LMFDB - Embedded newform 110.3.l.a.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,3,Mod(3,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([15, 16]))

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

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

chi := DirichletCharacter("110.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	110.l (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.99728290796$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.3
Character	$\chi$	$=$	110.37
Dual form			110.3.l.a.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.221232 - 1.39680i) q^{2} +(-0.190659 - 0.374189i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(4.53254 + 2.11095i) q^{5} +(-0.480488 + 0.349095i) q^{6} +(3.05982 - 6.00524i) q^{7} +(1.28408 + 2.52015i) q^{8} +(5.18640 - 7.13847i) q^{9} +(1.94584 - 6.79807i) q^{10} +(6.80666 - 8.64114i) q^{11} +(0.593916 + 0.593916i) q^{12} +(-22.7221 + 3.59882i) q^{13} +(-9.06507 - 2.94542i) q^{14} +(-0.0742729 - 2.09850i) q^{15} +(3.23607 - 2.35114i) q^{16} +(7.86061 + 1.24500i) q^{17} +(-11.1184 - 5.66512i) q^{18} +(14.9807 + 4.86752i) q^{19} +(-9.92604 - 1.21401i) q^{20} -2.83048 q^{21} +(-13.5758 - 7.59587i) q^{22} +(6.27408 - 6.27408i) q^{23} +(0.698191 - 0.960977i) q^{24} +(16.0878 + 19.1359i) q^{25} +(10.0537 + 30.9421i) q^{26} +(-7.39310 - 1.17095i) q^{27} +(-2.10869 + 13.3137i) q^{28} +(-41.8099 + 13.5849i) q^{29} +(-2.91475 + 0.567999i) q^{30} +(41.8975 + 30.4403i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-4.53117 - 0.899468i) q^{33} -11.2552i q^{34} +(26.5455 - 20.7598i) q^{35} +(-5.45330 + 16.7835i) q^{36} +(14.6166 - 28.6867i) q^{37} +(3.48476 - 22.0019i) q^{38} +(5.67881 + 7.81621i) q^{39} +(0.500225 + 14.1333i) q^{40} +(-16.7005 + 51.3988i) q^{41} +(0.626192 + 3.95362i) q^{42} +(-22.5790 + 22.5790i) q^{43} +(-7.60652 + 20.6432i) q^{44} +(38.5765 - 21.4071i) q^{45} +(-10.1517 - 7.37562i) q^{46} +(-81.3597 + 41.4548i) q^{47} +(-1.49676 - 0.762635i) q^{48} +(2.10105 + 2.89185i) q^{49} +(23.1700 - 26.7049i) q^{50} +(-1.03283 - 3.17872i) q^{51} +(40.9958 - 20.8884i) q^{52} +(-50.1741 + 7.94679i) q^{53} +10.5857i q^{54} +(49.0925 - 24.7978i) q^{55} +19.0632 q^{56} +(-1.03483 - 6.53365i) q^{57} +(28.2251 + 55.3948i) q^{58} +(-22.6016 + 7.34372i) q^{59} +(1.43822 + 3.94568i) q^{60} +(10.1157 - 7.34947i) q^{61} +(33.2501 - 65.2569i) q^{62} +(-26.9988 - 52.9881i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(-110.586 - 31.6534i) q^{65} +(-0.253940 + 6.52814i) q^{66} +(25.6290 + 25.6290i) q^{67} +(-15.7212 + 2.49000i) q^{68} +(-3.54390 - 1.15148i) q^{69} +(-34.8701 - 32.4861i) q^{70} +(91.6006 - 66.5517i) q^{71} +(24.6497 + 3.90413i) q^{72} +(-21.0787 - 10.7401i) q^{73} +(-43.3033 - 14.0701i) q^{74} +(4.09318 - 9.66830i) q^{75} -31.5033 q^{76} +(-31.0650 - 67.3160i) q^{77} +(9.66136 - 9.66136i) q^{78} +(17.0478 - 23.4642i) q^{79} +(19.6307 - 3.82545i) q^{80} +(-23.5685 - 72.5363i) q^{81} +(75.4887 + 11.9562i) q^{82} +(17.5698 - 110.932i) q^{83} +(5.38389 - 1.74933i) q^{84} +(33.0004 + 22.2364i) q^{85} +(36.5336 + 26.5432i) q^{86} +(13.0547 + 13.0547i) q^{87} +(30.5172 + 6.05788i) q^{88} +82.0644i q^{89} +(-38.4359 - 49.1478i) q^{90} +(-47.9138 + 147.463i) q^{91} +(-8.05641 + 15.8116i) q^{92} +(3.40231 - 21.4813i) q^{93} +(75.9035 + 104.472i) q^{94} +(57.6254 + 53.6858i) q^{95} +(-0.734121 + 2.25939i) q^{96} +(11.9595 + 75.5095i) q^{97} +(3.57452 - 3.57452i) q^{98} +(-26.3824 - 93.4056i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{2} + 2 q^{3} + 4 q^{5} + 4 q^{6} + 38 q^{7} + 24 q^{8} + 36 q^{10} + 80 q^{11} - 16 q^{12} - 16 q^{13} + 38 q^{15} + 48 q^{16} - 18 q^{17} - 44 q^{18} + 4 q^{20} + 24 q^{21} + 64 q^{23} + 70 q^{25}+ \cdots - 440 q^{98}+O(q^{100}) $ 48 * q - 12 * q^2 + 2 * q^3 + 4 * q^5 + 4 * q^6 + 38 * q^7 + 24 * q^8 + 36 * q^10 + 80 * q^11 - 16 * q^12 - 16 * q^13 + 38 * q^15 + 48 * q^16 - 18 * q^17 - 44 * q^18 + 4 * q^20 + 24 * q^21 + 64 * q^23 + 70 * q^25 + 8 * q^26 - 82 * q^27 + 64 * q^28 - 14 * q^30 - 116 * q^31 - 192 * q^32 - 312 * q^33 - 288 * q^35 - 88 * q^36 + 22 * q^37 - 72 * q^38 - 24 * q^40 - 196 * q^41 - 96 * q^42 - 484 * q^43 - 56 * q^45 - 132 * q^46 - 310 * q^47 - 8 * q^48 - 128 * q^50 + 256 * q^51 + 8 * q^52 - 82 * q^53 - 264 * q^55 + 48 * q^56 + 744 * q^57 + 168 * q^58 + 196 * q^60 + 528 * q^61 + 144 * q^62 + 814 * q^63 + 840 * q^65 + 436 * q^66 + 192 * q^67 + 36 * q^68 + 230 * q^70 - 292 * q^71 - 48 * q^72 - 108 * q^73 + 258 * q^75 + 96 * q^76 - 200 * q^77 + 88 * q^78 + 24 * q^80 + 628 * q^81 + 24 * q^82 + 360 * q^83 - 368 * q^85 + 532 * q^86 - 328 * q^87 - 40 * q^88 - 766 * q^90 + 72 * q^91 + 68 * q^92 - 66 * q^93 - 232 * q^95 - 16 * q^96 + 6 * q^97 - 440 * q^98

Character values

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

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.221232	−	1.39680i	−0.110616	−	0.698401i
$2$	−0.221232	−	1.39680i	−0.110616	−	0.698401i
$3$	−0.190659	−	0.374189i	−0.0635530	−	0.124730i	0.857045	−	0.515242i	$-0.172298\pi$
$3$	−0.190659	−	0.374189i	−0.0635530	−	0.124730i	−0.920598	+	0.390512i	$0.872298\pi$
$4$	−1.90211	+	0.618034i	−0.475528	+	0.154508i
$5$	4.53254	+	2.11095i	0.906507	+	0.422190i
$5$	4.53254	+	2.11095i	0.906507	+	0.422190i
$6$	−0.480488	+	0.349095i	−0.0800814	+	0.0581825i
$7$	3.05982	−	6.00524i	0.437118	−	0.857892i	−0.562401	−	0.826865i	$-0.690122\pi$
$7$	3.05982	−	6.00524i	0.437118	−	0.857892i	0.999519	−	0.0310272i	$-0.00987784\pi$
$8$	1.28408	+	2.52015i	0.160510	+	0.315018i
$9$	5.18640	−	7.13847i	0.576267	−	0.793163i
$10$	1.94584	−	6.79807i	0.194584	−	0.679807i
$11$	6.80666	−	8.64114i	0.618787	−	0.785558i
$11$	6.80666	−	8.64114i	0.618787	−	0.785558i
$12$	0.593916	+	0.593916i	0.0494930	+	0.0494930i
$13$	−22.7221	+	3.59882i	−1.74785	+	0.276833i	−0.946814	−	0.321781i	$-0.895719\pi$
$13$	−22.7221	+	3.59882i	−1.74785	+	0.276833i	−0.801038	+	0.598613i	$0.795719\pi$
$14$	−9.06507	−	2.94542i	−0.647505	−	0.210387i
$15$	−0.0742729	−	2.09850i	−0.00495153	−	0.139900i
$16$	3.23607	−	2.35114i	0.202254	−	0.146946i
$17$	7.86061	+	1.24500i	0.462389	+	0.0732352i	0.383283	−	0.923631i	$-0.374793\pi$
$17$	7.86061	+	1.24500i	0.462389	+	0.0732352i	0.0791060	+	0.996866i	$0.474793\pi$
$18$	−11.1184	−	5.66512i	−0.617690	−	0.314729i
$19$	14.9807	+	4.86752i	0.788458	+	0.256185i	0.675447	−	0.737408i	$-0.263951\pi$
$19$	14.9807	+	4.86752i	0.788458	+	0.256185i	0.113011	+	0.993594i	$0.463951\pi$
$20$	−9.92604	−	1.21401i	−0.496302	−	0.0607004i
$21$	−2.83048			−0.134785
$22$	−13.5758	−	7.59587i	−0.617083	−	0.345267i
$23$	6.27408	−	6.27408i	0.272786	−	0.272786i	−0.557435	−	0.830221i	$-0.688214\pi$
$23$	6.27408	−	6.27408i	0.272786	−	0.272786i	0.830221	+	0.557435i	$0.188214\pi$
$24$	0.698191	−	0.960977i	0.0290913	−	0.0400407i
$25$	16.0878	+	19.1359i	0.643510	+	0.765437i
$26$	10.0537	+	30.9421i	0.386680	+	1.19008i
$27$	−7.39310	−	1.17095i	−0.273818	−	0.0433686i
$28$	−2.10869	+	13.3137i	−0.0753103	+	0.475490i
$29$	−41.8099	+	13.5849i	−1.44172	+	0.468444i	−0.922434	−	0.386155i	$-0.873803\pi$
$29$	−41.8099	+	13.5849i	−1.44172	+	0.468444i	−0.519288	+	0.854599i	$0.673803\pi$
$30$	−2.91475	+	0.567999i	−0.0971585	+	0.0189333i
$31$	41.8975	+	30.4403i	1.35153	+	0.981946i	0.998934	+	0.0461720i	$0.0147022\pi$
$31$	41.8975	+	30.4403i	1.35153	+	0.981946i	0.352600	+	0.935774i	$0.385298\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−4.53117	−	0.899468i	−0.137308	−	0.0272566i
$34$		−	11.2552i		−	0.331034i
$35$	26.5455	−	20.7598i	0.758444	−	0.593138i
$36$	−5.45330	+	16.7835i	−0.151481	+	0.466210i
$37$	14.6166	−	28.6867i	0.395044	−	0.775317i	−0.604733	−	0.796428i	$-0.706720\pi$
$37$	14.6166	−	28.6867i	0.395044	−	0.775317i	0.999777	+	0.0211111i	$0.00672037\pi$
$38$	3.48476	−	22.0019i	0.0917043	−	0.578998i
$39$	5.67881	+	7.81621i	0.145610	+	0.200416i
$40$	0.500225	+	14.1333i	0.0125056	+	0.353332i
$41$	−16.7005	+	51.3988i	−0.407329	+	1.25363i	0.511605	+	0.859221i	$0.329051\pi$
$41$	−16.7005	+	51.3988i	−0.407329	+	1.25363i	−0.918935	+	0.394410i	$0.870949\pi$
$42$	0.626192	+	3.95362i	0.0149093	+	0.0941338i
$43$	−22.5790	+	22.5790i	−0.525094	+	0.525094i	−0.919105	−	0.394012i	$-0.871087\pi$
$43$	−22.5790	+	22.5790i	−0.525094	+	0.525094i	0.394012	+	0.919105i	$0.371087\pi$
$44$	−7.60652	+	20.6432i	−0.172875	+	0.469163i
$45$	38.5765	−	21.4071i	0.857256	−	0.475714i
$46$	−10.1517	−	7.37562i	−0.220689	−	0.160340i
$47$	−81.3597	+	41.4548i	−1.73106	+	0.882017i	−0.757738	+	0.652559i	$0.773696\pi$
$47$	−81.3597	+	41.4548i	−1.73106	+	0.882017i	−0.973318	+	0.229459i	$0.926304\pi$
$48$	−1.49676	−	0.762635i	−0.0311824	−	0.0158882i
$49$	2.10105	+	2.89185i	0.0428786	+	0.0590173i
$50$	23.1700	−	26.7049i	0.463400	−	0.534098i
$51$	−1.03283	−	3.17872i	−0.0202516	−	0.0623279i
$52$	40.9958	−	20.8884i	0.788380	−	0.401700i
$53$	−50.1741	+	7.94679i	−0.946681	+	0.149939i	−0.610640	−	0.791908i	$-0.709088\pi$
$53$	−50.1741	+	7.94679i	−0.946681	+	0.149939i	−0.336040	+	0.941848i	$0.609088\pi$
$54$			10.5857i			0.196032i
$55$	49.0925	−	24.7978i	0.892591	−	0.450868i
$56$	19.0632			0.340413
$57$	−1.03483	−	6.53365i	−0.0181549	−	0.114625i
$58$	28.2251	+	55.3948i	0.486639	+	0.955083i
$59$	−22.6016	+	7.34372i	−0.383079	+	0.124470i	−0.494225	−	0.869334i	$-0.664548\pi$
$59$	−22.6016	+	7.34372i	−0.383079	+	0.124470i	0.111146	+	0.993804i	$0.464548\pi$
$60$	1.43822	+	3.94568i	0.0239703	+	0.0657613i
$61$	10.1157	−	7.34947i	0.165831	−	0.120483i	−0.501775	−	0.864998i	$-0.667319\pi$
$61$	10.1157	−	7.34947i	0.165831	−	0.120483i	0.667605	+	0.744515i	$0.267319\pi$
$62$	33.2501	−	65.2569i	0.536291	−	1.05253i
$63$	−26.9988	−	52.9881i	−0.428552	−	0.841080i
$64$	−4.70228	+	6.47214i	−0.0734732	+	0.101127i
$65$	−110.586	−	31.6534i	−1.70132	−	0.486976i
$66$	−0.253940	+	6.52814i	−0.00384758	+	0.0989112i
$67$	25.6290	+	25.6290i	0.382523	+	0.382523i	0.872010	−	0.489487i	$-0.162816\pi$
$67$	25.6290	+	25.6290i	0.382523	+	0.382523i	−0.489487	+	0.872010i	$0.662816\pi$
$68$	−15.7212	+	2.49000i	−0.231194	+	0.0366176i
$69$	−3.54390	−	1.15148i	−0.0513609	−	0.0166882i
$70$	−34.8701	−	32.4861i	−0.498144	−	0.464088i
$71$	91.6006	−	66.5517i	1.29015	−	0.937348i	0.290340	−	0.956923i	$-0.406231\pi$
$71$	91.6006	−	66.5517i	1.29015	−	0.937348i	0.999808	+	0.0195754i	$0.00623145\pi$
$72$	24.6497	+	3.90413i	0.342357	+	0.0542241i
$73$	−21.0787	−	10.7401i	−0.288749	−	0.147125i	0.303617	−	0.952794i	$-0.401806\pi$
$73$	−21.0787	−	10.7401i	−0.288749	−	0.147125i	−0.592365	+	0.805669i	$0.701806\pi$
$74$	−43.3033	−	14.0701i	−0.585180	−	0.190137i
$75$	4.09318	−	9.66830i	0.0545758	−	0.128911i
$76$	−31.5033			−0.414517
$77$	−31.0650	−	67.3160i	−0.403441	−	0.874234i
$78$	9.66136	−	9.66136i	0.123864	−	0.123864i
$79$	17.0478	−	23.4642i	0.215794	−	0.297016i	−0.687372	−	0.726305i	$-0.741236\pi$
$79$	17.0478	−	23.4642i	0.215794	−	0.297016i	0.903167	+	0.429289i	$0.141236\pi$
$80$	19.6307	−	3.82545i	0.245384	−	0.0478181i
$81$	−23.5685	−	72.5363i	−0.290969	−	0.895510i
$82$	75.4887	+	11.9562i	0.920594	+	0.145808i
$83$	17.5698	−	110.932i	0.211685	−	1.33653i	−0.621449	−	0.783454i	$-0.713456\pi$
$83$	17.5698	−	110.932i	0.211685	−	1.33653i	0.833134	−	0.553071i	$-0.186544\pi$
$84$	5.38389	−	1.74933i	0.0640940	−	0.0208254i
$85$	33.0004	+	22.2364i	0.388240	+	0.261604i
$86$	36.5336	+	26.5432i	0.424810	+	0.308642i
$87$	13.0547	+	13.0547i	0.150055	+	0.150055i
$88$	30.5172	+	6.05788i	0.346787	+	0.0688395i
$89$			82.0644i			0.922072i	0.887381	+	0.461036i	$0.152522\pi$
$89$			82.0644i			0.922072i	−0.887381	+	0.461036i	$0.847478\pi$
$90$	−38.4359	−	49.1478i	−0.427065	−	0.546087i
$91$	−47.9138	+	147.463i	−0.526525	+	1.62048i
$92$	−8.05641	+	15.8116i	−0.0875697	+	0.171865i
$93$	3.40231	−	21.4813i	0.0365839	−	0.230982i
$94$	75.9035	+	104.472i	0.807484	+	1.11141i
$95$	57.6254	+	53.6858i	0.606584	+	0.565113i
$96$	−0.734121	+	2.25939i	−0.00764709	+	0.0235353i
$97$	11.9595	+	75.5095i	0.123294	+	0.778449i	0.969410	+	0.245449i	$0.0789354\pi$
$97$	11.9595	+	75.5095i	0.123294	+	0.778449i	−0.846115	+	0.533000i	$0.821065\pi$
$98$	3.57452	−	3.57452i	0.0364747	−	0.0364747i
$99$	−26.3824	−	93.4056i	−0.266489	−	0.943491i
$100$	−42.4274	−	26.4559i	−0.424274	−	0.264559i
$101$	−87.9754	−	63.9179i	−0.871044	−	0.632850i	0.0598230	−	0.998209i	$-0.480946\pi$
$101$	−87.9754	−	63.9179i	−0.871044	−	0.632850i	−0.930867	+	0.365359i	$0.880946\pi$
$102$	−4.21156	+	2.14589i	−0.0412898	+	0.0210382i
$103$	59.2699	+	30.1995i	0.575436	+	0.293199i	0.717388	−	0.696674i	$-0.245338\pi$
$103$	59.2699	+	30.1995i	0.575436	+	0.293199i	−0.141951	+	0.989874i	$0.545338\pi$
$104$	−38.2465	−	52.6418i	−0.367755	−	0.506171i
$105$	−12.8293	−	5.97501i	−0.122183	−	0.0569048i
$106$	22.2002	+	68.3252i	0.209436	+	0.644577i
$107$	24.0686	−	12.2635i	0.224940	−	0.114613i	−0.337889	−	0.941186i	$-0.609713\pi$
$107$	24.0686	−	12.2635i	0.224940	−	0.114613i	0.562829	+	0.826573i	$0.309713\pi$
$108$	14.7862	−	2.34190i	0.136909	−	0.0216843i
$109$			89.6334i			0.822325i	0.911562	+	0.411162i	$0.134877\pi$
$109$			89.6334i			0.822325i	−0.911562	+	0.411162i	$0.865123\pi$
$110$	−45.4984	−	63.0864i	−0.413622	−	0.573513i
$111$	−13.5210			−0.121811
$112$	−4.21737	−	26.6275i	−0.0376551	−	0.237745i
$113$	31.0697	+	60.9778i	0.274954	+	0.539627i	0.986649	−	0.162862i	$-0.0520724\pi$
$113$	31.0697	+	60.9778i	0.274954	+	0.539627i	−0.711695	+	0.702488i	$0.752072\pi$
$114$	−8.89728	+	2.89090i	−0.0780463	+	0.0253588i
$115$	41.6818	−	15.1932i	0.362450	−	0.132115i
$116$	71.1313	−	51.6799i	0.613201	−	0.445517i
$117$	−92.1557	+	180.866i	−0.787656	+	1.54586i
$118$	15.2579	+	29.9454i	0.129304	+	0.253774i
$119$	31.5286	−	43.3954i	0.264946	−	0.364667i
$120$	5.19315	−	2.88181i	0.0432762	−	0.0240151i
$121$	−28.3387	−	117.635i	−0.234204	−	0.972187i
$122$	−12.5037	−	12.5037i	−0.102489	−	0.102489i
$123$	22.4170	−	3.55050i	0.182252	−	0.0288659i
$124$	−98.5070	−	32.0069i	−0.794411	−	0.258120i
$125$	32.5233	+	120.695i	0.260187	+	0.965558i
$126$	−68.0409	+	49.4346i	−0.540007	+	0.392338i
$127$	−68.2792	−	10.8144i	−0.537632	−	0.0851525i	−0.118287	−	0.992979i	$-0.537740\pi$
$127$	−68.2792	−	10.8144i	−0.537632	−	0.0851525i	−0.419345	+	0.907827i	$0.637740\pi$
$128$	10.0806	+	5.13632i	0.0787546	+	0.0401275i
$129$	12.7537	+	4.14394i	0.0988661	+	0.0321235i
$130$	−19.7485	+	161.469i	−0.151912	+	1.24207i
$131$	−13.3454			−0.101873			−0.0509366	−	0.998702i	$-0.516221\pi$
$131$	−13.3454			−0.101873			−0.0509366	+	0.998702i	$0.516221\pi$
$132$	9.17470	−	1.08953i	0.0695053	−	0.00825400i
$133$	75.0690	−	75.0690i	0.564428	−	0.564428i
$134$	30.1287	−	41.4687i	0.224841	−	0.309468i
$135$	−31.0377	−	20.9139i	−0.229909	−	0.154917i
$136$	6.95607	+	21.4086i	0.0511475	+	0.157416i
$137$	95.9547	+	15.1977i	0.700399	+	0.110932i	0.496471	−	0.868054i	$-0.334629\pi$
$137$	95.9547	+	15.1977i	0.700399	+	0.110932i	0.203928	+	0.978986i	$0.434629\pi$
$138$	−0.824371	+	5.20487i	−0.00597370	+	0.0377165i
$139$	89.2331	−	28.9936i	0.641964	−	0.208587i	0.0300967	−	0.999547i	$-0.490418\pi$
$139$	89.2331	−	28.9936i	0.641964	−	0.208587i	0.611868	+	0.790960i	$0.290418\pi$
$140$	−37.6623	+	55.8936i	−0.269017	+	0.399240i
$141$	31.0239	+	22.5402i	0.220028	+	0.159859i
$142$	−113.225	−	113.225i	−0.797356	−	0.797356i
$143$	−123.564	+	220.841i	−0.864081	+	1.54434i
$144$		−	35.2945i		−	0.245101i
$145$	−218.182	−	26.6849i	−1.50470	−	0.184033i
$146$	−10.3385	+	31.8188i	−0.0708119	+	0.217937i
$147$	0.681514	−	1.33755i	0.00463615	−	0.00909895i
$148$	−10.0731	+	63.5990i	−0.0680614	+	0.429723i
$149$	17.5373	+	24.1381i	0.117700	+	0.162001i	0.863802	−	0.503831i	$-0.168077\pi$
$149$	17.5373	+	24.1381i	0.117700	+	0.162001i	−0.746102	+	0.665832i	$0.768077\pi$
$150$	−14.4102	−	3.57843i	−0.0960683	−	0.0238562i
$151$	23.0707	−	71.0042i	0.152786	−	0.470227i	−0.845144	−	0.534539i	$-0.820485\pi$
$151$	23.0707	−	71.0042i	0.152786	−	0.470227i	0.997930	+	0.0643122i	$0.0204854\pi$
$152$	6.96952	+	44.0038i	0.0458521	+	0.289499i
$153$	49.6557	−	49.6557i	0.324547	−	0.324547i
$154$	−87.1546	+	58.2841i	−0.565939	+	0.378468i
$155$	125.644	+	226.416i	0.810606	+	1.46075i
$156$	−15.6324	−	11.3576i	−0.100208	−	0.0728052i
$157$	−127.949	+	65.1934i	−0.814963	+	0.415244i	−0.811215	−	0.584749i	$-0.801193\pi$
$157$	−127.949	+	65.1934i	−0.814963	+	0.415244i	−0.00374840	+	0.999993i	$0.501193\pi$
$158$	−36.5464	−	18.6213i	−0.231306	−	0.117856i
$159$	12.5397	+	17.2595i	0.0788663	+	0.108550i
$160$	−9.68633	−	26.5740i	−0.0605396	−	0.166087i
$161$	−18.4798	−	56.8750i	−0.114781	−	0.353261i
$162$	−96.1048	+	48.9678i	−0.593239	+	0.302270i
$163$	81.2571	−	12.8699i	0.498510	−	0.0789562i	0.0978836	−	0.995198i	$-0.468793\pi$
$163$	81.2571	−	12.8699i	0.498510	−	0.0789562i	0.400626	+	0.916242i	$0.368793\pi$
$164$		−	108.088i		−	0.659073i
$165$	−18.6390	−	13.6420i	−0.112963	−	0.0826785i
$166$	−158.836			−0.956846
$167$	−1.82417	−	11.5173i	−0.0109232	−	0.0689661i	0.981625	−	0.190822i	$-0.0611154\pi$
$167$	−1.82417	−	11.5173i	−0.0109232	−	0.0689661i	−0.992548	+	0.121856i	$0.961115\pi$
$168$	−3.63456	−	7.13322i	−0.0216343	−	0.0424597i
$169$	342.613	−	111.322i	2.02730	−	0.658708i
$170$	23.7591	−	51.0144i	0.139759	−	0.300085i
$171$	112.443	−	81.6943i	0.657559	−	0.477744i
$172$	28.9933	−	56.9025i	0.168565	−	0.330828i
$173$	−61.3278	−	120.363i	−0.354496	−	0.695738i	0.643044	−	0.765829i	$-0.277671\pi$
$173$	−61.3278	−	120.363i	−0.354496	−	0.695738i	−0.997541	+	0.0700910i	$0.977671\pi$
$174$	15.3468	−	21.1230i	0.0881998	−	0.121397i
$175$	164.142	−	38.0583i	0.937952	−	0.217476i
$176$	1.71028	−	43.9667i	0.00971748	−	0.249811i
$177$	7.05715	+	7.05715i	0.0398709	+	0.0398709i
$178$	114.628	−	18.1553i	0.643976	−	0.101996i
$179$	−87.1758	−	28.3251i	−0.487016	−	0.158241i	0.0552086	−	0.998475i	$-0.482418\pi$
$179$	−87.1758	−	28.3251i	−0.487016	−	0.158241i	−0.542224	+	0.840234i	$0.682418\pi$
$180$	−60.1466	+	64.5604i	−0.334148	+	0.358669i
$181$	−68.5048	+	49.7717i	−0.378480	+	0.274982i	−0.760718	−	0.649082i	$-0.775153\pi$
$181$	−68.5048	+	49.7717i	−0.378480	+	0.274982i	0.382239	+	0.924064i	$0.375153\pi$
$182$	216.577	+	34.3025i	1.18998	+	0.188475i
$183$	−4.67874	−	2.38393i	−0.0255669	−	0.0130270i
$184$	23.8680	+	7.75519i	0.129717	+	0.0421478i
$185$	126.807	−	99.1686i	0.685441	−	0.536047i
$186$	−30.7579			−0.165365
$187$	64.2627	−	59.4504i	0.343651	−	0.317916i
$188$	129.135	−	129.135i	0.686887	−	0.686887i
$189$	−29.6534	+	40.8144i	−0.156896	+	0.215949i
$190$	62.2398	−	92.3683i	0.327578	−	0.486149i
$191$	−90.0948	−	277.283i	−0.471701	−	1.45175i	−0.850356	−	0.526208i	$-0.823613\pi$
$191$	−90.0948	−	277.283i	−0.471701	−	1.45175i	0.378655	−	0.925538i	$-0.376387\pi$
$192$	3.31833	+	0.525573i	0.0172830	+	0.00273736i
$193$	11.5070	−	72.6521i	0.0596215	−	0.376436i	−0.939778	−	0.341786i	$-0.888968\pi$
$193$	11.5070	−	72.6521i	0.0596215	−	0.376436i	0.999400	−	0.0346501i	$-0.0110317\pi$
$194$	102.826	−	33.4102i	0.530031	−	0.172218i
$195$	9.23976	+	47.4149i	0.0473834	+	0.243153i
$196$	−5.78369	−	4.20210i	−0.0295086	−	0.0214393i
$197$	−31.2521	−	31.2521i	−0.158640	−	0.158640i	0.623324	−	0.781964i	$-0.285782\pi$
$197$	−31.2521	−	31.2521i	−0.158640	−	0.158640i	−0.781964	+	0.623324i	$0.785782\pi$
$198$	−124.632	+	57.5153i	−0.629457	+	0.290481i
$199$			20.5865i			0.103450i	0.998661	+	0.0517249i	$0.0164719\pi$
$199$			20.5865i			0.103450i	−0.998661	+	0.0517249i	$0.983528\pi$
$200$	−27.5674	+	65.1156i	−0.137837	+	0.325578i
$201$	4.70370	−	14.4765i	0.0234015	−	0.0720225i
$202$	−69.8177	+	137.025i	−0.345632	+	0.678341i
$203$	−46.3506	+	292.646i	−0.228328	+	1.44161i
$204$	3.92912	+	5.40797i	0.0192604	+	0.0265097i
$205$	−184.196	+	197.713i	−0.898518	+	0.964454i
$206$	29.0704	−	89.4694i	0.141118	−	0.434318i
$207$	−12.2474	−	77.3272i	−0.0591663	−	0.373561i
$208$	−65.0689	+	65.0689i	−0.312831	+	0.312831i
$209$	144.030	−	96.3188i	0.689136	−	0.460855i
$210$	−5.50767	+	19.2418i	−0.0262270	+	0.0916276i
$211$	−88.6225	−	64.3880i	−0.420012	−	0.305156i	0.357631	−	0.933863i	$-0.383585\pi$
$211$	−88.6225	−	64.3880i	−0.420012	−	0.305156i	−0.777643	+	0.628707i	$0.783585\pi$
$212$	90.5254	−	46.1250i	0.427006	−	0.217571i
$213$	−42.3674	−	21.5873i	−0.198908	−	0.101349i
$214$	−22.4545	−	30.9059i	−0.104927	−	0.144420i
$215$	−150.004	+	54.6770i	−0.697691	+	0.254312i
$216$	−6.54235	−	20.1353i	−0.0302887	−	0.0932189i
$217$	311.001	−	158.463i	1.43318	−	0.730243i
$218$	125.200	−	19.8298i	0.574313	−	0.0909622i
$219$			9.93510i			0.0453658i
$220$	−78.0536	+	77.5089i	−0.354789	+	0.352313i
$221$	−183.090			−0.828461
$222$	2.99128	+	18.8862i	0.0134743	+	0.0850731i
$223$	−51.1067	−	100.303i	−0.229178	−	0.449787i	0.747568	−	0.664185i	$-0.231221\pi$
$223$	−51.1067	−	100.303i	−0.229178	−	0.449787i	−0.976746	+	0.214397i	$0.931221\pi$
$224$	−36.2603	+	11.7817i	−0.161876	+	0.0525968i
$225$	220.039	−	15.5954i	0.977950	−	0.0693127i
$226$	78.3003	−	56.8885i	0.346462	−	0.251719i
$227$	−14.0638	+	27.6018i	−0.0619552	+	0.121594i	−0.919908	−	0.392135i	$-0.871736\pi$
$227$	−14.0638	+	27.6018i	−0.0619552	+	0.121594i	0.857952	+	0.513729i	$0.171736\pi$
$228$	6.00638	+	11.7882i	0.0263438	+	0.0517026i
$229$	−30.0479	+	41.3573i	−0.131213	+	0.180600i	−0.869568	−	0.493813i	$-0.835603\pi$
$229$	−30.0479	+	41.3573i	−0.131213	+	0.180600i	0.738355	+	0.674412i	$0.235603\pi$
$230$	−30.4432	−	54.8600i	−0.132362	−	0.238522i
$231$	−19.2661	+	24.4586i	−0.0834031	+	0.105881i
$232$	−87.9231	−	87.9231i	−0.378979	−	0.378979i
$233$	329.799	−	52.2351i	1.41545	−	0.224185i	0.598604	−	0.801045i	$-0.295722\pi$
$233$	329.799	−	52.2351i	1.41545	−	0.224185i	0.816843	+	0.576860i	$0.195722\pi$
$234$	273.022	+	88.7101i	1.16676	+	0.379103i
$235$	−456.275	+	16.1491i	−1.94159	+	0.0687196i
$236$	38.4522	−	27.9372i	0.162933	−	0.118378i
$237$	−12.0304	−	1.90542i	−0.0507610	−	0.00803976i
$238$	−67.5899	−	34.4388i	−0.283991	−	0.144701i
$239$	−330.068	−	107.246i	−1.38104	−	0.448727i	−0.478028	−	0.878345i	$-0.658648\pi$
$239$	−330.068	−	107.246i	−1.38104	−	0.448727i	−0.903011	+	0.429618i	$0.858648\pi$
$240$	−5.17422	−	6.61625i	−0.0215592	−	0.0275677i
$241$	462.063			1.91727			0.958637	−	0.284630i	$-0.0918708\pi$
$241$	462.063			1.91727			0.958637	+	0.284630i	$0.0918708\pi$
$242$	−158.043	+	65.6081i	−0.653070	+	0.271108i
$243$	−70.2846	+	70.2846i	−0.289237	+	0.289237i
$244$	−14.6989	+	20.2314i	−0.0602416	+	0.0829154i
$245$	3.41853	+	17.5426i	0.0139532	+	0.0716025i
$246$	−9.91870	−	30.5266i	−0.0403199	−	0.124092i
$247$	−357.910	−	56.6874i	−1.44903	−	0.229504i
$248$	−22.9144	+	144.676i	−0.0923967	+	0.583370i
$249$	−44.8592	+	14.5756i	−0.180158	+	0.0585367i
$250$	161.392	−	72.1302i	0.645566	−	0.288521i
$251$	−106.956	−	77.7078i	−0.426118	−	0.309593i	0.353977	−	0.935254i	$-0.384829\pi$
$251$	−106.956	−	77.7078i	−0.426118	−	0.309593i	−0.780095	+	0.625661i	$0.784829\pi$
$252$	84.1031	+	84.1031i	0.333743	+	0.333743i
$253$	−11.5097	−	96.9208i	−0.0454928	−	0.383086i
$254$			97.7651i			0.384902i
$255$	2.02880	−	16.5879i	0.00795606	−	0.0650507i
$256$	4.94427	−	15.2169i	0.0193136	−	0.0594410i
$257$	−22.9082	+	44.9598i	−0.0891368	+	0.174941i	−0.931271	−	0.364327i	$-0.881299\pi$
$257$	−22.9082	+	44.9598i	−0.0891368	+	0.174941i	0.842134	+	0.539268i	$0.181299\pi$
$258$	2.96673	−	18.7312i	0.0114990	−	0.0726015i
$259$	−127.546	−	175.553i	−0.492457	−	0.677810i
$260$	229.909	−	8.13726i	0.884266	−	0.0312972i
$261$	−119.868	+	368.915i	−0.459264	+	1.41347i
$262$	2.95242	+	18.6409i	0.0112688	+	0.0711483i
$263$	−240.136	+	240.136i	−0.913065	+	0.913065i	−0.996512	−	0.0834472i	$-0.973407\pi$
$263$	−240.136	+	240.136i	−0.913065	+	0.913065i	0.0834472	+	0.996512i	$0.473407\pi$
$264$	−3.55159	−	12.5742i	−0.0134530	−	0.0476296i
$265$	−244.191	−	69.8959i	−0.921476	−	0.263758i
$266$	−121.464	−	88.2489i	−0.456632	−	0.331763i
$267$	30.7076	−	15.6463i	0.115010	−	0.0586004i
$268$	−64.5890	−	32.9097i	−0.241004	−	0.122797i
$269$	−156.947	−	216.019i	−0.583447	−	0.803046i	0.410621	−	0.911806i	$-0.365312\pi$
$269$	−156.947	−	216.019i	−0.583447	−	0.803046i	−0.994068	+	0.108760i	$0.965312\pi$
$270$	−22.3460	+	47.9803i	−0.0827630	+	0.177705i
$271$	98.7950	+	304.060i	0.364557	+	1.12199i	0.950258	+	0.311464i	$0.100819\pi$
$271$	98.7950	+	304.060i	0.364557	+	1.12199i	−0.585701	+	0.810527i	$0.699181\pi$
$272$	28.3646	−	14.4525i	0.104282	−	0.0531342i
$273$	64.3144	−	10.1864i	0.235584	−	0.0373128i
$274$		−	137.392i		−	0.501430i
$275$	274.860	−	8.76482i	0.999492	−	0.0318721i
$276$	7.45256			0.0270020
$277$	78.3422	+	494.633i	0.282824	+	1.78568i	0.563744	+	0.825949i	$0.309360\pi$
$277$	78.3422	+	494.633i	0.282824	+	1.78568i	−0.280920	+	0.959731i	$0.590640\pi$
$278$	−60.2395	−	118.227i	−0.216689	−	0.425276i
$279$	434.595	−	141.208i	1.55769	−	0.506123i
$280$	86.4044	+	40.2414i	0.308587	+	0.143719i
$281$	−313.089	+	227.473i	−1.11420	+	0.809511i	−0.983319	−	0.181888i	$-0.941779\pi$
$281$	−313.089	+	227.473i	−1.11420	+	0.809511i	−0.130877	+	0.991399i	$0.541779\pi$
$282$	24.6207	−	48.3208i	0.0873074	−	0.171350i
$283$	72.8205	+	142.918i	0.257316	+	0.505011i	0.983137	−	0.182873i	$-0.0585397\pi$
$283$	72.8205	+	142.918i	0.257316	+	0.505011i	−0.725820	+	0.687884i	$0.758540\pi$
$284$	−133.103	+	183.201i	−0.468674	+	0.645074i
$285$	9.10183	−	31.7985i	0.0319362	−	0.111574i
$286$	335.807	+	123.737i	1.17415	+	0.432647i
$287$	257.562	+	257.562i	0.897429	+	0.897429i
$288$	−49.2995	+	7.80827i	−0.171179	+	0.0271120i
$289$	−214.616	−	69.7330i	−0.742616	−	0.241291i
$290$	10.9953	+	310.661i	0.0379149	+	1.07124i
$291$	25.9747	−	18.8717i	0.0892600	−	0.0648512i
$292$	46.7317	+	7.40158i	0.160040	+	0.0253479i
$293$	266.394	+	135.735i	0.909196	+	0.463258i	0.845053	−	0.534682i	$-0.179569\pi$
$293$	266.394	+	135.735i	0.909196	+	0.463258i	0.0641425	+	0.997941i	$0.479569\pi$
$294$	−2.01906	−	0.656032i	−0.00686755	−	0.00223140i
$295$	−117.945	−	14.4253i	−0.399814	−	0.0488994i
$296$	91.0636			0.307647
$297$	−60.4407	+	55.9145i	−0.203504	+	0.188264i
$298$	29.8363	−	29.8363i	0.100122	−	0.100122i
$299$	−119.981	+	165.139i	−0.401274	+	0.552306i
$300$	−1.81036	+	20.9199i	−0.00603453	+	0.0697331i
$301$	66.5047	+	204.680i	0.220946	+	0.680002i
$302$	−104.283	−	16.5168i	−0.345307	−	0.0546913i
$303$	−7.14408	+	45.1060i	−0.0235778	+	0.148865i
$304$	59.9228	−	19.4701i	0.197114	−	0.0640464i
$305$	61.3641	−	11.9580i	0.201194	−	0.0392066i
$306$	−80.3445	−	58.3737i	−0.262564	−	0.190764i
$307$	−244.600	−	244.600i	−0.796743	−	0.796743i	0.185837	−	0.982581i	$-0.440500\pi$
$307$	−244.600	−	244.600i	−0.796743	−	0.796743i	−0.982581	+	0.185837i	$0.940500\pi$
$308$	100.693	+	108.844i	0.326924	+	0.353388i
$309$		−	27.9360i		−	0.0904077i
$310$	288.461	−	225.590i	0.930521	−	0.727710i
$311$	33.9242	−	104.408i	0.109081	−	0.335717i	−0.881585	−	0.472024i	$-0.843523\pi$
$311$	33.9242	−	104.408i	0.109081	−	0.335717i	0.990667	+	0.136307i	$0.0435234\pi$
$312$	−12.4060	+	24.3481i	−0.0397627	+	0.0780386i
$313$	68.8364	−	434.616i	0.219925	−	1.38855i	−0.592541	−	0.805540i	$-0.701875\pi$
$313$	68.8364	−	434.616i	0.219925	−	1.38855i	0.812466	−	0.583009i	$-0.198125\pi$
$314$	119.369	+	164.297i	0.380155	+	0.523238i
$315$	−10.5176	−	297.163i	−0.0333892	−	0.943376i
$316$	−17.9251	+	55.1677i	−0.0567249	+	0.174581i
$317$	−26.5148	−	167.408i	−0.0836428	−	0.528100i	−0.993560	−	0.113310i	$-0.963855\pi$
$317$	−26.5148	−	167.408i	−0.0836428	−	0.528100i	0.909917	−	0.414791i	$-0.136145\pi$
$318$	21.3339	−	21.3339i	0.0670876	−	0.0670876i
$319$	−167.197	+	453.753i	−0.524129	+	1.42242i
$320$	−34.9756	+	19.4089i	−0.109299	+	0.0606528i
$321$	−9.17777	−	6.66804i	−0.0285912	−	0.0207727i
$322$	−75.3548	+	38.3952i	−0.234021	+	0.119240i
$323$	111.697	+	56.9127i	0.345812	+	0.176200i
$324$	89.6598	+	123.406i	0.276728	+	0.380883i
$325$	−434.414	−	376.911i	−1.33666	−	1.15973i
$326$	−35.9533	−	110.653i	−0.110286	−	0.339426i
$327$	33.5399	−	17.0894i	0.102568	−	0.0522612i
$328$	−150.977	+	23.9125i	−0.460297	+	0.0729039i
$329$			615.429i			1.87061i
$330$	−14.9316	+	29.0530i	−0.0452472	+	0.0880393i
$331$	−175.923			−0.531491			−0.265745	−	0.964043i	$-0.585618\pi$
$331$	−175.923			−0.531491			−0.265745	+	0.964043i	$0.585618\pi$
$332$	35.1397	+	221.863i	0.105842	+	0.668263i
$333$	−128.972	−	253.121i	−0.387302	−	0.760123i
$334$	−15.6839	+	5.09600i	−0.0469577	+	0.0152575i
$335$	62.0629	+	170.266i	0.185262	+	0.508257i
$336$	−9.15962	+	6.65486i	−0.0272608	+	0.0198061i
$337$	248.391	−	487.495i	0.737065	−	1.44657i	−0.151804	−	0.988411i	$-0.548508\pi$
$337$	248.391	−	487.495i	0.737065	−	1.44657i	0.888869	−	0.458161i	$-0.151492\pi$
$338$	−231.291	−	453.935i	−0.684293	−	1.34300i
$339$	16.8935	−	23.2519i	0.0498334	−	0.0685897i
$340$	−76.5133	−	21.9007i	−0.225039	−	0.0644140i
$341$	548.222	−	154.845i	1.60769	−	0.454092i
$342$	−138.987	−	138.987i	−0.406394	−	0.406394i
$343$	349.981	−	55.4316i	1.02035	−	0.161608i
$344$	−85.8957	−	27.9092i	−0.249697	−	0.0811315i
$345$	−13.6321	−	12.7001i	−0.0395134	−	0.0368120i
$346$	−154.555	+	112.291i	−0.446691	+	0.324540i
$347$	−262.669	−	41.6027i	−0.756972	−	0.119893i	−0.233993	−	0.972238i	$-0.575179\pi$
$347$	−262.669	−	41.6027i	−0.756972	−	0.119893i	−0.522979	+	0.852346i	$0.675179\pi$
$348$	−32.8999	−	16.7633i	−0.0945399	−	0.0481705i
$349$	−53.5127	−	17.3873i	−0.153331	−	0.0498204i	0.231346	−	0.972872i	$-0.425687\pi$
$349$	−53.5127	−	17.3873i	−0.153331	−	0.0498204i	−0.384677	+	0.923051i	$0.625687\pi$
$350$	−89.4733	−	220.854i	−0.255638	−	0.631011i
$351$	172.201			0.490600
$352$	−61.7912	+	7.33792i	−0.175543	+	0.0208464i
$353$	110.322	−	110.322i	0.312527	−	0.312527i	−0.533361	−	0.845888i	$-0.679071\pi$
$353$	110.322	−	110.322i	0.312527	−	0.312527i	0.845888	+	0.533361i	$0.179071\pi$
$354$	8.29617	−	11.4187i	0.0234355	−	0.0322562i
$355$	555.670	−	108.284i	1.56527	−	0.305024i
$356$	−50.7186	−	156.096i	−0.142468	−	0.438471i
$357$	−22.2493	−	3.52394i	−0.0623230	−	0.00987099i
$358$	−20.2786	+	128.034i	−0.0566440	+	0.357636i
$359$	−217.473	+	70.6613i	−0.605775	+	0.196828i	−0.595814	−	0.803122i	$-0.703171\pi$
$359$	−217.473	+	70.6613i	−0.605775	+	0.196828i	−0.00996065	+	0.999950i	$0.503171\pi$
$360$	103.484	+	69.7300i	0.287457	+	0.193695i
$361$	−91.3266	−	66.3527i	−0.252982	−	0.183802i
$362$	84.6766	+	84.6766i	0.233913	+	0.233913i
$363$	−38.6146	+	33.0321i	−0.106376	+	0.0909976i
$364$		−	310.104i		−	0.851935i
$365$	−72.8679	−	93.1760i	−0.199638	−	0.255277i
$366$	−2.29480	+	7.06267i	−0.00626995	+	0.0192969i
$367$	278.041	−	545.686i	0.757604	−	1.48688i	−0.112306	−	0.993674i	$-0.535824\pi$
$367$	278.041	−	545.686i	0.757604	−	1.48688i	0.869911	−	0.493209i	$-0.164176\pi$
$368$	5.55210	−	35.0546i	0.0150872	−	0.0952571i
$369$	280.294	+	385.791i	0.759603	+	1.04550i
$370$	−166.573	−	155.185i	−0.450196	−	0.419418i
$371$	−105.801	+	325.623i	−0.285179	+	0.877691i
$372$	6.80461	+	42.9626i	0.0182920	+	0.115491i
$373$	−153.939	+	153.939i	−0.412705	+	0.412705i	−0.882680	−	0.469975i	$-0.844263\pi$
$373$	−153.939	+	153.939i	−0.412705	+	0.412705i	0.469975	+	0.882680i	$0.344263\pi$
$374$	−97.2574	−	76.6100i	−0.260046	−	0.204840i
$375$	38.9618	−	35.1814i	0.103898	−	0.0938171i
$376$	−208.944	−	151.807i	−0.555703	−	0.403742i
$377$	901.119	−	459.143i	2.39024	−	1.21789i
$378$	63.5700	+	32.3905i	0.168175	+	0.0856892i
$379$	7.30271	+	10.0513i	0.0192684	+	0.0265206i	0.818542	−	0.574446i	$-0.194782\pi$
$379$	7.30271	+	10.0513i	0.0192684	+	0.0265206i	−0.799274	+	0.600967i	$0.794782\pi$
$380$	−142.790	−	66.5019i	−0.375762	−	0.175005i
$381$	8.97142	+	27.6112i	0.0235470	+	0.0724703i
$382$	−367.378	+	187.189i	−0.961723	+	0.490022i
$383$	−476.120	+	75.4100i	−1.24313	+	0.196893i	−0.743140	−	0.669136i	$-0.766664\pi$
$383$	−476.120	+	75.4100i	−1.24313	+	0.196893i	−0.499993	+	0.866029i	$0.666664\pi$
$384$		−	4.75133i		−	0.0123733i
$385$	1.29783	−	370.689i	0.00337099	−	0.962829i
$386$	−104.026			−0.269498
$387$	44.0758	+	278.284i	0.113891	+	0.719079i
$388$	−69.4158	−	136.236i	−0.178907	−	0.351124i
$389$	−254.814	+	82.7941i	−0.655049	+	0.212838i	−0.617639	−	0.786462i	$-0.711911\pi$
$389$	−254.814	+	82.7941i	−0.655049	+	0.212838i	−0.0374100	+	0.999300i	$0.511911\pi$
$390$	64.1852	−	23.3958i	0.164577	−	0.0599892i
$391$	57.1293	−	41.5069i	0.146111	−	0.106156i
$392$	−4.58996	+	9.00831i	−0.0117091	+	0.0229804i
$393$	2.54441	+	4.99370i	0.00647434	+	0.0127066i
$394$	−36.7390	+	50.5670i	−0.0932463	+	0.128343i
$395$	126.801	−	70.3655i	0.321016	−	0.178140i
$396$	107.910	+	161.363i	0.272501	+	0.407482i
$397$	329.306	+	329.306i	0.829486	+	0.829486i	0.987446	−	0.157960i	$-0.0504917\pi$
$397$	329.306	+	329.306i	0.829486	+	0.829486i	−0.157960	+	0.987446i	$0.550492\pi$
$398$	28.7553	−	4.55439i	0.0722495	−	0.0114432i
$399$	−42.4026	−	13.7774i	−0.106272	−	0.0345299i
$400$	97.0524	+	24.1006i	0.242631	+	0.0602515i
$401$	−136.668	+	99.2952i	−0.340818	+	0.247619i	−0.745007	−	0.667057i	$-0.767554\pi$
$401$	−136.668	+	99.2952i	−0.340818	+	0.247619i	0.404189	+	0.914676i	$0.367554\pi$
$402$	−21.2614	−	3.36748i	−0.0528891	−	0.00837682i
$403$	−1061.55	−	540.886i	−2.63412	−	1.34215i
$404$	206.843	+	67.2072i	0.511987	+	0.166355i
$405$	46.2957	−	378.525i	0.114310	−	0.934630i
$406$	419.023			1.03208
$407$	−148.396	−	321.565i	−0.364609	−	0.790086i
$408$	6.68462	−	6.68462i	0.0163839	−	0.0163839i
$409$	−90.2543	+	124.224i	−0.220671	+	0.303727i	−0.904971	−	0.425473i	$-0.860108\pi$
$409$	−90.2543	+	124.224i	−0.220671	+	0.303727i	0.684300	+	0.729200i	$0.260108\pi$
$410$	316.916	+	213.545i	0.772966	+	0.520842i
$411$	−12.6078	−	38.8028i	−0.0306759	−	0.0944106i
$412$	−131.402	−	20.8121i	−0.318938	−	0.0505148i
$413$	−25.0562	+	158.199i	−0.0606689	+	0.383048i
$414$	−105.301	+	34.2145i	−0.254351	+	0.0826436i
$415$	313.807	−	465.712i	0.756162	−	1.12220i
$416$	105.284	+	76.4930i	0.253086	+	0.183877i
$417$	−27.8622	−	27.8622i	−0.0668157	−	0.0668157i
$418$	−166.402	−	179.872i	−0.398091	−	0.430316i
$419$		−	619.941i		−	1.47957i	−0.672841	−	0.739787i	$-0.734926\pi$
$419$		−	619.941i		−	1.47957i	0.672841	−	0.739787i	$-0.265074\pi$
$420$	28.0954	+	3.43623i	0.0668939	+	0.00818149i
$421$	−15.6596	+	48.1952i	−0.0371961	+	0.114478i	−0.967931	−	0.251218i	$-0.919169\pi$
$421$	−15.6596	+	48.1952i	−0.0371961	+	0.114478i	0.930734	+	0.365696i	$0.119169\pi$
$422$	−70.3312	+	138.033i	−0.166662	+	0.327092i
$423$	−126.040	+	795.785i	−0.297967	+	1.88129i
$424$	−84.4546	−	116.242i	−0.199185	−	0.274155i
$425$	102.635	+	170.449i	0.241495	+	0.401057i
$426$	−20.7801	+	63.9546i	−0.0487796	+	0.150128i
$427$	−13.1832	−	83.2352i	−0.0308739	−	0.194930i
$428$	−38.2018	+	38.2018i	−0.0892566	+	0.0892566i
$429$	106.195	+	4.13090i	0.247540	+	0.00962914i
$430$	109.559	+	197.429i	0.254787	+	0.459137i
$431$	654.100	+	475.231i	1.51763	+	1.10262i	0.962645	+	0.270766i	$0.0872770\pi$
$431$	654.100	+	475.231i	1.51763	+	1.10262i	0.554988	+	0.831859i	$0.312723\pi$
$432$	−26.6776	+	13.5929i	−0.0617538	+	0.0314651i
$433$	485.286	+	247.265i	1.12075	+	0.571052i	0.913338	−	0.407202i	$-0.133495\pi$
$433$	485.286	+	247.265i	1.12075	+	0.571052i	0.207414	+	0.978253i	$0.433495\pi$
$434$	−290.144	−	399.350i	−0.668535	−	0.920160i
$435$	31.6132	+	86.7290i	0.0726739	+	0.199377i
$436$	−55.3965	−	170.493i	−0.127056	−	0.391039i
$437$	124.529	−	63.4509i	0.284964	−	0.145196i
$438$	13.8774	−	2.19796i	0.0316835	−	0.00501817i
$439$		−	186.430i		−	0.424669i	−0.977197	−	0.212334i	$-0.931893\pi$
$439$		−	186.430i		−	0.424669i	0.977197	−	0.212334i	$-0.0681066\pi$
$440$	125.533	+	91.8780i	0.285301	+	0.208814i
$441$	31.5402			0.0715198
$442$	40.5053	+	255.740i	0.0916410	+	0.578598i
$443$	126.942	+	249.138i	0.286551	+	0.562388i	0.988747	−	0.149595i	$-0.0477971\pi$
$443$	126.942	+	249.138i	0.286551	+	0.562388i	−0.702196	+	0.711983i	$0.747797\pi$
$444$	25.7186	−	8.35647i	0.0579247	−	0.0188209i
$445$	−173.234	+	371.960i	−0.389290	+	0.835865i
$446$	−128.796	+	93.5761i	−0.288781	+	0.209812i
$447$	5.68856	−	11.1644i	0.0127261	−	0.0249763i
$448$	24.4786	+	48.0420i	0.0546397	+	0.107236i
$449$	33.3742	−	45.9357i	0.0743301	−	0.102307i	−0.770233	−	0.637762i	$-0.779860\pi$
$449$	33.3742	−	45.9357i	0.0743301	−	0.102307i	0.844563	+	0.535456i	$0.179860\pi$
$450$	−70.4632	−	303.901i	−0.156585	−	0.675335i
$451$	330.470	+	494.166i	0.732750	+	1.09571i
$452$	−96.7845	−	96.7845i	−0.214125	−	0.214125i
$453$	−30.9676	+	4.90479i	−0.0683612	+	0.0108274i
$454$	41.6657	+	13.5380i	0.0917746	+	0.0298194i
$455$	−528.459	+	567.240i	−1.16145	+	1.24668i
$456$	15.1370	−	10.9976i	0.0331951	−	0.0241176i
$457$	−457.322	−	72.4327i	−1.00070	−	0.158496i	−0.365476	−	0.930821i	$-0.619094\pi$
$457$	−457.322	−	72.4327i	−1.00070	−	0.158496i	−0.635228	+	0.772325i	$0.719094\pi$
$458$	64.4156	+	32.8214i	0.140645	+	0.0716624i
$459$	−56.6564	−	18.4088i	−0.123434	−	0.0401063i
$460$	−69.8935	+	54.6600i	−0.151942	+	0.118826i
$461$	397.386			0.862010			0.431005	−	0.902350i	$-0.358159\pi$
$461$	397.386			0.862010			0.431005	+	0.902350i	$0.358159\pi$
$462$	38.4261	+	21.4999i	0.0831733	+	0.0465367i
$463$	405.110	−	405.110i	0.874967	−	0.874967i	−0.118042	−	0.993009i	$-0.537662\pi$
$463$	405.110	−	405.110i	0.874967	−	0.874967i	0.993009	+	0.118042i	$0.0376617\pi$
$464$	−103.360	+	142.263i	−0.222758	+	0.306600i
$465$	60.7671	−	90.1827i	0.130682	−	0.193941i
$466$	−145.924	−	449.108i	−0.313142	−	0.963752i
$467$	−34.9158	−	5.53012i	−0.0747662	−	0.0118418i	0.118939	−	0.992902i	$-0.462051\pi$
$467$	−34.9158	−	5.53012i	−0.0747662	−	0.0118418i	−0.193705	+	0.981060i	$0.562051\pi$
$468$	63.5094	−	400.983i	0.135704	−	0.856800i
$469$	232.329	−	75.4883i	0.495371	−	0.160956i
$470$	123.500	+	633.753i	0.262765	+	1.34841i
$471$	48.7893	+	35.4475i	0.103587	+	0.0752601i
$472$	−47.5296	−	47.5296i	−0.100698	−	0.100698i
$473$	41.4208	+	348.796i	0.0875704	+	0.737413i
$474$			17.2256i			0.0363409i
$475$	147.861	+	364.977i	0.311287	+	0.768373i
$476$	−33.1511	+	102.029i	−0.0696453	+	0.214346i
$477$	−203.495	+	399.381i	−0.426614	+	0.837277i
$478$	−76.7794	+	484.766i	−0.160626	+	1.01415i
$479$	−40.0561	−	55.1325i	−0.0836244	−	0.115099i	0.765155	−	0.643846i	$-0.222662\pi$
$479$	−40.0561	−	55.1325i	−0.0836244	−	0.115099i	−0.848780	+	0.528747i	$0.822662\pi$
$480$	−8.09690	+	8.69108i	−0.0168685	+	0.0181064i
$481$	−228.881	+	704.425i	−0.475845	+	1.46450i
$482$	−102.223	−	645.411i	−0.212081	−	1.33903i
$483$	−17.7587	+	17.7587i	−0.0367674	+	0.0367674i
$484$	126.606	+	206.240i	0.261582	+	0.426116i
$485$	−105.190	+	367.496i	−0.216887	+	0.757723i
$486$	113.723	+	82.6245i	0.233998	+	0.170009i
$487$	−213.956	+	109.016i	−0.439335	+	0.223853i	−0.659645	−	0.751577i	$-0.729293\pi$
$487$	−213.956	+	109.016i	−0.439335	+	0.223853i	0.220309	+	0.975430i	$0.429293\pi$
$488$	31.5111	+	16.0557i	0.0645719	+	0.0329010i
$489$	−20.3081	−	27.9518i	−0.0415299	−	0.0571610i
$490$	23.7473	−	8.65600i	0.0484638	−	0.0176653i
$491$	−133.601	−	411.182i	−0.272100	−	0.837439i	−0.989972	−	0.141263i	$-0.954884\pi$
$491$	−133.601	−	411.182i	−0.272100	−	0.837439i	0.717872	−	0.696175i	$-0.245116\pi$
$492$	−40.4453	+	20.6079i	−0.0822059	+	0.0418860i
$493$	−345.565	+	54.7321i	−0.700943	+	0.111018i
$494$			512.470i			1.03739i
$495$	77.5953	−	479.056i	0.156758	−	0.967790i
$496$	207.153			0.417647
$497$	−119.378	−	753.720i	−0.240196	−	1.51654i
$498$	30.2836	+	59.4349i	0.0608104	+	0.119347i
$499$	154.234	−	50.1136i	0.309086	−	0.100428i	−0.150367	−	0.988630i	$-0.548046\pi$
$499$	154.234	−	50.1136i	0.309086	−	0.100428i	0.459453	+	0.888202i	$0.348046\pi$
$500$	−136.457	−	209.475i	−0.272913	−	0.418949i
$501$	−3.96187	+	2.87847i	−0.00790792	+	0.00574544i
$502$	−84.8805	+	166.587i	−0.169085	+	0.331847i
$503$	−10.4438	−	20.4971i	−0.0207630	−	0.0407497i	0.880392	−	0.474247i	$-0.157279\pi$
$503$	−10.4438	−	20.4971i	−0.0207630	−	0.0407497i	−0.901155	+	0.433497i	$0.857279\pi$
$504$	98.8692	−	136.082i	0.196169	−	0.270003i
$505$	−263.824	−	475.422i	−0.522424	−	0.941430i
$506$	−132.833	+	37.5187i	−0.262515	+	0.0741476i
$507$	−106.978	−	106.978i	−0.211001	−	0.211001i
$508$	136.558	−	21.6287i	0.268816	−	0.0425762i
$509$	−699.374	−	227.240i	−1.37402	−	0.446445i	−0.473318	−	0.880892i	$-0.656944\pi$
$509$	−699.374	−	227.240i	−1.37402	−	0.446445i	−0.900697	+	0.434447i	$0.856944\pi$
$510$	−23.6189	+	0.835953i	−0.0463116	+	0.00163912i
$511$	−128.994	+	93.7196i	−0.252434	+	0.183404i
$512$	−22.3488	−	3.53971i	−0.0436501	−	0.00691349i
$513$	−105.054	−	53.5277i	−0.204784	−	0.104343i
$514$	67.8680	+	22.0516i	0.132039	+	0.0429020i
$515$	204.893	+	261.996i	0.397851	+	0.508731i
$516$	−26.8201			−0.0519770
$517$	−195.571	+	985.209i	−0.378280	+	1.90563i
$518$	−216.995	+	216.995i	−0.418909	+	0.418909i
$519$	−33.3457	+	45.8964i	−0.0642499	+	0.0884324i
$520$	−62.2294	−	319.337i	−0.119672	−	0.614110i
$521$	−254.419	−	783.020i	−0.488327	−	1.50292i	−0.827103	−	0.562050i	$-0.810013\pi$
$521$	−254.419	−	783.020i	−0.488327	−	1.50292i	0.338776	−	0.940867i	$-0.389987\pi$
$522$	541.821	+	85.8159i	1.03797	+	0.164398i
$523$	−72.0197	+	454.715i	−0.137705	+	0.869435i	0.818023	+	0.575185i	$0.195070\pi$
$523$	−72.0197	+	454.715i	−0.137705	+	0.869435i	−0.955728	+	0.294250i	$0.904930\pi$
$524$	25.3844	−	8.24790i	0.0484435	−	0.0157403i
$525$	−45.5361	−	54.1639i	−0.0867354	−	0.103169i
$526$	388.548	+	282.297i	0.738685	+	0.536686i
$527$	291.442	+	291.442i	0.553021	+	0.553021i
$528$	−16.7780	+	7.74268i	−0.0317764	+	0.0146642i
$529$			450.272i			0.851176i
$530$	−43.6080	+	356.550i	−0.0822792	+	0.672736i
$531$	−64.7983	+	199.429i	−0.122031	+	0.375572i
$532$	−96.3945	+	189.185i	−0.181193	+	0.355611i
$533$	194.495	−	1227.99i	0.364906	−	2.30392i
$534$	−28.6483	−	39.4310i	−0.0536485	−	0.0738408i
$535$	134.979	−	4.77737i	0.252298	−	0.00892967i
$536$	−31.6792	+	97.4987i	−0.0591031	+	0.181901i
$537$	6.02188	+	38.0207i	0.0112139	+	0.0708020i
$538$	−267.015	+	267.015i	−0.496310	+	0.496310i
$539$	39.2900	+	1.52835i	0.0728942	+	0.00283554i
$540$	71.9626	+	20.5982i	0.133264	+	0.0381448i
$541$	−645.323	−	468.855i	−1.19283	−	0.866645i	−0.199273	−	0.979944i	$-0.563858\pi$
$541$	−645.323	−	468.855i	−1.19283	−	0.866645i	−0.993561	+	0.113299i	$0.963858\pi$
$542$	402.855	−	205.265i	0.743274	−	0.378717i
$543$	31.6851	+	16.1444i	0.0583519	+	0.0297318i
$544$	−26.4624	−	36.4224i	−0.0486442	−	0.0669530i
$545$	−189.212	+	406.267i	−0.347178	+	0.745443i
$546$	−28.4568	−	87.5809i	−0.0521186	−	0.160405i
$547$	361.782	−	184.337i	0.661393	−	0.336996i	−0.0908670	−	0.995863i	$-0.528964\pi$
$547$	361.782	−	184.337i	0.661393	−	0.336996i	0.752260	+	0.658867i	$0.228964\pi$
$548$	−191.909	+	30.3954i	−0.350199	+	0.0554661i
$549$		−	110.328i		−	0.200961i
$550$	−73.0505	−	381.986i	−0.132819	−	0.694521i
$551$	−692.467			−1.25675
$552$	−1.64874	−	10.4097i	−0.00298685	−	0.0188582i
$553$	−88.7453	−	174.172i	−0.160480	−	0.314959i
$554$	673.573	−	218.857i	1.21584	−	0.395049i
$555$	−61.2846	−	28.5423i	−0.110423	−	0.0514275i
$556$	−151.812	+	110.298i	−0.273044	+	0.198378i
$557$	26.1139	−	51.2514i	0.0468832	−	0.0920134i	−0.866376	−	0.499392i	$-0.833557\pi$
$557$	26.1139	−	51.2514i	0.0468832	−	0.0920134i	0.913260	+	0.407378i	$0.133557\pi$
$558$	−293.386	−	575.803i	−0.525782	−	1.03191i
$559$	431.785	−	594.301i	0.772423	−	1.06315i
$560$	37.0939	−	129.593i	0.0662391	−	0.231415i
$561$	−34.4979	−	12.7117i	−0.0614937	−	0.0226590i
$562$	386.999	+	386.999i	0.688611	+	0.688611i
$563$	874.081	−	138.441i	1.55254	−	0.245898i	0.679548	−	0.733631i	$-0.262176\pi$
$563$	874.081	−	138.441i	1.55254	−	0.245898i	0.872993	+	0.487733i	$0.162176\pi$
$564$	−72.9415	−	23.7001i	−0.129329	−	0.0420215i
$565$	12.1035	+	341.971i	0.0214221	+	0.605258i
$566$	183.518	−	133.334i	0.324237	−	0.235572i
$567$	−507.713	−	80.4139i	−0.895438	−	0.141823i
$568$	285.342	+	145.389i	0.502363	+	0.255967i
$569$	−282.727	−	91.8637i	−0.496884	−	0.161448i	0.0498448	−	0.998757i	$-0.484127\pi$
$569$	−282.727	−	91.8637i	−0.496884	−	0.161448i	−0.546729	+	0.837309i	$0.684127\pi$
$570$	−46.4298	−	5.67862i	−0.0814558	−	0.00996249i
$571$	104.209			0.182503			0.0912513	−	0.995828i	$-0.470913\pi$
$571$	104.209			0.182503			0.0912513	+	0.995828i	$0.470913\pi$
$572$	98.5448	−	496.431i	0.172281	−	0.867886i
$573$	−86.5791	+	86.5791i	−0.151098	+	0.151098i
$574$	302.782	−	416.744i	0.527495	−	0.726035i
$575$	220.996	+	19.1245i	0.384341	+	0.0332599i
$576$	21.8132	+	67.1342i	0.0378702	+	0.116552i
$577$	163.401	+	25.8802i	0.283191	+	0.0448530i	0.296414	−	0.955060i	$-0.404209\pi$
$577$	163.401	+	25.8802i	0.283191	+	0.0448530i	−0.0132231	+	0.999913i	$0.504209\pi$
$578$	−49.9233	+	315.203i	−0.0863725	+	0.545335i
$579$	−29.3795	+	9.54598i	−0.0507418	+	0.0164870i
$580$	431.499	−	84.0863i	0.743964	−	0.144976i
$581$	−612.411	−	444.942i	−1.05406	−	0.765822i
$582$	−32.1064	−	32.1064i	−0.0551657	−	0.0551657i
$583$	−272.849	+	487.652i	−0.468008	+	0.836454i
$584$		−	66.9125i		−	0.114576i
$585$	−799.498	+	625.244i	−1.36666	+	1.06879i
$586$	130.660	−	402.129i	0.222969	−	0.686227i
$587$	−263.114	+	516.391i	−0.448235	+	0.879711i	0.550750	+	0.834670i	$0.314342\pi$
$587$	−263.114	+	516.391i	−0.448235	+	0.879711i	−0.998985	+	0.0450410i	$0.985658\pi$
$588$	−0.469667	+	2.96536i	−0.000798754	+	0.00504313i
$589$	479.485	+	659.955i	0.814066	+	1.12047i
$590$	5.94386	+	167.937i	0.0100743	+	0.284639i
$591$	−5.73570	+	17.6527i	−0.00970508	+	0.0298692i
$592$	−20.1462	−	127.198i	−0.0340307	−	0.214861i
$593$	9.59595	−	9.59595i	0.0161820	−	0.0161820i	−0.698969	−	0.715152i	$-0.746358\pi$
$593$	9.59595	−	9.59595i	0.0161820	−	0.0161820i	0.715152	+	0.698969i	$0.246358\pi$
$594$	91.4729	+	72.0536i	0.153995	+	0.121302i
$595$	234.510	−	130.136i	0.394135	−	0.218716i
$596$	−48.2762	−	35.0747i	−0.0810003	−	0.0588502i
$597$	7.70325	−	3.92500i	0.0129033	−	0.00657454i
$598$	257.211	+	131.055i	0.430118	+	0.219156i
$599$	−379.677	−	522.580i	−0.633851	−	0.872421i	0.364418	−	0.931236i	$-0.381268\pi$
$599$	−379.677	−	522.580i	−0.633851	−	0.872421i	−0.998269	+	0.0588142i	$0.981268\pi$
$600$	29.6215	−	2.09944i	0.0493692	−	0.00349907i
$601$	187.429	+	576.846i	0.311862	+	0.959811i	0.977027	+	0.213115i	$0.0683610\pi$
$601$	187.429	+	576.846i	0.311862	+	0.959811i	−0.665166	+	0.746696i	$0.731639\pi$
$602$	271.185	−	138.176i	0.450474	−	0.229528i
$603$	315.875	−	50.0296i	0.523838	−	0.0829679i
$604$			149.316i			0.247213i
$605$	119.875	−	593.005i	0.198141	−	0.980174i
$606$	64.5846			0.106575
$607$	−94.1210	−	594.257i	−0.155059	−	0.979006i	−0.935385	−	0.353632i	$-0.884946\pi$
$607$	−94.1210	−	594.257i	−0.155059	−	0.979006i	0.780325	−	0.625374i	$-0.215054\pi$
$608$	−40.4527	−	79.3929i	−0.0665340	−	0.130580i
$609$	118.342	−	38.4517i	0.194322	−	0.0631391i
$610$	−30.2787	−	83.0680i	−0.0496372	−	0.136177i
$611$	1699.47	−	1234.74i	2.78146	−	2.02085i
$612$	−63.7618	+	125.140i	−0.104186	+	0.204476i
$613$	−280.446	−	550.407i	−0.457498	−	0.897891i	−0.998386	−	0.0567960i	$-0.981912\pi$
$613$	−280.446	−	550.407i	−0.457498	−	0.897891i	0.540887	−	0.841095i	$-0.318088\pi$
$614$	−287.545	+	395.771i	−0.468314	+	0.644579i
$615$	109.101	+	31.2284i	0.177400	+	0.0507779i
$616$	129.756	−	164.727i	0.210644	−	0.267415i
$617$	−317.829	−	317.829i	−0.515121	−	0.515121i	0.400970	−	0.916091i	$-0.368673\pi$
$617$	−317.829	−	317.829i	−0.515121	−	0.515121i	−0.916091	+	0.400970i	$0.868673\pi$
$618$	−39.0210	+	6.18032i	−0.0631408	+	0.0100005i
$619$	686.698	+	223.122i	1.10937	+	0.360455i	0.805700	−	0.592323i	$-0.201789\pi$
$619$	686.698	+	223.122i	1.10937	+	0.360455i	0.303667	+	0.952778i	$0.401789\pi$
$620$	−378.922	−	353.016i	−0.611164	−	0.569380i
$621$	−53.7315	+	39.0382i	−0.0865242	+	0.0628635i
$622$	−153.343	−	24.2871i	−0.246531	−	0.0390467i
$623$	492.817	+	251.103i	0.791038	+	0.403054i
$624$	36.7540	+	11.9421i	0.0589007	+	0.0191380i
$625$	−107.368	+	615.709i	−0.171788	+	0.985134i
$626$	−622.301			−0.994091
$627$	−63.5019	−	35.5302i	−0.101279	−	0.0566671i
$628$	203.082	−	203.082i	0.323379	−	0.323379i
$629$	150.610	−	207.297i	0.239444	−	0.329567i
$630$	−412.752	+	80.4330i	−0.655161	+	0.127671i
$631$	−323.379	−	995.259i	−0.512487	−	1.57727i	−0.787809	−	0.615920i	$-0.788785\pi$
$631$	−323.379	−	995.259i	−0.512487	−	1.57727i	0.275322	−	0.961352i	$-0.411215\pi$
$632$	81.0240	+	12.8329i	0.128203	+	0.0203053i
$633$	−7.19662	+	45.4377i	−0.0113691	+	0.0717815i
$634$	−227.970	+	74.0718i	−0.359573	+	0.116833i
$635$	−286.649	−	193.151i	−0.451416	−	0.304174i
$636$	−34.5189	−	25.0795i	−0.0542750	−	0.0394331i
$637$	−58.1475	−	58.1475i	−0.0912833	−	0.0912833i
$638$	670.793	+	133.157i	1.05140	+	0.208710i
$639$		−	999.052i		−	1.56346i
$640$	34.8481	+	44.5602i	0.0544502	+	0.0696253i
$641$	54.7325	−	168.449i	0.0853861	−	0.262791i	−0.899243	−	0.437449i	$-0.855882\pi$
$641$	54.7325	−	168.449i	0.0853861	−	0.262791i	0.984629	+	0.174658i	$0.0558819\pi$
$642$	−7.28352	+	14.2947i	−0.0113450	+	0.0222659i
$643$	45.5513	−	287.599i	0.0708418	−	0.447277i	−0.926615	−	0.376010i	$-0.877296\pi$
$643$	45.5513	−	287.599i	0.0708418	−	0.447277i	0.997457	−	0.0712671i	$-0.0227043\pi$
$644$	70.3013	+	96.7615i	0.109164	+	0.150251i
$645$	49.0590	+	45.7050i	0.0760605	+	0.0708605i
$646$	54.7847	−	168.610i	0.0848061	−	0.261006i
$647$	143.366	+	905.179i	0.221586	+	1.39904i	0.808073	+	0.589082i	$0.200510\pi$
$647$	143.366	+	905.179i	0.221586	+	1.39904i	−0.586487	+	0.809959i	$0.699490\pi$
$648$	152.538	−	152.538i	0.235399	−	0.235399i
$649$	−90.3836	+	245.290i	−0.139266	+	0.377951i
$650$	−430.364	+	690.176i	−0.662099	+	1.06181i
$651$	−118.590	−	86.1607i	−0.182166	−	0.132351i
$652$	−146.606	+	74.6995i	−0.224856	+	0.114570i
$653$	551.092	+	280.796i	0.843939	+	0.430009i	0.821820	−	0.569747i	$-0.192959\pi$
$653$	551.092	+	280.796i	0.843939	+	0.430009i	0.0221191	+	0.999755i	$0.492959\pi$
$654$	−31.2906	−	43.0678i	−0.0478450	−	0.0658529i
$655$	−60.4884	−	28.1715i	−0.0923487	−	0.0430099i
$656$	66.8020	+	205.595i	0.101832	+	0.313408i
$657$	−185.990	+	94.7668i	−0.283090	+	0.144242i
$658$	859.633	−	136.152i	1.30643	−	0.206919i
$659$			724.227i			1.09898i	0.835501	+	0.549490i	$0.185178\pi$
$659$			724.227i			1.09898i	−0.835501	+	0.549490i	$0.814822\pi$
$660$	43.8846	+	14.4290i	0.0664918	+	0.0218622i
$661$	−1142.32			−1.72816			−0.864082	−	0.503350i	$-0.832101\pi$
$661$	−1142.32			−1.72816			−0.864082	+	0.503350i	$0.832101\pi$
$662$	38.9199	+	245.730i	0.0587913	+	0.371194i
$663$	34.9077	+	68.5103i	0.0526512	+	0.103334i
$664$	302.125	−	98.1663i	0.455007	−	0.147841i
$665$	498.720	−	181.786i	0.749955	−	0.273362i
$666$	−325.027	+	236.146i	−0.488029	+	0.354574i
$667$	−177.086	+	347.551i	−0.265497	+	0.521067i
$668$	10.5879	+	20.7799i	0.0158501	+	0.0311076i
$669$	−27.7882	+	38.2472i	−0.0415369	+	0.0571706i
$670$	224.098	−	124.358i	0.334475	−	0.185609i
$671$	5.34618	−	137.436i	0.00796748	−	0.204823i
$672$	11.3219	+	11.3219i	0.0168481	+	0.0168481i
$673$	−748.711	+	118.584i	−1.11250	+	0.176202i	−0.685516	−	0.728058i	$-0.740423\pi$
$673$	−748.711	+	118.584i	−1.11250	+	0.176202i	−0.426982	+	0.904260i	$0.640423\pi$
$674$	−735.886	−	239.104i	−1.09182	−	0.354753i
$675$	−96.5311	−	160.312i	−0.143009	−	0.237499i
$676$	−582.888	+	423.493i	−0.862260	+	0.626469i
$677$	570.104	+	90.2956i	0.842104	+	0.133376i	0.562560	−	0.826757i	$-0.309817\pi$
$677$	570.104	+	90.2956i	0.842104	+	0.133376i	0.279544	+	0.960133i	$0.409817\pi$
$678$	−36.2157	−	18.4528i	−0.0534155	−	0.0272166i
$679$	490.047	+	159.226i	0.721719	+	0.234501i
$680$	−13.6638	+	111.719i	−0.0200939	+	0.164293i
$681$	13.0097			0.0191038
$682$	−337.572	−	731.500i	−0.494974	−	1.07258i
$683$	−126.987	+	126.987i	−0.185925	+	0.185925i	−0.793932	−	0.608007i	$-0.791969\pi$
$683$	−126.987	+	126.987i	−0.185925	+	0.185925i	0.608007	+	0.793932i	$0.291969\pi$
$684$	−163.389	+	224.885i	−0.238872	+	0.328779i
$685$	402.836	+	271.440i	0.588082	+	0.396263i
$686$	−154.854	−	476.592i	−0.225735	−	0.694740i
$687$	21.2044	+	3.35844i	0.0308651	+	0.00488856i
$688$	−19.9808	+	126.154i	−0.0290419	+	0.183363i
$689$	1111.46	−	361.135i	1.61315	−	0.524144i
$690$	−14.7237	+	21.8511i	−0.0213387	+	0.0316682i
$691$	−106.033	−	77.0373i	−0.153448	−	0.111487i	0.508412	−	0.861114i	$-0.330233\pi$
$691$	−106.033	−	77.0373i	−0.153448	−	0.111487i	−0.661860	+	0.749627i	$0.730233\pi$
$692$	191.041	+	191.041i	0.276070	+	0.276070i
$693$	−641.649	−	127.372i	−0.925900	−	0.183797i
$694$			376.101i			0.541932i
$695$	465.656	+	56.9523i	0.670009	+	0.0819457i
$696$	−16.1366	+	49.6632i	−0.0231847	+	0.0713552i
$697$	−195.268	+	383.234i	−0.280154	+	0.549834i
$698$	−12.4479	+	78.5932i	−0.0178337	+	0.112598i
$699$	−82.4249	−	113.448i	−0.117918	−	0.162301i
$700$	−288.695	+	173.836i	−0.412421	+	0.248338i
$701$	−79.5037	+	244.687i	−0.113415	+	0.349055i	−0.991613	−	0.129242i	$-0.958746\pi$
$701$	−79.5037	+	244.687i	−0.113415	+	0.349055i	0.878198	+	0.478297i	$0.158746\pi$
$702$	−38.0962	−	240.530i	−0.0542681	−	0.342636i
$703$	358.600	−	358.600i	0.510100	−	0.510100i
$704$	23.9198	+	84.6867i	0.0339770	+	0.120294i
$705$	93.0356	+	167.654i	0.131965	+	0.237807i
$706$	−178.505	−	129.691i	−0.252839	−	0.183699i
$707$	−653.032	+	332.736i	−0.923666	+	0.470631i
$708$	−17.7850	−	9.06193i	−0.0251201	−	0.0127993i
$709$	733.781	+	1009.96i	1.03495	+	1.42449i	0.901163	+	0.433479i	$0.142714\pi$
$709$	733.781	+	1009.96i	1.03495	+	1.42449i	0.133789	+	0.991010i	$0.457286\pi$
$710$	−274.183	−	752.206i	−0.386173	−	1.05944i
$711$	−79.0821	−	243.390i	−0.111227	−	0.342320i
$712$	−206.814	+	105.377i	−0.290470	+	0.148002i
$713$	453.854	−	71.8833i	0.636541	−	0.100818i
$714$			31.8575i			0.0446183i
$715$	−1026.24	+	740.132i	−1.43530	+	1.03515i
$716$	183.324			0.256039
$717$	22.8003	+	143.955i	0.0317995	+	0.200774i
$718$	146.812	+	288.135i	0.204473	+	0.401302i
$719$	−1051.85	+	341.767i	−1.46294	+	0.475337i	−0.928965	−	0.370166i	$-0.879301\pi$
$719$	−1051.85	+	341.767i	−1.46294	+	0.475337i	−0.533971	+	0.845503i	$0.679301\pi$
$720$	74.5051	−	159.974i	0.103479	−	0.222186i
$721$	362.711	−	263.525i	0.503067	−	0.365499i
$722$	−72.4772	+	142.245i	−0.100384	+	0.197015i
$723$	−88.0965	−	172.899i	−0.121848	−	0.239141i
$724$	99.5434	−	137.010i	0.137491	−	0.189240i
$725$	−932.587	−	581.522i	−1.28633	−	0.802099i
$726$	54.6821	+	46.6292i	0.0753197	+	0.0642275i
$727$	927.010	+	927.010i	1.27512	+	1.27512i	0.943368	+	0.331750i	$0.107639\pi$
$727$	927.010	+	927.010i	1.27512	+	1.27512i	0.331750	+	0.943368i	$0.392361\pi$
$728$	−433.155	+	68.6049i	−0.594992	+	0.0942376i
$729$	−613.126	−	199.217i	−0.841051	−	0.273274i
$730$	−114.028	+	122.396i	−0.156202	+	0.167665i
$731$	−205.596	+	149.374i	−0.281253	+	0.204342i
$732$	10.3728	+	1.64290i	0.0141705	+	0.00224439i
$733$	721.882	+	367.817i	0.984832	+	0.501797i	0.870777	−	0.491678i	$-0.163616\pi$
$733$	721.882	+	367.817i	0.984832	+	0.501797i	0.114054	+	0.993475i	$0.463616\pi$
$734$	−823.727	−	267.645i	−1.12224	−	0.364639i
$735$	5.91248	−	4.62383i	0.00804419	−	0.00629093i
$736$	−50.1926			−0.0681965
$737$	395.912	−	47.0160i	0.537195	−	0.0637937i
$738$	476.864	−	476.864i	0.646157	−	0.646157i
$739$	404.914	−	557.317i	0.547922	−	0.754150i	−0.441806	−	0.897110i	$-0.645662\pi$
$739$	404.914	−	557.317i	0.547922	−	0.754150i	0.989728	+	0.142960i	$0.0456621\pi$
$740$	−179.911	+	267.001i	−0.243123	+	0.360812i
$741$	47.0269	+	144.734i	0.0634641	+	0.195322i
$742$	478.238	+	75.7455i	0.644526	+	0.102083i
$743$	71.7204	−	452.825i	0.0965281	−	0.609454i	−0.891241	−	0.453530i	$-0.850164\pi$
$743$	71.7204	−	452.825i	0.0965281	−	0.609454i	0.987769	−	0.155924i	$-0.0498355\pi$
$744$	58.5049	−	19.0094i	0.0786356	−	0.0255503i
$745$	28.5343	+	146.427i	0.0383011	+	0.196547i
$746$	249.079	+	180.966i	0.333886	+	0.242582i
$747$	−700.757	−	700.757i	−0.938095	−	0.938095i
$748$	−85.4926	+	152.798i	−0.114295	+	0.204275i
$749$		−	182.062i		−	0.243073i
$750$	−57.7611	−	46.6387i	−0.0770147	−	0.0621849i
$751$	−318.680	+	980.796i	−0.424341	+	1.30599i	0.479283	+	0.877660i	$0.340897\pi$
$751$	−318.680	+	980.796i	−0.424341	+	1.30599i	−0.903624	+	0.428327i	$0.859103\pi$
$752$	−165.819	+	325.439i	−0.220504	+	0.432764i
$753$	−8.68538	+	54.8373i	−0.0115344	+	0.0728251i
$754$	−840.688	−	1157.11i	−1.11497	−	1.53463i
$755$	254.455	−	273.128i	0.337027	−	0.361759i
$756$	31.1795	−	95.9605i	0.0412427	−	0.126932i
$757$	157.537	+	994.652i	0.208108	+	1.31394i	0.841562	+	0.540160i	$0.181636\pi$
$757$	157.537	+	994.652i	0.208108	+	1.31394i	−0.633455	+	0.773780i	$0.718364\pi$
$758$	12.4241	−	12.4241i	0.0163906	−	0.0163906i
$759$	−34.0723	+	22.7856i	−0.0448910	+	0.0300206i
$760$	−61.3004	+	214.161i	−0.0806584	+	0.281791i
$761$	−287.933	−	209.196i	−0.378362	−	0.274896i	0.382308	−	0.924035i	$-0.375129\pi$
$761$	−287.933	−	209.196i	−0.378362	−	0.274896i	−0.760670	+	0.649139i	$0.775129\pi$
$762$	36.5826	−	18.6398i	0.0480087	−	0.0244616i
$763$	538.271	+	274.263i	0.705466	+	0.359453i
$764$	342.741	+	471.743i	0.448614	+	0.617464i
$765$	329.887	−	120.245i	0.431225	−	0.157183i
$766$	210.666	+	648.362i	0.275021	+	0.846426i
$767$	487.128	−	248.204i	0.635108	−	0.323604i
$768$	−6.63667	+	1.05115i	−0.00864150	+	0.00136868i
$769$		−	700.981i		−	0.911549i	−0.890095	−	0.455774i	$-0.849362\pi$
$769$		−	700.981i		−	0.911549i	0.890095	−	0.455774i	$-0.150638\pi$
$770$	−518.066	+	80.1954i	−0.672814	+	0.104150i
$771$	21.1911			0.0274852
$772$	23.0139	+	145.304i	0.0298108	+	0.188218i
$773$	−100.410	−	197.065i	−0.129896	−	0.254936i	0.816893	−	0.576789i	$-0.195694\pi$
$773$	−100.410	−	197.065i	−0.129896	−	0.254936i	−0.946790	+	0.321853i	$0.895694\pi$
$774$	378.956	−	123.130i	0.489607	−	0.159083i
$775$	91.5333	+	1291.47i	0.118107	+	1.66641i
$776$	−174.938	+	127.100i	−0.225436	+	0.163789i
$777$	−41.3720	+	81.1972i	−0.0532459	+	0.104501i
$778$	172.020	+	337.608i	0.221105	+	0.433944i
$779$	−500.370	+	688.700i	−0.642324	+	0.884083i
$780$	−46.8791	−	84.4781i	−0.0601014	−	0.108305i
$781$	48.4113	−	1244.53i	0.0619863	−	1.59351i
$782$	−70.6157	−	70.6157i	−0.0903014	−	0.0903014i
$783$	325.012	−	51.4769i	0.415086	−	0.0657431i
$784$	13.5983	+	4.41835i	0.0173447	+	0.00563565i
$785$	−717.554	+	25.3967i	−0.914082	+	0.0323524i
$786$	6.41230	−	4.65881i	0.00815814	−	0.00592724i
$787$	1138.17	+	180.269i	1.44622	+	0.229058i	0.829667	−	0.558258i	$-0.188530\pi$
$787$	1138.17	+	180.269i	1.44622	+	0.229058i	0.616549	+	0.787317i	$0.288530\pi$
$788$	78.7599	+	40.1302i	0.0999491	+	0.0509266i
$789$	135.640	+	44.0722i	0.171914	+	0.0558583i
$790$	−126.339	−	161.549i	−0.159923	−	0.204493i
$791$	461.255			0.583128
$792$	201.519	−	186.428i	0.254443	−	0.235389i
$793$	−203.400	+	203.400i	−0.256494	+	0.256494i
$794$	387.122	−	532.828i	0.487559	−	0.671068i
$795$	20.4029	+	104.700i	0.0256640	+	0.131698i
$796$	−12.7232	−	39.1579i	−0.0159839	−	0.0491933i
$797$	−1054.14	−	166.959i	−1.32263	−	0.209484i	−0.545122	−	0.838357i	$-0.683517\pi$
$797$	−1054.14	−	166.959i	−1.32263	−	0.209484i	−0.777508	+	0.628873i	$0.783517\pi$
$798$	−9.86355	+	62.2760i	−0.0123603	+	0.0780401i
$799$	−691.148	+	224.568i	−0.865016	+	0.281061i
$800$	12.1927	−	140.895i	0.0152409	−	0.176118i
$801$	585.814	+	425.619i	0.731354	+	0.531359i
$802$	168.931	+	168.931i	0.210637	+	0.210637i
$803$	−236.282	+	109.039i	−0.294249	+	0.135790i
$804$			30.4430i			0.0378644i
$805$	36.3000	−	296.798i	0.0450932	−	0.368693i
$806$	−520.662	+	1602.43i	−0.645983	+	1.98813i
$807$	−50.9087	+	99.9140i	−0.0630839	+	0.123809i
$808$	48.1151	−	303.787i	0.0595484	−	0.375974i
$809$	−36.5225	−	50.2689i	−0.0451452	−	0.0621370i	0.785848	−	0.618420i	$-0.212227\pi$
$809$	−36.5225	−	50.2689i	−0.0451452	−	0.0621370i	−0.830993	+	0.556283i	$0.812227\pi$
$810$	−538.967	+	19.0759i	−0.665391	+	0.0235504i
$811$	−89.6326	+	275.861i	−0.110521	+	0.340149i	−0.990987	−	0.133961i	$-0.957230\pi$
$811$	−89.6326	+	275.861i	−0.110521	+	0.340149i	0.880465	+	0.474110i	$0.157230\pi$
$812$	−92.7012	−	585.292i	−0.114164	−	0.720803i
$813$	94.9397	−	94.9397i	0.116777	−	0.116777i
$814$	−416.333	+	278.420i	−0.511466	+	0.342039i
$815$	395.468	+	113.197i	0.485237	+	0.138892i
$816$	−10.8159	−	7.85824i	−0.0132548	−	0.00963020i
$817$	−448.154	+	228.346i	−0.548536	+	0.279493i
$818$	193.484	+	98.5850i	0.236533	+	0.120520i
$819$	804.163	+	1106.84i	0.981884	+	1.35145i
$820$	228.168	−	489.912i	0.278254	−	0.597454i
$821$	42.2462	+	130.020i	0.0514570	+	0.158368i	0.973483	−	0.228760i	$-0.0734671\pi$
$821$	42.2462	+	130.020i	0.0514570	+	0.158368i	−0.922026	+	0.387128i	$0.873467\pi$
$822$	−51.4106	+	26.1950i	−0.0625433	+	0.0318674i
$823$	−681.893	+	108.001i	−0.828546	+	0.131229i	−0.556282	−	0.830994i	$-0.687772\pi$
$823$	−681.893	+	108.001i	−0.828546	+	0.131229i	−0.272264	+	0.962223i	$0.587772\pi$
$824$			188.147i			0.228334i
$825$	−55.6843	−	101.179i	−0.0674961	−	0.122641i
$826$	226.516			0.274232
$827$	−69.6609	−	439.821i	−0.0842332	−	0.531827i	−0.993336	−	0.115255i	$-0.963231\pi$
$827$	−69.6609	−	439.821i	−0.0842332	−	0.531827i	0.909103	−	0.416572i	$-0.136769\pi$
$828$	71.0868	+	139.516i	0.0858537	+	0.168497i
$829$	1026.54	−	333.543i	1.23829	−	0.402344i	0.384577	−	0.923093i	$-0.374347\pi$
$829$	1026.54	−	333.543i	1.23829	−	0.402344i	0.853710	+	0.520749i	$0.174347\pi$
$830$	−719.932	−	335.296i	−0.867388	−	0.403971i
$831$	170.150	−	123.621i	0.204753	−	0.148762i
$832$	83.5536	−	163.983i	0.100425	−	0.197095i
$833$	12.9152	+	25.3475i	0.0155044	+	0.0304291i
$834$	−32.7539	+	45.0819i	−0.0392733	+	0.0540551i
$835$	16.0444	−	56.0535i	0.0192149	−	0.0671299i
$836$	−214.432	+	272.224i	−0.256498	+	0.325627i
$837$	−274.108	−	274.108i	−0.327489	−	0.327489i
$838$	−865.935	+	137.151i	−1.03334	+	0.163664i
$839$	753.087	+	244.693i	0.897601	+	0.291648i	0.721246	−	0.692679i	$-0.243570\pi$
$839$	753.087	+	244.693i	0.897601	+	0.291648i	0.176354	+	0.984327i	$0.443570\pi$
$840$	−1.41588	−	40.0040i	−0.00168557	−	0.0476238i
$841$	883.139	−	641.638i	1.05011	−	0.762946i
$842$	70.7835	+	11.2110i	0.0840660	+	0.0133147i
$843$	144.811	+	73.7849i	0.171780	+	0.0875265i
$844$	208.364	+	67.7015i	0.246877	+	0.0802151i
$845$	1787.90	+	218.670i	2.11586	+	0.258781i
$846$	1139.44			1.34685
$847$	−793.136	−	189.761i	−0.936407	−	0.224039i
$848$	−143.683	+	143.683i	−0.169437	+	0.169437i
$849$	39.5946	−	54.4972i	0.0466367	−	0.0641899i
$850$	215.378	−	181.070i	0.253386	−	0.213024i
$851$	−88.2770	−	271.689i	−0.103733	−	0.319258i
$852$	93.9292	+	14.8769i	0.110246	+	0.0174612i
$853$	−104.470	+	659.600i	−0.122474	+	0.773271i	0.847631	+	0.530586i	$0.178028\pi$
$853$	−104.470	+	659.600i	−0.122474	+	0.773271i	−0.970105	+	0.242685i	$0.921972\pi$
$854$	−113.347	+	36.8285i	−0.132724	+	0.0431248i
$855$	682.103	−	132.921i	0.797781	−	0.155464i
$856$	61.8119	+	44.9089i	0.0722101	+	0.0524637i
$857$	−280.645	−	280.645i	−0.327474	−	0.327474i	0.524151	−	0.851625i	$-0.324383\pi$
$857$	−280.645	−	280.645i	−0.327474	−	0.327474i	−0.851625	+	0.524151i	$0.824383\pi$
$858$	−17.7236	−	149.247i	−0.0206569	−	0.173947i
$859$		−	1076.34i		−	1.25302i	−0.779413	−	0.626510i	$-0.784483\pi$
$859$		−	1076.34i		−	1.25302i	0.779413	−	0.626510i	$-0.215517\pi$
$860$	251.531	−	196.709i	0.292478	−	0.228732i
$861$	47.2704	−	145.483i	0.0549018	−	0.168970i
$862$	519.096	−	1018.78i	0.602200	−	1.18188i
$863$	173.277	−	1094.03i	0.200784	−	1.26770i	−0.657078	−	0.753823i	$-0.728208\pi$
$863$	173.277	−	1094.03i	0.200784	−	1.26770i	0.857862	−	0.513880i	$-0.171792\pi$
$864$	24.8886	+	34.2562i	0.0288062	+	0.0396484i
$865$	−23.8908	−	675.008i	−0.0276194	−	0.780356i
$866$	238.020	−	732.551i	0.274850	−	0.845902i
$867$	14.8251	+	93.6022i	0.0170994	+	0.107961i
$868$	−493.623	+	493.623i	−0.568690	+	0.568690i
$869$	−86.7194	−	307.025i	−0.0997922	−	0.353309i
$870$	114.149	−	63.3445i	0.131206	−	0.0728098i
$871$	−674.580	−	490.111i	−0.774489	−	0.562699i
$872$	−225.889	+	115.096i	−0.259047	+	0.131991i
$873$	601.049	+	306.250i	0.688487	+	0.350802i
$874$	−116.178	−	159.905i	−0.132927	−	0.182958i
$875$	824.317	+	173.994i	0.942077	+	0.198851i
$876$	−6.14023	−	18.8977i	−0.00700939	−	0.0215727i
$877$	758.112	−	386.277i	0.864437	−	0.440453i	0.0352204	−	0.999380i	$-0.488787\pi$
$877$	758.112	−	386.277i	0.864437	−	0.440453i	0.829217	+	0.558927i	$0.188787\pi$
$878$	−260.405	+	41.2441i	−0.296589	+	0.0469751i
$879$		−	125.561i		−	0.142845i
$880$	100.564	−	195.671i	0.114277	−	0.222353i
$881$	253.994			0.288302			0.144151	−	0.989556i	$-0.453955\pi$
$881$	253.994			0.288302			0.144151	+	0.989556i	$0.453955\pi$
$882$	−6.97770	−	44.0555i	−0.00791123	−	0.0499495i
$883$	−668.926	−	1312.84i	−0.757561	−	1.48680i	−0.869954	−	0.493133i	$-0.835852\pi$
$883$	−668.926	−	1312.84i	−0.757561	−	1.48680i	0.112393	−	0.993664i	$-0.464148\pi$
$884$	348.258	−	113.156i	0.393957	−	0.128004i
$885$	17.0895	+	46.8841i	0.0193101	+	0.0529763i
$886$	319.913	−	232.430i	0.361075	−	0.262337i
$887$	−9.28532	+	18.2235i	−0.0104682	+	0.0205450i	−0.896181	−	0.443688i	$-0.853670\pi$
$887$	−9.28532	+	18.2235i	−0.0104682	+	0.0205450i	0.885713	+	0.464233i	$0.153670\pi$
$888$	−17.3621	−	34.0750i	−0.0195519	−	0.0383728i
$889$	−273.865	+	376.943i	−0.308060	+	0.424008i
$890$	557.879	+	159.684i	0.626831	+	0.179421i
$891$	−787.219	−	290.071i	−0.883523	−	0.325557i
$892$	159.201	+	159.201i	0.178477	+	0.178477i
$893$	−1420.61	+	225.002i	−1.59082	+	0.251962i
$894$	−16.8530	−	5.47587i	−0.0188512	−	0.00612513i
$895$	−335.334	−	312.409i	−0.374675	−	0.349060i
$896$	61.6897	−	44.8202i	0.0688501	−	0.0500225i
$897$	84.6688	+	13.4102i	0.0943911	+	0.0149501i
$898$	−71.5465	−	36.4548i	−0.0796732	−	0.0405955i
$899$	−2165.26	−	703.536i	−2.40852	−	0.782576i
$900$	−408.900	+	165.656i	−0.454334	+	0.184062i
$901$	−404.293			−0.448715
$902$	617.142	−	570.927i	0.684193	−	0.632956i
$903$	63.9095	−	63.9095i	0.0707746	−	0.0707746i
$904$	−113.777	+	156.601i	−0.125860	+	0.173231i
$905$	−415.566	+	80.9815i	−0.459189	+	0.0894823i
$906$	13.7020	+	42.1706i	0.0151237	+	0.0465459i
$907$	−190.677	−	30.2002i	−0.210228	−	0.0332968i	0.0504321	−	0.998727i	$-0.483940\pi$
$907$	−190.677	−	30.2002i	−0.210228	−	0.0332968i	−0.260660	+	0.965431i	$0.583940\pi$
$908$	9.69214	−	61.1937i	0.0106742	−	0.0673940i
$909$	−912.552	+	296.506i	−1.00391	+	0.326189i
$910$	909.233	+	612.661i	0.999158	+	0.673254i
$911$	454.231	+	330.018i	0.498607	+	0.362259i	0.808485	−	0.588517i	$-0.200288\pi$
$911$	454.231	+	330.018i	0.498607	+	0.362259i	−0.309878	+	0.950776i	$0.600288\pi$
$912$	−18.7103	−	18.7103i	−0.0205157	−	0.0205157i
$913$	−838.984	−	906.897i	−0.918931	−	0.993316i
$914$			654.813i			0.716425i
$915$	−16.1742	−	20.6819i	−0.0176767	−	0.0226031i
$916$	31.5942	−	97.2369i	0.0344915	−	0.106154i
$917$	−40.8345	+	80.1423i	−0.0445306	+	0.0873961i
$918$	−13.1792	+	83.2104i	−0.0143565	+	0.0906432i
$919$	674.093	+	927.809i	0.733507	+	1.00959i	0.998966	+	0.0454632i	$0.0144764\pi$
$919$	674.093	+	927.809i	0.733507	+	1.00959i	−0.265459	+	0.964122i	$0.585524\pi$
$920$	91.8118	+	85.5349i	0.0997955	+	0.0929727i
$921$	−44.8915	+	138.162i	−0.0487422	+	0.150013i
$922$	−87.9145	−	555.070i	−0.0953519	−	0.602028i
$923$	−1841.85	+	1841.85i	−1.99550	+	1.99550i
$924$	21.5301	−	58.4301i	0.0233010	−	0.0632360i
$925$	784.096	−	181.803i	0.847671	−	0.196543i
$926$	−655.481	−	476.235i	−0.707863	−	0.514293i
$927$	522.976	−	266.470i	0.564160	−	0.287454i
$928$	221.579	+	112.900i	0.238771	+	0.121660i
$929$	−386.474	−	531.936i	−0.416011	−	0.572590i	0.548661	−	0.836045i	$-0.315138\pi$
$929$	−386.474	−	531.936i	−0.416011	−	0.572590i	−0.964672	+	0.263455i	$0.915138\pi$
$930$	−139.411	−	64.9284i	−0.149904	−	0.0698154i
$931$	17.3991	+	53.5488i	0.0186886	+	0.0575175i
$932$	−595.032	+	303.184i	−0.638447	+	0.325305i
$933$	−45.5363	+	7.21224i	−0.0488063	+	0.00773016i
$934$			49.9939i			0.0535267i
$935$	416.770	−	133.805i	0.445743	−	0.143107i
$936$	−574.144			−0.613401
$937$	−101.418	−	640.329i	−0.108237	−	0.683382i	−0.980820	−	0.194916i	$-0.937557\pi$
$937$	−101.418	−	640.329i	−0.108237	−	0.683382i	0.872583	−	0.488466i	$-0.162443\pi$
$938$	−156.841	−	307.817i	−0.167208	−	0.328163i
$939$	−175.753	+	57.1055i	−0.187170	+	0.0608153i
$940$	857.905	−	312.711i	0.912665	−	0.332671i
$941$	−126.100	+	91.6170i	−0.134006	+	0.0973613i	−0.652769	−	0.757557i	$-0.726393\pi$
$941$	−126.100	+	91.6170i	−0.134006	+	0.0973613i	0.518763	+	0.854918i	$0.326393\pi$
$942$	38.7194	−	75.9911i	0.0411034	−	0.0806700i
$943$	217.700	+	427.261i	0.230859	+	0.453087i
$944$	−55.8743	+	76.9044i	−0.0591889	+	0.0814666i
$945$	−220.563	+	122.396i	−0.233400	+	0.129520i
$946$	478.036	−	135.022i	0.505324	−	0.142729i
$947$	−570.332	−	570.332i	−0.602252	−	0.602252i	0.338658	−	0.940910i	$-0.390027\pi$
$947$	−570.332	−	570.332i	−0.602252	−	0.602252i	−0.940910	+	0.338658i	$0.890027\pi$
$948$	24.0607	−	3.81085i	0.0253805	−	0.00401988i
$949$	517.603	+	168.179i	0.545419	+	0.177217i
$950$	477.089	−	287.278i	0.502199	−	0.302397i
$951$	−57.5869	+	41.8393i	−0.0605540	+	0.0439951i
$952$	149.848	+	23.7336i	0.157403	+	0.0249302i
$953$	319.573	+	162.831i	0.335334	+	0.170861i	0.613547	−	0.789658i	$-0.289742\pi$
$953$	319.573	+	162.831i	0.335334	+	0.170861i	−0.278213	+	0.960519i	$0.589742\pi$
$954$	602.876	+	195.886i	0.631946	+	0.205332i
$955$	176.974	−	1446.98i	0.185313	−	1.51517i
$956$	694.108			0.726055
$957$	201.667	−	23.9487i	0.210728	−	0.0250247i
$958$	−68.1475	+	68.1475i	−0.0711351	+	0.0711351i
$959$	384.870	−	529.729i	0.401325	−	0.552376i
$960$	13.9310	+	9.38702i	0.0145115	+	0.00977815i
$961$	531.823	+	1636.78i	0.553406	+	1.70321i
$962$	1034.58	+	163.861i	1.07544	+	0.170334i
$963$	37.2863	−	235.416i	0.0387189	−	0.244461i
$964$	−878.896	+	285.571i	−0.911718	+	0.296235i
$965$	205.521	−	305.008i	0.212975	−	0.316070i
$966$	28.7341	+	20.8766i	0.0297455	+	0.0216113i
$967$	−1141.88	−	1141.88i	−1.18085	−	1.18085i	−0.979525	−	0.201322i	$-0.935476\pi$
$967$	−1141.88	−	1141.88i	−1.18085	−	1.18085i	−0.201322	−	0.979525i	$-0.564524\pi$
$968$	260.068	−	222.470i	0.268665	−	0.229824i
$969$		−	52.6468i		−	0.0543311i
$970$	536.590	+	65.6279i	0.553186	+	0.0676576i
$971$	−398.592	+	1226.74i	−0.410497	+	1.26338i	0.505721	+	0.862697i	$0.331227\pi$
$971$	−398.592	+	1226.74i	−0.410497	+	1.26338i	−0.916217	+	0.400682i	$0.868773\pi$
$972$	90.2510	−	177.128i	0.0928508	−	0.182230i
$973$	98.9240	−	624.582i	0.101669	−	0.641913i
$974$	199.608	+	274.737i	0.204936	+	0.282071i
$975$	−58.2111	+	234.415i	−0.0597037	+	0.240425i
$976$	15.4554	−	47.5668i	0.0158354	−	0.0487364i
$977$	84.9821	+	536.556i	0.0869827	+	0.549187i	0.992241	+	0.124326i	$0.0396770\pi$
$977$	84.9821	+	536.556i	0.0869827	+	0.549187i	−0.905259	+	0.424861i	$0.860323\pi$
$978$	−34.5503	+	34.5503i	−0.0353275	+	0.0353275i
$979$	709.130	+	558.585i	0.724342	+	0.570567i
$980$	−17.3444	−	31.2553i	−0.0176983	−	0.0318931i
$981$	639.845	+	464.875i	0.652238	+	0.473879i
$982$	−544.784	+	277.581i	−0.554770	+	0.282669i
$983$	−1590.09	−	810.191i	−1.61759	−	0.824203i	−0.999267	−	0.0382772i	$-0.987813\pi$
$983$	−1590.09	−	810.191i	−1.61759	−	0.824203i	−0.618321	−	0.785925i	$-0.712187\pi$
$984$	37.7330	+	51.9350i	0.0383465	+	0.0527794i
$985$	−75.6796	−	207.623i	−0.0768320	−	0.210785i
$986$	152.900	+	470.577i	0.155071	+	0.477259i
$987$	230.287	−	117.337i	0.233320	−	0.118882i
$988$	715.820	−	113.375i	0.724514	−	0.114752i
$989$			283.325i			0.286477i
$990$	−686.313	−	2.40287i	−0.693246	−	0.00242714i
$991$	946.609			0.955206			0.477603	−	0.878576i	$-0.341506\pi$
$991$	946.609			0.955206			0.477603	+	0.878576i	$0.341506\pi$
$992$	−45.8288	−	289.351i	−0.0461984	−	0.291685i
$993$	33.5414	+	65.8286i	0.0337778	+	0.0662927i
$994$	−1026.39	+	333.494i	−1.03258	+	0.335507i
$995$	−43.4572	+	93.3091i	−0.0436755	+	0.0937780i
$996$	76.3191	−	55.4491i	0.0766256	−	0.0556718i
$997$	−167.869	+	329.460i	−0.168374	+	0.330452i	−0.959740	−	0.280891i	$-0.909370\pi$
$997$	−167.869	+	329.460i	−0.168374	+	0.330452i	0.791366	+	0.611342i	$0.209370\pi$
$998$	−104.120	−	204.347i	−0.104329	−	0.204757i
$999$	−141.653	+	194.968i	−0.141795	+	0.195164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.3.l.a.37.3	yes	48
5.3	odd	4	inner	110.3.l.a.103.4	yes	48
11.3	even	5	inner	110.3.l.a.47.4	yes	48
55.3	odd	20	inner	110.3.l.a.3.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.3.l.a.3.3	✓	48	55.3	odd	20	inner
110.3.l.a.37.3	yes	48	1.1	even	1	trivial
110.3.l.a.47.4	yes	48	11.3	even	5	inner
110.3.l.a.103.4	yes	48	5.3	odd	4	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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	110.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.221232 - 1.39680i) q^{2} +(-0.190659 - 0.374189i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(4.53254 + 2.11095i) q^{5} +(-0.480488 + 0.349095i) q^{6} +(3.05982 - 6.00524i) q^{7} +(1.28408 + 2.52015i) q^{8} +(5.18640 - 7.13847i) q^{9} +(1.94584 - 6.79807i) q^{10} +(6.80666 - 8.64114i) q^{11} +(0.593916 + 0.593916i) q^{12} +(-22.7221 + 3.59882i) q^{13} +(-9.06507 - 2.94542i) q^{14} +(-0.0742729 - 2.09850i) q^{15} +(3.23607 - 2.35114i) q^{16} +(7.86061 + 1.24500i) q^{17} +(-11.1184 - 5.66512i) q^{18} +(14.9807 + 4.86752i) q^{19} +(-9.92604 - 1.21401i) q^{20} -2.83048 q^{21} +(-13.5758 - 7.59587i) q^{22} +(6.27408 - 6.27408i) q^{23} +(0.698191 - 0.960977i) q^{24} +(16.0878 + 19.1359i) q^{25} +(10.0537 + 30.9421i) q^{26} +(-7.39310 - 1.17095i) q^{27} +(-2.10869 + 13.3137i) q^{28} +(-41.8099 + 13.5849i) q^{29} +(-2.91475 + 0.567999i) q^{30} +(41.8975 + 30.4403i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-4.53117 - 0.899468i) q^{33} -11.2552i q^{34} +(26.5455 - 20.7598i) q^{35} +(-5.45330 + 16.7835i) q^{36} +(14.6166 - 28.6867i) q^{37} +(3.48476 - 22.0019i) q^{38} +(5.67881 + 7.81621i) q^{39} +(0.500225 + 14.1333i) q^{40} +(-16.7005 + 51.3988i) q^{41} +(0.626192 + 3.95362i) q^{42} +(-22.5790 + 22.5790i) q^{43} +(-7.60652 + 20.6432i) q^{44} +(38.5765 - 21.4071i) q^{45} +(-10.1517 - 7.37562i) q^{46} +(-81.3597 + 41.4548i) q^{47} +(-1.49676 - 0.762635i) q^{48} +(2.10105 + 2.89185i) q^{49} +(23.1700 - 26.7049i) q^{50} +(-1.03283 - 3.17872i) q^{51} +(40.9958 - 20.8884i) q^{52} +(-50.1741 + 7.94679i) q^{53} +10.5857i q^{54} +(49.0925 - 24.7978i) q^{55} +19.0632 q^{56} +(-1.03483 - 6.53365i) q^{57} +(28.2251 + 55.3948i) q^{58} +(-22.6016 + 7.34372i) q^{59} +(1.43822 + 3.94568i) q^{60} +(10.1157 - 7.34947i) q^{61} +(33.2501 - 65.2569i) q^{62} +(-26.9988 - 52.9881i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(-110.586 - 31.6534i) q^{65} +(-0.253940 + 6.52814i) q^{66} +(25.6290 + 25.6290i) q^{67} +(-15.7212 + 2.49000i) q^{68} +(-3.54390 - 1.15148i) q^{69} +(-34.8701 - 32.4861i) q^{70} +(91.6006 - 66.5517i) q^{71} +(24.6497 + 3.90413i) q^{72} +(-21.0787 - 10.7401i) q^{73} +(-43.3033 - 14.0701i) q^{74} +(4.09318 - 9.66830i) q^{75} -31.5033 q^{76} +(-31.0650 - 67.3160i) q^{77} +(9.66136 - 9.66136i) q^{78} +(17.0478 - 23.4642i) q^{79} +(19.6307 - 3.82545i) q^{80} +(-23.5685 - 72.5363i) q^{81} +(75.4887 + 11.9562i) q^{82} +(17.5698 - 110.932i) q^{83} +(5.38389 - 1.74933i) q^{84} +(33.0004 + 22.2364i) q^{85} +(36.5336 + 26.5432i) q^{86} +(13.0547 + 13.0547i) q^{87} +(30.5172 + 6.05788i) q^{88} +82.0644i q^{89} +(-38.4359 - 49.1478i) q^{90} +(-47.9138 + 147.463i) q^{91} +(-8.05641 + 15.8116i) q^{92} +(3.40231 - 21.4813i) q^{93} +(75.9035 + 104.472i) q^{94} +(57.6254 + 53.6858i) q^{95} +(-0.734121 + 2.25939i) q^{96} +(11.9595 + 75.5095i) q^{97} +(3.57452 - 3.57452i) q^{98} +(-26.3824 - 93.4056i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{2} + 2 q^{3} + 4 q^{5} + 4 q^{6} + 38 q^{7} + 24 q^{8} + 36 q^{10} + 80 q^{11} - 16 q^{12} - 16 q^{13} + 38 q^{15} + 48 q^{16} - 18 q^{17} - 44 q^{18} + 4 q^{20} + 24 q^{21} + 64 q^{23} + 70 q^{25}+ \cdots - 440 q^{98}+O(q^{100}) \) 48 * q - 12 * q^2 + 2 * q^3 + 4 * q^5 + 4 * q^6 + 38 * q^7 + 24 * q^8 + 36 * q^10 + 80 * q^11 - 16 * q^12 - 16 * q^13 + 38 * q^15 + 48 * q^16 - 18 * q^17 - 44 * q^18 + 4 * q^20 + 24 * q^21 + 64 * q^23 + 70 * q^25 + 8 * q^26 - 82 * q^27 + 64 * q^28 - 14 * q^30 - 116 * q^31 - 192 * q^32 - 312 * q^33 - 288 * q^35 - 88 * q^36 + 22 * q^37 - 72 * q^38 - 24 * q^40 - 196 * q^41 - 96 * q^42 - 484 * q^43 - 56 * q^45 - 132 * q^46 - 310 * q^47 - 8 * q^48 - 128 * q^50 + 256 * q^51 + 8 * q^52 - 82 * q^53 - 264 * q^55 + 48 * q^56 + 744 * q^57 + 168 * q^58 + 196 * q^60 + 528 * q^61 + 144 * q^62 + 814 * q^63 + 840 * q^65 + 436 * q^66 + 192 * q^67 + 36 * q^68 + 230 * q^70 - 292 * q^71 - 48 * q^72 - 108 * q^73 + 258 * q^75 + 96 * q^76 - 200 * q^77 + 88 * q^78 + 24 * q^80 + 628 * q^81 + 24 * q^82 + 360 * q^83 - 368 * q^85 + 532 * q^86 - 328 * q^87 - 40 * q^88 - 766 * q^90 + 72 * q^91 + 68 * q^92 - 66 * q^93 - 232 * q^95 - 16 * q^96 + 6 * q^97 - 440 * q^98

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