LMFDB - Embedded newform 45.4.e.b.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(16,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("45.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.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:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.15759792.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 16x^{4} - 27x^{3} + 52x^{2} - 39x + 9 $ x^6 - 3x^5 + 16x^4 - 27x^3 + 52x^2 - 39*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.3
Root			$0.500000 + 2.88506i$ of defining polynomial
Character	$\chi$	$=$	45.16
Dual form			45.4.e.b.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.28679 - 3.96084i) q^{2} +(3.36330 + 3.96084i) q^{3} +(-6.45882 - 11.1870i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(23.3794 - 4.26387i) q^{6} +(10.0573 - 17.4197i) q^{7} -22.4912 q^{8} +(-4.37646 + 26.6429i) q^{9} +O(q^{10})$	\(q+(2.28679 - 3.96084i) q^{2} +(3.36330 + 3.96084i) q^{3} +(-6.45882 - 11.1870i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(23.3794 - 4.26387i) q^{6} +(10.0573 - 17.4197i) q^{7} -22.4912 q^{8} +(-4.37646 + 26.6429i) q^{9} -22.8679 q^{10} +(-33.1708 + 57.4535i) q^{11} +(22.5870 - 63.2076i) q^{12} +(23.4003 + 40.5305i) q^{13} +(-45.9977 - 79.6704i) q^{14} +(8.74268 - 24.4656i) q^{15} +(0.237854 - 0.411975i) q^{16} -47.6233 q^{17} +(95.5203 + 78.2613i) q^{18} -9.95276 q^{19} +(-32.2941 + 55.9350i) q^{20} +(102.822 - 18.7524i) q^{21} +(151.709 + 262.768i) q^{22} +(-4.79602 - 8.30695i) q^{23} +(-75.6447 - 89.0841i) q^{24} +(-12.5000 + 21.6506i) q^{25} +214.046 q^{26} +(-120.248 + 72.2737i) q^{27} -259.832 q^{28} +(89.3675 - 154.789i) q^{29} +(-76.9116 - 90.5760i) q^{30} +(-77.0186 - 133.400i) q^{31} +(-91.0527 - 157.708i) q^{32} +(-339.127 + 61.8491i) q^{33} +(-108.905 + 188.628i) q^{34} -100.573 q^{35} +(326.322 - 123.123i) q^{36} +248.864 q^{37} +(-22.7599 + 39.4213i) q^{38} +(-81.8326 + 229.001i) q^{39} +(56.2280 + 97.3898i) q^{40} +(-124.832 - 216.216i) q^{41} +(160.857 - 450.145i) q^{42} +(106.122 - 183.809i) q^{43} +856.976 q^{44} +(126.308 - 47.6567i) q^{45} -43.8700 q^{46} +(-237.847 + 411.963i) q^{47} +(2.43174 - 0.443494i) q^{48} +(-30.7973 - 53.3425i) q^{49} +(57.1698 + 99.0209i) q^{50} +(-160.171 - 188.628i) q^{51} +(302.277 - 523.559i) q^{52} -546.314 q^{53} +(11.2831 + 641.556i) q^{54} +331.708 q^{55} +(-226.200 + 391.790i) q^{56} +(-33.4741 - 39.4213i) q^{57} +(-408.729 - 707.940i) q^{58} +(209.648 + 363.121i) q^{59} +(-330.164 + 60.2145i) q^{60} +(272.605 - 472.165i) q^{61} -704.502 q^{62} +(420.097 + 344.192i) q^{63} -829.068 q^{64} +(117.002 - 202.653i) q^{65} +(-530.538 + 1484.66i) q^{66} +(223.938 + 387.872i) q^{67} +(307.590 + 532.762i) q^{68} +(16.7720 - 46.9350i) q^{69} +(-229.989 + 398.352i) q^{70} +409.542 q^{71} +(98.4319 - 599.232i) q^{72} -358.548 q^{73} +(569.100 - 985.710i) q^{74} +(-127.796 + 23.3071i) q^{75} +(64.2831 + 111.342i) q^{76} +(667.215 + 1155.65i) q^{77} +(719.902 + 847.803i) q^{78} +(325.776 - 564.260i) q^{79} -2.37854 q^{80} +(-690.693 - 233.204i) q^{81} -1141.86 q^{82} +(406.571 - 704.202i) q^{83} +(-873.893 - 1029.15i) q^{84} +(119.058 + 206.215i) q^{85} +(-485.359 - 840.667i) q^{86} +(913.663 - 166.631i) q^{87} +(746.051 - 1292.20i) q^{88} -201.000 q^{89} +(100.080 - 609.268i) q^{90} +941.373 q^{91} +(-61.9532 + 107.306i) q^{92} +(269.340 - 753.723i) q^{93} +(1087.81 + 1884.14i) q^{94} +(24.8819 + 43.0967i) q^{95} +(318.418 - 891.064i) q^{96} +(-126.074 + 218.367i) q^{97} -281.708 q^{98} +(-1385.56 - 1135.21i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + 9 q^{3} - 11 q^{4} - 15 q^{5} + 84 q^{6} + 43 q^{7} - 54 q^{8} + 57 q^{9}+O(q^{10}) $ 6 * q + q^2 + 9 * q^3 - 11 * q^4 - 15 * q^5 + 84 * q^6 + 43 * q^7 - 54 * q^8 + 57 * q^9	\( 6 q + q^{2} + 9 q^{3} - 11 q^{4} - 15 q^{5} + 84 q^{6} + 43 q^{7} - 54 q^{8} + 57 q^{9} - 10 q^{10} - 14 q^{11} + 75 q^{12} - 40 q^{13} + 27 q^{14} - 15 q^{15} + 13 q^{16} - 332 q^{17} + 3 q^{18} - 328 q^{19} - 55 q^{20} - 144 q^{21} + 376 q^{22} - 171 q^{23} - 63 q^{24} - 75 q^{25} + 868 q^{26} + 162 q^{27} - 1034 q^{28} + 335 q^{29} - 315 q^{30} + 352 q^{31} + 77 q^{32} - 708 q^{33} + 52 q^{34} - 430 q^{35} + 1086 q^{36} + 804 q^{37} + 178 q^{38} - 390 q^{39} + 135 q^{40} - 187 q^{41} + 513 q^{42} + 602 q^{43} + 1964 q^{44} + 330 q^{45} - 402 q^{46} - 665 q^{47} - 1074 q^{48} - 430 q^{49} + 25 q^{50} - 180 q^{51} + 456 q^{52} - 1460 q^{53} + 639 q^{54} + 140 q^{55} - 705 q^{56} - 486 q^{57} - 217 q^{58} + 298 q^{59} - 150 q^{60} + 1439 q^{61} - 3228 q^{62} + 2205 q^{63} - 3138 q^{64} - 200 q^{65} - 966 q^{66} + 1849 q^{67} + 710 q^{68} - 873 q^{69} + 135 q^{70} + 140 q^{71} + 261 q^{72} - 736 q^{73} + 320 q^{74} - 150 q^{75} - 204 q^{76} + 948 q^{77} - 432 q^{78} + 382 q^{79} - 130 q^{80} - 1251 q^{81} - 1150 q^{82} + 831 q^{83} - 909 q^{84} + 830 q^{85} - 1580 q^{86} + 258 q^{87} + 1428 q^{88} + 3438 q^{89} + 375 q^{90} - 1420 q^{91} + 1623 q^{92} + 2178 q^{93} + 2077 q^{94} + 820 q^{95} + 1155 q^{96} + 282 q^{97} + 4328 q^{98} - 762 q^{99}+O(q^{100}) \) 6 * q + q^2 + 9 * q^3 - 11 * q^4 - 15 * q^5 + 84 * q^6 + 43 * q^7 - 54 * q^8 + 57 * q^9 - 10 * q^10 - 14 * q^11 + 75 * q^12 - 40 * q^13 + 27 * q^14 - 15 * q^15 + 13 * q^16 - 332 * q^17 + 3 * q^18 - 328 * q^19 - 55 * q^20 - 144 * q^21 + 376 * q^22 - 171 * q^23 - 63 * q^24 - 75 * q^25 + 868 * q^26 + 162 * q^27 - 1034 * q^28 + 335 * q^29 - 315 * q^30 + 352 * q^31 + 77 * q^32 - 708 * q^33 + 52 * q^34 - 430 * q^35 + 1086 * q^36 + 804 * q^37 + 178 * q^38 - 390 * q^39 + 135 * q^40 - 187 * q^41 + 513 * q^42 + 602 * q^43 + 1964 * q^44 + 330 * q^45 - 402 * q^46 - 665 * q^47 - 1074 * q^48 - 430 * q^49 + 25 * q^50 - 180 * q^51 + 456 * q^52 - 1460 * q^53 + 639 * q^54 + 140 * q^55 - 705 * q^56 - 486 * q^57 - 217 * q^58 + 298 * q^59 - 150 * q^60 + 1439 * q^61 - 3228 * q^62 + 2205 * q^63 - 3138 * q^64 - 200 * q^65 - 966 * q^66 + 1849 * q^67 + 710 * q^68 - 873 * q^69 + 135 * q^70 + 140 * q^71 + 261 * q^72 - 736 * q^73 + 320 * q^74 - 150 * q^75 - 204 * q^76 + 948 * q^77 - 432 * q^78 + 382 * q^79 - 130 * q^80 - 1251 * q^81 - 1150 * q^82 + 831 * q^83 - 909 * q^84 + 830 * q^85 - 1580 * q^86 + 258 * q^87 + 1428 * q^88 + 3438 * q^89 + 375 * q^90 - 1420 * q^91 + 1623 * q^92 + 2178 * q^93 + 2077 * q^94 + 820 * q^95 + 1155 * q^96 + 282 * q^97 + 4328 * q^98 - 762 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	2.28679	−	3.96084i	0.808502	−	1.40037i	−0.105398	−	0.994430i	$-0.533612\pi$
$2$	2.28679	−	3.96084i	0.808502	−	1.40037i	0.913901	−	0.405937i	$-0.133055\pi$
$3$	3.36330	+	3.96084i	0.647267	+	0.762263i
$3$	3.36330	+	3.96084i	0.647267	+	0.762263i
$4$	−6.45882	−	11.1870i	−0.807352	−	1.39838i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$	23.3794	−	4.26387i	1.59077	−	0.290120i
$7$	10.0573	−	17.4197i	0.543041	−	0.940575i	−0.455686	−	0.890141i	$-0.650606\pi$
$7$	10.0573	−	17.4197i	0.543041	−	0.940575i	0.998727	−	0.0504348i	$-0.0160607\pi$
$8$	−22.4912			−0.993981
$9$	−4.37646	+	26.6429i	−0.162091	+	0.986776i
$10$	−22.8679			−0.723147
$11$	−33.1708	+	57.4535i	−0.909215	+	1.57481i	−0.0940582	+	0.995567i	$0.529984\pi$
$11$	−33.1708	+	57.4535i	−0.909215	+	1.57481i	−0.815157	+	0.579240i	$0.803349\pi$
$12$	22.5870	−	63.2076i	0.543358	−	1.52054i
$13$	23.4003	+	40.5305i	0.499237	+	0.864703i	1.00000		0.000881222i	$-0.000280502\pi$
$13$	23.4003	+	40.5305i	0.499237	+	0.864703i	−0.500763	+	0.865584i	$0.666947\pi$
$14$	−45.9977	−	79.6704i	−0.878101	−	1.52092i
$15$	8.74268	−	24.4656i	0.150490	−	0.421133i
$16$	0.237854	−	0.411975i	0.00371647	−	0.00643711i
$17$	−47.6233			−0.679432			−0.339716	−	0.940528i	$-0.610331\pi$
$17$	−47.6233			−0.679432			−0.339716	+	0.940528i	$0.610331\pi$
$18$	95.5203	+	78.2613i	1.25080	+	1.02480i
$19$	−9.95276			−0.120175			−0.0600874	−	0.998193i	$-0.519138\pi$
$19$	−9.95276			−0.120175			−0.0600874	+	0.998193i	$0.519138\pi$
$20$	−32.2941	+	55.9350i	−0.361059	+	0.625373i
$21$	102.822	−	18.7524i	1.06846	−	0.194863i
$22$	151.709	+	262.768i	1.47021	+	2.54647i
$23$	−4.79602	−	8.30695i	−0.0434800	−	0.0753095i	0.843466	−	0.537182i	$-0.180511\pi$
$23$	−4.79602	−	8.30695i	−0.0434800	−	0.0753095i	−0.886946	+	0.461872i	$0.847178\pi$
$24$	−75.6447	−	89.0841i	−0.643371	−	0.757675i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	214.046			1.61454
$27$	−120.248	+	72.2737i	−0.857099	+	0.515151i
$28$	−259.832			−1.75370
$29$	89.3675	−	154.789i	0.572246	−	0.991158i	−0.424089	−	0.905620i	$-0.639406\pi$
$29$	89.3675	−	154.789i	0.572246	−	0.991158i	0.996335	−	0.0855380i	$-0.0272609\pi$
$30$	−76.9116	−	90.5760i	−0.468069	−	0.551228i
$31$	−77.0186	−	133.400i	−0.446224	−	0.772883i	0.551912	−	0.833902i	$-0.313898\pi$
$31$	−77.0186	−	133.400i	−0.446224	−	0.772883i	−0.998137	+	0.0610190i	$0.980565\pi$
$32$	−91.0527	−	157.708i	−0.503000	−	0.871222i
$33$	−339.127	+	61.8491i	−1.78892	+	0.326259i
$34$	−108.905	+	188.628i	−0.549323	+	0.951455i
$35$	−100.573			−0.485711
$36$	326.322	−	123.123i	1.51075	−	0.570012i
$37$	248.864			1.10576			0.552878	−	0.833262i	$-0.313529\pi$
$37$	248.864			1.10576			0.552878	+	0.833262i	$0.313529\pi$
$38$	−22.7599	+	39.4213i	−0.0971616	+	0.168289i
$39$	−81.8326	+	229.001i	−0.335992	+	0.940244i
$40$	56.2280	+	97.3898i	0.222261	+	0.384967i
$41$	−124.832	−	216.216i	−0.475500	−	0.823590i	0.524106	−	0.851653i	$-0.324400\pi$
$41$	−124.832	−	216.216i	−0.475500	−	0.823590i	−0.999606	+	0.0280628i	$0.991066\pi$
$42$	160.857	−	450.145i	0.590972	−	1.65378i
$43$	106.122	−	183.809i	0.376361	−	0.651876i	−0.614169	−	0.789175i	$-0.710509\pi$
$43$	106.122	−	183.809i	0.376361	−	0.651876i	0.990530	+	0.137299i	$0.0438420\pi$
$44$	856.976			2.93623
$45$	126.308	−	47.6567i	0.418421	−	0.157872i
$46$	−43.8700			−0.140615
$47$	−237.847	+	411.963i	−0.738160	+	1.27853i	0.215163	+	0.976578i	$0.430972\pi$
$47$	−237.847	+	411.963i	−0.738160	+	1.27853i	−0.953323	+	0.301953i	$0.902362\pi$
$48$	2.43174	−	0.443494i	0.00731232	−	0.00133360i
$49$	−30.7973	−	53.3425i	−0.0897880	−	0.155517i
$50$	57.1698	+	99.0209i	0.161700	+	0.280073i
$51$	−160.171	−	188.628i	−0.439774	−	0.517906i
$52$	302.277	−	523.559i	0.806120	−	1.39624i
$53$	−546.314			−1.41589			−0.707944	−	0.706269i	$-0.750377\pi$
$53$	−546.314			−1.41589			−0.707944	+	0.706269i	$0.750377\pi$
$54$	11.2831	+	641.556i	0.0284341	+	1.61675i
$55$	331.708			0.813227
$56$	−226.200	+	391.790i	−0.539773	+	0.934914i
$57$	−33.4741	−	39.4213i	−0.0777851	−	0.0916048i
$58$	−408.729	−	707.940i	−0.925324	−	1.60271i
$59$	209.648	+	363.121i	0.462608	+	0.801261i	0.999090	−	0.0426512i	$-0.0135804\pi$
$59$	209.648	+	363.121i	0.462608	+	0.801261i	−0.536482	+	0.843912i	$0.680247\pi$
$60$	−330.164	+	60.2145i	−0.710400	+	0.129561i
$61$	272.605	−	472.165i	0.572188	−	0.991059i	−0.424153	−	0.905591i	$-0.639428\pi$
$61$	272.605	−	472.165i	0.572188	−	0.991059i	0.996341	−	0.0854682i	$-0.0272386\pi$
$62$	−704.502			−1.44309
$63$	420.097	+	344.192i	0.840115	+	0.688319i
$64$	−829.068			−1.61927
$65$	117.002	−	202.653i	0.223265	−	0.386707i
$66$	−530.538	+	1484.66i	−0.989466	+	2.76893i
$67$	223.938	+	387.872i	0.408335	+	0.707256i	0.994703	−	0.102788i	$-0.0327764\pi$
$67$	223.938	+	387.872i	0.408335	+	0.707256i	−0.586369	+	0.810044i	$0.699443\pi$
$68$	307.590	+	532.762i	0.548541	+	0.950102i
$69$	16.7720	−	46.9350i	0.0292625	−	0.0818885i
$70$	−229.989	+	398.352i	−0.392699	+	0.680174i
$71$	409.542			0.684559			0.342279	−	0.939598i	$-0.388801\pi$
$71$	409.542			0.684559			0.342279	+	0.939598i	$0.388801\pi$
$72$	98.4319	−	599.232i	0.161115	−	0.980836i
$73$	−358.548			−0.574861			−0.287431	−	0.957801i	$-0.592801\pi$
$73$	−358.548			−0.574861			−0.287431	+	0.957801i	$0.592801\pi$
$74$	569.100	−	985.710i	0.894007	−	1.54847i
$75$	−127.796	+	23.3071i	−0.196755	+	0.0358836i
$76$	64.2831	+	111.342i	0.0970234	+	0.168049i
$77$	667.215	+	1155.65i	0.987483	+	1.71037i
$78$	719.902	+	847.803i	1.04504	+	1.23070i
$79$	325.776	−	564.260i	0.463958	−	0.803598i	−0.535196	−	0.844728i	$-0.679762\pi$
$79$	325.776	−	564.260i	0.463958	−	0.803598i	0.999154	+	0.0411297i	$0.0130957\pi$
$80$	−2.37854			−0.00332411
$81$	−690.693	−	233.204i	−0.947453	−	0.319895i
$82$	−1141.86			−1.53777
$83$	406.571	−	704.202i	0.537675	−	0.931280i	−0.461354	−	0.887216i	$-0.652636\pi$
$83$	406.571	−	704.202i	0.537675	−	0.931280i	0.999029	−	0.0440636i	$-0.0140304\pi$
$84$	−873.893	−	1029.15i	−1.13511	−	1.33678i
$85$	119.058	+	206.215i	0.151926	+	0.263143i
$86$	−485.359	−	840.667i	−0.608577	−	1.05409i
$87$	913.663	−	166.631i	1.12592	−	0.205342i
$88$	746.051	−	1292.20i	0.903743	−	1.56533i
$89$	−201.000			−0.239393			−0.119696	−	0.992811i	$-0.538192\pi$
$89$	−201.000			−0.239393			−0.119696	+	0.992811i	$0.538192\pi$
$90$	100.080	−	609.268i	0.117216	−	0.713584i
$91$	941.373			1.08442
$92$	−61.9532	+	107.306i	−0.0702073	+	0.121603i
$93$	269.340	−	753.723i	0.300314	−	0.840402i
$94$	1087.81	+	1884.14i	1.19361	+	2.06739i
$95$	24.8819	+	43.0967i	0.0268719	+	0.0465435i
$96$	318.418	−	891.064i	0.338525	−	0.947331i
$97$	−126.074	+	218.367i	−0.131968	+	0.228576i	−0.924435	−	0.381339i	$-0.875463\pi$
$97$	−126.074	+	218.367i	−0.131968	+	0.228576i	0.792467	+	0.609915i	$0.208796\pi$
$98$	−281.708			−0.290375
$99$	−1385.56	−	1135.21i	−1.40661	−	1.15245i
$100$	322.941			0.322941
$101$	−21.8013	+	37.7610i	−0.0214783	+	0.0372016i	−0.876565	−	0.481284i	$-0.840171\pi$
$101$	−21.8013	+	37.7610i	−0.0214783	+	0.0372016i	0.855086	+	0.518485i	$0.173504\pi$
$102$	−1113.40	+	203.060i	−1.08082	+	0.197117i
$103$	720.176	+	1247.38i	0.688942	+	1.19328i	0.972180	+	0.234233i	$0.0752579\pi$
$103$	720.176	+	1247.38i	0.688942	+	1.19328i	−0.283238	+	0.959050i	$0.591409\pi$
$104$	−526.301	−	911.581i	−0.496232	−	0.859498i
$105$	−338.256	−	398.352i	−0.314385	−	0.370240i
$106$	−1249.31	+	2163.86i	−1.14475	+	1.98276i
$107$	355.755			0.321422			0.160711	−	0.987002i	$-0.448621\pi$
$107$	355.755			0.321422			0.160711	+	0.987002i	$0.448621\pi$
$108$	1585.18	+	878.409i	1.41236	+	0.782638i
$109$	−1522.51			−1.33789			−0.668946	−	0.743311i	$-0.733254\pi$
$109$	−1522.51			−1.33789			−0.668946	+	0.743311i	$0.733254\pi$
$110$	758.546	−	1313.84i	0.657496	−	1.13882i
$111$	837.004	+	985.710i	0.715720	+	0.842878i
$112$	−4.78432	−	8.28669i	−0.00403639	−	0.00699124i
$113$	406.499	+	704.077i	0.338409	+	0.586142i	0.984134	−	0.177429i	$-0.0567779\pi$
$113$	406.499	+	704.077i	0.338409	+	0.586142i	−0.645725	+	0.763570i	$0.723445\pi$
$114$	−232.689	+	42.4373i	−0.191170	+	0.0348650i
$115$	−23.9801	+	41.5347i	−0.0194448	+	0.0336794i
$116$	−2308.83			−1.84802
$117$	−1182.26	+	446.073i	−0.934190	+	0.352474i
$118$	1917.69			1.49608
$119$	−478.960	+	829.584i	−0.368960	+	0.639057i
$120$	−196.634	+	550.261i	−0.149584	+	0.418598i
$121$	−1535.10	−	2658.87i	−1.15334	−	1.99765i
$122$	−1246.78	−	2159.49i	−0.925231	−	1.60255i
$123$	436.547	−	1221.64i	0.320017	−	0.895539i
$124$	−994.899	+	1723.22i	−0.720521	+	1.24798i
$125$	125.000			0.0894427
$126$	2323.96	−	876.841i	1.64313	−	0.619962i
$127$	−864.662			−0.604144			−0.302072	−	0.953285i	$-0.597678\pi$
$127$	−864.662			−0.604144			−0.302072	+	0.953285i	$0.597678\pi$
$128$	−1167.48	+	2022.14i	−0.806187	+	1.39636i
$129$	1084.96	−	197.872i	0.740507	−	0.135052i
$130$	−535.116	−	926.848i	−0.361021	−	0.625307i
$131$	1089.26	+	1886.65i	0.726482	+	1.25830i	0.958361	+	0.285559i	$0.0921792\pi$
$131$	1089.26	+	1886.65i	0.726482	+	1.25830i	−0.231879	+	0.972745i	$0.574487\pi$
$132$	2882.27	+	3394.34i	1.90052	+	2.23818i
$133$	−100.098	+	173.374i	−0.0652599	+	0.113033i
$134$	2048.40			1.32056
$135$	613.574	+	340.004i	0.391170	+	0.216762i
$136$	1071.11			0.675343
$137$	1149.58	−	1991.13i	0.716900	−	1.24171i	−0.245322	−	0.969442i	$-0.578894\pi$
$137$	1149.58	−	1991.13i	0.716900	−	1.24171i	0.962222	−	0.272266i	$-0.0877730\pi$
$138$	−147.548	−	173.762i	−0.0910152	−	0.107185i
$139$	1066.98	+	1848.06i	0.651077	+	1.12770i	0.982862	+	0.184343i	$0.0590157\pi$
$139$	1066.98	+	1848.06i	0.651077	+	1.12770i	−0.331785	+	0.943355i	$0.607651\pi$
$140$	649.581	+	1125.11i	0.392140	+	0.679206i
$141$	−2431.67	+	443.481i	−1.45236	+	0.264878i
$142$	936.536	−	1622.13i	0.553467	−	0.958634i
$143$	−3104.83			−1.81565
$144$	9.93528	+	8.14012i	0.00574958	+	0.00471072i
$145$	−893.675			−0.511832
$146$	−819.924	+	1420.15i	−0.464777	+	0.805017i
$147$	107.700	−	301.390i	0.0604284	−	0.169103i
$148$	−1607.37	−	2784.04i	−0.892735	−	1.54626i
$149$	−875.309	−	1516.08i	−0.481263	−	0.833572i	0.518506	−	0.855074i	$-0.326488\pi$
$149$	−875.309	−	1516.08i	−0.481263	−	0.833572i	−0.999769	+	0.0215024i	$0.993155\pi$
$150$	−199.927	+	559.477i	−0.108826	+	0.304541i
$151$	−437.977	+	758.598i	−0.236040	+	0.408833i	−0.959574	−	0.281455i	$-0.909183\pi$
$151$	−437.977	+	758.598i	−0.236040	+	0.408833i	0.723534	+	0.690288i	$0.242516\pi$
$152$	223.850			0.119451
$153$	208.421	−	1268.83i	0.110130	−	0.670447i
$154$	6103.12			3.19353
$155$	−385.093	+	667.001i	−0.199558	+	0.345644i
$156$	3090.38	−	563.615i	1.58608	−	0.289265i
$157$	129.697	+	224.642i	0.0659298	+	0.114194i	0.897106	−	0.441815i	$-0.145665\pi$
$157$	129.697	+	224.642i	0.0659298	+	0.114194i	−0.831176	+	0.556009i	$0.812332\pi$
$158$	−1489.96	−	2580.69i	−0.750222	−	1.29942i
$159$	−1837.42	−	2163.86i	−0.916457	−	1.07928i
$160$	−455.264	+	788.540i	−0.224948	+	0.389622i
$161$	−192.939			−0.0944457
$162$	−2503.15	+	2202.44i	−1.21399	+	1.06815i
$163$	−1201.80			−0.577498			−0.288749	−	0.957405i	$-0.593239\pi$
$163$	−1201.80			−0.577498			−0.288749	+	0.957405i	$0.593239\pi$
$164$	−1612.54	+	2792.99i	−0.767792	+	1.32986i
$165$	1115.63	+	1313.84i	0.526375	+	0.619893i
$166$	−1859.49	−	3220.72i	−0.869422	−	1.50588i
$167$	839.452	+	1453.97i	0.388975	+	0.673724i	0.992312	−	0.123762i	$-0.0394960\pi$
$167$	839.452	+	1453.97i	0.388975	+	0.673724i	−0.603337	+	0.797486i	$0.706163\pi$
$168$	−2312.60	+	421.765i	−1.06203	+	0.193690i
$169$	3.35162	−	5.80518i	0.00152554	−	0.00264232i
$170$	1089.05			0.491329
$171$	43.5578	−	265.171i	0.0194792	−	0.118586i
$172$	−2741.70			−1.21542
$173$	−465.899	+	806.961i	−0.204749	+	0.354636i	−0.950053	−	0.312089i	$-0.898971\pi$
$173$	−465.899	+	806.961i	−0.204749	+	0.354636i	0.745303	+	0.666725i	$0.232305\pi$
$174$	1429.36	−	3999.92i	0.622754	−	1.74272i
$175$	251.432	+	435.493i	0.108608	+	0.188115i
$176$	15.7796	+	27.3311i	0.00675814	+	0.0117054i
$177$	−733.155	+	2051.67i	−0.311341	+	0.871259i
$178$	−459.644	+	796.127i	−0.193549	+	0.335237i
$179$	1023.40			0.427333			0.213667	−	0.976907i	$-0.431459\pi$
$179$	1023.40			0.427333			0.213667	+	0.976907i	$0.431459\pi$
$180$	−1348.94	−	1105.21i	−0.558578	−	0.457652i
$181$	2639.93			1.08411			0.542056	−	0.840342i	$-0.317646\pi$
$181$	2639.93			1.08411			0.542056	+	0.840342i	$0.317646\pi$
$182$	2152.72	−	3728.62i	0.876760	−	1.51859i
$183$	2787.02	−	508.289i	1.12581	−	0.205322i
$184$	107.868	+	186.833i	0.0432182	+	0.0748562i
$185$	−622.160	−	1077.61i	−0.247255	−	0.428258i
$186$	−2369.45	−	2790.42i	−0.934067	−	1.10002i
$187$	1579.70	−	2736.13i	0.617750	−	1.06997i
$188$	6144.84			2.38382
$189$	49.6230	+	2821.56i	0.0190981	+	1.08591i
$190$	227.599			0.0869039
$191$	406.640	−	704.322i	0.154050	−	0.266822i	−0.778663	−	0.627442i	$-0.784102\pi$
$191$	406.640	−	704.322i	0.154050	−	0.266822i	0.932713	+	0.360621i	$0.117435\pi$
$192$	−2788.40	−	3283.80i	−1.04810	−	1.23431i
$193$	407.121	+	705.154i	0.151840	+	0.262995i	0.931904	−	0.362705i	$-0.118147\pi$
$193$	407.121	+	705.154i	0.151840	+	0.262995i	−0.780064	+	0.625700i	$0.784813\pi$
$194$	576.612	+	998.720i	0.213393	+	0.369608i
$195$	1196.18	−	218.157i	0.439285	−	0.0801156i
$196$	−397.828	+	689.059i	−0.144981	+	0.251115i
$197$	4078.41			1.47500			0.737499	−	0.675348i	$-0.236006\pi$
$197$	4078.41			1.47500			0.737499	+	0.675348i	$0.236006\pi$
$198$	−7664.87	+	2891.99i	−2.75110	+	1.03800i
$199$	−1342.49			−0.478224			−0.239112	−	0.970992i	$-0.576856\pi$
$199$	−1342.49			−0.478224			−0.239112	+	0.970992i	$0.576856\pi$
$200$	281.140	−	486.949i	0.0993981	−	0.172163i
$201$	−783.129	+	2191.51i	−0.274814	+	0.769042i
$202$	99.7101	+	172.703i	0.0347306	+	0.0601551i
$203$	−1797.58	−	3113.51i	−0.621506	−	1.07648i
$204$	−1075.67	+	3010.15i	−0.369175	+	1.03310i
$205$	−624.161	+	1081.08i	−0.212650	+	0.368321i
$206$	6587.56			2.22805
$207$	242.311	−	91.4250i	0.0813613	−	0.0306980i
$208$	22.2634			0.00742159
$209$	330.141	−	571.821i	0.109265	−	0.189252i
$210$	−2351.33	+	428.829i	−0.772652	+	0.140914i
$211$	1477.49	+	2559.08i	0.482059	+	0.834950i	0.999788	−	0.0205943i	$-0.00655583\pi$
$211$	1477.49	+	2559.08i	0.482059	+	0.834950i	−0.517729	+	0.855545i	$0.673222\pi$
$212$	3528.55	+	6111.62i	1.14312	+	1.97994i
$213$	1377.41	+	1622.13i	0.443092	+	0.521814i
$214$	813.536	−	1409.09i	0.259870	−	0.450108i
$215$	−1061.22			−0.336627
$216$	2704.52	−	1625.52i	0.851940	−	0.512050i
$217$	−3098.39			−0.969273
$218$	−3481.66	+	6030.42i	−1.08169	+	1.87354i
$219$	−1205.90	−	1420.15i	−0.372089	−	0.438196i
$220$	−2142.44	−	3710.82i	−0.656561	−	1.13720i
$221$	−1114.40	−	1930.20i	−0.339198	−	0.587507i
$222$	5818.29	−	1061.12i	1.75900	−	0.320802i
$223$	−1753.43	+	3037.03i	−0.526539	+	0.911993i	0.472982	+	0.881072i	$0.343177\pi$
$223$	−1753.43	+	3037.03i	−0.526539	+	0.911993i	−0.999522	+	0.0309212i	$0.990156\pi$
$224$	−3662.97			−1.09260
$225$	−522.131	−	427.790i	−0.154705	−	0.126753i
$226$	3718.31			1.09442
$227$	−326.413	+	565.364i	−0.0954396	+	0.165306i	−0.909792	−	0.415064i	$-0.863759\pi$
$227$	−326.413	+	565.364i	−0.0954396	+	0.165306i	0.814352	+	0.580371i	$0.197092\pi$
$228$	−224.803	+	629.090i	−0.0652979	+	0.182730i
$229$	−2291.78	−	3969.47i	−0.661331	−	1.14546i	−0.980266	−	0.197682i	$-0.936659\pi$
$229$	−2291.78	−	3969.47i	−0.661331	−	1.14546i	0.318935	−	0.947776i	$-0.396675\pi$
$230$	109.675	+	189.962i	0.0314424	+	0.0544598i
$231$	−2333.30	+	6529.52i	−0.664588	+	1.85979i
$232$	−2009.98	+	3481.39i	−0.568801	+	0.985192i
$233$	317.527			0.0892785			0.0446392	−	0.999003i	$-0.485786\pi$
$233$	317.527			0.0892785			0.0446392	+	0.999003i	$0.485786\pi$
$234$	−936.765	+	5702.83i	−0.261702	+	1.59319i
$235$	2378.47			0.660230
$236$	2708.16	−	4690.67i	0.746975	−	1.29380i
$237$	3330.62	−	607.430i	0.912858	−	0.166485i
$238$	2190.56	+	3794.17i	0.596610	+	1.03336i
$239$	−928.835	−	1608.79i	−0.251386	−	0.435414i	0.712521	−	0.701650i	$-0.247553\pi$
$239$	−928.835	−	1608.79i	−0.251386	−	0.435414i	−0.963908	+	0.266236i	$0.914220\pi$
$240$	−7.99974	−	9.42101i	−0.00215159	−	0.00253385i
$241$	1633.47	−	2829.25i	0.436602	−	0.756217i	−0.560823	−	0.827936i	$-0.689515\pi$
$241$	1633.47	−	2829.25i	0.436602	−	0.756217i	0.997425	+	0.0717190i	$0.0228485\pi$
$242$	−14041.8			−3.72993
$243$	−1399.33	−	3520.06i	−0.369411	−	0.929266i
$244$	−7042.82			−1.84783
$245$	−153.986	+	266.712i	−0.0401544	+	0.0695495i
$246$	−3840.41	−	4522.72i	−0.995349	−	1.17219i
$247$	−232.898	−	403.390i	−0.0599956	−	0.103915i
$248$	1732.24	+	3000.33i	0.443538	+	0.768231i
$249$	4156.65	−	758.079i	1.05790	−	0.192937i
$250$	285.849	−	495.105i	0.0723147	−	0.125253i
$251$	−5641.37			−1.41865			−0.709323	−	0.704884i	$-0.750999\pi$
$251$	−5641.37			−1.41865			−0.709323	+	0.704884i	$0.750999\pi$
$252$	1137.15	−	6922.70i	0.284260	−	1.73051i
$253$	636.351			0.158131
$254$	−1977.30	+	3424.78i	−0.488452	+	0.846024i
$255$	−416.356	+	1165.13i	−0.102248	+	0.286131i
$256$	2023.31	+	3504.47i	0.493971	+	0.855584i
$257$	586.731	+	1016.25i	0.142410	+	0.246661i	0.928404	−	0.371574i	$-0.121182\pi$
$257$	586.731	+	1016.25i	0.142410	+	0.246661i	−0.785994	+	0.618234i	$0.787848\pi$
$258$	1697.34	−	4749.84i	0.409580	−	1.14617i
$259$	2502.89	−	4335.14i	0.600472	−	1.04005i
$260$	−3022.77			−0.721016
$261$	3732.92	+	3058.44i	0.885295	+	0.725336i
$262$	9963.64			2.34945
$263$	1448.98	−	2509.71i	0.339726	−	0.588423i	−0.644655	−	0.764474i	$-0.722999\pi$
$263$	1448.98	−	2509.71i	0.339726	−	0.588423i	0.984381	+	0.176051i	$0.0563323\pi$
$264$	7627.38	−	1391.06i	1.77815	−	0.324295i
$265$	1365.79	+	2365.61i	0.316602	+	0.548371i
$266$	457.804	+	792.940i	0.105526	+	0.182776i
$267$	−676.022	−	796.127i	−0.154951	−	0.182480i
$268$	2892.75	−	5010.40i	0.659340	−	1.14201i
$269$	2930.13			0.664138			0.332069	−	0.943255i	$-0.392253\pi$
$269$	2930.13			0.664138			0.332069	+	0.943255i	$0.392253\pi$
$270$	2749.81	−	1652.75i	0.619808	−	0.372530i
$271$	−668.881			−0.149932			−0.0749661	−	0.997186i	$-0.523885\pi$
$271$	−668.881			−0.149932			−0.0749661	+	0.997186i	$0.523885\pi$
$272$	−11.3274	+	19.6196i	−0.00252509	+	0.00437358i
$273$	3166.12	+	3728.62i	0.701912	+	0.826617i
$274$	−5257.70	−	9106.60i	−1.15923	−	2.00785i
$275$	−829.270	−	1436.34i	−0.181843	−	0.314961i
$276$	−633.389	+	115.516i	−0.138136	+	0.0251929i
$277$	316.315	−	547.874i	0.0686121	−	0.118840i	−0.829679	−	0.558241i	$-0.811476\pi$
$277$	316.315	−	547.874i	0.0686121	−	0.118840i	0.898291	+	0.439402i	$0.144810\pi$
$278$	9759.80			2.10559
$279$	3891.24	−	1468.18i	0.834991	−	0.315046i
$280$	2262.00			0.482787
$281$	1797.65	−	3113.62i	0.381633	−	0.661007i	−0.609663	−	0.792661i	$-0.708695\pi$
$281$	1797.65	−	3113.62i	0.381633	−	0.661007i	0.991296	+	0.131653i	$0.0420286\pi$
$282$	−3804.16	+	10645.6i	−0.803313	+	2.24800i
$283$	−252.184	−	436.796i	−0.0529710	−	0.0917485i	0.838324	−	0.545172i	$-0.183536\pi$
$283$	−252.184	−	436.796i	−0.0529710	−	0.0917485i	−0.891295	+	0.453424i	$0.850202\pi$
$284$	−2645.16	−	4581.55i	−0.552680	−	0.957270i
$285$	−87.0138	+	243.500i	−0.0180851	+	0.0506095i
$286$	−7100.08	+	12297.7i	−1.46796	+	2.54258i
$287$	−5021.88			−1.03286
$288$	4600.29	−	1735.71i	0.941232	−	0.355131i
$289$	−2645.02			−0.538372
$290$	−2043.65	+	3539.70i	−0.413817	+	0.716753i
$291$	−1288.94	+	235.074i	−0.259654	+	0.0473549i
$292$	2315.80	+	4011.08i	0.464116	+	0.803872i
$293$	−3099.25	−	5368.06i	−0.617953	−	1.07033i	−0.989859	−	0.142055i	$-0.954629\pi$
$293$	−3099.25	−	5368.06i	−0.617953	−	1.07033i	0.371906	−	0.928270i	$-0.378704\pi$
$294$	−947.467	−	1115.80i	−0.187950	−	0.221343i
$295$	1048.24	−	1815.61i	0.206885	−	0.358335i
$296$	−5597.26			−1.09910
$297$	−163.666	−	9306.02i	−0.0319760	−	1.81815i
$298$	−8006.60			−1.55641
$299$	224.457	−	388.770i	0.0434136	−	0.0751945i
$300$	1086.15	+	1279.12i	0.209029	+	0.246166i
$301$	−2134.60	−	3697.24i	−0.408759	−	0.707991i
$302$	2003.12	+	3469.51i	0.381678	+	0.661086i
$303$	−222.889	+	40.6500i	−0.0422596	+	0.00770719i
$304$	−2.36730	+	4.10029i	−0.000446626	+	0.000773578i
$305$	−2726.05			−0.511781
$306$	−4548.99	−	3727.06i	−0.849832	−	0.696281i
$307$	−1966.79			−0.365636			−0.182818	−	0.983147i	$-0.558522\pi$
$307$	−1966.79			−0.365636			−0.182818	+	0.983147i	$0.558522\pi$
$308$	8618.84	−	14928.3i	1.59449	−	2.76174i
$309$	−2518.51	+	7047.81i	−0.463666	+	1.29753i
$310$	1761.25	+	3050.58i	0.322686	+	0.558908i
$311$	1153.05	+	1997.15i	0.210237	+	0.364141i	0.951789	−	0.306755i	$-0.0992431\pi$
$311$	1153.05	+	1997.15i	0.210237	+	0.364141i	−0.741552	+	0.670896i	$0.765910\pi$
$312$	1840.51	−	5150.51i	0.333970	−	0.934584i
$313$	−5151.20	+	8922.14i	−0.930234	+	1.61121i	−0.147314	+	0.989090i	$0.547063\pi$
$313$	−5151.20	+	8922.14i	−0.930234	+	1.61121i	−0.782920	+	0.622122i	$0.786271\pi$
$314$	1186.36			0.213218
$315$	440.152	−	2679.55i	0.0787294	−	0.479288i
$316$	−8416.51			−1.49831
$317$	850.916	−	1473.83i	0.150764	−	0.261131i	−0.780745	−	0.624850i	$-0.785160\pi$
$317$	850.916	−	1473.83i	0.150764	−	0.261131i	0.931509	+	0.363719i	$0.118493\pi$
$318$	−12772.5	+	2329.41i	−2.25235	+	0.410777i
$319$	5928.78	+	10268.9i	1.04059	+	1.80235i
$320$	2072.67	+	3589.97i	0.362081	+	0.627142i
$321$	1196.51	+	1409.09i	0.208046	+	0.245008i
$322$	−441.212	+	764.201i	−0.0763596	+	0.132259i
$323$	473.983			0.0816506
$324$	1852.21	+	9233.01i	0.317595	+	1.58316i
$325$	−1170.02			−0.199695
$326$	−2748.26	+	4760.13i	−0.466908	+	0.808709i
$327$	−5120.66	−	6030.42i	−0.865973	−	1.01983i
$328$	2807.63	+	4862.95i	0.472638	+	0.818633i
$329$	4784.18	+	8286.44i	0.801703	+	1.38859i
$330$	7755.12	−	1414.36i	1.29365	−	0.235933i
$331$	4175.74	−	7232.60i	0.693413	−	1.20103i	−0.277300	−	0.960783i	$-0.589440\pi$
$331$	4175.74	−	7232.60i	0.693413	−	1.20103i	0.970713	−	0.240243i	$-0.0772271\pi$
$332$	−10503.9			−1.73637
$333$	−1089.14	+	6630.47i	−0.179233	+	1.09113i
$334$	7678.61			1.25795
$335$	1119.69	−	1939.36i	0.182613	−	0.316295i
$336$	16.7311	−	46.8205i	0.00271654	−	0.00760199i
$337$	3928.71	+	6804.73i	0.635046	+	1.09993i	0.986505	+	0.163729i	$0.0523523\pi$
$337$	3928.71	+	6804.73i	0.635046	+	1.09993i	−0.351459	+	0.936203i	$0.614314\pi$
$338$	−15.3289	−	26.5504i	−0.00246681	−	0.00427264i
$339$	−1421.56	+	3978.10i	−0.227753	+	0.637347i
$340$	1537.95	−	2663.81i	0.245315	−	0.424898i
$341$	10219.1			1.62286
$342$	−950.691	−	778.916i	−0.150314	−	0.123155i
$343$	5660.34			0.891048
$344$	−2386.82	+	4134.10i	−0.374095	+	0.647952i
$345$	−245.164	+	44.7124i	−0.0382586	+	0.00697750i
$346$	2130.83	+	3690.70i	0.331081	+	0.573449i
$347$	−606.088	−	1049.78i	−0.0937652	−	0.162406i	0.815327	−	0.579000i	$-0.196557\pi$
$347$	−606.088	−	1049.78i	−0.0937652	−	0.162406i	−0.909093	+	0.416594i	$0.863224\pi$
$348$	−7765.29	−	9144.91i	−1.19616	−	1.40867i
$349$	−699.332	+	1211.28i	−0.107262	+	0.185783i	−0.914660	−	0.404224i	$-0.867542\pi$
$349$	−699.332	+	1211.28i	−0.107262	+	0.185783i	0.807398	+	0.590007i	$0.200875\pi$
$350$	2299.89			0.351240
$351$	−5743.12	−	3182.47i	−0.873348	−	0.483954i
$352$	12081.2			1.82934
$353$	−1314.21	+	2276.28i	−0.198154	+	0.343214i	−0.947930	−	0.318479i	$-0.896828\pi$
$353$	−1314.21	+	2276.28i	−0.198154	+	0.343214i	0.749776	+	0.661692i	$0.230161\pi$
$354$	6449.75	+	7595.64i	0.968362	+	1.14041i
$355$	−1023.85	−	1773.37i	−0.153072	−	0.265128i
$356$	1298.22	+	2248.59i	0.193274	+	0.334761i
$357$	−4896.73	+	893.053i	−0.725946	+	0.132396i
$358$	2340.31	−	4053.53i	0.345500	−	0.598424i
$359$	3677.48			0.540640			0.270320	−	0.962770i	$-0.412870\pi$
$359$	3677.48			0.540640			0.270320	+	0.962770i	$0.412870\pi$
$360$	−2840.83	+	1071.86i	−0.415903	+	0.156922i
$361$	−6759.94			−0.985558
$362$	6036.96	−	10456.3i	0.876507	−	1.51815i
$363$	5368.36	−	15022.9i	0.776215	−	2.17217i
$364$	−6080.16	−	10531.1i	−0.875513	−	1.51643i
$365$	896.370	+	1552.56i	0.128543	+	0.222643i
$366$	4360.08	−	12201.3i	0.622692	−	1.74255i
$367$	−5714.88	+	9898.47i	−0.812846	+	1.40789i	0.0980185	+	0.995185i	$0.468750\pi$
$367$	−5714.88	+	9898.47i	−0.812846	+	1.40789i	−0.910864	+	0.412706i	$0.864584\pi$
$368$	−4.56301			−0.000646368
$369$	6306.94	−	2379.64i	0.889773	−	0.335715i
$370$	−5691.00			−0.799624
$371$	−5494.43	+	9516.63i	−0.768886	+	1.33175i
$372$	−10171.5	+	1855.05i	−1.41766	+	0.258549i
$373$	−1129.95	−	1957.13i	−0.156854	−	0.271679i	0.776879	−	0.629650i	$-0.216802\pi$
$373$	−1129.95	−	1957.13i	−0.156854	−	0.271679i	−0.933733	+	0.357971i	$0.883469\pi$
$374$	−7224.90	−	12513.9i	−0.998905	−	1.73015i
$375$	420.412	+	495.105i	0.0578933	+	0.0681789i
$376$	5349.47	−	9265.55i	0.733717	−	1.27084i
$377$	8364.90			1.14274
$378$	11289.2	+	6255.76i	1.53612	+	0.851221i
$379$	−11815.8			−1.60142			−0.800709	−	0.599053i	$-0.795544\pi$
$379$	−11815.8			−1.60142			−0.800709	+	0.599053i	$0.795544\pi$
$380$	321.415	−	556.708i	0.0433902	−	0.0751540i
$381$	−2908.12	−	3424.78i	−0.391043	−	0.460517i
$382$	−1859.80	−	3221.27i	−0.249099	−	0.431452i
$383$	4040.11	+	6997.68i	0.539008	+	0.933589i	0.998958	+	0.0456440i	$0.0145340\pi$
$383$	4040.11	+	6997.68i	0.539008	+	0.933589i	−0.459950	+	0.887945i	$0.652133\pi$
$384$	−11936.0	+	2176.85i	−1.58621	+	0.289289i
$385$	3336.07	−	5778.25i	0.441616	−	0.764901i
$386$	3724.00			0.491054
$387$	4432.78	+	3631.85i	0.582251	+	0.477047i
$388$	3257.17			0.426180
$389$	−1550.22	+	2685.05i	−0.202054	+	0.349968i	−0.949190	−	0.314703i	$-0.898095\pi$
$389$	−1550.22	+	2685.05i	−0.202054	+	0.349968i	0.747136	+	0.664671i	$0.231428\pi$
$390$	1871.34	−	5236.77i	0.242972	−	0.679934i
$391$	228.402	+	395.604i	0.0295417	+	0.0511677i
$392$	692.669	+	1199.74i	0.0892476	+	0.154581i
$393$	−3809.22	+	10659.8i	−0.488931	+	1.36823i
$394$	9326.47	−	16153.9i	1.19254	−	2.06554i
$395$	−3257.76			−0.414976
$396$	−3750.52	+	22832.4i	−0.475936	+	2.89740i
$397$	−11990.1			−1.51578			−0.757890	−	0.652382i	$-0.773770\pi$
$397$	−11990.1			−1.51578			−0.757890	+	0.652382i	$0.773770\pi$
$398$	−3069.99	+	5317.38i	−0.386645	+	0.669689i
$399$	−1023.36	+	186.638i	−0.128402	+	0.0234176i
$400$	5.94635	+	10.2994i	0.000743294	+	0.00128742i
$401$	−6426.63	−	11131.3i	−0.800326	−	1.38620i	−0.919402	−	0.393320i	$-0.871327\pi$
$401$	−6426.63	−	11131.3i	−0.800326	−	1.38620i	0.119076	−	0.992885i	$-0.462007\pi$
$402$	6889.38	+	8113.38i	0.854753	+	1.00661i
$403$	3604.52	−	6243.21i	0.445543	−	0.771703i
$404$	563.243			0.0693623
$405$	716.932	+	3573.80i	0.0879621	+	0.438478i
$406$	−16442.8			−2.00996
$407$	−8255.02	+	14298.1i	−1.00537	+	1.74135i
$408$	3602.45	+	4242.48i	0.437127	+	0.514789i
$409$	−1112.54	−	1926.98i	−0.134503	−	0.232966i	0.790904	−	0.611940i	$-0.209610\pi$
$409$	−1112.54	−	1926.98i	−0.134503	−	0.232966i	−0.925408	+	0.378974i	$0.876277\pi$
$410$	2854.65	+	4944.40i	0.343856	+	0.595576i
$411$	11752.9	−	2143.47i	1.41053	−	0.257249i
$412$	9302.97	−	16113.2i	1.11244	−	1.92680i
$413$	8433.95			1.00486
$414$	191.995	−	1168.82i	0.0227924	−	0.138755i
$415$	−4065.71			−0.480911
$416$	4261.32	−	7380.83i	0.502232	−	0.869891i
$417$	−3731.29	+	10441.7i	−0.438183	+	1.22621i
$418$	−1509.93	−	2615.27i	−0.176682	−	0.306021i
$419$	−4838.33	−	8380.23i	−0.564123	−	0.977090i	−0.997131	−	0.0756998i	$-0.975881\pi$
$419$	−4838.33	−	8380.23i	−0.564123	−	0.977090i	0.433007	−	0.901390i	$-0.357452\pi$
$420$	−2271.63	+	6356.95i	−0.263915	+	0.738542i
$421$	4981.30	−	8627.87i	0.576660	−	0.998804i	−0.419199	−	0.907894i	$-0.637689\pi$
$421$	4981.30	−	8627.87i	0.576660	−	0.998804i	0.995859	−	0.0909098i	$-0.0289775\pi$
$422$	13514.8			1.55898
$423$	−9934.98	−	8139.88i	−1.14197	−	0.935637i
$424$	12287.3			1.40737
$425$	595.291	−	1031.08i	0.0679432	−	0.117681i
$426$	9574.84	−	1746.23i	1.08897	−	0.198604i
$427$	−5483.32	−	9497.39i	−0.621444	−	1.07637i
$428$	−2297.76	−	3979.83i	−0.259500	−	0.449468i
$429$	−10442.5	−	12297.7i	−1.17521	−	1.38401i
$430$	−2426.80	+	4203.33i	−0.272164	+	0.471402i
$431$	−2461.47			−0.275092			−0.137546	−	0.990495i	$-0.543922\pi$
$431$	−2461.47			−0.275092			−0.137546	+	0.990495i	$0.543922\pi$
$432$	1.17358	+	66.7297i	0.000130704	+	0.00743179i
$433$	7818.49			0.867743			0.433871	−	0.900975i	$-0.357147\pi$
$433$	7818.49			0.867743			0.433871	+	0.900975i	$0.357147\pi$
$434$	−7085.36	+	12272.2i	−0.783660	+	1.35734i
$435$	−3005.69	−	3539.70i	−0.331292	−	0.390151i
$436$	9833.63	+	17032.3i	1.08015	+	1.87087i
$437$	47.7336	+	82.6770i	0.00522519	+	0.00905030i
$438$	−8382.64	+	1528.80i	−0.914470	+	0.166779i
$439$	−3105.91	+	5379.60i	−0.337670	+	0.584862i	−0.983994	−	0.178201i	$-0.942972\pi$
$439$	−3105.91	+	5379.60i	−0.337670	+	0.584862i	0.646324	+	0.763063i	$0.276306\pi$
$440$	−7460.51			−0.808332
$441$	1555.98	−	587.080i	0.168015	−	0.0633927i
$442$	−10193.6			−1.09697
$443$	−1492.17	+	2584.52i	−0.160034	+	0.277188i	−0.934881	−	0.354962i	$-0.884494\pi$
$443$	−1492.17	+	2584.52i	−0.160034	+	0.277188i	0.774846	+	0.632150i	$0.217827\pi$
$444$	5621.08	−	15730.1i	0.600822	−	1.68134i
$445$	502.499	+	870.355i	0.0535298	+	0.0927163i
$446$	8019.45	+	13890.1i	0.851417	+	1.47470i
$447$	3061.02	−	8565.99i	0.323896	−	0.906392i
$448$	−8338.16	+	14442.1i	−0.879333	+	1.52305i
$449$	−810.476			−0.0851865			−0.0425932	−	0.999092i	$-0.513562\pi$
$449$	−810.476			−0.0851865			−0.0425932	+	0.999092i	$0.513562\pi$
$450$	−2888.41	+	1089.81i	−0.302580	+	0.114165i
$451$	16563.1			1.72933
$452$	5251.01	−	9095.01i	0.546431	−	0.946446i
$453$	−4477.73	+	816.637i	−0.464420	+	0.0846996i
$454$	1492.88	+	2585.74i	0.154326	+	0.267301i
$455$	−2353.43	−	4076.26i	−0.242485	−	0.419996i
$456$	752.873	+	886.632i	0.0773169	+	0.0910534i
$457$	−785.887	+	1361.20i	−0.0804425	+	0.139331i	−0.903440	−	0.428714i	$-0.858967\pi$
$457$	−785.887	+	1361.20i	−0.0804425	+	0.139331i	0.822998	+	0.568045i	$0.192300\pi$
$458$	−20963.2			−2.13875
$459$	5726.59	−	3441.91i	0.582341	−	0.350010i
$460$	619.532			0.0627953
$461$	−1031.35	+	1786.34i	−0.104196	+	0.180474i	−0.913410	−	0.407042i	$-0.866560\pi$
$461$	−1031.35	+	1786.34i	−0.104196	+	0.180474i	0.809213	+	0.587515i	$0.199894\pi$
$462$	20526.6	+	24173.5i	2.06707	+	2.43431i
$463$	−1391.62	−	2410.35i	−0.139684	−	0.241940i	0.787693	−	0.616068i	$-0.211275\pi$
$463$	−1391.62	−	2410.35i	−0.139684	−	0.241940i	−0.927377	+	0.374128i	$0.877942\pi$
$464$	−42.5128	−	73.6344i	−0.00425347	−	0.00736722i
$465$	−3937.06	+	718.031i	−0.392639	+	0.0716084i
$466$	726.118	−	1257.67i	0.0721819	−	0.125023i
$467$	10939.7			1.08400			0.541999	−	0.840379i	$-0.317668\pi$
$467$	10939.7			1.08400			0.541999	+	0.840379i	$0.317668\pi$
$468$	12626.2	+	10344.9i	1.24711	+	1.02178i
$469$	9008.83			0.886970
$470$	5439.06	−	9420.72i	0.533798	−	0.924565i
$471$	−453.561	+	1269.25i	−0.0443716	+	0.124170i
$472$	−4715.24	−	8167.04i	−0.459823	−	0.796438i
$473$	7040.33	+	12194.2i	0.684386	+	1.18539i
$474$	5210.51	−	14581.1i	0.504908	−	1.41294i
$475$	124.409	−	215.484i	0.0120175	−	0.0208149i
$476$	12374.1			1.19152
$477$	2390.92	−	14555.4i	0.229503	−	1.39716i
$478$	−8496.21			−0.812986
$479$	−7311.85	+	12664.5i	−0.697467	+	1.20805i	0.271875	+	0.962333i	$0.412356\pi$
$479$	−7311.85	+	12664.5i	−0.697467	+	1.20805i	−0.969342	+	0.245716i	$0.920977\pi$
$480$	−4654.46	+	848.869i	−0.442596	+	0.0807195i
$481$	5823.49	+	10086.6i	0.552034	+	0.956151i
$482$	−7470.81	−	12939.8i	−0.705987	−	1.22281i
$483$	−648.913	−	764.201i	−0.0611316	−	0.0719925i
$484$	−19829.9	+	34346.4i	−1.86231	+	3.22562i
$485$	1260.74			0.118036
$486$	−17142.3	−	2507.13i	−1.59998	−	0.234003i
$487$	16473.6			1.53284			0.766419	−	0.642341i	$-0.222037\pi$
$487$	16473.6			1.53284			0.766419	+	0.642341i	$0.222037\pi$
$488$	−6131.22	+	10619.6i	−0.568744	+	0.985093i
$489$	−4042.01	−	4760.13i	−0.373795	−	0.440206i
$490$	704.270	+	1219.83i	0.0649299	+	0.112462i
$491$	−10264.6	−	17778.8i	−0.943450	−	1.63410i	−0.758825	−	0.651295i	$-0.774226\pi$
$491$	−10264.6	−	17778.8i	−0.943450	−	1.63410i	−0.184626	−	0.982809i	$-0.559107\pi$
$492$	−16486.0	+	3006.68i	−1.51067	+	0.275511i
$493$	−4255.97	+	7371.56i	−0.388802	+	0.673425i
$494$	−2130.35			−0.194026
$495$	−1451.71	+	8837.67i	−0.131817	+	0.802473i
$496$	−73.2768			−0.00663352
$497$	4118.87	−	7134.10i	0.371744	−	0.643879i
$498$	6502.76	−	18197.4i	0.585132	−	1.63744i
$499$	7202.31	+	12474.8i	0.646131	+	1.11913i	0.984039	+	0.177953i	$0.0569475\pi$
$499$	7202.31	+	12474.8i	0.646131	+	1.11913i	−0.337908	+	0.941179i	$0.609719\pi$
$500$	−807.352	−	1398.38i	−0.0722118	−	0.125075i
$501$	−2935.63	+	8215.08i	−0.261785	+	0.732580i
$502$	−12900.6	+	22344.5i	−1.14698	+	1.98663i
$503$	−2953.63			−0.261821			−0.130910	−	0.991394i	$-0.541790\pi$
$503$	−2953.63			−0.261821			−0.130910	+	0.991394i	$0.541790\pi$
$504$	−9448.49	−	7741.30i	−0.835058	−	0.684176i
$505$	218.013			0.0192108
$506$	1455.20	−	2520.48i	0.127849	−	0.221441i
$507$	34.2659	−	6.24932i	0.00300158	−	0.000547420i
$508$	5584.69	+	9672.98i	0.487757	+	0.844821i
$509$	8684.44	+	15041.9i	0.756250	+	1.30986i	0.944750	+	0.327790i	$0.106304\pi$
$509$	8684.44	+	15041.9i	0.756250	+	1.30986i	−0.188500	+	0.982073i	$0.560363\pi$
$510$	3662.78	+	4313.53i	0.318021	+	0.374522i
$511$	−3606.02	+	6245.80i	−0.312174	+	0.540701i
$512$	−172.223			−0.0148657
$513$	1196.80	−	719.323i	0.103002	−	0.0619082i
$514$	5366.92			0.460554
$515$	3600.88	−	6236.91i	0.308104	−	0.533652i
$516$	−9221.16	−	10859.4i	−0.786703	−	0.926473i
$517$	−15779.1	−	27330.3i	−1.34229	−	2.32492i
$518$	−11447.2	−	19827.1i	−0.970966	−	1.68176i
$519$	−4763.20	+	868.699i	−0.402854	+	0.0734714i
$520$	−2631.51	+	4557.90i	−0.221922	+	0.384379i
$521$	−6146.30			−0.516841			−0.258421	−	0.966033i	$-0.583202\pi$
$521$	−6146.30			−0.516841			−0.258421	+	0.966033i	$0.583202\pi$
$522$	20650.4	−	7791.48i	1.73150	−	0.653303i
$523$	−4554.68			−0.380807			−0.190404	−	0.981706i	$-0.560980\pi$
$523$	−4554.68			−0.380807			−0.190404	+	0.981706i	$0.560980\pi$
$524$	14070.7	−	24371.1i	1.17305	−	2.03179i
$525$	−879.275	+	2460.57i	−0.0730947	+	0.204549i
$526$	−6627.03	−	11478.4i	−0.549339	−	0.951483i
$527$	3667.88	+	6352.96i	0.303179	+	0.525122i
$528$	−55.1824	+	154.423i	−0.00454831	+	0.0127280i
$529$	6037.50	−	10457.3i	0.496219	−	0.859476i
$530$	12493.1			1.02389
$531$	−10592.1	+	3996.46i	−0.865649	+	0.326613i
$532$	2586.05			0.210751
$533$	5842.22	−	10119.0i	0.474774	−	0.822333i
$534$	−4699.25	+	857.037i	−0.380817	+	0.0694525i
$535$	−889.387	−	1540.46i	−0.0718720	−	0.124486i
$536$	−5036.64	−	8723.72i	−0.405877	−	0.702999i
$537$	3442.01	+	4053.53i	0.276599	+	0.325741i
$538$	6700.59	−	11605.8i	0.536957	−	0.930037i
$539$	4086.28			0.326547
$540$	−159.341	−	9060.07i	−0.0126980	−	0.722006i
$541$	18091.8			1.43776			0.718879	−	0.695135i	$-0.244655\pi$
$541$	18091.8			1.43776			0.718879	+	0.695135i	$0.244655\pi$
$542$	−1529.59	+	2649.33i	−0.121221	+	0.209960i
$543$	8878.86	+	10456.3i	0.701710	+	0.826379i
$544$	4336.23	+	7510.58i	0.341754	+	0.591936i
$545$	3806.28	+	6592.67i	0.299162	+	0.518163i
$546$	22008.7	−	4013.89i	1.72507	−	0.314613i
$547$	−7890.69	+	13667.1i	−0.616786	+	1.06830i	0.373283	+	0.927718i	$0.378232\pi$
$547$	−7890.69	+	13667.1i	−0.616786	+	1.06830i	−0.990068	+	0.140586i	$0.955101\pi$
$548$	−29699.7			−2.31516
$549$	11386.8	+	9329.41i	0.885206	+	0.725263i
$550$	−7585.46			−0.588082
$551$	−889.453	+	1540.58i	−0.0687694	+	0.119112i
$552$	−377.223	+	1055.62i	−0.0290864	+	0.0813956i
$553$	−6552.83	−	11349.8i	−0.503896	−	0.872774i
$554$	−1446.69	−	2505.75i	−0.110946	−	0.192164i
$555$	2175.74	−	6088.61i	0.166405	−	0.465670i
$556$	13782.8	−	23872.5i	1.05130	−	1.82090i
$557$	−13954.5			−1.06153			−0.530766	−	0.847519i	$-0.678096\pi$
$557$	−13954.5			−1.06153			−0.530766	+	0.847519i	$0.678096\pi$
$558$	3083.22	−	18770.0i	0.233913	−	1.42401i
$559$	9933.18			0.751572
$560$	−23.9216	+	41.4335i	−0.00180513	+	0.00312658i
$561$	16150.4	−	2945.46i	1.21545	−	0.221671i
$562$	−8221.69	−	14240.4i	−0.617102	−	1.06885i
$563$	6801.97	+	11781.4i	0.509181	+	0.881927i	0.999943	+	0.0106339i	$0.00338494\pi$
$563$	6801.97	+	11781.4i	0.509181	+	0.881927i	−0.490762	+	0.871293i	$0.663282\pi$
$564$	20666.9	+	24338.7i	1.54297	+	1.81710i
$565$	2032.50	−	3520.39i	0.151341	−	0.262131i
$566$	−2306.77			−0.171309
$567$	−11008.8	+	9686.28i	−0.815392	+	0.717435i
$568$	−9211.10			−0.680438
$569$	6229.30	−	10789.5i	0.458956	−	0.794935i	−0.539950	−	0.841697i	$-0.681557\pi$
$569$	6229.30	−	10789.5i	0.458956	−	0.794935i	0.998906	+	0.0467619i	$0.0148902\pi$
$570$	765.482	+	901.482i	0.0562500	+	0.0662437i
$571$	6728.56	+	11654.2i	0.493137	+	0.854139i	0.999969	−	0.00790629i	$-0.00251668\pi$
$571$	6728.56	+	11654.2i	0.493137	+	0.854139i	−0.506831	+	0.862045i	$0.669183\pi$
$572$	20053.5	+	34733.7i	1.46587	+	2.53897i
$573$	4157.36	−	758.207i	0.303100	−	0.0552785i
$574$	−11484.0	+	19890.8i	−0.835074	+	1.44639i
$575$	239.801			0.0173920
$576$	3628.38	−	22088.8i	0.262470	−	1.59786i
$577$	3722.70			0.268592			0.134296	−	0.990941i	$-0.457123\pi$
$577$	3722.70			0.268592			0.134296	+	0.990941i	$0.457123\pi$
$578$	−6048.61	+	10476.5i	−0.435275	+	0.753918i
$579$	−1423.73	+	3984.18i	−0.102190	+	0.285971i
$580$	5772.08	+	9997.54i	0.413229	+	0.715733i
$581$	−8177.99	−	14164.7i	−0.583959	−	1.01145i
$582$	−2016.45	+	5642.86i	−0.143616	+	0.401897i
$583$	18121.7	−	31387.7i	1.28735	−	2.22975i
$584$	8064.19			0.571401
$585$	4887.21	+	4004.17i	0.345404	+	0.282995i
$586$	−28349.3			−1.99847
$587$	8770.16	−	15190.4i	0.616667	−	1.06810i	−0.373423	−	0.927661i	$-0.621816\pi$
$587$	8770.16	−	15190.4i	0.616667	−	1.06810i	0.990090	−	0.140437i	$-0.0448506\pi$
$588$	−4067.27	+	741.777i	−0.285257	+	0.0520244i
$589$	766.548	+	1327.70i	0.0536249	+	0.0928810i
$590$	−4794.21	−	8303.82i	−0.334533	−	0.579429i
$591$	13716.9	+	16153.9i	0.954718	+	1.12434i
$592$	59.1933	−	102.526i	0.00410951	−	0.00711788i
$593$	−22350.6			−1.54777			−0.773886	−	0.633325i	$-0.781690\pi$
$593$	−22350.6			−1.54777			−0.773886	+	0.633325i	$0.781690\pi$
$594$	−37233.9	−	20632.7i	−2.57193	−	1.42520i
$595$	4789.60			0.330008
$596$	−11306.9	+	19584.2i	−0.777097	+	1.34597i
$597$	−4515.19	−	5317.38i	−0.309539	−	0.364533i
$598$	−1026.57	−	1778.07i	−0.0702000	−	0.121590i
$599$	1280.81	+	2218.43i	0.0873665	+	0.151323i	0.906397	−	0.422427i	$-0.138822\pi$
$599$	1280.81	+	2218.43i	0.0873665	+	0.151323i	−0.819031	+	0.573750i	$0.805488\pi$
$600$	2874.28	−	524.204i	0.195570	−	0.0356676i
$601$	−6692.51	+	11591.8i	−0.454232	+	0.786752i	−0.998644	−	0.0520656i	$-0.983420\pi$
$601$	−6692.51	+	11591.8i	−0.454232	+	0.786752i	0.544412	+	0.838818i	$0.316753\pi$
$602$	−19525.6			−1.32193
$603$	−11314.1	+	4268.87i	−0.764091	+	0.288295i
$604$	11315.3			0.762270
$605$	−7675.51	+	13294.4i	−0.515791	+	0.893377i
$606$	−348.693	+	975.786i	−0.0233741	+	0.0654103i
$607$	14314.3	+	24793.1i	0.957166	+	1.65786i	0.729331	+	0.684161i	$0.239831\pi$
$607$	14314.3	+	24793.1i	0.957166	+	1.65786i	0.227835	+	0.973700i	$0.426835\pi$
$608$	906.226	+	1569.63i	0.0604479	+	0.104699i
$609$	6286.29	−	17591.6i	0.418281	−	1.17052i
$610$	−6233.90	+	10797.4i	−0.413776	+	0.716681i
$611$	−22262.8			−1.47407
$612$	−15540.5	+	5863.50i	−1.02645	+	0.387284i
$613$	7188.12			0.473614			0.236807	−	0.971557i	$-0.423899\pi$
$613$	7188.12			0.473614			0.236807	+	0.971557i	$0.423899\pi$
$614$	−4497.63	+	7790.12i	−0.295618	+	0.512025i
$615$	−6381.21	+	1163.79i	−0.418399	+	0.0763064i
$616$	−15006.5	−	25992.0i	−0.981539	−	1.70008i
$617$	−7766.88	−	13452.6i	−0.506779	−	0.877767i	−0.999969	−	0.00784559i	$-0.997503\pi$
$617$	−7766.88	−	13452.6i	−0.506779	−	0.877767i	0.493190	−	0.869922i	$-0.335831\pi$
$618$	22155.9	+	26092.3i	1.44214	+	1.69836i
$619$	11079.9	−	19191.0i	0.719450	−	1.24612i	−0.241769	−	0.970334i	$-0.577728\pi$
$619$	11079.9	−	19191.0i	0.719450	−	1.24612i	0.961218	−	0.275789i	$-0.0889392\pi$
$620$	9948.99			0.644453
$621$	1177.08	+	652.265i	0.0760624	+	0.0421490i
$622$	10547.2			0.679908
$623$	−2021.51	+	3501.36i	−0.130000	+	0.225167i
$624$	74.8785	+	88.1818i	0.00480375	+	0.00565721i
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	23559.4	+	40806.1i	1.50419	+	2.60534i
$627$	3375.25	−	615.569i	0.214983	−	0.0392081i
$628$	1675.38	−	2901.85i	0.106457	−	0.184389i
$629$	−11851.7			−0.751287
$630$	−9606.74	−	7870.95i	−0.607526	−	0.497756i
$631$	−25582.8			−1.61400			−0.807002	−	0.590549i	$-0.798911\pi$
$631$	−25582.8			−1.61400			−0.807002	+	0.590549i	$0.798911\pi$
$632$	−7327.10	+	12690.9i	−0.461165	+	0.798761i
$633$	−5166.88	+	14459.0i	−0.324431	+	0.907891i
$634$	−3891.73	−	6740.68i	−0.243786	−	0.422250i
$635$	2161.65	+	3744.10i	0.135091	+	0.233984i
$636$	−12339.6	+	34531.2i	−0.769334	+	2.15291i
$637$	1441.33	−	2496.46i	0.0896510	−	0.155280i
$638$	54231.5			3.36527
$639$	−1792.34	+	10911.4i	−0.110961	+	0.675506i
$640$	11674.8			0.721076
$641$	−1905.34	+	3300.14i	−0.117405	+	0.203351i	−0.918738	−	0.394867i	$-0.870791\pi$
$641$	−1905.34	+	3300.14i	−0.117405	+	0.203351i	0.801334	+	0.598217i	$0.204124\pi$
$642$	8317.33	−	1516.89i	0.511306	−	0.0932507i
$643$	−13360.0	−	23140.3i	−0.819391	−	1.41923i	−0.906131	−	0.422996i	$-0.860978\pi$
$643$	−13360.0	−	23140.3i	−0.819391	−	1.41923i	0.0867402	−	0.996231i	$-0.472355\pi$
$644$	1246.16	+	2158.41i	0.0762509	+	0.132071i
$645$	−3569.21	−	4203.33i	−0.217888	−	0.256599i
$646$	1083.90	−	1877.37i	0.0660147	−	0.114341i
$647$	5114.23			0.310759			0.155380	−	0.987855i	$-0.450340\pi$
$647$	5114.23			0.310759			0.155380	+	0.987855i	$0.450340\pi$
$648$	15534.5	+	5245.03i	0.941750	+	0.317970i
$649$	−27816.8			−1.68244
$650$	−2675.58	+	4634.24i	−0.161454	+	0.279646i
$651$	−10420.8	−	12272.2i	−0.627378	−	0.738842i
$652$	7762.20	+	13444.5i	0.466244	+	0.807559i
$653$	4435.53	+	7682.56i	0.265813	+	0.460401i	0.967776	−	0.251812i	$-0.0810264\pi$
$653$	4435.53	+	7682.56i	0.265813	+	0.460401i	−0.701964	+	0.712213i	$0.747693\pi$
$654$	−35595.4	+	6491.79i	−2.12827	+	0.388148i
$655$	5446.30	−	9433.27i	0.324893	−	0.562730i
$656$	−118.767			−0.00706872
$657$	1569.17	−	9552.78i	0.0931799	−	0.567259i
$658$	43761.7			2.59272
$659$	12102.2	−	20961.7i	0.715382	−	1.23908i	−0.247430	−	0.968906i	$-0.579586\pi$
$659$	12102.2	−	20961.7i	0.715382	−	1.23908i	0.962812	−	0.270172i	$-0.0870805\pi$
$660$	7492.27	−	20966.4i	0.441873	−	1.23654i
$661$	−10689.8	−	18515.2i	−0.629023	−	1.08950i	−0.987748	−	0.156056i	$-0.950122\pi$
$661$	−10689.8	−	18515.2i	−0.629023	−	1.08950i	0.358726	−	0.933443i	$-0.383211\pi$
$662$	−19098.1	−	33078.9i	−1.12125	−	1.94207i
$663$	3897.14	−	10905.8i	0.228284	−	0.638832i
$664$	−9144.28	+	15838.4i	−0.534438	+	0.925674i
$665$	1000.98			0.0583702
$666$	23771.6	+	19476.4i	1.38308	+	1.13318i
$667$	−1714.43			−0.0995248
$668$	10843.7	−	18781.9i	0.628079	−	1.08787i
$669$	−17926.5	+	3269.38i	−1.03599	+	0.188941i
$670$	−5121.00	−	8869.83i	−0.295286	−	0.511450i
$671$	18085.0	+	31324.2i	1.04048	+	1.80217i
$672$	−12319.6	−	14508.4i	−0.707203	−	0.832849i
$673$	−14850.7	+	25722.1i	−0.850597	+	1.47328i	0.0300732	+	0.999548i	$0.490426\pi$
$673$	−14850.7	+	25722.1i	−0.850597	+	1.47328i	−0.880670	+	0.473730i	$0.842907\pi$
$674$	35936.6			2.05375
$675$	−61.6756	−	3506.86i	−0.00351688	−	0.199969i
$676$	−86.5900			−0.00492661
$677$	−1330.74	+	2304.91i	−0.0755459	+	0.130849i	−0.901324	−	0.433147i	$-0.857403\pi$
$677$	−1330.74	+	2304.91i	−0.0755459	+	0.130849i	0.825778	+	0.563996i	$0.190737\pi$
$678$	12505.8	+	14727.6i	0.708381	+	0.834235i
$679$	2535.93	+	4392.36i	0.143328	+	0.248252i
$680$	−2677.77	−	4638.03i	−0.151011	−	0.261559i
$681$	−3337.14	+	608.618i	−0.187782	+	0.0342471i
$682$	23368.9	−	40476.1i	1.31208	−	2.27259i
$683$	28698.1			1.60776			0.803882	−	0.594789i	$-0.202765\pi$
$683$	28698.1			1.60776			0.803882	+	0.594789i	$0.202765\pi$
$684$	−3247.80	+	1225.41i	−0.181554	+	0.0685010i
$685$	−11495.8			−0.641215
$686$	12944.0	−	22419.7i	0.720415	−	1.24780i
$687$	8014.51	−	22427.9i	0.445084	−	1.24553i
$688$	−50.4833	−	87.4396i	−0.00279747	−	0.00484535i
$689$	−12783.9	−	22142.4i	−0.706863	−	1.22432i
$690$	−383.541	+	1073.30i	−0.0211611	+	0.0592174i
$691$	−8412.62	+	14571.1i	−0.463142	+	0.802186i	−0.999116	−	0.0420492i	$-0.986611\pi$
$691$	−8412.62	+	14571.1i	−0.463142	+	0.802186i	0.535973	+	0.844235i	$0.319945\pi$
$692$	12036.6			0.661220
$693$	−33710.0	+	12718.9i	−1.84781	+	0.697189i
$694$	−5543.99			−0.303238
$695$	5334.88	−	9240.28i	0.291170	−	0.504322i
$696$	−20549.4	+	3747.74i	−1.11914	+	0.204106i
$697$	5944.92	+	10296.9i	0.323070	+	0.559574i
$698$	3198.45	+	5539.88i	0.173443	+	0.300412i
$699$	1067.94	+	1257.67i	0.0577870	+	0.0680537i
$700$	3247.90	−	5625.54i	0.175370	−	0.303750i
$701$	−998.795			−0.0538145			−0.0269073	−	0.999638i	$-0.508566\pi$
$701$	−998.795			−0.0538145			−0.0269073	+	0.999638i	$0.508566\pi$
$702$	−25738.6	+	15469.9i	−1.38382	+	0.831730i
$703$	−2476.88			−0.132884
$704$	27500.8	−	47632.9i	1.47227	−	2.55004i
$705$	7999.50	+	9420.72i	0.427345	+	0.503270i
$706$	6010.66	+	10410.8i	0.320417	+	0.554978i
$707$	438.523	+	759.545i	0.0233272	+	0.0404040i
$708$	27687.3	−	5049.54i	1.46971	−	0.268041i
$709$	−16626.9	+	28798.6i	−0.880727	+	1.52546i	−0.0301937	+	0.999544i	$0.509612\pi$
$709$	−16626.9	+	28798.6i	−0.880727	+	1.52546i	−0.850534	+	0.525921i	$0.823721\pi$
$710$	−9365.36			−0.495036
$711$	13607.8	+	11149.1i	0.717768	+	0.588078i
$712$	4520.73			0.237952
$713$	−738.765	+	1279.58i	−0.0388036	+	0.0672099i
$714$	−7660.56	+	21437.4i	−0.401526	+	1.12363i
$715$	7762.06	+	13444.3i	0.405993	+	0.703200i
$716$	−6609.97	−	11448.8i	−0.345009	−	0.597573i
$717$	3248.21	−	9089.81i	0.169186	−	0.473452i
$718$	8409.62	−	14565.9i	0.437109	−	0.757095i
$719$	1178.94			0.0611503			0.0305752	−	0.999532i	$-0.490266\pi$
$719$	1178.94			0.0611503			0.0305752	+	0.999532i	$0.490266\pi$
$720$	10.4096	−	63.3713i	0.000538809	−	0.00328015i
$721$	28972.0			1.49650
$722$	−15458.6	+	26775.0i	−0.796826	+	1.38014i
$723$	16700.1	−	3045.71i	0.859034	−	0.156668i
$724$	−17050.8	−	29532.9i	−0.875260	−	1.51600i
$725$	2234.19	+	3869.72i	0.114449	+	0.198232i
$726$	−47226.8	−	55617.4i	−2.41426	−	2.84319i
$727$	−6338.35	+	10978.3i	−0.323351	+	0.560061i	−0.981177	−	0.193109i	$-0.938143\pi$
$727$	−6338.35	+	10978.3i	−0.323351	+	0.560061i	0.657826	+	0.753170i	$0.271476\pi$
$728$	−21172.6			−1.07790
$729$	9236.02	−	17381.5i	0.469238	−	0.883072i
$730$	8199.24			0.415709
$731$	−5053.90	+	8753.61i	−0.255712	+	0.442906i
$732$	−23687.1	−	27895.5i	−1.19604	−	1.40853i
$733$	−4903.42	−	8492.98i	−0.247083	−	0.427961i	0.715632	−	0.698478i	$-0.246139\pi$
$733$	−4903.42	−	8492.98i	−0.247083	−	0.427961i	−0.962715	+	0.270517i	$0.912805\pi$
$734$	26137.5	+	45271.4i	1.31438	+	2.27657i
$735$	−1574.31	+	287.118i	−0.0790057	+	0.0144088i
$736$	−873.381	+	1512.74i	−0.0437408	+	0.0757613i
$737$	−29712.8			−1.48506
$738$	4997.30	−	30422.5i	0.249259	−	1.51744i
$739$	−29970.4			−1.49185			−0.745927	−	0.666028i	$-0.767993\pi$
$739$	−29970.4			−1.49185			−0.745927	+	0.666028i	$0.767993\pi$
$740$	−8036.84	+	13920.2i	−0.399243	+	0.691510i
$741$	814.460	−	2279.19i	0.0403778	−	0.112994i
$742$	25129.2	+	43525.1i	1.24329	+	2.15345i
$743$	−10848.8	−	18790.6i	−0.535670	−	0.927808i	−0.999131	−	0.0416904i	$-0.986726\pi$
$743$	−10848.8	−	18790.6i	−0.535670	−	0.927808i	0.463460	−	0.886118i	$-0.346608\pi$
$744$	−6057.78	+	16952.1i	−0.298507	+	0.835344i
$745$	−4376.55	+	7580.40i	−0.215227	+	0.372785i
$746$	−10335.8			−0.507267
$747$	16982.7	+	13914.2i	0.831812	+	0.681516i
$748$	−40812.1			−1.99497
$749$	3577.92	−	6197.14i	0.174545	−	0.302321i
$750$	2922.42	−	532.984i	0.142282	−	0.0259491i
$751$	−8512.10	−	14743.4i	−0.413596	−	0.716370i	0.581684	−	0.813415i	$-0.302394\pi$
$751$	−8512.10	−	14743.4i	−0.413596	−	0.716370i	−0.995280	+	0.0970452i	$0.969061\pi$
$752$	113.146	+	195.974i	0.00548670	+	0.00950324i
$753$	−18973.6	−	22344.5i	−0.918243	−	1.08138i
$754$	19128.8	−	33132.0i	0.923911	−	1.60026i
$755$	4379.77			0.211121
$756$	31244.2	−	18779.0i	1.50310	−	0.903422i
$757$	30745.2			1.47616			0.738080	−	0.674714i	$-0.235733\pi$
$757$	30745.2			1.47616			0.738080	+	0.674714i	$0.235733\pi$
$758$	−27020.3	+	46800.5i	−1.29475	+	2.24257i
$759$	2140.24	+	2520.48i	0.102353	+	0.120537i
$760$	−559.624	−	969.298i	−0.0267101	−	0.0462633i
$761$	−10748.3	−	18616.6i	−0.511992	−	0.886797i	−0.999903	−	0.0139035i	$-0.995574\pi$
$761$	−10748.3	−	18616.6i	−0.511992	−	0.886797i	0.487911	−	0.872893i	$-0.337759\pi$
$762$	−20215.3	+	3686.81i	−0.961052	+	0.175274i
$763$	−15312.3	+	26521.7i	−0.726530	+	1.25839i
$764$	−10505.7			−0.497489
$765$	−6015.23	+	2269.57i	−0.284289	+	0.107263i
$766$	36955.5			1.74316
$767$	−9811.66	+	16994.3i	−0.461902	+	0.800037i
$768$	−7075.65	+	19800.6i	−0.332449	+	0.930327i
$769$	−11028.7	−	19102.4i	−0.517174	−	0.895772i	−0.999801	−	0.0199457i	$-0.993651\pi$
$769$	−11028.7	−	19102.4i	−0.517174	−	0.895772i	0.482627	−	0.875826i	$-0.339683\pi$
$770$	−15257.8	−	26427.3i	−0.714095	−	1.23685i
$771$	−2051.84	+	5741.89i	−0.0958434	+	0.268209i
$772$	5259.04	−	9108.93i	0.245178	−	0.424660i
$773$	30155.8			1.40314			0.701570	−	0.712601i	$-0.252483\pi$
$773$	30155.8			1.40314			0.701570	+	0.712601i	$0.252483\pi$
$774$	24522.0	−	9252.26i	1.13879	−	0.429671i
$775$	3850.93			0.178490
$776$	2835.57	−	4911.35i	0.131174	−	0.227200i
$777$	25588.7	−	4666.81i	1.18146	−	0.215471i
$778$	7090.04	+	12280.3i	0.326723	+	0.565900i
$779$	1242.42	+	2151.94i	0.0571431	+	0.0989747i
$780$	−10166.5	−	11972.7i	−0.466689	−	0.549604i
$781$	−13584.8	+	23529.6i	−0.622411	+	1.07805i
$782$	2089.23			0.0955381
$783$	440.943	+	25071.9i	0.0201252	+	1.14431i
$784$	−29.3010			−0.00133478
$785$	648.487	−	1123.21i	0.0294847	−	0.0510690i
$786$	33510.7	+	39464.4i	1.52072	+	1.79090i
$787$	1624.36	+	2813.47i	0.0735733	+	0.127433i	0.900465	−	0.434929i	$-0.143226\pi$
$787$	1624.36	+	2813.47i	0.0735733	+	0.127433i	−0.826892	+	0.562361i	$0.809893\pi$
$788$	−26341.7	−	45625.2i	−1.19084	−	2.06260i
$789$	14813.9	−	2701.72i	0.668427	−	0.121906i
$790$	−7449.81	+	12903.4i	−0.335509	+	0.581119i
$791$	16353.1			0.735081
$792$	31162.9	+	25532.3i	1.39814	+	1.14552i
$793$	25516.1			1.14263
$794$	−27418.8	+	47490.8i	−1.22551	+	2.12265i
$795$	−4776.25	+	13365.9i	−0.213077	+	0.596277i
$796$	8670.90	+	15018.4i	0.386095	+	0.668737i
$797$	13855.1	+	23997.7i	0.615775	+	1.06655i	0.990248	+	0.139316i	$0.0444904\pi$
$797$	13855.1	+	23997.7i	0.615775	+	1.06655i	−0.374473	+	0.927238i	$0.622176\pi$
$798$	−1600.98	+	4480.18i	−0.0710199	+	0.198743i
$799$	11327.1	−	19619.0i	0.501530	−	0.868675i
$800$	4552.64			0.201200
$801$	879.667	−	5355.23i	0.0388034	−	0.236227i
$802$	−58785.4			−2.58826
$803$	11893.3	−	20599.8i	0.522673	−	0.905296i
$804$	29574.6	−	5393.73i	1.29728	−	0.236595i
$805$	482.348	+	835.452i	0.0211187	+	0.0365786i
$806$	−16485.6	−	28553.8i	−0.720445	−	1.24785i
$807$	9854.90	+	11605.8i	0.429875	+	0.506248i
$808$	490.338	−	849.290i	0.0213491	−	0.0369776i
$809$	−2244.10			−0.0975259			−0.0487630	−	0.998810i	$-0.515528\pi$
$809$	−2244.10			−0.0975259			−0.0487630	+	0.998810i	$0.515528\pi$
$810$	15794.7	+	5332.88i	0.685147	+	0.231331i
$811$	−2739.73			−0.118625			−0.0593126	−	0.998239i	$-0.518891\pi$
$811$	−2739.73			−0.118625			−0.0593126	+	0.998239i	$0.518891\pi$
$812$	−23220.6	+	40219.2i	−1.00355	+	1.73820i
$813$	−2249.65	−	2649.33i	−0.0970462	−	0.114288i
$814$	37755.0	+	65393.5i	1.62569	+	2.81578i
$815$	3004.50	+	5203.94i	0.129132	+	0.223664i
$816$	−115.808	+	21.1207i	−0.00496823	+	0.000906092i
$817$	−1056.21	+	1829.41i	−0.0452290	+	0.0783390i
$818$	−10176.6			−0.434984
$819$	−4119.88	+	25080.9i	−0.175776	+	1.07008i
$820$	16125.4			0.686734
$821$	8616.06	−	14923.5i	0.366264	−	0.634388i	−0.622714	−	0.782449i	$-0.713970\pi$
$821$	8616.06	−	14923.5i	0.366264	−	0.634388i	0.988978	+	0.148062i	$0.0473034\pi$
$822$	18386.6	−	51453.1i	0.780177	−	2.18325i
$823$	−9642.94	−	16702.1i	−0.408422	−	0.707409i	0.586291	−	0.810101i	$-0.300588\pi$
$823$	−9642.94	−	16702.1i	−0.408422	−	0.707409i	−0.994713	+	0.102692i	$0.967254\pi$
$824$	−16197.6	−	28055.1i	−0.684795	−	1.18610i
$825$	2900.02	−	8115.43i	0.122383	−	0.342476i
$826$	19286.7	−	33405.5i	0.812433	−	1.40717i
$827$	26379.4			1.10919			0.554595	−	0.832120i	$-0.312873\pi$
$827$	26379.4			1.10919			0.554595	+	0.832120i	$0.312873\pi$
$828$	−2587.82	−	2120.24i	−0.108615	−	0.0889896i
$829$	−8718.15			−0.365252			−0.182626	−	0.983182i	$-0.558460\pi$
$829$	−8718.15			−0.365252			−0.182626	+	0.983182i	$0.558460\pi$
$830$	−9297.43	+	16103.6i	−0.388818	+	0.673452i
$831$	3233.90	−	589.790i	0.134997	−	0.0246205i
$832$	−19400.4	−	33602.6i	−0.808401	−	1.40019i
$833$	1466.67	+	2540.35i	0.0610049	+	0.105664i
$834$	32825.1	+	38657.0i	1.36288	+	1.60501i
$835$	4197.26	−	7269.87i	0.173955	−	0.301299i
$836$	−8529.28			−0.352860
$837$	18902.6	+	10474.6i	0.780610	+	0.432565i
$838$	−44256.9			−1.82438
$839$	6738.10	−	11670.7i	0.277265	−	0.480236i	−0.693439	−	0.720515i	$-0.743905\pi$
$839$	6738.10	−	11670.7i	0.277265	−	0.480236i	0.970704	+	0.240279i	$0.0772388\pi$
$840$	7607.79	+	8959.42i	0.312492	+	0.368011i
$841$	−3778.58	−	6544.70i	−0.154930	−	0.268346i
$842$	−22782.4	−	39460.2i	−0.932462	−	1.61507i
$843$	18378.6	−	3351.83i	0.750880	−	0.136943i
$844$	19085.6	−	33057.3i	0.778383	−	1.34820i
$845$	−33.5162			−0.00136449
$846$	−54959.9	+	20736.6i	−2.23352	+	0.842718i
$847$	−61755.7			−2.50526
$848$	−129.943	+	225.068i	−0.00526210	+	0.00911423i
$849$	881.907	−	2467.93i	0.0356501	−	0.0997636i
$850$	−2722.61	−	4715.70i	−0.109865	−	0.190291i
$851$	−1193.56	−	2067.30i	−0.0480783	−	0.0832740i
$852$	9250.31	−	25886.1i	0.371960	−	1.04090i
$853$	14118.3	−	24453.6i	0.566708	−	0.981567i	−0.430181	−	0.902743i	$-0.641550\pi$
$853$	14118.3	−	24453.6i	0.566708	−	0.981567i	0.996889	−	0.0788242i	$-0.0251166\pi$
$854$	−50156.8			−2.00975
$855$	−1257.12	+	474.316i	−0.0502837	+	0.0189722i
$856$	−8001.36			−0.319487
$857$	−4229.08	+	7324.98i	−0.168568	+	0.291968i	−0.937917	−	0.346861i	$-0.887248\pi$
$857$	−4229.08	+	7324.98i	−0.168568	+	0.291968i	0.769349	+	0.638829i	$0.220581\pi$
$858$	−72588.9	+	13238.6i	−2.88828	+	0.526757i
$859$	11527.2	+	19965.6i	0.457860	+	0.793036i	0.998848	−	0.0479940i	$-0.0152828\pi$
$859$	11527.2	+	19965.6i	0.457860	+	0.793036i	−0.540988	+	0.841030i	$0.681950\pi$
$860$	6854.25	+	11871.9i	0.271777	+	0.470731i
$861$	−16890.1	−	19890.8i	−0.668539	−	0.787315i
$862$	−5628.86	+	9749.48i	−0.222413	+	0.385230i
$863$	−42314.4			−1.66906			−0.834529	−	0.550963i	$-0.814260\pi$
$863$	−42314.4			−1.66906			−0.834529	+	0.550963i	$0.814260\pi$
$864$	22347.0	+	12383.3i	0.879932	+	0.487602i
$865$	4658.99			0.183133
$866$	17879.2	−	30967.8i	0.701572	−	1.21516i
$867$	−8895.99	−	10476.5i	−0.348470	−	0.410381i
$868$	20011.9	+	34661.7i	0.782545	+	1.35541i
$869$	21612.5	+	37433.9i	0.843674	+	1.46129i
$870$	−20893.6	+	3810.51i	−0.814205	+	0.148492i
$871$	−10480.4	+	18152.7i	−0.407711	+	0.706176i
$872$	34243.1			1.32984
$873$	−5266.19	−	4314.67i	−0.204162	−	0.167273i
$874$	436.627			0.0168983
$875$	1257.16	−	2177.46i	0.0485711	−	0.0841276i
$876$	−8098.51	+	22663.0i	−0.312356	+	0.874098i
$877$	5090.00	+	8816.15i	0.195983	+	0.339453i	0.947222	−	0.320577i	$-0.103877\pi$
$877$	5090.00	+	8816.15i	0.195983	+	0.339453i	−0.751239	+	0.660030i	$0.770544\pi$
$878$	14205.2	+	24604.0i	0.546014	+	0.945725i
$879$	10838.3	−	30330.0i	0.415890	−	1.16383i
$880$	78.8980	−	136.655i	0.00302233	−	0.00523483i
$881$	6030.64			0.230621			0.115311	−	0.993329i	$-0.463214\pi$
$881$	6030.64			0.230621			0.115311	+	0.993329i	$0.463214\pi$
$882$	1232.88	−	7505.53i	0.0470673	−	0.286535i
$883$	−30238.0			−1.15242			−0.576211	−	0.817301i	$-0.695469\pi$
$883$	−30238.0			−1.15242			−0.576211	+	0.817301i	$0.695469\pi$
$884$	−14395.4	+	24933.6i	−0.547704	+	0.948651i
$885$	10716.9	−	1954.51i	0.407055	−	0.0742376i
$886$	6824.57	+	11820.5i	0.258776	+	0.448214i
$887$	−9388.09	−	16260.7i	−0.355379	−	0.615535i	0.631804	−	0.775129i	$-0.282315\pi$
$887$	−9388.09	−	16260.7i	−0.355379	−	0.615535i	−0.987183	+	0.159594i	$0.948982\pi$
$888$	−18825.2	−	22169.8i	−0.711412	−	0.837805i
$889$	−8696.14	+	15062.1i	−0.328075	+	0.568243i
$890$	4596.44			0.173116
$891$	36309.2	−	31947.2i	1.36521	−	1.20120i
$892$	45300.3			1.70041
$893$	2367.23	−	4100.17i	0.0887082	−	0.153647i
$894$	−26928.6	−	31712.8i	−1.00741	−	1.18639i
$895$	−2558.51	−	4431.46i	−0.0955547	−	0.165506i
$896$	23483.4	+	40674.4i	0.875586	+	1.51656i
$897$	2294.77	−	418.514i	0.0854182	−	0.0155783i
$898$	−1853.39	+	3210.16i	−0.0688735	+	0.119292i
$899$	−27531.8			−1.02140
$900$	−1413.34	+	8604.10i	−0.0523459	+	0.318670i
$901$	26017.3			0.962000
$902$	37876.4	−	65603.8i	1.39817	−	2.42169i
$903$	7464.86	−	20889.7i	0.275100	−	0.769841i
$904$	−9142.66	−	15835.6i	−0.336372	−	0.582614i
$905$	−6599.82	−	11431.2i	−0.242415	−	0.419875i
$906$	−7005.07	+	19603.0i	−0.256874	+	0.718838i
$907$	18826.3	−	32608.1i	0.689213	−	1.19375i	−0.282880	−	0.959155i	$-0.591290\pi$
$907$	18826.3	−	32608.1i	0.689213	−	1.19375i	0.972093	−	0.234597i	$-0.0753769\pi$
$908$	8432.97			0.308214
$909$	−910.651	−	746.111i	−0.0332282	−	0.0272243i
$910$	−21527.2			−0.784198
$911$	23793.1	−	41210.8i	0.865312	−	1.49877i	−0.00142411	−	0.999999i	$-0.500453\pi$
$911$	23793.1	−	41210.8i	0.865312	−	1.49877i	0.866737	−	0.498766i	$-0.166213\pi$
$912$	−24.2025	+	4.41399i	−0.000878756	+	0.000160265i
$913$	26972.6	+	46717.9i	0.977724	+	1.69347i
$914$	3594.32	+	6225.54i	0.130076	+	0.225298i
$915$	−9168.51	−	10797.4i	−0.331259	−	0.390112i
$916$	−29604.3	+	51276.2i	−1.06785	+	1.84958i
$917$	43819.9			1.57804
$918$	−537.340	−	30553.0i	−0.0193190	−	1.09848i
$919$	32177.3			1.15499			0.577493	−	0.816396i	$-0.304031\pi$
$919$	32177.3			1.15499			0.577493	+	0.816396i	$0.304031\pi$
$920$	539.341	−	934.167i	0.0193278	−	0.0334767i
$921$	−6614.88	−	7790.12i	−0.236664	−	0.278711i
$922$	4716.94	+	8169.99i	0.168486	+	0.291827i
$923$	9583.40	+	16598.9i	0.341757	+	0.591940i
$924$	88116.2	−	16070.4i	3.13724	−	0.572161i
$925$	−3110.80	+	5388.07i	−0.110576	+	0.191523i
$926$	−12729.3			−0.451741
$927$	−36385.7	+	13728.5i	−1.28917	+	0.486411i
$928$	−32548.6			−1.15136
$929$	−20321.8	+	35198.4i	−0.717694	+	1.24308i	0.244218	+	0.969720i	$0.421469\pi$
$929$	−20321.8	+	35198.4i	−0.717694	+	1.24308i	−0.961911	+	0.273362i	$0.911864\pi$
$930$	−6159.24	+	17236.1i	−0.217171	+	0.607734i
$931$	306.518	+	530.905i	0.0107903	+	0.0186893i
$932$	−2050.85	−	3552.18i	−0.0720792	−	0.124845i
$933$	−4032.31	+	11284.1i	−0.141492	+	0.395952i
$934$	25016.7	−	43330.2i	0.876415	−	1.51799i
$935$	−15797.0			−0.552533
$936$	26590.5	−	10032.7i	0.928567	−	0.350352i
$937$	6077.87			0.211905			0.105953	−	0.994371i	$-0.466211\pi$
$937$	6077.87			0.211905			0.105953	+	0.994371i	$0.466211\pi$
$938$	20601.3	−	35682.5i	0.717118	−	1.24208i
$939$	−52664.2	+	9604.75i	−1.83028	+	0.333801i
$940$	−15362.1	−	26607.9i	−0.533039	−	0.923250i
$941$	−732.293	−	1268.37i	−0.0253688	−	0.0439401i	0.853062	−	0.521809i	$-0.174743\pi$
$941$	−732.293	−	1268.37i	−0.0253688	−	0.0439401i	−0.878431	+	0.477869i	$0.841409\pi$
$942$	3990.09	+	4698.99i	0.138009	+	0.162528i
$943$	−1197.39	+	2073.95i	−0.0413494	+	0.0716193i
$944$	199.463			0.00687707
$945$	12093.6	−	7268.76i	0.416303	−	0.250215i
$946$	64399.0			2.21331
$947$	5304.36	−	9187.43i	0.182015	−	0.315260i	−0.760551	−	0.649278i	$-0.775071\pi$
$947$	5304.36	−	9187.43i	0.182015	−	0.315260i	0.942567	+	0.334018i	$0.108405\pi$
$948$	−28307.2	−	33336.4i	−0.969806	−	1.14211i
$949$	−8390.14	−	14532.1i	−0.286992	−	0.497085i
$950$	−568.997	−	985.531i	−0.0194323	−	0.0336577i
$951$	8699.48	−	1586.59i	0.296635	−	0.0540995i
$952$	10772.4	−	18658.4i	0.366739	−	0.635211i
$953$	−43623.4			−1.48279			−0.741396	−	0.671068i	$-0.765836\pi$
$953$	−43623.4			−1.48279			−0.741396	+	0.671068i	$0.765836\pi$
$954$	−52184.1	−	42755.3i	−1.77099	−	1.45100i
$955$	−4066.40			−0.137786
$956$	−11998.4	+	20781.8i	−0.405915	+	0.703065i
$957$	−20733.4	+	58020.4i	−0.700329	+	1.95981i
$958$	33441.3	+	57922.1i	1.12781	+	1.95342i
$959$	−23123.3	−	40050.7i	−0.778613	−	1.34860i
$960$	−7248.28	+	20283.7i	−0.243685	+	0.681929i
$961$	3031.76	−	5251.17i	0.101768	−	0.176267i
$962$	53268.4			1.78528
$963$	−1556.95	+	9478.35i	−0.0520996	+	0.317171i
$964$	−42201.2			−1.40997
$965$	2035.61	−	3525.77i	0.0679051	−	0.117615i
$966$	−4510.80	+	822.668i	−0.150241	+	0.0274005i
$967$	−2540.19	−	4399.73i	−0.0844745	−	0.146314i	0.820693	−	0.571370i	$-0.193588\pi$
$967$	−2540.19	−	4399.73i	−0.0844745	−	0.146314i	−0.905167	+	0.425056i	$0.860254\pi$
$968$	34526.3	+	59801.3i	1.14640	+	1.98563i
$969$	1594.15	+	1877.37i	0.0528497	+	0.0622393i
$970$	2883.06	−	4993.60i	0.0954324	−	0.165294i
$971$	9875.60			0.326388			0.163194	−	0.986594i	$-0.447820\pi$
$971$	9875.60			0.326388			0.163194	+	0.986594i	$0.447820\pi$
$972$	−30340.9	+	38389.7i	−1.00122	+	1.26682i
$973$	42923.4			1.41425
$974$	37671.8	−	65249.4i	1.23930	−	2.14654i
$975$	−3935.11	−	4634.24i	−0.129256	−	0.152220i
$976$	−129.680	−	224.613i	−0.00425304	−	0.00736648i
$977$	−12290.4	−	21287.6i	−0.402461	−	0.697084i	0.591561	−	0.806260i	$-0.298512\pi$
$977$	−12290.4	−	21287.6i	−0.402461	−	0.697084i	−0.994022	+	0.109177i	$0.965179\pi$
$978$	−28097.3	+	5124.31i	−0.918664	+	0.167543i
$979$	6667.32	−	11548.1i	0.217659	−	0.376997i
$980$	3978.28			0.129675
$981$	6663.21	−	40564.2i	0.216860	−	1.32020i
$982$	−93891.8			−3.05113
$983$	15930.3	−	27592.1i	0.516885	−	0.895270i	−0.482923	−	0.875663i	$-0.660425\pi$
$983$	15930.3	−	27592.1i	0.516885	−	0.895270i	0.999808	−	0.0196076i	$-0.00624168\pi$
$984$	−9818.48	+	27476.1i	−0.318091	+	0.890149i
$985$	−10196.0	−	17660.0i	−0.329820	−	0.571265i
$986$	19465.0	+	33714.4i	0.628695	+	1.08893i
$987$	−16730.6	+	46819.1i	−0.539556	+	1.50990i
$988$	−3008.49	+	5210.85i	−0.0968752	+	0.167793i
$989$	−2035.86			−0.0654566
$990$	31684.8	+	25959.9i	1.01718	+	0.833393i
$991$	−36921.3			−1.18350			−0.591748	−	0.806123i	$-0.701562\pi$
$991$	−36921.3			−1.18350			−0.591748	+	0.806123i	$0.701562\pi$
$992$	−14025.5	+	24292.9i	−0.448902	+	0.777520i
$993$	42691.4	−	7785.95i	1.36432	−	0.248821i
$994$	−18838.0	−	32628.4i	−0.601112	−	1.04116i
$995$	3356.22	+	5813.15i	0.106934	+	0.185215i
$996$	−35327.7	−	41604.2i	−1.12390	−	1.32357i
$997$	1867.06	−	3233.84i	0.0593083	−	0.102725i	−0.834847	−	0.550482i	$-0.814444\pi$
$997$	1867.06	−	3233.84i	0.0593083	−	0.102725i	0.894155	+	0.447757i	$0.147777\pi$
$998$	65880.7			2.08959
$999$	−29925.3	+	17986.3i	−0.947743	+	0.569632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.e.b.16.3	✓	6
3.2	odd	2		135.4.e.b.46.1		6
5.2	odd	4		225.4.k.c.124.6		12
5.3	odd	4		225.4.k.c.124.1		12
5.4	even	2		225.4.e.c.151.1		6
9.2	odd	6		405.4.a.j.1.3		3
9.4	even	3	inner	45.4.e.b.31.3	yes	6
9.5	odd	6		135.4.e.b.91.1		6
9.7	even	3		405.4.a.h.1.1		3
45.4	even	6		225.4.e.c.76.1		6
45.13	odd	12		225.4.k.c.49.6		12
45.22	odd	12		225.4.k.c.49.1		12
45.29	odd	6		2025.4.a.q.1.1		3
45.34	even	6		2025.4.a.s.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.b.16.3	✓	6	1.1	even	1	trivial
45.4.e.b.31.3	yes	6	9.4	even	3	inner
135.4.e.b.46.1		6	3.2	odd	2
135.4.e.b.91.1		6	9.5	odd	6
225.4.e.c.76.1		6	45.4	even	6
225.4.e.c.151.1		6	5.4	even	2
225.4.k.c.49.1		12	45.22	odd	12
225.4.k.c.49.6		12	45.13	odd	12
225.4.k.c.124.1		12	5.3	odd	4
225.4.k.c.124.6		12	5.2	odd	4
405.4.a.h.1.1		3	9.7	even	3
405.4.a.j.1.3		3	9.2	odd	6
2025.4.a.q.1.1		3	45.29	odd	6
2025.4.a.s.1.3		3	45.34	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.28679 - 3.96084i) q^{2} +(3.36330 + 3.96084i) q^{3} +(-6.45882 - 11.1870i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(23.3794 - 4.26387i) q^{6} +(10.0573 - 17.4197i) q^{7} -22.4912 q^{8} +(-4.37646 + 26.6429i) q^{9} +O(q^{10})\)	\(q+(2.28679 - 3.96084i) q^{2} +(3.36330 + 3.96084i) q^{3} +(-6.45882 - 11.1870i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(23.3794 - 4.26387i) q^{6} +(10.0573 - 17.4197i) q^{7} -22.4912 q^{8} +(-4.37646 + 26.6429i) q^{9} -22.8679 q^{10} +(-33.1708 + 57.4535i) q^{11} +(22.5870 - 63.2076i) q^{12} +(23.4003 + 40.5305i) q^{13} +(-45.9977 - 79.6704i) q^{14} +(8.74268 - 24.4656i) q^{15} +(0.237854 - 0.411975i) q^{16} -47.6233 q^{17} +(95.5203 + 78.2613i) q^{18} -9.95276 q^{19} +(-32.2941 + 55.9350i) q^{20} +(102.822 - 18.7524i) q^{21} +(151.709 + 262.768i) q^{22} +(-4.79602 - 8.30695i) q^{23} +(-75.6447 - 89.0841i) q^{24} +(-12.5000 + 21.6506i) q^{25} +214.046 q^{26} +(-120.248 + 72.2737i) q^{27} -259.832 q^{28} +(89.3675 - 154.789i) q^{29} +(-76.9116 - 90.5760i) q^{30} +(-77.0186 - 133.400i) q^{31} +(-91.0527 - 157.708i) q^{32} +(-339.127 + 61.8491i) q^{33} +(-108.905 + 188.628i) q^{34} -100.573 q^{35} +(326.322 - 123.123i) q^{36} +248.864 q^{37} +(-22.7599 + 39.4213i) q^{38} +(-81.8326 + 229.001i) q^{39} +(56.2280 + 97.3898i) q^{40} +(-124.832 - 216.216i) q^{41} +(160.857 - 450.145i) q^{42} +(106.122 - 183.809i) q^{43} +856.976 q^{44} +(126.308 - 47.6567i) q^{45} -43.8700 q^{46} +(-237.847 + 411.963i) q^{47} +(2.43174 - 0.443494i) q^{48} +(-30.7973 - 53.3425i) q^{49} +(57.1698 + 99.0209i) q^{50} +(-160.171 - 188.628i) q^{51} +(302.277 - 523.559i) q^{52} -546.314 q^{53} +(11.2831 + 641.556i) q^{54} +331.708 q^{55} +(-226.200 + 391.790i) q^{56} +(-33.4741 - 39.4213i) q^{57} +(-408.729 - 707.940i) q^{58} +(209.648 + 363.121i) q^{59} +(-330.164 + 60.2145i) q^{60} +(272.605 - 472.165i) q^{61} -704.502 q^{62} +(420.097 + 344.192i) q^{63} -829.068 q^{64} +(117.002 - 202.653i) q^{65} +(-530.538 + 1484.66i) q^{66} +(223.938 + 387.872i) q^{67} +(307.590 + 532.762i) q^{68} +(16.7720 - 46.9350i) q^{69} +(-229.989 + 398.352i) q^{70} +409.542 q^{71} +(98.4319 - 599.232i) q^{72} -358.548 q^{73} +(569.100 - 985.710i) q^{74} +(-127.796 + 23.3071i) q^{75} +(64.2831 + 111.342i) q^{76} +(667.215 + 1155.65i) q^{77} +(719.902 + 847.803i) q^{78} +(325.776 - 564.260i) q^{79} -2.37854 q^{80} +(-690.693 - 233.204i) q^{81} -1141.86 q^{82} +(406.571 - 704.202i) q^{83} +(-873.893 - 1029.15i) q^{84} +(119.058 + 206.215i) q^{85} +(-485.359 - 840.667i) q^{86} +(913.663 - 166.631i) q^{87} +(746.051 - 1292.20i) q^{88} -201.000 q^{89} +(100.080 - 609.268i) q^{90} +941.373 q^{91} +(-61.9532 + 107.306i) q^{92} +(269.340 - 753.723i) q^{93} +(1087.81 + 1884.14i) q^{94} +(24.8819 + 43.0967i) q^{95} +(318.418 - 891.064i) q^{96} +(-126.074 + 218.367i) q^{97} -281.708 q^{98} +(-1385.56 - 1135.21i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + 9 q^{3} - 11 q^{4} - 15 q^{5} + 84 q^{6} + 43 q^{7} - 54 q^{8} + 57 q^{9}+O(q^{10}) \) 6 * q + q^2 + 9 * q^3 - 11 * q^4 - 15 * q^5 + 84 * q^6 + 43 * q^7 - 54 * q^8 + 57 * q^9	\( 6 q + q^{2} + 9 q^{3} - 11 q^{4} - 15 q^{5} + 84 q^{6} + 43 q^{7} - 54 q^{8} + 57 q^{9} - 10 q^{10} - 14 q^{11} + 75 q^{12} - 40 q^{13} + 27 q^{14} - 15 q^{15} + 13 q^{16} - 332 q^{17} + 3 q^{18} - 328 q^{19} - 55 q^{20} - 144 q^{21} + 376 q^{22} - 171 q^{23} - 63 q^{24} - 75 q^{25} + 868 q^{26} + 162 q^{27} - 1034 q^{28} + 335 q^{29} - 315 q^{30} + 352 q^{31} + 77 q^{32} - 708 q^{33} + 52 q^{34} - 430 q^{35} + 1086 q^{36} + 804 q^{37} + 178 q^{38} - 390 q^{39} + 135 q^{40} - 187 q^{41} + 513 q^{42} + 602 q^{43} + 1964 q^{44} + 330 q^{45} - 402 q^{46} - 665 q^{47} - 1074 q^{48} - 430 q^{49} + 25 q^{50} - 180 q^{51} + 456 q^{52} - 1460 q^{53} + 639 q^{54} + 140 q^{55} - 705 q^{56} - 486 q^{57} - 217 q^{58} + 298 q^{59} - 150 q^{60} + 1439 q^{61} - 3228 q^{62} + 2205 q^{63} - 3138 q^{64} - 200 q^{65} - 966 q^{66} + 1849 q^{67} + 710 q^{68} - 873 q^{69} + 135 q^{70} + 140 q^{71} + 261 q^{72} - 736 q^{73} + 320 q^{74} - 150 q^{75} - 204 q^{76} + 948 q^{77} - 432 q^{78} + 382 q^{79} - 130 q^{80} - 1251 q^{81} - 1150 q^{82} + 831 q^{83} - 909 q^{84} + 830 q^{85} - 1580 q^{86} + 258 q^{87} + 1428 q^{88} + 3438 q^{89} + 375 q^{90} - 1420 q^{91} + 1623 q^{92} + 2178 q^{93} + 2077 q^{94} + 820 q^{95} + 1155 q^{96} + 282 q^{97} + 4328 q^{98} - 762 q^{99}+O(q^{100}) \) 6 * q + q^2 + 9 * q^3 - 11 * q^4 - 15 * q^5 + 84 * q^6 + 43 * q^7 - 54 * q^8 + 57 * q^9 - 10 * q^10 - 14 * q^11 + 75 * q^12 - 40 * q^13 + 27 * q^14 - 15 * q^15 + 13 * q^16 - 332 * q^17 + 3 * q^18 - 328 * q^19 - 55 * q^20 - 144 * q^21 + 376 * q^22 - 171 * q^23 - 63 * q^24 - 75 * q^25 + 868 * q^26 + 162 * q^27 - 1034 * q^28 + 335 * q^29 - 315 * q^30 + 352 * q^31 + 77 * q^32 - 708 * q^33 + 52 * q^34 - 430 * q^35 + 1086 * q^36 + 804 * q^37 + 178 * q^38 - 390 * q^39 + 135 * q^40 - 187 * q^41 + 513 * q^42 + 602 * q^43 + 1964 * q^44 + 330 * q^45 - 402 * q^46 - 665 * q^47 - 1074 * q^48 - 430 * q^49 + 25 * q^50 - 180 * q^51 + 456 * q^52 - 1460 * q^53 + 639 * q^54 + 140 * q^55 - 705 * q^56 - 486 * q^57 - 217 * q^58 + 298 * q^59 - 150 * q^60 + 1439 * q^61 - 3228 * q^62 + 2205 * q^63 - 3138 * q^64 - 200 * q^65 - 966 * q^66 + 1849 * q^67 + 710 * q^68 - 873 * q^69 + 135 * q^70 + 140 * q^71 + 261 * q^72 - 736 * q^73 + 320 * q^74 - 150 * q^75 - 204 * q^76 + 948 * q^77 - 432 * q^78 + 382 * q^79 - 130 * q^80 - 1251 * q^81 - 1150 * q^82 + 831 * q^83 - 909 * q^84 + 830 * q^85 - 1580 * q^86 + 258 * q^87 + 1428 * q^88 + 3438 * q^89 + 375 * q^90 - 1420 * q^91 + 1623 * q^92 + 2178 * q^93 + 2077 * q^94 + 820 * q^95 + 1155 * q^96 + 282 * q^97 + 4328 * q^98 - 762 * q^99

Introduction

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