LMFDB - Embedded newform 201.4.e.b.37.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(37,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("201.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.e (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:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.8
Character	$\chi$	$=$	201.37
Dual form			201.4.e.b.163.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.561904 - 0.973245i) q^{2} -3.00000 q^{3} +(3.36853 - 5.83446i) q^{4} -9.21684 q^{5} +(1.68571 + 2.91974i) q^{6} +(2.79031 - 4.83295i) q^{7} -16.5616 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(-0.561904 - 0.973245i) q^{2} -3.00000 q^{3} +(3.36853 - 5.83446i) q^{4} -9.21684 q^{5} +(1.68571 + 2.91974i) q^{6} +(2.79031 - 4.83295i) q^{7} -16.5616 q^{8} +9.00000 q^{9} +(5.17897 + 8.97024i) q^{10} +(-15.6166 + 27.0487i) q^{11} +(-10.1056 + 17.5034i) q^{12} +(-35.5524 - 61.5785i) q^{13} -6.27153 q^{14} +27.6505 q^{15} +(-17.6422 - 30.5572i) q^{16} +(38.0096 + 65.8346i) q^{17} +(-5.05713 - 8.75921i) q^{18} +(44.2106 + 76.5751i) q^{19} +(-31.0472 + 53.7753i) q^{20} +(-8.37092 + 14.4989i) q^{21} +35.1001 q^{22} +(40.9889 + 70.9948i) q^{23} +49.6848 q^{24} -40.0499 q^{25} +(-39.9540 + 69.2024i) q^{26} -27.0000 q^{27} +(-18.7985 - 32.5599i) q^{28} +(-4.66534 + 8.08061i) q^{29} +(-15.5369 - 26.9107i) q^{30} +(-109.065 + 188.907i) q^{31} +(-86.0729 + 149.083i) q^{32} +(46.8498 - 81.1462i) q^{33} +(42.7155 - 73.9854i) q^{34} +(-25.7178 + 44.5445i) q^{35} +(30.3168 - 52.5102i) q^{36} +(103.370 + 179.042i) q^{37} +(49.6842 - 86.0556i) q^{38} +(106.657 + 184.736i) q^{39} +152.646 q^{40} +(7.08816 - 12.2771i) q^{41} +18.8146 q^{42} -257.822 q^{43} +(105.210 + 182.229i) q^{44} -82.9515 q^{45} +(46.0636 - 79.7844i) q^{46} +(-115.459 + 199.980i) q^{47} +(52.9266 + 91.6716i) q^{48} +(155.928 + 270.076i) q^{49} +(22.5042 + 38.9784i) q^{50} +(-114.029 - 197.504i) q^{51} -479.037 q^{52} -147.872 q^{53} +(15.1714 + 26.2776i) q^{54} +(143.936 - 249.304i) q^{55} +(-46.2120 + 80.0415i) q^{56} +(-132.632 - 229.725i) q^{57} +10.4859 q^{58} +211.586 q^{59} +(93.1415 - 161.326i) q^{60} +(-286.230 - 495.764i) q^{61} +245.137 q^{62} +(25.1128 - 43.4966i) q^{63} -88.8167 q^{64} +(327.680 + 567.559i) q^{65} -105.300 q^{66} +(282.586 - 470.009i) q^{67} +512.146 q^{68} +(-122.967 - 212.984i) q^{69} +57.8037 q^{70} +(27.4717 - 47.5824i) q^{71} -149.054 q^{72} +(-202.323 - 350.434i) q^{73} +(116.168 - 201.209i) q^{74} +120.150 q^{75} +595.699 q^{76} +(87.1501 + 150.948i) q^{77} +(119.862 - 207.607i) q^{78} +(-162.608 + 281.645i) q^{79} +(162.605 + 281.641i) q^{80} +81.0000 q^{81} -15.9315 q^{82} +(-653.525 - 1131.94i) q^{83} +(56.3954 + 97.6796i) q^{84} +(-350.329 - 606.787i) q^{85} +(144.871 + 250.924i) q^{86} +(13.9960 - 24.2418i) q^{87} +(258.636 - 447.970i) q^{88} -1647.40 q^{89} +(46.6108 + 80.7322i) q^{90} -396.808 q^{91} +552.289 q^{92} +(327.196 - 566.720i) q^{93} +259.507 q^{94} +(-407.482 - 705.780i) q^{95} +(258.219 - 447.248i) q^{96} +(-684.075 - 1184.85i) q^{97} +(175.233 - 303.513i) q^{98} +(-140.549 + 243.439i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9}+O(q^{10}) $ 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9} + 14 q^{10} - 16 q^{11} + 270 q^{12} - 46 q^{13} + 14 q^{14} + 12 q^{15} - 346 q^{16} - 8 q^{17} + 18 q^{18} - 154 q^{19} - 180 q^{20} - 66 q^{21} + 214 q^{22} - 104 q^{23} - 144 q^{24} + 1032 q^{25} - 333 q^{26} - 972 q^{27} - 473 q^{28} + 76 q^{29} - 42 q^{30} + 498 q^{31} - 285 q^{32} + 48 q^{33} + 26 q^{34} - 392 q^{35} - 810 q^{36} - 124 q^{37} + 20 q^{38} + 138 q^{39} + 638 q^{40} - 508 q^{41} - 42 q^{42} - 1400 q^{43} - 333 q^{44} - 36 q^{45} - 1372 q^{46} + 18 q^{47} + 1038 q^{48} - 238 q^{49} - 337 q^{50} + 24 q^{51} + 3640 q^{52} + 724 q^{53} - 54 q^{54} - 178 q^{55} - 829 q^{56} + 462 q^{57} - 1472 q^{58} + 720 q^{59} + 540 q^{60} + 232 q^{61} - 3882 q^{62} + 198 q^{63} + 3628 q^{64} - 1428 q^{65} - 642 q^{66} - 1164 q^{67} + 1634 q^{68} + 312 q^{69} + 2550 q^{70} + 406 q^{71} + 432 q^{72} - 2120 q^{73} + 1375 q^{74} - 3096 q^{75} + 4190 q^{76} - 800 q^{77} + 999 q^{78} + 1306 q^{79} - 1927 q^{80} + 2916 q^{81} - 794 q^{82} - 1010 q^{83} + 1419 q^{84} + 472 q^{85} + 737 q^{86} - 228 q^{87} - 1838 q^{88} + 1904 q^{89} + 126 q^{90} + 7340 q^{91} + 7368 q^{92} - 1494 q^{93} - 9862 q^{94} + 1678 q^{95} + 855 q^{96} - 2358 q^{97} - 2610 q^{98} - 144 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9 + 14 * q^10 - 16 * q^11 + 270 * q^12 - 46 * q^13 + 14 * q^14 + 12 * q^15 - 346 * q^16 - 8 * q^17 + 18 * q^18 - 154 * q^19 - 180 * q^20 - 66 * q^21 + 214 * q^22 - 104 * q^23 - 144 * q^24 + 1032 * q^25 - 333 * q^26 - 972 * q^27 - 473 * q^28 + 76 * q^29 - 42 * q^30 + 498 * q^31 - 285 * q^32 + 48 * q^33 + 26 * q^34 - 392 * q^35 - 810 * q^36 - 124 * q^37 + 20 * q^38 + 138 * q^39 + 638 * q^40 - 508 * q^41 - 42 * q^42 - 1400 * q^43 - 333 * q^44 - 36 * q^45 - 1372 * q^46 + 18 * q^47 + 1038 * q^48 - 238 * q^49 - 337 * q^50 + 24 * q^51 + 3640 * q^52 + 724 * q^53 - 54 * q^54 - 178 * q^55 - 829 * q^56 + 462 * q^57 - 1472 * q^58 + 720 * q^59 + 540 * q^60 + 232 * q^61 - 3882 * q^62 + 198 * q^63 + 3628 * q^64 - 1428 * q^65 - 642 * q^66 - 1164 * q^67 + 1634 * q^68 + 312 * q^69 + 2550 * q^70 + 406 * q^71 + 432 * q^72 - 2120 * q^73 + 1375 * q^74 - 3096 * q^75 + 4190 * q^76 - 800 * q^77 + 999 * q^78 + 1306 * q^79 - 1927 * q^80 + 2916 * q^81 - 794 * q^82 - 1010 * q^83 + 1419 * q^84 + 472 * q^85 + 737 * q^86 - 228 * q^87 - 1838 * q^88 + 1904 * q^89 + 126 * q^90 + 7340 * q^91 + 7368 * q^92 - 1494 * q^93 - 9862 * q^94 + 1678 * q^95 + 855 * q^96 - 2358 * q^97 - 2610 * q^98 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.561904	−	0.973245i	−0.198663	−	0.344094i	0.749432	−	0.662081i	$-0.230327\pi$
$2$	−0.561904	−	0.973245i	−0.198663	−	0.344094i	−0.948095	+	0.317987i	$0.896993\pi$
$3$	−3.00000			−0.577350
$3$	−3.00000			−0.577350
$4$	3.36853	−	5.83446i	0.421066	−	0.729308i
$5$	−9.21684			−0.824379			−0.412189	−	0.911098i	$-0.635236\pi$
$5$	−9.21684			−0.824379			−0.412189	+	0.911098i	$0.635236\pi$
$6$	1.68571	+	2.91974i	0.114698	+	0.198663i
$7$	2.79031	−	4.83295i	0.150662	−	0.260955i	−0.780809	−	0.624770i	$-0.785193\pi$
$7$	2.79031	−	4.83295i	0.150662	−	0.260955i	0.931471	+	0.363815i	$0.118526\pi$
$8$	−16.5616			−0.731927
$9$	9.00000			0.333333
$10$	5.17897	+	8.97024i	0.163773	+	0.283664i
$11$	−15.6166	+	27.0487i	−0.428053	+	0.741409i	−0.996700	−	0.0811725i	$-0.974134\pi$
$11$	−15.6166	+	27.0487i	−0.428053	+	0.741409i	0.568647	+	0.822581i	$0.307467\pi$
$12$	−10.1056	+	17.5034i	−0.243103	+	0.421066i
$13$	−35.5524	−	61.5785i	−0.758497	−	1.31375i	−0.943617	−	0.331039i	$-0.892601\pi$
$13$	−35.5524	−	61.5785i	−0.758497	−	1.31375i	0.185121	−	0.982716i	$-0.440732\pi$
$14$	−6.27153			−0.119724
$15$	27.6505			0.475955
$16$	−17.6422	−	30.5572i	−0.275659	−	0.477456i
$17$	38.0096	+	65.8346i	0.542276	+	0.939249i	0.998773	+	0.0495244i	$0.0157705\pi$
$17$	38.0096	+	65.8346i	0.542276	+	0.939249i	−0.456497	+	0.889725i	$0.650896\pi$
$18$	−5.05713	−	8.75921i	−0.0662210	−	0.114698i
$19$	44.2106	+	76.5751i	0.533822	+	0.924607i	0.999219	+	0.0395048i	$0.0125780\pi$
$19$	44.2106	+	76.5751i	0.533822	+	0.924607i	−0.465398	+	0.885102i	$0.654089\pi$
$20$	−31.0472	+	53.7753i	−0.347118	+	0.601226i
$21$	−8.37092	+	14.4989i	−0.0869850	+	0.150662i
$22$	35.1001			0.340153
$23$	40.9889	+	70.9948i	0.371599	+	0.643628i	0.989812	−	0.142383i	$-0.0454764\pi$
$23$	40.9889	+	70.9948i	0.371599	+	0.643628i	−0.618213	+	0.786011i	$0.712143\pi$
$24$	49.6848			0.422578
$25$	−40.0499			−0.320399
$26$	−39.9540	+	69.2024i	−0.301370	+	0.521989i
$27$	−27.0000			−0.192450
$28$	−18.7985	−	32.5599i	−0.126878	−	0.219759i
$29$	−4.66534	+	8.08061i	−0.0298735	+	0.0517425i	−0.880576	−	0.473906i	$-0.842844\pi$
$29$	−4.66534	+	8.08061i	−0.0298735	+	0.0517425i	0.850702	+	0.525648i	$0.176177\pi$
$30$	−15.5369	−	26.9107i	−0.0945547	−	0.163773i
$31$	−109.065	+	188.907i	−0.631894	+	1.09447i	0.355271	+	0.934764i	$0.384389\pi$
$31$	−109.065	+	188.907i	−0.631894	+	1.09447i	−0.987164	+	0.159708i	$0.948945\pi$
$32$	−86.0729	+	149.083i	−0.475490	+	0.823573i
$33$	46.8498	−	81.1462i	0.247136	−	0.428053i
$34$	42.7155	−	73.9854i	0.215460	−	0.373188i
$35$	−25.7178	+	44.5445i	−0.124203	+	0.215126i
$36$	30.3168	−	52.5102i	0.140355	−	0.243103i
$37$	103.370	+	179.042i	0.459295	+	0.795522i	0.998924	−	0.0463808i	$-0.0147688\pi$
$37$	103.370	+	179.042i	0.459295	+	0.795522i	−0.539629	+	0.841903i	$0.681435\pi$
$38$	49.6842	−	86.0556i	0.212101	−	0.367370i
$39$	106.657	+	184.736i	0.437918	+	0.758497i
$40$	152.646			0.603385
$41$	7.08816	−	12.2771i	0.0269996	−	0.0467647i	−0.852210	−	0.523200i	$-0.824738\pi$
$41$	7.08816	−	12.2771i	0.0269996	−	0.0467647i	0.879210	+	0.476435i	$0.158071\pi$
$42$	18.8146			0.0691227
$43$	−257.822			−0.914360			−0.457180	−	0.889374i	$-0.651140\pi$
$43$	−257.822			−0.914360			−0.457180	+	0.889374i	$0.651140\pi$
$44$	105.210	+	182.229i	0.360477	+	0.624364i
$45$	−82.9515			−0.274793
$46$	46.0636	−	79.7844i	0.147646	−	0.255730i
$47$	−115.459	+	199.980i	−0.358328	+	0.620641i	−0.987682	−	0.156477i	$-0.949986\pi$
$47$	−115.459	+	199.980i	−0.358328	+	0.620641i	0.629354	+	0.777119i	$0.283320\pi$
$48$	52.9266	+	91.6716i	0.159152	+	0.275659i
$49$	155.928	+	270.076i	0.454602	+	0.787393i
$50$	22.5042	+	38.9784i	0.0636515	+	0.110248i
$51$	−114.029	−	197.504i	−0.313083	−	0.542276i
$52$	−479.037			−1.27751
$53$	−147.872			−0.383242			−0.191621	−	0.981469i	$-0.561374\pi$
$53$	−147.872			−0.383242			−0.191621	+	0.981469i	$0.561374\pi$
$54$	15.1714	+	26.2776i	0.0382327	+	0.0662210i
$55$	143.936	−	249.304i	0.352878	−	0.611202i
$56$	−46.2120	+	80.0415i	−0.110274	+	0.191000i
$57$	−132.632	−	229.725i	−0.308202	−	0.533822i
$58$	10.4859			0.0237391
$59$	211.586			0.466884			0.233442	−	0.972371i	$-0.425001\pi$
$59$	211.586			0.466884			0.233442	+	0.972371i	$0.425001\pi$
$60$	93.1415	−	161.326i	0.200409	−	0.347118i
$61$	−286.230	−	495.764i	−0.600786	−	1.04059i	−0.992702	−	0.120591i	$-0.961521\pi$
$61$	−286.230	−	495.764i	−0.600786	−	1.04059i	0.391916	−	0.920001i	$-0.371812\pi$
$62$	245.137			0.502135
$63$	25.1128	−	43.4966i	0.0502208	−	0.0869850i
$64$	−88.8167			−0.173470
$65$	327.680	+	567.559i	0.625289	+	1.08303i
$66$	−105.300			−0.196387
$67$	282.586	−	470.009i	0.515273	−	0.857026i
$67$	282.586	−	470.009i	0.515273	−	0.857026i
$68$	512.146			0.913336
$69$	−122.967	−	212.984i	−0.214543	−	0.371599i
$70$	57.8037			0.0986980
$71$	27.4717	−	47.5824i	0.0459196	−	0.0795350i	−0.842152	−	0.539240i	$-0.818712\pi$
$71$	27.4717	−	47.5824i	0.0459196	−	0.0795350i	0.888072	+	0.459705i	$0.152045\pi$
$72$	−149.054			−0.243976
$73$	−202.323	−	350.434i	−0.324386	−	0.561853i	0.657002	−	0.753889i	$-0.271824\pi$
$73$	−202.323	−	350.434i	−0.324386	−	0.561853i	−0.981388	+	0.192036i	$0.938491\pi$
$74$	116.168	−	201.209i	0.182490	−	0.316082i
$75$	120.150			0.184983
$76$	595.699			0.899097
$77$	87.1501	+	150.948i	0.128983	+	0.223405i
$78$	119.862	−	207.607i	0.173996	−	0.301370i
$79$	−162.608	+	281.645i	−0.231580	+	0.401108i	−0.958273	−	0.285854i	$-0.907723\pi$
$79$	−162.608	+	281.645i	−0.231580	+	0.401108i	0.726693	+	0.686962i	$0.241056\pi$
$80$	162.605	+	281.641i	0.227248	+	0.393605i
$81$	81.0000			0.111111
$82$	−15.9315			−0.0214553
$83$	−653.525	−	1131.94i	−0.864262	−	1.49694i	−0.867779	−	0.496951i	$-0.834453\pi$
$83$	−653.525	−	1131.94i	−0.864262	−	1.49694i	0.00351704	−	0.999994i	$-0.498880\pi$
$84$	56.3954	+	97.6796i	0.0732528	+	0.126878i
$85$	−350.329	−	606.787i	−0.447041	−	0.774297i
$86$	144.871	+	250.924i	0.181649	+	0.314626i
$87$	13.9960	−	24.2418i	0.0172475	−	0.0298735i
$88$	258.636	−	447.970i	0.313303	−	0.542657i
$89$	−1647.40			−1.96206			−0.981032	−	0.193846i	$-0.937904\pi$
$89$	−1647.40			−1.96206			−0.981032	+	0.193846i	$0.937904\pi$
$90$	46.6108	+	80.7322i	0.0545912	+	0.0945547i
$91$	−396.808			−0.457108
$92$	552.289			0.625870
$93$	327.196	−	566.720i	0.364824	−	0.631894i
$94$	259.507			0.284746
$95$	−407.482	−	705.780i	−0.440071	−	0.762226i
$96$	258.219	−	447.248i	0.274524	−	0.475490i
$97$	−684.075	−	1184.85i	−0.716054	−	1.24024i	−0.962552	−	0.271099i	$-0.912613\pi$
$97$	−684.075	−	1184.85i	−0.716054	−	1.24024i	0.246497	−	0.969143i	$-0.420720\pi$
$98$	175.233	−	303.513i	0.180625	−	0.312852i
$99$	−140.549	+	243.439i	−0.142684	+	0.247136i
$100$	−134.909	+	233.670i	−0.134909	+	0.233670i
$101$	−583.118	+	1009.99i	−0.574480	+	0.995028i	0.421618	+	0.906773i	$0.361462\pi$
$101$	−583.118	+	1009.99i	−0.574480	+	0.995028i	−0.996098	+	0.0882545i	$0.971871\pi$
$102$	−128.146	+	221.956i	−0.124396	+	0.215460i
$103$	236.953	−	410.415i	0.226677	−	0.392615i	−0.730145	−	0.683293i	$-0.760547\pi$
$103$	236.953	−	410.415i	0.226677	−	0.392615i	0.956821	+	0.290677i	$0.0938806\pi$
$104$	588.805	+	1019.84i	0.555164	+	0.961572i
$105$	77.1534	−	133.634i	0.0717086	−	0.124203i
$106$	83.0899	+	143.916i	0.0761359	+	0.131871i
$107$	−301.954			−0.272813			−0.136407	−	0.990653i	$-0.543555\pi$
$107$	−301.954			−0.272813			−0.136407	+	0.990653i	$0.543555\pi$
$108$	−90.9503	+	157.531i	−0.0810342	+	0.140355i
$109$	1524.64			1.33976			0.669881	−	0.742468i	$-0.266345\pi$
$109$	1524.64			1.33976			0.669881	+	0.742468i	$0.266345\pi$
$110$	−323.512			−0.280415
$111$	−310.110	−	537.126i	−0.265174	−	0.459295i
$112$	−196.909			−0.166126
$113$	−593.034	+	1027.17i	−0.493699	+	0.855112i	−0.999974	−	0.00726059i	$-0.997689\pi$
$113$	−593.034	+	1027.17i	−0.493699	+	0.855112i	0.506275	+	0.862372i	$0.331022\pi$
$114$	−149.053	+	258.167i	−0.122457	+	0.212101i
$115$	−377.788	−	654.347i	−0.306338	−	0.530593i
$116$	31.4307	+	54.4396i	0.0251575	+	0.0435740i
$117$	−319.971	−	554.207i	−0.252832	−	0.437918i
$118$	−118.891	−	205.925i	−0.0927525	−	0.160652i
$119$	424.234			0.326802
$120$	−457.937			−0.348364
$121$	177.744	+	307.862i	0.133542	+	0.231301i
$122$	−321.667	+	557.143i	−0.238708	+	0.413454i
$123$	−21.2645	+	36.8312i	−0.0155882	+	0.0269996i
$124$	734.779	+	1272.67i	0.532138	+	0.921690i
$125$	1521.24			1.08851
$126$	−56.4438			−0.0399080
$127$	−54.2439	+	93.9531i	−0.0379005	+	0.0656456i	−0.884353	−	0.466818i	$-0.845400\pi$
$127$	−54.2439	+	93.9531i	−0.0379005	+	0.0656456i	0.846453	+	0.532464i	$0.178734\pi$
$128$	738.489	+	1279.10i	0.509952	+	0.883263i
$129$	773.466			0.527906
$130$	368.250	−	637.827i	0.248443	−	0.430316i
$131$	−913.462			−0.609233			−0.304616	−	0.952475i	$-0.598528\pi$
$131$	−913.462			−0.609233			−0.304616	+	0.952475i	$0.598528\pi$
$132$	−315.630	−	546.686i	−0.208121	−	0.360477i
$133$	493.445			0.321707
$134$	−616.220	−	10.9254i	−0.397263	−	0.00704336i
$135$	248.855			0.158652
$136$	−629.501	−	1090.33i	−0.396906	−	0.687462i
$137$	−851.617			−0.531084			−0.265542	−	0.964099i	$-0.585551\pi$
$137$	−851.617			−0.531084			−0.265542	+	0.964099i	$0.585551\pi$
$138$	−138.191	+	239.353i	−0.0852433	+	0.147646i
$139$	−599.053			−0.365547			−0.182773	−	0.983155i	$-0.558507\pi$
$139$	−599.053			−0.365547			−0.182773	+	0.983155i	$0.558507\pi$
$140$	173.262	+	300.099i	0.104595	+	0.181164i
$141$	346.376	−	599.941i	0.206880	−	0.358328i
$142$	−61.7457			−0.0364901
$143$	2220.83			1.29871
$144$	−158.780	−	275.015i	−0.0918865	−	0.159152i
$145$	42.9997	−	74.4777i	0.0246271	−	0.0426554i
$146$	−227.372	+	393.821i	−0.128887	+	0.223239i
$147$	−467.785	−	810.228i	−0.262464	−	0.454602i
$148$	1392.82			0.773574
$149$	−1506.27			−0.828180			−0.414090	−	0.910236i	$-0.635900\pi$
$149$	−1506.27			−0.828180			−0.414090	+	0.910236i	$0.635900\pi$
$150$	−67.5126	−	116.935i	−0.0367492	−	0.0636515i
$151$	826.695	+	1431.88i	0.445533	+	0.771686i	0.998089	−	0.0617897i	$-0.0196808\pi$
$151$	826.695	+	1431.88i	0.445533	+	0.771686i	−0.552556	+	0.833476i	$0.686347\pi$
$152$	−732.199	−	1268.21i	−0.390718	−	0.676744i
$153$	342.087	+	592.511i	0.180759	+	0.313083i
$154$	97.9399	−	169.637i	0.0512482	−	0.0887645i
$155$	1005.24	−	1741.12i	0.520920	−	0.902260i
$156$	1437.11			0.737570
$157$	694.142	+	1202.29i	0.352857	+	0.611167i	0.986749	−	0.162255i	$-0.0518768\pi$
$157$	694.142	+	1202.29i	0.352857	+	0.611167i	−0.633892	+	0.773422i	$0.718543\pi$
$158$	365.479			0.184025
$159$	443.617			0.221265
$160$	793.320	−	1374.07i	0.391984	−	0.678936i
$161$	457.486			0.223944
$162$	−45.5142	−	78.8329i	−0.0220737	−	0.0382327i
$163$	1251.09	−	2166.96i	0.601185	−	1.04128i	−0.391457	−	0.920196i	$-0.628029\pi$
$163$	1251.09	−	2166.96i	0.601185	−	1.04128i	0.992642	−	0.121087i	$-0.0386378\pi$
$164$	−47.7534	−	82.7112i	−0.0227373	−	0.0393821i
$165$	−431.807	+	747.911i	−0.203734	+	0.352878i
$166$	−734.436	+	1272.08i	−0.343393	+	0.594775i
$167$	−1498.06	+	2594.71i	−0.694151	+	1.20231i	0.276315	+	0.961067i	$0.410887\pi$
$167$	−1498.06	+	2594.71i	−0.694151	+	1.20231i	−0.970466	+	0.241238i	$0.922446\pi$
$168$	138.636	−	240.124i	0.0636666	−	0.110274i
$169$	−1429.44	+	2475.87i	−0.650634	+	1.12693i
$170$	−393.702	+	681.911i	−0.177621	+	0.307648i
$171$	397.896	+	689.176i	0.177941	+	0.308202i
$172$	−868.481	+	1504.25i	−0.385006	+	0.666850i
$173$	−83.7667	−	145.088i	−0.0368131	−	0.0637621i	0.847032	−	0.531542i	$-0.178387\pi$
$173$	−83.7667	−	145.088i	−0.0368131	−	0.0637621i	−0.883845	+	0.467780i	$0.845054\pi$
$174$	−31.4577			−0.0137057
$175$	−111.752	+	193.559i	−0.0482721	+	0.0836098i
$176$	1102.04			0.471987
$177$	−634.758			−0.269556
$178$	925.678	+	1603.32i	0.389789	+	0.675135i
$179$	−3038.82			−1.26889			−0.634447	−	0.772967i	$-0.718772\pi$
$179$	−3038.82			−1.26889			−0.634447	+	0.772967i	$0.718772\pi$
$180$	−279.425	+	483.978i	−0.115706	+	0.200409i
$181$	−1791.55	+	3103.06i	−0.735718	+	1.27430i	0.218690	+	0.975794i	$0.429822\pi$
$181$	−1791.55	+	3103.06i	−0.735718	+	1.27430i	−0.954408	+	0.298507i	$0.903512\pi$
$182$	222.968	+	386.192i	0.0908103	+	0.157288i
$183$	858.689	+	1487.29i	0.346864	+	0.600786i
$184$	−678.841	−	1175.79i	−0.271983	−	0.471088i
$185$	−952.744	−	1650.20i	−0.378633	−	0.655812i
$186$	−735.410			−0.289908
$187$	−2374.32			−0.928490
$188$	777.852	+	1347.28i	0.301759	+	0.522662i
$189$	−75.3383	+	130.490i	−0.0289950	+	0.0502208i
$190$	−457.931	+	793.160i	−0.174852	+	0.302852i
$191$	1592.61	+	2758.48i	0.603336	+	1.04501i	0.992312	+	0.123760i	$0.0394954\pi$
$191$	1592.61	+	2758.48i	0.603336	+	1.04501i	−0.388977	+	0.921248i	$0.627171\pi$
$192$	266.450			0.100153
$193$	−2470.95			−0.921569			−0.460784	−	0.887512i	$-0.652432\pi$
$193$	−2470.95			−0.921569			−0.460784	+	0.887512i	$0.652432\pi$
$194$	−768.768	+	1331.55i	−0.284507	+	0.492780i
$195$	−983.041	−	1702.68i	−0.361010	−	0.625289i
$196$	2101.00			0.765669
$197$	1144.33	−	1982.04i	0.413859	−	0.716824i	−0.581449	−	0.813583i	$-0.697514\pi$
$197$	1144.33	−	1982.04i	0.413859	−	0.716824i	0.995308	+	0.0967585i	$0.0308474\pi$
$198$	315.901			0.113384
$199$	1127.04	+	1952.09i	0.401476	+	0.695377i	0.993904	−	0.110246i	$-0.0351640\pi$
$199$	1127.04	+	1952.09i	0.401476	+	0.695377i	−0.592428	+	0.805623i	$0.701831\pi$
$200$	663.291			0.234509
$201$	−847.757	+	1410.03i	−0.297493	+	0.494804i
$202$	1310.63			0.456511
$203$	26.0355	+	45.0948i	0.00900164	+	0.0155913i
$204$	−1536.44			−0.527315
$205$	−65.3304	+	113.156i	−0.0222579	+	0.0385519i
$206$	−532.579			−0.180129
$207$	368.900	+	638.953i	0.123866	+	0.214543i
$208$	−1254.44	+	2172.76i	−0.418173	+	0.724298i
$209$	−2761.68			−0.914015
$210$	−173.411			−0.0569833
$211$	452.480	+	783.718i	0.147630	+	0.255703i	0.930351	−	0.366670i	$-0.119502\pi$
$211$	452.480	+	783.718i	0.147630	+	0.255703i	−0.782721	+	0.622373i	$0.786169\pi$
$212$	−498.112	+	862.755i	−0.161370	+	0.279501i
$213$	−82.4151	+	142.747i	−0.0265117	+	0.0459196i
$214$	169.669	+	293.876i	0.0541979	+	0.0938735i
$215$	2376.30			0.753779
$216$	447.163			0.140859
$217$	608.651	+	1054.21i	0.190405	+	0.329791i
$218$	−856.701	−	1483.85i	−0.266161	−	0.461004i
$219$	606.970	+	1051.30i	0.187284	+	0.324386i
$220$	−969.702	−	1679.57i	−0.297170	−	0.514713i
$221$	2702.67	−	4681.15i	0.822629	−	1.42483i
$222$	−348.504	+	603.626i	−0.105361	+	0.182490i
$223$	2104.41			0.631937			0.315968	−	0.948770i	$-0.397671\pi$
$223$	2104.41			0.631937			0.315968	+	0.948770i	$0.397671\pi$
$224$	480.339	+	831.972i	0.143277	+	0.248163i
$225$	−360.449			−0.106800
$226$	1332.91			0.392319
$227$	2936.81	−	5086.71i	0.858693	−	1.48730i	−0.0144839	−	0.999895i	$-0.504611\pi$
$227$	2936.81	−	5086.71i	0.858693	−	1.48730i	0.873177	−	0.487404i	$-0.162056\pi$
$228$	−1787.10			−0.519094
$229$	−718.775	−	1244.96i	−0.207415	−	0.359253i	0.743485	−	0.668753i	$-0.233172\pi$
$229$	−718.775	−	1244.96i	−0.207415	−	0.359253i	−0.950899	+	0.309500i	$0.899838\pi$
$230$	−424.560	+	735.360i	−0.121716	+	0.210818i
$231$	−261.450	−	452.845i	−0.0744683	−	0.128983i
$232$	77.2656	−	133.828i	0.0218652	−	0.0378717i
$233$	995.632	−	1724.49i	0.279940	−	0.484870i	−0.691429	−	0.722444i	$-0.743019\pi$
$233$	995.632	−	1724.49i	0.279940	−	0.484870i	0.971370	+	0.237574i	$0.0763521\pi$
$234$	−359.586	+	622.821i	−0.100457	+	0.173996i
$235$	1064.16	−	1843.19i	0.295398	−	0.511644i
$236$	712.734	−	1234.49i	0.196589	−	0.340502i
$237$	487.823	−	844.935i	0.133703	−	0.231580i
$238$	−238.379	−	412.884i	−0.0649235	−	0.112451i
$239$	471.046	−	815.876i	0.127487	−	0.220814i	−0.795215	−	0.606327i	$-0.792642\pi$
$239$	471.046	−	815.876i	0.127487	−	0.220814i	0.922702	+	0.385513i	$0.125976\pi$
$240$	−487.816	−	844.922i	−0.131202	−	0.227248i
$241$	−6787.19			−1.81411			−0.907056	−	0.421009i	$-0.861676\pi$
$241$	−6787.19			−1.81411			−0.907056	+	0.421009i	$0.861676\pi$
$242$	199.750	−	345.978i	0.0530596	−	0.0919020i
$243$	−243.000			−0.0641500
$244$	−3856.69			−1.01188
$245$	−1437.17	−	2489.25i	−0.374764	−	0.649110i
$246$	47.7944			0.0123872
$247$	3143.59	−	5444.85i	0.809804	−	1.40262i
$248$	1806.30	−	3128.60i	0.462500	−	0.801073i
$249$	1960.58	+	3395.82i	0.498982	+	0.864262i
$250$	−854.789	−	1480.54i	−0.216246	−	0.374550i
$251$	527.561	+	913.762i	0.132667	+	0.229785i	0.924704	−	0.380688i	$-0.124313\pi$
$251$	527.561	+	913.762i	0.132667	+	0.229785i	−0.792037	+	0.610473i	$0.790979\pi$
$252$	−169.186	−	293.039i	−0.0422925	−	0.0732528i
$253$	−2560.42			−0.636255
$254$	121.919			0.0301177
$255$	1050.99	+	1820.36i	0.258099	+	0.447041i
$256$	474.653	−	822.123i	0.115882	−	0.200714i
$257$	−1168.23	+	2023.44i	−0.283550	+	0.491124i	−0.972257	−	0.233917i	$-0.924846\pi$
$257$	−1168.23	+	2023.44i	−0.283550	+	0.491124i	0.688706	+	0.725041i	$0.258179\pi$
$258$	−434.613	−	752.772i	−0.104875	−	0.181649i
$259$	1153.74			0.276794
$260$	4415.20			1.05315
$261$	−41.9881	+	72.7255i	−0.00995785	+	0.0172475i
$262$	513.277	+	889.022i	0.121032	+	0.209634i
$263$	−3970.14			−0.930833			−0.465417	−	0.885092i	$-0.654096\pi$
$263$	−3970.14			−0.930833			−0.465417	+	0.885092i	$0.654096\pi$
$264$	−775.908	+	1343.91i	−0.180886	+	0.313303i
$265$	1362.91			0.315936
$266$	−277.268	−	480.243i	−0.0639113	−	0.110698i
$267$	4942.19			1.13280
$268$	−1790.35	−	3231.97i	−0.408072	−	0.736657i
$269$	2690.34			0.609788			0.304894	−	0.952386i	$-0.401379\pi$
$269$	2690.34			0.609788			0.304894	+	0.952386i	$0.401379\pi$
$270$	−139.832	−	242.197i	−0.0315182	−	0.0545912i
$271$	382.313			0.0856968			0.0428484	−	0.999082i	$-0.486357\pi$
$271$	382.313			0.0856968			0.0428484	+	0.999082i	$0.486357\pi$
$272$	1341.15	−	2322.94i	0.298967	−	0.517826i
$273$	1190.42			0.263911
$274$	478.526	+	828.832i	0.105507	+	0.182743i
$275$	625.443	−	1083.30i	0.137148	−	0.237547i
$276$	−1656.87			−0.361346
$277$	142.169			0.0308380			0.0154190	−	0.999881i	$-0.495092\pi$
$277$	142.169			0.0308380			0.0154190	+	0.999881i	$0.495092\pi$
$278$	336.610	+	583.026i	0.0726206	+	0.125783i
$279$	−981.588	+	1700.16i	−0.210631	+	0.364824i
$280$	425.928	−	737.729i	0.0909074	−	0.157456i
$281$	−2589.59	−	4485.30i	−0.549758	−	0.952209i	−0.998291	−	0.0584422i	$-0.981387\pi$
$281$	−2589.59	−	4485.30i	−0.549758	−	0.952209i	0.448533	−	0.893766i	$-0.351947\pi$
$282$	−778.520			−0.164398
$283$	8616.05			1.80979			0.904896	−	0.425634i	$-0.139949\pi$
$283$	8616.05			1.80979			0.904896	+	0.425634i	$0.139949\pi$
$284$	−185.078	−	320.565i	−0.0386703	−	0.0669790i
$285$	1222.45	+	2117.34i	0.254075	+	0.440071i
$286$	−1247.89	−	2161.41i	−0.258005	−	0.446877i
$287$	−39.5563	−	68.5135i	−0.00813566	−	0.0140914i
$288$	−774.656	+	1341.74i	−0.158497	+	0.274524i
$289$	−432.964	+	749.915i	−0.0881261	+	0.152639i
$290$	−96.6467			−0.0195700
$291$	2052.22	+	3554.56i	0.413414	+	0.716054i
$292$	−2726.13			−0.546351
$293$	−7355.41			−1.46658			−0.733290	−	0.679916i	$-0.762016\pi$
$293$	−7355.41			−1.46658			−0.733290	+	0.679916i	$0.762016\pi$
$294$	−525.700	+	910.540i	−0.104284	+	0.180625i
$295$	−1950.15			−0.384889
$296$	−1711.97	−	2965.22i	−0.336170	−	0.582264i
$297$	421.648	−	730.316i	0.0823788	−	0.142684i
$298$	846.381	+	1465.97i	0.164529	+	0.284972i
$299$	2914.50	−	5048.07i	0.563712	−	0.976379i
$300$	404.728	−	701.010i	0.0778900	−	0.134909i
$301$	−719.402	+	1246.04i	−0.137760	+	0.238607i
$302$	929.046	−	1609.15i	0.177022	−	0.306611i
$303$	1749.36	−	3029.97i	0.331676	−	0.574480i
$304$	1559.95	−	2701.91i	0.294306	−	0.509753i
$305$	2638.13	+	4569.38i	0.495275	+	0.857842i
$306$	384.439	−	665.869i	0.0718201	−	0.124396i
$307$	1219.97	+	2113.04i	0.226798	+	0.392826i	0.956857	−	0.290558i	$-0.0938408\pi$
$307$	1219.97	+	2113.04i	0.226798	+	0.392826i	−0.730059	+	0.683384i	$0.760508\pi$
$308$	1174.27			0.217241
$309$	−710.859	+	1231.24i	−0.130872	+	0.226677i
$310$	−2259.38			−0.413950
$311$	−1401.62			−0.255558			−0.127779	−	0.991803i	$-0.540785\pi$
$311$	−1401.62			−0.255558			−0.127779	+	0.991803i	$0.540785\pi$
$312$	−1766.41	−	3059.52i	−0.320524	−	0.555164i
$313$	−2230.69			−0.402831			−0.201416	−	0.979506i	$-0.564554\pi$
$313$	−2230.69			−0.402831			−0.201416	+	0.979506i	$0.564554\pi$
$314$	780.082	−	1351.14i	0.140199	−	0.242832i
$315$	−231.460	+	400.901i	−0.0414010	+	0.0717086i
$316$	1095.50	+	1897.46i	0.195021	+	0.337786i
$317$	−1982.74	−	3434.20i	−0.351299	−	0.608467i	0.635179	−	0.772365i	$-0.280927\pi$
$317$	−1982.74	−	3434.20i	−0.351299	−	0.608467i	−0.986477	+	0.163898i	$0.947593\pi$
$318$	−249.270	−	431.748i	−0.0439571	−	0.0761359i
$319$	−145.714	−	252.383i	−0.0255749	−	0.0442970i
$320$	818.609			0.143005
$321$	905.863			0.157509
$322$	−257.063	−	445.246i	−0.0444893	−	0.0770577i
$323$	−3360.86	+	5821.18i	−0.578957	+	1.00278i
$324$	272.851	−	472.592i	0.0467851	−	0.0810342i
$325$	1423.87	+	2466.22i	0.243022	+	0.420926i
$326$	−2811.97			−0.477733
$327$	−4573.92			−0.773512
$328$	−117.391	+	203.328i	−0.0197617	+	0.0342284i
$329$	644.331	+	1116.01i	0.107973	+	0.187015i
$330$	970.535			0.161897
$331$	1376.00	−	2383.31i	0.228495	−	0.395765i	−0.728867	−	0.684655i	$-0.759953\pi$
$331$	1376.00	−	2383.31i	0.228495	−	0.395765i	0.957362	+	0.288890i	$0.0932861\pi$
$332$	−8805.67			−1.45564
$333$	930.330	+	1611.38i	0.153098	+	0.265174i
$334$	3367.06			0.551609
$335$	−2604.54	+	4332.00i	−0.424780	+	0.706514i
$336$	590.726			0.0959129
$337$	6114.28	+	10590.2i	0.988326	+	1.71183i	0.626103	+	0.779741i	$0.284649\pi$
$337$	6114.28	+	10590.2i	0.988326	+	1.71183i	0.362224	+	0.932091i	$0.382018\pi$
$338$	3212.84			0.517027
$339$	1779.10	−	3081.50i	0.285037	−	0.493699i
$340$	−4720.37			−0.752935
$341$	−3406.46	−	5900.15i	−0.540968	−	0.936983i
$342$	447.158	−	774.500i	0.0707004	−	0.122457i
$343$	3654.50			0.575290
$344$	4269.95			0.669244
$345$	1133.36	+	1963.04i	0.176864	+	0.306338i
$346$	−94.1376	+	163.051i	−0.0146268	+	0.0253343i
$347$	5142.12	−	8906.40i	0.795514	−	1.37787i	−0.126999	−	0.991903i	$-0.540535\pi$
$347$	5142.12	−	8906.40i	0.795514	−	1.37787i	0.922513	−	0.385967i	$-0.126132\pi$
$348$	−94.2921	−	163.319i	−0.0145247	−	0.0251575i
$349$	−5123.16			−0.785777			−0.392889	−	0.919586i	$-0.628524\pi$
$349$	−5123.16			−0.785777			−0.392889	+	0.919586i	$0.628524\pi$
$350$	251.174			0.0383595
$351$	959.914	+	1662.62i	0.145973	+	0.252832i
$352$	−2688.33	−	4656.32i	−0.407069	−	0.705065i
$353$	−2253.08	−	3902.44i	−0.339714	−	0.588402i	0.644665	−	0.764466i	$-0.276997\pi$
$353$	−2253.08	−	3902.44i	−0.339714	−	0.588402i	−0.984379	+	0.176063i	$0.943664\pi$
$354$	356.673	+	617.775i	0.0535507	+	0.0927525i
$355$	−253.202	+	438.559i	−0.0378551	+	0.0655670i
$356$	−5549.30	+	9611.68i	−0.826159	+	1.43095i
$357$	−1272.70			−0.188679
$358$	1707.52	+	2957.52i	0.252082	+	0.436619i
$359$	10519.7			1.54654			0.773271	−	0.634076i	$-0.218619\pi$
$359$	10519.7			1.54654			0.773271	+	0.634076i	$0.218619\pi$
$360$	1373.81			0.201128
$361$	−479.661	+	830.797i	−0.0699316	+	0.121125i
$362$	4026.72			0.584639
$363$	−533.233	−	923.586i	−0.0771005	−	0.133542i
$364$	−1336.66	+	2315.16i	−0.192473	+	0.333372i
$365$	1864.78	+	3229.90i	0.267417	+	0.463179i
$366$	965.000	−	1671.43i	0.137818	−	0.238708i
$367$	5684.81	−	9846.38i	0.808568	−	1.40048i	−0.105287	−	0.994442i	$-0.533576\pi$
$367$	5684.81	−	9846.38i	0.808568	−	1.40048i	0.913856	−	0.406039i	$-0.133090\pi$
$368$	1446.27	−	2505.01i	0.204869	−	0.354844i
$369$	63.7935	−	110.494i	0.00899988	−	0.0155882i
$370$	−1070.70	+	1854.51i	−0.150441	+	0.260571i
$371$	−412.609	+	714.659i	−0.0577401	+	0.100009i
$372$	−2204.34	−	3818.02i	−0.307230	−	0.532138i
$373$	−1340.63	+	2322.03i	−0.186099	+	0.322333i	−0.943946	−	0.330099i	$-0.892918\pi$
$373$	−1340.63	+	2322.03i	−0.186099	+	0.322333i	0.757847	+	0.652432i	$0.226251\pi$
$374$	1334.14	+	2310.80i	0.184457	+	0.319488i
$375$	−4563.71			−0.628451
$376$	1912.18	−	3312.00i	0.262269	−	0.454264i
$377$	663.456			0.0906359
$378$	169.331			0.0230409
$379$	2191.62	+	3796.00i	0.297034	+	0.514478i	0.975456	−	0.220194i	$-0.0706691\pi$
$379$	2191.62	+	3796.00i	0.297034	+	0.514478i	−0.678422	+	0.734673i	$0.737336\pi$
$380$	−5490.46			−0.741197
$381$	162.732	−	281.859i	0.0218819	−	0.0379005i
$382$	1789.78	−	3100.00i	0.239721	−	0.415209i
$383$	−6116.34	−	10593.8i	−0.816006	−	1.41336i	−0.908604	−	0.417659i	$-0.862851\pi$
$383$	−6116.34	−	10593.8i	−0.816006	−	1.41336i	0.0925981	−	0.995704i	$-0.470483\pi$
$384$	−2215.47	−	3837.30i	−0.294421	−	0.509952i
$385$	−803.248	−	1391.27i	−0.106331	−	0.184170i
$386$	1388.43	+	2404.84i	0.183082	+	0.317106i
$387$	−2320.40			−0.304787
$388$	−9217.30			−1.20602
$389$	5653.14	+	9791.52i	0.736826	+	1.27622i	0.953917	+	0.300069i	$0.0970097\pi$
$389$	5653.14	+	9791.52i	0.736826	+	1.27622i	−0.217091	+	0.976151i	$0.569657\pi$
$390$	−1104.75	+	1913.48i	−0.143439	+	0.248443i
$391$	−3115.94	+	5396.97i	−0.403018	+	0.698047i
$392$	−2582.42	−	4472.89i	−0.332735	−	0.576314i
$393$	2740.38			0.351741
$394$	−2572.01			−0.328873
$395$	1498.73	−	2595.87i	0.190909	−	0.330665i
$396$	946.889	+	1640.06i	0.120159	+	0.208121i
$397$	−12752.9			−1.61222			−0.806110	−	0.591765i	$-0.798431\pi$
$397$	−12752.9			−1.61222			−0.806110	+	0.591765i	$0.798431\pi$
$398$	1266.57	−	2193.77i	0.159517	−	0.276291i
$399$	−1480.33			−0.185738
$400$	706.569	+	1223.81i	0.0883211	+	0.152977i
$401$	376.653			0.0469056			0.0234528	−	0.999725i	$-0.492534\pi$
$401$	376.653			0.0469056			0.0234528	+	0.999725i	$0.492534\pi$
$402$	1848.66	+	32.7762i	0.229360	+	0.00406649i
$403$	15510.1			1.91716
$404$	3928.50	+	6804.37i	0.483788	+	0.837945i
$405$	−746.564			−0.0915977
$406$	29.2589	−	50.6778i	0.00357658	−	0.00619482i
$407$	−6457.14			−0.786410
$408$	1888.50	+	3270.98i	0.229154	+	0.396906i
$409$	−5695.30	+	9864.54i	−0.688544	+	1.19259i	0.283765	+	0.958894i	$0.408416\pi$
$409$	−5695.30	+	9864.54i	−0.688544	+	1.19259i	−0.972309	+	0.233699i	$0.924917\pi$
$410$	146.838			0.0176873
$411$	2554.85			0.306622
$412$	−1596.37	−	2764.99i	−0.190892	−	0.330634i
$413$	590.390	−	1022.59i	0.0703419	−	0.121836i
$414$	414.572	−	718.060i	0.0492152	−	0.0852433i
$415$	6023.43	+	10432.9i	0.712479	+	1.23405i
$416$	12240.4			1.44263
$417$	1797.16			0.211049
$418$	1551.80	+	2687.79i	0.181581	+	0.314507i
$419$	−3494.86	−	6053.28i	−0.407483	−	0.705781i	0.587124	−	0.809497i	$-0.300260\pi$
$419$	−3494.86	−	6053.28i	−0.407483	−	0.705781i	−0.994607	+	0.103716i	$0.966927\pi$
$420$	−519.787	−	900.297i	−0.0603881	−	0.104595i
$421$	6389.30	+	11066.6i	0.739657	+	1.28112i	0.952650	+	0.304069i	$0.0983454\pi$
$421$	6389.30	+	11066.6i	0.739657	+	1.28112i	−0.212993	+	0.977054i	$0.568321\pi$
$422$	508.500	−	880.747i	0.0586573	−	0.101597i
$423$	−1039.13	+	1799.82i	−0.119443	+	0.206880i
$424$	2449.00			0.280505
$425$	−1522.28	−	2636.67i	−0.173745	−	0.300935i
$426$	185.237			0.0210675
$427$	−3194.67			−0.362063
$428$	−1017.14	+	1761.74i	−0.114872	+	0.198965i
$429$	−6662.48			−0.749808
$430$	−1335.25	−	2312.73i	−0.149748	−	0.259371i
$431$	−6942.30	+	12024.4i	−0.775867	+	1.34384i	0.158439	+	0.987369i	$0.449354\pi$
$431$	−6942.30	+	12024.4i	−0.775867	+	1.34384i	−0.934306	+	0.356472i	$0.883979\pi$
$432$	476.340	+	825.044i	0.0530507	+	0.0918865i
$433$	−4145.13	+	7179.58i	−0.460052	+	0.796833i	−0.998963	−	0.0455296i	$-0.985502\pi$
$433$	−4145.13	+	7179.58i	−0.460052	+	0.796833i	0.538911	+	0.842363i	$0.318836\pi$
$434$	684.006	−	1184.73i	0.0756529	−	0.131035i
$435$	−128.999	+	223.433i	−0.0142185	+	0.0246271i
$436$	5135.80	−	8895.46i	0.564129	−	0.977099i
$437$	−3624.29	+	6277.45i	−0.396735	+	0.687165i
$438$	682.117	−	1181.46i	0.0744128	−	0.128887i
$439$	−3848.20	−	6665.27i	−0.418370	−	0.724638i	0.577406	−	0.816457i	$-0.304065\pi$
$439$	−3848.20	−	6665.27i	−0.418370	−	0.724638i	−0.995776	+	0.0918195i	$0.970732\pi$
$440$	−2383.80	+	4128.87i	−0.258280	+	0.447355i
$441$	1403.36	+	2430.68i	0.151534	+	0.262464i
$442$	−6074.55			−0.653703
$443$	−8475.47	+	14679.9i	−0.908988	+	1.57441i	−0.0935163	+	0.995618i	$0.529811\pi$
$443$	−8475.47	+	14679.9i	−0.908988	+	1.57441i	−0.815472	+	0.578796i	$0.803523\pi$
$444$	−4178.46			−0.446623
$445$	15183.8			1.61748
$446$	−1182.48	−	2048.11i	−0.125542	−	0.217446i
$447$	4518.82			0.478150
$448$	−247.826	+	429.247i	−0.0261354	+	0.0452679i
$449$	−4667.29	+	8083.99i	−0.490564	+	0.849682i	−0.999941	−	0.0108617i	$-0.996543\pi$
$449$	−4667.29	+	8083.99i	−0.490564	+	0.849682i	0.509377	+	0.860543i	$0.329876\pi$
$450$	202.538	+	350.806i	0.0212172	+	0.0367492i
$451$	221.386	+	383.452i	0.0231145	+	0.0400355i
$452$	3995.31	+	6920.07i	0.415760	+	0.720117i
$453$	−2480.09	−	4295.63i	−0.257229	−	0.445533i
$454$	−6600.83			−0.682361
$455$	3657.31			0.376830
$456$	2196.60	+	3804.62i	0.225581	+	0.390718i
$457$	5426.39	−	9398.78i	0.555439	−	0.962049i	−0.442430	−	0.896803i	$-0.645883\pi$
$457$	5426.39	−	9398.78i	0.555439	−	0.962049i	0.997869	−	0.0652461i	$-0.0207832\pi$
$458$	−807.765	+	1399.09i	−0.0824113	+	0.142741i
$459$	−1026.26	−	1777.53i	−0.104361	−	0.180759i
$460$	−5090.35			−0.515954
$461$	−3722.45			−0.376078			−0.188039	−	0.982162i	$-0.560213\pi$
$461$	−3722.45			−0.376078			−0.188039	+	0.982162i	$0.560213\pi$
$462$	−293.820	+	508.911i	−0.0295882	+	0.0512482i
$463$	−2683.95	−	4648.74i	−0.269403	−	0.466620i	0.699305	−	0.714824i	$-0.253493\pi$
$463$	−2683.95	−	4648.74i	−0.269403	−	0.466620i	−0.968708	+	0.248204i	$0.920160\pi$
$464$	329.228			0.0329397
$465$	−3015.71	+	5223.36i	−0.300753	+	0.520920i
$466$	−2237.80			−0.222455
$467$	−5388.59	−	9333.31i	−0.533949	−	0.924827i	−0.999213	−	0.0396552i	$-0.987374\pi$
$467$	−5388.59	−	9333.31i	−0.533949	−	0.924827i	0.465264	−	0.885172i	$-0.345959\pi$
$468$	−4311.33			−0.425836
$469$	−1483.03	−	2677.19i	−0.146013	−	0.263585i
$470$	−2391.83			−0.234738
$471$	−2082.43	−	3606.87i	−0.203722	−	0.352857i
$472$	−3504.21			−0.341725
$473$	4026.30	−	6973.75i	0.391394	−	0.677915i
$474$	−1096.44			−0.106247
$475$	−1770.63	−	3066.83i	−0.171036	−	0.296243i
$476$	1429.04	−	2475.18i	0.137605	−	0.238339i
$477$	−1330.85			−0.127747
$478$	−1058.73			−0.101308
$479$	7585.56	+	13138.6i	0.723576	+	1.25327i	0.959557	+	0.281513i	$0.0908364\pi$
$479$	7585.56	+	13138.6i	0.723576	+	1.25327i	−0.235981	+	0.971758i	$0.575830\pi$
$480$	−2379.96	+	4122.21i	−0.226312	+	0.391984i
$481$	7350.09	−	12730.7i	0.696747	−	1.20680i
$482$	3813.74	+	6605.60i	0.360397	+	0.624226i
$483$	−1372.46			−0.129294
$484$	2394.95			0.224920
$485$	6305.00	+	10920.6i	0.590300	+	1.02243i
$486$	136.543	+	236.499i	0.0127442	+	0.0220737i
$487$	2344.55	+	4060.89i	0.218156	+	0.377857i	0.954244	−	0.299029i	$-0.0966626\pi$
$487$	2344.55	+	4060.89i	0.218156	+	0.377857i	−0.736088	+	0.676885i	$0.763329\pi$
$488$	4740.42	+	8210.65i	0.439731	+	0.761637i
$489$	−3753.28	+	6500.87i	−0.347094	+	0.601185i
$490$	−1615.10	+	2797.43i	−0.148903	+	0.257908i
$491$	14837.9			1.36380			0.681901	−	0.731445i	$-0.261154\pi$
$491$	14837.9			1.36380			0.681901	+	0.731445i	$0.261154\pi$
$492$	143.260	+	248.134i	0.0131274	+	0.0227373i
$493$	−709.312			−0.0647988
$494$	−7065.57			−0.643512
$495$	1295.42	−	2243.73i	0.117626	−	0.203734i
$496$	7696.61			0.696750
$497$	−153.309	−	265.539i	−0.0138367	−	0.0239659i
$498$	2203.31	−	3816.24i	0.198258	−	0.343393i
$499$	1086.40	+	1881.70i	0.0974626	+	0.168810i	0.910634	−	0.413215i	$-0.135594\pi$
$499$	1086.40	+	1881.70i	0.0974626	+	0.168810i	−0.813171	+	0.582025i	$0.802261\pi$
$500$	5124.33	−	8875.61i	0.458334	−	0.793859i
$501$	4494.18	−	7784.14i	0.400769	−	0.694151i
$502$	592.876	−	1026.89i	0.0527119	−	0.0912997i
$503$	−2648.07	+	4586.60i	−0.234735	+	0.406573i	−0.959196	−	0.282743i	$-0.908756\pi$
$503$	−2648.07	+	4586.60i	−0.234735	+	0.406573i	0.724461	+	0.689316i	$0.242089\pi$
$504$	−415.908	+	720.373i	−0.0367579	+	0.0636666i
$505$	5374.51	−	9308.92i	0.473589	−	0.820280i
$506$	1438.71	+	2491.92i	0.126400	+	0.218932i
$507$	4288.33	−	7427.60i	0.375644	−	0.650634i
$508$	365.444	+	632.968i	0.0319172	+	0.0552823i
$509$	11051.7			0.962389			0.481195	−	0.876614i	$-0.340203\pi$
$509$	11051.7			0.962389			0.481195	+	0.876614i	$0.340203\pi$
$510$	1181.10	−	2045.73i	0.102549	−	0.177621i
$511$	−2258.18			−0.195491
$512$	10749.0			0.927818
$513$	−1193.69	−	2067.53i	−0.102734	−	0.177941i
$514$	2625.74			0.225324
$515$	−2183.96	+	3782.73i	−0.186867	+	0.323664i
$516$	2605.44	−	4512.76i	0.222283	−	0.385006i
$517$	−3606.14	−	6246.03i	−0.306766	−	0.531334i
$518$	−648.288	−	1122.87i	−0.0549887	−	0.0952432i
$519$	251.300	+	435.264i	0.0212540	+	0.0368131i
$520$	−5426.92	−	9399.69i	−0.457665	−	0.792700i
$521$	−607.474			−0.0510824			−0.0255412	−	0.999674i	$-0.508131\pi$
$521$	−607.474			−0.0510824			−0.0255412	+	0.999674i	$0.508131\pi$
$522$	94.3730			0.00791302
$523$	5711.92	+	9893.34i	0.477562	+	0.827162i	0.999669	−	0.0257181i	$-0.00818722\pi$
$523$	5711.92	+	9893.34i	0.477562	+	0.827162i	−0.522107	+	0.852880i	$0.674854\pi$
$524$	−3077.02	+	5329.56i	−0.256527	+	0.444318i
$525$	335.255	−	580.678i	0.0278699	−	0.0482721i
$526$	2230.83	+	3863.92i	0.184922	+	0.320294i
$527$	−16582.1			−1.37064
$528$	−3306.13			−0.272502
$529$	2723.33	−	4716.94i	0.223829	−	0.387683i
$530$	−765.826	−	1326.45i	−0.0627648	−	0.108712i
$531$	1904.27			0.155628
$532$	1662.18	−	2878.99i	0.135460	−	0.234624i
$533$	−1008.00			−0.0819165
$534$	−2777.03	−	4809.96i	−0.225045	−	0.389789i
$535$	2783.06			0.224902
$536$	−4680.07	+	7784.10i	−0.377142	+	0.627280i
$537$	9116.45			0.732596
$538$	−1511.71	−	2618.36i	−0.121142	−	0.209825i
$539$	−9740.28			−0.778374
$540$	838.274	−	1451.93i	0.0668029	−	0.115706i
$541$	3506.19			0.278638			0.139319	−	0.990248i	$-0.455509\pi$
$541$	3506.19			0.278638			0.139319	+	0.990248i	$0.455509\pi$
$542$	−214.823	−	372.084i	−0.0170248	−	0.0294878i
$543$	5374.65	−	9309.17i	0.424767	−	0.735718i
$544$	−13086.4			−1.03139
$545$	−14052.4			−1.10447
$546$	−668.904	−	1158.57i	−0.0524294	−	0.0908103i
$547$	5692.44	−	9859.59i	0.444956	−	0.770687i	−0.553093	−	0.833120i	$-0.686553\pi$
$547$	5692.44	−	9859.59i	0.444956	−	0.770687i	0.998049	+	0.0624328i	$0.0198859\pi$
$548$	−2868.70	+	4968.73i	−0.223622	+	0.387324i
$549$	−2576.07	−	4461.88i	−0.200262	−	0.346864i
$550$	−1405.76			−0.108985
$551$	−825.031			−0.0637886
$552$	2036.52	+	3527.36i	0.157029	+	0.271983i
$553$	907.451	+	1571.75i	0.0697807	+	0.120864i
$554$	−79.8855	−	138.366i	−0.00612637	−	0.0106112i
$555$	2858.23	+	4950.60i	0.218604	+	0.378633i
$556$	−2017.93	+	3495.15i	−0.153919	+	0.266596i
$557$	10659.3	−	18462.4i	0.810858	−	1.40445i	−0.101406	−	0.994845i	$-0.532334\pi$
$557$	10659.3	−	18462.4i	0.810858	−	1.40445i	0.912264	−	0.409603i	$-0.134333\pi$
$558$	2206.23			0.167378
$559$	9166.18	+	15876.3i	0.693539	+	1.20124i
$560$	1814.87			0.136951
$561$	7122.97			0.536064
$562$	−2910.20	+	5040.61i	−0.218433	+	0.378337i
$563$	−10941.4			−0.819050			−0.409525	−	0.912299i	$-0.634306\pi$
$563$	−10941.4			−0.819050			−0.409525	+	0.912299i	$0.634306\pi$
$564$	−2333.56	−	4041.84i	−0.174221	−	0.301759i
$565$	5465.90	−	9467.22i	0.406995	−	0.704936i
$566$	−4841.39	−	8385.53i	−0.359538	−	0.622739i
$567$	226.015	−	391.469i	0.0167403	−	0.0289950i
$568$	−454.975	+	788.040i	−0.0336098	+	0.0582138i
$569$	−4599.33	+	7966.28i	−0.338865	+	0.586931i	−0.984219	−	0.176952i	$-0.943376\pi$
$569$	−4599.33	+	7966.28i	−0.338865	+	0.586931i	0.645355	+	0.763883i	$0.276710\pi$
$570$	1373.79	−	2379.48i	0.100951	−	0.174852i
$571$	−872.409	+	1511.06i	−0.0639390	+	0.110746i	−0.896223	−	0.443604i	$-0.853700\pi$
$571$	−872.409	+	1511.06i	−0.0639390	+	0.110746i	0.832284	+	0.554350i	$0.187033\pi$
$572$	7480.92	−	12957.3i	0.546841	−	0.947156i
$573$	−4777.83	−	8275.44i	−0.348336	−	0.603336i
$574$	−44.4536	+	76.9959i	−0.00323251	+	0.00559887i
$575$	−1641.60	−	2843.34i	−0.119060	−	0.206218i
$576$	−799.350			−0.0578234
$577$	−3238.10	+	5608.56i	−0.233629	+	0.404658i	−0.958873	−	0.283834i	$-0.908394\pi$
$577$	−3238.10	+	5608.56i	−0.233629	+	0.404658i	0.725244	+	0.688492i	$0.241727\pi$
$578$	973.135			0.0700296
$579$	7412.85			0.532068
$580$	−289.692	−	501.760i	−0.0207393	−	0.0359215i
$581$	−7294.14			−0.520847
$582$	2306.30	−	3994.64i	0.164260	−	0.284507i
$583$	2309.26	−	3999.75i	0.164048	−	0.284139i
$584$	3350.80	+	5803.76i	0.237427	+	0.411235i
$585$	2949.12	+	5108.03i	0.208430	+	0.361010i
$586$	4133.03	+	7158.62i	0.291355	+	0.504642i
$587$	−5394.60	−	9343.72i	−0.379317	−	0.656996i	0.611646	−	0.791131i	$-0.290508\pi$
$587$	−5394.60	−	9343.72i	−0.379317	−	0.656996i	−0.990963	+	0.134136i	$0.957174\pi$
$588$	−6302.99			−0.442059
$589$	−19287.4			−1.34927
$590$	1095.80	+	1897.98i	0.0764632	+	0.132438i
$591$	−3432.99	+	5946.11i	−0.238941	+	0.413859i
$592$	3647.35	−	6317.39i	0.253218	−	0.438586i
$593$	8933.36	+	15473.0i	0.618632	+	1.07150i	0.989736	+	0.142911i	$0.0456462\pi$
$593$	8933.36	+	15473.0i	0.618632	+	1.07150i	−0.371103	+	0.928592i	$0.621020\pi$
$594$	−947.702			−0.0654624
$595$	−3910.10			−0.269409
$596$	−5073.93	+	8788.30i	−0.348718	+	0.603998i
$597$	−3381.12	−	5856.27i	−0.231792	−	0.401476i
$598$	−6550.68			−0.447955
$599$	14113.3	−	24444.9i	0.962694	−	1.66743i	0.247006	−	0.969014i	$-0.420553\pi$
$599$	14113.3	−	24444.9i	0.962694	−	1.66743i	0.715688	−	0.698420i	$-0.246113\pi$
$600$	−1989.87			−0.135394
$601$	−9910.27	−	17165.1i	−0.672626	−	1.16502i	−0.977157	−	0.212520i	$-0.931833\pi$
$601$	−9910.27	−	17165.1i	−0.672626	−	1.16502i	0.304530	−	0.952503i	$-0.401500\pi$
$602$	1616.94			0.109471
$603$	2543.27	−	4230.08i	0.171758	−	0.285675i
$604$	11139.0			0.750396
$605$	−1638.24	−	2837.51i	−0.110089	−	0.190680i
$606$	−3931.88			−0.263567
$607$	2974.86	−	5152.61i	0.198922	−	0.344544i	−0.749257	−	0.662280i	$-0.769589\pi$
$607$	2974.86	−	5152.61i	0.198922	−	0.344544i	0.948179	+	0.317736i	$0.102922\pi$
$608$	−15221.3			−1.01531
$609$	−78.1064	−	135.284i	−0.00519710	−	0.00900164i
$610$	2964.75	−	5135.10i	0.196786	−	0.340843i
$611$	16419.3			1.08716
$612$	4609.32			0.304445
$613$	−9514.59	−	16479.7i	−0.626901	−	1.08582i	−0.988170	−	0.153363i	$-0.950990\pi$
$613$	−9514.59	−	16479.7i	−0.626901	−	1.08582i	0.361269	−	0.932462i	$-0.382344\pi$
$614$	1371.01	−	2374.65i	0.0901128	−	0.156080i
$615$	195.991	−	339.467i	0.0128506	−	0.0222579i
$616$	−1443.35	−	2499.95i	−0.0944060	−	0.163516i
$617$	−17161.2			−1.11975			−0.559873	−	0.828578i	$-0.689150\pi$
$617$	−17161.2			−1.11975			−0.559873	+	0.828578i	$0.689150\pi$
$618$	1597.74			0.103997
$619$	−11042.1	−	19125.6i	−0.716997	−	1.24188i	−0.962184	−	0.272400i	$-0.912183\pi$
$619$	−11042.1	−	19125.6i	−0.716997	−	1.24188i	0.245187	−	0.969476i	$-0.421151\pi$
$620$	−6772.34	−	11730.0i	−0.438683	−	0.759822i
$621$	−1106.70	−	1916.86i	−0.0715142	−	0.123866i
$622$	787.576	+	1364.12i	0.0507700	+	0.0879362i
$623$	−4596.74	+	7961.79i	−0.295609	+	0.512010i
$624$	3763.33	−	6518.29i	0.241433	−	0.418173i
$625$	−9014.76			−0.576945
$626$	1253.43	+	2171.01i	0.0800277	+	0.138612i
$627$	8285.03			0.527707
$628$	9352.95			0.594305
$629$	−7858.11	+	13610.6i	−0.498129	+	0.862785i
$630$	520.233			0.0328993
$631$	4373.98	+	7575.95i	0.275951	+	0.477962i	0.970375	−	0.241605i	$-0.0776738\pi$
$631$	4373.98	+	7575.95i	0.275951	+	0.477962i	−0.694423	+	0.719567i	$0.744340\pi$
$632$	2693.05	−	4664.49i	0.169499	−	0.293582i
$633$	−1357.44	−	2351.15i	−0.0852344	−	0.147630i
$634$	−2228.22	+	3859.38i	−0.139580	+	0.241760i
$635$	499.957	−	865.951i	0.0312444	−	0.0541169i
$636$	1494.34	−	2588.26i	0.0931671	−	0.161370i
$637$	11087.2	−	19203.7i	0.689628	−	1.19447i
$638$	−163.754	+	283.630i	−0.0101616	+	0.0176003i
$639$	247.245	−	428.241i	0.0153065	−	0.0265117i
$640$	−6806.54	−	11789.3i	−0.420394	−	0.728143i
$641$	14389.1	−	24922.7i	0.886641	−	1.53571i	0.0428205	−	0.999083i	$-0.486366\pi$
$641$	14389.1	−	24922.7i	0.886641	−	1.53571i	0.843821	−	0.536625i	$-0.180301\pi$
$642$	−509.008	−	881.627i	−0.0312912	−	0.0541979i
$643$	−4954.02			−0.303838			−0.151919	−	0.988393i	$-0.548545\pi$
$643$	−4954.02			−0.303838			−0.151919	+	0.988393i	$0.548545\pi$
$644$	1541.05	−	2669.18i	0.0942951	−	0.163324i
$645$	−7128.91			−0.435194
$646$	7553.92			0.460069
$647$	5267.80	+	9124.10i	0.320091	+	0.554413i	0.980506	−	0.196487i	$-0.0629533\pi$
$647$	5267.80	+	9124.10i	0.320091	+	0.554413i	−0.660416	+	0.750900i	$0.729620\pi$
$648$	−1341.49			−0.0813252
$649$	−3304.25	+	5723.13i	−0.199851	+	0.346152i
$650$	1600.16	−	2771.55i	0.0965589	−	0.167245i
$651$	−1825.95	−	3162.64i	−0.109930	−	0.190405i
$652$	−8428.68	−	14598.9i	−0.506277	−	0.876898i
$653$	11798.1	+	20435.0i	0.707040	+	1.22463i	0.965950	+	0.258728i	$0.0833033\pi$
$653$	11798.1	+	20435.0i	0.707040	+	1.22463i	−0.258910	+	0.965901i	$0.583363\pi$
$654$	2570.10	+	4451.55i	0.153668	+	0.266161i
$655$	8419.23			0.502239
$656$	−500.203			−0.0297708
$657$	−1820.91	−	3153.91i	−0.108129	−	0.187284i
$658$	724.103	−	1254.18i	0.0429004	−	0.0743057i
$659$	−8157.51	+	14129.2i	−0.482203	+	0.835199i	−0.999791	−	0.0204302i	$-0.993496\pi$
$659$	−8157.51	+	14129.2i	−0.482203	+	0.835199i	0.517589	+	0.855630i	$0.326830\pi$
$660$	2909.11	+	5038.72i	0.171571	+	0.297170i
$661$	−25511.7			−1.50120			−0.750598	−	0.660759i	$-0.770234\pi$
$661$	−25511.7			−1.50120			−0.750598	+	0.660759i	$0.770234\pi$
$662$	−3092.72			−0.181574
$663$	−8108.00	+	14043.5i	−0.474945	+	0.822629i
$664$	10823.4	+	18746.7i	0.632576	+	1.09565i
$665$	−4548.00			−0.265209
$666$	1045.51	−	1810.88i	0.0608299	−	0.105361i
$667$	−764.908			−0.0444039
$668$	10092.5	+	17480.7i	0.584567	+	1.01250i
$669$	−6313.24			−0.364849
$670$	5679.60	+	100.698i	0.327496	+	0.00580640i
$671$	17879.7			1.02867
$672$	−1441.02	−	2495.92i	−0.0827209	−	0.143277i
$673$	4669.16			0.267434			0.133717	−	0.991020i	$-0.457309\pi$
$673$	4669.16			0.267434			0.133717	+	0.991020i	$0.457309\pi$
$674$	6871.27	−	11901.4i	0.392688	−	0.680155i
$675$	1081.35			0.0616609
$676$	9630.24	+	16680.1i	0.547920	+	0.949025i
$677$	−1842.97	+	3192.12i	−0.104625	+	0.181216i	−0.913585	−	0.406648i	$-0.866698\pi$
$677$	−1842.97	+	3192.12i	−0.104625	+	0.181216i	0.808960	+	0.587864i	$0.200031\pi$
$678$	−3998.74			−0.226505
$679$	−7635.11			−0.431530
$680$	5802.00	+	10049.4i	0.327201	+	0.566729i
$681$	−8810.44	+	15260.1i	−0.495766	+	0.858693i
$682$	−3828.20	+	6630.64i	−0.214940	+	0.372288i
$683$	−768.851	−	1331.69i	−0.0430736	−	0.0746057i	0.843685	−	0.536839i	$-0.180382\pi$
$683$	−768.851	−	1331.69i	−0.0430736	−	0.0746057i	−0.886758	+	0.462233i	$0.847048\pi$
$684$	5361.29			0.299699
$685$	7849.21			0.437814
$686$	−2053.48	−	3556.73i	−0.114289	−	0.197954i
$687$	2156.33	+	3734.87i	0.119751	+	0.207415i
$688$	4548.55	+	7878.31i	0.252052	+	0.436567i
$689$	5257.21	+	9105.75i	0.290687	+	0.503485i
$690$	1273.68	−	2206.08i	0.0702728	−	0.121716i
$691$	15740.8	−	27263.8i	0.866580	−	1.50096i	0.00110966	−	0.999999i	$-0.499647\pi$
$691$	15740.8	−	27263.8i	0.866580	−	1.50096i	0.865470	−	0.500961i	$-0.167020\pi$
$692$	−1128.68			−0.0620029
$693$	784.351	+	1358.54i	0.0429943	+	0.0744683i
$694$	−11557.5			−0.632156
$695$	5521.37			0.301349
$696$	−231.797	+	401.484i	−0.0126239	+	0.0218652i
$697$	1077.67			0.0585650
$698$	2878.72	+	4986.09i	0.156105	+	0.270381i
$699$	−2986.90	+	5173.46i	−0.161623	+	0.279940i
$700$	752.877	+	1304.02i	0.0406515	+	0.0704105i
$701$	8504.45	−	14730.1i	0.458215	−	0.793652i	−0.540652	−	0.841247i	$-0.681822\pi$
$701$	8504.45	−	14730.1i	0.458215	−	0.793652i	0.998867	+	0.0475948i	$0.0151556\pi$
$702$	1078.76	−	1868.46i	0.0579987	−	0.100457i
$703$	−9140.10	+	15831.1i	−0.490363	+	0.849334i
$704$	1387.01	−	2402.38i	0.0742543	−	0.128612i
$705$	−3192.49	+	5529.56i	−0.170548	+	0.295398i
$706$	−2532.02	+	4385.59i	−0.134977	+	0.233787i
$707$	3254.16	+	5636.37i	0.173105	+	0.299827i
$708$	−2138.20	+	3703.47i	−0.113501	+	0.196589i
$709$	12405.0	+	21486.2i	0.657096	+	1.13812i	0.981364	+	0.192158i	$0.0615488\pi$
$709$	12405.0	+	21486.2i	0.657096	+	1.13812i	−0.324268	+	0.945965i	$0.605118\pi$
$710$	569.100			0.0300816
$711$	−1463.47	+	2534.80i	−0.0771933	+	0.133703i
$712$	27283.5			1.43609
$713$	−17881.8			−0.939243
$714$	715.136	+	1238.65i	0.0374836	+	0.0649235i
$715$	−20469.0			−1.07063
$716$	−10236.3	+	17729.9i	−0.534288	+	0.925414i
$717$	−1413.14	+	2447.63i	−0.0736048	+	0.127487i
$718$	−5911.06	−	10238.3i	−0.307240	−	0.532156i
$719$	−3108.45	−	5384.00i	−0.161232	−	0.279262i	0.774079	−	0.633089i	$-0.218213\pi$
$719$	−3108.45	−	5384.00i	−0.161232	−	0.279262i	−0.935311	+	0.353827i	$0.884880\pi$
$720$	1463.45	+	2534.77i	0.0757493	+	0.131202i
$721$	−1322.34	−	2290.37i	−0.0683033	−	0.118305i
$722$	1078.09			0.0555712
$723$	20361.6			1.04738
$724$	12069.8	+	20905.5i	0.619572	+	1.07313i
$725$	186.847	−	323.628i	0.00957147	−	0.0165783i
$726$	−599.251	+	1037.93i	−0.0306340	+	0.0530596i
$727$	−8732.05	−	15124.4i	−0.445466	−	0.771570i	0.552618	−	0.833434i	$-0.313629\pi$
$727$	−8732.05	−	15124.4i	−0.445466	−	0.771570i	−0.998085	+	0.0618643i	$0.980295\pi$
$728$	6571.78			0.334569
$729$	729.000			0.0370370
$730$	2095.65	−	3629.78i	0.106252	−	0.184033i
$731$	−9799.71	−	16973.6i	−0.495835	−	0.858812i
$732$	11570.1			0.584211
$733$	−14343.5	+	24843.6i	−0.722766	+	1.25187i	0.237120	+	0.971480i	$0.423796\pi$
$733$	−14343.5	+	24843.6i	−0.722766	+	1.25187i	−0.959887	+	0.280388i	$0.909537\pi$
$734$	−12777.3			−0.642530
$735$	4311.50	+	7467.74i	0.216370	+	0.374764i
$736$	−14112.1			−0.706766
$737$	8300.12	+	14983.5i	0.414842	+	0.748880i
$738$	−143.383			−0.00715177
$739$	−210.432	−	364.479i	−0.0104748	−	0.0181429i	0.860740	−	0.509044i	$-0.170001\pi$
$739$	−210.432	−	364.479i	−0.0104748	−	0.0181429i	−0.871215	+	0.490901i	$0.836668\pi$
$740$	−12837.4			−0.637718
$741$	−9430.76	+	16334.6i	−0.467541	+	0.809804i
$742$	927.385			0.0458833
$743$	−9337.77	−	16173.5i	−0.461063	−	0.798584i	0.537952	−	0.842976i	$-0.319198\pi$
$743$	−9337.77	−	16173.5i	−0.461063	−	0.798584i	−0.999014	+	0.0443919i	$0.985865\pi$
$744$	−5418.89	+	9385.79i	−0.267024	+	0.462500i
$745$	13883.1			0.682734
$746$	3013.21			0.147884
$747$	−5881.73	−	10187.4i	−0.288087	−	0.498982i
$748$	−7997.98	+	13852.9i	−0.390956	+	0.677155i
$749$	−842.545	+	1459.33i	−0.0411027	+	0.0711920i
$750$	2564.37	+	4441.61i	0.124850	+	0.216246i
$751$	23960.4			1.16422			0.582110	−	0.813110i	$-0.302227\pi$
$751$	23960.4			1.16422			0.582110	+	0.813110i	$0.302227\pi$
$752$	8147.79			0.395105
$753$	−1582.68	−	2741.29i	−0.0765951	−	0.132667i
$754$	−372.798	−	645.706i	−0.0180060	−	0.0311873i
$755$	−7619.51	−	13197.4i	−0.367288	−	0.636162i
$756$	507.558	+	879.117i	0.0244176	+	0.0422925i
$757$	−7427.89	+	12865.5i	−0.356633	+	0.617707i	−0.987396	−	0.158269i	$-0.949409\pi$
$757$	−7427.89	+	12865.5i	−0.356633	+	0.617707i	0.630763	+	0.775976i	$0.282742\pi$
$758$	2462.96	−	4265.97i	0.118019	−	0.204415i
$759$	7681.27			0.367342
$760$	6748.56	+	11688.8i	0.322100	+	0.557894i
$761$	12499.4			0.595404			0.297702	−	0.954659i	$-0.403780\pi$
$761$	12499.4			0.595404			0.297702	+	0.954659i	$0.403780\pi$
$762$	−365.758			−0.0173885
$763$	4254.21	−	7368.52i	0.201852	−	0.349618i
$764$	21459.0			1.01618
$765$	−3152.96	−	5461.08i	−0.149014	−	0.258099i
$766$	−6873.58	+	11905.4i	−0.324220	+	0.561566i
$767$	−7522.39	−	13029.2i	−0.354130	−	0.613371i
$768$	−1423.96	+	2466.37i	−0.0669045	+	0.115882i
$769$	−11384.2	+	19718.0i	−0.533842	+	0.924641i	0.465377	+	0.885113i	$0.345919\pi$
$769$	−11384.2	+	19718.0i	−0.533842	+	0.924641i	−0.999218	+	0.0395284i	$0.987414\pi$
$770$	−902.696	+	1563.52i	−0.0422479	+	0.0731756i
$771$	3504.70	−	6070.32i	0.163708	−	0.283550i
$772$	−8323.46	+	14416.7i	−0.388041	+	0.672107i
$773$	−2637.52	+	4568.33i	−0.122723	+	0.212563i	−0.920841	−	0.389939i	$-0.872496\pi$
$773$	−2637.52	+	4568.33i	−0.122723	+	0.212563i	0.798117	+	0.602502i	$0.205829\pi$
$774$	1303.84	+	2258.32i	0.0605498	+	0.104875i
$775$	4368.06	−	7565.70i	0.202458	−	0.350668i
$776$	11329.4	+	19623.1i	0.524099	+	0.907766i
$777$	−3461.21			−0.159807
$778$	6353.03	−	11003.8i	0.292760	−	0.507075i
$779$	1253.49			0.0576520
$780$	−13245.6			−0.608037
$781$	858.028	+	1486.15i	0.0393120	+	0.0680904i
$782$	7003.44			0.320259
$783$	125.964	−	218.177i	0.00574916	−	0.00995785i
$784$	5501.84	−	9529.47i	0.250631	−	0.434105i
$785$	−6397.80	−	11081.3i	−0.290888	−	0.503833i
$786$	−1539.83	−	2667.07i	−0.0698778	−	0.121032i
$787$	−19876.1	−	34426.4i	−0.900261	−	1.55930i	−0.827155	−	0.561974i	$-0.810042\pi$
$787$	−19876.1	−	34426.4i	−0.900261	−	1.55930i	−0.0731066	−	0.997324i	$-0.523291\pi$
$788$	−7709.42	−	13353.1i	−0.348524	−	0.603661i
$789$	11910.4			0.537417
$790$	−3368.56			−0.151707
$791$	3309.50	+	5732.21i	0.148764	+	0.257666i
$792$	2327.72	−	4031.73i	0.104434	−	0.180886i
$793$	−20352.3	+	35251.2i	−0.911388	+	1.57857i
$794$	7165.92	+	12411.7i	0.320288	+	0.554756i
$795$	−4088.74			−0.182406
$796$	15185.9			0.676192
$797$	7278.51	−	12606.7i	0.323485	−	0.560293i	−0.657719	−	0.753263i	$-0.728479\pi$
$797$	7278.51	−	12606.7i	0.323485	−	0.560293i	0.981205	+	0.192970i	$0.0618120\pi$
$798$	831.805	+	1440.73i	0.0368992	+	0.0639113i
$799$	−17554.2			−0.777249
$800$	3447.21	−	5970.75i	0.152347	−	0.263872i
$801$	−14826.6			−0.654021
$802$	−211.643	−	366.576i	−0.00931840	−	0.0161399i
$803$	12638.4			0.555417
$804$	5371.06	+	9695.92i	0.235600	+	0.425309i
$805$	−4216.57			−0.184614
$806$	−8715.19	−	15095.2i	−0.380868	−	0.659683i
$807$	−8071.02			−0.352061
$808$	9657.38	−	16727.1i	0.420477	−	0.728287i
$809$	1833.12			0.0796652			0.0398326	−	0.999206i	$-0.487318\pi$
$809$	1833.12			0.0796652			0.0398326	+	0.999206i	$0.487318\pi$
$810$	419.497	+	726.590i	0.0181971	+	0.0315182i
$811$	−16724.3	+	28967.3i	−0.724130	+	1.25423i	0.235202	+	0.971947i	$0.424425\pi$
$811$	−16724.3	+	28967.3i	−0.724130	+	1.25423i	−0.959331	+	0.282283i	$0.908908\pi$
$812$	350.805			0.0151611
$813$	−1146.94			−0.0494771
$814$	3628.29	+	6284.39i	0.156230	+	0.270599i
$815$	−11531.1	+	19972.5i	−0.495604	+	0.858412i
$816$	−4023.44	+	6968.81i	−0.172609	+	0.298967i
$817$	−11398.5	−	19742.7i	−0.488105	−	0.845423i
$818$	12800.8			0.547152
$819$	−3571.27			−0.152369
$820$	440.135	+	762.336i	0.0187441	+	0.0324658i
$821$	−11919.0	−	20644.3i	−0.506670	−	0.877577i	−0.999970	−	0.00771855i	$-0.997543\pi$
$821$	−11919.0	−	20644.3i	−0.506670	−	0.877577i	0.493301	−	0.869859i	$-0.335790\pi$
$822$	−1435.58	−	2486.50i	−0.0609143	−	0.105507i
$823$	16648.0	+	28835.3i	0.705121	+	1.22130i	0.966648	+	0.256109i	$0.0824405\pi$
$823$	16648.0	+	28835.3i	0.705121	+	1.22130i	−0.261527	+	0.965196i	$0.584226\pi$
$824$	−3924.33	+	6797.13i	−0.165911	+	0.287366i
$825$	−1876.33	+	3249.90i	−0.0791823	+	0.137148i
$826$	−1326.97			−0.0558973
$827$	1546.24	+	2678.16i	0.0650156	+	0.112610i	0.896701	−	0.442637i	$-0.145957\pi$
$827$	1546.24	+	2678.16i	0.0650156	+	0.112610i	−0.831685	+	0.555247i	$0.812624\pi$
$828$	4970.60			0.208623
$829$	−3332.81			−0.139630			−0.0698149	−	0.997560i	$-0.522241\pi$
$829$	−3332.81			−0.139630			−0.0698149	+	0.997560i	$0.522241\pi$
$830$	6769.18	−	11724.6i	0.283086	−	0.490320i
$831$	−426.508			−0.0178043
$832$	3157.64	+	5469.20i	0.131576	+	0.227897i
$833$	−11853.6	+	20531.0i	−0.493039	+	0.853969i
$834$	−1009.83	−	1749.08i	−0.0419275	−	0.0726206i
$835$	13807.4	−	23915.1i	0.572244	−	0.991155i
$836$	−9302.79	+	16112.9i	−0.384861	+	0.666599i
$837$	2944.76	−	5100.48i	0.121608	−	0.210631i
$838$	−3927.55	+	6802.72i	−0.161903	+	0.280425i
$839$	10474.1	−	18141.7i	0.430997	−	0.746508i	−0.565963	−	0.824431i	$-0.691495\pi$
$839$	10474.1	−	18141.7i	0.430997	−	0.746508i	0.996959	+	0.0779227i	$0.0248287\pi$
$840$	−1277.78	+	2213.19i	−0.0524854	+	0.0909074i
$841$	12151.0	+	21046.1i	0.498215	+	0.862934i
$842$	7180.34	−	12436.7i	0.293885	−	0.509023i
$843$	7768.77	+	13455.9i	0.317403	+	0.549758i
$844$	6096.76			0.248648
$845$	13174.9	−	22819.7i	0.536369	−	0.929018i
$846$	2335.56			0.0949152
$847$	1983.84			0.0804790
$848$	2608.79	+	4518.56i	0.105644	+	0.182981i
$849$	−25848.1			−1.04488
$850$	−1710.75	+	2963.11i	−0.0690333	+	0.119569i
$851$	−8474.03	+	14677.5i	−0.341347	+	0.591230i
$852$	555.235	+	961.695i	0.0223263	+	0.0386703i
$853$	16657.1	+	28850.9i	0.668615	+	1.15807i	0.978292	+	0.207233i	$0.0664457\pi$
$853$	16657.1	+	28850.9i	0.668615	+	1.15807i	−0.309677	+	0.950842i	$0.600221\pi$
$854$	1795.10	+	3109.20i	0.0719286	+	0.124584i
$855$	−3667.34	−	6352.02i	−0.146690	−	0.254075i
$856$	5000.85			0.199679
$857$	−15303.2			−0.609972			−0.304986	−	0.952357i	$-0.598652\pi$
$857$	−15303.2			−0.609972			−0.304986	+	0.952357i	$0.598652\pi$
$858$	3743.67	+	6484.23i	0.148959	+	0.258005i
$859$	2009.38	−	3480.35i	0.0798129	−	0.138240i	−0.823356	−	0.567525i	$-0.807901\pi$
$859$	2009.38	−	3480.35i	0.0798129	−	0.138240i	0.903169	+	0.429285i	$0.141234\pi$
$860$	8004.64	−	13864.4i	0.317391	−	0.549737i
$861$	118.669	+	205.540i	0.00469712	+	0.00813566i
$862$	15603.6			0.616544
$863$	−12932.2			−0.510103			−0.255051	−	0.966927i	$-0.582092\pi$
$863$	−12932.2			−0.510103			−0.255051	+	0.966927i	$0.582092\pi$
$864$	2323.97	−	4025.23i	0.0915081	−	0.158497i
$865$	772.063	+	1337.25i	0.0303479	+	0.0525641i
$866$	9316.66			0.365581
$867$	1298.89	−	2249.75i	0.0508796	−	0.0881261i
$868$	8201.04			0.320693
$869$	−5078.76	−	8796.67i	−0.198257	−	0.343391i
$870$	289.940			0.0112987
$871$	−38989.0	−	691.264i	−1.51675	−	0.0268916i
$872$	−25250.5			−0.980608
$873$	−6156.67	−	10663.7i	−0.238685	−	0.413414i
$874$	8146.00			0.315266
$875$	4244.72	−	7352.07i	0.163997	−	0.284052i
$876$	8178.39			0.315436
$877$	−14329.7	−	24819.8i	−0.551744	−	0.955649i	−0.998149	−	0.0608180i	$-0.980629\pi$
$877$	−14329.7	−	24819.8i	−0.551744	−	0.955649i	0.446405	−	0.894831i	$-0.352704\pi$
$878$	−4324.63	+	7490.48i	−0.166229	+	0.287917i
$879$	22066.2			0.846730
$880$	−10157.4			−0.389096
$881$	−20400.1	−	35334.1i	−0.780134	−	1.35123i	−0.931863	−	0.362810i	$-0.881817\pi$
$881$	−20400.1	−	35334.1i	−0.780134	−	1.35123i	0.151728	−	0.988422i	$-0.451516\pi$
$882$	1577.10	−	2731.62i	0.0602083	−	0.104284i
$883$	−15442.6	+	26747.4i	−0.588546	+	1.01939i	0.405877	+	0.913928i	$0.366966\pi$
$883$	−15442.6	+	26747.4i	−0.588546	+	1.01939i	−0.994423	+	0.105464i	$0.966367\pi$
$884$	−18208.0	−	31537.2i	−0.692762	−	1.19990i
$885$	5850.46			0.222216
$886$	19049.6			0.722329
$887$	12259.5	+	21234.0i	0.464072	+	0.803797i	0.999159	−	0.0410001i	$-0.0130544\pi$
$887$	12259.5	+	21234.0i	0.464072	+	0.803797i	−0.535087	+	0.844797i	$0.679721\pi$
$888$	5135.92	+	8895.67i	0.194088	+	0.336170i
$889$	302.714	+	524.316i	0.0114204	+	0.0197806i
$890$	−8531.82	−	14777.5i	−0.321334	−	0.556567i
$891$	−1264.94	+	2190.95i	−0.0475614	+	0.0823788i
$892$	7088.78	−	12278.1i	0.266087	−	0.460876i
$893$	−20418.0			−0.765132
$894$	−2539.14	−	4397.92i	−0.0949906	−	0.164529i
$895$	28008.3			1.04605
$896$	8242.45			0.307322
$897$	−8743.51	+	15144.2i	−0.325460	+	0.563712i
$898$	10490.3			0.389827
$899$	−1017.65	−	1762.63i	−0.0377538	−	0.0653915i
$900$	−1214.18	+	2103.03i	−0.0449698	+	0.0778900i
$901$	−5620.57	−	9735.11i	−0.207823	−	0.359959i
$902$	248.795	−	430.925i	0.00918400	−	0.0159072i
$903$	2158.21	−	3738.12i	0.0795356	−	0.137760i
$904$	9821.60	−	17011.5i	0.361351	−	0.625879i
$905$	16512.4	−	28600.4i	0.606510	−	1.05051i
$906$	−2787.14	+	4827.46i	−0.102204	+	0.177022i
$907$	3903.68	−	6761.38i	0.142910	−	0.247528i	−0.785681	−	0.618632i	$-0.787687\pi$
$907$	3903.68	−	6761.38i	0.142910	−	0.247528i	0.928591	+	0.371104i	$0.121021\pi$
$908$	−19785.5	−	34269.5i	−0.723133	−	1.25250i
$909$	−5248.07	+	9089.92i	−0.191493	+	0.331676i
$910$	−2055.06	−	3559.46i	−0.0748621	−	0.129665i
$911$	−9238.08			−0.335973			−0.167986	−	0.985789i	$-0.553726\pi$
$911$	−9238.08			−0.335973			−0.167986	+	0.985789i	$0.553726\pi$
$912$	−4679.84	+	8105.72i	−0.169918	+	0.294306i
$913$	40823.3			1.47980
$914$	−12196.4			−0.441381
$915$	−7914.39	−	13708.1i	−0.285947	−	0.495275i
$916$	−9684.86			−0.349342
$917$	−2548.84	+	4414.72i	−0.0917885	+	0.158982i
$918$	−1153.32	+	1997.61i	−0.0414653	+	0.0718201i
$919$	18022.1	+	31215.3i	0.646894	+	1.12045i	0.983861	+	0.178936i	$0.0572656\pi$
$919$	18022.1	+	31215.3i	0.646894	+	1.12045i	−0.336967	+	0.941517i	$0.609401\pi$
$920$	6256.77	+	10837.0i	0.224217	+	0.388355i
$921$	−3659.90	−	6339.12i	−0.130942	−	0.226798i
$922$	2091.66	+	3622.86i	0.0747127	+	0.129406i
$923$	−3906.73			−0.139319
$924$	−3522.81			−0.125424
$925$	−4139.96	−	7170.62i	−0.147158	−	0.254885i
$926$	−3016.24	+	5224.29i	−0.107041	+	0.185400i
$927$	2132.58	−	3693.73i	0.0755589	−	0.130872i
$928$	−803.119	−	1391.04i	−0.0284091	−	0.0492061i
$929$	52348.2			1.84875			0.924375	−	0.381486i	$-0.124587\pi$
$929$	52348.2			1.84875			0.924375	+	0.381486i	$0.124587\pi$
$930$	6778.15			0.238994
$931$	−13787.4	+	23880.5i	−0.485353	+	0.840655i
$932$	−6707.63	−	11618.0i	−0.235747	−	0.408325i
$933$	4204.86			0.147547
$934$	−6055.74	+	10488.8i	−0.212152	+	0.367458i
$935$	21883.7			0.765428
$936$	5299.24	+	9178.55i	0.185055	+	0.320524i
$937$	29475.4			1.02766			0.513831	−	0.857892i	$-0.328226\pi$
$937$	29475.4			1.02766			0.513831	+	0.857892i	$0.328226\pi$
$938$	−1772.24	+	2947.68i	−0.0616906	+	0.102607i
$939$	6692.08			0.232575
$940$	−7169.34	−	12417.7i	−0.248764	−	0.430872i
$941$	−13344.5			−0.462294			−0.231147	−	0.972919i	$-0.574248\pi$
$941$	−13344.5			−0.462294			−0.231147	+	0.972919i	$0.574248\pi$
$942$	−2340.25	+	4053.43i	−0.0809441	+	0.140199i
$943$	1162.14			0.0401321
$944$	−3732.84	−	6465.48i	−0.128701	−	0.222917i
$945$	694.380	−	1202.70i	0.0239029	−	0.0414010i
$946$	−9049.57			−0.311022
$947$	17281.2			0.592992			0.296496	−	0.955034i	$-0.404182\pi$
$947$	17281.2			0.592992			0.296496	+	0.955034i	$0.404182\pi$
$948$	−3286.49	−	5692.37i	−0.112595	−	0.195021i
$949$	−14386.2	+	24917.5i	−0.492091	+	0.852327i
$950$	−1989.85	+	3446.52i	−0.0679571	+	0.117705i
$951$	5948.22	+	10302.6i	0.202822	+	0.351299i
$952$	−7026.00			−0.239195
$953$	2459.72			0.0836077			0.0418038	−	0.999126i	$-0.486690\pi$
$953$	2459.72			0.0836077			0.0418038	+	0.999126i	$0.486690\pi$
$954$	747.809	+	1295.24i	0.0253786	+	0.0439571i
$955$	−14678.8	−	25424.4i	−0.497377	−	0.861482i
$956$	−3173.46	−	5496.60i	−0.107361	−	0.185955i
$957$	437.141	+	757.150i	0.0147657	+	0.0255749i
$958$	8524.71	−	14765.2i	0.287496	−	0.497957i
$959$	−2376.27	+	4115.82i	−0.0800144	+	0.138589i
$960$	−2455.83			−0.0825640
$961$	−8894.98	−	15406.6i	−0.298579	−	0.517155i
$962$	−16520.2			−0.553671
$963$	−2717.59			−0.0909378
$964$	−22862.8	+	39599.6i	−0.763861	+	1.32305i
$965$	22774.3			0.759722
$966$	771.189	+	1335.74i	0.0256859	+	0.0444893i
$967$	5737.42	−	9937.51i	0.190799	−	0.330474i	−0.754716	−	0.656052i	$-0.772225\pi$
$967$	5737.42	−	9937.51i	0.190799	−	0.330474i	0.945515	+	0.325577i	$0.105559\pi$
$968$	−2943.73	−	5098.69i	−0.0977429	−	0.169296i
$969$	10082.6	−	17463.5i	0.334261	−	0.578957i
$970$	7085.61	−	12272.6i	0.234541	−	0.406238i
$971$	−13325.0	+	23079.6i	−0.440392	+	0.762782i	−0.997718	−	0.0675118i	$-0.978494\pi$
$971$	−13325.0	+	23079.6i	−0.440392	+	0.762782i	0.557326	+	0.830294i	$0.311827\pi$
$972$	−818.553	+	1417.77i	−0.0270114	+	0.0467851i
$973$	−1671.54	+	2895.19i	−0.0550742	+	0.0953912i
$974$	2634.83	−	4563.65i	0.0866789	−	0.150132i
$975$	−4271.61	−	7398.65i	−0.140309	−	0.243022i
$976$	−10099.4	+	17492.7i	−0.331225	+	0.573698i
$977$	10402.8	+	18018.1i	0.340649	+	0.590021i	0.984553	−	0.175085i	$-0.0560199\pi$
$977$	10402.8	+	18018.1i	0.340649	+	0.590021i	−0.643904	+	0.765106i	$0.722687\pi$
$978$	8435.92			0.275819
$979$	25726.7	−	44560.0i	0.839867	−	1.45469i
$980$	−19364.5			−0.631202
$981$	13721.8			0.446587
$982$	−8337.48	−	14440.9i	−0.270937	−	0.469276i
$983$	8976.88			0.291270			0.145635	−	0.989338i	$-0.453478\pi$
$983$	8976.88			0.291270			0.145635	+	0.989338i	$0.453478\pi$
$984$	352.174	−	609.983i	0.0114095	−	0.0197617i
$985$	−10547.1	+	18268.1i	−0.341176	+	0.590935i
$986$	398.565	+	690.335i	0.0128731	+	0.0222969i
$987$	−1932.99	−	3348.04i	−0.0623382	−	0.107973i
$988$	−21178.5	−	36682.3i	−0.681962	−	1.18119i
$989$	−10567.8	−	18304.0i	−0.339775	−	0.588507i
$990$	−2911.60			−0.0934716
$991$	6673.07			0.213902			0.106951	−	0.994264i	$-0.465891\pi$
$991$	6673.07			0.213902			0.106951	+	0.994264i	$0.465891\pi$
$992$	−18775.1	−	32519.5i	−0.600918	−	1.04082i
$993$	−4128.01	+	7149.92i	−0.131922	+	0.228495i
$994$	−172.290	+	298.414i	−0.00549768	+	0.00952226i
$995$	−10387.7	−	17992.1i	−0.330968	−	0.573254i
$996$	26417.0			0.840417
$997$	−18217.4			−0.578688			−0.289344	−	0.957225i	$-0.593437\pi$
$997$	−18217.4			−0.578688			−0.289344	+	0.957225i	$0.593437\pi$
$998$	1220.90	−	2114.66i	0.0387244	−	0.0670726i
$999$	−2790.99	−	4834.13i	−0.0883914	−	0.153098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.e.b.37.8	✓	36
67.29	even	3	inner	201.4.e.b.163.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.e.b.37.8	✓	36	1.1	even	1	trivial
201.4.e.b.163.8	yes	36	67.29	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.561904 - 0.973245i) q^{2} -3.00000 q^{3} +(3.36853 - 5.83446i) q^{4} -9.21684 q^{5} +(1.68571 + 2.91974i) q^{6} +(2.79031 - 4.83295i) q^{7} -16.5616 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(-0.561904 - 0.973245i) q^{2} -3.00000 q^{3} +(3.36853 - 5.83446i) q^{4} -9.21684 q^{5} +(1.68571 + 2.91974i) q^{6} +(2.79031 - 4.83295i) q^{7} -16.5616 q^{8} +9.00000 q^{9} +(5.17897 + 8.97024i) q^{10} +(-15.6166 + 27.0487i) q^{11} +(-10.1056 + 17.5034i) q^{12} +(-35.5524 - 61.5785i) q^{13} -6.27153 q^{14} +27.6505 q^{15} +(-17.6422 - 30.5572i) q^{16} +(38.0096 + 65.8346i) q^{17} +(-5.05713 - 8.75921i) q^{18} +(44.2106 + 76.5751i) q^{19} +(-31.0472 + 53.7753i) q^{20} +(-8.37092 + 14.4989i) q^{21} +35.1001 q^{22} +(40.9889 + 70.9948i) q^{23} +49.6848 q^{24} -40.0499 q^{25} +(-39.9540 + 69.2024i) q^{26} -27.0000 q^{27} +(-18.7985 - 32.5599i) q^{28} +(-4.66534 + 8.08061i) q^{29} +(-15.5369 - 26.9107i) q^{30} +(-109.065 + 188.907i) q^{31} +(-86.0729 + 149.083i) q^{32} +(46.8498 - 81.1462i) q^{33} +(42.7155 - 73.9854i) q^{34} +(-25.7178 + 44.5445i) q^{35} +(30.3168 - 52.5102i) q^{36} +(103.370 + 179.042i) q^{37} +(49.6842 - 86.0556i) q^{38} +(106.657 + 184.736i) q^{39} +152.646 q^{40} +(7.08816 - 12.2771i) q^{41} +18.8146 q^{42} -257.822 q^{43} +(105.210 + 182.229i) q^{44} -82.9515 q^{45} +(46.0636 - 79.7844i) q^{46} +(-115.459 + 199.980i) q^{47} +(52.9266 + 91.6716i) q^{48} +(155.928 + 270.076i) q^{49} +(22.5042 + 38.9784i) q^{50} +(-114.029 - 197.504i) q^{51} -479.037 q^{52} -147.872 q^{53} +(15.1714 + 26.2776i) q^{54} +(143.936 - 249.304i) q^{55} +(-46.2120 + 80.0415i) q^{56} +(-132.632 - 229.725i) q^{57} +10.4859 q^{58} +211.586 q^{59} +(93.1415 - 161.326i) q^{60} +(-286.230 - 495.764i) q^{61} +245.137 q^{62} +(25.1128 - 43.4966i) q^{63} -88.8167 q^{64} +(327.680 + 567.559i) q^{65} -105.300 q^{66} +(282.586 - 470.009i) q^{67} +512.146 q^{68} +(-122.967 - 212.984i) q^{69} +57.8037 q^{70} +(27.4717 - 47.5824i) q^{71} -149.054 q^{72} +(-202.323 - 350.434i) q^{73} +(116.168 - 201.209i) q^{74} +120.150 q^{75} +595.699 q^{76} +(87.1501 + 150.948i) q^{77} +(119.862 - 207.607i) q^{78} +(-162.608 + 281.645i) q^{79} +(162.605 + 281.641i) q^{80} +81.0000 q^{81} -15.9315 q^{82} +(-653.525 - 1131.94i) q^{83} +(56.3954 + 97.6796i) q^{84} +(-350.329 - 606.787i) q^{85} +(144.871 + 250.924i) q^{86} +(13.9960 - 24.2418i) q^{87} +(258.636 - 447.970i) q^{88} -1647.40 q^{89} +(46.6108 + 80.7322i) q^{90} -396.808 q^{91} +552.289 q^{92} +(327.196 - 566.720i) q^{93} +259.507 q^{94} +(-407.482 - 705.780i) q^{95} +(258.219 - 447.248i) q^{96} +(-684.075 - 1184.85i) q^{97} +(175.233 - 303.513i) q^{98} +(-140.549 + 243.439i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9}+O(q^{10}) \) 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9	\( 36 q + 2 q^{2} - 108 q^{3} - 90 q^{4} - 4 q^{5} - 6 q^{6} + 22 q^{7} + 48 q^{8} + 324 q^{9} + 14 q^{10} - 16 q^{11} + 270 q^{12} - 46 q^{13} + 14 q^{14} + 12 q^{15} - 346 q^{16} - 8 q^{17} + 18 q^{18} - 154 q^{19} - 180 q^{20} - 66 q^{21} + 214 q^{22} - 104 q^{23} - 144 q^{24} + 1032 q^{25} - 333 q^{26} - 972 q^{27} - 473 q^{28} + 76 q^{29} - 42 q^{30} + 498 q^{31} - 285 q^{32} + 48 q^{33} + 26 q^{34} - 392 q^{35} - 810 q^{36} - 124 q^{37} + 20 q^{38} + 138 q^{39} + 638 q^{40} - 508 q^{41} - 42 q^{42} - 1400 q^{43} - 333 q^{44} - 36 q^{45} - 1372 q^{46} + 18 q^{47} + 1038 q^{48} - 238 q^{49} - 337 q^{50} + 24 q^{51} + 3640 q^{52} + 724 q^{53} - 54 q^{54} - 178 q^{55} - 829 q^{56} + 462 q^{57} - 1472 q^{58} + 720 q^{59} + 540 q^{60} + 232 q^{61} - 3882 q^{62} + 198 q^{63} + 3628 q^{64} - 1428 q^{65} - 642 q^{66} - 1164 q^{67} + 1634 q^{68} + 312 q^{69} + 2550 q^{70} + 406 q^{71} + 432 q^{72} - 2120 q^{73} + 1375 q^{74} - 3096 q^{75} + 4190 q^{76} - 800 q^{77} + 999 q^{78} + 1306 q^{79} - 1927 q^{80} + 2916 q^{81} - 794 q^{82} - 1010 q^{83} + 1419 q^{84} + 472 q^{85} + 737 q^{86} - 228 q^{87} - 1838 q^{88} + 1904 q^{89} + 126 q^{90} + 7340 q^{91} + 7368 q^{92} - 1494 q^{93} - 9862 q^{94} + 1678 q^{95} + 855 q^{96} - 2358 q^{97} - 2610 q^{98} - 144 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 108 * q^3 - 90 * q^4 - 4 * q^5 - 6 * q^6 + 22 * q^7 + 48 * q^8 + 324 * q^9 + 14 * q^10 - 16 * q^11 + 270 * q^12 - 46 * q^13 + 14 * q^14 + 12 * q^15 - 346 * q^16 - 8 * q^17 + 18 * q^18 - 154 * q^19 - 180 * q^20 - 66 * q^21 + 214 * q^22 - 104 * q^23 - 144 * q^24 + 1032 * q^25 - 333 * q^26 - 972 * q^27 - 473 * q^28 + 76 * q^29 - 42 * q^30 + 498 * q^31 - 285 * q^32 + 48 * q^33 + 26 * q^34 - 392 * q^35 - 810 * q^36 - 124 * q^37 + 20 * q^38 + 138 * q^39 + 638 * q^40 - 508 * q^41 - 42 * q^42 - 1400 * q^43 - 333 * q^44 - 36 * q^45 - 1372 * q^46 + 18 * q^47 + 1038 * q^48 - 238 * q^49 - 337 * q^50 + 24 * q^51 + 3640 * q^52 + 724 * q^53 - 54 * q^54 - 178 * q^55 - 829 * q^56 + 462 * q^57 - 1472 * q^58 + 720 * q^59 + 540 * q^60 + 232 * q^61 - 3882 * q^62 + 198 * q^63 + 3628 * q^64 - 1428 * q^65 - 642 * q^66 - 1164 * q^67 + 1634 * q^68 + 312 * q^69 + 2550 * q^70 + 406 * q^71 + 432 * q^72 - 2120 * q^73 + 1375 * q^74 - 3096 * q^75 + 4190 * q^76 - 800 * q^77 + 999 * q^78 + 1306 * q^79 - 1927 * q^80 + 2916 * q^81 - 794 * q^82 - 1010 * q^83 + 1419 * q^84 + 472 * q^85 + 737 * q^86 - 228 * q^87 - 1838 * q^88 + 1904 * q^89 + 126 * q^90 + 7340 * q^91 + 7368 * q^92 - 1494 * q^93 - 9862 * q^94 + 1678 * q^95 + 855 * q^96 - 2358 * q^97 - 2610 * q^98 - 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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