LMFDB - Embedded newform 690.2.m.g.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, 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:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.1
Character	$\chi$	$=$	690.121
Dual form			690.2.m.g.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.498068 + 3.46414i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.498068 + 3.46414i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.142315 - 0.989821i) q^{10} +(1.29808 + 2.84240i) q^{11} +(0.415415 + 0.909632i) q^{12} +(-0.133837 - 0.930855i) q^{13} +(2.94419 + 1.89212i) q^{14} +(-0.959493 + 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-4.81901 + 5.56143i) q^{17} +(0.841254 - 0.540641i) q^{18} +(1.23702 + 1.42759i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(1.45385 - 3.18350i) q^{21} +3.12478 q^{22} +(3.42329 + 3.35873i) q^{23} +1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(-0.902333 - 0.264949i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(2.94419 - 1.89212i) q^{28} +(-0.455579 + 0.525766i) q^{29} +(-0.142315 + 0.989821i) q^{30} +(4.98844 - 1.46474i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-0.444702 - 3.09297i) q^{33} +(3.05697 + 6.69383i) q^{34} +(1.45385 + 3.18350i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-0.958486 - 0.615982i) q^{37} +(1.81246 - 0.532186i) q^{38} +(-0.133837 + 0.930855i) q^{39} +(-0.654861 + 0.755750i) q^{40} +(1.73927 - 1.11776i) q^{41} +(-2.29186 - 2.64495i) q^{42} +(9.55053 + 2.80429i) q^{43} +(1.29808 - 2.84240i) q^{44} +1.00000 q^{45} +(4.47729 - 1.71867i) q^{46} -3.43994 q^{47} +(0.415415 - 0.909632i) q^{48} +(-5.03575 - 1.47863i) q^{49} +(-0.654861 - 0.755750i) q^{50} +(6.19064 - 3.97848i) q^{51} +(-0.615849 + 0.710727i) q^{52} +(-0.573236 + 3.98694i) q^{53} +(-0.959493 + 0.281733i) q^{54} +(2.62873 + 1.68938i) q^{55} +(-0.498068 - 3.46414i) q^{56} +(-0.784708 - 1.71827i) q^{57} +(0.288999 + 0.632820i) q^{58} +(-1.82681 - 12.7058i) q^{59} +(0.841254 + 0.540641i) q^{60} +(-2.91105 + 0.854761i) q^{61} +(0.739901 - 5.14612i) q^{62} +(-2.29186 + 2.64495i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.615849 - 0.710727i) q^{65} +(-2.99820 - 0.880352i) q^{66} +(1.53188 - 3.35435i) q^{67} +7.35883 q^{68} +(-2.33836 - 4.18713i) q^{69} +3.49976 q^{70} +(-1.92059 + 4.20550i) q^{71} +(-0.959493 - 0.281733i) q^{72} +(-0.931680 - 1.07522i) q^{73} +(-0.958486 + 0.615982i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(0.268829 - 1.86975i) q^{76} +(-10.4930 + 3.08102i) q^{77} +(0.791138 + 0.508433i) q^{78} +(2.40418 + 16.7215i) q^{79} +(0.415415 + 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.294231 - 2.04642i) q^{82} +(5.18106 + 3.32966i) q^{83} +(-3.35800 + 0.985998i) q^{84} +(-1.04727 + 7.28393i) q^{85} +(6.51831 - 7.52253i) q^{86} +(0.585250 - 0.376117i) q^{87} +(-2.04630 - 2.36155i) q^{88} +(-3.33736 - 0.979938i) q^{89} +(0.415415 - 0.909632i) q^{90} +3.29127 q^{91} +(0.296577 - 4.78665i) q^{92} -5.19904 q^{93} +(-1.42900 + 3.12908i) q^{94} +(1.81246 + 0.532186i) q^{95} +(-0.654861 - 0.755750i) q^{96} +(-4.25851 + 2.73678i) q^{97} +(-3.43694 + 3.96644i) q^{98} +(-0.444702 + 3.09297i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$6$	−0.654861	+	0.755750i	−0.267346	+	0.308533i
$7$	−0.498068	+	3.46414i	−0.188252	+	1.30932i	0.648279	+	0.761403i	$0.275489\pi$
$7$	−0.498068	+	3.46414i	−0.188252	+	1.30932i	−0.836531	+	0.547920i	$0.815420\pi$
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−0.142315	−	0.989821i	−0.0450039	−	0.313009i
$11$	1.29808	+	2.84240i	0.391386	+	0.857016i	0.998072	+	0.0620738i	$0.0197714\pi$
$11$	1.29808	+	2.84240i	0.391386	+	0.857016i	−0.606686	+	0.794942i	$0.707501\pi$
$12$	0.415415	+	0.909632i	0.119920	+	0.262588i
$13$	−0.133837	−	0.930855i	−0.0371196	−	0.258173i	0.962808	−	0.270186i	$-0.0870851\pi$
$13$	−0.133837	−	0.930855i	−0.0371196	−	0.258173i	−0.999928	+	0.0120131i	$0.996176\pi$
$14$	2.94419	+	1.89212i	0.786868	+	0.505689i
$15$	−0.959493	+	0.281733i	−0.247740	+	0.0727430i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−4.81901	+	5.56143i	−1.16878	+	1.34885i	−0.243346	+	0.969940i	$0.578245\pi$
$17$	−4.81901	+	5.56143i	−1.16878	+	1.34885i	−0.925435	+	0.378906i	$0.876300\pi$
$18$	0.841254	−	0.540641i	0.198285	−	0.127430i
$19$	1.23702	+	1.42759i	0.283791	+	0.327512i	0.879690	−	0.475547i	$-0.157750\pi$
$19$	1.23702	+	1.42759i	0.283791	+	0.327512i	−0.595900	+	0.803059i	$0.703204\pi$
$20$	−0.959493	−	0.281733i	−0.214549	−	0.0629973i
$21$	1.45385	−	3.18350i	0.317257	−	0.694696i
$22$	3.12478			0.666205
$23$	3.42329	+	3.35873i	0.713806	+	0.700343i
$23$	3.42329	+	3.35873i	0.713806	+	0.700343i
$24$	1.00000			0.204124
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	−0.902333	−	0.264949i	−0.176962	−	0.0519608i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	2.94419	−	1.89212i	0.556399	−	0.357576i
$29$	−0.455579	+	0.525766i	−0.0845988	+	0.0976322i	−0.796471	−	0.604677i	$-0.793302\pi$
$29$	−0.455579	+	0.525766i	−0.0845988	+	0.0976322i	0.711872	+	0.702309i	$0.247848\pi$
$30$	−0.142315	+	0.989821i	−0.0259830	+	0.180716i
$31$	4.98844	−	1.46474i	0.895951	−	0.263075i	0.198835	−	0.980033i	$-0.436284\pi$
$31$	4.98844	−	1.46474i	0.895951	−	0.263075i	0.697116	+	0.716958i	$0.254466\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$	−0.444702	−	3.09297i	−0.0774128	−	0.538418i
$34$	3.05697	+	6.69383i	0.524266	+	1.14798i
$35$	1.45385	+	3.18350i	0.245746	+	0.538109i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−0.958486	−	0.615982i	−0.157574	−	0.101267i	0.459477	−	0.888189i	$-0.348037\pi$
$37$	−0.958486	−	0.615982i	−0.157574	−	0.101267i	−0.617052	+	0.786923i	$0.711673\pi$
$38$	1.81246	−	0.532186i	0.294020	−	0.0863319i
$39$	−0.133837	+	0.930855i	−0.0214310	+	0.149056i
$40$	−0.654861	+	0.755750i	−0.103543	+	0.119494i
$41$	1.73927	−	1.11776i	0.271628	−	0.174564i	−0.397735	−	0.917500i	$-0.630204\pi$
$41$	1.73927	−	1.11776i	0.271628	−	0.174564i	0.669363	+	0.742936i	$0.266567\pi$
$42$	−2.29186	−	2.64495i	−0.353641	−	0.408124i
$43$	9.55053	+	2.80429i	1.45644	+	0.427650i	0.911666	−	0.410931i	$-0.134796\pi$
$43$	9.55053	+	2.80429i	1.45644	+	0.427650i	0.544776	+	0.838581i	$0.316615\pi$
$44$	1.29808	−	2.84240i	0.195693	−	0.428508i
$45$	1.00000			0.149071
$46$	4.47729	−	1.71867i	0.660141	−	0.253404i
$47$	−3.43994			−0.501767			−0.250883	−	0.968017i	$-0.580721\pi$
$47$	−3.43994			−0.501767			−0.250883	+	0.968017i	$0.580721\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	−5.03575	−	1.47863i	−0.719393	−	0.211233i
$50$	−0.654861	−	0.755750i	−0.0926113	−	0.106879i
$51$	6.19064	−	3.97848i	0.866863	−	0.557099i
$52$	−0.615849	+	0.710727i	−0.0854029	+	0.0985601i
$53$	−0.573236	+	3.98694i	−0.0787400	+	0.547649i	0.911822	+	0.410585i	$0.134676\pi$
$53$	−0.573236	+	3.98694i	−0.0787400	+	0.547649i	−0.990562	+	0.137063i	$0.956234\pi$
$54$	−0.959493	+	0.281733i	−0.130570	+	0.0383389i
$55$	2.62873	+	1.68938i	0.354458	+	0.227796i
$56$	−0.498068	−	3.46414i	−0.0665572	−	0.462915i
$57$	−0.784708	−	1.71827i	−0.103937	−	0.227591i
$58$	0.288999	+	0.632820i	0.0379474	+	0.0830933i
$59$	−1.82681	−	12.7058i	−0.237831	−	1.65415i	−0.662694	−	0.748890i	$-0.730587\pi$
$59$	−1.82681	−	12.7058i	−0.237831	−	1.65415i	0.424863	−	0.905257i	$-0.360322\pi$
$60$	0.841254	+	0.540641i	0.108605	+	0.0697964i
$61$	−2.91105	+	0.854761i	−0.372722	+	0.109441i	−0.462728	−	0.886500i	$-0.653129\pi$
$61$	−2.91105	+	0.854761i	−0.372722	+	0.109441i	0.0900064	+	0.995941i	$0.471311\pi$
$62$	0.739901	−	5.14612i	0.0939675	−	0.653558i
$63$	−2.29186	+	2.64495i	−0.288747	+	0.333232i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−0.615849	−	0.710727i	−0.0763866	−	0.0881549i
$66$	−2.99820	−	0.880352i	−0.369053	−	0.108364i
$67$	1.53188	−	3.35435i	0.187149	−	0.409799i	−0.792680	−	0.609638i	$-0.791315\pi$
$67$	1.53188	−	3.35435i	0.187149	−	0.409799i	0.979829	+	0.199839i	$0.0640421\pi$
$68$	7.35883			0.892389
$69$	−2.33836	−	4.18713i	−0.281506	−	0.504071i
$70$	3.49976			0.418302
$71$	−1.92059	+	4.20550i	−0.227932	+	0.499102i	−0.988697	−	0.149926i	$-0.952097\pi$
$71$	−1.92059	+	4.20550i	−0.227932	+	0.499102i	0.760765	+	0.649027i	$0.224824\pi$
$72$	−0.959493	−	0.281733i	−0.113077	−	0.0332025i
$73$	−0.931680	−	1.07522i	−0.109045	−	0.125845i	0.698603	−	0.715509i	$-0.253805\pi$
$73$	−0.931680	−	1.07522i	−0.109045	−	0.125845i	−0.807648	+	0.589665i	$0.799260\pi$
$74$	−0.958486	+	0.615982i	−0.111422	+	0.0716064i
$75$	−0.654861	+	0.755750i	−0.0756168	+	0.0872664i
$76$	0.268829	−	1.86975i	0.0308368	−	0.214475i
$77$	−10.4930	+	3.08102i	−1.19579	+	0.351115i
$78$	0.791138	+	0.508433i	0.0895787	+	0.0575687i
$79$	2.40418	+	16.7215i	0.270492	+	1.88131i	0.443327	+	0.896360i	$0.353798\pi$
$79$	2.40418	+	16.7215i	0.270492	+	1.88131i	−0.172836	+	0.984951i	$0.555293\pi$
$80$	0.415415	+	0.909632i	0.0464448	+	0.101700i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−0.294231	−	2.04642i	−0.0324924	−	0.225990i
$83$	5.18106	+	3.32966i	0.568695	+	0.365478i	0.793169	−	0.609002i	$-0.208430\pi$
$83$	5.18106	+	3.32966i	0.568695	+	0.365478i	−0.224474	+	0.974480i	$0.572066\pi$
$84$	−3.35800	+	0.985998i	−0.366388	+	0.107581i
$85$	−1.04727	+	7.28393i	−0.113592	+	0.790053i
$86$	6.51831	−	7.52253i	0.702887	−	0.811175i
$87$	0.585250	−	0.376117i	0.0627454	−	0.0403240i
$88$	−2.04630	−	2.36155i	−0.218136	−	0.251742i
$89$	−3.33736	−	0.979938i	−0.353760	−	0.103873i	0.100024	−	0.994985i	$-0.468108\pi$
$89$	−3.33736	−	0.979938i	−0.353760	−	0.103873i	−0.453784	+	0.891112i	$0.649926\pi$
$90$	0.415415	−	0.909632i	0.0437886	−	0.0958836i
$91$	3.29127			0.345019
$92$	0.296577	−	4.78665i	0.0309203	−	0.499043i
$93$	−5.19904			−0.539115
$94$	−1.42900	+	3.12908i	−0.147390	+	0.322740i
$95$	1.81246	+	0.532186i	0.185954	+	0.0546011i
$96$	−0.654861	−	0.755750i	−0.0668364	−	0.0771334i
$97$	−4.25851	+	2.73678i	−0.432386	+	0.277877i	−0.738676	−	0.674061i	$-0.764549\pi$
$97$	−4.25851	+	2.73678i	−0.432386	+	0.277877i	0.306290	+	0.951938i	$0.400912\pi$
$98$	−3.43694	+	3.96644i	−0.347183	+	0.400671i
$99$	−0.444702	+	3.09297i	−0.0446943	+	0.310856i
$100$	−0.959493	+	0.281733i	−0.0959493	+	0.0281733i
$101$	−1.58475	−	1.01846i	−0.157689	−	0.101340i	0.459417	−	0.888221i	$-0.348058\pi$
$101$	−1.58475	−	1.01846i	−0.157689	−	0.101340i	−0.617105	+	0.786880i	$0.711695\pi$
$102$	−1.04727	−	7.28393i	−0.103695	−	0.721216i
$103$	−0.363212	−	0.795324i	−0.0357884	−	0.0783656i	0.890894	−	0.454212i	$-0.150079\pi$
$103$	−0.363212	−	0.795324i	−0.0357884	−	0.0783656i	−0.926682	+	0.375847i	$0.877352\pi$
$104$	0.390668	+	0.855443i	0.0383081	+	0.0838830i
$105$	−0.498068	−	3.46414i	−0.0486065	−	0.338066i
$106$	3.38852	+	2.17767i	0.329122	+	0.211514i
$107$	−14.7565	+	4.33290i	−1.42656	+	0.418877i	−0.901720	−	0.432321i	$-0.857695\pi$
$107$	−14.7565	+	4.33290i	−1.42656	+	0.418877i	−0.524844	+	0.851198i	$0.675876\pi$
$108$	−0.142315	+	0.989821i	−0.0136943	+	0.0952456i
$109$	2.85960	−	3.30015i	0.273900	−	0.316097i	−0.602089	−	0.798429i	$-0.705665\pi$
$109$	2.85960	−	3.30015i	0.273900	−	0.316097i	0.875988	+	0.482332i	$0.160210\pi$
$110$	2.62873	−	1.68938i	0.250640	−	0.161076i
$111$	0.746119	+	0.861067i	0.0708185	+	0.0817289i
$112$	−3.35800	−	0.985998i	−0.317301	−	0.0931680i
$113$	−4.98183	+	10.9087i	−0.468652	+	1.02620i	0.516778	+	0.856119i	$0.327131\pi$
$113$	−4.98183	+	10.9087i	−0.468652	+	1.02620i	−0.985430	+	0.170084i	$0.945596\pi$
$114$	−1.88897			−0.176919
$115$	4.69572	+	0.974770i	0.437879	+	0.0908978i
$116$	0.695688			0.0645930
$117$	0.390668	−	0.855443i	0.0361172	−	0.0790857i
$118$	−12.3164	−	3.61643i	−1.13382	−	0.332920i
$119$	−16.8654	−	19.4637i	−1.54605	−	1.78423i
$120$	0.841254	−	0.540641i	0.0767956	−	0.0493535i
$121$	0.809248	−	0.933921i	0.0735680	−	0.0849020i
$122$	−0.431776	+	3.00307i	−0.0390911	+	0.271885i
$123$	−1.98372	+	0.582473i	−0.178866	+	0.0525198i
$124$	−4.37371	−	2.81081i	−0.392771	−	0.252418i
$125$	−0.142315	−	0.989821i	−0.0127290	−	0.0885323i
$126$	1.45385	+	3.18350i	0.129520	+	0.283608i
$127$	−0.674358	−	1.47664i	−0.0598396	−	0.131030i	0.877350	−	0.479851i	$-0.159309\pi$
$127$	−0.674358	−	1.47664i	−0.0598396	−	0.131030i	−0.937189	+	0.348821i	$0.886582\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$	−8.37361	−	5.38139i	−0.737255	−	0.473805i
$130$	−0.902333	+	0.264949i	−0.0791399	+	0.0232376i
$131$	1.86094	−	12.9431i	0.162591	−	1.13085i	−0.731135	−	0.682232i	$-0.761009\pi$
$131$	1.86094	−	12.9431i	0.162591	−	1.13085i	0.893726	−	0.448613i	$-0.148082\pi$
$132$	−2.04630	+	2.36155i	−0.178107	+	0.205547i
$133$	−5.56150	+	3.57416i	−0.482243	+	0.309919i
$134$	−2.41485	−	2.78689i	−0.208612	−	0.240751i
$135$	−0.959493	−	0.281733i	−0.0825800	−	0.0242477i
$136$	3.05697	−	6.69383i	0.262133	−	0.573991i
$137$	−18.5033			−1.58084			−0.790420	−	0.612565i	$-0.790138\pi$
$137$	−18.5033			−1.58084			−0.790420	+	0.612565i	$0.790138\pi$
$138$	−4.78014	+	0.387653i	−0.406912	+	0.0329992i
$139$	18.6522			1.58206			0.791028	−	0.611780i	$-0.209546\pi$
$139$	18.6522			1.58206			0.791028	+	0.611780i	$0.209546\pi$
$140$	1.45385	−	3.18350i	0.122873	−	0.269055i
$141$	3.30060	+	0.969143i	0.277960	+	0.0816165i
$142$	3.02762	+	3.49406i	0.254072	+	0.293215i
$143$	2.47213	−	1.58874i	0.206730	−	0.132857i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	−0.0990067	+	0.688607i	−0.00822206	+	0.0571857i
$146$	−1.36508	+	0.400825i	−0.112975	+	0.0331725i
$147$	4.41519	+	2.83747i	0.364159	+	0.234031i
$148$	0.162147	+	1.12776i	0.0133284	+	0.0927011i
$149$	−2.39180	−	5.23731i	−0.195944	−	0.429057i	0.786001	−	0.618225i	$-0.212148\pi$
$149$	−2.39180	−	5.23731i	−0.195944	−	0.429057i	−0.981945	+	0.189168i	$0.939421\pi$
$150$	0.415415	+	0.909632i	0.0339185	+	0.0742711i
$151$	−2.92385	−	20.3358i	−0.237940	−	1.65491i	−0.662171	−	0.749353i	$-0.730365\pi$
$151$	−2.92385	−	20.3358i	−0.237940	−	1.65491i	0.424232	−	0.905554i	$-0.360544\pi$
$152$	−1.58911	−	1.02126i	−0.128894	−	0.0828349i
$153$	−7.06075	+	2.07322i	−0.570827	+	0.167610i
$154$	−1.55635	+	10.8247i	−0.125415	+	0.872277i
$155$	3.40465	−	3.92917i	0.273468	−	0.315599i
$156$	0.791138	−	0.508433i	0.0633417	−	0.0407072i
$157$	5.29029	+	6.10532i	0.422211	+	0.487258i	0.926509	−	0.376272i	$-0.122794\pi$
$157$	5.29029	+	6.10532i	0.422211	+	0.487258i	−0.504298	+	0.863530i	$0.668249\pi$
$158$	16.2091	+	4.75942i	1.28953	+	0.378639i
$159$	1.67327	−	3.66394i	0.132699	−	0.290570i
$160$	1.00000			0.0790569
$161$	−13.3401	+	10.1859i	−1.05135	+	0.802761i
$162$	1.00000			0.0785674
$163$	0.691790	−	1.51481i	0.0541852	−	0.118649i	−0.880603	−	0.473855i	$-0.842862\pi$
$163$	0.691790	−	1.51481i	0.0541852	−	0.118649i	0.934788	+	0.355206i	$0.115589\pi$
$164$	−1.98372	−	0.582473i	−0.154903	−	0.0454835i
$165$	−2.04630	−	2.36155i	−0.159304	−	0.183846i
$166$	5.18106	−	3.32966i	0.402128	−	0.258432i
$167$	−8.77331	+	10.1249i	−0.678899	+	0.783491i	−0.985741	−	0.168269i	$-0.946182\pi$
$167$	−8.77331	+	10.1249i	−0.678899	+	0.783491i	0.306842	+	0.951760i	$0.400728\pi$
$168$	−0.498068	+	3.46414i	−0.0384268	+	0.267264i
$169$	11.6248	−	3.41336i	0.894218	−	0.262566i
$170$	6.19064	+	3.97848i	0.474801	+	0.305136i
$171$	0.268829	+	1.86975i	0.0205579	+	0.142983i
$172$	−4.13493	−	9.05423i	−0.315285	−	0.690379i
$173$	−0.769891	−	1.68583i	−0.0585337	−	0.128171i	0.878105	−	0.478468i	$-0.158808\pi$
$173$	−0.769891	−	1.68583i	−0.0585337	−	0.128171i	−0.936639	+	0.350297i	$0.886081\pi$
$174$	−0.0990067	−	0.688607i	−0.00750568	−	0.0522031i
$175$	2.94419	+	1.89212i	0.222560	+	0.143030i
$176$	−2.99820	+	0.880352i	−0.225998	+	0.0663590i
$177$	−1.82681	+	12.7058i	−0.137312	+	0.955023i
$178$	−2.27777	+	2.62869i	−0.170726	+	0.197029i
$179$	−9.04079	+	5.81016i	−0.675740	+	0.434272i	−0.832991	−	0.553287i	$-0.813373\pi$
$179$	−9.04079	+	5.81016i	−0.675740	+	0.434272i	0.157250	+	0.987559i	$0.449737\pi$
$180$	−0.654861	−	0.755750i	−0.0488104	−	0.0563302i
$181$	17.5956	+	5.16653i	1.30787	+	0.384025i	0.860101	−	0.510124i	$-0.170400\pi$
$181$	17.5956	+	5.16653i	1.30787	+	0.384025i	0.447769	+	0.894149i	$0.352219\pi$
$182$	1.36724	−	2.99385i	0.101347	−	0.221919i
$183$	3.03395			0.224276
$184$	−4.23089	−	2.25822i	−0.311905	−	0.166478i
$185$	−1.13935			−0.0837670
$186$	−2.15976	+	4.72921i	−0.158361	+	0.346763i
$187$	−22.0633	−	6.47836i	−1.61343	−	0.473745i
$188$	2.25268	+	2.59973i	0.164294	+	0.189605i
$189$	2.94419	−	1.89212i	0.214158	−	0.137631i
$190$	1.23702	−	1.42759i	0.0897425	−	0.103568i
$191$	2.40718	−	16.7423i	0.174178	−	1.21143i	−0.695762	−	0.718273i	$-0.744933\pi$
$191$	2.40718	−	16.7423i	0.174178	−	1.21143i	0.869939	−	0.493159i	$-0.164158\pi$
$192$	−0.959493	+	0.281733i	−0.0692454	+	0.0203323i
$193$	−4.59154	−	2.95081i	−0.330507	−	0.212404i	0.364854	−	0.931065i	$-0.381119\pi$
$193$	−4.59154	−	2.95081i	−0.330507	−	0.212404i	−0.695361	+	0.718661i	$0.744755\pi$
$194$	0.720411	+	5.01057i	0.0517225	+	0.359738i
$195$	0.390668	+	0.855443i	0.0279763	+	0.0612595i
$196$	2.18024	+	4.77407i	0.155732	+	0.341005i
$197$	−2.72360	−	18.9430i	−0.194048	−	1.34964i	−0.821156	−	0.570704i	$-0.806671\pi$
$197$	−2.72360	−	18.9430i	−0.194048	−	1.34964i	0.627108	−	0.778933i	$-0.284239\pi$
$198$	2.62873	+	1.68938i	0.186816	+	0.120059i
$199$	−9.50118	+	2.78980i	−0.673521	+	0.197763i	−0.600570	−	0.799572i	$-0.705060\pi$
$199$	−9.50118	+	2.78980i	−0.673521	+	0.197763i	−0.0729505	+	0.997336i	$0.523241\pi$
$200$	−0.142315	+	0.989821i	−0.0100632	+	0.0699909i
$201$	−2.41485	+	2.78689i	−0.170331	+	0.196572i
$202$	−1.58475	+	1.01846i	−0.111503	+	0.0716585i
$203$	−1.59442	−	1.84006i	−0.111906	−	0.129147i
$204$	−7.06075	−	2.07322i	−0.494351	−	0.145155i
$205$	0.858858	−	1.88064i	0.0599852	−	0.131349i
$206$	−0.874336			−0.0609178
$207$	1.06399	+	4.67631i	0.0739526	+	0.325026i
$208$	0.940427			0.0652069
$209$	−2.45204	+	5.36922i	−0.169611	+	0.371397i
$210$	−3.35800	−	0.985998i	−0.231724	−	0.0680403i
$211$	12.2086	+	14.0895i	0.840476	+	0.969961i	0.999851	−	0.0172569i	$-0.00549331\pi$
$211$	12.2086	+	14.0895i	0.840476	+	0.969961i	−0.159375	+	0.987218i	$0.550948\pi$
$212$	3.38852	−	2.17767i	0.232724	−	0.149563i
$213$	3.02762	−	3.49406i	0.207449	−	0.239409i
$214$	−2.18873	+	15.2229i	−0.149618	+	1.04062i
$215$	9.55053	−	2.80429i	0.651341	−	0.191251i
$216$	0.841254	+	0.540641i	0.0572401	+	0.0367859i
$217$	2.58948	+	18.0102i	0.175785	+	1.22261i
$218$	−1.81400	−	3.97211i	−0.122860	−	0.269025i
$219$	0.591017	+	1.29415i	0.0399372	+	0.0874503i
$220$	−0.444702	−	3.09297i	−0.0299818	−	0.208528i
$221$	5.82185	+	3.74147i	0.391620	+	0.251679i
$222$	1.09320	−	0.320993i	0.0733710	−	0.0215437i
$223$	0.835709	−	5.81248i	0.0559632	−	0.389233i	−0.942519	−	0.334153i	$-0.891550\pi$
$223$	0.835709	−	5.81248i	0.0559632	−	0.389233i	0.998482	−	0.0550794i	$-0.0175412\pi$
$224$	−2.29186	+	2.64495i	−0.153131	+	0.176723i
$225$	0.841254	−	0.540641i	0.0560836	−	0.0360427i
$226$	7.85337	+	9.06327i	0.522398	+	0.602880i
$227$	20.9634	+	6.15541i	1.39139	+	0.408549i	0.889718	−	0.456510i	$-0.150901\pi$
$227$	20.9634	+	6.15541i	1.39139	+	0.408549i	0.501671	+	0.865059i	$0.332719\pi$
$228$	−0.784708	+	1.71827i	−0.0519686	+	0.113795i
$229$	−16.9273			−1.11859			−0.559294	−	0.828969i	$-0.688928\pi$
$229$	−16.9273			−1.11859			−0.559294	+	0.828969i	$0.688928\pi$
$230$	2.83736	−	3.86645i	0.187090	−	0.254946i
$231$	10.9360			0.719535
$232$	0.288999	−	0.632820i	0.0189737	−	0.0415467i
$233$	14.5077	+	4.25984i	0.950429	+	0.279071i	0.719966	−	0.694010i	$-0.244158\pi$
$233$	14.5077	+	4.25984i	0.950429	+	0.279071i	0.230464	+	0.973081i	$0.425976\pi$
$234$	−0.615849	−	0.710727i	−0.0402593	−	0.0464617i
$235$	−2.89386	+	1.85977i	−0.188775	+	0.121318i
$236$	−8.40606	+	9.70111i	−0.547188	+	0.631488i
$237$	2.40418	−	16.7215i	0.156168	−	1.08618i
$238$	−24.7109	+	7.25579i	−1.60177	+	0.470323i
$239$	24.6441	+	15.8378i	1.59410	+	1.02446i	0.969997	+	0.243118i	$0.0781702\pi$
$239$	24.6441	+	15.8378i	1.59410	+	1.02446i	0.624099	+	0.781345i	$0.285466\pi$
$240$	−0.142315	−	0.989821i	−0.00918638	−	0.0638927i
$241$	−5.33912	−	11.6910i	−0.343923	−	0.753086i	0.656076	−	0.754695i	$-0.272215\pi$
$241$	−5.33912	−	11.6910i	−0.343923	−	0.753086i	−0.999999	+	0.00160918i	$0.999488\pi$
$242$	−0.513351	−	1.12408i	−0.0329995	−	0.0722588i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	2.55232	+	1.64028i	0.163395	+	0.105008i
$245$	−5.03575	+	1.47863i	−0.321723	+	0.0944663i
$246$	−0.294231	+	2.04642i	−0.0187595	+	0.130475i
$247$	1.16332	−	1.34255i	0.0740205	−	0.0854242i
$248$	−4.37371	+	2.81081i	−0.277731	+	0.178487i
$249$	−4.03311	−	4.65446i	−0.255588	−	0.294965i
$250$	−0.959493	−	0.281733i	−0.0606837	−	0.0178183i
$251$	−9.94980	+	21.7870i	−0.628026	+	1.37519i	0.281509	+	0.959559i	$0.409165\pi$
$251$	−9.94980	+	21.7870i	−0.628026	+	1.37519i	−0.909535	+	0.415627i	$0.863562\pi$
$252$	3.49976			0.220464
$253$	−5.10314	+	14.0903i	−0.320832	+	0.885847i
$254$	−1.62333			−0.101857
$255$	3.05697	−	6.69383i	0.191435	−	0.419184i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	10.5751	+	12.2044i	0.659659	+	0.761287i	0.982721	−	0.185091i	$-0.0592579\pi$
$257$	10.5751	+	12.2044i	0.659659	+	0.761287i	−0.323063	+	0.946378i	$0.604712\pi$
$258$	−8.37361	+	5.38139i	−0.521318	+	0.335031i
$259$	2.61124	−	3.01353i	0.162255	−	0.187252i
$260$	−0.133837	+	0.930855i	−0.00830020	+	0.0577292i
$261$	−0.667507	+	0.195998i	−0.0413177	+	0.0121320i
$262$	−11.0004	−	7.06953i	−0.679608	−	0.436757i
$263$	−4.05577	−	28.2085i	−0.250089	−	1.73941i	−0.597654	−	0.801754i	$-0.703900\pi$
$263$	−4.05577	−	28.2085i	−0.250089	−	1.73941i	0.347565	−	0.937656i	$-0.387009\pi$
$264$	1.29808	+	2.84240i	0.0798913	+	0.174938i
$265$	1.67327	+	3.66394i	0.102788	+	0.225074i
$266$	0.940839	+	6.54368i	0.0576865	+	0.401219i
$267$	2.92610	+	1.88049i	0.179074	+	0.115084i
$268$	−3.53821	+	1.03891i	−0.216131	+	0.0634617i
$269$	0.719583	−	5.00481i	0.0438738	−	0.305149i	−0.956055	−	0.293188i	$-0.905284\pi$
$269$	0.719583	−	5.00481i	0.0438738	−	0.305149i	0.999928	−	0.0119605i	$-0.00380722\pi$
$270$	−0.654861	+	0.755750i	−0.0398536	+	0.0459935i
$271$	6.71140	−	4.31316i	0.407689	−	0.262006i	−0.320685	−	0.947186i	$-0.603913\pi$
$271$	6.71140	−	4.31316i	0.407689	−	0.262006i	0.728373	+	0.685180i	$0.240277\pi$
$272$	−4.81901	−	5.56143i	−0.292195	−	0.337211i
$273$	−3.15795	−	0.927259i	−0.191128	−	0.0561203i
$274$	−7.68654	+	16.8312i	−0.464361	+	1.01681i
$275$	3.12478			0.188431
$276$	−1.63312	+	4.50920i	−0.0983023	+	0.271422i
$277$	4.81668			0.289406			0.144703	−	0.989475i	$-0.453777\pi$
$277$	4.81668			0.289406			0.144703	+	0.989475i	$0.453777\pi$
$278$	7.74839	−	16.9666i	0.464718	−	1.01759i
$279$	4.98844	+	1.46474i	0.298650	+	0.0876916i
$280$	−2.29186	−	2.64495i	−0.136965	−	0.158066i
$281$	21.8433	−	14.0378i	1.30306	−	0.837428i	0.309521	−	0.950893i	$-0.399831\pi$
$281$	21.8433	−	14.0378i	1.30306	−	0.837428i	0.993542	+	0.113465i	$0.0361949\pi$
$282$	2.25268	−	2.59973i	0.134145	−	0.154812i
$283$	2.96169	−	20.5990i	0.176054	−	1.22448i	−0.689730	−	0.724067i	$-0.742271\pi$
$283$	2.96169	−	20.5990i	0.176054	−	1.22448i	0.865784	−	0.500418i	$-0.166820\pi$
$284$	4.43603	−	1.30253i	0.263230	−	0.0772912i
$285$	−1.58911	−	1.02126i	−0.0941306	−	0.0604940i
$286$	−0.418210	−	2.90872i	−0.0247293	−	0.171996i
$287$	3.00580	+	6.58178i	0.177427	+	0.388510i
$288$	0.415415	+	0.909632i	0.0244786	+	0.0536006i
$289$	−5.28733	−	36.7742i	−0.311020	−	2.16319i
$290$	0.585250	+	0.376117i	0.0343670	+	0.0220864i
$291$	4.85704	−	1.42616i	0.284725	−	0.0836028i
$292$	−0.202473	+	1.40823i	−0.0118489	+	0.0824106i
$293$	17.0111	−	19.6319i	0.993801	−	1.14691i	0.00465191	−	0.999989i	$-0.498519\pi$
$293$	17.0111	−	19.6319i	0.993801	−	1.14691i	0.989149	−	0.146918i	$-0.0469353\pi$
$294$	4.41519	−	2.83747i	0.257499	−	0.165485i
$295$	−8.40606	−	9.70111i	−0.489420	−	0.564820i
$296$	1.09320	+	0.320993i	0.0635411	+	0.0186574i
$297$	1.29808	−	2.84240i	0.0753223	−	0.164933i
$298$	−5.75761			−0.333529
$299$	2.66833	−	3.63611i	0.154313	−	0.210282i
$300$	1.00000			0.0577350
$301$	−14.4713	+	31.6877i	−0.834110	+	1.82645i
$302$	−19.7127	−	5.78818i	−1.13434	−	0.333072i
$303$	1.23363	+	1.42368i	0.0708699	+	0.0817883i
$304$	−1.58911	+	1.02126i	−0.0911415	+	0.0585731i
$305$	−1.98681	+	2.29290i	−0.113765	+	0.131291i
$306$	−1.04727	+	7.28393i	−0.0598685	+	0.416394i
$307$	13.2473	−	3.88975i	0.756063	−	0.222000i	0.119087	−	0.992884i	$-0.462003\pi$
$307$	13.2473	−	3.88975i	0.756063	−	0.222000i	0.636976	+	0.770884i	$0.280185\pi$
$308$	9.19994	+	5.91244i	0.524215	+	0.336893i
$309$	0.124431	+	0.865436i	0.00707863	+	0.0492329i
$310$	−2.15976	−	4.72921i	−0.122666	−	0.268601i
$311$	−7.33931	−	16.0709i	−0.416174	−	0.911295i	−0.995371	−	0.0961068i	$-0.969361\pi$
$311$	−7.33931	−	16.0709i	−0.416174	−	0.911295i	0.579197	−	0.815188i	$-0.303366\pi$
$312$	−0.133837	−	0.930855i	−0.00757701	−	0.0526993i
$313$	−20.3440	−	13.0743i	−1.14991	−	0.739002i	−0.180288	−	0.983614i	$-0.557703\pi$
$313$	−20.3440	−	13.0743i	−1.14991	−	0.739002i	−0.969621	+	0.244612i	$0.921339\pi$
$314$	7.75126	−	2.27598i	0.437429	−	0.128441i
$315$	−0.498068	+	3.46414i	−0.0280630	+	0.195182i
$316$	11.0628	−	12.7672i	0.622333	−	0.718210i
$317$	11.3583	−	7.29954i	0.637946	−	0.409983i	−0.181298	−	0.983428i	$-0.558030\pi$
$317$	11.3583	−	7.29954i	0.637946	−	0.409983i	0.819244	+	0.573445i	$0.194394\pi$
$318$	−2.63774	−	3.04411i	−0.147917	−	0.170705i
$319$	−2.08581	−	0.612450i	−0.116783	−	0.0342906i
$320$	0.415415	−	0.909632i	0.0232224	−	0.0508500i
$321$	15.3795			0.858398
$322$	3.72372	+	16.3660i	0.207515	+	0.912041i
$323$	−13.9006			−0.773452
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	−0.902333	−	0.264949i	−0.0500524	−	0.0146967i
$326$	−1.09054	−	1.25855i	−0.0603994	−	0.0697046i
$327$	−3.67352	+	2.36083i	−0.203146	+	0.130554i
$328$	−1.35390	+	1.56249i	−0.0747568	+	0.0862740i
$329$	1.71332	−	11.9164i	0.0944586	−	0.656974i
$330$	−2.99820	+	0.880352i	−0.165046	+	0.0484618i
$331$	28.4875	+	18.3078i	1.56581	+	1.00629i	0.980742	+	0.195305i	$0.0625698\pi$
$331$	28.4875	+	18.3078i	1.56581	+	1.00629i	0.585071	+	0.810982i	$0.301067\pi$
$332$	−0.876479	−	6.09605i	−0.0481031	−	0.334564i
$333$	−0.473305	−	1.03639i	−0.0259370	−	0.0567940i
$334$	5.56540	+	12.1865i	0.304525	+	0.666818i
$335$	−0.524798	−	3.65005i	−0.0286728	−	0.199424i
$336$	2.94419	+	1.89212i	0.160619	+	0.103223i
$337$	10.3126	−	3.02804i	0.561761	−	0.164948i	0.0114901	−	0.999934i	$-0.496342\pi$
$337$	10.3126	−	3.02804i	0.561761	−	0.164948i	0.550271	+	0.834986i	$0.314524\pi$
$338$	1.72423	−	11.9923i	0.0937857	−	0.652294i
$339$	7.85337	−	9.06327i	0.426536	−	0.492249i
$340$	6.19064	−	3.97848i	0.335735	−	0.215764i
$341$	10.6388	+	12.2778i	0.576122	+	0.664880i
$342$	1.81246	+	0.532186i	0.0980065	+	0.0287773i
$343$	−2.54665	+	5.57637i	−0.137506	+	0.301096i
$344$	−9.95373			−0.536669
$345$	−4.23089	−	2.25822i	−0.227783	−	0.121579i
$346$	−1.85331			−0.0996343
$347$	−14.4227	+	31.5814i	−0.774253	+	1.69538i	−0.0571971	+	0.998363i	$0.518216\pi$
$347$	−14.4227	+	31.5814i	−0.774253	+	1.69538i	−0.717056	+	0.697015i	$0.754511\pi$
$348$	−0.667507	−	0.195998i	−0.0357822	−	0.0105066i
$349$	−18.9599	−	21.8809i	−1.01490	−	1.17126i	−0.985149	−	0.171700i	$-0.945074\pi$
$349$	−18.9599	−	21.8809i	−1.01490	−	1.17126i	−0.0297509	−	0.999557i	$-0.509471\pi$
$350$	2.94419	−	1.89212i	0.157374	−	0.101138i
$351$	−0.615849	+	0.710727i	−0.0328716	+	0.0379358i
$352$	−0.444702	+	3.09297i	−0.0237027	+	0.164856i
$353$	−17.9846	+	5.28074i	−0.957221	+	0.281065i	−0.722790	−	0.691067i	$-0.757141\pi$
$353$	−17.9846	+	5.28074i	−0.957221	+	0.281065i	−0.234431	+	0.972133i	$0.575323\pi$
$354$	10.7987	+	6.93989i	0.573943	+	0.368851i
$355$	0.657965	+	4.57624i	0.0349211	+	0.242882i
$356$	1.44492	+	3.16393i	0.0765806	+	0.167688i
$357$	10.6987	+	23.4268i	0.566234	+	1.23988i
$358$	1.52943	+	10.6374i	0.0808329	+	0.562205i
$359$	18.3361	+	11.7839i	0.967745	+	0.621932i	0.926131	−	0.377202i	$-0.123114\pi$
$359$	18.3361	+	11.7839i	0.967745	+	0.621932i	0.0416137	+	0.999134i	$0.486750\pi$
$360$	−0.959493	+	0.281733i	−0.0505697	+	0.0148486i
$361$	2.19617	−	15.2747i	0.115588	−	0.803932i
$362$	12.0091	−	13.8593i	0.631185	−	0.728427i
$363$	−1.03958	+	0.668100i	−0.0545640	+	0.0350661i
$364$	−2.15533	−	2.48738i	−0.112970	−	0.130374i
$365$	−1.36508	−	0.400825i	−0.0714518	−	0.0209801i
$366$	1.26035	−	2.75977i	0.0658794	−	0.144256i
$367$	22.9676			1.19890			0.599451	−	0.800412i	$-0.295386\pi$
$367$	22.9676			1.19890			0.599451	+	0.800412i	$0.295386\pi$
$368$	−3.81173	+	2.91045i	−0.198700	+	0.151718i
$369$	2.06747			0.107628
$370$	−0.473305	+	1.03639i	−0.0246060	+	0.0538795i
$371$	−13.5258	−	3.97154i	−0.702226	−	0.206192i
$372$	3.40465	+	3.92917i	0.176523	+	0.203718i
$373$	20.1745	−	12.9654i	1.04460	−	0.671321i	0.0984772	−	0.995139i	$-0.468603\pi$
$373$	20.1745	−	12.9654i	1.04460	−	0.671321i	0.946119	+	0.323818i	$0.104966\pi$
$374$	−15.0583	+	17.3782i	−0.778648	+	0.898608i
$375$	−0.142315	+	0.989821i	−0.00734911	+	0.0511142i
$376$	3.30060	−	0.969143i	0.170215	−	0.0499797i
$377$	0.550385	+	0.353711i	0.0283463	+	0.0182170i
$378$	−0.498068	−	3.46414i	−0.0256179	−	0.178176i
$379$	13.3948	+	29.3306i	0.688046	+	1.50661i	0.853887	+	0.520458i	$0.174239\pi$
$379$	13.3948	+	29.3306i	0.688046	+	1.50661i	−0.165841	+	0.986152i	$0.553034\pi$
$380$	−0.784708	−	1.71827i	−0.0402547	−	0.0881455i
$381$	0.231025	+	1.60681i	0.0118357	+	0.0823194i
$382$	−14.2294	−	9.14466i	−0.728038	−	0.467882i
$383$	20.6659	−	6.06805i	1.05598	−	0.310063i	0.292748	−	0.956190i	$-0.405430\pi$
$383$	20.6659	−	6.06805i	1.05598	−	0.310063i	0.763230	+	0.646127i	$0.223612\pi$
$384$	−0.142315	+	0.989821i	−0.00726247	+	0.0505116i
$385$	−7.16155	+	8.26487i	−0.364986	+	0.421217i
$386$	−4.59154	+	2.95081i	−0.233703	+	0.150192i
$387$	6.51831	+	7.52253i	0.331344	+	0.382392i
$388$	4.85704	+	1.42616i	0.246579	+	0.0724022i
$389$	−12.5386	+	27.4558i	−0.635734	+	1.39206i	0.267770	+	0.963483i	$0.413713\pi$
$389$	−12.5386	+	27.4558i	−0.635734	+	1.39206i	−0.903504	+	0.428580i	$0.859014\pi$
$390$	0.940427			0.0476204
$391$	−35.1762	+	2.85267i	−1.77894	+	0.144266i
$392$	5.24835			0.265082
$393$	−5.43205	+	11.8945i	−0.274011	+	0.600000i
$394$	−18.3626	−	5.39175i	−0.925096	−	0.271633i
$395$	11.0628	+	12.7672i	0.556631	+	0.642387i
$396$	2.62873	−	1.68938i	0.132099	−	0.0848947i
$397$	12.0498	−	13.9062i	0.604764	−	0.697934i	−0.367976	−	0.929835i	$-0.619949\pi$
$397$	12.0498	−	13.9062i	0.604764	−	0.697934i	0.972739	+	0.231901i	$0.0744945\pi$
$398$	−1.40924	+	9.80150i	−0.0706390	+	0.491305i
$399$	6.34318	−	1.86252i	0.317556	−	0.0932428i
$400$	0.841254	+	0.540641i	0.0420627	+	0.0270320i
$401$	−4.60231	−	32.0098i	−0.229828	−	1.59849i	−0.698826	−	0.715291i	$-0.746294\pi$
$401$	−4.60231	−	32.0098i	−0.229828	−	1.59849i	0.468998	−	0.883199i	$-0.344615\pi$
$402$	1.53188	+	3.35435i	0.0764031	+	0.167300i
$403$	−2.03110	−	4.44748i	−0.101176	−	0.221545i
$404$	0.268092	+	1.86462i	0.0133381	+	0.0927685i
$405$	0.841254	+	0.540641i	0.0418022	+	0.0268647i
$406$	−2.33612	+	0.685946i	−0.115940	+	0.0340429i
$407$	0.506674	−	3.52399i	0.0251149	−	0.174678i
$408$	−4.81901	+	5.56143i	−0.238576	+	0.275332i
$409$	14.6515	−	9.41594i	0.724469	−	0.465588i	−0.125720	−	0.992066i	$-0.540124\pi$
$409$	14.6515	−	9.41594i	0.724469	−	0.465588i	0.850189	+	0.526478i	$0.176488\pi$
$410$	−1.35390	−	1.56249i	−0.0668646	−	0.0771658i
$411$	17.7538	+	5.21297i	0.875728	+	0.257137i
$412$	−0.363212	+	0.795324i	−0.0178942	+	0.0391828i
$413$	44.9244			2.21059
$414$	4.69572	+	0.974770i	0.230782	+	0.0479073i
$415$	6.15874			0.302320
$416$	0.390668	−	0.855443i	0.0191541	−	0.0419415i
$417$	−17.8966	−	5.25492i	−0.876401	−	0.257335i
$418$	3.86540	+	4.46091i	0.189063	+	0.218190i
$419$	−15.3270	+	9.85004i	−0.748771	+	0.481206i	−0.858537	−	0.512751i	$-0.828626\pi$
$419$	−15.3270	+	9.85004i	−0.748771	+	0.481206i	0.109766	+	0.993957i	$0.464990\pi$
$420$	−2.29186	+	2.64495i	−0.111831	+	0.129060i
$421$	0.963535	−	6.70153i	0.0469598	−	0.326613i	−0.952777	−	0.303671i	$-0.901788\pi$
$421$	0.963535	−	6.70153i	0.0469598	−	0.326613i	0.999737	−	0.0229417i	$-0.00730322\pi$
$422$	17.8879	−	5.25236i	0.870770	−	0.255681i
$423$	−2.89386	−	1.85977i	−0.140704	−	0.0904252i
$424$	−0.573236	−	3.98694i	−0.0278388	−	0.193623i
$425$	3.05697	+	6.69383i	0.148285	+	0.324698i
$426$	−1.92059	−	4.20550i	−0.0930529	−	0.203757i
$427$	−1.51111	−	10.5100i	−0.0731279	−	0.508616i
$428$	12.9380	+	8.31477i	0.625383	+	0.401909i
$429$	−2.81959	+	0.827907i	−0.136131	+	0.0399717i
$430$	1.41656	−	9.85242i	0.0683128	−	0.475126i
$431$	−7.81480	+	9.01876i	−0.376426	+	0.434418i	−0.912076	−	0.410022i	$-0.865521\pi$
$431$	−7.81480	+	9.01876i	−0.376426	+	0.434418i	0.535650	+	0.844440i	$0.320067\pi$
$432$	0.841254	−	0.540641i	0.0404748	−	0.0260116i
$433$	−18.0283	−	20.8057i	−0.866383	−	0.999860i	−0.999961	−	0.00882128i	$-0.997192\pi$
$433$	−18.0283	−	20.8057i	−0.866383	−	0.999860i	0.133578	−	0.991038i	$-0.457353\pi$
$434$	17.4584	+	5.12624i	0.838029	+	0.246067i
$435$	0.288999	−	0.632820i	0.0138564	−	0.0303414i
$436$	−4.36672			−0.209128
$437$	−0.560227	+	9.04187i	−0.0267993	+	0.432531i
$438$	1.42271			0.0679799
$439$	2.05164	−	4.49246i	0.0979193	−	0.214413i	−0.854333	−	0.519727i	$-0.826034\pi$
$439$	2.05164	−	4.49246i	0.0979193	−	0.214413i	0.952252	+	0.305313i	$0.0987611\pi$
$440$	−2.99820	−	0.880352i	−0.142934	−	0.0419691i
$441$	−3.43694	−	3.96644i	−0.163664	−	0.188878i
$442$	5.82185	−	3.74147i	0.276917	−	0.177964i
$443$	−1.61866	+	1.86803i	−0.0769047	+	0.0887527i	−0.792898	−	0.609354i	$-0.791429\pi$
$443$	−1.61866	+	1.86803i	−0.0769047	+	0.0887527i	0.715993	+	0.698107i	$0.245974\pi$
$444$	0.162147	−	1.12776i	0.00769516	−	0.0535210i
$445$	−3.33736	+	0.979938i	−0.158206	+	0.0464535i
$446$	−4.94005	−	3.17478i	−0.233918	−	0.150330i
$447$	0.819393	+	5.69901i	0.0387560	+	0.269554i
$448$	1.45385	+	3.18350i	0.0686882	+	0.150406i
$449$	11.6403	+	25.4888i	0.549342	+	1.20289i	0.957088	+	0.289796i	$0.0935874\pi$
$449$	11.6403	+	25.4888i	0.549342	+	1.20289i	−0.407747	+	0.913095i	$0.633685\pi$
$450$	−0.142315	−	0.989821i	−0.00670879	−	0.0466606i
$451$	5.43482	+	3.49275i	0.255916	+	0.164467i
$452$	11.5066	−	3.37866i	0.541227	−	0.158919i
$453$	−2.92385	+	20.3358i	−0.137374	+	0.955461i
$454$	14.3077	−	16.5119i	0.671492	−	0.774943i
$455$	2.76879	−	1.77940i	0.129803	−	0.0834194i
$456$	1.23702	+	1.42759i	0.0579286	+	0.0668531i
$457$	−17.7754	−	5.21932i	−0.831497	−	0.244150i	−0.161837	−	0.986817i	$-0.551742\pi$
$457$	−17.7754	−	5.21932i	−0.831497	−	0.244150i	−0.669660	+	0.742668i	$0.733560\pi$
$458$	−7.03186	+	15.3976i	−0.328577	+	0.719484i
$459$	7.35883			0.343481
$460$	−2.33836	−	4.18713i	−0.109027	−	0.195226i
$461$	−16.4972			−0.768352			−0.384176	−	0.923260i	$-0.625514\pi$
$461$	−16.4972			−0.768352			−0.384176	+	0.923260i	$0.625514\pi$
$462$	4.54297	−	9.94773i	0.211358	−	0.462810i
$463$	−18.9504	−	5.56434i	−0.880700	−	0.258597i	−0.190040	−	0.981776i	$-0.560862\pi$
$463$	−18.9504	−	5.56434i	−0.880700	−	0.258597i	−0.690660	+	0.723180i	$0.742680\pi$
$464$	−0.455579	−	0.525766i	−0.0211497	−	0.0244081i
$465$	−4.37371	+	2.81081i	−0.202826	+	0.130348i
$466$	9.90159	−	11.4270i	0.458682	−	0.529348i
$467$	−0.288536	+	2.00681i	−0.0133518	+	0.0928641i	−0.995408	−	0.0957261i	$-0.969483\pi$
$467$	−0.288536	+	2.00681i	−0.0133518	+	0.0928641i	0.982056	+	0.188590i	$0.0603918\pi$
$468$	−0.902333	+	0.264949i	−0.0417104	+	0.0122473i
$469$	10.8569	+	6.97734i	0.501327	+	0.322184i
$470$	0.489554	+	3.40492i	0.0225815	+	0.157057i
$471$	−3.35593	−	7.34846i	−0.154633	−	0.338599i
$472$	5.33244	+	11.6764i	0.245445	+	0.537450i
$473$	4.42645	+	30.7866i	0.203528	+	1.41557i
$474$	−14.2116	−	9.13326i	−0.652762	−	0.419505i
$475$	1.81246	−	0.532186i	0.0831613	−	0.0244184i
$476$	−3.66520	+	25.4920i	−0.167994	+	1.16843i
$477$	−2.63774	+	3.04411i	−0.120774	+	0.139380i
$478$	24.6441	−	15.8378i	1.12720	−	0.724405i
$479$	−28.3123	−	32.6742i	−1.29362	−	1.49292i	−0.764937	−	0.644105i	$-0.777230\pi$
$479$	−28.3123	−	32.6742i	−1.29362	−	1.49292i	−0.528687	−	0.848817i	$-0.677315\pi$
$480$	−0.959493	−	0.281733i	−0.0437947	−	0.0128593i
$481$	−0.445109	+	0.974653i	−0.0202952	+	0.0444403i
$482$	−12.8525			−0.585415
$483$	15.6695	−	6.01494i	0.712986	−	0.273689i
$484$	−1.23576			−0.0561707
$485$	−2.10287	+	4.60464i	−0.0954864	+	0.209086i
$486$	−0.959493	−	0.281733i	−0.0435235	−	0.0127796i
$487$	−8.19025	−	9.45205i	−0.371135	−	0.428313i	0.539204	−	0.842175i	$-0.318725\pi$
$487$	−8.19025	−	9.45205i	−0.371135	−	0.428313i	−0.910340	+	0.413862i	$0.864180\pi$
$488$	2.55232	−	1.64028i	0.115538	−	0.0742518i
$489$	−1.09054	+	1.25855i	−0.0493159	+	0.0569135i
$490$	−0.746918	+	5.19493i	−0.0337423	+	0.234683i
$491$	−16.1593	+	4.74480i	−0.729259	+	0.214130i	−0.625225	−	0.780444i	$-0.714993\pi$
$491$	−16.1593	+	4.74480i	−0.729259	+	0.214130i	−0.104033	+	0.994574i	$0.533175\pi$
$492$	1.73927	+	1.11776i	0.0784121	+	0.0503924i
$493$	−0.728573	−	5.06734i	−0.0328133	−	0.228221i
$494$	−0.737961	−	1.61591i	−0.0332024	−	0.0727032i
$495$	1.29808	+	2.84240i	0.0583444	+	0.127756i
$496$	0.739901	+	5.14612i	0.0332225	+	0.231068i
$497$	−13.6119	−	8.74782i	−0.610576	−	0.392393i
$498$	−5.90926	+	1.73512i	−0.264800	+	0.0777524i
$499$	−1.18334	+	8.23033i	−0.0529737	+	0.368440i	0.946041	+	0.324048i	$0.105044\pi$
$499$	−1.18334	+	8.23033i	−0.0529737	+	0.368440i	−0.999014	+	0.0443917i	$0.985865\pi$
$500$	−0.654861	+	0.755750i	−0.0292863	+	0.0337981i
$501$	11.2705	−	7.24308i	0.503527	−	0.323597i
$502$	15.6849	+	18.1013i	0.700051	+	0.807902i
$503$	36.0087	+	10.5731i	1.60555	+	0.471431i	0.957083	−	0.289814i	$-0.0935935\pi$
$503$	36.0087	+	10.5731i	1.60555	+	0.471431i	0.648464	+	0.761245i	$0.275412\pi$
$504$	1.45385	−	3.18350i	0.0647598	−	0.141804i
$505$	−1.88380			−0.0838279
$506$	10.6970	+	10.4953i	0.475541	+	0.466572i
$507$	−12.1156			−0.538073
$508$	−0.674358	+	1.47664i	−0.0299198	+	0.0655152i
$509$	10.0351	+	2.94658i	0.444800	+	0.130605i	0.496460	−	0.868060i	$-0.334633\pi$
$509$	10.0351	+	2.94658i	0.444800	+	0.130605i	−0.0516601	+	0.998665i	$0.516451\pi$
$510$	−4.81901	−	5.56143i	−0.213389	−	0.246264i
$511$	4.18874	−	2.69194i	0.185299	−	0.119084i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	0.268829	−	1.86975i	0.0118691	−	0.0825514i
$514$	15.4945	−	4.54961i	0.683435	−	0.200675i
$515$	−0.735538	−	0.472702i	−0.0324117	−	0.0208297i
$516$	1.41656	+	9.85242i	0.0623607	+	0.433728i
$517$	−4.46532	−	9.77768i	−0.196384	−	0.430022i
$518$	−1.65646	−	3.62713i	−0.0727805	−	0.159367i
$519$	0.263753	+	1.83444i	0.0115775	+	0.0805230i
$520$	0.791138	+	0.508433i	0.0346937	+	0.0222963i
$521$	14.7293	−	4.32491i	0.645302	−	0.189478i	0.0573251	−	0.998356i	$-0.481743\pi$
$521$	14.7293	−	4.32491i	0.645302	−	0.189478i	0.587977	+	0.808878i	$0.299925\pi$
$522$	−0.0990067	+	0.688607i	−0.00433340	+	0.0301395i
$523$	26.3320	−	30.3888i	1.15142	−	1.32881i	0.215538	−	0.976495i	$-0.430850\pi$
$523$	26.3320	−	30.3888i	1.15142	−	1.32881i	0.935882	−	0.352314i	$-0.114605\pi$
$524$	−11.0004	+	7.06953i	−0.480555	+	0.308834i
$525$	−2.29186	−	2.64495i	−0.100025	−	0.115435i
$526$	−27.3442	−	8.02897i	−1.19226	−	0.350080i
$527$	−15.8933	+	34.8015i	−0.692323	+	1.51598i
$528$	3.12478			0.135989
$529$	0.437880	+	22.9958i	0.0190383	+	0.999819i
$530$	4.02794			0.174963
$531$	5.33244	−	11.6764i	0.231408	−	0.506713i
$532$	6.34318	+	1.86252i	0.275012	+	0.0807507i
$533$	−1.27325	−	1.46941i	−0.0551505	−	0.0636471i
$534$	2.92610	−	1.88049i	0.126625	−	0.0813767i
$535$	−10.0714	+	11.6230i	−0.435425	+	0.502507i
$536$	−0.524798	+	3.65005i	−0.0226678	+	0.157658i
$537$	10.3115	−	3.02773i	0.444973	−	0.130656i
$538$	−4.25361	−	2.73363i	−0.183386	−	0.117855i
$539$	−2.33395	−	16.2330i	−0.100531	−	0.699205i
$540$	0.415415	+	0.909632i	0.0178766	+	0.0391443i
$541$	1.90026	+	4.16098i	0.0816984	+	0.178895i	0.946073	−	0.323954i	$-0.105012\pi$
$541$	1.90026	+	4.16098i	0.0816984	+	0.178895i	−0.864374	+	0.502849i	$0.832285\pi$
$542$	−1.13537	−	7.89666i	−0.0487682	−	0.339190i
$543$	−15.4273	−	9.91450i	−0.662047	−	0.425472i
$544$	−7.06075	+	2.07322i	−0.302727	+	0.0888887i
$545$	0.621450	−	4.32228i	0.0266200	−	0.185146i
$546$	−2.15533	+	2.48738i	−0.0922394	+	0.106450i
$547$	−31.0863	+	19.9779i	−1.32915	+	0.854195i	−0.996059	−	0.0886986i	$-0.971729\pi$
$547$	−31.0863	+	19.9779i	−1.32915	+	0.854195i	−0.333095	+	0.942893i	$0.608093\pi$
$548$	12.1171	+	13.9838i	0.517615	+	0.597360i
$549$	−2.91105	−	0.854761i	−0.124241	−	0.0364803i
$550$	1.29808	−	2.84240i	0.0553503	−	0.121200i
$551$	−1.31414			−0.0559841
$552$	3.42329	+	3.35873i	0.145705	+	0.142957i
$553$	−59.1229			−2.51416
$554$	2.00092	−	4.38141i	0.0850110	−	0.186148i
$555$	1.09320	+	0.320993i	0.0464039	+	0.0136254i
$556$	−12.2146	−	14.0964i	−0.518013	−	0.597819i
$557$	16.5519	−	10.6372i	0.701326	−	0.450715i	−0.140770	−	0.990042i	$-0.544958\pi$
$557$	16.5519	−	10.6372i	0.701326	−	0.450715i	0.842096	+	0.539328i	$0.181322\pi$
$558$	3.40465	−	3.92917i	0.144130	−	0.166335i
$559$	1.33217	−	9.26548i	0.0563450	−	0.391888i
$560$	−3.35800	+	0.985998i	−0.141901	+	0.0416660i
$561$	19.3444	+	12.4319i	0.816721	+	0.524875i
$562$	−3.69523	−	25.7009i	−0.155874	−	1.08413i
$563$	6.63943	+	14.5383i	0.279818	+	0.612717i	0.996399	−	0.0847873i	$-0.0270211\pi$
$563$	6.63943	+	14.5383i	0.279818	+	0.612717i	−0.716581	+	0.697504i	$0.754294\pi$
$564$	−1.42900	−	3.12908i	−0.0601718	−	0.131758i
$565$	1.70670	+	11.8704i	0.0718014	+	0.499390i
$566$	−17.5072	−	11.2512i	−0.735882	−	0.472923i
$567$	−3.35800	+	0.985998i	−0.141023	+	0.0414080i
$568$	0.657965	−	4.57624i	0.0276076	−	0.192015i
$569$	3.74578	−	4.32286i	0.157031	−	0.181224i	−0.671782	−	0.740749i	$-0.734471\pi$
$569$	3.74578	−	4.32286i	0.157031	−	0.181224i	0.828814	+	0.559525i	$0.189016\pi$
$570$	−1.58911	+	1.02126i	−0.0665604	+	0.0427757i
$571$	11.0655	+	12.7703i	0.463078	+	0.534420i	0.938473	−	0.345352i	$-0.112240\pi$
$571$	11.0655	+	12.7703i	0.463078	+	0.534420i	−0.475396	+	0.879772i	$0.657695\pi$
$572$	−2.81959	−	0.827907i	−0.117893	−	0.0346165i
$573$	−7.02653	+	15.3860i	−0.293538	+	0.642758i
$574$	7.23565			0.302010
$575$	4.47729	−	1.71867i	0.186716	−	0.0716735i
$576$	1.00000			0.0416667
$577$	−0.922595	+	2.02020i	−0.0384081	+	0.0841020i	−0.927864	−	0.372920i	$-0.878357\pi$
$577$	−0.922595	+	2.02020i	−0.0384081	+	0.0841020i	0.889455	+	0.457022i	$0.151084\pi$
$578$	−35.6474	−	10.4670i	−1.48274	−	0.435371i
$579$	3.57422	+	4.12487i	0.148539	+	0.171424i
$580$	0.585250	−	0.376117i	0.0243012	−	0.0156174i
$581$	−14.1149	+	16.2895i	−0.585587	+	0.675803i
$582$	0.720411	−	5.01057i	0.0298620	−	0.207695i
$583$	−12.0766	+	3.54601i	−0.500161	+	0.146861i
$584$	1.19686	+	0.769178i	0.0495266	+	0.0318288i
$585$	−0.133837	−	0.930855i	−0.00553347	−	0.0384861i
$586$	−10.7911	−	23.6292i	−0.445777	−	0.976115i
$587$	−10.0691	−	22.0484i	−0.415598	−	0.910033i	−0.995448	−	0.0953094i	$-0.969616\pi$
$587$	−10.0691	−	22.0484i	−0.415598	−	0.910033i	0.579850	−	0.814724i	$-0.303111\pi$
$588$	−0.746918	−	5.19493i	−0.0308024	−	0.214235i
$589$	8.26183	+	5.30956i	0.340423	+	0.218776i
$590$	−12.3164	+	3.61643i	−0.507060	+	0.148886i
$591$	−2.72360	+	18.9430i	−0.112034	+	0.779213i
$592$	0.746119	−	0.861067i	0.0306653	−	0.0353896i
$593$	9.64933	−	6.20125i	0.396251	−	0.254655i	−0.327308	−	0.944918i	$-0.606141\pi$
$593$	9.64933	−	6.20125i	0.396251	−	0.254655i	0.723559	+	0.690263i	$0.242505\pi$
$594$	−2.04630	−	2.36155i	−0.0839605	−	0.0968956i
$595$	−24.7109	−	7.25579i	−1.01305	−	0.297458i
$596$	−2.39180	+	5.23731i	−0.0979718	+	0.214528i
$597$	9.90229			0.405274
$598$	−2.19906	−	3.93769i	−0.0899262	−	0.161024i
$599$	−22.1621			−0.905517			−0.452759	−	0.891633i	$-0.649560\pi$
$599$	−22.1621			−0.905517			−0.452759	+	0.891633i	$0.649560\pi$
$600$	0.415415	−	0.909632i	0.0169592	−	0.0371356i
$601$	−23.2472	−	6.82600i	−0.948274	−	0.278438i	−0.229206	−	0.973378i	$-0.573613\pi$
$601$	−23.2472	−	6.82600i	−0.948274	−	0.278438i	−0.719068	+	0.694940i	$0.755431\pi$
$602$	22.8125	+	26.3271i	0.929770	+	1.07301i
$603$	3.10219	−	1.99366i	0.126331	−	0.0811881i
$604$	−13.4541	+	15.5268i	−0.547439	+	0.631778i
$605$	0.175866	−	1.22318i	0.00714998	−	0.0497292i
$606$	1.80749	−	0.530727i	0.0734243	−	0.0215593i
$607$	25.1456	+	16.1601i	1.02063	+	0.655918i	0.940123	−	0.340836i	$-0.110710\pi$
$607$	25.1456	+	16.1601i	1.02063	+	0.655918i	0.0805060	+	0.996754i	$0.474346\pi$
$608$	0.268829	+	1.86975i	0.0109025	+	0.0758283i
$609$	1.01143	+	2.21472i	0.0409852	+	0.0897450i
$610$	1.26035	+	2.75977i	0.0510300	+	0.111740i
$611$	0.460390	+	3.20208i	0.0186254	+	0.129542i
$612$	6.19064	+	3.97848i	0.250242	+	0.160821i
$613$	−39.6205	+	11.6336i	−1.60026	+	0.469878i	−0.955618	−	0.294610i	$-0.904810\pi$
$613$	−39.6205	+	11.6336i	−1.60026	+	0.469878i	−0.644638	+	0.764488i	$0.722992\pi$
$614$	1.96488	−	13.6660i	0.0792960	−	0.551516i
$615$	−1.35390	+	1.56249i	−0.0545947	+	0.0630056i
$616$	9.19994	−	5.91244i	0.370676	−	0.238219i
$617$	9.24573	+	10.6701i	0.372219	+	0.429564i	0.910696	−	0.413076i	$-0.135546\pi$
$617$	9.24573	+	10.6701i	0.372219	+	0.429564i	−0.538477	+	0.842640i	$0.681000\pi$
$618$	0.838919	+	0.246329i	0.0337463	+	0.00990880i
$619$	−5.87007	+	12.8537i	−0.235938	+	0.516632i	−0.990152	−	0.139996i	$-0.955291\pi$
$619$	−5.87007	+	12.8537i	−0.235938	+	0.516632i	0.754214	+	0.656629i	$0.228018\pi$
$620$	−5.19904			−0.208798
$621$	0.296577	−	4.78665i	0.0119012	−	0.192082i
$622$	−17.6674			−0.708399
$623$	5.05688	−	11.0730i	0.202600	−	0.443631i
$624$	−0.902333	−	0.264949i	−0.0361222	−	0.0106064i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	−20.3440	+	13.0743i	−0.813109	+	0.522553i
$627$	3.86540	−	4.46091i	0.154369	−	0.178152i
$628$	1.14969	−	7.99627i	0.0458776	−	0.319086i
$629$	8.04470	−	2.36214i	0.320763	−	0.0941845i
$630$	2.94419	+	1.89212i	0.117299	+	0.0753837i
$631$	1.98725	+	13.8216i	0.0791112	+	0.550230i	0.990375	+	0.138408i	$0.0441985\pi$
$631$	1.98725	+	13.8216i	0.0791112	+	0.550230i	−0.911264	+	0.411822i	$0.864892\pi$
$632$	−7.01777	−	15.3668i	−0.279152	−	0.611258i
$633$	−7.74462	−	16.9583i	−0.307821	−	0.674034i
$634$	−1.92148	−	13.3642i	−0.0763119	−	0.530761i
$635$	−1.36564	−	0.877641i	−0.0541936	−	0.0348281i
$636$	−3.86478	+	1.13480i	−0.153249	+	0.0449978i
$637$	−0.702422	+	4.88545i	−0.0278310	+	0.193569i
$638$	−1.42358	+	1.64290i	−0.0563602	+	0.0650431i
$639$	−3.88937	+	2.49955i	−0.153861	+	0.0988805i
$640$	−0.654861	−	0.755750i	−0.0258856	−	0.0298736i
$641$	−18.6972	−	5.48998i	−0.738493	−	0.216841i	−0.109212	−	0.994019i	$-0.534833\pi$
$641$	−18.6972	−	5.48998i	−0.738493	−	0.216841i	−0.629282	+	0.777177i	$0.716651\pi$
$642$	6.38886	−	13.9897i	0.252148	−	0.552128i
$643$	34.3041			1.35282			0.676412	−	0.736524i	$-0.263534\pi$
$643$	34.3041			1.35282			0.676412	+	0.736524i	$0.263534\pi$
$644$	16.4339	+	3.41147i	0.647587	+	0.134431i
$645$	−9.95373			−0.391928
$646$	−5.77454	+	12.6445i	−0.227196	+	0.497490i
$647$	−34.8960	−	10.2464i	−1.37190	−	0.402828i	−0.488961	−	0.872306i	$-0.662624\pi$
$647$	−34.8960	−	10.2464i	−1.37190	−	0.402828i	−0.882944	+	0.469478i	$0.844442\pi$
$648$	−0.654861	−	0.755750i	−0.0257254	−	0.0296886i
$649$	33.7435	−	21.6856i	1.32455	−	0.851235i
$650$	−0.615849	+	0.710727i	−0.0241556	+	0.0278770i
$651$	2.58948	−	18.0102i	0.101490	−	0.705876i
$652$	−1.59784	+	0.469169i	−0.0625763	+	0.0183741i
$653$	−3.71540	−	2.38774i	−0.145395	−	0.0934395i	0.465921	−	0.884826i	$-0.345723\pi$
$653$	−3.71540	−	2.38774i	−0.145395	−	0.0934395i	−0.611316	+	0.791387i	$0.709359\pi$
$654$	0.621450	+	4.32228i	0.0243006	+	0.169014i
$655$	−5.43205	−	11.8945i	−0.212248	−	0.464758i
$656$	0.858858	+	1.88064i	0.0335328	+	0.0734265i
$657$	−0.202473	−	1.40823i	−0.00789924	−	0.0549404i
$658$	−10.1278	−	6.50876i	−0.394824	−	0.253738i
$659$	35.5989	−	10.4528i	1.38674	−	0.407183i	0.498629	−	0.866816i	$-0.333837\pi$
$659$	35.5989	−	10.4528i	1.38674	−	0.407183i	0.888109	+	0.459633i	$0.152019\pi$
$660$	−0.444702	+	3.09297i	−0.0173100	+	0.120394i
$661$	−6.65094	+	7.67559i	−0.258691	+	0.298546i	−0.870207	−	0.492687i	$-0.836015\pi$
$661$	−6.65094	+	7.67559i	−0.258691	+	0.298546i	0.611515	+	0.791233i	$0.290560\pi$
$662$	28.4875	−	18.3078i	1.10720	−	0.711553i
$663$	−4.53193	−	5.23012i	−0.176005	−	0.203121i
$664$	−5.90926	−	1.73512i	−0.229324	−	0.0673356i
$665$	−2.74629	+	6.01355i	−0.106497	+	0.233195i
$666$	−1.13935			−0.0441491
$667$	−3.32548	+	0.269685i	−0.128763	+	0.0104423i
$668$	13.3972			0.518354
$669$	−2.43942	+	5.34159i	−0.0943135	+	0.206518i
$670$	−3.53821	−	1.03891i	−0.136693	−	0.0401367i
$671$	−6.20835	−	7.16482i	−0.239671	−	0.276595i
$672$	2.94419	−	1.89212i	0.113575	−	0.0729899i
$673$	12.4364	−	14.3524i	0.479387	−	0.553243i	−0.463611	−	0.886039i	$-0.653447\pi$
$673$	12.4364	−	14.3524i	0.479387	−	0.553243i	0.942999	+	0.332796i	$0.107992\pi$
$674$	1.52959	−	10.6385i	0.0589176	−	0.409781i
$675$	−0.959493	+	0.281733i	−0.0369309	+	0.0108439i
$676$	−10.1923	−	6.55019i	−0.392011	−	0.251930i
$677$	0.512273	+	3.56293i	0.0196882	+	0.136935i	0.997295	−	0.0735066i	$-0.0234190\pi$
$677$	0.512273	+	3.56293i	0.0196882	+	0.136935i	−0.977606	+	0.210441i	$0.932510\pi$
$678$	−4.98183	−	10.9087i	−0.191326	−	0.418946i
$679$	−7.35955	−	16.1152i	−0.282434	−	0.618443i
$680$	−1.04727	−	7.28393i	−0.0401610	−	0.279326i
$681$	−18.3800	−	11.8121i	−0.704325	−	0.452642i
$682$	15.5878	−	4.57699i	0.596887	−	0.175262i
$683$	−2.06134	+	14.3369i	−0.0788750	+	0.548588i	0.911619	+	0.411035i	$0.134833\pi$
$683$	−2.06134	+	14.3369i	−0.0788750	+	0.548588i	−0.990494	+	0.137552i	$0.956076\pi$
$684$	1.23702	−	1.42759i	0.0472985	−	0.0545853i
$685$	−15.5659	+	10.0036i	−0.594744	+	0.382219i
$686$	4.01453	+	4.63302i	0.153276	+	0.176890i
$687$	16.2416	+	4.76898i	0.619657	+	0.181948i
$688$	−4.13493	+	9.05423i	−0.157643	+	0.345189i
$689$	3.78798			0.144311
$690$	−3.81173	+	2.91045i	−0.145110	+	0.110799i
$691$	−7.77848			−0.295907			−0.147954	−	0.988994i	$-0.547269\pi$
$691$	−7.77848			−0.295907			−0.147954	+	0.988994i	$0.547269\pi$
$692$	−0.769891	+	1.68583i	−0.0292669	+	0.0640855i
$693$	−10.4930	−	3.08102i	−0.398596	−	0.117038i
$694$	22.7360	+	26.2388i	0.863048	+	0.996010i
$695$	15.6912	−	10.0841i	0.595201	−	0.382513i
$696$	−0.455579	+	0.525766i	−0.0172687	+	0.0199291i
$697$	−2.16520	+	15.0593i	−0.0820128	+	0.570411i
$698$	−27.7798	+	8.15688i	−1.05148	+	0.308743i
$699$	−12.7199	−	8.17457i	−0.481110	−	0.309191i
$700$	−0.498068	−	3.46414i	−0.0188252	−	0.130932i
$701$	−4.74403	−	10.3880i	−0.179180	−	0.392349i	0.798636	−	0.601814i	$-0.205555\pi$
$701$	−4.74403	−	10.3880i	−0.179180	−	0.392349i	−0.977816	+	0.209465i	$0.932828\pi$
$702$	0.390668	+	0.855443i	0.0147448	+	0.0322866i
$703$	−0.306292	−	2.13031i	−0.0115520	−	0.0803460i
$704$	2.62873	+	1.68938i	0.0990740	+	0.0636710i
$705$	3.30060	−	0.969143i	0.124308	−	0.0365000i
$706$	−2.66752	+	18.5530i	−0.100394	+	0.698252i
$707$	4.31740	−	4.98254i	0.162373	−	0.187388i
$708$	10.7987	−	6.93989i	0.405839	−	0.260817i
$709$	−12.7841	−	14.7537i	−0.480118	−	0.554086i	0.463080	−	0.886317i	$-0.346744\pi$
$709$	−12.7841	−	14.7537i	−0.480118	−	0.554086i	−0.943198	+	0.332230i	$0.892199\pi$
$710$	4.43603	+	1.30253i	0.166481	+	0.0488833i
$711$	−7.01777	+	15.3668i	−0.263187	+	0.576299i
$712$	3.47826			0.130353
$713$	21.9966	+	11.7406i	0.823778	+	0.439689i
$714$	25.7542			0.963826
$715$	1.22075	−	2.67307i	0.0456534	−	0.0999671i
$716$	10.3115	+	3.02773i	0.385358	+	0.113151i
$717$	−19.1838	−	22.1393i	−0.716433	−	0.826808i
$718$	18.3361	−	11.7839i	0.684299	−	0.439772i
$719$	−14.3614	+	16.5740i	−0.535590	+	0.618104i	−0.957465	−	0.288550i	$-0.906827\pi$
$719$	−14.3614	+	16.5740i	−0.535590	+	0.618104i	0.421874	+	0.906654i	$0.361372\pi$
$720$	−0.142315	+	0.989821i	−0.00530376	+	0.0368885i
$721$	2.93602	−	0.862093i	0.109343	−	0.0321060i
$722$	−12.9820	−	8.34305i	−0.483141	−	0.310496i
$723$	1.82910	+	12.7217i	0.0680249	+	0.473124i
$724$	−7.61806	−	16.6812i	−0.283123	−	0.619953i
$725$	0.288999	+	0.632820i	0.0107332	+	0.0235023i
$726$	0.175866	+	1.22318i	0.00652701	+	0.0453964i
$727$	−21.1928	−	13.6198i	−0.785997	−	0.505130i	0.0850218	−	0.996379i	$-0.472904\pi$
$727$	−21.1928	−	13.6198i	−0.785997	−	0.505130i	−0.871019	+	0.491249i	$0.836540\pi$
$728$	−3.15795	+	0.927259i	−0.117042	+	0.0343665i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−0.931680	+	1.07522i	−0.0344830	+	0.0397955i
$731$	−61.6200	+	39.6008i	−2.27910	+	1.46469i
$732$	−1.98681	−	2.29290i	−0.0734347	−	0.0847482i
$733$	−37.5611	−	11.0289i	−1.38735	−	0.407363i	−0.499029	−	0.866585i	$-0.666310\pi$
$733$	−37.5611	−	11.0289i	−1.38735	−	0.407363i	−0.888321	+	0.459223i	$0.848128\pi$
$734$	9.54110	−	20.8921i	0.352169	−	0.771142i
$735$	5.24835			0.193588
$736$	1.06399	+	4.67631i	0.0392193	+	0.172371i
$737$	11.5229			0.424451
$738$	0.858858	−	1.88064i	0.0316150	−	0.0692272i
$739$	−19.2664	−	5.65713i	−0.708727	−	0.208101i	−0.0925492	−	0.995708i	$-0.529502\pi$
$739$	−19.2664	−	5.65713i	−0.708727	−	0.208101i	−0.616178	+	0.787607i	$0.711320\pi$
$740$	0.746119	+	0.861067i	0.0274279	+	0.0316535i
$741$	−1.49444	+	0.960418i	−0.0548996	+	0.0352818i
$742$	−9.23147	+	10.6537i	−0.338898	+	0.391109i
$743$	−0.798127	+	5.55109i	−0.0292804	+	0.203650i	−0.999210	−	0.0397349i	$-0.987349\pi$
$743$	−0.798127	+	5.55109i	−0.0292804	+	0.203650i	0.969930	+	0.243385i	$0.0782578\pi$
$744$	4.98844	−	1.46474i	0.182885	−	0.0536999i
$745$	−4.84361	−	3.11280i	−0.177456	−	0.114044i
$746$	−3.41292	−	23.7374i	−0.124956	−	0.869088i
$747$	2.55843	+	5.60218i	0.0936081	+	0.204973i
$748$	9.55235	+	20.9167i	0.349269	+	0.764791i
$749$	−7.66003	−	53.2767i	−0.279891	−	1.94669i
$750$	0.841254	+	0.540641i	0.0307182	+	0.0197414i
$751$	−35.6285	+	10.4615i	−1.30010	+	0.381744i	−0.857273	−	0.514862i	$-0.827843\pi$
$751$	−35.6285	+	10.4615i	−1.30010	+	0.381744i	−0.442829	+	0.896606i	$0.646025\pi$
$752$	0.489554	−	3.40492i	0.0178522	−	0.124165i
$753$	15.6849	−	18.1013i	0.571589	−	0.659649i
$754$	0.550385	−	0.353711i	0.0200438	−	0.0128814i
$755$	−13.4541	−	15.5268i	−0.489644	−	0.565079i
$756$	−3.35800	−	0.985998i	−0.122129	−	0.0358604i
$757$	18.3082	−	40.0893i	0.665422	−	1.45707i	−0.211960	−	0.977278i	$-0.567985\pi$
$757$	18.3082	−	40.0893i	0.665422	−	1.45707i	0.877382	−	0.479792i	$-0.159288\pi$
$758$	32.2444			1.17117
$759$	8.86611	−	12.0818i	0.321819	−	0.438541i
$760$	−1.88897			−0.0685203
$761$	0.707111	−	1.54836i	0.0256328	−	0.0561279i	−0.896383	−	0.443281i	$-0.853814\pi$
$761$	0.707111	−	1.54836i	0.0256328	−	0.0561279i	0.922015	+	0.387153i	$0.126542\pi$
$762$	1.55758	+	0.457346i	0.0564251	+	0.0165679i
$763$	10.0079	+	11.5497i	0.362311	+	0.418129i
$764$	−14.2294	+	9.14466i	−0.514801	+	0.330842i
$765$	−4.81901	+	5.56143i	−0.174232	+	0.201074i
$766$	3.06523	−	21.3191i	0.110751	−	0.770291i
$767$	−11.5827	+	3.40099i	−0.418228	+	0.122803i
$768$	0.841254	+	0.540641i	0.0303561	+	0.0195087i
$769$	0.673494	+	4.68425i	0.0242868	+	0.168919i	0.998355	−	0.0573365i	$-0.0182608\pi$
$769$	0.673494	+	4.68425i	0.0242868	+	0.168919i	−0.974068	+	0.226255i	$0.927352\pi$
$770$	4.54297	+	9.94773i	0.163717	+	0.358491i
$771$	−6.70840	−	14.6894i	−0.241597	−	0.529024i
$772$	0.776751	+	5.40243i	0.0279559	+	0.194438i
$773$	−28.7312	−	18.4645i	−1.03339	−	0.664120i	−0.0900475	−	0.995937i	$-0.528702\pi$
$773$	−28.7312	−	18.4645i	−1.03339	−	0.664120i	−0.943344	+	0.331817i	$0.892338\pi$
$774$	9.55053	−	2.80429i	0.343287	−	0.100798i
$775$	0.739901	−	5.14612i	0.0265780	−	0.184854i
$776$	3.31497	−	3.82568i	0.119000	−	0.137334i
$777$	−3.35448	+	2.15579i	−0.120341	+	0.0773386i
$778$	19.7659	+	22.8111i	0.708643	+	0.817817i
$779$	3.74720	+	1.10028i	0.134257	+	0.0394215i
$780$	0.390668	−	0.855443i	0.0139881	−	0.0306298i
$781$	−14.4468			−0.516947
$782$	−12.0178	+	33.1825i	−0.429757	+	1.18660i
$783$	0.695688			0.0248618
$784$	2.18024	−	4.77407i	0.0778658	−	0.170502i
$785$	7.75126	+	2.27598i	0.276654	+	0.0812331i
$786$	8.56310	+	9.88234i	0.305436	+	0.352491i
$787$	27.3067	−	17.5490i	0.973380	−	0.625553i	0.0457099	−	0.998955i	$-0.485445\pi$
$787$	27.3067	−	17.5490i	0.973380	−	0.625553i	0.927670	+	0.373402i	$0.121809\pi$
$788$	−12.5326	+	14.4634i	−0.446456	+	0.515238i
$789$	−4.05577	+	28.2085i	−0.144389	+	1.00425i
$790$	16.2091	−	4.75942i	0.576694	−	0.169333i
$791$	−35.3080	−	22.6911i	−1.25541	−	0.806801i
$792$	−0.444702	−	3.09297i	−0.0158018	−	0.109904i
$793$	1.18526	+	2.59537i	0.0420900	+	0.0921642i
$794$	−7.64389	−	16.7378i	−0.271271	−	0.594001i
$795$	−0.573236	−	3.98694i	−0.0203306	−	0.141402i
$796$	8.33034	+	5.35358i	0.295261	+	0.189753i
$797$	5.19463	−	1.52528i	0.184003	−	0.0540282i	−0.188433	−	0.982086i	$-0.560341\pi$
$797$	5.19463	−	1.52528i	0.184003	−	0.0540282i	0.372436	+	0.928058i	$0.378523\pi$
$798$	0.940839	−	6.54368i	0.0333053	−	0.231644i
$799$	16.5771	−	19.1310i	0.586455	−	0.676806i
$800$	0.841254	−	0.540641i	0.0297428	−	0.0191145i
$801$	−2.27777	−	2.62869i	−0.0804812	−	0.0928802i
$802$	−31.0290	−	9.11092i	−1.09567	−	0.321718i
$803$	1.84680	−	4.04392i	0.0651721	−	0.142707i
$804$	3.68759			0.130051
$805$	−5.71553	+	15.7812i	−0.201446	+	0.556212i
$806$	−4.88932			−0.172219
$807$	−2.10045	+	4.59935i	−0.0739395	+	0.161905i
$808$	1.80749	+	0.530727i	0.0635873	+	0.0186709i
$809$	33.8152	+	39.0248i	1.18888	+	1.37204i	0.911512	+	0.411274i	$0.134916\pi$
$809$	33.8152	+	39.0248i	1.18888	+	1.37204i	0.277366	+	0.960764i	$0.410539\pi$
$810$	0.841254	−	0.540641i	0.0295586	−	0.0189962i
$811$	−12.2922	+	14.1859i	−0.431637	+	0.498136i	−0.929347	−	0.369208i	$-0.879629\pi$
$811$	−12.2922	+	14.1859i	−0.431637	+	0.498136i	0.497710	+	0.867344i	$0.334174\pi$
$812$	−0.346500	+	2.40996i	−0.0121598	+	0.0845730i
$813$	−7.65470	+	2.24762i	−0.268462	+	0.0788276i
$814$	−2.99506	−	1.92481i	−0.104977	−	0.0674645i
$815$	−0.236997	−	1.64835i	−0.00830163	−	0.0577391i
$816$	3.05697	+	6.69383i	0.107015	+	0.234331i
$817$	7.81078	+	17.1032i	0.273264	+	0.598366i
$818$	−2.47859	−	17.2390i	−0.0866619	−	0.602747i
$819$	2.76879	+	1.77940i	0.0967495	+	0.0621771i
$820$	−1.98372	+	0.582473i	−0.0692746	+	0.0203408i
$821$	−3.06273	+	21.3018i	−0.106890	+	0.743437i	0.863927	+	0.503617i	$0.167998\pi$
$821$	−3.06273	+	21.3018i	−0.106890	+	0.743437i	−0.970817	+	0.239820i	$0.922911\pi$
$822$	12.1171	−	13.9838i	0.422631	−	0.487742i
$823$	21.6248	−	13.8974i	0.753793	−	0.484434i	−0.106450	−	0.994318i	$-0.533948\pi$
$823$	21.6248	−	13.8974i	0.753793	−	0.484434i	0.860243	+	0.509885i	$0.170312\pi$
$824$	0.572568	+	0.660779i	0.0199464	+	0.0230193i
$825$	−2.99820	−	0.880352i	−0.104384	−	0.0306499i
$826$	18.6623	−	40.8647i	0.649343	−	1.42186i
$827$	30.9864			1.07750			0.538751	−	0.842465i	$-0.318896\pi$
$827$	30.9864			1.07750			0.538751	+	0.842465i	$0.318896\pi$
$828$	2.83736	−	3.86645i	0.0986050	−	0.134368i
$829$	33.8413			1.17536			0.587679	−	0.809095i	$-0.300042\pi$
$829$	33.8413			1.17536			0.587679	+	0.809095i	$0.300042\pi$
$830$	2.55843	−	5.60218i	0.0888044	−	0.194455i
$831$	−4.62157	−	1.35702i	−0.160320	−	0.0470743i
$832$	−0.615849	−	0.710727i	−0.0213507	−	0.0246400i
$833$	32.4907	−	20.8805i	1.12573	−	0.723466i
$834$	−12.2146	+	14.0964i	−0.422956	+	0.488117i
$835$	−1.90662	+	13.2609i	−0.0659814	+	0.458911i
$836$	5.66353	−	1.66296i	0.195877	−	0.0575148i
$837$	−4.37371	−	2.81081i	−0.151178	−	0.0971559i
$838$	2.59286	+	18.0338i	0.0895690	+	0.622966i
$839$	−11.6166	−	25.4369i	−0.401051	−	0.878179i	−0.997163	−	0.0752774i	$-0.976016\pi$
$839$	−11.6166	−	25.4369i	−0.401051	−	0.878179i	0.596112	−	0.802901i	$-0.296712\pi$
$840$	1.45385	+	3.18350i	0.0501627	+	0.109841i
$841$	4.05825	+	28.2258i	0.139940	+	0.973302i
$842$	−5.69566	−	3.66038i	−0.196285	−	0.126145i
$843$	−24.9134	+	7.31524i	−0.858064	+	0.251950i
$844$	2.65319	−	18.4533i	0.0913265	−	0.635190i
$845$	7.93403	−	9.15636i	0.272939	−	0.314988i
$846$	−2.89386	+	1.85977i	−0.0994930	+	0.0639402i
$847$	2.83218	+	3.26850i	0.0973147	+	0.112307i
$848$	−3.86478	−	1.13480i	−0.132717	−	0.0389693i
$849$	−8.64514	+	18.9302i	−0.296700	+	0.649683i
$850$	7.35883			0.252406
$851$	−1.21226	−	5.32798i	−0.0415559	−	0.182641i
$852$	−4.62330			−0.158392
$853$	−20.7513	+	45.4390i	−0.710510	+	1.55580i	0.116233	+	0.993222i	$0.462918\pi$
$853$	−20.7513	+	45.4390i	−0.710510	+	1.55580i	−0.826744	+	0.562579i	$0.809809\pi$
$854$	−10.1880	−	2.99146i	−0.348626	−	0.102366i
$855$	1.23702	+	1.42759i	0.0423050	+	0.0488226i
$856$	12.9380	−	8.31477i	0.442213	−	0.284193i
$857$	26.9420	−	31.0927i	0.920321	−	1.06211i	−0.0775567	−	0.996988i	$-0.524712\pi$
$857$	26.9420	−	31.0927i	0.920321	−	1.06211i	0.997878	−	0.0651189i	$-0.0207427\pi$
$858$	−0.418210	+	2.90872i	−0.0142775	+	0.0993019i
$859$	13.6360	−	4.00390i	0.465256	−	0.136611i	−0.0406990	−	0.999171i	$-0.512958\pi$
$859$	13.6360	−	4.00390i	0.465256	−	0.136611i	0.505955	+	0.862560i	$0.331140\pi$
$860$	−8.37361	−	5.38139i	−0.285538	−	0.183504i
$861$	−1.02974	−	7.16200i	−0.0350935	−	0.244080i
$862$	4.95737	+	10.8551i	0.168849	+	0.369727i
$863$	11.5235	+	25.2330i	0.392266	+	0.858942i	0.997996	+	0.0632725i	$0.0201537\pi$
$863$	11.5235	+	25.2330i	0.392266	+	0.858942i	−0.605730	+	0.795670i	$0.707119\pi$
$864$	−0.142315	−	0.989821i	−0.00484165	−	0.0336744i
$865$	−1.55910	−	1.00197i	−0.0530110	−	0.0340681i
$866$	−26.4148	+	7.75608i	−0.897610	+	0.263562i
$867$	−5.28733	+	36.7742i	−0.179567	+	1.24892i
$868$	11.9155	−	13.7512i	0.404437	−	0.466745i
$869$	−44.4082	+	28.5394i	−1.50645	+	0.968134i
$870$	−0.455579	−	0.525766i	−0.0154456	−	0.0178251i
$871$	−3.32743	−	0.977022i	−0.112746	−	0.0331051i
$872$	−1.81400	+	3.97211i	−0.0614299	+	0.134513i
$873$	−5.06210			−0.171326
$874$	7.99204	+	4.26573i	0.270335	+	0.144290i
$875$	3.49976			0.118314
$876$	0.591017	−	1.29415i	0.0199686	−	0.0437252i
$877$	47.7235	+	14.0129i	1.61151	+	0.473182i	0.958719	−	0.284357i	$-0.0917800\pi$
$877$	47.7235	+	14.0129i	1.61151	+	0.473182i	0.652791	+	0.757538i	$0.273598\pi$
$878$	−3.23420	−	3.73247i	−0.109149	−	0.125965i
$879$	−21.8530	+	14.0441i	−0.737083	+	0.473695i
$880$	−2.04630	+	2.36155i	−0.0689806	+	0.0796079i
$881$	5.35415	−	37.2390i	0.180386	−	1.25461i	−0.675466	−	0.737391i	$-0.736057\pi$
$881$	5.35415	−	37.2390i	0.180386	−	1.25461i	0.855852	−	0.517221i	$-0.173034\pi$
$882$	−5.03575	+	1.47863i	−0.169563	+	0.0497881i
$883$	17.8907	+	11.4977i	0.602071	+	0.386928i	0.805876	−	0.592084i	$-0.201695\pi$
$883$	17.8907	+	11.4977i	0.602071	+	0.386928i	−0.203805	+	0.979011i	$0.565331\pi$
$884$	−0.984882	−	6.85000i	−0.0331252	−	0.230391i
$885$	5.33244	+	11.6764i	0.179248	+	0.392498i
$886$	1.02680	+	2.24839i	0.0344962	+	0.0755361i
$887$	−6.53544	−	45.4550i	−0.219438	−	1.52623i	−0.740119	−	0.672476i	$-0.765231\pi$
$887$	−6.53544	−	45.4550i	−0.219438	−	1.52623i	0.520680	−	0.853752i	$-0.325678\pi$
$888$	−0.958486	−	0.615982i	−0.0321647	−	0.0206710i
$889$	5.45116	−	1.60060i	0.182826	−	0.0536825i
$890$	−0.495008	+	3.44285i	−0.0165927	+	0.115405i
$891$	−2.04630	+	2.36155i	−0.0685535	+	0.0791149i
$892$	−4.94005	+	3.17478i	−0.165405	+	0.106299i
$893$	−4.25526	−	4.91083i	−0.142397	−	0.164335i
$894$	5.52439	+	1.62211i	0.184763	+	0.0542513i
$895$	−4.46439	+	9.77564i	−0.149228	+	0.326764i
$896$	3.49976			0.116919
$897$	−3.58465	+	2.73707i	−0.119688	+	0.0913881i
$898$	28.0210			0.935073
$899$	−1.50252	+	3.29006i	−0.0501118	+	0.109729i
$900$	−0.959493	−	0.281733i	−0.0319831	−	0.00939109i
$901$	−19.4107	−	22.4011i	−0.646664	−	0.746289i
$902$	5.43482	−	3.49275i	0.180960	−	0.116296i
$903$	22.8125	−	26.3271i	0.759154	−	0.876110i
$904$	1.70670	−	11.8704i	0.0567640	−	0.394802i
$905$	17.5956	−	5.16653i	0.584897	−	0.171741i
$906$	17.2835	+	11.1074i	0.574206	+	0.369020i
$907$	1.44933	+	10.0803i	0.0481241	+	0.334710i	0.999633	+	0.0270893i	$0.00862384\pi$
$907$	1.44933	+	10.0803i	0.0481241	+	0.334710i	−0.951509	+	0.307621i	$0.900467\pi$
$908$	−9.07615	−	19.8740i	−0.301203	−	0.659542i
$909$	−0.782558	−	1.71356i	−0.0259558	−	0.0568353i
$910$	−0.468397	−	3.25777i	−0.0155272	−	0.107994i
$911$	−12.8718	−	8.27217i	−0.426460	−	0.274069i	0.309756	−	0.950816i	$-0.399753\pi$
$911$	−12.8718	−	8.27217i	−0.426460	−	0.274069i	−0.736216	+	0.676747i	$0.763389\pi$
$912$	1.81246	−	0.532186i	0.0600165	−	0.0176224i
$913$	−2.73880	+	19.0488i	−0.0906412	+	0.630423i
$914$	−12.1318	+	14.0009i	−0.401285	+	0.463107i
$915$	2.55232	−	1.64028i	0.0843770	−	0.0542258i
$916$	11.0850	+	12.7928i	0.366260	+	0.422686i
$917$	43.9099	+	12.8931i	1.45003	+	0.425768i
$918$	3.05697	−	6.69383i	0.100895	−	0.220929i
$919$	−52.3844			−1.72800			−0.864001	−	0.503490i	$-0.832049\pi$
$919$	−52.3844			−1.72800			−0.864001	+	0.503490i	$0.832049\pi$
$920$	−4.78014	+	0.387653i	−0.157597	+	0.0127805i
$921$	−13.8066			−0.454941
$922$	−6.85319	+	15.0064i	−0.225698	+	0.494209i
$923$	4.17176	+	1.22494i	0.137315	+	0.0403194i
$924$	−7.16155	−	8.26487i	−0.235598	−	0.271894i
$925$	−0.958486	+	0.615982i	−0.0315148	+	0.0202534i
$926$	−12.9338	+	14.9264i	−0.425030	+	0.490511i
$927$	0.124431	−	0.865436i	0.00408685	−	0.0284247i
$928$	−0.667507	+	0.195998i	−0.0219120	+	0.00643395i
$929$	37.7084	+	24.2337i	1.23717	+	0.795083i	0.984992	−	0.172598i	$-0.0552160\pi$
$929$	37.7084	+	24.2337i	1.23717	+	0.795083i	0.252180	+	0.967680i	$0.418852\pi$
$930$	0.739901	+	5.14612i	0.0242623	+	0.168748i
$931$	−4.11842	−	9.01809i	−0.134976	−	0.295556i
$932$	−6.28114	−	13.7538i	−0.205745	−	0.450520i
$933$	2.51434	+	17.4876i	0.0823157	+	0.572518i
$934$	1.70560	+	1.09612i	0.0558088	+	0.0358661i
$935$	−22.0633	+	6.47836i	−0.721546	+	0.211865i
$936$	−0.133837	+	0.930855i	−0.00437459	+	0.0304259i
$937$	−3.37383	+	3.89361i	−0.110218	+	0.127199i	−0.808178	−	0.588938i	$-0.799546\pi$
$937$	−3.37383	+	3.89361i	−0.110218	+	0.127199i	0.697960	+	0.716137i	$0.254091\pi$
$938$	10.8569	−	6.97734i	0.354492	−	0.227818i
$939$	15.8365	+	18.2762i	0.516803	+	0.596422i
$940$	3.30060	+	0.969143i	0.107654	+	0.0316099i
$941$	−2.78867	+	6.10634i	−0.0909081	+	0.199061i	−0.949624	−	0.313390i	$-0.898535\pi$
$941$	−2.78867	+	6.10634i	−0.0909081	+	0.199061i	0.858716	+	0.512451i	$0.171262\pi$
$942$	−8.07850			−0.263212
$943$	9.70826	+	2.01531i	0.316145	+	0.0656274i
$944$	12.8364			0.417789
$945$	1.45385	−	3.18350i	0.0472939	−	0.103559i
$946$	29.8433	+	8.76279i	0.970290	+	0.284903i
$947$	16.7923	+	19.3793i	0.545676	+	0.629744i	0.959870	−	0.280445i	$-0.0904820\pi$
$947$	16.7923	+	19.3793i	0.545676	+	0.629744i	−0.414194	+	0.910189i	$0.635937\pi$
$948$	−14.2116	+	9.13326i	−0.461572	+	0.296635i
$949$	−0.876177	+	1.01116i	−0.0284419	+	0.0328237i
$950$	0.268829	−	1.86975i	0.00872197	−	0.0606626i
$951$	−12.9547	+	3.80385i	−0.420086	+	0.123348i
$952$	21.6658	+	13.9238i	0.702192	+	0.451271i
$953$	8.19147	+	56.9729i	0.265348	+	1.84553i	0.490790	+	0.871278i	$0.336708\pi$
$953$	8.19147	+	56.9729i	0.265348	+	1.84553i	−0.225442	+	0.974257i	$0.572383\pi$
$954$	1.67327	+	3.66394i	0.0541740	+	0.118625i
$955$	−7.02653	−	15.3860i	−0.227373	−	0.497878i
$956$	−4.16905	−	28.9964i	−0.134837	−	0.937809i
$957$	1.82878	+	1.17528i	0.0591159	+	0.0379915i
$958$	−41.4829	+	12.1805i	−1.34025	+	0.393533i
$959$	9.21589	−	64.0979i	0.297597	−	2.06983i
$960$	−0.654861	+	0.755750i	−0.0211355	+	0.0243917i
$961$	−3.33976	+	2.14633i	−0.107734	+	0.0692365i
$962$	0.701670	+	0.809771i	0.0226228	+	0.0261081i
$963$	−14.7565	−	4.33290i	−0.475521	−	0.139626i
$964$	−5.33912	+	11.6910i	−0.171961	+	0.376543i
$965$	−5.45798			−0.175699
$966$	1.03795	−	16.7522i	0.0333955	−	0.538992i
$967$	51.2434			1.64788			0.823938	−	0.566680i	$-0.191773\pi$
$967$	51.2434			1.64788			0.823938	+	0.566680i	$0.191773\pi$
$968$	−0.513351	+	1.12408i	−0.0164997	+	0.0361294i
$969$	13.3376	+	3.91626i	0.428464	+	0.125809i
$970$	3.31497	+	3.82568i	0.106437	+	0.122835i
$971$	17.1442	−	11.0179i	0.550185	−	0.353582i	−0.235826	−	0.971795i	$-0.575779\pi$
$971$	17.1442	−	11.0179i	0.550185	−	0.353582i	0.786011	+	0.618213i	$0.212143\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	−9.29005	+	64.6137i	−0.297825	+	2.07142i
$974$	−12.0002	+	3.52359i	−0.384512	+	0.112903i
$975$	0.791138	+	0.508433i	0.0253367	+	0.0162829i
$976$	−0.431776	−	3.00307i	−0.0138208	−	0.0961258i
$977$	2.48086	+	5.43232i	0.0793697	+	0.173795i	0.945157	−	0.326617i	$-0.105909\pi$
$977$	2.48086	+	5.43232i	0.0793697	+	0.173795i	−0.865787	+	0.500413i	$0.833182\pi$
$978$	0.691790	+	1.51481i	0.0221210	+	0.0484383i
$979$	−1.54679	−	10.7582i	−0.0494356	−	0.343832i
$980$	4.41519	+	2.83747i	0.141038	+	0.0906397i
$981$	4.18984	−	1.23025i	0.133771	−	0.0392788i
$982$	−2.39679	+	16.6701i	−0.0764848	+	0.531963i
$983$	22.0461	−	25.4426i	0.703162	−	0.811493i	−0.286014	−	0.958226i	$-0.592330\pi$
$983$	22.0461	−	25.4426i	0.703162	−	0.811493i	0.989176	+	0.146733i	$0.0468758\pi$
$984$	1.73927	−	1.11776i	0.0554458	−	0.0356328i
$985$	−12.5326	−	14.4634i	−0.399322	−	0.460843i
$986$	−4.91207	−	1.44231i	−0.156432	−	0.0459327i
$987$	−5.00117	+	10.9510i	−0.159189	+	0.348575i
$988$	−1.77644			−0.0565162
$989$	23.2754	+	41.6776i	0.740116	+	1.32527i
$990$	3.12478			0.0993120
$991$	−12.2097	+	26.7354i	−0.387853	+	0.849279i	0.610506	+	0.792011i	$0.290966\pi$
$991$	−12.2097	+	26.7354i	−0.387853	+	0.849279i	−0.998359	+	0.0572674i	$0.981761\pi$
$992$	4.98844	+	1.46474i	0.158383	+	0.0465055i
$993$	−22.1756	−	25.5921i	−0.703723	−	0.812139i
$994$	−13.6119	+	8.74782i	−0.431743	+	0.277464i
$995$	−6.48462	+	7.48365i	−0.205576	+	0.237248i
$996$	−0.876479	+	6.09605i	−0.0277723	+	0.193161i
$997$	9.33254	−	2.74028i	0.295565	−	0.0867856i	−0.130589	−	0.991437i	$-0.541687\pi$
$997$	9.33254	−	2.74028i	0.295565	−	0.0867856i	0.426153	+	0.904651i	$0.359868\pi$
$998$	6.99499	+	4.49541i	0.221423	+	0.142300i
$999$	0.162147	+	1.12776i	0.00513011	+	0.0356807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.g.121.1	✓	30
23.4	even	11	inner	690.2.m.g.211.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.g.121.1	✓	30	1.1	even	1	trivial
690.2.m.g.211.1	yes	30	23.4	even	11	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.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.498068 + 3.46414i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(-0.498068 + 3.46414i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.142315 - 0.989821i) q^{10} +(1.29808 + 2.84240i) q^{11} +(0.415415 + 0.909632i) q^{12} +(-0.133837 - 0.930855i) q^{13} +(2.94419 + 1.89212i) q^{14} +(-0.959493 + 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-4.81901 + 5.56143i) q^{17} +(0.841254 - 0.540641i) q^{18} +(1.23702 + 1.42759i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(1.45385 - 3.18350i) q^{21} +3.12478 q^{22} +(3.42329 + 3.35873i) q^{23} +1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(-0.902333 - 0.264949i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(2.94419 - 1.89212i) q^{28} +(-0.455579 + 0.525766i) q^{29} +(-0.142315 + 0.989821i) q^{30} +(4.98844 - 1.46474i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-0.444702 - 3.09297i) q^{33} +(3.05697 + 6.69383i) q^{34} +(1.45385 + 3.18350i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-0.958486 - 0.615982i) q^{37} +(1.81246 - 0.532186i) q^{38} +(-0.133837 + 0.930855i) q^{39} +(-0.654861 + 0.755750i) q^{40} +(1.73927 - 1.11776i) q^{41} +(-2.29186 - 2.64495i) q^{42} +(9.55053 + 2.80429i) q^{43} +(1.29808 - 2.84240i) q^{44} +1.00000 q^{45} +(4.47729 - 1.71867i) q^{46} -3.43994 q^{47} +(0.415415 - 0.909632i) q^{48} +(-5.03575 - 1.47863i) q^{49} +(-0.654861 - 0.755750i) q^{50} +(6.19064 - 3.97848i) q^{51} +(-0.615849 + 0.710727i) q^{52} +(-0.573236 + 3.98694i) q^{53} +(-0.959493 + 0.281733i) q^{54} +(2.62873 + 1.68938i) q^{55} +(-0.498068 - 3.46414i) q^{56} +(-0.784708 - 1.71827i) q^{57} +(0.288999 + 0.632820i) q^{58} +(-1.82681 - 12.7058i) q^{59} +(0.841254 + 0.540641i) q^{60} +(-2.91105 + 0.854761i) q^{61} +(0.739901 - 5.14612i) q^{62} +(-2.29186 + 2.64495i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.615849 - 0.710727i) q^{65} +(-2.99820 - 0.880352i) q^{66} +(1.53188 - 3.35435i) q^{67} +7.35883 q^{68} +(-2.33836 - 4.18713i) q^{69} +3.49976 q^{70} +(-1.92059 + 4.20550i) q^{71} +(-0.959493 - 0.281733i) q^{72} +(-0.931680 - 1.07522i) q^{73} +(-0.958486 + 0.615982i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(0.268829 - 1.86975i) q^{76} +(-10.4930 + 3.08102i) q^{77} +(0.791138 + 0.508433i) q^{78} +(2.40418 + 16.7215i) q^{79} +(0.415415 + 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.294231 - 2.04642i) q^{82} +(5.18106 + 3.32966i) q^{83} +(-3.35800 + 0.985998i) q^{84} +(-1.04727 + 7.28393i) q^{85} +(6.51831 - 7.52253i) q^{86} +(0.585250 - 0.376117i) q^{87} +(-2.04630 - 2.36155i) q^{88} +(-3.33736 - 0.979938i) q^{89} +(0.415415 - 0.909632i) q^{90} +3.29127 q^{91} +(0.296577 - 4.78665i) q^{92} -5.19904 q^{93} +(-1.42900 + 3.12908i) q^{94} +(1.81246 + 0.532186i) q^{95} +(-0.654861 - 0.755750i) q^{96} +(-4.25851 + 2.73678i) q^{97} +(-3.43694 + 3.96644i) q^{98} +(-0.444702 + 3.09297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more