LMFDB - Embedded newform 63.4.f.c.22.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(22,63)]

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([2, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("63.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.f (of order $3$, 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:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 6 x^{16} - 23 x^{15} - 6 x^{14} + 255 x^{13} - 56 x^{12} - 81 x^{11} + \cdots + 387420489 $ x^18 - 3x^17 + 6x^16 - 23x^15 - 6x^14 + 255x^13 - 56x^12 - 81x^11 + 5832x^10 - 32373x^9 + 52488x^8 - 6561x^7 - 40824x^6 + 1673055x^5 - 354294x^4 - 12223143x^3 + 28697814x^2 - 129140163*x + 387420489
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.3
Root			$-0.0718325 - 2.99914i$ of defining polynomial
Character	$\chi$	$=$	63.22
Dual form			63.4.f.c.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21836 - 2.11026i) q^{2} +(-2.70508 + 4.43650i) q^{3} +(1.03120 - 1.78609i) q^{4} +(2.61762 - 4.53384i) q^{5} +(12.6579 + 0.303171i) q^{6} +(-3.50000 - 6.06218i) q^{7} -24.5192 q^{8} +(-12.3651 - 24.0022i) q^{9} +O(q^{10})$	\(q+(-1.21836 - 2.11026i) q^{2} +(-2.70508 + 4.43650i) q^{3} +(1.03120 - 1.78609i) q^{4} +(2.61762 - 4.53384i) q^{5} +(12.6579 + 0.303171i) q^{6} +(-3.50000 - 6.06218i) q^{7} -24.5192 q^{8} +(-12.3651 - 24.0022i) q^{9} -12.7568 q^{10} +(-30.6689 - 53.1202i) q^{11} +(5.13450 + 9.40642i) q^{12} +(0.911402 - 1.57859i) q^{13} +(-8.52852 + 14.7718i) q^{14} +(13.0335 + 23.8775i) q^{15} +(21.6237 + 37.4533i) q^{16} -76.2501 q^{17} +(-35.5858 + 55.3369i) q^{18} +75.2316 q^{19} +(-5.39856 - 9.35058i) q^{20} +(36.3626 + 0.870923i) q^{21} +(-74.7316 + 129.439i) q^{22} +(65.7482 - 113.879i) q^{23} +(66.3265 - 108.780i) q^{24} +(48.7962 + 84.5175i) q^{25} -4.44166 q^{26} +(139.934 + 10.0701i) q^{27} -14.4368 q^{28} +(32.0266 + 55.4716i) q^{29} +(34.5082 - 56.5955i) q^{30} +(88.7151 - 153.659i) q^{31} +(-45.3861 + 78.6110i) q^{32} +(318.630 + 7.63151i) q^{33} +(92.9001 + 160.908i) q^{34} -36.6466 q^{35} +(-55.6208 - 2.66588i) q^{36} -337.434 q^{37} +(-91.6591 - 158.758i) q^{38} +(4.53802 + 8.31366i) q^{39} +(-64.1820 + 111.166i) q^{40} +(-22.8101 + 39.5083i) q^{41} +(-42.4649 - 77.7958i) q^{42} +(146.657 + 254.018i) q^{43} -126.503 q^{44} +(-141.189 - 6.76714i) q^{45} -320.420 q^{46} +(163.082 + 282.467i) q^{47} +(-224.655 - 5.38073i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(118.903 - 205.945i) q^{50} +(206.263 - 338.284i) q^{51} +(-1.87967 - 3.25568i) q^{52} -66.4388 q^{53} +(-149.240 - 307.567i) q^{54} -321.118 q^{55} +(85.8173 + 148.640i) q^{56} +(-203.507 + 333.765i) q^{57} +(78.0397 - 135.169i) q^{58} +(344.978 - 597.519i) q^{59} +(56.0874 + 1.34335i) q^{60} +(-336.245 - 582.394i) q^{61} -432.348 q^{62} +(-102.228 + 158.967i) q^{63} +567.165 q^{64} +(-4.77140 - 8.26430i) q^{65} +(-372.101 - 681.690i) q^{66} +(288.573 - 499.823i) q^{67} +(-78.6289 + 136.189i) q^{68} +(327.371 + 599.744i) q^{69} +(44.6488 + 77.3340i) q^{70} -4.08120 q^{71} +(303.182 + 588.515i) q^{72} +747.346 q^{73} +(411.116 + 712.074i) q^{74} +(-506.959 - 12.1422i) q^{75} +(77.5786 - 134.370i) q^{76} +(-214.683 + 371.841i) q^{77} +(12.0150 - 19.7054i) q^{78} +(-531.622 - 920.796i) q^{79} +226.410 q^{80} +(-423.209 + 593.578i) q^{81} +111.164 q^{82} +(415.955 + 720.455i) q^{83} +(39.0526 - 64.0487i) q^{84} +(-199.594 + 345.706i) q^{85} +(357.363 - 618.971i) q^{86} +(-332.734 - 7.96933i) q^{87} +(751.979 + 1302.47i) q^{88} -460.391 q^{89} +(157.739 + 306.191i) q^{90} -12.7596 q^{91} +(-135.599 - 234.864i) q^{92} +(441.727 + 809.244i) q^{93} +(397.386 - 688.292i) q^{94} +(196.927 - 341.088i) q^{95} +(-225.985 - 414.005i) q^{96} +(-431.419 - 747.240i) q^{97} +119.399 q^{98} +(-895.776 + 1392.96i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9}+O(q^{10}) $ 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9} + 111 q^{11} - 18 q^{13} + 42 q^{14} - 36 q^{15} - 144 q^{16} - 546 q^{17} - 45 q^{18} + 90 q^{19} + 402 q^{20} - 63 q^{21} + 162 q^{22} + 312 q^{23} - 36 q^{24} - 279 q^{25} + 102 q^{26} + 432 q^{27} + 504 q^{28} + 378 q^{29} - 864 q^{30} - 18 q^{31} + 891 q^{32} + 513 q^{33} + 324 q^{34} - 336 q^{35} + 414 q^{36} - 72 q^{37} + 147 q^{38} - 810 q^{39} - 405 q^{40} + 477 q^{41} + 315 q^{42} + 171 q^{43} - 1896 q^{44} - 720 q^{45} - 756 q^{46} + 654 q^{47} - 2709 q^{48} - 441 q^{49} + 429 q^{50} + 1341 q^{51} - 747 q^{52} - 1896 q^{53} - 108 q^{54} - 432 q^{55} + 525 q^{56} - 1143 q^{57} - 297 q^{58} + 957 q^{59} + 5400 q^{60} + 198 q^{61} - 600 q^{62} - 504 q^{63} + 4770 q^{64} + 2478 q^{65} - 2646 q^{66} + 333 q^{67} + 1443 q^{68} + 3366 q^{69} - 5652 q^{71} - 3681 q^{72} + 306 q^{73} + 2100 q^{74} - 4113 q^{75} + 144 q^{76} + 777 q^{77} + 6336 q^{78} - 1152 q^{79} - 8418 q^{80} - 1917 q^{81} - 6048 q^{82} + 1890 q^{83} + 1008 q^{84} + 648 q^{85} + 3837 q^{86} + 4212 q^{87} + 2268 q^{88} - 2604 q^{89} - 135 q^{90} + 252 q^{91} + 987 q^{92} + 378 q^{93} - 324 q^{94} + 3144 q^{95} + 5643 q^{96} + 1737 q^{97} - 588 q^{98} + 720 q^{99}+O(q^{100}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9 + 111 * q^11 - 18 * q^13 + 42 * q^14 - 36 * q^15 - 144 * q^16 - 546 * q^17 - 45 * q^18 + 90 * q^19 + 402 * q^20 - 63 * q^21 + 162 * q^22 + 312 * q^23 - 36 * q^24 - 279 * q^25 + 102 * q^26 + 432 * q^27 + 504 * q^28 + 378 * q^29 - 864 * q^30 - 18 * q^31 + 891 * q^32 + 513 * q^33 + 324 * q^34 - 336 * q^35 + 414 * q^36 - 72 * q^37 + 147 * q^38 - 810 * q^39 - 405 * q^40 + 477 * q^41 + 315 * q^42 + 171 * q^43 - 1896 * q^44 - 720 * q^45 - 756 * q^46 + 654 * q^47 - 2709 * q^48 - 441 * q^49 + 429 * q^50 + 1341 * q^51 - 747 * q^52 - 1896 * q^53 - 108 * q^54 - 432 * q^55 + 525 * q^56 - 1143 * q^57 - 297 * q^58 + 957 * q^59 + 5400 * q^60 + 198 * q^61 - 600 * q^62 - 504 * q^63 + 4770 * q^64 + 2478 * q^65 - 2646 * q^66 + 333 * q^67 + 1443 * q^68 + 3366 * q^69 - 5652 * q^71 - 3681 * q^72 + 306 * q^73 + 2100 * q^74 - 4113 * q^75 + 144 * q^76 + 777 * q^77 + 6336 * q^78 - 1152 * q^79 - 8418 * q^80 - 1917 * q^81 - 6048 * q^82 + 1890 * q^83 + 1008 * q^84 + 648 * q^85 + 3837 * q^86 + 4212 * q^87 + 2268 * q^88 - 2604 * q^89 - 135 * q^90 + 252 * q^91 + 987 * q^92 + 378 * q^93 - 324 * q^94 + 3144 * q^95 + 5643 * q^96 + 1737 * q^97 - 588 * q^98 + 720 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.21836	−	2.11026i	−0.430755	−	0.746090i	0.566183	−	0.824279i	$-0.308419\pi$
$2$	−1.21836	−	2.11026i	−0.430755	−	0.746090i	−0.996939	+	0.0781893i	$0.975086\pi$
$3$	−2.70508	+	4.43650i	−0.520593	+	0.853805i
$3$	−2.70508	+	4.43650i	−0.520593	+	0.853805i
$4$	1.03120	−	1.78609i	0.128900	−	0.223261i
$5$	2.61762	−	4.53384i	0.234127	−	0.405519i	−0.724892	−	0.688863i	$-0.758110\pi$
$5$	2.61762	−	4.53384i	0.234127	−	0.405519i	0.959019	+	0.283343i	$0.0914436\pi$
$6$	12.6579	+	0.303171i	0.861264	+	0.0206282i
$7$	−3.50000	−	6.06218i	−0.188982	−	0.327327i
$7$	−3.50000	−	6.06218i	−0.188982	−	0.327327i
$8$	−24.5192			−1.08361
$9$	−12.3651	−	24.0022i	−0.457966	−	0.888970i
$10$	−12.7568			−0.403405
$11$	−30.6689	−	53.1202i	−0.840639	−	1.45603i	−0.889355	−	0.457218i	$-0.848846\pi$
$11$	−30.6689	−	53.1202i	−0.840639	−	1.45603i	0.0487154	−	0.998813i	$-0.484487\pi$
$12$	5.13450	+	9.40642i	0.123517	+	0.226283i
$13$	0.911402	−	1.57859i	0.0194444	−	0.0336787i	−0.856139	−	0.516745i	$-0.827144\pi$
$13$	0.911402	−	1.57859i	0.0194444	−	0.0336787i	0.875584	+	0.483066i	$0.160477\pi$
$14$	−8.52852	+	14.7718i	−0.162810	+	0.281996i
$15$	13.0335	+	23.8775i	0.224350	+	0.411009i
$16$	21.6237	+	37.4533i	0.337870	+	0.585208i
$17$	−76.2501			−1.08785			−0.543923	−	0.839135i	$-0.683061\pi$
$17$	−76.2501			−1.08785			−0.543923	+	0.839135i	$0.683061\pi$
$18$	−35.5858	+	55.3369i	−0.465980	+	0.724612i
$19$	75.2316			0.908384			0.454192	−	0.890904i	$-0.349928\pi$
$19$	75.2316			0.908384			0.454192	+	0.890904i	$0.349928\pi$
$20$	−5.39856	−	9.35058i	−0.0603577	−	0.104543i
$21$	36.3626	+	0.870923i	0.377856	+	0.00905005i
$22$	−74.7316	+	129.439i	−0.724220	+	1.25439i
$23$	65.7482	−	113.879i	0.596063	−	1.03241i	−0.397333	−	0.917674i	$-0.630064\pi$
$23$	65.7482	−	113.879i	0.596063	−	1.03241i	0.993396	−	0.114737i	$-0.0366024\pi$
$24$	66.3265	−	108.780i	0.564118	−	0.925190i
$25$	48.7962	+	84.5175i	0.390369	+	0.676140i
$26$	−4.44166			−0.0335031
$27$	139.934	+	10.0701i	0.997421	+	0.0717776i
$28$	−14.4368			−0.0974390
$29$	32.0266	+	55.4716i	0.205075	+	0.355201i	0.950157	−	0.311773i	$-0.100923\pi$
$29$	32.0266	+	55.4716i	0.205075	+	0.355201i	−0.745081	+	0.666973i	$0.767589\pi$
$30$	34.5082	−	56.5955i	0.210010	−	0.344429i
$31$	88.7151	−	153.659i	0.513990	−	0.890257i	−0.485878	−	0.874027i	$-0.661500\pi$
$31$	88.7151	−	153.659i	0.513990	−	0.890257i	0.999868	−	0.0162305i	$-0.00516657\pi$
$32$	−45.3861	+	78.6110i	−0.250725	+	0.434269i
$33$	318.630	+	7.63151i	1.68080	+	0.0402568i
$34$	92.9001	+	160.908i	0.468595	+	0.811631i
$35$	−36.6466			−0.176983
$36$	−55.6208	−	2.66588i	−0.257504	−	0.0123420i
$37$	−337.434			−1.49929			−0.749646	−	0.661839i	$-0.769776\pi$
$37$	−337.434			−1.49929			−0.749646	+	0.661839i	$0.769776\pi$
$38$	−91.6591	−	158.758i	−0.391291	−	0.677737i
$39$	4.53802	+	8.31366i	0.0186324	+	0.0341346i
$40$	−64.1820	+	111.166i	−0.253701	+	0.439424i
$41$	−22.8101	+	39.5083i	−0.0868864	+	0.150492i	−0.906194	−	0.422863i	$-0.861025\pi$
$41$	−22.8101	+	39.5083i	−0.0868864	+	0.150492i	0.819307	+	0.573355i	$0.194358\pi$
$42$	−42.4649	−	77.7958i	−0.156011	−	0.285813i
$43$	146.657	+	254.018i	0.520117	+	0.900870i	0.999726	+	0.0233875i	$0.00744516\pi$
$43$	146.657	+	254.018i	0.520117	+	0.900870i	−0.479609	+	0.877482i	$0.659222\pi$
$44$	−126.503			−0.433433
$45$	−141.189	−	6.76714i	−0.467716	−	0.0224175i
$46$	−320.420			−1.02703
$47$	163.082	+	282.467i	0.506128	+	0.876639i	0.999975	+	0.00708997i	$0.00225683\pi$
$47$	163.082	+	282.467i	0.506128	+	0.876639i	−0.493847	+	0.869549i	$0.664410\pi$
$48$	−224.655	−	5.38073i	−0.675546	−	0.0161800i
$49$	−24.5000	+	42.4352i	−0.0714286	+	0.123718i
$50$	118.903	−	205.945i	0.336307	−	0.582501i
$51$	206.263	−	338.284i	0.566324	−	0.928808i
$52$	−1.87967	−	3.25568i	−0.00501276	−	0.00868235i
$53$	−66.4388			−0.172190			−0.0860950	−	0.996287i	$-0.527439\pi$
$53$	−66.4388			−0.172190			−0.0860950	+	0.996287i	$0.527439\pi$
$54$	−149.240	−	307.567i	−0.376092	−	0.775084i
$55$	−321.118			−0.787265
$56$	85.8173	+	148.640i	0.204783	+	0.354694i
$57$	−203.507	+	333.765i	−0.472898	+	0.775583i
$58$	78.0397	−	135.169i	0.176674	−	0.306009i
$59$	344.978	−	597.519i	0.761225	−	1.31848i	−0.180994	−	0.983484i	$-0.557932\pi$
$59$	344.978	−	597.519i	0.761225	−	1.31848i	0.942219	−	0.334996i	$-0.108735\pi$
$60$	56.0874	+	1.34335i	0.120681	+	0.00289043i
$61$	−336.245	−	582.394i	−0.705767	−	1.22242i	−0.966414	−	0.256990i	$-0.917269\pi$
$61$	−336.245	−	582.394i	−0.705767	−	1.22242i	0.260647	−	0.965434i	$-0.416064\pi$
$62$	−432.348			−0.885616
$63$	−102.228	+	158.967i	−0.204436	+	0.317904i
$64$	567.165			1.10774
$65$	−4.77140	−	8.26430i	−0.00910491	−	0.0157702i
$66$	−372.101	−	681.690i	−0.693977	−	1.27137i
$67$	288.573	−	499.823i	0.526191	−	0.911389i	−0.473344	−	0.880878i	$-0.656953\pi$
$67$	288.573	−	499.823i	0.526191	−	0.911389i	0.999534	−	0.0305114i	$-0.00971360\pi$
$68$	−78.6289	+	136.189i	−0.140223	+	0.242873i
$69$	327.371	+	599.744i	0.571172	+	1.04639i
$70$	44.6488	+	77.3340i	0.0762364	+	0.132045i
$71$	−4.08120			−0.00682183			−0.00341091	−	0.999994i	$-0.501086\pi$
$71$	−4.08120			−0.00682183			−0.00341091	+	0.999994i	$0.501086\pi$
$72$	303.182	+	588.515i	0.496255	+	0.963294i
$73$	747.346			1.19822			0.599112	−	0.800666i	$-0.295521\pi$
$73$	747.346			1.19822			0.599112	+	0.800666i	$0.295521\pi$
$74$	411.116	+	712.074i	0.645828	+	1.11861i
$75$	−506.959	−	12.1422i	−0.780515	−	0.0186941i
$76$	77.5786	−	134.370i	0.117090	−	0.202807i
$77$	−214.683	+	371.841i	−0.317732	+	0.550328i
$78$	12.0150	−	19.7054i	0.0174415	−	0.0286051i
$79$	−531.622	−	920.796i	−0.757115	−	1.31136i	−0.944316	−	0.329040i	$-0.893275\pi$
$79$	−531.622	−	920.796i	−0.757115	−	1.31136i	0.187201	−	0.982322i	$-0.440059\pi$
$80$	226.410			0.316418
$81$	−423.209	+	593.578i	−0.580534	+	0.814236i
$82$	111.164			0.149707
$83$	415.955	+	720.455i	0.550084	+	0.952774i	0.998268	+	0.0588326i	$0.0187378\pi$
$83$	415.955	+	720.455i	0.550084	+	0.952774i	−0.448183	+	0.893942i	$0.647929\pi$
$84$	39.0526	−	64.0487i	0.0507261	−	0.0831939i
$85$	−199.594	+	345.706i	−0.254694	+	0.441142i
$86$	357.363	−	618.971i	0.448087	−	0.776109i
$87$	−332.734	−	7.96933i	−0.410033	−	0.00982072i
$88$	751.979	+	1302.47i	0.910923	+	1.57777i
$89$	−460.391			−0.548329			−0.274165	−	0.961683i	$-0.588401\pi$
$89$	−460.391			−0.548329			−0.274165	+	0.961683i	$0.588401\pi$
$90$	157.739	+	306.191i	0.184746	+	0.358615i
$91$	−12.7596			−0.0146986
$92$	−135.599	−	234.864i	−0.153665	−	0.266155i
$93$	441.727	+	809.244i	0.492526	+	0.902309i
$94$	397.386	−	688.292i	0.436034	−	0.755233i
$95$	196.927	−	341.088i	0.212677	−	0.368367i
$96$	−225.985	−	414.005i	−0.240255	−	0.440148i
$97$	−431.419	−	747.240i	−0.451587	−	0.782172i	0.546897	−	0.837200i	$-0.315809\pi$
$97$	−431.419	−	747.240i	−0.451587	−	0.782172i	−0.998485	+	0.0550273i	$0.982475\pi$
$98$	119.399			0.123073
$99$	−895.776	+	1392.96i	−0.909382	+	1.41412i
$100$	201.274			0.201274
$101$	235.461	+	407.831i	0.231973	+	0.401789i	0.958389	−	0.285467i	$-0.0921485\pi$
$101$	235.461	+	407.831i	0.231973	+	0.401789i	−0.726416	+	0.687256i	$0.758815\pi$
$102$	−965.169	−	23.1168i	−0.936922	−	0.0224402i
$103$	418.304	−	724.524i	0.400162	−	0.693102i	−0.593583	−	0.804773i	$-0.702287\pi$
$103$	418.304	−	724.524i	0.400162	−	0.693102i	0.993745	+	0.111671i	$0.0356204\pi$
$104$	−22.3469	+	38.7059i	−0.0210701	+	0.0364945i
$105$	99.1321	−	162.583i	0.0921362	−	0.151109i
$106$	80.9464	+	140.203i	0.0741717	+	0.128469i
$107$	−72.6976			−0.0656817			−0.0328409	−	0.999461i	$-0.510455\pi$
$107$	−72.6976			−0.0656817			−0.0328409	+	0.999461i	$0.510455\pi$
$108$	162.286	−	239.550i	0.144592	−	0.213433i
$109$	546.680			0.480389			0.240195	−	0.970725i	$-0.422789\pi$
$109$	546.680			0.480389			0.240195	+	0.970725i	$0.422789\pi$
$110$	391.237	+	677.643i	0.339118	+	0.587370i
$111$	912.786	−	1497.03i	0.780521	−	1.28010i
$112$	151.366	−	262.173i	0.127703	−	0.221188i
$113$	766.977	−	1328.44i	0.638506	−	1.10592i	−0.347255	−	0.937771i	$-0.612886\pi$
$113$	766.977	−	1328.44i	0.638506	−	1.10592i	0.985761	−	0.168153i	$-0.0537804\pi$
$114$	952.276	+	22.8080i	0.782358	+	0.0187383i
$115$	−344.207	−	596.184i	−0.279108	−	0.483430i
$116$	132.103			0.105737
$117$	−49.1593	−	2.35618i	−0.0388442	−	0.00186179i
$118$	−1681.23			−1.31161
$119$	266.875	+	462.242i	0.205583	+	0.356081i
$120$	−319.573	−	585.457i	−0.243107	−	0.445372i
$121$	−1215.67	+	2105.60i	−0.913349	+	1.58197i
$122$	−819.335	+	1419.13i	−0.608026	+	1.05313i
$123$	−113.575	−	208.070i	−0.0832581	−	0.152529i
$124$	−182.966	−	316.906i	−0.132506	−	0.229508i
$125$	1165.32			0.833837
$126$	460.012	+	22.0482i	0.325247	+	0.0155890i
$127$	−466.368			−0.325854			−0.162927	−	0.986638i	$-0.552093\pi$
$127$	−466.368			−0.325854			−0.162927	+	0.986638i	$0.552093\pi$
$128$	−327.923	−	567.979i	−0.226442	−	0.392209i
$129$	−1523.67	−	36.4935i	−1.03994	−	0.0249076i
$130$	−11.6266	+	20.1378i	−0.00784398	+	0.0135862i
$131$	−303.754	+	526.118i	−0.202589	+	0.350894i	−0.949362	−	0.314185i	$-0.898269\pi$
$131$	−303.754	+	526.118i	−0.202589	+	0.350894i	0.746773	+	0.665079i	$0.231602\pi$
$132$	342.201	−	561.231i	0.225642	−	0.370067i
$133$	−263.310	−	456.067i	−0.171669	−	0.297339i
$134$	−1406.34			−0.906638
$135$	411.950	−	608.080i	0.262630	−	0.387668i
$136$	1869.59			1.17880
$137$	−237.673	−	411.661i	−0.148217	−	0.256720i	0.782351	−	0.622837i	$-0.214020\pi$
$137$	−237.673	−	411.661i	−0.148217	−	0.256720i	−0.930569	+	0.366118i	$0.880687\pi$
$138$	866.761	−	1421.54i	0.534664	−	0.876883i
$139$	−887.566	+	1537.31i	−0.541600	+	0.938078i	0.457213	+	0.889357i	$0.348848\pi$
$139$	−887.566	+	1537.31i	−0.541600	+	0.938078i	−0.998812	+	0.0487206i	$0.984486\pi$
$140$	−37.7899	+	65.4540i	−0.0228131	+	0.0395134i
$141$	−1694.31	−	40.5806i	−1.01196	−	0.0242376i
$142$	4.97238	+	8.61241i	0.00293854	+	0.00508970i
$143$	−111.807			−0.0653830
$144$	631.583	−	982.129i	0.365499	−	0.568362i
$145$	335.333			0.192054
$146$	−910.537	−	1577.10i	−0.516141	−	0.893982i
$147$	−121.990	−	223.485i	−0.0684458	−	0.125393i
$148$	−347.961	+	602.686i	−0.193258	+	0.334733i
$149$	1166.53	−	2020.49i	0.641383	−	1.11091i	−0.343742	−	0.939064i	$-0.611694\pi$
$149$	1166.53	−	2020.49i	0.641383	−	1.11091i	0.985124	−	0.171843i	$-0.0549722\pi$
$150$	592.036	+	1084.61i	0.322263	+	0.590387i
$151$	−786.732	−	1362.66i	−0.423995	−	0.734382i	0.572331	−	0.820023i	$-0.306039\pi$
$151$	−786.732	−	1362.66i	−0.423995	−	0.734382i	−0.996326	+	0.0856413i	$0.972706\pi$
$152$	−1844.62			−0.984332
$153$	942.839	+	1830.17i	0.498196	+	0.967061i
$154$	1046.24			0.547459
$155$	−464.444	−	804.440i	−0.240678	−	0.416866i
$156$	19.5285	+	0.467728i	0.0100226	+	0.000240053i
$157$	−1433.08	+	2482.17i	−0.728487	+	1.26178i	0.229036	+	0.973418i	$0.426443\pi$
$157$	−1433.08	+	2482.17i	−0.728487	+	1.26178i	−0.957523	+	0.288358i	$0.906891\pi$
$158$	−1295.41	+	2243.72i	−0.652263	+	1.12975i
$159$	179.722	−	294.756i	0.0896409	−	0.147017i
$160$	237.607	+	411.547i	0.117403	+	0.203348i
$161$	−920.475			−0.450581
$162$	1768.23	+	169.891i	0.857562	+	0.0823944i
$163$	−3070.11			−1.47527			−0.737637	−	0.675198i	$-0.764058\pi$
$163$	−3070.11			−1.47527			−0.737637	+	0.675198i	$0.764058\pi$
$164$	47.0435	+	81.4817i	0.0223993	+	0.0387967i
$165$	868.650	−	1424.64i	0.409844	−	0.672170i
$166$	1013.57	−	1755.55i	0.473904	−	0.820825i
$167$	712.701	−	1234.43i	0.330242	−	0.571997i	−0.652317	−	0.757946i	$-0.726203\pi$
$167$	712.701	−	1234.43i	0.330242	−	0.571997i	0.982559	+	0.185950i	$0.0595362\pi$
$168$	−891.584	−	21.3544i	−0.409448	−	0.00980670i
$169$	1096.84	+	1899.78i	0.499244	+	0.864716i
$170$	972.707			0.438842
$171$	−930.244	−	1805.72i	−0.416009	−	0.807526i
$172$	604.931			0.268172
$173$	1668.68	+	2890.23i	0.733336	+	1.27018i	0.955450	+	0.295154i	$0.0953711\pi$
$173$	1668.68	+	2890.23i	0.733336	+	1.27018i	−0.222114	+	0.975021i	$0.571296\pi$
$174$	388.573	+	711.866i	0.169297	+	0.310152i
$175$	341.573	−	591.622i	0.147546	−	0.255557i
$176$	1326.35	−	2297.31i	0.568054	−	0.983898i
$177$	1717.70	+	3146.83i	0.729437	+	1.33633i
$178$	560.922	+	971.545i	0.236196	+	0.409103i
$179$	−1060.27			−0.442726			−0.221363	−	0.975191i	$-0.571051\pi$
$179$	−1060.27			−0.442726			−0.221363	+	0.975191i	$0.571051\pi$
$180$	−157.681	+	245.198i	−0.0652934	+	0.101533i
$181$	531.013			0.218066			0.109033	−	0.994038i	$-0.465225\pi$
$181$	531.013			0.218066			0.109033	+	0.994038i	$0.465225\pi$
$182$	15.5458	+	26.9261i	0.00633150	+	0.0109665i
$183$	3493.36	+	83.6696i	1.41113	+	0.0337980i
$184$	−1612.10	+	2792.23i	−0.645898	+	1.11873i
$185$	−883.273	+	1529.87i	−0.351024	+	0.607992i
$186$	1169.53	−	1918.11i	0.461045	−	0.756143i
$187$	2338.51	+	4050.42i	0.914486	+	1.58394i
$188$	672.680			0.260959
$189$	−428.723	−	883.552i	−0.165000	−	0.340047i
$190$	−959.713			−0.366447
$191$	−1893.32	−	3279.33i	−0.717256	−	1.24232i	−0.962083	−	0.272757i	$-0.912065\pi$
$191$	−1893.32	−	3279.33i	−0.717256	−	1.24232i	0.244827	−	0.969567i	$-0.421269\pi$
$192$	−1534.23	+	2516.23i	−0.576684	+	0.945798i
$193$	1030.23	−	1784.41i	0.384237	−	0.665517i	−0.607426	−	0.794376i	$-0.707798\pi$
$193$	1030.23	−	1784.41i	0.384237	−	0.665517i	0.991663	+	0.128859i	$0.0411314\pi$
$194$	−1051.25	+	1820.81i	−0.389047	+	0.673850i
$195$	49.5716	+	1.18729i	0.0182046	+	0.000436019i
$196$	50.5287	+	87.5182i	0.0184142	+	0.0318944i
$197$	2441.58			0.883022			0.441511	−	0.897256i	$-0.354443\pi$
$197$	2441.58			0.883022			0.441511	+	0.897256i	$0.354443\pi$
$198$	4030.88	+	193.198i	1.44678	+	0.0693435i
$199$	3862.16			1.37579			0.687893	−	0.725812i	$-0.258536\pi$
$199$	3862.16			1.37579			0.687893	+	0.725812i	$0.258536\pi$
$200$	−1196.45	−	2072.30i	−0.423007	−	0.732670i
$201$	1436.85	+	2632.31i	0.504218	+	0.923727i
$202$	573.753	−	993.770i	0.199847	−	0.346146i
$203$	224.186	−	388.301i	0.0775111	−	0.134253i
$204$	−391.506	−	717.240i	−0.134367	−	0.246161i
$205$	119.416	+	206.835i	0.0406849	+	0.0704683i
$206$	−2038.58			−0.689488
$207$	−3546.33	−	169.974i	−1.19076	−	0.0570726i
$208$	78.8314			0.0262787
$209$	−2307.27	−	3996.31i	−0.763624	−	1.32264i
$210$	−463.871	−	11.1102i	−0.152429	−	0.00365084i
$211$	3006.19	−	5206.87i	0.980828	−	1.69884i	0.321645	−	0.946860i	$-0.395764\pi$
$211$	3006.19	−	5206.87i	0.980828	−	1.69884i	0.659182	−	0.751983i	$-0.270903\pi$
$212$	−68.5115	+	118.665i	−0.0221952	+	0.0384433i
$213$	11.0400	−	18.1063i	0.00355140	−	0.00582451i
$214$	88.5719	+	153.411i	0.0282928	+	0.0490045i
$215$	1535.57			0.487093
$216$	−3431.08	−	246.912i	−1.08081	−	0.0777788i
$217$	−1242.01			−0.388540
$218$	−666.053	−	1153.64i	−0.206930	−	0.358414i
$219$	−2021.63	+	3315.60i	−0.623786	+	1.02305i
$220$	−331.136	+	573.545i	−0.101478	+	0.175765i
$221$	−69.4945	+	120.368i	−0.0211525	+	0.0366372i
$222$	−4271.22	−	102.300i	−1.29129	−	0.0309276i
$223$	−402.431	−	697.032i	−0.120847	−	0.209313i	0.799255	−	0.600992i	$-0.205228\pi$
$223$	−402.431	−	697.032i	−0.120847	−	0.209313i	−0.920102	+	0.391679i	$0.871894\pi$
$224$	635.405			0.189530
$225$	1425.23	−	2216.28i	0.422292	−	0.656676i
$226$	−3737.82			−1.10016
$227$	2893.37	+	5011.46i	0.845990	+	1.46530i	0.884759	+	0.466050i	$0.154323\pi$
$227$	2893.37	+	5011.46i	0.845990	+	1.46530i	−0.0387685	+	0.999248i	$0.512343\pi$
$228$	386.277	+	707.659i	0.112201	+	0.205552i
$229$	−1034.85	+	1792.41i	−0.298623	+	0.517230i	−0.975821	−	0.218570i	$-0.929861\pi$
$229$	−1034.85	+	1792.41i	−0.298623	+	0.517230i	0.677198	+	0.735801i	$0.263194\pi$
$230$	−838.736	+	1452.73i	−0.240455	+	0.416480i
$231$	−1068.94	−	1958.30i	−0.304464	−	0.557778i
$232$	−785.267	−	1360.12i	−0.222221	−	0.384898i
$233$	−3387.11			−0.952348			−0.476174	−	0.879351i	$-0.657977\pi$
$233$	−3387.11			−0.952348			−0.476174	+	0.879351i	$0.657977\pi$
$234$	54.9215	+	106.610i	0.0153433	+	0.0297833i
$235$	1707.55			0.473992
$236$	−711.480	−	1232.32i	−0.196243	−	0.339903i
$237$	5523.19	+	132.286i	1.51380	+	0.0362570i
$238$	650.301	−	1126.35i	0.177112	−	0.306768i
$239$	−1550.85	+	2686.16i	−0.419734	+	0.727000i	−0.995912	−	0.0903237i	$-0.971210\pi$
$239$	−1550.85	+	2686.16i	−0.419734	+	0.727000i	0.576179	+	0.817324i	$0.304543\pi$
$240$	−612.457	+	1004.47i	−0.164725	+	0.270159i
$241$	−2732.22	−	4732.35i	−0.730282	−	1.26489i	−0.956763	−	0.290870i	$-0.906055\pi$
$241$	−2732.22	−	4732.35i	−0.730282	−	1.26489i	0.226481	−	0.974016i	$-0.427278\pi$
$242$	5924.49			1.57372
$243$	−1488.59	−	3483.25i	−0.392977	−	0.919548i
$244$	−1386.94			−0.363892
$245$	128.263	+	222.158i	0.0334467	+	0.0579313i
$246$	−300.707	+	493.178i	−0.0779365	+	0.127821i
$247$	68.5662	−	118.760i	0.0176630	−	0.0305932i
$248$	−2175.23	+	3767.60i	−0.556964	+	0.964689i
$249$	−4321.49	−	103.504i	−1.09985	−	0.0263426i
$250$	−1419.78	−	2459.14i	−0.359180	−	0.622117i
$251$	1890.69			0.475454			0.237727	−	0.971332i	$-0.423598\pi$
$251$	1890.69			0.475454			0.237727	+	0.971332i	$0.423598\pi$
$252$	178.512	+	346.514i	0.0446238	+	0.0866203i
$253$	−8065.71			−2.00430
$254$	568.204	+	984.158i	0.140363	+	0.243116i
$255$	−993.809	−	1820.66i	−0.244058	−	0.447114i
$256$	1469.61	−	2545.43i	0.358790	−	0.621443i
$257$	146.402	−	253.576i	0.0355343	−	0.0615472i	−0.847711	−	0.530458i	$-0.822020\pi$
$257$	146.402	−	253.576i	0.0355343	−	0.0615472i	0.883246	+	0.468911i	$0.155353\pi$
$258$	1779.37	+	3259.81i	0.429375	+	0.786616i
$259$	1181.02	+	2045.58i	0.283340	+	0.490758i
$260$	−19.6810			−0.00469448
$261$	935.429	−	1454.62i	0.221845	−	0.344976i
$262$	1480.33			0.349065
$263$	46.8905	+	81.2167i	0.0109939	+	0.0190420i	0.871470	−	0.490449i	$-0.163167\pi$
$263$	46.8905	+	81.2167i	0.0109939	+	0.0190420i	−0.860476	+	0.509491i	$0.829834\pi$
$264$	−7812.56	−	187.119i	−1.82132	−	0.0436226i
$265$	−173.911	+	301.223i	−0.0403143	+	0.0698264i
$266$	−641.614	+	1111.31i	−0.147894	+	0.256160i
$267$	1245.39	−	2042.52i	0.285456	−	0.468166i
$268$	−595.151	−	1030.83i	−0.135652	−	0.234956i
$269$	4956.81			1.12350			0.561751	−	0.827306i	$-0.310128\pi$
$269$	4956.81			1.12350			0.561751	+	0.827306i	$0.310128\pi$
$270$	−1785.11	−	128.462i	−0.402365	−	0.0289555i
$271$	8602.98			1.92839			0.964195	−	0.265195i	$-0.0854362\pi$
$271$	8602.98			1.92839			0.964195	+	0.265195i	$0.0854362\pi$
$272$	−1648.81	−	2855.82i	−0.367550	−	0.636616i
$273$	34.5158	−	56.6081i	0.00765198	−	0.0125497i
$274$	−579.142	+	1003.10i	−0.127691	+	0.221167i
$275$	2993.05	−	5184.12i	0.656320	−	1.13678i
$276$	1408.78	+	33.7417i	0.307241	+	0.00735875i
$277$	1069.42	+	1852.28i	0.231967	+	0.401779i	0.958387	−	0.285472i	$-0.0921504\pi$
$277$	1069.42	+	1852.28i	0.231967	+	0.401779i	−0.726420	+	0.687251i	$0.758817\pi$
$278$	4325.50			0.933188
$279$	−4785.12	−	229.349i	−1.02680	−	0.0492142i
$280$	898.547			0.191780
$281$	4011.86	+	6948.74i	0.851699	+	1.47519i	0.879674	+	0.475577i	$0.157761\pi$
$281$	4011.86	+	6948.74i	0.851699	+	1.47519i	−0.0279748	+	0.999609i	$0.508906\pi$
$282$	1978.65	+	3624.89i	0.417826	+	0.765457i
$283$	−274.059	+	474.684i	−0.0575657	+	0.0997068i	−0.893372	−	0.449317i	$-0.851667\pi$
$283$	−274.059	+	474.684i	−0.0575657	+	0.0997068i	0.835806	+	0.549024i	$0.185001\pi$
$284$	−4.20853	+	7.28938i	−0.000879332	+	0.00152305i
$285$	980.534	+	1796.34i	0.203796	+	0.373354i
$286$	136.221	+	235.942i	0.0281641	+	0.0487816i
$287$	319.342			0.0656800
$288$	2448.04	+	117.334i	0.500875	+	0.0240067i
$289$	901.079			0.183407
$290$	−408.556	−	707.640i	−0.0827284	−	0.143290i
$291$	4482.15	+	107.352i	0.902916	+	0.0216258i
$292$	770.662	−	1334.83i	0.154451	−	0.267516i
$293$	−37.1470	+	64.3404i	−0.00740665	+	0.0128287i	−0.869705	−	0.493572i	$-0.835691\pi$
$293$	−37.1470	+	64.3404i	−0.00740665	+	0.0128287i	0.862298	+	0.506401i	$0.169024\pi$
$294$	−322.985	+	529.715i	−0.0640709	+	0.105080i
$295$	−1806.04	−	3128.15i	−0.356446	−	0.617383i
$296$	8273.62			1.62464
$297$	−3756.71	−	7742.17i	−0.733961	−	1.51261i
$298$	−5685.02			−1.10512
$299$	−119.846	−	207.579i	−0.0231802	−	0.0401492i
$300$	−544.462	+	892.952i	−0.104782	+	0.171849i
$301$	1026.60	−	1778.13i	0.196586	−	0.340497i
$302$	−1917.04	+	3320.42i	−0.365277	+	0.632678i
$303$	−2446.28	−	58.5911i	−0.463813	−	0.0111088i
$304$	1626.78	+	2817.67i	0.306916	+	0.531594i
$305$	−3520.64			−0.660955
$306$	2713.42	−	4219.44i	0.506914	−	0.788266i
$307$	−4.58734			−0.000852812			−0.000426406	−	1.00000i	$-0.500136\pi$
$307$	−4.58734			−0.000852812			−0.000426406		1.00000i	$0.500136\pi$
$308$	442.760	+	766.883i	0.0819111	+	0.141874i
$309$	2082.80	+	3815.70i	0.383452	+	0.702484i
$310$	−1131.72	+	1960.20i	−0.207346	+	0.359134i
$311$	−4651.21	+	8056.13i	−0.848058	+	1.46888i	0.0348810	+	0.999391i	$0.488895\pi$
$311$	−4651.21	+	8056.13i	−0.848058	+	1.46888i	−0.882939	+	0.469488i	$0.844439\pi$
$312$	−111.269	−	203.845i	−0.0201902	−	0.0369885i
$313$	−920.407	−	1594.19i	−0.166212	−	0.287888i	0.770873	−	0.636989i	$-0.219820\pi$
$313$	−920.407	−	1594.19i	−0.166212	−	0.287888i	−0.937085	+	0.349101i	$0.886487\pi$
$314$	6984.04			1.25520
$315$	453.139	+	879.599i	0.0810523	+	0.157333i
$316$	−2192.83			−0.390368
$317$	−399.878	−	692.609i	−0.0708498	−	0.122715i	0.828424	−	0.560101i	$-0.189238\pi$
$317$	−399.878	−	692.609i	−0.0708498	−	0.122715i	−0.899274	+	0.437386i	$0.855904\pi$
$318$	−840.978	−	20.1423i	−0.148301	−	0.00355196i
$319$	1964.44	−	3402.51i	0.344789	−	0.597191i
$320$	1484.62	−	2571.44i	0.259353	−	0.449212i
$321$	196.653	−	322.523i	0.0341934	−	0.0560794i
$322$	1121.47	+	1942.44i	0.194090	+	0.336174i
$323$	−5736.41			−0.988182
$324$	623.769	+	1367.98i	0.106956	+	0.234565i
$325$	177.892			0.0303620
$326$	3740.50	+	6478.73i	0.635482	+	1.10069i
$327$	−1478.81	+	2425.35i	−0.250087	+	0.410159i
$328$	559.287	−	968.714i	0.0941508	−	0.163074i
$329$	1141.58	−	1977.27i	0.191298	−	0.331338i
$330$	−4064.69	−	97.3536i	−0.678042	−	0.0162398i
$331$	1653.85	+	2864.56i	0.274635	+	0.475681i	0.970043	−	0.242934i	$-0.0781098\pi$
$331$	1653.85	+	2864.56i	0.274635	+	0.475681i	−0.695408	+	0.718615i	$0.744776\pi$
$332$	1715.73			0.283623
$333$	4172.40	+	8099.15i	0.686625	+	1.33283i
$334$	−3473.31			−0.569015
$335$	−1510.75	−	2616.69i	−0.246391	−	0.426761i
$336$	753.675	+	1380.73i	0.122370	+	0.224182i
$337$	−1251.09	+	2166.95i	−0.202229	+	0.350271i	−0.949246	−	0.314534i	$-0.898152\pi$
$337$	−1251.09	+	2166.95i	−0.202229	+	0.350271i	0.747017	+	0.664805i	$0.231485\pi$
$338$	2672.69	−	4629.23i	0.430104	−	0.744962i
$339$	3818.91	+	6996.24i	0.611842	+	1.12090i
$340$	411.641	+	712.983i	0.0656599	+	0.113726i
$341$	−10883.2			−1.72832
$342$	−2677.17	+	4163.08i	−0.423289	+	0.658227i
$343$	343.000			0.0539949
$344$	−3595.93	−	6228.33i	−0.563603	−	0.976189i
$345$	3576.08	+	85.6508i	0.558057	+	0.0133660i
$346$	4066.10	−	7042.69i	0.631777	−	1.09427i
$347$	−6292.60	+	10899.1i	−0.973500	+	1.68615i	−0.288700	+	0.957420i	$0.593223\pi$
$347$	−6292.60	+	10899.1i	−0.973500	+	1.68615i	−0.684800	+	0.728731i	$0.740110\pi$
$348$	−357.349	+	586.074i	−0.0550457	+	0.0902784i
$349$	4801.86	+	8317.06i	0.736497	+	1.27565i	0.954063	+	0.299605i	$0.0968549\pi$
$349$	4801.86	+	8317.06i	0.736497	+	1.27565i	−0.217566	+	0.976046i	$0.569812\pi$
$350$	−1664.64			−0.254224
$351$	143.433	−	211.721i	0.0218116	−	0.0321962i
$352$	5567.77			0.843078
$353$	−5741.18	−	9944.01i	−0.865643	−	1.49934i	−0.866407	−	0.499338i	$-0.833577\pi$
$353$	−5741.18	−	9944.01i	−0.865643	−	1.49934i	0.000764501	−	1.00000i	$-0.499757\pi$
$354$	4547.86	−	7458.77i	0.682813	−	1.11986i
$355$	−10.6830	+	18.5035i	−0.00159717	+	0.00276638i
$356$	−474.754	+	822.297i	−0.0706795	+	0.122420i
$357$	−2772.66	−	66.4080i	−0.411049	−	0.00984505i
$358$	1291.79	+	2237.44i	0.190707	+	0.330314i
$359$	−7131.32			−1.04840			−0.524201	−	0.851594i	$-0.675636\pi$
$359$	−7131.32			−1.04840			−0.524201	+	0.851594i	$0.675636\pi$
$360$	3461.85	+	165.925i	0.506821	+	0.0242917i
$361$	−1199.21			−0.174838
$362$	−646.966	−	1120.58i	−0.0939330	−	0.162697i
$363$	−6053.01	−	11089.1i	−0.875209	−	1.60338i
$364$	−13.1577	+	22.7898i	−0.00189464	+	0.00328162i
$365$	1956.27	−	3388.35i	0.280536	−	0.485903i
$366$	−4079.61	−	7473.84i	−0.582635	−	1.06739i
$367$	−4212.57	−	7296.39i	−0.599168	−	1.03779i	−0.992944	−	0.118583i	$-0.962165\pi$
$367$	−4212.57	−	7296.39i	−0.599168	−	1.03779i	0.393776	−	0.919206i	$-0.371168\pi$
$368$	5686.87			0.805567
$369$	1230.33	+	58.9694i	0.173574	+	0.00831931i
$370$	4304.58			0.604822
$371$	232.536	+	402.764i	0.0325408	+	0.0563624i
$372$	1900.89	+	45.5283i	0.264937	+	0.00634551i
$373$	−1453.00	+	2516.68i	−0.201699	+	0.349353i	−0.949076	−	0.315047i	$-0.897980\pi$
$373$	−1453.00	+	2516.68i	−0.201699	+	0.349353i	0.747377	+	0.664400i	$0.231313\pi$
$374$	5698.30	−	9869.74i	0.787839	−	1.36458i
$375$	−3152.29	+	5169.95i	−0.434090	+	0.711934i
$376$	−3998.65	−	6925.87i	−0.548444	−	0.949932i
$377$	116.756			0.0159503
$378$	−1342.19	+	1981.20i	−0.182631	+	0.269582i
$379$	5329.37			0.722299			0.361149	−	0.932508i	$-0.382384\pi$
$379$	5329.37			0.722299			0.361149	+	0.932508i	$0.382384\pi$
$380$	−406.142	−	703.458i	−0.0548280	−	0.0949649i
$381$	1261.56	−	2069.04i	0.169637	−	0.278216i
$382$	−4613.49	+	7990.80i	−0.617924	+	1.07028i
$383$	2239.84	−	3879.51i	0.298826	−	0.517581i	−0.677042	−	0.735945i	$-0.736738\pi$
$383$	2239.84	−	3879.51i	0.298826	−	0.517581i	0.975868	+	0.218363i	$0.0700717\pi$
$384$	3406.90	+	81.5987i	0.452754	+	0.0108439i
$385$	1123.91	+	1946.67i	0.148779	+	0.257693i
$386$	−5020.77			−0.662048
$387$	4283.56	−	6661.05i	0.562650	−	0.874936i
$388$	−1779.51			−0.232838
$389$	−4453.75	−	7714.13i	−0.580499	−	1.00545i	−0.995420	−	0.0955967i	$-0.969524\pi$
$389$	−4453.75	−	7714.13i	−0.580499	−	1.00545i	0.414921	−	0.909858i	$-0.363809\pi$
$390$	−57.8906	−	106.056i	−0.00751642	−	0.0137701i
$391$	−5013.31	+	8683.30i	−0.648424	+	1.12310i
$392$	600.721	−	1040.48i	0.0774005	−	0.134062i
$393$	−1512.44	−	2770.80i	−0.194129	−	0.355645i
$394$	−2974.72	−	5152.37i	−0.380366	−	0.658814i
$395$	−5566.32			−0.709044
$396$	1564.22	+	3036.35i	0.198497	+	0.385309i
$397$	7639.09			0.965731			0.482865	−	0.875695i	$-0.339596\pi$
$397$	7639.09			0.965731			0.482865	+	0.875695i	$0.339596\pi$
$398$	−4705.50	−	8150.17i	−0.592627	−	1.02646i
$399$	2735.62	+	65.5209i	0.343239	+	0.00822092i
$400$	−2110.31	+	3655.16i	−0.263788	+	0.456895i
$401$	2496.88	−	4324.72i	0.310943	−	0.538569i	−0.667624	−	0.744499i	$-0.732688\pi$
$401$	2496.88	−	4324.72i	0.310943	−	0.538569i	0.978567	+	0.205930i	$0.0660218\pi$
$402$	3804.27	−	6239.24i	0.471989	−	0.774092i
$403$	−161.710	−	280.090i	−0.0199885	−	0.0346210i
$404$	971.229			0.119605
$405$	1583.39	+	3472.52i	0.194270	+	0.426052i
$406$	−1092.56			−0.133553
$407$	10348.7	+	17924.5i	1.26036	+	2.18301i
$408$	−5057.40	+	8294.46i	−0.613674	+	1.00646i
$409$	−1399.45	+	2423.91i	−0.169189	+	0.293043i	−0.938135	−	0.346270i	$-0.887448\pi$
$409$	−1399.45	+	2423.91i	−0.169189	+	0.293043i	0.768946	+	0.639313i	$0.220781\pi$
$410$	290.984	−	503.999i	0.0350504	−	0.0607092i
$411$	2469.26	+	59.1413i	0.296349	+	0.00709788i
$412$	−862.708	−	1494.25i	−0.103162	−	0.178681i
$413$	−4829.69			−0.575432
$414$	3962.02	+	7690.78i	0.470344	+	0.912998i
$415$	4355.24			0.515158
$416$	82.7299	+	143.292i	0.00975040	+	0.0168882i
$417$	−4419.34	−	8096.23i	−0.518983	−	0.950777i
$418$	−5622.18	+	9737.90i	−0.657870	+	1.13946i
$419$	−6447.88	+	11168.1i	−0.751789	+	1.30214i	0.195166	+	0.980770i	$0.437475\pi$
$419$	−6447.88	+	11168.1i	−0.751789	+	1.30214i	−0.946955	+	0.321366i	$0.895858\pi$
$420$	−188.162	−	344.713i	−0.0218604	−	0.0400483i
$421$	1380.97	+	2391.91i	0.159868	+	0.276899i	0.934821	−	0.355120i	$-0.115560\pi$
$421$	1380.97	+	2391.91i	0.159868	+	0.276899i	−0.774953	+	0.632019i	$0.782227\pi$
$422$	−14650.5			−1.68999
$423$	4763.29	−	7407.06i	0.547516	−	0.851403i
$424$	1629.03			0.186586
$425$	−3720.71	−	6444.47i	−0.424661	−	0.735535i
$426$	−51.6596	−	1.23730i	−0.00587539	−	0.000140722i
$427$	−2353.72	+	4076.76i	−0.266755	+	0.462033i
$428$	−74.9656	+	129.844i	−0.00846636	+	0.0146642i
$429$	302.447	−	496.031i	0.0340379	−	0.0558243i
$430$	−1870.88	−	3240.46i	−0.209818	−	0.363416i
$431$	−3024.37			−0.338002			−0.169001	−	0.985616i	$-0.554054\pi$
$431$	−3024.37			−0.338002			−0.169001	+	0.985616i	$0.554054\pi$
$432$	2648.73	+	5458.75i	0.294994	+	0.607950i
$433$	−17473.4			−1.93930			−0.969650	−	0.244496i	$-0.921378\pi$
$433$	−17473.4			−1.93930			−0.969650	+	0.244496i	$0.921378\pi$
$434$	1513.22	+	2620.97i	0.167366	+	0.289886i
$435$	−907.102	+	1487.70i	−0.0999821	+	0.163977i
$436$	563.735	−	976.417i	0.0619220	−	0.107252i
$437$	4946.34	−	8567.31i	0.541454	−	0.937826i
$438$	9459.87	+	226.574i	1.03199	+	0.0247171i
$439$	6448.27	+	11168.7i	0.701046	+	1.21425i	0.968100	+	0.250566i	$0.0806166\pi$
$439$	6448.27	+	11168.7i	0.701046	+	1.21425i	−0.267054	+	0.963682i	$0.586050\pi$
$440$	7873.57			0.853086
$441$	1321.48	+	63.3381i	0.142693	+	0.00683923i
$442$	338.677			0.0364462
$443$	4894.37	+	8477.30i	0.524918	+	0.909185i	0.999579	+	0.0290159i	$0.00923734\pi$
$443$	4894.37	+	8477.30i	0.524918	+	0.909185i	−0.474661	+	0.880169i	$0.657429\pi$
$444$	−1732.56	−	3174.04i	−0.185188	−	0.339265i
$445$	−1205.13	+	2087.34i	−0.128379	+	0.222358i
$446$	−980.613	+	1698.47i	−0.104111	+	0.180325i
$447$	5808.35	+	10640.9i	0.614599	+	1.12595i
$448$	−1985.08	−	3438.26i	−0.209344	−	0.362595i
$449$	3494.73			0.367319			0.183660	−	0.982990i	$-0.441206\pi$
$449$	3494.73			0.367319			0.183660	+	0.982990i	$0.441206\pi$
$450$	−6413.38	−	307.391i	−0.671844	−	0.0322012i
$451$	2798.25			0.292161
$452$	−1581.81	−	2739.77i	−0.164606	−	0.285107i
$453$	8173.61	+	195.767i	0.847748	+	0.0203044i
$454$	7050.33	−	12211.5i	0.728829	−	1.26237i
$455$	−33.3998	+	57.8501i	−0.00344133	+	0.00596056i
$456$	4989.85	−	8183.66i	0.512436	−	0.840428i
$457$	−4390.15	−	7603.96i	−0.449371	−	0.778333i	0.548975	−	0.835839i	$-0.315018\pi$
$457$	−4390.15	−	7603.96i	−0.449371	−	0.778333i	−0.998345	+	0.0575063i	$0.981685\pi$
$458$	5043.27			0.514534
$459$	−10670.0	−	767.848i	−1.08504	−	0.0780829i
$460$	−1419.78			−0.143908
$461$	6443.20	+	11160.0i	0.650954	+	1.12749i	0.982892	+	0.184184i	$0.0589644\pi$
$461$	6443.20	+	11160.0i	0.650954	+	1.12749i	−0.331937	+	0.943301i	$0.607702\pi$
$462$	−2830.17	+	4641.66i	−0.285003	+	0.467423i
$463$	4127.54	−	7149.11i	0.414305	−	0.717597i	−0.581051	−	0.813867i	$-0.697358\pi$
$463$	4127.54	−	7149.11i	0.414305	−	0.717597i	0.995355	+	0.0962708i	$0.0306915\pi$
$464$	−1385.06	+	2399.00i	−0.138578	+	0.240023i
$465$	4825.26	+	115.570i	0.481217	+	0.0115257i
$466$	4126.72	+	7147.69i	0.410229	+	0.710538i
$467$	6084.21			0.602877			0.301439	−	0.953486i	$-0.402533\pi$
$467$	6084.21			0.602877			0.301439	+	0.953486i	$0.402533\pi$
$468$	−54.9012	+	85.3730i	−0.00542267	+	0.00843241i
$469$	−4040.02			−0.397763
$470$	−2080.41	−	3603.37i	−0.204175	−	0.353641i
$471$	−7135.56	−	13072.3i	−0.698066	−	1.27886i
$472$	−8458.59	+	14650.7i	−0.824869	+	1.42872i
$473$	8995.66	−	15580.9i	0.874463	−	1.51461i
$474$	−6450.08	−	11816.5i	−0.625025	−	1.14505i
$475$	3671.01	+	6358.38i	0.354605	+	0.614195i
$476$	1100.80			0.105999
$477$	821.521	+	1594.68i	0.0788572	+	0.153072i
$478$	7557.99			0.723210
$479$	3791.31	+	6566.74i	0.361648	+	0.626393i	0.988232	−	0.152961i	$-0.0488809\pi$
$479$	3791.31	+	6566.74i	0.361648	+	0.626393i	−0.626584	+	0.779354i	$0.715548\pi$
$480$	−2468.57	−	59.1249i	−0.234738	−	0.00562223i
$481$	−307.538	+	532.671i	−0.0291528	+	0.0504942i
$482$	−6657.66	+	11531.4i	−0.629146	+	1.08971i
$483$	2489.96	−	4083.69i	0.234569	−	0.384708i
$484$	2507.19	+	4342.58i	0.235461	+	0.407830i
$485$	−4517.16			−0.422915
$486$	−5536.91	+	7385.17i	−0.516789	+	0.689296i
$487$	3413.33			0.317603			0.158802	−	0.987310i	$-0.449237\pi$
$487$	3413.33			0.317603			0.158802	+	0.987310i	$0.449237\pi$
$488$	8244.47	+	14279.8i	0.764774	+	1.32463i
$489$	8304.89	−	13620.5i	0.768017	−	1.25960i
$490$	312.541	−	541.338i	0.0288147	−	0.0499085i
$491$	4781.63	−	8282.02i	0.439495	−	0.761227i	−0.558156	−	0.829736i	$-0.688491\pi$
$491$	4781.63	−	8282.02i	0.439495	−	0.761227i	0.997650	+	0.0685092i	$0.0218242\pi$
$492$	−488.750	−	11.7061i	−0.0447857	−	0.00107266i
$493$	−2442.03	−	4229.72i	−0.223090	−	0.386403i
$494$	−334.153			−0.0304337
$495$	3970.65	+	7707.53i	0.360540	+	0.699854i
$496$	7673.39			0.694648
$497$	14.2842	+	24.7410i	0.00128920	+	0.00223297i
$498$	5046.71	+	9245.59i	0.454114	+	0.831937i
$499$	4159.25	−	7204.03i	0.373133	−	0.646286i	−0.616912	−	0.787032i	$-0.711617\pi$
$499$	4159.25	−	7204.03i	0.373133	−	0.646286i	0.990046	+	0.140746i	$0.0449501\pi$
$500$	1201.68	−	2081.37i	0.107481	−	0.186163i
$501$	3548.66	+	6501.15i	0.316452	+	0.579740i
$502$	−2303.54	−	3989.84i	−0.204805	−	0.354732i
$503$	−2698.02			−0.239163			−0.119581	−	0.992824i	$-0.538155\pi$
$503$	−2698.02			−0.239163			−0.119581	+	0.992824i	$0.538155\pi$
$504$	2506.55	−	3897.75i	0.221529	−	0.344483i
$505$	2465.39			0.217244
$506$	9826.94	+	17020.8i	0.863361	+	1.49539i
$507$	−11395.4	−	272.932i	−0.998201	−	0.0239080i
$508$	−480.917	+	832.973i	−0.0420025	+	0.0727504i
$509$	6412.04	−	11106.0i	0.558367	−	0.967120i	−0.439266	−	0.898357i	$-0.644762\pi$
$509$	6412.04	−	11106.0i	0.558367	−	0.967120i	0.997633	−	0.0687628i	$-0.0219052\pi$
$510$	−2631.25	+	4315.42i	−0.228458	+	0.374686i
$511$	−2615.71	−	4530.55i	−0.226443	−	0.392211i
$512$	−12408.8			−1.07109
$513$	10527.5	+	757.591i	0.906041	+	0.0652017i
$514$	−713.482			−0.0612263
$515$	−2189.92	−	3793.05i	−0.187377	−	0.324547i
$516$	−1636.39	+	2683.78i	−0.139608	+	0.228967i
$517$	10003.1	−	17325.9i	0.850942	−	1.47387i
$518$	2877.81	−	4984.52i	0.244100	−	0.422794i
$519$	−17336.4	−	415.225i	−1.46625	−	0.0351183i
$520$	116.991	+	202.634i	0.00986615	+	0.0170887i
$521$	5634.87			0.473836			0.236918	−	0.971530i	$-0.423863\pi$
$521$	5634.87			0.473836			0.236918	+	0.971530i	$0.423863\pi$
$522$	−4209.31	−	201.751i	−0.352944	−	0.0169165i
$523$	−20737.1			−1.73379			−0.866894	−	0.498492i	$-0.833887\pi$
$523$	−20737.1			−1.73379			−0.866894	+	0.498492i	$0.833887\pi$
$524$	626.462	+	1085.06i	0.0522273	+	0.0904603i
$525$	1700.75	+	3115.78i	0.141384	+	0.259016i
$526$	114.259	−	197.902i	0.00947134	−	0.0164048i
$527$	−6764.53	+	11716.5i	−0.559142	+	0.968462i
$528$	6604.12	+	12098.8i	0.544332	+	0.997218i
$529$	−2562.15	−	4437.77i	−0.210582	−	0.364738i
$530$	847.546			0.0694623
$531$	−18607.4	−	891.847i	−1.52070	−	0.0728867i
$532$	−1086.10			−0.0885121
$533$	41.5784	+	72.0159i	0.00337891	+	0.00585245i
$534$	−5827.60	−	139.577i	−0.472256	−	0.0113110i
$535$	−190.294	+	329.600i	−0.0153778	+	0.0266352i
$536$	−7075.59	+	12255.3i	−0.570184	+	0.987588i
$537$	2868.10	−	4703.87i	0.230480	−	0.378002i
$538$	−6039.18	−	10460.2i	−0.483955	−	0.838234i
$539$	3005.56			0.240183
$540$	−661.282	−	1362.83i	−0.0526982	−	0.108605i
$541$	10771.9			0.856047			0.428024	−	0.903768i	$-0.359210\pi$
$541$	10771.9			0.856047			0.428024	+	0.903768i	$0.359210\pi$
$542$	−10481.5	−	18154.5i	−0.830664	−	1.43875i
$543$	−1436.43	+	2355.84i	−0.113524	+	0.186186i
$544$	3460.70	−	5994.10i	0.272750	−	0.472417i
$545$	1431.00	−	2478.56i	0.112472	−	0.194807i
$546$	−161.511	−	3.86835i	−0.0126594	−	0.000303205i
$547$	3259.26	+	5645.21i	0.254764	+	0.441264i	0.964831	−	0.262869i	$-0.0846689\pi$
$547$	3259.26	+	5645.21i	0.254764	+	0.441264i	−0.710067	+	0.704134i	$0.751336\pi$
$548$	−980.350			−0.0764206
$549$	−9821.02	+	15272.0i	−0.763481	+	1.18723i
$550$	−14586.5			−1.13085
$551$	2409.41	+	4173.22i	0.186287	+	0.322659i
$552$	−8026.89	−	14705.3i	−0.618926	−	1.13387i
$553$	−3721.35	+	6445.57i	−0.286163	+	0.495648i
$554$	2605.87	−	4513.50i	0.199842	−	0.346137i
$555$	−4397.96	−	8057.07i	−0.336366	−	0.616223i
$556$	1830.51	+	3170.54i	0.139624	+	0.241836i
$557$	4472.98			0.340263			0.170131	−	0.985421i	$-0.445581\pi$
$557$	4472.98			0.340263			0.170131	+	0.985421i	$0.445581\pi$
$558$	5346.01	+	10377.3i	0.405582	+	0.787286i
$559$	534.655			0.0404535
$560$	−792.435	−	1372.54i	−0.0597973	−	0.103572i
$561$	−24295.5	−	581.904i	−1.82845	−	0.0437932i
$562$	9775.78	−	16932.1i	0.733748	−	1.27089i
$563$	2318.19	−	4015.22i	0.173534	−	0.300571i	−0.766119	−	0.642699i	$-0.777815\pi$
$563$	2318.19	−	4015.22i	0.173534	−	0.300571i	0.939653	+	0.342129i	$0.111148\pi$
$564$	−1819.65	+	2984.35i	−0.135853	+	0.222808i
$565$	−4015.30	−	6954.71i	−0.298982	−	0.517853i
$566$	1335.61			0.0991870
$567$	5079.61	+	488.048i	0.376232	+	0.0361483i
$568$	100.068			0.00739218
$569$	6615.33	+	11458.1i	0.487397	+	0.844197i	0.999895	−	0.0144917i	$-0.00461303\pi$
$569$	6615.33	+	11458.1i	0.487397	+	0.844197i	−0.512498	+	0.858689i	$0.671280\pi$
$570$	2596.10	−	4257.77i	0.190770	−	0.312874i
$571$	3335.30	−	5776.91i	0.244445	−	0.423391i	−0.717531	−	0.696527i	$-0.754728\pi$
$571$	3335.30	−	5776.91i	0.244445	−	0.423391i	0.961975	+	0.273136i	$0.0880610\pi$
$572$	−115.295	+	199.697i	−0.00842784	+	0.0145975i
$573$	19670.3	+	471.125i	1.43410	+	0.0343482i
$574$	−389.073	−	673.895i	−0.0282920	−	0.0490032i
$575$	12833.0			0.930739
$576$	−7013.05	−	13613.2i	−0.507310	−	0.984752i
$577$	−5729.30			−0.413369			−0.206684	−	0.978408i	$-0.566267\pi$
$577$	−5729.30			−0.413369			−0.206684	+	0.978408i	$0.566267\pi$
$578$	−1097.84	−	1901.51i	−0.0790036	−	0.136838i
$579$	5129.69	+	9397.60i	0.368191	+	0.674527i
$580$	345.794	−	598.934i	0.0247557	−	0.0428782i
$581$	2911.69	−	5043.19i	0.207912	−	0.360115i
$582$	−5234.34	−	9589.31i	−0.372801	−	0.682972i
$583$	2037.61	+	3529.24i	0.144750	+	0.250714i
$584$	−18324.4			−1.29840
$585$	−139.363	+	216.713i	−0.00984946	+	0.0153162i
$586$	181.034			0.0127618
$587$	−9338.88	−	16175.4i	−0.656655	−	1.13736i	−0.981476	−	0.191585i	$-0.938637\pi$
$587$	−9338.88	−	16175.4i	−0.656655	−	1.13736i	0.324821	−	0.945776i	$-0.394696\pi$
$588$	−524.959	−	12.5733i	−0.0368179	−	0.000881828i
$589$	6674.17	−	11560.0i	0.466901	−	0.808696i
$590$	−4400.81	+	7622.43i	−0.307082	+	0.531882i
$591$	−6604.67	+	10832.1i	−0.459695	+	0.753929i
$592$	−7296.57	−	12638.0i	−0.506566	−	0.877398i
$593$	−20326.8			−1.40763			−0.703814	−	0.710384i	$-0.748521\pi$
$593$	−20326.8			−1.40763			−0.703814	+	0.710384i	$0.748521\pi$
$594$	−11761.0	+	17360.4i	−0.812389	+	1.19917i
$595$	2794.31			0.192530
$596$	−2405.85	−	4167.05i	−0.165348	−	0.286391i
$597$	−10447.5	+	17134.5i	−0.716224	+	1.17465i
$598$	−292.031	+	505.813i	−0.0199700	+	0.0345890i
$599$	5866.86	−	10161.7i	0.400189	−	0.693148i	−0.593559	−	0.804790i	$-0.702278\pi$
$599$	5866.86	−	10161.7i	0.400189	−	0.693148i	0.993748	+	0.111642i	$0.0356110\pi$
$600$	12430.3	+	297.718i	0.845772	+	0.0202571i
$601$	3658.09	+	6335.99i	0.248280	+	0.430034i	0.963049	−	0.269327i	$-0.0868012\pi$
$601$	3658.09	+	6335.99i	0.248280	+	0.430034i	−0.714768	+	0.699361i	$0.753468\pi$
$602$	−5003.08			−0.338722
$603$	−15565.1	−	746.027i	−1.05118	−	0.0503824i
$604$	−3245.10			−0.218612
$605$	6364.30	+	11023.3i	0.427679	+	0.740762i
$606$	2856.81	+	5233.68i	0.191502	+	0.350832i
$607$	5039.46	−	8728.60i	0.336978	−	0.583662i	−0.646885	−	0.762588i	$-0.723929\pi$
$607$	5039.46	−	8728.60i	0.336978	−	0.583662i	0.983863	+	0.178925i	$0.0572620\pi$
$608$	−3414.47	+	5914.03i	−0.227755	+	0.394483i
$609$	1116.26	+	2044.99i	0.0742743	+	0.136071i
$610$	4289.41	+	7429.48i	0.284710	+	0.493132i
$611$	594.534			0.0393654
$612$	4241.09	+	203.274i	0.280124	+	0.0134262i
$613$	9125.73			0.601280			0.300640	−	0.953738i	$-0.402800\pi$
$613$	9125.73			0.601280			0.300640	+	0.953738i	$0.402800\pi$
$614$	5.58903	+	9.68049i	0.000367354	+	0.000636275i
$615$	−1240.66	−	29.7150i	−0.0813464	−	0.00194833i
$616$	5263.85	−	9117.26i	0.344297	−	0.596339i
$617$	6551.69	−	11347.9i	0.427490	−	0.740434i	−0.569159	−	0.822227i	$-0.692731\pi$
$617$	6551.69	−	11347.9i	0.427490	−	0.740434i	0.996649	+	0.0817929i	$0.0260646\pi$
$618$	5514.52	−	9044.16i	0.358943	−	0.588689i
$619$	10090.9	+	17478.0i	0.655233	+	1.13490i	0.981835	+	0.189735i	$0.0607628\pi$
$619$	10090.9	+	17478.0i	0.655233	+	1.13490i	−0.326603	+	0.945162i	$0.605904\pi$
$620$	−1915.73			−0.124093
$621$	10347.2	−	15273.5i	0.668629	−	0.986964i
$622$	22667.4			1.46122
$623$	1611.37	+	2790.97i	0.103624	+	0.179483i
$624$	−213.245	+	349.736i	−0.0136805	+	0.0224369i
$625$	−3049.15	+	5281.29i	−0.195146	+	0.338003i
$626$	−2242.78	+	3884.60i	−0.143194	+	0.248019i
$627$	23971.0	+	574.131i	1.52681	+	0.0365687i
$628$	2955.58	+	5119.22i	0.187804	+	0.325285i
$629$	25729.4			1.63100
$630$	1304.10	−	2027.91i	0.0824706	−	0.128244i
$631$	6629.61			0.418258			0.209129	−	0.977888i	$-0.432937\pi$
$631$	6629.61			0.418258			0.209129	+	0.977888i	$0.432937\pi$
$632$	13035.0	+	22577.2i	0.820416	+	1.42100i
$633$	14968.3	+	27422.0i	0.939869	+	1.72184i
$634$	−974.391	+	1687.69i	−0.0610379	+	0.105721i
$635$	−1220.77	+	2114.44i	−0.0762911	+	0.132140i
$636$	−341.130	−	624.951i	−0.0212684	−	0.0389637i
$637$	44.6587	+	77.3511i	0.00277777	+	0.00481124i
$638$	−9573.59			−0.594078
$639$	50.4644	+	97.9578i	0.00312417	+	0.00606440i
$640$	−3433.50			−0.212064
$641$	−47.9675	−	83.0821i	−0.00295569	−	0.00511941i	0.864544	−	0.502558i	$-0.167607\pi$
$641$	−47.9675	−	83.0821i	−0.00295569	−	0.00511941i	−0.867499	+	0.497438i	$0.834274\pi$
$642$	−920.202	−	22.0398i	−0.0565693	−	0.00135489i
$643$	−2610.70	+	4521.87i	−0.160118	+	0.277333i	−0.934911	−	0.354882i	$-0.884521\pi$
$643$	−2610.70	+	4521.87i	−0.160118	+	0.277333i	0.774793	+	0.632215i	$0.217854\pi$
$644$	−949.191	+	1644.05i	−0.0580798	+	0.100597i
$645$	−4153.84	+	6812.56i	−0.253577	+	0.415883i
$646$	6989.02	+	12105.3i	0.425664	+	0.737272i
$647$	20347.2			1.23637			0.618186	−	0.786032i	$-0.287868\pi$
$647$	20347.2			1.23637			0.618186	+	0.786032i	$0.287868\pi$
$648$	10376.8	−	14554.1i	0.629071	−	0.882312i
$649$	−42320.4			−2.55966
$650$	−216.736	−	375.398i	−0.0130786	−	0.0226528i
$651$	3359.74	−	5510.18i	0.202271	−	0.331737i
$652$	−3165.89	+	5483.48i	−0.190162	+	0.329371i
$653$	−1707.67	+	2957.76i	−0.102337	+	0.177253i	−0.912647	−	0.408748i	$-0.865965\pi$
$653$	−1707.67	+	2957.76i	−0.102337	+	0.177253i	0.810310	+	0.586001i	$0.199299\pi$
$654$	6919.84	+	165.737i	0.413742	+	0.00990955i
$655$	1590.23	+	2754.35i	0.0948630	+	0.164307i
$656$	−1972.96			−0.117425
$657$	−9241.00	−	17937.9i	−0.548745	−	1.06518i
$658$	−5563.40			−0.329611
$659$	−400.199	−	693.165i	−0.0236563	−	0.0409740i	0.853955	−	0.520347i	$-0.174197\pi$
$659$	−400.199	−	693.165i	−0.0236563	−	0.0409740i	−0.877611	+	0.479373i	$0.840864\pi$
$660$	−1648.78	−	3020.57i	−0.0972405	−	0.178145i
$661$	−8518.77	+	14754.9i	−0.501273	+	0.868231i	0.498726	+	0.866760i	$0.333802\pi$
$661$	−8518.77	+	14754.9i	−0.501273	+	0.868231i	−0.999999	+	0.00147083i	$0.999532\pi$
$662$	4029.98	−	6980.13i	0.236601	−	0.409804i
$663$	−346.024	−	633.917i	−0.0202692	−	0.0371332i
$664$	−10198.9	−	17665.0i	−0.596076	−	1.03243i
$665$	−2756.98			−0.160769
$666$	12007.8	−	18672.5i	0.698640	−	1.08641i
$667$	8422.75			0.488951
$668$	−1469.87	−	2545.89i	−0.0851363	−	0.147460i
$669$	4180.99	+	100.139i	0.241624	+	0.00578715i
$670$	−3681.27	+	6376.14i	−0.212268	+	0.367659i
$671$	−20624.6	+	35722.8i	−1.18659	+	2.05524i
$672$	−1718.82	+	2818.98i	−0.0986682	+	0.161822i
$673$	−10962.4	−	18987.4i	−0.627889	−	1.08754i	−0.987975	−	0.154616i	$-0.950586\pi$
$673$	−10962.4	−	18987.4i	−0.627889	−	1.08754i	0.360086	−	0.932919i	$-0.382747\pi$
$674$	6097.11			0.348445
$675$	5977.15	+	12318.3i	0.340831	+	0.702415i
$676$	4524.23			0.257410
$677$	−2882.05	−	4991.85i	−0.163613	−	0.283386i	0.772549	−	0.634955i	$-0.218982\pi$
$677$	−2882.05	−	4991.85i	−0.163613	−	0.283386i	−0.936162	+	0.351569i	$0.885648\pi$
$678$	10111.1	−	16582.8i	0.572735	−	0.939321i
$679$	−3019.93	+	5230.68i	−0.170684	+	0.295633i
$680$	4893.88	−	8476.45i	0.275988	−	0.478025i
$681$	−30060.2	−	719.972i	−1.69150	−	0.0405131i
$682$	13259.6	+	22966.4i	0.744484	+	1.28948i
$683$	19971.6			1.11887			0.559437	−	0.828873i	$-0.311017\pi$
$683$	19971.6			1.11887			0.559437	+	0.828873i	$0.311017\pi$
$684$	−4184.44	−	200.558i	−0.233912	−	0.0112113i
$685$	−2488.54			−0.138806
$686$	−417.897	−	723.820i	−0.0232586	−	0.0402851i
$687$	−5152.68	−	9439.71i	−0.286153	−	0.524232i
$688$	−6342.55	+	10985.6i	−0.351464	+	0.608754i
$689$	−60.5524	+	104.880i	−0.00334813	+	0.00579913i
$690$	−4176.21	−	7650.81i	−0.230414	−	0.422118i
$691$	−3819.22	−	6615.09i	−0.210261	−	0.364182i	0.741535	−	0.670914i	$-0.234098\pi$
$691$	−3819.22	−	6615.09i	−0.210261	−	0.364182i	−0.951796	+	0.306732i	$0.900765\pi$
$692$	6882.94			0.378107
$693$	11579.6	+	555.004i	0.634735	+	0.0304226i
$694$	30666.6			1.67736
$695$	4646.61	+	8048.17i	0.253606	+	0.439258i
$696$	8158.39	+	195.402i	0.444315	+	0.0106418i
$697$	1739.28	−	3012.51i	0.0945190	−	0.163712i
$698$	11700.8	−	20266.3i	0.634500	−	1.09899i
$699$	9162.41	−	15026.9i	0.495786	−	0.813120i
$700$	−704.459	−	1220.16i	−0.0380372	−	0.0658824i
$701$	−17637.3			−0.950288			−0.475144	−	0.879908i	$-0.657604\pi$
$701$	−17637.3			−0.950288			−0.475144	+	0.879908i	$0.657604\pi$
$702$	−621.540	−	44.7281i	−0.0334167	−	0.00240478i
$703$	−25385.7			−1.36193
$704$	−17394.4	−	30127.9i	−0.931214	−	1.61291i
$705$	−4619.05	+	7575.53i	−0.246757	+	0.404697i
$706$	−13989.6	+	24230.8i	−0.745761	+	1.29170i
$707$	1648.23	−	2854.82i	0.0876776	−	0.151862i
$708$	7391.80	+	177.041i	0.392374	+	0.00939777i
$709$	11338.0	+	19638.0i	0.600576	+	1.04023i	0.992734	+	0.120330i	$0.0383954\pi$
$709$	11338.0	+	19638.0i	0.600576	+	1.04023i	−0.392158	+	0.919898i	$0.628271\pi$
$710$	52.0631			0.00275196
$711$	−15527.6	+	24145.8i	−0.819028	+	1.27361i
$712$	11288.4			0.594174
$713$	−11665.7	−	20205.6i	−0.612741	−	1.06130i
$714$	3237.95	+	5931.94i	0.169716	+	0.310920i
$715$	−292.668	+	506.915i	−0.0153079	+	0.0265140i
$716$	−1093.34	+	1893.73i	−0.0570673	+	0.0988434i
$717$	−7721.95	−	14146.6i	−0.402206	−	0.736842i
$718$	8688.51	+	15048.9i	0.451605	+	0.782203i
$719$	−11860.2			−0.615172			−0.307586	−	0.951520i	$-0.599521\pi$
$719$	−11860.2			−0.615172			−0.307586	+	0.951520i	$0.599521\pi$
$720$	−2799.58	−	5434.33i	−0.144909	−	0.281286i
$721$	−5856.26			−0.302494
$722$	1461.07	+	2530.65i	0.0753124	+	0.130445i
$723$	28386.0	+	679.873i	1.46015	+	0.0349720i
$724$	547.580	−	948.436i	0.0281086	−	0.0486856i
$725$	−3125.55	+	5413.61i	−0.160110	+	0.277319i
$726$	−16026.2	+	26284.0i	−0.819268	+	1.34365i
$727$	−13648.2	−	23639.3i	−0.696262	−	1.20596i	−0.969753	−	0.244087i	$-0.921512\pi$
$727$	−13648.2	−	23639.3i	−0.696262	−	1.20596i	0.273491	−	0.961875i	$-0.411822\pi$
$728$	312.856			0.0159275
$729$	19480.2	+	2818.31i	0.989696	+	0.143185i
$730$	−9533.75			−0.483370
$731$	−11182.6	−	19368.9i	−0.565807	−	0.980007i
$732$	3751.79	−	6153.16i	0.189440	−	0.310693i
$733$	−16309.7	+	28249.2i	−0.821846	+	1.42348i	0.0824608	+	0.996594i	$0.473722\pi$
$733$	−16309.7	+	28249.2i	−0.821846	+	1.42348i	−0.904306	+	0.426884i	$0.859611\pi$
$734$	−10264.9	+	17779.3i	−0.516189	+	0.894066i
$735$	−1332.57	−	31.9164i	−0.0668742	−	0.00160171i
$736$	5968.11	+	10337.1i	0.298896	+	0.517703i
$737$	−35400.9			−1.76935
$738$	−1374.55	−	2668.17i	−0.0685608	−	0.133085i
$739$	−14629.4			−0.728216			−0.364108	−	0.931357i	$-0.618626\pi$
$739$	−14629.4			−0.728216			−0.364108	+	0.931357i	$0.618626\pi$
$740$	1821.66	+	3155.20i	0.0904938	+	0.156740i
$741$	341.402	+	625.449i	0.0169254	+	0.0310074i
$742$	566.624	−	981.422i	0.0280343	−	0.0485568i
$743$	4501.40	−	7796.66i	0.222262	−	0.384969i	−0.733233	−	0.679978i	$-0.761989\pi$
$743$	4501.40	−	7796.66i	0.222262	−	0.384969i	0.955494	+	0.295009i	$0.0953227\pi$
$744$	−10830.8	−	19842.1i	−0.533705	−	0.977749i
$745$	−6107.07	−	10577.7i	−0.300330	−	0.520186i
$746$	7081.13			0.347532
$747$	12149.2	−	18892.3i	0.595067	−	0.925347i
$748$	9645.86			0.471508
$749$	254.442	+	440.706i	0.0124127	+	0.0214994i
$750$	14750.6	+	353.292i	0.718153	+	0.0172005i
$751$	16692.2	−	28911.7i	0.811059	−	1.40480i	−0.101064	−	0.994880i	$-0.532225\pi$
$751$	16692.2	−	28911.7i	0.811059	−	1.40480i	0.912123	−	0.409916i	$-0.134442\pi$
$752$	−7052.88	+	12215.9i	−0.342011	+	0.592380i
$753$	−5114.46	+	8388.03i	−0.247518	+	0.405945i
$754$	−142.251	−	246.386i	−0.00687066	−	0.0119003i
$755$	−8237.45			−0.397075
$756$	−2020.20	−	145.380i	−0.0971877	−	0.00699394i
$757$	−10936.8			−0.525107			−0.262554	−	0.964917i	$-0.584565\pi$
$757$	−10936.8			−0.525107			−0.262554	+	0.964917i	$0.584565\pi$
$758$	−6493.09	−	11246.4i	−0.311134	−	0.538900i
$759$	21818.4	−	35783.5i	1.04342	−	1.71128i
$760$	−4828.51	+	8363.22i	−0.230458	+	0.399166i
$761$	−3392.08	+	5875.26i	−0.161581	+	0.279866i	−0.935436	−	0.353497i	$-0.884992\pi$
$761$	−3392.08	+	5875.26i	−0.161581	+	0.279866i	0.773855	+	0.633363i	$0.218326\pi$
$762$	−5903.26	−	141.389i	−0.280646	−	0.00672177i
$763$	−1913.38	−	3314.07i	−0.0907850	−	0.157244i
$764$	−7809.55			−0.369816
$765$	10765.7	+	515.995i	0.508803	+	0.0243867i
$766$	−10915.7			−0.514883
$767$	−628.827	−	1089.16i	−0.0296031	−	0.0512741i
$768$	7317.41	+	13405.5i	0.343808	+	0.629856i
$769$	−2130.16	+	3689.54i	−0.0998901	+	0.173015i	−0.911639	−	0.410992i	$-0.865182\pi$
$769$	−2130.16	+	3689.54i	−0.0998901	+	0.173015i	0.811749	+	0.584007i	$0.198516\pi$
$770$	2738.66	−	4743.50i	0.128175	−	0.222005i
$771$	728.960	+	1335.46i	0.0340504	+	0.0623804i
$772$	−2124.74	−	3680.16i	−0.0990559	−	0.171570i
$773$	18184.6			0.846124			0.423062	−	0.906101i	$-0.360955\pi$
$773$	18184.6			0.846124			0.423062	+	0.906101i	$0.360955\pi$
$774$	−19275.5	−	923.866i	−0.895146	−	0.0429040i
$775$	17315.8			0.802584
$776$	10578.1	+	18321.8i	0.489344	+	0.847568i
$777$	−12270.0	−	293.879i	−0.566517	−	0.0135687i
$778$	−10852.5	+	18797.2i	−0.500106	+	0.866210i
$779$	−1716.04	+	2972.27i	−0.0789263	+	0.136704i
$780$	53.2387	−	87.3149i	0.00244391	−	0.00400817i
$781$	125.166	+	216.794i	0.00573470	+	0.00993279i
$782$	24432.1			1.11725
$783$	3923.01	+	8084.89i	0.179051	+	0.369004i
$784$	−2119.12			−0.0965343
$785$	7502.52	+	12994.7i	0.341116	+	0.590831i
$786$	−4004.41	+	6567.48i	−0.181721	+	0.298033i
$787$	11479.7	−	19883.4i	0.519957	−	0.900592i	−0.479774	−	0.877392i	$-0.659281\pi$
$787$	11479.7	−	19883.4i	0.519957	−	0.900592i	0.999731	−	0.0231995i	$-0.00738530\pi$
$788$	2517.75	−	4360.87i	0.113821	−	0.197144i
$789$	−487.160	−	11.6680i	−0.0219815	−	0.000526479i
$790$	6781.79	+	11746.4i	0.305424	+	0.529010i
$791$	−10737.7			−0.482665
$792$	21963.7	−	34154.2i	0.985414	−	1.53235i
$793$	−1225.82			−0.0548929
$794$	−9307.17	−	16120.5i	−0.415994	−	0.720522i
$795$	−865.933	−	1586.39i	−0.0386308	−	0.0707716i
$796$	3982.65	−	6898.15i	0.177338	−	0.307159i
$797$	12428.1	−	21526.0i	0.552352	−	0.956701i	−0.445753	−	0.895156i	$-0.647064\pi$
$797$	12428.1	−	21526.0i	0.552352	−	0.956701i	0.998104	−	0.0615449i	$-0.0196027\pi$
$798$	−3194.70	−	5852.70i	−0.141718	−	0.259628i
$799$	−12435.0	−	21538.1i	−0.550588	−	0.953647i
$800$	−8858.67			−0.391502
$801$	5692.77	+	11050.4i	0.251116	+	0.487448i
$802$	−12168.4			−0.535761
$803$	−22920.3	−	39699.2i	−1.00727	−	1.74465i
$804$	6183.22	+	148.095i	0.271226	+	0.00649614i
$805$	−2409.45	+	4173.29i	−0.105493	+	0.182719i
$806$	−394.042	+	682.501i	−0.0172203	+	0.0298264i
$807$	−13408.6	+	21990.9i	−0.584888	+	0.959252i
$808$	−5773.33	−	9999.71i	−0.251368	−	0.435382i
$809$	10213.3			0.443856			0.221928	−	0.975063i	$-0.428765\pi$
$809$	10213.3			0.443856			0.221928	+	0.975063i	$0.428765\pi$
$810$	5398.80	−	7572.15i	0.234191	−	0.328467i
$811$	21616.4			0.935950			0.467975	−	0.883742i	$-0.344984\pi$
$811$	21616.4			0.935950			0.467975	+	0.883742i	$0.344984\pi$
$812$	−462.360	−	800.831i	−0.0199823	−	0.0346104i
$813$	−23271.7	+	38167.1i	−1.00391	+	1.64647i
$814$	25217.0	−	43677.1i	1.08582	−	1.88069i
$815$	−8036.37	+	13919.4i	−0.345401	+	0.598252i
$816$	17130.0	+	410.282i	0.734890	+	0.0176014i
$817$	11033.3	+	19110.2i	0.472467	+	0.818336i
$818$	6820.11			0.291515
$819$	157.774	+	306.259i	0.00673146	+	0.0130666i
$820$	492.567			0.0209771
$821$	−9086.29	−	15737.9i	−0.386253	−	0.669010i	0.605689	−	0.795701i	$-0.292897\pi$
$821$	−9086.29	−	15737.9i	−0.386253	−	0.669010i	−0.991942	+	0.126692i	$0.959564\pi$
$822$	−2883.64	−	5282.84i	−0.122358	−	0.224161i
$823$	−14425.5	+	24985.8i	−0.610988	+	1.05826i	0.380087	+	0.924951i	$0.375894\pi$
$823$	−14425.5	+	24985.8i	−0.610988	+	1.05826i	−0.991074	+	0.133311i	$0.957439\pi$
$824$	−10256.5	+	17764.8i	−0.433619	+	0.751050i
$825$	14902.9	+	27302.2i	0.628912	+	1.15217i
$826$	5884.30	+	10191.9i	0.247870	+	0.429324i
$827$	16577.1			0.697030			0.348515	−	0.937303i	$-0.386686\pi$
$827$	16577.1			0.697030			0.348515	+	0.937303i	$0.386686\pi$
$828$	−3960.56	+	6158.78i	−0.166231	+	0.258493i
$829$	17644.0			0.739206			0.369603	−	0.929190i	$-0.379494\pi$
$829$	17644.0			0.739206			0.369603	+	0.929190i	$0.379494\pi$
$830$	−5306.25	−	9190.70i	−0.221907	−	0.384354i
$831$	−11110.5	−	266.108i	−0.463802	−	0.0111085i
$832$	516.915	−	895.324i	0.0215394	−	0.0373074i
$833$	1868.13	−	3235.69i	0.0777032	−	0.134586i
$834$	−11700.8	+	19190.1i	−0.485811	+	0.796760i
$835$	−3731.16	−	6462.55i	−0.154637	−	0.267839i
$836$	−9517.01			−0.393723
$837$	13961.6	−	20608.8i	0.576565	−	0.851068i
$838$	31423.4			1.29535
$839$	−9335.66	−	16169.8i	−0.384151	−	0.665369i	0.607500	−	0.794320i	$-0.292172\pi$
$839$	−9335.66	−	16169.8i	−0.384151	−	0.665369i	−0.991651	+	0.128951i	$0.958839\pi$
$840$	−2430.64	+	3986.41i	−0.0998395	+	0.163743i
$841$	10143.1	−	17568.4i	0.415888	−	0.720340i
$842$	3365.04	−	5828.42i	0.137728	−	0.238552i
$843$	−41680.5	−	998.292i	−1.70291	−	0.0407865i
$844$	−6199.95	−	10738.6i	−0.252857	−	0.437961i
$845$	11484.4			0.467545
$846$	−21434.2	−	1027.33i	−0.871069	−	0.0417500i
$847$	17019.4			0.690427
$848$	−1436.65	−	2488.35i	−0.0581778	−	0.100767i
$849$	−1364.58	−	2499.92i	−0.0551618	−	0.101057i
$850$	−9066.34	+	15703.4i	−0.365850	+	0.633671i
$851$	−22185.7	+	38426.7i	−0.893672	+	1.54789i
$852$	−20.9550	−	38.3895i	−0.000842611	−	0.00154367i
$853$	7203.13	+	12476.2i	0.289133	+	0.500793i	0.973603	−	0.228248i	$-0.0732997\pi$
$853$	7203.13	+	12476.2i	0.289133	+	0.500793i	−0.684470	+	0.729041i	$0.739966\pi$
$854$	11470.7			0.459624
$855$	−10621.9	−	509.102i	−0.424866	−	0.0203637i
$856$	1782.49			0.0711732
$857$	3930.43	+	6807.70i	0.156664	+	0.271350i	0.933664	−	0.358151i	$-0.116593\pi$
$857$	3930.43	+	6807.70i	0.156664	+	0.271350i	−0.777000	+	0.629501i	$0.783259\pi$
$858$	−1415.24	−	33.8966i	−0.0563120	−	0.00134873i
$859$	−721.505	+	1249.68i	−0.0286582	+	0.0496375i	−0.879999	−	0.474976i	$-0.842457\pi$
$859$	−721.505	+	1249.68i	−0.0286582	+	0.0496375i	0.851341	+	0.524613i	$0.175790\pi$
$860$	1583.48	−	2742.66i	0.0627862	−	0.108749i
$861$	−863.845	+	1416.76i	−0.0341925	+	0.0560779i
$862$	3684.78	+	6382.22i	0.145596	+	0.252180i
$863$	34826.0			1.37369			0.686843	−	0.726806i	$-0.258996\pi$
$863$	34826.0			1.37369			0.686843	+	0.726806i	$0.258996\pi$
$864$	−7142.69	+	10543.3i	−0.281249	+	0.415152i
$865$	17471.8			0.686774
$866$	21288.9	+	36873.4i	0.835364	+	1.44689i
$867$	−2437.49	+	3997.64i	−0.0954805	+	0.156594i
$868$	−1280.76	+	2218.34i	−0.0500827	+	0.0867458i
$869$	−32608.5	+	56479.7i	−1.27292	+	2.20477i
$870$	4244.62	+	101.663i	0.165409	+	0.00396173i
$871$	−526.012	−	911.079i	−0.0204629	−	0.0354429i
$872$	−13404.2			−0.520553
$873$	−12600.9	+	19594.7i	−0.488516	+	0.759656i
$874$	−24105.7			−0.932937
$875$	−4078.63	−	7064.39i	−0.157580	−	0.272937i
$876$	3837.25	+	7029.85i	0.148001	+	0.271138i
$877$	−19376.0	+	33560.3i	−0.746046	+	1.29219i	0.203658	+	0.979042i	$0.434717\pi$
$877$	−19376.0	+	33560.3i	−0.746046	+	1.29219i	−0.949704	+	0.313148i	$0.898616\pi$
$878$	15712.6	−	27215.1i	0.603959	−	1.04609i
$879$	−184.961	−	338.849i	−0.00709736	−	0.0130024i
$880$	−6943.76	−	12026.9i	−0.265993	−	0.460714i
$881$	13310.3			0.509007			0.254503	−	0.967072i	$-0.418088\pi$
$881$	13310.3			0.509007			0.254503	+	0.967072i	$0.418088\pi$
$882$	−1476.38	−	2865.84i	−0.0563632	−	0.109408i
$883$	18152.4			0.691820			0.345910	−	0.938268i	$-0.387570\pi$
$883$	18152.4			0.691820			0.345910	+	0.938268i	$0.387570\pi$
$884$	143.325	+	248.246i	0.00545310	+	0.00944505i
$885$	18763.5	+	449.406i	0.712688	+	0.0170696i
$886$	11926.2	−	20656.8i	0.452222	−	0.783272i
$887$	15112.6	−	26175.8i	0.572075	−	0.990863i	−0.424277	−	0.905532i	$-0.639472\pi$
$887$	15112.6	−	26175.8i	0.572075	−	0.990863i	0.996353	−	0.0853310i	$-0.0271948\pi$
$888$	−22380.8	+	36705.9i	−0.845778	+	1.38713i
$889$	1632.29	+	2827.20i	0.0615806	+	0.106661i
$890$	5873.11			0.221199
$891$	44510.3	+	4276.55i	1.67357	+	0.160797i
$892$	−1659.95			−0.0623084
$893$	12268.9	+	21250.4i	0.459758	+	0.796325i
$894$	15378.4	−	25221.6i	0.575316	−	0.943554i
$895$	−2775.37	+	4807.08i	−0.103654	+	0.179534i
$896$	−2295.46	+	3975.85i	−0.0855870	+	0.148241i
$897$	1245.12	+	29.8219i	0.0463471	+	0.00111006i
$898$	−4257.84	−	7374.79i	−0.158225	−	0.274053i
$899$	11365.0			0.421627
$900$	−2488.77	−	4831.01i	−0.0921766	−	0.178926i
$901$	5065.96			0.187316
$902$	−3409.28	−	5905.04i	−0.125850	−	0.217978i
$903$	5111.62	+	9364.50i	0.188377	+	0.345106i
$904$	−18805.7	+	32572.4i	−0.691889	+	1.19839i
$905$	1389.99	−	2407.53i	0.0510550	−	0.0884299i
$906$	−9545.28	−	17487.0i	−0.350023	−	0.641242i
$907$	−22602.2	−	39148.2i	−0.827446	−	1.43318i	−0.900035	−	0.435817i	$-0.856460\pi$
$907$	−22602.2	−	39148.2i	−0.827446	−	1.43318i	0.0725891	−	0.997362i	$-0.476874\pi$
$908$	11934.5			0.436191
$909$	6877.33	−	10694.4i	0.250943	−	0.390223i
$910$	162.772			0.00592949
$911$	16787.2	+	29076.3i	0.610522	+	1.05745i	0.991153	+	0.132728i	$0.0423735\pi$
$911$	16787.2	+	29076.3i	0.610522	+	1.05745i	−0.380631	+	0.924727i	$0.624293\pi$
$912$	−16901.2	−	404.801i	−0.613656	−	0.0146977i
$913$	25513.8	−	44191.2i	0.924845	−	1.60188i
$914$	−10697.6	+	18528.7i	−0.387138	+	0.670542i
$915$	9523.62	−	15619.3i	0.344089	−	0.564327i
$916$	2134.26	+	3696.66i	0.0769848	+	0.133342i
$917$	4252.56			0.153143
$918$	11379.5	+	23452.0i	0.409130	+	0.843172i
$919$	−4708.51			−0.169009			−0.0845046	−	0.996423i	$-0.526931\pi$
$919$	−4708.51			−0.169009			−0.0845046	+	0.996423i	$0.526931\pi$
$920$	8439.69	+	14618.0i	0.302444	+	0.523848i
$921$	12.4091	−	20.3517i	0.000443968	−	0.000728136i
$922$	15700.3	−	27193.7i	0.560804	−	0.971341i
$923$	−3.71962	+	6.44256i	−0.000132646	+	0.000229750i
$924$	−4599.98	−	110.174i	−0.163775	−	0.00392259i
$925$	−16465.5	−	28519.1i	−0.585278	−	1.01373i
$926$	−20115.3			−0.713856
$927$	−22562.5	−	1081.41i	−0.799407	−	0.0383152i
$928$	−5814.24			−0.205670
$929$	5132.07	+	8889.00i	0.181246	+	0.313928i	0.942305	−	0.334755i	$-0.108654\pi$
$929$	5132.07	+	8889.00i	0.181246	+	0.313928i	−0.761059	+	0.648683i	$0.775320\pi$
$930$	−5635.02	−	10323.4i	−0.198688	−	0.363996i
$931$	−1843.17	+	3192.47i	−0.0648846	+	0.112383i
$932$	−3492.78	+	6049.68i	−0.122757	+	0.212622i
$933$	−23159.1	−	42427.6i	−0.812644	−	1.48876i
$934$	−7412.76	−	12839.3i	−0.259693	−	0.449801i
$935$	24485.3			0.856422
$936$	1205.35	+	57.7718i	0.0420919	+	0.00201745i
$937$	37985.5			1.32437			0.662183	−	0.749342i	$-0.269630\pi$
$937$	37985.5			1.32437			0.662183	+	0.749342i	$0.269630\pi$
$938$	4922.20	+	8525.50i	0.171338	+	0.296767i
$939$	9562.41	+	229.030i	0.332330	+	0.00795964i
$940$	1760.82	−	3049.83i	0.0610974	−	0.105824i
$941$	−3119.24	+	5402.67i	−0.108060	+	0.187165i	−0.914984	−	0.403490i	$-0.867797\pi$
$941$	−3119.24	+	5402.67i	−0.108060	+	0.187165i	0.806924	+	0.590655i	$0.201130\pi$
$942$	−18892.4	+	30984.7i	−0.653448	+	1.07169i
$943$	2999.45	+	5195.20i	0.103580	+	0.179405i
$944$	29838.8			1.02878
$945$	−5128.12	−	369.036i	−0.176527	−	0.0127034i
$946$	−43839.8			−1.50672
$947$	−6252.85	−	10830.3i	−0.214562	−	0.371632i	0.738575	−	0.674171i	$-0.235499\pi$
$947$	−6252.85	−	10830.3i	−0.214562	−	0.371632i	−0.953137	+	0.302539i	$0.902166\pi$
$948$	5931.77	−	9728.48i	0.203223	−	0.333298i
$949$	681.133	−	1179.76i	0.0232987	−	0.0403546i
$950$	8945.23	−	15493.6i	0.305496	−	0.529135i
$951$	4154.46	+	99.5037i	0.141659	+	0.00339288i
$952$	−6543.58	−	11333.8i	−0.222772	−	0.385852i
$953$	−18577.0			−0.631447			−0.315724	−	0.948851i	$-0.602247\pi$
$953$	−18577.0			−0.631447			−0.315724	+	0.948851i	$0.602247\pi$
$954$	2364.27	−	3676.51i	0.0802371	−	0.124771i
$955$	−19823.9			−0.671715
$956$	3198.47	+	5539.91i	0.108207	+	0.187420i
$957$	9781.28	+	17919.3i	0.330391	+	0.605276i
$958$	9238.36	−	16001.3i	0.311564	−	0.539644i
$959$	−1663.71	+	2881.63i	−0.0560208	+	0.0970309i
$960$	7392.17	+	13542.5i	0.248522	+	0.455293i
$961$	−845.226	−	1463.97i	−0.0283718	−	0.0491415i
$962$	1498.77			0.0502310
$963$	898.912	+	1744.90i	0.0300800	+	0.0583891i
$964$	−11269.8			−0.376532
$965$	−5393.50	−	9341.81i	−0.179920	−	0.311631i
$966$	−11651.3	−	279.061i	−0.388069	−	0.00929466i
$967$	−1863.09	+	3226.96i	−0.0619575	+	0.107314i	−0.895340	−	0.445383i	$-0.853068\pi$
$967$	−1863.09	+	3226.96i	−0.0619575	+	0.107314i	0.833383	+	0.552696i	$0.186401\pi$
$968$	29807.3	−	51627.7i	0.989712	−	1.71423i
$969$	15517.5	−	25449.6i	0.514440	−	0.843714i
$970$	5503.53	+	9532.39i	0.182173	+	0.315532i
$971$	−18655.2			−0.616555			−0.308278	−	0.951296i	$-0.599753\pi$
$971$	−18655.2			−0.616555			−0.308278	+	0.951296i	$0.599753\pi$
$972$	−7756.41	−	933.157i	−0.255954	−	0.0307932i
$973$	12425.9			0.409411
$974$	−4158.67	−	7203.02i	−0.136809	−	0.236961i
$975$	−481.211	+	789.216i	−0.0158062	+	0.0259232i
$976$	14541.7	−	25187.0i	0.476915	−	0.826041i
$977$	−12603.0	+	21829.0i	−0.412697	+	0.714812i	−0.995184	−	0.0980284i	$-0.968746\pi$
$977$	−12603.0	+	21829.0i	−0.412697	+	0.714812i	0.582487	+	0.812840i	$0.302080\pi$
$978$	−38861.3	−	930.768i	−1.27060	−	0.0304322i
$979$	14119.7	+	24456.0i	0.460947	+	0.798384i
$980$	529.059			0.0172451
$981$	−6759.74	−	13121.5i	−0.220002	−	0.427051i
$982$	−23303.0			−0.757258
$983$	−14511.0	−	25133.7i	−0.470832	−	0.815504i	0.528612	−	0.848864i	$-0.322713\pi$
$983$	−14511.0	−	25133.7i	−0.470832	−	0.815504i	−0.999443	+	0.0333594i	$0.989379\pi$
$984$	2784.78	+	5101.73i	0.0902191	+	0.165282i
$985$	6391.12	−	11069.7i	0.206739	−	0.358083i
$986$	−5950.54	+	10306.6i	−0.192194	+	0.332891i
$987$	5684.09	+	10413.3i	0.183310	+	0.335824i
$988$	−141.411	−	244.930i	−0.00455351	−	0.00788691i
$989$	38569.8			1.24009
$990$	11427.2	−	17769.7i	0.366850	−	0.570462i
$991$	27702.8			0.888000			0.444000	−	0.896027i	$-0.353559\pi$
$991$	27702.8			0.888000			0.444000	+	0.896027i	$0.353559\pi$
$992$	8052.86	+	13948.0i	0.257741	+	0.446420i
$993$	−17182.4	−	411.537i	−0.549112	−	0.0131518i
$994$	34.8066	−	60.2869i	0.00111066	−	0.00192373i
$995$	10109.7	−	17510.4i	0.322108	−	0.557908i
$996$	−4641.18	+	7611.83i	−0.147652	+	0.242159i
$997$	−5474.93	−	9482.86i	−0.173915	−	0.301229i	0.765871	−	0.642995i	$-0.222308\pi$
$997$	−5474.93	−	9482.86i	−0.173915	−	0.301229i	−0.939785	+	0.341766i	$0.888975\pi$
$998$	−20269.8			−0.642917
$999$	−47218.6	−	3398.00i	−1.49542	−	0.107616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.f.c.22.3	✓	18
3.2	odd	2		189.4.f.c.64.7		18
9.2	odd	6		189.4.f.c.127.7		18
9.4	even	3		567.4.a.j.1.7		9
9.5	odd	6		567.4.a.k.1.3		9
9.7	even	3	inner	63.4.f.c.43.3	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.f.c.22.3	✓	18	1.1	even	1	trivial
63.4.f.c.43.3	yes	18	9.7	even	3	inner
189.4.f.c.64.7		18	3.2	odd	2
189.4.f.c.127.7		18	9.2	odd	6
567.4.a.j.1.7		9	9.4	even	3
567.4.a.k.1.3		9	9.5	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21836 - 2.11026i) q^{2} +(-2.70508 + 4.43650i) q^{3} +(1.03120 - 1.78609i) q^{4} +(2.61762 - 4.53384i) q^{5} +(12.6579 + 0.303171i) q^{6} +(-3.50000 - 6.06218i) q^{7} -24.5192 q^{8} +(-12.3651 - 24.0022i) q^{9} +O(q^{10})\)	\(q+(-1.21836 - 2.11026i) q^{2} +(-2.70508 + 4.43650i) q^{3} +(1.03120 - 1.78609i) q^{4} +(2.61762 - 4.53384i) q^{5} +(12.6579 + 0.303171i) q^{6} +(-3.50000 - 6.06218i) q^{7} -24.5192 q^{8} +(-12.3651 - 24.0022i) q^{9} -12.7568 q^{10} +(-30.6689 - 53.1202i) q^{11} +(5.13450 + 9.40642i) q^{12} +(0.911402 - 1.57859i) q^{13} +(-8.52852 + 14.7718i) q^{14} +(13.0335 + 23.8775i) q^{15} +(21.6237 + 37.4533i) q^{16} -76.2501 q^{17} +(-35.5858 + 55.3369i) q^{18} +75.2316 q^{19} +(-5.39856 - 9.35058i) q^{20} +(36.3626 + 0.870923i) q^{21} +(-74.7316 + 129.439i) q^{22} +(65.7482 - 113.879i) q^{23} +(66.3265 - 108.780i) q^{24} +(48.7962 + 84.5175i) q^{25} -4.44166 q^{26} +(139.934 + 10.0701i) q^{27} -14.4368 q^{28} +(32.0266 + 55.4716i) q^{29} +(34.5082 - 56.5955i) q^{30} +(88.7151 - 153.659i) q^{31} +(-45.3861 + 78.6110i) q^{32} +(318.630 + 7.63151i) q^{33} +(92.9001 + 160.908i) q^{34} -36.6466 q^{35} +(-55.6208 - 2.66588i) q^{36} -337.434 q^{37} +(-91.6591 - 158.758i) q^{38} +(4.53802 + 8.31366i) q^{39} +(-64.1820 + 111.166i) q^{40} +(-22.8101 + 39.5083i) q^{41} +(-42.4649 - 77.7958i) q^{42} +(146.657 + 254.018i) q^{43} -126.503 q^{44} +(-141.189 - 6.76714i) q^{45} -320.420 q^{46} +(163.082 + 282.467i) q^{47} +(-224.655 - 5.38073i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(118.903 - 205.945i) q^{50} +(206.263 - 338.284i) q^{51} +(-1.87967 - 3.25568i) q^{52} -66.4388 q^{53} +(-149.240 - 307.567i) q^{54} -321.118 q^{55} +(85.8173 + 148.640i) q^{56} +(-203.507 + 333.765i) q^{57} +(78.0397 - 135.169i) q^{58} +(344.978 - 597.519i) q^{59} +(56.0874 + 1.34335i) q^{60} +(-336.245 - 582.394i) q^{61} -432.348 q^{62} +(-102.228 + 158.967i) q^{63} +567.165 q^{64} +(-4.77140 - 8.26430i) q^{65} +(-372.101 - 681.690i) q^{66} +(288.573 - 499.823i) q^{67} +(-78.6289 + 136.189i) q^{68} +(327.371 + 599.744i) q^{69} +(44.6488 + 77.3340i) q^{70} -4.08120 q^{71} +(303.182 + 588.515i) q^{72} +747.346 q^{73} +(411.116 + 712.074i) q^{74} +(-506.959 - 12.1422i) q^{75} +(77.5786 - 134.370i) q^{76} +(-214.683 + 371.841i) q^{77} +(12.0150 - 19.7054i) q^{78} +(-531.622 - 920.796i) q^{79} +226.410 q^{80} +(-423.209 + 593.578i) q^{81} +111.164 q^{82} +(415.955 + 720.455i) q^{83} +(39.0526 - 64.0487i) q^{84} +(-199.594 + 345.706i) q^{85} +(357.363 - 618.971i) q^{86} +(-332.734 - 7.96933i) q^{87} +(751.979 + 1302.47i) q^{88} -460.391 q^{89} +(157.739 + 306.191i) q^{90} -12.7596 q^{91} +(-135.599 - 234.864i) q^{92} +(441.727 + 809.244i) q^{93} +(397.386 - 688.292i) q^{94} +(196.927 - 341.088i) q^{95} +(-225.985 - 414.005i) q^{96} +(-431.419 - 747.240i) q^{97} +119.399 q^{98} +(-895.776 + 1392.96i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9}+O(q^{10}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9} + 111 q^{11} - 18 q^{13} + 42 q^{14} - 36 q^{15} - 144 q^{16} - 546 q^{17} - 45 q^{18} + 90 q^{19} + 402 q^{20} - 63 q^{21} + 162 q^{22} + 312 q^{23} - 36 q^{24} - 279 q^{25} + 102 q^{26} + 432 q^{27} + 504 q^{28} + 378 q^{29} - 864 q^{30} - 18 q^{31} + 891 q^{32} + 513 q^{33} + 324 q^{34} - 336 q^{35} + 414 q^{36} - 72 q^{37} + 147 q^{38} - 810 q^{39} - 405 q^{40} + 477 q^{41} + 315 q^{42} + 171 q^{43} - 1896 q^{44} - 720 q^{45} - 756 q^{46} + 654 q^{47} - 2709 q^{48} - 441 q^{49} + 429 q^{50} + 1341 q^{51} - 747 q^{52} - 1896 q^{53} - 108 q^{54} - 432 q^{55} + 525 q^{56} - 1143 q^{57} - 297 q^{58} + 957 q^{59} + 5400 q^{60} + 198 q^{61} - 600 q^{62} - 504 q^{63} + 4770 q^{64} + 2478 q^{65} - 2646 q^{66} + 333 q^{67} + 1443 q^{68} + 3366 q^{69} - 5652 q^{71} - 3681 q^{72} + 306 q^{73} + 2100 q^{74} - 4113 q^{75} + 144 q^{76} + 777 q^{77} + 6336 q^{78} - 1152 q^{79} - 8418 q^{80} - 1917 q^{81} - 6048 q^{82} + 1890 q^{83} + 1008 q^{84} + 648 q^{85} + 3837 q^{86} + 4212 q^{87} + 2268 q^{88} - 2604 q^{89} - 135 q^{90} + 252 q^{91} + 987 q^{92} + 378 q^{93} - 324 q^{94} + 3144 q^{95} + 5643 q^{96} + 1737 q^{97} - 588 q^{98} + 720 q^{99}+O(q^{100}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9 + 111 * q^11 - 18 * q^13 + 42 * q^14 - 36 * q^15 - 144 * q^16 - 546 * q^17 - 45 * q^18 + 90 * q^19 + 402 * q^20 - 63 * q^21 + 162 * q^22 + 312 * q^23 - 36 * q^24 - 279 * q^25 + 102 * q^26 + 432 * q^27 + 504 * q^28 + 378 * q^29 - 864 * q^30 - 18 * q^31 + 891 * q^32 + 513 * q^33 + 324 * q^34 - 336 * q^35 + 414 * q^36 - 72 * q^37 + 147 * q^38 - 810 * q^39 - 405 * q^40 + 477 * q^41 + 315 * q^42 + 171 * q^43 - 1896 * q^44 - 720 * q^45 - 756 * q^46 + 654 * q^47 - 2709 * q^48 - 441 * q^49 + 429 * q^50 + 1341 * q^51 - 747 * q^52 - 1896 * q^53 - 108 * q^54 - 432 * q^55 + 525 * q^56 - 1143 * q^57 - 297 * q^58 + 957 * q^59 + 5400 * q^60 + 198 * q^61 - 600 * q^62 - 504 * q^63 + 4770 * q^64 + 2478 * q^65 - 2646 * q^66 + 333 * q^67 + 1443 * q^68 + 3366 * q^69 - 5652 * q^71 - 3681 * q^72 + 306 * q^73 + 2100 * q^74 - 4113 * q^75 + 144 * q^76 + 777 * q^77 + 6336 * q^78 - 1152 * q^79 - 8418 * q^80 - 1917 * q^81 - 6048 * q^82 + 1890 * q^83 + 1008 * q^84 + 648 * q^85 + 3837 * q^86 + 4212 * q^87 + 2268 * q^88 - 2604 * q^89 - 135 * q^90 + 252 * q^91 + 987 * q^92 + 378 * q^93 - 324 * q^94 + 3144 * q^95 + 5643 * q^96 + 1737 * q^97 - 588 * q^98 + 720 * q^99

Introduction

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