LMFDB - Embedded newform 342.2.x.c.29.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(29,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([3, 17]))

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

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

chi := DirichletCharacter("342.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.x (of order $18$, degree $6$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.6
Character	$\chi$	$=$	342.29
Dual form			342.2.x.c.59.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(0.125873 - 1.72747i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.99507 + 0.351785i) q^{5} +(-0.709112 + 1.58024i) q^{6} +(2.49195 + 4.31618i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.96831 - 0.434885i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(0.125873 - 1.72747i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.99507 + 0.351785i) q^{5} +(-0.709112 + 1.58024i) q^{6} +(2.49195 + 4.31618i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.96831 - 0.434885i) q^{9} +(1.99507 + 0.351785i) q^{10} +5.23173i q^{11} +(1.20682 - 1.24241i) q^{12} +(-0.692178 - 0.122050i) q^{13} +(-0.865444 - 4.90817i) q^{14} +(0.356572 + 3.49071i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-1.86440 + 0.328744i) q^{17} +(2.64056 + 1.42388i) q^{18} +(2.66022 + 3.45300i) q^{19} +(-1.75444 - 1.01293i) q^{20} +(7.76974 - 3.76147i) q^{21} +(1.78936 - 4.91622i) q^{22} +(3.00539 - 3.58169i) q^{23} +(-1.55897 + 0.754726i) q^{24} +(-0.841900 + 0.306426i) q^{25} +(0.608691 + 0.351428i) q^{26} +(-1.12488 + 5.07293i) q^{27} +(-0.865444 + 4.90817i) q^{28} +(3.53489 + 2.96613i) q^{29} +(0.858825 - 3.40215i) q^{30} -7.59139i q^{31} +(0.173648 - 0.984808i) q^{32} +(9.03767 + 0.658535i) q^{33} +(1.86440 + 0.328744i) q^{34} +(-6.48998 - 7.73446i) q^{35} +(-1.99432 - 2.24114i) q^{36} +3.30669i q^{37} +(-1.31879 - 4.15461i) q^{38} +(-0.297964 + 1.18036i) q^{39} +(1.30219 + 1.55189i) q^{40} +(4.05564 + 1.47613i) q^{41} +(-8.58767 + 0.877221i) q^{42} +(2.20199 - 1.84769i) q^{43} +(-3.36289 + 4.00774i) q^{44} +(6.07498 - 0.176581i) q^{45} +(-4.04916 + 2.33778i) q^{46} +(-4.25457 + 5.07040i) q^{47} +(1.72308 - 0.176011i) q^{48} +(-8.91959 + 15.4492i) q^{49} +0.895931 q^{50} +(0.333218 + 3.26208i) q^{51} +(-0.451787 - 0.538419i) q^{52} +(1.34407 - 0.489201i) q^{53} +(2.79209 - 4.38226i) q^{54} +(-1.84045 - 10.4377i) q^{55} +(2.49195 - 4.31618i) q^{56} +(6.29982 - 4.16081i) q^{57} +(-2.30724 - 3.99625i) q^{58} +(-1.02155 + 0.857186i) q^{59} +(-1.97064 + 2.90324i) q^{60} +(-1.68420 + 9.55155i) q^{61} +(-2.59641 + 7.13358i) q^{62} +(-5.51983 - 13.8955i) q^{63} +(-0.500000 + 0.866025i) q^{64} +1.42388 q^{65} +(-8.26740 - 3.70989i) q^{66} +(-0.183340 - 0.503722i) q^{67} +(-1.63953 - 0.946581i) q^{68} +(-5.80896 - 5.64257i) q^{69} +(3.45325 + 9.48772i) q^{70} +(-8.50469 - 3.09546i) q^{71} +(1.10753 + 2.78808i) q^{72} +(7.85357 - 6.58993i) q^{73} +(1.13095 - 3.10727i) q^{74} +(0.423370 + 1.49293i) q^{75} +(-0.181703 + 4.35511i) q^{76} +(-22.5811 + 13.0372i) q^{77} +(0.683700 - 1.00726i) q^{78} +(-3.65947 + 0.645263i) q^{79} +(-0.692882 - 1.90368i) q^{80} +(8.62175 + 2.58175i) q^{81} +(-3.30619 - 2.77422i) q^{82} +(6.00455 - 3.46673i) q^{83} +(8.36979 + 2.11284i) q^{84} +(3.60397 - 1.31174i) q^{85} +(-2.70115 + 0.983137i) q^{86} +(5.56885 - 5.73307i) q^{87} +(4.53081 - 2.61587i) q^{88} +(-6.31073 - 5.29533i) q^{89} +(-5.76901 - 1.91183i) q^{90} +(-1.19808 - 3.29170i) q^{91} +(4.60453 - 0.811903i) q^{92} +(-13.1139 - 0.955553i) q^{93} +(5.73217 - 3.30947i) q^{94} +(-6.52204 - 5.95317i) q^{95} +(-1.67937 - 0.423933i) q^{96} +(6.36967 - 17.5005i) q^{97} +(13.6656 - 11.4668i) q^{98} +(2.27520 - 15.5294i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9}+O(q^{10}) $ 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9	$ 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9} + 3 q^{13} + 3 q^{14} + 27 q^{15} - 27 q^{17} - 18 q^{18} + 3 q^{19} + 18 q^{23} + 3 q^{24} - 6 q^{27} + 3 q^{28} + 57 q^{33} + 27 q^{34} + 9 q^{38} - 30 q^{39} + 9 q^{41} - 3 q^{43} - 9 q^{44} + 27 q^{45} - 30 q^{49} - 132 q^{50} - 66 q^{51} + 6 q^{52} + 27 q^{54} + 102 q^{57} - 54 q^{59} + 6 q^{60} - 24 q^{61} - 3 q^{62} - 30 q^{64} + 36 q^{65} - 63 q^{66} + 51 q^{67} - 18 q^{68} + 3 q^{69} - 18 q^{71} - 3 q^{72} - 66 q^{73} - 6 q^{74} + 3 q^{78} - 51 q^{79} - 30 q^{81} - 36 q^{83} + 60 q^{84} - 3 q^{86} + 54 q^{87} - 27 q^{89} + 36 q^{90} - 69 q^{91} + 69 q^{93} + 18 q^{94} - 27 q^{95} + 81 q^{97} + 60 q^{98} + 51 q^{99}+O(q^{100}) $ 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9 + 3 * q^13 + 3 * q^14 + 27 * q^15 - 27 * q^17 - 18 * q^18 + 3 * q^19 + 18 * q^23 + 3 * q^24 - 6 * q^27 + 3 * q^28 + 57 * q^33 + 27 * q^34 + 9 * q^38 - 30 * q^39 + 9 * q^41 - 3 * q^43 - 9 * q^44 + 27 * q^45 - 30 * q^49 - 132 * q^50 - 66 * q^51 + 6 * q^52 + 27 * q^54 + 102 * q^57 - 54 * q^59 + 6 * q^60 - 24 * q^61 - 3 * q^62 - 30 * q^64 + 36 * q^65 - 63 * q^66 + 51 * q^67 - 18 * q^68 + 3 * q^69 - 18 * q^71 - 3 * q^72 - 66 * q^73 - 6 * q^74 + 3 * q^78 - 51 * q^79 - 30 * q^81 - 36 * q^83 + 60 * q^84 - 3 * q^86 + 54 * q^87 - 27 * q^89 + 36 * q^90 - 69 * q^91 + 69 * q^93 + 18 * q^94 - 27 * q^95 + 81 * q^97 + 60 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	0.125873	−	1.72747i	0.0726730	−	0.997356i
$3$	0.125873	−	1.72747i	0.0726730	−	0.997356i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−1.99507	+	0.351785i	−0.892224	+	0.157323i	−0.600922	−	0.799308i	$-0.705200\pi$
$5$	−1.99507	+	0.351785i	−0.892224	+	0.157323i	−0.291302	+	0.956631i	$0.594089\pi$
$6$	−0.709112	+	1.58024i	−0.289494	+	0.645130i
$7$	2.49195	+	4.31618i	0.941867	+	1.63136i	0.761906	+	0.647688i	$0.224264\pi$
$7$	2.49195	+	4.31618i	0.941867	+	1.63136i	0.179961	+	0.983674i	$0.442403\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−2.96831	−	0.434885i	−0.989437	−	0.144962i
$10$	1.99507	+	0.351785i	0.630897	+	0.111244i
$11$			5.23173i			1.57743i	0.614761	+	0.788714i	$0.289253\pi$
$11$			5.23173i			1.57743i	−0.614761	+	0.788714i	$0.710747\pi$
$12$	1.20682	−	1.24241i	0.348379	−	0.358653i
$13$	−0.692178	−	0.122050i	−0.191976	−	0.0338505i	0.0768335	−	0.997044i	$-0.475519\pi$
$13$	−0.692178	−	0.122050i	−0.191976	−	0.0338505i	−0.268809	+	0.963193i	$0.586630\pi$
$14$	−0.865444	−	4.90817i	−0.231300	−	1.31176i
$15$	0.356572	+	3.49071i	0.0920666	+	0.901298i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−1.86440	+	0.328744i	−0.452184	+	0.0797322i	−0.395102	−	0.918637i	$-0.629291\pi$
$17$	−1.86440	+	0.328744i	−0.452184	+	0.0797322i	−0.0570819	+	0.998370i	$0.518180\pi$
$18$	2.64056	+	1.42388i	0.622386	+	0.335612i
$19$	2.66022	+	3.45300i	0.610296	+	0.792174i
$19$	2.66022	+	3.45300i	0.610296	+	0.792174i
$20$	−1.75444	−	1.01293i	−0.392304	−	0.226497i
$21$	7.76974	−	3.76147i	1.69550	−	0.820821i
$22$	1.78936	−	4.91622i	0.381492	−	1.04814i
$23$	3.00539	−	3.58169i	0.626668	−	0.746834i	−0.355534	−	0.934663i	$-0.615701\pi$
$23$	3.00539	−	3.58169i	0.626668	−	0.746834i	0.982202	+	0.187830i	$0.0601453\pi$
$24$	−1.55897	+	0.754726i	−0.318223	+	0.154058i
$25$	−0.841900	+	0.306426i	−0.168380	+	0.0612853i
$26$	0.608691	+	0.351428i	0.119374	+	0.0689207i
$27$	−1.12488	+	5.07293i	−0.216484	+	0.976286i
$28$	−0.865444	+	4.90817i	−0.163553	+	0.927558i
$29$	3.53489	+	2.96613i	0.656413	+	0.550796i	0.909009	−	0.416776i	$-0.136840\pi$
$29$	3.53489	+	2.96613i	0.656413	+	0.550796i	−0.252596	+	0.967572i	$0.581284\pi$
$30$	0.858825	−	3.40215i	0.156799	−	0.621145i
$31$		−	7.59139i		−	1.36345i	−0.731607	−	0.681727i	$-0.761229\pi$
$31$		−	7.59139i		−	1.36345i	0.731607	−	0.681727i	$-0.238771\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	9.03767	+	0.658535i	1.57326	+	0.114636i
$34$	1.86440	+	0.328744i	0.319742	+	0.0563792i
$35$	−6.48998	−	7.73446i	−1.09701	−	1.30736i
$36$	−1.99432	−	2.24114i	−0.332387	−	0.373523i
$37$			3.30669i			0.543616i	0.962352	+	0.271808i	$0.0876215\pi$
$37$			3.30669i			0.543616i	−0.962352	+	0.271808i	$0.912378\pi$
$38$	−1.31879	−	4.15461i	−0.213936	−	0.673967i
$39$	−0.297964	+	1.18036i	−0.0477124	+	0.189008i
$40$	1.30219	+	1.55189i	0.205895	+	0.245376i
$41$	4.05564	+	1.47613i	0.633384	+	0.230533i	0.638704	−	0.769453i	$-0.279471\pi$
$41$	4.05564	+	1.47613i	0.633384	+	0.230533i	−0.00531928	+	0.999986i	$0.501693\pi$
$42$	−8.58767	+	0.877221i	−1.32511	+	0.135358i
$43$	2.20199	−	1.84769i	0.335801	−	0.281771i	−0.459258	−	0.888303i	$-0.651885\pi$
$43$	2.20199	−	1.84769i	0.335801	−	0.281771i	0.795059	+	0.606533i	$0.207440\pi$
$44$	−3.36289	+	4.00774i	−0.506975	+	0.604190i
$45$	6.07498	−	0.176581i	0.905605	−	0.0263232i
$46$	−4.04916	+	2.33778i	−0.597015	+	0.344687i
$47$	−4.25457	+	5.07040i	−0.620593	+	0.739594i	−0.981172	−	0.193134i	$-0.938135\pi$
$47$	−4.25457	+	5.07040i	−0.620593	+	0.739594i	0.360579	+	0.932729i	$0.382579\pi$
$48$	1.72308	−	0.176011i	0.248706	−	0.0254050i
$49$	−8.91959	+	15.4492i	−1.27423	+	2.20703i
$50$	0.895931			0.126704
$51$	0.333218	+	3.26208i	0.0466598	+	0.456782i
$52$	−0.451787	−	0.538419i	−0.0626516	−	0.0746653i
$53$	1.34407	−	0.489201i	0.184622	−	0.0671969i	−0.248055	−	0.968746i	$-0.579791\pi$
$53$	1.34407	−	0.489201i	0.184622	−	0.0671969i	0.432677	+	0.901549i	$0.357569\pi$
$54$	2.79209	−	4.38226i	0.379955	−	0.596351i
$55$	−1.84045	−	10.4377i	−0.248166	−	1.40742i
$56$	2.49195	−	4.31618i	0.333000	−	0.576773i
$57$	6.29982	−	4.16081i	0.834431	−	0.551113i
$58$	−2.30724	−	3.99625i	−0.302955	−	0.524734i
$59$	−1.02155	+	0.857186i	−0.132995	+	0.111596i	−0.706859	−	0.707355i	$-0.749888\pi$
$59$	−1.02155	+	0.857186i	−0.132995	+	0.111596i	0.573864	+	0.818951i	$0.305444\pi$
$60$	−1.97064	+	2.90324i	−0.254408	+	0.374807i
$61$	−1.68420	+	9.55155i	−0.215639	+	1.22295i	0.664155	+	0.747595i	$0.268792\pi$
$61$	−1.68420	+	9.55155i	−0.215639	+	1.22295i	−0.879794	+	0.475356i	$0.842319\pi$
$62$	−2.59641	+	7.13358i	−0.329744	+	0.905965i
$63$	−5.51983	−	13.8955i	−0.695434	−	1.75066i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	1.42388			0.176611
$66$	−8.26740	−	3.70989i	−1.01765	−	0.456655i
$67$	−0.183340	−	0.503722i	−0.0223985	−	0.0615394i	0.927989	−	0.372606i	$-0.121536\pi$
$67$	−0.183340	−	0.503722i	−0.0223985	−	0.0615394i	−0.950388	+	0.311067i	$0.899314\pi$
$68$	−1.63953	−	0.946581i	−0.198822	−	0.114790i
$69$	−5.80896	−	5.64257i	−0.699317	−	0.679285i
$70$	3.45325	+	9.48772i	0.412742	+	1.13400i
$71$	−8.50469	−	3.09546i	−1.00932	−	0.367363i	−0.216149	−	0.976360i	$-0.569350\pi$
$71$	−8.50469	−	3.09546i	−1.00932	−	0.367363i	−0.793172	+	0.608997i	$0.791572\pi$
$72$	1.10753	+	2.78808i	0.130524	+	0.328578i
$73$	7.85357	−	6.58993i	0.919191	−	0.771293i	−0.0546545	−	0.998505i	$-0.517406\pi$
$73$	7.85357	−	6.58993i	0.919191	−	0.771293i	0.973845	+	0.227213i	$0.0729613\pi$
$74$	1.13095	−	3.10727i	0.131471	−	0.361213i
$75$	0.423370	+	1.49293i	0.0488866	+	0.172388i
$76$	−0.181703	+	4.35511i	−0.0208428	+	0.499565i
$77$	−22.5811	+	13.0372i	−2.57335	+	1.48573i
$78$	0.683700	−	1.00726i	0.0774138	−	0.114050i
$79$	−3.65947	+	0.645263i	−0.411722	+	0.0725978i	−0.375673	−	0.926752i	$-0.622588\pi$
$79$	−3.65947	+	0.645263i	−0.411722	+	0.0725978i	−0.0360494	+	0.999350i	$0.511477\pi$
$80$	−0.692882	−	1.90368i	−0.0774665	−	0.212838i
$81$	8.62175	+	2.58175i	0.957972	+	0.286861i
$82$	−3.30619	−	2.77422i	−0.365107	−	0.306361i
$83$	6.00455	−	3.46673i	0.659085	−	0.380523i	−0.132843	−	0.991137i	$-0.542411\pi$
$83$	6.00455	−	3.46673i	0.659085	−	0.380523i	0.791928	+	0.610614i	$0.209077\pi$
$84$	8.36979	+	2.11284i	0.913219	+	0.230529i
$85$	3.60397	−	1.31174i	0.390905	−	0.142278i
$86$	−2.70115	+	0.983137i	−0.291272	+	0.106014i
$87$	5.56885	−	5.73307i	0.597043	−	0.614649i
$88$	4.53081	−	2.61587i	0.482986	−	0.278852i
$89$	−6.31073	−	5.29533i	−0.668936	−	0.561304i	0.243814	−	0.969822i	$-0.421601\pi$
$89$	−6.31073	−	5.29533i	−0.668936	−	0.561304i	−0.912750	+	0.408518i	$0.866046\pi$
$90$	−5.76901	−	1.91183i	−0.608107	−	0.201525i
$91$	−1.19808	−	3.29170i	−0.125593	−	0.345064i
$92$	4.60453	−	0.811903i	0.480055	−	0.0846467i
$93$	−13.1139	−	0.955553i	−1.35985	−	0.0990862i
$94$	5.73217	−	3.30947i	0.591228	−	0.341346i
$95$	−6.52204	−	5.95317i	−0.669148	−	0.610782i
$96$	−1.67937	−	0.423933i	−0.171400	−	0.0432675i
$97$	6.36967	−	17.5005i	0.646742	−	1.77691i	0.0173130	−	0.999850i	$-0.494489\pi$
$97$	6.36967	−	17.5005i	0.646742	−	1.77691i	0.629429	−	0.777058i	$-0.283289\pi$
$98$	13.6656	−	11.4668i	1.38043	−	1.15832i
$99$	2.27520	−	15.5294i	0.228666	−	1.56077i
$100$	−0.841900	−	0.306426i	−0.0841900	−	0.0306426i
$101$	−1.72708	−	4.74513i	−0.171851	−	0.472158i	0.823629	−	0.567130i	$-0.191946\pi$
$101$	−1.72708	−	4.74513i	−0.171851	−	0.472158i	−0.995480	+	0.0949718i	$0.969724\pi$
$102$	0.802574	−	3.17932i	0.0794667	−	0.314799i
$103$	−10.9976	−	6.34945i	−1.08362	−	0.625630i	−0.151751	−	0.988419i	$-0.548491\pi$
$103$	−10.9976	−	6.34945i	−1.08362	−	0.625630i	−0.931871	+	0.362789i	$0.881825\pi$
$104$	0.240391	+	0.660469i	0.0235723	+	0.0647643i
$105$	−14.1780	+	10.2377i	−1.38363	+	0.999096i
$106$	−1.43033			−0.138926
$107$	−3.74730	+	6.49052i	−0.362266	+	0.627462i	−0.988333	−	0.152306i	$-0.951330\pi$
$107$	−3.74730	+	6.49052i	−0.362266	+	0.627462i	0.626068	+	0.779769i	$0.284663\pi$
$108$	−4.12253	+	3.16303i	−0.396690	+	0.304363i
$109$	−4.81544	+	13.2303i	−0.461236	+	1.26724i	0.463321	+	0.886191i	$0.346658\pi$
$109$	−4.81544	+	13.2303i	−0.461236	+	1.26724i	−0.924557	+	0.381045i	$0.875564\pi$
$110$	−1.84045	+	10.4377i	−0.175480	+	0.995195i
$111$	5.71220	+	0.416223i	0.542178	+	0.0395062i
$112$	−3.81788	+	3.20358i	−0.360756	+	0.302710i
$113$	7.65498	+	13.2588i	0.720120	+	1.24728i	0.960951	+	0.276717i	$0.0892465\pi$
$113$	7.65498	+	13.2588i	0.720120	+	1.24728i	−0.240832	+	0.970567i	$0.577420\pi$
$114$	−7.34297	+	1.75522i	−0.687732	+	0.164391i
$115$	−4.73599	+	8.20298i	−0.441634	+	0.764932i
$116$	0.801295	+	4.54437i	0.0743984	+	0.421934i
$117$	2.00152	+	0.663299i	0.185041	+	0.0613220i
$118$	1.25312	−	0.456099i	0.115359	−	0.0419873i
$119$	−6.06490	−	7.22787i	−0.555969	−	0.662578i
$120$	2.84476	−	2.05416i	0.259690	−	0.187518i
$121$	−16.3710			−1.48828
$122$	4.84945	−	8.39949i	0.439049	−	0.760454i
$123$	3.06047	−	6.82019i	0.275953	−	0.614956i
$124$	4.87965	−	5.81534i	0.438206	−	0.522233i
$125$	10.3440	−	5.97214i	0.925199	−	0.534164i
$126$	0.434416	+	14.9454i	0.0387009	+	1.33144i
$127$	6.91231	−	8.23777i	0.613368	−	0.730984i	−0.366547	−	0.930400i	$-0.619460\pi$
$127$	6.91231	−	8.23777i	0.613368	−	0.730984i	0.979915	+	0.199416i	$0.0639045\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	−2.91466	−	4.03646i	−0.256622	−	0.355390i
$130$	−1.33801	−	0.486996i	−0.117351	−	0.0427124i
$131$	9.45057	+	11.2628i	0.825700	+	0.984032i	1.00000		0.000661199i	$-0.000210466\pi$
$131$	9.45057	+	11.2628i	0.825700	+	0.984032i	−0.174299	+	0.984693i	$0.555766\pi$
$132$	6.49996	+	6.31377i	0.565749	+	0.549543i
$133$	−8.27466	+	20.0867i	−0.717504	+	1.74174i
$134$			0.536050i			0.0463076i
$135$	0.459639	−	10.5166i	0.0395594	−	0.905124i
$136$	1.21690	+	1.45025i	0.104348	+	0.124358i
$137$	20.6622	+	3.64330i	1.76529	+	0.311268i	0.959662	−	0.281156i	$-0.0907178\pi$
$137$	20.6622	+	3.64330i	1.76529	+	0.311268i	0.805626	+	0.592424i	$0.201829\pi$
$138$	3.52877	+	7.28906i	0.300389	+	0.620486i
$139$	1.71545	−	9.72878i	0.145502	−	0.825184i	−0.821460	−	0.570266i	$-0.806840\pi$
$139$	1.71545	−	9.72878i	0.145502	−	0.825184i	0.966963	−	0.254918i	$-0.0820486\pi$
$140$		−	10.0966i		−	0.853320i
$141$	8.22344	+	7.98788i	0.692538	+	0.672701i
$142$	6.93309	+	5.81755i	0.581812	+	0.488198i
$143$	0.638532	−	3.62129i	0.0533967	−	0.302828i
$144$	−0.0871641	−	2.99873i	−0.00726367	−	0.249894i
$145$	−8.09581	−	4.67412i	−0.672320	−	0.388164i
$146$	−9.63383	+	3.50643i	−0.797301	+	0.290194i
$147$	25.5653	+	17.3530i	2.10859	+	1.43125i
$148$	−2.12550	+	2.53307i	−0.174715	+	0.208217i
$149$	4.03017	−	11.0728i	0.330164	−	0.907119i	−0.657904	−	0.753102i	$-0.728557\pi$
$149$	4.03017	−	11.0728i	0.330164	−	0.907119i	0.988068	−	0.154017i	$-0.0492210\pi$
$150$	0.112774	−	1.54769i	0.00920794	−	0.126369i
$151$	3.78475	+	2.18513i	0.307999	+	0.177823i	0.646031	−	0.763312i	$-0.276428\pi$
$151$	3.78475	+	2.18513i	0.307999	+	0.177823i	−0.338032	+	0.941135i	$0.609761\pi$
$152$	1.66028	−	4.03032i	0.134667	−	0.326902i
$153$	5.67709	−	0.165016i	0.458966	−	0.0133407i
$154$	25.6783	−	4.52777i	2.06921	−	0.364858i
$155$	2.67054	+	15.1454i	0.214503	+	1.21651i
$156$	−0.986971	+	0.712677i	−0.0790209	+	0.0570598i
$157$	1.29803	+	7.36148i	0.103594	+	0.587510i	0.991773	+	0.128012i	$0.0408597\pi$
$157$	1.29803	+	7.36148i	0.103594	+	0.587510i	−0.888179	+	0.459498i	$0.848029\pi$
$158$	3.65947	+	0.645263i	0.291132	+	0.0513344i
$159$	−0.675898	−	2.38342i	−0.0536022	−	0.189017i
$160$			2.02585i			0.160158i
$161$	22.9485	+	4.04644i	1.80859	+	0.318904i
$162$	−7.21879	−	5.37486i	−0.567161	−	0.422289i
$163$	7.38205	+	12.7861i	0.578207	+	1.00148i	0.995685	+	0.0927967i	$0.0295807\pi$
$163$	7.38205	+	12.7861i	0.578207	+	1.00148i	−0.417478	+	0.908687i	$0.637086\pi$
$164$	2.15796	+	3.73770i	0.168508	+	0.291865i
$165$	−18.2625	+	1.86549i	−1.42173	+	0.145228i
$166$	−6.82812	+	1.20398i	−0.529965	+	0.0934471i
$167$	16.2464	+	13.6323i	1.25718	+	1.05490i	0.995976	+	0.0896179i	$0.0285646\pi$
$167$	16.2464	+	13.6323i	1.25718	+	1.05490i	0.261206	+	0.965283i	$0.415880\pi$
$168$	−7.14240	−	4.84805i	−0.551048	−	0.374036i
$169$	−11.7518	−	4.27730i	−0.903984	−	0.329023i
$170$	−3.83526			−0.294151
$171$	−6.39470	−	11.4065i	−0.489015	−	0.872276i
$172$	2.87450			0.219179
$173$	−1.14653	−	0.417304i	−0.0871693	−	0.0317270i	0.298067	−	0.954545i	$-0.403658\pi$
$173$	−1.14653	−	0.417304i	−0.0871693	−	0.0317270i	−0.385237	+	0.922818i	$0.625880\pi$
$174$	−7.19383	+	3.48266i	−0.545363	+	0.264020i
$175$	−3.42056	−	2.87019i	−0.258570	−	0.216966i
$176$	−5.15225	+	0.908481i	−0.388366	+	0.0684793i
$177$	1.35218	+	1.87260i	0.101636	+	0.140753i
$178$	4.11904	+	7.13438i	0.308735	+	0.534745i
$179$	5.93076	+	10.2724i	0.443286	+	0.767794i	0.997931	−	0.0642930i	$-0.0204792\pi$
$179$	5.93076	+	10.2724i	0.443286	+	0.767794i	−0.554645	+	0.832087i	$0.687146\pi$
$180$	4.76721	+	3.76966i	0.355327	+	0.280974i
$181$	−9.68919	−	1.70847i	−0.720192	−	0.126989i	−0.198472	−	0.980106i	$-0.563598\pi$
$181$	−9.68919	−	1.70847i	−0.720192	−	0.126989i	−0.521719	+	0.853117i	$0.674709\pi$
$182$			3.50296i			0.259657i
$183$	16.2880	+	4.11168i	1.20405	+	0.303944i
$184$	−4.60453	−	0.811903i	−0.339450	−	0.0598543i
$185$	−1.16324	−	6.59708i	−0.0855234	−	0.485027i
$186$	11.9962	+	5.38315i	0.879606	+	0.394712i
$187$	−1.71990	−	9.75405i	−0.125772	−	0.713287i
$188$	−6.51839	+	1.14937i	−0.475402	+	0.0838262i
$189$	−24.6988	+	7.78628i	−1.79657	+	0.566369i
$190$	4.09261	+	7.82482i	0.296909	+	0.567672i
$191$	−11.9428	−	6.89515i	−0.864147	−	0.498916i	0.00125155	−	0.999999i	$-0.499602\pi$
$191$	−11.9428	−	6.89515i	−0.864147	−	0.498916i	−0.865399	+	0.501083i	$0.832935\pi$
$192$	1.43310	+	0.972745i	0.103425	+	0.0702018i
$193$	8.16324	−	22.4283i	0.587603	−	1.61443i	−0.187270	−	0.982309i	$-0.559964\pi$
$193$	8.16324	−	22.4283i	0.587603	−	1.61443i	0.774873	−	0.632117i	$-0.217814\pi$
$194$	−11.9711	+	14.2666i	−0.859472	+	1.02428i
$195$	0.179229	−	2.45971i	0.0128348	−	0.176144i
$196$	−16.7633	+	6.10136i	−1.19738	+	0.435811i
$197$	−12.4705	−	7.19985i	−0.888486	−	0.512968i	−0.0150392	−	0.999887i	$-0.504787\pi$
$197$	−12.4705	−	7.19985i	−0.888486	−	0.512968i	−0.873447	+	0.486919i	$0.838121\pi$
$198$	−7.44936	+	13.8147i	−0.529403	+	0.981769i
$199$	4.77890	−	27.1025i	0.338767	−	1.92125i	−0.0475276	−	0.998870i	$-0.515134\pi$
$199$	4.77890	−	27.1025i	0.338767	−	1.92125i	0.386295	−	0.922375i	$-0.373755\pi$
$200$	0.686323	+	0.575893i	0.0485304	+	0.0407218i
$201$	−0.893243	+	0.253309i	−0.0630045	+	0.0178670i
$202$			5.04966i			0.355293i
$203$	−3.99357	+	22.6486i	−0.280293	+	1.58962i
$204$	−1.84156	+	2.71309i	−0.128935	+	0.189954i
$205$	−8.61058	−	1.51828i	−0.601389	−	0.106041i
$206$	8.16269	+	9.72792i	0.568722	+	0.677776i
$207$	−10.4786	+	9.32457i	−0.728311	+	0.648102i
$208$		−	0.702856i		−	0.0487343i
$209$	−18.0652	+	13.9176i	−1.24960	+	0.962697i
$210$	16.8244	−	4.77113i	1.16100	−	0.329239i
$211$	1.61745	+	1.92761i	0.111350	+	0.132702i	0.818841	−	0.574021i	$-0.194617\pi$
$211$	1.61745	+	1.92761i	0.111350	+	0.132702i	−0.707490	+	0.706723i	$0.750173\pi$
$212$	1.34407	+	0.489201i	0.0923110	+	0.0335985i
$213$	−6.41782	+	14.3020i	−0.439742	+	0.979955i
$214$	5.74120	−	4.81744i	0.392461	−	0.329314i
$215$	−3.74315	+	4.46091i	−0.255281	+	0.304232i
$216$	4.95573	−	1.56229i	0.337195	−	0.106300i
$217$	32.7658	−	18.9173i	2.22429	−	1.28419i
$218$	9.05007	−	10.7855i	0.612948	−	0.730483i
$219$	−10.3954	−	14.3963i	−0.702453	−	0.972812i
$220$	5.29935	−	9.17875i	0.357282	−	0.618831i
$221$	1.33062			0.0895073
$222$	−5.22536	−	2.34481i	−0.350703	−	0.157373i
$223$	−7.14764	−	8.51822i	−0.478641	−	0.570422i	0.471650	−	0.881786i	$-0.343659\pi$
$223$	−7.14764	−	8.51822i	−0.478641	−	0.570422i	−0.950291	+	0.311364i	$0.899214\pi$
$224$	4.68333	−	1.70459i	0.312918	−	0.113893i
$225$	2.63228	−	0.543440i	0.175485	−	0.0362293i
$226$	−2.65855	−	15.0774i	−0.176844	−	1.00293i
$227$	13.4468	−	23.2906i	0.892499	−	1.54585i	0.0556286	−	0.998452i	$-0.482284\pi$
$227$	13.4468	−	23.2906i	0.892499	−	1.54585i	0.836870	−	0.547402i	$-0.184383\pi$
$228$	7.50045	+	0.862079i	0.496730	+	0.0570926i
$229$	1.03989	+	1.80114i	0.0687179	+	0.119023i	0.898337	−	0.439307i	$-0.144776\pi$
$229$	1.03989	+	1.80114i	0.0687179	+	0.119023i	−0.829619	+	0.558330i	$0.811442\pi$
$230$	7.25596	−	6.08848i	0.478444	−	0.401462i
$231$	19.6790	+	40.6492i	1.29478	+	2.67452i
$232$	0.801295	−	4.54437i	0.0526076	−	0.298353i
$233$	−0.473869	+	1.30194i	−0.0310442	+	0.0852932i	−0.954246	−	0.299021i	$-0.903340\pi$
$233$	−0.473869	+	1.30194i	−0.0310442	+	0.0852932i	0.923202	+	0.384314i	$0.125562\pi$
$234$	−1.65396	−	1.30786i	−0.108122	−	0.0854974i
$235$	6.70449	−	11.6125i	0.437353	−	0.757517i
$236$	−1.33354			−0.0868064
$237$	0.654044	+	6.40285i	0.0424847	+	0.415910i
$238$	3.22707	+	8.86630i	0.209180	+	0.574717i
$239$	6.71568	+	3.87730i	0.434401	+	0.250802i	0.701220	−	0.712945i	$-0.252639\pi$
$239$	6.71568	+	3.87730i	0.434401	+	0.250802i	−0.266819	+	0.963747i	$0.585972\pi$
$240$	−3.37576	+	0.957311i	−0.217904	+	0.0617942i
$241$	4.49243	+	12.3428i	0.289383	+	0.795072i	0.996153	+	0.0876294i	$0.0279291\pi$
$241$	4.49243	+	12.3428i	0.289383	+	0.795072i	−0.706770	+	0.707443i	$0.749849\pi$
$242$	15.3837	+	5.59923i	0.988905	+	0.359932i
$243$	5.54514	−	14.5689i	0.355721	−	0.934592i
$244$	−7.42979	+	6.23433i	−0.475643	+	0.399112i
$245$	12.3604	−	33.9600i	0.789679	−	2.16963i
$246$	−5.20855	+	5.36214i	−0.332085	+	0.341878i
$247$	−1.41991	−	2.71477i	−0.0903465	−	0.172737i
$248$	−6.57434	+	3.79570i	−0.417471	+	0.241027i
$249$	−5.23286	−	10.8090i	−0.331619	−	0.684996i
$250$	−11.7628	+	2.07410i	−0.743946	+	0.131178i
$251$	−1.82997	−	5.02780i	−0.115507	−	0.317352i	0.868445	−	0.495785i	$-0.165120\pi$
$251$	−1.82997	−	5.02780i	−0.115507	−	0.317352i	−0.983952	+	0.178433i	$0.942897\pi$
$252$	4.70340	−	14.1926i	0.296286	−	0.894051i
$253$	18.7384	+	15.7234i	1.17808	+	0.988523i
$254$	−9.31293	+	5.37682i	−0.584345	+	0.337372i
$255$	−1.81235	−	6.39087i	−0.113493	−	0.400211i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	12.4283	−	4.52353i	0.775256	−	0.282170i	0.0760628	−	0.997103i	$-0.475765\pi$
$257$	12.4283	−	4.52353i	0.775256	−	0.282170i	0.699193	+	0.714933i	$0.253543\pi$
$258$	1.35834	+	4.78990i	0.0845664	+	0.298206i
$259$	−14.2722	+	8.24008i	−0.886834	+	0.512014i
$260$	1.09076	+	0.915253i	0.0676458	+	0.0567616i
$261$	−9.20274	−	10.3417i	−0.569635	−	0.640133i
$262$	−5.02855	−	13.8158i	−0.310665	−	0.853544i
$263$	5.18720	−	0.914644i	0.319857	−	0.0563993i	−0.0114148	−	0.999935i	$-0.503634\pi$
$263$	5.18720	−	0.914644i	0.319857	−	0.0563993i	0.331271	+	0.943536i	$0.392522\pi$
$264$	−3.94853	−	8.15612i	−0.243015	−	0.501974i
$265$	−2.50942	+	1.44881i	−0.154153	+	0.0890000i
$266$	14.6457	−	16.0452i	0.897984	−	0.983794i
$267$	−9.94189	+	10.2351i	−0.608434	+	0.626376i
$268$	0.183340	−	0.503722i	0.0111993	−	0.0307697i
$269$	−8.31923	+	6.98067i	−0.507233	+	0.425619i	−0.860154	−	0.510034i	$-0.829633\pi$
$269$	−8.31923	+	6.98067i	−0.507233	+	0.425619i	0.352921	+	0.935653i	$0.385188\pi$
$270$	−4.02880	+	9.72515i	−0.245185	+	0.591854i
$271$	−1.02271	−	0.372236i	−0.0621251	−	0.0226117i	0.310771	−	0.950485i	$-0.399413\pi$
$271$	−1.02271	−	0.372236i	−0.0621251	−	0.0226117i	−0.372896	+	0.927873i	$0.621635\pi$
$272$	−0.647500	−	1.77899i	−0.0392604	−	0.107867i
$273$	−5.83713	+	1.65532i	−0.353279	+	0.100184i
$274$	−18.1700	−	10.4905i	−1.09769	−	0.633752i
$275$	−1.60314	−	4.40459i	−0.0966731	−	0.265607i
$276$	−0.822951	−	8.05639i	−0.0495359	−	0.484938i
$277$	17.4909			1.05093			0.525463	−	0.850816i	$-0.323892\pi$
$277$	17.4909			1.05093			0.525463	+	0.850816i	$0.323892\pi$
$278$	−4.93943	+	8.55534i	−0.296247	+	0.513115i
$279$	−3.30138	+	22.5336i	−0.197648	+	1.34905i
$280$	−3.45325	+	9.48772i	−0.206371	+	0.567000i
$281$	−1.24214	+	7.04452i	−0.0740998	+	0.420241i	0.925081	+	0.379770i	$0.123997\pi$
$281$	−1.24214	+	7.04452i	−0.0740998	+	0.420241i	−0.999181	+	0.0404707i	$0.987114\pi$
$282$	−4.99549	−	10.3187i	−0.297477	−	0.614472i
$283$	14.8288	−	12.4429i	0.881482	−	0.739651i	−0.0850011	−	0.996381i	$-0.527089\pi$
$283$	14.8288	−	12.4429i	0.881482	−	0.739651i	0.966483	+	0.256729i	$0.0826449\pi$
$284$	−4.52525	−	7.83797i	−0.268524	−	0.465098i
$285$	−11.1049	+	10.5173i	−0.657796	+	0.622991i
$286$	−1.83858	+	3.18451i	−0.108717	+	0.188304i
$287$	3.73519	+	21.1833i	0.220481	+	1.25041i
$288$	−0.943720	+	2.84770i	−0.0556092	+	0.167802i
$289$	−12.6069	+	4.58852i	−0.741580	+	0.269913i
$290$	6.00893	+	7.16116i	0.352856	+	0.420518i
$291$	−29.4299	−	13.2063i	−1.72521	−	0.774165i
$292$	10.2521			0.599959
$293$	9.88366	−	17.1190i	0.577409	−	1.00010i	−0.418366	−	0.908279i	$-0.637397\pi$
$293$	9.88366	−	17.1190i	0.577409	−	1.00010i	0.995775	−	0.0918239i	$-0.0292697\pi$
$294$	−18.0884	−	25.0503i	−1.05494	−	1.46096i
$295$	1.73653	−	2.06952i	0.101105	−	0.120492i
$296$	2.86367	−	1.65334i	0.166448	−	0.0960986i
$297$	−26.5402	−	5.88508i	−1.54002	−	0.341487i
$298$	−7.57424	+	9.02663i	−0.438764	+	0.522898i
$299$	−2.51741	+	2.11236i	−0.145586	+	0.122161i
$300$	−0.635315	+	1.41579i	−0.0366799	+	0.0817405i
$301$	13.4622	+	4.89985i	0.775949	+	0.282422i
$302$	−2.80915	−	3.34781i	−0.161648	−	0.192645i
$303$	−8.41446	+	2.38620i	−0.483398	+	0.137084i
$304$	−2.93860	+	3.21941i	−0.168540	+	0.184646i
$305$		−	19.6485i		−	1.12507i
$306$	−5.39116	−	1.78662i	−0.308192	−	0.102134i
$307$	2.15688	+	2.57047i	0.123100	+	0.146704i	0.824074	−	0.566482i	$-0.191696\pi$
$307$	2.15688	+	2.57047i	0.123100	+	0.146704i	−0.700975	+	0.713186i	$0.747251\pi$
$308$	−25.6783	−	4.52777i	−1.46315	−	0.257994i
$309$	−12.3528	+	18.1988i	−0.702726	+	1.03529i
$310$	2.67054	−	15.1454i	0.151676	−	0.860200i
$311$		−	29.6318i		−	1.68026i	−0.542383	−	0.840131i	$-0.682478\pi$
$311$		−	29.6318i		−	1.68026i	0.542383	−	0.840131i	$-0.317522\pi$
$312$	1.17120	−	0.332133i	0.0663061	−	0.0188033i
$313$	−5.09937	−	4.27888i	−0.288233	−	0.241857i	0.487193	−	0.873294i	$-0.338021\pi$
$313$	−5.09937	−	4.27888i	−0.288233	−	0.241857i	−0.775427	+	0.631438i	$0.782465\pi$
$314$	1.29803	−	7.36148i	0.0732520	−	0.415433i
$315$	15.9007	+	25.7807i	0.895902	+	1.45258i
$316$	−3.21808	−	1.85796i	−0.181031	−	0.104518i
$317$	0.188455	−	0.0685920i	0.0105847	−	0.00385251i	−0.336722	−	0.941604i	$-0.609318\pi$
$317$	0.188455	−	0.0685920i	0.0105847	−	0.00385251i	0.347307	+	0.937751i	$0.387096\pi$
$318$	−0.180040	+	2.47085i	−0.0100961	+	0.138558i
$319$	−15.5180	+	18.4936i	−0.868840	+	1.03544i
$320$	0.692882	−	1.90368i	0.0387333	−	0.106419i
$321$	10.7405	+	7.29034i	0.599476	+	0.406907i
$322$	−20.1806	−	11.6512i	−1.12462	−	0.649299i
$323$	−6.09487	−	5.56325i	−0.339128	−	0.309548i
$324$	4.94513	+	7.51969i	0.274729	+	0.417760i
$325$	0.620144	−	0.109348i	0.0343994	−	0.00606554i
$326$	−2.56376	−	14.5398i	−0.141993	−	0.805285i
$327$	22.2489	+	9.98388i	1.23037	+	0.552110i
$328$	−0.749452	−	4.25035i	−0.0413816	−	0.234686i
$329$	−32.4869	−	5.72832i	−1.79106	−	0.315813i
$330$	17.7991	+	4.49314i	0.979811	+	0.247339i
$331$		−	4.93105i		−	0.271035i	−0.990775	−	0.135517i	$-0.956730\pi$
$331$		−	4.93105i		−	0.271035i	0.990775	−	0.135517i	$-0.0432697\pi$
$332$	6.82812	+	1.20398i	0.374742	+	0.0660771i
$333$	1.43803	−	9.81528i	0.0788034	−	0.537874i
$334$	−10.6041	−	18.3668i	−0.580229	−	1.00499i
$335$	0.542978	+	0.940466i	0.0296661	+	0.0513831i
$336$	5.05353	+	6.99853i	0.275693	+	0.381801i
$337$	4.52325	−	0.797570i	0.246397	−	0.0434464i	−0.0490856	−	0.998795i	$-0.515631\pi$
$337$	4.52325	−	0.797570i	0.246397	−	0.0434464i	0.295482	+	0.955348i	$0.404520\pi$
$338$	9.58015	+	8.03870i	0.521091	+	0.437247i
$339$	23.8678	−	11.5548i	1.29632	−	0.627572i
$340$	3.60397	+	1.31174i	0.195453	+	0.0711390i
$341$	39.7161			2.15075
$342$	2.10780	+	12.9057i	0.113977	+	0.697860i
$343$	−54.0213			−2.91687
$344$	−2.70115	−	0.983137i	−0.145636	−	0.0530072i
$345$	13.5743	+	9.21383i	0.730815	+	0.496056i
$346$	0.934662	+	0.784274i	0.0502477	+	0.0421629i
$347$	−28.2824	+	4.98695i	−1.51828	+	0.267713i	−0.869756	−	0.493482i	$-0.835724\pi$
$347$	−28.2824	+	4.98695i	−1.51828	+	0.267713i	−0.648522	+	0.761196i	$0.724613\pi$
$348$	7.95113	−	0.812199i	0.426225	−	0.0435385i
$349$	11.8161	+	20.4661i	0.632503	+	1.09553i	0.987038	+	0.160484i	$0.0513056\pi$
$349$	11.8161	+	20.4661i	0.632503	+	1.09553i	−0.354536	+	0.935042i	$0.615361\pi$
$350$	2.23261	+	3.86700i	0.119338	+	0.206700i
$351$	1.39777	−	3.37408i	0.0746074	−	0.180095i
$352$	5.15225	+	0.908481i	0.274616	+	0.0484222i
$353$			9.91051i			0.527483i	0.964593	+	0.263742i	$0.0849567\pi$
$353$			9.91051i			0.527483i	−0.964593	+	0.263742i	$0.915043\pi$
$354$	−0.630163	−	2.22214i	−0.0334928	−	0.118106i
$355$	18.0564	+	3.18383i	0.958335	+	0.168980i
$356$	−1.43053	−	8.11292i	−0.0758178	−	0.429984i
$357$	−13.2493	+	9.56715i	−0.701230	+	0.506347i
$358$	−2.05973	−	11.6813i	−0.108860	−	0.617377i
$359$	−27.1532	+	4.78785i	−1.43309	+	0.252693i	−0.835669	−	0.549233i	$-0.814920\pi$
$359$	−27.1532	+	4.78785i	−1.43309	+	0.252693i	−0.597423	+	0.801926i	$0.703809\pi$
$360$	−3.19042	−	5.17280i	−0.168150	−	0.272631i
$361$	−4.84648	+	18.3715i	−0.255078	+	0.966920i
$362$	8.52053	+	4.91933i	0.447829	+	0.258554i
$363$	−2.06068	+	28.2805i	−0.108157	+	1.48434i
$364$	1.19808	−	3.29170i	0.0627966	−	0.172532i
$365$	−13.3502	+	15.9102i	−0.698782	+	0.832775i
$366$	−13.8995	−	9.43455i	−0.726537	−	0.493152i
$367$	9.30588	−	3.38706i	0.485763	−	0.176803i	−0.0875167	−	0.996163i	$-0.527893\pi$
$367$	9.30588	−	3.38706i	0.485763	−	0.176803i	0.573280	+	0.819360i	$0.305671\pi$
$368$	4.04916	+	2.33778i	0.211077	+	0.121865i
$369$	−11.3965	−	6.14536i	−0.593276	−	0.319914i
$370$	−1.16324	+	6.59708i	−0.0604741	+	0.342966i
$371$	5.46082	+	4.58217i	0.283512	+	0.237895i
$372$	−9.43162	−	9.16146i	−0.489007	−	0.474999i
$373$		−	8.72330i		−	0.451675i	−0.974165	−	0.225838i	$-0.927488\pi$
$373$		−	8.72330i		−	0.451675i	0.974165	−	0.225838i	$-0.0725119\pi$
$374$	−1.71990	+	9.75405i	−0.0889340	+	0.504370i
$375$	−9.01465	−	18.6208i	−0.465515	−	0.961572i
$376$	6.51839	+	1.14937i	0.336160	+	0.0592741i
$377$	−2.08476	−	2.48452i	−0.107371	−	0.127959i
$378$	25.8724	+	1.13078i	1.33073	+	0.0581610i
$379$		−	27.0330i		−	1.38859i	−0.719688	−	0.694297i	$-0.755715\pi$
$379$		−	27.0330i		−	1.38859i	0.719688	−	0.694297i	$-0.244285\pi$
$380$	−1.16955	−	8.75268i	−0.0599967	−	0.449003i
$381$	−13.3604	−	12.9777i	−0.684476	−	0.664869i
$382$	8.86424	+	10.5640i	0.453534	+	0.540501i
$383$	−10.8750	−	3.95817i	−0.555685	−	0.202253i	0.0488855	−	0.998804i	$-0.484433\pi$
$383$	−10.8750	−	3.95817i	−0.555685	−	0.202253i	−0.604571	+	0.796552i	$0.706655\pi$
$384$	−1.01397	−	1.40423i	−0.0517441	−	0.0716593i
$385$	40.4646	−	33.9539i	2.06227	−	1.73045i
$386$	−15.3419	+	18.2837i	−0.780881	+	0.930618i
$387$	−7.33974	+	4.52691i	−0.373100	+	0.230116i
$388$	16.1286	−	9.31183i	0.818804	−	0.472737i
$389$	−2.57534	+	3.06917i	−0.130575	+	0.155613i	−0.827370	−	0.561657i	$-0.810164\pi$
$389$	−2.57534	+	3.06917i	−0.130575	+	0.155613i	0.696795	+	0.717270i	$0.254609\pi$
$390$	−1.00969	+	2.25008i	−0.0511277	+	0.113937i
$391$	−4.42580	+	7.66571i	−0.223822	+	0.387672i
$392$	17.8392			0.901014
$393$	20.6457	−	14.9079i	1.04144	−	0.752005i
$394$	9.25594	+	11.0308i	0.466308	+	0.555724i
$395$	7.07391	−	2.57469i	0.355927	−	0.129547i
$396$	11.7250	−	10.4338i	0.589205	−	0.524316i
$397$	2.37471	+	13.4677i	0.119184	+	0.675923i	0.984594	+	0.174859i	$0.0559469\pi$
$397$	2.37471	+	13.4677i	0.119184	+	0.675923i	−0.865410	+	0.501064i	$0.832942\pi$
$398$	−13.7603	+	23.8335i	−0.689741	+	1.19467i
$399$	33.6576	+	16.8226i	1.68499	+	0.842184i
$400$	−0.447965	−	0.775899i	−0.0223983	−	0.0387949i
$401$	2.26045	−	1.89674i	0.112882	−	0.0947188i	−0.584600	−	0.811322i	$-0.698748\pi$
$401$	2.26045	−	1.89674i	0.112882	−	0.0947188i	0.697481	+	0.716603i	$0.254304\pi$
$402$	0.926010	+	0.0674743i	0.0461852	+	0.00336531i
$403$	−0.926527	+	5.25460i	−0.0461536	+	0.261750i
$404$	1.72708	−	4.74513i	0.0859257	−	0.236079i
$405$	−18.1092	−	2.11777i	−0.899855	−	0.105233i
$406$	11.4990	−	19.9169i	0.570687	−	0.988458i
$407$	−17.2997			−0.857514
$408$	2.65843	−	1.91961i	0.131612	−	0.0950351i
$409$	10.0376	+	27.5781i	0.496329	+	1.36365i	0.894798	+	0.446470i	$0.147319\pi$
$409$	10.0376	+	27.5781i	0.496329	+	1.36365i	−0.398470	+	0.917181i	$0.630459\pi$
$410$	7.57201	+	4.37170i	0.373955	+	0.215903i
$411$	8.89451	−	35.2347i	0.438734	−	1.73800i
$412$	−4.34328	−	11.9331i	−0.213978	−	0.587900i
$413$	−6.24542	−	2.27315i	−0.307317	−	0.111854i
$414$	13.0358	−	5.17835i	0.640676	−	0.254502i
$415$	−10.7600	+	9.02868i	−0.528186	+	0.443201i
$416$	−0.240391	+	0.660469i	−0.0117861	+	0.0323821i
$417$	−16.5902	−	4.18798i	−0.812428	−	0.205086i
$418$	21.7358	−	6.89956i	1.06313	−	0.337468i
$419$	25.6107	−	14.7864i	1.25117	−	0.722361i	0.279825	−	0.960051i	$-0.409723\pi$
$419$	25.6107	−	14.7864i	1.25117	−	0.722361i	0.971341	+	0.237690i	$0.0763901\pi$
$420$	−17.4416	−	1.27089i	−0.851064	−	0.0620133i
$421$	−8.34480	+	1.47141i	−0.406701	+	0.0717123i	−0.373256	−	0.927728i	$-0.621759\pi$
$421$	−8.34480	+	1.47141i	−0.406701	+	0.0717123i	−0.0334445	+	0.999441i	$0.510648\pi$
$422$	−0.860630	−	2.36456i	−0.0418948	−	0.115105i
$423$	14.8339	−	13.2003i	0.721251	−	0.641820i
$424$	−1.09569	−	0.919397i	−0.0532116	−	0.0446499i
$425$	1.46890	−	0.848071i	0.0712523	−	0.0411375i
$426$	10.9223	−	11.2444i	0.529189	−	0.544795i
$427$	−45.4231	+	16.5327i	−2.19818	+	0.800071i
$428$	−7.04263	+	2.56331i	−0.340418	+	0.123902i
$429$	−6.17530	−	1.55887i	−0.298146	−	0.0752629i
$430$	5.04313	−	2.91165i	0.243201	−	0.140412i
$431$	8.03196	+	6.73961i	0.386886	+	0.324636i	0.815399	−	0.578900i	$-0.196518\pi$
$431$	8.03196	+	6.73961i	0.386886	+	0.324636i	−0.428513	+	0.903536i	$0.640962\pi$
$432$	−5.19120	−	0.226887i	−0.249762	−	0.0109161i
$433$	14.0736	+	38.6668i	0.676333	+	1.85821i	0.478832	+	0.877906i	$0.341060\pi$
$433$	14.0736	+	38.6668i	0.676333	+	1.85821i	0.197501	+	0.980303i	$0.436718\pi$
$434$	−37.2599	+	6.56992i	−1.78853	+	0.315366i
$435$	−9.09345	+	13.3969i	−0.435997	+	0.642333i
$436$	−12.1931	+	7.03971i	−0.583945	+	0.337141i
$437$	20.3626	+	0.849566i	0.974075	+	0.0406402i
$438$	4.84461	+	17.0835i	0.231484	+	0.816282i
$439$	−1.00953	+	2.77366i	−0.0481823	+	0.132380i	−0.961450	−	0.274981i	$-0.911329\pi$
$439$	−1.00953	+	2.77366i	−0.0481823	+	0.132380i	0.913267	+	0.407361i	$0.133551\pi$
$440$	−8.11908	+	6.81272i	−0.387062	+	0.324784i
$441$	33.1947	−	41.9790i	1.58070	−	1.99900i
$442$	−1.25037	−	0.455099i	−0.0594743	−	0.0216469i
$443$	7.31798	+	20.1060i	0.347688	+	0.955264i	0.983096	+	0.183088i	$0.0586094\pi$
$443$	7.31798	+	20.1060i	0.347688	+	0.955264i	−0.635409	+	0.772176i	$0.719168\pi$
$444$	4.10826	+	3.99058i	0.194969	+	0.189385i
$445$	14.4532	+	8.34456i	0.685147	+	0.395570i
$446$	3.80318	+	10.4491i	0.180086	+	0.494781i
$447$	−18.6206	−	8.35577i	−0.880726	−	0.395214i
$448$	−4.98389			−0.235467
$449$	14.5400	−	25.1840i	0.686184	−	1.18850i	−0.286880	−	0.957967i	$-0.592618\pi$
$449$	14.5400	−	25.1840i	0.686184	−	1.18850i	0.973063	−	0.230538i	$-0.0740487\pi$
$450$	−2.65940	−	0.389627i	−0.125365	−	0.0183672i
$451$	−7.72273	+	21.2180i	−0.363649	+	0.999118i
$452$	−2.65855	+	15.0774i	−0.125047	+	0.709180i
$453$	4.25114	−	6.26300i	0.199736	−	0.294261i
$454$	−20.6018	+	17.2869i	−0.966889	+	0.811316i
$455$	3.54824	+	6.14572i	0.166344	+	0.288116i
$456$	−6.75327	−	3.37540i	−0.316251	−	0.158067i
$457$	0.724837	−	1.25545i	0.0339065	−	0.0587277i	−0.848574	−	0.529076i	$-0.822539\pi$
$457$	0.724837	−	1.25545i	0.0339065	−	0.0587277i	0.882481	+	0.470349i	$0.155872\pi$
$458$	−0.361150	−	2.04819i	−0.0168754	−	0.0957054i
$459$	0.429534	−	9.82778i	0.0200489	−	0.458721i
$460$	−8.90076	+	3.23961i	−0.415000	+	0.151048i
$461$	0.895098	+	1.06674i	0.0416889	+	0.0496829i	0.786486	−	0.617608i	$-0.211898\pi$
$461$	0.895098	+	1.06674i	0.0416889	+	0.0496829i	−0.744797	+	0.667291i	$0.767454\pi$
$462$	−4.58939	−	44.9284i	−0.213518	−	2.09026i
$463$	31.8010			1.47792			0.738959	−	0.673750i	$-0.235318\pi$
$463$	31.8010			1.47792			0.738959	+	0.673750i	$0.235318\pi$
$464$	−2.30724	+	3.99625i	−0.107111	+	0.185521i
$465$	26.4994	−	2.70688i	1.22888	−	0.125529i
$466$	0.890583	−	1.06136i	0.0412554	−	0.0491663i
$467$	12.4117	−	7.16589i	0.574345	−	0.331598i	−0.184538	−	0.982825i	$-0.559079\pi$
$467$	12.4117	−	7.16589i	0.574345	−	0.331598i	0.758883	+	0.651227i	$0.225746\pi$
$468$	1.10690	+	1.79467i	0.0511663	+	0.0829587i
$469$	1.71728	−	2.04657i	0.0792966	−	0.0945021i
$470$	−10.2719	+	8.61913i	−0.473806	+	0.397571i
$471$	12.8801	−	1.31569i	0.593485	−	0.0606239i
$472$	1.25312	+	0.456099i	0.0576796	+	0.0209937i
$473$	9.66664	+	11.5202i	0.444472	+	0.529702i
$474$	1.57530	−	6.24041i	0.0723561	−	0.286631i
$475$	−3.29773	−	2.09192i	−0.151310	−	0.0959840i
$476$		−	9.43532i		−	0.432467i
$477$	−4.20236	+	0.867586i	−0.192413	+	0.0397240i
$478$	−4.98456	−	5.94037i	−0.227989	−	0.271706i
$479$	26.3474	+	4.64575i	1.20384	+	0.212270i	0.739359	−	0.673312i	$-0.235129\pi$
$479$	26.3474	+	4.64575i	1.20384	+	0.212270i	0.464484	+	0.885582i	$0.346240\pi$
$480$	3.49960	+	0.255000i	0.159734	+	0.0116391i
$481$	0.403580	−	2.28882i	0.0184017	−	0.104361i
$482$		−	13.1350i		−	0.598282i
$483$	9.87870	−	39.1335i	0.449496	−	1.78064i
$484$	−12.5409	−	10.5231i	−0.570043	−	0.478323i
$485$	−6.55153	+	37.1556i	−0.297490	+	1.68715i
$486$	−10.1936	+	11.7937i	−0.462390	+	0.534973i
$487$	−10.8262	−	6.25049i	−0.490581	−	0.283237i	0.234235	−	0.972180i	$-0.424742\pi$
$487$	−10.8262	−	6.25049i	−0.490581	−	0.283237i	−0.724815	+	0.688943i	$0.758075\pi$
$488$	9.11398	−	3.31722i	0.412571	−	0.150163i
$489$	23.0168	−	11.1429i	1.04086	−	0.503897i
$490$	−23.2300	+	27.6845i	−1.04943	+	1.25066i
$491$	−8.04783	+	22.1112i	−0.363194	+	0.997866i	0.614700	+	0.788761i	$0.289277\pi$
$491$	−8.04783	+	22.1112i	−0.363194	+	0.997866i	−0.977893	+	0.209105i	$0.932945\pi$
$492$	6.72839	−	3.25734i	0.303339	−	0.146852i
$493$	−7.56556	−	4.36798i	−0.340735	−	0.196724i
$494$	0.405769	+	3.03669i	0.0182564	+	0.136627i
$495$	0.923827	+	31.7827i	0.0415229	+	1.42853i
$496$	7.47606	−	1.31823i	0.335685	−	0.0591903i
$497$	−7.83270	−	44.4215i	−0.351345	−	1.99257i
$498$	1.22037	+	11.9469i	0.0546859	+	0.535355i
$499$	5.20898	+	29.5416i	0.233186	+	1.32246i	0.846400	+	0.532547i	$0.178765\pi$
$499$	5.20898	+	29.5416i	0.233186	+	1.32246i	−0.613215	+	0.789916i	$0.710124\pi$
$500$	11.7628	+	2.07410i	0.526049	+	0.0927566i
$501$	25.5944	−	26.3492i	1.14347	−	1.17720i
$502$			5.35048i			0.238804i
$503$	−34.9849	−	6.16877i	−1.55990	−	0.275052i	−0.673929	−	0.738796i	$-0.735395\pi$
$503$	−34.9849	−	6.16877i	−1.55990	−	0.275052i	−0.885969	+	0.463744i	$0.846506\pi$
$504$	−9.27391	+	11.7280i	−0.413093	+	0.522409i
$505$	5.11493	+	8.85931i	0.227611	+	0.394234i
$506$	−12.2306	−	21.1841i	−0.543719	−	0.941748i
$507$	−8.86815	+	19.7625i	−0.393848	+	0.877682i
$508$	10.5903	−	1.86735i	0.469867	−	0.0828503i
$509$	−29.8722	−	25.0658i	−1.32406	−	1.11102i	−0.985426	−	0.170104i	$-0.945590\pi$
$509$	−29.8722	−	25.0658i	−1.32406	−	1.11102i	−0.338637	−	0.940917i	$-0.609966\pi$
$510$	−0.482757	+	6.62531i	−0.0213768	+	0.293374i
$511$	48.0140	+	17.4756i	2.12401	+	0.773077i
$512$	1.00000			0.0441942
$513$	−20.5093	+	9.61088i	−0.905507	+	0.424331i
$514$	−13.2259			−0.583370
$515$	24.1746	+	8.79883i	1.06526	+	0.387723i
$516$	0.361823	−	4.96561i	0.0159284	−	0.218599i
$517$	−26.5270	−	22.2588i	−1.16666	−	0.978941i
$518$	16.2298	−	2.86175i	0.713096	−	0.125738i
$519$	−0.865198	+	1.92807i	−0.0379780	+	0.0846331i
$520$	−0.711941	−	1.23312i	−0.0312207	−	0.0540758i
$521$	18.1963	+	31.5169i	0.797193	+	1.38078i	0.921437	+	0.388528i	$0.127016\pi$
$521$	18.1963	+	31.5169i	0.797193	+	1.38078i	−0.124244	+	0.992252i	$0.539651\pi$
$522$	5.11069	+	12.8655i	0.223689	+	0.563108i
$523$	2.79512	+	0.492856i	0.122222	+	0.0215511i	0.234425	−	0.972134i	$-0.424679\pi$
$523$	2.79512	+	0.492856i	0.122222	+	0.0215511i	−0.112202	+	0.993685i	$0.535791\pi$
$524$			14.7025i			0.642281i
$525$	−5.38873	+	5.54764i	−0.235183	+	0.242119i
$526$	−5.18720	−	0.914644i	−0.226173	−	0.0398804i
$527$	2.49563	+	14.1534i	0.108711	+	0.616532i
$528$	0.920844	+	9.01472i	0.0400746	+	0.392315i
$529$	0.197806	+	1.12181i	0.00860027	+	0.0487745i
$530$	2.85361	−	0.503168i	0.123953	−	0.0218562i
$531$	3.40507	−	2.10014i	0.147767	−	0.0911382i
$532$	−19.2502	+	10.0684i	−0.834603	+	0.436522i
$533$	−2.62706	−	1.51674i	−0.113791	−	0.0656971i
$534$	12.8429	−	6.21749i	0.555767	−	0.269057i
$535$	5.19288	−	14.2673i	0.224508	−	0.616830i
$536$	−0.344566	+	0.410638i	−0.0148830	+	0.0177369i
$537$	18.4918	−	8.95220i	0.797979	−	0.386316i
$538$	10.2051	−	3.71433i	0.439971	−	0.160136i
$539$	−80.8260	−	46.6649i	−3.48142	−	2.01000i
$540$	7.11204	−	7.76072i	0.306053	−	0.333968i
$541$	−5.98007	+	33.9147i	−0.257103	+	1.45810i	0.533513	+	0.845792i	$0.320872\pi$
$541$	−5.98007	+	33.9147i	−0.257103	+	1.45810i	−0.790616	+	0.612313i	$0.790239\pi$
$542$	0.833720	+	0.699574i	0.0358113	+	0.0300493i
$543$	−4.17093	+	16.5227i	−0.178992	+	0.709059i
$544$			1.89316i			0.0811687i
$545$	4.95293	−	28.0895i	0.212160	−	1.20322i
$546$	6.05126	+	0.440929i	0.258970	+	0.0188700i
$547$	12.0556	+	2.12572i	0.515459	+	0.0908893i	0.425326	−	0.905040i	$-0.360160\pi$
$547$	12.0556	+	2.12572i	0.515459	+	0.0908893i	0.0901333	+	0.995930i	$0.471271\pi$
$548$	13.4863	+	16.0723i	0.576105	+	0.686575i
$549$	9.15304	−	27.6196i	0.390642	−	1.17877i
$550$			4.68727i			0.199866i
$551$	−0.838466	+	20.0965i	−0.0357198	+	0.856142i
$552$	−1.98213	+	7.85199i	−0.0843649	+	0.334203i
$553$	−11.9043	−	14.1870i	−0.506221	−	0.603291i
$554$	−16.4361	−	5.98224i	−0.698302	−	0.254161i
$555$	−11.5427	+	1.17907i	−0.489960	+	0.0500489i
$556$	7.56764	−	6.35001i	0.320940	−	0.269300i
$557$	−0.831684	+	0.991162i	−0.0352396	+	0.0419969i	−0.783376	−	0.621548i	$-0.786504\pi$
$557$	−0.831684	+	0.991162i	−0.0352396	+	0.0419969i	0.748137	+	0.663545i	$0.230949\pi$
$558$	10.8092	−	20.0455i	0.457591	−	0.848595i
$559$	−1.74968	+	1.01018i	−0.0740037	+	0.0427261i
$560$	6.48998	−	7.73446i	0.274252	−	0.326840i
$561$	−17.0663	+	1.74331i	−0.720541	+	0.0736025i
$562$	3.57659	−	6.19484i	0.150870	−	0.261314i
$563$	−29.0555			−1.22454			−0.612272	−	0.790647i	$-0.709744\pi$
$563$	−29.0555			−1.22454			−0.612272	+	0.790647i	$0.709744\pi$
$564$	1.16501	+	11.4050i	0.0490557	+	0.480237i
$565$	−19.9365	−	23.7594i	−0.838735	−	0.999565i
$566$	−18.1902	+	6.62071i	−0.764593	+	0.278289i
$567$	10.3417	+	43.6466i	0.434309	+	1.83298i
$568$	1.57160	+	8.91301i	0.0659430	+	0.373982i
$569$	−6.25445	+	10.8330i	−0.262200	+	0.454144i	−0.966826	−	0.255435i	$-0.917781\pi$
$569$	−6.25445	+	10.8330i	−0.262200	+	0.454144i	0.704626	+	0.709579i	$0.251115\pi$
$570$	14.0323	−	6.08493i	0.587748	−	0.254870i
$571$	−11.8381	−	20.5042i	−0.495409	−	0.858074i	0.504577	−	0.863367i	$-0.331649\pi$
$571$	−11.8381	−	20.5042i	−0.495409	−	0.858074i	−0.999986	+	0.00529301i	$0.998315\pi$
$572$	2.81687	−	2.36363i	0.117779	−	0.0988284i
$573$	−13.4144	+	19.7628i	−0.560397	+	0.825605i
$574$	3.73519	−	21.1833i	0.155904	−	0.884174i
$575$	−1.43272	+	3.93635i	−0.0597484	+	0.164157i
$576$	1.86078	−	2.35319i	0.0775324	−	0.0980496i
$577$	−16.4083	+	28.4200i	−0.683086	+	1.18314i	0.290948	+	0.956739i	$0.406029\pi$
$577$	−16.4083	+	28.4200i	−0.683086	+	1.18314i	−0.974034	+	0.226401i	$0.927304\pi$
$578$	13.4159			0.558029
$579$	−37.7167	−	16.9249i	−1.56745	−	0.703374i
$580$	−3.19728	−	8.78447i	−0.132760	−	0.364755i
$581$	29.9260	+	17.2778i	1.24154	+	0.716803i
$582$	23.1382	+	22.4754i	0.959110	+	0.931637i
$583$	2.55937	+	7.03181i	0.105998	+	0.291228i
$584$	−9.63383	−	3.50643i	−0.398651	−	0.145097i
$585$	−4.22652	−	0.619224i	−0.174745	−	0.0256018i
$586$	−15.1426	+	12.7062i	−0.625537	+	0.524888i
$587$	4.56360	−	12.5384i	0.188360	−	0.517515i	−0.809184	−	0.587555i	$-0.800091\pi$
$587$	4.56360	−	12.5384i	0.188360	−	0.517515i	0.997544	+	0.0700404i	$0.0223128\pi$
$588$	8.42986	+	29.7262i	0.347642	+	1.22589i
$589$	26.2131	−	20.1948i	1.08009	−	0.832111i
$590$	−2.33962	+	1.35078i	−0.0963207	+	0.0556108i
$591$	−14.0072	+	20.6362i	−0.576180	+	0.848858i
$592$	−3.25645	+	0.574200i	−0.133839	+	0.0235995i
$593$	0.498640	+	1.37000i	0.0204767	+	0.0562592i	0.949510	−	0.313737i	$-0.101581\pi$
$593$	0.498640	+	1.37000i	0.0204767	+	0.0562592i	−0.929033	+	0.369996i	$0.879359\pi$
$594$	22.9268	+	14.6075i	0.940700	+	0.599351i
$595$	14.6426	+	12.2866i	0.600288	+	0.503701i
$596$	10.2047	−	5.89171i	0.418003	−	0.241334i
$597$	−46.2172	−	11.6669i	−1.89155	−	0.477494i
$598$	3.08806	−	1.12396i	0.126280	−	0.0459623i
$599$	16.3597	−	5.95443i	0.668438	−	0.243292i	0.0145628	−	0.999894i	$-0.495364\pi$
$599$	16.3597	−	5.95443i	0.668438	−	0.243292i	0.653875	+	0.756602i	$0.273142\pi$
$600$	1.08123	−	1.11311i	0.0441410	−	0.0454427i
$601$	−0.811979	+	0.468797i	−0.0331213	+	0.0191226i	−0.516469	−	0.856306i	$-0.672754\pi$
$601$	−0.811979	+	0.468797i	−0.0331213	+	0.0191226i	0.483348	+	0.875428i	$0.339421\pi$
$602$	−10.9745	−	9.20870i	−0.447287	−	0.375319i
$603$	0.325149	+	1.57494i	0.0132411	+	0.0641363i
$604$	1.49471	+	4.10670i	0.0608191	+	0.167099i
$605$	32.6614	−	5.75909i	1.32788	−	0.234140i
$606$	8.72314	+	0.635617i	0.354353	+	0.0258202i
$607$	−1.58601	+	0.915683i	−0.0643741	+	0.0371664i	−0.531842	−	0.846844i	$-0.678500\pi$
$607$	−1.58601	+	0.915683i	−0.0643741	+	0.0371664i	0.467467	+	0.884010i	$0.345166\pi$
$608$	3.86249	−	2.02020i	0.156645	−	0.0819297i
$609$	38.6222	+	9.74963i	1.56505	+	0.395075i
$610$	−6.72019	+	18.4636i	−0.272092	+	0.747568i
$611$	3.56376	−	2.99035i	0.144174	−	0.120977i
$612$	4.45497	+	3.52275i	0.180082	+	0.142399i
$613$	−5.74857	−	2.09231i	−0.232183	−	0.0845076i	0.223309	−	0.974748i	$-0.428314\pi$
$613$	−5.74857	−	2.09231i	−0.232183	−	0.0845076i	−0.455491	+	0.890240i	$0.650536\pi$
$614$	−1.14765	−	3.15314i	−0.0463154	−	0.127251i
$615$	−3.70662	+	14.6834i	−0.149465	+	0.592092i
$616$	22.5811	+	13.0372i	0.909818	+	0.525284i
$617$	−4.55991	−	12.5282i	−0.183575	−	0.504368i	0.813434	−	0.581658i	$-0.197596\pi$
$617$	−4.55991	−	12.5282i	−0.183575	−	0.504368i	−0.997009	+	0.0772896i	$0.975373\pi$
$618$	17.8322	−	12.8763i	0.717315	−	0.517962i
$619$	−9.56809			−0.384574			−0.192287	−	0.981339i	$-0.561590\pi$
$619$	−9.56809			−0.384574			−0.192287	+	0.981339i	$0.561590\pi$
$620$	−7.68951	+	13.3186i	−0.308818	+	0.534889i
$621$	14.7889	+	19.2751i	0.593460	+	0.773484i
$622$	−10.1347	+	27.8447i	−0.406363	+	1.11647i
$623$	7.12959	−	40.4339i	0.285641	−	1.61995i
$624$	−1.21416	−	0.0884708i	−0.0486054	−	0.00354167i
$625$	−15.1046	+	12.6743i	−0.604184	+	0.506971i
$626$	3.32838	+	5.76492i	0.133029	+	0.230413i
$627$	21.7682	+	32.9590i	0.869340	+	1.31625i
$628$	−3.73752	+	6.47358i	−0.149143	+	0.258324i
$629$	−1.08705	−	6.16499i	−0.0433437	−	0.245814i
$630$	−6.12425	−	29.6643i	−0.243996	−	1.18185i
$631$	28.1453	−	10.2441i	1.12045	−	0.407810i	0.285632	−	0.958339i	$-0.407796\pi$
$631$	28.1453	−	10.2441i	1.12045	−	0.407810i	0.834816	+	0.550530i	$0.185574\pi$
$632$	2.38855	+	2.84656i	0.0950114	+	0.113230i
$633$	3.53348	−	2.55147i	0.140443	−	0.101412i
$634$	−0.200550			−0.00796484
$635$	−10.8926	+	18.8666i	−0.432261	+	0.748698i
$636$	1.01426	−	2.26026i	0.0402181	−	0.0896252i
$637$	8.05951	−	9.60495i	0.319329	−	0.380562i
$638$	20.9073	−	12.0709i	0.827729	−	0.477890i
$639$	23.8984	+	12.8868i	0.945407	+	0.509795i
$640$	−1.30219	+	1.55189i	−0.0514736	+	0.0613439i
$641$	−19.4630	+	16.3314i	−0.768742	+	0.645051i	−0.940386	−	0.340108i	$-0.889536\pi$
$641$	−19.4630	+	16.3314i	−0.768742	+	0.645051i	0.171644	+	0.985159i	$0.445092\pi$
$642$	−7.59933	−	10.5242i	−0.299922	−	0.415355i
$643$	8.21576	+	2.99029i	0.323998	+	0.117926i	0.498898	−	0.866660i	$-0.333738\pi$
$643$	8.21576	+	2.99029i	0.323998	+	0.117926i	−0.174900	+	0.984586i	$0.555960\pi$
$644$	14.9786	+	17.8507i	0.590238	+	0.703418i
$645$	7.23493	+	7.02769i	0.284875	+	0.276715i
$646$	3.82456	+	7.31232i	0.150475	+	0.287699i
$647$		−	35.1096i		−	1.38030i	−0.723666	−	0.690151i	$-0.757544\pi$
$647$		−	35.1096i		−	1.38030i	0.723666	−	0.690151i	$-0.242456\pi$
$648$	−2.07502	−	8.75753i	−0.0815144	−	0.344028i
$649$	−4.48457	−	5.34450i	−0.176035	−	0.209790i
$650$	−0.620144	−	0.109348i	−0.0243240	−	0.00428899i
$651$	−28.5548	−	58.9831i	−1.11915	−	2.31173i
$652$	−2.56376	+	14.5398i	−0.100405	+	0.569423i
$653$			8.94289i			0.349962i	0.984572	+	0.174981i	$0.0559864\pi$
$653$			8.94289i			0.349962i	−0.984572	+	0.174981i	$0.944014\pi$
$654$	−17.4924	−	16.9913i	−0.684007	−	0.664414i
$655$	−22.8167	−	19.1454i	−0.891521	−	0.748075i
$656$	−0.749452	+	4.25035i	−0.0292612	+	0.165948i
$657$	−26.1777	+	16.1456i	−1.02129	+	0.629898i
$658$	28.5685	+	16.4940i	1.11372	+	0.643005i
$659$	−3.05418	+	1.11163i	−0.118974	+	0.0433030i	−0.400821	−	0.916156i	$-0.631275\pi$
$659$	−3.05418	+	1.11163i	−0.118974	+	0.0433030i	0.281847	+	0.959459i	$0.409053\pi$
$660$	−15.1890	−	10.3098i	−0.591230	−	0.401310i
$661$	19.4940	−	23.2321i	0.758230	−	0.903624i	−0.239504	−	0.970895i	$-0.576985\pi$
$661$	19.4940	−	23.2321i	0.758230	−	0.903624i	0.997735	+	0.0672717i	$0.0214294\pi$
$662$	−1.68652	+	4.63367i	−0.0655484	+	0.180093i
$663$	0.167490	−	2.29861i	0.00650476	−	0.0892706i
$664$	−6.00455	−	3.46673i	−0.233022	−	0.134535i
$665$	9.44236	−	42.9853i	0.366159	−	1.66690i
$666$	−4.70833	+	8.73151i	−0.182444	+	0.338339i
$667$	21.2475	−	3.74650i	0.822706	−	0.145065i
$668$	3.68275	+	20.8859i	0.142490	+	0.808101i
$669$	−15.6147	+	11.2751i	−0.603698	+	0.435921i
$670$	−0.188574	−	1.06946i	−0.00728526	−	0.0413168i
$671$	−49.9712	−	8.81127i	−1.92912	−	0.340155i
$672$	−2.35513	−	8.30487i	−0.0908510	−	0.320367i
$673$			17.9140i			0.690532i	0.938505	+	0.345266i	$0.112211\pi$
$673$			17.9140i			0.690532i	−0.938505	+	0.345266i	$0.887789\pi$
$674$	−4.52325	−	0.797570i	−0.174229	−	0.0307213i
$675$	−0.607443	−	4.61559i	−0.0233805	−	0.177654i
$676$	−6.25300	−	10.8305i	−0.240500	−	0.416558i
$677$	−9.13745	−	15.8265i	−0.351181	−	0.608263i	0.635276	−	0.772285i	$-0.280886\pi$
$677$	−9.13745	−	15.8265i	−0.351181	−	0.608263i	−0.986457	+	0.164023i	$0.947553\pi$
$678$	−26.3803	+	2.69472i	−1.01313	+	0.103490i
$679$	91.4082	−	16.1177i	3.50792	−	0.618542i
$680$	−2.93798	−	2.46526i	−0.112666	−	0.0945384i
$681$	−38.5413	−	26.1607i	−1.47691	−	1.00248i
$682$	−37.3210	−	13.5837i	−1.42909	−	0.520148i
$683$	5.33391			0.204097			0.102048	−	0.994779i	$-0.467460\pi$
$683$	5.33391			0.204097			0.102048	+	0.994779i	$0.467460\pi$
$684$	2.43332	−	12.8483i	0.0930404	−	0.491267i
$685$	−42.5042			−1.62400
$686$	50.7634	+	18.4764i	1.93815	+	0.705431i
$687$	3.24232	−	1.56967i	0.123702	−	0.0598865i
$688$	2.20199	+	1.84769i	0.0839503	+	0.0704426i
$689$	−0.990042	+	0.174571i	−0.0377176	+	0.00665063i
$690$	−9.60433	−	13.3008i	−0.365631	−	0.506354i
$691$	21.2932	+	36.8810i	0.810033	+	1.40302i	0.912840	+	0.408316i	$0.133884\pi$
$691$	21.2932	+	36.8810i	0.810033	+	1.40302i	−0.102808	+	0.994701i	$0.532783\pi$
$692$	−0.610057	−	1.05665i	−0.0231909	−	0.0401678i
$693$	72.6974	−	28.8783i	2.76155	−	1.09700i
$694$	28.2824	+	4.98695i	1.07358	+	0.189302i
$695$			20.0131i			0.759140i
$696$	−7.74941	−	1.95623i	−0.293740	−	0.0741507i
$697$	−8.04661	−	1.41883i	−0.304787	−	0.0537422i
$698$	−4.10370	−	23.2732i	−0.155327	−	0.880905i
$699$	2.18942	+	0.982475i	0.0828116	+	0.0371606i
$700$	−0.775378	−	4.39739i	−0.0293065	−	0.166206i
$701$	1.30705	−	0.230469i	0.0493668	−	0.00870470i	−0.148910	−	0.988851i	$-0.547577\pi$
$701$	1.30705	−	0.230469i	0.0493668	−	0.00870470i	0.198277	+	0.980146i	$0.436465\pi$
$702$	−2.46748	+	2.69253i	−0.0931289	+	0.101623i
$703$	−11.4180	+	8.79651i	−0.430638	+	0.331767i
$704$	−4.53081	−	2.61587i	−0.170761	−	0.0985892i
$705$	−19.2164	−	13.0435i	−0.723731	−	0.491247i
$706$	3.38960	−	9.31284i	0.127569	−	0.350493i
$707$	16.1770	−	19.2790i	0.608399	−	0.725061i
$708$	−0.167858	+	2.30366i	−0.00630847	+	0.0865768i
$709$	12.4374	−	4.52684i	0.467096	−	0.170009i	−0.0977407	−	0.995212i	$-0.531162\pi$
$709$	12.4374	−	4.52684i	0.467096	−	0.170009i	0.564836	+	0.825203i	$0.308939\pi$
$710$	−15.8785	−	9.16748i	−0.595911	−	0.344050i
$711$	11.1431	−	0.323895i	0.417897	−	0.0121470i
$712$	−1.43053	+	8.11292i	−0.0536113	+	0.304045i
$713$	−27.1900	−	22.8151i	−1.01827	−	0.854433i
$714$	15.7225	−	4.45864i	0.588399	−	0.166860i
$715$			7.44937i			0.278591i
$716$	−2.05973	+	11.6813i	−0.0769758	+	0.436552i
$717$	7.54325	−	11.1131i	0.281708	−	0.415026i
$718$	27.1532	+	4.78785i	1.01335	+	0.178681i
$719$	10.2309	+	12.1927i	0.381546	+	0.454709i	0.922302	−	0.386471i	$-0.126306\pi$
$719$	10.2309	+	12.1927i	0.381546	+	0.454709i	−0.540755	+	0.841180i	$0.681861\pi$
$720$	1.22881	+	5.95203i	0.0457950	+	0.221819i
$721$		−	63.2899i		−	2.35704i
$722$	10.8376	−	15.6060i	0.403335	−	0.580794i
$723$	21.8874	−	6.20690i	0.814000	−	0.230837i
$724$	−6.32417	−	7.53685i	−0.235036	−	0.280105i
$725$	−3.88492	−	1.41400i	−0.144282	−	0.0525145i
$726$	11.6089	−	25.8702i	0.430847	−	0.960132i
$727$	2.08901	−	1.75289i	0.0774772	−	0.0650111i	−0.603227	−	0.797570i	$-0.706119\pi$
$727$	2.08901	−	1.75289i	0.0774772	−	0.0650111i	0.680704	+	0.732559i	$0.261674\pi$
$728$	−2.25166	+	2.68342i	−0.0834520	+	0.0994542i
$729$	−24.4693	−	11.4129i	−0.906270	−	0.422700i
$730$	17.9867	−	10.3846i	0.665717	−	0.384352i
$731$	−3.49798	+	4.16873i	−0.129378	+	0.154186i
$732$	9.83442	+	13.6195i	0.363490	+	0.503390i
$733$	−14.5115	+	25.1347i	−0.535995	+	0.928371i	0.463119	+	0.886296i	$0.346730\pi$
$733$	−14.5115	+	25.1347i	−0.535995	+	0.928371i	−0.999114	+	0.0420752i	$0.986603\pi$
$734$	−9.90311			−0.365530
$735$	−57.1091	−	25.6269i	−2.10650	−	0.945264i
$736$	−3.00539	−	3.58169i	−0.110780	−	0.132023i
$737$	2.63534	−	0.959185i	0.0970740	−	0.0353320i
$738$	8.60733	+	9.67256i	0.316840	+	0.356052i
$739$	−1.23260	−	6.99040i	−0.0453418	−	0.257146i	0.953708	−	0.300735i	$-0.0972320\pi$
$739$	−1.23260	−	6.99040i	−0.0453418	−	0.257146i	−0.999050	+	0.0435888i	$0.986121\pi$
$740$	3.34943	−	5.80138i	0.123127	−	0.213263i
$741$	−4.86842	+	2.11113i	−0.178846	+	0.0775543i
$742$	−3.56430	−	6.17355i	−0.130850	−	0.226638i
$743$	−30.3090	+	25.4323i	−1.11193	+	0.933019i	−0.998169	−	0.0604893i	$-0.980734\pi$
$743$	−30.3090	+	25.4323i	−1.11193	+	0.933019i	−0.113760	+	0.993508i	$0.536289\pi$
$744$	5.72942	+	11.8348i	0.210051	+	0.433883i
$745$	−4.14523	+	23.5088i	−0.151870	+	0.861295i
$746$	−2.98354	+	8.19722i	−0.109235	+	0.300121i
$747$	−19.3310	+	7.67904i	−0.707284	+	0.280961i
$748$	4.95226	−	8.57757i	0.181073	−	0.313627i
$749$	−37.3523			−1.36482
$750$	2.10233	+	20.5810i	0.0767661	+	0.751512i
$751$	2.12424	+	5.83630i	0.0775146	+	0.212970i	0.972397	−	0.233332i	$-0.0749630\pi$
$751$	2.12424	+	5.83630i	0.0775146	+	0.212970i	−0.894882	+	0.446302i	$0.852741\pi$
$752$	−5.73217	−	3.30947i	−0.209031	−	0.120684i
$753$	−8.91573	+	2.52836i	−0.324907	+	0.0921384i
$754$	1.10928	+	3.04772i	0.0403975	+	0.110991i
$755$	−8.31955	−	3.02807i	−0.302779	−	0.110203i
$756$	−23.9253	−	9.91145i	−0.870155	−	0.360476i
$757$	−0.344603	+	0.289157i	−0.0125248	+	0.0105096i	−0.649029	−	0.760764i	$-0.724824\pi$
$757$	−0.344603	+	0.289157i	−0.0125248	+	0.0105096i	0.636504	+	0.771274i	$0.280380\pi$
$758$	−9.24585	+	25.4028i	−0.335824	+	0.922670i
$759$	29.5204	−	30.3910i	1.07152	−	1.10312i
$760$	−1.89457	+	8.62484i	−0.0687235	+	0.312856i
$761$	11.0003	−	6.35101i	0.398759	−	0.230224i	−0.287189	−	0.957874i	$-0.592721\pi$
$761$	11.0003	−	6.35101i	0.398759	−	0.230224i	0.685948	+	0.727650i	$0.259388\pi$
$762$	8.11605	+	16.7646i	0.294014	+	0.607318i
$763$	−69.1042	+	12.1849i	−2.50174	+	0.441124i
$764$	−4.71656	−	12.9586i	−0.170639	−	0.468827i
$765$	−11.2682	+	2.32633i	−0.407401	+	0.0841088i
$766$	8.86536	+	7.43892i	0.320318	+	0.268779i
$767$	0.811717	−	0.468645i	0.0293094	−	0.0169218i
$768$	0.472548	+	1.66634i	0.0170516	+	0.0601290i
$769$	5.68544	−	2.06933i	0.205022	−	0.0746220i	−0.237468	−	0.971395i	$-0.576317\pi$
$769$	5.68544	−	2.06933i	0.205022	−	0.0746220i	0.442490	+	0.896773i	$0.354095\pi$
$770$	−49.6372	+	18.0665i	−1.78880	+	0.651070i
$771$	−6.24988	−	22.0389i	−0.225084	−	0.793712i
$772$	20.6701	−	11.9339i	0.743931	−	0.429509i
$773$	0.683524	+	0.573545i	0.0245847	+	0.0206290i	0.654997	−	0.755631i	$-0.272670\pi$
$773$	0.683524	+	0.573545i	0.0245847	+	0.0206290i	−0.630413	+	0.776260i	$0.717114\pi$
$774$	8.44540	−	1.74357i	0.303563	−	0.0626713i
$775$	2.32620	+	6.39119i	0.0835597	+	0.229578i
$776$	−18.3407	+	3.23396i	−0.658394	+	0.116093i
$777$	12.4380	+	25.6921i	0.446211	+	0.921699i
$778$	3.46975	−	2.00326i	0.124396	−	0.0718203i
$779$	5.69179	+	17.9310i	0.203930	+	0.642444i
$780$	1.71837	−	1.76904i	0.0615275	−	0.0633419i
$781$	16.1946	−	44.4943i	0.579488	−	1.59213i
$782$	6.78072	−	5.68970i	0.242478	−	0.203463i
$783$	−19.0233	+	14.5957i	−0.679837	+	0.521609i
$784$	−16.7633	−	6.10136i	−0.598691	−	0.217906i
$785$	−5.17932	−	14.2301i	−0.184858	−	0.507893i
$786$	−24.4994	+	6.94762i	−0.873864	+	0.247814i
$787$	0.346539	+	0.200075i	0.0123528	+	0.00713189i	0.506164	−	0.862437i	$-0.331063\pi$
$787$	0.346539	+	0.200075i	0.0123528	+	0.00713189i	−0.493811	+	0.869569i	$0.664396\pi$
$788$	−4.92498	−	13.5313i	−0.175445	−	0.482032i
$789$	−0.927090	−	9.07587i	−0.0330053	−	0.323110i
$790$	−7.52790			−0.267831
$791$	−38.1516	+	66.0805i	−1.35651	+	2.34955i
$792$	−14.5865	+	5.79433i	−0.518308	+	0.205892i
$793$	2.33153	−	6.40582i	0.0827950	−	0.227477i
$794$	2.37471	−	13.4677i	0.0842755	−	0.477950i
$795$	2.18692	+	4.51732i	0.0775619	+	0.160213i
$796$	21.0820	−	17.6899i	0.747232	−	0.627002i
$797$	15.0127	+	26.0027i	0.531777	+	0.921064i	0.999312	+	0.0370900i	$0.0118088\pi$
$797$	15.0127	+	26.0027i	0.531777	+	0.921064i	−0.467535	+	0.883975i	$0.654858\pi$
$798$	−25.8741	−	27.3197i	−0.915934	−	0.967105i
$799$	6.26537	−	10.8519i	0.221653	−	0.383914i
$800$	0.155577	+	0.882320i	0.00550047	+	0.0311947i
$801$	16.4294	+	18.4626i	0.580503	+	0.652345i
$802$	−2.77285	+	1.00924i	−0.0979129	+	0.0356374i
$803$	34.4767	+	41.0878i	1.21666	+	1.44996i
$804$	−0.847088	−	0.380119i	−0.0298745	−	0.0134058i
$805$	−47.2074			−1.66384
$806$	2.66783	−	4.62081i	0.0939703	−	0.162761i
$807$	11.0117	+	15.2499i	0.387631	+	0.536822i
$808$	−3.24586	+	3.86826i	−0.114189	+	0.136085i
$809$	3.27529	−	1.89099i	0.115153	−	0.0664836i	−0.441317	−	0.897351i	$-0.645489\pi$
$809$	3.27529	−	1.89099i	0.115153	−	0.0664836i	0.556470	+	0.830868i	$0.312155\pi$
$810$	16.2928	+	8.18378i	0.572471	+	0.287549i
$811$	2.90606	−	3.46330i	0.102045	−	0.121613i	−0.712605	−	0.701566i	$-0.752485\pi$
$811$	2.90606	−	3.46330i	0.102045	−	0.121613i	0.814650	+	0.579953i	$0.196929\pi$
$812$	−17.6175	+	14.7829i	−0.618254	+	0.518776i
$813$	−0.771758	+	1.71985i	−0.0270667	+	0.0603176i
$814$	16.2564	+	5.91685i	0.569787	+	0.207385i
$815$	−19.2257	−	22.9123i	−0.673446	−	0.802582i
$816$	−3.15466	+	0.894610i	−0.110435	+	0.0313176i
$817$	12.2379	+	2.68823i	0.428149	+	0.0940493i
$818$		−	29.3481i		−	1.02613i
$819$	2.12477	+	10.2918i	0.0742455	+	0.359626i
$820$	−5.62016	−	6.69784i	−0.196264	−	0.233899i
$821$	−16.6492	−	2.93571i	−0.581062	−	0.102457i	−0.124611	−	0.992206i	$-0.539768\pi$
$821$	−16.6492	−	2.93571i	−0.581062	−	0.102457i	−0.456451	+	0.889749i	$0.650880\pi$
$822$	−20.4091	+	30.0677i	−0.711849	+	1.04873i
$823$	−0.789274	+	4.47619i	−0.0275124	+	0.156030i	−0.995469	−	0.0950873i	$-0.969687\pi$
$823$	−0.789274	+	4.47619i	−0.0275124	+	0.156030i	0.967957	+	0.251118i	$0.0807981\pi$
$824$			12.6989i			0.442387i
$825$	−7.81060	+	2.21496i	−0.271930	+	0.0771150i
$826$	5.09132	+	4.27212i	0.177150	+	0.148646i
$827$	1.72008	−	9.75505i	0.0598130	−	0.339216i	−0.940186	−	0.340662i	$-0.889349\pi$
$827$	1.72008	−	9.75505i	0.0598130	−	0.339216i	0.999999	+	0.00144537i	$0.000460076\pi$
$828$	−14.0208	+	0.407541i	−0.487255	+	0.0141630i
$829$	−18.2261	−	10.5228i	−0.633018	−	0.365473i	0.148902	−	0.988852i	$-0.452426\pi$
$829$	−18.2261	−	10.5228i	−0.633018	−	0.365473i	−0.781920	+	0.623379i	$0.785759\pi$
$830$	13.1991	−	4.80406i	0.458146	−	0.166751i
$831$	2.20164	−	30.2150i	0.0763739	−	1.04815i
$832$	0.451787	−	0.538419i	0.0156629	−	0.0186663i
$833$	11.5509	−	31.7357i	0.400214	−	1.09958i
$834$	14.1574	+	9.60961i	0.490229	+	0.332754i
$835$	−37.2083	−	21.4823i	−1.28765	−	0.743424i
$836$	−22.7848	−	0.950624i	−0.788028	−	0.0328780i
$837$	38.5106	+	8.53942i	1.33112	+	0.295166i
$838$	−29.1235	+	5.13525i	−1.00605	+	0.177394i
$839$	−3.07681	−	17.4495i	−0.106223	−	0.602422i	−0.990725	−	0.135885i	$-0.956612\pi$
$839$	−3.07681	−	17.4495i	−0.106223	−	0.602422i	0.884501	−	0.466538i	$-0.154499\pi$
$840$	15.9551	+	7.15963i	0.550503	+	0.247031i
$841$	−1.33824	−	7.58954i	−0.0461463	−	0.261708i
$842$	8.34480	+	1.47141i	0.287581	+	0.0507083i
$843$	12.0128	+	3.03247i	0.413744	+	0.104444i
$844$			2.51631i			0.0866151i
$845$	24.9504	+	4.39942i	0.858319	+	0.151345i
$846$	−18.4541	+	7.33071i	−0.634465	+	0.252035i
$847$	−40.7957	−	70.6603i	−1.40176	−	2.42792i
$848$	0.715164	+	1.23870i	0.0245588	+	0.0425371i
$849$	−19.6281	−	27.1826i	−0.673636	−	0.932904i
$850$	−1.67037	+	0.294532i	−0.0572934	+	0.0101024i
$851$	11.8435	+	9.93789i	0.405991	+	0.340667i
$852$	−14.1095	+	6.83065i	−0.483382	+	0.234014i
$853$	−27.8675	−	10.1429i	−0.954164	−	0.347287i	−0.182420	−	0.983221i	$-0.558393\pi$
$853$	−27.8675	−	10.1429i	−0.954164	−	0.347287i	−0.771744	+	0.635933i	$0.780615\pi$
$854$	48.3383			1.65410
$855$	16.7705	+	20.5072i	0.573540	+	0.701332i
$856$	7.49461			0.256160
$857$	9.89346	+	3.60092i	0.337954	+	0.123005i	0.505422	−	0.862872i	$-0.331337\pi$
$857$	9.89346	+	3.60092i	0.337954	+	0.123005i	−0.167468	+	0.985878i	$0.553559\pi$
$858$	5.26972	+	3.57694i	0.179905	+	0.122115i
$859$	40.8751	+	34.2983i	1.39464	+	1.17024i	0.963420	+	0.267995i	$0.0863610\pi$
$859$	40.8751	+	34.2983i	1.39464	+	1.17024i	0.431220	+	0.902247i	$0.358083\pi$
$860$	−5.73484	+	1.01121i	−0.195556	+	0.0344819i
$861$	37.0637	−	3.78602i	1.26313	−	0.129027i
$862$	−5.24249	−	9.08025i	−0.178560	−	0.309275i
$863$	14.1160	+	24.4497i	0.480516	+	0.832278i	0.999750	−	0.0223540i	$-0.00711610\pi$
$863$	14.1160	+	24.4497i	0.480516	+	0.832278i	−0.519234	+	0.854632i	$0.673783\pi$
$864$	4.80053	+	1.98870i	0.163317	+	0.0676569i
$865$	2.43422	+	0.429218i	0.0827659	+	0.0145939i
$866$		−	41.1484i		−	1.39828i
$867$	6.33967	+	22.3555i	0.215306	+	0.759234i
$868$	37.2599	+	6.56992i	1.26468	+	0.222998i
$869$	−3.37585	−	19.1454i	−0.114518	−	0.649462i
$870$	13.1271	−	9.47885i	0.445049	−	0.321363i
$871$	0.0654247	+	0.371042i	0.00221683	+	0.0125723i
$872$	13.8655	−	2.44487i	0.469546	−	0.0827936i
$873$	−26.5179	+	49.1769i	−0.897494	+	1.66439i
$874$	−18.8440	−	7.76275i	−0.637408	−	0.262579i
$875$	51.5536	+	29.7645i	1.74283	+	1.00622i
$876$	1.29047	−	17.7102i	0.0436008	−	0.598373i
$877$	−4.85954	+	13.3515i	−0.164095	+	0.450847i	−0.994301	−	0.106610i	$-0.966001\pi$
$877$	−4.85954	+	13.3515i	−0.164095	+	0.450847i	0.830206	+	0.557457i	$0.188223\pi$
$878$	1.89730	−	2.26111i	0.0640307	−	0.0763088i
$879$	−28.3285	−	19.2286i	−0.955496	−	0.648563i
$880$	9.95953	−	3.62497i	0.335736	−	0.122198i
$881$	38.9269	+	22.4744i	1.31148	+	0.757183i	0.982341	−	0.187098i	$-0.0599083\pi$
$881$	38.9269	+	22.4744i	1.31148	+	0.757183i	0.329139	+	0.944282i	$0.393242\pi$
$882$	−45.5505	+	28.0941i	−1.53376	+	0.945977i
$883$	−2.13374	+	12.1010i	−0.0718060	+	0.407232i	0.927625	+	0.373512i	$0.121847\pi$
$883$	−2.13374	+	12.1010i	−0.0718060	+	0.407232i	−0.999431	+	0.0337200i	$0.989265\pi$
$884$	1.01931	+	0.855307i	0.0342833	+	0.0287671i
$885$	−3.35645	−	3.26030i	−0.112826	−	0.109594i
$886$		−	21.3963i		−	0.718824i
$887$	9.89238	−	56.1025i	0.332154	−	1.88374i	−0.121552	−	0.992585i	$-0.538787\pi$
$887$	9.89238	−	56.1025i	0.332154	−	1.88374i	0.453706	−	0.891152i	$-0.350102\pi$
$888$	−2.49564	−	5.15503i	−0.0837483	−	0.172991i
$889$	52.7808	+	9.30667i	1.77021	+	0.312136i
$890$	−10.7276	−	12.7846i	−0.359588	−	0.428541i
$891$	−13.5070	+	45.1067i	−0.452502	+	1.51113i
$892$		−	11.1198i		−	0.372317i
$893$	−28.8262	−	1.20268i	−0.964633	−	0.0402463i
$894$	14.6398	+	14.2205i	0.489629	+	0.475604i
$895$	−15.4460	−	18.4078i	−0.516302	−	0.615305i
$896$	4.68333	+	1.70459i	0.156459	+	0.0569464i
$897$	3.33216	+	4.61465i	0.111258	+	0.154079i
$898$	−22.2765	+	18.6922i	−0.743377	+	0.623768i
$899$	22.5170	−	26.8348i	0.750985	−	0.894989i
$900$	2.36576	+	1.27570i	0.0788587	+	0.0425233i
$901$	−2.34506	+	1.35392i	−0.0781253	+	0.0451057i
$902$	14.5140	−	17.2971i	0.483263	−	0.575930i
$903$	10.1589	−	22.6388i	0.338066	−	0.753373i
$904$	7.65498	−	13.2588i	0.254601	−	0.440981i
$905$	19.9316			0.662550
$906$	−6.13684	+	4.43132i	−0.203883	+	0.147221i
$907$	−17.5354	−	20.8979i	−0.582253	−	0.693903i	0.391844	−	0.920032i	$-0.371837\pi$
$907$	−17.5354	−	20.8979i	−0.582253	−	0.693903i	−0.974097	+	0.226129i	$0.927393\pi$
$908$	25.2718	−	9.19819i	0.838674	−	0.305253i
$909$	3.06294	+	14.8361i	0.101591	+	0.492082i
$910$	−1.23229	−	6.98866i	−0.0408500	−	0.231672i
$911$	16.1354	−	27.9474i	0.534591	−	0.925939i	−0.464592	−	0.885525i	$-0.653799\pi$
$911$	16.1354	−	27.9474i	0.534591	−	0.925939i	0.999183	−	0.0404141i	$-0.0128677\pi$
$912$	5.19155	+	5.48159i	0.171909	+	0.181514i
$913$	18.1370	+	31.4142i	0.600247	+	1.03966i
$914$	−1.11052	+	0.931833i	−0.0367326	+	0.0308223i
$915$	−33.9422	−	2.47322i	−1.12210	−	0.0817622i
$916$	−0.361150	+	2.04819i	−0.0119327	+	0.0676740i
$917$	−25.0617	+	68.8565i	−0.827611	+	2.27384i
$918$	−3.76493	+	9.08818i	−0.124261	+	0.299955i
$919$	−26.0562	+	45.1306i	−0.859513	+	1.48872i	0.0128806	+	0.999917i	$0.495900\pi$
$919$	−26.0562	+	45.1306i	−0.859513	+	1.48872i	−0.872394	+	0.488804i	$0.837433\pi$
$920$	9.47199			0.312282
$921$	4.71190	−	3.40239i	0.155262	−	0.112113i
$922$	−0.476272	−	1.30855i	−0.0156852	−	0.0430947i
$923$	5.50896	+	3.18060i	0.181330	+	0.104691i
$924$	−11.0538	+	43.7885i	−0.363643	+	1.44054i
$925$	−1.01326	−	2.78390i	−0.0333157	−	0.0915340i
$926$	−29.8832	−	10.8766i	−0.982022	−	0.357427i
$927$	29.8829	+	23.6298i	0.981484	+	0.776105i
$928$	3.53489	−	2.96613i	0.116039	−	0.0973679i
$929$	−2.96012	+	8.13285i	−0.0971182	+	0.266830i	−0.978733	−	0.205140i	$-0.934235\pi$
$929$	−2.96012	+	8.13285i	−0.0971182	+	0.266830i	0.881614	+	0.471971i	$0.156457\pi$
$930$	−25.8271	−	6.51968i	−0.846903	−	0.213789i
$931$	−77.0741	+	10.2988i	−2.52600	+	0.337530i
$932$	−1.19988	+	0.692750i	−0.0393033	+	0.0226918i
$933$	−51.1880	−	3.72984i	−1.67582	−	0.122110i
$934$	−14.1141	+	2.48869i	−0.461826	+	0.0814324i
$935$	6.86266	+	18.8550i	0.224433	+	0.616625i
$936$	−0.426328	−	2.06502i	−0.0139350	−	0.0674973i
$937$	−14.0902	−	11.8230i	−0.460305	−	0.386242i	0.382938	−	0.923774i	$-0.374912\pi$
$937$	−14.0902	−	11.8230i	−0.460305	−	0.386242i	−0.843243	+	0.537532i	$0.819357\pi$
$938$	−2.31369	+	1.33581i	−0.0755445	+	0.0436156i
$939$	−8.03352	+	8.27042i	−0.262164	+	0.269895i
$940$	12.6003	−	4.58614i	0.410977	−	0.149583i
$941$	22.0935	−	8.04137i	0.720227	−	0.262141i	0.0442049	−	0.999022i	$-0.485925\pi$
$941$	22.0935	−	8.04137i	0.720227	−	0.262141i	0.676022	+	0.736881i	$0.263702\pi$
$942$	−12.5534	−	3.16892i	−0.409011	−	0.103249i
$943$	17.4758	−	10.0897i	0.569092	−	0.328565i
$944$	−1.02155	−	0.857186i	−0.0332488	−	0.0278990i
$945$	46.5368	−	24.2229i	1.51384	−	0.787970i
$946$	−5.14351	−	14.1317i	−0.167230	−	0.459460i
$947$	−8.08048	+	1.42481i	−0.262580	+	0.0463000i	−0.303388	−	0.952867i	$-0.598118\pi$
$947$	−8.08048	+	1.42481i	−0.262580	+	0.0463000i	0.0408080	+	0.999167i	$0.487007\pi$
$948$	−3.61464	+	5.32528i	−0.117398	+	0.172957i
$949$	−6.24037	+	3.60288i	−0.202571	+	0.116954i
$950$	2.38337	+	3.09365i	0.0773268	+	0.100371i
$951$	−0.0947693	−	0.334184i	−0.00307310	−	0.0108367i
$952$	−3.22707	+	8.86630i	−0.104590	+	0.287358i
$953$	13.9544	−	11.7091i	0.452026	−	0.379295i	−0.388161	−	0.921592i	$-0.626890\pi$
$953$	13.9544	−	11.7091i	0.452026	−	0.379295i	0.840187	+	0.542297i	$0.182445\pi$
$954$	4.24566	+	0.622028i	0.137458	+	0.0201389i
$955$	26.2523	+	9.55505i	0.849504	+	0.309194i
$956$	2.65223	+	7.28694i	0.0857793	+	0.235677i
$957$	29.9939	+	29.1347i	0.969565	+	0.941792i
$958$	−23.1695	−	13.3769i	−0.748572	−	0.432189i
$959$	35.7639	+	98.2605i	1.15488	+	3.17300i
$960$	−3.20133	−	1.43655i	−0.103323	−	0.0463646i
$961$	−26.6292			−0.859008
$962$	−1.16206	+	2.01275i	−0.0374664	+	0.0648937i
$963$	13.9458	−	17.6362i	0.449397	−	0.568320i
$964$	−4.49243	+	12.3428i	−0.144691	+	0.397536i
$965$	−8.39631	+	47.6178i	−0.270287	+	1.53287i
$966$	−22.6674	+	33.3947i	−0.729311	+	1.07446i
$967$	13.5502	−	11.3700i	0.435745	−	0.365633i	−0.398370	−	0.917225i	$-0.630424\pi$
$967$	13.5502	−	11.3700i	0.435745	−	0.365633i	0.834114	+	0.551592i	$0.185979\pi$
$968$	8.18552	+	14.1777i	0.263093	+	0.455690i
$969$	−10.3775	+	9.82844i	−0.333375	+	0.315735i
$970$	18.8644	−	32.6741i	0.605699	−	1.04910i
$971$	−8.36101	−	47.4176i	−0.268317	−	1.52170i	−0.759419	−	0.650602i	$-0.774517\pi$
$971$	−8.36101	−	47.4176i	−0.268317	−	1.52170i	0.491102	−	0.871102i	$-0.336594\pi$
$972$	13.6125	−	7.59604i	0.436621	−	0.243643i
$973$	46.2659	−	16.8394i	1.48322	−	0.539847i
$974$	8.03548	+	9.57631i	0.257473	+	0.306845i
$975$	−0.110836	−	1.08504i	−0.00354960	−	0.0347492i
$976$	−9.69890			−0.310454
$977$	20.8809	−	36.1667i	0.668038	−	1.15708i	−0.310414	−	0.950602i	$-0.600468\pi$
$977$	20.8809	−	36.1667i	0.668038	−	1.15708i	0.978452	−	0.206475i	$-0.0661991\pi$
$978$	−25.4398	+	2.59865i	−0.813475	+	0.0830956i
$979$	27.7038	−	33.0161i	0.885417	−	1.05520i
$980$	31.2977	−	18.0697i	0.999769	−	0.577217i
$981$	20.0474	−	37.1776i	0.640064	−	1.18699i
$982$	15.1250	−	18.0252i	0.482657	−	0.575209i
$983$	0.921203	−	0.772981i	0.0293818	−	0.0246543i	−0.627978	−	0.778231i	$-0.716117\pi$
$983$	0.921203	−	0.772981i	0.0293818	−	0.0246543i	0.657360	+	0.753576i	$0.271673\pi$
$984$	−7.43670	+	0.759651i	−0.237073	+	0.0242168i
$985$	27.4124	+	9.97728i	0.873430	+	0.317903i
$986$	5.61536	+	6.69213i	0.178830	+	0.213121i
$987$	−13.9847	+	55.3992i	−0.445139	+	1.76338i
$988$	0.657311	−	2.99234i	0.0209119	−	0.0951989i
$989$		−	13.4399i		−	0.427364i
$990$	10.0022	−	30.1819i	0.317891	−	0.959245i
$991$	27.8712	+	33.2156i	0.885358	+	1.05513i	0.998107	+	0.0615055i	$0.0195902\pi$
$991$	27.8712	+	33.2156i	0.885358	+	1.05513i	−0.112748	+	0.993624i	$0.535965\pi$
$992$	−7.47606	−	1.31823i	−0.237365	−	0.0418539i
$993$	−8.51824	−	0.620687i	−0.270318	−	0.0196969i
$994$	−7.83270	+	44.4215i	−0.248438	+	1.40896i
$995$			55.7526i			1.76748i
$996$	2.93932	−	11.6438i	0.0931359	−	0.368949i
$997$	−16.0926	−	13.5033i	−0.509657	−	0.427653i	0.351351	−	0.936244i	$-0.385722\pi$
$997$	−16.0926	−	13.5033i	−0.509657	−	0.427653i	−0.861009	+	0.508590i	$0.830167\pi$
$998$	5.20898	−	29.5416i	0.164887	−	0.935123i
$999$	−16.7746	−	3.71963i	−0.530725	−	0.117684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.x.c.29.6	✓	60
9.5	odd	6		342.2.bf.c.257.1	yes	60
19.2	odd	18		342.2.bf.c.173.1	yes	60
171.59	even	18	inner	342.2.x.c.59.6	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.x.c.29.6	✓	60	1.1	even	1	trivial
342.2.x.c.59.6	yes	60	171.59	even	18	inner
342.2.bf.c.173.1	yes	60	19.2	odd	18
342.2.bf.c.257.1	yes	60	9.5	odd	6

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.125873 - 1.72747i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.99507 + 0.351785i) q^{5} +(-0.709112 + 1.58024i) q^{6} +(2.49195 + 4.31618i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.96831 - 0.434885i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.125873 - 1.72747i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.99507 + 0.351785i) q^{5} +(-0.709112 + 1.58024i) q^{6} +(2.49195 + 4.31618i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.96831 - 0.434885i) q^{9} +(1.99507 + 0.351785i) q^{10} +5.23173i q^{11} +(1.20682 - 1.24241i) q^{12} +(-0.692178 - 0.122050i) q^{13} +(-0.865444 - 4.90817i) q^{14} +(0.356572 + 3.49071i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-1.86440 + 0.328744i) q^{17} +(2.64056 + 1.42388i) q^{18} +(2.66022 + 3.45300i) q^{19} +(-1.75444 - 1.01293i) q^{20} +(7.76974 - 3.76147i) q^{21} +(1.78936 - 4.91622i) q^{22} +(3.00539 - 3.58169i) q^{23} +(-1.55897 + 0.754726i) q^{24} +(-0.841900 + 0.306426i) q^{25} +(0.608691 + 0.351428i) q^{26} +(-1.12488 + 5.07293i) q^{27} +(-0.865444 + 4.90817i) q^{28} +(3.53489 + 2.96613i) q^{29} +(0.858825 - 3.40215i) q^{30} -7.59139i q^{31} +(0.173648 - 0.984808i) q^{32} +(9.03767 + 0.658535i) q^{33} +(1.86440 + 0.328744i) q^{34} +(-6.48998 - 7.73446i) q^{35} +(-1.99432 - 2.24114i) q^{36} +3.30669i q^{37} +(-1.31879 - 4.15461i) q^{38} +(-0.297964 + 1.18036i) q^{39} +(1.30219 + 1.55189i) q^{40} +(4.05564 + 1.47613i) q^{41} +(-8.58767 + 0.877221i) q^{42} +(2.20199 - 1.84769i) q^{43} +(-3.36289 + 4.00774i) q^{44} +(6.07498 - 0.176581i) q^{45} +(-4.04916 + 2.33778i) q^{46} +(-4.25457 + 5.07040i) q^{47} +(1.72308 - 0.176011i) q^{48} +(-8.91959 + 15.4492i) q^{49} +0.895931 q^{50} +(0.333218 + 3.26208i) q^{51} +(-0.451787 - 0.538419i) q^{52} +(1.34407 - 0.489201i) q^{53} +(2.79209 - 4.38226i) q^{54} +(-1.84045 - 10.4377i) q^{55} +(2.49195 - 4.31618i) q^{56} +(6.29982 - 4.16081i) q^{57} +(-2.30724 - 3.99625i) q^{58} +(-1.02155 + 0.857186i) q^{59} +(-1.97064 + 2.90324i) q^{60} +(-1.68420 + 9.55155i) q^{61} +(-2.59641 + 7.13358i) q^{62} +(-5.51983 - 13.8955i) q^{63} +(-0.500000 + 0.866025i) q^{64} +1.42388 q^{65} +(-8.26740 - 3.70989i) q^{66} +(-0.183340 - 0.503722i) q^{67} +(-1.63953 - 0.946581i) q^{68} +(-5.80896 - 5.64257i) q^{69} +(3.45325 + 9.48772i) q^{70} +(-8.50469 - 3.09546i) q^{71} +(1.10753 + 2.78808i) q^{72} +(7.85357 - 6.58993i) q^{73} +(1.13095 - 3.10727i) q^{74} +(0.423370 + 1.49293i) q^{75} +(-0.181703 + 4.35511i) q^{76} +(-22.5811 + 13.0372i) q^{77} +(0.683700 - 1.00726i) q^{78} +(-3.65947 + 0.645263i) q^{79} +(-0.692882 - 1.90368i) q^{80} +(8.62175 + 2.58175i) q^{81} +(-3.30619 - 2.77422i) q^{82} +(6.00455 - 3.46673i) q^{83} +(8.36979 + 2.11284i) q^{84} +(3.60397 - 1.31174i) q^{85} +(-2.70115 + 0.983137i) q^{86} +(5.56885 - 5.73307i) q^{87} +(4.53081 - 2.61587i) q^{88} +(-6.31073 - 5.29533i) q^{89} +(-5.76901 - 1.91183i) q^{90} +(-1.19808 - 3.29170i) q^{91} +(4.60453 - 0.811903i) q^{92} +(-13.1139 - 0.955553i) q^{93} +(5.73217 - 3.30947i) q^{94} +(-6.52204 - 5.95317i) q^{95} +(-1.67937 - 0.423933i) q^{96} +(6.36967 - 17.5005i) q^{97} +(13.6656 - 11.4668i) q^{98} +(2.27520 - 15.5294i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9}+O(q^{10}) \) 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9	\( 60 q - 6 q^{3} - 30 q^{8} + 6 q^{9} + 3 q^{13} + 3 q^{14} + 27 q^{15} - 27 q^{17} - 18 q^{18} + 3 q^{19} + 18 q^{23} + 3 q^{24} - 6 q^{27} + 3 q^{28} + 57 q^{33} + 27 q^{34} + 9 q^{38} - 30 q^{39} + 9 q^{41} - 3 q^{43} - 9 q^{44} + 27 q^{45} - 30 q^{49} - 132 q^{50} - 66 q^{51} + 6 q^{52} + 27 q^{54} + 102 q^{57} - 54 q^{59} + 6 q^{60} - 24 q^{61} - 3 q^{62} - 30 q^{64} + 36 q^{65} - 63 q^{66} + 51 q^{67} - 18 q^{68} + 3 q^{69} - 18 q^{71} - 3 q^{72} - 66 q^{73} - 6 q^{74} + 3 q^{78} - 51 q^{79} - 30 q^{81} - 36 q^{83} + 60 q^{84} - 3 q^{86} + 54 q^{87} - 27 q^{89} + 36 q^{90} - 69 q^{91} + 69 q^{93} + 18 q^{94} - 27 q^{95} + 81 q^{97} + 60 q^{98} + 51 q^{99}+O(q^{100}) \) 60 * q - 6 * q^3 - 30 * q^8 + 6 * q^9 + 3 * q^13 + 3 * q^14 + 27 * q^15 - 27 * q^17 - 18 * q^18 + 3 * q^19 + 18 * q^23 + 3 * q^24 - 6 * q^27 + 3 * q^28 + 57 * q^33 + 27 * q^34 + 9 * q^38 - 30 * q^39 + 9 * q^41 - 3 * q^43 - 9 * q^44 + 27 * q^45 - 30 * q^49 - 132 * q^50 - 66 * q^51 + 6 * q^52 + 27 * q^54 + 102 * q^57 - 54 * q^59 + 6 * q^60 - 24 * q^61 - 3 * q^62 - 30 * q^64 + 36 * q^65 - 63 * q^66 + 51 * q^67 - 18 * q^68 + 3 * q^69 - 18 * q^71 - 3 * q^72 - 66 * q^73 - 6 * q^74 + 3 * q^78 - 51 * q^79 - 30 * q^81 - 36 * q^83 + 60 * q^84 - 3 * q^86 + 54 * q^87 - 27 * q^89 + 36 * q^90 - 69 * q^91 + 69 * q^93 + 18 * q^94 - 27 * q^95 + 81 * q^97 + 60 * q^98 + 51 * q^99

Introduction

L-functions

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