LMFDB - Embedded newform 197.3.f.a.20.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,3,Mod(20,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("197.20");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	197.f (of order $28$, degree $12$, 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:	$5.36786120790$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$32$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			20.18
Character	$\chi$	$=$	197.20
Dual form			197.3.f.a.69.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0564146 + 0.500693i) q^{2} +(-1.43240 - 0.161393i) q^{3} +(3.65220 - 0.833591i) q^{4} +(5.14385 + 8.18640i) q^{5} -0.726298i q^{6} +(3.28095 - 2.61647i) q^{7} +(1.28907 + 3.68395i) q^{8} +(-6.74863 - 1.54033i) q^{9} +(-3.80869 + 3.03733i) q^{10} +(-0.586365 - 5.20413i) q^{11} +(-5.36595 + 0.604597i) q^{12} +(-2.79225 + 7.97979i) q^{13} +(1.49514 + 1.49514i) q^{14} +(-6.04683 - 12.5564i) q^{15} +(11.7288 - 5.64827i) q^{16} +(2.77709 - 1.74496i) q^{17} +(0.390512 - 3.46589i) q^{18} +34.5904i q^{19} +(25.6105 + 25.6105i) q^{20} +(-5.12191 + 3.21831i) q^{21} +(2.57259 - 0.587178i) q^{22} +(19.5438 - 24.5072i) q^{23} +(-1.25190 - 5.48494i) q^{24} +(-29.7108 + 61.6950i) q^{25} +(-4.15295 - 0.947883i) q^{26} +(21.6633 + 7.58031i) q^{27} +(9.80162 - 12.2908i) q^{28} +(18.0930 - 22.6879i) q^{29} +(5.94576 - 3.73597i) q^{30} +(-1.54789 - 13.7379i) q^{31} +(11.7958 + 18.7728i) q^{32} +7.54903i q^{33} +(1.03036 + 1.29203i) q^{34} +(38.2962 + 13.4004i) q^{35} -25.9314 q^{36} +(-30.6891 - 14.7791i) q^{37} +(-17.3192 + 1.95141i) q^{38} +(5.28749 - 10.9796i) q^{39} +(-23.5275 + 29.5025i) q^{40} +(-2.62019 - 0.598040i) q^{41} +(-1.90034 - 2.38294i) q^{42} +(-40.4184 - 32.2326i) q^{43} +(-6.47964 - 18.5177i) q^{44} +(-22.1042 - 63.1702i) q^{45} +(13.3731 + 8.40289i) q^{46} +(-10.5007 + 21.8048i) q^{47} +(-17.7119 + 6.19765i) q^{48} +(-6.98481 + 30.6025i) q^{49} +(-32.5664 - 11.3955i) q^{50} +(-4.25952 + 2.05128i) q^{51} +(-3.54597 + 31.4714i) q^{52} +(-16.3541 - 71.6521i) q^{53} +(-2.57329 + 11.2743i) q^{54} +(39.5869 - 31.5695i) q^{55} +(13.8683 + 8.71404i) q^{56} +(5.58264 - 49.5473i) q^{57} +(12.3804 + 7.77911i) q^{58} +(29.1000 - 36.4902i) q^{59} +(-32.5511 - 40.8178i) q^{60} +(22.8496 - 28.6526i) q^{61} +(6.79116 - 1.55004i) q^{62} +(-26.1721 + 12.6038i) q^{63} +(31.9774 - 25.5011i) q^{64} +(-79.6886 + 18.1884i) q^{65} +(-3.77975 + 0.425875i) q^{66} +(35.9298 - 12.5724i) q^{67} +(8.68790 - 8.68790i) q^{68} +(-31.9498 + 31.9498i) q^{69} +(-4.54903 + 19.9306i) q^{70} +(32.1642 - 20.2101i) q^{71} +(-3.02495 - 26.8472i) q^{72} +(-60.5453 + 21.1857i) q^{73} +(5.66849 - 16.1996i) q^{74} +(52.5148 - 83.5769i) q^{75} +(28.8343 + 126.331i) q^{76} +(-15.5403 - 15.5403i) q^{77} +(5.79570 + 2.02800i) q^{78} +(45.4169 - 72.2806i) q^{79} +(106.570 + 66.9624i) q^{80} +(26.3230 + 12.6765i) q^{81} +(0.151618 - 1.34565i) q^{82} -114.741i q^{83} +(-16.0235 + 16.0235i) q^{84} +(28.5699 + 13.7585i) q^{85} +(13.8584 - 22.0556i) q^{86} +(-29.5780 + 29.5780i) q^{87} +(18.4159 - 8.86863i) q^{88} +(-5.87307 + 52.1250i) q^{89} +(30.3819 - 14.6311i) q^{90} +(11.7176 + 33.4871i) q^{91} +(50.9490 - 105.797i) q^{92} +19.9280i q^{93} +(-11.5099 - 4.02750i) q^{94} +(-283.171 + 177.928i) q^{95} +(-13.8664 - 28.7939i) q^{96} +(-98.2092 - 22.4156i) q^{97} +(-15.7165 - 1.77082i) q^{98} +(-4.05892 + 36.0239i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{2} - 12 q^{3} - 14 q^{4} - 4 q^{5} - 14 q^{7} + 48 q^{8} - 14 q^{9} - 14 q^{10} + 32 q^{11} - 26 q^{12} - 16 q^{13} - 68 q^{14} - 14 q^{15} + 70 q^{16} + 16 q^{17} + 180 q^{18} - 128 q^{20}+ \cdots - 662 q^{99}+O(q^{100}) $ 384 * q - 12 * q^2 - 12 * q^3 - 14 * q^4 - 4 * q^5 - 14 * q^7 + 48 * q^8 - 14 * q^9 - 14 * q^10 + 32 * q^11 - 26 * q^12 - 16 * q^13 - 68 * q^14 - 14 * q^15 + 70 * q^16 + 16 * q^17 + 180 * q^18 - 128 * q^20 + 6 * q^21 - 14 * q^22 - 62 * q^23 + 150 * q^24 - 14 * q^25 - 168 * q^26 + 6 * q^27 + 420 * q^28 + 140 * q^29 - 98 * q^30 + 50 * q^31 + 142 * q^32 + 38 * q^34 + 78 * q^35 - 2260 * q^36 - 64 * q^37 + 2 * q^38 - 14 * q^39 - 626 * q^40 - 126 * q^41 + 410 * q^42 - 14 * q^43 - 154 * q^44 + 544 * q^45 + 136 * q^46 - 364 * q^47 + 1114 * q^48 - 18 * q^49 - 140 * q^50 - 138 * q^51 - 214 * q^52 + 2 * q^53 + 90 * q^54 - 14 * q^55 + 26 * q^56 + 506 * q^57 - 364 * q^58 - 350 * q^59 + 348 * q^60 + 434 * q^61 + 756 * q^62 - 1122 * q^63 + 1330 * q^64 - 126 * q^65 - 742 * q^66 + 98 * q^67 + 1016 * q^68 + 454 * q^69 - 62 * q^70 - 682 * q^71 + 908 * q^72 - 32 * q^73 - 880 * q^74 - 78 * q^75 + 470 * q^76 - 410 * q^77 - 1626 * q^78 + 1100 * q^79 - 810 * q^80 + 1118 * q^81 - 86 * q^82 + 784 * q^84 - 1068 * q^85 - 632 * q^86 - 478 * q^87 - 274 * q^88 - 430 * q^89 + 308 * q^90 - 1570 * q^91 - 1022 * q^92 + 190 * q^94 + 1366 * q^95 - 462 * q^96 - 602 * q^97 + 1412 * q^98 - 662 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{28}\right)$

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 $

$2$	0.0564146	+	0.500693i	0.0282073	+	0.250347i	0.999901	+	0.0141007i	$0.00448853\pi$
$2$	0.0564146	+	0.500693i	0.0282073	+	0.250347i	−0.971693	+	0.236246i	$0.924083\pi$
$3$	−1.43240	−	0.161393i	−0.477467	−	0.0537976i	−0.130048	−	0.991508i	$-0.541513\pi$
$3$	−1.43240	−	0.161393i	−0.477467	−	0.0537976i	−0.347419	+	0.937710i	$0.612942\pi$
$4$	3.65220	−	0.833591i	0.913050	−	0.208398i
$5$	5.14385	+	8.18640i	1.02877	+	1.63728i	0.730651	+	0.682751i	$0.239217\pi$
$5$	5.14385	+	8.18640i	1.02877	+	1.63728i	0.298120	+	0.954528i	$0.403641\pi$
$6$		−	0.726298i		−	0.121050i
$7$	3.28095	−	2.61647i	0.468707	−	0.373781i	−0.360467	−	0.932772i	$-0.617383\pi$
$7$	3.28095	−	2.61647i	0.468707	−	0.373781i	0.829174	+	0.558991i	$0.188811\pi$
$8$	1.28907	+	3.68395i	0.161134	+	0.460494i
$9$	−6.74863	−	1.54033i	−0.749848	−	0.171148i
$10$	−3.80869	+	3.03733i	−0.380869	+	0.303733i
$11$	−0.586365	−	5.20413i	−0.0533059	−	0.473103i	−0.991799	−	0.127806i	$-0.959207\pi$
$11$	−0.586365	−	5.20413i	−0.0533059	−	0.473103i	0.938493	−	0.345297i	$-0.112222\pi$
$12$	−5.36595	+	0.604597i	−0.447162	+	0.0503831i
$13$	−2.79225	+	7.97979i	−0.214788	+	0.613830i	−0.999985	−	0.00541626i	$-0.998276\pi$
$13$	−2.79225	+	7.97979i	−0.214788	+	0.613830i	0.785197	+	0.619246i	$0.212562\pi$
$14$	1.49514	+	1.49514i	0.106796	+	0.106796i
$15$	−6.04683	−	12.5564i	−0.403122	−	0.837091i
$16$	11.7288	−	5.64827i	0.733047	−	0.353017i
$17$	2.77709	−	1.74496i	0.163358	−	0.102645i	−0.447872	−	0.894098i	$-0.647818\pi$
$17$	2.77709	−	1.74496i	0.163358	−	0.102645i	0.611230	+	0.791453i	$0.290675\pi$
$18$	0.390512	−	3.46589i	0.0216951	−	0.192549i
$19$			34.5904i			1.82055i	0.414005	+	0.910275i	$0.364130\pi$
$19$			34.5904i			1.82055i	−0.414005	+	0.910275i	$0.635870\pi$
$20$	25.6105	+	25.6105i	1.28052	+	1.28052i
$21$	−5.12191	+	3.21831i	−0.243900	+	0.153253i
$22$	2.57259	−	0.587178i	0.116936	−	0.0266899i
$23$	19.5438	−	24.5072i	0.849731	−	1.06553i	−0.147343	−	0.989085i	$-0.547072\pi$
$23$	19.5438	−	24.5072i	0.849731	−	1.06553i	0.997074	−	0.0764437i	$-0.0243565\pi$
$24$	−1.25190	−	5.48494i	−0.0521625	−	0.228539i
$25$	−29.7108	+	61.6950i	−1.18843	+	2.46780i
$26$	−4.15295	−	0.947883i	−0.159729	−	0.0364571i
$27$	21.6633	+	7.58031i	0.802344	+	0.280752i
$28$	9.80162	−	12.2908i	0.350058	−	0.438959i
$29$	18.0930	−	22.6879i	0.623896	−	0.782341i	−0.364991	−	0.931011i	$-0.618928\pi$
$29$	18.0930	−	22.6879i	0.623896	−	0.782341i	0.988887	+	0.148670i	$0.0474993\pi$
$30$	5.94576	−	3.73597i	0.198192	−	0.124532i
$31$	−1.54789	−	13.7379i	−0.0499320	−	0.443159i	−0.993659	−	0.112434i	$-0.964135\pi$
$31$	−1.54789	−	13.7379i	−0.0499320	−	0.443159i	0.943727	−	0.330725i	$-0.107293\pi$
$32$	11.7958	+	18.7728i	0.368617	+	0.586651i
$33$			7.54903i			0.228758i
$34$	1.03036	+	1.29203i	0.0303046	+	0.0380008i
$35$	38.2962	+	13.4004i	1.09418	+	0.382869i
$36$	−25.9314			−0.720315
$37$	−30.6891	−	14.7791i	−0.829436	−	0.399436i	−0.0295327	−	0.999564i	$-0.509402\pi$
$37$	−30.6891	−	14.7791i	−0.829436	−	0.399436i	−0.799904	+	0.600128i	$0.795116\pi$
$38$	−17.3192	+	1.95141i	−0.455768	+	0.0513528i
$39$	5.28749	−	10.9796i	0.135577	−	0.281528i
$40$	−23.5275	+	29.5025i	−0.588187	+	0.737564i
$41$	−2.62019	−	0.598040i	−0.0639070	−	0.0145863i	0.190448	−	0.981697i	$-0.439006\pi$
$41$	−2.62019	−	0.598040i	−0.0639070	−	0.0145863i	−0.254355	+	0.967111i	$0.581863\pi$
$42$	−1.90034	−	2.38294i	−0.0452461	−	0.0567368i
$43$	−40.4184	−	32.2326i	−0.939962	−	0.749595i	0.0282825	−	0.999600i	$-0.490996\pi$
$43$	−40.4184	−	32.2326i	−0.939962	−	0.749595i	−0.968244	+	0.250005i	$0.919568\pi$
$44$	−6.47964	−	18.5177i	−0.147264	−	0.420858i
$45$	−22.1042	−	63.1702i	−0.491205	−	1.40378i
$46$	13.3731	+	8.40289i	0.290720	+	0.182672i
$47$	−10.5007	+	21.8048i	−0.223418	+	0.463933i	−0.982305	−	0.187290i	$-0.940029\pi$
$47$	−10.5007	+	21.8048i	−0.223418	+	0.463933i	0.758886	+	0.651223i	$0.225744\pi$
$48$	−17.7119	+	6.19765i	−0.368997	+	0.129118i
$49$	−6.98481	+	30.6025i	−0.142547	+	0.624540i
$50$	−32.5664	−	11.3955i	−0.651328	−	0.227910i
$51$	−4.25952	+	2.05128i	−0.0835201	+	0.0402211i
$52$	−3.54597	+	31.4714i	−0.0681918	+	0.605219i
$53$	−16.3541	−	71.6521i	−0.308568	−	1.35193i	−0.856821	−	0.515614i	$-0.827564\pi$
$53$	−16.3541	−	71.6521i	−0.308568	−	1.35193i	0.548253	−	0.836313i	$-0.315293\pi$
$54$	−2.57329	+	11.2743i	−0.0476535	+	0.208783i
$55$	39.5869	−	31.5695i	0.719762	−	0.573991i
$56$	13.8683	+	8.71404i	0.247648	+	0.155608i
$57$	5.58264	−	49.5473i	0.0979411	−	0.869251i
$58$	12.3804	+	7.77911i	0.213455	+	0.134123i
$59$	29.1000	−	36.4902i	0.493220	−	0.618478i	−0.471465	−	0.881885i	$-0.656275\pi$
$59$	29.1000	−	36.4902i	0.493220	−	0.618478i	0.964685	+	0.263406i	$0.0848460\pi$
$60$	−32.5511	−	40.8178i	−0.542519	−	0.680297i
$61$	22.8496	−	28.6526i	0.374584	−	0.469714i	−0.558431	−	0.829551i	$-0.688596\pi$
$61$	22.8496	−	28.6526i	0.374584	−	0.469714i	0.933015	+	0.359837i	$0.117168\pi$
$62$	6.79116	−	1.55004i	0.109535	−	0.0250006i
$63$	−26.1721	+	12.6038i	−0.415431	+	0.200061i
$64$	31.9774	−	25.5011i	0.499646	−	0.398455i
$65$	−79.6886	+	18.1884i	−1.22598	+	0.279822i
$66$	−3.77975	+	0.425875i	−0.0572689	+	0.00645266i
$67$	35.9298	−	12.5724i	0.536265	−	0.187647i	−0.0485397	−	0.998821i	$-0.515457\pi$
$67$	35.9298	−	12.5724i	0.536265	−	0.187647i	0.584805	+	0.811174i	$0.301171\pi$
$68$	8.68790	−	8.68790i	0.127763	−	0.127763i
$69$	−31.9498	+	31.9498i	−0.463041	+	0.463041i
$70$	−4.54903	+	19.9306i	−0.0649862	+	0.284723i
$71$	32.1642	−	20.2101i	0.453017	−	0.284649i	−0.286134	−	0.958190i	$-0.592370\pi$
$71$	32.1642	−	20.2101i	0.453017	−	0.284649i	0.739150	+	0.673540i	$0.235227\pi$
$72$	−3.02495	−	26.8472i	−0.0420133	−	0.372878i
$73$	−60.5453	+	21.1857i	−0.829388	+	0.290215i	−0.711389	−	0.702798i	$-0.751934\pi$
$73$	−60.5453	+	21.1857i	−0.829388	+	0.290215i	−0.117999	+	0.993014i	$0.537648\pi$
$74$	5.66849	−	16.1996i	0.0766012	−	0.218914i
$75$	52.5148	−	83.5769i	0.700198	−	1.11436i
$76$	28.8343	+	126.331i	0.379398	+	1.66225i
$77$	−15.5403	−	15.5403i	−0.201822	−	0.201822i
$78$	5.79570	+	2.02800i	0.0743039	+	0.0260000i
$79$	45.4169	−	72.2806i	0.574898	−	0.914945i	−0.425054	−	0.905168i	$-0.639745\pi$
$79$	45.4169	−	72.2806i	0.574898	−	0.914945i	0.999952	−	0.00977703i	$-0.00311218\pi$
$80$	106.570	+	66.9624i	1.33213	+	0.837030i
$81$	26.3230	+	12.6765i	0.324975	+	0.156500i
$82$	0.151618	−	1.34565i	0.00184900	−	0.0164103i
$83$		−	114.741i		−	1.38242i	−0.722654	−	0.691210i	$-0.757078\pi$
$83$		−	114.741i		−	1.38242i	0.722654	−	0.691210i	$-0.242922\pi$
$84$	−16.0235	+	16.0235i	−0.190756	+	0.190756i
$85$	28.5699	+	13.7585i	0.336116	+	0.161865i
$86$	13.8584	−	22.0556i	0.161145	−	0.256460i
$87$	−29.5780	+	29.5780i	−0.339977	+	0.339977i
$88$	18.4159	−	8.86863i	0.209272	−	0.100780i
$89$	−5.87307	+	52.1250i	−0.0659896	+	0.585674i	0.916590	+	0.399829i	$0.130931\pi$
$89$	−5.87307	+	52.1250i	−0.0659896	+	0.585674i	−0.982579	+	0.185844i	$0.940498\pi$
$90$	30.3819	−	14.6311i	0.337577	−	0.162568i
$91$	11.7176	+	33.4871i	0.128765	+	0.367990i
$92$	50.9490	−	105.797i	0.553793	−	1.14996i
$93$			19.9280i			0.214280i
$94$	−11.5099	−	4.02750i	−0.122446	−	0.0428457i
$95$	−283.171	+	177.928i	−2.98075	+	1.87293i
$96$	−13.8664	−	28.7939i	−0.144442	−	0.299937i
$97$	−98.2092	−	22.4156i	−1.01247	−	0.231089i	−0.316062	−	0.948739i	$-0.602361\pi$
$97$	−98.2092	−	22.4156i	−1.01247	−	0.231089i	−0.696404	+	0.717650i	$0.745218\pi$
$98$	−15.7165	−	1.77082i	−0.160372	−	0.0180696i
$99$	−4.05892	+	36.0239i	−0.0409992	+	0.363878i
$100$	−57.0813	+	250.089i	−0.570813	+	2.50089i
$101$	−3.28055	+	1.57983i	−0.0324807	+	0.0156419i	−0.450054	−	0.893002i	$-0.648595\pi$
$101$	−3.28055	+	1.57983i	−0.0324807	+	0.0156419i	0.417573	+	0.908643i	$0.362881\pi$
$102$	−1.26736	−	2.01699i	−0.0124251	−	0.0197744i
$103$	−39.5110	+	112.916i	−0.383602	+	1.09627i	0.576615	+	0.817016i	$0.304373\pi$
$103$	−39.5110	+	112.916i	−0.383602	+	1.09627i	−0.960217	+	0.279255i	$0.909912\pi$
$104$	−32.9965			−0.317274
$105$	−52.6927	−	25.3755i	−0.501835	−	0.241671i
$106$	34.9531	−	12.2306i	0.329746	−	0.115383i
$107$	−9.17341	−	19.0488i	−0.0857328	−	0.178026i	0.853695	−	0.520774i	$-0.174357\pi$
$107$	−9.17341	−	19.0488i	−0.0857328	−	0.178026i	−0.939427	+	0.342748i	$0.888642\pi$
$108$	85.4376	+	9.62650i	0.791089	+	0.0891343i
$109$	−86.2751	−	179.152i	−0.791515	−	1.64360i	−0.765069	−	0.643948i	$-0.777295\pi$
$109$	−86.2751	−	179.152i	−0.791515	−	1.64360i	−0.0264456	−	0.999650i	$-0.508419\pi$
$110$	18.0399	+	18.0399i	0.163999	+	0.163999i
$111$	41.5739	+	26.1226i	0.374539	+	0.235339i
$112$	23.7029	−	49.2196i	0.211633	−	0.439461i
$113$	−121.391	−	121.391i	−1.07425	−	1.07425i	−0.997012	−	0.0772426i	$-0.975388\pi$
$113$	−121.391	−	121.391i	−1.07425	−	1.07425i	−0.0772426	−	0.997012i	$-0.524612\pi$
$114$	25.1230			0.220377
$115$	301.156	+	33.9321i	2.61875	+	0.295062i
$116$	47.1668	−	97.9429i	0.406610	−	0.844335i
$117$	31.1354	−	49.5516i	0.266114	−	0.423518i
$118$	19.9121	+	12.5116i	0.168746	+	0.106030i
$119$	4.54585	−	12.9913i	0.0382004	−	0.109170i
$120$	38.4623	−	38.4623i	0.320519	−	0.320519i
$121$	91.2271	−	20.8220i	0.753943	−	0.172083i
$122$	15.6352	+	9.82424i	0.128157	+	0.0805266i
$123$	3.65663	+	1.27951i	0.0297287	+	0.0104025i
$124$	−17.1050	−	48.8834i	−0.137944	−	0.394221i
$125$	−417.700	+	47.0635i	−3.34160	+	0.376508i
$126$	−7.78715	−	12.3932i	−0.0618027	−	0.0983585i
$127$	−24.3194	−	5.55074i	−0.191491	−	0.0437066i	0.125700	−	0.992068i	$-0.459882\pi$
$127$	−24.3194	−	5.55074i	−0.191491	−	0.0437066i	−0.317191	+	0.948362i	$0.602740\pi$
$128$	77.2816	+	77.2816i	0.603763	+	0.603763i
$129$	52.6931	+	52.6931i	0.408474	+	0.408474i
$130$	−13.6024	−	38.8735i	−0.104634	−	0.299027i
$131$	14.2193	+	126.200i	0.108545	+	0.963359i	0.923438	+	0.383748i	$0.125367\pi$
$131$	14.2193	+	126.200i	0.108545	+	0.963359i	−0.814893	+	0.579611i	$0.803204\pi$
$132$	6.29280	+	27.5706i	0.0476727	+	0.208868i
$133$	90.5048	+	113.489i	0.680487	+	0.853304i
$134$	8.32186	+	17.2805i	0.0621035	+	0.128959i
$135$	49.3774	+	216.336i	0.365758	+	1.60249i
$136$	10.0082	+	7.98128i	0.0735898	+	0.0586859i
$137$	102.881	−	82.0447i	0.750954	−	0.598866i	−0.171404	−	0.985201i	$-0.554830\pi$
$137$	102.881	−	82.0447i	0.750954	−	0.598866i	0.922359	+	0.386335i	$0.126259\pi$
$138$	−17.7995	−	14.1946i	−0.128982	−	0.102860i
$139$	63.1934	−	100.572i	0.454628	−	0.723537i	−0.538235	−	0.842795i	$-0.680909\pi$
$139$	63.1934	−	100.572i	0.454628	−	0.723537i	0.992863	+	0.119258i	$0.0380515\pi$
$140$	151.036	+	17.0176i	1.07883	+	0.121555i
$141$	18.5603	−	29.5385i	0.131633	−	0.209493i
$142$	11.9336	+	14.9643i	0.0840394	+	0.105382i
$143$	43.1651	+	9.85216i	0.301854	+	0.0688962i
$144$	−87.8533	+	20.0519i	−0.610092	+	0.139250i
$145$	278.800	+	31.4132i	1.92276	+	0.216643i
$146$	−14.0232	−	29.1194i	−0.0960492	−	0.199448i
$147$	14.9441	−	42.7077i	0.101660	−	0.290528i
$148$	−124.403	−	28.3941i	−0.840559	−	0.191852i
$149$	51.1740	+	146.247i	0.343450	+	0.981522i	0.977993	+	0.208636i	$0.0669023\pi$
$149$	51.1740	+	146.247i	0.343450	+	0.981522i	−0.634544	+	0.772887i	$0.718812\pi$
$150$	44.8090	+	21.5789i	0.298726	+	0.143859i
$151$	−56.6850	+	90.2137i	−0.375397	+	0.597441i	−0.979979	−	0.199102i	$-0.936198\pi$
$151$	−56.6850	+	90.2137i	−0.375397	+	0.597441i	0.604581	+	0.796543i	$0.293340\pi$
$152$	−127.429	+	44.5895i	−0.838352	+	0.293352i
$153$	−21.4294	+	7.49846i	−0.140061	+	0.0490095i
$154$	6.90421	−	8.65761i	0.0448326	−	0.0562182i
$155$	104.502	−	83.3376i	0.674207	−	0.537662i
$156$	10.1585	−	44.5073i	0.0651186	−	0.285303i
$157$	−11.9005	−	9.49036i	−0.0757996	−	0.0604482i	0.584857	−	0.811136i	$-0.301151\pi$
$157$	−11.9005	−	9.49036i	−0.0757996	−	0.0604482i	−0.660657	+	0.750688i	$0.729722\pi$
$158$	38.7526	+	18.6623i	0.245270	+	0.118116i
$159$	11.8615	+	105.274i	0.0746007	+	0.662100i
$160$	−93.0062	+	193.129i	−0.581289	+	1.20706i
$161$		−	131.543i		−	0.817034i
$162$	−4.86202	+	13.8949i	−0.0300125	+	0.0857708i
$163$	−230.779	+	184.041i	−1.41583	+	1.12908i	−0.443276	+	0.896385i	$0.646184\pi$
$163$	−230.779	+	184.041i	−1.41583	+	1.12908i	−0.972549	+	0.232698i	$0.925245\pi$
$164$	−10.0680			−0.0613900
$165$	−61.7994	+	38.8311i	−0.374542	+	0.235340i
$166$	57.4500	−	6.47306i	0.346084	−	0.0389943i
$167$	108.476	+	172.638i	0.649555	+	1.03376i	0.995431	+	0.0954813i	$0.0304390\pi$
$167$	108.476	+	172.638i	0.649555	+	1.03376i	−0.345876	+	0.938280i	$0.612418\pi$
$168$	−18.4586	−	14.7202i	−0.109873	−	0.0876204i
$169$	76.2492	+	60.8067i	0.451179	+	0.359803i
$170$	−5.27704	+	15.0809i	−0.0310414	+	0.0887113i
$171$	53.2807	−	233.438i	0.311583	−	1.36514i
$172$	−174.485	−	84.0274i	−1.01445	−	0.488532i
$173$	−33.9624	+	7.75170i	−0.196315	+	0.0448075i	−0.319548	−	0.947570i	$-0.603531\pi$
$173$	−33.9624	+	7.75170i	−0.196315	+	0.0448075i	0.123233	+	0.992378i	$0.460674\pi$
$174$	−16.4782	−	13.1409i	−0.0947020	−	0.0755224i
$175$	63.9437	+	280.156i	0.365392	+	1.60089i
$176$	−36.2717	−	57.7260i	−0.206089	−	0.327989i
$177$	−47.5721	+	47.5721i	−0.268769	+	0.268769i
$178$	−26.4299			−0.148483
$179$	79.8843	+	9.00080i	0.446281	+	0.0502838i	0.332246	−	0.943193i	$-0.392194\pi$
$179$	79.8843	+	9.00080i	0.446281	+	0.0502838i	0.114035	+	0.993477i	$0.463622\pi$
$180$	−133.387	−	212.284i	−0.741040	−	1.17936i
$181$	−118.623	−	246.324i	−0.655377	−	1.36091i	−0.918222	−	0.396067i	$-0.870375\pi$
$181$	−118.623	−	246.324i	−0.655377	−	1.36091i	0.262844	−	0.964838i	$-0.415339\pi$
$182$	−16.1057	+	7.75610i	−0.0884930	+	0.0426160i
$183$	−37.3541	+	37.3541i	−0.204121	+	0.204121i
$184$	115.477	+	40.4070i	0.627590	+	0.219603i
$185$	−36.8728	−	327.255i	−0.199312	−	1.76895i
$186$	−9.97783	+	1.12423i	−0.0536442	+	0.00604425i
$187$	−10.7094	−	13.4291i	−0.0572694	−	0.0718136i
$188$	−20.1742	+	88.3889i	−0.107310	+	0.470154i
$189$	90.9098	−	31.8107i	0.481004	−	0.168311i
$190$	−105.062	−	131.744i	−0.552960	−	0.693390i
$191$	221.262			1.15844			0.579220	−	0.815171i	$-0.303357\pi$
$191$	221.262			1.15844			0.579220	+	0.815171i	$0.303357\pi$
$192$	−49.9200	+	31.3668i	−0.260000	+	0.163369i
$193$	56.3687	+	246.967i	0.292066	+	1.27962i	0.881645	+	0.471913i	$0.156436\pi$
$193$	56.3687	+	246.967i	0.292066	+	1.27962i	−0.589579	+	0.807711i	$0.700706\pi$
$194$	5.68291	−	50.4373i	0.0292934	−	0.259986i
$195$	117.081	−	13.1919i	0.600418	−	0.0676508i
$196$			117.589i			0.599943i
$197$	186.225	+	64.2583i	0.945306	+	0.326184i
$197$	186.225	+	64.2583i	0.945306	+	0.326184i
$198$	−18.2659			−0.0922522
$199$	−24.0274	−	213.249i	−0.120741	−	1.07160i	−0.897257	−	0.441508i	$-0.854444\pi$
$199$	−24.0274	−	213.249i	−0.120741	−	1.07160i	0.776517	−	0.630097i	$-0.216985\pi$
$200$	−265.581	−	29.9238i	−1.32790	−	0.149619i
$201$	−53.4949	+	12.2099i	−0.266144	+	0.0607456i
$202$	−0.976080	−	1.55342i	−0.00483208	−	0.00769021i
$203$		−	121.778i		−	0.599889i
$204$	−13.8467	+	11.0424i	−0.0678760	+	0.0541293i
$205$	−8.58206	−	24.5261i	−0.0418637	−	0.119640i
$206$	−58.7652	−	13.4128i	−0.285268	−	0.0651106i
$207$	−169.643	+	135.286i	−0.819532	+	0.653555i
$208$	12.3224	+	109.364i	0.0592423	+	0.525790i
$209$	180.013	−	20.2826i	0.861307	−	0.0970460i
$210$	9.73269	−	27.8144i	0.0463461	−	0.132450i
$211$	76.0147	+	76.0147i	0.360259	+	0.360259i	0.863908	−	0.503649i	$-0.168010\pi$
$211$	76.0147	+	76.0147i	0.360259	+	0.360259i	−0.503649	+	0.863908i	$0.668010\pi$
$212$	−119.457	−	248.055i	−0.563477	−	1.17007i
$213$	−49.3337	+	23.7579i	−0.231614	+	0.111539i
$214$	9.02008	−	5.66769i	0.0421499	−	0.0264845i
$215$	55.9624	−	496.680i	0.260290	−	2.31014i
$216$			89.5781i			0.414713i
$217$	−41.0234	−	41.0234i	−0.189048	−	0.189048i
$218$	84.8331	−	53.3042i	0.389143	−	0.244515i
$219$	90.1443	−	20.5748i	0.411618	−	0.0939491i
$220$	118.263	−	148.297i	0.537560	−	0.674079i
$221$	6.17009	+	27.0329i	0.0279190	+	0.122321i
$222$	−10.7340	+	22.2895i	−0.0483515	+	0.100403i
$223$	−301.454	−	68.8048i	−1.35181	−	0.308542i	−0.515543	−	0.856864i	$-0.672410\pi$
$223$	−301.454	−	68.8048i	−1.35181	−	0.308542i	−0.836267	+	0.548322i	$0.815267\pi$
$224$	87.8198	+	30.7295i	0.392053	+	0.137185i
$225$	295.538	−	370.593i	1.31350	−	1.64708i
$226$	53.9313	−	67.6278i	0.238634	−	0.299238i
$227$	99.6661	−	62.6244i	0.439058	−	0.275878i	−0.294310	−	0.955710i	$-0.595090\pi$
$227$	99.6661	−	62.6244i	0.439058	−	0.275878i	0.733368	+	0.679832i	$0.237947\pi$
$228$	−20.9133	−	185.610i	−0.0917249	−	0.814081i
$229$	184.673	+	293.906i	0.806434	+	1.28343i	0.955614	+	0.294623i	$0.0951940\pi$
$229$	184.673	+	293.906i	0.806434	+	1.28343i	−0.149179	+	0.988810i	$0.547663\pi$
$230$			152.701i			0.663917i
$231$	19.7518	+	24.7680i	0.0855056	+	0.107221i
$232$	106.904	+	37.4074i	0.460794	+	0.161239i
$233$	−418.409			−1.79575			−0.897874	−	0.440252i	$-0.854889\pi$
$233$	−418.409			−1.79575			−0.897874	+	0.440252i	$0.854889\pi$
$234$	26.5667	+	12.7938i	0.113533	+	0.0546745i
$235$	−232.517	+	26.1984i	−0.989434	+	0.111482i
$236$	75.8610	−	157.527i	0.321445	−	0.667488i
$237$	−76.7208	+	96.2048i	−0.323716	+	0.405927i
$238$	6.76110	+	1.54318i	0.0284080	+	0.00648394i
$239$	82.7447	+	103.759i	0.346212	+	0.434136i	0.924200	−	0.381909i	$-0.124733\pi$
$239$	82.7447	+	103.759i	0.346212	+	0.434136i	−0.577988	+	0.816045i	$0.696162\pi$
$240$	−141.844	−	113.116i	−0.591015	−	0.471319i
$241$	3.83784	+	10.9679i	0.0159246	+	0.0455100i	0.951571	−	0.307428i	$-0.0994683\pi$
$241$	3.83784	+	10.9679i	0.0159246	+	0.0455100i	−0.935647	+	0.352938i	$0.885183\pi$
$242$	15.5720	+	44.5021i	0.0643470	+	0.183893i
$243$	−210.559	−	132.303i	−0.866500	−	0.544458i
$244$	59.5670	−	123.692i	0.244127	−	0.506935i
$245$	−286.453	+	100.234i	−1.16920	+	0.409119i
$246$	−0.434355	+	1.90303i	−0.00176567	+	0.00773591i
$247$	−276.024	−	96.5851i	−1.11751	−	0.391033i
$248$	48.6145	−	23.4115i	0.196026	−	0.0944013i
$249$	−18.5183	+	164.355i	−0.0743708	+	0.660059i
$250$	−47.1287	−	206.484i	−0.188515	−	0.825938i
$251$	−59.1988	+	259.367i	−0.235852	+	1.03333i	0.708838	+	0.705371i	$0.249220\pi$
$251$	−59.1988	+	259.367i	−0.235852	+	1.03333i	−0.944690	+	0.327964i	$0.893638\pi$
$252$	−85.0794	+	67.8486i	−0.337617	+	0.269240i
$253$	−138.998	−	87.3384i	−0.549400	−	0.345211i
$254$	1.40725	−	12.4897i	0.00554035	−	0.0491720i
$255$	−38.7029	−	24.3187i	−0.151776	−	0.0953674i
$256$	67.6698	−	84.8552i	0.264335	−	0.331466i
$257$	22.1548	+	27.7813i	0.0862056	+	0.108098i	0.823064	−	0.567949i	$-0.192263\pi$
$257$	22.1548	+	27.7813i	0.0862056	+	0.108098i	−0.736858	+	0.676047i	$0.763691\pi$
$258$	−23.4104	+	29.3558i	−0.0907381	+	0.113782i
$259$	−139.359	+	31.8077i	−0.538064	+	0.122810i
$260$	−275.877	+	132.855i	−1.06107	+	0.510982i
$261$	−157.050	+	125.243i	−0.601723	+	0.479858i
$262$	−62.3853	+	14.2390i	−0.238112	+	0.0543475i
$263$	−71.0108	+	8.00100i	−0.270003	+	0.0304220i	−0.245928	−	0.969288i	$-0.579093\pi$
$263$	−71.0108	+	8.00100i	−0.270003	+	0.0304220i	−0.0240751	+	0.999710i	$0.507664\pi$
$264$	−27.8103	+	9.73123i	−0.105342	+	0.0368607i
$265$	502.449	−	502.449i	1.89604	−	1.89604i
$266$	−51.7176	+	51.7176i	−0.194427	+	0.194427i
$267$	16.8252	−	73.7159i	0.0630156	−	0.276090i
$268$	120.743	−	75.8676i	0.450532	−	0.283088i
$269$	−28.3773	−	251.855i	−0.105492	−	0.936265i	−0.929282	−	0.369370i	$-0.879573\pi$
$269$	−28.3773	−	251.855i	−0.105492	−	0.936265i	0.823791	−	0.566894i	$-0.191855\pi$
$270$	−105.533	+	36.9274i	−0.390861	+	0.136768i
$271$	−157.053	+	448.832i	−0.579531	+	1.65621i	0.163182	+	0.986596i	$0.447824\pi$
$271$	−157.053	+	448.832i	−0.579531	+	1.65621i	−0.742713	+	0.669610i	$0.766461\pi$
$272$	22.7158	−	36.1520i	0.0835139	−	0.132912i
$273$	−11.3798	−	49.8580i	−0.0416842	−	0.182630i
$274$	46.8832	+	46.8832i	0.171107	+	0.171107i
$275$	338.490	+	118.443i	1.23087	+	0.430702i
$276$	−90.0541	+	143.320i	−0.326283	+	0.519276i
$277$	101.461	+	63.7520i	0.366284	+	0.230151i	0.702580	−	0.711605i	$-0.252031\pi$
$277$	101.461	+	63.7520i	0.366284	+	0.230151i	−0.336296	+	0.941756i	$0.609174\pi$
$278$	53.9206	+	25.9668i	0.193959	+	0.0934057i
$279$	−10.7148	+	95.0965i	−0.0384043	+	0.340848i
$280$			158.355i			0.565555i
$281$	−145.615	+	145.615i	−0.518201	+	0.518201i	−0.917027	−	0.398825i	$-0.869418\pi$
$281$	−145.615	+	145.615i	−0.518201	+	0.518201i	0.398825	+	0.917027i	$0.369418\pi$
$282$	15.8368	+	7.62660i	0.0561589	+	0.0270447i
$283$	40.0892	−	63.8016i	0.141658	−	0.225447i	−0.768358	−	0.640020i	$-0.778926\pi$
$283$	40.0892	−	63.8016i	0.141658	−	0.225447i	0.910016	+	0.414573i	$0.136069\pi$
$284$	100.623	−	100.623i	0.354307	−	0.354307i
$285$	434.330	−	209.163i	1.52397	−	0.733904i
$286$	−2.49777	+	22.1683i	−0.00873345	+	0.0775115i
$287$	−10.1614	+	4.89349i	−0.0354057	+	0.0170505i
$288$	−50.6888	−	144.860i	−0.176003	−	0.502987i
$289$	−120.725	+	250.688i	−0.417734	+	0.867433i
$290$			141.365i			0.487467i
$291$	137.057	+	47.9584i	0.470987	+	0.164805i
$292$	−203.463	+	127.844i	−0.696792	+	0.437824i
$293$	85.5367	+	177.619i	0.291934	+	0.606207i	0.994420	−	0.105490i	$-0.0336410\pi$
$293$	85.5367	+	177.619i	0.291934	+	0.606207i	−0.702486	+	0.711697i	$0.747927\pi$
$294$	22.2265	+	5.07305i	0.0756003	+	0.0172553i
$295$	448.410	+	50.5236i	1.52003	+	0.171266i
$296$	14.8851	−	132.109i	0.0502874	−	0.446313i
$297$	26.7464	−	117.183i	0.0900551	−	0.394557i
$298$	−70.3378	+	33.8729i	−0.236033	+	0.113668i
$299$	140.991	+	224.386i	0.471541	+	0.750454i
$300$	122.126	−	349.015i	0.407086	−	1.16338i
$301$	−216.946			−0.720751
$302$	−48.3672	−	23.2924i	−0.160156	−	0.0771272i
$303$	4.95403	−	1.73349i	0.0163499	−	0.00572109i
$304$	195.376	+	405.703i	0.642685	+	1.33455i
$305$	352.096	+	39.6717i	1.15441	+	0.130071i
$306$	−4.96335	−	10.3065i	−0.0162201	−	0.0336814i
$307$	−122.096	−	122.096i	−0.397706	−	0.397706i	0.479717	−	0.877423i	$-0.340739\pi$
$307$	−122.096	−	122.096i	−0.397706	−	0.397706i	−0.877423	+	0.479717i	$0.840739\pi$
$308$	−69.7104	−	43.8020i	−0.226333	−	0.142214i
$309$	74.8193	−	155.364i	0.242134	−	0.502796i
$310$	47.6220	+	47.6220i	0.153619	+	0.153619i
$311$	−346.843			−1.11525			−0.557625	−	0.830093i	$-0.688287\pi$
$311$	−346.843			−1.11525			−0.557625	+	0.830093i	$0.688287\pi$
$312$	47.2642	+	5.32540i	0.151488	+	0.0170686i
$313$	−97.3187	+	202.084i	−0.310922	+	0.645637i	−0.996611	−	0.0822578i	$-0.973787\pi$
$313$	−97.3187	+	202.084i	−0.310922	+	0.645637i	0.685689	+	0.727895i	$0.259501\pi$
$314$	4.08040	−	6.49391i	0.0129949	−	0.0206813i
$315$	−237.806	−	149.423i	−0.754939	−	0.474359i
$316$	105.619	−	301.843i	0.334238	−	0.955198i
$317$	147.079	−	147.079i	0.463972	−	0.463972i	−0.435983	−	0.899955i	$-0.643599\pi$
$317$	147.079	−	147.079i	0.463972	−	0.463972i	0.899955	+	0.435983i	$0.143599\pi$
$318$	−52.0408	+	11.8780i	−0.163650	+	0.0373521i
$319$	−128.680	−	80.8549i	−0.403385	−	0.253464i
$320$	373.249	+	130.605i	1.16640	+	0.408142i
$321$	10.0657	+	28.7660i	0.0313572	+	0.0896136i
$322$	65.8625	−	7.42092i	0.204542	−	0.0230463i
$323$	60.3589	+	96.0607i	0.186870	+	0.297402i
$324$	106.704	+	24.3544i	0.329333	+	0.0751680i
$325$	−409.354	−	409.354i	−1.25955	−	1.25955i
$326$	−105.167	−	105.167i	−0.322599	−	0.322599i
$327$	94.6666	+	270.542i	0.289500	+	0.827345i
$328$	−1.17445	−	10.4235i	−0.00358065	−	0.0317791i
$329$	22.5996	+	99.0152i	0.0686917	+	0.300958i
$330$	−22.9289	−	28.7519i	−0.0694814	−	0.0871269i
$331$	223.301	+	463.689i	0.674625	+	1.40087i	0.903999	+	0.427534i	$0.140618\pi$
$331$	223.301	+	463.689i	0.674625	+	1.40087i	−0.229375	+	0.973338i	$0.573668\pi$
$332$	−95.6470	−	419.057i	−0.288093	−	1.26222i
$333$	184.345	+	147.010i	0.553589	+	0.441472i
$334$	−80.3192	+	64.0524i	−0.240477	+	0.191774i
$335$	287.740	+	229.465i	0.858925	+	0.684970i
$336$	−41.8957	+	66.6767i	−0.124690	+	0.198442i
$337$	297.767	+	33.5503i	0.883582	+	0.0995557i	0.542081	−	0.840326i	$-0.317636\pi$
$337$	297.767	+	33.5503i	0.883582	+	0.0995557i	0.341500	+	0.939882i	$0.389065\pi$
$338$	−26.1439	+	41.6078i	−0.0773489	+	0.123100i
$339$	154.289	+	193.472i	0.455128	+	0.570713i
$340$	115.812	+	26.4333i	0.340623	+	0.0777450i
$341$	−70.5864	+	16.1109i	−0.206998	+	0.0472460i
$342$	119.887	+	13.5080i	0.350546	+	0.0394970i
$343$	146.372	+	303.945i	0.426741	+	0.886137i
$344$	66.6411	−	190.449i	0.193724	−	0.553632i
$345$	−425.899	−	97.2087i	−1.23449	−	0.281764i
$346$	−5.79720	−	16.5674i	−0.0167549	−	0.0478828i
$347$	−128.609	−	61.9346i	−0.370630	−	0.178486i	0.239292	−	0.970948i	$-0.423085\pi$
$347$	−128.609	−	61.9346i	−0.370630	−	0.178486i	−0.609922	+	0.792462i	$0.708799\pi$
$348$	−83.3689	+	132.681i	−0.239566	+	0.381267i
$349$	570.032	−	199.463i	1.63333	−	0.571527i	0.651065	−	0.759022i	$-0.274323\pi$
$349$	570.032	−	199.463i	1.63333	−	0.571527i	0.982266	+	0.187495i	$0.0600368\pi$
$350$	−136.665	+	47.8210i	−0.390470	+	0.136632i
$351$	−120.979	+	151.702i	−0.344668	+	0.432200i
$352$	90.7796	−	72.3943i	0.257897	−	0.205666i
$353$	−103.360	+	452.850i	−0.292805	+	1.28286i	0.587799	+	0.809007i	$0.299995\pi$
$353$	−103.360	+	452.850i	−0.292805	+	1.28286i	−0.880604	+	0.473854i	$0.842863\pi$
$354$	−26.5028	−	21.1352i	−0.0748666	−	0.0597041i
$355$	330.896	+	159.351i	0.932101	+	0.448876i
$356$	22.0013	+	195.267i	0.0618013	+	0.548502i
$357$	−8.60817	+	17.8751i	−0.0241125	+	0.0500702i
$358$			40.5053i			0.113143i
$359$	157.339	−	449.648i	0.438269	−	1.25250i	−0.487071	−	0.873363i	$-0.661935\pi$
$359$	157.339	−	449.648i	0.438269	−	1.25250i	0.925340	−	0.379139i	$-0.123780\pi$
$360$	204.222	−	162.862i	0.567283	−	0.452393i
$361$	−835.499			−2.31440
$362$	116.641	−	73.2901i	0.322212	−	0.202459i
$363$	−134.034	+	15.1020i	−0.369240	+	0.0416034i
$364$	70.7097	+	112.534i	0.194257	+	0.309159i
$365$	−484.871	−	386.672i	−1.32841	−	1.05937i
$366$	−20.8103	−	16.5956i	−0.0568587	−	0.0453433i
$367$	143.318	−	409.579i	0.390512	−	1.11602i	−0.566019	−	0.824392i	$-0.691517\pi$
$367$	143.318	−	409.579i	0.390512	−	1.11602i	0.956532	−	0.291628i	$-0.0941970\pi$
$368$	90.8015	−	397.827i	0.246743	−	1.08105i
$369$	16.7615	+	8.07190i	0.0454241	+	0.0218751i
$370$	161.774	−	36.9239i	0.437228	−	0.0997944i
$371$	−241.133	−	192.297i	−0.649953	−	0.518320i
$372$	16.6118	+	72.7811i	0.0446554	+	0.195648i
$373$	−6.94561	−	11.0539i	−0.0186209	−	0.0296350i	0.837284	−	0.546768i	$-0.184142\pi$
$373$	−6.94561	−	11.0539i	−0.0186209	−	0.0296350i	−0.855905	+	0.517133i	$0.826999\pi$
$374$	6.11972	−	6.11972i	0.0163629	−	0.0163629i
$375$	605.909			1.61576
$376$	−93.8640	−	10.5759i	−0.249638	−	0.0281275i
$377$	130.524	+	207.728i	0.346219	+	0.551004i
$378$	21.0560	+	43.7233i	0.0557038	+	0.115670i
$379$	15.1764	−	7.30857i	0.0400433	−	0.0192838i	−0.413755	−	0.910388i	$-0.635783\pi$
$379$	15.1764	−	7.30857i	0.0400433	−	0.0192838i	0.453798	+	0.891104i	$0.350069\pi$
$380$	−885.878	+	885.878i	−2.33126	+	2.33126i
$381$	33.9392	+	11.8758i	0.0890793	+	0.0311702i
$382$	12.4824	+	110.784i	0.0326764	+	0.290011i
$383$	−253.181	+	28.5267i	−0.661048	+	0.0744822i	−0.436113	−	0.899892i	$-0.643645\pi$
$383$	−253.181	+	28.5267i	−0.661048	+	0.0744822i	−0.224934	+	0.974374i	$0.572217\pi$
$384$	−98.2255	−	123.171i	−0.255796	−	0.320757i
$385$	47.2820	−	207.156i	0.122810	−	0.538067i
$386$	−120.475	+	42.1560i	−0.312111	+	0.109212i
$387$	223.120	+	279.783i	0.576537	+	0.722954i
$388$	−377.365			−0.972591
$389$	−408.216	+	256.499i	−1.04940	+	0.659380i	−0.942266	−	0.334865i	$-0.891309\pi$
$389$	−408.216	+	256.499i	−1.04940	+	0.659380i	−0.107131	+	0.994245i	$0.534166\pi$
$390$	13.2102	+	57.8777i	0.0338723	+	0.148404i
$391$	11.5109	−	102.162i	0.0294396	−	0.261283i
$392$	−121.742	+	13.7170i	−0.310566	+	0.0349924i
$393$		−	183.064i		−	0.465811i
$394$	−21.6679	+	96.8669i	−0.0549946	+	0.245855i
$395$	825.336			2.08946
$396$	15.2052	+	134.950i	0.0383971	+	0.340783i
$397$	−262.017	−	29.5222i	−0.659993	−	0.0743633i	−0.224386	−	0.974500i	$-0.572038\pi$
$397$	−262.017	−	29.5222i	−0.659993	−	0.0743633i	−0.435607	+	0.900137i	$0.643466\pi$
$398$	105.417	−	24.0607i	0.264867	−	0.0604541i
$399$	−111.323	−	177.169i	−0.279004	−	0.444033i
$400$			891.421i			2.22855i
$401$	18.0834	−	14.4210i	0.0450957	−	0.0359626i	−0.600683	−	0.799488i	$-0.705104\pi$
$401$	18.0834	−	14.4210i	0.0450957	−	0.0359626i	0.645778	+	0.763525i	$0.276533\pi$
$402$	−9.13128	−	26.0957i	−0.0227146	−	0.0649147i
$403$	113.948	+	26.0079i	0.282749	+	0.0645356i
$404$	−10.6643	+	8.50449i	−0.0263968	+	0.0210507i
$405$	31.6269	+	280.696i	0.0780910	+	0.693077i
$406$	60.9732	−	6.87003i	0.150180	−	0.0169212i
$407$	−58.9174	+	168.376i	−0.144760	+	0.413701i
$408$	−13.0476	−	13.0476i	−0.0319795	−	0.0319795i
$409$	246.102	+	511.035i	0.601716	+	1.24948i	0.950048	+	0.312104i	$0.101034\pi$
$409$	246.102	+	511.035i	0.601716	+	1.24948i	−0.348332	+	0.937371i	$0.613252\pi$
$410$	11.7959	−	5.68061i	0.0287705	−	0.0138551i
$411$	−160.608	+	100.917i	−0.390773	+	0.245539i
$412$	−50.1764	+	445.328i	−0.121787	+	1.08089i
$413$		−	195.862i		−	0.474241i
$414$	−77.3071	−	77.3071i	−0.186732	−	0.186732i
$415$	939.315	−	590.210i	2.26341	−	1.42219i
$416$	−182.740	+	41.7092i	−0.439278	+	0.100262i
$417$	−106.750	+	133.860i	−0.255994	+	0.321007i
$418$	20.3107	+	88.9871i	0.0485903	+	0.212888i
$419$	305.160	−	633.671i	0.728305	−	1.51234i	−0.125696	−	0.992069i	$-0.540116\pi$
$419$	305.160	−	633.671i	0.728305	−	1.51234i	0.854001	−	0.520272i	$-0.174169\pi$
$420$	−213.597	−	48.7521i	−0.508564	−	0.116077i
$421$	−714.242	−	249.924i	−1.69654	−	0.593644i	−0.703420	−	0.710774i	$-0.748345\pi$
$421$	−714.242	−	249.924i	−1.69654	−	0.593644i	−0.993117	+	0.117131i	$0.962630\pi$
$422$	−33.7717	+	42.3484i	−0.0800277	+	0.100352i
$423$	104.452	−	130.978i	0.246931	−	0.309641i
$424$	242.881	−	152.612i	0.572833	−	0.359935i
$425$	25.1460	+	223.177i	0.0591670	+	0.525122i
$426$	−14.6786	−	23.3608i	−0.0344567	−	0.0548375i
$427$		−	153.793i		−	0.360171i
$428$	−49.3820	−	61.9231i	−0.115379	−	0.144680i
$429$	−60.2396	−	21.0788i	−0.140419	−	0.0491346i
$430$	251.842			0.585678
$431$	279.908	+	134.797i	0.649439	+	0.312753i	0.729443	−	0.684041i	$-0.239779\pi$
$431$	279.908	+	134.797i	0.649439	+	0.312753i	−0.0800046	+	0.996794i	$0.525494\pi$
$432$	296.899	−	33.4525i	0.687267	−	0.0774363i
$433$	27.0646	−	56.2002i	0.0625048	−	0.129793i	−0.867376	−	0.497653i	$-0.834195\pi$
$433$	27.0646	−	56.2002i	0.0625048	−	0.129793i	0.929881	+	0.367860i	$0.119910\pi$
$434$	18.2258	−	22.8545i	0.0419950	−	0.0526601i
$435$	−394.283	−	89.9925i	−0.906397	−	0.206879i
$436$	−464.434	−	582.382i	−1.06522	−	1.33574i
$437$	847.714	+	676.029i	1.93985	+	1.54698i
$438$	15.3871	+	43.9739i	0.0351304	+	0.100397i
$439$	26.0692	+	74.5016i	0.0593832	+	0.169707i	0.969753	−	0.244088i	$-0.0784886\pi$
$439$	26.0692	+	74.5016i	0.0593832	+	0.169707i	−0.910370	+	0.413795i	$0.864203\pi$
$440$	167.331	+	105.141i	0.380297	+	0.238957i
$441$	94.2759	−	195.766i	0.213777	−	0.443913i
$442$	−13.1871	+	4.61437i	−0.0298351	+	0.0104398i
$443$	10.6763	−	46.7759i	0.0241000	−	0.105589i	−0.961447	−	0.274989i	$-0.911326\pi$
$443$	10.6763	−	46.7759i	0.0241000	−	0.105589i	0.985547	+	0.169400i	$0.0541830\pi$
$444$	173.612	+	60.7494i	0.391017	+	0.136823i
$445$	−456.926	+	220.044i	−1.02680	+	0.494481i
$446$	17.4437	−	154.817i	0.0391115	−	0.347124i
$447$	−49.6984	−	217.743i	−0.111182	−	0.487121i
$448$	38.1932	−	167.336i	0.0852528	−	0.373517i
$449$	−241.905	+	192.913i	−0.538764	+	0.429650i	−0.854694	−	0.519133i	$-0.826255\pi$
$449$	−241.905	+	192.913i	−0.538764	+	0.429650i	0.315930	+	0.948783i	$0.397684\pi$
$450$	202.226	+	127.067i	0.449391	+	0.282371i
$451$	−1.57590	+	13.9865i	−0.00349422	+	0.0310121i
$452$	−544.534	−	342.153i	−1.20472	−	0.756976i
$453$	95.7554	−	120.073i	0.211381	−	0.265063i
$454$	36.9782	+	46.3692i	0.0814498	+	0.102135i
$455$	−213.865	+	268.178i	−0.470033	+	0.589402i
$456$	189.726	−	43.3038i	0.416067	−	0.0949645i
$457$	−590.857	+	284.542i	−1.29290	+	0.622629i	−0.948674	−	0.316256i	$-0.897574\pi$
$457$	−590.857	+	284.542i	−1.29290	+	0.622629i	−0.344229	+	0.938886i	$0.611860\pi$
$458$	−136.739	+	109.045i	−0.298556	+	0.238090i
$459$	73.3882	−	16.7504i	0.159887	−	0.0364932i
$460$	1128.17	−	127.114i	2.45254	−	0.276335i
$461$	−374.564	+	131.066i	−0.812504	+	0.284307i	−0.704374	−	0.709829i	$-0.748772\pi$
$461$	−374.564	+	131.066i	−0.812504	+	0.284307i	−0.108130	+	0.994137i	$0.534486\pi$
$462$	−11.2869	+	11.2869i	−0.0244304	+	0.0244304i
$463$	230.481	−	230.481i	0.497799	−	0.497799i	−0.412954	−	0.910752i	$-0.635503\pi$
$463$	230.481	−	230.481i	0.497799	−	0.497799i	0.910752	+	0.412954i	$0.135503\pi$
$464$	84.0609	−	368.295i	0.181166	−	0.793739i
$465$	−163.139	+	102.507i	−0.350836	+	0.220445i
$466$	−23.6044	−	209.495i	−0.0506532	−	0.449559i
$467$	844.994	−	295.676i	1.80941	−	0.633139i	0.810534	−	0.585691i	$-0.199177\pi$
$467$	844.994	−	295.676i	1.80941	−	0.633139i	0.998874	−	0.0474483i	$-0.0151089\pi$
$468$	72.4068	−	206.927i	0.154715	−	0.442151i
$469$	84.9885	−	135.258i	0.181212	−	0.288398i
$470$	−26.2347	−	114.942i	−0.0558185	−	0.244557i
$471$	15.5147	+	15.5147i	0.0329398	+	0.0329398i
$472$	171.940	+	60.1644i	0.364280	+	0.127467i
$473$	−144.043	+	229.242i	−0.304530	+	0.484656i
$474$	−52.4973	−	32.9862i	−0.110754	−	0.0695912i
$475$	−2134.06	−	1027.71i	−4.49276	−	2.16360i
$476$	5.77293	−	51.2362i	0.0121280	−	0.107639i
$477$			508.744i			1.06655i
$478$	−47.2832	+	47.2832i	−0.0989188	+	0.0989188i
$479$	585.029	+	281.735i	1.22135	+	0.588173i	0.929688	−	0.368347i	$-0.120076\pi$
$479$	585.029	+	281.735i	1.22135	+	0.588173i	0.291666	+	0.956520i	$0.405790\pi$
$480$	164.392	−	261.628i	0.342483	−	0.545058i
$481$	203.626	−	203.626i	0.423339	−	0.423339i
$482$	−5.27505	+	2.54033i	−0.0109441	+	0.00527039i
$483$	−21.2300	+	188.421i	−0.0439545	+	0.390107i
$484$	315.823	−	152.092i	0.652526	−	0.314240i
$485$	−321.671	−	919.282i	−0.663239	−	1.89543i
$486$	54.3647	−	112.890i	0.111862	−	0.232283i
$487$		−	339.573i		−	0.697276i	−0.937257	−	0.348638i	$-0.886644\pi$
$487$		−	339.573i		−	0.697276i	0.937257	−	0.348638i	$-0.113356\pi$
$488$	135.009	+	47.2418i	0.276659	+	0.0968070i
$489$	360.271	−	226.373i	0.736751	−	0.462931i
$490$	−66.3467	−	137.770i	−0.135401	−	0.281164i
$491$	214.229	+	48.8963i	0.436311	+	0.0995852i	0.435034	−	0.900414i	$-0.356736\pi$
$491$	214.229	+	48.8963i	0.436311	+	0.0995852i	0.00127726	+	0.999999i	$0.499593\pi$
$492$	14.4213	+	1.62490i	0.0293117	+	0.00330263i
$493$	10.6564	−	94.5778i	0.0216153	−	0.191841i
$494$	32.7877	−	143.652i	0.0663719	−	0.290794i
$495$	−315.785	+	152.074i	−0.637949	+	0.307220i
$496$	−95.7504	−	152.386i	−0.193045	−	0.307230i
$497$	52.6500	−	150.465i	0.105936	−	0.302746i
$498$	−83.3360			−0.167341
$499$	142.157	+	68.4593i	0.284884	+	0.137193i	0.570869	−	0.821041i	$-0.306606\pi$
$499$	142.157	+	68.4593i	0.284884	+	0.137193i	−0.285985	+	0.958234i	$0.592321\pi$
$500$	−1486.29	+	520.076i	−2.97258	+	1.04015i
$501$	−127.518	−	264.794i	−0.254527	−	0.528531i
$502$	−133.203	−	15.0084i	−0.265345	−	0.0298971i
$503$	−39.6977	−	82.4331i	−0.0789218	−	0.163883i	0.857774	−	0.514027i	$-0.171847\pi$
$503$	−39.6977	−	82.4331i	−0.0789218	−	0.163883i	−0.936696	+	0.350144i	$0.886133\pi$
$504$	−80.1696	−	80.1696i	−0.159067	−	0.159067i
$505$	−29.8078	−	18.7295i	−0.0590253	−	0.0370880i
$506$	35.8882	−	74.5227i	0.0709254	−	0.147278i
$507$	−99.4055	−	99.4055i	−0.196066	−	0.196066i
$508$	−93.4463			−0.183949
$509$	−470.922	−	53.0602i	−0.925191	−	0.104244i	−0.363503	−	0.931593i	$-0.618419\pi$
$509$	−470.922	−	53.0602i	−0.925191	−	0.104244i	−0.561688	+	0.827349i	$0.689848\pi$
$510$	9.99278	−	20.7502i	0.0195937	−	0.0406867i
$511$	−143.214	+	227.924i	−0.280263	+	0.446035i
$512$	416.467	+	261.684i	0.813412	+	0.511101i
$513$	−262.206	+	749.343i	−0.511124	+	1.46071i
$514$	−12.6600	+	12.6600i	−0.0246304	+	0.0246304i
$515$	−1127.61	+	257.370i	−2.18954	+	0.499748i
$516$	236.370	+	148.521i	0.458082	+	0.287832i
$517$	119.632	+	41.8612i	0.231397	+	0.0809694i
$518$	−23.7878	−	67.9815i	−0.0459223	−	0.131238i
$519$	49.8988	−	5.62225i	0.0961442	−	0.0108328i
$520$	−169.729	−	270.123i	−0.326403	−	0.519467i
$521$	−936.628	−	213.779i	−1.79775	−	0.410325i	−0.812713	−	0.582664i	$-0.802011\pi$
$521$	−936.628	−	213.779i	−1.79775	−	0.410325i	−0.985038	+	0.172339i	$0.944868\pi$
$522$	−71.5682	−	71.5682i	−0.137104	−	0.137104i
$523$	−633.113	−	633.113i	−1.21054	−	1.21054i	−0.970849	−	0.239691i	$-0.922954\pi$
$523$	−633.113	−	633.113i	−1.21054	−	1.21054i	−0.239691	−	0.970849i	$-0.577046\pi$
$524$	157.131	+	449.055i	0.299869	+	0.856975i
$525$	−46.3778	−	411.615i	−0.0883388	−	0.784028i
$526$	−8.01209	−	35.1033i	−0.0152321	−	0.0667362i
$527$	−28.2708	−	35.4504i	−0.0536447	−	0.0672684i
$528$	42.6390	+	88.5407i	0.0807556	+	0.167691i
$529$	−100.927	−	442.190i	−0.190788	−	0.835899i
$530$	279.918	+	223.228i	0.528148	+	0.421184i
$531$	−252.592	+	201.435i	−0.475691	+	0.379351i
$532$	425.146	+	339.042i	0.799146	+	0.637297i
$533$	12.0884	−	19.2386i	0.0226800	−	0.0360950i
$534$	37.8582	+	4.26560i	0.0708956	+	0.00798801i
$535$	108.754	−	173.081i	0.203279	−	0.323516i
$536$	92.6320	+	116.157i	0.172821	+	0.216711i
$537$	−112.974	−	25.7855i	−0.210379	−	0.0480176i
$538$	124.501	−	28.4166i	0.231415	−	0.0528190i
$539$	163.355	+	18.4057i	0.303070	+	0.0341478i
$540$	360.672	+	748.943i	0.667911	+	1.38693i
$541$	−87.3552	+	249.647i	−0.161470	+	0.461454i	−0.995984	−	0.0895324i	$-0.971463\pi$
$541$	−87.3552	+	249.647i	−0.161470	+	0.461454i	0.834514	+	0.550987i	$0.185748\pi$
$542$	−233.587	−	53.3147i	−0.430972	−	0.0983666i
$543$	130.161	+	371.979i	0.239707	+	0.685044i
$544$	65.5157	+	31.5507i	0.120433	+	0.0579976i
$545$	1022.82	−	1627.82i	1.87674	−	2.98682i
$546$	24.3216	−	8.51050i	0.0445451	−	0.0155870i
$547$	−252.737	+	88.4365i	−0.462042	+	0.161676i	−0.551255	−	0.834337i	$-0.685851\pi$
$547$	−252.737	+	88.4365i	−0.462042	+	0.161676i	0.0892125	+	0.996013i	$0.471565\pi$
$548$	307.349	−	385.404i	0.560857	−	0.703292i
$549$	−198.338	+	158.169i	−0.361272	+	0.288105i
$550$	−40.2078	+	176.162i	−0.0731050	+	0.320294i
$551$	784.784	+	625.844i	1.42429	+	1.13583i
$552$	−158.887	−	76.5160i	−0.287839	−	0.138616i
$553$	−40.1094	−	355.981i	−0.0725306	−	0.643727i
$554$	−26.1963	+	54.3972i	−0.0472858	+	0.0981899i
$555$			474.711i			0.855335i
$556$	146.959	−	419.985i	0.264315	−	0.755369i
$557$	−103.199	+	82.2982i	−0.185276	+	0.147753i	−0.711736	−	0.702448i	$-0.752091\pi$
$557$	−103.199	+	82.2982i	−0.185276	+	0.147753i	0.526460	+	0.850200i	$0.323519\pi$
$558$	−48.2186			−0.0864133
$559$	370.067	−	232.529i	0.662016	−	0.415972i
$560$	524.856	−	59.1370i	0.937242	−	0.105602i
$561$	13.1728	+	20.9643i	0.0234808	+	0.0373696i
$562$	−81.1230	−	64.6935i	−0.144347	−	0.115113i
$563$	−411.010	−	327.770i	−0.730036	−	0.582185i	0.186348	−	0.982484i	$-0.440335\pi$
$563$	−411.010	−	327.770i	−0.730036	−	0.582185i	−0.916384	+	0.400299i	$0.868906\pi$
$564$	43.1628	−	123.352i	0.0765298	−	0.218710i
$565$	369.337	−	1618.17i	0.653693	−	2.86402i
$566$	34.2066	+	16.4731i	0.0604358	+	0.0291043i
$567$	119.532	−	27.2824i	0.210815	−	0.0481171i
$568$	115.915	+	92.4391i	0.204076	+	0.162745i
$569$	219.937	+	963.606i	0.386532	+	1.69351i	0.676477	+	0.736464i	$0.263506\pi$
$569$	219.937	+	963.606i	0.386532	+	1.69351i	−0.289945	+	0.957043i	$0.593637\pi$
$570$	129.229	+	205.666i	0.226717	+	0.360818i
$571$	−166.766	+	166.766i	−0.292060	+	0.292060i	−0.837894	−	0.545834i	$-0.816213\pi$
$571$	−166.766	+	166.766i	−0.292060	+	0.292060i	0.545834	+	0.837894i	$0.316213\pi$
$572$	165.860			0.289966
$573$	−316.936	−	35.7101i	−0.553116	−	0.0623212i
$574$	−3.02339	−	4.81170i	−0.00526724	−	0.00838276i
$575$	931.309	+	1933.88i	1.61967	+	3.36328i
$576$	−255.083	+	122.842i	−0.442853	+	0.213267i
$577$	11.2549	−	11.2549i	0.0195059	−	0.0195059i	−0.697287	−	0.716792i	$-0.745609\pi$
$577$	11.2549	−	11.2549i	0.0195059	−	0.0195059i	0.716792	+	0.697287i	$0.245609\pi$
$578$	−132.329	−	46.3038i	−0.228942	−	0.0801103i
$579$	−40.8838	−	362.854i	−0.0706110	−	0.626690i
$580$	1044.42	−	117.678i	1.80072	−	0.202893i
$581$	−300.216	−	376.459i	−0.516723	−	0.647950i
$582$	−16.2804	+	71.3291i	−0.0279732	+	0.122559i
$583$	−363.297	+	127.123i	−0.623152	+	0.218050i
$584$	−156.094	−	195.736i	−0.267285	−	0.335164i
$585$	565.805			0.967188
$586$	−84.1070	+	52.8479i	−0.143527	+	0.0901842i
$587$	−1.27936	−	5.60526i	−0.00217949	−	0.00954899i	0.973826	−	0.227293i	$-0.0729874\pi$
$587$	−1.27936	−	5.60526i	−0.00217949	−	0.00954899i	−0.976006	+	0.217744i	$0.930130\pi$
$588$	18.9780	−	168.434i	0.0322755	−	0.286453i
$589$	475.201	−	53.5423i	0.806793	−	0.0909037i
$590$			227.366i			0.385366i
$591$	−256.378	−	122.099i	−0.433804	−	0.206597i
$592$	−443.422			−0.749024
$593$	−21.8286	−	193.734i	−0.0368105	−	0.326702i	−0.998599	−	0.0529097i	$-0.983150\pi$
$593$	−21.8286	−	193.734i	−0.0368105	−	0.326702i	0.961789	−	0.273792i	$-0.0882781\pi$
$594$	60.1818	+	6.78086i	0.101316	+	0.0114156i
$595$	129.735	−	29.6112i	0.218042	−	0.0497667i
$596$	308.808	+	491.465i	0.518134	+	0.824605i
$597$			309.336i			0.518151i
$598$	−104.394	+	83.2518i	−0.174573	+	0.139217i
$599$	36.7105	+	104.912i	0.0612862	+	0.175146i	0.970455	−	0.241281i	$-0.0775677\pi$
$599$	36.7105	+	104.912i	0.0612862	+	0.175146i	−0.909169	+	0.416427i	$0.863282\pi$
$600$	375.588	+	85.7256i	0.625981	+	0.142876i
$601$	−139.399	+	111.167i	−0.231945	+	0.184970i	−0.732565	−	0.680697i	$-0.761677\pi$
$601$	−139.399	+	111.167i	−0.231945	+	0.184970i	0.500620	+	0.865667i	$0.333106\pi$
$602$	−12.2389	−	108.623i	−0.0203304	−	0.180438i
$603$	−261.842	+	29.5026i	−0.434233	+	0.0489263i
$604$	−131.824	+	376.730i	−0.218251	+	0.623726i
$605$	639.716	+	639.716i	1.05738	+	1.05738i
$606$	1.14743	+	2.38265i	0.00189344	+	0.00393177i
$607$	795.548	−	383.116i	1.31062	−	0.631163i	0.357547	−	0.933895i	$-0.383613\pi$
$607$	795.548	−	383.116i	1.31062	−	0.631163i	0.953076	+	0.302732i	$0.0978988\pi$
$608$	−649.360	+	408.020i	−1.06803	+	0.671086i
$609$	−19.6540	+	174.434i	−0.0322726	+	0.286427i
$610$			178.530i			0.292673i
$611$	−144.678	−	144.678i	−0.236788	−	0.236788i
$612$	−72.0137	+	45.2492i	−0.117669	+	0.0739366i
$613$	−118.763	+	27.1070i	−0.193741	+	0.0442202i	−0.318290	−	0.947993i	$-0.603109\pi$
$613$	−118.763	+	27.1070i	−0.193741	+	0.0442202i	0.124549	+	0.992213i	$0.460252\pi$
$614$	54.2445	−	68.0205i	0.0883461	−	0.110783i
$615$	8.33460	+	36.5163i	0.0135522	+	0.0593760i
$616$	37.2171	−	77.2821i	0.0604174	−	0.125458i
$617$	62.0940	+	14.1726i	0.100639	+	0.0229701i	0.272544	−	0.962143i	$-0.412135\pi$
$617$	62.0940	+	14.1726i	0.100639	+	0.0229701i	−0.171905	+	0.985114i	$0.554992\pi$
$618$	82.0106	+	28.6967i	0.132703	+	0.0464348i
$619$	−293.673	+	368.254i	−0.474431	+	0.594918i	−0.960250	−	0.279142i	$-0.909950\pi$
$619$	−293.673	+	368.254i	−0.474431	+	0.594918i	0.485819	+	0.874059i	$0.338521\pi$
$620$	312.193	−	391.477i	0.503537	−	0.631415i
$621$	609.156	−	382.758i	0.980927	−	0.616357i
$622$	−19.5670	−	173.662i	−0.0314582	−	0.279199i
$623$	117.114	+	186.386i	0.187984	+	0.299175i
$624$		−	158.642i		−	0.254234i
$625$	−1466.51	−	1838.95i	−2.34642	−	2.94231i
$626$	−106.673	−	37.3263i	−0.170403	−	0.0596267i
$627$	−261.124			−0.416466
$628$	−51.3742	−	24.7405i	−0.0818061	−	0.0393957i
$629$	−111.015	+	12.5084i	−0.176495	+	0.0198862i
$630$	61.3995	−	127.497i	0.0974595	−	0.202377i
$631$	−34.9450	+	43.8196i	−0.0553803	+	0.0694447i	−0.808750	−	0.588152i	$-0.799856\pi$
$631$	−34.9450	+	43.8196i	−0.0553803	+	0.0694447i	0.753370	+	0.657597i	$0.228427\pi$
$632$	324.824	+	74.1390i	0.513962	+	0.117308i
$633$	−96.6152	−	121.152i	−0.152631	−	0.191393i
$634$	81.9389	+	65.3441i	0.129241	+	0.103066i
$635$	−79.6548	−	227.640i	−0.125441	−	0.358488i
$636$	131.076	+	374.594i	0.206094	+	0.588984i
$637$	−224.698	−	141.187i	−0.352744	−	0.221644i
$638$	33.2241	−	68.9905i	0.0520753	−	0.108136i
$639$	−248.195	+	86.8470i	−0.388411	+	0.135911i
$640$	−235.133	+	1030.18i	−0.367395	+	1.60966i
$641$	909.994	+	318.421i	1.41965	+	0.496756i	0.927522	−	0.373768i	$-0.121935\pi$
$641$	909.994	+	318.421i	1.41965	+	0.496756i	0.492125	+	0.870525i	$0.336220\pi$
$642$	−13.8351	+	6.66262i	−0.0215500	+	0.0103779i
$643$	−20.6480	+	183.256i	−0.0321119	+	0.285001i	0.967386	+	0.253308i	$0.0815186\pi$
$643$	−20.6480	+	183.256i	−0.0321119	+	0.285001i	−0.999498	+	0.0316934i	$0.989910\pi$
$644$	−109.653	−	480.420i	−0.170268	−	0.745993i
$645$	−160.321	+	702.413i	−0.248560	+	1.08901i
$646$	−44.6918	+	35.6405i	−0.0691824	+	0.0551711i
$647$	−718.693	−	451.584i	−1.11081	−	0.697967i	−0.153821	−	0.988099i	$-0.549158\pi$
$647$	−718.693	−	451.584i	−1.11081	−	0.697967i	−0.956987	+	0.290132i	$0.906301\pi$
$648$	−12.7674	+	113.313i	−0.0197027	+	0.174866i
$649$	−206.963	−	130.044i	−0.318895	−	0.200375i
$650$	181.867	−	228.054i	0.279795	−	0.350852i
$651$	52.1411	+	65.3828i	0.0800938	+	0.100434i
$652$	−689.438	+	864.529i	−1.05742	+	1.32596i
$653$	594.326	−	135.651i	0.910147	−	0.207735i	0.258282	−	0.966070i	$-0.416844\pi$
$653$	594.326	−	135.651i	0.910147	−	0.207735i	0.651866	+	0.758334i	$0.273987\pi$
$654$	−130.118	+	62.6614i	−0.198957	+	0.0958126i
$655$	−959.982	+	765.560i	−1.46562	+	1.16879i
$656$	−34.1094	+	7.78525i	−0.0519960	+	0.0118678i
$657$	441.231	−	49.7148i	0.671584	−	0.0756694i
$658$	−48.3013	+	16.9014i	−0.0734062	+	0.0256859i
$659$	623.502	−	623.502i	0.946133	−	0.946133i	−0.0524883	−	0.998622i	$-0.516715\pi$
$659$	623.502	−	623.502i	0.946133	−	0.946133i	0.998622	+	0.0524883i	$0.0167152\pi$
$660$	−193.334	+	193.334i	−0.292931	+	0.292931i
$661$	−128.394	+	562.533i	−0.194243	+	0.851033i	0.780045	+	0.625724i	$0.215196\pi$
$661$	−128.394	+	562.533i	−0.194243	+	0.851033i	−0.974287	+	0.225309i	$0.927661\pi$
$662$	−219.568	+	137.964i	−0.331674	+	0.208405i
$663$	−4.47512	−	39.7178i	−0.00674980	−	0.0599061i
$664$	422.700	−	147.909i	0.636596	−	0.222755i
$665$	−463.526	+	1324.68i	−0.697032	+	1.99200i
$666$	−63.2073	+	100.594i	−0.0949058	+	0.151042i
$667$	−202.410	−	886.816i	−0.303463	−	1.32956i
$668$	540.085	+	540.085i	0.808510	+	0.808510i
$669$	420.697	+	147.208i	0.628845	+	0.220042i
$670$	−98.6588	+	157.015i	−0.147252	+	0.234350i
$671$	−162.510	−	102.112i	−0.242191	−	0.152178i
$672$	−120.833	−	58.1903i	−0.179812	−	0.0865928i
$673$	54.2966	−	481.896i	0.0806785	−	0.716041i	−0.886637	−	0.462466i	$-0.846965\pi$
$673$	54.2966	−	481.896i	0.0806785	−	0.716041i	0.967316	−	0.253575i	$-0.0816066\pi$
$674$			150.983i			0.224010i
$675$	−1111.30	+	1111.30i	−1.64637	+	1.64637i
$676$	329.165	+	158.518i	0.486931	+	0.234493i
$677$	19.5018	−	31.0369i	0.0288062	−	0.0458448i	−0.832011	−	0.554759i	$-0.812810\pi$
$677$	19.5018	−	31.0369i	0.0288062	−	0.0458448i	0.860817	+	0.508915i	$0.169953\pi$
$678$	−88.1659	+	88.1659i	−0.130038	+	0.130038i
$679$	−380.869	+	183.417i	−0.560927	+	0.270128i
$680$	−13.8572	+	122.986i	−0.0203782	+	0.180861i
$681$	−152.869	+	73.6178i	−0.224477	+	0.108102i
$682$	−12.0487	−	34.4332i	−0.0176667	−	0.0504886i
$683$	−51.8320	+	107.630i	−0.0758888	+	0.157585i	−0.935461	−	0.353429i	$-0.885016\pi$
$683$	−51.8320	+	107.630i	−0.0758888	+	0.157585i	0.859573	+	0.511014i	$0.170730\pi$
$684$		−	896.977i		−	1.31137i
$685$	1200.85	+	420.197i	1.75307	+	0.613426i
$686$	−143.926	+	90.4345i	−0.209804	+	0.131829i
$687$	−217.092	−	450.796i	−0.316000	−	0.656180i
$688$	−656.115	−	149.754i	−0.953656	−	0.217666i
$689$	617.433	+	69.5680i	0.896130	+	0.100970i
$690$	24.6448	−	218.729i	0.0357171	−	0.316998i
$691$	231.211	−	1013.00i	0.334604	−	1.46599i	−0.475504	−	0.879714i	$-0.657734\pi$
$691$	231.211	−	1013.00i	0.334604	−	1.46599i	0.810108	−	0.586281i	$-0.199409\pi$
$692$	−117.576	+	56.6215i	−0.169907	+	0.0818230i
$693$	80.9384	+	128.813i	0.116794	+	0.185877i
$694$	23.7548	−	67.8874i	0.0342289	−	0.0978205i
$695$	1148.38			1.65234
$696$	−147.092	−	70.8359i	−0.211339	−	0.101776i
$697$	−8.32004	+	2.91131i	−0.0119369	+	0.00417691i
$698$	132.028	+	274.159i	0.189152	+	0.392778i
$699$	599.329	+	67.5282i	0.857410	+	0.0966069i
$700$	467.070	+	969.881i	0.667243	+	1.38554i
$701$	658.602	+	658.602i	0.939517	+	0.939517i	0.998272	−	0.0587553i	$-0.0187132\pi$
$701$	658.602	+	658.602i	0.939517	+	0.939517i	−0.0587553	+	0.998272i	$0.518713\pi$
$702$	−82.7813	−	52.0149i	−0.117922	−	0.0740953i
$703$	511.216	−	1061.55i	0.727192	−	1.51003i
$704$	−151.461	−	151.461i	−0.215144	−	0.215144i
$705$	337.285			0.478419
$706$	−232.570	−	26.2043i	−0.329419	−	0.0371166i
$707$	−6.62974	+	13.7668i	−0.00937728	+	0.0194721i
$708$	−134.087	+	213.398i	−0.189388	+	0.301410i
$709$	−341.292	−	214.448i	−0.481371	−	0.302466i	0.269399	−	0.963029i	$-0.413175\pi$
$709$	−341.292	−	214.448i	−0.481371	−	0.302466i	−0.750771	+	0.660563i	$0.770318\pi$
$710$	−61.1186	+	174.667i	−0.0860826	+	0.246010i
$711$	−417.838	+	417.838i	−0.587677	+	0.587677i
$712$	−199.597	+	45.5566i	−0.280332	+	0.0639840i
$713$	−366.930	−	230.557i	−0.514628	−	0.323362i
$714$	−9.43554	−	3.30164i	−0.0132150	−	0.00462414i
$715$	141.381	+	404.045i	0.197736	+	0.565098i
$716$	299.256	−	33.7181i	0.417956	−	0.0470923i
$717$	−101.778	−	161.978i	−0.141949	−	0.225911i
$718$	234.012	+	53.4117i	0.325922	+	0.0743895i
$719$	−169.699	−	169.699i	−0.236021	−	0.236021i	0.579179	−	0.815200i	$-0.303373\pi$
$719$	−169.699	−	169.699i	−0.236021	−	0.236021i	−0.815200	+	0.579179i	$0.803373\pi$
$720$	−616.057	−	616.057i	−0.855635	−	0.855635i
$721$	165.807	+	473.851i	0.229969	+	0.657213i
$722$	−47.1343	−	418.328i	−0.0652830	−	0.579402i
$723$	−3.72718	−	16.3298i	−0.00515515	−	0.0225862i
$724$	−638.569	−	800.741i	−0.882002	−	1.10600i
$725$	862.174	+	1790.32i	1.18921	+	2.46941i
$726$	−15.1230	−	66.2580i	−0.0208305	−	0.0912645i
$727$	102.254	+	81.5445i	0.140651	+	0.112166i	0.691288	−	0.722579i	$-0.257044\pi$
$727$	102.254	+	81.5445i	0.140651	+	0.112166i	−0.550637	+	0.834745i	$0.685615\pi$
$728$	−108.260	+	86.3344i	−0.148709	+	0.118591i
$729$	74.6726	+	59.5494i	0.102431	+	0.0816864i
$730$	166.250	−	264.585i	0.227740	−	0.362446i
$731$	−168.490	−	18.9843i	−0.230492	−	0.0259703i
$732$	−105.287	+	167.563i	−0.143834	+	0.228911i
$733$	738.039	+	925.472i	1.00687	+	1.26258i	0.964667	+	0.263472i	$0.0848678\pi$
$733$	738.039	+	925.472i	1.00687	+	1.26258i	0.0422079	+	0.999109i	$0.486561\pi$
$734$	213.159	+	48.6521i	0.290407	+	0.0662835i
$735$	426.492	−	97.3440i	0.580261	−	0.132441i
$736$	690.603	+	77.8123i	0.938319	+	0.105723i
$737$	−86.4962	−	179.611i	−0.117363	−	0.243706i
$738$	−3.09596	+	8.84773i	−0.00419506	+	0.0119888i
$739$	−235.422	−	53.7335i	−0.318568	−	0.0727111i	0.0602470	−	0.998184i	$-0.480811\pi$
$739$	−235.422	−	53.7335i	−0.318568	−	0.0727111i	−0.378815	+	0.925472i	$0.623668\pi$
$740$	−407.464	−	1164.46i	−0.550627	−	1.57360i
$741$	379.789	+	182.897i	0.512536	+	0.246824i
$742$	82.6783	−	131.582i	0.111426	−	0.177334i
$743$	1380.66	−	483.114i	1.85822	−	0.650221i	0.870910	−	0.491443i	$-0.163530\pi$
$743$	1380.66	−	483.114i	1.85822	−	0.650221i	0.987314	−	0.158778i	$-0.0507553\pi$
$744$	−73.4139	+	25.6886i	−0.0986745	+	0.0345277i
$745$	−934.003	+	1171.20i	−1.25370	+	1.57208i
$746$	5.14276	−	4.10122i	0.00689379	−	0.00549761i
$747$	−176.739	+	774.344i	−0.236598	+	1.03660i
$748$	−50.3072	−	40.1187i	−0.0672557	−	0.0536346i
$749$	−79.9380	−	38.4961i	−0.106726	−	0.0513967i
$750$	34.1821	+	303.374i	0.0455761	+	0.404499i
$751$	352.690	−	732.368i	0.469627	−	0.975190i	−0.522812	−	0.852448i	$-0.675117\pi$
$751$	352.690	−	732.368i	0.469627	−	0.975190i	0.992439	−	0.122742i	$-0.0391688\pi$
$752$			315.054i			0.418955i
$753$	126.656	−	361.963i	0.168202	−	0.480694i
$754$	−96.6447	+	77.0716i	−0.128176	+	0.102217i
$755$	−1030.10			−1.36438
$756$	305.504	−	191.961i	0.404105	−	0.253916i
$757$	−942.188	+	106.159i	−1.24463	+	0.140237i	−0.709606	−	0.704598i	$-0.751127\pi$
$757$	−942.188	+	106.159i	−1.24463	+	0.140237i	−0.535027	+	0.844835i	$0.679699\pi$
$758$	4.51552	+	7.18641i	0.00595715	+	0.00948076i
$759$	185.005	+	147.537i	0.243749	+	0.194383i
$760$	−1020.51	−	813.826i	−1.34277	−	1.07082i
$761$	408.577	−	1167.65i	0.536895	−	1.53436i	−0.281418	−	0.959585i	$-0.590805\pi$
$761$	408.577	−	1167.65i	0.536895	−	1.53436i	0.818313	−	0.574773i	$-0.194910\pi$
$762$	−4.03149	+	17.6631i	−0.00529067	+	0.0231799i
$763$	−751.810	−	362.053i	−0.985335	−	0.474512i
$764$	808.093	−	184.442i	1.05771	−	0.241416i
$765$	−171.615	−	136.858i	−0.224333	−	0.178900i
$766$	−28.5662	−	125.157i	−0.0372927	−	0.163390i
$767$	209.930	+	334.101i	0.273703	+	0.435595i
$768$	−110.625	+	110.625i	−0.144043	+	0.144043i
$769$	1245.06			1.61906			0.809529	−	0.587080i	$-0.199723\pi$
$769$	1245.06			1.61906			0.809529	+	0.587080i	$0.199723\pi$
$770$	106.389	+	11.9872i	0.138167	+	0.0155677i
$771$	−27.2509	−	43.3695i	−0.0353448	−	0.0562510i
$772$	411.740	+	854.986i	0.533341	+	1.10749i
$773$	−363.118	+	174.868i	−0.469752	+	0.226220i	−0.653757	−	0.756705i	$-0.726808\pi$
$773$	−363.118	+	174.868i	−0.469752	+	0.226220i	0.184005	+	0.982925i	$0.441094\pi$
$774$	−127.498	+	127.498i	−0.164727	+	0.164727i
$775$	893.551	+	312.667i	1.15297	+	0.403441i
$776$	−44.0206	−	390.693i	−0.0567275	−	0.503471i
$777$	204.751	−	23.0699i	0.263514	−	0.0296909i
$778$	−151.457	−	189.920i	−0.194674	−	0.244114i
$779$	20.6865	−	90.6334i	0.0265552	−	0.116346i
$780$	416.608	−	145.778i	0.534113	−	0.186894i
$781$	−124.036	−	155.536i	−0.158817	−	0.199150i
$782$	51.8011			0.0662418
$783$	563.935	−	354.344i	0.720223	−	0.452546i
$784$	90.9279	+	398.381i	0.115979	+	0.508139i
$785$	16.4772	−	146.240i	0.0209901	−	0.186292i
$786$	91.6588	−	10.3275i	0.116614	−	0.0131393i
$787$		−	148.380i		−	0.188538i	−0.995547	−	0.0942691i	$-0.969949\pi$
$787$		−	148.380i		−	0.188538i	0.995547	−	0.0942691i	$-0.0300514\pi$
$788$	733.697	+	79.4485i	0.931088	+	0.100823i
$789$	103.007			0.130554
$790$	46.5610	+	413.240i	0.0589380	+	0.523089i
$791$	−715.892	−	80.6617i	−0.905047	−	0.101974i
$792$	−137.943	+	31.4845i	−0.174170	+	0.0397532i
$793$	164.839	+	262.340i	0.207868	+	0.330820i
$794$		−	132.856i		−	0.167324i
$795$	−800.800	+	638.617i	−1.00730	+	0.803291i
$796$	−265.516	−	758.800i	−0.333562	−	0.953266i
$797$	−1222.06	−	278.928i	−1.53333	−	0.349972i	−0.629204	−	0.777240i	$-0.716619\pi$
$797$	−1222.06	−	278.928i	−1.53333	−	0.349972i	−0.904125	+	0.427268i	$0.859476\pi$
$798$	82.4271	−	65.7334i	0.103292	−	0.0823727i
$799$	8.88732	+	78.8772i	0.0111231	+	0.0987199i
$800$	−1508.65	+	169.984i	−1.88581	+	0.212480i
$801$	119.925	−	342.726i	0.149719	−	0.427872i
$802$	8.24067	+	8.24067i	0.0102751	+	0.0102751i
$803$	145.755	+	302.663i	0.181513	+	0.376915i
$804$	−185.196	+	89.1857i	−0.230343	+	0.110927i
$805$	1076.86	−	676.636i	1.33771	−	0.840541i
$806$	−6.59364	+	58.5201i	−0.00818069	+	0.0726056i
$807$			365.337i			0.452710i
$808$	−10.0489	−	10.0489i	−0.0124367	−	0.0124367i
$809$	−742.599	+	466.606i	−0.917922	+	0.576768i	−0.906054	−	0.423161i	$-0.860920\pi$
$809$	−742.599	+	466.606i	−0.917922	+	0.576768i	−0.0118672	+	0.999930i	$0.503778\pi$
$810$	−138.758	+	31.6707i	−0.171307	+	0.0390996i
$811$	484.423	−	607.447i	0.597316	−	0.749010i	−0.387641	−	0.921810i	$-0.626710\pi$
$811$	484.423	−	607.447i	0.597316	−	0.749010i	0.984957	+	0.172800i	$0.0552815\pi$
$812$	−101.513	−	444.756i	−0.125016	−	0.547729i
$813$	297.401	−	617.559i	0.365807	−	0.759605i
$814$	−87.6287	−	20.0007i	−0.107652	−	0.0245708i
$815$	−2693.72	−	942.575i	−3.30518	−	1.15653i
$816$	−38.3727	+	48.1179i	−0.0470254	+	0.0589680i
$817$	1114.94	−	1398.09i	1.36467	−	1.71125i
$818$	−241.988	+	152.051i	−0.295829	+	0.185882i
$819$	−27.4968	−	244.041i	−0.0335737	−	0.297974i
$820$	−51.7881	−	82.4203i	−0.0631563	−	0.100513i
$821$		−	496.494i		−	0.604743i	−0.953190	−	0.302371i	$-0.902222\pi$
$821$		−	496.494i		−	0.604743i	0.953190	−	0.302371i	$-0.0977783\pi$
$822$	−59.5888	−	74.7221i	−0.0724925	−	0.0909027i
$823$	−550.003	−	192.454i	−0.668290	−	0.233845i	−0.0252545	−	0.999681i	$-0.508040\pi$
$823$	−550.003	−	192.454i	−0.668290	−	0.233845i	−0.643036	+	0.765836i	$0.722325\pi$
$824$	−466.909			−0.566637
$825$	−465.738	−	224.287i	−0.564531	−	0.271864i
$826$	98.0666	−	11.0495i	0.118725	−	0.0133771i
$827$	144.402	−	299.854i	0.174610	−	0.362581i	−0.795236	−	0.606300i	$-0.792653\pi$
$827$	144.402	−	299.854i	0.174610	−	0.362581i	0.969846	+	0.243719i	$0.0783674\pi$
$828$	−506.798	+	635.504i	−0.612075	+	0.767517i
$829$	−39.8269	−	9.09024i	−0.0480421	−	0.0109653i	0.198432	−	0.980115i	$-0.436415\pi$
$829$	−39.8269	−	9.09024i	−0.0480421	−	0.0109653i	−0.246474	+	0.969149i	$0.579272\pi$
$830$	348.505	+	437.012i	0.419886	+	0.526520i
$831$	−135.043	−	107.693i	−0.162507	−	0.129595i
$832$	114.205	+	326.378i	0.137265	+	0.392281i
$833$	34.0026	+	97.1740i	0.0408195	+	0.116655i
$834$	−73.0449	−	45.8972i	−0.0875839	−	0.0550326i
$835$	−855.301	+	1776.05i	−1.02431	+	2.12701i
$836$	640.537	−	224.134i	0.766192	−	0.268102i
$837$	70.6054	−	309.342i	0.0843553	−	0.369585i
$838$	334.490	+	117.043i	0.399153	+	0.139670i
$839$	66.4319	−	31.9919i	0.0791799	−	0.0381310i	−0.393875	−	0.919164i	$-0.628866\pi$
$839$	66.4319	−	31.9919i	0.0791799	−	0.0381310i	0.473055	+	0.881033i	$0.343151\pi$
$840$	25.5574	−	226.828i	0.0304255	−	0.270033i
$841$	−0.243933	−	1.06874i	−0.000290051	−	0.00127080i
$842$	84.8416	−	371.715i	0.100762	−	0.441467i
$843$	232.079	−	185.077i	0.275302	−	0.219546i
$844$	340.986	+	214.256i	0.404012	+	0.253858i
$845$	−105.573	+	936.987i	−0.124939	+	1.10886i
$846$	71.4725	+	44.9092i	0.0844829	+	0.0530841i
$847$	244.831	−	307.009i	0.289057	−	0.362466i
$848$	−596.524	−	748.018i	−0.703448	−	0.882096i
$849$	−67.7209	+	84.9193i	−0.0797654	+	0.100023i
$850$	−110.324	+	25.1808i	−0.129793	+	0.0296245i
$851$	−961.977	+	463.264i	−1.13041	+	0.544376i
$852$	−160.372	+	127.893i	−0.188230	+	0.150109i
$853$	−441.832	+	100.845i	−0.517974	+	0.118224i	−0.473513	−	0.880787i	$-0.657014\pi$
$853$	−441.832	+	100.845i	−0.517974	+	0.118224i	−0.0444612	+	0.999011i	$0.514157\pi$
$854$	77.0031	−	8.67616i	0.0901675	−	0.0101594i
$855$	2185.09	−	764.594i	2.55566	−	0.894263i
$856$	58.3496	−	58.3496i	0.0681654	−	0.0681654i
$857$	−399.359	+	399.359i	−0.465997	+	0.465997i	−0.900615	−	0.434618i	$-0.856883\pi$
$857$	−399.359	+	399.359i	−0.465997	+	0.465997i	0.434618	+	0.900615i	$0.356883\pi$
$858$	7.15560	−	31.3507i	0.00833986	−	0.0365393i
$859$	229.516	−	144.214i	0.267189	−	0.167886i	−0.391773	−	0.920062i	$-0.628138\pi$
$859$	229.516	−	144.214i	0.267189	−	0.167886i	0.658963	+	0.752176i	$0.270995\pi$
$860$	−209.642	−	1860.63i	−0.243770	−	2.16352i
$861$	15.3450	−	5.36946i	0.0178223	−	0.00623630i
$862$	−51.7009	+	147.753i	−0.0599778	+	0.171407i
$863$	627.585	−	998.796i	0.727213	−	1.15735i	−0.254516	−	0.967069i	$-0.581916\pi$
$863$	627.585	−	998.796i	0.727213	−	1.15735i	0.981729	−	0.190285i	$-0.0609411\pi$
$864$	113.231	+	496.097i	0.131054	+	0.574186i
$865$	−238.156	−	238.156i	−0.275325	−	0.275325i
$866$	29.6659	+	10.3805i	0.0342562	+	0.0119868i
$867$	213.386	−	339.601i	0.246120	−	0.391697i
$868$	−184.023	−	115.629i	−0.212008	−	0.133213i
$869$	−402.789	−	193.973i	−0.463508	−	0.223214i
$870$	22.8153	−	202.492i	0.0262245	−	0.232749i
$871$			321.817i			0.369480i
$872$	548.773	−	548.773i	0.629327	−	0.629327i
$873$	628.250	+	302.549i	0.719645	+	0.346563i
$874$	−290.660	+	462.582i	−0.332563	+	0.529271i
$875$	−1247.31	+	1247.31i	−1.42550	+	1.42550i
$876$	312.074	−	150.287i	0.356249	−	0.171560i
$877$	−104.696	+	929.198i	−0.119379	+	1.05952i	0.781036	+	0.624487i	$0.214692\pi$
$877$	−104.696	+	929.198i	−0.119379	+	1.05952i	−0.900415	+	0.435033i	$0.856737\pi$
$878$	−35.8318	+	17.2557i	−0.0408107	+	0.0196534i
$879$	−93.8564	−	268.226i	−0.106776	−	0.305149i
$880$	285.992	−	593.869i	0.324991	−	0.674851i
$881$			731.304i			0.830084i	0.909802	+	0.415042i	$0.136233\pi$
$881$			731.304i			0.830084i	−0.909802	+	0.415042i	$0.863767\pi$
$882$	103.337	+	36.1592i	0.117162	+	0.0409969i
$883$	−1237.12	+	777.334i	−1.40104	+	0.880333i	−0.999371	−	0.0354515i	$-0.988713\pi$
$883$	−1237.12	+	777.334i	−1.40104	+	0.880333i	−0.401670	+	0.915784i	$0.631570\pi$
$884$	45.0688	+	93.5864i	0.0509828	+	0.105867i
$885$	−634.147	−	144.740i	−0.716551	−	0.163548i
$886$	24.0227	+	2.70670i	0.0271136	+	0.00305497i
$887$	51.9223	−	460.823i	0.0585369	−	0.519530i	−0.929891	−	0.367836i	$-0.880099\pi$
$887$	51.9223	−	460.823i	0.0585369	−	0.519530i	0.988428	−	0.151694i	$-0.0484727\pi$
$888$	−42.6427	+	186.830i	−0.0480211	+	0.210394i
$889$	−94.3139	+	45.4192i	−0.106090	+	0.0510902i
$890$	−135.952	−	216.366i	−0.152755	−	0.243108i
$891$	50.5352	−	144.421i	0.0567173	−	0.162089i
$892$	−1158.32			−1.29857
$893$	−754.239	−	363.222i	−0.844612	−	0.406744i
$894$	106.219	−	37.1675i	0.118813	−	0.0415744i
$895$	337.229	+	700.263i	0.376792	+	0.782417i
$896$	455.762	+	51.3520i	0.508663	+	0.0573126i
$897$	−165.741	−	344.165i	−0.184773	−	0.383684i
$898$	−110.237	−	110.237i	−0.122759	−	0.122759i
$899$	−339.691	−	213.442i	−0.377854	−	0.237421i
$900$	770.441	−	1599.84i	0.856045	−	1.77760i
$901$	−170.447	−	170.447i	−0.189175	−	0.189175i
$902$	−7.09183			−0.00786234
$903$	310.753	+	35.0135i	0.344134	+	0.0387746i
$904$	290.717	−	603.679i	0.321589	−	0.667787i
$905$	1406.32	−	2238.15i	1.55395	−	2.47310i
$906$	65.5220	+	41.1702i	0.0723200	+	0.0454417i
$907$	−237.794	+	679.577i	−0.262177	+	0.749258i	0.735265	+	0.677779i	$0.237057\pi$
$907$	−237.794	+	679.577i	−0.262177	+	0.749258i	−0.997442	+	0.0714787i	$0.977228\pi$
$908$	311.798	−	311.798i	0.343389	−	0.343389i
$909$	24.5727	−	5.60855i	0.0270326	−	0.00617002i
$910$	−146.340	−	91.9515i	−0.160813	−	0.101046i
$911$	−359.263	−	125.712i	−0.394361	−	0.137993i	0.125811	−	0.992054i	$-0.459847\pi$
$911$	−359.263	−	125.712i	−0.394361	−	0.137993i	−0.520173	+	0.854061i	$0.674132\pi$
$912$	−214.379	−	612.661i	−0.235065	−	0.671777i
$913$	−597.127	+	67.2800i	−0.654027	+	0.0736911i
$914$	−175.801	−	279.786i	−0.192342	−	0.306111i
$915$	−497.940	−	113.652i	−0.544197	−	0.124209i
$916$	919.462	+	919.462i	1.00378	+	1.00378i
$917$	376.852	+	376.852i	0.410961	+	0.410961i
$918$	12.5270	+	35.8000i	0.0136459	+	0.0389978i
$919$	154.123	+	1367.88i	0.167708	+	1.48845i	0.742333	+	0.670031i	$0.233719\pi$
$919$	154.123	+	1367.88i	0.167708	+	1.48845i	−0.574625	+	0.818417i	$0.694852\pi$
$920$	263.207	+	1153.18i	0.286094	+	1.25346i
$921$	155.185	+	194.595i	0.168496	+	0.211287i
$922$	−86.7546	−	180.148i	−0.0940939	−	0.195388i
$923$	71.4619	+	313.095i	0.0774235	+	0.339215i
$924$	92.7839	+	73.9927i	0.100415	+	0.0800787i
$925$	1823.60	−	1454.27i	1.97146	−	1.57218i
$926$	128.403	+	102.398i	0.138664	+	0.110581i
$927$	440.573	−	701.168i	0.475267	−	0.756384i
$928$	639.336	+	72.0359i	0.688940	+	0.0776249i
$929$	−135.577	+	215.769i	−0.145938	+	0.232260i	−0.911692	−	0.410874i	$-0.865223\pi$
$929$	−135.577	+	215.769i	−0.145938	+	0.232260i	0.765753	+	0.643134i	$0.222366\pi$
$930$	−60.5279	−	75.8996i	−0.0650837	−	0.0816124i
$931$	−1058.55	−	241.608i	−1.13701	−	0.259514i
$932$	−1528.11	+	348.782i	−1.63961	+	0.374230i
$933$	496.817	+	55.9778i	0.532494	+	0.0599977i
$934$	195.713	+	406.402i	0.209543	+	0.435120i
$935$	54.8488	−	156.749i	0.0586618	−	0.167646i
$936$	222.682	+	50.8256i	0.237908	+	0.0543009i
$937$	517.446	+	1478.78i	0.552237	+	1.57820i	0.794032	+	0.607876i	$0.207978\pi$
$937$	517.446	+	1478.78i	0.552237	+	1.57820i	−0.241795	+	0.970327i	$0.577736\pi$
$938$	72.5176	+	34.9226i	0.0773108	+	0.0372309i
$939$	172.014	−	273.759i	0.183189	−	0.291543i
$940$	−827.360	+	289.506i	−0.880170	+	0.307985i
$941$	797.849	−	279.179i	0.847873	−	0.296684i	0.128845	−	0.991665i	$-0.458873\pi$
$941$	797.849	−	279.179i	0.847873	−	0.296684i	0.719028	+	0.694981i	$0.244587\pi$
$942$	−6.89283	+	8.64333i	−0.00731723	+	0.00917551i
$943$	−65.8647	+	52.5253i	−0.0698459	+	0.0557003i
$944$	135.200	−	592.350i	0.143220	−	0.627489i
$945$	728.042	+	580.594i	0.770415	+	0.614385i
$946$	−122.906	−	59.1885i	−0.129922	−	0.0625672i
$947$	50.9355	+	452.065i	0.0537862	+	0.477365i	0.991515	+	0.129996i	$0.0414964\pi$
$947$	50.9355	+	452.065i	0.0537862	+	0.477365i	−0.937728	+	0.347369i	$0.887075\pi$
$948$	−200.004	+	415.313i	−0.210975	+	0.438094i
$949$		−	542.294i		−	0.571438i
$950$	394.175	−	1126.49i	0.414921	−	1.18578i
$951$	−234.413	+	186.938i	−0.246492	+	0.196570i
$952$	53.7192			0.0564277
$953$	−9.52771	+	5.98666i	−0.00999760	+	0.00628191i	−0.537022	−	0.843568i	$-0.680451\pi$
$953$	−9.52771	+	5.98666i	−0.00999760	+	0.00628191i	0.527024	+	0.849850i	$0.323308\pi$
$954$	−254.725	+	28.7006i	−0.267007	+	0.0300845i
$955$	1138.14	+	1811.34i	1.19177	+	1.89669i
$956$	388.692	+	309.972i	0.406582	+	0.324238i
$957$	171.272	+	136.584i	0.178967	+	0.142721i
$958$	−108.059	+	308.814i	−0.112796	+	0.322353i
$959$	122.879	−	538.369i	0.128133	−	0.561385i
$960$	−513.563	−	247.319i	−0.534961	−	0.257624i
$961$	750.571	−	171.313i	0.781031	−	0.178265i
$962$	113.442	+	90.4666i	0.117923	+	0.0940402i
$963$	32.5665	+	142.683i	0.0338178	+	0.148165i
$964$	23.1593	+	36.8578i	0.0240242	+	0.0382343i
$965$	−1731.82	+	1731.82i	−1.79463	+	1.79463i
$966$	−95.5390			−0.0989017
$967$	−797.386	−	89.8438i	−0.824598	−	0.0929099i	−0.310427	−	0.950597i	$-0.600472\pi$
$967$	−797.386	−	89.8438i	−0.824598	−	0.0929099i	−0.514171	+	0.857688i	$0.671900\pi$
$968$	194.305	+	309.235i	0.200729	+	0.319458i
$969$	−70.9546	−	147.339i	−0.0732246	−	0.152052i
$970$	442.131	−	212.919i	0.455806	−	0.219504i
$971$	−684.744	+	684.744i	−0.705194	+	0.705194i	−0.965521	−	0.260326i	$-0.916170\pi$
$971$	−684.744	+	684.744i	−0.705194	+	0.705194i	0.260326	+	0.965521i	$0.416170\pi$
$972$	−879.292	−	307.678i	−0.904622	−	0.316541i
$973$	−55.8085	−	495.314i	−0.0573571	−	0.509058i
$974$	170.022	−	19.1569i	0.174561	−	0.0196683i
$975$	520.291	+	652.424i	0.533632	+	0.669153i
$976$	106.161	−	465.120i	0.108771	−	0.476557i
$977$	726.505	−	254.215i	0.743608	−	0.260200i	0.0682281	−	0.997670i	$-0.478265\pi$
$977$	726.505	−	254.215i	0.743608	−	0.260200i	0.675380	+	0.737470i	$0.263980\pi$
$978$	133.668	+	167.615i	0.136675	+	0.171385i
$979$	274.709			0.280601
$980$	−962.629	+	604.860i	−0.982274	+	0.617204i
$981$	306.285	+	1341.92i	0.312218	+	1.36791i
$982$	−12.3964	+	110.021i	−0.0126237	+	0.112038i
$983$	−1789.97	+	201.682i	−1.82093	+	0.205170i	−0.955325	−	0.295557i	$-0.904495\pi$
$983$	−1789.97	+	201.682i	−1.82093	+	0.205170i	−0.865606	+	0.500727i	$0.833066\pi$
$984$			15.1202i			0.0153661i
$985$	431.872	+	1855.05i	0.438449	+	1.88330i
$986$	47.9556			0.0486365
$987$	−16.3913	−	145.477i	−0.0166072	−	0.147393i
$988$	−1088.61	−	122.657i	−1.10183	−	0.124147i
$989$	−1579.86	+	360.592i	−1.59743	+	0.364603i
$990$	−93.9573	−	149.532i	−0.0949063	−	0.151043i
$991$		−	1739.28i		−	1.75507i	−0.479512	−	0.877535i	$-0.659186\pi$
$991$		−	1739.28i		−	1.75507i	0.479512	−	0.877535i	$-0.340814\pi$
$992$	239.641	−	191.108i	0.241574	−	0.192649i
$993$	−245.020	−	700.227i	−0.246747	−	0.705163i
$994$	78.3070	+	17.8731i	0.0787797	+	0.0179809i
$995$	1622.15	−	1293.62i	1.63030	−	1.30012i
$996$	69.3720	+	615.693i	0.0696506	+	0.618166i
$997$	265.513	−	29.9161i	0.266312	−	0.0300061i	0.0222011	−	0.999754i	$-0.492933\pi$
$997$	265.513	−	29.9161i	0.266312	−	0.0300061i	0.244111	+	0.969747i	$0.421504\pi$
$998$	−26.2574	+	75.0392i	−0.0263100	+	0.0751896i
$999$	−552.798	−	552.798i	−0.553351	−	0.553351i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.3.f.a.20.18	✓	384
197.69	odd	28	inner	197.3.f.a.69.18	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.3.f.a.20.18	✓	384	1.1	even	1	trivial
197.3.f.a.69.18	yes	384	197.69	odd	28	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	197.f (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0564146 + 0.500693i) q^{2} +(-1.43240 - 0.161393i) q^{3} +(3.65220 - 0.833591i) q^{4} +(5.14385 + 8.18640i) q^{5} -0.726298i q^{6} +(3.28095 - 2.61647i) q^{7} +(1.28907 + 3.68395i) q^{8} +(-6.74863 - 1.54033i) q^{9} +(-3.80869 + 3.03733i) q^{10} +(-0.586365 - 5.20413i) q^{11} +(-5.36595 + 0.604597i) q^{12} +(-2.79225 + 7.97979i) q^{13} +(1.49514 + 1.49514i) q^{14} +(-6.04683 - 12.5564i) q^{15} +(11.7288 - 5.64827i) q^{16} +(2.77709 - 1.74496i) q^{17} +(0.390512 - 3.46589i) q^{18} +34.5904i q^{19} +(25.6105 + 25.6105i) q^{20} +(-5.12191 + 3.21831i) q^{21} +(2.57259 - 0.587178i) q^{22} +(19.5438 - 24.5072i) q^{23} +(-1.25190 - 5.48494i) q^{24} +(-29.7108 + 61.6950i) q^{25} +(-4.15295 - 0.947883i) q^{26} +(21.6633 + 7.58031i) q^{27} +(9.80162 - 12.2908i) q^{28} +(18.0930 - 22.6879i) q^{29} +(5.94576 - 3.73597i) q^{30} +(-1.54789 - 13.7379i) q^{31} +(11.7958 + 18.7728i) q^{32} +7.54903i q^{33} +(1.03036 + 1.29203i) q^{34} +(38.2962 + 13.4004i) q^{35} -25.9314 q^{36} +(-30.6891 - 14.7791i) q^{37} +(-17.3192 + 1.95141i) q^{38} +(5.28749 - 10.9796i) q^{39} +(-23.5275 + 29.5025i) q^{40} +(-2.62019 - 0.598040i) q^{41} +(-1.90034 - 2.38294i) q^{42} +(-40.4184 - 32.2326i) q^{43} +(-6.47964 - 18.5177i) q^{44} +(-22.1042 - 63.1702i) q^{45} +(13.3731 + 8.40289i) q^{46} +(-10.5007 + 21.8048i) q^{47} +(-17.7119 + 6.19765i) q^{48} +(-6.98481 + 30.6025i) q^{49} +(-32.5664 - 11.3955i) q^{50} +(-4.25952 + 2.05128i) q^{51} +(-3.54597 + 31.4714i) q^{52} +(-16.3541 - 71.6521i) q^{53} +(-2.57329 + 11.2743i) q^{54} +(39.5869 - 31.5695i) q^{55} +(13.8683 + 8.71404i) q^{56} +(5.58264 - 49.5473i) q^{57} +(12.3804 + 7.77911i) q^{58} +(29.1000 - 36.4902i) q^{59} +(-32.5511 - 40.8178i) q^{60} +(22.8496 - 28.6526i) q^{61} +(6.79116 - 1.55004i) q^{62} +(-26.1721 + 12.6038i) q^{63} +(31.9774 - 25.5011i) q^{64} +(-79.6886 + 18.1884i) q^{65} +(-3.77975 + 0.425875i) q^{66} +(35.9298 - 12.5724i) q^{67} +(8.68790 - 8.68790i) q^{68} +(-31.9498 + 31.9498i) q^{69} +(-4.54903 + 19.9306i) q^{70} +(32.1642 - 20.2101i) q^{71} +(-3.02495 - 26.8472i) q^{72} +(-60.5453 + 21.1857i) q^{73} +(5.66849 - 16.1996i) q^{74} +(52.5148 - 83.5769i) q^{75} +(28.8343 + 126.331i) q^{76} +(-15.5403 - 15.5403i) q^{77} +(5.79570 + 2.02800i) q^{78} +(45.4169 - 72.2806i) q^{79} +(106.570 + 66.9624i) q^{80} +(26.3230 + 12.6765i) q^{81} +(0.151618 - 1.34565i) q^{82} -114.741i q^{83} +(-16.0235 + 16.0235i) q^{84} +(28.5699 + 13.7585i) q^{85} +(13.8584 - 22.0556i) q^{86} +(-29.5780 + 29.5780i) q^{87} +(18.4159 - 8.86863i) q^{88} +(-5.87307 + 52.1250i) q^{89} +(30.3819 - 14.6311i) q^{90} +(11.7176 + 33.4871i) q^{91} +(50.9490 - 105.797i) q^{92} +19.9280i q^{93} +(-11.5099 - 4.02750i) q^{94} +(-283.171 + 177.928i) q^{95} +(-13.8664 - 28.7939i) q^{96} +(-98.2092 - 22.4156i) q^{97} +(-15.7165 - 1.77082i) q^{98} +(-4.05892 + 36.0239i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{2} - 12 q^{3} - 14 q^{4} - 4 q^{5} - 14 q^{7} + 48 q^{8} - 14 q^{9} - 14 q^{10} + 32 q^{11} - 26 q^{12} - 16 q^{13} - 68 q^{14} - 14 q^{15} + 70 q^{16} + 16 q^{17} + 180 q^{18} - 128 q^{20}+ \cdots - 662 q^{99}+O(q^{100}) \) 384 * q - 12 * q^2 - 12 * q^3 - 14 * q^4 - 4 * q^5 - 14 * q^7 + 48 * q^8 - 14 * q^9 - 14 * q^10 + 32 * q^11 - 26 * q^12 - 16 * q^13 - 68 * q^14 - 14 * q^15 + 70 * q^16 + 16 * q^17 + 180 * q^18 - 128 * q^20 + 6 * q^21 - 14 * q^22 - 62 * q^23 + 150 * q^24 - 14 * q^25 - 168 * q^26 + 6 * q^27 + 420 * q^28 + 140 * q^29 - 98 * q^30 + 50 * q^31 + 142 * q^32 + 38 * q^34 + 78 * q^35 - 2260 * q^36 - 64 * q^37 + 2 * q^38 - 14 * q^39 - 626 * q^40 - 126 * q^41 + 410 * q^42 - 14 * q^43 - 154 * q^44 + 544 * q^45 + 136 * q^46 - 364 * q^47 + 1114 * q^48 - 18 * q^49 - 140 * q^50 - 138 * q^51 - 214 * q^52 + 2 * q^53 + 90 * q^54 - 14 * q^55 + 26 * q^56 + 506 * q^57 - 364 * q^58 - 350 * q^59 + 348 * q^60 + 434 * q^61 + 756 * q^62 - 1122 * q^63 + 1330 * q^64 - 126 * q^65 - 742 * q^66 + 98 * q^67 + 1016 * q^68 + 454 * q^69 - 62 * q^70 - 682 * q^71 + 908 * q^72 - 32 * q^73 - 880 * q^74 - 78 * q^75 + 470 * q^76 - 410 * q^77 - 1626 * q^78 + 1100 * q^79 - 810 * q^80 + 1118 * q^81 - 86 * q^82 + 784 * q^84 - 1068 * q^85 - 632 * q^86 - 478 * q^87 - 274 * q^88 - 430 * q^89 + 308 * q^90 - 1570 * q^91 - 1022 * q^92 + 190 * q^94 + 1366 * q^95 - 462 * q^96 - 602 * q^97 + 1412 * q^98 - 662 * q^99

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