LMFDB - Embedded newform 224.3.w.a.99.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(43,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("224.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.w (of order $8$, degree $4$, 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:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			99.19
Character	$\chi$	$=$	224.99
Dual form			224.3.w.a.43.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.518278 - 1.93168i) q^{2} +(-0.266183 + 0.642623i) q^{3} +(-3.46277 + 2.00230i) q^{4} +(-0.747592 - 1.80485i) q^{5} +(1.37930 + 0.181123i) q^{6} +(1.87083 + 1.87083i) q^{7} +(5.66248 + 5.65123i) q^{8} +(6.02185 + 6.02185i) q^{9} +O(q^{10})$	\(q+(-0.518278 - 1.93168i) q^{2} +(-0.266183 + 0.642623i) q^{3} +(-3.46277 + 2.00230i) q^{4} +(-0.747592 - 1.80485i) q^{5} +(1.37930 + 0.181123i) q^{6} +(1.87083 + 1.87083i) q^{7} +(5.66248 + 5.65123i) q^{8} +(6.02185 + 6.02185i) q^{9} +(-3.09892 + 2.37952i) q^{10} +(0.854581 + 2.06314i) q^{11} +(-0.364989 - 2.75824i) q^{12} +(-2.40343 + 5.80239i) q^{13} +(2.64423 - 4.58345i) q^{14} +1.35883 q^{15} +(7.98162 - 13.8670i) q^{16} -18.1690i q^{17} +(8.51129 - 14.7533i) q^{18} +(34.1345 + 14.1390i) q^{19} +(6.20258 + 4.75288i) q^{20} +(-1.70022 + 0.704255i) q^{21} +(3.54242 - 2.72006i) q^{22} +(6.06571 - 6.06571i) q^{23} +(-5.13887 + 2.13458i) q^{24} +(14.9791 - 14.9791i) q^{25} +(12.4540 + 1.63540i) q^{26} +(-11.2563 + 4.66252i) q^{27} +(-10.2242 - 2.73231i) q^{28} +(29.1695 + 12.0824i) q^{29} +(-0.704254 - 2.62483i) q^{30} +17.4712i q^{31} +(-30.9233 - 8.23097i) q^{32} -1.55330 q^{33} +(-35.0968 + 9.41662i) q^{34} +(1.97794 - 4.77517i) q^{35} +(-32.9098 - 8.79478i) q^{36} +(5.11785 + 12.3556i) q^{37} +(9.62079 - 73.2648i) q^{38} +(-3.08900 - 3.08900i) q^{39} +(5.96637 - 14.4447i) q^{40} +(-19.9681 - 19.9681i) q^{41} +(2.24158 + 2.91928i) q^{42} +(17.0934 + 41.2671i) q^{43} +(-7.09024 - 5.43307i) q^{44} +(6.36663 - 15.3704i) q^{45} +(-14.8607 - 8.57329i) q^{46} +35.7853 q^{47} +(6.78669 + 8.82034i) q^{48} +7.00000i q^{49} +(-36.6982 - 21.1715i) q^{50} +(11.6759 + 4.83630i) q^{51} +(-3.29557 - 24.9048i) q^{52} +(-87.6520 + 36.3066i) q^{53} +(14.8404 + 19.3271i) q^{54} +(3.08478 - 3.08478i) q^{55} +(0.0210475 + 21.1660i) q^{56} +(-18.1721 + 18.1721i) q^{57} +(8.22141 - 62.6082i) q^{58} +(62.7071 - 25.9741i) q^{59} +(-4.70533 + 2.72079i) q^{60} +(-91.3190 - 37.8256i) q^{61} +(33.7487 - 9.05493i) q^{62} +22.5317i q^{63} +(0.127283 + 63.9999i) q^{64} +12.2692 q^{65} +(0.805041 + 3.00048i) q^{66} +(-28.7890 + 69.5029i) q^{67} +(36.3798 + 62.9153i) q^{68} +(2.28338 + 5.51256i) q^{69} +(-10.2492 - 1.34588i) q^{70} +(47.0460 + 47.0460i) q^{71} +(0.0677481 + 68.1294i) q^{72} +(25.5379 + 25.5379i) q^{73} +(21.2146 - 16.2897i) q^{74} +(5.63873 + 13.6131i) q^{75} +(-146.510 + 19.3873i) q^{76} +(-2.26101 + 5.45856i) q^{77} +(-4.36600 + 7.56792i) q^{78} -8.38633 q^{79} +(-30.9948 - 4.03874i) q^{80} +68.1710i q^{81} +(-28.2230 + 48.9211i) q^{82} +(-12.8515 - 5.32326i) q^{83} +(4.47736 - 5.84302i) q^{84} +(-32.7923 + 13.5830i) q^{85} +(70.8556 - 54.4067i) q^{86} +(-15.5289 + 15.5289i) q^{87} +(-6.82023 + 16.5119i) q^{88} +(72.9437 - 72.9437i) q^{89} +(-32.9904 - 4.33214i) q^{90} +(-15.3517 + 6.35888i) q^{91} +(-8.85885 + 33.1496i) q^{92} +(-11.2274 - 4.65054i) q^{93} +(-18.5467 - 69.1257i) q^{94} -72.1777i q^{95} +(13.5207 - 17.6811i) q^{96} -102.626 q^{97} +(13.5218 - 3.62795i) q^{98} +(-7.27777 + 17.5701i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 80 q^{10} + 96 q^{12} - 20 q^{16} - 60 q^{18} - 260 q^{22} + 64 q^{23} - 144 q^{24} - 200 q^{26} + 192 q^{27} - 40 q^{30} + 40 q^{32} + 120 q^{34} + 464 q^{36} + 504 q^{38} - 384 q^{39} + 360 q^{40} - 96 q^{43} + 52 q^{44} + 64 q^{46} - 104 q^{48} - 312 q^{50} - 384 q^{51} - 320 q^{52} + 160 q^{53} - 576 q^{54} - 512 q^{55} - 196 q^{56} - 360 q^{58} - 872 q^{60} + 128 q^{61} - 408 q^{62} + 832 q^{66} + 160 q^{67} + 856 q^{68} - 384 q^{69} + 336 q^{70} + 1488 q^{72} + 308 q^{74} + 768 q^{75} + 1024 q^{76} - 224 q^{77} - 408 q^{78} + 1024 q^{79} - 1040 q^{80} - 240 q^{82} - 1384 q^{86} + 896 q^{87} - 560 q^{88} - 1320 q^{90} - 380 q^{92} - 936 q^{94} - 1088 q^{96} - 512 q^{99}+O(q^{100}) $ 192 * q + 80 * q^10 + 96 * q^12 - 20 * q^16 - 60 * q^18 - 260 * q^22 + 64 * q^23 - 144 * q^24 - 200 * q^26 + 192 * q^27 - 40 * q^30 + 40 * q^32 + 120 * q^34 + 464 * q^36 + 504 * q^38 - 384 * q^39 + 360 * q^40 - 96 * q^43 + 52 * q^44 + 64 * q^46 - 104 * q^48 - 312 * q^50 - 384 * q^51 - 320 * q^52 + 160 * q^53 - 576 * q^54 - 512 * q^55 - 196 * q^56 - 360 * q^58 - 872 * q^60 + 128 * q^61 - 408 * q^62 + 832 * q^66 + 160 * q^67 + 856 * q^68 - 384 * q^69 + 336 * q^70 + 1488 * q^72 + 308 * q^74 + 768 * q^75 + 1024 * q^76 - 224 * q^77 - 408 * q^78 + 1024 * q^79 - 1040 * q^80 - 240 * q^82 - 1384 * q^86 + 896 * q^87 - 560 * q^88 - 1320 * q^90 - 380 * q^92 - 936 * q^94 - 1088 * q^96 - 512 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−0.518278	−	1.93168i	−0.259139	−	0.965840i
$2$	−0.518278	−	1.93168i	−0.259139	−	0.965840i
$3$	−0.266183	+	0.642623i	−0.0887278	+	0.214208i	−0.962014	−	0.272999i	$-0.911984\pi$
$3$	−0.266183	+	0.642623i	−0.0887278	+	0.214208i	0.873286	+	0.487207i	$0.161984\pi$
$4$	−3.46277	+	2.00230i	−0.865694	+	0.500574i
$5$	−0.747592	−	1.80485i	−0.149518	−	0.360969i	0.831320	−	0.555795i	$-0.187586\pi$
$5$	−0.747592	−	1.80485i	−0.149518	−	0.360969i	−0.980838	+	0.194826i	$0.937586\pi$
$6$	1.37930	+	0.181123i	0.229883	+	0.0301872i
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$8$	5.66248	+	5.65123i	0.707810	+	0.706403i
$9$	6.02185	+	6.02185i	0.669094	+	0.669094i
$10$	−3.09892	+	2.37952i	−0.309892	+	0.237952i
$11$	0.854581	+	2.06314i	0.0776892	+	0.187558i	0.957952	−	0.286928i	$-0.0926339\pi$
$11$	0.854581	+	2.06314i	0.0776892	+	0.187558i	−0.880263	+	0.474486i	$0.842634\pi$
$12$	−0.364989	−	2.75824i	−0.0304158	−	0.229853i
$13$	−2.40343	+	5.80239i	−0.184879	+	0.446338i	−0.988960	−	0.148182i	$-0.952658\pi$
$13$	−2.40343	+	5.80239i	−0.184879	+	0.446338i	0.804081	+	0.594520i	$0.202658\pi$
$14$	2.64423	−	4.58345i	0.188874	−	0.327389i
$15$	1.35883			0.0905888
$16$	7.98162	−	13.8670i	0.498851	−	0.866688i
$17$		−	18.1690i		−	1.06877i	−0.845242	−	0.534384i	$-0.820544\pi$
$17$		−	18.1690i		−	1.06877i	0.845242	−	0.534384i	$-0.179456\pi$
$18$	8.51129	−	14.7533i	0.472850	−	0.819627i
$19$	34.1345	+	14.1390i	1.79655	+	0.744156i	0.987744	+	0.156083i	$0.0498868\pi$
$19$	34.1345	+	14.1390i	1.79655	+	0.744156i	0.808808	+	0.588073i	$0.200113\pi$
$20$	6.20258	+	4.75288i	0.310129	+	0.237644i
$21$	−1.70022	+	0.704255i	−0.0809629	+	0.0335359i
$22$	3.54242	−	2.72006i	0.161019	−	0.123639i
$23$	6.06571	−	6.06571i	0.263727	−	0.263727i	−0.562839	−	0.826566i	$-0.690291\pi$
$23$	6.06571	−	6.06571i	0.263727	−	0.263727i	0.826566	+	0.562839i	$0.190291\pi$
$24$	−5.13887	+	2.13458i	−0.214119	+	0.0889407i
$25$	14.9791	−	14.9791i	0.599164	−	0.599164i
$26$	12.4540	+	1.63540i	0.479000	+	0.0629001i
$27$	−11.2563	+	4.66252i	−0.416900	+	0.172686i
$28$	−10.2242	−	2.73231i	−0.365150	−	0.0975824i
$29$	29.1695	+	12.0824i	1.00584	+	0.416635i	0.823937	−	0.566681i	$-0.191773\pi$
$29$	29.1695	+	12.0824i	1.00584	+	0.416635i	0.181908	+	0.983316i	$0.441773\pi$
$30$	−0.704254	−	2.62483i	−0.0234751	−	0.0874943i
$31$			17.4712i			0.563586i	0.959475	+	0.281793i	$0.0909292\pi$
$31$			17.4712i			0.563586i	−0.959475	+	0.281793i	$0.909071\pi$
$32$	−30.9233	−	8.23097i	−0.966353	−	0.257218i
$33$	−1.55330			−0.0470697
$34$	−35.0968	+	9.41662i	−1.03226	+	0.276959i
$35$	1.97794	−	4.77517i	0.0565126	−	0.136434i
$36$	−32.9098	−	8.79478i	−0.914162	−	0.244300i
$37$	5.11785	+	12.3556i	0.138320	+	0.333935i	0.977827	−	0.209415i	$-0.0671558\pi$
$37$	5.11785	+	12.3556i	0.138320	+	0.333935i	−0.839507	+	0.543350i	$0.817156\pi$
$38$	9.62079	−	73.2648i	0.253179	−	1.92802i
$39$	−3.08900	−	3.08900i	−0.0792051	−	0.0792051i
$40$	5.96637	−	14.4447i	0.149159	−	0.361118i
$41$	−19.9681	−	19.9681i	−0.487028	−	0.487028i	0.420339	−	0.907367i	$-0.361911\pi$
$41$	−19.9681	−	19.9681i	−0.487028	−	0.487028i	−0.907367	+	0.420339i	$0.861911\pi$
$42$	2.24158	+	2.91928i	0.0533710	+	0.0695068i
$43$	17.0934	+	41.2671i	0.397520	+	0.959699i	0.988252	+	0.152831i	$0.0488390\pi$
$43$	17.0934	+	41.2671i	0.397520	+	0.959699i	−0.590732	+	0.806868i	$0.701161\pi$
$44$	−7.09024	−	5.43307i	−0.161142	−	0.123479i
$45$	6.36663	−	15.3704i	0.141481	−	0.341564i
$46$	−14.8607	−	8.57329i	−0.323060	−	0.186376i
$47$	35.7853			0.761389			0.380694	−	0.924701i	$-0.375685\pi$
$47$	35.7853			0.761389			0.380694	+	0.924701i	$0.375685\pi$
$48$	6.78669	+	8.82034i	0.141389	+	0.183757i
$49$			7.00000i			0.142857i
$50$	−36.6982	−	21.1715i	−0.733963	−	0.423430i
$51$	11.6759	+	4.83630i	0.228938	+	0.0948293i
$52$	−3.29557	−	24.9048i	−0.0633764	−	0.478938i
$53$	−87.6520	+	36.3066i	−1.65381	+	0.685031i	−0.997580	−	0.0695296i	$-0.977850\pi$
$53$	−87.6520	+	36.3066i	−1.65381	+	0.685031i	−0.656231	+	0.754560i	$0.727850\pi$
$54$	14.8404	+	19.3271i	0.274822	+	0.357909i
$55$	3.08478	−	3.08478i	0.0560868	−	0.0560868i
$56$	0.0210475	+	21.1660i	0.000375849	+	0.377964i
$57$	−18.1721	+	18.1721i	−0.318808	+	0.318808i
$58$	8.22141	−	62.6082i	0.141749	−	1.07945i
$59$	62.7071	−	25.9741i	1.06283	−	0.440240i	0.218377	−	0.975865i	$-0.429924\pi$
$59$	62.7071	−	25.9741i	1.06283	−	0.440240i	0.844456	+	0.535625i	$0.179924\pi$
$60$	−4.70533	+	2.72079i	−0.0784222	+	0.0453464i
$61$	−91.3190	−	37.8256i	−1.49703	−	0.620091i	−0.524199	−	0.851596i	$-0.675635\pi$
$61$	−91.3190	−	37.8256i	−1.49703	−	0.620091i	−0.972834	+	0.231504i	$0.925635\pi$
$62$	33.7487	−	9.05493i	0.544334	−	0.146047i
$63$			22.5317i			0.357646i
$64$	0.127283	+	63.9999i	0.00198880	+	0.999998i
$65$	12.2692			0.188757
$66$	0.805041	+	3.00048i	0.0121976	+	0.0454618i
$67$	−28.7890	+	69.5029i	−0.429687	+	1.03736i	0.549700	+	0.835362i	$0.314742\pi$
$67$	−28.7890	+	69.5029i	−0.429687	+	1.03736i	−0.979387	+	0.201994i	$0.935258\pi$
$68$	36.3798	+	62.9153i	0.534997	+	0.925225i
$69$	2.28338	+	5.51256i	0.0330924	+	0.0798922i
$70$	−10.2492	−	1.34588i	−0.146418	−	0.0192269i
$71$	47.0460	+	47.0460i	0.662620	+	0.662620i	0.955997	−	0.293377i	$-0.0947791\pi$
$71$	47.0460	+	47.0460i	0.662620	+	0.662620i	−0.293377	+	0.955997i	$0.594779\pi$
$72$	0.0677481	+	68.1294i	0.000940946	+	0.946242i
$73$	25.5379	+	25.5379i	0.349835	+	0.349835i	0.860048	−	0.510213i	$-0.170433\pi$
$73$	25.5379	+	25.5379i	0.349835	+	0.349835i	−0.510213	+	0.860048i	$0.670433\pi$
$74$	21.2146	−	16.2897i	0.286683	−	0.220131i
$75$	5.63873	+	13.6131i	0.0751831	+	0.181508i
$76$	−146.510	+	19.3873i	−1.92777	+	0.255096i
$77$	−2.26101	+	5.45856i	−0.0293638	+	0.0708904i
$78$	−4.36600	+	7.56792i	−0.0559743	+	0.0970246i
$79$	−8.38633			−0.106156			−0.0530780	−	0.998590i	$-0.516903\pi$
$79$	−8.38633			−0.106156			−0.0530780	+	0.998590i	$0.516903\pi$
$80$	−30.9948	−	4.03874i	−0.387435	−	0.0504843i
$81$			68.1710i			0.841617i
$82$	−28.2230	+	48.9211i	−0.344183	+	0.596599i
$83$	−12.8515	−	5.32326i	−0.154837	−	0.0641356i	0.303919	−	0.952698i	$-0.401705\pi$
$83$	−12.8515	−	5.32326i	−0.154837	−	0.0641356i	−0.458756	+	0.888562i	$0.651705\pi$
$84$	4.47736	−	5.84302i	0.0533019	−	0.0695598i
$85$	−32.7923	+	13.5830i	−0.385792	+	0.159800i
$86$	70.8556	−	54.4067i	0.823902	−	0.632637i
$87$	−15.5289	+	15.5289i	−0.178493	+	0.178493i
$88$	−6.82023	+	16.5119i	−0.0775027	+	0.187636i
$89$	72.9437	−	72.9437i	0.819592	−	0.819592i	−0.166457	−	0.986049i	$-0.553233\pi$
$89$	72.9437	−	72.9437i	0.819592	−	0.819592i	0.986049	+	0.166457i	$0.0532326\pi$
$90$	−32.9904	−	4.33214i	−0.366560	−	0.0481349i
$91$	−15.3517	+	6.35888i	−0.168700	+	0.0698778i
$92$	−8.85885	+	33.1496i	−0.0962918	+	0.360321i
$93$	−11.2274	−	4.65054i	−0.120725	−	0.0500058i
$94$	−18.5467	−	69.1257i	−0.197306	−	0.735380i
$95$		−	72.1777i		−	0.759765i
$96$	13.5207	−	17.6811i	0.140840	−	0.184178i
$97$	−102.626			−1.05800			−0.528998	−	0.848623i	$-0.677432\pi$
$97$	−102.626			−1.05800			−0.528998	+	0.848623i	$0.677432\pi$
$98$	13.5218	−	3.62795i	0.137977	−	0.0370199i
$99$	−7.27777	+	17.5701i	−0.0735128	+	0.177476i
$100$	−21.8767	+	81.8618i	−0.218767	+	0.818618i
$101$	−31.6698	−	76.4577i	−0.313563	−	0.757007i	−0.999567	−	0.0294102i	$-0.990637\pi$
$101$	−31.6698	−	76.4577i	−0.313563	−	0.757007i	0.686005	−	0.727597i	$-0.259363\pi$
$102$	3.29083	−	25.0606i	0.0322631	−	0.245692i
$103$	−36.0782	−	36.0782i	−0.350274	−	0.350274i	0.509937	−	0.860211i	$-0.329669\pi$
$103$	−36.0782	−	36.0782i	−0.350274	−	0.350274i	−0.860211	+	0.509937i	$0.829669\pi$
$104$	−46.4000	+	19.2736i	−0.446154	+	0.185323i
$105$	2.54214	+	2.54214i	0.0242109	+	0.0242109i
$106$	115.561	+	150.499i	1.09020	+	1.41980i
$107$	60.8944	+	147.012i	0.569107	+	1.37395i	0.902309	+	0.431090i	$0.141871\pi$
$107$	60.8944	+	147.012i	0.569107	+	1.37395i	−0.333202	+	0.942855i	$0.608129\pi$
$108$	29.6423	−	38.6837i	0.274466	−	0.358182i
$109$	−1.95510	+	4.72002i	−0.0179367	+	0.0433029i	−0.932594	−	0.360927i	$-0.882460\pi$
$109$	−1.95510	+	4.72002i	−0.0179367	+	0.0433029i	0.914657	+	0.404230i	$0.132460\pi$
$110$	−7.55757	−	4.36003i	−0.0687052	−	0.0396366i
$111$	−9.30228			−0.0838043
$112$	40.8750	−	11.0105i	0.364956	−	0.0983084i
$113$		−	191.128i		−	1.69140i	−0.533659	−	0.845700i	$-0.679183\pi$
$113$		−	191.128i		−	1.69140i	0.533659	−	0.845700i	$-0.320817\pi$
$114$	44.5208	+	25.6844i	0.390533	+	0.225302i
$115$	−15.4824	−	6.41300i	−0.134629	−	0.0557652i
$116$	−125.200	+	16.5673i	−1.07931	+	0.142822i
$117$	−49.4142	+	20.4680i	−0.422344	+	0.174941i
$118$	−82.6735	−	107.668i	−0.700623	−	0.912443i
$119$	33.9912	−	33.9912i	0.285640	−	0.285640i
$120$	7.69436	+	7.67907i	0.0641196	+	0.0639923i
$121$	82.0337	−	82.0337i	0.677964	−	0.677964i
$122$	−25.7382	+	196.003i	−0.210969	+	1.60658i
$123$	18.1472	−	7.51681i	0.147538	−	0.0611123i
$124$	−34.9825	−	60.4987i	−0.282117	−	0.487893i
$125$	−83.3543	−	34.5265i	−0.666835	−	0.276212i
$126$	43.5240	−	11.6777i	0.345429	−	0.0926801i
$127$		−	244.025i		−	1.92145i	−0.277494	−	0.960727i	$-0.589504\pi$
$127$		−	244.025i		−	1.92145i	0.277494	−	0.960727i	$-0.410496\pi$
$128$	123.561	−	33.4156i	0.965323	−	0.261060i
$129$	−31.0691			−0.240846
$130$	−6.35886	−	23.7002i	−0.0489143	−	0.182309i
$131$	46.8130	−	113.017i	0.357351	−	0.862721i	−0.638320	−	0.769771i	$-0.720370\pi$
$131$	46.8130	−	113.017i	0.357351	−	0.862721i	0.995671	−	0.0929502i	$-0.0296297\pi$
$132$	5.37872	−	3.11016i	0.0407479	−	0.0235618i
$133$	37.4082	+	90.3114i	0.281265	+	0.679033i
$134$	149.178	+	19.5894i	1.11327	+	0.146189i
$135$	16.8302	+	16.8302i	0.124668	+	0.124668i
$136$	102.677	−	102.882i	0.754981	−	0.756484i
$137$	18.6465	+	18.6465i	0.136106	+	0.136106i	0.771877	−	0.635771i	$-0.219318\pi$
$137$	18.6465	+	18.6465i	0.136106	+	0.136106i	−0.635771	+	0.771877i	$0.719318\pi$
$138$	9.46508	−	7.26780i	0.0685875	−	0.0526652i
$139$	10.7025	+	25.8382i	0.0769965	+	0.185886i	0.957691	−	0.287799i	$-0.0929235\pi$
$139$	10.7025	+	25.8382i	0.0769965	+	0.185886i	−0.880694	+	0.473685i	$0.842924\pi$
$140$	2.71214	+	20.4958i	0.0193725	+	0.146398i
$141$	−9.52545	+	22.9965i	−0.0675564	+	0.163095i
$142$	66.4949	−	115.261i	0.468274	−	0.811696i
$143$	−14.0251			−0.0980775
$144$	131.569	−	35.4409i	0.913674	−	0.246117i
$145$		−	61.6792i		−	0.425374i
$146$	36.0954	−	62.5669i	0.247229	−	0.428540i
$147$	−4.49836	−	1.86328i	−0.0306011	−	0.0126754i
$148$	−42.4615	−	32.5372i	−0.286902	−	0.219846i
$149$	−45.8596	+	18.9957i	−0.307782	+	0.127488i	−0.531228	−	0.847229i	$-0.678269\pi$
$149$	−45.8596	+	18.9957i	−0.307782	+	0.127488i	0.223446	+	0.974716i	$0.428269\pi$
$150$	23.3737	−	17.9476i	0.155825	−	0.119651i
$151$	−135.892	+	135.892i	−0.899945	+	0.899945i	−0.995431	−	0.0954859i	$-0.969560\pi$
$151$	−135.892	+	135.892i	−0.899945	+	0.899945i	0.0954859	+	0.995431i	$0.469560\pi$
$152$	113.383	+	272.963i	0.745942	+	1.79581i
$153$	109.411	−	109.411i	0.715106	−	0.715106i
$154$	11.7160	+	1.53849i	0.0760781	+	0.00999022i
$155$	31.5328	−	13.0613i	0.203437	−	0.0842665i
$156$	16.8816	+	4.51142i	0.108215	+	0.0289194i
$157$	−143.404	−	59.3999i	−0.913402	−	0.378343i	−0.124044	−	0.992277i	$-0.539586\pi$
$157$	−143.404	−	59.3999i	−0.913402	−	0.378343i	−0.789358	+	0.613933i	$0.789586\pi$
$158$	4.34645	+	16.1997i	0.0275092	+	0.102530i
$159$		−	65.9914i		−	0.415040i
$160$	8.26238	+	61.9652i	0.0516398	+	0.387283i
$161$	22.6958			0.140968
$162$	131.685	−	35.3315i	0.812867	−	0.218096i
$163$	29.7483	−	71.8186i	0.182505	−	0.440605i	−0.805977	−	0.591947i	$-0.798359\pi$
$163$	29.7483	−	71.8186i	0.182505	−	0.440605i	0.988481	+	0.151342i	$0.0483595\pi$
$164$	109.127	+	29.1631i	0.665411	+	0.177824i
$165$	1.16123	+	2.80346i	0.00703778	+	0.0169907i
$166$	−3.62218	+	27.5839i	−0.0218204	+	0.166168i
$167$	−219.438	−	219.438i	−1.31400	−	1.31400i	−0.918440	−	0.395560i	$-0.870550\pi$
$167$	−219.438	−	219.438i	−1.31400	−	1.31400i	−0.395560	−	0.918440i	$-0.629450\pi$
$168$	−13.6074	−	5.62051i	−0.0809962	−	0.0334554i
$169$	91.6098	+	91.6098i	0.542070	+	0.542070i
$170$	43.2336	+	56.3045i	0.254315	+	0.331203i
$171$	120.410	+	290.695i	0.704152	+	1.69997i
$172$	−141.819	−	108.673i	−0.824531	−	0.631817i
$173$	90.0139	−	217.313i	0.520311	−	1.25614i	−0.417399	−	0.908723i	$-0.637058\pi$
$173$	90.0139	−	217.313i	0.520311	−	1.25614i	0.937710	−	0.347419i	$-0.112942\pi$
$174$	38.0451	+	21.9485i	0.218650	+	0.126141i
$175$	56.0466			0.320267
$176$	35.4305	+	4.61674i	0.201310	+	0.0262315i
$177$			47.2110i			0.266729i
$178$	−178.709	−	103.099i	−1.00398	−	0.579206i
$179$	25.0102	+	10.3596i	0.139722	+	0.0578747i	0.451449	−	0.892297i	$-0.350907\pi$
$179$	25.0102	+	10.3596i	0.139722	+	0.0578747i	−0.311727	+	0.950172i	$0.600907\pi$
$180$	8.72989	+	65.9721i	0.0484994	+	0.366512i
$181$	−95.5125	+	39.5626i	−0.527693	+	0.218578i	−0.630593	−	0.776114i	$-0.717188\pi$
$181$	−95.5125	+	39.5626i	−0.527693	+	0.218578i	0.102899	+	0.994692i	$0.467188\pi$
$182$	20.2398	+	26.3589i	0.111207	+	0.144829i
$183$	48.6152	−	48.6152i	0.265657	−	0.265657i
$184$	68.6257	−	0.0682416i	0.372966	−	0.000370878i
$185$	18.4739	−	18.4739i	0.0998588	−	0.0998588i
$186$	−3.16443	+	24.0980i	−0.0170131	+	0.129559i
$187$	37.4853	−	15.5269i	0.200456	−	0.0830317i
$188$	−123.916	+	71.6527i	−0.659130	+	0.381132i
$189$	−29.7814	−	12.3359i	−0.157574	−	0.0652691i
$190$	−139.424	+	37.4081i	−0.733811	+	0.196885i
$191$			116.515i			0.610026i	0.952348	+	0.305013i	$0.0986609\pi$
$191$			116.515i			0.610026i	−0.952348	+	0.305013i	$0.901339\pi$
$192$	−41.1617	−	16.9539i	−0.214384	−	0.0883016i
$193$	−162.963			−0.844367			−0.422184	−	0.906510i	$-0.638736\pi$
$193$	−162.963			−0.844367			−0.422184	+	0.906510i	$0.638736\pi$
$194$	53.1887	+	198.240i	0.274168	+	1.02186i
$195$	−3.26586	+	7.88448i	−0.0167480	+	0.0404332i
$196$	−14.0161	−	24.2394i	−0.0715106	−	0.123671i
$197$	58.8448	+	142.064i	0.298704	+	0.721136i	0.999966	+	0.00823219i	$0.00262042\pi$
$197$	58.8448	+	142.064i	0.298704	+	0.721136i	−0.701262	+	0.712904i	$0.747380\pi$
$198$	37.7117	+	4.95212i	0.190463	+	0.0250107i
$199$	−16.3250	−	16.3250i	−0.0820353	−	0.0820353i	0.664898	−	0.746934i	$-0.268475\pi$
$199$	−16.3250	−	16.3250i	−0.0820353	−	0.0820353i	−0.746934	+	0.664898i	$0.768475\pi$
$200$	169.469	−	0.168521i	0.847345	−	0.000842603i
$201$	−37.0010	−	37.0010i	−0.184085	−	0.184085i
$202$	−131.278	+	100.802i	−0.649891	+	0.499022i
$203$	31.9670	+	77.1753i	0.157473	+	0.380174i
$204$	−50.1145	+	6.63151i	−0.245660	+	0.0325074i
$205$	−21.1114	+	50.9674i	−0.102982	+	0.248622i
$206$	−50.9930	+	88.3901i	−0.247539	+	0.429078i
$207$	73.0536			0.352916
$208$	61.2785	+	79.6408i	0.294608	+	0.382889i
$209$			82.5072i			0.394771i
$210$	3.59307	−	6.22814i	0.0171099	−	0.0296578i
$211$	−234.359	−	97.0747i	−1.11071	−	0.460070i	−0.249526	−	0.968368i	$-0.580275\pi$
$211$	−234.359	−	97.0747i	−1.11071	−	0.460070i	−0.861181	+	0.508299i	$0.830275\pi$
$212$	230.822	−	301.227i	1.08878	−	1.42088i
$213$	−42.7557	+	17.7100i	−0.200731	+	0.0831456i
$214$	252.420	−	193.822i	1.17953	−	0.905709i
$215$	61.7018	−	61.7018i	0.286985	−	0.286985i
$216$	−90.0875	−	37.2106i	−0.417072	−	0.172271i
$217$	−32.6856	+	32.6856i	−0.150625	+	0.150625i
$218$	10.1309	+	1.33034i	0.0464718	+	0.00610246i
$219$	−23.2091	+	9.61351i	−0.105977	+	0.0438973i
$220$	−4.50525	+	16.8585i	−0.0204784	+	0.0766296i
$221$	105.424	+	43.6680i	0.477031	+	0.197593i
$222$	4.82117	+	17.9690i	0.0217170	+	0.0809416i
$223$		−	298.537i		−	1.33873i	−0.742933	−	0.669366i	$-0.766566\pi$
$223$		−	298.537i		−	1.33873i	0.742933	−	0.669366i	$-0.233434\pi$
$224$	−42.4535	−	73.2510i	−0.189524	−	0.327013i
$225$	180.404			0.801794
$226$	−369.199	+	99.0576i	−1.63362	+	0.438308i
$227$	−108.709	+	262.446i	−0.478893	+	1.15615i	0.481236	+	0.876591i	$0.340188\pi$
$227$	−108.709	+	262.446i	−0.478893	+	1.15615i	−0.960129	+	0.279558i	$0.909812\pi$
$228$	26.5399	−	99.3116i	0.116403	−	0.435577i
$229$	60.2047	+	145.347i	0.262903	+	0.634703i	0.999116	−	0.0420469i	$-0.0133879\pi$
$229$	60.2047	+	145.347i	0.262903	+	0.634703i	−0.736213	+	0.676750i	$0.763388\pi$
$230$	−4.36370	+	33.2307i	−0.0189726	+	0.144481i
$231$	−2.90596	−	2.90596i	−0.0125799	−	0.0125799i
$232$	96.8912	+	233.260i	0.417635	+	1.00543i
$233$	118.214	+	118.214i	0.507357	+	0.507357i	0.913714	−	0.406357i	$-0.133201\pi$
$233$	118.214	+	118.214i	0.507357	+	0.507357i	−0.406357	+	0.913714i	$0.633201\pi$
$234$	65.1480	+	84.8443i	0.278410	+	0.362583i
$235$	−26.7528	−	64.5869i	−0.113842	−	0.274838i
$236$	−165.133	+	215.501i	−0.699715	+	0.913139i
$237$	2.23230	−	5.38925i	0.00941899	−	0.0227394i
$238$	−83.2769	−	48.0432i	−0.349903	−	0.201862i
$239$	−104.925			−0.439017			−0.219508	−	0.975611i	$-0.570445\pi$
$239$	−104.925			−0.439017			−0.219508	+	0.975611i	$0.570445\pi$
$240$	10.8457	−	18.8429i	0.0451904	−	0.0785122i
$241$		−	54.4361i		−	0.225876i	−0.993602	−	0.112938i	$-0.963974\pi$
$241$		−	54.4361i		−	0.225876i	0.993602	−	0.112938i	$-0.0360261\pi$
$242$	−200.979	−	115.947i	−0.830492	−	0.479118i
$243$	−145.115	−	60.1086i	−0.597181	−	0.247361i
$244$	391.955	−	51.8663i	1.60637	−	0.212567i
$245$	12.6339	−	5.23314i	0.0515670	−	0.0213598i
$246$	−23.9254	−	31.1588i	−0.0972576	−	0.126662i
$247$	−164.080	+	164.080i	−0.664290	+	0.664290i
$248$	−98.7336	+	98.9301i	−0.398119	+	0.398912i
$249$	6.84170	−	6.84170i	0.0274767	−	0.0274767i
$250$	−23.4934	+	178.908i	−0.0939736	+	0.715633i
$251$	151.730	−	62.8485i	0.604501	−	0.250392i	−0.0593744	−	0.998236i	$-0.518911\pi$
$251$	151.730	−	62.8485i	0.604501	−	0.250392i	0.663875	+	0.747843i	$0.268911\pi$
$252$	−45.1151	−	78.0222i	−0.179028	−	0.309612i
$253$	17.6981	+	7.33078i	0.0699529	+	0.0289754i
$254$	−471.378	+	126.473i	−1.85582	+	0.497924i
$255$		−	24.6887i		−	0.0968184i
$256$	−128.587	−	221.362i	−0.502295	−	0.864696i
$257$	185.282			0.720941			0.360470	−	0.932771i	$-0.382616\pi$
$257$	185.282			0.720941			0.360470	+	0.932771i	$0.382616\pi$
$258$	16.1025	+	60.0156i	0.0624127	+	0.232619i
$259$	−13.5406	+	32.6898i	−0.0522802	+	0.126216i
$260$	−42.4855	+	24.5666i	−0.163406	+	0.0944869i
$261$	102.896	+	248.413i	0.394237	+	0.951773i
$262$	−242.574	−	31.8537i	−0.925855	−	0.121579i
$263$	−142.962	−	142.962i	−0.543581	−	0.543581i	0.380995	−	0.924577i	$-0.375581\pi$
$263$	−142.962	−	142.962i	−0.543581	−	0.543581i	−0.924577	+	0.380995i	$0.875581\pi$
$264$	−8.79552	−	8.77804i	−0.0333164	−	0.0332502i
$265$	131.056	+	131.056i	0.494550	+	0.494550i
$266$	155.065	−	119.067i	0.582950	−	0.447621i
$267$	27.4589	+	66.2917i	0.102842	+	0.248284i
$268$	−39.4754	−	298.317i	−0.147296	−	1.11312i
$269$	19.0062	−	45.8851i	0.0706552	−	0.170577i	−0.884607	−	0.466338i	$-0.845573\pi$
$269$	19.0062	−	45.8851i	0.0706552	−	0.170577i	0.955262	+	0.295761i	$0.0955732\pi$
$270$	23.7879	−	41.2334i	0.0881033	−	0.152716i
$271$	18.7752			0.0692812			0.0346406	−	0.999400i	$-0.488971\pi$
$271$	18.7752			0.0692812			0.0346406	+	0.999400i	$0.488971\pi$
$272$	−251.950	−	145.018i	−0.926287	−	0.533156i
$273$		−	11.5580i		−	0.0423369i
$274$	26.3551	−	45.6833i	0.0961863	−	0.166727i
$275$	43.7049	+	18.1031i	0.158927	+	0.0658296i
$276$	−18.9446	−	14.5168i	−0.0686399	−	0.0525970i
$277$	−15.3036	+	6.33898i	−0.0552478	+	0.0228844i	−0.410136	−	0.912024i	$-0.634519\pi$
$277$	−15.3036	+	6.33898i	−0.0552478	+	0.0228844i	0.354888	+	0.934909i	$0.384519\pi$
$278$	44.3642	−	34.0652i	0.159583	−	0.122537i
$279$	−105.209	+	105.209i	−0.377092	+	0.377092i
$280$	38.1856	−	15.8615i	0.136377	−	0.0566483i
$281$	222.571	−	222.571i	0.792069	−	0.792069i	−0.189761	−	0.981830i	$-0.560771\pi$
$281$	222.571	−	222.571i	0.792069	−	0.792069i	0.981830	+	0.189761i	$0.0607714\pi$
$282$	49.3586	+	6.48154i	0.175031	+	0.0229842i
$283$	−249.110	+	103.185i	−0.880248	+	0.364611i	−0.776593	−	0.630003i	$-0.783054\pi$
$283$	−249.110	+	103.185i	−0.880248	+	0.364611i	−0.103655	+	0.994613i	$0.533054\pi$
$284$	−257.110	−	68.7097i	−0.905316	−	0.241936i
$285$	46.3831	+	19.2125i	0.162748	+	0.0674122i
$286$	7.26890	+	27.0920i	0.0254157	+	0.0947272i
$287$		−	74.7140i		−	0.260327i
$288$	−136.650	−	235.781i	−0.474479	−	0.818685i
$289$	−41.1141			−0.142263
$290$	−119.144	+	31.9670i	−0.410843	+	0.110231i
$291$	27.3172	−	65.9496i	0.0938737	−	0.226631i
$292$	−139.567	−	37.2976i	−0.477968	−	0.127732i
$293$	−34.5694	−	83.4579i	−0.117984	−	0.284839i	0.853844	−	0.520529i	$-0.174265\pi$
$293$	−34.5694	−	83.4579i	−0.117984	−	0.284839i	−0.971828	+	0.235690i	$0.924265\pi$
$294$	−1.26786	+	9.65510i	−0.00431246	+	0.0328405i
$295$	−93.7587	−	93.7587i	−0.317826	−	0.317826i
$296$	−40.8445	+	98.8854i	−0.137988	+	0.334072i
$297$	−19.2389	−	19.2389i	−0.0647773	−	0.0647773i
$298$	60.4616	+	78.7410i	0.202891	+	0.264231i
$299$	20.6171	+	49.7742i	0.0689536	+	0.166469i
$300$	−46.7831	−	35.8487i	−0.155944	−	0.119496i
$301$	−45.2248	+	109.182i	−0.150249	+	0.362732i
$302$	332.929	+	192.069i	1.10241	+	0.635992i
$303$	57.5635			0.189979
$304$	468.514	−	360.491i	1.54116	−	1.18583i
$305$			193.095i			0.633098i
$306$	−268.053	−	154.642i	−0.875990	−	0.505366i
$307$	−83.7613	−	34.6951i	−0.272838	−	0.113013i	0.242069	−	0.970259i	$-0.422174\pi$
$307$	−83.7613	−	34.6951i	−0.272838	−	0.113013i	−0.514908	+	0.857246i	$0.672174\pi$
$308$	−3.10029	−	23.4290i	−0.0100659	−	0.0760681i
$309$	32.7881	−	13.5813i	0.106110	−	0.0439524i
$310$	−41.5730	−	54.1418i	−0.134106	−	0.174651i
$311$	−431.656	+	431.656i	−1.38796	+	1.38796i	−0.558369	+	0.829593i	$0.688573\pi$
$311$	−431.656	+	431.656i	−1.38796	+	1.38796i	−0.829593	+	0.558369i	$0.811427\pi$
$312$	−0.0347524	−	34.9480i	−0.000111386	−	0.112013i
$313$	−2.33254	+	2.33254i	−0.00745219	+	0.00745219i	−0.710823	−	0.703371i	$-0.751677\pi$
$313$	−2.33254	+	2.33254i	−0.00745219	+	0.00745219i	0.703371	+	0.710823i	$0.251677\pi$
$314$	−40.4184	+	307.796i	−0.128721	+	0.980243i
$315$	40.6662	−	16.8445i	0.129099	−	0.0534746i
$316$	29.0400	−	16.7919i	0.0918986	−	0.0531389i
$317$	−210.177	−	87.0583i	−0.663020	−	0.274632i	0.0256887	−	0.999670i	$-0.491822\pi$
$317$	−210.177	−	87.0583i	−0.663020	−	0.274632i	−0.688709	+	0.725038i	$0.741822\pi$
$318$	−127.474	+	34.2019i	−0.400863	+	0.107553i
$319$			70.5062i			0.221023i
$320$	115.415	−	48.0755i	0.360671	−	0.150236i
$321$	−110.683			−0.344805
$322$	−11.7628	−	43.8411i	−0.0365303	−	0.136152i
$323$	256.891	−	620.191i	0.795330	−	1.92010i
$324$	−136.498	−	236.061i	−0.421292	−	0.728583i
$325$	50.9134	+	122.916i	0.156657	+	0.378202i
$326$	−154.148	−	20.2421i	−0.472848	−	0.0620922i
$327$	−2.51278	−	2.51278i	−0.00768435	−	0.00768435i
$328$	−0.224649	−	225.914i	−0.000684906	−	0.688761i
$329$	66.9481	+	66.9481i	0.203490	+	0.203490i
$330$	4.81355	−	3.69611i	0.0145865	−	0.0112003i
$331$	68.1626	+	164.559i	0.205929	+	0.497158i	0.992775	−	0.119993i	$-0.0382871\pi$
$331$	68.1626	+	164.559i	0.205929	+	0.497158i	−0.786845	+	0.617150i	$0.788287\pi$
$332$	55.1605	−	7.29922i	0.166146	−	0.0219856i
$333$	−43.5846	+	105.222i	−0.130885	+	0.315983i
$334$	−310.154	+	537.614i	−0.928605	+	1.60962i
$335$	146.964			0.438700
$336$	−3.80462	+	29.1981i	−0.0113233	+	0.0868990i
$337$			228.601i			0.678340i	0.940725	+	0.339170i	$0.110146\pi$
$337$			228.601i			0.678340i	−0.940725	+	0.339170i	$0.889854\pi$
$338$	129.481	−	224.440i	0.383081	−	0.664024i
$339$	122.823	+	50.8751i	0.362311	+	0.150074i
$340$	86.3552	−	112.695i	0.253986	−	0.331456i
$341$	−36.0455	+	14.9305i	−0.105705	+	0.0437846i
$342$	499.125	−	383.255i	1.45943	−	1.12063i
$343$	−13.0958	+	13.0958i	−0.0381802	+	0.0381802i
$344$	−136.419	+	330.272i	−0.396566	+	0.960094i
$345$	8.24229	−	8.24229i	0.0238907	−	0.0238907i
$346$	−466.431	−	61.2495i	−1.34807	−	0.177022i
$347$	205.523	−	85.1304i	0.592285	−	0.245333i	−0.0663482	−	0.997797i	$-0.521135\pi$
$347$	205.523	−	85.1304i	0.592285	−	0.245333i	0.658633	+	0.752464i	$0.271135\pi$
$348$	22.6796	−	84.8664i	0.0651712	−	0.243869i
$349$	470.881	+	195.045i	1.34923	+	0.558869i	0.936078	−	0.351793i	$-0.114428\pi$
$349$	470.881	+	195.045i	1.34923	+	0.558869i	0.413152	+	0.910662i	$0.364428\pi$
$350$	−29.0478	−	108.264i	−0.0829936	−	0.309326i
$351$		−	76.5195i		−	0.218004i
$352$	−9.44482	−	70.8332i	−0.0268319	−	0.201231i
$353$	−208.364			−0.590265			−0.295133	−	0.955456i	$-0.595364\pi$
$353$	−208.364			−0.590265			−0.295133	+	0.955456i	$0.595364\pi$
$354$	91.1965	−	24.4684i	0.257617	−	0.0691198i
$355$	49.7396	−	120.082i	0.140112	−	0.338259i
$356$	−106.533	+	398.642i	−0.299249	+	1.11978i
$357$	12.7956	+	30.8914i	0.0358421	+	0.0865305i
$358$	7.04912	−	53.6809i	0.0196903	−	0.149947i
$359$	266.013	+	266.013i	0.740984	+	0.740984i	0.972767	−	0.231784i	$-0.0744562\pi$
$359$	266.013	+	266.013i	0.740984	+	0.740984i	−0.231784	+	0.972767i	$0.574456\pi$
$360$	122.912	−	51.0553i	0.341423	−	0.141820i
$361$	709.987	+	709.987i	1.96672	+	1.96672i
$362$	125.924	+	163.995i	0.347857	+	0.453025i
$363$	30.8808	+	74.5528i	0.0850710	+	0.205380i
$364$	40.4271	−	52.7580i	0.111063	−	0.144939i
$365$	27.0001	−	65.1840i	0.0739729	−	0.178586i
$366$	−119.105	−	68.7128i	−0.325424	−	0.187740i
$367$	550.676			1.50048			0.750240	−	0.661165i	$-0.229938\pi$
$367$	550.676			1.50048			0.750240	+	0.661165i	$0.229938\pi$
$368$	−35.6990	−	132.528i	−0.0970082	−	0.360129i
$369$		−	240.490i		−	0.651735i
$370$	−45.2602	−	26.1110i	−0.122325	−	0.0705703i
$371$	−231.905	−	96.0583i	−0.625082	−	0.258917i
$372$	48.1897	−	6.37679i	0.129542	−	0.0171419i
$373$	−221.545	+	91.7668i	−0.593954	+	0.246024i	−0.659351	−	0.751836i	$-0.729169\pi$
$373$	−221.545	+	91.7668i	−0.593954	+	0.246024i	0.0653968	+	0.997859i	$0.479169\pi$
$374$	−49.4209	−	64.3624i	−0.132141	−	0.172092i
$375$	44.3751	−	44.3751i	0.118334	−	0.118334i
$376$	202.633	+	202.231i	0.538918	+	0.537848i
$377$	−140.214	+	140.214i	−0.371920	+	0.371920i
$378$	−8.39387	+	63.9215i	−0.0222060	+	0.169105i
$379$	−320.165	+	132.616i	−0.844761	+	0.349912i	−0.762729	−	0.646718i	$-0.776141\pi$
$379$	−320.165	+	132.616i	−0.844761	+	0.349912i	−0.0820322	+	0.996630i	$0.526141\pi$
$380$	144.521	+	249.935i	0.380319	+	0.657724i
$381$	156.816	+	64.9553i	0.411591	+	0.170486i
$382$	225.070	−	60.3872i	0.589188	−	0.158082i
$383$		−	470.646i		−	1.22884i	−0.788979	−	0.614420i	$-0.789390\pi$
$383$		−	470.646i		−	1.22884i	0.788979	−	0.614420i	$-0.210610\pi$
$384$	−11.4163	+	88.2981i	−0.0297299	+	0.229943i
$385$	11.5422			0.0299797
$386$	84.4601	+	314.792i	0.218809	+	0.815523i
$387$	−145.570	+	351.438i	−0.376151	+	0.908108i
$388$	355.370	−	205.487i	0.915901	−	0.529606i
$389$	109.044	+	263.254i	0.280318	+	0.676747i	0.999843	−	0.0177196i	$-0.00564061\pi$
$389$	109.044	+	263.254i	0.280318	+	0.676747i	−0.719525	+	0.694466i	$0.755641\pi$
$390$	16.9229	+	2.22224i	0.0433921	+	0.00569804i
$391$	−110.208	−	110.208i	−0.281862	−	0.281862i
$392$	−39.5586	+	39.6373i	−0.100915	+	0.101116i
$393$	60.1662	+	60.1662i	0.153095	+	0.153095i
$394$	243.924	−	187.298i	0.619096	−	0.475375i
$395$	6.26955	+	15.1360i	0.0158723	+	0.0383190i
$396$	−9.97924	−	75.4135i	−0.0252001	−	0.190438i
$397$	218.676	−	527.930i	0.550820	−	1.32980i	−0.366043	−	0.930598i	$-0.619288\pi$
$397$	218.676	−	527.930i	0.550820	−	1.32980i	0.916864	−	0.399200i	$-0.130712\pi$
$398$	−23.0738	+	39.9956i	−0.0579744	+	0.100492i
$399$	−67.9936			−0.170410
$400$	−88.1577	−	327.273i	−0.220394	−	0.818181i
$401$		−	633.058i		−	1.57870i	−0.613944	−	0.789350i	$-0.710418\pi$
$401$		−	633.058i		−	1.57870i	0.613944	−	0.789350i	$-0.289582\pi$
$402$	−52.2973	+	90.6510i	−0.130093	+	0.225500i
$403$	−101.375	−	41.9907i	−0.251550	−	0.104195i
$404$	262.756	+	201.344i	0.650387	+	0.498375i
$405$	123.038	−	50.9641i	0.303798	−	0.125837i
$406$	132.510	−	101.748i	0.326379	−	0.250612i
$407$	−21.1177	+	21.1177i	−0.0518863	+	0.0518863i
$408$	38.7832	+	93.3683i	0.0950569	+	0.228844i
$409$	324.224	−	324.224i	0.792725	−	0.792725i	−0.189212	−	0.981936i	$-0.560593\pi$
$409$	324.224	−	324.224i	0.792725	−	0.792725i	0.981936	+	0.189212i	$0.0605932\pi$
$410$	109.394	+	14.3652i	0.266816	+	0.0350370i
$411$	−16.9461	+	7.01931i	−0.0412314	+	0.0170786i
$412$	197.170	+	52.6915i	0.478568	+	0.127892i
$413$	165.908	+	68.7211i	0.401713	+	0.166395i
$414$	−37.8621	−	141.116i	−0.0914544	−	0.340861i
$415$			27.1746i			0.0654809i
$416$	122.081	−	159.647i	0.293465	−	0.383766i
$417$	−19.4530			−0.0466500
$418$	159.377	−	42.7617i	0.381286	−	0.102301i
$419$	15.1517	−	36.5795i	0.0361617	−	0.0873020i	−0.904767	−	0.425907i	$-0.859955\pi$
$419$	15.1517	−	36.5795i	0.0361617	−	0.0873020i	0.940929	+	0.338605i	$0.109955\pi$
$420$	−13.8930	−	3.71275i	−0.0330786	−	0.00883987i
$421$	195.396	+	471.728i	0.464124	+	1.12049i	0.966689	+	0.255954i	$0.0823897\pi$
$421$	195.396	+	471.728i	0.464124	+	1.12049i	−0.502565	+	0.864539i	$0.667610\pi$
$422$	−66.0540	+	503.018i	−0.156526	+	1.19199i
$423$	215.494	+	215.494i	0.509441	+	0.509441i
$424$	−701.504	−	289.756i	−1.65449	−	0.683386i
$425$	−272.156	−	272.156i	−0.640367	−	0.640367i
$426$	56.3694	+	73.4117i	0.132323	+	0.172328i
$427$	−100.077	−	241.607i	−0.234373	−	0.565825i
$428$	−505.226	−	387.141i	−1.18043	−	0.904536i
$429$	3.73324	−	9.01285i	0.00870220	−	0.0210090i
$430$	−151.167	−	87.2094i	−0.351551	−	0.202813i
$431$	−165.132			−0.383136			−0.191568	−	0.981479i	$-0.561357\pi$
$431$	−165.132			−0.383136			−0.191568	+	0.981479i	$0.561357\pi$
$432$	−25.1885	+	193.306i	−0.0583067	+	0.447467i
$433$			528.816i			1.22128i	0.791907	+	0.610642i	$0.209089\pi$
$433$			528.816i			1.22128i	−0.791907	+	0.610642i	$0.790911\pi$
$434$	80.0783	+	46.1978i	0.184512	+	0.106447i
$435$	39.6365	+	16.4180i	0.0911183	+	0.0377424i
$436$	−2.68082	−	20.2590i	−0.00614867	−	0.0464657i
$437$	292.813	−	121.287i	0.670053	−	0.277545i
$438$	30.5990	+	39.8500i	0.0698607	+	0.0909817i
$439$	−25.1536	+	25.1536i	−0.0572975	+	0.0572975i	−0.735175	−	0.677877i	$-0.762900\pi$
$439$	−25.1536	+	25.1536i	−0.0572975	+	0.0572975i	0.677877	+	0.735175i	$0.262900\pi$
$440$	34.9002	−	0.0347049i	0.0793187	−	7.88748e-5i
$441$	−42.1529	+	42.1529i	−0.0955849	+	0.0955849i
$442$	29.7137	−	226.277i	0.0672255	−	0.511940i
$443$	20.2440	−	8.38535i	0.0456976	−	0.0189286i	−0.359718	−	0.933061i	$-0.617127\pi$
$443$	20.2440	−	8.38535i	0.0456976	−	0.0189286i	0.405415	+	0.914133i	$0.367127\pi$
$444$	32.2117	−	18.6259i	0.0725489	−	0.0419503i
$445$	−186.184	−	77.1200i	−0.418391	−	0.173303i
$446$	−576.678	+	154.725i	−1.29300	+	0.346918i
$447$		−	34.5268i		−	0.0772411i
$448$	−119.495	+	119.971i	−0.266729	+	0.267792i
$449$	−822.991			−1.83294			−0.916471	−	0.400101i	$-0.868975\pi$
$449$	−822.991			−1.83294			−0.916471	+	0.400101i	$0.868975\pi$
$450$	−93.4993	−	348.482i	−0.207776	−	0.774405i
$451$	24.1327	−	58.2615i	0.0535093	−	0.129183i
$452$	382.695	+	661.834i	0.846671	+	1.46423i
$453$	−51.1551	−	123.499i	−0.112925	−	0.272625i
$454$	563.303	+	73.9703i	1.24075	+	0.162930i
$455$	22.9536	+	22.9536i	0.0504474	+	0.0504474i
$456$	−205.593	+	0.204443i	−0.450863	+	0.000448339i
$457$	−348.494	−	348.494i	−0.762568	−	0.762568i	0.214218	−	0.976786i	$-0.431280\pi$
$457$	−348.494	−	348.494i	−0.762568	−	0.762568i	−0.976786	+	0.214218i	$0.931280\pi$
$458$	249.561	−	191.626i	0.544893	−	0.418398i
$459$	84.7134	+	204.516i	0.184561	+	0.445569i
$460$	66.4526	−	8.79348i	0.144462	−	0.0191163i
$461$	309.271	−	746.645i	0.670869	−	1.61962i	−0.109268	−	0.994012i	$-0.534851\pi$
$461$	309.271	−	746.645i	0.670869	−	1.61962i	0.780137	−	0.625609i	$-0.215149\pi$
$462$	−4.10728	+	7.11947i	−0.00889022	+	0.0154101i
$463$	434.921			0.939354			0.469677	−	0.882838i	$-0.344370\pi$
$463$	434.921			0.939354			0.469677	+	0.882838i	$0.344370\pi$
$464$	400.367	−	308.056i	0.862859	−	0.663915i
$465$			23.7404i			0.0510546i
$466$	167.084	−	289.620i	0.358550	−	0.621502i
$467$	−671.182	−	278.013i	−1.43722	−	0.595316i	−0.478097	−	0.878307i	$-0.658673\pi$
$467$	−671.182	−	278.013i	−1.43722	−	0.595316i	−0.959123	+	0.282991i	$0.908673\pi$
$468$	130.127	−	169.818i	0.278050	−	0.362859i
$469$	−183.887	+	76.1686i	−0.392084	+	0.162406i
$470$	−110.896	+	85.1518i	−0.235949	+	0.181174i
$471$	76.3435	−	76.3435i	0.162088	−	0.162088i
$472$	501.864	+	207.294i	1.06327	+	0.439183i
$473$	−70.5321	+	70.5321i	−0.149116	+	0.149116i
$474$	−11.5673	−	1.51896i	−0.0244035	−	0.00320455i
$475$	723.093	−	299.515i	1.52230	−	0.630557i
$476$	−49.6434	+	185.764i	−0.104293	+	0.390261i
$477$	−746.460	−	309.194i	−1.56491	−	0.648205i
$478$	54.3803	+	202.681i	0.113766	+	0.424020i
$479$			498.738i			1.04121i	0.853799	+	0.520603i	$0.174293\pi$
$479$			498.738i			1.04121i	−0.853799	+	0.520603i	$0.825707\pi$
$480$	−42.0196	−	11.1845i	−0.0875408	−	0.0233011i
$481$	−83.9924			−0.174620
$482$	−105.153	+	28.2131i	−0.218160	+	0.0585333i
$483$	−6.04125	+	14.5849i	−0.0125078	+	0.0301964i
$484$	−119.808	+	448.320i	−0.247538	+	0.926281i
$485$	76.7221	+	185.223i	0.158190	+	0.381904i
$486$	−40.9006	+	311.469i	−0.0841577	+	0.640882i
$487$	−174.500	−	174.500i	−0.358316	−	0.358316i	0.504876	−	0.863192i	$-0.331538\pi$
$487$	−174.500	−	174.500i	−0.358316	−	0.358316i	−0.863192	+	0.504876i	$0.831538\pi$
$488$	−303.331	−	730.251i	−0.621580	−	1.49642i
$489$	38.2338	+	38.2338i	0.0781878	+	0.0781878i
$490$	−16.6566	−	21.6925i	−0.0339931	−	0.0442703i
$491$	−294.735	−	711.553i	−0.600275	−	1.44919i	−0.873299	−	0.487184i	$-0.838024\pi$
$491$	−294.735	−	711.553i	−0.600275	−	1.44919i	0.273025	−	0.962007i	$-0.411976\pi$
$492$	−47.7887	+	62.3651i	−0.0971316	+	0.126758i
$493$	219.526	−	529.982i	0.445285	−	1.07501i
$494$	401.988	+	231.910i	0.813741	+	0.469454i
$495$	37.1521			0.0750548
$496$	242.273	+	139.448i	0.488453	+	0.281146i
$497$			176.030i			0.354185i
$498$	−16.7619	−	9.67007i	−0.0336584	−	0.0194178i
$499$	−831.140	−	344.269i	−1.66561	−	0.689919i	−0.667126	−	0.744945i	$-0.732476\pi$
$499$	−831.140	−	344.269i	−1.66561	−	0.689919i	−0.998485	+	0.0550257i	$0.982476\pi$
$500$	357.770	−	47.3426i	0.715539	−	0.0946851i
$501$	199.427	−	82.6053i	0.398057	−	0.164881i
$502$	−200.041	−	260.520i	−0.398489	−	0.518965i
$503$	−391.784	+	391.784i	−0.778895	+	0.778895i	−0.979643	−	0.200748i	$-0.935663\pi$
$503$	−391.784	+	391.784i	−0.778895	+	0.778895i	0.200748	+	0.979643i	$0.435663\pi$
$504$	−127.332	+	127.585i	−0.252642	+	0.253145i
$505$	−114.318	+	114.318i	−0.226373	+	0.226373i
$506$	4.98820	−	37.9864i	0.00985809	−	0.0750719i
$507$	−83.2556	+	34.4856i	−0.164212	+	0.0680189i
$508$	488.610	+	845.003i	0.961830	+	1.66339i
$509$	−574.213	−	237.847i	−1.12812	−	0.467283i	−0.260979	−	0.965344i	$-0.584045\pi$
$509$	−574.213	−	237.847i	−1.12812	−	0.467283i	−0.867142	+	0.498062i	$0.834045\pi$
$510$	−47.6906	+	12.7956i	−0.0935111	+	0.0250894i
$511$			95.5542i			0.186995i
$512$	−360.957	+	363.117i	−0.704994	+	0.709213i
$513$	−450.151			−0.877488
$514$	−96.0275	−	357.905i	−0.186824	−	0.696313i
$515$	−38.1439	+	92.0874i	−0.0740657	+	0.178810i
$516$	107.585	−	62.2096i	0.208499	−	0.120561i
$517$	30.5814	+	73.8301i	0.0591517	+	0.142805i
$518$	70.1641	+	9.21362i	0.135452	+	0.0177869i
$519$	115.690	+	115.690i	0.222909	+	0.222909i
$520$	69.4741	+	69.3361i	0.133604	+	0.133339i
$521$	−237.942	−	237.942i	−0.456702	−	0.456702i	0.440869	−	0.897571i	$-0.354670\pi$
$521$	−237.942	−	237.942i	−0.456702	−	0.456702i	−0.897571	+	0.440869i	$0.854670\pi$
$522$	426.525	−	327.509i	0.817098	−	0.627412i
$523$	−22.1112	−	53.3811i	−0.0422775	−	0.102067i	0.901330	−	0.433133i	$-0.142592\pi$
$523$	−22.1112	−	53.3811i	−0.0422775	−	0.102067i	−0.943608	+	0.331066i	$0.892592\pi$
$524$	64.1897	+	485.084i	0.122499	+	0.925733i
$525$	−14.9187	+	36.0169i	−0.0284165	+	0.0686036i
$526$	−202.063	+	350.251i	−0.384149	+	0.665876i
$527$	317.434			0.602343
$528$	−12.3978	+	21.5396i	−0.0234808	+	0.0407947i
$529$			455.414i			0.860896i
$530$	185.234	−	321.081i	0.349499	−	0.605813i
$531$	534.025	+	221.201i	1.00570	+	0.416574i
$532$	−310.366	−	237.826i	−0.583395	−	0.447041i
$533$	163.855	−	67.8710i	0.307420	−	0.127338i
$534$	113.823	−	87.3994i	0.213152	−	0.163669i
$535$	219.810	−	219.810i	0.410860	−	0.410860i
$536$	−555.794	+	230.865i	−1.03693	+	0.430719i
$537$	−13.3146	+	13.3146i	−0.0247944	+	0.0247944i
$538$	−98.4859	−	12.9327i	−0.183059	−	0.0240385i
$539$	−14.4420	+	5.98207i	−0.0267941	+	0.0110985i
$540$	−91.9785	−	24.5802i	−0.170331	−	0.0455189i
$541$	354.065	+	146.658i	0.654464	+	0.271088i	0.685107	−	0.728443i	$-0.259756\pi$
$541$	354.065	+	146.658i	0.654464	+	0.271088i	−0.0306431	+	0.999530i	$0.509756\pi$
$542$	−9.73079	−	36.2677i	−0.0179535	−	0.0669146i
$543$		−	71.9095i		−	0.132430i
$544$	−149.549	+	561.847i	−0.274906	+	1.03281i
$545$	9.98052			0.0183129
$546$	−22.3263	+	5.99025i	−0.0408907	+	0.0109712i
$547$	103.588	−	250.083i	0.189374	−	0.457189i	−0.800465	−	0.599379i	$-0.795414\pi$
$547$	103.588	−	250.083i	0.189374	−	0.457189i	0.989839	+	0.142190i	$0.0454143\pi$
$548$	−101.905	−	27.2329i	−0.185957	−	0.0496951i
$549$	−322.130	−	777.689i	−0.586757	−	1.41656i
$550$	12.3182	−	93.8063i	0.0223967	−	0.170557i
$551$	824.853	+	824.853i	1.49701	+	1.49701i
$552$	−18.2232	+	44.1186i	−0.0330130	+	0.0799251i
$553$	−15.6894	−	15.6894i	−0.0283714	−	0.0283714i
$554$	20.1764	+	26.2764i	0.0364195	+	0.0474303i
$555$	6.95431	+	16.7892i	0.0125303	+	0.0302508i
$556$	−88.7961	−	68.0421i	−0.159705	−	0.122378i
$557$	120.210	−	290.214i	0.215818	−	0.521030i	−0.778480	−	0.627669i	$-0.784009\pi$
$557$	120.210	−	290.214i	0.215818	−	0.521030i	0.994298	+	0.106639i	$0.0340090\pi$
$558$	257.757	+	148.702i	0.461930	+	0.266492i
$559$	−280.530			−0.501843
$560$	−50.4302	−	65.5417i	−0.0900538	−	0.117039i
$561$			28.2219i			0.0503065i
$562$	−545.291	−	314.583i	−0.970268	−	0.559756i
$563$	79.9556	+	33.1187i	0.142017	+	0.0588254i	0.452560	−	0.891734i	$-0.350511\pi$
$563$	79.9556	+	33.1187i	0.142017	+	0.0588254i	−0.310543	+	0.950559i	$0.600511\pi$
$564$	−13.0612	−	98.7043i	−0.0231582	−	0.175008i
$565$	−344.957	+	142.886i	−0.610543	+	0.252895i
$566$	328.428	+	427.723i	0.580262	+	0.755694i
$567$	−127.536	+	127.536i	−0.224932	+	0.224932i
$568$	0.529286	+	532.265i	0.000931841	+	0.937086i
$569$	179.051	−	179.051i	0.314676	−	0.314676i	−0.532042	−	0.846718i	$-0.678575\pi$
$569$	179.051	−	179.051i	0.314676	−	0.314676i	0.846718	+	0.532042i	$0.178575\pi$
$570$	13.0730	−	99.5546i	0.0229352	−	0.174657i
$571$	377.516	−	156.372i	0.661149	−	0.273857i	−0.0267729	−	0.999642i	$-0.508523\pi$
$571$	377.516	−	156.372i	0.661149	−	0.273857i	0.687922	+	0.725785i	$0.258523\pi$
$572$	48.5657	−	28.0824i	0.0849051	−	0.0490950i
$573$	−74.8753	−	31.0144i	−0.130672	−	0.0541263i
$574$	−144.323	+	38.7226i	−0.251435	+	0.0674610i
$575$		−	181.718i		−	0.316031i
$576$	−384.631	+	386.164i	−0.667762	+	0.670424i
$577$	−876.819			−1.51962			−0.759808	−	0.650147i	$-0.774707\pi$
$577$	−876.819			−1.51962			−0.759808	+	0.650147i	$0.774707\pi$
$578$	21.3085	+	79.4193i	0.0368660	+	0.137404i
$579$	43.3780	−	104.724i	0.0749188	−	0.180870i
$580$	123.500	+	213.581i	0.212931	+	0.368243i
$581$	−14.0840	−	34.0018i	−0.0242410	−	0.0585229i
$582$	−141.552	−	18.5879i	−0.243216	−	0.0319379i
$583$	−149.811	−	149.811i	−0.256966	−	0.256966i
$584$	0.287312	+	288.929i	0.000491972	+	0.494741i
$585$	73.8833	+	73.8833i	0.126296	+	0.126296i
$586$	−143.297	+	110.031i	−0.244535	+	0.187767i
$587$	−2.16109	−	5.21733i	−0.00368158	−	0.00888812i	0.922028	−	0.387123i	$-0.126531\pi$
$587$	−2.16109	−	5.21733i	−0.00368158	−	0.00888812i	−0.925710	+	0.378235i	$0.876531\pi$
$588$	19.3077	−	2.55493i	0.0328362	−	0.00434511i
$589$	−247.024	+	596.370i	−0.419396	+	1.01251i
$590$	−132.519	+	229.705i	−0.224608	+	0.389330i
$591$	−106.957			−0.180976
$592$	212.184	+	27.6484i	0.358419	+	0.0467033i
$593$		−	925.041i		−	1.55993i	−0.625821	−	0.779967i	$-0.715236\pi$
$593$		−	925.041i		−	1.55993i	0.625821	−	0.779967i	$-0.284764\pi$
$594$	−27.1922	+	47.1344i	−0.0457782	+	0.0793509i
$595$	−86.7603	−	35.9373i	−0.145816	−	0.0603988i
$596$	120.766	−	157.602i	0.202628	−	0.264433i
$597$	14.8363	−	6.14539i	0.0248514	−	0.0102938i
$598$	85.4623	−	65.6226i	0.142914	−	0.109737i
$599$	26.4007	−	26.4007i	0.0440746	−	0.0440746i	−0.684726	−	0.728801i	$-0.740078\pi$
$599$	26.4007	−	26.4007i	0.0440746	−	0.0440746i	0.728801	+	0.684726i	$0.240078\pi$
$600$	−45.0015	+	108.950i	−0.0750026	+	0.181583i
$601$	−792.247	+	792.247i	−1.31821	+	1.31821i	−0.403026	+	0.915189i	$0.632041\pi$
$601$	−792.247	+	792.247i	−1.31821	+	1.31821i	−0.915189	+	0.403026i	$0.867959\pi$
$602$	234.344	+	30.7730i	0.389276	+	0.0511180i
$603$	−591.899	+	245.173i	−0.981591	+	0.406588i
$604$	198.467	−	742.658i	0.328588	−	1.22957i
$605$	−209.386	−	86.7304i	−0.346092	−	0.143356i
$606$	−29.8339	−	111.194i	−0.0492309	−	0.183489i
$607$			625.862i			1.03107i	0.856867	+	0.515537i	$0.172408\pi$
$607$			625.862i			1.03107i	−0.856867	+	0.515537i	$0.827592\pi$
$608$	−939.174	−	718.184i	−1.54469	−	1.18122i
$609$	−58.1037			−0.0954084
$610$	372.997	−	100.077i	0.611471	−	0.164060i
$611$	−86.0074	+	207.640i	−0.140765	+	0.339837i
$612$	−159.793	+	597.940i	−0.261099	+	0.977026i
$613$	−41.1666	−	99.3849i	−0.0671559	−	0.162129i	0.886738	−	0.462272i	$-0.152966\pi$
$613$	−41.1666	−	99.3849i	−0.0671559	−	0.162129i	−0.953894	+	0.300143i	$0.902966\pi$
$614$	−23.6081	+	179.782i	−0.0384497	+	0.292804i
$615$	−27.1334	−	27.1334i	−0.0441193	−	0.0441193i
$616$	−43.6505	+	18.1315i	−0.0708612	+	0.0294342i
$617$	−289.658	−	289.658i	−0.469462	−	0.469462i	0.432278	−	0.901740i	$-0.357710\pi$
$617$	−289.658	−	289.658i	−0.469462	−	0.469462i	−0.901740	+	0.432278i	$0.857710\pi$
$618$	−43.2281	−	56.2973i	−0.0699484	−	0.0910959i
$619$	259.369	+	626.173i	0.419013	+	1.01159i	0.982634	+	0.185554i	$0.0594079\pi$
$619$	259.369	+	626.173i	0.419013	+	1.01159i	−0.563621	+	0.826034i	$0.690592\pi$
$620$	−83.0383	+	108.366i	−0.133933	+	0.174784i
$621$	−39.9961	+	96.5590i	−0.0644059	+	0.155490i
$622$	1057.54	+	610.103i	1.70022	+	0.980874i
$623$	272.930			0.438090
$624$	−67.4904	+	18.1799i	−0.108158	+	0.0291345i
$625$		−	353.337i		−	0.565340i
$626$	5.71462	+	3.29681i	0.00912878	+	0.00526647i
$627$	−53.0210	−	21.9620i	−0.0845631	−	0.0350272i
$628$	615.512	−	81.4489i	0.980115	−	0.129696i
$629$	224.489	−	92.9865i	0.356899	−	0.147832i
$630$	−53.6146	−	69.8240i	−0.0851026	−	0.110832i
$631$	−196.095	+	196.095i	−0.310768	+	0.310768i	−0.845207	−	0.534439i	$-0.820523\pi$
$631$	−196.095	+	196.095i	−0.310768	+	0.310768i	0.534439	+	0.845207i	$0.320523\pi$
$632$	−47.4874	−	47.3930i	−0.0751382	−	0.0749890i
$633$	124.765	−	124.765i	0.197101	−	0.197101i
$634$	−59.2384	+	451.116i	−0.0934360	+	0.711539i
$635$	−440.427	+	182.431i	−0.693586	+	0.287293i
$636$	132.134	+	228.513i	0.207758	+	0.359298i
$637$	−40.6167	−	16.8240i	−0.0637625	−	0.0264113i
$638$	136.195	−	36.5419i	0.213472	−	0.0572756i
$639$			566.608i			0.886711i
$640$	−152.683	−	198.028i	−0.238568	−	0.309419i
$641$	−950.236			−1.48243			−0.741213	−	0.671270i	$-0.765749\pi$
$641$	−950.236			−1.48243			−0.741213	+	0.671270i	$0.765749\pi$
$642$	57.3644	+	213.803i	0.0893526	+	0.333027i
$643$	262.428	−	633.557i	0.408130	−	0.985314i	−0.577499	−	0.816391i	$-0.695971\pi$
$643$	262.428	−	633.557i	0.408130	−	0.985314i	0.985629	−	0.168923i	$-0.0540288\pi$
$644$	−78.5905	+	45.4438i	−0.122035	+	0.0705648i
$645$	23.2270	+	56.0750i	0.0360109	+	0.0869380i
$646$	−1331.15	−	174.801i	−2.06061	−	0.270589i
$647$	283.714	+	283.714i	0.438508	+	0.438508i	0.891510	−	0.453002i	$-0.149647\pi$
$647$	283.714	+	283.714i	0.438508	+	0.438508i	−0.453002	+	0.891510i	$0.649647\pi$
$648$	−385.250	+	386.017i	−0.594521	+	0.595705i
$649$	107.177	+	107.177i	0.165141	+	0.165141i
$650$	211.047	−	162.053i	0.324687	−	0.249312i
$651$	−12.3042	−	29.7049i	−0.0189004	−	0.0456296i
$652$	40.7907	+	308.257i	0.0625624	+	0.472786i
$653$	53.2215	−	128.488i	0.0815031	−	0.196766i	−0.877875	−	0.478890i	$-0.841039\pi$
$653$	53.2215	−	128.488i	0.0815031	−	0.196766i	0.959378	+	0.282124i	$0.0910391\pi$
$654$	−3.55157	+	6.15621i	−0.00543053	+	0.00941317i
$655$	−238.974			−0.364846
$656$	−436.277	+	117.520i	−0.665056	+	0.179147i
$657$			307.571i			0.468145i
$658$	94.6246	−	164.020i	0.143806	−	0.249271i
$659$	9.86433	+	4.08594i	0.0149686	+	0.00620021i	0.390155	−	0.920749i	$-0.372421\pi$
$659$	9.86433	+	4.08594i	0.0149686	+	0.00620021i	−0.375187	+	0.926949i	$0.622421\pi$
$660$	−9.63445	−	7.38263i	−0.0145977	−	0.0111858i
$661$	333.350	−	138.078i	0.504311	−	0.208892i	−0.115999	−	0.993249i	$-0.537007\pi$
$661$	333.350	−	138.078i	0.504311	−	0.208892i	0.620310	+	0.784357i	$0.287007\pi$
$662$	282.548	−	216.956i	0.426810	−	0.327728i
$663$	−56.1242	+	56.1242i	−0.0846518	+	0.0846518i
$664$	−42.6883	−	102.769i	−0.0642896	−	0.154773i
$665$	135.032	−	135.032i	0.203056	−	0.203056i
$666$	225.845	+	29.6569i	0.339107	+	0.0445299i
$667$	250.222	−	103.645i	0.375146	−	0.155391i
$668$	1199.24	+	320.485i	1.79528	+	0.479767i
$669$	191.847	+	79.4656i	0.286767	+	0.118783i
$670$	−76.1685	−	283.888i	−0.113684	−	0.423714i
$671$		−	220.729i		−	0.328956i
$672$	58.3732	−	7.78342i	0.0868649	−	0.0115825i
$673$	1036.18			1.53965			0.769824	−	0.638256i	$-0.220344\pi$
$673$	1036.18			1.53965			0.769824	+	0.638256i	$0.220344\pi$
$674$	441.583	−	118.479i	0.655168	−	0.175784i
$675$	−98.7690	+	238.450i	−0.146325	+	0.353259i
$676$	−500.654	−	133.794i	−0.740612	−	0.197920i
$677$	198.976	+	480.371i	0.293909	+	0.709559i	0.999999	+	0.00143687i	$0.000457372\pi$
$677$	198.976	+	480.371i	0.293909	+	0.709559i	−0.706090	+	0.708122i	$0.749543\pi$
$678$	34.6177	−	263.623i	0.0510586	−	0.388825i
$679$	−191.995	−	191.995i	−0.282761	−	0.282761i
$680$	−262.446	−	108.403i	−0.385951	−	0.159417i
$681$	−139.717	−	139.717i	−0.205165	−	0.205165i
$682$	47.5226	+	61.8902i	0.0696813	+	0.0907481i
$683$	−57.9171	−	139.824i	−0.0847980	−	0.204721i	0.875793	−	0.482688i	$-0.160339\pi$
$683$	−57.9171	−	139.824i	−0.0847980	−	0.204721i	−0.960591	+	0.277967i	$0.910339\pi$
$684$	−999.011	−	765.517i	−1.46054	−	1.11918i
$685$	19.7141	−	47.5941i	0.0287798	−	0.0694805i
$686$	32.0842	+	18.5096i	0.0467699	+	0.0269820i
$687$	−109.429			−0.159285
$688$	708.683	+	92.3442i	1.03006	+	0.134221i
$689$		−	595.851i		−	0.864806i
$690$	−20.1933	−	11.6497i	−0.0292656	−	0.0168836i
$691$	986.285	+	408.532i	1.42733	+	0.591219i	0.956691	−	0.291107i	$-0.0940235\pi$
$691$	986.285	+	408.532i	1.42733	+	0.591219i	0.470639	+	0.882326i	$0.344023\pi$
$692$	123.427	+	932.739i	0.178362	+	1.34789i
$693$	−46.4861	+	19.2552i	−0.0670795	+	0.0277852i
$694$	−270.963	−	352.883i	−0.390436	−	0.508477i
$695$	38.6328	−	38.6328i	0.0555867	−	0.0555867i
$696$	−175.689	+	0.174706i	−0.252427	+	0.000251014i
$697$	−362.802	+	362.802i	−0.520520	+	0.520520i
$698$	132.718	−	1010.68i	0.190140	−	1.44797i
$699$	−107.434	+	44.5006i	−0.153697	+	0.0636632i
$700$	−194.077	+	112.222i	−0.277253	+	0.160317i
$701$	1291.47	+	534.944i	1.84232	+	0.763115i	0.950494	+	0.310743i	$0.100578\pi$
$701$	1291.47	+	534.944i	1.84232	+	0.763115i	0.891829	+	0.452372i	$0.149422\pi$
$702$	−147.811	+	39.6584i	−0.210557	+	0.0564935i
$703$			494.113i			0.702863i
$704$	−131.932	+	54.9557i	−0.187403	+	0.0780621i
$705$	48.6262			0.0689733
$706$	107.990	+	402.492i	0.152961	+	0.570102i
$707$	83.7905	−	202.288i	0.118516	−	0.286122i
$708$	−94.5303	−	163.481i	−0.133517	−	0.230905i
$709$	−318.805	−	769.664i	−0.449655	−	1.08556i	−0.972451	−	0.233105i	$-0.925111\pi$
$709$	−318.805	−	769.664i	−0.449655	−	1.08556i	0.522797	−	0.852457i	$-0.324889\pi$
$710$	−257.739	−	33.8451i	−0.363013	−	0.0476691i
$711$	−50.5012	−	50.5012i	−0.0710284	−	0.0710284i
$712$	825.263	−	0.820644i	1.15908	−	0.00115259i
$713$	105.975	+	105.975i	0.148633	+	0.148633i
$714$	53.0406	−	40.7274i	0.0742866	−	0.0570412i
$715$	10.4850	+	25.3131i	0.0146644	+	0.0354030i
$716$	−107.348	+	14.2050i	−0.149927	+	0.0198394i
$717$	27.9293	−	67.4272i	0.0389530	−	0.0940408i
$718$	375.983	−	651.721i	0.523654	−	0.907689i
$719$	−171.790			−0.238929			−0.119465	−	0.992838i	$-0.538118\pi$
$719$	−171.790			−0.238929			−0.119465	+	0.992838i	$0.538118\pi$
$720$	−162.325	−	210.967i	−0.225452	−	0.293009i
$721$		−	134.992i		−	0.187229i
$722$	1003.50	−	1739.44i	1.38989	−	2.40920i
$723$	34.9819	+	14.4900i	0.0483844	+	0.0200415i
$724$	251.522	−	328.241i	0.347407	−	0.453371i
$725$	617.916	−	255.949i	0.852298	−	0.353033i
$726$	128.007	−	98.2908i	0.176319	−	0.135387i
$727$	168.124	−	168.124i	0.231258	−	0.231258i	−0.581960	−	0.813218i	$-0.697714\pi$
$727$	168.124	−	168.124i	0.231258	−	0.231258i	0.813218	+	0.581960i	$0.197714\pi$
$728$	−122.864	−	50.7489i	−0.168769	−	0.0697100i
$729$	−356.583	+	356.583i	−0.489140	+	0.489140i
$730$	−139.908	−	18.3721i	−0.191655	−	0.0251672i
$731$	749.783	−	310.570i	1.02569	−	0.424857i
$732$	−71.0015	+	265.686i	−0.0969966	+	0.362958i
$733$	690.214	+	285.896i	0.941629	+	0.390035i	0.800078	−	0.599896i	$-0.204791\pi$
$733$	690.214	+	285.896i	0.941629	+	0.390035i	0.141550	+	0.989931i	$0.454791\pi$
$734$	−285.404	−	1063.73i	−0.388833	−	1.44922i
$735$			9.51183i			0.0129413i
$736$	−237.499	+	137.645i	−0.322688	+	0.187018i
$737$	−167.997			−0.227947
$738$	−464.550	+	124.641i	−0.629472	+	0.168890i
$739$	317.679	−	766.944i	0.429876	−	1.03781i	−0.549450	−	0.835527i	$-0.685163\pi$
$739$	317.679	−	766.944i	0.429876	−	1.03781i	0.979326	−	0.202287i	$-0.0648373\pi$
$740$	−26.9807	+	100.961i	−0.0364604	+	0.136434i
$741$	−61.7662	−	149.117i	−0.0833551	−	0.201237i
$742$	−65.3624	+	497.752i	−0.0880895	+	0.670824i
$743$	286.566	+	286.566i	0.385688	+	0.385688i	0.873146	−	0.487458i	$-0.162076\pi$
$743$	286.566	+	286.566i	0.385688	+	0.385688i	−0.487458	+	0.873146i	$0.662076\pi$
$744$	−37.2936	−	89.7820i	−0.0501258	−	0.120675i
$745$	68.5685	+	68.5685i	0.0920382	+	0.0920382i
$746$	292.086	+	380.393i	0.391536	+	0.509910i
$747$	−45.3338	−	109.446i	−0.0606878	−	0.146513i
$748$	−98.7137	+	128.823i	−0.131970	+	0.172223i
$749$	−161.112	+	388.958i	−0.215102	+	0.519303i
$750$	−108.717	−	62.7198i	−0.144956	−	0.0836264i
$751$	1161.38			1.54645			0.773226	−	0.634131i	$-0.218642\pi$
$751$	1161.38			1.54645			0.773226	+	0.634131i	$0.218642\pi$
$752$	285.625	−	496.235i	0.379820	−	0.659886i
$753$			114.234i			0.151706i
$754$	343.518	+	198.178i	0.455594	+	0.262836i
$755$	346.855	+	143.672i	0.459411	+	0.190294i
$756$	127.826	−	16.9149i	0.169082	−	0.0223742i
$757$	−1034.46	+	428.489i	−1.36653	+	0.566035i	−0.940845	−	0.338836i	$-0.889967\pi$
$757$	−1034.46	+	428.489i	−1.36653	+	0.566035i	−0.425685	+	0.904871i	$0.639967\pi$
$758$	422.107	+	549.723i	0.556869	+	0.725228i
$759$	−9.42187	+	9.42187i	−0.0124135	+	0.0124135i
$760$	407.892	−	408.704i	0.536700	−	0.537769i
$761$	−295.368	+	295.368i	−0.388132	+	0.388132i	−0.874021	−	0.485889i	$-0.838496\pi$
$761$	−295.368	+	295.368i	−0.388132	+	0.388132i	0.485889	+	0.874021i	$0.338496\pi$
$762$	44.1985	−	336.583i	0.0580033	−	0.441710i
$763$	−12.4880	+	5.17270i	−0.0163670	+	0.00677942i
$764$	−233.298	−	403.465i	−0.305363	−	0.528096i
$765$	−279.265	−	115.675i	−0.365053	−	0.151210i
$766$	−909.137	+	243.925i	−1.18686	+	0.318440i
$767$			426.278i			0.555774i
$768$	176.480	−	23.7103i	0.229792	−	0.0308729i
$769$	990.349			1.28784			0.643920	−	0.765093i	$-0.277307\pi$
$769$	990.349			1.28784			0.643920	+	0.765093i	$0.277307\pi$
$770$	−5.98206	−	22.2958i	−0.00776891	−	0.0289556i
$771$	−49.3189	+	119.066i	−0.0639675	+	0.154431i
$772$	564.304	−	326.300i	0.730963	−	0.422668i
$773$	−344.890	−	832.639i	−0.446171	−	1.07715i	−0.973745	−	0.227643i	$-0.926898\pi$
$773$	−344.890	−	832.639i	−0.446171	−	1.07715i	0.527574	−	0.849509i	$-0.323102\pi$
$774$	754.311	+	99.0526i	0.974562	+	0.127975i
$775$	261.702	+	261.702i	0.337680	+	0.337680i
$776$	−581.115	−	579.961i	−0.748860	−	0.747372i
$777$	−17.4030	−	17.4030i	−0.0223977	−	0.0223977i
$778$	452.008	−	347.076i	0.580988	−	0.446114i
$779$	−399.273	−	963.931i	−0.512546	−	1.23740i
$780$	−4.47813	−	33.8414i	−0.00574119	−	0.0433864i
$781$	−56.8580	+	137.267i	−0.0728015	+	0.175758i
$782$	−155.768	+	270.006i	−0.199192	+	0.345276i
$783$	−384.675			−0.491284
$784$	97.0690	+	55.8713i	0.123813	+	0.0712645i
$785$			303.229i			0.386279i
$786$	85.0390	−	147.405i	0.108192	−	0.187538i
$787$	345.835	+	143.249i	0.439434	+	0.182020i	0.591421	−	0.806363i	$-0.298567\pi$
$787$	345.835	+	143.249i	0.439434	+	0.182020i	−0.151987	+	0.988383i	$0.548567\pi$
$788$	−488.220	−	374.110i	−0.619568	−	0.474759i
$789$	129.925	−	53.8166i	0.164670	−	0.0682086i
$790$	25.9886	−	19.9554i	0.0328969	−	0.0252600i
$791$	357.568	−	357.568i	0.452046	−	0.452046i
$792$	−140.503	+	58.3619i	−0.177402	+	0.0736893i
$793$	438.958	−	438.958i	0.553541	−	0.553541i
$794$	−1133.13	−	148.797i	−1.42711	−	0.187402i
$795$	−119.104	+	49.3346i	−0.149817	+	0.0620561i
$796$	89.2174	+	23.8424i	0.112082	+	0.0299527i
$797$	−490.684	−	203.248i	−0.615663	−	0.255016i	0.0529846	−	0.998595i	$-0.483127\pi$
$797$	−490.684	−	203.248i	−0.615663	−	0.255016i	−0.668648	+	0.743579i	$0.733127\pi$
$798$	35.2396	+	131.342i	0.0441599	+	0.164589i
$799$		−	650.184i		−	0.813748i
$800$	−586.496	+	339.911i	−0.733120	+	0.424888i
$801$	878.512			1.09677
$802$	−1222.87	+	328.100i	−1.52477	+	0.409103i
$803$	−30.8642	+	74.5127i	−0.0384361	+	0.0927929i
$804$	202.213	+	54.0392i	0.251509	+	0.0672130i
$805$	−16.9672	−	40.9625i	−0.0210773	−	0.0508850i
$806$	−28.5724	+	217.586i	−0.0354496	+	0.269958i
$807$	24.4277	+	24.4277i	0.0302698	+	0.0302698i
$808$	252.750	−	611.913i	0.312810	−	0.757319i
$809$	−628.886	−	628.886i	−0.777362	−	0.777362i	0.202019	−	0.979382i	$-0.435250\pi$
$809$	−628.886	−	628.886i	−0.777362	−	0.777362i	−0.979382	+	0.202019i	$0.935250\pi$
$810$	−162.214	−	211.257i	−0.200264	−	0.260811i
$811$	480.828	+	1160.82i	0.592883	+	1.43135i	0.880706	+	0.473663i	$0.157069\pi$
$811$	480.828	+	1160.82i	0.592883	+	1.43135i	−0.287822	+	0.957684i	$0.592931\pi$
$812$	−265.222	−	203.233i	−0.326629	−	0.250287i
$813$	−4.99765	+	12.0654i	−0.00614717	+	0.0148406i
$814$	51.7375	+	29.8478i	0.0635596	+	0.0366681i
$815$	−151.861			−0.186333
$816$	160.257	−	123.308i	0.196394	−	0.151112i
$817$			1650.31i			2.01997i
$818$	−794.336	−	458.259i	−0.971071	−	0.560219i
$819$	−130.738	−	54.1533i	−0.159631	−	0.0661213i
$820$	−28.9479	−	218.760i	−0.0353023	−	0.266781i
$821$	112.591	−	46.6367i	0.137139	−	0.0568048i	−0.313059	−	0.949734i	$-0.601354\pi$
$821$	112.591	−	46.6367i	0.137139	−	0.0568048i	0.450197	+	0.892929i	$0.351354\pi$
$822$	22.3419	+	29.0965i	0.0271799	+	0.0353972i
$823$	742.251	−	742.251i	0.901884	−	0.901884i	−0.0937147	−	0.995599i	$-0.529874\pi$
$823$	742.251	−	742.251i	0.901884	−	0.901884i	0.995599	+	0.0937147i	$0.0298742\pi$
$824$	−0.405894	−	408.178i	−0.000492590	−	0.495362i
$825$	−23.2670	+	23.2670i	−0.0282024	+	0.0282024i
$826$	46.7610	−	356.097i	0.0566113	−	0.431110i
$827$	794.518	−	329.100i	0.960723	−	0.397945i	0.153472	−	0.988153i	$-0.450954\pi$
$827$	794.518	−	329.100i	0.960723	−	0.397945i	0.807251	+	0.590208i	$0.200954\pi$
$828$	−252.968	+	146.275i	−0.305517	+	0.176661i
$829$	−304.267	−	126.031i	−0.367029	−	0.152028i	0.191544	−	0.981484i	$-0.438651\pi$
$829$	−304.267	−	126.031i	−0.367029	−	0.152028i	−0.558572	+	0.829456i	$0.688651\pi$
$830$	52.4925	−	14.0840i	0.0632440	−	0.0169687i
$831$		−	11.5218i		−	0.0138650i
$832$	−371.658	−	153.081i	−0.446705	−	0.183991i
$833$	127.183			0.152681
$834$	10.0821	+	37.5770i	0.0120888	+	0.0450564i
$835$	−232.002	+	560.102i	−0.277846	+	0.670781i
$836$	−165.204	−	285.704i	−0.197612	−	0.341751i
$837$	−81.4596	−	196.661i	−0.0973233	−	0.234959i
$838$	−78.5128	−	10.3099i	−0.0936906	−	0.0123030i
$839$	−171.772	−	171.772i	−0.204734	−	0.204734i	0.597291	−	0.802025i	$-0.296244\pi$
$839$	−171.772	−	171.772i	−0.204734	−	0.204734i	−0.802025	+	0.597291i	$0.796244\pi$
$840$	0.0286001	+	28.7611i	3.40477e−5	+	0.0342393i
$841$	110.199	+	110.199i	0.131033	+	0.131033i
$842$	809.958	−	621.929i	0.961945	−	0.738633i
$843$	83.7848	+	202.274i	0.0993888	+	0.239946i
$844$	1005.90	−	133.108i	1.19183	−	0.157711i
$845$	96.8548	−	233.828i	0.114621	−	0.276720i
$846$	304.579	−	527.950i	0.360022	−	0.624055i
$847$	306.942			0.362387
$848$	−196.141	+	1505.26i	−0.231298	+	1.77507i
$849$		−	187.550i		−	0.220907i
$850$	−384.665	+	666.770i	−0.452548	+	0.784436i
$851$	105.989	+	43.9021i	0.124546	+	0.0515888i
$852$	112.593	−	146.935i	0.132151	−	0.172459i
$853$	1081.19	−	447.845i	1.26752	−	0.525024i	0.355310	−	0.934748i	$-0.384375\pi$
$853$	1081.19	−	447.845i	1.26752	−	0.525024i	0.912209	+	0.409724i	$0.134375\pi$
$854$	−414.840	+	318.537i	−0.485762	+	0.372994i
$855$	434.643	−	434.643i	0.508354	−	0.508354i
$856$	−485.986	+	1176.58i	−0.567740	+	1.37451i
$857$	−804.153	+	804.153i	−0.938335	+	0.938335i	−0.998206	−	0.0598714i	$-0.980931\pi$
$857$	−804.153	+	804.153i	−0.938335	+	0.938335i	0.0598714	+	0.998206i	$0.480931\pi$
$858$	−19.3448	−	2.54027i	−0.0225464	−	0.00296068i
$859$	−1401.58	+	580.555i	−1.63164	+	0.675849i	−0.995415	−	0.0956500i	$-0.969507\pi$
$859$	−1401.58	+	580.555i	−1.63164	+	0.675849i	−0.636230	+	0.771499i	$0.719507\pi$
$860$	−90.1142	+	337.205i	−0.104784	+	0.392099i
$861$	48.0129	+	19.8876i	0.0557642	+	0.0230983i
$862$	85.5841	+	318.981i	0.0992855	+	0.370048i
$863$			1702.68i			1.97297i	0.163844	+	0.986486i	$0.447611\pi$
$863$			1702.68i			1.97297i	−0.163844	+	0.986486i	$0.552389\pi$
$864$	386.459	−	51.5301i	0.447291	−	0.0596413i
$865$	−459.509			−0.531225
$866$	1021.50	−	274.074i	1.17956	−	0.316483i
$867$	10.9439	−	26.4209i	0.0126227	−	0.0304739i
$868$	47.7366	−	178.629i	0.0549961	−	0.205794i
$869$	−7.16680	−	17.3022i	−0.00824718	−	0.0199104i
$870$	11.1715	−	85.0741i	0.0128408	−	0.0977863i
$871$	−334.091	−	334.091i	−0.383571	−	0.383571i
$872$	−37.7446	+	15.6783i	−0.0432851	+	0.0179797i
$873$	−617.996	−	617.996i	−0.707899	−	0.707899i
$874$	−386.047	−	502.760i	−0.441701	−	0.575241i
$875$	−91.3485	−	220.535i	−0.104398	−	0.252040i
$876$	61.1187	−	79.7608i	0.0697702	−	0.0910512i
$877$	−441.028	+	1064.74i	−0.502883	+	1.21407i	0.445024	+	0.895519i	$0.353195\pi$
$877$	−441.028	+	1064.74i	−0.502883	+	1.21407i	−0.947907	+	0.318548i	$0.896805\pi$
$878$	61.6253	+	35.5521i	0.0701883	+	0.0404922i
$879$	62.8338			0.0714832
$880$	−18.1551	−	67.3981i	−0.0206308	−	0.0765887i
$881$			1381.98i			1.56864i	0.620354	+	0.784322i	$0.286989\pi$
$881$			1381.98i			1.56864i	−0.620354	+	0.784322i	$0.713011\pi$
$882$	103.273	+	59.5790i	0.117090	+	0.0675499i
$883$	−1043.17	−	432.094i	−1.18139	−	0.489348i	−0.296448	−	0.955049i	$-0.595802\pi$
$883$	−1043.17	−	432.094i	−1.18139	−	0.489348i	−0.884942	+	0.465701i	$0.845802\pi$
$884$	−452.496	+	59.8774i	−0.511873	+	0.0677346i
$885$	85.2085	−	35.2945i	0.0962808	−	0.0398808i
$886$	−26.6899	−	34.7591i	−0.0301240	−	0.0392314i
$887$	68.5041	−	68.5041i	0.0772312	−	0.0772312i	−0.667436	−	0.744667i	$-0.732608\pi$
$887$	68.5041	−	68.5041i	0.0772312	−	0.0772312i	0.744667	+	0.667436i	$0.232608\pi$
$888$	−52.6740	−	52.5693i	−0.0593175	−	0.0591997i
$889$	456.529	−	456.529i	0.513530	−	0.513530i
$890$	−52.4759	+	399.618i	−0.0589617	+	0.449009i
$891$	−140.646	+	58.2576i	−0.157852	+	0.0653846i
$892$	597.760	+	1033.77i	0.670134	+	1.15893i
$893$	1221.51	+	505.967i	1.36787	+	0.566592i
$894$	−66.6947	+	17.8945i	−0.0746025	+	0.0200162i
$895$		−	52.8843i		−	0.0590886i
$896$	293.677	+	168.647i	0.327764	+	0.188222i
$897$	−37.4740			−0.0417770
$898$	426.539	+	1589.76i	0.474987	+	1.77033i
$899$	−211.094	+	509.625i	−0.234810	+	0.566880i
$900$	−624.697	+	361.222i	−0.694108	+	0.401357i
$901$	659.657	+	1592.55i	0.732138	+	1.76754i
$902$	−125.050	−	16.4210i	−0.138636	−	0.0182051i
$903$	−58.1250	−	58.1250i	−0.0643688	−	0.0643688i
$904$	1080.11	−	1082.26i	1.19481	−	1.19719i
$905$	142.809	+	142.809i	0.157800	+	0.157800i
$906$	−212.048	+	162.822i	−0.234049	+	0.179715i
$907$	−458.439	−	1106.77i	−0.505445	−	1.22025i	−0.946480	−	0.322763i	$-0.895388\pi$
$907$	−458.439	−	1106.77i	−0.505445	−	1.22025i	0.441034	−	0.897490i	$-0.354612\pi$
$908$	−149.061	−	1126.46i	−0.164164	−	1.24059i
$909$	269.706	−	651.128i	0.296706	−	0.716312i
$910$	32.4426	−	56.2353i	0.0356512	−	0.0617971i
$911$	202.975			0.222804			0.111402	−	0.993775i	$-0.464466\pi$
$911$	202.975			0.222804			0.111402	+	0.993775i	$0.464466\pi$
$912$	106.949	+	397.035i	0.117269	+	0.435345i
$913$		−	31.0636i		−	0.0340236i
$914$	−492.561	+	853.795i	−0.538907	+	0.934130i
$915$	−124.087	−	51.3986i	−0.135615	−	0.0561734i
$916$	−499.503	−	382.756i	−0.545309	−	0.417856i
$917$	299.014	−	123.855i	0.326078	−	0.135066i
$918$	351.155	−	269.636i	0.382522	−	0.293721i
$919$	−286.060	+	286.060i	−0.311273	+	0.311273i	−0.845403	−	0.534130i	$-0.820639\pi$
$919$	−286.060	+	286.060i	−0.311273	+	0.311273i	0.534130	+	0.845403i	$0.320639\pi$
$920$	−51.4272	−	123.808i	−0.0558991	−	0.134574i
$921$	44.5917	−	44.5917i	0.0484167	−	0.0484167i
$922$	−1602.57	−	210.442i	−1.73814	−	0.228245i
$923$	−386.051	+	159.908i	−0.418257	+	0.173248i
$924$	15.8813	+	4.24409i	0.0171875	+	0.00459317i
$925$	261.736	+	108.415i	0.282958	+	0.117205i
$926$	−225.410	−	840.128i	−0.243424	−	0.907266i
$927$		−	434.515i		−	0.468733i
$928$	−802.568	−	613.721i	−0.864836	−	0.661338i
$929$	945.820			1.01811			0.509053	−	0.860735i	$-0.329996\pi$
$929$	945.820			1.01811			0.509053	+	0.860735i	$0.329996\pi$
$930$	45.8589	−	12.3041i	0.0493106	−	0.0132303i
$931$	−98.9728	+	238.941i	−0.106308	+	0.256650i
$932$	−646.049	−	172.649i	−0.693186	−	0.185246i
$933$	−162.493	−	392.292i	−0.174161	−	0.420463i
$934$	−189.172	+	1440.60i	−0.202540	+	1.54239i
$935$	−56.0474	−	56.0474i	−0.0599438	−	0.0599438i
$936$	−395.476	−	163.351i	−0.422518	−	0.174520i
$937$	116.048	+	116.048i	0.123851	+	0.123851i	0.766315	−	0.642465i	$-0.222088\pi$
$937$	116.048	+	116.048i	0.123851	+	0.123851i	−0.642465	+	0.766315i	$0.722088\pi$
$938$	242.438	+	315.735i	0.258463	+	0.336604i
$939$	−0.878060	−	2.11983i	−0.000935102	−	0.00225753i
$940$	221.961	+	170.083i	0.236129	+	0.180939i
$941$	−223.040	+	538.465i	−0.237024	+	0.572226i	−0.996972	−	0.0777570i	$-0.975224\pi$
$941$	−223.040	+	538.465i	−0.237024	+	0.572226i	0.759948	+	0.649983i	$0.225224\pi$
$942$	−187.039	−	107.904i	−0.198555	−	0.114548i
$943$	−242.242			−0.256885
$944$	140.321	−	1076.88i	0.148645	−	1.14076i
$945$			62.9730i			0.0666381i
$946$	172.801	+	99.6902i	0.182665	+	0.105381i
$947$	335.222	+	138.853i	0.353983	+	0.146624i	0.552587	−	0.833455i	$-0.313641\pi$
$947$	335.222	+	138.853i	0.353983	+	0.146624i	−0.198604	+	0.980080i	$0.563641\pi$
$948$	3.06092	+	23.1315i	0.00322882	+	0.0244003i
$949$	−209.560	+	86.8025i	−0.220822	+	0.0914674i
$950$	−953.330	−	1241.55i	−1.00351	−	1.30690i
$951$	111.891	−	111.891i	0.117657	−	0.117657i
$952$	384.566	−	0.382414i	0.403956	−	0.000401695i
$953$	294.162	−	294.162i	0.308670	−	0.308670i	−0.535724	−	0.844393i	$-0.679961\pi$
$953$	294.162	−	294.162i	0.308670	−	0.308670i	0.844393	+	0.535724i	$0.179961\pi$
$954$	−210.389	+	1602.17i	−0.220534	+	1.67942i
$955$	210.292	−	87.1057i	0.220201	−	0.0912101i
$956$	363.331	−	210.091i	0.380054	−	0.219760i
$957$	−45.3089	−	18.7676i	−0.0473448	−	0.0196108i
$958$	963.402	−	258.485i	1.00564	−	0.269817i
$959$			69.7690i			0.0727518i
$960$	0.172957	+	86.9651i	0.000180164	+	0.0905887i
$961$	655.758			0.682371
$962$	43.5314	+	162.246i	0.0452510	+	0.168655i
$963$	−518.588	+	1251.98i	−0.538513	+	1.30009i
$964$	108.997	+	188.500i	0.113068	+	0.195539i
$965$	121.830	+	294.123i	0.126248	+	0.304790i
$966$	31.3043	+	4.11074i	0.0324062	+	0.00425542i
$967$	748.430	+	748.430i	0.773971	+	0.773971i	0.978798	−	0.204827i	$-0.0656633\pi$
$967$	748.430	+	748.430i	0.773971	+	0.773971i	−0.204827	+	0.978798i	$0.565663\pi$
$968$	928.105	−	0.922910i	0.958786	−	0.000953420i
$969$	330.169	+	330.169i	0.340732	+	0.340732i
$970$	318.029	−	244.200i	0.327865	−	0.251752i
$971$	207.061	+	499.889i	0.213245	+	0.514818i	0.993918	−	0.110121i	$-0.0351238\pi$
$971$	207.061	+	499.889i	0.213245	+	0.514818i	−0.780673	+	0.624939i	$0.785124\pi$
$972$	622.856	−	82.4207i	0.640798	−	0.0847949i
$973$	−28.3162	+	68.3613i	−0.0291019	+	0.0702583i
$974$	−246.639	+	427.518i	−0.253222	+	0.438930i
$975$	−92.5408			−0.0949137
$976$	−1253.40	+	964.412i	−1.28422	+	0.988127i
$977$		−	534.442i		−	0.547024i	−0.961869	−	0.273512i	$-0.911815\pi$
$977$		−	534.442i		−	0.547024i	0.961869	−	0.273512i	$-0.0881853\pi$
$978$	54.0398	−	93.6713i	0.0552554	−	0.0957785i
$979$	212.829	+	88.1569i	0.217395	+	0.0900479i
$980$	−33.2701	+	43.4180i	−0.0339491	+	0.0443041i
$981$	−40.1965	+	16.6500i	−0.0409751	+	0.0169724i
$982$	−1221.74	+	938.116i	−1.24413	+	0.955311i
$983$	−836.314	+	836.314i	−0.850777	+	0.850777i	−0.990229	−	0.139452i	$-0.955466\pi$
$983$	−836.314	+	836.314i	−0.850777	+	0.850777i	0.139452	+	0.990229i	$0.455466\pi$
$984$	145.237	+	59.9901i	0.147599	+	0.0609655i
$985$	212.411	−	212.411i	0.215646	−	0.215646i
$986$	−1137.53	−	149.375i	−1.15368	−	0.151496i
$987$	−60.8429	+	25.2020i	−0.0616443	+	0.0255339i
$988$	239.635	−	896.707i	0.242545	−	0.907598i
$989$	353.998	+	146.631i	0.357935	+	0.148262i
$990$	−19.2551	−	71.7660i	−0.0194496	−	0.0724909i
$991$		−	1779.43i		−	1.79559i	−0.440417	−	0.897793i	$-0.645169\pi$
$991$		−	1779.43i		−	1.79559i	0.440417	−	0.897793i	$-0.354831\pi$
$992$	143.805	−	540.267i	0.144964	−	0.544624i
$993$	−123.893			−0.124767
$994$	340.034	−	91.2326i	0.342086	−	0.0917833i
$995$	−17.2597	+	41.6686i	−0.0173464	+	0.0418780i
$996$	−9.99216	+	37.3904i	−0.0100323	+	0.0375405i
$997$	−347.706	−	839.437i	−0.348753	−	0.841963i	−0.996768	−	0.0803359i	$-0.974401\pi$
$997$	−347.706	−	839.437i	−0.348753	−	0.841963i	0.648015	−	0.761627i	$-0.275599\pi$
$998$	−234.257	+	1783.92i	−0.234726	+	1.78750i
$999$	−115.216	−	115.216i	−0.115332	−	0.115332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.w.a.99.19	yes	192
32.11	odd	8	inner	224.3.w.a.43.19	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.w.a.43.19	✓	192	32.11	odd	8	inner
224.3.w.a.99.19	yes	192	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.518278 - 1.93168i) q^{2} +(-0.266183 + 0.642623i) q^{3} +(-3.46277 + 2.00230i) q^{4} +(-0.747592 - 1.80485i) q^{5} +(1.37930 + 0.181123i) q^{6} +(1.87083 + 1.87083i) q^{7} +(5.66248 + 5.65123i) q^{8} +(6.02185 + 6.02185i) q^{9} +O(q^{10})\)	\(q+(-0.518278 - 1.93168i) q^{2} +(-0.266183 + 0.642623i) q^{3} +(-3.46277 + 2.00230i) q^{4} +(-0.747592 - 1.80485i) q^{5} +(1.37930 + 0.181123i) q^{6} +(1.87083 + 1.87083i) q^{7} +(5.66248 + 5.65123i) q^{8} +(6.02185 + 6.02185i) q^{9} +(-3.09892 + 2.37952i) q^{10} +(0.854581 + 2.06314i) q^{11} +(-0.364989 - 2.75824i) q^{12} +(-2.40343 + 5.80239i) q^{13} +(2.64423 - 4.58345i) q^{14} +1.35883 q^{15} +(7.98162 - 13.8670i) q^{16} -18.1690i q^{17} +(8.51129 - 14.7533i) q^{18} +(34.1345 + 14.1390i) q^{19} +(6.20258 + 4.75288i) q^{20} +(-1.70022 + 0.704255i) q^{21} +(3.54242 - 2.72006i) q^{22} +(6.06571 - 6.06571i) q^{23} +(-5.13887 + 2.13458i) q^{24} +(14.9791 - 14.9791i) q^{25} +(12.4540 + 1.63540i) q^{26} +(-11.2563 + 4.66252i) q^{27} +(-10.2242 - 2.73231i) q^{28} +(29.1695 + 12.0824i) q^{29} +(-0.704254 - 2.62483i) q^{30} +17.4712i q^{31} +(-30.9233 - 8.23097i) q^{32} -1.55330 q^{33} +(-35.0968 + 9.41662i) q^{34} +(1.97794 - 4.77517i) q^{35} +(-32.9098 - 8.79478i) q^{36} +(5.11785 + 12.3556i) q^{37} +(9.62079 - 73.2648i) q^{38} +(-3.08900 - 3.08900i) q^{39} +(5.96637 - 14.4447i) q^{40} +(-19.9681 - 19.9681i) q^{41} +(2.24158 + 2.91928i) q^{42} +(17.0934 + 41.2671i) q^{43} +(-7.09024 - 5.43307i) q^{44} +(6.36663 - 15.3704i) q^{45} +(-14.8607 - 8.57329i) q^{46} +35.7853 q^{47} +(6.78669 + 8.82034i) q^{48} +7.00000i q^{49} +(-36.6982 - 21.1715i) q^{50} +(11.6759 + 4.83630i) q^{51} +(-3.29557 - 24.9048i) q^{52} +(-87.6520 + 36.3066i) q^{53} +(14.8404 + 19.3271i) q^{54} +(3.08478 - 3.08478i) q^{55} +(0.0210475 + 21.1660i) q^{56} +(-18.1721 + 18.1721i) q^{57} +(8.22141 - 62.6082i) q^{58} +(62.7071 - 25.9741i) q^{59} +(-4.70533 + 2.72079i) q^{60} +(-91.3190 - 37.8256i) q^{61} +(33.7487 - 9.05493i) q^{62} +22.5317i q^{63} +(0.127283 + 63.9999i) q^{64} +12.2692 q^{65} +(0.805041 + 3.00048i) q^{66} +(-28.7890 + 69.5029i) q^{67} +(36.3798 + 62.9153i) q^{68} +(2.28338 + 5.51256i) q^{69} +(-10.2492 - 1.34588i) q^{70} +(47.0460 + 47.0460i) q^{71} +(0.0677481 + 68.1294i) q^{72} +(25.5379 + 25.5379i) q^{73} +(21.2146 - 16.2897i) q^{74} +(5.63873 + 13.6131i) q^{75} +(-146.510 + 19.3873i) q^{76} +(-2.26101 + 5.45856i) q^{77} +(-4.36600 + 7.56792i) q^{78} -8.38633 q^{79} +(-30.9948 - 4.03874i) q^{80} +68.1710i q^{81} +(-28.2230 + 48.9211i) q^{82} +(-12.8515 - 5.32326i) q^{83} +(4.47736 - 5.84302i) q^{84} +(-32.7923 + 13.5830i) q^{85} +(70.8556 - 54.4067i) q^{86} +(-15.5289 + 15.5289i) q^{87} +(-6.82023 + 16.5119i) q^{88} +(72.9437 - 72.9437i) q^{89} +(-32.9904 - 4.33214i) q^{90} +(-15.3517 + 6.35888i) q^{91} +(-8.85885 + 33.1496i) q^{92} +(-11.2274 - 4.65054i) q^{93} +(-18.5467 - 69.1257i) q^{94} -72.1777i q^{95} +(13.5207 - 17.6811i) q^{96} -102.626 q^{97} +(13.5218 - 3.62795i) q^{98} +(-7.27777 + 17.5701i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 80 q^{10} + 96 q^{12} - 20 q^{16} - 60 q^{18} - 260 q^{22} + 64 q^{23} - 144 q^{24} - 200 q^{26} + 192 q^{27} - 40 q^{30} + 40 q^{32} + 120 q^{34} + 464 q^{36} + 504 q^{38} - 384 q^{39} + 360 q^{40} - 96 q^{43} + 52 q^{44} + 64 q^{46} - 104 q^{48} - 312 q^{50} - 384 q^{51} - 320 q^{52} + 160 q^{53} - 576 q^{54} - 512 q^{55} - 196 q^{56} - 360 q^{58} - 872 q^{60} + 128 q^{61} - 408 q^{62} + 832 q^{66} + 160 q^{67} + 856 q^{68} - 384 q^{69} + 336 q^{70} + 1488 q^{72} + 308 q^{74} + 768 q^{75} + 1024 q^{76} - 224 q^{77} - 408 q^{78} + 1024 q^{79} - 1040 q^{80} - 240 q^{82} - 1384 q^{86} + 896 q^{87} - 560 q^{88} - 1320 q^{90} - 380 q^{92} - 936 q^{94} - 1088 q^{96} - 512 q^{99}+O(q^{100}) \) 192 * q + 80 * q^10 + 96 * q^12 - 20 * q^16 - 60 * q^18 - 260 * q^22 + 64 * q^23 - 144 * q^24 - 200 * q^26 + 192 * q^27 - 40 * q^30 + 40 * q^32 + 120 * q^34 + 464 * q^36 + 504 * q^38 - 384 * q^39 + 360 * q^40 - 96 * q^43 + 52 * q^44 + 64 * q^46 - 104 * q^48 - 312 * q^50 - 384 * q^51 - 320 * q^52 + 160 * q^53 - 576 * q^54 - 512 * q^55 - 196 * q^56 - 360 * q^58 - 872 * q^60 + 128 * q^61 - 408 * q^62 + 832 * q^66 + 160 * q^67 + 856 * q^68 - 384 * q^69 + 336 * q^70 + 1488 * q^72 + 308 * q^74 + 768 * q^75 + 1024 * q^76 - 224 * q^77 - 408 * q^78 + 1024 * q^79 - 1040 * q^80 - 240 * q^82 - 1384 * q^86 + 896 * q^87 - 560 * q^88 - 1320 * q^90 - 380 * q^92 - 936 * q^94 - 1088 * q^96 - 512 * q^99

Introduction

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