LMFDB - Embedded newform 690.2.w.a.103.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			103.3
Character	$\chi$	$=$	690.103
Dual form			690.2.w.a.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.212565 + 0.977147i) q^{2} +(0.800541 - 0.599278i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-0.402846 + 2.19948i) q^{5} +(0.415415 + 0.909632i) q^{6} +(0.263933 - 3.69027i) q^{7} +(0.599278 - 0.800541i) q^{8} +(0.281733 - 0.959493i) q^{9} +O(q^{10})$	\(q+(-0.212565 + 0.977147i) q^{2} +(0.800541 - 0.599278i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-0.402846 + 2.19948i) q^{5} +(0.415415 + 0.909632i) q^{6} +(0.263933 - 3.69027i) q^{7} +(0.599278 - 0.800541i) q^{8} +(0.281733 - 0.959493i) q^{9} +(-2.06358 - 0.861173i) q^{10} +(1.86704 - 2.90517i) q^{11} +(-0.977147 + 0.212565i) q^{12} +(-2.66017 + 0.190259i) q^{13} +(3.54983 + 1.04232i) q^{14} +(0.995605 + 2.00219i) q^{15} +(0.654861 + 0.755750i) q^{16} +(0.334391 - 0.896538i) q^{17} +(0.877679 + 0.479249i) q^{18} +(2.69056 - 5.89150i) q^{19} +(1.28014 - 1.83337i) q^{20} +(-2.00021 - 3.11238i) q^{21} +(2.44191 + 2.44191i) q^{22} +(4.65964 + 1.13477i) q^{23} -1.00000i q^{24} +(-4.67543 - 1.77210i) q^{25} +(0.379549 - 2.63982i) q^{26} +(-0.349464 - 0.936950i) q^{27} +(-1.77308 + 3.24715i) q^{28} +(4.39413 - 2.00673i) q^{29} +(-2.16807 + 0.547255i) q^{30} +(0.556612 + 3.87132i) q^{31} +(-0.877679 + 0.479249i) q^{32} +(-0.246361 - 3.44458i) q^{33} +(0.804969 + 0.517322i) q^{34} +(8.01035 + 2.06713i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(-2.21545 - 4.05729i) q^{37} +(5.18494 + 3.88140i) q^{38} +(-2.01556 + 1.74649i) q^{39} +(1.51936 + 1.64059i) q^{40} +(-6.58528 + 1.93361i) q^{41} +(3.46643 - 1.29291i) q^{42} +(4.64732 + 6.20809i) q^{43} +(-2.90517 + 1.86704i) q^{44} +(1.99689 + 1.00619i) q^{45} +(-2.09932 + 4.31194i) q^{46} +(3.84111 - 3.84111i) q^{47} +(0.977147 + 0.212565i) q^{48} +(-6.61968 - 0.951767i) q^{49} +(2.72544 - 4.19189i) q^{50} +(-0.269581 - 0.918108i) q^{51} +(2.49881 + 0.932010i) q^{52} +(7.17587 + 0.513229i) q^{53} +(0.989821 - 0.142315i) q^{54} +(5.63773 + 5.27685i) q^{55} +(-2.79604 - 2.42279i) q^{56} +(-1.37674 - 6.32878i) q^{57} +(1.02683 + 4.72027i) q^{58} +(0.242559 + 0.210178i) q^{59} +(-0.0738933 - 2.23485i) q^{60} +(9.95159 - 1.43082i) q^{61} +(-3.90117 - 0.279017i) q^{62} +(-3.46643 - 1.29291i) q^{63} +(-0.281733 - 0.959493i) q^{64} +(0.653169 - 5.92764i) q^{65} +(3.41823 + 0.491467i) q^{66} +(-15.6752 - 3.40993i) q^{67} +(-0.676608 + 0.676608i) q^{68} +(4.41028 - 1.88399i) q^{69} +(-3.72261 + 7.38789i) q^{70} +(7.16418 - 4.60414i) q^{71} +(-0.599278 - 0.800541i) q^{72} +(-6.81334 + 2.54125i) q^{73} +(4.43549 - 1.30238i) q^{74} +(-4.80486 + 1.38324i) q^{75} +(-4.89484 + 4.24140i) q^{76} +(-10.2281 - 7.65665i) q^{77} +(-1.27814 - 2.34074i) q^{78} +(8.69958 - 10.0398i) q^{79} +(-1.92606 + 1.13590i) q^{80} +(-0.841254 - 0.540641i) q^{81} +(-0.489622 - 6.84581i) q^{82} +(-9.45789 + 5.16440i) q^{83} +(0.526522 + 3.66204i) q^{84} +(1.83721 + 1.09665i) q^{85} +(-7.05407 + 3.22149i) q^{86} +(2.31509 - 4.23977i) q^{87} +(-1.20683 - 3.23565i) q^{88} +(-1.02032 + 7.09650i) q^{89} +(-1.40767 + 1.73737i) q^{90} +9.86697i q^{91} +(-3.76716 - 2.96791i) q^{92} +(2.76559 + 2.76559i) q^{93} +(2.93684 + 4.56982i) q^{94} +(11.8744 + 8.29120i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(6.69511 + 3.65581i) q^{97} +(2.33713 - 6.26609i) q^{98} +(-2.26148 - 2.60989i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{6}+O(q^{10}) $ 240 * q - 24 * q^6	$ 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.212565	+	0.977147i	−0.150306	+	0.690947i
$2$	−0.212565	+	0.977147i	−0.150306	+	0.690947i
$3$	0.800541	−	0.599278i	0.462193	−	0.345993i
$3$	0.800541	−	0.599278i	0.462193	−	0.345993i
$4$	−0.909632	−	0.415415i	−0.454816	−	0.207708i
$5$	−0.402846	+	2.19948i	−0.180158	+	0.983638i
$5$	−0.402846	+	2.19948i	−0.180158	+	0.983638i
$6$	0.415415	+	0.909632i	0.169592	+	0.371356i
$7$	0.263933	−	3.69027i	0.0997574	−	1.39479i	−0.663248	−	0.748399i	$-0.730823\pi$
$7$	0.263933	−	3.69027i	0.0997574	−	1.39479i	0.763006	−	0.646392i	$-0.223723\pi$
$8$	0.599278	−	0.800541i	0.211877	−	0.283034i
$9$	0.281733	−	0.959493i	0.0939109	−	0.319831i
$10$	−2.06358	−	0.861173i	−0.652563	−	0.272327i
$11$	1.86704	−	2.90517i	0.562933	−	0.875942i	−0.436787	−	0.899565i	$-0.643884\pi$
$11$	1.86704	−	2.90517i	0.562933	−	0.875942i	0.999721	+	0.0236231i	$0.00752018\pi$
$12$	−0.977147	+	0.212565i	−0.282078	+	0.0613623i
$13$	−2.66017	+	0.190259i	−0.737799	+	0.0527684i	−0.435180	−	0.900343i	$-0.643315\pi$
$13$	−2.66017	+	0.190259i	−0.737799	+	0.0527684i	−0.302619	+	0.953112i	$0.597861\pi$
$14$	3.54983	+	1.04232i	0.948733	+	0.278573i
$15$	0.995605	+	2.00219i	0.257064	+	0.516964i
$16$	0.654861	+	0.755750i	0.163715	+	0.188937i
$17$	0.334391	−	0.896538i	0.0811018	−	0.217442i	−0.890070	−	0.455825i	$-0.849344\pi$
$17$	0.334391	−	0.896538i	0.0811018	−	0.217442i	0.971171	+	0.238382i	$0.0766171\pi$
$18$	0.877679	+	0.479249i	0.206871	+	0.112960i
$19$	2.69056	−	5.89150i	0.617256	−	1.35160i	−0.300242	−	0.953863i	$-0.597067\pi$
$19$	2.69056	−	5.89150i	0.617256	−	1.35160i	0.917498	−	0.397740i	$-0.130205\pi$
$20$	1.28014	−	1.83337i	0.286248	−	0.409954i
$21$	−2.00021	−	3.11238i	−0.436481	−	0.679178i
$22$	2.44191	+	2.44191i	0.520617	+	0.520617i
$23$	4.65964	+	1.13477i	0.971603	+	0.236617i
$23$	4.65964	+	1.13477i	0.971603	+	0.236617i
$24$		−	1.00000i		−	0.204124i
$25$	−4.67543	−	1.77210i	−0.935086	−	0.354421i
$26$	0.379549	−	2.63982i	0.0744357	−	0.517712i
$27$	−0.349464	−	0.936950i	−0.0672544	−	0.180316i
$28$	−1.77308	+	3.24715i	−0.335080	+	0.613653i
$29$	4.39413	−	2.00673i	0.815969	−	0.372640i	0.0366968	−	0.999326i	$-0.488316\pi$
$29$	4.39413	−	2.00673i	0.815969	−	0.372640i	0.779272	+	0.626686i	$0.215589\pi$
$30$	−2.16807	+	0.547255i	−0.395833	+	0.0999147i
$31$	0.556612	+	3.87132i	0.0999705	+	0.695310i	0.976744	+	0.214407i	$0.0687820\pi$
$31$	0.556612	+	3.87132i	0.0999705	+	0.695310i	−0.876774	+	0.480903i	$0.840309\pi$
$32$	−0.877679	+	0.479249i	−0.155153	+	0.0847201i
$33$	−0.246361	−	3.44458i	−0.0428860	−	0.599625i
$34$	0.804969	+	0.517322i	0.138051	+	0.0887200i
$35$	8.01035	+	2.06713i	1.35400	+	0.349408i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	−2.21545	−	4.05729i	−0.364217	−	0.667014i	0.629737	−	0.776808i	$-0.283163\pi$
$37$	−2.21545	−	4.05729i	−0.364217	−	0.667014i	−0.993954	+	0.109794i	$0.964981\pi$
$38$	5.18494	+	3.88140i	0.841109	+	0.629646i
$39$	−2.01556	+	1.74649i	−0.322748	+	0.279663i
$40$	1.51936	+	1.64059i	0.240232	+	0.259401i
$41$	−6.58528	+	1.93361i	−1.02845	+	0.301980i	−0.752080	−	0.659072i	$-0.770949\pi$
$41$	−6.58528	+	1.93361i	−1.02845	+	0.301980i	−0.276369	+	0.961052i	$0.589131\pi$
$42$	3.46643	−	1.29291i	0.534882	−	0.199501i
$43$	4.64732	+	6.20809i	0.708709	+	0.946725i	0.999951	−	0.00992479i	$-0.00315921\pi$
$43$	4.64732	+	6.20809i	0.708709	+	0.946725i	−0.291241	+	0.956650i	$0.594068\pi$
$44$	−2.90517	+	1.86704i	−0.437971	+	0.281467i
$45$	1.99689	+	1.00619i	0.297679	+	0.149994i
$46$	−2.09932	+	4.31194i	−0.309528	+	0.635761i
$47$	3.84111	−	3.84111i	0.560284	−	0.560284i	−0.369104	−	0.929388i	$-0.620336\pi$
$47$	3.84111	−	3.84111i	0.560284	−	0.560284i	0.929388	+	0.369104i	$0.120336\pi$
$48$	0.977147	+	0.212565i	0.141039	+	0.0306812i
$49$	−6.61968	−	0.951767i	−0.945669	−	0.135967i
$50$	2.72544	−	4.19189i	0.385436	−	0.592823i
$51$	−0.269581	−	0.918108i	−0.0377489	−	0.128561i
$52$	2.49881	+	0.932010i	0.346523	+	0.129246i
$53$	7.17587	+	0.513229i	0.985682	+	0.0704974i	0.554864	−	0.831941i	$-0.312770\pi$
$53$	7.17587	+	0.513229i	0.985682	+	0.0704974i	0.430818	+	0.902439i	$0.358225\pi$
$54$	0.989821	−	0.142315i	0.134698	−	0.0193666i
$55$	5.63773	+	5.27685i	0.760192	+	0.711531i
$56$	−2.79604	−	2.42279i	−0.373637	−	0.323758i
$57$	−1.37674	−	6.32878i	−0.182354	−	0.838268i
$58$	1.02683	+	4.72027i	0.134830	+	0.619801i
$59$	0.242559	+	0.210178i	0.0315784	+	0.0273629i	0.670507	−	0.741903i	$-0.266077\pi$
$59$	0.242559	+	0.210178i	0.0315784	+	0.0273629i	−0.638929	+	0.769266i	$0.720622\pi$
$60$	−0.0738933	−	2.23485i	−0.00953959	−	0.288517i
$61$	9.95159	−	1.43082i	1.27417	−	0.183198i	0.528167	−	0.849140i	$-0.322879\pi$
$61$	9.95159	−	1.43082i	1.27417	−	0.183198i	0.746003	+	0.665942i	$0.231970\pi$
$62$	−3.90117	−	0.279017i	−0.495449	−	0.0354352i
$63$	−3.46643	−	1.29291i	−0.436729	−	0.162892i
$64$	−0.281733	−	0.959493i	−0.0352166	−	0.119937i
$65$	0.653169	−	5.92764i	0.0810156	−	0.735234i
$66$	3.41823	+	0.491467i	0.420755	+	0.0604955i
$67$	−15.6752	−	3.40993i	−1.91503	−	0.416589i	−0.999910	−	0.0134079i	$-0.995732\pi$
$67$	−15.6752	−	3.40993i	−1.91503	−	0.416589i	−0.915120	−	0.403181i	$-0.867904\pi$
$68$	−0.676608	+	0.676608i	−0.0820508	+	0.0820508i
$69$	4.41028	−	1.88399i	0.530936	−	0.226806i
$70$	−3.72261	+	7.38789i	−0.444937	+	0.883022i
$71$	7.16418	−	4.60414i	0.850231	−	0.546411i	−0.0414155	−	0.999142i	$-0.513187\pi$
$71$	7.16418	−	4.60414i	0.850231	−	0.546411i	0.891647	+	0.452731i	$0.149550\pi$
$72$	−0.599278	−	0.800541i	−0.0706256	−	0.0943447i
$73$	−6.81334	+	2.54125i	−0.797441	+	0.297430i	−0.714963	−	0.699163i	$-0.753556\pi$
$73$	−6.81334	+	2.54125i	−0.797441	+	0.297430i	−0.0824787	+	0.996593i	$0.526284\pi$
$74$	4.43549	−	1.30238i	0.515616	−	0.151398i
$75$	−4.80486	+	1.38324i	−0.554817	+	0.159723i
$76$	−4.89484	+	4.24140i	−0.561476	+	0.486522i
$77$	−10.2281	−	7.65665i	−1.16560	−	0.872556i
$78$	−1.27814	−	2.34074i	−0.144721	−	0.265037i
$79$	8.69958	−	10.0398i	0.978779	−	1.12957i	−0.0127803	−	0.999918i	$-0.504068\pi$
$79$	8.69958	−	10.0398i	0.978779	−	1.12957i	0.991559	−	0.129653i	$-0.0413863\pi$
$80$	−1.92606	+	1.13590i	−0.215341	+	0.126998i
$81$	−0.841254	−	0.540641i	−0.0934726	−	0.0600712i
$82$	−0.489622	−	6.84581i	−0.0540697	−	0.755993i
$83$	−9.45789	+	5.16440i	−1.03814	+	0.566866i	−0.905521	−	0.424301i	$-0.860520\pi$
$83$	−9.45789	+	5.16440i	−1.03814	+	0.566866i	−0.132617	+	0.991167i	$0.542338\pi$
$84$	0.526522	+	3.66204i	0.0574482	+	0.399561i
$85$	1.83721	+	1.09665i	0.199273	+	0.118949i
$86$	−7.05407	+	3.22149i	−0.760660	+	0.347382i
$87$	2.31509	−	4.23977i	0.248204	−	0.454551i
$88$	−1.20683	−	3.23565i	−0.128649	−	0.344921i
$89$	−1.02032	+	7.09650i	−0.108154	+	0.752228i	0.861502	+	0.507754i	$0.169524\pi$
$89$	−1.02032	+	7.09650i	−0.108154	+	0.752228i	−0.969656	+	0.244474i	$0.921385\pi$
$90$	−1.40767	+	1.73737i	−0.148381	+	0.183135i
$91$			9.86697i			1.03434i
$92$	−3.76716	−	2.96791i	−0.392754	−	0.309426i
$93$	2.76559	+	2.76559i	0.286778	+	0.286778i
$94$	2.93684	+	4.56982i	0.302912	+	0.471341i
$95$	11.8744	+	8.29120i	1.21828	+	0.850659i
$96$	−0.415415	+	0.909632i	−0.0423981	+	0.0928389i
$97$	6.69511	+	3.65581i	0.679786	+	0.371191i	0.781746	−	0.623597i	$-0.214330\pi$
$97$	6.69511	+	3.65581i	0.679786	+	0.371191i	−0.101960	+	0.994789i	$0.532511\pi$
$98$	2.33713	−	6.26609i	0.236086	−	0.632971i
$99$	−2.26148	−	2.60989i	−0.227288	−	0.262304i
$100$	3.51676	+	3.55421i	0.351676	+	0.355421i
$101$	−8.54473	−	2.50896i	−0.850233	−	0.249651i	−0.172546	−	0.985001i	$-0.555199\pi$
$101$	−8.54473	−	2.50896i	−0.850233	−	0.249651i	−0.677687	+	0.735351i	$0.737017\pi$
$102$	0.954430	−	0.0682622i	0.0945027	−	0.00675897i
$103$	−5.80596	+	1.26301i	−0.572079	+	0.124448i	−0.489293	−	0.872119i	$-0.662745\pi$
$103$	−5.80596	+	1.26301i	−0.572079	+	0.124448i	−0.0827853	+	0.996567i	$0.526382\pi$
$104$	−1.44187	+	2.24360i	−0.141387	+	0.220003i
$105$	7.65140	−	3.14560i	0.746700	−	0.306980i
$106$	−2.02684	+	6.90279i	−0.196864	+	0.670458i
$107$	−2.78346	+	3.71827i	−0.269088	+	0.359459i	−0.914649	−	0.404250i	$-0.867533\pi$
$107$	−2.78346	+	3.71827i	−0.269088	+	0.359459i	0.645561	+	0.763709i	$0.276624\pi$
$108$	−0.0713392	+	0.997452i	−0.00686462	+	0.0959799i
$109$	4.90708	+	10.7450i	0.470013	+	1.02918i	0.985090	+	0.172040i	$0.0550360\pi$
$109$	4.90708	+	10.7450i	0.470013	+	1.02918i	−0.515077	+	0.857144i	$0.672237\pi$
$110$	−6.35465	+	4.38722i	−0.605892	+	0.418305i
$111$	−4.20500	−	1.92036i	−0.399121	−	0.182272i
$112$	2.96176	−	2.21715i	0.279860	−	0.209501i
$113$	0.205405	−	0.944233i	0.0193229	−	0.0888260i	−0.966476	−	0.256759i	$-0.917345\pi$
$113$	0.205405	−	0.944233i	0.0193229	−	0.0888260i	0.985798	+	0.167933i	$0.0537091\pi$
$114$	6.47680			0.606608
$115$	−4.37303	+	9.79166i	−0.407787	+	0.913077i
$116$	−4.83066			−0.448516
$117$	−0.566905	+	2.60602i	−0.0524104	+	0.240927i
$118$	−0.256934	+	0.192339i	−0.0236527	+	0.0177062i
$119$	−3.22021	−	1.47062i	−0.295196	−	0.134812i
$120$	2.19948	+	0.402846i	0.200784	+	0.0367747i
$121$	−0.384610	−	0.842179i	−0.0349646	−	0.0765617i
$122$	−0.717239	+	10.0283i	−0.0649357	+	0.907920i
$123$	−4.11302	+	5.49435i	−0.370858	+	0.495409i
$124$	1.10189	−	3.75271i	0.0989530	−	0.337003i
$125$	5.78119	−	9.56963i	0.517085	−	0.855934i
$126$	2.00021	−	3.11238i	0.178193	−	0.277273i
$127$	−7.03267	+	1.52986i	−0.624049	+	0.135754i	−0.513461	−	0.858113i	$-0.671637\pi$
$127$	−7.03267	+	1.52986i	−0.624049	+	0.135754i	−0.110588	+	0.993866i	$0.535273\pi$
$128$	0.997452	−	0.0713392i	0.0881631	−	0.00630555i
$129$	7.44074	+	2.18480i	0.655121	+	0.192361i
$130$	5.65334	+	1.89825i	0.495830	+	0.166488i
$131$	4.06744	+	4.69408i	0.355374	+	0.410123i	0.905084	−	0.425232i	$-0.139807\pi$
$131$	4.06744	+	4.69408i	0.355374	+	0.410123i	−0.549711	+	0.835355i	$0.685262\pi$
$132$	−1.20683	+	3.23565i	−0.105041	+	0.281627i
$133$	−21.0311	−	11.4839i	−1.82363	−	0.995776i
$134$	6.66401	−	14.5921i	0.575682	−	1.26057i
$135$	2.20158	−	0.391193i	0.189482	−	0.0336685i
$136$	−0.517322	−	0.804969i	−0.0443600	−	0.0690255i
$137$	−1.95600	−	1.95600i	−0.167112	−	0.167112i	0.618597	−	0.785709i	$-0.287702\pi$
$137$	−1.95600	−	1.95600i	−0.167112	−	0.167112i	−0.785709	+	0.618597i	$0.787702\pi$
$138$	0.903460	+	4.70996i	0.0769076	+	0.400939i
$139$		−	1.29159i		−	0.109551i	−0.998499	−	0.0547757i	$-0.982556\pi$
$139$		−	1.29159i		−	0.109551i	0.998499	−	0.0547757i	$-0.0174444\pi$
$140$	−6.42776	−	5.20795i	−0.543245	−	0.440152i
$141$	0.773076	−	5.37686i	0.0651047	−	0.452813i
$142$	2.97606	+	7.97913i	0.249746	+	0.669594i
$143$	−4.41391	+	8.08347i	−0.369110	+	0.675974i
$144$	0.909632	−	0.415415i	0.0758027	−	0.0346179i
$145$	2.64361	+	10.4732i	0.219540	+	0.869752i
$146$	−1.03489	−	7.19782i	−0.0856481	−	0.595696i
$147$	−5.86970	+	3.20510i	−0.484125	+	0.264352i
$148$	0.329783	+	4.61097i	0.0271080	+	0.379019i
$149$	12.5386	+	8.05805i	1.02720	+	0.660141i	0.941789	−	0.336204i	$-0.109143\pi$
$149$	12.5386	+	8.05805i	1.02720	+	0.660141i	0.0854110	+	0.996346i	$0.472780\pi$
$150$	−0.330280	−	4.98908i	−0.0269673	−	0.407357i
$151$	−0.612254	+	0.706579i	−0.0498246	+	0.0575006i	−0.780115	−	0.625636i	$-0.784839\pi$
$151$	−0.612254	+	0.706579i	−0.0498246	+	0.0575006i	0.730290	+	0.683137i	$0.239385\pi$
$152$	−3.10400	−	5.68455i	−0.251767	−	0.461078i
$153$	−0.766013	−	0.573430i	−0.0619284	−	0.0463591i
$154$	9.65581	−	8.36680i	0.778087	−	0.674216i
$155$	−8.73913	−	0.335290i	−0.701944	−	0.0269312i
$156$	2.55894	−	0.751372i	0.204879	−	0.0601579i
$157$	−22.8278	+	8.51431i	−1.82185	+	0.679516i	−0.829136	+	0.559047i	$0.811167\pi$
$157$	−22.8278	+	8.51431i	−1.82185	+	0.679516i	−0.992717	+	0.120469i	$0.961560\pi$
$158$	7.96118	+	10.6349i	0.633357	+	0.846066i
$159$	6.05215	−	3.88948i	0.479967	−	0.308456i
$160$	−0.700529	−	2.12350i	−0.0553817	−	0.167878i
$161$	5.41746	−	16.8958i	0.426955	−	1.33158i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−22.3915	−	4.87097i	−1.75384	−	0.381524i	−0.783143	−	0.621842i	$-0.786385\pi$
$163$	−22.3915	−	4.87097i	−1.75384	−	0.381524i	−0.970694	+	0.240318i	$0.922748\pi$
$164$	6.79344	+	0.976749i	0.530478	+	0.0762713i
$165$	7.67554	+	0.845770i	0.597540	+	0.0658431i
$166$	−3.03596	−	10.3395i	−0.235636	−	0.802502i
$167$	4.61642	+	1.72183i	0.357229	+	0.133240i	0.521670	−	0.853147i	$-0.325309\pi$
$167$	4.61642	+	1.72183i	0.357229	+	0.133240i	−0.164441	+	0.986387i	$0.552582\pi$
$168$	−3.69027	−	0.263933i	−0.284711	−	0.0203629i
$169$	−5.82736	+	0.837848i	−0.448259	+	0.0644498i
$170$	−1.46212	+	1.56211i	−0.112139	+	0.119809i
$171$	−4.89484	−	4.24140i	−0.374317	−	0.324348i
$172$	−1.64842	−	7.57764i	−0.125690	−	0.577790i
$173$	−0.00984365	−	0.0452505i	−0.000748399	−	0.00344033i	0.976771	−	0.214285i	$-0.0687422\pi$
$173$	−0.00984365	−	0.0452505i	−0.000748399	−	0.00344033i	−0.977520	+	0.210845i	$0.932379\pi$
$174$	3.65077	+	3.16341i	0.276764	+	0.239818i
$175$	−7.77355	+	16.7859i	−0.587625	+	1.26889i
$176$	3.41823	−	0.491467i	0.257659	−	0.0370458i
$177$	0.320133	+	0.0228964i	0.0240627	+	0.00172100i
$178$	−6.71744	−	2.50548i	−0.503493	−	0.187793i
$179$	−0.550638	−	1.87530i	−0.0411566	−	0.140167i	0.936352	−	0.351063i	$-0.114180\pi$
$179$	−0.550638	−	1.87530i	−0.0411566	−	0.140167i	−0.977508	+	0.210897i	$0.932362\pi$
$180$	−1.39845	−	1.74480i	−0.104234	−	0.130050i
$181$	−19.1496	−	2.75329i	−1.42338	−	0.204651i	−0.612779	−	0.790254i	$-0.709949\pi$
$181$	−19.1496	−	2.75329i	−1.42338	−	0.204651i	−0.810598	+	0.585603i	$0.800858\pi$
$182$	−9.64148	−	2.09738i	−0.714674	−	0.155468i
$183$	7.10920	−	7.10920i	0.525527	−	0.525527i
$184$	3.70085	−	3.05019i	0.272831	−	0.224863i
$185$	9.81641	−	3.23837i	0.721717	−	0.238090i
$186$	−3.29026	+	2.11452i	−0.241253	+	0.155044i
$187$	−1.98027	−	2.64533i	−0.144812	−	0.193446i
$188$	−5.08965	+	1.89834i	−0.371201	+	0.138451i
$189$	−3.54983	+	1.04232i	−0.258212	+	0.0758180i
$190$	−10.6258	+	9.84057i	−0.770876	+	0.713910i
$191$	1.82046	−	1.57744i	0.131724	−	0.114140i	−0.586507	−	0.809944i	$-0.699497\pi$
$191$	1.82046	−	1.57744i	0.131724	−	0.114140i	0.718231	+	0.695804i	$0.244952\pi$
$192$	−0.800541	−	0.599278i	−0.0577741	−	0.0432491i
$193$	8.89021	+	16.2812i	0.639932	+	1.17195i	0.973384	+	0.229180i	$0.0736045\pi$
$193$	8.89021	+	16.2812i	0.639932	+	1.17195i	−0.333453	+	0.942767i	$0.608214\pi$
$194$	−4.99541	+	5.76501i	−0.358650	+	0.413904i
$195$	−3.02942	−	5.13675i	−0.216941	−	0.367850i
$196$	5.62610	+	3.61567i	0.401864	+	0.258262i
$197$	0.856904	+	11.9811i	0.0610519	+	0.853617i	0.932050	+	0.362330i	$0.118019\pi$
$197$	0.856904	+	11.9811i	0.0610519	+	0.853617i	−0.870998	+	0.491287i	$0.836527\pi$
$198$	3.03096	−	1.65503i	0.215401	−	0.117618i
$199$	1.25575	+	8.73390i	0.0890174	+	0.619130i	0.984677	+	0.174389i	$0.0557951\pi$
$199$	1.25575	+	8.73390i	0.0890174	+	0.619130i	−0.895659	+	0.444741i	$0.853296\pi$
$200$	−4.22052	+	2.68089i	−0.298436	+	0.189568i
$201$	−14.5921	+	6.66401i	−1.02925	+	0.470043i
$202$	4.26794	−	7.81614i	0.300291	−	0.549942i
$203$	−6.24562	−	16.7452i	−0.438356	−	1.17528i
$204$	−0.136177	+	0.947129i	−0.00953427	+	0.0663123i
$205$	−1.60009	−	15.2632i	−0.111755	−	1.06602i
$206$		−	5.94175i		−	0.413981i
$207$	2.40158	−	4.15119i	0.166921	−	0.288528i
$208$	−1.88583	−	1.88583i	−0.130759	−	0.130759i
$209$	−12.0924	−	18.8162i	−0.836451	−	1.30154i
$210$	1.44730	+	8.14519i	0.0998729	+	0.562071i
$211$	11.1963	−	24.5164i	0.770783	−	1.68778i	0.0458623	−	0.998948i	$-0.485396\pi$
$211$	11.1963	−	24.5164i	0.770783	−	1.68778i	0.724921	−	0.688832i	$-0.241876\pi$
$212$	−6.31420	−	3.44782i	−0.433661	−	0.236797i
$213$	2.97606	−	7.97913i	0.203916	−	0.546721i
$214$	−3.04163	−	3.51023i	−0.207922	−	0.239954i
$215$	−15.5267	+	7.72078i	−1.05891	+	0.526553i
$216$	−0.959493	−	0.281733i	−0.0652852	−	0.0191695i
$217$	14.4331	−	1.03228i	0.979785	−	0.0700756i
$218$	−11.5425	+	2.51092i	−0.781758	+	0.170061i
$219$	−3.93145	+	6.11746i	−0.265663	+	0.413379i
$220$	−2.93618	−	7.14199i	−0.197957	−	0.481513i
$221$	−0.718964	+	2.44857i	−0.0483627	+	0.164708i
$222$	2.77031	−	3.70070i	0.185931	−	0.248375i
$223$	1.97616	−	27.6303i	0.132334	−	1.85026i	−0.306716	−	0.951801i	$-0.599230\pi$
$223$	1.97616	−	27.6303i	0.132334	−	1.85026i	0.439049	−	0.898463i	$-0.355315\pi$
$224$	1.53691	+	3.36536i	0.102689	+	0.224858i
$225$	−3.01754	+	3.98678i	−0.201170	+	0.265785i
$226$	0.878993	+	0.401423i	0.0584697	+	0.0267022i
$227$	−18.2871	+	13.6896i	−1.21376	+	0.908609i	−0.997701	−	0.0677714i	$-0.978411\pi$
$227$	−18.2871	+	13.6896i	−1.21376	+	0.908609i	−0.216059	+	0.976380i	$0.569320\pi$
$228$	−1.37674	+	6.32878i	−0.0911770	+	0.419134i
$229$	17.8775			1.18138			0.590690	−	0.806899i	$-0.298856\pi$
$229$	17.8775			1.18138			0.590690	+	0.806899i	$0.298856\pi$
$230$	−8.63833	−	6.35446i	−0.569595	−	0.419001i
$231$	−12.7765			−0.840630
$232$	1.02683	−	4.72027i	0.0674148	−	0.309901i
$233$	19.4716	−	14.5763i	1.27563	−	0.954922i	0.275647	−	0.961259i	$-0.411108\pi$
$233$	19.4716	−	14.5763i	1.27563	−	0.954922i	0.999980	+	0.00633682i	$0.00201709\pi$
$234$	−2.42596	−	1.10790i	−0.158590	−	0.0724256i
$235$	6.90107	+	9.99583i	0.450176	+	0.652056i
$236$	−0.133328	−	0.291947i	−0.00867890	−	0.0190041i
$237$	0.947714	−	13.2508i	0.0615607	−	0.860730i
$238$	2.12152	−	2.83401i	0.137517	−	0.183702i
$239$	−0.699787	+	2.38326i	−0.0452655	+	0.154160i	−0.979025	−	0.203742i	$-0.934690\pi$
$239$	−0.699787	+	2.38326i	−0.0452655	+	0.154160i	0.933759	+	0.357902i	$0.116508\pi$
$240$	−0.861173	+	2.06358i	−0.0555885	+	0.133204i
$241$	−1.68053	+	2.61496i	−0.108253	+	0.168444i	−0.891153	−	0.453702i	$-0.850103\pi$
$241$	−1.68053	+	2.61496i	−0.108253	+	0.168444i	0.782901	+	0.622147i	$0.213739\pi$
$242$	0.904687	−	0.196803i	0.0581555	−	0.0126510i
$243$	−0.997452	+	0.0713392i	−0.0639866	+	0.00457641i
$244$	−9.64667	−	2.83252i	−0.617565	−	0.181333i
$245$	4.76011	−	14.1764i	0.304112	−	0.905700i
$246$	−4.49450	−	5.18693i	−0.286559	−	0.330707i
$247$	−6.03644	+	16.1843i	−0.384089	+	1.02978i
$248$	3.43272	+	1.87441i	0.217978	+	0.119025i
$249$	−4.47652	+	9.80222i	−0.283688	+	0.621190i
$250$	8.12206	+	7.68324i	0.513684	+	0.485931i
$251$	11.2173	+	17.4544i	0.708028	+	1.10171i	0.989832	+	0.142241i	$0.0454307\pi$
$251$	11.2173	+	17.4544i	0.708028	+	1.10171i	−0.281804	+	0.959472i	$0.590933\pi$
$252$	2.61608	+	2.61608i	0.164798	+	0.164798i
$253$	11.9964	−	11.4184i	0.754210	−	0.717868i
$254$		−	7.19715i		−	0.451589i
$255$	2.12796	−	0.223082i	0.133258	−	0.0139699i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	1.03885	+	2.78526i	0.0648015	+	0.173739i	0.965315	−	0.261089i	$-0.0840817\pi$
$257$	1.03885	+	2.78526i	0.0648015	+	0.173739i	−0.900513	+	0.434829i	$0.856809\pi$
$258$	−3.71651	+	6.80628i	−0.231380	+	0.423741i
$259$	−15.5572	+	7.10474i	−0.966679	+	0.441467i
$260$	−3.05657	+	5.12064i	−0.189561	+	0.317568i
$261$	−0.687475	−	4.78149i	−0.0425536	−	0.295967i
$262$	−5.45140	+	2.97669i	−0.336789	+	0.183900i
$263$	2.02904	+	28.3697i	0.125116	+	1.74935i	0.541989	+	0.840385i	$0.317671\pi$
$263$	2.02904	+	28.3697i	0.125116	+	1.74935i	−0.416873	+	0.908965i	$0.636874\pi$
$264$	−2.90517	−	1.86704i	−0.178801	−	0.114908i
$265$	−4.01961	+	15.5764i	−0.246923	+	0.956853i
$266$	15.6919	−	18.1094i	0.962132	−	1.11036i
$267$	3.43597	+	6.29250i	0.210278	+	0.385095i
$268$	12.8421	+	9.61349i	0.784458	+	0.587238i
$269$	8.62351	−	7.47231i	0.525784	−	0.455595i	−0.351071	−	0.936349i	$-0.614182\pi$
$269$	8.62351	−	7.47231i	0.525784	−	0.455595i	0.876856	+	0.480754i	$0.159637\pi$
$270$	−0.0857271	+	2.23442i	−0.00521718	+	0.135983i
$271$	2.26709	−	0.665678i	0.137716	−	0.0404371i	−0.212148	−	0.977238i	$-0.568046\pi$
$271$	2.26709	−	0.665678i	0.137716	−	0.0404371i	0.349864	+	0.936800i	$0.386228\pi$
$272$	0.896538	−	0.334391i	0.0543606	−	0.0202754i
$273$	5.91305	+	7.89892i	0.357874	+	0.478064i
$274$	2.32708	−	1.49552i	0.140584	−	0.0903477i
$275$	−13.8775	+	10.2743i	−0.836843	+	0.619565i
$276$	−4.79437	−	0.118361i	−0.288587	−	0.00712452i
$277$	9.73976	−	9.73976i	0.585205	−	0.585205i	−0.351124	−	0.936329i	$-0.614200\pi$
$277$	9.73976	−	9.73976i	0.585205	−	0.585205i	0.936329	+	0.351124i	$0.114200\pi$
$278$	1.26208	+	0.274548i	0.0756943	+	0.0164663i
$279$	3.87132	+	0.556612i	0.231770	+	0.0333235i
$280$	6.45525	−	5.17383i	0.385775	−	0.309196i
$281$	8.88391	+	30.2558i	0.529970	+	1.80491i	0.590869	+	0.806768i	$0.298785\pi$
$281$	8.88391	+	30.2558i	0.529970	+	1.80491i	−0.0608989	+	0.998144i	$0.519397\pi$
$282$	5.08965	+	1.89834i	0.303084	+	0.113045i
$283$	24.2191	+	1.73218i	1.43968	+	0.102968i	0.769221	−	0.638983i	$-0.220645\pi$
$283$	24.2191	+	1.73218i	1.43968	+	0.102968i	0.670455	+	0.741950i	$0.266099\pi$
$284$	−8.42939	+	1.21196i	−0.500192	+	0.0719168i
$285$	14.4746	−	0.478592i	0.857404	−	0.0283493i
$286$	−6.96050	−	6.03130i	−0.411583	−	0.356639i
$287$	5.39748	+	24.8118i	0.318603	+	1.46460i
$288$	0.212565	+	0.977147i	0.0125255	+	0.0575789i
$289$	12.1558	+	10.5330i	0.715046	+	0.619591i
$290$	−10.7958	+	0.356954i	−0.633951	+	0.0209610i
$291$	7.55056	−	1.08561i	0.442622	−	0.0636394i
$292$	7.25331	+	0.518767i	0.424468	+	0.0303585i
$293$	−15.7864	−	5.88801i	−0.922249	−	0.343981i	−0.156913	−	0.987612i	$-0.550154\pi$
$293$	−15.7864	−	5.88801i	−0.922249	−	0.343981i	−0.765336	+	0.643631i	$0.777427\pi$
$294$	−1.88416	−	6.41685i	−0.109886	−	0.374238i
$295$	−0.559997	+	0.448833i	−0.0326043	+	0.0261321i
$296$	−4.57569	−	0.657886i	−0.265957	−	0.0382388i
$297$	−3.37446	−	0.734069i	−0.195806	−	0.0425950i
$298$	−10.5392	+	10.5392i	−0.610517	+	0.610517i
$299$	−12.6114	−	2.13215i	−0.729334	−	0.123306i
$300$	4.94527	+	0.737773i	0.285515	+	0.0425953i
$301$	24.1361	−	15.5113i	1.39118	−	0.894058i
$302$	−0.560288	−	0.748457i	−0.0322409	−	0.0430688i
$303$	−8.34397	+	3.11214i	−0.479349	+	0.178788i
$304$	6.21444	−	1.82472i	0.356423	−	0.104655i
$305$	−0.861894	+	22.4647i	−0.0493519	+	1.28633i
$306$	0.723153	−	0.626616i	0.0413399	−	0.0358212i
$307$	6.53002	+	4.88831i	0.372688	+	0.278991i	0.769160	−	0.639056i	$-0.220675\pi$
$307$	6.53002	+	4.88831i	0.372688	+	0.278991i	−0.396472	+	0.918047i	$0.629766\pi$
$308$	6.12311	+	11.2136i	0.348896	+	0.638956i
$309$	−3.89102	+	4.49048i	−0.221352	+	0.255454i
$310$	2.18526	−	8.46814i	0.124115	−	0.480958i
$311$	24.0572	+	15.4606i	1.36416	+	0.876693i	0.998537	−	0.0540701i	$-0.0172194\pi$
$311$	24.0572	+	15.4606i	1.36416	+	0.876693i	0.365623	+	0.930763i	$0.380856\pi$
$312$	0.190259	+	2.66017i	0.0107713	+	0.150603i
$313$	16.1083	−	8.79577i	0.910492	−	0.497166i	0.0455072	−	0.998964i	$-0.485510\pi$
$313$	16.1083	−	8.79577i	0.910492	−	0.497166i	0.864985	+	0.501798i	$0.167328\pi$
$314$	−3.46735	−	24.1159i	−0.195674	−	1.36094i
$315$	4.24017	−	7.10350i	0.238907	−	0.400237i
$316$	−12.0841	+	5.51863i	−0.679785	+	0.310447i
$317$	−2.64215	+	4.83874i	−0.148398	+	0.271771i	−0.941295	−	0.337585i	$-0.890390\pi$
$317$	−2.64215	+	4.83874i	−0.148398	+	0.271771i	0.792897	+	0.609356i	$0.208572\pi$
$318$	2.51412	+	6.74061i	0.140985	+	0.377995i
$319$	2.37411	−	16.5123i	0.132925	−	0.924513i
$320$	2.22388	−	0.233137i	0.124319	−	0.0130328i
$321$			4.64470i			0.259242i
$322$	15.3582	+	8.88512i	0.855877	+	0.495148i
$323$	−4.38225	−	4.38225i	−0.243835	−	0.243835i
$324$	0.540641	+	0.841254i	0.0300356	+	0.0467363i
$325$	12.7746	+	3.82456i	0.708608	+	0.212148i
$326$	9.51931	−	20.8444i	0.527226	−	1.15446i
$327$	10.3676	+	5.66111i	0.573327	+	0.313060i
$328$	−2.39848	+	6.43056i	−0.132434	+	0.355068i
$329$	−13.1609	−	15.1885i	−0.725586	−	0.837371i
$330$	−2.45799	+	7.32035i	−0.135308	+	0.402972i
$331$	1.07928	+	0.316906i	0.0593228	+	0.0174188i	0.311259	−	0.950325i	$-0.399249\pi$
$331$	1.07928	+	0.316906i	0.0593228	+	0.0174188i	−0.251936	+	0.967744i	$0.581067\pi$
$332$	10.7486	−	0.768753i	0.589904	−	0.0421908i
$333$	−4.51710	+	0.982636i	−0.247536	+	0.0538481i
$334$	−2.66377	+	4.14491i	−0.145755	+	0.226800i
$335$	13.8148	−	33.1036i	0.754782	−	1.80864i
$336$	1.04232	−	3.54983i	0.0568635	−	0.193659i
$337$	12.4420	−	16.6205i	0.677757	−	0.905378i	−0.321378	−	0.946951i	$-0.604146\pi$
$337$	12.4420	−	16.6205i	0.677757	−	0.905378i	0.999135	+	0.0415734i	$0.0132370\pi$
$338$	0.419994	−	5.87228i	0.0228447	−	0.319410i
$339$	−0.401423	−	0.878993i	−0.0218023	−	0.0477403i
$340$	−1.21562	−	1.76076i	−0.0659261	−	0.0954904i
$341$	12.2861	+	5.61086i	0.665328	+	0.303845i
$342$	5.18494	−	3.88140i	0.280370	−	0.209882i
$343$	0.245559	−	1.12882i	0.0132590	−	0.0609504i
$344$	7.75487			0.418114
$345$	2.36713	+	10.4593i	0.127442	+	0.563109i
$346$	0.0463088			0.00248958
$347$	−7.58369	+	34.8616i	−0.407114	+	1.87147i	0.0778952	+	0.996962i	$0.475180\pi$
$347$	−7.58369	+	34.8616i	−0.407114	+	1.87147i	−0.485009	+	0.874509i	$0.661184\pi$
$348$	−3.86714	+	2.89491i	−0.207301	+	0.155183i
$349$	1.58353	+	0.723172i	0.0847642	+	0.0387105i	0.457346	−	0.889289i	$-0.348800\pi$
$349$	1.58353	+	0.723172i	0.0847642	+	0.0387105i	−0.372582	+	0.927999i	$0.621527\pi$
$350$	−14.7499	−	11.1640i	−0.788414	−	0.596741i
$351$	1.10790	+	2.42596i	0.0591352	+	0.129488i
$352$	−0.246361	+	3.44458i	−0.0131311	+	0.183597i
$353$	7.86025	−	10.5001i	0.418359	−	0.558862i	−0.541010	−	0.841016i	$-0.681958\pi$
$353$	7.86025	−	10.5001i	0.418359	−	0.558862i	0.959369	+	0.282154i	$0.0910489\pi$
$354$	−0.0904223	+	0.307950i	−0.00480589	+	0.0163674i
$355$	7.24065	+	17.6122i	0.384294	+	0.934760i
$356$	3.87611	−	6.03135i	0.205434	−	0.319661i
$357$	−3.45922	+	0.752507i	−0.183081	+	0.0398269i
$358$	1.94949	−	0.139430i	0.103034	−	0.00736912i
$359$	35.3429	+	10.3776i	1.86533	+	0.547710i	0.998821	+	0.0485474i	$0.0154592\pi$
$359$	35.3429	+	10.3776i	1.86533	+	0.547710i	0.866508	+	0.499163i	$0.166359\pi$
$360$	2.00219	−	0.995605i	0.105525	−	0.0524730i
$361$	−15.0283	−	17.3436i	−0.790965	−	0.912822i
$362$	6.76091	−	18.1267i	0.355345	−	0.952718i
$363$	−0.812595	−	0.443711i	−0.0426502	−	0.0232888i
$364$	4.09889	−	8.97531i	0.214840	−	0.470434i
$365$	−2.84469	−	16.0095i	−0.148898	−	0.837978i
$366$	5.43556	+	8.45790i	0.284121	+	0.442102i
$367$	−5.64568	−	5.64568i	−0.294702	−	0.294702i	0.544232	−	0.838935i	$-0.316821\pi$
$367$	−5.64568	−	5.64568i	−0.294702	−	0.294702i	−0.838935	+	0.544232i	$0.816821\pi$
$368$	2.19381	+	4.26464i	0.114360	+	0.222310i
$369$			6.86329i			0.357289i
$370$	1.07773	+	10.2804i	0.0560287	+	0.534455i
$371$	3.78790	−	26.3455i	0.196658	−	1.36779i
$372$	−1.36680	−	3.66454i	−0.0708653	−	0.189997i
$373$	−9.63986	+	17.6541i	−0.499133	+	0.914094i	0.499719	+	0.866188i	$0.333437\pi$
$373$	−9.63986	+	17.6541i	−0.499133	+	0.914094i	−0.998852	+	0.0479065i	$0.984745\pi$
$374$	3.00582	−	1.37271i	0.155427	−	0.0709812i
$375$	−1.10679	−	11.1254i	−0.0571542	−	0.574514i
$376$	−0.773076	−	5.37686i	−0.0398683	−	0.277290i
$377$	−11.3073	+	6.17427i	−0.582357	+	0.317991i
$378$	−0.263933	−	3.69027i	−0.0135753	−	0.189807i
$379$	20.8274	+	13.3850i	1.06983	+	0.687540i	0.952187	−	0.305516i	$-0.0988289\pi$
$379$	20.8274	+	13.3850i	1.06983	+	0.687540i	0.117646	+	0.993056i	$0.462465\pi$
$380$	−7.35701	−	12.4747i	−0.377407	−	0.639940i
$381$	−4.71313	+	5.43924i	−0.241461	+	0.278661i
$382$	1.15442	+	2.11417i	0.0590654	+	0.108170i
$383$	8.37505	+	6.26948i	0.427945	+	0.320356i	0.791447	−	0.611238i	$-0.209328\pi$
$383$	8.37505	+	6.26948i	0.427945	+	0.320356i	−0.363502	+	0.931593i	$0.618419\pi$
$384$	0.755750	−	0.654861i	0.0385667	−	0.0334182i
$385$	20.9610	−	19.4120i	1.06827	−	0.989328i
$386$	−17.7989	+	5.22622i	−0.905939	+	0.266008i
$387$	7.26592	−	2.71005i	0.369347	−	0.137759i
$388$	−4.57141	−	6.10669i	−0.232078	−	0.310020i
$389$	−16.3949	+	10.5364i	−0.831255	+	0.534215i	−0.885676	−	0.464303i	$-0.846305\pi$
$389$	−16.3949	+	10.5364i	−0.831255	+	0.534215i	0.0544218	+	0.998518i	$0.482668\pi$
$390$	5.66331	−	1.86829i	0.286773	−	0.0946045i
$391$	2.57551	−	3.79809i	0.130249	−	0.192078i
$392$	−4.72896	+	4.72896i	−0.238848	+	0.238848i
$393$	6.06921	+	1.32028i	0.306151	+	0.0665991i
$394$	−11.8894	−	1.70944i	−0.598980	−	0.0861204i
$395$	18.5779	+	23.1791i	0.934754	+	1.16627i
$396$	0.972930	+	3.31350i	0.0488916	+	0.166509i
$397$	−12.0441	−	4.49223i	−0.604477	−	0.225458i	0.0285443	−	0.999593i	$-0.490913\pi$
$397$	−12.0441	−	4.49223i	−0.604477	−	0.225458i	−0.633022	+	0.774134i	$0.718186\pi$
$398$	−8.80123	−	0.629477i	−0.441166	−	0.0315528i
$399$	−23.7183	+	3.41017i	−1.18740	+	0.170722i
$400$	−1.72249	−	4.69394i	−0.0861244	−	0.234697i
$401$	−12.1018	−	10.4863i	−0.604336	−	0.523660i	0.298072	−	0.954543i	$-0.403656\pi$
$401$	−12.1018	−	10.4863i	−0.604336	−	0.523660i	−0.902407	+	0.430884i	$0.858202\pi$
$402$	−3.40993	−	15.6752i	−0.170072	−	0.781808i
$403$	−2.21724	−	10.1925i	−0.110449	−	0.507724i
$404$	6.73030	+	5.83184i	0.334845	+	0.290145i
$405$	1.52802	−	1.63253i	0.0759282	−	0.0811209i
$406$	17.6901	−	2.54345i	0.877944	−	0.126229i
$407$	−15.9234	−	1.13887i	−0.789296	−	0.0564515i
$408$	−0.896538	−	0.334391i	−0.0443852	−	0.0165548i
$409$	−4.81438	−	16.3963i	−0.238056	−	0.810744i	−0.988683	−	0.150018i	$-0.952067\pi$
$409$	−4.81438	−	16.3963i	−0.238056	−	0.810744i	0.750627	−	0.660726i	$-0.229751\pi$
$410$	15.2545	+	1.68089i	0.753364	+	0.0830134i
$411$	−2.73804	−	0.393671i	−0.135058	−	0.0194184i
$412$	5.80596	+	1.26301i	0.286039	+	0.0622240i
$413$	0.839633	−	0.839633i	0.0413157	−	0.0413157i
$414$	3.54583	+	3.22910i	0.174268	+	0.158701i
$415$	−7.54892	−	22.8829i	−0.370562	−	1.12328i
$416$	2.24360	−	1.44187i	0.110001	−	0.0706936i
$417$	−0.774023	−	1.03397i	−0.0379040	−	0.0506339i
$418$	20.9566	−	7.81641i	1.02502	−	0.382313i
$419$	−29.5707	+	8.68275i	−1.44462	+	0.424180i	−0.907761	−	0.419489i	$-0.862209\pi$
$419$	−29.5707	+	8.68275i	−1.44462	+	0.424180i	−0.536864	+	0.843669i	$0.680391\pi$
$420$	−8.26669	−	0.317164i	−0.403373	−	0.0154760i
$421$	12.5155	−	10.8447i	0.609968	−	0.528541i	−0.294185	−	0.955748i	$-0.595048\pi$
$421$	12.5155	−	10.8447i	0.609968	−	0.528541i	0.904153	+	0.427208i	$0.140503\pi$
$422$	21.5762	+	16.1517i	1.05031	+	0.786255i
$423$	−2.60335	−	4.76768i	−0.126579	−	0.231813i
$424$	4.71120	−	5.43702i	0.228796	−	0.264045i
$425$	−3.15218	+	3.59912i	−0.152903	+	0.174583i
$426$	7.16418	+	4.60414i	0.347106	+	0.223071i
$427$	−2.65357	−	37.1017i	−0.128415	−	1.79548i
$428$	4.07655	−	2.22597i	0.197048	−	0.107596i
$429$	1.31073	+	9.11631i	0.0632825	+	0.440140i
$430$	−4.24389	−	16.8131i	−0.204659	−	0.810798i
$431$	0.292170	−	0.133430i	0.0140733	−	0.00642708i	−0.408366	−	0.912818i	$-0.633901\pi$
$431$	0.292170	−	0.133430i	0.0140733	−	0.00642708i	0.422439	+	0.906391i	$0.361174\pi$
$432$	0.479249	−	0.877679i	0.0230579	−	0.0422274i
$433$	−7.49485	−	20.0945i	−0.360179	−	0.965678i	−0.983047	−	0.183351i	$-0.941305\pi$
$433$	−7.49485	−	20.0945i	−0.360179	−	0.965678i	0.622868	−	0.782327i	$-0.285967\pi$
$434$	−2.05930	+	14.3227i	−0.0988494	+	0.687513i
$435$	8.39267	+	6.79997i	0.402398	+	0.326034i
$436$		−	11.8125i		−	0.565715i
$437$	19.2226	−	24.3991i	0.919540	−	1.16717i
$438$	−5.14196	−	5.14196i	−0.245693	−	0.245693i
$439$	8.47929	+	13.1940i	0.404695	+	0.629717i	0.982457	−	0.186488i	$-0.0597105\pi$
$439$	8.47929	+	13.1940i	0.404695	+	0.629717i	−0.577763	+	0.816205i	$0.696074\pi$
$440$	7.60291	−	1.35094i	0.362454	−	0.0644035i
$441$	−2.77819	+	6.08339i	−0.132295	+	0.289685i
$442$	−2.23978	−	1.22301i	−0.106536	−	0.0581728i
$443$	−5.97976	+	16.0323i	−0.284107	+	0.761720i	0.713996	+	0.700150i	$0.246883\pi$
$443$	−5.97976	+	16.0323i	−0.284107	+	0.761720i	−0.998103	+	0.0615699i	$0.980389\pi$
$444$	3.02726	+	3.49364i	0.143667	+	0.165801i
$445$	−15.1976	−	5.10298i	−0.720435	−	0.241904i
$446$	26.5788	+	7.80425i	1.25854	+	0.369542i
$447$	14.8667	−	1.06328i	0.703169	−	0.0502916i
$448$	−3.61515	+	0.786427i	−0.170800	+	0.0371552i
$449$	3.92587	−	6.10877i	0.185273	−	0.288291i	−0.736176	−	0.676791i	$-0.763370\pi$
$449$	3.92587	−	6.10877i	0.185273	−	0.288291i	0.921449	+	0.388500i	$0.127007\pi$
$450$	−3.25425	−	3.79603i	−0.153407	−	0.178947i
$451$	−6.67751	+	22.7415i	−0.314431	+	1.07086i
$452$	−0.579092	+	0.773576i	−0.0272382	+	0.0363860i
$453$	−0.0666977	+	0.932556i	−0.00313373	+	0.0438153i
$454$	−9.48952	−	20.7791i	−0.445365	−	0.975213i
$455$	−21.7022	−	3.97487i	−1.01742	−	0.186345i
$456$	−5.89150	−	2.69056i	−0.275895	−	0.125997i
$457$	6.82178	−	5.10672i	0.319109	−	0.238882i	−0.427700	−	0.903921i	$-0.640676\pi$
$457$	6.82178	−	5.10672i	0.319109	−	0.238882i	0.746809	+	0.665039i	$0.231585\pi$
$458$	−3.80014	+	17.4690i	−0.177569	+	0.816271i
$459$	−0.956868			−0.0446628
$460$	8.04545	−	7.09018i	0.375121	−	0.330581i
$461$	−22.4340			−1.04485			−0.522427	−	0.852684i	$-0.674973\pi$
$461$	−22.4340			−1.04485			−0.522427	+	0.852684i	$0.674973\pi$
$462$	2.71583	−	12.4845i	0.126352	−	0.580831i
$463$	−19.0642	+	14.2713i	−0.885991	+	0.663244i	−0.942155	−	0.335177i	$-0.891204\pi$
$463$	−19.0642	+	14.2713i	−0.885991	+	0.663244i	0.0561643	+	0.998422i	$0.482113\pi$
$464$	4.39413	+	2.00673i	0.203992	+	0.0931601i
$465$	−7.19697	+	4.96875i	−0.333751	+	0.230420i
$466$	10.1042	+	22.1250i	0.468066	+	1.02492i
$467$	−1.79917	+	25.1557i	−0.0832556	+	1.16407i	0.768402	+	0.639967i	$0.221052\pi$
$467$	−1.79917	+	25.1557i	−0.0832556	+	1.16407i	−0.851658	+	0.524098i	$0.824402\pi$
$468$	1.59825	−	2.13502i	0.0738793	−	0.0986912i
$469$	−16.7208	+	56.9457i	−0.772093	+	2.62951i
$470$	−11.2343	+	4.61860i	−0.518200	+	0.213040i
$471$	−13.1721	+	20.4962i	−0.606939	+	0.944416i
$472$	0.313616	−	0.0682230i	0.0144354	−	0.00314022i
$473$	26.7123	−	1.91050i	1.22823	−	0.0878449i
$474$	12.7465	+	3.74271i	0.585466	+	0.171908i
$475$	−23.0199	+	22.7773i	−1.05622	+	1.04510i
$476$	2.31829	+	2.67545i	0.106259	+	0.122629i
$477$	2.51412	−	6.74061i	0.115114	−	0.308631i
$478$	−2.18004	−	1.19039i	−0.0997128	−	0.0544473i
$479$	11.3105	−	24.7666i	0.516791	−	1.13161i	−0.453850	−	0.891078i	$-0.649950\pi$
$479$	11.3105	−	24.7666i	0.516791	−	1.13161i	0.970640	−	0.240535i	$-0.0773230\pi$
$480$	−1.83337	−	1.28014i	−0.0836815	−	0.0584301i
$481$	6.66541	+	10.3716i	0.303916	+	0.472903i
$482$	−2.19798	−	2.19798i	−0.100115	−	0.100115i
$483$	−5.78840	−	16.7724i	−0.263382	−	0.763170i
$484$			0.925846i			0.0420839i
$485$	−10.7380	+	13.2530i	−0.487587	+	0.601790i
$486$	0.142315	−	0.989821i	0.00645553	−	0.0448992i
$487$	−4.16884	−	11.1771i	−0.188908	−	0.506483i	0.807623	−	0.589699i	$-0.200754\pi$
$487$	−4.16884	−	11.1771i	−0.188908	−	0.506483i	−0.996532	+	0.0832161i	$0.973481\pi$
$488$	4.81833	−	8.82412i	0.218116	−	0.399449i
$489$	−20.8444	+	9.51931i	−0.942615	+	0.430478i
$490$	12.8406	+	7.66474i	0.580081	+	0.346258i
$491$	0.137365	+	0.955393i	0.00619918	+	0.0431163i	0.992686	−	0.120723i	$-0.0385213\pi$
$491$	0.137365	+	0.955393i	0.00619918	+	0.0431163i	−0.986487	+	0.163839i	$0.947612\pi$
$492$	6.02377	−	3.28923i	0.271573	−	0.148290i
$493$	−0.329752	−	4.61053i	−0.0148513	−	0.207648i
$494$	−14.5313	−	9.33871i	−0.653795	−	0.420168i
$495$	6.65144	−	3.92271i	0.298960	−	0.176312i
$496$	−2.56125	+	2.95584i	−0.115003	+	0.132721i
$497$	−15.0996	−	27.6529i	−0.677312	−	1.24040i
$498$	−8.62665	−	6.45783i	−0.386569	−	0.289382i
$499$	16.2390	−	14.0712i	0.726958	−	0.629913i	−0.210668	−	0.977558i	$-0.567564\pi$
$499$	16.2390	−	14.0712i	0.726958	−	0.629913i	0.937626	+	0.347645i	$0.113018\pi$
$500$	−9.23412	+	6.30325i	−0.412963	+	0.281890i
$501$	4.72749	−	1.38812i	0.211209	−	0.0620164i
$502$	−19.4399	+	7.25072i	−0.867646	+	0.323615i
$503$	23.6595	+	31.6054i	1.05492	+	1.40921i	0.907456	+	0.420148i	$0.138022\pi$
$503$	23.6595	+	31.6054i	1.05492	+	1.40921i	0.147469	+	0.989067i	$0.452887\pi$
$504$	−3.11238	+	2.00021i	−0.138637	+	0.0890963i
$505$	8.96062	−	17.7832i	0.398742	−	0.791344i
$506$	8.60742	+	14.1494i	0.382646	+	0.629020i
$507$	−4.16294	+	4.16294i	−0.184883	+	0.184883i
$508$	7.03267	+	1.52986i	0.312024	+	0.0678768i
$509$	20.8785	+	3.00188i	0.925425	+	0.133056i	0.588520	−	0.808483i	$-0.299711\pi$
$509$	20.8785	+	3.00188i	0.925425	+	0.133056i	0.336905	+	0.941539i	$0.390620\pi$
$510$	−0.234347	+	2.12675i	−0.0103771	+	0.0941741i
$511$	7.57961	+	25.8138i	0.335302	+	1.14194i
$512$	−0.936950	−	0.349464i	−0.0414077	−	0.0154443i
$513$	−6.46029	−	0.462049i	−0.285229	−	0.0204000i
$514$	−2.94243	+	0.423057i	−0.129785	+	0.0186602i
$515$	−0.439056	−	13.2789i	−0.0193471	−	0.585138i
$516$	−5.86074	−	5.07836i	−0.258005	−	0.223562i
$517$	−3.98757	−	18.3306i	−0.175373	−	0.806178i
$518$	−3.63545	−	16.7119i	−0.159733	−	0.734279i
$519$	−0.0349979	−	0.0303258i	−0.00153624	−	0.00133116i
$520$	−4.35389	−	4.07519i	−0.190931	−	0.178709i
$521$	−8.20926	+	1.18031i	−0.359654	+	0.0517105i	−0.319774	−	0.947494i	$-0.603607\pi$
$521$	−8.20926	+	1.18031i	−0.359654	+	0.0517105i	−0.0398806	+	0.999204i	$0.512698\pi$
$522$	4.81835	+	0.344616i	0.210894	+	0.0150834i
$523$	12.5516	+	4.68150i	0.548843	+	0.204708i	0.608560	−	0.793508i	$-0.291747\pi$
$523$	12.5516	+	4.68150i	0.548843	+	0.204708i	−0.0597177	+	0.998215i	$0.519020\pi$
$524$	−1.74988	−	5.95956i	−0.0764440	−	0.260344i
$525$	3.83636	+	18.0963i	0.167432	+	0.789787i
$526$	−28.1527	−	4.04774i	−1.22751	−	0.176490i
$527$	3.65691	+	0.795513i	0.159298	+	0.0346531i
$528$	2.44191	−	2.44191i	0.106270	−	0.106270i
$529$	20.4246	+	10.5753i	0.888025	+	0.459795i
$530$	−14.3660	−	7.23876i	−0.624021	−	0.314432i
$531$	0.270001	−	0.173519i	0.0117171	−	0.00753009i
$532$	14.3600	+	19.1827i	0.622585	+	0.831676i
$533$	17.1501	−	6.39666i	0.742853	−	0.277070i
$534$	−6.87906	+	2.01988i	−0.297686	+	0.0874086i
$535$	−7.05696	−	7.62007i	−0.305099	−	0.329444i
$536$	−12.1236	+	10.5051i	−0.523659	+	0.453753i
$537$	−1.56463	−	1.17127i	−0.0675190	−	0.0505441i
$538$	5.46849	+	10.0148i	0.235763	+	0.431768i
$539$	−15.1242	+	17.4543i	−0.651447	+	0.751810i
$540$	−2.16514	−	0.558729i	−0.0931727	−	0.0240439i
$541$	−20.8723	−	13.4138i	−0.897369	−	0.576704i	0.00864014	−	0.999963i	$-0.497250\pi$
$541$	−20.8723	−	13.4138i	−0.897369	−	0.576704i	−0.906009	+	0.423259i	$0.860886\pi$
$542$	0.168560	+	2.35678i	0.00724029	+	0.101232i
$543$	−16.9800	+	9.27179i	−0.728682	+	0.397891i
$544$	0.136177	+	0.947129i	0.00583852	+	0.0406078i
$545$	−25.6102	+	6.46444i	−1.09702	+	0.276906i
$546$	−8.97531	+	4.09889i	−0.384108	+	0.175416i
$547$	3.35019	−	6.13542i	0.143244	−	0.262332i	−0.796201	−	0.605033i	$-0.793160\pi$
$547$	3.35019	−	6.13542i	0.143244	−	0.262332i	0.939445	+	0.342701i	$0.111342\pi$
$548$	0.966688	+	2.59179i	0.0412949	+	0.110716i
$549$	1.43082	−	9.95159i	0.0610660	−	0.424724i
$550$	−7.08966	−	15.7443i	−0.302304	−	0.671339i
$551$		−	31.2872i		−	1.33288i
$552$	1.13477	−	4.65964i	0.0482992	−	0.198328i
$553$	−34.7536	−	34.7536i	−1.47788	−	1.47788i
$554$	7.44684	+	11.5875i	0.316386	+	0.492306i
$555$	5.91776	−	8.47521i	0.251195	−	0.359752i
$556$	−0.536547	+	1.17487i	−0.0227547	+	0.0498257i
$557$	20.4908	+	11.1888i	0.868222	+	0.474085i	0.850633	−	0.525760i	$-0.176219\pi$
$557$	20.4908	+	11.1888i	0.868222	+	0.474085i	0.0175889	+	0.999845i	$0.494401\pi$
$558$	−1.36680	+	3.66454i	−0.0578613	+	0.155132i
$559$	−13.5438	−	15.6304i	−0.572842	−	0.661095i
$560$	3.68343	+	7.40750i	0.155654	+	0.313024i
$561$	−3.17058	−	0.930966i	−0.133862	−	0.0393054i
$562$	−31.4528	+	2.24955i	−1.32676	+	0.0948915i
$563$	37.9918	−	8.26461i	1.60116	−	0.348312i	0.678706	−	0.734410i	$-0.262541\pi$
$563$	37.9918	−	8.26461i	1.60116	−	0.348312i	0.922457	+	0.386099i	$0.126178\pi$
$564$	−2.93684	+	4.56982i	−0.123663	+	0.192424i
$565$	1.99408	+	0.832166i	0.0838914	+	0.0350095i
$566$	−6.84074	+	23.2974i	−0.287538	+	0.979263i
$567$	−2.21715	+	2.96176i	−0.0931114	+	0.124382i
$568$	0.607530	−	8.49438i	0.0254914	−	0.356416i
$569$	−15.8519	−	34.7108i	−0.664545	−	1.45515i	−0.878225	−	0.478248i	$-0.841272\pi$
$569$	−15.8519	−	34.7108i	−0.664545	−	1.45515i	0.213680	−	0.976904i	$-0.431455\pi$
$570$	−2.60915	+	14.2456i	−0.109285	+	0.596682i
$571$	−17.1825	−	7.84697i	−0.719064	−	0.328385i	0.0220574	−	0.999757i	$-0.492978\pi$
$571$	−17.1825	−	7.84697i	−0.719064	−	0.328385i	−0.741121	+	0.671371i	$0.765706\pi$
$572$	7.37303	−	5.51938i	0.308282	−	0.230777i
$573$	0.512031	−	2.35377i	0.0213904	−	0.0983301i
$574$	−25.3921			−1.05985
$575$	−19.7749	−	13.5629i	−0.824671	−	0.565613i
$576$	−1.00000			−0.0416667
$577$	−7.33386	+	33.7132i	−0.305312	+	1.40350i	0.527317	+	0.849668i	$0.323198\pi$
$577$	−7.33386	+	33.7132i	−0.305312	+	1.40350i	−0.832630	+	0.553830i	$0.813166\pi$
$578$	−12.8762	+	9.63902i	−0.535580	+	0.400931i
$579$	16.8739	+	7.70607i	0.701257	+	0.320253i
$580$	1.94601	−	10.6249i	0.0808038	−	0.441177i
$581$	16.5618	+	36.2652i	0.687098	+	1.50453i
$582$	−0.544190	+	7.60877i	−0.0225574	+	0.315393i
$583$	14.8887	−	19.8889i	0.616625	−	0.823715i
$584$	−2.04871	+	6.97727i	−0.0847763	+	0.288722i
$585$	−5.50351	−	2.29672i	−0.227542	−	0.0949577i
$586$	9.10908	−	14.1740i	0.376293	−	0.585523i
$587$	−40.3318	+	8.77364i	−1.66467	+	0.362127i	−0.943690	−	0.330830i	$-0.892671\pi$
$587$	−40.3318	+	8.77364i	−1.66467	+	0.362127i	−0.720979	+	0.692957i	$0.756308\pi$
$588$	6.67071	−	0.477099i	0.275096	−	0.0196752i
$589$	24.3055	+	7.13674i	1.00149	+	0.294064i
$590$	−0.319540	−	0.642605i	−0.0131553	−	0.0264556i
$591$	7.86598	+	9.07782i	0.323563	+	0.373412i
$592$	1.61548	−	4.33128i	0.0663960	−	0.178015i
$593$	−41.5964	−	22.7134i	−1.70816	−	0.932727i	−0.964466	−	0.264208i	$-0.914889\pi$
$593$	−41.5964	−	22.7134i	−1.70816	−	0.932727i	−0.743696	−	0.668518i	$-0.766929\pi$
$594$	1.43459	−	3.14131i	0.0588618	−	0.128889i
$595$	4.53185	−	6.49035i	0.185788	−	0.266079i
$596$	−8.05805	−	12.5386i	−0.330071	−	0.513600i
$597$	6.23931	+	6.23931i	0.255358	+	0.255358i
$598$	4.76416	−	11.8699i	0.194821	−	0.485397i
$599$		−	18.8584i		−	0.770535i	−0.922805	−	0.385267i	$-0.874109\pi$
$599$		−	18.8584i		−	0.770535i	0.922805	−	0.385267i	$-0.125891\pi$
$600$	−1.77210	+	4.67543i	−0.0723459	+	0.190874i
$601$	0.615570	−	4.28138i	0.0251096	−	0.174641i	−0.973407	−	0.229081i	$-0.926428\pi$
$601$	0.615570	−	4.28138i	0.0251096	−	0.174641i	0.998517	+	0.0544393i	$0.0173372\pi$
$602$	10.0264	+	26.8817i	0.408644	+	1.09562i
$603$	−7.68802	+	14.0796i	−0.313080	+	0.573364i
$604$	0.850450	−	0.388387i	0.0346043	−	0.0158033i
$605$	2.00729	−	0.506674i	0.0816081	−	0.0205992i
$606$	−1.26738	−	8.81482i	−0.0514838	−	0.358078i
$607$	14.6514	−	8.00026i	0.594681	−	0.324721i	−0.153568	−	0.988138i	$-0.549076\pi$
$607$	14.6514	−	8.00026i	0.594681	−	0.324721i	0.748249	+	0.663418i	$0.230895\pi$
$608$	0.462049	+	6.46029i	0.0187386	+	0.262000i
$609$	−15.0349	−	9.66232i	−0.609244	−	0.391537i
$610$	−21.7681	−	5.61742i	−0.881366	−	0.227443i
$611$	−9.48721	+	10.9488i	−0.383811	+	0.442942i
$612$	0.458578	+	0.839823i	0.0185369	+	0.0339478i
$613$	−12.3274	−	9.22821i	−0.497901	−	0.372724i	0.320613	−	0.947210i	$-0.396111\pi$
$613$	−12.3274	−	9.22821i	−0.497901	−	0.372724i	−0.818514	+	0.574486i	$0.805202\pi$
$614$	−6.16465	+	5.34170i	−0.248785	+	0.215574i
$615$	−10.4278	−	11.2599i	−0.420490	−	0.454042i
$616$	−12.2589	+	3.59955i	−0.493926	+	0.145030i
$617$	27.0655	−	10.0949i	1.08962	−	0.406406i	0.260495	−	0.965475i	$-0.416114\pi$
$617$	27.0655	−	10.0949i	1.08962	−	0.406406i	0.829121	+	0.559070i	$0.188842\pi$
$618$	−3.56076	−	4.75662i	−0.143235	−	0.191339i
$619$	−28.4088	+	18.2572i	−1.14185	+	0.733820i	−0.968000	−	0.250952i	$-0.919256\pi$
$619$	−28.4088	+	18.2572i	−1.14185	+	0.733820i	−0.173847	+	0.984773i	$0.555620\pi$
$620$	7.81011	+	3.93536i	0.313662	+	0.158048i
$621$	−0.565153	−	4.76242i	−0.0226788	−	0.191109i
$622$	−20.2211	+	20.2211i	−0.810790	+	0.810790i
$623$	25.9187	+	5.63827i	1.03841	+	0.225893i
$624$	−2.63982	−	0.379549i	−0.105677	−	0.0151941i
$625$	18.7193	+	16.5707i	0.748772	+	0.662828i
$626$	5.17070	+	17.6098i	0.206663	+	0.703829i
$627$	−20.9566	−	7.81641i	−0.836927	−	0.312157i
$628$	24.3018	+	1.73810i	0.969748	+	0.0693578i
$629$	−4.37834	+	0.629510i	−0.174576	+	0.0251002i
$630$	6.03985	+	5.65323i	0.240633	+	0.225230i
$631$	22.9963	+	19.9264i	0.915468	+	0.793258i	0.978818	−	0.204734i	$-0.0656329\pi$
$631$	22.9963	+	19.9264i	0.915468	+	0.793258i	−0.0633496	+	0.997991i	$0.520178\pi$
$632$	−2.82385	−	12.9810i	−0.112327	−	0.516358i
$633$	−5.72906	−	26.3361i	−0.227710	−	1.04677i
$634$	−4.16653	−	3.61032i	−0.165474	−	0.143384i
$635$	−0.531821	−	16.0845i	−0.0211047	−	0.638295i
$636$	−7.12098	+	1.02384i	−0.282365	+	0.0405980i
$637$	17.7906	+	1.27241i	0.704888	+	0.0504146i
$638$	15.6303	+	5.82980i	0.618810	+	0.230804i
$639$	−2.39926	−	8.17111i	−0.0949131	−	0.323244i
$640$	−0.244911	+	2.22262i	−0.00968094	+	0.0878566i
$641$	−0.941471	−	0.135363i	−0.0371859	−	0.00534652i	0.123697	−	0.992320i	$-0.460525\pi$
$641$	−0.941471	−	0.135363i	−0.0371859	−	0.00534652i	−0.160883	+	0.986974i	$0.551434\pi$
$642$	−4.53855	−	0.987302i	−0.179122	−	0.0389657i
$643$	29.3408	−	29.3408i	1.15709	−	1.15709i	0.171988	−	0.985099i	$-0.444981\pi$
$643$	29.3408	−	29.3408i	1.15709	−	1.15709i	0.985099	−	0.171988i	$-0.0550189\pi$
$644$	−11.9467	+	13.1185i	−0.470765	+	0.516942i
$645$	−7.80289	+	15.4856i	−0.307239	+	0.609746i
$646$	5.21362	−	3.35059i	0.205127	−	0.131827i
$647$	12.3849	+	16.5443i	0.486902	+	0.650424i	0.974958	−	0.222387i	$-0.0713850\pi$
$647$	12.3849	+	16.5443i	0.486902	+	0.650424i	−0.488057	+	0.872812i	$0.662294\pi$
$648$	−0.936950	+	0.349464i	−0.0368069	+	0.0137282i
$649$	1.06347	−	0.312263i	0.0417448	−	0.0122574i
$650$	−6.45260	+	11.6697i	−0.253092	+	0.457723i
$651$	10.9357	−	9.47584i	0.428604	−	0.371387i
$652$	18.3445	+	13.7326i	0.718428	+	0.537808i
$653$	−6.06273	−	11.1031i	−0.237253	−	0.434496i	0.731740	−	0.681584i	$-0.238708\pi$
$653$	−6.06273	−	11.1031i	−0.237253	−	0.434496i	−0.968993	+	0.247087i	$0.920527\pi$
$654$	−7.73552	+	8.92727i	−0.302483	+	0.349084i
$655$	−11.9631	+	7.05527i	−0.467436	+	0.275672i
$656$	−5.77377	−	3.71058i	−0.225428	−	0.144874i
$657$	0.518767	+	7.25331i	0.0202390	+	0.282978i
$658$	17.6390	−	9.63162i	0.687639	−	0.375479i
$659$	−0.0192813	−	0.134104i	−0.000751091	−	0.00522395i	0.989442	−	0.144926i	$-0.0462945\pi$
$659$	−0.0192813	−	0.134104i	−0.000751091	−	0.00522395i	−0.990194	+	0.139702i	$0.955385\pi$
$660$	−6.63057	−	3.95787i	−0.258095	−	0.154060i
$661$	−16.4014	+	7.49027i	−0.637941	+	0.291338i	−0.708008	−	0.706204i	$-0.750406\pi$
$661$	−16.4014	+	7.49027i	−0.637941	+	0.291338i	0.0700670	+	0.997542i	$0.477679\pi$
$662$	−0.539082	+	0.987256i	−0.0209520	+	0.0383708i
$663$	0.891810	+	2.39104i	0.0346350	+	0.0928602i
$664$	−1.53359	+	10.6663i	−0.0595148	+	0.413934i
$665$	33.7308	−	41.6313i	1.30802	−	1.61439i
$666$		−	4.62275i		−	0.179128i
$667$	22.7522	−	4.36431i	0.880970	−	0.168987i
$668$	−3.48396	−	3.48396i	−0.134799	−	0.134799i
$669$	−14.9762	−	23.3035i	−0.579015	−	0.900965i
$670$	29.4106	+	20.5357i	1.13623	+	0.793365i
$671$	14.4232	−	31.5825i	0.556802	−	1.21923i
$672$	3.24715	+	1.77308i	0.125261	+	0.0683979i
$673$	1.53810	−	4.12381i	0.0592895	−	0.158961i	−0.903928	−	0.427685i	$-0.859329\pi$
$673$	1.53810	−	4.12381i	0.0592895	−	0.158961i	0.963217	+	0.268724i	$0.0866019\pi$
$674$	13.5960	+	15.6906i	0.523697	+	0.604378i
$675$	−0.0264779	+	4.99993i	−0.00101914	+	0.192447i
$676$	5.64881	+	1.65864i	0.217262	+	0.0637938i
$677$	33.2435	−	2.37762i	1.27765	−	0.0913794i	0.584038	−	0.811726i	$-0.301472\pi$
$677$	33.2435	−	2.37762i	1.27765	−	0.0913794i	0.693614	+	0.720347i	$0.256017\pi$
$678$	0.944233	−	0.205405i	0.0362631	−	0.00788855i
$679$	15.2580	−	23.7419i	0.585548	−	0.911130i
$680$	1.97891	−	0.813561i	0.0758879	−	0.0311986i
$681$	−6.43575	+	21.9181i	−0.246618	+	0.839905i
$682$	−8.09423	+	10.8126i	−0.309944	+	0.414037i
$683$	−0.756361	+	10.5753i	−0.0289413	+	0.404653i	0.962246	+	0.272183i	$0.0877455\pi$
$683$	−0.756361	+	10.5753i	−0.0289413	+	0.404653i	−0.991187	+	0.132470i	$0.957709\pi$
$684$	2.69056	+	5.89150i	0.102876	+	0.225267i
$685$	5.09015	−	3.51422i	0.194485	−	0.134271i
$686$	1.05082	+	0.479895i	0.0401206	+	0.0183225i
$687$	14.3117	−	10.7136i	0.546025	−	0.408749i
$688$	−1.64842	+	7.57764i	−0.0628452	+	0.288895i
$689$	−19.1867			−0.730955
$690$	−10.7234	+	0.0897523i	−0.408234	+	0.00341681i
$691$	−28.4714			−1.08310			−0.541551	−	0.840668i	$-0.682163\pi$
$691$	−28.4714			−1.08310			−0.541551	+	0.840668i	$0.682163\pi$
$692$	−0.00984365	+	0.0452505i	−0.000374199	+	0.00172017i
$693$	−10.2281	+	7.65665i	−0.388533	+	0.290852i
$694$	−32.4529	−	14.8207i	−1.23190	−	0.562588i
$695$	2.84083	+	0.520313i	0.107759	+	0.0197366i
$696$	−2.00673	−	4.39413i	−0.0760649	−	0.166559i
$697$	−0.468504	+	6.55054i	−0.0177458	+	0.248119i
$698$	−1.04325	+	1.39362i	−0.0394875	+	0.0527491i
$699$	6.85259	−	23.3378i	0.259189	−	0.882716i
$700$	14.0442	−	12.0397i	0.530820	−	0.455059i
$701$	0.500318	−	0.778510i	0.0188968	−	0.0294039i	−0.831677	−	0.555260i	$-0.812619\pi$
$701$	0.500318	−	0.778510i	0.0188968	−	0.0294039i	0.850573	+	0.525856i	$0.176255\pi$
$702$	−2.60602	+	0.566905i	−0.0983578	+	0.0213964i
$703$	−29.8643	+	2.13594i	−1.12635	+	0.0805584i
$704$	−3.31350	−	0.972930i	−0.124882	−	0.0366687i
$705$	11.5149	+	3.86641i	0.433675	+	0.145618i
$706$	8.58929	+	9.91257i	0.323262	+	0.373064i
$707$	−11.5140	+	30.8702i	−0.433028	+	1.16099i
$708$	−0.281692	−	0.153815i	−0.0105866	−	0.00578074i
$709$	−13.0851	+	28.6523i	−0.491419	+	1.07606i	0.487744	+	0.872986i	$0.337820\pi$
$709$	−13.0851	+	28.6523i	−0.491419	+	1.07606i	−0.979164	+	0.203072i	$0.934907\pi$
$710$	−18.7488	+	3.33143i	−0.703632	+	0.125026i
$711$	−7.18221	−	11.1757i	−0.269354	−	0.419123i
$712$	5.06959	+	5.06959i	0.189991	+	0.189991i
$713$	−1.79946	+	18.6706i	−0.0673903	+	0.699220i
$714$		−	3.54012i		−	0.132486i
$715$	−16.0013	−	12.9647i	−0.598415	−	0.484853i
$716$	−0.278150	+	1.93458i	−0.0103950	+	0.0722985i
$717$	0.868024	+	2.32726i	0.0324170	+	0.0869132i
$718$	−17.6531	+	32.3293i	−0.658810	+	1.20652i
$719$	−19.8035	+	9.04395i	−0.738546	+	0.337283i	−0.748917	−	0.662664i	$-0.769426\pi$
$719$	−19.8035	+	9.04395i	−0.738546	+	0.337283i	0.0103714	+	0.999946i	$0.496699\pi$
$720$	0.547255	+	2.16807i	0.0203950	+	0.0807991i
$721$	3.12846	+	21.7589i	0.116510	+	0.810345i
$722$	20.1418	−	10.9982i	0.749599	−	0.409312i
$723$	0.221752	+	3.10049i	0.00824703	+	0.115309i
$724$	16.2753	+	10.4595i	0.604867	+	0.388724i
$725$	−24.1006	+	1.59547i	−0.895072	+	0.0592544i
$726$	0.606300	−	0.699707i	0.0225019	−	0.0259686i
$727$	−16.4838	−	30.1878i	−0.611349	−	1.11960i	−0.981650	−	0.190690i	$-0.938927\pi$
$727$	−16.4838	−	30.1878i	−0.611349	−	1.11960i	0.370301	−	0.928912i	$-0.379254\pi$
$728$	7.89892	+	5.91305i	0.292753	+	0.219152i
$729$	−0.755750	+	0.654861i	−0.0279907	+	0.0242541i
$730$	16.2484	+	0.623393i	0.601379	+	0.0230728i
$731$	7.11981	−	2.09056i	0.263336	−	0.0773223i
$732$	−9.42002	+	3.51349i	−0.348174	+	0.129862i
$733$	20.0480	+	26.7810i	0.740491	+	0.989181i	0.999727	+	0.0233665i	$0.00743847\pi$
$733$	20.0480	+	26.7810i	0.740491	+	0.989181i	−0.259236	+	0.965814i	$0.583471\pi$
$734$	6.71674	−	4.31658i	0.247919	−	0.159328i
$735$	−4.68497	−	14.2015i	−0.172808	−	0.523829i
$736$	−4.63351	+	1.23716i	−0.170793	+	0.0456024i
$737$	−39.1726	+	39.1726i	−1.44294	+	1.44294i
$738$	−6.70645	−	1.45890i	−0.246868	−	0.0537028i
$739$	−48.2833	−	6.94209i	−1.77613	−	0.255369i	−0.825215	−	0.564819i	$-0.808946\pi$
$739$	−48.2833	−	6.94209i	−1.77613	−	0.255369i	−0.950916	+	0.309450i	$0.899855\pi$
$740$	−10.2746	−	1.13216i	−0.377701	−	0.0416190i
$741$	4.86648	+	16.5737i	0.178775	+	0.608850i
$742$	24.9382	+	9.30147i	0.915510	+	0.341468i
$743$	21.7442	+	1.55518i	0.797717	+	0.0570538i	0.464246	−	0.885706i	$-0.346325\pi$
$743$	21.7442	+	1.55518i	0.797717	+	0.0570538i	0.333471	+	0.942760i	$0.391780\pi$
$744$	3.87132	−	0.556612i	0.141930	−	0.0204064i
$745$	−22.7746	+	24.3322i	−0.834398	+	0.891463i
$746$	−15.2015	−	13.1722i	−0.556568	−	0.482269i
$747$	2.29061	+	10.5298i	0.0838090	+	0.385264i
$748$	0.702407	+	3.22892i	0.0256826	+	0.118061i
$749$	12.9868	+	11.2531i	0.474527	+	0.411180i
$750$	11.1064	+	1.28339i	0.405550	+	0.0468626i
$751$	3.58055	−	0.514805i	0.130656	−	0.0187855i	−0.0766766	−	0.997056i	$-0.524431\pi$
$751$	3.58055	−	0.514805i	0.130656	−	0.0187855i	0.207333	+	0.978271i	$0.433522\pi$
$752$	5.41831	+	0.387525i	0.197585	+	0.0141316i
$753$	19.4399	+	7.25072i	0.708430	+	0.264231i
$754$	−3.62962	−	12.3614i	−0.132183	−	0.450174i
$755$	−1.30746	−	1.63128i	−0.0475834	−	0.0593685i
$756$	3.66204	+	0.526522i	0.133187	+	0.0191494i
$757$	1.71988	+	0.374137i	0.0625100	+	0.0135982i	0.243712	−	0.969848i	$-0.421635\pi$
$757$	1.71988	+	0.374137i	0.0625100	+	0.0135982i	−0.181202	+	0.983446i	$0.557999\pi$
$758$	−17.5063	+	17.5063i	−0.635856	+	0.635856i
$759$	2.76086	−	16.3301i	0.100213	−	0.592745i
$760$	13.7535	−	4.53718i	0.498891	−	0.164581i
$761$	−1.16474	+	0.748531i	−0.0422217	+	0.0271342i	−0.561581	−	0.827421i	$-0.689807\pi$
$761$	−1.16474	+	0.748531i	−0.0422217	+	0.0271342i	0.519360	+	0.854556i	$0.326170\pi$
$762$	−4.31309	−	5.76162i	−0.156247	−	0.208721i
$763$	40.9471	−	15.2725i	1.48238	−	0.552901i
$764$	−2.31124	+	0.678642i	−0.0836178	+	0.0245524i
$765$	1.56983	−	1.45383i	0.0567574	−	0.0525632i
$766$	−7.90645	+	6.85098i	−0.285672	+	0.247536i
$767$	−0.685236	−	0.512961i	−0.0247424	−	0.0185220i
$768$	0.479249	+	0.877679i	0.0172934	+	0.0316705i
$769$	−33.8649	+	39.0822i	−1.22120	+	1.40934i	−0.337472	+	0.941335i	$0.609572\pi$
$769$	−33.8649	+	39.0822i	−1.22120	+	1.40934i	−0.883727	+	0.468003i	$0.844974\pi$
$770$	14.5128	+	24.6083i	0.523006	+	0.886821i
$771$	2.50078	+	1.60715i	0.0900634	+	0.0578802i
$772$	−1.32336	−	18.5030i	−0.0476289	−	0.665939i
$773$	−37.4556	+	20.4523i	−1.34718	+	0.735618i	−0.980831	−	0.194859i	$-0.937575\pi$
$773$	−37.4556	+	20.4523i	−1.34718	+	0.735618i	−0.366352	+	0.930476i	$0.619393\pi$
$774$	1.10363	+	7.67593i	0.0396692	+	0.275906i
$775$	4.25799	−	19.0865i	0.152952	−	0.685607i
$776$	6.93886	−	3.16887i	0.249090	−	0.113756i
$777$	−8.19648	+	15.0107i	−0.294047	+	0.538507i
$778$	−6.81059	−	18.2599i	−0.244171	−	0.654649i
$779$	−6.32620	+	43.9997i	−0.226660	+	1.57645i
$780$	0.621769	+	5.93102i	0.0222629	+	0.212365i
$781$		−	29.4093i		−	1.05235i
$782$	3.16383	+	3.32399i	0.113138	+	0.118866i
$783$	−3.41579	−	3.41579i	−0.122071	−	0.122071i
$784$	−3.61567	−	5.62610i	−0.129131	−	0.200932i
$785$	−9.53099	−	53.6392i	−0.340176	−	1.91446i
$786$	−2.58021	+	5.64986i	−0.0920329	+	0.201524i
$787$	−0.901626	−	0.492325i	−0.0321395	−	0.0175495i	0.463099	−	0.886307i	$-0.346737\pi$
$787$	−0.901626	−	0.492325i	−0.0321395	−	0.0175495i	−0.495238	+	0.868757i	$0.664919\pi$
$788$	4.19765	−	11.2543i	0.149535	−	0.400919i
$789$	18.6257	+	21.4951i	0.663091	+	0.765248i
$790$	−26.5984	+	13.2262i	−0.946327	+	0.470568i
$791$	−3.43026	−	1.00722i	−0.121966	−	0.0358125i
$792$	−3.44458	+	0.246361i	−0.122398	+	0.00875407i
$793$	−26.2007	+	5.69962i	−0.930415	+	0.202399i
$794$	6.94973	−	10.8140i	0.246637	−	0.383774i
$795$	6.11675	+	14.8784i	0.216939	+	0.527684i
$796$	2.48593	−	8.46629i	0.0881114	−	0.300080i
$797$	1.10274	−	1.47309i	0.0390610	−	0.0521794i	−0.780585	−	0.625049i	$-0.785079\pi$
$797$	1.10274	−	1.47309i	0.0390610	−	0.0521794i	0.819647	+	0.572870i	$0.194170\pi$
$798$	1.70944	−	23.9011i	0.0605136	−	0.846091i
$799$	−2.15927	−	4.72813i	−0.0763894	−	0.167269i
$800$	4.95281	−	0.685356i	0.175108	−	0.0242310i
$801$	6.52159	+	2.97831i	0.230429	+	0.105233i
$802$	12.8191	−	9.59623i	0.452657	−	0.338855i
$803$	−5.33803	+	24.5385i	−0.188375	+	0.865946i
$804$	16.0418			0.565751
$805$	34.9797	+	18.7220i	1.23287	+	0.659864i
$806$	10.4309			0.367412
$807$	2.42548	−	11.1498i	0.0853811	−	0.392490i
$808$	−7.12919	+	5.33685i	−0.250804	+	0.187750i
$809$	−17.4956	−	7.98997i	−0.615112	−	0.280912i	0.0833935	−	0.996517i	$-0.473424\pi$
$809$	−17.4956	−	7.98997i	−0.615112	−	0.280912i	−0.698506	+	0.715604i	$0.746151\pi$
$810$	1.27041	+	1.84012i	0.0446377	+	0.0646553i
$811$	16.8799	+	36.9619i	0.592734	+	1.29791i	0.933776	+	0.357858i	$0.116493\pi$
$811$	16.8799	+	36.9619i	0.592734	+	1.29791i	−0.341042	+	0.940048i	$0.610780\pi$
$812$	−1.27497	+	17.8264i	−0.0447428	+	0.625586i
$813$	1.41597	−	1.89152i	0.0496604	−	0.0663385i
$814$	4.49761	−	15.3175i	0.157641	−	0.536876i
$815$	19.7339	−	47.2874i	0.691249	−	1.65641i
$816$	0.517322	−	0.804969i	0.0181099	−	0.0281795i
$817$	49.0788	−	10.6764i	1.71705	−	0.373522i
$818$	17.0449	−	1.21908i	0.595963	−	0.0426241i
$819$	9.46729	+	2.77985i	0.330814	+	0.0971357i
$820$	−4.88505	+	14.5486i	−0.170593	+	0.508057i
$821$	5.42181	+	6.25710i	0.189222	+	0.218374i	0.842432	−	0.538803i	$-0.181123\pi$
$821$	5.42181	+	6.25710i	0.189222	+	0.218374i	−0.653209	+	0.757177i	$0.726578\pi$
$822$	0.966688	−	2.59179i	0.0337171	−	0.0903991i
$823$	−13.4841	−	7.36285i	−0.470025	−	0.256653i	0.226736	−	0.973956i	$-0.427194\pi$
$823$	−13.4841	−	7.36285i	−0.470025	−	0.256653i	−0.696761	+	0.717303i	$0.745376\pi$
$824$	−2.46829	+	5.40481i	−0.0859870	+	0.188285i
$825$	−4.95232	+	16.5415i	−0.172418	+	0.575901i
$826$	0.641968	+	0.998922i	0.0223369	+	0.0347569i
$827$	−5.53002	−	5.53002i	−0.192298	−	0.192298i	0.604391	−	0.796688i	$-0.293417\pi$
$827$	−5.53002	−	5.53002i	−0.192298	−	0.192298i	−0.796688	+	0.604391i	$0.793417\pi$
$828$	−3.90902	+	2.77841i	−0.135848	+	0.0965563i
$829$		−	27.8429i		−	0.967024i	−0.875338	−	0.483512i	$-0.839361\pi$
$829$		−	27.8429i		−	0.967024i	0.875338	−	0.483512i	$-0.160639\pi$
$830$	23.9646	−	2.51229i	0.831823	−	0.0872029i
$831$	1.96026	−	13.6339i	0.0680006	−	0.472955i
$832$	0.932010	+	2.49881i	0.0323116	+	0.0866308i
$833$	−3.06686	+	5.61653i	−0.106260	+	0.194601i
$834$	1.17487	−	0.536547i	0.0406826	−	0.0185791i
$835$	−5.64685	+	9.46008i	−0.195417	+	0.327380i
$836$	3.18313	+	22.1392i	0.110091	+	0.765700i
$837$	3.43272	−	1.87441i	0.118652	−	0.0647890i
$838$	−2.19861	−	30.7406i	−0.0759497	−	1.06192i
$839$	−34.1447	−	21.9434i	−1.17880	−	0.757572i	−0.203638	−	0.979046i	$-0.565277\pi$
$839$	−34.1447	−	21.9434i	−1.17880	−	0.757572i	−0.975166	+	0.221475i	$0.928913\pi$
$840$	2.06713	−	8.01035i	0.0713227	−	0.276383i
$841$	−3.70959	+	4.28109i	−0.127917	+	0.147624i
$842$	7.93655	+	14.5347i	0.273512	+	0.500899i
$843$	25.2436	+	18.8971i	0.869435	+	0.650851i
$844$	−20.3690	+	17.6498i	−0.701129	+	0.607532i
$845$	0.504700	−	13.1547i	0.0173622	−	0.452535i
$846$	5.21211	−	1.53041i	0.179196	−	0.0526167i
$847$	−3.20938	+	1.19704i	−0.110276	+	0.0411307i
$848$	4.31133	+	5.75926i	0.148052	+	0.197774i
$849$	20.4264	−	13.1273i	0.701034	−	0.450527i
$850$	−2.84683	−	3.84519i	−0.0976453	−	0.131889i
$851$	−5.71909	−	21.4196i	−0.196048	−	0.734253i
$852$	−6.02177	+	6.02177i	−0.206303	+	0.206303i
$853$	−34.6726	−	7.54257i	−1.18717	−	0.258253i	−0.424734	−	0.905318i	$-0.639632\pi$
$853$	−34.6726	−	7.54257i	−1.18717	−	0.258253i	−0.762434	+	0.647066i	$0.775996\pi$
$854$	36.8179	+	5.29361i	1.25988	+	0.181144i
$855$	11.3007	−	9.05746i	0.386477	−	0.309759i
$856$	1.30856	+	4.45656i	0.0447258	+	0.152322i
$857$	−19.3860	−	7.23059i	−0.662212	−	0.246992i	−0.00419026	−	0.999991i	$-0.501334\pi$
$857$	−19.3860	−	7.23059i	−0.662212	−	0.246992i	−0.658022	+	0.752999i	$0.728607\pi$
$858$	−9.18659	−	0.657038i	−0.313625	−	0.0224309i
$859$	−15.2408	+	2.19129i	−0.520008	+	0.0747659i	−0.397321	−	0.917679i	$-0.630060\pi$
$859$	−15.2408	+	2.19129i	−0.520008	+	0.0747659i	−0.122687	+	0.992445i	$0.539151\pi$
$860$	17.3309	−	0.573033i	0.590980	−	0.0195403i
$861$	19.1901	+	16.6283i	0.653996	+	0.566691i
$862$	0.0682751	+	0.313856i	0.00232546	+	0.0106900i
$863$	−9.18284	−	42.2128i	−0.312587	−	1.43694i	−0.818574	−	0.574400i	$-0.805235\pi$
$863$	−9.18284	−	42.2128i	−0.312587	−	1.43694i	0.505987	−	0.862541i	$-0.331128\pi$
$864$	0.755750	+	0.654861i	0.0257111	+	0.0222788i
$865$	0.103493	−	0.00342191i	0.00351887	−	0.000116349i
$866$	21.2284	−	3.05218i	0.721370	−	0.103717i
$867$	16.0434	+	1.14745i	0.544863	+	0.0389694i
$868$	−13.5577	−	5.05675i	−0.460177	−	0.171637i
$869$	−12.9250	−	44.0185i	−0.438451	−	1.49323i
$870$	−8.42856	+	6.75543i	−0.285755	+	0.229031i
$871$	42.3475	+	6.08865i	1.43489	+	0.206306i
$872$	11.5425	+	2.51092i	0.390879	+	0.0850305i
$873$	5.39395	−	5.39395i	0.182558	−	0.182558i
$874$	19.7555	+	23.9697i	0.668239	+	0.810786i
$875$	−33.7887	−	23.8599i	−1.14227	−	0.806612i
$876$	6.11746	−	3.93145i	0.206690	−	0.132831i
$877$	−22.7402	−	30.3774i	−0.767883	−	1.02577i	−0.998608	−	0.0527529i	$-0.983200\pi$
$877$	−22.7402	−	30.3774i	−0.767883	−	1.02577i	0.230724	−	0.973019i	$-0.425890\pi$
$878$	−14.6949	+	5.48092i	−0.495929	+	0.184972i
$879$	−16.1662	+	4.74682i	−0.545272	+	0.160106i
$880$	−0.296048	+	7.71632i	−0.00997979	+	0.260117i
$881$	5.09497	−	4.41481i	0.171654	−	0.148739i	−0.564797	−	0.825230i	$-0.691046\pi$
$881$	5.09497	−	4.41481i	0.171654	−	0.148739i	0.736451	+	0.676491i	$0.236500\pi$
$882$	−5.35382	−	4.00782i	−0.180273	−	0.134950i
$883$	8.58791	+	15.7276i	0.289006	+	0.529275i	0.981335	−	0.192307i	$-0.0615969\pi$
$883$	8.58791	+	15.7276i	0.289006	+	0.529275i	−0.692329	+	0.721582i	$0.743415\pi$
$884$	1.67116	−	1.92863i	0.0562073	−	0.0648667i
$885$	−0.179325	+	0.694903i	−0.00602793	+	0.0233589i
$886$	−14.3949	−	9.25102i	−0.483605	−	0.310794i
$887$	2.69807	+	37.7240i	0.0905925	+	1.26665i	0.815888	+	0.578210i	$0.196249\pi$
$887$	2.69807	+	37.7240i	0.0905925	+	1.26665i	−0.725295	+	0.688438i	$0.758297\pi$
$888$	−4.05729	+	2.21545i	−0.136154	+	0.0743455i
$889$	3.78946	+	26.3562i	0.127094	+	0.883960i
$890$	8.21684	−	13.7656i	0.275429	−	0.461423i
$891$	−3.14131	+	1.43459i	−0.105238	+	0.0480605i
$892$	−13.2756	+	24.3125i	−0.444501	+	0.814043i
$893$	−12.2952	−	32.9646i	−0.411442	−	1.10312i
$894$	−2.12115	+	14.7529i	−0.0709419	+	0.493412i
$895$	4.34651	−	0.455660i	0.145288	−	0.0152310i
$896$		−	3.69970i		−	0.123598i
$897$	−11.3737	+	5.85083i	−0.379756	+	0.195354i
$898$	5.13466	+	5.13466i	0.171346	+	0.171346i
$899$	10.2145	+	15.8941i	0.340674	+	0.530098i
$900$	4.40102	−	2.37297i	0.146701	−	0.0790991i
$901$	2.85968	−	6.26182i	0.0952697	−	0.208612i
$902$	−20.8024	−	11.3590i	−0.692643	−	0.378212i
$903$	10.0264	−	26.8817i	0.333656	−	0.894567i
$904$	−0.632803	−	0.730294i	−0.0210467	−	0.0242892i
$905$	13.7702	−	41.0100i	0.457735	−	1.36322i
$906$	−0.897067	−	0.263403i	−0.0298030	−	0.00875096i
$907$	13.1675	−	0.941760i	0.437221	−	0.0312706i	0.149006	−	0.988836i	$-0.452393\pi$
$907$	13.1675	−	0.941760i	0.437221	−	0.0312706i	0.288215	+	0.957566i	$0.406938\pi$
$908$	22.3214	−	4.85573i	0.740762	−	0.161143i
$909$	−4.81466	+	7.49175i	−0.159692	+	0.248486i
$910$	8.49717	−	20.3613i	0.281678	−	0.674971i
$911$	−4.41524	+	15.0369i	−0.146284	+	0.498196i	−0.999736	−	0.0229747i	$-0.992686\pi$
$911$	−4.41524	+	15.0369i	−0.146284	+	0.498196i	0.853453	+	0.521171i	$0.174504\pi$
$912$	3.88140	−	5.18494i	0.128526	−	0.171691i
$913$	−2.65480	+	37.1189i	−0.0878609	+	1.22846i
$914$	3.53994	+	7.75139i	0.117091	+	0.256393i
$915$	12.7726	+	18.5005i	0.422250	+	0.611606i
$916$	−16.2620	−	7.42659i	−0.537310	−	0.245381i
$917$	18.3959	−	13.7710i	0.607488	−	0.454759i
$918$	0.203397	−	0.935001i	0.00671310	−	0.0308596i
$919$	4.00671			0.132169			0.0660846	−	0.997814i	$-0.478949\pi$
$919$	4.00671			0.132169			0.0660846	+	0.997814i	$0.478949\pi$
$920$	5.21797	+	9.36872i	0.172031	+	0.308877i
$921$	8.15700			0.268782
$922$	4.76868	−	21.9213i	0.157048	−	0.721939i
$923$	−18.1820	+	13.6108i	−0.598467	+	0.448007i
$924$	11.6219	+	5.30753i	0.382332	+	0.174605i
$925$	3.16823	+	22.8956i	0.104171	+	0.752802i
$926$	−9.89278	−	21.6622i	−0.325097	−	0.711863i
$927$	−0.423880	+	5.92661i	−0.0139220	+	0.194655i
$928$	−2.89491	+	3.86714i	−0.0950300	+	0.126945i
$929$	−6.72307	+	22.8967i	−0.220577	+	0.751216i	0.772630	+	0.634856i	$0.218941\pi$
$929$	−6.72307	+	22.8967i	−0.220577	+	0.751216i	−0.993207	+	0.116360i	$0.962878\pi$
$930$	−3.32538	−	8.08868i	−0.109043	−	0.265238i
$931$	−23.4180	+	36.4391i	−0.767493	+	1.19424i
$932$	−23.7672	+	5.17023i	−0.778520	+	0.169357i
$933$	28.5240	−	2.04008i	0.933835	−	0.0667892i
$934$	−24.1983	−	7.10527i	−0.791794	−	0.232492i
$935$	6.61611	−	3.28991i	0.216370	−	0.107591i
$936$	1.74649	+	2.01556i	0.0570859	+	0.0658806i
$937$	7.56591	−	20.2850i	0.247167	−	0.662681i	−0.752823	−	0.658223i	$-0.771308\pi$
$937$	7.56591	−	20.2850i	0.247167	−	0.662681i	0.999990	−	0.00445804i	$-0.00141904\pi$
$938$	−52.0901	−	28.4433i	−1.70080	−	0.928708i
$939$	7.62421	−	16.6947i	0.248807	−	0.544811i
$940$	−2.12502	−	11.9593i	−0.0693105	−	0.390070i
$941$	26.6513	+	41.4702i	0.868807	+	1.35189i	0.935209	+	0.354098i	$0.115212\pi$
$941$	26.6513	+	41.4702i	0.868807	+	1.35189i	−0.0664012	+	0.997793i	$0.521152\pi$
$942$	−17.2279	−	17.2279i	−0.561315	−	0.561315i
$943$	−32.8793	+	1.53715i	−1.07070	+	0.0500565i
$944$			0.320951i			0.0104461i
$945$	−0.862537	−	8.22768i	−0.0280583	−	0.267647i
$946$	−3.81126	+	26.5079i	−0.123915	+	0.861847i
$947$	−10.3352	−	27.7099i	−0.335850	−	0.900449i	−0.989614	−	0.143751i	$-0.954084\pi$
$947$	−10.3352	−	27.7099i	−0.335850	−	0.900449i	0.653764	−	0.756699i	$-0.273189\pi$
$948$	−6.36664	+	11.6596i	−0.206779	+	0.378687i
$949$	17.6412	−	8.05645i	0.572657	−	0.261524i
$950$	−17.3636	−	27.3355i	−0.563349	−	0.886880i
$951$	0.784597	+	5.45699i	0.0254423	+	0.176955i
$952$	−3.10709	+	1.69660i	−0.100701	+	0.0549871i
$953$	−0.191604	−	2.67897i	−0.00620665	−	0.0867804i	0.993405	−	0.114662i	$-0.0365784\pi$
$953$	−0.191604	−	2.67897i	−0.00620665	−	0.0867804i	−0.999611	+	0.0278815i	$0.991124\pi$
$954$	6.05215	+	3.88948i	0.195946	+	0.125927i
$955$	2.73618	+	4.63954i	0.0885407	+	0.150132i
$956$	1.62659	−	1.87718i	0.0526077	−	0.0607125i
$957$	−7.99489	−	14.6415i	−0.258438	−	0.473294i
$958$	21.7964	+	16.3165i	0.704208	+	0.527164i
$959$	−7.73442	+	6.70191i	−0.249757	+	0.216416i
$960$	1.64059	−	1.51936i	0.0529500	−	0.0490371i
$961$	15.0669	−	4.42406i	0.486031	−	0.142711i
$962$	−11.5514	+	4.30845i	−0.372432	+	0.138910i
$963$	2.78346	+	3.71827i	0.0896959	+	0.119820i
$964$	2.61496	−	1.68053i	0.0842222	−	0.0541264i
$965$	−39.3916	+	12.9950i	−1.26806	+	0.418325i
$966$	17.6195	−	2.09090i	0.566898	−	0.0672735i
$967$	4.77853	−	4.77853i	0.153667	−	0.153667i	−0.626086	−	0.779754i	$-0.715344\pi$
$967$	4.77853	−	4.77853i	0.153667	−	0.153667i	0.779754	+	0.626086i	$0.215344\pi$
$968$	−0.904687	−	0.196803i	−0.0290777	−	0.00632548i
$969$	−6.13436	−	0.881988i	−0.197064	−	0.0283335i
$970$	−10.6676	−	13.3097i	−0.342517	−	0.427349i
$971$	−9.77766	−	33.2996i	−0.313780	−	1.06864i	−0.953841	−	0.300312i	$-0.902909\pi$
$971$	−9.77766	−	33.2996i	−0.313780	−	1.06864i	0.640061	−	0.768324i	$-0.278909\pi$
$972$	0.936950	+	0.349464i	0.0300527	+	0.0112091i
$973$	−4.76632	−	0.340894i	−0.152801	−	0.0109286i
$974$	11.8078	−	1.69771i	0.378347	−	0.0543981i
$975$	12.5186	−	4.59382i	0.400915	−	0.147120i
$976$	7.59825	+	6.58392i	0.243214	+	0.210746i
$977$	−7.34444	−	33.7619i	−0.234970	−	1.08014i	−0.931820	−	0.362921i	$-0.881779\pi$
$977$	−7.34444	−	33.7619i	−0.234970	−	1.08014i	0.696850	−	0.717217i	$-0.254584\pi$
$978$	−4.87097	−	22.3915i	−0.155756	−	0.716001i
$979$	18.7116	+	16.2137i	0.598024	+	0.518191i
$980$	−10.2191	+	10.9179i	−0.326436	+	0.348760i
$981$	11.6922	−	1.68109i	0.373304	−	0.0536731i
$982$	−0.962758	−	0.0688578i	−0.0307228	−	0.00219734i
$983$	37.0273	+	13.8105i	1.18099	+	0.440485i	0.861820	−	0.507213i	$-0.169324\pi$
$983$	37.0273	+	13.8105i	1.18099	+	0.440485i	0.319166	+	0.947699i	$0.396597\pi$
$984$	1.93361	+	6.58528i	0.0616414	+	0.209931i
$985$	−26.6974	−	2.94179i	−0.850648	−	0.0937332i
$986$	4.57526	+	0.657823i	0.145706	+	0.0209494i
$987$	−19.6380	−	4.27199i	−0.625085	−	0.135979i
$988$	12.2141	−	12.2141i	0.388584	−	0.388584i
$989$	14.6101	+	34.2011i	0.464573	+	1.08753i
$990$	2.41919	+	7.33326i	0.0768871	+	0.233066i
$991$	37.4411	−	24.0619i	1.18936	−	0.764353i	0.212273	−	0.977210i	$-0.431913\pi$
$991$	37.4411	−	24.0619i	1.18936	−	0.764353i	0.977083	+	0.212858i	$0.0682771\pi$
$992$	−2.34386	−	3.13102i	−0.0744175	−	0.0994101i
$993$	1.05393	−	0.393094i	0.0334453	−	0.0124745i
$994$	30.2306	−	8.87652i	0.958858	−	0.281546i
$995$	−19.7159	−	0.756431i	−0.625037	−	0.0239805i
$996$	8.14397	−	7.05679i	0.258052	−	0.223603i
$997$	31.3617	+	23.4771i	0.993234	+	0.743526i	0.966645	−	0.256121i	$-0.0824444\pi$
$997$	31.3617	+	23.4771i	0.993234	+	0.743526i	0.0265894	+	0.999646i	$0.491535\pi$
$998$	10.2978	+	18.8590i	0.325970	+	0.596970i
$999$	−3.02726	+	3.49364i	−0.0957781	+	0.110534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.103.3	yes	240
5.2	odd	4	inner	690.2.w.a.517.5	yes	240
23.21	odd	22	inner	690.2.w.a.343.5	yes	240
115.67	even	44	inner	690.2.w.a.67.3	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.67.3	✓	240	115.67	even	44	inner
690.2.w.a.103.3	yes	240	1.1	even	1	trivial
690.2.w.a.343.5	yes	240	23.21	odd	22	inner
690.2.w.a.517.5	yes	240	5.2	odd	4	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.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.212565 + 0.977147i) q^{2} +(0.800541 - 0.599278i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-0.402846 + 2.19948i) q^{5} +(0.415415 + 0.909632i) q^{6} +(0.263933 - 3.69027i) q^{7} +(0.599278 - 0.800541i) q^{8} +(0.281733 - 0.959493i) q^{9} +O(q^{10})\)	\(q+(-0.212565 + 0.977147i) q^{2} +(0.800541 - 0.599278i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-0.402846 + 2.19948i) q^{5} +(0.415415 + 0.909632i) q^{6} +(0.263933 - 3.69027i) q^{7} +(0.599278 - 0.800541i) q^{8} +(0.281733 - 0.959493i) q^{9} +(-2.06358 - 0.861173i) q^{10} +(1.86704 - 2.90517i) q^{11} +(-0.977147 + 0.212565i) q^{12} +(-2.66017 + 0.190259i) q^{13} +(3.54983 + 1.04232i) q^{14} +(0.995605 + 2.00219i) q^{15} +(0.654861 + 0.755750i) q^{16} +(0.334391 - 0.896538i) q^{17} +(0.877679 + 0.479249i) q^{18} +(2.69056 - 5.89150i) q^{19} +(1.28014 - 1.83337i) q^{20} +(-2.00021 - 3.11238i) q^{21} +(2.44191 + 2.44191i) q^{22} +(4.65964 + 1.13477i) q^{23} -1.00000i q^{24} +(-4.67543 - 1.77210i) q^{25} +(0.379549 - 2.63982i) q^{26} +(-0.349464 - 0.936950i) q^{27} +(-1.77308 + 3.24715i) q^{28} +(4.39413 - 2.00673i) q^{29} +(-2.16807 + 0.547255i) q^{30} +(0.556612 + 3.87132i) q^{31} +(-0.877679 + 0.479249i) q^{32} +(-0.246361 - 3.44458i) q^{33} +(0.804969 + 0.517322i) q^{34} +(8.01035 + 2.06713i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(-2.21545 - 4.05729i) q^{37} +(5.18494 + 3.88140i) q^{38} +(-2.01556 + 1.74649i) q^{39} +(1.51936 + 1.64059i) q^{40} +(-6.58528 + 1.93361i) q^{41} +(3.46643 - 1.29291i) q^{42} +(4.64732 + 6.20809i) q^{43} +(-2.90517 + 1.86704i) q^{44} +(1.99689 + 1.00619i) q^{45} +(-2.09932 + 4.31194i) q^{46} +(3.84111 - 3.84111i) q^{47} +(0.977147 + 0.212565i) q^{48} +(-6.61968 - 0.951767i) q^{49} +(2.72544 - 4.19189i) q^{50} +(-0.269581 - 0.918108i) q^{51} +(2.49881 + 0.932010i) q^{52} +(7.17587 + 0.513229i) q^{53} +(0.989821 - 0.142315i) q^{54} +(5.63773 + 5.27685i) q^{55} +(-2.79604 - 2.42279i) q^{56} +(-1.37674 - 6.32878i) q^{57} +(1.02683 + 4.72027i) q^{58} +(0.242559 + 0.210178i) q^{59} +(-0.0738933 - 2.23485i) q^{60} +(9.95159 - 1.43082i) q^{61} +(-3.90117 - 0.279017i) q^{62} +(-3.46643 - 1.29291i) q^{63} +(-0.281733 - 0.959493i) q^{64} +(0.653169 - 5.92764i) q^{65} +(3.41823 + 0.491467i) q^{66} +(-15.6752 - 3.40993i) q^{67} +(-0.676608 + 0.676608i) q^{68} +(4.41028 - 1.88399i) q^{69} +(-3.72261 + 7.38789i) q^{70} +(7.16418 - 4.60414i) q^{71} +(-0.599278 - 0.800541i) q^{72} +(-6.81334 + 2.54125i) q^{73} +(4.43549 - 1.30238i) q^{74} +(-4.80486 + 1.38324i) q^{75} +(-4.89484 + 4.24140i) q^{76} +(-10.2281 - 7.65665i) q^{77} +(-1.27814 - 2.34074i) q^{78} +(8.69958 - 10.0398i) q^{79} +(-1.92606 + 1.13590i) q^{80} +(-0.841254 - 0.540641i) q^{81} +(-0.489622 - 6.84581i) q^{82} +(-9.45789 + 5.16440i) q^{83} +(0.526522 + 3.66204i) q^{84} +(1.83721 + 1.09665i) q^{85} +(-7.05407 + 3.22149i) q^{86} +(2.31509 - 4.23977i) q^{87} +(-1.20683 - 3.23565i) q^{88} +(-1.02032 + 7.09650i) q^{89} +(-1.40767 + 1.73737i) q^{90} +9.86697i q^{91} +(-3.76716 - 2.96791i) q^{92} +(2.76559 + 2.76559i) q^{93} +(2.93684 + 4.56982i) q^{94} +(11.8744 + 8.29120i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(6.69511 + 3.65581i) q^{97} +(2.33713 - 6.26609i) q^{98} +(-2.26148 - 2.60989i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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