LMFDB - Embedded newform 1183.2.e.l.170.4

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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.4
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.l.508.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03405 + 1.79102i) q^{2} +(1.27200 + 2.20318i) q^{3} +(-1.13851 - 1.97195i) q^{4} +(-0.427895 + 0.741135i) q^{5} -5.26125 q^{6} +(0.562037 + 2.58537i) q^{7} +0.572885 q^{8} +(-1.73599 + 3.00682i) q^{9} +O(q^{10})$	\(q+(-1.03405 + 1.79102i) q^{2} +(1.27200 + 2.20318i) q^{3} +(-1.13851 - 1.97195i) q^{4} +(-0.427895 + 0.741135i) q^{5} -5.26125 q^{6} +(0.562037 + 2.58537i) q^{7} +0.572885 q^{8} +(-1.73599 + 3.00682i) q^{9} +(-0.884926 - 1.53274i) q^{10} +(3.02261 + 5.23531i) q^{11} +(2.89637 - 5.01666i) q^{12} +(-5.21162 - 1.66677i) q^{14} -2.17714 q^{15} +(1.68462 - 2.91785i) q^{16} +(-2.35073 - 4.07158i) q^{17} +(-3.59019 - 6.21839i) q^{18} +(-1.48430 + 2.57088i) q^{19} +1.94864 q^{20} +(-4.98110 + 4.52686i) q^{21} -12.5021 q^{22} +(-1.62726 + 2.81850i) q^{23} +(0.728712 + 1.26217i) q^{24} +(2.13381 + 3.69587i) q^{25} -1.20072 q^{27} +(4.45833 - 4.05176i) q^{28} +4.50008 q^{29} +(2.25126 - 3.89930i) q^{30} +(-0.970299 - 1.68061i) q^{31} +(4.05684 + 7.02665i) q^{32} +(-7.68954 + 13.3187i) q^{33} +9.72304 q^{34} +(-2.15660 - 0.689719i) q^{35} +7.90574 q^{36} +(4.23981 - 7.34356i) q^{37} +(-3.06966 - 5.31681i) q^{38} +(-0.245135 + 0.424586i) q^{40} -8.47502 q^{41} +(-2.95702 - 13.6022i) q^{42} +3.13983 q^{43} +(6.88251 - 11.9209i) q^{44} +(-1.48564 - 2.57321i) q^{45} +(-3.36533 - 5.82892i) q^{46} +(1.52221 - 2.63654i) q^{47} +8.57138 q^{48} +(-6.36823 + 2.90614i) q^{49} -8.82585 q^{50} +(5.98027 - 10.3581i) q^{51} +(3.98271 + 6.89825i) q^{53} +(1.24160 - 2.15052i) q^{54} -5.17343 q^{55} +(0.321983 + 1.48112i) q^{56} -7.55212 q^{57} +(-4.65329 + 8.05974i) q^{58} +(-3.32591 - 5.76064i) q^{59} +(2.47868 + 4.29320i) q^{60} +(5.60975 - 9.71638i) q^{61} +4.01334 q^{62} +(-8.74943 - 2.79822i) q^{63} -10.0414 q^{64} +(-15.9027 - 27.5443i) q^{66} +(-4.87200 - 8.43855i) q^{67} +(-5.35263 + 9.27103i) q^{68} -8.27953 q^{69} +(3.46532 - 3.14931i) q^{70} +5.35491 q^{71} +(-0.994523 + 1.72256i) q^{72} +(-1.78510 - 3.09188i) q^{73} +(8.76832 + 15.1872i) q^{74} +(-5.42844 + 9.40233i) q^{75} +6.75952 q^{76} +(-11.8364 + 10.7570i) q^{77} +(0.405540 - 0.702416i) q^{79} +(1.44168 + 2.49706i) q^{80} +(3.68065 + 6.37507i) q^{81} +(8.76357 - 15.1790i) q^{82} +17.0860 q^{83} +(14.5978 + 4.66862i) q^{84} +4.02345 q^{85} +(-3.24673 + 5.62350i) q^{86} +(5.72412 + 9.91447i) q^{87} +(1.73161 + 2.99923i) q^{88} +(-7.59999 + 13.1636i) q^{89} +6.14489 q^{90} +7.41058 q^{92} +(2.46845 - 4.27548i) q^{93} +(3.14807 + 5.45262i) q^{94} +(-1.27024 - 2.20013i) q^{95} +(-10.3206 + 17.8759i) q^{96} +15.2597 q^{97} +(1.38008 - 14.4107i) q^{98} -20.9889 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9}+O(q^{10}) $ 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9} - 5 q^{10} + q^{11} - 5 q^{12} - 2 q^{14} + 10 q^{15} - 17 q^{16} + 5 q^{17} - 24 q^{19} + 68 q^{20} - q^{21} - 28 q^{22} - 11 q^{23} - 32 q^{24} - 33 q^{25} - 42 q^{27} - 15 q^{28} + 8 q^{29} + 22 q^{30} - 40 q^{31} + 6 q^{32} - 24 q^{33} + 72 q^{34} + 44 q^{35} - 30 q^{36} + 4 q^{37} + 29 q^{38} + 4 q^{40} + 98 q^{41} - 9 q^{42} + 26 q^{43} - 10 q^{44} - 58 q^{45} + 10 q^{46} - 62 q^{47} + 178 q^{48} + 31 q^{49} - 46 q^{50} + 21 q^{51} + 18 q^{53} - 12 q^{54} - 28 q^{55} - 56 q^{56} - 26 q^{57} - 56 q^{58} - 79 q^{59} - 22 q^{60} - 13 q^{61} + 24 q^{62} + 22 q^{63} + 36 q^{64} + 38 q^{66} + 2 q^{67} + 12 q^{68} - 56 q^{69} + 85 q^{70} - 38 q^{71} - 81 q^{72} - 17 q^{73} - 17 q^{74} - 24 q^{75} + 116 q^{76} - 30 q^{77} + 9 q^{79} - 63 q^{80} - 16 q^{81} + 22 q^{82} + 162 q^{83} + 203 q^{84} - 68 q^{85} - 22 q^{86} - 70 q^{87} + 33 q^{88} - 72 q^{89} + 2 q^{90} - 8 q^{92} - 19 q^{93} + 30 q^{94} - 13 q^{95} - 11 q^{96} + 90 q^{97} + 81 q^{98} - 78 q^{99}+O(q^{100}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9 - 5 * q^10 + q^11 - 5 * q^12 - 2 * q^14 + 10 * q^15 - 17 * q^16 + 5 * q^17 - 24 * q^19 + 68 * q^20 - q^21 - 28 * q^22 - 11 * q^23 - 32 * q^24 - 33 * q^25 - 42 * q^27 - 15 * q^28 + 8 * q^29 + 22 * q^30 - 40 * q^31 + 6 * q^32 - 24 * q^33 + 72 * q^34 + 44 * q^35 - 30 * q^36 + 4 * q^37 + 29 * q^38 + 4 * q^40 + 98 * q^41 - 9 * q^42 + 26 * q^43 - 10 * q^44 - 58 * q^45 + 10 * q^46 - 62 * q^47 + 178 * q^48 + 31 * q^49 - 46 * q^50 + 21 * q^51 + 18 * q^53 - 12 * q^54 - 28 * q^55 - 56 * q^56 - 26 * q^57 - 56 * q^58 - 79 * q^59 - 22 * q^60 - 13 * q^61 + 24 * q^62 + 22 * q^63 + 36 * q^64 + 38 * q^66 + 2 * q^67 + 12 * q^68 - 56 * q^69 + 85 * q^70 - 38 * q^71 - 81 * q^72 - 17 * q^73 - 17 * q^74 - 24 * q^75 + 116 * q^76 - 30 * q^77 + 9 * q^79 - 63 * q^80 - 16 * q^81 + 22 * q^82 + 162 * q^83 + 203 * q^84 - 68 * q^85 - 22 * q^86 - 70 * q^87 + 33 * q^88 - 72 * q^89 + 2 * q^90 - 8 * q^92 - 19 * q^93 + 30 * q^94 - 13 * q^95 - 11 * q^96 + 90 * q^97 + 81 * q^98 - 78 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.03405	+	1.79102i	−0.731182	+	1.26644i	0.225197	+	0.974313i	$0.427697\pi$
$2$	−1.03405	+	1.79102i	−0.731182	+	1.26644i	−0.956379	+	0.292130i	$0.905636\pi$
$3$	1.27200	+	2.20318i	0.734392	+	1.27200i	0.954990	+	0.296639i	$0.0958660\pi$
$3$	1.27200	+	2.20318i	0.734392	+	1.27200i	−0.220597	+	0.975365i	$0.570801\pi$
$4$	−1.13851	−	1.97195i	−0.569253	−	0.985975i
$5$	−0.427895	+	0.741135i	−0.191360	+	0.331446i	−0.945701	−	0.325037i	$-0.894623\pi$
$5$	−0.427895	+	0.741135i	−0.191360	+	0.331446i	0.754341	+	0.656483i	$0.227957\pi$
$6$	−5.26125			−2.14790
$7$	0.562037	+	2.58537i	0.212430	+	0.977176i
$7$	0.562037	+	2.58537i	0.212430	+	0.977176i
$8$	0.572885			0.202546
$9$	−1.73599	+	3.00682i	−0.578663	+	1.00227i
$10$	−0.884926	−	1.53274i	−0.279838	−	0.484694i
$11$	3.02261	+	5.23531i	0.911350	+	1.57851i	0.812158	+	0.583437i	$0.198292\pi$
$11$	3.02261	+	5.23531i	0.911350	+	1.57851i	0.0991920	+	0.995068i	$0.468374\pi$
$12$	2.89637	−	5.01666i	0.836110	−	1.44818i
$13$		0			0
$13$		0			0
$14$	−5.21162	−	1.66677i	−1.39286	−	0.445462i
$15$	−2.17714			−0.562134
$16$	1.68462	−	2.91785i	0.421155	−	0.729462i
$17$	−2.35073	−	4.07158i	−0.570135	−	0.987503i	−0.996552	−	0.0829757i	$-0.973558\pi$
$17$	−2.35073	−	4.07158i	−0.570135	−	0.987503i	0.426417	−	0.904527i	$-0.359776\pi$
$18$	−3.59019	−	6.21839i	−0.846216	−	1.46569i
$19$	−1.48430	+	2.57088i	−0.340521	+	0.589799i	−0.984530	−	0.175219i	$-0.943937\pi$
$19$	−1.48430	+	2.57088i	−0.340521	+	0.589799i	0.644009	+	0.765018i	$0.277270\pi$
$20$	1.94864			0.435730
$21$	−4.98110	+	4.52686i	−1.08697	+	0.987843i
$22$	−12.5021			−2.66545
$23$	−1.62726	+	2.81850i	−0.339307	+	0.587698i	−0.984303	−	0.176489i	$-0.943526\pi$
$23$	−1.62726	+	2.81850i	−0.339307	+	0.587698i	0.644995	+	0.764187i	$0.276859\pi$
$24$	0.728712	+	1.26217i	0.148748	+	0.257639i
$25$	2.13381	+	3.69587i	0.426762	+	0.739174i
$26$		0			0
$27$	−1.20072			−0.231079
$28$	4.45833	−	4.05176i	0.842545	−	0.765711i
$29$	4.50008			0.835644			0.417822	−	0.908529i	$-0.362794\pi$
$29$	4.50008			0.835644			0.417822	+	0.908529i	$0.362794\pi$
$30$	2.25126	−	3.89930i	0.411022	−	0.711911i
$31$	−0.970299	−	1.68061i	−0.174271	−	0.301846i	0.765638	−	0.643272i	$-0.222424\pi$
$31$	−0.970299	−	1.68061i	−0.174271	−	0.301846i	−0.939909	+	0.341426i	$0.889090\pi$
$32$	4.05684	+	7.02665i	0.717155	+	1.24215i
$33$	−7.68954	+	13.3187i	−1.33858	+	2.31848i
$34$	9.72304			1.66749
$35$	−2.15660	−	0.689719i	−0.364532	−	0.116584i
$36$	7.90574			1.31762
$37$	4.23981	−	7.34356i	0.697020	−	1.20727i	−0.272475	−	0.962163i	$-0.587842\pi$
$37$	4.23981	−	7.34356i	0.697020	−	1.20727i	0.969495	−	0.245111i	$-0.0788244\pi$
$38$	−3.06966	−	5.31681i	−0.497965	−	0.862501i
$39$		0			0
$40$	−0.245135	+	0.424586i	−0.0387592	+	0.0671329i
$41$	−8.47502			−1.32358			−0.661788	−	0.749691i	$-0.730202\pi$
$41$	−8.47502			−1.32358			−0.661788	+	0.749691i	$0.730202\pi$
$42$	−2.95702	−	13.6022i	−0.456278	−	2.09887i
$43$	3.13983			0.478819			0.239410	−	0.970919i	$-0.423046\pi$
$43$	3.13983			0.478819			0.239410	+	0.970919i	$0.423046\pi$
$44$	6.88251	−	11.9209i	1.03758	−	1.79714i
$45$	−1.48564	−	2.57321i	−0.221466	−	0.383591i
$46$	−3.36533	−	5.82892i	−0.496191	−	0.859427i
$47$	1.52221	−	2.63654i	0.222037	−	0.384579i	−0.733389	−	0.679809i	$-0.762063\pi$
$47$	1.52221	−	2.63654i	0.222037	−	0.384579i	0.955426	+	0.295229i	$0.0953961\pi$
$48$	8.57138			1.23717
$49$	−6.36823	+	2.90614i	−0.909747	+	0.415163i
$50$	−8.82585			−1.24816
$51$	5.98027	−	10.3581i	0.837405	−	1.45043i
$52$		0			0
$53$	3.98271	+	6.89825i	0.547067	+	0.947547i	0.998474	+	0.0552291i	$0.0175889\pi$
$53$	3.98271	+	6.89825i	0.547067	+	0.947547i	−0.451407	+	0.892318i	$0.649078\pi$
$54$	1.24160	−	2.15052i	0.168961	−	0.292649i
$55$	−5.17343			−0.697585
$56$	0.321983	+	1.48112i	0.0430268	+	0.197923i
$57$	−7.55212			−1.00030
$58$	−4.65329	+	8.05974i	−0.611007	+	1.05830i
$59$	−3.32591	−	5.76064i	−0.432996	−	0.749972i	0.564133	−	0.825684i	$-0.309210\pi$
$59$	−3.32591	−	5.76064i	−0.432996	−	0.749972i	−0.997130	+	0.0757120i	$0.975877\pi$
$60$	2.47868	+	4.29320i	0.319996	+	0.554250i
$61$	5.60975	−	9.71638i	0.718256	−	1.24406i	−0.243435	−	0.969917i	$-0.578274\pi$
$61$	5.60975	−	9.71638i	0.718256	−	1.24406i	0.961690	−	0.274138i	$-0.0883924\pi$
$62$	4.01334			0.509695
$63$	−8.74943	−	2.79822i	−1.10232	−	0.352543i
$64$	−10.0414			−1.25517
$65$		0			0
$66$	−15.9027	−	27.5443i	−1.95749	−	3.39046i
$67$	−4.87200	−	8.43855i	−0.595209	−	1.03093i	−0.993517	−	0.113681i	$-0.963736\pi$
$67$	−4.87200	−	8.43855i	−0.595209	−	1.03093i	0.398308	−	0.917252i	$-0.369598\pi$
$68$	−5.35263	+	9.27103i	−0.649102	+	1.12428i
$69$	−8.27953			−0.996739
$70$	3.46532	−	3.14931i	0.414186	−	0.376415i
$71$	5.35491			0.635510			0.317755	−	0.948173i	$-0.397071\pi$
$71$	5.35491			0.635510			0.317755	+	0.948173i	$0.397071\pi$
$72$	−0.994523	+	1.72256i	−0.117206	+	0.203006i
$73$	−1.78510	−	3.09188i	−0.208930	−	0.361877i	0.742448	−	0.669904i	$-0.233665\pi$
$73$	−1.78510	−	3.09188i	−0.208930	−	0.361877i	−0.951378	+	0.308027i	$0.900331\pi$
$74$	8.76832	+	15.1872i	1.01930	+	1.76547i
$75$	−5.42844	+	9.40233i	−0.626822	+	1.08569i
$76$	6.75952			0.775370
$77$	−11.8364	+	10.7570i	−1.34888	+	1.22587i
$78$		0			0
$79$	0.405540	−	0.702416i	0.0456268	−	0.0790280i	−0.842310	−	0.538993i	$-0.818805\pi$
$79$	0.405540	−	0.702416i	0.0456268	−	0.0790280i	0.887937	+	0.459965i	$0.152138\pi$
$80$	1.44168	+	2.49706i	0.161185	+	0.279180i
$81$	3.68065	+	6.37507i	0.408961	+	0.708341i
$82$	8.76357	−	15.1790i	0.967775	−	1.67623i
$83$	17.0860			1.87543			0.937717	−	0.347399i	$-0.112935\pi$
$83$	17.0860			1.87543			0.937717	+	0.347399i	$0.112935\pi$
$84$	14.5978	+	4.66862i	1.59275	+	0.509388i
$85$	4.02345			0.436405
$86$	−3.24673	+	5.62350i	−0.350104	+	0.606397i
$87$	5.72412	+	9.91447i	0.613690	+	1.06294i
$88$	1.73161	+	2.99923i	0.184590	+	0.319719i
$89$	−7.59999	+	13.1636i	−0.805597	+	1.39533i	0.110291	+	0.993899i	$0.464822\pi$
$89$	−7.59999	+	13.1636i	−0.805597	+	1.39533i	−0.915887	+	0.401435i	$0.868511\pi$
$90$	6.14489			0.647729
$91$		0			0
$92$	7.41058			0.772607
$93$	2.46845	−	4.27548i	0.255966	−	0.443347i
$94$	3.14807	+	5.45262i	0.324699	+	0.562394i
$95$	−1.27024	−	2.20013i	−0.130324	−	0.225728i
$96$	−10.3206	+	17.8759i	−1.05335	+	1.82445i
$97$	15.2597			1.54939			0.774694	−	0.632336i	$-0.217904\pi$
$97$	15.2597			1.54939			0.774694	+	0.632336i	$0.217904\pi$
$98$	1.38008	−	14.4107i	0.139409	−	1.45570i
$99$	−20.9889			−2.10946
$100$	4.85871	−	8.41554i	0.485871	−	0.841554i
$101$	−3.77017	−	6.53013i	−0.375146	−	0.649773i	0.615203	−	0.788369i	$-0.289074\pi$
$101$	−3.77017	−	6.53013i	−0.375146	−	0.649773i	−0.990349	+	0.138597i	$0.955741\pi$
$102$	12.3678	+	21.4216i	1.22459	+	2.12105i
$103$	3.34143	−	5.78752i	0.329241	−	0.570262i	−0.653121	−	0.757254i	$-0.726541\pi$
$103$	3.34143	−	5.78752i	0.329241	−	0.570262i	0.982361	+	0.186992i	$0.0598739\pi$
$104$		0			0
$105$	−1.22363	−	5.62869i	−0.119414	−	0.549304i
$106$	−16.4732			−1.60002
$107$	−1.05379	+	1.82522i	−0.101874	+	0.176451i	−0.912457	−	0.409173i	$-0.865817\pi$
$107$	−1.05379	+	1.82522i	−0.101874	+	0.176451i	0.810583	+	0.585624i	$0.199150\pi$
$108$	1.36703	+	2.36776i	0.131542	+	0.227838i
$109$	−3.38646	−	5.86553i	−0.324364	−	0.561816i	0.657019	−	0.753874i	$-0.271817\pi$
$109$	−3.38646	−	5.86553i	−0.324364	−	0.561816i	−0.981384	+	0.192058i	$0.938484\pi$
$110$	5.34957	−	9.26573i	0.510062	−	0.883452i
$111$	21.5722			2.04754
$112$	8.49053	+	2.71542i	0.802279	+	0.256583i
$113$	−4.76130			−0.447905			−0.223953	−	0.974600i	$-0.571896\pi$
$113$	−4.76130			−0.447905			−0.223953	+	0.974600i	$0.571896\pi$
$114$	7.80925	−	13.5260i	0.731403	−	1.26683i
$115$	−1.39259	−	2.41204i	−0.129860	−	0.224924i
$116$	−5.12337	−	8.87393i	−0.475693	−	0.823924i
$117$		0			0
$118$	13.7566			1.26640
$119$	9.20532	−	8.36586i	0.843850	−	0.766898i
$120$	−1.24725			−0.113858
$121$	−12.7723	+	22.1223i	−1.16112	+	2.01112i
$122$	11.6015	+	20.0944i	1.05035	+	1.81926i
$123$	−10.7803	−	18.6720i	−0.972024	−	1.68359i
$124$	−2.20938	+	3.82676i	−0.198408	+	0.343653i
$125$	−7.93114			−0.709382
$126$	14.0590	−	12.7769i	1.25247	−	1.13826i
$127$	9.73157			0.863537			0.431769	−	0.901984i	$-0.357890\pi$
$127$	9.73157			0.863537			0.431769	+	0.901984i	$0.357890\pi$
$128$	2.26956	−	3.93099i	0.200603	−	0.347454i
$129$	3.99387	+	6.91759i	0.351641	+	0.609060i
$130$		0			0
$131$	3.43578	−	5.95095i	0.300186	−	0.519937i	−0.675992	−	0.736909i	$-0.736285\pi$
$131$	3.43578	−	5.95095i	0.300186	−	0.519937i	0.976178	+	0.216972i	$0.0696181\pi$
$132$	35.0183			3.04795
$133$	−7.48088	−	2.39252i	−0.648675	−	0.207458i
$134$	20.1515			1.74082
$135$	0.513783	−	0.889898i	0.0442194	−	0.0765902i
$136$	−1.34670	−	2.33255i	−0.115478	−	0.200014i
$137$	4.22628	+	7.32013i	0.361075	+	0.625401i	0.988138	−	0.153568i	$-0.0490764\pi$
$137$	4.22628	+	7.32013i	0.361075	+	0.625401i	−0.627063	+	0.778969i	$0.715743\pi$
$138$	8.56143	−	14.8288i	0.728797	−	1.26231i
$139$	3.83558			0.325330			0.162665	−	0.986681i	$-0.447991\pi$
$139$	3.83558			0.325330			0.162665	+	0.986681i	$0.447991\pi$
$140$	1.09521	+	5.03795i	0.0925621	+	0.425785i
$141$	7.74502			0.652249
$142$	−5.53722	+	9.59075i	−0.464674	+	0.804838i
$143$		0			0
$144$	5.84897	+	10.1307i	0.487414	+	0.844226i
$145$	−1.92556	+	3.33517i	−0.159909	+	0.276971i
$146$	7.38349			0.611062
$147$	−14.5032	−	10.3337i	−1.19620	−	0.852309i
$148$	−19.3082			−1.58712
$149$	−3.82554	+	6.62603i	−0.313400	+	0.542825i	−0.979096	−	0.203398i	$-0.934802\pi$
$149$	−3.82554	+	6.62603i	−0.313400	+	0.542825i	0.665696	+	0.746223i	$0.268135\pi$
$150$	−11.2265	−	19.4449i	−0.916641	−	1.58767i
$151$	−1.42054	−	2.46044i	−0.115602	−	0.200228i	0.802418	−	0.596762i	$-0.203546\pi$
$151$	−1.42054	−	2.46044i	−0.115602	−	0.200228i	−0.918020	+	0.396534i	$0.870213\pi$
$152$	−0.850331	+	1.47282i	−0.0689710	+	0.119461i
$153$	16.3234			1.31966
$154$	−7.02663	−	32.3224i	−0.566222	−	2.60461i
$155$	1.66074			0.133394
$156$		0			0
$157$	−0.589296	−	1.02069i	−0.0470309	−	0.0814600i	0.841552	−	0.540177i	$-0.181643\pi$
$157$	−0.589296	−	1.02069i	−0.0470309	−	0.0814600i	−0.888583	+	0.458717i	$0.848309\pi$
$158$	0.838695	+	1.45266i	0.0667230	+	0.115568i
$159$	−10.1320	+	17.5492i	−0.803523	+	1.39174i
$160$	−6.94360			−0.548940
$161$	−8.20143	−	2.62296i	−0.646363	−	0.206718i
$162$	−15.2238			−1.19610
$163$	−0.833975	+	1.44449i	−0.0653220	+	0.113141i	−0.896837	−	0.442362i	$-0.854141\pi$
$163$	−0.833975	+	1.44449i	−0.0653220	+	0.113141i	0.831515	+	0.555503i	$0.187474\pi$
$164$	9.64886	+	16.7123i	0.753450	+	1.30501i
$165$	−6.58063	−	11.3980i	−0.512301	−	0.887332i
$166$	−17.6678	+	30.6014i	−1.37128	+	2.37513i
$167$	7.52717			0.582470			0.291235	−	0.956652i	$-0.405934\pi$
$167$	7.52717			0.582470			0.291235	+	0.956652i	$0.405934\pi$
$168$	−2.85360	+	2.59337i	−0.220160	+	0.200083i
$169$		0			0
$170$	−4.16044	+	7.20609i	−0.319091	+	0.552682i
$171$	−5.15345	−	8.92603i	−0.394094	−	0.682591i
$172$	−3.57471	−	6.19158i	−0.272569	−	0.472104i
$173$	−6.61949	+	11.4653i	−0.503271	+	0.871690i	0.496722	+	0.867910i	$0.334537\pi$
$173$	−6.61949	+	11.4653i	−0.503271	+	0.871690i	−0.999993	+	0.00378072i	$0.998797\pi$
$174$	−23.6760			−1.79488
$175$	−8.35590	+	7.59390i	−0.631646	+	0.574045i
$176$	20.3678			1.53528
$177$	8.46114	−	14.6551i	0.635978	−	1.10155i
$178$	−15.7175	−	27.2235i	−1.17808	−	2.04049i
$179$	−1.29857	−	2.24919i	−0.0970596	−	0.168112i	0.813407	−	0.581695i	$-0.197610\pi$
$179$	−1.29857	−	2.24919i	−0.0970596	−	0.168112i	−0.910466	+	0.413583i	$0.864277\pi$
$180$	−3.38282	+	5.85922i	−0.252141	+	0.436721i
$181$	10.1531			0.754677			0.377338	−	0.926075i	$-0.376839\pi$
$181$	10.1531			0.754677			0.377338	+	0.926075i	$0.376839\pi$
$182$		0			0
$183$	28.5425			2.10992
$184$	−0.932234	+	1.61468i	−0.0687252	+	0.119036i
$185$	3.62838	+	6.28454i	0.266764	+	0.462049i
$186$	5.10499	+	8.84209i	0.374316	+	0.648334i
$187$	14.2106	−	24.6136i	1.03919	−	1.79992i
$188$	−6.93217			−0.505581
$189$	−0.674851	−	3.10431i	−0.0490882	−	0.225805i
$190$	5.25397			0.381163
$191$	−7.48870	+	12.9708i	−0.541863	+	0.938534i	0.456934	+	0.889501i	$0.348947\pi$
$191$	−7.48870	+	12.9708i	−0.541863	+	0.938534i	−0.998797	+	0.0490337i	$0.984386\pi$
$192$	−12.7727	−	22.1229i	−0.921787	−	1.59658i
$193$	−9.62654	−	16.6737i	−0.692934	−	1.20020i	−0.970872	−	0.239597i	$-0.922985\pi$
$193$	−9.62654	−	16.6737i	−0.692934	−	1.20020i	0.277939	−	0.960599i	$-0.410349\pi$
$194$	−15.7792	+	27.3305i	−1.13288	+	1.96221i
$195$		0			0
$196$	12.9810	+	9.24916i	0.927217	+	0.660655i
$197$	−8.92091			−0.635589			−0.317794	−	0.948160i	$-0.602942\pi$
$197$	−8.92091			−0.635589			−0.317794	+	0.948160i	$0.602942\pi$
$198$	21.7035	−	37.5915i	1.54240	−	2.67151i
$199$	8.00019	+	13.8567i	0.567118	+	0.982278i	0.996849	+	0.0793207i	$0.0252751\pi$
$199$	8.00019	+	13.8567i	0.567118	+	0.982278i	−0.429731	+	0.902957i	$0.641392\pi$
$200$	1.22243	+	2.11731i	0.0864388	+	0.149716i
$201$	12.3944	−	21.4677i	0.874234	−	1.51422i
$202$	15.5941			1.09720
$203$	2.52921	+	11.6343i	0.177516	+	0.816571i
$204$	−27.2343			−1.90678
$205$	3.62642	−	6.28114i	0.253280	−	0.438694i
$206$	6.91039	+	11.9691i	0.481469	+	0.833929i
$207$	−5.64982	−	9.78577i	−0.392690	−	0.680158i
$208$		0			0
$209$	−17.9458			−1.24134
$210$	11.3464	+	3.62878i	0.782976	+	0.250410i
$211$	−6.97420			−0.480124			−0.240062	−	0.970758i	$-0.577168\pi$
$211$	−6.97420			−0.480124			−0.240062	+	0.970758i	$0.577168\pi$
$212$	9.06866	−	15.7074i	0.622838	−	1.07879i
$213$	6.81146	+	11.7978i	0.466714	+	0.808372i
$214$	−2.17934	−	3.77473i	−0.148977	−	0.258035i
$215$	−1.34352	+	2.32704i	−0.0916270	+	0.158703i
$216$	−0.687876			−0.0468040
$217$	3.79964	−	3.45314i	0.257936	−	0.234415i
$218$	14.0070			0.948677
$219$	4.54130	−	7.86577i	0.306873	−	0.531519i
$220$	5.88998	+	10.2017i	0.397102	+	0.687802i
$221$		0			0
$222$	−22.3067	+	38.6363i	−1.49713	+	2.59310i
$223$	−2.51316			−0.168294			−0.0841470	−	0.996453i	$-0.526817\pi$
$223$	−2.51316			−0.168294			−0.0841470	+	0.996453i	$0.526817\pi$
$224$	−15.8864	+	14.4377i	−1.06145	+	0.964656i
$225$	−14.8171			−0.987807
$226$	4.92341	−	8.52759i	0.327500	−	0.567247i
$227$	1.37060	+	2.37394i	0.0909697	+	0.157564i	0.907919	−	0.419145i	$-0.137670\pi$
$227$	1.37060	+	2.37394i	0.0909697	+	0.157564i	−0.816950	+	0.576709i	$0.804337\pi$
$228$	8.59813	+	14.8924i	0.569425	+	0.986274i
$229$	−2.89243	+	5.00984i	−0.191137	+	0.331060i	−0.945627	−	0.325252i	$-0.894551\pi$
$229$	−2.89243	+	5.00984i	−0.191137	+	0.331060i	0.754490	+	0.656311i	$0.227884\pi$
$230$	5.76003			0.379805
$231$	−38.7554	−	12.3947i	−2.54992	−	0.815510i
$232$	2.57803			0.169256
$233$	0.284639	−	0.493009i	0.0186473	−	0.0322981i	−0.856551	−	0.516062i	$-0.827397\pi$
$233$	0.284639	−	0.493009i	0.0186473	−	0.0322981i	0.875198	+	0.483764i	$0.160731\pi$
$234$		0			0
$235$	1.30269	+	2.25633i	0.0849781	+	0.147186i
$236$	−7.57313	+	13.1170i	−0.492969	+	0.853847i
$237$	2.06339			0.134032
$238$	5.46471	+	25.1376i	0.354225	+	1.62943i
$239$	3.52059			0.227728			0.113864	−	0.993496i	$-0.463677\pi$
$239$	3.52059			0.227728			0.113864	+	0.993496i	$0.463677\pi$
$240$	−3.66765	+	6.35255i	−0.236746	+	0.410056i
$241$	−11.4960	−	19.9116i	−0.740522	−	1.28262i	−0.952258	−	0.305295i	$-0.901245\pi$
$241$	−11.4960	−	19.9116i	−0.740522	−	1.28262i	0.211736	−	0.977327i	$-0.432088\pi$
$242$	−26.4143	−	45.7510i	−1.69798	−	2.94098i
$243$	−11.1647	+	19.3378i	−0.716215	+	1.24052i
$244$	−25.5469			−1.63548
$245$	0.571086	−	5.96324i	0.0364853	−	0.380978i
$246$	44.5892			2.84290
$247$		0			0
$248$	−0.555870	−	0.962795i	−0.0352978	−	0.0611376i
$249$	21.7335	+	37.6435i	1.37730	+	2.38556i
$250$	8.20117	−	14.2048i	0.518687	−	0.898393i
$251$	1.64123			0.103594			0.0517968	−	0.998658i	$-0.483505\pi$
$251$	1.64123			0.103594			0.0517968	+	0.998658i	$0.483505\pi$
$252$	4.44332	+	20.4392i	0.279903	+	1.28755i
$253$	−19.6743			−1.23691
$254$	−10.0629	+	17.4295i	−0.631402	+	1.09362i
$255$	5.11785	+	8.86438i	0.320492	+	0.555109i
$256$	−5.34770	−	9.26249i	−0.334231	−	0.578905i
$257$	3.39787	−	5.88529i	0.211953	−	0.367114i	−0.740372	−	0.672197i	$-0.765351\pi$
$257$	3.39787	−	5.88529i	0.211953	−	0.367114i	0.952326	+	0.305083i	$0.0986842\pi$
$258$	−16.5194			−1.02845
$259$	21.3687	+	6.83409i	1.32779	+	0.424650i
$260$		0			0
$261$	−7.81209	+	13.5309i	−0.483556	+	0.837544i
$262$	7.10552	+	12.3071i	0.438980	+	0.760336i
$263$	−1.65183	−	2.86105i	−0.101856	−	0.176420i	0.810593	−	0.585609i	$-0.199145\pi$
$263$	−1.65183	−	2.86105i	−0.101856	−	0.176420i	−0.912449	+	0.409190i	$0.865811\pi$
$264$	−4.40522	+	7.63007i	−0.271123	+	0.469598i
$265$	−6.81671			−0.418747
$266$	12.0206	−	10.9244i	0.737032	−	0.669821i
$267$	−38.6689			−2.36650
$268$	−11.0936	+	19.2147i	−0.677649	+	1.17372i
$269$	14.3595	+	24.8713i	0.875512	+	1.51643i	0.856216	+	0.516618i	$0.172809\pi$
$269$	14.3595	+	24.8713i	0.875512	+	1.51643i	0.0192964	+	0.999814i	$0.493857\pi$
$270$	1.06255	+	1.84039i	0.0646648	+	0.112003i
$271$	−9.25883	+	16.0368i	−0.562434	+	0.974164i	0.434850	+	0.900503i	$0.356801\pi$
$271$	−9.25883	+	16.0368i	−0.562434	+	0.974164i	−0.997283	+	0.0736605i	$0.976532\pi$
$272$	−15.8403			−0.960461
$273$		0			0
$274$	−17.4807			−1.05605
$275$	−12.8994	+	22.3423i	−0.777860	+	1.34729i
$276$	9.42630	+	16.3268i	0.567396	+	0.982759i
$277$	−4.01139	−	6.94793i	−0.241021	−	0.417460i	0.719984	−	0.693990i	$-0.244149\pi$
$277$	−4.01139	−	6.94793i	−0.241021	−	0.417460i	−0.961005	+	0.276530i	$0.910816\pi$
$278$	−3.96617	+	6.86961i	−0.237875	+	0.412012i
$279$	6.73772			0.403377
$280$	−1.23548	−	0.395130i	−0.0738343	−	0.0236135i
$281$	3.32260			0.198210			0.0991049	−	0.995077i	$-0.468402\pi$
$281$	3.32260			0.198210			0.0991049	+	0.995077i	$0.468402\pi$
$282$	−8.00872	+	13.8715i	−0.476912	+	0.826036i
$283$	−7.49996	−	12.9903i	−0.445826	−	0.772194i	0.552283	−	0.833657i	$-0.313757\pi$
$283$	−7.49996	−	12.9903i	−0.445826	−	0.772194i	−0.998109	+	0.0614630i	$0.980423\pi$
$284$	−6.09659	−	10.5596i	−0.361766	−	0.626597i
$285$	3.23151	−	5.59715i	0.191418	−	0.331546i
$286$		0			0
$287$	−4.76328	−	21.9110i	−0.281167	−	1.29337i
$288$	−28.1705			−1.65996
$289$	−2.55183	+	4.41989i	−0.150108	+	0.259994i
$290$	−3.98224	−	6.89744i	−0.233845	−	0.405032i
$291$	19.4104	+	33.6198i	1.13786	+	1.97083i
$292$	−4.06469	+	7.04024i	−0.237868	+	0.411999i
$293$	−18.8858			−1.10332			−0.551659	−	0.834070i	$-0.686005\pi$
$293$	−18.8858			−1.10332			−0.551659	+	0.834070i	$0.686005\pi$
$294$	33.5048	−	15.2899i	1.95404	−	0.891728i
$295$	5.69255			0.331433
$296$	2.42892	−	4.20702i	0.141178	−	0.244528i
$297$	−3.62931	−	6.28615i	−0.210594	−	0.364760i
$298$	−7.91157	−	13.7032i	−0.458305	−	0.793808i
$299$		0			0
$300$	24.7212			1.42728
$301$	1.76470	+	8.11760i	0.101716	+	0.467891i
$302$	5.87561			0.338104
$303$	9.59136	−	16.6127i	0.551009	−	0.954376i
$304$	5.00095	+	8.66190i	0.286824	+	0.496794i
$305$	4.80077	+	8.31518i	0.274891	+	0.476126i
$306$	−16.8791	+	29.2355i	−0.964914	+	1.67128i
$307$	−2.18025			−0.124433			−0.0622166	−	0.998063i	$-0.519817\pi$
$307$	−2.18025			−0.124433			−0.0622166	+	0.998063i	$0.519817\pi$
$308$	34.6880	+	11.0938i	1.97653	+	0.632130i
$309$	17.0012			0.967167
$310$	−1.71729	+	2.97443i	−0.0975353	+	0.168936i
$311$	1.69753	+	2.94021i	0.0962582	+	0.166724i	0.910133	−	0.414316i	$-0.135979\pi$
$311$	1.69753	+	2.94021i	0.0962582	+	0.166724i	−0.813875	+	0.581040i	$0.802646\pi$
$312$		0			0
$313$	−11.7269	+	20.3115i	−0.662841	+	1.14807i	0.317025	+	0.948417i	$0.397316\pi$
$313$	−11.7269	+	20.3115i	−0.662841	+	1.14807i	−0.979866	+	0.199657i	$0.936017\pi$
$314$	2.43744			0.137553
$315$	5.81770	−	5.28717i	0.327790	−	0.297898i
$316$	−1.84684			−0.103893
$317$	−11.5380	+	19.9845i	−0.648041	+	1.12244i	0.335549	+	0.942023i	$0.391078\pi$
$317$	−11.5380	+	19.9845i	−0.648041	+	1.12244i	−0.983590	+	0.180417i	$0.942255\pi$
$318$	−20.9540	−	36.2934i	−1.17504	−	2.03523i
$319$	13.6020	+	23.5593i	0.761564	+	1.31907i
$320$	4.29665	−	7.44201i	0.240190	−	0.416021i
$321$	−5.36171			−0.299261
$322$	13.1784	−	11.9767i	0.734406	−	0.667434i
$323$	13.9567			0.776571
$324$	8.38087	−	14.5161i	0.465604	−	0.806450i
$325$		0			0
$326$	−1.72474	−	2.98733i	−0.0955244	−	0.165453i
$327$	8.61519	−	14.9220i	0.476421	−	0.825186i
$328$	−4.85522			−0.268084
$329$	7.67196	+	2.45363i	0.422969	+	0.135273i
$330$	27.2187			1.49834
$331$	−8.47814	+	14.6846i	−0.466001	+	0.807137i	−0.999246	−	0.0388236i	$-0.987639\pi$
$331$	−8.47814	+	14.6846i	−0.466001	+	0.807137i	0.533245	+	0.845961i	$0.320972\pi$
$332$	−19.4525	−	33.6928i	−1.06760	−	1.84913i
$333$	14.7205	+	25.4967i	0.806680	+	1.39721i
$334$	−7.78345	+	13.4813i	−0.425891	+	0.737666i
$335$	8.33881			0.455598
$336$	4.81744	+	22.1602i	0.262813	+	1.20894i
$337$	−2.51749			−0.137136			−0.0685682	−	0.997646i	$-0.521843\pi$
$337$	−2.51749			−0.137136			−0.0685682	+	0.997646i	$0.521843\pi$
$338$		0			0
$339$	−6.05639	−	10.4900i	−0.328938	−	0.569738i
$340$	−4.58072	−	7.93405i	−0.248425	−	0.430284i
$341$	5.86567	−	10.1596i	0.317644	−	0.550175i
$342$	21.3156			1.15262
$343$	−11.0926	−	14.8308i	−0.598945	−	0.800790i
$344$	1.79876			0.0969826
$345$	3.54277	−	6.13626i	0.190736	−	0.330365i
$346$	−13.6897	−	23.7113i	−0.735964	−	1.27473i
$347$	−6.78120	−	11.7454i	−0.364034	−	0.630525i	0.624587	−	0.780956i	$-0.285267\pi$
$347$	−6.78120	−	11.7454i	−0.364034	−	0.630525i	−0.988621	+	0.150430i	$0.951934\pi$
$348$	13.0339	−	22.5754i	0.698690	−	1.21017i
$349$	1.15064			0.0615923			0.0307962	−	0.999526i	$-0.490196\pi$
$349$	1.15064			0.0615923			0.0307962	+	0.999526i	$0.490196\pi$
$350$	−4.96045	−	22.8180i	−0.265147	−	1.21968i
$351$		0			0
$352$	−24.5245	+	42.4776i	−1.30716	+	2.26406i
$353$	−9.74295	−	16.8753i	−0.518565	−	0.898180i	−0.999767	−	0.0215710i	$-0.993133\pi$
$353$	−9.74295	−	16.8753i	−0.518565	−	0.898180i	0.481203	−	0.876609i	$-0.340200\pi$
$354$	17.4984	+	30.3082i	0.930031	+	1.61086i
$355$	−2.29134	+	3.96871i	−0.121612	+	0.210637i
$356$	34.6105			1.83435
$357$	30.1407	+	9.63952i	1.59521	+	0.510178i
$358$	5.37112			0.283873
$359$	−11.6483	+	20.1755i	−0.614775	+	1.06482i	0.375649	+	0.926762i	$0.377420\pi$
$359$	−11.6483	+	20.1755i	−0.614775	+	1.06482i	−0.990424	+	0.138059i	$0.955913\pi$
$360$	−0.851102	−	1.47415i	−0.0448570	−	0.0776947i
$361$	5.09373	+	8.82260i	0.268091	+	0.464347i
$362$	−10.4988	+	18.1845i	−0.551806	+	0.955755i
$363$	−64.9857			−3.41087
$364$		0			0
$365$	3.05533			0.159924
$366$	−29.5143	+	51.1203i	−1.54274	+	2.67210i
$367$	−18.0334	−	31.2348i	−0.941337	−	1.63044i	−0.762925	−	0.646487i	$-0.776238\pi$
$367$	−18.0334	−	31.2348i	−0.941337	−	1.63044i	−0.178412	−	0.983956i	$-0.557096\pi$
$368$	5.48264	+	9.49621i	0.285802	+	0.495024i
$369$	14.7126	−	25.4829i	0.765905	−	1.32659i
$370$	−15.0077			−0.780212
$371$	−15.5961	+	14.1738i	−0.809707	+	0.735868i
$372$	−11.2414			−0.582838
$373$	−14.7970	+	25.6291i	−0.766157	+	1.32702i	0.173475	+	0.984838i	$0.444500\pi$
$373$	−14.7970	+	25.6291i	−0.766157	+	1.32702i	−0.939633	+	0.342185i	$0.888833\pi$
$374$	29.3889	+	50.9031i	1.51967	+	2.63214i
$375$	−10.0884	−	17.4737i	−0.520965	−	0.902337i
$376$	0.872051	−	1.51044i	0.0449726	−	0.0778948i
$377$		0			0
$378$	6.25771	+	2.00133i	0.321862	+	0.102937i
$379$	12.0481			0.618869			0.309435	−	0.950921i	$-0.399860\pi$
$379$	12.0481			0.618869			0.309435	+	0.950921i	$0.399860\pi$
$380$	−2.89236	+	5.00972i	−0.148375	+	0.256993i
$381$	12.3786	+	21.4404i	0.634175	+	1.09842i
$382$	−15.4873	−	26.8248i	−0.792400	−	1.37248i
$383$	−7.87833	+	13.6457i	−0.402564	+	0.697261i	−0.994035	−	0.109065i	$-0.965214\pi$
$383$	−7.87833	+	13.6457i	−0.402564	+	0.697261i	0.591471	+	0.806327i	$0.298548\pi$
$384$	11.5476			0.589284
$385$	−2.90766	−	13.3752i	−0.148188	−	0.681664i
$386$	39.8172			2.02664
$387$	−5.45071	+	9.44090i	−0.277075	+	0.479908i
$388$	−17.3733	−	30.0914i	−0.881994	−	1.52766i
$389$	18.6554	+	32.3122i	0.945869	+	1.63829i	0.754002	+	0.656872i	$0.228121\pi$
$389$	18.6554	+	32.3122i	0.945869	+	1.63829i	0.191866	+	0.981421i	$0.438546\pi$
$390$		0			0
$391$	15.3010			0.773804
$392$	−3.64826	+	1.66489i	−0.184265	+	0.0840895i
$393$	17.4813			0.881816
$394$	9.22464	−	15.9775i	0.464731	−	0.804937i
$395$	0.347057	+	0.601120i	0.0174623	+	0.0302456i
$396$	23.8959	+	41.3890i	1.20082	+	2.07987i
$397$	12.1746	−	21.0871i	0.611027	−	1.05833i	−0.380041	−	0.924970i	$-0.624090\pi$
$397$	12.1746	−	21.0871i	0.611027	−	1.05833i	0.991068	−	0.133360i	$-0.0425766\pi$
$398$	−33.0903			−1.65867
$399$	−4.24457	−	19.5250i	−0.212495	−	0.977472i
$400$	14.3787			0.718933
$401$	16.2032	−	28.0648i	0.809151	−	1.40149i	−0.104301	−	0.994546i	$-0.533261\pi$
$401$	16.2032	−	28.0648i	0.809151	−	1.40149i	0.913452	−	0.406945i	$-0.133406\pi$
$402$	25.6328	+	44.3973i	1.27845	+	2.21434i
$403$		0			0
$404$	−8.58473	+	14.8692i	−0.427106	+	0.739770i
$405$	−6.29972			−0.313035
$406$	−23.4527	−	7.50059i	−1.16394	−	0.372248i
$407$	51.2611			2.54092
$408$	3.42601	−	5.93402i	0.169613	−	0.293778i
$409$	4.19912	+	7.27308i	0.207633	+	0.359631i	0.950968	−	0.309288i	$-0.100091\pi$
$409$	4.19912	+	7.27308i	0.207633	+	0.359631i	−0.743336	+	0.668919i	$0.766757\pi$
$410$	7.49977	+	12.9900i	0.370387	+	0.641530i
$411$	−10.7517	+	18.6225i	−0.530342	+	0.918578i
$412$	−15.2169			−0.749685
$413$	13.0241	−	11.8364i	0.640873	−	0.582430i
$414$	23.3687			1.14851
$415$	−7.31102	+	12.6631i	−0.358884	+	0.621605i
$416$		0			0
$417$	4.87888	+	8.45046i	0.238920	+	0.413821i
$418$	18.5568	−	32.1413i	0.907641	−	1.57208i
$419$	−13.8684			−0.677518			−0.338759	−	0.940873i	$-0.610007\pi$
$419$	−13.8684			−0.677518			−0.338759	+	0.940873i	$0.610007\pi$
$420$	−9.70639	+	8.82124i	−0.473623	+	0.430432i
$421$	−10.1628			−0.495305			−0.247653	−	0.968849i	$-0.579659\pi$
$421$	−10.1628			−0.495305			−0.247653	+	0.968849i	$0.579659\pi$
$422$	7.21165	−	12.4909i	0.351058	−	0.608050i
$423$	5.28508	+	9.15402i	0.256969	+	0.445084i
$424$	2.28163	+	3.95190i	0.110806	+	0.191921i
$425$	10.0320	−	17.3760i	0.486624	−	0.842858i
$426$	−28.1735			−1.36501
$427$	28.2733	+	9.04230i	1.36824	+	0.437587i
$428$	4.79899			0.231968
$429$		0			0
$430$	−2.77852	−	4.81253i	−0.133992	−	0.232081i
$431$	7.42802	+	12.8657i	0.357795	+	0.619719i	0.987592	−	0.157040i	$-0.0501953\pi$
$431$	7.42802	+	12.8657i	0.357795	+	0.619719i	−0.629797	+	0.776760i	$0.716862\pi$
$432$	−2.02276	+	3.50353i	−0.0973202	+	0.168564i
$433$	−24.5778			−1.18113			−0.590566	−	0.806989i	$-0.701096\pi$
$433$	−24.5778			−1.18113			−0.590566	+	0.806989i	$0.701096\pi$
$434$	2.25565	+	10.3759i	0.108275	+	0.498062i
$435$	−9.79728			−0.469744
$436$	−7.71102	+	13.3559i	−0.369291	+	0.639630i
$437$	−4.83067	−	8.36697i	−0.231082	−	0.400247i
$438$	9.39184	+	16.2671i	0.448759	+	0.777274i
$439$	−2.29085	+	3.96786i	−0.109336	+	0.189376i	−0.915502	−	0.402315i	$-0.868206\pi$
$439$	−2.29085	+	3.96786i	−0.109336	+	0.189376i	0.806165	+	0.591690i	$0.201539\pi$
$440$	−2.96378			−0.141293
$441$	2.31692	−	24.1932i	0.110330	−	1.15206i
$442$		0			0
$443$	9.57761	−	16.5889i	0.455046	−	0.788163i	−0.543645	−	0.839315i	$-0.682956\pi$
$443$	9.57761	−	16.5889i	0.455046	−	0.788163i	0.998691	+	0.0511527i	$0.0162895\pi$
$444$	−24.5601	−	42.5393i	−1.16557	−	2.01883i
$445$	−6.50399	−	11.2652i	−0.308319	−	0.534023i
$446$	2.59873	−	4.50113i	0.123053	−	0.213135i
$447$	−19.4644			−0.920635
$448$	−5.64362	−	25.9606i	−0.266636	−	1.22652i
$449$	−14.4360			−0.681276			−0.340638	−	0.940195i	$-0.610643\pi$
$449$	−14.4360			−0.681276			−0.340638	+	0.940195i	$0.610643\pi$
$450$	15.3216	−	26.5378i	0.722266	−	1.25100i
$451$	−25.6167	−	44.3694i	−1.20624	−	2.08927i
$452$	5.42077	+	9.38904i	0.254971	+	0.441623i
$453$	3.61386	−	6.25939i	0.169794	−	0.294092i
$454$	−5.66905			−0.266062
$455$		0			0
$456$	−4.32650			−0.202607
$457$	14.4953	−	25.1066i	0.678062	−	1.17444i	−0.297502	−	0.954721i	$-0.596154\pi$
$457$	14.4953	−	25.1066i	0.678062	−	1.17444i	0.975564	−	0.219716i	$-0.0705131\pi$
$458$	−5.98182	−	10.3608i	−0.279512	−	0.484129i
$459$	2.82257	+	4.88884i	0.131746	+	0.228191i
$460$	−3.17095	+	5.49225i	−0.147846	+	0.256077i
$461$	31.7874			1.48049			0.740243	−	0.672339i	$-0.234710\pi$
$461$	31.7874			1.48049			0.740243	+	0.672339i	$0.234710\pi$
$462$	62.2741	−	56.5952i	2.89725	−	2.63305i
$463$	35.1655			1.63428			0.817139	−	0.576441i	$-0.195559\pi$
$463$	35.1655			1.63428			0.817139	+	0.576441i	$0.195559\pi$
$464$	7.58093	−	13.1306i	0.351936	−	0.609571i
$465$	2.11247	+	3.65891i	0.0979636	+	0.169678i
$466$	0.588659	+	1.01959i	0.0272691	+	0.0472315i
$467$	13.6721	−	23.6807i	0.632668	−	1.09581i	−0.354336	−	0.935118i	$-0.615293\pi$
$467$	13.6721	−	23.6807i	0.632668	−	1.09581i	0.987004	−	0.160695i	$-0.0513737\pi$
$468$		0			0
$469$	19.0785	−	17.3387i	0.880963	−	0.800626i
$470$	−5.38817			−0.248538
$471$	1.49917	−	2.59665i	0.0690783	−	0.119647i
$472$	−1.90536	−	3.30019i	−0.0877015	−	0.151903i
$473$	9.49046	+	16.4380i	0.436372	+	0.755818i
$474$	−2.13365	+	3.69558i	−0.0980016	+	0.169744i
$475$	−12.6688			−0.581286
$476$	−26.9774	−	8.62784i	−1.23651	−	0.395456i
$477$	−27.6558			−1.26627
$478$	−3.64046	+	6.30546i	−0.166511	+	0.288405i
$479$	−4.77298	−	8.26705i	−0.218083	−	0.377731i	0.736139	−	0.676831i	$-0.236647\pi$
$479$	−4.77298	−	8.26705i	−0.218083	−	0.377731i	−0.954222	+	0.299100i	$0.903314\pi$
$480$	−8.83229	−	15.2980i	−0.403137	−	0.698254i
$481$		0			0
$482$	47.5496			2.16582
$483$	−4.65341	−	21.4056i	−0.211737	−	0.973989i
$484$	58.1654			2.64388
$485$	−6.52955	+	11.3095i	−0.296491	+	0.513538i
$486$	−23.0896	−	39.9924i	−1.04737	−	1.81409i
$487$	−8.01770	−	13.8871i	−0.363316	−	0.629283i	0.625188	−	0.780474i	$-0.285022\pi$
$487$	−8.01770	−	13.8871i	−0.363316	−	0.629283i	−0.988504	+	0.151192i	$0.951689\pi$
$488$	3.21375	−	5.56637i	0.145479	−	0.251978i
$489$	−4.24328			−0.191888
$490$	10.0898	+	7.18910i	0.455809	+	0.324770i
$491$	−14.4662			−0.652849			−0.326425	−	0.945223i	$-0.605844\pi$
$491$	−14.4662			−0.652849			−0.326425	+	0.945223i	$0.605844\pi$
$492$	−24.5468	+	42.5163i	−1.10665	+	1.91678i
$493$	−10.5785	−	18.3224i	−0.476430	−	0.825200i
$494$		0			0
$495$	8.98103	−	15.5556i	0.403667	−	0.699172i
$496$	−6.53835			−0.293580
$497$	3.00966	+	13.8444i	0.135002	+	0.621006i
$498$	−89.8938			−4.02824
$499$	5.37252	−	9.30547i	0.240507	−	0.416570i	−0.720352	−	0.693609i	$-0.756020\pi$
$499$	5.37252	−	9.30547i	0.240507	−	0.416570i	0.960859	+	0.277039i	$0.0893530\pi$
$500$	9.02964	+	15.6398i	0.403818	+	0.699433i
$501$	9.57460	+	16.5837i	0.427762	+	0.740905i
$502$	−1.69711	+	2.93948i	−0.0757458	+	0.131196i
$503$	37.0876			1.65366			0.826828	−	0.562455i	$-0.190143\pi$
$503$	37.0876			1.65366			0.826828	+	0.562455i	$0.190143\pi$
$504$	−5.01242	−	1.60306i	−0.223271	−	0.0714060i
$505$	6.45295			0.287153
$506$	20.3441	−	35.2371i	0.904407	−	1.56648i
$507$		0			0
$508$	−11.0794	−	19.1902i	−0.491571	−	0.851426i
$509$	−11.0408	+	19.1232i	−0.489373	+	0.847620i	−0.999925	−	0.0122273i	$-0.996108\pi$
$509$	−11.0408	+	19.1232i	−0.489373	+	0.847620i	0.510552	+	0.859847i	$0.329441\pi$
$510$	−21.1684			−0.937352
$511$	6.99034	−	6.35288i	0.309235	−	0.281035i
$512$	31.1973			1.37874
$513$	1.78223	−	3.08691i	0.0786873	−	0.136290i
$514$	7.02712	+	12.1713i	0.309953	+	0.536854i
$515$	2.85956	+	4.95290i	0.126007	+	0.218251i
$516$	9.09409	−	15.7514i	0.400345	−	0.693418i
$517$	18.4042			0.809414
$518$	−34.3363	+	31.2051i	−1.50865	+	1.37107i
$519$	−33.6801			−1.47839
$520$		0			0
$521$	−5.39996	−	9.35300i	−0.236576	−	0.409762i	0.723153	−	0.690688i	$-0.242692\pi$
$521$	−5.39996	−	9.35300i	−0.236576	−	0.409762i	−0.959730	+	0.280925i	$0.909359\pi$
$522$	−16.1561	−	27.9833i	−0.707135	−	1.22479i
$523$	−4.85729	+	8.41307i	−0.212394	+	0.367878i	−0.952463	−	0.304653i	$-0.901459\pi$
$523$	−4.85729	+	8.41307i	−0.212394	+	0.367878i	0.740069	+	0.672531i	$0.234793\pi$
$524$	−15.6466			−0.683526
$525$	−27.3594	−	8.75003i	−1.19406	−	0.381883i
$526$	6.83226			0.297901
$527$	−4.56182	+	7.90130i	−0.198716	+	0.344186i
$528$	25.9079	+	44.8738i	1.12750	+	1.95288i
$529$	6.20404	+	10.7457i	0.269741	+	0.467205i
$530$	7.04880	−	12.2089i	0.306180	−	0.530320i
$531$	23.0950			1.00224
$532$	3.79910	+	17.4758i	0.164712	+	0.757673i
$533$		0			0
$534$	39.9854	−	69.2568i	1.73034	−	2.99703i
$535$	−0.901824	−	1.56200i	−0.0389892	−	0.0675314i
$536$	−2.79110	−	4.83432i	−0.120557	−	0.208811i
$537$	3.30357	−	5.72195i	0.142560	−	0.246920i
$538$	−59.3935			−2.56063
$539$	−34.4632	−	24.5555i	−1.48444	−	1.05768i
$540$	−2.33978			−0.100688
$541$	1.64011	−	2.84076i	0.0705139	−	0.122134i	−0.828613	−	0.559822i	$-0.810869\pi$
$541$	1.64011	−	2.84076i	0.0705139	−	0.122134i	0.899127	+	0.437689i	$0.144203\pi$
$542$	−19.1481	−	33.1655i	−0.822482	−	1.42458i
$543$	12.9148	+	22.3692i	0.554229	+	0.959952i
$544$	19.0730	−	33.0355i	0.817750	−	1.41638i
$545$	5.79620			0.248282
$546$		0			0
$547$	−24.8189			−1.06118			−0.530589	−	0.847629i	$-0.678029\pi$
$547$	−24.8189			−1.06118			−0.530589	+	0.847629i	$0.678029\pi$
$548$	9.62328	−	16.6680i	0.411086	−	0.712022i
$549$	19.4770	+	33.7351i	0.831256	+	1.43978i
$550$	−26.6771	−	46.2060i	−1.13751	−	1.97023i
$551$	−6.67945	+	11.5691i	−0.284554	+	0.492862i
$552$	−4.74322			−0.201885
$553$	2.04393	+	0.653685i	0.0869168	+	0.0277975i
$554$	16.5918			0.704920
$555$	−9.23064	+	15.9879i	−0.391819	+	0.678650i
$556$	−4.36683	−	7.56357i	−0.185195	−	0.320767i
$557$	5.84664	+	10.1267i	0.247730	+	0.429081i	0.962896	−	0.269874i	$-0.0869820\pi$
$557$	5.84664	+	10.1267i	0.247730	+	0.429081i	−0.715165	+	0.698955i	$0.753649\pi$
$558$	−6.96712	+	12.0674i	−0.294942	+	0.510854i
$559$		0			0
$560$	−5.64555	+	5.13072i	−0.238568	+	0.216812i
$561$	72.3040			3.05268
$562$	−3.43572	+	5.95085i	−0.144927	+	0.251021i
$563$	−14.2543	−	24.6891i	−0.600745	−	1.04052i	−0.992708	−	0.120540i	$-0.961537\pi$
$563$	−14.2543	−	24.6891i	−0.600745	−	1.04052i	0.391963	−	0.919981i	$-0.371796\pi$
$564$	−8.81775	−	15.2728i	−0.371294	−	0.643101i
$565$	2.03733	−	3.52877i	0.0857113	−	0.148456i
$566$	31.0212			1.30392
$567$	−14.4132	+	13.0988i	−0.605298	+	0.550100i
$568$	3.06775			0.128720
$569$	−1.86852	+	3.23638i	−0.0783326	+	0.135676i	−0.902531	−	0.430626i	$-0.858293\pi$
$569$	−1.86852	+	3.23638i	−0.0783326	+	0.135676i	0.824198	+	0.566302i	$0.191626\pi$
$570$	6.68307	+	11.5754i	0.279923	+	0.484841i
$571$	17.0218	+	29.4827i	0.712341	+	1.23381i	0.963976	+	0.265989i	$0.0856984\pi$
$571$	17.0218	+	29.4827i	0.712341	+	1.23381i	−0.251635	+	0.967822i	$0.580968\pi$
$572$		0			0
$573$	−38.1026			−1.59176
$574$	44.1686	+	14.1259i	1.84356	+	0.589604i
$575$	−13.8891			−0.579215
$576$	17.4317	−	30.1926i	0.726321	−	1.25803i
$577$	8.83774	+	15.3074i	0.367920	+	0.637256i	0.989240	−	0.146301i	$-0.0467367\pi$
$577$	8.83774	+	15.3074i	0.367920	+	0.637256i	−0.621320	+	0.783557i	$0.713403\pi$
$578$	−5.27742	−	9.14076i	−0.219512	−	0.380205i
$579$	24.4900	−	42.4179i	1.01777	−	1.76283i
$580$	8.76904			0.364115
$581$	9.60298	+	44.1736i	0.398399	+	1.83263i
$582$	−80.2851			−3.32792
$583$	−24.0763	+	41.7014i	−0.997139	+	1.72710i
$584$	−1.02266	−	1.77129i	−0.0423178	−	0.0732966i
$585$		0			0
$586$	19.5288	−	33.8248i	0.806726	−	1.39729i
$587$	24.4054			1.00732			0.503660	−	0.863902i	$-0.331987\pi$
$587$	24.4054			1.00732			0.503660	+	0.863902i	$0.331987\pi$
$588$	−3.86561	+	40.3645i	−0.159415	+	1.66460i
$589$	5.76085			0.237371
$590$	−5.88637	+	10.1955i	−0.242338	+	0.419742i
$591$	−11.3474	−	19.6543i	−0.466771	−	0.808471i
$592$	−14.2849	−	24.7422i	−0.587107	−	1.01690i
$593$	8.96144	−	15.5217i	0.368002	−	0.637398i	−0.621251	−	0.783612i	$-0.713375\pi$
$593$	8.96144	−	15.5217i	0.368002	−	0.637398i	0.989253	+	0.146213i	$0.0467086\pi$
$594$	15.0115			0.615930
$595$	2.26133	+	10.4021i	0.0927055	+	0.426444i
$596$	17.4216			0.713616
$597$	−20.3525	+	35.2516i	−0.832974	+	1.44275i
$598$		0			0
$599$	−6.28984	−	10.8943i	−0.256996	−	0.445130i	0.708440	−	0.705771i	$-0.249399\pi$
$599$	−6.28984	−	10.8943i	−0.256996	−	0.445130i	−0.965436	+	0.260641i	$0.916066\pi$
$600$	−3.10987	+	5.38645i	−0.126960	+	0.219901i
$601$	−14.3960			−0.587227			−0.293614	−	0.955924i	$-0.594858\pi$
$601$	−14.3960			−0.587227			−0.293614	+	0.955924i	$0.594858\pi$
$602$	−16.3636	−	5.23336i	−0.666930	−	0.213296i
$603$	33.8310			1.37770
$604$	−3.23458	+	5.60246i	−0.131613	+	0.227961i
$605$	−10.9304	−	18.9320i	−0.444384	−	0.769696i
$606$	19.8358	+	34.3567i	0.805775	+	1.39564i
$607$	4.07222	−	7.05328i	0.165286	−	0.286284i	−0.771471	−	0.636265i	$-0.780479\pi$
$607$	4.07222	−	7.05328i	0.165286	−	0.286284i	0.936757	+	0.349981i	$0.113812\pi$
$608$	−24.0862			−0.976824
$609$	−22.4153	+	20.3712i	−0.908316	+	0.825484i
$610$	−19.8569			−0.803982
$611$		0			0
$612$	−18.5842	−	32.1888i	−0.751223	−	1.30116i
$613$	7.82108	+	13.5465i	0.315890	+	0.547138i	0.979626	−	0.200829i	$-0.0643635\pi$
$613$	7.82108	+	13.5465i	0.315890	+	0.547138i	−0.663736	+	0.747967i	$0.731030\pi$
$614$	2.25448	−	3.90487i	0.0909833	−	0.157588i
$615$	18.4513			0.744027
$616$	−6.78088	+	6.16252i	−0.273209	+	0.248295i
$617$	31.9466			1.28612			0.643062	−	0.765814i	$-0.277664\pi$
$617$	31.9466			1.28612			0.643062	+	0.765814i	$0.277664\pi$
$618$	−17.5801	+	30.4496i	−0.707175	+	1.22486i
$619$	−14.0634	−	24.3585i	−0.565255	−	0.979050i	−0.997026	−	0.0770668i	$-0.975445\pi$
$619$	−14.0634	−	24.3585i	−0.565255	−	0.979050i	0.431771	−	0.901983i	$-0.357889\pi$
$620$	−1.89077	−	3.27490i	−0.0759350	−	0.131523i
$621$	1.95389	−	3.38424i	0.0784069	−	0.135805i
$622$	−7.02131			−0.281529
$623$	−38.3041	−	12.2503i	−1.53462	−	0.490799i
$624$		0			0
$625$	−7.27537	+	12.6013i	−0.291015	+	0.504052i
$626$	−24.2522	−	42.0061i	−0.969314	−	1.67890i
$627$	−22.8271	−	39.5377i	−0.911627	−	1.57898i
$628$	−1.34183	+	2.32412i	−0.0535450	+	0.0927426i
$629$	−39.8665			−1.58958
$630$	3.45366	+	15.8868i	0.137597	+	0.632945i
$631$	43.5970			1.73557			0.867784	−	0.496941i	$-0.165544\pi$
$631$	43.5970			1.73557			0.867784	+	0.496941i	$0.165544\pi$
$632$	0.232328	−	0.402404i	0.00924151	−	0.0160068i
$633$	−8.87121	−	15.3654i	−0.352599	−	0.610719i
$634$	−23.8617	−	41.3298i	−0.947671	−	1.64141i
$635$	−4.16409	+	7.21241i	−0.165247	+	0.286216i
$636$	46.1415			1.82963
$637$		0			0
$638$	−56.2603			−2.22737
$639$	−9.29607	+	16.1013i	−0.367747	+	0.636956i
$640$	1.94227	+	3.36410i	0.0767748	+	0.132978i
$641$	7.25722	+	12.5699i	0.286643	+	0.496480i	0.973006	−	0.230779i	$-0.0741273\pi$
$641$	7.25722	+	12.5699i	0.286643	+	0.496480i	−0.686363	+	0.727259i	$0.740794\pi$
$642$	5.54426	−	9.60294i	0.218814	−	0.378998i
$643$	19.0778			0.752355			0.376177	−	0.926548i	$-0.377238\pi$
$643$	19.0778			0.752355			0.376177	+	0.926548i	$0.377238\pi$
$644$	4.16502	+	19.1591i	0.164125	+	0.754973i
$645$	−6.83583			−0.269161
$646$	−14.4319	+	24.9967i	−0.567814	+	0.983483i
$647$	−7.62798	−	13.2120i	−0.299887	−	0.519419i	0.676223	−	0.736697i	$-0.263616\pi$
$647$	−7.62798	−	13.2120i	−0.299887	−	0.519419i	−0.976110	+	0.217278i	$0.930282\pi$
$648$	2.10859	+	3.65218i	0.0828332	+	0.143471i
$649$	20.1058	−	34.8243i	0.789223	−	1.36697i
$650$		0			0
$651$	12.4410	+	3.97887i	0.487603	+	0.155944i
$652$	3.79794			0.148739
$653$	−4.08480	+	7.07509i	−0.159851	+	0.276870i	−0.934815	−	0.355136i	$-0.884435\pi$
$653$	−4.08480	+	7.07509i	−0.159851	+	0.276870i	0.774964	+	0.632005i	$0.217768\pi$
$654$	17.8170	+	30.8600i	0.696701	+	1.20672i
$655$	2.94031	+	5.09276i	0.114887	+	0.198991i
$656$	−14.2772	+	24.7288i	−0.557431	+	0.965499i
$657$	12.3956			0.483600
$658$	−12.3277	+	11.2035i	−0.480583	+	0.436757i
$659$	1.86780			0.0727590			0.0363795	−	0.999338i	$-0.488417\pi$
$659$	1.86780			0.0727590			0.0363795	+	0.999338i	$0.488417\pi$
$660$	−14.9842	+	25.9533i	−0.583258	+	1.01023i
$661$	4.86593	+	8.42804i	0.189263	+	0.327813i	0.945005	−	0.327057i	$-0.106057\pi$
$661$	4.86593	+	8.42804i	0.189263	+	0.327813i	−0.755742	+	0.654870i	$0.772724\pi$
$662$	−17.5336	−	30.3691i	−0.681462	−	1.18033i
$663$		0			0
$664$	9.78833			0.379861
$665$	4.97421	−	4.52060i	0.192892	−	0.175301i
$666$	−60.8869			−2.35932
$667$	−7.32280	+	12.6835i	−0.283540	+	0.491106i
$668$	−8.56973	−	14.8432i	−0.331573	−	0.574301i
$669$	−3.19676	−	5.53694i	−0.123594	−	0.214071i
$670$	−8.62272	+	14.9350i	−0.333125	+	0.576989i
$671$	67.8243			2.61833
$672$	−52.0162	−	16.6357i	−2.00657	−	0.641736i
$673$	−20.5640			−0.792683			−0.396341	−	0.918103i	$-0.629720\pi$
$673$	−20.5640			−0.792683			−0.396341	+	0.918103i	$0.629720\pi$
$674$	2.60320	−	4.50888i	0.100272	−	0.173675i
$675$	−2.56212	−	4.43772i	−0.0986159	−	0.170808i
$676$		0			0
$677$	19.4613	−	33.7080i	0.747959	−	1.29550i	−0.200841	−	0.979624i	$-0.564367\pi$
$677$	19.4613	−	33.7080i	0.747959	−	1.29550i	0.948800	−	0.315879i	$-0.102299\pi$
$678$	25.0504			0.962054
$679$	8.57652	+	39.4519i	0.329137	+	1.51403i
$680$	2.30498			0.0883918
$681$	−3.48681	+	6.03933i	−0.133615	+	0.231428i
$682$	12.1308	+	21.0111i	0.464510	+	0.804556i
$683$	−18.6339	−	32.2749i	−0.713008	−	1.23497i	−0.963723	−	0.266905i	$-0.913999\pi$
$683$	−18.6339	−	32.2749i	−0.713008	−	1.23497i	0.250715	−	0.968061i	$-0.419334\pi$
$684$	−11.7345	+	20.3247i	−0.448678	+	0.777133i
$685$	−7.23361			−0.276382
$686$	38.0326	−	4.53135i	1.45209	−	0.173008i
$687$	−14.7167			−0.561479
$688$	5.28942	−	9.16154i	0.201657	−	0.349280i
$689$		0			0
$690$	7.32678	+	12.6904i	0.278926	+	0.483113i
$691$	7.52824	−	13.0393i	0.286388	−	0.496038i	−0.686557	−	0.727076i	$-0.740879\pi$
$691$	7.52824	−	13.0393i	0.286388	−	0.496038i	0.972945	+	0.231038i	$0.0742121\pi$
$692$	30.1453			1.14595
$693$	−11.7965	−	54.2639i	−0.448113	−	2.06131i
$694$	28.0483			1.06470
$695$	−1.64123	+	2.84269i	−0.0622552	+	0.107829i
$696$	3.27926	+	5.67985i	0.124300	+	0.215294i
$697$	19.9225	+	34.5067i	0.754617	+	1.30703i
$698$	−1.18982	+	2.06082i	−0.0450352	+	0.0780032i
$699$	1.44825			0.0547777
$700$	24.4880	+	7.83170i	0.925560	+	0.296011i
$701$	27.1442			1.02522			0.512612	−	0.858621i	$-0.328678\pi$
$701$	27.1442			1.02522			0.512612	+	0.858621i	$0.328678\pi$
$702$		0			0
$703$	12.5863	+	21.8000i	0.474700	+	0.822204i
$704$	−30.3511	−	52.5696i	−1.14390	−	1.98129i
$705$	−3.31406	+	5.74011i	−0.124815	+	0.216185i
$706$	40.2987			1.51666
$707$	14.7638	−	13.4175i	0.555250	−	0.504615i
$708$	−38.5322			−1.44813
$709$	4.39865	−	7.61869i	0.165195	−	0.286126i	−0.771530	−	0.636193i	$-0.780508\pi$
$709$	4.39865	−	7.61869i	0.165195	−	0.286126i	0.936724	+	0.350067i	$0.113841\pi$
$710$	−4.73870	−	8.20767i	−0.177840	−	0.308028i
$711$	1.40803	+	2.43877i	0.0528051	+	0.0914612i
$712$	−4.35392	+	7.54121i	−0.163170	+	0.282619i
$713$	6.31572			0.236526
$714$	−48.4315	+	44.0149i	−1.81250	+	1.64722i
$715$		0			0
$716$	−2.95686	+	5.12142i	−0.110503	+	0.191397i
$717$	4.47821	+	7.75649i	0.167242	+	0.289671i
$718$	−24.0898	−	41.7248i	−0.899024	−	1.55716i
$719$	−11.2528	+	19.4905i	−0.419660	+	0.726872i	−0.995905	−	0.0904047i	$-0.971184\pi$
$719$	−11.2528	+	19.4905i	−0.419660	+	0.726872i	0.576245	+	0.817277i	$0.304517\pi$
$720$	−10.0110			−0.373087
$721$	16.8409	+	5.38601i	0.627187	+	0.200585i
$722$	−21.0686			−0.784093
$723$	29.2459	−	50.6554i	1.08767	−	1.88389i
$724$	−11.5594	−	20.0215i	−0.429602	−	0.744092i
$725$	9.60232	+	16.6317i	0.356621	+	0.617686i
$726$	67.1983	−	116.391i	2.49396	−	4.31967i
$727$	34.9184			1.29505			0.647525	−	0.762044i	$-0.275804\pi$
$727$	34.9184			1.29505			0.647525	+	0.762044i	$0.275804\pi$
$728$		0			0
$729$	−34.7222			−1.28601
$730$	−3.15936	+	5.47217i	−0.116933	+	0.202534i
$731$	−7.38087	−	12.7840i	−0.272991	−	0.472835i
$732$	−32.4958	−	56.2844i	−1.20108	−	2.08033i
$733$	23.4693	−	40.6501i	0.866859	−	1.50144i	0.00167001	−	0.999999i	$-0.499468\pi$
$733$	23.4693	−	40.6501i	0.866859	−	1.50144i	0.865189	−	0.501446i	$-0.167198\pi$
$734$	74.5896			2.75315
$735$	13.8645	−	6.32707i	0.511400	−	0.233377i
$736$	−26.4061			−0.973344
$737$	29.4523	−	51.0129i	1.08489	−	1.87908i
$738$	30.4269	+	52.7010i	1.12003	+	1.93995i
$739$	18.0506	+	31.2646i	0.664003	+	1.15009i	0.979555	+	0.201178i	$0.0644771\pi$
$739$	18.0506	+	31.2646i	0.664003	+	1.15009i	−0.315552	+	0.948908i	$0.602190\pi$
$740$	8.26187	−	14.3100i	0.303712	−	0.526045i
$741$		0			0
$742$	−9.25856	−	42.5893i	−0.339892	−	1.56350i
$743$	−24.6750			−0.905238			−0.452619	−	0.891704i	$-0.649510\pi$
$743$	−24.6750			−0.905238			−0.452619	+	0.891704i	$0.649510\pi$
$744$	1.41414	−	2.44936i	0.0518448	−	0.0897979i
$745$	−3.27386	−	5.67049i	−0.119945	−	0.207751i
$746$	−30.6015	−	53.0033i	−1.12040	−	1.94059i
$747$	−29.6612	+	51.3747i	−1.08525	+	1.87970i
$748$	−64.7156			−2.36624
$749$	−5.31113	−	1.69859i	−0.194065	−	0.0620653i
$750$	41.7277			1.52368
$751$	25.6685	−	44.4591i	0.936656	−	1.62234i	0.165001	−	0.986293i	$-0.447237\pi$
$751$	25.6685	−	44.4591i	0.936656	−	1.62234i	0.771655	−	0.636042i	$-0.219429\pi$
$752$	−5.12869	−	8.88315i	−0.187024	−	0.323935i
$753$	2.08765	+	3.61592i	0.0760784	+	0.131772i
$754$		0			0
$755$	2.43136			0.0884864
$756$	−5.35321	+	4.86504i	−0.194695	+	0.176940i
$757$	43.1811			1.56944			0.784722	−	0.619848i	$-0.212806\pi$
$757$	43.1811			1.56944			0.784722	+	0.619848i	$0.212806\pi$
$758$	−12.4583	+	21.5784i	−0.452506	+	0.783763i
$759$	−25.0258	−	43.3459i	−0.908378	−	1.57336i
$760$	−0.727704	−	1.26042i	−0.0263966	−	0.0457203i
$761$	−14.6293	+	25.3387i	−0.530311	+	0.918526i	0.469063	+	0.883165i	$0.344592\pi$
$761$	−14.6293	+	25.3387i	−0.530311	+	0.918526i	−0.999375	+	0.0353617i	$0.988742\pi$
$762$	−51.2002			−1.85479
$763$	13.2612	−	12.0519i	0.480088	−	0.436308i
$764$	34.1037			1.23383
$765$	−6.98468	+	12.0978i	−0.252532	+	0.437397i
$766$	−16.2931	−	28.2205i	−0.588695	−	1.01965i
$767$		0			0
$768$	13.6046	−	23.5638i	0.490913	−	0.850287i
$769$	−32.3727			−1.16739			−0.583695	−	0.811973i	$-0.698394\pi$
$769$	−32.3727			−1.16739			−0.583695	+	0.811973i	$0.698394\pi$
$770$	26.9619	+	8.62291i	0.971641	+	0.310748i
$771$	17.2884			0.622628
$772$	−21.9197	+	37.9661i	−0.788909	+	1.36643i
$773$	−3.84579	−	6.66110i	−0.138323	−	0.239583i	0.788539	−	0.614985i	$-0.210838\pi$
$773$	−3.84579	−	6.66110i	−0.138323	−	0.239583i	−0.926862	+	0.375402i	$0.877505\pi$
$774$	−11.2726	−	19.5247i	−0.405184	−	0.701800i
$775$	4.14087	−	7.17220i	0.148745	−	0.257633i
$776$	8.74206			0.313822
$777$	12.1244	+	55.7720i	0.434960	+	2.00081i
$778$	−77.1624			−2.76641
$779$	12.5794	−	21.7882i	0.450705	−	0.780644i
$780$		0			0
$781$	16.1858	+	28.0346i	0.579173	+	1.00316i
$782$	−15.8219	+	27.4044i	−0.565791	+	0.979979i
$783$	−5.40335			−0.193100
$784$	−2.24836	+	23.4773i	−0.0802987	+	0.838474i
$785$	1.00863			0.0359994
$786$	−18.0765	+	31.3094i	−0.644767	+	1.11677i
$787$	25.5919	+	44.3265i	0.912253	+	1.58007i	0.810874	+	0.585220i	$0.198992\pi$
$787$	25.5919	+	44.3265i	0.912253	+	1.58007i	0.101378	+	0.994848i	$0.467675\pi$
$788$	10.1565	+	17.5916i	0.361811	+	0.626674i
$789$	4.20226	−	7.27853i	0.149604	−	0.259122i
$790$	−1.43549			−0.0510725
$791$	−2.67603	−	12.3097i	−0.0951486	−	0.437682i
$792$	−12.0242			−0.427262
$793$		0			0
$794$	25.1783	+	43.6100i	0.893543	+	1.54766i
$795$	−8.67089	−	15.0184i	−0.307525	−	0.532649i
$796$	18.2165	−	31.5519i	0.645667	−	1.11833i
$797$	−3.10414			−0.109954			−0.0549771	−	0.998488i	$-0.517509\pi$
$797$	−3.10414			−0.109954			−0.0549771	+	0.998488i	$0.517509\pi$
$798$	39.3588	+	12.5876i	1.39329	+	0.445597i
$799$	−14.3132			−0.506364
$800$	−17.3131	+	29.9871i	−0.612109	+	1.06020i
$801$	−26.3870	−	45.7036i	−0.932339	−	1.61486i
$802$	33.5098	+	58.0407i	1.18327	+	2.04949i
$803$	10.7913	−	18.6911i	0.380816	−	0.659594i
$804$	−56.4444			−1.99064
$805$	5.45332	−	4.95602i	0.192204	−	0.174677i
$806$		0			0
$807$	−36.5306	+	63.2729i	−1.28594	+	2.22731i
$808$	−2.15988	−	3.74102i	−0.0759842	−	0.131609i
$809$	−18.8405	−	32.6327i	−0.662397	−	1.14731i	−0.979984	−	0.199076i	$-0.936206\pi$
$809$	−18.8405	−	32.6327i	−0.662397	−	1.14731i	0.317587	−	0.948229i	$-0.397127\pi$
$810$	6.51420	−	11.2829i	0.228886	−	0.396442i
$811$	22.0872			0.775587			0.387793	−	0.921746i	$-0.373237\pi$
$811$	22.0872			0.775587			0.387793	+	0.921746i	$0.373237\pi$
$812$	20.0628	−	18.2332i	0.704067	−	0.639862i
$813$	−47.1091			−1.65219
$814$	−53.0064	+	91.8097i	−1.85787	+	3.21793i
$815$	−0.713707	−	1.23618i	−0.0250001	−	0.0433014i
$816$	−20.1490	−	34.8990i	−0.705355	−	1.22171i
$817$	−4.66043	+	8.07210i	−0.163048	+	0.282407i
$818$	−17.3683			−0.607269
$819$		0			0
$820$	−16.5148			−0.576721
$821$	11.6792	−	20.2290i	0.407608	−	0.705998i	−0.587013	−	0.809578i	$-0.699696\pi$
$821$	11.6792	−	20.2290i	0.407608	−	0.705998i	0.994621	+	0.103579i	$0.0330296\pi$
$822$	−22.2355	−	38.5130i	−0.775552	−	1.34330i
$823$	23.1698	+	40.1312i	0.807647	+	1.39889i	0.914490	+	0.404609i	$0.132593\pi$
$823$	23.1698	+	40.1312i	0.807647	+	1.39889i	−0.106843	+	0.994276i	$0.534074\pi$
$824$	1.91425	−	3.31559i	0.0666862	−	0.115504i
$825$	−65.6321			−2.28502
$826$	7.73171	+	35.5658i	0.269021	+	1.23749i
$827$	−32.2703			−1.12215			−0.561074	−	0.827766i	$-0.689612\pi$
$827$	−32.2703			−1.12215			−0.561074	+	0.827766i	$0.689612\pi$
$828$	−12.8647	+	22.2823i	−0.447079	+	0.774364i
$829$	25.0902	+	43.4574i	0.871417	+	1.50934i	0.860531	+	0.509398i	$0.170132\pi$
$829$	25.0902	+	43.4574i	0.871417	+	1.50934i	0.0108858	+	0.999941i	$0.496535\pi$
$830$	−15.1199	−	26.1884i	−0.524819	−	0.909012i
$831$	10.2050	−	17.6756i	0.354008	−	0.613159i
$832$		0			0
$833$	26.8025	+	19.0972i	0.928653	+	0.661678i
$834$	−20.1800			−0.698775
$835$	−3.22084	+	5.57866i	−0.111462	+	0.193057i
$836$	20.4314	+	35.3882i	0.706634	+	1.22393i
$837$	1.16506	+	2.01794i	0.0402704	+	0.0697503i
$838$	14.3406	−	24.8387i	0.495389	−	0.858038i
$839$	33.2701			1.14861			0.574306	−	0.818640i	$-0.305272\pi$
$839$	33.2701			1.14861			0.574306	+	0.818640i	$0.305272\pi$
$840$	−0.701000	−	3.22459i	−0.0241868	−	0.111259i
$841$	−8.74929			−0.301700
$842$	10.5088	−	18.2018i	0.362158	−	0.627276i
$843$	4.22636	+	7.32027i	0.145564	+	0.252124i
$844$	7.94016	+	13.7528i	0.273312	+	0.473390i
$845$		0			0
$846$	−21.8601			−0.751565
$847$	−64.3727	−	20.5875i	−2.21187	−	0.707396i
$848$	26.8374			0.921600
$849$	19.0800	−	33.0475i	0.654822	−	1.13419i
$850$	20.7471	+	35.9351i	0.711621	+	1.23256i
$851$	13.7985	+	23.8998i	0.473008	+	0.819274i
$852$	15.5098	−	26.8637i	0.531356	−	0.920336i
$853$	50.9815			1.74557			0.872787	−	0.488102i	$-0.162310\pi$
$853$	50.9815			1.74557			0.872787	+	0.488102i	$0.162310\pi$
$854$	−45.4309	+	41.2879i	−1.55461	+	1.41284i
$855$	8.82053			0.301656
$856$	−0.603702	+	1.04564i	−0.0206341	+	0.0357393i
$857$	2.28231	+	3.95307i	0.0779621	+	0.135034i	0.902371	−	0.430961i	$-0.141825\pi$
$857$	2.28231	+	3.95307i	0.0779621	+	0.135034i	−0.824408	+	0.565995i	$0.808492\pi$
$858$		0			0
$859$	−5.63635	+	9.76245i	−0.192310	+	0.333090i	−0.946015	−	0.324122i	$-0.894931\pi$
$859$	−5.63635	+	9.76245i	−0.192310	+	0.333090i	0.753705	+	0.657212i	$0.228265\pi$
$860$	6.11840			0.208636
$861$	42.2150	−	38.3653i	1.43868	−	1.30748i
$862$	−30.7237			−1.04645
$863$	7.17807	−	12.4328i	0.244344	−	0.423217i	−0.717603	−	0.696453i	$-0.754761\pi$
$863$	7.17807	−	12.4328i	0.244344	−	0.423217i	0.961947	+	0.273236i	$0.0880940\pi$
$864$	−4.87114	−	8.43706i	−0.165720	−	0.287035i
$865$	−5.66489	−	9.81188i	−0.192612	−	0.333614i
$866$	25.4146	−	44.0193i	0.863622	−	1.49584i
$867$	−12.9837			−0.440951
$868$	−11.1353	−	3.56128i	−0.377958	−	0.120878i
$869$	4.90315			0.166328
$870$	10.1308	−	17.5471i	0.343468	−	0.594904i
$871$		0			0
$872$	−1.94005	−	3.36027i	−0.0656985	−	0.113793i
$873$	−26.4907	+	45.8832i	−0.896574	+	1.55291i
$874$	19.9806			0.675853
$875$	−4.45759	−	20.5049i	−0.150694	−	0.693192i
$876$	−20.6812			−0.698753
$877$	25.1533	−	43.5668i	0.849367	−	1.47115i	−0.0324068	−	0.999475i	$-0.510317\pi$
$877$	25.1533	−	43.5668i	0.849367	−	1.47115i	0.881774	−	0.471672i	$-0.156349\pi$
$878$	−4.73769	−	8.20591i	−0.159889	−	0.276936i
$879$	−24.0228	−	41.6087i	−0.810268	−	1.40343i
$880$	−8.71527	+	15.0953i	−0.293792	+	0.508862i
$881$	30.3462			1.02239			0.511194	−	0.859465i	$-0.329203\pi$
$881$	30.3462			1.02239			0.511194	+	0.859465i	$0.329203\pi$
$882$	40.9347	+	29.1665i	1.37834	+	0.982088i
$883$	−34.6742			−1.16688			−0.583440	−	0.812156i	$-0.698294\pi$
$883$	−34.6742			−1.16688			−0.583440	+	0.812156i	$0.698294\pi$
$884$		0			0
$885$	7.24095	+	12.5417i	0.243402	+	0.421585i
$886$	19.8074	+	34.3074i	0.665442	+	1.15258i
$887$	28.3867	−	49.1672i	0.953132	−	1.65087i	0.214546	−	0.976714i	$-0.431173\pi$
$887$	28.3867	−	49.1672i	0.953132	−	1.65087i	0.738586	−	0.674159i	$-0.235494\pi$
$888$	12.3584			0.414721
$889$	5.46951	+	25.1597i	0.183441	+	0.843828i
$890$	26.9017			0.901747
$891$	−22.2503	+	38.5386i	−0.745413	+	1.29109i
$892$	2.86125	+	4.95583i	0.0958018	+	0.165934i
$893$	4.51882	+	7.82682i	0.151216	+	0.261914i
$894$	20.1271	−	34.8612i	0.673151	−	1.16593i
$895$	2.22260			0.0742934
$896$	11.4386	+	3.65828i	0.382138	+	0.122214i
$897$		0			0
$898$	14.9275	−	25.8551i	0.498136	−	0.862797i
$899$	−4.36642	−	7.56287i	−0.145628	−	0.252236i
$900$	16.8694	+	29.2186i	0.562312	+	0.973953i
$901$	18.7245	−	32.4318i	0.623804	−	1.08046i
$902$	105.955			3.52793
$903$	−15.6398	+	14.2136i	−0.520460	+	0.472998i
$904$	−2.72768			−0.0907212
$905$	−4.34447	+	7.52485i	−0.144415	+	0.250134i
$906$	7.47381	+	12.9450i	0.248301	+	0.430069i
$907$	−4.68516	−	8.11494i	−0.155568	−	0.269452i	0.777698	−	0.628639i	$-0.216388\pi$
$907$	−4.68516	−	8.11494i	−0.155568	−	0.269452i	−0.933266	+	0.359186i	$0.883054\pi$
$908$	3.12086	−	5.40550i	0.103570	−	0.179388i
$909$	26.1799			0.868334
$910$		0			0
$911$	−10.0569			−0.333200			−0.166600	−	0.986025i	$-0.553279\pi$
$911$	−10.0569			−0.333200			−0.166600	+	0.986025i	$0.553279\pi$
$912$	−12.7225	+	22.0360i	−0.421283	+	0.729683i
$913$	51.6443	+	89.4506i	1.70918	+	2.96038i
$914$	29.9776	+	51.9228i	0.991572	+	1.71745i
$915$	−12.2132	+	21.1539i	−0.403756	+	0.699326i
$916$	13.1722			0.435222
$917$	17.3164	+	5.53810i	0.571838	+	0.182884i
$918$	−11.6747			−0.385322
$919$	−19.4310	+	33.6555i	−0.640969	+	1.11019i	0.344248	+	0.938879i	$0.388134\pi$
$919$	−19.4310	+	33.6555i	−0.640969	+	1.11019i	−0.985217	+	0.171312i	$0.945199\pi$
$920$	−0.797796	−	1.38182i	−0.0263026	−	0.0455574i
$921$	−2.77328	−	4.80347i	−0.0913828	−	0.158280i
$922$	−32.8696	+	56.9319i	−1.08250	+	1.87495i
$923$		0			0
$924$	19.6816	+	90.5352i	0.647477	+	2.97839i
$925$	36.1878			1.18985
$926$	−36.3627	+	62.9821i	−1.19495	+	2.06972i
$927$	11.6014	+	20.0942i	0.381039	+	0.659979i
$928$	18.2561	+	31.6205i	0.599286	+	1.03799i
$929$	−17.6449	+	30.5619i	−0.578912	+	1.00270i	0.416693	+	0.909047i	$0.363189\pi$
$929$	−17.6449	+	30.5619i	−0.578912	+	1.00270i	−0.995604	+	0.0936573i	$0.970144\pi$
$930$	−8.73759			−0.286517
$931$	1.98100	−	20.6855i	0.0649247	−	0.677940i
$932$	−1.29625			−0.0424601
$933$	−4.31853	+	7.47992i	−0.141382	+	0.244882i
$934$	28.2751	+	48.9740i	0.925191	+	1.60248i
$935$	12.1613	+	21.0640i	0.397718	+	0.688867i
$936$		0			0
$937$	12.0937			0.395085			0.197543	−	0.980294i	$-0.436704\pi$
$937$	12.0937			0.395085			0.197543	+	0.980294i	$0.436704\pi$
$938$	11.3259	+	52.0990i	0.369804	+	1.70109i
$939$	−59.6664			−1.94714
$940$	2.96624	−	5.13768i	0.0967481	−	0.167573i
$941$	2.85549	+	4.94585i	0.0930863	+	0.161230i	0.908808	−	0.417214i	$-0.136993\pi$
$941$	2.85549	+	4.94585i	0.0930863	+	0.161230i	−0.815722	+	0.578444i	$0.803660\pi$
$942$	3.10043	+	5.37011i	0.101018	+	0.174968i
$943$	13.7911	−	23.8868i	0.449099	−	0.777863i
$944$	−22.4116			−0.729435
$945$	2.58948	+	0.828161i	0.0842357	+	0.0269401i
$946$	−39.2543			−1.27627
$947$	5.36589	−	9.29400i	0.174368	−	0.302014i	−0.765574	−	0.643347i	$-0.777545\pi$
$947$	5.36589	−	9.29400i	0.174368	−	0.302014i	0.939942	+	0.341333i	$0.110878\pi$
$948$	−2.34919	−	4.06891i	−0.0762980	−	0.132152i
$949$		0			0
$950$	13.1002	−	22.6902i	0.425026	−	0.736166i
$951$	−58.7057			−1.90366
$952$	5.27359	−	4.79268i	0.170918	−	0.155332i
$953$	39.1509			1.26822			0.634111	−	0.773242i	$-0.281366\pi$
$953$	39.1509			1.26822			0.634111	+	0.773242i	$0.281366\pi$
$954$	28.5973	−	49.5320i	0.925873	−	1.60366i
$955$	−6.40875	−	11.1003i	−0.207382	−	0.359196i
$956$	−4.00822	−	6.94243i	−0.129635	−	0.224534i
$957$	−34.6035	+	59.9351i	−1.11857	+	1.93743i
$958$	19.7420			0.637834
$959$	−16.5499	+	15.0407i	−0.534423	+	0.485688i
$960$	21.8614			0.705574
$961$	13.6170	−	23.5854i	0.439259	−	0.760819i
$962$		0			0
$963$	−3.65874	−	6.33713i	−0.117901	−	0.204211i
$964$	−26.1765	+	45.3390i	−0.843088	+	1.46027i
$965$	16.4766			0.530400
$966$	43.1498	+	13.8001i	1.38832	+	0.444010i
$967$	−0.254316			−0.00817824			−0.00408912	−	0.999992i	$-0.501302\pi$
$967$	−0.254316			−0.00817824			−0.00408912	+	0.999992i	$0.501302\pi$
$968$	−7.31707	+	12.6735i	−0.235179	+	0.407343i
$969$	17.7530	+	30.7491i	0.570308	+	0.987802i
$970$	−13.5037	−	23.3891i	−0.433578	−	0.750979i
$971$	−3.32449	+	5.75819i	−0.106688	+	0.184789i	−0.914427	−	0.404752i	$-0.867358\pi$
$971$	−3.32449	+	5.75819i	−0.106688	+	0.184789i	0.807739	+	0.589541i	$0.200691\pi$
$972$	50.8442			1.63083
$973$	2.15574	+	9.91638i	0.0691099	+	0.317905i
$974$	33.1627			1.06260
$975$		0			0
$976$	−18.9006	−	32.7368i	−0.604994	−	1.04788i
$977$	3.15138	+	5.45835i	0.100822	+	0.174628i	0.912023	−	0.410138i	$-0.134520\pi$
$977$	3.15138	+	5.45835i	0.100822	+	0.174628i	−0.811202	+	0.584766i	$0.801186\pi$
$978$	4.38775	−	7.59980i	0.140305	−	0.243015i
$979$	−91.8871			−2.93672
$980$	−12.4094	+	5.66303i	−0.396404	+	0.180899i
$981$	23.5155			0.750791
$982$	14.9587	−	25.9092i	0.477351	−	0.826797i
$983$	10.1137	+	17.5174i	0.322575	+	0.558717i	0.981019	−	0.193913i	$-0.0621181\pi$
$983$	10.1137	+	17.5174i	0.322575	+	0.558717i	−0.658443	+	0.752630i	$0.728785\pi$
$984$	−6.17586	−	10.6969i	−0.196879	−	0.341005i
$985$	3.81721	−	6.61160i	0.121626	−	0.210663i
$986$	43.7545			1.39343
$987$	4.35299	+	20.0237i	0.138557	+	0.637362i
$988$		0			0
$989$	−5.10932	+	8.84960i	−0.162467	+	0.281401i
$990$	18.5736	+	32.1704i	0.590308	+	1.02244i
$991$	24.1825	+	41.8854i	0.768183	+	1.33053i	0.938547	+	0.345151i	$0.112172\pi$
$991$	24.1825	+	41.8854i	0.768183	+	1.33053i	−0.170364	+	0.985381i	$0.554494\pi$
$992$	7.87270	−	13.6359i	0.249958	−	0.432941i
$993$	−43.1369			−1.36891
$994$	−27.9077	−	8.92539i	−0.885179	−	0.283096i
$995$	−13.6930			−0.434096
$996$	49.4874	−	85.7147i	1.56807	−	2.71598i
$997$	−0.877445	−	1.51978i	−0.0277890	−	0.0481319i	0.851796	−	0.523873i	$-0.175513\pi$
$997$	−0.877445	−	1.51978i	−0.0277890	−	0.0481319i	−0.879585	+	0.475741i	$0.842180\pi$
$998$	11.1109	+	19.2446i	0.351708	+	0.609177i
$999$	−5.09083	+	8.81758i	−0.161067	+	0.278976i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.l.170.4	yes	48
7.2	even	3		8281.2.a.cu.1.21		24
7.4	even	3	inner	1183.2.e.l.508.4	yes	48
7.5	odd	6		8281.2.a.ct.1.21		24
13.12	even	2		1183.2.e.k.170.21	✓	48
91.12	odd	6		8281.2.a.cw.1.4		24
91.25	even	6		1183.2.e.k.508.21	yes	48
91.51	even	6		8281.2.a.cv.1.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.e.k.170.21	✓	48	13.12	even	2
1183.2.e.k.508.21	yes	48	91.25	even	6
1183.2.e.l.170.4	yes	48	1.1	even	1	trivial
1183.2.e.l.508.4	yes	48	7.4	even	3	inner
8281.2.a.ct.1.21		24	7.5	odd	6
8281.2.a.cu.1.21		24	7.2	even	3
8281.2.a.cv.1.4		24	91.51	even	6
8281.2.a.cw.1.4		24	91.12	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)

\(f(q)\)	\(=\)	\(q+(-1.03405 + 1.79102i) q^{2} +(1.27200 + 2.20318i) q^{3} +(-1.13851 - 1.97195i) q^{4} +(-0.427895 + 0.741135i) q^{5} -5.26125 q^{6} +(0.562037 + 2.58537i) q^{7} +0.572885 q^{8} +(-1.73599 + 3.00682i) q^{9} +O(q^{10})\)	\(q+(-1.03405 + 1.79102i) q^{2} +(1.27200 + 2.20318i) q^{3} +(-1.13851 - 1.97195i) q^{4} +(-0.427895 + 0.741135i) q^{5} -5.26125 q^{6} +(0.562037 + 2.58537i) q^{7} +0.572885 q^{8} +(-1.73599 + 3.00682i) q^{9} +(-0.884926 - 1.53274i) q^{10} +(3.02261 + 5.23531i) q^{11} +(2.89637 - 5.01666i) q^{12} +(-5.21162 - 1.66677i) q^{14} -2.17714 q^{15} +(1.68462 - 2.91785i) q^{16} +(-2.35073 - 4.07158i) q^{17} +(-3.59019 - 6.21839i) q^{18} +(-1.48430 + 2.57088i) q^{19} +1.94864 q^{20} +(-4.98110 + 4.52686i) q^{21} -12.5021 q^{22} +(-1.62726 + 2.81850i) q^{23} +(0.728712 + 1.26217i) q^{24} +(2.13381 + 3.69587i) q^{25} -1.20072 q^{27} +(4.45833 - 4.05176i) q^{28} +4.50008 q^{29} +(2.25126 - 3.89930i) q^{30} +(-0.970299 - 1.68061i) q^{31} +(4.05684 + 7.02665i) q^{32} +(-7.68954 + 13.3187i) q^{33} +9.72304 q^{34} +(-2.15660 - 0.689719i) q^{35} +7.90574 q^{36} +(4.23981 - 7.34356i) q^{37} +(-3.06966 - 5.31681i) q^{38} +(-0.245135 + 0.424586i) q^{40} -8.47502 q^{41} +(-2.95702 - 13.6022i) q^{42} +3.13983 q^{43} +(6.88251 - 11.9209i) q^{44} +(-1.48564 - 2.57321i) q^{45} +(-3.36533 - 5.82892i) q^{46} +(1.52221 - 2.63654i) q^{47} +8.57138 q^{48} +(-6.36823 + 2.90614i) q^{49} -8.82585 q^{50} +(5.98027 - 10.3581i) q^{51} +(3.98271 + 6.89825i) q^{53} +(1.24160 - 2.15052i) q^{54} -5.17343 q^{55} +(0.321983 + 1.48112i) q^{56} -7.55212 q^{57} +(-4.65329 + 8.05974i) q^{58} +(-3.32591 - 5.76064i) q^{59} +(2.47868 + 4.29320i) q^{60} +(5.60975 - 9.71638i) q^{61} +4.01334 q^{62} +(-8.74943 - 2.79822i) q^{63} -10.0414 q^{64} +(-15.9027 - 27.5443i) q^{66} +(-4.87200 - 8.43855i) q^{67} +(-5.35263 + 9.27103i) q^{68} -8.27953 q^{69} +(3.46532 - 3.14931i) q^{70} +5.35491 q^{71} +(-0.994523 + 1.72256i) q^{72} +(-1.78510 - 3.09188i) q^{73} +(8.76832 + 15.1872i) q^{74} +(-5.42844 + 9.40233i) q^{75} +6.75952 q^{76} +(-11.8364 + 10.7570i) q^{77} +(0.405540 - 0.702416i) q^{79} +(1.44168 + 2.49706i) q^{80} +(3.68065 + 6.37507i) q^{81} +(8.76357 - 15.1790i) q^{82} +17.0860 q^{83} +(14.5978 + 4.66862i) q^{84} +4.02345 q^{85} +(-3.24673 + 5.62350i) q^{86} +(5.72412 + 9.91447i) q^{87} +(1.73161 + 2.99923i) q^{88} +(-7.59999 + 13.1636i) q^{89} +6.14489 q^{90} +7.41058 q^{92} +(2.46845 - 4.27548i) q^{93} +(3.14807 + 5.45262i) q^{94} +(-1.27024 - 2.20013i) q^{95} +(-10.3206 + 17.8759i) q^{96} +15.2597 q^{97} +(1.38008 - 14.4107i) q^{98} -20.9889 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9}+O(q^{10}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9} - 5 q^{10} + q^{11} - 5 q^{12} - 2 q^{14} + 10 q^{15} - 17 q^{16} + 5 q^{17} - 24 q^{19} + 68 q^{20} - q^{21} - 28 q^{22} - 11 q^{23} - 32 q^{24} - 33 q^{25} - 42 q^{27} - 15 q^{28} + 8 q^{29} + 22 q^{30} - 40 q^{31} + 6 q^{32} - 24 q^{33} + 72 q^{34} + 44 q^{35} - 30 q^{36} + 4 q^{37} + 29 q^{38} + 4 q^{40} + 98 q^{41} - 9 q^{42} + 26 q^{43} - 10 q^{44} - 58 q^{45} + 10 q^{46} - 62 q^{47} + 178 q^{48} + 31 q^{49} - 46 q^{50} + 21 q^{51} + 18 q^{53} - 12 q^{54} - 28 q^{55} - 56 q^{56} - 26 q^{57} - 56 q^{58} - 79 q^{59} - 22 q^{60} - 13 q^{61} + 24 q^{62} + 22 q^{63} + 36 q^{64} + 38 q^{66} + 2 q^{67} + 12 q^{68} - 56 q^{69} + 85 q^{70} - 38 q^{71} - 81 q^{72} - 17 q^{73} - 17 q^{74} - 24 q^{75} + 116 q^{76} - 30 q^{77} + 9 q^{79} - 63 q^{80} - 16 q^{81} + 22 q^{82} + 162 q^{83} + 203 q^{84} - 68 q^{85} - 22 q^{86} - 70 q^{87} + 33 q^{88} - 72 q^{89} + 2 q^{90} - 8 q^{92} - 19 q^{93} + 30 q^{94} - 13 q^{95} - 11 q^{96} + 90 q^{97} + 81 q^{98} - 78 q^{99}+O(q^{100}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9 - 5 * q^10 + q^11 - 5 * q^12 - 2 * q^14 + 10 * q^15 - 17 * q^16 + 5 * q^17 - 24 * q^19 + 68 * q^20 - q^21 - 28 * q^22 - 11 * q^23 - 32 * q^24 - 33 * q^25 - 42 * q^27 - 15 * q^28 + 8 * q^29 + 22 * q^30 - 40 * q^31 + 6 * q^32 - 24 * q^33 + 72 * q^34 + 44 * q^35 - 30 * q^36 + 4 * q^37 + 29 * q^38 + 4 * q^40 + 98 * q^41 - 9 * q^42 + 26 * q^43 - 10 * q^44 - 58 * q^45 + 10 * q^46 - 62 * q^47 + 178 * q^48 + 31 * q^49 - 46 * q^50 + 21 * q^51 + 18 * q^53 - 12 * q^54 - 28 * q^55 - 56 * q^56 - 26 * q^57 - 56 * q^58 - 79 * q^59 - 22 * q^60 - 13 * q^61 + 24 * q^62 + 22 * q^63 + 36 * q^64 + 38 * q^66 + 2 * q^67 + 12 * q^68 - 56 * q^69 + 85 * q^70 - 38 * q^71 - 81 * q^72 - 17 * q^73 - 17 * q^74 - 24 * q^75 + 116 * q^76 - 30 * q^77 + 9 * q^79 - 63 * q^80 - 16 * q^81 + 22 * q^82 + 162 * q^83 + 203 * q^84 - 68 * q^85 - 22 * q^86 - 70 * q^87 + 33 * q^88 - 72 * q^89 + 2 * q^90 - 8 * q^92 - 19 * q^93 + 30 * q^94 - 13 * q^95 - 11 * q^96 + 90 * q^97 + 81 * q^98 - 78 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more