LMFDB - Embedded newform 115.3.k.a.108.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,3,Mod(2,115)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("115.2"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	115.k (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.13352304014$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			108.14
Character	$\chi$	$=$	115.108
Dual form			115.3.k.a.82.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0844762 + 1.18113i) q^{2} +(0.0419488 + 0.00912541i) q^{3} +(2.57135 - 0.369704i) q^{4} +(0.404279 - 4.98363i) q^{5} +(-0.00723463 + 0.0503180i) q^{6} +(5.16248 - 9.45438i) q^{7} +(1.66072 + 7.63422i) q^{8} +(-8.18501 - 3.73797i) q^{9} +(5.92048 + 0.0565084i) q^{10} +(5.39483 + 6.22596i) q^{11} +(0.111239 + 0.00795595i) q^{12} +(1.09337 + 2.00235i) q^{13} +(11.6030 + 5.29890i) q^{14} +(0.0624367 - 0.205368i) q^{15} +(1.09351 - 0.321084i) q^{16} +(15.3779 + 20.5425i) q^{17} +(3.72360 - 9.98335i) q^{18} +(-25.0190 + 3.59719i) q^{19} +(-0.802927 - 12.9641i) q^{20} +(0.302835 - 0.349490i) q^{21} +(-6.89795 + 6.89795i) q^{22} +(22.8336 + 2.76146i) q^{23} +0.335401i q^{24} +(-24.6731 - 4.02955i) q^{25} +(-2.27268 + 1.46056i) q^{26} +(-0.618545 - 0.463037i) q^{27} +(9.77921 - 26.2191i) q^{28} +(-29.9388 - 4.30454i) q^{29} +(0.247841 + 0.0563972i) q^{30} +(8.37844 + 5.38450i) q^{31} +(11.3928 + 30.5451i) q^{32} +(0.169492 + 0.310402i) q^{33} +(-22.9643 + 19.8987i) q^{34} +(-45.0300 - 29.5501i) q^{35} +(-22.4285 - 6.58559i) q^{36} +(6.55152 + 17.5653i) q^{37} +(-6.36226 - 29.2469i) q^{38} +(0.0275931 + 0.0939736i) q^{39} +(38.7175 - 5.19008i) q^{40} +(-10.8399 - 23.7360i) q^{41} +(0.438376 + 0.328165i) q^{42} +(-52.9680 - 11.5225i) q^{43} +(16.1737 + 14.0146i) q^{44} +(-21.9377 + 39.2799i) q^{45} +(-1.33275 + 27.2028i) q^{46} +(-7.72357 + 7.72357i) q^{47} +(0.0488016 - 0.00349036i) q^{48} +(-36.2426 - 56.3946i) q^{49} +(2.67514 - 29.4826i) q^{50} +(0.457626 + 1.00206i) q^{51} +(3.55170 + 4.74452i) q^{52} +(49.5464 + 27.0544i) q^{53} +(0.494656 - 0.769700i) q^{54} +(33.2089 - 24.3688i) q^{55} +(80.7503 + 23.7104i) q^{56} +(-1.08234 - 0.0774107i) q^{57} +(2.55512 - 35.7253i) q^{58} +(0.263087 - 0.895991i) q^{59} +(0.0846210 - 0.551156i) q^{60} +(41.2382 + 26.5022i) q^{61} +(-5.65202 + 10.3509i) q^{62} +(-77.5951 + 58.0870i) q^{63} +(-30.9687 + 14.1429i) q^{64} +(10.4210 - 4.63942i) q^{65} +(-0.352307 + 0.226414i) q^{66} +(-1.50797 - 21.0842i) q^{67} +(47.1366 + 47.1366i) q^{68} +(0.932644 + 0.324206i) q^{69} +(31.0986 - 55.6827i) q^{70} +(-82.6795 + 95.4173i) q^{71} +(14.9435 - 68.6939i) q^{72} +(46.7914 - 62.5059i) q^{73} +(-20.1935 + 9.22207i) q^{74} +(-0.998237 - 0.394187i) q^{75} +(-63.0027 + 18.4993i) q^{76} +(86.7133 - 18.8633i) q^{77} +(-0.108664 + 0.0405297i) q^{78} +(-15.9000 + 54.1505i) q^{79} +(-1.15808 - 5.57947i) q^{80} +(53.0111 + 61.1781i) q^{81} +(27.1196 - 14.8084i) q^{82} +(27.7348 - 10.3445i) q^{83} +(0.649486 - 1.01062i) q^{84} +(108.593 - 68.3328i) q^{85} +(9.13504 - 63.5356i) q^{86} +(-1.21661 - 0.453774i) q^{87} +(-38.5711 + 51.5249i) q^{88} +(50.4080 + 78.4364i) q^{89} +(-48.2479 - 22.5931i) q^{90} +24.5754 q^{91} +(59.7341 - 1.34100i) q^{92} +(0.302330 + 0.302330i) q^{93} +(-9.77501 - 8.47010i) q^{94} +(7.81240 + 126.140i) q^{95} +(0.199176 + 1.38530i) q^{96} +(61.3163 + 22.8698i) q^{97} +(63.5479 - 47.5713i) q^{98} +(-20.8843 - 71.1253i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 18 q^{2} - 22 q^{3} - 14 q^{5} - 44 q^{6} - 6 q^{7} - 34 q^{8} - 18 q^{10} - 20 q^{11} - 70 q^{12} - 26 q^{13} - 82 q^{15} + 180 q^{16} - 46 q^{17} - 286 q^{18} + 34 q^{20} - 52 q^{21} + 4 q^{22}+ \cdots + 606 q^{98}+O(q^{100}) $ 440 * q - 18 * q^2 - 22 * q^3 - 14 * q^5 - 44 * q^6 - 6 * q^7 - 34 * q^8 - 18 * q^10 - 20 * q^11 - 70 * q^12 - 26 * q^13 - 82 * q^15 + 180 * q^16 - 46 * q^17 - 286 * q^18 + 34 * q^20 - 52 * q^21 + 4 * q^22 + 22 * q^23 - 106 * q^25 - 100 * q^26 + 110 * q^27 + 302 * q^28 + 178 * q^30 - 144 * q^31 - 206 * q^32 + 288 * q^33 + 26 * q^35 - 596 * q^36 - 678 * q^37 + 30 * q^38 - 222 * q^40 + 88 * q^41 - 434 * q^42 - 150 * q^43 - 248 * q^45 - 44 * q^46 - 20 * q^47 + 566 * q^48 + 206 * q^50 + 220 * q^51 + 1238 * q^52 - 346 * q^53 + 134 * q^55 - 1316 * q^56 + 714 * q^57 - 386 * q^58 - 522 * q^60 - 692 * q^61 + 22 * q^62 + 198 * q^63 + 174 * q^65 + 156 * q^66 + 330 * q^67 + 572 * q^68 - 232 * q^70 + 508 * q^71 + 368 * q^72 - 190 * q^73 - 962 * q^75 + 900 * q^76 + 270 * q^77 - 618 * q^78 - 1884 * q^80 + 1432 * q^81 + 798 * q^82 + 122 * q^83 - 818 * q^85 + 212 * q^86 - 558 * q^87 + 462 * q^88 - 700 * q^90 - 400 * q^91 - 22 * q^92 + 372 * q^93 + 796 * q^95 + 1796 * q^96 + 480 * q^97 + 606 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.0844762	+	1.18113i	0.0422381	+	0.590566i	0.973862	+	0.227142i	$0.0729380\pi$
$2$	0.0844762	+	1.18113i	0.0422381	+	0.590566i	−0.931624	+	0.363425i	$0.881607\pi$
$3$	0.0419488	+	0.00912541i	0.0139829	+	0.00304180i	0.219551	−	0.975601i	$-0.429541\pi$
$3$	0.0419488	+	0.00912541i	0.0139829	+	0.00304180i	−0.205568	+	0.978643i	$0.565904\pi$
$4$	2.57135	−	0.369704i	0.642837	−	0.0924260i
$5$	0.404279	−	4.98363i	0.0808557	−	0.996726i
$5$	0.404279	−	4.98363i	0.0808557	−	0.996726i
$6$	−0.00723463	+	0.0503180i	−0.00120577	+	0.00838633i
$7$	5.16248	−	9.45438i	0.737497	−	1.35063i	−0.191852	−	0.981424i	$-0.561449\pi$
$7$	5.16248	−	9.45438i	0.737497	−	1.35063i	0.929349	−	0.369201i	$-0.120369\pi$
$8$	1.66072	+	7.63422i	0.207590	+	0.954278i
$9$	−8.18501	−	3.73797i	−0.909446	−	0.415330i
$10$	5.92048	+	0.0565084i	0.592048	+	0.00565084i
$11$	5.39483	+	6.22596i	0.490439	+	0.565997i	0.945983	−	0.324217i	$-0.105101\pi$
$11$	5.39483	+	6.22596i	0.490439	+	0.565997i	−0.455544	+	0.890213i	$0.650555\pi$
$12$	0.111239	+	0.00795595i	0.00926990	+	0.000662996i
$13$	1.09337	+	2.00235i	0.0841050	+	0.154027i	0.916346	−	0.400387i	$-0.131124\pi$
$13$	1.09337	+	2.00235i	0.0841050	+	0.154027i	−0.832241	+	0.554414i	$0.812942\pi$
$14$	11.6030	+	5.29890i	0.828784	+	0.378493i
$15$	0.0624367	−	0.205368i	0.00416244	−	0.0136912i
$16$	1.09351	−	0.321084i	0.0683446	−	0.0200678i
$17$	15.3779	+	20.5425i	0.904582	+	1.20838i	0.977477	+	0.211040i	$0.0676852\pi$
$17$	15.3779	+	20.5425i	0.904582	+	1.20838i	−0.0728953	+	0.997340i	$0.523224\pi$
$18$	3.72360	−	9.98335i	0.206867	−	0.554631i
$19$	−25.0190	+	3.59719i	−1.31679	+	0.189326i	−0.764661	−	0.644433i	$-0.777093\pi$
$19$	−25.0190	+	3.59719i	−1.31679	+	0.189326i	−0.552129	+	0.833759i	$0.686184\pi$
$20$	−0.802927	−	12.9641i	−0.0401463	−	0.648206i
$21$	0.302835	−	0.349490i	0.0144207	−	0.0166424i
$22$	−6.89795	+	6.89795i	−0.313543	+	0.313543i
$23$	22.8336	+	2.76146i	0.992766	+	0.120064i
$23$	22.8336	+	2.76146i	0.992766	+	0.120064i
$24$			0.335401i			0.0139751i
$25$	−24.6731	−	4.02955i	−0.986925	−	0.161182i
$26$	−2.27268	+	1.46056i	−0.0874106	+	0.0561754i
$27$	−0.618545	−	0.463037i	−0.0229091	−	0.0171495i
$28$	9.77921	−	26.2191i	0.349258	−	0.936396i
$29$	−29.9388	−	4.30454i	−1.03237	−	0.148433i	−0.394755	−	0.918787i	$-0.629170\pi$
$29$	−29.9388	−	4.30454i	−1.03237	−	0.148433i	−0.637616	+	0.770354i	$0.720079\pi$
$30$	0.247841	+	0.0563972i	0.00826138	+	0.00187991i
$31$	8.37844	+	5.38450i	0.270272	+	0.173693i	0.668756	−	0.743482i	$-0.266827\pi$
$31$	8.37844	+	5.38450i	0.270272	+	0.173693i	−0.398484	+	0.917175i	$0.630463\pi$
$32$	11.3928	+	30.5451i	0.356023	+	0.954536i
$33$	0.169492	+	0.310402i	0.00513613	+	0.00940611i
$34$	−22.9643	+	19.8987i	−0.675420	+	0.585255i
$35$	−45.0300	−	29.5501i	−1.28657	−	0.844288i
$36$	−22.4285	−	6.58559i	−0.623013	−	0.182933i
$37$	6.55152	+	17.5653i	0.177068	+	0.474738i	0.994917	−	0.100694i	$-0.0321064\pi$
$37$	6.55152	+	17.5653i	0.177068	+	0.474738i	−0.817849	+	0.575433i	$0.804834\pi$
$38$	−6.36226	−	29.2469i	−0.167428	−	0.769654i
$39$	0.0275931	+	0.0939736i	0.000707516	+	0.00240958i
$40$	38.7175	−	5.19008i	0.967938	−	0.129752i
$41$	−10.8399	−	23.7360i	−0.264387	−	0.578926i	0.730153	−	0.683284i	$-0.239449\pi$
$41$	−10.8399	−	23.7360i	−0.264387	−	0.578926i	−0.994540	+	0.104357i	$0.966721\pi$
$42$	0.438376	+	0.328165i	0.0104375	+	0.00781344i
$43$	−52.9680	−	11.5225i	−1.23181	−	0.267965i	−0.450884	−	0.892583i	$-0.648891\pi$
$43$	−52.9680	−	11.5225i	−1.23181	−	0.267965i	−0.780931	+	0.624618i	$0.785255\pi$
$44$	16.1737	+	14.0146i	0.367585	+	0.318514i
$45$	−21.9377	+	39.2799i	−0.487504	+	0.872886i
$46$	−1.33275	+	27.2028i	−0.0289729	+	0.591365i
$47$	−7.72357	+	7.72357i	−0.164331	+	0.164331i	−0.784482	−	0.620151i	$-0.787071\pi$
$47$	−7.72357	+	7.72357i	−0.164331	+	0.164331i	0.620151	+	0.784482i	$0.287071\pi$
$48$	0.0488016	−	0.00349036i	0.00101670	−	7.27158e-5i
$49$	−36.2426	−	56.3946i	−0.739646	−	1.15091i
$50$	2.67514	−	29.4826i	0.0535028	−	0.589652i
$51$	0.457626	+	1.00206i	0.00897306	+	0.0196483i
$52$	3.55170	+	4.74452i	0.0683019	+	0.0912407i
$53$	49.5464	+	27.0544i	0.934838	+	0.510460i	0.873051	−	0.487629i	$-0.162138\pi$
$53$	49.5464	+	27.0544i	0.934838	+	0.510460i	0.0617870	+	0.998089i	$0.480320\pi$
$54$	0.494656	−	0.769700i	0.00916029	−	0.0142537i
$55$	33.2089	−	24.3688i	0.603798	−	0.443069i
$56$	80.7503	+	23.7104i	1.44197	+	0.423400i
$57$	−1.08234	−	0.0774107i	−0.0189885	−	0.00135808i
$58$	2.55512	−	35.7253i	0.0440538	−	0.615953i
$59$	0.263087	−	0.895991i	0.00445910	−	0.0151863i	−0.957233	−	0.289317i	$-0.906572\pi$
$59$	0.263087	−	0.895991i	0.00445910	−	0.0151863i	0.961692	+	0.274131i	$0.0883901\pi$
$60$	0.0846210	−	0.551156i	0.00141035	−	0.00918594i
$61$	41.2382	+	26.5022i	0.676036	+	0.434462i	0.833097	−	0.553127i	$-0.186566\pi$
$61$	41.2382	+	26.5022i	0.676036	+	0.434462i	−0.157061	+	0.987589i	$0.550202\pi$
$62$	−5.65202	+	10.3509i	−0.0911616	+	0.166950i
$63$	−77.5951	+	58.0870i	−1.23167	+	0.922016i
$64$	−30.9687	+	14.1429i	−0.483886	+	0.220983i
$65$	10.4210	−	4.63942i	0.160323	−	0.0713757i
$66$	−0.352307	+	0.226414i	−0.00533799	+	0.00343052i
$67$	−1.50797	−	21.0842i	−0.0225070	−	0.314689i	−0.996217	−	0.0868986i	$-0.972304\pi$
$67$	−1.50797	−	21.0842i	−0.0225070	−	0.314689i	0.973710	−	0.227791i	$-0.0731502\pi$
$68$	47.1366	+	47.1366i	0.693185	+	0.693185i
$69$	0.932644	+	0.324206i	0.0135166	+	0.00469864i
$70$	31.0986	−	55.6827i	0.444266	−	0.795467i
$71$	−82.6795	+	95.4173i	−1.16450	+	1.34391i	−0.236364	+	0.971664i	$0.575956\pi$
$71$	−82.6795	+	95.4173i	−1.16450	+	1.34391i	−0.928136	+	0.372241i	$0.878590\pi$
$72$	14.9435	−	68.6939i	0.207548	−	0.954082i
$73$	46.7914	−	62.5059i	0.640978	−	0.856246i	−0.355956	−	0.934503i	$-0.615845\pi$
$73$	46.7914	−	62.5059i	0.640978	−	0.856246i	0.996933	+	0.0782571i	$0.0249355\pi$
$74$	−20.1935	+	9.22207i	−0.272885	+	0.124623i
$75$	−0.998237	−	0.394187i	−0.0133098	−	0.00525583i
$76$	−63.0027	+	18.4993i	−0.828982	+	0.243411i
$77$	86.7133	−	18.8633i	1.12615	−	0.244978i
$78$	−0.108664	+	0.0405297i	−0.00139313	+	0.000519611i
$79$	−15.9000	+	54.1505i	−0.201266	+	0.685449i	0.795563	+	0.605871i	$0.207175\pi$
$79$	−15.9000	+	54.1505i	−0.201266	+	0.685449i	−0.996829	+	0.0795779i	$0.974643\pi$
$80$	−1.15808	−	5.57947i	−0.0144760	−	0.0697434i
$81$	53.0111	+	61.1781i	0.654458	+	0.755285i
$82$	27.1196	−	14.8084i	0.330727	−	0.180591i
$83$	27.7348	−	10.3445i	0.334154	−	0.124633i	−0.176786	−	0.984249i	$-0.556570\pi$
$83$	27.7348	−	10.3445i	0.334154	−	0.124633i	0.510940	+	0.859616i	$0.329297\pi$
$84$	0.649486	−	1.01062i	0.00773198	−	0.0120312i
$85$	108.593	−	68.3328i	1.27756	−	0.803916i
$86$	9.13504	−	63.5356i	0.106221	−	0.738786i
$87$	−1.21661	−	0.453774i	−0.0139841	−	0.00521579i
$88$	−38.5711	+	51.5249i	−0.438308	+	0.585510i
$89$	50.4080	+	78.4364i	0.566382	+	0.881307i	0.999802	−	0.0198845i	$-0.00632985\pi$
$89$	50.4080	+	78.4364i	0.566382	+	0.881307i	−0.433420	+	0.901192i	$0.642693\pi$
$90$	−48.2479	−	22.5931i	−0.536088	−	0.251034i
$91$	24.5754			0.270060
$92$	59.7341	−	1.34100i	0.649284	−	0.0145761i
$93$	0.302330	+	0.302330i	0.00325086	+	0.00325086i
$94$	−9.77501	−	8.47010i	−0.103989	−	0.0901074i
$95$	7.81240	+	126.140i	0.0822358	+	1.32779i
$96$	0.199176	+	1.38530i	0.00207475	+	0.0144302i
$97$	61.3163	+	22.8698i	0.632127	+	0.235771i	0.645044	−	0.764145i	$-0.276839\pi$
$97$	61.3163	+	22.8698i	0.632127	+	0.235771i	−0.0129169	+	0.999917i	$0.504112\pi$
$98$	63.5479	−	47.5713i	0.648448	−	0.485422i
$99$	−20.8843	−	71.1253i	−0.210952	−	0.718437i
$100$	−64.9329	−	1.23963i	−0.649329	−	0.0123963i
$101$	72.6053	−	158.983i	0.718864	−	1.57409i	−0.0966255	−	0.995321i	$-0.530805\pi$
$101$	72.6053	−	158.983i	0.718864	−	1.57409i	0.815490	−	0.578772i	$-0.196468\pi$
$102$	−1.14491	+	0.625167i	−0.0112246	+	0.00612909i
$103$	8.69011	−	121.504i	0.0843700	−	1.17965i	−0.762190	−	0.647353i	$-0.775876\pi$
$103$	8.69011	−	121.504i	0.0843700	−	1.17965i	0.846560	−	0.532293i	$-0.178670\pi$
$104$	−13.4706	+	11.6723i	−0.129525	+	0.112234i
$105$	−1.61930	−	1.65051i	−0.0154219	−	0.0157191i
$106$	−27.7693	+	60.8063i	−0.261975	+	0.573644i
$107$	−174.763	+	38.0175i	−1.63330	+	0.355303i	−0.933373	−	0.358908i	$-0.883149\pi$
$107$	−174.763	+	38.0175i	−1.63330	+	0.355303i	−0.699930	+	0.714211i	$0.746785\pi$
$108$	−1.76168	−	0.961952i	−0.0163119	−	0.00890696i
$109$	−172.569	−	24.8117i	−1.58320	−	0.227630i	−0.706164	−	0.708048i	$-0.749576\pi$
$109$	−172.569	−	24.8117i	−1.58320	−	0.227630i	−0.877040	+	0.480418i	$0.840485\pi$
$110$	31.5881	+	37.1655i	0.287165	+	0.337868i
$111$	0.114538	+	0.796629i	0.00103187	+	0.00717684i
$112$	2.60959	−	11.9961i	0.0232999	−	0.107108i
$113$	−130.067	+	9.30259i	−1.15104	+	0.0823238i	−0.633785	−	0.773509i	$-0.718500\pi$
$113$	−130.067	+	9.30259i	−1.15104	+	0.0823238i	−0.517252	+	0.855833i	$0.673045\pi$
$114$		−	1.28493i		−	0.0112713i
$115$	22.9932	−	112.678i	0.199941	−	0.979808i
$116$	−78.5744			−0.677366
$117$	−1.46449	−	20.4762i	−0.0125170	−	0.175010i
$118$	1.08051	+	0.235050i	0.00915685	+	0.00199195i
$119$	273.604	−	39.3383i	2.29920	−	0.330574i
$120$	1.67152	+	0.135596i	0.0139293	+	0.00112996i
$121$	7.56165	−	52.5924i	0.0624930	−	0.434648i
$122$	−27.8189	+	50.9466i	−0.228024	+	0.417595i
$123$	−0.238119	−	1.09461i	−0.00193592	−	0.00889930i
$124$	23.5346	+	10.7479i	0.189795	+	0.0866764i
$125$	−30.0566	+	121.333i	−0.240453	+	0.970661i
$126$	−75.1634	−	86.7431i	−0.596535	−	0.688438i
$127$	−35.5127	−	2.53992i	−0.279628	−	0.0199994i	−0.0691791	−	0.997604i	$-0.522038\pi$
$127$	−35.5127	−	2.53992i	−0.279628	−	0.0199994i	−0.210449	+	0.977605i	$0.567493\pi$
$128$	43.1745	+	79.0682i	0.337301	+	0.617720i
$129$	−2.11680	−	0.966709i	−0.0164093	−	0.00749387i
$130$	6.36010	+	11.9166i	0.0489238	+	0.0916665i
$131$	−64.9168	+	19.0613i	−0.495548	+	0.145506i	−0.519951	−	0.854196i	$-0.674050\pi$
$131$	−64.9168	+	19.0613i	−0.495548	+	0.145506i	0.0244028	+	0.999702i	$0.492232\pi$
$132$	0.550580	+	0.735489i	0.00417106	+	0.00557189i
$133$	−95.1509	+	255.109i	−0.715420	+	1.91812i
$134$	24.7758	−	3.56222i	0.184894	−	0.0265838i
$135$	−2.55767	+	2.89541i	−0.0189457	+	0.0214474i
$136$	−131.287	+	151.514i	−0.965348	+	1.11407i
$137$	−6.21523	+	6.21523i	−0.0453667	+	0.0453667i	−0.729426	−	0.684060i	$-0.760213\pi$
$137$	−6.21523	+	6.21523i	−0.0453667	+	0.0453667i	0.684060	+	0.729426i	$0.260213\pi$
$138$	−0.304144	+	1.12896i	−0.00220394	+	0.00818090i
$139$			124.324i			0.894419i	0.894429	+	0.447209i	$0.147582\pi$
$139$			124.324i			0.894419i	−0.894429	+	0.447209i	$0.852418\pi$
$140$	−126.713	−	59.3358i	−0.905091	−	0.423827i
$141$	−0.394475	+	0.253514i	−0.00279770	+	0.00179797i
$142$	−119.685	−	89.5950i	−0.842851	−	0.630951i
$143$	−6.56803	+	17.6096i	−0.0459303	+	0.123144i
$144$	−10.1506	−	1.45944i	−0.0704904	−	0.0101350i
$145$	−33.5559	+	147.463i	−0.231420	+	1.01699i
$146$	77.7805	+	49.9865i	0.532743	+	0.342373i
$147$	−1.00571	−	2.69642i	−0.00684158	−	0.0183430i
$148$	23.3402	+	42.7444i	0.157704	+	0.288814i
$149$	178.095	−	154.320i	1.19527	−	1.03571i	0.196798	−	0.980444i	$-0.436946\pi$
$149$	178.095	−	154.320i	1.19527	−	1.03571i	0.998472	−	0.0552632i	$-0.0175998\pi$
$150$	0.381260	−	1.21235i	0.00254173	−	0.00808233i
$151$	−186.183	−	54.6682i	−1.23300	−	0.362041i	−0.400618	−	0.916245i	$-0.631205\pi$
$151$	−186.183	−	54.6682i	−1.23300	−	0.362041i	−0.832381	+	0.554204i	$0.813023\pi$
$152$	−69.0114	−	185.027i	−0.454022	−	1.21728i
$153$	−49.0811	−	225.622i	−0.320792	−	1.47466i
$154$	29.6053	+	100.826i	0.192242	+	0.654717i
$155$	30.2216	−	39.5782i	0.194978	−	0.255343i
$156$	0.105694	+	0.231438i	0.000677526	+	0.00148357i
$157$	22.4762	+	16.8255i	0.143160	+	0.107168i	0.668457	−	0.743750i	$-0.266955\pi$
$157$	22.4762	+	16.8255i	0.143160	+	0.107168i	−0.525297	+	0.850919i	$0.676046\pi$
$158$	−65.3021	−	14.2056i	−0.413304	−	0.0899088i
$159$	1.83153	+	1.58703i	0.0115191	+	0.00998132i
$160$	156.832	−	44.4285i	0.980197	−	0.277678i
$161$	143.986	−	201.622i	0.894323	−	1.25231i
$162$	−67.7813	+	67.7813i	−0.418403	+	0.418403i
$163$	33.4599	−	2.39310i	0.205275	−	0.0146816i	0.0316771	−	0.999498i	$-0.489915\pi$
$163$	33.4599	−	2.39310i	0.205275	−	0.0146816i	0.173598	+	0.984817i	$0.444461\pi$
$164$	−36.6483	−	57.0259i	−0.223466	−	0.347719i
$165$	1.61545	−	0.719197i	0.00979060	−	0.00435877i
$166$	14.5612	+	31.8846i	0.0877181	+	0.192076i
$167$	16.9603	+	22.6563i	0.101559	+	0.135666i	0.848441	−	0.529289i	$-0.177541\pi$
$167$	16.9603	+	22.6563i	0.101559	+	0.135666i	−0.746883	+	0.664956i	$0.768450\pi$
$168$	3.17101	+	1.73150i	0.0188751	+	0.0103066i
$169$	88.5543	−	137.793i	0.523990	−	0.815345i
$170$	89.8836	+	122.490i	0.528727	+	0.720530i
$171$	218.227	+	64.0772i	1.27618	+	0.374721i
$172$	−140.459	−	10.0458i	−0.816623	−	0.0584060i
$173$	4.46837	−	62.4759i	0.0258287	−	0.361132i	−0.968058	−	0.250727i	$-0.919330\pi$
$173$	4.46837	−	62.4759i	0.0258287	−	0.361132i	0.993887	−	0.110406i	$-0.0352150\pi$
$174$	0.433192	−	1.47532i	0.00248961	−	0.00847883i
$175$	−165.471	+	212.466i	−0.945551	+	1.21409i
$176$	7.89837	+	5.07598i	0.0448771	+	0.0288408i
$177$	0.0192125	−	0.0351850i	0.000108545	−	0.000198785i
$178$	−88.3854	+	66.1645i	−0.496547	+	0.371711i
$179$	−45.2215	+	20.6520i	−0.252634	+	0.115374i	−0.537707	−	0.843132i	$-0.680709\pi$
$179$	−45.2215	+	20.6520i	−0.252634	+	0.115374i	0.285073	+	0.958506i	$0.407982\pi$
$180$	−41.8875	+	109.113i	−0.232708	+	0.606182i
$181$	127.961	−	82.2353i	0.706965	−	0.454339i	−0.137116	−	0.990555i	$-0.543783\pi$
$181$	127.961	−	82.2353i	0.706965	−	0.454339i	0.844081	+	0.536216i	$0.180147\pi$
$182$	2.07604	+	29.0268i	0.0114068	+	0.159488i
$183$	1.48805	+	1.48805i	0.00813142	+	0.00813142i
$184$	16.8387	+	178.903i	0.0915148	+	0.972299i
$185$	90.1876	−	25.5491i	0.487501	−	0.138103i
$186$	−0.331552	+	0.382631i	−0.00178254	+	0.00205716i
$187$	−44.9355	+	206.565i	−0.240297	+	1.10463i
$188$	−17.0046	+	22.7154i	−0.0904497	+	0.120827i
$189$	−7.57096	+	3.45754i	−0.0400580	+	0.0182939i
$190$	−148.328	+	19.8833i	−0.780672	+	0.104649i
$191$	127.753	−	37.5116i	0.668863	−	0.196396i	0.0703666	−	0.997521i	$-0.477583\pi$
$191$	127.753	−	37.5116i	0.668863	−	0.196396i	0.598497	+	0.801125i	$0.295765\pi$
$192$	−1.42816	+	0.310677i	−0.00743833	+	0.00161811i
$193$	342.878	−	127.887i	1.77657	−	0.662627i	0.777125	−	0.629346i	$-0.216677\pi$
$193$	342.878	−	127.887i	1.77657	−	0.662627i	0.999446	−	0.0332806i	$-0.0105955\pi$
$194$	−21.8325	+	74.3547i	−0.112539	+	0.383271i
$195$	0.479485	−	0.0995224i	0.00245890	−	0.000510371i
$196$	−114.042	−	131.611i	−0.581846	−	0.671486i
$197$	153.204	−	83.6557i	0.777685	−	0.424648i	−0.0408064	−	0.999167i	$-0.512993\pi$
$197$	153.204	−	83.6557i	0.777685	−	0.424648i	0.818491	+	0.574519i	$0.194811\pi$
$198$	82.2441	−	30.6755i	0.415374	−	0.154927i
$199$	194.207	−	302.192i	0.975913	−	1.51855i	0.125729	−	0.992065i	$-0.459873\pi$
$199$	194.207	−	302.192i	0.975913	−	1.51855i	0.850184	−	0.526486i	$-0.176491\pi$
$200$	−10.2127	−	195.052i	−0.0510637	−	0.975260i
$201$	0.129144	−	0.898217i	0.000642508	−	0.00446874i
$202$	193.914	+	72.3261i	0.959969	+	0.358050i
$203$	−195.255	+	260.830i	−0.961847	+	1.28488i
$204$	1.54718	+	2.40746i	0.00758423	+	0.0118013i
$205$	−122.674	+	44.4259i	−0.598408	+	0.216712i
$206$	144.246			0.700223
$207$	−176.571	−	107.954i	−0.853001	−	0.521517i
$208$	1.83853	+	1.83853i	0.00883910	+	0.00883910i
$209$	−157.369	−	136.361i	−0.752962	−	0.652445i
$210$	1.81268	−	2.05204i	0.00863179	−	0.00977160i
$211$	−55.0095	−	382.599i	−0.260708	−	1.81327i	−0.527547	−	0.849526i	$-0.676888\pi$
$211$	−55.0095	−	382.599i	−0.260708	−	1.81327i	0.266839	−	0.963741i	$-0.414021\pi$
$212$	137.403	+	51.2487i	0.648128	+	0.241739i
$213$	−4.33903	+	3.24816i	−0.0203710	+	0.0152496i
$214$	−59.6670	−	203.207i	−0.278818	−	0.949566i
$215$	−78.8376	+	259.315i	−0.366687	+	1.20611i
$216$	2.50770	−	5.49109i	0.0116097	−	0.0254217i
$217$	94.1606	−	51.4156i	0.433920	−	0.236938i
$218$	14.7279	−	205.923i	0.0675592	−	0.944601i
$219$	2.53323	−	2.19506i	0.0115673	−	0.0100231i
$220$	76.3824	−	74.9381i	0.347193	−	0.340628i
$221$	−24.3195	+	53.2523i	−0.110043	+	0.240961i
$222$	−0.931249	+	0.202581i	−0.00419481	+	0.000912526i
$223$	203.849	+	111.310i	0.914119	+	0.499147i	0.866196	−	0.499704i	$-0.166558\pi$
$223$	203.849	+	111.310i	0.914119	+	0.499147i	0.0479229	+	0.998851i	$0.484740\pi$
$224$	347.600	+	49.9774i	1.55179	+	0.223113i
$225$	186.887	+	125.209i	0.830611	+	0.556486i
$226$	−21.9752	−	152.841i	−0.0972352	−	0.676286i
$227$	−21.4736	+	98.7124i	−0.0945972	+	0.434856i	0.905351	+	0.424664i	$0.139608\pi$
$227$	−21.4736	+	98.7124i	−0.0945972	+	0.434856i	−0.999948	+	0.0101920i	$0.996756\pi$
$228$	−2.81170	+	0.201097i	−0.0123320	+	0.000882003i
$229$			248.486i			1.08509i	0.840026	+	0.542546i	$0.182540\pi$
$229$			248.486i			1.08509i	−0.840026	+	0.542546i	$0.817460\pi$
$230$	135.030	+	17.6395i	0.587086	+	0.0766933i
$231$	3.80966			0.0164920
$232$	−16.8582	−	235.708i	−0.0726645	−	1.01598i
$233$	−257.666	−	56.0518i	−1.10586	−	0.240566i	−0.377671	−	0.925940i	$-0.623275\pi$
$233$	−257.666	−	56.0518i	−1.10586	−	0.240566i	−0.728191	+	0.685374i	$0.759639\pi$
$234$	24.0614	−	3.45951i	0.102827	−	0.0147842i
$235$	35.3689	+	41.6139i	0.150506	+	0.177080i
$236$	0.345236	−	2.40117i	0.00146286	−	0.0101744i
$237$	−1.16113	+	2.12646i	−0.00489929	+	0.00897239i
$238$	69.5768	+	319.840i	0.292340	+	1.34386i
$239$	−146.540	−	66.9227i	−0.613139	−	0.280011i	0.0845417	−	0.996420i	$-0.473057\pi$
$239$	−146.540	−	66.9227i	−0.613139	−	0.280011i	−0.697681	+	0.716409i	$0.745785\pi$
$240$	0.00233479	−	0.244620i	9.72830e−6	−	0.00101925i
$241$	140.040	+	161.614i	0.581077	+	0.670599i	0.967836	−	0.251582i	$-0.0809509\pi$
$241$	140.040	+	161.614i	0.581077	+	0.670599i	−0.386759	+	0.922181i	$0.626405\pi$
$242$	62.7574	+	4.48850i	0.259328	+	0.0185475i
$243$	4.99814	+	9.15342i	0.0205685	+	0.0376684i
$244$	115.836	+	52.9004i	0.474737	+	0.216805i
$245$	−295.702	+	157.821i	−1.20695	+	0.644166i
$246$	1.27277	−	0.373719i	0.00517386	−	0.00151918i
$247$	−34.5577	−	46.1637i	−0.139910	−	0.186898i
$248$	−27.1922	+	72.9050i	−0.109646	+	0.293972i
$249$	1.25784	−	0.180850i	0.00505157	−	0.000726306i
$250$	−145.849	−	25.2511i	−0.583396	−	0.101004i
$251$	−194.543	+	224.515i	−0.775073	+	0.894482i	−0.996743	−	0.0806394i	$-0.974304\pi$
$251$	−194.543	+	224.515i	−0.775073	+	0.894482i	0.221670	+	0.975122i	$0.428849\pi$
$252$	−178.049	+	178.049i	−0.706544	+	0.706544i
$253$	105.991	+	157.059i	0.418936	+	0.620786i
$254$		−	42.1598i		−	0.165984i
$255$	5.17891	−	1.87553i	0.0203095	−	0.00735501i
$256$	−204.306	+	131.299i	−0.798069	+	0.512888i
$257$	−32.0828	−	24.0169i	−0.124836	−	0.0934510i	0.535035	−	0.844830i	$-0.320298\pi$
$257$	−32.0828	−	24.0169i	−0.124836	−	0.0934510i	−0.659871	+	0.751379i	$0.729389\pi$
$258$	0.962992	−	2.58188i	0.00373253	−	0.0100073i
$259$	199.891	+	28.7400i	0.771781	+	0.110965i
$260$	25.0808	−	15.7823i	0.0964646	−	0.0607010i
$261$	228.959	+	147.143i	0.877237	+	0.563766i
$262$	−27.9978	−	75.0651i	−0.106862	−	0.286508i
$263$	49.4863	+	90.6274i	0.188161	+	0.344591i	0.954682	−	0.297629i	$-0.0961957\pi$
$263$	49.4863	+	90.6274i	0.188161	+	0.344591i	−0.766521	+	0.642219i	$0.778014\pi$
$264$	−2.08820	+	1.80943i	−0.00790983	+	0.00685391i
$265$	154.860	−	235.983i	0.584376	−	0.890503i
$266$	−309.356	−	90.8351i	−1.16299	−	0.341485i
$267$	1.39879	+	3.75031i	0.00523892	+	0.0140461i
$268$	−11.6724	−	53.6573i	−0.0435538	−	0.200214i
$269$	−19.8553	−	67.6209i	−0.0738115	−	0.251379i	0.914319	−	0.404994i	$-0.132727\pi$
$269$	−19.8553	−	67.6209i	−0.0738115	−	0.251379i	−0.988131	+	0.153615i	$0.950908\pi$
$270$	−3.63592	−	2.77635i	−0.0134664	−	0.0102828i
$271$	−121.749	−	266.593i	−0.449257	−	0.983736i	−0.989806	−	0.142424i	$-0.954510\pi$
$271$	−121.749	−	266.593i	−0.449257	−	0.983736i	0.540548	−	0.841313i	$-0.318217\pi$
$272$	23.4118	+	17.5258i	0.0860728	+	0.0644333i
$273$	1.03091	+	0.224261i	0.00377623	+	0.000821469i
$274$	−7.86605	−	6.81597i	−0.0287082	−	0.0248758i
$275$	−108.019	−	175.353i	−0.392798	−	0.637646i
$276$	2.51801	+	0.488845i	0.00912324	+	0.00177118i
$277$	−95.1231	+	95.1231i	−0.343405	+	0.343405i	−0.857646	−	0.514241i	$-0.828074\pi$
$277$	−95.1231	+	95.1231i	−0.343405	+	0.343405i	0.514241	+	0.857646i	$0.328074\pi$
$278$	−146.843	+	10.5024i	−0.528214	+	0.0377786i
$279$	−48.4505	−	75.3905i	−0.173658	−	0.270217i
$280$	150.810	−	392.844i	0.538605	−	1.40301i
$281$	19.5298	+	42.7642i	0.0695009	+	0.152186i	0.941194	−	0.337866i	$-0.109705\pi$
$281$	19.5298	+	42.7642i	0.0695009	+	0.152186i	−0.871693	+	0.490052i	$0.836978\pi$
$282$	−0.332757	−	0.444511i	−0.00117999	−	0.00157628i
$283$	−397.321	−	216.954i	−1.40396	−	0.766621i	−0.414313	−	0.910134i	$-0.635978\pi$
$283$	−397.321	−	216.954i	−1.40396	−	0.766621i	−0.989648	+	0.143513i	$0.954160\pi$
$284$	−177.322	+	275.918i	−0.624372	+	0.971543i
$285$	−0.823354	+	5.36270i	−0.00288896	+	0.0188165i
$286$	−21.3541	−	6.27013i	−0.0746646	−	0.0219235i
$287$	−280.369	−	20.0524i	−0.976897	−	0.0698690i
$288$	20.9270	−	292.598i	0.0726633	−	1.01597i
$289$	−104.092	+	354.506i	−0.360181	+	1.22666i
$290$	−177.008	−	27.1767i	−0.610374	−	0.0937129i
$291$	2.36345	+	1.51890i	0.00812183	+	0.00521958i
$292$	97.2082	−	178.024i	0.332905	−	0.609670i
$293$	−51.2077	+	38.3336i	−0.174770	+	0.130831i	−0.683082	−	0.730342i	$-0.739361\pi$
$293$	−51.2077	+	38.3336i	−0.174770	+	0.130831i	0.508312	+	0.861173i	$0.330270\pi$
$294$	3.09987	−	1.41566i	0.0105438	−	0.00481518i
$295$	−4.35893	−	1.67336i	−0.0147760	−	0.00567239i
$296$	−123.217	+	79.1869i	−0.416274	+	0.267523i
$297$	−0.454093	−	6.34905i	−0.00152893	−	0.0213773i
$298$	197.318	+	197.318i	0.662140	+	0.662140i
$299$	19.4361	+	48.7402i	0.0650036	+	0.163011i
$300$	−2.71255	−	0.644540i	−0.00904183	−	0.00214847i
$301$	−382.384	+	441.295i	−1.27038	+	1.46610i
$302$	48.8424	−	224.525i	0.161730	−	0.743460i
$303$	4.49649	−	6.00661i	0.0148399	−	0.0198238i
$304$	−26.2036	+	11.9668i	−0.0861960	+	0.0393644i
$305$	148.749	−	194.802i	0.487701	−	0.638694i
$306$	262.344	−	77.0310i	0.857332	−	0.251735i
$307$	−172.337	+	37.4897i	−0.561359	+	0.122116i	−0.484287	−	0.874909i	$-0.660921\pi$
$307$	−172.337	+	37.4897i	−0.561359	+	0.122116i	−0.0770721	+	0.997026i	$0.524557\pi$
$308$	215.996	−	80.5624i	0.701287	−	0.261566i
$309$	1.47331	−	5.01763i	0.00476799	−	0.0162383i
$310$	49.3001	+	32.3522i	0.159033	+	0.104362i
$311$	−111.631	−	128.829i	−0.358942	−	0.414242i	0.547343	−	0.836909i	$-0.315639\pi$
$311$	−111.631	−	128.829i	−0.358942	−	0.414242i	−0.906285	+	0.422667i	$0.861094\pi$
$312$	−0.671591	+	0.366716i	−0.00215253	+	0.00117537i
$313$	161.349	−	60.1801i	0.515493	−	0.192269i	−0.0782350	−	0.996935i	$-0.524928\pi$
$313$	161.349	−	60.1801i	0.515493	−	0.192269i	0.593728	+	0.804666i	$0.297656\pi$
$314$	−17.9744	+	27.9687i	−0.0572432	+	0.0890722i
$315$	258.114	+	410.189i	0.819409	+	1.30219i
$316$	−20.8648	+	145.118i	−0.0660280	+	0.459235i
$317$	−307.505	−	114.694i	−0.970048	−	0.361809i	−0.186028	−	0.982544i	$-0.559562\pi$
$317$	−307.505	−	114.694i	−0.970048	−	0.361809i	−0.784020	+	0.620735i	$0.786834\pi$
$318$	−1.71977	+	2.29735i	−0.00540809	+	0.00722436i
$319$	−134.715	−	209.620i	−0.422303	−	0.657116i
$320$	57.9631	+	160.054i	0.181135	+	0.500169i
$321$	−7.67804			−0.0239191
$322$	250.305	+	153.034i	0.777345	+	0.475262i
$323$	−458.635	−	458.635i	−1.41992	−	1.41992i
$324$	158.928	+	137.712i	0.490518	+	0.425037i
$325$	−18.9082	−	53.8100i	−0.0581790	−	0.165569i
$326$	5.65312	+	39.3183i	0.0173409	+	0.120608i
$327$	−7.01266	−	2.61559i	−0.0214454	−	0.00799873i
$328$	163.204	−	122.173i	0.497572	−	0.372478i
$329$	33.1488	+	112.894i	0.100756	+	0.343144i
$330$	0.985934	+	1.84730i	0.00298768	+	0.00559789i
$331$	63.1157	−	138.204i	0.190682	−	0.417535i	−0.790010	−	0.613094i	$-0.789925\pi$
$331$	63.1157	−	138.204i	0.190682	−	0.417535i	0.980692	+	0.195559i	$0.0626520\pi$
$332$	67.4914	−	36.8531i	0.203287	−	0.111003i
$333$	12.0343	−	168.262i	0.0361391	−	0.505290i
$334$	−25.3273	+	21.9462i	−0.0758303	+	0.0657073i
$335$	−105.685	−	1.00872i	−0.315479	−	0.00301111i
$336$	0.218938	−	0.479408i	0.000651602	−	0.00142681i
$337$	497.402	−	108.203i	1.47597	−	0.321078i	0.598661	−	0.801002i	$-0.295700\pi$
$337$	497.402	−	108.203i	1.47597	−	0.321078i	0.877310	+	0.479925i	$0.159336\pi$
$338$	170.233	+	92.9541i	0.503647	+	0.275012i
$339$	−5.54105	−	0.796683i	−0.0163453	−	0.00235010i
$340$	253.967	−	215.855i	0.746963	−	0.634867i
$341$	11.6766	+	81.2123i	0.0342421	+	0.238159i
$342$	−57.2487	+	263.168i	−0.167394	+	0.769497i
$343$	−193.794	+	13.8604i	−0.564997	+	0.0404094i
$344$		−	423.505i		−	1.23112i
$345$	1.99277	−	4.51688i	0.00577615	−	0.0130924i
$346$	74.1698			0.214364
$347$	19.2487	+	269.132i	0.0554717	+	0.775596i	0.946715	+	0.322071i	$0.104379\pi$
$347$	19.2487	+	269.132i	0.0554717	+	0.775596i	−0.891244	+	0.453525i	$0.850166\pi$
$348$	−3.29610	−	0.717023i	−0.00947156	−	0.00206041i
$349$	−245.271	+	35.2646i	−0.702782	+	0.101045i	−0.484436	−	0.874827i	$-0.660975\pi$
$349$	−245.271	+	35.2646i	−0.702782	+	0.101045i	−0.218346	+	0.975871i	$0.570066\pi$
$350$	−264.929	−	177.495i	−0.756941	−	0.507129i
$351$	0.250866	−	1.74481i	0.000714719	−	0.00497098i
$352$	−128.711	+	235.717i	−0.365656	+	0.669649i
$353$	−24.6555	−	113.339i	−0.0698456	−	0.321075i	0.928946	−	0.370214i	$-0.120716\pi$
$353$	−24.6555	−	113.339i	−0.0698456	−	0.321075i	−0.998792	+	0.0491395i	$0.984352\pi$
$354$	0.0431811	+	0.0197202i	0.000121981	+	5.57066e-5i
$355$	442.099	+	450.619i	1.24535	+	1.26935i
$356$	158.615	+	183.051i	0.445547	+	0.514189i
$357$	11.8364	+	0.846553i	0.0331550	+	0.00237130i
$358$	−28.2128	−	51.6679i	−0.0788068	−	0.144324i
$359$	−495.220	−	226.159i	−1.37944	−	0.629970i	−0.418881	−	0.908041i	$-0.637578\pi$
$359$	−495.220	−	226.159i	−1.37944	−	0.629970i	−0.960560	+	0.278071i	$0.910305\pi$
$360$	−336.304	−	102.244i	−0.934177	−	0.284011i
$361$	266.633	−	78.2906i	0.738596	−	0.216871i
$362$	107.940	+	144.192i	0.298178	+	0.398319i
$363$	0.797129	−	2.13719i	0.00219595	−	0.00588757i
$364$	63.1920	−	9.08564i	0.173605	−	0.0249606i
$365$	−292.590	−	258.461i	−0.801616	−	0.708111i
$366$	−1.63188	+	1.88329i	−0.00445869	+	0.00514560i
$367$	288.685	−	288.685i	0.786608	−	0.786608i	−0.194329	−	0.980936i	$-0.562253\pi$
$367$	288.685	−	288.685i	0.786608	−	0.786608i	0.980936	+	0.194329i	$0.0622529\pi$
$368$	25.8555	−	4.31183i	0.0702596	−	0.0117169i
$369$			234.798i			0.636310i
$370$	37.7956	+	104.365i	0.102150	+	0.282068i
$371$	511.565	−	328.763i	1.37888	−	0.886153i
$372$	0.889168	+	0.665623i	0.00239024	+	0.00178931i
$373$	−233.081	+	624.915i	−0.624882	+	1.67537i	0.107267	+	0.994230i	$0.465790\pi$
$373$	−233.081	+	624.915i	−0.624882	+	1.67537i	−0.732149	+	0.681144i	$0.761483\pi$
$374$	−247.777	−	35.6249i	−0.662505	−	0.0952538i
$375$	−2.36805	+	4.81548i	−0.00631480	+	0.0128413i
$376$	−71.7901	−	46.1367i	−0.190931	−	0.122704i
$377$	−24.1148	−	64.6543i	−0.0639650	−	0.171497i
$378$	−4.72338	−	8.65022i	−0.0124957	−	0.0228842i
$379$	−0.622115	+	0.539066i	−0.00164146	+	0.00142234i	−0.655681	−	0.755038i	$-0.727618\pi$
$379$	−0.622115	+	0.539066i	−0.00164146	+	0.00142234i	0.654040	+	0.756460i	$0.273073\pi$
$380$	66.7228	+	321.461i	0.175586	+	0.845949i
$381$	−1.46654	−	0.430615i	−0.00384919	−	0.00113022i
$382$	55.0983	+	147.724i	0.144236	+	0.386713i
$383$	6.31702	+	29.0389i	0.0164935	+	0.0758195i	0.984658	−	0.174496i	$-0.0558295\pi$
$383$	6.31702	+	29.0389i	0.0164935	+	0.0758195i	−0.968164	+	0.250315i	$0.919466\pi$
$384$	1.08959	+	3.71080i	0.00283747	+	0.00966354i
$385$	−58.9515	−	439.773i	−0.153121	−	1.14227i
$386$	180.016	+	394.181i	0.466364	+	1.02119i
$387$	390.473	+	292.305i	1.00897	+	0.755309i
$388$	166.121	+	36.1374i	0.428146	+	0.0931375i
$389$	−267.251	−	231.575i	−0.687022	−	0.595308i	0.239794	−	0.970824i	$-0.422920\pi$
$389$	−267.251	−	231.575i	−0.687022	−	0.595308i	−0.926816	+	0.375516i	$0.877465\pi$
$390$	0.158054	+	0.557928i	0.000405267	+	0.00143058i
$391$	294.406	+	511.524i	0.752956	+	1.30825i
$392$	370.340	−	370.340i	0.944745	−	0.944745i
$393$	−2.89712	+	0.207206i	−0.00737182	+	0.000527243i
$394$	111.750	+	173.887i	0.283631	+	0.441338i
$395$	263.438	+	101.132i	0.666932	+	0.256030i
$396$	−79.9960	−	175.167i	−0.202010	−	0.442341i
$397$	61.2704	+	81.8477i	0.154334	+	0.206166i	0.871043	−	0.491206i	$-0.163444\pi$
$397$	61.2704	+	81.8477i	0.154334	+	0.206166i	−0.716710	+	0.697371i	$0.754353\pi$
$398$	373.334	+	203.856i	0.938025	+	0.512200i
$399$	−6.31944	+	9.83325i	−0.0158382	+	0.0246447i
$400$	−28.2742	+	3.51579i	−0.0706855	+	0.00878947i
$401$	475.132	+	139.511i	1.18487	+	0.347909i	0.814049	−	0.580796i	$-0.197259\pi$
$401$	475.132	+	139.511i	1.18487	+	0.347909i	0.370820	+	0.928705i	$0.379077\pi$
$402$	1.07182	+	0.0766583i	0.00266623	+	0.000190692i
$403$	−1.62095	+	22.6638i	−0.00402220	+	0.0562377i
$404$	127.917	−	435.644i	0.316625	−	1.07833i
$405$	326.320	−	239.455i	0.805729	−	0.591246i
$406$	−324.569	−	208.588i	−0.799432	−	0.513764i
$407$	−74.0166	+	135.551i	−0.181859	+	0.333050i
$408$	−6.88997	+	5.15777i	−0.0168872	+	0.0126416i
$409$	−497.396	+	227.153i	−1.21613	+	0.555387i	−0.917023	−	0.398834i	$-0.869415\pi$
$409$	−497.396	+	227.153i	−1.21613	+	0.555387i	−0.299104	+	0.954220i	$0.596688\pi$
$410$	−62.8358	−	141.141i	−0.153258	−	0.344246i
$411$	−0.317438	+	0.204005i	−0.000772356	+	0.000496363i
$412$	−22.5751	−	315.641i	−0.0547939	−	0.766118i
$413$	−7.11286	−	7.11286i	−0.0172224	−	0.0172224i
$414$	112.592	−	217.673i	0.271961	−	0.525781i
$415$	−40.3408	−	142.402i	−0.0972067	−	0.343138i
$416$	−48.7056	+	56.2093i	−0.117081	+	0.135118i
$417$	−1.13451	+	5.21525i	−0.00272065	+	0.0125066i
$418$	147.767	−	197.393i	0.353508	−	0.472232i
$419$	−37.1505	+	16.9661i	−0.0886648	+	0.0404918i	−0.459254	−	0.888305i	$-0.651883\pi$
$419$	−37.1505	+	16.9661i	−0.0886648	+	0.0404918i	0.370589	+	0.928797i	$0.379156\pi$
$420$	−4.77398	−	3.64537i	−0.0113666	−	0.00867946i
$421$	−209.538	+	61.5260i	−0.497716	+	0.146142i	−0.520949	−	0.853588i	$-0.674422\pi$
$421$	−209.538	+	61.5260i	−0.497716	+	0.146142i	0.0232338	+	0.999730i	$0.492604\pi$
$422$	447.253	−	97.2940i	1.05984	−	0.230555i
$423$	92.0880	−	34.3470i	0.217702	−	0.0811987i
$424$	−124.256	+	423.178i	−0.293057	+	0.998062i
$425$	−296.644	−	568.813i	−0.697985	−	1.33838i
$426$	−4.20305	−	4.85058i	−0.00986631	−	0.0113863i
$427$	463.453	−	253.064i	1.08537	−	0.592657i
$428$	−435.322	+	162.367i	−1.01711	+	0.379362i
$429$	−0.436216	+	0.678765i	−0.00101682	+	0.00158220i
$430$	−312.945	−	71.2118i	−0.727779	−	0.165609i
$431$	−56.7902	+	394.984i	−0.131764	+	0.916437i	0.811491	+	0.584366i	$0.198657\pi$
$431$	−56.7902	+	394.984i	−0.131764	+	0.916437i	−0.943254	+	0.332071i	$0.892253\pi$
$432$	−0.825062	−	0.307732i	−0.00190987	−	0.000712343i
$433$	391.017	−	522.337i	0.903041	−	1.20632i	−0.0748471	−	0.997195i	$-0.523847\pi$
$433$	391.017	−	522.337i	0.903041	−	1.20632i	0.977888	−	0.209127i	$-0.0670622\pi$
$434$	68.6829	+	106.873i	0.158256	+	0.246250i
$435$	−2.75329	+	5.87971i	−0.00632941	+	0.0135166i
$436$	−452.909			−1.03878
$437$	−581.208	+	13.0479i	−1.32999	+	0.0298578i
$438$	2.80665	+	2.80665i	0.00640789	+	0.00640789i
$439$	582.528	+	504.763i	1.32694	+	1.14980i	0.977049	+	0.213013i	$0.0683278\pi$
$439$	582.528	+	504.763i	1.32694	+	1.14980i	0.349894	+	0.936789i	$0.386218\pi$
$440$	241.188	+	213.054i	0.548154	+	0.484214i
$441$	85.8449	+	597.065i	0.194660	+	1.35389i
$442$	−64.9525	−	24.2260i	−0.146951	−	0.0548100i
$443$	233.017	−	174.434i	0.525997	−	0.393757i	−0.303016	−	0.952985i	$-0.597994\pi$
$443$	233.017	−	174.434i	0.525997	−	0.393757i	0.829013	+	0.559229i	$0.188903\pi$
$444$	0.589034	+	2.00607i	0.00132665	+	0.00451817i
$445$	411.277	−	219.505i	0.924217	−	0.493269i
$446$	−114.251	+	250.175i	−0.256168	+	0.560931i
$447$	8.87912	−	4.84837i	0.0198638	−	0.0108465i
$448$	−26.1627	+	365.802i	−0.0583989	+	0.816523i
$449$	−31.1883	+	27.0248i	−0.0694617	+	0.0601889i	−0.688900	−	0.724857i	$-0.741906\pi$
$449$	−31.1883	+	27.0248i	−0.0694617	+	0.0601889i	0.619438	+	0.785046i	$0.287361\pi$
$450$	−132.101	+	231.316i	−0.293558	+	0.514035i
$451$	89.3001	−	195.540i	0.198005	−	0.433570i
$452$	−331.009	+	72.0066i	−0.732320	+	0.159307i
$453$	−7.31128	−	3.99226i	−0.0161397	−	0.00881294i
$454$	−118.406	−	17.0243i	−0.260807	−	0.0374984i
$455$	9.93533	−	122.475i	0.0218359	−	0.269176i
$456$	−1.20650	−	8.39140i	−0.00264584	−	0.0184022i
$457$	−69.3652	+	318.867i	−0.151784	+	0.697739i	0.836855	+	0.547425i	$0.184392\pi$
$457$	−69.3652	+	318.867i	−0.151784	+	0.697739i	−0.988638	+	0.150313i	$0.951972\pi$
$458$	−293.495	+	20.9912i	−0.640818	+	0.0458322i
$459$		−	19.8270i		−	0.0431960i
$460$	17.4662	−	298.235i	0.0379699	−	0.648337i
$461$	−566.861			−1.22963			−0.614817	−	0.788670i	$-0.710770\pi$
$461$	−566.861			−1.22963			−0.614817	+	0.788670i	$0.710770\pi$
$462$	0.321825	+	4.49971i	0.000696592	+	0.00973962i
$463$	144.704	+	31.4785i	0.312536	+	0.0679881i	0.366098	−	0.930576i	$-0.380694\pi$
$463$	144.704	+	31.4785i	0.312536	+	0.0679881i	−0.0535613	+	0.998565i	$0.517057\pi$
$464$	−34.1206	+	4.90579i	−0.0735357	+	0.0105728i
$465$	1.62893	−	1.38447i	0.00350307	−	0.00297736i
$466$	44.4379	−	309.073i	0.0953604	−	0.663246i
$467$	−6.83540	+	12.5181i	−0.0146368	+	0.0268053i	−0.884895	−	0.465790i	$-0.845770\pi$
$467$	−6.83540	+	12.5181i	−0.0146368	+	0.0268053i	0.870258	+	0.492596i	$0.163952\pi$
$468$	−11.3359	−	52.1101i	−0.0242219	−	0.111346i
$469$	−207.123	−	94.5897i	−0.441626	−	0.201684i
$470$	−46.1636	+	45.2908i	−0.0982205	+	0.0963633i
$471$	0.789310	+	0.910912i	0.00167582	+	0.00193400i
$472$	7.27711	+	0.520469i	0.0154176	+	0.00110269i
$473$	−214.015	−	391.939i	−0.452462	−	0.828623i
$474$	−2.60971	−	1.19182i	−0.00550572	−	0.00251438i
$475$	631.792	+	12.0614i	1.33009	+	0.0253925i
$476$	688.988	−	202.305i	1.44745	−	0.425011i
$477$	−304.409	−	406.643i	−0.638175	−	0.852502i
$478$	66.6654	−	178.737i	0.139467	−	0.373926i
$479$	−381.661	+	54.8745i	−0.796786	+	0.114561i	−0.528672	−	0.848826i	$-0.677310\pi$
$479$	−381.661	+	54.8745i	−0.796786	+	0.114561i	−0.268115	+	0.963387i	$0.586401\pi$
$480$	6.98432	−	0.432571i	0.0145507	−	0.000901190i
$481$	−28.0087	+	32.3237i	−0.0582301	+	0.0672011i
$482$	−179.058	+	179.058i	−0.371489	+	0.371489i
$483$	7.87992	−	7.14386i	0.0163145	−	0.0147906i
$484$		−	138.029i		−	0.285184i
$485$	138.764	−	296.332i	0.286110	−	0.610994i
$486$	−10.3892	+	6.67672i	−0.0213769	+	0.0137381i
$487$	−381.725	−	285.756i	−0.783831	−	0.586768i	0.130636	−	0.991430i	$-0.458298\pi$
$487$	−381.725	−	285.756i	−0.783831	−	0.586768i	−0.914466	+	0.404662i	$0.867389\pi$
$488$	−133.838	+	358.834i	−0.274259	+	0.735316i
$489$	1.42544	+	0.204947i	0.00291501	+	0.000419115i
$490$	−211.387	−	335.931i	−0.431402	−	0.685574i
$491$	−365.951	−	235.183i	−0.745318	−	0.478987i	0.112042	−	0.993703i	$-0.464261\pi$
$491$	−365.951	−	235.183i	−0.745318	−	0.478987i	−0.857360	+	0.514717i	$0.827897\pi$
$492$	−1.01697	−	2.72660i	−0.00206701	−	0.00554187i
$493$	−371.969	−	681.211i	−0.754501	−	1.38177i
$494$	51.6062	−	44.7170i	0.104466	−	0.0905202i
$495$	−362.905	+	75.3250i	−0.733142	+	0.152172i
$496$	10.8908	+	3.19783i	0.0219573	+	0.00644724i
$497$	475.279	+	1274.27i	0.956297	+	2.56393i
$498$	0.319866	+	1.47040i	0.000642300	+	0.00295261i
$499$	120.171	+	409.266i	0.240825	+	0.820173i	0.987854	+	0.155383i	$0.0496610\pi$
$499$	120.171	+	409.266i	0.240825	+	0.820173i	−0.747030	+	0.664791i	$0.768521\pi$
$500$	−32.4288	+	323.100i	−0.0648577	+	0.646201i
$501$	0.504716	+	1.10517i	0.00100742	+	0.00220594i
$502$	−281.616	−	210.815i	−0.560989	−	0.419951i
$503$	869.334	+	189.112i	1.72830	+	0.375968i	0.963376	−	0.268154i	$-0.0864135\pi$
$503$	869.334	+	189.112i	1.72830	+	0.375968i	0.764923	+	0.644122i	$0.222777\pi$
$504$	−572.313	−	495.912i	−1.13554	−	0.983953i
$505$	−762.961	−	426.111i	−1.51081	−	0.843785i
$506$	−176.554	+	138.457i	−0.348920	+	0.273630i
$507$	4.97217	−	4.97217i	0.00980704	−	0.00980704i
$508$	−92.2547	+	6.59819i	−0.181604	+	0.0129886i
$509$	74.0986	+	115.300i	0.145577	+	0.226522i	0.906383	−	0.422458i	$-0.138832\pi$
$509$	74.0986	+	115.300i	0.145577	+	0.226522i	−0.760806	+	0.648980i	$0.775196\pi$
$510$	2.65274	+	5.95854i	0.00520145	+	0.0116834i
$511$	−349.395	−	765.069i	−0.683748	−	1.49720i
$512$	43.6097	+	58.2557i	0.0851751	+	0.113781i
$513$	17.1410	+	9.35970i	0.0334133	+	0.0182450i
$514$	25.6569	−	39.9229i	0.0499162	−	0.0776711i
$515$	−602.015	−	92.4296i	−1.16896	−	0.179475i
$516$	−5.80042	−	1.70316i	−0.0112411	−	0.00330069i
$517$	−89.7540	−	6.41933i	−0.173605	−	0.0124165i
$518$	−17.0597	+	238.526i	−0.0329338	+	0.460474i
$519$	0.757561	−	2.58002i	0.00145965	−	0.00497113i
$520$	52.7248	+	71.8514i	0.101394	+	0.138176i
$521$	−360.363	−	231.591i	−0.691676	−	0.444513i	0.147005	−	0.989136i	$-0.453037\pi$
$521$	−360.363	−	231.591i	−0.691676	−	0.444513i	−0.838681	+	0.544623i	$0.816673\pi$
$522$	−154.454	+	282.861i	−0.295888	+	0.541879i
$523$	148.234	−	110.966i	0.283429	−	0.212173i	−0.448098	−	0.893984i	$-0.647899\pi$
$523$	148.234	−	110.966i	0.283429	−	0.212173i	0.731528	+	0.681812i	$0.238808\pi$
$524$	−159.877	+	73.0132i	−0.305108	+	0.139338i
$525$	−8.88017	+	7.40272i	−0.0169146	+	0.0141004i
$526$	−102.862	+	66.1057i	−0.195556	+	0.125676i
$527$	18.2319	+	254.916i	0.0345957	+	0.483711i
$528$	0.285007	+	0.285007i	0.000539786	+	0.000539786i
$529$	513.749	+	126.108i	0.971169	+	0.238390i
$530$	291.810	+	162.975i	0.550584	+	0.307499i
$531$	−5.50255	+	6.35029i	−0.0103626	+	0.0119591i
$532$	−150.351	+	691.153i	−0.282615	+	1.29916i
$533$	35.6758	−	47.6573i	0.0669340	−	0.0894133i
$534$	−4.31144	+	1.96897i	−0.00807386	+	0.00368721i
$535$	118.812	+	886.326i	0.222078	+	1.65668i
$536$	158.457	−	46.5272i	0.295629	−	0.0868044i
$537$	−2.08544	+	0.453661i	−0.00388351	+	0.000844806i
$538$	78.1920	−	29.1641i	0.145338	−	0.0542083i
$539$	155.588	−	529.885i	0.288661	−	0.983088i
$540$	−5.50622	+	8.39068i	−0.0101967	+	0.0155383i
$541$	−166.023	−	191.601i	−0.306881	−	0.354160i	0.581270	−	0.813711i	$-0.302556\pi$
$541$	−166.023	−	191.601i	−0.306881	−	0.354160i	−0.888152	+	0.459551i	$0.848010\pi$
$542$	304.596	−	166.322i	0.561986	−	0.306867i
$543$	6.11823	−	2.28198i	0.0112675	−	0.00420254i
$544$	−452.276	+	703.755i	−0.831390	+	1.29367i
$545$	−193.418	+	849.990i	−0.354896	+	1.55961i
$546$	−0.177794	+	1.23659i	−0.000325631	+	0.00226481i
$547$	−113.886	−	42.4772i	−0.208201	−	0.0776549i	0.243200	−	0.969976i	$-0.421803\pi$
$547$	−113.886	−	42.4772i	−0.208201	−	0.0776549i	−0.451401	+	0.892321i	$0.649076\pi$
$548$	−13.6837	+	18.2793i	−0.0249703	+	0.0333564i
$549$	−238.471	−	371.068i	−0.434373	−	0.675897i
$550$	197.990	−	142.398i	0.359981	−	0.258906i
$551$	764.522			1.38752
$552$	−0.926198	+	7.65843i	−0.00167789	+	0.0138740i
$553$	429.876	+	429.876i	0.777352	+	0.777352i
$554$	−120.389	−	104.317i	−0.217308	−	0.188298i
$555$	4.01641	−	0.248755i	0.00723678	−	0.000448207i
$556$	45.9632	+	319.681i	0.0826676	+	0.574966i
$557$	485.865	+	181.218i	0.872289	+	0.325347i	0.745438	−	0.666575i	$-0.232240\pi$
$557$	485.865	+	181.218i	0.872289	+	0.325347i	0.126851	+	0.991922i	$0.459513\pi$
$558$	84.9532	−	63.5952i	0.152246	−	0.113970i
$559$	−34.8414	−	118.659i	−0.0623280	−	0.212270i
$560$	−58.7290	−	17.8550i	−0.104873	−	0.0318839i
$561$	−3.76998	+	8.25511i	−0.00672011	+	0.0147150i
$562$	−48.8604	+	26.6798i	−0.0869402	+	0.0474729i
$563$	−30.8631	+	431.522i	−0.0548190	+	0.766469i	0.893482	+	0.449098i	$0.148255\pi$
$563$	−30.8631	+	431.522i	−0.0548190	+	0.766469i	−0.948301	+	0.317371i	$0.897200\pi$
$564$	−0.920608	+	0.797712i	−0.00163228	+	0.00141438i
$565$	−6.22274	+	651.967i	−0.0110137	+	1.15392i
$566$	222.687	−	487.616i	0.393440	−	0.861513i
$567$	852.070	−	185.356i	1.50277	−	0.326907i
$568$	−865.745	−	472.732i	−1.52420	−	0.832275i
$569$	1073.82	+	154.392i	1.88721	+	0.271339i	0.986583	−	0.163262i	$-0.0522015\pi$
$569$	1073.82	+	154.392i	1.88721	+	0.271339i	0.900623	+	0.434601i	$0.143111\pi$
$570$	−6.40361	−	0.519470i	−0.0112344	−	0.000911350i
$571$	31.5363	+	219.340i	0.0552299	+	0.384132i	0.998623	+	0.0524563i	$0.0167050\pi$
$571$	31.5363	+	219.340i	0.0552299	+	0.384132i	−0.943393	+	0.331676i	$0.892386\pi$
$572$	−10.3784	+	47.7086i	−0.0181440	+	0.0834067i
$573$	5.70139	−	0.407772i	0.00995007	−	0.000711643i
$574$		−	332.847i		−	0.579873i
$575$	−552.249	−	160.143i	−0.960433	−	0.278510i
$576$	306.345			0.531849
$577$	−51.4099	−	718.805i	−0.0890987	−	1.24576i	−0.823606	−	0.567162i	$-0.808041\pi$
$577$	−51.4099	−	718.805i	−0.0890987	−	1.24576i	0.734508	−	0.678601i	$-0.237413\pi$
$578$	−427.512	−	92.9995i	−0.739640	−	0.160899i
$579$	15.5504	−	2.23580i	0.0268573	−	0.00386149i
$580$	−31.7660	+	391.586i	−0.0547689	+	0.675148i
$581$	45.3791	−	315.619i	0.0781052	−	0.543234i
$582$	−1.59436	+	2.91986i	−0.00273946	+	0.00501694i
$583$	98.8547	+	454.428i	0.169562	+	0.779464i
$584$	554.892	+	253.411i	0.950157	+	0.433922i
$585$	−102.638	−	0.979634i	−0.175449	−	0.00167459i
$586$	−49.6028	−	57.2447i	−0.0846465	−	0.0976873i
$587$	−244.215	−	17.4666i	−0.416039	−	0.0297557i	−0.138249	−	0.990398i	$-0.544147\pi$
$587$	−244.215	−	17.4666i	−0.416039	−	0.0297557i	−0.277790	+	0.960642i	$0.589602\pi$
$588$	−3.58291	−	6.56161i	−0.00609339	−	0.0111592i
$589$	−228.989	−	104.576i	−0.388776	−	0.177548i
$590$	1.60823	−	5.28983i	0.00272581	−	0.00896581i
$591$	7.19012	−	2.11121i	0.0121660	−	0.00357226i
$592$	12.8041	+	17.1043i	0.0216286	+	0.0288924i
$593$	39.8210	−	106.764i	0.0671517	−	0.180041i	−0.899039	−	0.437868i	$-0.855734\pi$
$593$	39.8210	−	106.764i	0.0671517	−	0.180041i	0.966191	+	0.257827i	$0.0830065\pi$
$594$	7.46070	−	1.07269i	0.0125601	−	0.00180587i
$595$	−85.4354	−	1379.45i	−0.143589	−	2.31840i
$596$	400.892	−	462.654i	0.672638	−	0.776265i
$597$	10.9044	−	10.9044i	0.0182653	−	0.0182653i
$598$	−55.9267	+	27.0740i	−0.0935229	+	0.0452742i
$599$		−	252.895i		−	0.422196i	−0.977465	−	0.211098i	$-0.932296\pi$
$599$		−	252.895i		−	0.422196i	0.977465	−	0.211098i	$-0.0677039\pi$
$600$	1.35152	−	8.27540i	0.00225253	−	0.0137923i
$601$	−404.767	+	260.128i	−0.673490	+	0.432826i	−0.832182	−	0.554502i	$-0.812909\pi$
$601$	−404.767	+	260.128i	−0.673490	+	0.432826i	0.158692	+	0.987328i	$0.449272\pi$
$602$	−553.530	−	414.367i	−0.919485	−	0.688318i
$603$	−66.4692	+	178.211i	−0.110231	+	0.295541i
$604$	−498.952	−	71.7385i	−0.826080	−	0.118772i
$605$	−259.044	−	58.9464i	−0.428172	−	0.0974321i
$606$	7.47445	+	4.80354i	0.0123341	+	0.00792663i
$607$	80.4824	+	215.782i	0.132590	+	0.355489i	0.986231	−	0.165374i	$-0.0528831\pi$
$607$	80.4824	+	215.782i	0.132590	+	0.355489i	−0.853640	+	0.520863i	$0.825610\pi$
$608$	−394.912	−	723.227i	−0.649526	−	1.18952i
$609$	−10.5709	+	9.15974i	−0.0173578	+	0.0150406i
$610$	242.652	+	159.236i	0.397790	+	0.261042i
$611$	−23.9100	−	7.02060i	−0.0391325	−	0.0114903i
$612$	−209.618	−	562.008i	−0.342514	−	0.918314i
$613$	144.669	+	665.034i	0.236002	+	1.08488i	0.930757	+	0.365638i	$0.119149\pi$
$613$	144.669	+	665.034i	0.236002	+	1.08488i	−0.694755	+	0.719246i	$0.744487\pi$
$614$	−58.8386	−	200.386i	−0.0958284	−	0.326362i
$615$	−5.55142	+	0.744166i	−0.00902670	+	0.00121003i
$616$	288.014	+	630.662i	0.467554	+	1.02380i
$617$	277.426	+	207.679i	0.449637	+	0.336594i	0.799979	−	0.600028i	$-0.204844\pi$
$617$	277.426	+	207.679i	0.449637	+	0.336594i	−0.350342	+	0.936622i	$0.613935\pi$
$618$	6.05094	+	1.31630i	0.00979117	+	0.00212994i
$619$	856.339	+	742.022i	1.38342	+	1.19874i	0.955522	+	0.294918i	$0.0952924\pi$
$619$	856.339	+	742.022i	1.38342	+	1.19874i	0.427901	+	0.903825i	$0.359253\pi$
$620$	63.0779	−	112.942i	0.101739	−	0.182165i
$621$	−12.8450	−	12.2809i	−0.0206843	−	0.0197760i
$622$	142.734	−	142.734i	0.229476	−	0.229476i
$623$	1001.80	−	71.6499i	1.60802	−	0.115008i
$624$	0.0603469	+	0.0939016i	9.67098e−5	+	0.000150483i
$625$	592.525	+	198.843i	0.948041	+	0.318149i
$626$	84.7109	+	185.491i	0.135321	+	0.296311i
$627$	−5.35710	−	7.15624i	−0.00854401	−	0.0114135i
$628$	64.0145	+	34.9546i	0.101934	+	0.0556601i
$629$	−260.086	+	404.702i	−0.413491	+	0.643405i
$630$	−462.683	+	339.518i	−0.734417	+	0.538917i
$631$	−950.809	−	279.183i	−1.50683	−	0.442445i	−0.578961	−	0.815355i	$-0.696542\pi$
$631$	−950.809	−	279.183i	−1.50683	−	0.442445i	−0.927868	+	0.372910i	$0.878360\pi$
$632$	−439.803	−	31.4553i	−0.695890	−	0.0497710i
$633$	1.18379	−	16.5516i	0.00187013	−	0.0261478i
$634$	109.491	−	372.893i	0.172699	−	0.588160i
$635$	−27.0151	+	175.956i	−0.0425434	+	0.277095i
$636$	5.29624	+	3.40368i	0.00832742	+	0.00535171i
$637$	73.2953	−	134.230i	0.115063	−	0.210723i
$638$	236.209	−	176.824i	0.370233	−	0.277153i
$639$	1033.40	−	471.938i	1.61721	−	0.738557i
$640$	411.501	−	183.200i	0.642970	−	0.286250i
$641$	305.893	−	196.585i	0.477211	−	0.306685i	−0.279833	−	0.960049i	$-0.590279\pi$
$641$	305.893	−	196.585i	0.477211	−	0.306685i	0.757044	+	0.653364i	$0.226643\pi$
$642$	−0.648612	−	9.06878i	−0.00101030	−	0.0141258i
$643$	669.367	+	669.367i	1.04101	+	1.04101i	0.999123	+	0.0418833i	$0.0133358\pi$
$643$	669.367	+	669.367i	1.04101	+	1.04101i	0.0418833	+	0.999123i	$0.486664\pi$
$644$	295.698	−	571.672i	0.459158	−	0.887689i
$645$	−5.67350	+	10.1585i	−0.00879612	+	0.0157496i
$646$	502.964	−	580.452i	0.778582	−	0.898532i
$647$	270.454	−	1243.26i	0.418012	−	1.92157i	0.0309358	−	0.999521i	$-0.490151\pi$
$647$	270.454	−	1243.26i	0.418012	−	1.92157i	0.387076	−	0.922048i	$-0.373485\pi$
$648$	−379.010	+	506.299i	−0.584893	+	0.781325i
$649$	6.99771	−	3.19575i	0.0107823	−	0.00492411i
$650$	61.9594	−	26.8787i	0.0953222	−	0.0413519i
$651$	4.41911	−	1.29757i	0.00678819	−	0.00199319i
$652$	85.1522	−	18.5237i	0.130602	−	0.0284106i
$653$	−114.441	+	42.6843i	−0.175254	+	0.0653664i	−0.435560	−	0.900160i	$-0.643449\pi$
$653$	−114.441	+	42.6843i	−0.175254	+	0.0653664i	0.260305	+	0.965526i	$0.416177\pi$
$654$	2.49695	−	8.50383i	0.00381797	−	0.0130028i
$655$	68.7499	+	331.227i	0.104962	+	0.505691i
$656$	−19.4748	−	22.4751i	−0.0296872	−	0.0342608i
$657$	−616.633	+	336.707i	−0.938559	+	0.512492i
$658$	−130.543	+	48.6899i	−0.198393	+	0.0739969i
$659$	393.003	−	611.525i	0.596363	−	0.927959i	−0.403553	−	0.914956i	$-0.632225\pi$
$659$	393.003	−	611.525i	0.596363	−	0.927959i	0.999915	−	0.0130022i	$-0.00413885\pi$
$660$	3.88799	−	2.44655i	0.00589090	−	0.00370689i
$661$	−97.4263	+	677.615i	−0.147392	+	1.02514i	0.773075	+	0.634315i	$0.218718\pi$
$661$	−97.4263	+	677.615i	−0.147392	+	1.02514i	−0.920467	+	0.390821i	$0.872191\pi$
$662$	168.569	+	62.8731i	0.254636	+	0.0949744i
$663$	−1.50612	+	2.01195i	−0.00227168	+	0.00303461i
$664$	125.032	+	194.554i	0.188302	+	0.293003i
$665$	1232.90	+	577.332i	1.85399	+	0.868168i
$666$	199.756			0.299934
$667$	−671.724	−	180.963i	−1.00708	−	0.271309i
$668$	51.9869	+	51.9869i	0.0778247	+	0.0778247i
$669$	7.53546	+	6.52951i	0.0112638	+	0.00976011i
$670$	−7.73647	−	124.914i	−0.0115470	−	0.186438i
$671$	57.4714	+	399.722i	0.0856503	+	0.595711i
$672$	14.1254	+	5.26848i	0.0210199	+	0.00784001i
$673$	−769.712	+	576.199i	−1.14370	+	0.856165i	−0.991231	−	0.132142i	$-0.957814\pi$
$673$	−769.712	+	576.199i	−1.14370	+	0.856165i	−0.152472	+	0.988308i	$0.548724\pi$
$674$	169.821	+	578.357i	0.251960	+	0.858097i
$675$	13.3956	+	13.9170i	0.0198454	+	0.0206178i
$676$	176.761	−	387.053i	0.261481	−	0.572564i
$677$	−499.763	+	272.891i	−0.738202	+	0.403089i	−0.803911	−	0.594750i	$-0.797251\pi$
$677$	−499.763	+	272.891i	−0.738202	+	0.403089i	0.0657084	+	0.997839i	$0.479069\pi$
$678$	0.472901	−	6.61202i	0.000697494	−	0.00975224i
$679$	532.764	−	461.643i	0.784631	−	0.679886i
$680$	702.011	+	715.541i	1.03237	+	1.05227i
$681$	−1.80158	+	3.94491i	−0.00264549	+	0.00579282i
$682$	−94.9360	+	20.6521i	−0.139202	+	0.0302816i
$683$	−987.357	−	539.138i	−1.44562	−	0.789367i	−0.450956	−	0.892546i	$-0.648917\pi$
$683$	−987.357	−	539.138i	−1.44562	−	0.789367i	−0.994663	+	0.103179i	$0.967099\pi$
$684$	584.827	+	84.0854i	0.855010	+	0.122932i
$685$	28.4617	+	33.4871i	0.0415500	+	0.0488863i
$686$	−32.7419	−	227.725i	−0.0477288	−	0.331961i
$687$	−2.26754	+	10.4237i	−0.00330063	+	0.0151728i
$688$	−61.6209	+	4.40722i	−0.0895653	+	0.00640584i
$689$			128.790i			0.186922i
$690$	5.50338	+	1.97216i	0.00797591	+	0.00285820i
$691$	33.5901			0.0486109			0.0243055	−	0.999705i	$-0.492263\pi$
$691$	33.5901			0.0486109			0.0243055	+	0.999705i	$0.492263\pi$
$692$	−11.6079	−	162.299i	−0.0167744	−	0.234537i
$693$	−780.260	−	169.735i	−1.12592	−	0.244928i
$694$	−316.254	+	45.4705i	−0.455697	+	0.0655194i
$695$	619.586	+	50.2616i	0.891490	+	0.0723189i
$696$	1.44375	−	10.0415i	0.00207435	−	0.0144274i
$697$	320.901	−	587.687i	0.460403	−	0.843166i
$698$	−62.3718	−	286.718i	−0.0893578	−	0.410771i
$699$	−10.2973	−	4.70261i	−0.0147315	−	0.00672763i
$700$	−346.935	+	607.501i	−0.495621	+	0.867858i
$701$	677.554	+	781.939i	0.966553	+	1.11546i	0.993270	+	0.115819i	$0.0369492\pi$
$701$	677.554	+	781.939i	0.966553	+	1.11546i	−0.0267171	+	0.999643i	$0.508505\pi$
$702$	2.08205	+	0.148911i	0.00296588	+	0.000212124i
$703$	−227.098	−	415.899i	−0.323042	−	0.591607i
$704$	−255.124	−	116.511i	−0.362392	−	0.165499i
$705$	1.10394	+	2.06841i	0.00156587	+	0.00293391i
$706$	131.786	−	38.6959i	0.186666	−	0.0548100i
$707$	−1128.27	−	1507.19i	−1.59585	−	2.13180i
$708$	0.0363939	−	0.0975758i	5.14038e−5	−	0.000137819i
$709$	−598.145	+	86.0002i	−0.843645	+	0.121298i	−0.550567	−	0.834791i	$-0.685589\pi$
$709$	−598.145	+	86.0002i	−0.843645	+	0.121298i	−0.293078	+	0.956089i	$0.594680\pi$
$710$	−494.894	+	560.244i	−0.697034	+	0.789076i
$711$	332.555	−	383.789i	0.467728	−	0.539787i
$712$	−515.087	+	515.087i	−0.723437	+	0.723437i
$713$	176.441	+	146.084i	0.247463	+	0.204887i
$714$			14.0518i			0.0196804i
$715$	85.1043	+	39.8518i	0.119027	+	0.0557368i
$716$	−108.645	+	69.8219i	−0.151739	+	0.0975167i
$717$	−5.53649	−	4.14457i	−0.00772175	−	0.00578043i
$718$	225.290	−	604.025i	0.313774	−	0.841260i
$719$	84.7994	+	12.1923i	0.117941	+	0.0169573i	0.201032	−	0.979585i	$-0.435570\pi$
$719$	84.7994	+	12.1923i	0.117941	+	0.0169573i	−0.0830916	+	0.996542i	$0.526479\pi$
$720$	−11.3770	+	49.9969i	−0.0158014	+	0.0694402i
$721$	−1103.88	−	709.419i	−1.53104	−	0.983938i
$722$	114.996	+	308.315i	0.159274	+	0.427030i
$723$	4.39970	+	8.05744i	0.00608534	+	0.0111445i
$724$	298.629	−	258.763i	0.412471	−	0.357408i
$725$	721.337	+	226.846i	0.994948	+	0.312891i
$726$	2.59164	+	0.760974i	0.00356975	+	0.00104817i
$727$	146.839	+	393.689i	0.201979	+	0.541526i	0.997963	−	0.0637910i	$-0.0203191\pi$
$727$	146.839	+	393.689i	0.201979	+	0.541526i	−0.795985	+	0.605317i	$0.793046\pi$
$728$	40.8130	+	187.614i	0.0560618	+	0.257712i
$729$	−205.131	−	698.611i	−0.281386	−	0.958314i
$730$	280.559	−	367.421i	0.384328	−	0.503316i
$731$	−577.836	−	1265.29i	−0.790474	−	1.73090i
$732$	4.37643	+	3.27616i	0.00597874	+	0.00447563i
$733$	136.528	+	29.6999i	0.186259	+	0.0405182i	0.304727	−	0.952440i	$-0.401435\pi$
$733$	136.528	+	29.6999i	0.186259	+	0.0405182i	−0.118468	+	0.992958i	$0.537798\pi$
$734$	365.362	+	316.588i	0.497769	+	0.431319i
$735$	−13.8445	+	3.92199i	−0.0188361	+	0.00533604i
$736$	175.789	+	728.917i	0.238843	+	0.990376i
$737$	123.134	−	123.134i	0.167075	−	0.167075i
$738$	−277.328	+	19.8349i	−0.375783	+	0.0268765i
$739$	78.1353	+	121.581i	0.105731	+	0.164521i	0.890088	−	0.455789i	$-0.150643\pi$
$739$	78.1353	+	121.581i	0.105731	+	0.164521i	−0.784356	+	0.620310i	$0.787007\pi$
$740$	222.458	−	99.0383i	0.300619	−	0.133836i
$741$	−1.02839	−	2.25187i	−0.00138785	−	0.00303896i
$742$	431.527	+	576.453i	0.581573	+	0.776891i
$743$	−201.462	−	110.006i	−0.271146	−	0.148057i	0.337924	−	0.941174i	$-0.390275\pi$
$743$	−201.462	−	110.006i	−0.271146	−	0.148057i	−0.609070	+	0.793116i	$0.708457\pi$
$744$	−1.80597	+	2.81014i	−0.00242738	+	0.00377707i
$745$	−697.075	−	949.949i	−0.935672	−	1.27510i
$746$	−757.797	−	222.509i	−1.01581	−	0.298270i
$747$	−265.677	−	19.0016i	−0.355659	−	0.0254372i
$748$	−39.1769	+	547.764i	−0.0523755	+	0.732305i
$749$	−542.781	+	1848.54i	−0.724675	+	2.46802i
$750$	−5.88776	−	2.39018i	−0.00785035	−	0.00318691i
$751$	22.5609	+	14.4990i	0.0300412	+	0.0193063i	0.555575	−	0.831466i	$-0.312498\pi$
$751$	22.5609	+	14.4990i	0.0300412	+	0.0193063i	−0.525534	+	0.850773i	$0.676134\pi$
$752$	−5.96591	+	10.9257i	−0.00793339	+	0.0145289i
$753$	−10.2097	+	7.64285i	−0.0135586	+	0.0101499i
$754$	74.3281	−	33.9445i	0.0985784	−	0.0450193i
$755$	−347.716	+	905.765i	−0.460551	+	1.19969i
$756$	−18.1893	+	11.6896i	−0.0240599	+	0.0154624i
$757$	−10.5581	−	147.621i	−0.0139473	−	0.195008i	−0.999649	−	0.0265066i	$-0.991562\pi$
$757$	−10.5581	−	147.621i	−0.0139473	−	0.195008i	0.985701	−	0.168502i	$-0.0538928\pi$
$758$	−0.689262	−	0.689262i	−0.000909317	−	0.000909317i
$759$	3.01296	+	7.55564i	0.00396964	+	0.00995473i
$760$	−950.004	+	269.125i	−1.25001	+	0.354111i
$761$	−279.750	+	322.849i	−0.367608	+	0.424243i	−0.909174	−	0.416415i	$-0.863286\pi$
$761$	−279.750	+	322.849i	−0.367608	+	0.424243i	0.541566	+	0.840658i	$0.317832\pi$
$762$	0.384725	−	1.76855i	0.000504889	−	0.00232094i
$763$	−1125.46	+	1503.44i	−1.47505	+	1.97044i
$764$	314.629	−	143.686i	0.411818	−	0.188071i
$765$	−1144.26	+	153.388i	−1.49577	+	0.200507i
$766$	−33.7651	+	9.91433i	−0.0440798	+	0.0129430i
$767$	2.08174	−	0.452854i	0.00271413	−	0.000590423i
$768$	−9.76854	+	3.64348i	−0.0127195	+	0.00474411i
$769$	236.917	−	806.865i	0.308085	−	1.04924i	−0.649326	−	0.760510i	$-0.724949\pi$
$769$	236.917	−	806.865i	0.308085	−	1.04924i	0.957411	−	0.288730i	$-0.0932329\pi$
$770$	514.450	−	106.780i	0.668117	−	0.138675i
$771$	−1.12667	−	1.30025i	−0.00146131	−	0.00168645i
$772$	834.379	−	455.606i	1.08080	−	0.590163i
$773$	1160.04	−	432.672i	1.50070	−	0.559731i	0.541063	−	0.840982i	$-0.318022\pi$
$773$	1160.04	−	432.672i	1.50070	−	0.559731i	0.959634	+	0.281251i	$0.0907494\pi$
$774$	−312.265	+	485.893i	−0.403443	+	0.627769i
$775$	−185.025	−	166.614i	−0.238742	−	0.214985i
$776$	−72.7637	+	506.083i	−0.0937677	+	0.652169i
$777$	8.12293	+	3.02970i	0.0104542	+	0.00389923i
$778$	250.944	−	335.222i	0.322550	−	0.430876i
$779$	356.585	+	554.857i	0.457747	+	0.712269i
$780$	1.19613	−	0.433174i	0.00153350	−	0.000555352i
$781$	−1040.11			−1.33176
$782$	−579.307	+	390.944i	−0.740802	+	0.499928i
$783$	16.5253	+	16.5253i	0.0211051	+	0.0211051i
$784$	−57.7392	−	50.0313i	−0.0736470	−	0.0638155i
$785$	92.9384	−	105.211i	0.118393	−	0.134026i
$786$	−0.489476	−	3.40438i	−0.000622744	−	0.00433128i
$787$	−431.612	−	160.983i	−0.548427	−	0.204553i	0.0599495	−	0.998201i	$-0.480906\pi$
$787$	−431.612	−	160.983i	−0.548427	−	0.204553i	−0.608376	+	0.793649i	$0.708179\pi$
$788$	363.013	−	271.748i	0.460676	−	0.344858i
$789$	1.24888	+	4.25329i	0.00158286	+	0.00539074i
$790$	−97.1957	+	319.698i	−0.123032	+	0.404681i
$791$	−583.519	+	1277.73i	−0.737698	+	1.61533i
$792$	508.303	−	277.555i	0.641797	−	0.350448i
$793$	−7.97820	+	111.550i	−0.0100608	+	0.140668i
$794$	−91.4971	+	79.2827i	−0.115236	+	0.0998522i
$795$	8.64962	−	8.48607i	0.0108800	−	0.0106743i
$796$	387.652	−	848.839i	0.487000	−	1.06638i
$797$	−104.665	+	22.7685i	−0.131324	+	0.0285678i	−0.277747	−	0.960654i	$-0.589588\pi$
$797$	−104.665	+	22.7685i	−0.131324	+	0.0285678i	0.146423	+	0.989222i	$0.453224\pi$
$798$	−12.1482	−	6.63342i	−0.0152233	−	0.00831256i
$799$	−277.433	−	39.8889i	−0.347226	−	0.0499235i
$800$	−158.011	−	799.552i	−0.197514	−	0.999440i
$801$	−119.397	−	830.426i	−0.149060	−	1.03674i
$802$	−124.644	+	572.979i	−0.155417	+	0.714438i
$803$	641.591	−	45.8875i	0.798992	−	0.0571451i
$804$		−	2.35737i		−	0.00293206i
$805$	−946.597	−	799.084i	−1.17590	−	0.992651i
$806$	−26.9059			−0.0333820
$807$	−0.215838	−	3.01781i	−0.000267457	−	0.00373954i
$808$	1334.29	+	290.257i	1.65135	+	0.359229i
$809$	225.011	−	32.3517i	0.278135	−	0.0399897i	−0.00183585	−	0.999998i	$-0.500584\pi$
$809$	225.011	−	32.3517i	0.278135	−	0.0399897i	0.279971	+	0.960009i	$0.409675\pi$
$810$	310.394	+	365.199i	0.383203	+	0.450863i
$811$	95.3658	−	663.284i	0.117590	−	0.817859i	−0.842605	−	0.538531i	$-0.818979\pi$
$811$	95.3658	−	663.284i	0.117590	−	0.817859i	0.960196	−	0.279328i	$-0.0901116\pi$
$812$	−405.639	+	742.872i	−0.499555	+	0.914867i
$813$	−2.67445	−	12.2943i	−0.00328961	−	0.0151221i
$814$	−166.357	−	75.9726i	−0.204369	−	0.0933324i
$815$	1.60080	−	167.719i	0.00196418	−	0.205790i
$816$	0.822167	+	0.948831i	0.00100756	+	0.00116278i
$817$	1366.66	+	97.7451i	1.67277	+	0.119639i
$818$	−310.316	−	568.302i	−0.379360	−	0.694745i
$819$	−201.150	−	91.8623i	−0.245605	−	0.112164i
$820$	−299.012	+	159.587i	−0.364649	+	0.194619i
$821$	−584.880	+	171.736i	−0.712400	+	0.209179i	−0.617799	−	0.786336i	$-0.711976\pi$
$821$	−584.880	+	171.736i	−0.712400	+	0.209179i	−0.0946006	+	0.995515i	$0.530157\pi$
$822$	−0.267773	−	0.357703i	−0.000325758	−	0.000435162i
$823$	−361.987	+	970.525i	−0.439839	+	1.17925i	0.508239	+	0.861216i	$0.330296\pi$
$823$	−361.987	+	970.525i	−0.439839	+	1.17925i	−0.948078	+	0.318037i	$0.896976\pi$
$824$	942.017	−	135.442i	1.14322	−	0.164371i
$825$	−2.93112	−	8.34156i	−0.00355287	−	0.0101110i
$826$	7.80035	−	9.00209i	0.00944353	−	0.0108984i
$827$	−345.141	+	345.141i	−0.417341	+	0.417341i	−0.884286	−	0.466945i	$-0.845355\pi$
$827$	−345.141	+	345.141i	−0.417341	+	0.417341i	0.466945	+	0.884286i	$0.345355\pi$
$828$	−493.937	−	212.308i	−0.596543	−	0.256411i
$829$			828.397i			0.999273i	0.866235	+	0.499636i	$0.166533\pi$
$829$			828.397i			0.999273i	−0.866235	+	0.499636i	$0.833467\pi$
$830$	164.788	−	59.6774i	0.198540	−	0.0719005i
$831$	−4.85834	+	3.12226i	−0.00584638	+	0.00375724i
$832$	−62.1792	−	46.5467i	−0.0747346	−	0.0559456i
$833$	601.149	−	1611.74i	0.721668	−	1.93487i
$834$	−6.25574	−	0.899440i	−0.00750089	−	0.00107847i
$835$	119.767	−	75.3643i	0.143434	−	0.0902566i
$836$	−455.064	−	292.452i	−0.544335	−	0.349823i
$837$	−2.68922	−	7.21008i	−0.00321293	−	0.00861420i
$838$	−23.1775	−	42.4465i	−0.0276581	−	0.0506521i
$839$	−127.907	+	110.832i	−0.152452	+	0.132100i	−0.727747	−	0.685846i	$-0.759433\pi$
$839$	−127.907	+	110.832i	−0.152452	+	0.132100i	0.575295	+	0.817946i	$0.304887\pi$
$840$	9.91114	−	15.1031i	0.0117990	−	0.0179799i
$841$	70.8667	+	20.8083i	0.0842648	+	0.0247424i
$842$	−90.3713	−	242.295i	−0.107329	−	0.287761i
$843$	0.429010	+	1.97213i	0.000508908	+	0.00233941i
$844$	−282.897	−	963.459i	−0.335186	−	1.14154i
$845$	−650.910	−	497.029i	−0.770307	−	0.588200i
$846$	48.3476	+	105.867i	0.0571485	+	0.125138i
$847$	−458.192	−	342.998i	−0.540958	−	0.404956i
$848$	62.8664	+	13.6757i	0.0741349	+	0.0161271i
$849$	−14.6874	−	12.7267i	−0.0172996	−	0.0149902i
$850$	646.783	−	398.427i	0.760922	−	0.468737i
$851$	101.089	+	419.172i	0.118789	+	0.492563i
$852$	−9.95630	+	9.95630i	−0.0116858	+	0.0116858i
$853$	−493.893	+	35.3239i	−0.579007	+	0.0414114i	−0.357772	−	0.933809i	$-0.616463\pi$
$853$	−493.893	+	35.3239i	−0.579007	+	0.0414114i	−0.221235	+	0.975220i	$0.571009\pi$
$854$	338.053	+	526.021i	0.395847	+	0.615950i
$855$	407.562	−	1061.66i	0.476680	−	1.24170i
$856$	−580.467	−	1271.05i	−0.678116	−	1.48487i
$857$	706.747	+	944.104i	0.824676	+	1.10164i	0.993255	+	0.115950i	$0.0369913\pi$
$857$	706.747	+	944.104i	0.824676	+	1.10164i	−0.168579	+	0.985688i	$0.553918\pi$
$858$	−0.838561	−	0.457889i	−0.000977344	−	0.000533670i
$859$	619.516	−	963.986i	0.721207	−	1.12222i	−0.266185	−	0.963922i	$-0.585763\pi$
$859$	619.516	−	963.986i	0.721207	−	1.12222i	0.987391	−	0.158297i	$-0.0506005\pi$
$860$	−106.849	+	695.935i	−0.124243	+	0.809227i
$861$	−11.5782	−	3.39966i	−0.0134474	−	0.00394850i
$862$	−471.326	−	33.7099i	−0.546782	−	0.0391066i
$863$	−85.0160	+	1188.68i	−0.0985122	+	1.37738i	0.672282	+	0.740296i	$0.265314\pi$
$863$	−85.0160	+	1188.68i	−0.0985122	+	1.37738i	−0.770794	+	0.637085i	$0.780140\pi$
$864$	7.09661	−	24.1688i	0.00821367	−	0.0279732i
$865$	−309.550	−	47.5264i	−0.357862	−	0.0549438i
$866$	649.981	+	417.718i	0.750556	+	0.482353i
$867$	−7.60156	+	13.9212i	−0.00876766	+	0.0160568i
$868$	223.111	−	167.019i	0.257040	−	0.192418i
$869$	−422.917	+	193.140i	−0.486671	+	0.222255i
$870$	−7.17730	−	2.75531i	−0.00824977	−	0.00316702i
$871$	40.5691	−	26.0722i	0.0465776	−	0.0299336i
$872$	−97.1716	−	1358.64i	−0.111435	−	1.55807i
$873$	−416.388	−	416.388i	−0.476963	−	0.476963i
$874$	−64.5095	−	685.381i	−0.0738095	−	0.784189i
$875$	991.958	+	910.544i	1.13367	+	1.04062i
$876$	5.70231	−	6.58081i	0.00650948	−	0.00751234i
$877$	139.783	−	642.570i	0.159387	−	0.732691i	−0.826180	−	0.563406i	$-0.809491\pi$
$877$	139.783	−	642.570i	0.159387	−	0.732691i	0.985567	−	0.169285i	$-0.0541458\pi$
$878$	−546.983	+	730.683i	−0.622987	+	0.832213i
$879$	−2.49791	+	1.14076i	−0.00284176	+	0.00129779i
$880$	28.4899	−	37.3105i	0.0323749	−	0.0423982i
$881$	1182.98	−	347.354i	1.34277	−	0.394272i	0.470111	−	0.882607i	$-0.344214\pi$
$881$	1182.98	−	347.354i	1.34277	−	0.394272i	0.872656	+	0.488336i	$0.162396\pi$
$882$	−697.960	+	151.832i	−0.791338	+	0.172145i
$883$	174.769	−	65.1853i	0.197926	−	0.0738226i	−0.248546	−	0.968620i	$-0.579953\pi$
$883$	174.769	−	65.1853i	0.197926	−	0.0738226i	0.446472	+	0.894797i	$0.352680\pi$
$884$	−42.8464	+	145.921i	−0.0484688	+	0.165069i
$885$	−0.167582	−	0.109972i	−0.000189358	−	0.000124262i
$886$	225.714	+	260.488i	0.254757	+	0.294005i
$887$	1003.74	−	548.083i	1.13161	−	0.617906i	0.199434	−	0.979911i	$-0.436090\pi$
$887$	1003.74	−	548.083i	1.13161	−	0.617906i	0.932176	+	0.362005i	$0.117908\pi$
$888$	−5.89143	+	2.19739i	−0.00663449	+	0.00247454i
$889$	−207.347	+	322.639i	−0.233236	+	0.362923i
$890$	294.007	+	467.229i	0.330345	+	0.524976i
$891$	−94.9067	+	660.091i	−0.106517	+	0.740843i
$892$	565.317	+	210.852i	0.633764	+	0.236382i
$893$	165.453	−	221.019i	0.185277	−	0.247502i
$894$	6.47664	+	10.0778i	0.00724456	+	0.0112728i
$895$	84.6396	+	233.716i	0.0945694	+	0.261135i
$896$	970.428			1.08307
$897$	0.370547	+	2.22196i	0.000413096	+	0.00247710i
$898$	−34.5545	−	34.5545i	−0.0384794	−	0.0384794i
$899$	−227.662	−	197.270i	−0.253239	−	0.219433i
$900$	526.843	+	252.864i	0.585381	+	0.280960i
$901$	206.156	+	1433.84i	0.228808	+	1.59139i
$902$	238.502	+	88.9568i	0.264415	+	0.0986217i
$903$	−20.0676	+	15.0224i	−0.0222232	+	0.0166361i
$904$	−287.024	−	977.512i	−0.317504	−	1.08132i
$905$	−358.099	−	670.954i	−0.395689	−	0.741386i
$906$	4.09776	−	8.97284i	0.00452291	−	0.00990380i
$907$	751.069	−	410.115i	0.828081	−	0.452166i	−0.00853021	−	0.999964i	$-0.502715\pi$
$907$	751.069	−	410.115i	0.828081	−	0.452166i	0.836611	+	0.547797i	$0.184533\pi$
$908$	−18.7216	+	261.763i	−0.0206186	+	0.288285i
$909$	−1188.55	+	1029.88i	−1.30754	+	1.13299i
$910$	145.498	+	1.38872i	0.159888	+	0.00152606i
$911$	112.815	−	247.030i	0.123836	−	0.271163i	−0.837553	−	0.546356i	$-0.816014\pi$
$911$	112.815	−	247.030i	0.123836	−	0.271163i	0.961389	+	0.275193i	$0.0887418\pi$
$912$	−1.20841	+	0.262874i	−0.00132501	+	0.000288239i
$913$	214.029	+	116.869i	0.234424	+	0.128005i
$914$	−382.483	−	54.9928i	−0.418472	−	0.0601672i
$915$	8.01748	−	6.81430i	0.00876227	−	0.00744733i
$916$	91.8663	+	638.944i	0.100291	+	0.697537i
$917$	−154.919	+	712.151i	−0.168941	+	0.776610i
$918$	23.4183	−	1.67491i	0.0255101	−	0.00182452i
$919$			480.142i			0.522461i	0.965276	+	0.261230i	$0.0841283\pi$
$919$			480.142i			0.522461i	−0.965276	+	0.261230i	$0.915872\pi$
$920$	898.394	−	11.5913i	0.976515	−	0.0125992i
$921$	−7.57145			−0.00822090
$922$	−47.8863	−	669.538i	−0.0519374	−	0.726180i
$923$	−281.458	−	61.2274i	−0.304938	−	0.0663352i
$924$	9.79595	−	1.40845i	0.0106017	−	0.00152429i
$925$	−90.8662	−	459.791i	−0.0982337	−	0.497071i
$926$	−24.9562	+	173.574i	−0.0269505	+	0.187445i
$927$	−525.305	+	962.025i	−0.566672	+	1.03778i
$928$	−209.602	−	963.524i	−0.225864	−	1.03828i
$929$	−935.332	−	427.152i	−1.00682	−	0.459797i	−0.157407	−	0.987534i	$-0.550314\pi$
$929$	−935.332	−	427.152i	−1.00682	−	0.459797i	−0.849408	+	0.527737i	$0.823041\pi$
$930$	1.77285	+	1.80702i	0.00190629	+	0.00194303i
$931$	1109.62	+	1280.57i	1.19185	+	1.37547i
$932$	−683.272	−	48.8685i	−0.733124	−	0.0524341i
$933$	−3.50717	−	6.42291i	−0.00375903	−	0.00688415i
$934$	−15.3630	−	7.01602i	−0.0164486	−	0.00751180i
$935$	1011.28	+	307.452i	1.08158	+	0.328826i
$936$	153.888	−	45.1856i	0.164410	−	0.0482752i
$937$	−395.580	−	528.433i	−0.422177	−	0.563962i	0.538146	−	0.842851i	$-0.319125\pi$
$937$	−395.580	−	528.433i	−0.422177	−	0.563962i	−0.960323	+	0.278889i	$0.910034\pi$
$938$	94.2260	−	252.630i	0.100454	−	0.269328i
$939$	7.31757	−	1.05211i	0.00779294	−	0.00112046i
$940$	106.331	+	93.9277i	0.113118	+	0.0999231i
$941$	256.578	−	296.107i	0.272666	−	0.314673i	−0.602858	−	0.797849i	$-0.705971\pi$
$941$	256.578	−	296.107i	0.272666	−	0.314673i	0.875523	+	0.483176i	$0.160517\pi$
$942$	−1.00923	+	1.00923i	−0.00107137	+	0.00107137i
$943$	−181.967	−	571.912i	−0.192966	−	0.606482i
$944$		−	1.06425i		−	0.00112738i
$945$	14.1703	+	39.1287i	0.0149951	+	0.0414060i
$946$	444.852	−	285.889i	0.470246	−	0.302208i
$947$	144.084	+	107.860i	0.152148	+	0.113896i	0.672640	−	0.739970i	$-0.265160\pi$
$947$	144.084	+	107.860i	0.152148	+	0.113896i	−0.520492	+	0.853867i	$0.674251\pi$
$948$	−2.19952	+	5.89713i	−0.00232017	+	0.00622061i
$949$	176.319	+	25.3508i	0.185794	+	0.0267132i
$950$	39.1252	+	747.248i	0.0411844	+	0.786577i
$951$	−11.8529	−	7.61737i	−0.0124636	−	0.00800985i
$952$	754.699	+	2023.43i	0.792751	+	2.12545i
$953$	−78.1919	−	143.198i	−0.0820481	−	0.150260i	0.833433	−	0.552620i	$-0.186372\pi$
$953$	−78.1919	−	143.198i	−0.0820481	−	0.150260i	−0.915482	+	0.402360i	$0.868190\pi$
$954$	454.584	−	393.899i	0.476503	−	0.412893i
$955$	−135.296	−	651.838i	−0.141672	−	0.682553i
$956$	−401.548	−	117.905i	−0.420029	−	0.123332i
$957$	−3.73825	−	10.0226i	−0.00390622	−	0.0104730i
$958$	−97.0553	−	446.156i	−0.101310	−	0.465716i
$959$	26.6751	+	90.8471i	0.0278156	+	0.0947311i
$960$	0.970925	+	7.24302i	0.00101138	+	0.00754481i
$961$	−358.008	−	783.929i	−0.372537	−	0.815743i
$962$	−40.5447	−	30.3514i	−0.0421462	−	0.0315503i
$963$	1572.55	+	342.087i	1.63297	+	0.355231i
$964$	419.840	+	363.793i	0.435519	+	0.377379i
$965$	−498.723	−	1760.48i	−0.516811	−	1.82433i
$966$	9.10351	+	8.70374i	0.00942392	+	0.00901009i
$967$	−721.826	+	721.826i	−0.746459	+	0.746459i	−0.973812	−	0.227353i	$-0.926993\pi$
$967$	−721.826	+	721.826i	−0.746459	+	0.746459i	0.227353	+	0.973812i	$0.426993\pi$
$968$	414.060	−	29.6142i	0.427748	−	0.0305931i
$969$	−15.0539	−	23.4244i	−0.0155356	−	0.0241738i
$970$	361.730	+	138.865i	0.372917	+	0.143160i
$971$	327.957	+	718.125i	0.337752	+	0.739573i	0.999952	−	0.00975360i	$-0.00310472\pi$
$971$	327.957	+	718.125i	0.337752	+	0.739573i	−0.662201	+	0.749326i	$0.730377\pi$
$972$	16.2360	+	21.6888i	0.0167037	+	0.0223136i
$973$	1175.41	+	641.821i	1.20802	+	0.659631i
$974$	305.269	−	475.008i	0.313418	−	0.487688i
$975$	−0.302137	−	2.42981i	−0.000309885	−	0.00249211i
$976$	53.6039	+	15.7395i	0.0549221	+	0.0161266i
$977$	1363.65	+	97.5304i	1.39576	+	0.0998264i	0.748848	−	0.662742i	$-0.230607\pi$
$977$	1363.65	+	97.5304i	1.39576	+	0.0998264i	0.646908	+	0.762568i	$0.276062\pi$
$978$	−0.121654	+	1.70095i	−0.000124391	+	0.00173921i
$979$	−216.399	+	736.989i	−0.221041	+	0.752798i
$980$	−702.006	+	515.134i	−0.716333	+	0.525647i
$981$	1319.74	+	848.143i	1.34530	+	0.864569i
$982$	246.868	−	452.104i	0.251393	−	0.460391i
$983$	−916.535	+	686.109i	−0.932385	+	0.697975i	−0.953370	−	0.301805i	$-0.902411\pi$
$983$	−916.535	+	686.109i	−0.932385	+	0.697975i	0.0209843	+	0.999780i	$0.493320\pi$
$984$	7.96108	−	3.63570i	0.00809053	−	0.00369482i
$985$	−354.972	−	797.332i	−0.360377	−	0.809474i
$986$	773.177	−	496.891i	0.784155	−	0.503946i
$987$	0.360345	+	5.03828i	0.000365091	+	0.00510464i
$988$	−105.927	−	105.927i	−0.107213	−	0.107213i
$989$	−1177.63	−	409.369i	−1.19073	−	0.413922i
$990$	−119.626	−	422.276i	−0.120834	−	0.426541i
$991$	−43.2744	+	49.9413i	−0.0436674	+	0.0503949i	−0.777163	−	0.629299i	$-0.783342\pi$
$991$	−43.2744	+	49.9413i	−0.0436674	+	0.0503949i	0.733496	+	0.679694i	$0.237887\pi$
$992$	−69.0167	+	317.265i	−0.0695733	+	0.319823i
$993$	3.90880	−	5.22155i	0.00393636	−	0.00525835i
$994$	−1464.94	+	669.014i	−1.47378	+	0.673052i
$995$	−1427.50	−	1090.02i	−1.43467	−	1.09550i
$996$	3.16749	−	0.930058i	0.00318021	−	0.000933793i
$997$	1801.42	−	391.875i	1.80684	−	0.393055i	0.822421	−	0.568879i	$-0.192623\pi$
$997$	1801.42	−	391.875i	1.80684	−	0.393055i	0.984422	+	0.175824i	$0.0562591\pi$
$998$	−473.246	+	176.512i	−0.474194	+	0.176865i
$999$	4.08098	−	13.8985i	0.00408507	−	0.0139125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.k.a.108.14	yes	440
5.2	odd	4	inner	115.3.k.a.62.9	yes	440
23.13	even	11	inner	115.3.k.a.13.9	✓	440
115.82	odd	44	inner	115.3.k.a.82.14	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.k.a.13.9	✓	440	23.13	even	11	inner
115.3.k.a.62.9	yes	440	5.2	odd	4	inner
115.3.k.a.82.14	yes	440	115.82	odd	44	inner
115.3.k.a.108.14	yes	440	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	115.k (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0844762 + 1.18113i) q^{2} +(0.0419488 + 0.00912541i) q^{3} +(2.57135 - 0.369704i) q^{4} +(0.404279 - 4.98363i) q^{5} +(-0.00723463 + 0.0503180i) q^{6} +(5.16248 - 9.45438i) q^{7} +(1.66072 + 7.63422i) q^{8} +(-8.18501 - 3.73797i) q^{9} +(5.92048 + 0.0565084i) q^{10} +(5.39483 + 6.22596i) q^{11} +(0.111239 + 0.00795595i) q^{12} +(1.09337 + 2.00235i) q^{13} +(11.6030 + 5.29890i) q^{14} +(0.0624367 - 0.205368i) q^{15} +(1.09351 - 0.321084i) q^{16} +(15.3779 + 20.5425i) q^{17} +(3.72360 - 9.98335i) q^{18} +(-25.0190 + 3.59719i) q^{19} +(-0.802927 - 12.9641i) q^{20} +(0.302835 - 0.349490i) q^{21} +(-6.89795 + 6.89795i) q^{22} +(22.8336 + 2.76146i) q^{23} +0.335401i q^{24} +(-24.6731 - 4.02955i) q^{25} +(-2.27268 + 1.46056i) q^{26} +(-0.618545 - 0.463037i) q^{27} +(9.77921 - 26.2191i) q^{28} +(-29.9388 - 4.30454i) q^{29} +(0.247841 + 0.0563972i) q^{30} +(8.37844 + 5.38450i) q^{31} +(11.3928 + 30.5451i) q^{32} +(0.169492 + 0.310402i) q^{33} +(-22.9643 + 19.8987i) q^{34} +(-45.0300 - 29.5501i) q^{35} +(-22.4285 - 6.58559i) q^{36} +(6.55152 + 17.5653i) q^{37} +(-6.36226 - 29.2469i) q^{38} +(0.0275931 + 0.0939736i) q^{39} +(38.7175 - 5.19008i) q^{40} +(-10.8399 - 23.7360i) q^{41} +(0.438376 + 0.328165i) q^{42} +(-52.9680 - 11.5225i) q^{43} +(16.1737 + 14.0146i) q^{44} +(-21.9377 + 39.2799i) q^{45} +(-1.33275 + 27.2028i) q^{46} +(-7.72357 + 7.72357i) q^{47} +(0.0488016 - 0.00349036i) q^{48} +(-36.2426 - 56.3946i) q^{49} +(2.67514 - 29.4826i) q^{50} +(0.457626 + 1.00206i) q^{51} +(3.55170 + 4.74452i) q^{52} +(49.5464 + 27.0544i) q^{53} +(0.494656 - 0.769700i) q^{54} +(33.2089 - 24.3688i) q^{55} +(80.7503 + 23.7104i) q^{56} +(-1.08234 - 0.0774107i) q^{57} +(2.55512 - 35.7253i) q^{58} +(0.263087 - 0.895991i) q^{59} +(0.0846210 - 0.551156i) q^{60} +(41.2382 + 26.5022i) q^{61} +(-5.65202 + 10.3509i) q^{62} +(-77.5951 + 58.0870i) q^{63} +(-30.9687 + 14.1429i) q^{64} +(10.4210 - 4.63942i) q^{65} +(-0.352307 + 0.226414i) q^{66} +(-1.50797 - 21.0842i) q^{67} +(47.1366 + 47.1366i) q^{68} +(0.932644 + 0.324206i) q^{69} +(31.0986 - 55.6827i) q^{70} +(-82.6795 + 95.4173i) q^{71} +(14.9435 - 68.6939i) q^{72} +(46.7914 - 62.5059i) q^{73} +(-20.1935 + 9.22207i) q^{74} +(-0.998237 - 0.394187i) q^{75} +(-63.0027 + 18.4993i) q^{76} +(86.7133 - 18.8633i) q^{77} +(-0.108664 + 0.0405297i) q^{78} +(-15.9000 + 54.1505i) q^{79} +(-1.15808 - 5.57947i) q^{80} +(53.0111 + 61.1781i) q^{81} +(27.1196 - 14.8084i) q^{82} +(27.7348 - 10.3445i) q^{83} +(0.649486 - 1.01062i) q^{84} +(108.593 - 68.3328i) q^{85} +(9.13504 - 63.5356i) q^{86} +(-1.21661 - 0.453774i) q^{87} +(-38.5711 + 51.5249i) q^{88} +(50.4080 + 78.4364i) q^{89} +(-48.2479 - 22.5931i) q^{90} +24.5754 q^{91} +(59.7341 - 1.34100i) q^{92} +(0.302330 + 0.302330i) q^{93} +(-9.77501 - 8.47010i) q^{94} +(7.81240 + 126.140i) q^{95} +(0.199176 + 1.38530i) q^{96} +(61.3163 + 22.8698i) q^{97} +(63.5479 - 47.5713i) q^{98} +(-20.8843 - 71.1253i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 18 q^{2} - 22 q^{3} - 14 q^{5} - 44 q^{6} - 6 q^{7} - 34 q^{8} - 18 q^{10} - 20 q^{11} - 70 q^{12} - 26 q^{13} - 82 q^{15} + 180 q^{16} - 46 q^{17} - 286 q^{18} + 34 q^{20} - 52 q^{21} + 4 q^{22}+ \cdots + 606 q^{98}+O(q^{100}) \) 440 * q - 18 * q^2 - 22 * q^3 - 14 * q^5 - 44 * q^6 - 6 * q^7 - 34 * q^8 - 18 * q^10 - 20 * q^11 - 70 * q^12 - 26 * q^13 - 82 * q^15 + 180 * q^16 - 46 * q^17 - 286 * q^18 + 34 * q^20 - 52 * q^21 + 4 * q^22 + 22 * q^23 - 106 * q^25 - 100 * q^26 + 110 * q^27 + 302 * q^28 + 178 * q^30 - 144 * q^31 - 206 * q^32 + 288 * q^33 + 26 * q^35 - 596 * q^36 - 678 * q^37 + 30 * q^38 - 222 * q^40 + 88 * q^41 - 434 * q^42 - 150 * q^43 - 248 * q^45 - 44 * q^46 - 20 * q^47 + 566 * q^48 + 206 * q^50 + 220 * q^51 + 1238 * q^52 - 346 * q^53 + 134 * q^55 - 1316 * q^56 + 714 * q^57 - 386 * q^58 - 522 * q^60 - 692 * q^61 + 22 * q^62 + 198 * q^63 + 174 * q^65 + 156 * q^66 + 330 * q^67 + 572 * q^68 - 232 * q^70 + 508 * q^71 + 368 * q^72 - 190 * q^73 - 962 * q^75 + 900 * q^76 + 270 * q^77 - 618 * q^78 - 1884 * q^80 + 1432 * q^81 + 798 * q^82 + 122 * q^83 - 818 * q^85 + 212 * q^86 - 558 * q^87 + 462 * q^88 - 700 * q^90 - 400 * q^91 - 22 * q^92 + 372 * q^93 + 796 * q^95 + 1796 * q^96 + 480 * q^97 + 606 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more