LMFDB - Embedded newform 690.2.m.b.601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			601.1
Root			$-0.415415 - 0.909632i$ of defining polynomial
Character	$\chi$	$=$	690.601
Dual form			690.2.m.b.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-2.31329 + 1.48666i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-2.31329 + 1.48666i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-0.841254 - 0.540641i) q^{10} +(0.0681534 - 0.474017i) q^{11} +(-0.142315 + 0.989821i) q^{12} +(-3.48325 - 2.23855i) q^{13} +(-1.80075 - 2.07817i) q^{14} +(0.415415 + 0.909632i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-2.59792 - 0.762819i) q^{17} +(0.654861 - 0.755750i) q^{18} +(-0.983568 + 0.288802i) q^{19} +(0.415415 - 0.909632i) q^{20} +(0.391340 + 2.72183i) q^{21} +0.478891 q^{22} +(-3.77831 - 2.95371i) q^{23} -1.00000 q^{24} +(-0.142315 - 0.989821i) q^{25} +(1.72005 - 3.76638i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(1.80075 - 2.07817i) q^{28} +(-3.20870 - 0.942161i) q^{29} +(-0.841254 + 0.540641i) q^{30} +(0.829365 + 1.81606i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-0.402869 - 0.258908i) q^{33} +(0.385331 - 2.68004i) q^{34} +(0.391340 - 2.72183i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-0.403660 - 0.465849i) q^{37} +(-0.425839 - 0.932456i) q^{38} +(-3.48325 + 2.23855i) q^{39} +(0.959493 + 0.281733i) q^{40} +(-1.49078 + 1.72045i) q^{41} +(-2.63843 + 0.774713i) q^{42} +(1.25013 - 2.73740i) q^{43} +(0.0681534 + 0.474017i) q^{44} +1.00000 q^{45} +(2.38594 - 4.16021i) q^{46} -3.04936 q^{47} +(-0.142315 - 0.989821i) q^{48} +(0.233250 - 0.510747i) q^{49} +(0.959493 - 0.281733i) q^{50} +(-1.77310 + 2.04627i) q^{51} +(3.97283 + 1.16653i) q^{52} +(-9.58797 + 6.16182i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(0.313607 + 0.361922i) q^{55} +(2.31329 + 1.48666i) q^{56} +(-0.145886 + 1.01466i) q^{57} +(0.475925 - 3.31013i) q^{58} +(-8.64662 - 5.55685i) q^{59} +(-0.654861 - 0.755750i) q^{60} +(4.15426 + 9.09656i) q^{61} +(-1.67954 + 1.07937i) q^{62} +(2.63843 + 0.774713i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(3.97283 - 1.16653i) q^{65} +(0.198939 - 0.435615i) q^{66} +(0.109917 + 0.764490i) q^{67} +2.70760 q^{68} +(-4.25635 + 2.20985i) q^{69} +2.74982 q^{70} +(-1.16375 - 8.09403i) q^{71} +(-0.415415 + 0.909632i) q^{72} +(8.90793 - 2.61561i) q^{73} +(0.403660 - 0.465849i) q^{74} +(-0.959493 - 0.281733i) q^{75} +(0.862362 - 0.554206i) q^{76} +(0.547045 + 1.19786i) q^{77} +(-2.71148 - 3.12922i) q^{78} +(6.15853 + 3.95785i) q^{79} +(-0.142315 + 0.989821i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-1.91510 - 1.23076i) q^{82} +(2.46990 + 2.85041i) q^{83} +(-1.14231 - 2.50132i) q^{84} +(2.27778 - 1.46384i) q^{85} +(2.88745 + 0.847833i) q^{86} +(-2.18996 + 2.52735i) q^{87} +(-0.459493 + 0.134919i) q^{88} +(0.300142 - 0.657220i) q^{89} +(0.142315 + 0.989821i) q^{90} +11.3858 q^{91} +(4.45741 + 1.76959i) q^{92} +1.99647 q^{93} +(-0.433969 - 3.01832i) q^{94} +(0.425839 - 0.932456i) q^{95} +(0.959493 - 0.281733i) q^{96} +(-3.39399 + 3.91688i) q^{97} +(0.538744 + 0.158189i) q^{98} +(-0.402869 + 0.258908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{8} - q^{9}+O(q^{10}) $ 10 * q + q^2 - q^3 - q^4 - q^5 + q^6 + q^8 - q^9	$ 10 q + q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{8} - q^{9} + q^{10} - 4 q^{11} - q^{12} + 2 q^{13} - q^{15} - q^{16} - 2 q^{17} + q^{18} - q^{20} + 4 q^{22} - q^{23} - 10 q^{24} - q^{25} + 9 q^{26} - q^{27} - 6 q^{29} + q^{30} + 22 q^{31} + q^{32} - 4 q^{33} - 9 q^{34} - q^{36} + 20 q^{37} + 2 q^{39} + q^{40} + 9 q^{41} - 11 q^{42} + 12 q^{43} - 4 q^{44} + 10 q^{45} + q^{46} - 8 q^{47} - q^{48} + 7 q^{49} + q^{50} - 13 q^{51} + 2 q^{52} - 20 q^{53} + q^{54} + 7 q^{55} + 11 q^{57} + 6 q^{58} - 22 q^{59} - q^{60} + 49 q^{61} + 11 q^{63} - q^{64} + 2 q^{65} - 7 q^{66} + 10 q^{67} - 2 q^{68} - q^{69} - q^{71} + q^{72} + 17 q^{73} - 20 q^{74} - q^{75} - 13 q^{78} + 18 q^{79} - q^{80} - q^{81} + 13 q^{82} + 15 q^{83} - 11 q^{84} + 9 q^{85} + 10 q^{86} - 6 q^{87} + 4 q^{88} - 5 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 22 q^{93} - 3 q^{94} + q^{96} - q^{97} - 7 q^{98} - 4 q^{99}+O(q^{100}) $ 10 * q + q^2 - q^3 - q^4 - q^5 + q^6 + q^8 - q^9 + q^10 - 4 * q^11 - q^12 + 2 * q^13 - q^15 - q^16 - 2 * q^17 + q^18 - q^20 + 4 * q^22 - q^23 - 10 * q^24 - q^25 + 9 * q^26 - q^27 - 6 * q^29 + q^30 + 22 * q^31 + q^32 - 4 * q^33 - 9 * q^34 - q^36 + 20 * q^37 + 2 * q^39 + q^40 + 9 * q^41 - 11 * q^42 + 12 * q^43 - 4 * q^44 + 10 * q^45 + q^46 - 8 * q^47 - q^48 + 7 * q^49 + q^50 - 13 * q^51 + 2 * q^52 - 20 * q^53 + q^54 + 7 * q^55 + 11 * q^57 + 6 * q^58 - 22 * q^59 - q^60 + 49 * q^61 + 11 * q^63 - q^64 + 2 * q^65 - 7 * q^66 + 10 * q^67 - 2 * q^68 - q^69 - q^71 + q^72 + 17 * q^73 - 20 * q^74 - q^75 - 13 * q^78 + 18 * q^79 - q^80 - q^81 + 13 * q^82 + 15 * q^83 - 11 * q^84 + 9 * q^85 + 10 * q^86 - 6 * q^87 + 4 * q^88 - 5 * q^89 + q^90 + 22 * q^91 - 12 * q^92 - 22 * q^93 - 3 * q^94 + q^96 - q^97 - 7 * q^98 - 4 * 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 $

$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$6$	0.959493	+	0.281733i	0.391711	+	0.115017i
$7$	−2.31329	+	1.48666i	−0.874342	+	0.561906i	−0.899078	−	0.437788i	$-0.855762\pi$
$7$	−2.31329	+	1.48666i	−0.874342	+	0.561906i	0.0247357	+	0.999694i	$0.492126\pi$
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	−0.841254	−	0.540641i	−0.266028	−	0.170966i
$11$	0.0681534	−	0.474017i	0.0205490	−	0.142922i	−0.976964	−	0.213404i	$-0.931545\pi$
$11$	0.0681534	−	0.474017i	0.0205490	−	0.142922i	0.997513	+	0.0704827i	$0.0224540\pi$
$12$	−0.142315	+	0.989821i	−0.0410828	+	0.285737i
$13$	−3.48325	−	2.23855i	−0.966081	−	0.620862i	−0.0404062	−	0.999183i	$-0.512865\pi$
$13$	−3.48325	−	2.23855i	−0.966081	−	0.620862i	−0.925674	+	0.378321i	$0.876502\pi$
$14$	−1.80075	−	2.07817i	−0.481270	−	0.555415i
$15$	0.415415	+	0.909632i	0.107260	+	0.234866i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−2.59792	−	0.762819i	−0.630089	−	0.185011i	−0.0489316	−	0.998802i	$-0.515582\pi$
$17$	−2.59792	−	0.762819i	−0.630089	−	0.185011i	−0.581157	+	0.813791i	$0.697400\pi$
$18$	0.654861	−	0.755750i	0.154352	−	0.178132i
$19$	−0.983568	+	0.288802i	−0.225646	+	0.0662557i	−0.392601	−	0.919709i	$-0.628425\pi$
$19$	−0.983568	+	0.288802i	−0.225646	+	0.0662557i	0.166955	+	0.985965i	$0.446607\pi$
$20$	0.415415	−	0.909632i	0.0928896	−	0.203400i
$21$	0.391340	+	2.72183i	0.0853973	+	0.593951i
$22$	0.478891			0.102100
$23$	−3.77831	−	2.95371i	−0.787831	−	0.615891i
$23$	−3.77831	−	2.95371i	−0.787831	−	0.615891i
$24$	−1.00000			−0.204124
$25$	−0.142315	−	0.989821i	−0.0284630	−	0.197964i
$26$	1.72005	−	3.76638i	0.337329	−	0.738648i
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$	1.80075	−	2.07817i	0.340309	−	0.392738i
$29$	−3.20870	−	0.942161i	−0.595842	−	0.174955i	−0.0301131	−	0.999546i	$-0.509587\pi$
$29$	−3.20870	−	0.942161i	−0.595842	−	0.174955i	−0.565728	+	0.824592i	$0.691405\pi$
$30$	−0.841254	+	0.540641i	−0.153591	+	0.0987071i
$31$	0.829365	+	1.81606i	0.148958	+	0.326173i	0.969372	−	0.245597i	$-0.0789841\pi$
$31$	0.829365	+	1.81606i	0.148958	+	0.326173i	−0.820414	+	0.571770i	$0.806257\pi$
$32$	0.654861	+	0.755750i	0.115764	+	0.133599i
$33$	−0.402869	−	0.258908i	−0.0701305	−	0.0450701i
$34$	0.385331	−	2.68004i	0.0660838	−	0.459623i
$35$	0.391340	−	2.72183i	0.0661485	−	0.460073i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	−0.403660	−	0.465849i	−0.0663613	−	0.0765851i	0.721598	−	0.692312i	$-0.243408\pi$
$37$	−0.403660	−	0.465849i	−0.0663613	−	0.0765851i	−0.787960	+	0.615727i	$0.788862\pi$
$38$	−0.425839	−	0.932456i	−0.0690801	−	0.151264i
$39$	−3.48325	+	2.23855i	−0.557767	+	0.358455i
$40$	0.959493	+	0.281733i	0.151709	+	0.0445458i
$41$	−1.49078	+	1.72045i	−0.232821	+	0.268689i	−0.860123	−	0.510086i	$-0.829613\pi$
$41$	−1.49078	+	1.72045i	−0.232821	+	0.268689i	0.627303	+	0.778776i	$0.284159\pi$
$42$	−2.63843	+	0.774713i	−0.407118	+	0.119541i
$43$	1.25013	−	2.73740i	0.190643	−	0.417450i	−0.790039	−	0.613056i	$-0.789940\pi$
$43$	1.25013	−	2.73740i	0.190643	−	0.417450i	0.980683	+	0.195606i	$0.0626673\pi$
$44$	0.0681534	+	0.474017i	0.0102745	+	0.0714608i
$45$	1.00000			0.149071
$46$	2.38594	−	4.16021i	0.351787	−	0.613389i
$47$	−3.04936			−0.444795			−0.222397	−	0.974956i	$-0.571388\pi$
$47$	−3.04936			−0.444795			−0.222397	+	0.974956i	$0.571388\pi$
$48$	−0.142315	−	0.989821i	−0.0205414	−	0.142868i
$49$	0.233250	−	0.510747i	0.0333215	−	0.0729639i
$50$	0.959493	−	0.281733i	0.135693	−	0.0398430i
$51$	−1.77310	+	2.04627i	−0.248284	+	0.286535i
$52$	3.97283	+	1.16653i	0.550932	+	0.161768i
$53$	−9.58797	+	6.16182i	−1.31701	+	0.846391i	−0.994954	−	0.100330i	$-0.968010\pi$
$53$	−9.58797	+	6.16182i	−1.31701	+	0.846391i	−0.322055	+	0.946721i	$0.604374\pi$
$54$	−0.415415	−	0.909632i	−0.0565308	−	0.123785i
$55$	0.313607	+	0.361922i	0.0422868	+	0.0488016i
$56$	2.31329	+	1.48666i	0.309127	+	0.198664i
$57$	−0.145886	+	1.01466i	−0.0193230	+	0.134395i
$58$	0.475925	−	3.31013i	0.0624920	−	0.434641i
$59$	−8.64662	−	5.55685i	−1.12569	−	0.723440i	−0.161037	−	0.986948i	$-0.551484\pi$
$59$	−8.64662	−	5.55685i	−1.12569	−	0.723440i	−0.964657	+	0.263508i	$0.915120\pi$
$60$	−0.654861	−	0.755750i	−0.0845422	−	0.0975669i
$61$	4.15426	+	9.09656i	0.531899	+	1.16470i	0.964735	+	0.263223i	$0.0847855\pi$
$61$	4.15426	+	9.09656i	0.531899	+	1.16470i	−0.432836	+	0.901473i	$0.642487\pi$
$62$	−1.67954	+	1.07937i	−0.213302	+	0.137081i
$63$	2.63843	+	0.774713i	0.332411	+	0.0976046i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	3.97283	−	1.16653i	0.492769	−	0.144690i
$66$	0.198939	−	0.435615i	0.0244877	−	0.0536205i
$67$	0.109917	+	0.764490i	0.0134285	+	0.0933974i	0.995433	−	0.0954577i	$-0.0304315\pi$
$67$	0.109917	+	0.764490i	0.0134285	+	0.0933974i	−0.982005	+	0.188855i	$0.939522\pi$
$68$	2.70760			0.328345
$69$	−4.25635	+	2.20985i	−0.512405	+	0.266035i
$70$	2.74982			0.328666
$71$	−1.16375	−	8.09403i	−0.138111	−	0.960585i	−0.934541	−	0.355854i	$-0.884190\pi$
$71$	−1.16375	−	8.09403i	−0.138111	−	0.960585i	0.796430	−	0.604731i	$-0.206719\pi$
$72$	−0.415415	+	0.909632i	−0.0489571	+	0.107201i
$73$	8.90793	−	2.61561i	1.04259	−	0.306133i	0.284773	−	0.958595i	$-0.408082\pi$
$73$	8.90793	−	2.61561i	1.04259	−	0.306133i	0.757822	+	0.652462i	$0.226264\pi$
$74$	0.403660	−	0.465849i	0.0469246	−	0.0541538i
$75$	−0.959493	−	0.281733i	−0.110793	−	0.0325317i
$76$	0.862362	−	0.554206i	0.0989197	−	0.0635718i
$77$	0.547045	+	1.19786i	0.0623415	+	0.136509i
$78$	−2.71148	−	3.12922i	−0.307015	−	0.354314i
$79$	6.15853	+	3.95785i	0.692889	+	0.445293i	0.839112	−	0.543959i	$-0.183075\pi$
$79$	6.15853	+	3.95785i	0.692889	+	0.445293i	−0.146223	+	0.989252i	$0.546712\pi$
$80$	−0.142315	+	0.989821i	−0.0159113	+	0.110665i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−1.91510	−	1.23076i	−0.211487	−	0.135915i
$83$	2.46990	+	2.85041i	0.271106	+	0.312873i	0.874935	−	0.484241i	$-0.160904\pi$
$83$	2.46990	+	2.85041i	0.271106	+	0.312873i	−0.603828	+	0.797114i	$0.706359\pi$
$84$	−1.14231	−	2.50132i	−0.124637	−	0.272916i
$85$	2.27778	−	1.46384i	0.247060	−	0.158776i
$86$	2.88745	+	0.847833i	0.311362	+	0.0914242i
$87$	−2.18996	+	2.52735i	−0.234789	+	0.270961i
$88$	−0.459493	+	0.134919i	−0.0489821	+	0.0143824i
$89$	0.300142	−	0.657220i	0.0318150	−	0.0696652i	−0.893057	−	0.449943i	$-0.851444\pi$
$89$	0.300142	−	0.657220i	0.0318150	−	0.0696652i	0.924872	+	0.380278i	$0.124172\pi$
$90$	0.142315	+	0.989821i	0.0150013	+	0.104336i
$91$	11.3858			1.19355
$92$	4.45741	+	1.76959i	0.464718	+	0.184493i
$93$	1.99647			0.207025
$94$	−0.433969	−	3.01832i	−0.0447605	−	0.311316i
$95$	0.425839	−	0.932456i	0.0436901	−	0.0956680i
$96$	0.959493	−	0.281733i	0.0979278	−	0.0287542i
$97$	−3.39399	+	3.91688i	−0.344608	+	0.397698i	−0.901424	−	0.432937i	$-0.857477\pi$
$97$	−3.39399	+	3.91688i	−0.344608	+	0.397698i	0.556816	+	0.830636i	$0.312023\pi$
$98$	0.538744	+	0.158189i	0.0544213	+	0.0159795i
$99$	−0.402869	+	0.258908i	−0.0404899	+	0.0260213i
$100$	0.415415	+	0.909632i	0.0415415	+	0.0909632i
$101$	3.83750	+	4.42871i	0.381846	+	0.440673i	0.913840	−	0.406075i	$-0.133103\pi$
$101$	3.83750	+	4.42871i	0.381846	+	0.440673i	−0.531994	+	0.846748i	$0.678557\pi$
$102$	−2.27778	−	1.46384i	−0.225534	−	0.144942i
$103$	0.404118	−	2.81070i	0.0398189	−	0.276947i	−0.960178	−	0.279389i	$-0.909868\pi$
$103$	0.404118	−	2.81070i	0.0398189	−	0.276947i	0.999997	+	0.00244196i	$0.000777300\pi$
$104$	−0.589262	+	4.09841i	−0.0577819	+	0.401882i
$105$	−2.31329	−	1.48666i	−0.225754	−	0.145083i
$106$	−7.46361	−	8.61347i	−0.724930	−	0.836614i
$107$	−6.01284	−	13.1663i	−0.581283	−	1.27283i	−0.940569	−	0.339604i	$-0.889707\pi$
$107$	−6.01284	−	13.1663i	−0.581283	−	1.27283i	0.359286	−	0.933228i	$-0.383020\pi$
$108$	0.841254	−	0.540641i	0.0809497	−	0.0520232i
$109$	9.78108	+	2.87198i	0.936857	+	0.275086i	0.714305	−	0.699835i	$-0.246743\pi$
$109$	9.78108	+	2.87198i	0.936857	+	0.275086i	0.222552	+	0.974921i	$0.428561\pi$
$110$	−0.313607	+	0.361922i	−0.0299013	+	0.0345079i
$111$	−0.591438	+	0.173662i	−0.0561368	+	0.0164832i
$112$	−1.14231	+	2.50132i	−0.107939	+	0.236353i
$113$	1.39380	+	9.69412i	0.131118	+	0.911946i	0.944100	+	0.329658i	$0.106933\pi$
$113$	1.39380	+	9.69412i	0.131118	+	0.911946i	−0.812982	+	0.582288i	$0.802157\pi$
$114$	−1.02509			−0.0960086
$115$	4.70653	−	0.921186i	0.438886	−	0.0859010i
$116$	3.34417			0.310498
$117$	0.589262	+	4.09841i	0.0544773	+	0.378898i
$118$	4.26974	−	9.34944i	0.393062	−	0.860685i
$119$	7.14381	−	2.09761i	0.654872	−	0.192288i
$120$	0.654861	−	0.755750i	0.0597803	−	0.0689902i
$121$	10.3344	+	3.03445i	0.939489	+	0.275859i
$122$	−8.41276	+	5.40655i	−0.761656	+	0.489486i
$123$	0.945686	+	2.07076i	0.0852696	+	0.186714i
$124$	−1.30741	−	1.50883i	−0.117409	−	0.135497i
$125$	0.841254	+	0.540641i	0.0752440	+	0.0483564i
$126$	−0.391340	+	2.72183i	−0.0348633	+	0.242480i
$127$	−0.157812	+	1.09761i	−0.0140036	+	0.0973971i	−0.995625	−	0.0934439i	$-0.970212\pi$
$127$	−0.157812	+	1.09761i	−0.0140036	+	0.0973971i	0.981621	+	0.190841i	$0.0611215\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$	−1.97071	−	2.27432i	−0.173511	−	0.200243i
$130$	1.72005	+	3.76638i	0.150858	+	0.330333i
$131$	1.80527	−	1.16018i	0.157727	−	0.101365i	−0.459396	−	0.888231i	$-0.651934\pi$
$131$	1.80527	−	1.16018i	0.157727	−	0.101365i	0.617124	+	0.786866i	$0.288298\pi$
$132$	0.459493	+	0.134919i	0.0399937	+	0.0117432i
$133$	1.84593	−	2.13032i	0.160062	−	0.184722i
$134$	−0.741066	+	0.217597i	−0.0640184	+	0.0187975i
$135$	0.415415	−	0.909632i	0.0357532	−	0.0782887i
$136$	0.385331	+	2.68004i	0.0330419	+	0.229811i
$137$	10.6596			0.910708			0.455354	−	0.890310i	$-0.349513\pi$
$137$	10.6596			0.910708			0.455354	+	0.890310i	$0.349513\pi$
$138$	−2.79310	−	3.89854i	−0.237765	−	0.331865i
$139$	1.03969			0.0881857			0.0440929	−	0.999027i	$-0.485960\pi$
$139$	1.03969			0.0881857			0.0440929	+	0.999027i	$0.485960\pi$
$140$	0.391340	+	2.72183i	0.0330742	+	0.230036i
$141$	−1.26675	+	2.77379i	−0.106680	+	0.233596i
$142$	7.84603	−	2.30380i	0.658424	−	0.193331i
$143$	−1.29851	+	1.49856i	−0.108587	+	0.125316i
$144$	−0.959493	−	0.281733i	−0.0799577	−	0.0234777i
$145$	2.81329	−	1.80799i	0.233631	−	0.150146i
$146$	3.85671	+	8.44502i	0.319184	+	0.698915i
$147$	−0.367696	−	0.424344i	−0.0303271	−	0.0349993i
$148$	0.518554	+	0.333254i	0.0426249	+	0.0273933i
$149$	−1.33978	+	9.31837i	−0.109759	+	0.763391i	0.858387	+	0.513003i	$0.171467\pi$
$149$	−1.33978	+	9.31837i	−0.109759	+	0.763391i	−0.968146	+	0.250387i	$0.919442\pi$
$150$	0.142315	−	0.989821i	0.0116200	−	0.0808186i
$151$	−4.28533	−	2.75402i	−0.348735	−	0.224119i	0.354532	−	0.935044i	$-0.384640\pi$
$151$	−4.28533	−	2.75402i	−0.348735	−	0.224119i	−0.703268	+	0.710925i	$0.748276\pi$
$152$	0.671292	+	0.774713i	0.0544490	+	0.0628375i
$153$	1.12478	+	2.46292i	0.0909328	+	0.199115i
$154$	−1.10782	+	0.711950i	−0.0892704	+	0.0573706i
$155$	−1.91560	−	0.562472i	−0.153865	−	0.0451788i
$156$	2.71148	−	3.12922i	0.217093	−	0.250538i
$157$	−11.5474	+	3.39062i	−0.921581	+	0.270601i	−0.707908	−	0.706305i	$-0.750361\pi$
$157$	−11.5474	+	3.39062i	−0.921581	+	0.270601i	−0.213673	+	0.976905i	$0.568543\pi$
$158$	−3.04111	+	6.65910i	−0.241938	+	0.529770i
$159$	1.62200	+	11.2812i	0.128633	+	0.894661i
$160$	−1.00000			−0.0790569
$161$	13.1315	+	1.21573i	1.03491	+	0.0958126i
$162$	−1.00000			−0.0785674
$163$	−1.15784	−	8.05296i	−0.0906890	−	0.630756i	−0.983579	−	0.180480i	$-0.942235\pi$
$163$	−1.15784	−	8.05296i	−0.0906890	−	0.630756i	0.892890	−	0.450276i	$-0.148674\pi$
$164$	0.945686	−	2.07076i	0.0738456	−	0.161699i
$165$	0.459493	−	0.134919i	0.0357715	−	0.0105035i
$166$	−2.46990	+	2.85041i	−0.191701	+	0.221235i
$167$	−16.1184	−	4.73280i	−1.24728	−	0.366235i	−0.409536	−	0.912294i	$-0.634309\pi$
$167$	−16.1184	−	4.73280i	−1.24728	−	0.366235i	−0.837747	+	0.546059i	$0.816128\pi$
$168$	2.31329	−	1.48666i	0.178474	−	0.114699i
$169$	1.72155	+	3.76967i	0.132427	+	0.289974i
$170$	1.77310	+	2.04627i	0.135991	+	0.156941i
$171$	0.862362	+	0.554206i	0.0659465	+	0.0423812i
$172$	−0.428276	+	2.97872i	−0.0326557	+	0.227125i
$173$	−1.85151	+	12.8775i	−0.140768	+	0.979061i	0.789910	+	0.613222i	$0.210127\pi$
$173$	−1.85151	+	12.8775i	−0.140768	+	0.979061i	−0.930678	+	0.365839i	$0.880782\pi$
$174$	−2.81329	−	1.80799i	−0.213275	−	0.137064i
$175$	1.80075	+	2.07817i	0.136124	+	0.157095i
$176$	−0.198939	−	0.435615i	−0.0149956	−	0.0328357i
$177$	−8.64662	+	5.55685i	−0.649920	+	0.417678i
$178$	0.693245	+	0.203555i	0.0519609	+	0.0152571i
$179$	−6.36641	+	7.34723i	−0.475848	+	0.549158i	−0.942029	−	0.335532i	$-0.891084\pi$
$179$	−6.36641	+	7.34723i	−0.475848	+	0.549158i	0.466181	+	0.884689i	$0.345629\pi$
$180$	−0.959493	+	0.281733i	−0.0715164	+	0.0209991i
$181$	0.823476	−	1.80316i	0.0612085	−	0.134028i	−0.876556	−	0.481300i	$-0.840165\pi$
$181$	0.823476	−	1.80316i	0.0612085	−	0.134028i	0.937764	+	0.347272i	$0.112892\pi$
$182$	1.62036	+	11.2699i	0.120109	+	0.835378i
$183$	10.0003			0.739241
$184$	−1.11722	+	4.66388i	−0.0823628	+	0.343826i
$185$	0.616406			0.0453191
$186$	0.284128	+	1.97615i	0.0208333	+	0.144899i
$187$	−0.538646	+	1.17947i	−0.0393897	+	0.0862514i
$188$	2.92584	−	0.859104i	0.213389	−	0.0626566i
$189$	1.80075	−	2.07817i	0.130985	−	0.151165i
$190$	0.983568	+	0.288802i	0.0713555	+	0.0209519i
$191$	−7.08893	+	4.55578i	−0.512937	+	0.329644i	−0.771372	−	0.636384i	$-0.780429\pi$
$191$	−7.08893	+	4.55578i	−0.512937	+	0.329644i	0.258436	+	0.966028i	$0.416793\pi$
$192$	0.415415	+	0.909632i	0.0299800	+	0.0656470i
$193$	−13.7502	−	15.8686i	−0.989763	−	1.14225i	−0.989831	−	0.142247i	$-0.954567\pi$
$193$	−13.7502	−	15.8686i	−0.989763	−	1.14225i	6.85072e−5	−	1.00000i	$-0.499978\pi$
$194$	−4.36002	−	2.80202i	−0.313031	−	0.201173i
$195$	0.589262	−	4.09841i	0.0421979	−	0.293493i
$196$	−0.0799081	+	0.555773i	−0.00570772	+	0.0396981i
$197$	−21.6578	−	13.9186i	−1.54305	−	0.991659i	−0.987038	−	0.160486i	$-0.948694\pi$
$197$	−21.6578	−	13.9186i	−1.54305	−	0.991659i	−0.556014	−	0.831173i	$-0.687670\pi$
$198$	−0.313607	−	0.361922i	−0.0222871	−	0.0257207i
$199$	8.38313	+	18.3565i	0.594264	+	1.30126i	0.932831	+	0.360314i	$0.117331\pi$
$199$	8.38313	+	18.3565i	0.594264	+	1.30126i	−0.338567	+	0.940942i	$0.609942\pi$
$200$	−0.841254	+	0.540641i	−0.0594856	+	0.0382291i
$201$	0.741066	+	0.217597i	0.0522708	+	0.0153481i
$202$	−3.83750	+	4.42871i	−0.270006	+	0.311603i
$203$	8.82335	−	2.59077i	0.619278	−	0.181836i
$204$	1.12478	−	2.46292i	0.0787502	−	0.172439i
$205$	−0.323977	−	2.25331i	−0.0226276	−	0.157378i
$206$	2.83961			0.197845
$207$	0.242000	+	4.78972i	0.0168202	+	0.332909i
$208$	−4.14055			−0.287096
$209$	0.0698634	+	0.485911i	0.00483256	+	0.0336112i
$210$	1.14231	−	2.50132i	0.0788272	−	0.172608i
$211$	20.2644	−	5.95016i	1.39506	−	0.409626i	0.504074	−	0.863660i	$-0.331834\pi$
$211$	20.2644	−	5.95016i	1.39506	−	0.409626i	0.890984	+	0.454034i	$0.150016\pi$
$212$	7.46361	−	8.61347i	0.512603	−	0.591575i
$213$	−7.84603	−	2.30380i	−0.537601	−	0.157854i
$214$	12.1765	−	7.82539i	0.832371	−	0.534933i
$215$	1.25013	+	2.73740i	0.0852582	+	0.186689i
$216$	0.654861	+	0.755750i	0.0445576	+	0.0514222i
$217$	−4.61843	−	2.96808i	−0.313519	−	0.201487i
$218$	−1.45076	+	10.0902i	−0.0982578	+	0.683398i
$219$	1.32125	−	9.18950i	0.0892819	−	0.620969i
$220$	−0.402869	−	0.258908i	−0.0271614	−	0.0174556i
$221$	7.34161	+	8.47267i	0.493850	+	0.569934i
$222$	−0.256064	−	0.560703i	−0.0171859	−	0.0376319i
$223$	−20.8129	+	13.3757i	−1.39374	+	0.895700i	−0.999726	−	0.0234061i	$-0.992549\pi$
$223$	−20.8129	+	13.3757i	−1.39374	+	0.895700i	−0.394010	+	0.919106i	$0.628913\pi$
$224$	−2.63843	−	0.774713i	−0.176287	−	0.0517627i
$225$	−0.654861	+	0.755750i	−0.0436574	+	0.0503833i
$226$	−9.39709	+	2.75924i	−0.625085	+	0.183542i
$227$	1.90950	−	4.18123i	0.126738	−	0.277518i	−0.835617	−	0.549312i	$-0.814890\pi$
$227$	1.90950	−	4.18123i	0.126738	−	0.277518i	0.962355	+	0.271794i	$0.0876170\pi$
$228$	−0.145886	−	1.01466i	−0.00966152	−	0.0671974i
$229$	5.75305			0.380172			0.190086	−	0.981767i	$-0.439123\pi$
$229$	5.75305			0.380172			0.190086	+	0.981767i	$0.439123\pi$
$230$	1.58162	+	4.52753i	0.104289	+	0.298536i
$231$	1.31686			0.0866432
$232$	0.475925	+	3.31013i	0.0312460	+	0.217321i
$233$	−7.61611	+	16.6770i	−0.498948	+	1.09254i	0.477862	+	0.878435i	$0.341412\pi$
$233$	−7.61611	+	16.6770i	−0.498948	+	1.09254i	−0.976810	+	0.214109i	$0.931315\pi$
$234$	−3.97283	+	1.16653i	−0.259712	+	0.0762583i
$235$	1.99691	−	2.30455i	0.130264	−	0.150332i
$236$	9.86192	+	2.89572i	0.641956	+	0.188495i
$237$	6.15853	−	3.95785i	0.400039	−	0.257090i
$238$	3.09293	+	6.77257i	0.200485	+	0.439001i
$239$	−1.51131	−	1.74415i	−0.0977587	−	0.112820i	0.704762	−	0.709444i	$-0.251054\pi$
$239$	−1.51131	−	1.74415i	−0.0977587	−	0.112820i	−0.802521	+	0.596624i	$0.796508\pi$
$240$	0.841254	+	0.540641i	0.0543027	+	0.0348982i
$241$	−2.82547	+	19.6516i	−0.182005	+	1.26587i	0.670010	+	0.742352i	$0.266290\pi$
$241$	−2.82547	+	19.6516i	−0.182005	+	1.26587i	−0.852015	+	0.523518i	$0.824619\pi$
$242$	−1.53283	+	10.6610i	−0.0985337	+	0.685317i
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$	−6.54878	−	7.55770i	−0.419243	−	0.483832i
$245$	0.233250	+	0.510747i	0.0149018	+	0.0326305i
$246$	−1.91510	+	1.23076i	−0.122102	+	0.0784704i
$247$	4.07252	+	1.19580i	0.259128	+	0.0760868i
$248$	1.30741	−	1.50883i	0.0830207	−	0.0958110i
$249$	3.61886	−	1.06259i	0.229336	−	0.0673391i
$250$	−0.415415	+	0.909632i	−0.0262732	+	0.0575302i
$251$	−4.14088	−	28.8005i	−0.261370	−	1.81787i	−0.522583	−	0.852589i	$-0.675031\pi$
$251$	−4.14088	−	28.8005i	−0.261370	−	1.81787i	0.261212	−	0.965281i	$-0.415878\pi$
$252$	−2.74982			−0.173222
$253$	−1.65761	+	1.58968i	−0.104213	+	0.0999421i
$254$	−1.10890			−0.0695783
$255$	−0.385331	−	2.68004i	−0.0241304	−	0.167831i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	23.6658	−	6.94891i	1.47623	−	0.433461i	0.558113	−	0.829765i	$-0.311525\pi$
$257$	23.6658	−	6.94891i	1.47623	−	0.433461i	0.918119	+	0.396304i	$0.129707\pi$
$258$	1.97071	−	2.27432i	0.122691	−	0.141593i
$259$	1.62634	+	0.477538i	0.101056	+	0.0296728i
$260$	−3.48325	+	2.23855i	−0.216022	+	0.138829i
$261$	1.38922	+	3.04196i	0.0859904	+	0.188293i
$262$	1.40529	+	1.62179i	0.0868189	+	0.100194i
$263$	8.23984	+	5.29542i	0.508090	+	0.326530i	0.769445	−	0.638713i	$-0.220533\pi$
$263$	8.23984	+	5.29542i	0.508090	+	0.326530i	−0.261355	+	0.965243i	$0.584169\pi$
$264$	−0.0681534	+	0.474017i	−0.00419455	+	0.0291737i
$265$	1.62200	−	11.2812i	0.0996385	−	0.693001i
$266$	2.37134	+	1.52397i	0.145396	+	0.0934403i
$267$	−0.473145	−	0.546038i	−0.0289560	−	0.0334170i
$268$	−0.320847	−	0.702556i	−0.0195988	−	0.0429154i
$269$	−13.0653	+	8.39654i	−0.796604	+	0.511946i	−0.874506	−	0.485015i	$-0.838814\pi$
$269$	−13.0653	+	8.39654i	−0.796604	+	0.511946i	0.0779021	+	0.996961i	$0.475178\pi$
$270$	0.959493	+	0.281733i	0.0583929	+	0.0171457i
$271$	18.3444	−	21.1705i	1.11434	−	1.28602i	0.160059	−	0.987107i	$-0.448832\pi$
$271$	18.3444	−	21.1705i	1.11434	−	1.28602i	0.954281	−	0.298910i	$-0.0966230\pi$
$272$	−2.59792	+	0.762819i	−0.157522	+	0.0462527i
$273$	4.72981	−	10.3568i	0.286261	−	0.626825i
$274$	1.51701	+	10.5511i	0.0916462	+	0.637413i
$275$	−0.478891			−0.0288782
$276$	3.46135	−	3.31949i	0.208349	−	0.199810i
$277$	−18.5401			−1.11396			−0.556982	−	0.830525i	$-0.688041\pi$
$277$	−18.5401			−1.11396			−0.556982	+	0.830525i	$0.688041\pi$
$278$	0.147964	+	1.02911i	0.00887429	+	0.0617220i
$279$	0.829365	−	1.81606i	0.0496528	−	0.108724i
$280$	−2.63843	+	0.774713i	−0.157676	+	0.0462979i
$281$	18.5420	−	21.3986i	1.10612	−	1.27653i	0.148369	−	0.988932i	$-0.452598\pi$
$281$	18.5420	−	21.3986i	1.10612	−	1.27653i	0.957751	−	0.287599i	$-0.0928569\pi$
$282$	−2.92584	−	0.859104i	−0.174231	−	0.0511589i
$283$	−7.59826	+	4.88311i	−0.451670	+	0.290271i	−0.746631	−	0.665239i	$-0.768330\pi$
$283$	−7.59826	+	4.88311i	−0.451670	+	0.290271i	0.294961	+	0.955509i	$0.404693\pi$
$284$	3.39696	+	7.43830i	0.201572	+	0.441382i
$285$	−0.671292	−	0.774713i	−0.0397639	−	0.0458900i
$286$	−1.66810	−	1.07202i	−0.0986368	−	0.0633900i
$287$	0.890878	−	6.19620i	0.0525869	−	0.365750i
$288$	0.142315	−	0.989821i	0.00838598	−	0.0583258i
$289$	−8.13400	−	5.22741i	−0.478471	−	0.307495i
$290$	2.18996	+	2.52735i	0.128599	+	0.148411i
$291$	2.15300	+	4.71441i	0.126211	+	0.276364i
$292$	−7.81020	+	5.01931i	−0.457057	+	0.293733i
$293$	−17.6278	−	5.17599i	−1.02983	−	0.302385i	−0.277187	−	0.960816i	$-0.589402\pi$
$293$	−17.6278	−	5.17599i	−1.02983	−	0.302385i	−0.752641	+	0.658431i	$0.771220\pi$
$294$	0.367696	−	0.424344i	0.0214445	−	0.0247483i
$295$	9.86192	−	2.89572i	0.574183	−	0.168595i
$296$	−0.256064	+	0.560703i	−0.0148834	+	0.0325902i
$297$	0.0681534	+	0.474017i	0.00395466	+	0.0275053i
$298$	−9.41419			−0.545350
$299$	6.54877	+	18.7465i	0.378725	+	1.08414i
$300$	1.00000			0.0577350
$301$	1.17768	+	8.19094i	0.0678803	+	0.472118i
$302$	2.11612	−	4.63365i	0.121769	−	0.266637i
$303$	5.62265	−	1.65096i	0.323013	−	0.0948452i
$304$	−0.671292	+	0.774713i	−0.0385013	+	0.0444328i
$305$	−9.59519	−	2.81740i	−0.549419	−	0.161324i
$306$	−2.27778	+	1.46384i	−0.130212	+	0.0836821i
$307$	−8.52437	−	18.6658i	−0.486512	−	1.06531i	−0.980621	−	0.195912i	$-0.937233\pi$
$307$	−8.52437	−	18.6658i	−0.486512	−	1.06531i	0.494110	−	0.869400i	$-0.335494\pi$
$308$	−0.862362	−	0.995219i	−0.0491376	−	0.0567079i
$309$	−2.38883	−	1.53521i	−0.135896	−	0.0873348i
$310$	0.284128	−	1.97615i	0.0161374	−	0.112238i
$311$	3.73564	−	25.9819i	0.211829	−	1.47330i	−0.555216	−	0.831706i	$-0.687364\pi$
$311$	3.73564	−	25.9819i	0.211829	−	1.47330i	0.767045	−	0.641594i	$-0.221726\pi$
$312$	3.48325	+	2.23855i	0.197200	+	0.126733i
$313$	11.4831	+	13.2522i	0.649063	+	0.749059i	0.980950	−	0.194260i	$-0.0622306\pi$
$313$	11.4831	+	13.2522i	0.649063	+	0.749059i	−0.331887	+	0.943319i	$0.607685\pi$
$314$	−4.99947	−	10.9473i	−0.282136	−	0.617792i
$315$	−2.31329	+	1.48666i	−0.130339	+	0.0837640i
$316$	−7.02412	−	2.06247i	−0.395138	−	0.116023i
$317$	−2.70121	+	3.11737i	−0.151715	+	0.175089i	−0.826520	−	0.562908i	$-0.809683\pi$
$317$	−2.70121	+	3.11737i	−0.151715	+	0.175089i	0.674804	+	0.737997i	$0.264228\pi$
$318$	−10.9356	+	3.21098i	−0.613237	+	0.180063i
$319$	−0.665284	+	1.45677i	−0.0372488	+	0.0815634i
$320$	−0.142315	−	0.989821i	−0.00795564	−	0.0553327i
$321$	−14.4743			−0.807876
$322$	0.665456	+	13.1709i	0.0370844	+	0.733983i
$323$	2.77554			0.154435
$324$	−0.142315	−	0.989821i	−0.00790638	−	0.0549901i
$325$	−1.72005	+	3.76638i	−0.0954111	+	0.208921i
$326$	7.80621	−	2.29211i	0.432346	−	0.126948i
$327$	6.67565	−	7.70412i	0.369165	−	0.426039i
$328$	2.18427	+	0.641360i	0.120606	+	0.0354132i
$329$	7.05406	−	4.53337i	0.388903	−	0.249933i
$330$	0.198939	+	0.435615i	0.0109512	+	0.0239798i
$331$	−11.4539	−	13.2185i	−0.629561	−	0.726552i	0.347932	−	0.937520i	$-0.386884\pi$
$331$	−11.4539	−	13.2185i	−0.629561	−	0.726552i	−0.977493	+	0.210968i	$0.932339\pi$
$332$	−3.17290	−	2.03910i	−0.174136	−	0.111910i
$333$	−0.0877238	+	0.610132i	−0.00480723	+	0.0334350i
$334$	2.39074	−	16.6279i	0.130815	−	0.909840i
$335$	−0.649744	−	0.417565i	−0.0354993	−	0.0228140i
$336$	1.80075	+	2.07817i	0.0982388	+	0.113374i
$337$	−14.7031	−	32.1952i	−0.800928	−	1.75379i	−0.642308	−	0.766447i	$-0.722023\pi$
$337$	−14.7031	−	32.1952i	−0.800928	−	1.75379i	−0.158620	−	0.987340i	$-0.550704\pi$
$338$	−3.48629	+	2.24051i	−0.189629	+	0.121867i
$339$	9.39709	+	2.75924i	0.510380	+	0.149861i
$340$	−1.77310	+	2.04627i	−0.0961599	+	0.110974i
$341$	0.917365	−	0.269363i	0.0496781	−	0.0145868i
$342$	−0.425839	+	0.932456i	−0.0230267	+	0.0504215i
$343$	−2.51964	−	17.5245i	−0.136048	−	0.946235i
$344$	−3.00935			−0.162253
$345$	1.11722	−	4.66388i	0.0601493	−	0.251095i
$346$	−13.0100			−0.699420
$347$	−4.40299	−	30.6235i	−0.236365	−	1.64395i	−0.669635	−	0.742690i	$-0.733550\pi$
$347$	−4.40299	−	30.6235i	−0.236365	−	1.64395i	0.433271	−	0.901264i	$-0.357359\pi$
$348$	1.38922	−	3.04196i	0.0744699	−	0.163066i
$349$	−2.38299	+	0.699709i	−0.127559	+	0.0374546i	−0.344889	−	0.938644i	$-0.612083\pi$
$349$	−2.38299	+	0.699709i	−0.127559	+	0.0374546i	0.217330	+	0.976098i	$0.430265\pi$
$350$	−1.80075	+	2.07817i	−0.0962539	+	0.111083i
$351$	3.97283	+	1.16653i	0.212054	+	0.0622647i
$352$	0.402869	−	0.258908i	0.0214730	−	0.0137999i
$353$	4.62459	+	10.1264i	0.246142	+	0.538976i	0.991867	−	0.127278i	$-0.0406240\pi$
$353$	4.62459	+	10.1264i	0.246142	+	0.538976i	−0.745725	+	0.666254i	$0.767897\pi$
$354$	−6.73083	−	7.76779i	−0.357740	−	0.412853i
$355$	6.87915	+	4.42096i	0.365108	+	0.234640i
$356$	−0.102824	+	0.715158i	−0.00544967	+	0.0379033i
$357$	1.05959	−	7.36962i	0.0560795	−	0.390041i
$358$	−8.17848	−	5.25599i	−0.432246	−	0.277788i
$359$	−18.2965	−	21.1153i	−0.965651	−	1.11442i	−0.993388	−	0.114805i	$-0.963376\pi$
$359$	−18.2965	−	21.1153i	−0.965651	−	1.11442i	0.0277374	−	0.999615i	$-0.491170\pi$
$360$	−0.415415	−	0.909632i	−0.0218943	−	0.0479418i
$361$	−15.0998	+	9.70406i	−0.794727	+	0.510740i
$362$	1.90200	+	0.558477i	0.0999669	+	0.0293529i
$363$	7.05328	−	8.13992i	0.370201	−	0.427235i
$364$	−10.9246	+	3.20774i	−0.572602	+	0.168131i
$365$	−3.85671	+	8.44502i	−0.201870	+	0.442033i
$366$	1.42319	+	9.89848i	0.0743911	+	0.517402i
$367$	4.34188			0.226644			0.113322	−	0.993558i	$-0.463851\pi$
$367$	4.34188			0.226644			0.113322	+	0.993558i	$0.463851\pi$
$368$	−4.77541	−	0.442111i	−0.248935	−	0.0230467i
$369$	2.27648			0.118509
$370$	0.0877238	+	0.610132i	0.00456054	+	0.0317193i
$371$	13.0192	−	28.5082i	0.675926	−	1.48007i
$372$	−1.91560	+	0.562472i	−0.0993193	+	0.0291628i
$373$	7.44750	−	8.59488i	0.385617	−	0.445026i	−0.529442	−	0.848346i	$-0.677599\pi$
$373$	7.44750	−	8.59488i	0.385617	−	0.445026i	0.915059	+	0.403320i	$0.132144\pi$
$374$	−1.24412	−	0.365307i	−0.0643321	−	0.0188896i
$375$	0.841254	−	0.540641i	0.0434421	−	0.0279186i
$376$	1.26675	+	2.77379i	0.0653276	+	0.143048i
$377$	9.06766	+	10.4646i	0.467008	+	0.538956i
$378$	2.31329	+	1.48666i	0.118983	+	0.0764657i
$379$	1.99499	−	13.8755i	0.102476	−	0.712736i	−0.872206	−	0.489139i	$-0.837311\pi$
$379$	1.99499	−	13.8755i	0.102476	−	0.712736i	0.974682	−	0.223597i	$-0.0717798\pi$
$380$	−0.145886	+	1.01466i	−0.00748378	+	0.0520508i
$381$	0.932863	+	0.599515i	0.0477920	+	0.0307141i
$382$	−5.51827	−	6.36842i	−0.282339	−	0.325837i
$383$	1.89579	+	4.15120i	0.0968704	+	0.212117i	0.951863	−	0.306523i	$-0.0991658\pi$
$383$	1.89579	+	4.15120i	0.0968704	+	0.212117i	−0.854993	+	0.518640i	$0.826438\pi$
$384$	−0.841254	+	0.540641i	−0.0429300	+	0.0275895i
$385$	−1.26352	−	0.371003i	−0.0643950	−	0.0189081i
$386$	13.7502	−	15.8686i	0.699868	−	0.807691i
$387$	−2.88745	+	0.847833i	−0.146778	+	0.0430978i
$388$	2.15300	−	4.71441i	0.109302	−	0.239338i
$389$	0.794976	+	5.52918i	0.0403069	+	0.280341i	1.00000		0.000710333i	$-0.000226106\pi$
$389$	0.794976	+	5.52918i	0.0403069	+	0.280341i	−0.959693	+	0.281051i	$0.909317\pi$
$390$	4.14055			0.209665
$391$	7.56260	+	10.5557i	0.382457	+	0.533823i
$392$	−0.561488			−0.0283594
$393$	−0.305398	−	2.12409i	−0.0154053	−	0.107146i
$394$	10.6947	−	23.4181i	0.538792	−	1.17979i
$395$	−7.02412	+	2.06247i	−0.353422	+	0.103774i
$396$	0.313607	−	0.361922i	0.0157594	−	0.0181873i
$397$	4.78156	+	1.40399i	0.239980	+	0.0704644i	0.399511	−	0.916728i	$-0.369180\pi$
$397$	4.78156	+	1.40399i	0.239980	+	0.0704644i	−0.159531	+	0.987193i	$0.550998\pi$
$398$	−16.9766	+	10.9102i	−0.850960	+	0.546879i
$399$	−1.17098	−	2.56408i	−0.0586222	−	0.128365i
$400$	−0.654861	−	0.755750i	−0.0327430	−	0.0377875i
$401$	−2.28032	−	1.46547i	−0.113874	−	0.0731823i	0.482464	−	0.875916i	$-0.339742\pi$
$401$	−2.28032	−	1.46547i	−0.113874	−	0.0731823i	−0.596338	+	0.802733i	$0.703378\pi$
$402$	−0.109917	+	0.764490i	−0.00548217	+	0.0381293i
$403$	1.17645	−	8.18236i	0.0586029	−	0.407592i
$404$	−4.92977	−	3.16817i	−0.245265	−	0.157622i
$405$	−0.654861	−	0.755750i	−0.0325403	−	0.0375535i
$406$	3.82009	+	8.36483i	0.189588	+	0.415140i
$407$	−0.248331	+	0.159593i	−0.0123093	+	0.00791072i
$408$	2.59792	+	0.762819i	0.128616	+	0.0377652i
$409$	−20.7734	+	23.9738i	−1.02718	+	1.18543i	−0.0447091	+	0.999000i	$0.514236\pi$
$409$	−20.7734	+	23.9738i	−1.02718	+	1.18543i	−0.982469	+	0.186427i	$0.940309\pi$
$410$	2.18427	−	0.641360i	0.107873	−	0.0316745i
$411$	4.42814	−	9.69628i	0.218424	−	0.478282i
$412$	0.404118	+	2.81070i	0.0199095	+	0.138473i
$413$	28.2633			1.39075
$414$	−4.70653	+	0.921186i	−0.231313	+	0.0452738i
$415$	−3.77164			−0.185142
$416$	−0.589262	−	4.09841i	−0.0288909	−	0.200941i
$417$	0.431905	−	0.945739i	0.0211505	−	0.0463130i
$418$	−0.471022	+	0.138305i	−0.0230385	+	0.00676470i
$419$	4.40657	−	5.08546i	0.215275	−	0.248441i	−0.637833	−	0.770175i	$-0.720169\pi$
$419$	4.40657	−	5.08546i	0.215275	−	0.248441i	0.853108	+	0.521734i	$0.174715\pi$
$420$	2.63843	+	0.774713i	0.128742	+	0.0378021i
$421$	−27.3378	+	17.5689i	−1.33236	+	0.856258i	−0.996330	−	0.0855928i	$-0.972722\pi$
$421$	−27.3378	+	17.5689i	−1.33236	+	0.856258i	−0.336033	+	0.941850i	$0.609085\pi$
$422$	8.77352	+	19.2113i	0.427088	+	0.935193i
$423$	1.99691	+	2.30455i	0.0970929	+	0.112051i
$424$	9.58797	+	6.16182i	0.465633	+	0.299244i
$425$	−0.385331	+	2.68004i	−0.0186913	+	0.130001i
$426$	1.16375	−	8.09403i	0.0563837	−	0.392157i
$427$	−23.1335	−	14.8670i	−1.11951	−	0.719466i
$428$	9.47864	+	10.9389i	0.458167	+	0.528753i
$429$	0.823716	+	1.80369i	0.0397694	+	0.0870828i
$430$	−2.53163	+	1.62698i	−0.122086	+	0.0784599i
$431$	−17.0919	−	5.01864i	−0.823289	−	0.241739i	−0.157157	−	0.987574i	$-0.550233\pi$
$431$	−17.0919	−	5.01864i	−0.823289	−	0.241739i	−0.666132	+	0.745834i	$0.732051\pi$
$432$	−0.654861	+	0.755750i	−0.0315070	+	0.0363610i
$433$	−8.21324	+	2.41162i	−0.394703	+	0.115895i	−0.473060	−	0.881030i	$-0.656851\pi$
$433$	−8.21324	+	2.41162i	−0.394703	+	0.115895i	0.0783572	+	0.996925i	$0.475033\pi$
$434$	2.28060	−	4.99382i	0.109472	−	0.239711i
$435$	−0.475925	−	3.31013i	−0.0228188	−	0.158709i
$436$	−10.1940			−0.488204
$437$	4.56926	+	1.81399i	0.218577	+	0.0867751i
$438$	9.28400			0.443607
$439$	−0.294283	−	2.04678i	−0.0140454	−	0.0976876i	0.981593	−	0.190985i	$-0.0611683\pi$
$439$	−0.294283	−	2.04678i	−0.0140454	−	0.0976876i	−0.995638	+	0.0932977i	$0.970259\pi$
$440$	0.198939	−	0.435615i	0.00948403	−	0.0207671i
$441$	−0.538744	+	0.158189i	−0.0256545	+	0.00753283i
$442$	−7.34161	+	8.47267i	−0.349205	+	0.403004i
$443$	27.2420	+	7.99897i	1.29431	+	0.380043i	0.855156	−	0.518371i	$-0.173461\pi$
$443$	27.2420	+	7.99897i	1.29431	+	0.380043i	0.439151	+	0.898413i	$0.355279\pi$
$444$	0.518554	−	0.333254i	0.0246095	−	0.0158156i
$445$	0.300142	+	0.657220i	0.0142281	+	0.0311552i
$446$	−16.2015	−	18.6975i	−0.767163	−	0.885353i
$447$	7.91972	+	5.08970i	0.374590	+	0.240734i
$448$	0.391340	−	2.72183i	0.0184891	−	0.128594i
$449$	0.259864	−	1.80739i	0.0122637	−	0.0852960i	−0.982770	−	0.184831i	$-0.940826\pi$
$449$	0.259864	−	1.80739i	0.0122637	−	0.0852960i	0.995034	+	0.0995347i	$0.0317354\pi$
$450$	−0.841254	−	0.540641i	−0.0396571	−	0.0254861i
$451$	0.713922	+	0.823910i	0.0336173	+	0.0387964i
$452$	−4.06850	−	8.90876i	−0.191366	−	0.419033i
$453$	−4.28533	+	2.75402i	−0.201342	+	0.129395i
$454$	4.41042	+	1.29502i	0.206991	+	0.0607782i
$455$	−7.45608	+	8.60478i	−0.349547	+	0.403398i
$456$	0.983568	−	0.288802i	0.0460598	−	0.0135244i
$457$	−3.27423	+	7.16957i	−0.153162	+	0.335378i	−0.970623	−	0.240606i	$-0.922654\pi$
$457$	−3.27423	+	7.16957i	−0.153162	+	0.335378i	0.817461	+	0.575984i	$0.195381\pi$
$458$	0.818744	+	5.69449i	0.0382574	+	0.266086i
$459$	2.70760			0.126380
$460$	−4.25635	+	2.20985i	−0.198454	+	0.103035i
$461$	−19.9072			−0.927170			−0.463585	−	0.886053i	$-0.653437\pi$
$461$	−19.9072			−0.927170			−0.463585	+	0.886053i	$0.653437\pi$
$462$	0.187409	+	1.30346i	0.00871906	+	0.0606424i
$463$	−16.4657	+	36.0549i	−0.765228	+	1.67561i	−0.0283410	+	0.999598i	$0.509022\pi$
$463$	−16.4657	+	36.0549i	−0.765228	+	1.67561i	−0.736887	+	0.676016i	$0.763705\pi$
$464$	−3.20870	+	0.942161i	−0.148960	+	0.0437387i
$465$	−1.30741	+	1.50883i	−0.0606298	+	0.0699705i
$466$	−17.5911	−	5.16521i	−0.814892	−	0.239274i
$467$	−8.00465	+	5.14428i	−0.370411	+	0.238049i	−0.712582	−	0.701589i	$-0.752474\pi$
$467$	−8.00465	+	5.14428i	−0.370411	+	0.238049i	0.342171	+	0.939638i	$0.388838\pi$
$468$	−1.72005	−	3.76638i	−0.0795092	−	0.174101i
$469$	−1.39081	−	1.60508i	−0.0642216	−	0.0741157i
$470$	2.56528	+	1.64861i	0.118328	+	0.0760446i
$471$	−1.71274	+	11.9124i	−0.0789190	+	0.548893i
$472$	−1.46275	+	10.1736i	−0.0673285	+	0.468280i
$473$	−1.21238	−	0.779147i	−0.0557451	−	0.0358252i
$474$	4.79401	+	5.53258i	0.220196	+	0.254120i
$475$	0.425839	+	0.932456i	0.0195388	+	0.0427840i
$476$	−6.26347	+	4.02529i	−0.287086	+	0.184499i
$477$	10.9356	+	3.21098i	0.500706	+	0.147020i
$478$	1.51131	−	1.74415i	0.0691258	−	0.0797754i
$479$	26.2547	−	7.70908i	1.19961	−	0.352237i	0.379905	−	0.925025i	$-0.375957\pi$
$479$	26.2547	−	7.70908i	1.19961	−	0.352237i	0.819703	+	0.572789i	$0.194138\pi$
$480$	−0.415415	+	0.909632i	−0.0189610	+	0.0415188i
$481$	0.363225	+	2.52628i	0.0165616	+	0.115189i
$482$	−19.8537			−0.904309
$483$	6.56088	−	11.4398i	0.298531	−	0.520529i
$484$	−10.7707			−0.489576
$485$	−0.737585	−	5.13002i	−0.0334920	−	0.232942i
$486$	−0.415415	+	0.909632i	−0.0188436	+	0.0412617i
$487$	0.773470	−	0.227111i	0.0350493	−	0.0102914i	−0.264161	−	0.964479i	$-0.585095\pi$
$487$	0.773470	−	0.227111i	0.0350493	−	0.0102914i	0.299210	+	0.954187i	$0.403277\pi$
$488$	6.54878	−	7.55770i	0.296449	−	0.342121i
$489$	−7.80621	−	2.29211i	−0.353009	−	0.103653i
$490$	−0.472354	+	0.303563i	−0.0213388	+	0.0137136i
$491$	2.18102	+	4.77576i	0.0984279	+	0.215527i	0.952440	−	0.304726i	$-0.0985649\pi$
$491$	2.18102	+	4.77576i	0.0984279	+	0.215527i	−0.854012	+	0.520253i	$0.825838\pi$
$492$	−1.49078	−	1.72045i	−0.0672096	−	0.0775640i
$493$	7.61727	+	4.89532i	0.343064	+	0.220474i
$494$	−0.604048	+	4.20124i	−0.0271774	+	0.189023i
$495$	0.0681534	−	0.474017i	0.00306327	−	0.0213055i
$496$	1.67954	+	1.07937i	0.0754136	+	0.0484654i
$497$	14.7252	+	16.9938i	0.660515	+	0.762275i
$498$	1.56679	+	3.43080i	0.0702097	+	0.153738i
$499$	−27.0586	+	17.3895i	−1.21131	+	0.778461i	−0.980877	−	0.194628i	$-0.937650\pi$
$499$	−27.0586	+	17.3895i	−1.21131	+	0.778461i	−0.230431	+	0.973089i	$0.574014\pi$
$500$	−0.959493	−	0.281733i	−0.0429098	−	0.0125995i
$501$	−11.0010	+	12.6958i	−0.491486	+	0.567205i
$502$	27.9180	−	8.19747i	1.24604	−	0.365871i
$503$	−10.3682	+	22.7033i	−0.462296	+	1.01229i	0.524662	+	0.851311i	$0.324192\pi$
$503$	−10.3682	+	22.7033i	−0.462296	+	1.01229i	−0.986958	+	0.160977i	$0.948535\pi$
$504$	−0.391340	−	2.72183i	−0.0174317	−	0.121240i
$505$	−5.86003			−0.260768
$506$	−1.80940	−	1.41451i	−0.0804376	−	0.0628825i
$507$	4.14417			0.184049
$508$	−0.157812	−	1.09761i	−0.00700179	−	0.0486985i
$509$	7.55792	−	16.5495i	0.334999	−	0.733545i	−0.664912	−	0.746922i	$-0.731531\pi$
$509$	7.55792	−	16.5495i	0.334999	−	0.733545i	0.999911	+	0.0133767i	$0.00425805\pi$
$510$	2.59792	−	0.762819i	0.115038	−	0.0337782i
$511$	−16.7181	+	19.2938i	−0.739567	+	0.853505i
$512$	0.959493	+	0.281733i	0.0424040	+	0.0124509i
$513$	0.862362	−	0.554206i	0.0380742	−	0.0244688i
$514$	10.2462	+	22.4360i	0.451939	+	0.989609i
$515$	1.85955	+	2.14603i	0.0819414	+	0.0945654i
$516$	2.53163	+	1.62698i	0.111449	+	0.0716238i
$517$	−0.207824	+	1.44545i	−0.00914009	+	0.0635707i
$518$	−0.241224	+	1.67775i	−0.0105988	+	0.0737162i
$519$	10.9447	+	7.03372i	0.480418	+	0.308746i
$520$	−2.71148	−	3.12922i	−0.118906	−	0.137225i
$521$	−10.4624	−	22.9094i	−0.458364	−	1.00368i	−0.987857	−	0.155363i	$-0.950345\pi$
$521$	−10.4624	−	22.9094i	−0.458364	−	1.00368i	0.529493	−	0.848314i	$-0.322382\pi$
$522$	−2.81329	+	1.80799i	−0.123134	+	0.0791337i
$523$	40.2560	+	11.8202i	1.76027	+	0.516862i	0.992326	−	0.123652i	$-0.0394606\pi$
$523$	40.2560	+	11.8202i	1.76027	+	0.516862i	0.767946	+	0.640514i	$0.221279\pi$
$524$	−1.40529	+	1.62179i	−0.0613902	+	0.0708481i
$525$	2.63843	−	0.774713i	0.115150	−	0.0338112i
$526$	−4.06887	+	8.90959i	−0.177411	+	0.388477i
$527$	−0.769304	−	5.35063i	−0.0335114	−	0.233077i
$528$	−0.478891			−0.0208411
$529$	5.55120	+	22.3200i	0.241357	+	0.970436i
$530$	11.3972			0.495065
$531$	1.46275	+	10.1736i	0.0634779	+	0.441499i
$532$	−1.17098	+	2.56408i	−0.0507683	+	0.111167i
$533$	9.04408	−	2.65558i	0.391743	−	0.115026i
$534$	0.473145	−	0.546038i	0.0204750	−	0.0236294i
$535$	13.8880	+	4.07788i	0.600429	+	0.176302i
$536$	0.649744	−	0.417565i	0.0280647	−	0.0180361i
$537$	4.03857	+	8.84324i	0.174277	+	0.381614i
$538$	−10.1705	−	11.7373i	−0.438480	−	0.506032i
$539$	−0.226206	−	0.145374i	−0.00974339	−	0.00626170i
$540$	−0.142315	+	0.989821i	−0.00612426	+	0.0425951i
$541$	0.247850	−	1.72383i	0.0106559	−	0.0741134i	−0.983800	−	0.179272i	$-0.942626\pi$
$541$	0.247850	−	1.72383i	0.0106559	−	0.0741134i	0.994455	+	0.105158i	$0.0335349\pi$
$542$	23.5657	+	15.1448i	1.01223	+	0.650523i
$543$	−1.29813	−	1.49812i	−0.0557080	−	0.0642905i
$544$	−1.12478	−	2.46292i	−0.0482244	−	0.105597i
$545$	−8.57574	+	5.51130i	−0.367345	+	0.236078i
$546$	10.9246	+	3.20774i	0.467528	+	0.137279i
$547$	18.3367	−	21.1617i	0.784022	−	0.904810i	−0.213371	−	0.976971i	$-0.568444\pi$
$547$	18.3367	−	21.1617i	0.784022	−	0.904810i	0.997393	+	0.0721617i	$0.0229898\pi$
$548$	−10.2278	+	3.00315i	−0.436909	+	0.128288i
$549$	4.15426	−	9.09656i	0.177300	−	0.388232i
$550$	−0.0681534	−	0.474017i	−0.00290607	−	0.0202122i
$551$	3.42808			0.146041
$552$	3.77831	+	2.95371i	0.160815	+	0.125718i
$553$	−20.1305			−0.856034
$554$	−2.63852	−	18.3513i	−0.112100	−	0.779674i
$555$	0.256064	−	0.560703i	0.0108693	−	0.0238005i
$556$	−0.997579	+	0.292916i	−0.0423068	+	0.0124224i
$557$	26.7164	−	30.8324i	1.13201	−	1.30641i	0.185900	−	0.982569i	$-0.440480\pi$
$557$	26.7164	−	30.8324i	1.13201	−	1.30641i	0.946111	−	0.323842i	$-0.104975\pi$
$558$	1.91560	+	0.562472i	0.0810939	+	0.0238113i
$559$	−10.4823	+	6.73659i	−0.443356	+	0.284928i
$560$	−1.14231	−	2.50132i	−0.0482716	−	0.105700i
$561$	0.849122	+	0.979940i	0.0358500	+	0.0413731i
$562$	23.8195	+	15.3079i	1.00477	+	0.645724i
$563$	−1.99103	+	13.8479i	−0.0839119	+	0.583620i	0.903874	+	0.427800i	$0.140711\pi$
$563$	−1.99103	+	13.8479i	−0.0839119	+	0.583620i	−0.987785	+	0.155820i	$0.950198\pi$
$564$	0.433969	−	3.01832i	0.0182734	−	0.127094i
$565$	−8.23908	−	5.29493i	−0.346621	−	0.222760i
$566$	−5.91475	−	6.82598i	−0.248615	−	0.286918i
$567$	−1.14231	−	2.50132i	−0.0479727	−	0.105046i
$568$	−6.87915	+	4.42096i	−0.288643	+	0.185499i
$569$	−0.247496	−	0.0726713i	−0.0103756	−	0.00304654i	0.276541	−	0.961002i	$-0.410812\pi$
$569$	−0.247496	−	0.0726713i	−0.0103756	−	0.00304654i	−0.286916	+	0.957956i	$0.592630\pi$
$570$	0.671292	−	0.774713i	0.0281173	−	0.0324491i
$571$	−6.43240	+	1.88872i	−0.269187	+	0.0790406i	−0.413541	−	0.910486i	$-0.635708\pi$
$571$	−6.43240	+	1.88872i	−0.269187	+	0.0790406i	0.144353	+	0.989526i	$0.453890\pi$
$572$	0.823716	−	1.80369i	0.0344413	−	0.0754159i
$573$	1.19923	+	8.34085i	0.0500987	+	0.348444i
$574$	6.25991			0.261284
$575$	−2.38594	+	4.16021i	−0.0995004	+	0.173493i
$576$	1.00000			0.0416667
$577$	3.65742	+	25.4379i	0.152260	+	1.05899i	0.912419	+	0.409257i	$0.134212\pi$
$577$	3.65742	+	25.4379i	0.152260	+	1.05899i	−0.760159	+	0.649738i	$0.774879\pi$
$578$	4.01661	−	8.79515i	0.167069	−	0.365830i
$579$	−20.1466	+	5.91559i	−0.837266	+	0.245843i
$580$	−2.18996	+	2.52735i	−0.0909333	+	0.104943i
$581$	−9.95120	−	2.92193i	−0.412845	−	0.121222i
$582$	−4.36002	+	2.80202i	−0.180729	+	0.116147i
$583$	2.26735	+	4.96481i	0.0939042	+	0.205621i
$584$	−6.07973	−	7.01638i	−0.251581	−	0.290340i
$585$	−3.48325	−	2.23855i	−0.144015	−	0.0925527i
$586$	2.61461	−	18.1850i	0.108009	−	0.751216i
$587$	1.86241	−	12.9533i	0.0768698	−	0.534641i	−0.914606	−	0.404347i	$-0.867499\pi$
$587$	1.86241	−	12.9533i	0.0768698	−	0.534641i	0.991475	−	0.130294i	$-0.0415921\pi$
$588$	0.472354	+	0.303563i	0.0194795	+	0.0125187i
$589$	−1.34022	−	1.54669i	−0.0552227	−	0.0637304i
$590$	4.26974	+	9.34944i	0.175783	+	0.384910i
$591$	−21.6578	+	13.9186i	−0.890881	+	0.572535i
$592$	−0.591438	−	0.173662i	−0.0243079	−	0.00713745i
$593$	−13.8574	+	15.9923i	−0.569055	+	0.656724i	−0.965215	−	0.261457i	$-0.915797\pi$
$593$	−13.8574	+	15.9923i	−0.569055	+	0.656724i	0.396160	+	0.918181i	$0.370342\pi$
$594$	−0.459493	+	0.134919i	−0.0188532	+	0.00553581i
$595$	−3.09293	+	6.77257i	−0.126798	+	0.277648i
$596$	−1.33978	−	9.31837i	−0.0548795	−	0.381695i
$597$	20.1801			0.825917
$598$	−17.6237	+	9.15001i	−0.720685	+	0.374172i
$599$	−15.3835			−0.628555			−0.314277	−	0.949331i	$-0.601762\pi$
$599$	−15.3835			−0.628555			−0.314277	+	0.949331i	$0.601762\pi$
$600$	0.142315	+	0.989821i	0.00580998	+	0.0404093i
$601$	4.64678	−	10.1750i	0.189546	−	0.415048i	−0.790870	−	0.611984i	$-0.790372\pi$
$601$	4.64678	−	10.1750i	0.189546	−	0.415048i	0.980416	+	0.196936i	$0.0630990\pi$
$602$	−7.93997	+	2.33138i	−0.323609	+	0.0950201i
$603$	0.505783	−	0.583705i	0.0205971	−	0.0237703i
$604$	4.88764	+	1.43514i	0.198875	+	0.0583951i
$605$	−9.06086	+	5.82306i	−0.368376	+	0.236741i
$606$	2.43434	+	5.33047i	0.0988884	+	0.216535i
$607$	15.2471	+	17.5961i	0.618862	+	0.714205i	0.975491	−	0.220041i	$-0.0706192\pi$
$607$	15.2471	+	17.5961i	0.618862	+	0.714205i	−0.356628	+	0.934246i	$0.616074\pi$
$608$	−0.862362	−	0.554206i	−0.0349734	−	0.0224760i
$609$	1.30871	−	9.10224i	0.0530314	−	0.368842i
$610$	1.42319	−	9.89848i	0.0576231	−	0.400778i
$611$	10.6217	+	6.82615i	0.429708	+	0.276156i
$612$	−1.77310	−	2.04627i	−0.0716733	−	0.0827154i
$613$	−18.1158	−	39.6682i	−0.731692	−	1.60218i	−0.796756	−	0.604301i	$-0.793452\pi$
$613$	−18.1158	−	39.6682i	−0.731692	−	1.60218i	0.0650637	−	0.997881i	$-0.479275\pi$
$614$	17.2626	−	11.0940i	0.696663	−	0.447718i
$615$	−2.18427	−	0.641360i	−0.0880783	−	0.0258621i
$616$	0.862362	−	0.995219i	0.0347456	−	0.0400985i
$617$	11.3199	−	3.32382i	0.455721	−	0.133812i	−0.0458122	−	0.998950i	$-0.514588\pi$
$617$	11.3199	−	3.32382i	0.455721	−	0.133812i	0.501533	+	0.865138i	$0.332769\pi$
$618$	1.17961	−	2.58300i	0.0474511	−	0.103903i
$619$	−1.20858	−	8.40585i	−0.0485769	−	0.337860i	−0.999588	−	0.0287030i	$-0.990862\pi$
$619$	−1.20858	−	8.40585i	−0.0485769	−	0.337860i	0.951011	−	0.309157i	$-0.100047\pi$
$620$	1.99647			0.0801803
$621$	4.45741	+	1.76959i	0.178870	+	0.0710112i
$622$	26.2491			1.05249
$623$	0.282748	+	1.96655i	0.0113280	+	0.0787883i
$624$	−1.72005	+	3.76638i	−0.0688570	+	0.150776i
$625$	−0.959493	+	0.281733i	−0.0383797	+	0.0112693i
$626$	−11.4831	+	13.2522i	−0.458957	+	0.529665i
$627$	0.471022	+	0.138305i	0.0188108	+	0.00552336i
$628$	10.1244	−	6.50654i	0.404007	−	0.259639i
$629$	0.693320	+	1.51816i	0.0276445	+	0.0605329i
$630$	−1.80075	−	2.07817i	−0.0717435	−	0.0827964i
$631$	6.36297	+	4.08923i	0.253306	+	0.162790i	0.661132	−	0.750270i	$-0.270077\pi$
$631$	6.36297	+	4.08923i	0.253306	+	0.162790i	−0.407826	+	0.913060i	$0.633713\pi$
$632$	1.04184	−	7.24614i	0.0414421	−	0.288236i
$633$	3.00568	−	20.9049i	0.119465	−	0.830896i
$634$	−3.47006	−	2.23007i	−0.137814	−	0.0885675i
$635$	−0.726173	−	0.838048i	−0.0288173	−	0.0332569i
$636$	−4.73459	−	10.3673i	−0.187739	−	0.411090i
$637$	−1.95580	+	1.25692i	−0.0774918	+	0.0498010i
$638$	−1.53662	−	0.451193i	−0.0608354	−	0.0178629i
$639$	−5.35497	+	6.17996i	−0.211839	+	0.244476i
$640$	0.959493	−	0.281733i	0.0379273	−	0.0111365i
$641$	−10.6262	+	23.2681i	−0.419708	+	0.919033i	0.575178	+	0.818028i	$0.304933\pi$
$641$	−10.6262	+	23.2681i	−0.419708	+	0.919033i	−0.994886	+	0.101004i	$0.967794\pi$
$642$	−2.05991	−	14.3270i	−0.0812980	−	0.565440i
$643$	17.0930			0.674081			0.337041	−	0.941490i	$-0.390574\pi$
$643$	17.0930			0.674081			0.337041	+	0.941490i	$0.390574\pi$
$644$	−12.9421	+	2.53309i	−0.509990	+	0.0998178i
$645$	3.00935			0.118493
$646$	0.395000	+	2.74729i	0.0155411	+	0.108091i
$647$	−3.74104	+	8.19174i	−0.147076	+	0.322051i	−0.968804	−	0.247829i	$-0.920283\pi$
$647$	−3.74104	+	8.19174i	−0.147076	+	0.322051i	0.821728	+	0.569880i	$0.193010\pi$
$648$	0.959493	−	0.281733i	0.0376924	−	0.0110675i
$649$	−3.22334	+	3.71993i	−0.126527	+	0.146020i
$650$	−3.97283	−	1.16653i	−0.155827	−	0.0457550i
$651$	−4.61843	+	2.96808i	−0.181010	+	0.116328i
$652$	3.37972	+	7.40055i	0.132360	+	0.289828i
$653$	−30.7568	−	35.4952i	−1.20361	−	1.38903i	−0.899801	−	0.436300i	$-0.856289\pi$
$653$	−30.7568	−	35.4952i	−1.20361	−	1.38903i	−0.303804	−	0.952735i	$-0.598257\pi$
$654$	8.57574	+	5.51130i	0.335338	+	0.215509i
$655$	−0.305398	+	2.12409i	−0.0119329	+	0.0829950i
$656$	−0.323977	+	2.25331i	−0.0126492	+	0.0879771i
$657$	−7.81020	−	5.01931i	−0.304705	−	0.195822i
$658$	5.49112	+	6.33709i	0.214066	+	0.247046i
$659$	−5.24618	−	11.4875i	−0.204362	−	0.447490i	0.779504	−	0.626397i	$-0.215471\pi$
$659$	−5.24618	−	11.4875i	−0.204362	−	0.447490i	−0.983866	+	0.178907i	$0.942744\pi$
$660$	−0.402869	+	0.258908i	−0.0156817	+	0.0100780i
$661$	41.4869	+	12.1817i	1.61365	+	0.473812i	0.959303	−	0.282378i	$-0.0911234\pi$
$661$	41.4869	+	12.1817i	1.61365	+	0.473812i	0.654352	+	0.756190i	$0.272942\pi$
$662$	11.4539	−	13.2185i	0.445167	−	0.513750i
$663$	10.7568	−	3.15849i	0.417761	−	0.122666i
$664$	1.56679	−	3.43080i	0.0608034	−	0.133141i
$665$	0.401159	+	2.79012i	0.0155563	+	0.108196i
$666$	−0.616406			−0.0238853
$667$	9.34060	+	13.0374i	0.361670	+	0.504808i
$668$	16.7989			0.649970
$669$	3.52092	+	24.4885i	0.136127	+	0.946782i
$670$	0.320847	−	0.702556i	0.0123954	−	0.0271421i
$671$	4.59505	−	1.34923i	0.177390	−	0.0520864i
$672$	−1.80075	+	2.07817i	−0.0694653	+	0.0801672i
$673$	37.2523	+	10.9383i	1.43597	+	0.421639i	0.904877	−	0.425674i	$-0.139963\pi$
$673$	37.2523	+	10.9383i	1.43597	+	0.421639i	0.531094	+	0.847313i	$0.321781\pi$
$674$	29.7751	−	19.1353i	1.14689	−	0.737063i
$675$	0.415415	+	0.909632i	0.0159893	+	0.0350118i
$676$	−2.71385	−	3.13195i	−0.104379	−	0.120460i
$677$	31.5756	+	20.2924i	1.21355	+	0.779901i	0.981249	−	0.192743i	$-0.0617385\pi$
$677$	31.5756	+	20.2924i	1.21355	+	0.779901i	0.232300	+	0.972644i	$0.425375\pi$
$678$	−1.39380	+	9.69412i	−0.0535287	+	0.372301i
$679$	2.02822	−	14.1066i	0.0778360	−	0.541362i
$680$	−2.27778	−	1.46384i	−0.0873488	−	0.0561356i
$681$	−3.01015	−	3.47389i	−0.115349	−	0.133120i
$682$	0.397176	+	0.869694i	0.0152086	+	0.0333023i
$683$	−25.0066	+	16.0708i	−0.956851	+	0.614931i	−0.923125	−	0.384500i	$-0.874374\pi$
$683$	−25.0066	+	16.0708i	−0.956851	+	0.614931i	−0.0337260	+	0.999431i	$0.510737\pi$
$684$	−0.983568	−	0.288802i	−0.0376077	−	0.0110426i
$685$	−6.98053	+	8.05596i	−0.266712	+	0.307803i
$686$	16.9876	−	4.98800i	0.648588	−	0.190443i
$687$	2.38990	−	5.23316i	0.0911805	−	0.199657i
$688$	−0.428276	−	2.97872i	−0.0163279	−	0.113563i
$689$	47.1909			1.79783
$690$	4.77541	+	0.442111i	0.181797	+	0.0168309i
$691$	−44.7642			−1.70291			−0.851456	−	0.524427i	$-0.824280\pi$
$691$	−44.7642			−1.70291			−0.851456	+	0.524427i	$0.824280\pi$
$692$	−1.85151	−	12.8775i	−0.0703839	−	0.489531i
$693$	0.547045	−	1.19786i	0.0207805	−	0.0455030i
$694$	29.6852	−	8.71635i	1.12683	−	0.330868i
$695$	−0.680855	+	0.785748i	−0.0258263	+	0.0298051i
$696$	3.20870	+	0.942161i	0.121626	+	0.0357125i
$697$	5.18532	−	3.33240i	0.196408	−	0.126224i
$698$	−1.03172	−	2.25916i	−0.0390512	−	0.0855103i
$699$	12.0060	+	13.8557i	0.454110	+	0.524071i
$700$	−2.31329	−	1.48666i	−0.0874342	−	0.0561906i
$701$	−5.81815	+	40.4661i	−0.219748	+	1.52838i	0.519218	+	0.854642i	$0.326223\pi$
$701$	−5.81815	+	40.4661i	−0.219748	+	1.52838i	−0.738967	+	0.673742i	$0.764686\pi$
$702$	−0.589262	+	4.09841i	−0.0222403	+	0.154684i
$703$	0.531565	+	0.341616i	0.0200484	+	0.0128843i
$704$	0.313607	+	0.361922i	0.0118195	+	0.0136404i
$705$	−1.26675	−	2.77379i	−0.0477085	−	0.104467i
$706$	−9.36521	+	6.01866i	−0.352464	+	0.226515i
$707$	−15.4613	−	4.53984i	−0.581481	−	0.170738i
$708$	6.73083	−	7.76779i	0.252960	−	0.291931i
$709$	−4.32715	+	1.27057i	−0.162509	+	0.0477171i	−0.361975	−	0.932188i	$-0.617898\pi$
$709$	−4.32715	+	1.27057i	−0.162509	+	0.0477171i	0.199466	+	0.979905i	$0.436079\pi$
$710$	−3.39696	+	7.43830i	−0.127486	+	0.279154i
$711$	−1.04184	−	7.24614i	−0.0390720	−	0.271752i
$712$	−0.722512			−0.0270773
$713$	2.23051	−	9.31132i	0.0835331	−	0.348712i
$714$	7.44540			0.278637
$715$	−0.282192	−	1.96269i	−0.0105534	−	0.0734005i
$716$	4.03857	−	8.84324i	0.150929	−	0.330487i
$717$	−2.21435	+	0.650193i	−0.0826966	+	0.0242819i
$718$	18.2965	−	21.1153i	0.682818	−	0.788014i
$719$	5.21066	+	1.52999i	0.194325	+	0.0570589i	0.377447	−	0.926031i	$-0.376802\pi$
$719$	5.21066	+	1.52999i	0.194325	+	0.0570589i	−0.183122	+	0.983090i	$0.558620\pi$
$720$	0.841254	−	0.540641i	0.0313517	−	0.0201485i
$721$	3.24372	+	7.10276i	0.120803	+	0.264521i
$722$	−11.7542	−	13.5651i	−0.437447	−	0.504840i
$723$	16.7020	+	10.7337i	0.621153	+	0.399191i
$724$	−0.282110	+	1.96212i	−0.0104845	+	0.0729216i
$725$	−0.475925	+	3.31013i	−0.0176754	+	0.122935i
$726$	9.06086	+	5.82306i	0.336280	+	0.216114i
$727$	14.8591	+	17.1483i	0.551093	+	0.635996i	0.961138	−	0.276070i	$-0.0890322\pi$
$727$	14.8591	+	17.1483i	0.551093	+	0.635996i	−0.410044	+	0.912066i	$0.634487\pi$
$728$	−4.72981	−	10.3568i	−0.175299	−	0.383850i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	−8.90793	−	2.61561i	−0.329697	−	0.0968079i
$731$	−5.33589	+	6.15794i	−0.197355	+	0.227760i
$732$	−9.59519	+	2.81740i	−0.354648	+	0.104134i
$733$	11.3439	−	24.8396i	0.418995	−	0.917471i	−0.575991	−	0.817456i	$-0.695384\pi$
$733$	11.3439	−	24.8396i	0.418995	−	0.917471i	0.994986	−	0.100015i	$-0.0318890\pi$
$734$	0.617914	+	4.29768i	0.0228076	+	0.158630i
$735$	0.561488			0.0207108
$736$	−0.242000	−	4.78972i	−0.00892025	−	0.176551i
$737$	0.369873			0.0136244
$738$	0.323977	+	2.25331i	0.0119258	+	0.0829456i
$739$	7.79551	−	17.0698i	0.286762	−	0.627922i	−0.710351	−	0.703848i	$-0.751464\pi$
$739$	7.79551	−	17.0698i	0.286762	−	0.627922i	0.997113	+	0.0759254i	$0.0241911\pi$
$740$	−0.591438	+	0.173662i	−0.0217417	+	0.00638393i
$741$	2.77952	−	3.20774i	0.102108	−	0.117839i
$742$	30.0708	+	8.82959i	1.10393	+	0.324145i
$743$	−25.4800	+	16.3750i	−0.934771	+	0.600741i	−0.916908	−	0.399099i	$-0.869323\pi$
$743$	−25.4800	+	16.3750i	−0.934771	+	0.600741i	−0.0178635	+	0.999840i	$0.505686\pi$
$744$	−0.829365	−	1.81606i	−0.0304060	−	0.0665798i
$745$	−6.16499	−	7.11477i	−0.225868	−	0.260665i
$746$	9.56729	+	6.14852i	0.350283	+	0.225113i
$747$	0.536760	−	3.73325i	0.0196390	−	0.136592i
$748$	0.184532	−	1.28345i	0.00674716	−	0.0469275i
$749$	33.4833	+	21.5184i	1.22345	+	0.786264i
$750$	0.654861	+	0.755750i	0.0239121	+	0.0275961i
$751$	0.663803	+	1.45353i	0.0242225	+	0.0530399i	0.921357	−	0.388718i	$-0.127082\pi$
$751$	0.663803	+	1.45353i	0.0242225	+	0.0530399i	−0.897134	+	0.441758i	$0.854355\pi$
$752$	−2.56528	+	1.64861i	−0.0935463	+	0.0601185i
$753$	−27.9180	−	8.19747i	−1.01739	−	0.298732i
$754$	−9.06766	+	10.4646i	−0.330225	+	0.381100i
$755$	4.88764	−	1.43514i	0.177879	−	0.0522301i
$756$	−1.14231	+	2.50132i	−0.0415456	+	0.0909722i
$757$	0.329965	+	2.29496i	0.0119928	+	0.0834116i	0.994939	−	0.100483i	$-0.0320387\pi$
$757$	0.329965	+	2.29496i	0.0119928	+	0.0834116i	−0.982946	+	0.183894i	$0.941130\pi$
$758$	14.0182			0.509163
$759$	0.757423	+	2.16819i	0.0274927	+	0.0787004i
$760$	−1.02509			−0.0371840
$761$	2.97955	+	20.7232i	0.108008	+	0.751216i	0.969791	+	0.243938i	$0.0784392\pi$
$761$	2.97955	+	20.7232i	0.108008	+	0.751216i	−0.861782	+	0.507278i	$0.830652\pi$
$762$	−0.460652	+	1.00869i	−0.0166877	+	0.0365409i
$763$	−26.8962	+	7.89743i	−0.973706	+	0.285906i
$764$	5.51827	−	6.36842i	0.199644	−	0.230401i
$765$	−2.59792	−	0.762819i	−0.0939281	−	0.0275798i
$766$	−3.83915	+	2.46727i	−0.138714	+	0.0891462i
$767$	17.6791	+	38.7118i	0.638355	+	1.39780i
$768$	−0.654861	−	0.755750i	−0.0236303	−	0.0272708i
$769$	14.8879	+	9.56790i	0.536873	+	0.345027i	0.780815	−	0.624763i	$-0.214804\pi$
$769$	14.8879	+	9.56790i	0.536873	+	0.345027i	−0.243942	+	0.969790i	$0.578441\pi$
$770$	0.187409	−	1.30346i	0.00675376	−	0.0469734i
$771$	3.51018	−	24.4139i	0.126416	−	0.879244i
$772$	17.6639	+	11.3519i	0.635739	+	0.408565i
$773$	1.42947	+	1.64970i	0.0514145	+	0.0593354i	0.780874	−	0.624688i	$-0.214774\pi$
$773$	1.42947	+	1.64970i	0.0514145	+	0.0593354i	−0.729460	+	0.684024i	$0.760228\pi$
$774$	−1.25013	−	2.73740i	−0.0449350	−	0.0983940i
$775$	1.67954	−	1.07937i	0.0603309	−	0.0387723i
$776$	4.97283	+	1.46015i	0.178514	+	0.0524165i
$777$	1.10999	−	1.28100i	0.0398207	−	0.0459556i
$778$	−5.35976	+	1.57377i	−0.192157	+	0.0564223i
$779$	0.969415	−	2.12272i	0.0347329	−	0.0760544i
$780$	0.589262	+	4.09841i	0.0210990	+	0.146746i
$781$	−3.91602			−0.140126
$782$	−9.37196	+	8.98785i	−0.335141	+	0.321405i
$783$	3.34417			0.119511
$784$	−0.0799081	−	0.555773i	−0.00285386	−	0.0198490i
$785$	4.99947	−	10.9473i	0.178439	−	0.390726i
$786$	2.05901	−	0.604579i	0.0734423	−	0.0215646i
$787$	−29.1297	+	33.6175i	−1.03836	+	1.19833i	−0.0585758	+	0.998283i	$0.518656\pi$
$787$	−29.1297	+	33.6175i	−1.03836	+	1.19833i	−0.979786	+	0.200050i	$0.935890\pi$
$788$	24.7018	+	7.25310i	0.879965	+	0.258381i
$789$	8.23984	−	5.29542i	0.293346	−	0.188522i
$790$	−3.04111	−	6.65910i	−0.108198	−	0.236920i
$791$	−17.6362	−	20.3532i	−0.627070	−	0.723677i
$792$	0.402869	+	0.258908i	0.0143153	+	0.00919990i
$793$	5.89278	−	40.9852i	0.209259	−	1.45543i
$794$	−0.709216	+	4.93270i	−0.0251691	+	0.175055i
$795$	−9.58797	−	6.16182i	−0.340050	−	0.218537i
$796$	−13.2152	−	15.2511i	−0.468399	−	0.540562i
$797$	−4.66970	−	10.2252i	−0.165409	−	0.362196i	0.808718	−	0.588197i	$-0.200162\pi$
$797$	−4.66970	−	10.2252i	−0.165409	−	0.362196i	−0.974127	+	0.226001i	$0.927435\pi$
$798$	2.37134	−	1.52397i	0.0839444	−	0.0539478i
$799$	7.92200	+	2.32611i	0.280260	+	0.0822918i
$800$	0.654861	−	0.755750i	0.0231528	−	0.0267198i
$801$	−0.693245	+	0.203555i	−0.0244946	+	0.00719227i
$802$	1.12603	−	2.46567i	0.0397616	−	0.0870658i
$803$	−0.632736	−	4.40077i	−0.0223288	−	0.155300i
$804$	−0.772352			−0.0272388
$805$	−9.51809	+	9.12799i	−0.335468	+	0.321719i
$806$	8.26650			0.291175
$807$	2.21025	+	15.3726i	0.0778046	+	0.541143i
$808$	2.43434	−	5.33047i	0.0856399	−	0.187525i
$809$	23.5124	−	6.90386i	0.826652	−	0.242727i	0.159074	−	0.987267i	$-0.449149\pi$
$809$	23.5124	−	6.90386i	0.826652	−	0.242727i	0.667578	+	0.744540i	$0.267331\pi$
$810$	0.654861	−	0.755750i	0.0230095	−	0.0265543i
$811$	−34.1831	−	10.0371i	−1.20033	−	0.352449i	−0.380352	−	0.924842i	$-0.624197\pi$
$811$	−34.1831	−	10.0371i	−1.20033	−	0.352449i	−0.819980	+	0.572393i	$0.806015\pi$
$812$	−7.73604	+	4.97165i	−0.271482	+	0.174471i
$813$	−11.6369	−	25.4812i	−0.408122	−	0.893663i
$814$	−0.193309	−	0.223091i	−0.00677549	−	0.00781934i
$815$	6.84424	+	4.39853i	0.239743	+	0.154074i
$816$	−0.385331	+	2.68004i	−0.0134893	+	0.0938201i
$817$	−0.439022	+	3.05346i	−0.0153594	+	0.106827i
$818$	−26.6861	−	17.1501i	−0.933058	−	0.599640i
$819$	−7.45608	−	8.60478i	−0.260537	−	0.300675i
$820$	0.945686	+	2.07076i	0.0330248	+	0.0723142i
$821$	12.8237	−	8.24128i	0.447550	−	0.287623i	−0.297388	−	0.954757i	$-0.596116\pi$
$821$	12.8237	−	8.24128i	0.447550	−	0.287623i	0.744938	+	0.667134i	$0.232479\pi$
$822$	10.2278	+	3.00315i	0.356735	+	0.104747i
$823$	10.1041	−	11.6607i	0.352207	−	0.406468i	−0.551807	−	0.833972i	$-0.686061\pi$
$823$	10.1041	−	11.6607i	0.352207	−	0.406468i	0.904014	+	0.427504i	$0.140607\pi$
$824$	−2.72458	+	0.800009i	−0.0949153	+	0.0278696i
$825$	−0.198939	+	0.435615i	−0.00692616	+	0.0151662i
$826$	4.02229	+	27.9756i	0.139953	+	0.973397i
$827$	23.2847			0.809689			0.404845	−	0.914385i	$-0.367326\pi$
$827$	23.2847			0.809689			0.404845	+	0.914385i	$0.367326\pi$
$828$	−1.58162	−	4.52753i	−0.0549650	−	0.157342i
$829$	−13.4992			−0.468845			−0.234423	−	0.972135i	$-0.575320\pi$
$829$	−13.4992			−0.468845			−0.234423	+	0.972135i	$0.575320\pi$
$830$	−0.536760	−	3.73325i	−0.0186312	−	0.129583i
$831$	−7.70182	+	16.8646i	−0.267173	+	0.585027i
$832$	3.97283	−	1.16653i	0.137733	−	0.0404421i
$833$	−0.995574	+	1.14895i	−0.0344946	+	0.0398089i
$834$	0.997579	+	0.292916i	0.0345433	+	0.0101428i
$835$	14.1322	−	9.08218i	0.489063	−	0.314302i
$836$	−0.203930	−	0.446545i	−0.00705308	−	0.0154441i
$837$	−1.30741	−	1.50883i	−0.0451908	−	0.0521529i
$838$	5.66082	+	3.63799i	0.195550	+	0.125672i
$839$	−3.91726	+	27.2451i	−0.135239	+	0.940606i	0.803335	+	0.595527i	$0.203057\pi$
$839$	−3.91726	+	27.2451i	−0.135239	+	0.940606i	−0.938574	+	0.345079i	$0.887852\pi$
$840$	−0.391340	+	2.72183i	−0.0135025	+	0.0939119i
$841$	−14.9882	−	9.63235i	−0.516836	−	0.332150i
$842$	−21.2807	−	24.5592i	−0.733381	−	0.846367i
$843$	−11.7622	−	25.7556i	−0.405112	−	0.887071i
$844$	−17.7672	+	11.4183i	−0.611572	+	0.393033i
$845$	−3.97630	−	1.16755i	−0.136789	−	0.0401648i
$846$	−1.99691	+	2.30455i	−0.0686550	+	0.0792321i
$847$	−28.4176	+	8.34417i	−0.976441	+	0.286709i
$848$	−4.73459	+	10.3673i	−0.162586	+	0.356015i
$849$	1.28540	+	8.94014i	0.0441147	+	0.306825i
$850$	−2.70760			−0.0928699
$851$	0.149170	+	2.95241i	0.00511350	+	0.101207i
$852$	8.17726			0.280148
$853$	−0.741293	−	5.15580i	−0.0253814	−	0.176531i	0.973187	−	0.230014i	$-0.0738771\pi$
$853$	−0.741293	−	5.15580i	−0.0253814	−	0.176531i	−0.998569	+	0.0534822i	$0.982968\pi$
$854$	11.4235	−	25.0139i	0.390903	−	0.855957i
$855$	−0.983568	+	0.288802i	−0.0336373	+	0.00987681i
$856$	−9.47864	+	10.9389i	−0.323973	+	0.373885i
$857$	3.61233	+	1.06068i	0.123395	+	0.0362320i	0.342847	−	0.939391i	$-0.388609\pi$
$857$	3.61233	+	1.06068i	0.123395	+	0.0362320i	−0.219452	+	0.975623i	$0.570427\pi$
$858$	−1.66810	+	1.07202i	−0.0569480	+	0.0365983i
$859$	−15.5383	−	34.0242i	−0.530160	−	1.16089i	−0.965448	−	0.260598i	$-0.916080\pi$
$859$	−15.5383	−	34.0242i	−0.530160	−	1.16089i	0.435287	−	0.900292i	$-0.356647\pi$
$860$	−1.97071	−	2.27432i	−0.0672006	−	0.0775536i
$861$	−5.26617	−	3.38436i	−0.179471	−	0.115339i
$862$	2.53512	−	17.6322i	0.0863467	−	0.600554i
$863$	−4.21422	+	29.3105i	−0.143454	+	0.997741i	0.783185	+	0.621789i	$0.213594\pi$
$863$	−4.21422	+	29.3105i	−0.143454	+	0.997741i	−0.926639	+	0.375953i	$0.877315\pi$
$864$	−0.841254	−	0.540641i	−0.0286200	−	0.0183930i
$865$	−8.51971	−	9.83227i	−0.289679	−	0.334307i
$866$	−3.55594	−	7.78643i	−0.120836	−	0.264594i
$867$	−8.13400	+	5.22741i	−0.276245	+	0.177532i
$868$	5.26755	+	1.54669i	0.178792	+	0.0524982i
$869$	2.29581	−	2.64951i	0.0778801	−	0.0898784i
$870$	3.20870	−	0.942161i	0.108785	−	0.0319422i
$871$	1.32848	−	2.90897i	0.0450139	−	0.0985667i
$872$	−1.45076	−	10.0902i	−0.0491289	−	0.341699i
$873$	5.18277			0.175410
$874$	−1.14526	+	4.78091i	−0.0387389	+	0.161717i
$875$	−2.74982			−0.0929607
$876$	1.32125	+	9.18950i	0.0446409	+	0.310485i
$877$	13.1899	−	28.8818i	0.445391	−	0.975269i	−0.545187	−	0.838315i	$-0.683541\pi$
$877$	13.1899	−	28.8818i	0.445391	−	0.975269i	0.990577	−	0.136955i	$-0.0437315\pi$
$878$	1.98407	−	0.582575i	0.0669590	−	0.0196609i
$879$	−12.0311	+	13.8846i	−0.405799	+	0.468317i
$880$	0.459493	+	0.134919i	0.0154895	+	0.00454813i
$881$	−29.4045	+	18.8971i	−0.990663	+	0.636660i	−0.932319	−	0.361636i	$-0.882218\pi$
$881$	−29.4045	+	18.8971i	−0.990663	+	0.636660i	−0.0583437	+	0.998297i	$0.518582\pi$
$882$	−0.233250	−	0.510747i	−0.00785395	−	0.0171978i
$883$	−0.853635	−	0.985147i	−0.0287271	−	0.0331529i	0.741204	−	0.671280i	$-0.234255\pi$
$883$	−0.853635	−	0.985147i	−0.0287271	−	0.0331529i	−0.769931	+	0.638127i	$0.779710\pi$
$884$	−9.43125	−	6.06110i	−0.317207	−	0.203857i
$885$	1.46275	−	10.1736i	0.0491698	−	0.341983i
$886$	−4.04061	+	28.1031i	−0.135747	+	0.944142i
$887$	18.9847	+	12.2007i	0.637444	+	0.409661i	0.819059	−	0.573709i	$-0.194496\pi$
$887$	18.9847	+	12.2007i	0.637444	+	0.409661i	−0.181615	+	0.983370i	$0.558132\pi$
$888$	0.403660	+	0.465849i	0.0135460	+	0.0156329i
$889$	−1.26671	−	2.77371i	−0.0424841	−	0.0930271i
$890$	−0.607816	+	0.390620i	−0.0203740	+	0.0130936i
$891$	0.459493	+	0.134919i	0.0153936	+	0.00451997i
$892$	16.2015	−	18.6975i	0.542466	−	0.626039i
$893$	2.99925	−	0.880660i	0.100366	−	0.0294702i
$894$	−3.91080	+	8.56345i	−0.130797	+	0.286405i
$895$	−1.38355	−	9.62282i	−0.0462471	−	0.321655i
$896$	2.74982			0.0918649
$897$	19.7728	+	1.83059i	0.660196	+	0.0611215i
$898$	1.82598			0.0609336
$899$	−0.950171	−	6.60858i	−0.0316900	−	0.220409i
$900$	0.415415	−	0.909632i	0.0138472	−	0.0303211i
$901$	29.6092	−	8.69403i	0.986424	−	0.289640i
$902$	−0.713922	+	0.823910i	−0.0237710	+	0.0274332i
$903$	7.93997	+	2.33138i	0.264226	+	0.0775836i
$904$	8.23908	−	5.29493i	0.274028	−	0.176107i
$905$	0.823476	+	1.80316i	0.0273733	+	0.0599391i
$906$	−3.33585	−	3.84978i	−0.110826	−	0.127900i
$907$	−5.27996	−	3.39322i	−0.175318	−	0.112670i	0.450039	−	0.893009i	$-0.351410\pi$
$907$	−5.27996	−	3.39322i	−0.175318	−	0.112670i	−0.625357	+	0.780339i	$0.715047\pi$
$908$	−0.654167	+	4.54983i	−0.0217093	+	0.150991i
$909$	0.833969	−	5.80038i	0.0276610	−	0.192386i
$910$	−9.57831	−	6.15560i	−0.317518	−	0.204056i
$911$	−9.85414	−	11.3723i	−0.326482	−	0.376781i	0.568651	−	0.822579i	$-0.307465\pi$
$911$	−9.85414	−	11.3723i	−0.326482	−	0.376781i	−0.895134	+	0.445798i	$0.852920\pi$
$912$	0.425839	+	0.932456i	0.0141009	+	0.0308767i
$913$	1.51948	−	0.976508i	0.0502873	−	0.0323177i
$914$	−7.56257	−	2.22057i	−0.250147	−	0.0734499i
$915$	−6.54878	+	7.55770i	−0.216496	+	0.249850i
$916$	−5.52001	+	1.62082i	−0.182386	+	0.0535534i
$917$	−2.45133	+	5.36766i	−0.0809500	+	0.177256i
$918$	0.385331	+	2.68004i	0.0127178	+	0.0884545i
$919$	47.7529			1.57522			0.787611	−	0.616173i	$-0.211318\pi$
$919$	47.7529			1.57522			0.787611	+	0.616173i	$0.211318\pi$
$920$	−2.79310	−	3.89854i	−0.0920859	−	0.128531i
$921$	−20.5201			−0.676162
$922$	−2.83309	−	19.7045i	−0.0933027	−	0.648935i
$923$	−14.0653	+	30.7987i	−0.462964	+	1.01375i
$924$	−1.26352	+	0.371003i	−0.0415668	+	0.0122051i
$925$	−0.403660	+	0.465849i	−0.0132723	+	0.0153170i
$926$	−38.0313	−	11.1670i	−1.24978	−	0.366970i
$927$	−2.38883	+	1.53521i	−0.0784594	+	0.0504228i
$928$	−1.38922	−	3.04196i	−0.0456033	−	0.0998573i
$929$	32.4507	+	37.4501i	1.06467	+	1.22870i	0.972487	+	0.232956i	$0.0748397\pi$
$929$	32.4507	+	37.4501i	1.06467	+	1.22870i	0.0921850	+	0.995742i	$0.470615\pi$
$930$	−1.67954	−	1.07937i	−0.0550743	−	0.0353941i
$931$	−0.0819131	+	0.569718i	−0.00268459	+	0.0186718i
$932$	2.60916	−	18.1471i	0.0854660	−	0.594429i
$933$	−22.0821	−	14.1913i	−0.722937	−	0.464603i
$934$	−6.23109	−	7.19107i	−0.203888	−	0.235299i
$935$	−0.538646	−	1.17947i	−0.0176156	−	0.0385728i
$936$	3.48325	−	2.23855i	0.113854	−	0.0731693i
$937$	−22.1988	−	6.51814i	−0.725202	−	0.212938i	−0.101761	−	0.994809i	$-0.532448\pi$
$937$	−22.1988	−	6.51814i	−0.725202	−	0.212938i	−0.623441	+	0.781870i	$0.714266\pi$
$938$	1.39081	−	1.60508i	0.0454116	−	0.0524077i
$939$	16.8249	−	4.94023i	0.549059	−	0.161218i
$940$	−1.26675	+	2.77379i	−0.0413168	+	0.0904712i
$941$	3.76446	+	26.1824i	0.122718	+	0.853521i	0.954456	+	0.298353i	$0.0964371\pi$
$941$	3.76446	+	26.1824i	0.122718	+	0.853521i	−0.831738	+	0.555168i	$0.812654\pi$
$942$	−12.0349			−0.392117
$943$	10.7143	−	2.09706i	0.348907	−	0.0682898i
$944$	−10.2783			−0.334529
$945$	0.391340	+	2.72183i	0.0127303	+	0.0885410i
$946$	0.598677	−	1.31092i	0.0194647	−	0.0426217i
$947$	14.7926	−	4.34351i	0.480696	−	0.141145i	−0.0324024	−	0.999475i	$-0.510316\pi$
$947$	14.7926	−	4.34351i	0.480696	−	0.141145i	0.513098	+	0.858330i	$0.328498\pi$
$948$	−4.79401	+	5.53258i	−0.155702	+	0.179690i
$949$	−36.8838	−	10.8300i	−1.19730	−	0.351558i
$950$	−0.862362	+	0.554206i	−0.0279787	+	0.0179808i
$951$	1.71353	+	3.75211i	0.0555651	+	0.121671i
$952$	−4.87570	−	5.62686i	−0.158022	−	0.182367i
$953$	−12.0739	−	7.75943i	−0.391112	−	0.251353i	0.330275	−	0.943885i	$-0.392859\pi$
$953$	−12.0739	−	7.75943i	−0.391112	−	0.251353i	−0.721387	+	0.692532i	$0.756495\pi$
$954$	−1.62200	+	11.2812i	−0.0525141	+	0.365244i
$955$	1.19923	−	8.34085i	0.0388063	−	0.269904i
$956$	1.94148	+	1.24771i	0.0627918	+	0.0403539i
$957$	1.04875	+	1.21033i	0.0339014	+	0.0391243i
$958$	11.3670	+	24.8904i	0.367253	+	0.804171i
$959$	−24.6587	+	15.8472i	−0.796271	+	0.511732i
$960$	−0.959493	−	0.281733i	−0.0309675	−	0.00909288i
$961$	17.6905	−	20.4159i	0.570660	−	0.658577i
$962$	−2.44888	+	0.719055i	−0.0789550	+	0.0231833i
$963$	−6.01284	+	13.1663i	−0.193761	+	0.424277i
$964$	−2.82547	−	19.6516i	−0.0910023	−	0.632935i
$965$	20.9972			0.675923
$966$	12.2571	+	4.86605i	0.394365	+	0.156563i
$967$	23.9515			0.770227			0.385114	−	0.922869i	$-0.374162\pi$
$967$	23.9515			0.770227			0.385114	+	0.922869i	$0.374162\pi$
$968$	−1.53283	−	10.6610i	−0.0492669	−	0.342659i
$969$	1.15300	−	2.52472i	0.0370397	−	0.0811056i
$970$	4.97283	−	1.46015i	0.159668	−	0.0468827i
$971$	−25.8373	+	29.8178i	−0.829159	+	0.956900i	−0.999595	−	0.0284687i	$-0.990937\pi$
$971$	−25.8373	+	29.8178i	−0.829159	+	0.956900i	0.170436	+	0.985369i	$0.445482\pi$
$972$	−0.959493	−	0.281733i	−0.0307758	−	0.00903658i
$973$	−2.40512	+	1.54567i	−0.0771045	+	0.0495521i
$974$	0.334876	+	0.733276i	0.0107301	+	0.0234957i
$975$	2.71148	+	3.12922i	0.0868370	+	0.100215i
$976$	8.41276	+	5.40655i	0.269286	+	0.173060i
$977$	−8.24423	+	57.3399i	−0.263756	+	1.83447i	0.240184	+	0.970727i	$0.422792\pi$
$977$	−8.24423	+	57.3399i	−0.263756	+	1.83447i	−0.503940	+	0.863739i	$0.668117\pi$
$978$	1.15784	−	8.05296i	0.0370236	−	0.257505i
$979$	−0.291078	−	0.187064i	−0.00930289	−	0.00597860i
$980$	−0.367696	−	0.424344i	−0.0117456	−	0.0135552i
$981$	−4.23474	−	9.27279i	−0.135205	−	0.296058i
$982$	−4.41676	+	2.83848i	−0.140944	+	0.0905795i
$983$	0.0733842	+	0.0215475i	0.00234059	+	0.000687260i	0.282903	−	0.959149i	$-0.408703\pi$
$983$	0.0733842	+	0.0215475i	0.00234059	+	0.000687260i	−0.280562	+	0.959836i	$0.590521\pi$
$984$	1.49078	−	1.72045i	0.0475243	−	0.0548460i
$985$	24.7018	−	7.25310i	0.787065	−	0.231103i
$986$	−3.76144	+	8.23641i	−0.119789	+	0.262301i
$987$	−1.19333	−	8.29983i	−0.0379843	−	0.264186i
$988$	−4.24445			−0.135034
$989$	−12.8089	+	6.65023i	−0.407299	+	0.211465i
$990$	0.478891			0.0152202
$991$	4.27693	+	29.7467i	0.135861	+	0.944935i	0.937713	+	0.347412i	$0.112939\pi$
$991$	4.27693	+	29.7467i	0.135861	+	0.944935i	−0.801852	+	0.597523i	$0.796152\pi$
$992$	−0.829365	+	1.81606i	−0.0263324	+	0.0576598i
$993$	−16.7820	+	4.92765i	−0.532562	+	0.156374i
$994$	−14.7252	+	16.9938i	−0.467054	+	0.539009i
$995$	−19.3627	−	5.68540i	−0.613838	−	0.180239i
$996$	−3.17290	+	2.03910i	−0.100537	+	0.0646114i
$997$	−14.3120	−	31.3389i	−0.453265	−	0.992513i	−0.988971	−	0.148108i	$-0.952682\pi$
$997$	−14.3120	−	31.3389i	−0.453265	−	0.992513i	0.535706	−	0.844405i	$-0.320046\pi$
$998$	−21.0633	−	24.3084i	−0.666748	−	0.769468i
$999$	0.518554	+	0.333254i	0.0164063	+	0.0105437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.b.601.1	yes	10
23.8	even	11	inner	690.2.m.b.31.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.b.31.1	✓	10	23.8	even	11	inner
690.2.m.b.601.1	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-2.31329 + 1.48666i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-2.31329 + 1.48666i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-0.841254 - 0.540641i) q^{10} +(0.0681534 - 0.474017i) q^{11} +(-0.142315 + 0.989821i) q^{12} +(-3.48325 - 2.23855i) q^{13} +(-1.80075 - 2.07817i) q^{14} +(0.415415 + 0.909632i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-2.59792 - 0.762819i) q^{17} +(0.654861 - 0.755750i) q^{18} +(-0.983568 + 0.288802i) q^{19} +(0.415415 - 0.909632i) q^{20} +(0.391340 + 2.72183i) q^{21} +0.478891 q^{22} +(-3.77831 - 2.95371i) q^{23} -1.00000 q^{24} +(-0.142315 - 0.989821i) q^{25} +(1.72005 - 3.76638i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(1.80075 - 2.07817i) q^{28} +(-3.20870 - 0.942161i) q^{29} +(-0.841254 + 0.540641i) q^{30} +(0.829365 + 1.81606i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-0.402869 - 0.258908i) q^{33} +(0.385331 - 2.68004i) q^{34} +(0.391340 - 2.72183i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-0.403660 - 0.465849i) q^{37} +(-0.425839 - 0.932456i) q^{38} +(-3.48325 + 2.23855i) q^{39} +(0.959493 + 0.281733i) q^{40} +(-1.49078 + 1.72045i) q^{41} +(-2.63843 + 0.774713i) q^{42} +(1.25013 - 2.73740i) q^{43} +(0.0681534 + 0.474017i) q^{44} +1.00000 q^{45} +(2.38594 - 4.16021i) q^{46} -3.04936 q^{47} +(-0.142315 - 0.989821i) q^{48} +(0.233250 - 0.510747i) q^{49} +(0.959493 - 0.281733i) q^{50} +(-1.77310 + 2.04627i) q^{51} +(3.97283 + 1.16653i) q^{52} +(-9.58797 + 6.16182i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(0.313607 + 0.361922i) q^{55} +(2.31329 + 1.48666i) q^{56} +(-0.145886 + 1.01466i) q^{57} +(0.475925 - 3.31013i) q^{58} +(-8.64662 - 5.55685i) q^{59} +(-0.654861 - 0.755750i) q^{60} +(4.15426 + 9.09656i) q^{61} +(-1.67954 + 1.07937i) q^{62} +(2.63843 + 0.774713i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(3.97283 - 1.16653i) q^{65} +(0.198939 - 0.435615i) q^{66} +(0.109917 + 0.764490i) q^{67} +2.70760 q^{68} +(-4.25635 + 2.20985i) q^{69} +2.74982 q^{70} +(-1.16375 - 8.09403i) q^{71} +(-0.415415 + 0.909632i) q^{72} +(8.90793 - 2.61561i) q^{73} +(0.403660 - 0.465849i) q^{74} +(-0.959493 - 0.281733i) q^{75} +(0.862362 - 0.554206i) q^{76} +(0.547045 + 1.19786i) q^{77} +(-2.71148 - 3.12922i) q^{78} +(6.15853 + 3.95785i) q^{79} +(-0.142315 + 0.989821i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-1.91510 - 1.23076i) q^{82} +(2.46990 + 2.85041i) q^{83} +(-1.14231 - 2.50132i) q^{84} +(2.27778 - 1.46384i) q^{85} +(2.88745 + 0.847833i) q^{86} +(-2.18996 + 2.52735i) q^{87} +(-0.459493 + 0.134919i) q^{88} +(0.300142 - 0.657220i) q^{89} +(0.142315 + 0.989821i) q^{90} +11.3858 q^{91} +(4.45741 + 1.76959i) q^{92} +1.99647 q^{93} +(-0.433969 - 3.01832i) q^{94} +(0.425839 - 0.932456i) q^{95} +(0.959493 - 0.281733i) q^{96} +(-3.39399 + 3.91688i) q^{97} +(0.538744 + 0.158189i) q^{98} +(-0.402869 + 0.258908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{8} - q^{9}+O(q^{10}) \) 10 * q + q^2 - q^3 - q^4 - q^5 + q^6 + q^8 - q^9	\( 10 q + q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{8} - q^{9} + q^{10} - 4 q^{11} - q^{12} + 2 q^{13} - q^{15} - q^{16} - 2 q^{17} + q^{18} - q^{20} + 4 q^{22} - q^{23} - 10 q^{24} - q^{25} + 9 q^{26} - q^{27} - 6 q^{29} + q^{30} + 22 q^{31} + q^{32} - 4 q^{33} - 9 q^{34} - q^{36} + 20 q^{37} + 2 q^{39} + q^{40} + 9 q^{41} - 11 q^{42} + 12 q^{43} - 4 q^{44} + 10 q^{45} + q^{46} - 8 q^{47} - q^{48} + 7 q^{49} + q^{50} - 13 q^{51} + 2 q^{52} - 20 q^{53} + q^{54} + 7 q^{55} + 11 q^{57} + 6 q^{58} - 22 q^{59} - q^{60} + 49 q^{61} + 11 q^{63} - q^{64} + 2 q^{65} - 7 q^{66} + 10 q^{67} - 2 q^{68} - q^{69} - q^{71} + q^{72} + 17 q^{73} - 20 q^{74} - q^{75} - 13 q^{78} + 18 q^{79} - q^{80} - q^{81} + 13 q^{82} + 15 q^{83} - 11 q^{84} + 9 q^{85} + 10 q^{86} - 6 q^{87} + 4 q^{88} - 5 q^{89} + q^{90} + 22 q^{91} - 12 q^{92} - 22 q^{93} - 3 q^{94} + q^{96} - q^{97} - 7 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q + q^2 - q^3 - q^4 - q^5 + q^6 + q^8 - q^9 + q^10 - 4 * q^11 - q^12 + 2 * q^13 - q^15 - q^16 - 2 * q^17 + q^18 - q^20 + 4 * q^22 - q^23 - 10 * q^24 - q^25 + 9 * q^26 - q^27 - 6 * q^29 + q^30 + 22 * q^31 + q^32 - 4 * q^33 - 9 * q^34 - q^36 + 20 * q^37 + 2 * q^39 + q^40 + 9 * q^41 - 11 * q^42 + 12 * q^43 - 4 * q^44 + 10 * q^45 + q^46 - 8 * q^47 - q^48 + 7 * q^49 + q^50 - 13 * q^51 + 2 * q^52 - 20 * q^53 + q^54 + 7 * q^55 + 11 * q^57 + 6 * q^58 - 22 * q^59 - q^60 + 49 * q^61 + 11 * q^63 - q^64 + 2 * q^65 - 7 * q^66 + 10 * q^67 - 2 * q^68 - q^69 - q^71 + q^72 + 17 * q^73 - 20 * q^74 - q^75 - 13 * q^78 + 18 * q^79 - q^80 - q^81 + 13 * q^82 + 15 * q^83 - 11 * q^84 + 9 * q^85 + 10 * q^86 - 6 * q^87 + 4 * q^88 - 5 * q^89 + q^90 + 22 * q^91 - 12 * q^92 - 22 * q^93 - 3 * q^94 + q^96 - q^97 - 7 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more