LMFDB - Embedded newform 63.3.j.b.23.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(11,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 4]))

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

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

chi := DirichletCharacter("63.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.j (of order $6$, degree $2$, 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:	$1.71662566547$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.10
Character	$\chi$	$=$	63.23
Dual form			63.3.j.b.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.22356i q^{2} +(-2.32685 - 1.89361i) q^{3} -6.39137 q^{4} +(-4.79167 + 2.76647i) q^{5} +(6.10417 - 7.50076i) q^{6} +(-6.99696 - 0.206413i) q^{7} -7.70873i q^{8} +(1.82848 + 8.81230i) q^{9} +O(q^{10})$	\(q+3.22356i q^{2} +(-2.32685 - 1.89361i) q^{3} -6.39137 q^{4} +(-4.79167 + 2.76647i) q^{5} +(6.10417 - 7.50076i) q^{6} +(-6.99696 - 0.206413i) q^{7} -7.70873i q^{8} +(1.82848 + 8.81230i) q^{9} +(-8.91790 - 15.4463i) q^{10} +(15.3189 + 8.84435i) q^{11} +(14.8718 + 12.1028i) q^{12} +(2.03775 - 3.52949i) q^{13} +(0.665386 - 22.5551i) q^{14} +(16.3881 + 2.63638i) q^{15} -0.715882 q^{16} +(-14.3348 + 8.27617i) q^{17} +(-28.4070 + 5.89424i) q^{18} +(-3.92096 + 6.79130i) q^{19} +(30.6253 - 17.6815i) q^{20} +(15.8900 + 13.7298i) q^{21} +(-28.5103 + 49.3813i) q^{22} +(8.71877 - 5.03378i) q^{23} +(-14.5973 + 17.9371i) q^{24} +(2.80674 - 4.86141i) q^{25} +(11.3775 + 6.56882i) q^{26} +(12.4324 - 23.9674i) q^{27} +(44.7201 + 1.31926i) q^{28} +(-39.9040 + 23.0386i) q^{29} +(-8.49854 + 52.8282i) q^{30} +29.6235 q^{31} -33.1426i q^{32} +(-18.8970 - 49.5874i) q^{33} +(-26.6788 - 46.2090i) q^{34} +(34.0981 - 18.3678i) q^{35} +(-11.6865 - 56.3227i) q^{36} +(15.5948 - 27.0110i) q^{37} +(-21.8922 - 12.6395i) q^{38} +(-11.4250 + 4.35389i) q^{39} +(21.3260 + 36.9377i) q^{40} +(27.8184 + 16.0609i) q^{41} +(-44.2589 + 51.2225i) q^{42} +(3.35243 + 5.80658i) q^{43} +(-97.9085 - 56.5275i) q^{44} +(-33.1405 - 37.1672i) q^{45} +(16.2267 + 28.1055i) q^{46} +16.4402i q^{47} +(1.66575 + 1.35560i) q^{48} +(48.9148 + 2.88853i) q^{49} +(15.6711 + 9.04769i) q^{50} +(49.0267 + 7.88699i) q^{51} +(-13.0240 + 22.5583i) q^{52} +(-32.5897 + 18.8157i) q^{53} +(77.2603 + 40.0768i) q^{54} -97.8706 q^{55} +(-1.59118 + 53.9377i) q^{56} +(21.9836 - 8.37759i) q^{57} +(-74.2663 - 128.633i) q^{58} +95.0557i q^{59} +(-104.743 - 16.8501i) q^{60} -73.7679 q^{61} +95.4932i q^{62} +(-10.9749 - 62.0367i) q^{63} +103.974 q^{64} +22.5495i q^{65} +(159.848 - 60.9156i) q^{66} -12.1909 q^{67} +(91.6187 - 52.8961i) q^{68} +(-29.8193 - 4.79707i) q^{69} +(59.2099 + 109.918i) q^{70} +20.0140i q^{71} +(67.9317 - 14.0953i) q^{72} +(-11.4932 - 19.9068i) q^{73} +(87.0715 + 50.2708i) q^{74} +(-15.7365 + 5.99692i) q^{75} +(25.0603 - 43.4057i) q^{76} +(-105.360 - 65.0455i) q^{77} +(-14.0351 - 36.8293i) q^{78} +138.880 q^{79} +(3.43027 - 1.98047i) q^{80} +(-74.3133 + 32.2263i) q^{81} +(-51.7735 + 89.6743i) q^{82} +(13.6928 - 7.90552i) q^{83} +(-101.559 - 87.7522i) q^{84} +(45.7916 - 79.3134i) q^{85} +(-18.7179 + 10.8068i) q^{86} +(136.477 + 21.9552i) q^{87} +(68.1787 - 118.089i) q^{88} +(-46.9444 - 27.1034i) q^{89} +(119.811 - 106.830i) q^{90} +(-14.9866 + 24.2750i) q^{91} +(-55.7249 + 32.1728i) q^{92} +(-68.9294 - 56.0953i) q^{93} -52.9962 q^{94} -43.3889i q^{95} +(-62.7592 + 77.1180i) q^{96} +(86.1189 + 149.162i) q^{97} +(-9.31136 + 157.680i) q^{98} +(-49.9287 + 151.166i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 19 q^{3} - 24 q^{4} + 12 q^{5} - 8 q^{6} - 37 q^{9}+O(q^{10}) $ 22 * q - 19 * q^3 - 24 * q^4 + 12 * q^5 - 8 * q^6 - 37 * q^9	\( 22 q - 19 q^{3} - 24 q^{4} + 12 q^{5} - 8 q^{6} - 37 q^{9} + 25 q^{10} + 24 q^{11} + 40 q^{12} - 18 q^{13} - 60 q^{14} + 53 q^{15} - 24 q^{16} - 6 q^{17} + 40 q^{18} + 3 q^{19} - 39 q^{20} - 11 q^{21} - 59 q^{22} + 81 q^{23} + 126 q^{24} + 57 q^{25} + 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 38 q^{30} + 58 q^{31} - 4 q^{33} - 99 q^{34} + 27 q^{35} + 76 q^{36} - 20 q^{37} - 48 q^{38} - 76 q^{39} - 105 q^{40} - 51 q^{41} + 68 q^{42} + 65 q^{43} - 54 q^{44} - 214 q^{45} + 75 q^{46} - 113 q^{48} + 4 q^{49} + 63 q^{50} + 141 q^{51} - 46 q^{52} + 63 q^{53} + 433 q^{54} - 100 q^{55} + 192 q^{56} + 224 q^{57} + 40 q^{58} - 482 q^{60} - 156 q^{61} + 19 q^{63} + 106 q^{64} + 61 q^{66} + 264 q^{67} + 27 q^{68} - 297 q^{69} + 236 q^{70} - 222 q^{72} + q^{73} + 342 q^{74} - 296 q^{75} + 233 q^{76} - 531 q^{77} - 440 q^{78} - 280 q^{79} - 96 q^{80} - 169 q^{81} - 157 q^{82} + 255 q^{83} - 13 q^{84} + 102 q^{85} + 504 q^{86} + 704 q^{87} + 408 q^{88} + 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} - 36 q^{93} - 522 q^{94} - 397 q^{96} + 178 q^{97} - 483 q^{98} - 103 q^{99}+O(q^{100}) \) 22 * q - 19 * q^3 - 24 * q^4 + 12 * q^5 - 8 * q^6 - 37 * q^9 + 25 * q^10 + 24 * q^11 + 40 * q^12 - 18 * q^13 - 60 * q^14 + 53 * q^15 - 24 * q^16 - 6 * q^17 + 40 * q^18 + 3 * q^19 - 39 * q^20 - 11 * q^21 - 59 * q^22 + 81 * q^23 + 126 * q^24 + 57 * q^25 + 3 * q^26 - 97 * q^27 + 34 * q^28 - 63 * q^29 - 38 * q^30 + 58 * q^31 - 4 * q^33 - 99 * q^34 + 27 * q^35 + 76 * q^36 - 20 * q^37 - 48 * q^38 - 76 * q^39 - 105 * q^40 - 51 * q^41 + 68 * q^42 + 65 * q^43 - 54 * q^44 - 214 * q^45 + 75 * q^46 - 113 * q^48 + 4 * q^49 + 63 * q^50 + 141 * q^51 - 46 * q^52 + 63 * q^53 + 433 * q^54 - 100 * q^55 + 192 * q^56 + 224 * q^57 + 40 * q^58 - 482 * q^60 - 156 * q^61 + 19 * q^63 + 106 * q^64 + 61 * q^66 + 264 * q^67 + 27 * q^68 - 297 * q^69 + 236 * q^70 - 222 * q^72 + q^73 + 342 * q^74 - 296 * q^75 + 233 * q^76 - 531 * q^77 - 440 * q^78 - 280 * q^79 - 96 * q^80 - 169 * q^81 - 157 * q^82 + 255 * q^83 - 13 * q^84 + 102 * q^85 + 504 * q^86 + 704 * q^87 + 408 * q^88 + 720 * q^89 + 418 * q^90 - 70 * q^91 - 1239 * q^92 - 36 * q^93 - 522 * q^94 - 397 * q^96 + 178 * q^97 - 483 * q^98 - 103 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			3.22356i			1.61178i	0.592064	+	0.805891i	$0.298313\pi$
$2$			3.22356i			1.61178i	−0.592064	+	0.805891i	$0.701687\pi$
$3$	−2.32685	−	1.89361i	−0.775617	−	0.631203i
$3$	−2.32685	−	1.89361i	−0.775617	−	0.631203i
$4$	−6.39137			−1.59784
$5$	−4.79167	+	2.76647i	−0.958334	+	0.553294i	−0.895660	−	0.444740i	$-0.853296\pi$
$5$	−4.79167	+	2.76647i	−0.958334	+	0.553294i	−0.0626741	+	0.998034i	$0.519963\pi$
$6$	6.10417	−	7.50076i	1.01736	−	1.25013i
$7$	−6.99696	−	0.206413i	−0.999565	−	0.0294876i
$7$	−6.99696	−	0.206413i	−0.999565	−	0.0294876i
$8$		−	7.70873i		−	0.963591i
$9$	1.82848	+	8.81230i	0.203165	+	0.979145i
$10$	−8.91790	−	15.4463i	−0.891790	−	1.54463i
$11$	15.3189	+	8.84435i	1.39262	+	0.804032i	0.993605	−	0.112911i	$-0.0360176\pi$
$11$	15.3189	+	8.84435i	1.39262	+	0.804032i	0.399018	+	0.916943i	$0.369351\pi$
$12$	14.8718	+	12.1028i	1.23931	+	1.00856i
$13$	2.03775	−	3.52949i	0.156750	−	0.271499i	−0.776945	−	0.629569i	$-0.783232\pi$
$13$	2.03775	−	3.52949i	0.156750	−	0.271499i	0.933695	+	0.358070i	$0.116565\pi$
$14$	0.665386	−	22.5551i	0.0475276	−	1.61108i
$15$	16.3881	+	2.63638i	1.09254	+	0.175759i
$16$	−0.715882			−0.0447426
$17$	−14.3348	+	8.27617i	−0.843221	+	0.486834i	−0.858358	−	0.513052i	$-0.828515\pi$
$17$	−14.3348	+	8.27617i	−0.843221	+	0.486834i	0.0151370	+	0.999885i	$0.495182\pi$
$18$	−28.4070	+	5.89424i	−1.57817	+	0.327458i
$19$	−3.92096	+	6.79130i	−0.206366	+	0.357437i	−0.950567	−	0.310519i	$-0.899497\pi$
$19$	−3.92096	+	6.79130i	−0.206366	+	0.357437i	0.744201	+	0.667956i	$0.232830\pi$
$20$	30.6253	−	17.6815i	1.53127	−	0.884077i
$21$	15.8900	+	13.7298i	0.756668	+	0.653800i
$22$	−28.5103	+	49.3813i	−1.29592	+	2.24461i
$23$	8.71877	−	5.03378i	0.379077	−	0.218860i	−0.298340	−	0.954460i	$-0.596433\pi$
$23$	8.71877	−	5.03378i	0.379077	−	0.218860i	0.677417	+	0.735600i	$0.263099\pi$
$24$	−14.5973	+	17.9371i	−0.608222	+	0.747378i
$25$	2.80674	−	4.86141i	0.112269	−	0.194456i
$26$	11.3775	+	6.56882i	0.437597	+	0.252647i
$27$	12.4324	−	23.9674i	0.460461	−	0.887680i
$28$	44.7201	+	1.31926i	1.59715	+	0.0471165i
$29$	−39.9040	+	23.0386i	−1.37600	+	0.794434i	−0.991675	−	0.128764i	$-0.958899\pi$
$29$	−39.9040	+	23.0386i	−1.37600	+	0.794434i	−0.384324	+	0.923198i	$0.625566\pi$
$30$	−8.49854	+	52.8282i	−0.283285	+	1.76094i
$31$	29.6235			0.955596			0.477798	−	0.878470i	$-0.341435\pi$
$31$	29.6235			0.955596			0.477798	+	0.878470i	$0.341435\pi$
$32$		−	33.1426i		−	1.03571i
$33$	−18.8970	−	49.5874i	−0.572636	−	1.50265i
$34$	−26.6788	−	46.2090i	−0.784670	−	1.35909i
$35$	34.0981	−	18.3678i	0.974233	−	0.524795i
$36$	−11.6865	−	56.3227i	−0.324626	−	1.56452i
$37$	15.5948	−	27.0110i	0.421481	−	0.730026i	−0.574604	−	0.818432i	$-0.694844\pi$
$37$	15.5948	−	27.0110i	0.421481	−	0.730026i	0.996085	+	0.0884059i	$0.0281772\pi$
$38$	−21.8922	−	12.6395i	−0.576110	−	0.332617i
$39$	−11.4250	+	4.35389i	−0.292949	+	0.111638i
$40$	21.3260	+	36.9377i	0.533150	+	0.923442i
$41$	27.8184	+	16.0609i	0.678497	+	0.391730i	0.799288	−	0.600948i	$-0.205210\pi$
$41$	27.8184	+	16.0609i	0.678497	+	0.391730i	−0.120792	+	0.992678i	$0.538543\pi$
$42$	−44.2589	+	51.2225i	−1.05378	+	1.21958i
$43$	3.35243	+	5.80658i	0.0779635	+	0.135037i	0.902371	−	0.430960i	$-0.141825\pi$
$43$	3.35243	+	5.80658i	0.0779635	+	0.135037i	−0.824408	+	0.565997i	$0.808492\pi$
$44$	−97.9085	−	56.5275i	−2.22519	−	1.28472i
$45$	−33.1405	−	37.1672i	−0.736455	−	0.825937i
$46$	16.2267	+	28.1055i	0.352755	+	0.610990i
$47$			16.4402i			0.349792i	0.984587	+	0.174896i	$0.0559590\pi$
$47$			16.4402i			0.349792i	−0.984587	+	0.174896i	$0.944041\pi$
$48$	1.66575	+	1.35560i	0.0347032	+	0.0282417i
$49$	48.9148	+	2.88853i	0.998261	+	0.0589496i
$50$	15.6711	+	9.04769i	0.313421	+	0.180954i
$51$	49.0267	+	7.88699i	0.961308	+	0.154647i
$52$	−13.0240	+	22.5583i	−0.250462	+	0.433813i
$53$	−32.5897	+	18.8157i	−0.614900	+	0.355013i	−0.774881	−	0.632108i	$-0.782190\pi$
$53$	−32.5897	+	18.8157i	−0.614900	+	0.355013i	0.159981	+	0.987120i	$0.448857\pi$
$54$	77.2603	+	40.0768i	1.43075	+	0.742163i
$55$	−97.8706			−1.77946
$56$	−1.59118	+	53.9377i	−0.0284140	+	0.963172i
$57$	21.9836	−	8.37759i	0.385676	−	0.146975i
$58$	−74.2663	−	128.633i	−1.28045	−	2.21781i
$59$			95.0557i			1.61111i	0.592519	+	0.805557i	$0.298134\pi$
$59$			95.0557i			1.61111i	−0.592519	+	0.805557i	$0.701866\pi$
$60$	−104.743	−	16.8501i	−1.74571	−	0.280835i
$61$	−73.7679			−1.20931			−0.604655	−	0.796488i	$-0.706689\pi$
$61$	−73.7679			−1.20931			−0.604655	+	0.796488i	$0.706689\pi$
$62$			95.4932i			1.54021i
$63$	−10.9749	−	62.0367i	−0.174204	−	0.984710i
$64$	103.974			1.62459
$65$			22.5495i			0.346916i
$66$	159.848	−	60.9156i	2.42194	−	0.922964i
$67$	−12.1909			−0.181954			−0.0909769	−	0.995853i	$-0.528999\pi$
$67$	−12.1909			−0.181954			−0.0909769	+	0.995853i	$0.528999\pi$
$68$	91.6187	−	52.8961i	1.34733	−	0.777883i
$69$	−29.8193	−	4.79707i	−0.432164	−	0.0695228i
$70$	59.2099	+	109.918i	0.845855	+	1.57025i
$71$			20.0140i			0.281887i	0.990018	+	0.140944i	$0.0450136\pi$
$71$			20.0140i			0.281887i	−0.990018	+	0.140944i	$0.954986\pi$
$72$	67.9317	−	14.0953i	0.943495	−	0.195768i
$73$	−11.4932	−	19.9068i	−0.157441	−	0.272696i	0.776504	−	0.630112i	$-0.216991\pi$
$73$	−11.4932	−	19.9068i	−0.157441	−	0.272696i	−0.933945	+	0.357416i	$0.883658\pi$
$74$	87.0715	+	50.2708i	1.17664	+	0.679335i
$75$	−15.7365	+	5.99692i	−0.209820	+	0.0799589i
$76$	25.0603	−	43.4057i	0.329741	−	0.571128i
$77$	−105.360	−	65.0455i	−1.36831	−	0.844747i
$78$	−14.0351	−	36.8293i	−0.179937	−	0.472170i
$79$	138.880			1.75798			0.878988	−	0.476844i	$-0.158219\pi$
$79$	138.880			1.75798			0.878988	+	0.476844i	$0.158219\pi$
$80$	3.43027	−	1.98047i	0.0428784	−	0.0247559i
$81$	−74.3133	+	32.2263i	−0.917448	+	0.397856i
$82$	−51.7735	+	89.6743i	−0.631384	+	1.09359i
$83$	13.6928	−	7.90552i	0.164973	−	0.0952472i	−0.415240	−	0.909712i	$-0.636303\pi$
$83$	13.6928	−	7.90552i	0.164973	−	0.0952472i	0.580213	+	0.814465i	$0.302969\pi$
$84$	−101.559	−	87.7522i	−1.20904	−	1.04467i
$85$	45.7916	−	79.3134i	0.538725	−	0.933099i
$86$	−18.7179	+	10.8068i	−0.217650	+	0.125660i
$87$	136.477	+	21.9552i	1.56870	+	0.252359i
$88$	68.1787	−	118.089i	0.774758	−	1.34192i
$89$	−46.9444	−	27.1034i	−0.527466	−	0.304532i	0.212518	−	0.977157i	$-0.431834\pi$
$89$	−46.9444	−	27.1034i	−0.527466	−	0.304532i	−0.739984	+	0.672625i	$0.765167\pi$
$90$	119.811	−	106.830i	1.33123	−	1.18701i
$91$	−14.9866	+	24.2750i	−0.164688	+	0.266759i
$92$	−55.7249	+	32.1728i	−0.605705	+	0.349704i
$93$	−68.9294	−	56.0953i	−0.741177	−	0.603175i
$94$	−52.9962			−0.563789
$95$		−	43.3889i		−	0.456725i
$96$	−62.7592	+	77.1180i	−0.653741	+	0.803312i
$97$	86.1189	+	149.162i	0.887823	+	1.53776i	0.842443	+	0.538785i	$0.181117\pi$
$97$	86.1189	+	149.162i	0.887823	+	1.53776i	0.0453802	+	0.998970i	$0.485550\pi$
$98$	−9.31136	+	157.680i	−0.0950139	+	1.60898i
$99$	−49.9287	+	151.166i	−0.504331	+	1.52693i
$100$	−17.9389	+	31.0710i	−0.179389	+	0.310710i
$101$	−14.9975	−	8.65880i	−0.148490	−	0.0857307i	0.423914	−	0.905702i	$-0.360656\pi$
$101$	−14.9975	−	8.65880i	−0.148490	−	0.0857307i	−0.572404	+	0.819972i	$0.693989\pi$
$102$	−25.4242	+	158.041i	−0.249257	+	1.54942i
$103$	13.7999	+	23.9021i	0.133979	+	0.232059i	0.925207	−	0.379463i	$-0.123891\pi$
$103$	13.7999	+	23.9021i	0.133979	+	0.232059i	−0.791228	+	0.611521i	$0.790558\pi$
$104$	−27.2079	−	15.7085i	−0.261614	−	0.151043i
$105$	−114.123	−	21.8294i	−1.08688	−	0.207899i
$106$	−60.6535	−	105.055i	−0.572203	−	0.991085i
$107$	−106.089	−	61.2506i	−0.991488	−	0.572436i	−0.0857691	−	0.996315i	$-0.527335\pi$
$107$	−106.089	−	61.2506i	−0.991488	−	0.572436i	−0.905719	+	0.423879i	$0.860668\pi$
$108$	−79.4603	+	153.184i	−0.735744	+	1.41837i
$109$	−17.0725	−	29.5705i	−0.156629	−	0.271289i	0.777022	−	0.629473i	$-0.216729\pi$
$109$	−17.0725	−	29.5705i	−0.156629	−	0.271289i	−0.933651	+	0.358184i	$0.883396\pi$
$110$		−	315.492i		−	2.86811i
$111$	−87.4350	+	33.3201i	−0.787702	+	0.300181i
$112$	5.00900	+	0.147768i	0.0447232	+	0.00131935i
$113$	67.4250	+	38.9278i	0.596681	+	0.344494i	0.767735	−	0.640768i	$-0.221384\pi$
$113$	67.4250	+	38.9278i	0.596681	+	0.344494i	−0.171054	+	0.985262i	$0.554717\pi$
$114$	27.0057	+	70.8654i	0.236892	+	0.621626i
$115$	−27.8516	+	48.2405i	−0.242188	+	0.419482i
$116$	255.041	−	147.248i	2.19863	−	1.26938i
$117$	34.8289	+	11.5037i	0.297683	+	0.0983218i
$118$	−306.418			−2.59676
$119$	102.008	−	54.9491i	0.857210	−	0.461757i
$120$	20.3231	−	126.332i	0.169360	−	1.05276i
$121$	95.9449	+	166.182i	0.792933	+	1.37340i
$122$		−	237.795i		−	1.94914i
$123$	−34.3161	−	90.0486i	−0.278992	−	0.732102i
$124$	−189.335			−1.52689
$125$		−	107.265i		−	0.858117i
$126$	199.979	−	35.3781i	1.58714	−	0.280779i
$127$	14.0742			0.110821			0.0554103	−	0.998464i	$-0.482353\pi$
$127$	14.0742			0.110821			0.0554103	+	0.998464i	$0.482353\pi$
$128$			202.596i			1.58278i
$129$	3.19479	−	19.8593i	0.0247658	−	0.153948i
$130$	−72.6898			−0.559152
$131$	19.2863	−	11.1349i	0.147223	−	0.0849995i	−0.424579	−	0.905391i	$-0.639578\pi$
$131$	19.2863	−	11.1349i	0.147223	−	0.0849995i	0.571802	+	0.820391i	$0.306244\pi$
$132$	120.778	+	316.932i	0.914982	+	2.40100i
$133$	28.8366	−	46.7091i	0.216816	−	0.351196i
$134$		−	39.2982i		−	0.293270i
$135$	6.73286	+	149.238i	0.0498731	+	1.10546i
$136$	63.7988	+	110.503i	0.469109	+	0.812520i
$137$	32.1175	+	18.5430i	0.234434	+	0.135351i	0.612616	−	0.790381i	$-0.290117\pi$
$137$	32.1175	+	18.5430i	0.234434	+	0.135351i	−0.378182	+	0.925731i	$0.623451\pi$
$138$	15.4637	−	96.1245i	0.112056	−	0.696554i
$139$	70.5358	−	122.172i	0.507451	−	0.878932i	−0.492511	−	0.870306i	$-0.663921\pi$
$139$	70.5358	−	122.172i	0.507451	−	0.878932i	0.999963	−	0.00862568i	$-0.00274567\pi$
$140$	−217.934	+	117.396i	−1.55667	+	0.838539i
$141$	31.1314	−	38.2540i	0.220790	−	0.271305i
$142$	−64.5164			−0.454341
$143$	62.4320	−	36.0451i	0.436587	−	0.252064i
$144$	−1.30898	−	6.30857i	−0.00909014	−	0.0438095i
$145$	127.471	−	220.787i	0.879111	−	1.52267i
$146$	64.1710	−	37.0491i	0.439527	−	0.253761i
$147$	−108.348	−	99.3467i	−0.737060	−	0.675828i
$148$	−99.6720	+	172.637i	−0.673459	+	1.16647i
$149$	100.215	−	57.8590i	0.672582	−	0.388315i	−0.124472	−	0.992223i	$-0.539724\pi$
$149$	100.215	−	57.8590i	0.672582	−	0.388315i	0.797054	+	0.603908i	$0.206390\pi$
$150$	−19.3315	−	50.7275i	−0.128876	−	0.338183i
$151$	75.1579	−	130.177i	0.497734	−	0.862101i	−0.502262	−	0.864715i	$-0.667499\pi$
$151$	75.1579	−	130.177i	0.497734	−	0.862101i	0.999997	+	0.00261420i	$0.000832125\pi$
$152$	52.3523	+	30.2256i	0.344423	+	0.198853i
$153$	−99.1430	−	111.189i	−0.647993	−	0.726727i
$154$	209.678	−	339.634i	1.36155	−	2.20542i
$155$	−141.946	+	81.9525i	−0.915780	+	0.528726i
$156$	73.0215	−	27.8273i	0.468086	−	0.178380i
$157$	−274.056			−1.74558			−0.872788	−	0.488099i	$-0.837691\pi$
$157$	−274.056			−1.74558			−0.872788	+	0.488099i	$0.837691\pi$
$158$			447.689i			2.83347i
$159$	111.461	+	17.9309i	0.701012	+	0.112773i
$160$	91.6881	+	158.808i	0.573051	+	0.992553i
$161$	−62.0439	+	33.4215i	−0.385366	+	0.207587i
$162$	−103.884	−	239.554i	−0.641257	−	1.47873i
$163$	−111.326	+	192.822i	−0.682981	+	1.18296i	0.291085	+	0.956697i	$0.405984\pi$
$163$	−111.326	+	192.822i	−0.682981	+	1.18296i	−0.974067	+	0.226261i	$0.927350\pi$
$164$	−177.797	−	102.651i	−1.08413	−	0.625923i
$165$	227.730	+	185.329i	1.38018	+	1.12320i
$166$	25.4839	+	44.1395i	0.153518	+	0.265900i
$167$	62.7878	+	36.2506i	0.375975	+	0.217069i	0.676066	−	0.736841i	$-0.263684\pi$
$167$	62.7878	+	36.2506i	0.375975	+	0.217069i	−0.300091	+	0.953911i	$0.597017\pi$
$168$	105.839	−	122.492i	0.629996	−	0.729118i
$169$	76.1951	+	131.974i	0.450859	+	0.780910i
$170$	255.672	+	147.612i	1.50395	+	0.868307i
$171$	−67.0164	−	22.1349i	−0.391909	−	0.129444i
$172$	−21.4266	−	37.1120i	−0.124573	−	0.215768i
$173$			211.173i			1.22066i	0.792149	+	0.610328i	$0.208962\pi$
$173$			211.173i			1.22066i	−0.792149	+	0.610328i	$0.791038\pi$
$174$	−70.7740	+	439.942i	−0.406747	+	2.52840i
$175$	−20.6421	+	33.4357i	−0.117955	+	0.191061i
$176$	−10.9665	−	6.33151i	−0.0623096	−	0.0359745i
$177$	179.998	−	221.181i	1.01694	−	1.24961i
$178$	87.3695	−	151.328i	0.490840	−	0.850160i
$179$	69.5967	−	40.1817i	0.388809	−	0.224479i	−0.292835	−	0.956163i	$-0.594599\pi$
$179$	69.5967	−	40.1817i	0.388809	−	0.224479i	0.681644	+	0.731684i	$0.261265\pi$
$180$	211.813	+	237.549i	1.17674	+	1.31972i
$181$	122.944			0.679250			0.339625	−	0.940561i	$-0.389700\pi$
$181$	122.944			0.679250			0.339625	+	0.940561i	$0.389700\pi$
$182$	−78.2522	−	48.3102i	−0.429957	−	0.265441i
$183$	171.647	+	139.688i	0.937961	+	0.763320i
$184$	−38.8041	−	67.2107i	−0.210892	−	0.365275i
$185$			172.570i			0.932811i
$186$	180.827	−	222.199i	0.972187	−	1.19462i
$187$	−292.789			−1.56572
$188$		−	105.076i		−	0.558913i
$189$	−91.9364	+	165.132i	−0.486436	+	0.873716i
$190$	139.867			0.736141
$191$		−	355.490i		−	1.86120i	−0.366032	−	0.930602i	$-0.619284\pi$
$191$		−	355.490i		−	1.86120i	0.366032	−	0.930602i	$-0.380716\pi$
$192$	−241.932	−	196.886i	−1.26006	−	1.02545i
$193$	−39.6593			−0.205488			−0.102744	−	0.994708i	$-0.532762\pi$
$193$	−39.6593			−0.205488			−0.102744	+	0.994708i	$0.532762\pi$
$194$	−480.834	+	277.610i	−2.47853	+	1.43098i
$195$	42.7000	−	52.4694i	0.218974	−	0.269074i
$196$	−312.632	−	18.4617i	−1.59506	−	0.0941921i
$197$		−	130.634i		−	0.663119i	−0.943434	−	0.331559i	$-0.892425\pi$
$197$		−	130.634i		−	0.663119i	0.943434	−	0.331559i	$-0.107575\pi$
$198$	−487.294	−	160.949i	−2.46108	−	0.812871i
$199$	108.521	+	187.964i	0.545331	+	0.944540i	0.998586	+	0.0531596i	$0.0169292\pi$
$199$	108.521	+	187.964i	0.545331	+	0.944540i	−0.453255	+	0.891381i	$0.649737\pi$
$200$	−37.4753	−	21.6364i	−0.187376	−	0.108182i
$201$	28.3664	+	23.0848i	0.141127	+	0.114850i
$202$	27.9122	−	48.3454i	0.138179	−	0.239333i
$203$	283.962	−	152.963i	1.39883	−	0.753513i
$204$	−313.348	−	50.4087i	−1.53602	−	0.247101i
$205$	−177.729			−0.866969
$206$	−77.0498	+	44.4847i	−0.374028	+	0.215945i
$207$	60.3014	+	67.6282i	0.291311	+	0.326706i
$208$	−1.45879	+	2.52670i	−0.00701341	+	0.0121476i
$209$	−120.129	+	69.3566i	−0.574781	+	0.331850i
$210$	70.3684	−	367.882i	0.335087	−	1.75182i
$211$	54.6113	−	94.5895i	0.258821	−	0.448292i	−0.707105	−	0.707108i	$-0.749999\pi$
$211$	54.6113	−	94.5895i	0.258821	−	0.448292i	0.965926	+	0.258817i	$0.0833326\pi$
$212$	208.293	−	120.258i	0.982513	−	0.567254i
$213$	37.8987	−	46.5696i	0.177928	−	0.218637i
$214$	197.445	−	341.985i	0.922642	−	1.59806i
$215$	−32.1275	−	18.5488i	−0.149430	−	0.0862736i
$216$	−184.758	−	95.8384i	−0.855361	−	0.443696i
$217$	−207.274	−	6.11468i	−0.955180	−	0.0281782i
$218$	95.3224	−	55.0344i	0.437259	−	0.252451i
$219$	−10.9528	+	68.0839i	−0.0500126	+	0.310885i
$220$	625.527			2.84330
$221$			67.4591i			0.305245i
$222$	−107.409	−	281.852i	−0.483826	−	1.26960i
$223$	−93.3685	−	161.719i	−0.418693	−	0.725197i	0.577115	−	0.816663i	$-0.304178\pi$
$223$	−93.3685	−	161.719i	−0.418693	−	0.725197i	−0.995808	+	0.0914653i	$0.970845\pi$
$224$	−6.84107	+	231.897i	−0.0305405	+	1.03526i
$225$	47.9723	+	15.8448i	0.213210	+	0.0704213i
$226$	−125.486	+	217.349i	−0.555249	+	0.961720i
$227$	175.411	+	101.274i	0.772737	+	0.446140i	0.833850	−	0.551991i	$-0.186132\pi$
$227$	175.411	+	101.274i	0.772737	+	0.446140i	−0.0611131	+	0.998131i	$0.519465\pi$
$228$	−140.505	+	53.5442i	−0.616250	+	0.234843i
$229$	39.6366	+	68.6525i	0.173085	+	0.299793i	0.939497	−	0.342557i	$-0.111293\pi$
$229$	39.6366	+	68.6525i	0.173085	+	0.299793i	−0.766412	+	0.642350i	$0.777960\pi$
$230$	−155.506	−	89.7816i	−0.676114	−	0.390355i
$231$	121.986	+	350.862i	0.528077	+	1.51888i
$232$	177.598	+	307.609i	0.765509	+	1.32590i
$233$	282.430	+	163.061i	1.21215	+	0.699833i	0.963227	−	0.268690i	$-0.0865909\pi$
$233$	282.430	+	163.061i	1.21215	+	0.699833i	0.248921	+	0.968524i	$0.419924\pi$
$234$	−37.0828	+	112.273i	−0.158473	+	0.479800i
$235$	−45.4814	−	78.7762i	−0.193538	−	0.335218i
$236$		−	607.536i		−	2.57430i
$237$	−323.154	−	262.985i	−1.36352	−	1.10964i
$238$	177.132	+	328.829i	0.744252	+	1.38164i
$239$	−210.918	−	121.774i	−0.882503	−	0.509514i	−0.0110203	−	0.999939i	$-0.503508\pi$
$239$	−210.918	−	121.774i	−0.882503	−	0.509514i	−0.871483	+	0.490426i	$0.836841\pi$
$240$	−11.7320	−	1.88734i	−0.0488832	−	0.00786391i
$241$	−14.1702	+	24.5436i	−0.0587976	+	0.101840i	−0.893926	−	0.448215i	$-0.852060\pi$
$241$	−14.1702	+	24.5436i	−0.0587976	+	0.101840i	0.835128	+	0.550055i	$0.185393\pi$
$242$	−535.697	+	309.285i	−2.21362	+	1.27804i
$243$	233.940	+	65.7345i	0.962717	+	0.270512i
$244$	471.478			1.93229
$245$	−242.375	+	121.481i	−0.989284	+	0.495839i
$246$	290.277	−	110.620i	1.17999	−	0.449675i
$247$	15.9799	+	27.6779i	0.0646958	+	0.112056i
$248$		−	228.359i		−	0.920804i
$249$	−46.8310	−	7.53377i	−0.188076	−	0.0302561i
$250$	345.774			1.38310
$251$			140.132i			0.558294i	0.960248	+	0.279147i	$0.0900516\pi$
$251$			140.132i			0.558294i	−0.960248	+	0.279147i	$0.909948\pi$
$252$	70.1443	+	396.499i	0.278350	+	1.57341i
$253$	178.082			0.703882
$254$			45.3692i			0.178619i
$255$	−256.739	+	97.8391i	−1.00682	+	0.383683i
$256$	−237.186			−0.926506
$257$	95.8445	−	55.3359i	0.372936	−	0.215315i	−0.301804	−	0.953370i	$-0.597589\pi$
$257$	95.8445	−	55.3359i	0.372936	−	0.215315i	0.674740	+	0.738055i	$0.264256\pi$
$258$	64.0176	+	10.2986i	0.248130	+	0.0399171i
$259$	−114.691	+	185.775i	−0.442824	+	0.717280i
$260$		−	144.122i		−	0.554316i
$261$	−275.987	−	309.520i	−1.05742	−	1.18590i
$262$	35.8942	+	62.1705i	0.137001	+	0.237292i
$263$	−42.7543	−	24.6842i	−0.162564	−	0.0938563i	0.416511	−	0.909131i	$-0.363253\pi$
$263$	−42.7543	−	24.6842i	−0.162564	−	0.0938563i	−0.579075	+	0.815274i	$0.696586\pi$
$264$	−382.256	+	145.672i	−1.44794	+	0.551787i
$265$	104.106	−	180.317i	0.392853	−	0.680441i
$266$	150.570	+	92.9566i	0.566052	+	0.349461i
$267$	57.9095	+	151.960i	0.216890	+	0.569139i
$268$	77.9166			0.290734
$269$	−162.040	+	93.5538i	−0.602379	+	0.347784i	−0.769977	−	0.638072i	$-0.779732\pi$
$269$	−162.040	+	93.5538i	−0.602379	+	0.347784i	0.167598	+	0.985855i	$0.446399\pi$
$270$	−481.077	+	21.7038i	−1.78177	+	0.0803845i
$271$	108.146	−	187.315i	0.399064	−	0.691199i	−0.594547	−	0.804061i	$-0.702668\pi$
$271$	108.146	−	187.315i	0.399064	−	0.691199i	0.993611	+	0.112862i	$0.0360018\pi$
$272$	10.2620	−	5.92476i	0.0377279	−	0.0217822i
$273$	80.8390	−	28.1057i	0.296114	−	0.102951i
$274$	−59.7747	+	103.533i	−0.218156	+	0.377857i
$275$	85.9920	−	49.6475i	0.312698	−	0.180536i
$276$	190.586	+	30.6599i	0.690530	+	0.111086i
$277$	−39.0618	+	67.6570i	−0.141017	+	0.244249i	−0.927880	−	0.372879i	$-0.878371\pi$
$277$	−39.0618	+	67.6570i	−0.141017	+	0.244249i	0.786863	+	0.617128i	$0.211704\pi$
$278$	393.828	+	227.377i	1.41665	+	0.817901i
$279$	54.1661	+	261.051i	0.194144	+	0.935666i
$280$	−141.593	−	262.853i	−0.505688	−	0.938762i
$281$	−385.051	+	222.309i	−1.37029	+	0.791135i	−0.990964	−	0.134129i	$-0.957176\pi$
$281$	−385.051	+	222.309i	−1.37029	+	0.791135i	−0.379323	+	0.925264i	$0.623843\pi$
$282$	123.314	+	100.354i	0.437285	+	0.355865i
$283$	−128.424			−0.453796			−0.226898	−	0.973919i	$-0.572858\pi$
$283$	−128.424			−0.453796			−0.226898	+	0.973919i	$0.572858\pi$
$284$		−	127.917i		−	0.450411i
$285$	−82.1616	+	100.960i	−0.288286	+	0.354244i
$286$	116.194	+	201.254i	0.406272	+	0.703684i
$287$	−191.329	−	118.120i	−0.666650	−	0.411567i
$288$	292.063	−	60.6008i	1.01411	−	0.210419i
$289$	−7.50994	+	13.0076i	−0.0259859	+	0.0450090i
$290$	711.720	+	410.912i	2.45421	+	1.41694i
$291$	82.0692	−	510.154i	0.282025	−	1.75311i
$292$	73.4574	+	127.232i	0.251566	+	0.435726i
$293$	−42.6510	−	24.6246i	−0.145567	−	0.0840429i	0.425448	−	0.904983i	$-0.360117\pi$
$293$	−42.6510	−	24.6246i	−0.145567	−	0.0840429i	−0.571014	+	0.820940i	$0.693450\pi$
$294$	320.250	−	349.266i	1.08929	−	1.18798i
$295$	−262.969	−	455.475i	−0.891420	−	1.54398i
$296$	−208.220	−	120.216i	−0.703446	−	0.406135i
$297$	402.426	−	257.196i	1.35497	−	0.865979i
$298$	186.512	+	323.049i	0.625880	+	1.08406i
$299$		−	41.0304i		−	0.137225i
$300$	100.578	−	38.3285i	0.335259	−	0.127762i
$301$	−22.2583	−	41.3204i	−0.0739477	−	0.137277i
$302$	419.635	+	242.276i	1.38952	+	0.802239i
$303$	18.5005	+	48.5471i	0.0610579	+	0.160222i
$304$	2.80694	−	4.86177i	0.00923337	−	0.0159927i
$305$	353.471	−	204.077i	1.15892	−	0.669104i
$306$	358.426	−	319.594i	1.17133	−	1.04442i
$307$	−387.296			−1.26155			−0.630776	−	0.775965i	$-0.717263\pi$
$307$	−387.296			−1.26155			−0.630776	+	0.775965i	$0.717263\pi$
$308$	673.393	+	415.730i	2.18634	+	1.34977i
$309$	13.1509	−	81.7481i	0.0425596	−	0.264557i
$310$	−264.179	−	457.572i	−0.852191	−	1.47604i
$311$		−	101.097i		−	0.325070i	−0.986703	−	0.162535i	$-0.948033\pi$
$311$		−	101.097i		−	0.325070i	0.986703	−	0.162535i	$-0.0519671\pi$
$312$	33.5630	+	88.0724i	0.107574	+	0.282283i
$313$	364.791			1.16547			0.582733	−	0.812663i	$-0.301983\pi$
$313$	364.791			1.16547			0.582733	+	0.812663i	$0.301983\pi$
$314$		−	883.436i		−	2.81349i
$315$	224.211	+	266.898i	0.711780	+	0.847295i
$316$	−887.634			−2.80897
$317$		−	33.1510i		−	0.104577i	−0.998632	−	0.0522886i	$-0.983348\pi$
$317$		−	33.1510i		−	0.104577i	0.998632	−	0.0522886i	$-0.0166516\pi$
$318$	−57.8013	+	359.301i	−0.181765	+	1.12988i
$319$	−815.045			−2.55500
$320$	−498.208	+	287.641i	−1.55690	+	0.898877i
$321$	130.869	+	343.413i	0.407692	+	1.06982i
$322$	−107.736	−	200.003i	−0.334585	−	0.621126i
$323$		−	129.802i		−	0.401864i
$324$	474.964	−	205.970i	1.46594	−	0.635711i
$325$	−11.4388	−	19.8127i	−0.0351965	−	0.0609621i
$326$	−621.575	−	358.866i	−1.90667	−	1.10082i
$327$	−16.2697	+	101.135i	−0.0497545	+	0.309281i
$328$	123.809	−	214.444i	0.377468	−	0.653794i
$329$	3.39348	−	115.032i	0.0103145	−	0.349640i
$330$	−597.419	+	734.103i	−1.81036	+	2.22456i
$331$	−90.5077			−0.273437			−0.136719	−	0.990610i	$-0.543656\pi$
$331$	−90.5077			−0.273437			−0.136719	+	0.990610i	$0.543656\pi$
$332$	−87.5154	+	50.5271i	−0.263601	+	0.152190i
$333$	266.543	+	88.0368i	0.800431	+	0.264375i
$334$	−116.856	+	202.401i	−0.349869	+	0.605990i
$335$	58.4148	−	33.7258i	0.174373	−	0.100674i
$336$	−11.3754	−	9.82892i	−0.0338553	−	0.0292527i
$337$	216.839	−	375.576i	0.643438	−	1.11447i	−0.341221	−	0.939983i	$-0.610841\pi$
$337$	216.839	−	375.576i	0.643438	−	1.11447i	0.984660	−	0.174485i	$-0.0558261\pi$
$338$	−425.426	+	245.620i	−1.25866	+	0.726686i
$339$	−83.1738	−	218.256i	−0.245351	−	0.643822i
$340$	−292.671	+	506.921i	−0.860797	+	1.49094i
$341$	453.798	+	262.000i	1.33079	+	0.768329i
$342$	71.3532	−	216.032i	0.208635	−	0.631671i
$343$	−341.658	−	30.3076i	−0.996089	−	0.0883603i
$344$	44.7614	−	25.8430i	0.130120	−	0.0751250i
$345$	156.155	−	59.5083i	0.452624	−	0.172488i
$346$	−680.731			−1.96743
$347$		−	11.6949i		−	0.0337029i	−0.999858	−	0.0168514i	$-0.994636\pi$
$347$		−	11.6949i		−	0.0337029i	0.999858	−	0.0168514i	$-0.00536423\pi$
$348$	−872.273	−	140.324i	−2.50653	−	0.403229i
$349$	91.7075	+	158.842i	0.262772	+	0.455135i	0.966978	−	0.254862i	$-0.0820299\pi$
$349$	91.7075	+	158.842i	0.262772	+	0.455135i	−0.704205	+	0.709996i	$0.748697\pi$
$350$	−107.782	−	66.5410i	−0.307949	−	0.190117i
$351$	−59.2583	−	92.7196i	−0.168827	−	0.264159i
$352$	293.125	−	507.707i	0.832741	−	1.44235i
$353$	−58.9619	−	34.0417i	−0.167031	−	0.0964353i	0.414154	−	0.910207i	$-0.364077\pi$
$353$	−58.9619	−	34.0417i	−0.167031	−	0.0964353i	−0.581185	+	0.813771i	$0.697411\pi$
$354$	712.990	+	580.236i	2.01410	+	1.63909i
$355$	−55.3681	−	95.9004i	−0.155967	−	0.270142i
$356$	300.039	+	173.228i	0.842807	+	0.486595i
$357$	−341.410	−	65.3047i	−0.956329	−	0.182926i
$358$	129.528	+	224.350i	0.361811	+	0.626675i
$359$	−386.169	−	222.955i	−1.07568	−	0.621044i	−0.145952	−	0.989292i	$-0.546625\pi$
$359$	−386.169	−	222.955i	−1.07568	−	0.621044i	−0.929728	+	0.368247i	$0.879958\pi$
$360$	−286.512	+	255.471i	−0.795866	+	0.709642i
$361$	149.752	+	259.378i	0.414826	+	0.718500i
$362$			396.319i			1.09480i
$363$	91.4332	−	568.362i	0.251882	−	1.56574i
$364$	95.7848	−	155.151i	0.263145	−	0.426238i
$365$	110.143	+	63.5913i	0.301763	+	0.174223i
$366$	−450.292	+	553.315i	−1.23031	+	1.51179i
$367$	−63.3424	+	109.712i	−0.172595	+	0.298943i	−0.939326	−	0.343025i	$-0.888549\pi$
$367$	−63.3424	+	109.712i	−0.172595	+	0.298943i	0.766731	+	0.641968i	$0.221882\pi$
$368$	−6.24161	+	3.60360i	−0.0169609	+	0.00979238i
$369$	−90.6684	+	274.511i	−0.245714	+	0.743932i
$370$	−556.291			−1.50349
$371$	231.912	−	124.925i	0.625101	−	0.336726i
$372$	440.553	+	358.526i	1.18428	+	0.963779i
$373$	306.165	+	530.293i	0.820817	+	1.42170i	0.905075	+	0.425252i	$0.139815\pi$
$373$	306.165	+	530.293i	0.820817	+	1.42170i	−0.0842582	+	0.996444i	$0.526852\pi$
$374$		−	943.825i		−	2.52360i
$375$	−203.117	+	249.589i	−0.541646	+	0.665570i
$376$	126.733			0.337057
$377$			187.787i			0.498110i
$378$	−532.315	−	296.363i	−1.40824	−	0.784029i
$379$	410.847			1.08403			0.542015	−	0.840369i	$-0.317662\pi$
$379$	410.847			1.08403			0.542015	+	0.840369i	$0.317662\pi$
$380$			277.314i			0.729775i
$381$	−32.7486	−	26.6511i	−0.0859544	−	0.0699504i
$382$	1145.95			2.99986
$383$	190.627	−	110.059i	0.497722	−	0.287360i	−0.230051	−	0.973179i	$-0.573889\pi$
$383$	190.627	−	110.059i	0.497722	−	0.287360i	0.727772	+	0.685819i	$0.240556\pi$
$384$	383.638	−	471.411i	0.999056	−	1.22763i
$385$	684.796	+	20.2018i	1.77869	+	0.0524721i
$386$		−	127.844i		−	0.331203i
$387$	−45.0395	+	40.1599i	−0.116381	+	0.103772i
$388$	−550.417	−	953.351i	−1.41860	−	2.45709i
$389$	149.180	+	86.1293i	0.383497	+	0.221412i	0.679339	−	0.733825i	$-0.262267\pi$
$389$	149.180	+	86.1293i	0.383497	+	0.221412i	−0.295842	+	0.955237i	$0.595600\pi$
$390$	169.138	+	137.646i	0.433688	+	0.352939i
$391$	−83.3209	+	144.316i	−0.213097	+	0.369095i
$392$	22.2669	−	377.071i	0.0568033	−	0.961916i
$393$	−65.9615	−	10.6113i	−0.167841	−	0.0270008i
$394$	421.109			1.06880
$395$	−665.468	+	384.208i	−1.68473	+	0.972678i
$396$	319.113	−	966.159i	0.805841	−	2.43979i
$397$	−185.521	+	321.332i	−0.467308	+	0.809401i	−0.999302	−	0.0373470i	$-0.988109\pi$
$397$	−185.521	+	321.332i	−0.467308	+	0.809401i	0.531995	+	0.846748i	$0.321443\pi$
$398$	−605.912	+	349.824i	−1.52239	+	0.878954i
$399$	−155.547	+	54.0799i	−0.389843	+	0.135539i
$400$	−2.00929	+	3.48020i	−0.00502323	+	0.00870049i
$401$	−259.303	+	149.708i	−0.646640	+	0.373338i	−0.787168	−	0.616739i	$-0.788453\pi$
$401$	−259.303	+	149.708i	−0.646640	+	0.373338i	0.140528	+	0.990077i	$0.455120\pi$
$402$	−74.4154	+	91.4411i	−0.185113	+	0.227465i
$403$	60.3652	−	104.556i	0.149790	−	0.259443i
$404$	95.8544	+	55.3416i	0.237263	+	0.136984i
$405$	266.932	−	360.004i	0.659090	−	0.888898i
$406$	493.087	+	915.370i	1.21450	+	2.25460i
$407$	477.788	−	275.851i	1.17393	−	0.677767i
$408$	60.7987	−	377.934i	0.149016	−	0.926308i
$409$	−374.401			−0.915407			−0.457703	−	0.889105i	$-0.651328\pi$
$409$	−374.401			−0.915407			−0.457703	+	0.889105i	$0.651328\pi$
$410$		−	572.919i		−	1.39736i
$411$	−39.6194	−	103.965i	−0.0963975	−	0.252956i
$412$	−88.2000	−	152.767i	−0.214078	−	0.370793i
$413$	19.6208	−	665.100i	0.0475079	−	1.61041i
$414$	−218.004	+	194.385i	−0.526580	+	0.469530i
$415$	−43.7408	+	75.7613i	−0.105399	+	0.182557i
$416$	−116.976	−	67.5364i	−0.281193	−	0.162347i
$417$	−395.471	+	150.708i	−0.948373	+	0.361410i
$418$	−223.576	−	387.244i	−0.534870	−	0.926422i
$419$	350.317	+	202.256i	0.836080	+	0.482711i	0.855930	−	0.517092i	$-0.172986\pi$
$419$	350.317	+	202.256i	0.836080	+	0.482711i	−0.0198501	+	0.999803i	$0.506319\pi$
$420$	729.401	+	139.520i	1.73667	+	0.332189i
$421$	−231.002	−	400.107i	−0.548698	−	0.950372i	−0.998364	−	0.0571757i	$-0.981790\pi$
$421$	−231.002	−	400.107i	−0.548698	−	0.950372i	0.449666	−	0.893197i	$-0.351543\pi$
$422$	304.916	+	176.043i	0.722549	+	0.417164i
$423$	−144.876	+	30.0607i	−0.342497	+	0.0710655i
$424$	145.045	+	251.225i	0.342087	+	0.592512i
$425$			92.9161i			0.218626i
$426$	150.120	+	122.169i	0.352395	+	0.286781i
$427$	516.150	+	15.2267i	1.20878	+	0.0356596i
$428$	678.055	+	391.475i	1.58424	+	0.914662i
$429$	−213.525	−	34.3501i	−0.497728	−	0.0800703i
$430$	59.7933	−	103.565i	0.139054	−	0.240849i
$431$	197.559	−	114.061i	0.458374	−	0.264643i	−0.252986	−	0.967470i	$-0.581413\pi$
$431$	197.559	−	114.061i	0.458374	−	0.264643i	0.711360	+	0.702827i	$0.248079\pi$
$432$	−8.90017	+	17.1578i	−0.0206022	+	0.0397171i
$433$	777.626			1.79590			0.897951	−	0.440095i	$-0.145055\pi$
$433$	777.626			1.79590			0.897951	+	0.440095i	$0.145055\pi$
$434$	19.7111	−	668.161i	0.0454172	−	1.53954i
$435$	−714.690	+	272.357i	−1.64297	+	0.626108i
$436$	109.117	+	188.996i	0.250268	+	0.433477i
$437$			78.9490i			0.180661i
$438$	−219.473	−	35.3069i	−0.501080	−	0.0806094i
$439$	68.8012			0.156722			0.0783612	−	0.996925i	$-0.475031\pi$
$439$	68.8012			0.156722			0.0783612	+	0.996925i	$0.475031\pi$
$440$			754.458i			1.71468i
$441$	63.9854	+	436.333i	0.145092	+	0.989418i
$442$	−217.459			−0.491988
$443$			208.330i			0.470271i	0.971963	+	0.235136i	$0.0755534\pi$
$443$			208.330i			0.470271i	−0.971963	+	0.235136i	$0.924447\pi$
$444$	558.829	−	212.961i	1.25862	−	0.479642i
$445$	299.923			0.673984
$446$	521.312	−	300.979i	1.16886	−	0.674842i
$447$	−342.747	−	55.1382i	−0.766772	−	0.123352i
$448$	−727.500	−	21.4616i	−1.62388	−	0.0479053i
$449$			259.045i			0.576937i	0.957489	+	0.288469i	$0.0931461\pi$
$449$			259.045i			0.576937i	−0.957489	+	0.288469i	$0.906854\pi$
$450$	−51.0767	+	154.642i	−0.113504	+	0.343648i
$451$	284.097	+	492.071i	0.629927	+	1.09107i
$452$	−430.938	−	248.802i	−0.953402	−	0.550447i
$453$	−421.386	+	160.584i	−0.930212	+	0.354489i
$454$	−326.463	+	565.450i	−0.719081	+	1.24548i
$455$	4.65452	−	157.778i	0.0102297	−	0.346765i
$456$	−64.5806	−	169.465i	−0.141624	−	0.371635i
$457$	159.437			0.348878			0.174439	−	0.984668i	$-0.444189\pi$
$457$	159.437			0.348878			0.174439	+	0.984668i	$0.444189\pi$
$458$	−221.306	+	127.771i	−0.483201	+	0.278976i
$459$	20.1420	+	446.459i	0.0438824	+	0.972678i
$460$	178.010	−	308.323i	0.386979	−	0.670267i
$461$	−176.910	+	102.139i	−0.383752	+	0.221559i	−0.679449	−	0.733722i	$-0.737781\pi$
$461$	−176.910	+	102.139i	−0.383752	+	0.221559i	0.295697	+	0.955282i	$0.404448\pi$
$462$	−1131.03	+	393.229i	−2.44811	+	0.851146i
$463$	−381.105	+	660.092i	−0.823120	+	1.42569i	0.0802276	+	0.996777i	$0.474435\pi$
$463$	−381.105	+	660.092i	−0.823120	+	1.42569i	−0.903348	+	0.428909i	$0.858898\pi$
$464$	28.5666	−	16.4929i	0.0615659	−	0.0355451i
$465$	485.473	+	78.0987i	1.04403	+	0.167954i
$466$	−525.638	+	910.432i	−1.12798	+	1.95372i
$467$	−462.046	−	266.762i	−0.989391	−	0.571225i	−0.0842988	−	0.996441i	$-0.526865\pi$
$467$	−462.046	−	266.762i	−0.989391	−	0.571225i	−0.905092	+	0.425215i	$0.860198\pi$
$468$	−222.604	−	73.5241i	−0.475650	−	0.157103i
$469$	85.2993	+	2.51636i	0.181875	+	0.00536538i
$470$	253.940	−	146.612i	0.540298	−	0.311941i
$471$	637.687	+	518.954i	1.35390	+	1.10181i
$472$	732.759			1.55245
$473$			118.600i			0.250741i
$474$	847.748	−	1041.71i	1.78850	−	2.19769i
$475$	22.0102	+	38.1228i	0.0463372	+	0.0802584i
$476$	−651.970	+	351.200i	−1.36969	+	0.737815i
$477$	−225.399	−	252.786i	−0.472535	−	0.529950i
$478$	392.545	−	679.909i	0.821225	−	1.42240i
$479$	523.526	+	302.258i	1.09296	+	0.631019i	0.934362	−	0.356325i	$-0.115970\pi$
$479$	523.526	+	302.258i	1.09296	+	0.631019i	0.158595	+	0.987344i	$0.449304\pi$
$480$	87.3766	−	543.145i	0.182034	−	1.13155i
$481$	−63.5565	−	110.083i	−0.132134	−	0.228863i
$482$	−79.1177	−	45.6787i	−0.164145	−	0.0947690i
$483$	207.654	+	39.7200i	0.429926	+	0.0822361i
$484$	−613.220	−	1062.13i	−1.26698	−	2.19448i
$485$	−825.306	−	476.491i	−1.70166	−	0.982455i
$486$	−211.899	+	754.121i	−0.436007	+	1.55169i
$487$	−78.1017	−	135.276i	−0.160373	−	0.277774i	0.774629	−	0.632415i	$-0.217936\pi$
$487$	−78.1017	−	135.276i	−0.160373	−	0.277774i	−0.935002	+	0.354641i	$0.884603\pi$
$488$			568.657i			1.16528i
$489$	624.169	−	237.861i	1.27642	−	0.486423i
$490$	−391.600	−	781.310i	−0.799184	−	1.59451i
$491$	−346.903	−	200.285i	−0.706523	−	0.407911i	0.103249	−	0.994656i	$-0.467076\pi$
$491$	−346.903	−	200.285i	−0.706523	−	0.407911i	−0.809772	+	0.586744i	$0.800409\pi$
$492$	219.327	+	575.534i	0.445786	+	1.16978i
$493$	381.342	−	660.505i	0.773514	−	1.33977i
$494$	−89.2216	+	51.5121i	−0.180611	+	0.104276i
$495$	−178.955	−	862.465i	−0.361525	−	1.74235i
$496$	−21.2069			−0.0427559
$497$	4.13115	−	140.037i	0.00831218	−	0.281765i
$498$	24.2856	−	150.963i	0.0487662	−	0.303138i
$499$	61.1444	+	105.905i	0.122534	+	0.212235i	0.920766	−	0.390115i	$-0.127565\pi$
$499$	61.1444	+	105.905i	0.122534	+	0.212235i	−0.798232	+	0.602350i	$0.794231\pi$
$500$			685.567i			1.37113i
$501$	−77.4536	−	203.245i	−0.154598	−	0.405680i
$502$	−451.724			−0.899848
$503$			786.814i			1.56424i	0.623126	+	0.782121i	$0.285862\pi$
$503$			786.814i			1.56424i	−0.623126	+	0.782121i	$0.714138\pi$
$504$	−478.224	+	84.6022i	−0.948858	+	0.167861i
$505$	95.8173			0.189737
$506$			574.059i			1.13450i
$507$	72.6121	−	451.368i	0.143219	−	0.890271i
$508$	−89.9536			−0.177074
$509$	−781.867	+	451.411i	−1.53609	+	0.886859i	−0.537023	+	0.843568i	$0.680451\pi$
$509$	−781.867	+	451.411i	−1.53609	+	0.886859i	−0.999062	+	0.0432914i	$0.986216\pi$
$510$	−315.391	−	827.614i	−0.618413	−	1.62277i
$511$	76.3085	+	141.660i	0.149332	+	0.277220i
$512$			45.8004i			0.0894539i
$513$	114.022	+	178.407i	0.222266	+	0.347773i
$514$	178.379	+	308.961i	0.347040	+	0.601092i
$515$	−132.249	−	76.3539i	−0.256794	−	0.148260i
$516$	−20.4191	+	126.928i	−0.0395718	+	0.245984i
$517$	−145.403	+	251.846i	−0.281244	+	0.487129i
$518$	−598.859	−	369.715i	−1.15610	−	0.713736i
$519$	399.880	−	491.369i	0.770482	−	0.946762i
$520$	173.828			0.334285
$521$	442.743	−	255.618i	0.849795	−	0.490630i	−0.0107865	−	0.999942i	$-0.503434\pi$
$521$	442.743	−	255.618i	0.849795	−	0.490630i	0.860582	+	0.509312i	$0.170100\pi$
$522$	997.759	−	889.661i	1.91141	−	1.70433i
$523$	489.654	−	848.105i	0.936240	−	1.62162i	0.163833	−	0.986488i	$-0.447614\pi$
$523$	489.654	−	848.105i	0.936240	−	1.62162i	0.772407	−	0.635128i	$-0.219053\pi$
$524$	−123.266	+	71.1675i	−0.235240	+	0.135816i
$525$	111.345	−	38.7120i	0.212086	−	0.0737371i
$526$	79.5711	−	137.821i	0.151276	−	0.262018i
$527$	−424.645	+	245.169i	−0.805778	+	0.465216i
$528$	13.5280	+	35.4988i	0.0256212	+	0.0672325i
$529$	−213.822	+	370.351i	−0.404200	+	0.700096i
$530$	581.263	+	335.592i	1.09672	+	0.633193i
$531$	−837.659	+	173.808i	−1.57751	+	0.327322i
$532$	−184.305	+	298.535i	−0.346438	+	0.561156i
$533$	113.374	−	65.4564i	0.212709	−	0.122807i
$534$	−489.853	+	186.675i	−0.917327	+	0.349579i
$535$	677.793			1.26690
$536$			93.9764i			0.175329i
$537$	−238.030	−	38.2922i	−0.443258	−	0.0713076i
$538$	−301.577	−	522.346i	−0.560552	−	0.970904i
$539$	723.772	+	476.868i	1.34280	+	0.884728i
$540$	−43.0322	−	953.833i	−0.0796893	−	1.76636i
$541$	350.265	−	606.676i	0.647439	−	1.12140i	−0.336293	−	0.941757i	$-0.609173\pi$
$541$	350.265	−	606.676i	0.647439	−	1.12140i	0.983732	−	0.179640i	$-0.0574934\pi$
$542$	603.822	+	348.617i	1.11406	+	0.643204i
$543$	−286.073	−	232.808i	−0.526838	−	0.428745i
$544$	274.294	+	475.091i	0.504217	+	0.873329i
$545$	163.612	+	94.4613i	0.300205	+	0.173324i
$546$	90.6006	+	260.590i	0.165935	+	0.477271i
$547$	294.015	+	509.248i	0.537504	+	0.930984i	0.999038	+	0.0438616i	$0.0139660\pi$
$547$	294.015	+	509.248i	0.537504	+	0.930984i	−0.461534	+	0.887123i	$0.652701\pi$
$548$	−205.275	−	118.515i	−0.374589	−	0.216269i
$549$	−134.883	−	650.065i	−0.245689	−	1.18409i
$550$	160.042	+	277.201i	0.290985	+	0.504001i
$551$		−	361.333i		−	0.655777i
$552$	−36.9794	+	229.869i	−0.0669916	+	0.416430i
$553$	−971.738	−	28.6667i	−1.75721	−	0.0518385i
$554$	−218.097	−	125.918i	−0.393676	−	0.227289i
$555$	326.780	−	401.545i	0.588794	−	0.723505i
$556$	−450.820	+	780.843i	−0.810827	+	1.40439i
$557$	347.042	−	200.365i	0.623055	−	0.359721i	−0.155002	−	0.987914i	$-0.549539\pi$
$557$	347.042	−	200.365i	0.623055	−	0.359721i	0.778057	+	0.628193i	$0.216205\pi$
$558$	−841.514	+	174.608i	−1.50809	+	0.312917i
$559$	27.3257			0.0488831
$560$	−24.4103	+	13.1492i	−0.0435897	+	0.0234807i
$561$	681.278	+	554.429i	1.21440	+	0.988287i
$562$	−716.628	−	1241.24i	−1.27514	−	2.20860i
$563$		−	91.1620i		−	0.161922i	−0.996717	−	0.0809609i	$-0.974201\pi$
$563$		−	91.1620i		−	0.161922i	0.996717	−	0.0809609i	$-0.0257989\pi$
$564$	−198.972	+	244.495i	−0.352788	+	0.433502i
$565$	−430.771			−0.762426
$566$		−	413.984i		−	0.731421i
$567$	526.619	−	210.147i	0.928781	−	0.370629i
$568$	154.282			0.271624
$569$		−	295.137i		−	0.518693i	−0.965784	−	0.259347i	$-0.916493\pi$
$569$		−	295.137i		−	0.518693i	0.965784	−	0.259347i	$-0.0835072\pi$
$570$	−325.450	−	264.853i	−0.570964	−	0.464655i
$571$	914.813			1.60212			0.801062	−	0.598581i	$-0.204268\pi$
$571$	914.813			1.60212			0.801062	+	0.598581i	$0.204268\pi$
$572$	−399.026	+	230.378i	−0.697598	+	0.402758i
$573$	−673.159	+	827.173i	−1.17480	+	1.44358i
$574$	380.767	−	616.760i	0.663357	−	1.07450i
$575$		−	56.5140i		−	0.0982852i
$576$	190.115	+	916.249i	0.330060	+	1.59071i
$577$	−267.301	−	462.978i	−0.463259	−	0.802389i	0.535862	−	0.844306i	$-0.319987\pi$
$577$	−267.301	−	462.978i	−0.463259	−	0.802389i	−0.999121	+	0.0419171i	$0.986653\pi$
$578$	−41.9308	−	24.2088i	−0.0725447	−	0.0418837i
$579$	92.2812	+	75.0992i	0.159380	+	0.129705i
$580$	−814.715	+	1411.13i	−1.40468	+	2.43298i
$581$	−97.4394	+	52.4882i	−0.167710	+	0.0903411i
$582$	1644.51	+	264.555i	2.82563	+	0.454562i
$583$	−665.649			−1.14177
$584$	−153.456	+	88.5981i	−0.262768	+	0.151709i
$585$	−198.713	+	41.2314i	−0.339681	+	0.0704811i
$586$	79.3789	−	137.488i	0.135459	−	0.234622i
$587$	299.889	−	173.141i	0.510884	−	0.294959i	−0.222313	−	0.974975i	$-0.571361\pi$
$587$	299.889	−	173.141i	0.510884	−	0.294959i	0.733197	+	0.680016i	$0.238027\pi$
$588$	692.490	+	634.961i	1.17770	+	1.07987i
$589$	−116.152	+	201.182i	−0.197203	+	0.341565i
$590$	1468.25	−	847.697i	2.48857	−	1.43677i
$591$	−247.371	+	303.967i	−0.418563	+	0.514327i
$592$	−11.1640	+	19.3367i	−0.0188582	+	0.0326633i
$593$	3.55214	+	2.05083i	0.00599012	+	0.00345840i	0.502992	−	0.864291i	$-0.332232\pi$
$593$	3.55214	+	2.05083i	0.00599012	+	0.00345840i	−0.497002	+	0.867749i	$0.665566\pi$
$594$	829.087	+	1297.25i	1.39577	+	2.18392i
$595$	−336.773	+	545.500i	−0.566005	+	0.916807i
$596$	−640.509	+	369.798i	−1.07468	+	0.620467i
$597$	103.418	−	642.859i	0.173229	−	1.07682i
$598$	132.264			0.221177
$599$			169.572i			0.283091i	0.989932	+	0.141546i	$0.0452072\pi$
$599$			169.572i			0.283091i	−0.989932	+	0.141546i	$0.954793\pi$
$600$	46.2286	+	121.308i	0.0770477	+	0.202180i
$601$	−312.975	−	542.089i	−0.520757	−	0.901978i	−0.999709	−	0.0241366i	$-0.992316\pi$
$601$	−312.975	−	542.089i	−0.520757	−	0.901978i	0.478951	−	0.877841i	$-0.341017\pi$
$602$	133.199	−	71.7510i	0.221261	−	0.119188i
$603$	−22.2909	−	107.430i	−0.0369667	−	0.178159i
$604$	−480.362	+	832.011i	−0.795301	+	1.37750i
$605$	−919.473	−	530.858i	−1.51979	−	0.877451i
$606$	−156.495	+	59.6377i	−0.258242	+	0.0984120i
$607$	18.8059	+	32.5727i	0.0309817	+	0.0536618i	0.881101	−	0.472929i	$-0.156803\pi$
$607$	18.8059	+	32.5727i	0.0309817	+	0.0536618i	−0.850119	+	0.526591i	$0.823470\pi$
$608$	225.081	+	129.951i	0.370200	+	0.213735i
$609$	−950.390	−	181.790i	−1.56057	−	0.298506i
$610$	657.855	+	1139.44i	1.07845	+	1.86793i
$611$	58.0256	+	33.5011i	0.0949682	+	0.0548299i
$612$	633.659	+	710.652i	1.03539	+	1.16120i
$613$	−149.019	−	258.108i	−0.243098	−	0.421057i	0.718497	−	0.695530i	$-0.244830\pi$
$613$	−149.019	−	258.108i	−0.243098	−	0.421057i	−0.961595	+	0.274472i	$0.911497\pi$
$614$		−	1248.48i		−	2.03335i
$615$	413.548	+	336.549i	0.672436	+	0.547233i
$616$	−501.418	+	812.190i	−0.813991	+	1.31849i
$617$	818.560	+	472.596i	1.32668	+	0.765957i	0.984784	−	0.173782i	$-0.0555987\pi$
$617$	818.560	+	472.596i	1.32668	+	0.765957i	0.341893	+	0.939739i	$0.388932\pi$
$618$	263.520	+	42.3929i	0.426408	+	0.0685969i
$619$	596.799	−	1033.69i	0.964133	−	1.66993i	0.252208	−	0.967673i	$-0.418843\pi$
$619$	596.799	−	1033.69i	0.964133	−	1.66993i	0.711926	−	0.702255i	$-0.247823\pi$
$620$	907.229	−	523.789i	1.46327	−	0.844820i
$621$	−12.2509	−	271.548i	−0.0197277	−	0.437276i
$622$	325.892			0.523943
$623$	322.874	+	199.331i	0.518256	+	0.319954i
$624$	8.17896	−	3.11687i	0.0131073	−	0.00499499i
$625$	366.913	+	635.512i	0.587061	+	1.01682i
$626$			1175.93i			1.87848i
$627$	410.857	+	66.0952i	0.655275	+	0.105415i
$628$	1751.59			2.78916
$629$			516.260i			0.820764i
$630$	−860.362	+	722.758i	−1.36565	+	1.14723i
$631$	−823.055			−1.30437			−0.652183	−	0.758062i	$-0.726147\pi$
$631$	−823.055			−1.30437			−0.652183	+	0.758062i	$0.726147\pi$
$632$		−	1070.59i		−	1.69397i
$633$	−306.188	+	116.683i	−0.483709	+	0.184334i
$634$	106.864			0.168556
$635$	−67.4390	+	38.9359i	−0.106203	+	0.0613165i
$636$	−712.388	−	114.603i	−1.12011	−	0.180193i
$637$	109.871	−	166.758i	0.172482	−	0.261786i
$638$		−	2627.35i		−	4.11810i
$639$	−176.369	+	36.5953i	−0.276008	+	0.0572696i
$640$	−560.476	−	970.773i	−0.875744	−	1.51683i
$641$	−617.070	−	356.265i	−0.962667	−	0.555796i	−0.0656744	−	0.997841i	$-0.520920\pi$
$641$	−617.070	−	356.265i	−0.962667	−	0.555796i	−0.896993	+	0.442045i	$0.854253\pi$
$642$	−1107.01	+	421.865i	−1.72432	+	0.657111i
$643$	534.902	−	926.478i	0.831885	−	1.44087i	−0.0646564	−	0.997908i	$-0.520595\pi$
$643$	534.902	−	926.478i	0.831885	−	1.44087i	0.896542	−	0.442960i	$-0.146072\pi$
$644$	396.545	−	213.609i	0.615754	−	0.331691i
$645$	39.6317	+	103.997i	0.0614445	+	0.161236i
$646$	418.425			0.647717
$647$	973.422	−	562.006i	1.50452	−	0.868633i	0.504531	−	0.863394i	$-0.331666\pi$
$647$	973.422	−	562.006i	1.50452	−	0.868633i	0.999986	−	0.00523936i	$-0.00166775\pi$
$648$	248.424	+	572.861i	0.383370	+	0.884045i
$649$	−840.705	+	1456.14i	−1.29539	+	2.24367i
$650$	63.8674	−	36.8739i	0.0982576	−	0.0567290i
$651$	470.717	+	406.724i	0.723068	+	0.624768i
$652$	711.525	−	1232.40i	1.09130	−	1.89018i
$653$	41.9432	−	24.2159i	0.0642315	−	0.0370841i	−0.467540	−	0.883972i	$-0.654860\pi$
$653$	41.9432	−	24.2159i	0.0642315	−	0.0370841i	0.531772	+	0.846888i	$0.321526\pi$
$654$	−326.015	−	52.4464i	−0.498494	−	0.0801933i
$655$	−61.6090	+	106.710i	−0.0940595	+	0.162916i
$656$	−19.9147	−	11.4977i	−0.0303577	−	0.0175270i
$657$	154.410	−	137.681i	0.235023	−	0.209560i
$658$	370.812	+	10.9391i	0.563544	+	0.0166248i
$659$	−818.128	+	472.346i	−1.24147	+	0.716762i	−0.969393	−	0.245514i	$-0.921043\pi$
$659$	−818.128	+	472.346i	−1.24147	+	0.716762i	−0.272076	+	0.962276i	$0.587710\pi$
$660$	−1455.51	−	1184.50i	−2.20532	−	1.79470i
$661$	281.194			0.425407			0.212703	−	0.977117i	$-0.431773\pi$
$661$	281.194			0.425407			0.212703	+	0.977117i	$0.431773\pi$
$662$		−	291.757i		−	0.440721i
$663$	127.741	−	156.967i	0.192671	−	0.236753i
$664$	−60.9415	−	105.554i	−0.0917794	−	0.158967i
$665$	−8.95604	+	303.590i	−0.0134677	+	0.456526i
$666$	−283.792	+	859.220i	−0.426114	+	1.29012i
$667$	−231.942	+	401.736i	−0.347740	+	0.602303i
$668$	−401.300	−	231.691i	−0.600749	−	0.346843i
$669$	−88.9779	+	553.100i	−0.133001	+	0.826756i
$670$	108.717	+	188.304i	0.162265	+	0.281051i
$671$	−1130.04	−	652.429i	−1.68411	−	0.972323i
$672$	455.041	−	526.637i	0.677145	−	0.783686i
$673$	246.892	+	427.630i	0.366854	+	0.635409i	0.989072	−	0.147435i	$-0.0471017\pi$
$673$	246.892	+	427.630i	0.366854	+	0.635409i	−0.622218	+	0.782844i	$0.713768\pi$
$674$	1210.69	+	698.994i	1.79628	+	1.03708i
$675$	−81.6205	−	127.709i	−0.120919	−	0.189199i
$676$	−486.991	−	843.494i	−0.720401	−	1.24777i
$677$			705.620i			1.04227i	0.853473	+	0.521137i	$0.174492\pi$
$677$			705.620i			1.04227i	−0.853473	+	0.521137i	$0.825508\pi$
$678$	703.562	−	268.116i	1.03770	−	0.395452i
$679$	−571.781	−	1061.46i	−0.842093	−	1.56327i
$680$	−611.405	−	352.995i	−0.899126	−	0.519110i
$681$	−216.383	−	567.810i	−0.317743	−	0.833788i
$682$	−844.575	+	1462.85i	−1.23838	+	2.14494i
$683$	−1010.24	+	583.260i	−1.47912	+	0.853968i	−0.999721	−	0.0236320i	$-0.992477\pi$
$683$	−1010.24	+	583.260i	−1.47912	+	0.853968i	−0.479394	+	0.877600i	$0.659144\pi$
$684$	428.326	+	141.472i	0.626208	+	0.206831i
$685$	−205.195			−0.299555
$686$	97.6984	−	1101.36i	0.142417	−	1.60548i
$687$	37.7727	−	234.800i	0.0549821	−	0.341777i
$688$	−2.39995	−	4.15683i	−0.00348829	−	0.00604190i
$689$			153.366i			0.222593i
$690$	191.829	+	503.377i	0.278013	+	0.729531i
$691$	365.668			0.529186			0.264593	−	0.964360i	$-0.414762\pi$
$691$	365.668			0.529186			0.264593	+	0.964360i	$0.414762\pi$
$692$		−	1349.69i		−	1.95041i
$693$	380.552	−	1047.40i	0.549137	−	1.51140i
$694$	37.6993			0.0543217
$695$			780.541i			1.12308i
$696$	169.247	−	1052.06i	0.243171	−	1.51158i
$697$	−531.692			−0.762830
$698$	−512.038	+	295.625i	−0.733578	+	0.423532i
$699$	−348.399	−	914.232i	−0.498425	−	1.30791i
$700$	131.931	−	213.700i	0.188473	−	0.305286i
$701$			254.519i			0.363080i	0.983384	+	0.181540i	$0.0581083\pi$
$701$			254.519i			0.363080i	−0.983384	+	0.181540i	$0.941892\pi$
$702$	298.888	−	191.023i	0.425766	−	0.272112i
$703$	122.293	+	211.818i	0.173959	+	0.301305i
$704$	1592.76	+	919.581i	2.26244	+	1.30622i
$705$	−43.3427	+	269.425i	−0.0614790	+	0.382163i
$706$	109.735	−	190.067i	0.155433	−	0.269217i
$707$	103.149	+	63.6809i	0.145897	+	0.0900720i
$708$	−1150.44	+	1413.65i	−1.62491	+	1.99668i
$709$	−1040.99			−1.46825			−0.734124	−	0.679015i	$-0.762407\pi$
$709$	−1040.99			−1.46825			−0.734124	+	0.679015i	$0.762407\pi$
$710$	309.141	−	178.483i	0.435410	−	0.251384i
$711$	253.940	+	1223.85i	0.357159	+	1.72131i
$712$	−208.933	+	361.882i	−0.293445	+	0.508261i
$713$	258.280	−	149.118i	0.362244	−	0.209142i
$714$	210.514	−	1100.56i	0.294837	−	1.54139i
$715$	−199.436	+	345.433i	−0.278931	+	0.483123i
$716$	−444.818	+	256.816i	−0.621255	+	0.358682i
$717$	260.184	+	682.746i	0.362878	+	0.952227i
$718$	718.710	−	1244.84i	1.00099	−	1.73376i
$719$	653.543	+	377.323i	0.908961	+	0.524789i	0.880097	−	0.474795i	$-0.157478\pi$
$719$	653.543	+	377.323i	0.908961	+	0.524789i	0.0288642	+	0.999583i	$0.490811\pi$
$720$	23.7247	+	26.6073i	0.0329509	+	0.0369546i
$721$	−91.6233	−	170.090i	−0.127078	−	0.235909i
$722$	−836.123	+	482.736i	−1.15807	+	0.668609i
$723$	79.4480	−	30.2764i	0.109887	−	0.0418760i
$724$	−785.782			−1.08533
$725$			258.653i			0.356762i
$726$	1832.15	+	294.741i	2.52363	+	0.405979i
$727$	698.773	+	1210.31i	0.961174	+	1.66480i	0.719561	+	0.694429i	$0.244343\pi$
$727$	698.773	+	1210.31i	0.961174	+	1.66480i	0.241612	+	0.970373i	$0.422324\pi$
$728$	187.130	+	115.528i	0.257046	+	0.158692i
$729$	−419.869	−	595.946i	−0.575952	−	0.817484i
$730$	−204.991	+	355.054i	−0.280809	+	0.486376i
$731$	−96.1126	−	55.4906i	−0.131481	−	0.0759106i
$732$	−1097.06	−	892.795i	−1.49871	−	1.21966i
$733$	−626.744	−	1085.55i	−0.855039	−	1.48097i	−0.876609	−	0.481204i	$-0.840200\pi$
$733$	−626.744	−	1085.55i	−0.855039	−	1.48097i	0.0215697	−	0.999767i	$-0.493134\pi$
$734$	−353.664	−	204.188i	−0.481832	−	0.278186i
$735$	794.007	+	176.296i	1.08028	+	0.239858i
$736$	−166.833	−	288.963i	−0.226675	−	0.392613i
$737$	−186.751	−	107.821i	−0.253393	−	0.146297i
$738$	−884.904	−	292.275i	−1.19906	−	0.396037i
$739$	−534.999	−	926.646i	−0.723950	−	1.25392i	−0.959405	−	0.282033i	$-0.908991\pi$
$739$	−534.999	−	926.646i	−0.723950	−	1.25392i	0.235454	−	0.971885i	$-0.424342\pi$
$740$		−	1102.96i		−	1.49049i
$741$	15.2284	−	94.6621i	0.0205512	−	0.127749i
$742$	402.705	+	747.585i	0.542729	+	1.00753i
$743$	−620.266	−	358.111i	−0.834813	−	0.481980i	0.0206847	−	0.999786i	$-0.493415\pi$
$743$	−620.266	−	358.111i	−0.834813	−	0.481980i	−0.855498	+	0.517806i	$0.826749\pi$
$744$	−432.423	+	531.359i	−0.581214	+	0.714192i
$745$	−320.131	+	554.483i	−0.429706	+	0.744272i
$746$	−1709.43	+	986.941i	−2.29146	+	1.32298i
$747$	94.7028	+	106.210i	0.126777	+	0.142181i
$748$	1871.32			2.50177
$749$	729.659	+	450.466i	0.974177	+	0.601423i
$750$	−804.566	−	654.762i	−1.07275	−	0.873015i
$751$	60.3209	+	104.479i	0.0803208	+	0.139120i	0.903388	−	0.428825i	$-0.141072\pi$
$751$	60.3209	+	104.479i	0.0803208	+	0.139120i	−0.823067	+	0.567944i	$0.807739\pi$
$752$		−	11.7693i		−	0.0156506i
$753$	265.355	−	326.066i	0.352397	−	0.433022i
$754$	−605.345			−0.802845
$755$			831.689i			1.10157i
$756$	587.600	−	1055.42i	0.777248	−	1.39606i
$757$	−369.403			−0.487983			−0.243992	−	0.969777i	$-0.578457\pi$
$757$	−369.403			−0.487983			−0.243992	+	0.969777i	$0.578457\pi$
$758$			1324.39i			1.74722i
$759$	−414.371	−	337.218i	−0.545943	−	0.444293i
$760$	−334.473			−0.440096
$761$	992.067	−	572.770i	1.30364	−	0.752655i	0.322610	−	0.946532i	$-0.395440\pi$
$761$	992.067	−	572.770i	1.30364	−	0.752655i	0.981026	+	0.193877i	$0.0621063\pi$
$762$	85.9115	−	105.567i	0.112745	−	0.138540i
$763$	113.352	+	210.427i	0.148561	+	0.275790i
$764$			2272.07i			2.97391i
$765$	782.663	+	258.506i	1.02309	+	0.337916i
$766$	354.782	+	614.500i	0.463161	+	0.802219i
$767$	335.498	+	193.700i	0.437416	+	0.252542i
$768$	551.896	+	449.137i	0.718615	+	0.584814i
$769$	319.295	−	553.035i	0.415208	−	0.719162i	−0.580242	−	0.814444i	$-0.697042\pi$
$769$	319.295	−	553.035i	0.415208	−	0.719162i	0.995450	+	0.0952822i	$0.0303754\pi$
$770$	−65.1217	+	2207.48i	−0.0845737	+	2.86686i
$771$	−327.801	−	52.7337i	−0.425163	−	0.0683966i
$772$	253.477			0.328338
$773$	169.438	−	97.8250i	0.219195	−	0.126552i	−0.386382	−	0.922339i	$-0.626275\pi$
$773$	169.438	−	97.8250i	0.219195	−	0.126552i	0.605578	+	0.795786i	$0.292942\pi$
$774$	−129.458	−	145.188i	−0.167258	−	0.187581i
$775$	83.1452	−	144.012i	0.107284	−	0.185822i
$776$	1149.85	−	663.867i	1.48177	−	0.855499i
$777$	618.656	−	215.091i	0.796211	−	0.276823i
$778$	−277.643	+	480.892i	−0.356868	+	0.618114i
$779$	−218.149	+	125.949i	−0.280038	+	0.161680i
$780$	−272.911	+	335.351i	−0.349886	+	0.429937i
$781$	−177.011	+	306.591i	−0.226646	+	0.392563i
$782$	−465.212	−	268.590i	−0.594901	−	0.343466i
$783$	56.0698	+	1242.82i	0.0716090	+	1.58725i
$784$	−35.0172	−	2.06785i	−0.0446648	−	0.00263756i
$785$	1313.18	−	758.167i	1.67285	−	0.965818i
$786$	34.2063	−	212.631i	0.0435194	−	0.270523i
$787$	−17.3655			−0.0220654			−0.0110327	−	0.999939i	$-0.503512\pi$
$787$	−17.3655			−0.0220654			−0.0110327	+	0.999939i	$0.503512\pi$
$788$			834.933i			1.05956i
$789$	52.7407	+	138.396i	0.0668450	+	0.175407i
$790$	−1238.52	−	2145.18i	−1.56775	−	2.71542i
$791$	−463.734	−	286.294i	−0.586263	−	0.361939i
$792$	1165.30	+	384.887i	1.47134	+	0.485969i
$793$	−150.320	+	260.363i	−0.189559	+	0.328326i
$794$	−1035.83	−	598.040i	−1.30458	−	0.753198i
$795$	−583.689	+	222.435i	−0.734200	+	0.279792i
$796$	−693.596	−	1201.34i	−0.871352	−	1.50923i
$797$	−871.920	−	503.403i	−1.09400	−	0.631622i	−0.159363	−	0.987220i	$-0.550944\pi$
$797$	−871.920	−	503.403i	−1.09400	−	0.631622i	−0.934639	+	0.355598i	$0.884277\pi$
$798$	−174.330	−	501.417i	−0.218459	−	0.628342i
$799$	−136.062	−	235.667i	−0.170291	−	0.294952i
$800$	−161.120	−	93.0225i	−0.201400	−	0.116278i
$801$	153.006	−	463.247i	0.191019	−	0.578335i
$802$	−482.595	−	835.879i	−0.601739	−	1.04224i
$803$		−	406.600i		−	0.506351i
$804$	−181.300	−	147.544i	−0.225498	−	0.183512i
$805$	204.834	−	331.788i	0.254452	−	0.412158i
$806$	337.042	+	194.591i	0.418166	+	0.241428i
$807$	554.198	+	89.1545i	0.686738	+	0.110477i
$808$	−66.7484	+	115.612i	−0.0826094	+	0.143084i
$809$	364.210	−	210.277i	0.450198	−	0.259922i	−0.257716	−	0.966221i	$-0.582970\pi$
$809$	364.210	−	210.277i	0.450198	−	0.259922i	0.707914	+	0.706299i	$0.249636\pi$
$810$	1160.49	+	860.471i	1.43271	+	1.06231i
$811$	1318.39			1.62564			0.812819	−	0.582517i	$-0.197932\pi$
$811$	1318.39			1.62564			0.812819	+	0.582517i	$0.197932\pi$
$812$	−1814.91	+	977.644i	−2.23510	+	1.20400i
$813$	−606.342	+	231.067i	−0.745808	+	0.284216i
$814$	889.224	+	1540.18i	1.09241	+	1.89212i
$815$		−	1231.92i		−	1.51156i
$816$	−35.0973	−	5.64616i	−0.0430114	−	0.00691931i
$817$	−52.5790			−0.0643562
$818$		−	1206.91i		−	1.47544i
$819$	−241.322	−	87.6797i	−0.294654	−	0.107057i
$820$	1135.93			1.38528
$821$		−	771.778i		−	0.940047i	−0.882654	−	0.470023i	$-0.844245\pi$
$821$		−	771.778i		−	0.940047i	0.882654	−	0.470023i	$-0.155755\pi$
$822$	335.137	−	127.716i	0.407710	−	0.155372i
$823$	906.455			1.10140			0.550702	−	0.834702i	$-0.314360\pi$
$823$	906.455			1.10140			0.550702	+	0.834702i	$0.314360\pi$
$824$	184.255	−	106.379i	0.223610	−	0.129101i
$825$	−294.104	−	47.3128i	−0.356489	−	0.0573489i
$826$	2143.99	+	63.2488i	2.59563	+	0.0765723i
$827$			509.463i			0.616038i	0.951380	+	0.308019i	$0.0996660\pi$
$827$			509.463i			0.616038i	−0.951380	+	0.308019i	$0.900334\pi$
$828$	−385.408	−	432.237i	−0.465469	−	0.522025i
$829$	332.585	+	576.054i	0.401188	+	0.694878i	0.993870	−	0.110559i	$-0.0352641\pi$
$829$	332.585	+	576.054i	0.401188	+	0.694878i	−0.592682	+	0.805437i	$0.701931\pi$
$830$	−244.221	−	141.001i	−0.294243	−	0.169881i
$831$	219.007	−	83.4600i	0.263546	−	0.100433i
$832$	211.873	−	366.974i	0.254655	−	0.441075i
$833$	−725.087	+	363.421i	−0.870453	+	0.436280i
$834$	−485.817	−	1274.83i	−0.582514	−	1.52857i
$835$	−401.145			−0.480413
$836$	767.790	−	443.284i	0.918409	−	0.530244i
$837$	368.292	−	709.996i	0.440014	−	0.848263i
$838$	−651.985	+	1129.27i	−0.778025	+	1.34758i
$839$	1237.78	−	714.635i	1.47531	−	0.851770i	0.475696	−	0.879610i	$-0.342196\pi$
$839$	1237.78	−	714.635i	1.47531	−	0.851770i	0.999612	+	0.0278396i	$0.00886276\pi$
$840$	−168.277	+	879.742i	−0.200329	+	1.04731i
$841$	641.052	−	1110.33i	0.762250	−	1.32026i
$842$	1289.77	−	744.649i	1.53179	−	0.884381i
$843$	1316.92	+	211.855i	1.56219	+	0.251311i
$844$	−349.041	+	604.557i	−0.413556	+	0.716299i
$845$	−730.204	−	421.583i	−0.864147	−	0.498915i
$846$	−96.9027	−	467.018i	−0.114542	−	0.552031i
$847$	−637.020	−	1182.57i	−0.752090	−	1.39619i
$848$	23.3304	−	13.4698i	0.0275122	−	0.0158842i
$849$	298.824	+	243.186i	0.351972	+	0.286438i
$850$	−299.521			−0.352378
$851$		−	314.003i		−	0.368981i
$852$	−242.224	+	297.643i	−0.284301	+	0.349347i
$853$	485.171	+	840.341i	0.568782	+	0.985159i	0.996687	+	0.0813353i	$0.0259185\pi$
$853$	485.171	+	840.341i	0.568782	+	0.985159i	−0.427905	+	0.903824i	$0.640748\pi$
$854$	−49.0841	+	1663.84i	−0.0574756	+	1.94830i
$855$	382.356	−	79.3359i	0.447200	−	0.0927905i
$856$	−472.165	+	817.813i	−0.551594	+	0.955389i
$857$	−1308.06	−	755.208i	−1.52632	−	0.881223i	−0.999512	−	0.0312415i	$-0.990054\pi$
$857$	−1308.06	−	755.208i	−1.52632	−	0.881223i	−0.526812	−	0.849982i	$-0.676613\pi$
$858$	110.730	−	688.313i	0.129056	−	0.802230i
$859$	614.191	+	1063.81i	0.715007	+	1.23843i	0.962957	+	0.269655i	$0.0869097\pi$
$859$	614.191	+	1063.81i	0.715007	+	1.23843i	−0.247950	+	0.968773i	$0.579757\pi$
$860$	205.339	+	118.552i	0.238766	+	0.137852i
$861$	221.521	+	637.149i	0.257283	+	0.740011i
$862$	367.683	+	636.845i	0.426546	+	0.738800i
$863$	1292.69	+	746.335i	1.49790	+	0.864815i	0.999997	−	0.00241587i	$-0.000768995\pi$
$863$	1292.69	+	746.335i	1.49790	+	0.864815i	0.497906	+	0.867231i	$0.334102\pi$
$864$	−794.341	−	412.044i	−0.919376	−	0.476902i
$865$	−584.205	−	1011.87i	−0.675382	−	1.16980i
$866$			2506.73i			2.89460i
$867$	42.1058	−	16.0459i	0.0485650	−	0.0185073i
$868$	1324.77	+	39.0811i	1.52623	+	0.0450244i
$869$	2127.48	+	1228.30i	2.44820	+	1.41347i
$870$	−877.961	−	2303.85i	−1.00915	−	2.64810i
$871$	−24.8420	+	43.0277i	−0.0285213	+	0.0494003i
$872$	−227.951	+	131.608i	−0.261412	+	0.150926i
$873$	−1157.00	+	1031.65i	−1.32531	+	1.18173i
$874$	−254.497			−0.291187
$875$	−22.1408	+	750.526i	−0.0253038	+	0.857744i
$876$	70.0031	−	435.149i	0.0799122	−	0.496746i
$877$	173.474	+	300.466i	0.197804	+	0.342607i	0.947816	−	0.318817i	$-0.103286\pi$
$877$	173.474	+	300.466i	0.197804	+	0.342607i	−0.750012	+	0.661424i	$0.769952\pi$
$878$			221.785i			0.252602i
$879$	52.6133	+	138.062i	0.0598558	+	0.157067i
$880$	70.0638			0.0796179
$881$		−	738.403i		−	0.838142i	−0.907953	−	0.419071i	$-0.862356\pi$
$881$		−	738.403i		−	0.838142i	0.907953	−	0.419071i	$-0.137644\pi$
$882$	−1406.55	+	206.261i	−1.59473	+	0.233856i
$883$	872.215			0.987786			0.493893	−	0.869523i	$-0.335573\pi$
$883$	872.215			0.987786			0.493893	+	0.869523i	$0.335573\pi$
$884$		−	431.156i		−	0.487733i
$885$	−250.603	+	1557.78i	−0.283167	+	1.76021i
$886$	−671.566			−0.757975
$887$	548.437	−	316.640i	0.618306	−	0.356979i	−0.157903	−	0.987455i	$-0.550473\pi$
$887$	548.437	−	316.640i	0.618306	−	0.356979i	0.776209	+	0.630476i	$0.217140\pi$
$888$	256.855	+	674.013i	0.289252	+	0.759023i
$889$	−98.4767	−	2.90511i	−0.110772	−	0.00326784i
$890$			966.821i			1.08632i
$891$	−1423.42	−	163.582i	−1.59755	−	0.183594i
$892$	596.753	+	1033.61i	0.669005	+	1.15875i
$893$	−111.651	−	64.4615i	−0.125029	−	0.0721853i
$894$	177.742	−	1104.87i	0.198816	−	1.23587i
$895$	−222.323	+	385.075i	−0.248406	+	0.430251i
$896$	41.8185	−	1417.55i	0.0466724	−	1.58209i
$897$	−77.6955	+	95.4716i	−0.0866171	+	0.106434i
$898$	−835.048			−0.929897
$899$	−1182.09	+	682.483i	−1.31490	+	0.759158i
$900$	−306.608	−	101.270i	−0.340676	−	0.112522i
$901$	311.443	−	539.436i	0.345664	−	0.598708i
$902$	−1586.22	+	915.805i	−1.75856	+	1.01531i
$903$	−26.4530	+	138.295i	−0.0292946	+	0.153151i
$904$	300.084	−	519.761i	0.331951	−	0.574957i
$905$	−589.108	+	340.122i	−0.650948	+	0.375825i
$906$	−517.652	−	1358.37i	−0.571359	−	1.49930i
$907$	−560.854	+	971.427i	−0.618361	+	1.07103i	0.371424	+	0.928464i	$0.378870\pi$
$907$	−560.854	+	971.427i	−0.618361	+	1.07103i	−0.989785	+	0.142570i	$0.954464\pi$
$908$	−1121.12	−	647.278i	−1.23471	−	0.712861i
$909$	48.8813	−	147.995i	0.0537748	−	0.162811i
$910$	508.607	+	15.0041i	0.558909	+	0.0164881i
$911$	−770.852	+	445.052i	−0.846160	+	0.488531i	−0.859353	−	0.511382i	$-0.829134\pi$
$911$	−770.852	+	445.052i	−0.846160	+	0.488531i	0.0131931	+	0.999913i	$0.495800\pi$
$912$	−15.7376	+	5.99736i	−0.0172562	+	0.00657606i
$913$	279.677			0.306327
$914$			513.956i			0.562315i
$915$	−1208.92	−	194.480i	−1.32122	−	0.212547i
$916$	−253.332	−	438.784i	−0.276563	−	0.479021i
$917$	−137.244	+	73.9297i	−0.149666	+	0.0806213i
$918$	−1439.19	+	64.9291i	−1.56775	+	0.0707289i
$919$	567.953	−	983.724i	0.618012	−	1.07043i	−0.371836	−	0.928299i	$-0.621271\pi$
$919$	567.953	−	983.724i	0.618012	−	1.07043i	0.989848	−	0.142130i	$-0.0453952\pi$
$920$	371.873	+	214.701i	0.404210	+	0.233371i
$921$	901.182	+	733.388i	0.978482	+	0.796296i
$922$	−329.251	−	570.280i	−0.357105	−	0.618525i
$923$	70.6391	+	40.7835i	0.0765321	+	0.0441858i
$924$	−779.657	−	2242.49i	−0.843784	−	2.42693i
$925$	−87.5408	−	151.625i	−0.0946387	−	0.163919i
$926$	−2127.85	−	1228.52i	−2.29790	−	1.32669i
$927$	−185.399	+	165.313i	−0.199999	+	0.178331i
$928$	763.559	+	1322.52i	0.822800	+	1.42513i
$929$		−	719.197i		−	0.774162i	−0.922046	−	0.387081i	$-0.873483\pi$
$929$		−	719.197i		−	0.774162i	0.922046	−	0.387081i	$-0.126517\pi$
$930$	−251.756	+	1564.95i	−0.270706	+	1.68275i
$931$	−211.410	+	320.869i	−0.227078	+	0.344650i
$932$	−1805.12	−	1042.18i	−1.93682	−	1.11822i
$933$	−191.438	+	235.238i	−0.205186	+	0.252130i
$934$	859.925	−	1489.43i	0.920691	−	1.59468i
$935$	1402.95	−	809.994i	1.50048	−	0.866303i
$936$	88.6786	−	268.487i	0.0947421	−	0.286845i
$937$	−1522.34			−1.62470			−0.812348	−	0.583172i	$-0.801811\pi$
$937$	−1522.34			−1.62470			−0.812348	+	0.583172i	$0.801811\pi$
$938$	−8.11166	+	274.968i	−0.00864783	+	0.293142i
$939$	−848.815	−	690.772i	−0.903957	−	0.735646i
$940$	290.689	+	503.488i	0.309243	+	0.535625i
$941$		−	1023.51i		−	1.08768i	−0.839188	−	0.543841i	$-0.816970\pi$
$941$		−	1023.51i		−	1.08768i	0.839188	−	0.543841i	$-0.183030\pi$
$942$	−1672.88	+	2055.62i	−1.77588	+	2.18219i
$943$	323.389			0.342937
$944$		−	68.0487i		−	0.0720855i
$945$	−16.3049	−	1045.60i	−0.0172539	−	1.10645i
$946$	−382.316			−0.404139
$947$		−	1572.43i		−	1.66043i	−0.557441	−	0.830217i	$-0.688217\pi$
$947$		−	1572.43i		−	1.66043i	0.557441	−	0.830217i	$-0.311783\pi$
$948$	2065.39	+	1680.83i	2.17868	+	1.77303i
$949$	−93.6812			−0.0987157
$950$	−122.891	+	70.9512i	−0.129359	+	0.0746855i
$951$	−62.7750	+	77.1374i	−0.0660095	+	0.0811119i
$952$	−423.588	−	786.352i	−0.444945	−	0.826000i
$953$		−	1342.92i		−	1.40915i	−0.709629	−	0.704576i	$-0.751137\pi$
$953$		−	1342.92i		−	1.40915i	0.709629	−	0.704576i	$-0.248863\pi$
$954$	814.872	−	726.588i	0.854163	−	0.761623i
$955$	983.453	+	1703.39i	1.02979	+	1.78366i
$956$	1348.06	+	778.301i	1.41010	+	0.814122i
$957$	1896.49	+	1543.38i	1.98170	+	1.61272i
$958$	−974.348	+	1687.62i	−1.01706	+	1.76161i
$959$	−220.897	−	136.374i	−0.230341	−	0.142205i
$960$	1703.94	+	274.115i	1.77493	+	0.285536i
$961$	−83.4501			−0.0868367
$962$	354.860	−	204.879i	0.368877	−	0.212971i
$963$	345.776	−	1046.89i	0.359062	−	1.08711i
$964$	90.5672	−	156.867i	0.0939493	−	0.162725i
$965$	190.034	−	109.716i	0.196927	−	0.113696i
$966$	−128.040	+	669.387i	−0.132547	+	0.692947i
$967$	−867.804	+	1503.08i	−0.897418	+	1.55437i	−0.0666355	+	0.997777i	$0.521226\pi$
$967$	−867.804	+	1503.08i	−0.897418	+	1.55437i	−0.830783	+	0.556597i	$0.812107\pi$
$968$	1281.05	−	739.614i	1.32340	−	0.764064i
$969$	−245.795	+	302.030i	−0.253658	+	0.311693i
$970$	1536.00	−	2660.43i	1.58350	−	2.74271i
$971$	−43.8474	−	25.3153i	−0.0451569	−	0.0260714i	0.477252	−	0.878767i	$-0.341633\pi$
$971$	−43.8474	−	25.3153i	−0.0451569	−	0.0260714i	−0.522409	+	0.852695i	$0.674966\pi$
$972$	−1495.20	−	420.133i	−1.53827	−	0.432236i
$973$	−518.753	+	840.269i	−0.533148	+	0.863586i
$974$	436.071	−	251.766i	0.447712	−	0.258486i
$975$	−10.9009	+	67.7619i	−0.0111805	+	0.0694994i
$976$	52.8091			0.0541077
$977$			585.107i			0.598881i	0.954115	+	0.299440i	$0.0968000\pi$
$977$			585.107i			0.598881i	−0.954115	+	0.299440i	$0.903200\pi$
$978$	766.760	+	2012.05i	0.784008	+	2.05731i
$979$	−479.423	−	830.386i	−0.489707	−	0.848198i
$980$	1549.11	−	776.427i	1.58072	−	0.792272i
$981$	229.367	−	204.517i	0.233810	−	0.208479i
$982$	645.630	−	1118.26i	0.657464	−	1.13876i
$983$	839.089	+	484.448i	0.853600	+	0.492826i	0.861864	−	0.507140i	$-0.169297\pi$
$983$	839.089	+	484.448i	0.853600	+	0.492826i	−0.00826378	+	0.999966i	$0.502630\pi$
$984$	−694.160	+	264.533i	−0.705447	+	0.268835i
$985$	361.397	+	625.957i	0.366900	+	0.635489i
$986$	2129.18	+	1229.28i	2.15941	+	1.24674i
$987$	−225.721	+	261.236i	−0.228694	+	0.264676i
$988$	−102.133	−	176.900i	−0.103374	−	0.179048i
$989$	58.4582	+	33.7508i	0.0591084	+	0.0341262i
$990$	2780.21	−	576.872i	2.80829	−	0.582699i
$991$	−104.448	−	180.910i	−0.105397	−	0.182553i	0.808503	−	0.588492i	$-0.200278\pi$
$991$	−104.448	−	180.910i	−0.105397	−	0.182553i	−0.913900	+	0.405939i	$0.866945\pi$
$992$		−	981.799i		−	0.989717i
$993$	210.598	+	171.386i	0.212083	+	0.172594i
$994$	451.418	+	13.3170i	0.454143	+	0.0133974i
$995$	−1039.99	−	600.439i	−1.04522	−	0.603457i
$996$	299.314	+	48.1511i	0.300516	+	0.0483444i
$997$	−76.0851	+	131.783i	−0.0763140	+	0.132180i	−0.901657	−	0.432452i	$-0.857648\pi$
$997$	−76.0851	+	131.783i	−0.0763140	+	0.132180i	0.825343	+	0.564632i	$0.190982\pi$
$998$	−341.392	+	197.103i	−0.342077	+	0.197498i
$999$	−453.500	−	709.578i	−0.453954	−	0.710288i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.j.b.23.10	yes	22
3.2	odd	2		189.3.j.b.44.2		22
7.2	even	3		441.3.r.g.50.10		22
7.3	odd	6		441.3.n.f.410.2		22
7.4	even	3		63.3.n.b.32.2	yes	22
7.5	odd	6		441.3.r.f.50.10		22
7.6	odd	2		441.3.j.f.275.10		22
9.2	odd	6		63.3.n.b.2.2	yes	22
9.7	even	3		189.3.n.b.170.10		22
21.11	odd	6		189.3.n.b.179.10		22
63.2	odd	6		441.3.r.g.344.10		22
63.11	odd	6	inner	63.3.j.b.11.2	✓	22
63.20	even	6		441.3.n.f.128.2		22
63.25	even	3		189.3.j.b.116.10		22
63.38	even	6		441.3.j.f.263.2		22
63.47	even	6		441.3.r.f.344.10		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.2	✓	22	63.11	odd	6	inner
63.3.j.b.23.10	yes	22	1.1	even	1	trivial
63.3.n.b.2.2	yes	22	9.2	odd	6
63.3.n.b.32.2	yes	22	7.4	even	3
189.3.j.b.44.2		22	3.2	odd	2
189.3.j.b.116.10		22	63.25	even	3
189.3.n.b.170.10		22	9.7	even	3
189.3.n.b.179.10		22	21.11	odd	6
441.3.j.f.263.2		22	63.38	even	6
441.3.j.f.275.10		22	7.6	odd	2
441.3.n.f.128.2		22	63.20	even	6
441.3.n.f.410.2		22	7.3	odd	6
441.3.r.f.50.10		22	7.5	odd	6
441.3.r.f.344.10		22	63.47	even	6
441.3.r.g.50.10		22	7.2	even	3
441.3.r.g.344.10		22	63.2	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+3.22356i q^{2} +(-2.32685 - 1.89361i) q^{3} -6.39137 q^{4} +(-4.79167 + 2.76647i) q^{5} +(6.10417 - 7.50076i) q^{6} +(-6.99696 - 0.206413i) q^{7} -7.70873i q^{8} +(1.82848 + 8.81230i) q^{9} +O(q^{10})\)	\(q+3.22356i q^{2} +(-2.32685 - 1.89361i) q^{3} -6.39137 q^{4} +(-4.79167 + 2.76647i) q^{5} +(6.10417 - 7.50076i) q^{6} +(-6.99696 - 0.206413i) q^{7} -7.70873i q^{8} +(1.82848 + 8.81230i) q^{9} +(-8.91790 - 15.4463i) q^{10} +(15.3189 + 8.84435i) q^{11} +(14.8718 + 12.1028i) q^{12} +(2.03775 - 3.52949i) q^{13} +(0.665386 - 22.5551i) q^{14} +(16.3881 + 2.63638i) q^{15} -0.715882 q^{16} +(-14.3348 + 8.27617i) q^{17} +(-28.4070 + 5.89424i) q^{18} +(-3.92096 + 6.79130i) q^{19} +(30.6253 - 17.6815i) q^{20} +(15.8900 + 13.7298i) q^{21} +(-28.5103 + 49.3813i) q^{22} +(8.71877 - 5.03378i) q^{23} +(-14.5973 + 17.9371i) q^{24} +(2.80674 - 4.86141i) q^{25} +(11.3775 + 6.56882i) q^{26} +(12.4324 - 23.9674i) q^{27} +(44.7201 + 1.31926i) q^{28} +(-39.9040 + 23.0386i) q^{29} +(-8.49854 + 52.8282i) q^{30} +29.6235 q^{31} -33.1426i q^{32} +(-18.8970 - 49.5874i) q^{33} +(-26.6788 - 46.2090i) q^{34} +(34.0981 - 18.3678i) q^{35} +(-11.6865 - 56.3227i) q^{36} +(15.5948 - 27.0110i) q^{37} +(-21.8922 - 12.6395i) q^{38} +(-11.4250 + 4.35389i) q^{39} +(21.3260 + 36.9377i) q^{40} +(27.8184 + 16.0609i) q^{41} +(-44.2589 + 51.2225i) q^{42} +(3.35243 + 5.80658i) q^{43} +(-97.9085 - 56.5275i) q^{44} +(-33.1405 - 37.1672i) q^{45} +(16.2267 + 28.1055i) q^{46} +16.4402i q^{47} +(1.66575 + 1.35560i) q^{48} +(48.9148 + 2.88853i) q^{49} +(15.6711 + 9.04769i) q^{50} +(49.0267 + 7.88699i) q^{51} +(-13.0240 + 22.5583i) q^{52} +(-32.5897 + 18.8157i) q^{53} +(77.2603 + 40.0768i) q^{54} -97.8706 q^{55} +(-1.59118 + 53.9377i) q^{56} +(21.9836 - 8.37759i) q^{57} +(-74.2663 - 128.633i) q^{58} +95.0557i q^{59} +(-104.743 - 16.8501i) q^{60} -73.7679 q^{61} +95.4932i q^{62} +(-10.9749 - 62.0367i) q^{63} +103.974 q^{64} +22.5495i q^{65} +(159.848 - 60.9156i) q^{66} -12.1909 q^{67} +(91.6187 - 52.8961i) q^{68} +(-29.8193 - 4.79707i) q^{69} +(59.2099 + 109.918i) q^{70} +20.0140i q^{71} +(67.9317 - 14.0953i) q^{72} +(-11.4932 - 19.9068i) q^{73} +(87.0715 + 50.2708i) q^{74} +(-15.7365 + 5.99692i) q^{75} +(25.0603 - 43.4057i) q^{76} +(-105.360 - 65.0455i) q^{77} +(-14.0351 - 36.8293i) q^{78} +138.880 q^{79} +(3.43027 - 1.98047i) q^{80} +(-74.3133 + 32.2263i) q^{81} +(-51.7735 + 89.6743i) q^{82} +(13.6928 - 7.90552i) q^{83} +(-101.559 - 87.7522i) q^{84} +(45.7916 - 79.3134i) q^{85} +(-18.7179 + 10.8068i) q^{86} +(136.477 + 21.9552i) q^{87} +(68.1787 - 118.089i) q^{88} +(-46.9444 - 27.1034i) q^{89} +(119.811 - 106.830i) q^{90} +(-14.9866 + 24.2750i) q^{91} +(-55.7249 + 32.1728i) q^{92} +(-68.9294 - 56.0953i) q^{93} -52.9962 q^{94} -43.3889i q^{95} +(-62.7592 + 77.1180i) q^{96} +(86.1189 + 149.162i) q^{97} +(-9.31136 + 157.680i) q^{98} +(-49.9287 + 151.166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 19 q^{3} - 24 q^{4} + 12 q^{5} - 8 q^{6} - 37 q^{9}+O(q^{10}) \) 22 * q - 19 * q^3 - 24 * q^4 + 12 * q^5 - 8 * q^6 - 37 * q^9	\( 22 q - 19 q^{3} - 24 q^{4} + 12 q^{5} - 8 q^{6} - 37 q^{9} + 25 q^{10} + 24 q^{11} + 40 q^{12} - 18 q^{13} - 60 q^{14} + 53 q^{15} - 24 q^{16} - 6 q^{17} + 40 q^{18} + 3 q^{19} - 39 q^{20} - 11 q^{21} - 59 q^{22} + 81 q^{23} + 126 q^{24} + 57 q^{25} + 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 38 q^{30} + 58 q^{31} - 4 q^{33} - 99 q^{34} + 27 q^{35} + 76 q^{36} - 20 q^{37} - 48 q^{38} - 76 q^{39} - 105 q^{40} - 51 q^{41} + 68 q^{42} + 65 q^{43} - 54 q^{44} - 214 q^{45} + 75 q^{46} - 113 q^{48} + 4 q^{49} + 63 q^{50} + 141 q^{51} - 46 q^{52} + 63 q^{53} + 433 q^{54} - 100 q^{55} + 192 q^{56} + 224 q^{57} + 40 q^{58} - 482 q^{60} - 156 q^{61} + 19 q^{63} + 106 q^{64} + 61 q^{66} + 264 q^{67} + 27 q^{68} - 297 q^{69} + 236 q^{70} - 222 q^{72} + q^{73} + 342 q^{74} - 296 q^{75} + 233 q^{76} - 531 q^{77} - 440 q^{78} - 280 q^{79} - 96 q^{80} - 169 q^{81} - 157 q^{82} + 255 q^{83} - 13 q^{84} + 102 q^{85} + 504 q^{86} + 704 q^{87} + 408 q^{88} + 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} - 36 q^{93} - 522 q^{94} - 397 q^{96} + 178 q^{97} - 483 q^{98} - 103 q^{99}+O(q^{100}) \) 22 * q - 19 * q^3 - 24 * q^4 + 12 * q^5 - 8 * q^6 - 37 * q^9 + 25 * q^10 + 24 * q^11 + 40 * q^12 - 18 * q^13 - 60 * q^14 + 53 * q^15 - 24 * q^16 - 6 * q^17 + 40 * q^18 + 3 * q^19 - 39 * q^20 - 11 * q^21 - 59 * q^22 + 81 * q^23 + 126 * q^24 + 57 * q^25 + 3 * q^26 - 97 * q^27 + 34 * q^28 - 63 * q^29 - 38 * q^30 + 58 * q^31 - 4 * q^33 - 99 * q^34 + 27 * q^35 + 76 * q^36 - 20 * q^37 - 48 * q^38 - 76 * q^39 - 105 * q^40 - 51 * q^41 + 68 * q^42 + 65 * q^43 - 54 * q^44 - 214 * q^45 + 75 * q^46 - 113 * q^48 + 4 * q^49 + 63 * q^50 + 141 * q^51 - 46 * q^52 + 63 * q^53 + 433 * q^54 - 100 * q^55 + 192 * q^56 + 224 * q^57 + 40 * q^58 - 482 * q^60 - 156 * q^61 + 19 * q^63 + 106 * q^64 + 61 * q^66 + 264 * q^67 + 27 * q^68 - 297 * q^69 + 236 * q^70 - 222 * q^72 + q^73 + 342 * q^74 - 296 * q^75 + 233 * q^76 - 531 * q^77 - 440 * q^78 - 280 * q^79 - 96 * q^80 - 169 * q^81 - 157 * q^82 + 255 * q^83 - 13 * q^84 + 102 * q^85 + 504 * q^86 + 704 * q^87 + 408 * q^88 + 720 * q^89 + 418 * q^90 - 70 * q^91 - 1239 * q^92 - 36 * q^93 - 522 * q^94 - 397 * q^96 + 178 * q^97 - 483 * q^98 - 103 * q^99

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