LMFDB - Embedded newform 90.3.k.b.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,3,Mod(7,90)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 3]))

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

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

chi := DirichletCharacter("90.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	90.k (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.45232237924$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.1
Character	$\chi$	$=$	90.7
Dual form			90.3.k.b.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36603 - 0.366025i) q^{2} +(-2.94504 + 0.571623i) q^{3} +(1.73205 - 1.00000i) q^{4} +(4.17929 - 2.74473i) q^{5} +(-3.81377 + 1.85881i) q^{6} +(8.06163 - 2.16011i) q^{7} +(2.00000 - 2.00000i) q^{8} +(8.34650 - 3.36690i) q^{9} +(4.70437 - 5.27910i) q^{10} +(-2.87538 + 4.98030i) q^{11} +(-4.52933 + 3.93512i) q^{12} +(-6.01206 - 1.61093i) q^{13} +(10.2217 - 5.90153i) q^{14} +(-10.7392 + 10.4723i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-7.29884 - 7.29884i) q^{17} +(10.1692 - 7.65430i) q^{18} +30.1705i q^{19} +(4.49400 - 8.93331i) q^{20} +(-22.5070 + 10.9698i) q^{21} +(-2.10492 + 7.85567i) q^{22} +(-38.1793 - 10.2301i) q^{23} +(-4.74683 + 7.03332i) q^{24} +(9.93287 - 22.9421i) q^{25} -8.80226 q^{26} +(-22.6561 + 14.6867i) q^{27} +(11.8031 - 11.8031i) q^{28} +(13.3150 + 7.68744i) q^{29} +(-10.8369 + 18.2363i) q^{30} +(19.4198 + 33.6360i) q^{31} +(1.46410 - 5.46410i) q^{32} +(5.62124 - 16.3108i) q^{33} +(-12.6420 - 7.29884i) q^{34} +(27.7630 - 31.1548i) q^{35} +(11.0897 - 14.1781i) q^{36} +(23.3594 + 23.3594i) q^{37} +(11.0432 + 41.2136i) q^{38} +(18.6266 + 1.30761i) q^{39} +(2.86910 - 13.8480i) q^{40} +(-23.6254 - 40.9204i) q^{41} +(-26.7300 + 23.2232i) q^{42} +(2.80496 + 10.4683i) q^{43} +11.5015i q^{44} +(25.6411 - 36.9802i) q^{45} -55.8984 q^{46} +(-63.8022 + 17.0957i) q^{47} +(-3.90992 + 11.3452i) q^{48} +(17.8886 - 10.3280i) q^{49} +(5.17117 - 34.9751i) q^{50} +(25.6675 + 17.3232i) q^{51} +(-12.0241 + 3.22185i) q^{52} +(0.227111 - 0.227111i) q^{53} +(-25.5732 + 28.3551i) q^{54} +(1.65257 + 28.7062i) q^{55} +(11.8031 - 20.4435i) q^{56} +(-17.2461 - 88.8531i) q^{57} +(21.0025 + 5.62760i) q^{58} +(11.0663 - 6.38914i) q^{59} +(-8.12852 + 28.8778i) q^{60} +(-41.0215 + 71.0513i) q^{61} +(38.8395 + 38.8395i) q^{62} +(60.0135 - 45.1721i) q^{63} -8.00000i q^{64} +(-29.5477 + 9.76898i) q^{65} +(1.70859 - 24.3385i) q^{66} +(28.5011 - 106.367i) q^{67} +(-19.9408 - 5.34312i) q^{68} +(118.287 + 8.30392i) q^{69} +(26.5215 - 52.7201i) q^{70} +87.7370 q^{71} +(9.95919 - 23.4268i) q^{72} +(15.8257 - 15.8257i) q^{73} +(40.4597 + 23.3594i) q^{74} +(-16.1385 + 73.2431i) q^{75} +(30.1705 + 52.2568i) q^{76} +(-12.4222 + 46.3604i) q^{77} +(25.9230 - 5.03157i) q^{78} +(-72.6039 - 41.9179i) q^{79} +(-1.14947 - 19.9669i) q^{80} +(58.3280 - 56.2036i) q^{81} +(-47.2508 - 47.2508i) q^{82} +(3.11595 + 11.6289i) q^{83} +(-28.0135 + 41.5073i) q^{84} +(-50.5373 - 10.4706i) q^{85} +(7.66330 + 13.2732i) q^{86} +(-43.6076 - 15.0286i) q^{87} +(4.20984 + 15.7113i) q^{88} +59.4813i q^{89} +(21.4908 - 59.9011i) q^{90} -51.9468 q^{91} +(-76.3586 + 20.4602i) q^{92} +(-76.4190 - 87.9586i) q^{93} +(-80.8979 + 46.7064i) q^{94} +(82.8099 + 126.091i) q^{95} +(-1.18843 + 16.9289i) q^{96} +(107.430 - 28.7859i) q^{97} +(20.6560 - 20.6560i) q^{98} +(-7.23114 + 51.2491i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} + 4 q^{3} + 16 q^{6} + 6 q^{7} + 48 q^{8} + 12 q^{10} - 12 q^{11} + 8 q^{12} - 38 q^{15} + 48 q^{16} - 36 q^{17} - 20 q^{18} + 12 q^{20} - 128 q^{21} + 12 q^{22} - 66 q^{23} - 42 q^{25}+ \cdots + 264 q^{98}+O(q^{100}) $ 24 * q + 12 * q^2 + 4 * q^3 + 16 * q^6 + 6 * q^7 + 48 * q^8 + 12 * q^10 - 12 * q^11 + 8 * q^12 - 38 * q^15 + 48 * q^16 - 36 * q^17 - 20 * q^18 + 12 * q^20 - 128 * q^21 + 12 * q^22 - 66 * q^23 - 42 * q^25 + 10 * q^27 + 24 * q^28 - 48 * q^30 + 72 * q^31 - 48 * q^32 - 122 * q^33 - 240 * q^35 - 8 * q^36 + 36 * q^37 - 36 * q^38 - 12 * q^40 - 24 * q^41 - 16 * q^42 - 108 * q^43 + 158 * q^45 - 264 * q^46 - 36 * q^47 + 32 * q^48 + 42 * q^50 + 380 * q^51 + 384 * q^53 + 288 * q^55 + 24 * q^56 + 154 * q^57 - 108 * q^58 - 56 * q^60 + 360 * q^61 + 144 * q^62 - 68 * q^63 + 144 * q^65 - 80 * q^66 + 144 * q^67 - 36 * q^68 - 174 * q^70 + 216 * q^71 + 32 * q^72 + 432 * q^73 - 184 * q^75 + 72 * q^76 - 48 * q^77 - 240 * q^78 + 416 * q^81 - 48 * q^82 - 378 * q^83 - 228 * q^85 + 216 * q^86 + 52 * q^87 - 24 * q^88 + 124 * q^90 - 1560 * q^91 - 132 * q^92 + 580 * q^93 + 264 * q^95 + 32 * q^96 - 294 * q^97 + 264 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.36603	−	0.366025i	0.683013	−	0.183013i
$2$	1.36603	−	0.366025i	0.683013	−	0.183013i
$3$	−2.94504	+	0.571623i	−0.981679	+	0.190541i
$3$	−2.94504	+	0.571623i	−0.981679	+	0.190541i
$4$	1.73205	−	1.00000i	0.433013	−	0.250000i
$5$	4.17929	−	2.74473i	0.835857	−	0.548947i
$5$	4.17929	−	2.74473i	0.835857	−	0.548947i
$6$	−3.81377	+	1.85881i	−0.635628	+	0.309802i
$7$	8.06163	−	2.16011i	1.15166	−	0.308587i	0.368031	−	0.929814i	$-0.380032\pi$
$7$	8.06163	−	2.16011i	1.15166	−	0.308587i	0.783631	+	0.621227i	$0.213365\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	8.34650	−	3.36690i	0.927388	−	0.374100i
$10$	4.70437	−	5.27910i	0.470437	−	0.527910i
$11$	−2.87538	+	4.98030i	−0.261398	+	0.452754i	−0.966614	−	0.256239i	$-0.917517\pi$
$11$	−2.87538	+	4.98030i	−0.261398	+	0.452754i	0.705216	+	0.708993i	$0.250850\pi$
$12$	−4.52933	+	3.93512i	−0.377444	+	0.327926i
$13$	−6.01206	−	1.61093i	−0.462466	−	0.123917i	0.0200606	−	0.999799i	$-0.493614\pi$
$13$	−6.01206	−	1.61093i	−0.462466	−	0.123917i	−0.482526	+	0.875881i	$0.660281\pi$
$14$	10.2217	−	5.90153i	0.730124	−	0.421538i
$15$	−10.7392	+	10.4723i	−0.715947	+	0.698155i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	−7.29884	−	7.29884i	−0.429343	−	0.429343i	0.459061	−	0.888405i	$-0.348186\pi$
$17$	−7.29884	−	7.29884i	−0.429343	−	0.429343i	−0.888405	+	0.459061i	$0.848186\pi$
$18$	10.1692	−	7.65430i	0.564953	−	0.425239i
$19$			30.1705i			1.58792i	0.607971	+	0.793959i	$0.291984\pi$
$19$			30.1705i			1.58792i	−0.607971	+	0.793959i	$0.708016\pi$
$20$	4.49400	−	8.93331i	0.224700	−	0.446665i
$21$	−22.5070	+	10.9698i	−1.07176	+	0.522372i
$22$	−2.10492	+	7.85567i	−0.0956782	+	0.357076i
$23$	−38.1793	−	10.2301i	−1.65997	−	0.444788i	−0.697590	−	0.716497i	$-0.745744\pi$
$23$	−38.1793	−	10.2301i	−1.65997	−	0.444788i	−0.962379	+	0.271709i	$0.912411\pi$
$24$	−4.74683	+	7.03332i	−0.197785	+	0.293055i
$25$	9.93287	−	22.9421i	0.397315	−	0.917682i
$26$	−8.80226			−0.338548
$27$	−22.6561	+	14.6867i	−0.839117	+	0.543952i
$28$	11.8031	−	11.8031i	0.421538	−	0.421538i
$29$	13.3150	+	7.68744i	0.459139	+	0.265084i	0.711682	−	0.702501i	$-0.247934\pi$
$29$	13.3150	+	7.68744i	0.459139	+	0.265084i	−0.252543	+	0.967586i	$0.581267\pi$
$30$	−10.8369	+	18.2363i	−0.361230	+	0.607876i
$31$	19.4198	+	33.6360i	0.626444	+	1.08503i	0.988260	+	0.152783i	$0.0488236\pi$
$31$	19.4198	+	33.6360i	0.626444	+	1.08503i	−0.361816	+	0.932250i	$0.617843\pi$
$32$	1.46410	−	5.46410i	0.0457532	−	0.170753i
$33$	5.62124	−	16.3108i	0.170341	−	0.494266i
$34$	−12.6420	−	7.29884i	−0.371822	−	0.214672i
$35$	27.7630	−	31.1548i	0.793227	−	0.890136i
$36$	11.0897	−	14.1781i	0.308046	−	0.393837i
$37$	23.3594	+	23.3594i	0.631336	+	0.631336i	0.948403	−	0.317067i	$-0.102698\pi$
$37$	23.3594	+	23.3594i	0.631336	+	0.631336i	−0.317067	+	0.948403i	$0.602698\pi$
$38$	11.0432	+	41.2136i	0.290609	+	1.08457i
$39$	18.6266	+	1.30761i	0.477604	+	0.0335284i
$40$	2.86910	−	13.8480i	0.0717276	−	0.346201i
$41$	−23.6254	−	40.9204i	−0.576229	−	0.998058i	−0.995907	−	0.0903851i	$-0.971190\pi$
$41$	−23.6254	−	40.9204i	−0.576229	−	0.998058i	0.419678	−	0.907673i	$-0.362143\pi$
$42$	−26.7300	+	23.2232i	−0.636428	+	0.552933i
$43$	2.80496	+	10.4683i	0.0652317	+	0.243448i	0.990841	−	0.135032i	$-0.0431137\pi$
$43$	2.80496	+	10.4683i	0.0652317	+	0.243448i	−0.925610	+	0.378480i	$0.876447\pi$
$44$			11.5015i			0.261398i
$45$	25.6411	−	36.9802i	0.569803	−	0.821781i
$46$	−55.8984			−1.21518
$47$	−63.8022	+	17.0957i	−1.35749	+	0.363739i	−0.862895	−	0.505383i	$-0.831351\pi$
$47$	−63.8022	+	17.0957i	−1.35749	+	0.363739i	−0.494598	+	0.869122i	$0.664685\pi$
$48$	−3.90992	+	11.3452i	−0.0814566	+	0.236357i
$49$	17.8886	−	10.3280i	0.365074	−	0.210776i
$50$	5.17117	−	34.9751i	0.103423	−	0.699502i
$51$	25.6675	+	17.3232i	0.503285	+	0.339670i
$52$	−12.0241	+	3.22185i	−0.231233	+	0.0619587i
$53$	0.227111	−	0.227111i	0.00428512	−	0.00428512i	−0.704961	−	0.709246i	$-0.749036\pi$
$53$	0.227111	−	0.227111i	0.00428512	−	0.00428512i	0.709246	+	0.704961i	$0.249036\pi$
$54$	−25.5732	+	28.3551i	−0.473577	+	0.525095i
$55$	1.65257	+	28.7062i	0.0300468	+	0.521931i
$56$	11.8031	−	20.4435i	0.210769	−	0.365062i
$57$	−17.2461	−	88.8531i	−0.302563	−	1.55883i
$58$	21.0025	+	5.62760i	0.362112	+	0.0970276i
$59$	11.0663	−	6.38914i	0.187565	−	0.108291i	−0.403277	−	0.915078i	$-0.632129\pi$
$59$	11.0663	−	6.38914i	0.187565	−	0.108291i	0.590842	+	0.806787i	$0.298796\pi$
$60$	−8.12852	+	28.8778i	−0.135475	+	0.481297i
$61$	−41.0215	+	71.0513i	−0.672483	+	1.16478i	0.304714	+	0.952444i	$0.401439\pi$
$61$	−41.0215	+	71.0513i	−0.672483	+	1.16478i	−0.977198	+	0.212332i	$0.931894\pi$
$62$	38.8395	+	38.8395i	0.626444	+	0.626444i
$63$	60.0135	−	45.1721i	0.952596	−	0.717017i
$64$		−	8.00000i		−	0.125000i
$65$	−29.5477	+	9.76898i	−0.454579	+	0.150292i
$66$	1.70859	−	24.3385i	0.0258877	−	0.368765i
$67$	28.5011	−	106.367i	0.425389	−	1.58757i	−0.337683	−	0.941260i	$-0.609643\pi$
$67$	28.5011	−	106.367i	0.425389	−	1.58757i	0.763072	−	0.646314i	$-0.223690\pi$
$68$	−19.9408	−	5.34312i	−0.293247	−	0.0785753i
$69$	118.287	+	8.30392i	1.71431	+	0.120347i
$70$	26.5215	−	52.7201i	0.378878	−	0.753145i
$71$	87.7370			1.23573			0.617866	−	0.786283i	$-0.287997\pi$
$71$	87.7370			1.23573			0.617866	+	0.786283i	$0.287997\pi$
$72$	9.95919	−	23.4268i	0.138322	−	0.325372i
$73$	15.8257	−	15.8257i	0.216791	−	0.216791i	−0.590354	−	0.807145i	$-0.701012\pi$
$73$	15.8257	−	15.8257i	0.216791	−	0.216791i	0.807145	+	0.590354i	$0.201012\pi$
$74$	40.4597	+	23.3594i	0.546753	+	0.315668i
$75$	−16.1385	+	73.2431i	−0.215180	+	0.976575i
$76$	30.1705	+	52.2568i	0.396980	+	0.687589i
$77$	−12.4222	+	46.3604i	−0.161328	+	0.602084i
$78$	25.9230	−	5.03157i	0.332346	−	0.0645073i
$79$	−72.6039	−	41.9179i	−0.919037	−	0.530606i	−0.0357094	−	0.999362i	$-0.511369\pi$
$79$	−72.6039	−	41.9179i	−0.919037	−	0.530606i	−0.883328	+	0.468756i	$0.844702\pi$
$80$	−1.14947	−	19.9669i	−0.0143683	−	0.249587i
$81$	58.3280	−	56.2036i	0.720098	−	0.693872i
$82$	−47.2508	−	47.2508i	−0.576229	−	0.576229i
$83$	3.11595	+	11.6289i	0.0375416	+	0.140107i	0.982153	−	0.188084i	$-0.0602277\pi$
$83$	3.11595	+	11.6289i	0.0375416	+	0.140107i	−0.944611	+	0.328191i	$0.893561\pi$
$84$	−28.0135	+	41.5073i	−0.333495	+	0.494135i
$85$	−50.5373	−	10.4706i	−0.594556	−	0.123183i
$86$	7.66330	+	13.2732i	0.0891081	+	0.154340i
$87$	−43.6076	−	15.0286i	−0.501237	−	0.172743i
$88$	4.20984	+	15.7113i	0.0478391	+	0.178538i
$89$			59.4813i			0.668330i	0.942515	+	0.334165i	$0.108454\pi$
$89$			59.4813i			0.668330i	−0.942515	+	0.334165i	$0.891546\pi$
$90$	21.4908	−	59.9011i	0.238786	−	0.665568i
$91$	−51.9468			−0.570844
$92$	−76.3586	+	20.4602i	−0.829985	+	0.222394i
$93$	−76.4190	−	87.9586i	−0.821710	−	0.945791i
$94$	−80.8979	+	46.7064i	−0.860616	+	0.496877i
$95$	82.8099	+	126.091i	0.871683	+	1.32727i
$96$	−1.18843	+	16.9289i	−0.0123795	+	0.176343i
$97$	107.430	−	28.7859i	1.10753	−	0.296762i	0.341703	−	0.939808i	$-0.388996\pi$
$97$	107.430	−	28.7859i	1.10753	−	0.296762i	0.765827	+	0.643046i	$0.222330\pi$
$98$	20.6560	−	20.6560i	0.210776	−	0.210776i
$99$	−7.23114	+	51.2491i	−0.0730419	+	0.517668i
$100$	−5.73783	−	49.6697i	−0.0573783	−	0.496697i
$101$	−46.1762	+	79.9796i	−0.457191	+	0.791877i	−0.998811	−	0.0487458i	$-0.984478\pi$
$101$	−46.1762	+	79.9796i	−0.457191	+	0.791877i	0.541621	+	0.840623i	$0.317811\pi$
$102$	41.4032	+	14.2689i	0.405914	+	0.139891i
$103$	−127.449	−	34.1499i	−1.23737	−	0.331553i	−0.419926	−	0.907558i	$-0.637944\pi$
$103$	−127.449	−	34.1499i	−1.23737	−	0.331553i	−0.817446	+	0.576006i	$0.804611\pi$
$104$	−15.2460	+	8.80226i	−0.146596	+	0.0846371i
$105$	−63.9542	+	107.622i	−0.609087	+	1.02497i
$106$	0.227111	−	0.393368i	0.00214256	−	0.00371102i
$107$	106.237	+	106.237i	0.992872	+	0.992872i	0.999975	−	0.00710243i	$-0.00226079\pi$
$107$	106.237	+	106.237i	0.992872	+	0.992872i	−0.00710243	+	0.999975i	$0.502261\pi$
$108$	−24.5549	+	48.0942i	−0.227360	+	0.445317i
$109$		−	138.393i		−	1.26966i	−0.772653	−	0.634829i	$-0.781071\pi$
$109$		−	138.393i		−	1.26966i	0.772653	−	0.634829i	$-0.218929\pi$
$110$	12.7647	+	38.6085i	0.116042	+	0.350987i
$111$	−82.1471	−	55.4416i	−0.740064	−	0.499474i
$112$	8.64043	−	32.2465i	0.0771467	−	0.287915i
$113$	−134.628	−	36.0734i	−1.19140	−	0.319234i	−0.391958	−	0.919983i	$-0.628202\pi$
$113$	−134.628	−	36.0734i	−1.19140	−	0.319234i	−0.799437	+	0.600749i	$0.794869\pi$
$114$	−56.0811	−	115.063i	−0.491940	−	1.00933i
$115$	−187.641	+	62.0375i	−1.63166	+	0.539456i
$116$	30.7498			0.265084
$117$	−55.6034	+	6.79641i	−0.475243	+	0.0580890i
$118$	12.7783	−	12.7783i	0.108291	−	0.108291i
$119$	−74.6068	−	43.0743i	−0.626948	−	0.361969i
$120$	−0.533764	+	42.4230i	−0.00444804	+	0.353525i
$121$	43.9644	+	76.1486i	0.363342	+	0.629328i
$122$	−30.0298	+	112.073i	−0.246146	+	0.918629i
$123$	92.9687	+	107.007i	0.755843	+	0.869978i
$124$	67.2720	+	38.8395i	0.542516	+	0.313222i
$125$	−21.4576	−	123.145i	−0.171661	−	0.985156i
$126$	65.4459	−	83.6726i	0.519412	−	0.664069i
$127$	66.9076	+	66.9076i	0.526832	+	0.526832i	0.919626	−	0.392795i	$-0.128492\pi$
$127$	66.9076	+	66.9076i	0.526832	+	0.526832i	−0.392795	+	0.919626i	$0.628492\pi$
$128$	−2.92820	−	10.9282i	−0.0228766	−	0.0853766i
$129$	−14.2446	−	29.2260i	−0.110423	−	0.226558i
$130$	−36.7872	+	24.1599i	−0.282978	+	0.185845i
$131$	−92.0091	−	159.364i	−0.702360	−	1.21652i	−0.967636	−	0.252350i	$-0.918796\pi$
$131$	−92.0091	−	159.364i	−0.702360	−	1.21652i	0.265276	−	0.964172i	$-0.414537\pi$
$132$	−6.57452	−	33.8724i	−0.0498070	−	0.256609i
$133$	65.1714	+	243.223i	0.490011	+	1.82875i
$134$		−	155.733i		−	1.16218i
$135$	−54.3754	+	123.565i	−0.402781	+	0.915296i
$136$	−29.1953			−0.214672
$137$	147.628	−	39.5568i	1.07758	−	0.288736i	0.323974	−	0.946066i	$-0.394981\pi$
$137$	147.628	−	39.5568i	1.07758	−	0.288736i	0.753603	+	0.657330i	$0.228314\pi$
$138$	164.623	−	31.9528i	1.19292	−	0.231542i
$139$	3.48356	−	2.01123i	0.0250616	−	0.0144693i	−0.487417	−	0.873169i	$-0.662061\pi$
$139$	3.48356	−	2.01123i	0.0250616	−	0.0144693i	0.512478	+	0.858700i	$0.328727\pi$
$140$	16.9321	−	81.7246i	0.120943	−	0.583747i
$141$	178.128	−	86.8184i	1.26332	−	0.615733i
$142$	119.851	−	32.1140i	0.844021	−	0.226155i
$143$	25.3098	−	25.3098i	0.176992	−	0.176992i
$144$	5.02970	−	35.6469i	0.0349285	−	0.247548i
$145$	76.7474	−	4.41823i	0.529292	−	0.0304705i
$146$	15.8257	−	27.4110i	0.108395	−	0.187746i
$147$	−46.7790	+	40.6419i	−0.318224	+	0.276476i
$148$	63.8191	+	17.1003i	0.431210	+	0.115542i
$149$	89.1479	−	51.4696i	0.598308	−	0.345433i	−0.170068	−	0.985432i	$-0.554399\pi$
$149$	89.1479	−	51.4696i	0.598308	−	0.345433i	0.768376	+	0.639999i	$0.221065\pi$
$150$	4.76328	+	105.959i	0.0317552	+	0.706393i
$151$	73.5398	−	127.375i	0.487019	−	0.843541i	−0.512870	−	0.858466i	$-0.671418\pi$
$151$	73.5398	−	127.375i	0.487019	−	0.843541i	0.999889	+	0.0149251i	$0.00475098\pi$
$152$	60.3409	+	60.3409i	0.396980	+	0.396980i
$153$	−85.4942	−	36.3452i	−0.558785	−	0.237551i
$154$			67.8764i			0.440756i
$155$	173.483	+	87.2725i	1.11924	+	0.563048i
$156$	33.5698	−	16.3617i	0.215191	−	0.104883i
$157$	5.66833	−	21.1545i	0.0361040	−	0.134742i	−0.945521	−	0.325560i	$-0.894447\pi$
$157$	5.66833	−	21.1545i	0.0361040	−	0.134742i	0.981625	+	0.190818i	$0.0611139\pi$
$158$	−114.522	−	30.6860i	−0.724822	−	0.194215i
$159$	−0.539029	+	0.798673i	−0.00339012	+	0.00502310i
$160$	−8.87861	−	26.8546i	−0.0554913	−	0.167841i
$161$	−329.886			−2.04898
$162$	59.1055	−	98.1251i	0.364849	−	0.605711i
$163$	−51.4648	+	51.4648i	−0.315735	+	0.315735i	−0.847127	−	0.531391i	$-0.821669\pi$
$163$	−51.4648	+	51.4648i	−0.315735	+	0.315735i	0.531391	+	0.847127i	$0.321669\pi$
$164$	−81.8408	−	47.2508i	−0.499029	−	0.288115i
$165$	−21.2760	−	83.5963i	−0.128946	−	0.506644i
$166$	8.51293	+	14.7448i	0.0512827	+	0.0888243i
$167$	35.4672	−	132.365i	0.212378	−	0.792607i	−0.774695	−	0.632335i	$-0.782096\pi$
$167$	35.4672	−	132.365i	0.212378	−	0.792607i	0.987073	−	0.160271i	$-0.0512369\pi$
$168$	−23.0745	+	66.9537i	−0.137348	+	0.398534i
$169$	−112.809	−	65.1301i	−0.667506	−	0.385385i
$170$	−72.8677	+	4.19488i	−0.428634	+	0.0246758i
$171$	101.581	+	251.818i	0.594040	+	1.47262i
$172$	15.3266	+	15.3266i	0.0891081	+	0.0891081i
$173$	46.6155	+	173.971i	0.269454	+	1.00562i	0.959468	+	0.281819i	$0.0909378\pi$
$173$	46.6155	+	173.971i	0.269454	+	1.00562i	−0.690014	+	0.723796i	$0.742396\pi$
$174$	−65.0700	−	4.56800i	−0.373965	−	0.0262528i
$175$	30.5178	−	206.407i	0.174387	−	1.17947i
$176$	11.5015	+	19.9212i	0.0653494	+	0.113189i
$177$	−28.9386	+	25.1420i	−0.163495	+	0.142045i
$178$	21.7717	+	81.2530i	0.122313	+	0.456478i
$179$			6.72775i			0.0375852i	0.999823	+	0.0187926i	$0.00598222\pi$
$179$			6.72775i			0.0375852i	−0.999823	+	0.0187926i	$0.994018\pi$
$180$	7.43161	−	89.6926i	0.0412867	−	0.498292i
$181$	153.631			0.848789			0.424395	−	0.905477i	$-0.360487\pi$
$181$	153.631			0.848789			0.424395	+	0.905477i	$0.360487\pi$
$182$	−70.9606	+	19.0138i	−0.389893	+	0.104472i
$183$	80.1953	−	232.698i	0.438226	−	1.27157i
$184$	−96.8188	+	55.8984i	−0.526189	+	0.303796i
$185$	161.741	+	33.5103i	0.874276	+	0.181137i
$186$	−136.585	−	92.1823i	−0.734330	−	0.495604i
$187$	57.3373	−	15.3635i	0.306616	−	0.0821576i
$188$	−93.4129	+	93.4129i	−0.496877	+	0.496877i
$189$	−150.921	+	167.338i	−0.798522	+	0.885389i
$190$	159.273	+	141.933i	0.838278	+	0.747015i
$191$	180.317	−	312.319i	0.944070	−	1.63518i	0.186468	−	0.982461i	$-0.440296\pi$
$191$	180.317	−	312.319i	0.944070	−	1.63518i	0.757602	−	0.652717i	$-0.226371\pi$
$192$	4.57298	+	23.5603i	0.0238176	+	0.122710i
$193$	226.571	+	60.7095i	1.17394	+	0.314557i	0.792522	−	0.609844i	$-0.208768\pi$
$193$	226.571	+	60.7095i	1.17394	+	0.314557i	0.381422	+	0.924401i	$0.375435\pi$
$194$	136.216	−	78.6446i	0.702146	−	0.405384i
$195$	81.4348	−	45.6601i	0.417614	−	0.234154i
$196$	20.6560	−	35.7773i	0.105388	−	0.182537i
$197$	−54.2664	−	54.2664i	−0.275464	−	0.275464i	0.555831	−	0.831295i	$-0.312400\pi$
$197$	−54.2664	−	54.2664i	−0.275464	−	0.275464i	−0.831295	+	0.555831i	$0.812400\pi$
$198$	8.88055	+	72.6544i	0.0448513	+	0.366941i
$199$		−	205.980i		−	1.03507i	−0.855661	−	0.517537i	$-0.826849\pi$
$199$		−	205.980i		−	1.03507i	0.855661	−	0.517537i	$-0.173151\pi$
$200$	−26.0184	−	65.7499i	−0.130092	−	0.328749i
$201$	−23.1347	+	329.548i	−0.115098	+	1.63954i
$202$	−33.8034	+	126.156i	−0.167343	+	0.624534i
$203$	123.947	+	33.2114i	0.610575	+	0.163603i
$204$	61.7806	+	4.33708i	0.302846	+	0.0212602i
$205$	−211.053	−	106.173i	−1.02953	−	0.517915i
$206$	−186.599			−0.905819
$207$	−353.107	+	43.1603i	−1.70583	+	0.208504i
$208$	−17.6045	+	17.6045i	−0.0846371	+	0.0846371i
$209$	−150.258	−	86.7514i	−0.718937	−	0.415078i
$210$	−47.9707	+	170.423i	−0.228432	+	0.811538i
$211$	−3.70438	−	6.41617i	−0.0175563	−	0.0304084i	0.857114	−	0.515127i	$-0.172255\pi$
$211$	−3.70438	−	6.41617i	−0.0175563	−	0.0304084i	−0.874670	+	0.484719i	$0.838922\pi$
$212$	0.166257	−	0.620479i	0.000784231	−	0.00292679i
$213$	−258.389	+	50.1524i	−1.21309	+	0.235457i
$214$	184.008	+	106.237i	0.859853	+	0.496436i
$215$	40.4553	+	36.0510i	0.188164	+	0.167679i
$216$	−15.9389	+	74.6857i	−0.0737912	+	0.345767i
$217$	229.212	+	229.212i	1.05628	+	1.05628i
$218$	−50.6552	−	189.048i	−0.232363	−	0.867192i
$219$	−37.5610	+	55.6537i	−0.171511	+	0.254126i
$220$	31.5686	+	48.0681i	0.143493	+	0.218491i
$221$	32.1231	+	55.6389i	0.145354	+	0.251760i
$222$	−132.508	−	45.6667i	−0.596883	−	0.205706i
$223$	−35.7743	−	133.511i	−0.160423	−	0.598705i	−0.998580	−	0.0532767i	$-0.983033\pi$
$223$	−35.7743	−	133.511i	−0.160423	−	0.598705i	0.838157	−	0.545429i	$-0.183633\pi$
$224$		−	47.2122i		−	0.210769i
$225$	5.66098	−	224.929i	0.0251599	−	0.999683i
$226$	−197.109			−0.872162
$227$	−65.8723	+	17.6504i	−0.290186	+	0.0777552i	−0.400976	−	0.916089i	$-0.631329\pi$
$227$	−65.8723	+	17.6504i	−0.290186	+	0.0777552i	0.110789	+	0.993844i	$0.464662\pi$
$228$	−118.724	−	136.652i	−0.520720	−	0.599351i
$229$	−170.779	+	98.5996i	−0.745762	+	0.430566i	−0.824161	−	0.566356i	$-0.808353\pi$
$229$	−170.779	+	98.5996i	−0.745762	+	0.430566i	0.0783986	+	0.996922i	$0.475019\pi$
$230$	−233.615	+	153.426i	−1.01572	+	0.667070i
$231$	10.0833	−	143.634i	0.0436506	−	0.621793i
$232$	42.0050	−	11.2552i	0.181056	−	0.0485138i
$233$	47.1109	−	47.1109i	0.202193	−	0.202193i	−0.598746	−	0.800939i	$-0.704334\pi$
$233$	47.1109	−	47.1109i	0.202193	−	0.202193i	0.800939	+	0.598746i	$0.204334\pi$
$234$	−73.4680	+	29.6363i	−0.313966	+	0.126651i
$235$	−219.724	+	246.568i	−0.934997	+	1.04923i
$236$	12.7783	−	22.1326i	0.0541453	−	0.0937824i
$237$	237.783	+	81.9478i	1.00330	+	0.345771i
$238$	−117.681	−	31.5326i	−0.494458	−	0.132490i
$239$	3.11197	−	1.79669i	0.0130208	−	0.00751755i	−0.493475	−	0.869760i	$-0.664274\pi$
$239$	3.11197	−	1.79669i	0.0130208	−	0.00751755i	0.506496	+	0.862242i	$0.330940\pi$
$240$	14.7988	+	58.1463i	0.0616616	+	0.242276i
$241$	33.8177	−	58.5741i	0.140323	−	0.243046i	−0.787296	−	0.616576i	$-0.788519\pi$
$241$	33.8177	−	58.5741i	0.140323	−	0.243046i	0.927618	+	0.373530i	$0.121853\pi$
$242$	87.9289	+	87.9289i	0.363342	+	0.363342i
$243$	−139.651	+	198.863i	−0.574695	+	0.818368i
$244$			164.086i			0.672483i
$245$	46.4141	−	92.2632i	0.189445	−	0.376585i
$246$	166.165	+	112.146i	0.675468	+	0.455877i
$247$	48.6023	−	181.386i	0.196771	−	0.734358i
$248$	106.112	+	28.4325i	0.427869	+	0.114647i
$249$	−15.8239	−	32.4663i	−0.0635499	−	0.130387i
$250$	−74.3856	−	160.365i	−0.297542	−	0.641458i
$251$	15.9799			0.0636649			0.0318324	−	0.999493i	$-0.489866\pi$
$251$	15.9799			0.0636649			0.0318324	+	0.999493i	$0.489866\pi$
$252$	58.7744	−	138.254i	0.233232	−	0.548626i
$253$	160.729	−	160.729i	0.635292	−	0.635292i
$254$	115.887	+	66.9076i	0.456249	+	0.263416i
$255$	154.819	+	1.94793i	0.607135	+	0.00763894i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−45.7242	+	170.645i	−0.177915	+	0.663989i	0.818122	+	0.575045i	$0.195016\pi$
$257$	−45.7242	+	170.645i	−0.177915	+	0.663989i	−0.996037	+	0.0889431i	$0.971651\pi$
$258$	−30.1560	−	34.7096i	−0.116884	−	0.134533i
$259$	238.774	+	137.856i	0.921907	+	0.532263i
$260$	−41.4091	+	46.4680i	−0.159266	+	0.178723i
$261$	137.017	+	19.3328i	0.524969	+	0.0740720i
$262$	−184.018	−	184.018i	−0.702360	−	0.702360i
$263$	−45.3709	−	169.327i	−0.172513	−	0.643827i	−0.996962	−	0.0778908i	$-0.975181\pi$
$263$	−45.3709	−	169.327i	−0.172513	−	0.643827i	0.824449	−	0.565936i	$-0.191485\pi$
$264$	−21.3791	−	43.8641i	−0.0809814	−	0.166152i
$265$	0.325803	−	1.57252i	0.00122944	−	0.00593405i
$266$	178.052	+	308.395i	0.669367	+	1.15938i
$267$	−34.0009	−	175.175i	−0.127344	−	0.656085i
$268$	−57.0021	−	212.735i	−0.212695	−	0.793787i
$269$			245.869i			0.914011i	0.889464	+	0.457006i	$0.151078\pi$
$269$			245.869i			0.914011i	−0.889464	+	0.457006i	$0.848922\pi$
$270$	−29.0503	+	188.696i	−0.107594	+	0.698873i
$271$	−120.153			−0.443371			−0.221685	−	0.975118i	$-0.571156\pi$
$271$	−120.153			−0.443371			−0.221685	+	0.975118i	$0.571156\pi$
$272$	−39.8816	+	10.6862i	−0.146623	+	0.0392876i
$273$	152.985	−	29.6939i	0.560385	−	0.108769i
$274$	187.185	−	108.071i	0.683156	−	0.394421i
$275$	85.6975	+	115.436i	0.311627	+	0.419766i
$276$	213.183	−	103.904i	0.772404	−	0.376465i
$277$	−427.888	+	114.652i	−1.54472	+	0.413907i	−0.927788	−	0.373107i	$-0.878293\pi$
$277$	−427.888	+	114.652i	−1.54472	+	0.413907i	−0.616935	+	0.787014i	$0.711626\pi$
$278$	4.02247	−	4.02247i	0.0144693	−	0.0144693i
$279$	275.336	+	215.358i	0.986868	+	0.771894i
$280$	−6.78361	−	117.835i	−0.0242272	−	0.420841i
$281$	−133.612	+	231.422i	−0.475486	+	0.823566i	−0.999606	−	0.0280785i	$-0.991061\pi$
$281$	−133.612	+	231.422i	−0.475486	+	0.823566i	0.524120	+	0.851645i	$0.324394\pi$
$282$	211.549	−	183.795i	0.750174	−	0.651756i
$283$	−4.65544	−	1.24742i	−0.0164503	−	0.00440785i	0.250585	−	0.968095i	$-0.419377\pi$
$283$	−4.65544	−	1.24742i	−0.0164503	−	0.00440785i	−0.267035	+	0.963687i	$0.586044\pi$
$284$	151.965	−	87.7370i	0.535088	−	0.308933i
$285$	−315.955	−	324.007i	−1.10861	−	1.13687i
$286$	25.3098	−	43.8379i	0.0884958	−	0.153279i
$287$	−278.852	−	278.852i	−0.971609	−	0.971609i
$288$	−6.17697	−	50.5356i	−0.0214478	−	0.175471i
$289$		−	182.454i		−	0.631329i
$290$	103.222	−	34.1269i	0.355937	−	0.117679i
$291$	−299.932	+	146.185i	−1.03069	+	0.502355i
$292$	11.5852	−	43.2367i	0.0396755	−	0.148071i
$293$	74.9920	+	20.0940i	0.255945	+	0.0685804i	0.384510	−	0.923121i	$-0.374370\pi$
$293$	74.9920	+	20.0940i	0.255945	+	0.0685804i	−0.128565	+	0.991701i	$0.541037\pi$
$294$	−49.0253	+	72.6402i	−0.166753	+	0.247075i
$295$	28.7128	−	57.0762i	0.0973316	−	0.193479i
$296$	93.4377			0.315668
$297$	−7.99916	−	155.064i	−0.0269332	−	0.522101i
$298$	102.939	−	102.939i	0.345433	−	0.345433i
$299$	213.056	+	123.008i	0.712562	+	0.411398i
$300$	45.2904	+	142.999i	0.150968	+	0.476664i
$301$	45.2251	+	78.3323i	0.150250	+	0.260240i
$302$	53.8349	−	200.915i	0.178261	−	0.665280i
$303$	90.2726	−	261.938i	0.297929	−	0.864483i
$304$	104.514	+	60.3409i	0.343794	+	0.198490i
$305$	23.5764	+	409.537i	0.0772997	+	1.34274i
$306$	−130.090	−	18.3555i	−0.425132	−	0.0599853i
$307$	−214.620	−	214.620i	−0.699088	−	0.699088i	0.265126	−	0.964214i	$-0.414586\pi$
$307$	−214.620	−	214.620i	−0.699088	−	0.699088i	−0.964214	+	0.265126i	$0.914586\pi$
$308$	24.8445	+	92.7209i	0.0806639	+	0.301042i
$309$	394.864	+	27.7199i	1.27788	+	0.0897086i
$310$	268.926	+	55.7173i	0.867502	+	0.179733i
$311$	47.5516	+	82.3617i	0.152899	+	0.264829i	0.932292	−	0.361707i	$-0.117806\pi$
$311$	47.5516	+	82.3617i	0.152899	+	0.264829i	−0.779393	+	0.626535i	$0.784472\pi$
$312$	39.8684	−	34.6379i	0.127783	−	0.111019i
$313$	120.559	+	449.931i	0.385172	+	1.43748i	0.837896	+	0.545830i	$0.183786\pi$
$313$	120.559	+	449.931i	0.385172	+	1.43748i	−0.452724	+	0.891651i	$0.649548\pi$
$314$		−	30.9723i		−	0.0986380i
$315$	126.828	−	353.508i	0.402630	−	1.12225i
$316$	−167.672			−0.530606
$317$	140.067	−	37.5308i	0.441852	−	0.118394i	−0.0310325	−	0.999518i	$-0.509880\pi$
$317$	140.067	−	37.5308i	0.441852	−	0.118394i	0.472884	+	0.881125i	$0.343213\pi$
$318$	−0.443993	+	1.28831i	−0.00139620	+	0.00405128i
$319$	−76.5715	+	44.2086i	−0.240036	+	0.138585i
$320$	−21.9579	−	33.4343i	−0.0686184	−	0.104482i
$321$	−373.601	−	252.145i	−1.16386	−	0.785499i
$322$	−450.632	+	120.747i	−1.39948	+	0.374989i
$323$	220.209	−	220.209i	0.681762	−	0.681762i
$324$	44.8234	−	155.676i	0.138344	−	0.480480i
$325$	−96.6749	+	121.928i	−0.297461	+	0.375163i
$326$	−51.4648	+	89.1397i	−0.157868	+	0.273435i
$327$	79.1084	+	407.572i	0.241922	+	1.24640i
$328$	−129.092	−	34.5900i	−0.393572	−	0.105457i
$329$	−477.421	+	275.639i	−1.45113	+	0.837809i
$330$	−59.6619	−	106.407i	−0.180794	−	0.322446i
$331$	221.369	−	383.422i	0.668788	−	1.15838i	−0.309455	−	0.950914i	$-0.600147\pi$
$331$	221.369	−	383.422i	0.668788	−	1.15838i	0.978243	−	0.207461i	$-0.0665200\pi$
$332$	17.0259	+	17.0259i	0.0512827	+	0.0512827i
$333$	273.618	+	116.320i	0.821676	+	0.349311i
$334$		−	193.796i		−	0.580228i
$335$	−172.836	−	522.768i	−0.515929	−	1.56050i
$336$	−7.01355	+	99.9063i	−0.0208737	+	0.297340i
$337$	−35.0491	+	130.805i	−0.104003	+	0.388145i	−0.998230	−	0.0594686i	$-0.981059\pi$
$337$	−35.0491	+	130.805i	−0.104003	+	0.388145i	0.894227	+	0.447614i	$0.147726\pi$
$338$	−177.939	−	47.6785i	−0.526446	−	0.141061i
$339$	417.104	+	29.2812i	1.23040	+	0.0863753i
$340$	−98.0037	+	32.4018i	−0.288246	+	0.0952993i
$341$	−223.356			−0.655004
$342$	230.934	+	306.808i	0.675245	+	0.897099i
$343$	−167.273	+	167.273i	−0.487676	+	0.487676i
$344$	26.5464	+	15.3266i	0.0771699	+	0.0445541i
$345$	517.148	−	289.963i	1.49898	−	0.840471i
$346$	127.356	+	220.587i	0.368081	+	0.637535i
$347$	−108.480	+	404.853i	−0.312623	+	1.16672i	0.613560	+	0.789648i	$0.289737\pi$
$347$	−108.480	+	404.853i	−0.312623	+	1.16672i	−0.926182	+	0.377076i	$0.876930\pi$
$348$	−90.5592	+	17.5773i	−0.260228	+	0.0505094i
$349$	206.863	+	119.432i	0.592731	+	0.342213i	0.766176	−	0.642630i	$-0.222157\pi$
$349$	206.863	+	119.432i	0.592731	+	0.342213i	−0.173446	+	0.984843i	$0.555490\pi$
$350$	−33.8620	−	293.127i	−0.0967485	−	0.837505i
$351$	159.869	−	51.7999i	0.455468	−	0.147578i
$352$	23.0030	+	23.0030i	0.0653494	+	0.0653494i
$353$	16.9753	+	63.3528i	0.0480887	+	0.179470i	0.985793	−	0.167965i	$-0.0537195\pi$
$353$	16.9753	+	63.3528i	0.0480887	+	0.179470i	−0.937704	+	0.347435i	$0.887053\pi$
$354$	−30.3282	+	44.9369i	−0.0856728	+	0.126940i
$355$	366.678	−	240.815i	1.03290	−	0.678351i
$356$	59.4813	+	103.025i	0.167082	+	0.289395i
$357$	244.342	+	84.2084i	0.684432	+	0.235878i
$358$	2.46253	+	9.19028i	0.00687857	+	0.0256712i
$359$			269.424i			0.750484i	0.926927	+	0.375242i	$0.122440\pi$
$359$			269.424i			0.750484i	−0.926927	+	0.375242i	$0.877560\pi$
$360$	−22.6780	−	125.243i	−0.0629945	−	0.347896i
$361$	−549.256			−1.52149
$362$	209.864	−	56.2328i	0.579734	−	0.155339i
$363$	−173.005	−	199.130i	−0.476598	−	0.548566i
$364$	−89.9744	+	51.9468i	−0.247183	+	0.142711i
$365$	22.7028	−	109.578i	0.0621995	−	0.300213i
$366$	24.3756	−	347.224i	0.0666000	−	0.948700i
$367$	−437.004	+	117.095i	−1.19075	+	0.319059i	−0.799181	−	0.601091i	$-0.794733\pi$
$367$	−437.004	+	117.095i	−1.19075	+	0.319059i	−0.391565	+	0.920150i	$0.628066\pi$
$368$	−111.797	+	111.797i	−0.303796	+	0.303796i
$369$	−334.964	−	261.997i	−0.907762	−	0.710020i
$370$	233.208	−	13.4254i	0.630292	−	0.0362850i
$371$	1.34030	−	2.32147i	0.00361268	−	0.00625734i
$372$	−220.320	−	75.9297i	−0.592259	−	0.204112i
$373$	−589.150	−	157.862i	−1.57949	−	0.423224i	−0.640723	−	0.767772i	$-0.721365\pi$
$373$	−589.150	−	157.862i	−1.57949	−	0.423224i	−0.938769	+	0.344548i	$0.888032\pi$
$374$	72.7007	−	41.9738i	0.194387	−	0.112229i
$375$	133.586	+	350.400i	0.356228	+	0.934399i
$376$	−93.4129	+	161.796i	−0.248439	+	0.430308i
$377$	−67.6669	−	67.6669i	−0.179488	−	0.179488i
$378$	−144.911	+	283.829i	−0.383363	+	0.750872i
$379$			444.508i			1.17284i	0.810006	+	0.586422i	$0.199464\pi$
$379$			444.508i			1.17284i	−0.810006	+	0.586422i	$0.800536\pi$
$380$	269.522	+	135.586i	0.709268	+	0.356805i
$381$	−235.291	−	158.800i	−0.617563	−	0.416797i
$382$	132.002	−	492.636i	0.345554	−	1.28962i
$383$	234.373	+	62.8001i	0.611940	+	0.163969i	0.551461	−	0.834201i	$-0.314071\pi$
$383$	234.373	+	62.8001i	0.611940	+	0.163969i	0.0604790	+	0.998169i	$0.480737\pi$
$384$	14.8705	+	30.5101i	0.0387252	+	0.0794535i
$385$	75.3310	+	227.849i	0.195665	+	0.591816i
$386$	331.723			0.859386
$387$	58.6572	+	77.9292i	0.151569	+	0.201368i
$388$	157.289	−	157.289i	0.405384	−	0.405384i
$389$	−565.614	−	326.557i	−1.45402	−	0.839479i	−0.455314	−	0.890331i	$-0.650473\pi$
$389$	−565.614	−	326.557i	−1.45402	−	0.839479i	−0.998706	+	0.0508516i	$0.983806\pi$
$390$	94.5293	−	92.1801i	0.242383	−	0.236359i
$391$	203.997	+	353.332i	0.521730	+	0.903663i
$392$	15.1212	−	56.4333i	0.0385746	−	0.143962i
$393$	362.067	+	416.740i	0.921289	+	1.06041i
$394$	−93.9921	−	54.2664i	−0.238559	−	0.137732i
$395$	−418.486	+	24.0916i	−1.05946	+	0.0609914i
$396$	38.7244	+	95.9972i	0.0977889	+	0.242417i
$397$	362.820	+	362.820i	0.913903	+	0.913903i	0.996577	−	0.0826735i	$-0.0263458\pi$
$397$	362.820	+	362.820i	0.913903	+	0.913903i	−0.0826735	+	0.996577i	$0.526346\pi$
$398$	−75.3938	−	281.373i	−0.189432	−	0.706968i
$399$	−330.964	−	679.048i	−0.829484	−	1.70187i
$400$	−59.6079	−	80.2926i	−0.149020	−	0.200731i
$401$	130.663	+	226.315i	0.325842	+	0.564375i	0.981682	−	0.190524i	$-0.0610188\pi$
$401$	130.663	+	226.315i	0.325842	+	0.564375i	−0.655840	+	0.754900i	$0.727685\pi$
$402$	89.0204	+	458.639i	0.221444	+	1.14089i
$403$	−62.5676	−	233.505i	−0.155255	−	0.579418i
$404$			184.705i			0.457191i
$405$	89.5052	−	394.986i	0.221000	−	0.975274i
$406$	181.471			0.446972
$407$	−183.504	+	49.1697i	−0.450869	+	0.120810i
$408$	85.9814	−	16.6887i	0.210739	−	0.0409037i
$409$	248.853	−	143.675i	0.608442	−	0.351284i	−0.163913	−	0.986475i	$-0.552412\pi$
$409$	248.853	−	143.675i	0.608442	−	0.351284i	0.772355	+	0.635191i	$0.219078\pi$
$410$	−327.166	−	67.7837i	−0.797965	−	0.165326i
$411$	−412.159	+	200.884i	−1.00282	+	0.488768i
$412$	−254.899	+	68.2999i	−0.618686	+	0.165776i
$413$	75.4114	−	75.4114i	0.182594	−	0.182594i
$414$	−466.556	+	188.204i	−1.12695	+	0.454600i
$415$	44.9406	+	40.0480i	0.108291	+	0.0965011i
$416$	−17.6045	+	30.4919i	−0.0423186	+	0.0732979i
$417$	−9.10954	+	7.91444i	−0.0218454	+	0.0189795i
$418$	−237.009	−	63.5064i	−0.567007	−	0.151929i
$419$	−172.948	+	99.8517i	−0.412764	+	0.238310i	−0.691977	−	0.721920i	$-0.743260\pi$
$419$	−172.948	+	99.8517i	−0.412764	+	0.238310i	0.279212	+	0.960229i	$0.409927\pi$
$420$	−3.15002	+	250.361i	−0.00750006	+	0.596097i
$421$	244.456	−	423.411i	0.580656	−	1.00573i	−0.414745	−	0.909937i	$-0.636129\pi$
$421$	244.456	−	423.411i	0.580656	−	1.00573i	0.995402	−	0.0957886i	$-0.0305373\pi$
$422$	−7.40876	−	7.40876i	−0.0175563	−	0.0175563i
$423$	−474.965	+	357.505i	−1.12285	+	0.845166i
$424$		−	0.908445i		−	0.00214256i
$425$	−239.949	+	94.9520i	−0.564585	+	0.223416i
$426$	−334.608	+	163.086i	−0.785466	+	0.382832i
$427$	−177.222	+	661.400i	−0.415039	+	1.54895i
$428$	290.246	+	77.7711i	0.678144	+	0.181708i
$429$	−60.0707	+	89.0060i	−0.140025	+	0.207473i
$430$	68.4586	+	34.4389i	0.159206	+	0.0800904i
$431$	504.045			1.16948			0.584739	−	0.811221i	$-0.301197\pi$
$431$	504.045			1.16948			0.584739	+	0.811221i	$0.301197\pi$
$432$	5.56391	+	107.857i	0.0128794	+	0.249668i
$433$	379.677	−	379.677i	0.876851	−	0.876851i	−0.116356	−	0.993208i	$-0.537121\pi$
$433$	379.677	−	379.677i	0.876851	−	0.876851i	0.993208	+	0.116356i	$0.0371214\pi$
$434$	397.008	+	229.212i	0.914764	+	0.528139i
$435$	−223.498	+	56.8824i	−0.513789	+	0.130764i
$436$	−138.393	−	239.703i	−0.317414	−	0.549778i
$437$	308.647	−	1151.89i	0.706286	−	2.63590i
$438$	−30.9386	+	89.7727i	−0.0706361	+	0.204960i
$439$	−285.924	−	165.078i	−0.651308	−	0.376033i	0.137649	−	0.990481i	$-0.456045\pi$
$439$	−285.924	−	165.078i	−0.651308	−	0.376033i	−0.788957	+	0.614448i	$0.789379\pi$
$440$	60.7176	+	54.1073i	0.137995	+	0.122971i
$441$	114.534	−	146.432i	0.259714	−	0.332045i
$442$	64.2463	+	64.2463i	0.145354	+	0.145354i
$443$	109.435	+	408.416i	0.247031	+	0.921932i	0.972352	+	0.233521i	$0.0750248\pi$
$443$	109.435	+	408.416i	0.247031	+	0.921932i	−0.725321	+	0.688411i	$0.758308\pi$
$444$	−197.725	−	13.8805i	−0.445326	−	0.0312624i
$445$	163.261	+	248.590i	0.366878	+	0.558628i
$446$	−97.7371	−	169.286i	−0.219141	−	0.379564i
$447$	−233.123	+	202.539i	−0.521527	+	0.453107i
$448$	−17.2809	−	64.4931i	−0.0385734	−	0.143958i
$449$		−	177.792i		−	0.395972i	−0.980205	−	0.197986i	$-0.936560\pi$
$449$		−	177.792i		−	0.395972i	0.980205	−	0.197986i	$-0.0634401\pi$
$450$	−74.5966	−	309.330i	−0.165770	−	0.687401i
$451$	271.728			0.602500
$452$	−269.255	+	72.1468i	−0.595698	+	0.159617i
$453$	−143.767	+	417.160i	−0.317367	+	0.920884i
$454$	−83.5227	+	48.2219i	−0.183971	+	0.106216i
$455$	−217.100	+	142.580i	−0.477144	+	0.313363i
$456$	−212.198	−	143.214i	−0.465347	−	0.314066i
$457$	831.978	−	222.928i	1.82052	−	0.487807i	0.823666	−	0.567075i	$-0.191925\pi$
$457$	831.978	−	222.928i	1.82052	−	0.487807i	0.996853	+	0.0792678i	$0.0252582\pi$
$458$	−197.199	+	197.199i	−0.430566	+	0.430566i
$459$	272.559	+	58.1677i	0.593811	+	0.126727i
$460$	−262.967	+	295.093i	−0.571666	+	0.641507i
$461$	59.9057	−	103.760i	0.129947	−	0.225075i	−0.793709	−	0.608298i	$-0.791853\pi$
$461$	59.9057	−	103.760i	0.129947	−	0.225075i	0.923656	+	0.383223i	$0.125186\pi$
$462$	−38.7997	−	199.899i	−0.0839820	−	0.432681i
$463$	−358.368	−	96.0243i	−0.774012	−	0.207396i	−0.149869	−	0.988706i	$-0.547885\pi$
$463$	−358.368	−	96.0243i	−0.774012	−	0.207396i	−0.624143	+	0.781310i	$0.714552\pi$
$464$	53.2602	−	30.7498i	0.114785	−	0.0662711i
$465$	−560.800	−	157.854i	−1.20602	−	0.339471i
$466$	47.1109	−	81.5984i	0.101096	−	0.175104i
$467$	−221.252	−	221.252i	−0.473772	−	0.473772i	0.429361	−	0.903133i	$-0.358739\pi$
$467$	−221.252	−	221.252i	−0.473772	−	0.473772i	−0.903133	+	0.429361i	$0.858739\pi$
$468$	−89.5115	+	67.3751i	−0.191264	+	0.143964i
$469$		−	919.061i		−	1.95962i
$470$	−209.899	+	417.243i	−0.446593	+	0.887751i
$471$	−4.60106	+	65.5410i	−0.00976870	+	0.139153i
$472$	9.35435	−	34.9109i	0.0198185	−	0.0739638i
$473$	−60.2003	−	16.1306i	−0.127273	−	0.0341028i
$474$	354.812	+	24.9083i	0.748548	+	0.0525491i
$475$	692.172	+	299.679i	1.45720	+	0.630903i
$476$	−172.297			−0.361969
$477$	1.13092	−	2.66024i	0.00237091	−	0.00557703i
$478$	3.59339	−	3.59339i	0.00751755	−	0.00751755i
$479$	466.040	+	269.068i	0.972943	+	0.561729i	0.900132	−	0.435617i	$-0.143470\pi$
$479$	466.040	+	269.068i	0.972943	+	0.561729i	0.0728106	+	0.997346i	$0.476803\pi$
$480$	41.4985	+	74.0126i	0.0864553	+	0.154193i
$481$	−102.808	−	178.068i	−0.213738	−	0.370205i
$482$	24.7563	−	92.3918i	0.0513616	−	0.191684i
$483$	971.526	−	188.570i	2.01144	−	0.390414i
$484$	152.297	+	87.9289i	0.314664	+	0.181671i
$485$	369.973	−	415.173i	0.762831	−	0.856026i
$486$	−117.977	+	322.768i	−0.242752	+	0.664132i
$487$	142.335	+	142.335i	0.292268	+	0.292268i	0.837976	−	0.545708i	$-0.183739\pi$
$487$	142.335	+	142.335i	0.292268	+	0.292268i	−0.545708	+	0.837976i	$0.683739\pi$
$488$	60.0596	+	224.146i	0.123073	+	0.459315i
$489$	122.147	−	180.984i	0.249790	−	0.370111i
$490$	29.6321	−	143.023i	0.0604737	−	0.291883i
$491$	−235.845	−	408.495i	−0.480335	−	0.831965i	0.519410	−	0.854525i	$-0.326152\pi$
$491$	−235.845	−	408.495i	−0.480335	−	0.831965i	−0.999745	+	0.0225601i	$0.992818\pi$
$492$	268.034	+	92.3733i	0.544784	+	0.187751i
$493$	−41.0749	−	153.294i	−0.0833163	−	0.310941i
$494$		−	265.568i		−	0.537587i
$495$	110.444	+	234.032i	0.223120	+	0.472793i
$496$	155.358			0.313222
$497$	707.303	−	189.521i	1.42315	−	0.381331i
$498$	−33.4994	−	38.5579i	−0.0672678	−	0.0774255i
$499$	−227.181	+	131.163i	−0.455273	+	0.262852i	−0.710055	−	0.704147i	$-0.751330\pi$
$499$	−227.181	+	131.163i	−0.455273	+	0.262852i	0.254782	+	0.966999i	$0.417996\pi$
$500$	−160.310	−	191.835i	−0.320620	−	0.383670i
$501$	−28.7892	+	410.095i	−0.0574634	+	0.818552i
$502$	21.8289	−	5.84904i	0.0434839	−	0.0116515i
$503$	92.4744	−	92.4744i	0.183846	−	0.183846i	−0.609184	−	0.793029i	$-0.708503\pi$
$503$	92.4744	−	92.4744i	0.183846	−	0.183846i	0.793029	+	0.609184i	$0.208503\pi$
$504$	29.6829	−	210.371i	0.0588947	−	0.417403i
$505$	26.5390	+	460.999i	0.0525525	+	0.912870i
$506$	160.729	−	278.390i	0.317646	−	0.550179i
$507$	369.455	+	127.327i	0.728709	+	0.251137i
$508$	182.795	+	48.9798i	0.359833	+	0.0964169i
$509$	379.182	−	218.921i	0.744955	−	0.430100i	−0.0789130	−	0.996882i	$-0.525145\pi$
$509$	379.182	−	218.921i	0.744955	−	0.430100i	0.823868	+	0.566781i	$0.191812\pi$
$510$	212.200	−	54.0069i	0.416079	−	0.105896i
$511$	93.3959	−	161.766i	0.182771	−	0.316568i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−443.104	−	683.546i	−0.863751	−	1.33245i
$514$			249.842i			0.486073i
$515$	−626.380	+	207.092i	−1.21627	+	0.402121i
$516$	−53.8984	−	36.3764i	−0.104454	−	0.0704968i
$517$	98.3134	−	366.910i	0.190161	−	0.709691i
$518$	376.630	+	100.918i	0.727085	+	0.194822i
$519$	−236.730	−	485.706i	−0.456128	−	0.935850i
$520$	−39.5574	+	78.6333i	−0.0760719	+	0.151218i
$521$	943.155			1.81028			0.905139	−	0.425115i	$-0.139766\pi$
$521$	943.155			1.81028			0.905139	+	0.425115i	$0.139766\pi$
$522$	194.245	−	23.7426i	0.372116	−	0.0454838i
$523$	217.654	−	217.654i	0.416165	−	0.416165i	−0.467715	−	0.883879i	$-0.654923\pi$
$523$	217.654	−	217.654i	0.416165	−	0.416165i	0.883879	+	0.467715i	$0.154923\pi$
$524$	−318.729	−	184.018i	−0.608261	−	0.351180i
$525$	28.1106	+	625.320i	0.0535440	+	1.19109i
$526$	−123.956	−	214.697i	−0.235657	−	0.408170i
$527$	103.762	−	387.245i	0.196892	−	0.734811i
$528$	−45.2598	−	52.0941i	−0.0857192	−	0.0986631i
$529$	894.876	+	516.657i	1.69164	+	0.976667i
$530$	−0.130528	−	2.26736i	−0.000246280	−	0.00427803i
$531$	70.8534	−	90.5861i	0.133434	−	0.170595i
$532$	356.103	+	356.103i	0.669367	+	0.669367i
$533$	76.1175	+	284.074i	0.142810	+	0.532973i
$534$	−110.565	−	226.848i	−0.207050	−	0.424809i
$535$	735.590	+	152.403i	1.37493	+	0.284865i
$536$	−155.733	−	269.737i	−0.290546	−	0.503241i
$537$	−3.84573	−	19.8135i	−0.00716152	−	0.0368966i
$538$	89.9943	+	335.863i	0.167276	+	0.624281i
$539$			118.788i			0.220385i
$540$	29.3840	+	268.396i	0.0544148	+	0.497030i
$541$	−249.489			−0.461162			−0.230581	−	0.973053i	$-0.574063\pi$
$541$	−249.489			−0.461162			−0.230581	+	0.973053i	$0.574063\pi$
$542$	−164.133	+	43.9792i	−0.302828	+	0.0811424i
$543$	−452.449	+	87.8189i	−0.833239	+	0.161729i
$544$	−50.5678	+	29.1953i	−0.0929555	+	0.0536679i
$545$	−379.851	−	578.383i	−0.696975	−	1.06125i
$546$	198.113	−	96.5591i	0.362844	−	0.176848i
$547$	−543.268	+	145.568i	−0.993178	+	0.266121i	−0.718585	−	0.695439i	$-0.755210\pi$
$547$	−543.268	+	145.568i	−0.993178	+	0.266121i	−0.274593	+	0.961561i	$0.588543\pi$
$548$	216.142	−	216.142i	0.394421	−	0.394421i
$549$	−103.163	+	731.145i	−0.187911	+	1.33178i
$550$	159.317	+	126.321i	0.289668	+	0.229674i
$551$	−231.934	+	401.721i	−0.420932	+	0.729076i
$552$	253.182	−	219.967i	0.458664	−	0.398490i
$553$	−675.854	−	181.094i	−1.22216	−	0.327476i
$554$	−542.541	+	313.236i	−0.979316	+	0.565408i
$555$	−495.489	−	6.23421i	−0.892773	−	0.0112328i
$556$	4.02247	−	6.96711i	0.00723465	−	0.0125308i
$557$	−268.053	−	268.053i	−0.481244	−	0.481244i	0.424285	−	0.905529i	$-0.360525\pi$
$557$	−268.053	−	268.053i	−0.481244	−	0.481244i	−0.905529	+	0.424285i	$0.860525\pi$
$558$	454.943	+	193.405i	0.815310	+	0.346604i
$559$		−	67.4543i		−	0.120670i
$560$	−52.3973	−	158.483i	−0.0935667	−	0.283006i
$561$	−160.078	+	78.0213i	−0.285344	+	0.139075i
$562$	−97.8105	+	365.034i	−0.174040	+	0.649526i
$563$	−644.580	−	172.715i	−1.14490	−	0.306776i	−0.363982	−	0.931406i	$-0.618583\pi$
$563$	−644.580	−	172.715i	−1.14490	−	0.306776i	−0.780920	+	0.624630i	$0.785250\pi$
$564$	221.708	−	328.501i	0.393099	−	0.582449i
$565$	−661.660	+	218.756i	−1.17108	+	0.387179i
$566$	−6.81604			−0.0120425
$567$	348.813	−	579.088i	0.615190	−	1.02132i
$568$	175.474	−	175.474i	0.308933	−	0.308933i
$569$	−222.641	−	128.542i	−0.391284	−	0.225908i	0.291432	−	0.956591i	$-0.405868\pi$
$569$	−222.641	−	128.542i	−0.391284	−	0.225908i	−0.682716	+	0.730684i	$0.739201\pi$
$570$	−550.197	−	326.954i	−0.965257	−	0.573603i
$571$	438.771	+	759.974i	0.768426	+	1.33095i	0.938416	+	0.345507i	$0.112293\pi$
$571$	438.771	+	759.974i	0.768426	+	1.33095i	−0.169991	+	0.985446i	$0.554374\pi$
$572$	18.5281	−	69.1477i	0.0323917	−	0.120888i
$573$	−352.513	+	1022.86i	−0.615206	+	1.78510i
$574$	−482.985	−	278.852i	−0.841438	−	0.485805i
$575$	−613.930	+	774.297i	−1.06770	+	1.34660i
$576$	−26.9352	−	66.7720i	−0.0467625	−	0.115924i
$577$	−687.574	−	687.574i	−1.19164	−	1.19164i	−0.976608	−	0.215027i	$-0.931016\pi$
$577$	−687.574	−	687.574i	−1.19164	−	1.19164i	−0.215027	−	0.976608i	$-0.568984\pi$
$578$	−66.7828	−	249.237i	−0.115541	−	0.431206i
$579$	−701.963	−	49.2787i	−1.21237	−	0.0851101i
$580$	128.512	−	84.4000i	0.221573	−	0.145517i
$581$	50.2393	+	87.0170i	0.0864704	+	0.149771i
$582$	−356.207	+	309.476i	−0.612040	+	0.531745i
$583$	0.478051	+	1.78411i	0.000819985	+	0.00306023i
$584$		−	63.3029i		−	0.108395i
$585$	−213.728	+	181.021i	−0.365347	+	0.309437i
$586$	109.796			0.187365
$587$	93.9197	−	25.1657i	0.159999	−	0.0428717i	−0.177930	−	0.984043i	$-0.556940\pi$
$587$	93.9197	−	25.1657i	0.159999	−	0.0428717i	0.337930	+	0.941171i	$0.390273\pi$
$588$	−40.3816	+	117.173i	−0.0686762	+	0.199273i
$589$	−1014.81	+	585.903i	−1.72294	+	0.994742i
$590$	18.3311	−	88.4771i	0.0310697	−	0.149961i
$591$	190.836	+	128.797i	0.322904	+	0.217930i
$592$	127.638	−	34.2006i	0.215605	−	0.0577712i
$593$	−196.612	+	196.612i	−0.331555	+	0.331555i	−0.853177	−	0.521622i	$-0.825327\pi$
$593$	−196.612	+	196.612i	−0.331555	+	0.331555i	0.521622	+	0.853177i	$0.325327\pi$
$594$	−67.6844	−	208.894i	−0.113947	−	0.351673i
$595$	−430.031	+	24.7562i	−0.722741	+	0.0416071i
$596$	102.939	−	178.296i	0.172717	−	0.299154i
$597$	117.743	+	606.618i	0.197224	+	1.01611i
$598$	336.064	+	90.0481i	0.561980	+	0.150582i
$599$	−95.2202	+	54.9754i	−0.158965	+	0.0917787i	−0.577372	−	0.816481i	$-0.695922\pi$
$599$	−95.2202	+	54.9754i	−0.158965	+	0.0917787i	0.418407	+	0.908260i	$0.362589\pi$
$600$	114.209	+	178.763i	0.190349	+	0.297939i
$601$	24.2179	−	41.9466i	0.0402960	−	0.0697946i	−0.845174	−	0.534491i	$-0.820503\pi$
$601$	24.2179	−	41.9466i	0.0402960	−	0.0697946i	0.885470	+	0.464697i	$0.153837\pi$
$602$	90.4503	+	90.4503i	0.150250	+	0.150250i
$603$	−120.245	−	983.756i	−0.199411	−	1.63144i
$604$		−	294.159i		−	0.487019i
$605$	392.748	+	197.576i	0.649170	+	0.326572i
$606$	27.4386	−	390.856i	0.0452783	−	0.644978i
$607$	33.6276	−	125.500i	0.0553997	−	0.206754i	−0.932678	−	0.360710i	$-0.882535\pi$
$607$	33.6276	−	125.500i	0.0553997	−	0.206754i	0.988078	+	0.153955i	$0.0492012\pi$
$608$	164.854	+	44.1726i	0.271142	+	0.0726523i
$609$	−384.012	−	26.9581i	−0.630562	−	0.0442662i
$610$	182.107	+	550.808i	0.298536	+	0.902964i
$611$	411.122			0.672868
$612$	−184.425	+	22.5423i	−0.301349	+	0.0368339i
$613$	68.4305	−	68.4305i	0.111632	−	0.111632i	−0.649084	−	0.760716i	$-0.724848\pi$
$613$	68.4305	−	68.4305i	0.111632	−	0.111632i	0.760716	+	0.649084i	$0.224848\pi$
$614$	−371.733	−	214.620i	−0.605428	−	0.349544i
$615$	682.249	+	192.040i	1.10935	+	0.312260i
$616$	67.8764	+	117.565i	0.110189	+	0.190853i
$617$	−239.548	+	894.007i	−0.388247	+	1.44896i	0.444737	+	0.895661i	$0.353297\pi$
$617$	−239.548	+	894.007i	−0.388247	+	1.44896i	−0.832984	+	0.553297i	$0.813370\pi$
$618$	549.540	−	106.664i	0.889224	−	0.172596i
$619$	−352.357	−	203.433i	−0.569235	−	0.328648i	0.187609	−	0.982244i	$-0.439926\pi$
$619$	−352.357	−	203.433i	−0.569235	−	0.328648i	−0.756844	+	0.653596i	$0.773260\pi$
$620$	387.753	−	22.3224i	0.625409	−	0.0360038i
$621$	1015.24	−	328.953i	1.63485	−	0.529715i
$622$	95.1032	+	95.1032i	0.152899	+	0.152899i
$623$	128.486	+	479.517i	0.206238	+	0.769690i
$624$	41.7828	−	61.9091i	0.0669597	−	0.0992133i
$625$	−427.676	−	455.761i	−0.684282	−	0.729217i
$626$	329.373	+	570.490i	0.526154	+	0.911326i
$627$	492.104	+	169.595i	0.784855	+	0.270487i
$628$	−11.3367	−	42.3090i	−0.0180520	−	0.0673710i
$629$		−	340.993i		−	0.542119i
$630$	43.8578	−	529.323i	0.0696156	−	0.840196i
$631$	39.5574			0.0626900			0.0313450	−	0.999509i	$-0.490021\pi$
$631$	39.5574			0.0626900			0.0313450	+	0.999509i	$0.490021\pi$
$632$	−229.044	+	61.3721i	−0.362411	+	0.0971077i
$633$	14.5772	+	16.7784i	0.0230287	+	0.0265061i
$634$	177.598	−	102.536i	0.280123	−	0.161729i
$635$	463.270	+	95.9824i	0.729558	+	0.151153i
$636$	−0.134953	+	1.92237i	−0.000212190	+	0.00302260i
$637$	−124.185	+	33.2753i	−0.194953	+	0.0522375i
$638$	−88.4171	+	88.4171i	−0.138585	+	0.138585i
$639$	732.296	−	295.402i	1.14600	−	0.462287i
$640$	−42.2328	−	37.6349i	−0.0659888	−	0.0588046i
$641$	−416.098	+	720.703i	−0.649139	+	1.12434i	0.334190	+	0.942506i	$0.391537\pi$
$641$	−416.098	+	720.703i	−0.649139	+	1.12434i	−0.983329	+	0.181836i	$0.941796\pi$
$642$	−602.640	−	207.690i	−0.938691	−	0.323504i
$643$	892.066	+	239.028i	1.38735	+	0.371739i	0.873785	−	0.486312i	$-0.161658\pi$
$643$	892.066	+	239.028i	1.38735	+	0.371739i	0.513564	+	0.858051i	$0.328325\pi$
$644$	−571.379	+	329.886i	−0.887234	+	0.512245i
$645$	−139.750	−	83.0463i	−0.216667	−	0.128754i
$646$	220.209	−	381.413i	0.340881	−	0.590423i
$647$	−4.82533	−	4.82533i	−0.00745800	−	0.00745800i	0.703368	−	0.710826i	$-0.251679\pi$
$647$	−4.82533	−	4.82533i	−0.00745800	−	0.00745800i	−0.710826	+	0.703368i	$0.751679\pi$
$648$	4.24865	−	229.063i	0.00655655	−	0.353493i
$649$			73.4847i			0.113228i
$650$	−87.4317	+	201.942i	−0.134510	+	0.310680i
$651$	−806.062	−	544.016i	−1.23819	−	0.835663i
$652$	−37.6749	+	140.605i	−0.0577836	+	0.215651i
$653$	−179.600	−	48.1238i	−0.275039	−	0.0736965i	0.118663	−	0.992935i	$-0.462139\pi$
$653$	−179.600	−	48.1238i	−0.275039	−	0.0736965i	−0.393702	+	0.919238i	$0.628806\pi$
$654$	257.246	+	527.798i	0.393342	+	0.807030i
$655$	−821.946	−	413.489i	−1.25488	−	0.631281i
$656$	−189.003			−0.288115
$657$	78.8057	−	185.373i	0.119948	−	0.282151i
$658$	−551.279	+	551.279i	−0.837809	+	0.837809i
$659$	274.113	+	158.259i	0.415953	+	0.240151i	0.693344	−	0.720606i	$-0.256137\pi$
$659$	274.113	+	158.259i	0.415953	+	0.240151i	−0.277391	+	0.960757i	$0.589470\pi$
$660$	−120.447	−	123.517i	−0.182496	−	0.187147i
$661$	−435.173	−	753.742i	−0.658356	−	1.14031i	−0.981041	−	0.193800i	$-0.937919\pi$
$661$	−435.173	−	753.742i	−0.658356	−	1.14031i	0.322685	−	0.946506i	$-0.395414\pi$
$662$	162.053	−	604.791i	0.244793	−	0.913582i
$663$	−126.408	−	145.496i	−0.190661	−	0.219451i
$664$	29.4897	+	17.0259i	0.0444121	+	0.0256414i
$665$	939.953	+	837.621i	1.41346	+	1.25958i
$666$	416.345	+	58.7455i	0.625143	+	0.0882064i
$667$	−429.716	−	429.716i	−0.644251	−	0.644251i
$668$	−70.9344	−	264.731i	−0.106189	−	0.396303i
$669$	181.675	+	372.747i	0.271561	+	0.557170i
$670$	−427.445	−	650.852i	−0.637978	−	0.971420i
$671$	−235.904	−	408.598i	−0.351571	−	0.608939i
$672$	26.9876	+	139.042i	0.0401601	+	0.206907i
$673$	65.2386	+	243.474i	0.0969371	+	0.361774i	0.997306	−	0.0733532i	$-0.0233700\pi$
$673$	65.2386	+	243.474i	0.0969371	+	0.361774i	−0.900369	+	0.435127i	$0.856703\pi$
$674$			191.512i			0.284142i
$675$	111.903	+	665.660i	0.165782	+	0.986162i
$676$	−260.520			−0.385385
$677$	291.869	−	78.2062i	0.431122	−	0.115519i	−0.0367309	−	0.999325i	$-0.511694\pi$
$677$	291.869	−	78.2062i	0.431122	−	0.115519i	0.467853	+	0.883806i	$0.345028\pi$
$678$	580.493	−	112.672i	0.856184	−	0.166183i
$679$	803.884	−	464.123i	1.18392	−	0.683539i
$680$	−122.016	+	80.1335i	−0.179435	+	0.117843i
$681$	183.907	−	89.6353i	0.270054	−	0.131623i
$682$	−305.111	+	81.7541i	−0.447376	+	0.119874i
$683$	−56.0495	+	56.0495i	−0.0820637	+	0.0820637i	−0.746947	−	0.664883i	$-0.768481\pi$
$683$	−56.0495	+	56.0495i	−0.0820637	+	0.0820637i	0.664883	+	0.746947i	$0.268481\pi$
$684$	427.761	+	334.580i	0.625381	+	0.489152i
$685$	508.407	−	570.519i	0.742200	−	0.832874i
$686$	−167.273	+	289.725i	−0.243838	+	0.422340i
$687$	446.590	−	388.001i	0.650059	−	0.564776i
$688$	41.8730	+	11.2198i	0.0608620	+	0.0163079i
$689$	−1.73126	+	0.999546i	−0.00251272	+	0.00145072i
$690$	600.304	−	585.386i	0.870006	−	0.848385i
$691$	−15.4812	+	26.8142i	−0.0224041	+	0.0388050i	−0.877010	−	0.480472i	$-0.840465\pi$
$691$	−15.4812	+	26.8142i	−0.0224041	+	0.0388050i	0.854606	+	0.519277i	$0.173799\pi$
$692$	254.712	+	254.712i	0.368081	+	0.368081i
$693$	52.4088	+	428.772i	0.0756260	+	0.618718i
$694$			592.746i			0.854101i
$695$	9.03848	−	17.9670i	0.0130050	−	0.0258517i
$696$	−117.273	+	57.1580i	−0.168495	+	0.0821235i
$697$	−126.233	+	471.109i	−0.181109	+	0.675910i
$698$	326.295	+	87.4306i	0.467472	+	0.125259i
$699$	−111.814	+	165.673i	−0.159962	+	0.237014i
$700$	−153.548	−	388.024i	−0.219355	−	0.554321i
$701$	395.892			0.564753			0.282376	−	0.959304i	$-0.408877\pi$
$701$	395.892			0.564753			0.282376	+	0.959304i	$0.408877\pi$
$702$	199.425	−	129.276i	0.284082	−	0.184154i
$703$	−704.764	+	704.764i	−1.00251	+	1.00251i
$704$	39.8424	+	23.0030i	0.0565943	+	0.0326747i
$705$	506.153	−	851.752i	0.717947	−	1.20816i
$706$	46.3775	+	80.3281i	0.0656904	+	0.113779i
$707$	−199.491	+	744.512i	−0.282166	+	1.05306i
$708$	−24.9810	+	72.4858i	−0.0352839	+	0.102381i
$709$	−315.081	−	181.912i	−0.444403	−	0.256576i	0.261061	−	0.965322i	$-0.415928\pi$
$709$	−315.081	−	181.912i	−0.444403	−	0.256576i	−0.705463	+	0.708746i	$0.749261\pi$
$710$	412.747	−	463.172i	0.581334	−	0.652355i
$711$	−747.122	−	105.417i	−1.05080	−	0.148266i
$712$	118.963	+	118.963i	0.167082	+	0.167082i
$713$	−397.333	−	1482.87i	−0.557269	−	2.07976i
$714$	364.600	+	25.5954i	0.510644	+	0.0358479i
$715$	36.3082	−	175.246i	0.0507807	−	0.245099i
$716$	6.72775	+	11.6528i	0.00939630	+	0.0162749i
$717$	−8.13782	+	7.07020i	−0.0113498	+	0.00986081i
$718$	98.6160	+	368.040i	0.137348	+	0.512590i
$719$		−	509.086i		−	0.708048i	−0.935236	−	0.354024i	$-0.884813\pi$
$719$		−	509.086i		−	0.708048i	0.935236	−	0.354024i	$-0.115187\pi$
$720$	−76.8207	−	162.784i	−0.106695	−	0.226089i
$721$	−1101.22			−1.52735
$722$	−750.298	+	201.042i	−1.03919	+	0.278451i
$723$	−66.1123	+	191.834i	−0.0914416	+	0.265330i
$724$	266.096	−	153.631i	0.367536	−	0.212197i
$725$	308.622	−	229.116i	0.425686	−	0.316022i
$726$	−309.216	−	208.692i	−0.425917	−	0.287454i
$727$	407.908	−	109.299i	0.561084	−	0.150342i	0.0328794	−	0.999459i	$-0.489532\pi$
$727$	407.908	−	109.299i	0.561084	−	0.150342i	0.528204	+	0.849117i	$0.322866\pi$
$728$	−103.894	+	103.894i	−0.142711	+	0.142711i
$729$	297.602	−	665.488i	0.408233	−	0.912878i
$730$	−9.09557	−	157.996i	−0.0124597	−	0.216432i
$731$	55.9332	−	96.8791i	0.0765159	−	0.132529i
$732$	−93.7952	−	483.239i	−0.128136	−	0.660163i
$733$	750.335	+	201.052i	1.02365	+	0.274286i	0.731322	−	0.682032i	$-0.238904\pi$
$733$	750.335	+	201.052i	1.02365	+	0.274286i	0.292328	+	0.956318i	$0.405570\pi$
$734$	−554.099	+	319.909i	−0.754903	+	0.435843i
$735$	−83.9514	+	298.250i	−0.114220	+	0.405782i
$736$	−111.797	+	193.638i	−0.151898	+	0.263095i
$737$	447.790	+	447.790i	0.607585	+	0.607585i
$738$	−553.467	−	235.290i	−0.749956	−	0.318821i
$739$			365.394i			0.494444i	0.968959	+	0.247222i	$0.0795176\pi$
$739$			365.394i			0.494444i	−0.968959	+	0.247222i	$0.920482\pi$
$740$	313.654	−	103.700i	0.423857	−	0.140135i
$741$	−39.4512	+	561.972i	−0.0532404	+	0.758397i
$742$	0.981170	−	3.66178i	0.00132233	−	0.00493501i
$743$	587.633	+	157.456i	0.790892	+	0.211919i	0.631581	−	0.775310i	$-0.282406\pi$
$743$	587.633	+	157.456i	0.790892	+	0.211919i	0.159311	+	0.987229i	$0.449073\pi$
$744$	−328.755	−	23.0790i	−0.441875	−	0.0310202i
$745$	231.304	−	459.793i	0.310476	−	0.617172i
$746$	−862.576			−1.15627
$747$	65.1605	+	86.5693i	0.0872296	+	0.115889i
$748$	83.9476	−	83.9476i	0.112229	−	0.112229i
$749$	1085.93	+	626.962i	1.44984	+	0.837066i
$750$	310.736	+	429.759i	0.414315	+	0.573012i
$751$	404.776	+	701.092i	0.538983	+	0.933545i	0.998959	+	0.0456141i	$0.0145245\pi$
$751$	404.776	+	701.092i	0.538983	+	0.933545i	−0.459977	+	0.887931i	$0.652142\pi$
$752$	−68.3830	+	255.209i	−0.0909348	+	0.339373i
$753$	−47.0614	+	9.13447i	−0.0624985	+	0.0121308i
$754$	−117.202	−	67.6669i	−0.155441	−	0.0897439i
$755$	−42.2658	−	734.183i	−0.0559812	−	0.972428i
$756$	−94.0638	+	440.759i	−0.124423	+	0.583015i
$757$	−491.291	−	491.291i	−0.648997	−	0.648997i	0.303753	−	0.952751i	$-0.401760\pi$
$757$	−491.291	−	491.291i	−0.648997	−	0.648997i	−0.952751	+	0.303753i	$0.901760\pi$
$758$	162.701	+	607.209i	0.214645	+	0.801068i
$759$	−381.476	+	565.229i	−0.502604	+	0.744702i
$760$	417.802	+	86.5621i	0.549739	+	0.113898i
$761$	188.782	+	326.981i	0.248072	+	0.429673i	0.962991	−	0.269535i	$-0.0868698\pi$
$761$	188.782	+	326.981i	0.248072	+	0.429673i	−0.714919	+	0.699207i	$0.753537\pi$
$762$	−379.539	−	130.802i	−0.498082	−	0.171656i
$763$	−298.943	−	1115.67i	−0.391800	−	1.46222i
$764$		−	721.270i		−	0.944070i
$765$	−457.063	+	82.7616i	−0.597467	+	0.108185i
$766$	343.146			0.447971
$767$	−76.8238	+	20.5849i	−0.100161	+	0.0268382i
$768$	31.4809	+	36.2347i	0.0409908	+	0.0471805i
$769$	1249.73	−	721.531i	1.62513	−	0.938271i	0.639617	−	0.768694i	$-0.279093\pi$
$769$	1249.73	−	721.531i	1.62513	−	0.938271i	0.985517	−	0.169577i	$-0.0542402\pi$
$770$	186.303	+	283.675i	0.241952	+	0.368409i
$771$	37.1149	−	528.693i	0.0481387	−	0.685724i
$772$	453.142	−	121.419i	0.586972	−	0.157279i
$773$	369.006	−	369.006i	0.477369	−	0.477369i	−0.426920	−	0.904289i	$-0.640402\pi$
$773$	369.006	−	369.006i	0.477369	−	0.477369i	0.904289	+	0.426920i	$0.140402\pi$
$774$	108.651	+	84.9833i	0.140376	+	0.109798i
$775$	964.574	−	111.427i	1.24461	−	0.143777i
$776$	157.289	−	272.433i	0.202692	−	0.351073i
$777$	−782.000	−	269.503i	−1.00643	−	0.346851i
$778$	−892.171	−	239.057i	−1.14675	−	0.307271i
$779$	1234.59	−	712.789i	1.58484	−	0.915005i
$780$	95.3891	−	160.520i	0.122294	−	0.205795i
$781$	−252.277	+	436.956i	−0.323017	+	0.559483i
$782$	407.993	+	407.993i	0.521730	+	0.521730i
$783$	−414.571	+	21.3861i	−0.529465	+	0.0273131i
$784$		−	82.6240i		−	0.105388i
$785$	−34.3739	−	103.969i	−0.0437884	−	0.132444i
$786$	647.130	+	436.752i	0.823320	+	0.555664i
$787$	298.330	−	1113.38i	0.379072	−	1.41472i	−0.468230	−	0.883607i	$-0.655108\pi$
$787$	298.330	−	1113.38i	0.379072	−	1.41472i	0.847302	−	0.531111i	$-0.178225\pi$
$788$	−148.259	−	39.7258i	−0.188145	−	0.0504134i
$789$	230.410	+	472.738i	0.292028	+	0.599161i
$790$	−562.845	+	186.086i	−0.712461	+	0.235552i
$791$	−1163.24			−1.47060
$792$	88.0359	+	116.961i	0.111156	+	0.147677i
$793$	361.082	−	361.082i	0.455336	−	0.455336i
$794$	628.422	+	362.820i	0.791463	+	0.456952i
$795$	−0.0606120	+	4.81738i	−7.62415e−5	+	0.00605959i
$796$	−205.980	−	356.767i	−0.258768	−	0.448200i
$797$	−400.142	+	1493.35i	−0.502061	+	1.87372i	−0.0158493	+	0.999874i	$0.505045\pi$
$797$	−400.142	+	1493.35i	−0.502061	+	1.87372i	−0.486211	+	0.873841i	$0.661621\pi$
$798$	−700.654	−	806.455i	−0.878013	−	1.01060i
$799$	590.461	+	340.903i	0.739000	+	0.426662i
$800$	−110.815	−	87.8637i	−0.138519	−	0.109830i
$801$	200.268	+	496.461i	0.250022	+	0.619801i
$802$	261.326	+	261.326i	0.325842	+	0.325842i
$803$	33.3119	+	124.322i	0.0414843	+	0.154822i
$804$	289.478	+	593.929i	0.360047	+	0.738717i
$805$	−1378.69	+	905.449i	−1.71265	+	1.12478i
$806$	−170.938	−	296.073i	−0.212082	−	0.367336i
$807$	−140.544	−	724.093i	−0.174156	−	0.897266i
$808$	67.6067	+	252.312i	0.0836717	+	0.312267i
$809$		−	132.217i		−	0.163433i	−0.996656	−	0.0817163i	$-0.973960\pi$
$809$		−	132.217i		−	0.163433i	0.996656	−	0.0817163i	$-0.0260401\pi$
$810$	−22.3085	−	572.322i	−0.0275414	−	0.706570i
$811$	99.9069			0.123190			0.0615949	−	0.998101i	$-0.480381\pi$
$811$	99.9069			0.123190			0.0615949	+	0.998101i	$0.480381\pi$
$812$	247.893	−	66.4228i	0.305287	−	0.0818015i
$813$	353.856	−	68.6824i	0.435248	−	0.0844802i
$814$	−232.674	+	134.334i	−0.285840	+	0.165030i
$815$	−73.8290	+	356.344i	−0.0905877	+	0.437231i
$816$	111.344	−	54.2686i	0.136451	−	0.0665056i
$817$	−315.832	+	84.6270i	−0.386575	+	0.103583i
$818$	287.350	−	287.350i	0.351284	−	0.351284i
$819$	−433.573	+	174.900i	−0.529394	+	0.213553i
$820$	−471.727	+	27.1566i	−0.575277	+	0.0331178i
$821$	−300.172	+	519.913i	−0.365618	+	0.633268i	−0.988875	−	0.148748i	$-0.952476\pi$
$821$	−300.172	+	519.913i	−0.365618	+	0.633268i	0.623257	+	0.782017i	$0.285809\pi$
$822$	−489.490	+	425.273i	−0.595487	+	0.517364i
$823$	101.960	+	27.3202i	0.123889	+	0.0331959i	0.320231	−	0.947340i	$-0.396240\pi$
$823$	101.960	+	27.3202i	0.123889	+	0.0331959i	−0.196342	+	0.980535i	$0.562906\pi$
$824$	−323.198	+	186.599i	−0.392231	+	0.226455i
$825$	−318.368	−	290.976i	−0.385901	−	0.352698i
$826$	75.4114	−	130.616i	0.0912971	−	0.158131i
$827$	199.922	+	199.922i	0.241743	+	0.241743i	0.817571	−	0.575828i	$-0.195320\pi$
$827$	199.922	+	199.922i	0.241743	+	0.241743i	−0.575828	+	0.817571i	$0.695320\pi$
$828$	−568.439	+	427.863i	−0.686521	+	0.516743i
$829$			444.676i			0.536400i	0.963363	+	0.268200i	$0.0864288\pi$
$829$			444.676i			0.536400i	−0.963363	+	0.268200i	$0.913571\pi$
$830$	76.0486	+	38.2571i	0.0916248	+	0.0460929i
$831$	1194.61	−	582.246i	1.43756	−	0.700657i
$832$	−12.8874	+	48.0964i	−0.0154897	+	0.0578082i
$833$	−205.949	−	55.1837i	−0.247237	−	0.0662470i
$834$	−9.54698	+	14.1456i	−0.0114472	+	0.0169612i
$835$	−215.080	−	650.541i	−0.257581	−	0.779091i
$836$	−347.005			−0.415078
$837$	−933.979	−	476.850i	−1.11586	−	0.569714i
$838$	−199.703	+	199.703i	−0.238310	+	0.238310i
$839$	−795.475	−	459.268i	−0.948123	−	0.547399i	−0.0556257	−	0.998452i	$-0.517715\pi$
$839$	−795.475	−	459.268i	−0.948123	−	0.547399i	−0.892497	+	0.451053i	$0.851049\pi$
$840$	87.3354	+	343.152i	0.103971	+	0.408514i
$841$	−302.306	−	523.610i	−0.359461	−	0.622604i
$842$	178.954	−	667.867i	0.212535	−	0.793191i
$843$	261.205	−	757.922i	0.309852	−	0.899077i
$844$	−12.8323	−	7.40876i	−0.0152042	−	0.00877815i
$845$	−650.224	+	37.4324i	−0.769496	+	0.0442987i
$846$	−517.958	+	662.210i	−0.612244	+	0.782755i
$847$	518.914	+	518.914i	0.612650	+	0.612650i
$848$	−0.332514	−	1.24096i	−0.000392116	−	0.00146339i
$849$	14.4235	+	1.01255i	0.0169888	+	0.00119264i
$850$	−293.021	+	217.534i	−0.344731	+	0.255923i
$851$	−652.877	−	1130.82i	−0.767188	−	1.32881i
$852$	−397.390	+	345.255i	−0.466420	+	0.405229i
$853$	10.2946	+	38.4199i	0.0120687	+	0.0450409i	0.971698	−	0.236228i	$-0.0759113\pi$
$853$	10.2946	+	38.4199i	0.0120687	+	0.0450409i	−0.959629	+	0.281269i	$0.909245\pi$
$854$			968.357i			1.13391i
$855$	1115.71	+	773.605i	1.30492	+	0.904801i
$856$	424.949			0.496436
$857$	168.243	−	45.0806i	0.196316	−	0.0526028i	−0.159321	−	0.987227i	$-0.550930\pi$
$857$	168.243	−	45.0806i	0.196316	−	0.0526028i	0.355637	+	0.934624i	$0.384264\pi$
$858$	−49.4796	+	143.572i	−0.0576685	+	0.167333i
$859$	−1152.81	+	665.578i	−1.34204	+	0.774829i	−0.987107	−	0.160062i	$-0.948831\pi$
$859$	−1152.81	+	665.578i	−1.34204	+	0.774829i	−0.354936	+	0.934891i	$0.615497\pi$
$860$	106.122	+	21.9868i	0.123397	+	0.0255660i
$861$	980.627	+	661.831i	1.13894	+	0.768677i
$862$	688.539	−	184.493i	0.798769	−	0.214029i
$863$	−980.185	+	980.185i	−1.13579	+	1.13579i	−0.146591	+	0.989197i	$0.546830\pi$
$863$	−980.185	+	980.185i	−1.13579	+	1.13579i	−0.989197	+	0.146591i	$0.953170\pi$
$864$	47.0787	+	145.298i	0.0544892	+	0.168169i
$865$	672.325	+	599.129i	0.777254	+	0.692635i
$866$	379.677	−	657.619i	0.438426	−	0.759376i
$867$	104.295	+	537.334i	0.120294	+	0.619762i
$868$	626.220	+	167.795i	0.721452	+	0.193312i
$869$	417.527	−	241.059i	0.480468	−	0.277399i
$870$	−284.484	+	159.509i	−0.326993	+	0.183344i
$871$	−342.700	+	593.574i	−0.393456	+	0.681486i
$872$	−276.785	−	276.785i	−0.317414	−	0.317414i
$873$	799.748	−	601.969i	0.916092	−	0.689541i
$874$		−	1686.48i		−	1.92961i
$875$	−438.989	−	946.395i	−0.501701	−	1.08159i
$876$	−9.40389	+	133.956i	−0.0107350	+	0.152918i
$877$	−326.118	+	1217.09i	−0.371856	+	1.38779i	0.486027	+	0.873944i	$0.338446\pi$
$877$	−326.118	+	1217.09i	−0.371856	+	1.38779i	−0.857884	+	0.513844i	$0.828221\pi$
$878$	−451.003	−	120.846i	−0.513670	−	0.137638i
$879$	−232.340	−	16.3106i	−0.264324	−	0.0185559i
$880$	102.746	+	51.6878i	0.116757	+	0.0587361i
$881$	−482.151			−0.547277			−0.273639	−	0.961833i	$-0.588227\pi$
$881$	−482.151			−0.547277			−0.273639	+	0.961833i	$0.588227\pi$
$882$	102.859	−	241.952i	0.116620	−	0.274322i
$883$	−20.8159	+	20.8159i	−0.0235740	+	0.0235740i	−0.718796	−	0.695222i	$-0.755306\pi$
$883$	−20.8159	+	20.8159i	−0.0235740	+	0.0235740i	0.695222	+	0.718796i	$0.255306\pi$
$884$	111.278	+	64.2463i	0.125880	+	0.0726768i
$885$	−51.9343	+	184.504i	−0.0586828	+	0.208480i
$886$	298.981	+	517.851i	0.337451	+	0.584482i
$887$	−31.4487	+	117.368i	−0.0354552	+	0.132320i	−0.981385	−	0.192051i	$-0.938486\pi$
$887$	−31.4487	+	117.368i	−0.0354552	+	0.132320i	0.945930	+	0.324371i	$0.105153\pi$
$888$	−275.177	+	53.4111i	−0.309885	+	0.0601476i
$889$	683.912	+	394.857i	0.769305	+	0.444159i
$890$	314.008	+	279.822i	0.352818	+	0.314407i
$891$	112.196	+	452.097i	0.125921	+	0.507404i
$892$	−195.474	−	195.474i	−0.219141	−	0.219141i
$893$	−515.786	−	1924.94i	−0.577588	−	2.15559i
$894$	−244.317	+	362.002i	−0.273286	+	0.404924i
$895$	18.4659	+	28.1172i	0.0206323	+	0.0314159i
$896$	−47.2122	−	81.7739i	−0.0526922	−	0.0912656i
$897$	−697.772	−	240.476i	−0.777896	−	0.268089i
$898$	−65.0762	−	242.868i	−0.0724679	−	0.270454i
$899$			597.153i			0.664242i
$900$	−215.124	−	395.249i	−0.239026	−	0.439166i
$901$	−3.31530			−0.00367957
$902$	371.187	−	99.4592i	0.411515	−	0.110265i
$903$	−177.966	−	204.840i	−0.197083	−	0.226844i
$904$	−341.402	+	197.109i	−0.377657	+	0.218041i
$905$	642.067	−	421.676i	0.709466	−	0.465940i
$906$	−43.6985	+	622.474i	−0.0482323	+	0.687058i
$907$	1106.27	−	296.423i	1.21970	−	0.326817i	0.409138	−	0.912472i	$-0.365829\pi$
$907$	1106.27	−	296.423i	1.21970	−	0.326817i	0.810560	+	0.585655i	$0.199163\pi$
$908$	−96.4437	+	96.4437i	−0.106216	+	0.106216i
$909$	−116.126	+	823.020i	−0.127752	+	0.905413i
$910$	−244.377	+	274.232i	−0.268546	+	0.301354i
$911$	33.3225	−	57.7163i	0.0365780	−	0.0633549i	−0.847157	−	0.531343i	$-0.821688\pi$
$911$	33.3225	−	57.7163i	0.0365780	−	0.0633549i	0.883735	+	0.467988i	$0.155021\pi$
$912$	−342.288	−	117.964i	−0.375316	−	0.129346i
$913$	−66.8748	−	17.9190i	−0.0732473	−	0.0196266i
$914$	1054.91	−	609.050i	1.15416	−	0.666356i
$915$	−303.534	−	1192.62i	−0.331731	−	1.30341i
$916$	−197.199	+	341.559i	−0.215283	+	0.372881i
$917$	−1085.99	−	1085.99i	−1.18428	−	1.18428i
$918$	393.614	−	20.3050i	0.428773	−	0.0221188i
$919$			1575.30i			1.71415i	0.515194	+	0.857074i	$0.327720\pi$
$919$			1575.30i			1.71415i	−0.515194	+	0.857074i	$0.672280\pi$
$920$	−251.207	+	499.357i	−0.273052	+	0.542780i
$921$	754.745	+	509.382i	0.819485	+	0.553075i
$922$	43.8540	−	163.665i	0.0475640	−	0.177511i
$923$	−527.479	−	141.338i	−0.571484	−	0.153129i
$924$	−126.169	−	258.865i	−0.136547	−	0.280157i
$925$	767.939	−	303.887i	0.830204	−	0.328527i
$926$	−524.687			−0.566616
$927$	−1178.73	+	144.077i	−1.27156	+	0.155423i
$928$	61.4995	−	61.4995i	0.0662711	−	0.0662711i
$929$	−614.392	−	354.719i	−0.661348	−	0.381829i	0.131443	−	0.991324i	$-0.458039\pi$
$929$	−614.392	−	354.719i	−0.661348	−	0.381829i	−0.792790	+	0.609494i	$0.791372\pi$
$930$	−823.846	−	10.3656i	−0.885855	−	0.0111458i
$931$	311.601	+	539.708i	0.334694	+	0.579708i
$932$	34.4876	−	128.709i	0.0370038	−	0.138100i
$933$	−187.121	−	215.377i	−0.200558	−	0.230843i
$934$	−383.219	−	221.252i	−0.410299	−	0.236886i
$935$	197.460	−	221.584i	0.211187	−	0.236988i
$936$	−97.6140	+	124.800i	−0.104288	+	0.133333i
$937$	716.809	+	716.809i	0.765004	+	0.765004i	0.977222	−	0.212218i	$-0.0680688\pi$
$937$	716.809	+	716.809i	0.765004	+	0.765004i	−0.212218	+	0.977222i	$0.568069\pi$
$938$	−336.400	−	1255.46i	−0.358635	−	1.33844i
$939$	−612.241	−	1256.15i	−0.652014	−	1.33775i
$940$	−134.006	+	646.793i	−0.142559	+	0.688077i
$941$	−137.643	−	238.405i	−0.146273	−	0.253353i	0.783574	−	0.621298i	$-0.213395\pi$
$941$	−137.643	−	238.405i	−0.146273	−	0.253353i	−0.929847	+	0.367946i	$0.880061\pi$
$942$	17.7045	+	91.2147i	0.0187946	+	0.0968309i
$943$	483.381	+	1804.00i	0.512599	+	1.91305i
$944$		−	51.1131i		−	0.0541453i
$945$	−171.441	+	1113.59i	−0.181419	+	1.17840i
$946$	−88.1394			−0.0931706
$947$	61.8292	−	16.5671i	0.0652896	−	0.0174943i	−0.226026	−	0.974121i	$-0.572574\pi$
$947$	61.8292	−	16.5671i	0.0652896	−	0.0174943i	0.291316	+	0.956627i	$0.405907\pi$
$948$	493.799	−	95.8449i	0.520885	−	0.101102i
$949$	−120.639	+	69.6511i	−0.127122	+	0.0733942i
$950$	1055.22	+	156.017i	1.11075	+	0.164228i
$951$	−391.049	+	190.595i	−0.411198	+	0.200416i
$952$	−235.362	+	63.0651i	−0.247229	+	0.0662449i
$953$	−578.229	+	578.229i	−0.606746	+	0.606746i	−0.942094	−	0.335348i	$-0.891146\pi$
$953$	−578.229	+	578.229i	−0.606746	+	0.606746i	0.335348	+	0.942094i	$0.391146\pi$
$954$	0.571151	−	4.04791i	0.000598691	−	0.00424309i
$955$	−103.634	−	1800.19i	−0.108518	−	1.88502i
$956$	3.59339	−	6.22393i	0.00375877	−	0.00651039i
$957$	200.235	−	173.966i	0.209232	−	0.181783i
$958$	735.108	+	196.971i	0.767336	+	0.205607i
$959$	1104.68	−	637.785i	1.15190	−	0.665052i
$960$	83.7786	+	85.9136i	0.0872693	+	0.0894934i
$961$	−273.754	+	474.157i	−0.284864	+	0.493399i
$962$	−205.616	−	205.616i	−0.213738	−	0.213738i
$963$	1244.40	+	529.019i	1.29221	+	0.549345i
$964$		−	135.271i		−	0.140323i
$965$	1113.54	−	368.155i	1.15392	−	0.381508i
$966$	1258.11	−	613.195i	1.30239	−	0.634777i
$967$	370.649	−	1383.28i	0.383298	−	1.43049i	−0.457535	−	0.889192i	$-0.651267\pi$
$967$	370.649	−	1383.28i	0.383298	−	1.43049i	0.840833	−	0.541295i	$-0.182066\pi$
$968$	240.226	+	64.3684i	0.248168	+	0.0664963i
$969$	−522.648	+	774.401i	−0.539368	+	0.799175i
$970$	353.429	−	702.556i	0.364360	−	0.724284i
$971$	−435.010			−0.448002			−0.224001	−	0.974589i	$-0.571912\pi$
$971$	−435.010			−0.448002			−0.224001	+	0.974589i	$0.571912\pi$
$972$	−43.0188	+	484.092i	−0.0442580	+	0.498037i
$973$	23.7387	−	23.7387i	0.0243974	−	0.0243974i
$974$	246.531	+	142.335i	0.253112	+	0.146134i
$975$	215.014	−	414.344i	0.220528	−	0.424968i
$976$	164.086	+	284.205i	0.168121	+	0.291194i
$977$	−446.328	+	1665.72i	−0.456835	+	1.70493i	0.225801	+	0.974173i	$0.427500\pi$
$977$	−446.328	+	1665.72i	−0.456835	+	1.70493i	−0.682636	+	0.730759i	$0.739167\pi$
$978$	100.612	−	291.938i	0.102875	−	0.298505i
$979$	−296.235	−	171.031i	−0.302589	−	0.174700i
$980$	−11.8717	−	206.219i	−0.0121140	−	0.210427i
$981$	−465.954	−	1155.09i	−0.474979	−	1.17747i
$982$	−471.689	−	471.689i	−0.480335	−	0.480335i
$983$	380.122	+	1418.63i	0.386696	+	1.44317i	0.835476	+	0.549526i	$0.185192\pi$
$983$	380.122	+	1418.63i	0.386696	+	1.44317i	−0.448781	+	0.893642i	$0.648142\pi$
$984$	399.952	+	28.0771i	0.406455	+	0.0285337i
$985$	−375.742	−	77.8479i	−0.381464	−	0.0790334i
$986$	−112.219	−	194.369i	−0.113812	−	0.197128i
$987$	1248.46	−	1084.67i	1.26491	−	1.09896i
$988$	−97.2047	−	362.773i	−0.0983853	−	0.367179i
$989$		−	428.366i		−	0.433130i
$990$	236.531	+	279.269i	0.238921	+	0.282090i
$991$	877.590			0.885560			0.442780	−	0.896630i	$-0.353992\pi$
$991$	877.590			0.885560			0.442780	+	0.896630i	$0.353992\pi$
$992$	212.223	−	56.8650i	0.213935	−	0.0573236i
$993$	−432.767	+	1255.73i	−0.435818	+	1.26458i
$994$	896.825	−	517.782i	0.902238	−	0.520907i
$995$	−565.359	−	860.848i	−0.568200	−	0.865174i
$996$	−59.8742	−	40.4094i	−0.0601146	−	0.0405717i
$997$	−274.662	+	73.5956i	−0.275489	+	0.0738170i	−0.393918	−	0.919145i	$-0.628881\pi$
$997$	−274.662	+	73.5956i	−0.275489	+	0.0738170i	0.118429	+	0.992962i	$0.462214\pi$
$998$	−262.326	+	262.326i	−0.262852	+	0.262852i
$999$	−872.307	−	186.162i	−0.873180	−	0.186348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.3.k.b.7.1	✓	24
3.2	odd	2		270.3.l.a.127.1		24
5.3	odd	4	inner	90.3.k.b.43.3	yes	24
9.2	odd	6		810.3.g.j.487.4		12
9.4	even	3	inner	90.3.k.b.67.3	yes	24
9.5	odd	6		270.3.l.a.37.5		24
9.7	even	3		810.3.g.h.487.3		12
15.8	even	4		270.3.l.a.73.5		24
45.13	odd	12	inner	90.3.k.b.13.1	yes	24
45.23	even	12		270.3.l.a.253.1		24
45.38	even	12		810.3.g.j.163.4		12
45.43	odd	12		810.3.g.h.163.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.k.b.7.1	✓	24	1.1	even	1	trivial
90.3.k.b.13.1	yes	24	45.13	odd	12	inner
90.3.k.b.43.3	yes	24	5.3	odd	4	inner
90.3.k.b.67.3	yes	24	9.4	even	3	inner
270.3.l.a.37.5		24	9.5	odd	6
270.3.l.a.73.5		24	15.8	even	4
270.3.l.a.127.1		24	3.2	odd	2
270.3.l.a.253.1		24	45.23	even	12
810.3.g.h.163.3		12	45.43	odd	12
810.3.g.h.487.3		12	9.7	even	3
810.3.g.j.163.4		12	45.38	even	12
810.3.g.j.487.4		12	9.2	odd	6

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:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	90.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 0.366025i) q^{2} +(-2.94504 + 0.571623i) q^{3} +(1.73205 - 1.00000i) q^{4} +(4.17929 - 2.74473i) q^{5} +(-3.81377 + 1.85881i) q^{6} +(8.06163 - 2.16011i) q^{7} +(2.00000 - 2.00000i) q^{8} +(8.34650 - 3.36690i) q^{9} +(4.70437 - 5.27910i) q^{10} +(-2.87538 + 4.98030i) q^{11} +(-4.52933 + 3.93512i) q^{12} +(-6.01206 - 1.61093i) q^{13} +(10.2217 - 5.90153i) q^{14} +(-10.7392 + 10.4723i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-7.29884 - 7.29884i) q^{17} +(10.1692 - 7.65430i) q^{18} +30.1705i q^{19} +(4.49400 - 8.93331i) q^{20} +(-22.5070 + 10.9698i) q^{21} +(-2.10492 + 7.85567i) q^{22} +(-38.1793 - 10.2301i) q^{23} +(-4.74683 + 7.03332i) q^{24} +(9.93287 - 22.9421i) q^{25} -8.80226 q^{26} +(-22.6561 + 14.6867i) q^{27} +(11.8031 - 11.8031i) q^{28} +(13.3150 + 7.68744i) q^{29} +(-10.8369 + 18.2363i) q^{30} +(19.4198 + 33.6360i) q^{31} +(1.46410 - 5.46410i) q^{32} +(5.62124 - 16.3108i) q^{33} +(-12.6420 - 7.29884i) q^{34} +(27.7630 - 31.1548i) q^{35} +(11.0897 - 14.1781i) q^{36} +(23.3594 + 23.3594i) q^{37} +(11.0432 + 41.2136i) q^{38} +(18.6266 + 1.30761i) q^{39} +(2.86910 - 13.8480i) q^{40} +(-23.6254 - 40.9204i) q^{41} +(-26.7300 + 23.2232i) q^{42} +(2.80496 + 10.4683i) q^{43} +11.5015i q^{44} +(25.6411 - 36.9802i) q^{45} -55.8984 q^{46} +(-63.8022 + 17.0957i) q^{47} +(-3.90992 + 11.3452i) q^{48} +(17.8886 - 10.3280i) q^{49} +(5.17117 - 34.9751i) q^{50} +(25.6675 + 17.3232i) q^{51} +(-12.0241 + 3.22185i) q^{52} +(0.227111 - 0.227111i) q^{53} +(-25.5732 + 28.3551i) q^{54} +(1.65257 + 28.7062i) q^{55} +(11.8031 - 20.4435i) q^{56} +(-17.2461 - 88.8531i) q^{57} +(21.0025 + 5.62760i) q^{58} +(11.0663 - 6.38914i) q^{59} +(-8.12852 + 28.8778i) q^{60} +(-41.0215 + 71.0513i) q^{61} +(38.8395 + 38.8395i) q^{62} +(60.0135 - 45.1721i) q^{63} -8.00000i q^{64} +(-29.5477 + 9.76898i) q^{65} +(1.70859 - 24.3385i) q^{66} +(28.5011 - 106.367i) q^{67} +(-19.9408 - 5.34312i) q^{68} +(118.287 + 8.30392i) q^{69} +(26.5215 - 52.7201i) q^{70} +87.7370 q^{71} +(9.95919 - 23.4268i) q^{72} +(15.8257 - 15.8257i) q^{73} +(40.4597 + 23.3594i) q^{74} +(-16.1385 + 73.2431i) q^{75} +(30.1705 + 52.2568i) q^{76} +(-12.4222 + 46.3604i) q^{77} +(25.9230 - 5.03157i) q^{78} +(-72.6039 - 41.9179i) q^{79} +(-1.14947 - 19.9669i) q^{80} +(58.3280 - 56.2036i) q^{81} +(-47.2508 - 47.2508i) q^{82} +(3.11595 + 11.6289i) q^{83} +(-28.0135 + 41.5073i) q^{84} +(-50.5373 - 10.4706i) q^{85} +(7.66330 + 13.2732i) q^{86} +(-43.6076 - 15.0286i) q^{87} +(4.20984 + 15.7113i) q^{88} +59.4813i q^{89} +(21.4908 - 59.9011i) q^{90} -51.9468 q^{91} +(-76.3586 + 20.4602i) q^{92} +(-76.4190 - 87.9586i) q^{93} +(-80.8979 + 46.7064i) q^{94} +(82.8099 + 126.091i) q^{95} +(-1.18843 + 16.9289i) q^{96} +(107.430 - 28.7859i) q^{97} +(20.6560 - 20.6560i) q^{98} +(-7.23114 + 51.2491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} + 4 q^{3} + 16 q^{6} + 6 q^{7} + 48 q^{8} + 12 q^{10} - 12 q^{11} + 8 q^{12} - 38 q^{15} + 48 q^{16} - 36 q^{17} - 20 q^{18} + 12 q^{20} - 128 q^{21} + 12 q^{22} - 66 q^{23} - 42 q^{25}+ \cdots + 264 q^{98}+O(q^{100}) \) 24 * q + 12 * q^2 + 4 * q^3 + 16 * q^6 + 6 * q^7 + 48 * q^8 + 12 * q^10 - 12 * q^11 + 8 * q^12 - 38 * q^15 + 48 * q^16 - 36 * q^17 - 20 * q^18 + 12 * q^20 - 128 * q^21 + 12 * q^22 - 66 * q^23 - 42 * q^25 + 10 * q^27 + 24 * q^28 - 48 * q^30 + 72 * q^31 - 48 * q^32 - 122 * q^33 - 240 * q^35 - 8 * q^36 + 36 * q^37 - 36 * q^38 - 12 * q^40 - 24 * q^41 - 16 * q^42 - 108 * q^43 + 158 * q^45 - 264 * q^46 - 36 * q^47 + 32 * q^48 + 42 * q^50 + 380 * q^51 + 384 * q^53 + 288 * q^55 + 24 * q^56 + 154 * q^57 - 108 * q^58 - 56 * q^60 + 360 * q^61 + 144 * q^62 - 68 * q^63 + 144 * q^65 - 80 * q^66 + 144 * q^67 - 36 * q^68 - 174 * q^70 + 216 * q^71 + 32 * q^72 + 432 * q^73 - 184 * q^75 + 72 * q^76 - 48 * q^77 - 240 * q^78 + 416 * q^81 - 48 * q^82 - 378 * q^83 - 228 * q^85 + 216 * q^86 + 52 * q^87 - 24 * q^88 + 124 * q^90 - 1560 * q^91 - 132 * q^92 + 580 * q^93 + 264 * q^95 + 32 * q^96 - 294 * q^97 + 264 * q^98

Introduction

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