
$406$	20.2010	−	9.22547i	1.00256	−	0.457853i
$407$	−6.80602	+	4.37397i	−0.337362	+	0.216809i
$408$	1.25950	−	2.72227i	0.0623544	−	0.134772i
$409$	−0.427761	+	0.493663i	−0.0211514	+	0.0244101i	−0.766227	−	0.642570i	$-0.777868\pi$
$409$	−0.427761	+	0.493663i	−0.0211514	+	0.0244101i	0.745075	+	0.666980i	$0.232414\pi$
$410$	0.287359	−	0.649816i	0.0141916	−	0.0320921i
$411$	−3.41308	−	2.21734i	−0.168355	−	0.109373i
$412$	−2.60682	−	18.1308i	−0.128429	−	0.893241i
$413$			28.0334i			1.37943i
$414$	−11.7172	−	8.34914i	−0.575867	−	0.410338i
$415$	−22.8973	+	27.0767i	−1.12398	+	1.32914i
$416$	1.46092	−	0.210049i	0.0716277	−	0.0102985i
$417$	0.865352	−	1.33201i	0.0423765	−	0.0652287i
$418$	1.20823	+	4.11485i	0.0590965	+	0.201264i
$419$	17.0320	−	19.6560i	0.832069	−	0.960259i	−0.167603	−	0.985855i	$-0.553603\pi$
$419$	17.0320	−	19.6560i	0.832069	−	0.960259i	0.999672	+	0.0255957i	$0.00814825\pi$
$420$	−5.33657	−	11.4692i	−0.260398	−	0.559642i
$421$	−1.48052	−	2.30373i	−0.0721561	−	0.112277i	0.803300	−	0.595574i	$-0.203075\pi$
$421$	−1.48052	−	2.30373i	−0.0721561	−	0.112277i	−0.875456	+	0.483297i	$0.839439\pi$
$422$	−6.68284	−	14.6334i	−0.325315	−	0.712342i
$423$	0.360915	+	0.811402i	0.0175483	+	0.0394517i
$424$	1.32976	−	2.06915i	0.0645788	−	0.100487i
$425$	0.208441	+	8.65633i	0.0101109	+	0.419894i
$426$	−13.3838	−	4.00173i	−0.648449	−	0.193884i
$427$	8.20186	−	12.7623i	0.396916	−	0.617613i
$428$	−7.76145	+	6.72534i	−0.375164	+	0.325081i
$429$	1.78641	−	0.514971i	0.0862487	−	0.0248630i
$430$	−20.5641	−	2.70444i	−0.991690	−	0.130420i
$431$	3.54845	+	1.04192i	0.170923	+	0.0501875i	0.366074	−	0.930586i	$-0.380702\pi$
$431$	3.54845	+	1.04192i	0.170923	+	0.0501875i	−0.195151	+	0.980773i	$0.562520\pi$
$432$	−4.75804	+	2.08832i	−0.228921	+	0.100474i
$433$	26.7068	−	7.84183i	1.28345	−	0.376854i	0.432276	−	0.901742i	$-0.357711\pi$
$433$	26.7068	−	7.84183i	1.28345	−	0.376854i	0.851172	+	0.524887i	$0.175893\pi$
$434$	5.28849	−	11.5802i	0.253856	−	0.555867i
$435$	20.0234	+	17.1030i	0.960049	+	0.820025i
$436$		−	12.2247i		−	0.585456i
$437$	−22.0619	+	17.6940i	−1.05537	+	0.846419i
$438$	−0.731361	+	4.91437i	−0.0349458	+	0.234818i
$439$	4.14197	+	28.8080i	0.197686	+	1.37493i	0.810978	+	0.585077i	$0.198936\pi$
$439$	4.14197	+	28.8080i	0.197686	+	1.37493i	−0.613292	+	0.789856i	$0.710155\pi$
$440$	−1.47099	+	0.693297i	−0.0701266	+	0.0330516i
$441$	−11.0040	−	0.108659i	−0.523999	−	0.00517425i
$442$	−1.67382	+	1.93169i	−0.0796156	+	0.0918814i
$443$	−32.1145	−	9.42968i	−1.52581	−	0.448017i	−0.592043	−	0.805906i	$-0.701679\pi$
$443$	−32.1145	−	9.42968i	−1.52581	−	0.448017i	−0.933764	+	0.357889i	$0.883497\pi$
$444$	−17.5664	+	7.91771i	−0.833662	+	0.375758i
$445$	5.18038	−	18.4620i	0.245574	−	0.875184i
$446$	2.62919	−	2.27821i	0.124496	−	0.107876i
$447$	−13.2835	−	11.6256i	−0.628289	−	0.549870i
$448$	−0.464831	+	3.23297i	−0.0219612	+	0.152744i
$449$	−38.0510	−	5.47090i	−1.79574	−	0.258188i	−0.837966	−	0.545722i	$-0.816255\pi$
$449$	−38.0510	−	5.47090i	−1.79574	−	0.258188i	−0.957770	+	0.287534i	$0.907165\pi$
$450$	9.66094	−	11.4746i	0.455421	−	0.540917i
$451$	−0.174643	+	0.151329i	−0.00822363	+	0.00712581i
$452$	−8.59593	+	3.92563i	−0.404319	+	0.184646i
$453$	−33.3441	+	15.0292i	−1.56664	+	0.706136i
$454$	−5.70685	+	19.4357i	−0.267836	+	0.912164i
$455$	1.66241	+	10.6506i	0.0779352	+	0.499307i
$456$	1.40365	+	10.1169i	0.0657320	+	0.473769i
$457$	−3.10118	+	6.79064i	−0.145067	+	0.317653i	−0.968192	−	0.250207i	$-0.919501\pi$
$457$	−3.10118	+	6.79064i	−0.145067	+	0.317653i	0.823125	+	0.567860i	$0.192229\pi$
$458$	−9.34534	+	1.34366i	−0.436679	+	0.0627850i
$459$	3.85895	−	8.12909i	0.180120	−	0.379434i
$460$	−7.91926	−	7.23086i	−0.369237	−	0.337141i
$461$		−	23.1040i		−	1.07606i	−0.842925	−	0.538030i	$-0.819169\pi$
$461$		−	23.1040i		−	1.07606i	0.842925	−	0.538030i	$-0.180831\pi$
$462$	−0.0203124	+	4.11419i	−0.000945017	+	0.191409i
$463$	−9.46248	−	4.32137i	−0.439759	−	0.200831i	0.183217	−	0.983073i	$-0.441349\pi$
$463$	−9.46248	−	4.32137i	−0.439759	−	0.200831i	−0.622975	+	0.782242i	$0.714076\pi$
$464$	−1.91557	−	6.52384i	−0.0889282	−	0.302862i
$465$	15.0952	−	0.107183i	0.700024	−	0.00497051i
$466$	11.4807	+	3.37105i	0.531834	+	0.156161i
$467$	16.4551	+	25.6047i	0.761453	+	1.18484i	0.978007	+	0.208573i	$0.0668819\pi$
$467$	16.4551	+	25.6047i	0.761453	+	1.18484i	−0.216554	+	0.976271i	$0.569482\pi$
$468$	4.38878	−	0.586841i	0.202871	−	0.0271267i
$469$	0.869283	+	1.00321i	0.0401397	+	0.0463237i
$470$	0.194114	+	0.632811i	0.00895381	+	0.0291894i
$471$	7.96306	−	26.6326i	0.366918	−	1.22716i
$472$	8.49547	+	1.22146i	0.391036	+	0.0562224i
$473$	5.67492	+	3.64705i	0.260933	+	0.167692i
$474$	−4.83061	+	3.07085i	−0.221877	+	0.141049i
$475$	−16.5332	−	24.4133i	−0.758595	−	1.12016i
$476$	−3.05804	−	4.75841i	−0.140165	−	0.218101i
$477$	4.05038	−	6.16774i	0.185454	−	0.282402i
$478$	15.5939	+	13.5122i	0.713251	+	0.618035i
$479$	−11.3558	+	3.33437i	−0.518861	+	0.152351i	−0.530669	−	0.847579i	$-0.678059\pi$
$479$	−11.3558	+	3.33437i	−0.518861	+	0.152351i	0.0118082	+	0.999930i	$0.496241\pi$
$480$	−3.70826	+	1.11750i	−0.169258	+	0.0510068i
$481$	16.2521	−	2.33670i	0.741033	−	0.106544i
$482$		−	9.38833i		−	0.427627i
$483$	−25.1408	+	10.2002i	−1.14395	+	0.464127i
$484$	−10.4711			−0.475959
$485$	15.8427	−	25.3166i	0.719380	−	1.14957i
$486$	−14.3353	+	6.12371i	−0.650261	+	0.277777i
$487$	0.399122	+	1.35928i	0.0180859	+	0.0615951i	0.968042	−	0.250790i	$-0.0806903\pi$
$487$	0.399122	+	1.35928i	0.0180859	+	0.0615951i	−0.949956	+	0.312385i	$0.898872\pi$
$488$	−3.51024	−	3.04164i	−0.158901	−	0.137688i
$489$	10.6810	−	23.0857i	0.483010	−	1.04397i
$490$	−8.13225	−	1.06949i	−0.367378	−	0.0483148i
$491$	12.9167	−	5.89886i	0.582922	−	0.266212i	−0.102052	−	0.994779i	$-0.532541\pi$
$491$	12.9167	−	5.89886i	0.582922	−	0.266212i	0.684974	+	0.728567i	$0.259813\pi$
$492$	−0.464459	+	0.295260i	−0.0209395	+	0.0133114i
$493$	9.90554	+	6.36591i	0.446123	+	0.286706i
$494$	1.23865	−	8.61502i	0.0557296	−	0.387608i
$495$	−4.43329	+	2.03622i	−0.199261	+	0.0915211i
$496$	−3.27893	−	2.10724i	−0.147228	−	0.0946178i
$497$	−19.9084	+	17.2507i	−0.893014	+	0.773801i
$498$	26.3927	−	7.60827i	1.18269	−	0.340935i
$499$	27.0882	−	17.4085i	1.21263	−	0.779312i	0.231536	−	0.972826i	$-0.425625\pi$
$499$	27.0882	−	17.4085i	1.21263	−	0.779312i	0.981098	+	0.193514i	$0.0619885\pi$
$500$	8.17969	−	7.62186i	0.365807	−	0.340860i
$501$	−5.65215	+	4.84896i	−0.252519	+	0.216636i
$502$	−23.6999	+	6.95893i	−1.05778	+	0.310592i
$503$	−36.7413	−	16.7792i	−1.63821	−	0.748146i	−0.638444	−	0.769669i	$-0.720421\pi$
$503$	−36.7413	−	16.7792i	−1.63821	−	0.748146i	−0.999768	+	0.0215221i	$0.993149\pi$
$504$	−1.49019	+	9.68467i	−0.0663785	+	0.431390i
$505$	−8.06192	+	9.53345i	−0.358751	+	0.424233i
$506$	1.32720	+	3.22538i	0.0590012	+	0.143386i
$507$	18.5394	+	2.75905i	0.823361	+	0.122534i
$508$	11.0052	−	1.58231i	0.488276	−	0.0702035i
$509$	−17.8004	−	8.12919i	−0.788991	−	0.360320i	−0.0201799	−	0.999796i	$-0.506424\pi$
$509$	−17.8004	−	8.12919i	−0.788991	−	0.360320i	−0.768811	+	0.639476i	$0.779151\pi$
$510$	3.58598	−	5.66799i	0.158790	−	0.250983i
$511$	7.08087	+	6.13561i	0.313239	+	0.271423i
$512$	0.959493	+	0.281733i	0.0424040	+	0.0124509i
$513$	3.91106	+	30.3909i	0.172678	+	1.34179i
$514$	−0.841392	−	1.84239i	−0.0371122	−	0.0812644i
$515$	−0.493027	−	40.9557i	−0.0217253	−	1.80472i
$516$	12.0898	+	10.5809i	0.532225	+	0.465796i
$517$	0.0306373	−	0.213087i	0.00134743	−	0.00937156i
$518$	−5.17104	+	35.9654i	−0.227202	+	1.58023i
$519$	20.8315	+	18.2314i	0.914401	+	0.800271i
$520$	3.30008	−	0.0397265i	0.144718	−	0.00174212i
$521$	−13.6630	−	29.9179i	−0.598588	−	1.31073i	−0.930111	−	0.367279i	$-0.880290\pi$
$521$	−13.6630	−	29.9179i	−0.598588	−	1.31073i	0.331522	−	0.943447i	$-0.392438\pi$
$522$	−5.55319	−	19.6273i	−0.243056	−	0.859064i
$523$	−25.0573	−	7.35747i	−1.09568	−	0.321720i	−0.316544	−	0.948578i	$-0.602522\pi$
$523$	−25.0573	−	7.35747i	−1.09568	−	0.321720i	−0.779134	+	0.626858i	$0.784341\pi$
$524$	−9.80767	−	8.49840i	−0.428450	−	0.371254i
$525$	−8.48708	−	26.9830i	−0.370407	−	1.17763i
$526$	18.2690	+	8.34319i	0.796568	+	0.363780i
$527$	6.68115	−	0.960605i	0.291036	−	0.0418446i
$528$	1.24591	+	0.185418i	0.0542214	+	0.00806929i
$529$	−16.3391	+	16.1875i	−0.710395	+	0.703803i
$530$	3.55133	−	4.19954i	0.154260	−	0.182417i
$531$	25.4490	+	3.91587i	1.10439	+	0.169934i
$532$	17.5202	+	8.00121i	0.759597	+	0.346897i
$533$	0.449989	−	0.132129i	0.0194912	−	0.00572313i
$534$	−11.2730	+	9.67106i	−0.487829	+	0.418508i
$535$	−19.1678	+	12.6470i	−0.828697	+	0.546777i
$536$	0.341896	−	0.219723i	0.0147677	−	0.00949060i
$537$	29.4190	−	8.48065i	1.26952	−	0.365967i
$538$	11.1591	−	9.66937i	0.481101	−	0.416876i
$539$	2.24419	+	1.44226i	0.0966643	+	0.0621224i
$540$	−11.1573	+	3.24250i	−0.480135	+	0.139535i
$541$	−2.56904	+	17.8681i	−0.110452	+	0.768209i	0.857030	+	0.515267i	$0.172307\pi$
$541$	−2.56904	+	17.8681i	−0.110452	+	0.768209i	−0.967481	+	0.252942i	$0.918602\pi$
$542$	−7.54262	−	4.84735i	−0.323983	−	0.208212i
$543$	−29.6338	+	18.8384i	−1.27171	+	0.808433i
$544$	−1.57527	+	0.719403i	−0.0675392	+	0.0308441i
$545$	3.56424	−	27.1019i	0.152675	−	1.16092i
$546$	3.50609	−	7.57803i	0.150047	−	0.324310i
$547$	8.62440	+	7.47309i	0.368753	+	0.319526i	0.819450	−	0.573151i	$-0.194279\pi$
$547$	8.62440	+	7.47309i	0.368753	+	0.319526i	−0.450697	+	0.892677i	$0.648825\pi$
$548$	0.662036	+	2.25469i	0.0282808	+	0.0963154i
$549$	−10.4401	−	9.22845i	−0.445572	−	0.393860i
$550$	−3.46329	+	1.10814i	−0.147675	+	0.0472513i
$551$	−40.0950			−1.70810
$552$	1.99573	+	8.06331i	0.0849441	+	0.343197i
$553$			10.7942i			0.459014i
$554$	32.3324	−	4.64870i	1.37367	−	0.197504i
$555$	−41.2527	+	12.4317i	−1.75108	+	0.527697i
$556$	−0.879927	+	0.258370i	−0.0373172	+	0.0109573i
$557$	15.3807	+	13.3275i	0.651703	+	0.564704i	0.916715	−	0.399541i	$-0.130831\pi$
$557$	15.3807	+	13.3275i	0.651703	+	0.564704i	−0.265012	+	0.964245i	$0.585376\pi$
$558$	−9.77388	−	6.41853i	−0.413761	−	0.271718i
$559$	−7.40165	−	11.5172i	−0.313056	−	0.487125i
$560$	−1.97313	+	7.03190i	−0.0833798	+	0.297152i
$561$	−1.84091	+	1.17028i	−0.0777232	+	0.0494091i
$562$	4.16266	+	2.67518i	0.175591	+	0.112846i
$563$	10.7639	+	1.54761i	0.453643	+	0.0652241i	0.365350	−	0.930870i	$-0.380949\pi$
$563$	10.7639	+	1.54761i	0.453643	+	0.0652241i	0.0882938	+	0.996094i	$0.471859\pi$
$564$	0.146876	−	0.491228i	0.00618459	−	0.0206844i
$565$	−20.2016	+	6.19680i	−0.849886	+	0.260701i
$566$	6.06889	+	7.00387i	0.255094	+	0.294395i
$567$	−4.75724	+	29.0085i	−0.199785	+	1.21824i
$568$	4.36036	+	6.78485i	0.182957	+	0.284686i
$569$	25.0014	+	7.34108i	1.04811	+	0.307754i	0.760055	−	0.649859i	$-0.225172\pi$
$569$	25.0014	+	7.34108i	1.04811	+	0.307754i	0.288059	+	0.957613i	$0.406990\pi$
$570$	0.162163	+	22.8383i	0.00679225	+	0.956590i
$571$	−0.973707	−	3.31614i	−0.0407484	−	0.138776i	0.936607	−	0.350383i	$-0.113949\pi$
$571$	−0.973707	−	3.31614i	−0.0407484	−	0.138776i	−0.977355	+	0.211607i	$0.932130\pi$
$572$	−0.976383	−	0.445899i	−0.0408246	−	0.0186440i
$573$	0.00407656	−	0.825690i	0.000170301	−	0.0344937i
$574$			1.03785i			0.0433190i
$575$	−15.4486	−	18.3396i	−0.644251	−	0.764815i
$576$	2.86999	+	0.873579i	0.119583	+	0.0363991i
$577$	−28.9240	+	4.15865i	−1.20412	+	0.173127i	−0.715023	−	0.699101i	$-0.753584\pi$
$577$	−28.9240	+	4.15865i	−1.20412	+	0.173127i	−0.489100	+	0.872227i	$0.662675\pi$
$578$	−5.81622	+	12.7357i	−0.241923	+	0.529737i
$579$	0.787905	+	5.67889i	0.0327442	+	0.236007i
$580$	−2.34469	−	15.0217i	−0.0973578	−	0.623743i
$581$	14.5928	−	49.6987i	0.605413	−	2.06185i
$582$	−21.0901	+	9.50595i	−0.874211	+	0.394034i
$583$	−1.62710	+	0.743071i	−0.0673875	+	0.0307749i
$584$	2.16791	−	1.87851i	0.0897088	−	0.0777331i
$585$	9.90093	−	0.0214182i	0.409353	−	0.000885534i
$586$	22.5820	+	3.24680i	0.932852	+	0.134124i
$587$	−0.787458	+	5.47689i	−0.0325019	+	0.226056i	−0.999598	−	0.0283562i	$-0.990973\pi$
$587$	−0.787458	+	5.47689i	−0.0325019	+	0.226056i	0.967096	+	0.254412i	$0.0818818\pi$
$588$	4.78102	+	4.18428i	0.197166	+	0.172557i
$589$	−17.3705	+	15.0516i	−0.715737	+	0.620190i
$590$	18.4781	+	5.18490i	0.760733	+	0.213459i
$591$	−4.05735	+	1.82877i	−0.166897	+	0.0752258i
$592$	10.6739	+	3.13415i	0.438696	+	0.128813i
$593$	−21.7749	+	25.1296i	−0.894189	+	1.03195i	0.105108	+	0.994461i	$0.466481\pi$
$593$	−21.7749	+	25.1296i	−0.894189	+	1.03195i	−0.999297	+	0.0374879i	$0.988064\pi$
$594$	3.73206	+	0.593134i	0.153128	+	0.0243366i
$595$	−5.39225	−	11.4409i	−0.221061	−	0.469031i
$596$	1.45041	+	10.0879i	0.0594113	+	0.413215i
$597$	2.29745	−	15.4376i	0.0940282	−	0.631820i
$598$	0.269129	−	7.07327i	0.0110055	−	0.289248i
$599$		−	17.0942i		−	0.698449i	−0.937039	−	0.349224i	$-0.886445\pi$
$599$		−	17.0942i		−	0.698449i	0.937039	−	0.349224i	$-0.113555\pi$
$600$	−8.54695	+	1.39630i	−0.348928	+	0.0570036i
$601$	4.53694	−	9.93452i	0.185066	−	0.405237i	−0.794246	−	0.607597i	$-0.792134\pi$
$601$	4.53694	−	9.93452i	0.185066	−	0.405237i	0.979311	+	0.202359i	$0.0648609\pi$
$602$	29.0694	−	8.53554i	1.18478	−	0.347883i
$603$	1.03215	−	0.649010i	0.0420323	−	0.0264297i
$604$	20.2611	+	5.94918i	0.824411	+	0.242069i
$605$	−23.2142	−	3.05296i	−0.943792	−	0.124121i
$606$	9.29262	−	2.67880i	0.377487	−	0.108819i
$607$	−13.4570	+	11.6605i	−0.546202	+	0.473287i	−0.883709	−	0.468036i	$-0.844962\pi$
$607$	−13.4570	+	11.6605i	−0.546202	+	0.473287i	0.337507	+	0.941323i	$0.390416\pi$
$608$	3.18814	−	4.96084i	0.129296	−	0.201189i
$609$	−36.8531	−	11.0190i	−1.49336	−	0.446511i
$610$	−6.89530	−	7.76669i	−0.279182	−	0.314464i
$611$	−0.236209	+	0.367548i	−0.00955598	+	0.0148694i
$612$	−4.74690	+	2.11144i	−0.191882	+	0.0853499i
$613$	−16.4861	−	36.0995i	−0.665867	−	1.45805i	−0.876952	−	0.480577i	$-0.840427\pi$
$613$	−16.4861	−	36.0995i	−0.665867	−	1.45805i	0.211085	−	0.977468i	$-0.432300\pi$
$614$	9.54336	+	14.8498i	0.385138	+	0.599287i
$615$	−1.11578	+	0.519167i	−0.0449927	+	0.0209348i
$616$	1.55553	−	1.79518i	0.0626740	−	0.0723297i
$617$	−7.78003	−	26.4963i	−0.313212	−	1.06670i	−0.954205	−	0.299155i	$-0.903295\pi$
$617$	−7.78003	−	26.4963i	−0.313212	−	1.06670i	0.640992	−	0.767547i	$-0.278523\pi$
$618$	−17.2842	+	26.6050i	−0.695271	+	1.07021i
$619$	12.4756	−	1.79372i	0.501437	−	0.0720958i	0.113045	−	0.993590i	$-0.463940\pi$
$619$	12.4756	−	1.79372i	0.501437	−	0.0720958i	0.388392	+	0.921494i	$0.373030\pi$
$620$	−6.65492	−	5.62771i	−0.267268	−	0.226014i
$621$	5.74806	+	24.2479i	0.230662	+	0.973034i
$622$		−	22.6892i		−	0.909754i
$623$	3.98609	+	27.7238i	0.159699	+	1.11073i
$624$	−2.14374	−	1.39270i	−0.0858184	−	0.0557527i
$625$	20.3564	−	14.5126i	0.814257	−	0.580505i
$626$	−6.80241	+	7.85039i	−0.271879	+	0.313765i
$627$	3.11903	−	6.74145i	0.124562	−	0.269228i
$628$	−13.5012	+	8.67670i	−0.538757	+	0.346238i
$629$	−17.5242	+	8.00303i	−0.698736	+	0.319102i
$630$	−6.12739	+	21.0362i	−0.244121	+	0.838103i
$631$	24.5281	−	38.1665i	0.976449	−	1.51938i	0.126872	−	0.991919i	$-0.459506\pi$
$631$	24.5281	−	38.1665i	0.976449	−	1.51938i	0.849577	−	0.527465i	$-0.176857\pi$
$632$	3.27115	+	0.470321i	0.130119	+	0.0187083i
$633$	−7.98202	+	26.6960i	−0.317257	+	1.06107i
$634$	2.56523	+	1.64857i	0.101878	+	0.0654731i
$635$	24.8596	−	0.299261i	0.986523	−	0.0118758i
$636$	−4.09346	+	1.18003i	−0.162316	+	0.0467911i
$637$	−2.92704	−	4.55457i	−0.115974	−	0.180459i
$638$	−1.39310	+	4.74447i	−0.0551534	+	0.187835i
$639$	12.8795	+	20.4827i	0.509504	+	0.810284i
$640$	2.04503	+	0.904345i	0.0808370	+	0.0357474i
$641$	−15.0340	+	32.9199i	−0.593808	+	1.30026i	0.339305	+	0.940676i	$0.389808\pi$
$641$	−15.0340	+	32.9199i	−0.593808	+	1.30026i	−0.933113	+	0.359582i	$0.882919\pi$
$642$	17.7877	+	0.0878207i	0.702025	+	0.00346601i
$643$	−21.0704			−0.830935			−0.415468	−	0.909608i	$-0.636382\pi$
$643$	−21.0704			−0.830935			−0.415468	+	0.909608i	$0.636382\pi$
$644$	14.8511	+	4.98138i	0.585213	+	0.196294i
$645$	23.7179	+	26.9824i	0.933893	+	1.06243i
$646$	1.45335	+	10.1082i	0.0571811	+	0.397703i
$647$	−11.0528	+	24.2022i	−0.434530	+	0.951487i	0.558040	+	0.829814i	$0.311553\pi$
$647$	−11.0528	+	24.2022i	−0.434530	+	0.951487i	−0.992570	+	0.121674i	$0.961174\pi$
$648$	8.58368	+	2.70562i	0.337199	+	0.106287i
$649$	−4.71729	−	4.08755i	−0.185170	−	0.160450i
$650$	7.32778	+	0.874100i	0.287419	+	0.0342850i
$651$	−20.1024	+	9.06080i	−0.787877	+	0.355121i
$652$	−13.3588	+	6.10077i	−0.523172	+	0.238925i
$653$	−24.4803	−	28.2518i	−0.957989	−	1.10558i	−0.994341	−	0.106239i	$-0.966119\pi$
$653$	−24.4803	−	28.2518i	−0.957989	−	1.10558i	0.0363521	−	0.999339i	$-0.488426\pi$
$654$	−13.9447	+	15.9334i	−0.545281	+	0.623046i
$655$	−19.2656	−	21.7003i	−0.752769	−	0.847900i
$656$	0.314519	+	0.0452210i	0.0122799	+	0.00176558i
$657$	6.55906	−	5.57103i	0.255893	−	0.217346i
$658$	−0.633155	−	0.730700i	−0.0246830	−	0.0284857i
$659$	3.52585	+	7.72053i	0.137347	+	0.300749i	0.965790	−	0.259325i	$-0.0835000\pi$
$659$	3.52585	+	7.72053i	0.137347	+	0.300749i	−0.828443	+	0.560074i	$0.810773\pi$
$660$	2.70810	+	0.774327i	0.105413	+	0.0301406i
$661$	−14.1762	+	48.2796i	−0.551389	+	1.87786i	−0.0781093	+	0.996945i	$0.524888\pi$
$661$	−14.1762	+	48.2796i	−0.551389	+	1.87786i	−0.473279	+	0.880912i	$0.656930\pi$
$662$	20.2113	−	23.3251i	0.785534	−	0.906554i
$663$	4.38512	−	0.608403i	0.170304	−	0.0236284i
$664$	−14.4253	−	6.58779i	−0.559809	−	0.255656i
$665$	36.5091	+	22.8467i	1.41576	+	0.885958i
$666$	31.9274	+	9.71817i	1.23716	+	0.376572i
$667$	−32.4293	+	3.41008i	−1.25567	+	0.132039i
$668$	4.29958			0.166356
$669$	−6.02559	−	0.0297493i	−0.232963	−	0.00115017i
$670$	0.822039	−	0.387438i	0.0317581	−	0.0149680i
$671$	0.951655	+	3.24104i	0.0367382	+	0.125119i
$672$	4.29370	−	3.68356i	0.165633	−	0.142096i
$673$	−10.3983	+	35.4134i	−0.400825	+	1.36509i	0.473948	+	0.880553i	$0.342828\pi$
$673$	−10.3983	+	35.4134i	−0.400825	+	1.36509i	−0.874773	+	0.484532i	$0.838990\pi$
$674$	−13.0322	+	8.37530i	−0.501982	+	0.322605i
$675$	−25.6810	+	3.93551i	−0.988461	+	0.151478i
$676$	−7.08663	−	8.17841i	−0.272563	−	0.314554i
$677$	8.84282	−	13.7597i	0.339857	−	0.528828i	−0.628691	−	0.777656i	$-0.716409\pi$
$677$	8.84282	−	13.7597i	0.339857	−	0.528828i	0.968548	+	0.248827i	$0.0800452\pi$
$678$	15.6817	+	4.68880i	0.602254	+	0.180072i
$679$	−6.20832	+	43.1798i	−0.238253	+	1.65709i
$680$	−3.70209	+	1.13561i	−0.141969	+	0.0435488i
$681$	29.6086	−	18.8224i	1.13460	−	0.721275i
$682$	1.17753	+	2.57842i	0.0450898	+	0.0987330i
$683$	11.3707	−	7.30751i	0.435088	−	0.279614i	−0.304707	−	0.952446i	$-0.598559\pi$
$683$	11.3707	−	7.30751i	0.435088	−	0.279614i	0.739795	+	0.672832i	$0.234922\pi$
$684$	9.71091	−	14.7874i	0.371306	−	0.565409i
$685$	0.810341	+	5.19161i	0.0309615	+	0.198361i
$686$	−10.4417	+	3.06595i	−0.398664	+	0.117058i
$687$	13.7132	+	8.90894i	0.523193	+	0.339897i
$688$	−1.32008	−	9.18133i	−0.0503274	−	0.350035i
$689$	3.63024			0.138301
$690$	2.07356	+	18.4581i	0.0789389	+	0.702687i
$691$	22.9769			0.874082			0.437041	−	0.899442i	$-0.356027\pi$
$691$	22.9769			0.874082			0.437041	+	0.899442i	$0.356027\pi$
$692$	−2.27457	−	15.8200i	−0.0864661	−	0.601385i
$693$	4.71953	−	5.33919i	0.179280	−	0.202819i
$694$	23.1405	−	6.79466i	0.878401	−	0.257922i
$695$	−2.02611	+	0.316248i	−0.0768547	+	0.0119960i
$696$	−4.94503	+	10.6881i	−0.187441	+	0.405133i
$697$	−0.462921	+	0.297501i	−0.0175344	+	0.0112687i
$698$	−2.09425	−	4.58577i	−0.0792686	−	0.173574i
$699$	−11.1184	−	17.4898i	−0.420537	−	0.661526i
$700$	−6.42461	+	15.0143i	−0.242827	+	0.567487i
$701$	−2.66198	+	18.5145i	−0.100542	+	0.699283i	0.875741	+	0.482782i	$0.160374\pi$
$701$	−2.66198	+	18.5145i	−0.100542	+	0.699283i	−0.976282	+	0.216501i	$0.930536\pi$
$702$	−6.38966	−	4.24141i	−0.241162	−	0.160082i
$703$	35.4666	−	55.1872i	1.33765	−	2.08142i
$704$	−0.476248	−	0.549619i	−0.0179493	−	0.0207146i
$705$	0.468843	−	1.04622i	0.0176577	−	0.0394029i
$706$	−13.2875	+	8.53936i	−0.500082	+	0.321383i
$707$	5.13800	−	17.4984i	0.193234	−	0.658095i
$708$	−9.67950	−	11.2828i	−0.363778	−	0.424034i
$709$	−7.26287	−	24.7351i	−0.272763	−	0.928945i	−0.975960	−	0.217950i	$-0.930063\pi$
$709$	−7.26287	−	24.7351i	−0.272763	−	0.928945i	0.703197	−	0.710995i	$-0.251755\pi$
$710$	7.68863	+	16.3132i	0.288549	+	0.612223i
$711$	9.79904	+	1.50779i	0.367493	+	0.0565466i
$712$	8.57534			0.321375
$713$	−12.7693	+	13.6513i	−0.478214	+	0.511244i
$714$	−1.44213	+	9.69033i	−0.0539702	+	0.362652i
$715$	−2.03461	−	1.27322i	−0.0760903	−	0.0476159i
$716$	−16.0793	−	7.34317i	−0.600912	−	0.274427i
$717$	−4.91144	−	35.3996i	−0.183421	−	1.32202i
$718$	−1.03639	+	1.19605i	−0.0386776	+	0.0446364i
$719$	9.22894	−	31.4309i	0.344181	−	1.17217i	−0.587599	−	0.809152i	$-0.699927\pi$
$719$	9.22894	−	31.4309i	0.344181	−	1.17217i	0.931781	−	0.363022i	$-0.118255\pi$
$720$	6.10801	+	2.77348i	0.227632	+	0.103362i
$721$	24.8535	+	54.4216i	0.925593	+	2.02677i
$722$	−10.3299	−	11.9214i	−0.384439	−	0.443667i
$723$	−10.7093	+	12.2366i	−0.398282	+	0.455083i
$724$	20.0672	+	2.88522i	0.745790	+	0.107228i
$725$	−0.818380	−	33.9864i	−0.0303939	−	1.26222i
$726$	13.6478	+	11.9444i	0.506519	+	0.443298i
$727$	7.08273	+	8.17391i	0.262684	+	0.303154i	0.871735	−	0.489977i	$-0.162995\pi$
$727$	7.08273	+	8.17391i	0.262684	+	0.303154i	−0.609051	+	0.793131i	$0.708450\pi$
$728$	−4.38512	+	2.00262i	−0.162523	+	0.0742219i
$729$	25.6696	+	8.37074i	0.950728	+	0.310028i
$730$	5.35391	−	3.53253i	0.198157	−	0.130745i
$731$	12.1399	+	10.5193i	0.449012	+	0.389071i
$732$	1.10558	+	7.96854i	0.0408633	+	0.294526i
$733$	−1.90844	+	4.17890i	−0.0704898	+	0.154351i	−0.941597	−	0.336742i	$-0.890675\pi$
$733$	−1.90844	+	4.17890i	−0.0704898	+	0.154351i	0.871107	+	0.491093i	$0.163402\pi$
$734$	4.85103	+	33.7397i	0.179055	+	1.24535i
$735$	9.37945	+	10.6704i	0.345966	+	0.393585i
$736$	2.15669	−	4.28354i	0.0794965	−	0.157893i
$737$	−0.295564			−0.0108872
$738$	0.942171	+	0.144973i	0.0346818	+	0.00533653i
$739$	−6.55482	+	14.3531i	−0.241123	+	0.527986i	−0.991043	−	0.133543i	$-0.957365\pi$
$739$	−6.55482	+	14.3531i	−0.241123	+	0.527986i	0.749920	+	0.661529i	$0.230092\pi$
$740$	22.7501	+	10.0604i	0.836309	+	0.369829i
$741$	−11.4416	+	9.81572i	−0.420318	+	0.360589i
$742$	−2.26332	+	7.70816i	−0.0830891	+	0.282976i
$743$	11.1301	+	17.3188i	0.408324	+	0.635364i	0.983126	−	0.182928i	$-0.0585575\pi$
$743$	11.1301	+	17.3188i	0.408324	+	0.635364i	−0.574802	+	0.818292i	$0.694921\pi$
$744$	1.86996	+	6.48681i	0.0685561	+	0.237818i
$745$	0.274316	+	22.7874i	0.0100502	+	0.834867i
$746$	−9.62282	−	6.18421i	−0.352316	−	0.226420i
$747$	−43.0785	−	20.1897i	−1.57616	−	0.738704i
$748$	1.24661	+	0.179236i	0.0455806	+	0.00655350i
$749$	18.1351	−	28.2187i	0.662640	−	1.03109i
$750$	−19.3555	+	0.603609i	−0.706763	+	0.0220407i
$751$	−3.21312	+	1.46738i	−0.117249	+	0.0535456i	−0.473176	−	0.880968i	$-0.656892\pi$
$751$	−3.21312	+	1.46738i	−0.117249	+	0.0535456i	0.355927	+	0.934514i	$0.384165\pi$
$752$	−0.249025	+	0.160039i	−0.00908101	+	0.00583601i
$753$	38.8281	+	17.9644i	1.41497	+	0.654659i
$754$	6.57175	−	7.58421i	0.239329	−	0.276201i
$755$	43.1838	+	19.0965i	1.57162	+	0.694994i
$756$	12.9896	−	10.9230i	0.472427	−	0.397264i
$757$	−3.07665	−	21.3986i	−0.111823	−	0.777745i	−0.966145	−	0.258000i	$-0.916936\pi$
$757$	−3.07665	−	21.3986i	−0.111823	−	0.777745i	0.854322	−	0.519744i	$-0.173973\pi$
$758$			26.7233i			0.970633i
$759$	1.94935	−	5.71784i	0.0707569	−	0.207544i
$760$	8.51442	−	10.0685i	0.308851	−	0.365225i
$761$	20.1120	−	2.89166i	0.729058	−	0.104823i	0.232217	−	0.972664i	$-0.425402\pi$
$761$	20.1120	−	2.89166i	0.729058	−	0.104823i	0.496841	+	0.867841i	$0.334493\pi$
$762$	−16.1489	−	10.4913i	−0.585013	−	0.380059i
$763$	11.2492	+	38.3111i	0.407247	+	1.38695i
$764$	−0.312184	+	0.360280i	−0.0112944	+	0.0130345i
$765$	−11.1394	+	3.29701i	−0.402745	+	0.119204i
$766$	6.98678	+	10.8716i	0.252443	+	0.392808i
$767$	5.26239	+	11.5230i	0.190014	+	0.416073i
$768$	−0.929212	−	1.46170i	−0.0335301	−	0.0527445i
$769$	0.712759	−	1.10907i	0.0257027	−	0.0399942i	−0.828164	−	0.560485i	$-0.810615\pi$
$769$	0.712759	−	1.10907i	0.0257027	−	0.0399942i	0.853867	+	0.520491i	$0.174251\pi$
$770$	3.97197	−	3.52633i	0.143140	−	0.127080i
$771$	−1.00496	+	3.36111i	−0.0361929	+	0.121048i
$772$	1.78958	−	2.78465i	0.0644085	−	0.100222i
$773$	3.24542	−	2.81217i	0.116729	−	0.101147i	−0.594540	−	0.804066i	$-0.702666\pi$
$773$	3.24542	−	2.81217i	0.116729	−	0.101147i	0.711270	+	0.702919i	$0.248120\pi$
$774$	−3.68806	−	27.5818i	−0.132565	−	0.991406i
$775$	−13.1130	−	14.4168i	−0.471033	−	0.517867i
$776$	12.8151	+	3.76284i	0.460034	+	0.135078i
$777$	47.7655	−	40.9779i	1.71358	−	1.47008i
$778$	−25.7642	+	7.56506i	−0.923692	+	0.271220i
$779$	0.778396	−	1.70445i	0.0278889	−	0.0610682i
$780$	−4.34657	−	3.71262i	−0.155632	−	0.132933i
$781$		−	5.86540i		−	0.209880i
$782$	2.03519	+	8.05205i	0.0727782	+	0.287941i
$783$	−15.1510	+	31.9164i	−0.541452	+	1.14060i
$784$	−0.522035	−	3.63083i	−0.0186441	−	0.129673i
$785$	−32.4617	+	15.2996i	−1.15861	+	0.546067i
$786$	3.08900	+	22.2643i	0.110181	+	0.794140i
$787$	2.36241	−	2.72636i	0.0842107	−	0.0971843i	−0.712080	−	0.702098i	$-0.752247\pi$
$787$	2.36241	−	2.72636i	0.0842107	−	0.0971843i	0.796291	+	0.604914i	$0.206792\pi$
$788$	2.46539	+	0.723903i	0.0878258	+	0.0257880i
$789$	−14.2944	−	31.7139i	−0.508895	−	1.12904i
$790$	7.11494	+	1.99643i	0.253138	+	0.0710298i
$791$	23.3265	−	20.2126i	0.829396	−	0.718676i
$792$	−1.41239	−	1.66288i	−0.0501872	−	0.0590880i
$793$	0.975617	−	6.78556i	0.0346452	−	0.240962i
$794$	−23.5649	−	3.38812i	−0.836288	−	0.120240i
$795$	−9.41916	+	1.42260i	−0.334063	+	0.0504545i
$796$	−6.81012	+	5.90100i	−0.241378	+	0.209156i
$797$	−16.0810	+	7.34397i	−0.569620	+	0.260137i	−0.679337	−	0.733826i	$-0.737733\pi$
$797$	−16.0810	+	7.34397i	−0.569620	+	0.260137i	0.109717	+	0.993963i	$0.465005\pi$
$798$	−13.7085	−	30.4139i	−0.485276	−	1.07664i
$799$	0.144425	−	0.491867i	0.00510940	−	0.0174010i
$800$	4.27012	+	2.60116i	0.150972	+	0.0919651i
$801$	25.7248	+	0.254020i	0.908940	+	0.00897537i
$802$	−13.7695	+	30.1509i	−0.486216	+	1.06467i
$803$	−2.06493	+	0.296892i	−0.0728697	+	0.0104771i
$804$	−0.696259	−	0.103618i	−0.0245552	−	0.00365433i
$805$	31.4721	+	15.3736i	1.10925	+	0.541848i
$806$		−	5.75275i		−	0.202632i
$807$	−25.5744	−	0.126265i	−0.900260	−	0.00444472i
$808$	−5.07899	−	2.31950i	−0.178678	−	0.0815997i
$809$	9.54583	+	32.5101i	0.335613	+	1.14299i	0.938532	+	0.345192i	$0.112186\pi$
$809$	9.54583	+	32.5101i	0.335613	+	1.14299i	−0.602919	+	0.797803i	$0.705996\pi$
$810$	18.2410	+	8.50097i	0.640923	+	0.298694i
$811$	−33.3775	−	9.80052i	−1.17204	−	0.344143i	−0.362942	−	0.931812i	$-0.618228\pi$
$811$	−33.3775	−	9.80052i	−1.17204	−	0.344143i	−0.809101	+	0.587669i	$0.800046\pi$
$812$	12.0065	+	18.6824i	0.421344	+	0.655625i
$813$	4.30153	+	14.9218i	0.150861	+	0.523331i
$814$	−5.29804	−	6.11427i	−0.185696	−	0.214305i
$815$	−31.3950	+	9.63037i	−1.09972	+	0.337337i
$816$	2.87380	+	0.859259i	0.100603	+	0.0300801i
$817$	−54.1420	−	7.78445i	−1.89419	−	0.272343i
$818$	−0.549515	−	0.353152i	−0.0192133	−	0.0123477i
$819$	−13.2140	+	5.87766i	−0.461736	+	0.205382i
$820$	0.684097	+	0.191955i	0.0238897	+	0.00670337i
$821$	8.99520	+	13.9968i	0.313935	+	0.488492i	0.961984	−	0.273107i	$-0.0880512\pi$
$821$	8.99520	+	13.9968i	0.313935	+	0.488492i	−0.648049	+	0.761599i	$0.724415\pi$
$822$	1.70904	−	3.69390i	0.0596096	−	0.128840i
$823$	15.7420	+	13.6405i	0.548732	+	0.475479i	0.884548	−	0.466449i	$-0.154467\pi$
$823$	15.7420	+	13.6405i	0.548732	+	0.475479i	−0.335817	+	0.941927i	$0.609012\pi$
$824$	17.5753	−	5.16057i	0.612264	−	0.179777i
$825$	5.77804	+	2.50624i	0.201166	+	0.0872562i
$826$	−27.7480	+	3.98957i	−0.965478	+	0.138815i
$827$		−	28.5676i		−	0.993394i	−0.867924	−	0.496697i	$-0.834546\pi$
$827$		−	28.5676i		−	0.993394i	0.867924	−	0.496697i	$-0.165454\pi$
$828$	6.59663	−	12.7861i	0.229249	−	0.444348i
$829$	−13.7720			−0.478322			−0.239161	−	0.970980i	$-0.576872\pi$
$829$	−13.7720			−0.478322			−0.239161	+	0.970980i	$0.576872\pi$
$830$	−30.0597	−	18.8108i	−1.04339	−	0.652934i
$831$	−47.4442	−	30.8226i	−1.64582	−	1.06922i
$832$	0.415822	+	1.41616i	0.0144160	+	0.0490965i
$833$	4.80084	+	4.15995i	0.166339	+	0.144134i
$834$	1.44160	+	0.666979i	0.0499186	+	0.0230956i
$835$	9.53208	+	1.25359i	0.329871	+	0.0433822i
$836$	−3.90102	+	1.78154i	−0.134920	+	0.0616157i
$837$	5.41746	+	19.5149i	0.187255	+	0.674532i
$838$	21.8798	+	14.0613i	0.755827	+	0.485740i
$839$	−2.77281	+	19.2853i	−0.0957281	+	0.665804i	0.884296	+	0.466926i	$0.154639\pi$
$839$	−2.77281	+	19.2853i	−0.0957281	+	0.665804i	−0.980024	+	0.198877i	$0.936270\pi$
$840$	10.5930	−	6.91450i	0.365494	−	0.238573i
$841$	−14.4947	−	9.31519i	−0.499818	−	0.321214i
$842$	2.06958	−	1.79331i	0.0713226	−	0.0618014i
$843$	−2.37395	−	8.23513i	−0.0817633	−	0.283633i
$844$	13.5334	−	8.69736i	0.465837	−	0.299376i
$845$	−13.3264	−	20.1975i	−0.458442	−	0.694816i
$846$	−0.751780	+	0.472716i	−0.0258467	+	0.0162523i
$847$	32.8155	−	9.63551i	1.12755	−	0.331080i
$848$	2.23733	+	1.02175i	0.0768302	+	0.0350872i
$849$	0.0792487	−	16.0515i	0.00271981	−	0.550886i
$850$	−8.53856	+	1.43824i	−0.292870	+	0.0493314i
$851$	23.9922	−	47.6525i	0.822440	−	1.63351i
$852$	2.05628	−	13.8171i	0.0704469	−	0.473367i
$853$	−37.9732	+	5.45972i	−1.30018	+	0.186937i	−0.757407	−	0.652944i	$-0.773534\pi$
$853$	−37.9732	+	5.45972i	−1.30018	+	0.186937i	−0.542771	+	0.839881i	$0.682625\pi$
$854$	13.7997	+	6.30210i	0.472215	+	0.215654i
$855$	25.8403	−	29.9520i	0.883719	−	1.02434i
$856$	−7.76145	−	6.72534i	−0.265281	−	0.229867i
$857$	−1.10896	−	0.325621i	−0.0378815	−	0.0111230i	0.262737	−	0.964868i	$-0.415375\pi$
$857$	−1.10896	−	0.325621i	−0.0378815	−	0.0111230i	−0.300618	+	0.953745i	$0.597193\pi$
$858$	0.763962	+	1.69494i	0.0260812	+	0.0578642i
$859$	1.84217	+	4.03379i	0.0628541	+	0.137631i	0.938452	−	0.345409i	$-0.112260\pi$
$859$	1.84217	+	4.03379i	0.0628541	+	0.137631i	−0.875598	+	0.483040i	$0.839533\pi$
$860$	−0.249666	−	20.7397i	−0.00851353	−	0.707218i
$861$	1.18388	−	1.35271i	0.0403464	−	0.0461004i
$862$	−0.526317	+	3.66062i	−0.0179264	+	0.124681i
$863$	−8.00726	+	55.6917i	−0.272570	+	1.89577i	0.148782	+	0.988870i	$0.452465\pi$
$863$	−8.00726	+	55.6917i	−0.272570	+	1.89577i	−0.421352	+	0.906897i	$0.638444\pi$
$864$	−2.74420	−	4.41241i	−0.0933596	−	0.150113i
$865$	−0.430188	−	35.7357i	−0.0146268	−	1.21505i
$866$	11.5628	+	25.3190i	0.392919	+	0.860373i
$867$	22.1084	−	9.96495i	0.750841	−	0.338428i
$868$	12.2149	+	3.58663i	0.414602	+	0.121738i
$869$	−1.81638	−	1.57390i	−0.0616163	−	0.0533908i
$870$	−14.0793	+	22.2536i	−0.477332	+	0.754468i
$871$	0.545637	+	0.249184i	0.0184882	+	0.00844328i
$872$	12.1003	−	1.73975i	0.409767	−	0.0589155i
$873$	38.3318	+	11.6676i	1.29734	+	0.394888i
$874$	−20.6536	−	19.3193i	−0.698620	−	0.653484i
$875$	−18.6208	+	31.4132i	−0.629497	+	1.06196i
$876$	−4.96843	−	0.0245299i	−0.167868	−	0.000828788i
$877$	36.2487	+	16.5542i	1.22403	+	0.558996i	0.919343	−	0.393456i	$-0.128721\pi$
$877$	36.2487	+	16.5542i	1.22403	+	0.558996i	0.304687	+	0.952452i	$0.401448\pi$
$878$	−27.9254	+	8.19962i	−0.942435	+	0.276724i
$879$	−25.7293	−	29.9911i	−0.867827	−	1.01157i
$880$	−0.895584	−	1.35735i	−0.0301901	−	0.0457562i
$881$	−34.2315	+	21.9993i	−1.15329	+	0.741174i	−0.970291	−	0.241940i	$-0.922216\pi$
$881$	−34.2315	+	21.9993i	−1.15329	+	0.741174i	−0.182997	+	0.983113i	$0.558580\pi$
$882$	−1.45848	−	10.9074i	−0.0491094	−	0.367272i
$883$	5.05124	−	4.37693i	0.169988	−	0.147295i	−0.565712	−	0.824603i	$-0.691399\pi$
$883$	5.05124	−	4.37693i	0.169988	−	0.147295i	0.735700	+	0.677307i	$0.236853\pi$
$884$	−2.15024	−	1.38188i	−0.0723205	−	0.0464776i
$885$	−18.1696	−	27.8359i	−0.610765	−	0.935694i
$886$	4.76332	−	33.1296i	0.160027	−	1.11301i
$887$	−43.5714	−	28.0016i	−1.46298	−	0.940203i	−0.998507	−	0.0546172i	$-0.982606\pi$
$887$	−43.5714	−	28.0016i	−1.46298	−	0.940203i	−0.464476	−	0.885585i	$-0.653757\pi$
$888$	−10.3371	−	16.2607i	−0.346889	−	0.545675i
$889$	−33.0332	+	15.0858i	−1.10790	+	0.505961i
$890$	19.0113	+	2.50023i	0.637262	+	0.0838080i
$891$	−4.18771	−	5.03025i	−0.140294	−	0.168520i
$892$	2.62919	+	2.27821i	0.0880319	+	0.0762801i
$893$	0.491793	+	1.67489i	0.0164572	+	0.0560481i
$894$	9.61678	−	14.8028i	0.321633	−	0.495080i
$895$	−33.5065	−	20.9677i	−1.12000	−	0.700874i
$896$	−3.26622			−0.109117
$897$	−8.41927	+	8.91217i	−0.281111	+	0.297569i
$898$		−	38.4423i		−	1.28284i
$899$	−26.2315	+	3.77152i	−0.874869	+	0.125787i
$900$	12.7327	+	7.92960i	0.424423	+	0.264320i
$901$	−4.08692	+	1.20003i	−0.136155	+	0.0399787i
$902$	−0.174643	−	0.151329i	−0.00581498	−	0.00503871i
$903$	−47.6250	−	22.0344i	−1.58486	−	0.733259i
$904$	−5.10900	−	7.94976i	−0.169923	−	0.264405i
$905$	43.6472	+	12.2473i	1.45088	+	0.407113i
$906$	−19.6216	−	30.8659i	−0.651885	−	1.02545i
$907$	39.9731	+	25.6892i	1.32729	+	0.852994i	0.995896	−	0.0905000i	$-0.0288465\pi$
$907$	39.9731	+	25.6892i	1.32729	+	0.852994i	0.331389	+	0.943494i	$0.392483\pi$
$908$	−20.0501	−	2.88277i	−0.665385	−	0.0956680i
$909$	−15.1675	−	7.10861i	−0.503075	−	0.235778i
$910$	−10.3056	+	3.16123i	−0.341627	+	0.104794i
$911$	−27.2784	−	31.4810i	−0.903774	−	1.04301i	−0.998869	−	0.0475426i	$-0.984861\pi$
$911$	−27.2784	−	31.4810i	−0.903774	−	1.04301i	0.0950953	−	0.995468i	$-0.469684\pi$
$912$	−9.81420	+	2.82915i	−0.324981	+	0.0936826i
$913$	6.23520	+	9.70217i	0.206355	+	0.321095i
$914$	−7.16287	−	2.10321i	−0.236927	−	0.0695679i
$915$	0.127726	+	17.9884i	0.00422251	+	0.594679i
$916$	−2.65996	−	9.05900i	−0.0878876	−	0.299318i
$917$	38.5566	+	17.6082i	1.27325	+	0.581474i
$918$	8.59554	+	2.66278i	0.283695	+	0.0878848i
$919$			1.30308i			0.0429847i	0.999769	+	0.0214923i	$0.00684175\pi$
$919$			1.30308i			0.0429847i	−0.999769	+	0.0214923i	$0.993158\pi$
$920$	6.03024	−	8.86771i	0.198811	−	0.292360i
$921$	4.50050	−	30.2410i	0.148296	−	0.996475i
$922$	22.8688	−	3.28804i	0.753145	−	0.108286i
$923$	−4.94500	+	10.8280i	−0.162767	+	0.356409i
$924$	−4.07520	+	0.565405i	−0.134064	+	0.0186004i
$925$	47.5032	+	28.9368i	1.56190	+	0.951436i
$926$	2.93073	−	9.98116i	0.0963098	−	0.328001i
$927$	52.8761	−	14.9603i	1.73668	−	0.491362i
$928$	6.18482	−	2.82451i	0.203027	−	0.0927192i
$929$	8.19025	−	7.09689i	0.268713	−	0.232841i	−0.510072	−	0.860131i	$-0.670381\pi$
$929$	8.19025	−	7.09689i	0.268713	−	0.232841i	0.778786	+	0.627290i	$0.215836\pi$
$930$	2.25437	+	14.9263i	0.0739236	+	0.489453i
$931$	−21.4109	−	3.07842i	−0.701714	−	0.100891i
$932$	−1.70286	+	11.8436i	−0.0557789	+	0.387951i
$933$	−25.8816	+	29.5727i	−0.847325	+	0.968165i
$934$	−23.0023	+	19.9316i	−0.752657	+	0.652181i
$935$	2.71145	+	0.760824i	0.0886739	+	0.0248816i
$936$	1.20546	+	4.26059i	0.0394016	+	0.139262i
$937$	−19.7668	−	5.80405i	−0.645752	−	0.189610i	−0.0575740	−	0.998341i	$-0.518337\pi$
$937$	−19.7668	−	5.80405i	−0.645752	−	0.189610i	−0.588178	+	0.808731i	$0.700155\pi$
$938$	−0.869283	+	1.00321i	−0.0283831	+	0.0327558i
$939$	17.8211	−	2.47254i	0.581569	−	0.0806884i
$940$	−0.598744	+	0.282196i	−0.0195289	+	0.00920423i
$941$	5.45299	+	37.9264i	0.177762	+	1.23636i	0.861925	+	0.507035i	$0.169259\pi$
$941$	5.45299	+	37.9264i	0.177762	+	1.23636i	−0.684163	+	0.729329i	$0.739832\pi$
$942$	27.4947	+	4.09180i	0.895827	+	0.133318i
$943$	0.484612	−	1.44478i	0.0157811	−	0.0470485i
$944$			8.58283i			0.279347i
$945$	31.9824	−	20.4287i	1.04039	−	0.664545i
$946$	−2.80230	+	6.13619i	−0.0911107	+	0.199505i
$947$	14.1055	−	4.14174i	0.458366	−	0.134588i	−0.0443948	−	0.999014i	$-0.514136\pi$
$947$	14.1055	−	4.14174i	0.458366	−	0.134588i	0.502760	+	0.864426i	$0.332318\pi$
$948$	−3.72706	−	4.34441i	−0.121049	−	0.141100i
$949$	4.06234	+	1.19281i	0.131869	+	0.0387203i
$950$	21.8119	−	19.8393i	0.707671	−	0.643671i
$951$	−1.46294	−	5.07487i	−0.0474391	−	0.164564i
$952$	4.27477	−	3.70411i	0.138546	−	0.120051i
$953$	22.3031	−	34.7043i	0.722467	−	1.12418i	−0.264675	−	0.964338i	$-0.585265\pi$
$953$	22.3031	−	34.7043i	0.722467	−	1.12418i	0.987142	−	0.159843i	$-0.0510989\pi$
$954$	6.68139	+	3.13139i	0.216318	+	0.101382i
$955$	−0.797149	+	0.707712i	−0.0257951	+	0.0229010i
$956$	−11.1554	+	17.3582i	−0.360793	+	0.561405i
$957$	7.22776	−	4.59473i	0.233640	−	0.148527i
$958$	−4.91654	−	10.7657i	−0.158846	−	0.347824i
$959$	−4.14952	−	6.45678i	−0.133995	−	0.208500i
$960$	−1.63387	−	3.51148i	−0.0527329	−	0.113332i
$961$	10.3522	−	11.9470i	0.333941	−	0.385388i
$962$	4.62584	+	15.7542i	0.149143	+	0.507934i
$963$	−23.0840	−	20.4049i	−0.743871	−	0.657540i
$964$	9.29277	−	1.33610i	0.299300	−	0.0430329i
$965$	4.77936	−	5.65173i	0.153853	−	0.181936i
$966$	−13.6743	−	23.4332i	−0.439964	−	0.753952i
$967$			36.3789i			1.16987i	0.811082	+	0.584933i	$0.198879\pi$
$967$			36.3789i			1.16987i	−0.811082	+	0.584933i	$0.801121\pi$
$968$	−1.49019	−	10.3645i	−0.0478966	−	0.333128i
$969$	9.63621	−	14.8327i	0.309560	−	0.476495i
$970$	27.3136	+	12.0785i	0.876987	+	0.387817i
$971$	−16.7981	+	19.3861i	−0.539078	+	0.622130i	−0.958303	−	0.285753i	$-0.907756\pi$
$971$	−16.7981	+	19.3861i	−0.539078	+	0.622130i	0.419225	+	0.907882i	$0.362302\pi$
$972$	−8.10150	−	13.3179i	−0.259856	−	0.427171i
$973$	2.51986	−	1.61942i	0.0807831	−	0.0519161i
$974$	−1.28865	+	0.588506i	−0.0412909	+	0.0188569i
$975$	−8.55381	−	9.49810i	−0.273941	−	0.304182i
$976$	2.51112	−	3.90738i	0.0803789	−	0.125072i
$977$	−22.1530	−	3.18512i	−0.708738	−	0.101901i	−0.221487	−	0.975163i	$-0.571091\pi$
$977$	−22.1530	−	3.18512i	−0.708738	−	0.101901i	−0.487251	+	0.873262i	$0.662000\pi$
$978$	24.3708	+	7.28680i	0.779292	+	0.233006i
$979$	−5.24641	−	3.37166i	−0.167676	−	0.107759i
$980$	−0.0987323	−	8.20168i	−0.00315389	−	0.261993i
$981$	36.3505	−	4.86057i	1.16058	−	0.155186i
$982$	7.67705	+	11.9457i	0.244985	+	0.381204i
$983$	−1.72652	+	5.88000i	−0.0550676	+	0.187543i	−0.982434	−	0.186612i	$-0.940249\pi$
$983$	−1.72652	+	5.88000i	−0.0550676	+	0.187543i	0.927366	+	0.374155i	$0.122067\pi$
$984$	−0.358354	−	0.417712i	−0.0114239	−	0.0133162i
$985$	5.25465	+	2.32369i	0.167427	+	0.0740388i
$986$	−4.89141	+	10.7107i	−0.155774	+	0.341098i
$987$	−0.00826786	+	1.67462i	−0.000263169	+	0.0533038i
$988$	8.70361			0.276899
$989$	−44.4527	−	1.69137i	−1.41352	−	0.0537824i
$990$	−2.64641	−	4.09838i	−0.0841085	−	0.130255i
$991$	2.14252	+	14.9016i	0.0680595	+	0.473364i	0.995137	+	0.0984958i	$0.0314031\pi$
$991$	2.14252	+	14.9016i	0.0680595	+	0.473364i	−0.927078	+	0.374869i	$0.877688\pi$
$992$	1.61915	−	3.54544i	0.0514080	−	0.112568i
$993$	−52.9499	+	7.34641i	−1.68031	+	0.233131i
$994$	−19.9084	−	17.2507i	−0.631456	−	0.547160i
$995$	−16.8184	+	11.0968i	−0.533179	+	0.351793i
$996$	11.2869	+	25.0413i	0.357639	+	0.793464i
$997$	−20.8895	+	9.53992i	−0.661577	+	0.302132i	−0.717762	−	0.696288i	$-0.754834\pi$
$997$	−20.8895	+	9.53992i	−0.661577	+	0.302132i	0.0561851	+	0.998420i	$0.482106\pi$
$998$	21.0864	+	24.3350i	0.667478	+	0.770310i
$999$	−30.5280	−	49.0861i	−0.965864	−	1.55301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.n.b.89.17	yes	240
3.2	odd	2		690.2.n.a.89.10	yes	240
5.4	even	2		690.2.n.a.89.8	✓	240
15.14	odd	2	inner	690.2.n.b.89.15	yes	240
23.15	odd	22	inner	690.2.n.b.659.15	yes	240
69.38	even	22		690.2.n.a.659.8	yes	240
115.84	odd	22		690.2.n.a.659.10	yes	240
345.314	even	22	inner	690.2.n.b.659.17	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.n.a.89.8	✓	240	5.4	even	2
690.2.n.a.89.10	yes	240	3.2	odd	2
690.2.n.a.659.8	yes	240	69.38	even	22
690.2.n.a.659.10	yes	240	115.84	odd	22
690.2.n.b.89.15	yes	240	15.14	odd	2	inner
690.2.n.b.89.17	yes	240	1.1	even	1	trivial
690.2.n.b.659.15	yes	240	23.15	odd	22	inner
690.2.n.b.659.17	yes	240	345.314	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.n (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(0.943600 - 1.45245i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.20932 + 0.344845i) q^{5} +(1.57196 + 0.727290i) q^{6} +(2.74772 - 1.76585i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-1.21924 - 2.74107i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(0.943600 - 1.45245i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.20932 + 0.344845i) q^{5} +(1.57196 + 0.727290i) q^{6} +(2.74772 - 1.76585i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-1.21924 - 2.74107i) q^{9} +(-0.655753 - 2.13775i) q^{10} +(-0.103499 + 0.719848i) q^{11} +(-0.496174 + 1.65946i) q^{12} +(0.797957 - 1.24165i) q^{13} +(2.13892 + 2.46844i) q^{14} +(-1.58384 + 3.53432i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-0.487896 + 1.66162i) q^{17} +(2.53965 - 1.59692i) q^{18} +(-1.66137 - 5.65810i) q^{19} +(2.02267 - 0.953313i) q^{20} +(0.0279304 - 5.65718i) q^{21} -0.727250 q^{22} +(-1.82495 - 4.43504i) q^{23} +(-1.71318 - 0.254958i) q^{24} +(4.76216 - 1.52374i) q^{25} +(1.34257 + 0.613130i) q^{26} +(-5.13175 - 0.815584i) q^{27} +(-2.13892 + 2.46844i) q^{28} +(1.91557 - 6.52384i) q^{29} +(-3.72375 - 1.06473i) q^{30} +(-1.61915 - 3.54544i) q^{31} +(0.654861 + 0.755750i) q^{32} +(0.947884 + 0.829575i) q^{33} +(-1.71414 - 0.246456i) q^{34} +(-5.46163 + 4.84886i) q^{35} +(1.94210 + 2.28654i) q^{36} +(7.28503 + 8.40738i) q^{37} +(5.36407 - 2.44969i) q^{38} +(-1.05048 - 2.33061i) q^{39} +(1.23147 + 1.86641i) q^{40} +(0.240142 + 0.208084i) q^{41} +(5.60358 - 0.777455i) q^{42} +(3.85328 - 8.43752i) q^{43} +(-0.103499 - 0.719848i) q^{44} +(3.63893 + 5.63544i) q^{45} +(4.13018 - 2.43755i) q^{46} -0.296017 q^{47} +(0.00855129 - 1.73203i) q^{48} +(1.52381 - 3.33668i) q^{49} +(2.18596 + 4.49684i) q^{50} +(1.95305 + 2.27655i) q^{51} +(-0.415822 + 1.41616i) q^{52} +(1.32976 + 2.06915i) q^{53} +(0.0769591 - 5.19558i) q^{54} +(-0.0195746 - 1.62606i) q^{55} +(-2.74772 - 1.76585i) q^{56} +(-9.78579 - 2.92592i) q^{57} +(6.73005 + 0.967635i) q^{58} +(-4.64023 + 7.22033i) q^{59} +(0.523950 - 3.83738i) q^{60} +(4.22497 - 1.92948i) q^{61} +(3.27893 - 2.10724i) q^{62} +(-8.19044 - 5.37868i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-1.33477 + 3.01836i) q^{65} +(-0.686233 + 1.05630i) q^{66} +(0.0578385 + 0.402276i) q^{67} -1.73177i q^{68} +(-8.16371 - 1.53424i) q^{69} +(-5.57677 - 4.71598i) q^{70} +(-7.98308 + 1.14779i) q^{71} +(-1.98687 + 2.24774i) q^{72} +(0.808166 + 2.75236i) q^{73} +(-7.28503 + 8.40738i) q^{74} +(2.28041 - 8.35462i) q^{75} +(3.18814 + 4.96084i) q^{76} +(0.986759 + 2.16070i) q^{77} +(2.15739 - 1.37147i) q^{78} +(-1.78670 + 2.78017i) q^{79} +(-1.67216 + 1.48455i) q^{80} +(-6.02691 + 6.68404i) q^{81} +(-0.171790 + 0.267311i) q^{82} +(11.9849 - 10.3850i) q^{83} +(1.56701 + 5.43590i) q^{84} +(0.504916 - 3.83929i) q^{85} +(8.90001 + 2.61328i) q^{86} +(-7.66804 - 8.93817i) q^{87} +(0.697792 - 0.204890i) q^{88} +(-3.56233 + 7.80041i) q^{89} +(-5.06021 + 4.40390i) q^{90} -4.82076i q^{91} +(3.00053 + 3.74124i) q^{92} +(-6.67742 - 0.993741i) q^{93} +(-0.0421276 - 0.293004i) q^{94} +(5.62165 + 11.9276i) q^{95} +(1.71562 - 0.238029i) q^{96} +(-8.74637 + 10.0938i) q^{97} +(3.51958 + 1.03344i) q^{98} +(2.09934 - 0.593970i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9}+O(q^{10}) \) 240 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 + 24 * q^8 - 6 * q^9	\( 240 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} + 24 q^{8} - 6 q^{9} + 9 q^{12} + 11 q^{15} - 24 q^{16} + 6 q^{18} + 4 q^{23} + 2 q^{24} - 12 q^{25} - 2 q^{27} + 22 q^{30} + 28 q^{31} + 24 q^{32} + 36 q^{35} - 6 q^{36} - 4 q^{46} - 104 q^{47} + 9 q^{48} + 70 q^{49} - 54 q^{50} - 9 q^{54} - 26 q^{55} + 44 q^{57} - 11 q^{60} + 44 q^{61} - 28 q^{62} + 121 q^{63} - 24 q^{64} - 44 q^{65} + 44 q^{66} - 102 q^{69} - 36 q^{70} - 16 q^{72} - 102 q^{75} - 8 q^{77} - 44 q^{79} + 74 q^{81} - 11 q^{84} + 22 q^{85} + 93 q^{87} + 4 q^{92} - 172 q^{93} + 16 q^{94} - 26 q^{95} + 2 q^{96} - 4 q^{98}+O(q^{100}) \) 240 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 + 24 * q^8 - 6 * q^9 + 9 * q^12 + 11 * q^15 - 24 * q^16 + 6 * q^18 + 4 * q^23 + 2 * q^24 - 12 * q^25 - 2 * q^27 + 22 * q^30 + 28 * q^31 + 24 * q^32 + 36 * q^35 - 6 * q^36 - 4 * q^46 - 104 * q^47 + 9 * q^48 + 70 * q^49 - 54 * q^50 - 9 * q^54 - 26 * q^55 + 44 * q^57 - 11 * q^60 + 44 * q^61 - 28 * q^62 + 121 * q^63 - 24 * q^64 - 44 * q^65 + 44 * q^66 - 102 * q^69 - 36 * q^70 - 16 * q^72 - 102 * q^75 - 8 * q^77 - 44 * q^79 + 74 * q^81 - 11 * q^84 + 22 * q^85 + 93 * q^87 + 4 * q^92 - 172 * q^93 + 16 * q^94 - 26 * q^95 + 2 * q^96 - 4 * q^98

Introduction

L-functions

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