LMFDB - Embedded newform 690.2.r.b.49.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(49,690)]

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, 11, 16]))

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

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

chi := DirichletCharacter("690.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			49.7
Character	$\chi$	$=$	690.49
Dual form			690.2.r.b.169.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.989821 - 0.142315i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(-2.14372 - 0.635975i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(2.47408 + 3.84974i) q^{7} +(0.909632 - 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.989821 - 0.142315i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(-2.14372 - 0.635975i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(2.47408 + 3.84974i) q^{7} +(0.909632 - 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-2.21241 - 0.324418i) q^{10} +(-0.00211055 + 0.0146792i) q^{11} +(-0.989821 - 0.142315i) q^{12} +(-1.93109 + 3.00483i) q^{13} +(2.99677 + 3.45846i) q^{14} +(1.68580 + 1.46904i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-0.817835 + 2.78529i) q^{17} +(0.755750 + 0.654861i) q^{18} +(7.13628 - 2.09540i) q^{19} +(-2.23606 - 0.00625769i) q^{20} +(-0.651260 - 4.52962i) q^{21} +0.0148302i q^{22} +(-4.29463 + 2.13452i) q^{23} -1.00000 q^{24} +(4.19107 + 2.72670i) q^{25} +(-1.48380 + 3.24907i) q^{26} +(-0.281733 - 0.959493i) q^{27} +(3.45846 + 2.99677i) q^{28} +(6.47189 + 1.90032i) q^{29} +(1.87771 + 1.21417i) q^{30} +(1.24883 + 2.73455i) q^{31} +(0.755750 - 0.654861i) q^{32} +(0.00801779 - 0.0124759i) q^{33} +(-0.413122 + 2.87333i) q^{34} +(-2.85539 - 9.82622i) q^{35} +(0.841254 + 0.540641i) q^{36} +(2.52487 - 2.18781i) q^{37} +(6.76544 - 3.08967i) q^{38} +(3.00483 - 1.93109i) q^{39} +(-2.21419 + 0.312030i) q^{40} +(-2.38170 + 2.74863i) q^{41} +(-1.28926 - 4.39083i) q^{42} +(6.63915 + 3.03200i) q^{43} +(0.00211055 + 0.0146792i) q^{44} +(-0.923200 - 2.03659i) q^{45} +(-3.94714 + 2.72399i) q^{46} -0.920854i q^{47} +(-0.989821 + 0.142315i) q^{48} +(-5.79153 + 12.6817i) q^{49} +(4.53646 + 2.10250i) q^{50} +(1.90098 - 2.19385i) q^{51} +(-1.00631 + 3.42716i) q^{52} +(-4.07432 - 6.33977i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(0.0138600 - 0.0301259i) q^{55} +(3.84974 + 2.47408i) q^{56} +(-7.36185 - 1.05847i) q^{57} +(6.67646 + 0.959930i) q^{58} +(7.23748 + 4.65125i) q^{59} +(2.03139 + 0.934585i) q^{60} +(-2.74195 - 6.00403i) q^{61} +(1.62528 + 2.52899i) q^{62} +(-1.28926 + 4.39083i) q^{63} +(0.654861 - 0.755750i) q^{64} +(6.05070 - 5.21339i) q^{65} +(0.00616067 - 0.0134900i) q^{66} +(-5.29761 + 0.761682i) q^{67} +2.90288i q^{68} +(4.79324 - 0.157578i) q^{69} +(-4.22474 - 9.31983i) q^{70} +(-1.86038 - 12.9392i) q^{71} +(0.909632 + 0.415415i) q^{72} +(1.35080 + 4.60039i) q^{73} +(2.18781 - 2.52487i) q^{74} +(-2.67962 - 4.22133i) q^{75} +(6.25687 - 4.02105i) q^{76} +(-0.0617328 + 0.0281924i) q^{77} +(2.69942 - 2.33906i) q^{78} +(-13.4044 - 8.61449i) q^{79} +(-2.14725 + 0.623966i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-1.96629 + 3.05961i) q^{82} +(-10.6189 + 9.20132i) q^{83} +(-1.90102 - 4.16265i) q^{84} +(3.52458 - 5.45076i) q^{85} +(7.00307 + 2.05629i) q^{86} +(-5.09762 - 4.41711i) q^{87} +(0.00417814 + 0.0142294i) q^{88} +(-3.94429 + 8.63679i) q^{89} +(-1.20364 - 1.88448i) q^{90} -16.3455 q^{91} +(-3.51930 + 3.25800i) q^{92} -3.00621i q^{93} +(-0.131051 - 0.911481i) q^{94} +(-16.6308 - 0.0465419i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(-4.85804 - 4.20952i) q^{97} +(-3.92779 + 13.3768i) q^{98} +(-0.0124759 + 0.00801779i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9	$ 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9} - 18 q^{10} - 8 q^{11} - 4 q^{15} - 12 q^{16} + 16 q^{19} + 14 q^{20} - 22 q^{21} - 120 q^{24} + 28 q^{25} + 8 q^{26} + 8 q^{29} + 8 q^{30} + 8 q^{31} + 44 q^{34} + 58 q^{35} - 12 q^{36} + 14 q^{39} - 4 q^{40} + 8 q^{44} - 8 q^{45} + 12 q^{49} - 4 q^{50} + 12 q^{54} + 92 q^{55} - 94 q^{59} + 4 q^{60} - 60 q^{61} + 12 q^{64} - 44 q^{65} - 8 q^{66} + 16 q^{70} - 16 q^{74} + 4 q^{75} - 16 q^{76} + 172 q^{79} + 8 q^{80} - 12 q^{81} - 32 q^{85} - 40 q^{86} + 48 q^{89} - 4 q^{90} + 288 q^{91} + 24 q^{94} - 78 q^{95} - 12 q^{96} - 36 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9 - 18 * q^10 - 8 * q^11 - 4 * q^15 - 12 * q^16 + 16 * q^19 + 14 * q^20 - 22 * q^21 - 120 * q^24 + 28 * q^25 + 8 * q^26 + 8 * q^29 + 8 * q^30 + 8 * q^31 + 44 * q^34 + 58 * q^35 - 12 * q^36 + 14 * q^39 - 4 * q^40 + 8 * q^44 - 8 * q^45 + 12 * q^49 - 4 * q^50 + 12 * q^54 + 92 * q^55 - 94 * q^59 + 4 * q^60 - 60 * q^61 + 12 * q^64 - 44 * q^65 - 8 * q^66 + 16 * q^70 - 16 * q^74 + 4 * q^75 - 16 * q^76 + 172 * q^79 + 8 * q^80 - 12 * q^81 - 32 * q^85 - 40 * q^86 + 48 * q^89 - 4 * q^90 + 288 * q^91 + 24 * q^94 - 78 * q^95 - 12 * q^96 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	0.989821	−	0.142315i	0.699909	−	0.100632i
$2$	0.989821	−	0.142315i	0.699909	−	0.100632i
$3$	−0.909632	−	0.415415i	−0.525176	−	0.239840i
$3$	−0.909632	−	0.415415i	−0.525176	−	0.239840i
$4$	0.959493	−	0.281733i	0.479746	−	0.140866i
$5$	−2.14372	−	0.635975i	−0.958701	−	0.284417i
$5$	−2.14372	−	0.635975i	−0.958701	−	0.284417i
$6$	−0.959493	−	0.281733i	−0.391711	−	0.115017i
$7$	2.47408	+	3.84974i	0.935113	+	1.45506i	0.889936	+	0.456086i	$0.150749\pi$
$7$	2.47408	+	3.84974i	0.935113	+	1.45506i	0.0451776	+	0.998979i	$0.485615\pi$
$8$	0.909632	−	0.415415i	0.321603	−	0.146871i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	−2.21241	−	0.324418i	−0.699625	−	0.102590i
$11$	−0.00211055	+	0.0146792i	−0.000636355	+	0.00442595i	−0.990137	−	0.140102i	$-0.955257\pi$
$11$	−0.00211055	+	0.0146792i	−0.000636355	+	0.00442595i	0.989501	+	0.144527i	$0.0461662\pi$
$12$	−0.989821	−	0.142315i	−0.285737	−	0.0410828i
$13$	−1.93109	+	3.00483i	−0.535587	+	0.833390i	−0.998596	−	0.0529637i	$-0.983133\pi$
$13$	−1.93109	+	3.00483i	−0.535587	+	0.833390i	0.463009	+	0.886353i	$0.346770\pi$
$14$	2.99677	+	3.45846i	0.800920	+	0.924312i
$15$	1.68580	+	1.46904i	0.435272	+	0.379304i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−0.817835	+	2.78529i	−0.198354	+	0.675532i	0.798899	+	0.601465i	$0.205416\pi$
$17$	−0.817835	+	2.78529i	−0.198354	+	0.675532i	−0.997253	+	0.0740670i	$0.976402\pi$
$18$	0.755750	+	0.654861i	0.178132	+	0.154352i
$19$	7.13628	−	2.09540i	1.63718	−	0.480718i	0.671616	−	0.740900i	$-0.265601\pi$
$19$	7.13628	−	2.09540i	1.63718	−	0.480718i	0.965560	+	0.260182i	$0.0837825\pi$
$20$	−2.23606	−	0.00625769i	−0.499998	−	0.00139926i
$21$	−0.651260	−	4.52962i	−0.142117	−	0.988443i
$22$			0.0148302i			0.00316180i
$23$	−4.29463	+	2.13452i	−0.895491	+	0.445079i
$23$	−4.29463	+	2.13452i	−0.895491	+	0.445079i
$24$	−1.00000			−0.204124
$25$	4.19107	+	2.72670i	0.838214	+	0.545341i
$26$	−1.48380	+	3.24907i	−0.290997	+	0.637194i
$27$	−0.281733	−	0.959493i	−0.0542195	−	0.184655i
$28$	3.45846	+	2.99677i	0.653587	+	0.566336i
$29$	6.47189	+	1.90032i	1.20180	+	0.352880i	0.820541	−	0.571588i	$-0.193672\pi$
$29$	6.47189	+	1.90032i	1.20180	+	0.352880i	0.381259	+	0.924468i	$0.375491\pi$
$30$	1.87771	+	1.21417i	0.342821	+	0.221676i
$31$	1.24883	+	2.73455i	0.224296	+	0.491139i	0.988005	−	0.154421i	$-0.0493513\pi$
$31$	1.24883	+	2.73455i	0.224296	+	0.491139i	−0.763710	+	0.645560i	$0.776624\pi$
$32$	0.755750	−	0.654861i	0.133599	−	0.115764i
$33$	0.00801779	−	0.0124759i	0.00139572	−	0.00217178i
$34$	−0.413122	+	2.87333i	−0.0708499	+	0.492772i
$35$	−2.85539	−	9.82622i	−0.482649	−	1.66093i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	2.52487	−	2.18781i	0.415086	−	0.359674i	−0.422140	−	0.906531i	$-0.638721\pi$
$37$	2.52487	−	2.18781i	0.415086	−	0.359674i	0.837227	+	0.546856i	$0.184176\pi$
$38$	6.76544	−	3.08967i	1.09750	−	0.501211i
$39$	3.00483	−	1.93109i	0.481158	−	0.309221i
$40$	−2.21419	+	0.312030i	−0.350094	+	0.0493363i
$41$	−2.38170	+	2.74863i	−0.371959	+	0.429264i	−0.910611	−	0.413265i	$-0.864388\pi$
$41$	−2.38170	+	2.74863i	−0.371959	+	0.429264i	0.538652	+	0.842529i	$0.318934\pi$
$42$	−1.28926	−	4.39083i	−0.198938	−	0.677519i
$43$	6.63915	+	3.03200i	1.01246	+	0.462375i	0.851371	−	0.524565i	$-0.175772\pi$
$43$	6.63915	+	3.03200i	1.01246	+	0.462375i	0.161090	+	0.986940i	$0.448499\pi$
$44$	0.00211055	+	0.0146792i	0.000318178	+	0.00221297i
$45$	−0.923200	−	2.03659i	−0.137623	−	0.303597i
$46$	−3.94714	+	2.72399i	−0.581974	+	0.401630i
$47$		−	0.920854i		−	0.134320i	−0.997742	−	0.0671602i	$-0.978606\pi$
$47$		−	0.920854i		−	0.134320i	0.997742	−	0.0671602i	$-0.0213938\pi$
$48$	−0.989821	+	0.142315i	−0.142868	+	0.0205414i
$49$	−5.79153	+	12.6817i	−0.827362	+	1.81167i
$50$	4.53646	+	2.10250i	0.641553	+	0.297338i
$51$	1.90098	−	2.19385i	0.266190	−	0.307200i
$52$	−1.00631	+	3.42716i	−0.139549	+	0.475262i
$53$	−4.07432	−	6.33977i	−0.559651	−	0.870835i	0.439979	−	0.898008i	$-0.354986\pi$
$53$	−4.07432	−	6.33977i	−0.559651	−	0.870835i	−0.999631	+	0.0271733i	$0.991349\pi$
$54$	−0.415415	−	0.909632i	−0.0565308	−	0.123785i
$55$	0.0138600	−	0.0301259i	0.00186889	−	0.00406217i
$56$	3.84974	+	2.47408i	0.514443	+	0.330613i
$57$	−7.36185	−	1.05847i	−0.975101	−	0.140198i
$58$	6.67646	+	0.959930i	0.876662	+	0.126045i
$59$	7.23748	+	4.65125i	0.942240	+	0.605541i	0.919029	−	0.394190i	$-0.128975\pi$
$59$	7.23748	+	4.65125i	0.942240	+	0.605541i	0.0232108	+	0.999731i	$0.492611\pi$
$60$	2.03139	+	0.934585i	0.262252	+	0.120654i
$61$	−2.74195	−	6.00403i	−0.351071	−	0.768737i	−0.999969	−	0.00786238i	$-0.997497\pi$
$61$	−2.74195	−	6.00403i	−0.351071	−	0.768737i	0.648899	−	0.760875i	$-0.275230\pi$
$62$	1.62528	+	2.52899i	0.206411	+	0.321181i
$63$	−1.28926	+	4.39083i	−0.162432	+	0.553192i
$64$	0.654861	−	0.755750i	0.0818576	−	0.0944687i
$65$	6.05070	−	5.21339i	0.750498	−	0.646641i
$66$	0.00616067	−	0.0134900i	0.000758326	−	0.00166050i
$67$	−5.29761	+	0.761682i	−0.647206	+	0.0930542i	−0.458098	−	0.888902i	$-0.651469\pi$
$67$	−5.29761	+	0.761682i	−0.647206	+	0.0930542i	−0.189109	+	0.981956i	$0.560560\pi$
$68$			2.90288i			0.352025i
$69$	4.79324	−	0.157578i	0.577039	−	0.0189702i
$70$	−4.22474	−	9.31983i	−0.504954	−	1.11393i
$71$	−1.86038	−	12.9392i	−0.220786	−	1.53560i	−0.735075	−	0.677986i	$-0.762853\pi$
$71$	−1.86038	−	12.9392i	−0.220786	−	1.53560i	0.514289	−	0.857617i	$-0.328056\pi$
$72$	0.909632	+	0.415415i	0.107201	+	0.0489571i
$73$	1.35080	+	4.60039i	0.158099	+	0.538435i	0.999999	−	0.00119755i	$-0.000381194\pi$
$73$	1.35080	+	4.60039i	0.158099	+	0.538435i	−0.841900	+	0.539633i	$0.818563\pi$
$74$	2.18781	−	2.52487i	0.254328	−	0.293510i
$75$	−2.67962	−	4.22133i	−0.309416	−	0.487437i
$76$	6.25687	−	4.02105i	0.717712	−	0.461246i
$77$	−0.0617328	+	0.0281924i	−0.00703510	+	0.00321282i
$78$	2.69942	−	2.33906i	0.305649	−	0.264847i
$79$	−13.4044	−	8.61449i	−1.50811	−	0.969206i	−0.993749	−	0.111635i	$-0.964391\pi$
$79$	−13.4044	−	8.61449i	−1.50811	−	0.969206i	−0.514365	−	0.857571i	$-0.671972\pi$
$80$	−2.14725	+	0.623966i	−0.240069	+	0.0697616i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−1.96629	+	3.05961i	−0.217140	+	0.337877i
$83$	−10.6189	+	9.20132i	−1.16557	+	1.00998i	−0.165858	+	0.986150i	$0.553039\pi$
$83$	−10.6189	+	9.20132i	−1.16557	+	1.00998i	−0.999716	+	0.0238265i	$0.992415\pi$
$84$	−1.90102	−	4.16265i	−0.207418	−	0.454183i
$85$	3.52458	−	5.45076i	0.382295	−	0.591218i
$86$	7.00307	+	2.05629i	0.755160	+	0.221735i
$87$	−5.09762	−	4.41711i	−0.546522	−	0.473564i
$88$	0.00417814	+	0.0142294i	0.000445391	+	0.00151686i
$89$	−3.94429	+	8.63679i	−0.418094	+	0.915498i	0.577017	+	0.816732i	$0.304217\pi$
$89$	−3.94429	+	8.63679i	−0.418094	+	0.915498i	−0.995111	+	0.0987660i	$0.968510\pi$
$90$	−1.20364	−	1.88448i	−0.126875	−	0.198641i
$91$	−16.3455			−1.71347
$92$	−3.51930	+	3.25800i	−0.366912	+	0.339670i
$93$		−	3.00621i		−	0.311730i
$94$	−0.131051	−	0.911481i	−0.0135169	−	0.0940121i
$95$	−16.6308	−	0.0465419i	−1.70629	−	0.00477510i
$96$	−0.959493	+	0.281733i	−0.0979278	+	0.0287542i
$97$	−4.85804	−	4.20952i	−0.493259	−	0.427412i	0.372380	−	0.928081i	$-0.378542\pi$
$97$	−4.85804	−	4.20952i	−0.493259	−	0.427412i	−0.865639	+	0.500669i	$0.833087\pi$
$98$	−3.92779	+	13.3768i	−0.396767	+	1.35126i
$99$	−0.0124759	+	0.00801779i	−0.00125388	+	0.000805818i
$100$	4.78951	+	1.43549i	0.478951	+	0.143549i
$101$	−4.91898	−	5.67680i	−0.489456	−	0.564863i	0.456264	−	0.889845i	$-0.349187\pi$
$101$	−4.91898	−	5.67680i	−0.489456	−	0.564863i	−0.945720	+	0.324982i	$0.894642\pi$
$102$	1.56941	−	2.44205i	0.155395	−	0.241799i
$103$	−19.7907	−	2.84547i	−1.95003	−	0.280373i	−0.950495	−	0.310740i	$-0.899423\pi$
$103$	−19.7907	−	2.84547i	−1.95003	−	0.280373i	−0.999539	+	0.0303672i	$0.990332\pi$
$104$	−0.508327	+	3.53549i	−0.0498455	+	0.346683i
$105$	−1.48460	+	10.1244i	−0.144882	+	0.988042i
$106$	−4.93510	−	5.69541i	−0.479339	−	0.553187i
$107$	8.01342	−	3.65961i	0.774687	−	0.353788i	0.0114734	−	0.999934i	$-0.496348\pi$
$107$	8.01342	−	3.65961i	0.774687	−	0.353788i	0.763213	+	0.646147i	$0.223621\pi$
$108$	−0.540641	−	0.841254i	−0.0520232	−	0.0809497i
$109$	6.68967	+	1.96426i	0.640754	+	0.188142i	0.585940	−	0.810354i	$-0.300725\pi$
$109$	6.68967	+	1.96426i	0.640754	+	0.188142i	0.0548139	+	0.998497i	$0.482543\pi$
$110$	0.00943161	−	0.0317917i	0.000899268	−	0.00303122i
$111$	−3.20555	+	0.941236i	−0.304258	+	0.0893381i
$112$	4.16265	+	1.90102i	0.393334	+	0.179629i
$113$	19.8624	−	2.85578i	1.86849	−	0.268649i	0.887232	−	0.461323i	$-0.152625\pi$
$113$	19.8624	−	2.85578i	1.86849	−	0.268649i	0.981263	+	0.192674i	$0.0617161\pi$
$114$	−7.43755			−0.696591
$115$	10.5640	−	1.84455i	0.985096	−	0.172005i
$116$	6.74512			0.626268
$117$	−3.53549	+	0.508327i	−0.326856	+	0.0469948i
$118$	7.82576	+	3.57390i	0.720419	+	0.329004i
$119$	−12.7460	+	3.74257i	−1.16843	+	0.343081i
$120$	2.14372	+	0.635975i	0.195694	+	0.0580563i
$121$	10.5542	+	3.09900i	0.959474	+	0.281727i
$122$	−3.56850	−	5.55270i	−0.323077	−	0.502718i
$123$	3.30830	−	1.51085i	0.298299	−	0.136229i
$124$	1.96865	+	2.27194i	0.176790	+	0.204026i
$125$	−7.25037	−	8.51071i	−0.648493	−	0.761221i
$126$	−0.651260	+	4.52962i	−0.0580189	+	0.403530i
$127$	2.82813	+	0.406624i	0.250956	+	0.0360821i	0.266645	−	0.963795i	$-0.414085\pi$
$127$	2.82813	+	0.406624i	0.250956	+	0.0360821i	−0.0156886	+	0.999877i	$0.504994\pi$
$128$	0.540641	−	0.841254i	0.0477863	−	0.0743570i
$129$	−4.77964	−	5.51600i	−0.420824	−	0.485657i
$130$	5.24717	−	6.02143i	0.460208	−	0.528114i
$131$	4.49523	−	2.88891i	0.392750	−	0.252405i	−0.329330	−	0.944215i	$-0.606823\pi$
$131$	4.49523	−	2.88891i	0.392750	−	0.252405i	0.722080	+	0.691810i	$0.243186\pi$
$132$	0.00417814	−	0.0142294i	0.000363660	−	0.00123851i
$133$	25.7225	+	22.2886i	2.23042	+	1.93267i
$134$	−5.13529	+	1.50786i	−0.443622	+	0.130259i
$135$	−0.00625769	+	2.23606i	−0.000538576	+	0.192449i
$136$	0.413122	+	2.87333i	0.0354250	+	0.246386i
$137$		−	5.96460i		−	0.509590i	−0.966995	−	0.254795i	$-0.917992\pi$
$137$		−	5.96460i		−	0.509590i	0.966995	−	0.254795i	$-0.0820080\pi$
$138$	4.72203	−	0.838124i	0.401966	−	0.0713458i
$139$	−8.45609			−0.717236			−0.358618	−	0.933484i	$-0.616752\pi$
$139$	−8.45609			−0.717236			−0.358618	+	0.933484i	$0.616752\pi$
$140$	−5.50809	−	8.62373i	−0.465519	−	0.728838i
$141$	−0.382536	+	0.837638i	−0.0322154	+	0.0705418i
$142$	−3.68289	−	12.5428i	−0.309061	−	1.05256i
$143$	−0.0400328	−	0.0346887i	−0.00334771	−	0.00290081i
$144$	0.959493	+	0.281733i	0.0799577	+	0.0234777i
$145$	−12.6654	−	8.18971i	−1.05180	−	0.680119i
$146$	1.99175	+	4.36133i	0.164839	+	0.360946i
$147$	10.5363	−	9.12978i	0.869021	−	0.753011i
$148$	1.80622	−	2.81053i	0.148470	−	0.231024i
$149$	1.17559	−	8.17640i	0.0963080	−	0.669837i	−0.883284	−	0.468839i	$-0.844672\pi$
$149$	1.17559	−	8.17640i	0.0963080	−	0.669837i	0.979592	−	0.200998i	$-0.0644185\pi$
$150$	−3.25310	−	3.79702i	−0.265615	−	0.310025i
$151$	−0.645427	−	0.414791i	−0.0525241	−	0.0337552i	0.514115	−	0.857721i	$-0.328120\pi$
$151$	−0.645427	−	0.414791i	−0.0525241	−	0.0337552i	−0.566639	+	0.823966i	$0.691757\pi$
$152$	5.62093	−	4.87056i	0.455918	−	0.395055i
$153$	−2.64055	+	1.20590i	−0.213476	+	0.0974911i
$154$	−0.0570922	+	0.0366910i	−0.00460062	+	0.00295664i
$155$	−0.938029	−	6.65632i	−0.0753443	−	0.534649i
$156$	2.33906	−	2.69942i	0.187275	−	0.216127i
$157$	5.52292	+	18.8093i	0.440777	+	1.50115i	0.818105	+	0.575069i	$0.195025\pi$
$157$	5.52292	+	18.8093i	0.440777	+	1.50115i	−0.377328	+	0.926080i	$0.623157\pi$
$158$	−14.4939	−	6.61916i	−1.15308	−	0.526592i
$159$	1.07250	+	7.45939i	0.0850547	+	0.591568i
$160$	−2.03659	+	0.923200i	−0.161007	+	0.0729854i
$161$	−18.8426	−	11.2522i	−1.48500	−	0.886799i
$162$			1.00000i			0.0785674i
$163$	10.6817	−	1.53580i	0.836657	−	0.120293i	0.289348	−	0.957224i	$-0.406562\pi$
$163$	10.6817	−	1.53580i	0.836657	−	0.120293i	0.547309	+	0.836931i	$0.315652\pi$
$164$	−1.51085	+	3.30830i	−0.117977	+	0.258334i
$165$	−0.0251223	+	0.0216458i	−0.00195577	+	0.00168512i
$166$	−9.20132	+	10.6189i	−0.714161	+	0.824186i
$167$	3.69618	−	12.5880i	0.286019	−	0.974092i	−0.683678	−	0.729784i	$-0.739621\pi$
$167$	3.69618	−	12.5880i	0.286019	−	0.974092i	0.969698	−	0.244309i	$-0.0785610\pi$
$168$	−2.47408	−	3.84974i	−0.190879	−	0.297014i
$169$	0.100492	+	0.220048i	0.00773018	+	0.0169267i
$170$	2.71298	−	5.89688i	0.208076	−	0.452270i
$171$	6.25687	+	4.02105i	0.478475	+	0.307497i
$172$	7.22443	+	1.03872i	0.550857	+	0.0792013i
$173$	12.3234	+	1.77184i	0.936933	+	0.134711i	0.593833	−	0.804588i	$-0.297614\pi$
$173$	12.3234	+	1.77184i	0.936933	+	0.134711i	0.343100	+	0.939299i	$0.388523\pi$
$174$	−5.67435	−	3.64669i	−0.430172	−	0.276454i
$175$	−0.128065	+	22.8806i	−0.00968083	+	1.72961i
$176$	0.00616067	+	0.0134900i	0.000464378	+	0.00101685i
$177$	−4.65125	−	7.23748i	−0.349609	−	0.544002i
$178$	−2.67500	+	9.11022i	−0.200500	+	0.682840i
$179$	−7.35888	+	8.49261i	−0.550029	+	0.634767i	−0.960890	−	0.276931i	$-0.910683\pi$
$179$	−7.35888	+	8.49261i	−0.550029	+	0.634767i	0.410861	+	0.911698i	$0.365228\pi$
$180$	−1.45958	−	1.69400i	−0.108791	−	0.126263i
$181$	6.14801	−	13.4623i	0.456978	−	1.00064i	−0.531188	−	0.847254i	$-0.678254\pi$
$181$	6.14801	−	13.4623i	0.456978	−	1.00064i	0.988166	−	0.153388i	$-0.0490185\pi$
$182$	−16.1791	+	2.32620i	−1.19927	+	0.172430i
$183$			6.60051i			0.487923i
$184$	−3.01982	+	3.72568i	−0.222624	+	0.274661i
$185$	−6.80401	+	3.08430i	−0.500241	+	0.226763i
$186$	−0.427828	−	2.97561i	−0.0313699	−	0.218182i
$187$	−0.0391598	−	0.0178837i	−0.00286364	−	0.00130778i
$188$	−0.259434	−	0.883553i	−0.0189212	−	0.0644397i
$189$	2.99677	−	3.45846i	0.217983	−	0.251566i
$190$	−16.4682	+	2.32074i	−1.19473	+	0.168364i
$191$	−2.36772	+	1.52164i	−0.171322	+	0.110102i	−0.623492	−	0.781830i	$-0.714287\pi$
$191$	−2.36772	+	1.52164i	−0.171322	+	0.110102i	0.452170	+	0.891932i	$0.350650\pi$
$192$	−0.909632	+	0.415415i	−0.0656470	+	0.0299800i
$193$	15.9895	−	13.8550i	1.15095	−	0.997304i	0.150988	−	0.988536i	$-0.451754\pi$
$193$	15.9895	−	13.8550i	1.15095	−	0.997304i	0.999962	−	0.00876797i	$-0.00279097\pi$
$194$	−5.40767	−	3.47530i	−0.388248	−	0.249512i
$195$	−7.66963	+	2.22871i	−0.549234	+	0.159601i
$196$	−1.98409	+	13.7997i	−0.141721	+	0.985689i
$197$	12.5263	−	19.4914i	0.892464	−	1.38870i	−0.0287255	−	0.999587i	$-0.509145\pi$
$197$	12.5263	−	19.4914i	0.892464	−	1.38870i	0.921190	−	0.389114i	$-0.127219\pi$
$198$	−0.0112079	+	0.00971169i	−0.000796510	+	0.000690179i
$199$	−7.62100	−	16.6877i	−0.540238	−	1.18296i	−0.961193	−	0.275875i	$-0.911032\pi$
$199$	−7.62100	−	16.6877i	−0.540238	−	1.18296i	0.420955	−	0.907081i	$-0.361695\pi$
$200$	4.94505	+	0.739263i	0.349668	+	0.0522738i
$201$	5.13529	+	1.50786i	0.362216	+	0.106356i
$202$	−5.67680	−	4.91898i	−0.399418	−	0.346098i
$203$	8.69623	+	29.6166i	0.610356	+	2.07868i
$204$	1.20590	−	2.64055i	0.0844298	−	0.184875i
$205$	6.85376	−	4.37759i	0.478688	−	0.305744i
$206$	−19.9942			−1.39306
$207$	−4.42555	−	1.84785i	−0.307597	−	0.128434i
$208$			3.57185i			0.247663i
$209$	0.0156973	+	0.109177i	0.00108581	+	0.00755196i
$210$	−0.0286364	+	10.2326i	−0.00197610	+	0.706119i
$211$	−10.2713	+	3.01593i	−0.707106	+	0.207625i	−0.615462	−	0.788167i	$-0.711030\pi$
$211$	−10.2713	+	3.01593i	−0.707106	+	0.207625i	−0.0916441	+	0.995792i	$0.529212\pi$
$212$	−5.69541	−	4.93510i	−0.391162	−	0.338944i
$213$	−3.68289	+	12.5428i	−0.252347	+	0.859415i
$214$	7.41104	−	4.76279i	0.506608	−	0.325577i
$215$	−12.3042	−	10.7221i	−0.839140	−	0.731240i
$216$	−0.654861	−	0.755750i	−0.0445576	−	0.0514222i
$217$	−7.43760	+	11.5731i	−0.504897	+	0.785635i
$218$	6.90112	+	0.992232i	0.467403	+	0.0672024i
$219$	0.682344	−	4.74581i	0.0461085	−	0.320692i
$220$	0.00481118	−	0.0328104i	0.000324369	−	0.00221207i
$221$	−6.79001	−	7.83609i	−0.456745	−	0.527112i
$222$	−3.03897	+	1.38785i	−0.203963	+	0.0931466i
$223$	−8.65920	−	13.4740i	−0.579863	−	0.902285i	0.420123	−	0.907467i	$-0.361987\pi$
$223$	−8.65920	−	13.4740i	−0.579863	−	0.902285i	−0.999987	+	0.00518222i	$0.998350\pi$
$224$	4.39083	+	1.28926i	0.293374	+	0.0861425i
$225$	0.683863	+	4.95301i	0.0455909	+	0.330201i
$226$	19.2538	−	5.65342i	1.28074	−	0.376060i
$227$	−21.2364	−	9.69834i	−1.40951	−	0.643701i	−0.442111	−	0.896960i	$-0.645770\pi$
$227$	−21.2364	−	9.69834i	−1.40951	−	0.643701i	−0.967399	+	0.253259i	$0.918498\pi$
$228$	−7.36185	+	1.05847i	−0.487551	+	0.0700992i
$229$	9.72610			0.642719			0.321359	−	0.946957i	$-0.395860\pi$
$229$	9.72610			0.642719			0.321359	+	0.946957i	$0.395860\pi$
$230$	10.1939	−	3.32918i	0.672169	−	0.219520i
$231$	0.0678657			0.00446523
$232$	6.67646	−	0.959930i	0.438331	−	0.0630225i
$233$	4.22035	+	1.92737i	0.276485	+	0.126266i	0.548832	−	0.835933i	$-0.315073\pi$
$233$	4.22035	+	1.92737i	0.276485	+	0.126266i	−0.272347	+	0.962199i	$0.587800\pi$
$234$	−3.42716	+	1.00631i	−0.224041	+	0.0657843i
$235$	−0.585640	+	1.97405i	−0.0382029	+	0.128773i
$236$	8.25472	+	2.42380i	0.537337	+	0.157776i
$237$	8.61449	+	13.4044i	0.559571	+	0.870710i
$238$	−12.0837	+	5.51843i	−0.783268	+	0.357706i
$239$	15.8634	+	18.3073i	1.02612	+	1.18420i	0.982711	+	0.185144i	$0.0592751\pi$
$239$	15.8634	+	18.3073i	1.02612	+	1.18420i	0.0434049	+	0.999058i	$0.486179\pi$
$240$	2.21241	+	0.324418i	0.142810	+	0.0209411i
$241$	−1.77061	+	12.3149i	−0.114055	+	0.793271i	0.849850	+	0.527025i	$0.176693\pi$
$241$	−1.77061	+	12.3149i	−0.114055	+	0.793271i	−0.963905	+	0.266246i	$0.914216\pi$
$242$	10.8878	+	1.56543i	0.699895	+	0.100630i
$243$	0.540641	−	0.841254i	0.0346821	−	0.0539664i
$244$	−4.32241	−	4.98833i	−0.276714	−	0.319345i
$245$	20.4807	−	23.5027i	1.30846	−	1.50153i
$246$	3.05961	−	1.96629i	0.195073	−	0.125366i
$247$	−7.48445	+	25.4897i	−0.476224	+	1.62187i
$248$	2.27194	+	1.96865i	0.144268	+	0.125009i
$249$	13.4816	−	3.95857i	0.854365	−	0.250864i
$250$	−8.38777	−	7.39225i	−0.530489	−	0.467527i
$251$	0.980076	+	6.81658i	0.0618618	+	0.430258i	0.997091	+	0.0762163i	$0.0242840\pi$
$251$	0.980076	+	6.81658i	0.0618618	+	0.430258i	−0.935229	+	0.354042i	$0.884807\pi$
$252$			4.57619i			0.288273i
$253$	−0.0222691	−	0.0675467i	−0.00140004	−	0.00424663i
$254$	2.85722			0.179278
$255$	−5.47040	+	3.49402i	−0.342570	+	0.218804i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	0.217513	+	0.740781i	0.0135681	+	0.0462086i	0.965999	−	0.258547i	$-0.0832435\pi$
$257$	0.217513	+	0.740781i	0.0135681	+	0.0462086i	−0.952431	+	0.304755i	$0.901425\pi$
$258$	−5.51600	−	4.77964i	−0.343411	−	0.297568i
$259$	14.6692	+	4.30728i	0.911502	+	0.267641i
$260$	4.33683	−	6.70689i	0.268959	−	0.415944i
$261$	2.80202	+	6.13557i	0.173441	+	0.379782i
$262$	4.03834	−	3.49924i	0.249489	−	0.216184i
$263$	−1.04841	+	1.63135i	−0.0646476	+	0.100594i	−0.872072	−	0.489377i	$-0.837224\pi$
$263$	−1.04841	+	1.63135i	−0.0646476	+	0.100594i	0.807425	+	0.589970i	$0.200861\pi$
$264$	0.00211055	−	0.0146792i	0.000129895	−	0.000903443i
$265$	4.70227	+	16.1819i	0.288858	+	0.994044i
$266$	28.6326	+	18.4011i	1.75558	+	1.12824i
$267$	7.17571	−	6.21779i	0.439146	−	0.380522i
$268$	−4.86843	+	2.22334i	−0.297387	+	0.135812i
$269$	4.33368	−	2.78509i	0.264229	−	0.169810i	−0.401818	−	0.915720i	$-0.631621\pi$
$269$	4.33368	−	2.78509i	0.264229	−	0.169810i	0.666047	+	0.745910i	$0.267985\pi$
$270$	0.312030	+	2.21419i	0.0189896	+	0.134751i
$271$	5.14236	−	5.93460i	0.312376	−	0.360501i	−0.577751	−	0.816213i	$-0.696070\pi$
$271$	5.14236	−	5.93460i	0.312376	−	0.360501i	0.890127	+	0.455712i	$0.150615\pi$
$272$	0.817835	+	2.78529i	0.0495885	+	0.168883i
$273$	14.8684	+	6.79015i	0.899874	+	0.410959i
$274$	−0.848851	−	5.90389i	−0.0512809	−	0.356667i
$275$	−0.0488713	+	0.0557668i	−0.00294705	+	0.00336286i
$276$	4.55469	−	1.50161i	0.274160	−	0.0903862i
$277$		−	0.855020i		−	0.0513732i	−0.999670	−	0.0256866i	$-0.991823\pi$
$277$		−	0.855020i		−	0.0513732i	0.999670	−	0.0256866i	$-0.00817719\pi$
$278$	−8.37002	+	1.20343i	−0.502000	+	0.0721768i
$279$	−1.24883	+	2.73455i	−0.0747652	+	0.163713i
$280$	−6.67931	−	7.75207i	−0.399165	−	0.463275i
$281$	−12.6069	+	14.5491i	−0.752065	+	0.867929i	−0.994767	−	0.102172i	$-0.967421\pi$
$281$	−12.6069	+	14.5491i	−0.752065	+	0.867929i	0.242702	+	0.970101i	$0.421966\pi$
$282$	−0.259434	+	0.883553i	−0.0154491	+	0.0526148i
$283$	−5.53606	−	8.61428i	−0.329085	−	0.512066i	0.636803	−	0.771026i	$-0.280256\pi$
$283$	−5.53606	−	8.61428i	−0.329085	−	0.512066i	−0.965888	+	0.258961i	$0.916620\pi$
$284$	−5.43042	−	11.8910i	−0.322236	−	0.705599i
$285$	15.1086	+	6.95103i	0.894955	+	0.411743i
$286$	−0.0445621	−	0.0286383i	−0.00263501	−	0.00169342i
$287$	−16.4740	−	2.36861i	−0.972431	−	0.139815i
$288$	0.989821	+	0.142315i	0.0583258	+	0.00838598i
$289$	7.21233	+	4.63508i	0.424255	+	0.272652i
$290$	−13.7020	−	6.30388i	−0.804608	−	0.370177i
$291$	2.67033	+	5.84721i	0.156538	+	0.342770i
$292$	2.59216	+	4.03348i	0.151695	+	0.236042i
$293$	4.80460	−	16.3630i	0.280688	−	0.955935i	−0.691626	−	0.722256i	$-0.743105\pi$
$293$	4.80460	−	16.3630i	0.280688	−	0.955935i	0.972314	−	0.233679i	$-0.0750765\pi$
$294$	9.12978	−	10.5363i	0.532459	−	0.614491i
$295$	−12.5571	−	14.5738i	−0.731100	−	0.848521i
$296$	1.38785	−	3.03897i	0.0806673	−	0.176637i
$297$	0.0146792	−	0.00211055i	0.000851774	−	0.000122467i
$298$		−	8.26048i		−	0.478517i
$299$	1.87942	−	17.0266i	0.108689	−	0.984672i
$300$	−3.76036	−	3.29540i	−0.217105	−	0.190260i
$301$	4.75337	+	33.0604i	0.273979	+	1.90557i
$302$	−0.697888	−	0.318715i	−0.0401590	−	0.0183400i
$303$	2.11623	+	7.20722i	0.121574	+	0.414044i
$304$	4.87056	−	5.62093i	0.279346	−	0.322382i
$305$	2.05956	+	14.6148i	0.117930	+	0.836839i
$306$	−2.44205	+	1.56941i	−0.139603	+	0.0897174i
$307$	26.1517	−	11.9431i	1.49256	−	0.681629i	0.508761	−	0.860908i	$-0.330104\pi$
$307$	26.1517	−	11.9431i	1.49256	−	0.681629i	0.983798	+	0.179279i	$0.0573765\pi$
$308$	−0.0512895	+	0.0444426i	−0.00292249	+	0.00253235i
$309$	16.8202	+	10.8097i	0.956867	+	0.614941i
$310$	−1.87577	−	6.45507i	−0.106537	−	0.366624i
$311$	0.681277	−	4.73839i	0.0386317	−	0.268689i	−0.961346	−	0.275343i	$-0.911209\pi$
$311$	0.681277	−	4.73839i	0.0386317	−	0.268689i	0.999978	+	0.00665332i	$0.00211783\pi$
$312$	1.93109	−	3.00483i	0.109326	−	0.170115i
$313$	14.6429	−	12.6882i	0.827668	−	0.717178i	−0.134123	−	0.990965i	$-0.542822\pi$
$313$	14.6429	−	12.6882i	0.827668	−	0.717178i	0.961791	+	0.273786i	$0.0882761\pi$
$314$	8.14356	+	17.8319i	0.459567	+	1.00631i
$315$	5.55627	−	8.59276i	0.313061	−	0.484147i
$316$	−15.2884	−	4.48909i	−0.860041	−	0.252531i
$317$	−5.01542	−	4.34588i	−0.281694	−	0.244089i	0.502541	−	0.864554i	$-0.332399\pi$
$317$	−5.01542	−	4.34588i	−0.281694	−	0.244089i	−0.784235	+	0.620464i	$0.786944\pi$
$318$	2.12317	+	7.23084i	0.119061	+	0.405485i
$319$	−0.0415544	+	0.0909915i	−0.00232660	+	0.00509455i
$320$	−1.88448	+	1.20364i	−0.105345	+	0.0672856i
$321$	−8.80952			−0.491699
$322$	−20.2522	−	8.45610i	−1.12861	−	0.471240i
$323$			21.5903i			1.20132i
$324$	0.142315	+	0.989821i	0.00790638	+	0.0549901i
$325$	−16.2866	+	7.32795i	−0.903418	+	0.406482i
$326$	10.3544	−	3.04033i	0.573479	−	0.168388i
$327$	−5.26915	−	4.56575i	−0.291385	−	0.252486i
$328$	−1.02465	+	3.48964i	−0.0565768	+	0.192683i
$329$	3.54505	−	2.27826i	0.195445	−	0.125605i
$330$	−0.0217860	+	0.0250007i	−0.00119928	+	0.00137624i
$331$	−6.49261	−	7.49288i	−0.356866	−	0.411846i	0.548721	−	0.836006i	$-0.315115\pi$
$331$	−6.49261	−	7.49288i	−0.356866	−	0.411846i	−0.905587	+	0.424160i	$0.860569\pi$
$332$	−7.59644	+	11.8203i	−0.416909	+	0.648723i
$333$	3.30688	+	0.475457i	0.181216	+	0.0260549i
$334$	1.86710	−	12.9859i	0.102163	−	0.710559i
$335$	11.8410	+	1.73632i	0.646943	+	0.0948651i
$336$	−2.99677	−	3.45846i	−0.163487	−	0.188674i
$337$	−4.22162	+	1.92795i	−0.229966	+	0.105022i	−0.527066	−	0.849824i	$-0.676708\pi$
$337$	−4.22162	+	1.92795i	−0.229966	+	0.105022i	0.297100	+	0.954846i	$0.403981\pi$
$338$	0.130786	+	0.203506i	0.00711380	+	0.0110693i
$339$	−19.2538	−	5.65342i	−1.04572	−	0.307052i
$340$	1.84616	−	6.22295i	0.100122	−	0.337487i
$341$	−0.0427767	+	0.0125604i	−0.00231649	+	0.000680182i
$342$	6.76544	+	3.08967i	0.365833	+	0.167070i
$343$	−31.4426	+	4.52076i	−1.69774	+	0.244098i
$344$	7.29872			0.393521
$345$	−10.3756	−	2.71058i	−0.558603	−	0.145933i
$346$	12.4502			0.669325
$347$	2.53653	−	0.364698i	0.136168	−	0.0195780i	−0.0738937	−	0.997266i	$-0.523543\pi$
$347$	2.53653	−	0.364698i	0.136168	−	0.0195780i	0.210062	+	0.977688i	$0.432633\pi$
$348$	−6.13557	−	2.80202i	−0.328901	−	0.150204i
$349$	−11.4008	+	3.34757i	−0.610269	+	0.179191i	−0.572241	−	0.820085i	$-0.693926\pi$
$349$	−11.4008	+	3.34757i	−0.610269	+	0.179191i	−0.0380281	+	0.999277i	$0.512108\pi$
$350$	3.12949	+	22.6659i	0.167278	+	1.21155i
$351$	3.42716	+	1.00631i	0.182928	+	0.0537126i
$352$	0.00801779	+	0.0124759i	0.000427349	+	0.000664969i
$353$	−7.73691	+	3.53333i	−0.411794	+	0.188060i	−0.610530	−	0.791993i	$-0.709044\pi$
$353$	−7.73691	+	3.53333i	−0.411794	+	0.188060i	0.198736	+	0.980053i	$0.436316\pi$
$354$	−5.63391	−	6.50187i	−0.299439	−	0.345571i
$355$	−4.24089	+	28.9212i	−0.225083	+	1.53498i
$356$	−1.35125	+	9.39818i	−0.0716163	+	0.498102i
$357$	13.1489	+	1.89053i	0.695914	+	0.100057i
$358$	−6.07536	+	9.45344i	−0.321093	+	0.499630i
$359$	3.36968	+	3.88882i	0.177845	+	0.205244i	0.837672	−	0.546173i	$-0.183916\pi$
$359$	3.36968	+	3.88882i	0.177845	+	0.205244i	−0.659827	+	0.751417i	$0.729371\pi$
$360$	−1.68580	−	1.46904i	−0.0888496	−	0.0774250i
$361$	30.5520	−	19.6346i	1.60800	−	1.03340i
$362$	4.16955	−	14.2002i	0.219147	−	0.746346i
$363$	−8.31308	−	7.20332i	−0.436323	−	0.378076i
$364$	−15.6834	+	4.60505i	−0.822031	+	0.241370i
$365$	0.0300032	−	10.7210i	0.00157044	−	0.561164i
$366$	0.939350	+	6.53332i	0.0491006	+	0.341502i
$367$			25.1961i			1.31523i	0.753355	+	0.657614i	$0.228434\pi$
$367$			25.1961i			1.31523i	−0.753355	+	0.657614i	$0.771566\pi$
$368$	−2.45886	+	4.11753i	−0.128177	+	0.214641i
$369$	−3.63696			−0.189333
$370$	−6.29581	+	4.02122i	−0.327304	+	0.209053i
$371$	14.3263	−	31.3702i	0.743783	−	1.62866i
$372$	−0.846947	−	2.88444i	−0.0439122	−	0.149551i
$373$	−13.3694	−	11.5847i	−0.692242	−	0.599831i	0.236025	−	0.971747i	$-0.424155\pi$
$373$	−13.3694	−	11.5847i	−0.692242	−	0.599831i	−0.928266	+	0.371916i	$0.878701\pi$
$374$	−0.0413063	−	0.0121286i	−0.00213590	−	0.000627156i
$375$	3.05969	+	10.7535i	0.158002	+	0.555310i
$376$	−0.382536	−	0.837638i	−0.0197278	−	0.0431979i
$377$	−18.2079	+	15.7772i	−0.937755	+	0.812570i
$378$	2.47408	−	3.84974i	0.127253	−	0.198009i
$379$	4.48220	−	31.1744i	0.230235	−	1.60132i	−0.466852	−	0.884336i	$-0.654612\pi$
$379$	4.48220	−	31.1744i	0.230235	−	1.60132i	0.697087	−	0.716987i	$-0.254479\pi$
$380$	−15.9703	+	4.64078i	−0.819257	+	0.238067i
$381$	−2.40364	−	1.54473i	−0.123142	−	0.0791388i
$382$	−2.12707	+	1.84312i	−0.108830	+	0.0943020i
$383$	31.8123	−	14.5282i	1.62553	−	0.742355i	0.626226	−	0.779641i	$-0.284599\pi$
$383$	31.8123	−	14.5282i	1.62553	−	0.742355i	0.999305	+	0.0372863i	$0.0118714\pi$
$384$	−0.841254	+	0.540641i	−0.0429300	+	0.0275895i
$385$	0.150267	−	0.0211762i	0.00765834	−	0.00107924i
$386$	13.8550	−	15.9895i	0.705200	−	0.813844i
$387$	2.05629	+	7.00307i	0.104527	+	0.355986i
$388$	−5.84721	−	2.67033i	−0.296847	−	0.135566i
$389$	3.46164	+	24.0762i	0.175512	+	1.22071i	0.866994	+	0.498319i	$0.166049\pi$
$389$	3.46164	+	24.0762i	0.175512	+	1.22071i	−0.691482	+	0.722394i	$0.743042\pi$
$390$	−7.27439	+	3.29753i	−0.368353	+	0.166977i
$391$	−2.43297	−	13.7075i	−0.123041	−	0.693216i
$392$			13.9416i			0.704155i
$393$	−5.28910	+	0.760458i	−0.266800	+	0.0383600i
$394$	9.62492	−	21.0756i	0.484897	−	1.06178i
$395$	23.2567	+	26.9919i	1.17017	+	1.35811i
$396$	−0.00971169	+	0.0112079i	−0.000488031	+	0.000563217i
$397$	2.93854	−	10.0077i	0.147481	−	0.502274i	−0.852303	−	0.523048i	$-0.824795\pi$
$397$	2.93854	−	10.0077i	0.147481	−	0.502274i	0.999784	+	0.0207739i	$0.00661300\pi$
$398$	−9.91833	−	15.4332i	−0.497161	−	0.773597i
$399$	−14.1389	−	30.9600i	−0.707832	−	1.54994i
$400$	4.99992	+	0.0279851i	0.249996	+	0.00139926i
$401$	−6.69952	−	4.30552i	−0.334558	−	0.215007i	0.362566	−	0.931958i	$-0.381901\pi$
$401$	−6.69952	−	4.30552i	−0.334558	−	0.215007i	−0.697124	+	0.716951i	$0.745537\pi$
$402$	5.29761	+	0.761682i	0.264221	+	0.0379892i
$403$	−10.6284	−	1.52814i	−0.529440	−	0.0761220i
$404$	−6.31906	−	4.06101i	−0.314385	−	0.202043i
$405$	0.934585	−	2.03139i	0.0464399	−	0.100941i
$406$	12.8226	+	28.0776i	0.636375	+	1.39347i
$407$	0.0267865	+	0.0416806i	0.00132776	+	0.00206603i
$408$	0.817835	−	2.78529i	0.0404889	−	0.137892i
$409$	−7.84771	+	9.05674i	−0.388044	+	0.447827i	−0.915839	−	0.401545i	$-0.868473\pi$
$409$	−7.84771	+	9.05674i	−0.388044	+	0.447827i	0.527795	+	0.849372i	$0.323019\pi$
$410$	6.16101	−	5.30843i	0.304270	−	0.262165i
$411$	−2.47778	+	5.42559i	−0.122220	+	0.267624i
$412$	−19.7907	+	2.84547i	−0.975017	+	0.140186i
$413$			39.3700i			1.93727i
$414$	−4.64348	−	1.19922i	−0.228214	−	0.0589383i
$415$	28.6157	−	12.9717i	1.40469	−	0.636756i
$416$	0.508327	+	3.53549i	0.0249228	+	0.173342i
$417$	7.69193	+	3.51279i	0.376675	+	0.172022i
$418$	0.0310751	+	0.105832i	0.00151993	+	0.00517642i
$419$	−20.9279	+	24.1521i	−1.02240	+	1.17991i	−0.0388521	+	0.999245i	$0.512370\pi$
$419$	−20.9279	+	24.1521i	−1.02240	+	1.17991i	−0.983545	+	0.180664i	$0.942175\pi$
$420$	1.42791	+	10.1326i	0.0696750	+	0.494418i
$421$	25.0834	−	16.1201i	1.22249	−	0.785646i	0.239784	−	0.970826i	$-0.422923\pi$
$421$	25.0834	−	16.1201i	1.22249	−	0.785646i	0.982705	+	0.185181i	$0.0592870\pi$
$422$	−9.73755	+	4.44699i	−0.474016	+	0.216476i
$423$	0.695935	−	0.603031i	0.0338375	−	0.0293204i
$424$	−6.33977	−	4.07432i	−0.307887	−	0.197867i
$425$	−11.0223	+	9.44335i	−0.534658	+	0.458070i
$426$	−1.86038	+	12.9392i	−0.0901356	+	0.626907i
$427$	16.3302	−	25.4102i	0.790272	−	1.22969i
$428$	6.65779	−	5.76901i	0.321816	−	0.278856i
$429$	0.0220050	+	0.0481842i	0.00106241	+	0.00232635i
$430$	−13.7049	−	8.86188i	−0.660908	−	0.427358i
$431$	6.31202	+	1.85338i	0.304040	+	0.0892741i	0.430194	−	0.902737i	$-0.358445\pi$
$431$	6.31202	+	1.85338i	0.304040	+	0.0892741i	−0.126154	+	0.992011i	$0.540263\pi$
$432$	−0.755750	−	0.654861i	−0.0363610	−	0.0315070i
$433$	0.0310993	+	0.105915i	0.00149454	+	0.00508993i	0.960237	−	0.279187i	$-0.0900648\pi$
$433$	0.0310993	+	0.105915i	0.00149454	+	0.00508993i	−0.958742	+	0.284277i	$0.908247\pi$
$434$	−5.71487	+	12.5138i	−0.274322	+	0.600682i
$435$	8.11870	+	12.7110i	0.389262	+	0.609446i
$436$	6.97209			0.333903
$437$	−26.1750	+	24.2315i	−1.25212	+	1.15915i
$438$		−	4.79461i		−	0.229095i
$439$	0.254332	+	1.76892i	0.0121386	+	0.0844258i	0.994990	−	0.0999725i	$-0.0318755\pi$
$439$	0.254332	+	1.76892i	0.0121386	+	0.0844258i	−0.982852	+	0.184398i	$0.940966\pi$
$440$	9.28025e−5	−	0.0331611i	4.42418e−6	−	0.00158089i
$441$	−13.3768	+	3.92779i	−0.636992	+	0.187038i
$442$	−7.83609	−	6.79001i	−0.372725	−	0.322968i
$443$	6.99475	−	23.8219i	0.332331	−	1.13181i	−0.608674	−	0.793421i	$-0.708298\pi$
$443$	6.99475	−	23.8219i	0.332331	−	1.13181i	0.941005	−	0.338394i	$-0.109884\pi$
$444$	−2.81053	+	1.80622i	−0.133382	+	0.0857193i
$445$	13.9482	−	16.0064i	0.661210	−	0.758776i
$446$	−10.4886	−	12.1045i	−0.496650	−	0.573165i
$447$	−4.46595	+	6.94916i	−0.211232	+	0.328684i
$448$	4.52962	+	0.651260i	0.214004	+	0.0307692i
$449$	−3.39760	+	23.6308i	−0.160343	+	1.11521i	0.737645	+	0.675188i	$0.235938\pi$
$449$	−3.39760	+	23.6308i	−0.160343	+	1.11521i	−0.897988	+	0.440020i	$0.854971\pi$
$450$	1.38179	+	4.80527i	0.0651382	+	0.226523i
$451$	−0.0353210	−	0.0407626i	−0.00166320	−	0.00191944i
$452$	18.2532	−	8.33598i	0.858560	−	0.392091i
$453$	0.414791	+	0.645427i	0.0194886	+	0.0303248i
$454$	−22.4005	−	6.57737i	−1.05131	−	0.308691i
$455$	35.0401	+	10.3953i	1.64271	+	0.487339i
$456$	−7.13628	+	2.09540i	−0.334187	+	0.0981262i
$457$	−5.85944	−	2.67591i	−0.274093	−	0.125174i	0.273627	−	0.961836i	$-0.411777\pi$
$457$	−5.85944	−	2.67591i	−0.274093	−	0.125174i	−0.547720	+	0.836662i	$0.684504\pi$
$458$	9.62710	−	1.38417i	0.449845	−	0.0646780i
$459$	2.90288			0.135495
$460$	9.61640	−	4.74605i	0.448367	−	0.221286i
$461$	−10.1128			−0.470998			−0.235499	−	0.971875i	$-0.575672\pi$
$461$	−10.1128			−0.470998			−0.235499	+	0.971875i	$0.575672\pi$
$462$	0.0671749	−	0.00965829i	0.00312526	−	0.000449344i
$463$	−9.79466	−	4.47307i	−0.455196	−	0.207881i	0.174603	−	0.984639i	$-0.444136\pi$
$463$	−9.79466	−	4.47307i	−0.455196	−	0.207881i	−0.629800	+	0.776758i	$0.716863\pi$
$464$	6.47189	−	1.90032i	0.300450	−	0.0882201i
$465$	−1.91187	+	6.44447i	−0.0886611	+	0.298855i
$466$	4.45169	+	1.30713i	0.206221	+	0.0605518i
$467$	17.5752	+	27.3475i	0.813283	+	1.26549i	0.961023	+	0.276467i	$0.0891635\pi$
$467$	17.5752	+	27.3475i	0.813283	+	1.26549i	−0.147741	+	0.989026i	$0.547200\pi$
$468$	−3.24907	+	1.48380i	−0.150188	+	0.0685886i
$469$	−16.0390	−	18.5100i	−0.740611	−	0.854711i
$470$	−0.298742	+	2.03730i	−0.0137799	+	0.0939739i
$471$	2.78986	−	19.4039i	0.128550	−	0.894084i
$472$	8.51564	+	1.22436i	0.391964	+	0.0563560i
$473$	−0.0585196	+	0.0910582i	−0.00269073	+	0.00418686i
$474$	10.4345	+	12.0420i	0.479270	+	0.553108i
$475$	35.6222	+	10.6766i	1.63446	+	0.489874i
$476$	−11.1753	+	7.18194i	−0.512220	+	0.329184i
$477$	2.12317	−	7.23084i	0.0972130	−	0.331077i
$478$	18.3073	+	15.8634i	0.837357	+	0.725574i
$479$	12.4206	−	3.64701i	0.567511	−	0.166636i	0.0146250	−	0.999893i	$-0.495345\pi$
$479$	12.4206	−	3.64701i	0.567511	−	0.166636i	0.552886	+	0.833257i	$0.313526\pi$
$480$	2.23606	+	0.00625769i	0.102062	+	0.000285623i
$481$	1.69826	+	11.8117i	0.0774340	+	0.538565i
$482$			12.4415i			0.566696i
$483$	12.4655	+	18.0629i	0.567199	+	0.821889i
$484$	10.9998			0.499990
$485$	7.73713	+	12.1136i	0.351325	+	0.550051i
$486$	0.415415	−	0.909632i	0.0188436	−	0.0412617i
$487$	2.69127	+	9.16562i	0.121953	+	0.415334i	0.997727	−	0.0673877i	$-0.0214664\pi$
$487$	2.69127	+	9.16562i	0.121953	+	0.415334i	−0.875774	+	0.482722i	$0.839648\pi$
$488$	−4.98833	−	4.32241i	−0.225811	−	0.195666i
$489$	−10.3544	−	3.04033i	−0.468243	−	0.137489i
$490$	16.9274	−	26.1782i	0.764702	−	1.18261i
$491$	−5.76985	−	12.6342i	−0.260390	−	0.570174i	0.733608	−	0.679573i	$-0.237835\pi$
$491$	−5.76985	−	12.6342i	−0.260390	−	0.570174i	−0.993998	+	0.109399i	$0.965107\pi$
$492$	2.74863	−	2.38170i	0.123918	−	0.107375i
$493$	−10.5859	+	16.4719i	−0.476764	+	0.741859i
$494$	−3.78071	+	26.2954i	−0.170102	+	1.18309i
$495$	0.0318440	−	0.00925352i	0.00143128	−	0.000415915i
$496$	2.52899	+	1.62528i	0.113555	+	0.0729772i
$497$	45.2099	−	39.1746i	2.02794	−	1.75722i
$498$	12.7811	−	5.83692i	0.572733	−	0.261558i
$499$	23.7810	−	15.2831i	1.06458	−	0.684167i	0.113638	−	0.993522i	$-0.463750\pi$
$499$	23.7810	−	15.2831i	1.06458	−	0.684167i	0.950947	+	0.309355i	$0.100113\pi$
$500$	−9.35442	−	6.12330i	−0.418342	−	0.273842i
$501$	−8.59143	+	9.91504i	−0.383837	+	0.442971i
$502$	1.94020	+	6.60771i	0.0865954	+	0.294917i
$503$	−9.64950	−	4.40678i	−0.430250	−	0.196489i	0.188506	−	0.982072i	$-0.439636\pi$
$503$	−9.64950	−	4.40678i	−0.430250	−	0.196489i	−0.618756	+	0.785584i	$0.712363\pi$
$504$	0.651260	+	4.52962i	0.0290094	+	0.201765i
$505$	6.93460	+	15.2978i	0.308586	+	0.680744i
$506$	−0.0316553	−	0.0636900i	−0.00140725	−	0.00283136i
$507$		−	0.241908i		−	0.0107435i
$508$	2.82813	−	0.406624i	0.125478	−	0.0180410i
$509$	−13.2120	+	28.9303i	−0.585613	+	1.28231i	0.352444	+	0.935833i	$0.385351\pi$
$509$	−13.2120	+	28.9303i	−0.585613	+	1.28231i	−0.938057	+	0.346481i	$0.887376\pi$
$510$	−4.91747	+	4.23697i	−0.217749	+	0.187616i
$511$	−14.3683	+	16.5820i	−0.635618	+	0.733542i
$512$	0.281733	−	0.959493i	0.0124509	−	0.0424040i
$513$	−4.02105	−	6.25687i	−0.177534	−	0.276248i
$514$	0.320723	+	0.702285i	0.0141465	+	0.0309765i
$515$	40.6160	+	18.6863i	1.78976	+	0.823415i
$516$	−6.14007	−	3.94599i	−0.270302	−	0.173712i
$517$	0.0135174	+	0.00194351i	0.000594495	+	8.54754e-5i
$518$	15.1329	+	2.17578i	0.664902	+	0.0955985i
$519$	−10.4737	−	6.73106i	−0.459746	−	0.295461i
$520$	3.33819	−	7.25582i	0.146389	−	0.318189i
$521$	4.17760	+	9.14766i	0.183024	+	0.400766i	0.978798	−	0.204827i	$-0.0656631\pi$
$521$	4.17760	+	9.14766i	0.183024	+	0.400766i	−0.795774	+	0.605593i	$0.792936\pi$
$522$	3.64669	+	5.67435i	0.159611	+	0.248360i
$523$	3.99855	−	13.6178i	0.174844	−	0.595465i	−0.824708	−	0.565558i	$-0.808661\pi$
$523$	3.99855	−	13.6178i	0.174844	−	0.595465i	0.999553	−	0.0299067i	$-0.00952102\pi$
$524$	3.49924	−	4.03834i	0.152865	−	0.176416i
$525$	9.62144	−	20.7597i	0.419914	−	0.906029i
$526$	−0.805570	+	1.76395i	−0.0351245	+	0.0769120i
$527$	−8.63783	+	1.24193i	−0.376270	+	0.0540994i
$528$		−	0.0148302i		−	0.000645400i
$529$	13.8876	−	18.3340i	0.603810	−	0.797128i
$530$	6.95733	+	15.3480i	0.302207	+	0.666672i
$531$	1.22436	+	8.51564i	0.0531329	+	0.369547i
$532$	30.9600	+	14.1389i	1.34228	+	0.613001i
$533$	−3.65989	−	12.4645i	−0.158528	−	0.539895i
$534$	6.21779	−	7.17571i	0.269070	−	0.310523i
$535$	−19.5059	+	2.74884i	−0.843316	+	0.118843i
$536$	−4.50246	+	2.89356i	−0.194477	+	0.124983i
$537$	10.2218	−	4.66815i	0.441105	−	0.201446i
$538$	3.89321	−	3.37349i	0.167848	−	0.145441i
$539$	−0.173934	−	0.111780i	−0.00749186	−	0.00481472i
$540$	0.623966	+	2.14725i	0.0268512	+	0.0924028i
$541$	−0.943040	+	6.55899i	−0.0405445	+	0.281993i	0.959456	+	0.281860i	$0.0909514\pi$
$541$	−0.943040	+	6.55899i	−0.0405445	+	0.281993i	−1.00000		0.000132901i	$0.999958\pi$
$542$	4.24544	−	6.60603i	0.182357	−	0.283753i
$543$	−11.1849	+	9.69173i	−0.479988	+	0.415912i
$544$	1.20590	+	2.64055i	0.0517025	+	0.113213i
$545$	−13.0916	−	8.46530i	−0.560781	−	0.362613i
$546$	15.6834	+	4.60505i	0.671186	+	0.197078i
$547$	−19.6822	−	17.0547i	−0.841550	−	0.729207i	0.123198	−	0.992382i	$-0.460685\pi$
$547$	−19.6822	−	17.0547i	−0.841550	−	0.729207i	−0.964748	+	0.263175i	$0.915230\pi$
$548$	−1.68042	−	5.72299i	−0.0717840	−	0.244474i
$549$	2.74195	−	6.00403i	0.117024	−	0.256246i
$550$	−0.0404374	+	0.0621542i	−0.00172426	+	0.00265027i
$551$	50.1672			2.13719
$552$	4.29463	−	2.13452i	0.182791	−	0.0908513i
$553$		−	72.9164i		−	3.10072i
$554$	−0.121682	−	0.846317i	−0.00516977	−	0.0359566i
$555$	7.47041	+	0.0209062i	0.317101	+	0.000887419i
$556$	−8.11356	+	2.38236i	−0.344092	+	0.101034i
$557$	−8.62103	−	7.47017i	−0.365285	−	0.316521i	0.452807	−	0.891609i	$-0.350423\pi$
$557$	−8.62103	−	7.47017i	−0.365285	−	0.316521i	−0.818092	+	0.575087i	$0.804968\pi$
$558$	−0.846947	+	2.88444i	−0.0358541	+	0.122108i
$559$	−21.9314	+	14.0945i	−0.927599	+	0.596132i
$560$	−7.71456	−	6.72260i	−0.326000	−	0.284082i
$561$	0.0281918	+	0.0325351i	0.00119026	+	0.00137363i
$562$	−10.4080	+	16.1952i	−0.439036	+	0.683153i
$563$	−22.9603	−	3.30119i	−0.967662	−	0.139129i	−0.359677	−	0.933077i	$-0.617113\pi$
$563$	−22.9603	−	3.30119i	−0.967662	−	0.139129i	−0.607985	+	0.793948i	$0.708022\pi$
$564$	−0.131051	+	0.911481i	−0.00551825	+	0.0383803i
$565$	−44.3956	−	6.50998i	−1.86774	−	0.273877i
$566$	−6.70565	−	7.73873i	−0.281860	−	0.325283i
$567$	−4.16265	+	1.90102i	−0.174815	+	0.0798353i
$568$	−7.06740	−	10.9971i	−0.296542	−	0.461428i
$569$	−21.0427	−	6.17871i	−0.882158	−	0.259025i	−0.190879	−	0.981614i	$-0.561134\pi$
$569$	−21.0427	−	6.17871i	−0.882158	−	0.259025i	−0.691278	+	0.722589i	$0.742952\pi$
$570$	15.9440	+	4.73010i	0.667822	+	0.198122i
$571$	−21.7226	+	6.37833i	−0.909062	+	0.266925i	−0.702646	−	0.711539i	$-0.747998\pi$
$571$	−21.7226	+	6.37833i	−0.909062	+	0.266925i	−0.206416	+	0.978464i	$0.566180\pi$
$572$	−0.0481842	−	0.0220050i	−0.00201468	−	0.000920074i
$573$	2.78587	−	0.400547i	0.116381	−	0.0167331i
$574$	−16.6434			−0.694684
$575$	−23.8193	−	2.76424i	−0.993333	−	0.115277i
$576$	1.00000			0.0416667
$577$	7.34368	−	1.05586i	0.305721	−	0.0439561i	0.0122531	−	0.999925i	$-0.496100\pi$
$577$	7.34368	−	1.05586i	0.305721	−	0.0439561i	0.293468	+	0.955969i	$0.405191\pi$
$578$	7.79856	+	3.56148i	0.324377	+	0.148138i
$579$	−20.3001	+	5.96066i	−0.843645	+	0.247716i
$580$	−14.4596	−	4.28972i	−0.600404	−	0.178121i
$581$	−61.6946	−	18.1152i	−2.55953	−	0.751544i
$582$	3.47530	+	5.40767i	0.144056	+	0.224155i
$583$	0.101662	−	0.0464274i	0.00421040	−	0.00192283i
$584$	3.13980	+	3.62352i	0.129926	+	0.149942i
$585$	7.90239	+	1.15877i	0.326723	+	0.0479094i
$586$	2.42700	−	16.8802i	0.100259	−	0.697314i
$587$	7.58031	+	1.08988i	0.312873	+	0.0449843i	0.296963	−	0.954889i	$-0.404026\pi$
$587$	7.58031	+	1.08988i	0.312873	+	0.0449843i	0.0159101	+	0.999873i	$0.494935\pi$
$588$	7.53737	−	11.7284i	0.310836	−	0.483670i
$589$	14.6419	+	16.8977i	0.603310	+	0.696257i
$590$	−14.5033	−	12.6384i	−0.597092	−	0.520316i
$591$	−19.4914	+	12.5263i	−0.801767	+	0.515264i
$592$	0.941236	−	3.20555i	0.0386845	−	0.131747i
$593$	24.3459	+	21.0959i	0.999768	+	0.866304i	0.991028	−	0.133658i	$-0.0426722\pi$
$593$	24.3459	+	21.0959i	0.999768	+	0.866304i	0.00874074	+	0.999962i	$0.497218\pi$
$594$	0.0142294	−	0.00417814i	0.000583841	−	0.000171431i
$595$	29.7041	+	0.0831279i	1.21775	+	0.00340791i
$596$	−1.17559	−	8.17640i	−0.0481540	−	0.334919i
$597$			18.3455i			0.750831i
$598$	−0.562845	−	17.1207i	−0.0230165	−	0.700119i
$599$	−8.02915			−0.328062			−0.164031	−	0.986455i	$-0.552450\pi$
$599$	−8.02915			−0.328062			−0.164031	+	0.986455i	$0.552450\pi$
$600$	−4.19107	−	2.72670i	−0.171100	−	0.111317i
$601$	−12.0305	+	26.3431i	−0.490734	+	1.07456i	0.488637	+	0.872487i	$0.337494\pi$
$601$	−12.0305	+	26.3431i	−0.490734	+	1.07456i	−0.979371	+	0.202070i	$0.935233\pi$
$602$	9.40997	+	32.0474i	0.383522	+	1.30615i
$603$	−4.04484	−	3.50487i	−0.164719	−	0.142729i
$604$	−0.736143	−	0.216151i	−0.0299532	−	0.00879506i
$605$	−20.6544	−	13.3556i	−0.839720	−	0.542982i
$606$	3.12038	+	6.83269i	0.126757	+	0.277559i
$607$	−31.6462	+	27.4216i	−1.28448	+	1.11301i	−0.297064	+	0.954858i	$0.596007\pi$
$607$	−31.6462	+	27.4216i	−1.28448	+	1.11301i	−0.987415	+	0.158150i	$0.949447\pi$
$608$	4.02105	−	6.25687i	0.163075	−	0.253750i
$609$	4.39283	−	30.5528i	0.178006	−	1.23806i
$610$	4.11849	+	14.1729i	0.166753	+	0.573844i
$611$	2.76701	+	1.77825i	0.111941	+	0.0719402i
$612$	−2.19385	+	1.90098i	−0.0886810	+	0.0768425i
$613$	−36.4567	+	16.6492i	−1.47247	+	0.672455i	−0.980204	−	0.197990i	$-0.936559\pi$
$613$	−36.4567	+	16.6492i	−1.47247	+	0.672455i	−0.492266	+	0.870445i	$0.663831\pi$
$614$	24.1859	−	15.5433i	0.976063	−	0.627277i
$615$	−8.05292	+	1.13484i	−0.324725	+	0.0457613i
$616$	−0.0444426	+	0.0512895i	−0.00179064	+	0.00206651i
$617$	10.7674	+	36.6703i	0.433478	+	1.47629i	0.829738	+	0.558152i	$0.188490\pi$
$617$	10.7674	+	36.6703i	0.433478	+	1.47629i	−0.396260	+	0.918138i	$0.629692\pi$
$618$	18.1874	+	8.30589i	0.731603	+	0.334112i
$619$	−3.82211	−	26.5833i	−0.153623	−	1.06847i	−0.910081	−	0.414431i	$-0.863981\pi$
$619$	−3.82211	−	26.5833i	−0.153623	−	1.06847i	0.756457	−	0.654043i	$-0.226929\pi$
$620$	−2.77533	−	6.12242i	−0.111460	−	0.245882i
$621$	3.25800	+	3.51930i	0.130739	+	0.141225i
$622$		−	4.78711i		−	0.191946i
$623$	−43.0079	+	6.18360i	−1.72307	+	0.247741i
$624$	1.48380	−	3.24907i	0.0593995	−	0.130067i
$625$	10.1302	+	22.8556i	0.405207	+	0.914225i
$626$	12.6882	−	14.6429i	0.507122	−	0.585250i
$627$	0.0310751	−	0.105832i	0.00124102	−	0.00422653i
$628$	10.5984	+	16.4914i	0.422923	+	0.658080i
$629$	4.02877	+	8.82177i	0.160637	+	0.351747i
$630$	4.27684	−	9.29604i	0.170393	−	0.370363i
$631$	−21.2884	−	13.6813i	−0.847480	−	0.544642i	0.0433081	−	0.999062i	$-0.486210\pi$
$631$	−21.2884	−	13.6813i	−0.847480	−	0.544642i	−0.890788	+	0.454420i	$0.849847\pi$
$632$	−15.7717	−	2.26762i	−0.627363	−	0.0902012i
$633$	10.5960	+	1.52347i	0.421152	+	0.0605525i
$634$	−5.58285	−	3.58788i	−0.221723	−	0.142493i
$635$	−5.80412	−	2.67031i	−0.230330	−	0.105968i
$636$	3.13061	+	6.85508i	0.124137	+	0.271822i
$637$	−26.9223	−	41.8920i	−1.06670	−	1.65982i
$638$	−0.0281820	+	0.0959792i	−0.00111574	+	0.00379985i
$639$	8.56052	−	9.87937i	0.338649	−	0.390822i
$640$	−1.69400	+	1.45958i	−0.0669612	+	0.0576949i
$641$	7.65167	−	16.7548i	0.302223	−	0.661775i	−0.696204	−	0.717844i	$-0.745129\pi$
$641$	7.65167	−	16.7548i	0.302223	−	0.661775i	0.998427	+	0.0560684i	$0.0178565\pi$
$642$	−8.71985	+	1.25373i	−0.344145	+	0.0494806i
$643$		−	48.9713i		−	1.93124i	−0.259956	−	0.965621i	$-0.583708\pi$
$643$		−	48.9713i		−	1.93124i	0.259956	−	0.965621i	$-0.416292\pi$
$644$	−21.2495	−	5.48785i	−0.837346	−	0.216252i
$645$	6.73818	+	14.8645i	0.265316	+	0.585289i
$646$	3.07262	+	21.3705i	0.120891	+	0.840813i
$647$	29.5217	+	13.4821i	1.16062	+	0.530035i	0.900207	−	0.435463i	$-0.143415\pi$
$647$	29.5217	+	13.4821i	1.16062	+	0.530035i	0.260409	+	0.965498i	$0.416143\pi$
$648$	0.281733	+	0.959493i	0.0110675	+	0.0376924i
$649$	−0.0835517	+	0.0964238i	−0.00327969	+	0.00378496i
$650$	−15.0780	+	9.57119i	−0.591406	+	0.375413i
$651$	11.5731	−	7.43760i	0.453587	−	0.291502i
$652$	9.81635	−	4.48298i	0.384438	−	0.175567i
$653$	2.13136	−	1.84684i	0.0834066	−	0.0722722i	−0.612160	−	0.790734i	$-0.709699\pi$
$653$	2.13136	−	1.84684i	0.0834066	−	0.0722722i	0.695566	+	0.718462i	$0.255154\pi$
$654$	−5.86530	−	3.76940i	−0.229351	−	0.147395i
$655$	−11.4738	+	3.33416i	−0.448318	+	0.130276i
$656$	−0.517593	+	3.59994i	−0.0202086	+	0.140554i
$657$	−2.59216	+	4.03348i	−0.101130	+	0.157361i
$658$	3.18473	−	2.75959i	0.124154	−	0.107580i
$659$	5.49972	+	12.0427i	0.214239	+	0.469117i	0.985989	−	0.166808i	$-0.0533459\pi$
$659$	5.49972	+	12.0427i	0.214239	+	0.469117i	−0.771751	+	0.635925i	$0.780619\pi$
$660$	−0.0180063	+	0.0278467i	−0.000700895	+	0.00108393i
$661$	−41.1214	−	12.0743i	−1.59944	−	0.469637i	−0.644048	−	0.764985i	$-0.722746\pi$
$661$	−41.1214	−	12.0743i	−1.59944	−	0.469637i	−0.955390	+	0.295348i	$0.904564\pi$
$662$	−7.49288	−	6.49261i	−0.291219	−	0.252343i
$663$	2.92118	+	9.94863i	0.113449	+	0.386373i
$664$	−5.83692	+	12.7811i	−0.226516	+	0.496001i
$665$	−40.9667	−	64.1394i	−1.58862	−	2.48722i
$666$	3.34088			0.129457
$667$	−31.8506	+	5.65324i	−1.23326	+	0.218894i
$668$		−	13.1195i		−	0.507608i
$669$	2.27939	+	15.8535i	0.0881265	+	0.612933i
$670$	11.9676	+	0.0334917i	0.462348	+	0.00129390i
$671$	0.0939214	−	0.0275778i	0.00362580	−	0.00106463i
$672$	−3.45846	−	2.99677i	−0.133413	−	0.115603i
$673$	−6.73450	+	22.9356i	−0.259596	+	0.884102i	0.721799	+	0.692103i	$0.243315\pi$
$673$	−6.73450	+	22.9356i	−0.259596	+	0.884102i	−0.981395	+	0.192000i	$0.938503\pi$
$674$	−3.90427	+	2.50912i	−0.150387	+	0.0966478i
$675$	1.43549	−	4.78951i	0.0552521	−	0.184348i
$676$	0.158416	+	0.182822i	0.00609294	+	0.00703162i
$677$	18.4622	−	28.7278i	0.709560	−	1.10410i	−0.280003	−	0.959999i	$-0.590335\pi$
$677$	18.4622	−	28.7278i	0.709560	−	1.10410i	0.989563	−	0.144098i	$-0.0460282\pi$
$678$	−19.8624	−	2.85578i	−0.762810	−	0.109675i
$679$	4.18637	−	29.1169i	0.160658	−	1.11740i
$680$	0.941746	−	6.42235i	0.0361143	−	0.246286i
$681$	15.2885	+	17.6438i	0.585856	+	0.676113i
$682$	−0.0405537	+	0.0185203i	−0.00155288	+	0.000709178i
$683$	−21.4148	−	33.3221i	−0.819416	−	1.27504i	−0.958596	−	0.284769i	$-0.908083\pi$
$683$	−21.4148	−	33.3221i	−0.819416	−	1.27504i	0.139180	−	0.990267i	$-0.455553\pi$
$684$	7.13628	+	2.09540i	0.272863	+	0.0801197i
$685$	−3.79333	+	12.7864i	−0.144936	+	0.488544i
$686$	−30.4792	+	8.94949i	−1.16370	+	0.341693i
$687$	−8.84717	−	4.04037i	−0.337541	−	0.154150i
$688$	7.22443	−	1.03872i	0.275429	−	0.0396007i
$689$	26.9178			1.02549
$690$	−10.6557	−	1.20639i	−0.405657	−	0.0459264i
$691$	−23.4616			−0.892522			−0.446261	−	0.894903i	$-0.647245\pi$
$691$	−23.4616			−0.892522			−0.446261	+	0.894903i	$0.647245\pi$
$692$	12.3234	−	1.77184i	0.468467	−	0.0673553i
$693$	−0.0617328	−	0.0281924i	−0.00234503	−	0.00107094i
$694$	2.45881	−	0.721973i	0.0933353	−	0.0274057i
$695$	18.1275	+	5.37786i	0.687615	+	0.203994i
$696$	−6.47189	−	1.90032i	−0.245316	−	0.0720314i
$697$	−5.70789	−	8.88166i	−0.216202	−	0.336417i
$698$	−10.8083	+	4.93599i	−0.409101	+	0.186830i
$699$	−3.03831	−	3.50640i	−0.114919	−	0.132624i
$700$	6.32334	+	21.9899i	0.239000	+	0.831139i
$701$	1.61932	−	11.2626i	0.0611608	−	0.425382i	−0.936120	−	0.351682i	$-0.885610\pi$
$701$	1.61932	−	11.2626i	0.0611608	−	0.425382i	0.997280	−	0.0737007i	$-0.0234810\pi$
$702$	3.53549	+	0.508327i	0.133439	+	0.0191856i
$703$	13.4338	−	20.9035i	0.506667	−	0.788389i
$704$	0.00971169	+	0.0112079i	0.000366023	+	0.000422413i
$705$	1.35277	−	1.55238i	0.0509482	−	0.0584659i
$706$	−7.15532	+	4.59844i	−0.269294	+	0.173065i
$707$	9.68428	−	32.9816i	0.364215	−	1.24040i
$708$	−6.50187	−	5.63391i	−0.244355	−	0.211735i
$709$	31.2658	−	9.18047i	1.17421	−	0.344780i	0.364272	−	0.931292i	$-0.381318\pi$
$709$	31.2658	−	9.18047i	1.17421	−	0.344780i	0.809940	+	0.586513i	$0.199500\pi$
$710$	−0.0818022	+	29.2304i	−0.00306998	+	1.09700i
$711$	−2.26762	−	15.7717i	−0.0850425	−	0.591484i
$712$			9.49482i			0.355834i
$713$	−11.2002	−	9.07820i	−0.419450	−	0.339981i
$714$	13.2841			0.497146
$715$	0.0637581	+	0.0998227i	0.00238442	+	0.00373316i
$716$	−4.66815	+	10.2218i	−0.174457	+	0.382008i
$717$	−6.82470	−	23.2428i	−0.254873	−	0.868018i
$718$	3.88882	+	3.36968i	0.145130	+	0.125755i
$719$	8.90966	+	2.61611i	0.332274	+	0.0975645i	0.443614	−	0.896218i	$-0.353696\pi$
$719$	8.90966	+	2.61611i	0.332274	+	0.0975645i	−0.111340	+	0.993782i	$0.535514\pi$
$720$	−1.87771	−	1.21417i	−0.0699781	−	0.0452494i
$721$	−38.0094	−	83.2289i	−1.41554	−	3.09961i
$722$	27.4467	−	23.7827i	1.02146	−	0.885101i
$723$	6.72639	−	10.4665i	0.250157	−	0.389252i
$724$	2.10621	−	14.6490i	0.0782768	−	0.544427i
$725$	21.9426	+	25.6113i	0.814926	+	0.951180i
$726$	−9.25360	−	5.94693i	−0.343433	−	0.220711i
$727$	33.3710	−	28.9161i	1.23766	−	1.07244i	0.242917	−	0.970047i	$-0.421896\pi$
$727$	33.3710	−	28.9161i	1.23766	−	1.07244i	0.994744	−	0.102392i	$-0.0326496\pi$
$728$	−14.8684	+	6.79015i	−0.551058	+	0.251660i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	−1.49606	−	10.6162i	−0.0553718	−	0.392922i
$731$	−13.8747	+	16.0123i	−0.513175	+	0.592235i
$732$	1.85958	+	6.33314i	0.0687320	+	0.234080i
$733$	−35.4262	−	16.1786i	−1.30850	−	0.597570i	−0.365636	−	0.930758i	$-0.619148\pi$
$733$	−35.4262	−	16.1786i	−1.30850	−	0.597570i	−0.942861	+	0.333188i	$0.891876\pi$
$734$	3.58578	+	24.9397i	0.132354	+	0.920540i
$735$	−28.3932	+	12.8708i	−1.04730	+	0.474748i
$736$	−1.84785	+	4.42555i	−0.0681125	+	0.163128i
$737$		−	0.0793723i		−	0.00292372i
$738$	−3.59994	+	0.517593i	−0.132516	+	0.0190529i
$739$	−11.0207	+	24.1319i	−0.405403	+	0.887708i	0.591291	+	0.806458i	$0.298618\pi$
$739$	−11.0207	+	24.1319i	−0.405403	+	0.887708i	−0.996694	+	0.0812498i	$0.974109\pi$
$740$	−5.65945	+	4.87628i	−0.208046	+	0.179256i
$741$	17.3969	−	20.0771i	0.639091	−	0.737551i
$742$	9.71602	−	33.0897i	0.356686	−	1.21476i
$743$	−11.8932	−	18.5062i	−0.436320	−	0.678927i	0.551562	−	0.834134i	$-0.314032\pi$
$743$	−11.8932	−	18.5062i	−0.436320	−	0.678927i	−0.987882	+	0.155207i	$0.950396\pi$
$744$	−1.24883	−	2.73455i	−0.0457841	−	0.100253i
$745$	−7.72012	+	16.7803i	−0.282843	+	0.614782i
$746$	−14.8820	−	9.56408i	−0.544869	−	0.350166i
$747$	−13.9078	−	1.99964i	−0.508859	−	0.0731629i
$748$	−0.0426119	−	0.00612667i	−0.00155805	−	0.000224013i
$749$	33.9144	+	21.7954i	1.23920	+	0.796388i
$750$	4.55894	+	10.2086i	0.166469	+	0.372766i
$751$	−11.5407	−	25.2706i	−0.421126	−	0.922137i	−0.994684	−	0.102972i	$-0.967165\pi$
$751$	−11.5407	−	25.2706i	−0.421126	−	0.922137i	0.573559	−	0.819165i	$-0.305562\pi$
$752$	−0.497851	−	0.774671i	−0.0181548	−	0.0282494i
$753$	1.94020	−	6.60771i	0.0707048	−	0.240798i
$754$	−15.7772	+	18.2079i	−0.574573	+	0.663093i
$755$	1.11982	+	1.29967i	0.0407543	+	0.0472998i
$756$	1.90102	−	4.16265i	0.0691394	−	0.151394i
$757$	−31.5746	+	4.53974i	−1.14760	+	0.164999i	−0.689761	−	0.724037i	$-0.742284\pi$
$757$	−31.5746	+	4.53974i	−1.14760	+	0.164999i	−0.457836	+	0.889037i	$0.651375\pi$
$758$		−	31.4950i		−	1.14395i
$759$	−0.00780326	+	0.0706936i	−0.000283240	+	0.00256601i
$760$	−15.1473	+	6.86635i	−0.549449	+	0.249069i
$761$	−7.21184	−	50.1594i	−0.261429	−	1.81828i	−0.522138	−	0.852861i	$-0.674866\pi$
$761$	−7.21184	−	50.1594i	−0.261429	−	1.81828i	0.260709	−	0.965417i	$-0.416044\pi$
$762$	−2.59901	−	1.18693i	−0.0941524	−	0.0429980i
$763$	8.98886	+	30.6132i	0.325418	+	1.10827i
$764$	−1.84312	+	2.12707i	−0.0666816	+	0.0769547i
$765$	6.42752	−	0.905786i	0.232387	−	0.0327487i
$766$	29.4209	−	18.9077i	1.06302	−	0.683161i
$767$	−27.9524	+	12.7654i	−1.00930	+	0.460933i
$768$	−0.755750	+	0.654861i	−0.0272708	+	0.0236303i
$769$	21.4845	+	13.8072i	0.774749	+	0.497901i	0.867287	−	0.497808i	$-0.165862\pi$
$769$	21.4845	+	13.8072i	0.774749	+	0.497901i	−0.0925380	+	0.995709i	$0.529498\pi$
$770$	0.145724	−	0.0423459i	0.00525154	−	0.00152604i
$771$	0.109875	−	0.764196i	0.00395704	−	0.0275218i
$772$	11.4384	−	17.7985i	0.411678	−	0.640583i
$773$	−20.7981	+	18.0217i	−0.748057	+	0.648195i	−0.943066	−	0.332606i	$-0.892072\pi$
$773$	−20.7981	+	18.0217i	−0.748057	+	0.648195i	0.195009	+	0.980802i	$0.437527\pi$
$774$	3.03200	+	6.63915i	0.108983	+	0.238639i
$775$	−2.22238	+	14.8659i	−0.0798303	+	0.533997i
$776$	−6.16773	−	1.81101i	−0.221408	−	0.0650114i
$777$	−11.5543	−	10.0119i	−0.414508	−	0.359173i
$778$	6.85280	+	23.3385i	0.245685	+	0.836726i
$779$	−11.2370	+	24.6056i	−0.402608	+	0.881588i
$780$	−6.73106	+	4.29922i	−0.241011	+	0.153937i
$781$	0.193864			0.00693699
$782$	−4.35898	−	13.2217i	−0.155877	−	0.472807i
$783$		−	6.74512i		−	0.241051i
$784$	1.98409	+	13.7997i	0.0708604	+	0.492845i
$785$	0.122672	−	43.8344i	0.00437835	−	1.56452i
$786$	−5.12704	+	1.50543i	−0.182875	+	0.0536971i
$787$	2.48519	+	2.15343i	0.0885874	+	0.0767614i	0.698029	−	0.716070i	$-0.254061\pi$
$787$	2.48519	+	2.15343i	0.0885874	+	0.0767614i	−0.609441	+	0.792831i	$0.708606\pi$
$788$	6.52758	−	22.2309i	0.232535	−	0.791943i
$789$	1.63135	−	1.04841i	0.0580777	−	0.0373243i
$790$	26.8613	+	23.4074i	0.955684	+	0.832799i
$791$	60.1351	+	69.3995i	2.13816	+	2.46756i
$792$	−0.00801779	+	0.0124759i	−0.000284900	+	0.000443313i
$793$	23.3360	+	3.35521i	0.828687	+	0.119147i
$794$	1.48438	−	10.3241i	0.0526786	−	0.366388i
$795$	2.44485	−	16.6729i	0.0867099	−	0.591328i
$796$	−12.0137	−	13.8646i	−0.425816	−	0.491418i
$797$	−19.8313	+	9.05666i	−0.702462	+	0.320803i	−0.734429	−	0.678685i	$-0.762550\pi$
$797$	−19.8313	+	9.05666i	−0.702462	+	0.320803i	0.0319675	+	0.999489i	$0.489823\pi$
$798$	−18.4011	−	28.6326i	−0.651391	−	1.01358i
$799$	2.56484	+	0.753106i	0.0907377	+	0.0266430i
$800$	4.95301	−	0.683863i	0.175115	−	0.0241782i
$801$	−9.11022	+	2.67500i	−0.321894	+	0.0945165i
$802$	−7.24407	−	3.30826i	−0.255797	−	0.116819i
$803$	−0.0703811	+	0.0101193i	−0.00248369	+	0.000357101i
$804$	5.35209			0.188754
$805$	33.2371	+	36.1050i	1.17145	+	1.27253i
$806$	−10.7377			−0.378220
$807$	−5.09903	+	0.733129i	−0.179494	+	0.0258074i
$808$	−6.83269	−	3.12038i	−0.240373	−	0.109775i
$809$	−4.12486	+	1.21117i	−0.145022	+	0.0425824i	−0.353438	−	0.935458i	$-0.614987\pi$
$809$	−4.12486	+	1.21117i	−0.145022	+	0.0425824i	0.208416	+	0.978040i	$0.433169\pi$
$810$	0.635975	−	2.14372i	0.0223459	−	0.0753226i
$811$	43.1072	+	12.6574i	1.51370	+	0.444462i	0.930016	−	0.367520i	$-0.119793\pi$
$811$	43.1072	+	12.6574i	1.51370	+	0.444462i	0.583683	+	0.811982i	$0.301611\pi$
$812$	16.6879	+	25.9669i	0.585632	+	0.911261i
$813$	−7.14297	+	3.26209i	−0.250515	+	0.114406i
$814$	0.0324456	+	0.0374442i	0.00113722	+	0.00131242i
$815$	−23.8753	−	3.50098i	−0.836317	−	0.122634i
$816$	0.413122	−	2.87333i	0.0144622	−	0.100587i
$817$	53.7321	+	7.72551i	1.87985	+	0.270281i
$818$	−6.47892	+	10.0814i	−0.226530	+	0.352488i
$819$	−10.7040	−	12.3531i	−0.374028	−	0.431652i
$820$	5.34283	−	6.13120i	0.186580	−	0.214111i
$821$	11.6099	−	7.46126i	0.405190	−	0.260400i	−0.322134	−	0.946694i	$-0.604400\pi$
$821$	11.6099	−	7.46126i	0.405190	−	0.260400i	0.727324	+	0.686294i	$0.240764\pi$
$822$	−1.68042	+	5.72299i	−0.0586114	+	0.199612i
$823$	−0.433501	−	0.375630i	−0.0151109	−	0.0130937i	0.647273	−	0.762259i	$-0.275910\pi$
$823$	−0.433501	−	0.375630i	−0.0151109	−	0.0130937i	−0.662383	+	0.749165i	$0.730455\pi$
$824$	−19.1843	+	5.63302i	−0.668316	+	0.196235i
$825$	0.0676213	−	0.0304253i	0.00235427	−	0.00105927i
$826$	5.60293	+	38.9692i	0.194951	+	1.35591i
$827$			52.7565i			1.83452i	0.398284	+	0.917262i	$0.369606\pi$
$827$			52.7565i			1.83452i	−0.398284	+	0.917262i	$0.630394\pi$
$828$	−4.76688	−	0.526175i	−0.165661	−	0.0182858i
$829$	38.5039			1.33729			0.668647	−	0.743580i	$-0.266874\pi$
$829$	38.5039			1.33729			0.668647	+	0.743580i	$0.266874\pi$
$830$	26.4784	−	16.9121i	0.919079	−	0.587028i
$831$	−0.355188	+	0.777753i	−0.0123213	+	0.0269800i
$832$	1.00631	+	3.42716i	0.0348874	+	0.118815i
$833$	−30.5856	−	26.5026i	−1.05973	−	0.918261i
$834$	8.11356	+	2.38236i	0.280950	+	0.0824943i
$835$	−15.9293	+	24.6346i	−0.551255	+	0.852514i
$836$	0.0458203	+	0.100332i	0.00158473	+	0.00347007i
$837$	2.27194	−	1.96865i	0.0785298	−	0.0680465i
$838$	−17.2777	+	26.8847i	−0.596849	+	0.928715i
$839$	5.99132	−	41.6706i	0.206843	−	1.43863i	−0.576530	−	0.817076i	$-0.695594\pi$
$839$	5.99132	−	41.6706i	0.206843	−	1.43863i	0.783373	−	0.621552i	$-0.213497\pi$
$840$	2.85539	+	9.82622i	0.0985204	+	0.339037i
$841$	13.8778	+	8.91873i	0.478546	+	0.307543i
$842$	22.5339	−	19.5258i	0.776570	−	0.672902i
$843$	17.5116	−	7.99727i	0.603131	−	0.275441i
$844$	−9.00556	+	5.78752i	−0.309984	+	0.199215i
$845$	−0.0754828	−	0.535631i	−0.00259669	−	0.0184263i
$846$	0.603031	−	0.695935i	0.0207326	−	0.0239267i
$847$	14.1816	+	48.2981i	0.487286	+	1.65954i
$848$	−6.85508	−	3.13061i	−0.235404	−	0.107506i
$849$	1.45728	+	10.1356i	0.0500136	+	0.347852i
$850$	−9.56614	+	10.9159i	−0.328116	+	0.374411i
$851$	−6.17344	+	14.7852i	−0.211623	+	0.506831i
$852$			13.0723i			0.447849i
$853$	−3.15122	+	0.453077i	−0.107896	+	0.0155130i	−0.196051	−	0.980594i	$-0.562812\pi$
$853$	−3.15122	+	0.453077i	−0.107896	+	0.0155130i	0.0881555	+	0.996107i	$0.471903\pi$
$854$	12.5477	−	27.4756i	0.429373	−	0.940196i
$855$	−10.8557	−	12.5992i	−0.371257	−	0.430884i
$856$	5.76901	−	6.65779i	0.197181	−	0.227559i
$857$	−4.68678	+	15.9617i	−0.160097	+	0.545242i	0.839899	+	0.542742i	$0.182614\pi$
$857$	−4.68678	+	15.9617i	−0.160097	+	0.545242i	−0.999997	+	0.00249978i	$0.999204\pi$
$858$	0.0286383	+	0.0445621i	0.000977696	+	0.00152132i
$859$	9.33700	+	20.4452i	0.318574	+	0.697580i	0.999392	−	0.0348728i	$-0.0111026\pi$
$859$	9.33700	+	20.4452i	0.318574	+	0.697580i	−0.680818	+	0.732453i	$0.738375\pi$
$860$	−14.8266	−	6.82127i	−0.505581	−	0.232603i
$861$	14.0014	+	8.99812i	0.477165	+	0.306655i
$862$	6.51154	+	0.936218i	0.221784	+	0.0318877i
$863$	−16.5866	−	2.38480i	−0.564616	−	0.0811795i	−0.145904	−	0.989299i	$-0.546609\pi$
$863$	−16.5866	−	2.38480i	−0.564616	−	0.0811795i	−0.418712	+	0.908119i	$0.637518\pi$
$864$	−0.841254	−	0.540641i	−0.0286200	−	0.0183930i
$865$	−25.2911	−	11.6357i	−0.859925	−	0.395627i
$866$	0.0458560	+	0.100411i	0.00155825	+	0.00341209i
$867$	−4.63508	−	7.21233i	−0.157416	−	0.244943i
$868$	−3.87580	+	13.1997i	−0.131553	+	0.448029i
$869$	0.154745	−	0.178585i	0.00524935	−	0.00605807i
$870$	9.84502	+	11.4262i	0.333778	+	0.387385i
$871$	7.94142	−	17.3893i	0.269085	−	0.589214i
$872$	6.90112	−	0.992232i	0.233702	−	0.0336012i
$873$		−	6.42811i		−	0.217559i
$874$	−22.4600	+	27.7100i	−0.759722	+	0.937304i
$875$	14.8260	−	48.9682i	0.501211	−	1.65543i
$876$	−0.682344	−	4.74581i	−0.0230543	−	0.160346i
$877$	26.9633	+	12.3137i	0.910487	+	0.415806i	0.814891	−	0.579615i	$-0.196797\pi$
$877$	26.9633	+	12.3137i	0.910487	+	0.415806i	0.0955964	+	0.995420i	$0.469524\pi$
$878$	0.503486	+	1.71472i	0.0169918	+	0.0578689i
$879$	−11.1678	+	12.8884i	−0.376682	+	0.434714i
$880$	−0.00462746	−	0.0328368i	−0.000155992	−	0.00110693i
$881$	−14.8048	+	9.51448i	−0.498787	+	0.320551i	−0.765731	−	0.643161i	$-0.777623\pi$
$881$	−14.8048	+	9.51448i	−0.498787	+	0.320551i	0.266944	+	0.963712i	$0.413986\pi$
$882$	−12.6817	+	5.79153i	−0.427015	+	0.195011i
$883$	36.8328	−	31.9158i	1.23952	−	1.07405i	0.244999	−	0.969523i	$-0.421212\pi$
$883$	36.8328	−	31.9158i	1.23952	−	1.07405i	0.994522	−	0.104528i	$-0.0333332\pi$
$884$	−8.72265	−	5.60570i	−0.293374	−	0.188540i
$885$	5.36812	+	18.4732i	0.180447	+	0.620970i
$886$	3.53334	−	24.5749i	0.118705	−	0.825611i
$887$	−18.4568	+	28.7193i	−0.619717	+	0.964299i	0.379517	+	0.925185i	$0.376090\pi$
$887$	−18.4568	+	28.7193i	−0.619717	+	0.964299i	−0.999235	+	0.0391144i	$0.987546\pi$
$888$	−2.52487	+	2.18781i	−0.0847291	+	0.0734182i
$889$	5.43162	+	11.8936i	0.182171	+	0.398898i
$890$	11.5283	−	17.8285i	0.386430	−	0.597613i
$891$	−0.0142294	−	0.00417814i	−0.000476704	−	0.000139973i
$892$	−12.1045	−	10.4886i	−0.405289	−	0.351185i
$893$	−1.92956	−	6.57147i	−0.0645702	−	0.219906i
$894$	−3.43153	+	7.51400i	−0.114767	+	0.251306i
$895$	21.1765	−	13.5257i	0.707851	−	0.452114i
$896$	4.57619			0.152880
$897$	−8.78267	+	14.7072i	−0.293245	+	0.491058i
$898$			23.8738i			0.796680i
$899$	2.88575	+	20.0708i	0.0962452	+	0.669400i
$900$	2.05159	+	4.55971i	0.0683862	+	0.151990i
$901$	20.9902	−	6.16329i	0.699286	−	0.205329i
$902$	−0.0407626	−	0.0353210i	−0.00135725	−	0.00117606i
$903$	9.40997	−	32.0474i	0.313144	−	1.06647i
$904$	16.8811	−	10.8488i	0.561458	−	0.360827i
$905$	−21.7413	+	24.9493i	−0.722705	+	0.829344i
$906$	0.502422	+	0.579826i	0.0166919	+	0.0192634i
$907$	−16.1497	+	25.1294i	−0.536242	+	0.834409i	−0.998633	−	0.0522674i	$-0.983355\pi$
$907$	−16.1497	+	25.1294i	−0.536242	+	0.834409i	0.462391	+	0.886676i	$0.346992\pi$
$908$	−23.1085	−	3.32250i	−0.766883	−	0.110261i
$909$	1.06900	−	7.43503i	0.0354563	−	0.246604i
$910$	36.1629	+	5.30277i	1.19879	+	0.175785i
$911$	2.95632	+	3.41178i	0.0979474	+	0.113037i	0.802607	−	0.596508i	$-0.203446\pi$
$911$	2.95632	+	3.41178i	0.0979474	+	0.113037i	−0.704660	+	0.709546i	$0.748900\pi$
$912$	−6.76544	+	3.08967i	−0.224026	+	0.102309i
$913$	−0.112656	−	0.175297i	−0.00372838	−	0.00580147i
$914$	−6.18062	−	1.81479i	−0.204437	−	0.0600280i
$915$	4.19776	−	14.1496i	0.138774	−	0.467773i
$916$	9.33213	−	2.74016i	0.308342	−	0.0905374i
$917$	22.2431	+	10.1581i	0.734531	+	0.335449i
$918$	2.87333	−	0.413122i	0.0948340	−	0.0136351i
$919$	−31.6282			−1.04332			−0.521659	−	0.853154i	$-0.674687\pi$
$919$	−31.6282			−1.04332			−0.521659	+	0.853154i	$0.674687\pi$
$920$	8.84308	−	6.06629i	0.291548	−	0.200000i
$921$	−28.7498			−0.947338
$922$	−10.0098	+	1.43920i	−0.329656	+	0.0473974i
$923$	42.4727	+	19.3966i	1.39801	+	0.638448i
$924$	0.0651166	−	0.0191200i	0.00214218	−	0.000629001i
$925$	16.5474	−	2.28471i	0.544076	−	0.0751207i
$926$	−10.3315	−	3.03362i	−0.339516	−	0.0996908i
$927$	−10.8097	−	16.8202i	−0.355036	−	0.552447i
$928$	6.13557	−	2.80202i	0.201410	−	0.0919809i
$929$	21.7712	+	25.1253i	0.714290	+	0.824335i	0.990608	−	0.136731i	$-0.0436597\pi$
$929$	21.7712	+	25.1253i	0.714290	+	0.824335i	−0.276318	+	0.961066i	$0.589114\pi$
$930$	−0.975270	+	6.65097i	−0.0319804	+	0.218094i
$931$	−14.7568	+	102.636i	−0.483634	+	3.36375i
$932$	4.59240	+	0.660288i	0.150429	+	0.0216284i
$933$	−2.58811	+	4.02717i	−0.0847308	+	0.131844i
$934$	21.2883	+	24.5680i	0.696573	+	0.803888i
$935$	0.0725740	+	0.0632422i	0.00237342	+	0.00206824i
$936$	−3.00483	+	1.93109i	−0.0982159	+	0.0631195i
$937$	2.74124	−	9.33579i	0.0895523	−	0.304987i	−0.902521	−	0.430645i	$-0.858286\pi$
$937$	2.74124	−	9.33579i	0.0895523	−	0.304987i	0.992074	+	0.125658i	$0.0401042\pi$
$938$	−18.5100	−	16.0390i	−0.604372	−	0.523691i
$939$	−18.5905	+	5.45868i	−0.606680	+	0.178137i
$940$	−0.00576241	+	2.05908i	−0.000187949	+	0.0671599i
$941$	−5.53312	−	38.4837i	−0.180375	−	1.25453i	−0.855879	−	0.517177i	$-0.826983\pi$
$941$	−5.53312	−	38.4837i	−0.180375	−	1.25453i	0.675504	−	0.737356i	$-0.263926\pi$
$942$		−	19.6034i		−	0.638714i
$943$	4.36150	−	16.8881i	0.142030	−	0.549954i
$944$	8.60321			0.280011
$945$	−8.62373	+	5.50809i	−0.280530	+	0.179178i
$946$	−0.0449650	+	0.0984596i	−0.00146194	+	0.00320120i
$947$	1.83066	+	6.23466i	0.0594885	+	0.202599i	0.983875	−	0.178858i	$-0.0572404\pi$
$947$	1.83066	+	6.23466i	0.0594885	+	0.202599i	−0.924386	+	0.381458i	$0.875422\pi$
$948$	12.0420	+	10.4345i	0.391106	+	0.338895i
$949$	−16.4319	−	4.82484i	−0.533402	−	0.156621i
$950$	36.7791	+	5.49831i	1.19327	+	0.178389i
$951$	2.75684	+	6.03663i	0.0893966	+	0.195751i
$952$	−10.0395	+	8.69925i	−0.325381	+	0.281944i
$953$	7.52355	−	11.7069i	0.243712	−	0.379223i	−0.697751	−	0.716341i	$-0.745816\pi$
$953$	7.52355	−	11.7069i	0.243712	−	0.379223i	0.941463	+	0.337118i	$0.109452\pi$
$954$	1.07250	−	7.45939i	0.0347234	−	0.241507i
$955$	6.04346	−	1.75616i	0.195562	−	0.0568281i
$956$	20.3786	+	13.0965i	0.659090	+	0.423571i
$957$	0.0755985	−	0.0655065i	0.00244375	−	0.00211752i
$958$	11.7751	−	5.37753i	0.380438	−	0.173740i
$959$	22.9621	−	14.7569i	0.741486	−	0.476524i
$960$	2.21419	−	0.312030i	0.0714627	−	0.0100707i
$961$	14.3825	−	16.5983i	0.463952	−	0.535429i
$962$	3.36195	+	11.4497i	0.108394	+	0.369155i
$963$	8.01342	+	3.65961i	0.258229	+	0.117929i
$964$	1.77061	+	12.3149i	0.0570276	+	0.396636i
$965$	−43.0884	+	19.5323i	−1.38707	+	0.628766i
$966$	14.9092	+	16.1050i	0.479696	+	0.518170i
$967$		−	50.9924i		−	1.63980i	−0.572504	−	0.819902i	$-0.694028\pi$
$967$		−	50.9924i		−	1.63980i	0.572504	−	0.819902i	$-0.305972\pi$
$968$	10.8878	−	1.56543i	0.349948	−	0.0503149i
$969$	8.96894	−	19.6392i	0.288124	−	0.630903i
$970$	9.38233	+	10.8892i	0.301248	+	0.349631i
$971$	38.1164	−	43.9887i	1.22321	−	1.41166i	0.341497	−	0.939883i	$-0.389066\pi$
$971$	38.1164	−	43.9887i	1.22321	−	1.41166i	0.881716	−	0.471781i	$-0.156389\pi$
$972$	0.281733	−	0.959493i	0.00903658	−	0.0307758i
$973$	−20.9210	−	32.5538i	−0.670697	−	1.04363i
$974$	3.96828	+	8.68932i	0.127152	+	0.278424i
$975$	17.8590	+	0.0999586i	0.571944	+	0.00320124i
$976$	−5.55270	−	3.56850i	−0.177738	−	0.114225i
$977$	18.8208	+	2.70603i	0.602131	+	0.0865734i	0.436638	−	0.899637i	$-0.356169\pi$
$977$	18.8208	+	2.70603i	0.602131	+	0.0865734i	0.165494	+	0.986211i	$0.447078\pi$
$978$	−10.6817	−	1.53580i	−0.341564	−	0.0491094i
$979$	−0.118457	−	0.0761275i	−0.00378589	−	0.00243304i
$980$	13.0296	−	28.3208i	0.416214	−	0.904673i
$981$	2.89631	+	6.34204i	0.0924721	+	0.202486i
$982$	−7.50915	−	11.6845i	−0.239627	−	0.372866i
$983$	−7.98875	+	27.2072i	−0.254802	+	0.867775i	0.728384	+	0.685169i	$0.240272\pi$
$983$	−7.98875	+	27.2072i	−0.254802	+	0.867775i	−0.983186	+	0.182606i	$0.941547\pi$
$984$	2.38170	−	2.74863i	0.0759259	−	0.0876232i
$985$	−39.2490	+	33.8176i	−1.25058	+	1.07752i
$986$	−8.13392	+	17.8108i	−0.259037	+	0.567212i
$987$	−4.17111	+	0.599716i	−0.132768	+	0.0190892i
$988$			26.5658i			0.845171i
$989$	−34.9845	+	1.15012i	−1.11244	+	0.0365717i
$990$	0.0302030	−	0.0136912i	0.000959913	−	0.000435135i
$991$	7.41211	+	51.5523i	0.235453	+	1.63761i	0.673876	+	0.738845i	$0.264628\pi$
$991$	7.41211	+	51.5523i	0.235453	+	1.63761i	−0.438422	+	0.898769i	$0.644463\pi$
$992$	2.73455	+	1.24883i	0.0868219	+	0.0396502i
$993$	2.79324	+	9.51289i	0.0886407	+	0.301882i
$994$	39.1746	−	45.2099i	1.24254	−	1.43397i
$995$	5.72435	+	40.6204i	0.181474	+	1.28775i
$996$	11.8203	−	7.59644i	0.374540	−	0.240702i
$997$	−24.7287	+	11.2932i	−0.783165	+	0.357660i	−0.766535	−	0.642202i	$-0.778021\pi$
$997$	−24.7287	+	11.2932i	−0.783165	+	0.357660i	−0.0166300	+	0.999862i	$0.505294\pi$
$998$	21.3639	−	18.5120i	0.676264	−	0.585986i
$999$	−2.81053	−	1.80622i	−0.0889212	−	0.0571462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.r.b.49.7	yes	120
5.4	even	2	inner	690.2.r.b.49.4	✓	120
23.8	even	11	inner	690.2.r.b.169.4	yes	120
115.54	even	22	inner	690.2.r.b.169.7	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.r.b.49.4	✓	120	5.4	even	2	inner
690.2.r.b.49.7	yes	120	1.1	even	1	trivial
690.2.r.b.169.4	yes	120	23.8	even	11	inner
690.2.r.b.169.7	yes	120	115.54	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.989821 - 0.142315i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(-2.14372 - 0.635975i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(2.47408 + 3.84974i) q^{7} +(0.909632 - 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.989821 - 0.142315i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(-2.14372 - 0.635975i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(2.47408 + 3.84974i) q^{7} +(0.909632 - 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +(-2.21241 - 0.324418i) q^{10} +(-0.00211055 + 0.0146792i) q^{11} +(-0.989821 - 0.142315i) q^{12} +(-1.93109 + 3.00483i) q^{13} +(2.99677 + 3.45846i) q^{14} +(1.68580 + 1.46904i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-0.817835 + 2.78529i) q^{17} +(0.755750 + 0.654861i) q^{18} +(7.13628 - 2.09540i) q^{19} +(-2.23606 - 0.00625769i) q^{20} +(-0.651260 - 4.52962i) q^{21} +0.0148302i q^{22} +(-4.29463 + 2.13452i) q^{23} -1.00000 q^{24} +(4.19107 + 2.72670i) q^{25} +(-1.48380 + 3.24907i) q^{26} +(-0.281733 - 0.959493i) q^{27} +(3.45846 + 2.99677i) q^{28} +(6.47189 + 1.90032i) q^{29} +(1.87771 + 1.21417i) q^{30} +(1.24883 + 2.73455i) q^{31} +(0.755750 - 0.654861i) q^{32} +(0.00801779 - 0.0124759i) q^{33} +(-0.413122 + 2.87333i) q^{34} +(-2.85539 - 9.82622i) q^{35} +(0.841254 + 0.540641i) q^{36} +(2.52487 - 2.18781i) q^{37} +(6.76544 - 3.08967i) q^{38} +(3.00483 - 1.93109i) q^{39} +(-2.21419 + 0.312030i) q^{40} +(-2.38170 + 2.74863i) q^{41} +(-1.28926 - 4.39083i) q^{42} +(6.63915 + 3.03200i) q^{43} +(0.00211055 + 0.0146792i) q^{44} +(-0.923200 - 2.03659i) q^{45} +(-3.94714 + 2.72399i) q^{46} -0.920854i q^{47} +(-0.989821 + 0.142315i) q^{48} +(-5.79153 + 12.6817i) q^{49} +(4.53646 + 2.10250i) q^{50} +(1.90098 - 2.19385i) q^{51} +(-1.00631 + 3.42716i) q^{52} +(-4.07432 - 6.33977i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(0.0138600 - 0.0301259i) q^{55} +(3.84974 + 2.47408i) q^{56} +(-7.36185 - 1.05847i) q^{57} +(6.67646 + 0.959930i) q^{58} +(7.23748 + 4.65125i) q^{59} +(2.03139 + 0.934585i) q^{60} +(-2.74195 - 6.00403i) q^{61} +(1.62528 + 2.52899i) q^{62} +(-1.28926 + 4.39083i) q^{63} +(0.654861 - 0.755750i) q^{64} +(6.05070 - 5.21339i) q^{65} +(0.00616067 - 0.0134900i) q^{66} +(-5.29761 + 0.761682i) q^{67} +2.90288i q^{68} +(4.79324 - 0.157578i) q^{69} +(-4.22474 - 9.31983i) q^{70} +(-1.86038 - 12.9392i) q^{71} +(0.909632 + 0.415415i) q^{72} +(1.35080 + 4.60039i) q^{73} +(2.18781 - 2.52487i) q^{74} +(-2.67962 - 4.22133i) q^{75} +(6.25687 - 4.02105i) q^{76} +(-0.0617328 + 0.0281924i) q^{77} +(2.69942 - 2.33906i) q^{78} +(-13.4044 - 8.61449i) q^{79} +(-2.14725 + 0.623966i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-1.96629 + 3.05961i) q^{82} +(-10.6189 + 9.20132i) q^{83} +(-1.90102 - 4.16265i) q^{84} +(3.52458 - 5.45076i) q^{85} +(7.00307 + 2.05629i) q^{86} +(-5.09762 - 4.41711i) q^{87} +(0.00417814 + 0.0142294i) q^{88} +(-3.94429 + 8.63679i) q^{89} +(-1.20364 - 1.88448i) q^{90} -16.3455 q^{91} +(-3.51930 + 3.25800i) q^{92} -3.00621i q^{93} +(-0.131051 - 0.911481i) q^{94} +(-16.6308 - 0.0465419i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(-4.85804 - 4.20952i) q^{97} +(-3.92779 + 13.3768i) q^{98} +(-0.0124759 + 0.00801779i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9	\( 120 q + 12 q^{4} + 8 q^{5} - 12 q^{6} + 12 q^{9} - 18 q^{10} - 8 q^{11} - 4 q^{15} - 12 q^{16} + 16 q^{19} + 14 q^{20} - 22 q^{21} - 120 q^{24} + 28 q^{25} + 8 q^{26} + 8 q^{29} + 8 q^{30} + 8 q^{31} + 44 q^{34} + 58 q^{35} - 12 q^{36} + 14 q^{39} - 4 q^{40} + 8 q^{44} - 8 q^{45} + 12 q^{49} - 4 q^{50} + 12 q^{54} + 92 q^{55} - 94 q^{59} + 4 q^{60} - 60 q^{61} + 12 q^{64} - 44 q^{65} - 8 q^{66} + 16 q^{70} - 16 q^{74} + 4 q^{75} - 16 q^{76} + 172 q^{79} + 8 q^{80} - 12 q^{81} - 32 q^{85} - 40 q^{86} + 48 q^{89} - 4 q^{90} + 288 q^{91} + 24 q^{94} - 78 q^{95} - 12 q^{96} - 36 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 + 8 * q^5 - 12 * q^6 + 12 * q^9 - 18 * q^10 - 8 * q^11 - 4 * q^15 - 12 * q^16 + 16 * q^19 + 14 * q^20 - 22 * q^21 - 120 * q^24 + 28 * q^25 + 8 * q^26 + 8 * q^29 + 8 * q^30 + 8 * q^31 + 44 * q^34 + 58 * q^35 - 12 * q^36 + 14 * q^39 - 4 * q^40 + 8 * q^44 - 8 * q^45 + 12 * q^49 - 4 * q^50 + 12 * q^54 + 92 * q^55 - 94 * q^59 + 4 * q^60 - 60 * q^61 + 12 * q^64 - 44 * q^65 - 8 * q^66 + 16 * q^70 - 16 * q^74 + 4 * q^75 - 16 * q^76 + 172 * q^79 + 8 * q^80 - 12 * q^81 - 32 * q^85 - 40 * q^86 + 48 * q^89 - 4 * q^90 + 288 * q^91 + 24 * q^94 - 78 * q^95 - 12 * q^96 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more