LMFDB - Embedded newform 1183.2.e.g.508.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, degree $2$, 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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.1
Root			$-0.181721 + 0.314749i$ of defining polynomial
Character	$\chi$	$=$	1183.508
Dual form			1183.2.e.g.170.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.19402 - 2.06810i) q^{2} +(1.37574 - 2.38285i) q^{3} +(-1.85136 + 3.20665i) q^{4} +(0.491140 + 0.850679i) q^{5} -6.57063 q^{6} +(1.69505 + 2.03145i) q^{7} +4.06616 q^{8} +(-2.28532 - 3.95828i) q^{9} +(1.17286 - 2.03145i) q^{10} +(-0.293901 + 0.509052i) q^{11} +(5.09398 + 8.82303i) q^{12} +(2.17733 - 5.93113i) q^{14} +2.70272 q^{15} +(-1.15235 - 1.99593i) q^{16} +(3.22710 - 5.58950i) q^{17} +(-5.45742 + 9.45253i) q^{18} +(-1.91345 - 3.31419i) q^{19} -3.63711 q^{20} +(7.17260 - 1.24430i) q^{21} +1.40369 q^{22} +(-4.13001 - 7.15338i) q^{23} +(5.59398 - 9.68906i) q^{24} +(2.01756 - 3.49452i) q^{25} -4.32156 q^{27} +(-9.65231 + 1.67448i) q^{28} -3.96018 q^{29} +(-3.22710 - 5.58950i) q^{30} +(-1.49436 + 2.58831i) q^{31} +(1.31430 - 2.27644i) q^{32} +(0.808663 + 1.40065i) q^{33} -15.4129 q^{34} +(-0.895609 + 2.43967i) q^{35} +16.9238 q^{36} +(0.877941 + 1.52064i) q^{37} +(-4.56938 + 7.91440i) q^{38} +(1.99705 + 3.45900i) q^{40} -3.67169 q^{41} +(-11.1376 - 13.3479i) q^{42} +6.38085 q^{43} +(-1.08823 - 1.88488i) q^{44} +(2.24482 - 3.88814i) q^{45} +(-9.86261 + 17.0825i) q^{46} +(-2.17030 - 3.75906i) q^{47} -6.34134 q^{48} +(-1.25361 + 6.88683i) q^{49} -9.63603 q^{50} +(-8.87930 - 15.3794i) q^{51} +(-0.212770 + 0.368529i) q^{53} +(5.16002 + 8.93742i) q^{54} -0.577387 q^{55} +(6.89235 + 8.26022i) q^{56} -10.5296 q^{57} +(4.72853 + 8.19006i) q^{58} +(3.00431 - 5.20362i) q^{59} +(-5.00371 + 8.66669i) q^{60} +(-1.10337 - 1.91109i) q^{61} +7.13717 q^{62} +(4.16735 - 11.3520i) q^{63} -10.8866 q^{64} +(1.93112 - 3.34479i) q^{66} +(3.50651 - 6.07346i) q^{67} +(11.9491 + 20.6964i) q^{68} -22.7272 q^{69} +(6.11486 - 1.06080i) q^{70} -3.60253 q^{71} +(-9.29247 - 16.0950i) q^{72} +(2.46714 - 4.27321i) q^{73} +(2.09656 - 3.63134i) q^{74} +(-5.55128 - 9.61510i) q^{75} +14.1699 q^{76} +(-1.53229 + 0.265822i) q^{77} +(-1.39270 - 2.41223i) q^{79} +(1.13193 - 1.96056i) q^{80} +(0.910609 - 1.57722i) q^{81} +(4.38406 + 7.59342i) q^{82} +2.86819 q^{83} +(-9.28903 + 25.3037i) q^{84} +6.33983 q^{85} +(-7.61885 - 13.1962i) q^{86} +(-5.44818 + 9.43652i) q^{87} +(-1.19505 + 2.06989i) q^{88} +(-1.04656 - 1.81269i) q^{89} -10.7214 q^{90} +30.5845 q^{92} +(4.11170 + 7.12167i) q^{93} +(-5.18275 + 8.97679i) q^{94} +(1.87954 - 3.25546i) q^{95} +(-3.61628 - 6.26357i) q^{96} -7.69704 q^{97} +(15.7395 - 5.63041i) q^{98} +2.68663 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} + 5 q^{12} - 2 q^{14} - 4 q^{15} + 8 q^{16} + 5 q^{17} - 3 q^{18} + q^{19} - 2 q^{20} + 9 q^{21}+ \cdots + 20 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 - 18 * q^6 + 6 * q^7 + 6 * q^8 + 3 * q^9 + 4 * q^10 - 4 * q^11 + 5 * q^12 - 2 * q^14 - 4 * q^15 + 8 * q^16 + 5 * q^17 - 3 * q^18 + q^19 - 2 * q^20 + 9 * q^21 + 10 * q^22 - q^23 + 11 * q^24 + 7 * q^25 - 8 * q^27 - 8 * q^28 - 6 * q^29 - 5 * q^30 - 16 * q^31 - 8 * q^32 - 16 * q^33 - 32 * q^34 - 28 * q^35 + 42 * q^36 + 13 * q^37 - 17 * q^38 - 5 * q^40 - 16 * q^41 - 52 * q^42 + 22 * q^43 - 21 * q^44 + 7 * q^45 - 16 * q^46 + q^47 - 42 * q^48 + 6 * q^49 + 12 * q^50 - 20 * q^51 - 2 * q^53 + 18 * q^54 - 18 * q^55 + 9 * q^56 - 42 * q^57 + 8 * q^58 - 13 * q^59 - 20 * q^60 - 5 * q^61 - 10 * q^62 - 8 * q^63 - 30 * q^64 + 18 * q^66 + 11 * q^67 + 29 * q^68 - 46 * q^69 + 39 * q^70 + 12 * q^71 - 25 * q^72 + 30 * q^73 - 3 * q^74 - 3 * q^75 - 18 * q^76 + 11 * q^77 + 7 * q^79 + 7 * q^80 - 6 * q^81 + q^82 + 54 * q^83 - 41 * q^84 - 2 * q^85 + 7 * q^86 + 16 * q^87 - 4 * q^89 - 16 * q^90 + 54 * q^92 + 7 * q^93 + 45 * q^94 - 6 * q^95 - 19 * q^96 - 70 * q^97 + 82 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.19402	−	2.06810i	−0.844299	−	1.46237i	−0.886229	−	0.463248i	$-0.846684\pi$
$2$	−1.19402	−	2.06810i	−0.844299	−	1.46237i	0.0419302	−	0.999121i	$-0.486649\pi$
$3$	1.37574	−	2.38285i	0.794283	−	1.37574i	−0.129010	−	0.991643i	$-0.541180\pi$
$3$	1.37574	−	2.38285i	0.794283	−	1.37574i	0.923293	−	0.384096i	$-0.125487\pi$
$4$	−1.85136	+	3.20665i	−0.925680	+	1.60333i
$5$	0.491140	+	0.850679i	0.219644	+	0.380435i	0.954699	−	0.297572i	$-0.0961769\pi$
$5$	0.491140	+	0.850679i	0.219644	+	0.380435i	−0.735055	+	0.678008i	$0.762844\pi$
$6$	−6.57063			−2.68245
$7$	1.69505	+	2.03145i	0.640669	+	0.767817i
$7$	1.69505	+	2.03145i	0.640669	+	0.767817i
$8$	4.06616			1.43761
$9$	−2.28532	−	3.95828i	−0.761772	−	1.31943i
$10$	1.17286	−	2.03145i	0.370891	−	0.642402i
$11$	−0.293901	+	0.509052i	−0.0886146	+	0.153485i	−0.906926	−	0.421291i	$-0.861577\pi$
$11$	−0.293901	+	0.509052i	−0.0886146	+	0.153485i	0.818311	+	0.574775i	$0.194911\pi$
$12$	5.09398	+	8.82303i	1.47051	+	2.54699i
$13$		0			0
$13$		0			0
$14$	2.17733	−	5.93113i	0.581916	−	1.58516i
$15$	2.70272			0.697840
$16$	−1.15235	−	1.99593i	−0.288088	−	0.498983i
$17$	3.22710	−	5.58950i	0.782687	−	1.35565i	−0.147685	−	0.989035i	$-0.547182\pi$
$17$	3.22710	−	5.58950i	0.782687	−	1.35565i	0.930371	−	0.366619i	$-0.119485\pi$
$18$	−5.45742	+	9.45253i	−1.28633	+	2.22798i
$19$	−1.91345	−	3.31419i	−0.438975	−	0.760327i	0.558636	−	0.829413i	$-0.311325\pi$
$19$	−1.91345	−	3.31419i	−0.438975	−	0.760327i	−0.997611	+	0.0690863i	$0.977992\pi$
$20$	−3.63711			−0.813282
$21$	7.17260	−	1.24430i	1.56519	−	0.271528i
$22$	1.40369			0.299269
$23$	−4.13001	−	7.15338i	−0.861166	−	1.49158i	−0.870805	−	0.491629i	$-0.836402\pi$
$23$	−4.13001	−	7.15338i	−0.861166	−	1.49158i	0.00963902	−	0.999954i	$-0.496932\pi$
$24$	5.59398	−	9.68906i	1.14187	−	1.97777i
$25$	2.01756	−	3.49452i	0.403513	−	0.698904i
$26$		0			0
$27$	−4.32156			−0.831685
$28$	−9.65231	+	1.67448i	−1.82412	+	0.316447i
$29$	−3.96018			−0.735387			−0.367694	−	0.929947i	$-0.619853\pi$
$29$	−3.96018			−0.735387			−0.367694	+	0.929947i	$0.619853\pi$
$30$	−3.22710	−	5.58950i	−0.589185	−	1.02050i
$31$	−1.49436	+	2.58831i	−0.268395	+	0.464874i	−0.968448	−	0.249218i	$-0.919827\pi$
$31$	−1.49436	+	2.58831i	−0.268395	+	0.464874i	0.700053	+	0.714091i	$0.253160\pi$
$32$	1.31430	−	2.27644i	0.232338	−	0.402421i
$33$	0.808663	+	1.40065i	0.140770	+	0.243821i
$34$	−15.4129			−2.64329
$35$	−0.895609	+	2.43967i	−0.151386	+	0.412380i
$36$	16.9238			2.82063
$37$	0.877941	+	1.52064i	0.144333	+	0.249991i	0.929124	−	0.369769i	$-0.120563\pi$
$37$	0.877941	+	1.52064i	0.144333	+	0.249991i	−0.784791	+	0.619760i	$0.787230\pi$
$38$	−4.56938	+	7.91440i	−0.741252	+	1.28389i
$39$		0			0
$40$	1.99705	+	3.45900i	0.315762	+	0.546916i
$41$	−3.67169			−0.573421			−0.286710	−	0.958017i	$-0.592562\pi$
$41$	−3.67169			−0.573421			−0.286710	+	0.958017i	$0.592562\pi$
$42$	−11.1376	−	13.3479i	−1.71856	−	2.05963i
$43$	6.38085			0.973070			0.486535	−	0.873661i	$-0.338261\pi$
$43$	6.38085			0.973070			0.486535	+	0.873661i	$0.338261\pi$
$44$	−1.08823	−	1.88488i	−0.164058	−	0.284156i
$45$	2.24482	−	3.88814i	0.334638	−	0.579610i
$46$	−9.86261	+	17.0825i	−1.45416	+	2.51868i
$47$	−2.17030	−	3.75906i	−0.316570	−	0.548316i	0.663200	−	0.748442i	$-0.269198\pi$
$47$	−2.17030	−	3.75906i	−0.316570	−	0.548316i	−0.979770	+	0.200127i	$0.935865\pi$
$48$	−6.34134			−0.915294
$49$	−1.25361	+	6.88683i	−0.179087	+	0.983833i
$50$	−9.63603			−1.36274
$51$	−8.87930	−	15.3794i	−1.24335	−	2.15355i
$52$		0			0
$53$	−0.212770	+	0.368529i	−0.0292263	+	0.0506214i	−0.880269	−	0.474476i	$-0.842638\pi$
$53$	−0.212770	+	0.368529i	−0.0292263	+	0.0506214i	0.851042	+	0.525097i	$0.175971\pi$
$54$	5.16002	+	8.93742i	0.702190	+	1.21623i
$55$	−0.577387			−0.0778548
$56$	6.89235	+	8.26022i	0.921029	+	1.10382i
$57$	−10.5296			−1.39468
$58$	4.72853	+	8.19006i	0.620887	+	1.07541i
$59$	3.00431	−	5.20362i	0.391128	−	0.677454i	−0.601470	−	0.798895i	$-0.705418\pi$
$59$	3.00431	−	5.20362i	0.391128	−	0.677454i	0.992599	+	0.121441i	$0.0387516\pi$
$60$	−5.00371	+	8.66669i	−0.645977	+	1.11886i
$61$	−1.10337	−	1.91109i	−0.141272	−	0.244691i	0.786704	−	0.617331i	$-0.211786\pi$
$61$	−1.10337	−	1.91109i	−0.141272	−	0.244691i	−0.927976	+	0.372640i	$0.878453\pi$
$62$	7.13717			0.906422
$63$	4.16735	−	11.3520i	0.525036	−	1.43022i
$64$	−10.8866			−1.36083
$65$		0			0
$66$	1.93112	−	3.34479i	0.237704	−	0.411716i
$67$	3.50651	−	6.07346i	0.428389	−	0.741991i	−0.568341	−	0.822793i	$-0.692415\pi$
$67$	3.50651	−	6.07346i	0.428389	−	0.741991i	0.996730	+	0.0808015i	$0.0257480\pi$
$68$	11.9491	+	20.6964i	1.44904	+	2.50980i
$69$	−22.7272			−2.73604
$70$	6.11486	−	1.06080i	0.730866	−	0.126790i
$71$	−3.60253			−0.427542			−0.213771	−	0.976884i	$-0.568575\pi$
$71$	−3.60253			−0.427542			−0.213771	+	0.976884i	$0.568575\pi$
$72$	−9.29247	−	16.0950i	−1.09513	−	1.89682i
$73$	2.46714	−	4.27321i	0.288756	−	0.500141i	−0.684757	−	0.728772i	$-0.740092\pi$
$73$	2.46714	−	4.27321i	0.288756	−	0.500141i	0.973513	+	0.228631i	$0.0734249\pi$
$74$	2.09656	−	3.63134i	0.243720	−	0.422135i
$75$	−5.55128	−	9.61510i	−0.641007	−	1.11026i
$76$	14.1699			1.62540
$77$	−1.53229	+	0.265822i	−0.174621	+	0.0302932i
$78$		0			0
$79$	−1.39270	−	2.41223i	−0.156691	−	0.271397i	0.776982	−	0.629522i	$-0.216749\pi$
$79$	−1.39270	−	2.41223i	−0.156691	−	0.271397i	−0.933674	+	0.358125i	$0.883416\pi$
$80$	1.13193	−	1.96056i	0.126554	−	0.219198i
$81$	0.910609	−	1.57722i	0.101179	−	0.175247i
$82$	4.38406	+	7.59342i	0.484138	+	0.838552i
$83$	2.86819			0.314825			0.157412	−	0.987533i	$-0.449685\pi$
$83$	2.86819			0.314825			0.157412	+	0.987533i	$0.449685\pi$
$84$	−9.28903	+	25.3037i	−1.01352	+	2.76086i
$85$	6.33983			0.687651
$86$	−7.61885	−	13.1962i	−0.821562	−	1.42299i
$87$	−5.44818	+	9.43652i	−0.584106	+	1.01170i
$88$	−1.19505	+	2.06989i	−0.127393	+	0.220651i
$89$	−1.04656	−	1.81269i	−0.110935	−	0.192145i	0.805213	−	0.592986i	$-0.202051\pi$
$89$	−1.04656	−	1.81269i	−0.110935	−	0.192145i	−0.916147	+	0.400842i	$0.868718\pi$
$90$	−10.7214			−1.13014
$91$		0			0
$92$	30.5845			3.18866
$93$	4.11170	+	7.12167i	0.426363	+	0.738483i
$94$	−5.18275	+	8.97679i	−0.534560	+	0.925885i
$95$	1.87954	−	3.25546i	0.192837	−	0.334003i
$96$	−3.61628	−	6.26357i	−0.369085	−	0.639273i
$97$	−7.69704			−0.781516			−0.390758	−	0.920493i	$-0.627787\pi$
$97$	−7.69704			−0.781516			−0.390758	+	0.920493i	$0.627787\pi$
$98$	15.7395	−	5.63041i	1.58993	−	0.568758i
$99$	2.68663			0.270016
$100$	7.47047	+	12.9392i	0.747047	+	1.29392i
$101$	1.31866	−	2.28399i	0.131212	−	0.227265i	−0.792932	−	0.609310i	$-0.791447\pi$
$101$	1.31866	−	2.28399i	0.131212	−	0.227265i	0.924144	+	0.382045i	$0.124780\pi$
$102$	−21.2041	+	36.7266i	−2.09952	+	3.63647i
$103$	5.43095	+	9.40669i	0.535128	+	0.926868i	0.999157	+	0.0410486i	$0.0130699\pi$
$103$	5.43095	+	9.40669i	0.535128	+	0.926868i	−0.464029	+	0.885820i	$0.653597\pi$
$104$		0			0
$105$	4.58125	+	5.49045i	0.447084	+	0.535813i
$106$	1.01621			0.0987027
$107$	7.99024	+	13.8395i	0.772446	+	1.33792i	0.936219	+	0.351418i	$0.114300\pi$
$107$	7.99024	+	13.8395i	0.772446	+	1.33792i	−0.163773	+	0.986498i	$0.552366\pi$
$108$	8.00077	−	13.8577i	0.769874	−	1.33346i
$109$	4.61738	−	7.99754i	0.442265	−	0.766026i	−0.555592	−	0.831455i	$-0.687508\pi$
$109$	4.61738	−	7.99754i	0.442265	−	0.766026i	0.997857	+	0.0654294i	$0.0208417\pi$
$110$	0.689410	+	1.19409i	0.0657327	+	0.113852i
$111$	4.83127			0.458564
$112$	2.10135	−	5.72416i	0.198559	−	0.540882i
$113$	10.1802			0.957677			0.478838	−	0.877903i	$-0.341058\pi$
$113$	10.1802			0.957677			0.478838	+	0.877903i	$0.341058\pi$
$114$	12.5726	+	21.7763i	1.17753	+	2.03954i
$115$	4.05682	−	7.02662i	0.378301	−	0.655236i
$116$	7.33173	−	12.6989i	0.680734	−	1.17907i
$117$		0			0
$118$	−14.3488			−1.32092
$119$	16.8249	−	2.91878i	1.54234	−	0.267564i
$120$	10.9897			1.00322
$121$	5.32724	+	9.22706i	0.484295	+	0.838823i
$122$	−2.63489	+	4.56376i	−0.238552	+	0.413184i
$123$	−5.05128	+	8.74908i	−0.455459	+	0.788878i
$124$	−5.53320	−	9.58378i	−0.496896	−	0.860649i
$125$	8.87502			0.793806
$126$	−28.4530	+	4.93601i	−2.53479	+	0.439735i
$127$	4.25026			0.377149			0.188575	−	0.982059i	$-0.439613\pi$
$127$	4.25026			0.377149			0.188575	+	0.982059i	$0.439613\pi$
$128$	10.3702	+	17.9617i	0.916606	+	1.58761i
$129$	8.77838	−	15.2046i	0.772893	−	1.33869i
$130$		0			0
$131$	1.08478	+	1.87890i	0.0947779	+	0.164160i	0.909516	−	0.415669i	$-0.136453\pi$
$131$	1.08478	+	1.87890i	0.0947779	+	0.164160i	−0.814738	+	0.579829i	$0.803119\pi$
$132$	−5.98851			−0.521233
$133$	3.48923	−	9.50479i	0.302555	−	0.824170i
$134$	−16.7474			−1.44675
$135$	−2.12249	−	3.67626i	−0.182675	−	0.316402i
$136$	13.1219	−	22.7278i	1.12519	−	1.94889i
$137$	4.18158	−	7.24271i	0.357257	−	0.618787i	−0.630245	−	0.776396i	$-0.717045\pi$
$137$	4.18158	−	7.24271i	0.357257	−	0.618787i	0.987501	+	0.157610i	$0.0503788\pi$
$138$	27.1367	+	47.0022i	2.31003	+	4.00110i
$139$	−0.576914			−0.0489332			−0.0244666	−	0.999701i	$-0.507789\pi$
$139$	−0.576914			−0.0489332			−0.0244666	+	0.999701i	$0.507789\pi$
$140$	−6.16508	−	7.38862i	−0.521045	−	0.624452i
$141$	−11.9430			−1.00579
$142$	4.30149	+	7.45040i	0.360973	+	0.625224i
$143$		0			0
$144$	−5.26698	+	9.12267i	−0.438915	+	0.760223i
$145$	−1.94500	−	3.36885i	−0.161524	−	0.279767i
$146$	−11.7832			−0.975187
$147$	14.6856	+	12.4616i	1.21125	+	1.02782i
$148$	−6.50154			−0.534423
$149$	1.40331	+	2.43061i	0.114964	+	0.199123i	0.917765	−	0.397123i	$-0.129991\pi$
$149$	1.40331	+	2.43061i	0.114964	+	0.199123i	−0.802801	+	0.596246i	$0.796658\pi$
$150$	−13.2567	+	22.9612i	−1.08240	+	1.87478i
$151$	−11.5054	+	19.9280i	−0.936300	+	1.62172i	−0.164000	+	0.986460i	$0.552440\pi$
$151$	−11.5054	+	19.9280i	−0.936300	+	1.62172i	−0.772300	+	0.635258i	$0.780894\pi$
$152$	−7.78039	−	13.4760i	−0.631073	−	1.09305i
$153$	−29.4998			−2.38492
$154$	2.37933	+	2.85154i	0.191732	+	0.229784i
$155$	−2.93576			−0.235806
$156$		0			0
$157$	−11.2880	+	19.5513i	−0.900879	+	1.56037i	−0.0745227	+	0.997219i	$0.523743\pi$
$157$	−11.2880	+	19.5513i	−0.900879	+	1.56037i	−0.826356	+	0.563148i	$0.809590\pi$
$158$	−3.32583	+	5.76050i	−0.264588	+	0.458281i
$159$	0.585433	+	1.01400i	0.0464278	+	0.0804154i
$160$	2.58203			0.204127
$161$	7.53119	−	20.5153i	0.593541	−	1.61683i
$162$	−4.34913			−0.341700
$163$	4.08857	+	7.08161i	0.320242	+	0.554675i	0.980538	−	0.196331i	$-0.0629026\pi$
$163$	4.08857	+	7.08161i	0.320242	+	0.554675i	−0.660296	+	0.751005i	$0.729569\pi$
$164$	6.79761	−	11.7738i	0.530804	−	0.919380i
$165$	−0.794333	+	1.37583i	−0.0618388	+	0.107108i
$166$	−3.42467	−	5.93170i	−0.265806	−	0.460389i
$167$	2.32771			0.180124			0.0900619	−	0.995936i	$-0.471293\pi$
$167$	2.32771			0.180124			0.0900619	+	0.995936i	$0.471293\pi$
$168$	29.1649	−	5.05953i	2.25012	−	0.390351i
$169$		0			0
$170$	−7.56988	−	13.1114i	−0.580583	−	1.00560i
$171$	−8.74566	+	15.1479i	−0.668798	+	1.15839i
$172$	−11.8133	+	20.4611i	−0.900752	+	1.56015i
$173$	4.06686	+	7.04401i	0.309198	+	0.535546i	0.978187	−	0.207726i	$-0.0666061\pi$
$173$	4.06686	+	7.04401i	0.309198	+	0.535546i	−0.668989	+	0.743272i	$0.733273\pi$
$174$	26.0209			1.97264
$175$	10.5188	−	1.82480i	0.795149	−	0.137942i
$176$	1.35471			0.102115
$177$	−8.26630	−	14.3177i	−0.621333	−	1.07618i
$178$	−2.49922	+	4.32877i	−0.187324	+	0.324455i
$179$	10.4963	−	18.1801i	0.784528	−	1.35884i	−0.144752	−	0.989468i	$-0.546239\pi$
$179$	10.4963	−	18.1801i	0.784528	−	1.35884i	0.929281	−	0.369375i	$-0.120428\pi$
$180$	8.31194	+	14.3967i	0.619536	+	1.07307i
$181$	−1.60807			−0.119527			−0.0597635	−	0.998213i	$-0.519035\pi$
$181$	−1.60807			−0.119527			−0.0597635	+	0.998213i	$0.519035\pi$
$182$		0			0
$183$	−6.07180			−0.448841
$184$	−16.7933	−	29.0868i	−1.23802	−	2.14431i
$185$	−0.862384	+	1.49369i	−0.0634037	+	0.109818i
$186$	9.81889	−	17.0068i	0.719956	−	1.24700i
$187$	1.89690	+	3.28552i	0.138715	+	0.240261i
$188$	16.0720			1.17217
$189$	−7.32526	−	8.77905i	−0.532834	−	0.638582i
$190$	−8.97683			−0.651247
$191$	5.78111	+	10.0132i	0.418307	+	0.724529i	0.995769	−	0.0918886i	$-0.0292904\pi$
$191$	5.78111	+	10.0132i	0.418307	+	0.724529i	−0.577463	+	0.816417i	$0.695957\pi$
$192$	−14.9771	+	25.9412i	−1.08088	+	1.87214i
$193$	11.7894	−	20.4199i	0.848621	−	1.46985i	−0.0338178	−	0.999428i	$-0.510767\pi$
$193$	11.7894	−	20.4199i	0.848621	−	1.46985i	0.882439	−	0.470427i	$-0.155900\pi$
$194$	9.19041	+	15.9183i	0.659833	+	1.14286i
$195$		0			0
$196$	−19.7628	−	16.7699i	−1.41163	−	1.19785i
$197$	1.47094			0.104800			0.0524002	−	0.998626i	$-0.483313\pi$
$197$	1.47094			0.104800			0.0524002	+	0.998626i	$0.483313\pi$
$198$	−3.20788	−	5.55622i	−0.227974	−	0.394863i
$199$	−4.69700	+	8.13543i	−0.332961	+	0.576706i	−0.983091	−	0.183117i	$-0.941381\pi$
$199$	−4.69700	+	8.13543i	−0.332961	+	0.576706i	0.650130	+	0.759823i	$0.274714\pi$
$200$	8.20374	−	14.2093i	0.580092	−	1.00475i
$201$	−9.64810	−	16.7110i	−0.680524	−	1.17870i
$202$	−6.29802			−0.443127
$203$	−6.71271	−	8.04493i	−0.471140	−	0.564643i
$204$	65.7551			4.60378
$205$	−1.80331	−	3.12343i	−0.125949	−	0.218150i
$206$	12.9693	−	22.4635i	0.903615	−	1.56511i
$207$	−18.8767	+	32.6955i	−1.31202	+	2.27249i
$208$		0			0
$209$	2.24946			0.155598
$210$	5.88472	−	16.0302i	0.406084	−	1.10619i
$211$	−8.94219			−0.615605			−0.307803	−	0.951450i	$-0.599594\pi$
$211$	−8.94219			−0.615605			−0.307803	+	0.951450i	$0.599594\pi$
$212$	−0.787829	−	1.36456i	−0.0541083	−	0.0937184i
$213$	−4.95615	+	8.58430i	−0.339589	+	0.588186i
$214$	19.0810	−	33.0493i	1.30435	−	2.25920i
$215$	3.13389	+	5.42805i	0.213729	+	0.370190i
$216$	−17.5722			−1.19563
$217$	−7.79104	+	1.35159i	−0.528890	+	0.0917518i
$218$	−22.0530			−1.49362
$219$	−6.78827	−	11.7576i	−0.458709	−	0.794507i
$220$	1.06895	−	1.85148i	0.0720686	−	0.124827i
$221$		0			0
$222$	−5.76863	−	9.99156i	−0.387165	−	0.670589i
$223$	−21.8196			−1.46115			−0.730574	−	0.682833i	$-0.760748\pi$
$223$	−21.8196			−1.46115			−0.730574	+	0.682833i	$0.760748\pi$
$224$	6.85229	−	1.18873i	0.457838	−	0.0794256i
$225$	−18.4431			−1.22954
$226$	−12.1554	−	21.0538i	−0.808565	−	1.40048i
$227$	−9.27627	+	16.0670i	−0.615687	+	1.06640i	0.374576	+	0.927196i	$0.377788\pi$
$227$	−9.27627	+	16.0670i	−0.615687	+	1.06640i	−0.990263	+	0.139206i	$0.955545\pi$
$228$	19.4941	−	33.7648i	1.29103	−	2.23613i
$229$	9.67525	+	16.7580i	0.639359	+	1.10740i	0.985574	+	0.169247i	$0.0541334\pi$
$229$	9.67525	+	16.7580i	0.639359	+	1.10740i	−0.346215	+	0.938155i	$0.612533\pi$
$230$	−19.3757			−1.27759
$231$	−1.47462	+	4.01692i	−0.0970230	+	0.264294i
$232$	−16.1027			−1.05720
$233$	−8.08170	−	13.9979i	−0.529450	−	0.917034i	−0.999410	−	0.0343462i	$-0.989065\pi$
$233$	−8.08170	−	13.9979i	−0.529450	−	0.917034i	0.469960	−	0.882688i	$-0.344268\pi$
$234$		0			0
$235$	2.13184	−	3.69245i	0.139066	−	0.240869i
$236$	11.1241	+	19.2676i	0.724119	+	1.25421i
$237$	−7.66398			−0.497829
$238$	−26.1256	−	31.3105i	−1.69347	−	2.02956i
$239$	−16.1037			−1.04166			−0.520831	−	0.853660i	$-0.674378\pi$
$239$	−16.1037			−1.04166			−0.520831	+	0.853660i	$0.674378\pi$
$240$	−3.11449	−	5.39445i	−0.201039	−	0.348210i
$241$	−2.00300	+	3.46930i	−0.129025	+	0.223477i	−0.923299	−	0.384082i	$-0.874518\pi$
$241$	−2.00300	+	3.46930i	−0.129025	+	0.223477i	0.794274	+	0.607559i	$0.207851\pi$
$242$	12.7217	−	22.0346i	0.817779	−	1.41643i
$243$	−8.98786	−	15.5674i	−0.576572	−	0.998651i
$244$	8.17095			0.523092
$245$	−6.47418	+	2.31598i	−0.413620	+	0.147962i
$246$	24.1253			1.53817
$247$		0			0
$248$	−6.07631	+	10.5245i	−0.385846	+	0.668305i
$249$	3.94588	−	6.83446i	0.250060	−	0.433116i
$250$	−10.5969	−	18.3544i	−0.670209	−	1.16084i
$251$	3.24688			0.204941			0.102471	−	0.994736i	$-0.467325\pi$
$251$	3.24688			0.204941			0.102471	+	0.994736i	$0.467325\pi$
$252$	28.6867	+	34.3799i	1.80709	+	2.16573i
$253$	4.85525			0.305247
$254$	−5.07489	−	8.78996i	−0.318427	−	0.551531i
$255$	8.72195	−	15.1069i	0.546190	−	0.946029i
$256$	13.8778	−	24.0371i	0.867365	−	1.50232i
$257$	13.4462	+	23.2895i	0.838751	+	1.45276i	0.890940	+	0.454122i	$0.150047\pi$
$257$	13.4462	+	23.2895i	0.838751	+	1.45276i	−0.0521891	+	0.998637i	$0.516620\pi$
$258$	−41.9262			−2.61021
$259$	−1.60095	+	4.36106i	−0.0994784	+	0.270983i
$260$		0			0
$261$	9.05027	+	15.6755i	0.560198	+	0.970291i
$262$	2.59050	−	4.48688i	0.160042	−	0.277200i
$263$	1.90353	−	3.29701i	0.117377	−	0.203302i	−0.801351	−	0.598195i	$-0.795885\pi$
$263$	1.90353	−	3.29701i	0.117377	−	0.203302i	0.918727	+	0.394893i	$0.129218\pi$
$264$	3.28815	+	5.69525i	0.202372	+	0.350518i
$265$	−0.418000			−0.0256775
$266$	−23.8231	+	4.13282i	−1.46069	+	0.253399i
$267$	−5.75915			−0.352455
$268$	12.9836	+	22.4883i	0.793102	+	1.37369i
$269$	11.9190	−	20.6444i	0.726716	−	1.25871i	−0.231548	−	0.972824i	$-0.574379\pi$
$269$	11.9190	−	20.6444i	0.726716	−	1.25871i	0.958264	−	0.285886i	$-0.0922878\pi$
$270$	−5.06859	+	8.77905i	−0.308464	+	0.534276i
$271$	4.95068	+	8.57482i	0.300732	+	0.520883i	0.976302	−	0.216413i	$-0.0694357\pi$
$271$	4.95068	+	8.57482i	0.300732	+	0.520883i	−0.675570	+	0.737296i	$0.736102\pi$
$272$	−14.8750			−0.901931
$273$		0			0
$274$	−19.9715			−1.20653
$275$	1.18593	+	2.05409i	0.0715142	+	0.123866i
$276$	42.0763	−	72.8783i	2.53270	−	4.38676i
$277$	−5.89289	+	10.2068i	−0.354069	+	0.613266i	−0.986958	−	0.160977i	$-0.948536\pi$
$277$	−5.89289	+	10.2068i	−0.354069	+	0.613266i	0.632889	+	0.774243i	$0.281869\pi$
$278$	0.688846	+	1.19312i	0.0413142	+	0.0715584i
$279$	13.6603			0.817823
$280$	−3.64169	+	9.92010i	−0.217633	+	0.592840i
$281$	−12.9976			−0.775372			−0.387686	−	0.921791i	$-0.626726\pi$
$281$	−12.9976			−0.775372			−0.387686	+	0.921791i	$0.626726\pi$
$282$	14.2602	+	24.6994i	0.849184	+	1.47083i
$283$	8.40249	−	14.5535i	0.499476	−	0.865118i	−0.500524	−	0.865723i	$-0.666859\pi$
$283$	8.40249	−	14.5535i	0.499476	−	0.865118i	1.00000		0.000604910i	$0.000192549\pi$
$284$	6.66959	−	11.5521i	0.395767	−	0.685489i
$285$	−5.17151	−	8.95733i	−0.306334	−	0.530586i
$286$		0			0
$287$	−6.22369	−	7.45886i	−0.367373	−	0.440283i
$288$	−12.0144			−0.707955
$289$	−12.3283	−	21.3533i	−0.725197	−	1.25608i
$290$	−4.64474	+	8.04493i	−0.272749	+	0.472414i
$291$	−10.5891	+	18.3409i	−0.620746	+	1.07516i
$292$	9.13512	+	15.8225i	0.534592	+	0.925941i
$293$	14.0956			0.823476			0.411738	−	0.911302i	$-0.364922\pi$
$293$	14.0956			0.823476			0.411738	+	0.911302i	$0.364922\pi$
$294$	8.23701	−	45.2508i	0.480392	−	2.63908i
$295$	5.90215			0.343637
$296$	3.56985	+	6.18316i	0.207493	+	0.359389i
$297$	1.27011	−	2.19990i	0.0736994	−	0.127651i
$298$	3.35116	−	5.80438i	0.194128	−	0.336239i
$299$		0			0
$300$	41.1097			2.37347
$301$	10.8159	+	12.9624i	0.623416	+	0.747140i
$302$	54.9508			3.16207
$303$	−3.62827	−	6.28434i	−0.208439	−	0.361026i
$304$	−4.40993	+	7.63822i	−0.252927	+	0.438082i
$305$	1.08382	−	1.87723i	0.0620593	−	0.107490i
$306$	35.2233	+	61.0085i	2.01358	+	3.48762i
$307$	−15.8786			−0.906240			−0.453120	−	0.891450i	$-0.649689\pi$
$307$	−15.8786			−0.906240			−0.453120	+	0.891450i	$0.649689\pi$
$308$	1.98443	−	5.40566i	0.113073	−	0.308016i
$309$	29.8863			1.70017
$310$	3.50535	+	6.07145i	0.199091	+	0.344835i
$311$	14.3017	−	24.7713i	0.810975	−	1.40465i	−0.101208	−	0.994865i	$-0.532271\pi$
$311$	14.3017	−	24.7713i	0.810975	−	1.40465i	0.912183	−	0.409784i	$-0.134396\pi$
$312$		0			0
$313$	9.28962	+	16.0901i	0.525080	+	0.909465i	0.999573	+	0.0292063i	$0.00929798\pi$
$313$	9.28962	+	16.0901i	0.525080	+	0.909465i	−0.474493	+	0.880259i	$0.657369\pi$
$314$	53.9122			3.04244
$315$	11.7037	−	2.03035i	0.659427	−	0.114397i
$316$	10.3136			0.580184
$317$	15.3223	+	26.5389i	0.860584	+	1.49057i	0.871366	+	0.490633i	$0.163234\pi$
$317$	15.3223	+	26.5389i	0.860584	+	1.49057i	−0.0107826	+	0.999942i	$0.503432\pi$
$318$	1.39804	−	2.42147i	0.0783979	−	0.135789i
$319$	1.16390	−	2.01594i	0.0651660	−	0.112871i
$320$	−5.34685	−	9.26102i	−0.298898	−	0.517707i
$321$	43.9700			2.45416
$322$	−51.4200	+	8.92033i	−2.86552	+	0.497110i
$323$	−24.6995			−1.37432
$324$	3.37173	+	5.84001i	0.187318	+	0.324445i
$325$		0			0
$326$	9.76366	−	16.9112i	0.540759	−	0.936622i
$327$	−12.7046	−	22.0051i	−0.702568	−	1.21688i
$328$	−14.9297			−0.824353
$329$	3.95760	−	10.7807i	0.218190	−	0.594357i
$330$	3.79379			0.208842
$331$	13.6138	+	23.5799i	0.748284	+	1.29607i	0.948644	+	0.316344i	$0.102455\pi$
$331$	13.6138	+	23.5799i	0.748284	+	1.29607i	−0.200360	+	0.979722i	$0.564211\pi$
$332$	−5.31005	+	9.19728i	−0.291427	+	0.504766i
$333$	4.01275	−	6.95028i	0.219897	−	0.380873i
$334$	−2.77933	−	4.81395i	−0.152078	−	0.263407i
$335$	6.88876			0.376373
$336$	−10.7489	−	12.8821i	−0.586400	−	0.702779i
$337$	−12.3160			−0.670898			−0.335449	−	0.942058i	$-0.608888\pi$
$337$	−12.3160			−0.670898			−0.335449	+	0.942058i	$0.608888\pi$
$338$		0			0
$339$	14.0054	−	24.2580i	0.760666	−	1.31751i
$340$	−11.7373	+	20.3296i	−0.636545	+	1.10253i
$341$	−0.878389	−	1.52141i	−0.0475674	−	0.0823892i
$342$	41.7699			2.25866
$343$	−16.1152	+	9.12688i	−0.870140	+	0.492805i
$344$	25.9456			1.39889
$345$	−11.1623	−	19.3336i	−0.600956	−	1.04089i
$346$	9.71182	−	16.8214i	0.522111	−	0.904322i
$347$	−3.07253	+	5.32177i	−0.164942	+	0.285688i	−0.936635	−	0.350308i	$-0.886077\pi$
$347$	−3.07253	+	5.32177i	−0.164942	+	0.285688i	0.771693	+	0.635996i	$0.219410\pi$
$348$	−20.1731	−	34.9408i	−1.08139	−	1.87302i
$349$	−13.0313			−0.697547			−0.348774	−	0.937207i	$-0.613402\pi$
$349$	−13.0313			−0.697547			−0.348774	+	0.937207i	$0.613402\pi$
$350$	−16.3336	−	19.5752i	−0.873065	−	1.04634i
$351$		0			0
$352$	0.772550	+	1.33810i	0.0411771	+	0.0713208i
$353$	15.8332	−	27.4240i	0.842718	−	1.45963i	−0.0448710	−	0.998993i	$-0.514288\pi$
$353$	15.8332	−	27.4240i	0.842718	−	1.45963i	0.887589	−	0.460637i	$-0.152379\pi$
$354$	−19.7402	+	34.1911i	−1.04918	+	1.81724i
$355$	−1.76935	−	3.06460i	−0.0939072	−	0.162652i
$356$	7.75021			0.410761
$357$	16.1917	−	44.1067i	0.856954	−	2.33438i
$358$	−50.1310			−2.64950
$359$	9.96610	+	17.2618i	0.525991	+	0.911043i	0.999542	+	0.0302764i	$0.00963874\pi$
$359$	9.96610	+	17.2618i	0.525991	+	0.911043i	−0.473551	+	0.880767i	$0.657028\pi$
$360$	9.12780	−	15.8098i	0.481077	−	0.833251i
$361$	2.17744	−	3.77144i	0.114602	−	0.198497i
$362$	1.92007	+	3.32566i	0.100917	+	0.174793i
$363$	29.3156			1.53867
$364$		0			0
$365$	4.84684			0.253695
$366$	7.24984	+	12.5571i	0.378955	+	0.656370i
$367$	−9.85950	+	17.0772i	−0.514662	+	0.891420i	0.485194	+	0.874407i	$0.338749\pi$
$367$	−9.85950	+	17.0772i	−0.514662	+	0.891420i	−0.999855	+	0.0170133i	$0.994584\pi$
$368$	−9.51844	+	16.4864i	−0.496183	+	0.859414i
$369$	8.39096	+	14.5336i	0.436816	+	0.756588i
$370$	4.11881			0.214127
$371$	−1.10931	+	0.192442i	−0.0575923	+	0.00999109i
$372$	−30.4490			−1.57870
$373$	−8.77345	−	15.1961i	−0.454272	−	0.786823i	0.544374	−	0.838843i	$-0.316767\pi$
$373$	−8.77345	−	15.1961i	−0.454272	−	0.786823i	−0.998646	+	0.0520202i	$0.983434\pi$
$374$	4.52986	−	7.84595i	0.234234	−	0.405704i
$375$	12.2097	−	21.1478i	0.630507	−	1.09207i
$376$	−8.82478	−	15.2850i	−0.455103	−	0.788262i
$377$		0			0
$378$	−9.40946	+	25.6317i	−0.483971	+	1.31835i
$379$	11.7014			0.601058			0.300529	−	0.953773i	$-0.402837\pi$
$379$	11.7014			0.601058			0.300529	+	0.953773i	$0.402837\pi$
$380$	6.95942	+	12.0541i	0.357010	+	0.618360i
$381$	5.84725	−	10.1277i	0.299563	−	0.518859i
$382$	13.8055	−	23.9119i	0.706352	−	1.22344i
$383$	−10.7644	−	18.6445i	−0.550036	−	0.952690i	−0.998271	−	0.0587748i	$-0.981281\pi$
$383$	−10.7644	−	18.6445i	−0.550036	−	0.952690i	0.448235	−	0.893916i	$-0.352053\pi$
$384$	57.0669			2.91218
$385$	−0.978699	−	1.17293i	−0.0498791	−	0.0597783i
$386$	−56.3072			−2.86596
$387$	−14.5823	−	25.2572i	−0.741258	−	1.28390i
$388$	14.2500	−	24.6817i	0.723435	−	1.25303i
$389$	−13.2455	+	22.9419i	−0.671574	+	1.16320i	0.305884	+	0.952069i	$0.401048\pi$
$389$	−13.2455	+	22.9419i	−0.671574	+	1.16320i	−0.977458	+	0.211131i	$0.932285\pi$
$390$		0			0
$391$	−53.3118			−2.69609
$392$	−5.09738	+	28.0030i	−0.257457	+	1.41436i
$393$	5.96951			0.301122
$394$	−1.75633	−	3.04206i	−0.0884828	−	0.153257i
$395$	1.36802	−	2.36949i	0.0688327	−	0.119222i
$396$	−4.97392	+	8.61508i	−0.249949	+	0.432924i
$397$	−16.8995	−	29.2707i	−0.848160	−	1.46906i	−0.882849	−	0.469658i	$-0.844377\pi$
$397$	−16.8995	−	29.2707i	−0.848160	−	1.46906i	0.0346887	−	0.999398i	$-0.488956\pi$
$398$	22.4332			1.12447
$399$	−17.8482	−	21.3904i	−0.893529	−	1.07086i
$400$	−9.29977			−0.464989
$401$	10.8059	+	18.7164i	0.539623	+	0.934655i	0.998924	+	0.0463741i	$0.0147666\pi$
$401$	10.8059	+	18.7164i	0.539623	+	0.934655i	−0.459301	+	0.888281i	$0.651900\pi$
$402$	−23.0400	+	39.9065i	−1.14913	+	1.99035i
$403$		0			0
$404$	4.88264	+	8.45697i	0.242920	+	0.420750i
$405$	1.78895			0.0888934
$406$	−8.62262	+	23.4884i	−0.427934	+	1.16571i
$407$	−1.03211			−0.0511599
$408$	−36.1047	−	62.5351i	−1.78745	−	3.09595i
$409$	3.87109	−	6.70492i	0.191413	−	0.331537i	−0.754306	−	0.656523i	$-0.772026\pi$
$409$	3.87109	−	6.70492i	0.191413	−	0.331537i	0.945719	+	0.324986i	$0.105360\pi$
$410$	−4.30637	+	7.45886i	−0.212677	+	0.368367i
$411$	−11.5055	−	19.9282i	−0.567526	−	0.982984i
$412$	−40.2186			−1.98143
$413$	15.6634	−	2.71728i	0.770744	−	0.133709i
$414$	90.1567			4.43096
$415$	1.40868	+	2.43991i	0.0691495	+	0.119770i
$416$		0			0
$417$	−0.793683	+	1.37470i	−0.0388668	+	0.0673193i
$418$	−2.68589	−	4.65211i	−0.131371	−	0.227542i
$419$	−8.10194			−0.395806			−0.197903	−	0.980222i	$-0.563413\pi$
$419$	−8.10194			−0.395806			−0.197903	+	0.980222i	$0.563413\pi$
$420$	−26.0875	+	4.52565i	−1.27294	+	0.220829i
$421$	32.1124			1.56506			0.782530	−	0.622612i	$-0.213929\pi$
$421$	32.1124			1.56506			0.782530	+	0.622612i	$0.213929\pi$
$422$	10.6771	+	18.4933i	0.519755	+	0.900242i
$423$	−9.91963	+	17.1813i	−0.482309	+	0.835384i
$424$	−0.865159	+	1.49850i	−0.0420158	+	0.0727735i
$425$	−13.0218	−	22.5543i	−0.631648	−	1.09405i
$426$	23.6709			1.14686
$427$	2.01203	−	5.48085i	0.0973690	−	0.265237i
$428$	−59.1713			−2.86015
$429$		0			0
$430$	7.48384	−	12.9624i	0.360903	−	0.625102i
$431$	−14.7640	+	25.5721i	−0.711159	+	1.23176i	0.253263	+	0.967397i	$0.418496\pi$
$431$	−14.7640	+	25.5721i	−0.711159	+	1.23176i	−0.964422	+	0.264366i	$0.914837\pi$
$432$	4.97996	+	8.62554i	0.239598	+	0.414997i
$433$	22.0910			1.06163			0.530813	−	0.847489i	$-0.321887\pi$
$433$	22.0910			1.06163			0.530813	+	0.847489i	$0.321887\pi$
$434$	12.0979	+	14.4988i	0.580716	+	0.695967i
$435$	−10.7033			−0.513183
$436$	17.0969	+	29.6127i	0.818792	+	1.41819i
$437$	−15.8051	+	27.3752i	−0.756060	+	1.30953i
$438$	−16.2106	+	28.0777i	−0.774575	+	1.34160i
$439$	3.17790	+	5.50428i	0.151673	+	0.262705i	0.931843	−	0.362863i	$-0.118201\pi$
$439$	3.17790	+	5.50428i	0.151673	+	0.262705i	−0.780170	+	0.625568i	$0.784867\pi$
$440$	−2.34775			−0.111924
$441$	30.1249	−	10.7764i	1.43452	−	0.513164i
$442$		0			0
$443$	6.78135	+	11.7456i	0.322192	+	0.558052i	0.980940	−	0.194311i	$-0.0622472\pi$
$443$	6.78135	+	11.7456i	0.322192	+	0.558052i	−0.658748	+	0.752363i	$0.728914\pi$
$444$	−8.94443	+	15.4922i	−0.424484	+	0.735227i
$445$	1.02801	−	1.78057i	0.0487324	−	0.0844070i
$446$	26.0530	+	45.1251i	1.23365	+	2.13674i
$447$	7.72237			0.365255
$448$	−18.4534	−	22.1157i	−0.871839	−	1.04487i
$449$	−21.9118			−1.03408			−0.517041	−	0.855961i	$-0.672966\pi$
$449$	−21.9118			−1.03408			−0.517041	+	0.855961i	$0.672966\pi$
$450$	22.0214	+	38.1421i	1.03810	+	1.79804i
$451$	1.07911	−	1.86908i	0.0508134	−	0.0880115i
$452$	−18.8473	+	32.6445i	−0.886502	+	1.53547i
$453$	31.6570	+	54.8315i	1.48737	+	2.57621i
$454$	44.3041			2.07930
$455$		0			0
$456$	−42.8151			−2.00500
$457$	7.60732	+	13.1763i	0.355855	+	0.616359i	0.987264	−	0.159091i	$-0.0508563\pi$
$457$	7.60732	+	13.1763i	0.355855	+	0.616359i	−0.631409	+	0.775450i	$0.717523\pi$
$458$	23.1049	−	40.0188i	1.07962	−	1.86996i
$459$	−13.9461	+	24.1554i	−0.650949	+	1.12748i
$460$	15.0213	+	26.0176i	0.700371	+	1.21308i
$461$	16.2163			0.755267			0.377633	−	0.925955i	$-0.376738\pi$
$461$	16.2163			0.755267			0.377633	+	0.925955i	$0.376738\pi$
$462$	10.0681	−	1.74662i	0.468412	−	0.0812600i
$463$	1.44769			0.0672799			0.0336400	−	0.999434i	$-0.489290\pi$
$463$	1.44769			0.0672799			0.0336400	+	0.999434i	$0.489290\pi$
$464$	4.56353	+	7.90426i	0.211856	+	0.366946i
$465$	−4.03884	+	6.99547i	−0.187297	+	0.324407i
$466$	−19.2994	+	33.4275i	−0.894027	+	1.54850i
$467$	−7.00337	−	12.1302i	−0.324078	−	0.561319i	0.657248	−	0.753675i	$-0.271721\pi$
$467$	−7.00337	−	12.1302i	−0.324078	−	0.561319i	−0.981325	+	0.192356i	$0.938387\pi$
$468$		0			0
$469$	18.2817	−	3.17150i	0.844169	−	0.146446i
$470$	−10.1818			−0.469652
$471$	31.0586	+	53.7951i	1.43111	+	2.47875i
$472$	12.2160	−	21.1588i	0.562288	−	0.973912i
$473$	−1.87534	+	3.24818i	−0.0862282	+	0.149352i
$474$	9.15094	+	15.8499i	0.420316	+	0.728009i
$475$	−15.4420			−0.708528
$476$	−21.7895	+	59.3553i	−0.998719	+	2.72055i
$477$	1.94499			0.0890550
$478$	19.2281	+	33.3041i	0.879474	+	1.52329i
$479$	−15.0122	+	26.0018i	−0.685923	+	1.18805i	0.287223	+	0.957864i	$0.407268\pi$
$479$	−15.0122	+	26.0018i	−0.685923	+	1.18805i	−0.973146	+	0.230189i	$0.926065\pi$
$480$	3.55219	−	6.15258i	0.162135	−	0.280826i
$481$		0			0
$482$	9.56649			0.435742
$483$	−38.5238	−	46.1693i	−1.75289	−	2.10078i
$484$	−39.4506			−1.79321
$485$	−3.78033	−	6.54772i	−0.171656	−	0.297317i
$486$	−21.4633	+	37.1756i	−0.973597	+	1.68632i
$487$	−14.2452	+	24.6733i	−0.645510	+	1.11806i	0.338674	+	0.940904i	$0.390022\pi$
$487$	−14.2452	+	24.6733i	−0.645510	+	1.11806i	−0.984184	+	0.177152i	$0.943312\pi$
$488$	−4.48649	−	7.77082i	−0.203094	−	0.351769i
$489$	22.4992			1.01745
$490$	12.5200	+	10.6239i	0.565595	+	0.479941i
$491$	−28.4677			−1.28473			−0.642365	−	0.766399i	$-0.722047\pi$
$491$	−28.4677			−1.28473			−0.642365	+	0.766399i	$0.722047\pi$
$492$	−18.7035	−	32.3954i	−0.843218	−	1.46050i
$493$	−12.7799	+	22.1354i	−0.575578	+	0.996930i
$494$		0			0
$495$	1.31951	+	2.28546i	0.0593076	+	0.102724i
$496$	6.88812			0.309286
$497$	−6.10647	−	7.31838i	−0.273913	−	0.328274i
$498$	−18.8458			−0.844501
$499$	−13.1164	−	22.7183i	−0.587172	−	1.01701i	−0.994601	−	0.103775i	$-0.966908\pi$
$499$	−13.1164	−	22.7183i	−0.587172	−	1.01701i	0.407429	−	0.913237i	$-0.366425\pi$
$500$	−16.4309	+	28.4591i	−0.734811	+	1.27273i
$501$	3.20233	−	5.54659i	0.143069	−	0.247803i
$502$	−3.87684	−	6.71488i	−0.173032	−	0.299700i
$503$	8.53175			0.380412			0.190206	−	0.981744i	$-0.439084\pi$
$503$	8.53175			0.380412			0.190206	+	0.981744i	$0.439084\pi$
$504$	16.9451	−	46.1591i	0.754795	−	2.05609i
$505$	2.59059			0.115280
$506$	−5.79726	−	10.0412i	−0.257720	−	0.446384i
$507$		0			0
$508$	−7.86876	+	13.6291i	−0.349120	+	0.604693i
$509$	−6.51298	−	11.2808i	−0.288683	−	0.500014i	0.684813	−	0.728719i	$-0.259884\pi$
$509$	−6.51298	−	11.2808i	−0.288683	−	0.500014i	−0.973496	+	0.228706i	$0.926551\pi$
$510$	−41.6567			−1.84459
$511$	12.8627	−	2.23142i	0.569014	−	0.0987124i
$512$	−24.8008			−1.09605
$513$	8.26908	+	14.3225i	0.365089	+	0.632352i
$514$	32.1100	−	55.6162i	1.41631	−	2.45312i
$515$	−5.33472	+	9.24000i	−0.235076	+	0.407163i
$516$	32.5039	+	56.2984i	1.43090	+	2.47840i
$517$	2.55141			0.112211
$518$	10.9307	−	1.89625i	0.480266	−	0.0833164i
$519$	22.3798			0.982363
$520$		0			0
$521$	−2.23285	+	3.86741i	−0.0978230	+	0.169434i	−0.910783	−	0.412885i	$-0.864521\pi$
$521$	−2.23285	+	3.86741i	−0.0978230	+	0.169434i	0.812960	+	0.582319i	$0.197855\pi$
$522$	21.6124	−	37.4337i	0.945948	−	1.63843i
$523$	1.45406	+	2.51850i	0.0635815	+	0.110126i	0.896064	−	0.443925i	$-0.146414\pi$
$523$	1.45406	+	2.51850i	0.0635815	+	0.110126i	−0.832482	+	0.554051i	$0.813081\pi$
$524$	−8.03330			−0.350936
$525$	10.1229	−	27.5752i	0.441801	−	1.20348i
$526$	−9.09140			−0.396404
$527$	9.64490	+	16.7055i	0.420138	+	0.727701i
$528$	1.86373	−	3.22807i	0.0811084	−	0.140484i
$529$	−22.6139	+	39.1684i	−0.983213	+	1.70297i
$530$	0.499100	+	0.864466i	0.0216795	+	0.0375500i
$531$	−27.4632			−1.19180
$532$	24.0187	+	28.7855i	1.04134	+	1.24801i
$533$		0			0
$534$	6.87654	+	11.9105i	0.297577	+	0.515418i
$535$	−7.84866	+	13.5943i	−0.339327	+	0.587732i
$536$	14.2581	−	24.6957i	0.615854	−	1.06669i
$537$	−28.8803	−	50.0221i	−1.24628	−	2.15861i
$538$	−56.9262			−2.45426
$539$	−3.13732	−	2.66220i	−0.135134	−	0.114669i
$540$	15.7180			0.676394
$541$	−9.23193	−	15.9902i	−0.396912	−	0.687471i	0.596431	−	0.802664i	$-0.296585\pi$
$541$	−9.23193	−	15.9902i	−0.396912	−	0.687471i	−0.993343	+	0.115193i	$0.963251\pi$
$542$	11.8224	−	20.4770i	0.507815	−	0.879562i
$543$	−2.21229	+	3.83180i	−0.0949384	+	0.164438i
$544$	−8.48277	−	14.6926i	−0.363696	−	0.629940i
$545$	9.07112			0.388564
$546$		0			0
$547$	34.9817			1.49571			0.747856	−	0.663861i	$-0.231083\pi$
$547$	34.9817			1.49571			0.747856	+	0.663861i	$0.231083\pi$
$548$	15.4832	+	26.8177i	0.661411	+	1.14560i
$549$	−5.04310	+	8.73491i	−0.215234	+	0.372797i
$550$	2.83204	−	4.90524i	0.120759	−	0.209160i
$551$	7.57760	+	13.1248i	0.322817	+	0.559135i
$552$	−92.4127			−3.93334
$553$	2.53964	−	6.91806i	0.107996	−	0.294186i
$554$	28.1449			1.19576
$555$	2.37283	+	4.10986i	0.100721	+	0.174454i
$556$	1.06808	−	1.84996i	0.0452965	−	0.0784559i
$557$	0.0265706	−	0.0460217i	0.00112583	−	0.00195000i	−0.865462	−	0.500975i	$-0.832975\pi$
$557$	0.0265706	−	0.0460217i	0.00112583	−	0.00195000i	0.866588	+	0.499025i	$0.166308\pi$
$558$	−16.3107	−	28.2510i	−0.690487	−	1.19596i
$559$		0			0
$560$	5.90148	−	1.02379i	0.249383	−	0.0432629i
$561$	10.4385			0.440716
$562$	15.5194	+	26.8804i	0.654646	+	1.13388i
$563$	−3.99253	+	6.91527i	−0.168265	+	0.291444i	−0.937810	−	0.347149i	$-0.887150\pi$
$563$	−3.99253	+	6.91527i	−0.168265	+	0.291444i	0.769545	+	0.638593i	$0.220483\pi$
$564$	22.1109	−	38.2972i	0.931037	−	1.61260i
$565$	4.99992	+	8.66012i	0.210348	+	0.364334i
$566$	−40.1309			−1.68683
$567$	4.74758	−	0.823608i	0.199380	−	0.0345883i
$568$	−14.6485			−0.614637
$569$	13.3621	+	23.1438i	0.560167	+	0.970237i	0.997481	+	0.0709285i	$0.0225962\pi$
$569$	13.3621	+	23.1438i	0.560167	+	0.970237i	−0.437315	+	0.899308i	$0.644070\pi$
$570$	−12.3498	+	21.3904i	−0.517275	+	0.895946i
$571$	−6.74647	+	11.6852i	−0.282331	+	0.489012i	−0.971958	−	0.235153i	$-0.924441\pi$
$571$	−6.74647	+	11.6852i	−0.282331	+	0.489012i	0.689627	+	0.724164i	$0.257774\pi$
$572$		0			0
$573$	31.8132			1.32902
$574$	−7.99447	+	21.7772i	−0.333683	+	0.908964i
$575$	−33.3302			−1.38996
$576$	24.8794	+	43.0923i	1.03664	+	1.79551i
$577$	6.00662	−	10.4038i	0.250059	−	0.433115i	−0.713483	−	0.700673i	$-0.752883\pi$
$577$	6.00662	−	10.4038i	0.250059	−	0.433115i	0.963542	+	0.267558i	$0.0862167\pi$
$578$	−29.4406	+	50.9925i	−1.22457	+	2.12101i
$579$	−32.4383	−	56.1848i	−1.34809	−	2.33496i
$580$	14.4036			0.598078
$581$	4.86172	+	5.82659i	0.201698	+	0.241728i
$582$	50.5745			2.09638
$583$	−0.125067	−	0.216622i	−0.00517974	−	0.00897158i
$584$	10.0318	−	17.3756i	0.415118	−	0.719005i
$585$		0			0
$586$	−16.8305	−	29.1512i	−0.695260	−	1.20422i
$587$	−10.4235			−0.430225			−0.215113	−	0.976589i	$-0.569012\pi$
$587$	−10.4235			−0.430225			−0.215113	+	0.976589i	$0.569012\pi$
$588$	−67.1486	+	24.0207i	−2.76916	+	0.990599i
$589$	11.4375			0.471275
$590$	−7.04728	−	12.2062i	−0.290132	−	0.502523i
$591$	2.02364	−	3.50504i	0.0832412	−	0.144178i
$592$	2.02339	−	3.50462i	0.0831610	−	0.144039i
$593$	−11.1751	−	19.3558i	−0.458905	−	0.794847i	0.539998	−	0.841666i	$-0.318425\pi$
$593$	−11.1751	−	19.3558i	−0.458905	−	0.794847i	−0.998903	+	0.0468194i	$0.985091\pi$
$594$	−6.06615			−0.248897
$595$	10.7463	+	12.8791i	0.440557	+	0.527991i
$596$	−10.3921			−0.425679
$597$	12.9237	+	22.3845i	0.528931	+	0.916135i
$598$		0			0
$599$	−0.579463	+	1.00366i	−0.0236762	+	0.0410084i	−0.877621	−	0.479356i	$-0.840870\pi$
$599$	−0.579463	+	1.00366i	−0.0236762	+	0.0410084i	0.853945	+	0.520364i	$0.174204\pi$
$600$	−22.5724	−	39.0966i	−0.921515	−	1.59611i
$601$	42.1813			1.72061			0.860306	−	0.509778i	$-0.170272\pi$
$601$	42.1813			1.72061			0.860306	+	0.509778i	$0.170272\pi$
$602$	13.8932	−	37.8456i	0.566245	−	1.54247i
$603$	−32.0540			−1.30534
$604$	−42.6014	−	73.7879i	−1.73343	−	3.00239i
$605$	−5.23284	+	9.06355i	−0.212745	+	0.368486i
$606$	−8.66444	+	15.0072i	−0.351969	+	0.609628i
$607$	9.07844	+	15.7243i	0.368482	+	0.638230i	0.989328	−	0.145702i	$-0.0465441\pi$
$607$	9.07844	+	15.7243i	0.368482	+	0.638230i	−0.620846	+	0.783932i	$0.713211\pi$
$608$	−10.0594			−0.407962
$609$	−28.4048	+	4.92765i	−1.15102	+	0.199679i
$610$	−5.17640			−0.209586
$611$		0			0
$612$	54.6147	−	94.5955i	2.20767	−	3.82380i
$613$	−0.451323	+	0.781714i	−0.0182288	+	0.0315731i	−0.874996	−	0.484130i	$-0.839136\pi$
$613$	−0.451323	+	0.781714i	−0.0182288	+	0.0315731i	0.856767	+	0.515703i	$0.172469\pi$
$614$	18.9594	+	32.8386i	0.765137	+	1.32526i
$615$	−9.92354			−0.400156
$616$	−6.23055	+	1.08087i	−0.251036	+	0.0435497i
$617$	26.0436			1.04848			0.524238	−	0.851572i	$-0.324350\pi$
$617$	26.0436			1.04848			0.524238	+	0.851572i	$0.324350\pi$
$618$	−35.6848	−	61.8079i	−1.43545	−	2.48628i
$619$	13.4171	−	23.2390i	0.539277	−	0.934056i	−0.459666	−	0.888092i	$-0.652031\pi$
$619$	13.4171	−	23.2390i	0.539277	−	0.934056i	0.998943	−	0.0459638i	$-0.0146359\pi$
$620$	5.43515	−	9.41396i	0.218281	−	0.378074i
$621$	17.8481	+	30.9138i	0.716218	+	1.24053i
$622$	−68.3060			−2.73882
$623$	1.90843	−	5.19863i	0.0764596	−	0.208279i
$624$		0			0
$625$	−5.72894	−	9.92281i	−0.229158	−	0.396912i
$626$	22.1839	−	38.4237i	0.886649	−	1.53572i
$627$	3.09467	−	5.36012i	0.123589	−	0.214063i
$628$	−41.7962	−	72.3932i	−1.66785	−	2.88880i
$629$	11.3328			0.451869
$630$	−18.1734	−	21.7801i	−0.724044	−	0.867739i
$631$	33.6121			1.33808			0.669039	−	0.743228i	$-0.266706\pi$
$631$	33.6121			1.33808			0.669039	+	0.743228i	$0.266706\pi$
$632$	−5.66296	−	9.80853i	−0.225260	−	0.390162i
$633$	−12.3021	+	21.3079i	−0.488965	+	0.846913i
$634$	36.5901	−	63.3760i	1.45318	−	2.51698i
$635$	2.08747	+	3.61561i	0.0828388	+	0.143481i
$636$	−4.33539			−0.171909
$637$		0			0
$638$	−5.55889			−0.220078
$639$	8.23293	+	14.2598i	0.325690	+	0.564111i
$640$	−10.1865	+	17.6435i	−0.402655	+	0.697419i
$641$	−10.5921	+	18.3460i	−0.418361	+	0.724622i	−0.995775	−	0.0918294i	$-0.970729\pi$
$641$	−10.5921	+	18.3460i	−0.418361	+	0.724622i	0.577414	+	0.816452i	$0.304062\pi$
$642$	−52.5010	−	90.9343i	−2.07205	−	3.58889i
$643$	−0.661539			−0.0260886			−0.0130443	−	0.999915i	$-0.504152\pi$
$643$	−0.661539			−0.0260886			−0.0130443	+	0.999915i	$0.504152\pi$
$644$	51.8423	+	62.1310i	2.04287	+	2.44831i
$645$	17.2457			0.679047
$646$	29.4917	+	51.0811i	1.16034	+	2.00976i
$647$	20.0162	−	34.6690i	0.786916	−	1.36298i	−0.140931	−	0.990019i	$-0.545010\pi$
$647$	20.0162	−	34.6690i	0.786916	−	1.36298i	0.927848	−	0.372960i	$-0.121657\pi$
$648$	3.70268	−	6.41323i	0.145455	−	0.251936i
$649$	1.76594	+	3.05870i	0.0693193	+	0.120065i
$650$		0			0
$651$	−7.49781	+	20.4243i	−0.293862	+	0.800492i
$652$	−30.2777			−1.18577
$653$	−6.35602	−	11.0089i	−0.248730	−	0.430813i	0.714444	−	0.699693i	$-0.246680\pi$
$653$	−6.35602	−	11.0089i	−0.248730	−	0.430813i	−0.963174	+	0.268880i	$0.913347\pi$
$654$	−30.3391	+	52.5489i	−1.18635	+	2.05482i
$655$	−1.06556	+	1.84560i	−0.0416349	+	0.0721138i
$656$	4.23107	+	7.32844i	0.165196	+	0.286127i
$657$	−22.5527			−0.879867
$658$	−27.0209	+	4.68759i	−1.05339	+	0.182741i
$659$	−14.1904			−0.552781			−0.276391	−	0.961045i	$-0.589138\pi$
$659$	−14.1904			−0.552781			−0.276391	+	0.961045i	$0.589138\pi$
$660$	−2.94119	−	5.09430i	−0.114486	−	0.198295i
$661$	25.0890	−	43.4554i	0.975848	−	1.69022i	0.298742	−	0.954334i	$-0.403433\pi$
$661$	25.0890	−	43.4554i	0.975848	−	1.69022i	0.677106	−	0.735885i	$-0.263234\pi$
$662$	32.5104	−	56.3096i	1.26355	−	2.18853i
$663$		0			0
$664$	11.6625			0.452594
$665$	9.79923	−	1.69997i	0.379998	−	0.0659219i
$666$	−19.1652			−0.742635
$667$	16.3556	+	28.3287i	0.633290	+	1.09689i
$668$	−4.30944	+	7.46417i	−0.166737	+	0.288797i
$669$	−30.0181	+	51.9928i	−1.16057	+	2.01016i
$670$	−8.22530	−	14.2466i	−0.317771	−	0.550396i
$671$	1.29713			0.0500751
$672$	6.59439	−	17.9634i	0.254384	−	0.692952i
$673$	−1.87427			−0.0722479			−0.0361240	−	0.999347i	$-0.511501\pi$
$673$	−1.87427			−0.0722479			−0.0361240	+	0.999347i	$0.511501\pi$
$674$	14.7056	+	25.4708i	0.566438	+	0.981100i
$675$	−8.71902	+	15.1018i	−0.335595	+	0.581268i
$676$		0			0
$677$	1.00439	+	1.73966i	0.0386020	+	0.0668607i	0.884681	−	0.466197i	$-0.154376\pi$
$677$	1.00439	+	1.73966i	0.0386020	+	0.0668607i	−0.846079	+	0.533058i	$0.821043\pi$
$678$	−66.8906			−2.56892
$679$	−13.0469	−	15.6362i	−0.500693	−	0.600062i
$680$	25.7788			0.988571
$681$	25.5234	+	44.2079i	0.978061	+	1.69405i
$682$	−2.09762	+	3.63319i	−0.0803222	+	0.139122i
$683$	−7.05061	+	12.2120i	−0.269784	+	0.467280i	−0.968806	−	0.247820i	$-0.920286\pi$
$683$	−7.05061	+	12.2120i	−0.269784	+	0.467280i	0.699022	+	0.715100i	$0.253619\pi$
$684$	−32.3828	−	56.0886i	−1.23819	−	2.14460i
$685$	8.21497			0.313878
$686$	38.1172	+	22.4302i	1.45532	+	0.856390i
$687$	53.2425			2.03133
$688$	−7.35298	−	12.7357i	−0.280330	−	0.485546i
$689$		0			0
$690$	−26.6559	+	46.1693i	−1.01477	+	1.75764i
$691$	−17.8460	−	30.9102i	−0.678895	−	1.17588i	−0.975314	−	0.220822i	$-0.929126\pi$
$691$	−17.8460	−	30.9102i	−0.678895	−	1.17588i	0.296419	−	0.955058i	$-0.404207\pi$
$692$	−30.1169			−1.14487
$693$	4.55397	+	5.45776i	0.172991	+	0.207323i
$694$	14.6746			0.557041
$695$	−0.283346	−	0.490769i	−0.0107479	−	0.0186159i
$696$	−22.1532	+	38.3704i	−0.839714	+	1.45443i
$697$	−11.8489	+	20.5229i	−0.448809	+	0.777360i
$698$	15.5596	+	26.9500i	0.588938	+	1.02007i
$699$	−44.4732			−1.68213
$700$	−13.6226	+	37.1086i	−0.514888	+	1.40257i
$701$	−6.15865			−0.232609			−0.116305	−	0.993214i	$-0.537105\pi$
$701$	−6.15865			−0.232609			−0.116305	+	0.993214i	$0.537105\pi$
$702$		0			0
$703$	3.35979	−	5.81932i	0.126717	−	0.219480i
$704$	3.19959	−	5.54185i	0.120589	−	0.208866i
$705$	−5.86571	−	10.1597i	−0.220915	−	0.382637i
$706$	−75.6207			−2.84602
$707$	6.87501	−	1.19268i	0.258561	−	0.0448552i
$708$	61.2156			2.30062
$709$	17.0185	+	29.4770i	0.639144	+	1.10703i	0.985621	+	0.168972i	$0.0540447\pi$
$709$	17.0185	+	29.4770i	0.639144	+	1.10703i	−0.346477	+	0.938059i	$0.612622\pi$
$710$	−4.22527	+	7.31838i	−0.158571	+	0.274654i
$711$	−6.36553	+	11.0254i	−0.238726	+	0.413486i
$712$	−4.25547	−	7.37069i	−0.159480	−	0.276228i
$713$	24.6869			0.924530
$714$	−110.550	+	19.1782i	−4.13724	+	0.717727i
$715$		0			0
$716$	38.8648	+	67.3158i	1.45244	+	2.51571i
$717$	−22.1545	+	38.3727i	−0.827375	+	1.43306i
$718$	23.7994	−	41.2218i	0.888187	−	1.53838i
$719$	11.4824	+	19.8881i	0.428222	+	0.741702i	0.996715	−	0.0809859i	$-0.0258069\pi$
$719$	11.4824	+	19.8881i	0.428222	+	0.741702i	−0.568493	+	0.822688i	$0.692474\pi$
$720$	−10.3473			−0.385621
$721$	−9.90351	+	26.9775i	−0.368826	+	1.00470i
$722$	−10.3996			−0.387034
$723$	5.51122	+	9.54571i	0.204964	+	0.355009i
$724$	2.97712	−	5.15653i	0.110644	−	0.191641i
$725$	−7.98992	+	13.8389i	−0.296738	+	0.513966i
$726$	−35.0034	−	60.6276i	−1.29910	−	2.25010i
$727$	1.06558			0.0395203			0.0197601	−	0.999805i	$-0.493710\pi$
$727$	1.06558			0.0395203			0.0197601	+	0.999805i	$0.493710\pi$
$728$		0			0
$729$	−43.9962			−1.62949
$730$	−5.78721	−	10.0237i	−0.214194	−	0.370996i
$731$	20.5916	−	35.6658i	0.761609	−	1.31915i
$732$	11.2411	−	19.4702i	0.415483	−	0.719637i
$733$	−13.1689	−	22.8092i	−0.486404	−	0.842476i	0.513474	−	0.858105i	$-0.328358\pi$
$733$	−13.1689	−	22.8092i	−0.486404	−	0.842476i	−0.999878	+	0.0156289i	$0.995025\pi$
$734$	47.0897			1.73811
$735$	−3.38816	+	18.6132i	−0.124974	+	0.686558i
$736$	−21.7123			−0.800326
$737$	2.06114	+	3.57000i	0.0759230	+	0.131502i
$738$	20.0379	−	34.7067i	0.737606	−	1.27757i
$739$	17.1075	−	29.6310i	0.629308	−	1.08999i	−0.358383	−	0.933575i	$-0.616672\pi$
$739$	17.1075	−	29.6310i	0.629308	−	1.08999i	0.987691	−	0.156419i	$-0.0499950\pi$
$740$	−3.19317	−	5.53073i	−0.117383	−	0.203314i
$741$		0			0
$742$	1.72252	+	2.06438i	0.0632358	+	0.0757857i
$743$	−22.4782			−0.824644			−0.412322	−	0.911038i	$-0.635282\pi$
$743$	−22.4782			−0.824644			−0.412322	+	0.911038i	$0.635282\pi$
$744$	16.7188	+	28.9579i	0.612942	+	1.06165i
$745$	−1.37845	+	2.38754i	−0.0505023	+	0.0874726i
$746$	−20.9513	+	36.2888i	−0.767083	+	1.32863i
$747$	−6.55472	−	11.3531i	−0.239825	−	0.415388i
$748$	−14.0474			−0.513623
$749$	−14.5705	+	39.6905i	−0.532393	+	1.45026i
$750$	−58.3145			−2.12934
$751$	21.2712	+	36.8428i	0.776197	+	1.34441i	0.934119	+	0.356961i	$0.116187\pi$
$751$	21.2712	+	36.8428i	0.776197	+	1.34441i	−0.157923	+	0.987451i	$0.550480\pi$
$752$	−5.00189	+	8.66353i	−0.182400	+	0.315927i
$753$	4.46686	−	7.73683i	0.162781	−	0.281946i
$754$		0			0
$755$	−22.6031			−0.822612
$756$	41.7131	−	7.23637i	1.51709	−	0.263184i
$757$	−11.2380			−0.408454			−0.204227	−	0.978924i	$-0.565468\pi$
$757$	−11.2380			−0.408454			−0.204227	+	0.978924i	$0.565468\pi$
$758$	−13.9716	−	24.1996i	−0.507473	−	0.878969i
$759$	6.67956	−	11.5693i	0.242453	−	0.419941i
$760$	7.64252	−	13.2372i	0.277223	−	0.480165i
$761$	6.40422	+	11.0924i	0.232153	+	0.402101i	0.958441	−	0.285289i	$-0.0920897\pi$
$761$	6.40422	+	11.0924i	0.232153	+	0.402101i	−0.726289	+	0.687390i	$0.758756\pi$
$762$	−27.9269			−1.01168
$763$	24.0733	−	4.17623i	0.871513	−	0.151190i
$764$	−42.8117			−1.54887
$765$	−14.4885	−	25.0948i	−0.523833	−	0.907306i
$766$	−25.7058	+	44.5238i	−0.928789	+	1.60871i
$767$		0			0
$768$	−38.1846	−	66.1377i	−1.37787	−	2.38654i
$769$	51.3517			1.85179			0.925895	−	0.377781i	$-0.123313\pi$
$769$	51.3517			1.85179			0.925895	+	0.377781i	$0.123313\pi$
$770$	−1.25716	+	3.42455i	−0.0453049	+	0.123412i
$771$	73.9938			2.66482
$772$	43.6529	+	75.6091i	1.57110	+	2.72123i
$773$	10.0023	−	17.3245i	0.359759	−	0.623120i	−0.628162	−	0.778083i	$-0.716192\pi$
$773$	10.0023	−	17.3245i	0.359759	−	0.623120i	0.987920	+	0.154963i	$0.0495257\pi$
$774$	−34.8230	+	60.3151i	−1.25169	+	2.16798i
$775$	6.02993	+	10.4441i	0.216602	+	0.375165i
$776$	−31.2974			−1.12351
$777$	8.18925	+	9.81450i	0.293788	+	0.352093i
$778$	63.2615			2.26804
$779$	7.02558	+	12.1687i	0.251717	+	0.435987i
$780$		0			0
$781$	1.05879	−	1.83388i	0.0378864	−	0.0656212i
$782$	63.6552	+	110.254i	2.27631	+	3.94268i
$783$	17.1142			0.611611
$784$	15.1903	−	5.43394i	0.542509	−	0.194069i
$785$	−22.1759			−0.791492
$786$	−7.12771	−	12.3456i	−0.254237	−	0.440351i
$787$	14.6596	−	25.3911i	0.522558	−	0.905096i	−0.477098	−	0.878850i	$-0.658311\pi$
$787$	14.6596	−	25.3911i	0.522558	−	0.905096i	0.999656	−	0.0262462i	$-0.00835537\pi$
$788$	−2.72325	+	4.71680i	−0.0970117	+	0.168029i
$789$	−5.23752	−	9.07166i	−0.186461	−	0.322959i
$790$	−6.53378			−0.232462
$791$	17.2560	+	20.6807i	0.613553	+	0.735321i
$792$	10.9243			0.388177
$793$		0			0
$794$	−40.3566	+	69.8996i	−1.43220	+	2.48064i
$795$	−0.575059	+	0.996031i	−0.0203952	+	0.0353256i
$796$	−17.3917	−	30.1232i	−0.616431	−	1.06769i
$797$	3.10100			0.109843			0.0549215	−	0.998491i	$-0.482509\pi$
$797$	3.10100			0.109843			0.0549215	+	0.998491i	$0.482509\pi$
$798$	−22.9264	+	62.4525i	−0.811588	+	2.21079i
$799$	−28.0151			−0.991102
$800$	−5.30338	−	9.18572i	−0.187503	−	0.324764i
$801$	−4.78343	+	8.28514i	−0.169014	+	0.292741i
$802$	25.8050	−	44.6956i	0.911206	−	1.57826i
$803$	1.45019	+	2.51180i	0.0511761	+	0.0886395i
$804$	71.4484			2.51979
$805$	21.1508	−	3.66923i	0.745467	−	0.129323i
$806$		0			0
$807$	−32.7950	−	56.8025i	−1.15444	−	1.99954i
$808$	5.36189	−	9.28707i	0.188631	−	0.326718i
$809$	−3.99501	+	6.91957i	−0.140457	+	0.243279i	−0.927669	−	0.373404i	$-0.878191\pi$
$809$	−3.99501	+	6.91957i	−0.140457	+	0.243279i	0.787212	+	0.616683i	$0.211524\pi$
$810$	−2.13603	−	3.69972i	−0.0750526	−	0.129995i
$811$	48.2554			1.69448			0.847239	−	0.531213i	$-0.178263\pi$
$811$	48.2554			1.69448			0.847239	+	0.531213i	$0.178263\pi$
$812$	38.2249	−	6.63125i	1.34143	−	0.232711i
$813$	27.2434			0.955466
$814$	1.23236	+	2.13451i	0.0431942	+	0.0748146i
$815$	−4.01612	+	6.95612i	−0.140679	+	0.243662i
$816$	−20.4642	+	35.4449i	−0.716389	+	1.24082i
$817$	−12.2094	−	21.1473i	−0.427153	−	0.739851i
$818$	−18.4886			−0.646439
$819$		0			0
$820$	13.3543			0.466353
$821$	−13.7760	−	23.8607i	−0.480785	−	0.832743i	0.518972	−	0.854791i	$-0.326315\pi$
$821$	−13.7760	−	23.8607i	−0.480785	−	0.832743i	−0.999757	+	0.0220477i	$0.992981\pi$
$822$	−27.4756	+	47.5892i	−0.958323	+	1.65986i
$823$	−10.2137	+	17.6907i	−0.356028	+	0.616659i	−0.987293	−	0.158908i	$-0.949203\pi$
$823$	−10.2137	+	17.6907i	−0.356028	+	0.616659i	0.631265	+	0.775567i	$0.282536\pi$
$824$	22.0831	+	38.2491i	0.769303	+	1.33247i
$825$	6.52611			0.227210
$826$	−24.3220	−	29.1490i	−0.846270	−	1.01422i
$827$	27.7142			0.963719			0.481859	−	0.876249i	$-0.339962\pi$
$827$	27.7142			0.963719			0.481859	+	0.876249i	$0.339962\pi$
$828$	−69.8953	−	121.062i	−2.42903	−	4.20720i
$829$	−4.62832	+	8.01648i	−0.160748	+	0.278424i	−0.935137	−	0.354286i	$-0.884724\pi$
$829$	−4.62832	+	8.01648i	−0.160748	+	0.278424i	0.774389	+	0.632710i	$0.218057\pi$
$830$	3.36398	−	5.82659i	0.116766	−	0.202244i
$831$	16.2142	+	28.0837i	0.562463	+	0.974214i
$832$		0			0
$833$	34.4484	+	29.2315i	1.19357	+	1.01281i
$834$	3.79069			0.131261
$835$	1.14323	+	1.98014i	0.0395632	+	0.0685255i
$836$	−4.16456	+	7.21323i	−0.144034	+	0.249475i
$837$	6.45797	−	11.1855i	0.223220	−	0.386628i
$838$	9.67387	+	16.7556i	0.334178	+	0.578814i
$839$	30.3739			1.04862			0.524312	−	0.851526i	$-0.324323\pi$
$839$	30.3739			1.04862			0.524312	+	0.851526i	$0.324323\pi$
$840$	18.6281	+	22.3251i	0.642731	+	0.770288i
$841$	−13.3170			−0.459205
$842$	−38.3428	−	66.4116i	−1.32138	−	2.28869i
$843$	−17.8813	+	30.9713i	−0.615865	+	1.06671i
$844$	16.5552	−	28.6745i	0.569854	−	0.987016i
$845$		0			0
$846$	47.3769			1.62885
$847$	−9.71440	+	26.4624i	−0.333791	+	0.909258i
$848$	0.980745			0.0336789
$849$	−23.1193	−	40.0437i	−0.793451	−	1.37430i
$850$	−31.0964	+	53.8606i	−1.06660	+	1.84740i
$851$	7.25180	−	12.5605i	0.248589	−	0.430568i
$852$	−18.3512	−	31.7853i	−0.628703	−	1.08894i
$853$	5.30773			0.181733			0.0908666	−	0.995863i	$-0.471036\pi$
$853$	5.30773			0.181733			0.0908666	+	0.995863i	$0.471036\pi$
$854$	−13.7374	+	2.38315i	−0.470082	+	0.0815498i
$855$	−17.1814			−0.587591
$856$	32.4896	+	56.2737i	1.11047	+	1.92340i
$857$	8.31857	−	14.4082i	0.284157	−	0.492175i	−0.688247	−	0.725476i	$-0.741620\pi$
$857$	8.31857	−	14.4082i	0.284157	−	0.492175i	0.972404	+	0.233302i	$0.0749529\pi$
$858$		0			0
$859$	5.29426	+	9.16993i	0.180638	+	0.312874i	0.942098	−	0.335338i	$-0.108850\pi$
$859$	5.29426	+	9.16993i	0.180638	+	0.312874i	−0.761460	+	0.648212i	$0.775517\pi$
$860$	−23.2078			−0.791381
$861$	−26.3355	+	4.56868i	−0.897512	+	0.155700i
$862$	70.5142			2.40172
$863$	−28.0316	−	48.5522i	−0.954207	−	1.65273i	−0.736173	−	0.676793i	$-0.763369\pi$
$863$	−28.0316	−	48.5522i	−0.954207	−	1.65273i	−0.218033	−	0.975941i	$-0.569964\pi$
$864$	−5.67984	+	9.83777i	−0.193232	+	0.334688i
$865$	−3.99480	+	6.91919i	−0.135827	+	0.235260i
$866$	−26.3771	−	45.6864i	−0.896329	−	1.55249i
$867$	−67.8424			−2.30405
$868$	10.0900	−	27.4854i	0.342476	−	0.932916i
$869$	1.63727			0.0555405
$870$	12.7799	+	22.1354i	0.433279	+	0.750462i
$871$		0			0
$872$	18.7750	−	32.5193i	0.635803	−	1.10124i
$873$	17.5902	+	30.4671i	0.595337	+	1.03115i
$874$	75.4863			2.55336
$875$	15.0436	+	18.0292i	0.508567	+	0.609498i
$876$	50.2702			1.69847
$877$	−1.83026	−	3.17010i	−0.0618033	−	0.107047i	0.833468	−	0.552567i	$-0.186352\pi$
$877$	−1.83026	−	3.17010i	−0.0618033	−	0.107047i	−0.895272	+	0.445521i	$0.853018\pi$
$878$	7.58894	−	13.1444i	0.256114	−	0.443603i
$879$	19.3919	−	33.5878i	0.654073	−	1.13289i
$880$	0.665353	+	1.15242i	0.0224290	+	0.0388482i
$881$	10.2299			0.344653			0.172326	−	0.985040i	$-0.444872\pi$
$881$	10.2299			0.344653			0.172326	+	0.985040i	$0.444872\pi$
$882$	−58.2565	−	49.4341i	−1.96160	−	1.66453i
$883$	−3.98979			−0.134267			−0.0671335	−	0.997744i	$-0.521385\pi$
$883$	−3.98979			−0.134267			−0.0671335	+	0.997744i	$0.521385\pi$
$884$		0			0
$885$	8.11982	−	14.0639i	0.272945	−	0.472754i
$886$	16.1941	−	28.0490i	0.544052	−	0.942325i
$887$	7.11039	+	12.3155i	0.238743	+	0.413516i	0.960354	−	0.278784i	$-0.0899312\pi$
$887$	7.11039	+	12.3155i	0.238743	+	0.413516i	−0.721611	+	0.692299i	$0.756598\pi$
$888$	19.6447			0.659234
$889$	7.20440	+	8.63420i	0.241628	+	0.289582i
$890$	−4.90986			−0.164579
$891$	0.535258	+	0.927094i	0.0179318	+	0.0310588i
$892$	40.3960	−	69.9678i	1.35256	−	2.34270i
$893$	−8.30550	+	14.3855i	−0.277933	+	0.481394i
$894$	−9.22065	−	15.9706i	−0.308385	−	0.534138i
$895$	20.6206			0.689269
$896$	−18.9104	+	51.5127i	−0.631753	+	1.72092i
$897$		0			0
$898$	26.1631	+	45.3158i	0.873074	+	1.51221i
$899$	5.91794	−	10.2502i	0.197374	−	0.341862i
$900$	34.1448	−	59.1405i	1.13816	−	1.97135i
$901$	1.37326	+	2.37856i	0.0457500	+	0.0792413i
$902$	−5.15392			−0.171607
$903$	45.7672	−	7.93969i	1.52304	−	0.264216i
$904$	41.3945			1.37676
$905$	−0.789789	−	1.36795i	−0.0262535	−	0.0454723i
$906$	75.5980	−	130.940i	2.51158	−	4.35018i
$907$	−21.7126	+	37.6074i	−0.720956	+	1.24873i	0.239661	+	0.970857i	$0.422964\pi$
$907$	−21.7126	+	37.6074i	−0.720956	+	1.24873i	−0.960617	+	0.277876i	$0.910370\pi$
$908$	−34.3474	−	59.4915i	−1.13986	−	1.97429i
$909$	−12.0542			−0.399814
$910$		0			0
$911$	24.8617			0.823706			0.411853	−	0.911250i	$-0.364882\pi$
$911$	24.8617			0.823706			0.411853	+	0.911250i	$0.364882\pi$
$912$	12.1338	+	21.0164i	0.401791	+	0.695923i
$913$	−0.842964	+	1.46006i	−0.0278980	+	0.0483208i
$914$	18.1666	−	31.4654i	0.600896	−	1.04078i
$915$	−2.98210	−	5.16516i	−0.0985853	−	0.170755i
$916$	−71.6495			−2.36737
$917$	−1.97814	+	5.38852i	−0.0653238	+	0.177944i
$918$	66.6076			2.19838
$919$	0.831637	+	1.44044i	0.0274332	+	0.0475157i	0.879416	−	0.476054i	$-0.157933\pi$
$919$	0.831637	+	1.44044i	0.0274332	+	0.0475157i	−0.851983	+	0.523570i	$0.824600\pi$
$920$	16.4957	−	28.5714i	0.543847	−	0.941971i
$921$	−21.8448	+	37.8363i	−0.719811	+	1.24675i
$922$	−19.3625	−	33.5369i	−0.637671	−	1.10448i
$923$		0			0
$924$	−10.1508	−	12.1654i	−0.333937	−	0.400211i
$925$	7.08521			0.232960
$926$	−1.72857	−	2.99397i	−0.0568044	−	0.0983880i
$927$	24.8229	−	42.9945i	0.815291	−	1.41212i
$928$	−5.20488	+	9.01512i	−0.170859	+	0.295936i
$929$	4.74761	+	8.22310i	0.155764	+	0.269791i	0.933337	−	0.359002i	$-0.116883\pi$
$929$	4.74761	+	8.22310i	0.155764	+	0.269791i	−0.777573	+	0.628793i	$0.783549\pi$
$930$	19.2898			0.632537
$931$	25.2230	−	9.02289i	0.826649	−	0.295713i
$932$	59.8486			1.96040
$933$	−39.3508	−	68.1576i	−1.28829	−	2.23138i
$934$	−16.7243	+	28.9674i	−0.547236	+	0.947841i
$935$	−1.86328	+	3.22730i	−0.0609359	+	0.105544i
$936$		0			0
$937$	−6.41678			−0.209627			−0.104813	−	0.994492i	$-0.533425\pi$
$937$	−6.41678			−0.209627			−0.104813	+	0.994492i	$0.533425\pi$
$938$	−28.3876	−	34.0215i	−0.926889	−	1.11084i
$939$	51.1203			1.66825
$940$	7.89361	+	13.6721i	0.257461	+	0.445936i
$941$	−25.7593	+	44.6164i	−0.839730	+	1.45445i	0.0503911	+	0.998730i	$0.483953\pi$
$941$	−25.7593	+	44.6164i	−0.839730	+	1.45445i	−0.890121	+	0.455725i	$0.849380\pi$
$942$	74.1691	−	128.465i	2.41656	−	4.18561i
$943$	15.1641	+	26.2650i	0.493810	+	0.855305i
$944$	−13.8481			−0.450717
$945$	3.87043	−	10.5432i	0.125905	−	0.342970i
$946$	8.95676			0.291209
$947$	−4.20109	−	7.27651i	−0.136517	−	0.236455i	0.789659	−	0.613546i	$-0.210258\pi$
$947$	−4.20109	−	7.27651i	−0.136517	−	0.236455i	−0.926176	+	0.377091i	$0.876924\pi$
$948$	14.1888	−	24.5757i	0.460831	−	0.798182i
$949$		0			0
$950$	18.4380	+	31.9356i	0.598209	+	1.03613i
$951$	84.3177			2.73419
$952$	68.4128	−	11.8682i	2.21727	−	0.384652i
$953$	−36.0911			−1.16910			−0.584552	−	0.811356i	$-0.698730\pi$
$953$	−36.0911			−1.16910			−0.584552	+	0.811356i	$0.698730\pi$
$954$	−2.32235	−	4.02244i	−0.0751890	−	0.130231i
$955$	−5.67867	+	9.83575i	−0.183758	+	0.318277i
$956$	29.8138	−	51.6390i	0.964246	−	1.67012i
$957$	−3.20245	−	5.54681i	−0.103521	−	0.179303i
$958$	71.6991			2.31649
$959$	21.8012	−	3.78207i	0.703998	−	0.122129i
$960$	−29.4235			−0.949639
$961$	11.0338	+	19.1111i	0.355928	+	0.616486i
$962$		0			0
$963$	36.5205	−	63.2553i	1.17686	−	2.03837i
$964$	−7.41656	−	12.8459i	−0.238871	−	0.413737i
$965$	23.1610			0.745580
$966$	−49.4847	+	134.798i	−1.59214	+	4.33706i
$967$	−3.18338			−0.102371			−0.0511853	−	0.998689i	$-0.516300\pi$
$967$	−3.18338			−0.102371			−0.0511853	+	0.998689i	$0.516300\pi$
$968$	21.6614	+	37.5187i	0.696225	+	1.20590i
$969$	−33.9801	+	58.8553i	−1.09160	+	1.89070i
$970$	−9.02756	+	15.6362i	−0.289857	+	0.502048i
$971$	−18.8738	−	32.6904i	−0.605690	−	1.04909i	−0.991942	−	0.126692i	$-0.959564\pi$
$971$	−18.8738	−	32.6904i	−0.605690	−	1.04909i	0.386253	−	0.922393i	$-0.373769\pi$
$972$	66.5591			2.13488
$973$	−0.977898	−	1.17197i	−0.0313500	−	0.0375718i
$974$	68.0359			2.18001
$975$		0			0
$976$	−2.54294	+	4.40451i	−0.0813977	+	0.140985i
$977$	−10.6538	+	18.4530i	−0.340846	+	0.590363i	−0.984590	−	0.174878i	$-0.944047\pi$
$977$	−10.6538	+	18.4530i	−0.340846	+	0.590363i	0.643744	+	0.765241i	$0.277380\pi$
$978$	−26.8645	−	46.5307i	−0.859032	−	1.48789i
$979$	1.23034			0.0393217
$980$	4.55951	−	25.0482i	0.145648	−	0.800134i
$981$	−42.2087			−1.34762
$982$	33.9910	+	58.8741i	1.08470	+	1.87875i
$983$	−11.0158	+	19.0799i	−0.351350	+	0.608556i	−0.986486	−	0.163844i	$-0.947611\pi$
$983$	−11.0158	+	19.0799i	−0.351350	+	0.608556i	0.635136	+	0.772400i	$0.280944\pi$
$984$	−20.5393	+	35.5752i	−0.654770	+	1.13409i
$985$	0.722439	+	1.25130i	0.0230188	+	0.0398698i
$986$	61.0378			1.94384
$987$	−20.2441	−	24.2618i	−0.644376	−	0.772260i
$988$		0			0
$989$	−26.3529	−	45.6446i	−0.837975	−	1.45141i
$990$	3.15104	−	5.45776i	0.100147	−	0.173459i
$991$	11.0129	−	19.0750i	0.349838	−	0.605937i	−0.636383	−	0.771374i	$-0.719570\pi$
$991$	11.0129	−	19.0750i	0.349838	−	0.605937i	0.986220	+	0.165437i	$0.0529033\pi$
$992$	3.92808	+	6.80364i	0.124717	+	0.216016i
$993$	74.9164			2.37740
$994$	−7.84390	+	21.3671i	−0.248793	+	0.677723i
$995$	−9.22753			−0.292532
$996$	14.6105	+	25.3061i	0.462951	+	0.801855i
$997$	−5.04102	+	8.73130i	−0.159651	+	0.276523i	−0.934743	−	0.355325i	$-0.884370\pi$
$997$	−5.04102	+	8.73130i	−0.159651	+	0.276523i	0.775092	+	0.631848i	$0.217703\pi$
$998$	−31.3225	+	54.2522i	−0.991497	+	1.71732i
$999$	−3.79408	−	6.57153i	−0.120039	−	0.207914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.g.508.1		12
7.2	even	3	inner	1183.2.e.g.170.1		12
7.3	odd	6		8281.2.a.cf.1.6		6
7.4	even	3		8281.2.a.ce.1.6		6
13.4	even	6		91.2.g.b.81.6	yes	12
13.10	even	6		91.2.h.b.74.1	yes	12
13.12	even	2		1183.2.e.h.508.6		12
39.17	odd	6		819.2.n.d.172.1		12
39.23	odd	6		819.2.s.d.802.6		12
91.4	even	6		637.2.f.k.393.6		12
91.10	odd	6		637.2.f.j.295.6		12
91.17	odd	6		637.2.f.j.393.6		12
91.23	even	6		91.2.g.b.9.6	✓	12
91.25	even	6		8281.2.a.bz.1.1		6
91.30	even	6		91.2.h.b.16.1	yes	12
91.38	odd	6		8281.2.a.ca.1.1		6
91.51	even	6		1183.2.e.h.170.6		12
91.62	odd	6		637.2.h.l.165.1		12
91.69	odd	6		637.2.g.l.263.6		12
91.75	odd	6		637.2.g.l.373.6		12
91.82	odd	6		637.2.h.l.471.1		12
91.88	even	6		637.2.f.k.295.6		12
273.23	odd	6		819.2.n.d.100.1		12
273.212	odd	6		819.2.s.d.289.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.6	✓	12	91.23	even	6
91.2.g.b.81.6	yes	12	13.4	even	6
91.2.h.b.16.1	yes	12	91.30	even	6
91.2.h.b.74.1	yes	12	13.10	even	6
637.2.f.j.295.6		12	91.10	odd	6
637.2.f.j.393.6		12	91.17	odd	6
637.2.f.k.295.6		12	91.88	even	6
637.2.f.k.393.6		12	91.4	even	6
637.2.g.l.263.6		12	91.69	odd	6
637.2.g.l.373.6		12	91.75	odd	6
637.2.h.l.165.1		12	91.62	odd	6
637.2.h.l.471.1		12	91.82	odd	6
819.2.n.d.100.1		12	273.23	odd	6
819.2.n.d.172.1		12	39.17	odd	6
819.2.s.d.289.6		12	273.212	odd	6
819.2.s.d.802.6		12	39.23	odd	6
1183.2.e.g.170.1		12	7.2	even	3	inner
1183.2.e.g.508.1		12	1.1	even	1	trivial
1183.2.e.h.170.6		12	91.51	even	6
1183.2.e.h.508.6		12	13.12	even	2
8281.2.a.bz.1.1		6	91.25	even	6
8281.2.a.ca.1.1		6	91.38	odd	6
8281.2.a.ce.1.6		6	7.4	even	3
8281.2.a.cf.1.6		6	7.3	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19402 - 2.06810i) q^{2} +(1.37574 - 2.38285i) q^{3} +(-1.85136 + 3.20665i) q^{4} +(0.491140 + 0.850679i) q^{5} -6.57063 q^{6} +(1.69505 + 2.03145i) q^{7} +4.06616 q^{8} +(-2.28532 - 3.95828i) q^{9} +(1.17286 - 2.03145i) q^{10} +(-0.293901 + 0.509052i) q^{11} +(5.09398 + 8.82303i) q^{12} +(2.17733 - 5.93113i) q^{14} +2.70272 q^{15} +(-1.15235 - 1.99593i) q^{16} +(3.22710 - 5.58950i) q^{17} +(-5.45742 + 9.45253i) q^{18} +(-1.91345 - 3.31419i) q^{19} -3.63711 q^{20} +(7.17260 - 1.24430i) q^{21} +1.40369 q^{22} +(-4.13001 - 7.15338i) q^{23} +(5.59398 - 9.68906i) q^{24} +(2.01756 - 3.49452i) q^{25} -4.32156 q^{27} +(-9.65231 + 1.67448i) q^{28} -3.96018 q^{29} +(-3.22710 - 5.58950i) q^{30} +(-1.49436 + 2.58831i) q^{31} +(1.31430 - 2.27644i) q^{32} +(0.808663 + 1.40065i) q^{33} -15.4129 q^{34} +(-0.895609 + 2.43967i) q^{35} +16.9238 q^{36} +(0.877941 + 1.52064i) q^{37} +(-4.56938 + 7.91440i) q^{38} +(1.99705 + 3.45900i) q^{40} -3.67169 q^{41} +(-11.1376 - 13.3479i) q^{42} +6.38085 q^{43} +(-1.08823 - 1.88488i) q^{44} +(2.24482 - 3.88814i) q^{45} +(-9.86261 + 17.0825i) q^{46} +(-2.17030 - 3.75906i) q^{47} -6.34134 q^{48} +(-1.25361 + 6.88683i) q^{49} -9.63603 q^{50} +(-8.87930 - 15.3794i) q^{51} +(-0.212770 + 0.368529i) q^{53} +(5.16002 + 8.93742i) q^{54} -0.577387 q^{55} +(6.89235 + 8.26022i) q^{56} -10.5296 q^{57} +(4.72853 + 8.19006i) q^{58} +(3.00431 - 5.20362i) q^{59} +(-5.00371 + 8.66669i) q^{60} +(-1.10337 - 1.91109i) q^{61} +7.13717 q^{62} +(4.16735 - 11.3520i) q^{63} -10.8866 q^{64} +(1.93112 - 3.34479i) q^{66} +(3.50651 - 6.07346i) q^{67} +(11.9491 + 20.6964i) q^{68} -22.7272 q^{69} +(6.11486 - 1.06080i) q^{70} -3.60253 q^{71} +(-9.29247 - 16.0950i) q^{72} +(2.46714 - 4.27321i) q^{73} +(2.09656 - 3.63134i) q^{74} +(-5.55128 - 9.61510i) q^{75} +14.1699 q^{76} +(-1.53229 + 0.265822i) q^{77} +(-1.39270 - 2.41223i) q^{79} +(1.13193 - 1.96056i) q^{80} +(0.910609 - 1.57722i) q^{81} +(4.38406 + 7.59342i) q^{82} +2.86819 q^{83} +(-9.28903 + 25.3037i) q^{84} +6.33983 q^{85} +(-7.61885 - 13.1962i) q^{86} +(-5.44818 + 9.43652i) q^{87} +(-1.19505 + 2.06989i) q^{88} +(-1.04656 - 1.81269i) q^{89} -10.7214 q^{90} +30.5845 q^{92} +(4.11170 + 7.12167i) q^{93} +(-5.18275 + 8.97679i) q^{94} +(1.87954 - 3.25546i) q^{95} +(-3.61628 - 6.26357i) q^{96} -7.69704 q^{97} +(15.7395 - 5.63041i) q^{98} +2.68663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} + 5 q^{12} - 2 q^{14} - 4 q^{15} + 8 q^{16} + 5 q^{17} - 3 q^{18} + q^{19} - 2 q^{20} + 9 q^{21}+ \cdots + 20 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 - 18 * q^6 + 6 * q^7 + 6 * q^8 + 3 * q^9 + 4 * q^10 - 4 * q^11 + 5 * q^12 - 2 * q^14 - 4 * q^15 + 8 * q^16 + 5 * q^17 - 3 * q^18 + q^19 - 2 * q^20 + 9 * q^21 + 10 * q^22 - q^23 + 11 * q^24 + 7 * q^25 - 8 * q^27 - 8 * q^28 - 6 * q^29 - 5 * q^30 - 16 * q^31 - 8 * q^32 - 16 * q^33 - 32 * q^34 - 28 * q^35 + 42 * q^36 + 13 * q^37 - 17 * q^38 - 5 * q^40 - 16 * q^41 - 52 * q^42 + 22 * q^43 - 21 * q^44 + 7 * q^45 - 16 * q^46 + q^47 - 42 * q^48 + 6 * q^49 + 12 * q^50 - 20 * q^51 - 2 * q^53 + 18 * q^54 - 18 * q^55 + 9 * q^56 - 42 * q^57 + 8 * q^58 - 13 * q^59 - 20 * q^60 - 5 * q^61 - 10 * q^62 - 8 * q^63 - 30 * q^64 + 18 * q^66 + 11 * q^67 + 29 * q^68 - 46 * q^69 + 39 * q^70 + 12 * q^71 - 25 * q^72 + 30 * q^73 - 3 * q^74 - 3 * q^75 - 18 * q^76 + 11 * q^77 + 7 * q^79 + 7 * q^80 - 6 * q^81 + q^82 + 54 * q^83 - 41 * q^84 - 2 * q^85 + 7 * q^86 + 16 * q^87 - 4 * q^89 - 16 * q^90 + 54 * q^92 + 7 * q^93 + 45 * q^94 - 6 * q^95 - 19 * q^96 - 70 * q^97 + 82 * q^98 + 20 * q^99

Introduction

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