LMFDB - Embedded newform 231.4.u.a.20.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [231,4,Mod(20,231)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("231.20"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(231, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 6])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	231.u (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$13.6294412113$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$92$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			20.1
Character	$\chi$	$=$	231.20
Dual form			231.4.u.a.104.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.23865 - 1.70214i) q^{2} +(-5.19044 - 0.243508i) q^{3} +(18.0740 + 13.1315i) q^{4} +(-3.51328 - 10.8128i) q^{5} +(26.7764 + 10.1105i) q^{6} +(18.1267 - 3.79766i) q^{7} +(-46.4303 - 63.9058i) q^{8} +(26.8814 + 2.52783i) q^{9} +62.6244i q^{10} +(36.4742 - 0.793165i) q^{11} +(-90.6144 - 72.5596i) q^{12} +(-61.2668 - 19.9068i) q^{13} +(-101.424 - 10.9596i) q^{14} +(15.6025 + 56.9786i) q^{15} +(79.2260 + 243.832i) q^{16} +(22.9593 + 70.6614i) q^{17} +(-136.519 - 58.9983i) q^{18} +(44.9190 + 61.8257i) q^{19} +(78.4891 - 241.565i) q^{20} +(-95.0105 + 15.2975i) q^{21} +(-192.426 - 57.9291i) q^{22} +87.5177i q^{23} +(225.432 + 343.005i) q^{24} +(-3.44574 + 2.50348i) q^{25} +(287.071 + 208.569i) q^{26} +(-138.911 - 19.6664i) q^{27} +(377.491 + 169.393i) q^{28} +(-120.023 + 165.197i) q^{29} +(15.2495 - 325.048i) q^{30} +(11.6382 + 3.78147i) q^{31} -780.270i q^{32} +(-189.511 - 4.76490i) q^{33} -409.250i q^{34} +(-104.747 - 182.658i) q^{35} +(452.660 + 398.682i) q^{36} +(-39.5701 - 28.7493i) q^{37} +(-130.079 - 400.341i) q^{38} +(313.154 + 118.244i) q^{39} +(-527.876 + 726.559i) q^{40} +(132.224 - 96.0665i) q^{41} +(523.765 + 81.5828i) q^{42} +252.173 q^{43} +(669.651 + 464.627i) q^{44} +(-67.1091 - 299.543i) q^{45} +(148.967 - 458.474i) q^{46} +(69.7013 - 50.6409i) q^{47} +(-351.843 - 1284.89i) q^{48} +(314.156 - 137.678i) q^{49} +(22.3123 - 7.24969i) q^{50} +(-101.962 - 372.355i) q^{51} +(-845.929 - 1164.32i) q^{52} +(213.123 + 69.2479i) q^{53} +(694.230 + 339.471i) q^{54} +(-136.721 - 391.601i) q^{55} +(-1084.32 - 982.076i) q^{56} +(-218.094 - 331.841i) q^{57} +(909.947 - 661.115i) q^{58} +(317.968 + 231.017i) q^{59} +(-466.216 + 1234.72i) q^{60} +(-77.7467 + 25.2614i) q^{61} +(-54.5317 - 39.6196i) q^{62} +(496.871 - 56.2650i) q^{63} +(-694.321 + 2136.90i) q^{64} +732.402i q^{65} +(984.669 + 347.535i) q^{66} +80.9414 q^{67} +(-512.926 + 1578.62i) q^{68} +(21.3113 - 454.256i) q^{69} +(237.826 + 1135.17i) q^{70} +(566.163 - 183.958i) q^{71} +(-1086.57 - 1835.25i) q^{72} +(-503.012 + 692.337i) q^{73} +(158.358 + 217.961i) q^{74} +(18.4945 - 12.1551i) q^{75} +1707.29i q^{76} +(658.146 - 152.894i) q^{77} +(-1439.24 - 1152.47i) q^{78} +(-210.755 + 648.639i) q^{79} +(2358.16 - 1713.30i) q^{80} +(716.220 + 135.903i) q^{81} +(-856.194 + 278.194i) q^{82} +(50.3375 + 154.923i) q^{83} +(-1918.10 - 971.145i) q^{84} +(683.383 - 496.507i) q^{85} +(-1321.05 - 429.234i) q^{86} +(663.199 - 828.221i) q^{87} +(-1744.20 - 2294.09i) q^{88} +340.730 q^{89} +(-158.304 + 1683.43i) q^{90} +(-1186.16 - 128.175i) q^{91} +(-1149.24 + 1581.79i) q^{92} +(-59.4865 - 22.4615i) q^{93} +(-451.338 + 146.649i) q^{94} +(510.694 - 702.910i) q^{95} +(-190.002 + 4049.95i) q^{96} +(1508.77 + 490.228i) q^{97} +(-1880.10 + 186.510i) q^{98} +(982.484 + 70.8794i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 340 q^{4} - 18 q^{7} + 42 q^{9} + 42 q^{15} - 1116 q^{16} - 262 q^{18} - 222 q^{21} + 696 q^{22} - 1516 q^{25} + 38 q^{28} + 624 q^{30} + 1430 q^{36} + 36 q^{37} + 390 q^{39} + 2130 q^{42} - 1376 q^{43}+ \cdots - 6218 q^{99}+O(q^{100}) $ 368 * q + 340 * q^4 - 18 * q^7 + 42 * q^9 + 42 * q^15 - 1116 * q^16 - 262 * q^18 - 222 * q^21 + 696 * q^22 - 1516 * q^25 + 38 * q^28 + 624 * q^30 + 1430 * q^36 + 36 * q^37 + 390 * q^39 + 2130 * q^42 - 1376 * q^43 + 1716 * q^46 + 474 * q^49 + 782 * q^51 + 670 * q^57 + 5576 * q^58 - 2708 * q^60 - 739 * q^63 + 5256 * q^64 - 2432 * q^67 + 2280 * q^70 - 3706 * q^72 - 10900 * q^78 + 732 * q^79 - 262 * q^81 - 510 * q^84 + 8008 * q^85 - 832 * q^88 - 5446 * q^91 + 2510 * q^93 - 6218 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−5.23865	−	1.70214i	−1.85214	−	0.601797i	−0.996438	−	0.0843295i	$-0.973125\pi$
$2$	−5.23865	−	1.70214i	−1.85214	−	0.601797i	−0.855703	−	0.517467i	$-0.826875\pi$
$3$	−5.19044	−	0.243508i	−0.998901	−	0.0468632i
$3$	−5.19044	−	0.243508i	−0.998901	−	0.0468632i
$4$	18.0740	+	13.1315i	2.25925	+	1.64144i
$5$	−3.51328	−	10.8128i	−0.314238	−	0.967124i	−0.976067	−	0.217469i	$-0.930220\pi$
$5$	−3.51328	−	10.8128i	−0.314238	−	0.967124i	0.661830	−	0.749654i	$-0.269780\pi$
$6$	26.7764	+	10.1105i	1.82190	+	0.687933i
$7$	18.1267	−	3.79766i	0.978751	−	0.205054i
$7$	18.1267	−	3.79766i	0.978751	−	0.205054i
$8$	−46.4303	−	63.9058i	−2.05195	−	2.82426i
$9$	26.8814	+	2.52783i	0.995608	+	0.0936234i
$10$			62.6244i			1.98036i
$11$	36.4742	−	0.793165i	0.999764	−	0.0217408i
$11$	36.4742	−	0.793165i	0.999764	−	0.0217408i
$12$	−90.6144	−	72.5596i	−2.17984	−	1.74551i
$13$	−61.2668	−	19.9068i	−1.30710	−	0.424704i	−0.429057	−	0.903278i	$-0.641154\pi$
$13$	−61.2668	−	19.9068i	−1.30710	−	0.424704i	−0.878047	+	0.478574i	$0.841154\pi$
$14$	−101.424	−	10.9596i	−1.93618	−	0.209220i
$15$	15.6025	+	56.9786i	0.268570	+	0.980787i
$16$	79.2260	+	243.832i	1.23791	+	3.80988i
$17$	22.9593	+	70.6614i	0.327555	+	1.00811i	0.970274	+	0.242009i	$0.0778064\pi$
$17$	22.9593	+	70.6614i	0.327555	+	1.00811i	−0.642719	+	0.766102i	$0.722194\pi$
$18$	−136.519	−	58.9983i	−1.78766	−	0.772557i
$19$	44.9190	+	61.8257i	0.542375	+	0.746515i	0.988953	−	0.148230i	$-0.0473575\pi$
$19$	44.9190	+	61.8257i	0.542375	+	0.746515i	−0.446578	+	0.894745i	$0.647358\pi$
$20$	78.4891	−	241.565i	0.877535	−	2.70078i
$21$	−95.0105	+	15.2975i	−0.987285	+	0.158961i
$22$	−192.426	−	57.9291i	−1.86479	−	0.561388i
$23$			87.5177i			0.793422i	0.917944	+	0.396711i	$0.129848\pi$
$23$			87.5177i			0.793422i	−0.917944	+	0.396711i	$0.870152\pi$
$24$	225.432	+	343.005i	1.91734	+	2.91732i
$25$	−3.44574	+	2.50348i	−0.0275659	+	0.0200278i
$26$	287.071	+	208.569i	2.16536	+	1.57322i
$27$	−138.911	−	19.6664i	−0.990126	−	0.140178i
$28$	377.491	+	169.393i	2.54783	+	1.14329i
$29$	−120.023	+	165.197i	−0.768541	+	1.05781i	0.227914	+	0.973681i	$0.426810\pi$
$29$	−120.023	+	165.197i	−0.768541	+	1.05781i	−0.996455	+	0.0841252i	$0.973190\pi$
$30$	15.2495	−	325.048i	0.0928058	−	1.97818i
$31$	11.6382	+	3.78147i	0.0674283	+	0.0219088i	0.342537	−	0.939504i	$-0.388714\pi$
$31$	11.6382	+	3.78147i	0.0674283	+	0.0219088i	−0.275109	+	0.961413i	$0.588714\pi$
$32$		−	780.270i		−	4.31042i
$33$	−189.511	−	4.76490i	−0.999684	−	0.0251352i
$34$		−	409.250i		−	2.06429i
$35$	−104.747	−	182.658i	−0.505873	−	0.882137i
$36$	452.660	+	398.682i	2.09565	+	1.84575i
$37$	−39.5701	−	28.7493i	−0.175818	−	0.127740i	0.496396	−	0.868096i	$-0.334657\pi$
$37$	−39.5701	−	28.7493i	−0.175818	−	0.127740i	−0.672214	+	0.740357i	$0.734657\pi$
$38$	−130.079	−	400.341i	−0.555304	−	1.70905i
$39$	313.154	+	118.244i	1.28576	+	0.485492i
$40$	−527.876	+	726.559i	−2.08661	+	2.87198i
$41$	132.224	−	96.0665i	0.503657	−	0.365929i	−0.306755	−	0.951789i	$-0.599243\pi$
$41$	132.224	−	96.0665i	0.503657	−	0.365929i	0.810412	+	0.585860i	$0.199243\pi$
$42$	523.765	+	81.5828i	1.92425	+	0.299726i
$43$	252.173			0.894327			0.447163	−	0.894452i	$-0.352434\pi$
$43$	252.173			0.894327			0.447163	+	0.894452i	$0.352434\pi$
$44$	669.651	+	464.627i	2.29440	+	1.59193i
$45$	−67.1091	−	299.543i	−0.222312	−	0.992296i
$46$	148.967	−	458.474i	0.477479	−	1.46953i
$47$	69.7013	−	50.6409i	0.216319	−	0.157165i	−0.474349	−	0.880337i	$-0.657317\pi$
$47$	69.7013	−	50.6409i	0.216319	−	0.157165i	0.690668	+	0.723172i	$0.257317\pi$
$48$	−351.843	−	1284.89i	−1.05800	−	3.86371i
$49$	314.156	−	137.678i	0.915906	−	0.401394i
$50$	22.3123	−	7.24969i	0.0631086	−	0.0205052i
$51$	−101.962	−	372.355i	−0.279952	−	1.02235i
$52$	−845.929	−	1164.32i	−2.25595	−	3.10504i
$53$	213.123	+	69.2479i	0.552353	+	0.179470i	0.571878	−	0.820339i	$-0.306215\pi$
$53$	213.123	+	69.2479i	0.552353	+	0.179470i	−0.0195244	+	0.999809i	$0.506215\pi$
$54$	694.230	+	339.471i	1.74949	+	0.855484i
$55$	−136.721	−	391.601i	−0.335189	−	0.960063i
$56$	−1084.32	−	982.076i	−2.58747	−	2.34349i
$57$	−218.094	−	331.841i	−0.506795	−	0.771112i
$58$	909.947	−	661.115i	2.06003	−	1.49670i
$59$	317.968	+	231.017i	0.701625	+	0.509760i	0.880461	−	0.474119i	$-0.157233\pi$
$59$	317.968	+	231.017i	0.701625	+	0.509760i	−0.178836	+	0.983879i	$0.557233\pi$
$60$	−466.216	+	1234.72i	−1.00314	+	2.65668i
$61$	−77.7467	+	25.2614i	−0.163188	+	0.0530229i	−0.389471	−	0.921039i	$-0.627342\pi$
$61$	−77.7467	+	25.2614i	−0.163188	+	0.0530229i	0.226284	+	0.974061i	$0.427342\pi$
$62$	−54.5317	−	39.6196i	−0.111702	−	0.0811563i
$63$	496.871	−	56.2650i	0.993650	−	0.112520i
$64$	−694.321	+	2136.90i	−1.35610	+	4.17363i
$65$			732.402i			1.39759i
$66$	984.669	+	347.535i	1.83643	+	0.648161i
$67$	80.9414			0.147590			0.0737952	−	0.997273i	$-0.476489\pi$
$67$	80.9414			0.147590			0.0737952	+	0.997273i	$0.476489\pi$
$68$	−512.926	+	1578.62i	−0.914726	+	2.81524i
$69$	21.3113	−	454.256i	0.0371823	−	0.792550i
$70$	237.826	+	1135.17i	0.406080	+	1.93828i
$71$	566.163	−	183.958i	0.946355	−	0.307489i	0.205121	−	0.978737i	$-0.434241\pi$
$71$	566.163	−	183.958i	0.946355	−	0.307489i	0.741234	+	0.671247i	$0.234241\pi$
$72$	−1086.57	−	1835.25i	−1.77852	−	3.00397i
$73$	−503.012	+	692.337i	−0.806481	+	1.11003i	0.185375	+	0.982668i	$0.440650\pi$
$73$	−503.012	+	692.337i	−0.806481	+	1.11003i	−0.991857	+	0.127359i	$0.959350\pi$
$74$	158.358	+	217.961i	0.248767	+	0.342399i
$75$	18.4945	−	12.1551i	0.0284742	−	0.0187140i
$76$			1707.29i			2.57684i
$77$	658.146	−	152.894i	0.974061	−	0.226284i
$78$	−1439.24	−	1152.47i	−2.08925	−	1.67297i
$79$	−210.755	+	648.639i	−0.300150	+	0.923766i	0.681293	+	0.732011i	$0.261418\pi$
$79$	−210.755	+	648.639i	−0.300150	+	0.923766i	−0.981443	+	0.191755i	$0.938582\pi$
$80$	2358.16	−	1713.30i	3.29563	−	2.39442i
$81$	716.220	+	135.903i	0.982469	+	0.186424i
$82$	−856.194	+	278.194i	−1.15306	+	0.374652i
$83$	50.3375	+	154.923i	0.0665693	+	0.204879i	0.978808	−	0.204780i	$-0.0656477\pi$
$83$	50.3375	+	154.923i	0.0665693	+	0.204879i	−0.912239	+	0.409659i	$0.865648\pi$
$84$	−1918.10	−	971.145i	−2.49145	−	1.26144i
$85$	683.383	−	496.507i	0.872038	−	0.633573i
$86$	−1321.05	−	429.234i	−1.65642	−	0.538203i
$87$	663.199	−	828.221i	0.817269	−	1.02063i
$88$	−1744.20	−	2294.09i	−2.11286	−	2.77898i
$89$	340.730			0.405813			0.202906	−	0.979198i	$-0.434961\pi$
$89$	340.730			0.405813			0.202906	+	0.979198i	$0.434961\pi$
$90$	−158.304	+	1683.43i	−0.185408	+	1.97166i
$91$	−1186.16	−	128.175i	−1.36642	−	0.147652i
$92$	−1149.24	+	1581.79i	−1.30235	+	1.79254i
$93$	−59.4865	−	22.4615i	−0.0663275	−	0.0250446i
$94$	−451.338	+	146.649i	−0.495234	+	0.160911i
$95$	510.694	−	702.910i	0.551538	−	0.759126i
$96$	−190.002	+	4049.95i	−0.202000	+	4.30569i
$97$	1508.77	+	490.228i	1.57930	+	0.513146i	0.961876	−	0.273486i	$-0.0881766\pi$
$97$	1508.77	+	490.228i	1.57930	+	0.513146i	0.617423	+	0.786631i	$0.288177\pi$
$98$	−1880.10	+	186.510i	−1.93794	+	0.192248i
$99$	982.484	+	70.8794i	0.997408	+	0.0719560i
$100$	−95.1527			−0.0951527
$101$	480.399	−	1478.52i	0.473282	−	1.45661i	−0.374978	−	0.927034i	$-0.622350\pi$
$101$	480.399	−	1478.52i	0.473282	−	1.45661i	0.848260	−	0.529579i	$-0.177650\pi$
$102$	−99.6557	+	2124.19i	−0.0967390	+	2.06202i
$103$	234.624	−	322.932i	0.224448	−	0.308927i	−0.681910	−	0.731436i	$-0.738851\pi$
$103$	234.624	−	322.932i	0.224448	−	0.308927i	0.906359	+	0.422509i	$0.138851\pi$
$104$	1572.47	+	4839.58i	1.48263	+	4.56307i
$105$	499.207	+	973.582i	0.463977	+	0.904875i
$106$	−998.607	−	725.531i	−0.915031	−	0.664809i
$107$	−405.149	−	557.639i	−0.366049	−	0.503823i	0.585773	−	0.810475i	$-0.300791\pi$
$107$	−405.149	−	557.639i	−0.366049	−	0.503823i	−0.951822	+	0.306653i	$0.900791\pi$
$108$	−2252.42	−	2179.56i	−2.00685	−	1.94193i
$109$	151.796			0.133389			0.0666946	−	0.997773i	$-0.478755\pi$
$109$	151.796			0.133389			0.0666946	+	0.997773i	$0.478755\pi$
$110$	49.6715	+	2284.18i	0.0430544	+	1.97989i
$111$	198.386	+	158.857i	0.169639	+	0.135839i
$112$	2362.10	+	4119.01i	1.99283	+	3.47509i
$113$	179.511	+	247.076i	0.149442	+	0.205690i	0.877175	−	0.480172i	$-0.159426\pi$
$113$	179.511	+	247.076i	0.149442	+	0.205690i	−0.727732	+	0.685861i	$0.759426\pi$
$114$	577.680	+	2109.62i	0.474602	+	1.73320i
$115$	946.309	−	307.474i	0.767337	−	0.249323i
$116$	−4338.59	+	1409.69i	−3.47265	+	1.12833i
$117$	−1596.62	−	689.995i	−1.26160	−	0.545214i
$118$	−1272.50	−	1751.44i	−0.992735	−	1.36638i
$119$	684.524	+	1193.67i	0.527312	+	0.919523i
$120$	2916.83	−	3642.62i	2.21891	−	2.77104i
$121$	1329.74	−	57.8602i	0.999055	−	0.0434712i
$122$	450.286			0.334155
$123$	−709.695	+	466.430i	−0.520253	+	0.341924i
$124$	160.692	+	221.173i	0.116375	+	0.160177i
$125$	−1110.56	−	806.870i	−0.794653	−	0.577349i
$126$	−2698.70	−	550.992i	−1.90809	−	0.389573i
$127$	−560.260	−	1724.30i	−0.391457	−	1.20478i	−0.931686	−	0.363264i	$-0.881662\pi$
$127$	−560.260	−	1724.30i	−0.391457	−	1.20478i	0.540229	−	0.841518i	$-0.318338\pi$
$128$	3605.55	−	4962.61i	2.48975	−	3.42685i
$129$	−1308.89	−	61.4062i	−0.893344	−	0.0419110i
$130$	1246.65	−	3836.79i	0.841065	−	2.58853i
$131$	−1191.16			−0.794446			−0.397223	−	0.917722i	$-0.630026\pi$
$131$	−1191.16			−0.794446			−0.397223	+	0.917722i	$0.630026\pi$
$132$	−3362.64	−	2574.68i	−2.21728	−	1.69771i
$133$	1049.03	+	950.110i	0.683926	+	0.619436i
$134$	−424.023	−	137.773i	−0.273358	−	0.0888195i
$135$	275.385	+	1571.11i	0.175566	+	1.00162i
$136$	3449.66	−	4748.06i	2.17505	−	2.99369i
$137$	2927.97	−	951.354i	1.82593	−	0.593282i	0.826390	−	0.563097i	$-0.190390\pi$
$137$	2927.97	−	951.354i	1.82593	−	0.593282i	0.999544	−	0.0301847i	$-0.00960956\pi$
$138$	−884.849	+	2343.41i	−0.545821	+	1.44554i
$139$	1239.81	−	1706.45i	0.756541	−	1.04129i	−0.240953	−	0.970537i	$-0.577460\pi$
$139$	1239.81	−	1706.45i	0.756541	−	1.04129i	0.997494	−	0.0707521i	$-0.0225399\pi$
$140$	505.371	−	4676.85i	0.305083	−	2.82333i
$141$	−374.112	+	245.876i	−0.223446	+	0.146855i
$142$	−3279.05			−1.93783
$143$	−2250.45	−	677.490i	−1.31603	−	0.396186i
$144$	1513.34	+	6754.83i	0.875774	+	3.90904i
$145$	2207.92	+	717.395i	1.26453	+	0.410872i
$146$	3813.56	−	2770.71i	2.16173	−	1.57059i
$147$	−1664.13	+	638.111i	−0.933710	+	0.358030i
$148$	−337.666	−	1039.23i	−0.187541	−	0.577191i
$149$	−1778.81	+	577.971i	−0.978027	+	0.317780i	−0.754052	−	0.656815i	$-0.771903\pi$
$149$	−1778.81	+	577.971i	−0.978027	+	0.317780i	−0.223975	+	0.974595i	$0.571903\pi$
$150$	−117.576	+	32.1959i	−0.0640002	+	0.0175252i
$151$	−1286.09	+	934.398i	−0.693115	+	0.503578i	−0.877683	−	0.479242i	$-0.840912\pi$
$151$	−1286.09	+	934.398i	−0.693115	+	0.503578i	0.184568	+	0.982820i	$0.440912\pi$
$152$	1865.42	−	5741.16i	0.995430	−	3.06362i
$153$	438.557	+	1957.51i	0.231734	+	1.03435i
$154$	−3708.04	−	319.298i	−1.94028	−	0.167077i
$155$		−	139.126i		−	0.0720961i
$156$	4107.22	+	6249.34i	2.10796	+	3.20735i
$157$	676.942	+	931.731i	0.344114	+	0.473632i	0.945637	−	0.325223i	$-0.105439\pi$
$157$	676.942	+	931.731i	0.344114	+	0.473632i	−0.601524	+	0.798855i	$0.705439\pi$
$158$	2208.15	−	3039.25i	1.11184	−	1.53032i
$159$	−1089.34	−	411.325i	−0.543336	−	0.205158i
$160$	−8436.88	+	2741.31i	−4.16871	+	1.35450i
$161$	332.362	+	1586.41i	0.162694	+	0.776562i
$162$	−3520.70	−	1931.06i	−1.70748	−	0.936531i
$163$	641.676	−	1974.88i	0.308343	−	0.948983i	−0.670065	−	0.742302i	$-0.733734\pi$
$163$	641.676	−	1974.88i	0.308343	−	0.948983i	0.978408	−	0.206681i	$-0.0662662\pi$
$164$	3651.32			1.73854
$165$	614.283	+	2065.88i	0.289829	+	0.974717i
$166$		−	897.267i		−	0.419527i
$167$	595.465	−	1832.65i	0.275919	−	0.849191i	−0.713056	−	0.701107i	$-0.752690\pi$
$167$	595.465	−	1832.65i	0.275919	−	0.849191i	0.988975	−	0.148084i	$-0.0473105\pi$
$168$	5388.96	+	5361.45i	2.47481	+	2.46217i
$169$	1579.93	+	1147.89i	0.719130	+	0.522479i
$170$	−4425.12	+	1437.81i	−1.99642	+	0.648676i
$171$	1051.20	+	1775.51i	0.470101	+	0.794015i
$172$	4557.78	+	3311.42i	2.02051	+	1.46798i
$173$	−2522.87	+	1832.97i	−1.10873	+	0.805540i	−0.982463	−	0.186456i	$-0.940300\pi$
$173$	−2522.87	+	1832.97i	−1.10873	+	0.805540i	−0.126267	+	0.991996i	$0.540300\pi$
$174$	−4884.01	+	3209.90i	−2.12791	+	1.39852i
$175$	−52.9526	+	58.4655i	−0.0228734	+	0.0252547i
$176$	3083.11	+	8830.77i	1.32044	+	3.78207i
$177$	−1594.14	−	1276.51i	−0.676965	−	0.542080i
$178$	−1784.97	−	579.971i	−0.751623	−	0.244217i
$179$	−1598.22	−	2199.76i	−0.667354	−	0.918534i	0.332343	−	0.943159i	$-0.392161\pi$
$179$	−1598.22	−	2199.76i	−0.667354	−	0.918534i	−0.999697	+	0.0246249i	$0.992161\pi$
$180$	2720.53	−	6295.19i	1.12654	−	2.60675i
$181$	2076.75	−	674.778i	0.852839	−	0.277104i	0.150204	−	0.988655i	$-0.452007\pi$
$181$	2076.75	−	674.778i	0.852839	−	0.277104i	0.702634	+	0.711551i	$0.252007\pi$
$182$	5995.73	+	2690.48i	2.44194	+	1.09578i
$183$	409.691	−	112.186i	0.165493	−	0.0453171i
$184$	5592.89	−	4063.47i	2.24083	−	1.62806i
$185$	−171.839	+	528.867i	−0.0682912	+	0.210179i
$186$	273.396	+	218.922i	0.107776	+	0.0863019i
$187$	893.468	+	2559.11i	0.349395	+	1.00075i
$188$	1924.77			0.746694
$189$	−2592.68	+	171.048i	−0.997831	+	0.0658303i
$190$	−3871.79	+	2813.02i	−1.47837	+	1.07410i
$191$	879.463	−	1210.48i	0.333171	−	0.458571i	−0.609260	−	0.792970i	$-0.708533\pi$
$191$	879.463	−	1210.48i	0.333171	−	0.458571i	0.942431	+	0.334399i	$0.108533\pi$
$192$	4124.18	−	10922.4i	1.55019	−	4.10549i
$193$	−145.310	−	447.219i	−0.0541951	−	0.166795i	0.920295	−	0.391224i	$-0.127948\pi$
$193$	−145.310	−	447.219i	−0.0541951	−	0.166795i	−0.974490	+	0.224429i	$0.927948\pi$
$194$	−7069.46	−	5136.26i	−2.61628	−	1.90084i
$195$	178.346	−	3801.49i	0.0654955	−	1.39605i
$196$	7485.97	+	1636.95i	2.72812	+	0.596556i
$197$			863.376i			0.312249i	0.987737	+	0.156124i	$0.0499001\pi$
$197$			863.376i			0.312249i	−0.987737	+	0.156124i	$0.950100\pi$
$198$	−5026.24	−	2043.64i	−1.80404	−	0.733510i
$199$			2310.73i			0.823131i	0.911380	+	0.411566i	$0.135018\pi$
$199$			2310.73i			0.823131i	−0.911380	+	0.411566i	$0.864982\pi$
$200$	319.973	+	103.966i	0.113128	+	0.0367574i
$201$	−420.122	−	19.7099i	−0.147428	−	0.00691656i
$202$	−5033.28	+	6927.72i	−1.75317	+	2.41303i
$203$	−1548.26	+	3450.29i	−0.535303	+	1.19292i
$204$	3046.72	−	8068.85i	1.04565	−	2.76928i
$205$	−1503.29	−	1092.20i	−0.512166	−	0.372111i
$206$	−1778.79	+	1292.36i	−0.601621	+	0.437104i
$207$	−221.230	+	2352.60i	−0.0742828	+	0.789937i
$208$		−	16516.0i		−	5.50565i
$209$	1687.42	+	2219.42i	0.558476	+	0.734547i
$210$	−957.997	−	5949.97i	−0.314800	−	1.95518i
$211$	−859.385	+	2644.91i	−0.280391	+	0.862955i	0.707351	+	0.706862i	$0.249890\pi$
$211$	−859.385	+	2644.91i	−0.280391	+	0.862955i	−0.987742	+	0.156093i	$0.950110\pi$
$212$	2942.66	+	4050.22i	0.953313	+	1.31212i
$213$	−2983.43	+	816.956i	−0.959725	+	0.262802i
$214$	1173.25	+	3610.89i	0.374774	+	1.15344i
$215$	−885.955	−	2726.69i	−0.281031	−	0.864924i
$216$	5192.87	+	9790.32i	1.63579	+	3.08401i
$217$	225.323	+	24.3479i	0.0704880	+	0.00761679i
$218$	−795.205	−	258.378i	−0.247055	−	0.0802732i
$219$	2779.45	−	3471.05i	0.857615	−	1.07101i
$220$	2671.23	−	8873.14i	0.818611	−	2.71922i
$221$		−	4786.24i		−	1.45682i
$222$	−768.874	−	1169.88i	−0.232448	−	0.353680i
$223$	−446.121	−	614.034i	−0.133966	−	0.184389i	0.736763	−	0.676151i	$-0.236353\pi$
$223$	−446.121	−	614.034i	−0.133966	−	0.184389i	−0.870730	+	0.491762i	$0.836353\pi$
$224$	−2963.20	−	14143.7i	−0.883870	−	4.21883i
$225$	−98.9547	+	58.5867i	−0.0293199	+	0.0173590i
$226$	−519.838	−	1599.90i	−0.153005	−	0.470900i
$227$	2873.18	+	2087.49i	0.840086	+	0.610358i	0.922395	−	0.386249i	$-0.126229\pi$
$227$	2873.18	+	2087.49i	0.840086	+	0.610358i	−0.0823090	+	0.996607i	$0.526229\pi$
$228$	415.740	−	8861.60i	0.120759	−	2.57401i
$229$	4206.71	+	1366.84i	1.21392	+	0.394426i	0.844864	−	0.534981i	$-0.179681\pi$
$229$	4206.71	+	1366.84i	1.21392	+	0.394426i	0.369055	+	0.929408i	$0.379681\pi$
$230$	−5480.74			−1.57126
$231$	−3453.30	+	633.324i	−0.983595	+	0.180388i
$232$	16129.8			4.56453
$233$	2992.54	+	972.336i	0.841407	+	0.273390i	0.697843	−	0.716251i	$-0.254143\pi$
$233$	2992.54	+	972.336i	0.841407	+	0.273390i	0.143565	+	0.989641i	$0.454143\pi$
$234$	7189.64	+	6332.30i	2.00855	+	1.76904i
$235$	−792.449	−	575.748i	−0.219973	−	0.159820i
$236$	2713.34	+	8350.80i	0.748404	+	2.30335i
$237$	1251.86	−	3315.40i	0.343111	−	0.908686i
$238$	−1554.19	−	7418.35i	−0.423290	−	2.02042i
$239$	−543.813	−	748.494i	−0.147181	−	0.202578i	0.729061	−	0.684449i	$-0.239957\pi$
$239$	−543.813	−	748.494i	−0.147181	−	0.202578i	−0.876242	+	0.481871i	$0.839957\pi$
$240$	−12657.1	+	8318.58i	−3.40422	+	2.23734i
$241$			2453.24i			0.655715i	0.944727	+	0.327858i	$0.106327\pi$
$241$			2453.24i			0.655715i	−0.944727	+	0.327858i	$0.893673\pi$
$242$	−7064.53	−	1960.30i	−1.87655	−	0.520713i
$243$	−3684.41	−	879.804i	−0.972653	−	0.232261i
$244$	−1736.91	−	564.357i	−0.455715	−	0.148071i
$245$	−2592.40	−	2913.19i	−0.676009	−	0.759661i
$246$	4511.77	−	1235.46i	1.16935	−	0.320204i
$247$	−1521.29	−	4682.05i	−0.391893	−	1.20612i
$248$	−298.706	−	919.322i	−0.0764832	−	0.235391i
$249$	−223.549	−	816.376i	−0.0568949	−	0.207774i
$250$	4444.43	+	6117.23i	1.12436	+	1.54755i
$251$	−1125.11	+	3462.73i	−0.282933	+	0.870778i	0.704078	+	0.710123i	$0.251361\pi$
$251$	−1125.11	+	3462.73i	−0.282933	+	0.870778i	−0.987011	+	0.160655i	$0.948639\pi$
$252$	9719.30	+	5507.75i	2.42960	+	1.37681i
$253$	69.4160	+	3192.14i	0.0172496	+	0.793234i
$254$			9986.66i			2.46700i
$255$	−3667.96	+	2410.68i	−0.900772	+	0.592010i
$256$	−12793.2	+	9294.81i	−3.12334	+	2.26924i
$257$	4057.52	+	2947.96i	0.984829	+	0.715520i	0.958783	−	0.284141i	$-0.0917082\pi$
$257$	4057.52	+	2947.96i	0.984829	+	0.715520i	0.0260464	+	0.999661i	$0.491708\pi$
$258$	6752.29	+	2549.60i	1.62938	+	0.615237i
$259$	−826.455	−	370.858i	−0.198276	−	0.0889729i
$260$	−9617.55	+	13237.4i	−2.29406	+	3.15750i
$261$	−3643.98	+	4137.34i	−0.864201	+	0.981207i
$262$	6240.08	+	2027.53i	1.47143	+	0.478095i
$263$			865.568i			0.202940i	0.994839	+	0.101470i	$0.0323546\pi$
$263$			865.568i			0.202940i	−0.994839	+	0.101470i	$0.967645\pi$
$264$	8494.53	+	12332.1i	1.98031	+	2.87495i
$265$		−	2547.74i		−	0.590590i
$266$	−3878.26	−	6762.88i	−0.893952	−	1.55887i
$267$	−1768.54	−	82.9707i	−0.405367	−	0.0190177i
$268$	1462.93	+	1062.88i	0.333444	+	0.242261i
$269$	−1651.17	−	5081.79i	−0.374252	−	1.15183i	−0.943982	−	0.329998i	$-0.892952\pi$
$269$	−1651.17	−	5081.79i	−0.374252	−	1.15183i	0.569729	−	0.821832i	$-0.307048\pi$
$270$	1231.60	−	8699.21i	0.277602	−	1.96080i
$271$	−551.716	+	759.372i	−0.123669	+	0.170216i	−0.866363	−	0.499416i	$-0.833548\pi$
$271$	−551.716	+	759.372i	−0.123669	+	0.170216i	0.742693	+	0.669632i	$0.233548\pi$
$272$	−15410.6	+	11196.4i	−3.43530	+	2.49589i
$273$	6125.51	+	954.123i	1.35800	+	0.211524i
$274$	−16957.9			−3.73892
$275$	−123.695	+	94.0454i	−0.0271240	+	0.0206224i
$276$	6350.25	−	7930.36i	1.38493	−	1.72954i
$277$	1242.14	−	3822.91i	0.269433	−	0.829229i	−0.721206	−	0.692720i	$-0.756412\pi$
$277$	1242.14	−	3822.91i	0.269433	−	0.829229i	0.990639	−	0.136508i	$-0.0435880\pi$
$278$	−9399.53	+	6829.16i	−2.02786	+	1.47333i
$279$	303.292	+	131.071i	0.0650810	+	0.0281254i
$280$	−6809.44	+	15174.8i	−1.45336	+	3.23882i
$281$	3221.71	−	1046.80i	0.683954	−	0.222230i	0.0536281	−	0.998561i	$-0.482921\pi$
$281$	3221.71	−	1046.80i	0.683954	−	0.222230i	0.630325	+	0.776331i	$0.282921\pi$
$282$	2378.35	−	651.267i	0.502230	−	0.137526i
$283$	−4414.00	−	6075.36i	−0.927157	−	1.27612i	−0.960958	−	0.276693i	$-0.910761\pi$
$283$	−4414.00	−	6075.36i	−0.927157	−	1.27612i	0.0338018	−	0.999429i	$-0.489239\pi$
$284$	12648.5	+	4109.74i	2.64278	+	0.858690i
$285$	−2821.89	+	3524.05i	−0.586507	+	0.732446i
$286$	10636.1	+	7379.71i	2.19905	+	1.52577i
$287$	2031.96	−	2243.51i	0.417920	−	0.461430i
$288$	1972.39	−	20974.8i	0.403557	−	4.29149i
$289$	−491.199	+	356.877i	−0.0999794	+	0.0726393i
$290$	−10345.4	−	7516.36i	−2.09483	−	1.52199i
$291$	−7711.79	−	2911.90i	−1.55352	−	0.586593i
$292$	−18182.9	+	5907.98i	−3.64408	+	1.18403i
$293$	4172.51	+	3031.51i	0.831948	+	0.604445i	0.920110	−	0.391661i	$-0.128099\pi$
$293$	4172.51	+	3031.51i	0.831948	+	0.604445i	−0.0881620	+	0.996106i	$0.528099\pi$
$294$	9803.95	−	510.250i	1.94482	−	0.101219i
$295$	1380.82	−	4249.74i	0.272524	−	0.838743i
$296$			3863.60i			0.758672i
$297$	−5082.27	−	607.138i	−0.992940	−	0.118619i
$298$	10302.4			2.00268
$299$	1742.20	−	5361.93i	0.336969	−	1.03708i
$300$	493.885	+	23.1705i	0.0950482	+	0.00445916i
$301$	4571.07	−	957.667i	0.875323	−	0.183385i
$302$	8327.83	−	2705.88i	1.58680	−	0.515582i
$303$	−2853.52	+	7557.18i	−0.541024	+	1.43283i
$304$	−11516.4	+	15850.9i	−2.17272	+	2.99050i
$305$	546.292	+	751.906i	0.102559	+	0.141161i
$306$	1034.51	−	11001.2i	0.193265	−	2.05522i
$307$			3240.56i			0.602438i	0.953555	+	0.301219i	$0.0973936\pi$
$307$			3240.56i			0.602438i	−0.953555	+	0.301219i	$0.902606\pi$
$308$	13903.1	+	5879.05i	2.57208	+	1.08763i
$309$	−1296.44	+	1619.03i	−0.238679	+	0.298069i
$310$	−236.812	+	728.833i	−0.0433872	+	0.133532i
$311$	−3911.78	+	2842.08i	−0.713237	+	0.518197i	−0.884216	−	0.467078i	$-0.845307\pi$
$311$	−3911.78	+	2842.08i	−0.713237	+	0.518197i	0.170979	+	0.985275i	$0.445307\pi$
$312$	−6983.36	−	25502.5i	−1.26716	−	4.62754i
$313$	−4709.16	+	1530.10i	−0.850408	+	0.276314i	−0.701617	−	0.712554i	$-0.747538\pi$
$313$	−4709.16	+	1530.10i	−0.850408	+	0.276314i	−0.148791	+	0.988869i	$0.547538\pi$
$314$	−1960.32	−	6033.26i	−0.352317	−	1.08432i
$315$	−2354.03	−	5174.88i	−0.421062	−	0.925624i
$316$	−12326.8	+	8955.95i	−2.19442	+	1.59434i
$317$	1376.51	+	447.255i	0.243888	+	0.0792439i	0.428410	−	0.903584i	$-0.359074\pi$
$317$	1376.51	+	447.255i	0.243888	+	0.0792439i	−0.184522	+	0.982828i	$0.559074\pi$
$318$	5006.54	+	4008.99i	0.882871	+	0.706960i
$319$	−4246.72	+	6120.65i	−0.745362	+	1.07427i
$320$	25545.1			4.46255
$321$	1967.11	+	2993.05i	0.342036	+	0.520423i
$322$	959.161	−	8876.36i	0.166000	−	1.53621i
$323$	−3337.38	+	4593.51i	−0.574913	+	0.791299i
$324$	11160.3	+	11861.4i	1.91364	+	2.03384i
$325$	260.946	−	84.7863i	0.0445374	−	0.0144711i
$326$	−6723.03	+	9253.45i	−1.14219	+	1.57209i
$327$	−787.888	−	36.9636i	−0.133243	−	0.00625104i
$328$	−12278.4	−	3989.50i	−2.06696	−	0.671595i
$329$	1071.14	−	1182.66i	0.179495	−	0.198182i
$330$	298.399	−	11868.0i	0.0497767	−	1.97973i
$331$	6859.03			1.13899			0.569496	−	0.821994i	$-0.307138\pi$
$331$	6859.03			1.13899			0.569496	+	0.821994i	$0.307138\pi$
$332$	−1124.57	+	3461.08i	−0.185901	+	0.572143i
$333$	−991.026	−	872.849i	−0.163087	−	0.143639i
$334$	−6238.85	+	8587.05i	−1.02208	+	1.40677i
$335$	−284.370	−	875.200i	−0.0463785	−	0.142738i
$336$	−11257.3	−	21954.7i	−1.82779	−	3.56466i
$337$	7636.58	+	5548.30i	1.23439	+	0.896840i	0.997212	−	0.0746249i	$-0.0237759\pi$
$337$	7636.58	+	5548.30i	1.23439	+	0.896840i	0.237183	+	0.971465i	$0.423776\pi$
$338$	−6322.83	−	8702.63i	−1.01750	−	1.40047i
$339$	−871.577	−	1326.15i	−0.139639	−	0.212467i
$340$	18871.3			3.01012
$341$	427.493	+	128.695i	0.0678887	+	0.0204377i
$342$	−2484.70	−	11090.6i	−0.392858	−	1.75353i
$343$	5171.76	−	3688.71i	0.814136	−	0.580675i
$344$	−11708.5	−	16115.3i	−1.83511	−	2.52581i
$345$	−4986.63	+	1365.49i	−0.778178	+	0.213089i
$346$	16336.4	−	5308.02i	2.53830	−	0.824743i
$347$	500.995	−	162.783i	0.0775067	−	0.0251834i	−0.270007	−	0.962858i	$-0.587026\pi$
$347$	500.995	−	162.783i	0.0775067	−	0.0251834i	0.347514	+	0.937675i	$0.387026\pi$
$348$	22862.5	−	6260.45i	3.52171	−	0.964354i
$349$	−3935.20	−	5416.33i	−0.603571	−	0.830744i	0.392459	−	0.919770i	$-0.371625\pi$
$349$	−3935.20	−	5416.33i	−0.603571	−	0.830744i	−0.996029	+	0.0890259i	$0.971625\pi$
$350$	376.916	−	216.147i	0.0575629	−	0.0330102i
$351$	8119.13	+	3970.17i	1.23466	+	0.603737i
$352$	−618.883	−	28459.8i	−0.0937119	−	4.30941i
$353$	−248.832			−0.0375184			−0.0187592	−	0.999824i	$-0.505972\pi$
$353$	−248.832			−0.0375184			−0.0187592	+	0.999824i	$0.505972\pi$
$354$	6178.33	+	9400.62i	0.927612	+	1.41140i
$355$	−3978.18	−	5475.50i	−0.594760	−	0.818618i
$356$	6158.36	+	4474.31i	0.916832	+	0.666118i
$357$	−3262.31	−	6362.35i	−0.483641	−	0.943225i
$358$	4628.20	+	14244.1i	0.683262	+	2.10287i
$359$	4779.70	−	6578.70i	0.702683	−	0.967160i	−0.297241	−	0.954802i	$-0.596066\pi$
$359$	4779.70	−	6578.70i	0.702683	−	0.967160i	0.999924	−	0.0123572i	$-0.00393353\pi$
$360$	−16026.7	+	18196.5i	−2.34633	+	2.66401i
$361$	314.848	−	969.004i	0.0459030	−	0.141275i
$362$	−12027.9			−1.74634
$363$	−6916.04	−	23.4829i	−0.999994	−	0.00339541i
$364$	−19755.6	−	17892.8i	−2.84471	−	2.57647i
$365$	9253.31	+	3006.58i	1.32696	+	0.431155i
$366$	−2337.18	−	109.648i	−0.333788	−	0.0156596i
$367$	−4485.03	+	6173.12i	−0.637920	+	0.878022i	−0.998503	−	0.0547056i	$-0.982578\pi$
$367$	−4485.03	+	6173.12i	−0.637920	+	0.878022i	0.360582	+	0.932727i	$0.382578\pi$
$368$	−21339.7	+	6933.67i	−3.02284	+	0.982181i
$369$	3797.21	−	2248.16i	0.535705	−	0.317167i
$370$	1800.41	−	2478.05i	0.252970	−	0.348183i
$371$	4126.20	+	445.869i	0.577417	+	0.0623945i
$372$	−780.204	−	1187.12i	−0.108741	−	0.165455i
$373$	−1251.37			−0.173709			−0.0868547	−	0.996221i	$-0.527682\pi$
$373$	−1251.37			−0.173709			−0.0868547	+	0.996221i	$0.527682\pi$
$374$	−324.603	−	14927.1i	−0.0448791	−	2.06380i
$375$	5567.83	+	4458.44i	0.766723	+	0.613955i
$376$	−6472.50	−	2103.04i	−0.887749	−	0.288447i
$377$	10642.0	−	7731.84i	1.45382	−	1.05626i
$378$	13873.3	+	3517.05i	1.88774	+	0.478565i
$379$	−4285.81	−	13190.4i	−0.580863	−	1.78771i	−0.615284	−	0.788306i	$-0.710959\pi$
$379$	−4285.81	−	13190.4i	−0.580863	−	1.78771i	0.0344207	−	0.999407i	$-0.489041\pi$
$380$	18460.5	−	5998.20i	2.49212	−	0.809739i
$381$	2488.12	+	9086.33i	0.334567	+	1.22180i
$382$	−6667.60	+	4844.29i	−0.893047	+	0.648837i
$383$	−2617.35	+	8055.36i	−0.349191	+	1.07470i	0.610111	+	0.792316i	$0.291125\pi$
$383$	−2617.35	+	8055.36i	−0.349191	+	1.07470i	−0.959302	+	0.282383i	$0.908875\pi$
$384$	−19922.8	+	24880.2i	−2.64761	+	3.30641i
$385$	−3965.46	−	6579.22i	−0.524932	−	0.870931i
$386$			2590.16i			0.341543i
$387$	6778.77	+	637.451i	0.890398	+	0.0837299i
$388$	20832.0	+	28672.8i	2.72573	+	3.75165i
$389$	−2552.60	+	3513.36i	−0.332705	+	0.457929i	−0.942293	−	0.334790i	$-0.891335\pi$
$389$	−2552.60	+	3513.36i	−0.332705	+	0.457929i	0.609588	+	0.792718i	$0.291335\pi$
$390$	−7404.96	+	19611.1i	−0.961448	+	2.54627i
$391$	−6184.12	+	2009.34i	−0.799858	+	0.259890i
$392$	−23384.8	−	13683.9i	−3.01303	−	1.76312i
$393$	6182.66	+	290.058i	0.793573	+	0.0372303i
$394$	1469.59	−	4522.92i	0.187910	−	0.578329i
$395$	7754.02			0.987715
$396$	16826.7	+	14182.6i	2.13528	+	1.79975i
$397$			5690.26i			0.719360i	0.933076	+	0.359680i	$0.117114\pi$
$397$			5690.26i			0.719360i	−0.933076	+	0.359680i	$0.882886\pi$
$398$	3933.18	−	12105.1i	0.495358	−	1.52456i
$399$	−5213.55	−	5186.94i	−0.654145	−	0.650806i
$400$	−883.421	−	641.843i	−0.110428	−	0.0802303i
$401$	−10119.3	+	3287.95i	−1.26018	+	0.409457i	−0.861558	−	0.507659i	$-0.830511\pi$
$401$	−10119.3	+	3287.95i	−1.26018	+	0.409457i	−0.398620	+	0.917116i	$0.630511\pi$
$402$	2167.32	+	818.358i	0.268896	+	0.101532i
$403$	−637.757	−	463.357i	−0.0788311	−	0.0572741i
$404$	28097.9	−	20414.3i	3.46021	−	2.51399i
$405$	−1046.79	−	8221.79i	−0.128433	−	1.00875i
$406$	13983.7	−	15439.5i	1.70935	−	1.88731i
$407$	−1466.09	−	1017.22i	−0.178554	−	0.123887i
$408$	−19061.5	+	23804.5i	−2.31295	+	2.88848i
$409$	6840.67	+	2222.67i	0.827015	+	0.268714i	0.691788	−	0.722101i	$-0.256823\pi$
$409$	6840.67	+	2222.67i	0.827015	+	0.268714i	0.135228	+	0.990815i	$0.456823\pi$
$410$	6016.11	+	8280.46i	0.724669	+	0.997421i
$411$	−15429.1	+	4224.97i	−1.85173	+	0.507061i
$412$	8481.18	−	2755.70i	1.01417	−	0.329524i
$413$	6641.03	+	2980.05i	0.791244	+	0.355057i
$414$	5163.40	−	11947.9i	0.612964	−	1.41837i
$415$	1498.29	−	1088.58i	0.177225	−	0.128762i
$416$	−15532.7	+	47804.7i	−1.83065	+	5.63417i
$417$	−6850.69	+	8555.33i	−0.804507	+	1.00469i
$418$	−5062.06	−	14499.0i	−0.592329	−	1.69657i
$419$	−7454.41			−0.869145			−0.434572	−	0.900637i	$-0.643100\pi$
$419$	−7454.41			−0.869145			−0.434572	+	0.900637i	$0.643100\pi$
$420$	−3761.95	+	24151.9i	−0.437058	+	2.80593i
$421$	−281.970	+	204.864i	−0.0326423	+	0.0237160i	−0.603987	−	0.796994i	$-0.706422\pi$
$421$	−281.970	+	204.864i	−0.0326423	+	0.0237160i	0.571344	+	0.820710i	$0.306422\pi$
$422$	9004.02	−	12393.0i	1.03865	−	1.42958i
$423$	2001.68	−	1185.11i	0.230083	−	0.136222i
$424$	−5470.02	−	16835.0i	−0.626528	−	1.92825i
$425$	−256.011	−	186.003i	−0.0292196	−	0.0212293i
$426$	17019.7	+	798.476i	1.93570	+	0.0908128i
$427$	−1313.36	+	753.162i	−0.148847	+	0.0853584i
$428$		−	15399.0i		−	1.73911i
$429$	11515.9	+	4064.48i	1.29602	+	0.457424i
$430$			15792.2i			1.77109i
$431$	−2205.80	−	716.707i	−0.246519	−	0.0800988i	0.183151	−	0.983085i	$-0.441370\pi$
$431$	−2205.80	−	716.707i	−0.246519	−	0.0800988i	−0.429670	+	0.902986i	$0.641370\pi$
$432$	−6210.04	−	35429.1i	−0.691622	−	3.94579i
$433$	9736.49	−	13401.1i	1.08061	−	1.48734i	0.221772	−	0.975099i	$-0.428816\pi$
$433$	9736.49	−	13401.1i	1.08061	−	1.48734i	0.858843	−	0.512240i	$-0.171184\pi$
$434$	−1138.94	−	511.080i	−0.125970	−	0.0565268i
$435$	−11285.4	−	4261.25i	−1.24389	−	0.469681i
$436$	2743.56	+	1993.31i	0.301359	+	0.218950i
$437$	−5410.84	+	3931.21i	−0.592301	+	0.430332i
$438$	−20468.7	+	13452.6i	−2.23296	+	1.46756i
$439$			15339.8i			1.66772i	0.551977	+	0.833860i	$0.313874\pi$
$439$			15339.8i			1.66772i	−0.551977	+	0.833860i	$0.686126\pi$
$440$	−18677.6	+	26919.4i	−2.02368	+	2.91666i
$441$	8792.97	−	2906.85i	0.949463	−	0.313880i
$442$	−8146.85	+	25073.4i	−0.876710	+	2.69824i
$443$	3289.70	+	4527.89i	0.352818	+	0.485612i	0.948130	−	0.317882i	$-0.102972\pi$
$443$	3289.70	+	4527.89i	0.352818	+	0.485612i	−0.595312	+	0.803495i	$0.702972\pi$
$444$	1499.58	+	5476.29i	0.160286	+	0.585345i
$445$	−1197.08	−	3684.24i	−0.127522	−	0.392471i
$446$	1291.90	+	3976.06i	0.137160	+	0.422135i
$447$	9373.57	−	2566.77i	0.991845	−	0.271598i
$448$	−4470.55	+	41371.8i	−0.471459	+	4.36302i
$449$	−8514.10	−	2766.40i	−0.894889	−	0.290767i	−0.174763	−	0.984611i	$-0.555916\pi$
$449$	−8514.10	−	2766.40i	−0.894889	−	0.290767i	−0.720126	+	0.693844i	$0.755916\pi$
$450$	618.111	−	138.480i	0.0647512	−	0.0145067i
$451$	4746.58	−	3608.83i	0.495583	−	0.376792i
$452$			6822.90i			0.710005i
$453$	6902.90	−	4536.77i	0.715953	−	0.470543i
$454$	−11498.4	−	15826.1i	−1.18865	−	1.63603i
$455$	2781.41	+	13276.0i	0.286581	+	1.36789i
$456$	−11080.4	+	29344.9i	−1.13791	+	3.01360i
$457$	−1982.78	−	6102.37i	−0.202955	−	0.624632i	−0.999791	−	0.0204364i	$-0.993494\pi$
$457$	−1982.78	−	6102.37i	−0.202955	−	0.624632i	0.796836	−	0.604196i	$-0.206506\pi$
$458$	−19710.9	−	14320.8i	−2.01098	−	1.46107i
$459$	−1799.64	−	10267.2i	−0.183006	−	1.04407i
$460$	21141.2	+	6869.19i	2.14285	+	0.696255i
$461$	17706.2			1.78885			0.894426	−	0.447217i	$-0.147585\pi$
$461$	17706.2			1.78885			0.894426	+	0.447217i	$0.147585\pi$
$462$	19168.6	+	2560.24i	1.93031	+	0.257820i
$463$	386.852			0.0388305			0.0194153	−	0.999812i	$-0.493820\pi$
$463$	386.852			0.0388305			0.0194153	+	0.999812i	$0.493820\pi$
$464$	−49789.4	−	16177.6i	−4.98150	−	1.61859i
$465$	−33.8784	+	722.127i	−0.00337865	+	0.0720169i
$466$	−14021.8	−	10187.4i	−1.39388	−	1.01271i
$467$	−805.103	−	2477.85i	−0.0797768	−	0.245528i	0.903212	−	0.429196i	$-0.141203\pi$
$467$	−805.103	−	2477.85i	−0.0797768	−	0.245528i	−0.982988	+	0.183668i	$0.941203\pi$
$468$	−19796.6	−	33437.0i	−1.95533	−	3.30262i
$469$	1467.20	−	307.387i	0.144454	−	0.0302640i
$470$	3171.36	+	4365.00i	0.311242	+	0.428388i
$471$	−3286.74	−	5000.94i	−0.321540	−	0.489238i
$472$		−	31046.1i		−	3.02757i
$473$	9197.83	−	200.015i	0.894115	−	0.0194433i
$474$	−12201.3	+	15237.4i	−1.18233	+	1.47653i
$475$	−309.558	−	100.582i	−0.0299021	−	0.00971578i
$476$	−3302.59	+	30563.2i	−0.318013	+	2.94298i
$477$	5554.00	+	2400.22i	0.533124	+	0.230395i
$478$	1574.80	+	4846.74i	0.150690	+	0.463775i
$479$	4302.18	+	13240.8i	0.410380	+	1.26302i	0.916319	+	0.400449i	$0.131146\pi$
$479$	4302.18	+	13240.8i	0.410380	+	1.26302i	−0.505939	+	0.862569i	$0.668854\pi$
$480$	44458.7	−	12174.2i	4.22761	−	1.15765i
$481$	1852.02	+	2549.09i	0.175561	+	0.241640i
$482$	4175.76	−	12851.7i	0.394608	−	1.21448i
$483$	−1338.80	−	8315.10i	−0.126123	−	0.783333i
$484$	24793.5	+	16415.8i	2.32847	+	1.54168i
$485$		−	18036.3i		−	1.68863i
$486$	17803.7	+	10880.4i	1.66172	+	1.01552i
$487$	8902.01	−	6467.69i	0.828313	−	0.601805i	−0.0907684	−	0.995872i	$-0.528932\pi$
$487$	8902.01	−	6467.69i	0.828313	−	0.601805i	0.919082	+	0.394067i	$0.128932\pi$
$488$	5224.15	+	3795.57i	0.484603	+	0.352085i
$489$	−3811.48	+	10094.2i	−0.352477	+	0.933491i
$490$	8622.00	+	19673.8i	0.794903	+	1.81382i
$491$	9333.99	−	12847.1i	0.857917	−	1.18082i	−0.124145	−	0.992264i	$-0.539619\pi$
$491$	9333.99	−	12847.1i	0.857917	−	1.18082i	0.982062	−	0.188557i	$-0.0603812\pi$
$492$	−18952.0	−	889.126i	−1.73663	−	0.0814734i
$493$	−14428.7	−	4688.17i	−1.31813	−	0.428285i
$494$			27117.1i			2.46975i
$495$	−2685.34	−	10872.4i	−0.243833	−	0.987228i
$496$			3137.36i			0.284015i
$497$	9564.07	−	5484.64i	0.863194	−	0.495009i
$498$	−218.492	+	4657.21i	−0.0196604	+	0.419066i
$499$	2224.04	+	1615.86i	0.199522	+	0.144961i	0.683060	−	0.730362i	$-0.260649\pi$
$499$	2224.04	+	1615.86i	0.199522	+	0.144961i	−0.483538	+	0.875323i	$0.660649\pi$
$500$	−9476.84	−	29166.7i	−0.847634	−	2.60875i
$501$	−3536.99	+	9367.27i	−0.315411	+	0.835327i
$502$	11788.1	−	16224.9i	1.04806	−	1.44254i
$503$	−4054.37	+	2945.67i	−0.359394	+	0.261115i	−0.752799	−	0.658250i	$-0.771297\pi$
$503$	−4054.37	+	2945.67i	−0.359394	+	0.261115i	0.393405	+	0.919365i	$0.371297\pi$
$504$	−26665.5	−	29140.6i	−2.35670	−	2.57544i
$505$	−17674.6			−1.55745
$506$	5069.82	−	16840.7i	0.445417	−	1.47956i
$507$	−7921.01	−	6342.76i	−0.693855	−	0.555606i
$508$	12516.6	−	38522.1i	1.09318	−	3.36446i
$509$	−4471.31	+	3248.60i	−0.389366	+	0.282891i	−0.765196	−	0.643798i	$-0.777358\pi$
$509$	−4471.31	+	3248.60i	−0.389366	+	0.282891i	0.375830	+	0.926689i	$0.377358\pi$
$510$	23318.5	−	6385.32i	2.02463	−	0.554405i
$511$	−6488.70	+	14460.1i	−0.561729	+	1.25181i
$512$	36168.9	−	11752.0i	3.12198	−	1.01439i
$513$	−5023.85	−	9471.65i	−0.432375	−	0.815173i
$514$	−16238.1	−	22349.8i	−1.39344	−	1.91791i
$515$	−4316.09	−	1402.38i	−0.369301	−	0.119993i
$516$	−22850.5	−	18297.6i	−1.94949	−	1.56106i
$517$	2502.13	−	1902.37i	0.212851	−	0.161830i
$518$	3698.26	+	3349.53i	0.313691	+	0.284112i
$519$	13541.2	−	8899.61i	1.14526	−	0.752696i
$520$	46804.7	−	34005.6i	3.94716	−	2.86778i
$521$	−5110.89	−	3713.28i	−0.429774	−	0.312249i	0.351785	−	0.936081i	$-0.385575\pi$
$521$	−5110.89	−	3713.28i	−0.429774	−	0.312249i	−0.781558	+	0.623832i	$0.785575\pi$
$522$	26131.8	−	15471.5i	2.19111	−	1.29726i
$523$	97.0733	−	31.5410i	0.00811610	−	0.00263708i	−0.304956	−	0.952366i	$-0.598642\pi$
$523$	97.0733	−	31.5410i	0.00811610	−	0.00263708i	0.313072	+	0.949729i	$0.398642\pi$
$524$	−21529.1	−	15641.8i	−1.79485	−	1.30404i
$525$	289.084	−	290.568i	0.0240318	−	0.0241551i
$526$	1473.32	−	4534.40i	0.122129	−	0.375873i
$527$			909.189i			0.0751516i
$528$	−13852.3	−	46586.4i	−1.14175	−	3.83979i
$529$	4507.65			0.370482
$530$	−4336.61	+	13346.7i	−0.355415	+	1.09386i
$531$	7963.44	+	7013.83i	0.650817	+	0.573210i
$532$	6483.70	+	30947.6i	0.528391	+	2.52208i
$533$	−10013.3	+	3253.53i	−0.813744	+	0.264401i
$534$	9123.54	+	3444.96i	0.739352	+	0.279172i
$535$	−4606.22	+	6339.92i	−0.372233	+	0.512334i
$536$	−3758.13	−	5172.62i	−0.302848	−	0.416834i
$537$	7759.80	+	11806.9i	0.623575	+	0.948799i
$538$			29432.2i			2.35858i
$539$	11349.4	−	5270.88i	0.906963	−	0.421211i
$540$	−15653.7	+	32012.4i	−1.24746	+	2.55110i
$541$	−5795.14	+	17835.6i	−0.460541	+	1.41740i	0.403964	+	0.914775i	$0.367632\pi$
$541$	−5795.14	+	17835.6i	−0.460541	+	1.41740i	−0.864505	+	0.502625i	$0.832368\pi$
$542$	4182.80	−	3038.98i	0.331488	−	0.240840i
$543$	−10943.6	+	2996.69i	−0.864887	+	0.236833i
$544$	55135.0	−	17914.4i	4.34539	−	1.41190i
$545$	−533.302	−	1641.33i	−0.0419159	−	0.129004i
$546$	−30465.3	−	15424.8i	−2.38790	−	1.20901i
$547$	7417.55	−	5389.17i	0.579802	−	0.421251i	−0.258851	−	0.965917i	$-0.583344\pi$
$547$	7417.55	−	5389.17i	0.579802	−	0.421251i	0.838653	+	0.544667i	$0.183344\pi$
$548$	65412.8	+	21253.9i	5.09908	+	1.65679i
$549$	−2153.80	+	482.532i	−0.167435	+	0.0375118i
$550$	808.073	−	282.124i	0.0626479	−	0.0218724i
$551$	−15604.7			−1.20651
$552$	−30019.0	+	19729.3i	−2.31467	+	1.52126i
$553$	−1357.00	+	12558.1i	−0.104350	+	0.965684i
$554$	−13014.2	+	17912.6i	−0.998055	+	1.37370i
$555$	1020.70	−	2703.21i	0.0780658	−	0.206747i
$556$	44816.6	−	14561.8i	3.41843	−	1.11071i
$557$	−9062.90	+	12474.0i	−0.689421	+	0.948906i	−0.999999	−	0.00164167i	$-0.999477\pi$
$557$	−9062.90	+	12474.0i	−0.689421	+	0.948906i	0.310578	+	0.950548i	$0.399477\pi$
$558$	−1365.74	−	1202.88i	−0.103613	−	0.0912578i
$559$	−15449.8	−	5019.96i	−1.16898	−	0.379824i
$560$	36239.2	−	40012.1i	2.73462	−	3.01932i
$561$	−4014.33	−	13500.5i	−0.302113	−	1.01603i
$562$	−18659.2			−1.40052
$563$	−4634.90	+	14264.8i	−0.346959	+	1.06783i	0.613568	+	0.789642i	$0.289734\pi$
$563$	−4634.90	+	14264.8i	−0.346959	+	1.06783i	−0.960527	+	0.278187i	$0.910266\pi$
$564$	−9990.42	−	468.698i	−0.745874	−	0.0349925i
$565$	2040.90	−	2809.06i	0.151967	−	0.209165i
$566$	12782.3	+	39339.9i	0.949258	+	2.92152i
$567$	13498.8	−	256.476i	0.999820	−	0.0189964i
$568$	−38043.1	−	27639.9i	−2.81030	−	2.04180i
$569$	10152.4	+	13973.5i	0.747995	+	1.02953i	0.998119	+	0.0613133i	$0.0195289\pi$
$569$	10152.4	+	13973.5i	0.747995	+	1.02953i	−0.250123	+	0.968214i	$0.580471\pi$
$570$	20781.3	−	13658.0i	1.52708	−	1.00363i
$571$	−11829.7			−0.867002			−0.433501	−	0.901153i	$-0.642722\pi$
$571$	−11829.7			−0.867002			−0.433501	+	0.901153i	$0.642722\pi$
$572$	−31778.1	−	41796.8i	−2.32292	−	3.05526i
$573$	−4859.57	+	6068.76i	−0.354295	+	0.442454i
$574$	−14463.5	+	8294.28i	−1.05173	+	0.603130i
$575$	−219.098	−	301.563i	−0.0158905	−	0.0218714i
$576$	−24066.0	+	55687.7i	−1.74089	+	4.02834i
$577$	−22417.3	+	7283.81i	−1.61741	+	0.525527i	−0.971328	−	0.237745i	$-0.923592\pi$
$577$	−22417.3	+	7283.81i	−1.61741	+	0.525527i	−0.646078	+	0.763272i	$0.723592\pi$
$578$	3180.67	−	1033.46i	0.228890	−	0.0743709i
$579$	645.323	+	2356.65i	0.0463190	+	0.169152i
$580$	30485.4	+	41959.5i	2.18248	+	3.00392i
$581$	1500.80	+	2617.08i	0.107166	+	0.186875i
$582$	35442.9	+	28380.9i	2.52432	+	2.02135i
$583$	7828.43	+	2356.72i	0.556124	+	0.167419i
$584$	67599.3			4.78986
$585$	−1851.39	+	19688.0i	−0.130847	+	1.39145i
$586$	−16698.3	−	22983.2i	−1.17713	−	1.62018i
$587$	13644.8	+	9913.50i	0.959420	+	0.697059i	0.953016	−	0.302920i	$-0.0979616\pi$
$587$	13644.8	+	9913.50i	0.959420	+	0.697059i	0.00640387	+	0.999979i	$0.497962\pi$
$588$	−38456.9	−	10319.4i	−2.69717	−	0.723749i
$589$	288.983	+	889.398i	0.0202162	+	0.0622190i
$590$	−14467.3	+	19912.5i	−1.00951	+	1.38947i
$591$	210.239	−	4481.31i	0.0146330	−	0.311906i
$592$	3875.04	−	11926.2i	0.269026	−	0.827977i
$593$	−19664.8			−1.36178			−0.680890	−	0.732386i	$-0.738407\pi$
$593$	−19664.8			−1.36178			−0.680890	+	0.732386i	$0.738407\pi$
$594$	25590.8	+	11831.3i	1.76768	+	0.817247i
$595$	10501.9	−	11595.3i	0.723591	−	0.798925i
$596$	−39739.9	−	12912.3i	−2.73122	−	0.887428i
$597$	562.681	−	11993.7i	0.0385746	−	0.822227i
$598$	−18253.5	+	25123.8i	−1.24823	+	1.71804i
$599$	1479.33	−	480.664i	0.100908	−	0.0327870i	−0.258128	−	0.966111i	$-0.583106\pi$
$599$	1479.33	−	480.664i	0.100908	−	0.0327870i	0.359036	+	0.933324i	$0.383106\pi$
$600$	−1635.49	−	617.543i	−0.111281	−	0.0420185i
$601$	−633.065	+	871.339i	−0.0429671	+	0.0591392i	−0.829960	−	0.557823i	$-0.811637\pi$
$601$	−633.065	+	871.339i	−0.0429671	+	0.0591392i	0.786993	+	0.616962i	$0.211637\pi$
$602$	−25576.3	−	2763.72i	−1.73158	−	0.187111i
$603$	2175.82	+	204.606i	0.146942	+	0.0138179i
$604$	−35514.8			−2.39251
$605$	−5297.39	−	14174.9i	−0.355983	−	0.952549i
$606$	27811.9	−	34732.3i	1.86433	−	2.32822i
$607$	−1514.13	−	491.970i	−0.101246	−	0.0328969i	0.257956	−	0.966157i	$-0.416951\pi$
$607$	−1514.13	−	491.970i	−0.101246	−	0.0328969i	−0.359202	+	0.933260i	$0.616951\pi$
$608$	48240.7	−	35048.9i	3.21780	−	2.33787i
$609$	8876.32	−	17531.5i	0.590619	−	1.16652i
$610$	−1581.98	−	4868.84i	−0.105004	−	0.323170i
$611$	−5278.47	+	1715.08i	−0.349499	+	0.113559i
$612$	−17778.7	+	41139.0i	−1.17428	+	2.71723i
$613$	−8555.02	+	6215.59i	−0.563677	+	0.409535i	−0.832803	−	0.553570i	$-0.813265\pi$
$613$	−8555.02	+	6215.59i	−0.563677	+	0.409535i	0.269126	+	0.963105i	$0.413265\pi$
$614$	5515.88	−	16976.1i	0.362546	−	1.11580i
$615$	7536.76	+	6035.07i	0.494165	+	0.395703i
$616$	−40328.7	−	34960.4i	−2.63781	−	2.28668i
$617$		−	5138.53i		−	0.335282i	−0.985848	−	0.167641i	$-0.946385\pi$
$617$		−	5138.53i		−	0.335282i	0.985848	−	0.167641i	$-0.0536150\pi$
$618$	9547.40	−	6274.80i	0.621444	−	0.408429i
$619$	−5725.02	−	7879.81i	−0.371741	−	0.511658i	0.581632	−	0.813452i	$-0.302414\pi$
$619$	−5725.02	−	7879.81i	−0.371741	−	0.511658i	−0.953373	+	0.301794i	$0.902414\pi$
$620$	1826.94	−	2514.57i	0.118341	−	0.162883i
$621$	1721.16	−	12157.2i	0.111220	−	0.785588i
$622$	25330.0	−	8230.23i	1.63287	−	0.530550i
$623$	6176.32	−	1293.98i	0.397190	−	0.0832136i
$624$	−4021.77	+	85725.2i	−0.258013	+	5.49961i
$625$	−4987.30	+	15349.3i	−0.319187	+	0.982358i
$626$	27274.1			1.74136
$627$	−8218.03	−	11930.7i	−0.523440	−	0.759912i
$628$			25729.4i			1.63489i
$629$	1122.97	−	3456.14i	0.0711854	−	0.219086i
$630$	3523.56	+	31116.3i	0.222829	+	1.96778i
$631$	−20332.3	−	14772.3i	−1.28275	−	0.931972i	−0.283117	−	0.959085i	$-0.591368\pi$
$631$	−20332.3	−	14772.3i	−1.28275	−	0.931972i	−0.999632	+	0.0271136i	$0.991368\pi$
$632$	51237.2	−	16648.0i	3.22485	−	1.04782i
$633$	5104.65	−	13519.0i	0.320524	−	0.848867i
$634$	−6449.75	−	4686.02i	−0.404026	−	0.293542i
$635$	−16676.2	+	12115.9i	−1.04216	+	0.757175i
$636$	−14287.4	−	21739.0i	−0.890776	−	1.35536i
$637$	−21988.0	+	2181.26i	−1.36766	+	0.135675i
$638$	32665.2	−	24835.4i	2.02701	−	1.54113i
$639$	15684.3	−	3513.87i	0.970987	−	0.217538i
$640$	−66326.9	−	21550.9i	−4.09656	−	1.33105i
$641$	2636.79	+	3629.23i	0.162476	+	0.223629i	0.882491	−	0.470330i	$-0.155865\pi$
$641$	2636.79	+	3629.23i	0.162476	+	0.223629i	−0.720015	+	0.693959i	$0.755865\pi$
$642$	−5210.41	−	19027.8i	−0.320309	−	1.16973i
$643$	9359.19	−	3040.98i	0.574013	−	0.186508i	−0.00760372	−	0.999971i	$-0.502420\pi$
$643$	9359.19	−	3040.98i	0.574013	−	0.186508i	0.581617	+	0.813463i	$0.302420\pi$
$644$	−14824.8	+	33037.2i	−0.907113	+	2.02150i
$645$	3934.53	+	14368.5i	0.240189	+	0.877144i
$646$	25302.1	−	18383.1i	1.54102	−	1.11962i
$647$	−2668.48	+	8212.75i	−0.162147	+	0.499036i	−0.998815	−	0.0486740i	$-0.984500\pi$
$647$	−2668.48	+	8212.75i	−0.162147	+	0.499036i	0.836668	+	0.547710i	$0.184500\pi$
$648$	−24569.3	−	52080.6i	−1.48946	−	3.15728i
$649$	11780.9	+	8173.97i	0.712541	+	0.494386i
$650$	−1511.32			−0.0911982
$651$	−1163.60	−	181.244i	−0.0700536	−	0.0109117i
$652$	37530.8	−	27267.7i	2.25432	−	1.63786i
$653$	−6936.49	+	9547.26i	−0.415691	+	0.572149i	−0.964595	−	0.263736i	$-0.915045\pi$
$653$	−6936.49	+	9547.26i	−0.415691	+	0.572149i	0.548904	+	0.835885i	$0.315045\pi$
$654$	4064.55	+	1534.73i	0.243022	+	0.0917628i
$655$	4184.89	+	12879.8i	0.249645	+	0.768327i
$656$	33899.7	+	24629.6i	2.01763	+	1.46589i
$657$	−15271.8	+	17339.5i	−0.906864	+	1.02965i
$658$	−7624.36	+	4372.28i	−0.451715	+	0.259042i
$659$		−	7723.28i		−	0.456534i	−0.973599	−	0.228267i	$-0.926694\pi$
$659$		−	7723.28i		−	0.456534i	0.973599	−	0.228267i	$-0.0733060\pi$
$660$	−16025.6	+	45405.1i	−0.945142	+	2.67786i
$661$		−	7862.36i		−	0.462648i	−0.972877	−	0.231324i	$-0.925694\pi$
$661$		−	7862.36i		−	0.462648i	0.972877	−	0.231324i	$-0.0743057\pi$
$662$	−35932.0	−	11675.0i	−2.10957	−	0.685442i
$663$	−1165.49	+	24842.7i	−0.0682713	+	1.45522i
$664$	7563.28	−	10410.0i	0.442036	−	0.608411i
$665$	6587.79	−	14680.9i	0.384156	−	0.856091i
$666$	3705.92	+	6259.41i	0.215618	+	0.364185i
$667$	−14457.7	−	10504.1i	−0.839287	−	0.609778i
$668$	34827.9	−	25304.0i	2.01726	−	1.46563i
$669$	2166.05	+	3295.74i	0.125178	+	0.190464i
$670$			5068.90i			0.292282i
$671$	−2815.72	+	983.058i	−0.161996	+	0.0565581i
$672$	11936.2	+	74133.8i	0.685191	+	4.25562i
$673$	−9381.81	+	28874.2i	−0.537358	+	1.65382i	0.201140	+	0.979563i	$0.435535\pi$
$673$	−9381.81	+	28874.2i	−0.537358	+	1.65382i	−0.738498	+	0.674256i	$0.764465\pi$
$674$	−30561.4	−	42064.1i	−1.74656	−	2.40393i
$675$	527.885	−	279.995i	0.0301012	−	0.0159659i
$676$	13482.1	+	41493.8i	0.767077	+	2.36082i
$677$	−7169.21	−	22064.6i	−0.406994	−	1.25260i	−0.919218	−	0.393748i	$-0.871178\pi$
$677$	−7169.21	−	22064.6i	−0.406994	−	1.25260i	0.512224	−	0.858852i	$-0.328822\pi$
$678$	2308.60	+	8430.75i	0.130769	+	0.477553i
$679$	29210.7	+	3156.45i	1.65096	+	0.178400i
$680$	−63459.3	−	20619.2i	−3.57875	−	1.16281i
$681$	−14404.7	−	11534.6i	−0.810559	−	0.649056i
$682$	−2020.43	−	1401.84i	−0.113440	−	0.0787087i
$683$			4519.03i			0.253171i	0.991956	+	0.126586i	$0.0404018\pi$
$683$			4519.03i			0.253171i	−0.991956	+	0.126586i	$0.959598\pi$
$684$	−4315.74	+	45894.4i	−0.241252	+	2.56552i
$685$	−20573.5	−	28317.1i	−1.14755	−	1.57947i
$686$	−33371.7	+	10520.8i	−1.85734	+	0.585547i
$687$	−21501.9	−	8118.90i	−1.19410	−	0.450881i
$688$	19978.7	+	61488.0i	1.10709	+	3.40728i
$689$	−11678.9	−	8485.20i	−0.645761	−	0.469173i
$690$	28447.5	+	1334.61i	1.56953	+	0.0736341i
$691$	12359.5	+	4015.83i	0.680429	+	0.221085i	0.628783	−	0.777581i	$-0.283553\pi$
$691$	12359.5	+	4015.83i	0.680429	+	0.221085i	0.0516457	+	0.998665i	$0.483553\pi$
$692$	−69668.1			−3.82714
$693$	18078.4	−	2446.33i	0.990968	−	0.134096i
$694$	−2901.61			−0.158709
$695$	−22807.2	−	7410.52i	−1.24479	−	0.404456i
$696$	−83720.6	−	3927.73i	−4.55951	−	0.213908i
$697$	9823.96	+	7137.53i	0.533872	+	0.387881i
$698$	11395.7	+	35072.5i	0.617959	+	1.90188i
$699$	−15295.8	−	5775.56i	−0.827671	−	0.312520i
$700$	−1724.81	+	361.357i	−0.0931308	+	0.0195115i
$701$	−11843.1	−	16300.6i	−0.638097	−	0.878266i	0.360415	−	0.932792i	$-0.382635\pi$
$701$	−11843.1	−	16300.6i	−0.638097	−	0.878266i	−0.998512	+	0.0545265i	$0.982635\pi$
$702$	−35775.5	−	34618.2i	−1.92344	−	1.86122i
$703$		−	3737.84i		−	0.200534i
$704$	−23629.9	+	78492.5i	−1.26504	+	4.20213i
$705$	3972.96	+	3181.35i	0.212242	+	0.169953i
$706$	1303.54	+	423.546i	0.0694893	+	0.0225784i
$707$	3093.16	−	28625.0i	0.164541	−	1.52271i
$708$	−12049.9	−	44005.1i	−0.639639	−	2.33589i
$709$	10849.9	+	33392.5i	0.574719	+	1.76880i	0.637133	+	0.770754i	$0.280120\pi$
$709$	10849.9	+	33392.5i	0.574719	+	1.76880i	−0.0624130	+	0.998050i	$0.519880\pi$
$710$	11520.2	+	35455.6i	0.608939	+	1.87412i
$711$	−7305.05	+	16903.6i	−0.385318	+	0.891608i
$712$	−15820.2	−	21774.6i	−0.832707	−	1.14612i
$713$	−330.946	+	1018.55i	−0.0173829	+	0.0534991i
$714$	6260.50	+	38883.0i	0.328142	+	2.03804i
$715$	580.916	+	26713.8i	0.0303846	+	1.39726i
$716$		−	60745.4i		−	3.17062i
$717$	2640.36	+	4017.44i	0.137526	+	0.209252i
$718$	−36237.0	+	26327.7i	−1.88350	+	1.36844i
$719$	8454.13	+	6142.28i	0.438506	+	0.318593i	0.785041	−	0.619444i	$-0.212642\pi$
$719$	8454.13	+	6142.28i	0.438506	+	0.318593i	−0.346535	+	0.938037i	$0.612642\pi$
$720$	67721.6	−	40095.0i	3.50533	−	2.07535i
$721$	3026.58	−	6744.72i	0.156332	−	0.348386i
$722$	−3298.76	+	4540.35i	−0.170038	+	0.234037i
$723$	597.385	−	12733.4i	0.0307289	−	0.654995i
$724$	46396.1	+	15075.0i	2.38162	+	0.773837i
$725$		−	869.702i		−	0.0445516i
$726$	36190.7	+	11895.1i	1.85009	+	0.608082i
$727$		−	18994.6i		−	0.969012i	−0.874788	−	0.484506i	$-0.838999\pi$
$727$		−	18994.6i		−	0.969012i	0.874788	−	0.484506i	$-0.161001\pi$
$728$	46882.9	+	81754.0i	2.38681	+	4.16209i
$729$	18909.5	+	5463.76i	0.960700	+	0.277588i
$730$	−43357.2	−	31500.8i	−2.19825	−	1.59712i
$731$	5789.71	+	17818.9i	0.292941	+	0.901581i
$732$	8877.93	+	3352.22i	0.448275	+	0.169264i
$733$	−18765.2	+	25828.1i	−0.945578	+	1.30148i	0.00788511	+	0.999969i	$0.497490\pi$
$733$	−18765.2	+	25828.1i	−0.945578	+	1.30148i	−0.953464	+	0.301508i	$0.902510\pi$
$734$	34003.0	−	24704.6i	1.70991	−	1.24232i
$735$	12746.3	+	15752.0i	0.639666	+	0.790506i
$736$	68287.5			3.41998
$737$	2952.28	−	64.1999i	0.147556	−	0.00320873i
$738$	−23718.9	+	5313.94i	−1.18307	+	0.265053i
$739$	5400.87	−	16622.2i	0.268842	−	0.827411i	−0.721941	−	0.691954i	$-0.756750\pi$
$739$	5400.87	−	16622.2i	0.268842	−	0.827411i	0.990783	−	0.135456i	$-0.0432500\pi$
$740$	−10050.6	+	7302.22i	−0.499282	+	0.362750i
$741$	6756.06	+	24672.4i	0.334939	+	1.22316i
$742$	−20856.8	−	9359.12i	−1.03191	−	0.463051i
$743$	26481.3	−	8604.30i	1.30754	−	0.424847i	0.429344	−	0.903141i	$-0.358745\pi$
$743$	26481.3	−	8604.30i	1.30754	−	0.424847i	0.878200	+	0.478294i	$0.158745\pi$
$744$	1326.55	+	4844.42i	0.0653680	+	0.238717i
$745$	12498.9	+	17203.3i	0.614665	+	0.846014i
$746$	6555.50	+	2130.01i	0.321734	+	0.104538i
$747$	961.523	+	4291.79i	0.0470954	+	0.210212i
$748$	−17456.5	+	57985.9i	−0.853304	+	2.83446i
$749$	−9461.73	−	8569.55i	−0.461581	−	0.418057i
$750$	−21579.0	−	32833.4i	−1.05060	−	1.59854i
$751$	10523.2	−	7645.52i	0.511312	−	0.371490i	−0.302009	−	0.953305i	$-0.597657\pi$
$751$	10523.2	−	7645.52i	0.511312	−	0.371490i	0.813321	+	0.581815i	$0.197657\pi$
$752$	17870.1	+	12983.4i	0.866561	+	0.629593i
$753$	6683.01	−	17699.1i	0.323429	−	0.856562i
$754$	−68910.2	+	22390.3i	−3.32833	+	1.08144i
$755$	14621.8	+	10623.4i	0.704824	+	0.512085i
$756$	−49106.3	−	30954.4i	−2.36240	−	1.48915i
$757$	−9448.20	+	29078.6i	−0.453634	+	1.39614i	0.419098	+	0.907941i	$0.362346\pi$
$757$	−9448.20	+	29078.6i	−0.453634	+	1.39614i	−0.872732	+	0.488200i	$0.837654\pi$
$758$			76394.7i			3.66066i
$759$	417.013	−	16585.5i	0.0199428	−	0.793171i
$760$	−68631.6			−3.27570
$761$	12472.6	−	38386.9i	0.594130	−	1.82854i	0.0351213	−	0.999383i	$-0.488818\pi$
$761$	12472.6	−	38386.9i	0.594130	−	1.82854i	0.559009	−	0.829162i	$-0.311182\pi$
$762$	2431.83	−	51835.2i	0.115612	−	2.46429i
$763$	2751.56	−	576.469i	0.130555	−	0.0273520i
$764$	31790.8	−	10329.5i	1.50543	−	0.489145i
$765$	19625.4	−	11619.3i	0.927525	−	0.549147i
$766$	27422.7	−	37744.1i	1.29350	−	1.78035i
$767$	−14882.0	−	20483.4i	−0.700599	−	0.964292i
$768$	68665.8	−	45128.9i	3.22625	−	2.12038i
$769$			7719.01i			0.361970i	0.983486	+	0.180985i	$0.0579285\pi$
$769$			7719.01i			0.361970i	−0.983486	+	0.180985i	$0.942071\pi$
$770$	9574.90	+	41216.0i	0.448124	+	1.92899i
$771$	−20342.5	−	16289.3i	−0.950215	−	0.760886i
$772$	3246.33	−	9991.17i	0.151344	−	0.465790i
$773$	−10474.1	+	7609.90i	−0.487359	+	0.354087i	−0.804168	−	0.594402i	$-0.797389\pi$
$773$	−10474.1	+	7609.90i	−0.487359	+	0.354087i	0.316809	+	0.948489i	$0.397389\pi$
$774$	−34426.5	−	14877.8i	−1.59875	−	0.690919i
$775$	−49.5689	+	16.1059i	−0.00229751	+	0.000746506i
$776$	−38724.0	−	119180.i	−1.79138	−	5.51330i
$777$	4199.36	+	2126.16i	0.193888	+	0.0981669i
$778$	19352.4	−	14060.3i	0.891796	−	0.647928i
$779$	11878.8	+	3859.64i	0.546342	+	0.177517i
$780$	53142.8	−	66366.2i	2.43951	−	3.04653i
$781$	20504.5	−	7158.77i	0.939446	−	0.327991i
$782$	35816.6			1.63785
$783$	19921.3	−	20587.3i	0.909234	−	0.939630i
$784$	58459.7	+	65693.7i	2.66307	+	2.99260i
$785$	7696.30	−	10593.1i	0.349927	−	0.481633i
$786$	−31895.1	−	12043.3i	−1.44740	−	0.546526i
$787$	−12689.4	+	4123.03i	−0.574749	+	0.186747i	−0.581947	−	0.813227i	$-0.697709\pi$
$787$	−12689.4	+	4123.03i	−0.574749	+	0.186747i	0.00719769	+	0.999974i	$0.497709\pi$
$788$	−11337.4	+	15604.7i	−0.512538	+	0.705448i
$789$	210.773	−	4492.68i	0.00951041	−	0.202717i
$790$	−40620.6	−	13198.4i	−1.82939	−	0.594404i
$791$	4192.26	+	3796.95i	0.188444	+	0.170675i
$792$	−41087.4	−	66077.4i	−1.84341	−	2.96459i
$793$	5266.16			0.235822
$794$	9685.61	−	29809.2i	0.432908	−	1.33236i
$795$	−620.396	+	13223.9i	−0.0276769	+	0.589941i
$796$	−30343.4	+	41764.1i	−1.35112	+	1.85966i
$797$	7633.97	+	23494.9i	0.339284	+	1.04421i	0.964573	+	0.263815i	$0.0849808\pi$
$797$	7633.97	+	23494.9i	0.339284	+	1.04421i	−0.625290	+	0.780393i	$0.715019\pi$
$798$	18483.1	+	36046.7i	0.819916	+	1.59905i
$799$	5178.65	+	3762.51i	0.229296	+	0.166593i
$800$	1953.39	+	2688.61i	0.0863283	+	0.118821i
$801$	9159.31	+	861.309i	0.404030	+	0.0379936i
$802$	58607.7			2.58044
$803$	−17797.9	+	25651.4i	−0.782158	+	1.12730i
$804$	−7334.45	−	5873.07i	−0.321724	−	0.257621i
$805$	15985.8	−	9167.26i	0.699907	−	0.401371i
$806$	2552.28	+	3512.92i	0.111539	+	0.153520i
$807$	7332.87	+	26778.8i	0.319863	+	1.16810i
$808$	−116791.	+	37947.6i	−5.08501	+	1.65222i
$809$	41167.5	−	13376.1i	1.78909	−	0.581310i	0.789611	−	0.613608i	$-0.210282\pi$
$809$	41167.5	−	13376.1i	1.78909	−	0.581310i	0.999478	+	0.0322973i	$0.0102823\pi$
$810$	−8510.86	+	44852.8i	−0.369187	+	1.94564i
$811$	−17292.9	−	23801.6i	−0.748749	−	1.03056i	−0.998067	−	0.0621429i	$-0.980207\pi$
$811$	−17292.9	−	23801.6i	−0.748749	−	1.03056i	0.249318	−	0.968422i	$-0.419793\pi$
$812$	−73290.8	+	42029.6i	−3.16749	+	1.81644i
$813$	3048.56	−	3807.13i	0.131510	−	0.164234i
$814$	5948.88	+	7824.37i	0.256152	+	0.336909i
$815$	−23608.3			−1.01468
$816$	82714.1	−	54361.8i	3.54849	−	2.33216i
$817$	11327.4	+	15590.8i	0.485060	+	0.667628i
$818$	−32052.5	−	23287.5i	−1.37004	−	0.995391i
$819$	−31561.8	−	6443.94i	−1.34659	−	0.274932i
$820$	−12828.1	−	39480.9i	−0.546314	−	1.68138i
$821$	−2286.62	+	3147.27i	−0.0972030	+	0.133789i	−0.854848	−	0.518878i	$-0.826350\pi$
$821$	−2286.62	+	3147.27i	−0.0972030	+	0.133789i	0.757645	+	0.652667i	$0.226350\pi$
$822$	88019.1	+	4129.39i	3.73482	+	0.175218i
$823$	−4750.00	+	14619.0i	−0.201184	+	0.619181i	0.798664	+	0.601777i	$0.205540\pi$
$823$	−4750.00	+	14619.0i	−0.201184	+	0.619181i	−0.999849	+	0.0174046i	$0.994460\pi$
$824$	−31530.9			−1.33305
$825$	664.933	−	458.017i	0.0280606	−	0.0193286i
$826$	−29717.5	−	26915.4i	−1.25182	−	1.13378i
$827$	42150.0	+	13695.4i	1.77231	+	0.575858i	0.998352	−	0.0573807i	$-0.0182749\pi$
$827$	42150.0	+	13695.4i	1.77231	+	0.575858i	0.773957	+	0.633239i	$0.218275\pi$
$828$	−34891.7	+	39615.8i	−1.46446	+	1.66273i
$829$	14855.4	−	20446.7i	0.622374	−	0.856625i	−0.375149	−	0.926965i	$-0.622408\pi$
$829$	14855.4	−	20446.7i	0.622374	−	0.856625i	0.997523	+	0.0703398i	$0.0224083\pi$
$830$	−9701.94	+	3152.35i	−0.405734	+	0.131831i
$831$	−7378.16	+	19540.1i	−0.307997	+	0.815691i
$832$	85077.6	−	117099.i	3.54511	−	4.87943i
$833$	16941.3	+	19037.7i	0.704659	+	0.791856i
$834$	50450.7	−	33157.5i	2.09468	−	1.37668i
$835$	−21908.1			−0.907976
$836$	1354.16	+	62272.2i	0.0560224	+	2.57623i
$837$	−1542.30	−	754.169i	−0.0636914	−	0.0311444i
$838$	39051.0	+	12688.4i	1.60978	+	0.523049i
$839$	7939.93	−	5768.70i	0.326719	−	0.237375i	−0.412318	−	0.911040i	$-0.635281\pi$
$839$	7939.93	−	5768.70i	0.326719	−	0.237375i	0.739037	+	0.673665i	$0.235281\pi$
$840$	39039.2	−	77105.9i	1.60355	−	3.16715i
$841$	−5348.06	−	16459.6i	−0.219282	−	0.674880i
$842$	1825.85	−	593.254i	0.0747303	−	0.0242813i
$843$	−16977.0	+	4648.82i	−0.693616	+	0.189934i
$844$	−50264.3	+	36519.1i	−2.04996	+	1.48938i
$845$	6861.09	−	21116.3i	0.279324	−	0.859670i
$846$	−12503.3	+	2801.21i	−0.508124	+	0.113839i
$847$	23884.1	−	6098.72i	0.968911	−	0.247408i
$848$			57452.6i			2.32657i
$849$	21431.2	+	32608.6i	0.866335	+	1.31817i
$850$	1024.55	+	1410.17i	0.0413431	+	0.0569039i
$851$	2516.08	−	3463.08i	0.101351	−	0.139498i
$852$	−64650.4	−	24411.4i	−2.59963	−	0.981596i
$853$	14830.5	−	4818.71i	0.595294	−	0.193423i	0.00415354	−	0.999991i	$-0.498678\pi$
$853$	14830.5	−	4818.71i	0.595294	−	0.193423i	0.591140	+	0.806569i	$0.298678\pi$
$854$	8162.20	−	1710.03i	0.327055	−	0.0685199i
$855$	15505.0	−	17604.3i	0.620187	−	0.704155i
$856$	−16825.2	+	51782.7i	−0.671815	+	2.06763i
$857$	35599.3			1.41896			0.709480	−	0.704726i	$-0.248930\pi$
$857$	35599.3			1.41896			0.709480	+	0.704726i	$0.248930\pi$
$858$	−53409.2	−	40894.0i	−2.12513	−	1.62715i
$859$		−	42673.7i		−	1.69500i	−0.530794	−	0.847501i	$-0.678106\pi$
$859$		−	42673.7i		−	1.69500i	0.530794	−	0.847501i	$-0.321894\pi$
$860$	19792.8	−	60916.1i	0.784803	−	2.41537i
$861$	−11093.1	+	11150.0i	−0.439085	+	0.441338i
$862$	10335.5	+	7509.15i	0.408384	+	0.296708i
$863$	−38936.0	+	12651.1i	−1.53580	+	0.499012i	−0.950214	−	0.311598i	$-0.899136\pi$
$863$	−38936.0	+	12651.1i	−1.53580	+	0.499012i	−0.585587	+	0.810610i	$0.699136\pi$
$864$	−15345.1	+	108388.i	−0.604226	+	4.26786i
$865$	28683.1	+	20839.5i	1.12746	+	0.819149i
$866$	−73816.6	+	53630.9i	−2.89653	+	2.10445i
$867$	2636.44	−	1732.74i	0.103274	−	0.0678742i
$868$	3752.75	+	3398.89i	0.146747	+	0.132910i
$869$	−7172.67	+	23825.8i	−0.279996	+	0.930074i
$870$	51866.8	+	41532.4i	2.02121	+	1.61848i
$871$	−4959.02	−	1611.28i	−0.192916	−	0.0626822i
$872$	−7047.93	−	9700.64i	−0.273707	−	0.376726i
$873$	39318.6	+	16991.9i	1.52432	+	0.658751i
$874$	35036.9	−	11384.2i	1.35600	−	0.440590i
$875$	−23195.0	−	10408.4i	−0.896155	−	0.402134i
$876$	95815.9	−	26237.3i	3.69557	−	1.01196i
$877$	−2395.61	+	1740.51i	−0.0922393	+	0.0670158i	−0.632949	−	0.774193i	$-0.718156\pi$
$877$	−2395.61	+	1740.51i	−0.0922393	+	0.0670158i	0.540710	+	0.841209i	$0.318156\pi$
$878$	26110.5	−	80359.8i	1.00363	−	3.08885i
$879$	−20919.0	−	16750.9i	−0.802707	−	0.642769i
$880$	84653.2	−	64361.9i	3.24279	−	2.46550i
$881$	15924.0			0.608960			0.304480	−	0.952519i	$-0.401517\pi$
$881$	15924.0			0.608960			0.304480	+	0.952519i	$0.401517\pi$
$882$	−51011.1	+	261.079i	−1.94743	+	0.00996712i
$883$	−25727.9	+	18692.4i	−0.980534	+	0.712400i	−0.957828	−	0.287343i	$-0.907228\pi$
$883$	−25727.9	+	18692.4i	−0.980534	+	0.712400i	−0.0227060	+	0.999742i	$0.507228\pi$
$884$	62850.6	−	86506.5i	2.39128	−	3.29132i
$885$	−8201.93	+	21721.8i	−0.311531	+	0.825051i
$886$	−9526.49	−	29319.5i	−0.361229	−	1.11175i
$887$	−13269.5	−	9640.88i	−0.502308	−	0.364948i	0.307590	−	0.951519i	$-0.400478\pi$
$887$	−13269.5	−	9640.88i	−0.502308	−	0.364948i	−0.809898	+	0.586571i	$0.800478\pi$
$888$	940.817	−	20053.8i	0.0355538	−	0.757838i
$889$	−16704.0	−	29128.3i	−0.630185	−	1.09891i
$890$			21338.0i			0.803654i
$891$	26231.4	+	4388.89i	0.986290	+	0.165021i
$892$		−	16956.3i		−	0.636478i
$893$	6261.82	+	2034.59i	0.234652	+	0.0762429i
$894$	−53473.8	−	2508.71i	−2.00048	−	0.0938521i
$895$	−18170.5	+	25009.5i	−0.678628	+	0.934051i
$896$	46510.5	−	103648.i	1.73416	−	3.86457i
$897$	−10348.4	+	27406.5i	−0.385200	+	1.02015i
$898$	39893.5	+	28984.3i	1.48248	+	1.07708i
$899$	−2021.54	+	1468.73i	−0.0749967	+	0.0544883i
$900$	−2557.84	−	240.530i	−0.0947348	−	0.00890852i
$901$			16649.5i			0.615620i
$902$	−31008.4	+	10826.0i	−1.14464	+	0.399631i
$903$	−23959.1	+	3857.62i	−0.882955	+	0.142163i
$904$	7454.83	−	22943.6i	0.274274	−	0.844129i
$905$	−14592.4	−	20084.8i	−0.535988	−	0.737724i
$906$	−43884.1	+	12016.8i	−1.60922	+	0.440653i
$907$	−14049.7	−	43240.5i	−0.514347	−	1.58300i	−0.784467	−	0.620170i	$-0.787064\pi$
$907$	−14049.7	−	43240.5i	−0.514347	−	1.58300i	0.270121	−	0.962827i	$-0.412936\pi$
$908$	24517.9	+	75458.4i	0.896096	+	2.75790i
$909$	16651.2	−	38530.2i	0.607576	−	1.40590i
$910$	8026.85	−	74282.8i	0.292404	−	2.70599i
$911$	1466.35	+	476.448i	0.0533288	+	0.0173276i	0.335560	−	0.942019i	$-0.391075\pi$
$911$	1466.35	+	476.448i	0.0533288	+	0.0173276i	−0.282231	+	0.959346i	$0.591075\pi$
$912$	63634.8	−	79468.9i	2.31048	−	2.88539i
$913$	1958.90	+	5610.77i	0.0710078	+	0.203384i
$914$			35343.1i			1.27905i
$915$	−2652.40	−	4035.75i	−0.0958314	−	0.145812i
$916$	58083.4	+	79944.9i	2.09512	+	2.88368i
$917$	−21591.9	+	4523.63i	−0.777564	+	0.162904i
$918$	−8048.47	+	56849.2i	−0.289367	+	2.04390i
$919$	−16034.6	−	49349.4i	−0.575552	−	1.77137i	−0.634293	−	0.773093i	$-0.718709\pi$
$919$	−16034.6	−	49349.4i	−0.575552	−	1.77137i	0.0587412	−	0.998273i	$-0.481291\pi$
$920$	−63586.8	−	46198.5i	−2.27869	−	1.65556i
$921$	789.103	−	16819.9i	0.0282322	−	0.601776i
$922$	−92756.6	−	30138.4i	−3.31320	−	1.07653i
$923$	−38349.0			−1.36758
$924$	−70731.5	−	33900.4i	−2.51828	−	1.20697i
$925$	208.321			0.00740493
$926$	−2026.58	−	658.476i	−0.0719196	−	0.0233681i
$927$	7123.34	−	8087.78i	0.252385	−	0.286556i
$928$	128899.	+	93650.3i	4.55960	+	3.31274i
$929$	−3686.17	−	11344.9i	−0.130182	−	0.400660i	0.864627	−	0.502414i	$-0.167555\pi$
$929$	−3686.17	−	11344.9i	−0.130182	−	0.400660i	−0.994810	+	0.101754i	$0.967555\pi$
$930$	1406.64	−	3725.30i	0.0495973	−	0.131352i
$931$	22623.6	+	13238.5i	0.796410	+	0.466031i
$932$	41318.9	+	56870.6i	1.45220	+	1.99878i
$933$	20995.9	−	13799.1i	0.736738	−	0.484203i
$934$			14351.0i			0.502761i
$935$	24532.1	−	18651.7i	0.858058	−	0.652382i
$936$	30036.7	+	134070.i	1.04891	+	4.68184i
$937$	10361.0	+	3366.48i	0.361236	+	0.117373i	0.484011	−	0.875062i	$-0.339179\pi$
$937$	10361.0	+	3366.48i	0.361236	+	0.117373i	−0.122775	+	0.992435i	$0.539179\pi$
$938$	−8209.36	−	887.086i	−0.285762	−	0.0308789i
$939$	24815.2	−	6795.18i	0.862423	−	0.236158i
$940$	−6762.27	−	20812.1i	−0.234639	−	0.722145i
$941$	8872.26	+	27306.0i	0.307362	+	0.945962i	0.978785	+	0.204888i	$0.0656832\pi$
$941$	8872.26	+	27306.0i	0.307362	+	0.945962i	−0.671424	+	0.741074i	$0.734317\pi$
$942$	8705.80	+	31792.6i	0.301115	+	1.09964i
$943$	8407.52	+	11572.0i	0.290336	+	0.399613i
$944$	−31138.1	+	95833.3i	−1.07358	+	3.30414i
$945$	10958.3	+	27433.2i	0.377222	+	0.944339i
$946$	−48524.6	−	14608.2i	−1.66773	−	0.502064i
$947$			24157.4i			0.828946i	0.910062	+	0.414473i	$0.136034\pi$
$947$			24157.4i			0.828946i	−0.910062	+	0.414473i	$0.863966\pi$
$948$	66162.4	−	43483.7i	2.26673	−	1.48975i
$949$	44600.2	−	32403.9i	1.52559	−	1.10840i
$950$	1450.46	+	1053.82i	0.0495360	+	0.0359900i
$951$	−7035.78	−	2656.64i	−0.239906	−	0.0905862i
$952$	44499.6	−	99167.3i	1.51496	−	3.37608i
$953$	−28368.0	+	39045.2i	−0.964248	+	1.32717i	−0.0193491	+	0.999813i	$0.506159\pi$
$953$	−28368.0	+	39045.2i	−0.964248	+	1.32717i	−0.944899	+	0.327361i	$0.893841\pi$
$954$	−25009.9	−	22027.6i	−0.848770	−	0.747557i
$955$	−16178.4	−	5256.69i	−0.548190	−	0.178118i
$956$		−	20669.4i		−	0.699262i
$957$	23532.8	−	30734.8i	0.794887	−	1.03815i
$958$		−	76686.6i		−	2.58625i
$959$	49461.5	−	28364.3i	1.66548	−	0.955091i
$960$	−132591.	−	6220.45i	−4.45765	−	0.209129i
$961$	−23980.3	−	17422.7i	−0.804950	−	0.584831i
$962$	−5363.19	−	16506.2i	−0.179746	−	0.553203i
$963$	−9481.35	−	16014.3i	−0.317271	−	0.535880i
$964$	−32214.8	+	44339.9i	−1.07632	+	1.48142i
$965$	−4325.16	+	3142.41i	−0.144282	+	0.104827i
$966$	−7139.94	+	45838.7i	−0.237809	+	1.52674i
$967$	−19616.4			−0.652348			−0.326174	−	0.945310i	$-0.605759\pi$
$967$	−19616.4			−0.652348			−0.326174	+	0.945310i	$0.605759\pi$
$968$	−65437.9	−	82291.7i	−2.17278	−	2.73239i
$969$	18441.0	−	23029.7i	0.611364	−	0.763488i
$970$	−30700.2	+	94485.6i	−1.01621	+	3.12758i
$971$	43323.0	−	31476.0i	1.43182	−	1.04028i	0.442150	−	0.896941i	$-0.354216\pi$
$971$	43323.0	−	31476.0i	1.43182	−	1.04028i	0.989674	−	0.143340i	$-0.0457842\pi$
$972$	−55038.8	−	64283.4i	−1.81622	−	2.12129i
$973$	15993.1	−	35640.7i	0.526944	−	1.17429i
$974$	−57643.4	+	18729.5i	−1.89632	+	0.616151i
$975$	−1375.07	+	376.536i	−0.0451666	+	0.0123680i
$976$	−12319.1	−	16955.8i	−0.404022	−	0.556088i
$977$	−16468.9	−	5351.08i	−0.539291	−	0.175226i	0.0266911	−	0.999644i	$-0.491503\pi$
$977$	−16468.9	−	5351.08i	−0.539291	−	0.175226i	−0.565982	+	0.824417i	$0.691503\pi$
$978$	37148.8	−	46392.4i	1.21461	−	1.51684i
$979$	12427.9	−	270.256i	0.405717	−	0.00882268i
$980$	−8600.35	−	86695.1i	−0.280335	−	2.82589i
$981$	4080.49	+	383.715i	0.132803	+	0.0124883i
$982$	−70765.1	+	51413.9i	−2.29960	+	1.67076i
$983$	−9493.51	−	6897.44i	−0.308032	−	0.223799i	0.423019	−	0.906121i	$-0.360970\pi$
$983$	−9493.51	−	6897.44i	−0.308032	−	0.223799i	−0.731052	+	0.682322i	$0.760970\pi$
$984$	62758.9	+	23697.2i	2.03321	+	0.767721i
$985$	9335.49	−	3033.28i	0.301983	−	0.0981203i
$986$	67607.0	+	49119.3i	2.18362	+	1.58649i
$987$	−5847.67	+	5877.67i	−0.188585	+	0.189553i
$988$	33986.7	−	104600.i	1.09439	−	3.36820i
$989$			22069.6i			0.709578i
$990$	−4438.78	+	61527.4i	−0.142499	+	1.97522i
$991$	29554.0			0.947339			0.473670	−	0.880703i	$-0.342929\pi$
$991$	29554.0			0.947339			0.473670	+	0.880703i	$0.342929\pi$
$992$	2950.57	−	9080.92i	0.0944362	−	0.290645i
$993$	−35601.4	−	1670.23i	−1.13774	−	0.0533768i
$994$	−59438.4	+	12452.7i	−1.89665	+	0.397360i
$995$	24985.4	−	8118.24i	0.796070	−	0.258659i
$996$	6679.84	−	17690.7i	0.212509	−	0.562803i
$997$	8008.04	−	11022.1i	0.254380	−	0.350124i	−0.662659	−	0.748921i	$-0.730572\pi$
$997$	8008.04	−	11022.1i	0.254380	−	0.350124i	0.917039	+	0.398797i	$0.130572\pi$
$998$	−8900.52	−	12250.5i	−0.282306	−	0.388561i
$999$	4931.32	+	4771.80i	0.156176	+	0.151124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.4.u.a.20.1	✓	368
3.2	odd	2	inner	231.4.u.a.20.92	yes	368
7.6	odd	2	inner	231.4.u.a.20.2	yes	368
11.5	even	5	inner	231.4.u.a.104.91	yes	368
21.20	even	2	inner	231.4.u.a.20.91	yes	368
33.5	odd	10	inner	231.4.u.a.104.2	yes	368
77.27	odd	10	inner	231.4.u.a.104.92	yes	368
231.104	even	10	inner	231.4.u.a.104.1	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.u.a.20.1	✓	368	1.1	even	1	trivial
231.4.u.a.20.2	yes	368	7.6	odd	2	inner
231.4.u.a.20.91	yes	368	21.20	even	2	inner
231.4.u.a.20.92	yes	368	3.2	odd	2	inner
231.4.u.a.104.1	yes	368	231.104	even	10	inner
231.4.u.a.104.2	yes	368	33.5	odd	10	inner
231.4.u.a.104.91	yes	368	11.5	even	5	inner
231.4.u.a.104.92	yes	368	77.27	odd	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	231.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.23865 - 1.70214i) q^{2} +(-5.19044 - 0.243508i) q^{3} +(18.0740 + 13.1315i) q^{4} +(-3.51328 - 10.8128i) q^{5} +(26.7764 + 10.1105i) q^{6} +(18.1267 - 3.79766i) q^{7} +(-46.4303 - 63.9058i) q^{8} +(26.8814 + 2.52783i) q^{9} +62.6244i q^{10} +(36.4742 - 0.793165i) q^{11} +(-90.6144 - 72.5596i) q^{12} +(-61.2668 - 19.9068i) q^{13} +(-101.424 - 10.9596i) q^{14} +(15.6025 + 56.9786i) q^{15} +(79.2260 + 243.832i) q^{16} +(22.9593 + 70.6614i) q^{17} +(-136.519 - 58.9983i) q^{18} +(44.9190 + 61.8257i) q^{19} +(78.4891 - 241.565i) q^{20} +(-95.0105 + 15.2975i) q^{21} +(-192.426 - 57.9291i) q^{22} +87.5177i q^{23} +(225.432 + 343.005i) q^{24} +(-3.44574 + 2.50348i) q^{25} +(287.071 + 208.569i) q^{26} +(-138.911 - 19.6664i) q^{27} +(377.491 + 169.393i) q^{28} +(-120.023 + 165.197i) q^{29} +(15.2495 - 325.048i) q^{30} +(11.6382 + 3.78147i) q^{31} -780.270i q^{32} +(-189.511 - 4.76490i) q^{33} -409.250i q^{34} +(-104.747 - 182.658i) q^{35} +(452.660 + 398.682i) q^{36} +(-39.5701 - 28.7493i) q^{37} +(-130.079 - 400.341i) q^{38} +(313.154 + 118.244i) q^{39} +(-527.876 + 726.559i) q^{40} +(132.224 - 96.0665i) q^{41} +(523.765 + 81.5828i) q^{42} +252.173 q^{43} +(669.651 + 464.627i) q^{44} +(-67.1091 - 299.543i) q^{45} +(148.967 - 458.474i) q^{46} +(69.7013 - 50.6409i) q^{47} +(-351.843 - 1284.89i) q^{48} +(314.156 - 137.678i) q^{49} +(22.3123 - 7.24969i) q^{50} +(-101.962 - 372.355i) q^{51} +(-845.929 - 1164.32i) q^{52} +(213.123 + 69.2479i) q^{53} +(694.230 + 339.471i) q^{54} +(-136.721 - 391.601i) q^{55} +(-1084.32 - 982.076i) q^{56} +(-218.094 - 331.841i) q^{57} +(909.947 - 661.115i) q^{58} +(317.968 + 231.017i) q^{59} +(-466.216 + 1234.72i) q^{60} +(-77.7467 + 25.2614i) q^{61} +(-54.5317 - 39.6196i) q^{62} +(496.871 - 56.2650i) q^{63} +(-694.321 + 2136.90i) q^{64} +732.402i q^{65} +(984.669 + 347.535i) q^{66} +80.9414 q^{67} +(-512.926 + 1578.62i) q^{68} +(21.3113 - 454.256i) q^{69} +(237.826 + 1135.17i) q^{70} +(566.163 - 183.958i) q^{71} +(-1086.57 - 1835.25i) q^{72} +(-503.012 + 692.337i) q^{73} +(158.358 + 217.961i) q^{74} +(18.4945 - 12.1551i) q^{75} +1707.29i q^{76} +(658.146 - 152.894i) q^{77} +(-1439.24 - 1152.47i) q^{78} +(-210.755 + 648.639i) q^{79} +(2358.16 - 1713.30i) q^{80} +(716.220 + 135.903i) q^{81} +(-856.194 + 278.194i) q^{82} +(50.3375 + 154.923i) q^{83} +(-1918.10 - 971.145i) q^{84} +(683.383 - 496.507i) q^{85} +(-1321.05 - 429.234i) q^{86} +(663.199 - 828.221i) q^{87} +(-1744.20 - 2294.09i) q^{88} +340.730 q^{89} +(-158.304 + 1683.43i) q^{90} +(-1186.16 - 128.175i) q^{91} +(-1149.24 + 1581.79i) q^{92} +(-59.4865 - 22.4615i) q^{93} +(-451.338 + 146.649i) q^{94} +(510.694 - 702.910i) q^{95} +(-190.002 + 4049.95i) q^{96} +(1508.77 + 490.228i) q^{97} +(-1880.10 + 186.510i) q^{98} +(982.484 + 70.8794i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 340 q^{4} - 18 q^{7} + 42 q^{9} + 42 q^{15} - 1116 q^{16} - 262 q^{18} - 222 q^{21} + 696 q^{22} - 1516 q^{25} + 38 q^{28} + 624 q^{30} + 1430 q^{36} + 36 q^{37} + 390 q^{39} + 2130 q^{42} - 1376 q^{43}+ \cdots - 6218 q^{99}+O(q^{100}) \) 368 * q + 340 * q^4 - 18 * q^7 + 42 * q^9 + 42 * q^15 - 1116 * q^16 - 262 * q^18 - 222 * q^21 + 696 * q^22 - 1516 * q^25 + 38 * q^28 + 624 * q^30 + 1430 * q^36 + 36 * q^37 + 390 * q^39 + 2130 * q^42 - 1376 * q^43 + 1716 * q^46 + 474 * q^49 + 782 * q^51 + 670 * q^57 + 5576 * q^58 - 2708 * q^60 - 739 * q^63 + 5256 * q^64 - 2432 * q^67 + 2280 * q^70 - 3706 * q^72 - 10900 * q^78 + 732 * q^79 - 262 * q^81 - 510 * q^84 + 8008 * q^85 - 832 * q^88 - 5446 * q^91 + 2510 * q^93 - 6218 * q^99

Introduction

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