LMFDB - Embedded newform 138.2.f.a.113.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(5,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

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

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

chi := DirichletCharacter("138.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.f (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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			113.5
Character	$\chi$	$=$	138.113
Dual form			138.2.f.a.11.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540641 - 0.841254i) q^{2} +(-1.71919 + 0.210651i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-2.84902 - 0.836549i) q^{5} +(-0.752255 + 1.56016i) q^{6} +(-3.02354 - 2.61991i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(2.91125 - 0.724301i) q^{9} +O(q^{10})$	\(q+(0.540641 - 0.841254i) q^{2} +(-1.71919 + 0.210651i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-2.84902 - 0.836549i) q^{5} +(-0.752255 + 1.56016i) q^{6} +(-3.02354 - 2.61991i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(2.91125 - 0.724301i) q^{9} +(-2.24405 + 1.94448i) q^{10} +(2.79349 - 1.79527i) q^{11} +(0.905794 + 1.47633i) q^{12} +(1.31691 + 1.51980i) q^{13} +(-3.83866 + 1.12713i) q^{14} +(5.07424 + 0.838038i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(0.139786 - 0.306088i) q^{17} +(0.964621 - 2.84069i) q^{18} +(-4.42768 + 2.02205i) q^{19} +(0.422576 + 2.93908i) q^{20} +(5.74994 + 3.86723i) q^{21} -3.32063i q^{22} +(-0.384545 - 4.78039i) q^{23} +(1.73167 + 0.0361594i) q^{24} +(3.21085 + 2.06349i) q^{25} +(1.99051 - 0.286192i) q^{26} +(-4.85243 + 1.85847i) q^{27} +(-1.12713 + 3.83866i) q^{28} +(6.14380 + 2.80578i) q^{29} +(3.44834 - 3.81565i) q^{30} +(1.10880 - 7.71186i) q^{31} +(0.281733 + 0.959493i) q^{32} +(-4.42438 + 3.67487i) q^{33} +(-0.181924 - 0.283079i) q^{34} +(6.42246 + 9.99354i) q^{35} +(-1.86823 - 2.34728i) q^{36} +(-2.31258 - 7.87592i) q^{37} +(-0.692724 + 4.81800i) q^{38} +(-2.58417 - 2.33542i) q^{39} +(2.70097 + 1.23349i) q^{40} +(0.321149 - 1.09373i) q^{41} +(6.36197 - 2.74638i) q^{42} +(-0.439950 + 0.0632552i) q^{43} +(-2.79349 - 1.79527i) q^{44} +(-8.90014 - 0.371853i) q^{45} +(-4.22942 - 2.26097i) q^{46} -8.33095i q^{47} +(0.966633 - 1.43723i) q^{48} +(1.28165 + 8.91409i) q^{49} +(3.47183 - 1.58553i) q^{50} +(-0.175841 + 0.555670i) q^{51} +(0.835391 - 1.82925i) q^{52} +(-0.581719 + 0.671339i) q^{53} +(-1.05997 + 5.08689i) q^{54} +(-9.46055 + 2.77787i) q^{55} +(2.61991 + 3.02354i) q^{56} +(7.18608 - 4.40899i) q^{57} +(5.68196 - 3.65157i) q^{58} +(-3.38202 + 2.93054i) q^{59} +(-1.34561 - 4.96383i) q^{60} +(7.37119 + 1.05982i) q^{61} +(-5.88816 - 5.10212i) q^{62} +(-10.6999 - 5.43728i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-2.48053 - 5.43160i) q^{65} +(0.699496 + 5.70880i) q^{66} +(-6.97092 + 10.8470i) q^{67} -0.336496 q^{68} +(1.66810 + 8.13741i) q^{69} +11.8793 q^{70} +(-6.79016 + 10.5657i) q^{71} +(-2.98470 + 0.302614i) q^{72} +(4.56063 + 9.98639i) q^{73} +(-7.87592 - 2.31258i) q^{74} +(-5.95475 - 2.87117i) q^{75} +(3.67865 + 3.18756i) q^{76} +(-13.1497 - 1.89064i) q^{77} +(-3.36179 + 0.911324i) q^{78} +(11.8282 - 10.2492i) q^{79} +(2.49793 - 1.60533i) q^{80} +(7.95078 - 4.21725i) q^{81} +(-0.746481 - 0.861485i) q^{82} +(5.91068 - 1.73553i) q^{83} +(1.12914 - 6.83684i) q^{84} +(-0.654309 + 0.755113i) q^{85} +(-0.184641 + 0.404308i) q^{86} +(-11.1534 - 3.52947i) q^{87} +(-3.02055 + 1.37944i) q^{88} +(-1.63266 - 11.3554i) q^{89} +(-5.12460 + 7.28623i) q^{90} -8.04537i q^{91} +(-4.18865 + 2.33564i) q^{92} +(-0.281724 + 13.4917i) q^{93} +(-7.00844 - 4.50405i) q^{94} +(14.3061 - 2.05691i) q^{95} +(-0.686471 - 1.59021i) q^{96} +(1.88225 - 6.41036i) q^{97} +(8.19193 + 3.74113i) q^{98} +(6.83224 - 7.24981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{13}{22}\right)$

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
$3$	−1.71919	+	0.210651i	−0.992577	+	0.121620i
$3$	−1.71919	+	0.210651i	−0.992577	+	0.121620i
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	−2.84902	−	0.836549i	−1.27412	−	0.374116i	−0.426389	−	0.904540i	$-0.640215\pi$
$5$	−2.84902	−	0.836549i	−1.27412	−	0.374116i	−0.847733	+	0.530424i	$0.822033\pi$
$6$	−0.752255	+	1.56016i	−0.307107	+	0.636934i
$7$	−3.02354	−	2.61991i	−1.14279	−	0.990235i	−1.00000		0.000481787i	$-0.999847\pi$
$7$	−3.02354	−	2.61991i	−1.14279	−	0.990235i	−0.142792	−	0.989753i	$-0.545608\pi$
$8$	−0.989821	−	0.142315i	−0.349955	−	0.0503159i
$9$	2.91125	−	0.724301i	0.970417	−	0.241434i
$10$	−2.24405	+	1.94448i	−0.709630	+	0.614898i
$11$	2.79349	−	1.79527i	0.842269	−	0.541294i	−0.0468854	−	0.998900i	$-0.514930\pi$
$11$	2.79349	−	1.79527i	0.842269	−	0.541294i	0.889155	+	0.457607i	$0.151293\pi$
$12$	0.905794	+	1.47633i	0.261480	+	0.426178i
$13$	1.31691	+	1.51980i	0.365246	+	0.421516i	0.908390	−	0.418123i	$-0.137312\pi$
$13$	1.31691	+	1.51980i	0.365246	+	0.421516i	−0.543145	+	0.839639i	$0.682767\pi$
$14$	−3.83866	+	1.12713i	−1.02593	+	0.301239i
$15$	5.07424	+	0.838038i	1.31016	+	0.216380i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	0.139786	−	0.306088i	0.0339030	−	0.0742371i	−0.891923	−	0.452188i	$-0.850644\pi$
$17$	0.139786	−	0.306088i	0.0339030	−	0.0742371i	0.925826	+	0.377950i	$0.123371\pi$
$18$	0.964621	−	2.84069i	0.227363	−	0.669557i
$19$	−4.42768	+	2.02205i	−1.01578	+	0.463890i	−0.852521	−	0.522693i	$-0.824927\pi$
$19$	−4.42768	+	2.02205i	−1.01578	+	0.463890i	−0.163257	+	0.986584i	$0.552200\pi$
$20$	0.422576	+	2.93908i	0.0944908	+	0.657198i
$21$	5.74994	+	3.86723i	1.25474	+	0.843898i
$22$		−	3.32063i		−	0.707961i
$23$	−0.384545	−	4.78039i	−0.0801833	−	0.996780i
$23$	−0.384545	−	4.78039i	−0.0801833	−	0.996780i
$24$	1.73167	+	0.0361594i	0.353476	+	0.00738101i
$25$	3.21085	+	2.06349i	0.642170	+	0.412698i
$26$	1.99051	−	0.286192i	0.390371	−	0.0561269i
$27$	−4.85243	+	1.85847i	−0.933851	+	0.357663i
$28$	−1.12713	+	3.83866i	−0.213008	+	0.725439i
$29$	6.14380	+	2.80578i	1.14087	+	0.521020i	0.894017	−	0.448032i	$-0.147875\pi$
$29$	6.14380	+	2.80578i	1.14087	+	0.521020i	0.246857	+	0.969052i	$0.420602\pi$
$30$	3.44834	−	3.81565i	0.629579	−	0.696639i
$31$	1.10880	−	7.71186i	0.199146	−	1.38509i	−0.607624	−	0.794225i	$-0.707877\pi$
$31$	1.10880	−	7.71186i	0.199146	−	1.38509i	0.806770	−	0.590865i	$-0.201214\pi$
$32$	0.281733	+	0.959493i	0.0498038	+	0.169616i
$33$	−4.42438	+	3.67487i	−0.770185	+	0.639712i
$34$	−0.181924	−	0.283079i	−0.0311996	−	0.0485476i
$35$	6.42246	+	9.99354i	1.08559	+	1.68922i
$36$	−1.86823	−	2.34728i	−0.311371	−	0.391214i
$37$	−2.31258	−	7.87592i	−0.380186	−	1.29479i	−0.898263	−	0.439459i	$-0.855170\pi$
$37$	−2.31258	−	7.87592i	−0.380186	−	1.29479i	0.518077	−	0.855334i	$-0.326648\pi$
$38$	−0.692724	+	4.81800i	−0.112375	+	0.781583i
$39$	−2.58417	−	2.33542i	−0.413799	−	0.373966i
$40$	2.70097	+	1.23349i	0.427061	+	0.195032i
$41$	0.321149	−	1.09373i	0.0501551	−	0.170813i	−0.930607	−	0.366021i	$-0.880720\pi$
$41$	0.321149	−	1.09373i	0.0501551	−	0.170813i	0.980762	+	0.195208i	$0.0625382\pi$
$42$	6.36197	−	2.74638i	0.981673	−	0.423776i
$43$	−0.439950	+	0.0632552i	−0.0670917	+	0.00964633i	−0.175779	−	0.984430i	$-0.556244\pi$
$43$	−0.439950	+	0.0632552i	−0.0670917	+	0.00964633i	0.108687	+	0.994076i	$0.465335\pi$
$44$	−2.79349	−	1.79527i	−0.421135	−	0.270647i
$45$	−8.90014	−	0.371853i	−1.32675	−	0.0554326i
$46$	−4.22942	−	2.26097i	−0.623594	−	0.333362i
$47$		−	8.33095i		−	1.21519i	−0.794245	−	0.607597i	$-0.792134\pi$
$47$		−	8.33095i		−	1.21519i	0.794245	−	0.607597i	$-0.207866\pi$
$48$	0.966633	−	1.43723i	0.139521	−	0.207446i
$49$	1.28165	+	8.91409i	0.183093	+	1.27344i
$50$	3.47183	−	1.58553i	0.490991	−	0.224228i
$51$	−0.175841	+	0.555670i	−0.0246226	+	0.0778093i
$52$	0.835391	−	1.82925i	0.115848	−	0.253671i
$53$	−0.581719	+	0.671339i	−0.0799052	+	0.0922155i	−0.794294	−	0.607533i	$-0.792159\pi$
$53$	−0.581719	+	0.671339i	−0.0799052	+	0.0922155i	0.714389	+	0.699749i	$0.246705\pi$
$54$	−1.05997	+	5.08689i	−0.144244	+	0.692238i
$55$	−9.46055	+	2.77787i	−1.27566	+	0.374568i
$56$	2.61991	+	3.02354i	0.350101	+	0.404038i
$57$	7.18608	−	4.40899i	0.951820	−	0.583985i
$58$	5.68196	−	3.65157i	0.746077	−	0.479475i
$59$	−3.38202	+	2.93054i	−0.440302	+	0.381524i	−0.846611	−	0.532212i	$-0.821361\pi$
$59$	−3.38202	+	2.93054i	−0.440302	+	0.381524i	0.406309	+	0.913736i	$0.366815\pi$
$60$	−1.34561	−	4.96383i	−0.173718	−	0.640827i
$61$	7.37119	+	1.05982i	0.943784	+	0.135696i	0.596993	−	0.802247i	$-0.296362\pi$
$61$	7.37119	+	1.05982i	0.943784	+	0.135696i	0.346791	+	0.937942i	$0.387271\pi$
$62$	−5.88816	−	5.10212i	−0.747798	−	0.647970i
$63$	−10.6999	−	5.43728i	−1.34806	−	0.685032i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	−2.48053	−	5.43160i	−0.307672	−	0.673707i
$66$	0.699496	+	5.70880i	0.0861019	+	0.702705i
$67$	−6.97092	+	10.8470i	−0.851634	+	1.32517i	0.0925361	+	0.995709i	$0.470503\pi$
$67$	−6.97092	+	10.8470i	−0.851634	+	1.32517i	−0.944170	+	0.329459i	$0.893134\pi$
$68$	−0.336496			−0.0408061
$69$	1.66810	+	8.13741i	0.200816	+	0.979629i
$70$	11.8793			1.41985
$71$	−6.79016	+	10.5657i	−0.805843	+	1.25392i	0.157998	+	0.987439i	$0.449496\pi$
$71$	−6.79016	+	10.5657i	−0.805843	+	1.25392i	−0.963841	+	0.266477i	$0.914140\pi$
$72$	−2.98470	+	0.302614i	−0.351750	+	0.0356635i
$73$	4.56063	+	9.98639i	0.533782	+	1.16882i	0.963953	+	0.266072i	$0.0857257\pi$
$73$	4.56063	+	9.98639i	0.533782	+	1.16882i	−0.430172	+	0.902747i	$0.641547\pi$
$74$	−7.87592	−	2.31258i	−0.915557	−	0.268832i
$75$	−5.95475	−	2.87117i	−0.687595	−	0.331534i
$76$	3.67865	+	3.18756i	0.421970	+	0.365639i
$77$	−13.1497	−	1.89064i	−1.49855	−	0.215458i
$78$	−3.36179	+	0.911324i	−0.380647	+	0.103187i
$79$	11.8282	−	10.2492i	1.33078	−	1.15313i	0.354877	−	0.934913i	$-0.384523\pi$
$79$	11.8282	−	10.2492i	1.33078	−	1.15313i	0.975901	−	0.218213i	$-0.0700227\pi$
$80$	2.49793	−	1.60533i	0.279278	−	0.179481i
$81$	7.95078	−	4.21725i	0.883420	−	0.468583i
$82$	−0.746481	−	0.861485i	−0.0824351	−	0.0951351i
$83$	5.91068	−	1.73553i	0.648781	−	0.190499i	0.0592477	−	0.998243i	$-0.481130\pi$
$83$	5.91068	−	1.73553i	0.648781	−	0.190499i	0.589533	+	0.807744i	$0.299312\pi$
$84$	1.12914	−	6.83684i	0.123199	−	0.745960i
$85$	−0.654309	+	0.755113i	−0.0709698	+	0.0819035i
$86$	−0.184641	+	0.404308i	−0.0199104	+	0.0435976i
$87$	−11.1534	−	3.52947i	−1.19577	−	0.378399i
$88$	−3.02055	+	1.37944i	−0.321992	+	0.147049i
$89$	−1.63266	−	11.3554i	−0.173061	−	1.20367i	−0.872370	−	0.488847i	$-0.837418\pi$
$89$	−1.63266	−	11.3554i	−0.173061	−	1.20367i	0.699309	−	0.714820i	$-0.253491\pi$
$90$	−5.12460	+	7.28623i	−0.540180	+	0.768036i
$91$		−	8.04537i		−	0.843383i
$92$	−4.18865	+	2.33564i	−0.436697	+	0.243507i
$93$	−0.281724	+	13.4917i	−0.0292134	+	1.39903i
$94$	−7.00844	−	4.50405i	−0.722866	−	0.464558i
$95$	14.3061	−	2.05691i	1.46777	−	0.211034i
$96$	−0.686471	−	1.59021i	−0.0700627	−	0.162300i
$97$	1.88225	−	6.41036i	0.191114	−	0.650874i	−0.807060	−	0.590469i	$-0.798943\pi$
$97$	1.88225	−	6.41036i	0.191114	−	0.650874i	0.998174	−	0.0604046i	$-0.0192391\pi$
$98$	8.19193	+	3.74113i	0.827510	+	0.377911i
$99$	6.83224	−	7.24981i	0.686666	−	0.728633i
$100$	0.543180	−	3.77790i	0.0543180	−	0.377790i
$101$	−0.162410	−	0.553117i	−0.0161604	−	0.0550372i	0.951018	−	0.309135i	$-0.100040\pi$
$101$	−0.162410	−	0.553117i	−0.0161604	−	0.0550372i	−0.967178	+	0.254098i	$0.918221\pi$
$102$	0.372393	+	0.448344i	0.0368724	+	0.0443927i
$103$	3.74407	+	5.82588i	0.368914	+	0.574041i	0.975233	−	0.221180i	$-0.0709910\pi$
$103$	3.74407	+	5.82588i	0.368914	+	0.574041i	−0.606319	+	0.795221i	$0.707355\pi$
$104$	−1.08722	−	1.69174i	−0.106610	−	0.165889i
$105$	−13.1466	−	15.8279i	−1.28298	−	1.54465i
$106$	0.250266	+	0.852326i	0.0243079	+	0.0827852i
$107$	0.163240	−	1.13536i	0.0157810	−	0.109759i	−0.980408	−	0.196976i	$-0.936888\pi$
$107$	0.163240	−	1.13536i	0.0157810	−	0.109759i	0.996189	+	0.0872163i	$0.0277971\pi$
$108$	3.70630	+	3.64189i	0.356639	+	0.350441i
$109$	−9.88716	−	4.51532i	−0.947019	−	0.432489i	−0.118815	−	0.992916i	$-0.537910\pi$
$109$	−9.88716	−	4.51532i	−0.947019	−	0.432489i	−0.828203	+	0.560427i	$0.810637\pi$
$110$	−2.77787	+	9.46055i	−0.264859	+	0.902028i
$111$	5.63484	+	13.0531i	0.534836	+	1.23894i
$112$	3.96000	−	0.569362i	0.374185	−	0.0537996i
$113$	−3.76459	−	2.41935i	−0.354142	−	0.227594i	0.351458	−	0.936204i	$-0.385686\pi$
$113$	−3.76459	−	2.41935i	−0.354142	−	0.227594i	−0.705600	+	0.708610i	$0.749322\pi$
$114$	0.176008	−	8.42900i	0.0164846	−	0.789448i
$115$	−2.90345	+	13.9411i	−0.270748	+	1.30002i
$116$		−	6.75416i		−	0.627108i
$117$	4.93465	+	3.47067i	0.456209	+	0.320864i
$118$	0.636867	+	4.42951i	0.0586283	+	0.407769i
$119$	−1.22457	+	0.559243i	−0.112256	+	0.0512657i
$120$	−4.90333	−	1.55165i	−0.447611	−	0.141645i
$121$	0.0110428	−	0.0241804i	0.00100389	−	0.00219822i
$122$	4.87674	−	5.62806i	0.441519	−	0.509540i
$123$	−0.321721	+	1.94799i	−0.0290086	+	0.175644i
$124$	−7.47556	+	2.19502i	−0.671325	+	0.197119i
$125$	2.30081	+	2.65528i	0.205791	+	0.237495i
$126$	−10.3589	+	6.06172i	−0.922847	+	0.540021i
$127$	8.81530	−	5.66525i	0.782232	−	0.502710i	−0.0875418	−	0.996161i	$-0.527901\pi$
$127$	8.81530	−	5.66525i	0.782232	−	0.502710i	0.869774	+	0.493451i	$0.164265\pi$
$128$	0.755750	−	0.654861i	0.0667995	−	0.0578821i
$129$	0.743034	−	0.201424i	0.0654205	−	0.0177344i
$130$	−5.91042	−	0.849791i	−0.518378	−	0.0745316i
$131$	7.37999	+	6.39480i	0.644793	+	0.558716i	0.914682	−	0.404175i	$-0.132441\pi$
$131$	7.37999	+	6.39480i	0.644793	+	0.558716i	−0.269889	+	0.962892i	$0.586987\pi$
$132$	5.18073	+	2.49796i	0.450925	+	0.217420i
$133$	18.6849	+	5.48637i	1.62018	+	0.475729i
$134$	5.35628	+	11.7286i	0.462713	+	1.01320i
$135$	15.3794	−	1.23554i	1.32365	−	0.106338i
$136$	−0.181924	+	0.283079i	−0.0155998	+	0.0242738i
$137$	9.33315			0.797385			0.398692	−	0.917085i	$-0.369464\pi$
$137$	9.33315			0.797385			0.398692	+	0.917085i	$0.369464\pi$
$138$	7.74747	+	2.99612i	0.659508	+	0.255046i
$139$	20.0639			1.70180			0.850900	−	0.525328i	$-0.176057\pi$
$139$	20.0639			1.70180			0.850900	+	0.525328i	$0.176057\pi$
$140$	6.42246	−	9.99354i	0.542797	−	0.844608i
$141$	1.75493	+	14.3225i	0.147792	+	1.20617i
$142$	5.21739	+	11.4245i	0.437834	+	0.958722i
$143$	6.40722	+	1.88133i	0.535799	+	0.157325i
$144$	−1.35907	+	2.67449i	−0.113256	+	0.222874i
$145$	−15.1566	−	13.1333i	−1.25869	−	1.09066i
$146$	10.8668	+	1.56240i	0.899339	+	0.129305i
$147$	−4.08118	−	15.0551i	−0.336610	−	1.24172i
$148$	−6.20351	+	5.37537i	−0.509925	+	0.441853i
$149$	−1.22356	+	0.786335i	−0.100238	+	0.0644191i	−0.589800	−	0.807550i	$-0.700793\pi$
$149$	−1.22356	+	0.786335i	−0.100238	+	0.0644191i	0.489561	+	0.871969i	$0.337157\pi$
$150$	−5.63476	+	3.45719i	−0.460076	+	0.282278i
$151$	−1.87590	−	2.16490i	−0.152658	−	0.176177i	0.674269	−	0.738486i	$-0.264459\pi$
$151$	−1.87590	−	2.16490i	−0.152658	−	0.176177i	−0.826927	+	0.562309i	$0.809913\pi$
$152$	4.67038	−	1.37135i	0.378817	−	0.111231i
$153$	0.185251	−	0.992345i	0.0149767	−	0.0802263i
$154$	−8.69977	+	10.0401i	−0.701047	+	0.809051i
$155$	−9.61033	+	21.0437i	−0.771920	+	1.69027i
$156$	−1.05086	+	3.32081i	−0.0841365	+	0.265878i
$157$	−4.03655	+	1.84343i	−0.322152	+	0.147122i	−0.569926	−	0.821696i	$-0.693028\pi$
$157$	−4.03655	+	1.84343i	−0.322152	+	0.147122i	0.247774	+	0.968818i	$0.420301\pi$
$158$	−2.22737	−	15.4917i	−0.177200	−	1.23245i
$159$	0.858668	−	1.27670i	0.0680968	−	0.101249i
$160$		−	2.96930i		−	0.234744i
$161$	−11.3615	+	15.4612i	−0.895413	+	1.21851i
$162$	0.750740	−	8.96863i	0.0589837	−	0.704642i
$163$	1.84628	+	1.18653i	0.144612	+	0.0929363i	0.610946	−	0.791672i	$-0.290789\pi$
$163$	1.84628	+	1.18653i	0.144612	+	0.0929363i	−0.466334	+	0.884609i	$0.654426\pi$
$164$	−1.12831	+	0.162226i	−0.0881059	+	0.0126677i
$165$	15.6794	−	6.76857i	1.22064	−	0.526933i
$166$	1.73553	−	5.91068i	0.134703	−	0.458758i
$167$	−11.6185	−	5.30598i	−0.899065	−	0.410589i	−0.0883904	−	0.996086i	$-0.528172\pi$
$167$	−11.6185	−	5.30598i	−0.899065	−	0.410589i	−0.810675	+	0.585497i	$0.800900\pi$
$168$	−5.14105	−	4.64617i	−0.396641	−	0.358459i
$169$	1.27457	−	8.86480i	0.0980436	−	0.681908i
$170$	0.281495	+	0.958685i	0.0215897	+	0.0735278i
$171$	−11.4255	+	9.09367i	−0.873730	+	0.695410i
$172$	0.240301	+	0.373915i	0.0183228	+	0.0285108i
$173$	−9.24628	−	14.3875i	−0.702982	−	1.09386i	−0.990689	−	0.136142i	$-0.956530\pi$
$173$	−9.24628	−	14.3875i	−0.702982	−	1.09386i	0.287708	−	0.957718i	$-0.407107\pi$
$174$	−8.99917	+	7.47467i	−0.682226	+	0.566653i
$175$	−4.30198	−	14.6512i	−0.325199	−	1.10753i
$176$	−0.472575	+	3.28683i	−0.0356217	+	0.247754i
$177$	5.19703	−	5.75059i	0.390632	−	0.432241i
$178$	−10.4354	−	4.76570i	−0.782168	−	0.357204i
$179$	4.74950	−	16.1753i	0.354994	−	1.20900i	−0.567625	−	0.823287i	$-0.692138\pi$
$179$	4.74950	−	16.1753i	0.354994	−	1.20900i	0.922619	−	0.385712i	$-0.126044\pi$
$180$	3.35900	+	8.25032i	0.250365	+	0.614943i
$181$	−22.3862	+	3.21865i	−1.66395	+	0.239240i	−0.909077	−	0.416629i	$-0.863211\pi$
$181$	−22.3862	+	3.21865i	−1.66395	+	0.239240i	−0.754875	+	0.655869i	$0.772302\pi$
$182$	−6.76819	−	4.34965i	−0.501692	−	0.322418i
$183$	−12.8957	−	0.269279i	−0.953281	−	0.0199056i
$184$	−0.299689	+	4.78646i	−0.0220934	+	0.352862i
$185$			24.3733i			1.79196i
$186$	11.1977	+	7.53119i	0.821053	+	0.552213i
$187$	−0.159020	−	1.10601i	−0.0116287	−	0.0808791i
$188$	−7.57810	+	3.46080i	−0.552690	+	0.252405i
$189$	19.5406	+	7.09378i	1.42137	+	0.515996i
$190$	6.00408	−	13.1471i	0.435582	−	0.953791i
$191$	−5.13683	+	5.92822i	−0.371688	+	0.428951i	−0.910522	−	0.413461i	$-0.864320\pi$
$191$	−5.13683	+	5.92822i	−0.371688	+	0.428951i	0.538834	+	0.842412i	$0.318865\pi$
$192$	−1.70890	−	0.282234i	−0.123329	−	0.0203685i
$193$	4.35595	−	1.27902i	0.313548	−	0.0920661i	−0.121172	−	0.992632i	$-0.538665\pi$
$193$	4.35595	−	1.27902i	0.313548	−	0.0920661i	0.434721	+	0.900565i	$0.356847\pi$
$194$	−4.37512	−	5.04916i	−0.314115	−	0.362508i
$195$	5.40868	+	8.81544i	0.387324	+	0.631287i
$196$	7.57613	−	4.86888i	0.541152	−	0.347777i
$197$	4.14385	−	3.59067i	0.295237	−	0.255825i	−0.494628	−	0.869105i	$-0.664696\pi$
$197$	4.14385	−	3.59067i	0.295237	−	0.255825i	0.789865	+	0.613280i	$0.210150\pi$
$198$	−2.40514	−	9.66719i	−0.170926	−	0.687017i
$199$	9.25058	+	1.33003i	0.655756	+	0.0942835i	0.462158	−	0.886797i	$-0.347075\pi$
$199$	9.25058	+	1.33003i	0.655756	+	0.0942835i	0.193598	+	0.981081i	$0.437984\pi$
$200$	−2.88450	−	2.49944i	−0.203965	−	0.176737i
$201$	9.69944	−	20.1165i	0.684145	−	1.41891i
$202$	−0.553117	−	0.162410i	−0.0389172	−	0.0114271i
$203$	−11.2251	−	24.5796i	−0.787850	−	1.72515i
$204$	0.578502	−	0.0708834i	0.0405032	−	0.00496283i
$205$	−1.82992	+	2.84742i	−0.127807	+	0.198872i
$206$	6.92524			0.482504
$207$	−4.58195	−	13.6384i	−0.318468	−	0.947934i
$208$	−2.01098			−0.139436
$209$	−8.73855	+	13.5974i	−0.604458	+	0.940555i
$210$	−20.4229	+	2.50240i	−1.40931	+	0.172682i
$211$	−0.549711	−	1.20370i	−0.0378437	−	0.0828661i	0.889766	−	0.456417i	$-0.150867\pi$
$211$	−0.549711	−	1.20370i	−0.0378437	−	0.0828661i	−0.927610	+	0.373551i	$0.878140\pi$
$212$	0.852326	+	0.250266i	0.0585380	+	0.0171883i
$213$	9.44792	−	19.5948i	0.647360	−	1.34262i
$214$	−0.866870	−	0.751148i	−0.0592580	−	0.0513474i
$215$	1.30634	+	0.187824i	0.0890919	+	0.0128095i
$216$	5.06753	−	1.14898i	0.344802	−	0.0781785i
$217$	−23.5569	+	20.4122i	−1.59915	+	1.38567i
$218$	−9.14393	+	5.87645i	−0.619305	+	0.398003i
$219$	−9.94426	−	16.2078i	−0.671971	−	1.09522i
$220$	6.45689	+	7.45165i	0.435324	+	0.502390i
$221$	0.649276	−	0.190645i	0.0436750	−	0.0128241i
$222$	14.0274	+	2.31670i	0.941456	+	0.155486i
$223$	−3.43565	+	3.96496i	−0.230068	+	0.265513i	−0.859032	−	0.511921i	$-0.828934\pi$
$223$	−3.43565	+	3.96496i	−0.230068	+	0.265513i	0.628964	+	0.777435i	$0.283479\pi$
$224$	1.66196	−	3.63918i	0.111044	−	0.243153i
$225$	10.8422	+	3.68171i	0.722812	+	0.245447i
$226$	−4.07058	+	1.85897i	−0.270771	+	0.123657i
$227$	−0.0525893	−	0.365766i	−0.00349047	−	0.0242768i	0.988002	−	0.154443i	$-0.0493581\pi$
$227$	−0.0525893	−	0.365766i	−0.00349047	−	0.0242768i	−0.991492	+	0.130166i	$0.958449\pi$
$228$	−6.99577	−	4.70513i	−0.463306	−	0.311605i
$229$		−	24.3543i		−	1.60938i	−0.593698	−	0.804688i	$-0.702332\pi$
$229$		−	24.3543i		−	1.60938i	0.593698	−	0.804688i	$-0.297668\pi$
$230$	10.1583	+	9.97968i	0.669819	+	0.658041i
$231$	23.0051	+	0.480374i	1.51363	+	0.0316063i
$232$	−5.68196	−	3.65157i	−0.373039	−	0.239737i
$233$	1.72714	−	0.248325i	0.113149	−	0.0162683i	−0.0855079	−	0.996337i	$-0.527251\pi$
$233$	1.72714	−	0.248325i	0.113149	−	0.0162683i	0.198656	+	0.980069i	$0.436342\pi$
$234$	5.58759	−	2.27491i	0.365272	−	0.148715i
$235$	−6.96925	+	23.7351i	−0.454624	+	1.54831i
$236$	4.07065	+	1.85901i	0.264977	+	0.121011i
$237$	−18.1760	+	20.1120i	−1.18066	+	1.30641i
$238$	−0.191588	+	1.33252i	−0.0124188	+	0.0863747i
$239$	6.95175	+	23.6755i	0.449672	+	1.53144i	0.803022	+	0.595950i	$0.203224\pi$
$239$	6.95175	+	23.6755i	0.449672	+	1.53144i	−0.353350	+	0.935491i	$0.614958\pi$
$240$	−3.95627	+	3.28606i	−0.255376	+	0.212114i
$241$	−1.26781	−	1.97275i	−0.0816666	−	0.127076i	0.798017	−	0.602634i	$-0.205882\pi$
$241$	−1.26781	−	1.97275i	−0.0816666	−	0.127076i	−0.879684	+	0.475559i	$0.842246\pi$
$242$	−0.0143716	−	0.0223627i	−0.000923843	−	0.00143753i
$243$	−12.7806	+	8.92510i	−0.819873	+	0.572546i
$244$	−2.09806	−	7.14533i	−0.134314	−	0.457433i
$245$	3.80561	−	26.4686i	0.243132	−	1.69102i
$246$	1.46482	+	1.32381i	0.0933934	+	0.0844032i
$247$	−8.90396	−	4.06630i	−0.566546	−	0.258733i
$248$	−2.19502	+	7.47556i	−0.139384	+	0.474699i
$249$	−9.79600	+	4.22881i	−0.620797	+	0.267990i
$250$	3.47768	−	0.500014i	0.219948	−	0.0316237i
$251$	8.50239	+	5.46416i	0.536666	+	0.344894i	0.780734	−	0.624864i	$-0.214845\pi$
$251$	8.50239	+	5.46416i	0.536666	+	0.344894i	−0.244068	+	0.969758i	$0.578482\pi$
$252$	−0.501020	+	11.9917i	−0.0315613	+	0.755406i
$253$	−9.65630	−	12.6636i	−0.607087	−	0.796155i
$254$		−	10.4788i		−	0.657497i
$255$	0.965819	−	1.43602i	0.0604819	−	0.0899269i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	1.49729	−	0.683789i	0.0933983	−	0.0426536i	−0.368168	−	0.929759i	$-0.620015\pi$
$257$	1.49729	−	0.683789i	0.0933983	−	0.0426536i	0.461566	+	0.887106i	$0.347288\pi$
$258$	0.232266	−	0.733978i	0.0144602	−	0.0456955i
$259$	−13.6421	+	29.8719i	−0.847676	+	1.85615i
$260$	−3.91031	+	4.51273i	−0.242507	+	0.279868i
$261$	19.9184	+	3.71837i	1.23292	+	0.230161i
$262$	9.36957	−	2.75116i	0.578854	−	0.169967i
$263$	−3.18074	−	3.67076i	−0.196133	−	0.226349i	0.649161	−	0.760651i	$-0.275120\pi$
$263$	−3.18074	−	3.67076i	−0.196133	−	0.226349i	−0.845294	+	0.534302i	$0.820575\pi$
$264$	4.90233	−	3.00781i	0.301718	−	0.185118i
$265$	2.21894	−	1.42602i	0.136308	−	0.0876000i
$266$	14.7172	−	12.7526i	0.902371	−	0.781909i
$267$	5.19888	+	19.1782i	0.318166	+	1.17368i
$268$	12.7626	+	1.83498i	0.779598	+	0.112089i
$269$	−7.36354	−	6.38054i	−0.448963	−	0.389028i	0.400824	−	0.916155i	$-0.368724\pi$
$269$	−7.36354	−	6.38054i	−0.448963	−	0.389028i	−0.849787	+	0.527127i	$0.823269\pi$
$270$	7.27532	−	13.6059i	0.442762	−	0.828032i
$271$	−14.8160	−	4.35037i	−0.900007	−	0.264266i	−0.201178	−	0.979555i	$-0.564477\pi$
$271$	−14.8160	−	4.35037i	−0.900007	−	0.264266i	−0.698829	+	0.715289i	$0.746295\pi$
$272$	0.139786	+	0.306088i	0.00847574	+	0.0185593i
$273$	1.69477	+	13.8315i	0.102572	+	0.837123i
$274$	5.04588	−	7.85154i	0.304833	−	0.474329i
$275$	12.6740			0.764271
$276$	6.70909	−	4.89776i	0.403840	−	0.294811i
$277$	1.96700			0.118185			0.0590927	−	0.998252i	$-0.481179\pi$
$277$	1.96700			0.118185			0.0590927	+	0.998252i	$0.481179\pi$
$278$	10.8474	−	16.8788i	0.650582	−	1.01233i
$279$	−2.35772	−	23.2543i	−0.141153	−	1.39220i
$280$	−4.93486	−	10.8058i	−0.294914	−	0.645772i
$281$	6.61909	+	1.94354i	0.394862	+	0.115942i	0.473135	−	0.880990i	$-0.343122\pi$
$281$	6.61909	+	1.94354i	0.394862	+	0.115942i	−0.0782730	+	0.996932i	$0.524941\pi$
$282$	12.9977	+	6.26700i	0.773999	+	0.373194i
$283$	8.48295	+	7.35052i	0.504259	+	0.436943i	0.869473	−	0.493981i	$-0.164459\pi$
$283$	8.48295	+	7.35052i	0.504259	+	0.436943i	−0.365214	+	0.930924i	$0.619004\pi$
$284$	12.4316	+	1.78740i	0.737681	+	0.106063i
$285$	−24.1617	+	6.54982i	−1.43121	+	0.387978i
$286$	5.04668	−	4.37298i	0.298417	−	0.258579i
$287$	−3.83650	+	2.46557i	−0.226461	+	0.145538i
$288$	1.51516	+	2.58927i	0.0892814	+	0.152574i
$289$	11.0585	+	12.7622i	0.650499	+	0.750716i
$290$	−19.2427	+	5.65018i	−1.12997	+	0.331790i
$291$	−1.88560	+	11.4172i	−0.110536	+	0.669285i
$292$	7.18939	−	8.29699i	0.420727	−	0.485545i
$293$	−4.76749	+	10.4393i	−0.278520	+	0.609873i	−0.996257	−	0.0864410i	$-0.972451\pi$
$293$	−4.76749	+	10.4393i	−0.278520	+	0.609873i	0.717737	+	0.696314i	$0.245178\pi$
$294$	−14.8716	−	4.70608i	−0.867328	−	0.274464i
$295$	12.0870	−	5.51995i	0.703732	−	0.321384i
$296$	1.16818	+	8.12487i	0.0678991	+	0.472248i
$297$	−10.2188	+	13.9030i	−0.592953	+	0.806736i
$298$			1.45445i			0.0842541i
$299$	6.75881	−	6.87978i	0.390872	−	0.397868i
$300$	−0.138011	+	6.60936i	−0.00796808	+	0.381591i
$301$	1.49593	+	0.961376i	0.0862240	+	0.0554128i
$302$	−2.83542	+	0.407671i	−0.163160	+	0.0234589i
$303$	0.395729	+	0.916703i	0.0227340	+	0.0526632i
$304$	1.37135	−	4.67038i	0.0786521	−	0.267864i
$305$	−20.1141	−	9.18580i	−1.15173	−	0.525977i
$306$	−0.734659	−	0.692345i	−0.0419977	−	0.0395788i
$307$	1.11094	−	7.72674i	0.0634046	−	0.440989i	−0.933248	−	0.359233i	$-0.883038\pi$
$307$	1.11094	−	7.72674i	0.0634046	−	0.440989i	0.996652	−	0.0817554i	$-0.0260526\pi$
$308$	3.74279	+	12.7468i	0.213265	+	0.726315i
$309$	−7.66400	−	9.22712i	−0.435990	−	0.524913i
$310$	12.5073	+	19.4618i	0.710369	+	1.10536i
$311$	15.3196	+	23.8377i	0.868694	+	1.35171i	0.935271	+	0.353933i	$0.115156\pi$
$311$	15.3196	+	23.8377i	0.868694	+	1.35171i	−0.0665772	+	0.997781i	$0.521208\pi$
$312$	2.22551	+	2.67941i	0.125994	+	0.151692i
$313$	−3.74744	−	12.7626i	−0.211818	−	0.721385i	−0.995025	−	0.0996245i	$-0.968236\pi$
$313$	−3.74744	−	12.7626i	−0.211818	−	0.721385i	0.783207	−	0.621761i	$-0.213582\pi$
$314$	−0.631532	+	4.39240i	−0.0356394	+	0.247878i
$315$	25.9357	+	24.4419i	1.46131	+	1.37715i
$316$	−14.2366	−	6.50165i	−0.800873	−	0.365746i
$317$	1.67282	−	5.69709i	0.0939547	−	0.319980i	−0.899083	−	0.437779i	$-0.855765\pi$
$317$	1.67282	−	5.69709i	0.0939547	−	0.319980i	0.993038	+	0.117798i	$0.0375836\pi$
$318$	−0.609799	−	1.41259i	−0.0341958	−	0.0792144i
$319$	22.1998	−	3.19184i	1.24295	−	0.178709i
$320$	−2.49793	−	1.60533i	−0.139639	−	0.0897404i
$321$	−0.0414761	+	1.98629i	−0.00231497	+	0.110864i
$322$	6.86427	+	17.9169i	0.382531	+	0.998468i
$323$			1.63791i			0.0911357i
$324$	−7.13901	−	5.48037i	−0.396612	−	0.304465i
$325$	1.09232	+	7.59727i	0.0605912	+	0.421421i
$326$	1.99635	−	0.911701i	0.110567	−	0.0504944i
$327$	17.9491	+	5.67996i	0.992588	+	0.314102i
$328$	−0.473535	+	1.03690i	−0.0261466	+	0.0572531i
$329$	−21.8264	+	25.1890i	−1.20333	+	1.38871i
$330$	2.78281	−	16.8497i	0.153189	−	0.927544i
$331$	−6.96421	+	2.04488i	−0.382788	+	0.112397i	−0.467464	−	0.884012i	$-0.654832\pi$
$331$	−6.96421	+	2.04488i	−0.382788	+	0.112397i	0.0846768	+	0.996408i	$0.473014\pi$
$332$	−4.03408	−	4.65558i	−0.221399	−	0.255508i
$333$	−12.4370	−	21.2538i	−0.681545	−	1.16470i
$334$	−10.7451	+	6.90546i	−0.587946	+	0.377850i
$335$	28.9343	−	25.0717i	1.58085	−	1.36982i
$336$	−6.68807	+	1.81302i	−0.364864	+	0.0989085i
$337$	−3.18413	−	0.457809i	−0.173451	−	0.0249385i	0.0550421	−	0.998484i	$-0.482471\pi$
$337$	−3.18413	−	0.457809i	−0.173451	−	0.0249385i	−0.228493	+	0.973546i	$0.573380\pi$
$338$	−6.76846	−	5.86491i	−0.368156	−	0.319009i
$339$	6.98169	+	3.36632i	0.379193	+	0.182833i
$340$	0.958685	+	0.281495i	0.0519920	+	0.0152662i
$341$	−10.7474	−	23.5336i	−0.582006	−	1.27442i
$342$	1.47299	+	14.5282i	0.0796502	+	0.785593i
$343$	4.33836	−	6.75062i	0.234250	−	0.364499i
$344$	0.444474			0.0239644
$345$	2.05487	−	24.5791i	0.110631	−	1.32330i
$346$	−17.1024			−0.919433
$347$	6.87059	−	10.6908i	0.368833	−	0.573915i	−0.606383	−	0.795173i	$-0.707380\pi$
$347$	6.87059	−	10.6908i	0.368833	−	0.573915i	0.975215	+	0.221258i	$0.0710164\pi$
$348$	1.42277	+	11.6117i	0.0762686	+	0.622452i
$349$	−8.25417	−	18.0741i	−0.441836	−	0.967486i	−0.991258	−	0.131940i	$-0.957879\pi$
$349$	−8.25417	−	18.0741i	−0.441836	−	0.967486i	0.549422	−	0.835545i	$-0.314848\pi$
$350$	−14.6512	−	4.30198i	−0.783140	−	0.229951i
$351$	−9.21472	−	4.92726i	−0.491845	−	0.262998i
$352$	2.50956	+	2.17455i	0.133760	+	0.115904i
$353$	26.6533	+	3.83217i	1.41861	+	0.203966i	0.808568	−	0.588402i	$-0.200243\pi$
$353$	26.6533	+	3.83217i	1.41861	+	0.203966i	0.610044	+	0.792368i	$0.291152\pi$
$354$	−2.02798	−	7.48102i	−0.107786	−	0.397612i
$355$	28.1840	−	24.4216i	1.49585	−	1.29616i
$356$	−9.65098	+	6.20231i	−0.511501	+	0.328722i
$357$	1.98747	−	1.21940i	0.105188	−	0.0645377i
$358$	−11.0398	−	12.7406i	−0.583469	−	0.673359i
$359$	2.98130	−	0.875389i	0.157347	−	0.0462013i	−0.202110	−	0.979363i	$-0.564780\pi$
$359$	2.98130	−	0.875389i	0.157347	−	0.0462013i	0.359457	+	0.933161i	$0.382962\pi$
$360$	8.75663	+	1.63469i	0.461515	+	0.0861557i
$361$	3.07326	−	3.54673i	0.161751	−	0.186670i
$362$	−9.39518	+	20.5726i	−0.493800	+	1.08127i
$363$	−0.0138911	+	0.0438969i	−0.000729093	+	0.00230399i
$364$	−7.31832	+	3.34217i	−0.383584	+	0.175177i
$365$	−4.63924	−	32.2666i	−0.242829	−	1.68891i
$366$	−7.19850	+	10.7030i	−0.376272	+	0.559455i
$367$			17.1813i			0.896858i	0.893818	+	0.448429i	$0.148016\pi$
$367$			17.1813i			0.896858i	−0.893818	+	0.448429i	$0.851984\pi$
$368$	3.86460	+	2.83987i	0.201456	+	0.148038i
$369$	0.142754	−	3.41674i	0.00743146	−	0.177869i
$370$	20.5041	+	13.1772i	1.06596	+	0.685049i
$371$	3.51770	−	0.505769i	0.182630	−	0.0262582i
$372$	12.3896	−	5.34841i	0.642368	−	0.277302i
$373$	−3.31040	+	11.2742i	−0.171406	+	0.583756i	0.828318	+	0.560259i	$0.189298\pi$
$373$	−3.31040	+	11.2742i	−0.171406	+	0.583756i	−0.999724	+	0.0234971i	$0.992520\pi$
$374$	−1.01640	−	0.464176i	−0.0525570	−	0.0240020i
$375$	−4.51488	−	4.08027i	−0.233147	−	0.210704i
$376$	−1.18562	+	8.24616i	−0.0611436	+	0.425263i
$377$	3.82662	+	13.0323i	0.197081	+	0.671197i
$378$	16.5321	−	12.6034i	0.850319	−	0.648248i
$379$	4.97611	+	7.74298i	0.255606	+	0.397730i	0.945214	−	0.326453i	$-0.105853\pi$
$379$	4.97611	+	7.74298i	0.255606	+	0.397730i	−0.689608	+	0.724183i	$0.742217\pi$
$380$	−7.81399	−	12.1588i	−0.400849	−	0.623734i
$381$	−13.9618	+	11.5966i	−0.715286	+	0.594113i
$382$	2.20996	+	7.52642i	0.113071	+	0.385085i
$383$	−2.55660	+	17.7815i	−0.130636	+	0.908594i	0.814091	+	0.580737i	$0.197236\pi$
$383$	−2.55660	+	17.7815i	−0.130636	+	0.908594i	−0.944727	+	0.327857i	$0.893674\pi$
$384$	−1.16133	+	1.28503i	−0.0592640	+	0.0655765i
$385$	35.8822	+	16.3868i	1.82872	+	0.835150i
$386$	1.27902	−	4.35595i	0.0651006	−	0.221712i
$387$	−1.23499	+	0.502808i	−0.0627780	+	0.0255592i
$388$	−6.61299	+	0.950804i	−0.335724	+	0.0482698i
$389$	13.0570	+	8.39122i	0.662016	+	0.425452i	0.828039	−	0.560670i	$-0.189456\pi$
$389$	13.0570	+	8.39122i	0.662016	+	0.425452i	−0.166023	+	0.986122i	$0.553093\pi$
$390$	10.3402	+	0.215915i	0.523595	+	0.0109333i
$391$	−1.51697	−	0.550525i	−0.0767166	−	0.0278412i
$392$		−	9.00576i		−	0.454860i
$393$	−14.0347	−	9.43929i	−0.707957	−	0.476149i
$394$	−0.780327	−	5.42729i	−0.0393123	−	0.273423i
$395$	−42.2728	+	19.3053i	−2.12698	+	0.971357i
$396$	−9.43287	−	3.20315i	−0.474020	−	0.160964i
$397$	2.27392	−	4.97920i	0.114125	−	0.249899i	−0.843947	−	0.536427i	$-0.819774\pi$
$397$	2.27392	−	4.97920i	0.114125	−	0.249899i	0.958072	+	0.286528i	$0.0925011\pi$
$398$	6.12014	−	7.06301i	0.306775	−	0.354037i
$399$	−33.2786	−	5.49614i	−1.66601	−	0.275151i
$400$	−3.66214	+	1.07530i	−0.183107	+	0.0537651i
$401$	−1.43577	−	1.65697i	−0.0716992	−	0.0827452i	0.718767	−	0.695251i	$-0.244707\pi$
$401$	−1.43577	−	1.65697i	−0.0716992	−	0.0827452i	−0.790466	+	0.612506i	$0.790161\pi$
$402$	−11.6791	−	19.0355i	−0.582503	−	0.949403i
$403$	13.1806	−	8.47068i	0.656575	−	0.421955i
$404$	−0.435665	+	0.377506i	−0.0216752	+	0.0187816i
$405$	−26.1799	+	5.36382i	−1.30089	+	0.266530i
$406$	−26.7464	−	3.84556i	−1.32740	−	0.190852i
$407$	−20.5996	−	17.8496i	−1.02108	−	0.884773i
$408$	0.253131	−	0.524989i	0.0125318	−	0.0259908i
$409$	−3.48616	−	1.02363i	−0.172380	−	0.0506152i	0.194404	−	0.980922i	$-0.437723\pi$
$409$	−3.48616	−	1.02363i	−0.172380	−	0.0506152i	−0.366783	+	0.930306i	$0.619541\pi$
$410$	1.40607	+	3.07886i	0.0694407	+	0.152054i
$411$	−16.0455	+	1.96604i	−0.791466	+	0.0969777i
$412$	3.74407	−	5.82588i	0.184457	−	0.287020i
$413$	17.9034			0.880971
$414$	−13.9505	−	3.51889i	−0.685631	−	0.172944i
$415$	−18.2915			−0.897895
$416$	−1.08722	+	1.69174i	−0.0533052	+	0.0829446i
$417$	−34.4938	+	4.22649i	−1.68917	+	0.206972i
$418$	6.71448	+	14.7027i	0.328416	+	0.719131i
$419$	−20.3765	−	5.98307i	−0.995456	−	0.292292i	−0.256866	−	0.966447i	$-0.582690\pi$
$419$	−20.3765	−	5.98307i	−0.995456	−	0.292292i	−0.738590	+	0.674155i	$0.764508\pi$
$420$	−8.93629	+	18.5337i	−0.436046	+	0.904353i
$421$	28.7303	+	24.8950i	1.40023	+	1.21331i	0.946721	+	0.322054i	$0.104373\pi$
$421$	28.7303	+	24.8950i	1.40023	+	1.21331i	0.453508	+	0.891252i	$0.350172\pi$
$422$	−1.30981	−	0.188323i	−0.0637607	−	0.00916741i
$423$	−6.03412	−	24.2535i	−0.293389	−	1.17925i
$424$	0.671339	−	0.581719i	0.0326031	−	0.0282508i
$425$	1.08044	−	0.694356i	0.0524090	−	0.0336812i
$426$	−11.3763	−	18.5419i	−0.551183	−	0.898356i
$427$	−19.5105	−	22.5163i	−0.944178	−	1.08964i
$428$	−1.10057	+	0.323157i	−0.0531981	+	0.0156204i
$429$	−11.4116	−	1.88468i	−0.550955	−	0.0909932i
$430$	0.864270	−	0.997421i	0.0416788	−	0.0480999i
$431$	13.9684	−	30.5865i	0.672833	−	1.47330i	−0.197230	−	0.980357i	$-0.563195\pi$
$431$	13.9684	−	30.5865i	0.672833	−	1.47330i	0.870063	−	0.492941i	$-0.164078\pi$
$432$	1.77313	−	4.88426i	0.0853095	−	0.234994i
$433$	28.2901	−	12.9196i	1.35953	−	0.620878i	0.403729	−	0.914879i	$-0.367714\pi$
$433$	28.2901	−	12.9196i	1.35953	−	0.620878i	0.955805	+	0.294000i	$0.0949867\pi$
$434$	4.43599	+	30.8530i	0.212934	+	1.48099i
$435$	28.8238	+	19.3859i	1.38199	+	0.929484i
$436$			10.8694i			0.520550i
$437$	11.3688	+	20.3884i	0.543845	+	0.975311i
$438$	−19.0112	−	0.396976i	−0.908389	−	0.0189682i
$439$	−18.2095	−	11.7025i	−0.869093	−	0.558532i	0.0283821	−	0.999597i	$-0.490964\pi$
$439$	−18.2095	−	11.7025i	−0.869093	−	0.558532i	−0.897475	+	0.441065i	$0.854601\pi$
$440$	9.75959	−	1.40322i	0.465270	−	0.0668957i
$441$	10.1877	+	25.0229i	0.485129	+	1.19157i
$442$	0.190645	−	0.649276i	0.00906804	−	0.0308829i
$443$	23.3040	+	10.6426i	1.10721	+	0.505645i	0.883225	−	0.468949i	$-0.155367\pi$
$443$	23.3040	+	10.6426i	1.10721	+	0.505645i	0.223982	+	0.974593i	$0.428094\pi$
$444$	9.53270	−	10.5481i	0.452402	−	0.500590i
$445$	−4.84785	+	33.7175i	−0.229810	+	1.59836i
$446$	1.47808	+	5.03387i	0.0699891	+	0.238361i
$447$	1.93790	−	1.60961i	0.0916594	−	0.0761318i
$448$	−2.16295	−	3.36562i	−0.102190	−	0.159011i
$449$	−6.30751	−	9.81467i	−0.297670	−	0.463183i	0.659913	−	0.751342i	$-0.270593\pi$
$449$	−6.30751	−	9.81467i	−0.297670	−	0.463183i	−0.957583	+	0.288159i	$0.906957\pi$
$450$	8.95898	−	7.13054i	0.422330	−	0.336137i
$451$	−1.06642	−	3.63189i	−0.0502157	−	0.171019i
$452$	−0.636855	+	4.42942i	−0.0299551	+	0.208343i
$453$	3.68107	+	3.32672i	0.172952	+	0.156303i
$454$	−0.336134	−	0.153507i	−0.0157756	−	0.00720446i
$455$	−6.73034	+	22.9214i	−0.315523	+	1.07457i
$456$	−7.74040	+	3.34143i	−0.362478	+	0.156477i
$457$	−10.3483	+	1.48786i	−0.484074	+	0.0695993i	−0.380031	−	0.924974i	$-0.624087\pi$
$457$	−10.3483	+	1.48786i	−0.484074	+	0.0695993i	−0.104042	+	0.994573i	$0.533178\pi$
$458$	−20.4881	−	13.1669i	−0.957347	−	0.615250i
$459$	−0.109444	+	1.74506i	−0.00510840	+	0.0814523i
$460$	13.8874	−	3.15028i	0.647505	−	0.146883i
$461$		−	22.6459i		−	1.05472i	−0.849641	−	0.527362i	$-0.823181\pi$
$461$		−	22.6459i		−	1.05472i	0.849641	−	0.527362i	$-0.176819\pi$
$462$	12.8416	−	19.0934i	0.597446	−	0.888307i
$463$	5.52918	+	38.4563i	0.256963	+	1.78721i	0.554173	+	0.832402i	$0.313035\pi$
$463$	5.52918	+	38.4563i	0.256963	+	1.78721i	−0.297210	+	0.954812i	$0.596056\pi$
$464$	−6.14380	+	2.80578i	−0.285219	+	0.130255i
$465$	12.0891	−	38.2026i	0.560620	−	1.77160i
$466$	0.724857	−	1.58721i	0.0335783	−	0.0735263i
$467$	−2.32240	+	2.68019i	−0.107468	+	0.124025i	−0.806935	−	0.590640i	$-0.798875\pi$
$467$	−2.32240	+	2.68019i	−0.107468	+	0.124025i	0.699467	+	0.714665i	$0.253421\pi$
$468$	1.10710	−	5.93049i	0.0511759	−	0.274137i
$469$	49.4950	−	14.5330i	2.28547	−	0.671074i
$470$	16.1994	+	18.6951i	0.747221	+	0.862339i
$471$	6.55130	−	4.01952i	0.301868	−	0.185210i
$472$	3.76466	−	2.41940i	0.173282	−	0.111362i
$473$	−1.11544	+	0.966531i	−0.0512878	+	0.0444411i
$474$	7.09261	+	26.1640i	0.325775	+	1.20175i
$475$	−18.3891	−	2.64395i	−0.843749	−	0.121313i
$476$	1.01741	+	0.881591i	0.0466329	+	0.0404077i
$477$	−1.20728	+	2.37578i	−0.0552775	+	0.108779i
$478$	23.6755	+	6.95175i	1.08289	+	0.317966i
$479$	−11.7548	−	25.7394i	−0.537090	−	1.17606i	−0.962555	−	0.271088i	$-0.912617\pi$
$479$	−11.7548	−	25.7394i	−0.537090	−	1.17606i	0.425465	−	0.904975i	$-0.360111\pi$
$480$	0.625487	+	5.10480i	0.0285495	+	0.233001i
$481$	8.92434	−	13.8865i	0.406915	−	0.633172i
$482$	−2.34501			−0.106812
$483$	16.2757	−	28.9741i	0.740571	−	1.31837i
$484$	−0.0265826			−0.00120830
$485$	−10.7252	+	16.6887i	−0.487005	+	0.757794i
$486$	0.598588	+	15.5770i	0.0271525	+	0.706585i
$487$	−1.56441	−	3.42558i	−0.0708903	−	0.155228i	0.870870	−	0.491514i	$-0.163556\pi$
$487$	−1.56441	−	3.42558i	−0.0708903	−	0.155228i	−0.941760	+	0.336286i	$0.890829\pi$
$488$	−7.14533	−	2.09806i	−0.323454	−	0.0949746i
$489$	−3.42405	−	1.65095i	−0.154841	−	0.0746587i
$490$	−20.2094	−	17.5115i	−0.912966	−	0.791089i
$491$	−37.1255	−	5.33784i	−1.67545	−	0.240893i	−0.761922	−	0.647668i	$-0.775744\pi$
$491$	−37.1255	−	5.33784i	−1.67545	−	0.240893i	−0.913528	+	0.406775i	$0.866653\pi$
$492$	1.90560	−	0.516577i	0.0859112	−	0.0232891i
$493$	1.71763	−	1.48833i	0.0773580	−	0.0670311i
$494$	−8.23464	+	5.29208i	−0.370494	+	0.238102i
$495$	−25.5300	+	14.9394i	−1.14749	+	0.671474i
$496$	5.10212	+	5.88816i	0.229092	+	0.264386i
$497$	48.2115	−	14.1562i	2.16258	−	0.634992i
$498$	−1.73862	+	10.5272i	−0.0779095	+	0.471735i
$499$	−16.0723	+	18.5485i	−0.719496	+	0.830343i	−0.991246	−	0.132025i	$-0.957852\pi$
$499$	−16.0723	+	18.5485i	−0.719496	+	0.830343i	0.271750	+	0.962368i	$0.412398\pi$
$500$	1.45953	−	3.19593i	0.0652724	−	0.142927i
$501$	21.0921	+	6.67456i	0.942327	+	0.298197i
$502$	9.19348	−	4.19852i	0.410325	−	0.187389i
$503$	3.03450	+	21.1054i	0.135302	+	0.941045i	0.938487	+	0.345315i	$0.112228\pi$
$503$	3.03450	+	21.1054i	0.135302	+	0.941045i	−0.803185	+	0.595730i	$0.796863\pi$
$504$	9.81719	+	6.90469i	0.437292	+	0.307559i
$505$			1.71171i			0.0761699i
$506$	−15.8739	+	1.27693i	−0.705681	+	0.0567666i
$507$	−0.323842	+	15.5088i	−0.0143823	+	0.688770i
$508$	−8.81530	−	5.66525i	−0.391116	−	0.251355i
$509$	42.4766	−	6.10722i	1.88274	−	0.270698i	0.897393	−	0.441233i	$-0.145459\pi$
$509$	42.4766	−	6.10722i	1.88274	−	0.270698i	0.985352	+	0.170535i	$0.0545497\pi$
$510$	−0.685893	−	1.58887i	−0.0303719	−	0.0703562i
$511$	12.3742	−	42.1427i	0.547403	−	1.86429i
$512$	−0.909632	−	0.415415i	−0.0402004	−	0.0183589i
$513$	17.7271	−	18.0406i	0.782669	−	0.796511i
$514$	0.234256	−	1.62928i	0.0103326	−	0.0718646i
$515$	−5.79330	−	19.7302i	−0.255283	−	0.869415i
$516$	−0.491889	−	0.592213i	−0.0216542	−	0.0260707i
$517$	−14.9563	−	23.2724i	−0.657777	−	1.02352i
$518$	17.7544	+	27.6264i	0.780084	+	1.21383i
$519$	18.9269	+	22.7871i	0.830798	+	1.00024i
$520$	1.68228	+	5.72933i	0.0737729	+	0.251248i
$521$	−2.73795	+	19.0428i	−0.119952	+	0.834282i	0.837654	+	0.546201i	$0.183926\pi$
$521$	−2.73795	+	19.0428i	−0.119952	+	0.834282i	−0.957606	+	0.288081i	$0.906983\pi$
$522$	13.8968	−	14.7461i	0.608245	−	0.645419i
$523$	16.0627	+	7.33557i	0.702371	+	0.320762i	0.734392	−	0.678725i	$-0.237467\pi$
$523$	16.0627	+	7.33557i	0.702371	+	0.320762i	−0.0320215	+	0.999487i	$0.510194\pi$
$524$	2.75116	−	9.36957i	0.120185	−	0.409312i
$525$	10.4822	+	24.2820i	0.457482	+	1.05975i
$526$	−4.80768	+	0.691240i	−0.209625	+	0.0301395i
$527$	−2.20551	−	1.41739i	−0.0960735	−	0.0617427i
$528$	0.120072	−	5.75025i	0.00522546	−	0.250247i
$529$	−22.7042	+	3.67655i	−0.987141	+	0.159850i
$530$		−	2.63766i		−	0.114572i
$531$	−7.72332	+	10.9811i	−0.335164	+	0.476541i
$532$	−2.77139	−	19.2755i	−0.120155	−	0.835698i
$533$	2.08518	−	0.952269i	0.0903191	−	0.0412474i
$534$	18.9444	+	5.99492i	0.819805	+	0.259426i
$535$	−1.41486	+	3.09811i	−0.0611696	+	0.133943i
$536$	8.44365	−	9.74450i	0.364710	−	0.420898i
$537$	−4.75795	+	28.8090i	−0.205321	+	1.24320i
$538$	−9.34868	+	2.74502i	−0.403050	+	0.118346i
$539$	19.5835	+	22.6005i	0.843520	+	0.973474i
$540$	−7.51271	−	13.4763i	−0.323296	−	0.579929i
$541$	−36.5312	+	23.4772i	−1.57060	+	1.00936i	−0.591420	+	0.806363i	$0.701433\pi$
$541$	−36.5312	+	23.4772i	−1.57060	+	1.00936i	−0.979179	+	0.202999i	$0.934931\pi$
$542$	−11.6699	+	10.1120i	−0.501265	+	0.434348i
$543$	37.8081	−	10.2492i	1.62250	−	0.439833i
$544$	0.333071	+	0.0478884i	0.0142803	+	0.00205320i
$545$	24.3915	+	21.1353i	1.04482	+	0.905338i
$546$	12.5521	+	6.05217i	0.537180	+	0.259009i
$547$	−35.4346	−	10.4045i	−1.51507	−	0.444866i	−0.584630	−	0.811300i	$-0.698760\pi$
$547$	−35.4346	−	10.4045i	−1.51507	−	0.444866i	−0.930444	+	0.366434i	$0.880578\pi$
$548$	−3.87713	−	8.48973i	−0.165623	−	0.362663i
$549$	22.2270	−	2.25357i	0.948625	−	0.0961798i
$550$	6.85208	−	10.6620i	0.292174	−	0.454631i
$551$	−32.8762			−1.40057
$552$	−0.493051	−	8.29198i	−0.0209856	−	0.352930i
$553$	−62.6151			−2.66267
$554$	1.06344	−	1.65474i	0.0451812	−	0.0703033i
$555$	−5.13426	−	41.9023i	−0.217937	−	1.77866i
$556$	−8.33485	−	18.2508i	−0.353477	−	0.774006i
$557$	18.1238	+	5.32163i	0.767931	+	0.225485i	0.642156	−	0.766574i	$-0.278040\pi$
$557$	18.1238	+	5.32163i	0.767931	+	0.225485i	0.125775	+	0.992059i	$0.459858\pi$
$558$	−20.8374	−	10.5888i	−0.882118	−	0.448258i
$559$	−0.675510	−	0.585333i	−0.0285710	−	0.0247569i
$560$	−11.7584	−	1.69061i	−0.496884	−	0.0714412i
$561$	0.506367	+	1.86794i	0.0213788	+	0.0788645i
$562$	5.21356	−	4.51758i	0.219921	−	0.190562i
$563$	23.9202	−	15.3726i	1.00812	−	0.647878i	0.0712125	−	0.997461i	$-0.477313\pi$
$563$	23.9202	−	15.3726i	1.00812	−	0.647878i	0.936905	+	0.349583i	$0.113677\pi$
$564$	12.2992	−	7.54613i	0.517890	−	0.317749i
$565$	8.70148	+	10.0420i	0.366074	+	0.422472i
$566$	10.7699	−	3.16232i	0.452692	−	0.132922i
$567$	−35.0883	−	8.07933i	−1.47357	−	0.339300i
$568$	8.22470	−	9.49181i	0.345101	−	0.398267i
$569$	−13.9582	+	30.5643i	−0.585160	+	1.28132i	0.353163	+	0.935562i	$0.385106\pi$
$569$	−13.9582	+	30.5643i	−0.585160	+	1.28132i	−0.938323	+	0.345760i	$0.887621\pi$
$570$	−7.55272	+	23.8672i	−0.316349	+	0.999686i
$571$	4.45035	−	2.03241i	0.186241	−	0.0850536i	−0.320112	−	0.947380i	$-0.603720\pi$
$571$	4.45035	−	2.03241i	0.186241	−	0.0850536i	0.506353	+	0.862326i	$0.330993\pi$
$572$	−0.950338	−	6.60975i	−0.0397356	−	0.276367i
$573$	7.58242	−	11.2738i	0.316760	−	0.470971i
$574$			4.56045i			0.190350i
$575$	8.62956	−	16.1426i	0.359878	−	0.673194i
$576$	2.99738	+	0.125233i	0.124891	+	0.00521802i
$577$	23.8380	+	15.3197i	0.992387	+	0.637769i	0.932777	−	0.360453i	$-0.117378\pi$
$577$	23.8380	+	15.3197i	0.992387	+	0.637769i	0.0596101	+	0.998222i	$0.481014\pi$
$578$	16.7149	−	2.40324i	0.695248	−	0.0999615i
$579$	−7.21930	+	3.11648i	−0.300024	+	0.129516i
$580$	−5.65018	+	19.2427i	−0.234611	+	0.799011i
$581$	−22.4181	−	10.2380i	−0.930061	−	0.424744i
$582$	8.58529	+	7.75885i	0.355872	+	0.321615i
$583$	−0.419793	+	2.91972i	−0.0173860	+	0.120922i
$584$	−3.09300	−	10.5338i	−0.127989	−	0.435891i
$585$	−11.1556	−	14.0161i	−0.461225	−	0.579494i
$586$	6.20464	+	9.65460i	0.256311	+	0.398828i
$587$	−3.26296	−	5.07727i	−0.134677	−	0.209561i	0.767364	−	0.641211i	$-0.221568\pi$
$587$	−3.26296	−	5.07727i	−0.134677	−	0.209561i	−0.902041	+	0.431650i	$0.857932\pi$
$588$	−11.9992	+	9.96647i	−0.494838	+	0.411010i
$589$	10.6844	+	36.3876i	0.440242	+	1.49933i
$590$	1.89105	−	13.1525i	0.0778533	−	0.541481i
$591$	−6.36770	+	7.04596i	−0.261932	+	0.289832i
$592$	7.46664	+	3.40990i	0.306877	+	0.140146i
$593$	0.946543	−	3.22363i	0.0388699	−	0.132379i	−0.937772	−	0.347251i	$-0.887115\pi$
$593$	0.946543	−	3.22363i	0.0388699	−	0.132379i	0.976642	+	0.214872i	$0.0689335\pi$
$594$	6.17130	+	16.1131i	0.253212	+	0.661129i
$595$	3.95666	−	0.568882i	0.162207	−	0.0233219i
$596$	1.22356	+	0.786335i	0.0501190	+	0.0322095i
$597$	−16.1837	−	0.337935i	−0.662355	−	0.0138308i
$598$	−2.13355	−	9.40536i	−0.0872474	−	0.384614i
$599$		−	25.0545i		−	1.02370i	−0.859075	−	0.511849i	$-0.828961\pi$
$599$		−	25.0545i		−	1.02370i	0.859075	−	0.511849i	$-0.171039\pi$
$600$	5.48553	+	3.68939i	0.223946	+	0.150619i
$601$	−5.44515	−	37.8719i	−0.222112	−	1.54483i	−0.730027	−	0.683418i	$-0.760493\pi$
$601$	−5.44515	−	37.8719i	−0.222112	−	1.54483i	0.507915	−	0.861407i	$-0.330417\pi$
$602$	1.61752	−	0.738698i	0.0659253	−	0.0301071i
$603$	−12.4376	+	36.6273i	−0.506500	+	1.49158i
$604$	−1.18999	+	2.60571i	−0.0484199	+	0.106025i
$605$	−0.0516893	+	0.0596526i	−0.00210147	+	0.00242522i
$606$	0.985127	+	0.162699i	0.0400180	+	0.00660919i
$607$	1.78539	−	0.524237i	0.0724666	−	0.0212781i	−0.245298	−	0.969448i	$-0.578886\pi$
$607$	1.78539	−	0.524237i	0.0724666	−	0.0212781i	0.317765	+	0.948170i	$0.397068\pi$
$608$	−3.18756	−	3.67865i	−0.129273	−	0.149189i
$609$	24.4759	+	39.8925i	0.991813	+	1.61653i
$610$	−18.6021	+	11.9548i	−0.753176	+	0.484037i
$611$	12.6614	−	10.9711i	0.512224	−	0.443844i
$612$	−0.979625	+	0.243725i	−0.0395990	+	0.00985198i
$613$	28.6602	+	4.12071i	1.15757	+	0.166434i	0.694236	−	0.719748i	$-0.255742\pi$
$613$	28.6602	+	4.12071i	1.15757	+	0.166434i	0.463338	+	0.886182i	$0.346652\pi$
$614$	−5.89953	−	5.11197i	−0.238086	−	0.206302i
$615$	2.54618	−	5.28074i	0.102672	−	0.212940i
$616$	12.7468	+	3.74279i	0.513582	+	0.150801i
$617$	14.9187	+	32.6675i	0.600606	+	1.31514i	0.928817	+	0.370538i	$0.120827\pi$
$617$	14.9187	+	32.6675i	0.600606	+	1.31514i	−0.328212	+	0.944604i	$0.606446\pi$
$618$	−11.9058	+	1.45881i	−0.478922	+	0.0586820i
$619$	4.15672	−	6.46799i	0.167073	−	0.259970i	−0.747614	−	0.664133i	$-0.768801\pi$
$619$	4.15672	−	6.46799i	0.167073	−	0.259970i	0.914687	+	0.404163i	$0.132437\pi$
$620$	23.1343			0.929095
$621$	10.7502	+	22.4818i	0.431391	+	0.902165i
$622$	28.3360			1.13617
$623$	−24.8137	+	38.6109i	−0.994140	+	1.54691i
$624$	3.45726	−	0.423616i	0.138401	−	0.0169582i
$625$	−12.2615	−	26.8489i	−0.490459	−	1.07395i
$626$	−12.7626	−	3.74744i	−0.510096	−	0.149778i
$627$	12.1589	−	25.2174i	0.485581	−	1.00709i
$628$	3.35369	+	2.90599i	0.133827	+	0.115962i
$629$	−2.73399	−	0.393088i	−0.109011	−	0.0156734i
$630$	34.5838	−	8.60422i	1.37785	−	0.342800i
$631$	−15.4012	+	13.3452i	−0.613113	+	0.531266i	−0.905123	−	0.425150i	$-0.860221\pi$
$631$	−15.4012	+	13.3452i	−0.613113	+	0.531266i	0.292010	+	0.956415i	$0.405676\pi$
$632$	−13.1664	+	8.46155i	−0.523733	+	0.336583i
$633$	1.19862	+	1.95360i	0.0476409	+	0.0776485i
$634$	−3.88830	−	4.48734i	−0.154424	−	0.178215i
$635$	−29.8543	+	8.76600i	−1.18473	+	0.347868i
$636$	−1.51803	−	0.250711i	−0.0601939	−	0.00994134i
$637$	−11.8598	+	13.6869i	−0.469902	+	0.542296i
$638$	9.31695	−	20.4013i	0.368862	−	0.807694i
$639$	−12.1151	+	35.6775i	−0.479267	+	1.41138i
$640$	−2.70097	+	1.23349i	−0.106765	+	0.0487581i
$641$	−4.08684	−	28.4246i	−0.161421	−	1.12270i	−0.895959	−	0.444137i	$-0.853510\pi$
$641$	−4.08684	−	28.4246i	−0.161421	−	1.12270i	0.734538	−	0.678567i	$-0.237399\pi$
$642$	1.64855	+	1.10876i	0.0650630	+	0.0437593i
$643$			12.9601i			0.511097i	0.966796	+	0.255548i	$0.0822560\pi$
$643$			12.9601i			0.511097i	−0.966796	+	0.255548i	$0.917744\pi$
$644$	18.7837	+	3.91200i	0.740183	+	0.154154i
$645$	−2.28542	−	0.0477223i	−0.0899884	−	0.00187907i
$646$	1.37790	+	0.885521i	0.0542127	+	0.0348404i
$647$	41.5048	−	5.96749i	1.63172	−	0.234606i	0.735279	−	0.677764i	$-0.237051\pi$
$647$	41.5048	−	5.96749i	1.63172	−	0.234606i	0.896443	+	0.443158i	$0.146142\pi$
$648$	−8.47002	+	3.04281i	−0.332734	+	0.119533i
$649$	−4.18655	+	14.2581i	−0.164336	+	0.559678i
$650$	6.98179	+	3.18848i	0.273848	+	0.125062i
$651$	36.1990	−	40.0548i	1.41875	−	1.56987i
$652$	0.312335	−	2.17234i	0.0122320	−	0.0850752i
$653$	−8.75808	−	29.8273i	−0.342730	−	1.16723i	−0.932955	−	0.359993i	$-0.882779\pi$
$653$	−8.75808	−	29.8273i	−0.342730	−	1.16723i	0.590225	−	0.807239i	$-0.299039\pi$
$654$	14.4823	−	12.0289i	0.566303	−	0.470368i
$655$	−15.6762	−	24.3927i	−0.612520	−	0.953100i
$656$	0.616281	+	0.958952i	0.0240617	+	0.0374408i
$657$	20.5103	+	25.7696i	0.800183	+	1.00537i
$658$	9.39009	+	31.9797i	0.366064	+	1.24670i
$659$	−1.41394	+	9.83414i	−0.0550791	+	0.383084i	0.943572	+	0.331167i	$0.107442\pi$
$659$	−1.41394	+	9.83414i	−0.0550791	+	0.383084i	−0.998651	+	0.0519171i	$0.983467\pi$
$660$	−12.6703	−	11.4507i	−0.493193	−	0.445717i
$661$	3.03210	+	1.38472i	0.117935	+	0.0538592i	0.473509	−	0.880789i	$-0.342987\pi$
$661$	3.03210	+	1.38472i	0.117935	+	0.0538592i	−0.355574	+	0.934648i	$0.615714\pi$
$662$	−2.04488	+	6.96421i	−0.0794764	+	0.270672i
$663$	−1.07607	+	0.464526i	−0.0417912	+	0.0180407i
$664$	−6.09751	+	0.876689i	−0.236629	+	0.0340221i
$665$	−48.6440	−	31.2616i	−1.88633	−	1.21227i
$666$	−24.6038	−	1.02796i	−0.953377	−	0.0398327i
$667$	11.0501	−	30.4487i	0.427863	−	1.17898i
$668$			12.7727i			0.494192i
$669$	5.07133	−	7.54025i	0.196069	−	0.291523i
$670$	−5.44861	−	37.8959i	−0.210498	−	1.46405i
$671$	22.4940	−	10.2727i	0.868371	−	0.396572i
$672$	−2.09063	+	6.60655i	−0.0806478	+	0.254853i
$673$	1.47408	−	3.22779i	0.0568217	−	0.124422i	−0.879091	−	0.476653i	$-0.841850\pi$
$673$	1.47408	−	3.22779i	0.0568217	−	0.124422i	0.935913	+	0.352231i	$0.114577\pi$
$674$	−2.10661	+	2.43115i	−0.0811434	+	0.0936445i
$675$	−19.4154	−	4.04565i	−0.747298	−	0.155717i
$676$	−8.59318	+	2.52319i	−0.330507	+	0.0970456i
$677$	6.25498	+	7.21864i	0.240399	+	0.277435i	0.863109	−	0.505018i	$-0.168514\pi$
$677$	6.25498	+	7.21864i	0.240399	+	0.277435i	−0.622710	+	0.782452i	$0.713969\pi$
$678$	6.60651	−	4.05340i	0.253722	−	0.155670i
$679$	−22.4857	+	14.4507i	−0.862921	+	0.554566i
$680$	0.755113	−	0.654309i	0.0289573	−	0.0250916i
$681$	0.167460	+	0.617745i	0.00641709	+	0.0236720i
$682$	−25.6082	−	3.68191i	−0.980589	−	0.140987i
$683$	−26.7419	−	23.1720i	−1.02325	−	0.886651i	−0.0296448	−	0.999560i	$-0.509438\pi$
$683$	−26.7419	−	23.1720i	−1.02325	−	0.886651i	−0.993605	+	0.112909i	$0.963983\pi$
$684$	13.0182	+	6.61536i	0.497764	+	0.252944i
$685$	−26.5904	−	7.80763i	−1.01597	−	0.298314i
$686$	−3.33349	−	7.29933i	−0.127273	−	0.278690i
$687$	5.13027	+	41.8697i	0.195732	+	1.59743i
$688$	0.240301	−	0.373915i	0.00916138	−	0.0142554i
$689$	−1.78637			−0.0680553
$690$	−19.5663	−	15.0171i	−0.744877	−	0.571693i
$691$	−16.2491			−0.618147			−0.309073	−	0.951038i	$-0.600019\pi$
$691$	−16.2491			−0.618147			−0.309073	+	0.951038i	$0.600019\pi$
$692$	−9.24628	+	14.3875i	−0.351491	+	0.546930i
$693$	−39.6514	+	4.02021i	−1.50623	+	0.152715i
$694$	−5.27919	−	11.5598i	−0.200395	−	0.438805i
$695$	−57.1626	−	16.7844i	−2.16830	−	0.636670i
$696$	10.5376	+	5.08085i	0.399426	+	0.192589i
$697$	−0.289886	−	0.251188i	−0.0109802	−	0.00951442i
$698$	−19.6675	−	2.82775i	−0.744424	−	0.107032i
$699$	−2.91697	+	0.790742i	−0.110330	+	0.0299086i
$700$	−11.5401	+	9.99955i	−0.436175	+	0.377947i
$701$	−25.1960	+	16.1925i	−0.951641	+	0.611583i	−0.921673	−	0.387968i	$-0.873177\pi$
$701$	−25.1960	+	16.1925i	−0.951641	+	0.611583i	−0.0299686	+	0.999551i	$0.509541\pi$
$702$	−9.12693	+	5.08804i	−0.344474	+	0.192036i
$703$	26.1649	+	30.1959i	0.986826	+	1.13886i
$704$	3.18612	−	0.935530i	0.120081	−	0.0352591i
$705$	6.98166	−	42.2733i	0.262944	−	1.59210i
$706$	17.6337	−	20.3504i	0.663652	−	0.765896i
$707$	−0.958066	+	2.09787i	−0.0360318	+	0.0788986i
$708$	−7.38984	−	2.33850i	−0.277727	−	0.0878862i
$709$	−23.8693	+	10.9007i	−0.896429	+	0.409385i	−0.809698	−	0.586846i	$-0.800369\pi$
$709$	−23.8693	+	10.9007i	−0.896429	+	0.409385i	−0.0867306	+	0.996232i	$0.527642\pi$
$710$	−5.30732	−	36.9132i	−0.199180	−	1.38533i
$711$	27.0114	−	38.4052i	1.01301	−	1.44031i
$712$			11.4721i			0.429937i
$713$	−37.2921	−	2.33493i	−1.39660	−	0.0874436i
$714$	0.0486788	−	2.33122i	0.00182176	−	0.0872439i
$715$	−16.6805	−	10.7199i	−0.623815	−	0.400902i
$716$	−16.6866	+	2.39917i	−0.623607	+	0.0896611i
$717$	−16.9387	−	39.2384i	−0.632587	−	1.46538i
$718$	0.875389	−	2.98130i	0.0326692	−	0.111261i
$719$	22.9762	+	10.4929i	0.856868	+	0.391319i	0.794886	−	0.606759i	$-0.207531\pi$
$719$	22.9762	+	10.4929i	0.856868	+	0.391319i	0.0619820	+	0.998077i	$0.480258\pi$
$720$	6.10938	−	6.48276i	0.227683	−	0.241598i
$721$	3.94297	−	27.4239i	0.146844	−	1.02132i
$722$	−1.32217	−	4.50290i	−0.0492061	−	0.167581i
$723$	2.59517	+	3.12447i	0.0965153	+	0.116200i
$724$	12.2273	+	19.0261i	0.454425	+	0.707100i
$725$	13.9371	+	21.6866i	0.517612	+	0.805420i
$726$	0.0294183	+	0.0354184i	0.00109182	+	0.00131450i
$727$	3.47428	+	11.8323i	0.128854	+	0.438836i	0.998495	−	0.0548492i	$-0.0174678\pi$
$727$	3.47428	+	11.8323i	0.128854	+	0.438836i	−0.869641	+	0.493685i	$0.835650\pi$
$728$	−1.14497	+	7.96348i	−0.0424356	+	0.295146i
$729$	20.0922	−	18.0362i	0.744154	−	0.668008i
$730$	−29.6526	−	13.5419i	−1.09749	−	0.501208i
$731$	−0.0421370	+	0.143505i	−0.00155849	+	0.00530774i
$732$	5.11214	+	11.8422i	0.188950	+	0.437702i
$733$	5.86820	−	0.843720i	0.216747	−	0.0311635i	−0.0330858	−	0.999453i	$-0.510533\pi$
$733$	5.86820	−	0.843720i	0.216747	−	0.0311635i	0.249833	+	0.968289i	$0.419624\pi$
$734$	14.4539	+	9.28893i	0.533502	+	0.342861i
$735$	−0.966932	+	46.3063i	−0.0356658	+	1.70804i
$736$	4.47841	−	1.71576i	0.165076	−	0.0632438i
$737$			42.8156i			1.57713i
$738$	−2.79717	−	1.96732i	−0.102965	−	0.0724182i
$739$	−5.65645	−	39.3415i	−0.208076	−	1.44720i	−0.779427	−	0.626494i	$-0.784489\pi$
$739$	−5.65645	−	39.3415i	−0.208076	−	1.44720i	0.571351	−	0.820706i	$-0.306420\pi$
$740$	22.1707	−	10.1250i	0.815011	−	0.372203i
$741$	16.1642	+	5.11513i	0.593807	+	0.187909i
$742$	1.47633	−	3.23272i	0.0541979	−	0.118677i
$743$	−3.48982	+	4.02746i	−0.128029	+	0.147753i	−0.816145	−	0.577848i	$-0.803893\pi$
$743$	−3.48982	+	4.02746i	−0.128029	+	0.147753i	0.688116	+	0.725601i	$0.258438\pi$
$744$	2.19893	−	13.3143i	0.0806167	−	0.488127i
$745$	4.14376	−	1.21672i	0.151816	−	0.0445771i
$746$	7.69472	+	8.88018i	0.281724	+	0.325126i
$747$	15.9504	−	9.33368i	0.583595	−	0.341501i
$748$	−0.939999	+	0.604101i	−0.0343698	+	0.0220881i
$749$	−3.46811	+	3.00513i	−0.126722	+	0.109805i
$750$	−5.87347	+	1.59220i	−0.214469	+	0.0581389i
$751$	8.36986	+	1.20340i	0.305421	+	0.0439128i	0.293321	−	0.956014i	$-0.405239\pi$
$751$	8.36986	+	1.20340i	0.305421	+	0.0439128i	0.0120994	+	0.999927i	$0.496149\pi$
$752$	6.29611	+	5.45561i	0.229596	+	0.198946i
$753$	−15.7683	−	7.60290i	−0.574628	−	0.277065i
$754$	13.0323	+	3.82662i	0.474608	+	0.139357i
$755$	3.53343	+	7.73713i	0.128595	+	0.281583i
$756$	−1.66472	−	20.7216i	−0.0605452	−	0.753637i
$757$	13.9286	−	21.6733i	0.506242	−	0.787729i	−0.490235	−	0.871590i	$-0.663089\pi$
$757$	13.9286	−	21.6733i	0.506242	−	0.787729i	0.996477	+	0.0838617i	$0.0267254\pi$
$758$	9.20410			0.334308
$759$	19.2687	+	19.7371i	0.699408	+	0.716411i
$760$	−14.4532			−0.524273
$761$	22.6031	−	35.1712i	0.819363	−	1.27495i	−0.139255	−	0.990257i	$-0.544471\pi$
$761$	22.6031	−	35.1712i	0.819363	−	1.27495i	0.958618	−	0.284697i	$-0.0918929\pi$
$762$	2.20737	+	18.0150i	0.0799645	+	0.652616i
$763$	18.0645	+	39.5558i	0.653979	+	1.43202i
$764$	7.52642	+	2.20996i	0.272296	+	0.0799534i
$765$	−1.35793	+	2.67224i	−0.0490961	+	0.0966151i
$766$	13.5766	+	11.7642i	0.490542	+	0.425057i
$767$	−8.90765	−	1.28073i	−0.321636	−	0.0462443i
$768$	0.453174	+	1.67172i	0.0163525	+	0.0603228i
$769$	16.0631	−	13.9187i	0.579249	−	0.501922i	−0.315240	−	0.949012i	$-0.602085\pi$
$769$	16.0631	−	13.9187i	0.579249	−	0.501922i	0.894489	+	0.447090i	$0.147540\pi$
$770$	33.1848	−	21.3266i	1.19590	−	0.768557i
$771$	−2.43009	+	1.49097i	−0.0875175	+	0.0536960i
$772$	−2.97297	−	3.43099i	−0.106999	−	0.123484i
$773$	−19.9728	+	5.86455i	−0.718372	+	0.210933i	−0.620433	−	0.784259i	$-0.713043\pi$
$773$	−19.9728	+	5.86455i	−0.718372	+	0.210933i	−0.0979390	+	0.995192i	$0.531225\pi$
$774$	−0.244696	+	1.31078i	−0.00879543	+	0.0471149i
$775$	19.4735	−	22.4736i	0.699509	−	0.807277i
$776$	−2.77538	+	6.07724i	−0.0996305	+	0.218160i
$777$	17.1608	−	54.2294i	0.615639	−	1.94547i
$778$	14.1183	−	6.44761i	0.506165	−	0.231158i
$779$	0.789642	+	5.49208i	0.0282919	+	0.196774i
$780$	5.77196	−	8.58197i	0.206669	−	0.307284i
$781$			41.7053i			1.49233i
$782$	−1.28327	+	0.978522i	−0.0458896	+	0.0349919i
$783$	−35.0268	−	2.19676i	−1.25176	−	0.0785058i
$784$	−7.57613	−	4.86888i	−0.270576	−	0.173889i
$785$	13.0424	−	1.87521i	0.465502	−	0.0669290i
$786$	−15.5286	+	6.70348i	−0.553886	+	0.239105i
$787$	1.92259	−	6.54775i	0.0685330	−	0.233402i	−0.918103	−	0.396342i	$-0.870279\pi$
$787$	1.92259	−	6.54775i	0.0685330	−	0.233402i	0.986636	+	0.162940i	$0.0520977\pi$
$788$	−4.98761	−	2.27776i	−0.177676	−	0.0811419i
$789$	6.24155	+	5.64073i	0.222205	+	0.200815i
$790$	−6.61372	+	45.9994i	−0.235305	+	1.63659i
$791$	5.04389	+	17.1779i	0.179340	+	0.610776i
$792$	−7.79446	+	6.20368i	−0.276964	+	0.220438i
$793$	8.09649	+	12.5984i	0.287515	+	0.447382i
$794$	−2.95939	−	4.60490i	−0.105025	−	0.163422i
$795$	−3.51439	+	2.91903i	−0.124643	+	0.103527i
$796$	−2.63299	−	8.96714i	−0.0933239	−	0.317832i
$797$	−1.65794	+	11.5313i	−0.0587274	+	0.408458i	0.939159	+	0.343482i	$0.111606\pi$
$797$	−1.65794	+	11.5313i	−0.0587274	+	0.408458i	−0.997887	+	0.0649764i	$0.979303\pi$
$798$	−22.6154	+	25.0243i	−0.800577	+	0.885851i
$799$	−2.55000	−	1.16455i	−0.0902126	−	0.0411987i
$800$	−1.07530	+	3.66214i	−0.0380177	+	0.129476i
$801$	−12.9778	−	31.8758i	−0.458547	−	1.12628i
$802$	−2.17017	+	0.312024i	−0.0766314	+	0.0110179i
$803$	30.6683	+	19.7093i	1.08226	+	0.695528i
$804$	−22.3279	−	0.466233i	−0.787444	−	0.0164428i
$805$	45.3033	−	34.5448i	1.59673	−	1.21754i
$806$		−	15.6679i		−	0.551877i
$807$	14.0034	+	9.41824i	0.492943	+	0.331538i
$808$	0.0820399	+	0.570600i	0.00288615	+	0.0200736i
$809$	−4.55250	+	2.07906i	−0.160057	+	0.0730957i	−0.493833	−	0.869557i	$-0.664405\pi$
$809$	−4.55250	+	2.07906i	−0.160057	+	0.0730957i	0.333775	+	0.942653i	$0.391677\pi$
$810$	−9.64157	+	24.9238i	−0.338770	+	0.875734i
$811$	3.68193	−	8.06230i	0.129290	−	0.283106i	−0.833906	−	0.551907i	$-0.813900\pi$
$811$	3.68193	−	8.06230i	0.129290	−	0.283106i	0.963196	+	0.268802i	$0.0866276\pi$
$812$	−17.6953	+	20.4215i	−0.620984	+	0.716653i
$813$	26.3880	+	4.35811i	0.925466	+	0.152846i
$814$	−26.1530	+	7.67922i	−0.916663	+	0.269156i
$815$	−4.26750	−	4.92495i	−0.149484	−	0.172514i
$816$	−0.304796	−	0.496778i	−0.0106700	−	0.0173907i
$817$	1.82005	−	1.16967i	0.0636755	−	0.0409217i
$818$	−2.74589	+	2.37933i	−0.0960079	+	0.0831913i
$819$	−5.82727	−	23.4221i	−0.203621	−	0.818434i
$820$	3.35028	+	0.481697i	0.116997	+	0.0168216i
$821$	16.8253	+	14.5792i	0.587206	+	0.508817i	0.897026	−	0.441979i	$-0.145723\pi$
$821$	16.8253	+	14.5792i	0.587206	+	0.508817i	−0.309820	+	0.950795i	$0.600269\pi$
$822$	−7.02091	+	14.5612i	−0.244882	+	0.507882i
$823$	27.4492	+	8.05981i	0.956819	+	0.280947i	0.722623	−	0.691242i	$-0.242936\pi$
$823$	27.4492	+	8.05981i	0.956819	+	0.280947i	0.234196	+	0.972189i	$0.424754\pi$
$824$	−2.87685	−	6.29942i	−0.100220	−	0.219451i
$825$	−21.7891	+	2.66980i	−0.758598	+	0.0929504i
$826$	9.67933	−	15.0613i	0.336787	−	0.524051i
$827$	30.2864			1.05316			0.526581	−	0.850125i	$-0.323474\pi$
$827$	30.2864			1.05316			0.526581	+	0.850125i	$0.323474\pi$
$828$	−10.5025	+	9.83348i	−0.364987	+	0.341737i
$829$	9.73151			0.337989			0.168995	−	0.985617i	$-0.445948\pi$
$829$	9.73151			0.337989			0.168995	+	0.985617i	$0.445948\pi$
$830$	−9.88914	+	15.3878i	−0.343257	+	0.534118i
$831$	−3.38165	+	0.414351i	−0.117308	+	0.0143737i
$832$	0.835391	+	1.82925i	0.0289620	+	0.0634179i
$833$	2.90765	+	0.853763i	0.100744	+	0.0295811i
$834$	−15.0932	+	31.3030i	−0.522634	+	1.08393i
$835$	28.6626	+	24.8363i	0.991911	+	0.859496i
$836$	15.9988	+	2.30028i	0.553330	+	0.0795568i
$837$	8.95192	+	39.4819i	0.309423	+	1.36469i
$838$	−16.0496	+	13.9071i	−0.554425	+	0.480412i
$839$	25.1182	−	16.1425i	0.867175	−	0.557300i	−0.0297121	−	0.999558i	$-0.509459\pi$
$839$	25.1182	−	16.1425i	0.867175	−	0.557300i	0.896888	+	0.442259i	$0.145823\pi$
$840$	10.7602	+	17.5378i	0.371263	+	0.605111i
$841$	10.8829	+	12.5595i	0.375272	+	0.433086i
$842$	36.4758	−	10.7102i	1.25704	−	0.369099i
$843$	−11.7889	−	1.94700i	−0.406031	−	0.0670583i
$844$	−0.866566	+	1.00007i	−0.0298284	+	0.0344238i
$845$	−11.0471	+	24.1898i	−0.380032	+	0.832154i
$846$	−23.6656	−	8.03621i	−0.813641	−	0.276291i
$847$	−0.0967389	+	0.0441792i	−0.00332399	+	0.00151801i
$848$	−0.126420	−	0.879267i	−0.00434127	−	0.0301942i
$849$	−16.1322	−	10.8500i	−0.553656	−	0.372371i
$850$		−	1.28432i		−	0.0440518i
$851$	−36.7607	+	14.0837i	−1.26014	+	0.482782i
$852$	−21.7489	−	0.454143i	−0.745104	−	0.0155587i
$853$	−13.4788	−	8.66233i	−0.461507	−	0.296592i	0.289151	−	0.957283i	$-0.406627\pi$
$853$	−13.4788	−	8.66233i	−0.461507	−	0.296592i	−0.750658	+	0.660691i	$0.770263\pi$
$854$	−29.4901	+	4.24003i	−1.00913	+	0.145091i
$855$	40.1588	−	16.3501i	1.37340	−	0.559161i
$856$	−0.323157	+	1.10057i	−0.0110453	+	0.0376167i
$857$	43.5545	+	19.8907i	1.48779	+	0.679452i	0.982969	−	0.183771i	$-0.0588303\pi$
$857$	43.5545	+	19.8907i	1.48779	+	0.679452i	0.504823	+	0.863223i	$0.331558\pi$
$858$	−7.75505	+	8.58108i	−0.264753	+	0.292953i
$859$	−0.0392731	+	0.273151i	−0.00133998	+	0.00931978i	−0.990480	−	0.137653i	$-0.956044\pi$
$859$	−0.0392731	+	0.273151i	−0.00133998	+	0.00931978i	0.989140	+	0.146973i	$0.0469531\pi$
$860$	−0.371824	−	1.26632i	−0.0126791	−	0.0431810i
$861$	6.07631	−	5.04695i	0.207080	−	0.172000i
$862$	−18.1791	−	28.2872i	−0.619182	−	0.963467i
$863$	15.6209	+	24.3066i	0.531741	+	0.827405i	0.998371	−	0.0570475i	$-0.0181686\pi$
$863$	15.6209	+	24.3066i	0.531741	+	0.827405i	−0.466631	+	0.884452i	$0.654532\pi$
$864$	−3.15028	−	4.13228i	−0.107175	−	0.140583i
$865$	14.3070	+	48.7253i	0.486453	+	1.65671i
$866$	4.42607	−	30.7840i	0.150404	−	1.04608i
$867$	−21.7000	−	19.6112i	−0.736972	−	0.666030i
$868$	28.3534	+	12.9486i	0.962379	+	0.439504i
$869$	14.6419	−	49.8659i	0.496694	−	1.69158i
$870$	31.8918	−	13.7673i	1.08123	−	0.466754i
$871$	−25.6653	+	3.69011i	−0.869635	+	0.125035i
$872$	9.14393	+	5.87645i	0.309653	+	0.199002i
$873$	0.836678	−	20.0255i	0.0283172	−	0.677761i
$874$	23.2983	+	1.45875i	0.788077	+	0.0493430i
$875$		−	14.0563i		−	0.475189i
$876$	−10.6122	+	15.7786i	−0.358552	+	0.533109i
$877$	0.931736	+	6.48037i	0.0314625	+	0.218826i	0.999487	−	0.0320295i	$-0.0101970\pi$
$877$	0.931736	+	6.48037i	0.0314625	+	0.218826i	−0.968024	+	0.250856i	$0.919288\pi$
$878$	−19.6896	+	8.99195i	−0.664493	+	0.303464i
$879$	5.99717	−	18.9515i	0.202280	−	0.639219i
$880$	4.09597	−	8.96892i	0.138075	−	0.302342i
$881$	10.8764	−	12.5521i	0.366437	−	0.422891i	−0.542349	−	0.840153i	$-0.682465\pi$
$881$	10.8764	−	12.5521i	0.366437	−	0.422891i	0.908786	+	0.417263i	$0.137010\pi$
$882$	26.5585	+	4.95794i	0.894270	+	0.166943i
$883$	15.5044	−	4.55251i	0.521765	−	0.153204i	−0.0102361	−	0.999948i	$-0.503258\pi$
$883$	15.5044	−	4.55251i	0.521765	−	0.153204i	0.532001	+	0.846744i	$0.321440\pi$
$884$	−0.443136	−	0.511406i	−0.0149043	−	0.0172004i
$885$	−19.6171	+	12.0360i	−0.659422	+	0.404586i
$886$	21.5522	−	13.8508i	0.724061	−	0.465326i
$887$	−43.3698	+	37.5802i	−1.45622	+	1.26182i	−0.552619	+	0.833434i	$0.686371\pi$
$887$	−43.3698	+	37.5802i	−1.45622	+	1.26182i	−0.903597	+	0.428384i	$0.859083\pi$
$888$	−3.71984	−	13.7221i	−0.124830	−	0.460485i
$889$	−41.4959	−	5.96621i	−1.39173	−	0.200100i
$890$	25.7440	+	22.3073i	0.862942	+	0.747743i
$891$	14.6393	−	26.0546i	0.490436	−	0.872862i
$892$	5.03387	+	1.47808i	0.168547	+	0.0494897i
$893$	16.8456	+	36.8867i	0.563717	+	1.23437i
$894$	−0.306382	−	2.50048i	−0.0102470	−	0.0836286i
$895$	−27.0629	+	42.1106i	−0.904611	+	1.40760i
$896$	−4.00072			−0.133655
$897$	−10.1705	+	13.2514i	−0.339582	+	0.442452i
$898$	−11.6667			−0.389324
$899$	28.4500	−	44.2690i	0.948860	−	1.47645i
$900$	−1.15500	−	11.3918i	−0.0385001	−	0.379728i
$901$	0.124173	+	0.271900i	0.00413679	+	0.00905831i
$902$	−3.63189	−	1.06642i	−0.120929	−	0.0355078i
$903$	−2.77431	−	1.33767i	−0.0923232	−	0.0445149i
$904$	3.38196	+	2.93048i	0.112482	+	0.0974664i
$905$	66.4713	+	9.55713i	2.20958	+	0.317690i
$906$	4.78875	−	1.29815i	0.159096	−	0.0431282i
$907$	19.7733	−	17.1337i	0.656561	−	0.568914i	−0.261573	−	0.965184i	$-0.584241\pi$
$907$	19.7733	−	17.1337i	0.656561	−	0.568914i	0.918134	+	0.396270i	$0.129696\pi$
$908$	−0.310866	+	0.199782i	−0.0103165	+	0.00662999i
$909$	−0.873439	−	1.49263i	−0.0289701	−	0.0495074i
$910$	15.6440	+	18.0542i	0.518595	+	0.598490i
$911$	−38.0462	+	11.1714i	−1.26053	+	0.370125i	−0.842691	−	0.538397i	$-0.819030\pi$
$911$	−38.0462	+	11.1714i	−1.26053	+	0.370125i	−0.417837	+	0.908522i	$0.637212\pi$
$912$	−1.37379	+	8.31816i	−0.0454907	+	0.275442i
$913$	13.3957	−	15.4594i	0.443332	−	0.511633i
$914$	−4.34305	+	9.50995i	−0.143655	+	0.314561i
$915$	36.5150	+	11.5551i	1.20715	+	0.382000i
$916$	−22.1534	+	10.1171i	−0.731970	+	0.334280i
$917$	−5.55989	−	38.6699i	−0.183604	−	1.27699i
$918$	1.40886	+	1.03552i	0.0464995	+	0.0341772i
$919$			10.6628i			0.351732i	0.984414	+	0.175866i	$0.0562725\pi$
$919$			10.6628i			0.351732i	−0.984414	+	0.175866i	$0.943727\pi$
$920$	4.85793	−	13.3860i	0.160161	−	0.441324i
$921$	−0.282268	+	13.5178i	−0.00930103	+	0.445426i
$922$	−19.0509	−	12.2433i	−0.627408	−	0.403211i
$923$	−24.9997	+	3.59442i	−0.822876	+	0.118312i
$924$	−9.11971	−	21.1258i	−0.300016	−	0.694986i
$925$	8.82653	−	30.0604i	0.290214	−	0.988379i
$926$	35.3408	+	16.1396i	1.16137	+	0.530380i
$927$	15.1196	+	14.2488i	0.496593	+	0.467991i
$928$	−0.961216	+	6.68541i	−0.0315535	+	0.219459i
$929$	15.6787	+	53.3969i	0.514403	+	1.75190i	0.648791	+	0.760966i	$0.275275\pi$
$929$	15.6787	+	53.3969i	0.514403	+	1.75190i	−0.134388	+	0.990929i	$0.542907\pi$
$930$	−25.6022	−	30.8239i	−0.839529	−	1.01076i
$931$	−23.6995	−	36.8771i	−0.776720	−	1.20860i
$932$	−0.943363	−	1.46790i	−0.0309009	−	0.0480827i
$933$	−31.3588	−	37.7546i	−1.02664	−	1.23603i
$934$	0.999138	+	3.40275i	0.0326928	+	0.111341i
$935$	−0.472177	+	3.28406i	−0.0154418	+	0.107400i
$936$	−4.39050	−	4.13762i	−0.143508	−	0.135242i
$937$	51.2203	+	23.3915i	1.67329	+	0.764168i	0.999685	+	0.0250802i	$0.00798412\pi$
$937$	51.2203	+	23.3915i	1.67329	+	0.764168i	0.673609	+	0.739088i	$0.264743\pi$
$938$	14.5330	−	49.4950i	0.474521	−	1.61607i
$939$	9.13103	+	21.1520i	0.297980	+	0.690269i
$940$	24.4853	−	3.52046i	0.798623	−	0.114825i
$941$	−34.9124	−	22.4369i	−1.13811	−	0.731421i	−0.170875	−	0.985293i	$-0.554659\pi$
$941$	−34.9124	−	22.4369i	−1.13811	−	0.731421i	−0.967238	+	0.253872i	$0.918296\pi$
$942$	0.160460	−	7.68442i	0.00522806	−	0.250372i
$943$	−5.35197	−	1.11463i	−0.174284	−	0.0362973i
$944$		−	4.47506i		−	0.145651i
$945$	−49.7372	−	36.5570i	−1.61795	−	1.18920i
$946$	0.210047	+	1.46091i	0.00682922	+	0.0474983i
$947$	−26.7684	+	12.2247i	−0.869855	+	0.397249i	−0.799781	−	0.600292i	$-0.795051\pi$
$947$	−26.7684	+	12.2247i	−0.869855	+	0.397249i	−0.0700742	+	0.997542i	$0.522324\pi$
$948$	25.8451	+	8.17863i	0.839410	+	0.265629i
$949$	−9.17134	+	20.0824i	−0.297714	+	0.651903i
$950$	−12.1661	+	14.0405i	−0.394721	+	0.455533i
$951$	−1.67579	+	10.1468i	−0.0543414	+	0.329032i
$952$	1.29169	−	0.379276i	0.0418641	−	0.0122924i
$953$	−18.2066	−	21.0115i	−0.589770	−	0.680631i	0.379906	−	0.925025i	$-0.375956\pi$
$953$	−18.2066	−	21.0115i	−0.589770	−	0.680631i	−0.969676	+	0.244394i	$0.921411\pi$
$954$	1.34593	+	2.30007i	0.0435760	+	0.0744675i
$955$	19.5942	−	12.5924i	0.634053	−	0.407481i
$956$	18.6481	−	16.1587i	0.603124	−	0.522610i
$957$	−37.4933	+	10.1638i	−1.21199	+	0.328549i
$958$	−28.0085	−	4.02701i	−0.904912	−	0.130107i
$959$	−28.2192	−	24.4521i	−0.911245	−	0.789598i
$960$	4.63260	+	2.23367i	0.149516	+	0.0720914i
$961$	−28.4990	−	8.36806i	−0.919323	−	0.269937i
$962$	−6.85724	−	15.0153i	−0.221086	−	0.484111i
$963$	−0.347109	−	3.42355i	−0.0111854	−	0.110322i
$964$	−1.26781	+	1.97275i	−0.0408333	+	0.0635378i
$965$	−13.4802			−0.433942
$966$	−15.5752	−	29.3566i	−0.501125	−	0.944533i
$967$	13.5242			0.434908			0.217454	−	0.976071i	$-0.430225\pi$
$967$	13.5242			0.434908			0.217454	+	0.976071i	$0.430225\pi$
$968$	−0.0143716	+	0.0223627i	−0.000461922	+	0.000718764i
$969$	−0.345028	−	2.81588i	−0.0110839	−	0.0904592i
$970$	8.24095	+	18.0452i	0.264601	+	0.579395i
$971$	−0.222806	−	0.0654217i	−0.00715018	−	0.00209948i	0.278156	−	0.960536i	$-0.410277\pi$
$971$	−0.222806	−	0.0654217i	−0.00715018	−	0.00209948i	−0.285306	+	0.958437i	$0.592095\pi$
$972$	13.4278	+	7.91798i	0.430697	+	0.253969i
$973$	−60.6641	−	52.5658i	−1.94480	−	1.68518i
$974$	−3.72757	−	0.535943i	−0.119439	−	0.0171727i
$975$	−3.47829	−	12.8311i	−0.111394	−	0.410923i
$976$	−5.62806	+	4.87674i	−0.180150	+	0.156101i
$977$	−28.0911	+	18.0530i	−0.898713	+	0.577568i	−0.906408	−	0.422402i	$-0.861187\pi$
$977$	−28.0911	+	18.0530i	−0.898713	+	0.577568i	0.00769511	+	0.999970i	$0.497551\pi$
$978$	−3.24005	+	1.98792i	−0.103606	+	0.0635668i
$979$	−24.9467	−	28.7901i	−0.797301	−	0.920135i
$980$	−25.6576	+	7.53376i	−0.819602	+	0.240657i
$981$	−32.0545	−	5.98394i	−1.02342	−	0.191052i
$982$	−24.5620	+	28.3461i	−0.783806	+	0.904561i
$983$	3.75446	−	8.22112i	0.119749	−	0.262213i	−0.840260	−	0.542184i	$-0.817598\pi$
$983$	3.75446	−	8.22112i	0.119749	−	0.262213i	0.960008	+	0.279971i	$0.0903249\pi$
$984$	0.595674	−	1.88238i	0.0189894	−	0.0600080i
$985$	−14.8097	+	6.76336i	−0.471876	+	0.215499i
$986$	−0.323446	−	2.24961i	−0.0103006	−	0.0716423i
$987$	32.2177	−	47.9025i	1.02550	−	1.52475i
$988$			9.78853i			0.311415i
$989$	0.471565	+	2.07881i	0.0149949	+	0.0661022i
$990$	−1.23479	+	29.5541i	−0.0392441	+	0.939290i
$991$	29.7144	+	19.0963i	0.943908	+	0.606613i	0.919500	−	0.393089i	$-0.128594\pi$
$991$	29.7144	+	19.0963i	0.943908	+	0.606613i	0.0244077	+	0.999702i	$0.492230\pi$
$992$	7.71186	−	1.10880i	0.244852	−	0.0352044i
$993$	11.5421	−	4.98256i	0.366276	−	0.158117i
$994$	14.1562	−	48.2115i	0.449007	−	1.52918i
$995$	−25.2425	−	11.5279i	−0.800240	−	0.365458i
$996$	7.91607	+	7.15405i	0.250830	+	0.226685i
$997$	−1.36746	+	9.51092i	−0.0433080	+	0.301214i	0.956643	+	0.291265i	$0.0940760\pi$
$997$	−1.36746	+	9.51092i	−0.0433080	+	0.301214i	−0.999951	+	0.00994905i	$0.996833\pi$
$998$	6.91460	+	23.5490i	0.218878	+	0.745429i
$999$	25.8588	+	33.9195i	0.818137	+	1.07316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.f.a.113.5	yes	80
3.2	odd	2	inner	138.2.f.a.113.4	yes	80
23.11	odd	22	inner	138.2.f.a.11.4	✓	80
69.11	even	22	inner	138.2.f.a.11.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.11.4	✓	80	23.11	odd	22	inner
138.2.f.a.11.5	yes	80	69.11	even	22	inner
138.2.f.a.113.4	yes	80	3.2	odd	2	inner
138.2.f.a.113.5	yes	80	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 - 0.841254i) q^{2} +(-1.71919 + 0.210651i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-2.84902 - 0.836549i) q^{5} +(-0.752255 + 1.56016i) q^{6} +(-3.02354 - 2.61991i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(2.91125 - 0.724301i) q^{9} +O(q^{10})\)	\(q+(0.540641 - 0.841254i) q^{2} +(-1.71919 + 0.210651i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-2.84902 - 0.836549i) q^{5} +(-0.752255 + 1.56016i) q^{6} +(-3.02354 - 2.61991i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(2.91125 - 0.724301i) q^{9} +(-2.24405 + 1.94448i) q^{10} +(2.79349 - 1.79527i) q^{11} +(0.905794 + 1.47633i) q^{12} +(1.31691 + 1.51980i) q^{13} +(-3.83866 + 1.12713i) q^{14} +(5.07424 + 0.838038i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(0.139786 - 0.306088i) q^{17} +(0.964621 - 2.84069i) q^{18} +(-4.42768 + 2.02205i) q^{19} +(0.422576 + 2.93908i) q^{20} +(5.74994 + 3.86723i) q^{21} -3.32063i q^{22} +(-0.384545 - 4.78039i) q^{23} +(1.73167 + 0.0361594i) q^{24} +(3.21085 + 2.06349i) q^{25} +(1.99051 - 0.286192i) q^{26} +(-4.85243 + 1.85847i) q^{27} +(-1.12713 + 3.83866i) q^{28} +(6.14380 + 2.80578i) q^{29} +(3.44834 - 3.81565i) q^{30} +(1.10880 - 7.71186i) q^{31} +(0.281733 + 0.959493i) q^{32} +(-4.42438 + 3.67487i) q^{33} +(-0.181924 - 0.283079i) q^{34} +(6.42246 + 9.99354i) q^{35} +(-1.86823 - 2.34728i) q^{36} +(-2.31258 - 7.87592i) q^{37} +(-0.692724 + 4.81800i) q^{38} +(-2.58417 - 2.33542i) q^{39} +(2.70097 + 1.23349i) q^{40} +(0.321149 - 1.09373i) q^{41} +(6.36197 - 2.74638i) q^{42} +(-0.439950 + 0.0632552i) q^{43} +(-2.79349 - 1.79527i) q^{44} +(-8.90014 - 0.371853i) q^{45} +(-4.22942 - 2.26097i) q^{46} -8.33095i q^{47} +(0.966633 - 1.43723i) q^{48} +(1.28165 + 8.91409i) q^{49} +(3.47183 - 1.58553i) q^{50} +(-0.175841 + 0.555670i) q^{51} +(0.835391 - 1.82925i) q^{52} +(-0.581719 + 0.671339i) q^{53} +(-1.05997 + 5.08689i) q^{54} +(-9.46055 + 2.77787i) q^{55} +(2.61991 + 3.02354i) q^{56} +(7.18608 - 4.40899i) q^{57} +(5.68196 - 3.65157i) q^{58} +(-3.38202 + 2.93054i) q^{59} +(-1.34561 - 4.96383i) q^{60} +(7.37119 + 1.05982i) q^{61} +(-5.88816 - 5.10212i) q^{62} +(-10.6999 - 5.43728i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-2.48053 - 5.43160i) q^{65} +(0.699496 + 5.70880i) q^{66} +(-6.97092 + 10.8470i) q^{67} -0.336496 q^{68} +(1.66810 + 8.13741i) q^{69} +11.8793 q^{70} +(-6.79016 + 10.5657i) q^{71} +(-2.98470 + 0.302614i) q^{72} +(4.56063 + 9.98639i) q^{73} +(-7.87592 - 2.31258i) q^{74} +(-5.95475 - 2.87117i) q^{75} +(3.67865 + 3.18756i) q^{76} +(-13.1497 - 1.89064i) q^{77} +(-3.36179 + 0.911324i) q^{78} +(11.8282 - 10.2492i) q^{79} +(2.49793 - 1.60533i) q^{80} +(7.95078 - 4.21725i) q^{81} +(-0.746481 - 0.861485i) q^{82} +(5.91068 - 1.73553i) q^{83} +(1.12914 - 6.83684i) q^{84} +(-0.654309 + 0.755113i) q^{85} +(-0.184641 + 0.404308i) q^{86} +(-11.1534 - 3.52947i) q^{87} +(-3.02055 + 1.37944i) q^{88} +(-1.63266 - 11.3554i) q^{89} +(-5.12460 + 7.28623i) q^{90} -8.04537i q^{91} +(-4.18865 + 2.33564i) q^{92} +(-0.281724 + 13.4917i) q^{93} +(-7.00844 - 4.50405i) q^{94} +(14.3061 - 2.05691i) q^{95} +(-0.686471 - 1.59021i) q^{96} +(1.88225 - 6.41036i) q^{97} +(8.19193 + 3.74113i) q^{98} +(6.83224 - 7.24981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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