LMFDB - Embedded newform 63.3.n.b.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(2,63)]

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, 2]))

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

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

chi := DirichletCharacter("63.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.n (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			2.2
Character	$\chi$	$=$	63.2
Dual form			63.3.n.b.32.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.79169 + 1.61178i) q^{2} +(-0.476488 - 2.96192i) q^{3} +(3.19568 - 5.53509i) q^{4} +5.53294i q^{5} +(6.10417 + 7.50076i) q^{6} +(3.31972 + 6.16275i) q^{7} +7.70873i q^{8} +(-8.54592 + 2.82264i) q^{9} +O(q^{10})$	\(q+(-2.79169 + 1.61178i) q^{2} +(-0.476488 - 2.96192i) q^{3} +(3.19568 - 5.53509i) q^{4} +5.53294i q^{5} +(6.10417 + 7.50076i) q^{6} +(3.31972 + 6.16275i) q^{7} +7.70873i q^{8} +(-8.54592 + 2.82264i) q^{9} +(-8.91790 - 15.4463i) q^{10} +17.6887i q^{11} +(-17.9172 - 6.82795i) q^{12} +(2.03775 + 3.52949i) q^{13} +(-19.2006 - 11.8538i) q^{14} +(16.3881 - 2.63638i) q^{15} +(0.357941 + 0.619972i) q^{16} +(14.3348 - 8.27617i) q^{17} +(19.3081 - 21.6541i) q^{18} +(-3.92096 + 6.79130i) q^{19} +(30.6253 + 17.6815i) q^{20} +(16.6718 - 12.7692i) q^{21} +(-28.5103 - 49.3813i) q^{22} -10.0676i q^{23} +(22.8326 - 3.67312i) q^{24} -5.61347 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} +(-41.5013 + 33.7740i) q^{30} +(-14.8117 + 25.6547i) q^{31} +(-28.7023 - 16.5713i) q^{32} +(52.3925 - 8.42845i) 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} -25.2789i q^{38} +(9.48309 - 7.71741i) q^{39} -42.6520 q^{40} +(27.8184 - 16.0609i) q^{41} +(-25.9612 + 62.5189i) q^{42} +(3.35243 - 5.80658i) q^{43} +(97.9085 + 56.5275i) q^{44} +(-15.6175 - 47.2841i) q^{45} +(16.2267 + 28.1055i) q^{46} +(-14.2377 + 8.22012i) q^{47} +(1.66575 - 1.35560i) q^{48} +(-26.9589 + 40.9172i) q^{49} +(15.6711 - 9.04769i) q^{50} +(-31.3437 - 38.5149i) q^{51} +26.0480 q^{52} +(32.5897 - 18.8157i) q^{53} +(-73.3377 - 46.8710i) q^{54} -97.8706 q^{55} +(-47.5070 + 25.5908i) q^{56} +(21.9836 + 8.37759i) q^{57} +148.533 q^{58} +(82.3206 + 47.5278i) q^{59} +(37.7787 - 99.1348i) q^{60} +(36.8839 + 63.8848i) q^{61} -95.4932i q^{62} +(-45.7652 - 43.2960i) q^{63} +103.974 q^{64} +(-19.5285 + 11.2748i) q^{65} +(-132.679 + 107.975i) q^{66} +(6.09545 - 10.5576i) q^{67} -105.792i q^{68} +(-29.8193 + 4.79707i) q^{69} +(65.5865 - 106.236i) q^{70} -20.0140i q^{71} +(-21.7589 - 65.8782i) q^{72} +(-11.4932 - 19.9068i) q^{73} +100.542i q^{74} +(2.67475 + 16.6266i) q^{75} +(25.0603 + 43.4057i) q^{76} +(-109.011 + 58.7215i) q^{77} +(-14.0351 + 36.8293i) q^{78} +(-69.4400 - 120.274i) q^{79} +(-3.43027 + 1.98047i) q^{80} +(65.0655 - 48.2440i) q^{81} +(-51.7735 + 89.6743i) q^{82} +(13.6928 + 7.90552i) q^{83} +(-17.4010 - 133.086i) q^{84} +(45.7916 + 79.3134i) q^{85} +21.6136i q^{86} +(-49.2246 + 129.170i) q^{87} -136.357 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} +(83.0447 + 31.6470i) q^{93} +(26.4981 - 45.8960i) q^{94} +(-37.5759 - 21.6944i) q^{95} +(-35.4065 + 92.9100i) 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 - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9}+O(q^{10}) $ 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9} + 25 q^{10} - 20 q^{12} - 18 q^{13} - 90 q^{14} + 53 q^{15} + 12 q^{16} + 6 q^{17} - 56 q^{18} + 3 q^{19} - 39 q^{20} - 2 q^{21} - 59 q^{22} + 15 q^{24} - 114 q^{25} - 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 20 q^{30} - 29 q^{31} + 246 q^{32} + 77 q^{33} - 99 q^{34} - 27 q^{35} + 76 q^{36} - 20 q^{37} + 200 q^{39} + 210 q^{40} - 51 q^{41} + 80 q^{42} + 65 q^{43} + 54 q^{44} + 71 q^{45} + 75 q^{46} + 261 q^{47} - 113 q^{48} - 131 q^{49} + 63 q^{50} - 78 q^{51} + 92 q^{52} - 63 q^{53} - 485 q^{54} - 100 q^{55} + 153 q^{56} + 224 q^{57} - 80 q^{58} - 102 q^{59} + 103 q^{60} + 78 q^{61} + 421 q^{63} + 106 q^{64} - 225 q^{65} - 401 q^{66} - 132 q^{67} - 297 q^{69} + 179 q^{70} - 66 q^{72} + q^{73} - 245 q^{75} + 233 q^{76} - 447 q^{77} - 440 q^{78} + 140 q^{79} + 96 q^{80} + 104 q^{81} - 157 q^{82} + 255 q^{83} - 316 q^{84} + 102 q^{85} - 136 q^{87} - 816 q^{88} - 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} + 210 q^{93} + 261 q^{94} + 642 q^{95} + 539 q^{96} + 178 q^{97} + 483 q^{98} - 103 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9 + 25 * q^10 - 20 * q^12 - 18 * q^13 - 90 * q^14 + 53 * q^15 + 12 * q^16 + 6 * q^17 - 56 * q^18 + 3 * q^19 - 39 * q^20 - 2 * q^21 - 59 * q^22 + 15 * q^24 - 114 * q^25 - 3 * q^26 - 97 * q^27 + 34 * q^28 - 63 * q^29 - 20 * q^30 - 29 * q^31 + 246 * q^32 + 77 * q^33 - 99 * q^34 - 27 * q^35 + 76 * q^36 - 20 * q^37 + 200 * q^39 + 210 * q^40 - 51 * q^41 + 80 * q^42 + 65 * q^43 + 54 * q^44 + 71 * q^45 + 75 * q^46 + 261 * q^47 - 113 * q^48 - 131 * q^49 + 63 * q^50 - 78 * q^51 + 92 * q^52 - 63 * q^53 - 485 * q^54 - 100 * q^55 + 153 * q^56 + 224 * q^57 - 80 * q^58 - 102 * q^59 + 103 * q^60 + 78 * q^61 + 421 * q^63 + 106 * q^64 - 225 * q^65 - 401 * q^66 - 132 * q^67 - 297 * q^69 + 179 * q^70 - 66 * q^72 + q^73 - 245 * q^75 + 233 * q^76 - 447 * q^77 - 440 * q^78 + 140 * q^79 + 96 * q^80 + 104 * q^81 - 157 * q^82 + 255 * q^83 - 316 * q^84 + 102 * q^85 - 136 * q^87 - 816 * q^88 - 720 * q^89 + 418 * q^90 - 70 * q^91 - 1239 * q^92 + 210 * q^93 + 261 * q^94 + 642 * q^95 + 539 * 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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.79169	+	1.61178i	−1.39584	+	0.805891i	−0.993954	−	0.109797i	$-0.964980\pi$
$2$	−2.79169	+	1.61178i	−1.39584	+	0.805891i	−0.401890	+	0.915688i	$0.631647\pi$
$3$	−0.476488	−	2.96192i	−0.158829	−	0.987306i
$3$	−0.476488	−	2.96192i	−0.158829	−	0.987306i
$4$	3.19568	−	5.53509i	0.798921	−	1.38377i
$5$			5.53294i			1.10659i	0.832986	+	0.553294i	$0.186630\pi$
$5$			5.53294i			1.10659i	−0.832986	+	0.553294i	$0.813370\pi$
$6$	6.10417	+	7.50076i	1.01736	+	1.25013i
$7$	3.31972	+	6.16275i	0.474246	+	0.880393i
$7$	3.31972	+	6.16275i	0.474246	+	0.880393i
$8$			7.70873i			0.963591i
$9$	−8.54592	+	2.82264i	−0.949547	+	0.313626i
$10$	−8.91790	−	15.4463i	−0.891790	−	1.54463i
$11$			17.6887i			1.60806i	0.594587	+	0.804032i	$0.297316\pi$
$11$			17.6887i			1.60806i	−0.594587	+	0.804032i	$0.702684\pi$
$12$	−17.9172	−	6.82795i	−1.49310	−	0.568996i
$13$	2.03775	+	3.52949i	0.156750	+	0.271499i	0.933695	−	0.358070i	$-0.116565\pi$
$13$	2.03775	+	3.52949i	0.156750	+	0.271499i	−0.776945	+	0.629569i	$0.783232\pi$
$14$	−19.2006	−	11.8538i	−1.37147	−	0.846701i
$15$	16.3881	−	2.63638i	1.09254	−	0.175759i
$16$	0.357941	+	0.619972i	0.0223713	+	0.0387483i
$17$	14.3348	−	8.27617i	0.843221	−	0.486834i	−0.0151370	−	0.999885i	$-0.504818\pi$
$17$	14.3348	−	8.27617i	0.843221	−	0.486834i	0.858358	+	0.513052i	$0.171485\pi$
$18$	19.3081	−	21.6541i	1.07267	−	1.20300i
$19$	−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
$21$	16.6718	−	12.7692i	0.793893	−	0.608058i
$22$	−28.5103	−	49.3813i	−1.29592	−	2.24461i
$23$		−	10.0676i		−	0.437720i	−0.975756	−	0.218860i	$-0.929766\pi$
$23$		−	10.0676i		−	0.437720i	0.975756	−	0.218860i	$-0.0702339\pi$
$24$	22.8326	−	3.67312i	0.951360	−	0.153047i
$25$	−5.61347			−0.224539
$26$	−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	−0.384324	−	0.923198i	$-0.625566\pi$
$29$	−39.9040	−	23.0386i	−1.37600	−	0.794434i	−0.991675	+	0.128764i	$0.958899\pi$
$30$	−41.5013	+	33.7740i	−1.38338	+	1.12580i
$31$	−14.8117	+	25.6547i	−0.477798	+	0.827570i	−0.999676	−	0.0254498i	$-0.991898\pi$
$31$	−14.8117	+	25.6547i	−0.477798	+	0.827570i	0.521878	+	0.853020i	$0.325232\pi$
$32$	−28.7023	−	16.5713i	−0.896948	−	0.517853i
$33$	52.3925	−	8.42845i	1.58765	−	0.255408i
$34$	−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	$0.0281772\pi$
$38$		−	25.2789i		−	0.665235i
$39$	9.48309	−	7.71741i	0.243156	−	0.197882i
$40$	−42.6520			−1.06630
$41$	27.8184	−	16.0609i	0.678497	−	0.391730i	−0.120792	−	0.992678i	$-0.538543\pi$
$41$	27.8184	−	16.0609i	0.678497	−	0.391730i	0.799288	+	0.600948i	$0.205210\pi$
$42$	−25.9612	+	62.5189i	−0.618123	+	1.48855i
$43$	3.35243	−	5.80658i	0.0779635	−	0.135037i	−0.824408	−	0.565997i	$-0.808492\pi$
$43$	3.35243	−	5.80658i	0.0779635	−	0.135037i	0.902371	+	0.430960i	$0.141825\pi$
$44$	97.9085	+	56.5275i	2.22519	+	1.28472i
$45$	−15.6175	−	47.2841i	−0.347055	−	1.05076i
$46$	16.2267	+	28.1055i	0.352755	+	0.610990i
$47$	−14.2377	+	8.22012i	−0.302929	+	0.174896i	−0.643758	−	0.765229i	$-0.722626\pi$
$47$	−14.2377	+	8.22012i	−0.302929	+	0.174896i	0.340829	+	0.940125i	$0.389292\pi$
$48$	1.66575	−	1.35560i	0.0347032	−	0.0282417i
$49$	−26.9589	+	40.9172i	−0.550182	+	0.835045i
$50$	15.6711	−	9.04769i	0.313421	−	0.180954i
$51$	−31.3437	−	38.5149i	−0.614582	−	0.755193i
$52$	26.0480			0.500924
$53$	32.5897	−	18.8157i	0.614900	−	0.355013i	−0.159981	−	0.987120i	$-0.551143\pi$
$53$	32.5897	−	18.8157i	0.614900	−	0.355013i	0.774881	+	0.632108i	$0.217810\pi$
$54$	−73.3377	−	46.8710i	−1.35811	−	0.867982i
$55$	−97.8706			−1.77946
$56$	−47.5070	+	25.5908i	−0.848339	+	0.456979i
$57$	21.9836	+	8.37759i	0.385676	+	0.146975i
$58$	148.533			2.56091
$59$	82.3206	+	47.5278i	1.39527	+	0.805557i	0.993892	−	0.110358i	$-0.0351997\pi$
$59$	82.3206	+	47.5278i	1.39527	+	0.805557i	0.401373	+	0.915915i	$0.368533\pi$
$60$	37.7787	−	99.1348i	0.629645	−	1.65225i
$61$	36.8839	+	63.8848i	0.604655	+	1.04729i	0.992106	+	0.125402i	$0.0400222\pi$
$61$	36.8839	+	63.8848i	0.604655	+	1.04729i	−0.387451	+	0.921890i	$0.626644\pi$
$62$		−	95.4932i		−	1.54021i
$63$	−45.7652	−	43.2960i	−0.726432	−	0.687238i
$64$	103.974			1.62459
$65$	−19.5285	+	11.2748i	−0.300438	+	0.173458i
$66$	−132.679	+	107.975i	−2.01028	+	1.63598i
$67$	6.09545	−	10.5576i	0.0909769	−	0.157577i	−0.816946	−	0.576715i	$-0.804334\pi$
$67$	6.09545	−	10.5576i	0.0909769	−	0.157577i	0.907922	+	0.419138i	$0.137668\pi$
$68$		−	105.792i		−	1.55577i
$69$	−29.8193	+	4.79707i	−0.432164	+	0.0695228i
$70$	65.5865	−	106.236i	0.936950	−	1.51766i
$71$		−	20.0140i		−	0.281887i	−0.990018	−	0.140944i	$-0.954986\pi$
$71$		−	20.0140i		−	0.281887i	0.990018	−	0.140944i	$-0.0450136\pi$
$72$	−21.7589	−	65.8782i	−0.302208	−	0.914975i
$73$	−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	$0.883658\pi$
$74$			100.542i			1.35867i
$75$	2.67475	+	16.6266i	0.0356633	+	0.221689i
$76$	25.0603	+	43.4057i	0.329741	+	0.571128i
$77$	−109.011	+	58.7215i	−1.41573	+	0.762617i
$78$	−14.0351	+	36.8293i	−0.179937	+	0.472170i
$79$	−69.4400	−	120.274i	−0.878988	−	1.52245i	−0.852453	−	0.522804i	$-0.824886\pi$
$79$	−69.4400	−	120.274i	−0.878988	−	1.52245i	−0.0265350	−	0.999648i	$-0.508447\pi$
$80$	−3.43027	+	1.98047i	−0.0428784	+	0.0247559i
$81$	65.0655	−	48.2440i	0.803277	−	0.595605i
$82$	−51.7735	+	89.6743i	−0.631384	+	1.09359i
$83$	13.6928	+	7.90552i	0.164973	+	0.0952472i	0.580213	−	0.814465i	$-0.302969\pi$
$83$	13.6928	+	7.90552i	0.164973	+	0.0952472i	−0.415240	+	0.909712i	$0.636303\pi$
$84$	−17.4010	−	133.086i	−0.207155	−	1.58436i
$85$	45.7916	+	79.3134i	0.538725	+	0.933099i
$86$			21.6136i			0.251320i
$87$	−49.2246	+	129.170i	−0.565800	+	1.48471i
$88$	−136.357			−1.54952
$89$	46.9444	+	27.1034i	0.527466	+	0.304532i	0.739984	−	0.672625i	$-0.234833\pi$
$89$	46.9444	+	27.1034i	0.527466	+	0.304532i	−0.212518	+	0.977157i	$0.568166\pi$
$90$	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
$93$	83.0447	+	31.6470i	0.892953	+	0.340290i
$94$	26.4981	−	45.8960i	0.281894	−	0.488256i
$95$	−37.5759	−	21.6944i	−0.395536	−	0.228363i
$96$	−35.4065	+	92.9100i	−0.368818	+	0.967813i
$97$	86.1189	−	149.162i	0.887823	−	1.53776i	0.0453802	−	0.998970i	$-0.485550\pi$
$97$	86.1189	−	149.162i	0.887823	−	1.53776i	0.842443	−	0.538785i	$-0.181117\pi$
$98$	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
$101$		−	17.3176i		−	0.171461i	−0.996318	−	0.0857307i	$-0.972678\pi$
$101$		−	17.3176i		−	0.171461i	0.996318	−	0.0857307i	$-0.0273225\pi$
$102$	149.579	+	57.0023i	1.46646	+	0.558846i
$103$	−27.5997			−0.267958			−0.133979	−	0.990984i	$-0.542776\pi$
$103$	−27.5997			−0.267958			−0.133979	+	0.990984i	$0.542776\pi$
$104$	−27.2079	+	15.7085i	−0.261614	+	0.151043i
$105$	70.6513	+	92.2439i	0.672870	+	0.878513i
$106$	−60.6535	+	105.055i	−0.572203	+	0.991085i
$107$	106.089	+	61.2506i	0.991488	+	0.572436i	0.905719	−	0.423879i	$-0.139332\pi$
$107$	106.089	+	61.2506i	0.991488	+	0.572436i	0.0857691	+	0.996315i	$0.472665\pi$
$108$	172.392	+	7.77745i	1.59622	+	0.0720134i
$109$	−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	$0.883396\pi$
$110$	273.224	−	157.746i	2.48386	−	1.43405i
$111$	−87.4350	−	33.3201i	−0.787702	−	0.300181i
$112$	−2.63247	+	4.26403i	−0.0235042	+	0.0380717i
$113$	67.4250	−	38.9278i	0.596681	−	0.344494i	−0.171054	−	0.985262i	$-0.554717\pi$
$113$	67.4250	−	38.9278i	0.596681	−	0.344494i	0.767735	+	0.640768i	$0.221384\pi$
$114$	−74.8741	+	12.0451i	−0.656790	+	0.105659i
$115$	55.7033			0.484377
$116$	−255.041	+	147.248i	−2.19863	+	1.26938i
$117$	−27.3769	−	24.4109i	−0.233991	−	0.208640i
$118$	−306.418			−2.59676
$119$	98.5913	+	60.8669i	0.828498	+	0.511487i
$120$	20.3231	+	126.332i	0.169360	+	1.05276i
$121$	−191.890			−1.58587
$122$	−205.937	−	118.898i	−1.68801	−	0.974572i
$123$	−60.8263	−	74.7429i	−0.494523	−	0.607666i
$124$	94.6673	+	163.968i	0.763446	+	1.32233i
$125$			107.265i			0.858117i
$126$	197.546	+	47.1053i	1.56783	+	0.373852i
$127$	14.0742			0.110821			0.0554103	−	0.998464i	$-0.482353\pi$
$127$	14.0742			0.110821			0.0554103	+	0.998464i	$0.482353\pi$
$128$	−175.453	+	101.298i	−1.37073	+	0.791390i
$129$	−18.7960	−	7.16286i	−0.145706	−	0.0555261i
$130$	36.3449	−	62.9512i	0.279576	−	0.484240i
$131$		−	22.2699i		−	0.169999i	−0.996381	−	0.0849995i	$-0.972911\pi$
$131$		−	22.2699i		−	0.169999i	0.996381	−	0.0849995i	$-0.0270889\pi$
$132$	120.778	−	316.932i	0.914982	−	2.40100i
$133$	−54.8695	−	1.61868i	−0.412553	−	0.0121705i
$134$			39.2982i			0.293270i
$135$	−132.610	+	68.7880i	−0.982297	+	0.509541i
$136$	63.7988	+	110.503i	0.469109	+	0.812520i
$137$			37.0861i			0.270701i	0.990798	+	0.135351i	$0.0432161\pi$
$137$			37.0861i			0.270701i	−0.990798	+	0.135351i	$0.956784\pi$
$138$	75.5144	−	61.4542i	0.547206	−	0.445320i
$139$	70.5358	+	122.172i	0.507451	+	0.878932i	0.999963	+	0.00862568i	$0.00274567\pi$
$139$	70.5358	+	122.172i	0.507451	+	0.878932i	−0.492511	+	0.870306i	$0.663921\pi$
$140$	−7.29941	+	247.434i	−0.0521386	+	1.76739i
$141$	31.1314	+	38.2540i	0.220790	+	0.271305i
$142$	32.2582	+	55.8728i	0.227170	+	0.393471i
$143$	−62.4320	+	36.0451i	−0.436587	+	0.252064i
$144$	−4.80889	−	4.28789i	−0.0333951	−	0.0297770i
$145$	127.471	−	220.787i	0.879111	−	1.52267i
$146$	64.1710	+	37.0491i	0.439527	+	0.253761i
$147$	134.039	+	60.3536i	0.911830	+	0.410569i
$148$	−99.6720	−	172.637i	−0.673459	−	1.16647i
$149$		−	115.718i		−	0.776631i	−0.921526	−	0.388315i	$-0.873057\pi$
$149$		−	115.718i		−	0.776631i	0.921526	−	0.388315i	$-0.126943\pi$
$150$	−34.2656	−	42.1053i	−0.228437	−	0.280702i
$151$	−150.316			−0.995469			−0.497734	−	0.867330i	$-0.665835\pi$
$151$	−150.316			−0.995469			−0.497734	+	0.867330i	$0.665835\pi$
$152$	−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
$156$	−12.4116	−	77.1521i	−0.0795613	−	0.494565i
$157$	137.028	−	237.339i	0.872788	−	1.51171i	0.0136883	−	0.999906i	$-0.495643\pi$
$157$	137.028	−	237.339i	0.872788	−	1.51171i	0.859100	−	0.511808i	$-0.171024\pi$
$158$	387.710	+	223.844i	2.45386	+	1.41674i
$159$	−71.2591	−	87.5626i	−0.448170	−	0.550708i
$160$	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	$0.927350\pi$
$164$		−	205.303i		−	1.25185i
$165$	46.6341	+	289.885i	0.282631	+	1.75688i
$166$	−50.9679			−0.307035
$167$	62.7878	−	36.2506i	0.375975	−	0.217069i	−0.300091	−	0.953911i	$-0.597017\pi$
$167$	62.7878	−	36.2506i	0.375975	−	0.217069i	0.676066	+	0.736841i	$0.263684\pi$
$168$	98.4344	+	128.518i	0.585919	+	0.764988i
$169$	76.1951	−	131.974i	0.450859	−	0.780910i
$170$	−255.672	−	147.612i	−1.50395	−	0.868307i
$171$	14.3388	−	69.1053i	0.0838528	−	0.404125i
$172$	−21.4266	−	37.1120i	−0.124573	−	0.215768i
$173$	−182.881	+	105.587i	−1.05712	+	0.610328i	−0.924634	−	0.380857i	$-0.875629\pi$
$173$	−182.881	+	105.587i	−1.05712	+	0.610328i	−0.132485	+	0.991185i	$0.542296\pi$
$174$	−70.7740	−	439.942i	−0.406747	−	2.52840i
$175$	−18.6351	−	34.5944i	−0.106487	−	0.197682i
$176$	−10.9665	+	6.33151i	−0.0623096	+	0.0359745i
$177$	101.549	−	266.473i	0.573722	−	1.50550i
$178$	−174.739			−0.981680
$179$	−69.5967	+	40.1817i	−0.388809	+	0.224479i	−0.681644	−	0.731684i	$-0.738735\pi$
$179$	−69.5967	+	40.1817i	−0.388809	+	0.224479i	0.292835	+	0.956163i	$0.405401\pi$
$180$	−311.630	−	64.6609i	−1.73128	−	0.359227i
$181$	122.944			0.679250			0.339625	−	0.940561i	$-0.389700\pi$
$181$	122.944			0.679250			0.339625	+	0.940561i	$0.389700\pi$
$182$	2.71178	−	91.9235i	0.0148999	−	0.505074i
$183$	171.647	−	139.688i	0.937961	−	0.763320i
$184$	77.6082			0.421784
$185$	149.450	+	86.2850i	0.807838	+	0.466406i
$186$	−282.843	+	45.5013i	−1.52066	+	0.244631i
$187$	146.395	+	253.563i	0.782859	+	1.35595i
$188$			105.076i			0.558913i
$189$	−106.433	+	156.183i	−0.563135	+	0.826365i
$190$	139.867			0.736141
$191$	307.863	−	177.745i	1.61185	−	0.930602i	0.622909	−	0.782294i	$-0.285951\pi$
$191$	307.863	−	177.745i	1.61185	−	0.930602i	0.988941	−	0.148308i	$-0.0473827\pi$
$192$	−49.5423	−	307.962i	−0.258033	−	1.60397i
$193$	19.8296	−	34.3459i	0.102744	−	0.177958i	−0.810070	−	0.586333i	$-0.800571\pi$
$193$	19.8296	−	34.3459i	0.102744	−	0.177958i	0.912814	+	0.408375i	$0.133904\pi$
$194$			555.219i			2.86196i
$195$	42.7000	+	52.4694i	0.218974	+	0.269074i
$196$	140.328	+	279.978i	0.715959	+	1.42846i
$197$			130.634i			0.663119i	0.943434	+	0.331559i	$0.107575\pi$
$197$			130.634i			0.663119i	−0.943434	+	0.331559i	$0.892425\pi$
$198$	383.032	+	341.535i	1.93451	+	1.72492i
$199$	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	$0.649737\pi$
$200$		−	43.2727i		−	0.216364i
$201$	−34.1753	−	13.0237i	−0.170026	−	0.0647943i
$202$	27.9122	+	48.3454i	0.138179	+	0.239333i
$203$	9.51093	−	322.400i	0.0468519	−	1.58818i
$204$	−313.348	+	50.4087i	−1.53602	+	0.247101i
$205$	88.8643	+	153.917i	0.433484	+	0.750817i
$206$	77.0498	−	44.4847i	0.374028	−	0.215945i
$207$	28.4171	+	86.0366i	0.137281	+	0.415636i
$208$	−1.45879	+	2.52670i	−0.00701341	+	0.0121476i
$209$	−120.129	−	69.3566i	−0.574781	−	0.331850i
$210$	−345.914	−	143.642i	−1.64721	−	0.684008i
$211$	54.6113	+	94.5895i	0.258821	+	0.448292i	0.965926	−	0.258817i	$-0.0833326\pi$
$211$	54.6113	+	94.5895i	0.258821	+	0.448292i	−0.707105	+	0.707108i	$0.749999\pi$
$212$		−	240.516i		−	1.13451i
$213$	−59.2798	+	9.53642i	−0.278309	+	0.0447719i
$214$	−394.891			−1.84528
$215$	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
$219$	−53.4860	+	43.5273i	−0.244228	+	0.198755i
$220$	−312.763	+	541.722i	−1.42165	+	2.46237i
$221$	58.4213	+	33.7295i	0.264350	+	0.152622i
$222$	297.796	−	47.9068i	1.34142	−	0.215797i
$223$	−93.3685	+	161.719i	−0.418693	+	0.725197i	−0.995808	−	0.0914653i	$-0.970845\pi$
$223$	−93.3685	+	161.719i	−0.418693	+	0.725197i	0.577115	+	0.816663i	$0.304178\pi$
$224$	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
$227$			202.548i			0.892280i	0.894963	+	0.446140i	$0.147202\pi$
$227$			202.548i			0.892280i	−0.894963	+	0.446140i	$0.852798\pi$
$228$	116.623	−	94.9088i	0.511505	−	0.416267i
$229$	−79.2731			−0.346171			−0.173085	−	0.984907i	$-0.555374\pi$
$229$	−79.2731			−0.346171			−0.173085	+	0.984907i	$0.555374\pi$
$230$	−155.506	+	89.7816i	−0.676114	+	0.390355i
$231$	225.871	+	294.901i	0.977795	+	1.27663i
$232$	177.598	−	307.609i	0.765509	−	1.32590i
$233$	−282.430	−	163.061i	−1.21215	−	0.699833i	−0.248921	−	0.968524i	$-0.580076\pi$
$233$	−282.430	−	163.061i	−1.21215	−	0.699833i	−0.963227	+	0.268690i	$0.913409\pi$
$234$	115.773	+	24.0220i	0.494756	+	0.102658i
$235$	−45.4814	−	78.7762i	−0.193538	−	0.335218i
$236$	526.142	−	303.768i	2.22941	−	1.28715i
$237$	−323.154	+	262.985i	−1.36352	+	1.10964i
$238$	−373.340	−	11.0137i	−1.56866	−	0.0462761i
$239$	−210.918	+	121.774i	−0.882503	+	0.509514i	−0.871483	−	0.490426i	$-0.836841\pi$
$239$	−210.918	+	121.774i	−0.882503	+	0.509514i	−0.0110203	+	0.999939i	$0.503508\pi$
$240$	7.50047	+	9.21651i	0.0312519	+	0.0384021i
$241$	28.3405			0.117595			0.0587976	−	0.998270i	$-0.481273\pi$
$241$	28.3405			0.117595			0.0587976	+	0.998270i	$0.481273\pi$
$242$	535.697	−	309.285i	2.21362	−	1.27804i
$243$	−173.898	−	169.731i	−0.715629	−	0.698481i
$244$	471.478			1.93229
$245$	−226.392	−	149.162i	−0.924051	−	0.608826i
$246$	290.277	+	110.620i	1.17999	+	0.449675i
$247$	−31.9597			−0.129392
$248$	−197.765	−	114.180i	−0.797440	−	0.460402i
$249$	16.8911	−	44.3237i	0.0678356	−	0.178007i
$250$	−172.887	−	299.449i	−0.691549	−	1.19780i
$251$		−	140.132i		−	0.558294i	−0.960248	−	0.279147i	$-0.909948\pi$
$251$		−	140.132i		−	0.558294i	0.960248	−	0.279147i	$-0.0900516\pi$
$252$	−385.898	+	114.954i	−1.53134	+	0.456168i
$253$	178.082			0.703882
$254$	−39.2909	+	22.6846i	−0.154688	+	0.0893094i
$255$	213.101	−	173.423i	0.835689	−	0.680090i
$256$	118.593	−	205.409i	0.463253	−	0.802378i
$257$		−	110.672i		−	0.430629i	−0.976545	−	0.215315i	$-0.930922\pi$
$257$		−	110.672i		−	0.430629i	0.976545	−	0.215315i	$-0.0690777\pi$
$258$	64.0176	−	10.2986i	0.248130	−	0.0399171i
$259$	218.232	+	6.43794i	0.842595	+	0.0248569i
$260$			144.122i			0.554316i
$261$	406.046	+	84.2514i	1.55573	+	0.322802i
$262$	35.8942	+	62.1705i	0.137001	+	0.237292i
$263$		−	49.3684i		−	0.187713i	−0.995586	−	0.0938563i	$-0.970081\pi$
$263$		−	49.3684i		−	0.187713i	0.995586	−	0.0938563i	$-0.0299194\pi$
$264$	64.9726	+	403.879i	0.246108	+	1.52985i
$265$	104.106	+	180.317i	0.392853	+	0.680441i
$266$	155.788	−	83.9189i	0.585668	−	0.315485i
$267$	57.9095	−	151.960i	0.216890	−	0.569139i
$268$	−38.9583	−	67.4777i	−0.145367	−	0.251783i
$269$	162.040	−	93.5538i	0.602379	−	0.347784i	−0.167598	−	0.985855i	$-0.553601\pi$
$269$	162.040	−	93.5538i	0.602379	−	0.347784i	0.769977	+	0.638072i	$0.220268\pi$
$270$	259.335	−	405.773i	0.960499	−	1.50286i
$271$	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
$273$	79.0416	+	32.8223i	0.289530	+	0.120228i
$274$	−59.7747	−	103.533i	−0.218156	−	0.377857i
$275$		−	99.2950i		−	0.361073i
$276$	−68.7409	+	180.382i	−0.249061	+	0.653560i
$277$	78.1235			0.282034			0.141017	−	0.990007i	$-0.454963\pi$
$277$	78.1235			0.282034			0.141017	+	0.990007i	$0.454963\pi$
$278$	−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	−0.379323	−	0.925264i	$-0.623843\pi$
$281$	−385.051	−	222.309i	−1.37029	−	0.791135i	−0.990964	+	0.134129i	$0.957176\pi$
$282$	−148.566	−	56.6162i	−0.526831	−	0.200767i
$283$	64.2122	−	111.219i	0.226898	−	0.392999i	−0.729989	−	0.683459i	$-0.760475\pi$
$283$	64.2122	−	111.219i	0.226898	−	0.392999i	0.956887	+	0.290460i	$0.0938082\pi$
$284$	−110.779	−	63.9584i	−0.390068	−	0.225206i
$285$	−46.3527	+	121.634i	−0.162641	+	0.426785i
$286$	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
$290$			821.823i			2.83387i
$291$	−482.841	−	184.003i	−1.65925	−	0.632313i
$292$	−146.915			−0.503133
$293$	−42.6510	+	24.6246i	−0.145567	+	0.0840429i	−0.571014	−	0.820940i	$-0.693450\pi$
$293$	−42.6510	+	24.6246i	−0.145567	+	0.0840429i	0.425448	+	0.904983i	$0.360117\pi$
$294$	−471.472	+	47.5531i	−1.60365	+	0.161745i
$295$	−262.969	+	455.475i	−0.891420	+	1.54398i
$296$	208.220	+	120.216i	0.703446	+	0.406135i
$297$	−423.951	+	219.914i	−1.42745	+	0.740450i
$298$	186.512	+	323.049i	0.625880	+	1.08406i
$299$	35.5334	−	20.5152i	0.118841	−	0.0686127i
$300$	100.578	+	38.3285i	0.335259	+	0.127762i
$301$	46.9136	+	1.38397i	0.155859	+	0.00459792i
$302$	419.635	−	242.276i	1.38952	−	0.802239i
$303$	−51.2933	+	8.25163i	−0.169285	+	0.0272331i
$304$	−5.61389			−0.0184667
$305$	−353.471	+	204.077i	−1.15892	+	0.669104i
$306$	97.5635	−	470.203i	0.318835	−	1.53661i
$307$	−387.296			−1.26155			−0.630776	−	0.775965i	$-0.717263\pi$
$307$	−387.296			−1.26155			−0.630776	+	0.775965i	$0.717263\pi$
$308$	−23.3360	+	791.041i	−0.0757664	+	2.56831i
$309$	13.1509	+	81.7481i	0.0425596	+	0.264557i
$310$	528.358			1.70438
$311$	−87.5525	−	50.5485i	−0.281519	−	0.162535i	0.352592	−	0.935777i	$-0.385300\pi$
$311$	−87.5525	−	50.5485i	−0.281519	−	0.162535i	−0.634111	+	0.773242i	$0.718634\pi$
$312$	59.4914	+	73.1026i	0.190678	+	0.234303i
$313$	−182.396	−	315.918i	−0.582733	−	1.00932i	−0.995154	−	0.0983303i	$-0.968650\pi$
$313$	−182.396	−	315.918i	−0.582733	−	1.00932i	0.412420	−	0.910994i	$-0.364684\pi$
$314$			883.436i			2.81349i
$315$	239.554	−	253.217i	0.760490	−	0.803862i
$316$	−887.634			−2.80897
$317$	28.7096	−	16.5755i	0.0905665	−	0.0522886i	−0.454033	−	0.890985i	$-0.650015\pi$
$317$	28.7096	−	16.5755i	0.0905665	−	0.0522886i	0.544599	+	0.838696i	$0.316682\pi$
$318$	340.065	+	129.593i	1.06939	+	0.407526i
$319$	407.522	−	705.849i	1.27750	−	2.21269i
$320$			575.281i			1.79775i
$321$	130.869	−	343.413i	0.407692	−	1.06982i
$322$	−119.339	+	193.304i	−0.370618	+	0.600322i
$323$			129.802i			0.401864i
$324$	−59.1063	−	514.316i	−0.182427	−	1.58739i
$325$	−11.4388	−	19.8127i	−0.0351965	−	0.0609621i
$326$		−	717.733i		−	2.20163i
$327$	−79.4505	+	64.6574i	−0.242968	+	0.197729i
$328$	123.809	+	214.444i	0.377468	+	0.653794i
$329$	−97.9235	−	60.4546i	−0.297640	−	0.183753i
$330$	−597.419	−	734.103i	−1.81036	−	2.22456i
$331$	45.2538	+	78.3820i	0.136719	+	0.236804i	0.926253	−	0.376903i	$-0.123011\pi$
$331$	45.2538	+	78.3820i	0.136719	+	0.236804i	−0.789534	+	0.613707i	$0.789678\pi$
$332$	87.5154	−	50.5271i	0.263601	−	0.152190i
$333$	−57.0296	+	274.852i	−0.171260	+	0.825381i
$334$	−116.856	+	202.401i	−0.349869	+	0.605990i
$335$	58.4148	+	33.7258i	0.174373	+	0.100674i
$336$	13.8841	+	5.76540i	0.0413216	+	0.0171589i
$337$	216.839	+	375.576i	0.643438	+	1.11447i	0.984660	+	0.174485i	$0.0558261\pi$
$337$	216.839	+	375.576i	0.643438	+	1.11447i	−0.341221	+	0.939983i	$0.610841\pi$
$338$			491.240i			1.45337i
$339$	−147.428	−	181.159i	−0.434891	−	0.534391i
$340$	585.342			1.72159
$341$	−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
$345$	−26.5419	−	164.989i	−0.0769332	−	0.478228i
$346$	340.365	−	589.530i	0.983715	−	1.70384i
$347$	−10.1281	−	5.84745i	−0.0291876	−	0.0168514i	0.485335	−	0.874328i	$-0.338698\pi$
$347$	−10.1281	−	5.84745i	−0.0291876	−	0.0168514i	−0.514523	+	0.857477i	$0.672031\pi$
$348$	557.661	+	685.249i	1.60247	+	1.96911i
$349$	91.7075	−	158.842i	0.262772	−	0.455135i	−0.704205	−	0.709996i	$-0.748697\pi$
$349$	91.7075	−	158.842i	0.262772	−	0.455135i	0.966978	+	0.254862i	$0.0820299\pi$
$350$	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
$353$		−	68.0833i		−	0.192871i	−0.995339	−	0.0964353i	$-0.969256\pi$
$353$		−	68.0833i		−	0.192871i	0.995339	−	0.0964353i	$-0.0307441\pi$
$354$	146.005	+	907.585i	0.412442	+	2.56380i
$355$	110.736			0.311933
$356$	300.039	−	173.228i	0.842807	−	0.486595i
$357$	133.305	−	321.022i	0.373404	−	0.899221i
$358$	129.528	−	224.350i	0.361811	−	0.626675i
$359$	386.169	+	222.955i	1.07568	+	0.621044i	0.929728	−	0.368247i	$-0.120042\pi$
$359$	386.169	+	222.955i	1.07568	+	0.621044i	0.145952	+	0.989292i	$0.453375\pi$
$360$	364.500	−	120.391i	1.01250	−	0.334419i
$361$	149.752	+	259.378i	0.414826	+	0.718500i
$362$	−343.222	+	198.159i	−0.948127	+	0.547401i
$363$	91.4332	+	568.362i	0.251882	+	1.56574i
$364$	86.4721	+	160.527i	0.237561	+	0.441009i
$365$	110.143	−	63.5913i	0.301763	−	0.174223i
$366$	−254.039	+	666.622i	−0.694095	+	1.82137i
$367$	126.685			0.345190			0.172595	−	0.984993i	$-0.444785\pi$
$367$	126.685			0.345190			0.172595	+	0.984993i	$0.444785\pi$
$368$	6.24161	−	3.60360i	0.0169609	−	0.00979238i
$369$	−192.399	+	215.777i	−0.521407	+	0.584760i
$370$	−556.291			−1.50349
$371$	224.145	+	138.379i	0.604164	+	0.372990i
$372$	440.553	−	358.526i	1.18428	−	0.963779i
$373$	−612.329			−1.64163			−0.820817	−	0.571192i	$-0.806481\pi$
$373$	−612.329			−1.64163			−0.820817	+	0.571192i	$0.806481\pi$
$374$	−817.377	−	471.913i	−2.18550	−	1.26180i
$375$	317.709	−	51.1103i	0.847224	−	0.136294i
$376$	−63.3667	−	109.754i	−0.168528	−	0.291900i
$377$		−	187.787i		−	0.498110i
$378$	45.3938	−	607.560i	0.120089	−	1.60730i
$379$	410.847			1.08403			0.542015	−	0.840369i	$-0.317662\pi$
$379$	410.847			1.08403			0.542015	+	0.840369i	$0.317662\pi$
$380$	−240.161	+	138.657i	−0.632003	+	0.364887i
$381$	−6.70620	−	41.6867i	−0.0176016	−	0.109414i
$382$	−572.973	+	992.418i	−1.49993	+	2.59795i
$383$		−	220.118i		−	0.574720i	−0.957823	−	0.287360i	$-0.907222\pi$
$383$		−	220.118i		−	0.574720i	0.957823	−	0.287360i	$-0.0927775\pi$
$384$	383.638	+	471.411i	0.999056	+	1.22763i
$385$	−324.903	−	603.152i	−0.843903	−	1.56663i
$386$			127.844i			0.331203i
$387$	−12.2597	+	59.0853i	−0.0316789	+	0.152675i
$388$	−550.417	−	953.351i	−1.41860	−	2.45709i
$389$			172.259i			0.442824i	0.975180	+	0.221412i	$0.0710666\pi$
$389$			172.259i			0.442824i	−0.975180	+	0.221412i	$0.928933\pi$
$390$	−203.774	−	77.6551i	−0.522498	−	0.199116i
$391$	−83.3209	−	144.316i	−0.213097	−	0.369095i
$392$	−315.420	−	207.819i	−0.804642	−	0.530151i
$393$	−65.9615	+	10.6113i	−0.167841	+	0.0270008i
$394$	−210.554	−	364.691i	−0.534402	−	0.925611i
$395$	665.468	−	384.208i	1.68473	−	0.972678i
$396$	−996.274	−	206.719i	−2.51584	−	0.522018i
$397$	−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
$399$	21.3503	+	163.290i	0.0535095	+	0.409249i
$400$	−2.00929	−	3.48020i	−0.00502323	−	0.00870049i
$401$			299.417i			0.746675i	0.927696	+	0.373338i	$0.121787\pi$
$401$			299.417i			0.746675i	−0.927696	+	0.373338i	$0.878213\pi$
$402$	116.398	−	18.7251i	0.289547	−	0.0465799i
$403$	−120.730			−0.299579
$404$	−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
$408$	296.901	−	241.620i	0.727698	−	0.592206i
$409$	187.201	−	324.241i	0.457703	−	0.792766i	−0.541136	−	0.840935i	$-0.682005\pi$
$409$	187.201	−	324.241i	0.457703	−	0.792766i	0.998839	+	0.0481696i	$0.0153388\pi$
$410$	−496.163	−	286.460i	−1.21015	−	0.698682i
$411$	109.846	−	17.6711i	0.267265	−	0.0429953i
$412$	−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
$416$		−	135.073i		−	0.324694i
$417$	328.253	−	267.134i	0.787176	−	0.640610i
$418$	447.151			1.06974
$419$	350.317	−	202.256i	0.836080	−	0.482711i	−0.0198501	−	0.999803i	$-0.506319\pi$
$419$	350.317	−	202.256i	0.836080	−	0.482711i	0.855930	+	0.517092i	$0.172986\pi$
$420$	736.357	−	96.2790i	1.75323	−	0.229236i
$421$	−231.002	+	400.107i	−0.548698	+	0.950372i	0.449666	+	0.893197i	$0.351543\pi$
$421$	−231.002	+	400.107i	−0.548698	+	0.950372i	−0.998364	+	0.0571757i	$0.981790\pi$
$422$	−304.916	−	176.043i	−0.722549	−	0.417164i
$423$	98.4715	−	110.436i	0.232793	−	0.261078i
$424$	145.045	+	251.225i	0.342087	+	0.592512i
$425$	−80.4677	+	46.4580i	−0.189336	+	0.109313i
$426$	150.120	−	122.169i	0.352395	−	0.286781i
$427$	−271.262	+	439.386i	−0.635274	+	1.02901i
$428$	678.055	−	391.475i	1.58424	−	0.914662i
$429$	136.511	+	167.743i	0.318207	+	0.391010i
$430$	−119.587			−0.278108
$431$	−197.559	+	114.061i	−0.458374	+	0.264643i	−0.711360	−	0.702827i	$-0.751921\pi$
$431$	−197.559	+	114.061i	−0.458374	+	0.264643i	0.252986	+	0.967470i	$0.418587\pi$
$432$	−10.4090	+	16.2867i	−0.0240949	+	0.0377006i
$433$	777.626			1.79590			0.897951	−	0.440095i	$-0.145055\pi$
$433$	777.626			1.79590			0.897951	+	0.440095i	$0.145055\pi$
$434$	588.500	−	317.010i	1.35599	−	0.730439i
$435$	−714.690	−	272.357i	−1.64297	−	0.626108i
$436$	−218.234			−0.500536
$437$	68.3719	+	39.4745i	0.156457	+	0.0903307i
$438$	79.1598	−	207.723i	0.180730	−	0.474252i
$439$	−34.4006	−	59.5836i	−0.0783612	−	0.135726i	0.824182	−	0.566325i	$-0.191635\pi$
$439$	−34.4006	−	59.5836i	−0.0783612	−	0.135726i	−0.902543	+	0.430600i	$0.858302\pi$
$440$		−	754.458i		−	1.71468i
$441$	114.895	−	425.770i	0.260532	−	0.965465i
$442$	−217.459			−0.491988
$443$	−180.419	+	104.165i	−0.407267	+	0.235136i	−0.689615	−	0.724176i	$-0.742220\pi$
$443$	−180.419	+	104.165i	−0.407267	+	0.235136i	0.282348	+	0.959312i	$0.408887\pi$
$444$	−463.844	+	377.480i	−1.04469	+	0.850179i
$445$	−149.961	+	259.741i	−0.336992	+	0.583687i
$446$		−	601.959i		−	1.34968i
$447$	−342.747	+	55.1382i	−0.766772	+	0.123352i
$448$	345.164	+	640.765i	0.770455	+	1.43028i
$449$		−	259.045i		−	0.576937i	−0.957489	−	0.288469i	$-0.906854\pi$
$449$		−	259.045i		−	0.576937i	0.957489	−	0.288469i	$-0.0931461\pi$
$450$	−108.385	+	121.555i	−0.240856	+	0.270121i
$451$	284.097	+	492.071i	0.629927	+	1.09107i
$452$		−	497.604i		−	1.10089i
$453$	71.6236	+	445.223i	0.158110	+	0.982832i
$454$	−326.463	−	565.450i	−0.719081	−	1.24548i
$455$	−134.312	−	82.9199i	−0.295192	−	0.182242i
$456$	−64.5806	+	169.465i	−0.141624	+	0.371635i
$457$	−79.7186	−	138.077i	−0.174439	−	0.302137i	0.765528	−	0.643403i	$-0.222478\pi$
$457$	−79.7186	−	138.077i	−0.174439	−	0.302137i	−0.939967	+	0.341265i	$0.889144\pi$
$458$	221.306	−	127.771i	0.483201	−	0.278976i
$459$	376.574	+	240.673i	0.820423	+	0.524342i
$460$	178.010	−	308.323i	0.386979	−	0.670267i
$461$	−176.910	−	102.139i	−0.383752	−	0.221559i	0.295697	−	0.955282i	$-0.404448\pi$
$461$	−176.910	−	102.139i	−0.383752	−	0.221559i	−0.679449	+	0.733722i	$0.737781\pi$
$462$	−1105.88	−	459.219i	−2.39367	−	0.993980i
$463$	−381.105	−	660.092i	−0.823120	−	1.42569i	−0.903348	−	0.428909i	$-0.858898\pi$
$463$	−381.105	−	660.092i	−0.823120	−	1.42569i	0.0802276	−	0.996777i	$-0.474435\pi$
$464$		−	32.9858i		−	0.0710901i
$465$	−175.101	+	459.481i	−0.376562	+	0.988132i
$466$	1051.28			2.25596
$467$	462.046	+	266.762i	0.989391	+	0.571225i	0.905092	−	0.425215i	$-0.139802\pi$
$467$	462.046	+	266.762i	0.989391	+	0.571225i	0.0842988	+	0.996441i	$0.473135\pi$
$468$	−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
$471$	−768.271	−	292.776i	−1.63115	−	0.621605i
$472$	−366.379	+	634.588i	−0.776227	+	1.34447i
$473$	102.711	+	59.3001i	0.217148	+	0.125370i
$474$	478.270	−	1255.02i	1.00901	−	2.64773i
$475$	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
$479$			604.516i			1.26204i	0.775768	+	0.631019i	$0.217363\pi$
$479$			604.516i			1.26204i	−0.775768	+	0.631019i	$0.782637\pi$
$480$	−514.066	−	195.902i	−1.07097	−	0.408130i
$481$	127.113			0.264268
$482$	−79.1177	+	45.6787i	−0.164145	+	0.0947690i
$483$	−128.555	−	167.844i	−0.266159	−	0.347503i
$484$	−613.220	+	1062.13i	−1.26698	+	2.19448i
$485$	825.306	+	476.491i	1.70166	+	0.982455i
$486$	759.038	+	193.550i	1.56181	+	0.398252i
$487$	−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	$0.884603\pi$
$488$	−492.471	+	284.328i	−1.00916	+	0.582640i
$489$	624.169	+	237.861i	1.27642	+	0.486423i
$490$	872.434	+	51.5192i	1.78048	+	0.105141i
$491$	−346.903	+	200.285i	−0.706523	+	0.407911i	−0.809772	−	0.586744i	$-0.800409\pi$
$491$	−346.903	+	200.285i	−0.706523	+	0.407911i	0.103249	+	0.994656i	$0.467076\pi$
$492$	−608.090	+	97.8243i	−1.23596	+	0.198830i
$493$	−762.685			−1.54703
$494$	89.2216	−	51.5121i	0.180611	−	0.104276i
$495$	836.394	−	276.253i	1.68968	−	0.558087i
$496$	−21.2069			−0.0427559
$497$	123.341	−	66.4408i	0.248171	−	0.133684i
$498$	24.2856	+	150.963i	0.0487662	+	0.303138i
$499$	−122.289			−0.245068			−0.122534	−	0.992464i	$-0.539102\pi$
$499$	−122.289			−0.245068			−0.122534	+	0.992464i	$0.539102\pi$
$500$	593.719	+	342.784i	1.18744	+	0.685567i
$501$	−137.289	−	168.700i	−0.274030	−	0.336726i
$502$	225.862	+	391.204i	0.449924	+	0.779291i
$503$		−	786.814i		−	1.56424i	−0.623126	−	0.782121i	$-0.714138\pi$
$503$		−	786.814i		−	1.56424i	0.623126	−	0.782121i	$-0.285862\pi$
$504$	333.757	−	352.792i	0.662216	−	0.699984i
$505$	95.8173			0.189737
$506$	−497.150	+	287.030i	−0.982510	+	0.567252i
$507$	−427.202	−	162.800i	−0.842607	−	0.321104i
$508$	44.9768	−	77.9021i	0.0885370	−	0.153351i
$509$			902.823i			1.77372i	0.462040	+	0.886859i	$0.347118\pi$
$509$			902.823i			1.77372i	−0.462040	+	0.886859i	$0.652882\pi$
$510$	−315.391	+	827.614i	−0.618413	+	1.62277i
$511$	84.5265	−	136.915i	0.165414	−	0.267935i
$512$		−	45.8004i		−	0.0894539i
$513$	−211.517	−	9.54258i	−0.412313	−	0.0186015i
$514$	178.379	+	308.961i	0.347040	+	0.601092i
$515$		−	152.708i		−	0.296520i
$516$	−99.7132	+	81.1473i	−0.193243	+	0.157262i
$517$	−145.403	−	251.846i	−0.281244	−	0.487129i
$518$	−619.612	+	333.770i	−1.19616	+	0.644343i
$519$	399.880	+	491.369i	0.770482	+	0.946762i
$520$	−86.9141	−	150.540i	−0.167142	−	0.289499i
$521$	−442.743	+	255.618i	−0.849795	+	0.490630i	−0.860582	−	0.509312i	$-0.829900\pi$
$521$	−442.743	+	255.618i	−0.849795	+	0.490630i	0.0107865	+	0.999942i	$0.496566\pi$
$522$	−1269.35	+	419.254i	−2.43170	+	0.803168i
$523$	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
$525$	−93.5864	+	71.6796i	−0.178260	+	0.136533i
$526$	79.5711	+	137.821i	0.151276	+	0.262018i
$527$			490.338i			0.930432i
$528$	23.9788	+	29.4650i	0.0454144	+	0.0558049i
$529$	427.644			0.808401
$530$	−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
$534$	83.2610	+	517.563i	0.155919	+	0.969218i
$535$	−338.896	+	586.986i	−0.633451	+	1.09717i
$536$	81.3860	+	46.9882i	0.151840	+	0.0876646i
$537$	152.177	+	186.994i	0.283383	+	0.348219i
$538$	−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	$-0.0574934\pi$
$542$			697.234i			1.28641i
$543$	−58.5814	−	364.151i	−0.107885	−	0.670628i
$544$	−548.588			−1.00843
$545$	163.612	−	94.4613i	0.300205	−	0.173324i
$546$	−273.562	+	35.7683i	−0.501029	+	0.0655098i
$547$	294.015	−	509.248i	0.537504	−	0.930984i	−0.461534	−	0.887123i	$-0.652701\pi$
$547$	294.015	−	509.248i	0.537504	−	0.930984i	0.999038	−	0.0438616i	$-0.0139660\pi$
$548$	205.275	+	118.515i	0.374589	+	0.216269i
$549$	−495.531	−	441.845i	−0.902606	−	0.804817i
$550$	160.042	+	277.201i	0.290985	+	0.504001i
$551$	312.924	−	180.667i	0.567920	−	0.327889i
$552$	−36.9794	−	229.869i	−0.0669916	−	0.416430i
$553$	510.695	−	827.216i	0.923499	−	1.49587i
$554$	−218.097	+	125.918i	−0.393676	+	0.227289i
$555$	184.358	−	483.773i	0.332177	−	0.871663i
$556$	901.640			1.62165
$557$	−347.042	+	200.365i	−0.623055	+	0.359721i	−0.778057	−	0.628193i	$-0.783795\pi$
$557$	−347.042	+	200.365i	−0.623055	+	0.359721i	0.155002	+	0.987914i	$0.450461\pi$
$558$	269.542	+	816.077i	0.483051	+	1.46250i
$559$	27.3257			0.0488831
$560$	−23.5927	−	14.5653i	−0.0421298	−	0.0260095i
$561$	681.278	−	554.429i	1.21440	−	0.988287i
$562$	1433.26			2.55028
$563$	−78.9486	−	45.5810i	−0.140228	−	0.0809609i	0.428244	−	0.903663i	$-0.359132\pi$
$563$	−78.9486	−	45.5810i	−0.140228	−	0.0809609i	−0.568473	+	0.822702i	$0.692466\pi$
$564$	311.225	−	50.0672i	0.551818	−	0.0887717i
$565$	215.385	+	373.058i	0.381213	+	0.660281i
$566$			413.984i			0.731421i
$567$	513.315	+	240.825i	0.905317	+	0.424736i
$568$	154.282			0.271624
$569$	255.596	−	147.568i	0.449202	−	0.259347i	−0.258291	−	0.966067i	$-0.583159\pi$
$569$	255.596	−	147.568i	0.449202	−	0.259347i	0.707493	+	0.706720i	$0.249826\pi$
$570$	−66.6449	−	414.274i	−0.116921	−	0.726797i
$571$	−457.407	+	792.252i	−0.801062	+	1.38748i	0.117855	+	0.993031i	$0.462398\pi$
$571$	−457.407	+	792.252i	−0.801062	+	1.38748i	−0.918917	+	0.394450i	$0.870935\pi$
$572$			460.756i			0.805517i
$573$	−673.159	−	827.173i	−1.17480	−	1.44358i
$574$	−724.513	−	21.3735i	−1.26222	−	0.0372360i
$575$			56.5140i			0.0982852i
$576$	−888.552	+	293.480i	−1.54262	+	0.509514i
$577$	−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	$0.986653\pi$
$578$		−	48.4175i		−	0.0837674i
$579$	−111.178	−	42.3683i	−0.192018	−	0.0731750i
$580$	−814.715	−	1411.13i	−1.40468	−	2.43298i
$581$	−3.26361	+	110.629i	−0.00561722	+	0.190412i
$582$	1644.51	−	264.555i	2.82563	−	0.454562i
$583$	332.825	+	576.469i	0.570883	+	0.988798i
$584$	153.456	−	88.5981i	0.262768	−	0.151709i
$585$	135.064	−	151.475i	0.230879	−	0.258931i
$586$	79.3789	−	137.488i	0.135459	−	0.234622i
$587$	299.889	+	173.141i	0.510884	+	0.294959i	0.733197	−	0.680016i	$-0.238027\pi$
$587$	299.889	+	173.141i	0.510884	+	0.294959i	−0.222313	+	0.974975i	$0.571361\pi$
$588$	762.409	−	549.046i	1.29661	−	0.933752i
$589$	−116.152	−	201.182i	−0.197203	−	0.341565i
$590$		−	1695.39i		−	2.87355i
$591$	386.929	−	62.2457i	0.654701	−	0.105323i
$592$	22.3281			0.0377163
$593$	−3.55214	−	2.05083i	−0.00599012	−	0.00345840i	0.497002	−	0.867749i	$-0.334434\pi$
$593$	−3.55214	−	2.05083i	−0.00599012	−	0.00345840i	−0.502992	+	0.864291i	$0.667768\pi$
$594$	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
$597$	505.024	−	410.992i	0.845936	−	0.688429i
$598$	−66.1320	+	114.544i	−0.110589	+	0.191545i
$599$	146.853	+	84.7858i	0.245164	+	0.141546i	0.617548	−	0.786533i	$-0.288126\pi$
$599$	146.853	+	84.7858i	0.245164	+	0.141546i	−0.372384	+	0.928079i	$0.621459\pi$
$600$	−128.170	+	20.6189i	−0.213617	+	0.0343649i
$601$	−312.975	+	542.089i	−0.520757	+	0.901978i	0.478951	+	0.877841i	$0.341017\pi$
$601$	−312.975	+	542.089i	−0.520757	+	0.901978i	−0.999709	+	0.0241366i	$0.992316\pi$
$602$	−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
$605$		−	1061.72i		−	1.75490i
$606$	129.895	−	105.710i	0.214348	−	0.174438i
$607$	−37.6117			−0.0619633			−0.0309817	−	0.999520i	$-0.509863\pi$
$607$	−37.6117			−0.0619633			−0.0309817	+	0.999520i	$0.509863\pi$
$608$	225.081	−	129.951i	0.370200	−	0.213735i
$609$	−959.454	+	125.449i	−1.57546	+	0.205992i
$610$	657.855	−	1139.44i	1.07845	−	1.86793i
$611$	−58.0256	−	33.5011i	−0.0949682	−	0.0548299i
$612$	298.613	+	904.091i	0.487929	+	1.47727i
$613$	−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	$0.911497\pi$
$614$	1081.21	−	624.238i	1.76093	−	1.01667i
$615$	413.548	−	336.549i	0.672436	−	0.547233i
$616$	−452.668	−	840.336i	−0.734851	−	1.36418i
$617$	818.560	−	472.596i	1.32668	−	0.765957i	0.341893	−	0.939739i	$-0.388932\pi$
$617$	818.560	−	472.596i	1.32668	−	0.765957i	0.984784	+	0.173782i	$0.0555987\pi$
$618$	−168.473	−	207.019i	−0.272611	−	0.334982i
$619$	−1193.60			−1.92827			−0.964133	−	0.265418i	$-0.914490\pi$
$619$	−1193.60			−1.92827			−0.964133	+	0.265418i	$0.914490\pi$
$620$	−907.229	+	523.789i	−1.46327	+	0.844820i
$621$	241.293	−	125.164i	0.388556	−	0.201553i
$622$	325.892			0.523943
$623$	−11.1890	+	379.282i	−0.0179599	+	0.608800i
$624$	8.17896	+	3.11687i	0.0131073	+	0.00499499i
$625$	−733.826			−1.17412
$626$	1018.38	+	587.964i	1.62681	+	0.939239i
$627$	−148.189	+	388.860i	−0.236345	+	0.620192i
$628$	−875.795	−	1516.92i	−1.39458	−	2.41548i
$629$		−	516.260i		−	0.820764i
$630$	−260.631	+	1093.01i	−0.413700	+	1.73494i
$631$	−823.055			−1.30437			−0.652183	−	0.758062i	$-0.726147\pi$
$631$	−823.055			−1.30437			−0.652183	+	0.758062i	$0.726147\pi$
$632$	927.158	−	535.295i	1.46702	−	0.846985i
$633$	254.145	−	206.825i	0.401493	−	0.326738i
$634$	−53.4322	+	92.5472i	−0.0842779	+	0.145974i
$635$			77.8719i			0.122633i
$636$	−712.388	+	114.603i	−1.12011	+	0.180193i
$637$	−199.352	−	11.7722i	−0.312955	−	0.0184807i
$638$			2627.35i			4.11810i
$639$	56.4922	+	171.038i	0.0884072	+	0.267665i
$640$	−560.476	−	970.773i	−0.875744	−	1.51683i
$641$		−	712.531i		−	1.11159i	−0.831319	−	0.555796i	$-0.812413\pi$
$641$		−	712.531i		−	1.11159i	0.831319	−	0.555796i	$-0.187587\pi$
$642$	188.161	+	1169.63i	0.293085	+	1.82186i
$643$	534.902	+	926.478i	0.831885	+	1.44087i	0.896542	+	0.442960i	$0.146072\pi$
$643$	534.902	+	926.478i	0.831885	+	1.44087i	−0.0646564	+	0.997908i	$0.520595\pi$
$644$	13.2818	−	450.223i	0.0206239	−	0.699104i
$645$	39.6317	−	103.997i	0.0614445	−	0.161236i
$646$	−209.213	−	362.367i	−0.323859	−	0.560940i
$647$	−973.422	+	562.006i	−1.50452	+	0.868633i	−0.504531	+	0.863394i	$0.668334\pi$
$647$	−973.422	+	562.006i	−1.50452	+	0.868633i	−0.999986	+	0.00523936i	$0.998332\pi$
$648$	371.900	+	501.572i	0.573920	+	0.774031i
$649$	−840.705	+	1456.14i	−1.29539	+	2.24367i
$650$	63.8674	+	36.8739i	0.0982576	+	0.0567290i
$651$	80.6524	+	616.843i	0.123890	+	0.947531i
$652$	711.525	+	1232.40i	1.09130	+	1.89018i
$653$		−	48.4318i		−	0.0741682i	−0.999312	−	0.0370841i	$-0.988193\pi$
$653$		−	48.4318i		−	0.0741682i	0.999312	−	0.0370841i	$-0.0118069\pi$
$654$	117.587	−	308.560i	0.179797	−	0.471805i
$655$	123.218			0.188119
$656$	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	−0.272076	−	0.962276i	$-0.587710\pi$
$659$	−818.128	−	472.346i	−1.24147	−	0.716762i	−0.969393	+	0.245514i	$0.921043\pi$
$660$	1753.56	+	668.256i	2.65692	+	1.01251i
$661$	−140.597	+	243.521i	−0.212703	+	0.368413i	−0.952560	−	0.304352i	$-0.901560\pi$
$661$	−140.597	+	243.521i	−0.212703	+	0.368413i	0.739856	+	0.672765i	$0.234893\pi$
$662$	−252.669	−	145.879i	−0.381676	−	0.220361i
$663$	72.0671	−	189.111i	0.108699	−	0.285235i
$664$	−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
$668$		−	463.382i		−	0.693685i
$669$	523.487	+	199.493i	0.782492	+	0.298195i
$670$	−217.435			−0.324529
$671$	−1130.04	+	652.429i	−1.68411	+	0.972323i
$672$	−690.121	+	90.2336i	−1.02697	+	0.134276i
$673$	246.892	−	427.630i	0.366854	−	0.635409i	−0.622218	−	0.782844i	$-0.713768\pi$
$673$	246.892	−	427.630i	0.366854	−	0.635409i	0.989072	+	0.147435i	$0.0471017\pi$
$674$	−1210.69	−	698.994i	−1.79628	−	1.03708i
$675$	−69.7892	−	134.540i	−0.103391	−	0.199319i
$676$	−486.991	−	843.494i	−0.720401	−	1.24777i
$677$	−611.085	+	352.810i	−0.902636	+	0.521137i	−0.878055	−	0.478561i	$-0.841159\pi$
$677$	−611.085	+	352.810i	−0.902636	+	0.521137i	−0.0245816	+	0.999698i	$0.507825\pi$
$678$	703.562	+	268.116i	1.03770	+	0.395452i
$679$	1205.14	+	35.5521i	1.77487	+	0.0523596i
$680$	−611.405	+	352.995i	−0.899126	+	0.519110i
$681$	599.929	−	96.5114i	0.880953	−	0.141720i
$682$	1689.15			2.47676
$683$	1010.24	−	583.260i	1.47912	−	0.853968i	0.479394	−	0.877600i	$-0.340856\pi$
$683$	1010.24	−	583.260i	1.47912	−	0.853968i	0.999721	+	0.0236320i	$0.00752300\pi$
$684$	−336.682	−	300.205i	−0.492225	−	0.438897i
$685$	−205.195			−0.299555
$686$	1002.65	−	466.070i	1.46159	−	0.679402i
$687$	37.7727	+	234.800i	0.0549821	+	0.341777i
$688$	4.79989			0.00697659
$689$	132.819	+	76.6832i	0.192771	+	0.111296i
$690$	340.023	+	417.817i	0.492786	+	0.605532i
$691$	−182.834	−	316.677i	−0.264593	−	0.458289i	0.702864	−	0.711324i	$-0.251904\pi$
$691$	−182.834	−	316.677i	−0.264593	−	0.458289i	−0.967457	+	0.253036i	$0.918571\pi$
$692$			1349.69i			1.95041i
$693$	765.849	−	809.527i	1.10512	−	1.16815i
$694$	37.6993			0.0543217
$695$	−675.968	+	390.270i	−0.972616	+	0.561540i
$696$	−995.736	−	379.459i	−1.43066	−	0.545200i
$697$	265.846	−	460.459i	0.381415	−	0.660630i
$698$			591.250i			0.847063i
$699$	−348.399	+	914.232i	−0.498425	+	1.30791i
$700$	−251.035	−	7.40564i	−0.358622	−	0.0105795i
$701$		−	254.519i		−	0.363080i	−0.983384	−	0.181540i	$-0.941892\pi$
$701$		−	254.519i		−	0.363080i	0.983384	−	0.181540i	$-0.0581083\pi$
$702$	15.9868	−	354.356i	0.0227732	−	0.504780i
$703$	122.293	+	211.818i	0.173959	+	0.301305i
$704$			1839.16i			2.61245i
$705$	−211.657	+	172.248i	−0.300223	+	0.244324i
$706$	109.735	+	190.067i	0.155433	+	0.269217i
$707$	106.724	−	57.4896i	0.150953	−	0.0813148i
$708$	−1150.44	−	1413.65i	−1.62491	−	1.99668i
$709$	520.494	+	901.522i	0.734124	+	1.27154i	0.955107	+	0.296263i	$0.0957403\pi$
$709$	520.494	+	901.522i	0.734124	+	1.27154i	−0.220982	+	0.975278i	$0.570926\pi$
$710$	−309.141	+	178.483i	−0.435410	+	0.251384i
$711$	932.918	+	831.845i	1.31212	+	1.16997i
$712$	−208.933	+	361.882i	−0.293445	+	0.508261i
$713$	258.280	+	149.118i	0.362244	+	0.209142i
$714$	145.270	+	1111.05i	0.203460	+	1.55609i
$715$	−199.436	−	345.433i	−0.278931	−	0.483123i
$716$			513.632i			0.717363i
$717$	461.184	+	566.699i	0.643213	+	0.790375i
$718$	−1437.42			−2.00198
$719$	−653.543	−	377.323i	−0.908961	−	0.524789i	−0.0288642	−	0.999583i	$-0.509189\pi$
$719$	−653.543	−	377.323i	−0.908961	−	0.524789i	−0.880097	+	0.474795i	$0.842522\pi$
$720$	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
$723$	−13.5039	−	83.9421i	−0.0186776	−	0.116103i
$724$	392.891	−	680.507i	0.542667	−	0.939927i
$725$	224.000	+	129.326i	0.308965	+	0.178381i
$726$	−1171.33	−	1439.32i	−1.61340	−	1.98253i
$727$	698.773	−	1210.31i	0.961174	−	1.66480i	0.241612	−	0.970373i	$-0.422324\pi$
$727$	698.773	−	1210.31i	0.961174	−	1.66480i	0.719561	−	0.694429i	$-0.244343\pi$
$728$	−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
$731$		−	110.981i		−	0.151821i
$732$	−224.653	−	1396.48i	−0.306903	−	1.90776i
$733$	1253.49			1.71008			0.855039	−	0.518564i	$-0.173533\pi$
$733$	1253.49			1.71008			0.855039	+	0.518564i	$0.173533\pi$
$734$	−353.664	+	204.188i	−0.481832	+	0.278186i
$735$	−333.933	+	741.630i	−0.454331	+	1.00902i
$736$	−166.833	+	288.963i	−0.226675	+	0.392613i
$737$	186.751	+	107.821i	0.253393	+	0.146297i
$738$	189.334	−	912.487i	0.256550	−	1.23643i
$739$	−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	$-0.424342\pi$
$740$	955.191	−	551.480i	1.29080	−	0.745243i
$741$	15.2284	+	94.6621i	0.0205512	+	0.127749i
$742$	−848.780	−	25.0394i	−1.14391	−	0.0337458i
$743$	−620.266	+	358.111i	−0.834813	+	0.481980i	−0.855498	−	0.517806i	$-0.826749\pi$
$743$	−620.266	+	358.111i	−0.834813	+	0.481980i	0.0206847	+	0.999786i	$0.493415\pi$
$744$	−243.958	+	640.169i	−0.327901	+	0.860442i
$745$	640.261			0.859411
$746$	1709.43	−	986.941i	2.29146	−	1.32298i
$747$	−139.332	−	28.9102i	−0.186522	−	0.0387018i
$748$	1871.32			2.50177
$749$	−25.2859	+	857.136i	−0.0337595	+	1.14437i
$750$	−804.566	+	654.762i	−1.07275	+	0.873015i
$751$	−120.642			−0.160642			−0.0803208	−	0.996769i	$-0.525594\pi$
$751$	−120.642			−0.160642			−0.0803208	+	0.996769i	$0.525594\pi$
$752$	−10.1925	−	5.88464i	−0.0135538	−	0.00782531i
$753$	−415.059	+	66.7711i	−0.551207	+	0.0886734i
$754$	302.672	+	524.244i	0.401422	+	0.695284i
$755$		−	831.689i		−	1.10157i
$756$	524.361	+	1088.22i	0.693599	+	1.43945i
$757$	−369.403			−0.487983			−0.243992	−	0.969777i	$-0.578457\pi$
$757$	−369.403			−0.487983			−0.243992	+	0.969777i	$0.578457\pi$
$758$	−1146.96	+	662.196i	−1.51314	+	0.873610i
$759$	−84.8540	−	527.465i	−0.111797	−	0.694947i
$760$	167.237	−	289.662i	0.220048	−	0.381135i
$761$		−	1145.54i		−	1.50531i	−0.658415	−	0.752655i	$-0.728773\pi$
$761$		−	1145.54i		−	1.50531i	0.658415	−	0.752655i	$-0.271227\pi$
$762$	85.9115	+	105.567i	0.112745	+	0.138540i
$763$	125.559	−	203.379i	0.164560	−	0.266552i
$764$		−	2272.07i		−	2.97391i
$765$	−615.204	−	548.553i	−0.804188	−	0.717062i
$766$	354.782	+	614.500i	0.463161	+	0.802219i
$767$			387.399i			0.505084i
$768$	−664.912	−	253.387i	−0.865771	−	0.329932i
$769$	319.295	+	553.035i	0.415208	+	0.719162i	0.995450	−	0.0952822i	$-0.0303754\pi$
$769$	319.295	+	553.035i	0.415208	+	0.719162i	−0.580242	+	0.814444i	$0.697042\pi$
$770$	1879.18	+	1160.14i	2.44049	+	1.50667i
$771$	−327.801	+	52.7337i	−0.425163	+	0.0683966i
$772$	−126.738	−	219.517i	−0.164169	−	0.284349i
$773$	−169.438	+	97.8250i	−0.219195	+	0.126552i	−0.605578	−	0.795786i	$-0.707058\pi$
$773$	−169.438	+	97.8250i	−0.219195	+	0.126552i	0.386382	+	0.922339i	$0.373725\pi$
$774$	−61.0072	−	184.708i	−0.0788207	−	0.238641i
$775$	83.1452	−	144.012i	0.107284	−	0.185822i
$776$	1149.85	+	663.867i	1.48177	+	0.855499i
$777$	−84.9162	−	649.453i	−0.109287	−	0.835847i
$778$	−277.643	−	480.892i	−0.356868	−	0.618114i
$779$			251.897i			0.323360i
$780$	426.878	−	68.6725i	0.547280	−	0.0880417i
$781$	354.021			0.453292
$782$	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
$786$	167.041	−	135.939i	0.212520	−	0.172951i
$787$	8.68274	−	15.0389i	0.0110327	−	0.0191092i	−0.860456	−	0.509524i	$-0.829821\pi$
$787$	8.68274	−	15.0389i	0.0110327	−	0.0191092i	0.871489	+	0.490415i	$0.163155\pi$
$788$	723.073	+	417.466i	0.917605	+	0.529780i
$789$	−146.225	+	23.5235i	−0.185330	+	0.0298143i
$790$	−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
$794$		−	1196.08i		−	1.50640i
$795$	484.479	−	394.272i	0.609407	−	0.495940i
$796$	1387.19			1.74270
$797$	−871.920	+	503.403i	−1.09400	+	0.631622i	−0.934639	−	0.355598i	$-0.884277\pi$
$797$	−871.920	+	503.403i	−1.09400	+	0.631622i	−0.159363	+	0.987220i	$0.550944\pi$
$798$	−322.792	−	421.444i	−0.404501	−	0.528125i
$799$	−136.062	+	235.667i	−0.170291	+	0.294952i
$800$	161.120	+	93.0225i	0.201400	+	0.116278i
$801$	−477.686	−	99.1162i	−0.596362	−	0.123741i
$802$	−482.595	−	835.879i	−0.601739	−	1.04224i
$803$	352.126	−	203.300i	0.438513	−	0.253176i
$804$	−181.300	+	147.544i	−0.225498	+	0.183512i
$805$	184.919	+	343.285i	0.229713	+	0.426442i
$806$	337.042	−	194.591i	0.418166	−	0.241428i
$807$	−354.309	−	435.372i	−0.439045	−	0.539494i
$808$	133.497			0.165219
$809$	−364.210	+	210.277i	−0.450198	+	0.259922i	−0.707914	−	0.706299i	$-0.750364\pi$
$809$	−364.210	+	210.277i	−0.450198	+	0.259922i	0.257716	+	0.966221i	$0.417030\pi$
$810$	−1325.44	−	574.782i	−1.63634	−	0.709608i
$811$	1318.39			1.62564			0.812819	−	0.582517i	$-0.197932\pi$
$811$	1318.39			1.62564			0.812819	+	0.582517i	$0.197932\pi$
$812$	−1754.12	−	1082.93i	−2.16024	−	1.33366i
$813$	−606.342	−	231.067i	−0.745808	−	0.284216i
$814$	−1778.45			−2.18483
$815$	−1066.87	−	615.960i	−1.30905	−	0.755780i
$816$	12.6590	−	33.2183i	0.0155134	−	0.0407087i
$817$	26.2895	+	45.5347i	0.0321781	+	0.0557341i
$818$			1206.91i			1.47544i
$819$	59.5545	−	249.754i	0.0727161	−	0.304950i
$820$	1135.93			1.38528
$821$	668.380	−	385.889i	0.814104	−	0.470023i	−0.0342747	−	0.999412i	$-0.510912\pi$
$821$	668.380	−	385.889i	0.814104	−	0.470023i	0.848379	+	0.529389i	$0.177579\pi$
$822$	−278.174	+	226.380i	−0.338411	+	0.275401i
$823$	−453.227	+	785.013i	−0.550702	+	0.953843i	0.447522	+	0.894273i	$0.352306\pi$
$823$	−453.227	+	785.013i	−0.550702	+	0.953843i	−0.998224	+	0.0595705i	$0.981027\pi$
$824$		−	212.759i		−	0.258202i
$825$	−294.104	+	47.3128i	−0.356489	+	0.0573489i
$826$	−1017.22	−	1888.38i	−1.23150	−	2.28617i
$827$		−	509.463i		−	0.616038i	−0.951380	−	0.308019i	$-0.900334\pi$
$827$		−	509.463i		−	0.616038i	0.951380	−	0.308019i	$-0.0996660\pi$
$828$	567.032	+	117.655i	0.684822	+	0.142095i
$829$	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	$0.701931\pi$
$830$		−	282.002i		−	0.339762i
$831$	−37.2249	−	231.396i	−0.0447953	−	0.278454i
$832$	211.873	+	366.974i	0.254655	+	0.441075i
$833$	−47.8119	+	809.654i	−0.0573973	+	0.971974i
$834$	−485.817	+	1274.83i	−0.582514	+	1.52857i
$835$	200.572	+	347.402i	0.240207	+	0.416050i
$836$	−767.790	+	443.284i	−0.918409	+	0.530244i
$837$	−799.021	−	36.0479i	−0.954625	−	0.0430679i
$838$	−651.985	+	1129.27i	−0.778025	+	1.34758i
$839$	1237.78	+	714.635i	1.47531	+	0.851770i	0.999612	−	0.0278396i	$-0.00886276\pi$
$839$	1237.78	+	714.635i	1.47531	+	0.851770i	0.475696	+	0.879610i	$0.342196\pi$
$840$	−711.083	+	544.632i	−0.846528	+	0.648372i
$841$	641.052	+	1110.33i	0.762250	+	1.32026i
$842$		−	1489.30i		−	1.76876i
$843$	−474.989	+	1246.42i	−0.563451	+	1.47855i
$844$	698.082			0.827111
$845$	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
$849$	−360.017	−	137.197i	−0.424048	−	0.161598i
$850$	149.761	−	259.393i	0.176189	−	0.305168i
$851$	−271.935	−	157.002i	−0.319547	−	0.184491i
$852$	−136.655	+	358.594i	−0.160393	+	0.420885i
$853$	485.171	−	840.341i	0.568782	−	0.985159i	−0.427905	−	0.903824i	$-0.640748\pi$
$853$	485.171	−	840.341i	0.568782	−	0.985159i	0.996687	−	0.0813353i	$-0.0259185\pi$
$854$	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
$857$		−	1510.42i		−	1.76245i	−0.472700	−	0.881223i	$-0.656721\pi$
$857$		−	1510.42i		−	1.76245i	0.472700	−	0.881223i	$-0.343279\pi$
$858$	−651.462	−	248.262i	−0.759279	−	0.289349i
$859$	−1228.38			−1.43001			−0.715007	−	0.699118i	$-0.753576\pi$
$859$	−1228.38			−1.43001			−0.715007	+	0.699118i	$0.753576\pi$
$860$	205.339	−	118.552i	0.238766	−	0.137852i
$861$	258.695	−	622.983i	0.300459	−	0.723557i
$862$	367.683	−	636.845i	0.426546	−	0.738800i
$863$	−1292.69	−	746.335i	−1.49790	−	0.864815i	−0.497906	−	0.867231i	$-0.665898\pi$
$863$	−1292.69	−	746.335i	−1.49790	−	0.864815i	−0.999997	+	0.00241587i	$0.999231\pi$
$864$	40.3302	−	893.941i	0.0466785	−	1.03465i
$865$	−584.205	−	1011.87i	−0.675382	−	1.16980i
$866$	−2170.89	+	1253.36i	−2.50680	+	1.44730i
$867$	42.1058	+	16.0459i	0.0485650	+	0.0185073i
$868$	−696.228	+	1127.74i	−0.802106	+	1.29924i
$869$	2127.48	−	1228.30i	2.44820	−	1.41347i
$870$	2434.17	−	391.589i	2.79790	−	0.450102i
$871$	49.6841			0.0570425
$872$	227.951	−	131.608i	0.261412	−	0.150926i
$873$	−314.934	+	1517.81i	−0.360749	+	1.73861i
$874$	−254.497			−0.291187
$875$	−661.045	+	356.088i	−0.755480	+	0.406958i
$876$	70.0031	+	435.149i	0.0799122	+	0.496746i
$877$	−346.948			−0.395608			−0.197804	−	0.980242i	$-0.563381\pi$
$877$	−346.948			−0.395608			−0.197804	+	0.980242i	$0.563381\pi$
$878$	192.071	+	110.892i	0.218760	+	0.126301i
$879$	93.2586	+	114.595i	0.106096	+	0.130370i
$880$	−35.0319	−	60.6770i	−0.0398090	−	0.0689512i
$881$			738.403i			0.838142i	0.907953	+	0.419071i	$0.137644\pi$
$881$			738.403i			0.838142i	−0.907953	+	0.419071i	$0.862356\pi$
$882$	365.499	+	1373.80i	0.414398	+	1.55760i
$883$	872.215			0.987786			0.493893	−	0.869523i	$-0.335573\pi$
$883$	872.215			0.987786			0.493893	+	0.869523i	$0.335573\pi$
$884$	373.392	−	215.578i	0.422389	−	0.243866i
$885$	1474.38	+	561.864i	1.66597	+	0.634874i
$886$	335.783	−	581.593i	0.378987	−	0.656426i
$887$		−	633.281i		−	0.713958i	−0.934112	−	0.356979i	$-0.883807\pi$
$887$		−	633.281i		−	0.713958i	0.934112	−	0.356979i	$-0.116193\pi$
$888$	256.855	−	674.013i	0.289252	−	0.759023i
$889$	46.7225	+	86.7359i	0.0525562	+	0.0975657i
$890$		−	966.821i		−	1.08632i
$891$	853.374	+	1150.92i	0.957771	+	1.29172i
$892$	596.753	+	1033.61i	0.669005	+	1.15875i
$893$		−	128.923i		−	0.144371i
$894$	867.973	−	706.363i	0.970887	−	0.790115i
$895$	−222.323	−	385.075i	−0.248406	−	0.430251i
$896$	−1206.73	−	744.993i	−1.34680	−	0.831466i
$897$	−77.6955	−	95.4716i	−0.0866171	−	0.106434i
$898$	417.524	+	723.172i	0.464949	+	0.805314i
$899$	1182.09	−	682.483i	1.31490	−	0.759158i
$900$	65.6019	−	316.166i	0.0728910	−	0.351295i
$901$	311.443	−	539.436i	0.345664	−	0.598708i
$902$	−1586.22	−	915.805i	−1.75856	−	1.01531i
$903$	−18.2546	−	139.614i	−0.0202155	−	0.154611i
$904$	300.084	+	519.761i	0.331951	+	0.574957i
$905$			680.244i			0.751650i
$906$	−917.553	−	1127.48i	−1.01275	−	1.24446i
$907$	1121.71			1.23672			0.618361	−	0.785894i	$-0.287797\pi$
$907$	1121.71			1.23672			0.618361	+	0.785894i	$0.287797\pi$
$908$	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	0.0131931	−	0.999913i	$-0.495800\pi$
$911$	−770.852	−	445.052i	−0.846160	−	0.488531i	−0.859353	+	0.511382i	$0.829134\pi$
$912$	2.67495	+	16.6279i	0.00293306	+	0.0182323i
$913$	−139.838	+	242.207i	−0.153163	+	0.265287i
$914$	445.099	+	256.978i	0.486979	+	0.281158i
$915$	772.883	+	949.713i	0.844681	+	1.03794i
$916$	−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	$-0.0453952\pi$
$920$			429.402i			0.466741i
$921$	184.542	+	1147.14i	0.200371	+	1.24554i
$922$	658.502			0.714211
$923$	70.6391	−	40.7835i	0.0765321	−	0.0441858i
$924$	2354.12	−	307.802i	2.54775	−	0.333119i
$925$	−87.5408	+	151.625i	−0.0946387	+	0.163919i
$926$	2127.85	+	1228.52i	2.29790	+	1.32669i
$927$	235.865	−	77.9040i	0.254439	−	0.0840388i
$928$	763.559	+	1322.52i	0.822800	+	1.42513i
$929$	622.843	−	359.598i	0.670444	−	0.387081i	−0.125801	−	0.992056i	$-0.540150\pi$
$929$	622.843	−	359.598i	0.670444	−	0.387081i	0.796245	+	0.604974i	$0.206817\pi$
$930$	−251.756	−	1564.95i	−0.270706	−	1.68275i
$931$	−172.176	−	343.521i	−0.184937	−	0.368980i
$932$	−1805.12	+	1042.18i	−1.93682	+	1.11822i
$933$	−108.003	+	283.409i	−0.115759	+	0.303761i
$934$	−1719.85			−1.84138
$935$	−1402.95	+	809.994i	−1.50048	+	0.866303i
$936$	188.177	−	211.041i	0.201044	−	0.225471i
$937$	−1522.34			−1.62470			−0.812348	−	0.583172i	$-0.801811\pi$
$937$	−1522.34			−1.62470			−0.812348	+	0.583172i	$0.801811\pi$
$938$	−242.185	+	130.459i	−0.258193	+	0.139082i
$939$	−848.815	+	690.772i	−0.903957	+	0.735646i
$940$	−581.377			−0.618487
$941$	−886.384	−	511.754i	−0.941960	−	0.543841i	−0.0513858	−	0.998679i	$-0.516364\pi$
$941$	−886.384	−	511.754i	−0.941960	−	0.543841i	−0.890574	+	0.454838i	$0.849697\pi$
$942$	2616.66	−	420.946i	2.77778	−	0.446865i
$943$	−161.695	−	280.063i	−0.171468	−	0.296992i
$944$			68.0487i			0.0720855i
$945$	−864.151	−	588.886i	−0.914446	−	0.623159i
$946$	−382.316			−0.404139
$947$	1361.76	−	786.215i	1.43798	−	0.830217i	0.440268	−	0.897866i	$-0.354883\pi$
$947$	1361.76	−	786.215i	1.43798	−	0.830217i	0.997709	+	0.0676499i	$0.0215501\pi$
$948$	422.947	+	2629.10i	0.446146	+	2.77331i
$949$	46.8406	−	81.1303i	0.0493578	−	0.0854903i
$950$			141.902i			0.149371i
$951$	−62.7750	−	77.1374i	−0.0660095	−	0.0811119i
$952$	−469.207	+	760.014i	−0.492864	+	0.798334i
$953$			1342.92i			1.40915i	0.709629	+	0.704576i	$0.248863\pi$
$953$			1342.92i			1.40915i	−0.709629	+	0.704576i	$0.751137\pi$
$954$	221.808	−	1068.99i	0.232503	−	1.12054i
$955$	983.453	+	1703.39i	1.02979	+	1.78366i
$956$			1556.60i			1.62824i
$957$	−2284.85	−	870.719i	−2.38751	−	0.909842i
$958$	−974.348	−	1687.62i	−1.01706	−	1.76161i
$959$	−228.552	+	123.115i	−0.238323	+	0.128379i
$960$	1703.94	−	274.115i	1.77493	−	0.285536i
$961$	41.7250	+	72.2699i	0.0434183	+	0.0752028i
$962$	−354.860	+	204.879i	−0.368877	+	0.212971i
$963$	−1079.52	−	223.992i	−1.12099	−	0.232598i
$964$	90.5672	−	156.867i	0.0939493	−	0.162725i
$965$	190.034	+	109.716i	0.196927	+	0.113696i
$966$	629.413	+	261.366i	0.651567	+	0.270565i
$967$	−867.804	−	1503.08i	−0.897418	−	1.55437i	−0.830783	−	0.556597i	$-0.812107\pi$
$967$	−867.804	−	1503.08i	−0.897418	−	1.55437i	−0.0666355	−	0.997777i	$-0.521226\pi$
$968$		−	1479.23i		−	1.52813i
$969$	384.463	−	61.8491i	0.396763	−	0.0638278i
$970$	−3072.00			−3.16701
$971$	43.8474	+	25.3153i	0.0451569	+	0.0260714i	0.522409	−	0.852695i	$-0.325034\pi$
$971$	43.8474	+	25.3153i	0.0451569	+	0.0260714i	−0.477252	+	0.878767i	$0.658367\pi$
$972$	−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
$975$	−53.2330	+	43.3214i	−0.0545980	+	0.0444322i
$976$	−26.4045	+	45.7340i	−0.0270538	+	0.0468586i
$977$	506.717	+	292.553i	0.518646	+	0.299440i	0.736381	−	0.676568i	$-0.236533\pi$
$977$	506.717	+	292.553i	0.518646	+	0.299440i	−0.217734	+	0.976008i	$0.569867\pi$
$978$	−2125.87	+	341.991i	−2.17369	+	0.349684i
$979$	−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
$983$			968.896i			0.985653i	0.870128	+	0.492826i	$0.164036\pi$
$983$			968.896i			0.985653i	−0.870128	+	0.492826i	$0.835964\pi$
$984$	576.173	−	468.894i	0.585541	−	0.476518i
$985$	−722.793			−0.733800
$986$	2129.18	−	1229.28i	2.15941	−	1.24674i
$987$	−132.402	+	318.847i	−0.134146	+	0.323047i
$988$	−102.133	+	176.900i	−0.103374	+	0.179048i
$989$	−58.4582	−	33.7508i	−0.0591084	−	0.0341262i
$990$	−1889.69	+	2119.30i	−1.90878	+	2.14070i
$991$	−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	$0.866945\pi$
$992$	850.263	−	490.900i	0.857120	−	0.494859i
$993$	210.598	−	171.386i	0.212083	−	0.172594i
$994$	−237.242	+	384.281i	−0.238674	+	0.386601i
$995$	−1039.99	+	600.439i	−1.04522	+	0.603457i
$996$	−191.357	−	235.138i	−0.192126	−	0.236082i
$997$	152.170			0.152628			0.0763140	−	0.997084i	$-0.475685\pi$
$997$	152.170			0.152628			0.0763140	+	0.997084i	$0.475685\pi$
$998$	341.392	−	197.103i	0.342077	−	0.197498i
$999$	841.262	+	37.9536i	0.842105	+	0.0379916i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.n.b.2.2	yes	22
3.2	odd	2		189.3.n.b.170.10		22
7.2	even	3		441.3.r.g.344.10		22
7.3	odd	6		441.3.j.f.263.2		22
7.4	even	3		63.3.j.b.11.2	✓	22
7.5	odd	6		441.3.r.f.344.10		22
7.6	odd	2		441.3.n.f.128.2		22
9.4	even	3		189.3.j.b.44.2		22
9.5	odd	6		63.3.j.b.23.10	yes	22
21.11	odd	6		189.3.j.b.116.10		22
63.4	even	3		189.3.n.b.179.10		22
63.5	even	6		441.3.r.f.50.10		22
63.23	odd	6		441.3.r.g.50.10		22
63.32	odd	6	inner	63.3.n.b.32.2	yes	22
63.41	even	6		441.3.j.f.275.10		22
63.59	even	6		441.3.n.f.410.2		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.2	✓	22	7.4	even	3
63.3.j.b.23.10	yes	22	9.5	odd	6
63.3.n.b.2.2	yes	22	1.1	even	1	trivial
63.3.n.b.32.2	yes	22	63.32	odd	6	inner
189.3.j.b.44.2		22	9.4	even	3
189.3.j.b.116.10		22	21.11	odd	6
189.3.n.b.170.10		22	3.2	odd	2
189.3.n.b.179.10		22	63.4	even	3
441.3.j.f.263.2		22	7.3	odd	6
441.3.j.f.275.10		22	63.41	even	6
441.3.n.f.128.2		22	7.6	odd	2
441.3.n.f.410.2		22	63.59	even	6
441.3.r.f.50.10		22	63.5	even	6
441.3.r.f.344.10		22	7.5	odd	6
441.3.r.g.50.10		22	63.23	odd	6
441.3.r.g.344.10		22	7.2	even	3

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.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.79169 + 1.61178i) q^{2} +(-0.476488 - 2.96192i) q^{3} +(3.19568 - 5.53509i) q^{4} +5.53294i q^{5} +(6.10417 + 7.50076i) q^{6} +(3.31972 + 6.16275i) q^{7} +7.70873i q^{8} +(-8.54592 + 2.82264i) q^{9} +O(q^{10})\)	\(q+(-2.79169 + 1.61178i) q^{2} +(-0.476488 - 2.96192i) q^{3} +(3.19568 - 5.53509i) q^{4} +5.53294i q^{5} +(6.10417 + 7.50076i) q^{6} +(3.31972 + 6.16275i) q^{7} +7.70873i q^{8} +(-8.54592 + 2.82264i) q^{9} +(-8.91790 - 15.4463i) q^{10} +17.6887i q^{11} +(-17.9172 - 6.82795i) q^{12} +(2.03775 + 3.52949i) q^{13} +(-19.2006 - 11.8538i) q^{14} +(16.3881 - 2.63638i) q^{15} +(0.357941 + 0.619972i) q^{16} +(14.3348 - 8.27617i) q^{17} +(19.3081 - 21.6541i) q^{18} +(-3.92096 + 6.79130i) q^{19} +(30.6253 + 17.6815i) q^{20} +(16.6718 - 12.7692i) q^{21} +(-28.5103 - 49.3813i) q^{22} -10.0676i q^{23} +(22.8326 - 3.67312i) q^{24} -5.61347 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} +(-41.5013 + 33.7740i) q^{30} +(-14.8117 + 25.6547i) q^{31} +(-28.7023 - 16.5713i) q^{32} +(52.3925 - 8.42845i) 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} -25.2789i q^{38} +(9.48309 - 7.71741i) q^{39} -42.6520 q^{40} +(27.8184 - 16.0609i) q^{41} +(-25.9612 + 62.5189i) q^{42} +(3.35243 - 5.80658i) q^{43} +(97.9085 + 56.5275i) q^{44} +(-15.6175 - 47.2841i) q^{45} +(16.2267 + 28.1055i) q^{46} +(-14.2377 + 8.22012i) q^{47} +(1.66575 - 1.35560i) q^{48} +(-26.9589 + 40.9172i) q^{49} +(15.6711 - 9.04769i) q^{50} +(-31.3437 - 38.5149i) q^{51} +26.0480 q^{52} +(32.5897 - 18.8157i) q^{53} +(-73.3377 - 46.8710i) q^{54} -97.8706 q^{55} +(-47.5070 + 25.5908i) q^{56} +(21.9836 + 8.37759i) q^{57} +148.533 q^{58} +(82.3206 + 47.5278i) q^{59} +(37.7787 - 99.1348i) q^{60} +(36.8839 + 63.8848i) q^{61} -95.4932i q^{62} +(-45.7652 - 43.2960i) q^{63} +103.974 q^{64} +(-19.5285 + 11.2748i) q^{65} +(-132.679 + 107.975i) q^{66} +(6.09545 - 10.5576i) q^{67} -105.792i q^{68} +(-29.8193 + 4.79707i) q^{69} +(65.5865 - 106.236i) q^{70} -20.0140i q^{71} +(-21.7589 - 65.8782i) q^{72} +(-11.4932 - 19.9068i) q^{73} +100.542i q^{74} +(2.67475 + 16.6266i) q^{75} +(25.0603 + 43.4057i) q^{76} +(-109.011 + 58.7215i) q^{77} +(-14.0351 + 36.8293i) q^{78} +(-69.4400 - 120.274i) q^{79} +(-3.43027 + 1.98047i) q^{80} +(65.0655 - 48.2440i) q^{81} +(-51.7735 + 89.6743i) q^{82} +(13.6928 + 7.90552i) q^{83} +(-17.4010 - 133.086i) q^{84} +(45.7916 + 79.3134i) q^{85} +21.6136i q^{86} +(-49.2246 + 129.170i) q^{87} -136.357 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} +(83.0447 + 31.6470i) q^{93} +(26.4981 - 45.8960i) q^{94} +(-37.5759 - 21.6944i) q^{95} +(-35.4065 + 92.9100i) q^{96} +(86.1189 - 149.162i) q^{97} +(9.31136 - 157.680i) q^{98} +(-49.9287 - 151.166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9}+O(q^{10}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9} + 25 q^{10} - 20 q^{12} - 18 q^{13} - 90 q^{14} + 53 q^{15} + 12 q^{16} + 6 q^{17} - 56 q^{18} + 3 q^{19} - 39 q^{20} - 2 q^{21} - 59 q^{22} + 15 q^{24} - 114 q^{25} - 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 20 q^{30} - 29 q^{31} + 246 q^{32} + 77 q^{33} - 99 q^{34} - 27 q^{35} + 76 q^{36} - 20 q^{37} + 200 q^{39} + 210 q^{40} - 51 q^{41} + 80 q^{42} + 65 q^{43} + 54 q^{44} + 71 q^{45} + 75 q^{46} + 261 q^{47} - 113 q^{48} - 131 q^{49} + 63 q^{50} - 78 q^{51} + 92 q^{52} - 63 q^{53} - 485 q^{54} - 100 q^{55} + 153 q^{56} + 224 q^{57} - 80 q^{58} - 102 q^{59} + 103 q^{60} + 78 q^{61} + 421 q^{63} + 106 q^{64} - 225 q^{65} - 401 q^{66} - 132 q^{67} - 297 q^{69} + 179 q^{70} - 66 q^{72} + q^{73} - 245 q^{75} + 233 q^{76} - 447 q^{77} - 440 q^{78} + 140 q^{79} + 96 q^{80} + 104 q^{81} - 157 q^{82} + 255 q^{83} - 316 q^{84} + 102 q^{85} - 136 q^{87} - 816 q^{88} - 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} + 210 q^{93} + 261 q^{94} + 642 q^{95} + 539 q^{96} + 178 q^{97} + 483 q^{98} - 103 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9 + 25 * q^10 - 20 * q^12 - 18 * q^13 - 90 * q^14 + 53 * q^15 + 12 * q^16 + 6 * q^17 - 56 * q^18 + 3 * q^19 - 39 * q^20 - 2 * q^21 - 59 * q^22 + 15 * q^24 - 114 * q^25 - 3 * q^26 - 97 * q^27 + 34 * q^28 - 63 * q^29 - 20 * q^30 - 29 * q^31 + 246 * q^32 + 77 * q^33 - 99 * q^34 - 27 * q^35 + 76 * q^36 - 20 * q^37 + 200 * q^39 + 210 * q^40 - 51 * q^41 + 80 * q^42 + 65 * q^43 + 54 * q^44 + 71 * q^45 + 75 * q^46 + 261 * q^47 - 113 * q^48 - 131 * q^49 + 63 * q^50 - 78 * q^51 + 92 * q^52 - 63 * q^53 - 485 * q^54 - 100 * q^55 + 153 * q^56 + 224 * q^57 - 80 * q^58 - 102 * q^59 + 103 * q^60 + 78 * q^61 + 421 * q^63 + 106 * q^64 - 225 * q^65 - 401 * q^66 - 132 * q^67 - 297 * q^69 + 179 * q^70 - 66 * q^72 + q^73 - 245 * q^75 + 233 * q^76 - 447 * q^77 - 440 * q^78 + 140 * q^79 + 96 * q^80 + 104 * q^81 - 157 * q^82 + 255 * q^83 - 316 * q^84 + 102 * q^85 - 136 * q^87 - 816 * q^88 - 720 * q^89 + 418 * q^90 - 70 * q^91 - 1239 * q^92 + 210 * q^93 + 261 * q^94 + 642 * q^95 + 539 * q^96 + 178 * q^97 + 483 * q^98 - 103 * q^99

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