LMFDB - Embedded newform 63.4.i.a.5.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(5,63)]

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([5, 5]))

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

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

chi := DirichletCharacter("63.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.i (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:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.11
Character	$\chi$	$=$	63.5
Dual form			63.4.i.a.38.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.747815i q^{2} +(4.77381 - 2.05201i) q^{3} +7.44077 q^{4} +(4.35110 + 7.53632i) q^{5} +(-1.53452 - 3.56993i) q^{6} +(-11.6200 + 14.4213i) q^{7} -11.5468i q^{8} +(18.5785 - 19.5918i) q^{9} +O(q^{10})$	\(q-0.747815i q^{2} +(4.77381 - 2.05201i) q^{3} +7.44077 q^{4} +(4.35110 + 7.53632i) q^{5} +(-1.53452 - 3.56993i) q^{6} +(-11.6200 + 14.4213i) q^{7} -11.5468i q^{8} +(18.5785 - 19.5918i) q^{9} +(5.63577 - 3.25382i) q^{10} +(-35.9461 - 20.7535i) q^{11} +(35.5208 - 15.2685i) q^{12} +(33.0053 + 19.0556i) q^{13} +(10.7845 + 8.68963i) q^{14} +(36.2359 + 27.0485i) q^{15} +50.8913 q^{16} +(-39.9685 - 69.2274i) q^{17} +(-14.6510 - 13.8933i) q^{18} +(-49.4113 - 28.5276i) q^{19} +(32.3755 + 56.0761i) q^{20} +(-25.8791 + 92.6891i) q^{21} +(-15.5198 + 26.8811i) q^{22} +(-153.298 + 88.5068i) q^{23} +(-23.6942 - 55.1224i) q^{24} +(24.6359 - 42.6706i) q^{25} +(14.2501 - 24.6818i) q^{26} +(48.4877 - 131.651i) q^{27} +(-86.4620 + 107.306i) q^{28} +(-60.1430 + 34.7236i) q^{29} +(20.2272 - 27.0978i) q^{30} +260.805i q^{31} -130.432i q^{32} +(-214.186 - 25.3115i) q^{33} +(-51.7693 + 29.8890i) q^{34} +(-159.244 - 24.8237i) q^{35} +(138.238 - 145.778i) q^{36} +(-74.9359 + 129.793i) q^{37} +(-21.3334 + 36.9505i) q^{38} +(196.663 + 23.2407i) q^{39} +(87.0207 - 50.2414i) q^{40} +(54.7122 - 94.7643i) q^{41} +(69.3143 + 19.3528i) q^{42} +(124.193 + 215.108i) q^{43} +(-267.467 - 154.422i) q^{44} +(228.487 + 54.7678i) q^{45} +(66.1867 + 114.639i) q^{46} +295.057 q^{47} +(242.945 - 104.429i) q^{48} +(-72.9497 - 335.153i) q^{49} +(-31.9097 - 18.4231i) q^{50} +(-332.857 - 248.463i) q^{51} +(245.585 + 141.788i) q^{52} +(-263.613 + 152.197i) q^{53} +(-98.4504 - 36.2598i) q^{54} -361.202i q^{55} +(166.521 + 134.175i) q^{56} +(-294.419 - 34.7930i) q^{57} +(25.9668 + 44.9759i) q^{58} +720.693 q^{59} +(269.623 + 201.262i) q^{60} -648.357i q^{61} +195.034 q^{62} +(66.6571 + 495.584i) q^{63} +309.591 q^{64} +331.651i q^{65} +(-18.9283 + 160.172i) q^{66} -194.853 q^{67} +(-297.396 - 515.106i) q^{68} +(-550.200 + 737.084i) q^{69} +(-18.5635 + 119.085i) q^{70} +98.7349i q^{71} +(-226.223 - 214.523i) q^{72} +(226.289 - 130.648i) q^{73} +(97.0610 + 56.0382i) q^{74} +(30.0465 - 254.255i) q^{75} +(-367.658 - 212.268i) q^{76} +(716.989 - 277.235i) q^{77} +(17.3797 - 147.068i) q^{78} -1154.25 q^{79} +(221.433 + 383.533i) q^{80} +(-38.6779 - 727.973i) q^{81} +(-70.8661 - 40.9146i) q^{82} +(285.406 + 494.337i) q^{83} +(-192.560 + 689.679i) q^{84} +(347.813 - 602.431i) q^{85} +(160.861 - 92.8731i) q^{86} +(-215.858 + 289.178i) q^{87} +(-239.638 + 415.064i) q^{88} +(-89.5115 + 155.038i) q^{89} +(40.9561 - 170.866i) q^{90} +(-658.330 + 254.553i) q^{91} +(-1140.66 + 658.559i) q^{92} +(535.175 + 1245.04i) q^{93} -220.648i q^{94} -496.506i q^{95} +(-267.648 - 622.657i) q^{96} +(956.569 - 552.275i) q^{97} +(-250.632 + 54.5529i) q^{98} +(-1074.42 + 318.681i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 3 q^{3} - 162 q^{4} - 3 q^{5} + 24 q^{6} + 5 q^{7} - 45 q^{9}+O(q^{10}) $ 44 * q - 3 * q^3 - 162 * q^4 - 3 * q^5 + 24 * q^6 + 5 * q^7 - 45 * q^9	\( 44 q - 3 q^{3} - 162 q^{4} - 3 q^{5} + 24 q^{6} + 5 q^{7} - 45 q^{9} - 6 q^{10} + 9 q^{11} + 186 q^{12} - 36 q^{13} + 54 q^{14} - 141 q^{15} + 526 q^{16} - 72 q^{17} - 54 q^{18} - 6 q^{19} + 24 q^{20} - 81 q^{21} + 14 q^{22} - 285 q^{23} - 114 q^{24} - 349 q^{25} - 96 q^{26} + 432 q^{27} - 156 q^{28} - 132 q^{29} - 447 q^{30} - 3 q^{33} + 24 q^{34} + 765 q^{35} + 1122 q^{36} + 82 q^{37} - 873 q^{38} + 306 q^{39} + 420 q^{40} + 618 q^{41} - 282 q^{42} + 82 q^{43} + 603 q^{44} + 291 q^{45} + 266 q^{46} - 402 q^{47} - 1569 q^{48} - 79 q^{49} - 1845 q^{50} + 453 q^{51} + 189 q^{52} + 564 q^{53} - 2385 q^{54} + 66 q^{56} + 1170 q^{57} + 269 q^{58} + 1494 q^{59} + 2265 q^{60} - 2904 q^{62} - 636 q^{63} - 1144 q^{64} - 372 q^{66} - 590 q^{67} + 3504 q^{68} - 1005 q^{69} - 105 q^{70} + 1830 q^{72} - 6 q^{73} + 1515 q^{74} - 33 q^{75} - 144 q^{76} - 4443 q^{77} - 5985 q^{78} + 1102 q^{79} - 4239 q^{80} - 4017 q^{81} + 18 q^{82} + 1830 q^{83} + 3165 q^{84} - 237 q^{85} + 1209 q^{86} + 2013 q^{87} - 623 q^{88} + 4266 q^{89} + 9993 q^{90} - 1140 q^{91} + 7896 q^{92} - 729 q^{93} + 3975 q^{96} - 792 q^{97} + 5667 q^{98} + 4335 q^{99}+O(q^{100}) \) 44 * q - 3 * q^3 - 162 * q^4 - 3 * q^5 + 24 * q^6 + 5 * q^7 - 45 * q^9 - 6 * q^10 + 9 * q^11 + 186 * q^12 - 36 * q^13 + 54 * q^14 - 141 * q^15 + 526 * q^16 - 72 * q^17 - 54 * q^18 - 6 * q^19 + 24 * q^20 - 81 * q^21 + 14 * q^22 - 285 * q^23 - 114 * q^24 - 349 * q^25 - 96 * q^26 + 432 * q^27 - 156 * q^28 - 132 * q^29 - 447 * q^30 - 3 * q^33 + 24 * q^34 + 765 * q^35 + 1122 * q^36 + 82 * q^37 - 873 * q^38 + 306 * q^39 + 420 * q^40 + 618 * q^41 - 282 * q^42 + 82 * q^43 + 603 * q^44 + 291 * q^45 + 266 * q^46 - 402 * q^47 - 1569 * q^48 - 79 * q^49 - 1845 * q^50 + 453 * q^51 + 189 * q^52 + 564 * q^53 - 2385 * q^54 + 66 * q^56 + 1170 * q^57 + 269 * q^58 + 1494 * q^59 + 2265 * q^60 - 2904 * q^62 - 636 * q^63 - 1144 * q^64 - 372 * q^66 - 590 * q^67 + 3504 * q^68 - 1005 * q^69 - 105 * q^70 + 1830 * q^72 - 6 * q^73 + 1515 * q^74 - 33 * q^75 - 144 * q^76 - 4443 * q^77 - 5985 * q^78 + 1102 * q^79 - 4239 * q^80 - 4017 * q^81 + 18 * q^82 + 1830 * q^83 + 3165 * q^84 - 237 * q^85 + 1209 * q^86 + 2013 * q^87 - 623 * q^88 + 4266 * q^89 + 9993 * q^90 - 1140 * q^91 + 7896 * q^92 - 729 * q^93 + 3975 * q^96 - 792 * q^97 + 5667 * q^98 + 4335 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	0.747815i		−	0.264392i	−0.991224	−	0.132196i	$-0.957797\pi$
$2$		−	0.747815i		−	0.264392i	0.991224	−	0.132196i	$-0.0422029\pi$
$3$	4.77381	−	2.05201i	0.918720	−	0.394910i
$3$	4.77381	−	2.05201i	0.918720	−	0.394910i
$4$	7.44077			0.930097
$5$	4.35110	+	7.53632i	0.389174	+	0.674069i	0.992339	−	0.123548i	$-0.0394271\pi$
$5$	4.35110	+	7.53632i	0.389174	+	0.674069i	−0.603165	+	0.797617i	$0.706094\pi$
$6$	−1.53452	−	3.56993i	−0.104411	−	0.242903i
$7$	−11.6200	+	14.4213i	−0.627423	+	0.778679i
$7$	−11.6200	+	14.4213i	−0.627423	+	0.778679i
$8$		−	11.5468i		−	0.510303i
$9$	18.5785	−	19.5918i	0.688093	−	0.725623i
$10$	5.63577	−	3.25382i	0.178219	−	0.102895i
$11$	−35.9461	−	20.7535i	−0.985288	−	0.568856i	−0.0814258	−	0.996679i	$-0.525947\pi$
$11$	−35.9461	−	20.7535i	−0.985288	−	0.568856i	−0.903863	+	0.427823i	$0.859281\pi$
$12$	35.5208	−	15.2685i	0.854498	−	0.367304i
$13$	33.0053	+	19.0556i	0.704155	+	0.406544i	0.808893	−	0.587956i	$-0.200067\pi$
$13$	33.0053	+	19.0556i	0.704155	+	0.406544i	−0.104738	+	0.994500i	$0.533400\pi$
$14$	10.7845	+	8.68963i	0.205877	+	0.165886i
$15$	36.2359	+	27.0485i	0.623738	+	0.465592i
$16$	50.8913			0.795176
$17$	−39.9685	−	69.2274i	−0.570222	−	0.987654i	−0.996543	−	0.0830818i	$-0.973524\pi$
$17$	−39.9685	−	69.2274i	−0.570222	−	0.987654i	0.426320	−	0.904572i	$-0.359810\pi$
$18$	−14.6510	−	13.8933i	−0.191849	−	0.181927i
$19$	−49.4113	−	28.5276i	−0.596617	−	0.344457i	0.171092	−	0.985255i	$-0.445270\pi$
$19$	−49.4113	−	28.5276i	−0.596617	−	0.344457i	−0.767710	+	0.640798i	$0.778604\pi$
$20$	32.3755	+	56.0761i	0.361969	+	0.626949i
$21$	−25.8791	+	92.6891i	−0.268918	+	0.963163i
$22$	−15.5198	+	26.8811i	−0.150401	+	0.260503i
$23$	−153.298	+	88.5068i	−1.38978	+	0.802389i	−0.993290	−	0.115651i	$-0.963105\pi$
$23$	−153.298	+	88.5068i	−1.38978	+	0.802389i	−0.396488	+	0.918040i	$0.629771\pi$
$24$	−23.6942	−	55.1224i	−0.201523	−	0.468826i
$25$	24.6359	−	42.6706i	0.197087	−	0.341365i
$26$	14.2501	−	24.6818i	0.107487	−	0.186173i
$27$	48.4877	−	131.651i	0.345610	−	0.938378i
$28$	−86.4620	+	107.306i	−0.583564	+	0.724247i
$29$	−60.1430	+	34.7236i	−0.385113	+	0.222345i	−0.680041	−	0.733174i	$-0.738038\pi$
$29$	−60.1430	+	34.7236i	−0.385113	+	0.222345i	0.294927	+	0.955520i	$0.404705\pi$
$30$	20.2272	−	27.0978i	0.123099	−	0.164912i
$31$			260.805i			1.51103i	0.655130	+	0.755517i	$0.272614\pi$
$31$			260.805i			1.51103i	−0.655130	+	0.755517i	$0.727386\pi$
$32$		−	130.432i		−	0.720542i
$33$	−214.186	−	25.3115i	−1.12985	−	0.133520i
$34$	−51.7693	+	29.8890i	−0.261128	+	0.150762i
$35$	−159.244	−	24.8237i	−0.769060	−	0.119885i
$36$	138.238	−	145.778i	0.639993	−	0.674899i
$37$	−74.9359	+	129.793i	−0.332957	+	0.576698i	−0.983090	−	0.183122i	$-0.941380\pi$
$37$	−74.9359	+	129.793i	−0.332957	+	0.576698i	0.650134	+	0.759820i	$0.274713\pi$
$38$	−21.3334	+	36.9505i	−0.0910719	+	0.157741i
$39$	196.663	+	23.2407i	0.807469	+	0.0954227i
$40$	87.0207	−	50.2414i	0.343980	−	0.198597i
$41$	54.7122	−	94.7643i	0.208405	−	0.360968i	−0.742807	−	0.669505i	$-0.766506\pi$
$41$	54.7122	−	94.7643i	0.208405	−	0.360968i	0.951212	+	0.308537i	$0.0998395\pi$
$42$	69.3143	+	19.3528i	0.254653	+	0.0710999i
$43$	124.193	+	215.108i	0.440446	+	0.762875i	0.997723	−	0.0674517i	$-0.0214869\pi$
$43$	124.193	+	215.108i	0.440446	+	0.762875i	−0.557276	+	0.830327i	$0.688154\pi$
$44$	−267.467	−	154.422i	−0.916413	−	0.529092i
$45$	228.487	+	54.7678i	0.756908	+	0.181429i
$46$	66.1867	+	114.639i	0.212146	+	0.367447i
$47$	295.057			0.915711			0.457855	−	0.889027i	$-0.348618\pi$
$47$	295.057			0.915711			0.457855	+	0.889027i	$0.348618\pi$
$48$	242.945	−	104.429i	0.730544	−	0.314023i
$49$	−72.9497	−	335.153i	−0.212681	−	0.977122i
$50$	−31.9097	−	18.4231i	−0.0902543	−	0.0521084i
$51$	−332.857	−	248.463i	−0.913909	−	0.682191i
$52$	245.585	+	141.788i	0.654932	+	0.378125i
$53$	−263.613	+	152.197i	−0.683208	+	0.394450i	−0.801062	−	0.598581i	$-0.795732\pi$
$53$	−263.613	+	152.197i	−0.683208	+	0.394450i	0.117855	+	0.993031i	$0.462398\pi$
$54$	−98.4504	−	36.2598i	−0.248100	−	0.0913766i
$55$		−	361.202i		−	0.885537i
$56$	166.521	+	134.175i	0.397362	+	0.320176i
$57$	−294.419	−	34.7930i	−0.684154	−	0.0808499i
$58$	25.9668	+	44.9759i	0.0587864	+	0.101821i
$59$	720.693			1.59027			0.795137	−	0.606429i	$-0.207399\pi$
$59$	720.693			1.59027			0.795137	+	0.606429i	$0.207399\pi$
$60$	269.623	+	201.262i	0.580137	+	0.433046i
$61$		−	648.357i		−	1.36088i	−0.732804	−	0.680440i	$-0.761789\pi$
$61$		−	648.357i		−	1.36088i	0.732804	−	0.680440i	$-0.238211\pi$
$62$	195.034			0.399506
$63$	66.6571	+	495.584i	0.133302	+	0.991075i
$64$	309.591			0.604671
$65$			331.651i			0.632866i
$66$	−18.9283	+	160.172i	−0.0353017	+	0.298724i
$67$	−194.853			−0.355299			−0.177649	−	0.984094i	$-0.556849\pi$
$67$	−194.853			−0.355299			−0.177649	+	0.984094i	$0.556849\pi$
$68$	−297.396	−	515.106i	−0.530362	−	0.918614i
$69$	−550.200	+	737.084i	−0.959946	+	1.28601i
$70$	−18.5635	+	119.085i	−0.0316966	+	0.203334i
$71$			98.7349i			0.165038i	0.996590	+	0.0825188i	$0.0262965\pi$
$71$			98.7349i			0.165038i	−0.996590	+	0.0825188i	$0.973704\pi$
$72$	−226.223	−	214.523i	−0.370287	−	0.351136i
$73$	226.289	−	130.648i	0.362809	−	0.209468i	−0.307503	−	0.951547i	$-0.599493\pi$
$73$	226.289	−	130.648i	0.362809	−	0.209468i	0.670312	+	0.742079i	$0.266160\pi$
$74$	97.0610	+	56.0382i	0.152475	+	0.0880312i
$75$	30.0465	−	254.255i	0.0462597	−	0.391450i
$76$	−367.658	−	212.268i	−0.554912	−	0.320379i
$77$	716.989	−	277.235i	1.06115	−	0.410310i
$78$	17.3797	−	147.068i	0.0252290	−	0.213489i
$79$	−1154.25			−1.64384			−0.821918	−	0.569606i	$-0.807096\pi$
$79$	−1154.25			−1.64384			−0.821918	+	0.569606i	$0.807096\pi$
$80$	221.433	+	383.533i	0.309462	+	0.536004i
$81$	−38.6779	−	727.973i	−0.0530561	−	0.998592i
$82$	−70.8661	−	40.9146i	−0.0954372	−	0.0551007i
$83$	285.406	+	494.337i	0.377438	+	0.653741i	0.990689	−	0.136147i	$-0.0434719\pi$
$83$	285.406	+	494.337i	0.377438	+	0.653741i	−0.613251	+	0.789888i	$0.710139\pi$
$84$	−192.560	+	689.679i	−0.250120	+	0.895835i
$85$	347.813	−	602.431i	0.443831	−	0.768739i
$86$	160.861	−	92.8731i	0.201699	−	0.116451i
$87$	−215.858	+	289.178i	−0.266005	+	0.356358i
$88$	−239.638	+	415.064i	−0.290289	+	0.502796i
$89$	−89.5115	+	155.038i	−0.106609	+	0.184652i	−0.914394	−	0.404824i	$-0.867333\pi$
$89$	−89.5115	+	155.038i	−0.106609	+	0.184652i	0.807785	+	0.589477i	$0.200666\pi$
$90$	40.9561	−	170.866i	0.0479684	−	0.200121i
$91$	−658.330	+	254.553i	−0.758370	+	0.293236i
$92$	−1140.66	+	658.559i	−1.29263	+	0.746299i
$93$	535.175	+	1245.04i	0.596721	+	1.38822i
$94$		−	220.648i		−	0.242107i
$95$		−	496.506i		−	0.536215i
$96$	−267.648	−	622.657i	−0.284549	−	0.661976i
$97$	956.569	−	552.275i	1.00129	−	0.578093i	0.0926581	−	0.995698i	$-0.470464\pi$
$97$	956.569	−	552.275i	1.00129	−	0.578093i	0.908629	+	0.417605i	$0.137130\pi$
$98$	−250.632	+	54.5529i	−0.258344	+	0.0562314i
$99$	−1074.42	+	318.681i	−1.09075	+	0.323521i
$100$	183.310	−	317.502i	0.183310	−	0.317502i
$101$	−0.375397	+	0.650207i	−0.000369836	+	0.000640575i	−0.866210	−	0.499680i	$-0.833451\pi$
$101$	−0.375397	+	0.650207i	−0.000369836	+	0.000640575i	0.865840	+	0.500320i	$0.166784\pi$
$102$	−185.804	+	248.916i	−0.180366	+	0.241631i
$103$	652.141	−	376.514i	0.623858	−	0.360184i	−0.154512	−	0.987991i	$-0.549380\pi$
$103$	652.141	−	376.514i	0.623858	−	0.360184i	0.778369	+	0.627807i	$0.216047\pi$
$104$	220.032	−	381.107i	0.207461	−	0.359332i
$105$	−811.138	+	208.266i	−0.753894	+	0.193569i
$106$	113.815	+	197.134i	0.104290	+	0.180635i
$107$	−1089.54	−	629.045i	−0.984388	−	0.568337i	−0.0807962	−	0.996731i	$-0.525746\pi$
$107$	−1089.54	−	629.045i	−0.984388	−	0.568337i	−0.903592	+	0.428394i	$0.859080\pi$
$108$	360.786	−	979.584i	0.321450	−	0.872783i
$109$	−110.812	−	191.932i	−0.0973748	−	0.168658i	0.813222	−	0.581953i	$-0.197711\pi$
$109$	−110.812	−	191.932i	−0.0973748	−	0.168658i	−0.910597	+	0.413295i	$0.864378\pi$
$110$	−270.112			−0.234129
$111$	−91.3937	+	773.376i	−0.0781505	+	0.661311i
$112$	−591.358	+	733.920i	−0.498912	+	0.619187i
$113$	1345.36	+	776.746i	1.12001	+	0.646638i	0.941404	−	0.337282i	$-0.109508\pi$
$113$	1345.36	+	776.746i	1.12001	+	0.646638i	0.178607	+	0.983921i	$0.442841\pi$
$114$	−26.0187	+	220.171i	−0.0213761	+	0.180885i
$115$	−1334.03	−	770.203i	−1.08173	−	0.624538i
$116$	−447.511	+	258.370i	−0.358192	+	0.206803i
$117$	986.523	−	292.608i	0.779522	−	0.231211i
$118$		−	538.945i		−	0.420457i
$119$	1462.79	+	228.026i	1.12684	+	0.175657i
$120$	312.324	−	418.410i	0.237593	−	0.318296i
$121$	195.917	+	339.338i	0.147195	+	0.254950i
$122$	−484.851			−0.359806
$123$	66.7283	−	564.656i	0.0489161	−	0.413930i
$124$			1940.59i			1.40541i
$125$	1516.55			1.08515
$126$	370.605	−	49.8472i	0.262033	−	0.0352440i
$127$	2425.06			1.69440			0.847202	−	0.531271i	$-0.178285\pi$
$127$	2425.06			1.69440			0.847202	+	0.531271i	$0.178285\pi$
$128$		−	1274.97i		−	0.880412i
$129$	1034.28	+	772.040i	0.705914	+	0.526933i
$130$	248.014			0.167325
$131$	−24.4173	−	42.2921i	−0.0162851	−	0.0282067i	0.857768	−	0.514037i	$-0.171851\pi$
$131$	−24.4173	−	42.2921i	−0.0162851	−	0.0282067i	−0.874053	+	0.485830i	$0.838517\pi$
$132$	−1593.71	−	188.337i	−1.05087	−	0.124187i
$133$	985.567	−	381.085i	0.642553	−	0.248453i
$134$			145.714i			0.0939384i
$135$	1203.14	−	207.407i	0.767034	−	0.132228i
$136$	−799.358	+	461.510i	−0.504003	+	0.290986i
$137$	1327.03	+	766.160i	0.827559	+	0.477792i	0.853016	−	0.521884i	$-0.174771\pi$
$137$	1327.03	+	766.160i	0.827559	+	0.477792i	−0.0254569	+	0.999676i	$0.508104\pi$
$138$	551.202	+	411.448i	0.340011	+	0.253802i
$139$	−638.674	−	368.739i	−0.389724	−	0.225007i	0.292317	−	0.956322i	$-0.405574\pi$
$139$	−638.674	−	368.739i	−0.389724	−	0.225007i	−0.682040	+	0.731314i	$0.738907\pi$
$140$	−1184.90	−	184.707i	−0.715300	−	0.111504i
$141$	1408.54	−	605.459i	0.841282	−	0.361623i
$142$	73.8354			0.0436347
$143$	−790.942	−	1369.95i	−0.462531	−	0.801126i
$144$	945.484	−	997.052i	0.547155	−	0.576998i
$145$	−523.376	−	302.172i	−0.299752	−	0.173062i
$146$	−97.7003	−	169.222i	−0.0553817	−	0.0959240i
$147$	−1035.98	−	1450.26i	−0.581269	−	0.813711i
$148$	−557.581	+	965.759i	−0.309682	+	0.536385i
$149$	1278.04	−	737.878i	0.702693	−	0.405700i	−0.105657	−	0.994403i	$-0.533694\pi$
$149$	1278.04	−	737.878i	0.702693	−	0.405700i	0.808350	+	0.588703i	$0.200361\pi$
$150$	−190.135	−	22.4692i	−0.103497	−	0.0122307i
$151$	637.438	−	1104.08i	0.343536	−	0.595022i	−0.641550	−	0.767081i	$-0.721709\pi$
$151$	637.438	−	1104.08i	0.343536	−	0.595022i	0.985087	+	0.172059i	$0.0550418\pi$
$152$	−329.404	+	570.544i	−0.175778	+	0.304456i
$153$	−2098.85	−	503.088i	−1.10903	−	0.265832i
$154$	−207.320	−	536.175i	−0.108483	−	0.280560i
$155$	−1965.51	+	1134.79i	−1.01854	+	0.588055i
$156$	1463.33	+	172.929i	0.751025	+	0.0887523i
$157$			1984.00i			1.00854i	0.863547	+	0.504268i	$0.168238\pi$
$157$			1984.00i			1.00854i	−0.863547	+	0.504268i	$0.831762\pi$
$158$			863.164i			0.434618i
$159$	−946.128	+	1267.49i	−0.471904	+	0.632194i
$160$	982.977	−	567.522i	0.485695	−	0.280416i
$161$	504.945	−	3239.22i	0.247175	−	1.58563i
$162$	−544.389	+	28.9239i	−0.264020	+	0.0140276i
$163$	−1836.59	+	3181.06i	−0.882532	+	1.52859i	−0.0340145	+	0.999421i	$0.510829\pi$
$163$	−1836.59	+	3181.06i	−0.882532	+	1.52859i	−0.848517	+	0.529168i	$0.822504\pi$
$164$	407.101	−	705.119i	0.193837	−	0.335735i
$165$	−741.191	−	1724.31i	−0.349707	−	0.813560i
$166$	369.673	−	213.431i	0.172844	−	0.0997917i
$167$	−2007.55	+	3477.17i	−0.930231	+	1.61121i	−0.147306	+	0.989091i	$0.547060\pi$
$167$	−2007.55	+	3477.17i	−0.930231	+	1.61121i	−0.782925	+	0.622116i	$0.786273\pi$
$168$	1070.27	+	298.822i	0.491505	+	0.137230i
$169$	−372.268	−	644.787i	−0.169444	−	0.293485i
$170$	−450.507	−	260.100i	−0.203249	−	0.117346i
$171$	−1476.90	+	438.056i	−0.660474	+	0.195900i
$172$	924.089	+	1600.57i	0.409658	+	0.709548i
$173$	−2093.51			−0.920037			−0.460019	−	0.887909i	$-0.652157\pi$
$173$	−2093.51			−0.920037			−0.460019	+	0.887909i	$0.652157\pi$
$174$	216.252	+	161.422i	0.0942183	+	0.0703297i
$175$	329.097	+	851.117i	0.142157	+	0.367648i
$176$	−1829.35	−	1056.17i	−0.783478	−	0.452341i
$177$	3440.45	−	1478.87i	1.46102	−	0.628015i
$178$	115.940	+	66.9380i	0.0488206	+	0.0281866i
$179$	−3194.00	+	1844.06i	−1.33369	+	0.770008i	−0.985863	−	0.167551i	$-0.946414\pi$
$179$	−3194.00	+	1844.06i	−1.33369	+	0.770008i	−0.347829	+	0.937558i	$0.613081\pi$
$180$	1700.12	+	407.515i	0.703997	+	0.168746i
$181$		−	1648.55i		−	0.676995i	−0.940967	−	0.338497i	$-0.890081\pi$
$181$		−	1648.55i		−	0.676995i	0.940967	−	0.338497i	$-0.109919\pi$
$182$	190.359	+	492.309i	0.0775293	+	0.200507i
$183$	−1330.44	−	3095.13i	−0.537424	−	1.25027i
$184$	1021.97	+	1770.11i	0.409461	+	0.709208i
$185$	−1304.21			−0.518312
$186$	931.056	−	400.212i	0.367034	−	0.157769i
$187$			3317.95i			1.29750i
$188$	2195.45			0.851700
$189$	1335.15	+	2229.04i	0.513852	+	0.857879i
$190$	−371.295			−0.141771
$191$		−	3667.20i		−	1.38926i	−0.719366	−	0.694631i	$-0.755568\pi$
$191$		−	3667.20i		−	1.38926i	0.719366	−	0.694631i	$-0.244432\pi$
$192$	1477.93	−	635.285i	0.555523	−	0.238790i
$193$	−342.125			−0.127600			−0.0637998	−	0.997963i	$-0.520322\pi$
$193$	−342.125			−0.127600			−0.0637998	+	0.997963i	$0.520322\pi$
$194$	−413.000	−	715.336i	−0.152844	−	0.264733i
$195$	680.551	+	1583.24i	0.249925	+	0.581426i
$196$	−542.802	−	2493.80i	−0.197814	−	0.908817i
$197$			468.339i			0.169380i	0.996407	+	0.0846898i	$0.0269899\pi$
$197$			468.339i			0.169380i	−0.996407	+	0.0846898i	$0.973010\pi$
$198$	238.314	+	803.471i	0.0855366	+	0.288385i
$199$	−1359.11	+	784.682i	−0.484144	+	0.279521i	−0.722142	−	0.691745i	$-0.756842\pi$
$199$	−1359.11	+	784.682i	−0.484144	+	0.279521i	0.237998	+	0.971266i	$0.423509\pi$
$200$	−492.711	−	284.467i	−0.174200	−	0.100574i
$201$	−930.189	+	399.839i	−0.326420	+	0.140311i
$202$	0.486235	+	0.280728i	0.000169363	+	9.77818e-5i
$203$	198.103	−	1270.83i	0.0684933	−	0.439384i
$204$	−2476.72	−	1848.76i	−0.850023	−	0.634504i
$205$	952.232			0.324423
$206$	−281.563	−	487.681i	−0.0952300	−	0.164943i
$207$	−1114.05	+	4647.71i	−0.374065	+	1.56057i
$208$	1679.68	+	969.764i	0.559927	+	0.323274i
$209$	1184.10	+	2050.92i	0.391893	+	0.678779i
$210$	155.745	+	606.581i	0.0511781	+	0.199324i
$211$	1244.68	−	2155.85i	0.406101	−	0.703387i	−0.588348	−	0.808608i	$-0.700222\pi$
$211$	1244.68	−	2155.85i	0.406101	−	0.703387i	0.994449	+	0.105221i	$0.0335549\pi$
$212$	−1961.48	+	1132.46i	−0.635449	+	0.366877i
$213$	202.605	+	471.341i	0.0651749	+	0.151623i
$214$	−470.409	+	814.772i	−0.150264	+	0.260265i
$215$	−1080.75	+	1871.91i	−0.342821	+	0.593783i
$216$	−1520.15	−	559.879i	−0.478857	−	0.176366i
$217$	−3761.16	−	3030.57i	−1.17661	−	0.948057i
$218$	−143.530	+	82.8668i	−0.0445920	+	0.0257452i
$219$	812.168	−	1088.03i	0.250599	−	0.335719i
$220$		−	2687.62i		−	0.823635i
$221$		−	3046.49i		−	0.927282i
$222$	578.342	+	68.3455i	0.174846	+	0.0206624i
$223$	−858.894	+	495.883i	−0.257918	+	0.148909i	−0.623385	−	0.781915i	$-0.714243\pi$
$223$	−858.894	+	495.883i	−0.257918	+	0.148909i	0.365466	+	0.930825i	$0.380910\pi$
$224$	1881.00	+	1515.62i	0.561071	+	0.452084i
$225$	−378.296	−	1275.42i	−0.112088	−	0.377902i
$226$	580.862	−	1006.08i	0.170966	−	0.296122i
$227$	301.732	−	522.616i	0.0882233	−	0.152807i	−0.818537	−	0.574454i	$-0.805214\pi$
$227$	301.732	−	522.616i	0.0882233	−	0.152807i	0.906760	+	0.421647i	$0.138548\pi$
$228$	−2190.71	−	258.887i	−0.636329	−	0.0751982i
$229$	−1121.72	+	647.623i	−0.323690	+	0.186883i	−0.653036	−	0.757327i	$-0.726505\pi$
$229$	−1121.72	+	647.623i	−0.323690	+	0.186883i	0.329346	+	0.944209i	$0.393172\pi$
$230$	−575.969	+	997.608i	−0.165123	+	0.286002i
$231$	2853.88	−	2794.73i	0.812863	−	0.796017i
$232$	400.948	+	694.462i	0.113463	+	0.196524i
$233$	3699.70	+	2136.02i	1.04024	+	0.600581i	0.919900	−	0.392152i	$-0.128269\pi$
$233$	3699.70	+	2136.02i	1.04024	+	0.600581i	0.120336	+	0.992733i	$0.461603\pi$
$234$	−218.817	−	737.736i	−0.0611303	−	0.206100i
$235$	1283.82	+	2223.64i	0.356371	+	0.617253i
$236$	5362.51			1.47911
$237$	−5510.16	+	2368.53i	−1.51022	+	0.649166i
$238$	170.521	−	1093.89i	0.0464423	−	0.297927i
$239$	2074.66	+	1197.80i	0.561500	+	0.324182i	0.753747	−	0.657164i	$-0.228244\pi$
$239$	2074.66	+	1197.80i	0.561500	+	0.324182i	−0.192247	+	0.981346i	$0.561578\pi$
$240$	1844.09	+	1376.53i	0.495982	+	0.370228i
$241$	708.518	+	409.063i	0.189376	+	0.109336i	0.591690	−	0.806165i	$-0.298461\pi$
$241$	708.518	+	409.063i	0.189376	+	0.109336i	−0.402314	+	0.915502i	$0.631794\pi$
$242$	253.762	−	146.510i	0.0674068	−	0.0389174i
$243$	−1678.45	−	3395.84i	−0.443097	−	0.896474i
$244$		−	4824.28i		−	1.26575i
$245$	2208.41	−	2008.05i	0.575877	−	0.523632i
$246$	−422.258	−	49.9004i	−0.109440	−	0.0129331i
$247$	−1087.22	−	1883.12i	−0.280074	−	0.485103i
$248$	3011.48			0.771085
$249$	2376.86	+	1774.22i	0.604928	+	0.451552i
$250$		−	1134.10i		−	0.286906i
$251$	7516.24			1.89012			0.945062	−	0.326891i	$-0.106001\pi$
$251$	7516.24			1.89012			0.945062	+	0.326891i	$0.106001\pi$
$252$	495.981	+	3687.53i	0.123984	+	0.921796i
$253$	7347.31			1.82578
$254$		−	1813.50i		−	0.447988i
$255$	424.202	−	3589.61i	0.104175	−	0.881529i
$256$	1523.29			0.371896
$257$	2774.31	+	4805.24i	0.673372	+	1.16631i	0.976942	+	0.213505i	$0.0684879\pi$
$257$	2774.31	+	4805.24i	0.673372	+	1.16631i	−0.303570	+	0.952809i	$0.598179\pi$
$258$	577.343	−	773.446i	0.139317	−	0.186638i
$259$	−1001.03	−	2588.87i	−0.240158	−	0.621099i
$260$			2467.74i			0.588626i
$261$	−437.070	+	1823.42i	−0.103655	+	0.432441i
$262$	−31.6267	+	18.2597i	−0.00745764	+	0.00430567i
$263$	−5519.74	−	3186.82i	−1.29415	−	0.747179i	−0.314764	−	0.949170i	$-0.601925\pi$
$263$	−5519.74	−	3186.82i	−1.29415	−	0.747179i	−0.979387	+	0.201991i	$0.935259\pi$
$264$	−292.268	+	2473.18i	−0.0681357	+	0.576566i
$265$	−2294.01	−	1324.45i	−0.531773	−	0.307019i
$266$	−284.981	−	737.022i	−0.0656891	−	0.169886i
$267$	−109.170	+	923.802i	−0.0250229	+	0.211745i
$268$	−1449.85			−0.330462
$269$	−2137.07	−	3701.52i	−0.484385	−	0.838979i	0.515454	−	0.856917i	$-0.327623\pi$
$269$	−2137.07	−	3701.52i	−0.484385	−	0.838979i	−0.999839	+	0.0179379i	$0.994290\pi$
$270$	−155.102	−	899.724i	−0.0349600	−	0.202798i
$271$	−1818.38	−	1049.84i	−0.407597	−	0.235326i	0.282160	−	0.959367i	$-0.408949\pi$
$271$	−1818.38	−	1049.84i	−0.407597	−	0.235326i	−0.689757	+	0.724041i	$0.742283\pi$
$272$	−2034.05	−	3523.07i	−0.453427	−	0.785359i
$273$	−2620.39	+	2566.09i	−0.580928	+	0.568889i
$274$	572.946	−	992.371i	0.126325	−	0.218800i
$275$	−1771.13	+	1022.56i	−0.388375	+	0.224229i
$276$	−4093.91	+	5484.48i	−0.892843	+	1.19611i
$277$	−2205.33	+	3819.74i	−0.478359	+	0.828542i	−0.999692	−	0.0248113i	$-0.992102\pi$
$277$	−2205.33	+	3819.74i	−0.478359	+	0.828542i	0.521333	+	0.853353i	$0.325435\pi$
$278$	−275.748	+	477.610i	−0.0594902	+	0.103040i
$279$	5109.65	+	4845.38i	1.09644	+	1.03973i
$280$	−286.635	+	1838.76i	−0.0611775	+	0.392454i
$281$	−4392.19	+	2535.83i	−0.932443	+	0.538346i	−0.887583	−	0.460647i	$-0.847617\pi$
$281$	−4392.19	+	2535.83i	−0.932443	+	0.538346i	−0.0448593	+	0.998993i	$0.514284\pi$
$282$	−452.771	−	1053.33i	−0.0956104	−	0.222429i
$283$		−	552.595i		−	0.116072i	−0.998314	−	0.0580360i	$-0.981516\pi$
$283$		−	552.595i		−	0.116072i	0.998314	−	0.0580360i	$-0.0184838\pi$
$284$			734.664i			0.153501i
$285$	−1018.84	−	2370.23i	−0.211756	−	0.492632i
$286$	−1024.47	+	591.478i	−0.211812	+	0.122290i
$287$	730.870	+	1890.19i	0.150320	+	0.388760i
$288$	−2555.40	−	2423.23i	−0.522841	−	0.495800i
$289$	−738.458	+	1279.05i	−0.150307	+	0.260339i
$290$	−225.968	+	391.389i	−0.0457563	+	0.0792522i
$291$	3433.20	−	4599.34i	0.691608	−	0.926524i
$292$	1683.76	−	972.120i	0.337448	−	0.194825i
$293$	−496.106	+	859.280i	−0.0989174	+	0.171330i	−0.911237	−	0.411883i	$-0.864871\pi$
$293$	−496.106	+	859.280i	−0.0989174	+	0.171330i	0.812319	+	0.583213i	$0.198205\pi$
$294$	−1084.53	+	774.725i	−0.215139	+	0.153683i
$295$	3135.80	+	5431.37i	0.618894	+	1.07196i
$296$	1498.70	+	865.273i	0.294291	+	0.169909i
$297$	−4475.16	+	3726.05i	−0.874328	+	0.727971i
$298$	−551.796	−	955.739i	−0.107264	−	0.185787i
$299$	−6746.20			−1.30483
$300$	223.569	−	1891.85i	0.0430259	−	0.364087i
$301$	−4545.26	−	708.538i	−0.870381	−	0.135679i
$302$	−825.644	−	476.686i	−0.157319	−	0.0908284i
$303$	−0.457843	+	3.87428i	−8.68067e−5	+	0.000734560i
$304$	−2514.60	−	1451.81i	−0.474416	−	0.273904i
$305$	4886.23	−	2821.07i	0.917327	−	0.529619i
$306$	−376.217	+	1569.55i	−0.0702839	+	0.293219i
$307$		−	256.830i		−	0.0477462i	−0.999715	−	0.0238731i	$-0.992400\pi$
$307$		−	256.830i		−	0.0477462i	0.999715	−	0.0238731i	$-0.00759977\pi$
$308$	5334.95	−	2062.84i	0.986971	−	0.381628i
$309$	2340.59	−	3135.60i	0.430910	−	0.577276i
$310$	848.612	+	1469.84i	0.155477	+	0.269295i
$311$	−723.484			−0.131913			−0.0659566	−	0.997822i	$-0.521010\pi$
$311$	−723.484			−0.131913			−0.0659566	+	0.997822i	$0.521010\pi$
$312$	268.356	−	2270.84i	0.0486945	−	0.412054i
$313$		−	6884.30i		−	1.24321i	−0.783332	−	0.621604i	$-0.786481\pi$
$313$		−	6884.30i		−	1.24321i	0.783332	−	0.621604i	$-0.213519\pi$
$314$	1483.66			0.266649
$315$	−3444.85	+	2658.69i	−0.616176	+	0.475555i
$316$	−8588.50			−1.52893
$317$			367.366i			0.0650893i	0.999470	+	0.0325447i	$0.0103611\pi$
$317$			367.366i			0.0650893i	−0.999470	+	0.0325447i	$0.989639\pi$
$318$	947.852	+	707.528i	0.167147	+	0.124768i
$319$	2882.55			0.505930
$320$	1347.06	+	2333.18i	0.235322	+	0.407590i
$321$	−6492.05	−	767.198i	−1.12882	−	0.133398i
$322$	−2422.33	−	377.605i	−0.419228	−	0.0653513i
$323$			4560.82i			0.785669i
$324$	−287.794	−	5416.68i	−0.0493473	−	0.928787i
$325$	1626.23	−	938.904i	0.277560	−	0.160249i
$326$	2378.85	+	1373.43i	0.404148	+	0.233335i
$327$	−922.841	−	688.859i	−0.156065	−	0.116495i
$328$	−1094.23	−	631.753i	−0.184203	−	0.106350i
$329$	−3428.57	+	4255.11i	−0.574538	+	0.713045i
$330$	−1289.47	+	554.273i	−0.215099	+	0.0924599i
$331$	3825.76			0.635295			0.317647	−	0.948209i	$-0.397107\pi$
$331$	3825.76			0.635295			0.317647	+	0.948209i	$0.397107\pi$
$332$	2123.64	+	3678.25i	0.351054	+	0.608043i
$333$	1150.68	+	3879.49i	0.189360	+	0.638422i
$334$	2600.28	+	1501.27i	0.425991	+	0.245946i
$335$	−847.823	−	1468.47i	−0.138273	−	0.239496i
$336$	−1317.02	+	4717.07i	−0.213837	+	0.765884i
$337$	−477.374	+	826.836i	−0.0771639	+	0.133652i	−0.902025	−	0.431683i	$-0.857920\pi$
$337$	−477.374	+	826.836i	−0.0771639	+	0.133652i	0.824861	+	0.565335i	$0.191253\pi$
$338$	−482.181	+	278.388i	−0.0775953	+	0.0447997i
$339$	8016.40	+	947.338i	1.28434	+	0.151777i
$340$	2588.00	−	4482.55i	0.412806	−	0.715001i
$341$	5412.63	−	9374.95i	0.859561	−	1.48880i
$342$	327.585	+	1104.44i	0.0517946	+	0.174624i
$343$	5681.03	+	2842.45i	0.894305	+	0.447458i
$344$	2483.82	−	1434.03i	0.389298	−	0.224761i
$345$	−7948.88	−	939.358i	−1.24044	−	0.146589i
$346$			1565.56i			0.243251i
$347$		−	5672.80i		−	0.877614i	−0.898581	−	0.438807i	$-0.855401\pi$
$347$		−	5672.80i		−	0.877614i	0.898581	−	0.438807i	$-0.144599\pi$
$348$	−1606.15	+	2151.71i	−0.247410	+	0.331447i
$349$	163.883	−	94.6178i	0.0251360	−	0.0145123i	−0.487379	−	0.873190i	$-0.662047\pi$
$349$	163.883	−	94.6178i	0.0251360	−	0.0145123i	0.512515	+	0.858678i	$0.328714\pi$
$350$	636.478	−	246.104i	0.0972033	−	0.0375852i
$351$	4109.04	−	3421.21i	0.624855	−	0.520258i
$352$	−2706.92	+	4688.53i	−0.409885	+	0.709941i
$353$	−5220.33	+	9041.87i	−0.787110	+	1.36331i	0.140620	+	0.990064i	$0.455090\pi$
$353$	−5220.33	+	9041.87i	−0.787110	+	1.36331i	−0.927730	+	0.373251i	$0.878243\pi$
$354$	−1105.92	−	2572.82i	−0.166042	−	0.386282i
$355$	−744.098	+	429.605i	−0.111247	+	0.0642284i
$356$	−666.035	+	1153.61i	−0.0991566	+	0.171744i
$357$	7450.98	−	1913.10i	1.10461	−	0.283619i
$358$	1379.01	+	2388.52i	0.203584	+	0.352618i
$359$	−9191.43	−	5306.67i	−1.35127	−	0.780155i	−0.362840	−	0.931851i	$-0.618193\pi$
$359$	−9191.43	−	5306.67i	−1.35127	−	0.780155i	−0.988427	+	0.151697i	$0.951526\pi$
$360$	632.395	−	2638.30i	0.0925837	−	0.386252i
$361$	−1801.85	−	3120.89i	−0.262698	−	0.455007i
$362$	−1232.81			−0.178992
$363$	1631.60	+	1217.91i	0.235914	+	0.176099i
$364$	−4898.48	+	1894.07i	−0.705358	+	0.272737i
$365$	1969.21	+	1136.92i	0.282392	+	0.163039i
$366$	−2314.59	+	994.919i	−0.330561	+	0.142091i
$367$	764.470	+	441.367i	0.108733	+	0.0627770i	0.553380	−	0.832929i	$-0.313338\pi$
$367$	764.470	+	441.367i	0.108733	+	0.0627770i	−0.444647	+	0.895706i	$0.646671\pi$
$368$	−7801.55	+	4504.22i	−1.10512	+	0.638041i
$369$	−840.133	−	2832.49i	−0.118525	−	0.399603i
$370$			975.311i			0.137038i
$371$	868.306	−	5570.18i	0.121510	−	0.779486i
$372$	3982.12	+	9264.02i	0.555009	+	1.29118i
$373$	−1308.08	−	2265.66i	−0.181581	−	0.314507i	0.760838	−	0.648942i	$-0.224788\pi$
$373$	−1308.08	−	2265.66i	−0.181581	−	0.314507i	−0.942419	+	0.334434i	$0.891455\pi$
$374$	2481.21			0.343049
$375$	7239.71	−	3111.97i	0.996952	−	0.428537i
$376$		−	3406.97i		−	0.467290i
$377$	−2646.72			−0.361573
$378$	1666.91	−	998.447i	0.226817	−	0.135859i
$379$	636.672			0.0862892			0.0431446	−	0.999069i	$-0.486262\pi$
$379$	636.672			0.0862892			0.0431446	+	0.999069i	$0.486262\pi$
$380$		−	3694.39i		−	0.498732i
$381$	11576.8	−	4976.25i	1.55668	−	0.669136i
$382$	−2742.38			−0.367310
$383$	−3784.88	−	6555.61i	−0.504957	−	0.874611i	−0.999984	−	0.00573317i	$-0.998175\pi$
$383$	−3784.88	−	6555.61i	−0.504957	−	0.874611i	0.495027	−	0.868878i	$-0.335158\pi$
$384$	−2616.26	−	6086.48i	−0.347683	−	0.808852i
$385$	5209.02	+	4197.18i	0.689549	+	0.555606i
$386$			255.846i			0.0337364i
$387$	6521.67	+	1563.23i	0.856628	+	0.205331i
$388$	7117.61	−	4109.35i	0.931294	−	0.537683i
$389$	9643.62	+	5567.75i	1.25694	+	0.725697i	0.972479	−	0.232990i	$-0.0748509\pi$
$389$	9643.62	+	5567.75i	1.25694	+	0.725697i	0.284464	+	0.958687i	$0.408184\pi$
$390$	1183.97	−	508.926i	0.153725	−	0.0660782i
$391$	12254.2	+	7074.96i	1.58496	+	0.915080i
$392$	−3869.95	+	842.339i	−0.498628	+	0.108532i
$393$	−203.348	−	151.790i	−0.0261006	−	0.0194829i
$394$	350.231			0.0447827
$395$	−5022.24	−	8698.78i	−0.639738	−	1.10806i
$396$	−7994.55	+	2371.23i	−1.01450	+	0.300906i
$397$	−777.013	−	448.609i	−0.0982297	−	0.0567129i	0.450080	−	0.892988i	$-0.351395\pi$
$397$	−777.013	−	448.609i	−0.0982297	−	0.0567129i	−0.548310	+	0.836275i	$0.684729\pi$
$398$	586.797	+	1016.36i	0.0739032	+	0.128004i
$399$	3922.92	−	3841.62i	0.492210	−	0.482009i
$400$	1253.75	−	2171.56i	0.156719	−	0.271445i
$401$	−3487.06	+	2013.25i	−0.434253	+	0.250716i	−0.701157	−	0.713007i	$-0.747333\pi$
$401$	−3487.06	+	2013.25i	−0.434253	+	0.250716i	0.266904	+	0.963723i	$0.413999\pi$
$402$	299.006	+	695.609i	0.0370972	+	0.0863031i
$403$	−4969.80	+	8607.95i	−0.614302	+	1.06400i
$404$	−2.79325	+	4.83804i	−0.000343983	+	0.000595796i
$405$	5317.95	−	3458.97i	0.652472	−	0.424389i
$406$	−950.347	−	148.145i	−0.116170	−	0.0181091i
$407$	5387.32	−	3110.37i	0.656116	−	0.378809i
$408$	−2868.96	+	3843.45i	−0.348124	+	0.466370i
$409$			10933.5i			1.32182i	0.750463	+	0.660912i	$0.229830\pi$
$409$			10933.5i			1.32182i	−0.750463	+	0.660912i	$0.770170\pi$
$410$		−	712.093i		−	0.0857751i
$411$	7907.15	+	934.427i	0.948980	+	0.112146i
$412$	4852.43	−	2801.55i	0.580248	−	0.335006i
$413$	−8374.47	+	10393.4i	−0.997774	+	1.23831i
$414$	3475.63	+	833.099i	0.412604	+	0.0989000i
$415$	−2483.66	+	4301.82i	−0.293778	+	0.508838i
$416$	2485.46	−	4304.94i	0.292932	−	0.507373i
$417$	−3805.56	−	449.722i	−0.446905	−	0.0528129i
$418$	1533.71	−	885.486i	0.179464	−	0.103614i
$419$	2433.63	−	4215.18i	0.283749	−	0.491467i	−0.688556	−	0.725183i	$-0.741755\pi$
$419$	2433.63	−	4215.18i	0.283749	−	0.491467i	0.972305	+	0.233716i	$0.0750885\pi$
$420$	−6035.49	+	1549.66i	−0.701195	+	0.180037i
$421$	−5868.66	−	10164.8i	−0.679385	−	1.17673i	−0.975166	−	0.221474i	$-0.928913\pi$
$421$	−5868.66	−	10164.8i	−0.679385	−	1.17673i	0.295781	−	0.955256i	$-0.404420\pi$
$422$	−1612.17	−	930.789i	−0.185970	−	0.107370i
$423$	5481.71	−	5780.69i	0.630094	−	0.664461i
$424$	1757.39	+	3043.89i	0.201289	+	0.348643i
$425$	−3938.64			−0.449534
$426$	352.476	−	151.511i	0.0400881	−	0.0172318i
$427$	9350.18	+	7533.93i	1.05969	+	0.853847i
$428$	−8107.00	−	4680.58i	−0.915576	−	0.528608i
$429$	−6586.96	−	4916.87i	−0.741308	−	0.553353i
$430$	1399.84	+	808.200i	0.156992	+	0.0906392i
$431$	−8093.99	+	4673.07i	−0.904580	+	0.522260i	−0.878683	−	0.477405i	$-0.841577\pi$
$431$	−8093.99	+	4673.07i	−0.904580	+	0.522260i	−0.0258967	+	0.999665i	$0.508244\pi$
$432$	2467.60	−	6699.88i	0.274821	−	0.746176i
$433$		−	582.680i		−	0.0646693i	−0.999477	−	0.0323346i	$-0.989706\pi$
$433$		−	582.680i		−	0.0646693i	0.999477	−	0.0323346i	$-0.0102942\pi$
$434$	−2266.30	+	2812.65i	−0.250659	+	0.311087i
$435$	−3118.56	−	368.536i	−0.343732	−	0.0406205i
$436$	−824.526	−	1428.12i	−0.0905680	−	0.156868i
$437$	10099.6			1.10555
$438$	−813.648	−	607.351i	−0.0887616	−	0.0662565i
$439$			6440.25i			0.700174i	0.936717	+	0.350087i	$0.113848\pi$
$439$			6440.25i			0.700174i	−0.936717	+	0.350087i	$0.886152\pi$
$440$	−4170.75			−0.451892
$441$	−7921.55	−	4797.42i	−0.855366	−	0.518024i
$442$	−2278.21			−0.245166
$443$			11722.1i			1.25719i	0.777734	+	0.628593i	$0.216369\pi$
$443$			11722.1i			1.25719i	−0.777734	+	0.628593i	$0.783631\pi$
$444$	−680.039	+	5754.51i	−0.0726875	+	0.615083i
$445$	−1557.89			−0.165958
$446$	370.828	+	642.293i	0.0393705	+	0.0681917i
$447$	4587.00	−	6145.04i	0.485364	−	0.650225i
$448$	−3597.46	+	4464.72i	−0.379384	+	0.470844i
$449$		−	10126.0i		−	1.06431i	−0.846648	−	0.532153i	$-0.821383\pi$
$449$		−	10126.0i		−	1.06431i	0.846648	−	0.532153i	$-0.178617\pi$
$450$	−953.777	+	282.896i	−0.0999144	+	0.0296352i
$451$	−3933.38	+	2270.94i	−0.410678	+	0.237105i
$452$	10010.5	+	5779.59i	1.04172	+	0.601436i
$453$	777.435	−	6578.67i	0.0806337	−	0.682325i
$454$	−390.820	−	225.640i	−0.0404011	−	0.0233256i
$455$	−4782.85	−	3853.80i	−0.492799	−	0.397074i
$456$	−401.749	+	3399.61i	−0.0412579	+	0.349126i
$457$	−7054.77			−0.722119			−0.361059	−	0.932543i	$-0.617585\pi$
$457$	−7054.77			−0.722119			−0.361059	+	0.932543i	$0.617585\pi$
$458$	484.302	+	838.835i	0.0494104	+	0.0855812i
$459$	−11051.8	+	1905.21i	−1.12387	+	0.193742i
$460$	−9926.22	−	5730.91i	−1.00611	−	0.580880i
$461$	−1300.85	−	2253.14i	−0.131425	−	0.227634i	0.792801	−	0.609480i	$-0.208622\pi$
$461$	−1300.85	−	2253.14i	−0.131425	−	0.227634i	−0.924226	+	0.381846i	$0.875288\pi$
$462$	−2089.94	−	2134.17i	−0.210461	−	0.214915i
$463$	−4858.94	+	8415.93i	−0.487719	+	0.844755i	−0.999900	−	0.0141228i	$-0.995504\pi$
$463$	−4858.94	+	8415.93i	−0.487719	+	0.844755i	0.512181	+	0.858878i	$0.328838\pi$
$464$	−3060.76	+	1767.13i	−0.306233	+	0.176804i
$465$	−7054.39	+	9450.52i	−0.703525	+	0.942489i
$466$	1597.35	−	2766.69i	0.158789	−	0.275031i
$467$	4239.34	−	7342.76i	0.420072	−	0.727585i	−0.575874	−	0.817538i	$-0.695338\pi$
$467$	4239.34	−	7342.76i	0.420072	−	0.727585i	0.995946	+	0.0899527i	$0.0286716\pi$
$468$	7340.49	−	2177.23i	0.725031	−	0.215048i
$469$	2264.19	−	2810.03i	0.222923	−	0.276664i
$470$	1662.87	−	960.059i	0.163197	−	0.0942218i
$471$	4071.18	+	9471.23i	0.398281	+	0.926563i
$472$		−	8321.72i		−	0.811522i
$473$		−	10309.7i		−	1.00220i
$474$	1771.22	+	4120.58i	0.171635	+	0.399292i
$475$	−2434.58	+	1405.61i	−0.235171	+	0.135776i
$476$	10884.3	+	1696.69i	1.04807	+	0.163378i
$477$	−1915.72	+	7992.24i	−0.183888	+	0.767169i
$478$	895.736	−	1551.46i	0.0857113	−	0.148456i
$479$	−9850.70	+	17061.9i	−0.939645	+	1.62751i	−0.173512	+	0.984832i	$0.555512\pi$
$479$	−9850.70	+	17061.9i	−0.939645	+	1.62751i	−0.766133	+	0.642682i	$0.777822\pi$
$480$	3527.99	−	4726.32i	0.335479	−	0.449429i
$481$	−4946.56	+	2855.90i	−0.468906	+	0.270723i
$482$	305.903	−	529.840i	0.0289077	−	0.0500696i
$483$	−4236.40	−	16499.6i	−0.399095	−	1.55436i
$484$	1457.77	+	2524.94i	0.136906	+	0.237128i
$485$	8324.25	+	4806.01i	0.779350	+	0.449958i
$486$	−2539.46	+	1255.17i	−0.237021	+	0.117152i
$487$	−7141.08	−	12368.7i	−0.664463	−	1.15088i	−0.979431	−	0.201781i	$-0.935327\pi$
$487$	−7141.08	−	12368.7i	−0.664463	−	1.15088i	0.314968	−	0.949102i	$-0.398006\pi$
$488$	−7486.48			−0.694461
$489$	−2239.95	+	18954.5i	−0.207145	+	1.75287i
$490$	−1501.65	−	1651.48i	−0.138444	−	0.152258i
$491$	9090.51	+	5248.41i	0.835537	+	0.482398i	0.855745	−	0.517398i	$-0.173099\pi$
$491$	9090.51	+	5248.41i	0.835537	+	0.482398i	−0.0202074	+	0.999796i	$0.506433\pi$
$492$	496.510	−	4201.48i	0.0454967	−	0.384995i
$493$	4807.65	+	2775.70i	0.439200	+	0.253572i
$494$	−1408.23	+	813.041i	−0.128257	+	0.0740495i
$495$	−7076.61	−	6710.60i	−0.642565	−	0.609332i
$496$			13272.7i			1.20154i
$497$	−1423.89	−	1147.30i	−0.128511	−	0.103548i
$498$	1326.78	−	1777.45i	0.119387	−	0.159938i
$499$	−8414.18	−	14573.8i	−0.754850	−	1.30744i	−0.945449	−	0.325771i	$-0.894376\pi$
$499$	−8414.18	−	14573.8i	−0.754850	−	1.30744i	0.190598	−	0.981668i	$-0.438957\pi$
$500$	11284.3			1.00930
$501$	−2448.45	+	20718.9i	−0.218341	+	1.84761i
$502$		−	5620.76i		−	0.499735i
$503$	−12335.3			−1.09344			−0.546722	−	0.837314i	$-0.684125\pi$
$503$	−12335.3			−1.09344			−0.546722	+	0.837314i	$0.684125\pi$
$504$	5722.43	−	769.679i	0.505749	−	0.0680243i
$505$	−6.53356			−0.000575722
$506$		−	5494.43i		−	0.482721i
$507$	−3100.25	−	2314.19i	−0.271572	−	0.202716i
$508$	18044.3			1.57596
$509$	7226.55	+	12516.8i	0.629295	+	1.08997i	0.987693	+	0.156402i	$0.0499897\pi$
$509$	7226.55	+	12516.8i	0.629295	+	1.08997i	−0.358398	+	0.933569i	$0.616677\pi$
$510$	−2684.36	−	317.224i	−0.233070	−	0.0275430i
$511$	−745.365	+	4781.51i	−0.0645264	+	0.413937i
$512$		−	11338.9i		−	0.978739i
$513$	−6151.53	+	5121.80i	−0.529428	+	0.440805i
$514$	3593.43	−	2074.67i	0.308365	−	0.178034i
$515$	5675.06	+	3276.50i	0.485578	+	0.280349i
$516$	7695.81	+	5744.57i	0.656568	+	0.490098i
$517$	−10606.1	−	6123.46i	−0.902239	−	0.520908i
$518$	−1936.00	+	748.584i	−0.164214	+	0.0634959i
$519$	−9994.01	+	4295.90i	−0.845257	+	0.363332i
$520$	3829.52			0.322953
$521$	−3797.90	−	6578.16i	−0.319365	−	0.553156i	0.660991	−	0.750394i	$-0.270136\pi$
$521$	−3797.90	−	6578.16i	−0.319365	−	0.553156i	−0.980356	+	0.197238i	$0.936803\pi$
$522$	1363.58	+	326.847i	0.114334	+	0.0274056i
$523$	15947.4	+	9207.24i	1.33333	+	0.769799i	0.985809	−	0.167873i	$-0.0536900\pi$
$523$	15947.4	+	9207.24i	1.33333	+	0.769799i	0.347522	+	0.937672i	$0.387023\pi$
$524$	−181.684	−	314.686i	−0.0151468	−	0.0262350i
$525$	3317.55	+	3387.76i	0.275790	+	0.281626i
$526$	−2383.15	+	4127.74i	−0.197548	+	0.342164i
$527$	18054.9	−	10424.0i	1.49238	−	0.861625i
$528$	−10900.2	−	1288.13i	−0.898431	−	0.106172i
$529$	9583.40	−	16598.9i	0.787655	−	1.36426i
$530$	−990.441	+	1715.49i	−0.0811736	+	0.140597i
$531$	13389.4	−	14119.7i	1.09426	−	1.15394i
$532$	7333.38	−	2835.57i	0.597636	−	0.231085i
$533$	3611.58	−	2085.15i	0.293499	−	0.169452i
$534$	690.833	+	81.6392i	0.0559837	+	0.00661587i
$535$		−	10948.1i		−	0.884728i
$536$			2249.93i			0.181310i
$537$	−11463.5	+	15357.3i	−0.921206	+	1.23411i
$538$	−2768.05	+	1598.13i	−0.221820	+	0.128068i
$539$	−4333.34	+	13561.4i	−0.346289	+	1.08373i
$540$	8952.28	−	1543.27i	0.713416	−	0.122985i
$541$	10525.6	−	18230.9i	0.836474	−	1.44882i	−0.0563503	−	0.998411i	$-0.517946\pi$
$541$	10525.6	−	18230.9i	0.836474	−	1.44882i	0.892825	−	0.450405i	$-0.148720\pi$
$542$	−785.088	+	1359.81i	−0.0622185	+	0.107766i
$543$	−3382.85	−	7869.88i	−0.267352	−	0.621969i
$544$	−9029.47	+	5213.17i	−0.711646	+	0.410869i
$545$	964.307	−	1670.23i	0.0757915	−	0.131275i
$546$	1918.96	+	1959.57i	0.150410	+	0.153593i
$547$	−8242.69	−	14276.8i	−0.644300	−	1.11596i	−0.984463	−	0.175594i	$-0.943815\pi$
$547$	−8242.69	−	14276.8i	−0.644300	−	1.11596i	0.340163	−	0.940367i	$-0.389518\pi$
$548$	9874.11	+	5700.82i	0.769710	+	0.444392i
$549$	−12702.5	−	12045.5i	−0.987485	−	0.936412i
$550$	764.688	+	1324.48i	0.0592844	+	0.102684i
$551$	3962.33			0.306354
$552$	8510.99	+	6353.07i	0.656253	+	0.489863i
$553$	13412.4	−	16645.8i	1.03138	−	1.28002i
$554$	2856.46	+	1649.18i	0.219060	+	0.126474i
$555$	−6226.07	+	2676.26i	−0.476184	+	0.204686i
$556$	−4752.23	−	2743.70i	−0.362481	−	0.209278i
$557$	5731.63	−	3309.16i	0.436009	−	0.251730i	−0.265894	−	0.964002i	$-0.585667\pi$
$557$	5731.63	−	3309.16i	0.436009	−	0.251730i	0.701903	+	0.712272i	$0.252334\pi$
$558$	3623.44	−	3821.07i	0.274897	−	0.289890i
$559$			9466.26i			0.716243i
$560$	−8104.12	−	1263.31i	−0.611538	−	0.0953295i
$561$	6808.46	+	15839.2i	0.512395	+	1.19204i
$562$	1896.33	+	3284.55i	0.142335	+	0.246531i
$563$	17006.6			1.27308			0.636540	−	0.771244i	$-0.280365\pi$
$563$	17006.6			1.27308			0.636540	+	0.771244i	$0.280365\pi$
$564$	10480.7	−	4505.08i	0.782474	−	0.336344i
$565$			13518.8i			1.00662i
$566$	−413.239			−0.0306885
$567$	10947.8	+	7901.28i	0.810871	+	0.585225i
$568$	1140.08			0.0842192
$569$			11281.2i			0.831164i	0.909556	+	0.415582i	$0.136422\pi$
$569$			11281.2i			0.831164i	−0.909556	+	0.415582i	$0.863578\pi$
$570$	−1772.49	+	761.900i	−0.130248	+	0.0559868i
$571$	−24466.3			−1.79314			−0.896571	−	0.442900i	$-0.853950\pi$
$571$	−24466.3			−1.79314			−0.896571	+	0.442900i	$0.853950\pi$
$572$	−5885.22	−	10193.5i	−0.430198	−	0.745125i
$573$	−7525.13	−	17506.5i	−0.548633	−	1.27634i
$574$	1413.51	−	546.555i	0.102785	−	0.0397435i
$575$			8721.78i			0.632562i
$576$	5751.75	−	6065.45i	0.416070	−	0.438763i
$577$	−14445.8	+	8340.28i	−1.04226	+	0.601751i	−0.920474	−	0.390805i	$-0.872197\pi$
$577$	−14445.8	+	8340.28i	−1.04226	+	0.601751i	−0.121790	+	0.992556i	$0.538863\pi$
$578$	956.490	+	552.230i	0.0688317	+	0.0397400i
$579$	−1633.24	+	702.045i	−0.117228	+	0.0503903i
$580$	−3894.33	−	2248.39i	−0.278798	−	0.160964i
$581$	−10445.4	−	1628.28i	−0.745868	−	0.116269i
$582$	−3439.46	−	2567.40i	−0.244966	−	0.182856i
$583$	12634.5			0.897542
$584$	−1508.57	−	2612.92i	−0.106892	−	0.185143i
$585$	6497.65	+	6161.58i	0.459222	+	0.435470i
$586$	642.582	+	370.995i	0.0452984	+	0.0261530i
$587$	−7866.86	−	13625.8i	−0.553152	−	0.958087i	−0.998045	−	0.0625029i	$-0.980092\pi$
$587$	−7866.86	−	13625.8i	−0.553152	−	0.958087i	0.444893	−	0.895584i	$-0.353242\pi$
$588$	−7708.53	−	10791.1i	−0.540637	−	0.756830i
$589$	7440.16	−	12886.7i	0.520486	−	0.901509i
$590$	4061.66	−	2345.00i	0.283417	−	0.163631i
$591$	961.036	+	2235.76i	0.0668896	+	0.155612i
$592$	−3813.59	+	6605.33i	−0.264759	+	0.458576i
$593$	−2335.26	+	4044.79i	−0.161716	+	0.280101i	−0.935484	−	0.353368i	$-0.885036\pi$
$593$	−2335.26	+	4044.79i	−0.161716	+	0.280101i	0.773768	+	0.633469i	$0.218370\pi$
$594$	2786.40	+	3346.59i	0.192470	+	0.231166i
$595$	4646.25	+	12016.2i	0.320131	+	0.827926i
$596$	9509.62	−	5490.38i	0.653573	−	0.377340i
$597$	−4877.95	+	6534.83i	−0.334408	+	0.447995i
$598$			5044.91i			0.344986i
$599$		−	12756.3i		−	0.870131i	−0.900399	−	0.435066i	$-0.856725\pi$
$599$		−	12756.3i		−	0.870131i	0.900399	−	0.435066i	$-0.143275\pi$
$600$	−2935.84	−	346.942i	−0.199758	−	0.0236064i
$601$	−17937.2	+	10356.0i	−1.21743	+	0.702882i	−0.964367	−	0.264569i	$-0.914770\pi$
$601$	−17937.2	+	10356.0i	−1.21743	+	0.702882i	−0.253060	+	0.967451i	$0.581437\pi$
$602$	−529.855	+	3399.02i	−0.0358725	+	0.230122i
$603$	−3620.07	+	3817.51i	−0.244479	+	0.257813i
$604$	4743.03	−	8215.17i	0.319522	−	0.553428i
$605$	−1704.91	+	2952.99i	−0.114569	+	0.198440i
$606$	2.89725	+	0.342382i	0.000194212	+	2.29510e-5i
$607$	21204.6	−	12242.5i	1.41790	−	0.818628i	0.421790	−	0.906694i	$-0.361402\pi$
$607$	21204.6	−	12242.5i	1.41790	−	0.818628i	0.996115	+	0.0880658i	$0.0280686\pi$
$608$	−3720.91	+	6444.81i	−0.248196	+	0.429888i
$609$	−1662.05	−	6473.22i	−0.110591	−	0.430719i
$610$	−2109.63	−	3653.99i	−0.140027	−	0.242534i
$611$	9738.42	+	5622.48i	0.644803	+	0.372277i
$612$	−15617.0	−	3743.36i	−1.03151	−	0.247249i
$613$	−2415.65	−	4184.03i	−0.159164	−	0.275679i	0.775404	−	0.631466i	$-0.217546\pi$
$613$	−2415.65	−	4184.03i	−0.159164	−	0.275679i	−0.934567	+	0.355786i	$0.884213\pi$
$614$	−192.062			−0.0126237
$615$	4545.77	−	1953.99i	0.298054	−	0.128118i
$616$	−3201.19	−	8278.95i	−0.209382	−	0.541507i
$617$	−5042.06	−	2911.04i	−0.328988	−	0.189942i	0.326404	−	0.945231i	$-0.394163\pi$
$617$	−5042.06	−	2911.04i	−0.328988	−	0.189942i	−0.655392	+	0.755289i	$0.727497\pi$
$618$	−2344.85	−	1750.32i	−0.152627	−	0.113929i
$619$	1254.22	+	724.124i	0.0814400	+	0.0470194i	0.540167	−	0.841558i	$-0.318361\pi$
$619$	1254.22	+	724.124i	0.0814400	+	0.0470194i	−0.458727	+	0.888577i	$0.651694\pi$
$620$	−14624.9	+	8443.71i	−0.947341	+	0.546948i
$621$	4218.92	+	24473.3i	0.272624	+	1.58145i
$622$			541.032i			0.0348769i
$623$	−1195.73	−	3092.43i	−0.0768958	−	0.198869i
$624$	10008.4	+	1182.75i	0.642081	+	0.0758779i
$625$	3519.16	+	6095.36i	0.225226	+	0.390103i
$626$	−5148.18			−0.328695
$627$	9861.16	+	7360.91i	0.628097	+	0.468846i
$628$			14762.5i			0.938037i
$629$	11980.3			0.759437
$630$	1988.20	+	2576.11i	0.125733	+	0.162912i
$631$	−22632.9			−1.42790			−0.713948	−	0.700199i	$-0.753095\pi$
$631$	−22632.9			−1.42790			−0.713948	+	0.700199i	$0.753095\pi$
$632$			13327.9i			0.838854i
$633$	1518.04	−	12845.7i	0.0953186	−	0.806588i
$634$	274.721			0.0172091
$635$	10551.7	+	18276.0i	0.659418	+	1.14215i
$636$	−7039.92	+	9431.14i	−0.438917	+	0.588002i
$637$	3978.81	−	12451.9i	0.247482	−	0.774509i
$638$		−	2155.61i		−	0.133764i
$639$	1934.39	+	1834.35i	0.119755	+	0.113561i
$640$	9608.61	−	5547.53i	0.593459	−	0.342633i
$641$	13191.2	+	7615.95i	0.812826	+	0.469286i	0.847936	−	0.530098i	$-0.177845\pi$
$641$	13191.2	+	7615.95i	0.812826	+	0.469286i	−0.0351100	+	0.999383i	$0.511178\pi$
$642$	−573.722	+	4854.85i	−0.0352695	+	0.298451i
$643$	12428.6	+	7175.65i	0.762264	+	0.440093i	0.830108	−	0.557603i	$-0.188279\pi$
$643$	12428.6	+	7175.65i	0.762264	+	0.440093i	−0.0678441	+	0.997696i	$0.521612\pi$
$644$	3757.18	−	24102.3i	0.229897	−	1.47479i
$645$	−1318.11	+	11153.9i	−0.0804657	+	0.680903i
$646$	3410.65			0.207725
$647$	−14009.3	−	24264.9i	−0.851258	−	1.47442i	−0.880073	−	0.474838i	$-0.842507\pi$
$647$	−14009.3	−	24264.9i	−0.851258	−	1.47442i	0.0288151	−	0.999585i	$-0.490827\pi$
$648$	−8405.79	+	446.608i	−0.509584	+	0.0270747i
$649$	−25906.1	−	14956.9i	−1.56688	−	0.904638i
$650$	−702.126	−	1216.12i	−0.0423687	−	0.0733847i
$651$	−24173.8	−	6749.41i	−1.45537	−	0.406344i
$652$	−13665.6	+	23669.6i	−0.820840	+	1.42174i
$653$	−10579.8	+	6108.27i	−0.634029	+	0.366057i	−0.782311	−	0.622888i	$-0.785959\pi$
$653$	−10579.8	+	6108.27i	−0.634029	+	0.366057i	0.148282	+	0.988945i	$0.452626\pi$
$654$	−515.139	+	690.114i	−0.0308005	+	0.0412624i
$655$	212.485	−	368.034i	0.0126755	−	0.0219546i
$656$	2784.37	−	4822.67i	0.165719	−	0.287033i
$657$	1644.48	−	6860.64i	0.0976517	−	0.407396i
$658$	3182.03	+	2563.93i	0.188524	+	0.151903i
$659$	5703.43	−	3292.88i	0.337138	−	0.194647i	−0.321868	−	0.946785i	$-0.604311\pi$
$659$	5703.43	−	3292.88i	0.337138	−	0.194647i	0.659006	+	0.752138i	$0.270977\pi$
$660$	−5515.03	−	12830.2i	−0.325261	−	0.756690i
$661$			7317.01i			0.430558i	0.976553	+	0.215279i	$0.0690661\pi$
$661$			7317.01i			0.430558i	−0.976553	+	0.215279i	$0.930934\pi$
$662$		−	2860.96i		−	0.167967i
$663$	−6251.44	−	14543.4i	−0.366193	−	0.851913i
$664$	5708.03	−	3295.53i	0.333606	−	0.192608i
$665$	7160.28	+	5769.42i	0.417539	+	0.336434i
$666$	2901.14	−	860.494i	0.168794	−	0.0500653i
$667$	6146.55	−	10646.1i	0.356815	−	0.618021i
$668$	−14937.7	+	25872.8i	−0.865205	+	1.49858i
$669$	−3082.64	+	4129.71i	−0.178149	+	0.238660i
$670$	−1098.14	+	634.014i	−0.0633210	+	0.0365584i
$671$	−13455.7	+	23305.9i	−0.774145	+	1.34086i
$672$	12089.6	+	3375.46i	0.693999	+	0.193767i
$673$	1486.23	+	2574.23i	0.0851263	+	0.147443i	0.905445	−	0.424464i	$-0.139537\pi$
$673$	1486.23	+	2574.23i	0.0851263	+	0.147443i	−0.820319	+	0.571907i	$0.806204\pi$
$674$	618.320	+	356.987i	0.0353365	+	0.0204015i
$675$	−4423.09	−	5312.34i	−0.252214	−	0.302921i
$676$	−2769.96	−	4797.71i	−0.157599	−	0.272970i
$677$	17108.8			0.971261			0.485630	−	0.874164i	$-0.338590\pi$
$677$	17108.8			0.971261			0.485630	+	0.874164i	$0.338590\pi$
$678$	708.433	−	5994.78i	0.0401286	−	0.339570i
$679$	−3150.81	+	20212.5i	−0.178081	+	1.14239i
$680$	−6956.17	−	4016.15i	−0.392290	−	0.226488i
$681$	368.000	−	3114.03i	0.0207075	−	0.175227i
$682$	−7010.73	−	4047.64i	−0.393628	−	0.227261i
$683$	−4555.42	+	2630.07i	−0.255210	+	0.147346i	−0.622147	−	0.782900i	$-0.713740\pi$
$683$	−4555.42	+	2630.07i	−0.255210	+	0.147346i	0.366938	+	0.930246i	$0.380406\pi$
$684$	−10989.3	+	3259.47i	−0.614305	+	0.182206i
$685$			13334.5i			0.743776i
$686$	2125.63	−	4248.36i	0.118304	−	0.236448i
$687$	−4025.93	+	5393.40i	−0.223579	+	0.299521i
$688$	6320.32	+	10947.1i	0.350233	+	0.606621i
$689$	−11600.8			−0.641445
$690$	−702.466	+	5944.29i	−0.0387571	+	0.327964i
$691$		−	19364.5i		−	1.06608i	−0.846090	−	0.533040i	$-0.821050\pi$
$691$		−	19364.5i		−	1.06608i	0.846090	−	0.533040i	$-0.178950\pi$
$692$	−15577.3			−0.855724
$693$	7889.05	−	19197.7i	0.432439	−	1.05232i
$694$	−4242.21			−0.232034
$695$		−	6417.67i		−	0.350268i
$696$	3339.09	+	2492.48i	0.181850	+	0.135743i
$697$	−8747.05			−0.475349
$698$	−70.7566	−	122.554i	−0.00383693	−	0.00664576i
$699$	22044.8	+	2605.14i	1.19286	+	0.140966i
$700$	2448.74	+	6332.96i	0.132219	+	0.341948i
$701$		−	23797.7i		−	1.28221i	−0.767455	−	0.641103i	$-0.778477\pi$
$701$		−	23797.7i		−	1.28221i	0.767455	−	0.641103i	$-0.221523\pi$
$702$	−2558.43	−	3072.80i	−0.137552	−	0.165207i
$703$	7405.36	−	4275.49i	0.397295	−	0.229379i
$704$	−11128.6	−	6425.11i	−0.595775	−	0.343971i
$705$	10691.6	+	7980.83i	0.571164	+	0.426348i
$706$	6761.64	+	3903.84i	0.360450	+	0.208106i
$707$	−5.01473	−	12.9692i	−0.000266758	−	0.000689894i
$708$	25599.6	−	11003.9i	1.35889	−	0.584114i
$709$	14427.0			0.764201			0.382100	−	0.924121i	$-0.375201\pi$
$709$	14427.0			0.764201			0.382100	+	0.924121i	$0.375201\pi$
$710$	321.265	+	556.447i	0.0169815	+	0.0294128i
$711$	−21444.2	+	22613.8i	−1.13111	+	1.19280i
$712$	1790.20	+	1033.57i	0.0942285	+	0.0544029i
$713$	−23083.0	−	39981.0i	−1.21244	−	2.10000i
$714$	−1430.64	−	5571.95i	−0.0749867	−	0.292052i
$715$	6882.93	−	11921.6i	0.360010	−	0.623555i
$716$	−23765.8	+	13721.2i	−1.24046	+	0.716181i
$717$	12361.9	+	1460.87i	0.643884	+	0.0760909i
$718$	−3968.41	+	6873.49i	−0.206267	+	0.357265i
$719$	−2139.85	+	3706.33i	−0.110992	+	0.192243i	−0.916170	−	0.400789i	$-0.868736\pi$
$719$	−2139.85	+	3706.33i	−0.110992	+	0.192243i	0.805179	+	0.593032i	$0.202069\pi$
$720$	11628.0	+	2787.20i	0.601875	+	0.144268i
$721$	−2148.07	+	13779.8i	−0.110955	+	0.711773i
$722$	−2333.85	+	1347.45i	−0.120300	+	0.0694555i
$723$	4221.73	+	498.903i	0.217162	+	0.0256631i
$724$		−	12266.5i		−	0.629671i
$725$			3421.79i			0.175286i
$726$	910.773	−	1220.13i	0.0465592	−	0.0623738i
$727$	−8438.47	+	4871.95i	−0.430489	+	0.248543i	−0.699555	−	0.714579i	$-0.746618\pi$
$727$	−8438.47	+	4871.95i	−0.430489	+	0.248543i	0.269066	+	0.963122i	$0.413285\pi$
$728$	2939.29	+	7601.62i	0.149639	+	0.386999i
$729$	−14980.9	−	12766.9i	−0.761108	−	0.648625i
$730$	850.207	−	1472.60i	0.0431063	−	0.0746623i
$731$	9927.58	−	17195.1i	0.502305	−	0.870017i
$732$	−9899.47	−	23030.2i	−0.499856	−	1.16287i
$733$	−3927.82	+	2267.73i	−0.197923	+	0.114271i	−0.595686	−	0.803217i	$-0.703120\pi$
$733$	−3927.82	+	2267.73i	−0.197923	+	0.114271i	0.397764	+	0.917488i	$0.369786\pi$
$734$	330.061	−	571.682i	0.0165978	−	0.0287482i
$735$	6421.97	−	14117.7i	0.322283	−	0.708491i
$736$	11544.1	+	19995.0i	0.578154	+	1.00139i
$737$	7004.20	+	4043.88i	0.350072	+	0.202114i
$738$	−2118.18	+	628.264i	−0.105652	+	0.0313370i
$739$	15942.1	+	27612.6i	0.793561	+	1.37449i	0.923749	+	0.382998i	$0.125108\pi$
$739$	15942.1	+	27612.6i	0.793561	+	1.37449i	−0.130189	+	0.991489i	$0.541558\pi$
$740$	−9704.36			−0.482080
$741$	−9054.38	−	6758.69i	−0.448881	−	0.335070i
$742$	−4165.46	−	649.332i	−0.206090	−	0.0321263i
$743$	−10135.3	−	5851.64i	−0.500444	−	0.288931i	0.228453	−	0.973555i	$-0.426633\pi$
$743$	−10135.3	−	5851.64i	−0.500444	−	0.288931i	−0.728897	+	0.684624i	$0.759967\pi$
$744$	14376.2	−	6179.58i	0.708411	−	0.304509i
$745$	11121.8	+	6421.16i	0.546940	+	0.315776i
$746$	−1694.29	+	978.200i	−0.0831534	+	0.0480086i
$747$	14987.4	+	3592.43i	0.734082	+	0.175958i
$748$			24688.1i			1.20680i
$749$	21732.1	−	8403.06i	1.06018	−	0.409935i
$750$	−2327.18	−	5413.96i	−0.113302	−	0.263586i
$751$	8290.26	+	14359.1i	0.402817	+	0.697700i	0.994065	−	0.108790i	$-0.0346977\pi$
$751$	8290.26	+	14359.1i	0.402817	+	0.697700i	−0.591247	+	0.806490i	$0.701364\pi$
$752$	15015.8			0.728152
$753$	35881.1	−	15423.4i	1.73649	−	0.746428i
$754$			1979.25i			0.0955970i
$755$	11094.2			0.534782
$756$	9934.57	+	16585.8i	0.477932	+	0.797910i
$757$	−16410.7			−0.787923			−0.393962	−	0.919127i	$-0.628896\pi$
$757$	−16410.7			−0.787923			−0.393962	+	0.919127i	$0.628896\pi$
$758$		−	476.112i		−	0.0228142i
$759$	35074.7	−	15076.8i	1.67738	−	0.721016i
$760$	−5733.07			−0.273632
$761$	10595.5	+	18351.9i	0.504713	+	0.874188i	0.999985	+	0.00545022i	$0.00173487\pi$
$761$	10595.5	+	18351.9i	0.504713	+	0.874188i	−0.495273	+	0.868738i	$0.664932\pi$
$762$	−3721.31	−	8657.29i	−0.176915	−	0.411575i
$763$	4055.55	+	632.199i	0.192426	+	0.0299962i
$764$		−	27286.8i		−	1.29215i
$765$	−5340.85	−	18006.6i	−0.252417	−	0.851018i
$766$	−4902.38	+	2830.39i	−0.231241	+	0.133507i
$767$	23786.7	+	13733.2i	1.11980	+	0.646517i
$768$	7271.88	−	3125.80i	0.341669	−	0.146865i
$769$	4457.86	+	2573.75i	0.209044	+	0.120691i	0.600867	−	0.799349i	$-0.294822\pi$
$769$	4457.86	+	2573.75i	0.209044	+	0.120691i	−0.391823	+	0.920041i	$0.628156\pi$
$770$	3138.72	−	3895.38i	0.146898	−	0.182311i
$771$	23104.4	+	17246.4i	1.07923	+	0.805595i
$772$	−2545.68			−0.118680
$773$	13537.8	+	23448.2i	0.629912	+	1.09104i	0.987569	+	0.157187i	$0.0502425\pi$
$773$	13537.8	+	23448.2i	0.629912	+	1.09104i	−0.357657	+	0.933853i	$0.616424\pi$
$774$	1169.00	−	4877.00i	0.0542881	−	0.226486i
$775$	11128.7	+	6425.17i	0.515814	+	0.297805i
$776$	−6377.03	−	11045.3i	−0.295003	−	0.510960i
$777$	−10091.1	−	10304.7i	−0.465916	−	0.475776i
$778$	4163.64	−	7211.64i	0.191869	−	0.332326i
$779$	−5406.80	+	3121.62i	−0.248676	+	0.143573i
$780$	5063.83	+	11780.5i	0.232454	+	0.540783i
$781$	2049.10	−	3549.14i	0.0938827	−	0.162610i
$782$	5290.76	−	9163.87i	0.241940	−	0.419053i
$783$	1655.19	+	9601.55i	0.0755451	+	0.438227i
$784$	−3712.51	−	17056.4i	−0.169119	−	0.776984i
$785$	−14952.0	+	8632.57i	−0.679823	+	0.392496i
$786$	−113.511	+	152.066i	−0.00515113	+	0.00690080i
$787$			10863.1i			0.492030i	0.969266	+	0.246015i	$0.0791213\pi$
$787$			10863.1i			0.492030i	−0.969266	+	0.246015i	$0.920879\pi$
$788$			3484.80i			0.157539i
$789$	−32889.6	−	3886.73i	−1.48403	−	0.175375i
$790$	−6505.08	+	3755.71i	−0.292962	+	0.169142i
$791$	−26834.9	+	10376.1i	−1.20624	+	0.466413i
$792$	3679.75	+	12406.2i	0.165094	+	0.556610i
$793$	12354.8	−	21399.2i	0.553257	−	0.958270i
$794$	−335.476	+	581.062i	−0.0149945	+	0.0259712i
$795$	−13668.9	−	1615.33i	−0.609796	−	0.0720626i
$796$	−10112.8	+	5838.64i	−0.450301	+	0.259981i
$797$	−3869.66	+	6702.44i	−0.171983	+	0.297883i	−0.939113	−	0.343608i	$-0.888351\pi$
$797$	−3869.66	+	6702.44i	−0.171983	+	0.297883i	0.767130	+	0.641491i	$0.221684\pi$
$798$	−2872.82	−	2933.62i	−0.127440	−	0.130137i
$799$	−11793.0	−	20426.0i	−0.522159	−	0.904406i
$800$	−5565.61	−	3213.31i	−0.245968	−	0.142010i
$801$	1374.49	+	4634.08i	0.0606309	+	0.204416i
$802$	1505.54	+	2607.67i	0.0662874	+	0.114813i
$803$	−10845.6			−0.476629
$804$	−6921.33	+	2975.11i	−0.303602	+	0.130503i
$805$	26608.8	−	10288.7i	1.16502	−	0.450472i
$806$	6437.15	+	3716.49i	0.281314	+	0.162417i
$807$	−17797.5	−	13285.0i	−0.776335	−	0.579499i
$808$	7.50784	+	4.33465i	0.000326887	+	0.000188728i
$809$	18111.7	−	10456.8i	0.787114	−	0.454440i	−0.0518317	−	0.998656i	$-0.516506\pi$
$809$	18111.7	−	10456.8i	0.787114	−	0.454440i	0.838945	+	0.544215i	$0.183173\pi$
$810$	−2586.67	−	3976.84i	−0.112205	−	0.172509i
$811$		−	31359.1i		−	1.35779i	−0.734235	−	0.678895i	$-0.762459\pi$
$811$		−	31359.1i		−	1.35779i	0.734235	−	0.678895i	$-0.237541\pi$
$812$	1474.04	−	9455.97i	0.0637053	−	0.408669i
$813$	−10834.9	−	1280.41i	−0.467400	−	0.0552350i
$814$	−2325.98	−	4028.72i	−0.100154	−	0.173472i
$815$	−31964.7			−1.37383
$816$	−16939.5	−	12644.6i	−0.726719	−	0.542462i
$817$		−	14171.7i		−	0.606860i
$818$	8176.22			0.349480
$819$	−7243.62	+	17627.1i	−0.309051	+	0.752064i
$820$	7085.34			0.301745
$821$		−	18888.1i		−	0.802920i	−0.915876	−	0.401460i	$-0.868503\pi$
$821$		−	18888.1i		−	0.802920i	0.915876	−	0.401460i	$-0.131497\pi$
$822$	698.778	−	5913.08i	0.0296505	−	0.250903i
$823$	−13485.3			−0.571163			−0.285582	−	0.958354i	$-0.592187\pi$
$823$	−13485.3			−0.571163			−0.285582	+	0.958354i	$0.592187\pi$
$824$	−4347.54	−	7530.16i	−0.183803	−	0.318356i
$825$	−6356.73	+	8515.90i	−0.268258	+	0.359376i
$826$	7772.30	+	6262.55i	0.327401	+	0.263804i
$827$			17296.9i			0.727292i	0.931537	+	0.363646i	$0.118468\pi$
$827$			17296.9i			0.727292i	−0.931537	+	0.363646i	$0.881532\pi$
$828$	−8289.36	+	34582.6i	−0.347917	+	1.45148i
$829$	−4067.89	+	2348.59i	−0.170426	+	0.0983957i	−0.582787	−	0.812625i	$-0.698038\pi$
$829$	−4067.89	+	2348.59i	−0.170426	+	0.0983957i	0.412360	+	0.911021i	$0.364704\pi$
$830$	3216.96	+	1857.31i	0.134533	+	0.0776727i
$831$	−2689.67	+	22760.1i	−0.112279	+	0.950106i
$832$	10218.1	+	5899.45i	0.425782	+	0.245825i
$833$	−20286.1	+	18445.7i	−0.843782	+	0.767232i
$834$	−336.309	+	2845.86i	−0.0139633	+	0.118158i
$835$	−34940.1			−1.44809
$836$	8810.60	+	15260.4i	0.364499	+	0.631330i
$837$	34335.2	+	12645.8i	1.41792	+	0.522227i
$838$	−3152.17	−	1819.91i	−0.129940	−	0.0750210i
$839$	−1606.27	−	2782.14i	−0.0660960	−	0.114482i	0.831084	−	0.556147i	$-0.187721\pi$
$839$	−1606.27	−	2782.14i	−0.0660960	−	0.114482i	−0.897180	+	0.441666i	$0.854388\pi$
$840$	2404.82	+	9366.07i	0.0987786	+	0.384715i
$841$	−9783.04	+	16944.7i	−0.401125	+	0.694769i
$842$	−7601.40	+	4388.67i	−0.311118	+	0.179624i
$843$	−15763.9	+	21118.4i	−0.644056	+	0.862820i
$844$	9261.37	−	16041.2i	0.377713	−	0.654218i
$845$	3239.55	−	5611.06i	0.131886	−	0.228434i
$846$	−4322.89	−	4099.30i	−0.175678	−	0.166592i
$847$	−7170.28	−	1117.74i	−0.290878	−	0.0453434i
$848$	−13415.6	+	7745.50i	−0.543270	+	0.313657i
$849$	−1133.93	−	2637.98i	−0.0458379	−	0.106638i
$850$			2945.37i			0.118853i
$851$		−	26529.4i		−	1.06864i
$852$	1507.54	+	3507.14i	0.0606190	+	0.141024i
$853$	34142.7	−	19712.3i	1.37048	−	0.791249i	0.379495	−	0.925194i	$-0.376098\pi$
$853$	34142.7	−	19712.3i	1.37048	−	0.791249i	0.990989	+	0.133945i	$0.0427646\pi$
$854$	5633.99	−	6992.20i	0.225751	−	0.280173i
$855$	−9727.45	−	9224.34i	−0.389090	−	0.368966i
$856$	−7263.48	+	12580.7i	−0.290024	+	0.502336i
$857$	−879.891	+	1524.02i	−0.0350718	+	0.0607461i	−0.883029	−	0.469319i	$-0.844499\pi$
$857$	−879.891	+	1524.02i	−0.0350718	+	0.0607461i	0.847957	+	0.530065i	$0.177833\pi$
$858$	−3676.90	+	4925.82i	−0.146302	+	0.195996i
$859$	4451.77	−	2570.23i	0.176825	−	0.102090i	−0.408975	−	0.912545i	$-0.634114\pi$
$859$	4451.77	−	2570.23i	0.176825	−	0.102090i	0.585800	+	0.810456i	$0.300780\pi$
$860$	−8041.60	+	13928.5i	−0.318856	+	0.552275i
$861$	7367.71	+	7523.64i	0.291627	+	0.297799i
$862$	3494.59	+	6052.81i	0.138081	+	0.239164i
$863$	30321.8	+	17506.3i	1.19602	+	0.690523i	0.959666	−	0.281144i	$-0.0907139\pi$
$863$	30321.8	+	17506.3i	1.19602	+	0.690523i	0.236355	+	0.971667i	$0.424047\pi$
$864$	−17171.5	−	6324.34i	−0.676141	−	0.249026i
$865$	−9109.06	−	15777.4i	−0.358055	−	0.620169i
$866$	−435.736			−0.0170981
$867$	−900.641	+	7621.25i	−0.0352796	+	0.298537i
$868$	−27985.9	−	22549.8i	−1.09436	−	0.881784i
$869$	41490.8	+	23954.7i	1.61965	+	0.935107i
$870$	−275.596	+	2332.10i	−0.0107398	+	0.0908802i
$871$	−6431.16	−	3713.03i	−0.250186	−	0.144445i
$872$	−2216.21	+	1279.53i	−0.0860668	+	0.0496907i
$873$	6951.55	−	29001.4i	0.269501	−	1.12434i
$874$		−	7552.60i		−	0.292300i
$875$	−17622.3	+	21870.6i	−0.680850	+	0.844986i
$876$	6043.16	−	8095.81i	0.233081	−	0.312251i
$877$	−8670.90	−	15018.4i	−0.333860	−	0.578263i	0.649405	−	0.760443i	$-0.275018\pi$
$877$	−8670.90	−	15018.4i	−0.333860	−	0.578263i	−0.983265	+	0.182180i	$0.941685\pi$
$878$	4816.12			0.185121
$879$	−605.062	+	5120.05i	−0.0232176	+	0.196468i
$880$		−	18382.1i		−	0.704158i
$881$	38797.9			1.48369			0.741846	−	0.670570i	$-0.233950\pi$
$881$	38797.9			1.48369			0.741846	+	0.670570i	$0.233950\pi$
$882$	−3587.58	+	5923.85i	−0.136962	+	0.226152i
$883$	27338.7			1.04193			0.520963	−	0.853579i	$-0.325573\pi$
$883$	27338.7			1.04193			0.520963	+	0.853579i	$0.325573\pi$
$884$		−	22668.3i		−	0.862462i
$885$	26115.0	+	19493.6i	0.991915	+	0.740420i
$886$	8765.96			0.332391
$887$	−21705.1	−	37594.4i	−0.821631	−	1.42311i	−0.904467	−	0.426544i	$-0.859731\pi$
$887$	−21705.1	−	37594.4i	−0.821631	−	1.42311i	0.0828354	−	0.996563i	$-0.473602\pi$
$888$	8930.04	+	1055.31i	0.337469	+	0.0398804i
$889$	−28179.3	+	34972.6i	−1.06311	+	1.31940i
$890$			1165.02i			0.0438780i
$891$	−13717.7	+	26970.5i	−0.515780	+	1.01408i
$892$	−6390.83	+	3689.75i	−0.239889	+	0.138500i
$893$	−14579.1	−	8417.26i	−0.546329	−	0.315423i
$894$	−4595.35	−	3430.22i	−0.171915	−	0.128326i
$895$	−27794.8	−	16047.4i	−1.03808	−	0.599334i
$896$	18386.8	+	14815.2i	0.685558	+	0.552390i
$897$	−32205.1	+	13843.3i	−1.19877	+	0.515288i
$898$	−7572.34			−0.281394
$899$	−9056.10	−	15685.6i	−0.335971	−	0.581919i
$900$	−2814.82	−	9490.10i	−0.104253	−	0.351485i
$901$	21072.4	+	12166.2i	0.779160	+	0.449848i
$902$	1698.24	+	2941.44i	0.0626888	+	0.108580i
$903$	−23152.2	+	5944.50i	−0.853217	+	0.219071i
$904$	8968.96	−	15534.7i	0.329981	−	0.571545i
$905$	12424.0	−	7173.02i	0.456341	−	0.263469i
$906$	−4919.63	−	581.377i	−0.180401	−	0.0213189i
$907$	2565.11	−	4442.90i	0.0939064	−	0.162651i	−0.815245	−	0.579116i	$-0.803398\pi$
$907$	2565.11	−	4442.90i	0.0939064	−	0.162651i	0.909152	+	0.416465i	$0.136731\pi$
$908$	2245.12	−	3888.67i	0.0820562	−	0.142125i
$909$	5.76441	+	19.4346i	0.000210334	+	0.000709136i
$910$	−2881.93	+	3576.69i	−0.104983	+	0.130292i
$911$	20476.8	−	11822.3i	0.744707	−	0.429957i	−0.0790715	−	0.996869i	$-0.525196\pi$
$911$	20476.8	−	11822.3i	0.744707	−	0.429957i	0.823778	+	0.566912i	$0.191862\pi$
$912$	−14983.4	−	1770.66i	−0.544023	−	0.0642899i
$913$		−	23692.7i		−	0.858832i
$914$			5275.66i			0.190923i
$915$	17537.1	−	23493.8i	0.633615	−	0.848833i
$916$	−8346.43	+	4818.81i	−0.301063	+	0.173819i
$917$	893.639	+	139.305i	0.0321816	+	0.00501663i
$918$	1424.74	+	8264.72i	0.0512238	+	0.297142i
$919$	−22890.0	+	39646.7i	−0.821623	+	1.42309i	0.0828494	+	0.996562i	$0.473598\pi$
$919$	−22890.0	+	39646.7i	−0.821623	+	1.42309i	−0.904473	+	0.426531i	$0.859735\pi$
$920$	−8893.41	+	15403.8i	−0.318703	+	0.552011i
$921$	−527.019	−	1226.06i	−0.0188554	−	0.0438654i
$922$	−1684.93	+	972.797i	−0.0601847	+	0.0347477i
$923$	−1881.45	+	3258.77i	−0.0670951	+	0.116212i
$924$	21235.1	−	20795.0i	0.756042	−	0.740373i
$925$	3692.23	+	6395.13i	0.131243	+	0.227319i
$926$	6293.56	+	3633.59i	0.223347	+	0.128949i
$927$	4739.22	−	19771.7i	0.167914	−	0.700526i
$928$	4529.07	+	7844.57i	0.160209	+	0.277490i
$929$	−28665.2			−1.01235			−0.506176	−	0.862430i	$-0.668942\pi$
$929$	−28665.2			−1.01235			−0.506176	+	0.862430i	$0.668942\pi$
$930$	7067.24	+	5275.37i	0.249187	+	0.186007i
$931$	−5956.57	+	18641.4i	−0.209687	+	0.656227i
$932$	27528.6	+	15893.6i	0.967521	+	0.558598i
$933$	−3453.77	+	1484.60i	−0.121191	+	0.0520938i
$934$	−5491.02	−	3170.24i	−0.192368	−	0.111064i
$935$	−25005.1	+	14436.7i	−0.874604	+	0.504953i
$936$	−3378.70	−	11391.2i	−0.117987	−	0.397792i
$937$		−	20013.0i		−	0.697754i	−0.937168	−	0.348877i	$-0.886563\pi$
$937$		−	20013.0i		−	0.697754i	0.937168	−	0.348877i	$-0.113437\pi$
$938$	−2101.39	−	1693.20i	−0.0731478	−	0.0589391i
$939$	−14126.7	−	32864.4i	−0.490954	−	1.14216i
$940$	9552.61	+	16545.6i	0.331459	+	0.574105i
$941$	23886.9			0.827513			0.413757	−	0.910388i	$-0.364216\pi$
$941$	23886.9			0.827513			0.413757	+	0.910388i	$0.364216\pi$
$942$	7082.72	−	3044.49i	0.244976	−	0.105302i
$943$			19369.6i			0.668887i
$944$	36677.0			1.26455
$945$	−10989.4	+	19760.9i	−0.378292	+	0.680236i
$946$	−7709.77			−0.264975
$947$		−	9423.94i		−	0.323376i	−0.986842	−	0.161688i	$-0.948306\pi$
$947$		−	9423.94i		−	0.323376i	0.986842	−	0.161688i	$-0.0516938\pi$
$948$	−40999.8	+	17623.7i	−1.40466	+	0.603787i
$949$	9958.29			0.340632
$950$	1051.13	+	1820.62i	0.0358982	+	0.0621775i
$951$	753.838	+	1753.73i	0.0257044	+	0.0597988i
$952$	2632.98	−	16890.6i	0.0896381	−	0.575028i
$953$			42523.4i			1.44540i	0.691161	+	0.722701i	$0.257100\pi$
$953$			42523.4i			1.44540i	−0.691161	+	0.722701i	$0.742900\pi$
$954$	5976.72	+	1432.60i	0.202834	+	0.0486187i
$955$	27637.2	−	15956.3i	0.936459	−	0.540665i
$956$	15437.1	+	8912.59i	0.522249	+	0.301521i
$957$	13760.7	−	5915.02i	0.464808	−	0.199797i
$958$	12759.2	+	7366.50i	0.430302	+	0.248435i
$959$	−26469.2	+	10234.7i	−0.891276	+	0.344626i
$960$	11218.3	+	8373.97i	0.377156	+	0.281530i
$961$	−38228.4			−1.28322
$962$	2135.68	+	3699.11i	0.0715771	+	0.123975i
$963$	−32566.1	+	9659.29i	−1.08975	+	0.323226i
$964$	5271.92	+	3043.75i	0.176138	+	0.101693i
$965$	−1488.62	−	2578.37i	−0.0496584	−	0.0860109i
$966$	−12338.6	+	3168.04i	−0.410961	+	0.105518i
$967$	−2110.16	+	3654.91i	−0.0701739	+	0.121545i	−0.898977	−	0.437995i	$-0.855689\pi$
$967$	−2110.16	+	3654.91i	−0.0701739	+	0.121545i	0.828803	+	0.559540i	$0.189022\pi$
$968$	3918.29	−	2262.22i	0.130102	−	0.0751143i
$969$	9358.86	+	21772.5i	0.310268	+	0.721810i
$970$	3594.00	−	6225.00i	0.118965	−	0.206054i
$971$	−5026.42	+	8706.01i	−0.166123	+	0.287733i	−0.937054	−	0.349186i	$-0.886458\pi$
$971$	−5026.42	+	8706.01i	−0.166123	+	0.287733i	0.770931	+	0.636919i	$0.219792\pi$
$972$	−12489.0	−	25267.7i	−0.412123	−	0.833807i
$973$	12739.1	−	4925.78i	0.419730	−	0.162295i
$974$	−9249.51	+	5340.21i	−0.304285	+	0.175679i
$975$	5836.67	−	7819.19i	0.191716	−	0.256835i
$976$		−	32995.7i		−	1.08214i
$977$		−	21845.4i		−	0.715348i	−0.933847	−	0.357674i	$-0.883570\pi$
$977$		−	21845.4i		−	0.715348i	0.933847	−	0.357674i	$-0.116430\pi$
$978$	14174.4	+	1675.06i	0.463444	+	0.0547675i
$979$	6435.19	−	3715.36i	0.210081	−	0.121290i
$980$	16432.3	−	14941.5i	0.535622	−	0.487029i
$981$	−5819.01	−	1394.80i	−0.189385	−	0.0453951i
$982$	3924.84	−	6798.02i	0.127542	−	0.220910i
$983$	22362.1	−	38732.3i	0.725575	−	1.25673i	−0.233162	−	0.972438i	$-0.574907\pi$
$983$	22362.1	−	38732.3i	0.725575	−	1.25673i	0.958737	−	0.284295i	$-0.0917595\pi$
$984$	−6520.00	−	770.500i	−0.211230	−	0.0249621i
$985$	−3529.55	+	2037.79i	−0.114174	+	0.0659181i
$986$	2075.71	−	3595.23i	0.0670426	−	0.116121i
$987$	−7635.80	+	27348.5i	−0.246251	+	0.881979i
$988$	−8089.78	−	14011.9i	−0.260496	−	0.451192i
$989$	−38077.0	−	21983.8i	−1.22425	−	0.706818i
$990$	−5018.29	+	5291.99i	−0.161103	+	0.169889i
$991$	−8670.77	−	15018.2i	−0.277937	−	0.481402i	0.692935	−	0.721000i	$-0.256317\pi$
$991$	−8670.77	−	15018.2i	−0.277937	−	0.481402i	−0.970872	+	0.239599i	$0.922984\pi$
$992$	34017.4			1.08876
$993$	18263.4	−	7850.49i	0.583658	−	0.250884i
$994$	−857.970	+	1064.80i	−0.0273774	+	0.0339774i
$995$	−11827.2	−	6828.46i	−0.376833	−	0.217565i
$996$	17685.6	+	13201.5i	0.562642	+	0.419987i
$997$	48754.0	+	28148.1i	1.54870	+	0.894142i	0.998241	+	0.0592792i	$0.0188802\pi$
$997$	48754.0	+	28148.1i	1.54870	+	0.894142i	0.550458	+	0.834863i	$0.314453\pi$
$998$	−10898.5	+	6292.25i	−0.345677	+	0.199577i
$999$	13453.9	+	16158.7i	0.426088	+	0.511751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.i.a.5.11	✓	44
3.2	odd	2		189.4.i.a.152.12		44
7.3	odd	6		63.4.s.a.59.12	yes	44
9.2	odd	6		63.4.s.a.47.12	yes	44
9.7	even	3		189.4.s.a.89.11		44
21.17	even	6		189.4.s.a.17.11		44
63.38	even	6	inner	63.4.i.a.38.12	yes	44
63.52	odd	6		189.4.i.a.143.11		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.11	✓	44	1.1	even	1	trivial
63.4.i.a.38.12	yes	44	63.38	even	6	inner
63.4.s.a.47.12	yes	44	9.2	odd	6
63.4.s.a.59.12	yes	44	7.3	odd	6
189.4.i.a.143.11		44	63.52	odd	6
189.4.i.a.152.12		44	3.2	odd	2
189.4.s.a.17.11		44	21.17	even	6
189.4.s.a.89.11		44	9.7	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.747815i q^{2} +(4.77381 - 2.05201i) q^{3} +7.44077 q^{4} +(4.35110 + 7.53632i) q^{5} +(-1.53452 - 3.56993i) q^{6} +(-11.6200 + 14.4213i) q^{7} -11.5468i q^{8} +(18.5785 - 19.5918i) q^{9} +O(q^{10})\)	\(q-0.747815i q^{2} +(4.77381 - 2.05201i) q^{3} +7.44077 q^{4} +(4.35110 + 7.53632i) q^{5} +(-1.53452 - 3.56993i) q^{6} +(-11.6200 + 14.4213i) q^{7} -11.5468i q^{8} +(18.5785 - 19.5918i) q^{9} +(5.63577 - 3.25382i) q^{10} +(-35.9461 - 20.7535i) q^{11} +(35.5208 - 15.2685i) q^{12} +(33.0053 + 19.0556i) q^{13} +(10.7845 + 8.68963i) q^{14} +(36.2359 + 27.0485i) q^{15} +50.8913 q^{16} +(-39.9685 - 69.2274i) q^{17} +(-14.6510 - 13.8933i) q^{18} +(-49.4113 - 28.5276i) q^{19} +(32.3755 + 56.0761i) q^{20} +(-25.8791 + 92.6891i) q^{21} +(-15.5198 + 26.8811i) q^{22} +(-153.298 + 88.5068i) q^{23} +(-23.6942 - 55.1224i) q^{24} +(24.6359 - 42.6706i) q^{25} +(14.2501 - 24.6818i) q^{26} +(48.4877 - 131.651i) q^{27} +(-86.4620 + 107.306i) q^{28} +(-60.1430 + 34.7236i) q^{29} +(20.2272 - 27.0978i) q^{30} +260.805i q^{31} -130.432i q^{32} +(-214.186 - 25.3115i) q^{33} +(-51.7693 + 29.8890i) q^{34} +(-159.244 - 24.8237i) q^{35} +(138.238 - 145.778i) q^{36} +(-74.9359 + 129.793i) q^{37} +(-21.3334 + 36.9505i) q^{38} +(196.663 + 23.2407i) q^{39} +(87.0207 - 50.2414i) q^{40} +(54.7122 - 94.7643i) q^{41} +(69.3143 + 19.3528i) q^{42} +(124.193 + 215.108i) q^{43} +(-267.467 - 154.422i) q^{44} +(228.487 + 54.7678i) q^{45} +(66.1867 + 114.639i) q^{46} +295.057 q^{47} +(242.945 - 104.429i) q^{48} +(-72.9497 - 335.153i) q^{49} +(-31.9097 - 18.4231i) q^{50} +(-332.857 - 248.463i) q^{51} +(245.585 + 141.788i) q^{52} +(-263.613 + 152.197i) q^{53} +(-98.4504 - 36.2598i) q^{54} -361.202i q^{55} +(166.521 + 134.175i) q^{56} +(-294.419 - 34.7930i) q^{57} +(25.9668 + 44.9759i) q^{58} +720.693 q^{59} +(269.623 + 201.262i) q^{60} -648.357i q^{61} +195.034 q^{62} +(66.6571 + 495.584i) q^{63} +309.591 q^{64} +331.651i q^{65} +(-18.9283 + 160.172i) q^{66} -194.853 q^{67} +(-297.396 - 515.106i) q^{68} +(-550.200 + 737.084i) q^{69} +(-18.5635 + 119.085i) q^{70} +98.7349i q^{71} +(-226.223 - 214.523i) q^{72} +(226.289 - 130.648i) q^{73} +(97.0610 + 56.0382i) q^{74} +(30.0465 - 254.255i) q^{75} +(-367.658 - 212.268i) q^{76} +(716.989 - 277.235i) q^{77} +(17.3797 - 147.068i) q^{78} -1154.25 q^{79} +(221.433 + 383.533i) q^{80} +(-38.6779 - 727.973i) q^{81} +(-70.8661 - 40.9146i) q^{82} +(285.406 + 494.337i) q^{83} +(-192.560 + 689.679i) q^{84} +(347.813 - 602.431i) q^{85} +(160.861 - 92.8731i) q^{86} +(-215.858 + 289.178i) q^{87} +(-239.638 + 415.064i) q^{88} +(-89.5115 + 155.038i) q^{89} +(40.9561 - 170.866i) q^{90} +(-658.330 + 254.553i) q^{91} +(-1140.66 + 658.559i) q^{92} +(535.175 + 1245.04i) q^{93} -220.648i q^{94} -496.506i q^{95} +(-267.648 - 622.657i) q^{96} +(956.569 - 552.275i) q^{97} +(-250.632 + 54.5529i) q^{98} +(-1074.42 + 318.681i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{3} - 162 q^{4} - 3 q^{5} + 24 q^{6} + 5 q^{7} - 45 q^{9}+O(q^{10}) \) 44 * q - 3 * q^3 - 162 * q^4 - 3 * q^5 + 24 * q^6 + 5 * q^7 - 45 * q^9	\( 44 q - 3 q^{3} - 162 q^{4} - 3 q^{5} + 24 q^{6} + 5 q^{7} - 45 q^{9} - 6 q^{10} + 9 q^{11} + 186 q^{12} - 36 q^{13} + 54 q^{14} - 141 q^{15} + 526 q^{16} - 72 q^{17} - 54 q^{18} - 6 q^{19} + 24 q^{20} - 81 q^{21} + 14 q^{22} - 285 q^{23} - 114 q^{24} - 349 q^{25} - 96 q^{26} + 432 q^{27} - 156 q^{28} - 132 q^{29} - 447 q^{30} - 3 q^{33} + 24 q^{34} + 765 q^{35} + 1122 q^{36} + 82 q^{37} - 873 q^{38} + 306 q^{39} + 420 q^{40} + 618 q^{41} - 282 q^{42} + 82 q^{43} + 603 q^{44} + 291 q^{45} + 266 q^{46} - 402 q^{47} - 1569 q^{48} - 79 q^{49} - 1845 q^{50} + 453 q^{51} + 189 q^{52} + 564 q^{53} - 2385 q^{54} + 66 q^{56} + 1170 q^{57} + 269 q^{58} + 1494 q^{59} + 2265 q^{60} - 2904 q^{62} - 636 q^{63} - 1144 q^{64} - 372 q^{66} - 590 q^{67} + 3504 q^{68} - 1005 q^{69} - 105 q^{70} + 1830 q^{72} - 6 q^{73} + 1515 q^{74} - 33 q^{75} - 144 q^{76} - 4443 q^{77} - 5985 q^{78} + 1102 q^{79} - 4239 q^{80} - 4017 q^{81} + 18 q^{82} + 1830 q^{83} + 3165 q^{84} - 237 q^{85} + 1209 q^{86} + 2013 q^{87} - 623 q^{88} + 4266 q^{89} + 9993 q^{90} - 1140 q^{91} + 7896 q^{92} - 729 q^{93} + 3975 q^{96} - 792 q^{97} + 5667 q^{98} + 4335 q^{99}+O(q^{100}) \) 44 * q - 3 * q^3 - 162 * q^4 - 3 * q^5 + 24 * q^6 + 5 * q^7 - 45 * q^9 - 6 * q^10 + 9 * q^11 + 186 * q^12 - 36 * q^13 + 54 * q^14 - 141 * q^15 + 526 * q^16 - 72 * q^17 - 54 * q^18 - 6 * q^19 + 24 * q^20 - 81 * q^21 + 14 * q^22 - 285 * q^23 - 114 * q^24 - 349 * q^25 - 96 * q^26 + 432 * q^27 - 156 * q^28 - 132 * q^29 - 447 * q^30 - 3 * q^33 + 24 * q^34 + 765 * q^35 + 1122 * q^36 + 82 * q^37 - 873 * q^38 + 306 * q^39 + 420 * q^40 + 618 * q^41 - 282 * q^42 + 82 * q^43 + 603 * q^44 + 291 * q^45 + 266 * q^46 - 402 * q^47 - 1569 * q^48 - 79 * q^49 - 1845 * q^50 + 453 * q^51 + 189 * q^52 + 564 * q^53 - 2385 * q^54 + 66 * q^56 + 1170 * q^57 + 269 * q^58 + 1494 * q^59 + 2265 * q^60 - 2904 * q^62 - 636 * q^63 - 1144 * q^64 - 372 * q^66 - 590 * q^67 + 3504 * q^68 - 1005 * q^69 - 105 * q^70 + 1830 * q^72 - 6 * q^73 + 1515 * q^74 - 33 * q^75 - 144 * q^76 - 4443 * q^77 - 5985 * q^78 + 1102 * q^79 - 4239 * q^80 - 4017 * q^81 + 18 * q^82 + 1830 * q^83 + 3165 * q^84 - 237 * q^85 + 1209 * q^86 + 2013 * q^87 - 623 * q^88 + 4266 * q^89 + 9993 * q^90 - 1140 * q^91 + 7896 * q^92 - 729 * q^93 + 3975 * q^96 - 792 * q^97 + 5667 * q^98 + 4335 * q^99

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