LMFDB - Embedded newform 230.2.g.d.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(31,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([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("230.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.g (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:	$1.83655924649$
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			71.1
Character	$\chi$	$=$	230.71
Dual form			230.2.g.d.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 + 0.540641i) q^{2} +(-0.369448 - 2.56957i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(1.07841 - 2.36139i) q^{6} +(1.04688 - 1.20816i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-3.58770 + 1.05344i) q^{9} +O(q^{10})$	\(q+(0.841254 + 0.540641i) q^{2} +(-0.369448 - 2.56957i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(1.07841 - 2.36139i) q^{6} +(1.04688 - 1.20816i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-3.58770 + 1.05344i) q^{9} +(0.654861 + 0.755750i) q^{10} +(1.45913 - 0.937726i) q^{11} +(2.18389 - 1.40350i) q^{12} +(-2.84790 - 3.28665i) q^{13} +(1.53387 - 0.450385i) q^{14} +(0.369448 - 2.56957i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-0.474450 + 1.03890i) q^{17} +(-3.58770 - 1.05344i) q^{18} +(1.47276 + 3.22489i) q^{19} +(0.142315 + 0.989821i) q^{20} +(-3.49122 - 2.24367i) q^{21} +1.73447 q^{22} +(4.79580 + 0.0163991i) q^{23} +2.59599 q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.618907 - 4.30459i) q^{26} +(0.797119 + 1.74545i) q^{27} +(1.53387 + 0.450385i) q^{28} +(-3.12354 + 6.83959i) q^{29} +(1.70001 - 1.96192i) q^{30} +(-0.936553 + 6.51387i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(-2.94862 - 3.40289i) q^{33} +(-0.960805 + 0.617472i) q^{34} +(1.34485 - 0.864283i) q^{35} +(-2.44863 - 2.82587i) q^{36} +(-5.21650 + 1.53170i) q^{37} +(-0.504544 + 3.50918i) q^{38} +(-7.39311 + 8.53210i) q^{39} +(-0.415415 + 0.909632i) q^{40} +(-2.55719 - 0.750859i) q^{41} +(-1.72398 - 3.77499i) q^{42} +(0.942858 + 6.55772i) q^{43} +(1.45913 + 0.937726i) q^{44} -3.73916 q^{45} +(4.02562 + 2.60660i) q^{46} +10.5533 q^{47} +(2.18389 + 1.40350i) q^{48} +(0.632503 + 4.39915i) q^{49} +(0.415415 + 0.909632i) q^{50} +(2.84481 + 0.835311i) q^{51} +(1.80658 - 3.95586i) q^{52} +(-1.27165 + 1.46756i) q^{53} +(-0.273081 + 1.89932i) q^{54} +(1.66421 - 0.488657i) q^{55} +(1.04688 + 1.20816i) q^{56} +(7.74245 - 4.97577i) q^{57} +(-6.32545 + 4.06512i) q^{58} +(-7.22782 - 8.34135i) q^{59} +(2.49083 - 0.731375i) q^{60} +(0.704444 - 4.89951i) q^{61} +(-4.30954 + 4.97348i) q^{62} +(-2.48315 + 5.43735i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.80658 - 3.95586i) q^{65} +(-0.640797 - 4.45684i) q^{66} +(-3.88786 - 2.49858i) q^{67} -1.14211 q^{68} +(-1.72966 - 12.3292i) q^{69} +1.59863 q^{70} +(6.30235 + 4.05027i) q^{71} +(-0.532138 - 3.70110i) q^{72} +(1.34963 + 2.95528i) q^{73} +(-5.21650 - 1.53170i) q^{74} +(1.07841 - 2.36139i) q^{75} +(-2.32165 + 2.67933i) q^{76} +(0.394607 - 2.74455i) q^{77} +(-10.8323 + 3.18064i) q^{78} +(-10.2348 - 11.8116i) q^{79} +(-0.841254 + 0.540641i) q^{80} +(-5.24620 + 3.37152i) q^{81} +(-1.74530 - 2.01418i) q^{82} +(-3.60813 + 1.05944i) q^{83} +(0.590609 - 4.10778i) q^{84} +(-0.747924 + 0.863150i) q^{85} +(-2.75219 + 6.02645i) q^{86} +(18.7288 + 5.49926i) q^{87} +(0.720525 + 1.57773i) q^{88} +(-2.05573 - 14.2979i) q^{89} +(-3.14558 - 2.02154i) q^{90} -6.95220 q^{91} +(1.97733 + 4.36923i) q^{92} +17.0838 q^{93} +(8.87797 + 5.70552i) q^{94} +(0.504544 + 3.50918i) q^{95} +(1.07841 + 2.36139i) q^{96} +(-4.93151 - 1.44802i) q^{97} +(-1.84627 + 4.04276i) q^{98} +(-4.24708 + 4.90139i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) $ 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9	\( 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} - q^{12} + 12 q^{13} - 3 q^{14} + q^{15} - 3 q^{16} - 26 q^{17} + 12 q^{18} - 25 q^{19} + 3 q^{20} - 11 q^{21} - 14 q^{22} + 14 q^{23} + 10 q^{24} - 3 q^{25} - 10 q^{26} - 52 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} + 5 q^{31} - 3 q^{32} + 9 q^{33} + 7 q^{34} + 3 q^{35} + 12 q^{36} - 20 q^{37} + 19 q^{38} + 41 q^{39} + 3 q^{40} + 32 q^{41} + 22 q^{42} - 46 q^{43} - 3 q^{44} - 56 q^{45} + 3 q^{46} + 80 q^{47} - q^{48} - 41 q^{49} - 3 q^{50} - 34 q^{51} - 21 q^{52} + 29 q^{53} + 47 q^{54} + 3 q^{55} + 8 q^{56} - 33 q^{57} - 7 q^{58} - 3 q^{59} + q^{60} - q^{61} - 28 q^{62} - 8 q^{63} - 3 q^{64} + 21 q^{65} - 46 q^{66} - 63 q^{67} - 4 q^{68} + 78 q^{69} - 8 q^{70} + 55 q^{71} - 32 q^{72} - 36 q^{73} - 20 q^{74} - q^{75} - 3 q^{76} - 9 q^{77} - 80 q^{78} - 29 q^{79} + 3 q^{80} + 15 q^{81} - 23 q^{82} - 63 q^{83} + 4 q^{85} + 31 q^{86} + 63 q^{87} - 3 q^{88} - 95 q^{89} + 10 q^{90} - 12 q^{91} + 14 q^{92} + 126 q^{93} + 3 q^{94} - 19 q^{95} - q^{96} + 11 q^{97} + 58 q^{98} + 97 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 - q^12 + 12 * q^13 - 3 * q^14 + q^15 - 3 * q^16 - 26 * q^17 + 12 * q^18 - 25 * q^19 + 3 * q^20 - 11 * q^21 - 14 * q^22 + 14 * q^23 + 10 * q^24 - 3 * q^25 - 10 * q^26 - 52 * q^27 - 3 * q^28 + 4 * q^29 + q^30 + 5 * q^31 - 3 * q^32 + 9 * q^33 + 7 * q^34 + 3 * q^35 + 12 * q^36 - 20 * q^37 + 19 * q^38 + 41 * q^39 + 3 * q^40 + 32 * q^41 + 22 * q^42 - 46 * q^43 - 3 * q^44 - 56 * q^45 + 3 * q^46 + 80 * q^47 - q^48 - 41 * q^49 - 3 * q^50 - 34 * q^51 - 21 * q^52 + 29 * q^53 + 47 * q^54 + 3 * q^55 + 8 * q^56 - 33 * q^57 - 7 * q^58 - 3 * q^59 + q^60 - q^61 - 28 * q^62 - 8 * q^63 - 3 * q^64 + 21 * q^65 - 46 * q^66 - 63 * q^67 - 4 * q^68 + 78 * q^69 - 8 * q^70 + 55 * q^71 - 32 * q^72 - 36 * q^73 - 20 * q^74 - q^75 - 3 * q^76 - 9 * q^77 - 80 * q^78 - 29 * q^79 + 3 * q^80 + 15 * q^81 - 23 * q^82 - 63 * q^83 + 4 * q^85 + 31 * q^86 + 63 * q^87 - 3 * q^88 - 95 * q^89 + 10 * q^90 - 12 * q^91 + 14 * q^92 + 126 * q^93 + 3 * q^94 - 19 * q^95 - q^96 + 11 * q^97 + 58 * q^98 + 97 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$

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 $

$2$	0.841254	+	0.540641i	0.594856	+	0.382291i
$2$	0.841254	+	0.540641i	0.594856	+	0.382291i
$3$	−0.369448	−	2.56957i	−0.213301	−	1.48354i	−0.762031	−	0.647540i	$-0.775798\pi$
$3$	−0.369448	−	2.56957i	−0.213301	−	1.48354i	0.548731	−	0.835999i	$-0.315111\pi$
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	0.959493	+	0.281733i	0.429098	+	0.125995i
$5$	0.959493	+	0.281733i	0.429098	+	0.125995i
$6$	1.07841	−	2.36139i	0.440260	−	0.964035i
$7$	1.04688	−	1.20816i	0.395683	−	0.456642i	−0.522594	−	0.852582i	$-0.675036\pi$
$7$	1.04688	−	1.20816i	0.395683	−	0.456642i	0.918277	+	0.395939i	$0.129581\pi$
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	−3.58770	+	1.05344i	−1.19590	+	0.351148i
$10$	0.654861	+	0.755750i	0.207085	+	0.238989i
$11$	1.45913	−	0.937726i	0.439944	−	0.282735i	−0.301859	−	0.953353i	$-0.597607\pi$
$11$	1.45913	−	0.937726i	0.439944	−	0.282735i	0.741803	+	0.670618i	$0.233971\pi$
$12$	2.18389	−	1.40350i	0.630433	−	0.405155i
$13$	−2.84790	−	3.28665i	−0.789864	−	0.911552i	0.207916	−	0.978147i	$-0.433332\pi$
$13$	−2.84790	−	3.28665i	−0.789864	−	0.911552i	−0.997780	+	0.0665949i	$0.978786\pi$
$14$	1.53387	−	0.450385i	0.409944	−	0.120371i
$15$	0.369448	−	2.56957i	0.0953910	−	0.663459i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−0.474450	+	1.03890i	−0.115071	+	0.251971i	−0.958401	−	0.285426i	$-0.907865\pi$
$17$	−0.474450	+	1.03890i	−0.115071	+	0.251971i	0.843330	+	0.537397i	$0.180592\pi$
$18$	−3.58770	−	1.05344i	−0.845628	−	0.248299i
$19$	1.47276	+	3.22489i	0.337873	+	0.739839i	0.999954	−	0.00959315i	$-0.00305364\pi$
$19$	1.47276	+	3.22489i	0.337873	+	0.739839i	−0.662081	+	0.749433i	$0.730326\pi$
$20$	0.142315	+	0.989821i	0.0318226	+	0.221331i
$21$	−3.49122	−	2.24367i	−0.761846	−	0.489609i
$22$	1.73447			0.369791
$23$	4.79580	+	0.0163991i	0.999994	+	0.00341945i
$23$	4.79580	+	0.0163991i	0.999994	+	0.00341945i
$24$	2.59599			0.529904
$25$	0.841254	+	0.540641i	0.168251	+	0.108128i
$26$	−0.618907	−	4.30459i	−0.121378	−	0.844200i
$27$	0.797119	+	1.74545i	0.153406	+	0.335912i
$28$	1.53387	+	0.450385i	0.289875	+	0.0851148i
$29$	−3.12354	+	6.83959i	−0.580026	+	1.27008i	0.361259	+	0.932466i	$0.382347\pi$
$29$	−3.12354	+	6.83959i	−0.580026	+	1.27008i	−0.941285	+	0.337614i	$0.890380\pi$
$30$	1.70001	−	1.96192i	0.310378	−	0.358196i
$31$	−0.936553	+	6.51387i	−0.168210	+	1.16993i	0.714372	+	0.699767i	$0.246713\pi$
$31$	−0.936553	+	6.51387i	−0.168210	+	1.16993i	−0.882582	+	0.470159i	$0.844196\pi$
$32$	−0.959493	+	0.281733i	−0.169616	+	0.0498038i
$33$	−2.94862	−	3.40289i	−0.513289	−	0.592367i
$34$	−0.960805	+	0.617472i	−0.164777	+	0.105896i
$35$	1.34485	−	0.864283i	0.227321	−	0.146091i
$36$	−2.44863	−	2.82587i	−0.408105	−	0.470978i
$37$	−5.21650	+	1.53170i	−0.857588	+	0.251811i	−0.680828	−	0.732443i	$-0.738380\pi$
$37$	−5.21650	+	1.53170i	−0.857588	+	0.251811i	−0.176760	+	0.984254i	$0.556562\pi$
$38$	−0.504544	+	3.50918i	−0.0818478	+	0.569264i
$39$	−7.39311	+	8.53210i	−1.18384	+	1.36623i
$40$	−0.415415	+	0.909632i	−0.0656829	+	0.143825i
$41$	−2.55719	−	0.750859i	−0.399366	−	0.117264i	0.0758810	−	0.997117i	$-0.475823\pi$
$41$	−2.55719	−	0.750859i	−0.399366	−	0.117264i	−0.475247	+	0.879852i	$0.657641\pi$
$42$	−1.72398	−	3.77499i	−0.266016	−	0.582494i
$43$	0.942858	+	6.55772i	0.143784	+	1.00004i	0.926132	+	0.377200i	$0.123113\pi$
$43$	0.942858	+	6.55772i	0.143784	+	1.00004i	−0.782347	+	0.622842i	$0.785978\pi$
$44$	1.45913	+	0.937726i	0.219972	+	0.141368i
$45$	−3.73916			−0.557401
$46$	4.02562	+	2.60660i	0.593545	+	0.384323i
$47$	10.5533			1.53935			0.769675	−	0.638435i	$-0.220418\pi$
$47$	10.5533			1.53935			0.769675	+	0.638435i	$0.220418\pi$
$48$	2.18389	+	1.40350i	0.315217	+	0.202577i
$49$	0.632503	+	4.39915i	0.0903575	+	0.628450i
$50$	0.415415	+	0.909632i	0.0587486	+	0.128641i
$51$	2.84481	+	0.835311i	0.398353	+	0.116967i
$52$	1.80658	−	3.95586i	0.250528	−	0.548579i
$53$	−1.27165	+	1.46756i	−0.174675	+	0.201585i	−0.836336	−	0.548218i	$-0.815306\pi$
$53$	−1.27165	+	1.46756i	−0.174675	+	0.201585i	0.661661	+	0.749803i	$0.269852\pi$
$54$	−0.273081	+	1.89932i	−0.0371616	+	0.258465i
$55$	1.66421	−	0.488657i	0.224402	−	0.0658905i
$56$	1.04688	+	1.20816i	0.139895	+	0.161447i
$57$	7.74245	−	4.97577i	1.02551	−	0.659057i
$58$	−6.32545	+	4.06512i	−0.830572	+	0.533776i
$59$	−7.22782	−	8.34135i	−0.940982	−	1.08595i	−0.996167	−	0.0874748i	$-0.972120\pi$
$59$	−7.22782	−	8.34135i	−0.940982	−	1.08595i	0.0551849	−	0.998476i	$-0.482425\pi$
$60$	2.49083	−	0.731375i	0.321565	−	0.0944201i
$61$	0.704444	−	4.89951i	0.0901948	−	0.627318i	−0.893713	−	0.448640i	$-0.851909\pi$
$61$	0.704444	−	4.89951i	0.0901948	−	0.627318i	0.983907	−	0.178679i	$-0.0571823\pi$
$62$	−4.30954	+	4.97348i	−0.547313	+	0.631632i
$63$	−2.48315	+	5.43735i	−0.312848	+	0.685041i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−1.80658	−	3.95586i	−0.224079	−	0.490664i
$66$	−0.640797	−	4.45684i	−0.0788766	−	0.548599i
$67$	−3.88786	−	2.49858i	−0.474978	−	0.305250i	0.281161	−	0.959661i	$-0.409280\pi$
$67$	−3.88786	−	2.49858i	−0.474978	−	0.305250i	−0.756139	+	0.654411i	$0.772917\pi$
$68$	−1.14211			−0.138501
$69$	−1.72966	−	12.3292i	−0.208227	−	1.48426i
$70$	1.59863			0.191073
$71$	6.30235	+	4.05027i	0.747951	+	0.480679i	0.858258	−	0.513219i	$-0.171547\pi$
$71$	6.30235	+	4.05027i	0.747951	+	0.480679i	−0.110307	+	0.993898i	$0.535183\pi$
$72$	−0.532138	−	3.70110i	−0.0627131	−	0.436179i
$73$	1.34963	+	2.95528i	0.157962	+	0.345889i	0.972021	−	0.234893i	$-0.0754740\pi$
$73$	1.34963	+	2.95528i	0.157962	+	0.345889i	−0.814059	+	0.580782i	$0.802747\pi$
$74$	−5.21650	−	1.53170i	−0.606406	−	0.178057i
$75$	1.07841	−	2.36139i	0.124524	−	0.272670i
$76$	−2.32165	+	2.67933i	−0.266312	+	0.307340i
$77$	0.394607	−	2.74455i	0.0449696	−	0.312771i
$78$	−10.8323	+	3.18064i	−1.22651	+	0.360137i
$79$	−10.2348	−	11.8116i	−1.15151	−	1.32891i	−0.935832	−	0.352447i	$-0.885350\pi$
$79$	−10.2348	−	11.8116i	−1.15151	−	1.32891i	−0.215676	−	0.976465i	$-0.569196\pi$
$80$	−0.841254	+	0.540641i	−0.0940550	+	0.0604455i
$81$	−5.24620	+	3.37152i	−0.582911	+	0.374614i
$82$	−1.74530	−	2.01418i	−0.192736	−	0.222429i
$83$	−3.60813	+	1.05944i	−0.396044	+	0.116289i	−0.473689	−	0.880692i	$-0.657078\pi$
$83$	−3.60813	+	1.05944i	−0.396044	+	0.116289i	0.0776452	+	0.996981i	$0.475260\pi$
$84$	0.590609	−	4.10778i	0.0644408	−	0.448195i
$85$	−0.747924	+	0.863150i	−0.0811237	+	0.0936218i
$86$	−2.75219	+	6.02645i	−0.296776	+	0.649849i
$87$	18.7288	+	5.49926i	2.00793	+	0.589582i
$88$	0.720525	+	1.57773i	0.0768083	+	0.168187i
$89$	−2.05573	−	14.2979i	−0.217907	−	1.51558i	−0.745745	−	0.666231i	$-0.767906\pi$
$89$	−2.05573	−	14.2979i	−0.217907	−	1.51558i	0.527839	−	0.849345i	$-0.323003\pi$
$90$	−3.14558	−	2.02154i	−0.331573	−	0.213089i
$91$	−6.95220			−0.728789
$92$	1.97733	+	4.36923i	0.206151	+	0.455524i
$93$	17.0838			1.77151
$94$	8.87797	+	5.70552i	0.915692	+	0.588480i
$95$	0.504544	+	3.50918i	0.0517651	+	0.360034i
$96$	1.07841	+	2.36139i	0.110065	+	0.241009i
$97$	−4.93151	−	1.44802i	−0.500719	−	0.147024i	0.0216135	−	0.999766i	$-0.493120\pi$
$97$	−4.93151	−	1.44802i	−0.500719	−	0.147024i	−0.522332	+	0.852742i	$0.674938\pi$
$98$	−1.84627	+	4.04276i	−0.186501	+	0.408380i
$99$	−4.24708	+	4.90139i	−0.426847	+	0.492608i
$100$	−0.142315	+	0.989821i	−0.0142315	+	0.0989821i
$101$	16.6681	−	4.89420i	1.65854	−	0.486991i	0.687555	−	0.726133i	$-0.258684\pi$
$101$	16.6681	−	4.89420i	1.65854	−	0.486991i	0.970985	+	0.239142i	$0.0768660\pi$
$102$	1.94160	+	2.24073i	0.192247	+	0.221865i
$103$	13.5982	−	8.73903i	1.33987	−	0.861082i	0.342938	−	0.939358i	$-0.388578\pi$
$103$	13.5982	−	8.73903i	1.33987	−	0.861082i	0.996932	+	0.0782758i	$0.0249415\pi$
$104$	3.65849	−	2.35117i	0.358745	−	0.230551i
$105$	−2.71768	−	3.13638i	−0.265219	−	0.306079i
$106$	−1.86321	+	0.547087i	−0.180971	+	0.0531378i
$107$	2.53340	−	17.6202i	0.244913	−	1.70340i	−0.381875	−	0.924214i	$-0.624721\pi$
$107$	2.53340	−	17.6202i	0.244913	−	1.70340i	0.626787	−	0.779190i	$-0.284369\pi$
$108$	−1.25658	+	1.45017i	−0.120914	+	0.139543i
$109$	−6.80702	+	14.9053i	−0.651994	+	1.42767i	0.237804	+	0.971313i	$0.423572\pi$
$109$	−6.80702	+	14.9053i	−0.651994	+	1.42767i	−0.889798	+	0.456355i	$0.849155\pi$
$110$	1.66421	+	0.488657i	0.158676	+	0.0465916i
$111$	5.86304	+	12.8383i	0.556495	+	1.21855i
$112$	0.227508	+	1.58236i	0.0214975	+	0.149519i
$113$	6.44191	+	4.13996i	0.606003	+	0.389455i	0.807357	−	0.590064i	$-0.200897\pi$
$113$	6.44191	+	4.13996i	0.606003	+	0.389455i	−0.201353	+	0.979519i	$0.564534\pi$
$114$	9.20347			0.861984
$115$	4.59692	+	1.36687i	0.428665	+	0.127461i
$116$	−7.51907			−0.698128
$117$	13.6797	+	8.79140i	1.26469	+	0.812765i
$118$	−1.57076	−	10.9248i	−0.144600	−	1.00571i
$119$	0.758469	+	1.66082i	0.0695288	+	0.152247i
$120$	2.49083	+	0.731375i	0.227381	+	0.0667651i
$121$	−3.31983	+	7.26942i	−0.301803	+	0.660857i
$122$	3.24149	−	3.74088i	0.293471	−	0.338684i
$123$	−0.984632	+	6.84827i	−0.0887813	+	0.617488i
$124$	−6.31428	+	1.85404i	−0.567039	+	0.166498i
$125$	0.654861	+	0.755750i	0.0585725	+	0.0675963i
$126$	−5.02861	+	3.23169i	−0.447984	+	0.287902i
$127$	−11.4264	+	7.34332i	−1.01393	+	0.651614i	−0.938408	−	0.345530i	$-0.887699\pi$
$127$	−11.4264	+	7.34332i	−1.01393	+	0.651614i	−0.0755239	+	0.997144i	$0.524063\pi$
$128$	−0.654861	−	0.755750i	−0.0578821	−	0.0667995i
$129$	16.5022	−	4.84547i	1.45293	−	0.426620i
$130$	0.618907	−	4.30459i	0.0542817	−	0.377538i
$131$	−2.54221	+	2.93387i	−0.222114	+	0.256334i	−0.855860	−	0.517208i	$-0.826971\pi$
$131$	−2.54221	+	2.93387i	−0.222114	+	0.256334i	0.633745	+	0.773542i	$0.281517\pi$
$132$	1.87048	−	4.09577i	0.162804	−	0.356491i
$133$	5.43798	+	1.59674i	0.471533	+	0.138454i
$134$	−1.91985	−	4.20387i	−0.165849	−	0.363159i
$135$	0.273081	+	1.89932i	0.0235031	+	0.163467i
$136$	−0.960805	−	0.617472i	−0.0823884	−	0.0529478i
$137$	−13.1481			−1.12332			−0.561659	−	0.827369i	$-0.689837\pi$
$137$	−13.1481			−1.12332			−0.561659	+	0.827369i	$0.689837\pi$
$138$	5.21058	−	11.3071i	0.443554	−	0.962524i
$139$	−10.5815			−0.897511			−0.448756	−	0.893654i	$-0.648133\pi$
$139$	−10.5815			−0.897511			−0.448756	+	0.893654i	$0.648133\pi$
$140$	1.34485	+	0.864283i	0.113661	+	0.0730453i
$141$	−3.89888	−	27.1173i	−0.328345	−	2.28369i
$142$	3.11213	+	6.81461i	0.261164	+	0.571870i
$143$	−7.23742	−	2.12510i	−0.605224	−	0.177710i
$144$	1.55330	−	3.40126i	0.129442	−	0.283438i
$145$	−4.92395	+	5.68254i	−0.408911	+	0.471909i
$146$	−0.462363	+	3.21580i	−0.0382654	+	0.266142i
$147$	11.0702	−	3.25051i	0.913058	−	0.268098i
$148$	−3.56030	−	4.10881i	−0.292655	−	0.337742i
$149$	13.3484	−	8.57852i	1.09355	−	0.702780i	0.135899	−	0.990723i	$-0.456608\pi$
$149$	13.3484	−	8.57852i	1.09355	−	0.702780i	0.957648	+	0.287943i	$0.0929713\pi$
$150$	2.18389	−	1.40350i	0.178313	−	0.114595i
$151$	14.0036	+	16.1611i	1.13960	+	1.31517i	0.942278	+	0.334830i	$0.108679\pi$
$151$	14.0036	+	16.1611i	1.13960	+	1.31517i	0.197322	+	0.980339i	$0.436775\pi$
$152$	−3.40166	+	0.998816i	−0.275911	+	0.0810147i
$153$	0.607761	−	4.22707i	0.0491345	−	0.341738i
$154$	1.81578	−	2.09552i	0.146320	−	0.168862i
$155$	−2.73379	+	5.98616i	−0.219583	+	0.480820i
$156$	−10.8323	−	3.18064i	−0.867276	−	0.254655i
$157$	−7.68699	−	16.8322i	−0.613489	−	1.34335i	−0.920162	−	0.391538i	$-0.871943\pi$
$157$	−7.68699	−	16.8322i	−0.613489	−	1.34335i	0.306673	−	0.951815i	$-0.400784\pi$
$158$	−2.22424	−	15.4699i	−0.176951	−	1.23072i
$159$	4.24081	+	2.72540i	0.336318	+	0.216139i
$160$	−1.00000			−0.0790569
$161$	5.04044	−	5.77694i	0.397242	−	0.455287i
$162$	−6.23616			−0.489959
$163$	−6.65182	−	4.27486i	−0.521010	−	0.334833i	0.253561	−	0.967319i	$-0.418398\pi$
$163$	−6.65182	−	4.27486i	−0.521010	−	0.334833i	−0.774572	+	0.632486i	$0.782034\pi$
$164$	−0.379290	−	2.63802i	−0.0296176	−	0.205995i
$165$	−1.87048	−	4.09577i	−0.145616	−	0.318855i
$166$	−3.60813	−	1.05944i	−0.280046	−	0.0822288i
$167$	8.33227	−	18.2451i	0.644771	−	1.41185i	−0.251287	−	0.967913i	$-0.580854\pi$
$167$	8.33227	−	18.2451i	0.644771	−	1.41185i	0.896057	−	0.443938i	$-0.146419\pi$
$168$	2.71768	−	3.13638i	0.209674	−	0.241977i
$169$	−0.841444	+	5.85237i	−0.0647265	+	0.450183i
$170$	−1.09585	+	0.321770i	−0.0840477	+	0.0246786i
$171$	−8.68104	−	10.0184i	−0.663855	−	0.766130i
$172$	−5.57343	+	3.58183i	−0.424970	+	0.273112i
$173$	−4.35740	+	2.80033i	−0.331287	+	0.212905i	−0.695700	−	0.718332i	$-0.744906\pi$
$173$	−4.35740	+	2.80033i	−0.331287	+	0.212905i	0.364413	+	0.931237i	$0.381269\pi$
$174$	12.7825	+	14.7518i	0.969040	+	1.11833i
$175$	1.53387	−	0.450385i	0.115950	−	0.0340459i
$176$	−0.246841	+	1.71682i	−0.0186063	+	0.129410i
$177$	−18.7633	+	21.6540i	−1.41034	+	1.62762i
$178$	6.00065	−	13.1396i	0.449767	−	0.984853i
$179$	7.13019	+	2.09361i	0.532936	+	0.156484i	0.537118	−	0.843507i	$-0.319513\pi$
$179$	7.13019	+	2.09361i	0.532936	+	0.156484i	−0.00418223	+	0.999991i	$0.501331\pi$
$180$	−1.55330	−	3.40126i	−0.115776	−	0.253515i
$181$	−1.05898	−	7.36537i	−0.0787134	−	0.547464i	−0.990576	−	0.136967i	$-0.956265\pi$
$181$	−1.05898	−	7.36537i	−0.0787134	−	0.547464i	0.911862	−	0.410496i	$-0.134645\pi$
$182$	−5.84856	−	3.75864i	−0.433524	−	0.278609i
$183$	−12.8499			−0.949890
$184$	−0.698746	+	4.74466i	−0.0515123	+	0.349781i
$185$	−5.43673			−0.399716
$186$	14.3718	+	9.23622i	1.05379	+	0.677232i
$187$	0.281920	+	1.96080i	0.0206160	+	0.143388i
$188$	4.38398	+	9.59958i	0.319735	+	0.700121i
$189$	2.94327	+	0.864222i	0.214091	+	0.0628629i
$190$	−1.47276	+	3.22489i	−0.106845	+	0.233958i
$191$	0.0112171	−	0.0129452i	0.000811640	−	0.000936683i	−0.755344	−	0.655329i	$-0.772530\pi$
$191$	0.0112171	−	0.0129452i	0.000811640	−	0.000936683i	0.756155	+	0.654392i	$0.227075\pi$
$192$	−0.369448	+	2.56957i	−0.0266626	+	0.185442i
$193$	−7.68073	+	2.25527i	−0.552871	+	0.162338i	−0.546222	−	0.837640i	$-0.683935\pi$
$193$	−7.68073	+	2.25527i	−0.552871	+	0.162338i	−0.00664895	+	0.999978i	$0.502116\pi$
$194$	−3.36579	−	3.88433i	−0.241649	−	0.278878i
$195$	−9.49740	+	6.10361i	−0.680123	+	0.437089i
$196$	−3.73886	+	2.40282i	−0.267061	+	0.171630i
$197$	−7.62018	−	8.79416i	−0.542916	−	0.626558i	0.416302	−	0.909226i	$-0.363326\pi$
$197$	−7.62018	−	8.79416i	−0.542916	−	0.626558i	−0.959218	+	0.282668i	$0.908780\pi$
$198$	−6.22276	+	1.82717i	−0.442232	+	0.129851i
$199$	−2.58460	+	17.9763i	−0.183218	+	1.27431i	0.665876	+	0.746063i	$0.268058\pi$
$199$	−2.58460	+	17.9763i	−0.183218	+	1.27431i	−0.849093	+	0.528243i	$0.822851\pi$
$200$	−0.654861	+	0.755750i	−0.0463056	+	0.0534396i
$201$	−4.98390	+	10.9132i	−0.351537	+	0.769759i
$202$	16.6681	+	4.89420i	1.17276	+	0.344355i
$203$	4.99337	+	10.9340i	0.350466	+	0.767413i
$204$	0.421951	+	2.93473i	0.0295424	+	0.205472i
$205$	−2.24206	−	1.44089i	−0.156593	−	0.100636i
$206$	16.1642			1.12621
$207$	−17.2232	+	4.99327i	−1.19709	+	0.347056i
$208$	4.34886			0.301539
$209$	5.17300	+	3.32449i	0.357824	+	0.229960i
$210$	−0.590609	−	4.10778i	−0.0407559	−	0.283464i
$211$	−5.50556	−	12.0555i	−0.379018	−	0.829935i	−0.998974	−	0.0452974i	$-0.985576\pi$
$211$	−5.50556	−	12.0555i	−0.379018	−	0.829935i	0.619955	−	0.784637i	$-0.287151\pi$
$212$	−1.86321	−	0.547087i	−0.127966	−	0.0375741i
$213$	8.07905	−	17.6907i	0.553568	−	1.21214i
$214$	11.6574	−	13.4534i	0.796884	−	0.919653i
$215$	−0.942858	+	6.55772i	−0.0643024	+	0.447233i
$216$	−1.84112	+	0.540603i	−0.125273	+	0.0367833i
$217$	6.88935	+	7.95074i	0.467680	+	0.539731i
$218$	−13.7848	+	8.85898i	−0.933627	+	0.600006i
$219$	7.09517	−	4.55979i	0.479447	−	0.308122i
$220$	1.13584	+	1.31083i	0.0765781	+	0.0883759i
$221$	4.76569	−	1.39933i	0.320575	−	0.0941292i
$222$	−2.00859	+	13.9700i	−0.134808	+	0.937607i
$223$	−2.92599	+	3.37677i	−0.195938	+	0.226125i	−0.845214	−	0.534428i	$-0.820527\pi$
$223$	−2.92599	+	3.37677i	−0.195938	+	0.226125i	0.649275	+	0.760554i	$0.275072\pi$
$224$	−0.664094	+	1.45416i	−0.0443716	+	0.0971603i
$225$	−3.58770	−	1.05344i	−0.239180	−	0.0702295i
$226$	3.18104	+	6.96551i	0.211600	+	0.463339i
$227$	−0.319214	−	2.22018i	−0.0211870	−	0.147359i	0.976482	−	0.215599i	$-0.0691705\pi$
$227$	−0.319214	−	2.22018i	−0.0211870	−	0.147359i	−0.997669	+	0.0682407i	$0.978261\pi$
$228$	7.74245	+	4.97577i	0.512756	+	0.329528i
$229$	4.41437			0.291710			0.145855	−	0.989306i	$-0.453407\pi$
$229$	4.41437			0.291710			0.145855	+	0.989306i	$0.453407\pi$
$230$	3.12819	+	3.63517i	0.206267	+	0.239696i
$231$	−7.19809			−0.473600
$232$	−6.32545	−	4.06512i	−0.415286	−	0.266888i
$233$	−0.637729	−	4.43550i	−0.0417790	−	0.290579i	−0.999990	−	0.00451625i	$-0.998562\pi$
$233$	−0.637729	−	4.43550i	−0.0417790	−	0.290579i	0.958211	−	0.286063i	$-0.0923467\pi$
$234$	6.75509	+	14.7916i	0.441594	+	0.966956i
$235$	10.1258	+	2.97320i	0.660533	+	0.193950i
$236$	4.58501	−	10.0398i	0.298459	−	0.653534i
$237$	−26.5695	+	30.6628i	−1.72588	+	1.99177i
$238$	−0.259840	+	1.80723i	−0.0168429	+	0.117145i
$239$	−4.79415	+	1.40769i	−0.310108	+	0.0910559i	−0.433083	−	0.901354i	$-0.642574\pi$
$239$	−4.79415	+	1.40769i	−0.310108	+	0.0910559i	0.122976	+	0.992410i	$0.460756\pi$
$240$	1.70001	+	1.96192i	0.109735	+	0.126641i
$241$	−13.0916	+	8.41343i	−0.843301	+	0.541957i	−0.889479	−	0.456977i	$-0.848932\pi$
$241$	−13.0916	+	8.41343i	−0.843301	+	0.541957i	0.0461777	+	0.998933i	$0.485296\pi$
$242$	−6.72297	+	4.32059i	−0.432169	+	0.277738i
$243$	14.3713	+	16.5854i	0.921919	+	1.06395i
$244$	4.74939	−	1.39455i	0.304049	−	0.0892767i
$245$	−0.632503	+	4.39915i	−0.0404091	+	0.281052i
$246$	−4.53078	+	5.22880i	−0.288872	+	0.333376i
$247$	6.40480	−	14.0246i	0.407528	−	0.892362i
$248$	−6.31428	−	1.85404i	−0.400957	−	0.117732i
$249$	4.05533	+	8.87993i	0.256996	+	0.562743i
$250$	0.142315	+	0.989821i	0.00900078	+	0.0626018i
$251$	−6.26460	−	4.02602i	−0.395418	−	0.254120i	0.327789	−	0.944751i	$-0.393696\pi$
$251$	−6.26460	−	4.02602i	−0.395418	−	0.254120i	−0.723207	+	0.690631i	$0.757333\pi$
$252$	−5.97752			−0.376549
$253$	7.01308	−	4.47322i	0.440909	−	0.281229i
$254$	−13.5826			−0.852250
$255$	2.49424	+	1.60295i	0.156195	+	0.100381i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	9.40745	+	20.5994i	0.586820	+	1.28496i	0.937345	+	0.348404i	$0.113276\pi$
$257$	9.40745	+	20.5994i	0.586820	+	1.28496i	−0.350524	+	0.936554i	$0.613997\pi$
$258$	16.5022	+	4.84547i	1.02738	+	0.301666i
$259$	−3.61050	+	7.90589i	−0.224346	+	0.491248i
$260$	2.84790	−	3.28665i	0.176619	−	0.203829i
$261$	4.00118	−	27.8288i	0.247667	−	1.72256i
$262$	−3.72482	+	1.09371i	−0.230120	+	0.0675693i
$263$	−11.1987	−	12.9240i	−0.690543	−	0.796929i	0.296900	−	0.954909i	$-0.404047\pi$
$263$	−11.1987	−	12.9240i	−0.690543	−	0.796929i	−0.987442	+	0.157980i	$0.949502\pi$
$264$	3.78789	−	2.43433i	0.233128	−	0.149822i
$265$	−1.63360	+	1.04985i	−0.100351	+	0.0644919i
$266$	3.71146	+	4.28325i	0.227564	+	0.262623i
$267$	−35.9799	+	10.5647i	−2.20194	+	0.646547i
$268$	0.657710	−	4.57447i	0.0401760	−	0.279430i
$269$	2.51716	−	2.90495i	0.153474	−	0.177118i	−0.673806	−	0.738908i	$-0.735342\pi$
$269$	2.51716	−	2.90495i	0.153474	−	0.177118i	0.827280	+	0.561790i	$0.189887\pi$
$270$	−0.797119	+	1.74545i	−0.0485111	+	0.106225i
$271$	13.1821	+	3.87061i	0.800755	+	0.235123i	0.656410	−	0.754405i	$-0.272074\pi$
$271$	13.1821	+	3.87061i	0.800755	+	0.235123i	0.144345	+	0.989527i	$0.453892\pi$
$272$	−0.474450	−	1.03890i	−0.0287678	−	0.0629926i
$273$	2.56848	+	17.8641i	0.155451	+	1.08119i
$274$	−11.0609	−	7.10840i	−0.668213	−	0.429434i
$275$	1.73447			0.104593
$276$	10.4965	−	6.69509i	0.631815	−	0.402997i
$277$	−8.92770			−0.536413			−0.268207	−	0.963361i	$-0.586431\pi$
$277$	−8.92770			−0.536413			−0.268207	+	0.963361i	$0.586431\pi$
$278$	−8.90173	−	5.72079i	−0.533890	−	0.343110i
$279$	−3.50192	−	24.3564i	−0.209655	−	1.45818i
$280$	0.664094	+	1.45416i	0.0396872	+	0.0869028i
$281$	−1.81328	−	0.532428i	−0.108171	−	0.0317620i	0.227199	−	0.973848i	$-0.427043\pi$
$281$	−1.81328	−	0.532428i	−0.108171	−	0.0317620i	−0.335370	+	0.942086i	$0.608861\pi$
$282$	11.3808	−	24.9204i	0.677715	−	1.48399i
$283$	16.0225	−	18.4910i	0.952442	−	1.09918i	−0.0425375	−	0.999095i	$-0.513544\pi$
$283$	16.0225	−	18.4910i	0.952442	−	1.09918i	0.994979	−	0.100081i	$-0.0319103\pi$
$284$	−1.06617	+	7.41536i	−0.0632654	+	0.440021i
$285$	8.83066	−	2.59292i	0.523083	−	0.153591i
$286$	−4.93959	−	5.70059i	−0.292084	−	0.337083i
$287$	−3.58423	+	2.30344i	−0.211570	+	0.135968i
$288$	3.14558	−	2.02154i	0.185355	−	0.119121i
$289$	10.2784	+	11.8619i	0.604613	+	0.697761i
$290$	−7.21450	+	2.11837i	−0.423650	+	0.124395i
$291$	−1.89885	+	13.2068i	−0.111313	+	0.774196i
$292$	−2.12756	+	2.45533i	−0.124506	+	0.143688i
$293$	−10.7429	+	23.5237i	−0.627607	+	1.37427i	0.282247	+	0.959342i	$0.408920\pi$
$293$	−10.7429	+	23.5237i	−0.627607	+	1.37427i	−0.909855	+	0.414927i	$0.863807\pi$
$294$	11.0702	+	3.25051i	0.645629	+	0.189574i
$295$	−4.58501	−	10.0398i	−0.266950	−	0.584538i
$296$	−0.773727	−	5.38139i	−0.0449720	−	0.312787i
$297$	2.79985	+	1.79936i	0.162464	+	0.104409i
$298$	15.8673			0.919169
$299$	−13.6040	−	15.8088i	−0.786742	−	0.914247i
$300$	2.59599			0.149880
$301$	8.90984	+	5.72601i	0.513555	+	0.330042i
$302$	3.04328	+	21.1665i	0.175121	+	1.21800i
$303$	−18.7340	−	41.0217i	−1.07624	−	2.35663i
$304$	−3.40166	−	0.998816i	−0.195098	−	0.0572860i
$305$	2.05626	−	4.50258i	0.117741	−	0.257817i
$306$	2.79661	−	3.22746i	0.159871	−	0.184501i
$307$	0.425397	−	2.95870i	0.0242787	−	0.168862i	−0.974075	−	0.226227i	$-0.927361\pi$
$307$	0.425397	−	2.95870i	0.0242787	−	0.168862i	0.998353	+	0.0573652i	$0.0182700\pi$
$308$	2.66046	−	0.781181i	0.151594	−	0.0445119i
$309$	−27.4793	−	31.7128i	−1.56324	−	1.80408i
$310$	−5.53617	+	3.55788i	−0.314433	+	0.202074i
$311$	25.7891	−	16.5737i	1.46237	−	0.939806i	0.463819	−	0.885930i	$-0.346479\pi$
$311$	25.7891	−	16.5737i	1.46237	−	0.939806i	0.998548	−	0.0538762i	$-0.0171576\pi$
$312$	−7.39311	−	8.53210i	−0.418552	−	0.483035i
$313$	−7.45722	+	2.18964i	−0.421507	+	0.123766i	−0.485606	−	0.874178i	$-0.661401\pi$
$313$	−7.45722	+	2.18964i	−0.421507	+	0.123766i	0.0640988	+	0.997944i	$0.479583\pi$
$314$	2.63345	−	18.3160i	0.148614	−	1.03363i
$315$	−3.91445	+	4.51751i	−0.220554	+	0.254533i
$316$	6.49253	−	14.2167i	0.365233	−	0.799749i
$317$	16.7363	+	4.91422i	0.940004	+	0.276010i	0.715619	−	0.698490i	$-0.246145\pi$
$317$	16.7363	+	4.91422i	0.940004	+	0.276010i	0.224385	+	0.974501i	$0.427963\pi$
$318$	2.09413	+	4.58551i	0.117433	+	0.257143i
$319$	1.85602	+	12.9089i	0.103917	+	0.722758i
$320$	−0.841254	−	0.540641i	−0.0470275	−	0.0302227i
$321$	−46.2121			−2.57931
$322$	7.36353	−	2.13481i	0.410354	−	0.118968i
$323$	−4.04909			−0.225297
$324$	−5.24620	−	3.37152i	−0.291455	−	0.187307i
$325$	−0.618907	−	4.30459i	−0.0343308	−	0.238776i
$326$	−3.28470	−	7.19249i	−0.181923	−	0.398355i
$327$	40.8150	+	11.9844i	2.25707	+	0.662736i
$328$	1.10714	−	2.42430i	0.0611317	−	0.133860i
$329$	11.0480	−	12.7500i	0.609095	−	0.702933i
$330$	0.640797	−	4.45684i	0.0352747	−	0.245341i
$331$	11.2441	−	3.30157i	0.618032	−	0.181471i	0.0422947	−	0.999105i	$-0.486533\pi$
$331$	11.2441	−	3.30157i	0.618032	−	0.181471i	0.575738	+	0.817635i	$0.304715\pi$
$332$	−2.46258	−	2.84197i	−0.135151	−	0.155973i
$333$	17.1017	−	10.9906i	0.937166	−	0.602280i
$334$	16.8736	−	10.8440i	0.923283	−	0.593358i
$335$	−3.02645	−	3.49271i	−0.165352	−	0.190827i
$336$	3.98191	−	1.16920i	0.217231	−	0.0637848i
$337$	−3.14858	+	21.8989i	−0.171514	+	1.19291i	0.704173	+	0.710029i	$0.251318\pi$
$337$	−3.14858	+	21.8989i	−0.171514	+	1.19291i	−0.875687	+	0.482879i	$0.839591\pi$
$338$	−3.87190	+	4.46841i	−0.210604	+	0.243050i
$339$	8.25795	−	18.0824i	0.448511	−	0.982101i
$340$	−1.09585	−	0.321770i	−0.0594307	−	0.0174504i
$341$	4.74167	+	10.3828i	0.256776	+	0.562261i
$342$	−1.88657	−	13.1214i	−0.102014	−	0.709523i
$343$	15.3910	+	9.89119i	0.831036	+	0.534074i
$344$	−6.62515			−0.357204
$345$	1.81394	−	12.3171i	0.0976591	−	0.663129i
$346$	−5.17965			−0.278460
$347$	−20.9048	−	13.4347i	−1.12223	−	0.721214i	−0.158306	−	0.987390i	$-0.550603\pi$
$347$	−20.9048	−	13.4347i	−1.12223	−	0.721214i	−0.963924	+	0.266176i	$0.914240\pi$
$348$	2.77790	+	19.3208i	0.148911	+	1.03570i
$349$	4.02531	+	8.81420i	0.215470	+	0.471813i	0.986244	−	0.165295i	$-0.0528576\pi$
$349$	4.02531	+	8.81420i	0.215470	+	0.471813i	−0.770774	+	0.637108i	$0.780130\pi$
$350$	1.53387	+	0.450385i	0.0819889	+	0.0240741i
$351$	3.46656	−	7.59070i	0.185031	−	0.405162i
$352$	−1.13584	+	1.31083i	−0.0605403	+	0.0698673i
$353$	−4.48168	+	31.1708i	−0.238536	+	1.65905i	0.420762	+	0.907171i	$0.361763\pi$
$353$	−4.48168	+	31.1708i	−0.238536	+	1.65905i	−0.659298	+	0.751882i	$0.729146\pi$
$354$	−27.4918	+	8.07232i	−1.46117	+	0.429039i
$355$	4.90596	+	5.66178i	0.260382	+	0.300496i
$356$	12.1519	−	7.80953i	0.644047	−	0.413904i
$357$	3.98736	−	2.56252i	0.211034	−	0.135623i
$358$	4.86641	+	5.61613i	0.257198	+	0.296822i
$359$	23.4141	−	6.87499i	1.23575	−	0.362848i	0.402331	−	0.915494i	$-0.368200\pi$
$359$	23.4141	−	6.87499i	1.23575	−	0.362848i	0.833416	+	0.552646i	$0.186382\pi$
$360$	0.532138	−	3.70110i	0.0280461	−	0.195065i
$361$	4.21148	−	4.86030i	0.221657	−	0.255805i
$362$	3.09115	−	6.76867i	0.162467	−	0.355753i
$363$	19.9058	+	5.84486i	1.04478	+	0.306776i
$364$	−2.88805	−	6.32395i	−0.151375	−	0.331465i
$365$	0.462363	+	3.21580i	0.0242012	+	0.168323i
$366$	−10.8100	−	6.94717i	−0.565048	−	0.363134i
$367$	−22.4667			−1.17275			−0.586376	−	0.810039i	$-0.699446\pi$
$367$	−22.4667			−1.17275			−0.586376	+	0.810039i	$0.699446\pi$
$368$	−3.15298	+	3.61369i	−0.164360	+	0.188376i
$369$	9.96541			0.518778
$370$	−4.57367	−	2.93932i	−0.237774	−	0.152808i
$371$	0.441791	+	3.07272i	0.0229366	+	0.159528i
$372$	7.09688	+	15.5400i	0.367956	+	0.805711i
$373$	−10.7549	−	3.15794i	−0.556870	−	0.163512i	−0.00882556	−	0.999961i	$-0.502809\pi$
$373$	−10.7549	−	3.15794i	−0.556870	−	0.163512i	−0.548044	+	0.836449i	$0.684627\pi$
$374$	−0.822920	+	1.80194i	−0.0425522	+	0.0931763i
$375$	1.70001	−	1.96192i	0.0877882	−	0.101313i
$376$	−1.50189	+	10.4458i	−0.0774538	+	0.538703i
$377$	31.3748	−	9.21248i	1.61589	−	0.474467i
$378$	2.00880	+	2.31828i	0.103322	+	0.119240i
$379$	18.2617	−	11.7361i	0.938042	−	0.602843i	0.0202028	−	0.999796i	$-0.493569\pi$
$379$	18.2617	−	11.7361i	0.938042	−	0.602843i	0.917839	+	0.396953i	$0.129932\pi$
$380$	−2.98247	+	1.91671i	−0.152997	+	0.0983254i
$381$	23.0906	+	26.6480i	1.18297	+	1.36522i
$382$	0.0164351	−	0.00482579i	0.000840894	−	0.000246909i
$383$	−0.114861	+	0.798878i	−0.00586914	+	0.0408208i	−0.992546	−	0.121874i	$-0.961110\pi$
$383$	−0.114861	+	0.798878i	−0.00586914	+	0.0408208i	0.986676	+	0.162695i	$0.0520186\pi$
$384$	−1.70001	+	1.96192i	−0.0867533	+	0.100119i
$385$	1.15185	−	2.52220i	0.0587038	−	0.128543i
$386$	−7.68073	−	2.25527i	−0.390939	−	0.114790i
$387$	−10.2909	−	22.5339i	−0.523114	−	1.14546i
$388$	−0.731456	−	5.08739i	−0.0371340	−	0.258273i
$389$	25.6842	+	16.5062i	1.30224	+	0.836898i	0.993454	−	0.114234i	$-0.0364414\pi$
$389$	25.6842	+	16.5062i	1.30224	+	0.836898i	0.308785	+	0.951132i	$0.400078\pi$
$390$	−11.2896			−0.571670
$391$	−2.29241	+	4.97459i	−0.115932	+	0.251576i
$392$	−4.44439			−0.224476
$393$	8.47799	+	5.44848i	0.427658	+	0.274839i
$394$	−1.65602	−	11.5179i	−0.0834293	−	0.580263i
$395$	−6.49253	−	14.2167i	−0.326675	−	0.715318i
$396$	−6.22276	−	1.82717i	−0.312705	−	0.0918186i
$397$	2.94209	−	6.44229i	0.147659	−	0.323329i	−0.821321	−	0.570466i	$-0.806763\pi$
$397$	2.94209	−	6.44229i	0.147659	−	0.323329i	0.968981	+	0.247137i	$0.0794898\pi$
$398$	−11.8930	+	13.7253i	−0.596143	+	0.687986i
$399$	2.09387	−	14.5632i	0.104824	−	0.729070i
$400$	−0.959493	+	0.281733i	−0.0479746	+	0.0140866i
$401$	8.54020	+	9.85592i	0.426477	+	0.492181i	0.927799	−	0.373080i	$-0.121698\pi$
$401$	8.54020	+	9.85592i	0.426477	+	0.492181i	−0.501322	+	0.865261i	$0.667153\pi$
$402$	−10.0928	+	6.48628i	−0.503386	+	0.323506i
$403$	24.0760	−	15.4727i	1.19931	−	0.770750i
$404$	11.3761	+	13.1287i	0.565982	+	0.653179i
$405$	−5.98356	+	1.75693i	−0.297325	+	0.0873026i
$406$	−1.71065	+	11.8978i	−0.0848982	+	0.590480i
$407$	−6.17524	+	7.12661i	−0.306095	+	0.353253i
$408$	−1.23167	+	2.69698i	−0.0609766	+	0.133520i
$409$	−8.94302	−	2.62591i	−0.442204	−	0.129843i	0.0530486	−	0.998592i	$-0.483106\pi$
$409$	−8.94302	−	2.62591i	−0.442204	−	0.129843i	−0.495252	+	0.868749i	$0.664924\pi$
$410$	−1.10714	−	2.42430i	−0.0546778	−	0.119728i
$411$	4.85754	+	33.7849i	0.239605	+	1.66649i
$412$	13.5982	+	8.73903i	0.669935	+	0.430541i
$413$	−17.6443			−0.868221
$414$	−17.1886	−	5.11094i	−0.844774	−	0.251189i
$415$	−3.76046			−0.184594
$416$	3.65849	+	2.35117i	0.179372	+	0.115276i
$417$	3.90931	+	27.1899i	0.191440	+	1.33149i
$418$	2.55445	+	5.59347i	0.124942	+	0.273586i
$419$	9.00197	+	2.64322i	0.439775	+	0.129130i	0.494122	−	0.869392i	$-0.335490\pi$
$419$	9.00197	+	2.64322i	0.439775	+	0.129130i	−0.0543471	+	0.998522i	$0.517308\pi$
$420$	1.72398	−	3.77499i	0.0841216	−	0.184201i
$421$	18.3333	−	21.1577i	0.893508	−	1.03116i	−0.105815	−	0.994386i	$-0.533745\pi$
$421$	18.3333	−	21.1577i	0.893508	−	1.03116i	0.999323	−	0.0367774i	$-0.0117093\pi$
$422$	1.88612	−	13.1183i	0.0918149	−	0.638587i
$423$	−37.8619	+	11.1173i	−1.84091	+	0.540539i
$424$	−1.27165	−	1.46756i	−0.0617569	−	0.0712712i
$425$	−0.960805	+	0.617472i	−0.0466059	+	0.0299518i
$426$	16.3608	−	10.5145i	0.792685	−	0.509427i
$427$	−5.18194	−	5.98028i	−0.250772	−	0.289406i
$428$	17.0803	−	5.01522i	0.825606	−	0.242420i
$429$	−2.78673	+	19.3822i	−0.134545	+	0.935779i
$430$	−4.33855	+	5.00696i	−0.209224	+	0.241457i
$431$	−1.46588	+	3.20982i	−0.0706087	+	0.154612i	−0.941645	−	0.336606i	$-0.890721\pi$
$431$	−1.46588	+	3.20982i	−0.0706087	+	0.154612i	0.871037	+	0.491218i	$0.163448\pi$
$432$	−1.84112	−	0.540603i	−0.0885811	−	0.0260098i
$433$	−14.8815	−	32.5860i	−0.715160	−	1.56598i	−0.820566	−	0.571552i	$-0.806341\pi$
$433$	−14.8815	−	32.5860i	−0.715160	−	1.56598i	0.105406	−	0.994429i	$-0.466386\pi$
$434$	1.49720	+	10.4133i	0.0718679	+	0.499852i
$435$	16.4208	+	10.5530i	0.787317	+	0.505978i
$436$	−16.3861			−0.784750
$437$	7.01016	+	15.4901i	0.335342	+	0.740990i
$438$	8.43404			0.402994
$439$	−24.0442	−	15.4522i	−1.14757	−	0.737495i	−0.178412	−	0.983956i	$-0.557096\pi$
$439$	−24.0442	−	15.4522i	−1.14757	−	0.737495i	−0.969153	+	0.246460i	$0.920732\pi$
$440$	0.246841	+	1.71682i	0.0117677	+	0.0818460i
$441$	−6.90348	−	15.1165i	−0.328737	−	0.719834i
$442$	4.76569	+	1.39933i	0.226681	+	0.0665594i
$443$	−12.1439	+	26.5915i	−0.576976	+	1.26340i	0.366022	+	0.930606i	$0.380719\pi$
$443$	−12.1439	+	26.5915i	−0.576976	+	1.26340i	−0.942999	+	0.332796i	$0.892008\pi$
$444$	−9.24250	+	10.6664i	−0.438630	+	0.506206i
$445$	2.05573	−	14.2979i	0.0974509	−	0.677786i
$446$	−4.28711	+	1.25881i	−0.203001	+	0.0596064i
$447$	−26.9746	−	31.1304i	−1.27586	−	1.47242i
$448$	−1.34485	+	0.864283i	−0.0635382	+	0.0408335i
$449$	−29.0280	+	18.6552i	−1.36992	+	0.880392i	−0.998837	−	0.0482084i	$-0.984649\pi$
$449$	−29.0280	+	18.6552i	−1.36992	+	0.880392i	−0.371080	+	0.928601i	$0.621012\pi$
$450$	−2.44863	−	2.82587i	−0.115429	−	0.133213i
$451$	−4.43537	+	1.30234i	−0.208854	+	0.0613249i
$452$	−1.08978	+	7.57957i	−0.0512588	+	0.356513i
$453$	36.3533	−	41.9540i	1.70803	−	1.97117i
$454$	0.931781	−	2.04032i	0.0437306	−	0.0957568i
$455$	−6.67059	−	1.95866i	−0.312722	−	0.0918235i
$456$	3.82326	+	8.37177i	0.179040	+	0.392044i
$457$	−2.20909	−	15.3645i	−0.103337	−	0.718722i	−0.973951	−	0.226757i	$-0.927188\pi$
$457$	−2.20909	−	15.3645i	−0.103337	−	0.718722i	0.870615	−	0.491965i	$-0.163721\pi$
$458$	3.71360	+	2.38659i	0.173525	+	0.111518i
$459$	−2.19154			−0.102292
$460$	0.666282	+	4.74932i	0.0310656	+	0.221438i
$461$	−20.9031			−0.973553			−0.486777	−	0.873526i	$-0.661827\pi$
$461$	−20.9031			−0.973553			−0.486777	+	0.873526i	$0.661827\pi$
$462$	−6.05542	−	3.89158i	−0.281724	−	0.181053i
$463$	−2.63214	−	18.3070i	−0.122326	−	0.850797i	−0.954909	−	0.296897i	$-0.904048\pi$
$463$	−2.63214	−	18.3070i	−0.122326	−	0.850797i	0.832583	−	0.553900i	$-0.186861\pi$
$464$	−3.12354	−	6.83959i	−0.145007	−	0.317520i
$465$	16.3918	+	4.81307i	0.760152	+	0.223201i
$466$	1.86152	−	4.07616i	0.0862333	−	0.188825i
$467$	1.24054	−	1.43166i	0.0574054	−	0.0662494i	−0.726321	−	0.687356i	$-0.758771\pi$
$467$	1.24054	−	1.43166i	0.0574054	−	0.0662494i	0.783726	+	0.621107i	$0.213317\pi$
$468$	−2.31419	+	16.0956i	−0.106974	+	0.744017i
$469$	−7.08881	+	2.08146i	−0.327331	+	0.0961130i
$470$	6.91091	+	7.97562i	0.318777	+	0.367888i
$471$	−40.4114	+	25.9708i	−1.86206	+	1.19667i
$472$	9.28507	−	5.96715i	0.427380	−	0.274660i
$473$	7.52510	+	8.68442i	0.346004	+	0.399310i
$474$	−38.9293	+	11.4307i	−1.78808	+	0.525028i
$475$	−0.504544	+	3.50918i	−0.0231501	+	0.161012i
$476$	−1.19565	+	1.37986i	−0.0548026	+	0.0632456i
$477$	3.01631	−	6.60479i	0.138107	−	0.302413i
$478$	−4.79415	−	1.40769i	−0.219279	−	0.0643862i
$479$	9.22805	+	20.2066i	0.421641	+	0.923264i	0.994610	+	0.103687i	$0.0330641\pi$
$479$	9.22805	+	20.2066i	0.421641	+	0.923264i	−0.572969	+	0.819577i	$0.694209\pi$
$480$	0.369448	+	2.56957i	0.0168629	+	0.117284i
$481$	19.8902	+	12.7827i	0.906916	+	0.582840i
$482$	−15.5620			−0.708828
$483$	−16.7064	−	10.8175i	−0.760168	−	0.492211i
$484$	−7.99161			−0.363255
$485$	−4.32379	−	2.77873i	−0.196333	−	0.126176i
$486$	3.12318	+	21.7222i	0.141670	+	0.985339i
$487$	2.63028	+	5.75951i	0.119189	+	0.260988i	0.959818	−	0.280624i	$-0.0905414\pi$
$487$	2.63028	+	5.75951i	0.119189	+	0.260988i	−0.840628	+	0.541612i	$0.817814\pi$
$488$	4.74939	+	1.39455i	0.214995	+	0.0631282i
$489$	−8.52704	+	18.6716i	−0.385606	+	0.844360i
$490$	−2.91046	+	3.35885i	−0.131481	+	0.151737i
$491$	−0.550384	+	3.82800i	−0.0248385	+	0.172755i	−0.998465	−	0.0553942i	$-0.982358\pi$
$491$	−0.550384	+	3.82800i	−0.0248385	+	0.172755i	0.973626	+	0.228150i	$0.0732675\pi$
$492$	−6.63844	+	1.94922i	−0.299284	+	0.0878777i
$493$	−5.62369	−	6.49009i	−0.253278	−	0.292299i
$494$	12.9703	−	8.33552i	0.583562	−	0.375033i
$495$	−5.45592	+	3.50631i	−0.245225	+	0.157597i
$496$	−4.30954	−	4.97348i	−0.193504	−	0.223316i
$497$	11.4912	−	3.37411i	0.515450	−	0.151350i
$498$	−1.38929	+	9.66275i	−0.0622557	+	0.432998i
$499$	12.3442	−	14.2460i	0.552604	−	0.637739i	−0.408884	−	0.912587i	$-0.634082\pi$
$499$	12.3442	−	14.2460i	0.552604	−	0.637739i	0.961488	+	0.274847i	$0.0886273\pi$
$500$	−0.415415	+	0.909632i	−0.0185779	+	0.0406800i
$501$	−49.9604	−	14.6697i	−2.23207	−	0.655394i
$502$	−3.09349	−	6.77380i	−0.138069	−	0.302329i
$503$	−1.62170	−	11.2792i	−0.0723080	−	0.502913i	−0.993502	−	0.113811i	$-0.963694\pi$
$503$	−1.62170	−	11.2792i	−0.0723080	−	0.502913i	0.921195	−	0.389102i	$-0.127215\pi$
$504$	−5.02861	−	3.23169i	−0.223992	−	0.143951i
$505$	17.3718			0.773035
$506$	8.31818	+	0.0284438i	0.369788	+	0.00126448i
$507$	15.3489			0.681670
$508$	−11.4264	−	7.34332i	−0.506966	−	0.325807i
$509$	2.50481	+	17.4213i	0.111024	+	0.772186i	0.966928	+	0.255051i	$0.0820923\pi$
$509$	2.50481	+	17.4213i	0.111024	+	0.772186i	−0.855904	+	0.517135i	$0.826999\pi$
$510$	1.23167	+	2.69698i	0.0545392	+	0.119424i
$511$	4.98336	+	1.46325i	0.220451	+	0.0647302i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	−4.45491	+	5.14124i	−0.196689	+	0.226991i
$514$	−3.22285	+	22.4154i	−0.142154	+	0.988701i
$515$	15.5094	−	4.55398i	0.683428	−	0.200672i
$516$	11.2628	+	12.9980i	0.495819	+	0.572205i
$517$	15.3986	−	9.89606i	0.677229	−	0.435228i
$518$	−7.31159	+	4.69888i	−0.321253	+	0.206457i
$519$	8.80546	+	10.1620i	0.386517	+	0.446064i
$520$	4.17270	−	1.22521i	0.182985	−	0.0537292i
$521$	2.40160	−	16.7035i	0.105216	−	0.731792i	−0.867102	−	0.498130i	$-0.834020\pi$
$521$	2.40160	−	16.7035i	0.105216	−	0.731792i	0.972318	−	0.233662i	$-0.0750708\pi$
$522$	18.4114	−	21.2479i	0.805846	−	0.929996i
$523$	−8.52168	+	18.6599i	−0.372627	+	0.815939i	0.626700	+	0.779261i	$0.284405\pi$
$523$	−8.52168	+	18.6599i	−0.372627	+	0.815939i	−0.999327	+	0.0366788i	$0.988322\pi$
$524$	−3.72482	−	1.09371i	−0.162719	−	0.0477787i
$525$	−1.72398	−	3.77499i	−0.0752407	−	0.164754i
$526$	−2.43371	−	16.9269i	−0.106115	−	0.738046i
$527$	−6.32292	−	4.06349i	−0.275431	−	0.177009i
$528$	4.50267			0.195954
$529$	22.9995	+	0.157294i	0.999977	+	0.00683885i
$530$	−1.94187			−0.0843493
$531$	34.7184	+	22.3121i	1.50665	+	0.968264i
$532$	0.806577	+	5.60987i	0.0349696	+	0.243219i
$533$	4.81480	+	10.5429i	0.208552	+	0.456666i
$534$	−35.9799	−	10.5647i	−1.55700	−	0.457178i
$535$	7.39495	−	16.1927i	0.319711	−	0.700070i
$536$	3.02645	−	3.49271i	0.130723	−	0.150862i
$537$	2.74544	−	19.0950i	0.118475	−	0.824009i
$538$	3.68810	−	1.08293i	0.159005	−	0.0466882i
$539$	5.04810	+	5.82582i	0.217437	+	0.250936i
$540$	−1.61424	+	1.03741i	−0.0694658	+	0.0446430i
$541$	−21.7488	+	13.9771i	−0.935054	+	0.600923i	−0.916988	−	0.398914i	$-0.869387\pi$
$541$	−21.7488	+	13.9771i	−0.935054	+	0.600923i	−0.0180656	+	0.999837i	$0.505751\pi$
$542$	8.99687	+	10.3829i	0.386449	+	0.445985i
$543$	−18.5346	+	5.44224i	−0.795394	+	0.233549i
$544$	0.162539	−	1.13049i	0.00696882	−	0.0484692i
$545$	−10.7306	+	12.3838i	−0.459648	+	0.530462i
$546$	−7.49734	+	16.4169i	−0.320857	+	0.702578i
$547$	1.48827	+	0.436997i	0.0636340	+	0.0186846i	0.313395	−	0.949623i	$-0.398534\pi$
$547$	1.48827	+	0.436997i	0.0636340	+	0.0186846i	−0.249761	+	0.968308i	$0.580352\pi$
$548$	−5.46192	−	11.9599i	−0.233322	−	0.510903i
$549$	2.63403	+	18.3201i	0.112418	+	0.781881i
$550$	1.45913	+	0.937726i	0.0622175	+	0.0399848i
$551$	−26.6571			−1.13563
$552$	12.4499	+	0.0425719i	0.529901	+	0.00181198i
$553$	−24.9850			−1.06247
$554$	−7.51046	−	4.82668i	−0.319089	−	0.205066i
$555$	2.00859	+	13.9700i	0.0852598	+	0.592995i
$556$	−4.39572	−	9.62527i	−0.186420	−	0.408203i
$557$	32.3138	+	9.48817i	1.36918	+	0.402027i	0.881989	−	0.471270i	$-0.156204\pi$
$557$	32.3138	+	9.48817i	1.36918	+	0.402027i	0.487189	+	0.873297i	$0.338022\pi$
$558$	10.2221	−	22.3832i	0.432734	−	0.947556i
$559$	18.8677	−	21.7745i	0.798021	−	0.920965i
$560$	−0.227508	+	1.58236i	−0.00961398	+	0.0668667i
$561$	4.93424	−	1.44882i	0.208324	−	0.0611694i
$562$	−1.23758	−	1.42824i	−0.0522041	−	0.0602468i
$563$	−21.0148	+	13.5054i	−0.885667	+	0.569183i	−0.902507	−	0.430675i	$-0.858276\pi$
$563$	−21.0148	+	13.5054i	−0.885667	+	0.569183i	0.0168405	+	0.999858i	$0.494639\pi$
$564$	23.0471	−	14.8115i	0.970458	−	0.623676i
$565$	5.01460	+	5.78716i	0.210966	+	0.243468i
$566$	23.4760	−	6.89318i	0.986771	−	0.289742i
$567$	−1.41878	+	9.86783i	−0.0595832	+	0.414410i
$568$	−4.90596	+	5.66178i	−0.205850	+	0.237563i
$569$	−8.86653	+	19.4150i	−0.371704	+	0.813919i	0.627668	+	0.778481i	$0.284010\pi$
$569$	−8.86653	+	19.4150i	−0.371704	+	0.813919i	−0.999372	+	0.0354374i	$0.988718\pi$
$570$	8.83066	+	2.59292i	0.369876	+	0.108605i
$571$	−5.45492	−	11.9446i	−0.228281	−	0.499866i	0.760482	−	0.649360i	$-0.224963\pi$
$571$	−5.45492	−	11.9446i	−0.228281	−	0.499866i	−0.988763	+	0.149494i	$0.952236\pi$
$572$	−1.07348	−	7.46619i	−0.0448843	−	0.312177i
$573$	−0.0374077	−	0.0240405i	−0.00156273	−	0.00100431i
$574$	−4.26058			−0.177833
$575$	4.02562	+	2.60660i	0.167880	+	0.108703i
$576$	3.73916			0.155798
$577$	16.2588	+	10.4489i	0.676863	+	0.434994i	0.833394	−	0.552679i	$-0.186395\pi$
$577$	16.2588	+	10.4489i	0.676863	+	0.434994i	−0.156531	+	0.987673i	$0.550031\pi$
$578$	2.23371	+	15.5358i	0.0929103	+	0.646205i
$579$	8.63269	+	18.9029i	0.358762	+	0.785580i
$580$	−7.21450	−	2.11837i	−0.299566	−	0.0879604i
$581$	−2.49730	+	5.46832i	−0.103605	+	0.226864i
$582$	−8.73755	+	10.0837i	−0.362183	+	0.417982i
$583$	−0.479332	+	3.33383i	−0.0198519	+	0.138073i
$584$	−3.11727	+	0.915313i	−0.128994	+	0.0378759i
$585$	10.6487	+	12.2893i	0.440271	+	0.508100i
$586$	−21.7554	+	13.9813i	−0.898706	+	0.577563i
$587$	−7.55513	+	4.85539i	−0.311834	+	0.200403i	−0.687191	−	0.726477i	$-0.741156\pi$
$587$	−7.55513	+	4.85539i	−0.311834	+	0.200403i	0.375357	+	0.926880i	$0.377520\pi$
$588$	7.55551	+	8.71953i	0.311584	+	0.359587i
$589$	−22.3858	+	6.57307i	−0.922391	+	0.270838i
$590$	1.57076	−	10.9248i	0.0646670	−	0.449769i
$591$	−19.7819	+	22.8295i	−0.813719	+	0.939082i
$592$	2.25850	−	4.94542i	0.0928238	−	0.203256i
$593$	4.27926	+	1.25651i	0.175728	+	0.0515985i	0.368413	−	0.929662i	$-0.379901\pi$
$593$	4.27926	+	1.25651i	0.175728	+	0.0515985i	−0.192685	+	0.981261i	$0.561719\pi$
$594$	1.38258	+	3.02743i	0.0567280	+	0.124217i
$595$	0.259840	+	1.80723i	0.0106524	+	0.0740891i
$596$	13.3484	+	8.57852i	0.546773	+	0.351390i
$597$	47.1461			1.92956
$598$	−2.89756	−	20.6541i	−0.118490	−	0.844610i
$599$	−22.9114			−0.936133			−0.468066	−	0.883693i	$-0.655049\pi$
$599$	−22.9114			−0.936133			−0.468066	+	0.883693i	$0.655049\pi$
$600$	2.18389	+	1.40350i	0.0891567	+	0.0572976i
$601$	−3.19314	−	22.2088i	−0.130251	−	0.905915i	−0.945225	−	0.326418i	$-0.894158\pi$
$601$	−3.19314	−	22.2088i	−0.130251	−	0.905915i	0.814975	−	0.579497i	$-0.196751\pi$
$602$	4.39972	+	9.63405i	0.179319	+	0.392655i
$603$	16.5806	+	4.86850i	0.675214	+	0.198261i
$604$	−8.88330	+	19.4517i	−0.361456	+	0.791479i
$605$	−5.23339	+	6.03966i	−0.212768	+	0.245547i
$606$	6.41797	−	44.6380i	0.260712	−	1.81329i
$607$	29.6131	−	8.69518i	1.20196	−	0.352927i	0.381356	−	0.924428i	$-0.375457\pi$
$607$	29.6131	−	8.69518i	1.20196	−	0.352927i	0.820601	+	0.571502i	$0.193639\pi$
$608$	−2.32165	−	2.67933i	−0.0941555	−	0.108661i
$609$	26.2507	−	16.8703i	1.06373	−	0.683620i
$610$	4.16412	−	2.67612i	0.168600	−	0.108353i
$611$	−30.0546	−	34.6848i	−1.21588	−	1.40320i
$612$	4.09755	−	1.20315i	0.165634	−	0.0486344i
$613$	6.07593	−	42.2590i	0.245405	−	1.70683i	−0.378728	−	0.925508i	$-0.623638\pi$
$613$	6.07593	−	42.2590i	0.245405	−	1.70683i	0.624133	−	0.781318i	$-0.285452\pi$
$614$	1.95746	−	2.25903i	0.0789966	−	0.0911670i
$615$	−2.87413	+	6.29346i	−0.115896	+	0.253777i
$616$	2.66046	+	0.781181i	0.107193	+	0.0314747i
$617$	−18.7684	−	41.0971i	−0.755588	−	1.65451i	−0.756055	−	0.654508i	$-0.772876\pi$
$617$	−18.7684	−	41.0971i	−0.755588	−	1.65451i	0.000466890	−	1.00000i	$-0.499851\pi$
$618$	−5.97183	−	41.5350i	−0.240222	−	1.67078i
$619$	−4.17253	−	2.68152i	−0.167708	−	0.107779i	0.454094	−	0.890954i	$-0.349963\pi$
$619$	−4.17253	−	2.68152i	−0.167708	−	0.107779i	−0.621802	+	0.783174i	$0.713599\pi$
$620$	−6.58086			−0.264294
$621$	3.79420	+	8.38390i	0.152256	+	0.336434i
$622$	30.6556			1.22918
$623$	−19.4263	−	12.4845i	−0.778298	−	0.500182i
$624$	−1.60668	−	11.1747i	−0.0643185	−	0.447345i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	−7.45722	−	2.18964i	−0.298050	−	0.0875155i
$627$	6.63133	−	14.5206i	0.264830	−	0.579897i
$628$	12.1178	−	13.9847i	0.483552	−	0.558049i
$629$	0.883683	−	6.14615i	0.0352347	−	0.245063i
$630$	−5.73539	+	1.68406i	−0.228503	+	0.0670947i
$631$	17.1773	+	19.8236i	0.683816	+	0.789165i	0.986471	−	0.163935i	$-0.0524186\pi$
$631$	17.1773	+	19.8236i	0.683816	+	0.789165i	−0.302656	+	0.953100i	$0.597873\pi$
$632$	13.1480	−	8.44969i	0.522998	−	0.336110i
$633$	−28.9434	+	18.6008i	−1.15040	+	0.739315i
$634$	11.4226	+	13.1824i	0.453651	+	0.523541i
$635$	−13.0324	+	3.82667i	−0.517176	+	0.151857i
$636$	−0.717418	+	4.98975i	−0.0284475	+	0.197857i
$637$	12.6572	−	14.6071i	0.501495	−	0.578756i
$638$	−5.41768	+	11.8631i	−0.214488	+	0.469664i
$639$	−26.8776	−	7.89199i	−1.06326	−	0.312202i
$640$	−0.415415	−	0.909632i	−0.0164207	−	0.0359564i
$641$	−1.50954	−	10.4991i	−0.0596234	−	0.414690i	−0.997673	−	0.0681875i	$-0.978278\pi$
$641$	−1.50954	−	10.4991i	−0.0596234	−	0.414690i	0.938049	−	0.346502i	$-0.112631\pi$
$642$	−38.8761	−	24.9841i	−1.53432	−	0.986046i
$643$	32.1679			1.26858			0.634288	−	0.773097i	$-0.281293\pi$
$643$	32.1679			1.26858			0.634288	+	0.773097i	$0.281293\pi$
$644$	7.34876	+	2.18511i	0.289582	+	0.0861056i
$645$	17.1988			0.677203
$646$	−3.40631	−	2.18910i	−0.134019	−	0.0861290i
$647$	−3.89356	−	27.0803i	−0.153072	−	1.06464i	−0.911032	−	0.412336i	$-0.864713\pi$
$647$	−3.89356	−	27.0803i	−0.153072	−	1.06464i	0.757960	−	0.652301i	$-0.226196\pi$
$648$	−2.59060	−	5.67261i	−0.101768	−	0.222841i
$649$	−18.3682	−	5.39340i	−0.721016	−	0.211709i
$650$	1.80658	−	3.95586i	0.0708599	−	0.155162i
$651$	17.8847	−	20.6400i	0.700956	−	0.808947i
$652$	1.12529	−	7.82655i	0.0440697	−	0.306511i
$653$	−32.3088	+	9.48672i	−1.26434	+	0.371244i	−0.844108	−	0.536173i	$-0.819870\pi$
$653$	−32.3088	+	9.48672i	−1.26434	+	0.371244i	−0.420232	+	0.907417i	$0.638051\pi$
$654$	27.8565	+	32.1481i	1.08928	+	1.25709i
$655$	−3.26580	+	2.09881i	−0.127606	+	0.0820071i
$656$	2.24206	−	1.44089i	0.0875379	−	0.0562572i
$657$	−7.95529	−	9.18089i	−0.310365	−	0.358181i
$658$	16.1873	−	4.75303i	0.631048	−	0.185293i
$659$	−6.71009	+	46.6697i	−0.261388	+	1.81799i	0.261061	+	0.965322i	$0.415928\pi$
$659$	−6.71009	+	46.6697i	−0.261388	+	1.81799i	−0.522449	+	0.852671i	$0.674981\pi$
$660$	2.94862	−	3.40289i	0.114775	−	0.132457i
$661$	14.7649	−	32.3305i	0.574287	−	1.25751i	−0.370197	−	0.928953i	$-0.620710\pi$
$661$	14.7649	−	32.3305i	0.574287	−	1.25751i	0.944483	−	0.328559i	$-0.106563\pi$
$662$	11.2441	+	3.30157i	0.437015	+	0.128319i
$663$	−5.35635	−	11.7288i	−0.208023	−	0.455507i
$664$	−0.535169	−	3.72218i	−0.0207686	−	0.144449i
$665$	4.76785	+	3.06411i	0.184889	+	0.118821i
$666$	20.3288			0.787725
$667$	−15.0920	+	32.7501i	−0.584366	+	1.26809i
$668$	20.0577			0.776056
$669$	9.75782	+	6.27097i	0.377259	+	0.242450i
$670$	−0.657710	−	4.57447i	−0.0254095	−	0.176727i
$671$	−3.56653	−	7.80960i	−0.137684	−	0.301486i
$672$	3.98191	+	1.16920i	0.153606	+	0.0451027i
$673$	−20.9307	+	45.8319i	−0.806820	+	1.76669i	−0.186308	+	0.982491i	$0.559652\pi$
$673$	−20.9307	+	45.8319i	−0.806820	+	1.76669i	−0.620512	+	0.784197i	$0.713075\pi$
$674$	−14.4882	+	16.7203i	−0.558064	+	0.644040i
$675$	−0.273081	+	1.89932i	−0.0105109	+	0.0731048i
$676$	−5.67306	+	1.66576i	−0.218194	+	0.0640677i
$677$	9.94454	+	11.4766i	0.382200	+	0.441082i	0.913955	−	0.405816i	$-0.133013\pi$
$677$	9.94454	+	11.4766i	0.382200	+	0.441082i	−0.531755	+	0.846898i	$0.678467\pi$
$678$	16.7231	−	10.7473i	0.642247	−	0.412747i
$679$	−6.91213	+	4.44216i	−0.265263	+	0.170474i
$680$	−0.747924	−	0.863150i	−0.0286816	−	0.0331003i
$681$	−5.58697	+	1.64048i	−0.214093	+	0.0628634i
$682$	−1.62442	+	11.2981i	−0.0622024	+	0.432628i
$683$	7.22247	−	8.33517i	0.276360	−	0.318937i	−0.600554	−	0.799585i	$-0.705053\pi$
$683$	7.22247	−	8.33517i	0.276360	−	0.318937i	0.876914	+	0.480648i	$0.159599\pi$
$684$	5.50687	−	12.0584i	0.210560	−	0.461063i
$685$	−12.6155	−	3.70425i	−0.482014	−	0.141532i
$686$	7.60015	+	16.6420i	0.290175	+	0.635395i
$687$	−1.63088	−	11.3430i	−0.0622219	−	0.432763i
$688$	−5.57343	−	3.58183i	−0.212485	−	0.136556i
$689$	8.44490			0.321725
$690$	8.18509	−	9.38109i	0.311601	−	0.357132i
$691$	−32.0587			−1.21957			−0.609785	−	0.792567i	$-0.708744\pi$
$691$	−32.0587			−1.21957			−0.609785	+	0.792567i	$0.708744\pi$
$692$	−4.35740	−	2.80033i	−0.165643	−	0.106453i
$693$	1.47550	+	10.2623i	0.0560495	+	0.389833i
$694$	−10.3229	−	22.6040i	−0.391852	−	0.858037i
$695$	−10.1529	−	2.98115i	−0.385121	−	0.113082i
$696$	−8.10866	+	17.7555i	−0.307358	+	0.673020i
$697$	1.99333	−	2.30042i	0.0755026	−	0.0871347i
$698$	−1.37901	+	9.59122i	−0.0521963	+	0.363033i
$699$	−11.1617	+	3.27737i	−0.422174	+	0.123962i
$700$	1.04688	+	1.20816i	0.0395683	+	0.0456642i
$701$	33.2863	−	21.3918i	1.25721	−	0.807957i	0.269306	−	0.963055i	$-0.413206\pi$
$701$	33.2863	−	21.3918i	1.25721	−	0.807957i	0.987899	+	0.155098i	$0.0495693\pi$
$702$	7.02010	−	4.51154i	0.264956	−	0.170277i
$703$	−12.6222	−	14.5668i	−0.476056	−	0.549397i
$704$	−1.66421	+	0.488657i	−0.0627224	+	0.0184170i
$705$	3.89888	−	27.1173i	0.146840	−	1.02130i
$706$	−20.6224	+	23.7995i	−0.776135	+	0.895708i
$707$	11.5365	−	25.2614i	0.433875	−	0.950053i
$708$	−27.4918	−	8.07232i	−1.03320	−	0.303376i
$709$	4.98169	+	10.9084i	0.187091	+	0.409673i	0.979814	−	0.199909i	$-0.0640647\pi$
$709$	4.98169	+	10.9084i	0.187091	+	0.409673i	−0.792723	+	0.609582i	$0.791337\pi$
$710$	1.06617	+	7.41536i	0.0400126	+	0.278294i
$711$	49.1623	+	31.5947i	1.84373	+	1.18489i
$712$	14.4449			0.541347
$713$	−4.59835	+	31.2239i	−0.172209	+	1.16934i
$714$	4.73979			0.177382
$715$	−6.34555	−	4.07804i	−0.237310	−	0.152510i
$716$	1.05757	+	7.35557i	0.0395233	+	0.274891i
$717$	5.38834	+	11.7988i	0.201231	+	0.440635i
$718$	23.4141	+	6.87499i	0.873806	+	0.256572i
$719$	9.63967	−	21.1079i	0.359499	−	0.787193i	−0.640319	−	0.768109i	$-0.721198\pi$
$719$	9.63967	−	21.1079i	0.359499	−	0.787193i	0.999818	−	0.0190837i	$-0.00607489\pi$
$720$	2.44863	−	2.82587i	0.0912550	−	0.105314i
$721$	3.67749	−	25.5775i	0.136957	−	0.952557i
$722$	6.17060	−	1.81185i	0.229646	−	0.0674301i
$723$	26.4555	+	30.5313i	0.983891	+	1.13547i
$724$	6.25986	−	4.02297i	0.232646	−	0.149512i
$725$	−6.32545	+	4.06512i	−0.234921	+	0.150975i
$726$	13.5858	+	15.6789i	0.504217	+	0.581898i
$727$	−45.5370	+	13.3709i	−1.68888	+	0.495899i	−0.978208	−	0.207629i	$-0.933425\pi$
$727$	−45.5370	+	13.3709i	−1.68888	+	0.495899i	−0.710668	+	0.703528i	$0.751607\pi$
$728$	0.989401	−	6.88144i	0.0366697	−	0.255043i
$729$	25.0563	−	28.9165i	0.928009	−	1.07098i
$730$	−1.34963	+	2.95528i	−0.0499521	+	0.109380i
$731$	−7.26016	−	2.13178i	−0.268527	−	0.0788466i
$732$	−5.33803	−	11.6887i	−0.197299	−	0.432025i
$733$	0.0150415	+	0.104616i	0.000555570	+	0.00386407i	0.990097	−	0.140383i	$-0.0448332\pi$
$733$	0.0150415	+	0.104616i	0.000555570	+	0.00386407i	−0.989542	+	0.144247i	$0.953924\pi$
$734$	−18.9002	−	12.1464i	−0.697618	−	0.448332i
$735$	11.5376			0.425570
$736$	−4.60616	+	1.33540i	−0.169785	+	0.0492235i
$737$	−8.01588			−0.295269
$738$	8.38344	+	5.38771i	0.308599	+	0.198324i
$739$	−1.01845	−	7.08344i	−0.0374641	−	0.260569i	0.962478	−	0.271361i	$-0.0874737\pi$
$739$	−1.01845	−	7.08344i	−0.0374641	−	0.260569i	−0.999942	+	0.0107923i	$0.996565\pi$
$740$	−2.25850	−	4.94542i	−0.0830241	−	0.181797i
$741$	−38.4033	−	11.2762i	−1.41078	−	0.414242i
$742$	−1.28958	+	2.82379i	−0.0473420	+	0.103665i
$743$	8.14367	−	9.39830i	0.298762	−	0.344790i	−0.586443	−	0.809990i	$-0.699472\pi$
$743$	8.14367	−	9.39830i	0.298762	−	0.344790i	0.885205	+	0.465200i	$0.154018\pi$
$744$	−2.43128	+	16.9099i	−0.0891351	+	0.619948i
$745$	15.2246	−	4.47034i	0.557786	−	0.163781i
$746$	−7.34032	−	8.47119i	−0.268748	−	0.310152i
$747$	11.8288	−	7.60193i	0.432794	−	0.278140i
$748$	−1.66649	+	1.07099i	−0.0609329	+	0.0391592i
$749$	−18.6358	−	21.5069i	−0.680939	−	0.785845i
$750$	2.49083	−	0.731375i	0.0909524	−	0.0267060i
$751$	0.825322	−	5.74024i	0.0301164	−	0.209464i	−0.969207	−	0.246248i	$-0.920802\pi$
$751$	0.825322	−	5.74024i	0.0301164	−	0.209464i	0.999323	+	0.0367837i	$0.0117113\pi$
$752$	−6.91091	+	7.97562i	−0.252015	+	0.290841i
$753$	−8.03067	+	17.5847i	−0.292654	+	0.640822i
$754$	31.3748	+	9.21248i	1.14260	+	0.335499i
$755$	8.88330	+	19.4517i	0.323296	+	0.707920i
$756$	0.436555	+	3.03630i	0.0158773	+	0.110429i
$757$	−24.7813	−	15.9260i	−0.900693	−	0.578840i	0.00630264	−	0.999980i	$-0.497994\pi$
$757$	−24.7813	−	15.9260i	−0.900693	−	0.578840i	−0.906996	+	0.421140i	$0.861630\pi$
$758$	21.7078			0.788461
$759$	−14.0852	−	16.3679i	−0.511260	−	0.594119i
$760$	−3.54526			−0.128600
$761$	−8.05368	−	5.17578i	−0.291946	−	0.187622i	0.386467	−	0.922303i	$-0.373695\pi$
$761$	−8.05368	−	5.17578i	−0.291946	−	0.187622i	−0.678412	+	0.734681i	$0.737332\pi$
$762$	5.01807	+	34.9014i	0.181786	+	1.26435i
$763$	10.8819	+	23.8280i	0.393951	+	0.862632i
$764$	0.0164351	+	0.00482579i	0.000594602	+	0.000174591i
$765$	1.77405	−	3.88462i	0.0641407	−	0.140449i
$766$	−0.528534	+	0.609960i	−0.0190967	+	0.0220388i
$767$	−6.83099	+	47.5106i	−0.246653	+	1.71551i
$768$	−2.49083	+	0.731375i	−0.0898802	+	0.0263912i
$769$	−13.8825	−	16.0213i	−0.500617	−	0.577743i	0.448054	−	0.894006i	$-0.352117\pi$
$769$	−13.8825	−	16.0213i	−0.500617	−	0.577743i	−0.948671	+	0.316263i	$0.897572\pi$
$770$	2.33261	−	1.49907i	0.0840613	−	0.0540229i
$771$	49.4560	−	31.7835i	1.78112	−	1.14465i
$772$	−5.24215	−	6.04977i	−0.188669	−	0.217736i
$773$	8.92689	−	2.62117i	0.321078	−	0.0942769i	−0.117222	−	0.993106i	$-0.537399\pi$
$773$	8.92689	−	2.62117i	0.321078	−	0.0942769i	0.438300	+	0.898829i	$0.355581\pi$
$774$	3.52549	−	24.5204i	0.126721	−	0.881366i
$775$	−4.30954	+	4.97348i	−0.154803	+	0.178653i
$776$	2.13511	−	4.67524i	0.0766459	−	0.167831i
$777$	21.6486	+	6.35660i	0.776639	+	0.228042i
$778$	12.6830	+	27.7718i	0.454706	+	0.995668i
$779$	−1.34468	−	9.35247i	−0.0481783	−	0.335087i
$780$	−9.49740	−	6.10361i	−0.340062	−	0.218544i
$781$	12.9940			0.464962
$782$	−4.61796	+	2.94552i	−0.165138	+	0.105332i
$783$	−14.4280			−0.515614
$784$	−3.73886	−	2.40282i	−0.133531	−	0.0858150i
$785$	−2.63345	−	18.3160i	−0.0939917	−	0.653727i
$786$	4.18647	+	9.16710i	0.149327	+	0.326980i
$787$	−24.7756	−	7.27477i	−0.883155	−	0.259318i	−0.191454	−	0.981502i	$-0.561320\pi$
$787$	−24.7756	−	7.27477i	−0.883155	−	0.259318i	−0.691701	+	0.722184i	$0.743138\pi$
$788$	4.83391	−	10.5848i	0.172201	−	0.377067i
$789$	−29.0718	+	33.5506i	−1.03498	+	1.19443i
$790$	2.22424	−	15.4699i	0.0791349	−	0.550396i
$791$	11.7456	−	3.44883i	0.417627	−	0.122626i
$792$	−4.24708	−	4.90139i	−0.150913	−	0.174163i
$793$	−18.1092	+	11.6380i	−0.643075	+	0.413279i
$794$	5.95801	−	3.82898i	0.211442	−	0.135885i
$795$	3.30119	+	3.80978i	0.117081	+	0.135119i
$796$	−17.4255	+	5.11659i	−0.617630	+	0.181353i
$797$	4.77137	−	33.1856i	0.169011	−	1.17549i	−0.711924	−	0.702256i	$-0.752176\pi$
$797$	4.77137	−	33.1856i	0.169011	−	1.17549i	0.880935	−	0.473238i	$-0.156915\pi$
$798$	9.63491	−	11.1193i	0.341072	−	0.393618i
$799$	−5.00700	+	10.9638i	−0.177135	+	0.387871i
$800$	−0.959493	−	0.281733i	−0.0339232	−	0.00996075i
$801$	22.4374	+	49.1310i	0.792786	+	1.73596i
$802$	1.85596	+	12.9085i	0.0655363	+	0.455815i
$803$	4.74053	+	3.04655i	0.167290	+	0.107511i
$804$	−11.9974			−0.423115
$805$	6.46381	−	4.12288i	0.227820	−	0.145312i
$806$	28.6192			1.00807
$807$	−8.39443	−	5.39477i	−0.295498	−	0.189905i
$808$	2.47226	+	17.1950i	0.0869739	+	0.604917i
$809$	−4.95950	−	10.8598i	−0.174367	−	0.381810i	0.802190	−	0.597068i	$-0.203668\pi$
$809$	−4.95950	−	10.8598i	−0.174367	−	0.381810i	−0.976557	+	0.215258i	$0.930941\pi$
$810$	−5.98356	−	1.75693i	−0.210241	−	0.0617322i
$811$	−7.96606	+	17.4432i	−0.279726	+	0.612515i	−0.996389	−	0.0849046i	$-0.972941\pi$
$811$	−7.96606	+	17.4432i	−0.279726	+	0.612515i	0.716663	+	0.697420i	$0.245669\pi$
$812$	−7.87155	+	9.08426i	−0.276237	+	0.318795i
$813$	5.07569	−	35.3022i	0.178012	−	1.23810i
$814$	−9.04788	+	2.65670i	−0.317128	+	0.0931172i
$815$	−5.17800	−	5.97573i	−0.181378	−	0.209321i
$816$	−2.49424	+	1.60295i	−0.0873159	+	0.0561145i
$817$	−19.7593	+	12.6985i	−0.691290	+	0.444265i
$818$	−6.10367	−	7.04401i	−0.213410	−	0.246288i
$819$	24.9424	−	7.32375i	0.871558	−	0.255912i
$820$	0.379290	−	2.63802i	0.0132454	−	0.0921236i
$821$	−24.7886	+	28.6076i	−0.865130	+	0.998413i	0.134842	+	0.990867i	$0.456947\pi$
$821$	−24.7886	+	28.6076i	−0.865130	+	0.998413i	−0.999972	+	0.00754569i	$0.997598\pi$
$822$	−14.1791	+	31.0479i	−0.494552	+	1.08292i
$823$	36.0348	+	10.5808i	1.25609	+	0.368823i	0.841039	−	0.540974i	$-0.181944\pi$
$823$	36.0348	+	10.5808i	1.25609	+	0.368823i	0.415055	+	0.909796i	$0.363762\pi$
$824$	6.71485	+	14.7035i	0.233923	+	0.512220i
$825$	−0.640797	−	4.45684i	−0.0223097	−	0.155167i
$826$	−14.8434	−	9.53925i	−0.516467	−	0.331913i
$827$	10.0150			0.348256			0.174128	−	0.984723i	$-0.444289\pi$
$827$	10.0150			0.348256			0.174128	+	0.984723i	$0.444289\pi$
$828$	−11.6968	−	13.5925i	−0.406492	−	0.472371i
$829$	13.4848			0.468348			0.234174	−	0.972195i	$-0.424761\pi$
$829$	13.4848			0.468348			0.234174	+	0.972195i	$0.424761\pi$
$830$	−3.16350	−	2.03306i	−0.109807	−	0.0705685i
$831$	3.29832	+	22.9403i	0.114417	+	0.795790i
$832$	1.80658	+	3.95586i	0.0626319	+	0.137145i
$833$	−4.87038	−	1.43007i	−0.168749	−	0.0495490i
$834$	−11.4112	+	24.9871i	−0.395139	+	0.865233i
$835$	13.1350	−	15.1586i	0.454556	−	0.524585i
$836$	−0.875117	+	6.08657i	−0.0302665	+	0.210508i
$837$	−12.1162	+	3.55763i	−0.418796	+	0.122970i
$838$	6.14391	+	7.09045i	0.212238	+	0.244936i
$839$	32.8284	−	21.0975i	1.13336	−	0.728368i	0.167103	−	0.985939i	$-0.446559\pi$
$839$	32.8284	−	21.0975i	1.13336	−	0.728368i	0.966259	+	0.257572i	$0.0829224\pi$
$840$	3.49122	−	2.24367i	0.120458	−	0.0774140i
$841$	−18.0325	−	20.8107i	−0.621812	−	0.717609i
$842$	26.8616	−	7.88729i	0.925713	−	0.271814i
$843$	−0.698196	+	4.85606i	−0.0240471	+	0.167252i
$844$	8.67897	−	10.0161i	0.298743	−	0.344767i
$845$	−2.45616	+	5.37825i	−0.0844946	+	0.185017i
$846$	−37.8619	−	11.1173i	−1.30172	−	0.382219i
$847$	5.30718	+	11.6211i	0.182357	+	0.399306i
$848$	−0.276356	−	1.92210i	−0.00949012	−	0.0660052i
$849$	−53.4334	−	34.3395i	−1.83383	−	1.17853i
$850$	−1.14211			−0.0391741
$851$	−25.0425	+	7.26021i	−0.858444	+	0.248877i
$852$	19.4482			0.666283
$853$	24.3971	+	15.6790i	0.835340	+	0.536840i	0.886971	−	0.461826i	$-0.152806\pi$
$853$	24.3971	+	15.6790i	0.835340	+	0.536840i	−0.0516308	+	0.998666i	$0.516442\pi$
$854$	−1.12614	−	7.83250i	−0.0385358	−	0.268023i
$855$	−5.50687	−	12.0584i	−0.188331	−	0.412387i
$856$	17.0803	+	5.01522i	0.583791	+	0.171417i
$857$	−15.6689	+	34.3101i	−0.535240	+	1.17201i	0.428101	+	0.903731i	$0.359183\pi$
$857$	−15.6689	+	34.3101i	−0.535240	+	1.17201i	−0.963341	+	0.268281i	$0.913544\pi$
$858$	−12.8231	+	14.7987i	−0.437774	+	0.505219i
$859$	0.247461	−	1.72113i	0.00844325	−	0.0587241i	−0.985164	−	0.171614i	$-0.945102\pi$
$859$	0.247461	−	1.72113i	0.00844325	−	0.0587241i	0.993607	+	0.112890i	$0.0360108\pi$
$860$	−6.35679	+	1.86652i	−0.216765	+	0.0636478i
$861$	7.24303	+	8.35890i	0.246842	+	0.284871i
$862$	−2.96853	+	1.90776i	−0.101109	+	0.0649786i
$863$	7.70132	−	4.94934i	0.262156	−	0.168477i	−0.402960	−	0.915218i	$-0.632019\pi$
$863$	7.70132	−	4.94934i	0.262156	−	0.168477i	0.665116	+	0.746740i	$0.268382\pi$
$864$	−1.25658	−	1.45017i	−0.0427497	−	0.0493358i
$865$	−4.96984	+	1.45928i	−0.168980	+	0.0496169i
$866$	5.09818	−	35.4586i	0.173243	−	1.20493i
$867$	26.6827	−	30.7934i	0.906191	−	1.04580i
$868$	−4.37031	+	9.56963i	−0.148338	+	0.324815i
$869$	−26.0100	−	7.63723i	−0.882329	−	0.259075i
$870$	8.10866	+	17.7555i	0.274909	+	0.601968i
$871$	2.86029	+	19.8937i	0.0969171	+	0.674073i
$872$	−13.7848	−	8.85898i	−0.466814	−	0.300003i
$873$	19.2182			0.650436
$874$	−2.47724	+	16.8211i	−0.0837939	+	0.568981i
$875$	1.59863			0.0540435
$876$	7.09517	+	4.55979i	0.239723	+	0.154061i
$877$	−1.58883	−	11.0505i	−0.0536509	−	0.373150i	−0.998904	−	0.0468113i	$-0.985094\pi$
$877$	−1.58883	−	11.0505i	−0.0536509	−	0.373150i	0.945253	−	0.326339i	$-0.105815\pi$
$878$	−11.8731	−	25.9985i	−0.400698	−	0.877407i
$879$	64.4146	+	18.9138i	2.17265	+	0.637948i
$880$	−0.720525	+	1.57773i	−0.0242889	+	0.0531853i
$881$	29.1046	−	33.5885i	0.980559	−	1.13163i	−0.0107329	−	0.999942i	$-0.503416\pi$
$881$	29.1046	−	33.5885i	0.980559	−	1.13163i	0.991292	−	0.131683i	$-0.0420381\pi$
$882$	2.36503	−	16.4491i	0.0796347	−	0.553871i
$883$	−2.57093	+	0.754894i	−0.0865188	+	0.0254042i	−0.324705	−	0.945815i	$-0.605265\pi$
$883$	−2.57093	+	0.754894i	−0.0865188	+	0.0254042i	0.238187	+	0.971219i	$0.423447\pi$
$884$	3.25261	+	3.75372i	0.109397	+	0.126251i
$885$	−24.1039	+	15.4907i	−0.810245	+	0.520713i
$886$	−24.5926	+	15.8047i	−0.826205	+	0.530970i
$887$	−2.32107	−	2.67866i	−0.0779339	−	0.0899405i	0.715443	−	0.698671i	$-0.246225\pi$
$887$	−2.32107	−	2.67866i	−0.0779339	−	0.0899405i	−0.793377	+	0.608730i	$0.791679\pi$
$888$	−13.5420	+	3.97629i	−0.454439	+	0.133435i
$889$	−3.09016	+	21.4925i	−0.103641	+	0.720837i
$890$	9.45943	−	10.9168i	0.317081	−	0.365931i
$891$	−4.49332	+	9.83899i	−0.150532	+	0.329618i
$892$	−4.28711	−	1.25881i	−0.143543	−	0.0421481i
$893$	15.5424	+	34.0330i	0.520106	+	1.13887i
$894$	−5.86215	−	40.7721i	−0.196060	−	1.36362i
$895$	6.25153	+	4.01761i	0.208966	+	0.134294i
$896$	−1.59863			−0.0534064
$897$	−35.5958	+	40.7970i	−1.18851	+	1.36217i
$898$	−34.5057			−1.15147
$899$	−41.6268	−	26.7520i	−1.38833	−	0.892228i
$900$	−0.532138	−	3.70110i	−0.0177379	−	0.123370i
$901$	−0.921319	−	2.01741i	−0.0306936	−	0.0672096i
$902$	−4.43537	−	1.30234i	−0.147682	−	0.0433633i
$903$	11.4216	−	25.0099i	0.380088	−	0.832277i
$904$	−5.01460	+	5.78716i	−0.166783	+	0.192478i
$905$	1.05898	−	7.36537i	0.0352017	−	0.244833i
$906$	53.2644	−	15.6398i	1.76959	−	0.519599i
$907$	21.3564	+	24.6466i	0.709127	+	0.818376i	0.989955	−	0.141382i	$-0.0451545\pi$
$907$	21.3564	+	24.6466i	0.709127	+	0.818376i	−0.280828	+	0.959758i	$0.590609\pi$
$908$	1.88694	−	1.21266i	0.0626204	−	0.0402437i
$909$	−54.6444	+	35.1178i	−1.81244	+	1.16478i
$910$	−4.55272	−	5.25412i	−0.150921	−	0.174173i
$911$	25.3225	−	7.43534i	0.838970	−	0.246344i	0.166104	−	0.986108i	$-0.446881\pi$
$911$	25.3225	−	7.43534i	0.838970	−	0.246344i	0.672866	+	0.739764i	$0.265063\pi$
$912$	−1.30979	+	9.10979i	−0.0433715	+	0.301655i
$913$	−4.27127	+	4.92931i	−0.141358	+	0.163136i
$914$	6.44829	−	14.1198i	0.213290	−	0.467041i
$915$	−12.3294	−	3.62023i	−0.407596	−	0.119681i
$916$	1.83379	+	4.01545i	0.0605903	+	0.132674i
$917$	0.883203	+	6.14282i	0.0291659	+	0.202854i
$918$	−1.84364	−	1.18484i	−0.0608492	−	0.0391054i
$919$	40.1988			1.32604			0.663019	−	0.748603i	$-0.269275\pi$
$919$	40.1988			1.32604			0.663019	+	0.748603i	$0.269275\pi$
$920$	−2.00717	+	4.35560i	−0.0661743	+	0.143600i
$921$	−7.75973			−0.255692
$922$	−17.5848	−	11.3011i	−0.579124	−	0.372180i
$923$	−4.63661	−	32.2483i	−0.152616	−	1.06147i
$924$	−2.99019	−	6.54761i	−0.0983702	−	0.215401i
$925$	−5.21650	−	1.53170i	−0.171518	−	0.0503621i
$926$	7.68319	−	16.8238i	0.252485	−	0.552866i
$927$	−39.5801	+	45.6779i	−1.29998	+	1.50026i
$928$	1.07008	−	7.44254i	0.0351270	−	0.244313i
$929$	16.6979	−	4.90293i	0.547839	−	0.160860i	0.00391161	−	0.999992i	$-0.498755\pi$
$929$	16.6979	−	4.90293i	0.547839	−	0.160860i	0.543927	+	0.839132i	$0.316937\pi$
$930$	11.1875	+	12.9111i	0.366854	+	0.423372i
$931$	−13.2552	+	8.51863i	−0.434423	+	0.279187i
$932$	3.76975	−	2.42267i	0.123482	−	0.0793572i
$933$	−52.1148	−	60.1437i	−1.70616	−	1.96902i
$934$	1.81762	−	0.533702i	0.0594745	−	0.0174633i
$935$	−0.281920	+	1.96080i	−0.00921977	+	0.0641249i
$936$	−10.6487	+	12.2893i	−0.348065	+	0.401688i
$937$	−19.4826	+	42.6610i	−0.636470	+	1.39368i	0.266442	+	0.963851i	$0.414152\pi$
$937$	−19.4826	+	42.6610i	−0.636470	+	1.39368i	−0.902912	+	0.429825i	$0.858575\pi$
$938$	−7.08881	−	2.08146i	−0.231458	−	0.0679621i
$939$	8.38147	+	18.3529i	0.273519	+	0.598923i
$940$	1.50189	+	10.4458i	0.0489861	+	0.340706i
$941$	0.492573	+	0.316557i	0.0160574	+	0.0103195i	0.548645	−	0.836055i	$-0.315144\pi$
$941$	0.492573	+	0.316557i	0.0160574	+	0.0103195i	−0.532587	+	0.846375i	$0.678780\pi$
$942$	−48.0371			−1.56513
$943$	−12.2515	−	3.64291i	−0.398963	−	0.118629i
$944$	11.0372			0.359230
$945$	2.58057	+	1.65843i	0.0839459	+	0.0539487i
$946$	1.63536	+	11.3742i	0.0531701	+	0.369806i
$947$	1.98784	+	4.35277i	0.0645962	+	0.141446i	0.939177	−	0.343435i	$-0.111590\pi$
$947$	1.98784	+	4.35277i	0.0645962	+	0.141446i	−0.874580	+	0.484881i	$0.838863\pi$
$948$	−38.9293	−	11.4307i	−1.26436	−	0.371251i
$949$	5.86935	−	12.8521i	0.190527	−	0.417196i
$950$	−2.32165	+	2.67933i	−0.0753244	+	0.0869290i
$951$	6.44423	−	44.8206i	0.208968	−	1.45341i
$952$	−1.75185	+	0.514390i	−0.0567779	+	0.0166715i
$953$	15.5341	+	17.9273i	0.503200	+	0.580723i	0.949344	−	0.314237i	$-0.101749\pi$
$953$	15.5341	+	17.9273i	0.503200	+	0.580723i	−0.446145	+	0.894961i	$0.647203\pi$
$954$	6.10830	−	3.92556i	0.197763	−	0.127095i
$955$	0.0144098	−	0.00926062i	0.000466291	−	0.000299667i
$956$	−3.27204	−	3.77614i	−0.105825	−	0.122129i
$957$	32.4845	−	9.53831i	1.05007	−	0.308330i
$958$	−3.16139	+	21.9880i	−0.102140	+	0.710399i
$959$	−13.7645	+	15.8850i	−0.444478	+	0.512955i
$960$	−1.07841	+	2.36139i	−0.0348056	+	0.0762137i
$961$	−11.8091	−	3.46747i	−0.380939	−	0.111854i
$962$	9.82189	+	21.5069i	0.316670	+	0.693412i
$963$	9.47277	+	65.8846i	0.305256	+	2.12310i
$964$	−13.0916	−	8.41343i	−0.421651	−	0.270978i
$965$	−8.00499			−0.257690
$966$	−8.20596	−	18.1324i	−0.264023	−	0.583400i
$967$	26.4416			0.850305			0.425153	−	0.905122i	$-0.360220\pi$
$967$	26.4416			0.850305			0.425153	+	0.905122i	$0.360220\pi$
$968$	−6.72297	−	4.32059i	−0.216084	−	0.138869i
$969$	1.49593	+	10.4044i	0.0480561	+	0.334237i
$970$	−2.13511	−	4.67524i	−0.0685542	−	0.150113i
$971$	−46.5531	−	13.6692i	−1.49396	−	0.438666i	−0.570157	−	0.821535i	$-0.693118\pi$
$971$	−46.5531	−	13.6692i	−1.49396	−	0.438666i	−0.923803	+	0.382869i	$0.874936\pi$
$972$	−9.11652	+	19.9624i	−0.292412	+	0.640294i
$973$	−11.0775	+	12.7842i	−0.355130	+	0.409842i
$974$	−0.901094	+	6.26725i	−0.0288729	+	0.200816i
$975$	−10.8323	+	3.18064i	−0.346911	+	0.101862i
$976$	3.24149	+	3.74088i	0.103758	+	0.119743i
$977$	42.5110	−	27.3202i	1.36005	−	0.874050i	0.361745	−	0.932277i	$-0.382181\pi$
$977$	42.5110	−	27.3202i	1.36005	−	0.874050i	0.998303	+	0.0582270i	$0.0185447\pi$
$978$	−17.2680	+	11.0975i	−0.552171	+	0.354859i
$979$	−16.4071	−	18.9348i	−0.524373	−	0.605159i
$980$	−4.26436	+	1.25213i	−0.136220	+	0.0399978i
$981$	8.71965	−	60.6465i	0.278397	−	1.93629i
$982$	−2.53259	+	2.92276i	−0.0808181	+	0.0932691i
$983$	−2.75867	+	6.04065i	−0.0879880	+	0.192667i	−0.948511	−	0.316745i	$-0.897410\pi$
$983$	−2.75867	+	6.04065i	−0.0879880	+	0.192667i	0.860523	+	0.509412i	$0.170137\pi$
$984$	−6.63844	−	1.94922i	−0.211626	−	0.0621389i
$985$	−4.83391	−	10.5848i	−0.154021	−	0.337259i
$986$	−1.22215	−	8.50021i	−0.0389210	−	0.270702i
$987$	−36.8437	−	23.6780i	−1.17275	−	0.753680i
$988$	15.4178			0.490507
$989$	4.41422	+	31.4650i	0.140364	+	1.00053i
$990$	−6.48547			−0.206122
$991$	51.3452	+	32.9975i	1.63103	+	1.04820i	0.948223	+	0.317606i	$0.102879\pi$
$991$	51.3452	+	32.9975i	1.63103	+	1.04820i	0.682811	+	0.730595i	$0.260757\pi$
$992$	−0.936553	−	6.51387i	−0.0297356	−	0.206816i
$993$	−12.6377	−	27.6727i	−0.401046	−	0.878167i
$994$	11.4912	+	3.37411i	0.364478	+	0.107020i
$995$	−7.54441	+	16.5200i	−0.239174	+	0.523718i
$996$	−6.39282	+	7.37771i	−0.202564	+	0.233772i
$997$	−5.27926	+	36.7180i	−0.167196	+	1.16287i	0.717451	+	0.696609i	$0.245309\pi$
$997$	−5.27926	+	36.7180i	−0.167196	+	1.16287i	−0.884646	+	0.466263i	$0.845600\pi$
$998$	18.0866	−	5.31071i	0.572522	−	0.168108i
$999$	−6.83169	−	7.88419i	−0.216145	−	0.249445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.g.d.71.1	✓	30
23.9	even	11		5290.2.a.bk.1.11		15
23.12	even	11	inner	230.2.g.d.81.1	yes	30
23.14	odd	22		5290.2.a.bl.1.11		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.d.71.1	✓	30	1.1	even	1	trivial
230.2.g.d.81.1	yes	30	23.12	even	11	inner
5290.2.a.bk.1.11		15	23.9	even	11
5290.2.a.bl.1.11		15	23.14	odd	22

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 + 0.540641i) q^{2} +(-0.369448 - 2.56957i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(1.07841 - 2.36139i) q^{6} +(1.04688 - 1.20816i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-3.58770 + 1.05344i) q^{9} +O(q^{10})\)	\(q+(0.841254 + 0.540641i) q^{2} +(-0.369448 - 2.56957i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(1.07841 - 2.36139i) q^{6} +(1.04688 - 1.20816i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-3.58770 + 1.05344i) q^{9} +(0.654861 + 0.755750i) q^{10} +(1.45913 - 0.937726i) q^{11} +(2.18389 - 1.40350i) q^{12} +(-2.84790 - 3.28665i) q^{13} +(1.53387 - 0.450385i) q^{14} +(0.369448 - 2.56957i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-0.474450 + 1.03890i) q^{17} +(-3.58770 - 1.05344i) q^{18} +(1.47276 + 3.22489i) q^{19} +(0.142315 + 0.989821i) q^{20} +(-3.49122 - 2.24367i) q^{21} +1.73447 q^{22} +(4.79580 + 0.0163991i) q^{23} +2.59599 q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.618907 - 4.30459i) q^{26} +(0.797119 + 1.74545i) q^{27} +(1.53387 + 0.450385i) q^{28} +(-3.12354 + 6.83959i) q^{29} +(1.70001 - 1.96192i) q^{30} +(-0.936553 + 6.51387i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(-2.94862 - 3.40289i) q^{33} +(-0.960805 + 0.617472i) q^{34} +(1.34485 - 0.864283i) q^{35} +(-2.44863 - 2.82587i) q^{36} +(-5.21650 + 1.53170i) q^{37} +(-0.504544 + 3.50918i) q^{38} +(-7.39311 + 8.53210i) q^{39} +(-0.415415 + 0.909632i) q^{40} +(-2.55719 - 0.750859i) q^{41} +(-1.72398 - 3.77499i) q^{42} +(0.942858 + 6.55772i) q^{43} +(1.45913 + 0.937726i) q^{44} -3.73916 q^{45} +(4.02562 + 2.60660i) q^{46} +10.5533 q^{47} +(2.18389 + 1.40350i) q^{48} +(0.632503 + 4.39915i) q^{49} +(0.415415 + 0.909632i) q^{50} +(2.84481 + 0.835311i) q^{51} +(1.80658 - 3.95586i) q^{52} +(-1.27165 + 1.46756i) q^{53} +(-0.273081 + 1.89932i) q^{54} +(1.66421 - 0.488657i) q^{55} +(1.04688 + 1.20816i) q^{56} +(7.74245 - 4.97577i) q^{57} +(-6.32545 + 4.06512i) q^{58} +(-7.22782 - 8.34135i) q^{59} +(2.49083 - 0.731375i) q^{60} +(0.704444 - 4.89951i) q^{61} +(-4.30954 + 4.97348i) q^{62} +(-2.48315 + 5.43735i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-1.80658 - 3.95586i) q^{65} +(-0.640797 - 4.45684i) q^{66} +(-3.88786 - 2.49858i) q^{67} -1.14211 q^{68} +(-1.72966 - 12.3292i) q^{69} +1.59863 q^{70} +(6.30235 + 4.05027i) q^{71} +(-0.532138 - 3.70110i) q^{72} +(1.34963 + 2.95528i) q^{73} +(-5.21650 - 1.53170i) q^{74} +(1.07841 - 2.36139i) q^{75} +(-2.32165 + 2.67933i) q^{76} +(0.394607 - 2.74455i) q^{77} +(-10.8323 + 3.18064i) q^{78} +(-10.2348 - 11.8116i) q^{79} +(-0.841254 + 0.540641i) q^{80} +(-5.24620 + 3.37152i) q^{81} +(-1.74530 - 2.01418i) q^{82} +(-3.60813 + 1.05944i) q^{83} +(0.590609 - 4.10778i) q^{84} +(-0.747924 + 0.863150i) q^{85} +(-2.75219 + 6.02645i) q^{86} +(18.7288 + 5.49926i) q^{87} +(0.720525 + 1.57773i) q^{88} +(-2.05573 - 14.2979i) q^{89} +(-3.14558 - 2.02154i) q^{90} -6.95220 q^{91} +(1.97733 + 4.36923i) q^{92} +17.0838 q^{93} +(8.87797 + 5.70552i) q^{94} +(0.504544 + 3.50918i) q^{95} +(1.07841 + 2.36139i) q^{96} +(-4.93151 - 1.44802i) q^{97} +(-1.84627 + 4.04276i) q^{98} +(-4.24708 + 4.90139i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) \) 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9	\( 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} - q^{12} + 12 q^{13} - 3 q^{14} + q^{15} - 3 q^{16} - 26 q^{17} + 12 q^{18} - 25 q^{19} + 3 q^{20} - 11 q^{21} - 14 q^{22} + 14 q^{23} + 10 q^{24} - 3 q^{25} - 10 q^{26} - 52 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} + 5 q^{31} - 3 q^{32} + 9 q^{33} + 7 q^{34} + 3 q^{35} + 12 q^{36} - 20 q^{37} + 19 q^{38} + 41 q^{39} + 3 q^{40} + 32 q^{41} + 22 q^{42} - 46 q^{43} - 3 q^{44} - 56 q^{45} + 3 q^{46} + 80 q^{47} - q^{48} - 41 q^{49} - 3 q^{50} - 34 q^{51} - 21 q^{52} + 29 q^{53} + 47 q^{54} + 3 q^{55} + 8 q^{56} - 33 q^{57} - 7 q^{58} - 3 q^{59} + q^{60} - q^{61} - 28 q^{62} - 8 q^{63} - 3 q^{64} + 21 q^{65} - 46 q^{66} - 63 q^{67} - 4 q^{68} + 78 q^{69} - 8 q^{70} + 55 q^{71} - 32 q^{72} - 36 q^{73} - 20 q^{74} - q^{75} - 3 q^{76} - 9 q^{77} - 80 q^{78} - 29 q^{79} + 3 q^{80} + 15 q^{81} - 23 q^{82} - 63 q^{83} + 4 q^{85} + 31 q^{86} + 63 q^{87} - 3 q^{88} - 95 q^{89} + 10 q^{90} - 12 q^{91} + 14 q^{92} + 126 q^{93} + 3 q^{94} - 19 q^{95} - q^{96} + 11 q^{97} + 58 q^{98} + 97 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 - q^12 + 12 * q^13 - 3 * q^14 + q^15 - 3 * q^16 - 26 * q^17 + 12 * q^18 - 25 * q^19 + 3 * q^20 - 11 * q^21 - 14 * q^22 + 14 * q^23 + 10 * q^24 - 3 * q^25 - 10 * q^26 - 52 * q^27 - 3 * q^28 + 4 * q^29 + q^30 + 5 * q^31 - 3 * q^32 + 9 * q^33 + 7 * q^34 + 3 * q^35 + 12 * q^36 - 20 * q^37 + 19 * q^38 + 41 * q^39 + 3 * q^40 + 32 * q^41 + 22 * q^42 - 46 * q^43 - 3 * q^44 - 56 * q^45 + 3 * q^46 + 80 * q^47 - q^48 - 41 * q^49 - 3 * q^50 - 34 * q^51 - 21 * q^52 + 29 * q^53 + 47 * q^54 + 3 * q^55 + 8 * q^56 - 33 * q^57 - 7 * q^58 - 3 * q^59 + q^60 - q^61 - 28 * q^62 - 8 * q^63 - 3 * q^64 + 21 * q^65 - 46 * q^66 - 63 * q^67 - 4 * q^68 + 78 * q^69 - 8 * q^70 + 55 * q^71 - 32 * q^72 - 36 * q^73 - 20 * q^74 - q^75 - 3 * q^76 - 9 * q^77 - 80 * q^78 - 29 * q^79 + 3 * q^80 + 15 * q^81 - 23 * q^82 - 63 * q^83 + 4 * q^85 + 31 * q^86 + 63 * q^87 - 3 * q^88 - 95 * q^89 + 10 * q^90 - 12 * q^91 + 14 * q^92 + 126 * q^93 + 3 * q^94 - 19 * q^95 - q^96 + 11 * q^97 + 58 * q^98 + 97 * q^99

Introduction

L-functions

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