LMFDB - Embedded newform 186.2.m.d.175.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [186,2,Mod(7,186)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(186, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([0, 28])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("186.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 186 = 2 \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	186.m (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,2,1,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$1.48521747760$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			175.1
Root			$-0.978148 - 0.207912i$ of defining polynomial
Character	$\chi$	$=$	186.175
Dual form			186.2.m.d.169.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.951057i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.01807 + 1.76336i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.0180739 - 0.171962i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(1.36245 - 1.51315i) q^{10} +(4.46320 + 1.98714i) q^{11} +(-0.978148 - 0.207912i) q^{12} +(-3.16535 + 0.672816i) q^{13} +(-0.157960 + 0.0703285i) q^{14} +(-0.629204 + 1.93649i) q^{15} +(0.309017 - 0.951057i) q^{16} +(6.29456 - 2.80252i) q^{17} +(0.978148 - 0.207912i) q^{18} +(-3.16535 - 0.672816i) q^{19} +(-1.86011 - 0.828176i) q^{20} +(0.115699 - 0.128496i) q^{21} +(0.510682 - 4.85882i) q^{22} +(-4.85410 - 3.52671i) q^{23} +(0.104528 + 0.994522i) q^{24} +(0.427051 - 0.739674i) q^{25} +(1.61803 + 2.80252i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.115699 + 0.128496i) q^{28} +(0.760744 + 2.34133i) q^{29} +2.03615 q^{30} +(-2.76627 - 4.83195i) q^{31} -1.00000 q^{32} +(1.50973 + 4.64646i) q^{33} +(-4.61048 - 5.12045i) q^{34} +(0.284829 - 0.206941i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-0.547318 + 0.947983i) q^{37} +(0.338261 + 3.21834i) q^{38} +(-2.61803 - 1.90211i) q^{39} +(-0.212835 + 2.02499i) q^{40} +(-7.25841 + 8.06128i) q^{41} +(-0.157960 - 0.0703285i) q^{42} +(-6.58347 - 1.39936i) q^{43} +(-4.77882 + 1.01577i) q^{44} +(-1.86011 + 0.828176i) q^{45} +(-1.85410 + 5.70634i) q^{46} +(2.46182 - 7.57670i) q^{47} +(0.913545 - 0.406737i) q^{48} +(6.81779 - 1.44917i) q^{49} +(-0.835438 - 0.177578i) q^{50} +(6.29456 + 2.80252i) q^{51} +(2.16535 - 2.40487i) q^{52} +(-0.413079 + 3.93018i) q^{53} +(0.809017 + 0.587785i) q^{54} +(1.03982 + 9.89327i) q^{55} +(0.0864545 - 0.149744i) q^{56} +(-1.61803 - 2.80252i) q^{57} +(1.99165 - 1.44702i) q^{58} +(-4.44746 - 4.93940i) q^{59} +(-0.629204 - 1.93649i) q^{60} -3.84029 q^{61} +(-3.74064 + 4.12403i) q^{62} +0.172909 q^{63} +(0.309017 + 0.951057i) q^{64} +(-4.40898 - 4.89667i) q^{65} +(3.95252 - 2.87167i) q^{66} +(-1.46747 - 2.54172i) q^{67} +(-3.44512 + 5.96713i) q^{68} +(-0.627171 - 5.96713i) q^{69} +(-0.284829 - 0.206941i) q^{70} +(0.336681 - 3.20331i) q^{71} +(-0.669131 + 0.743145i) q^{72} +(-1.19644 - 0.532691i) q^{73} +(1.07072 + 0.227588i) q^{74} +(0.835438 - 0.177578i) q^{75} +(2.95630 - 1.31623i) q^{76} +(0.261046 - 0.803416i) q^{77} +(-1.00000 + 3.07768i) q^{78} +(6.02353 - 2.68185i) q^{79} +(1.99165 - 0.423339i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(9.90970 + 4.41208i) q^{82} +(4.53079 - 5.03195i) q^{83} +(-0.0180739 + 0.171962i) q^{84} +(11.3502 + 8.24637i) q^{85} +(0.703533 + 6.69367i) q^{86} +(-1.23091 + 2.13200i) q^{87} +(2.44279 + 4.23104i) q^{88} +(8.72490 - 6.33901i) q^{89} +(1.36245 + 1.51315i) q^{90} +(0.172909 + 0.532159i) q^{91} +6.00000 q^{92} +(1.73985 - 5.28894i) q^{93} -7.96661 q^{94} +(-2.03615 - 6.26662i) q^{95} +(-0.669131 - 0.743145i) q^{96} +(9.39813 - 6.82814i) q^{97} +(-3.48505 - 6.03629i) q^{98} +(-2.44279 + 4.23104i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + q^{3} - 2 q^{4} + 4 q^{6} + 8 q^{7} + 2 q^{8} + q^{9} + 6 q^{11} + q^{12} - 4 q^{13} + 7 q^{14} - 2 q^{16} + 24 q^{17} - q^{18} - 4 q^{19} - 15 q^{20} + 3 q^{21} + 9 q^{22} - 12 q^{23}+ \cdots - 9 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 + q^3 - 2 * q^4 + 4 * q^6 + 8 * q^7 + 2 * q^8 + q^9 + 6 * q^11 + q^12 - 4 * q^13 + 7 * q^14 - 2 * q^16 + 24 * q^17 - q^18 - 4 * q^19 - 15 * q^20 + 3 * q^21 + 9 * q^22 - 12 * q^23 - q^24 - 10 * q^25 + 4 * q^26 - 2 * q^27 + 3 * q^28 - 15 * q^29 - 29 * q^31 - 8 * q^32 - 12 * q^33 + 6 * q^34 - 4 * q^36 + 8 * q^37 - 6 * q^38 - 12 * q^39 - 15 * q^40 - 48 * q^41 + 7 * q^42 - 24 * q^43 - 9 * q^44 - 15 * q^45 + 12 * q^46 + 30 * q^47 + q^48 - 3 * q^49 - 10 * q^50 + 24 * q^51 - 4 * q^52 + 33 * q^53 + 2 * q^54 + 30 * q^55 + 7 * q^56 - 4 * q^57 - 3 * q^59 - 28 * q^61 - 11 * q^62 + 14 * q^63 - 2 * q^64 - 30 * q^65 - 3 * q^66 + 2 * q^67 - 6 * q^68 + 6 * q^69 + 30 * q^71 - q^72 + 26 * q^73 + 12 * q^74 + 10 * q^75 + 6 * q^76 - 36 * q^77 - 8 * q^78 + q^81 - 12 * q^82 + 39 * q^83 + 8 * q^84 - 26 * q^86 - 15 * q^87 + 9 * q^88 + 48 * q^89 + 14 * q^91 + 48 * q^92 + 13 * q^93 - q^96 + 18 * q^97 - 7 * q^98 - 9 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/186\mathbb{Z}\right)^\times$.

$n$	$125$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{15}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	1.01807	+	1.76336i	0.455296	+	0.788597i	0.998705	−	0.0508716i	$-0.0161999\pi$
$5$	1.01807	+	1.76336i	0.455296	+	0.788597i	−0.543409	+	0.839468i	$0.682867\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−0.0180739	−	0.171962i	−0.00683130	−	0.0649955i	0.990575	−	0.136970i	$-0.0437365\pi$
$7$	−0.0180739	−	0.171962i	−0.00683130	−	0.0649955i	−0.997406	+	0.0719749i	$0.977070\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	1.36245	−	1.51315i	0.430844	−	0.478501i
$11$	4.46320	+	1.98714i	1.34571	+	0.599147i	0.947972	−	0.318355i	$-0.103130\pi$
$11$	4.46320	+	1.98714i	1.34571	+	0.599147i	0.397733	+	0.917501i	$0.369797\pi$
$12$	−0.978148	−	0.207912i	−0.282367	−	0.0600189i
$13$	−3.16535	+	0.672816i	−0.877911	+	0.186606i	−0.624756	−	0.780820i	$-0.714802\pi$
$13$	−3.16535	+	0.672816i	−0.877911	+	0.186606i	−0.253155	+	0.967426i	$0.581468\pi$
$14$	−0.157960	+	0.0703285i	−0.0422167	+	0.0187961i
$15$	−0.629204	+	1.93649i	−0.162460	+	0.500000i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	6.29456	−	2.80252i	1.52665	−	0.679710i	0.539870	−	0.841749i	$-0.318473\pi$
$17$	6.29456	−	2.80252i	1.52665	−	0.679710i	0.986784	+	0.162038i	$0.0518068\pi$
$18$	0.978148	−	0.207912i	0.230552	−	0.0490053i
$19$	−3.16535	−	0.672816i	−0.726182	−	0.154355i	−0.170034	−	0.985438i	$-0.554388\pi$
$19$	−3.16535	−	0.672816i	−0.726182	−	0.154355i	−0.556148	+	0.831084i	$0.687721\pi$
$20$	−1.86011	−	0.828176i	−0.415934	−	0.185186i
$21$	0.115699	−	0.128496i	0.0252475	−	0.0280402i
$22$	0.510682	−	4.85882i	0.108878	−	1.03590i
$23$	−4.85410	−	3.52671i	−1.01215	−	0.735370i	−0.0474912	−	0.998872i	$-0.515123\pi$
$23$	−4.85410	−	3.52671i	−1.01215	−	0.735370i	−0.964659	+	0.263501i	$0.915123\pi$
$24$	0.104528	+	0.994522i	0.0213368	+	0.203006i
$25$	0.427051	−	0.739674i	0.0854102	−	0.147935i
$26$	1.61803	+	2.80252i	0.317323	+	0.549619i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	0.115699	+	0.128496i	0.0218650	+	0.0242836i
$29$	0.760744	+	2.34133i	0.141267	+	0.434774i	0.996512	−	0.0834493i	$-0.0265937\pi$
$29$	0.760744	+	2.34133i	0.141267	+	0.434774i	−0.855245	+	0.518223i	$0.826594\pi$
$30$	2.03615			0.371748
$31$	−2.76627	−	4.83195i	−0.496836	−	0.867844i
$31$	−2.76627	−	4.83195i	−0.496836	−	0.867844i
$32$	−1.00000			−0.176777
$33$	1.50973	+	4.64646i	0.262810	+	0.808845i
$34$	−4.61048	−	5.12045i	−0.790690	−	0.878151i
$35$	0.284829	−	0.206941i	0.0481450	−	0.0349794i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−0.547318	+	0.947983i	−0.0899785	+	0.155847i	−0.907502	−	0.420048i	$-0.862013\pi$
$37$	−0.547318	+	0.947983i	−0.0899785	+	0.155847i	0.817523	+	0.575896i	$0.195347\pi$
$38$	0.338261	+	3.21834i	0.0548732	+	0.522084i
$39$	−2.61803	−	1.90211i	−0.419221	−	0.304582i
$40$	−0.212835	+	2.02499i	−0.0336522	+	0.320180i
$41$	−7.25841	+	8.06128i	−1.13357	+	1.25896i	−0.171794	+	0.985133i	$0.554956\pi$
$41$	−7.25841	+	8.06128i	−1.13357	+	1.25896i	−0.961779	+	0.273827i	$0.911710\pi$
$42$	−0.157960	−	0.0703285i	−0.0243738	−	0.0108519i
$43$	−6.58347	−	1.39936i	−1.00397	−	0.213400i	−0.323540	−	0.946214i	$-0.604873\pi$
$43$	−6.58347	−	1.39936i	−1.00397	−	0.213400i	−0.680429	+	0.732814i	$0.738206\pi$
$44$	−4.77882	+	1.01577i	−0.720434	+	0.153133i
$45$	−1.86011	+	0.828176i	−0.277289	+	0.123457i
$46$	−1.85410	+	5.70634i	−0.273372	+	0.841354i
$47$	2.46182	−	7.57670i	0.359093	−	1.10518i	−0.594505	−	0.804092i	$-0.702652\pi$
$47$	2.46182	−	7.57670i	0.359093	−	1.10518i	0.953598	−	0.301083i	$-0.0973481\pi$
$48$	0.913545	−	0.406737i	0.131859	−	0.0587074i
$49$	6.81779	−	1.44917i	0.973970	−	0.207024i
$50$	−0.835438	−	0.177578i	−0.118149	−	0.0251133i
$51$	6.29456	+	2.80252i	0.881414	+	0.392431i
$52$	2.16535	−	2.40487i	0.300280	−	0.333495i
$53$	−0.413079	+	3.93018i	−0.0567407	+	0.539852i	0.928820	+	0.370531i	$0.120824\pi$
$53$	−0.413079	+	3.93018i	−0.0567407	+	0.539852i	−0.985561	+	0.169321i	$0.945843\pi$
$54$	0.809017	+	0.587785i	0.110093	+	0.0799874i
$55$	1.03982	+	9.89327i	0.140210	+	1.33401i
$56$	0.0864545	−	0.149744i	0.0115530	−	0.0200103i
$57$	−1.61803	−	2.80252i	−0.214314	−	0.371202i
$58$	1.99165	−	1.44702i	0.261517	−	0.190003i
$59$	−4.44746	−	4.93940i	−0.579010	−	0.643056i	0.380483	−	0.924788i	$-0.375758\pi$
$59$	−4.44746	−	4.93940i	−0.579010	−	0.643056i	−0.959493	+	0.281732i	$0.909091\pi$
$60$	−0.629204	−	1.93649i	−0.0812299	−	0.250000i
$61$	−3.84029			−0.491699			−0.245850	−	0.969308i	$-0.579067\pi$
$61$	−3.84029			−0.491699			−0.245850	+	0.969308i	$0.579067\pi$
$62$	−3.74064	+	4.12403i	−0.475061	+	0.523753i
$63$	0.172909			0.0217845
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−4.40898	−	4.89667i	−0.546866	−	0.607357i
$66$	3.95252	−	2.87167i	0.486521	−	0.353478i
$67$	−1.46747	−	2.54172i	−0.179279	−	0.310521i	0.762355	−	0.647160i	$-0.224043\pi$
$67$	−1.46747	−	2.54172i	−0.179279	−	0.310521i	−0.941634	+	0.336639i	$0.890710\pi$
$68$	−3.44512	+	5.96713i	−0.417783	+	0.723621i
$69$	−0.627171	−	5.96713i	−0.0755025	−	0.718358i
$70$	−0.284829	−	0.206941i	−0.0340436	−	0.0247341i
$71$	0.336681	−	3.20331i	0.0399567	−	0.380163i	−0.956210	−	0.292683i	$-0.905452\pi$
$71$	0.336681	−	3.20331i	0.0399567	−	0.380163i	0.996166	−	0.0874800i	$-0.0278814\pi$
$72$	−0.669131	+	0.743145i	−0.0788578	+	0.0875805i
$73$	−1.19644	−	0.532691i	−0.140033	−	0.0623468i	0.335524	−	0.942032i	$-0.391087\pi$
$73$	−1.19644	−	0.532691i	−0.140033	−	0.0623468i	−0.475557	+	0.879685i	$0.657753\pi$
$74$	1.07072	+	0.227588i	0.124468	+	0.0264565i
$75$	0.835438	−	0.177578i	0.0964680	−	0.0205049i
$76$	2.95630	−	1.31623i	0.339110	−	0.150982i
$77$	0.261046	−	0.803416i	0.0297489	−	0.0915577i
$78$	−1.00000	+	3.07768i	−0.113228	+	0.348479i
$79$	6.02353	−	2.68185i	0.677701	−	0.301732i	−0.0388721	−	0.999244i	$-0.512376\pi$
$79$	6.02353	−	2.68185i	0.677701	−	0.301732i	0.716573	+	0.697512i	$0.245710\pi$
$80$	1.99165	−	0.423339i	0.222674	−	0.0473307i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	9.90970	+	4.41208i	1.09434	+	0.487233i
$83$	4.53079	−	5.03195i	0.497319	−	0.552328i	−0.441266	−	0.897376i	$-0.645471\pi$
$83$	4.53079	−	5.03195i	0.497319	−	0.552328i	0.938585	+	0.345048i	$0.112137\pi$
$84$	−0.0180739	+	0.171962i	−0.00197203	+	0.0187626i
$85$	11.3502	+	8.24637i	1.23110	+	0.894445i
$86$	0.703533	+	6.69367i	0.0758640	+	0.721797i
$87$	−1.23091	+	2.13200i	−0.131967	+	0.228574i
$88$	2.44279	+	4.23104i	0.260402	+	0.451030i
$89$	8.72490	−	6.33901i	0.924837	−	0.671934i	−0.0198860	−	0.999802i	$-0.506330\pi$
$89$	8.72490	−	6.33901i	0.924837	−	0.671934i	0.944723	+	0.327869i	$0.106330\pi$
$90$	1.36245	+	1.51315i	0.143615	+	0.159500i
$91$	0.172909	+	0.532159i	0.0181258	+	0.0557855i
$92$	6.00000			0.625543
$93$	1.73985	−	5.28894i	0.180414	−	0.548438i
$94$	−7.96661			−0.821693
$95$	−2.03615	−	6.26662i	−0.208904	−	0.642942i
$96$	−0.669131	−	0.743145i	−0.0682929	−	0.0758469i
$97$	9.39813	−	6.82814i	0.954236	−	0.693293i	0.00243068	−	0.999997i	$-0.499226\pi$
$97$	9.39813	−	6.82814i	0.954236	−	0.693293i	0.951805	+	0.306704i	$0.0992263\pi$
$98$	−3.48505	−	6.03629i	−0.352043	−	0.609757i
$99$	−2.44279	+	4.23104i	−0.245510	+	0.425235i
$100$	0.0892780	+	0.849423i	0.00892780	+	0.0849423i
$101$	5.78716	+	4.20462i	0.575844	+	0.418375i	0.837224	−	0.546861i	$-0.184177\pi$
$101$	5.78716	+	4.20462i	0.575844	+	0.418375i	−0.261379	+	0.965236i	$0.584177\pi$
$102$	0.720227	−	6.85250i	0.0713131	−	0.678499i
$103$	−2.11426	+	2.34812i	−0.208324	+	0.231367i	−0.838247	−	0.545290i	$-0.816420\pi$
$103$	−2.11426	+	2.34812i	−0.208324	+	0.231367i	0.629924	+	0.776657i	$0.283086\pi$
$104$	−2.95630	−	1.31623i	−0.289889	−	0.129067i
$105$	0.344375	+	0.0731991i	0.0336076	+	0.00714351i
$106$	3.86547	−	0.821631i	0.375448	−	0.0798039i
$107$	0.204790	−	0.0911785i	0.0197978	−	0.00881456i	−0.396814	−	0.917899i	$-0.629884\pi$
$107$	0.204790	−	0.0911785i	0.0197978	−	0.00881456i	0.416612	+	0.909085i	$0.363217\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	−3.13834	+	9.65882i	−0.300599	+	0.925147i	0.680685	+	0.732577i	$0.261682\pi$
$109$	−3.13834	+	9.65882i	−0.300599	+	0.925147i	−0.981283	+	0.192571i	$0.938318\pi$
$110$	9.08773	−	4.04612i	0.866481	−	0.385782i
$111$	−1.07072	+	0.227588i	−0.101628	+	0.0216017i
$112$	−0.169131	−	0.0359498i	−0.0159813	−	0.00339694i
$113$	11.1681	+	4.97236i	1.05061	+	0.467761i	0.858072	−	0.513529i	$-0.171662\pi$
$113$	11.1681	+	4.97236i	1.05061	+	0.467761i	0.192536	+	0.981290i	$0.438329\pi$
$114$	−2.16535	+	2.40487i	−0.202804	+	0.225236i
$115$	1.27701	−	12.1500i	0.119082	−	1.13299i
$116$	−1.99165	−	1.44702i	−0.184920	−	0.134352i
$117$	−0.338261	−	3.21834i	−0.0312723	−	0.297536i
$118$	−3.32331	+	5.75615i	−0.305936	+	0.529896i
$119$	−0.595693	−	1.03177i	−0.0546071	−	0.0945823i
$120$	−1.64728	+	1.19682i	−0.150375	+	0.109254i
$121$	8.61097	+	9.56345i	0.782815	+	0.869404i
$122$	1.18672	+	3.65234i	0.107440	+	0.330667i
$123$	−10.8475			−0.978088
$124$	5.07811	+	2.28316i	0.456028	+	0.205034i
$125$	11.9198			1.06614
$126$	−0.0534318	−	0.164446i	−0.00476009	−	0.0146500i
$127$	−7.85476	−	8.72359i	−0.696997	−	0.774093i	0.285898	−	0.958260i	$-0.407708\pi$
$127$	−7.85476	−	8.72359i	−0.696997	−	0.774093i	−0.982895	+	0.184167i	$0.941041\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−3.36527	−	5.82882i	−0.296296	−	0.513199i
$130$	−3.29456	+	5.70634i	−0.288952	+	0.500479i
$131$	−0.286863	−	2.72932i	−0.0250633	−	0.238462i	−0.999881	−	0.0154563i	$-0.995080\pi$
$131$	−0.286863	−	2.72932i	−0.0250633	−	0.238462i	0.974817	−	0.223005i	$-0.0715867\pi$
$132$	−3.95252	−	2.87167i	−0.344022	−	0.249947i
$133$	−0.0584884	+	0.556480i	−0.00507159	+	0.0482530i
$134$	−1.96385	+	2.18108i	−0.169651	+	0.188417i
$135$	−1.86011	−	0.828176i	−0.160093	−	0.0712780i
$136$	6.73968	+	1.43256i	0.577923	+	0.122841i
$137$	−22.1046	+	4.69848i	−1.88853	+	0.401418i	−0.998513	−	0.0545175i	$-0.982638\pi$
$137$	−22.1046	+	4.69848i	−1.88853	+	0.401418i	−0.890013	+	0.455936i	$0.849305\pi$
$138$	−5.48127	+	2.44042i	−0.466597	+	0.207742i
$139$	−6.45893	+	19.8785i	−0.547839	+	1.68608i	0.166302	+	0.986075i	$0.446817\pi$
$139$	−6.45893	+	19.8785i	−0.547839	+	1.68608i	−0.714141	+	0.700002i	$0.753183\pi$
$140$	−0.108795	+	0.334837i	−0.00919487	+	0.0282989i
$141$	7.27786	−	3.24031i	0.612907	−	0.272884i
$142$	−3.15057	+	0.669674i	−0.264390	+	0.0561978i
$143$	−15.4646	−	3.28710i	−1.29321	−	0.274881i
$144$	0.913545	+	0.406737i	0.0761288	+	0.0338947i
$145$	−3.35410	+	3.72511i	−0.278543	+	0.309353i
$146$	−0.136898	+	1.30250i	−0.0113297	+	0.107795i
$147$	5.63893	+	4.09692i	0.465091	+	0.337909i
$148$	−0.114421	−	1.08864i	−0.00940532	−	0.0894856i
$149$	−9.47388	+	16.4092i	−0.776131	+	1.34430i	0.158026	+	0.987435i	$0.449487\pi$
$149$	−9.47388	+	16.4092i	−0.776131	+	1.34430i	−0.934157	+	0.356863i	$0.883846\pi$
$150$	−0.427051	−	0.739674i	−0.0348686	−	0.0603941i
$151$	−9.84809	+	7.15506i	−0.801426	+	0.582270i	−0.911332	−	0.411672i	$-0.864945\pi$
$151$	−9.84809	+	7.15506i	−0.801426	+	0.582270i	0.109906	+	0.993942i	$0.464945\pi$
$152$	−2.16535	−	2.40487i	−0.175633	−	0.195060i
$153$	2.12920	+	6.55302i	0.172136	+	0.529780i
$154$	−0.844761			−0.0680728
$155$	5.70419	−	9.79720i	0.458171	−	0.786930i
$156$	3.23607			0.259093
$157$	−5.40707	−	16.6412i	−0.431531	−	1.32812i	−0.896600	−	0.442841i	$-0.853971\pi$
$157$	−5.40707	−	16.6412i	−0.431531	−	1.32812i	0.465069	−	0.885274i	$-0.346029\pi$
$158$	−4.41197	−	4.89998i	−0.350997	−	0.389822i
$159$	−3.19710	+	2.32283i	−0.253546	+	0.184212i
$160$	−1.01807	−	1.76336i	−0.0804858	−	0.139406i
$161$	−0.518727	+	0.898462i	−0.0408814	+	0.0708087i
$162$	0.104528	+	0.994522i	0.00821253	+	0.0781370i
$163$	19.1213	+	13.8925i	1.49770	+	1.08814i	0.971287	+	0.237910i	$0.0764622\pi$
$163$	19.1213	+	13.8925i	1.49770	+	1.08814i	0.526410	+	0.850231i	$0.323538\pi$
$164$	1.13387	−	10.7881i	0.0885407	−	0.842409i
$165$	−6.65635	+	7.39263i	−0.518196	+	0.575515i
$166$	−6.18576	−	2.75408i	−0.480108	−	0.213758i
$167$	−17.6828	−	3.75859i	−1.36833	−	0.290848i	−0.535577	−	0.844487i	$-0.679906\pi$
$167$	−17.6828	−	3.75859i	−1.36833	−	0.290848i	−0.832757	+	0.553638i	$0.813239\pi$
$168$	0.169131	−	0.0359498i	0.0130487	−	0.00277359i
$169$	−2.30932	+	1.02817i	−0.177640	+	0.0790904i
$170$	4.33537	−	13.3429i	0.332508	−	1.02335i
$171$	1.00000	−	3.07768i	0.0764719	−	0.235356i
$172$	6.14866	−	2.73756i	0.468831	−	0.208737i
$173$	15.1751	−	3.22557i	1.15374	−	0.245236i	0.408966	−	0.912550i	$-0.365889\pi$
$173$	15.1751	−	3.22557i	1.15374	−	0.245236i	0.744776	+	0.667314i	$0.232556\pi$
$174$	2.40802	+	0.511841i	0.182552	+	0.0388026i
$175$	−0.134914	−	0.0600677i	−0.0101986	−	0.00454069i
$176$	3.26909	−	3.63069i	0.246417	−	0.273674i
$177$	0.694761	−	6.61021i	0.0522215	−	0.496854i
$178$	−8.72490	−	6.33901i	−0.653959	−	0.475129i
$179$	1.77112	+	16.8511i	0.132380	+	1.25951i	0.835918	+	0.548854i	$0.184936\pi$
$179$	1.77112	+	16.8511i	0.132380	+	1.25951i	−0.703538	+	0.710658i	$0.748398\pi$
$180$	1.01807	−	1.76336i	0.0758827	−	0.131433i
$181$	−11.4209	−	19.7815i	−0.848907	−	1.47035i	−0.882185	−	0.470904i	$-0.843928\pi$
$181$	−11.4209	−	19.7815i	−0.848907	−	1.47035i	0.0332777	−	0.999446i	$-0.489405\pi$
$182$	0.452682	−	0.328893i	0.0335550	−	0.0243791i
$183$	−2.56966	−	2.85390i	−0.189955	−	0.210966i
$184$	−1.85410	−	5.70634i	−0.136686	−	0.420677i
$185$	−2.22884			−0.163868
$186$	−5.56773	−	0.0203186i	−0.408246	−	0.00148983i
$187$	33.6629			2.46167
$188$	2.46182	+	7.57670i	0.179547	+	0.552588i
$189$	0.115699	+	0.128496i	0.00841585	+	0.00934674i
$190$	−5.33070	+	3.87298i	−0.386730	+	0.280976i
$191$	6.80126	+	11.7801i	0.492122	+	0.852380i	0.999959	−	0.00907305i	$-0.00288808\pi$
$191$	6.80126	+	11.7801i	0.492122	+	0.852380i	−0.507837	+	0.861453i	$0.669555\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−0.213421	−	2.03057i	−0.0153624	−	0.146163i	0.984152	−	0.177328i	$-0.0567452\pi$
$193$	−0.213421	−	2.03057i	−0.0153624	−	0.146163i	−0.999514	+	0.0311641i	$0.990079\pi$
$194$	−9.39813	−	6.82814i	−0.674746	−	0.490232i
$195$	0.688750	−	6.55302i	0.0493224	−	0.469271i
$196$	−4.66391	+	5.17980i	−0.333136	+	0.369985i
$197$	7.67400	+	3.41669i	0.546750	+	0.243429i	0.661473	−	0.749969i	$-0.269931\pi$
$197$	7.67400	+	3.41669i	0.546750	+	0.243429i	−0.114723	+	0.993397i	$0.536598\pi$
$198$	4.77882	+	1.01577i	0.339616	+	0.0721876i
$199$	0.761067	−	0.161770i	0.0539506	−	0.0114676i	−0.180857	−	0.983509i	$-0.557887\pi$
$199$	0.761067	−	0.161770i	0.0539506	−	0.0114676i	0.234808	+	0.972042i	$0.424554\pi$
$200$	0.780261	−	0.347395i	0.0551728	−	0.0245645i
$201$	0.906944	−	2.79129i	0.0639709	−	0.196882i
$202$	2.21050	−	6.80322i	0.155530	−	0.478673i
$203$	0.388870	−	0.173136i	0.0272933	−	0.0121518i
$204$	−6.73968	+	1.43256i	−0.471872	+	0.100300i
$205$	−21.6045	−	4.59218i	−1.50892	−	0.320732i
$206$	2.88653	+	1.28517i	0.201114	+	0.0895419i
$207$	4.01478	−	4.45887i	0.279047	−	0.309913i
$208$	−0.338261	+	3.21834i	−0.0234542	+	0.223152i
$209$	−12.7906	−	9.29292i	−0.884745	−	0.642805i
$210$	−0.0368012	−	0.350140i	−0.00253952	−	0.0241619i
$211$	−7.43757	+	12.8822i	−0.512023	+	0.886850i	0.487880	+	0.872911i	$0.337771\pi$
$211$	−7.43757	+	12.8822i	−0.512023	+	0.886850i	−0.999903	+	0.0139394i	$0.995563\pi$
$212$	−1.97591	−	3.42238i	−0.135706	−	0.235050i
$213$	2.60581	−	1.89323i	0.178547	−	0.129722i
$214$	−0.150000	−	0.166591i	−0.0102538	−	0.0113880i
$215$	−4.23489	−	13.0336i	−0.288817	−	0.888887i
$216$	−1.00000			−0.0680414
$217$	−0.780914	+	0.563025i	−0.0530119	+	0.0382206i
$218$	10.1559			0.687843
$219$	−0.404710	−	1.24557i	−0.0273478	−	0.0841679i
$220$	−6.65635	−	7.39263i	−0.448771	−	0.498411i
$221$	−18.0389	+	13.1060i	−1.21343	+	0.881607i
$222$	0.547318	+	0.947983i	0.0367336	+	0.0636244i
$223$	−13.1660	+	22.8041i	−0.881659	+	1.52708i	−0.0321634	+	0.999483i	$0.510240\pi$
$223$	−13.1660	+	22.8041i	−0.881659	+	1.52708i	−0.849496	+	0.527596i	$0.823094\pi$
$224$	0.0180739	+	0.171962i	0.00120761	+	0.0114897i
$225$	0.690983	+	0.502029i	0.0460655	+	0.0334686i
$226$	1.27786	−	12.1581i	0.0850022	−	0.808742i
$227$	17.5368	−	19.4766i	1.16396	−	1.29271i	0.215252	−	0.976559i	$-0.430943\pi$
$227$	17.5368	−	19.4766i	1.16396	−	1.29271i	0.948709	−	0.316151i	$-0.102391\pi$
$228$	2.95630	+	1.31623i	0.195785	+	0.0871693i
$229$	20.5303	+	4.36385i	1.35668	+	0.288371i	0.828132	−	0.560532i	$-0.189403\pi$
$229$	20.5303	+	4.36385i	1.35668	+	0.288371i	0.528548	+	0.848904i	$0.322737\pi$
$230$	−11.9499	+	2.54003i	−0.787954	+	0.167485i
$231$	0.771728	−	0.343595i	0.0507759	−	0.0226069i
$232$	−0.760744	+	2.34133i	−0.0499453	+	0.153716i
$233$	0.243625	−	0.749800i	0.0159604	−	0.0491211i	−0.942759	−	0.333474i	$-0.891779\pi$
$233$	0.243625	−	0.749800i	0.0159604	−	0.0491211i	0.958720	+	0.284353i	$0.0917789\pi$
$234$	−2.95630	+	1.31623i	−0.193259	+	0.0860445i
$235$	15.8667	−	3.37258i	1.03503	−	0.220003i
$236$	6.50138	+	1.38191i	0.423204	+	0.0899547i
$237$	6.02353	+	2.68185i	0.391271	+	0.174205i
$238$	−0.797193	+	0.885373i	−0.0516744	+	0.0573902i
$239$	−3.08899	+	29.3898i	−0.199810	+	1.90107i	0.192602	+	0.981277i	$0.438307\pi$
$239$	−3.08899	+	29.3898i	−0.199810	+	1.90107i	−0.392412	+	0.919789i	$0.628359\pi$
$240$	1.64728	+	1.19682i	0.106331	+	0.0772542i
$241$	0.991063	+	9.42933i	0.0638400	+	0.607397i	0.978937	+	0.204163i	$0.0654472\pi$
$241$	0.991063	+	9.42933i	0.0638400	+	0.607397i	−0.915097	+	0.403234i	$0.867886\pi$
$242$	6.43444	−	11.1448i	0.413622	−	0.716414i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	3.10686	−	2.25727i	0.198897	−	0.144507i
$245$	9.49641	+	10.5468i	0.606703	+	0.673812i
$246$	3.35207	+	10.3166i	0.213720	+	0.657763i
$247$	10.4721			0.666326
$248$	0.602193	−	5.53510i	0.0382393	−	0.351479i
$249$	6.77116			0.429105
$250$	−3.68343	−	11.3364i	−0.232960	−	0.716978i
$251$	−0.792790	−	0.880483i	−0.0500405	−	0.0555756i	0.717605	−	0.696450i	$-0.245238\pi$
$251$	−0.792790	−	0.880483i	−0.0500405	−	0.0555756i	−0.767645	+	0.640875i	$0.778572\pi$
$252$	−0.139886	+	0.101633i	−0.00881201	+	0.00640230i
$253$	−14.6567	−	25.3862i	−0.921461	−	1.59602i
$254$	−5.86937	+	10.1661i	−0.368277	+	0.637875i
$255$	1.46649	+	13.9527i	0.0918351	+	0.873753i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−0.739681	+	7.03760i	−0.0461401	+	0.438993i	0.946927	+	0.321447i	$0.104169\pi$
$257$	−0.739681	+	7.03760i	−0.0461401	+	0.438993i	−0.993067	+	0.117546i	$0.962497\pi$
$258$	−4.50361	+	5.00177i	−0.280383	+	0.311397i
$259$	0.172909	+	0.0769841i	0.0107440	+	0.00478356i
$260$	6.44512	+	1.36995i	0.399710	+	0.0849609i
$261$	−2.40802	+	0.511841i	−0.149053	+	0.0316822i
$262$	−2.50709	+	1.11623i	−0.154889	+	0.0689608i
$263$	2.31125	−	7.11330i	0.142518	−	0.438625i	−0.854166	−	0.520001i	$-0.825932\pi$
$263$	2.31125	−	7.11330i	0.142518	−	0.438625i	0.996683	+	0.0813763i	$0.0259316\pi$
$264$	−1.50973	+	4.64646i	−0.0929173	+	0.285970i
$265$	−7.35085	+	3.27281i	−0.451559	+	0.201047i
$266$	0.547318	−	0.116336i	0.0335582	−	0.00713302i
$267$	10.5489	+	2.24224i	0.645582	+	0.137223i
$268$	2.68119	+	1.19374i	0.163780	+	0.0729195i
$269$	−15.2360	+	16.9213i	−0.928956	+	1.03171i	0.0704596	+	0.997515i	$0.477553\pi$
$269$	−15.2360	+	16.9213i	−0.928956	+	1.03171i	−0.999415	+	0.0341951i	$0.989113\pi$
$270$	−0.212835	+	2.02499i	−0.0129528	+	0.123237i
$271$	−24.2244	−	17.6001i	−1.47153	−	1.06913i	−0.980167	−	0.198171i	$-0.936500\pi$
$271$	−24.2244	−	17.6001i	−1.47153	−	1.06913i	−0.491360	−	0.870956i	$-0.663500\pi$
$272$	−0.720227	−	6.85250i	−0.0436702	−	0.415494i
$273$	−0.279773	+	0.484581i	−0.0169326	+	0.0293282i
$274$	11.2992	+	19.5708i	0.682611	+	1.18232i
$275$	3.37585	−	2.45270i	0.203572	−	0.147903i
$276$	4.01478	+	4.45887i	0.241662	+	0.268392i
$277$	−6.19861	−	19.0774i	−0.372439	−	1.14625i	−0.945191	−	0.326519i	$-0.894124\pi$
$277$	−6.19861	−	19.0774i	−0.372439	−	1.14625i	0.572752	−	0.819729i	$-0.305876\pi$
$278$	20.9015			1.25359
$279$	5.09464	−	2.24604i	0.305008	−	0.134467i
$280$	0.352068			0.0210401
$281$	6.35207	+	19.5497i	0.378933	+	1.16623i	0.940787	+	0.338999i	$0.110088\pi$
$281$	6.35207	+	19.5497i	0.378933	+	1.16623i	−0.561854	+	0.827236i	$0.689912\pi$
$282$	−5.33070	−	5.92035i	−0.317439	−	0.352552i
$283$	19.4225	−	14.1112i	1.15455	−	0.838826i	0.165466	−	0.986215i	$-0.447087\pi$
$283$	19.4225	−	14.1112i	1.15455	−	0.838826i	0.989079	+	0.147389i	$0.0470870\pi$
$284$	1.61048	+	2.78943i	0.0955642	+	0.165522i
$285$	3.29456	−	5.70634i	0.195153	−	0.338014i
$286$	1.65260	+	15.7235i	0.0977204	+	0.929748i
$287$	1.51742	+	1.10247i	0.0895705	+	0.0650768i
$288$	0.104528	−	0.994522i	0.00615940	−	0.0586028i
$289$	20.3921	−	22.6477i	1.19954	−	1.33222i
$290$	4.57926	+	2.03882i	0.268904	+	0.119724i
$291$	11.3629	+	2.41525i	0.666103	+	0.141585i
$292$	1.28105	−	0.272296i	0.0749678	−	0.0159349i
$293$	−12.8559	+	5.72382i	−0.751050	+	0.334389i	−0.746309	−	0.665600i	$-0.768176\pi$
$293$	−12.8559	+	5.72382i	−0.751050	+	0.334389i	−0.00474118	+	0.999989i	$0.501509\pi$
$294$	2.15388	−	6.62896i	0.125617	−	0.386609i
$295$	4.18208	−	12.8711i	0.243490	−	0.749386i
$296$	−1.00000	+	0.445229i	−0.0581238	+	0.0258784i
$297$	−4.77882	+	1.01577i	−0.277295	+	0.0589409i
$298$	18.5337	+	3.93946i	1.07363	+	0.228207i
$299$	17.7378	+	7.89736i	1.02580	+	0.456716i
$300$	−0.571506	+	0.634721i	−0.0329959	+	0.0366457i
$301$	−0.121647	+	1.15740i	−0.00701164	+	0.0667113i
$302$	9.84809	+	7.15506i	0.566694	+	0.411727i
$303$	0.747726	+	7.11414i	0.0429558	+	0.408697i
$304$	−1.61803	+	2.80252i	−0.0928006	+	0.160735i
$305$	−3.90970	−	6.77181i	−0.223869	−	0.387752i
$306$	5.57433	−	4.04999i	0.318663	−	0.231522i
$307$	−0.843454	−	0.936751i	−0.0481385	−	0.0534632i	0.718595	−	0.695429i	$-0.244786\pi$
$307$	−0.843454	−	0.936751i	−0.0481385	−	0.0534632i	−0.766733	+	0.641966i	$0.778119\pi$
$308$	0.261046	+	0.803416i	0.0148744	+	0.0457788i
$309$	−3.15971			−0.179749
$310$	−11.0804	−	2.39750i	−0.629323	−	0.136169i
$311$	18.4419			1.04574			0.522872	−	0.852411i	$-0.324860\pi$
$311$	18.4419			1.04574			0.522872	+	0.852411i	$0.324860\pi$
$312$	−1.00000	−	3.07768i	−0.0566139	−	0.174240i
$313$	−12.6933	−	14.0973i	−0.717465	−	0.796826i	0.268588	−	0.963255i	$-0.413443\pi$
$313$	−12.6933	−	14.0973i	−0.717465	−	0.796826i	−0.986053	+	0.166429i	$0.946776\pi$
$314$	−14.1559	+	10.2849i	−0.798863	+	0.580408i
$315$	0.176034	+	0.304900i	0.00991841	+	0.0171792i
$316$	−3.29679	+	5.71021i	−0.185459	+	0.321224i
$317$	0.271460	+	2.58277i	0.0152467	+	0.145063i	0.999497	−	0.0317186i	$-0.0100980\pi$
$317$	0.271460	+	2.58277i	0.0152467	+	0.145063i	−0.984250	+	0.176782i	$0.943431\pi$
$318$	3.19710	+	2.32283i	0.179284	+	0.130258i
$319$	−1.25721	+	11.9615i	−0.0703901	+	0.669717i
$320$	−1.36245	+	1.51315i	−0.0761632	+	0.0845878i
$321$	0.204790	+	0.0911785i	0.0114303	+	0.00508909i
$322$	1.01478	+	0.215699i	0.0565517	+	0.0120204i
$323$	−21.8101	+	4.63587i	−1.21354	+	0.257947i
$324$	0.913545	−	0.406737i	0.0507525	−	0.0225965i
$325$	−0.854102	+	2.62866i	−0.0473771	+	0.145812i
$326$	7.30369	−	22.4785i	0.404514	−	1.24497i
$327$	−9.27786	+	4.13077i	−0.513067	+	0.228432i
$328$	−10.6105	+	2.25533i	−0.585866	+	0.124530i
$329$	−1.34740	−	0.286398i	−0.0742845	−	0.0157896i
$330$	9.08773	+	4.04612i	0.500263	+	0.222732i
$331$	−0.479159	+	0.532159i	−0.0263369	+	0.0292501i	−0.756169	−	0.654376i	$-0.772931\pi$
$331$	−0.479159	+	0.532159i	−0.0263369	+	0.0292501i	0.729832	+	0.683626i	$0.239598\pi$
$332$	−0.707779	+	6.73407i	−0.0388444	+	0.369580i
$333$	−0.885579	−	0.643411i	−0.0485294	−	0.0352587i
$334$	1.88965	+	17.9788i	0.103397	+	0.983755i
$335$	2.98798	−	5.17533i	0.163251	−	0.282758i
$336$	−0.0864545	−	0.149744i	−0.00471648	−	0.00816919i
$337$	10.4811	−	7.61495i	0.570940	−	0.414813i	−0.264506	−	0.964384i	$-0.585209\pi$
$337$	10.4811	−	7.61495i	0.570940	−	0.414813i	0.835447	+	0.549571i	$0.185209\pi$
$338$	1.69147	+	1.87857i	0.0920039	+	0.102181i
$339$	3.77774	+	11.6267i	0.205179	+	0.631475i
$340$	−14.0296			−0.760860
$341$	−2.74461	−	27.0629i	−0.148629	−	1.46554i
$342$	−3.23607			−0.174987
$343$	−0.746448	−	2.29733i	−0.0403044	−	0.124044i
$344$	−4.50361	−	5.00177i	−0.242819	−	0.269677i
$345$	9.88367	−	7.18091i	0.532119	−	0.386607i
$346$	−7.75707	−	13.4356i	−0.417023	−	0.722304i
$347$	1.36314	−	2.36102i	0.0731770	−	0.126746i	−0.827115	−	0.562033i	$-0.810020\pi$
$347$	1.36314	−	2.36102i	0.0731770	−	0.126746i	0.900292	+	0.435286i	$0.143353\pi$
$348$	−0.257330	−	2.44833i	−0.0137943	−	0.131244i
$349$	−3.32657	−	2.41689i	−0.178067	−	0.129373i	0.495181	−	0.868790i	$-0.335102\pi$
$349$	−3.32657	−	2.41689i	−0.178067	−	0.129373i	−0.673249	+	0.739416i	$0.735102\pi$
$350$	−0.0154370	+	0.146873i	−0.000825141	+	0.00785069i
$351$	2.16535	−	2.40487i	0.115578	−	0.128362i
$352$	−4.46320	−	1.98714i	−0.237889	−	0.105915i
$353$	−11.1615	−	2.37246i	−0.594068	−	0.126273i	−0.0989407	−	0.995093i	$-0.531545\pi$
$353$	−11.1615	−	2.37246i	−0.594068	−	0.126273i	−0.495128	+	0.868820i	$0.664879\pi$
$354$	−6.50138	+	1.38191i	−0.345544	+	0.0734477i
$355$	5.99134	−	2.66752i	0.317987	−	0.141577i
$356$	−3.33261	+	10.2567i	−0.176628	+	0.543606i
$357$	0.368159	−	1.13308i	0.0194850	−	0.0599688i
$358$	15.4791	−	6.89172i	0.818094	−	0.364239i
$359$	1.64195	−	0.349008i	0.0866590	−	0.0184199i	−0.164378	−	0.986397i	$-0.552562\pi$
$359$	1.64195	−	0.349008i	0.0866590	−	0.0184199i	0.251037	+	0.967977i	$0.419228\pi$
$360$	−1.99165	−	0.423339i	−0.104969	−	0.0223119i
$361$	−7.79059	−	3.46859i	−0.410031	−	0.182558i
$362$	−15.2841	+	16.9747i	−0.803315	+	0.892172i
$363$	−1.34516	+	12.7984i	−0.0706028	+	0.671741i
$364$	−0.452682	−	0.328893i	−0.0237270	−	0.0172387i
$365$	−0.278744	−	2.65207i	−0.0145901	−	0.138816i
$366$	−1.92015	+	3.32579i	−0.100368	+	0.173842i
$367$	8.16877	+	14.1487i	0.426406	+	0.738557i	0.996551	−	0.0829874i	$-0.0264461\pi$
$367$	8.16877	+	14.1487i	0.426406	+	0.738557i	−0.570144	+	0.821544i	$0.693113\pi$
$368$	−4.85410	+	3.52671i	−0.253038	+	0.183843i
$369$	−7.25841	−	8.06128i	−0.377858	−	0.419653i
$370$	0.688750	+	2.11975i	0.0358064	+	0.110201i
$371$	0.683307			0.0354755
$372$	1.70120	+	5.30150i	0.0882030	+	0.274870i
$373$	−16.5313			−0.855957			−0.427978	−	0.903789i	$-0.640774\pi$
$373$	−16.5313			−0.855957			−0.427978	+	0.903789i	$0.640774\pi$
$374$	−10.4024	−	32.0153i	−0.537895	−	1.65547i
$375$	7.97591	+	8.85815i	0.411874	+	0.457433i
$376$	6.44512	−	4.68266i	0.332382	−	0.241490i
$377$	−3.98331	−	6.89929i	−0.205151	−	0.355331i
$378$	0.0864545	−	0.149744i	0.00444674	−	0.00770198i
$379$	−3.41523	−	32.4937i	−0.175428	−	1.66909i	−0.628647	−	0.777691i	$-0.716391\pi$
$379$	−3.41523	−	32.4937i	−0.175428	−	1.66909i	0.453219	−	0.891399i	$-0.350276\pi$
$380$	5.33070	+	3.87298i	0.273459	+	0.198680i
$381$	1.22703	−	11.6744i	0.0628628	−	0.598100i
$382$	9.10186	−	10.1086i	0.465692	−	0.517203i
$383$	−6.29456	−	2.80252i	−0.321637	−	0.143202i	0.239566	−	0.970880i	$-0.422995\pi$
$383$	−6.29456	−	2.80252i	−0.321637	−	0.143202i	−0.561203	+	0.827678i	$0.689661\pi$
$384$	0.978148	+	0.207912i	0.0499159	+	0.0106099i
$385$	1.68247	−	0.357620i	0.0857467	−	0.0182260i
$386$	−1.86523	+	0.830455i	−0.0949379	+	0.0422691i
$387$	2.07985	−	6.40113i	0.105725	−	0.325388i
$388$	−3.58977	+	11.0482i	−0.182243	+	0.560886i
$389$	19.5246	−	8.69293i	0.989938	−	0.440749i	0.153107	−	0.988210i	$-0.451072\pi$
$389$	19.5246	−	8.69293i	0.989938	−	0.440749i	0.836831	+	0.547461i	$0.184405\pi$
$390$	−6.44512	+	1.36995i	−0.326362	+	0.0693703i
$391$	−40.4381	−	8.59538i	−2.04504	−	0.434687i
$392$	6.36751	+	2.83500i	0.321608	+	0.143189i
$393$	1.83633	−	2.03945i	0.0926306	−	0.102877i
$394$	0.878064	−	8.35422i	0.0442362	−	0.420880i
$395$	10.8615	+	7.89131i	0.546499	+	0.397055i
$396$	−0.510682	−	4.85882i	−0.0256627	−	0.244165i
$397$	−16.5130	+	28.6013i	−0.828761	+	1.43546i	0.0702489	+	0.997529i	$0.477621\pi$
$397$	−16.5130	+	28.6013i	−0.828761	+	1.43546i	−0.899010	+	0.437927i	$0.855713\pi$
$398$	−0.389035	−	0.673828i	−0.0195006	−	0.0337759i
$399$	−0.452682	+	0.328893i	−0.0226624	+	0.0164652i
$400$	−0.571506	−	0.634721i	−0.0285753	−	0.0317361i
$401$	−6.30658	−	19.4097i	−0.314936	−	0.969272i	−0.975781	−	0.218750i	$-0.929802\pi$
$401$	−6.30658	−	19.4097i	−0.314936	−	0.969272i	0.660845	−	0.750522i	$-0.270198\pi$
$402$	−2.93493			−0.146381
$403$	12.0072	+	13.4336i	0.598123	+	0.669177i
$404$	−7.15333			−0.355891
$405$	−0.629204	−	1.93649i	−0.0312654	−	0.0962250i
$406$	−0.284829	−	0.316335i	−0.0141358	−	0.0156994i
$407$	−4.32657	+	3.14344i	−0.214460	+	0.155814i
$408$	3.44512	+	5.96713i	0.170559	+	0.295417i
$409$	−10.6426	+	18.4336i	−0.526245	+	0.911483i	0.473287	+	0.880908i	$0.343067\pi$
$409$	−10.6426	+	18.4336i	−0.526245	+	0.911483i	−0.999532	+	0.0305751i	$0.990266\pi$
$410$	2.30874	+	21.9662i	0.114020	+	1.08483i
$411$	−18.2825	−	13.2830i	−0.901811	−	0.655204i
$412$	0.330279	−	3.14240i	0.0162717	−	0.154815i
$413$	−0.769006	+	0.854068i	−0.0378403	+	0.0420259i
$414$	−5.48127	−	2.44042i	−0.269390	−	0.119940i
$415$	13.4858	+	2.86650i	0.661992	+	0.140711i
$416$	3.16535	−	0.672816i	0.155194	−	0.0329875i
$417$	−19.0945	+	8.50142i	−0.935062	+	0.416317i
$418$	−4.88558	+	15.0363i	−0.238961	+	0.735448i
$419$	−0.573943	+	1.76642i	−0.0280390	+	0.0862950i	−0.964097	−	0.265551i	$-0.914446\pi$
$419$	−0.573943	+	1.76642i	−0.0280390	+	0.0862950i	0.936058	+	0.351846i	$0.114446\pi$
$420$	−0.321631	+	0.143199i	−0.0156940	+	0.00698740i
$421$	20.1883	−	4.29115i	0.983917	−	0.209138i	0.312257	−	0.949998i	$-0.398915\pi$
$421$	20.1883	−	4.29115i	0.983917	−	0.209138i	0.671660	+	0.740859i	$0.265582\pi$
$422$	14.5501	+	3.09271i	0.708287	+	0.150551i
$423$	7.27786	+	3.24031i	0.353862	+	0.157549i
$424$	−2.64429	+	2.93678i	−0.128418	+	0.142623i
$425$	0.615147	−	5.85274i	0.0298390	−	0.283899i
$426$	−2.60581	−	1.89323i	−0.126252	−	0.0917273i
$427$	0.0694092	+	0.660384i	0.00335895	+	0.0319582i
$428$	−0.112085	+	0.194138i	−0.00541785	+	0.00938400i
$429$	−7.90503	−	13.6919i	−0.381659	−	0.661052i
$430$	−11.0871	+	8.05523i	−0.534666	+	0.388458i
$431$	5.42376	+	6.02370i	0.261253	+	0.290151i	0.859473	−	0.511181i	$-0.170792\pi$
$431$	5.42376	+	6.02370i	0.261253	+	0.290151i	−0.598220	+	0.801332i	$0.704125\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	−26.8320			−1.28946			−0.644732	−	0.764409i	$-0.723031\pi$
$433$	−26.8320			−1.28946			−0.644732	+	0.764409i	$0.723031\pi$
$434$	0.776784	+	0.568709i	0.0372868	+	0.0272989i
$435$	−5.01263			−0.240337
$436$	−3.13834	−	9.65882i	−0.150299	−	0.462574i
$437$	12.9921	+	14.4292i	0.621497	+	0.690242i
$438$	−1.05955	+	0.769805i	−0.0506270	+	0.0367827i
$439$	−1.31365	−	2.27531i	−0.0626970	−	0.108594i	0.832973	−	0.553314i	$-0.186637\pi$
$439$	−1.31365	−	2.27531i	−0.0626970	−	0.108594i	−0.895670	+	0.444719i	$0.853304\pi$
$440$	−4.97388	+	8.61501i	−0.237120	+	0.410705i
$441$	0.728574	+	6.93192i	0.0346940	+	0.330091i
$442$	18.0389	+	13.1060i	0.858023	+	0.623390i
$443$	2.31643	−	22.0394i	0.110057	−	1.04712i	−0.790523	−	0.612432i	$-0.790191\pi$
$443$	2.31643	−	22.0394i	0.110057	−	1.04712i	0.900580	−	0.434690i	$-0.143142\pi$
$444$	0.732455	−	0.813473i	0.0347608	−	0.0386057i
$445$	20.0605	+	8.93152i	0.950960	+	0.423395i
$446$	25.7565	+	5.47472i	1.21961	+	0.259236i
$447$	−18.5337	+	3.93946i	−0.876614	+	0.186330i
$448$	0.157960	−	0.0703285i	0.00746292	−	0.00332271i
$449$	−2.21024	+	6.80241i	−0.104308	+	0.321026i	−0.989567	−	0.144071i	$-0.953981\pi$
$449$	−2.21024	+	6.80241i	−0.104308	+	0.321026i	0.885260	+	0.465097i	$0.153981\pi$
$450$	0.263932	−	0.812299i	0.0124419	−	0.0382922i
$451$	−48.4146	+	21.5556i	−2.27976	+	1.01501i
$452$	−11.9579	+	2.54172i	−0.562451	+	0.119553i
$453$	−11.9069	−	2.53089i	−0.559435	−	0.118912i
$454$	−23.9426	−	10.6599i	−1.12368	−	0.500295i
$455$	−0.762352	+	0.846678i	−0.0357396	+	0.0396929i
$456$	0.338261	−	3.21834i	0.0158405	−	0.150713i
$457$	31.2932	+	22.7359i	1.46384	+	1.06354i	0.982343	+	0.187089i	$0.0599054\pi$
$457$	31.2932	+	22.7359i	1.46384	+	1.06354i	0.481493	+	0.876450i	$0.340095\pi$
$458$	−2.19394	−	20.8740i	−0.102516	−	0.975377i
$459$	−3.44512	+	5.96713i	−0.160805	+	0.278522i
$460$	6.10844	+	10.5801i	0.284808	+	0.493301i
$461$	14.3458	−	10.4228i	0.668148	−	0.485438i	−0.201256	−	0.979539i	$-0.564502\pi$
$461$	14.3458	−	10.4228i	0.668148	−	0.485438i	0.869405	+	0.494100i	$0.164502\pi$
$462$	−0.565255	−	0.627780i	−0.0262981	−	0.0292070i
$463$	−2.18737	−	6.73203i	−0.101656	−	0.312864i	0.887275	−	0.461240i	$-0.152595\pi$
$463$	−2.18737	−	6.73203i	−0.101656	−	0.312864i	−0.988931	+	0.148376i	$0.952595\pi$
$464$	2.46182			0.114287
$465$	11.0976	−	2.31657i	0.514638	−	0.107428i
$466$	−0.788387			−0.0365213
$467$	−4.89928	−	15.0784i	−0.226712	−	0.697747i	−0.998113	−	0.0613986i	$-0.980444\pi$
$467$	−4.89928	−	15.0784i	−0.226712	−	0.697747i	0.771401	−	0.636349i	$-0.219556\pi$
$468$	2.16535	+	2.40487i	0.100093	+	0.111165i
$469$	−0.410557	+	0.298287i	−0.0189578	+	0.0137736i
$470$	−8.11060	−	14.0480i	−0.374114	−	0.647985i
$471$	8.74882	−	15.1534i	0.403124	−	0.698232i
$472$	−0.694761	−	6.61021i	−0.0319790	−	0.304260i
$473$	−26.6026	−	19.3279i	−1.22319	−	0.888698i
$474$	0.689217	−	6.55746i	0.0316568	−	0.301194i
$475$	−1.84943	+	2.05400i	−0.0848577	+	0.0942441i
$476$	1.08839	+	0.484581i	0.0498861	+	0.0222107i
$477$	−3.86547	−	0.821631i	−0.176988	−	0.0376199i
$478$	28.9059	−	6.14414i	1.32212	−	0.281026i
$479$	−17.6902	+	7.87619i	−0.808286	+	0.359872i	−0.768914	−	0.639352i	$-0.779202\pi$
$479$	−17.6902	+	7.87619i	−0.808286	+	0.359872i	−0.0393723	+	0.999225i	$0.512536\pi$
$480$	0.629204	−	1.93649i	0.0287191	−	0.0883883i
$481$	1.09464	−	3.36894i	0.0499111	−	0.153611i
$482$	8.66157	−	3.85638i	0.394524	−	0.175653i
$483$	−1.01478	+	0.215699i	−0.0461743	+	0.00981464i
$484$	−12.5877	−	2.67559i	−0.572167	−	0.121618i
$485$	21.6084	+	9.62069i	0.981188	+	0.436853i
$486$	−0.669131	+	0.743145i	−0.0303524	+	0.0337097i
$487$	0.144166	−	1.37165i	0.00653280	−	0.0621554i	−0.990770	−	0.135555i	$-0.956718\pi$
$487$	0.144166	−	1.37165i	0.00653280	−	0.0621554i	0.997303	+	0.0733997i	$0.0233849\pi$
$488$	−3.10686	−	2.25727i	−0.140641	−	0.102182i
$489$	2.47056	+	23.5058i	0.111722	+	1.06297i
$490$	7.09608	−	12.2908i	0.320568	−	0.555240i
$491$	7.57697	+	13.1237i	0.341944	+	0.592264i	0.984794	−	0.173728i	$-0.0555815\pi$
$491$	7.57697	+	13.1237i	0.341944	+	0.592264i	−0.642850	+	0.765992i	$0.722248\pi$
$492$	8.77583	−	6.37601i	0.395645	−	0.287453i
$493$	11.3502	+	12.6056i	0.511185	+	0.567729i
$494$	−3.23607	−	9.95959i	−0.145598	−	0.448103i
$495$	−9.94776			−0.447119
$496$	−5.45028	+	1.13772i	−0.244725	+	0.0510852i
$497$	−0.556932			−0.0249818
$498$	−2.09240	−	6.43975i	−0.0937628	−	0.288572i
$499$	26.5076	+	29.4397i	1.18664	+	1.31790i	0.936903	+	0.349589i	$0.113679\pi$
$499$	26.5076	+	29.4397i	1.18664	+	1.31790i	0.249741	+	0.968313i	$0.419654\pi$
$500$	−9.64333	+	7.00629i	−0.431263	+	0.313331i
$501$	−9.03891	−	15.6558i	−0.403829	−	0.699452i
$502$	−0.592403	+	1.02607i	−0.0264402	+	0.0457958i
$503$	1.20999	+	11.5123i	0.0539508	+	0.513308i	0.987810	+	0.155666i	$0.0497524\pi$
$503$	1.20999	+	11.5123i	0.0539508	+	0.513308i	−0.933859	+	0.357642i	$0.883581\pi$
$504$	0.139886	+	0.101633i	0.00623103	+	0.00452711i
$505$	−1.52248	+	14.4854i	−0.0677495	+	0.644594i
$506$	−19.6145	+	21.7842i	−0.871973	+	0.968424i
$507$	−2.30932	−	1.02817i	−0.102560	−	0.0456629i
$508$	11.4822	+	2.44062i	0.509441	+	0.108285i
$509$	9.91775	−	2.10808i	0.439596	−	0.0934391i	0.0172037	−	0.999852i	$-0.494524\pi$
$509$	9.91775	−	2.10808i	0.439596	−	0.0934391i	0.422393	+	0.906413i	$0.361190\pi$
$510$	12.8166	−	5.70634i	0.567531	−	0.252681i
$511$	−0.0699781	+	0.215370i	−0.00309565	+	0.00952743i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	2.95630	−	1.31623i	0.130524	−	0.0581129i
$514$	6.92173	−	1.47126i	0.305304	−	0.0648944i
$515$	−6.29304	−	1.33763i	−0.277304	−	0.0589429i
$516$	6.14866	+	2.73756i	0.270680	+	0.120514i
$517$	26.0436	−	28.9243i	1.14540	−	1.27209i
$518$	0.0197844	−	0.188236i	0.000869275	−	0.00827060i
$519$	12.5512	+	9.11898i	0.550936	+	0.400279i
$520$	−0.688750	−	6.55302i	−0.0302037	−	0.287369i
$521$	5.29923	−	9.17853i	0.232163	−	0.402119i	−0.726281	−	0.687398i	$-0.758753\pi$
$521$	5.29923	−	9.17853i	0.232163	−	0.402119i	0.958445	+	0.285279i	$0.0920863\pi$
$522$	1.23091	+	2.13200i	0.0538754	+	0.0933150i
$523$	−11.3140	+	8.22011i	−0.494727	+	0.359440i	−0.806999	−	0.590552i	$-0.798910\pi$
$523$	−11.3140	+	8.22011i	−0.494727	+	0.359440i	0.312272	+	0.949993i	$0.398910\pi$
$524$	1.83633	+	2.03945i	0.0802204	+	0.0890938i
$525$	−0.0456362	−	0.140454i	−0.00199173	−	0.00612991i
$526$	−7.47936			−0.326116
$527$	−30.9541	−	22.6625i	−1.34838	−	0.987193i
$528$	4.88558			0.212618
$529$	4.01722	+	12.3637i	0.174662	+	0.537554i
$530$	5.38416	+	5.97972i	0.233873	+	0.259742i
$531$	5.37723	−	3.90679i	0.233352	−	0.169540i
$532$	−0.279773	−	0.484581i	−0.0121297	−	0.0210092i
$533$	17.5517	−	30.4004i	0.760247	−	1.31679i
$534$	−1.12729	−	10.7255i	−0.0487828	−	0.464137i
$535$	0.369272	+	0.268292i	0.0159650	+	0.0115993i
$536$	0.306784	−	2.91885i	0.0132510	−	0.126075i
$537$	−11.3377	+	12.5918i	−0.489258	+	0.543376i
$538$	20.8013	+	9.26133i	0.896808	+	0.399284i
$539$	33.3088	+	7.08001i	1.43471	+	0.304958i
$540$	1.99165	−	0.423339i	0.0857071	−	0.0182176i
$541$	29.6900	−	13.2188i	1.27647	−	0.568322i	0.347226	−	0.937782i	$-0.387124\pi$
$541$	29.6900	−	13.2188i	1.27647	−	0.568322i	0.929247	+	0.369459i	$0.120457\pi$
$542$	−9.25290	+	28.4775i	−0.397446	+	1.22321i
$543$	7.05849	−	21.7238i	0.302909	−	0.932257i
$544$	−6.29456	+	2.80252i	−0.269877	+	0.120157i
$545$	−20.2270	+	4.29938i	−0.866429	+	0.184165i
$546$	0.547318	+	0.116336i	0.0234231	+	0.00497872i
$547$	20.4069	+	9.08576i	0.872538	+	0.388479i	0.793628	−	0.608403i	$-0.208190\pi$
$547$	20.4069	+	9.08576i	0.872538	+	0.388479i	0.0789095	+	0.996882i	$0.474856\pi$
$548$	15.1213	−	16.7939i	0.645951	−	0.717401i
$549$	0.401420	−	3.81926i	0.0171322	−	0.163002i
$550$	−3.37585	−	2.45270i	−0.143947	−	0.104583i
$551$	−0.832738	−	7.92297i	−0.0354758	−	0.337530i
$552$	3.00000	−	5.19615i	0.127688	−	0.221163i
$553$	−0.570045	−	0.987347i	−0.0242408	−	0.0419863i
$554$	−16.2282	+	11.7905i	−0.689469	+	0.500929i
$555$	−1.49139	−	1.65635i	−0.0633058	−	0.0703082i
$556$	−6.45893	−	19.8785i	−0.273920	−	0.843038i
$557$	−27.2218			−1.15342			−0.576712	−	0.816947i	$-0.695665\pi$
$557$	−27.2218			−1.15342			−0.576712	+	0.816947i	$0.695665\pi$
$558$	−3.71044	−	4.15122i	−0.157075	−	0.175735i
$559$	21.7805			0.921217
$560$	−0.108795	−	0.334837i	−0.00459743	−	0.0141494i
$561$	22.5249	+	25.0164i	0.951000	+	1.05619i
$562$	16.6299	−	12.0824i	0.701491	−	0.509663i
$563$	9.63089	+	16.6812i	0.405893	+	0.703028i	0.994425	−	0.105446i	$-0.0336271\pi$
$563$	9.63089	+	16.6812i	0.405893	+	0.703028i	−0.588532	+	0.808474i	$0.700294\pi$
$564$	−3.98331	+	6.89929i	−0.167727	+	0.290512i
$565$	2.60192	+	24.7556i	0.109463	+	1.04148i
$566$	−19.4225	−	14.1112i	−0.816387	−	0.593140i
$567$	−0.0180739	+	0.171962i	−0.000759033	+	0.00722172i
$568$	2.15524	−	2.39364i	0.0904318	−	0.100435i
$569$	23.7452	+	10.5720i	0.995451	+	0.443203i	0.838793	−	0.544450i	$-0.183262\pi$
$569$	23.7452	+	10.5720i	0.995451	+	0.443203i	0.156657	+	0.987653i	$0.449928\pi$
$570$	−6.44512	−	1.36995i	−0.269957	−	0.0573810i
$571$	−3.12960	+	0.665218i	−0.130970	+	0.0278385i	−0.272930	−	0.962034i	$-0.587993\pi$
$571$	−3.12960	+	0.665218i	−0.130970	+	0.0278385i	0.141960	+	0.989872i	$0.454659\pi$
$572$	14.4432	−	6.43053i	0.603901	−	0.268874i
$573$	−4.20341	+	12.9368i	−0.175600	+	0.540441i
$574$	0.579603	−	1.78383i	0.0241922	−	0.0744558i
$575$	−4.68157	+	2.08437i	−0.195235	+	0.0869241i
$576$	−0.978148	+	0.207912i	−0.0407562	+	0.00866299i
$577$	30.4282	+	6.46772i	1.26674	+	0.269255i	0.791811	−	0.610767i	$-0.209139\pi$
$577$	30.4282	+	6.46772i	1.26674	+	0.269255i	0.474934	+	0.880022i	$0.342472\pi$
$578$	−27.8408	−	12.3955i	−1.15802	−	0.515586i
$579$	1.36620	−	1.51732i	0.0567773	−	0.0630576i
$580$	0.523962	−	4.98517i	0.0217563	−	0.206998i
$581$	−0.947193	−	0.688176i	−0.0392962	−	0.0285503i
$582$	−1.21428	−	11.5531i	−0.0503335	−	0.478891i
$583$	−9.65349	+	16.7203i	−0.399807	+	0.692485i
$584$	−0.654835	−	1.13421i	−0.0270973	−	0.0469339i
$585$	5.33070	−	3.87298i	0.220397	−	0.160128i
$586$	9.41637	+	10.4579i	0.388987	+	0.432013i
$587$	7.48824	+	23.0464i	0.309073	+	0.951228i	0.978126	+	0.208014i	$0.0666998\pi$
$587$	7.48824	+	23.0464i	0.309073	+	0.951228i	−0.669053	+	0.743214i	$0.733300\pi$
$588$	−6.97010			−0.287442
$589$	5.50519	+	17.1560i	0.226838	+	0.706902i
$590$	−13.5335			−0.557166
$591$	2.59582	+	7.98910i	0.106778	+	0.328628i
$592$	0.732455	+	0.813473i	0.0301037	+	0.0334335i
$593$	6.97673	−	5.06889i	0.286500	−	0.208154i	−0.435248	−	0.900311i	$-0.643339\pi$
$593$	6.97673	−	5.06889i	0.286500	−	0.208154i	0.721747	+	0.692156i	$0.243339\pi$
$594$	2.44279	+	4.23104i	0.100229	+	0.173602i
$595$	1.21292	−	2.10084i	0.0497249	−	0.0861260i
$596$	−1.98058	−	18.8440i	−0.0811277	−	0.771879i
$597$	0.629471	+	0.457338i	0.0257626	+	0.0187176i
$598$	2.02957	−	19.3100i	0.0829952	−	0.789646i
$599$	17.6868	−	19.6432i	0.722665	−	0.802600i	−0.264145	−	0.964483i	$-0.585090\pi$
$599$	17.6868	−	19.6432i	0.722665	−	0.802600i	0.986810	+	0.161882i	$0.0517565\pi$
$600$	0.780261	+	0.347395i	0.0318540	+	0.0141823i
$601$	−43.7312	−	9.29536i	−1.78383	−	0.379165i	−0.806561	−	0.591152i	$-0.798674\pi$
$601$	−43.7312	−	9.29536i	−1.78383	−	0.379165i	−0.977273	+	0.211986i	$0.932007\pi$
$602$	1.13834	−	0.241962i	0.0463953	−	0.00986163i
$603$	2.68119	−	1.19374i	0.109187	−	0.0486130i
$604$	3.76164	−	11.5771i	0.153059	−	0.471067i
$605$	−8.09716	+	24.9205i	−0.329196	+	1.01316i
$606$	6.53489	−	2.90952i	0.265462	−	0.118191i
$607$	25.9250	−	5.51054i	1.05226	−	0.223666i	0.350859	−	0.936428i	$-0.385890\pi$
$607$	25.9250	−	5.51054i	1.05226	−	0.223666i	0.701406	+	0.712762i	$0.252556\pi$
$608$	3.16535	+	0.672816i	0.128372	+	0.0272863i
$609$	0.388870	+	0.173136i	0.0157578	+	0.00701582i
$610$	−5.23221	+	5.81095i	−0.211846	+	0.235279i
$611$	−2.69480	+	25.6393i	−0.109020	+	1.03725i
$612$	−5.57433	−	4.04999i	−0.225329	−	0.163711i
$613$	1.64444	+	15.6458i	0.0664184	+	0.631929i	0.976205	+	0.216851i	$0.0695787\pi$
$613$	1.64444	+	15.6458i	0.0664184	+	0.631929i	−0.909786	+	0.415077i	$0.863755\pi$
$614$	−0.630261	+	1.09164i	−0.0254353	+	0.0440552i
$615$	−11.0436	−	19.1280i	−0.445320	−	0.771317i
$616$	0.683426	−	0.496538i	0.0275360	−	0.0200061i
$617$	−22.3621	−	24.8356i	−0.900265	−	0.999845i	−0.999988	−	0.00483012i	$-0.998463\pi$
$617$	−22.3621	−	24.8356i	−0.900265	−	0.999845i	0.0997236	−	0.995015i	$-0.468204\pi$
$618$	0.976403	+	3.00506i	0.0392767	+	0.120881i
$619$	−12.5821			−0.505719			−0.252859	−	0.967503i	$-0.581371\pi$
$619$	−12.5821			−0.505719			−0.252859	+	0.967503i	$0.581371\pi$
$620$	1.14386	+	11.2789i	0.0459387	+	0.452973i
$621$	6.00000			0.240772
$622$	−5.69886	−	17.5393i	−0.228504	−	0.703262i
$623$	−1.24776	−	1.38578i	−0.0499905	−	0.0555201i
$624$	−2.61803	+	1.90211i	−0.104805	+	0.0761455i
$625$	10.0000	+	17.3205i	0.400000	+	0.692820i
$626$	−9.48489	+	16.4283i	−0.379092	+	0.656607i
$627$	−1.65260	−	15.7235i	−0.0659986	−	0.627934i
$628$	14.1559	+	10.2849i	0.564881	+	0.410410i
$629$	−0.788387	+	7.50100i	−0.0314350	+	0.299084i
$630$	0.235580	−	0.261638i	0.00938572	−	0.0104239i
$631$	−15.9797	−	7.11460i	−0.636140	−	0.283228i	0.0632176	−	0.998000i	$-0.479864\pi$
$631$	−15.9797	−	7.11460i	−0.636140	−	0.283228i	−0.699358	+	0.714772i	$0.746530\pi$
$632$	6.44949	+	1.37088i	0.256547	+	0.0545308i
$633$	−14.5501	+	3.09271i	−0.578314	+	0.122924i
$634$	2.37248	−	1.05630i	0.0942231	−	0.0419508i
$635$	7.38607	−	22.7320i	0.293107	−	0.902091i
$636$	1.22118	−	3.75841i	0.0484230	−	0.149031i
$637$	−20.6057	+	9.17424i	−0.816427	+	0.363497i
$638$	11.7646	−	2.50064i	0.465764	−	0.0990013i
$639$	3.15057	+	0.669674i	0.124635	+	0.0264919i
$640$	1.86011	+	0.828176i	0.0735274	+	0.0327365i
$641$	15.9767	−	17.7440i	0.631043	−	0.700844i	−0.339817	−	0.940491i	$-0.610365\pi$
$641$	15.9767	−	17.7440i	0.631043	−	0.700844i	0.970860	+	0.239648i	$0.0770319\pi$
$642$	0.0234322	−	0.222943i	0.000924796	−	0.00879885i
$643$	−5.40451	−	3.92661i	−0.213133	−	0.154850i	0.476097	−	0.879393i	$-0.342051\pi$
$643$	−5.40451	−	3.92661i	−0.213133	−	0.154850i	−0.689230	+	0.724542i	$0.742051\pi$
$644$	−0.108444	−	1.03177i	−0.00427327	−	0.0406575i
$645$	6.85219	−	11.8683i	0.269805	−	0.467316i
$646$	11.1487	+	19.3100i	0.438638	+	0.759743i
$647$	33.7299	−	24.5062i	1.32606	−	0.963438i	0.326223	−	0.945293i	$-0.394224\pi$
$647$	33.7299	−	24.5062i	1.32606	−	0.963438i	0.999835	−	0.0181452i	$-0.00577611\pi$
$648$	−0.669131	−	0.743145i	−0.0262859	−	0.0291935i
$649$	−10.0346	−	30.8833i	−0.393892	−	1.21228i
$650$	2.76393			0.108410
$651$	−0.940943	−	0.203595i	−0.0368784	−	0.00797953i
$652$	−23.6352			−0.925628
$653$	12.7695	+	39.3004i	0.499708	+	1.53794i	0.809489	+	0.587136i	$0.199744\pi$
$653$	12.7695	+	39.3004i	0.499708	+	1.53794i	−0.309780	+	0.950808i	$0.600256\pi$
$654$	6.79561	+	7.54729i	0.265730	+	0.295123i
$655$	4.52071	−	3.28449i	0.176639	−	0.128336i
$656$	5.42376	+	9.39423i	0.211762	+	0.366783i
$657$	0.654835	−	1.13421i	0.0255476	−	0.0442497i
$658$	0.143988	+	1.36995i	0.00561323	+	0.0534064i
$659$	−16.2594	−	11.8131i	−0.633376	−	0.460175i	0.224192	−	0.974545i	$-0.428026\pi$
$659$	−16.2594	−	11.8131i	−0.633376	−	0.460175i	−0.857568	+	0.514370i	$0.828026\pi$
$660$	1.03982	−	9.89327i	0.0404751	−	0.385095i
$661$	27.3285	−	30.3513i	1.06295	−	1.18053i	0.0799779	−	0.996797i	$-0.474515\pi$
$661$	27.3285	−	30.3513i	1.06295	−	1.18053i	0.982976	−	0.183733i	$-0.0588183\pi$
$662$	0.654182	+	0.291261i	0.0254255	+	0.0113202i
$663$	−21.8101	−	4.63587i	−0.847033	−	0.180042i
$664$	6.62319	−	1.40780i	0.257030	−	0.0546334i
$665$	−1.04082	+	0.463402i	−0.0403612	+	0.0179700i
$666$	−0.338261	+	1.04106i	−0.0131074	+	0.0403403i
$667$	4.56446	−	14.0480i	0.176737	−	0.543940i
$668$	16.5149	−	7.35291i	0.638981	−	0.284493i
$669$	−25.7565	+	5.47472i	−0.995805	+	0.211665i
$670$	−5.84536	−	1.24247i	−0.225826	−	0.0480008i
$671$	−17.1400	−	7.63122i	−0.661682	−	0.294600i
$672$	−0.115699	+	0.128496i	−0.00446318	+	0.00495686i
$673$	−0.954516	+	9.08161i	−0.0367939	+	0.350070i	0.960601	+	0.277932i	$0.0896490\pi$
$673$	−0.954516	+	9.08161i	−0.0367939	+	0.350070i	−0.997395	+	0.0721384i	$0.977018\pi$
$674$	−10.4811	−	7.61495i	−0.403716	−	0.293317i
$675$	0.0892780	+	0.849423i	0.00343631	+	0.0326943i
$676$	1.26393	−	2.18919i	0.0486128	−	0.0841998i
$677$	1.20790	+	2.09215i	0.0464235	+	0.0804078i	0.888303	−	0.459257i	$-0.151884\pi$
$677$	1.20790	+	2.09215i	0.0464235	+	0.0804078i	−0.841880	+	0.539665i	$0.818551\pi$
$678$	9.89025	−	7.18569i	0.379833	−	0.275965i
$679$	−1.34404	−	1.49271i	−0.0515796	−	0.0572849i
$680$	4.33537	+	13.3429i	0.166254	+	0.511677i
$681$	26.2084			1.00431
$682$	−24.8902	+	10.9732i	−0.953097	+	0.420185i
$683$	−21.5262			−0.823676			−0.411838	−	0.911257i	$-0.635113\pi$
$683$	−21.5262			−0.823676			−0.411838	+	0.911257i	$0.635113\pi$
$684$	1.00000	+	3.07768i	0.0382360	+	0.117678i
$685$	−30.7892	−	34.1949i	−1.17640	−	1.30652i
$686$	−1.95423	+	1.41983i	−0.0746127	+	0.0542093i
$687$	10.4945	+	18.1770i	0.400389	+	0.693495i
$688$	−3.36527	+	5.82882i	−0.128300	+	0.222222i
$689$	−1.33675	−	12.7183i	−0.0509261	−	0.484530i
$690$	−9.88367	−	7.18091i	−0.376265	−	0.273372i
$691$	−2.05902	+	19.5903i	−0.0783289	+	0.745250i	0.882912	+	0.469539i	$0.155580\pi$
$691$	−2.05902	+	19.5903i	−0.0783289	+	0.745250i	−0.961241	+	0.275711i	$0.911087\pi$
$692$	−10.3810	+	11.5292i	−0.394626	+	0.438276i
$693$	0.771728	+	0.343595i	0.0293155	+	0.0130521i
$694$	−2.66670	−	0.566824i	−0.101226	−	0.0215163i
$695$	−41.6286	+	8.84844i	−1.57906	+	0.335640i
$696$	−2.24898	+	1.00131i	−0.0852475	+	0.0379546i
$697$	−23.0966	+	71.0840i	−0.874846	+	2.69250i
$698$	−1.27064	+	3.91062i	−0.0480943	+	0.148019i
$699$	0.720227	−	0.320666i	0.0272415	−	0.0121287i
$700$	0.144455	−	0.0307048i	0.00545988	−	0.00116053i
$701$	−5.79045	−	1.23080i	−0.218702	−	0.0464866i	0.0972571	−	0.995259i	$-0.468993\pi$
$701$	−5.79045	−	1.23080i	−0.218702	−	0.0464866i	−0.315960	+	0.948773i	$0.602326\pi$
$702$	−2.95630	−	1.31623i	−0.111578	−	0.0496778i
$703$	2.37027	−	2.63245i	0.0893965	−	0.0992849i
$704$	−0.510682	+	4.85882i	−0.0192471	+	0.183124i
$705$	13.1232	+	9.53458i	0.494249	+	0.359093i
$706$	1.19276	+	11.3484i	0.0448902	+	0.427102i
$707$	0.618438	−	1.07117i	0.0232587	−	0.0402853i
$708$	3.32331	+	5.75615i	0.124898	+	0.216329i
$709$	−17.9167	+	13.0173i	−0.672877	+	0.488874i	−0.870987	−	0.491306i	$-0.836520\pi$
$709$	−17.9167	+	13.0173i	−0.672877	+	0.488874i	0.198110	+	0.980180i	$0.436520\pi$
$710$	−4.38839	−	4.87380i	−0.164693	−	0.182910i
$711$	2.03753	+	6.27087i	0.0764133	+	0.235176i
$712$	10.7846			0.404169
$713$	−3.61316	+	33.2106i	−0.135314	+	1.24375i
$714$	−1.19139			−0.0445865
$715$	−9.94776	−	30.6161i	−0.372025	−	1.14498i
$716$	−11.3377	−	12.5918i	−0.423710	−	0.470578i
$717$	−23.9078	+	17.3700i	−0.892853	+	0.648696i
$718$	−0.839318	−	1.45374i	−0.0313231	−	0.0542532i
$719$	11.0135	−	19.0759i	0.410733	−	0.711411i	−0.584237	−	0.811583i	$-0.698606\pi$
$719$	11.0135	−	19.0759i	0.410733	−	0.711411i	0.994970	+	0.100172i	$0.0319394\pi$
$720$	0.212835	+	2.02499i	0.00793191	+	0.0754671i
$721$	0.442000	+	0.321132i	0.0164609	+	0.0119596i
$722$	−0.891405	+	8.48115i	−0.0331746	+	0.315636i
$723$	−6.34421	+	7.04596i	−0.235944	+	0.262042i
$724$	20.8670	+	9.29058i	0.775515	+	0.345282i
$725$	2.05670	+	0.437164i	0.0763838	+	0.0162359i
$726$	12.5877	−	2.67559i	0.467172	−	0.0993005i
$727$	10.7589	−	4.79015i	0.399024	−	0.177657i	−0.197406	−	0.980322i	$-0.563252\pi$
$727$	10.7589	−	4.79015i	0.399024	−	0.177657i	0.596430	+	0.802665i	$0.296585\pi$
$728$	−0.172909	+	0.532159i	−0.00640844	+	0.0197231i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−2.43614	+	1.08464i	−0.0901654	+	0.0401442i
$731$	−45.3617	+	9.64193i	−1.67776	+	0.356620i
$732$	3.75638	+	0.798442i	0.138840	+	0.0295113i
$733$	−28.8444	−	12.8424i	−1.06539	−	0.474344i	−0.202266	−	0.979331i	$-0.564831\pi$
$733$	−28.8444	−	12.8424i	−1.06539	−	0.474344i	−0.863127	+	0.504987i	$0.831497\pi$
$734$	10.9319	−	12.1412i	0.403505	−	0.448138i
$735$	−1.48348	+	14.1144i	−0.0547192	+	0.520618i
$736$	4.85410	+	3.52671i	0.178925	+	0.129996i
$737$	−1.49882	−	14.2603i	−0.0552096	−	0.525284i
$738$	−5.42376	+	9.39423i	−0.199651	+	0.345806i
$739$	−2.16824	−	3.75550i	−0.0797599	−	0.138148i	0.823386	−	0.567481i	$-0.192082\pi$
$739$	−2.16824	−	3.75550i	−0.0797599	−	0.138148i	−0.903146	+	0.429333i	$0.858749\pi$
$740$	1.80317	−	1.31008i	0.0662859	−	0.0481595i
$741$	7.00723	+	7.78231i	0.257417	+	0.285890i
$742$	−0.211154	−	0.649864i	−0.00775169	−	0.0238572i
$743$	45.2856			1.66137			0.830684	−	0.556744i	$-0.187950\pi$
$743$	45.2856			1.66137			0.830684	+	0.556744i	$0.187950\pi$
$744$	4.51633	−	3.25619i	0.165577	−	0.119378i
$745$	−38.5804			−1.41348
$746$	5.10844	+	15.7222i	0.187033	+	0.575630i
$747$	4.53079	+	5.03195i	0.165773	+	0.184109i
$748$	−27.2338	+	19.7865i	−0.995767	+	0.723467i
$749$	−0.0193806	−	0.0335682i	−0.000708151	−	0.00122655i
$750$	5.95991	−	10.3229i	0.217625	−	0.376938i
$751$	0.430850	+	4.09926i	0.0157219	+	0.149584i	0.999567	−	0.0294403i	$-0.00937251\pi$
$751$	0.430850	+	4.09926i	0.0157219	+	0.149584i	−0.983845	+	0.179025i	$0.942706\pi$
$752$	−6.44512	−	4.68266i	−0.235030	−	0.170759i
$753$	0.123846	−	1.17832i	0.00451320	−	0.0429402i
$754$	−5.33070	+	5.92035i	−0.194133	+	0.215606i
$755$	−22.6430	−	10.0813i	−0.824063	−	0.366896i
$756$	−0.169131	−	0.0359498i	−0.00615122	−	0.00130748i
$757$	−5.57624	+	1.18527i	−0.202672	+	0.0430792i	−0.308129	−	0.951345i	$-0.599703\pi$
$757$	−5.57624	+	1.18527i	−0.202672	+	0.0430792i	0.105457	+	0.994424i	$0.466369\pi$
$758$	−29.8480	+	13.2892i	−1.08413	+	0.482685i
$759$	9.05836	−	27.8788i	0.328798	−	1.01194i
$760$	2.03615	−	6.26662i	0.0738588	−	0.227314i
$761$	9.02688	−	4.01903i	0.327224	−	0.145690i	−0.236548	−	0.971620i	$-0.576016\pi$
$761$	9.02688	−	4.01903i	0.327224	−	0.145690i	0.563773	+	0.825930i	$0.309349\pi$
$762$	−11.4822	+	2.44062i	−0.415957	+	0.0884144i
$763$	1.71767	+	0.365102i	0.0621839	+	0.0132176i
$764$	−12.4265	−	5.53264i	−0.449576	−	0.200164i
$765$	−9.38761	+	10.4260i	−0.339410	+	0.376953i
$766$	−0.720227	+	6.85250i	−0.0260229	+	0.247591i
$767$	17.4011	+	12.6426i	0.628317	+	0.456499i
$768$	−0.104528	−	0.994522i	−0.00377185	−	0.0358867i
$769$	21.8960	−	37.9250i	0.789591	−	1.36761i	−0.136627	−	0.990623i	$-0.543626\pi$
$769$	21.8960	−	37.9250i	0.789591	−	1.36761i	0.926218	−	0.376989i	$-0.123040\pi$
$770$	−0.860029	−	1.48961i	−0.0309933	−	0.0536820i
$771$	−5.72490	+	4.15938i	−0.206177	+	0.149796i
$772$	1.36620	+	1.51732i	0.0491706	+	0.0546094i
$773$	3.81125	+	11.7298i	0.137081	+	0.421892i	0.995908	−	0.0903737i	$-0.0288062\pi$
$773$	3.81125	+	11.7298i	0.137081	+	0.421892i	−0.858827	+	0.512266i	$0.828806\pi$
$774$	−6.73054			−0.241924
$775$	−4.75541	−	0.0173541i	−0.170819	−	0.000623379i
$776$	11.6167			0.417016
$777$	0.0584884	+	0.180009i	0.00209826	+	0.00645778i
$778$	−14.3009	−	15.8828i	−0.512712	−	0.569425i
$779$	28.3992	−	20.6332i	1.01751	−	0.739262i
$780$	3.29456	+	5.70634i	0.117964	+	0.204320i
$781$	7.86811	−	13.6280i	0.281543	−	0.487647i
$782$	4.32136	+	41.1150i	0.154532	+	1.47027i
$783$	−1.99165	−	1.44702i	−0.0711759	−	0.0517123i
$784$	0.728574	−	6.93192i	0.0260205	−	0.247569i
$785$	23.8396	−	26.4766i	0.850873	−	0.944990i
$786$	−2.50709	−	1.11623i	−0.0894249	−	0.0398145i
$787$	−40.1527	−	8.53471i	−1.43129	−	0.304230i	−0.573911	−	0.818918i	$-0.694574\pi$
$787$	−40.1527	−	8.53471i	−1.43129	−	0.304230i	−0.857377	+	0.514688i	$0.827908\pi$
$788$	−8.21667	+	1.74651i	−0.292707	+	0.0622168i
$789$	6.83274	−	3.04213i	0.243252	−	0.108303i
$790$	4.14871	−	12.7684i	0.147604	−	0.454280i
$791$	0.653205	−	2.01036i	0.0232253	−	0.0714802i
$792$	−4.46320	+	1.98714i	−0.158593	+	0.0706101i
$793$	12.1559	−	2.58381i	0.431668	−	0.0917539i
$794$	32.3042	+	6.86647i	1.14643	+	0.243682i
$795$	−7.35085	−	3.27281i	−0.260708	−	0.116075i
$796$	−0.520630	+	0.578218i	−0.0184532	+	0.0204944i
$797$	−0.607173	+	5.77686i	−0.0215072	+	0.204627i	−0.999999	−	0.00166037i	$-0.999471\pi$
$797$	−0.607173	+	5.77686i	−0.0215072	+	0.204627i	0.978491	+	0.206287i	$0.0661382\pi$
$798$	0.452682	+	0.328893i	0.0160248	+	0.0116427i
$799$	−5.73777	−	54.5912i	−0.202988	−	1.93130i
$800$	−0.427051	+	0.739674i	−0.0150985	+	0.0261514i
$801$	5.39228	+	9.33971i	0.190527	+	0.330002i
$802$	−16.5108	+	11.9958i	−0.583018	+	0.423587i
$803$	−4.28143	−	4.75501i	−0.151088	−	0.167801i
$804$	0.906944	+	2.79129i	0.0319854	+	0.0984410i
$805$	−2.11241			−0.0744527
$806$	9.06572	−	15.5708i	0.319326	−	0.548457i
$807$	−22.7699			−0.801537
$808$	2.21050	+	6.80322i	0.0777651	+	0.239336i
$809$	−4.14812	−	4.60696i	−0.145840	−	0.161972i	0.665799	−	0.746131i	$-0.268091\pi$
$809$	−4.14812	−	4.60696i	−0.145840	−	0.161972i	−0.811639	+	0.584159i	$0.801424\pi$
$810$	−1.64728	+	1.19682i	−0.0578795	+	0.0420519i
$811$	−15.5897	−	27.0022i	−0.547429	−	0.948175i	−0.998450	−	0.0556613i	$-0.982273\pi$
$811$	−15.5897	−	27.0022i	−0.547429	−	0.948175i	0.451021	−	0.892513i	$-0.351060\pi$
$812$	−0.212835	+	0.368642i	−0.00746906	+	0.0129368i
$813$	−3.12990	−	29.7790i	−0.109770	−	1.04439i
$814$	4.32657	+	3.14344i	0.151646	+	0.110177i
$815$	−5.03042	+	47.8612i	−0.176208	+	1.67651i
$816$	4.61048	−	5.12045i	0.161399	−	0.179252i
$817$	19.8975	+	8.85893i	0.696125	+	0.309935i
$818$	20.8202	+	4.42546i	0.727960	+	0.154733i
$819$	−0.547318	+	0.116336i	−0.0191248	+	0.00406511i
$820$	20.1776	−	8.98366i	0.704633	−	0.313723i
$821$	0.120773	−	0.371701i	0.00421501	−	0.0129725i	−0.948927	−	0.315496i	$-0.897829\pi$
$821$	0.120773	−	0.371701i	0.00421501	−	0.0129725i	0.953142	+	0.302524i	$0.0978291\pi$
$822$	−6.98331	+	21.4924i	−0.243571	+	0.749634i
$823$	2.94806	−	1.31256i	0.102763	−	0.0457531i	−0.354711	−	0.934976i	$-0.615421\pi$
$823$	2.94806	−	1.31256i	0.102763	−	0.0457531i	0.457474	+	0.889223i	$0.348754\pi$
$824$	−3.09066	+	0.656940i	−0.107668	+	0.0228856i
$825$	4.08160	+	0.867570i	0.142103	+	0.0302049i
$826$	1.04990	+	0.467447i	0.0365308	+	0.0162646i
$827$	−24.6757	+	27.4051i	−0.858058	+	0.952970i	−0.999315	−	0.0370033i	$-0.988219\pi$
$827$	−24.6757	+	27.4051i	−0.858058	+	0.952970i	0.141257	+	0.989973i	$0.454885\pi$
$828$	−0.627171	+	5.96713i	−0.0217957	+	0.207372i
$829$	−12.6328	−	9.17828i	−0.438756	−	0.318775i	0.346385	−	0.938093i	$-0.387409\pi$
$829$	−12.6328	−	9.17828i	−0.438756	−	0.318775i	−0.785140	+	0.619318i	$0.787409\pi$
$830$	−1.44114	−	13.7116i	−0.0500228	−	0.475935i
$831$	10.0296	−	17.3717i	0.347922	−	0.602618i
$832$	−1.61803	−	2.80252i	−0.0560952	−	0.0971598i
$833$	38.8536	−	28.2288i	1.34620	−	0.978071i
$834$	13.9859	+	15.5329i	0.484291	+	0.537859i
$835$	−11.3746	−	35.0075i	−0.393636	−	1.21149i
$836$	15.8101			0.546803
$837$	5.07811	+	2.28316i	0.175525	+	0.0789176i
$838$	1.85732			0.0641600
$839$	10.2697	+	31.6070i	0.354550	+	1.09119i	0.956270	+	0.292486i	$0.0944826\pi$
$839$	10.2697	+	31.6070i	0.354550	+	1.09119i	−0.601719	+	0.798708i	$0.705517\pi$
$840$	0.235580	+	0.261638i	0.00812827	+	0.00902736i
$841$	18.5584	−	13.4835i	0.639945	−	0.464947i
$842$	−10.3197	−	17.8742i	−0.355639	−	0.615985i
$843$	−10.2779	+	17.8018i	−0.353988	+	0.613126i
$844$	−1.55488	−	14.7936i	−0.0535210	−	0.509218i
$845$	−4.16410	−	3.02539i	−0.143249	−	0.104077i
$846$	0.832738	−	7.92297i	0.0286301	−	0.272397i
$847$	1.48891	−	1.65361i	0.0511597	−	0.0568186i
$848$	3.61018	+	1.60735i	0.123974	+	0.0551967i
$849$	23.4829	+	4.99143i	0.805929	+	0.171306i
$850$	−5.75638	+	1.22356i	−0.197442	+	0.0419676i
$851$	6.00000	−	2.67137i	0.205677	−	0.0915735i
$852$	−0.995330	+	3.06331i	−0.0340994	+	0.104947i
$853$	7.00565	−	21.5612i	0.239869	−	0.738240i	−0.756569	−	0.653913i	$-0.773126\pi$
$853$	7.00565	−	21.5612i	0.239869	−	0.738240i	0.996438	−	0.0843268i	$-0.0268740\pi$
$854$	0.606614	−	0.270082i	0.0207579	−	0.00924202i
$855$	6.44512	−	1.36995i	0.220419	−	0.0468514i
$856$	0.219272	+	0.0466077i	0.00749457	+	0.00159302i
$857$	−38.0718	−	16.9507i	−1.30051	−	0.579024i	−0.364567	−	0.931177i	$-0.618783\pi$
$857$	−38.0718	−	16.9507i	−1.30051	−	0.579024i	−0.935942	+	0.352153i	$0.885450\pi$
$858$	−10.5790	+	11.7492i	−0.361161	+	0.401110i
$859$	1.36746	−	13.0105i	0.0466570	−	0.443912i	−0.946109	−	0.323848i	$-0.895023\pi$
$859$	1.36746	−	13.0105i	0.0466570	−	0.443912i	0.992766	−	0.120064i	$-0.0383099\pi$
$860$	11.0871	+	8.05523i	0.378066	+	0.274681i
$861$	0.196057	+	1.86536i	0.00668161	+	0.0635713i
$862$	4.05284	−	7.01973i	0.138040	−	0.239093i
$863$	−16.0578	−	27.8129i	−0.546612	−	0.946761i	−0.998504	−	0.0546874i	$-0.982584\pi$
$863$	−16.0578	−	27.8129i	−0.546612	−	0.946761i	0.451891	−	0.892073i	$-0.350750\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	21.1372	+	23.4753i	0.718687	+	0.798183i
$866$	8.29155	+	25.5188i	0.281758	+	0.867163i
$867$	30.4755			1.03500
$868$	0.300835	−	0.914507i	0.0102110	−	0.0310404i
$869$	32.2135			1.09277
$870$	1.54899	+	4.76729i	0.0525156	+	0.161626i
$871$	6.35516	+	7.05812i	0.215336	+	0.239155i
$872$	−8.21628	+	5.96948i	−0.278238	+	0.202152i
$873$	5.80836	+	10.0604i	0.196583	+	0.340492i
$874$	9.70820	−	16.8151i	0.328385	−	0.568779i
$875$	−0.215438	−	2.04975i	−0.00728313	−	0.0692943i
$876$	1.05955	+	0.769805i	0.0357987	+	0.0260093i
$877$	−5.73468	+	54.5618i	−0.193646	+	1.84242i	0.277935	+	0.960600i	$0.410350\pi$
$877$	−5.73468	+	54.5618i	−0.193646	+	1.84242i	−0.471581	+	0.881823i	$0.656317\pi$
$878$	−1.75800	+	1.95246i	−0.0593298	+	0.0658924i
$879$	−12.8559	−	5.72382i	−0.433619	−	0.193060i
$880$	9.73038	+	2.06826i	0.328011	+	0.0697209i
$881$	42.4575	−	9.02461i	1.43043	−	0.304047i	0.573383	−	0.819287i	$-0.305631\pi$
$881$	42.4575	−	9.02461i	1.43043	−	0.304047i	0.857046	+	0.515240i	$0.172297\pi$
$882$	6.36751	−	2.83500i	0.214405	−	0.0954593i
$883$	10.7286	−	33.0193i	0.361047	−	1.11119i	−0.591372	−	0.806399i	$-0.701414\pi$
$883$	10.7286	−	33.0193i	0.361047	−	1.11119i	0.952419	−	0.304791i	$-0.0985865\pi$
$884$	6.89025	−	21.2060i	0.231744	−	0.713235i
$885$	12.3635	−	5.50457i	0.415594	−	0.185034i
$886$	−21.6765	+	4.60748i	−0.728236	+	0.154791i
$887$	−8.16320	−	1.73514i	−0.274093	−	0.0582603i	0.0688143	−	0.997629i	$-0.478078\pi$
$887$	−8.16320	−	1.73514i	−0.274093	−	0.0582603i	−0.342908	+	0.939369i	$0.611412\pi$
$888$	−1.00000	−	0.445229i	−0.0335578	−	0.0149409i
$889$	−1.35816	+	1.50839i	−0.0455512	+	0.0505897i
$890$	2.29534	−	21.8387i	0.0769399	−	0.732034i
$891$	−3.95252	−	2.87167i	−0.132414	−	0.0962046i
$892$	−2.75244	−	26.1877i	−0.0921585	−	0.876829i
$893$	−12.8902	+	22.3266i	−0.431356	+	0.747130i
$894$	9.47388	+	16.4092i	0.316854	+	0.548807i
$895$	−27.9114	+	20.2788i	−0.932975	+	0.677846i
$896$	−0.115699	−	0.128496i	−0.00386522	−	0.00429277i
$897$	6.00000	+	18.4661i	0.200334	+	0.616565i
$898$	7.15248			0.238681
$899$	9.20877	−	10.1526i	0.307130	−	0.338609i
$900$	−0.854102			−0.0284701
$901$	8.41425	+	25.8964i	0.280319	+	0.862734i
$902$	35.4615	+	39.3840i	1.18074	+	1.31134i
$903$	−0.941512	+	0.684048i	−0.0313315	+	0.0227637i
$904$	6.11251	+	10.5872i	0.203299	+	0.352124i
$905$	23.2546	−	40.2781i	0.773009	−	1.33889i
$906$	1.27242	+	12.1062i	0.0422732	+	0.402202i
$907$	25.1225	+	18.2526i	0.834179	+	0.606066i	0.920738	−	0.390180i	$-0.127587\pi$
$907$	25.1225	+	18.2526i	0.834179	+	0.606066i	−0.0865596	+	0.996247i	$0.527587\pi$
$908$	−2.73952	+	26.0648i	−0.0909143	+	0.864992i
$909$	−4.78651	+	5.31596i	−0.158759	+	0.176319i
$910$	1.04082	+	0.463402i	0.0345028	+	0.0153616i
$911$	−8.15135	−	1.73262i	−0.270066	−	0.0574044i	0.0708879	−	0.997484i	$-0.477417\pi$
$911$	−8.15135	−	1.73262i	−0.270066	−	0.0574044i	−0.340954	+	0.940080i	$0.610750\pi$
$912$	−3.16535	+	0.672816i	−0.104815	+	0.0222792i
$913$	30.2210	−	13.4553i	1.00017	−	0.445304i
$914$	11.9530	−	36.7874i	0.395369	−	1.21682i
$915$	2.41633	−	7.43670i	0.0798814	−	0.245850i
$916$	−19.1744	+	8.53698i	−0.633539	+	0.282070i
$917$	−0.464154	+	0.0986590i	−0.0153277	+	0.00325801i
$918$	6.73968	+	1.43256i	0.222443	+	0.0472816i
$919$	−27.9125	−	12.4274i	−0.920748	−	0.409943i	−0.109060	−	0.994035i	$-0.534784\pi$
$919$	−27.9125	−	12.4274i	−0.920748	−	0.409943i	−0.811688	+	0.584092i	$0.801451\pi$
$920$	8.17469	−	9.07892i	0.269512	−	0.299323i
$921$	0.131761	−	1.25362i	0.00434166	−	0.0413081i
$922$	−14.3458	−	10.4228i	−0.472452	−	0.343257i
$923$	1.08952	+	10.3661i	0.0358621	+	0.341205i
$924$	−0.422381	+	0.731585i	−0.0138953	+	0.0240674i
$925$	0.467465	+	0.809674i	0.0153702	+	0.0266219i
$926$	−5.72661	+	4.16062i	−0.188188	+	0.136727i
$927$	−2.11426	−	2.34812i	−0.0694413	−	0.0771223i
$928$	−0.760744	−	2.34133i	−0.0249726	−	0.0768579i
$929$	−47.3672			−1.55407			−0.777034	−	0.629458i	$-0.783277\pi$
$929$	−47.3672			−1.55407			−0.777034	+	0.629458i	$0.783277\pi$
$930$	−5.63253	−	9.83857i	−0.184698	−	0.322619i
$931$	−22.5557			−0.739234
$932$	0.243625	+	0.749800i	0.00798020	+	0.0245605i
$933$	12.3400	+	13.7050i	0.403995	+	0.448682i
$934$	−12.8265	+	9.31899i	−0.419696	+	0.304927i
$935$	34.2713	+	59.3596i	1.12079	+	1.94127i
$936$	1.61803	−	2.80252i	0.0528871	−	0.0916031i
$937$	−0.339992	−	3.23481i	−0.0111071	−	0.105677i	0.987564	−	0.157219i	$-0.0502529\pi$
$937$	−0.339992	−	3.23481i	−0.0111071	−	0.105677i	−0.998671	+	0.0515425i	$0.983586\pi$
$938$	0.410557	+	0.298287i	0.0134052	+	0.00973942i
$939$	1.98288	−	18.8659i	0.0647089	−	0.615664i
$940$	−10.8541	+	12.0547i	−0.354022	+	0.393181i
$941$	30.3697	+	13.5215i	0.990024	+	0.440787i	0.836862	−	0.547414i	$-0.184388\pi$
$941$	30.3697	+	13.5215i	0.990024	+	0.440787i	0.153162	+	0.988201i	$0.451054\pi$
$942$	−17.1153	−	3.63796i	−0.557646	−	0.118531i
$943$	63.6629	−	13.5320i	2.07315	−	0.440661i
$944$	−6.07199	+	2.70343i	−0.197627	+	0.0879890i
$945$	−0.108795	+	0.334837i	−0.00353911	+	0.0108922i
$946$	−10.1613	+	31.2732i	−0.330372	+	1.01678i
$947$	−21.8003	+	9.70614i	−0.708416	+	0.315407i	−0.729127	−	0.684378i	$-0.760074\pi$
$947$	−21.8003	+	9.70614i	−0.708416	+	0.315407i	0.0207111	+	0.999786i	$0.493407\pi$
$948$	−6.44949	+	1.37088i	−0.209470	+	0.0445242i
$949$	4.14557	+	0.881168i	0.134571	+	0.0286039i
$950$	2.52498	+	1.12419i	0.0819211	+	0.0364736i
$951$	−1.73773	+	1.92995i	−0.0563498	+	0.0625828i
$952$	0.124534	−	1.18486i	0.00403616	−	0.0384015i
$953$	−5.82676	−	4.23339i	−0.188747	−	0.137133i	0.489399	−	0.872060i	$-0.337216\pi$
$953$	−5.82676	−	4.23339i	−0.188747	−	0.137133i	−0.678146	+	0.734927i	$0.737216\pi$
$954$	0.413079	+	3.93018i	0.0133739	+	0.127244i
$955$	−13.8484	+	23.9861i	−0.448123	+	0.776171i
$956$	−14.7758	−	25.5925i	−0.477884	−	0.827720i
$957$	−9.73038	+	7.06953i	−0.314538	+	0.228526i
$958$	12.9573	+	14.3905i	0.418630	+	0.464936i
$959$	1.20748	+	3.71623i	0.0389915	+	0.120003i
$960$	−2.03615			−0.0657164
$961$	−15.6955	+	26.7329i	−0.506307	+	0.862353i
$962$	−3.54232			−0.114209
$963$	0.0692726	+	0.213199i	0.00223228	+	0.00687025i
$964$	−6.34421	−	7.04596i	−0.204333	−	0.226935i
$965$	3.36333	−	2.44360i	0.108270	−	0.0786624i
$966$	0.518727	+	0.898462i	0.0166898	+	0.0289075i
$967$	−3.04061	+	5.26650i	−0.0977796	+	0.169359i	−0.910765	−	0.412924i	$-0.864507\pi$
$967$	−3.04061	+	5.26650i	−0.0977796	+	0.169359i	0.812986	+	0.582284i	$0.197841\pi$
$968$	1.34516	+	12.7984i	0.0432352	+	0.411356i
$969$	−18.0389	−	13.1060i	−0.579493	−	0.421026i
$970$	2.47245	−	23.5238i	0.0793856	−	0.755304i
$971$	−24.5680	+	27.2855i	−0.788425	+	0.875634i	−0.994696	−	0.102860i	$-0.967200\pi$
$971$	−24.5680	+	27.2855i	−0.788425	+	0.875634i	0.206271	+	0.978495i	$0.433867\pi$
$972$	0.913545	+	0.406737i	0.0293020	+	0.0130461i
$973$	3.53509	+	0.751407i	0.113330	+	0.0240890i
$974$	−1.34907	+	0.286753i	−0.0432269	+	0.00918816i
$975$	−2.52498	+	1.12419i	−0.0808640	+	0.0360030i
$976$	−1.18672	+	3.65234i	−0.0379859	+	0.116908i
$977$	−7.88894	+	24.2797i	−0.252390	+	0.776775i	0.741943	+	0.670463i	$0.233904\pi$
$977$	−7.88894	+	24.2797i	−0.252390	+	0.776775i	−0.994333	+	0.106313i	$0.966096\pi$
$978$	21.5919	−	9.61332i	0.690432	−	0.307400i
$979$	51.5375	−	10.9546i	1.64714	−	0.350111i
$980$	−13.8820	−	2.95072i	−0.443445	−	0.0942572i
$981$	−9.27786	−	4.13077i	−0.296219	−	0.131885i
$982$	10.1400	−	11.2616i	0.323579	−	0.359371i
$983$	−0.485696	+	4.62109i	−0.0154913	+	0.147390i	−0.999533	−	0.0305461i	$-0.990275\pi$
$983$	−0.485696	+	4.62109i	−0.0154913	+	0.147390i	0.984042	+	0.177936i	$0.0569420\pi$
$984$	−8.77583	−	6.37601i	−0.279763	−	0.203260i
$985$	1.78787	+	17.0104i	0.0569662	+	0.541997i
$986$	8.48127	−	14.6900i	0.270099	−	0.467825i
$987$	−0.688750	−	1.19295i	−0.0219231	−	0.0379720i
$988$	−8.47214	+	6.15537i	−0.269535	+	0.195828i
$989$	27.0217	+	30.0106i	0.859239	+	0.954282i
$990$	3.07403	+	9.46088i	0.0976990	+	0.300687i
$991$	22.9819			0.730043			0.365022	−	0.930999i	$-0.381062\pi$
$991$	22.9819			0.730043			0.365022	+	0.930999i	$0.381062\pi$
$992$	2.76627	+	4.83195i	0.0878291	+	0.153415i
$993$	−0.716091			−0.0227245
$994$	0.172102	+	0.529674i	0.00545873	+	0.0168002i
$995$	1.06008	+	1.17734i	0.0336068	+	0.0373241i
$996$	−5.47798	+	3.97999i	−0.173577	+	0.126111i
$997$	−22.6954	−	39.3097i	−0.718772	−	1.24495i	−0.961487	−	0.274852i	$-0.911371\pi$
$997$	−22.6954	−	39.3097i	−0.718772	−	1.24495i	0.242715	−	0.970098i	$-0.421962\pi$
$998$	19.8075	−	34.3076i	0.626996	−	1.08599i
$999$	−0.114421	−	1.08864i	−0.00362011	−	0.0344430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	186.2.m.d.175.1	yes	8
3.2	odd	2		558.2.ba.b.361.1		8
31.13	odd	30		5766.2.a.x.1.2		4
31.14	even	15	inner	186.2.m.d.169.1	✓	8
31.18	even	15		5766.2.a.ba.1.2		4
93.14	odd	30		558.2.ba.b.541.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.m.d.169.1	✓	8	31.14	even	15	inner
186.2.m.d.175.1	yes	8	1.1	even	1	trivial
558.2.ba.b.361.1		8	3.2	odd	2
558.2.ba.b.541.1		8	93.14	odd	30
5766.2.a.x.1.2		4	31.13	odd	30
5766.2.a.ba.1.2		4	31.18	even	15

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 186 = 2 \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	186.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.01807 + 1.76336i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.0180739 - 0.171962i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(1.36245 - 1.51315i) q^{10} +(4.46320 + 1.98714i) q^{11} +(-0.978148 - 0.207912i) q^{12} +(-3.16535 + 0.672816i) q^{13} +(-0.157960 + 0.0703285i) q^{14} +(-0.629204 + 1.93649i) q^{15} +(0.309017 - 0.951057i) q^{16} +(6.29456 - 2.80252i) q^{17} +(0.978148 - 0.207912i) q^{18} +(-3.16535 - 0.672816i) q^{19} +(-1.86011 - 0.828176i) q^{20} +(0.115699 - 0.128496i) q^{21} +(0.510682 - 4.85882i) q^{22} +(-4.85410 - 3.52671i) q^{23} +(0.104528 + 0.994522i) q^{24} +(0.427051 - 0.739674i) q^{25} +(1.61803 + 2.80252i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.115699 + 0.128496i) q^{28} +(0.760744 + 2.34133i) q^{29} +2.03615 q^{30} +(-2.76627 - 4.83195i) q^{31} -1.00000 q^{32} +(1.50973 + 4.64646i) q^{33} +(-4.61048 - 5.12045i) q^{34} +(0.284829 - 0.206941i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-0.547318 + 0.947983i) q^{37} +(0.338261 + 3.21834i) q^{38} +(-2.61803 - 1.90211i) q^{39} +(-0.212835 + 2.02499i) q^{40} +(-7.25841 + 8.06128i) q^{41} +(-0.157960 - 0.0703285i) q^{42} +(-6.58347 - 1.39936i) q^{43} +(-4.77882 + 1.01577i) q^{44} +(-1.86011 + 0.828176i) q^{45} +(-1.85410 + 5.70634i) q^{46} +(2.46182 - 7.57670i) q^{47} +(0.913545 - 0.406737i) q^{48} +(6.81779 - 1.44917i) q^{49} +(-0.835438 - 0.177578i) q^{50} +(6.29456 + 2.80252i) q^{51} +(2.16535 - 2.40487i) q^{52} +(-0.413079 + 3.93018i) q^{53} +(0.809017 + 0.587785i) q^{54} +(1.03982 + 9.89327i) q^{55} +(0.0864545 - 0.149744i) q^{56} +(-1.61803 - 2.80252i) q^{57} +(1.99165 - 1.44702i) q^{58} +(-4.44746 - 4.93940i) q^{59} +(-0.629204 - 1.93649i) q^{60} -3.84029 q^{61} +(-3.74064 + 4.12403i) q^{62} +0.172909 q^{63} +(0.309017 + 0.951057i) q^{64} +(-4.40898 - 4.89667i) q^{65} +(3.95252 - 2.87167i) q^{66} +(-1.46747 - 2.54172i) q^{67} +(-3.44512 + 5.96713i) q^{68} +(-0.627171 - 5.96713i) q^{69} +(-0.284829 - 0.206941i) q^{70} +(0.336681 - 3.20331i) q^{71} +(-0.669131 + 0.743145i) q^{72} +(-1.19644 - 0.532691i) q^{73} +(1.07072 + 0.227588i) q^{74} +(0.835438 - 0.177578i) q^{75} +(2.95630 - 1.31623i) q^{76} +(0.261046 - 0.803416i) q^{77} +(-1.00000 + 3.07768i) q^{78} +(6.02353 - 2.68185i) q^{79} +(1.99165 - 0.423339i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(9.90970 + 4.41208i) q^{82} +(4.53079 - 5.03195i) q^{83} +(-0.0180739 + 0.171962i) q^{84} +(11.3502 + 8.24637i) q^{85} +(0.703533 + 6.69367i) q^{86} +(-1.23091 + 2.13200i) q^{87} +(2.44279 + 4.23104i) q^{88} +(8.72490 - 6.33901i) q^{89} +(1.36245 + 1.51315i) q^{90} +(0.172909 + 0.532159i) q^{91} +6.00000 q^{92} +(1.73985 - 5.28894i) q^{93} -7.96661 q^{94} +(-2.03615 - 6.26662i) q^{95} +(-0.669131 - 0.743145i) q^{96} +(9.39813 - 6.82814i) q^{97} +(-3.48505 - 6.03629i) q^{98} +(-2.44279 + 4.23104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + q^{3} - 2 q^{4} + 4 q^{6} + 8 q^{7} + 2 q^{8} + q^{9} + 6 q^{11} + q^{12} - 4 q^{13} + 7 q^{14} - 2 q^{16} + 24 q^{17} - q^{18} - 4 q^{19} - 15 q^{20} + 3 q^{21} + 9 q^{22} - 12 q^{23}+ \cdots - 9 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + q^3 - 2 * q^4 + 4 * q^6 + 8 * q^7 + 2 * q^8 + q^9 + 6 * q^11 + q^12 - 4 * q^13 + 7 * q^14 - 2 * q^16 + 24 * q^17 - q^18 - 4 * q^19 - 15 * q^20 + 3 * q^21 + 9 * q^22 - 12 * q^23 - q^24 - 10 * q^25 + 4 * q^26 - 2 * q^27 + 3 * q^28 - 15 * q^29 - 29 * q^31 - 8 * q^32 - 12 * q^33 + 6 * q^34 - 4 * q^36 + 8 * q^37 - 6 * q^38 - 12 * q^39 - 15 * q^40 - 48 * q^41 + 7 * q^42 - 24 * q^43 - 9 * q^44 - 15 * q^45 + 12 * q^46 + 30 * q^47 + q^48 - 3 * q^49 - 10 * q^50 + 24 * q^51 - 4 * q^52 + 33 * q^53 + 2 * q^54 + 30 * q^55 + 7 * q^56 - 4 * q^57 - 3 * q^59 - 28 * q^61 - 11 * q^62 + 14 * q^63 - 2 * q^64 - 30 * q^65 - 3 * q^66 + 2 * q^67 - 6 * q^68 + 6 * q^69 + 30 * q^71 - q^72 + 26 * q^73 + 12 * q^74 + 10 * q^75 + 6 * q^76 - 36 * q^77 - 8 * q^78 + q^81 - 12 * q^82 + 39 * q^83 + 8 * q^84 - 26 * q^86 - 15 * q^87 + 9 * q^88 + 48 * q^89 + 14 * q^91 + 48 * q^92 + 13 * q^93 - q^96 + 18 * q^97 - 7 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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