LMFDB - Embedded newform 368.2.i.b.91.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(91,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("368.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.i (of order $4$, 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:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			91.3
Character	$\chi$	$=$	368.91
Dual form			368.2.i.b.275.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39222 + 0.248418i) q^{2} +(2.02263 + 2.02263i) q^{3} +(1.87658 - 0.691707i) q^{4} +(-2.65107 + 2.65107i) q^{5} +(-3.31841 - 2.31349i) q^{6} -3.33656i q^{7} +(-2.44078 + 1.42919i) q^{8} +5.18204i q^{9} +(3.03230 - 4.34945i) q^{10} +(0.724926 + 0.724926i) q^{11} +(5.19468 + 2.39655i) q^{12} +(-3.53283 + 3.53283i) q^{13} +(0.828863 + 4.64525i) q^{14} -10.7242 q^{15} +(3.04308 - 2.59608i) q^{16} +4.76111i q^{17} +(-1.28731 - 7.21456i) q^{18} +(-3.17635 + 3.17635i) q^{19} +(-3.14117 + 6.80869i) q^{20} +(6.74862 - 6.74862i) q^{21} +(-1.18935 - 0.829176i) q^{22} +(3.43211 - 3.34972i) q^{23} +(-7.82751 - 2.04608i) q^{24} -9.05629i q^{25} +(4.04087 - 5.79611i) q^{26} +(-4.41345 + 4.41345i) q^{27} +(-2.30793 - 6.26132i) q^{28} +(-1.84414 + 1.84414i) q^{29} +(14.9305 - 2.66409i) q^{30} -1.38478i q^{31} +(-3.59174 + 4.37029i) q^{32} +2.93251i q^{33} +(-1.18275 - 6.62854i) q^{34} +(8.84545 + 8.84545i) q^{35} +(3.58445 + 9.72449i) q^{36} +(4.39510 - 4.39510i) q^{37} +(3.63313 - 5.21125i) q^{38} -14.2912 q^{39} +(2.68181 - 10.2595i) q^{40} -5.77253i q^{41} +(-7.71912 + 11.0721i) q^{42} +(4.73707 + 4.73707i) q^{43} +(1.86182 + 0.858944i) q^{44} +(-13.7379 - 13.7379i) q^{45} +(-3.94613 + 5.51616i) q^{46} +2.53821i q^{47} +(11.4059 + 0.904113i) q^{48} -4.13266 q^{49} +(2.24975 + 12.6084i) q^{50} +(-9.62995 + 9.62995i) q^{51} +(-4.18594 + 9.07331i) q^{52} +(-6.81151 + 6.81151i) q^{53} +(5.04813 - 7.24089i) q^{54} -3.84365 q^{55} +(4.76857 + 8.14383i) q^{56} -12.8491 q^{57} +(2.10934 - 3.02558i) q^{58} +(0.361229 - 0.361229i) q^{59} +(-20.1248 + 7.41803i) q^{60} +(8.75210 + 8.75210i) q^{61} +(0.344003 + 1.92792i) q^{62} +17.2902 q^{63} +(3.91485 - 6.97667i) q^{64} -18.7315i q^{65} +(-0.728489 - 4.08271i) q^{66} +(3.41462 - 3.41462i) q^{67} +(3.29330 + 8.93460i) q^{68} +(13.7171 + 0.166637i) q^{69} +(-14.5122 - 10.1175i) q^{70} +9.57678 q^{71} +(-7.40610 - 12.6482i) q^{72} +8.39374i q^{73} +(-5.02715 + 7.21079i) q^{74} +(18.3175 - 18.3175i) q^{75} +(-3.76356 + 8.15776i) q^{76} +(2.41876 - 2.41876i) q^{77} +(19.8965 - 3.55019i) q^{78} +4.67231 q^{79} +(-1.18502 + 14.9498i) q^{80} -2.30741 q^{81} +(1.43400 + 8.03666i) q^{82} +(-0.0994634 + 0.0994634i) q^{83} +(7.99624 - 17.3324i) q^{84} +(-12.6220 - 12.6220i) q^{85} +(-7.77184 - 5.41829i) q^{86} -7.46003 q^{87} +(-2.80544 - 0.733333i) q^{88} +17.0806 q^{89} +(22.5390 + 15.7135i) q^{90} +(11.7875 + 11.7875i) q^{91} +(4.12359 - 8.66002i) q^{92} +(2.80088 - 2.80088i) q^{93} +(-0.630536 - 3.53375i) q^{94} -16.8414i q^{95} +(-16.1042 + 1.57471i) q^{96} -1.61185i q^{97} +(5.75359 - 1.02663i) q^{98} +(-3.75660 + 3.75660i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{2} - 4 q^{3} - 16 q^{6} - 4 q^{8} + 20 q^{12} - 4 q^{13} - 16 q^{16} + 24 q^{18} + 4 q^{23} + 4 q^{24} - 24 q^{26} + 44 q^{27} - 20 q^{29} - 24 q^{32} + 16 q^{35} + 104 q^{36} - 128 q^{39} - 16 q^{46}+ \cdots - 88 q^{98}+O(q^{100}) $ 80 * q - 4 * q^2 - 4 * q^3 - 16 * q^6 - 4 * q^8 + 20 * q^12 - 4 * q^13 - 16 * q^16 + 24 * q^18 + 4 * q^23 + 4 * q^24 - 24 * q^26 + 44 * q^27 - 20 * q^29 - 24 * q^32 + 16 * q^35 + 104 * q^36 - 128 * q^39 - 16 * q^46 + 56 * q^48 - 160 * q^49 + 8 * q^50 - 72 * q^52 + 52 * q^54 - 8 * q^55 - 44 * q^58 + 80 * q^59 - 92 * q^62 - 24 * q^69 - 12 * q^70 - 8 * q^71 - 120 * q^72 - 12 * q^75 + 40 * q^77 + 136 * q^78 + 40 * q^81 + 132 * q^82 - 16 * q^85 - 8 * q^87 + 4 * q^92 - 28 * q^93 - 60 * q^94 + 24 * q^96 - 88 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.39222	+	0.248418i	−0.984451	+	0.175658i
$2$	−1.39222	+	0.248418i	−0.984451	+	0.175658i
$3$	2.02263	+	2.02263i	1.16776	+	1.16776i	0.982733	+	0.185032i	$0.0592387\pi$
$3$	2.02263	+	2.02263i	1.16776	+	1.16776i	0.185032	+	0.982733i	$0.440761\pi$
$4$	1.87658	−	0.691707i	0.938289	−	0.345854i
$5$	−2.65107	+	2.65107i	−1.18559	+	1.18559i	−0.207319	+	0.978273i	$0.566474\pi$
$5$	−2.65107	+	2.65107i	−1.18559	+	1.18559i	−0.978273	+	0.207319i	$0.933526\pi$
$6$	−3.31841	−	2.31349i	−1.35473	−	0.944480i
$7$		−	3.33656i		−	1.26110i	−0.776148	−	0.630551i	$-0.782829\pi$
$7$		−	3.33656i		−	1.26110i	0.776148	−	0.630551i	$-0.217171\pi$
$8$	−2.44078	+	1.42919i	−0.862947	+	0.505294i
$9$			5.18204i			1.72735i
$10$	3.03230	−	4.34945i	0.958899	−	1.37542i
$11$	0.724926	+	0.724926i	0.218574	+	0.218574i	0.807897	−	0.589324i	$-0.200606\pi$
$11$	0.724926	+	0.724926i	0.218574	+	0.218574i	−0.589324	+	0.807897i	$0.700606\pi$
$12$	5.19468	+	2.39655i	1.49958	+	0.691824i
$13$	−3.53283	+	3.53283i	−0.979830	+	0.979830i	−0.999801	−	0.0199701i	$-0.993643\pi$
$13$	−3.53283	+	3.53283i	−0.979830	+	0.979830i	0.0199701	+	0.999801i	$0.493643\pi$
$14$	0.828863	+	4.64525i	0.221523	+	1.24149i
$15$	−10.7242			−2.76898
$16$	3.04308	−	2.59608i	0.760771	−	0.649021i
$17$			4.76111i			1.15474i	0.816483	+	0.577370i	$0.195921\pi$
$17$			4.76111i			1.15474i	−0.816483	+	0.577370i	$0.804079\pi$
$18$	−1.28731	−	7.21456i	−0.303422	−	1.70049i
$19$	−3.17635	+	3.17635i	−0.728704	+	0.728704i	−0.970362	−	0.241657i	$-0.922309\pi$
$19$	−3.17635	+	3.17635i	−0.728704	+	0.728704i	0.241657	+	0.970362i	$0.422309\pi$
$20$	−3.14117	+	6.80869i	−0.702386	+	1.52247i
$21$	6.74862	−	6.74862i	1.47267	−	1.47267i
$22$	−1.18935	−	0.829176i	−0.253569	−	0.176781i
$23$	3.43211	−	3.34972i	0.715644	−	0.698465i
$23$	3.43211	−	3.34972i	0.715644	−	0.698465i
$24$	−7.82751	−	2.04608i	−1.59778	−	0.417655i
$25$		−	9.05629i		−	1.81126i
$26$	4.04087	−	5.79611i	0.792480	−	1.13671i
$27$	−4.41345	+	4.41345i	−0.849369	+	0.849369i
$28$	−2.30793	−	6.26132i	−0.436157	−	1.18328i
$29$	−1.84414	+	1.84414i	−0.342449	+	0.342449i	−0.857287	−	0.514838i	$-0.827852\pi$
$29$	−1.84414	+	1.84414i	−0.342449	+	0.342449i	0.514838	+	0.857287i	$0.327852\pi$
$30$	14.9305	−	2.66409i	2.72593	−	0.486394i
$31$		−	1.38478i		−	0.248713i	−0.992238	−	0.124357i	$-0.960313\pi$
$31$		−	1.38478i		−	0.248713i	0.992238	−	0.124357i	$-0.0396867\pi$
$32$	−3.59174	+	4.37029i	−0.634936	+	0.772565i
$33$			2.93251i			0.510485i
$34$	−1.18275	−	6.62854i	−0.202839	−	1.13678i
$35$	8.84545	+	8.84545i	1.49515	+	1.49515i
$36$	3.58445	+	9.72449i	0.597409	+	1.62075i
$37$	4.39510	−	4.39510i	0.722550	−	0.722550i	−0.246574	−	0.969124i	$-0.579305\pi$
$37$	4.39510	−	4.39510i	0.722550	−	0.722550i	0.969124	+	0.246574i	$0.0793048\pi$
$38$	3.63313	−	5.21125i	0.589371	−	0.845376i
$39$	−14.2912			−2.28842
$40$	2.68181	−	10.2595i	0.424031	−	1.62218i
$41$		−	5.77253i		−	0.901518i	−0.892646	−	0.450759i	$-0.851153\pi$
$41$		−	5.77253i		−	0.901518i	0.892646	−	0.450759i	$-0.148847\pi$
$42$	−7.71912	+	11.0721i	−1.19109	+	1.70846i
$43$	4.73707	+	4.73707i	0.722396	+	0.722396i	0.969093	−	0.246697i	$-0.0793451\pi$
$43$	4.73707	+	4.73707i	0.722396	+	0.722396i	−0.246697	+	0.969093i	$0.579345\pi$
$44$	1.86182	+	0.858944i	0.280680	+	0.129491i
$45$	−13.7379	−	13.7379i	−2.04793	−	2.04793i
$46$	−3.94613	+	5.51616i	−0.581826	+	0.813314i
$47$			2.53821i			0.370235i	0.982716	+	0.185118i	$0.0592666\pi$
$47$			2.53821i			0.370235i	−0.982716	+	0.185118i	$0.940733\pi$
$48$	11.4059	+	0.904113i	1.64630	+	0.130497i
$49$	−4.13266			−0.590380
$50$	2.24975	+	12.6084i	0.318162	+	1.78310i
$51$	−9.62995	+	9.62995i	−1.34846	+	1.34846i
$52$	−4.18594	+	9.07331i	−0.580486	+	1.25824i
$53$	−6.81151	+	6.81151i	−0.935633	+	0.935633i	−0.998050	−	0.0624169i	$-0.980119\pi$
$53$	−6.81151	+	6.81151i	−0.935633	+	0.935633i	0.0624169	+	0.998050i	$0.480119\pi$
$54$	5.04813	−	7.24089i	0.686964	−	0.985360i
$55$	−3.84365			−0.518278
$56$	4.76857	+	8.14383i	0.637227	+	1.08827i
$57$	−12.8491			−1.70191
$58$	2.10934	−	3.02558i	0.276970	−	0.397278i
$59$	0.361229	−	0.361229i	0.0470280	−	0.0470280i	−0.683202	−	0.730230i	$-0.739413\pi$
$59$	0.361229	−	0.361229i	0.0470280	−	0.0470280i	0.730230	+	0.683202i	$0.239413\pi$
$60$	−20.1248	+	7.41803i	−2.59811	+	0.957663i
$61$	8.75210	+	8.75210i	1.12059	+	1.12059i	0.991653	+	0.128939i	$0.0411570\pi$
$61$	8.75210	+	8.75210i	1.12059	+	1.12059i	0.128939	+	0.991653i	$0.458843\pi$
$62$	0.344003	+	1.92792i	0.0436884	+	0.244846i
$63$	17.2902			2.17836
$64$	3.91485	−	6.97667i	0.489356	−	0.872084i
$65$		−	18.7315i		−	2.32336i
$66$	−0.728489	−	4.08271i	−0.0896707	−	0.502547i
$67$	3.41462	−	3.41462i	0.417163	−	0.417163i	−0.467062	−	0.884225i	$-0.654687\pi$
$67$	3.41462	−	3.41462i	0.417163	−	0.417163i	0.884225	+	0.467062i	$0.154687\pi$
$68$	3.29330	+	8.93460i	0.399371	+	1.08348i
$69$	13.7171	+	0.166637i	1.65135	+	0.0200608i
$70$	−14.5122	−	10.1175i	−1.73454	−	1.20927i
$71$	9.57678			1.13655			0.568277	−	0.822837i	$-0.307610\pi$
$71$	9.57678			1.13655			0.568277	+	0.822837i	$0.307610\pi$
$72$	−7.40610	−	12.6482i	−0.872817	−	1.49061i
$73$			8.39374i			0.982413i	0.871043	+	0.491207i	$0.163444\pi$
$73$			8.39374i			0.982413i	−0.871043	+	0.491207i	$0.836556\pi$
$74$	−5.02715	+	7.21079i	−0.584394	+	0.838237i
$75$	18.3175	−	18.3175i	2.11512	−	2.11512i
$76$	−3.76356	+	8.15776i	−0.431710	+	0.935760i
$77$	2.41876	−	2.41876i	0.275644	−	0.275644i
$78$	19.8965	−	3.55019i	2.25284	−	0.401980i
$79$	4.67231			0.525676			0.262838	−	0.964840i	$-0.415342\pi$
$79$	4.67231			0.525676			0.262838	+	0.964840i	$0.415342\pi$
$80$	−1.18502	+	14.9498i	−0.132490	+	1.67144i
$81$	−2.30741			−0.256378
$82$	1.43400	+	8.03666i	0.158359	+	0.887501i
$83$	−0.0994634	+	0.0994634i	−0.0109175	+	0.0109175i	−0.712544	−	0.701627i	$-0.752457\pi$
$83$	−0.0994634	+	0.0994634i	−0.0109175	+	0.0109175i	0.701627	+	0.712544i	$0.252457\pi$
$84$	7.99624	−	17.3324i	0.872461	−	1.89112i
$85$	−12.6220	−	12.6220i	−1.36905	−	1.36905i
$86$	−7.77184	−	5.41829i	−0.838059	−	0.584269i
$87$	−7.46003			−0.799799
$88$	−2.80544	−	0.733333i	−0.299061	−	0.0781736i
$89$	17.0806			1.81054			0.905271	−	0.424835i	$-0.139668\pi$
$89$	17.0806			1.81054			0.905271	+	0.424835i	$0.139668\pi$
$90$	22.5390	+	15.7135i	2.37582	+	1.65635i
$91$	11.7875	+	11.7875i	1.23567	+	1.23567i
$92$	4.12359	−	8.66002i	0.429914	−	0.902870i
$93$	2.80088	−	2.80088i	0.290438	−	0.290438i
$94$	−0.630536	−	3.53375i	−0.0650348	−	0.364479i
$95$		−	16.8414i		−	1.72789i
$96$	−16.1042	+	1.57471i	−1.64363	+	0.160718i
$97$		−	1.61185i		−	0.163658i	−0.996646	−	0.0818291i	$-0.973924\pi$
$97$		−	1.61185i		−	0.163658i	0.996646	−	0.0818291i	$-0.0260762\pi$
$98$	5.75359	−	1.02663i	0.581200	−	0.103705i
$99$	−3.75660	+	3.75660i	−0.377552	+	0.377552i
$100$	−6.26430	−	16.9948i	−0.626430	−	1.69948i
$101$	−5.35837	−	5.35837i	−0.533178	−	0.533178i	0.388339	−	0.921517i	$-0.373049\pi$
$101$	−5.35837	−	5.35837i	−0.533178	−	0.533178i	−0.921517	+	0.388339i	$0.873049\pi$
$102$	11.0148	−	15.7993i	1.09063	−	1.56436i
$103$			8.44890i			0.832495i	0.909251	+	0.416247i	$0.136655\pi$
$103$			8.44890i			0.832495i	−0.909251	+	0.416247i	$0.863345\pi$
$104$	3.57380	−	13.6719i	0.350440	−	1.34064i
$105$			35.7821i			3.49197i
$106$	7.79105	−	11.1753i	0.756734	−	1.08544i
$107$	1.03089	+	1.03089i	0.0996602	+	0.0996602i	0.755179	−	0.655519i	$-0.227550\pi$
$107$	1.03089	+	1.03089i	0.0996602	+	0.0996602i	−0.655519	+	0.755179i	$0.727550\pi$
$108$	−5.22936	+	11.3350i	−0.503196	+	1.09071i
$109$	−11.2714	−	11.2714i	−1.07960	−	1.07960i	−0.996545	−	0.0830581i	$-0.973531\pi$
$109$	−11.2714	−	11.2714i	−1.07960	−	1.07960i	−0.0830581	−	0.996545i	$-0.526469\pi$
$110$	5.35123	−	0.954833i	0.510220	−	0.0910397i
$111$	17.7793			1.68754
$112$	−8.66200	−	10.1534i	−0.818482	−	0.959410i
$113$			4.99401i			0.469797i	0.972020	+	0.234899i	$0.0754758\pi$
$113$			4.99401i			0.469797i	−0.972020	+	0.234899i	$0.924524\pi$
$114$	17.8889	−	3.19196i	1.67545	−	0.298954i
$115$	−0.218412	+	17.9791i	−0.0203670	+	1.67656i
$116$	−2.18507	+	4.73629i	−0.202879	+	0.439753i
$117$	−18.3073	−	18.3073i	−1.69251	−	1.69251i
$118$	−0.413176	+	0.592647i	−0.0380359	+	0.0545576i
$119$	15.8858			1.45625
$120$	26.1755	−	15.3269i	2.38949	−	1.39915i
$121$		−	9.94896i		−	0.904451i
$122$	−14.3591	−	10.0107i	−1.30001	−	0.906327i
$123$	11.6757	−	11.6757i	1.05276	−	1.05276i
$124$	−0.957859	−	2.59864i	−0.0860183	−	0.233365i
$125$	10.7535	+	10.7535i	0.961822	+	0.961822i
$126$	−24.0718	+	4.29520i	−2.14449	+	0.382647i
$127$			22.1487i			1.96538i	0.185253	+	0.982691i	$0.440689\pi$
$127$			22.1487i			1.96538i	−0.185253	+	0.982691i	$0.559311\pi$
$128$	−3.71722	+	10.6856i	−0.328559	+	0.944484i
$129$			19.1626i			1.68718i
$130$	4.65325	+	26.0785i	0.408117	+	2.28723i
$131$	−1.96314	−	1.96314i	−0.171521	−	0.171521i	0.616127	−	0.787647i	$-0.288701\pi$
$131$	−1.96314	−	1.96314i	−0.171521	−	0.171521i	−0.787647	+	0.616127i	$0.788701\pi$
$132$	2.02844	+	5.50308i	0.176553	+	0.478982i
$133$	10.5981	+	10.5981i	0.918971	+	0.918971i
$134$	−3.90567	+	5.60218i	−0.337398	+	0.483954i
$135$		−	23.4007i		−	2.01401i
$136$	−6.80452	−	11.6208i	−0.583483	−	0.996479i
$137$	−11.2546			−0.961550			−0.480775	−	0.876844i	$-0.659645\pi$
$137$	−11.2546			−0.961550			−0.480775	+	0.876844i	$0.659645\pi$
$138$	−19.1387	+	3.17558i	−1.62919	+	0.270323i
$139$	8.77465	−	8.77465i	0.744256	−	0.744256i	−0.229138	−	0.973394i	$-0.573591\pi$
$139$	8.77465	−	8.77465i	0.744256	−	0.744256i	0.973394	+	0.229138i	$0.0735906\pi$
$140$	22.7176	+	10.4807i	1.91999	+	0.885781i
$141$	−5.13384	+	5.13384i	−0.432347	+	0.432347i
$142$	−13.3330	+	2.37904i	−1.11888	+	0.199645i
$143$	−5.12208			−0.428330
$144$	13.4530	+	15.7694i	1.12108	+	1.31411i
$145$		−	9.77789i		−	0.812010i
$146$	−2.08516	−	11.6860i	−0.172569	−	0.967138i
$147$	−8.35883	−	8.35883i	−0.689424	−	0.689424i
$148$	5.20762	−	11.2879i	0.428064	−	0.927857i
$149$	−4.04590	+	4.04590i	−0.331453	+	0.331453i	−0.853138	−	0.521685i	$-0.825304\pi$
$149$	−4.04590	+	4.04590i	−0.331453	+	0.331453i	0.521685	+	0.853138i	$0.325304\pi$
$150$	−20.9517	+	30.0525i	−1.71070	+	2.45377i
$151$	6.54463			0.532594			0.266297	−	0.963891i	$-0.414200\pi$
$151$	6.54463			0.532594			0.266297	+	0.963891i	$0.414200\pi$
$152$	3.21318	−	12.2924i	0.260624	−	0.997043i
$153$	−24.6723			−1.99463
$154$	−2.76660	+	3.96833i	−0.222939	+	0.319777i
$155$	3.67113	+	3.67113i	0.294872	+	0.294872i
$156$	−26.8185	+	9.88532i	−2.14720	+	0.791459i
$157$	9.66599	+	9.66599i	0.771430	+	0.771430i	0.978356	−	0.206927i	$-0.0663461\pi$
$157$	9.66599	+	9.66599i	0.771430	+	0.771430i	−0.206927	+	0.978356i	$0.566346\pi$
$158$	−6.50490	+	1.16069i	−0.517502	+	0.0923392i
$159$	−27.5543			−2.18520
$160$	−2.06398	−	21.1078i	−0.163172	−	1.66872i
$161$	−11.1766	−	11.4514i	−0.880836	−	0.902501i
$162$	3.21243	−	0.573201i	0.252392	−	0.0450349i
$163$	−7.61293	−	7.61293i	−0.596291	−	0.596291i	0.343033	−	0.939323i	$-0.388546\pi$
$163$	−7.61293	−	7.61293i	−0.596291	−	0.596291i	−0.939323	+	0.343033i	$0.888546\pi$
$164$	−3.99290	−	10.8326i	−0.311793	−	0.845884i
$165$	−7.77428	−	7.77428i	−0.605227	−	0.605227i
$166$	0.113767	−	0.163184i	0.00883003	−	0.0126655i
$167$	−21.1158			−1.63399			−0.816993	−	0.576647i	$-0.804361\pi$
$167$	−21.1158			−1.63399			−0.816993	+	0.576647i	$0.804361\pi$
$168$	−6.82689	+	26.1170i	−0.526706	+	2.01497i
$169$		−	11.9618i		−	0.920136i
$170$	20.7082	+	14.4371i	1.58825	+	1.10728i
$171$	−16.4600	−	16.4600i	−1.25872	−	1.25872i
$172$	12.1661	+	5.61281i	0.927659	+	0.427973i
$173$	11.0112	−	11.0112i	0.837170	−	0.837170i	−0.151316	−	0.988485i	$-0.548351\pi$
$173$	11.0112	−	11.0112i	0.837170	−	0.837170i	0.988485	+	0.151316i	$0.0483510\pi$
$174$	10.3860	−	1.85321i	0.787363	−	0.140491i
$175$	−30.2169			−2.28418
$176$	4.08798	+	0.324042i	0.308143	+	0.0244256i
$177$	1.46126			0.109835
$178$	−23.7800	+	4.24313i	−1.78239	+	0.318036i
$179$	1.58311	+	1.58311i	0.118327	+	0.118327i	0.763791	−	0.645464i	$-0.223336\pi$
$179$	1.58311	+	1.58311i	0.118327	+	0.118327i	−0.645464	+	0.763791i	$0.723336\pi$
$180$	−35.2829	−	16.2776i	−2.62983	−	1.21326i
$181$	15.2514	−	15.2514i	1.13363	−	1.13363i	0.144056	−	0.989570i	$-0.453985\pi$
$181$	15.2514	−	15.2514i	1.13363	−	1.13363i	0.989570	−	0.144056i	$-0.0460145\pi$
$182$	−19.3391	−	13.4826i	−1.43351	−	0.999399i
$183$			35.4045i			2.61717i
$184$	−3.58965	+	13.0811i	−0.264633	+	0.964349i
$185$			23.3034i			1.71330i
$186$	−3.20367	+	4.59525i	−0.234904	+	0.336940i
$187$	−3.45146	+	3.45146i	−0.252396	+	0.252396i
$188$	1.75569	+	4.76314i	0.128047	+	0.347388i
$189$	14.7258	+	14.7258i	1.07114	+	1.07114i
$190$	4.18371	+	23.4470i	0.303518	+	1.70103i
$191$	8.75780			0.633692			0.316846	−	0.948477i	$-0.397376\pi$
$191$	8.75780			0.633692			0.316846	+	0.948477i	$0.397376\pi$
$192$	22.0295	−	6.19292i	1.58984	−	0.446936i
$193$	16.3352			1.17583			0.587916	−	0.808922i	$-0.299949\pi$
$193$	16.3352			1.17583			0.587916	+	0.808922i	$0.299949\pi$
$194$	0.400412	+	2.24405i	0.0287479	+	0.161114i
$195$	37.8869	−	37.8869i	2.71314	−	2.71314i
$196$	−7.75525	+	2.85859i	−0.553947	+	0.204185i
$197$	−6.28542	−	6.28542i	−0.447818	−	0.447818i	0.446811	−	0.894629i	$-0.352560\pi$
$197$	−6.28542	−	6.28542i	−0.447818	−	0.447818i	−0.894629	+	0.446811i	$0.852560\pi$
$198$	4.29682	−	6.16323i	0.305362	−	0.438002i
$199$		−	2.38340i		−	0.168954i	−0.996425	−	0.0844772i	$-0.973078\pi$
$199$		−	2.38340i		−	0.168954i	0.996425	−	0.0844772i	$-0.0269220\pi$
$200$	12.9431	+	22.1044i	0.915218	+	1.56302i
$201$	13.8130			0.974295
$202$	8.79117	+	6.12894i	0.618545	+	0.431231i
$203$	6.15311	+	6.15311i	0.431863	+	0.431863i
$204$	−11.4102	+	24.7325i	−0.798877	+	1.73162i
$205$	15.3034	+	15.3034i	1.06883	+	1.06883i
$206$	−2.09886	−	11.7628i	−0.146234	−	0.819550i
$207$	17.3584	+	17.7853i	1.20649	+	1.23616i
$208$	−1.57917	+	19.9222i	−0.109496	+	1.38136i
$209$	−4.60524			−0.318551
$210$	−8.88891	−	49.8167i	−0.613393	−	3.43768i
$211$	−9.61479	−	9.61479i	−0.661910	−	0.661910i	0.293920	−	0.955830i	$-0.405040\pi$
$211$	−9.61479	−	9.61479i	−0.661910	−	0.661910i	−0.955830	+	0.293920i	$0.905040\pi$
$212$	−8.07076	+	17.4939i	−0.554302	+	1.20149i
$213$	19.3703	+	19.3703i	1.32723	+	1.32723i
$214$	−1.69133	−	1.17914i	−0.115617	−	0.0806045i
$215$	−25.1166			−1.71293
$216$	4.46463	−	17.0799i	0.303780	−	1.16214i
$217$	−4.62039			−0.313653
$218$	18.4923	+	12.8923i	1.25246	+	0.873175i
$219$	−16.9774	+	16.9774i	−1.14723	+	1.14723i
$220$	−7.21291	+	2.65868i	−0.486295	+	0.179248i
$221$	−16.8202	−	16.8202i	−1.13145	−	1.13145i
$222$	−24.7528	+	4.41670i	−1.66130	+	0.296429i
$223$			6.52831i			0.437168i	0.975818	+	0.218584i	$0.0701437\pi$
$223$			6.52831i			0.437168i	−0.975818	+	0.218584i	$0.929856\pi$
$224$	14.5817	+	11.9841i	0.974284	+	0.800719i
$225$	46.9300			3.12867
$226$	−1.24060	−	6.95279i	−0.0825236	−	0.462492i
$227$	−0.435048	+	0.435048i	−0.0288751	+	0.0288751i	−0.721397	−	0.692522i	$-0.756500\pi$
$227$	−0.435048	+	0.435048i	−0.0288751	+	0.0288751i	0.692522	+	0.721397i	$0.256500\pi$
$228$	−24.1124	+	8.88784i	−1.59688	+	0.588611i
$229$	1.06296	−	1.06296i	0.0702425	−	0.0702425i	−0.671113	−	0.741355i	$-0.734183\pi$
$229$	1.06296	−	1.06296i	0.0702425	−	0.0702425i	0.741355	+	0.671113i	$0.234183\pi$
$230$	−4.16225	−	25.0852i	−0.274450	−	1.65407i
$231$	9.78451			0.643774
$232$	1.86553	−	7.13678i	0.122478	−	0.468553i
$233$			8.67745i			0.568479i	0.958753	+	0.284239i	$0.0917410\pi$
$233$			8.67745i			0.568479i	−0.958753	+	0.284239i	$0.908259\pi$
$234$	30.0357	+	20.9400i	1.96349	+	1.36889i
$235$	−6.72895	−	6.72895i	−0.438948	−	0.438948i
$236$	0.428009	−	0.927738i	0.0278610	−	0.0603906i
$237$	9.45034	+	9.45034i	0.613865	+	0.613865i
$238$	−22.1165	+	3.94631i	−1.43360	+	0.255801i
$239$			6.71842i			0.434578i	0.976107	+	0.217289i	$0.0697215\pi$
$239$			6.71842i			0.434578i	−0.976107	+	0.217289i	$0.930279\pi$
$240$	−32.6347	+	27.8410i	−2.10656	+	1.79713i
$241$		−	20.1173i		−	1.29587i	−0.761697	−	0.647934i	$-0.775633\pi$
$241$		−	20.1173i		−	1.29587i	0.761697	−	0.647934i	$-0.224367\pi$
$242$	2.47150	+	13.8512i	0.158874	+	0.890388i
$243$	8.57333	+	8.57333i	0.549979	+	0.549979i
$244$	22.4779	+	10.3701i	1.43900	+	0.663877i
$245$	10.9559	−	10.9559i	0.699950	−	0.699950i
$246$	−13.3547	+	19.1556i	−0.851466	+	1.22132i
$247$		−	22.4430i		−	1.42801i
$248$	1.97910	+	3.37994i	0.125673	+	0.214626i
$249$	−0.402355			−0.0254982
$250$	−17.6426	−	12.2999i	−1.11582	−	0.777915i
$251$	−8.60917	−	8.60917i	−0.543406	−	0.543406i	0.381120	−	0.924526i	$-0.375539\pi$
$251$	−8.60917	−	8.60917i	−0.543406	−	0.543406i	−0.924526	+	0.381120i	$0.875539\pi$
$252$	32.4464	−	11.9598i	2.04393	−	0.753394i
$253$	4.91633	+	0.0597242i	0.309087	+	0.00375483i
$254$	−5.50214	−	30.8360i	−0.345235	−	1.93482i
$255$		−	51.0593i		−	3.19746i
$256$	2.52070	−	15.8002i	0.157544	−	0.987512i
$257$	−14.3731			−0.896568			−0.448284	−	0.893891i	$-0.647965\pi$
$257$	−14.3731			−0.896568			−0.448284	+	0.893891i	$0.647965\pi$
$258$	−4.76035	−	26.6787i	−0.296366	−	1.66094i
$259$	−14.6645	−	14.6645i	−0.911210	−	0.911210i
$260$	−12.9567	−	35.1511i	−0.803542	−	2.17998i
$261$	−9.55643	−	9.55643i	−0.591528	−	0.591528i
$262$	3.22081	+	2.24545i	0.198983	+	0.138725i
$263$		−	8.95880i		−	0.552423i	−0.961097	−	0.276212i	$-0.910921\pi$
$263$		−	8.95880i		−	0.552423i	0.961097	−	0.276212i	$-0.0890790\pi$
$264$	−4.19111	−	7.15763i	−0.257945	−	0.440521i
$265$		−	36.1155i		−	2.21856i
$266$	−17.3877	−	12.1222i	−1.06611	−	0.743257i
$267$	34.5477	+	34.5477i	2.11428	+	2.11428i
$268$	4.04588	−	8.76972i	0.247142	−	0.535696i
$269$	−0.236554	+	0.236554i	−0.0144230	+	0.0144230i	−0.714281	−	0.699859i	$-0.753246\pi$
$269$	−0.236554	+	0.236554i	−0.0144230	+	0.0144230i	0.699859	+	0.714281i	$0.253246\pi$
$270$	5.81315	+	32.5790i	0.353777	+	1.98269i
$271$			30.0599i			1.82601i	0.407951	+	0.913004i	$0.366243\pi$
$271$			30.0599i			1.82601i	−0.407951	+	0.913004i	$0.633757\pi$
$272$	12.3602	+	14.4885i	0.749450	+	0.878492i
$273$			47.6835i			2.88593i
$274$	15.6690	−	2.79586i	0.946599	−	0.168904i
$275$	6.56515	−	6.56515i	0.395893	−	0.395893i
$276$	25.8565	−	9.17552i	1.55638	−	0.552301i
$277$	−15.3614	−	15.3614i	−0.922978	−	0.922978i	0.0742611	−	0.997239i	$-0.476340\pi$
$277$	−15.3614	−	15.3614i	−0.922978	−	0.922978i	−0.997239	+	0.0742611i	$0.976340\pi$
$278$	−10.0365	+	14.3961i	−0.601950	+	0.863419i
$279$	7.17596			0.429614
$280$	−34.2316	−	8.94803i	−2.04573	−	0.534747i
$281$	−9.88650			−0.589779			−0.294890	−	0.955531i	$-0.595283\pi$
$281$	−9.88650			−0.589779			−0.294890	+	0.955531i	$0.595283\pi$
$282$	5.87212	−	8.42280i	0.349680	−	0.501570i
$283$	−22.6260	−	22.6260i	−1.34497	−	1.34497i	−0.891030	−	0.453944i	$-0.850017\pi$
$283$	−22.6260	−	22.6260i	−1.34497	−	1.34497i	−0.453944	−	0.891030i	$-0.649983\pi$
$284$	17.9716	−	6.62433i	1.06642	−	0.393082i
$285$	34.0639	−	34.0639i	2.01777	−	2.01777i
$286$	7.13109	−	1.27242i	0.421670	−	0.0752396i
$287$	−19.2604			−1.13691
$288$	−22.6470	−	18.6125i	−1.33449	−	1.09675i
$289$	−5.66820			−0.333423
$290$	2.42900	+	13.6130i	0.142636	+	0.799384i
$291$	3.26016	−	3.26016i	0.191114	−	0.191114i
$292$	5.80601	+	15.7515i	0.339771	+	0.921787i
$293$	−12.5307	+	12.5307i	−0.732053	+	0.732053i	−0.971026	−	0.238973i	$-0.923189\pi$
$293$	−12.5307	+	12.5307i	−0.732053	+	0.732053i	0.238973	+	0.971026i	$0.423189\pi$
$294$	13.7138	+	9.56088i	0.799808	+	0.557602i
$295$			1.91528i			0.111512i
$296$	−4.44607	+	17.0089i	−0.258423	+	0.988623i
$297$	−6.39885			−0.371299
$298$	4.62773	−	6.63788i	0.268077	−	0.384522i
$299$	−0.291057	+	23.9590i	−0.0168323	+	1.38559i
$300$	21.7039	−	47.0445i	1.25307	−	2.71612i
$301$	15.8055	−	15.8055i	0.911016	−	0.911016i
$302$	−9.11159	+	1.62580i	−0.524313	+	0.0935545i
$303$		−	21.6760i		−	1.24525i
$304$	−1.41982	+	17.9120i	−0.0814325	+	1.02732i
$305$	−46.4048			−2.65713
$306$	34.3493	−	6.12904i	1.96362	−	0.350374i
$307$	14.4518	+	14.4518i	0.824811	+	0.824811i	0.986794	−	0.161983i	$-0.0517890\pi$
$307$	14.4518	+	14.4518i	0.824811	+	0.824811i	−0.161983	+	0.986794i	$0.551789\pi$
$308$	2.86592	−	6.21207i	0.163301	−	0.353966i
$309$	−17.0890	+	17.0890i	−0.972157	+	0.972157i
$310$	−6.02301	−	4.19906i	−0.342084	−	0.238491i
$311$	−6.40275			−0.363067			−0.181533	−	0.983385i	$-0.558106\pi$
$311$	−6.40275			−0.363067			−0.181533	+	0.983385i	$0.558106\pi$
$312$	34.8817	−	20.4248i	1.97479	−	1.15633i
$313$	8.62414			0.487465			0.243733	−	0.969842i	$-0.421628\pi$
$313$	8.62414			0.487465			0.243733	+	0.969842i	$0.421628\pi$
$314$	−15.8584	−	11.0560i	−0.894943	−	0.623927i
$315$	−45.8375	+	45.8375i	−2.58265	+	2.58265i
$316$	8.76795	−	3.23187i	0.493235	−	0.181807i
$317$	14.8751	−	14.8751i	0.835469	−	0.835469i	−0.152789	−	0.988259i	$-0.548826\pi$
$317$	14.8751	−	14.8751i	0.835469	−	0.835469i	0.988259	+	0.152789i	$0.0488256\pi$
$318$	38.3618	−	6.84498i	2.15122	−	0.383848i
$319$	−2.67374			−0.149701
$320$	8.11709	+	28.8741i	0.453759	+	1.61411i
$321$			4.17022i			0.232759i
$322$	18.4050	+	13.1665i	1.02567	+	0.733742i
$323$	−15.1230	−	15.1230i	−0.841463	−	0.841463i
$324$	−4.33002	+	1.59605i	−0.240557	+	0.0886694i
$325$	31.9943	+	31.9943i	1.77473	+	1.77473i
$326$	12.4901	+	8.70772i	0.691763	+	0.482276i
$327$		−	45.5956i		−	2.52144i
$328$	8.25003	+	14.0895i	0.455532	+	0.777963i
$329$	8.46888			0.466905
$330$	12.7548	+	8.89227i	0.702129	+	0.489503i
$331$	−12.8004	+	12.8004i	−0.703574	+	0.703574i	−0.965176	−	0.261602i	$-0.915749\pi$
$331$	−12.8004	+	12.8004i	−0.703574	+	0.703574i	0.261602	+	0.965176i	$0.415749\pi$
$332$	−0.117851	+	0.255450i	−0.00646793	+	0.0140197i
$333$	22.7756	+	22.7756i	1.24809	+	1.24809i
$334$	29.3979	−	5.24553i	1.60858	−	0.287023i
$335$			18.1048i			0.989170i
$336$	3.01663	−	38.0566i	0.164571	−	2.07616i
$337$		−	0.815882i		−	0.0444439i	−0.999753	−	0.0222220i	$-0.992926\pi$
$337$		−	0.815882i		−	0.0444439i	0.999753	−	0.0222220i	$-0.00707405\pi$
$338$	2.97152	+	16.6535i	0.161629	+	0.905829i
$339$	−10.1010	+	10.1010i	−0.548612	+	0.548612i
$340$	−32.4169	−	14.9555i	−1.75806	−	0.811073i
$341$	1.00386	−	1.00386i	0.0543621	−	0.0543621i
$342$	27.0049	+	18.8270i	1.46026	+	1.01805i
$343$		−	9.56707i		−	0.516573i
$344$	−18.3323	−	4.79200i	−0.988412	−	0.258368i
$345$	−36.8067	+	35.9232i	−1.98161	+	1.93404i
$346$	−12.5947	+	18.0655i	−0.677097	+	0.971208i
$347$	16.3645	−	16.3645i	0.878493	−	0.878493i	−0.114886	−	0.993379i	$-0.536650\pi$
$347$	16.3645	−	16.3645i	0.878493	−	0.878493i	0.993379	+	0.114886i	$0.0366503\pi$
$348$	−13.9993	+	5.16016i	−0.750442	+	0.276613i
$349$	14.0377	−	14.0377i	0.751422	−	0.751422i	−0.223323	−	0.974745i	$-0.571690\pi$
$349$	14.0377	−	14.0377i	0.751422	−	0.751422i	0.974745	+	0.223323i	$0.0716903\pi$
$350$	42.0687	−	7.50642i	2.24867	−	0.401235i
$351$		−	31.1839i		−	1.66447i
$352$	−5.77188	+	0.564389i	−0.307642	+	0.0300821i
$353$	−8.06763			−0.429397			−0.214698	−	0.976680i	$-0.568877\pi$
$353$	−8.06763			−0.429397			−0.214698	+	0.976680i	$0.568877\pi$
$354$	−2.03440	+	0.363004i	−0.108127	+	0.0192934i
$355$	−25.3887	+	25.3887i	−1.34749	+	1.34749i
$356$	32.0531	−	11.8148i	1.69881	−	0.626182i
$357$	32.1310	+	32.1310i	1.70055	+	1.70055i
$358$	−2.59732	−	1.81077i	−0.137273	−	0.0957023i
$359$		−	20.6672i		−	1.09078i	−0.838184	−	0.545388i	$-0.816382\pi$
$359$		−	20.6672i		−	1.09078i	0.838184	−	0.545388i	$-0.183618\pi$
$360$	53.1653	+	13.8972i	2.80206	+	0.732449i
$361$		−	1.17837i		−	0.0620195i
$362$	−17.4446	+	25.0220i	−0.916869	+	1.31513i
$363$	20.1230	−	20.1230i	1.05619	−	1.05619i
$364$	30.2737	+	13.9667i	1.58677	+	0.732052i
$365$	−22.2524	−	22.2524i	−1.16474	−	1.16474i
$366$	−8.79510	−	49.2909i	−0.459727	−	2.57648i
$367$	−15.8615			−0.827965			−0.413983	−	0.910285i	$-0.635863\pi$
$367$	−15.8615			−0.827965			−0.413983	+	0.910285i	$0.635863\pi$
$368$	1.74803	−	19.1035i	0.0911225	−	0.995840i
$369$	29.9135			1.55723
$370$	−5.78898	−	32.4436i	−0.300955	−	1.68666i
$371$	22.7270	+	22.7270i	1.17993	+	1.17993i
$372$	3.31868	−	7.19347i	0.172066	−	0.372964i
$373$	−7.88793	+	7.88793i	−0.408421	+	0.408421i	−0.881188	−	0.472766i	$-0.843255\pi$
$373$	−7.88793	+	7.88793i	−0.408421	+	0.408421i	0.472766	+	0.881188i	$0.343255\pi$
$374$	3.94780	−	5.66261i	0.204136	−	0.292806i
$375$			43.5006i			2.24636i
$376$	−3.62757	−	6.19521i	−0.187078	−	0.319494i
$377$		−	13.0301i		−	0.671084i
$378$	−24.1597	−	16.8434i	−1.24264	−	0.866332i
$379$	−18.6264	−	18.6264i	−0.956776	−	0.956776i	0.0423274	−	0.999104i	$-0.486523\pi$
$379$	−18.6264	−	18.6264i	−0.956776	−	0.956776i	−0.999104	+	0.0423274i	$0.986523\pi$
$380$	−11.6493	−	31.6042i	−0.597598	−	1.62126i
$381$	−44.7986	+	44.7986i	−2.29510	+	2.29510i
$382$	−12.1928	+	2.17559i	−0.623839	+	0.111313i
$383$	33.7608			1.72510			0.862548	−	0.505974i	$-0.168867\pi$
$383$	33.7608			1.72510			0.862548	+	0.505974i	$0.168867\pi$
$384$	−29.1315	+	14.0945i	−1.48661	+	0.719255i
$385$			12.8246i			0.653602i
$386$	−22.7422	+	4.05795i	−1.15755	+	0.206544i
$387$	−24.5477	+	24.5477i	−1.24783	+	1.24783i
$388$	−1.11493	−	3.02475i	−0.0566018	−	0.153559i
$389$	10.4259	−	10.4259i	0.528613	−	0.528613i	−0.391545	−	0.920159i	$-0.628059\pi$
$389$	10.4259	−	10.4259i	0.528613	−	0.528613i	0.920159	+	0.391545i	$0.128059\pi$
$390$	−43.3352	+	62.1588i	−2.19437	+	3.14753i
$391$	15.9484	+	16.3407i	0.806545	+	0.826382i
$392$	10.0869	−	5.90634i	0.509467	−	0.298315i
$393$		−	7.94141i		−	0.400591i
$394$	10.3121	+	7.18931i	0.519518	+	0.362192i
$395$	−12.3866	+	12.3866i	−0.623237	+	0.623237i
$396$	−4.45108	+	9.64801i	−0.223675	+	0.484831i
$397$	−22.2360	+	22.2360i	−1.11599	+	1.11599i	−0.123668	+	0.992324i	$0.539466\pi$
$397$	−22.2360	+	22.2360i	−1.11599	+	1.11599i	−0.992324	+	0.123668i	$0.960534\pi$
$398$	0.592078	+	3.31822i	0.0296782	+	0.166327i
$399$			42.8720i			2.14628i
$400$	−23.5109	−	27.5590i	−1.17554	−	1.37795i
$401$			3.36340i			0.167960i	0.996467	+	0.0839801i	$0.0267632\pi$
$401$			3.36340i			0.167960i	−0.996467	+	0.0839801i	$0.973237\pi$
$402$	−19.2308	+	3.43140i	−0.959146	+	0.171143i
$403$	4.89218	+	4.89218i	0.243697	+	0.243697i
$404$	−13.7618	−	6.34897i	−0.684676	−	0.315873i
$405$	6.11708	−	6.11708i	0.303960	−	0.303960i
$406$	−10.0950	−	7.03796i	−0.501009	−	0.349288i
$407$	6.37225			0.315861
$408$	9.74163	−	37.2676i	0.482283	−	1.84502i
$409$			15.4010i			0.761529i	0.924672	+	0.380765i	$0.124339\pi$
$409$			15.4010i			0.761529i	−0.924672	+	0.380765i	$0.875661\pi$
$410$	−25.1073	−	17.5041i	−1.23996	−	0.864465i
$411$	−22.7640	−	22.7640i	−1.12286	−	1.12286i
$412$	5.84416	+	15.8550i	0.287921	+	0.781120i
$413$	−1.20526	−	1.20526i	−0.0593071	−	0.0593071i
$414$	−28.5850	−	20.4490i	−1.40487	−	1.00501i
$415$		−	0.527368i		−	0.0258875i
$416$	−2.75047	−	28.1285i	−0.134853	−	1.37911i
$417$	35.4957			1.73823
$418$	6.41152	−	1.14402i	0.313598	−	0.0559560i
$419$	−0.0418387	+	0.0418387i	−0.00204395	+	0.00204395i	−0.708128	−	0.706084i	$-0.750460\pi$
$419$	−0.0418387	+	0.0418387i	−0.00204395	+	0.00204395i	0.706084	+	0.708128i	$0.250460\pi$
$420$	24.7507	+	67.1478i	1.20771	+	3.27648i
$421$	1.65570	−	1.65570i	0.0806937	−	0.0806937i	−0.665608	−	0.746302i	$-0.731828\pi$
$421$	1.65570	−	1.65570i	0.0806937	−	0.0806937i	0.746302	+	0.665608i	$0.231828\pi$
$422$	15.7744	+	10.9975i	0.767887	+	0.535348i
$423$	−13.1531			−0.639524
$424$	6.89050	−	26.3604i	0.334632	−	1.28017i
$425$	43.1180			2.09153
$426$	−31.7797	−	22.1558i	−1.53973	−	1.07345i
$427$	29.2019	−	29.2019i	1.41318	−	1.41318i
$428$	2.64763	+	1.22147i	0.127978	+	0.0590422i
$429$	−10.3601	−	10.3601i	−0.500188	−	0.500188i
$430$	34.9679	−	6.23940i	1.68630	−	0.300891i
$431$	−1.19137			−0.0573863			−0.0286932	−	0.999588i	$-0.509135\pi$
$431$	−1.19137			−0.0573863			−0.0286932	+	0.999588i	$0.509135\pi$
$432$	−1.97281	+	24.8882i	−0.0949168	+	1.19743i
$433$			1.62961i			0.0783140i	0.999233	+	0.0391570i	$0.0124673\pi$
$433$			1.62961i			0.0783140i	−0.999233	+	0.0391570i	$0.987533\pi$
$434$	6.43262	−	1.14779i	0.308776	−	0.0550956i
$435$	19.7770	−	19.7770i	0.948236	−	0.948236i
$436$	−28.9481	−	13.3551i	−1.38636	−	0.639594i
$437$	−0.261688	+	21.5414i	−0.0125182	+	1.03047i
$438$	19.4189	−	27.8539i	0.927869	−	1.33091i
$439$	35.3423			1.68680			0.843398	−	0.537289i	$-0.180552\pi$
$439$	35.3423			1.68680			0.843398	+	0.537289i	$0.180552\pi$
$440$	9.38153	−	5.49330i	0.447247	−	0.261883i
$441$		−	21.4156i		−	1.01979i
$442$	27.5959	+	19.2390i	1.31260	+	0.915108i
$443$	10.8099	−	10.8099i	0.513596	−	0.513596i	−0.402031	−	0.915626i	$-0.631695\pi$
$443$	10.8099	−	10.8099i	0.513596	−	0.513596i	0.915626	+	0.402031i	$0.131695\pi$
$444$	33.3642	−	12.2981i	1.58340	−	0.583641i
$445$	−45.2818	+	45.2818i	−2.14656	+	2.14656i
$446$	−1.62175	−	9.08887i	−0.0767920	−	0.430370i
$447$	−16.3667			−0.774118
$448$	−23.2781	−	13.0621i	−1.09979	−	0.617128i
$449$	−30.1491			−1.42282			−0.711412	−	0.702775i	$-0.751944\pi$
$449$	−30.1491			−1.42282			−0.711412	+	0.702775i	$0.751944\pi$
$450$	−65.3372	+	11.6583i	−3.08002	+	0.549576i
$451$	4.18466	−	4.18466i	0.197048	−	0.197048i
$452$	3.45439	+	9.37165i	0.162481	+	0.440805i
$453$	13.2373	+	13.2373i	0.621945	+	0.621945i
$454$	0.497610	−	0.713758i	0.0233540	−	0.0334983i
$455$	−62.4989			−2.92999
$456$	31.3620	−	18.3638i	1.46866	−	0.859964i
$457$	13.5869			0.635568			0.317784	−	0.948163i	$-0.397061\pi$
$457$	13.5869			0.635568			0.317784	+	0.948163i	$0.397061\pi$
$458$	−1.21582	+	1.74394i	−0.0568117	+	0.0814890i
$459$	−21.0129	−	21.0129i	−0.980800	−	0.980800i
$460$	12.0264	+	33.8902i	0.560733	+	1.58014i
$461$	−8.61292	+	8.61292i	−0.401144	+	0.401144i	−0.878636	−	0.477492i	$-0.841546\pi$
$461$	−8.61292	+	8.61292i	−0.401144	+	0.401144i	0.477492	+	0.878636i	$0.341546\pi$
$462$	−13.6222	+	2.43065i	−0.633764	+	0.113084i
$463$		−	0.601238i		−	0.0279419i	−0.999902	−	0.0139710i	$-0.995553\pi$
$463$		−	0.601238i		−	0.0279419i	0.999902	−	0.0139710i	$-0.00444724\pi$
$464$	−0.824331	+	10.3994i	−0.0382686	+	0.482782i
$465$			14.8507i			0.688683i
$466$	−2.15563	−	12.0810i	−0.0998579	−	0.559640i
$467$	19.1134	−	19.1134i	0.884462	−	0.884462i	−0.109522	−	0.993984i	$-0.534932\pi$
$467$	19.1134	−	19.1134i	0.884462	−	0.884462i	0.993984	+	0.109522i	$0.0349322\pi$
$468$	−47.0182	−	21.6917i	−2.17342	−	1.00270i
$469$	−11.3931	−	11.3931i	−0.526085	−	0.526085i
$470$	11.0398	+	7.69661i	0.509228	+	0.355018i
$471$			39.1014i			1.80170i
$472$	−0.365418	+	1.39794i	−0.0168197	+	0.0643456i
$473$			6.86805i			0.315793i
$474$	−15.5046	−	10.8094i	−0.712151	−	0.496490i
$475$	28.7659	+	28.7659i	1.31987	+	1.31987i
$476$	29.8108	−	10.9883i	1.36638	−	0.503648i
$477$	−35.2975	−	35.2975i	−1.61616	−	1.61616i
$478$	−1.66898	−	9.35355i	−0.0763372	−	0.427821i
$479$	18.6712			0.853111			0.426555	−	0.904461i	$-0.359727\pi$
$479$	18.6712			0.853111			0.426555	+	0.904461i	$0.359727\pi$
$480$	38.5186	−	46.8680i	1.75813	−	2.13922i
$481$			31.0543i			1.41595i
$482$	4.99749	+	28.0078i	0.227630	+	1.27572i
$483$	0.555996	−	45.7680i	0.0252987	−	2.08252i
$484$	−6.88177	−	18.6700i	−0.312808	−	0.848636i
$485$	4.27311	+	4.27311i	0.194032	+	0.194032i
$486$	−14.0658	−	9.80622i	−0.638036	−	0.444819i
$487$	−10.7741			−0.488222			−0.244111	−	0.969747i	$-0.578496\pi$
$487$	−10.7741			−0.488222			−0.244111	+	0.969747i	$0.578496\pi$
$488$	−33.8704	−	8.85359i	−1.53324	−	0.400783i
$489$		−	30.7962i		−	1.39265i
$490$	−12.5315	+	17.9748i	−0.566115	+	0.812018i
$491$	2.61700	−	2.61700i	0.118103	−	0.118103i	−0.645585	−	0.763688i	$-0.723386\pi$
$491$	2.61700	−	2.61700i	0.118103	−	0.118103i	0.763688	+	0.645585i	$0.223386\pi$
$492$	13.8342	−	29.9865i	0.623692	−	1.35189i
$493$	−8.78018	−	8.78018i	−0.395439	−	0.395439i
$494$	5.57524	+	31.2457i	0.250842	+	1.40581i
$495$		−	19.9180i		−	0.895246i
$496$	−3.59499	−	4.21399i	−0.161420	−	0.189214i
$497$		−	31.9535i		−	1.43331i
$498$	0.560168	−	0.0999522i	0.0251017	−	0.00447896i
$499$	−5.63012	−	5.63012i	−0.252039	−	0.252039i	0.569767	−	0.821806i	$-0.307033\pi$
$499$	−5.63012	−	5.63012i	−0.252039	−	0.252039i	−0.821806	+	0.569767i	$0.807033\pi$
$500$	27.6180	+	12.7415i	1.23512	+	0.569817i
$501$	−42.7093	−	42.7093i	−1.90811	−	1.90811i
$502$	14.1246	+	9.84722i	0.630410	+	0.439503i
$503$		−	17.6384i		−	0.786455i	−0.919441	−	0.393228i	$-0.871358\pi$
$503$		−	17.6384i		−	0.786455i	0.919441	−	0.393228i	$-0.128642\pi$
$504$	−42.2016	+	24.7109i	−1.87981	+	1.10071i
$505$	28.4108			1.26426
$506$	−6.85947	+	1.13815i	−0.304941	+	0.0505972i
$507$	24.1942	−	24.1942i	1.07450	−	1.07450i
$508$	15.3204	+	41.5638i	0.679734	+	1.84409i
$509$	−13.0082	+	13.0082i	−0.576578	+	0.576578i	−0.933959	−	0.357381i	$-0.883670\pi$
$509$	−13.0082	+	13.0082i	−0.576578	+	0.576578i	0.357381	+	0.933959i	$0.383670\pi$
$510$	12.6840	+	71.0860i	0.561659	+	3.14774i
$511$	28.0063			1.23892
$512$	0.415668	+	22.6236i	0.0183701	+	0.999831i
$513$		−	28.0373i		−	1.23788i
$514$	20.0106	−	3.57053i	0.882628	−	0.157489i
$515$	−22.3986	−	22.3986i	−0.986999	−	0.986999i
$516$	13.2549	+	35.9602i	0.583516	+	1.58306i
$517$	−1.84001	+	1.84001i	−0.0809236	+	0.0809236i
$518$	24.0593	+	16.7734i	1.05710	+	0.736980i
$519$	44.5433			1.95523
$520$	26.7708	+	45.7196i	1.17398	+	2.00494i
$521$	−32.7075			−1.43294			−0.716471	−	0.697617i	$-0.754244\pi$
$521$	−32.7075			−1.43294			−0.716471	+	0.697617i	$0.754244\pi$
$522$	15.6787	+	10.9307i	0.686237	+	0.478424i
$523$	2.61273	+	2.61273i	0.114247	+	0.114247i	0.761919	−	0.647672i	$-0.224257\pi$
$523$	2.61273	+	2.61273i	0.114247	+	0.114247i	−0.647672	+	0.761919i	$0.724257\pi$
$524$	−5.04191	−	2.32607i	−0.220257	−	0.101615i
$525$	−61.1175	−	61.1175i	−2.66739	−	2.66739i
$526$	2.22553	+	12.4727i	0.0970375	+	0.543834i
$527$	6.59307			0.287199
$528$	7.61304	+	8.92387i	0.331315	+	0.388362i
$529$	0.558731	−	22.9932i	0.0242927	−	0.999705i
$530$	8.97175	+	50.2809i	0.389708	+	2.18406i
$531$	1.87190	+	1.87190i	0.0812336	+	0.0812336i
$532$	27.2189	+	12.5574i	1.18009	+	0.544430i
$533$	20.3934	+	20.3934i	0.883335	+	0.883335i
$534$	−56.6804	−	39.5159i	−2.45280	−	1.71002i
$535$	−5.46593			−0.236313
$536$	−3.45422	+	13.2145i	−0.149200	+	0.570779i
$537$			6.40408i			0.276357i
$538$	0.270572	−	0.388101i	0.0116652	−	0.0167322i
$539$	−2.99587	−	2.99587i	−0.129041	−	0.129041i
$540$	−16.1864	−	43.9132i	−0.696553	−	1.88972i
$541$	2.19297	−	2.19297i	0.0942830	−	0.0942830i	−0.658392	−	0.752675i	$-0.728763\pi$
$541$	2.19297	−	2.19297i	0.0942830	−	0.0942830i	0.752675	+	0.658392i	$0.228763\pi$
$542$	−7.46742	−	41.8501i	−0.320753	−	1.79762i
$543$	61.6957			2.64761
$544$	−20.8074	−	17.1007i	−0.892111	−	0.733186i
$545$	59.7623			2.55994
$546$	−11.8454	−	66.3861i	−0.506938	−	2.84106i
$547$	5.56175	+	5.56175i	0.237803	+	0.237803i	0.815940	−	0.578137i	$-0.196220\pi$
$547$	5.56175	+	5.56175i	0.237803	+	0.237803i	−0.578137	+	0.815940i	$0.696220\pi$
$548$	−21.1202	+	7.78492i	−0.902211	+	0.332555i
$549$	−45.3537	+	45.3537i	−1.93565	+	1.93565i
$550$	−7.50926	+	10.7711i	−0.320196	+	0.459279i
$551$		−	11.7153i		−	0.499088i
$552$	−33.7187	+	19.1976i	−1.43516	+	0.817104i
$553$		−	15.5895i		−	0.662931i
$554$	25.2026	+	17.5705i	1.07075	+	0.746498i
$555$	−47.1341	+	47.1341i	−2.00073	+	2.00073i
$556$	10.3968	−	22.5358i	0.440923	−	0.955731i
$557$	3.45796	+	3.45796i	0.146519	+	0.146519i	0.776561	−	0.630042i	$-0.216962\pi$
$557$	3.45796	+	3.45796i	0.146519	+	0.146519i	−0.630042	+	0.776561i	$0.716962\pi$
$558$	−9.99055	+	1.78264i	−0.422934	+	0.0754651i
$559$	−33.4705			−1.41565
$560$	49.8809	+	3.95391i	2.10785	+	0.167083i
$561$	−13.9620			−0.589477
$562$	13.7642	−	2.45599i	0.580609	−	0.103599i
$563$	−30.1071	+	30.1071i	−1.26886	+	1.26886i	−0.322185	+	0.946677i	$0.604417\pi$
$563$	−30.1071	+	30.1071i	−1.26886	+	1.26886i	−0.946677	+	0.322185i	$0.895583\pi$
$564$	−6.08293	+	13.1852i	−0.256138	+	0.555196i
$565$	−13.2395	−	13.2395i	−0.556988	−	0.556988i
$566$	37.1211	+	25.8797i	1.56032	+	1.08781i
$567$			7.69881i			0.323319i
$568$	−23.3749	+	13.6870i	−0.980787	+	0.574294i
$569$	5.74701			0.240927			0.120464	−	0.992718i	$-0.461562\pi$
$569$	5.74701			0.240927			0.120464	+	0.992718i	$0.461562\pi$
$570$	−38.9625	+	55.8867i	−1.63196	+	2.34083i
$571$	3.60376	+	3.60376i	0.150813	+	0.150813i	0.778481	−	0.627668i	$-0.215991\pi$
$571$	3.60376	+	3.60376i	0.150813	+	0.150813i	−0.627668	+	0.778481i	$0.715991\pi$
$572$	−9.61198	+	3.54298i	−0.401897	+	0.148139i
$573$	17.7138	+	17.7138i	0.740003	+	0.740003i
$574$	26.8148	−	4.78464i	1.11923	−	0.199707i
$575$	−30.3361	−	31.0822i	−1.26510	−	1.29622i
$576$	36.1534	+	20.2869i	1.50639	+	0.845287i
$577$	−16.8250			−0.700433			−0.350217	−	0.936669i	$-0.613892\pi$
$577$	−16.8250			−0.700433			−0.350217	+	0.936669i	$0.613892\pi$
$578$	7.89140	−	1.40808i	0.328239	−	0.0585685i
$579$	33.0400	+	33.0400i	1.37309	+	1.37309i
$580$	−6.76344	−	18.3490i	−0.280836	−	0.761899i
$581$	0.331866	+	0.331866i	0.0137681	+	0.0137681i
$582$	−3.72900	+	5.34876i	−0.154572	+	0.221713i
$583$	−9.87569			−0.409009
$584$	−11.9962	−	20.4873i	−0.496407	−	0.847771i
$585$	97.0674			4.01325
$586$	14.3327	−	20.5584i	0.592079	−	0.849261i
$587$	9.63278	−	9.63278i	0.397587	−	0.397587i	−0.479794	−	0.877381i	$-0.659289\pi$
$587$	9.63278	−	9.63278i	0.397587	−	0.397587i	0.877381	+	0.479794i	$0.159289\pi$
$588$	−21.4678	−	9.90412i	−0.885319	−	0.408439i
$589$	4.39853	+	4.39853i	0.181238	+	0.181238i
$590$	−0.475790	−	2.66650i	−0.0195880	−	0.109778i
$591$		−	25.4261i		−	1.04589i
$592$	1.96461	−	24.7847i	0.0807448	−	1.01865i
$593$	18.4259			0.756661			0.378330	−	0.925671i	$-0.376498\pi$
$593$	18.4259			0.756661			0.378330	+	0.925671i	$0.376498\pi$
$594$	8.90864	−	1.58959i	0.365526	−	0.0652217i
$595$	−42.1142	+	42.1142i	−1.72651	+	1.72651i
$596$	−4.79387	+	10.3910i	−0.196364	+	0.425633i
$597$	4.82072	−	4.82072i	0.197299	−	0.197299i
$598$	−5.54664	−	33.4287i	−0.226819	−	1.36700i
$599$	17.9963			0.735308			0.367654	−	0.929963i	$-0.380161\pi$
$599$	17.9963			0.735308			0.367654	+	0.929963i	$0.380161\pi$
$600$	−18.5299	+	70.8882i	−0.756481	+	2.89400i
$601$		−	11.1111i		−	0.453231i	−0.973984	−	0.226616i	$-0.927234\pi$
$601$		−	11.1111i		−	0.453231i	0.973984	−	0.226616i	$-0.0727661\pi$
$602$	−18.0785	+	25.9312i	−0.736823	+	1.05688i
$603$	17.6947	+	17.6947i	0.720584	+	0.720584i
$604$	12.2815	−	4.52697i	0.499727	−	0.184200i
$605$	26.3753	+	26.3753i	1.07231	+	1.07231i
$606$	5.38470	+	30.1778i	0.218739	+	1.22589i
$607$			38.7254i			1.57182i	0.618344	+	0.785908i	$0.287804\pi$
$607$			38.7254i			1.57182i	−0.618344	+	0.785908i	$0.712196\pi$
$608$	−2.47294	−	25.2902i	−0.100291	−	1.02565i
$609$			24.8909i			1.00863i
$610$	64.6058	−	11.5278i	2.61581	−	0.466746i
$611$	−8.96705	−	8.96705i	−0.362768	−	0.362768i
$612$	−46.2994	+	17.0660i	−1.87154	+	0.689852i
$613$	−24.3045	+	24.3045i	−0.981648	+	0.981648i	−0.999835	−	0.0181862i	$-0.994211\pi$
$613$	−24.3045	+	24.3045i	−0.981648	+	0.981648i	0.0181862	+	0.999835i	$0.494211\pi$
$614$	−23.7103	−	16.5301i	−0.956870	−	0.667101i
$615$			61.9060i			2.49629i
$616$	−2.44681	+	9.36054i	−0.0985849	+	0.377147i
$617$	22.0090			0.886048			0.443024	−	0.896510i	$-0.353906\pi$
$617$	22.0090			0.886048			0.443024	+	0.896510i	$0.353906\pi$
$618$	19.5465	−	28.0369i	0.786274	−	1.12781i
$619$	19.6897	+	19.6897i	0.791395	+	0.791395i	0.981721	−	0.190326i	$-0.0609545\pi$
$619$	19.6897	+	19.6897i	0.791395	+	0.791395i	−0.190326	+	0.981721i	$0.560954\pi$
$620$	9.42851	+	4.34981i	0.378658	+	0.174693i
$621$	−0.363609	+	29.9313i	−0.0145911	+	1.20110i
$622$	8.91407	−	1.59056i	0.357422	−	0.0637756i
$623$		−	56.9906i		−	2.28328i
$624$	−43.4893	+	37.1011i	−1.74096	+	1.48523i
$625$	−11.7350			−0.469398
$626$	−12.0067	+	2.14239i	−0.479886	+	0.0856272i
$627$	−9.31468	−	9.31468i	−0.371992	−	0.371992i
$628$	24.8250	+	11.4529i	0.990626	+	0.457022i
$629$	20.9256	+	20.9256i	0.834357	+	0.834357i
$630$	52.4292	−	75.2029i	2.08883	−	2.99615i
$631$		−	14.3670i		−	0.571939i	−0.958239	−	0.285970i	$-0.907684\pi$
$631$		−	14.3670i		−	0.571939i	0.958239	−	0.285970i	$-0.0923157\pi$
$632$	−11.4041	+	6.67760i	−0.453630	+	0.265621i
$633$		−	38.8943i		−	1.54591i
$634$	−17.0142	+	24.4047i	−0.675722	+	0.969236i
$635$	−58.7177	−	58.7177i	−2.33014	−	2.33014i
$636$	−51.7078	+	19.0595i	−2.05035	+	0.755758i
$637$	14.6000	−	14.6000i	0.578472	−	0.578472i
$638$	3.72244	−	0.664205i	0.147373	−	0.0262961i
$639$			49.6272i			1.96322i
$640$	−18.4737	−	38.1828i	−0.730236	−	1.50931i
$641$		−	33.8585i		−	1.33733i	−0.743563	−	0.668666i	$-0.766866\pi$
$641$		−	33.8585i		−	1.33733i	0.743563	−	0.668666i	$-0.233134\pi$
$642$	−1.03596	−	5.80589i	−0.0408860	−	0.229140i
$643$	12.8687	−	12.8687i	0.507492	−	0.507492i	−0.406264	−	0.913756i	$-0.633169\pi$
$643$	12.8687	−	12.8687i	0.507492	−	0.507492i	0.913756	+	0.406264i	$0.133169\pi$
$644$	−28.8947	−	13.7586i	−1.13861	−	0.542166i
$645$	−50.8014	−	50.8014i	−2.00030	−	2.00030i
$646$	24.8114	+	17.2977i	0.976190	+	0.680570i
$647$	25.5975			1.00634			0.503171	−	0.864187i	$-0.332167\pi$
$647$	25.5975			1.00634			0.503171	+	0.864187i	$0.332167\pi$
$648$	5.63188	−	3.29771i	0.221241	−	0.129546i
$649$	0.523728			0.0205581
$650$	−52.4913	−	36.5953i	−2.05888	−	1.43539i
$651$	−9.34533	−	9.34533i	−0.366272	−	0.366272i
$652$	−19.5522	−	9.02033i	−0.765722	−	0.353264i
$653$	0.269034	−	0.269034i	0.0105281	−	0.0105281i	−0.701823	−	0.712351i	$-0.747630\pi$
$653$	0.269034	−	0.269034i	0.0105281	−	0.0105281i	0.712351	+	0.701823i	$0.247630\pi$
$654$	11.3268	+	63.4793i	0.442912	+	2.48224i
$655$	10.4088			0.406707
$656$	−14.9860	−	17.5663i	−0.585104	−	0.685849i
$657$	−43.4967			−1.69697
$658$	−11.7906	+	2.10382i	−0.459645	+	0.0820156i
$659$	15.7070	−	15.7070i	0.611858	−	0.611858i	−0.331572	−	0.943430i	$-0.607579\pi$
$659$	15.7070	−	15.7070i	0.611858	−	0.611858i	0.943430	+	0.331572i	$0.107579\pi$
$660$	−19.9666	−	9.21151i	−0.777197	−	0.358557i
$661$	−0.147912	+	0.147912i	−0.00575309	+	0.00575309i	−0.709977	−	0.704224i	$-0.751295\pi$
$661$	−0.147912	+	0.147912i	−0.00575309	+	0.00575309i	0.704224	+	0.709977i	$0.251295\pi$
$662$	14.6412	−	21.0009i	0.569046	−	0.816222i
$663$		−	68.0420i		−	2.64253i
$664$	0.100617	−	0.384921i	0.00390469	−	0.0149378i
$665$	−56.1924			−2.17905
$666$	−37.3666	−	26.0509i	−1.44793	−	1.00945i
$667$	−0.151933	+	12.5067i	−0.00588285	+	0.484260i
$668$	−39.6253	+	14.6059i	−1.53315	+	0.565120i
$669$	−13.2043	+	13.2043i	−0.510509	+	0.510509i
$670$	−4.49755	−	25.2059i	−0.173756	−	0.973789i
$671$			12.6893i			0.489863i
$672$	5.25412	+	53.7327i	0.202682	+	2.07278i
$673$	13.3291			0.513801			0.256900	−	0.966438i	$-0.417299\pi$
$673$	13.3291			0.513801			0.256900	+	0.966438i	$0.417299\pi$
$674$	0.202680	+	1.13589i	0.00780693	+	0.0437529i
$675$	39.9695	+	39.9695i	1.53843	+	1.53843i
$676$	−8.27404	−	22.4472i	−0.318232	−	0.863353i
$677$	17.7399	−	17.7399i	0.681799	−	0.681799i	−0.278607	−	0.960405i	$-0.589873\pi$
$677$	17.7399	−	17.7399i	0.681799	−	0.681799i	0.960405	+	0.278607i	$0.0898725\pi$
$678$	11.5536	−	16.5722i	0.443714	−	0.636450i
$679$	−5.37803			−0.206390
$680$	48.8468	+	12.7684i	1.87319	+	0.489646i
$681$	−1.75988			−0.0674387
$682$	−1.14822	+	1.64698i	−0.0439677	+	0.0630660i
$683$	−4.41251	+	4.41251i	−0.168840	+	0.168840i	−0.786469	−	0.617629i	$-0.788093\pi$
$683$	−4.41251	+	4.41251i	−0.168840	+	0.168840i	0.617629	+	0.786469i	$0.288093\pi$
$684$	−42.2738	−	19.5029i	−1.61638	−	0.745712i
$685$	29.8368	−	29.8368i	1.14001	−	1.14001i
$686$	2.37663	+	13.3195i	0.0907402	+	0.508541i
$687$	4.29995			0.164053
$688$	26.7131	+	2.11747i	1.01843	+	0.0807276i
$689$		−	48.1278i		−	1.83352i
$690$	42.3192	−	59.1566i	1.61107	−	2.25205i
$691$	24.1438	+	24.1438i	0.918475	+	0.918475i	0.996919	−	0.0784438i	$-0.0249951\pi$
$691$	24.1438	+	24.1438i	0.918475	+	0.918475i	−0.0784438	+	0.996919i	$0.524995\pi$
$692$	13.0469	−	28.2800i	0.495969	−	1.07504i
$693$	12.5341	+	12.5341i	0.476132	+	0.476132i
$694$	−18.7178	+	26.8483i	−0.710519	+	1.01915i
$695$			46.5244i			1.76477i
$696$	18.2083	−	10.6618i	0.690185	−	0.404134i
$697$	27.4837			1.04102
$698$	−16.0564	+	23.0309i	−0.607745	+	0.871732i
$699$	−17.5512	+	17.5512i	−0.663849	+	0.663849i
$700$	−56.7043	+	20.9012i	−2.14322	+	0.789993i
$701$	−14.3308	−	14.3308i	−0.541266	−	0.541266i	0.382634	−	0.923900i	$-0.375017\pi$
$701$	−14.3308	−	14.3308i	−0.541266	−	0.541266i	−0.923900	+	0.382634i	$0.875017\pi$
$702$	7.74665	+	43.4150i	0.292378	+	1.63859i
$703$			27.9207i			1.05305i
$704$	7.89555	−	2.21960i	0.297575	−	0.0836542i
$705$		−	27.2203i		−	1.02518i
$706$	11.2320	−	2.00415i	0.422720	−	0.0754270i
$707$	−17.8786	+	17.8786i	−0.672392	+	0.672392i
$708$	2.74217	−	1.01076i	0.103057	−	0.0379869i
$709$	−29.3716	+	29.3716i	−1.10307	+	1.10307i	−0.109036	+	0.994038i	$0.534776\pi$
$709$	−29.3716	+	29.3716i	−1.10307	+	1.10307i	−0.994038	+	0.109036i	$0.965224\pi$
$710$	29.0397	−	41.6537i	1.08984	−	1.56324i
$711$			24.2121i			0.908024i
$712$	−41.6901	+	24.4114i	−1.56240	+	0.914855i
$713$	−4.63861	−	4.75270i	−0.173717	−	0.177990i
$714$	−52.7154	−	36.7516i	−1.97282	−	1.37539i
$715$	13.5790	−	13.5790i	0.507825	−	0.507825i
$716$	4.06588	+	1.87578i	0.151949	+	0.0701012i
$717$	−13.5889	+	13.5889i	−0.507485	+	0.507485i
$718$	5.13411	+	28.7734i	0.191603	+	1.07381i
$719$		−	16.4243i		−	0.612523i	−0.951947	−	0.306261i	$-0.900922\pi$
$719$		−	16.4243i		−	0.612523i	0.951947	−	0.306261i	$-0.0990781\pi$
$720$	−77.4704	−	6.14084i	−2.88715	−	0.228856i
$721$	28.1903			1.04986
$722$	0.292728	+	1.64056i	0.0108942	+	0.0610552i
$723$	40.6897	−	40.6897i	1.51327	−	1.51327i
$724$	18.0709	−	39.1699i	0.671599	−	1.45574i
$725$	16.7011	+	16.7011i	0.620264	+	0.620264i
$726$	−23.0169	+	33.0147i	−0.854236	+	1.22529i
$727$			22.2516i			0.825268i	0.910897	+	0.412634i	$0.135391\pi$
$727$			22.2516i			0.825268i	−0.910897	+	0.412634i	$0.864609\pi$
$728$	−45.6173	−	11.9242i	−1.69069	−	0.441940i
$729$			41.6035i			1.54087i
$730$	36.5082	+	25.4524i	1.35123	+	0.942035i
$731$	−22.5537	+	22.5537i	−0.834180	+	0.834180i
$732$	24.4895	+	66.4392i	0.905158	+	2.45566i
$733$	19.9631	+	19.9631i	0.737354	+	0.737354i	0.972065	−	0.234711i	$-0.0754144\pi$
$733$	19.9631	+	19.9631i	0.737354	+	0.737354i	−0.234711	+	0.972065i	$0.575414\pi$
$734$	22.0828	−	3.94029i	0.815091	−	0.145439i
$735$	44.3196			1.63475
$736$	2.31200	+	27.0306i	0.0852216	+	0.996362i
$737$	4.95070			0.182361
$738$	−41.6463	+	7.43105i	−1.53302	+	0.273541i
$739$	−5.44473	−	5.44473i	−0.200288	−	0.200288i	0.599836	−	0.800123i	$-0.295233\pi$
$739$	−5.44473	−	5.44473i	−0.200288	−	0.200288i	−0.800123	+	0.599836i	$0.795233\pi$
$740$	16.1191	+	43.7306i	0.592551	+	1.60757i
$741$	45.3938	−	45.3938i	1.66758	−	1.66758i
$742$	−37.2870	−	25.9953i	−1.36885	−	0.954319i
$743$			19.3179i			0.708704i	0.935112	+	0.354352i	$0.115299\pi$
$743$			19.3179i			0.708704i	−0.935112	+	0.354352i	$0.884701\pi$
$744$	−2.83337	+	10.8393i	−0.103876	+	0.397390i
$745$		−	21.4519i		−	0.785937i
$746$	9.02226	−	12.9413i	0.330328	−	0.473813i
$747$	−0.515423	−	0.515423i	−0.0188584	−	0.0188584i
$748$	−4.08953	+	8.86432i	−0.149528	+	0.324112i
$749$	3.43964	−	3.43964i	0.125682	−	0.125682i
$750$	−10.8063	−	60.5626i	−0.394591	−	2.21143i
$751$	−27.9364			−1.01942			−0.509708	−	0.860348i	$-0.670246\pi$
$751$	−27.9364			−1.01942			−0.509708	+	0.860348i	$0.670246\pi$
$752$	6.58939	+	7.72397i	0.240290	+	0.281664i
$753$		−	34.8263i		−	1.26914i
$754$	3.23691	+	18.1408i	0.117881	+	0.660649i
$755$	−17.3502	+	17.3502i	−0.631440	+	0.631440i
$756$	37.8199	+	17.4481i	1.37550	+	0.634581i
$757$	8.69654	−	8.69654i	0.316081	−	0.316081i	−0.531179	−	0.847260i	$-0.678251\pi$
$757$	8.69654	−	8.69654i	0.316081	−	0.316081i	0.847260	+	0.531179i	$0.178251\pi$
$758$	30.5593	+	21.3051i	1.10997	+	0.773834i
$759$	9.82310	+	10.0647i	0.356556	+	0.365325i
$760$	24.0695	+	41.1062i	0.873093	+	1.49108i
$761$		−	19.1635i		−	0.694675i	−0.937740	−	0.347338i	$-0.887086\pi$
$761$		−	19.1635i		−	0.694675i	0.937740	−	0.347338i	$-0.112914\pi$
$762$	51.2409	−	73.4985i	1.85626	−	2.66257i
$763$	−37.6077	+	37.6077i	−1.36149	+	1.36149i
$764$	16.4347	−	6.05783i	0.594586	−	0.219165i
$765$	65.4078	−	65.4078i	2.36482	−	2.36482i
$766$	−47.0026	+	8.38679i	−1.69827	+	0.303027i
$767$			2.55232i			0.0921588i
$768$	37.0563	−	26.8595i	1.33716	−	0.969207i
$769$			29.6065i			1.06764i	0.845599	+	0.533819i	$0.179244\pi$
$769$			29.6065i			1.06764i	−0.845599	+	0.533819i	$0.820756\pi$
$770$	−3.18586	−	17.8547i	−0.114810	−	0.643439i
$771$	−29.0714	−	29.0714i	−1.04698	−	1.04698i
$772$	30.6542	−	11.2992i	1.10327	−	0.406666i
$773$	−16.0331	+	16.0331i	−0.576672	+	0.576672i	−0.933985	−	0.357313i	$-0.883693\pi$
$773$	−16.0331	+	16.0331i	−0.576672	+	0.576672i	0.357313	+	0.933985i	$0.383693\pi$
$774$	28.0778	−	40.2740i	1.00924	−	1.44762i
$775$	−12.5409			−0.450484
$776$	2.30363	+	3.93417i	0.0826955	+	0.141228i
$777$		−	59.3218i		−	2.12816i
$778$	−11.9252	+	17.1051i	−0.427539	+	0.613249i
$779$	18.3356	+	18.3356i	0.656940	+	0.656940i
$780$	44.8910	−	97.3043i	1.60736	−	3.48405i
$781$	6.94246	+	6.94246i	0.248421	+	0.248421i
$782$	−26.2631	−	18.7880i	−0.939165	−	0.671857i
$783$		−	16.2781i		−	0.581731i
$784$	−12.5760	+	10.7287i	−0.449144	+	0.383169i
$785$	−51.2503			−1.82920
$786$	1.97279	+	11.0562i	0.0703670	+	0.394362i
$787$	37.3676	−	37.3676i	1.33201	−	1.33201i	0.428441	−	0.903570i	$-0.359063\pi$
$787$	37.3676	−	37.3676i	1.33201	−	1.33201i	0.903570	−	0.428441i	$-0.140937\pi$
$788$	−16.1428	−	7.44741i	−0.575062	−	0.265303i
$789$	18.1203	−	18.1203i	0.645100	−	0.645100i
$790$	14.1679	−	20.3220i	0.504070	−	0.723023i
$791$	16.6628			0.592462
$792$	3.80016	−	14.5379i	0.135033	−	0.516582i
$793$	−61.8393			−2.19598
$794$	25.4336	−	36.4813i	0.902606	−	1.29467i
$795$	73.0482	−	73.0482i	2.59075	−	2.59075i
$796$	−1.64861	−	4.47263i	−0.0584335	−	0.158528i
$797$	22.7840	+	22.7840i	0.807052	+	0.807052i	0.984187	−	0.177134i	$-0.0566827\pi$
$797$	22.7840	+	22.7840i	0.807052	+	0.807052i	−0.177134	+	0.984187i	$0.556683\pi$
$798$	−10.6502	−	59.6874i	−0.377012	−	2.11291i
$799$	−12.0847			−0.427525
$800$	39.5786	+	32.5278i	1.39931	+	1.15003i
$801$			88.5124i			3.12743i
$802$	−0.835530	−	4.68261i	−0.0295036	−	0.165349i
$803$	−6.08485	+	6.08485i	−0.214730	+	0.214730i
$804$	25.9212	−	9.55456i	0.914170	−	0.336963i
$805$	59.9883	+	0.728746i	2.11431	+	0.0256849i
$806$	−8.02631	−	5.59570i	−0.282715	−	0.197100i
$807$	−0.956922			−0.0336852
$808$	20.7367	+	5.42051i	0.729516	+	0.190693i
$809$		−	53.9640i		−	1.89727i	−0.316367	−	0.948637i	$-0.602463\pi$
$809$		−	53.9640i		−	1.89727i	0.316367	−	0.948637i	$-0.397537\pi$
$810$	−6.99676	+	10.0359i	−0.245841	+	0.352627i
$811$	−17.1133	+	17.1133i	−0.600928	+	0.600928i	−0.940559	−	0.339631i	$-0.889698\pi$
$811$	−17.1133	+	17.1133i	−0.600928	+	0.600928i	0.339631	+	0.940559i	$0.389698\pi$
$812$	15.8029	+	7.29063i	0.554574	+	0.255851i
$813$	−60.7999	+	60.7999i	−2.13235	+	2.13235i
$814$	−8.87160	+	1.58298i	−0.310950	+	0.0554835i
$815$	40.3648			1.41392
$816$	−4.30458	+	54.3049i	−0.150691	+	1.90105i
$817$	−30.0932			−1.05283
$818$	−3.82588	−	21.4416i	−0.133769	−	0.749689i
$819$	−61.0833	+	61.0833i	−2.13442	+	2.13442i
$820$	39.3034	+	18.1325i	1.37253	+	0.633214i
$821$	8.58987	+	8.58987i	0.299789	+	0.299789i	0.840931	−	0.541142i	$-0.182008\pi$
$821$	8.58987	+	8.58987i	0.299789	+	0.299789i	−0.541142	+	0.840931i	$0.682008\pi$
$822$	37.3475	+	26.0376i	1.30264	+	0.908164i
$823$	17.2375			0.600862			0.300431	−	0.953804i	$-0.402870\pi$
$823$	17.2375			0.600862			0.300431	+	0.953804i	$0.402870\pi$
$824$	−12.0751	−	20.6219i	−0.420654	−	0.718399i
$825$	26.5577			0.924620
$826$	1.97740	+	1.37859i	0.0688027	+	0.0479672i
$827$	9.74911	+	9.74911i	0.339010	+	0.339010i	0.855995	−	0.516985i	$-0.172946\pi$
$827$	9.74911	+	9.74911i	0.339010	+	0.339010i	−0.516985	+	0.855995i	$0.672946\pi$
$828$	44.8766	+	21.3686i	1.55957	+	0.742610i
$829$	8.87586	−	8.87586i	0.308271	−	0.308271i	−0.535967	−	0.844239i	$-0.680053\pi$
$829$	8.87586	−	8.87586i	0.308271	−	0.308271i	0.844239	+	0.535967i	$0.180053\pi$
$830$	0.131008	+	0.734215i	0.00454734	+	0.0254850i
$831$		−	62.1408i		−	2.15564i
$832$	10.8169	+	38.4779i	0.375008	+	1.33398i
$833$		−	19.6761i		−	0.681735i
$834$	−49.4180	+	8.81777i	−1.71120	+	0.305334i
$835$	55.9792	−	55.9792i	1.93724	−	1.93724i
$836$	−8.64208	+	3.18548i	−0.298893	+	0.110172i
$837$	6.11164	+	6.11164i	0.211249	+	0.211249i
$838$	0.0478553	−	0.0686423i	0.00165313	−	0.00237121i
$839$			24.4174i			0.842982i	0.906833	+	0.421491i	$0.138493\pi$
$839$			24.4174i			0.842982i	−0.906833	+	0.421491i	$0.861507\pi$
$840$	−51.1393	−	87.3363i	−1.76447	−	3.01339i
$841$			22.1983i			0.765457i
$842$	−1.89380	+	2.71641i	−0.0652645	+	0.0936136i
$843$	−19.9967	−	19.9967i	−0.688723	−	0.688723i
$844$	−24.6935	−	11.3923i	−0.849986	−	0.392138i
$845$	31.7114	+	31.7114i	1.09091	+	1.09091i
$846$	18.3120	−	3.26746i	0.629581	−	0.112338i
$847$	−33.1954			−1.14061
$848$	−3.04474	+	38.4113i	−0.104557	+	1.31905i
$849$		−	91.5278i		−	3.14123i
$850$	−60.0300	+	10.7113i	−2.05901	+	0.367394i
$851$	0.362097	−	29.8068i	0.0124125	−	1.02176i
$852$	49.7483	+	22.9512i	1.70435	+	0.786296i
$853$	32.5416	+	32.5416i	1.11420	+	1.11420i	0.992576	+	0.121626i	$0.0388109\pi$
$853$	32.5416	+	32.5416i	1.11420	+	1.11420i	0.121626	+	0.992576i	$0.461189\pi$
$854$	−33.4014	+	47.9099i	−1.14297	+	1.63944i
$855$	87.2728			2.98467
$856$	−3.98953	−	1.04285i	−0.136359	−	0.0356438i
$857$			24.9215i			0.851302i	0.904887	+	0.425651i	$0.139955\pi$
$857$			24.9215i			0.851302i	−0.904887	+	0.425651i	$0.860045\pi$
$858$	16.9972	+	11.8499i	0.580273	+	0.404549i
$859$	2.23055	−	2.23055i	0.0761052	−	0.0761052i	−0.668030	−	0.744135i	$-0.732862\pi$
$859$	2.23055	−	2.23055i	0.0761052	−	0.0761052i	0.744135	+	0.668030i	$0.232862\pi$
$860$	−47.1332	+	17.3733i	−1.60723	+	0.592425i
$861$	−38.9567	−	38.9567i	−1.32764	−	1.32764i
$862$	1.65866	−	0.295958i	0.0564940	−	0.0100804i
$863$		−	24.8408i		−	0.845591i	−0.906225	−	0.422795i	$-0.861049\pi$
$863$		−	24.8408i		−	0.845591i	0.906225	−	0.422795i	$-0.138951\pi$
$864$	−3.43608	−	35.1400i	−0.116898	−	1.19549i
$865$			58.3831i			1.98508i
$866$	−0.404824	−	2.26878i	−0.0137565	−	0.0770963i
$867$	−11.4646	−	11.4646i	−0.389360	−	0.389360i
$868$	−8.67052	+	3.19596i	−0.294297	+	0.108478i
$869$	3.38708	+	3.38708i	0.114899	+	0.114899i
$870$	−22.6211	+	32.4470i	−0.766927	+	1.10006i
$871$			24.1266i			0.817497i
$872$	43.6199	+	11.4021i	1.47716	+	0.386124i
$873$	8.35265			0.282694
$874$	−4.98695	−	30.0555i	−0.168686	−	1.01664i
$875$	35.8797	−	35.8797i	1.21296	−	1.21296i
$876$	−20.1160	+	43.6028i	−0.679657	+	1.47320i
$877$	9.02193	−	9.02193i	0.304649	−	0.304649i	−0.538181	−	0.842829i	$-0.680888\pi$
$877$	9.02193	−	9.02193i	0.304649	−	0.304649i	0.842829	+	0.538181i	$0.180888\pi$
$878$	−49.2044	+	8.77967i	−1.66057	+	0.296299i
$879$	−50.6900			−1.70973
$880$	−11.6966	+	9.97845i	−0.394291	+	0.336373i
$881$			52.0359i			1.75313i	0.481280	+	0.876567i	$0.340172\pi$
$881$			52.0359i			1.75313i	−0.481280	+	0.876567i	$0.659828\pi$
$882$	5.32002	+	29.8153i	0.179134	+	1.00393i
$883$	−3.22463	−	3.22463i	−0.108518	−	0.108518i	0.650763	−	0.759281i	$-0.274449\pi$
$883$	−3.22463	−	3.22463i	−0.108518	−	0.108518i	−0.759281	+	0.650763i	$0.774449\pi$
$884$	−43.1990	−	19.9297i	−1.45294	−	0.670310i
$885$	−3.87390	+	3.87390i	−0.130220	+	0.130220i
$886$	−12.3645	+	17.7352i	−0.415393	+	0.595827i
$887$	−50.5351			−1.69680			−0.848401	−	0.529354i	$-0.822434\pi$
$887$	−50.5351			−1.69680			−0.848401	+	0.529354i	$0.822434\pi$
$888$	−43.3954	+	25.4099i	−1.45626	+	0.852702i
$889$	73.9006			2.47855
$890$	51.7936	−	74.2913i	1.73613	−	2.49025i
$891$	−1.67270	−	1.67270i	−0.0560375	−	0.0560375i
$892$	4.51568	+	12.2509i	0.151196	+	0.410189i
$893$	−8.06222	−	8.06222i	−0.269792	−	0.269792i
$894$	22.7861	−	4.06578i	0.762082	−	0.135980i
$895$	−8.39386			−0.280576
$896$	35.6532	+	12.4027i	1.19109	+	0.414346i
$897$	−49.0489	+	47.8715i	−1.63770	+	1.59838i
$898$	41.9743	−	7.48958i	1.40070	−	0.249930i
$899$	2.55373	+	2.55373i	0.0851715	+	0.0851715i
$900$	88.0679	−	32.4618i	2.93560	−	1.08206i
$901$	−32.4304	−	32.4304i	−1.08041	−	1.08041i
$902$	−4.78644	+	6.86553i	−0.159371	+	0.228597i
$903$	63.9374			2.12770
$904$	−7.13738	−	12.1893i	−0.237386	−	0.405410i
$905$			80.8648i			2.68804i
$906$	−21.7177	−	15.1410i	−0.721524	−	0.503025i
$907$	−5.08536	−	5.08536i	−0.168857	−	0.168857i	0.617620	−	0.786477i	$-0.288097\pi$
$907$	−5.08536	−	5.08536i	−0.168857	−	0.168857i	−0.786477	+	0.617620i	$0.788097\pi$
$908$	−0.515475	+	1.11733i	−0.0171066	+	0.0370798i
$909$	27.7673	−	27.7673i	0.920983	−	0.920983i
$910$	87.0125	−	15.5259i	2.88444	−	0.514677i
$911$	4.64753			0.153980			0.0769898	−	0.997032i	$-0.475469\pi$
$911$	4.64753			0.153980			0.0769898	+	0.997032i	$0.475469\pi$
$912$	−39.1010	+	33.3574i	−1.29476	+	1.10457i
$913$	−0.144207			−0.00477257
$914$	−18.9160	+	3.37523i	−0.625686	+	0.111643i
$915$	−93.8595	−	93.8595i	−3.10290	−	3.10290i
$916$	1.25947	−	2.72999i	0.0416141	−	0.0902014i
$917$	−6.55015	+	6.55015i	−0.216305	+	0.216305i
$918$	34.4747	+	24.0347i	1.13783	+	0.793264i
$919$		−	8.05446i		−	0.265692i	−0.991137	−	0.132846i	$-0.957588\pi$
$919$		−	8.05446i		−	0.265692i	0.991137	−	0.132846i	$-0.0424116\pi$
$920$	−25.1624	−	44.1952i	−0.829578	−	1.45707i
$921$			58.4614i			1.92637i
$922$	9.85152	−	14.1307i	0.324442	−	0.465371i
$923$	−33.8331	+	33.8331i	−1.11363	+	1.11363i
$924$	18.3614	−	6.76802i	0.604045	−	0.222651i
$925$	−39.8033	−	39.8033i	−1.30873	−	1.30873i
$926$	0.149358	+	0.837059i	0.00490822	+	0.0275075i
$927$	−43.7825			−1.43801
$928$	−1.43575	−	14.6831i	−0.0471309	−	0.481997i
$929$	21.3638			0.700923			0.350461	−	0.936577i	$-0.386025\pi$
$929$	21.3638			0.700923			0.350461	+	0.936577i	$0.386025\pi$
$930$	−3.68917	−	20.6754i	−0.120973	−	0.677974i
$931$	13.1268	−	13.1268i	0.430212	−	0.430212i
$932$	6.00225	+	16.2839i	0.196610	+	0.533397i
$933$	−12.9504	−	12.9504i	−0.423976	−	0.423976i
$934$	−21.8620	+	31.3582i	−0.715347	+	1.02607i
$935$		−	18.3001i		−	0.598476i
$936$	70.8485	+	18.5196i	2.31576	+	0.605331i
$937$	−11.6112			−0.379321			−0.189661	−	0.981850i	$-0.560739\pi$
$937$	−11.6112			−0.379321			−0.189661	+	0.981850i	$0.560739\pi$
$938$	18.6920	+	13.0315i	0.610316	+	0.425494i
$939$	17.4434	+	17.4434i	0.569245	+	0.569245i
$940$	−17.2818	−	7.97293i	−0.563672	−	0.260048i
$941$	23.2864	+	23.2864i	0.759115	+	0.759115i	0.976161	−	0.217047i	$-0.0696424\pi$
$941$	23.2864	+	23.2864i	0.759115	+	0.759115i	−0.217047	+	0.976161i	$0.569642\pi$
$942$	−9.71348	−	54.4379i	−0.316482	−	1.77368i
$943$	−19.3364	−	19.8120i	−0.629679	−	0.645166i
$944$	0.161469	−	2.03703i	0.00525536	−	0.0662996i
$945$	−78.0779			−2.53987
$946$	−1.70615	−	9.56187i	−0.0554717	−	0.310883i
$947$	13.9678	+	13.9678i	0.453894	+	0.453894i	0.896645	−	0.442751i	$-0.145997\pi$
$947$	13.9678	+	13.9678i	0.453894	+	0.453894i	−0.442751	+	0.896645i	$0.645997\pi$
$948$	24.2711	+	11.1974i	0.788290	+	0.363675i
$949$	−29.6537	−	29.6537i	−0.962598	−	0.962598i
$950$	−47.1946	−	32.9027i	−1.53120	−	1.06750i
$951$	60.1736			1.95126
$952$	−38.7737	+	22.7037i	−1.25666	+	0.735832i
$953$	−49.4038			−1.60035			−0.800173	−	0.599769i	$-0.795259\pi$
$953$	−49.4038			−1.60035			−0.800173	+	0.599769i	$0.795259\pi$
$954$	57.9106	+	40.3735i	1.87493	+	1.30714i
$955$	−23.2175	+	23.2175i	−0.751300	+	0.751300i
$956$	4.64718	+	12.6076i	0.150300	+	0.407760i
$957$	−5.40797	−	5.40797i	−0.174815	−	0.174815i
$958$	−25.9946	+	4.63827i	−0.839846	+	0.149856i
$959$			37.5519i			1.21261i
$960$	−41.9837	+	74.8194i	−1.35502	+	2.41479i
$961$	29.0824			0.938142
$962$	−7.71444	−	43.2345i	−0.248724	−	1.39394i
$963$	−5.34213	+	5.34213i	−0.172148	+	0.172148i
$964$	−13.9153	−	37.7516i	−0.448180	−	1.21590i
$965$	−43.3056	+	43.3056i	−1.39406	+	1.39406i
$966$	10.5955	+	63.8575i	0.340906	+	2.05458i
$967$	9.85370			0.316874			0.158437	−	0.987369i	$-0.449355\pi$
$967$	9.85370			0.316874			0.158437	+	0.987369i	$0.449355\pi$
$968$	14.2189	+	24.2833i	0.457014	+	0.780494i
$969$		−	61.1762i		−	1.96526i
$970$	−7.01064	−	4.88761i	−0.225098	−	0.156932i
$971$	18.3483	+	18.3483i	0.588824	+	0.588824i	0.937313	−	0.348489i	$-0.113305\pi$
$971$	18.3483	+	18.3483i	0.588824	+	0.588824i	−0.348489	+	0.937313i	$0.613305\pi$
$972$	22.0187	+	10.1583i	0.706251	+	0.325827i
$973$	−29.2772	−	29.2772i	−0.938584	−	0.938584i
$974$	15.0000	−	2.67649i	0.480631	−	0.0857601i
$975$			129.425i			4.14492i
$976$	49.3545	+	3.91218i	1.57980	+	0.125226i
$977$		−	57.4749i		−	1.83879i	−0.393340	−	0.919393i	$-0.628681\pi$
$977$		−	57.4749i		−	1.83879i	0.393340	−	0.919393i	$-0.371319\pi$
$978$	7.65034	+	42.8753i	0.244631	+	1.37100i
$979$	12.3822	+	12.3822i	0.395736	+	0.395736i
$980$	12.9814	−	28.1380i	0.414675	−	0.898835i
$981$	58.4087	−	58.4087i	1.86485	−	1.86485i
$982$	−2.99334	+	4.29355i	−0.0955212	+	0.137013i
$983$		−	61.4676i		−	1.96051i	−0.197736	−	0.980255i	$-0.563359\pi$
$983$		−	61.4676i		−	1.96051i	0.197736	−	0.980255i	$-0.436641\pi$
$984$	−11.8111	+	45.1845i	−0.376523	+	1.44043i
$985$	33.3261			1.06186
$986$	14.4051	+	10.0428i	0.458753	+	0.319829i
$987$	17.1294	+	17.1294i	0.545235	+	0.545235i
$988$	−15.5240	−	42.1160i	−0.493883	−	1.33989i
$989$	32.1260	+	0.390271i	1.02155	+	0.0124099i
$990$	4.94798	+	27.7303i	0.157257	+	0.881326i
$991$			29.2375i			0.928761i	0.885636	+	0.464381i	$0.153723\pi$
$991$			29.2375i			0.928761i	−0.885636	+	0.464381i	$0.846277\pi$
$992$	6.05187	+	4.97375i	0.192147	+	0.157917i
$993$	−51.7809			−1.64322
$994$	7.93783	+	44.4865i	0.251773	+	1.41103i
$995$	6.31854	+	6.31854i	0.200311	+	0.200311i
$996$	−0.755050	+	0.278312i	−0.0239247	+	0.00881864i
$997$	−28.5363	−	28.5363i	−0.903753	−	0.903753i	0.0920054	−	0.995759i	$-0.470672\pi$
$997$	−28.5363	−	28.5363i	−0.903753	−	0.903753i	−0.995759	+	0.0920054i	$0.970672\pi$
$998$	9.23701	+	6.43977i	0.292393	+	0.203847i
$999$			38.7951i			1.22742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.i.b.91.3	✓	80
4.3	odd	2		1472.2.i.b.1103.2		80
16.3	odd	4	inner	368.2.i.b.275.4	yes	80
16.13	even	4		1472.2.i.b.367.1		80
23.22	odd	2	inner	368.2.i.b.91.4	yes	80
92.91	even	2		1472.2.i.b.1103.1		80
368.45	odd	4		1472.2.i.b.367.2		80
368.275	even	4	inner	368.2.i.b.275.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
368.2.i.b.91.3	✓	80	1.1	even	1	trivial
368.2.i.b.91.4	yes	80	23.22	odd	2	inner
368.2.i.b.275.3	yes	80	368.275	even	4	inner
368.2.i.b.275.4	yes	80	16.3	odd	4	inner
1472.2.i.b.367.1		80	16.13	even	4
1472.2.i.b.367.2		80	368.45	odd	4
1472.2.i.b.1103.1		80	92.91	even	2
1472.2.i.b.1103.2		80	4.3	odd	2

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39222 + 0.248418i) q^{2} +(2.02263 + 2.02263i) q^{3} +(1.87658 - 0.691707i) q^{4} +(-2.65107 + 2.65107i) q^{5} +(-3.31841 - 2.31349i) q^{6} -3.33656i q^{7} +(-2.44078 + 1.42919i) q^{8} +5.18204i q^{9} +(3.03230 - 4.34945i) q^{10} +(0.724926 + 0.724926i) q^{11} +(5.19468 + 2.39655i) q^{12} +(-3.53283 + 3.53283i) q^{13} +(0.828863 + 4.64525i) q^{14} -10.7242 q^{15} +(3.04308 - 2.59608i) q^{16} +4.76111i q^{17} +(-1.28731 - 7.21456i) q^{18} +(-3.17635 + 3.17635i) q^{19} +(-3.14117 + 6.80869i) q^{20} +(6.74862 - 6.74862i) q^{21} +(-1.18935 - 0.829176i) q^{22} +(3.43211 - 3.34972i) q^{23} +(-7.82751 - 2.04608i) q^{24} -9.05629i q^{25} +(4.04087 - 5.79611i) q^{26} +(-4.41345 + 4.41345i) q^{27} +(-2.30793 - 6.26132i) q^{28} +(-1.84414 + 1.84414i) q^{29} +(14.9305 - 2.66409i) q^{30} -1.38478i q^{31} +(-3.59174 + 4.37029i) q^{32} +2.93251i q^{33} +(-1.18275 - 6.62854i) q^{34} +(8.84545 + 8.84545i) q^{35} +(3.58445 + 9.72449i) q^{36} +(4.39510 - 4.39510i) q^{37} +(3.63313 - 5.21125i) q^{38} -14.2912 q^{39} +(2.68181 - 10.2595i) q^{40} -5.77253i q^{41} +(-7.71912 + 11.0721i) q^{42} +(4.73707 + 4.73707i) q^{43} +(1.86182 + 0.858944i) q^{44} +(-13.7379 - 13.7379i) q^{45} +(-3.94613 + 5.51616i) q^{46} +2.53821i q^{47} +(11.4059 + 0.904113i) q^{48} -4.13266 q^{49} +(2.24975 + 12.6084i) q^{50} +(-9.62995 + 9.62995i) q^{51} +(-4.18594 + 9.07331i) q^{52} +(-6.81151 + 6.81151i) q^{53} +(5.04813 - 7.24089i) q^{54} -3.84365 q^{55} +(4.76857 + 8.14383i) q^{56} -12.8491 q^{57} +(2.10934 - 3.02558i) q^{58} +(0.361229 - 0.361229i) q^{59} +(-20.1248 + 7.41803i) q^{60} +(8.75210 + 8.75210i) q^{61} +(0.344003 + 1.92792i) q^{62} +17.2902 q^{63} +(3.91485 - 6.97667i) q^{64} -18.7315i q^{65} +(-0.728489 - 4.08271i) q^{66} +(3.41462 - 3.41462i) q^{67} +(3.29330 + 8.93460i) q^{68} +(13.7171 + 0.166637i) q^{69} +(-14.5122 - 10.1175i) q^{70} +9.57678 q^{71} +(-7.40610 - 12.6482i) q^{72} +8.39374i q^{73} +(-5.02715 + 7.21079i) q^{74} +(18.3175 - 18.3175i) q^{75} +(-3.76356 + 8.15776i) q^{76} +(2.41876 - 2.41876i) q^{77} +(19.8965 - 3.55019i) q^{78} +4.67231 q^{79} +(-1.18502 + 14.9498i) q^{80} -2.30741 q^{81} +(1.43400 + 8.03666i) q^{82} +(-0.0994634 + 0.0994634i) q^{83} +(7.99624 - 17.3324i) q^{84} +(-12.6220 - 12.6220i) q^{85} +(-7.77184 - 5.41829i) q^{86} -7.46003 q^{87} +(-2.80544 - 0.733333i) q^{88} +17.0806 q^{89} +(22.5390 + 15.7135i) q^{90} +(11.7875 + 11.7875i) q^{91} +(4.12359 - 8.66002i) q^{92} +(2.80088 - 2.80088i) q^{93} +(-0.630536 - 3.53375i) q^{94} -16.8414i q^{95} +(-16.1042 + 1.57471i) q^{96} -1.61185i q^{97} +(5.75359 - 1.02663i) q^{98} +(-3.75660 + 3.75660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{2} - 4 q^{3} - 16 q^{6} - 4 q^{8} + 20 q^{12} - 4 q^{13} - 16 q^{16} + 24 q^{18} + 4 q^{23} + 4 q^{24} - 24 q^{26} + 44 q^{27} - 20 q^{29} - 24 q^{32} + 16 q^{35} + 104 q^{36} - 128 q^{39} - 16 q^{46}+ \cdots - 88 q^{98}+O(q^{100}) \) 80 * q - 4 * q^2 - 4 * q^3 - 16 * q^6 - 4 * q^8 + 20 * q^12 - 4 * q^13 - 16 * q^16 + 24 * q^18 + 4 * q^23 + 4 * q^24 - 24 * q^26 + 44 * q^27 - 20 * q^29 - 24 * q^32 + 16 * q^35 + 104 * q^36 - 128 * q^39 - 16 * q^46 + 56 * q^48 - 160 * q^49 + 8 * q^50 - 72 * q^52 + 52 * q^54 - 8 * q^55 - 44 * q^58 + 80 * q^59 - 92 * q^62 - 24 * q^69 - 12 * q^70 - 8 * q^71 - 120 * q^72 - 12 * q^75 + 40 * q^77 + 136 * q^78 + 40 * q^81 + 132 * q^82 - 16 * q^85 - 8 * q^87 + 4 * q^92 - 28 * q^93 - 60 * q^94 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

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Database

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