LMFDB - Embedded newform 690.2.q.b.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(11,690)]

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([11, 0, 9]))

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

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

chi := DirichletCharacter("690.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	690.11
Dual form			690.2.q.b.251.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540641 - 0.841254i) q^{2} +(1.72873 - 0.107190i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-1.02480 - 1.39635i) q^{6} +(1.12640 - 0.976034i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.97702 - 0.370607i) q^{9} +O(q^{10})$	\(q+(-0.540641 - 0.841254i) q^{2} +(1.72873 - 0.107190i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-1.02480 - 1.39635i) q^{6} +(1.12640 - 0.976034i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.97702 - 0.370607i) q^{9} +(-0.755750 - 0.654861i) q^{10} +(2.69175 + 1.72988i) q^{11} +(-0.620637 + 1.61704i) q^{12} +(-0.301686 + 0.348165i) q^{13} +(-1.43007 - 0.419907i) q^{14} +(1.62851 - 0.589888i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(0.993222 + 2.17485i) q^{17} +(-1.92127 - 2.30406i) q^{18} +(-2.25092 - 1.02796i) q^{19} +(-0.142315 + 0.989821i) q^{20} +(1.84263 - 1.80804i) q^{21} -3.19969i q^{22} +(-1.51739 + 4.54945i) q^{23} +(1.69588 - 0.352123i) q^{24} +(0.841254 - 0.540641i) q^{25} +(0.455999 + 0.0655627i) q^{26} +(5.10674 - 0.959787i) q^{27} +(0.419907 + 1.43007i) q^{28} +(-4.48945 + 2.05026i) q^{29} +(-1.37668 - 1.05107i) q^{30} +(-0.946047 - 6.57990i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(4.83874 + 2.70197i) q^{33} +(1.29263 - 2.01137i) q^{34} +(0.805795 - 1.25384i) q^{35} +(-0.899583 + 2.86195i) q^{36} +(3.37397 - 11.4907i) q^{37} +(0.352164 + 2.44935i) q^{38} +(-0.484215 + 0.634221i) q^{39} +(0.909632 - 0.415415i) q^{40} +(-0.984332 - 3.35233i) q^{41} +(-2.51722 - 0.572616i) q^{42} +(3.53652 + 0.508475i) q^{43} +(-2.69175 + 1.72988i) q^{44} +(2.75202 - 1.19432i) q^{45} +(4.64761 - 1.18311i) q^{46} +2.26918i q^{47} +(-1.21309 - 1.23629i) q^{48} +(-0.680062 + 4.72993i) q^{49} +(-0.909632 - 0.415415i) q^{50} +(1.95014 + 3.65327i) q^{51} +(-0.191377 - 0.419056i) q^{52} +(4.51643 + 5.21223i) q^{53} +(-3.56834 - 3.77716i) q^{54} +(3.07008 + 0.901458i) q^{55} +(0.976034 - 1.12640i) q^{56} +(-4.00142 - 1.53579i) q^{57} +(4.15197 + 2.66831i) q^{58} +(4.54854 + 3.94133i) q^{59} +(-0.139925 + 1.72639i) q^{60} +(-6.06637 + 0.872212i) q^{61} +(-5.02389 + 4.35323i) q^{62} +(2.99160 - 3.32313i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-0.191377 + 0.419056i) q^{65} +(-0.342976 - 5.53141i) q^{66} +(-3.93607 - 6.12464i) q^{67} -2.39092 q^{68} +(-2.13551 + 8.02743i) q^{69} -1.49044 q^{70} +(-3.37290 - 5.24833i) q^{71} +(2.89398 - 0.790509i) q^{72} +(-0.392136 + 0.858657i) q^{73} +(-11.4907 + 3.37397i) q^{74} +(1.39635 - 1.02480i) q^{75} +(1.87013 - 1.62048i) q^{76} +(4.72043 - 0.678695i) q^{77} +(0.795327 + 0.0644616i) q^{78} +(-6.33721 - 5.49123i) q^{79} +(-0.841254 - 0.540641i) q^{80} +(8.72530 - 2.20661i) q^{81} +(-2.28799 + 2.64048i) q^{82} +(-7.60990 - 2.23447i) q^{83} +(0.879196 + 2.42720i) q^{84} +(1.56572 + 1.80693i) q^{85} +(-1.48423 - 3.25001i) q^{86} +(-7.54128 + 4.02558i) q^{87} +(2.91054 + 1.32920i) q^{88} +(1.46103 - 10.1617i) q^{89} +(-2.49258 - 1.66945i) q^{90} +0.686630i q^{91} +(-3.50798 - 3.27018i) q^{92} +(-2.34076 - 11.2735i) q^{93} +(1.90895 - 1.22681i) q^{94} +(-2.44935 - 0.352164i) q^{95} +(-0.384191 + 1.68890i) q^{96} +(0.334672 + 1.13979i) q^{97} +(4.34674 - 1.98509i) q^{98} +(8.65451 + 4.15232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{4} + 16 q^{5} - 2 q^{6} - 46 q^{9}+O(q^{10}) $ 160 * q + 16 * q^4 + 16 * q^5 - 2 * q^6 - 46 * q^9	$ 160 q + 16 q^{4} + 16 q^{5} - 2 q^{6} - 46 q^{9} + 12 q^{11} + 12 q^{14} - 16 q^{16} - 8 q^{18} - 16 q^{20} + 70 q^{21} - 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} + 2 q^{30} - 4 q^{31} - 16 q^{33} + 2 q^{36} - 72 q^{38} + 140 q^{39} - 44 q^{41} + 44 q^{43} - 12 q^{44} + 2 q^{45} + 4 q^{46} + 70 q^{49} + 2 q^{51} + 52 q^{53} - 62 q^{54} + 10 q^{55} + 54 q^{56} - 94 q^{57} - 36 q^{58} - 44 q^{61} + 16 q^{64} - 54 q^{66} - 44 q^{67} - 30 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} + 24 q^{74} + 88 q^{77} - 54 q^{78} - 44 q^{79} + 16 q^{80} - 66 q^{81} - 28 q^{82} - 4 q^{83} - 4 q^{84} - 158 q^{86} + 156 q^{87} - 80 q^{89} + 8 q^{90} + 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} + 88 q^{98} - 58 q^{99}+O(q^{100}) $ 160 * q + 16 * q^4 + 16 * q^5 - 2 * q^6 - 46 * q^9 + 12 * q^11 + 12 * q^14 - 16 * q^16 - 8 * q^18 - 16 * q^20 + 70 * q^21 - 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 + 2 * q^30 - 4 * q^31 - 16 * q^33 + 2 * q^36 - 72 * q^38 + 140 * q^39 - 44 * q^41 + 44 * q^43 - 12 * q^44 + 2 * q^45 + 4 * q^46 + 70 * q^49 + 2 * q^51 + 52 * q^53 - 62 * q^54 + 10 * q^55 + 54 * q^56 - 94 * q^57 - 36 * q^58 - 44 * q^61 + 16 * q^64 - 54 * q^66 - 44 * q^67 - 30 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 + 24 * q^74 + 88 * q^77 - 54 * q^78 - 44 * q^79 + 16 * q^80 - 66 * q^81 - 28 * q^82 - 4 * q^83 - 4 * q^84 - 158 * q^86 + 156 * q^87 - 80 * q^89 + 8 * q^90 + 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 + 88 * q^98 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.540641	−	0.841254i	−0.382291	−	0.594856i
$2$	−0.540641	−	0.841254i	−0.382291	−	0.594856i
$3$	1.72873	−	0.107190i	0.998083	−	0.0618864i
$3$	1.72873	−	0.107190i	0.998083	−	0.0618864i
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	0.959493	−	0.281733i	0.429098	−	0.125995i
$5$	0.959493	−	0.281733i	0.429098	−	0.125995i
$6$	−1.02480	−	1.39635i	−0.418372	−	0.570057i
$7$	1.12640	−	0.976034i	0.425740	−	0.368906i	−0.415477	−	0.909604i	$-0.636385\pi$
$7$	1.12640	−	0.976034i	0.425740	−	0.368906i	0.841217	+	0.540698i	$0.181840\pi$
$8$	0.989821	−	0.142315i	0.349955	−	0.0503159i
$9$	2.97702	−	0.370607i	0.992340	−	0.123536i
$10$	−0.755750	−	0.654861i	−0.238989	−	0.207085i
$11$	2.69175	+	1.72988i	0.811594	+	0.521580i	0.879380	−	0.476120i	$-0.157957\pi$
$11$	2.69175	+	1.72988i	0.811594	+	0.521580i	−0.0677862	+	0.997700i	$0.521594\pi$
$12$	−0.620637	+	1.61704i	−0.179162	+	0.466798i
$13$	−0.301686	+	0.348165i	−0.0836727	+	0.0965635i	−0.796042	−	0.605241i	$-0.793077\pi$
$13$	−0.301686	+	0.348165i	−0.0836727	+	0.0965635i	0.712369	+	0.701805i	$0.247622\pi$
$14$	−1.43007	−	0.419907i	−0.382203	−	0.112225i
$15$	1.62851	−	0.589888i	0.420478	−	0.152308i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	0.993222	+	2.17485i	0.240892	+	0.527479i	0.991004	−	0.133831i	$-0.0427279\pi$
$17$	0.993222	+	2.17485i	0.240892	+	0.527479i	−0.750112	+	0.661310i	$0.770001\pi$
$18$	−1.92127	−	2.30406i	−0.452848	−	0.543073i
$19$	−2.25092	−	1.02796i	−0.516397	−	0.235831i	0.140130	−	0.990133i	$-0.455248\pi$
$19$	−2.25092	−	1.02796i	−0.516397	−	0.235831i	−0.656527	+	0.754303i	$0.727975\pi$
$20$	−0.142315	+	0.989821i	−0.0318226	+	0.221331i
$21$	1.84263	−	1.80804i	0.402094	−	0.394547i
$22$		−	3.19969i		−	0.682177i
$23$	−1.51739	+	4.54945i	−0.316398	+	0.948626i
$23$	−1.51739	+	4.54945i	−0.316398	+	0.948626i
$24$	1.69588	−	0.352123i	0.346170	−	0.0718769i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	0.455999	+	0.0655627i	0.0894287	+	0.0128579i
$27$	5.10674	−	0.959787i	0.982793	−	0.184711i
$28$	0.419907	+	1.43007i	0.0793549	+	0.270258i
$29$	−4.48945	+	2.05026i	−0.833670	+	0.380724i	−0.786066	−	0.618142i	$-0.787886\pi$
$29$	−4.48945	+	2.05026i	−0.833670	+	0.380724i	−0.0476034	+	0.998866i	$0.515158\pi$
$30$	−1.37668	−	1.05107i	−0.251347	−	0.191898i
$31$	−0.946047	−	6.57990i	−0.169915	−	1.18179i	−0.879056	−	0.476718i	$-0.841826\pi$
$31$	−0.946047	−	6.57990i	−0.169915	−	1.18179i	0.709141	−	0.705067i	$-0.249083\pi$
$32$	−0.281733	+	0.959493i	−0.0498038	+	0.169616i
$33$	4.83874	+	2.70197i	0.842317	+	0.470353i
$34$	1.29263	−	2.01137i	0.221684	−	0.344947i
$35$	0.805795	−	1.25384i	0.136204	−	0.211938i
$36$	−0.899583	+	2.86195i	−0.149931	+	0.476991i
$37$	3.37397	−	11.4907i	0.554677	−	1.88906i	0.108539	−	0.994092i	$-0.465383\pi$
$37$	3.37397	−	11.4907i	0.554677	−	1.88906i	0.446138	−	0.894964i	$-0.352799\pi$
$38$	0.352164	+	2.44935i	0.0571285	+	0.397338i
$39$	−0.484215	+	0.634221i	−0.0775364	+	0.101557i
$40$	0.909632	−	0.415415i	0.143825	−	0.0656829i
$41$	−0.984332	−	3.35233i	−0.153727	−	0.523545i	0.846230	−	0.532817i	$-0.178867\pi$
$41$	−0.984332	−	3.35233i	−0.153727	−	0.523545i	−0.999957	+	0.00927203i	$0.997049\pi$
$42$	−2.51722	−	0.572616i	−0.388415	−	0.0883566i
$43$	3.53652	+	0.508475i	0.539314	+	0.0775417i	0.406589	−	0.913611i	$-0.366718\pi$
$43$	3.53652	+	0.508475i	0.539314	+	0.0775417i	0.132725	+	0.991153i	$0.457627\pi$
$44$	−2.69175	+	1.72988i	−0.405797	+	0.260790i
$45$	2.75202	−	1.19432i	0.410247	−	0.178038i
$46$	4.64761	−	1.18311i	0.685252	−	0.174440i
$47$			2.26918i			0.330993i	0.986210	+	0.165497i	$0.0529227\pi$
$47$			2.26918i			0.330993i	−0.986210	+	0.165497i	$0.947077\pi$
$48$	−1.21309	−	1.23629i	−0.175094	−	0.178443i
$49$	−0.680062	+	4.72993i	−0.0971517	+	0.675705i
$50$	−0.909632	−	0.415415i	−0.128641	−	0.0587486i
$51$	1.95014	+	3.65327i	0.273074	+	0.511560i
$52$	−0.191377	−	0.419056i	−0.0265392	−	0.0581127i
$53$	4.51643	+	5.21223i	0.620379	+	0.715956i	0.975779	−	0.218759i	$-0.0702008\pi$
$53$	4.51643	+	5.21223i	0.620379	+	0.715956i	−0.355400	+	0.934714i	$0.615655\pi$
$54$	−3.56834	−	3.77716i	−0.485589	−	0.514007i
$55$	3.07008	+	0.901458i	0.413970	+	0.121553i
$56$	0.976034	−	1.12640i	0.130428	−	0.150522i
$57$	−4.00142	−	1.53579i	−0.530002	−	0.203421i
$58$	4.15197	+	2.66831i	0.545180	+	0.350366i
$59$	4.54854	+	3.94133i	0.592169	+	0.513118i	0.898596	−	0.438777i	$-0.144588\pi$
$59$	4.54854	+	3.94133i	0.592169	+	0.513118i	−0.306427	+	0.951894i	$0.599134\pi$
$60$	−0.139925	+	1.72639i	−0.0180642	+	0.222876i
$61$	−6.06637	+	0.872212i	−0.776718	+	0.111675i	−0.519263	−	0.854615i	$-0.673793\pi$
$61$	−6.06637	+	0.872212i	−0.776718	+	0.111675i	−0.257456	+	0.966290i	$0.582884\pi$
$62$	−5.02389	+	4.35323i	−0.638035	+	0.552861i
$63$	2.99160	−	3.32313i	0.376906	−	0.418674i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	−0.191377	+	0.419056i	−0.0237373	+	0.0519775i
$66$	−0.342976	−	5.53141i	−0.0422175	−	0.680869i
$67$	−3.93607	−	6.12464i	−0.480867	−	0.748244i	0.513052	−	0.858358i	$-0.328515\pi$
$67$	−3.93607	−	6.12464i	−0.480867	−	0.748244i	−0.993919	+	0.110113i	$0.964879\pi$
$68$	−2.39092			−0.289941
$69$	−2.13551	+	8.02743i	−0.257085	+	0.966389i
$70$	−1.49044			−0.178142
$71$	−3.37290	−	5.24833i	−0.400289	−	0.622863i	0.581340	−	0.813661i	$-0.302529\pi$
$71$	−3.37290	−	5.24833i	−0.400289	−	0.622863i	−0.981629	+	0.190798i	$0.938892\pi$
$72$	2.89398	−	0.790509i	0.341058	−	0.0931623i
$73$	−0.392136	+	0.858657i	−0.0458960	+	0.100498i	−0.931191	−	0.364532i	$-0.881229\pi$
$73$	−0.392136	+	0.858657i	−0.0458960	+	0.100498i	0.885295	+	0.465030i	$0.153956\pi$
$74$	−11.4907	+	3.37397i	−1.33576	+	0.392216i
$75$	1.39635	−	1.02480i	0.161237	−	0.118333i
$76$	1.87013	−	1.62048i	0.214519	−	0.185882i
$77$	4.72043	−	0.678695i	0.537942	−	0.0773444i
$78$	0.795327	+	0.0644616i	0.0900530	+	0.00729884i
$79$	−6.33721	−	5.49123i	−0.712992	−	0.617811i	0.220929	−	0.975290i	$-0.429091\pi$
$79$	−6.33721	−	5.49123i	−0.712992	−	0.617811i	−0.933921	+	0.357479i	$0.883637\pi$
$80$	−0.841254	−	0.540641i	−0.0940550	−	0.0604455i
$81$	8.72530	−	2.20661i	0.969478	−	0.245179i
$82$	−2.28799	+	2.64048i	−0.252666	+	0.291592i
$83$	−7.60990	−	2.23447i	−0.835296	−	0.245265i	−0.164005	−	0.986459i	$-0.552441\pi$
$83$	−7.60990	−	2.23447i	−0.835296	−	0.245265i	−0.671290	+	0.741195i	$0.734260\pi$
$84$	0.879196	+	2.42720i	0.0959281	+	0.264829i
$85$	1.56572	+	1.80693i	0.169826	+	0.195989i
$86$	−1.48423	−	3.25001i	−0.160049	−	0.350458i
$87$	−7.54128	+	4.02558i	−0.808510	+	0.431587i
$88$	2.91054	+	1.32920i	0.310265	+	0.141693i
$89$	1.46103	−	10.1617i	0.154869	−	1.07714i	−0.753042	−	0.657972i	$-0.771414\pi$
$89$	1.46103	−	10.1617i	0.154869	−	1.07714i	0.907911	−	0.419163i	$-0.137676\pi$
$90$	−2.49258	−	1.66945i	−0.262741	−	0.175975i
$91$			0.686630i			0.0719783i
$92$	−3.50798	−	3.27018i	−0.365732	−	0.340940i
$93$	−2.34076	−	11.2735i	−0.242726	−	1.16900i
$94$	1.90895	−	1.22681i	0.196893	−	0.126536i
$95$	−2.44935	−	0.352164i	−0.251298	−	0.0361313i
$96$	−0.384191	+	1.68890i	−0.0392114	+	0.172373i
$97$	0.334672	+	1.13979i	0.0339808	+	0.115728i	0.974737	−	0.223356i	$-0.0717012\pi$
$97$	0.334672	+	1.13979i	0.0339808	+	0.115728i	−0.940756	+	0.339084i	$0.889883\pi$
$98$	4.34674	−	1.98509i	0.439087	−	0.200525i
$99$	8.65451	+	4.15232i	0.869811	+	0.417324i
$100$	0.142315	+	0.989821i	0.0142315	+	0.0989821i
$101$	3.16884	−	10.7921i	0.315311	−	1.07385i	−0.637541	−	0.770416i	$-0.720048\pi$
$101$	3.16884	−	10.7921i	0.315311	−	1.07385i	0.952852	−	0.303435i	$-0.0981334\pi$
$102$	2.01900	−	3.61567i	0.199911	−	0.358005i
$103$	−8.49723	+	13.2219i	−0.837257	+	1.30280i	0.113713	+	0.993514i	$0.463726\pi$
$103$	−8.49723	+	13.2219i	−0.837257	+	1.30280i	−0.950970	+	0.309283i	$0.899911\pi$
$104$	−0.249067	+	0.387555i	−0.0244230	+	0.0380029i
$105$	1.25860	−	2.25393i	0.122827	−	0.219961i
$106$	1.94305	−	6.61741i	0.188725	−	0.642739i
$107$	2.59085	+	18.0197i	0.250467	+	1.74203i	0.595421	+	0.803414i	$0.296985\pi$
$107$	2.59085	+	18.0197i	0.250467	+	1.74203i	−0.344954	+	0.938619i	$0.612106\pi$
$108$	−1.24836	+	5.04397i	−0.120124	+	0.485356i
$109$	−14.2659	+	6.51502i	−1.36643	+	0.624025i	−0.957471	−	0.288530i	$-0.906834\pi$
$109$	−14.2659	+	6.51502i	−1.36643	+	0.624025i	−0.408954	+	0.912555i	$0.634106\pi$
$110$	−0.901458	−	3.07008i	−0.0859506	−	0.292721i
$111$	4.60099	−	20.2260i	0.436707	−	1.91976i
$112$	−1.47527	−	0.212112i	−0.139400	−	0.0200427i
$113$	−6.60972	+	4.24781i	−0.621790	+	0.399600i	−0.813262	−	0.581898i	$-0.802310\pi$
$113$	−6.60972	+	4.24781i	−0.621790	+	0.399600i	0.191472	+	0.981498i	$0.438674\pi$
$114$	0.871344	+	4.19652i	0.0816088	+	0.393041i
$115$	−0.174199	+	4.79267i	−0.0162441	+	0.446918i
$116$		−	4.93546i		−	0.458246i
$117$	−0.769094	+	1.14830i	−0.0711028	+	0.106160i
$118$	0.856533	−	5.95732i	0.0788503	−	0.548416i
$119$	3.24150	+	1.48034i	0.297148	+	0.135703i
$120$	1.52798	−	0.815645i	0.139485	−	0.0744578i
$121$	−0.316531	−	0.693107i	−0.0287756	−	0.0630097i
$122$	4.01348	+	4.63180i	0.363363	+	0.419343i
$123$	−2.06098	−	5.68976i	−0.185832	−	0.513028i
$124$	6.37829	+	1.87283i	0.572787	+	0.168186i
$125$	0.654861	−	0.755750i	0.0585725	−	0.0675963i
$126$	−4.41297	−	0.720077i	−0.393139	−	0.0641496i
$127$	10.5887	+	6.80493i	0.939593	+	0.603840i	0.918279	−	0.395933i	$-0.129579\pi$
$127$	10.5887	+	6.80493i	0.939593	+	0.603840i	0.0213139	+	0.999773i	$0.493215\pi$
$128$	−0.755750	−	0.654861i	−0.0667995	−	0.0578821i
$129$	6.16819	+	0.499935i	0.543079	+	0.0440168i
$130$	0.455999	−	0.0655627i	0.0399937	−	0.00575023i
$131$	−2.50812	+	2.17330i	−0.219135	+	0.189882i	−0.757510	−	0.652824i	$-0.773584\pi$
$131$	−2.50812	+	2.17330i	−0.219135	+	0.189882i	0.538374	+	0.842706i	$0.319039\pi$
$132$	−4.46789	+	3.27903i	−0.388880	+	0.285403i
$133$	−3.53877	+	1.03908i	−0.306850	+	0.0900994i
$134$	−3.02438	+	6.62246i	−0.261266	+	0.572094i
$135$	4.62948	−	2.35964i	0.398442	−	0.203086i
$136$	1.29263	+	2.01137i	0.110842	+	0.172473i
$137$	−3.06689			−0.262022			−0.131011	−	0.991381i	$-0.541822\pi$
$137$	−3.06689			−0.262022			−0.131011	+	0.991381i	$0.541822\pi$
$138$	7.90764	−	2.54345i	0.673143	−	0.216513i
$139$	−3.86632			−0.327937			−0.163969	−	0.986466i	$-0.552430\pi$
$139$	−3.86632			−0.327937			−0.163969	+	0.986466i	$0.552430\pi$
$140$	0.805795	+	1.25384i	0.0681021	+	0.105969i
$141$	0.243234	+	3.92279i	0.0204840	+	0.330359i
$142$	−2.59165	+	5.67493i	−0.217487	+	0.476229i
$143$	−1.41435	+	0.415291i	−0.118274	+	0.0347283i
$144$	−2.22962	−	2.00719i	−0.185802	−	0.167266i
$145$	−3.72997	+	3.23204i	−0.309757	+	0.268406i
$146$	0.934353	−	0.134340i	0.0773276	−	0.0111180i
$147$	−0.668641	+	8.24968i	−0.0551485	+	0.680422i
$148$	9.05069	+	7.84247i	0.743962	+	0.644647i
$149$	−6.52444	−	4.19300i	−0.534503	−	0.343504i	0.245383	−	0.969426i	$-0.421086\pi$
$149$	−6.52444	−	4.19300i	−0.534503	−	0.343504i	−0.779886	+	0.625922i	$0.784723\pi$
$150$	−1.61704	−	0.620637i	−0.132031	−	0.0506748i
$151$	7.57909	−	8.74674i	0.616778	−	0.711800i	−0.358314	−	0.933601i	$-0.616648\pi$
$151$	7.57909	−	8.74674i	0.616778	−	0.711800i	0.975092	+	0.221802i	$0.0711937\pi$
$152$	−2.37430	−	0.697159i	−0.192582	−	0.0565470i
$153$	3.76286	+	6.10649i	0.304209	+	0.493680i
$154$	−3.12301	−	3.60414i	−0.251659	−	0.290430i
$155$	−2.76150	−	6.04684i	−0.221809	−	0.485694i
$156$	−0.375757	−	0.703922i	−0.0300847	−	0.0563589i
$157$	2.86966	+	1.31053i	0.229024	+	0.104592i	0.526622	−	0.850100i	$-0.323458\pi$
$157$	2.86966	+	1.31053i	0.229024	+	0.104592i	−0.297598	+	0.954691i	$0.596186\pi$
$158$	−1.19336	+	8.29999i	−0.0949384	+	0.660311i
$159$	8.36639	+	8.52643i	0.663498	+	0.676190i
$160$			1.00000i			0.0790569i
$161$	2.73122	+	6.60554i	0.215251	+	0.520590i
$162$	−6.57357	−	6.14721i	−0.516468	−	0.482970i
$163$	−17.9461	+	11.5333i	−1.40565	+	0.903356i	−0.999943	−	0.0106483i	$-0.996610\pi$
$163$	−17.9461	+	11.5333i	−1.40565	+	0.903356i	−0.405705	+	0.914004i	$0.632974\pi$
$164$	3.45829	+	0.497227i	0.270047	+	0.0388269i
$165$	5.40397	+	1.22929i	0.420699	+	0.0957004i
$166$	2.23447	+	7.60990i	0.173428	+	0.590643i
$167$	−22.4942	+	10.2727i	−1.74065	+	0.794929i	−0.749530	+	0.661971i	$0.769720\pi$
$167$	−22.4942	+	10.2727i	−1.74065	+	0.794929i	−0.991122	+	0.132958i	$0.957552\pi$
$168$	1.56656	−	2.05187i	0.120863	−	0.158305i
$169$	1.81989	+	12.6576i	0.139991	+	0.973662i
$170$	0.673599	−	2.29407i	0.0516627	−	0.175947i
$171$	−7.08201	−	2.22606i	−0.541575	−	0.170231i
$172$	−1.93165	+	3.00570i	−0.147287	+	0.229183i
$173$	−4.21538	+	6.55927i	−0.320490	+	0.498692i	−0.963696	−	0.267001i	$-0.913967\pi$
$173$	−4.21538	+	6.55927i	−0.320490	+	0.498692i	0.643207	+	0.765693i	$0.277604\pi$
$174$	7.46366	+	4.16774i	0.565818	+	0.315955i
$175$	0.419907	−	1.43007i	0.0317420	−	0.108103i
$176$	−0.455364	−	3.16712i	−0.0343243	−	0.238731i
$177$	8.28567	+	6.32594i	0.622789	+	0.475487i
$178$	−9.33844	+	4.26472i	−0.699945	+	0.319654i
$179$	0.471157	+	1.60461i	0.0352159	+	0.119934i	0.975225	−	0.221215i	$-0.0710021\pi$
$179$	0.471157	+	1.60461i	0.0352159	+	0.119934i	−0.940009	+	0.341149i	$0.889184\pi$
$180$	−0.0568398	+	2.99946i	−0.00423659	+	0.223567i
$181$	−5.01373	−	0.720865i	−0.372667	−	0.0535815i	−0.0465633	−	0.998915i	$-0.514827\pi$
$181$	−5.01373	−	0.720865i	−0.372667	−	0.0535815i	−0.326104	+	0.945334i	$0.605736\pi$
$182$	0.577630	−	0.371220i	0.0428168	−	0.0275167i
$183$	−10.3936	+	2.15808i	−0.768318	+	0.159530i
$184$	−0.854493	+	4.71909i	−0.0629941	+	0.347896i
$185$		−	11.9758i		−	0.880477i
$186$	−8.21833	+	8.06407i	−0.602598	+	0.591286i
$187$	−1.08874	+	7.57233i	−0.0796163	+	0.553744i
$188$	−2.06411	−	0.942650i	−0.150541	−	0.0687498i
$189$	4.81546	−	6.06546i	0.350274	−	0.441197i
$190$	1.02796	+	2.25092i	0.0745762	+	0.163299i
$191$	−1.59327	−	1.83873i	−0.115285	−	0.133046i	0.695174	−	0.718842i	$-0.255327\pi$
$191$	−1.59327	−	1.83873i	−0.115285	−	0.133046i	−0.810459	+	0.585796i	$0.800782\pi$
$192$	1.62851	−	0.589888i	0.117527	−	0.0425715i
$193$	10.8065	+	3.17308i	0.777870	+	0.228403i	0.646484	−	0.762928i	$-0.276239\pi$
$193$	10.8065	+	3.17308i	0.777870	+	0.228403i	0.131387	+	0.991331i	$0.458057\pi$
$194$	0.777914	−	0.897760i	0.0558510	−	0.0644554i
$195$	−0.285920	+	0.744949i	−0.0204751	+	0.0533469i
$196$	−4.01999	−	2.58349i	−0.287142	−	0.184535i
$197$	15.4010	+	13.3450i	1.09728	+	0.950795i	0.999015	−	0.0443657i	$-0.0141267\pi$
$197$	15.4010	+	13.3450i	1.09728	+	0.950795i	0.0982606	+	0.995161i	$0.468672\pi$
$198$	−1.18583	−	9.52555i	−0.0842731	−	0.676951i
$199$	1.63691	−	0.235352i	0.116037	−	0.0166836i	−0.0840515	−	0.996461i	$-0.526786\pi$
$199$	1.63691	−	0.235352i	0.116037	−	0.0166836i	0.200089	+	0.979778i	$0.435877\pi$
$200$	0.755750	−	0.654861i	0.0534396	−	0.0463056i
$201$	−7.46091	−	10.1660i	−0.526252	−	0.717051i
$202$	−10.7921	+	3.16884i	−0.759327	+	0.222959i
$203$	−3.05580	+	6.69128i	−0.214475	+	0.469636i
$204$	−4.13325	+	0.256283i	−0.289385	+	0.0179434i
$205$	−1.88892	−	2.93922i	−0.131928	−	0.205284i
$206$	15.7170			1.09505
$207$	−2.83125	+	14.1062i	−0.196786	+	0.980447i
$208$	0.460688			0.0319429
$209$	−4.28067	−	6.66085i	−0.296100	−	0.460741i
$210$	−2.57658	+	0.159761i	−0.177801	+	0.0110246i
$211$	1.39424	−	3.05296i	0.0959833	−	0.210174i	−0.855550	−	0.517721i	$-0.826781\pi$
$211$	1.39424	−	3.05296i	0.0959833	−	0.210174i	0.951533	+	0.307546i	$0.0995080\pi$
$212$	−6.61741	+	1.94305i	−0.454485	+	0.133449i
$213$	−6.39340	−	8.71141i	−0.438069	−	0.596896i
$214$	13.7584	−	11.9218i	0.940508	−	0.814955i
$215$	3.53652	−	0.508475i	0.241189	−	0.0346777i
$216$	4.91817	−	1.67678i	0.334639	−	0.114091i
$217$	−7.48784	−	6.48825i	−0.508307	−	0.440451i
$218$	13.1935	+	8.47895i	0.893577	+	0.574267i
$219$	−0.585857	+	1.52642i	−0.0395886	+	0.103146i
$220$	−2.09535	+	2.41817i	−0.141269	+	0.163033i
$221$	−1.05685	−	0.310319i	−0.0710913	−	0.0208743i
$222$	−19.5026	+	7.06437i	−1.30893	+	0.474130i
$223$	−8.85527	−	10.2195i	−0.592992	−	0.684350i	0.377354	−	0.926069i	$-0.376834\pi$
$223$	−8.85527	−	10.2195i	−0.592992	−	0.684350i	−0.970346	+	0.241719i	$0.922289\pi$
$224$	0.619153	+	1.35576i	0.0413689	+	0.0905853i
$225$	2.30406	−	1.92127i	0.153604	−	0.128085i
$226$	7.14697	+	3.26391i	0.475410	+	0.217112i
$227$	−1.94294	+	13.5134i	−0.128957	+	0.896917i	0.817922	+	0.575328i	$0.195126\pi$
$227$	−1.94294	+	13.5134i	−0.128957	+	0.896917i	−0.946880	+	0.321588i	$0.895783\pi$
$228$	3.05926	−	3.00183i	0.202604	−	0.198801i
$229$		−	1.73080i		−	0.114375i	−0.998363	−	0.0571873i	$-0.981787\pi$
$229$		−	1.73080i		−	0.114375i	0.998363	−	0.0571873i	$-0.0182132\pi$
$230$	4.12603	−	2.44457i	0.272062	−	0.161190i
$231$	8.08759	−	1.67926i	0.532125	−	0.110487i
$232$	−4.15197	+	2.66831i	−0.272590	+	0.175183i
$233$	14.8144	+	2.12999i	0.970525	+	0.139540i	0.609302	−	0.792939i	$-0.291450\pi$
$233$	14.8144	+	2.12999i	0.970525	+	0.139540i	0.361224	+	0.932479i	$0.382359\pi$
$234$	1.38182	+	0.0261854i	0.0903321	+	0.00171179i
$235$	0.639301	+	2.17726i	0.0417034	+	0.142029i
$236$	−5.47469	+	2.50021i	−0.356372	+	0.162750i
$237$	−11.5439	−	8.81357i	−0.749860	−	0.572503i
$238$	−0.507143	−	3.52726i	−0.0328732	−	0.228638i
$239$	−7.10618	+	24.2014i	−0.459661	+	1.56546i	0.325111	+	0.945676i	$0.394598\pi$
$239$	−7.10618	+	24.2014i	−0.459661	+	1.56546i	−0.784772	+	0.619785i	$0.787220\pi$
$240$	−1.51225	−	0.844448i	−0.0976155	−	0.0545089i
$241$	−0.659232	+	1.02579i	−0.0424649	+	0.0660766i	−0.861837	−	0.507185i	$-0.830686\pi$
$241$	−0.659232	+	1.02579i	−0.0424649	+	0.0660766i	0.819372	+	0.573262i	$0.194322\pi$
$242$	−0.411949	+	0.641005i	−0.0264811	+	0.0412054i
$243$	14.8472	−	4.74990i	0.952446	−	0.304706i
$244$	1.72667	−	5.88049i	0.110539	−	0.376460i
$245$	0.680062	+	4.72993i	0.0434476	+	0.302184i
$246$	−3.67228	+	4.80992i	−0.234136	+	0.306670i
$247$	1.03697	−	0.473569i	0.0659809	−	0.0301325i
$248$	−1.87283	−	6.37829i	−0.118925	−	0.405022i
$249$	−13.3950	−	3.04709i	−0.848873	−	0.193101i
$250$	−0.989821	−	0.142315i	−0.0626018	−	0.00900078i
$251$	5.36013	−	3.44475i	0.338328	−	0.217430i	−0.360433	−	0.932785i	$-0.617371\pi$
$251$	5.36013	−	3.44475i	0.338328	−	0.217430i	0.698762	+	0.715355i	$0.253735\pi$
$252$	1.78007	+	4.10173i	0.112134	+	0.258385i
$253$	−11.9545	+	9.62109i	−0.751571	+	0.604873i
$254$		−	12.5868i		−	0.789765i
$255$	2.90039	+	2.95587i	0.181629	+	0.185104i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−6.14023	−	2.80415i	−0.383017	−	0.174918i	0.214596	−	0.976703i	$-0.431157\pi$
$257$	−6.14023	−	2.80415i	−0.383017	−	0.174918i	−0.597613	+	0.801785i	$0.703884\pi$
$258$	−2.91420	−	5.45930i	−0.181430	−	0.339881i
$259$	−7.41485	−	16.2362i	−0.460736	−	1.00887i
$260$	−0.301686	−	0.348165i	−0.0187098	−	0.0215922i
$261$	−12.6053	+	7.76749i	−0.780251	+	0.480796i
$262$	3.18429	+	0.934991i	0.196726	+	0.0577639i
$263$	4.85550	−	5.60355i	0.299403	−	0.345530i	−0.586036	−	0.810285i	$-0.699312\pi$
$263$	4.85550	−	5.60355i	0.299403	−	0.345530i	0.885439	+	0.464755i	$0.153858\pi$
$264$	5.17402	+	1.98585i	0.318439	+	0.122220i
$265$	5.80194	+	3.72868i	0.356410	+	0.229051i
$266$	2.78733	+	2.41524i	0.170902	+	0.148088i
$267$	1.43649	−	17.7234i	0.0879118	−	1.08465i
$268$	7.20627	−	1.03611i	0.440193	−	0.0632902i
$269$	19.5675	−	16.9553i	1.19305	−	1.03379i	0.194450	−	0.980912i	$-0.437708\pi$
$269$	19.5675	−	16.9553i	1.19305	−	1.03379i	0.998601	−	0.0528727i	$-0.0168378\pi$
$270$	−4.48794	−	2.61885i	−0.273128	−	0.159378i
$271$	−5.34510	+	1.56946i	−0.324691	+	0.0953380i	−0.440016	−	0.897990i	$-0.645027\pi$
$271$	−5.34510	+	1.56946i	−0.324691	+	0.0953380i	0.115325	+	0.993328i	$0.463209\pi$
$272$	0.993222	−	2.17485i	0.0602230	−	0.131870i
$273$	0.0736001	+	1.18700i	0.00445448	+	0.0718404i
$274$	1.65809	+	2.58003i	0.100169	+	0.155865i
$275$	3.19969			0.192949
$276$	−6.41489	−	5.27724i	−0.386131	−	0.317652i
$277$	17.1356			1.02958			0.514790	−	0.857316i	$-0.327870\pi$
$277$	17.1356			1.02958			0.514790	+	0.857316i	$0.327870\pi$
$278$	2.09029	+	3.25256i	0.125367	+	0.195076i
$279$	−5.25496	−	19.2379i	−0.314606	−	1.15174i
$280$	0.619153	−	1.35576i	0.0370015	−	0.0810219i
$281$	−7.96339	+	2.33826i	−0.475056	+	0.139489i	−0.510491	−	0.859883i	$-0.670536\pi$
$281$	−7.96339	+	2.33826i	−0.475056	+	0.139489i	0.0354351	+	0.999372i	$0.488718\pi$
$282$	3.16856	−	2.32544i	0.188685	−	0.138478i
$283$	−17.0131	+	14.7419i	−1.01132	+	0.876317i	−0.992344	−	0.123503i	$-0.960587\pi$
$283$	−17.0131	+	14.7419i	−1.01132	+	0.876317i	−0.0189799	+	0.999820i	$0.506042\pi$
$284$	6.17520	−	0.887860i	0.366431	−	0.0526848i
$285$	−4.27202	−	0.346249i	−0.253053	−	0.0205100i
$286$	1.11402	+	0.965304i	0.0658734	+	0.0570796i
$287$	−4.38074	−	2.81533i	−0.258587	−	0.166184i
$288$	−0.483129	+	2.96084i	−0.0284687	+	0.174469i
$289$	7.38913	−	8.52752i	0.434655	−	0.501619i
$290$	4.73554	+	1.39048i	0.278080	+	0.0816517i
$291$	0.700732	+	1.93451i	0.0410777	+	0.113403i
$292$	−0.618163	−	0.713398i	−0.0361753	−	0.0417485i
$293$	−12.6712	−	27.7461i	−0.740261	−	1.62095i	−0.783125	−	0.621865i	$-0.786375\pi$
$293$	−12.6712	−	27.7461i	−0.740261	−	1.62095i	0.0428636	−	0.999081i	$-0.486352\pi$
$294$	7.30157	−	3.89762i	0.425836	−	0.227314i
$295$	5.47469	+	2.50021i	0.318749	+	0.145568i
$296$	1.70433	−	11.8539i	0.0990623	−	0.688993i
$297$	15.4064	+	6.25056i	0.893970	+	0.362695i
$298$			7.75562i			0.449271i
$299$	−1.12618	−	1.90081i	−0.0651288	−	0.109927i
$300$	0.352123	+	1.69588i	0.0203299	+	0.0979117i
$301$	4.47983	−	2.87901i	0.258213	−	0.165944i
$302$	−11.4558	−	1.64709i	−0.659207	−	0.0947796i
$303$	4.32126	−	18.9962i	0.248250	−	1.09131i
$304$	0.697159	+	2.37430i	0.0399848	+	0.136176i
$305$	−5.57490	+	2.54597i	−0.319218	+	0.145782i
$306$	3.10275	−	6.46694i	0.177372	−	0.369690i
$307$	0.215682	+	1.50010i	0.0123096	+	0.0856151i	0.995050	−	0.0993741i	$-0.0316841\pi$
$307$	0.215682	+	1.50010i	0.0123096	+	0.0856151i	−0.982741	+	0.184989i	$0.940775\pi$
$308$	−1.34357	+	4.57579i	−0.0765572	+	0.260730i
$309$	−13.2722	+	23.7680i	−0.755027	+	1.35211i
$310$	−3.59394	+	5.59229i	−0.204122	+	0.317620i
$311$	−0.504859	+	0.785576i	−0.0286279	+	0.0445459i	−0.855273	−	0.518178i	$-0.826610\pi$
$311$	−0.504859	+	0.785576i	−0.0286279	+	0.0445459i	0.826645	+	0.562724i	$0.190247\pi$
$312$	−0.389027	+	0.696676i	−0.0220243	+	0.0394415i
$313$	7.96321	−	27.1202i	0.450107	−	1.53292i	−0.352148	−	0.935944i	$-0.614549\pi$
$313$	7.96321	−	27.1202i	0.450107	−	1.53292i	0.802256	−	0.596981i	$-0.203633\pi$
$314$	−0.448967	−	3.12263i	−0.0253367	−	0.176220i
$315$	1.93419	−	4.03135i	0.108979	−	0.227141i
$316$	7.62757	−	3.48339i	0.429084	−	0.195956i
$317$	−8.12969	−	27.6872i	−0.456609	−	1.55507i	−0.790504	−	0.612457i	$-0.790181\pi$
$317$	−8.12969	−	27.6872i	−0.456609	−	1.55507i	0.333895	−	0.942610i	$-0.391637\pi$
$318$	2.64968	−	11.6480i	0.148587	−	0.653187i
$319$	−15.6312	−	2.24743i	−0.875180	−	0.125832i
$320$	0.841254	−	0.540641i	0.0470275	−	0.0302227i
$321$	6.41042	+	30.8736i	0.357795	+	1.72319i
$322$	4.08033	−	5.86888i	0.227388	−	0.327060i
$323$		−	5.91642i		−	0.329198i
$324$	−1.61742	+	8.85347i	−0.0898567	+	0.491860i
$325$	−0.0655627	+	0.455999i	−0.00363676	+	0.0252943i
$326$	19.4048	+	8.86188i	1.07473	+	0.490814i
$327$	−23.9635	+	12.7919i	−1.32519	+	0.707392i
$328$	−1.45140	−	3.17812i	−0.0801401	−	0.175482i
$329$	2.21479	+	2.55601i	0.122105	+	0.140917i
$330$	−1.88746	−	5.21072i	−0.103901	−	0.286841i
$331$	26.6680	+	7.83042i	1.46580	+	0.430399i	0.914733	−	0.404059i	$-0.132401\pi$
$331$	26.6680	+	7.83042i	1.46580	+	0.430399i	0.551071	+	0.834458i	$0.314219\pi$
$332$	5.19381	−	5.99398i	0.285048	−	0.328962i
$333$	5.78585	−	35.4584i	0.317063	−	1.94311i
$334$	20.8033	+	13.3694i	1.13830	+	0.731543i
$335$	−5.50214	−	4.76763i	−0.300614	−	0.260484i
$336$	−2.57309	−	0.208550i	−0.140373	−	0.0113773i
$337$	27.1460	−	3.90301i	1.47874	−	0.212610i	0.644750	−	0.764393i	$-0.276961\pi$
$337$	27.1460	−	3.90301i	1.47874	−	0.212610i	0.833988	+	0.551783i	$0.186052\pi$
$338$	9.66435	−	8.37421i	0.525671	−	0.455497i
$339$	−10.9711	+	8.05182i	−0.595869	+	0.437315i
$340$	−2.29407	+	0.673599i	−0.124413	+	0.0365310i
$341$	8.83594	−	19.3480i	0.478493	−	1.04775i
$342$	1.95615	+	7.16126i	0.105776	+	0.387237i
$343$	9.49112	+	14.7685i	0.512472	+	0.797423i
$344$	3.57289			0.192637
$345$	0.212585	+	8.30390i	0.0114452	+	0.447067i
$346$	7.79701			0.419170
$347$	6.63793	+	10.3288i	0.356343	+	0.554480i	0.972429	−	0.233198i	$-0.0749192\pi$
$347$	6.63793	+	10.3288i	0.356343	+	0.554480i	−0.616086	+	0.787679i	$0.711283\pi$
$348$	−0.529033	−	8.53208i	−0.0283592	−	0.457367i
$349$	5.44380	−	11.9203i	0.291400	−	0.638076i	−0.706148	−	0.708064i	$-0.749569\pi$
$349$	5.44380	−	11.9203i	0.291400	−	0.638076i	0.997548	+	0.0699878i	$0.0222960\pi$
$350$	−1.43007	+	0.419907i	−0.0764405	+	0.0224450i
$351$	−1.20647	+	2.06754i	−0.0643966	+	0.110357i
$352$	−2.41817	+	2.09535i	−0.128889	+	0.111683i
$353$	22.5811	−	3.24668i	1.20187	−	0.172803i	0.487851	−	0.872927i	$-0.337781\pi$
$353$	22.5811	−	3.24668i	1.20187	−	0.172803i	0.714022	+	0.700124i	$0.246872\pi$
$354$	0.842148	−	10.3904i	0.0447597	−	0.552244i
$355$	−4.71490	−	4.08548i	−0.250241	−	0.216835i
$356$	8.63645	+	5.55031i	0.457731	+	0.294166i
$357$	5.76236	+	2.21166i	0.304976	+	0.117053i
$358$	1.09516	−	1.26388i	0.0578810	−	0.0667982i
$359$	−17.0544	−	5.00762i	−0.900096	−	0.264292i	−0.201230	−	0.979544i	$-0.564494\pi$
$359$	−17.0544	−	5.00762i	−0.900096	−	0.264292i	−0.698867	+	0.715252i	$0.746312\pi$
$360$	2.55404	−	1.57381i	0.134610	−	0.0829473i
$361$	−8.43241	−	9.73152i	−0.443811	−	0.512185i
$362$	2.10419	+	4.60754i	0.110594	+	0.242167i
$363$	−0.621492	−	1.16427i	−0.0326199	−	0.0611081i
$364$	−0.624580	−	0.285236i	−0.0327369	−	0.0149504i
$365$	−0.134340	+	0.934353i	−0.00703166	+	0.0489063i
$366$	7.43470	+	7.57693i	0.388618	+	0.396052i
$367$		−	20.4214i		−	1.06599i	−0.846119	−	0.532994i	$-0.821067\pi$
$367$		−	20.4214i		−	1.06599i	0.846119	−	0.532994i	$-0.178933\pi$
$368$	4.43193	−	1.83249i	0.231030	−	0.0955251i
$369$	−4.17277	−	9.61514i	−0.217226	−	0.500544i
$370$	−10.0747	+	6.47460i	−0.523757	+	0.336598i
$371$	10.1746	+	1.46289i	0.528241	+	0.0759496i
$372$	11.2271	+	2.55394i	0.582098	+	0.132415i
$373$	−7.45040	−	25.3737i	−0.385767	−	1.31380i	−0.892246	−	0.451549i	$-0.850871\pi$
$373$	−7.45040	−	25.3737i	−0.385767	−	1.31380i	0.506479	−	0.862252i	$-0.330947\pi$
$374$	6.95886	−	3.17801i	0.359834	−	0.164331i
$375$	1.05107	−	1.37668i	0.0542770	−	0.0710916i
$376$	0.322937	+	2.24608i	0.0166542	+	0.115833i
$377$	0.640576	−	2.18160i	0.0329914	−	0.112358i
$378$	−7.70603	−	0.771792i	−0.396355	−	0.0396967i
$379$	−1.53770	+	2.39271i	−0.0789864	+	0.122905i	−0.878499	−	0.477744i	$-0.841455\pi$
$379$	−1.53770	+	2.39271i	−0.0789864	+	0.122905i	0.799513	+	0.600649i	$0.205091\pi$
$380$	1.33784	−	2.08172i	0.0686296	−	0.106790i
$381$	19.0344	+	10.6289i	0.975162	+	0.544535i
$382$	−0.685453	+	2.33444i	−0.0350708	+	0.119440i
$383$	2.60995	+	18.1526i	0.133362	+	0.927556i	0.941128	+	0.338051i	$0.109768\pi$
$383$	2.60995	+	18.1526i	0.133362	+	0.927556i	−0.807765	+	0.589504i	$0.799323\pi$
$384$	−1.37668	−	1.05107i	−0.0702535	−	0.0536371i
$385$	4.33800	−	1.98110i	0.221085	−	0.100966i
$386$	−3.17308	−	10.8065i	−0.161506	−	0.550037i
$387$	10.7167	+	0.203082i	0.544762	+	0.0103232i
$388$	−1.17582	−	0.169057i	−0.0596930	−	0.00858256i
$389$	−5.15795	+	3.31482i	−0.261519	+	0.168068i	−0.664829	−	0.746995i	$-0.731496\pi$
$389$	−5.15795	+	3.31482i	−0.261519	+	0.168068i	0.403311	+	0.915063i	$0.367859\pi$
$390$	0.781271	−	0.162219i	0.0395612	−	0.00821427i
$391$	−11.4015	+	1.21851i	−0.576599	+	0.0616228i
$392$			4.77857i			0.241354i
$393$	−4.10291	+	4.02589i	−0.206964	+	0.203080i
$394$	2.90016	−	20.1710i	0.146108	−	1.01620i
$395$	−7.62757	−	3.48339i	−0.383785	−	0.175269i
$396$	−7.37230	+	6.14748i	−0.370472	+	0.308923i
$397$	4.31403	+	9.44640i	0.216515	+	0.474101i	0.986459	−	0.164011i	$-0.0524431\pi$
$397$	4.31403	+	9.44640i	0.216515	+	0.474101i	−0.769944	+	0.638112i	$0.779716\pi$
$398$	−1.08297	−	1.24981i	−0.0542843	−	0.0626474i
$399$	−6.00620	+	2.17561i	−0.300686	+	0.108917i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	−10.4864	+	12.1020i	−0.523668	+	0.604345i	−0.954545	−	0.298066i	$-0.903659\pi$
$401$	−10.4864	+	12.1020i	−0.523668	+	0.604345i	0.430878	+	0.902410i	$0.358204\pi$
$402$	−4.51847	+	11.7726i	−0.225361	+	0.587166i
$403$	2.57630	+	1.65569i	0.128335	+	0.0824756i
$404$	8.50043	+	7.36566i	0.422912	+	0.366455i
$405$	7.75019	−	4.57543i	0.385110	−	0.227355i
$406$	7.28115	−	1.04687i	0.361358	−	0.0519554i
$407$	28.9594	−	25.0935i	1.43547	−	1.24384i
$408$	2.45020	+	3.33855i	0.121303	+	0.165283i
$409$	22.0048	−	6.46120i	1.08807	−	0.319486i	0.311967	−	0.950093i	$-0.399012\pi$
$409$	22.0048	−	6.46120i	1.08807	−	0.319486i	0.776102	+	0.630607i	$0.217194\pi$
$410$	−1.45140	+	3.17812i	−0.0716795	+	0.156956i
$411$	−5.30182	+	0.328741i	−0.261520	+	0.0162156i
$412$	−8.49723	−	13.2219i	−0.418628	−	0.651398i
$413$	8.97036			0.441403
$414$	13.3976	−	5.24457i	0.658454	−	0.257757i
$415$	−7.93117			−0.389326
$416$	−0.249067	−	0.387555i	−0.0122115	−	0.0190015i
$417$	−6.68383	+	0.414433i	−0.327309	+	0.0202949i
$418$	−3.28916	+	7.20226i	−0.160878	+	0.352274i
$419$	−29.0624	+	8.53348i	−1.41979	+	0.416888i	−0.899432	−	0.437061i	$-0.856019\pi$
$419$	−29.0624	+	8.53348i	−1.41979	+	0.416888i	−0.520357	+	0.853949i	$0.674201\pi$
$420$	1.52740	+	2.08118i	0.0745296	+	0.101551i
$421$	29.3756	−	25.4541i	1.43168	−	1.24056i	0.505850	−	0.862621i	$-0.331179\pi$
$421$	29.3756	−	25.4541i	1.43168	−	1.24056i	0.925831	−	0.377938i	$-0.123367\pi$
$422$	−3.32209	+	0.477645i	−0.161717	+	0.0232514i
$423$	0.840971	+	6.75538i	0.0408894	+	0.328458i
$424$	5.21223	+	4.51643i	0.253128	+	0.219337i
$425$	2.01137	+	1.29263i	0.0975656	+	0.0627016i
$426$	−3.87197	+	10.0882i	−0.187598	+	0.488776i
$427$	−5.98186	+	6.90344i	−0.289483	+	0.334081i
$428$	−17.4676	−	5.12895i	−0.844328	−	0.247917i
$429$	−2.40051	+	0.869530i	−0.115898	+	0.0419813i
$430$	−2.33974	−	2.70021i	−0.112832	−	0.130216i
$431$	−14.9985	−	32.8420i	−0.722450	−	1.58195i	−0.810438	−	0.585824i	$-0.800771\pi$
$431$	−14.9985	−	32.8420i	−0.722450	−	1.58195i	0.0879879	−	0.996122i	$-0.471956\pi$
$432$	−4.06956	−	3.23089i	−0.195797	−	0.155446i
$433$	−10.7052	−	4.88890i	−0.514459	−	0.234945i	0.141230	−	0.989977i	$-0.454894\pi$
$433$	−10.7052	−	4.88890i	−0.514459	−	0.234945i	−0.655689	+	0.755031i	$0.727622\pi$
$434$	−1.41003	+	9.80698i	−0.0676836	+	0.470750i
$435$	−6.10167	+	5.98714i	−0.292553	+	0.287061i
$436$		−	15.6832i		−	0.751087i
$437$	8.09219	−	8.68064i	0.387102	−	0.415251i
$438$	1.60084	−	0.332391i	0.0764913	−	0.0158822i
$439$	−15.1935	+	9.76428i	−0.725147	+	0.466024i	−0.850424	−	0.526098i	$-0.823654\pi$
$439$	−15.1935	+	9.76428i	−0.725147	+	0.466024i	0.125277	+	0.992122i	$0.460018\pi$
$440$	3.16712	+	0.455364i	0.150987	+	0.0217086i
$441$	−0.271613	+	14.3331i	−0.0129340	+	0.682531i
$442$	0.310319	+	1.05685i	0.0147604	+	0.0502692i
$443$	4.43826	−	2.02689i	0.210868	−	0.0963003i	−0.307181	−	0.951651i	$-0.599386\pi$
$443$	4.43826	−	2.02689i	0.210868	−	0.0963003i	0.518049	+	0.855351i	$0.326658\pi$
$444$	16.4869	+	12.5874i	0.782431	+	0.597370i
$445$	−1.46103	−	10.1617i	−0.0692594	−	0.481710i
$446$	−3.80969	+	12.9746i	−0.180394	+	0.614366i
$447$	−11.7284	−	6.54922i	−0.554737	−	0.309767i
$448$	0.805795	−	1.25384i	0.0380703	−	0.0592385i
$449$	19.1070	−	29.7311i	0.901715	−	1.40310i	−0.0134037	−	0.999910i	$-0.504267\pi$
$449$	19.1070	−	29.7311i	0.901715	−	1.40310i	0.915118	−	0.403185i	$-0.132097\pi$
$450$	−2.86195	−	0.899583i	−0.134914	−	0.0424068i
$451$	3.14956	−	10.7264i	0.148307	−	0.505087i
$452$	−1.11817	−	7.77702i	−0.0525941	−	0.365800i
$453$	12.1646	−	15.9332i	0.571545	−	0.748605i
$454$	12.4186	−	5.67140i	0.582835	−	0.266172i
$455$	0.193446	+	0.658816i	0.00906889	+	0.0308858i
$456$	−4.17926	−	0.950697i	−0.195712	−	0.0445205i
$457$	−22.0690	−	3.17305i	−1.03235	−	0.148429i	−0.394741	−	0.918792i	$-0.629166\pi$
$457$	−22.0690	−	3.17305i	−1.03235	−	0.148429i	−0.637605	+	0.770364i	$0.720075\pi$
$458$	−1.45604	+	0.935742i	−0.0680365	+	0.0437244i
$459$	7.15953	+	10.1531i	0.334178	+	0.473908i
$460$	−4.28720	−	2.14940i	−0.199892	−	0.100216i
$461$			7.65706i			0.356625i	0.983974	+	0.178312i	$0.0570637\pi$
$461$			7.65706i			0.356625i	−0.983974	+	0.178312i	$0.942936\pi$
$462$	−5.78517	−	5.89584i	−0.269151	−	0.274299i
$463$	−4.90050	+	34.0837i	−0.227746	+	1.58401i	0.479826	+	0.877364i	$0.340700\pi$
$463$	−4.90050	+	34.0837i	−0.227746	+	1.58401i	−0.707572	+	0.706642i	$0.750209\pi$
$464$	4.48945	+	2.05026i	0.208417	+	0.0951811i
$465$	−5.42205	−	10.1573i	−0.251441	−	0.471036i
$466$	−6.21742	−	13.6143i	−0.288016	−	0.630668i
$467$	15.2617	+	17.6130i	0.706228	+	0.815030i	0.989580	−	0.143986i	$-0.0459919\pi$
$467$	15.2617	+	17.6130i	0.706228	+	0.815030i	−0.283352	+	0.959016i	$0.591446\pi$
$468$	−0.725037	−	1.17661i	−0.0335149	−	0.0543890i
$469$	−10.4115	−	3.05708i	−0.480757	−	0.141163i
$470$	1.48599	−	1.71493i	0.0685438	−	0.0791038i
$471$	5.10134	+	1.95795i	0.235057	+	0.0902176i
$472$	5.06315	+	3.25389i	0.233050	+	0.149772i
$473$	8.63983	+	7.48646i	0.397260	+	0.344228i
$474$	−1.17332	+	14.4764i	−0.0538922	+	0.664921i
$475$	−2.44935	+	0.352164i	−0.112384	+	0.0161584i
$476$	−2.69314	+	2.33361i	−0.123440	+	0.106961i
$477$	15.3772	+	13.8431i	0.704073	+	0.633833i
$478$	24.2014	−	7.10618i	1.10695	−	0.325029i
$479$	2.83658	−	6.21125i	0.129607	−	0.283799i	−0.833692	−	0.552229i	$-0.813777\pi$
$479$	2.83658	−	6.21125i	0.129607	−	0.283799i	0.963299	+	0.268430i	$0.0865047\pi$
$480$	0.107190	+	1.72873i	0.00489255	+	0.0789054i
$481$	2.98277	+	4.64128i	0.136003	+	0.211624i
$482$	1.21935			0.0555400
$483$	5.42960	+	11.1264i	0.247055	+	0.506271i
$484$	0.761964			0.0346347
$485$	0.642231	+	0.999331i	0.0291622	+	0.0453773i
$486$	−12.0229	−	9.92225i	−0.545368	−	0.450082i
$487$	5.04845	−	11.0546i	0.228767	−	0.500930i	−0.760086	−	0.649822i	$-0.774843\pi$
$487$	5.04845	−	11.0546i	0.228767	−	0.500930i	0.988853	+	0.148892i	$0.0475707\pi$
$488$	−5.88049	+	1.72667i	−0.266197	+	0.0781626i
$489$	−29.7878	+	21.8616i	−1.34705	+	0.988615i
$490$	3.61141	−	3.12930i	0.163147	−	0.141367i
$491$	−30.4523	+	4.37837i	−1.37429	+	0.197593i	−0.789580	−	0.613648i	$-0.789701\pi$
$491$	−30.4523	+	4.37837i	−1.37429	+	0.197593i	−0.584712	+	0.811241i	$0.698792\pi$
$492$	6.03175	+	0.488876i	0.271932	+	0.0220402i
$493$	−8.91804	−	7.72753i	−0.401648	−	0.348030i
$494$	−0.959021	−	0.616325i	−0.0431484	−	0.0277298i
$495$	9.47379	+	1.54586i	0.425815	+	0.0694815i
$496$	−4.35323	+	5.02389i	−0.195466	+	0.225579i
$497$	−8.92179	−	2.61968i	−0.400197	−	0.117508i
$498$	4.67850	+	12.9160i	0.209649	+	0.578778i
$499$	14.0785	+	16.2475i	0.630241	+	0.727337i	0.977618	−	0.210389i	$-0.0674730\pi$
$499$	14.0785	+	16.2475i	0.630241	+	0.727337i	−0.347377	+	0.937726i	$0.612928\pi$
$500$	0.415415	+	0.909632i	0.0185779	+	0.0406800i
$501$	−37.7852	+	20.1700i	−1.68812	+	0.901128i
$502$	−5.79581	−	2.64686i	−0.258680	−	0.118135i
$503$	−3.04247	+	21.1609i	−0.135657	+	0.943516i	0.802338	+	0.596869i	$0.203589\pi$
$503$	−3.04247	+	21.1609i	−0.135657	+	0.943516i	−0.937996	+	0.346647i	$0.887320\pi$
$504$	2.48822	−	3.71505i	0.110834	−	0.165481i
$505$		−	11.2477i		−	0.500515i
$506$	14.5569	+	4.85519i	0.647131	+	0.215840i
$507$	4.50287	+	21.6865i	0.199980	+	0.963132i
$508$	−10.5887	+	6.80493i	−0.469797	+	0.301920i
$509$	−0.606624	−	0.0872193i	−0.0268881	−	0.00386593i	0.128858	−	0.991663i	$-0.458869\pi$
$509$	−0.606624	−	0.0872193i	−0.0268881	−	0.00386593i	−0.155746	+	0.987797i	$0.549778\pi$
$510$	0.918569	−	4.03803i	0.0406749	−	0.178807i
$511$	0.396376	+	1.34993i	0.0175346	+	0.0597175i
$512$	0.909632	−	0.415415i	0.0402004	−	0.0183589i
$513$	−12.4815	−	3.08913i	−0.551072	−	0.136388i
$514$	0.960659	+	6.68153i	0.0423728	+	0.294710i
$515$	−4.42798	+	15.0803i	−0.195120	+	0.664518i
$516$	−3.01712	+	5.40310i	−0.132821	+	0.237858i
$517$	−3.92541	+	6.10806i	−0.172639	+	0.268632i
$518$	−9.65003	+	15.0157i	−0.423998	+	0.659754i
$519$	−6.58417	+	11.7911i	−0.289013	+	0.517570i
$520$	−0.129791	+	0.442027i	−0.00569170	+	0.0193842i
$521$	3.27469	+	22.7760i	0.143467	+	0.997834i	0.926618	+	0.376003i	$0.122702\pi$
$521$	3.27469	+	22.7760i	0.143467	+	0.997834i	−0.783152	+	0.621831i	$0.786389\pi$
$522$	13.3494	+	6.40486i	0.584287	+	0.280333i
$523$	−25.8751	+	11.8168i	−1.13144	+	0.516711i	−0.891023	−	0.453958i	$-0.850011\pi$
$523$	−25.8751	+	11.8168i	−1.13144	+	0.516711i	−0.240417	+	0.970670i	$0.577284\pi$
$524$	−0.934991	−	3.18429i	−0.0408453	−	0.139106i
$525$	0.572616	−	2.51722i	0.0249910	−	0.109860i
$526$	−7.33909	−	1.05520i	−0.320000	−	0.0460090i
$527$	13.3707	−	8.59282i	0.582436	−	0.374309i
$528$	−1.12669	−	5.42630i	−0.0490327	−	0.236149i
$529$	−18.3950	−	13.8066i	−0.799784	−	0.600287i
$530$		−	6.89677i		−	0.299577i
$531$	15.0018	+	10.0477i	0.651022	+	0.436033i
$532$	0.524881	−	3.65063i	0.0227565	−	0.158275i
$533$	1.46412	+	0.668642i	0.0634181	+	0.0289621i
$534$	−15.6865	+	8.37355i	−0.678821	+	0.362359i
$535$	7.56264	+	16.5599i	0.326962	+	0.715946i
$536$	−4.76763	−	5.50214i	−0.205930	−	0.237656i
$537$	0.986502	+	2.72344i	0.0425707	+	0.117525i
$538$	−24.8427	−	7.29448i	−1.07105	−	0.314487i
$539$	−10.0128	+	11.5554i	−0.431282	+	0.497726i
$540$	0.223253	+	5.19135i	0.00960726	+	0.223400i
$541$	7.38317	+	4.74487i	0.317427	+	0.203998i	0.689646	−	0.724147i	$-0.257766\pi$
$541$	7.38317	+	4.74487i	0.317427	+	0.203998i	−0.372218	+	0.928145i	$0.621403\pi$
$542$	4.21009	+	3.64807i	0.180839	+	0.156698i
$543$	−8.74465	−	0.708758i	−0.375269	−	0.0304157i
$544$	−2.36658	+	0.340263i	−0.101466	+	0.0145886i
$545$	−11.8525	+	10.2703i	−0.507707	+	0.439930i
$546$	0.958775	−	0.703656i	0.0410318	−	0.0301137i
$547$	−15.7179	+	4.61518i	−0.672048	+	0.197331i	−0.599915	−	0.800064i	$-0.704799\pi$
$547$	−15.7179	+	4.61518i	−0.672048	+	0.197331i	−0.0721330	+	0.997395i	$0.522981\pi$
$548$	1.27403	−	2.78974i	0.0544239	−	0.119172i
$549$	−17.7364	+	4.84483i	−0.756973	+	0.206772i
$550$	−1.72988	−	2.69175i	−0.0737625	−	0.114777i
$551$	12.2130			0.520291
$552$	−0.971347	+	8.24964i	−0.0413433	+	0.351128i
$553$	−12.4979			−0.531464
$554$	−9.26422	−	14.4154i	−0.393599	−	0.612452i
$555$	−1.28369	−	20.7029i	−0.0544896	−	0.878790i
$556$	1.60613	−	3.51693i	0.0681151	−	0.149151i
$557$	−2.42774	+	0.712847i	−0.102866	+	0.0302043i	−0.332761	−	0.943011i	$-0.607980\pi$
$557$	−2.42774	+	0.712847i	−0.102866	+	0.0302043i	0.229894	+	0.973216i	$0.426162\pi$
$558$	−13.3429	+	14.8215i	−0.564850	+	0.627446i
$559$	−1.24395	+	1.07789i	−0.0526136	+	0.0455899i
$560$	−1.47527	+	0.212112i	−0.0623417	+	0.00896339i
$561$	−1.07045	+	13.2072i	−0.0451945	+	0.557609i
$562$	6.27241	+	5.43507i	0.264586	+	0.229265i
$563$	25.7404	+	16.5424i	1.08483	+	0.697178i	0.955668	−	0.294446i	$-0.0951350\pi$
$563$	25.7404	+	16.5424i	1.08483	+	0.697178i	0.129162	+	0.991624i	$0.458771\pi$
$564$	−3.66934	−	1.40833i	−0.154507	−	0.0593016i
$565$	−5.14524	+	5.93792i	−0.216462	+	0.249810i
$566$	21.5997	+	6.34224i	0.907903	+	0.266584i
$567$	7.67448	−	11.0017i	0.322298	−	0.462029i
$568$	−4.08548	−	4.71490i	−0.171423	−	0.197833i
$569$	−1.40975	−	3.08691i	−0.0590997	−	0.129410i	0.877778	−	0.479068i	$-0.159025\pi$
$569$	−1.40975	−	3.08691i	−0.0590997	−	0.129410i	−0.936878	+	0.349658i	$0.886298\pi$
$570$	2.01835	+	3.78105i	0.0845392	+	0.158371i
$571$	−7.57671	−	3.46017i	−0.317075	−	0.144803i	0.250519	−	0.968112i	$-0.419399\pi$
$571$	−7.57671	−	3.46017i	−0.317075	−	0.144803i	−0.567595	+	0.823308i	$0.692126\pi$
$572$	0.209781	−	1.45906i	0.00877136	−	0.0610062i
$573$	−2.95143	−	3.00789i	−0.123298	−	0.125656i
$574$			5.20739i			0.217352i
$575$	1.18311	+	4.64761i	0.0493390	+	0.193819i
$576$	2.75202	−	1.19432i	0.114667	−	0.0497633i
$577$	31.2127	−	20.0592i	1.29940	−	0.835075i	0.306255	−	0.951950i	$-0.400924\pi$
$577$	31.2127	−	20.0592i	1.29940	−	0.835075i	0.993147	+	0.116875i	$0.0372876\pi$
$578$	−11.1687	−	1.60581i	−0.464555	−	0.0667930i
$579$	19.0217	+	4.32705i	0.790514	+	0.179826i
$580$	−1.39048	−	4.73554i	−0.0577365	−	0.196632i
$581$	−10.7527	+	4.91061i	−0.446099	+	0.203726i
$582$	1.24857	−	1.63537i	0.0517550	−	0.0677883i
$583$	3.14054	+	21.8429i	0.130068	+	0.904642i
$584$	−0.265945	+	0.905724i	−0.0110049	+	0.0374791i
$585$	−0.414427	+	1.31846i	−0.0171344	+	0.0545118i
$586$	−16.4909	+	25.6604i	−0.681234	+	1.06002i
$587$	22.7267	−	35.3634i	0.938030	−	1.45960i	0.0505680	−	0.998721i	$-0.483897\pi$
$587$	22.7267	−	35.3634i	0.938030	−	1.45960i	0.887462	−	0.460882i	$-0.152467\pi$
$588$	−7.22641	−	4.03526i	−0.298012	−	0.166411i
$589$	−4.63441	+	15.7833i	−0.190957	+	0.650341i
$590$	−0.856533	−	5.95732i	−0.0352629	−	0.245259i
$591$	28.0546	+	21.4191i	1.15401	+	0.881066i
$592$	−10.8936	+	4.97492i	−0.447722	+	0.204468i
$593$	−7.08148	−	24.1173i	−0.290801	−	0.990379i	−0.967237	−	0.253876i	$-0.918294\pi$
$593$	−7.08148	−	24.1173i	−0.290801	−	0.990379i	0.676435	−	0.736502i	$-0.263524\pi$
$594$	−3.07102	−	16.3400i	−0.126006	−	0.670439i
$595$	3.52726	+	0.507143i	0.144603	+	0.0207908i
$596$	6.52444	−	4.19300i	0.267251	−	0.171752i
$597$	2.80454	−	0.582320i	0.114782	−	0.0238328i
$598$	−0.990203	+	1.97506i	−0.0404924	+	0.0807662i
$599$		−	35.7148i		−	1.45927i	−0.683838	−	0.729634i	$-0.739691\pi$
$599$		−	35.7148i		−	1.45927i	0.683838	−	0.729634i	$-0.260309\pi$
$600$	1.23629	−	1.21309i	0.0504714	−	0.0495241i
$601$	−1.44415	+	10.0443i	−0.0589081	+	0.409715i	0.938936	+	0.344091i	$0.111813\pi$
$601$	−1.44415	+	10.0443i	−0.0589081	+	0.409715i	−0.997844	+	0.0656240i	$0.979096\pi$
$602$	−4.84396	−	2.21216i	−0.197425	−	0.0901611i
$603$	−13.9876	−	16.7745i	−0.569619	−	0.683109i
$604$	4.80784	+	10.5277i	0.195628	+	0.428367i
$605$	−0.498981	−	0.575854i	−0.0202864	−	0.0234118i
$606$	−18.3169	+	6.63487i	−0.744074	+	0.269523i
$607$	12.4598	+	3.65854i	0.505729	+	0.148496i	0.524638	−	0.851326i	$-0.324201\pi$
$607$	12.4598	+	3.65854i	0.505729	+	0.148496i	−0.0189082	+	0.999821i	$0.506019\pi$
$608$	1.62048	−	1.87013i	0.0657191	−	0.0758439i
$609$	−4.56542	+	11.8950i	−0.185000	+	0.482008i
$610$	5.15583	+	3.31345i	0.208753	+	0.134158i
$611$	−0.790046	−	0.684579i	−0.0319619	−	0.0276951i
$612$	−7.11781	+	0.886089i	−0.287720	+	0.0358180i
$613$	15.2521	−	2.19292i	0.616026	−	0.0885712i	0.172764	−	0.984963i	$-0.444730\pi$
$613$	15.2521	−	2.19292i	0.616026	−	0.0885712i	0.443262	+	0.896392i	$0.353821\pi$
$614$	1.14536	−	0.992457i	0.0462228	−	0.0400523i
$615$	−3.58049	−	4.87864i	−0.144379	−	0.196726i
$616$	4.57579	−	1.34357i	0.184364	−	0.0541341i
$617$	−7.65030	+	16.7518i	−0.307989	+	0.674403i	−0.998818	−	0.0486162i	$-0.984519\pi$
$617$	−7.65030	+	16.7518i	−0.307989	+	0.674403i	0.690828	+	0.723019i	$0.257246\pi$
$618$	27.1704	−	1.68471i	1.09295	−	0.0677688i
$619$	1.24050	+	1.93026i	0.0498600	+	0.0775837i	0.865289	−	0.501274i	$-0.167135\pi$
$619$	1.24050	+	1.93026i	0.0498600	+	0.0775837i	−0.815429	+	0.578858i	$0.803499\pi$
$620$	6.64756			0.266973
$621$	−3.38243	+	24.6893i	−0.135732	+	0.990746i
$622$	0.933816			0.0374426
$623$	−8.27243	−	12.8722i	−0.331428	−	0.515712i
$624$	0.796405	−	0.0493813i	0.0318817	−	0.00197683i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−27.1202	+	7.96321i	−1.08394	+	0.318274i
$627$	−8.11411	−	11.0560i	−0.324046	−	0.441533i
$628$	−2.38420	+	2.06592i	−0.0951398	+	0.0824391i
$629$	28.3417	−	4.07491i	1.13006	−	0.162477i
$630$	−4.43709	+	0.552369i	−0.176778	+	0.0220069i
$631$	−25.6931	−	22.2632i	−1.02283	−	0.886285i	−0.0292650	−	0.999572i	$-0.509317\pi$
$631$	−25.6931	−	22.2632i	−1.02283	−	0.886285i	−0.993562	+	0.113287i	$0.963862\pi$
$632$	−7.05419	−	4.53346i	−0.280601	−	0.180331i
$633$	2.08301	−	5.42719i	0.0827924	−	0.215711i
$634$	−18.8967	+	21.8080i	−0.750484	+	0.866105i
$635$	12.0769	+	3.54611i	0.479259	+	0.140723i
$636$	−11.2314	+	4.06833i	−0.445356	+	0.161320i
$637$	−1.44163	−	1.66373i	−0.0571195	−	0.0659194i
$638$	6.56021	+	14.3649i	0.259721	+	0.568710i
$639$	−11.9863	−	14.3744i	−0.474169	−	0.568642i
$640$	−0.909632	−	0.415415i	−0.0359564	−	0.0164207i
$641$	−4.16956	+	28.9999i	−0.164688	+	1.14543i	0.724963	+	0.688787i	$0.241857\pi$
$641$	−4.16956	+	28.9999i	−0.164688	+	1.14543i	−0.889651	+	0.456641i	$0.849052\pi$
$642$	22.5068	−	22.0843i	0.888271	−	0.871597i
$643$			25.0540i			0.988034i	0.869452	+	0.494017i	$0.164472\pi$
$643$			25.0540i			0.988034i	−0.869452	+	0.494017i	$0.835528\pi$
$644$	−7.14321	−	0.259633i	−0.281482	−	0.0102310i
$645$	6.05919	−	1.25810i	0.238580	−	0.0495375i
$646$	−4.97721	+	3.19866i	−0.195826	+	0.125850i
$647$	34.5400	+	4.96610i	1.35791	+	0.195238i	0.782511	−	0.622637i	$-0.213939\pi$
$647$	34.5400	+	4.96610i	1.35791	+	0.195238i	0.575396	+	0.817875i	$0.304848\pi$
$648$	8.32246	−	3.42589i	0.326937	−	0.134582i
$649$	5.42549	+	18.4775i	0.212969	+	0.725307i
$650$	0.419056	−	0.191377i	0.0164367	−	0.00750641i
$651$	−13.6399	−	10.4138i	−0.534591	−	0.408149i
$652$	−3.03595	−	21.1155i	−0.118897	−	0.826945i
$653$	−1.01562	+	3.45889i	−0.0397443	+	0.135357i	−0.976975	−	0.213352i	$-0.931562\pi$
$653$	−1.01562	+	3.45889i	−0.0397443	+	0.135357i	0.937231	+	0.348709i	$0.113380\pi$
$654$	23.7169	+	13.2436i	0.927404	+	0.517866i
$655$	−1.79423	+	2.79188i	−0.0701066	+	0.109088i
$656$	−1.88892	+	2.93922i	−0.0737499	+	0.114757i
$657$	−0.849172	+	2.70157i	−0.0331293	+	0.105398i
$658$	0.952842	−	3.24508i	0.0371457	−	0.126507i
$659$	−0.272927	−	1.89825i	−0.0106317	−	0.0739453i	0.983815	−	0.179188i	$-0.0573471\pi$
$659$	−0.272927	−	1.89825i	−0.0106317	−	0.0739453i	−0.994447	+	0.105243i	$0.966438\pi$
$660$	−3.36310	+	4.40496i	−0.130908	+	0.171463i
$661$	0.940382	−	0.429458i	0.0365766	−	0.0167040i	−0.397043	−	0.917800i	$-0.629964\pi$
$661$	0.940382	−	0.429458i	0.0365766	−	0.0167040i	0.433619	+	0.901096i	$0.357236\pi$
$662$	−7.83042	−	26.6680i	−0.304338	−	1.03648i
$663$	−1.86027	−	0.423174i	−0.0722469	−	0.0164347i
$664$	−7.85044	−	1.12872i	−0.304656	−	0.0438030i
$665$	−3.10268	+	1.99397i	−0.120317	+	0.0773230i
$666$	−32.9576	+	14.3029i	−1.27708	+	0.554226i
$667$	−2.51532	−	23.5356i	−0.0973934	−	0.911302i
$668$		−	24.7289i		−	0.956789i
$669$	−16.4038	−	16.7176i	−0.634208	−	0.646340i
$670$	−1.03611	+	7.20627i	−0.0400283	+	0.278403i
$671$	−17.8380	−	8.14633i	−0.688628	−	0.314486i
$672$	1.21567	+	2.27737i	0.0468956	+	0.0878515i
$673$	12.9075	+	28.2635i	0.497548	+	1.08948i	0.977258	+	0.212052i	$0.0680145\pi$
$673$	12.9075	+	28.2635i	0.497548	+	1.08948i	−0.479710	+	0.877427i	$0.659258\pi$
$674$	−17.9597	−	20.7266i	−0.691780	−	0.798357i
$675$	3.77716	−	3.56834i	0.145383	−	0.137345i
$676$	−12.2698	−	3.60273i	−0.471914	−	0.138567i
$677$	19.5229	−	22.5306i	0.750326	−	0.865923i	−0.244274	−	0.969706i	$-0.578549\pi$
$677$	19.5229	−	22.5306i	0.750326	−	0.865923i	0.994600	+	0.103784i	$0.0330949\pi$
$678$	12.7051	+	4.87634i	0.487935	+	0.187275i
$679$	1.48945	+	0.957210i	0.0571598	+	0.0367344i
$680$	1.80693	+	1.56572i	0.0692927	+	0.0600425i
$681$	−1.91030	+	23.5693i	−0.0732030	+	0.903178i
$682$	−21.0537	+	3.02706i	−0.806186	+	0.115912i
$683$	26.4593	−	22.9271i	1.01244	−	0.877281i	0.0199702	−	0.999801i	$-0.493643\pi$
$683$	26.4593	−	22.9271i	1.01244	−	0.877281i	0.992466	+	0.122519i	$0.0390974\pi$
$684$	4.96686	−	5.51728i	0.189913	−	0.210959i
$685$	−2.94266	+	0.864042i	−0.112433	+	0.0330134i
$686$	7.29274	−	15.9689i	0.278438	−	0.609695i
$687$	−0.185525	−	2.99209i	−0.00707823	−	0.114155i
$688$	−1.93165	−	3.00570i	−0.0736434	−	0.114591i
$689$	−3.17726			−0.121044
$690$	6.87076	−	4.66827i	0.261565	−	0.177718i
$691$	40.0560			1.52380			0.761902	−	0.647693i	$-0.224266\pi$
$691$	40.0560			1.52380			0.761902	+	0.647693i	$0.224266\pi$
$692$	−4.21538	−	6.55927i	−0.160245	−	0.249346i
$693$	13.8013	−	3.76991i	0.524267	−	0.143207i
$694$	5.10042	−	11.1684i	0.193609	−	0.423945i
$695$	−3.70971	+	1.08927i	−0.140717	+	0.0413183i
$696$	−6.89162	+	5.05784i	−0.261226	+	0.191717i
$697$	6.31316	−	5.47038i	0.239128	−	0.207206i
$698$	−12.9711	+	1.86496i	−0.490963	+	0.0705898i
$699$	25.8385	+	2.09422i	0.977301	+	0.0792107i
$700$	1.12640	+	0.976034i	0.0425740	+	0.0368906i
$701$	−11.1144	−	7.14280i	−0.419786	−	0.269780i	0.313650	−	0.949539i	$-0.398448\pi$
$701$	−11.1144	−	7.14280i	−0.419786	−	0.269780i	−0.733436	+	0.679759i	$0.762085\pi$
$702$	2.39159	−	0.102850i	0.0902649	−	0.00388181i
$703$	−19.4065	+	22.3963i	−0.731931	+	0.844693i
$704$	3.07008	+	0.901458i	0.115708	+	0.0339750i
$705$	1.33856	+	3.69537i	0.0504131	+	0.139176i
$706$	−14.9396	−	17.2412i	−0.562258	−	0.648880i
$707$	−6.96403	−	15.2491i	−0.261909	−	0.573502i
$708$	−9.19627	+	4.90902i	−0.345617	+	0.184492i
$709$	32.6447	+	14.9083i	1.22600	+	0.559894i	0.919918	−	0.392112i	$-0.128255\pi$
$709$	32.6447	+	14.9083i	1.22600	+	0.559894i	0.306080	+	0.952006i	$0.400983\pi$
$710$	−0.887860	+	6.17520i	−0.0333208	+	0.231751i
$711$	−20.9011	−	13.9989i	−0.783853	−	0.524999i
$712$		−	10.2662i		−	0.384741i
$713$	31.3705	+	5.68030i	1.17483	+	0.212729i
$714$	−1.25480	−	6.04332i	−0.0469598	−	0.226165i
$715$	−1.24006	+	0.796937i	−0.0463755	+	0.0298037i
$716$	−1.65533	−	0.238001i	−0.0618627	−	0.00889451i
$717$	−9.69051	+	42.5995i	−0.361899	+	1.59091i
$718$	5.00762	+	17.0544i	0.186883	+	0.636464i
$719$	28.3164	−	12.9317i	1.05602	−	0.482270i	0.189747	−	0.981833i	$-0.439233\pi$
$719$	28.3164	−	12.9317i	1.05602	−	0.482270i	0.866278	+	0.499563i	$0.166506\pi$
$720$	−2.70479	−	1.29772i	−0.100802	−	0.0483633i
$721$	3.33376	+	23.1868i	0.124156	+	0.863522i
$722$	−3.62777	+	12.3551i	−0.135012	+	0.459807i
$723$	−1.02968	+	1.84397i	−0.0382942	+	0.0685780i
$724$	2.73850	−	4.26119i	0.101776	−	0.158366i
$725$	−2.66831	+	4.15197i	−0.0990985	+	0.154200i
$726$	−0.643439	+	1.15228i	−0.0238803	+	0.0427652i
$727$	5.52536	−	18.8176i	0.204924	−	0.697908i	−0.791326	−	0.611394i	$-0.790609\pi$
$727$	5.52536	−	18.8176i	0.204924	−	0.697908i	0.996251	−	0.0865140i	$-0.0275727\pi$
$728$	0.0977176	+	0.679641i	0.00362165	+	0.0251892i
$729$	25.1576	−	9.80277i	0.931764	−	0.363065i
$730$	0.858657	−	0.392136i	0.0317803	−	0.0145136i
$731$	2.40669	+	8.19644i	0.0890147	+	0.303156i
$732$	2.35461	−	10.3509i	0.0870289	−	0.382579i
$733$	52.1034	+	7.49134i	1.92448	+	0.276699i	0.995602	−	0.0936798i	$-0.0298630\pi$
$733$	52.1034	+	7.49134i	1.92448	+	0.276699i	0.928881	+	0.370379i	$0.120772\pi$
$734$	−17.1796	+	11.0406i	−0.634110	+	0.407517i
$735$	1.68265	+	8.10389i	0.0620654	+	0.298916i
$736$	−3.93767	−	2.73766i	−0.145144	−	0.100911i
$737$		−	23.2950i		−	0.858081i
$738$	−5.83280	+	8.70870i	−0.214708	+	0.320572i
$739$	−1.05168	+	7.31457i	−0.0386865	+	0.269071i	−0.999979	−	0.00645879i	$-0.997944\pi$
$739$	−1.05168	+	7.31457i	−0.0386865	+	0.269071i	0.961293	+	0.275530i	$0.0888532\pi$
$740$	10.8936	+	4.97492i	0.400455	+	0.182882i
$741$	1.74188	−	0.929827i	0.0639897	−	0.0341581i
$742$	−4.27016	−	9.35035i	−0.156763	−	0.343262i
$743$	−28.4811	−	32.8689i	−1.04487	−	1.20584i	−0.978113	−	0.208074i	$-0.933280\pi$
$743$	−28.4811	−	32.8689i	−1.04487	−	1.20584i	−0.0667563	−	0.997769i	$-0.521265\pi$
$744$	−3.92132	−	10.8256i	−0.143763	−	0.396886i
$745$	−7.44146	−	2.18501i	−0.272634	−	0.0800525i
$746$	−17.3177	+	19.9857i	−0.634048	+	0.731730i
$747$	−23.4830	−	3.83178i	−0.859196	−	0.140198i
$748$	−6.43576	−	4.13601i	−0.235315	−	0.151227i
$749$	20.5062	+	17.7687i	0.749280	+	0.649255i
$750$	−1.72639	−	0.139925i	−0.0630388	−	0.00510933i
$751$	−11.3818	+	1.63645i	−0.415327	+	0.0597150i	−0.346811	−	0.937935i	$-0.612735\pi$
$751$	−11.3818	+	1.63645i	−0.415327	+	0.0597150i	−0.0685159	+	0.997650i	$0.521826\pi$
$752$	1.71493	−	1.48599i	0.0625370	−	0.0541886i
$753$	8.89698	−	6.52959i	0.324224	−	0.237952i
$754$	−2.18160	+	0.640576i	−0.0794493	+	0.0233284i
$755$	4.80784	−	10.5277i	0.174975	−	0.383143i
$756$	3.51692	+	6.89998i	0.127909	+	0.250950i
$757$	3.02307	+	4.70399i	0.109875	+	0.170969i	0.891837	−	0.452358i	$-0.149417\pi$
$757$	3.02307	+	4.70399i	0.109875	+	0.170969i	−0.781961	+	0.623327i	$0.785781\pi$
$758$	2.84422			0.103307
$759$	−19.6348	+	17.9137i	−0.712697	+	0.650225i
$760$	−2.47454			−0.0897610
$761$	24.6505	+	38.3568i	0.893578	+	1.39043i	0.920477	+	0.390797i	$0.127800\pi$
$761$	24.6505	+	38.3568i	0.893578	+	1.39043i	−0.0268989	+	0.999638i	$0.508563\pi$
$762$	−1.34918	−	21.7592i	−0.0488757	−	0.788252i
$763$	−9.71027	+	21.2625i	−0.351536	+	0.769755i
$764$	2.33444	−	0.685453i	0.0844570	−	0.0247988i
$765$	5.33083	+	4.79901i	0.192737	+	0.173509i
$766$	13.8599	−	12.0097i	0.500779	−	0.433927i
$767$	−2.74446	+	0.394594i	−0.0990968	+	0.0142480i
$768$	−0.139925	+	1.72639i	−0.00504910	+	0.0622957i
$769$	−36.1389	−	31.3146i	−1.30320	−	1.12923i	−0.983342	−	0.181768i	$-0.941818\pi$
$769$	−36.1389	−	31.3146i	−1.30320	−	1.12923i	−0.319862	−	0.947464i	$-0.603636\pi$
$770$	−4.01191	−	2.57830i	−0.144579	−	0.0929154i
$771$	−10.9154	−	4.18944i	−0.393108	−	0.150879i
$772$	−7.37553	+	8.51181i	−0.265451	+	0.306347i
$773$	−31.2031	−	9.16205i	−1.12230	−	0.329536i	−0.332621	−	0.943061i	$-0.607933\pi$
$773$	−31.2031	−	9.16205i	−1.12230	−	0.329536i	−0.789676	+	0.613525i	$0.789751\pi$
$774$	−5.62306	−	9.12528i	−0.202117	−	0.328002i
$775$	−4.35323	−	5.02389i	−0.156373	−	0.180464i
$776$	0.493475	+	1.08056i	0.0177147	+	0.0387898i
$777$	−14.5586	−	27.2733i	−0.522288	−	0.978424i
$778$	5.57720	+	2.54702i	0.199952	+	0.0913152i
$779$	−1.23041	+	8.55768i	−0.0440840	+	0.306611i
$780$	−0.558854	−	0.569545i	−0.0200102	−	0.0203930i
$781$		−	19.9619i		−	0.714294i
$782$	7.18919	+	8.93278i	0.257085	+	0.319435i
$783$	−20.9586	+	14.7791i	−0.749001	+	0.528161i
$784$	4.01999	−	2.58349i	0.143571	−	0.0922676i
$785$	3.12263	+	0.448967i	0.111452	+	0.0160243i
$786$	5.60500	+	1.27502i	0.199924	+	0.0454786i
$787$	−1.86703	−	6.35853i	−0.0665525	−	0.226657i	0.919500	−	0.393089i	$-0.128594\pi$
$787$	−1.86703	−	6.35853i	−0.0665525	−	0.226657i	−0.986053	+	0.166432i	$0.946775\pi$
$788$	−18.5369	+	8.46551i	−0.660349	+	0.301571i
$789$	7.79321	−	10.2075i	0.277446	−	0.363396i
$790$	1.19336	+	8.29999i	0.0424578	+	0.295300i
$791$	−3.29921	+	11.2361i	−0.117306	+	0.399508i
$792$	9.15736	+	2.87839i	0.325393	+	0.102279i
$793$	1.52647	−	2.37523i	0.0542064	−	0.0843468i
$794$	5.61448	−	8.73630i	0.199250	−	0.310040i
$795$	10.4297	+	5.82397i	0.369902	+	0.206555i
$796$	−0.465912	+	1.58675i	−0.0165138	+	0.0562409i
$797$	0.354525	+	2.46578i	0.0125579	+	0.0873423i	0.995137	−	0.0985051i	$-0.0314061\pi$
$797$	0.354525	+	2.46578i	0.0125579	+	0.0873423i	−0.982579	+	0.185847i	$0.940497\pi$
$798$	5.07743	+	3.87652i	0.179739	+	0.137227i
$799$	−4.93512	+	2.25380i	−0.174592	+	0.0797336i
$800$	0.281733	+	0.959493i	0.00996075	+	0.0339232i
$801$	0.583527	−	30.7930i	0.0206179	−	1.08802i
$802$	15.8502	+	2.27892i	0.559692	+	0.0804715i
$803$	−2.54091	+	1.63294i	−0.0896668	+	0.0576253i
$804$	12.3466	−	2.56359i	0.435433	−	0.0904109i
$805$	4.48159	+	5.56850i	0.157955	+	0.196264i
$806$		−	3.06245i		−	0.107870i
$807$	32.0095	−	31.4087i	1.12679	−	1.10564i
$808$	1.60071	−	11.1332i	0.0563128	−	0.391664i
$809$	3.47383	+	1.58645i	0.122134	+	0.0557765i	0.475545	−	0.879692i	$-0.342251\pi$
$809$	3.47383	+	1.58645i	0.122134	+	0.0557765i	−0.353411	+	0.935468i	$0.614978\pi$
$810$	−8.03916	−	4.04622i	−0.282467	−	0.142170i
$811$	−19.3604	−	42.3935i	−0.679837	−	1.48864i	−0.862816	−	0.505519i	$-0.831301\pi$
$811$	−19.3604	−	42.3935i	−0.679837	−	1.48864i	0.182978	−	0.983117i	$-0.441426\pi$
$812$	−4.81717	−	5.55931i	−0.169050	−	0.195094i
$813$	−9.07200	+	3.28612i	−0.318169	+	0.115249i
$814$	−36.7667	−	10.7957i	−1.28867	−	0.378388i
$815$	−13.9699	+	16.1221i	−0.489344	+	0.564733i
$816$	1.48389	−	3.86620i	0.0519466	−	0.135344i
$817$	−7.43773	−	4.77994i	−0.260213	−	0.167229i
$818$	−17.3322	−	15.0185i	−0.606007	−	0.525108i
$819$	0.254470	+	2.04411i	0.00889188	+	0.0714270i
$820$	3.45829	−	0.497227i	0.120769	−	0.0173639i
$821$	−36.1370	+	31.3129i	−1.26119	+	1.09283i	−0.269658	+	0.962956i	$0.586911\pi$
$821$	−36.1370	+	31.3129i	−1.26119	+	1.09283i	−0.991531	+	0.129870i	$0.958544\pi$
$822$	3.14294	+	4.28245i	0.109623	+	0.149368i
$823$	50.8534	−	14.9319i	1.77264	−	0.520494i	0.778409	−	0.627758i	$-0.216027\pi$
$823$	50.8534	−	14.9319i	1.77264	−	0.520494i	0.994231	+	0.107264i	$0.0342090\pi$
$824$	−6.52906	+	14.2966i	−0.227451	+	0.498047i
$825$	5.53141	−	0.342976i	0.192579	−	0.0119409i
$826$	−4.84974	−	7.54635i	−0.168744	−	0.262571i
$827$	2.11165			0.0734293			0.0367146	−	0.999326i	$-0.488311\pi$
$827$	2.11165			0.0734293			0.0367146	+	0.999326i	$0.488311\pi$
$828$	−11.6553	−	8.43531i	−0.405049	−	0.293147i
$829$	−4.03347			−0.140088			−0.0700442	−	0.997544i	$-0.522314\pi$
$829$	−4.03347			−0.140088			−0.0700442	+	0.997544i	$0.522314\pi$
$830$	4.28792	+	6.67213i	0.148836	+	0.231593i
$831$	29.6229	−	1.83677i	1.02761	−	0.0637170i
$832$	−0.191377	+	0.419056i	−0.00663479	+	0.0145282i
$833$	−10.9624	+	3.21884i	−0.379824	+	0.111526i
$834$	3.96220	+	5.39874i	0.137200	+	0.186943i
$835$	−18.6888	+	16.1940i	−0.646754	+	0.560415i
$836$	7.83718	−	1.12682i	0.271055	−	0.0389718i
$837$	−11.1465	−	32.6938i	−0.385280	−	1.13006i
$838$	22.8911	+	19.8353i	0.790761	+	0.685198i
$839$	14.4812	+	9.30653i	0.499948	+	0.321297i	0.766195	−	0.642608i	$-0.222147\pi$
$839$	14.4812	+	9.30653i	0.499948	+	0.321297i	−0.266247	+	0.963905i	$0.585784\pi$
$840$	0.925025	−	2.41011i	0.0319164	−	0.0831565i
$841$	−3.03939	+	3.50764i	−0.104806	+	0.120953i
$842$	−37.2951	−	10.9508i	−1.28527	−	0.377390i
$843$	−13.5159	+	4.89583i	−0.465513	+	0.168621i
$844$	2.19788	+	2.53649i	0.0756541	+	0.0873095i
$845$	5.31223	+	11.6322i	0.182746	+	0.400159i
$846$	5.22833	−	4.35971i	0.179754	−	0.149890i
$847$	−1.03304	−	0.471773i	−0.0354956	−	0.0162103i
$848$	0.981513	−	6.82658i	0.0337053	−	0.234426i
$849$	−27.8309	+	27.3085i	−0.955154	+	0.937225i
$850$		−	2.39092i		−	0.0820077i
$851$	47.1567	+	32.7856i	1.61651	+	1.12388i
$852$	10.5801	−	2.19679i	0.362468	−	0.0752609i
$853$	−4.09969	+	2.63471i	−0.140371	+	0.0902107i	−0.608941	−	0.793215i	$-0.708405\pi$
$853$	−4.09969	+	2.63471i	−0.140371	+	0.0902107i	0.468571	+	0.883426i	$0.344769\pi$
$854$	9.04158	+	1.29998i	0.309397	+	0.0444845i
$855$	−7.42229	−	0.140652i	−0.253837	−	0.00481021i
$856$	5.12895	+	17.4676i	0.175304	+	0.597030i
$857$	−12.4339	+	5.67836i	−0.424733	+	0.193969i	−0.616302	−	0.787510i	$-0.711370\pi$
$857$	−12.4339	+	5.67836i	−0.424733	+	0.193969i	0.191569	+	0.981479i	$0.438642\pi$
$858$	2.02931	+	1.54934i	0.0692796	+	0.0528935i
$859$	5.69801	+	39.6306i	0.194414	+	1.35218i	0.820153	+	0.572145i	$0.193888\pi$
$859$	5.69801	+	39.6306i	0.194414	+	1.35218i	−0.625739	+	0.780032i	$0.715202\pi$
$860$	−1.00660	+	3.42816i	−0.0343247	+	0.116899i
$861$	−7.87489	−	4.39737i	−0.268376	−	0.149862i
$862$	−19.5197	+	30.3733i	−0.664844	+	1.03452i
$863$	4.65635	−	7.24542i	0.158504	−	0.246637i	−0.752914	−	0.658119i	$-0.771352\pi$
$863$	4.65635	−	7.24542i	0.158504	−	0.246637i	0.911418	+	0.411482i	$0.134989\pi$
$864$	−0.517826	+	5.17029i	−0.0176168	+	0.175897i
$865$	−2.19667	+	7.48118i	−0.0746891	+	0.254368i
$866$	1.67486	+	11.6489i	0.0569141	+	0.395846i
$867$	11.8598	−	15.5338i	0.402778	−	0.527556i
$868$	9.01248	−	4.11586i	0.305903	−	0.139701i
$869$	−7.55903	−	25.7437i	−0.256422	−	0.873295i
$870$	8.33551	+	1.89616i	0.282600	+	0.0642858i
$871$	3.31984	+	0.477321i	0.112489	+	0.0161734i
$872$	−13.1935	+	8.47895i	−0.446789	+	0.287134i
$873$	1.41874	+	3.26914i	0.0480170	+	0.110644i
$874$	−11.6776	−	2.11448i	−0.395000	−	0.0715233i
$875$		−	1.49044i		−	0.0503862i
$876$	−1.14511	−	1.16701i	−0.0386896	−	0.0394297i
$877$	−3.35239	+	23.3164i	−0.113202	+	0.787338i	0.851568	+	0.524244i	$0.175652\pi$
$877$	−3.35239	+	23.3164i	−0.113202	+	0.787338i	−0.964770	+	0.263094i	$0.915257\pi$
$878$	16.4285	+	7.50263i	0.554434	+	0.253202i
$879$	−24.8793	−	46.6073i	−0.839157	−	1.57203i
$880$	−1.32920	−	2.91054i	−0.0448073	−	0.0981144i
$881$	−13.7549	−	15.8740i	−0.463414	−	0.534808i	0.475154	−	0.879903i	$-0.342392\pi$
$881$	−13.7549	−	15.8740i	−0.463414	−	0.534808i	−0.938568	+	0.345094i	$0.887847\pi$
$882$	12.2047	−	7.52059i	0.410952	−	0.253231i
$883$	21.4104	+	6.28667i	0.720518	+	0.211563i	0.621379	−	0.783510i	$-0.286573\pi$
$883$	21.4104	+	6.28667i	0.720518	+	0.211563i	0.0991396	+	0.995074i	$0.468391\pi$
$884$	0.721307	−	0.832432i	0.0242602	−	0.0279977i
$885$	9.73227	+	3.73535i	0.327147	+	0.125563i
$886$	−4.10463	−	2.63789i	−0.137898	−	0.0886215i
$887$	−12.8971	−	11.1754i	−0.433042	−	0.375233i	0.410888	−	0.911686i	$-0.365219\pi$
$887$	−12.8971	−	11.1754i	−0.433042	−	0.375233i	−0.843931	+	0.536452i	$0.819764\pi$
$888$	1.67571	−	20.6749i	0.0562331	−	0.693803i
$889$	18.5690	−	2.66981i	0.622783	−	0.0895427i
$890$	−7.75865	+	6.72291i	−0.260071	+	0.225353i
$891$	27.3035	+	9.15412i	0.914703	+	0.306675i
$892$	12.9746	−	3.80969i	0.434422	−	0.127558i
$893$	2.33262	−	5.10774i	0.0780583	−	0.170924i
$894$	0.831327	+	13.4074i	0.0278037	+	0.448410i
$895$	0.904143	+	1.40687i	0.0302222	+	0.0470266i
$896$	−1.49044			−0.0497923
$897$	−2.15061	−	3.16527i	−0.0718069	−	0.105685i
$898$	−35.3414			−1.17936
$899$	17.7378	+	27.6005i	0.591587	+	0.920528i
$900$	0.790509	+	2.89398i	0.0263503	+	0.0964659i
$901$	−6.85003	+	14.9995i	−0.228208	+	0.499705i
$902$	−10.7264	+	3.14956i	−0.357151	+	0.104869i
$903$	7.43582	−	5.45724i	0.247449	−	0.181605i
$904$	−5.93792	+	5.14524i	−0.197492	+	0.171128i
$905$	−5.01373	+	0.720865i	−0.166662	+	0.0239624i
$906$	−19.9805	−	1.61943i	−0.663809	−	0.0538020i
$907$	6.05708	+	5.24849i	0.201122	+	0.174273i	0.749599	−	0.661893i	$-0.230247\pi$
$907$	6.05708	+	5.24849i	0.201122	+	0.174273i	−0.548477	+	0.836166i	$0.684792\pi$
$908$	−11.4851	−	7.38103i	−0.381147	−	0.244948i
$909$	5.43408	−	33.3026i	0.180237	−	1.10458i
$910$	0.449647	−	0.518920i	0.0149056	−	0.0172020i
$911$	−15.5569	−	4.56793i	−0.515424	−	0.151342i	0.0136679	−	0.999907i	$-0.495649\pi$
$911$	−15.5569	−	4.56793i	−0.515424	−	0.151342i	−0.529092	+	0.848564i	$0.677467\pi$
$912$	1.45970	+	4.02980i	0.0483356	+	0.133440i
$913$	−16.6186	−	19.1789i	−0.549996	−	0.634729i
$914$	9.26208	+	20.2811i	0.306362	+	0.670840i
$915$	−9.36461	+	4.99888i	−0.309584	+	0.165258i
$916$	1.57439	+	0.719001i	0.0520194	+	0.0237565i
$917$	−0.703941	+	4.89602i	−0.0232462	+	0.161681i
$918$	4.67063	−	11.5122i	0.154154	−	0.379958i
$919$		−	10.4529i		−	0.344808i	−0.985026	−	0.172404i	$-0.944847\pi$
$919$		−	10.4529i		−	0.344808i	0.985026	−	0.172404i	$-0.0551535\pi$
$920$	0.509642	+	4.76868i	0.0168024	+	0.157219i
$921$	0.533651	+	2.57015i	0.0175844	+	0.0846892i
$922$	6.44153	−	4.13972i	0.212140	−	0.136334i
$923$	2.84484	+	0.409026i	0.0936391	+	0.0134633i
$924$	−1.83220	+	8.05433i	−0.0602748	+	0.264968i
$925$	−3.37397	−	11.4907i	−0.110935	−	0.377811i
$926$	31.3225	−	14.3045i	1.02932	−	0.470075i
$927$	−20.3963	+	42.5111i	−0.669902	+	1.39625i
$928$	−0.702389	−	4.88522i	−0.0230570	−	0.160365i
$929$	−4.63240	+	15.7765i	−0.151984	+	0.517611i	−0.999922	−	0.0124849i	$-0.996026\pi$
$929$	−4.63240	+	15.7765i	−0.151984	+	0.517611i	0.847938	+	0.530096i	$0.177844\pi$
$930$	−5.61352	+	10.0528i	−0.184075	+	0.329644i
$931$	6.39296	−	9.94763i	0.209521	−	0.326021i
$932$	−8.09165	+	12.5908i	−0.265051	+	0.412427i
$933$	−0.788559	+	1.41217i	−0.0258163	+	0.0462322i
$934$	6.56586	−	22.3613i	0.214841	−	0.731683i
$935$	1.08874	+	7.57233i	0.0356055	+	0.247642i
$936$	−0.597846	+	1.24607i	−0.0195412	+	0.0407289i
$937$	5.04682	−	2.30481i	0.164872	−	0.0752947i	−0.331269	−	0.943536i	$-0.607477\pi$
$937$	5.04682	−	2.30481i	0.164872	−	0.0752947i	0.496142	+	0.868242i	$0.334750\pi$
$938$	3.05708	+	10.4115i	0.0998172	+	0.339946i
$939$	10.8592	−	47.7371i	0.354377	−	1.55784i
$940$	−2.24608	−	0.322937i	−0.0732590	−	0.0105331i
$941$	−47.9847	+	30.8379i	−1.56426	+	1.00529i	−0.583023	+	0.812455i	$0.698130\pi$
$941$	−47.9847	+	30.8379i	−1.56426	+	1.00529i	−0.981232	+	0.192830i	$0.938233\pi$
$942$	−1.11086	−	5.35007i	−0.0361938	−	0.174315i
$943$	16.7449	+	0.608624i	0.545288	+	0.0198195i
$944$		−	6.01858i		−	0.195888i
$945$	2.91157	−	7.17644i	0.0947133	−	0.233450i
$946$	1.62696	−	11.3158i	0.0528971	−	0.367908i
$947$	25.1729	+	11.4961i	0.818010	+	0.373573i	0.780058	−	0.625707i	$-0.215189\pi$
$947$	25.1729	+	11.4961i	0.818010	+	0.373573i	0.0379520	+	0.999280i	$0.487917\pi$
$948$	12.8126	−	6.83945i	0.416135	−	0.222135i
$949$	−0.180652	−	0.395573i	−0.00586421	−	0.0128408i
$950$	1.62048	+	1.87013i	0.0525753	+	0.0606751i
$951$	−17.0219	−	46.9923i	−0.551971	−	1.52383i
$952$	3.41918	+	1.00396i	0.110816	+	0.0325386i
$953$	−10.4379	+	12.0460i	−0.338118	+	0.390209i	−0.899190	−	0.437558i	$-0.855844\pi$
$953$	−10.4379	+	12.0460i	−0.338118	+	0.390209i	0.561072	+	0.827767i	$0.310389\pi$
$954$	3.33203	−	20.4203i	0.107879	−	0.661130i
$955$	−2.04676	−	1.31537i	−0.0662317	−	0.0425645i
$956$	−19.0624	−	16.5176i	−0.616522	−	0.534219i
$957$	−27.2631	−	2.20968i	−0.881289	−	0.0714289i
$958$	−6.75881	+	0.971770i	−0.218367	+	0.0313965i
$959$	−3.45455	+	2.99339i	−0.111553	+	0.0966615i
$960$	1.39635	−	1.02480i	0.0450670	−	0.0330752i
$961$	−12.6558	+	3.71608i	−0.408252	+	0.119874i
$962$	2.29188	−	5.01853i	0.0738933	−	0.161804i
$963$	14.3912	+	52.6849i	0.463751	+	1.69775i
$964$	−0.659232	−	1.02579i	−0.0212324	−	0.0330383i
$965$	11.2627			0.362560
$966$	6.42470	−	10.5831i	0.206711	−	0.340505i
$967$	24.0592			0.773692			0.386846	−	0.922144i	$-0.373565\pi$
$967$	24.0592			0.773692			0.386846	+	0.922144i	$0.373565\pi$
$968$	−0.411949	−	0.641005i	−0.0132405	−	0.0206027i
$969$	−0.634183	−	10.2279i	−0.0203729	−	0.328567i
$970$	0.493475	−	1.08056i	0.0158445	−	0.0346946i
$971$	−35.3126	+	10.3687i	−1.13324	+	0.332748i	−0.793979	−	0.607946i	$-0.791994\pi$
$971$	−35.3126	+	10.3687i	−1.13324	+	0.332748i	−0.339257	+	0.940694i	$0.610176\pi$
$972$	−1.84708	+	15.4786i	−0.0592451	+	0.496478i
$973$	−4.35504	+	3.77366i	−0.139616	+	0.120978i
$974$	−12.0291	+	1.72952i	−0.385437	+	0.0554174i
$975$	−0.0644616	+	0.795327i	−0.00206442	+	0.0254708i
$976$	4.63180	+	4.01348i	0.148260	+	0.128468i
$977$	21.6173	+	13.8926i	0.691599	+	0.444464i	0.838654	−	0.544665i	$-0.183343\pi$
$977$	21.6173	+	13.8926i	0.691599	+	0.444464i	−0.147055	+	0.989128i	$0.546979\pi$
$978$	34.4956	+	13.2398i	1.10305	+	0.423362i
$979$	21.5113	−	24.8253i	0.687503	−	0.793420i
$980$	−4.58501	−	1.34628i	−0.146463	−	0.0430053i
$981$	−40.0554	+	24.6824i	−1.27887	+	0.788048i
$982$	20.1471	+	23.2509i	0.642918	+	0.741967i
$983$	−24.9934	−	54.7280i	−0.797167	−	1.74555i	−0.654888	−	0.755726i	$-0.727284\pi$
$983$	−24.9934	−	54.7280i	−0.797167	−	1.74555i	−0.142279	−	0.989827i	$-0.545443\pi$
$984$	−2.84974	−	5.33854i	−0.0908464	−	0.170186i
$985$	18.5369	+	8.46551i	0.590634	+	0.269734i
$986$	−1.67935	+	11.6802i	−0.0534815	+	0.371972i
$987$	4.10276	+	4.18124i	0.130592	+	0.133090i
$988$			1.13999i			0.0362679i
$989$	−7.67957	+	15.3177i	−0.244196	+	0.487074i
$990$	−3.82145	−	8.80561i	−0.121454	−	0.279861i
$991$	20.8033	−	13.3695i	0.660838	−	0.424695i	−0.166774	−	0.985995i	$-0.553335\pi$
$991$	20.8033	−	13.3695i	0.660838	−	0.424695i	0.827612	+	0.561300i	$0.189699\pi$
$992$	6.57990	+	0.946047i	0.208912	+	0.0300370i
$993$	46.9411	+	10.6781i	1.48963	+	0.338861i
$994$	2.61968	+	8.92179i	0.0830910	+	0.282982i
$995$	1.50429	−	0.686988i	0.0476893	−	0.0217790i
$996$	8.33621	−	10.9187i	0.264143	−	0.345972i
$997$	6.28624	+	43.7218i	0.199087	+	1.38468i	0.806941	+	0.590633i	$0.201122\pi$
$997$	6.28624	+	43.7218i	0.199087	+	1.38468i	−0.607853	+	0.794049i	$0.707969\pi$
$998$	6.05682	−	20.6276i	0.191725	−	0.652957i
$999$	6.20138	−	61.9182i	0.196203	−	1.95901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.q.b.11.8	yes	160
3.2	odd	2		690.2.q.a.11.9	✓	160
23.21	odd	22		690.2.q.a.251.9	yes	160
69.44	even	22	inner	690.2.q.b.251.8	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.q.a.11.9	✓	160	3.2	odd	2
690.2.q.a.251.9	yes	160	23.21	odd	22
690.2.q.b.11.8	yes	160	1.1	even	1	trivial
690.2.q.b.251.8	yes	160	69.44	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.540641 - 0.841254i) q^{2} +(1.72873 - 0.107190i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-1.02480 - 1.39635i) q^{6} +(1.12640 - 0.976034i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.97702 - 0.370607i) q^{9} +O(q^{10})\)	\(q+(-0.540641 - 0.841254i) q^{2} +(1.72873 - 0.107190i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-1.02480 - 1.39635i) q^{6} +(1.12640 - 0.976034i) q^{7} +(0.989821 - 0.142315i) q^{8} +(2.97702 - 0.370607i) q^{9} +(-0.755750 - 0.654861i) q^{10} +(2.69175 + 1.72988i) q^{11} +(-0.620637 + 1.61704i) q^{12} +(-0.301686 + 0.348165i) q^{13} +(-1.43007 - 0.419907i) q^{14} +(1.62851 - 0.589888i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(0.993222 + 2.17485i) q^{17} +(-1.92127 - 2.30406i) q^{18} +(-2.25092 - 1.02796i) q^{19} +(-0.142315 + 0.989821i) q^{20} +(1.84263 - 1.80804i) q^{21} -3.19969i q^{22} +(-1.51739 + 4.54945i) q^{23} +(1.69588 - 0.352123i) q^{24} +(0.841254 - 0.540641i) q^{25} +(0.455999 + 0.0655627i) q^{26} +(5.10674 - 0.959787i) q^{27} +(0.419907 + 1.43007i) q^{28} +(-4.48945 + 2.05026i) q^{29} +(-1.37668 - 1.05107i) q^{30} +(-0.946047 - 6.57990i) q^{31} +(-0.281733 + 0.959493i) q^{32} +(4.83874 + 2.70197i) q^{33} +(1.29263 - 2.01137i) q^{34} +(0.805795 - 1.25384i) q^{35} +(-0.899583 + 2.86195i) q^{36} +(3.37397 - 11.4907i) q^{37} +(0.352164 + 2.44935i) q^{38} +(-0.484215 + 0.634221i) q^{39} +(0.909632 - 0.415415i) q^{40} +(-0.984332 - 3.35233i) q^{41} +(-2.51722 - 0.572616i) q^{42} +(3.53652 + 0.508475i) q^{43} +(-2.69175 + 1.72988i) q^{44} +(2.75202 - 1.19432i) q^{45} +(4.64761 - 1.18311i) q^{46} +2.26918i q^{47} +(-1.21309 - 1.23629i) q^{48} +(-0.680062 + 4.72993i) q^{49} +(-0.909632 - 0.415415i) q^{50} +(1.95014 + 3.65327i) q^{51} +(-0.191377 - 0.419056i) q^{52} +(4.51643 + 5.21223i) q^{53} +(-3.56834 - 3.77716i) q^{54} +(3.07008 + 0.901458i) q^{55} +(0.976034 - 1.12640i) q^{56} +(-4.00142 - 1.53579i) q^{57} +(4.15197 + 2.66831i) q^{58} +(4.54854 + 3.94133i) q^{59} +(-0.139925 + 1.72639i) q^{60} +(-6.06637 + 0.872212i) q^{61} +(-5.02389 + 4.35323i) q^{62} +(2.99160 - 3.32313i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-0.191377 + 0.419056i) q^{65} +(-0.342976 - 5.53141i) q^{66} +(-3.93607 - 6.12464i) q^{67} -2.39092 q^{68} +(-2.13551 + 8.02743i) q^{69} -1.49044 q^{70} +(-3.37290 - 5.24833i) q^{71} +(2.89398 - 0.790509i) q^{72} +(-0.392136 + 0.858657i) q^{73} +(-11.4907 + 3.37397i) q^{74} +(1.39635 - 1.02480i) q^{75} +(1.87013 - 1.62048i) q^{76} +(4.72043 - 0.678695i) q^{77} +(0.795327 + 0.0644616i) q^{78} +(-6.33721 - 5.49123i) q^{79} +(-0.841254 - 0.540641i) q^{80} +(8.72530 - 2.20661i) q^{81} +(-2.28799 + 2.64048i) q^{82} +(-7.60990 - 2.23447i) q^{83} +(0.879196 + 2.42720i) q^{84} +(1.56572 + 1.80693i) q^{85} +(-1.48423 - 3.25001i) q^{86} +(-7.54128 + 4.02558i) q^{87} +(2.91054 + 1.32920i) q^{88} +(1.46103 - 10.1617i) q^{89} +(-2.49258 - 1.66945i) q^{90} +0.686630i q^{91} +(-3.50798 - 3.27018i) q^{92} +(-2.34076 - 11.2735i) q^{93} +(1.90895 - 1.22681i) q^{94} +(-2.44935 - 0.352164i) q^{95} +(-0.384191 + 1.68890i) q^{96} +(0.334672 + 1.13979i) q^{97} +(4.34674 - 1.98509i) q^{98} +(8.65451 + 4.15232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{4} + 16 q^{5} - 2 q^{6} - 46 q^{9}+O(q^{10}) \) 160 * q + 16 * q^4 + 16 * q^5 - 2 * q^6 - 46 * q^9	\( 160 q + 16 q^{4} + 16 q^{5} - 2 q^{6} - 46 q^{9} + 12 q^{11} + 12 q^{14} - 16 q^{16} - 8 q^{18} - 16 q^{20} + 70 q^{21} - 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} + 2 q^{30} - 4 q^{31} - 16 q^{33} + 2 q^{36} - 72 q^{38} + 140 q^{39} - 44 q^{41} + 44 q^{43} - 12 q^{44} + 2 q^{45} + 4 q^{46} + 70 q^{49} + 2 q^{51} + 52 q^{53} - 62 q^{54} + 10 q^{55} + 54 q^{56} - 94 q^{57} - 36 q^{58} - 44 q^{61} + 16 q^{64} - 54 q^{66} - 44 q^{67} - 30 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} + 24 q^{74} + 88 q^{77} - 54 q^{78} - 44 q^{79} + 16 q^{80} - 66 q^{81} - 28 q^{82} - 4 q^{83} - 4 q^{84} - 158 q^{86} + 156 q^{87} - 80 q^{89} + 8 q^{90} + 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} + 88 q^{98} - 58 q^{99}+O(q^{100}) \) 160 * q + 16 * q^4 + 16 * q^5 - 2 * q^6 - 46 * q^9 + 12 * q^11 + 12 * q^14 - 16 * q^16 - 8 * q^18 - 16 * q^20 + 70 * q^21 - 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 + 2 * q^30 - 4 * q^31 - 16 * q^33 + 2 * q^36 - 72 * q^38 + 140 * q^39 - 44 * q^41 + 44 * q^43 - 12 * q^44 + 2 * q^45 + 4 * q^46 + 70 * q^49 + 2 * q^51 + 52 * q^53 - 62 * q^54 + 10 * q^55 + 54 * q^56 - 94 * q^57 - 36 * q^58 - 44 * q^61 + 16 * q^64 - 54 * q^66 - 44 * q^67 - 30 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 + 24 * q^74 + 88 * q^77 - 54 * q^78 - 44 * q^79 + 16 * q^80 - 66 * q^81 - 28 * q^82 - 4 * q^83 - 4 * q^84 - 158 * q^86 + 156 * q^87 - 80 * q^89 + 8 * q^90 + 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 + 88 * q^98 - 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more