LMFDB - Embedded newform 690.2.r.b.49.4

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			49.4
Character	$\chi$	$=$	690.49
Dual form			690.2.r.b.169.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.989821 + 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(0.934585 + 2.03139i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-2.47408 - 3.84974i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.989821 + 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(0.934585 + 2.03139i) 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} +(-1.21417 - 1.87771i) 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} +(0.00625769 + 2.23606i) 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} +(1.46904 + 1.68580i) q^{20} +(-0.651260 - 4.52962i) q^{21} -0.0148302i q^{22} +(4.29463 - 2.13452i) q^{23} -1.00000 q^{24} +(-3.25310 + 3.79702i) 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} +(-0.324418 - 2.21241i) 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} +(5.50809 - 8.62373i) 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} +(-1.69400 - 1.45958i) 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} +(2.67962 - 4.22133i) 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} +(-0.0317917 + 0.00943161i) 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} +(0.635975 + 2.14372i) 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} +(7.90875 + 1.11452i) 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} +(-4.53646 + 2.10250i) 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} +(1.88448 + 1.20364i) 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} +(6.42235 - 0.941746i) 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} +(0.623966 - 2.14725i) q^{90} -16.3455 q^{91} +(3.51930 - 3.25800i) q^{92} +3.00621i q^{93} +(-0.131051 - 0.911481i) q^{94} +(10.9260 + 12.5383i) 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
$5$	0.934585	+	2.03139i	0.417959	+	0.908466i
$5$	0.934585	+	2.03139i	0.417959	+	0.908466i
$6$	−0.959493	−	0.281733i	−0.391711	−	0.115017i
$7$	−2.47408	−	3.84974i	−0.935113	−	1.45506i	−0.889936	−	0.456086i	$-0.849251\pi$
$7$	−2.47408	−	3.84974i	−0.935113	−	1.45506i	−0.0451776	−	0.998979i	$-0.514385\pi$
$8$	−0.909632	+	0.415415i	−0.321603	+	0.146871i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	−1.21417	−	1.87771i	−0.383954	−	0.593784i
$11$	−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	−0.463009	−	0.886353i	$-0.653230\pi$
$13$	1.93109	−	3.00483i	0.535587	−	0.833390i	0.998596	+	0.0529637i	$0.0168668\pi$
$14$	2.99677	+	3.45846i	0.800920	+	0.924312i
$15$	0.00625769	+	2.23606i	0.00161573	+	0.577348i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	0.817835	−	2.78529i	0.198354	−	0.675532i	−0.798899	−	0.601465i	$-0.794584\pi$
$17$	0.817835	−	2.78529i	0.198354	−	0.675532i	0.997253	−	0.0740670i	$-0.0235979\pi$
$18$	−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	$0.0837825\pi$
$20$	1.46904	+	1.68580i	0.328487	+	0.376957i
$21$	−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
$25$	−3.25310	+	3.79702i	−0.650621	+	0.759403i
$26$	−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	$0.375491\pi$
$30$	−0.324418	−	2.21241i	−0.0592304	−	0.403929i
$31$	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
$35$	5.50809	−	8.62373i	0.931038	−	1.45768i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	−2.52487	+	2.18781i	−0.415086	+	0.359674i	−0.837227	−	0.546856i	$-0.815824\pi$
$37$	−2.52487	+	2.18781i	−0.415086	+	0.359674i	0.422140	+	0.906531i	$0.361279\pi$
$38$	−6.76544	+	3.08967i	−1.09750	+	0.501211i
$39$	3.00483	−	1.93109i	0.481158	−	0.309221i
$40$	−1.69400	−	1.45958i	−0.267845	−	0.230780i
$41$	−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	−0.161090	−	0.986940i	$-0.551501\pi$
$43$	−6.63915	−	3.03200i	−1.01246	−	0.462375i	−0.851371	+	0.524565i	$0.824228\pi$
$44$	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	$0.0213938\pi$
$47$			0.920854i			0.134320i	−0.997742	+	0.0671602i	$0.978606\pi$
$48$	0.989821	−	0.142315i	0.142868	−	0.0205414i
$49$	−5.79153	+	12.6817i	−0.827362	+	1.81167i
$50$	2.67962	−	4.22133i	0.378955	−	0.596986i
$51$	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	0.999631	−	0.0271733i	$-0.00865059\pi$
$53$	4.07432	+	6.33977i	0.559651	+	0.870835i	−0.439979	+	0.898008i	$0.645014\pi$
$54$	−0.415415	−	0.909632i	−0.0565308	−	0.123785i
$55$	−0.0317917	+	0.00943161i	−0.00428679	+	0.00127176i
$56$	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	$0.492611\pi$
$60$	0.635975	+	2.14372i	0.0821040	+	0.276753i
$61$	−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
$65$	7.90875	+	1.11452i	0.980959	+	0.138240i
$66$	0.00616067	−	0.0134900i	0.000758326	−	0.00166050i
$67$	5.29761	−	0.761682i	0.647206	−	0.0930542i	0.189109	−	0.981956i	$-0.439440\pi$
$67$	5.29761	−	0.761682i	0.647206	−	0.0930542i	0.458098	+	0.888902i	$0.348531\pi$
$68$		−	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	0.841900	−	0.539633i	$-0.181437\pi$
$73$	−1.35080	−	4.60039i	−0.158099	−	0.538435i	−0.999999	+	0.00119755i	$0.999619\pi$
$74$	2.18781	−	2.52487i	0.254328	−	0.293510i
$75$	−4.53646	+	2.10250i	−0.523826	+	0.242776i
$76$	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	$-0.671972\pi$
$80$	1.88448	+	1.20364i	0.210691	+	0.134571i
$81$	−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	$-0.446961\pi$
$83$	10.6189	−	9.20132i	1.16557	−	1.00998i	0.999716	−	0.0238265i	$-0.00758493\pi$
$84$	−1.90102	−	4.16265i	−0.207418	−	0.454183i
$85$	6.42235	−	0.941746i	0.696602	−	0.102147i
$86$	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	$0.968510\pi$
$90$	0.623966	−	2.14725i	0.0657718	−	0.226340i
$91$	−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
$95$	10.9260	+	12.5383i	1.12099	+	1.28640i
$96$	−0.959493	+	0.281733i	−0.0979278	+	0.0287542i
$97$	4.85804	+	4.20952i	0.493259	+	0.427412i	0.865639	−	0.500669i	$-0.166913\pi$
$97$	4.85804	+	4.20952i	0.493259	+	0.427412i	−0.372380	+	0.928081i	$0.621458\pi$
$98$	3.92779	−	13.3768i	0.396767	−	1.35126i
$99$	−0.0124759	+	0.00801779i	−0.00125388	+	0.000805818i
$100$	−2.05159	+	4.55971i	−0.205159	+	0.455971i
$101$	−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	0.999539	−	0.0303672i	$-0.00966767\pi$
$103$	19.7907	+	2.84547i	1.95003	+	0.280373i	0.950495	+	0.310740i	$0.100577\pi$
$104$	−0.508327	+	3.53549i	−0.0498455	+	0.346683i
$105$	8.59276	−	5.55627i	0.838568	−	0.542237i
$106$	−4.93510	−	5.69541i	−0.479339	−	0.553187i
$107$	−8.01342	+	3.65961i	−0.774687	+	0.353788i	−0.763213	−	0.646147i	$-0.776379\pi$
$107$	−8.01342	+	3.65961i	−0.774687	+	0.353788i	−0.0114734	+	0.999934i	$0.503652\pi$
$108$	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	$0.482543\pi$
$110$	0.0301259	−	0.0138600i	0.00287239	−	0.00132150i
$111$	−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	−0.981263	−	0.192674i	$-0.938284\pi$
$113$	−19.8624	+	2.85578i	−1.86849	+	0.268649i	−0.887232	+	0.461323i	$0.847375\pi$
$114$	−7.43755			−0.696591
$115$	8.34974	+	6.72917i	0.778618	+	0.627499i
$116$	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
$120$	−0.934585	−	2.03139i	−0.0853155	−	0.185440i
$121$	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
$125$	−10.7535	−	3.05969i	−0.961824	−	0.273667i
$126$	−0.651260	+	4.52962i	−0.0580189	+	0.403530i
$127$	−2.82813	−	0.406624i	−0.250956	−	0.0360821i	0.0156886	−	0.999877i	$-0.495006\pi$
$127$	−2.82813	−	0.406624i	−0.250956	−	0.0360821i	−0.266645	+	0.963795i	$0.585915\pi$
$128$	−0.540641	+	0.841254i	−0.0477863	+	0.0743570i
$129$	−4.77964	−	5.51600i	−0.420824	−	0.485657i
$130$	−7.98686	+	0.0223515i	−0.700494	+	0.00196036i
$131$	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
$135$	−1.68580	+	1.46904i	−0.145091	+	0.126435i
$136$	0.413122	+	2.87333i	0.0354250	+	0.246386i
$137$			5.96460i			0.509590i	0.966995	+	0.254795i	$0.0820080\pi$
$137$			5.96460i			0.509590i	−0.966995	+	0.254795i	$0.917992\pi$
$138$	−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	$0.616752\pi$
$140$	2.85539	−	9.82622i	0.241325	−	0.830467i
$141$	−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
$145$	2.18824	+	14.9230i	0.181723	+	1.23928i
$146$	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	$-0.0644185\pi$
$150$	4.19107	−	2.72670i	0.342200	−	0.222634i
$151$	−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
$155$	−4.38780	+	5.09252i	−0.352437	+	0.409041i
$156$	2.33906	−	2.69942i	0.187275	−	0.216127i
$157$	−5.52292	−	18.8093i	−0.440777	−	1.50115i	−0.818105	−	0.575069i	$-0.804975\pi$
$157$	−5.52292	−	18.8093i	−0.440777	−	1.50115i	0.377328	−	0.926080i	$-0.376843\pi$
$158$	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	−0.547309	−	0.836931i	$-0.684348\pi$
$163$	−10.6817	+	1.53580i	−0.836657	+	0.120293i	−0.289348	+	0.957224i	$0.593438\pi$
$164$	−1.51085	+	3.30830i	−0.117977	+	0.258334i
$165$	−0.0328368	−	0.00462746i	−0.00255634	−	0.000360247i
$166$	−9.20132	+	10.6189i	−0.714161	+	0.824186i
$167$	−3.69618	+	12.5880i	−0.286019	+	0.974092i	0.683678	+	0.729784i	$0.260379\pi$
$167$	−3.69618	+	12.5880i	−0.286019	+	0.974092i	−0.969698	+	0.244309i	$0.921439\pi$
$168$	2.47408	+	3.84974i	0.190879	+	0.297014i
$169$	0.100492	+	0.220048i	0.00773018	+	0.0169267i
$170$	−6.22295	+	1.84616i	−0.477279	+	0.141594i
$171$	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	−0.343100	−	0.939299i	$-0.611477\pi$
$173$	−12.3234	−	1.77184i	−0.936933	−	0.134711i	−0.593833	+	0.804588i	$0.702386\pi$
$174$	−5.67435	−	3.64669i	−0.430172	−	0.276454i
$175$	22.6659	+	3.12949i	1.71338	+	0.236567i
$176$	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	$0.365228\pi$
$180$	−0.312030	+	2.21419i	−0.0232574	+	0.165036i
$181$	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
$190$	−12.5992	−	10.8557i	−0.914043	−	0.787555i
$191$	−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	$0.548246\pi$
$193$	−15.9895	+	13.8550i	−1.15095	+	0.997304i	−0.999962	+	0.00876797i	$0.997209\pi$
$194$	−5.40767	−	3.47530i	−0.388248	−	0.249512i
$195$	6.73106	+	4.29922i	0.482021	+	0.307874i
$196$	−1.98409	+	13.7997i	−0.141721	+	0.985689i
$197$	−12.5263	+	19.4914i	−0.892464	+	1.38870i	0.0287255	+	0.999587i	$0.490855\pi$
$197$	−12.5263	+	19.4914i	−0.892464	+	1.38870i	−0.921190	+	0.389114i	$0.872781\pi$
$198$	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	$-0.361695\pi$
$200$	1.38179	−	4.80527i	0.0977073	−	0.339784i
$201$	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
$205$	−7.80945	−	2.26934i	−0.545436	−	0.158498i
$206$	−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
$210$	−7.71456	+	6.72260i	−0.532355	+	0.463903i
$211$	−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
$215$	−0.0456731	−	16.3204i	−0.00311488	−	1.11304i
$216$	−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
$220$	−0.0278467	+	0.0180063i	−0.00187743	+	0.00121399i
$221$	−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	0.999987	−	0.00518222i	$-0.00164956\pi$
$223$	8.65920	+	13.4740i	0.579863	+	0.902285i	−0.420123	+	0.907467i	$0.638013\pi$
$224$	4.39083	+	1.28926i	0.293374	+	0.0861425i
$225$	−4.99992	+	0.0279851i	−0.333328	+	0.00186567i
$226$	19.2538	−	5.65342i	1.28074	−	0.376060i
$227$	21.2364	+	9.69834i	1.40951	+	0.643701i	0.967399	−	0.253259i	$-0.0815025\pi$
$227$	21.2364	+	9.69834i	1.40951	+	0.643701i	0.442111	+	0.896960i	$0.354230\pi$
$228$	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	$0.395860\pi$
$230$	−9.22242	−	5.47239i	−0.608108	−	0.360839i
$231$	0.0678657			0.00446523
$232$	−6.67646	+	0.959930i	−0.438331	+	0.0630225i
$233$	−4.22035	−	1.92737i	−0.276485	−	0.126266i	0.272347	−	0.962199i	$-0.412200\pi$
$233$	−4.22035	−	1.92737i	−0.276485	−	0.126266i	−0.548832	+	0.835933i	$0.684927\pi$
$234$	−3.42716	+	1.00631i	−0.224041	+	0.0657843i
$235$	−1.87061	+	0.860616i	−0.122025	+	0.0561404i
$236$	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	$0.486179\pi$
$240$	1.21417	+	1.87771i	0.0783743	+	0.121206i
$241$	−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
$245$	−31.1741	+	0.0872419i	−1.99164	+	0.00557368i
$246$	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
$250$	11.0795	+	1.49816i	0.700730	+	0.0947522i
$251$	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
$255$	6.23319	+	1.81130i	0.390337	+	0.113428i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−0.217513	−	0.740781i	−0.0135681	−	0.0462086i	0.952431	−	0.304755i	$-0.0985746\pi$
$257$	−0.217513	−	0.740781i	−0.0135681	−	0.0462086i	−0.965999	+	0.258547i	$0.916756\pi$
$258$	5.51600	+	4.77964i	0.343411	+	0.297568i
$259$	14.6692	+	4.30728i	0.911502	+	0.267641i
$260$	7.90239	−	1.15877i	0.490085	−	0.0718640i
$261$	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	−0.807425	−	0.589970i	$-0.799139\pi$
$263$	1.04841	−	1.63135i	0.0646476	−	0.100594i	0.872072	+	0.489377i	$0.162776\pi$
$264$	0.00211055	−	0.0146792i	0.000129895	−	0.000903443i
$265$	−9.07076	+	14.2016i	−0.557212	+	0.872397i
$266$	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	$0.267985\pi$
$270$	1.45958	−	1.69400i	0.0888271	−	0.103093i
$271$	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	$0.00817719\pi$
$277$			0.855020i			0.0513732i	−0.999670	+	0.0256866i	$0.991823\pi$
$278$	8.37002	−	1.20343i	0.502000	−	0.0721768i
$279$	−1.24883	+	2.73455i	−0.0747652	+	0.163713i
$280$	−1.42791	+	10.1326i	−0.0853341	+	0.605536i
$281$	−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	0.965888	−	0.258961i	$-0.0833800\pi$
$283$	5.53606	+	8.61428i	0.329085	+	0.512066i	−0.636803	+	0.771026i	$0.719744\pi$
$284$	−5.43042	−	11.8910i	−0.322236	−	0.705599i
$285$	4.73010	+	15.9440i	0.280187	+	0.944443i
$286$	−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
$290$	−4.28972	−	14.4596i	−0.251901	−	0.849099i
$291$	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	$0.256895\pi$
$293$	−4.80460	+	16.3630i	−0.280688	+	0.955935i	−0.972314	+	0.233679i	$0.924924\pi$
$294$	9.12978	−	10.5363i	0.532459	−	0.614491i
$295$	−2.68446	+	19.0491i	−0.156296	+	1.10908i
$296$	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
$305$	9.63395	−	11.1812i	0.551639	−	0.640236i
$306$	−2.44205	+	1.56941i	−0.139603	+	0.0897174i
$307$	−26.1517	+	11.9431i	−1.49256	+	0.681629i	−0.983798	−	0.179279i	$-0.942623\pi$
$307$	−26.1517	+	11.9431i	−1.49256	+	0.681629i	−0.508761	+	0.860908i	$0.669896\pi$
$308$	0.0512895	−	0.0444426i	0.00292249	−	0.00253235i
$309$	16.8202	+	10.8097i	0.956867	+	0.614941i
$310$	3.61840	−	5.66513i	0.205511	−	0.321758i
$311$	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	−0.961791	−	0.273786i	$-0.911724\pi$
$313$	−14.6429	+	12.6882i	−0.827668	+	0.717178i	0.134123	+	0.990965i	$0.457178\pi$
$314$	8.14356	+	17.8319i	0.459567	+	1.00631i
$315$	10.1244	−	1.48460i	0.570446	−	0.0836478i
$316$	−15.2884	−	4.48909i	−0.860041	−	0.252531i
$317$	5.01542	+	4.34588i	0.281694	+	0.244089i	0.784235	−	0.620464i	$-0.213056\pi$
$317$	5.01542	+	4.34588i	0.281694	+	0.244089i	−0.502541	+	0.864554i	$0.667601\pi$
$318$	−2.12317	−	7.23084i	−0.119061	−	0.405485i
$319$	−0.0415544	+	0.0909915i	−0.00232660	+	0.00509455i
$320$	2.14725	+	0.623966i	0.120035	+	0.0348808i
$321$	−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
$325$	5.12736	+	17.1074i	0.284415	+	0.948947i
$326$	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
$330$	0.0331611		9.28025e-5i	0.00182546		5.10861e-6i
$331$	−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
$335$	6.49834	+	10.0497i	0.355042	+	0.549072i
$336$	−2.99677	−	3.45846i	−0.163487	−	0.188674i
$337$	4.22162	−	1.92795i	0.229966	−	0.105022i	−0.297100	−	0.954846i	$-0.596019\pi$
$337$	4.22162	−	1.92795i	0.229966	−	0.105022i	0.527066	+	0.849824i	$0.323292\pi$
$338$	−0.130786	−	0.203506i	−0.00711380	−	0.0110693i
$339$	−19.2538	−	5.65342i	−1.04572	−	0.307052i
$340$	5.89688	−	2.71298i	0.319803	−	0.147132i
$341$	−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
$345$	4.79979	+	9.58968i	0.258412	+	0.516291i
$346$	12.4502			0.669325
$347$	−2.53653	+	0.364698i	−0.136168	+	0.0195780i	−0.210062	−	0.977688i	$-0.567367\pi$
$347$	−2.53653	+	0.364698i	−0.136168	+	0.0195780i	0.0738937	+	0.997266i	$0.476457\pi$
$348$	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	$0.512108\pi$
$350$	−22.8806	+	0.128065i	−1.22302	+	0.00684538i
$351$	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	−0.198736	−	0.980053i	$-0.563684\pi$
$353$	7.73691	−	3.53333i	0.411794	−	0.188060i	0.610530	+	0.791993i	$0.290956\pi$
$354$	−5.63391	−	6.50187i	−0.299439	−	0.345571i
$355$	24.5459	−	15.8720i	1.30276	−	0.842396i
$356$	−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	$0.729371\pi$
$360$	−0.00625769	−	2.23606i	−0.000329809	−	0.117851i
$361$	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
$365$	8.08277	−	7.04346i	0.423071	−	0.368671i
$366$	0.939350	+	6.53332i	0.0491006	+	0.341502i
$367$		−	25.1961i		−	1.31523i	−0.753355	−	0.657614i	$-0.771566\pi$
$367$		−	25.1961i		−	1.31523i	0.753355	−	0.657614i	$-0.228434\pi$
$368$	2.45886	−	4.11753i	0.128177	−	0.214641i
$369$	−3.63696			−0.189333
$370$	7.17370	+	2.08460i	0.372943	+	0.108373i
$371$	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	0.928266	−	0.371916i	$-0.121299\pi$
$373$	13.3694	+	11.5847i	0.692242	+	0.599831i	−0.236025	+	0.971747i	$0.575845\pi$
$374$	−0.0413063	−	0.0121286i	−0.00213590	−	0.000627156i
$375$	−8.51071	−	7.25037i	−0.439491	−	0.374407i
$376$	−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	$-0.254479\pi$
$380$	14.0159	+	8.95214i	0.719000	+	0.459235i
$381$	−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	−0.999305	−	0.0372863i	$-0.988129\pi$
$383$	−31.8123	+	14.5282i	−1.62553	+	0.742355i	−0.626226	+	0.779641i	$0.715401\pi$
$384$	−0.841254	+	0.540641i	−0.0429300	+	0.0275895i
$385$	0.114964	+	0.0990553i	0.00585913	+	0.00504832i
$386$	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
$395$	4.97185	−	35.2806i	0.250161	−	1.77516i
$396$	−0.00971169	+	0.0112079i	−0.000488031	+	0.000563217i
$397$	−2.93854	+	10.0077i	−0.147481	+	0.502274i	−0.999784	−	0.0207739i	$-0.993387\pi$
$397$	−2.93854	+	10.0077i	−0.147481	+	0.502274i	0.852303	+	0.523048i	$0.175205\pi$
$398$	9.91833	+	15.4332i	0.497161	+	0.773597i
$399$	−14.1389	−	30.9600i	−0.707832	−	1.54994i
$400$	−0.683863	+	4.95301i	−0.0341931	+	0.247651i
$401$	−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
$405$	−2.14372	+	0.635975i	−0.106522	+	0.0316018i
$406$	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	$0.323019\pi$
$410$	8.05292	+	1.13484i	0.397705	+	0.0560459i
$411$	−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	$0.942175\pi$
$420$	6.67931	−	7.75207i	0.325917	−	0.378262i
$421$	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
$425$	7.91529	+	12.1662i	0.383948	+	0.590146i
$426$	−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
$430$	2.36784	+	16.1477i	0.114187	+	0.778714i
$431$	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	0.958742	−	0.284277i	$-0.0917534\pi$
$433$	−0.0310993	−	0.105915i	−0.00149454	−	0.00508993i	−0.960237	+	0.279187i	$0.909935\pi$
$434$	−5.71487	+	12.5138i	−0.274322	+	0.600682i
$435$	−4.20873	+	14.4834i	−0.201793	+	0.694427i
$436$	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	$0.940966\pi$
$440$	0.0250007	−	0.0217860i	0.00119186	−	0.00103861i
$441$	−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	$0.291702\pi$
$443$	−6.99475	+	23.8219i	−0.332331	+	1.13181i	−0.941005	+	0.338394i	$0.890116\pi$
$444$	−2.81053	+	1.80622i	−0.133382	+	0.0857193i
$445$	−21.2310	+	0.0594156i	−1.00645	+	0.00281657i
$446$	−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	$0.854971\pi$
$450$	4.94505	−	0.739263i	0.233112	−	0.0348492i
$451$	−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
$455$	−15.2762	−	33.2040i	−0.716160	−	1.55663i
$456$	−7.13628	+	2.09540i	−0.334187	+	0.0981262i
$457$	5.85944	+	2.67591i	0.274093	+	0.125174i	0.547720	−	0.836662i	$-0.315496\pi$
$457$	5.85944	+	2.67591i	0.274093	+	0.125174i	−0.273627	+	0.961836i	$0.588223\pi$
$458$	−9.62710	+	1.38417i	−0.449845	+	0.0646780i
$459$	2.90288			0.135495
$460$	9.90735	+	4.10420i	0.461932	+	0.191359i
$461$	−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	0.629800	−	0.776758i	$-0.283137\pi$
$463$	9.79466	+	4.47307i	0.455196	+	0.207881i	−0.174603	+	0.984639i	$0.555864\pi$
$464$	6.47189	−	1.90032i	0.300450	−	0.0882201i
$465$	−6.10679	+	2.80956i	−0.283196	+	0.130290i
$466$	4.45169	+	1.30713i	0.206221	+	0.0605518i
$467$	−17.5752	−	27.3475i	−0.813283	−	1.26549i	−0.961023	−	0.276467i	$-0.910836\pi$
$467$	−17.5752	−	27.3475i	−0.813283	−	1.26549i	0.147741	−	0.989026i	$-0.452800\pi$
$468$	3.24907	−	1.48380i	0.150188	−	0.0685886i
$469$	−16.0390	−	18.5100i	−0.740611	−	0.854711i
$470$	1.72910	−	1.11807i	0.0797572	−	0.0515728i
$471$	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
$475$	−15.2588	+	33.9131i	−0.700121	+	1.55604i
$476$	−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	$0.313526\pi$
$480$	−1.46904	−	1.68580i	−0.0670520	−	0.0769460i
$481$	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
$485$	−4.01093	+	13.8027i	−0.182127	+	0.626750i
$486$	0.415415	−	0.909632i	0.0188436	−	0.0412617i
$487$	−2.69127	−	9.16562i	−0.121953	−	0.415334i	0.875774	−	0.482722i	$-0.160352\pi$
$487$	−2.69127	−	9.16562i	−0.121953	−	0.415334i	−0.997727	+	0.0673877i	$0.978534\pi$
$488$	4.98833	+	4.32241i	0.225811	+	0.195666i
$489$	−10.3544	−	3.04033i	−0.468243	−	0.137489i
$490$	30.8444	−	4.52290i	1.39341	−	0.204324i
$491$	−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
$495$	−0.0279471	−	0.0178502i	−0.00125613	−	0.000802306i
$496$	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	$0.100113\pi$
$500$	−11.1799	+	0.0938643i	−0.499982	+	0.00419774i
$501$	−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	0.618756	−	0.785584i	$-0.287637\pi$
$503$	9.64950	+	4.40678i	0.430250	+	0.196489i	−0.188506	+	0.982072i	$0.560364\pi$
$504$	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	$0.887376\pi$
$510$	−6.42752	−	0.905786i	−0.284615	−	0.0401089i
$511$	−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
$515$	12.7158	+	42.8620i	0.560325	+	1.88872i
$516$	−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
$520$	−7.65704	+	2.27161i	−0.335783	+	0.0996165i
$521$	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	$0.191339\pi$
$523$	−3.99855	+	13.6178i	−0.174844	+	0.595465i	−0.999553	+	0.0299067i	$0.990479\pi$
$524$	3.49924	−	4.03834i	0.152865	−	0.176416i
$525$	19.3176	+	12.2625i	0.843091	+	0.535178i
$526$	−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
$535$	−14.9233	−	12.8582i	−0.645191	−	0.555908i
$536$	−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
$540$	−1.20364	+	1.88448i	−0.0517964	+	0.0810949i
$541$	−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
$545$	2.26187	+	15.4251i	0.0968881	+	0.660739i
$546$	15.6834	+	4.60505i	0.671186	+	0.197078i
$547$	19.6822	+	17.0547i	0.841550	+	0.729207i	0.964748	−	0.263175i	$-0.0847697\pi$
$547$	19.6822	+	17.0547i	0.841550	+	0.729207i	−0.123198	+	0.992382i	$0.539315\pi$
$548$	1.68042	+	5.72299i	0.0717840	+	0.244474i
$549$	2.74195	−	6.00403i	0.117024	−	0.256246i
$550$	0.0563103	+	0.0482440i	0.00240108	+	0.00205713i
$551$	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
$555$	−4.90788	−	5.63207i	−0.208328	−	0.239068i
$556$	−8.11356	+	2.38236i	−0.344092	+	0.101034i
$557$	8.62103	+	7.47017i	0.365285	+	0.316521i	0.818092	−	0.575087i	$-0.195032\pi$
$557$	8.62103	+	7.47017i	0.365285	+	0.316521i	−0.452807	+	0.891609i	$0.649577\pi$
$558$	0.846947	−	2.88444i	0.0358541	−	0.122108i
$559$	−21.9314	+	14.0945i	−0.927599	+	0.596132i
$560$	−0.0286364	−	10.2326i	−0.00121011	−	0.432408i
$561$	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	0.607985	−	0.793948i	$-0.291978\pi$
$563$	22.9603	+	3.30119i	0.967662	+	0.139129i	0.359677	+	0.933077i	$0.382887\pi$
$564$	−0.131051	+	0.911481i	−0.00551825	+	0.0383803i
$565$	−24.3643	−	37.6793i	−1.02501	−	1.58518i
$566$	−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	$0.742952\pi$
$570$	−6.95103	−	15.1086i	−0.291146	−	0.632829i
$571$	−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
$575$	−5.86604	+	23.2506i	−0.244631	+	0.969616i
$576$	1.00000			0.0416667
$577$	−7.34368	+	1.05586i	−0.305721	+	0.0439561i	−0.293468	−	0.955969i	$-0.594809\pi$
$577$	−7.34368	+	1.05586i	−0.305721	+	0.0439561i	−0.0122531	+	0.999925i	$0.503900\pi$
$578$	−7.79856	−	3.56148i	−0.324377	−	0.148138i
$579$	−20.3001	+	5.96066i	−0.843645	+	0.247716i
$580$	6.30388	+	13.7020i	0.261754	+	0.568943i
$581$	−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
$585$	4.33683	+	6.70689i	0.179306	+	0.277296i
$586$	2.42700	−	16.8802i	0.100259	−	0.697314i
$587$	−7.58031	−	1.08988i	−0.312873	−	0.0449843i	−0.0159101	−	0.999873i	$-0.505065\pi$
$587$	−7.58031	−	1.08988i	−0.312873	−	0.0449843i	−0.296963	+	0.954889i	$0.595974\pi$
$588$	−7.53737	+	11.7284i	−0.310836	+	0.483670i
$589$	14.6419	+	16.8977i	0.603310	+	0.696257i
$590$	−0.0538362	−	19.2373i	−0.00221640	−	0.791987i
$591$	−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	−0.00874074	−	0.999962i	$-0.502782\pi$
$593$	−24.3459	−	21.0959i	−0.999768	−	0.866304i	−0.991028	+	0.133658i	$0.957328\pi$
$594$	0.0142294	−	0.00417814i	0.000583841	−	0.000171431i
$595$	−19.5149	−	22.3944i	−0.800032	−	0.918082i
$596$	−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	$0.552450\pi$
$600$	3.25310	−	3.79702i	0.132807	−	0.155012i
$601$	−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
$605$	3.56853	+	24.3360i	0.145081	+	0.989400i
$606$	3.12038	+	6.83269i	0.126757	+	0.277559i
$607$	31.6462	−	27.4216i	1.28448	−	1.11301i	0.297064	−	0.954858i	$-0.403993\pi$
$607$	31.6462	−	27.4216i	1.28448	−	1.11301i	0.987415	−	0.158150i	$-0.0505529\pi$
$608$	−4.02105	+	6.25687i	−0.163075	+	0.253750i
$609$	4.39283	−	30.5528i	0.178006	−	1.23806i
$610$	−7.94464	+	12.4385i	−0.321669	+	0.503620i
$611$	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	0.492266	−	0.870445i	$-0.336169\pi$
$613$	36.4567	−	16.6492i	1.47247	−	0.672455i	0.980204	+	0.197990i	$0.0634413\pi$
$614$	24.1859	−	15.5433i	0.976063	−	0.627277i
$615$	−6.16101	−	5.30843i	−0.248436	−	0.214056i
$616$	−0.0444426	+	0.0512895i	−0.00179064	+	0.00206651i
$617$	−10.7674	−	36.6703i	−0.433478	−	1.47629i	−0.829738	−	0.558152i	$-0.811510\pi$
$617$	−10.7674	−	36.6703i	−0.433478	−	1.47629i	0.396260	−	0.918138i	$-0.370308\pi$
$618$	−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
$625$	−3.83465	−	24.7042i	−0.153386	−	0.988166i
$626$	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
$630$	−9.81008	+	2.91034i	−0.390843	+	0.115951i
$631$	−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
$635$	−1.81712	−	6.12507i	−0.0721101	−	0.243066i
$636$	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
$640$	−2.21419	−	0.312030i	−0.0875235	−	0.0123341i
$641$	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	$0.416292\pi$
$643$			48.9713i			1.93124i	−0.259956	+	0.965621i	$0.583708\pi$
$644$	−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	−0.260409	−	0.965498i	$-0.583857\pi$
$647$	−29.5217	−	13.4821i	−1.16062	−	0.530035i	−0.900207	+	0.435463i	$0.856585\pi$
$648$	−0.281733	−	0.959493i	−0.0110675	−	0.0376924i
$649$	−0.0835517	+	0.0964238i	−0.00327969	+	0.00378496i
$650$	−7.50980	−	16.2036i	−0.294559	−	0.635556i
$651$	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	−0.695566	−	0.718462i	$-0.744846\pi$
$653$	−2.13136	+	1.84684i	−0.0834066	+	0.0722722i	0.612160	+	0.790734i	$0.290301\pi$
$654$	−5.86530	−	3.76940i	−0.229351	−	0.147395i
$655$	10.0697	+	6.43164i	0.393455	+	0.251305i
$656$	−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	$0.780619\pi$
$660$	−0.0328104	+	0.00481118i	−0.00127714	+	0.000187275i
$661$	−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
$665$	21.2371	−	73.0830i	0.823541	−	2.83404i
$666$	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
$670$	−7.86242	−	9.02257i	−0.303752	−	0.348572i
$671$	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	$-0.756685\pi$
$673$	6.73450	−	22.9356i	0.259596	−	0.884102i	0.981395	−	0.192000i	$-0.0614973\pi$
$674$	−3.90427	+	2.50912i	−0.150387	+	0.0966478i
$675$	−4.55971	−	2.05159i	−0.175503	−	0.0789656i
$676$	0.158416	+	0.182822i	0.00609294	+	0.00703162i
$677$	−18.4622	+	28.7278i	−0.709560	+	1.10410i	0.280003	+	0.959999i	$0.409665\pi$
$677$	−18.4622	+	28.7278i	−0.709560	+	1.10410i	−0.989563	+	0.144098i	$0.953972\pi$
$678$	19.8624	+	2.85578i	0.762810	+	0.109675i
$679$	4.18637	−	29.1169i	0.160658	−	1.11740i
$680$	−5.45076	+	3.52458i	−0.209027	+	0.135162i
$681$	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	$0.0919169\pi$
$683$	21.4148	+	33.3221i	0.819416	+	1.27504i	−0.139180	+	0.990267i	$0.544447\pi$
$684$	7.13628	+	2.09540i	0.272863	+	0.0801197i
$685$	−12.1164	+	5.57442i	−0.462945	+	0.212988i
$686$	−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
$690$	−6.11569	−	8.80899i	−0.232820	−	0.335353i
$691$	−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
$695$	−7.90293	−	17.1776i	−0.299775	−	0.651585i
$696$	−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
$700$	22.6295	−	3.38301i	0.855315	−	0.127866i
$701$	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
$705$	−2.05908	+	0.00576241i	−0.0775496	+	0.000217025i
$706$	−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	$0.199500\pi$
$710$	−22.0373	+	19.2036i	−0.827044	+	0.720700i
$711$	−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
$715$	−0.0330522	+	0.113742i	−0.00123608	+	0.00425370i
$716$	−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	$0.535514\pi$
$720$	0.324418	+	2.21241i	0.0120904	+	0.0824516i
$721$	−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
$725$	−28.2693	+	18.3919i	−1.04989	+	0.683059i
$726$	−9.25360	−	5.94693i	−0.343433	−	0.220711i
$727$	−33.3710	+	28.9161i	−1.23766	+	1.07244i	−0.242917	+	0.970047i	$0.578104\pi$
$727$	−33.3710	+	28.9161i	−1.23766	+	1.07244i	−0.994744	+	0.102392i	$0.967350\pi$
$728$	14.8684	−	6.79015i	0.551058	−	0.251660i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	−6.99811	+	8.12206i	−0.259012	+	0.300611i
$731$	−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	0.942861	−	0.333188i	$-0.108124\pi$
$733$	35.4262	+	16.1786i	1.30850	+	0.597570i	0.365636	+	0.930758i	$0.380852\pi$
$734$	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	$0.974109\pi$
$740$	−7.39735	−	1.04246i	−0.271932	−	0.0383215i
$741$	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	0.987882	−	0.155207i	$-0.0496043\pi$
$743$	11.8932	+	18.5062i	0.436320	+	0.678927i	−0.551562	+	0.834134i	$0.685968\pi$
$744$	−1.24883	−	2.73455i	−0.0457841	−	0.100253i
$745$	17.7082	−	5.25346i	0.648777	−	0.192472i
$746$	−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
$750$	9.45592	+	5.96537i	0.345281	+	0.217825i
$751$	−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
$755$	0.239396	−	1.69877i	0.00871252	−	0.0618246i
$756$	1.90102	−	4.16265i	0.0691394	−	0.151394i
$757$	31.5746	−	4.53974i	1.14760	−	0.164999i	0.457836	−	0.889037i	$-0.348625\pi$
$757$	31.5746	−	4.53974i	1.14760	−	0.164999i	0.689761	+	0.724037i	$0.257716\pi$
$758$			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
$765$	4.91747	+	4.23697i	0.177791	+	0.153188i
$766$	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	$0.529498\pi$
$770$	−0.127891	−	0.0816859i	−0.00460888	−	0.00294375i
$771$	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	−0.195009	−	0.980802i	$-0.562473\pi$
$773$	20.7981	−	18.0217i	0.748057	−	0.648195i	0.943066	+	0.332606i	$0.107928\pi$
$774$	3.03200	+	6.63915i	0.108983	+	0.238639i
$775$	−14.4457	−	4.15395i	−0.518904	−	0.149214i
$776$	−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
$780$	7.66963	+	2.22871i	0.274617	+	0.0798007i
$781$	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
$785$	33.0475	−	28.7981i	1.17952	−	1.02785i
$786$	−5.12704	+	1.50543i	−0.182875	+	0.0536971i
$787$	−2.48519	−	2.15343i	−0.0885874	−	0.0767614i	0.609441	−	0.792831i	$-0.291394\pi$
$787$	−2.48519	−	2.15343i	−0.0885874	−	0.0767614i	−0.698029	+	0.716070i	$0.745939\pi$
$788$	−6.52758	+	22.2309i	−0.232535	+	0.791943i
$789$	1.63135	−	1.04841i	0.0580777	−	0.0373243i
$790$	0.0997091	+	35.6290i	0.00354749	+	1.26762i
$791$	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
$795$	−14.1506	+	9.15010i	−0.501870	+	0.324521i
$796$	−12.0137	−	13.8646i	−0.425816	−	0.491418i
$797$	19.8313	−	9.05666i	0.702462	−	0.320803i	−0.0319675	−	0.999489i	$-0.510177\pi$
$797$	19.8313	−	9.05666i	0.702462	−	0.320803i	0.734429	+	0.678685i	$0.237450\pi$
$798$	18.4011	+	28.6326i	0.651391	+	1.01358i
$799$	2.56484	+	0.753106i	0.0907377	+	0.0266430i
$800$	−0.0279851	−	4.99992i	−0.000989423	−	0.176774i
$801$	−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
$805$	5.24766	−	48.7928i	0.184956	−	1.71972i
$806$	−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	$0.433169\pi$
$810$	2.03139	−	0.934585i	0.0713758	−	0.0328380i
$811$	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
$815$	−13.1028	−	20.2634i	−0.458970	−	0.709796i
$816$	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
$820$	−8.13246	+	0.0227590i	−0.283998	+	0.000794777i
$821$	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	0.662383	−	0.749165i	$-0.269545\pi$
$823$	0.433501	+	0.375630i	0.0151109	+	0.0130937i	−0.647273	+	0.762259i	$0.724090\pi$
$824$	−19.1843	+	5.63302i	−0.668316	+	0.196235i
$825$	−0.0212886	−	0.0710291i	−0.000741173	−	0.00247292i
$826$	5.60293	+	38.9692i	0.194951	+	1.35591i
$827$		−	52.7565i		−	1.83452i	−0.398284	−	0.917262i	$-0.630394\pi$
$827$		−	52.7565i		−	1.83452i	0.398284	−	0.917262i	$-0.369606\pi$
$828$	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	$0.266874\pi$
$830$	−30.1705	−	8.76723i	−1.04723	−	0.304315i
$831$	−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
$835$	−29.0256	+	4.25620i	−1.00447	+	0.147292i
$836$	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	$-0.213497\pi$
$840$	−5.50809	+	8.62373i	−0.190047	+	0.297547i
$841$	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
$845$	−0.353084	+	0.409793i	−0.0121465	+	0.0140973i
$846$	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	−0.0881555	−	0.996107i	$-0.528097\pi$
$853$	3.15122	−	0.453077i	0.107896	−	0.0155130i	0.196051	+	0.980594i	$0.437188\pi$
$854$	12.5477	−	27.4756i	0.429373	−	0.940196i
$855$	−2.32074	+	16.4682i	−0.0793677	+	0.563199i
$856$	5.76901	−	6.65779i	0.197181	−	0.227559i
$857$	4.68678	−	15.9617i	0.160097	−	0.545242i	−0.839899	−	0.542742i	$-0.817386\pi$
$857$	4.68678	−	15.9617i	0.160097	−	0.545242i	0.999997	−	0.00249978i	$-0.000795706\pi$
$858$	−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	$0.738375\pi$
$860$	−4.64180	−	15.6464i	−0.158284	−	0.533538i
$861$	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	0.418712	−	0.908119i	$-0.362482\pi$
$863$	16.5866	+	2.38480i	0.564616	+	0.0811795i	0.145904	+	0.989299i	$0.453391\pi$
$864$	−0.841254	−	0.540641i	−0.0286200	−	0.0183930i
$865$	−7.91799	−	26.6897i	−0.269220	−	0.907476i
$866$	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
$870$	2.10468	−	14.9350i	0.0713554	−	0.506343i
$871$	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	−0.0955964	−	0.995420i	$-0.530476\pi$
$877$	−26.9633	−	12.3137i	−0.910487	−	0.415806i	−0.814891	+	0.579615i	$0.803203\pi$
$878$	−0.503486	−	1.71472i	−0.0169918	−	0.0578689i
$879$	−11.1678	+	12.8884i	−0.376682	+	0.434714i
$880$	−0.0216458	+	0.0251223i	−0.000729679	+	0.000846871i
$881$	−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	$0.578788\pi$
$883$	−36.8328	+	31.9158i	−1.23952	+	1.07405i	−0.994522	+	0.104528i	$0.966667\pi$
$884$	−8.72265	−	5.60570i	−0.293374	−	0.188540i
$885$	−10.3552	+	16.2125i	−0.348085	+	0.544979i
$886$	3.53334	−	24.5749i	0.118705	−	0.825611i
$887$	18.4568	−	28.7193i	0.619717	−	0.964299i	−0.379517	−	0.925185i	$-0.623910\pi$
$887$	18.4568	−	28.7193i	0.619717	−	0.964299i	0.999235	−	0.0391144i	$-0.0124537\pi$
$888$	2.52487	−	2.18781i	0.0847291	−	0.0734182i
$889$	5.43162	+	11.8936i	0.182171	+	0.398898i
$890$	21.0064	−	3.08030i	0.704137	−	0.103252i
$891$	−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
$895$	−24.1293	−	7.01172i	−0.806554	−	0.234376i
$896$	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
$900$	−4.78951	+	1.43549i	−0.159650	+	0.0478497i
$901$	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
$905$	33.0930	−	0.0926118i	1.10005	−	0.00307852i
$906$	0.502422	+	0.579826i	0.0166919	+	0.0192634i
$907$	16.1497	−	25.1294i	0.536242	−	0.834409i	−0.462391	−	0.886676i	$-0.653008\pi$
$907$	16.1497	−	25.1294i	0.536242	−	0.834409i	0.998633	+	0.0522674i	$0.0166448\pi$
$908$	23.1085	+	3.32250i	0.766883	+	0.110261i
$909$	1.06900	−	7.43503i	0.0354563	−	0.246604i
$910$	19.8462	+	30.6920i	0.657894	+	1.01743i
$911$	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
$915$	13.4082	−	6.16873i	0.443262	−	0.203932i
$916$	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	$0.674687\pi$
$920$	−10.3906	−	2.65246i	−0.342568	−	0.0874491i
$921$	−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
$925$	−0.0934950	−	16.7042i	−0.00307410	−	0.549229i
$926$	−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	$0.589114\pi$
$930$	5.64479	−	3.65005i	0.185100	−	0.119690i
$931$	−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
$935$	0.000269394		0.0962626i	8.81013e−6		0.00314812i
$936$	−3.00483	+	1.93109i	−0.0982159	+	0.0631195i
$937$	−2.74124	+	9.33579i	−0.0895523	+	0.304987i	−0.992074	−	0.125658i	$-0.959896\pi$
$937$	−2.74124	+	9.33579i	−0.0895523	+	0.304987i	0.902521	+	0.430645i	$0.141714\pi$
$938$	18.5100	+	16.0390i	0.604372	+	0.523691i
$939$	−18.5905	+	5.45868i	−0.606680	+	0.178137i
$940$	−1.55238	+	1.35277i	−0.0506330	+	0.0441224i
$941$	−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
$945$	9.82622	+	2.85539i	0.319647	+	0.0928859i
$946$	−0.0449650	+	0.0984596i	−0.00146194	+	0.00320120i
$947$	−1.83066	−	6.23466i	−0.0594885	−	0.202599i	0.924386	−	0.381458i	$-0.124578\pi$
$947$	−1.83066	−	6.23466i	−0.0594885	−	0.202599i	−0.983875	+	0.178858i	$0.942760\pi$
$948$	−12.0420	−	10.4345i	−0.391106	−	0.338895i
$949$	−16.4319	−	4.82484i	−0.533402	−	0.156621i
$950$	10.2771	−	35.7395i	0.333434	−	1.15954i
$951$	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	−0.941463	−	0.337118i	$-0.890548\pi$
$953$	−7.52355	+	11.7069i	−0.243712	+	0.379223i	0.697751	+	0.716341i	$0.254184\pi$
$954$	1.07250	−	7.45939i	0.0347234	−	0.241507i
$955$	−5.30389	−	3.38767i	−0.171630	−	0.109622i
$956$	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
$960$	1.69400	+	1.45958i	0.0546736	+	0.0471077i
$961$	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	$0.305972\pi$
$967$			50.9924i			1.63980i	−0.572504	+	0.819902i	$0.694028\pi$
$968$	−10.8878	+	1.56543i	−0.349948	+	0.0503149i
$969$	8.96894	−	19.6392i	0.288124	−	0.630903i
$970$	2.00577	−	14.2331i	0.0644013	−	0.456996i
$971$	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
$975$	−2.44265	+	17.6914i	−0.0782275	+	0.566578i
$976$	−5.55270	−	3.56850i	−0.177738	−	0.114225i
$977$	−18.8208	−	2.70603i	−0.602131	−	0.0865734i	−0.165494	−	0.986211i	$-0.552922\pi$
$977$	−18.8208	−	2.70603i	−0.602131	−	0.0865734i	−0.436638	+	0.899637i	$0.643831\pi$
$978$	10.6817	+	1.53580i	0.341564	+	0.0491094i
$979$	−0.118457	−	0.0761275i	−0.00378589	−	0.00243304i
$980$	−29.8868	+	8.86648i	−0.954699	+	0.283229i
$981$	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	$-0.759728\pi$
$983$	7.98875	−	27.2072i	0.254802	−	0.867775i	0.983186	−	0.182606i	$-0.0584533\pi$
$984$	2.38170	−	2.74863i	0.0759259	−	0.0876232i
$985$	−51.3015	−	7.22956i	−1.63460	−	0.230353i
$986$	−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
$995$	26.7767	−	31.0773i	0.848878	−	0.985215i
$996$	11.8203	−	7.59644i	0.374540	−	0.240702i
$997$	24.7287	−	11.2932i	0.783165	−	0.357660i	0.0166300	−	0.999862i	$-0.494706\pi$
$997$	24.7287	−	11.2932i	0.783165	−	0.357660i	0.766535	+	0.642202i	$0.221979\pi$
$998$	−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.49.4	✓	120
5.4	even	2	inner	690.2.r.b.49.7	yes	120
23.8	even	11	inner	690.2.r.b.169.7	yes	120
115.54	even	22	inner	690.2.r.b.169.4	yes	120

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.989821 + 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(0.934585 + 2.03139i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-2.47408 - 3.84974i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.989821 + 0.142315i) q^{2} +(0.909632 + 0.415415i) q^{3} +(0.959493 - 0.281733i) q^{4} +(0.934585 + 2.03139i) 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} +(-1.21417 - 1.87771i) 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} +(0.00625769 + 2.23606i) 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} +(1.46904 + 1.68580i) q^{20} +(-0.651260 - 4.52962i) q^{21} -0.0148302i q^{22} +(4.29463 - 2.13452i) q^{23} -1.00000 q^{24} +(-3.25310 + 3.79702i) 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} +(-0.324418 - 2.21241i) 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} +(5.50809 - 8.62373i) 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} +(-1.69400 - 1.45958i) 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} +(2.67962 - 4.22133i) 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} +(-0.0317917 + 0.00943161i) 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} +(0.635975 + 2.14372i) 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} +(7.90875 + 1.11452i) 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} +(-4.53646 + 2.10250i) 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} +(1.88448 + 1.20364i) 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} +(6.42235 - 0.941746i) 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} +(0.623966 - 2.14725i) q^{90} -16.3455 q^{91} +(3.51930 - 3.25800i) q^{92} +3.00621i q^{93} +(-0.131051 - 0.911481i) q^{94} +(10.9260 + 12.5383i) 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

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