LMFDB - Embedded newform 110.4.k.a.73.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,4,Mod(7,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 14])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.7"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	110.k (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.49021010063$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			73.2
Character	$\chi$	$=$	110.73
Dual form			110.4.k.a.107.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.312869 - 1.97538i) q^{2} +(-6.00362 + 3.05899i) q^{3} +(-3.80423 + 1.23607i) q^{4} +(-0.773319 - 11.1536i) q^{5} +(7.92101 + 10.9023i) q^{6} +(-3.41066 + 6.69380i) q^{7} +(3.63192 + 7.12805i) q^{8} +(10.8157 - 14.8866i) q^{9} +(-21.7905 + 5.01720i) q^{10} +(-10.0463 + 35.0724i) q^{11} +(19.0580 - 19.0580i) q^{12} +(83.6339 - 13.2463i) q^{13} +(14.2899 + 4.64306i) q^{14} +(38.7614 + 64.5961i) q^{15} +(12.9443 - 9.40456i) q^{16} +(112.655 + 17.8428i) q^{17} +(-32.7906 - 16.7076i) q^{18} +(-17.8986 + 55.0863i) q^{19} +(16.7284 + 41.4748i) q^{20} -50.6202i q^{21} +(72.4243 + 8.87209i) q^{22} +(4.14181 + 4.14181i) q^{23} +(-43.6094 - 31.6840i) q^{24} +(-123.804 + 17.2505i) q^{25} +(-52.3329 - 161.064i) q^{26} +(9.06400 - 57.2279i) q^{27} +(4.70094 - 29.6806i) q^{28} +(84.3925 + 259.733i) q^{29} +(115.474 - 96.7785i) q^{30} +(-42.6332 - 30.9749i) q^{31} +(-22.6274 - 22.6274i) q^{32} +(-46.9724 - 241.293i) q^{33} -228.119i q^{34} +(77.2973 + 32.8646i) q^{35} +(-22.7447 + 70.0010i) q^{36} +(-233.230 - 118.837i) q^{37} +(114.416 + 18.1217i) q^{38} +(-461.586 + 335.362i) q^{39} +(76.6945 - 46.0212i) q^{40} +(98.2775 + 31.9323i) q^{41} +(-99.9940 + 15.8375i) q^{42} +(14.0489 - 14.0489i) q^{43} +(-5.13362 - 145.841i) q^{44} +(-174.403 - 109.122i) q^{45} +(6.88580 - 9.47749i) q^{46} +(260.647 + 511.548i) q^{47} +(-48.9439 + 96.0578i) q^{48} +(168.436 + 231.832i) q^{49} +(72.8107 + 239.162i) q^{50} +(-730.919 + 237.490i) q^{51} +(-301.789 + 153.769i) q^{52} +(-4.68216 - 29.5620i) q^{53} -115.882 q^{54} +(398.951 + 84.9295i) q^{55} -60.1011 q^{56} +(-61.0523 - 385.469i) q^{57} +(486.668 - 247.970i) q^{58} +(-14.7271 + 4.78513i) q^{59} +(-227.302 - 197.827i) q^{60} +(-240.012 - 330.347i) q^{61} +(-47.8484 + 93.9078i) q^{62} +(62.7591 + 123.172i) q^{63} +(-37.6183 + 51.7771i) q^{64} +(-212.419 - 922.573i) q^{65} +(-461.948 + 168.281i) q^{66} +(459.956 - 459.956i) q^{67} +(-450.620 + 71.3712i) q^{68} +(-37.5357 - 12.1961i) q^{69} +(40.7361 - 162.974i) q^{70} +(58.0796 - 42.1973i) q^{71} +(145.394 + 23.0282i) q^{72} +(314.716 + 160.356i) q^{73} +(-161.777 + 497.898i) q^{74} +(690.502 - 482.281i) q^{75} -231.685i q^{76} +(-200.503 - 186.868i) q^{77} +(806.881 + 806.881i) q^{78} +(407.935 + 296.382i) q^{79} +(-114.904 - 137.102i) q^{80} +(274.170 + 843.807i) q^{81} +(32.3303 - 204.126i) q^{82} +(-131.768 + 831.952i) q^{83} +(62.5700 + 192.571i) q^{84} +(111.893 - 1270.30i) q^{85} +(-32.1474 - 23.3565i) q^{86} +(-1301.18 - 1301.18i) q^{87} +(-286.485 + 55.7700i) q^{88} -642.498i q^{89} +(-160.992 + 378.652i) q^{90} +(-196.579 + 605.008i) q^{91} +(-20.8760 - 10.6368i) q^{92} +(350.705 + 55.5463i) q^{93} +(928.952 - 674.923i) q^{94} +(628.250 + 157.034i) q^{95} +(205.063 + 66.6292i) q^{96} +(341.497 - 54.0877i) q^{97} +(405.258 - 405.258i) q^{98} +(413.451 + 528.889i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{3} + 32 q^{5} - 40 q^{7} - 44 q^{11} + 128 q^{12} - 256 q^{15} + 576 q^{16} - 640 q^{17} - 64 q^{20} + 312 q^{22} - 984 q^{23} - 520 q^{25} + 304 q^{26} - 364 q^{27} + 240 q^{28} - 432 q^{31}+ \cdots + 7044 q^{97}+O(q^{100}) $ 144 * q + 8 * q^3 + 32 * q^5 - 40 * q^7 - 44 * q^11 + 128 * q^12 - 256 * q^15 + 576 * q^16 - 640 * q^17 - 64 * q^20 + 312 * q^22 - 984 * q^23 - 520 * q^25 + 304 * q^26 - 364 * q^27 + 240 * q^28 - 432 * q^31 + 2368 * q^33 + 1808 * q^36 - 960 * q^37 + 72 * q^38 + 740 * q^41 + 2440 * q^42 + 2656 * q^45 + 720 * q^46 - 1980 * q^47 - 128 * q^48 - 1360 * q^50 - 3880 * q^51 - 1920 * q^52 - 3060 * q^53 - 3044 * q^55 - 64 * q^56 - 4400 * q^57 - 2016 * q^58 - 1120 * q^60 - 960 * q^61 + 80 * q^62 + 1800 * q^63 + 1552 * q^66 + 10160 * q^67 + 2560 * q^68 + 2304 * q^70 + 1312 * q^71 - 2460 * q^73 + 8644 * q^75 - 1272 * q^77 - 5312 * q^78 + 768 * q^80 + 2116 * q^81 + 1280 * q^82 + 320 * q^85 - 5488 * q^86 + 1248 * q^88 - 8480 * q^90 + 11796 * q^91 - 704 * q^92 + 688 * q^93 - 1280 * q^95 + 7044 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.312869	−	1.97538i	−0.110616	−	0.698401i
$2$	−0.312869	−	1.97538i	−0.110616	−	0.698401i
$3$	−6.00362	+	3.05899i	−1.15540	+	0.588704i	−0.923334	−	0.383997i	$-0.874547\pi$
$3$	−6.00362	+	3.05899i	−1.15540	+	0.588704i	−0.232062	+	0.972701i	$0.574547\pi$
$4$	−3.80423	+	1.23607i	−0.475528	+	0.154508i
$5$	−0.773319	−	11.1536i	−0.0691678	−	0.997605i
$5$	−0.773319	−	11.1536i	−0.0691678	−	0.997605i
$6$	7.92101	+	10.9023i	0.538957	+	0.741810i
$7$	−3.41066	+	6.69380i	−0.184159	+	0.361431i	−0.964567	−	0.263839i	$-0.915011\pi$
$7$	−3.41066	+	6.69380i	−0.184159	+	0.361431i	0.780408	+	0.625270i	$0.215011\pi$
$8$	3.63192	+	7.12805i	0.160510	+	0.315018i
$9$	10.8157	−	14.8866i	0.400583	−	0.551356i
$10$	−21.7905	+	5.01720i	−0.689077	+	0.158658i
$11$	−10.0463	+	35.0724i	−0.275369	+	0.961339i
$11$	−10.0463	+	35.0724i	−0.275369	+	0.961339i
$12$	19.0580	−	19.0580i	0.458464	−	0.458464i
$13$	83.6339	−	13.2463i	1.78430	−	0.282605i	0.825028	−	0.565092i	$-0.191160\pi$
$13$	83.6339	−	13.2463i	1.78430	−	0.282605i	0.959271	+	0.282487i	$0.0911595\pi$
$14$	14.2899	+	4.64306i	0.272795	+	0.0886365i
$15$	38.7614	+	64.5961i	0.667210	+	1.11191i
$16$	12.9443	−	9.40456i	0.202254	−	0.146946i
$17$	112.655	+	17.8428i	1.60723	+	0.254560i	0.894562	−	0.446944i	$-0.147488\pi$
$17$	112.655	+	17.8428i	1.60723	+	0.254560i	0.712665	+	0.701504i	$0.247488\pi$
$18$	−32.7906	−	16.7076i	−0.429378	−	0.218779i
$19$	−17.8986	+	55.0863i	−0.216117	+	0.665140i	0.782955	+	0.622078i	$0.213711\pi$
$19$	−17.8986	+	55.0863i	−0.216117	+	0.665140i	−0.999072	+	0.0430622i	$0.986289\pi$
$20$	16.7284	+	41.4748i	0.187030	+	0.463702i
$21$		−	50.6202i		−	0.526011i
$22$	72.4243	+	8.87209i	0.701860	+	0.0859789i
$23$	4.14181	+	4.14181i	0.0375490	+	0.0375490i	0.725632	−	0.688083i	$-0.241548\pi$
$23$	4.14181	+	4.14181i	0.0375490	+	0.0375490i	−0.688083	+	0.725632i	$0.741548\pi$
$24$	−43.6094	−	31.6840i	−0.370905	−	0.269478i
$25$	−123.804	+	17.2505i	−0.990432	+	0.138004i
$26$	−52.3329	−	161.064i	−0.394743	−	1.21490i
$27$	9.06400	−	57.2279i	0.0646062	−	0.407908i
$28$	4.70094	−	29.6806i	0.0317284	−	0.200325i
$29$	84.3925	+	259.733i	0.540390	+	1.66315i	0.731707	+	0.681620i	$0.238724\pi$
$29$	84.3925	+	259.733i	0.540390	+	1.66315i	−0.191317	+	0.981528i	$0.561276\pi$
$30$	115.474	−	96.7785i	0.702755	−	0.588975i
$31$	−42.6332	−	30.9749i	−0.247005	−	0.179460i	0.457393	−	0.889264i	$-0.348783\pi$
$31$	−42.6332	−	30.9749i	−0.247005	−	0.179460i	−0.704398	+	0.709805i	$0.748783\pi$
$32$	−22.6274	−	22.6274i	−0.125000	−	0.125000i
$33$	−46.9724	−	241.293i	−0.247783	−	1.27284i
$34$		−	228.119i		−	1.15065i
$35$	77.2973	+	32.8646i	0.373304	+	0.158718i
$36$	−22.7447	+	70.0010i	−0.105300	+	0.324079i
$37$	−233.230	−	118.837i	−1.03629	−	0.528018i	−0.148814	−	0.988865i	$-0.547546\pi$
$37$	−233.230	−	118.837i	−1.03629	−	0.528018i	−0.887479	+	0.460847i	$0.847546\pi$
$38$	114.416	+	18.1217i	0.488441	+	0.0773614i
$39$	−461.586	+	335.362i	−1.89520	+	1.37694i
$40$	76.6945	−	46.0212i	0.303162	−	0.181915i
$41$	98.2775	+	31.9323i	0.374350	+	0.121634i	0.490148	−	0.871639i	$-0.336943\pi$
$41$	98.2775	+	31.9323i	0.374350	+	0.121634i	−0.115798	+	0.993273i	$0.536943\pi$
$42$	−99.9940	+	15.8375i	−0.367367	+	0.0581852i
$43$	14.0489	−	14.0489i	0.0498243	−	0.0498243i	−0.681756	−	0.731580i	$-0.738783\pi$
$43$	14.0489	−	14.0489i	0.0498243	−	0.0498243i	0.731580	+	0.681756i	$0.238783\pi$
$44$	−5.13362	−	145.841i	−0.0175891	−	0.499691i
$45$	−174.403	−	109.122i	−0.577743	−	0.361488i
$46$	6.88580	−	9.47749i	0.0220708	−	0.0303778i
$47$	260.647	+	511.548i	0.808920	+	1.58759i	0.809156	+	0.587594i	$0.199925\pi$
$47$	260.647	+	511.548i	0.808920	+	1.58759i	−0.000235997		1.00000i	$0.500075\pi$
$48$	−48.9439	+	96.0578i	−0.147176	+	0.288849i
$49$	168.436	+	231.832i	0.491067	+	0.675896i
$50$	72.8107	+	239.162i	0.205940	+	0.676453i
$51$	−730.919	+	237.490i	−2.00684	+	0.652063i
$52$	−301.789	+	153.769i	−0.804820	+	0.410076i
$53$	−4.68216	−	29.5620i	−0.0121348	−	0.0766161i	0.980878	−	0.194625i	$-0.0623489\pi$
$53$	−4.68216	−	29.5620i	−0.0121348	−	0.0766161i	−0.993013	+	0.118009i	$0.962349\pi$
$54$	−115.882			−0.292030
$55$	398.951	+	84.9295i	0.978083	+	0.208216i
$56$	−60.1011			−0.143417
$57$	−61.0523	−	385.469i	−0.141870	−	0.895730i
$58$	486.668	−	247.970i	1.10177	−	0.561379i
$59$	−14.7271	+	4.78513i	−0.0324967	+	0.0105588i	−0.325220	−	0.945638i	$-0.605438\pi$
$59$	−14.7271	+	4.78513i	−0.0324967	+	0.0105588i	0.292724	+	0.956197i	$0.405438\pi$
$60$	−227.302	−	197.827i	−0.489077	−	0.425655i
$61$	−240.012	−	330.347i	−0.503776	−	0.693388i	0.479078	−	0.877772i	$-0.340971\pi$
$61$	−240.012	−	330.347i	−0.503776	−	0.693388i	−0.982854	+	0.184384i	$0.940971\pi$
$62$	−47.8484	+	93.9078i	−0.0980121	+	0.192360i
$63$	62.7591	+	123.172i	0.125506	+	0.246320i
$64$	−37.6183	+	51.7771i	−0.0734732	+	0.101127i
$65$	−212.419	−	922.573i	−0.405344	−	1.76048i
$66$	−461.948	+	168.281i	−0.861543	+	0.313848i
$67$	459.956	−	459.956i	0.838695	−	0.838695i	−0.149992	−	0.988687i	$-0.547925\pi$
$67$	459.956	−	459.956i	0.838695	−	0.838695i	0.988687	+	0.149992i	$0.0479249\pi$
$68$	−450.620	+	71.3712i	−0.803614	+	0.127280i
$69$	−37.5357	−	12.1961i	−0.0654893	−	0.0212788i
$70$	40.7361	−	162.974i	0.0695556	−	0.278272i
$71$	58.0796	−	42.1973i	0.0970814	−	0.0705337i	−0.538186	−	0.842826i	$-0.680890\pi$
$71$	58.0796	−	42.1973i	0.0970814	−	0.0705337i	0.635267	+	0.772293i	$0.280890\pi$
$72$	145.394	+	23.0282i	0.237985	+	0.0376931i
$73$	314.716	+	160.356i	0.504585	+	0.257099i	0.687703	−	0.725992i	$-0.258619\pi$
$73$	314.716	+	160.356i	0.504585	+	0.257099i	−0.183118	+	0.983091i	$0.558619\pi$
$74$	−161.777	+	497.898i	−0.254138	+	0.782156i
$75$	690.502	−	482.281i	1.06310	−	0.742520i
$76$		−	231.685i		−	0.349685i
$77$	−200.503	−	186.868i	−0.296746	−	0.276566i
$78$	806.881	+	806.881i	1.17130	+	1.17130i
$79$	407.935	+	296.382i	0.580965	+	0.422096i	0.839072	−	0.544020i	$-0.183099\pi$
$79$	407.935	+	296.382i	0.580965	+	0.422096i	−0.258107	+	0.966116i	$0.583099\pi$
$80$	−114.904	−	137.102i	−0.160584	−	0.191606i
$81$	274.170	+	843.807i	0.376090	+	1.15749i
$82$	32.3303	−	204.126i	0.0435401	−	0.274901i
$83$	−131.768	+	831.952i	−0.174258	+	1.10022i	0.733179	+	0.680036i	$0.238036\pi$
$83$	−131.768	+	831.952i	−0.174258	+	1.10022i	−0.907437	+	0.420188i	$0.861964\pi$
$84$	62.5700	+	192.571i	0.0812732	+	0.250133i
$85$	111.893	−	1270.30i	0.142782	−	1.62099i
$86$	−32.1474	−	23.3565i	−0.0403087	−	0.0292860i
$87$	−1301.18	−	1301.18i	−1.60347	−	1.60347i
$88$	−286.485	+	55.7700i	−0.347039	+	0.0675580i
$89$		−	642.498i		−	0.765221i	−0.923910	−	0.382611i	$-0.875025\pi$
$89$		−	642.498i		−	0.765221i	0.923910	−	0.382611i	$-0.124975\pi$
$90$	−160.992	+	378.652i	−0.188556	+	0.443482i
$91$	−196.579	+	605.008i	−0.226451	+	0.696946i
$92$	−20.8760	−	10.6368i	−0.0236573	−	0.0120540i
$93$	350.705	+	55.5463i	0.391037	+	0.0619342i
$94$	928.952	−	674.923i	1.01930	−	0.740564i
$95$	628.250	+	157.034i	0.678496	+	0.169593i
$96$	205.063	+	66.6292i	0.218013	+	0.0708366i
$97$	341.497	−	54.0877i	0.357461	−	0.0566163i	0.0248787	−	0.999690i	$-0.492080\pi$
$97$	341.497	−	54.0877i	0.357461	−	0.0566163i	0.332582	+	0.943074i	$0.392080\pi$
$98$	405.258	−	405.258i	0.417726	−	0.417726i
$99$	413.451	+	528.889i	0.419731	+	0.536922i
$100$	449.655	−	218.655i	0.449655	−	0.218655i
$101$	−1010.27	+	1390.52i	−0.995303	+	1.36992i	−0.0671397	+	0.997744i	$0.521387\pi$
$101$	−1010.27	+	1390.52i	−0.995303	+	1.36992i	−0.928163	+	0.372173i	$0.878613\pi$
$102$	697.814	+	1369.54i	0.677391	+	1.32945i
$103$	−519.455	+	1019.49i	−0.496926	+	0.975273i	0.497260	+	0.867602i	$0.334339\pi$
$103$	−519.455	+	1019.49i	−0.496926	+	0.975273i	−0.994187	+	0.107672i	$0.965661\pi$
$104$	398.173	+	548.037i	0.375423	+	0.516726i
$105$	−564.596	+	39.1456i	−0.524752	+	0.0363830i
$106$	−56.9312	+	18.4981i	−0.0521664	+	0.0169499i
$107$	1421.99	−	724.541i	1.28476	−	0.654617i	0.327774	−	0.944756i	$-0.393701\pi$
$107$	1421.99	−	724.541i	1.28476	−	0.654617i	0.956985	+	0.290139i	$0.0937014\pi$
$108$	36.2560	+	228.911i	0.0323031	+	0.203954i
$109$	1038.01			0.912137			0.456068	−	0.889945i	$-0.349257\pi$
$109$	1038.01			0.912137			0.456068	+	0.889945i	$0.349257\pi$
$110$	42.9483	−	814.651i	0.0372269	−	0.706126i
$111$	1763.75			1.50818
$112$	18.8038	+	118.722i	0.0158642	+	0.100162i
$113$	−198.100	+	100.937i	−0.164918	+	0.0840299i	−0.534501	−	0.845168i	$-0.679500\pi$
$113$	−198.100	+	100.937i	−0.164918	+	0.0840299i	0.369583	+	0.929198i	$0.379500\pi$
$114$	−742.345	+	241.202i	−0.609886	+	0.198164i
$115$	42.9931	−	49.3989i	0.0348619	−	0.0400563i
$116$	−642.096	−	883.770i	−0.513941	−	0.707379i
$117$	707.371	−	1388.29i	0.558944	−	1.09699i
$118$	14.0601	+	27.5945i	0.0109689	+	0.0215278i
$119$	−503.665	+	693.235i	−0.387990	+	0.534023i
$120$	−319.666	+	510.902i	−0.243178	+	0.388656i
$121$	−1129.15	−	704.693i	−0.848344	−	0.529446i
$122$	−577.469	+	577.469i	−0.428537	+	0.428537i
$123$	−687.701	+	108.921i	−0.504129	+	0.0798462i
$124$	200.473	+	65.1378i	0.145186	+	0.0471738i
$125$	288.145	+	1367.52i	0.206180	+	0.978514i
$126$	223.675	−	162.509i	0.158147	−	0.114901i
$127$	1120.94	+	177.540i	0.783209	+	0.124048i	0.535218	−	0.844714i	$-0.320230\pi$
$127$	1120.94	+	177.540i	0.783209	+	0.124048i	0.247991	+	0.968762i	$0.420230\pi$
$128$	114.049	+	58.1108i	0.0787546	+	0.0401275i
$129$	−41.3688	+	127.320i	−0.0282351	+	0.0868986i
$130$	−1755.97	+	708.253i	−1.18468	+	0.477830i
$131$		−	1449.08i		−	0.966464i	−0.875492	−	0.483232i	$-0.839463\pi$
$131$		−	1449.08i		−	0.966464i	0.875492	−	0.483232i	$-0.160537\pi$
$132$	476.948	+	859.871i	0.314492	+	0.566986i
$133$	−307.691	−	307.691i	−0.200603	−	0.200603i
$134$	−1052.49	−	764.680i	−0.678518	−	0.492972i
$135$	−645.304	−	56.8405i	−0.411399	−	0.0362374i
$136$	281.970	+	867.815i	0.177785	+	0.547165i
$137$	−324.626	+	2049.61i	−0.202443	+	1.27817i	0.651836	+	0.758360i	$0.273999\pi$
$137$	−324.626	+	2049.61i	−0.202443	+	1.27817i	−0.854279	+	0.519815i	$0.826001\pi$
$138$	−12.3481	+	77.9628i	−0.00761696	+	0.0480916i
$139$	−590.482	−	1817.32i	−0.360317	−	1.10894i	−0.952862	−	0.303404i	$-0.901877\pi$
$139$	−590.482	−	1817.32i	−0.360317	−	1.10894i	0.592545	−	0.805537i	$-0.298123\pi$
$140$	−334.679	−	29.4797i	−0.202040	−	0.0177963i
$141$	−3129.64	−	2273.82i	−1.86925	−	1.35809i
$142$	−101.527	−	101.527i	−0.0599996	−	0.0599996i
$143$	−375.628	+	3066.32i	−0.219662	+	1.79314i
$144$		−	294.414i		−	0.170378i
$145$	2831.69	−	1142.13i	1.62179	−	0.654132i
$146$	218.298	−	671.853i	0.123743	−	0.380842i
$147$	−1720.40	−	876.587i	−0.965279	−	0.491834i
$148$	1034.15	+	163.794i	0.574370	+	0.0909713i
$149$	−1066.45	+	774.824i	−0.586357	+	0.426014i	−0.841010	−	0.541019i	$-0.818039\pi$
$149$	−1066.45	+	774.824i	−0.586357	+	0.426014i	0.254653	+	0.967033i	$0.418039\pi$
$150$	−1168.72	−	1213.11i	−0.636173	−	0.660334i
$151$	−1578.54	−	512.900i	−0.850728	−	0.276418i	−0.148977	−	0.988841i	$-0.547598\pi$
$151$	−1578.54	−	512.900i	−0.850728	−	0.276418i	−0.701751	+	0.712422i	$0.747598\pi$
$152$	−457.665	+	72.4869i	−0.244220	+	0.0386807i
$153$	1484.07	−	1484.07i	0.784181	−	0.784181i
$154$	−306.403	+	454.535i	−0.160329	+	0.237841i
$155$	−312.511	+	499.466i	−0.161945	+	0.258826i
$156$	1341.45	−	1846.34i	0.688472	−	0.947601i
$157$	−484.795	−	951.464i	−0.246439	−	0.483663i	0.734341	−	0.678780i	$-0.237491\pi$
$157$	−484.795	−	951.464i	−0.246439	−	0.483663i	−0.980780	+	0.195117i	$0.937491\pi$
$158$	457.836	−	898.554i	0.230528	−	0.452437i
$159$	118.540	+	163.156i	0.0591247	+	0.0813781i
$160$	−234.878	+	269.875i	−0.116055	+	0.133347i
$161$	−41.8508	+	13.5982i	−0.0204864	+	0.00665643i
$162$	1581.06	−	805.589i	0.766788	−	0.390698i
$163$	−504.689	−	3186.48i	−0.242517	−	1.53119i	−0.745270	−	0.666763i	$-0.767679\pi$
$163$	−504.689	−	3186.48i	−0.242517	−	1.53119i	0.502753	−	0.864430i	$-0.332321\pi$
$164$	−413.340			−0.196808
$165$	−2654.95	+	710.506i	−1.25265	+	0.335229i
$166$	1684.65			0.787674
$167$	192.640	+	1216.28i	0.0892632	+	0.563586i	0.991268	+	0.131860i	$0.0420950\pi$
$167$	192.640	+	1216.28i	0.0892632	+	0.563586i	−0.902005	+	0.431725i	$0.857905\pi$
$168$	360.824	−	183.849i	0.165703	−	0.0844300i
$169$	4729.70	−	1536.77i	2.15280	−	0.699487i
$170$	−2544.34	+	176.408i	−1.14789	+	0.0795877i
$171$	626.461	+	862.249i	0.280156	+	0.385601i
$172$	−36.0799	+	70.8108i	−0.0159946	+	0.0313911i
$173$	−855.347	−	1678.71i	−0.375901	−	0.737746i	0.623114	−	0.782131i	$-0.285867\pi$
$173$	−855.347	−	1678.71i	−0.375901	−	0.737746i	−0.999015	+	0.0443847i	$0.985867\pi$
$174$	−2163.23	+	2977.43i	−0.942494	+	1.29723i
$175$	306.782	−	887.555i	0.132517	−	0.383388i
$176$	199.799	+	548.467i	0.0855706	+	0.234899i
$177$	73.7782	−	73.7782i	0.0313306	−	0.0313306i
$178$	−1269.18	+	201.018i	−0.534431	+	0.0846456i
$179$	−472.240	−	153.440i	−0.197189	−	0.0640706i	0.208757	−	0.977967i	$-0.433058\pi$
$179$	−472.240	−	153.440i	−0.197189	−	0.0640706i	−0.405947	+	0.913897i	$0.633058\pi$
$180$	798.349	+	199.551i	0.330586	+	0.0826316i
$181$	−1227.80	+	892.047i	−0.504207	+	0.366328i	−0.810622	−	0.585570i	$-0.800871\pi$
$181$	−1227.80	+	892.047i	−0.504207	+	0.366328i	0.306415	+	0.951898i	$0.400871\pi$
$182$	1256.62	+	199.029i	0.511797	+	0.0810607i
$183$	2451.47	+	1249.09i	0.990261	+	0.504563i
$184$	−14.4803	+	44.5658i	−0.00580165	+	0.0178556i
$185$	−1145.09	+	2693.25i	−0.455075	+	1.07033i
$186$		−	710.154i		−	0.279952i
$187$	−1757.55	+	3771.83i	−0.687299	+	1.47499i
$188$	−1623.87	−	1623.87i	−0.629961	−	0.629961i
$189$	352.158	+	255.858i	0.135533	+	0.0984704i
$190$	113.642	−	1290.16i	0.0433918	−	0.492622i
$191$	195.594	+	601.975i	0.0740977	+	0.228049i	0.981245	−	0.192763i	$-0.0617450\pi$
$191$	195.594	+	601.975i	0.0740977	+	0.228049i	−0.907148	+	0.420813i	$0.861745\pi$
$192$	67.4597	−	425.924i	0.0253567	−	0.160096i
$193$	−83.8216	+	529.229i	−0.0312622	+	0.197382i	−0.998376	−	0.0569606i	$-0.981859\pi$
$193$	−83.8216	+	529.229i	−0.0312622	+	0.197382i	0.967114	+	0.254343i	$0.0818591\pi$
$194$	−213.687	−	657.662i	−0.0790817	−	0.243389i
$195$	4097.43	+	4888.98i	1.50473	+	1.79542i
$196$	−927.329	−	673.744i	−0.337948	−	0.245533i
$197$	−1151.01	−	1151.01i	−0.416275	−	0.416275i	0.467643	−	0.883918i	$-0.345103\pi$
$197$	−1151.01	−	1151.01i	−0.416275	−	0.416275i	−0.883918	+	0.467643i	$0.845103\pi$
$198$	915.399	−	982.194i	0.328558	−	0.352533i
$199$			1820.60i			0.648539i	0.945965	+	0.324269i	$0.105118\pi$
$199$			1820.60i			0.648539i	−0.945965	+	0.324269i	$0.894882\pi$
$200$	−572.609	−	819.828i	−0.202448	−	0.289853i
$201$	−1354.40	+	4168.40i	−0.475282	+	1.46277i
$202$	3062.88	+	1560.61i	1.06685	+	0.543586i
$203$	−2026.44	−	320.956i	−0.700631	−	0.110969i
$204$	2487.03	−	1806.93i	0.853562	−	0.620149i
$205$	280.159	−	1120.84i	0.0954495	−	0.381867i
$206$	2176.39	+	707.153i	0.736100	+	0.239173i
$207$	106.454	−	16.8607i	0.0357444	−	0.00566136i
$208$	958.005	−	958.005i	0.319354	−	0.319354i
$209$	−1752.19	−	1181.16i	−0.579913	−	0.390921i
$210$	253.972	+	1103.04i	0.0834558	+	0.362463i
$211$	−171.507	+	236.060i	−0.0559576	+	0.0770190i	−0.836079	−	0.548609i	$-0.815157\pi$
$211$	−171.507	+	236.060i	−0.0559576	+	0.0770190i	0.780121	+	0.625628i	$0.215157\pi$
$212$	54.3526	+	106.673i	0.0176083	+	0.0345582i
$213$	−219.606	+	431.001i	−0.0706440	+	0.138647i
$214$	−1876.14	−	2582.28i	−0.599300	−	0.824866i
$215$	−167.560	−	145.832i	−0.0531512	−	0.0462587i
$216$	440.843	−	143.239i	0.138868	−	0.0451211i
$217$	352.747	−	179.734i	0.110350	−	0.0562264i
$218$	−324.760	−	2050.45i	−0.100897	−	0.637037i
$219$	−2379.96			−0.734351
$220$	−1622.68	+	170.040i	−0.497277	+	0.0521095i
$221$	9658.14			2.93971
$222$	−551.822	−	3484.07i	−0.166828	−	1.05331i
$223$	−3368.65	+	1716.41i	−1.01157	+	0.515423i	−0.879542	−	0.475822i	$-0.842151\pi$
$223$	−3368.65	+	1716.41i	−1.01157	+	0.515423i	−0.132033	+	0.991245i	$0.542151\pi$
$224$	228.638	−	74.2890i	0.0681987	−	0.0221591i
$225$	−1082.23	+	2029.60i	−0.320661	+	0.601362i
$226$	261.369	+	359.743i	0.0769291	+	0.105884i
$227$	2037.61	−	3999.03i	0.595775	−	1.16927i	−0.374491	−	0.927231i	$-0.622182\pi$
$227$	2037.61	−	3999.03i	0.595775	−	1.16927i	0.970265	−	0.242043i	$-0.0778176\pi$
$228$	708.722	+	1390.95i	0.205861	+	0.404025i
$229$	−437.764	+	602.530i	−0.126324	+	0.173870i	−0.867495	−	0.497447i	$-0.834271\pi$
$229$	−437.764	+	602.530i	−0.126324	+	0.173870i	0.741170	+	0.671317i	$0.234271\pi$
$230$	−111.033	−	69.4721i	−0.0318316	−	0.0199168i
$231$	1775.37	+	508.544i	0.505675	+	0.144847i
$232$	−1544.89	+	1544.89i	−0.437184	+	0.437184i
$233$	1626.53	−	257.617i	0.457328	−	0.0724336i	0.0764795	−	0.997071i	$-0.475632\pi$
$233$	1626.53	−	257.617i	0.457328	−	0.0724336i	0.380848	+	0.924638i	$0.375632\pi$
$234$	−2963.72	−	962.970i	−0.827967	−	0.269023i
$235$	5504.02	−	3302.73i	1.52784	−	0.916793i
$236$	50.1105	−	36.4074i	0.0138217	−	0.0100420i
$237$	−3355.72	−	531.493i	−0.919735	−	0.145672i
$238$	1526.98	+	778.036i	0.415880	+	0.211902i
$239$	8.53436	−	26.2661i	0.00230980	−	0.00710883i	−0.949895	−	0.312569i	$-0.898810\pi$
$239$	8.53436	−	26.2661i	0.00230980	−	0.00710883i	0.952205	+	0.305460i	$0.0988104\pi$
$240$	1109.24	+	471.616i	0.298337	+	0.126844i
$241$			1580.59i			0.422467i	0.977436	+	0.211233i	$0.0677480\pi$
$241$			1580.59i			0.422467i	−0.977436	+	0.211233i	$0.932252\pi$
$242$	−1038.76	+	2450.96i	−0.275925	+	0.651049i
$243$	−3121.01	−	3121.01i	−0.823920	−	0.823920i
$244$	1321.39	+	960.046i	0.346694	+	0.251888i
$245$	2455.50	−	2057.94i	0.640311	−	0.536641i
$246$	430.320	+	1324.39i	0.111529	+	0.343252i
$247$	−767.242	+	4844.18i	−0.197646	+	1.24788i
$248$	65.9497	−	416.390i	0.0168863	−	0.106616i
$249$	−1753.85	−	5397.80i	−0.446369	−	1.37378i
$250$	2611.21	−	997.047i	0.660589	−	0.252235i
$251$	683.210	+	496.381i	0.171808	+	0.124826i	0.670366	−	0.742030i	$-0.266137\pi$
$251$	683.210	+	496.381i	0.171808	+	0.124826i	−0.498558	+	0.866856i	$0.666137\pi$
$252$	−390.998	−	390.998i	−0.0977404	−	0.0977404i
$253$	−186.873	+	103.654i	−0.0464372	+	0.0257575i
$254$		−	2269.83i		−	0.560715i
$255$	3214.09	+	7968.69i	0.789311	+	1.95694i
$256$	79.1084	−	243.470i	0.0193136	−	0.0594410i
$257$	−5474.58	−	2789.44i	−1.32877	−	0.677045i	−0.361881	−	0.932224i	$-0.617865\pi$
$257$	−5474.58	−	2789.44i	−1.32877	−	0.677045i	−0.966894	+	0.255180i	$0.917865\pi$
$258$	264.448	+	41.8845i	0.0638133	+	0.0101070i
$259$	1590.94	−	1155.89i	0.381685	−	0.277310i
$260$	1948.45	+	3247.11i	0.464761	+	0.774528i
$261$	4779.32	+	1552.89i	1.13346	+	0.368282i
$262$	−2862.48	+	453.372i	−0.674979	+	0.106906i
$263$	−2517.68	+	2517.68i	−0.590292	+	0.590292i	−0.937710	−	0.347418i	$-0.887059\pi$
$263$	−2517.68	+	2517.68i	−0.590292	+	0.590292i	0.347418	+	0.937710i	$0.387059\pi$
$264$	1549.35	−	1211.18i	0.361196	−	0.282359i
$265$	−326.101	+	75.0836i	−0.0755932	+	0.0174051i
$266$	−511.538	+	704.072i	−0.117911	+	0.162291i
$267$	1965.40	+	3857.31i	0.450489	+	0.884134i
$268$	−1181.24	+	2318.31i	−0.269238	+	0.528408i
$269$	2594.79	+	3571.43i	0.588132	+	0.809494i	0.994557	−	0.104190i	$-0.0332250\pi$
$269$	2594.79	+	3571.43i	0.588132	+	0.809494i	−0.406426	+	0.913684i	$0.633225\pi$
$270$	89.6141	+	1292.50i	0.0201990	+	0.291330i
$271$	5798.41	−	1884.02i	1.29974	−	0.422310i	0.424246	−	0.905547i	$-0.360539\pi$
$271$	5798.41	−	1884.02i	1.29974	−	0.422310i	0.875489	+	0.483237i	$0.160539\pi$
$272$	1626.04	−	828.509i	0.362475	−	0.184690i
$273$	−670.531	−	4233.57i	−0.148654	−	0.938561i
$274$	4150.32			0.915072
$275$	638.750	−	4515.40i	0.140066	−	0.990142i
$276$	157.869			0.0344298
$277$	−1356.52	−	8564.73i	−0.294243	−	1.85778i	−0.482818	−	0.875721i	$-0.660387\pi$
$277$	−1356.52	−	8564.73i	−0.294243	−	1.85778i	0.188575	−	0.982059i	$-0.439613\pi$
$278$	−3405.14	+	1735.01i	−0.734629	+	0.374312i
$279$	−922.221	+	299.648i	−0.197892	+	0.0642991i
$280$	46.4773	+	670.341i	0.00991982	+	0.143073i
$281$	−1933.62	−	2661.40i	−0.410499	−	0.565004i	0.552841	−	0.833287i	$-0.313544\pi$
$281$	−1933.62	−	2661.40i	−0.410499	−	0.565004i	−0.963340	+	0.268283i	$0.913544\pi$
$282$	−3512.48	+	6893.64i	−0.741721	+	1.45571i
$283$	−1216.43	−	2387.38i	−0.255510	−	0.501467i	0.727245	−	0.686378i	$-0.240800\pi$
$283$	−1216.43	−	2387.38i	−0.255510	−	0.501467i	−0.982755	+	0.184911i	$0.940800\pi$
$284$	−168.789	+	232.318i	−0.0352669	+	0.0485407i
$285$	−4252.14	+	979.041i	−0.883772	+	0.203485i
$286$	6174.66	−	217.348i	1.27663	−	0.0449373i
$287$	−548.940	+	548.940i	−0.112902	+	0.112902i
$288$	−581.578	+	92.1129i	−0.118992	+	0.0188465i
$289$	7700.25	+	2501.96i	1.56732	+	0.509254i
$290$	−3142.09	−	5236.32i	−0.636242	−	1.06030i
$291$	−1884.76	+	1369.36i	−0.379679	+	0.275853i
$292$	−1395.46	−	221.019i	−0.279668	−	0.0442951i
$293$	−673.917	−	343.378i	−0.134371	−	0.0684653i	0.385513	−	0.922703i	$-0.374025\pi$
$293$	−673.917	−	343.378i	−0.134371	−	0.0684653i	−0.519883	+	0.854237i	$0.674025\pi$
$294$	−1193.33	+	3672.69i	−0.236722	+	0.728557i
$295$	64.7600	+	160.559i	0.0127813	+	0.0316885i
$296$		−	2094.09i		−	0.411204i
$297$	1916.06	+	892.822i	0.374347	+	0.174434i
$298$	1864.23	+	1864.23i	0.362389	+	0.362389i
$299$	401.260	+	291.533i	0.0776103	+	0.0563872i
$300$	−2030.69	+	2688.21i	−0.390807	+	0.517347i
$301$	46.1247	+	141.957i	0.00883250	+	0.0271836i
$302$	−519.293	+	3278.69i	−0.0989469	+	0.624726i
$303$	1811.69	−	11438.5i	0.343494	−	2.16874i
$304$	286.378	+	881.381i	0.0540293	+	0.166285i
$305$	−3498.95	+	2932.45i	−0.656882	+	0.550529i
$306$	−3395.91	−	2467.27i	−0.634416	−	0.460930i
$307$	−5621.21	−	5621.21i	−1.04501	−	1.04501i	−0.998938	−	0.0460758i	$-0.985328\pi$
$307$	−5621.21	−	5621.21i	−1.04501	−	1.04501i	−0.0460758	−	0.998938i	$-0.514672\pi$
$308$	993.741	+	463.052i	0.183843	+	0.0856650i
$309$		−	7709.62i		−	1.41937i
$310$	1084.41	+	461.059i	0.198678	+	0.0844723i
$311$	2703.67	−	8321.05i	0.492962	−	1.51718i	−0.327146	−	0.944974i	$-0.606087\pi$
$311$	2703.67	−	8321.05i	0.492962	−	1.51718i	0.820109	−	0.572208i	$-0.193913\pi$
$312$	−4066.92	−	2072.20i	−0.737961	−	0.376010i
$313$	1521.96	+	241.055i	0.274845	+	0.0435311i	0.292335	−	0.956316i	$-0.405568\pi$
$313$	1521.96	+	241.055i	0.274845	+	0.0435311i	−0.0174906	+	0.999847i	$0.505568\pi$
$314$	−1727.82	+	1255.34i	−0.310531	+	0.225614i
$315$	1325.27	−	795.239i	0.237049	−	0.142243i
$316$	−1918.22	−	623.269i	−0.341483	−	0.110955i
$317$	10605.5	−	1679.74i	1.87906	−	0.297614i	0.891279	−	0.453456i	$-0.149809\pi$
$317$	10605.5	−	1679.74i	1.87906	−	0.297614i	0.987782	+	0.155842i	$0.0498090\pi$
$318$	285.207	−	285.207i	0.0502944	−	0.0502944i
$319$	−9957.30	+	350.498i	−1.74766	+	0.0615175i
$320$	606.590	+	379.537i	0.105967	+	0.0663025i
$321$	−6320.73	+	8699.74i	−1.09903	+	1.51269i
$322$	39.9553	+	78.4167i	0.00691498	+	0.0135714i
$323$	−2999.26	+	5886.39i	−0.516667	+	1.01402i
$324$	−2086.01	−	2871.14i	−0.357683	−	0.492308i
$325$	−10125.7	+	3082.68i	−1.72823	+	0.526142i
$326$	−6136.60	+	1993.90i	−1.04256	+	0.338749i
$327$	−6231.79	+	3175.25i	−1.05388	+	0.536978i
$328$	129.321	+	816.502i	0.0217700	+	0.137451i
$329$	−4313.18			−0.722776
$330$	2234.17	+	5022.23i	0.372687	+	0.837771i
$331$	−1937.09			−0.321667			−0.160834	−	0.986982i	$-0.551418\pi$
$331$	−1937.09			−0.321667			−0.160834	+	0.986982i	$0.551418\pi$
$332$	−527.073	−	3327.81i	−0.0871292	−	0.550112i
$333$	−4291.64	+	2186.70i	−0.706247	+	0.359851i
$334$	2342.35	−	761.074i	0.383735	−	0.124683i
$335$	−5485.84	−	4774.45i	−0.894697	−	0.778675i
$336$	−476.061	−	655.242i	−0.0772954	−	0.106388i
$337$	−525.030	+	1030.43i	−0.0848670	+	0.166561i	−0.929539	−	0.368723i	$-0.879795\pi$
$337$	−525.030	+	1030.43i	−0.0848670	+	0.166561i	0.844672	+	0.535284i	$0.179795\pi$
$338$	−4515.48	−	8862.13i	−0.726656	−	1.42614i
$339$	880.553	−	1211.98i	0.141077	−	0.194176i
$340$	1144.52	+	4970.83i	0.182559	+	0.792885i
$341$	1514.67	−	1184.07i	0.240539	−	0.188038i
$342$	1507.27	−	1507.27i	0.238315	−	0.238315i
$343$	−4671.43	+	739.881i	−0.735374	+	0.116472i
$344$	151.166	+	49.1169i	0.0236929	+	0.00769828i
$345$	−107.003	+	428.088i	−0.0166981	+	0.0668043i
$346$	−3048.48	+	2214.85i	−0.473662	+	0.344136i
$347$	5729.52	+	907.467i	0.886389	+	0.140390i	0.582996	−	0.812475i	$-0.301880\pi$
$347$	5729.52	+	907.467i	0.886389	+	0.140390i	0.303393	+	0.952865i	$0.401880\pi$
$348$	6558.35	+	3341.65i	1.01024	+	0.514744i
$349$	−558.207	+	1717.99i	−0.0856165	+	0.263500i	−0.984695	−	0.174287i	$-0.944238\pi$
$349$	−558.207	+	1717.99i	−0.0856165	+	0.263500i	0.899078	+	0.437788i	$0.144238\pi$
$350$	−1849.24	−	328.322i	−0.282417	−	0.0501415i
$351$		−	4906.26i		−	0.746087i
$352$	1020.92	−	566.277i	0.154588	−	0.0857462i
$353$	8280.99	+	8280.99i	1.24859	+	1.24859i	0.956342	+	0.292249i	$0.0944036\pi$
$353$	8280.99	+	8280.99i	1.24859	+	1.24859i	0.292249	+	0.956342i	$0.405596\pi$
$354$	−168.823	−	122.657i	−0.0253470	−	0.0184156i
$355$	−515.564	−	615.162i	−0.0770797	−	0.0919702i
$356$	794.171	+	2444.21i	0.118233	+	0.363884i
$357$	903.207	−	5702.62i	0.133901	−	0.845420i
$358$	−155.353	+	980.858i	−0.0229347	+	0.144804i
$359$	2926.34	+	9006.36i	0.430213	+	1.32406i	0.897913	+	0.440173i	$0.145083\pi$
$359$	2926.34	+	9006.36i	0.430213	+	1.32406i	−0.467700	+	0.883887i	$0.654917\pi$
$360$	144.410	−	1639.47i	0.0211419	−	0.240022i
$361$	2834.91	+	2059.68i	0.413312	+	0.300289i
$362$	2146.27	+	2146.27i	0.311617	+	0.311617i
$363$	8934.61	+	776.655i	1.29186	+	0.112297i
$364$		−	2544.57i		−	0.366406i
$365$	1545.16	−	3634.21i	0.221582	−	0.521160i
$366$	1700.43	−	5233.37i	0.242849	−	0.747412i
$367$	−9.53873	−	4.86023i	−0.00135672	−	0.000691285i	0.453312	−	0.891352i	$-0.350242\pi$
$367$	−9.53873	−	4.86023i	−0.00135672	−	0.000691285i	−0.454669	+	0.890661i	$0.650242\pi$
$368$	92.5647	+	14.6608i	0.0131121	+	0.00207676i
$369$	1538.31	−	1117.65i	0.217022	−	0.157676i
$370$	5678.45	+	1419.36i	0.797861	+	0.199429i
$371$	213.851	+	69.4845i	0.0299262	+	0.00972361i
$372$	−1402.82	+	222.185i	−0.195519	+	0.0309671i
$373$	−353.978	+	353.978i	−0.0491375	+	0.0491375i	−0.731249	−	0.682111i	$-0.761062\pi$
$373$	−353.978	+	353.978i	−0.0491375	+	0.0491375i	0.682111	+	0.731249i	$0.261062\pi$
$374$	8000.66	+	2291.74i	1.10616	+	0.316853i
$375$	−5913.13	−	7328.60i	−0.814274	−	1.00919i
$376$	−2699.69	+	3715.81i	−0.370282	+	0.509649i
$377$	10498.6	+	20604.6i	1.43423	+	2.81484i
$378$	395.236	−	775.694i	0.0537797	−	0.105549i
$379$	−2554.79	−	3516.37i	−0.346255	−	0.476580i	0.600000	−	0.800000i	$-0.295167\pi$
$379$	−2554.79	−	3516.37i	−0.346255	−	0.476580i	−0.946255	+	0.323420i	$0.895167\pi$
$380$	−2584.11	+	179.166i	−0.348847	+	0.0241869i
$381$	−7272.80	+	2363.07i	−0.977944	+	0.317753i
$382$	1127.93	−	574.710i	0.151073	−	0.0769758i
$383$	−1830.19	−	11555.3i	−0.244173	−	1.54164i	−0.739631	−	0.673013i	$-0.765000\pi$
$383$	−1830.19	−	11555.3i	−0.244173	−	1.54164i	0.495458	−	0.868632i	$-0.335000\pi$
$384$	−862.466			−0.114616
$385$	−1929.19	+	2380.83i	−0.255378	+	0.315165i
$386$	1071.65			0.141310
$387$	−57.1912	−	361.091i	−0.00751212	−	0.0474297i
$388$	−1232.27	+	627.875i	−0.161235	+	0.0821534i
$389$	−1474.44	+	479.075i	−0.192178	+	0.0624423i	−0.403525	−	0.914969i	$-0.632215\pi$
$389$	−1474.44	+	479.075i	−0.192178	+	0.0624423i	0.211347	+	0.977411i	$0.432215\pi$
$390$	8375.62	−	9623.58i	1.08748	−	1.24951i
$391$	392.695	+	540.498i	0.0507914	+	0.0699083i
$392$	−1040.77	+	2042.62i	−0.134098	+	0.263183i
$393$	4432.73	+	8699.72i	0.568961	+	1.11665i
$394$	−1913.57	+	2633.80i	−0.244680	+	0.336773i
$395$	2990.25	−	4779.13i	0.380901	−	0.608769i
$396$	−2226.60	−	1500.96i	−0.282553	−	0.190470i
$397$	−2722.88	+	2722.88i	−0.344225	+	0.344225i	−0.857953	−	0.513728i	$-0.828264\pi$
$397$	−2722.88	+	2722.88i	−0.344225	+	0.344225i	0.513728	+	0.857953i	$0.328264\pi$
$398$	3596.38	−	569.610i	0.452940	−	0.0717387i
$399$	2788.48	+	906.033i	0.349871	+	0.113680i
$400$	−1440.32	+	1387.62i	−0.180040	+	0.173452i
$401$	3606.99	−	2620.63i	0.449189	−	0.326355i	−0.340087	−	0.940394i	$-0.610456\pi$
$401$	3606.99	−	2620.63i	0.449189	−	0.326355i	0.789275	+	0.614039i	$0.210456\pi$
$402$	8657.91	+	1371.28i	1.07417	+	0.170132i
$403$	−3975.89	−	2025.82i	−0.491447	−	0.250405i
$404$	2124.52	−	6538.60i	0.261631	−	0.805217i
$405$	9199.44	−	3710.50i	1.12870	−	0.455250i
$406$			4103.40i			0.501597i
$407$	6510.99	−	6986.08i	0.792967	−	0.850829i
$408$	−4347.48	−	4347.48i	−0.527530	−	0.527530i
$409$	4265.26	+	3098.89i	0.515656	+	0.374646i	0.814965	−	0.579510i	$-0.196756\pi$
$409$	4265.26	+	3098.89i	0.515656	+	0.374646i	−0.299309	+	0.954156i	$0.596756\pi$
$410$	−2301.73	−	202.744i	−0.277254	−	0.0244215i
$411$	−4320.81	−	13298.1i	−0.518564	−	1.59598i
$412$	715.968	−	4520.44i	0.0856146	−	0.540549i
$413$	18.1985	−	114.901i	0.00216826	−	0.0136898i
$414$	−66.6125	−	205.012i	−0.00790779	−	0.0243377i
$415$	9381.13	+	826.321i	1.10964	+	0.0977410i
$416$	−2192.15	−	1592.69i	−0.258363	−	0.187712i
$417$	9104.19	+	9104.19i	1.06915	+	1.06915i
$418$	−1785.03	+	3830.79i	−0.208872	+	0.448254i
$419$			14770.7i			1.72218i	0.508450	+	0.861092i	$0.330219\pi$
$419$			14770.7i			1.72218i	−0.508450	+	0.861092i	$0.669781\pi$
$420$	2099.46	−	846.798i	0.243913	−	0.0983797i
$421$	3429.15	−	10553.8i	0.396975	−	1.22176i	−0.530437	−	0.847724i	$-0.677972\pi$
$421$	3429.15	−	10553.8i	0.396975	−	1.22176i	0.927413	−	0.374040i	$-0.122028\pi$
$422$	519.966	+	264.936i	0.0599799	+	0.0305613i
$423$	10434.3	+	1652.63i	1.19937	+	0.189961i
$424$	193.714	−	140.742i	0.0221877	−	0.0161203i
$425$	−14254.9	−	265.651i	−1.62698	−	0.0303200i
$426$	920.098	+	298.958i	0.104645	+	0.0340013i
$427$	3029.88	−	479.886i	0.343387	−	0.0543871i
$428$	−4514.00	+	4514.00i	−0.509795	+	0.509795i
$429$	−7124.72	−	19558.0i	−0.801830	−	2.20110i
$430$	−235.648	+	376.621i	−0.0264278	+	0.0422378i
$431$	−2912.77	+	4009.09i	−0.325530	+	0.448053i	−0.940145	−	0.340773i	$-0.889311\pi$
$431$	−2912.77	+	4009.09i	−0.325530	+	0.448053i	0.614616	+	0.788827i	$0.289311\pi$
$432$	−420.876	−	826.016i	−0.0468736	−	0.0919947i
$433$	−7454.20	+	14629.7i	−0.827311	+	1.62369i	−0.0465041	+	0.998918i	$0.514808\pi$
$433$	−7454.20	+	14629.7i	−0.827311	+	1.62369i	−0.780807	+	0.624772i	$0.785192\pi$
$434$	−465.405	−	640.576i	−0.0514751	−	0.0708493i
$435$	−13506.6	+	15519.1i	−1.48872	+	1.71053i
$436$	−3948.81	+	1283.05i	−0.433747	+	0.140933i
$437$	−302.290	+	154.024i	−0.0330904	+	0.0168604i
$438$	744.616	+	4701.32i	0.0812309	+	0.512872i
$439$	−4799.77			−0.521823			−0.260912	−	0.965363i	$-0.584023\pi$
$439$	−4799.77			−0.521823			−0.260912	+	0.965363i	$0.584023\pi$
$440$	843.579	+	3152.20i	0.0914001	+	0.341535i
$441$	5272.95			0.569372
$442$	−3021.73	−	19078.5i	−0.325179	−	2.05310i
$443$	13594.2	−	6926.61i	1.45797	−	0.742874i	0.467945	−	0.883757i	$-0.344994\pi$
$443$	13594.2	−	6926.61i	1.45797	−	0.742874i	0.990026	+	0.140884i	$0.0449944\pi$
$444$	−6709.69	+	2180.11i	−0.717180	+	0.233026i
$445$	−7166.14	+	496.856i	−0.763388	+	0.0529286i
$446$	4444.50	+	6117.33i	0.471868	+	0.649471i
$447$	4032.39	−	7914.02i	0.426679	−	0.837406i
$448$	−218.282	−	428.403i	−0.0230198	−	0.0451789i
$449$	−4895.24	+	6737.72i	−0.514522	+	0.708179i	−0.984674	−	0.174407i	$-0.944199\pi$
$449$	−4895.24	+	6737.72i	−0.514522	+	0.708179i	0.470151	+	0.882586i	$0.344199\pi$
$450$	4347.82	+	1502.82i	0.455462	+	0.157430i
$451$	−2107.26	+	3126.03i	−0.220016	+	0.326383i
$452$	628.854	−	628.854i	0.0654398	−	0.0654398i
$453$	11045.9	−	1749.50i	1.14566	−	0.181454i
$454$	−8537.10	−	2773.87i	−0.882524	−	0.286750i
$455$	6900.01	+	1724.69i	0.710940	+	0.177703i
$456$	2525.90	−	1835.18i	0.259400	−	0.188465i
$457$	6199.01	+	981.827i	0.634524	+	0.100499i	0.465406	−	0.885097i	$-0.345908\pi$
$457$	6199.01	+	981.827i	0.634524	+	0.100499i	0.169118	+	0.985596i	$0.445908\pi$
$458$	1327.19	+	676.235i	0.135405	+	0.0689921i
$459$	2042.21	−	6285.28i	0.207674	−	0.639154i
$460$	−102.495	+	241.067i	−0.0103888	+	0.0244344i
$461$			11510.8i			1.16293i	0.813570	+	0.581467i	$0.197521\pi$
$461$			11510.8i			1.16293i	−0.813570	+	0.581467i	$0.802479\pi$
$462$	449.107	−	3666.14i	0.0452259	−	0.369186i
$463$	−8635.81	−	8635.81i	−0.866825	−	0.866825i	0.125295	−	0.992120i	$-0.460012\pi$
$463$	−8635.81	−	8635.81i	−0.866825	−	0.866825i	−0.992120	+	0.125295i	$0.960012\pi$
$464$	3535.08	+	2568.39i	0.353690	+	0.256971i
$465$	348.332	−	3954.57i	0.0347387	−	0.394385i
$466$	−1017.78	−	3132.40i	−0.101175	−	0.311386i
$467$	−1133.07	+	7153.93i	−0.112275	+	0.708875i	0.865764	+	0.500452i	$0.166833\pi$
$467$	−1133.07	+	7153.93i	−0.112275	+	0.708875i	−0.978039	+	0.208422i	$0.933167\pi$
$468$	−974.974	+	6155.74i	−0.0962995	+	0.608011i
$469$	1510.10	+	4647.61i	0.148678	+	0.457583i
$470$	−8246.17	−	9839.19i	−0.809292	−	0.965634i
$471$	5821.05	+	4229.24i	0.569469	+	0.413743i
$472$	−87.5964	−	87.5964i	−0.00854227	−	0.00854227i
$473$	351.591	+	633.870i	0.0341779	+	0.0616181i
$474$			6795.09i			0.658457i
$475$	1265.65	−	7128.66i	0.122257	−	0.688601i
$476$	1059.17	−	3259.79i	0.101989	−	0.313891i
$477$	−490.719	−	250.034i	−0.0471037	−	0.0240005i
$478$	−54.5555	−	8.64075i	−0.00522032	−	0.000826817i
$479$	10929.3	−	7940.61i	1.04253	−	0.757444i	0.0717545	−	0.997422i	$-0.477140\pi$
$479$	10929.3	−	7940.61i	1.04253	−	0.757444i	0.970778	+	0.239978i	$0.0771402\pi$
$480$	584.573	−	2338.71i	0.0555875	−	0.222390i
$481$	−21080.1	−	6849.35i	−1.99828	−	0.649280i
$482$	3122.25	−	494.516i	0.295051	−	0.0467315i
$483$	209.660	−	209.660i	0.0197512	−	0.0197512i
$484$	5166.57	+	1285.11i	0.485215	+	0.120690i
$485$	−867.357	−	3767.08i	−0.0812054	−	0.352689i
$486$	−5188.70	+	7141.63i	−0.484288	+	0.666565i
$487$	−4130.82	−	8107.19i	−0.384364	−	0.754357i	0.615053	−	0.788485i	$-0.289134\pi$
$487$	−4130.82	−	8107.19i	−0.384364	−	0.754357i	−0.999417	+	0.0341286i	$0.989134\pi$
$488$	1483.03	−	2910.61i	0.137569	−	0.269994i
$489$	12777.4	+	17586.6i	1.18162	+	1.62636i
$490$	−4833.46	−	4206.67i	−0.445619	−	0.387833i
$491$	−10202.8	+	3315.08i	−0.937768	+	0.304699i	−0.737735	−	0.675090i	$-0.764105\pi$
$491$	−10202.8	+	3315.08i	−0.937768	+	0.304699i	−0.200032	+	0.979789i	$0.564105\pi$
$492$	2481.54	−	1264.41i	0.227391	−	0.115861i
$493$	4872.87	+	30766.1i	0.445158	+	2.81062i
$494$	9809.12			0.893387
$495$	5579.27	−	5020.45i	0.506605	−	0.455864i
$496$	−843.161			−0.0763287
$497$	84.3704	+	532.694i	0.00761475	+	0.0480776i
$498$	−10114.0	+	5153.32i	−0.910075	+	0.463706i
$499$	5114.63	−	1661.84i	0.458842	−	0.149087i	−0.0704702	−	0.997514i	$-0.522450\pi$
$499$	5114.63	−	1661.84i	0.458842	−	0.149087i	0.529312	+	0.848427i	$0.322450\pi$
$500$	−2786.51	−	4846.17i	−0.249233	−	0.433455i
$501$	−4877.14	−	6712.81i	−0.434919	−	0.598615i
$502$	766.784	−	1504.90i	0.0681738	−	0.133799i
$503$	−5883.66	−	11547.3i	−0.521550	−	1.02360i	−0.990127	−	0.140176i	$-0.955233\pi$
$503$	−5883.66	−	11547.3i	−0.521550	−	1.02360i	0.468577	−	0.883423i	$-0.344767\pi$
$504$	−650.038	+	894.700i	−0.0574504	+	0.0790737i
$505$	16290.5	+	10192.8i	1.43548	+	0.898165i
$506$	263.222	+	336.715i	0.0231258	+	0.0295826i
$507$	−23694.3	+	23694.3i	−2.07555	+	2.07555i
$508$	−4483.77	+	710.159i	−0.391604	+	0.0620240i
$509$	−17582.5	−	5712.90i	−1.53110	−	0.497485i	−0.582197	−	0.813048i	$-0.697807\pi$
$509$	−17582.5	−	5712.90i	−1.53110	−	0.497485i	−0.948905	+	0.315563i	$0.897807\pi$
$510$	14735.6	−	8842.20i	1.27942	−	0.767724i
$511$	−2146.78	+	1559.73i	−0.185847	+	0.135026i
$512$	−505.696	−	80.0944i	−0.0436501	−	0.00691349i
$513$	2990.24	+	1523.60i	0.257353	+	0.131128i
$514$	−3797.37	+	11687.1i	−0.325865	+	1.00291i
$515$	11772.6	+	5005.39i	1.00731	+	0.428279i
$516$		−	535.489i		−	0.0456853i
$517$	−20559.7	+	4002.36i	−1.74897	+	0.340471i
$518$	−2781.07	−	2781.07i	−0.235894	−	0.235894i
$519$	10270.3	+	7461.84i	0.868628	+	0.631095i
$520$	5804.66	−	4864.85i	0.489521	−	0.410265i
$521$	478.973	+	1474.13i	0.0402768	+	0.123959i	0.969173	−	0.246381i	$-0.0792413\pi$
$521$	478.973	+	1474.13i	0.0402768	+	0.123959i	−0.928896	+	0.370340i	$0.879241\pi$
$522$	1572.25	−	9926.80i	0.131831	−	0.832346i
$523$	−2400.08	+	15153.5i	−0.200665	+	1.26695i	0.657451	+	0.753497i	$0.271635\pi$
$523$	−2400.08	+	15153.5i	−0.200665	+	1.26695i	−0.858117	+	0.513455i	$0.828365\pi$
$524$	1791.16	+	5512.63i	0.149327	+	0.459581i
$525$	873.225	+	6266.98i	0.0725918	+	0.520978i
$526$	5761.07	+	4185.67i	0.477557	+	0.346965i
$527$	−4250.17	−	4250.17i	−0.351310	−	0.351310i
$528$	−2877.28	−	2681.60i	−0.237154	−	0.221026i
$529$		−	12132.7i		−	0.997180i
$530$	250.345	+	620.680i	0.0205175	+	0.0508691i
$531$	−88.0504	+	270.991i	−0.00719597	+	0.0221469i
$532$	1550.85	+	790.199i	0.126387	+	0.0643975i
$533$	8642.32	+	1368.81i	0.702327	+	0.111238i
$534$	7004.73	−	5089.24i	0.567649	−	0.412421i
$535$	−9180.87	−	15300.0i	−0.741914	−	1.23640i
$536$	4949.11	+	1608.06i	0.398823	+	0.129585i
$537$	3304.52	−	523.384i	0.265550	−	0.0420590i
$538$	6243.08	−	6243.08i	0.500295	−	0.500295i
$539$	−9823.06	+	3578.41i	−0.784989	+	0.285961i
$540$	2525.14	−	581.405i	0.201231	−	0.0463328i
$541$	−6750.13	+	9290.76i	−0.536434	+	0.738338i	−0.988094	−	0.153852i	$-0.950832\pi$
$541$	−6750.13	+	9290.76i	−0.536434	+	0.738338i	0.451660	+	0.892190i	$0.350832\pi$
$542$	−5535.79	−	10864.6i	−0.438713	−	0.861023i
$543$	4642.46	−	9111.33i	0.366900	−	0.720082i
$544$	−2145.36	−	2952.83i	−0.169083	−	0.232723i
$545$	−802.709	−	11577.5i	−0.0630904	−	0.909952i
$546$	−8153.11	+	2649.10i	−0.639049	+	0.207640i
$547$	−20114.8	+	10249.0i	−1.57230	+	0.801126i	−0.999823	−	0.0187970i	$-0.994016\pi$
$547$	−20114.8	+	10249.0i	−1.57230	+	0.801126i	−0.572474	+	0.819923i	$0.694016\pi$
$548$	−1298.50	−	8198.44i	−0.101221	−	0.639087i
$549$	−7513.65			−0.584107
$550$	−9119.47	+	150.959i	−0.707010	+	0.0117034i
$551$	−15818.3			−1.22301
$552$	−49.3924	−	311.851i	−0.00380848	−	0.0240458i
$553$	−3375.25	+	1719.78i	−0.259549	+	0.132247i
$554$	−16494.2	+	5359.28i	−1.26493	+	0.411000i
$555$	−1363.94	−	19672.1i	−0.104317	−	1.50456i
$556$	4492.65	+	6183.61i	0.342681	+	0.471661i
$557$	8894.79	−	17457.0i	0.676632	−	1.32797i	−0.255838	−	0.966720i	$-0.582351\pi$
$557$	8894.79	−	17457.0i	0.676632	−	1.32797i	0.932471	−	0.361246i	$-0.117649\pi$
$558$	880.451	+	1727.98i	0.0667965	+	0.131096i
$559$	988.872	−	1361.07i	0.0748208	−	0.102982i
$560$	1309.63	−	301.539i	0.0988253	−	0.0227542i
$561$	−986.339	−	28020.9i	−0.0742304	−	2.10882i
$562$	−4652.31	+	4652.31i	−0.349192	+	0.349192i
$563$	12825.1	−	2031.29i	0.960056	−	0.152058i	0.343312	−	0.939221i	$-0.388451\pi$
$563$	12825.1	−	2031.29i	0.960056	−	0.152058i	0.616744	+	0.787163i	$0.288451\pi$
$564$	14716.5	+	4781.67i	1.09872	+	0.356994i
$565$	1279.00	+	2131.47i	0.0952356	+	0.158711i
$566$	−4335.39	+	3149.85i	−0.321961	+	0.233919i
$567$	−6583.38	−	1042.71i	−0.487612	−	0.0772302i
$568$	511.725	+	260.737i	0.0378019	+	0.0192611i
$569$	−4429.91	+	13633.8i	−0.326382	+	1.00450i	0.644431	+	0.764662i	$0.277094\pi$
$569$	−4429.91	+	13633.8i	−0.326382	+	1.00450i	−0.970813	+	0.239838i	$0.922906\pi$
$570$	3264.34	+	8093.26i	0.239874	+	0.594718i
$571$			1875.04i			0.137422i	0.997637	+	0.0687110i	$0.0218886\pi$
$571$			1875.04i			0.137422i	−0.997637	+	0.0687110i	$0.978111\pi$
$572$	−2361.20	−	12129.3i	−0.172599	−	0.886626i
$573$	−3015.71	−	3015.71i	−0.219866	−	0.219866i
$574$	1256.11	+	912.617i	0.0913397	+	0.0663622i
$575$	−584.222	−	441.325i	−0.0423717	−	0.0320078i
$576$	363.915	+	1120.02i	0.0263249	+	0.0810197i
$577$	3089.58	−	19506.8i	0.222913	−	1.40742i	−0.581596	−	0.813478i	$-0.697571\pi$
$577$	3089.58	−	19506.8i	0.222913	−	1.40742i	0.804509	−	0.593941i	$-0.202429\pi$
$578$	2533.15	−	15993.7i	0.182293	−	1.15095i
$579$	−1115.67	−	3433.69i	−0.0800792	−	0.246458i
$580$	−9360.64	+	7845.10i	−0.670137	+	0.561638i
$581$	−5119.51	−	3719.54i	−0.365564	−	0.265598i
$582$	3294.68	+	3294.68i	0.234655	+	0.234655i
$583$	1083.85	+	132.773i	0.0769955	+	0.00943206i
$584$			2825.71i			0.200221i
$585$	−16031.4	−	6816.11i	−1.13302	−	0.481729i
$586$	−467.453	+	1438.67i	−0.0329527	+	0.101418i
$587$	−603.795	−	307.649i	−0.0424554	−	0.0216321i	0.432634	−	0.901570i	$-0.357584\pi$
$587$	−603.795	−	307.649i	−0.0424554	−	0.0216321i	−0.475089	+	0.879938i	$0.657584\pi$
$588$	7628.30	+	1208.20i	0.535010	+	0.0847373i
$589$	2469.37	−	1794.10i	0.172748	−	0.125509i
$590$	296.904	−	178.159i	0.0207175	−	0.0124317i
$591$	10431.2	+	3389.29i	0.726025	+	0.235900i
$592$	−4136.61	+	655.174i	−0.287185	+	0.0454856i
$593$	4583.31	−	4583.31i	0.317393	−	0.317393i	−0.530372	−	0.847765i	$-0.677948\pi$
$593$	4583.31	−	4583.31i	0.317393	−	0.317393i	0.847765	+	0.530372i	$0.177948\pi$
$594$	1164.18	−	4064.27i	0.0804160	−	0.280739i
$595$	8121.53	+	5081.56i	0.559581	+	0.350124i
$596$	3099.29	−	4265.81i	0.213007	−	0.293179i
$597$	−5569.22	−	10930.2i	−0.381797	−	0.749319i
$598$	450.345	−	883.851i	0.0307959	−	0.0604404i
$599$	6705.15	+	9228.84i	0.457370	+	0.629516i	0.973961	−	0.226716i	$-0.0727990\pi$
$599$	6705.15	+	9228.84i	0.457370	+	0.629516i	−0.516590	+	0.856233i	$0.672799\pi$
$600$	5945.58	+	3170.33i	0.404545	+	0.215713i
$601$	6261.06	−	2034.34i	0.424949	−	0.138074i	−0.0887322	−	0.996056i	$-0.528282\pi$
$601$	6261.06	−	2034.34i	0.424949	−	0.138074i	0.513681	+	0.857981i	$0.328282\pi$
$602$	265.988	−	135.528i	0.0180081	−	0.00917557i
$603$	−1872.41	−	11821.9i	−0.126452	−	0.798386i
$604$	6639.11			0.447254
$605$	−6986.65	+	13138.9i	−0.469500	+	0.882932i
$606$	−23162.2			−1.55264
$607$	3682.32	+	23249.3i	0.246229	+	1.55463i	0.732468	+	0.680802i	$0.238368\pi$
$607$	3682.32	+	23249.3i	0.246229	+	1.55463i	−0.486239	+	0.873826i	$0.661632\pi$
$608$	1651.46	−	841.461i	0.110157	−	0.0561279i
$609$	13147.8	−	4271.97i	0.874835	−	0.284251i
$610$	6887.40	+	5994.27i	0.457152	+	0.397870i
$611$	28575.0	+	39330.2i	1.89202	+	2.60414i
$612$	−3811.32	+	7480.14i	−0.251738	+	0.494063i
$613$	−10044.7	−	19713.8i	−0.661828	−	1.29891i	−0.940914	−	0.338644i	$-0.890032\pi$
$613$	−10044.7	−	19713.8i	−0.661828	−	1.29891i	0.279087	−	0.960266i	$-0.409968\pi$
$614$	−9345.30	+	12862.7i	−0.614244	+	0.845434i
$615$	1746.67	+	7586.08i	0.114524	+	0.497399i
$616$	603.791	−	2107.89i	0.0394926	−	0.137872i
$617$	3218.68	−	3218.68i	0.210015	−	0.210015i	−0.594259	−	0.804274i	$-0.702555\pi$
$617$	3218.68	−	3218.68i	0.210015	−	0.210015i	0.804274	+	0.594259i	$0.202555\pi$
$618$	−15229.4	+	2412.10i	−0.991289	+	0.157005i
$619$	−4244.92	−	1379.26i	−0.275635	−	0.0895592i	0.167938	−	0.985798i	$-0.446289\pi$
$619$	−4244.92	−	1379.26i	−0.275635	−	0.0895592i	−0.443573	+	0.896238i	$0.646289\pi$
$620$	571.488	−	2286.37i	0.0370186	−	0.148101i
$621$	274.569	−	199.486i	0.0177424	−	0.0128906i
$622$	−17283.1	−	2737.37i	−1.11413	−	0.176461i
$623$	4300.76	+	2191.35i	0.276575	+	0.140922i
$624$	−2820.96	+	8682.02i	−0.180976	+	0.556986i
$625$	15029.8	−	4271.37i	0.961910	−	0.273367i
$626$		−	3081.87i		−	0.196767i
$627$	14132.7	+	1731.27i	0.900166	+	0.110272i
$628$	3020.34	+	3020.34i	0.191919	+	0.191919i
$629$	−24154.2	−	17549.1i	−1.53115	−	1.11244i
$630$	−1985.53	−	2369.10i	−0.125564	−	0.149821i
$631$	−1817.41	−	5593.40i	−0.114659	−	0.352884i	0.877217	−	0.480094i	$-0.159398\pi$
$631$	−1817.41	−	5593.40i	−0.114659	−	0.352884i	−0.991876	+	0.127211i	$0.959398\pi$
$632$	−631.038	+	3984.22i	−0.0397173	+	0.250765i
$633$	307.559	−	1941.85i	0.0193118	−	0.121930i
$634$	−6636.24	−	20424.3i	−0.415708	−	1.27942i
$635$	1113.36	−	12639.8i	0.0695782	−	0.789913i
$636$	−652.624	−	474.159i	−0.0406891	−	0.0295623i
$637$	17157.9	+	17157.9i	1.06722	+	1.06722i
$638$	3807.70	+	19559.8i	0.236282	+	1.21376i
$639$		−	1321.00i		−	0.0817810i
$640$	559.946	−	1316.99i	0.0345841	−	0.0813415i
$641$	8626.00	−	26548.1i	0.531524	−	1.63586i	−0.219519	−	0.975608i	$-0.570449\pi$
$641$	8626.00	−	26548.1i	0.531524	−	1.63586i	0.751043	−	0.660254i	$-0.229551\pi$
$642$	19162.8	+	9763.94i	1.17803	+	0.600237i
$643$	21843.8	+	3459.71i	1.33971	+	0.212189i	0.784815	−	0.619730i	$-0.212758\pi$
$643$	21843.8	+	3459.71i	1.33971	+	0.212189i	0.554896	+	0.831920i	$0.312758\pi$
$644$	142.402	−	103.461i	0.00871338	−	0.00633064i
$645$	1452.06	+	362.951i	0.0886434	+	0.0221569i
$646$	12566.2	+	4083.01i	0.765342	+	0.248675i
$647$	17494.2	−	2770.80i	1.06301	−	0.168364i	0.399652	−	0.916667i	$-0.369131\pi$
$647$	17494.2	−	2770.80i	1.06301	−	0.168364i	0.663357	+	0.748303i	$0.269131\pi$
$648$	−5018.94	+	5018.94i	−0.304263	+	0.304263i
$649$	−19.8735	−	564.587i	−0.00120201	−	0.0341479i
$650$	9257.46	+	19037.6i	0.558627	+	1.14879i
$651$	−1567.95	+	2158.10i	−0.0943978	+	0.129927i
$652$	5858.66	+	11498.3i	0.351906	+	0.690655i
$653$	−2230.18	+	4376.97i	−0.133650	+	0.262304i	−0.948126	−	0.317894i	$-0.897025\pi$
$653$	−2230.18	+	4376.97i	−0.133650	+	0.262304i	0.814476	+	0.580197i	$0.197025\pi$
$654$	8222.05	+	11316.7i	0.491602	+	0.676632i
$655$	−16162.4	+	1120.60i	−0.964149	+	0.0668481i
$656$	1572.44	−	510.917i	0.0935876	−	0.0304084i
$657$	5791.04	−	2950.68i	0.343881	−	0.175216i
$658$	1349.46	+	8520.15i	0.0799505	+	0.504788i
$659$	4997.03			0.295382			0.147691	−	0.989034i	$-0.452816\pi$
$659$	4997.03			0.295382			0.147691	+	0.989034i	$0.452816\pi$
$660$	9221.79	−	5984.62i	0.543875	−	0.352956i
$661$	29077.8			1.71104			0.855520	−	0.517770i	$-0.173238\pi$
$661$	29077.8			1.71104			0.855520	+	0.517770i	$0.173238\pi$
$662$	606.054	+	3826.47i	0.0355815	+	0.224653i
$663$	−57983.7	+	29544.2i	−3.39653	+	1.73062i
$664$	−6408.77	+	2082.34i	−0.374561	+	0.121702i
$665$	−3193.91	+	3669.79i	−0.186247	+	0.213998i
$666$	5662.28	+	7793.45i	0.329443	+	0.453439i
$667$	−726.230	+	1425.31i	−0.0421585	+	0.0827407i
$668$	−2236.26	−	4388.90i	−0.129526	−	0.254209i
$669$	14973.6	−	20609.3i	0.865338	−	1.19104i
$670$	−7715.00	+	12330.4i	−0.444860	+	0.710991i
$671$	13997.3	−	5099.02i	0.805305	−	0.293361i
$672$	−1145.41	+	1145.41i	−0.0657514	+	0.0657514i
$673$	30198.9	−	4783.03i	1.72969	−	0.273956i	0.789288	−	0.614023i	$-0.210450\pi$
$673$	30198.9	−	4783.03i	1.72969	−	0.273956i	0.940401	+	0.340067i	$0.110450\pi$
$674$	2199.75	+	714.742i	0.125714	+	0.0408469i
$675$	−134.949	+	7241.39i	−0.00769508	+	0.412921i
$676$	−16093.3	+	11692.5i	−0.915640	+	0.665252i
$677$	2990.70	+	473.680i	0.169781	+	0.0268907i	0.240746	−	0.970588i	$-0.422608\pi$
$677$	2990.70	+	473.680i	0.169781	+	0.0268907i	−0.0709650	+	0.997479i	$0.522608\pi$
$678$	−2669.61	−	1360.23i	−0.151218	−	0.0770493i
$679$	−802.677	+	2470.39i	−0.0453666	+	0.139624i
$680$	9461.17	−	3816.07i	0.533558	−	0.215205i
$681$			30241.7i			1.70171i
$682$	−2812.87	−	2621.58i	−0.157933	−	0.147193i
$683$	−15516.2	−	15516.2i	−0.869270	−	0.869270i	0.123122	−	0.992392i	$-0.460709\pi$
$683$	−15516.2	−	15516.2i	−0.869270	−	0.869270i	−0.992392	+	0.123122i	$0.960709\pi$
$684$	−3449.00	−	2505.84i	−0.192801	−	0.140078i
$685$	23111.5	+	2035.74i	1.28912	+	0.113550i
$686$	2923.09	+	8996.34i	0.162688	+	0.500702i
$687$	785.028	−	4956.47i	0.0435964	−	0.275257i
$688$	49.7292	−	313.978i	0.00275568	−	0.0173987i
$689$	−783.175	−	2410.36i	−0.0433042	−	0.133277i
$690$	879.112	+	77.4352i	0.0485032	+	0.00427233i
$691$	−8128.46	−	5905.67i	−0.447498	−	0.325126i	0.341109	−	0.940024i	$-0.389197\pi$
$691$	−8128.46	−	5905.67i	−0.447498	−	0.325126i	−0.788607	+	0.614897i	$0.789197\pi$
$692$	5328.93	+	5328.93i	0.292739	+	0.292739i
$693$	−4950.42	+	963.697i	−0.271358	+	0.0528252i
$694$		−	11601.9i		−	0.634584i
$695$	−19812.9	+	7991.34i	−1.08136	+	0.436157i
$696$	4549.10	−	14000.7i	0.247749	−	0.762493i
$697$	10501.7	+	5350.88i	0.570703	+	0.290788i
$698$	3568.31	+	565.165i	0.193500	+	0.0306473i
$699$	−8977.00	+	6522.17i	−0.485753	+	0.352920i
$700$	−69.9896	+	3755.66i	−0.00377908	+	0.202787i
$701$	−15863.8	−	5154.48i	−0.854735	−	0.277720i	−0.151307	−	0.988487i	$-0.548348\pi$
$701$	−15863.8	−	5154.48i	−0.854735	−	0.277720i	−0.703428	+	0.710767i	$0.748348\pi$
$702$	−9691.70	+	1535.01i	−0.521068	+	0.0825291i
$703$	10720.8	−	10720.8i	0.575167	−	0.575167i
$704$	−1438.02	−	1839.53i	−0.0769852	−	0.0984799i
$705$	−22941.0	+	36665.1i	−1.22554	+	1.95870i
$706$	13767.2	−	18948.9i	0.733904	−	1.01013i
$707$	−5862.16	−	11505.1i	−0.311838	−	0.612016i
$708$	−189.474	+	371.864i	−0.0100577	+	0.0197394i
$709$	−11429.6	−	15731.6i	−0.605429	−	0.833302i	0.390763	−	0.920491i	$-0.372211\pi$
$709$	−11429.6	−	15731.6i	−0.605429	−	0.833302i	−0.996192	+	0.0871899i	$0.972211\pi$
$710$	−1053.87	+	1210.90i	−0.0557059	+	0.0640059i
$711$	8824.24	−	2867.17i	0.465450	−	0.151234i
$712$	4579.76	−	2333.50i	0.241059	−	0.122826i
$713$	−48.2868	−	304.871i	−0.00253626	−	0.0160133i
$714$	−11547.4			−0.605254
$715$	34490.9	+	1818.35i	1.80403	+	0.0951085i
$716$	1986.17			0.103668
$717$	29.1107	+	183.798i	0.00151626	+	0.00957331i
$718$	16875.4	−	8598.44i	0.877137	−	0.446923i
$719$	−25487.3	+	8281.32i	−1.32200	+	0.429543i	−0.883180	−	0.469034i	$-0.844602\pi$
$719$	−25487.3	+	8281.32i	−1.32200	+	0.429543i	−0.438817	+	0.898577i	$0.644602\pi$
$720$	−3283.76	+	227.676i	−0.169970	+	0.0117847i
$721$	−5052.57	−	6954.26i	−0.260981	−	0.359210i
$722$	3181.69	−	6244.42i	0.164003	−	0.321874i
$723$	−4835.00	−	9489.23i	−0.248708	−	0.488117i
$724$	3568.19	−	4911.19i	0.183164	−	0.252103i
$725$	−14928.7	−	30700.2i	−0.764740	−	1.57266i
$726$	−1261.18	−	17892.2i	−0.0644719	−	0.914658i
$727$	9901.76	−	9901.76i	0.505139	−	0.505139i	−0.407892	−	0.913030i	$-0.633736\pi$
$727$	9901.76	−	9901.76i	0.505139	−	0.505139i	0.913030	+	0.407892i	$0.133736\pi$
$728$	−5026.49	+	796.118i	−0.255898	+	0.0405303i
$729$	5501.65	+	1787.60i	0.279513	+	0.0908193i
$730$	−7662.37	−	1915.25i	−0.388489	−	0.0971047i
$731$	1833.36	−	1332.01i	0.0927622	−	0.0673957i
$732$	−10869.9	−	1721.62i	−0.548856	−	0.0869303i
$733$	3463.45	+	1764.72i	0.174523	+	0.0889239i	0.539070	−	0.842261i	$-0.318776\pi$
$733$	3463.45	+	1764.72i	0.174523	+	0.0889239i	−0.364547	+	0.931185i	$0.618776\pi$
$734$	−6.61641	+	20.3632i	−0.000332719	+	0.00102400i
$735$	−8446.65	+	19866.5i	−0.423890	+	0.996987i
$736$		−	187.437i		−	0.00938726i
$737$	11510.9	+	20752.6i	0.575319	+	1.03722i
$738$	−2689.06	−	2689.06i	−0.134127	−	0.134127i
$739$	−16569.2	−	12038.2i	−0.824775	−	0.599234i	0.0933012	−	0.995638i	$-0.470258\pi$
$739$	−16569.2	−	12038.2i	−0.824775	−	0.599234i	−0.918076	+	0.396404i	$0.870258\pi$
$740$	1027.15	−	11661.1i	0.0510255	−	0.579287i
$741$	−10212.1	−	31429.6i	−0.506276	−	1.55816i
$742$	70.3507	−	444.177i	0.00348067	−	0.0219761i
$743$	3818.84	−	24111.2i	0.188559	−	1.19052i	−0.693880	−	0.720090i	$-0.744100\pi$
$743$	3818.84	−	24111.2i	0.188559	−	1.19052i	0.882440	−	0.470426i	$-0.155900\pi$
$744$	877.799	+	2701.59i	0.0432549	+	0.133125i
$745$	9466.75	+	11295.6i	0.465550	+	0.555487i
$746$	809.989	+	588.492i	0.0397531	+	0.0288823i
$747$	10959.8	+	10959.8i	0.536810	+	0.536810i
$748$	2023.89	−	16521.3i	0.0989314	−	0.807594i
$749$			11989.7i			0.584906i
$750$	−12626.7	+	13973.6i	−0.614750	+	0.680323i
$751$	−2131.84	+	6561.12i	−0.103584	+	0.318800i	−0.989396	−	0.145246i	$-0.953603\pi$
$751$	−2131.84	+	6561.12i	−0.103584	+	0.318800i	0.885811	+	0.464046i	$0.153603\pi$
$752$	8184.77	+	4170.35i	0.396899	+	0.202230i
$753$	−5620.15	−	890.145i	−0.271992	−	0.0430793i
$754$	37417.3	−	27185.2i	1.80724	−	1.31303i
$755$	−4499.94	+	18003.0i	−0.216913	+	0.867810i
$756$	−1655.95	−	538.049i	−0.0796642	−	0.0258845i
$757$	−11287.9	+	1787.83i	−0.541964	+	0.0858386i	−0.421413	−	0.906869i	$-0.638466\pi$
$757$	−11287.9	+	1787.83i	−0.541964	+	0.0858386i	−0.120550	+	0.992707i	$0.538466\pi$
$758$	−6146.84	+	6146.84i	−0.294542	+	0.294542i
$759$	804.838	−	1193.94i	0.0384898	−	0.0570979i
$760$	1162.41	+	5048.53i	0.0554802	+	0.240960i
$761$	4054.89	−	5581.08i	0.193153	−	0.265853i	−0.701445	−	0.712723i	$-0.747462\pi$
$761$	4054.89	−	5581.08i	0.193153	−	0.265853i	0.894599	+	0.446871i	$0.147462\pi$
$762$	6943.40	+	13627.2i	0.330095	+	0.647849i
$763$	−3540.29	+	6948.21i	−0.167978	+	0.329675i
$764$	−1488.16	−	2048.28i	−0.0704711	−	0.0969951i
$765$	−17700.3	−	15405.0i	−0.836543	−	0.728063i
$766$	−22253.5	+	7230.61i	−1.04968	+	0.341061i
$767$	−1168.30	+	595.279i	−0.0549999	+	0.0280238i
$768$	269.839	+	1703.70i	0.0126783	+	0.0800479i
$769$	−716.792			−0.0336127			−0.0168063	−	0.999859i	$-0.505350\pi$
$769$	−716.792			−0.0336127			−0.0168063	+	0.999859i	$0.505350\pi$
$770$	5306.63	+	3065.99i	0.248361	+	0.143494i
$771$	41400.2			1.93384
$772$	−335.286	−	2116.91i	−0.0156311	−	0.0986909i
$773$	290.752	−	148.145i	0.0135286	−	0.00689317i	−0.447213	−	0.894427i	$-0.647583\pi$
$773$	290.752	−	148.145i	0.0135286	−	0.00689317i	0.460742	+	0.887534i	$0.347583\pi$
$774$	−695.397	+	225.948i	−0.0322940	+	0.0104929i
$775$	5812.50	+	3099.36i	0.269408	+	0.143655i
$776$	1625.83	+	2237.76i	0.0752112	+	0.103519i
$777$	−6015.55	+	11806.2i	−0.277743	+	0.545102i
$778$	1407.66	+	2762.69i	0.0648677	+	0.127310i
$779$	−3518.06	+	4842.20i	−0.161807	+	0.222708i
$780$	−21630.7	−	13534.1i	−0.992951	−	0.621280i
$781$	896.477	+	2460.91i	0.0410736	+	0.112751i
$782$	944.825	−	944.825i	0.0432057	−	0.0432057i
$783$	15628.9	−	2475.38i	0.713323	−	0.112979i
$784$	4360.56	+	1416.83i	0.198641	+	0.0645423i
$785$	−10237.3	+	6142.98i	−0.465459	+	0.279302i
$786$	15798.4	−	11478.2i	0.716933	−	0.520882i
$787$	−22538.4	−	3569.73i	−1.02085	−	0.161686i	−0.376497	−	0.926418i	$-0.622872\pi$
$787$	−22538.4	−	3569.73i	−1.02085	−	0.161686i	−0.644349	+	0.764731i	$0.722872\pi$
$788$	5801.44	+	2955.98i	0.262268	+	0.133632i
$789$	7413.62	−	22816.8i	0.334514	−	1.02953i
$790$	−10376.1	−	4411.63i	−0.467299	−	0.198682i
$791$		−	1670.31i		−	0.0750813i
$792$	−2268.32	+	4867.98i	−0.101769	+	0.218404i
$793$	−24449.0	−	24449.0i	−1.09484	−	1.09484i
$794$	6230.62	+	4526.81i	0.278484	+	0.202330i
$795$	1728.10	−	1448.31i	0.0770937	−	0.0646118i
$796$	−2250.39	−	6925.99i	−0.100205	−	0.308398i
$797$	3042.82	−	19211.6i	0.135235	−	0.853840i	−0.823038	−	0.567986i	$-0.807723\pi$
$797$	3042.82	−	19211.6i	0.135235	−	0.853840i	0.958273	−	0.285854i	$-0.0922773\pi$
$798$	917.326	−	5791.77i	0.0406930	−	0.256925i
$799$	20235.7	+	62279.1i	0.895980	+	2.75754i
$800$	3191.70	+	2411.03i	0.141054	+	0.106553i
$801$	−9564.61	−	6949.10i	−0.421909	−	0.306535i
$802$	−6305.26	−	6305.26i	−0.277614	−	0.277614i
$803$	−8785.78	+	9426.86i	−0.386106	+	0.414280i
$804$		−	17531.7i		−	0.769022i
$805$	184.032	+	456.270i	0.00805748	+	0.0199769i
$806$	−2757.82	+	8487.69i	−0.120521	+	0.370926i
$807$	−26503.1	−	13504.0i	−1.15608	−	0.589051i
$808$	−13580.9	−	2151.00i	−0.591305	−	0.0936535i
$809$	12423.6	−	9026.26i	0.539914	−	0.392270i	−0.284139	−	0.958783i	$-0.591708\pi$
$809$	12423.6	−	9026.26i	0.539914	−	0.392270i	0.824053	+	0.566513i	$0.191708\pi$
$810$	−10207.9	−	17011.5i	−0.442799	−	0.737928i
$811$	−2469.28	−	802.318i	−0.106915	−	0.0347388i	0.255071	−	0.966922i	$-0.417901\pi$
$811$	−2469.28	−	802.318i	−0.106915	−	0.0347388i	−0.361986	+	0.932184i	$0.617901\pi$
$812$	8105.76	−	1283.83i	0.350316	−	0.0554846i
$813$	−29048.2	+	29048.2i	−1.25309	+	1.25309i
$814$	−15837.2	−	10675.9i	−0.681935	−	0.459694i
$815$	−35150.3	+	8093.25i	−1.51075	+	0.347846i
$816$	−7227.72	+	9948.10i	−0.310075	+	0.426781i
$817$	522.448	+	1025.36i	0.0223723	+	0.0439080i
$818$	4787.01	−	9395.04i	0.204614	−	0.401577i
$819$	6880.36	+	9470.01i	0.293552	+	0.404040i
$820$	319.644	+	4610.22i	0.0136127	+	0.196336i
$821$	−24082.1	+	7824.76i	−1.02372	+	0.332626i	−0.772304	−	0.635253i	$-0.780896\pi$
$821$	−24082.1	+	7824.76i	−1.02372	+	0.332626i	−0.251414	+	0.967880i	$0.580896\pi$
$822$	−24916.9	+	12695.8i	−1.05727	+	0.538706i
$823$	−2450.33	−	15470.8i	−0.103783	−	0.655258i	−0.983657	−	0.180052i	$-0.942373\pi$
$823$	−2450.33	−	15470.8i	−0.103783	−	0.655258i	0.879874	−	0.475206i	$-0.157627\pi$
$824$	−9153.58			−0.386991
$825$	9977.79	+	29062.7i	0.421069	+	1.22646i
$826$	−232.666			−0.00980084
$827$	4331.73	+	27349.5i	0.182139	+	1.14998i	0.894135	+	0.447798i	$0.147792\pi$
$827$	4331.73	+	27349.5i	0.182139	+	1.14998i	−0.711996	+	0.702184i	$0.752208\pi$
$828$	−384.135	+	195.727i	−0.0161227	+	0.00821495i
$829$	23902.8	−	7766.50i	1.00142	−	0.325382i	0.237989	−	0.971268i	$-0.423512\pi$
$829$	23902.8	−	7766.50i	1.00142	−	0.325382i	0.763434	+	0.645886i	$0.223512\pi$
$830$	−1302.77	−	18789.8i	−0.0544816	−	0.785787i
$831$	34343.5	+	47269.8i	1.43365	+	1.97325i
$832$	−2460.31	+	4828.63i	−0.102519	+	0.201205i
$833$	14838.6	+	29122.4i	0.617200	+	1.21132i
$834$	15135.8	−	20832.6i	0.628428	−	0.864957i
$835$	13416.9	−	3089.20i	0.556062	−	0.128031i
$836$	8125.74	+	2327.56i	0.336166	+	0.0962925i
$837$	−2159.05	+	2159.05i	−0.0891610	+	0.0891610i
$838$	29177.7	−	4621.29i	1.20277	−	0.190501i
$839$	27152.4	+	8822.34i	1.11729	+	0.363029i	0.808732	−	0.588177i	$-0.200154\pi$
$839$	27152.4	+	8822.34i	1.11729	+	0.363029i	0.308556	+	0.951206i	$0.400154\pi$
$840$	−2329.60	−	3882.30i	−0.0956891	−	0.159467i
$841$	−40608.3	+	29503.6i	−1.66502	+	1.20971i
$842$	−21920.7	−	3471.90i	−0.897193	−	0.142101i
$843$	19750.0	+	10063.1i	0.806909	+	0.411141i
$844$	360.667	−	1110.02i	0.0147093	−	0.0452706i
$845$	−20798.1	−	51564.6i	−0.846716	−	2.09926i
$846$		−	21128.7i		−	0.858653i
$847$	8568.21	−	5154.81i	0.347588	−	0.209116i
$848$	−338.625	−	338.625i	−0.0137128	−	0.0137128i
$849$	14606.0	+	10611.9i	0.590431	+	0.428973i
$850$	3935.17	+	28242.0i	0.158794	+	1.13964i
$851$	−473.797	−	1458.20i	−0.0190853	−	0.0587384i
$852$	302.684	−	1911.07i	0.0121711	−	0.0768455i
$853$	1532.22	−	9674.05i	0.0615032	−	0.388316i	−0.937665	−	0.347540i	$-0.887017\pi$
$853$	1532.22	−	9674.05i	0.0615032	−	0.388316i	0.999168	−	0.0407757i	$-0.0129829\pi$
$854$	−1895.91	−	5835.01i	−0.0759681	−	0.233806i
$855$	9132.70	−	7654.06i	0.365300	−	0.306156i
$856$	10329.1	+	7504.56i	0.412433	+	0.299650i
$857$	−23049.9	−	23049.9i	−0.918750	−	0.918750i	0.0781883	−	0.996939i	$-0.475086\pi$
$857$	−23049.9	−	23049.9i	−0.918750	−	0.918750i	−0.996939	+	0.0781883i	$0.975086\pi$
$858$	−36405.4	+	20193.1i	−1.44855	+	0.803475i
$859$		−	48969.2i		−	1.94506i	−0.232775	−	0.972531i	$-0.574781\pi$
$859$		−	48969.2i		−	1.94506i	0.232775	−	0.972531i	$-0.425219\pi$
$860$	817.694	+	347.660i	0.0324223	+	0.0137850i
$861$	1616.42	−	4974.83i	0.0639808	−	0.196913i
$862$	8830.77	+	4499.50i	0.348930	+	0.177789i
$863$	−26961.3	−	4270.25i	−1.06347	−	0.168437i	−0.399905	−	0.916556i	$-0.630957\pi$
$863$	−26961.3	−	4270.25i	−1.06347	−	0.168437i	−0.663564	+	0.748120i	$0.730957\pi$
$864$	−1500.01	+	1089.82i	−0.0590642	+	0.0429127i
$865$	−18062.2	+	10838.3i	−0.709979	+	0.426029i
$866$	31231.3	+	10147.7i	1.22550	+	0.398189i
$867$	−53882.8	+	8534.20i	−2.11068	+	0.334298i
$868$	−1119.77	+	1119.77i	−0.0437873	+	0.0437873i
$869$	−14493.0	+	11329.7i	−0.565757	+	0.442272i
$870$	34881.8	+	21825.2i	1.35931	+	0.850510i
$871$	32375.2	−	44560.6i	1.25946	−	1.73350i
$872$	3769.96	+	7398.96i	0.146407	+	0.287340i
$873$	2888.36	−	5668.72i	0.111977	−	0.219768i
$874$	398.834	+	548.947i	0.0154356	+	0.0212453i
$875$	−10136.6	−	2735.35i	−0.391636	−	0.105682i
$876$	9053.91	−	2941.79i	0.349205	−	0.113463i
$877$	−8555.88	+	4359.44i	−0.329432	+	0.167854i	−0.610881	−	0.791722i	$-0.709185\pi$
$877$	−8555.88	+	4359.44i	−0.329432	+	0.167854i	0.281450	+	0.959576i	$0.409185\pi$
$878$	1501.70	+	9481.35i	0.0577219	+	0.364442i
$879$	5096.33			0.195557
$880$	5962.86	−	2652.61i	0.228418	−	0.101613i
$881$	26264.4			1.00439			0.502196	−	0.864754i	$-0.332526\pi$
$881$	26264.4			1.00439			0.502196	+	0.864754i	$0.332526\pi$
$882$	−1649.74	−	10416.1i	−0.0629816	−	0.397650i
$883$	−8150.66	+	4152.97i	−0.310636	+	0.158277i	−0.602358	−	0.798226i	$-0.705772\pi$
$883$	−8150.66	+	4152.97i	−0.310636	+	0.158277i	0.291722	+	0.956503i	$0.405772\pi$
$884$	−36741.7	+	11938.1i	−1.39792	+	0.454211i
$885$	−879.944	−	765.836i	−0.0334226	−	0.0290885i
$886$	−17935.9	−	24686.6i	−0.680099	−	0.936075i
$887$	18714.9	−	36730.0i	0.708437	−	1.39039i	−0.203096	−	0.979159i	$-0.565101\pi$
$887$	18714.9	−	36730.0i	0.708437	−	1.39039i	0.911533	−	0.411227i	$-0.134899\pi$
$888$	6405.80	+	12572.1i	0.242077	+	0.475103i
$889$	−5011.57	+	6897.84i	−0.189069	+	0.260232i
$890$	3223.54	+	14000.4i	0.121408	+	0.527297i
$891$	−32348.7	+	1138.68i	−1.21630	+	0.0428138i
$892$	10693.5	−	10693.5i	0.401395	−	0.401395i
$893$	−32844.5	+	5202.06i	−1.23079	+	0.194939i
$894$	−16894.8	−	5489.45i	−0.632042	−	0.205363i
$895$	−1346.21	+	5385.81i	−0.0502780	+	0.201148i
$896$	−777.964	+	565.224i	−0.0290067	+	0.0210746i
$897$	−3300.81	−	522.797i	−0.122866	−	0.0194601i
$898$	14841.1	+	7561.91i	0.551507	+	0.281007i
$899$	4447.28	−	13687.3i	0.164989	−	0.507784i
$900$	1608.33	−	9058.76i	0.0595678	−	0.335510i
$901$		−	3413.85i		−	0.126228i
$902$	6834.38	+	3184.60i	0.252284	+	0.117556i
$903$	−711.161	−	711.161i	−0.0262081	−	0.0262081i
$904$	−1438.97	−	1045.47i	−0.0529419	−	0.0384645i
$905$	10899.0	+	13004.5i	0.400325	+	0.477661i
$906$	−6911.85	−	21272.5i	−0.253456	−	0.780056i
$907$	3717.71	−	23472.7i	0.136102	−	0.859315i	−0.821287	−	0.570515i	$-0.806744\pi$
$907$	3717.71	−	23472.7i	0.136102	−	0.859315i	0.957389	−	0.288800i	$-0.0932564\pi$
$908$	−2808.45	+	17731.9i	−0.102645	+	0.648075i
$909$	9773.25	+	30079.0i	0.356610	+	1.09753i
$910$	1248.12	−	14169.7i	0.0454667	−	0.516178i
$911$	38180.2	+	27739.5i	1.38855	+	1.00884i	0.996023	+	0.0890950i	$0.0283975\pi$
$911$	38180.2	+	27739.5i	1.38855	+	1.00884i	0.392522	+	0.919742i	$0.371603\pi$
$912$	−4415.44	−	4415.44i	−0.160318	−	0.160318i
$913$	−27854.8	−	12979.4i	−1.00970	−	0.470489i
$914$		−	12552.6i		−	0.454269i
$915$	12036.0	−	28308.5i	0.434861	−	1.02279i
$916$	920.584	−	2833.27i	0.0332063	−	0.102198i
$917$	9699.86	+	4942.33i	0.349310	+	0.177983i
$918$	−13054.7	−	2067.67i	−0.469358	−	0.0743390i
$919$	−11769.2	+	8550.82i	−0.422448	+	0.306927i	−0.778622	−	0.627493i	$-0.784081\pi$
$919$	−11769.2	+	8550.82i	−0.422448	+	0.306927i	0.356174	+	0.934420i	$0.384081\pi$
$920$	508.266	+	127.044i	0.0182142	+	0.00455272i
$921$	50942.8	+	16552.3i	1.82261	+	0.592201i
$922$	22738.2	−	3601.38i	0.812195	−	0.128639i
$923$	4298.46	−	4298.46i	0.153289	−	0.153289i
$924$	−7382.51	+	259.865i	−0.262843	+	0.00925208i
$925$	30924.9	+	10689.1i	1.09925	+	0.379953i
$926$	−14357.1	+	19760.8i	−0.509507	+	0.701276i
$927$	9558.41	+	18759.4i	0.338662	+	0.664661i
$928$	3967.51	−	7786.68i	0.140345	−	0.275442i
$929$	−15669.6	−	21567.4i	−0.553395	−	0.761683i	0.437073	−	0.899426i	$-0.356015\pi$
$929$	−15669.6	−	21567.4i	−0.553395	−	0.761683i	−0.990468	+	0.137743i	$0.956015\pi$
$930$	−7920.75	+	549.176i	−0.279281	+	0.0193636i
$931$	−15785.6	+	5129.04i	−0.555693	+	0.180556i
$932$	−5869.25	+	2990.53i	−0.206281	+	0.105105i
$933$	9222.24	+	58226.9i	0.323604	+	2.04315i
$934$	14486.2			0.507498
$935$	43428.5	+	16686.1i	1.51900	+	0.583631i
$936$	12464.9			0.435288
$937$	4725.60	+	29836.2i	0.164758	+	1.04024i	0.922023	+	0.387135i	$0.126535\pi$
$937$	4725.60	+	29836.2i	0.164758	+	1.04024i	−0.757265	+	0.653108i	$0.773465\pi$
$938$	8708.31	−	4437.11i	0.303131	−	0.154453i
$939$	−9874.66	+	3208.47i	−0.343181	+	0.111506i
$940$	−16856.1	+	19367.7i	−0.584879	+	0.672025i
$941$	−6079.01	−	8367.03i	−0.210595	−	0.289859i	0.690632	−	0.723206i	$-0.257332\pi$
$941$	−6079.01	−	8367.03i	−0.210595	−	0.289859i	−0.901227	+	0.433347i	$0.857332\pi$
$942$	6533.11	−	12822.0i	0.225966	−	0.443484i
$943$	274.789	+	539.305i	0.00948926	+	0.0186237i
$944$	−145.630	+	200.442i	−0.00502102	+	0.00691084i
$945$	2581.39	−	4125.67i	0.0888600	−	0.142019i
$946$	1142.13	−	892.842i	0.0392535	−	0.0306858i
$947$	−6886.74	+	6886.74i	−0.236314	+	0.236314i	−0.815322	−	0.579008i	$-0.803440\pi$
$947$	−6886.74	+	6886.74i	−0.236314	+	0.236314i	0.579008	+	0.815322i	$0.303440\pi$
$948$	13422.9	−	2125.97i	0.459867	−	0.0728358i
$949$	28445.1	+	9242.36i	0.972988	+	0.316143i
$950$	−14477.8	−	269.804i	−0.494443	−	0.00921432i
$951$	−58532.8	+	42526.6i	−1.99585	+	1.45007i
$952$	−6770.69	−	1072.37i	−0.230503	−	0.0365081i
$953$	−264.638	−	134.840i	−0.00899524	−	0.00458331i	0.449487	−	0.893287i	$-0.351607\pi$
$953$	−264.638	−	134.840i	−0.00899524	−	0.00458331i	−0.458482	+	0.888704i	$0.651607\pi$
$954$	−340.380	+	1047.58i	−0.0115516	+	0.0355521i
$955$	6562.91	−	2647.08i	0.222378	−	0.0896939i
$956$			110.471i			0.00373733i
$957$	58707.7	−	32563.6i	1.98302	−	1.09993i
$958$	−19105.1	−	19105.1i	−0.644321	−	0.644321i
$959$	−12612.5	−	9163.51i	−0.424691	−	0.308556i
$960$	−4802.74	−	423.041i	−0.161466	−	0.0142225i
$961$	−8347.77	−	25691.8i	−0.280211	−	0.862402i
$962$	−6934.73	+	43784.2i	−0.232416	+	1.46742i
$963$	4593.96	−	29005.1i	0.153726	−	0.970588i
$964$	−1953.71	−	6012.91i	−0.0652747	−	0.200895i
$965$	5967.60	+	525.647i	0.199071	+	0.0175349i
$966$	−479.753	−	348.561i	−0.0159791	−	0.0116095i
$967$	−31358.1	−	31358.1i	−1.04282	−	1.04282i	−0.999041	−	0.0437810i	$-0.986060\pi$
$967$	−31358.1	−	31358.1i	−1.04282	−	1.04282i	−0.0437810	−	0.999041i	$-0.513940\pi$
$968$	922.117	−	10608.0i	0.0306177	−	0.352225i
$969$		−	44514.3i		−	1.47576i
$970$	−7170.03	+	2891.96i	−0.237336	+	0.0957270i
$971$	−12188.8	+	37513.1i	−0.402838	+	1.23981i	0.519849	+	0.854258i	$0.325988\pi$
$971$	−12188.8	+	37513.1i	−0.402838	+	1.23981i	−0.922687	+	0.385550i	$0.874012\pi$
$972$	15730.8	+	8015.23i	0.519100	+	0.264495i
$973$	14178.7	+	2245.68i	0.467161	+	0.0739911i
$974$	−14722.3	+	10696.4i	−0.484327	+	0.351884i
$975$	51361.0	−	49481.7i	1.68704	−	1.62532i
$976$	−6213.55	−	2018.90i	−0.203782	−	0.0662127i
$977$	−28522.3	+	4517.48i	−0.933990	+	0.147929i	−0.604839	−	0.796348i	$-0.706762\pi$
$977$	−28522.3	+	4517.48i	−0.933990	+	0.147929i	−0.329151	+	0.944277i	$0.606762\pi$
$978$	30742.4	−	30742.4i	1.00515	−	1.00515i
$979$	22533.9	+	6454.70i	0.735636	+	0.210718i
$980$	−6797.52	+	10864.0i	−0.221570	+	0.354121i
$981$	11226.8	−	15452.4i	0.365387	−	0.502912i
$982$	9740.65	+	19117.1i	0.316534	+	0.621233i
$983$	−4380.00	+	8596.23i	−0.142116	+	0.278919i	−0.951083	−	0.308936i	$-0.900027\pi$
$983$	−4380.00	+	8596.23i	−0.142116	+	0.278919i	0.808967	+	0.587854i	$0.200027\pi$
$984$	−3274.07	−	4506.37i	−0.106071	−	0.145994i
$985$	−11947.8	+	13728.0i	−0.386485	+	0.444071i
$986$	59250.0	−	19251.5i	1.91370	−	0.621798i
$987$	25894.7	−	13194.0i	0.835093	−	0.425501i
$988$	−3068.97	−	19376.7i	−0.0988228	−	0.623942i
$989$	116.376			0.00374171
$990$	−11662.9	−	9450.41i	−0.374414	−	0.303388i
$991$	38768.3			1.24270			0.621351	−	0.783533i	$-0.286584\pi$
$991$	38768.3			1.24270			0.621351	+	0.783533i	$0.286584\pi$
$992$	263.799	+	1665.56i	0.00844317	+	0.0533081i
$993$	11629.5	−	5925.54i	0.371653	−	0.189367i
$994$	1025.87	−	333.327i	0.0327352	−	0.0106363i
$995$	20306.2	−	1407.91i	0.646985	−	0.0448580i
$996$	13344.1	+	18366.6i	0.424522	+	0.584304i
$997$	−7725.92	+	15163.0i	−0.245419	+	0.481661i	−0.980551	−	0.196262i	$-0.937120\pi$
$997$	−7725.92	+	15163.0i	−0.245419	+	0.481661i	0.735133	+	0.677923i	$0.237120\pi$
$998$	−4882.98	−	9583.38i	−0.154878	−	0.303964i
$999$	−8914.78	+	12270.1i	−0.282334	+	0.388599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.4.k.a.73.2	yes	144
5.2	odd	4	inner	110.4.k.a.7.17	✓	144
11.8	odd	10	inner	110.4.k.a.63.17	yes	144
55.52	even	20	inner	110.4.k.a.107.2	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.4.k.a.7.17	✓	144	5.2	odd	4	inner
110.4.k.a.63.17	yes	144	11.8	odd	10	inner
110.4.k.a.73.2	yes	144	1.1	even	1	trivial
110.4.k.a.107.2	yes	144	55.52	even	20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	110.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.312869 - 1.97538i) q^{2} +(-6.00362 + 3.05899i) q^{3} +(-3.80423 + 1.23607i) q^{4} +(-0.773319 - 11.1536i) q^{5} +(7.92101 + 10.9023i) q^{6} +(-3.41066 + 6.69380i) q^{7} +(3.63192 + 7.12805i) q^{8} +(10.8157 - 14.8866i) q^{9} +(-21.7905 + 5.01720i) q^{10} +(-10.0463 + 35.0724i) q^{11} +(19.0580 - 19.0580i) q^{12} +(83.6339 - 13.2463i) q^{13} +(14.2899 + 4.64306i) q^{14} +(38.7614 + 64.5961i) q^{15} +(12.9443 - 9.40456i) q^{16} +(112.655 + 17.8428i) q^{17} +(-32.7906 - 16.7076i) q^{18} +(-17.8986 + 55.0863i) q^{19} +(16.7284 + 41.4748i) q^{20} -50.6202i q^{21} +(72.4243 + 8.87209i) q^{22} +(4.14181 + 4.14181i) q^{23} +(-43.6094 - 31.6840i) q^{24} +(-123.804 + 17.2505i) q^{25} +(-52.3329 - 161.064i) q^{26} +(9.06400 - 57.2279i) q^{27} +(4.70094 - 29.6806i) q^{28} +(84.3925 + 259.733i) q^{29} +(115.474 - 96.7785i) q^{30} +(-42.6332 - 30.9749i) q^{31} +(-22.6274 - 22.6274i) q^{32} +(-46.9724 - 241.293i) q^{33} -228.119i q^{34} +(77.2973 + 32.8646i) q^{35} +(-22.7447 + 70.0010i) q^{36} +(-233.230 - 118.837i) q^{37} +(114.416 + 18.1217i) q^{38} +(-461.586 + 335.362i) q^{39} +(76.6945 - 46.0212i) q^{40} +(98.2775 + 31.9323i) q^{41} +(-99.9940 + 15.8375i) q^{42} +(14.0489 - 14.0489i) q^{43} +(-5.13362 - 145.841i) q^{44} +(-174.403 - 109.122i) q^{45} +(6.88580 - 9.47749i) q^{46} +(260.647 + 511.548i) q^{47} +(-48.9439 + 96.0578i) q^{48} +(168.436 + 231.832i) q^{49} +(72.8107 + 239.162i) q^{50} +(-730.919 + 237.490i) q^{51} +(-301.789 + 153.769i) q^{52} +(-4.68216 - 29.5620i) q^{53} -115.882 q^{54} +(398.951 + 84.9295i) q^{55} -60.1011 q^{56} +(-61.0523 - 385.469i) q^{57} +(486.668 - 247.970i) q^{58} +(-14.7271 + 4.78513i) q^{59} +(-227.302 - 197.827i) q^{60} +(-240.012 - 330.347i) q^{61} +(-47.8484 + 93.9078i) q^{62} +(62.7591 + 123.172i) q^{63} +(-37.6183 + 51.7771i) q^{64} +(-212.419 - 922.573i) q^{65} +(-461.948 + 168.281i) q^{66} +(459.956 - 459.956i) q^{67} +(-450.620 + 71.3712i) q^{68} +(-37.5357 - 12.1961i) q^{69} +(40.7361 - 162.974i) q^{70} +(58.0796 - 42.1973i) q^{71} +(145.394 + 23.0282i) q^{72} +(314.716 + 160.356i) q^{73} +(-161.777 + 497.898i) q^{74} +(690.502 - 482.281i) q^{75} -231.685i q^{76} +(-200.503 - 186.868i) q^{77} +(806.881 + 806.881i) q^{78} +(407.935 + 296.382i) q^{79} +(-114.904 - 137.102i) q^{80} +(274.170 + 843.807i) q^{81} +(32.3303 - 204.126i) q^{82} +(-131.768 + 831.952i) q^{83} +(62.5700 + 192.571i) q^{84} +(111.893 - 1270.30i) q^{85} +(-32.1474 - 23.3565i) q^{86} +(-1301.18 - 1301.18i) q^{87} +(-286.485 + 55.7700i) q^{88} -642.498i q^{89} +(-160.992 + 378.652i) q^{90} +(-196.579 + 605.008i) q^{91} +(-20.8760 - 10.6368i) q^{92} +(350.705 + 55.5463i) q^{93} +(928.952 - 674.923i) q^{94} +(628.250 + 157.034i) q^{95} +(205.063 + 66.6292i) q^{96} +(341.497 - 54.0877i) q^{97} +(405.258 - 405.258i) q^{98} +(413.451 + 528.889i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{3} + 32 q^{5} - 40 q^{7} - 44 q^{11} + 128 q^{12} - 256 q^{15} + 576 q^{16} - 640 q^{17} - 64 q^{20} + 312 q^{22} - 984 q^{23} - 520 q^{25} + 304 q^{26} - 364 q^{27} + 240 q^{28} - 432 q^{31}+ \cdots + 7044 q^{97}+O(q^{100}) \) 144 * q + 8 * q^3 + 32 * q^5 - 40 * q^7 - 44 * q^11 + 128 * q^12 - 256 * q^15 + 576 * q^16 - 640 * q^17 - 64 * q^20 + 312 * q^22 - 984 * q^23 - 520 * q^25 + 304 * q^26 - 364 * q^27 + 240 * q^28 - 432 * q^31 + 2368 * q^33 + 1808 * q^36 - 960 * q^37 + 72 * q^38 + 740 * q^41 + 2440 * q^42 + 2656 * q^45 + 720 * q^46 - 1980 * q^47 - 128 * q^48 - 1360 * q^50 - 3880 * q^51 - 1920 * q^52 - 3060 * q^53 - 3044 * q^55 - 64 * q^56 - 4400 * q^57 - 2016 * q^58 - 1120 * q^60 - 960 * q^61 + 80 * q^62 + 1800 * q^63 + 1552 * q^66 + 10160 * q^67 + 2560 * q^68 + 2304 * q^70 + 1312 * q^71 - 2460 * q^73 + 8644 * q^75 - 1272 * q^77 - 5312 * q^78 + 768 * q^80 + 2116 * q^81 + 1280 * q^82 + 320 * q^85 - 5488 * q^86 + 1248 * q^88 - 8480 * q^90 + 11796 * q^91 - 704 * q^92 + 688 * q^93 - 1280 * q^95 + 7044 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more