LMFDB - Embedded newform 349.2.c.a.122.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(122,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("349.122");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.c (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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			122.8
Character	$\chi$	$=$	349.122
Dual form			349.2.c.a.226.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.770318 + 1.33423i) q^{2} +(-1.33797 - 2.31743i) q^{3} +(-0.186780 - 0.323513i) q^{4} +(0.251334 + 0.435324i) q^{5} +4.12265 q^{6} +(0.615403 - 1.06591i) q^{7} -2.50575 q^{8} +(-2.08032 + 3.60322i) q^{9} +O(q^{10})$	\(q+(-0.770318 + 1.33423i) q^{2} +(-1.33797 - 2.31743i) q^{3} +(-0.186780 - 0.323513i) q^{4} +(0.251334 + 0.435324i) q^{5} +4.12265 q^{6} +(0.615403 - 1.06591i) q^{7} -2.50575 q^{8} +(-2.08032 + 3.60322i) q^{9} -0.774430 q^{10} +2.76483 q^{11} +(-0.499812 + 0.865701i) q^{12} +(0.877958 - 1.52067i) q^{13} +(0.948113 + 1.64218i) q^{14} +(0.672555 - 1.16490i) q^{15} +(2.30379 - 3.99028i) q^{16} -5.56673 q^{17} +(-3.20502 - 5.55126i) q^{18} +(-3.62143 - 6.27250i) q^{19} +(0.0938886 - 0.162620i) q^{20} -3.29356 q^{21} +(-2.12980 + 3.68892i) q^{22} +(3.14889 - 5.45404i) q^{23} +(3.35262 + 5.80690i) q^{24} +(2.37366 - 4.11130i) q^{25} +(1.35261 + 2.34280i) q^{26} +3.10581 q^{27} -0.459781 q^{28} +(-1.02924 - 1.78269i) q^{29} +(1.03616 + 1.79469i) q^{30} +6.41655 q^{31} +(1.04355 + 1.80747i) q^{32} +(-3.69925 - 6.40729i) q^{33} +(4.28816 - 7.42730i) q^{34} +0.618688 q^{35} +1.55425 q^{36} -1.52580 q^{37} +11.1586 q^{38} -4.69872 q^{39} +(-0.629782 - 1.09081i) q^{40} +1.58931 q^{41} +(2.53709 - 4.39437i) q^{42} +(-3.65915 - 6.33783i) q^{43} +(-0.516415 - 0.894458i) q^{44} -2.09143 q^{45} +(4.85130 + 8.40269i) q^{46} -3.36994 q^{47} -12.3296 q^{48} +(2.74256 + 4.75025i) q^{49} +(3.65695 + 6.33402i) q^{50} +(7.44811 + 12.9005i) q^{51} -0.655941 q^{52} +2.56573 q^{53} +(-2.39246 + 4.14386i) q^{54} +(0.694896 + 1.20360i) q^{55} +(-1.54205 + 2.67091i) q^{56} +(-9.69073 + 16.7848i) q^{57} +3.17136 q^{58} +(3.73160 + 6.46333i) q^{59} -0.502480 q^{60} -13.0144 q^{61} +(-4.94278 + 8.56115i) q^{62} +(2.56047 + 4.43487i) q^{63} +5.99970 q^{64} +0.882644 q^{65} +11.3984 q^{66} +7.37522 q^{67} +(1.03976 + 1.80091i) q^{68} -16.8525 q^{69} +(-0.476587 + 0.825473i) q^{70} +(-1.47352 + 2.55220i) q^{71} +(5.21277 - 9.02878i) q^{72} +(-6.32845 - 10.9612i) q^{73} +(1.17536 - 2.03577i) q^{74} -12.7035 q^{75} +(-1.35282 + 2.34316i) q^{76} +(1.70148 - 2.94706i) q^{77} +(3.61951 - 6.26918i) q^{78} +5.73756 q^{79} +2.31608 q^{80} +(2.08549 + 3.61218i) q^{81} +(-1.22427 + 2.12051i) q^{82} +(-8.04944 + 13.9420i) q^{83} +(0.615173 + 1.06551i) q^{84} +(-1.39911 - 2.42333i) q^{85} +11.2748 q^{86} +(-2.75417 + 4.77036i) q^{87} -6.92797 q^{88} +(-2.05322 - 3.55627i) q^{89} +(1.61106 - 2.79044i) q^{90} +(-1.08060 - 1.87165i) q^{91} -2.35260 q^{92} +(-8.58514 - 14.8699i) q^{93} +(2.59593 - 4.49628i) q^{94} +(1.82038 - 3.15299i) q^{95} +(2.79246 - 4.83669i) q^{96} +(1.21173 - 2.09877i) q^{97} -8.45057 q^{98} +(-5.75173 + 9.96229i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) $ 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9} - 2 q^{10} - 2 q^{11} + 11 q^{12} - 2 q^{13} + 2 q^{14} + 9 q^{15} - 34 q^{16} + 18 q^{18} - 5 q^{19} + 14 q^{20} + 12 q^{21} - 7 q^{22} - 11 q^{23} - 30 q^{24} - 6 q^{25} - 11 q^{26} - 30 q^{27} - 52 q^{28} + 8 q^{29} - 21 q^{30} - 48 q^{31} - 6 q^{32} + 12 q^{33} - 14 q^{34} + 42 q^{35} + 66 q^{36} + 14 q^{37} + 60 q^{38} - 26 q^{39} + 24 q^{40} - 3 q^{42} - 23 q^{43} - 20 q^{44} + 18 q^{45} + 5 q^{46} - 26 q^{47} - 22 q^{48} - 26 q^{49} + 11 q^{50} + 14 q^{51} + 6 q^{52} - 12 q^{53} - 7 q^{54} + 10 q^{55} - 19 q^{56} + 25 q^{57} - 12 q^{58} - 16 q^{59} - 12 q^{60} + 42 q^{61} - 27 q^{62} + 31 q^{63} + 54 q^{64} + 72 q^{65} - 66 q^{66} - 34 q^{67} - 57 q^{68} + 10 q^{69} - 52 q^{70} - 10 q^{71} + 47 q^{72} + 23 q^{73} - 17 q^{74} - 26 q^{75} + 9 q^{76} - 10 q^{77} + 25 q^{78} + 48 q^{79} - 32 q^{80} - 12 q^{81} - 8 q^{82} + 14 q^{83} + 10 q^{84} - 3 q^{85} + 46 q^{86} + 14 q^{87} + 58 q^{88} + 8 q^{89} + 68 q^{90} + 54 q^{91} + 48 q^{92} - 57 q^{93} + 33 q^{94} + 54 q^{95} - 72 q^{96} + 32 q^{98} + 73 q^{99}+O(q^{100}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9 - 2 * q^10 - 2 * q^11 + 11 * q^12 - 2 * q^13 + 2 * q^14 + 9 * q^15 - 34 * q^16 + 18 * q^18 - 5 * q^19 + 14 * q^20 + 12 * q^21 - 7 * q^22 - 11 * q^23 - 30 * q^24 - 6 * q^25 - 11 * q^26 - 30 * q^27 - 52 * q^28 + 8 * q^29 - 21 * q^30 - 48 * q^31 - 6 * q^32 + 12 * q^33 - 14 * q^34 + 42 * q^35 + 66 * q^36 + 14 * q^37 + 60 * q^38 - 26 * q^39 + 24 * q^40 - 3 * q^42 - 23 * q^43 - 20 * q^44 + 18 * q^45 + 5 * q^46 - 26 * q^47 - 22 * q^48 - 26 * q^49 + 11 * q^50 + 14 * q^51 + 6 * q^52 - 12 * q^53 - 7 * q^54 + 10 * q^55 - 19 * q^56 + 25 * q^57 - 12 * q^58 - 16 * q^59 - 12 * q^60 + 42 * q^61 - 27 * q^62 + 31 * q^63 + 54 * q^64 + 72 * q^65 - 66 * q^66 - 34 * q^67 - 57 * q^68 + 10 * q^69 - 52 * q^70 - 10 * q^71 + 47 * q^72 + 23 * q^73 - 17 * q^74 - 26 * q^75 + 9 * q^76 - 10 * q^77 + 25 * q^78 + 48 * q^79 - 32 * q^80 - 12 * q^81 - 8 * q^82 + 14 * q^83 + 10 * q^84 - 3 * q^85 + 46 * q^86 + 14 * q^87 + 58 * q^88 + 8 * q^89 + 68 * q^90 + 54 * q^91 + 48 * q^92 - 57 * q^93 + 33 * q^94 + 54 * q^95 - 72 * q^96 + 32 * q^98 + 73 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.770318	+	1.33423i	−0.544697	+	0.943443i	0.453929	+	0.891038i	$0.350022\pi$
$2$	−0.770318	+	1.33423i	−0.544697	+	0.943443i	−0.998626	+	0.0524053i	$0.983311\pi$
$3$	−1.33797	−	2.31743i	−0.772477	−	1.33797i	−0.936202	−	0.351463i	$-0.885684\pi$
$3$	−1.33797	−	2.31743i	−0.772477	−	1.33797i	0.163725	−	0.986506i	$-0.447649\pi$
$4$	−0.186780	−	0.323513i	−0.0933902	−	0.161756i
$5$	0.251334	+	0.435324i	0.112400	+	0.194683i	0.916738	−	0.399490i	$-0.130813\pi$
$5$	0.251334	+	0.435324i	0.112400	+	0.194683i	−0.804337	+	0.594173i	$0.797479\pi$
$6$	4.12265			1.68306
$7$	0.615403	−	1.06591i	0.232601	−	0.402876i	−0.725972	−	0.687724i	$-0.758610\pi$
$7$	0.615403	−	1.06591i	0.232601	−	0.402876i	0.958573	+	0.284848i	$0.0919432\pi$
$8$	−2.50575			−0.885917
$9$	−2.08032	+	3.60322i	−0.693440	+	1.20107i
$10$	−0.774430			−0.244896
$11$	2.76483			0.833627			0.416813	−	0.908992i	$-0.363147\pi$
$11$	2.76483			0.833627			0.416813	+	0.908992i	$0.363147\pi$
$12$	−0.499812	+	0.865701i	−0.144283	+	0.249906i
$13$	0.877958	−	1.52067i	0.243502	−	0.421757i	−0.718208	−	0.695829i	$-0.755037\pi$
$13$	0.877958	−	1.52067i	0.243502	−	0.421757i	0.961709	+	0.274072i	$0.0883705\pi$
$14$	0.948113	+	1.64218i	0.253394	+	0.438891i
$15$	0.672555	−	1.16490i	0.173653	−	0.300776i
$16$	2.30379	−	3.99028i	0.575947	−	0.997569i
$17$	−5.56673			−1.35013			−0.675065	−	0.737758i	$-0.735885\pi$
$17$	−5.56673			−1.35013			−0.675065	+	0.737758i	$0.735885\pi$
$18$	−3.20502	−	5.55126i	−0.755430	−	1.30844i
$19$	−3.62143	−	6.27250i	−0.830814	−	1.43901i	−0.897394	−	0.441230i	$-0.854542\pi$
$19$	−3.62143	−	6.27250i	−0.830814	−	1.43901i	0.0665805	−	0.997781i	$-0.478791\pi$
$20$	0.0938886	−	0.162620i	0.0209941	−	0.0363629i
$21$	−3.29356			−0.718714
$22$	−2.12980	+	3.68892i	−0.454074	+	0.786480i
$23$	3.14889	−	5.45404i	0.656589	−	1.13725i	−0.324904	−	0.945747i	$-0.605332\pi$
$23$	3.14889	−	5.45404i	0.656589	−	1.13725i	0.981493	−	0.191499i	$-0.0613347\pi$
$24$	3.35262	+	5.80690i	0.684350	+	1.18533i
$25$	2.37366	−	4.11130i	0.474732	−	0.822261i
$26$	1.35261	+	2.34280i	0.265269	+	0.459460i
$27$	3.10581			0.597713
$28$	−0.459781			−0.0868904
$29$	−1.02924	−	1.78269i	−0.191124	−	0.331037i	0.754499	−	0.656301i	$-0.227880\pi$
$29$	−1.02924	−	1.78269i	−0.191124	−	0.331037i	−0.945623	+	0.325264i	$0.894547\pi$
$30$	1.03616	+	1.79469i	0.189177	+	0.327664i
$31$	6.41655			1.15245			0.576223	−	0.817293i	$-0.304526\pi$
$31$	6.41655			1.15245			0.576223	+	0.817293i	$0.304526\pi$
$32$	1.04355	+	1.80747i	0.184475	+	0.319519i
$33$	−3.69925	−	6.40729i	−0.643957	−	1.11537i
$34$	4.28816	−	7.42730i	0.735413	−	1.27377i
$35$	0.618688			0.104577
$36$	1.55425			0.259042
$37$	−1.52580			−0.250841			−0.125420	−	0.992104i	$-0.540028\pi$
$37$	−1.52580			−0.250841			−0.125420	+	0.992104i	$0.540028\pi$
$38$	11.1586			1.81017
$39$	−4.69872			−0.752398
$40$	−0.629782	−	1.09081i	−0.0995772	−	0.172473i
$41$	1.58931			0.248209			0.124104	−	0.992269i	$-0.460394\pi$
$41$	1.58931			0.248209			0.124104	+	0.992269i	$0.460394\pi$
$42$	2.53709	−	4.39437i	0.391482	−	0.678066i
$43$	−3.65915	−	6.33783i	−0.558015	−	0.966511i	−0.997662	−	0.0683399i	$-0.978230\pi$
$43$	−3.65915	−	6.33783i	−0.558015	−	0.966511i	0.439647	−	0.898171i	$-0.355104\pi$
$44$	−0.516415	−	0.894458i	−0.0778525	−	0.134845i
$45$	−2.09143			−0.311771
$46$	4.85130	+	8.40269i	0.715284	+	1.23891i
$47$	−3.36994			−0.491557			−0.245778	−	0.969326i	$-0.579044\pi$
$47$	−3.36994			−0.491557			−0.245778	+	0.969326i	$0.579044\pi$
$48$	−12.3296			−1.77962
$49$	2.74256	+	4.75025i	0.391794	+	0.678607i
$50$	3.65695	+	6.33402i	0.517171	+	0.895766i
$51$	7.44811	+	12.9005i	1.04294	+	1.80643i
$52$	−0.655941			−0.0909627
$53$	2.56573			0.352430			0.176215	−	0.984352i	$-0.443615\pi$
$53$	2.56573			0.352430			0.176215	+	0.984352i	$0.443615\pi$
$54$	−2.39246	+	4.14386i	−0.325572	+	0.563908i
$55$	0.694896	+	1.20360i	0.0936998	+	0.162293i
$56$	−1.54205	+	2.67091i	−0.206065	+	0.356915i
$57$	−9.69073	+	16.7848i	−1.28357	+	2.22321i
$58$	3.17136			0.416419
$59$	3.73160	+	6.46333i	0.485813	+	0.841453i	0.999867	−	0.0163047i	$-0.00519017\pi$
$59$	3.73160	+	6.46333i	0.485813	+	0.841453i	−0.514054	+	0.857758i	$0.671857\pi$
$60$	−0.502480			−0.0648699
$61$	−13.0144			−1.66632			−0.833160	−	0.553033i	$-0.813470\pi$
$61$	−13.0144			−1.66632			−0.833160	+	0.553033i	$0.813470\pi$
$62$	−4.94278	+	8.56115i	−0.627734	+	1.08727i
$63$	2.56047	+	4.43487i	0.322589	+	0.558741i
$64$	5.99970			0.749962
$65$	0.882644			0.109479
$66$	11.3984			1.40305
$67$	7.37522			0.901026			0.450513	−	0.892770i	$-0.351241\pi$
$67$	7.37522			0.901026			0.450513	+	0.892770i	$0.351241\pi$
$68$	1.03976	+	1.80091i	0.126089	+	0.218392i
$69$	−16.8525			−2.02880
$70$	−0.476587	+	0.825473i	−0.0569630	+	0.0986629i
$71$	−1.47352	+	2.55220i	−0.174874	+	0.302891i	−0.940118	−	0.340850i	$-0.889285\pi$
$71$	−1.47352	+	2.55220i	−0.174874	+	0.302891i	0.765244	+	0.643741i	$0.222619\pi$
$72$	5.21277	−	9.02878i	0.614331	−	1.06405i
$73$	−6.32845	−	10.9612i	−0.740688	−	1.28291i	−0.952182	−	0.305531i	$-0.901166\pi$
$73$	−6.32845	−	10.9612i	−0.740688	−	1.28291i	0.211494	−	0.977379i	$-0.432167\pi$
$74$	1.17536	−	2.03577i	0.136632	−	0.236654i
$75$	−12.7035			−1.46688
$76$	−1.35282	+	2.34316i	−0.155180	+	0.268779i
$77$	1.70148	−	2.94706i	0.193902	−	0.335848i
$78$	3.61951	−	6.26918i	0.409829	−	0.709844i
$79$	5.73756			0.645525			0.322763	−	0.946480i	$-0.395388\pi$
$79$	5.73756			0.645525			0.322763	+	0.946480i	$0.395388\pi$
$80$	2.31608			0.258946
$81$	2.08549	+	3.61218i	0.231721	+	0.401353i
$82$	−1.22427	+	2.12051i	−0.135199	+	0.234171i
$83$	−8.04944	+	13.9420i	−0.883541	+	1.53034i	−0.0361634	+	0.999346i	$0.511514\pi$
$83$	−8.04944	+	13.9420i	−0.883541	+	1.53034i	−0.847377	+	0.530991i	$0.821820\pi$
$84$	0.615173	+	1.06551i	0.0671208	+	0.116257i
$85$	−1.39911	−	2.42333i	−0.151755	−	0.262847i
$86$	11.2748			1.21580
$87$	−2.75417	+	4.77036i	−0.295278	+	0.511437i
$88$	−6.92797			−0.738524
$89$	−2.05322	−	3.55627i	−0.217640	−	0.376964i	0.736446	−	0.676497i	$-0.236503\pi$
$89$	−2.05322	−	3.55627i	−0.217640	−	0.376964i	−0.954086	+	0.299532i	$0.903169\pi$
$90$	1.61106	−	2.79044i	0.169821	−	0.294139i
$91$	−1.08060	−	1.87165i	−0.113277	−	0.196202i
$92$	−2.35260			−0.245276
$93$	−8.58514	−	14.8699i	−0.890238	−	1.54194i
$94$	2.59593	−	4.49628i	0.267750	−	0.463756i
$95$	1.82038	−	3.15299i	0.186767	−	0.323490i
$96$	2.79246	−	4.83669i	0.285005	−	0.493643i
$97$	1.21173	−	2.09877i	0.123032	−	0.213098i	−0.797930	−	0.602750i	$-0.794071\pi$
$97$	1.21173	−	2.09877i	0.123032	−	0.213098i	0.920962	+	0.389652i	$0.127405\pi$
$98$	−8.45057			−0.853636
$99$	−5.75173	+	9.96229i	−0.578071	+	1.00125i
$100$	−1.77341			−0.177341
$101$	11.7163			1.16582			0.582908	−	0.812538i	$-0.301915\pi$
$101$	11.7163			1.16582			0.582908	+	0.812538i	$0.301915\pi$
$102$	−22.9497			−2.27236
$103$	11.5141			1.13451			0.567257	−	0.823541i	$-0.308005\pi$
$103$	11.5141			1.13451			0.567257	+	0.823541i	$0.308005\pi$
$104$	−2.19994	+	3.81042i	−0.215722	+	0.373642i
$105$	−0.827786	−	1.43377i	−0.0807836	−	0.139921i
$106$	−1.97643	+	3.42327i	−0.191968	+	0.332498i
$107$	−1.39747	+	2.42049i	−0.135098	+	0.233997i	−0.925635	−	0.378417i	$-0.876468\pi$
$107$	−1.39747	+	2.42049i	−0.135098	+	0.233997i	0.790537	+	0.612415i	$0.209802\pi$
$108$	−0.580103	−	1.00477i	−0.0558205	−	0.0966839i
$109$	−0.976978	−	1.69218i	−0.0935775	−	0.162081i	0.815437	−	0.578847i	$-0.196497\pi$
$109$	−0.976978	−	1.69218i	−0.0935775	−	0.162081i	−0.909014	+	0.416765i	$0.863164\pi$
$110$	−2.14117			−0.204152
$111$	2.04148	+	3.53595i	0.193769	+	0.335617i
$112$	−2.83552	−	4.91126i	−0.267931	−	0.464070i
$113$	−4.90749	+	8.50002i	−0.461658	+	0.799615i	−0.999044	−	0.0437215i	$-0.986079\pi$
$113$	−4.90749	+	8.50002i	−0.461658	+	0.799615i	0.537386	+	0.843337i	$0.319412\pi$
$114$	−14.9299	−	25.8593i	−1.39831	−	2.42195i
$115$	3.16570			0.295203
$116$	−0.384482	+	0.665942i	−0.0356982	+	0.0618312i
$117$	3.65287	+	6.32695i	0.337708	+	0.584927i
$118$	−11.4981			−1.05848
$119$	−3.42579	+	5.93364i	−0.314041	+	0.543936i
$120$	−1.68526	+	2.91895i	−0.153842	+	0.266462i
$121$	−3.35573			−0.305066
$122$	10.0252	−	17.3642i	0.907639	−	1.57208i
$123$	−2.12645	−	3.68312i	−0.191735	−	0.332095i
$124$	−1.19848	−	2.07584i	−0.107627	−	0.186416i
$125$	4.89968			0.438240
$126$	−7.88952			−0.702854
$127$	12.4922			1.10850			0.554252	−	0.832349i	$-0.313004\pi$
$127$	12.4922			1.10850			0.554252	+	0.832349i	$0.313004\pi$
$128$	−6.70877	+	11.6199i	−0.592977	+	1.02707i
$129$	−9.79166	+	16.9596i	−0.862107	+	1.49321i
$130$	−0.679917	+	1.17765i	−0.0596327	+	0.103287i
$131$	−5.70663			−0.498590			−0.249295	−	0.968428i	$-0.580199\pi$
$131$	−5.70663			−0.498590			−0.249295	+	0.968428i	$0.580199\pi$
$132$	−1.38190	+	2.39351i	−0.120279	+	0.208329i
$133$	−8.91457			−0.772991
$134$	−5.68126	+	9.84024i	−0.490786	+	0.850067i
$135$	0.780596	+	1.35203i	0.0671830	+	0.116364i
$136$	13.9488			1.19610
$137$	7.95431	+	13.7773i	0.679583	+	1.17707i	0.975107	+	0.221736i	$0.0711725\pi$
$137$	7.95431	+	13.7773i	0.679583	+	1.17707i	−0.295524	+	0.955335i	$0.595494\pi$
$138$	12.9818	−	22.4851i	1.10508	−	1.91406i
$139$	10.9413			0.928032			0.464016	−	0.885827i	$-0.346408\pi$
$139$	10.9413			0.928032			0.464016	+	0.885827i	$0.346408\pi$
$140$	−0.115559	−	0.200154i	−0.00976650	−	0.0169161i
$141$	4.50888	+	7.80961i	0.379716	+	0.657687i
$142$	−2.27015	−	3.93202i	−0.190507	−	0.329968i
$143$	2.42740	−	4.20438i	0.202990	−	0.351588i
$144$	9.58523	+	16.6021i	0.798769	+	1.38351i
$145$	0.517365	−	0.896102i	0.0429648	−	0.0744172i
$146$	19.4997			1.61380
$147$	7.33891	−	12.7114i	0.605303	−	1.04842i
$148$	0.284990	+	0.493618i	0.0234261	+	0.0405751i
$149$	5.63927	−	9.76750i	0.461987	−	0.800185i	−0.537073	−	0.843536i	$-0.680470\pi$
$149$	5.63927	−	9.76750i	0.461987	−	0.800185i	0.999060	+	0.0433508i	$0.0138033\pi$
$150$	9.78577	−	16.9495i	0.799005	−	1.38392i
$151$	6.26979	+	10.8596i	0.510228	+	0.883741i	0.999930	+	0.0118512i	$0.00377245\pi$
$151$	6.26979	+	10.8596i	0.510228	+	0.883741i	−0.489701	+	0.871890i	$0.662894\pi$
$152$	9.07441	+	15.7173i	0.736032	+	1.27484i
$153$	11.5806	−	20.0582i	0.936235	−	1.62161i
$154$	2.62137	+	4.54034i	0.211236	+	0.365871i
$155$	1.61270	+	2.79328i	0.129535	+	0.224361i
$156$	0.877629	+	1.52010i	0.0702665	+	0.121705i
$157$	−8.54703	−	14.8039i	−0.682127	−	1.18148i	−0.974330	−	0.225123i	$-0.927722\pi$
$157$	−8.54703	−	14.8039i	−0.682127	−	1.18148i	0.292203	−	0.956356i	$-0.405612\pi$
$158$	−4.41974	+	7.65522i	−0.351616	+	0.609017i
$159$	−3.43286	−	5.94589i	−0.272244	−	0.471540i
$160$	−0.524558	+	0.908561i	−0.0414700	+	0.0718281i
$161$	−3.87568	−	6.71287i	−0.305446	−	0.529048i
$162$	−6.42597			−0.504872
$163$	7.45717			0.584091			0.292045	−	0.956404i	$-0.405664\pi$
$163$	7.45717			0.584091			0.292045	+	0.956404i	$0.405664\pi$
$164$	−0.296852	−	0.514163i	−0.0231802	−	0.0401494i
$165$	1.85950	−	3.22075i	0.144762	−	0.250735i
$166$	−12.4013	−	21.4796i	−0.962524	−	1.66714i
$167$	1.88732			0.146045			0.0730226	−	0.997330i	$-0.476735\pi$
$167$	1.88732			0.146045			0.0730226	+	0.997330i	$0.476735\pi$
$168$	8.25285			0.636721
$169$	4.95838	+	8.58817i	0.381414	+	0.660628i
$170$	4.31104			0.330642
$171$	30.1350			2.30448
$172$	−1.36691	+	2.36757i	−0.104226	+	0.180525i
$173$	3.04978	−	5.28238i	0.231871	−	0.401612i	−0.726488	−	0.687179i	$-0.758849\pi$
$173$	3.04978	−	5.28238i	0.231871	−	0.401612i	0.958359	+	0.285567i	$0.0921821\pi$
$174$	−4.24317	−	7.34939i	−0.321674	−	0.557156i
$175$	−2.92152	−	5.06022i	−0.220846	−	0.382517i
$176$	6.36957	−	11.0324i	0.480125	−	0.831600i
$177$	9.98554	−	17.2955i	0.750559	−	1.30001i
$178$	6.32652			0.474193
$179$	−9.65122			−0.721366			−0.360683	−	0.932688i	$-0.617456\pi$
$179$	−9.65122			−0.721366			−0.360683	+	0.932688i	$0.617456\pi$
$180$	0.390637	+	0.676603i	0.0291164	+	0.0504310i
$181$	−21.6540			−1.60953			−0.804766	−	0.593592i	$-0.797709\pi$
$181$	−21.6540			−1.60953			−0.804766	+	0.593592i	$0.797709\pi$
$182$	3.32961			0.246807
$183$	17.4128	+	30.1599i	1.28719	+	2.22948i
$184$	−7.89034	+	13.6665i	−0.581683	+	1.00751i
$185$	−0.383487	−	0.664219i	−0.0281945	−	0.0488344i
$186$	26.4532			1.93964
$187$	−15.3911			−1.12551
$188$	0.629439	+	1.09022i	0.0459065	+	0.0795125i
$189$	1.91132	−	3.31051i	0.139028	−	0.240804i
$190$	2.80455	+	4.85762i	0.203463	+	0.352408i
$191$	9.81865	−	17.0064i	0.710452	−	1.23054i	−0.254235	−	0.967142i	$-0.581824\pi$
$191$	9.81865	−	17.0064i	0.710452	−	1.23054i	0.964687	−	0.263397i	$-0.0848429\pi$
$192$	−8.02741	−	13.9039i	−0.579328	−	1.00343i
$193$	1.28271	+	2.22172i	0.0923315	+	0.159923i	0.908492	−	0.417903i	$-0.137235\pi$
$193$	1.28271	+	2.22172i	0.0923315	+	0.159923i	−0.816160	+	0.577826i	$0.803901\pi$
$194$	1.86683	+	3.23345i	0.134031	+	0.232148i
$195$	−1.18095	−	2.04547i	−0.0845696	−	0.146479i
$196$	1.02451	−	1.77451i	0.0731794	−	0.126750i
$197$	2.34612	+	4.06359i	0.167154	+	0.289519i	0.937418	−	0.348206i	$-0.113209\pi$
$197$	2.34612	+	4.06359i	0.167154	+	0.289519i	−0.770264	+	0.637725i	$0.779876\pi$
$198$	−8.86132	−	15.3483i	−0.629747	−	1.09075i
$199$	−8.32159	+	14.4134i	−0.589902	+	1.02174i	0.404343	+	0.914608i	$0.367500\pi$
$199$	−8.32159	+	14.4134i	−0.589902	+	1.02174i	−0.994245	+	0.107133i	$0.965833\pi$
$200$	−5.94781	+	10.3019i	−0.420574	+	0.728455i
$201$	−9.86781	−	17.0915i	−0.696022	−	1.20554i
$202$	−9.02528	+	15.6322i	−0.635016	+	1.09988i
$203$	−2.53358			−0.177822
$204$	2.78232	−	4.81912i	0.194802	−	0.337406i
$205$	0.399448	+	0.691865i	0.0278987	+	0.0483219i
$206$	−8.86949	+	15.3624i	−0.617967	+	1.07035i
$207$	13.1014	+	22.6923i	0.910611	+	1.57722i
$208$	−4.04526	−	7.00659i	−0.280488	−	0.485820i
$209$	−10.0126	−	17.3424i	−0.692588	−	1.19960i
$210$	2.55063			0.176010
$211$	5.66556	−	9.81304i	0.390033	−	0.675558i	−0.602420	−	0.798179i	$-0.705797\pi$
$211$	5.66556	−	9.81304i	0.390033	−	0.675558i	0.992454	+	0.122621i	$0.0391301\pi$
$212$	−0.479227	−	0.830046i	−0.0329135	−	0.0570078i
$213$	7.88607			0.540345
$214$	−2.15299	−	3.72909i	−0.147176	−	0.254916i
$215$	1.83934	−	3.18583i	0.125442	−	0.217272i
$216$	−7.78238			−0.529524
$217$	3.94877	−	6.83946i	0.268060	−	0.464293i
$218$	3.01034			0.203886
$219$	−16.9345	+	29.3315i	−1.14433	+	1.98204i
$220$	0.259586	−	0.449616i	0.0175013	−	0.0303131i
$221$	−4.88736	+	8.46515i	−0.328759	+	0.569428i
$222$	−6.29035			−0.422181
$223$	−5.28559			−0.353950			−0.176975	−	0.984215i	$-0.556631\pi$
$223$	−5.28559			−0.353950			−0.176975	+	0.984215i	$0.556631\pi$
$224$	2.56881			0.171636
$225$	9.87596	+	17.1057i	0.658397	+	1.14038i
$226$	−7.56066	−	13.0954i	−0.502928	−	0.871096i
$227$	12.8421	−	22.2432i	0.852363	−	1.47634i	−0.0267078	−	0.999643i	$-0.508502\pi$
$227$	12.8421	−	22.2432i	0.852363	−	1.47634i	0.879070	−	0.476692i	$-0.158164\pi$
$228$	7.24015			0.479490
$229$	−10.1239	+	17.5352i	−0.669008	+	1.15876i	0.309174	+	0.951006i	$0.399948\pi$
$229$	−10.1239	+	17.5352i	−0.669008	+	1.15876i	−0.978182	+	0.207751i	$0.933386\pi$
$230$	−2.43859	+	4.22377i	−0.160796	+	0.278507i
$231$	−9.10613			−0.599139
$232$	2.57901	+	4.46697i	0.169320	+	0.293271i
$233$	3.66530	−	6.34848i	0.240122	−	0.415903i	−0.720627	−	0.693323i	$-0.756146\pi$
$233$	3.66530	−	6.34848i	0.240122	−	0.415903i	0.960749	+	0.277420i	$0.0894793\pi$
$234$	−11.2555			−0.735794
$235$	−0.846983	−	1.46702i	−0.0552511	−	0.0956976i
$236$	1.39398	−	2.41444i	0.0907404	−	0.157167i
$237$	−7.67667	−	13.2964i	−0.498653	−	0.863693i
$238$	−5.27789	−	9.14158i	−0.342115	−	0.592560i
$239$	0.329707			0.0213270			0.0106635	−	0.999943i	$-0.496606\pi$
$239$	0.329707			0.0213270			0.0106635	+	0.999943i	$0.496606\pi$
$240$	−3.09885	−	5.36736i	−0.200030	−	0.346462i
$241$	2.09855	+	3.63480i	0.135180	+	0.234138i	0.925666	−	0.378342i	$-0.123506\pi$
$241$	2.09855	+	3.63480i	0.135180	+	0.234138i	−0.790486	+	0.612480i	$0.790172\pi$
$242$	2.58498	−	4.47732i	0.166169	−	0.287813i
$243$	10.2394	−	17.7351i	0.656855	−	1.13771i
$244$	2.43083	+	4.21032i	0.155618	+	0.269538i
$245$	−1.37860	+	2.38780i	−0.0880754	+	0.152551i
$246$	6.55217			0.417751
$247$	−12.7179			−0.809218
$248$	−16.0783			−1.02097
$249$	43.0796			2.73006
$250$	−3.77431	+	6.53730i	−0.238708	+	0.413455i
$251$	−22.7400			−1.43534			−0.717669	−	0.696384i	$-0.754791\pi$
$251$	−22.7400			−1.43534			−0.717669	+	0.696384i	$0.754791\pi$
$252$	0.956492	−	1.65669i	0.0602533	−	0.104362i
$253$	8.70614	−	15.0795i	0.547350	−	0.948038i
$254$	−9.62297	+	16.6675i	−0.603799	+	1.04581i
$255$	−3.74394	+	6.48469i	−0.234454	+	0.406087i
$256$	−4.33608	−	7.51030i	−0.271005	−	0.469394i
$257$	−12.5008			−0.779779			−0.389889	−	0.920862i	$-0.627487\pi$
$257$	−12.5008			−0.779779			−0.389889	+	0.920862i	$0.627487\pi$
$258$	−15.0854	−	26.1287i	−0.939175	−	1.62670i
$259$	−0.938986	+	1.62637i	−0.0583457	+	0.101058i
$260$	−0.164861	−	0.285547i	−0.0102242	−	0.0177089i
$261$	8.56456			0.530133
$262$	4.39592	−	7.61396i	0.271581	−	0.470392i
$263$	−7.04871			−0.434642			−0.217321	−	0.976100i	$-0.569732\pi$
$263$	−7.04871			−0.434642			−0.217321	+	0.976100i	$0.569732\pi$
$264$	9.26941	+	16.0551i	0.570493	+	0.988122i
$265$	0.644856	+	1.11692i	0.0396132	+	0.0686120i
$266$	6.86705	−	11.8941i	0.421046	−	0.729273i
$267$	−5.49428	+	9.51637i	−0.336244	+	0.582392i
$268$	−1.37755	−	2.38598i	−0.0841470	−	0.145747i
$269$	12.2527			0.747063			0.373532	−	0.927617i	$-0.378147\pi$
$269$	12.2527			0.747063			0.373532	+	0.927617i	$0.378147\pi$
$270$	−2.40523			−0.146378
$271$	15.2953	−	26.4922i	0.929122	−	1.60929i	0.144327	−	0.989530i	$-0.453898\pi$
$271$	15.2953	−	26.4922i	0.929122	−	1.60929i	0.784795	−	0.619756i	$-0.212768\pi$
$272$	−12.8246	+	22.2128i	−0.777603	+	1.34685i
$273$	−2.89161	+	5.00841i	−0.175008	+	0.303123i
$274$	−24.5094			−1.48067
$275$	6.56277	−	11.3670i	0.395750	−	0.685459i
$276$	3.14771	+	5.45199i	0.189470	+	0.328171i
$277$	2.21508	−	3.83663i	0.133091	−	0.230521i	−0.791775	−	0.610812i	$-0.790843\pi$
$277$	2.21508	−	3.83663i	0.133091	−	0.230521i	0.924867	+	0.380291i	$0.124176\pi$
$278$	−8.42831	+	14.5983i	−0.505497	+	0.875546i
$279$	−13.3485	+	23.1202i	−0.799153	+	1.38417i
$280$	−1.55028			−0.0926469
$281$	1.27652	+	2.21100i	0.0761507	+	0.131897i	0.901586	−	0.432600i	$-0.142404\pi$
$281$	1.27652	+	2.21100i	0.0761507	+	0.131897i	−0.825435	+	0.564497i	$0.809070\pi$
$282$	−13.8931			−0.827321
$283$	−19.4314			−1.15507			−0.577537	−	0.816364i	$-0.695986\pi$
$283$	−19.4314			−1.15507			−0.577537	+	0.816364i	$0.695986\pi$
$284$	1.10090			0.0653261
$285$	−9.74245			−0.577093
$286$	3.73974	+	6.47743i	0.221136	+	0.383018i
$287$	0.978067	−	1.69406i	0.0577335	−	0.0999973i
$288$	−8.68364			−0.511689
$289$	13.9885			0.822853
$290$	0.797071	+	1.38057i	0.0468056	+	0.0810697i
$291$	−6.48502			−0.380158
$292$	−2.36406	+	4.09467i	−0.138346	+	0.239622i
$293$	3.12996	−	5.42125i	0.182854	−	0.316713i	−0.759997	−	0.649926i	$-0.774800\pi$
$293$	3.12996	−	5.42125i	0.182854	−	0.316713i	0.942851	+	0.333214i	$0.108133\pi$
$294$	11.3066	+	19.5836i	0.659414	+	1.14214i
$295$	−1.87576	+	3.24891i	−0.109211	+	0.189159i
$296$	3.82329			0.222224
$297$	8.58702			0.498269
$298$	8.68807	+	15.0482i	0.503286	+	0.871717i
$299$	−5.52919	−	9.57683i	−0.319761	−	0.553843i
$300$	2.37277	+	4.10976i	0.136992	+	0.237277i
$301$	−9.00741			−0.519179
$302$	−19.3189			−1.11168
$303$	−15.6760	−	27.1517i	−0.900565	−	1.55982i
$304$	−33.3720			−1.91402
$305$	−3.27096	−	5.66547i	−0.187295	−	0.324404i
$306$	17.8415	+	30.9024i	1.01993	+	1.76657i
$307$	13.3705	−	23.1585i	0.763097	−	1.32172i	−0.178150	−	0.984003i	$-0.557011\pi$
$307$	13.3705	−	23.1585i	0.763097	−	1.32172i	0.941247	−	0.337719i	$-0.109655\pi$
$308$	−1.27122			−0.0724342
$309$	−15.4055	−	26.6830i	−0.876386	−	1.51795i
$310$	−4.96917			−0.282230
$311$	−6.29459			−0.356934			−0.178467	−	0.983946i	$-0.557114\pi$
$311$	−6.29459			−0.356934			−0.178467	+	0.983946i	$0.557114\pi$
$312$	11.7738			0.666562
$313$	3.34403			0.189016			0.0945078	−	0.995524i	$-0.469872\pi$
$313$	3.34403			0.189016			0.0945078	+	0.995524i	$0.469872\pi$
$314$	26.3357			1.48621
$315$	−1.28707	+	2.22927i	−0.0725182	+	0.125605i
$316$	−1.07166	−	1.85617i	−0.0602857	−	0.104418i
$317$	7.37118	+	12.7673i	0.414007	+	0.717081i	0.995324	−	0.0965964i	$-0.0307956\pi$
$317$	7.37118	+	12.7673i	0.414007	+	0.717081i	−0.581317	+	0.813677i	$0.697462\pi$
$318$	10.5776			0.593162
$319$	−2.84566	−	4.92882i	−0.159326	−	0.275961i
$320$	1.50793	+	2.61181i	0.0842959	+	0.146005i
$321$	7.47908			0.417442
$322$	11.9420			0.665502
$323$	20.1595	+	34.9174i	1.12171	+	1.94285i
$324$	0.779057	−	1.34937i	0.0432810	−	0.0749648i
$325$	−4.16795	−	7.21910i	−0.231196	−	0.400444i
$326$	−5.74439	+	9.94958i	−0.318153	+	0.551056i
$327$	−2.61433	+	4.52816i	−0.144573	+	0.250408i
$328$	−3.98242			−0.219892
$329$	−2.07387	+	3.59206i	−0.114336	+	0.198036i
$330$	2.86481	+	4.96200i	0.157703	+	0.273149i
$331$	13.6314	+	23.6102i	0.749248	+	1.29774i	0.948183	+	0.317724i	$0.102918\pi$
$331$	13.6314	+	23.6102i	0.749248	+	1.29774i	−0.198935	+	0.980013i	$0.563748\pi$
$332$	6.01391			0.330056
$333$	3.17416	−	5.49781i	0.173943	−	0.301278i
$334$	−1.45384	+	2.51812i	−0.0795504	+	0.137785i
$335$	1.85365	+	3.21061i	0.101275	+	0.175414i
$336$	−7.58767	+	13.1422i	−0.413941	+	0.716967i
$337$	−14.1164	+	24.4504i	−0.768970	+	1.33190i	0.169151	+	0.985590i	$0.445897\pi$
$337$	−14.1164	+	24.4504i	−0.768970	+	1.33190i	−0.938122	+	0.346306i	$0.887436\pi$
$338$	−15.2781			−0.831020
$339$	26.2643			1.42648
$340$	−0.522653	+	0.905261i	−0.0283448	+	0.0490947i
$341$	17.7406			0.960710
$342$	−23.2135	+	40.2070i	−1.25524	+	2.17414i
$343$	15.3668			0.829727
$344$	9.16892	+	15.8810i	0.494355	+	0.856248i
$345$	−4.23561	−	7.33628i	−0.228037	−	0.394972i
$346$	4.69861	+	8.13822i	0.252599	+	0.437514i
$347$	9.63717	−	16.6921i	0.517350	−	0.896077i	−0.482447	−	0.875925i	$-0.660252\pi$
$347$	9.63717	−	16.6921i	0.517350	−	0.896077i	0.999797	−	0.0201515i	$-0.00641484\pi$
$348$	2.05770			0.110304
$349$	−8.35855	−	16.7073i	−0.447423	−	0.894323i
$349$	−8.35855	−	16.7073i	−0.447423	−	0.894323i
$350$	9.00200			0.481177
$351$	2.72677	−	4.72290i	0.145544	−	0.252090i
$352$	2.88523	+	4.99736i	0.153783	+	0.266360i
$353$	1.50363	+	2.60436i	0.0800299	+	0.138616i	0.903263	−	0.429088i	$-0.141165\pi$
$353$	1.50363	+	2.60436i	0.0800299	+	0.138616i	−0.823233	+	0.567704i	$0.807832\pi$
$354$	15.3841	+	26.6460i	0.817655	+	1.41622i
$355$	−1.48138			−0.0786235
$356$	−0.767001	+	1.32848i	−0.0406509	+	0.0704095i
$357$	18.3344			0.970358
$358$	7.43451	−	12.8769i	0.392926	−	0.680568i
$359$	−33.2361			−1.75414			−0.877068	−	0.480366i	$-0.840504\pi$
$359$	−33.2361			−1.75414			−0.877068	+	0.480366i	$0.840504\pi$
$360$	5.24059			0.276203
$361$	−16.7295	+	28.9764i	−0.880502	+	1.52507i
$362$	16.6805	−	28.8915i	0.876708	−	1.51850i
$363$	4.48986	+	7.77667i	0.235657	+	0.408169i
$364$	−0.403668	+	0.699174i	−0.0211580	+	0.0366467i
$365$	3.18111	−	5.50985i	0.166507	−	0.288399i
$366$	−53.6536			−2.80452
$367$	14.6081	+	25.3020i	0.762538	+	1.32075i	0.941539	+	0.336905i	$0.109380\pi$
$367$	14.6081	+	25.3020i	0.762538	+	1.32075i	−0.179001	+	0.983849i	$0.557286\pi$
$368$	−14.5087	−	25.1299i	−0.756321	−	1.30999i
$369$	−3.30628	+	5.72664i	−0.172118	+	0.298117i
$370$	1.18163			0.0614300
$371$	1.57896	−	2.73483i	0.0819754	−	0.141986i
$372$	−3.20707	+	5.55481i	−0.166279	+	0.288003i
$373$	18.0603	+	31.2814i	0.935128	+	1.61969i	0.774405	+	0.632691i	$0.218049\pi$
$373$	18.0603	+	31.2814i	0.935128	+	1.61969i	0.160724	+	0.986999i	$0.448617\pi$
$374$	11.8560	−	20.5352i	0.613060	−	1.06185i
$375$	−6.55561	−	11.3547i	−0.338530	−	0.586352i
$376$	8.44424			0.435478
$377$	−3.61450			−0.186156
$378$	2.94466	+	5.10029i	0.151457	+	0.262331i
$379$	3.03731	+	5.26077i	0.156016	+	0.270228i	0.933429	−	0.358763i	$-0.116802\pi$
$379$	3.03731	+	5.26077i	0.156016	+	0.270228i	−0.777413	+	0.628991i	$0.783468\pi$
$380$	−1.36005			−0.0697689
$381$	−16.7142	−	28.9498i	−0.856293	−	1.48314i
$382$	15.1270	+	26.2007i	0.773963	+	1.34054i
$383$	−15.6499	+	27.1065i	−0.799674	+	1.38508i	0.120154	+	0.992755i	$0.461661\pi$
$383$	−15.6499	+	27.1065i	−0.799674	+	1.38508i	−0.919828	+	0.392321i	$0.871672\pi$
$384$	35.9045			1.83224
$385$	1.71057			0.0871785
$386$	−3.95238			−0.201171
$387$	30.4488			1.54780
$388$	−0.905307			−0.0459600
$389$	−16.2584	−	28.1603i	−0.824333	−	1.42779i	−0.902428	−	0.430840i	$-0.858217\pi$
$389$	−16.2584	−	28.1603i	−0.824333	−	1.42779i	0.0780957	−	0.996946i	$-0.475116\pi$
$390$	3.63883			0.184259
$391$	−17.5290	+	30.3612i	−0.886481	+	1.53543i
$392$	−6.87217	−	11.9029i	−0.347097	−	0.601189i
$393$	7.63529	+	13.2247i	0.385149	+	0.667098i
$394$	−7.22903			−0.364193
$395$	1.44205	+	2.49770i	0.0725572	+	0.125673i
$396$	4.29724			0.215944
$397$	12.9528			0.650084			0.325042	−	0.945700i	$-0.394622\pi$
$397$	12.9528			0.650084			0.325042	+	0.945700i	$0.394622\pi$
$398$	−12.8205	−	22.2058i	−0.642636	−	1.11308i
$399$	11.9274	+	20.6589i	0.597118	+	1.03424i
$400$	−10.9368	−	18.9431i	−0.546841	−	0.947157i
$401$	1.99572			0.0996613			0.0498307	−	0.998758i	$-0.484132\pi$
$401$	1.99572			0.0996613			0.0498307	+	0.998758i	$0.484132\pi$
$402$	30.4054			1.51648
$403$	5.63346	−	9.75744i	0.280623	−	0.486053i
$404$	−2.18837	−	3.79038i	−0.108876	−	0.188578i
$405$	−1.04831	+	1.81573i	−0.0520910	+	0.0902243i
$406$	1.95166	−	3.38038i	0.0968594	−	0.167765i
$407$	−4.21859			−0.209108
$408$	−18.6631	−	32.3255i	−0.923962	−	1.60035i
$409$	23.4907			1.16154			0.580771	−	0.814067i	$-0.302751\pi$
$409$	23.4907			1.16154			0.580771	+	0.814067i	$0.302751\pi$
$410$	−1.23081			−0.0607854
$411$	21.2852	−	36.8671i	1.04992	−	1.81852i
$412$	−2.15060	−	3.72495i	−0.105952	−	0.183515i
$413$	9.18576			0.452002
$414$	−40.3690			−1.98403
$415$	−8.09240			−0.397240
$416$	3.66476			0.179680
$417$	−14.6392	−	25.3558i	−0.716883	−	1.24168i
$418$	30.8517			1.50900
$419$	18.6325	−	32.2725i	0.910258	−	1.57661i	0.0965575	−	0.995327i	$-0.469217\pi$
$419$	18.6325	−	32.2725i	0.910258	−	1.57661i	0.813700	−	0.581285i	$-0.197450\pi$
$420$	−0.309228	+	0.535599i	−0.0150888	+	0.0261345i
$421$	−10.4583	+	18.1143i	−0.509706	+	0.882836i	0.490231	+	0.871592i	$0.336912\pi$
$421$	−10.4583	+	18.1143i	−0.509706	+	0.882836i	−0.999937	+	0.0112435i	$0.996421\pi$
$422$	8.72857	+	15.1183i	0.424900	+	0.735949i
$423$	7.01056	−	12.1427i	0.340865	−	0.590396i
$424$	−6.42908			−0.312224
$425$	−13.2135	+	22.8865i	−0.640951	+	1.11016i
$426$	−6.07479	+	10.5218i	−0.294324	+	0.509785i
$427$	−8.00909	+	13.8721i	−0.387587	+	0.671320i
$428$	1.04408			0.0504675
$429$	−12.9912			−0.627219
$430$	2.83376	+	4.90821i	0.136656	+	0.236695i
$431$	17.1489	−	29.7028i	0.826034	−	1.43073i	−0.0750919	−	0.997177i	$-0.523925\pi$
$431$	17.1489	−	29.7028i	0.826034	−	1.43073i	0.901126	−	0.433557i	$-0.142742\pi$
$432$	7.15512	−	12.3930i	0.344251	−	0.596260i
$433$	20.0567	+	34.7393i	0.963866	+	1.66946i	0.712632	+	0.701538i	$0.247503\pi$
$433$	20.0567	+	34.7393i	0.963866	+	1.66946i	0.251233	+	0.967927i	$0.419164\pi$
$434$	6.08361	+	10.5371i	0.292023	+	0.505798i
$435$	−2.76887			−0.132757
$436$	−0.364961	+	0.632130i	−0.0174784	+	0.0302736i
$437$	−45.6140			−2.18201
$438$	−26.0899	−	45.1891i	−1.24663	−	2.15922i
$439$	−6.51316	+	11.2811i	−0.310856	+	0.538418i	−0.978548	−	0.206019i	$-0.933949\pi$
$439$	−6.51316	+	11.2811i	−0.310856	+	0.538418i	0.667692	+	0.744438i	$0.267282\pi$
$440$	−1.74124	−	3.01591i	−0.0830102	−	0.143778i
$441$	−22.8216			−1.08674
$442$	−7.52964	−	13.0417i	−0.358148	−	0.620331i
$443$	7.15334	−	12.3899i	0.339865	−	0.588664i	−0.644542	−	0.764569i	$-0.722952\pi$
$443$	7.15334	−	12.3899i	0.339865	−	0.588664i	0.984407	+	0.175905i	$0.0562851\pi$
$444$	0.762616	−	1.32089i	0.0361922	−	0.0626867i
$445$	1.03209	−	1.78763i	0.0489256	−	0.0847417i
$446$	4.07159	−	7.05220i	0.192795	−	0.333931i
$447$	−30.1807			−1.42750
$448$	3.69223	−	6.39514i	0.174442	−	0.302142i
$449$	31.5171			1.48738			0.743692	−	0.668522i	$-0.233073\pi$
$449$	31.5171			1.48738			0.743692	+	0.668522i	$0.233073\pi$
$450$	−30.4305			−1.43451
$451$	4.39417			0.206913
$452$	3.66649			0.172457
$453$	16.7776	−	29.0596i	0.788279	−	1.36534i
$454$	19.7851	+	34.2687i	0.928559	+	1.60831i
$455$	0.543182	−	0.940819i	0.0254648	−	0.0441063i
$456$	24.2826	−	42.0586i	1.13713	−	1.96958i
$457$	10.7811	+	18.6734i	0.504317	+	0.873503i	0.999988	+	0.00499255i	$0.00158919\pi$
$457$	10.7811	+	18.6734i	0.504317	+	0.873503i	−0.495670	+	0.868511i	$0.665077\pi$
$458$	−15.5973	−	27.0153i	−0.728814	−	1.26234i
$459$	−17.2892			−0.806990
$460$	−0.591290	−	1.02414i	−0.0275690	−	0.0477510i
$461$	5.16849	+	8.95209i	0.240721	+	0.416940i	0.960920	−	0.276827i	$-0.0892829\pi$
$461$	5.16849	+	8.95209i	0.240721	+	0.416940i	−0.720199	+	0.693767i	$0.755950\pi$
$462$	7.01462	−	12.1497i	0.326350	−	0.565254i
$463$	−13.4651	−	23.3222i	−0.625776	−	1.08388i	−0.988390	−	0.151937i	$-0.951449\pi$
$463$	−13.4651	−	23.3222i	−0.625776	−	1.08388i	0.362614	−	0.931939i	$-0.381884\pi$
$464$	−9.48456			−0.440309
$465$	4.31548	−	7.47464i	0.200126	−	0.346628i
$466$	5.64689	+	9.78070i	0.261587	+	0.453082i
$467$	3.62403			0.167700			0.0838500	−	0.996478i	$-0.473278\pi$
$467$	3.62403			0.167700			0.0838500	+	0.996478i	$0.473278\pi$
$468$	1.36457	−	2.36350i	0.0630772	−	0.109253i
$469$	4.53873	−	7.86132i	0.209579	−	0.363002i
$470$	2.60978			0.120380
$471$	−22.8713	+	39.6143i	−1.05385	+	1.82533i
$472$	−9.35047	−	16.1955i	−0.430390	−	0.745458i
$473$	−10.1169	−	17.5230i	−0.465176	−	0.805709i
$474$	23.6539			1.08646
$475$	−34.3842			−1.57766
$476$	2.55948			0.117313
$477$	−5.33754	+	9.24489i	−0.244389	+	0.423294i
$478$	−0.253980	+	0.439906i	−0.0116168	+	0.0201208i
$479$	2.22250	−	3.84948i	0.101549	−	0.175887i	−0.810774	−	0.585359i	$-0.800954\pi$
$479$	2.22250	−	3.84948i	0.101549	−	0.175887i	0.912323	+	0.409472i	$0.134287\pi$
$480$	2.80737			0.128138
$481$	−1.33959	+	2.32024i	−0.0610802	+	0.105794i
$482$	−6.46621			−0.294528
$483$	−10.3711	+	17.9632i	−0.471900	+	0.817355i
$484$	0.626784	+	1.08562i	0.0284902	+	0.0493465i
$485$	1.21820			0.0553154
$486$	15.7751	+	27.3233i	0.715574	+	1.23941i
$487$	−2.81011	+	4.86725i	−0.127338	+	0.220556i	−0.922644	−	0.385652i	$-0.873977\pi$
$487$	−2.81011	+	4.86725i	−0.127338	+	0.220556i	0.795306	+	0.606208i	$0.207310\pi$
$488$	32.6108			1.47622
$489$	−9.97746	−	17.2815i	−0.451196	−	0.781495i
$490$	−2.12392	−	3.67873i	−0.0959489	−	0.166188i
$491$	10.2758	+	17.7982i	0.463740	+	0.803221i	0.999144	−	0.0413755i	$-0.0131740\pi$
$491$	10.2758	+	17.7982i	0.463740	+	0.803221i	−0.535404	+	0.844596i	$0.679841\pi$
$492$	−0.794357	+	1.37587i	−0.0358124	+	0.0620289i
$493$	5.72948	+	9.92375i	0.258043	+	0.446943i
$494$	9.79680	−	16.9686i	0.440779	−	0.763451i
$495$	−5.78243			−0.259901
$496$	14.7824	−	25.6038i	0.663747	−	1.14964i
$497$	1.81361	+	3.14127i	0.0813517	+	0.140905i
$498$	−33.1850	+	57.4781i	−1.48706	+	2.57565i
$499$	15.5215	−	26.8841i	0.694839	−	1.20350i	−0.275396	−	0.961331i	$-0.588809\pi$
$499$	15.5215	−	26.8841i	0.694839	−	1.20350i	0.970235	−	0.242166i	$-0.0778578\pi$
$500$	−0.915163	−	1.58511i	−0.0409273	−	0.0708882i
$501$	−2.52517	−	4.37373i	−0.112816	−	0.195404i
$502$	17.5171	−	30.3405i	0.781825	−	1.35416i
$503$	3.31544	+	5.74251i	0.147828	+	0.256046i	0.930425	−	0.366484i	$-0.119438\pi$
$503$	3.31544	+	5.74251i	0.147828	+	0.256046i	−0.782596	+	0.622530i	$0.786105\pi$
$504$	−6.41591	−	11.1127i	−0.285787	−	0.494998i
$505$	2.94471	+	5.10039i	0.131038	+	0.226964i
$506$	13.4130	+	23.2320i	0.596280	+	1.03279i
$507$	13.2683	−	22.9814i	0.589267	−	1.02064i
$508$	−2.33330	−	4.04139i	−0.103523	−	0.179308i
$509$	15.0909	−	26.1382i	0.668892	−	1.15856i	−0.309322	−	0.950957i	$-0.600102\pi$
$509$	15.0909	−	26.1382i	0.668892	−	1.15856i	0.978214	−	0.207598i	$-0.0665646\pi$
$510$	−5.76804	−	9.99054i	−0.255413	−	0.442389i
$511$	−15.5782			−0.689138
$512$	−13.4744			−0.595492
$513$	−11.2475	−	19.4812i	−0.496588	−	0.860115i
$514$	9.62960	−	16.6790i	0.424743	−	0.735677i
$515$	2.89388	+	5.01235i	0.127520	+	0.220870i
$516$	7.31555			0.322049
$517$	−9.31731			−0.409775
$518$	−1.44664	−	2.50565i	−0.0635615	−	0.110092i
$519$	−16.3221			−0.716459
$520$	−2.21169			−0.0969889
$521$	−15.6070	+	27.0322i	−0.683757	+	1.18430i	0.290068	+	0.957006i	$0.406322\pi$
$521$	−15.6070	+	27.0322i	−0.683757	+	1.18430i	−0.973826	+	0.227296i	$0.927011\pi$
$522$	−6.59744	+	11.4271i	−0.288762	+	0.500150i
$523$	11.1229	+	19.2655i	0.486371	+	0.842420i	0.999877	−	0.0156661i	$-0.00498687\pi$
$523$	11.1229	+	19.2655i	0.486371	+	0.842420i	−0.513506	+	0.858086i	$0.671654\pi$
$524$	1.06589	+	1.84617i	0.0465634	+	0.0806502i
$525$	−7.81780	+	13.5408i	−0.341197	+	0.590970i
$526$	5.42975	−	9.40460i	0.236748	−	0.410060i
$527$	−35.7192			−1.55595
$528$	−34.0892			−1.48354
$529$	−8.33102	−	14.4298i	−0.362218	−	0.627380i
$530$	−1.98698			−0.0863087
$531$	−31.0517			−1.34753
$532$	1.66507	+	2.88398i	0.0721898	+	0.125036i
$533$	1.39535	−	2.41681i	0.0604392	−	0.104684i
$534$	−8.46468	−	14.6613i	−0.366303	−	0.634455i
$535$	−1.40493			−0.0607404
$536$	−18.4805			−0.798234
$537$	12.9130	+	22.3660i	0.557238	+	0.965165i
$538$	−9.43852	+	16.3480i	−0.406923	+	0.704812i
$539$	7.58270	+	13.1336i	0.326610	+	0.565705i
$540$	0.291600	−	0.505066i	0.0125485	−	0.0217346i
$541$	−0.200008	−	0.346424i	−0.00859901	−	0.0148939i	0.861694	−	0.507428i	$-0.169404\pi$
$541$	−0.200008	−	0.346424i	−0.00859901	−	0.0148939i	−0.870293	+	0.492535i	$0.836071\pi$
$542$	23.5645	+	40.8148i	1.01218	+	1.75315i
$543$	28.9724	+	50.1817i	1.24333	+	2.15350i
$544$	−5.80914	−	10.0617i	−0.249065	−	0.431393i
$545$	0.491097	−	0.850604i	0.0210363	−	0.0364359i
$546$	−4.45492	−	7.71615i	−0.190653	−	0.330221i
$547$	−9.42357	−	16.3221i	−0.402923	−	0.697883i	0.591155	−	0.806558i	$-0.298672\pi$
$547$	−9.42357	−	16.3221i	−0.402923	−	0.697883i	−0.994077	+	0.108676i	$0.965339\pi$
$548$	2.97142	−	5.14665i	0.126933	−	0.219854i
$549$	27.0741	−	46.8937i	1.15549	−	2.00137i
$550$	10.1108	+	17.5125i	0.431127	+	0.746735i
$551$	−7.45461	+	12.9118i	−0.317577	+	0.550060i
$552$	42.2281			1.79735
$553$	3.53091	−	6.11572i	0.150150	−	0.260067i
$554$	3.41264	+	5.91086i	0.144989	+	0.251128i
$555$	−1.02619	+	1.77741i	−0.0435593	+	0.0754468i
$556$	−2.04363	−	3.53966i	−0.0866691	−	0.150115i
$557$	−8.87993	−	15.3805i	−0.376255	−	0.651692i	0.614259	−	0.789104i	$-0.289455\pi$
$557$	−8.87993	−	15.3805i	−0.376255	−	0.651692i	−0.990514	+	0.137412i	$0.956122\pi$
$558$	−20.5652	−	35.6199i	−0.870592	−	1.50791i
$559$	−12.8503			−0.543511
$560$	1.42533	−	2.46874i	0.0602310	−	0.104323i
$561$	20.5928	+	35.6677i	0.869427	+	1.50589i
$562$	−3.93330			−0.165916
$563$	−7.47512	−	12.9473i	−0.315039	−	0.545663i	0.664407	−	0.747371i	$-0.268684\pi$
$563$	−7.47512	−	12.9473i	−0.315039	−	0.545663i	−0.979446	+	0.201708i	$0.935351\pi$
$564$	1.68434	−	2.91736i	0.0709235	−	0.122843i
$565$	−4.93369			−0.207562
$566$	14.9683	−	25.9259i	0.629166	−	1.08975i
$567$	5.13367			0.215594
$568$	3.69227	−	6.39519i	0.154924	−	0.268336i
$569$	7.43539	−	12.8785i	0.311708	−	0.539894i	−0.667024	−	0.745036i	$-0.732432\pi$
$569$	7.43539	−	12.8785i	0.311708	−	0.539894i	0.978732	+	0.205142i	$0.0657657\pi$
$570$	7.50479	−	12.9987i	0.314341	−	0.544455i
$571$	4.70713			0.196987			0.0984935	−	0.995138i	$-0.468598\pi$
$571$	4.70713			0.196987			0.0984935	+	0.995138i	$0.468598\pi$
$572$	−1.81356			−0.0758289
$573$	−52.5482			−2.19523
$574$	1.50685	+	2.60993i	0.0628945	+	0.108937i
$575$	−14.9488	−	25.8921i	−0.623408	−	1.07977i
$576$	−12.4813	+	21.6182i	−0.520054	+	0.900760i
$577$	34.0798			1.41876			0.709381	−	0.704826i	$-0.248975\pi$
$577$	34.0798			1.41876			0.709381	+	0.704826i	$0.248975\pi$
$578$	−10.7756	+	18.6639i	−0.448206	+	0.776316i
$579$	3.43245	−	5.94518i	0.142648	−	0.247073i
$580$	−0.386534			−0.0160500
$581$	9.90730	+	17.1600i	0.411024	+	0.711915i
$582$	4.99553	−	8.65250i	0.207071	−	0.358658i
$583$	7.09379			0.293795
$584$	15.8575	+	27.4660i	0.656189	+	1.13655i
$585$	−1.83618	+	3.18036i	−0.0759168	+	0.131492i
$586$	4.82213	+	8.35217i	0.199200	+	0.345025i
$587$	−12.4452	−	21.5557i	−0.513669	−	0.889701i	−0.999874	−	0.0158563i	$-0.994953\pi$
$587$	−12.4452	−	21.5557i	−0.513669	−	0.889701i	0.486205	−	0.873845i	$-0.338381\pi$
$588$	−5.48306			−0.226117
$589$	−23.2371	−	40.2478i	−0.957468	−	1.65838i
$590$	−2.88986	−	5.00539i	−0.118974	−	0.206069i
$591$	6.27806	−	10.8739i	0.258245	−	0.447293i
$592$	−3.51513	+	6.08838i	−0.144471	+	0.250231i
$593$	−6.36066	−	11.0170i	−0.261201	−	0.452414i	0.705360	−	0.708849i	$-0.250785\pi$
$593$	−6.36066	−	11.0170i	−0.261201	−	0.452414i	−0.966561	+	0.256435i	$0.917452\pi$
$594$	−6.61474	+	11.4571i	−0.271406	+	0.470089i
$595$	−3.44407			−0.141193
$596$	−4.21322			−0.172580
$597$	44.5361			1.82274
$598$	17.0369			0.696692
$599$	7.22513	−	12.5143i	0.295211	−	0.511320i	−0.679823	−	0.733376i	$-0.737943\pi$
$599$	7.22513	−	12.5143i	0.295211	−	0.511320i	0.975034	+	0.222056i	$0.0712768\pi$
$600$	31.8319			1.29953
$601$	14.2064	−	24.6061i	0.579490	−	1.00371i	−0.416048	−	0.909343i	$-0.636585\pi$
$601$	14.2064	−	24.6061i	0.579490	−	1.00371i	0.995538	−	0.0943631i	$-0.0300815\pi$
$602$	6.93858	−	12.0180i	0.282795	−	0.489816i
$603$	−15.3428	+	26.5745i	−0.624808	+	1.08220i
$604$	2.34215	−	4.05672i	0.0953006	−	0.165065i
$605$	−0.843410	−	1.46083i	−0.0342895	−	0.0593912i
$606$	48.3022			1.96214
$607$	19.5530	+	33.8668i	0.793632	+	1.37461i	0.923704	+	0.383106i	$0.125146\pi$
$607$	19.5530	+	33.8668i	0.793632	+	1.37461i	−0.130072	+	0.991504i	$0.541521\pi$
$608$	7.55826	−	13.0913i	0.306528	−	0.530922i
$609$	3.38985	+	5.87139i	0.137364	+	0.237921i
$610$	10.0787			0.408075
$611$	−2.95867	+	5.12456i	−0.119695	+	0.207318i
$612$	−8.65211			−0.349741
$613$	22.2933	+	38.6132i	0.900419	+	1.55957i	0.826951	+	0.562274i	$0.190073\pi$
$613$	22.2933	+	38.6132i	0.900419	+	1.55957i	0.0734683	+	0.997298i	$0.476593\pi$
$614$	20.5991	+	35.6788i	0.831314	+	1.43988i
$615$	1.06890	−	1.85139i	0.0431022	−	0.0746552i
$616$	−4.26350	+	7.38459i	−0.171781	+	0.297534i
$617$	2.22200	+	3.84862i	0.0894544	+	0.154940i	0.907281	−	0.420526i	$-0.138154\pi$
$617$	2.22200	+	3.84862i	0.0894544	+	0.154940i	−0.817826	+	0.575465i	$0.804821\pi$
$618$	47.4684			1.90946
$619$	46.6507			1.87505			0.937525	−	0.347918i	$-0.113111\pi$
$619$	46.6507			1.87505			0.937525	+	0.347918i	$0.113111\pi$
$620$	0.602441	−	1.04346i	0.0241946	−	0.0419063i
$621$	9.77984	−	16.9392i	0.392452	−	0.679746i
$622$	4.84884	−	8.39844i	0.194421	−	0.336747i
$623$	−5.05422			−0.202493
$624$	−10.8249	+	18.7492i	−0.433341	+	0.750568i
$625$	−10.6369	−	18.4236i	−0.425474	−	0.736943i
$626$	−2.57597	+	4.46170i	−0.102956	+	0.178326i
$627$	−26.7932	+	46.4072i	−1.07002	+	1.85332i
$628$	−3.19283	+	5.53015i	−0.127408	+	0.220677i
$629$	8.49375			0.338668
$630$	−1.98291	−	3.43450i	−0.0790009	−	0.136834i
$631$	3.58867			0.142863			0.0714313	−	0.997446i	$-0.477243\pi$
$631$	3.58867			0.142863			0.0714313	+	0.997446i	$0.477243\pi$
$632$	−14.3769			−0.571882
$633$	−30.3214			−1.20517
$634$	−22.7126			−0.902034
$635$	3.13972	+	5.43816i	0.124596	+	0.215807i
$636$	−1.28238	+	2.22115i	−0.0508498	+	0.0880744i
$637$	9.63140			0.381610
$638$	8.76825			0.347138
$639$	−6.13077	−	10.6188i	−0.242530	−	0.420074i
$640$	−6.74458			−0.266603
$641$	−1.69243	+	2.93138i	−0.0668470	+	0.115782i	−0.897512	−	0.440990i	$-0.854627\pi$
$641$	−1.69243	+	2.93138i	−0.0668470	+	0.115782i	0.830665	+	0.556773i	$0.187961\pi$
$642$	−5.76127	+	9.97882i	−0.227379	+	0.393833i
$643$	−19.8300	−	34.3466i	−0.782020	−	1.35450i	−0.930763	−	0.365623i	$-0.880856\pi$
$643$	−19.8300	−	34.3466i	−0.782020	−	1.35450i	0.148743	−	0.988876i	$-0.452477\pi$
$644$	−1.44780	+	2.50766i	−0.0570513	+	0.0988158i
$645$	−9.84392			−0.387604
$646$	−62.1171			−2.44396
$647$	18.1411	+	31.4213i	0.713201	+	1.23530i	0.963649	+	0.267171i	$0.0860887\pi$
$647$	18.1411	+	31.4213i	0.713201	+	1.23530i	−0.250448	+	0.968130i	$0.580578\pi$
$648$	−5.22572	−	9.05122i	−0.205286	−	0.355565i
$649$	10.3172	+	17.8700i	0.404987	+	0.701458i
$650$	12.8426			0.503728
$651$	−21.1333			−0.828279
$652$	−1.39285	−	2.41249i	−0.0545483	−	0.0944805i
$653$	−47.7453			−1.86842			−0.934209	−	0.356726i	$-0.883893\pi$
$653$	−47.7453			−1.86842			−0.934209	+	0.356726i	$0.883893\pi$
$654$	−4.02774	−	6.97624i	−0.157497	−	0.272793i
$655$	−1.43427	−	2.48423i	−0.0560416	−	0.0970670i
$656$	3.66143	−	6.34179i	0.142955	−	0.247605i
$657$	52.6608			2.05449
$658$	−3.19509	−	5.53405i	−0.124557	−	0.215740i
$659$	24.4989			0.954342			0.477171	−	0.878810i	$-0.341662\pi$
$659$	24.4989			0.954342			0.477171	+	0.878810i	$0.341662\pi$
$660$	−1.38927			−0.0540773
$661$	29.5356			1.14880			0.574402	−	0.818574i	$-0.305235\pi$
$661$	29.5356			1.14880			0.574402	+	0.818574i	$0.305235\pi$
$662$	−42.0020			−1.63245
$663$	26.1565			1.01584
$664$	20.1699	−	34.9353i	0.782744	−	1.35575i
$665$	−2.24054	−	3.88073i	−0.0868843	−	0.150488i
$666$	4.89023	+	8.47013i	0.189493	+	0.328211i
$667$	−12.9638			−0.501960
$668$	−0.352514	−	0.610572i	−0.0136392	−	0.0236238i
$669$	7.07196	+	12.2490i	0.273418	+	0.473574i
$670$	−5.71159			−0.220658
$671$	−35.9825			−1.38909
$672$	−3.43698	−	5.95303i	−0.132585	−	0.229643i
$673$	14.5855	−	25.2629i	0.562230	−	0.973812i	−0.435071	−	0.900396i	$-0.643277\pi$
$673$	14.5855	−	25.2629i	0.562230	−	0.973812i	0.997301	−	0.0734154i	$-0.0233899\pi$
$674$	−21.7483	−	37.6691i	−0.837712	−	1.45096i
$675$	7.37213	−	12.7689i	0.283754	−	0.491476i
$676$	1.85226	−	3.20820i	0.0712406	−	0.123392i
$677$	13.2721			0.510089			0.255045	−	0.966929i	$-0.417910\pi$
$677$	13.2721			0.510089			0.255045	+	0.966929i	$0.417910\pi$
$678$	−20.2319	+	35.0426i	−0.777000	+	1.34580i
$679$	−1.49140	−	2.58319i	−0.0572348	−	0.0991336i
$680$	3.50583	+	6.07227i	0.134442	+	0.232861i
$681$	−68.7295			−2.63372
$682$	−13.6659	+	23.6701i	−0.523296	+	0.906375i
$683$	18.0569	−	31.2754i	0.690928	−	1.19672i	−0.280607	−	0.959823i	$-0.590536\pi$
$683$	18.0569	−	31.2754i	0.690928	−	1.19672i	0.971534	−	0.236899i	$-0.0761310\pi$
$684$	−5.62862	−	9.74905i	−0.215216	−	0.372764i
$685$	−3.99838	+	6.92541i	−0.152770	+	0.264606i
$686$	−11.8373	+	20.5028i	−0.451950	+	0.782801i
$687$	54.1820			2.06717
$688$	−33.7196			−1.28555
$689$	2.25260	−	3.90162i	0.0858173	−	0.148640i
$690$	13.0511			0.496845
$691$	4.20285	−	7.27954i	0.159884	−	0.276927i	−0.774943	−	0.632031i	$-0.782221\pi$
$691$	4.20285	−	7.27954i	0.159884	−	0.276927i	0.934827	+	0.355105i	$0.115555\pi$
$692$	−2.27856			−0.0866177
$693$	7.07927	+	12.2617i	0.268919	+	0.465782i
$694$	14.8474	+	25.7164i	0.563598	+	0.976181i
$695$	2.74993	+	4.76303i	0.104311	+	0.180672i
$696$	6.90127	−	11.9533i	0.261592	−	0.453090i
$697$	−8.84727			−0.335114
$698$	28.7302	+	1.71773i	1.08745	+	0.0650169i
$699$	−19.6162			−0.741954
$700$	−1.09136	+	1.89030i	−0.0412497	+	0.0714466i
$701$	7.64379	+	13.2394i	0.288702	+	0.500046i	0.973500	−	0.228686i	$-0.0734430\pi$
$701$	7.64379	+	13.2394i	0.288702	+	0.500046i	−0.684798	+	0.728733i	$0.740110\pi$
$702$	4.20096	+	7.27627i	0.158555	+	0.274625i
$703$	5.52560	+	9.57062i	0.208402	+	0.360963i
$704$	16.5881			0.625189
$705$	−2.26647	+	3.92565i	−0.0853603	+	0.147848i
$706$	−4.63308			−0.174368
$707$	7.21025	−	12.4885i	0.271169	−	0.469679i
$708$	−7.46041			−0.280379
$709$	−30.4026			−1.14179			−0.570897	−	0.821021i	$-0.693405\pi$
$709$	−30.4026			−1.14179			−0.570897	+	0.821021i	$0.693405\pi$
$710$	1.14113	−	1.97650i	0.0428260	−	0.0741769i
$711$	−11.9360	+	20.6737i	−0.447633	+	0.775324i
$712$	5.14485	+	8.91114i	0.192811	+	0.333959i
$713$	20.2050	−	34.9961i	0.756683	−	1.31061i
$714$	−14.1233	+	24.4623i	−0.528552	+	0.915478i
$715$	2.44036			0.0912643
$716$	1.80266	+	3.12229i	0.0673685	+	0.116686i
$717$	−0.441138	−	0.764074i	−0.0164746	−	0.0285349i
$718$	25.6024	−	44.3446i	0.955473	−	1.65493i
$719$	9.81789			0.366145			0.183073	−	0.983099i	$-0.441396\pi$
$719$	9.81789			0.366145			0.183073	+	0.983099i	$0.441396\pi$
$720$	−4.81820	+	8.34536i	−0.179564	+	0.311013i
$721$	7.08580	−	12.2730i	0.263889	−	0.457069i
$722$	−25.7741	−	44.6421i	−0.959214	−	1.66141i
$723$	5.61559	−	9.72649i	0.208846	−	0.361732i
$724$	4.04455	+	7.00536i	0.150314	+	0.260352i
$725$	−9.77223			−0.362931
$726$	−13.8345			−0.513446
$727$	14.6992	+	25.4598i	0.545164	+	0.944253i	0.998597	+	0.0529617i	$0.0168661\pi$
$727$	14.6992	+	25.4598i	0.545164	+	0.944253i	−0.453432	+	0.891291i	$0.649801\pi$
$728$	2.70771	+	4.68989i	0.100354	+	0.173819i
$729$	−42.2868			−1.56618
$730$	4.90094	+	8.48867i	0.181392	+	0.314180i
$731$	20.3695	+	35.2810i	0.753393	+	1.30492i
$732$	6.50474	−	11.2665i	0.240422	−	0.416424i
$733$	−24.1554			−0.892199			−0.446099	−	0.894983i	$-0.647187\pi$
$733$	−24.1554			−0.892199			−0.446099	+	0.894983i	$0.647187\pi$
$734$	−45.0116			−1.66141
$735$	7.37808			0.272145
$736$	13.1440			0.484496
$737$	20.3912			0.751120
$738$	−5.09377	−	8.82267i	−0.187504	−	0.324767i
$739$	31.6103			1.16280			0.581401	−	0.813617i	$-0.302505\pi$
$739$	31.6103			1.16280			0.581401	+	0.813617i	$0.302505\pi$
$740$	−0.143256	+	0.248126i	−0.00526619	+	0.00912130i
$741$	17.0161	+	29.4728i	0.625102	+	1.08271i
$742$	2.43260	+	4.21339i	0.0893035	+	0.154678i
$743$	14.7359			0.540606			0.270303	−	0.962775i	$-0.412876\pi$
$743$	14.7359			0.540606			0.270303	+	0.962775i	$0.412876\pi$
$744$	21.5122	+	37.2603i	0.788677	+	1.36603i
$745$	5.66937			0.207710
$746$	−55.6488			−2.03745
$747$	−33.4908	−	58.0078i	−1.22537	−	2.12240i
$748$	2.87475	+	4.97921i	0.105111	+	0.182058i
$749$	1.72002	+	2.97915i	0.0628480	+	0.108856i
$750$	20.1996			0.737586
$751$	−41.5695			−1.51689			−0.758447	−	0.651735i	$-0.774041\pi$
$751$	−41.5695			−1.51689			−0.758447	+	0.651735i	$0.774041\pi$
$752$	−7.76363	+	13.4470i	−0.283110	+	0.490362i
$753$	30.4255	+	52.6985i	1.10877	+	1.92044i
$754$	2.78432	−	4.82258i	0.101399	−	0.175628i
$755$	−3.15163	+	5.45878i	−0.114700	+	0.198665i
$756$	−1.42799			−0.0519355
$757$	−5.03075	−	8.71351i	−0.182846	−	0.316698i	0.760003	−	0.649920i	$-0.225198\pi$
$757$	−5.03075	−	8.71351i	−0.182846	−	0.316698i	−0.942848	+	0.333222i	$0.891864\pi$
$758$	−9.35877			−0.339926
$759$	−46.5942			−1.69126
$760$	−4.56142	+	7.90062i	−0.165460	+	0.286585i
$761$	−4.29864	−	7.44547i	−0.155826	−	0.269898i	0.777534	−	0.628841i	$-0.216471\pi$
$761$	−4.29864	−	7.44547i	−0.155826	−	0.269898i	−0.933359	+	0.358943i	$0.883137\pi$
$762$	51.5010			1.86568
$763$	−2.40494			−0.0870648
$764$	−7.33572			−0.265397
$765$	11.6424			0.420932
$766$	−24.1109	−	41.7612i	−0.871161	−	1.50889i
$767$	13.1048			0.473185
$768$	−11.6031	+	20.0971i	−0.418690	+	0.725192i
$769$	−1.50978	+	2.61502i	−0.0544441	+	0.0943000i	−0.891963	−	0.452108i	$-0.850672\pi$
$769$	−1.50978	+	2.61502i	−0.0544441	+	0.0943000i	0.837519	+	0.546408i	$0.184005\pi$
$770$	−1.31768	+	2.28229i	−0.0474859	+	0.0822480i
$771$	16.7257	+	28.9697i	0.602361	+	1.04332i
$772$	0.479170	−	0.829947i	0.0172457	−	0.0298704i
$773$	−50.6154			−1.82051			−0.910256	−	0.414047i	$-0.864115\pi$
$773$	−50.6154			−1.82051			−0.910256	+	0.414047i	$0.864115\pi$
$774$	−23.4553	+	40.6257i	−0.843083	+	1.46026i
$775$	15.2307	−	26.3804i	0.547103	−	0.947611i
$776$	−3.03629	+	5.25901i	−0.108996	+	0.188787i
$777$	5.02533			0.180283
$778$	50.0965			1.79605
$779$	−5.75558	−	9.96896i	−0.206215	−	0.357175i
$780$	−0.441157	+	0.764106i	−0.0157959	+	0.0273594i
$781$	−4.07402	+	7.05640i	−0.145780	+	0.252498i
$782$	−27.0059	−	46.7755i	−0.965728	−	1.67269i
$783$	−3.19661	−	5.53668i	−0.114237	−	0.197865i
$784$	25.2731			0.902610
$785$	4.29633	−	7.44145i	0.153342	−	0.265597i
$786$	−23.5264			−0.839159
$787$	9.09852	+	15.7591i	0.324327	+	0.561751i	0.981376	−	0.192097i	$-0.0615288\pi$
$787$	9.09852	+	15.7591i	0.324327	+	0.561751i	−0.657049	+	0.753848i	$0.728195\pi$
$788$	0.876417	−	1.51800i	0.0312211	−	0.0540765i
$789$	9.43096	+	16.3349i	0.335751	+	0.581538i
$790$	−4.44334			−0.158087
$791$	6.04017	+	10.4619i	0.214764	+	0.371982i
$792$	14.4124	−	24.9630i	0.512123	−	0.887022i
$793$	−11.4261	+	19.7905i	−0.405752	+	0.702782i
$794$	−9.97781	+	17.2821i	−0.354099	+	0.613318i
$795$	1.72559	−	2.98882i	0.0612005	−	0.106002i
$796$	6.21724			0.220364
$797$	21.8984	−	37.9291i	0.775681	−	1.34352i	−0.158730	−	0.987322i	$-0.550740\pi$
$797$	21.8984	−	37.9291i	0.775681	−	1.34352i	0.934411	−	0.356196i	$-0.115927\pi$
$798$	−36.7516			−1.30099
$799$	18.7596			0.663666
$800$	9.90810			0.350304
$801$	17.0854			0.603683
$802$	−1.53734	+	2.66275i	−0.0542853	+	0.0940248i
$803$	−17.4971	−	30.3058i	−0.617458	−	1.06947i
$804$	−3.68623	+	6.38473i	−0.130003	+	0.225172i
$805$	1.94818	−	3.37435i	0.0686644	−	0.118930i
$806$	8.67911	+	15.0327i	0.305709	+	0.529503i
$807$	−16.3938	−	28.3949i	−0.577089	−	0.999547i
$808$	−29.3581			−1.03282
$809$	5.43374	+	9.41151i	0.191040	+	0.330891i	0.945595	−	0.325346i	$-0.105481\pi$
$809$	5.43374	+	9.41151i	0.191040	+	0.330891i	−0.754555	+	0.656237i	$0.772147\pi$
$810$	−1.61507	−	2.79738i	−0.0567477	−	0.0982898i
$811$	−12.8154	+	22.1969i	−0.450009	+	0.779439i	−0.998386	−	0.0567926i	$-0.981913\pi$
$811$	−12.8154	+	22.1969i	−0.450009	+	0.779439i	0.548377	+	0.836231i	$0.315246\pi$
$812$	0.473223	+	0.819646i	0.0166069	+	0.0287639i
$813$	−81.8584			−2.87090
$814$	3.24965	−	5.62857i	0.113900	−	0.197281i
$815$	1.87424	+	3.24629i	0.0656519	+	0.113712i
$816$	68.6355			2.40272
$817$	−26.5027	+	45.9041i	−0.927213	+	1.60598i
$818$	−18.0953	+	31.3421i	−0.632689	+	1.09585i
$819$	8.99195			0.314204
$820$	0.149218	−	0.258454i	0.00521093	−	0.00902559i
$821$	13.9073	+	24.0881i	0.485368	+	0.840681i	0.999859	−	0.0168145i	$-0.00535247\pi$
$821$	13.9073	+	24.0881i	0.485368	+	0.840681i	−0.514491	+	0.857496i	$0.672019\pi$
$822$	32.7928	+	56.7988i	1.14378	+	1.98109i
$823$	−12.3025			−0.428839			−0.214419	−	0.976742i	$-0.568786\pi$
$823$	−12.3025			−0.428839			−0.214419	+	0.976742i	$0.568786\pi$
$824$	−28.8514			−1.00509
$825$	−35.1231			−1.22283
$826$	−7.07596	+	12.2559i	−0.246204	+	0.426438i
$827$	−13.3866	+	23.1864i	−0.465499	+	0.806269i	−0.999224	−	0.0393898i	$-0.987459\pi$
$827$	−13.3866	+	23.1864i	−0.465499	+	0.806269i	0.533725	+	0.845658i	$0.320792\pi$
$828$	4.89417	−	8.47695i	0.170084	−	0.294594i
$829$	24.3636			0.846182			0.423091	−	0.906087i	$-0.360945\pi$
$829$	24.3636			0.846182			0.423091	+	0.906087i	$0.360945\pi$
$830$	6.23373	−	10.7971i	0.216376	−	0.374774i
$831$	−11.8548			−0.411240
$832$	5.26748	−	9.12355i	0.182617	−	0.316302i
$833$	−15.2671	−	26.4434i	−0.528973	−	0.916208i
$834$	45.1073			1.56194
$835$	0.474348	+	0.821595i	0.0164155	+	0.0284325i
$836$	−3.74033	+	6.47843i	−0.129362	+	0.224061i
$837$	19.9286			0.688832
$838$	28.7059	+	49.7201i	0.991630	+	1.71755i
$839$	−20.6056	−	35.6900i	−0.711384	−	1.23215i	−0.964338	−	0.264675i	$-0.914735\pi$
$839$	−20.6056	−	35.6900i	−0.711384	−	1.23215i	0.252953	−	0.967479i	$-0.418598\pi$
$840$	2.07423	+	3.59266i	0.0715676	+	0.123959i
$841$	12.3813	−	21.4451i	0.426943	−	0.739487i
$842$	−16.1124	−	27.9075i	−0.555270	−	0.961757i
$843$	3.41588	−	5.91649i	0.117649	−	0.203775i
$844$	−4.23286			−0.145701
$845$	−2.49242	+	4.31700i	−0.0857420	+	0.148509i
$846$	10.8007	+	18.7074i	0.371337	+	0.643174i
$847$	−2.06513	+	3.57691i	−0.0709586	+	0.122904i
$848$	5.91089	−	10.2380i	0.202981	−	0.351573i
$849$	25.9986	+	45.0308i	0.892268	+	1.54545i
$850$	−20.3573	−	35.2598i	−0.698248	−	1.20940i
$851$	−4.80459	+	8.32180i	−0.164699	+	0.285268i
$852$	−1.47296	−	2.55125i	−0.0504629	−	0.0874043i
$853$	−17.8232	−	30.8706i	−0.610253	−	1.05699i	−0.991197	−	0.132392i	$-0.957734\pi$
$853$	−17.8232	−	30.8706i	−0.610253	−	1.05699i	0.380944	−	0.924598i	$-0.375599\pi$
$854$	−12.3391	−	21.3719i	−0.422235	−	0.731332i
$855$	7.57395	+	13.1185i	0.259024	+	0.448642i
$856$	3.50171	−	6.06514i	0.119686	−	0.207302i
$857$	8.29971	+	14.3755i	0.283513	+	0.491058i	0.972247	−	0.233955i	$-0.0751669\pi$
$857$	8.29971	+	14.3755i	0.283513	+	0.491058i	−0.688735	+	0.725013i	$0.741834\pi$
$858$	10.0073	−	17.3332i	0.341644	−	0.591745i
$859$	14.3855	+	24.9165i	0.490828	+	0.850138i	0.999944	−	0.0105591i	$-0.00336112\pi$
$859$	14.3855	+	24.9165i	0.490828	+	0.850138i	−0.509117	+	0.860698i	$0.670028\pi$
$860$	−1.37421			−0.0468602
$861$	−5.23449			−0.178391
$862$	26.4202	+	45.7612i	0.899877	+	1.55863i
$863$	−6.30309	+	10.9173i	−0.214560	+	0.371628i	−0.953136	−	0.302541i	$-0.902165\pi$
$863$	−6.30309	+	10.9173i	−0.214560	+	0.371628i	0.738577	+	0.674170i	$0.235498\pi$
$864$	3.24105	+	5.61367i	0.110263	+	0.190981i
$865$	3.06606			0.104249
$866$	−61.8003			−2.10006
$867$	−18.7162	−	32.4174i	−0.635635	−	1.10095i
$868$	−2.95021			−0.100137
$869$	15.8634			0.538127
$870$	2.13291	−	3.69431i	0.0723125	−	0.125249i
$871$	6.47513	−	11.2153i	0.219401	−	0.380014i
$872$	2.44806	+	4.24017i	0.0829019	+	0.143590i
$873$	5.04157	+	8.73225i	0.170631	+	0.295542i
$874$	35.1373	−	60.8595i	1.18854	−	2.05860i
$875$	3.01528	−	5.22261i	0.101935	−	0.176557i
$876$	12.6521			0.427476
$877$	−34.4891			−1.16461			−0.582307	−	0.812969i	$-0.697850\pi$
$877$	−34.4891			−1.16461			−0.582307	+	0.812969i	$0.697850\pi$
$878$	−10.0344	−	17.3801i	−0.338645	−	0.586550i
$879$	−16.7512			−0.565002
$880$	6.40357			0.215864
$881$	26.2279	+	45.4281i	0.883641	+	1.53051i	0.847264	+	0.531172i	$0.178248\pi$
$881$	26.2279	+	45.4281i	0.883641	+	1.53051i	0.0363766	+	0.999338i	$0.488418\pi$
$882$	17.5799	−	30.4493i	0.591946	−	1.02528i
$883$	−19.4187	−	33.6341i	−0.653490	−	1.13188i	−0.982270	−	0.187471i	$-0.939971\pi$
$883$	−19.4187	−	33.6341i	−0.653490	−	1.13188i	0.328780	−	0.944406i	$-0.393362\pi$
$884$	3.65145			0.122811
$885$	10.0388			0.337452
$886$	11.0207	+	19.0884i	0.370248	+	0.641288i
$887$	8.61184	−	14.9161i	0.289157	−	0.500835i	−0.684452	−	0.729058i	$-0.739958\pi$
$887$	8.61184	−	14.9161i	0.289157	−	0.500835i	0.973609	+	0.228223i	$0.0732916\pi$
$888$	−5.11544	−	8.86020i	−0.171663	−	0.297329i
$889$	7.68775	−	13.3156i	0.257839	−	0.446590i
$890$	1.59007	+	2.75409i	0.0532993	+	0.0923171i
$891$	5.76602	+	9.98705i	0.193169	+	0.334579i
$892$	0.987245	+	1.70996i	0.0330554	+	0.0572536i
$893$	12.2040	+	21.1380i	0.408392	+	0.707356i
$894$	23.2487	−	40.2680i	0.777554	−	1.34676i
$895$	−2.42568	−	4.20141i	−0.0810817	−	0.140438i
$896$	8.25720	+	14.3019i	0.275854	+	0.477793i
$897$	−14.7958	+	25.6270i	−0.494016	+	0.855661i
$898$	−24.2782	+	42.0511i	−0.810174	+	1.40326i
$899$	−6.60414	−	11.4387i	−0.220260	−	0.381502i
$900$	3.68927	−	6.39000i	0.122976	−	0.213000i
$901$	−14.2827			−0.475826
$902$	−3.38491	+	5.86283i	−0.112705	+	0.195211i
$903$	12.0516	+	20.8741i	0.401053	+	0.694645i
$904$	12.2970	−	21.2990i	0.408991	−	0.708393i
$905$	−5.44241	−	9.42653i	−0.180912	−	0.313348i
$906$	25.8481	+	44.7703i	0.858747	+	1.48739i
$907$	−5.32292	−	9.21957i	−0.176745	−	0.306131i	0.764019	−	0.645194i	$-0.223223\pi$
$907$	−5.32292	−	9.21957i	−0.176745	−	0.306131i	−0.940764	+	0.339063i	$0.889890\pi$
$908$	−9.59463			−0.318409
$909$	−24.3737	+	42.2164i	−0.808424	+	1.40023i
$910$	0.836846	+	1.44946i	0.0277412	+	0.0480492i
$911$	−3.43978			−0.113965			−0.0569825	−	0.998375i	$-0.518148\pi$
$911$	−3.43978			−0.113965			−0.0569825	+	0.998375i	$0.518148\pi$
$912$	44.6507	+	77.3373i	1.47853	+	2.56090i
$913$	−22.2553	+	38.5473i	−0.736543	+	1.27573i
$914$	−33.2194			−1.09880
$915$	−8.75288	+	15.1604i	−0.289361	+	0.501189i
$916$	7.56380			0.249915
$917$	−3.51188	+	6.08275i	−0.115972	+	0.200870i
$918$	13.3182	−	23.0678i	0.439565	−	0.761350i
$919$	8.19221	−	14.1893i	0.270236	−	0.468062i	−0.698686	−	0.715428i	$-0.746232\pi$
$919$	8.19221	−	14.1893i	0.270236	−	0.468062i	0.968922	+	0.247366i	$0.0795650\pi$
$920$	−7.93245			−0.261525
$921$	−71.5575			−2.35790
$922$	−15.9255			−0.524480
$923$	2.58737	+	4.48146i	0.0851643	+	0.147509i
$924$	1.70085	+	2.94595i	0.0559537	+	0.0969147i
$925$	−3.62174	+	6.27305i	−0.119082	+	0.206256i
$926$	41.4896			1.36343
$927$	−23.9530	+	41.4877i	−0.786718	+	1.36264i
$928$	2.14811	−	3.72063i	0.0705151	−	0.122136i
$929$	−35.7224			−1.17201			−0.586007	−	0.810306i	$-0.699301\pi$
$929$	−35.7224			−1.17201			−0.586007	+	0.810306i	$0.699301\pi$
$930$	6.64859	+	11.5157i	0.218016	+	0.377615i
$931$	19.8640	−	34.4054i	0.651015	−	1.12759i
$932$	−2.73842			−0.0897000
$933$	8.42197	+	14.5873i	0.275723	+	0.477566i
$934$	−2.79165	+	4.83529i	−0.0913457	+	0.158215i
$935$	−3.86830	−	6.70010i	−0.126507	−	0.219117i
$936$	−9.15318	−	15.8538i	−0.299181	−	0.518197i
$937$	0.813684			0.0265819			0.0132909	−	0.999912i	$-0.495769\pi$
$937$	0.813684			0.0265819			0.0132909	+	0.999912i	$0.495769\pi$
$938$	6.99254	+	12.1114i	0.228314	+	0.395452i
$939$	−4.47420	−	7.74955i	−0.146010	−	0.252897i
$940$	−0.316399	+	0.548020i	−0.0103198	+	0.0178744i
$941$	−27.2686	+	47.2305i	−0.888930	+	1.53967i	−0.0477872	+	0.998858i	$0.515217\pi$
$941$	−27.2686	+	47.2305i	−0.888930	+	1.53967i	−0.841142	+	0.540814i	$0.818116\pi$
$942$	−35.2364	−	61.0312i	−1.14806	−	1.98850i
$943$	5.00456	−	8.66816i	0.162971	−	0.282274i
$944$	34.3873			1.11921
$945$	1.92153			0.0625073
$946$	31.1730			1.01352
$947$	−11.0928			−0.360469			−0.180234	−	0.983624i	$-0.557686\pi$
$947$	−11.0928			−0.360469			−0.180234	+	0.983624i	$0.557686\pi$
$948$	−2.86770	+	4.96701i	−0.0931386	+	0.161321i
$949$	−22.2244			−0.721436
$950$	26.4868	−	45.8765i	0.859345	−	1.48843i
$951$	19.7248	−	34.1644i	0.639621	−	1.10786i
$952$	8.58417	−	14.8682i	0.278215	−	0.481882i
$953$	−25.6560	+	44.4376i	−0.831081	+	1.43947i	0.0661016	+	0.997813i	$0.478944\pi$
$953$	−25.6560	+	44.4376i	−0.831081	+	1.43947i	−0.897182	+	0.441661i	$0.854389\pi$
$954$	−8.22320	−	14.2430i	−0.266236	−	0.461134i
$955$	9.87106			0.319420
$956$	−0.0615828	−	0.106665i	−0.00199173	−	0.00344978i
$957$	−7.61480	+	13.1892i	−0.246152	+	0.426347i
$958$	3.42406	+	5.93065i	0.110626	+	0.191611i
$959$	19.5804			0.632285
$960$	4.03513	−	6.98905i	0.130233	−	0.225570i
$961$	10.1721			0.328132
$962$	−2.06382	−	3.57465i	−0.0665404	−	0.115251i
$963$	−5.81437	−	10.0708i	−0.187365	−	0.324527i
$964$	0.783936	−	1.35782i	0.0252489	−	0.0437324i
$965$	−0.644779	+	1.11679i	−0.0207562	+	0.0359507i
$966$	−15.9780	−	27.6748i	−0.514085	−	0.890422i
$967$	−15.5412			−0.499770			−0.249885	−	0.968276i	$-0.580393\pi$
$967$	−15.5412			−0.499770			−0.249885	+	0.968276i	$0.580393\pi$
$968$	8.40863			0.270263
$969$	53.9457	−	93.4367i	1.73298	−	3.00162i
$970$	−0.938398	+	1.62535i	−0.0301301	+	0.0521869i
$971$	24.7749	−	42.9114i	0.795065	−	1.37709i	−0.127733	−	0.991809i	$-0.540770\pi$
$971$	24.7749	−	42.9114i	0.795065	−	1.37709i	0.922798	−	0.385284i	$-0.125897\pi$
$972$	−7.65004			−0.245375
$973$	6.73334	−	11.6625i	0.215861	−	0.373882i
$974$	−4.32936	−	7.49866i	−0.138722	−	0.240273i
$975$	−11.1532	+	19.3179i	−0.357188	+	0.618667i
$976$	−29.9823	+	51.9309i	−0.959711	+	1.66227i
$977$	16.0195	−	27.7466i	0.512509	−	0.887692i	−0.487386	−	0.873187i	$-0.662049\pi$
$977$	16.0195	−	27.7466i	0.512509	−	0.887692i	0.999895	−	0.0145052i	$-0.00461730\pi$
$978$	30.7433			0.983062
$979$	−5.67679	−	9.83248i	−0.181431	−	0.314248i
$980$	1.02998			0.0329015
$981$	8.12971			0.259562
$982$	−31.6625			−1.01039
$983$	1.30798			0.0417181			0.0208590	−	0.999782i	$-0.493360\pi$
$983$	1.30798			0.0417181			0.0208590	+	0.999782i	$0.493360\pi$
$984$	5.32835	+	9.22897i	0.169862	+	0.294209i
$985$	−1.17932	+	2.04264i	−0.0375763	+	0.0650840i
$986$	−17.6541			−0.562221
$987$	11.0991			0.353289
$988$	2.37545	+	4.11439i	0.0755730	+	0.130896i
$989$	−46.0890			−1.46555
$990$	4.45431	−	7.71509i	0.141567	−	0.245202i
$991$	−2.41627	+	4.18511i	−0.0767554	+	0.132944i	−0.901848	−	0.432053i	$-0.857789\pi$
$991$	−2.41627	+	4.18511i	−0.0767554	+	0.132944i	0.825093	+	0.564997i	$0.191123\pi$
$992$	6.69596	+	11.5977i	0.212597	+	0.368229i
$993$	36.4767	−	63.1795i	1.15755	−	2.00494i
$994$	−5.58824			−0.177248
$995$	−8.36601			−0.265220
$996$	−8.04642	−	13.9368i	−0.254961	−	0.441605i
$997$	1.30403	+	2.25864i	0.0412989	+	0.0715318i	0.885936	−	0.463808i	$-0.153517\pi$
$997$	1.30403	+	2.25864i	0.0412989	+	0.0715318i	−0.844637	+	0.535339i	$0.820184\pi$
$998$	23.9130	+	41.4186i	0.756954	+	1.31108i
$999$	−4.73885			−0.149931

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.c.a.122.8	✓	56
349.226	even	3	inner	349.2.c.a.226.8	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.c.a.122.8	✓	56	1.1	even	1	trivial
349.2.c.a.226.8	yes	56	349.226	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.770318 + 1.33423i) q^{2} +(-1.33797 - 2.31743i) q^{3} +(-0.186780 - 0.323513i) q^{4} +(0.251334 + 0.435324i) q^{5} +4.12265 q^{6} +(0.615403 - 1.06591i) q^{7} -2.50575 q^{8} +(-2.08032 + 3.60322i) q^{9} +O(q^{10})\)	\(q+(-0.770318 + 1.33423i) q^{2} +(-1.33797 - 2.31743i) q^{3} +(-0.186780 - 0.323513i) q^{4} +(0.251334 + 0.435324i) q^{5} +4.12265 q^{6} +(0.615403 - 1.06591i) q^{7} -2.50575 q^{8} +(-2.08032 + 3.60322i) q^{9} -0.774430 q^{10} +2.76483 q^{11} +(-0.499812 + 0.865701i) q^{12} +(0.877958 - 1.52067i) q^{13} +(0.948113 + 1.64218i) q^{14} +(0.672555 - 1.16490i) q^{15} +(2.30379 - 3.99028i) q^{16} -5.56673 q^{17} +(-3.20502 - 5.55126i) q^{18} +(-3.62143 - 6.27250i) q^{19} +(0.0938886 - 0.162620i) q^{20} -3.29356 q^{21} +(-2.12980 + 3.68892i) q^{22} +(3.14889 - 5.45404i) q^{23} +(3.35262 + 5.80690i) q^{24} +(2.37366 - 4.11130i) q^{25} +(1.35261 + 2.34280i) q^{26} +3.10581 q^{27} -0.459781 q^{28} +(-1.02924 - 1.78269i) q^{29} +(1.03616 + 1.79469i) q^{30} +6.41655 q^{31} +(1.04355 + 1.80747i) q^{32} +(-3.69925 - 6.40729i) q^{33} +(4.28816 - 7.42730i) q^{34} +0.618688 q^{35} +1.55425 q^{36} -1.52580 q^{37} +11.1586 q^{38} -4.69872 q^{39} +(-0.629782 - 1.09081i) q^{40} +1.58931 q^{41} +(2.53709 - 4.39437i) q^{42} +(-3.65915 - 6.33783i) q^{43} +(-0.516415 - 0.894458i) q^{44} -2.09143 q^{45} +(4.85130 + 8.40269i) q^{46} -3.36994 q^{47} -12.3296 q^{48} +(2.74256 + 4.75025i) q^{49} +(3.65695 + 6.33402i) q^{50} +(7.44811 + 12.9005i) q^{51} -0.655941 q^{52} +2.56573 q^{53} +(-2.39246 + 4.14386i) q^{54} +(0.694896 + 1.20360i) q^{55} +(-1.54205 + 2.67091i) q^{56} +(-9.69073 + 16.7848i) q^{57} +3.17136 q^{58} +(3.73160 + 6.46333i) q^{59} -0.502480 q^{60} -13.0144 q^{61} +(-4.94278 + 8.56115i) q^{62} +(2.56047 + 4.43487i) q^{63} +5.99970 q^{64} +0.882644 q^{65} +11.3984 q^{66} +7.37522 q^{67} +(1.03976 + 1.80091i) q^{68} -16.8525 q^{69} +(-0.476587 + 0.825473i) q^{70} +(-1.47352 + 2.55220i) q^{71} +(5.21277 - 9.02878i) q^{72} +(-6.32845 - 10.9612i) q^{73} +(1.17536 - 2.03577i) q^{74} -12.7035 q^{75} +(-1.35282 + 2.34316i) q^{76} +(1.70148 - 2.94706i) q^{77} +(3.61951 - 6.26918i) q^{78} +5.73756 q^{79} +2.31608 q^{80} +(2.08549 + 3.61218i) q^{81} +(-1.22427 + 2.12051i) q^{82} +(-8.04944 + 13.9420i) q^{83} +(0.615173 + 1.06551i) q^{84} +(-1.39911 - 2.42333i) q^{85} +11.2748 q^{86} +(-2.75417 + 4.77036i) q^{87} -6.92797 q^{88} +(-2.05322 - 3.55627i) q^{89} +(1.61106 - 2.79044i) q^{90} +(-1.08060 - 1.87165i) q^{91} -2.35260 q^{92} +(-8.58514 - 14.8699i) q^{93} +(2.59593 - 4.49628i) q^{94} +(1.82038 - 3.15299i) q^{95} +(2.79246 - 4.83669i) q^{96} +(1.21173 - 2.09877i) q^{97} -8.45057 q^{98} +(-5.75173 + 9.96229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9} - 2 q^{10} - 2 q^{11} + 11 q^{12} - 2 q^{13} + 2 q^{14} + 9 q^{15} - 34 q^{16} + 18 q^{18} - 5 q^{19} + 14 q^{20} + 12 q^{21} - 7 q^{22} - 11 q^{23} - 30 q^{24} - 6 q^{25} - 11 q^{26} - 30 q^{27} - 52 q^{28} + 8 q^{29} - 21 q^{30} - 48 q^{31} - 6 q^{32} + 12 q^{33} - 14 q^{34} + 42 q^{35} + 66 q^{36} + 14 q^{37} + 60 q^{38} - 26 q^{39} + 24 q^{40} - 3 q^{42} - 23 q^{43} - 20 q^{44} + 18 q^{45} + 5 q^{46} - 26 q^{47} - 22 q^{48} - 26 q^{49} + 11 q^{50} + 14 q^{51} + 6 q^{52} - 12 q^{53} - 7 q^{54} + 10 q^{55} - 19 q^{56} + 25 q^{57} - 12 q^{58} - 16 q^{59} - 12 q^{60} + 42 q^{61} - 27 q^{62} + 31 q^{63} + 54 q^{64} + 72 q^{65} - 66 q^{66} - 34 q^{67} - 57 q^{68} + 10 q^{69} - 52 q^{70} - 10 q^{71} + 47 q^{72} + 23 q^{73} - 17 q^{74} - 26 q^{75} + 9 q^{76} - 10 q^{77} + 25 q^{78} + 48 q^{79} - 32 q^{80} - 12 q^{81} - 8 q^{82} + 14 q^{83} + 10 q^{84} - 3 q^{85} + 46 q^{86} + 14 q^{87} + 58 q^{88} + 8 q^{89} + 68 q^{90} + 54 q^{91} + 48 q^{92} - 57 q^{93} + 33 q^{94} + 54 q^{95} - 72 q^{96} + 32 q^{98} + 73 q^{99}+O(q^{100}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9 - 2 * q^10 - 2 * q^11 + 11 * q^12 - 2 * q^13 + 2 * q^14 + 9 * q^15 - 34 * q^16 + 18 * q^18 - 5 * q^19 + 14 * q^20 + 12 * q^21 - 7 * q^22 - 11 * q^23 - 30 * q^24 - 6 * q^25 - 11 * q^26 - 30 * q^27 - 52 * q^28 + 8 * q^29 - 21 * q^30 - 48 * q^31 - 6 * q^32 + 12 * q^33 - 14 * q^34 + 42 * q^35 + 66 * q^36 + 14 * q^37 + 60 * q^38 - 26 * q^39 + 24 * q^40 - 3 * q^42 - 23 * q^43 - 20 * q^44 + 18 * q^45 + 5 * q^46 - 26 * q^47 - 22 * q^48 - 26 * q^49 + 11 * q^50 + 14 * q^51 + 6 * q^52 - 12 * q^53 - 7 * q^54 + 10 * q^55 - 19 * q^56 + 25 * q^57 - 12 * q^58 - 16 * q^59 - 12 * q^60 + 42 * q^61 - 27 * q^62 + 31 * q^63 + 54 * q^64 + 72 * q^65 - 66 * q^66 - 34 * q^67 - 57 * q^68 + 10 * q^69 - 52 * q^70 - 10 * q^71 + 47 * q^72 + 23 * q^73 - 17 * q^74 - 26 * q^75 + 9 * q^76 - 10 * q^77 + 25 * q^78 + 48 * q^79 - 32 * q^80 - 12 * q^81 - 8 * q^82 + 14 * q^83 + 10 * q^84 - 3 * q^85 + 46 * q^86 + 14 * q^87 + 58 * q^88 + 8 * q^89 + 68 * q^90 + 54 * q^91 + 48 * q^92 - 57 * q^93 + 33 * q^94 + 54 * q^95 - 72 * q^96 + 32 * q^98 + 73 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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