LMFDB - Embedded newform 42.4.e.c.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,4,Mod(25,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("42.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	42.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:	$2.47808022024$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{1345})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 337x^{2} + 336x + 112896 $ x^4 - x^3 + 337x^2 + 336x + 112896
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$-8.91856 + 15.4474i$ of defining polynomial
Character	$\chi$	$=$	42.37
Dual form			42.4.e.c.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-10.4186 + 18.0455i) q^{5} +6.00000 q^{6} +(-18.3371 + 2.59808i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-10.4186 + 18.0455i) q^{5} +6.00000 q^{6} +(-18.3371 + 2.59808i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-20.8371 - 36.0910i) q^{10} +(-7.58144 - 13.1314i) q^{11} +(-6.00000 + 10.3923i) q^{12} +2.16288 q^{13} +(13.8371 - 34.3589i) q^{14} +62.5114 q^{15} +(-8.00000 + 13.8564i) q^{16} +(59.6742 + 103.359i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(16.7557 - 29.0217i) q^{19} +83.3485 q^{20} +(34.2557 + 43.7441i) q^{21} +30.3258 q^{22} +(-0.325758 + 0.564230i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(-154.593 - 267.763i) q^{25} +(-2.16288 + 3.74622i) q^{26} +27.0000 q^{27} +(45.6742 + 58.3255i) q^{28} -163.208 q^{29} +(-62.5114 + 108.273i) q^{30} +(111.663 + 193.406i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(-22.7443 + 39.3943i) q^{33} -238.697 q^{34} +(144.163 - 357.970i) q^{35} +36.0000 q^{36} +(-84.2670 + 145.955i) q^{37} +(33.5114 + 58.0434i) q^{38} +(-3.24432 - 5.61932i) q^{39} +(-83.3485 + 144.364i) q^{40} -323.023 q^{41} +(-110.023 + 15.5885i) q^{42} +221.557 q^{43} +(-30.3258 + 52.5258i) q^{44} +(-93.7670 - 162.409i) q^{45} +(-0.651517 - 1.12846i) q^{46} +(-254.023 + 439.980i) q^{47} +48.0000 q^{48} +(329.500 - 95.2825i) q^{49} +618.371 q^{50} +(179.023 - 310.076i) q^{51} +(-4.32576 - 7.49243i) q^{52} +(88.2557 + 152.863i) q^{53} +(-27.0000 + 46.7654i) q^{54} +315.951 q^{55} +(-146.697 + 20.7846i) q^{56} -100.534 q^{57} +(163.208 - 282.685i) q^{58} +(-227.464 - 393.979i) q^{59} +(-125.023 - 216.546i) q^{60} +(-19.3258 + 33.4732i) q^{61} -446.652 q^{62} +(62.2670 - 154.615i) q^{63} +64.0000 q^{64} +(-22.5341 + 39.0302i) q^{65} +(-45.4886 - 78.7886i) q^{66} +(-70.8958 - 122.795i) q^{67} +(238.697 - 413.435i) q^{68} +1.95455 q^{69} +(475.860 + 607.668i) q^{70} +602.742 q^{71} +(-36.0000 + 62.3538i) q^{72} +(551.150 + 954.619i) q^{73} +(-168.534 - 291.910i) q^{74} +(-463.778 + 803.288i) q^{75} -134.045 q^{76} +(173.138 + 221.096i) q^{77} +12.9773 q^{78} +(58.1515 - 100.721i) q^{79} +(-166.697 - 288.728i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(323.023 - 559.492i) q^{82} -568.928 q^{83} +(83.0227 - 206.153i) q^{84} -2486.88 q^{85} +(-221.557 + 383.748i) q^{86} +(244.812 + 424.028i) q^{87} +(-60.6515 - 105.052i) q^{88} +(191.580 - 331.825i) q^{89} +375.068 q^{90} +(-39.6610 + 5.61932i) q^{91} +2.60607 q^{92} +(334.989 - 580.217i) q^{93} +(-508.045 - 879.961i) q^{94} +(349.140 + 604.728i) q^{95} +(-48.0000 + 83.1384i) q^{96} +334.701 q^{97} +(-164.466 + 665.993i) q^{98} +136.466 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 5 q^{5} + 24 q^{6} + 32 q^{8} - 18 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 6 * q^3 - 8 * q^4 - 5 * q^5 + 24 * q^6 + 32 * q^8 - 18 * q^9	\( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 5 q^{5} + 24 q^{6} + 32 q^{8} - 18 q^{9} - 10 q^{10} - 67 q^{11} - 24 q^{12} + 82 q^{13} - 18 q^{14} + 30 q^{15} - 32 q^{16} + 92 q^{17} - 36 q^{18} - 43 q^{19} + 40 q^{20} + 27 q^{21} + 268 q^{22} - 148 q^{23} - 48 q^{24} - 435 q^{25} - 82 q^{26} + 108 q^{27} + 36 q^{28} + 154 q^{29} - 30 q^{30} + 520 q^{31} - 64 q^{32} - 201 q^{33} - 368 q^{34} + 650 q^{35} + 144 q^{36} - 7 q^{37} - 86 q^{38} - 123 q^{39} - 40 q^{40} - 852 q^{41} - 214 q^{43} - 268 q^{44} - 45 q^{45} - 296 q^{46} - 576 q^{47} + 192 q^{48} + 1318 q^{49} + 1740 q^{50} + 276 q^{51} - 164 q^{52} + 243 q^{53} - 108 q^{54} - 1010 q^{55} + 258 q^{57} - 154 q^{58} + 7 q^{59} - 60 q^{60} - 224 q^{61} - 2080 q^{62} - 81 q^{63} + 256 q^{64} + 570 q^{65} - 402 q^{66} - 687 q^{67} + 368 q^{68} + 888 q^{69} + 1390 q^{70} + 944 q^{71} - 144 q^{72} + 921 q^{73} - 14 q^{74} - 1305 q^{75} + 344 q^{76} - 371 q^{77} + 492 q^{78} + 526 q^{79} - 80 q^{80} - 162 q^{81} + 852 q^{82} - 442 q^{83} - 108 q^{84} - 5840 q^{85} + 214 q^{86} - 231 q^{87} - 536 q^{88} - 774 q^{89} + 180 q^{90} + 1345 q^{91} + 1184 q^{92} + 1560 q^{93} - 1152 q^{94} + 1910 q^{95} - 192 q^{96} + 3906 q^{97} - 1318 q^{98} + 1206 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 6 * q^3 - 8 * q^4 - 5 * q^5 + 24 * q^6 + 32 * q^8 - 18 * q^9 - 10 * q^10 - 67 * q^11 - 24 * q^12 + 82 * q^13 - 18 * q^14 + 30 * q^15 - 32 * q^16 + 92 * q^17 - 36 * q^18 - 43 * q^19 + 40 * q^20 + 27 * q^21 + 268 * q^22 - 148 * q^23 - 48 * q^24 - 435 * q^25 - 82 * q^26 + 108 * q^27 + 36 * q^28 + 154 * q^29 - 30 * q^30 + 520 * q^31 - 64 * q^32 - 201 * q^33 - 368 * q^34 + 650 * q^35 + 144 * q^36 - 7 * q^37 - 86 * q^38 - 123 * q^39 - 40 * q^40 - 852 * q^41 - 214 * q^43 - 268 * q^44 - 45 * q^45 - 296 * q^46 - 576 * q^47 + 192 * q^48 + 1318 * q^49 + 1740 * q^50 + 276 * q^51 - 164 * q^52 + 243 * q^53 - 108 * q^54 - 1010 * q^55 + 258 * q^57 - 154 * q^58 + 7 * q^59 - 60 * q^60 - 224 * q^61 - 2080 * q^62 - 81 * q^63 + 256 * q^64 + 570 * q^65 - 402 * q^66 - 687 * q^67 + 368 * q^68 + 888 * q^69 + 1390 * q^70 + 944 * q^71 - 144 * q^72 + 921 * q^73 - 14 * q^74 - 1305 * q^75 + 344 * q^76 - 371 * q^77 + 492 * q^78 + 526 * q^79 - 80 * q^80 - 162 * q^81 + 852 * q^82 - 442 * q^83 - 108 * q^84 - 5840 * q^85 + 214 * q^86 - 231 * q^87 - 536 * q^88 - 774 * q^89 + 180 * q^90 + 1345 * q^91 + 1184 * q^92 + 1560 * q^93 - 1152 * q^94 + 1910 * q^95 - 192 * q^96 + 3906 * q^97 - 1318 * q^98 + 1206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−10.4186	+	18.0455i	−0.931864	+	1.61404i	−0.151732	+	0.988422i	$0.548485\pi$
$5$	−10.4186	+	18.0455i	−0.931864	+	1.61404i	−0.780132	+	0.625615i	$0.784848\pi$
$6$	6.00000			0.408248
$7$	−18.3371	+	2.59808i	−0.990111	+	0.140283i
$7$	−18.3371	+	2.59808i	−0.990111	+	0.140283i
$8$	8.00000			0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−20.8371	−	36.0910i	−0.658928	−	1.14130i
$11$	−7.58144	−	13.1314i	−0.207808	−	0.359934i	0.743216	−	0.669052i	$-0.233300\pi$
$11$	−7.58144	−	13.1314i	−0.207808	−	0.359934i	−0.951024	+	0.309118i	$0.899966\pi$
$12$	−6.00000	+	10.3923i	−0.144338	+	0.250000i
$13$	2.16288			0.0461442			0.0230721	−	0.999734i	$-0.492655\pi$
$13$	2.16288			0.0461442			0.0230721	+	0.999734i	$0.492655\pi$
$14$	13.8371	−	34.3589i	0.264152	−	0.655914i
$15$	62.5114			1.07602
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	59.6742	+	103.359i	0.851361	+	1.47460i	0.879981	+	0.475009i	$0.157555\pi$
$17$	59.6742	+	103.359i	0.851361	+	1.47460i	−0.0286202	+	0.999590i	$0.509111\pi$
$18$	−9.00000	−	15.5885i	−0.117851	−	0.204124i
$19$	16.7557	−	29.0217i	0.202317	−	0.350423i	−0.746958	−	0.664871i	$-0.768486\pi$
$19$	16.7557	−	29.0217i	0.202317	−	0.350423i	0.949274	+	0.314449i	$0.101820\pi$
$20$	83.3485			0.931864
$21$	34.2557	+	43.7441i	0.355962	+	0.454560i
$22$	30.3258			0.293885
$23$	−0.325758	+	0.564230i	−0.00295327	+	0.00511522i	−0.867498	−	0.497440i	$-0.834273\pi$
$23$	−0.325758	+	0.564230i	−0.00295327	+	0.00511522i	0.864545	+	0.502555i	$0.167607\pi$
$24$	−12.0000	−	20.7846i	−0.102062	−	0.176777i
$25$	−154.593	−	267.763i	−1.23674	−	2.14210i
$26$	−2.16288	+	3.74622i	−0.0163144	+	0.0282574i
$27$	27.0000			0.192450
$28$	45.6742	+	58.3255i	0.308272	+	0.393660i
$29$	−163.208			−1.04507			−0.522535	−	0.852618i	$-0.675014\pi$
$29$	−163.208			−1.04507			−0.522535	+	0.852618i	$0.675014\pi$
$30$	−62.5114	+	108.273i	−0.380432	+	0.658928i
$31$	111.663	+	193.406i	0.646943	+	1.12054i	0.983849	+	0.179000i	$0.0572863\pi$
$31$	111.663	+	193.406i	0.646943	+	1.12054i	−0.336906	+	0.941538i	$0.609380\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	−22.7443	+	39.3943i	−0.119978	+	0.207808i
$34$	−238.697			−1.20401
$35$	144.163	−	357.970i	0.696228	−	1.72880i
$36$	36.0000			0.166667
$37$	−84.2670	+	145.955i	−0.374417	+	0.648509i	−0.990240	−	0.139376i	$-0.955490\pi$
$37$	−84.2670	+	145.955i	−0.374417	+	0.648509i	0.615823	+	0.787885i	$0.288824\pi$
$38$	33.5114	+	58.0434i	0.143059	+	0.247786i
$39$	−3.24432	−	5.61932i	−0.0133207	−	0.0230721i
$40$	−83.3485	+	144.364i	−0.329464	+	0.570648i
$41$	−323.023			−1.23043			−0.615216	−	0.788359i	$-0.710931\pi$
$41$	−323.023			−1.23043			−0.615216	+	0.788359i	$0.710931\pi$
$42$	−110.023	+	15.5885i	−0.404211	+	0.0572703i
$43$	221.557			0.785746			0.392873	−	0.919593i	$-0.371481\pi$
$43$	221.557			0.785746			0.392873	+	0.919593i	$0.371481\pi$
$44$	−30.3258	+	52.5258i	−0.103904	+	0.179967i
$45$	−93.7670	−	162.409i	−0.310621	−	0.538012i
$46$	−0.651517	−	1.12846i	−0.00208828	−	0.00361701i
$47$	−254.023	+	439.980i	−0.788362	+	1.36548i	0.138608	+	0.990347i	$0.455737\pi$
$47$	−254.023	+	439.980i	−0.788362	+	1.36548i	−0.926970	+	0.375136i	$0.877596\pi$
$48$	48.0000			0.144338
$49$	329.500	−	95.2825i	0.960641	−	0.277791i
$50$	618.371			1.74902
$51$	179.023	−	310.076i	0.491533	−	0.851361i
$52$	−4.32576	−	7.49243i	−0.0115361	−	0.0199810i
$53$	88.2557	+	152.863i	0.228733	+	0.396177i	0.957433	−	0.288656i	$-0.0932084\pi$
$53$	88.2557	+	152.863i	0.228733	+	0.396177i	−0.728700	+	0.684833i	$0.759875\pi$
$54$	−27.0000	+	46.7654i	−0.0680414	+	0.117851i
$55$	315.951			0.774596
$56$	−146.697	+	20.7846i	−0.350057	+	0.0495975i
$57$	−100.534			−0.233615
$58$	163.208	−	282.685i	0.369488	−	0.639972i
$59$	−227.464	−	393.979i	−0.501920	−	0.869351i	−0.999998	−	0.00221868i	$-0.999294\pi$
$59$	−227.464	−	393.979i	−0.501920	−	0.869351i	0.498077	−	0.867133i	$-0.334040\pi$
$60$	−125.023	−	216.546i	−0.269006	−	0.465932i
$61$	−19.3258	+	33.4732i	−0.0405641	+	0.0702591i	−0.885595	−	0.464459i	$-0.846249\pi$
$61$	−19.3258	+	33.4732i	−0.0405641	+	0.0702591i	0.845031	+	0.534718i	$0.179582\pi$
$62$	−446.652			−0.914916
$63$	62.2670	−	154.615i	0.124522	−	0.309201i
$64$	64.0000			0.125000
$65$	−22.5341	+	39.0302i	−0.0430001	+	0.0744784i
$66$	−45.4886	−	78.7886i	−0.0848373	−	0.146943i
$67$	−70.8958	−	122.795i	−0.129273	−	0.223908i	0.794122	−	0.607758i	$-0.207931\pi$
$67$	−70.8958	−	122.795i	−0.129273	−	0.223908i	−0.923395	+	0.383851i	$0.874598\pi$
$68$	238.697	−	413.435i	0.425680	−	0.737300i
$69$	1.95455			0.00341015
$70$	475.860	+	607.668i	0.812516	+	1.03757i
$71$	602.742			1.00750			0.503749	−	0.863850i	$-0.331954\pi$
$71$	602.742			1.00750			0.503749	+	0.863850i	$0.331954\pi$
$72$	−36.0000	+	62.3538i	−0.0589256	+	0.102062i
$73$	551.150	+	954.619i	0.883660	+	1.53054i	0.847242	+	0.531207i	$0.178262\pi$
$73$	551.150	+	954.619i	0.883660	+	1.53054i	0.0364183	+	0.999337i	$0.488405\pi$
$74$	−168.534	−	291.910i	−0.264753	−	0.458565i
$75$	−463.778	+	803.288i	−0.714034	+	1.23674i
$76$	−134.045			−0.202317
$77$	173.138	+	221.096i	0.256246	+	0.327223i
$78$	12.9773			0.0188383
$79$	58.1515	−	100.721i	0.0828172	−	0.143444i	−0.821642	−	0.570004i	$-0.806942\pi$
$79$	58.1515	−	100.721i	0.0828172	−	0.143444i	0.904459	+	0.426561i	$0.140275\pi$
$80$	−166.697	−	288.728i	−0.232966	−	0.403509i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	323.023	−	559.492i	0.435023	−	0.753482i
$83$	−568.928			−0.752385			−0.376193	−	0.926542i	$-0.622767\pi$
$83$	−568.928			−0.752385			−0.376193	+	0.926542i	$0.622767\pi$
$84$	83.0227	−	206.153i	0.107840	−	0.267776i
$85$	−2486.88			−3.17341
$86$	−221.557	+	383.748i	−0.277803	+	0.481169i
$87$	244.812	+	424.028i	0.301686	+	0.522535i
$88$	−60.6515	−	105.052i	−0.0734713	−	0.127256i
$89$	191.580	−	331.825i	0.228173	−	0.395207i	−0.729094	−	0.684414i	$-0.760058\pi$
$89$	191.580	−	331.825i	0.228173	−	0.395207i	0.957267	+	0.289207i	$0.0933915\pi$
$90$	375.068			0.439285
$91$	−39.6610	+	5.61932i	−0.0456879	+	0.00647325i
$92$	2.60607			0.00295327
$93$	334.989	−	580.217i	0.373513	−	0.646943i
$94$	−508.045	−	879.961i	−0.557456	−	0.965543i
$95$	349.140	+	604.728i	0.377063	+	0.653093i
$96$	−48.0000	+	83.1384i	−0.0510310	+	0.0883883i
$97$	334.701			0.350348			0.175174	−	0.984538i	$-0.443951\pi$
$97$	334.701			0.350348			0.175174	+	0.984538i	$0.443951\pi$
$98$	−164.466	+	665.993i	−0.169526	+	0.686484i
$99$	136.466			0.138539
$100$	−618.371	+	1071.05i	−0.618371	+	1.07105i
$101$	7.37121	+	12.7673i	0.00726201	+	0.0125782i	0.869634	−	0.493698i	$-0.164355\pi$
$101$	7.37121	+	12.7673i	0.00726201	+	0.0125782i	−0.862372	+	0.506276i	$0.831022\pi$
$102$	358.045	+	620.153i	0.347566	+	0.602003i
$103$	420.710	−	728.691i	0.402464	−	0.697088i	−0.591559	−	0.806262i	$-0.701487\pi$
$103$	420.710	−	728.691i	0.402464	−	0.697088i	0.994023	+	0.109174i	$0.0348205\pi$
$104$	17.3030			0.0163144
$105$	−1146.28	+	162.409i	−1.06538	+	0.150948i
$106$	−353.023			−0.323477
$107$	357.835	−	619.789i	0.323301	−	0.559974i	−0.657866	−	0.753135i	$-0.728541\pi$
$107$	357.835	−	619.789i	0.323301	−	0.559974i	0.981167	+	0.193161i	$0.0618739\pi$
$108$	−54.0000	−	93.5307i	−0.0481125	−	0.0833333i
$109$	−300.009	−	519.632i	−0.263630	−	0.456621i	0.703574	−	0.710622i	$-0.251587\pi$
$109$	−300.009	−	519.632i	−0.263630	−	0.456621i	−0.967204	+	0.254001i	$0.918253\pi$
$110$	−315.951	+	547.243i	−0.273861	+	0.474341i
$111$	505.602			0.432339
$112$	110.697	−	274.871i	0.0933918	−	0.231901i
$113$	622.644			0.518349			0.259174	−	0.965831i	$-0.416550\pi$
$113$	622.644			0.518349			0.259174	+	0.965831i	$0.416550\pi$
$114$	100.534	−	174.130i	0.0825954	−	0.143059i
$115$	−6.78787	−	11.7569i	−0.00550410	−	0.00953339i
$116$	326.417	+	565.370i	0.261267	+	0.452529i
$117$	−9.73296	+	16.8580i	−0.00769070	+	0.0133207i
$118$	909.856			0.709822
$119$	−1362.79	−	1740.26i	−1.04980	−	1.34059i
$120$	500.091			0.380432
$121$	550.544	−	953.569i	0.413632	−	0.716431i
$122$	−38.6515	−	66.9464i	−0.0286831	−	0.0496807i
$123$	484.534	+	839.238i	0.355195	+	0.615216i
$124$	446.652	−	773.623i	0.323472	−	0.560269i
$125$	3837.90			2.74618
$126$	205.534	+	262.465i	0.145321	+	0.185573i
$127$	−180.076			−0.125820			−0.0629100	−	0.998019i	$-0.520038\pi$
$127$	−180.076			−0.125820			−0.0629100	+	0.998019i	$0.520038\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	−332.335	−	575.621i	−0.226825	−	0.392873i
$130$	−45.0682	−	78.0604i	−0.0304057	−	0.0526642i
$131$	−108.930	+	188.672i	−0.0726508	+	0.125835i	−0.900062	−	0.435761i	$-0.856479\pi$
$131$	−108.930	+	188.672i	−0.0726508	+	0.125835i	0.827411	+	0.561596i	$0.189813\pi$
$132$	181.955			0.119978
$133$	−231.850	+	575.707i	−0.151158	+	0.375339i
$134$	283.583			0.182820
$135$	−281.301	+	487.228i	−0.179337	+	0.310621i
$136$	477.394	+	826.871i	0.301001	+	0.521350i
$137$	1300.93	+	2253.27i	0.811283	+	1.40518i	0.911966	+	0.410265i	$0.134564\pi$
$137$	1300.93	+	2253.27i	0.811283	+	1.40518i	−0.100683	+	0.994919i	$0.532103\pi$
$138$	−1.95455	+	3.38538i	−0.00120567	+	0.00208828i
$139$	−2651.55			−1.61800			−0.808998	−	0.587811i	$-0.799990\pi$
$139$	−2651.55			−1.61800			−0.808998	+	0.587811i	$0.799990\pi$
$140$	−1528.37	+	216.546i	−0.922650	+	0.130725i
$141$	1524.14			0.910322
$142$	−602.742	+	1043.98i	−0.356204	+	0.616964i
$143$	−16.3977	−	28.4017i	−0.00958914	−	0.0166089i
$144$	−72.0000	−	124.708i	−0.0416667	−	0.0721688i
$145$	1700.40	−	2945.17i	0.973863	−	1.68678i
$146$	−2204.60			−1.24968
$147$	−741.801	−	713.142i	−0.416209	−	0.400129i
$148$	674.136			0.374417
$149$	−290.511	+	503.180i	−0.159729	+	0.276659i	−0.934771	−	0.355251i	$-0.884395\pi$
$149$	−290.511	+	503.180i	−0.159729	+	0.276659i	0.775042	+	0.631910i	$0.217729\pi$
$150$	−927.557	−	1606.58i	−0.504898	−	0.874509i
$151$	307.695	+	532.943i	0.165827	+	0.287221i	0.936949	−	0.349467i	$-0.113637\pi$
$151$	307.695	+	532.943i	0.165827	+	0.287221i	−0.771122	+	0.636688i	$0.780304\pi$
$152$	134.045	−	232.174i	0.0715297	−	0.123893i
$153$	−1074.14			−0.567574
$154$	−556.087	+	78.7886i	−0.290979	+	0.0412271i
$155$	−4653.47			−2.41145
$156$	−12.9773	+	22.4773i	−0.00666034	+	0.0115361i
$157$	153.466	+	265.811i	0.0780122	+	0.135121i	0.902392	−	0.430916i	$-0.141809\pi$
$157$	153.466	+	265.811i	0.0780122	+	0.135121i	−0.824380	+	0.566037i	$0.808476\pi$
$158$	116.303	+	201.443i	0.0585606	+	0.101430i
$159$	264.767	−	458.590i	0.132059	−	0.228733i
$160$	666.788			0.329464
$161$	4.50756	−	11.1927i	0.00220649	−	0.00547893i
$162$	162.000			0.0785674
$163$	−1757.25	+	3043.65i	−0.844408	+	1.46256i	0.0417271	+	0.999129i	$0.486714\pi$
$163$	−1757.25	+	3043.65i	−0.844408	+	1.46256i	−0.886135	+	0.463428i	$0.846619\pi$
$164$	646.045	+	1118.98i	0.307608	+	0.532792i
$165$	−473.926	−	820.864i	−0.223607	−	0.387298i
$166$	568.928	−	985.412i	0.266008	−	0.460740i
$167$	1123.30			0.520502			0.260251	−	0.965541i	$-0.416195\pi$
$167$	1123.30			0.520502			0.260251	+	0.965541i	$0.416195\pi$
$168$	274.045	+	349.953i	0.125852	+	0.160711i
$169$	−2192.32			−0.997871
$170$	2486.88	−	4307.40i	1.12197	−	1.94331i
$171$	150.801	+	261.195i	0.0674389	+	0.116808i
$172$	−443.114	−	767.495i	−0.196437	−	0.340238i
$173$	−765.299	+	1325.54i	−0.336327	+	0.582536i	−0.983739	−	0.179605i	$-0.942518\pi$
$173$	−765.299	+	1325.54i	−0.336327	+	0.582536i	0.647412	+	0.762141i	$0.275852\pi$
$174$	−979.250			−0.426648
$175$	3530.45	+	4508.35i	1.52501	+	1.94742i
$176$	242.606			0.103904
$177$	−682.392	+	1181.94i	−0.289784	+	0.501920i
$178$	383.159	+	663.651i	0.161343	+	0.279454i
$179$	−1706.72	−	2956.12i	−0.712659	−	1.23436i	−0.963856	−	0.266425i	$-0.914157\pi$
$179$	−1706.72	−	2956.12i	−0.712659	−	1.23436i	0.251197	−	0.967936i	$-0.419176\pi$
$180$	−375.068	+	649.637i	−0.155311	+	0.269006i
$181$	1286.71			0.528399			0.264200	−	0.964468i	$-0.414892\pi$
$181$	1286.71			0.528399			0.264200	+	0.964468i	$0.414892\pi$
$182$	29.9280	−	74.3142i	0.0121891	−	0.0302667i
$183$	115.955			0.0468394
$184$	−2.60607	+	4.51384i	−0.00104414	+	0.00180850i
$185$	−1755.88	−	3041.28i	−0.697811	−	1.20864i
$186$	669.977	+	1160.43i	0.264114	+	0.457458i
$187$	904.833	−	1567.22i	0.353839	−	0.612868i
$188$	2032.18			0.788362
$189$	−495.102	+	70.1481i	−0.190547	+	0.0269975i
$190$	−1396.56			−0.533248
$191$	−527.648	+	913.913i	−0.199891	+	0.346222i	−0.948493	−	0.316798i	$-0.897392\pi$
$191$	−527.648	+	913.913i	−0.199891	+	0.346222i	0.748602	+	0.663020i	$0.230726\pi$
$192$	−96.0000	−	166.277i	−0.0360844	−	0.0625000i
$193$	2385.42	+	4131.67i	0.889670	+	1.54095i	0.840266	+	0.542175i	$0.182399\pi$
$193$	2385.42	+	4131.67i	0.889670	+	1.54095i	0.0494044	+	0.998779i	$0.484268\pi$
$194$	−334.701	+	579.719i	−0.123867	+	0.214543i
$195$	135.205			0.0496523
$196$	−989.068	−	950.857i	−0.360448	−	0.346522i
$197$	1622.31			0.586725			0.293363	−	0.956001i	$-0.405226\pi$
$197$	1622.31			0.586725			0.293363	+	0.956001i	$0.405226\pi$
$198$	−136.466	+	236.366i	−0.0489809	+	0.0848373i
$199$	1775.07	+	3074.51i	0.632318	+	1.09521i	0.987077	+	0.160249i	$0.0512296\pi$
$199$	1775.07	+	3074.51i	0.632318	+	1.09521i	−0.354759	+	0.934958i	$0.615437\pi$
$200$	−1236.74	−	2142.10i	−0.437254	−	0.757347i
$201$	−212.688	+	368.386i	−0.0746359	+	0.129273i
$202$	−29.4848			−0.0102700
$203$	2992.77	−	424.028i	1.03474	−	0.146605i
$204$	−1432.18			−0.491533
$205$	3365.43	−	5829.10i	1.14659	−	1.98596i
$206$	841.420	+	1457.38i	0.284585	+	0.492916i
$207$	−2.93183	−	5.07807i	−0.000984425	−	0.00170507i
$208$	−17.3030	+	29.9697i	−0.00576803	+	0.00999051i
$209$	−508.129			−0.168172
$210$	864.977	−	2147.82i	0.284234	−	0.705780i
$211$	4653.39			1.51826			0.759129	−	0.650941i	$-0.225625\pi$
$211$	4653.39			1.51826			0.759129	+	0.650941i	$0.225625\pi$
$212$	353.023	−	611.453i	0.114367	−	0.198089i
$213$	−904.114	−	1565.97i	−0.290840	−	0.503749i
$214$	715.670	+	1239.58i	0.228609	+	0.395962i
$215$	−2308.30	+	3998.10i	−0.732209	+	1.26822i
$216$	216.000			0.0680414
$217$	−2550.06	−	3256.40i	−0.797739	−	1.01870i
$218$	1200.04			0.372829
$219$	1653.45	−	2863.86i	0.510181	−	0.883660i
$220$	−631.901	−	1094.49i	−0.193649	−	0.335410i
$221$	129.068	+	223.553i	0.0392854	+	0.0680442i
$222$	−505.602	+	875.729i	−0.152855	+	0.264753i
$223$	−4649.53			−1.39621			−0.698107	−	0.715993i	$-0.745974\pi$
$223$	−4649.53			−1.39621			−0.698107	+	0.715993i	$0.745974\pi$
$224$	365.394	+	466.604i	0.108991	+	0.139180i
$225$	2782.67			0.824495
$226$	−622.644	+	1078.45i	−0.183264	+	0.317423i
$227$	−2075.86	−	3595.49i	−0.606958	−	1.05128i	−0.991739	−	0.128274i	$-0.959056\pi$
$227$	−2075.86	−	3595.49i	−0.606958	−	1.05128i	0.384780	−	0.923008i	$-0.374277\pi$
$228$	201.068	+	348.260i	0.0584038	+	0.101158i
$229$	−2131.82	+	3692.41i	−0.615172	+	1.06551i	0.375182	+	0.926951i	$0.377580\pi$
$229$	−2131.82	+	3692.41i	−0.615172	+	1.06551i	−0.990354	+	0.138558i	$0.955753\pi$
$230$	27.1515			0.00778398
$231$	314.716	−	781.470i	0.0896398	−	0.222584i
$232$	−1305.67			−0.369488
$233$	−1524.95	+	2641.29i	−0.428768	+	0.742647i	−0.996764	−	0.0803838i	$-0.974385\pi$
$233$	−1524.95	+	2641.29i	−0.428768	+	0.742647i	0.567996	+	0.823031i	$0.307719\pi$
$234$	−19.4659	−	33.7159i	−0.00543815	−	0.00941915i
$235$	−5293.10	−	9167.92i	−1.46929	−	2.54489i
$236$	−909.856	+	1575.92i	−0.250960	+	0.434676i
$237$	−348.909			−0.0956290
$238$	4377.02	−	620.153i	1.19210	−	0.168901i
$239$	3987.20			1.07912			0.539562	−	0.841946i	$-0.318590\pi$
$239$	3987.20			1.07912			0.539562	+	0.841946i	$0.318590\pi$
$240$	−500.091	+	866.183i	−0.134503	+	0.232966i
$241$	312.324	+	540.961i	0.0834795	+	0.144591i	0.904742	−	0.425959i	$-0.140063\pi$
$241$	312.324	+	540.961i	0.0834795	+	0.144591i	−0.821263	+	0.570550i	$0.806730\pi$
$242$	1101.09	+	1907.14i	0.292482	+	0.506593i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	154.606			0.0405641
$245$	−1713.50	+	6938.69i	−0.446822	+	1.80937i
$246$	−1938.14			−0.502321
$247$	36.2405	−	62.7704i	0.00933574	−	0.0161700i
$248$	893.303	+	1547.25i	0.228729	+	0.396170i
$249$	853.392	+	1478.12i	0.217195	+	0.376193i
$250$	−3837.90	+	6647.43i	−0.970920	+	1.68168i
$251$	−1328.78			−0.334152			−0.167076	−	0.985944i	$-0.553432\pi$
$251$	−1328.78			−0.334152			−0.167076	+	0.985944i	$0.553432\pi$
$252$	−660.136	+	93.5307i	−0.165019	+	0.0233805i
$253$	9.87887			0.00245486
$254$	180.076	−	311.900i	0.0444841	−	0.0770487i
$255$	3730.32	+	6461.10i	0.916085	+	1.58671i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	1613.09	−	2793.96i	0.391525	−	0.678141i	−0.601126	−	0.799154i	$-0.705281\pi$
$257$	1613.09	−	2793.96i	0.391525	−	0.678141i	0.992651	+	0.121013i	$0.0386144\pi$
$258$	1329.34			0.320780
$259$	1166.01	−	2895.32i	0.279740	−	0.694620i
$260$	180.273			0.0430001
$261$	734.437	−	1272.08i	0.174178	−	0.301686i
$262$	−217.860	−	377.344i	−0.0513719	−	0.0889787i
$263$	−1625.31	−	2815.11i	−0.381067	−	0.660028i	0.610148	−	0.792288i	$-0.291110\pi$
$263$	−1625.31	−	2815.11i	−0.381067	−	0.660028i	−0.991215	+	0.132260i	$0.957777\pi$
$264$	−181.955	+	315.155i	−0.0424187	+	0.0734713i
$265$	−3677.99			−0.852593
$266$	−765.303	−	977.283i	−0.176405	−	0.225267i
$267$	−1149.48			−0.263471
$268$	−283.583	+	491.181i	−0.0646366	+	0.111954i
$269$	−1413.02	−	2447.42i	−0.320273	−	0.554729i	0.660271	−	0.751027i	$-0.270441\pi$
$269$	−1413.02	−	2447.42i	−0.320273	−	0.554729i	−0.980544	+	0.196298i	$0.937108\pi$
$270$	−562.602	−	974.456i	−0.126811	−	0.219643i
$271$	1198.38	−	2075.66i	0.268622	−	0.465268i	−0.699884	−	0.714257i	$-0.746765\pi$
$271$	1198.38	−	2075.66i	0.268622	−	0.465268i	0.968506	+	0.248989i	$0.0800983\pi$
$272$	−1909.58			−0.425680
$273$	74.0909	+	94.6133i	0.0164256	+	0.0209753i
$274$	−5203.71			−1.14733
$275$	−2344.07	+	4060.05i	−0.514010	+	0.890292i
$276$	−3.90910	−	6.77076i	−0.000852537	−	0.00147664i
$277$	−910.233	−	1576.57i	−0.197439	−	0.341974i	0.750258	−	0.661145i	$-0.229929\pi$
$277$	−910.233	−	1576.57i	−0.197439	−	0.341974i	−0.947697	+	0.319170i	$0.896596\pi$
$278$	2651.55	−	4592.62i	0.572048	−	0.990816i
$279$	−2009.93			−0.431296
$280$	1153.30	−	2863.76i	0.246154	−	0.611223i
$281$	3083.81			0.654679			0.327339	−	0.944907i	$-0.393848\pi$
$281$	3083.81			0.654679			0.327339	+	0.944907i	$0.393848\pi$
$282$	−1524.14	+	2639.88i	−0.321848	+	0.557456i
$283$	−1277.38	−	2212.49i	−0.268313	−	0.464732i	0.700113	−	0.714032i	$-0.253133\pi$
$283$	−1277.38	−	2212.49i	−0.268313	−	0.464732i	−0.968426	+	0.249300i	$0.919800\pi$
$284$	−1205.48	−	2087.96i	−0.251875	−	0.436259i
$285$	1047.42	−	1814.19i	0.217698	−	0.377063i
$286$	65.5910			0.0135611
$287$	5923.31	−	839.238i	1.21826	−	0.172608i
$288$	288.000			0.0589256
$289$	−4665.53	+	8080.94i	−0.949630	+	1.64481i
$290$	3400.79	+	5890.34i	0.688625	+	1.19273i
$291$	−502.051	−	869.578i	−0.101137	−	0.175174i
$292$	2204.60	−	3818.48i	0.441830	−	0.765272i
$293$	−1846.47			−0.368163			−0.184081	−	0.982911i	$-0.558931\pi$
$293$	−1846.47			−0.368163			−0.184081	+	0.982911i	$0.558931\pi$
$294$	1977.00	−	571.695i	0.392180	−	0.113408i
$295$	9479.39			1.87089
$296$	−674.136	+	1167.64i	−0.132376	+	0.229282i
$297$	−204.699	−	354.549i	−0.0399927	−	0.0692694i
$298$	−581.023	−	1006.36i	−0.112945	−	0.195627i
$299$	−0.704576	+	1.22036i	−0.000136277	+	0.000236038i
$300$	3710.23			0.714034
$301$	−4062.71	+	575.621i	−0.777977	+	0.110227i
$302$	−1230.78			−0.234515
$303$	22.1136	−	38.3019i	0.00419272	−	0.00726201i
$304$	268.091	+	464.347i	0.0505792	+	0.0876057i
$305$	−402.693	−	697.485i	−0.0756005	−	0.130944i
$306$	1074.14	−	1860.46i	0.200668	−	0.347566i
$307$	7041.50			1.30905			0.654527	−	0.756039i	$-0.272868\pi$
$307$	7041.50			1.30905			0.654527	+	0.756039i	$0.272868\pi$
$308$	419.621	−	1041.96i	0.0776303	−	0.192764i
$309$	−2524.26			−0.464726
$310$	4653.47	−	8060.04i	0.852578	−	1.47671i
$311$	1343.00	+	2326.14i	0.244869	+	0.424126i	0.962095	−	0.272715i	$-0.0879216\pi$
$311$	1343.00	+	2326.14i	0.244869	+	0.424126i	−0.717226	+	0.696841i	$0.754588\pi$
$312$	−25.9546	−	44.9546i	−0.00470957	−	0.00815722i
$313$	−1109.59	+	1921.87i	−0.200377	+	0.347063i	−0.948650	−	0.316328i	$-0.897550\pi$
$313$	−1109.59	+	1921.87i	−0.200377	+	0.347063i	0.748273	+	0.663391i	$0.230883\pi$
$314$	−613.864			−0.110326
$315$	2141.37	+	2734.50i	0.383024	+	0.489117i
$316$	−465.212			−0.0828172
$317$	−1110.63	+	1923.67i	−0.196780	+	0.340833i	−0.947483	−	0.319807i	$-0.896382\pi$
$317$	−1110.63	+	1923.67i	−0.196780	+	0.340833i	0.750703	+	0.660640i	$0.229715\pi$
$318$	529.534	+	917.180i	0.0933799	+	0.161739i
$319$	1237.35	+	2143.16i	0.217174	+	0.376157i
$320$	−666.788	+	1154.91i	−0.116483	+	0.201755i
$321$	−2147.01			−0.373316
$322$	14.8788	+	19.0000i	0.00257503	+	0.00328829i
$323$	3999.53			0.688978
$324$	−162.000	+	280.592i	−0.0277778	+	0.0481125i
$325$	−334.366	−	579.138i	−0.0570685	−	0.0988455i
$326$	−3514.50	−	6087.29i	−0.597086	−	1.03418i
$327$	−900.028	+	1558.89i	−0.152207	+	0.263630i
$328$	−2584.18			−0.435023
$329$	3514.94	−	8727.94i	0.589012	−	1.46257i
$330$	1895.70			0.316228
$331$	−2077.03	+	3597.52i	−0.344906	+	0.597394i	−0.985337	−	0.170622i	$-0.945422\pi$
$331$	−2077.03	+	3597.52i	−0.344906	+	0.597394i	0.640431	+	0.768016i	$0.278756\pi$
$332$	1137.86	+	1970.82i	0.188096	+	0.325792i
$333$	−758.403	−	1313.59i	−0.124806	−	0.216170i
$334$	−1123.30	+	1945.62i	−0.184025	+	0.318741i
$335$	2954.53			0.481860
$336$	−880.182	+	124.708i	−0.142910	+	0.0202481i
$337$	−254.167			−0.0410841			−0.0205420	−	0.999789i	$-0.506539\pi$
$337$	−254.167			−0.0410841			−0.0205420	+	0.999789i	$0.506539\pi$
$338$	2192.32	−	3797.21i	0.352801	−	0.611069i
$339$	−933.966	−	1617.68i	−0.149634	−	0.259174i
$340$	4973.76	+	8614.80i	0.793353	+	1.37413i
$341$	1693.13	−	2932.59i	0.268880	−	0.465714i
$342$	−603.205			−0.0953730
$343$	−5794.53	+	2603.27i	−0.912173	+	0.409806i
$344$	1772.45			0.277803
$345$	−20.3636	+	35.2708i	−0.00317780	+	0.00550410i
$346$	−1530.60	−	2651.07i	−0.237819	−	0.411915i
$347$	3112.32	+	5390.69i	0.481493	+	0.833970i	0.999774	−	0.0212401i	$-0.00676143\pi$
$347$	3112.32	+	5390.69i	0.481493	+	0.833970i	−0.518282	+	0.855210i	$0.673428\pi$
$348$	979.250	−	1696.11i	0.150843	−	0.261267i
$349$	9732.21			1.49270			0.746352	−	0.665552i	$-0.231804\pi$
$349$	9732.21			1.49270			0.746352	+	0.665552i	$0.231804\pi$
$350$	−11339.1	+	1606.58i	−1.73172	+	0.245357i
$351$	58.3977			0.00888046
$352$	−242.606	+	420.206i	−0.0367356	+	0.0636280i
$353$	−712.807	−	1234.62i	−0.107476	−	0.186153i	0.807271	−	0.590180i	$-0.200943\pi$
$353$	−712.807	−	1234.62i	−0.107476	−	0.186153i	−0.914747	+	0.404027i	$0.867610\pi$
$354$	−1364.78	−	2363.88i	−0.204908	−	0.354911i
$355$	−6279.71	+	10876.8i	−0.938852	+	1.62614i
$356$	−1532.64			−0.228173
$357$	−2477.16	+	6151.02i	−0.367241	+	0.911896i
$358$	6826.86			1.00785
$359$	2883.25	−	4993.93i	0.423877	−	0.734177i	−0.572438	−	0.819948i	$-0.694002\pi$
$359$	2883.25	−	4993.93i	0.423877	−	0.734177i	0.996315	+	0.0857714i	$0.0273355\pi$
$360$	−750.136	−	1299.27i	−0.109821	−	0.190216i
$361$	2867.99	+	4967.51i	0.418136	+	0.724233i
$362$	−1286.71	+	2228.64i	−0.186817	+	0.323577i
$363$	−3303.26			−0.477621
$364$	98.7879	+	126.151i	0.0142250	+	0.0181651i
$365$	−22968.7			−3.29381
$366$	−115.955	+	200.839i	−0.0165602	+	0.0286831i
$367$	−5772.67	−	9998.56i	−0.821065	−	1.42213i	−0.904890	−	0.425646i	$-0.860047\pi$
$367$	−5772.67	−	9998.56i	−0.821065	−	1.42213i	0.0838244	−	0.996481i	$-0.473287\pi$
$368$	−5.21213	−	9.02768i	−0.000738319	−	0.00127881i
$369$	1453.60	−	2517.71i	0.205072	−	0.355195i
$370$	7023.53			0.986854
$371$	−2015.51	−	2573.78i	−0.282048	−	0.360172i
$372$	−2679.91			−0.373513
$373$	3239.79	−	5611.47i	0.449731	−	0.778957i	−0.548637	−	0.836061i	$-0.684853\pi$
$373$	3239.79	−	5611.47i	0.449731	−	0.778957i	0.998368	+	0.0571033i	$0.0181864\pi$
$374$	1809.67	+	3134.43i	0.250202	+	0.433363i
$375$	−5756.85	−	9971.15i	−0.792753	−	1.37309i
$376$	−2032.18	+	3519.84i	−0.278728	+	0.482771i
$377$	−353.000			−0.0482239
$378$	373.602	−	927.690i	0.0508360	−	0.126231i
$379$	611.996			0.0829449			0.0414725	−	0.999140i	$-0.486795\pi$
$379$	611.996			0.0829449			0.0414725	+	0.999140i	$0.486795\pi$
$380$	1396.56	−	2418.91i	0.188532	−	0.326546i
$381$	270.114	+	467.851i	0.0363211	+	0.0629100i
$382$	−1055.30	−	1827.83i	−0.141345	−	0.244816i
$383$	−2180.41	+	3776.57i	−0.290897	+	0.503848i	−0.974022	−	0.226453i	$-0.927287\pi$
$383$	−2180.41	+	3776.57i	−0.290897	+	0.503848i	0.683125	+	0.730301i	$0.260620\pi$
$384$	384.000			0.0510310
$385$	−5793.63	+	820.864i	−0.766937	+	0.108663i
$386$	−9541.68			−1.25818
$387$	−997.006	+	1726.86i	−0.130958	+	0.226825i
$388$	−669.402	−	1159.44i	−0.0875869	−	0.151705i
$389$	6573.46	+	11385.6i	0.856781	+	1.48399i	0.874983	+	0.484154i	$0.160872\pi$
$389$	6573.46	+	11385.6i	0.856781	+	1.48399i	−0.0182021	+	0.999834i	$0.505794\pi$
$390$	−135.205	+	234.181i	−0.0175547	+	0.0304057i
$391$	−77.7575			−0.0100572
$392$	2636.00	−	762.260i	0.339638	−	0.0982141i
$393$	653.580			0.0838899
$394$	−1622.31	+	2809.92i	−0.207439	+	0.359294i
$395$	1211.71	+	2098.74i	0.154349	+	0.267340i
$396$	−272.932	−	472.732i	−0.0346347	−	0.0599891i
$397$	4239.02	−	7342.20i	0.535895	−	0.928198i	−0.463224	−	0.886241i	$-0.653308\pi$
$397$	4239.02	−	7342.20i	0.535895	−	0.928198i	0.999119	−	0.0419565i	$-0.0133591\pi$
$398$	−7100.27			−0.894232
$399$	1843.51	−	261.195i	0.231305	−	0.0327722i
$400$	4946.97			0.618371
$401$	−1401.50	+	2427.47i	−0.174533	+	0.302299i	−0.939999	−	0.341176i	$-0.889175\pi$
$401$	−1401.50	+	2427.47i	−0.174533	+	0.302299i	0.765467	+	0.643475i	$0.222508\pi$
$402$	−425.375	−	736.771i	−0.0527756	−	0.0914100i
$403$	241.513	+	418.313i	0.0298527	+	0.0517064i
$404$	29.4848	−	51.0692i	0.00363100	−	0.00628908i
$405$	1687.81			0.207081
$406$	−2258.33	+	5607.66i	−0.276057	+	0.685476i
$407$	2555.46			0.311227
$408$	1432.18	−	2480.61i	0.173783	−	0.301001i
$409$	3192.69	+	5529.91i	0.385987	+	0.668548i	0.991906	−	0.126978i	$-0.0405278\pi$
$409$	3192.69	+	5529.91i	0.385987	+	0.668548i	−0.605919	+	0.795526i	$0.707194\pi$
$410$	6730.86	+	11658.2i	0.810765	+	1.40429i
$411$	3902.78	−	6759.82i	0.468395	−	0.811283i
$412$	−3365.68			−0.402464
$413$	5194.62	+	6633.48i	0.618912	+	0.790344i
$414$	11.7273			0.00139219
$415$	5927.41	−	10266.6i	0.701121	−	1.21438i
$416$	−34.6061	−	59.9395i	−0.00407861	−	0.00706436i
$417$	3977.32	+	6888.93i	0.467075	+	0.808998i
$418$	508.129	−	880.105i	0.0594579	−	0.102984i
$419$	4831.66			0.563346			0.281673	−	0.959510i	$-0.409111\pi$
$419$	4831.66			0.563346			0.281673	+	0.959510i	$0.409111\pi$
$420$	2855.16	+	3646.01i	0.331708	+	0.423588i
$421$	7475.37			0.865385			0.432693	−	0.901542i	$-0.357564\pi$
$421$	7475.37			0.865385			0.432693	+	0.901542i	$0.357564\pi$
$422$	−4653.39	+	8059.90i	−0.536785	+	0.929739i
$423$	−2286.20	−	3959.82i	−0.262787	−	0.455161i
$424$	706.045	+	1222.91i	0.0808693	+	0.140070i
$425$	18450.4	−	31957.1i	2.10583	−	3.64740i
$426$	3616.45			0.411309
$427$	267.413	−	664.012i	0.0303068	−	0.0752548i
$428$	−2862.68			−0.323301
$429$	−49.1932	+	85.2051i	−0.00553630	+	0.00958914i
$430$	−4616.61	−	7996.20i	−0.517750	−	0.896769i
$431$	−3495.97	−	6055.19i	−0.390707	−	0.676725i	0.601836	−	0.798620i	$-0.294436\pi$
$431$	−3495.97	−	6055.19i	−0.390707	−	0.676725i	−0.992543	+	0.121895i	$0.961103\pi$
$432$	−216.000	+	374.123i	−0.0240563	+	0.0416667i
$433$	−7699.26			−0.854510			−0.427255	−	0.904131i	$-0.640519\pi$
$433$	−7699.26			−0.854510			−0.427255	+	0.904131i	$0.640519\pi$
$434$	8190.30	−	1160.43i	0.905869	−	0.128347i
$435$	−10202.4			−1.12452
$436$	−1200.04	+	2078.53i	−0.131815	+	0.228310i
$437$	10.9166	+	18.9081i	0.00119499	+	0.00206979i
$438$	3306.90	+	5727.71i	0.360753	+	0.624842i
$439$	−4706.16	+	8151.31i	−0.511646	+	0.886198i	0.488262	+	0.872697i	$0.337631\pi$
$439$	−4706.16	+	8151.31i	−0.511646	+	0.886198i	−0.999909	+	0.0135008i	$0.995702\pi$
$440$	2527.61			0.273861
$441$	−740.097	+	2996.97i	−0.0799154	+	0.323612i
$442$	−516.273			−0.0555579
$443$	3129.09	−	5419.74i	0.335593	−	0.581263i	−0.648006	−	0.761635i	$-0.724397\pi$
$443$	3129.09	−	5419.74i	0.335593	−	0.581263i	0.983598	+	0.180372i	$0.0577301\pi$
$444$	−1011.20	−	1751.46i	−0.108085	−	0.187208i
$445$	3991.97	+	6914.29i	0.425252	+	0.736559i
$446$	4649.53	−	8053.23i	0.493636	−	0.855003i
$447$	1743.07			0.184439
$448$	−1173.58	+	166.277i	−0.123764	+	0.0175354i
$449$	−11633.8			−1.22279			−0.611396	−	0.791325i	$-0.709392\pi$
$449$	−11633.8			−1.22279			−0.611396	+	0.791325i	$0.709392\pi$
$450$	−2782.67	+	4819.73i	−0.291503	+	0.504898i
$451$	2448.98	+	4241.75i	0.255694	+	0.442874i
$452$	−1245.29	−	2156.90i	−0.129587	−	0.224452i
$453$	923.085	−	1598.83i	0.0957402	−	0.165827i
$454$	8303.43			0.858369
$455$	311.807	−	774.246i	0.0321269	−	0.0797741i
$456$	−804.273			−0.0825954
$457$	6552.31	−	11348.9i	0.670688	−	1.16167i	−0.307022	−	0.951703i	$-0.599332\pi$
$457$	6552.31	−	11348.9i	0.670688	−	1.16167i	0.977709	−	0.209963i	$-0.0673343\pi$
$458$	−4263.63	−	7384.83i	−0.434992	−	0.753429i
$459$	1611.20	+	2790.69i	0.163844	+	0.283787i
$460$	−27.1515	+	47.0277i	−0.00275205	+	0.00476669i
$461$	−2594.63			−0.262134			−0.131067	−	0.991373i	$-0.541840\pi$
$461$	−2594.63			−0.262134			−0.131067	+	0.991373i	$0.541840\pi$
$462$	1038.83	+	1326.57i	0.104612	+	0.133588i
$463$	−14136.2			−1.41893			−0.709465	−	0.704741i	$-0.751063\pi$
$463$	−14136.2			−1.41893			−0.709465	+	0.704741i	$0.751063\pi$
$464$	1305.67	−	2261.48i	0.130634	−	0.226264i
$465$	6980.20	+	12090.1i	0.696127	+	1.20573i
$466$	−3049.90	−	5282.58i	−0.303184	−	0.525131i
$467$	−7795.12	+	13501.5i	−0.772409	+	1.33785i	0.163830	+	0.986489i	$0.447615\pi$
$467$	−7795.12	+	13501.5i	−0.772409	+	1.33785i	−0.936239	+	0.351363i	$0.885718\pi$
$468$	77.8637			0.00769070
$469$	1619.06	+	2067.52i	0.159405	+	0.203559i
$470$	21172.4			2.07789
$471$	460.398	−	797.432i	0.0450404	−	0.0780122i
$472$	−1819.71	−	3151.83i	−0.177456	−	0.307362i
$473$	−1679.72	−	2909.36i	−0.163285	−	0.282817i
$474$	348.909	−	604.328i	0.0338100	−	0.0585606i
$475$	−10361.2			−1.00085
$476$	−3302.88	+	8201.37i	−0.318040	+	0.789725i
$477$	−1588.60			−0.152489
$478$	−3987.20	+	6906.04i	−0.381528	+	0.660826i
$479$	4226.75	+	7320.95i	0.403184	+	0.698336i	0.994108	−	0.108391i	$-0.0345700\pi$
$479$	4226.75	+	7320.95i	0.403184	+	0.698336i	−0.590924	+	0.806727i	$0.701237\pi$
$480$	−1000.18	−	1732.37i	−0.0951080	−	0.164732i
$481$	−182.259	+	315.683i	−0.0172772	+	0.0299249i
$482$	−1249.30			−0.118058
$483$	−35.8408	+	5.07807i	−0.00337643	+	0.000478386i
$484$	−4404.35			−0.413632
$485$	−3487.10	+	6039.83i	−0.326476	+	0.565474i
$486$	−243.000	−	420.888i	−0.0226805	−	0.0392837i
$487$	2005.53	+	3473.69i	0.186611	+	0.323219i	0.944118	−	0.329607i	$-0.106916\pi$
$487$	2005.53	+	3473.69i	0.186611	+	0.323219i	−0.757507	+	0.652827i	$0.773583\pi$
$488$	−154.606	+	267.786i	−0.0143416	+	0.0248403i
$489$	10543.5			0.975038
$490$	−10304.7	−	9906.56i	−0.950035	−	0.913332i
$491$	13927.9			1.28016			0.640079	−	0.768309i	$-0.278902\pi$
$491$	13927.9			1.28016			0.640079	+	0.768309i	$0.278902\pi$
$492$	1938.14	−	3356.95i	0.177597	−	0.307608i
$493$	−9739.33	−	16869.0i	−0.889731	−	1.54106i
$494$	72.4810	+	125.541i	0.00660137	+	0.0114339i
$495$	−1421.78	+	2462.59i	−0.129099	+	0.223607i
$496$	−3573.21			−0.323472
$497$	−11052.6	+	1565.97i	−0.997535	+	0.141335i
$498$	−3413.57			−0.307160
$499$	1973.77	−	3418.68i	0.177071	−	0.306695i	−0.763805	−	0.645447i	$-0.776671\pi$
$499$	1973.77	−	3418.68i	0.177071	−	0.306695i	0.940876	+	0.338751i	$0.110005\pi$
$500$	−7675.80	−	13294.9i	−0.686544	−	1.18913i
$501$	−1684.95	−	2918.43i	−0.150256	−	0.260251i
$502$	1328.78	−	2301.52i	0.118141	−	0.204625i
$503$	−13725.3			−1.21666			−0.608331	−	0.793684i	$-0.708161\pi$
$503$	−13725.3			−1.21666			−0.608331	+	0.793684i	$0.708161\pi$
$504$	498.136	−	1236.92i	0.0440253	−	0.109319i
$505$	−307.190			−0.0270688
$506$	−9.87887	+	17.1107i	−0.000867924	+	0.00150329i
$507$	3288.48	+	5695.82i	0.288060	+	0.498935i
$508$	360.152	+	623.801i	0.0314550	+	0.0544817i
$509$	−3915.05	+	6781.07i	−0.340926	+	0.590502i	−0.984605	−	0.174794i	$-0.944074\pi$
$509$	−3915.05	+	6781.07i	−0.340926	+	0.590502i	0.643679	+	0.765296i	$0.277407\pi$
$510$	−14921.3			−1.29554
$511$	−12586.7	−	16073.0i	−1.08963	−	1.39145i
$512$	512.000			0.0441942
$513$	452.403	−	783.586i	0.0389359	−	0.0674389i
$514$	3226.18	+	5587.91i	0.276850	+	0.479518i
$515$	8766.39	+	15183.8i	0.750084	+	1.29918i
$516$	−1329.34	+	2302.49i	−0.113413	+	0.196437i
$517$	7703.43			0.655312
$518$	3848.83	+	4914.92i	0.326463	+	0.416890i
$519$	4591.80			0.388357
$520$	−180.273	+	312.241i	−0.0152028	+	0.0263321i
$521$	2953.69	+	5115.95i	0.248376	+	0.430199i	0.963075	−	0.269232i	$-0.0867700\pi$
$521$	2953.69	+	5115.95i	0.248376	+	0.430199i	−0.714700	+	0.699431i	$0.753437\pi$
$522$	1468.87	+	2544.17i	0.123163	+	0.213324i
$523$	−3954.03	+	6848.58i	−0.330588	+	0.572595i	−0.982627	−	0.185590i	$-0.940580\pi$
$523$	−3954.03	+	6848.58i	−0.330588	+	0.572595i	0.652039	+	0.758185i	$0.273914\pi$
$524$	871.439			0.0726508
$525$	6417.36	−	15934.9i	0.533479	−	1.32468i
$526$	6501.23			0.538911
$527$	−13326.8	+	23082.7i	−1.10156	+	1.90797i
$528$	−363.909	−	630.309i	−0.0299945	−	0.0519520i
$529$	6083.29	+	10536.6i	0.499983	+	0.865995i
$530$	3677.99	−	6370.46i	0.301437	−	0.522104i
$531$	4094.35			0.334613
$532$	2458.01	−	348.260i	0.200316	−	0.0283816i
$533$	−698.659			−0.0567773
$534$	1149.48	−	1990.95i	0.0931512	−	0.161343i
$535$	7456.26	+	12914.6i	0.602546	+	1.04364i
$536$	−567.167	−	982.362i	−0.0457050	−	0.0791633i
$537$	−5120.15	+	8868.36i	−0.411454	+	0.712659i
$538$	5652.08			0.452934
$539$	−3749.28	−	3604.43i	−0.299616	−	0.288040i
$540$	2250.41			0.179337
$541$	1970.52	−	3413.04i	0.156598	−	0.271235i	−0.777042	−	0.629449i	$-0.783281\pi$
$541$	1970.52	−	3413.04i	0.156598	−	0.271235i	0.933640	+	0.358214i	$0.116614\pi$
$542$	2396.77	+	4151.33i	0.189945	+	0.328994i
$543$	−1930.06	−	3342.97i	−0.152536	−	0.264200i
$544$	1909.58	−	3307.48i	0.150501	−	0.260675i
$545$	12502.7			0.982670
$546$	−237.966	+	33.7159i	−0.0186520	+	0.00264269i
$547$	−1828.71			−0.142943			−0.0714717	−	0.997443i	$-0.522770\pi$
$547$	−1828.71			−0.142943			−0.0714717	+	0.997443i	$0.522770\pi$
$548$	5203.71	−	9013.09i	0.405642	−	0.702592i
$549$	−173.932	−	301.259i	−0.0135214	−	0.0234197i
$550$	−4688.14	−	8120.10i	−0.363460	−	0.629532i
$551$	−2734.67	+	4736.58i	−0.211435	+	0.366216i
$552$	15.6364			0.00120567
$553$	−804.650	+	1998.02i	−0.0618756	+	0.153643i
$554$	3640.93			0.279221
$555$	−5267.65	+	9123.83i	−0.402881	+	0.697811i
$556$	5303.10	+	9185.24i	0.404499	+	0.700613i
$557$	−11266.0	−	19513.3i	−0.857011	−	1.48439i	−0.874767	−	0.484544i	$-0.838985\pi$
$557$	−11266.0	−	19513.3i	−0.857011	−	1.48439i	0.0177556	−	0.999842i	$-0.494348\pi$
$558$	2009.93	−	3481.30i	0.152486	−	0.264114i
$559$	479.201			0.0362577
$560$	3806.88	+	4861.34i	0.287268	+	0.366838i
$561$	−5429.00			−0.408579
$562$	−3083.81	+	5341.32i	−0.231464	+	0.400907i
$563$	−11677.9	−	20226.6i	−0.874179	−	1.51412i	−0.857635	−	0.514260i	$-0.828067\pi$
$563$	−11677.9	−	20226.6i	−0.874179	−	1.51412i	−0.0165446	−	0.999863i	$-0.505267\pi$
$564$	−3048.27	−	5279.76i	−0.227581	−	0.394181i
$565$	−6487.05	+	11235.9i	−0.483031	+	0.836634i
$566$	5109.54			0.379452
$567$	924.903	+	1181.09i	0.0685049	+	0.0874800i
$568$	4821.94			0.356204
$569$	10443.8	−	18089.2i	0.769468	−	1.33276i	−0.168384	−	0.985721i	$-0.553855\pi$
$569$	10443.8	−	18089.2i	0.769468	−	1.33276i	0.937852	−	0.347036i	$-0.112812\pi$
$570$	2094.84	+	3628.37i	0.153935	+	0.266624i
$571$	−11872.6	−	20564.0i	−0.870147	−	1.50714i	−0.861844	−	0.507173i	$-0.830690\pi$
$571$	−11872.6	−	20564.0i	−0.870147	−	1.50714i	−0.00830301	−	0.999966i	$-0.502643\pi$
$572$	−65.5910	+	113.607i	−0.00479457	+	0.00830444i
$573$	3165.89			0.230815
$574$	−4469.70	+	11098.7i	−0.325021	+	0.807058i
$575$	201.440			0.0146098
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	−1227.20	−	2125.57i	−0.0885422	−	0.153360i	0.818353	−	0.574716i	$-0.194887\pi$
$577$	−1227.20	−	2125.57i	−0.0885422	−	0.153360i	−0.906895	+	0.421356i	$0.861554\pi$
$578$	−9331.06	−	16161.9i	−0.671490	−	1.16305i
$579$	7156.26	−	12395.0i	0.513651	−	0.889670i
$580$	−13603.2			−0.973863
$581$	10432.5	−	1478.12i	0.744945	−	0.105547i
$582$	2008.20			0.143029
$583$	1338.21	−	2317.85i	0.0950652	−	0.164658i
$584$	4409.20	+	7636.95i	0.312421	+	0.541129i
$585$	−202.807	−	351.272i	−0.0143334	−	0.0248261i
$586$	1846.47	−	3198.17i	0.130165	−	0.225453i
$587$	18567.5			1.30556			0.652780	−	0.757547i	$-0.273603\pi$
$587$	18567.5			1.30556			0.652780	+	0.757547i	$0.273603\pi$
$588$	−986.795	+	3995.96i	−0.0692088	+	0.280256i
$589$	7483.95			0.523550
$590$	−9479.39	+	16418.8i	−0.661458	+	1.14568i
$591$	−2433.47	−	4214.89i	−0.169373	−	0.293363i
$592$	−1348.27	−	2335.28i	−0.0936042	−	0.162127i
$593$	−8556.47	+	14820.2i	−0.592533	+	1.02630i	0.401357	+	0.915922i	$0.368539\pi$
$593$	−8556.47	+	14820.2i	−0.592533	+	1.02630i	−0.993890	+	0.110375i	$0.964795\pi$
$594$	818.795			0.0565582
$595$	45602.2	−	6461.10i	3.14203	−	0.445175i
$596$	2324.09			0.159729
$597$	5325.20	−	9223.52i	0.365069	−	0.632318i
$598$	−1.40915	−	2.44072i	−9.63621e−5	−	0.000166904i
$599$	−11632.4	−	20147.9i	−0.793469	−	1.37433i	−0.923807	−	0.382859i	$-0.874940\pi$
$599$	−11632.4	−	20147.9i	−0.793469	−	1.37433i	0.130338	−	0.991470i	$-0.458394\pi$
$600$	−3710.23	+	6426.30i	−0.252449	+	0.437254i
$601$	25322.3			1.71867			0.859334	−	0.511416i	$-0.170879\pi$
$601$	25322.3			1.71867			0.859334	+	0.511416i	$0.170879\pi$
$602$	3065.71	−	7612.45i	0.207556	−	0.515382i
$603$	1276.13			0.0861821
$604$	1230.78	−	2131.77i	0.0829135	−	0.143610i
$605$	11471.7	+	19869.6i	0.770897	+	1.33523i
$606$	44.2272	+	76.6038i	0.00296470	+	0.00513501i
$607$	10867.2	−	18822.5i	0.726665	−	1.25862i	−0.231620	−	0.972806i	$-0.574403\pi$
$607$	10867.2	−	18822.5i	0.726665	−	1.25862i	0.958285	−	0.285814i	$-0.0922639\pi$
$608$	−1072.36			−0.0715297
$609$	−5590.81	−	7139.41i	−0.372005	−	0.475046i
$610$	1610.77			0.106915
$611$	−549.420	+	951.624i	−0.0363784	+	0.0630092i
$612$	2148.27	+	3720.92i	0.141893	+	0.245767i
$613$	6786.19	+	11754.0i	0.447131	+	0.774454i	0.998198	−	0.0600072i	$-0.0191124\pi$
$613$	6786.19	+	11754.0i	0.447131	+	0.774454i	−0.551067	+	0.834461i	$0.685779\pi$
$614$	−7041.50	+	12196.2i	−0.462820	+	0.801628i
$615$	−20192.6			−1.32397
$616$	1385.11	+	1768.76i	0.0905966	+	0.115691i
$617$	−8497.12			−0.554427			−0.277213	−	0.960808i	$-0.589411\pi$
$617$	−8497.12			−0.554427			−0.277213	+	0.960808i	$0.589411\pi$
$618$	2524.26	−	4372.15i	0.164305	−	0.284585i
$619$	11491.5	+	19903.8i	0.746173	+	1.29241i	0.949645	+	0.313329i	$0.101444\pi$
$619$	11491.5	+	19903.8i	0.746173	+	1.29241i	−0.203472	+	0.979081i	$0.565223\pi$
$620$	9306.93	+	16120.1i	0.602863	+	1.04419i
$621$	−8.79548	+	15.2342i	−0.000568358	+	0.000984425i
$622$	−5371.98			−0.346297
$623$	−2650.91	+	6582.46i	−0.170476	+	0.423308i
$624$	103.818			0.00666034
$625$	−20661.3	+	35786.4i	−1.32232	+	2.29033i
$626$	−2219.19	−	3843.75i	−0.141688	−	0.245411i
$627$	762.193	+	1320.16i	0.0485471	+	0.0840861i
$628$	613.864	−	1063.24i	0.0390061	−	0.0675605i
$629$	−20114.3			−1.27505
$630$	−6877.67	+	974.456i	−0.434941	+	0.0616242i
$631$	−15717.9			−0.991635			−0.495817	−	0.868427i	$-0.665131\pi$
$631$	−15717.9			−0.991635			−0.495817	+	0.868427i	$0.665131\pi$
$632$	465.212	−	805.771i	0.0292803	−	0.0507150i
$633$	−6980.08	−	12089.9i	−0.438283	−	0.759129i
$634$	−2221.26	−	3847.34i	−0.139144	−	0.241005i
$635$	1876.13	−	3249.55i	0.117247	−	0.203078i
$636$	−2118.14			−0.132059
$637$	712.669	−	206.084i	0.0443280	−	0.0128185i
$638$	−4949.42			−0.307131
$639$	−2712.34	+	4697.91i	−0.167916	+	0.290840i
$640$	−1333.58	−	2309.82i	−0.0823660	−	0.142662i
$641$	−14553.7	−	25207.7i	−0.896780	−	1.55327i	−0.831587	−	0.555395i	$-0.812567\pi$
$641$	−14553.7	−	25207.7i	−0.896780	−	1.55327i	−0.0651930	−	0.997873i	$-0.520766\pi$
$642$	2147.01	−	3718.73i	0.131987	−	0.228609i
$643$	−3112.26			−0.190880			−0.0954398	−	0.995435i	$-0.530426\pi$
$643$	−3112.26			−0.190880			−0.0954398	+	0.995435i	$0.530426\pi$
$644$	−47.7878	+	6.77076i	−0.00292407	+	0.000414294i
$645$	13849.8			0.845482
$646$	−3999.53	+	6927.39i	−0.243590	+	0.421911i
$647$	3928.80	+	6804.87i	0.238728	+	0.413489i	0.960349	−	0.278799i	$-0.0899363\pi$
$647$	3928.80	+	6804.87i	0.238728	+	0.413489i	−0.721622	+	0.692288i	$0.756603\pi$
$648$	−324.000	−	561.184i	−0.0196419	−	0.0340207i
$649$	−3449.01	+	5973.86i	−0.208606	+	0.361317i
$650$	1337.46			0.0807071
$651$	−4635.28	+	11509.8i	−0.279064	+	0.692944i
$652$	14058.0			0.844408
$653$	9761.01	−	16906.6i	0.584958	−	1.01318i	−0.409923	−	0.912120i	$-0.634444\pi$
$653$	9761.01	−	16906.6i	0.584958	−	1.01318i	0.994881	−	0.101057i	$-0.0322224\pi$
$654$	−1800.06	−	3117.79i	−0.107627	−	0.186415i
$655$	−2269.79	−	3931.38i	−0.135401	−	0.234522i
$656$	2584.18	−	4475.93i	0.153804	−	0.266396i
$657$	−9920.69			−0.589107
$658$	11602.3	+	14816.0i	0.687393	+	0.877793i
$659$	664.061			0.0392536			0.0196268	−	0.999807i	$-0.493752\pi$
$659$	664.061			0.0392536			0.0196268	+	0.999807i	$0.493752\pi$
$660$	−1895.70	+	3283.46i	−0.111803	+	0.193649i
$661$	−7960.82	−	13788.5i	−0.468442	−	0.811365i	0.530908	−	0.847430i	$-0.321851\pi$
$661$	−7960.82	−	13788.5i	−0.468442	−	0.811365i	−0.999349	+	0.0360650i	$0.988518\pi$
$662$	−4154.06	−	7195.04i	−0.243885	−	0.422422i
$663$	387.205	−	670.658i	0.0226814	−	0.0392854i
$664$	−4551.42			−0.266008
$665$	−7973.36	−	10181.9i	−0.464953	−	0.593739i
$666$	3033.61			0.176502
$667$	53.1665	−	92.0870i	0.00308638	−	0.00534576i
$668$	−2246.61	−	3891.24i	−0.130125	−	0.225384i
$669$	6974.30	+	12079.8i	0.403052	+	0.698107i
$670$	−2954.53	+	5117.40i	−0.170363	+	0.295078i
$671$	586.068			0.0337182
$672$	664.182	−	1649.23i	0.0381270	−	0.0946731i
$673$	24631.0			1.41078			0.705391	−	0.708819i	$-0.250771\pi$
$673$	24631.0			1.41078			0.705391	+	0.708819i	$0.250771\pi$
$674$	254.167	−	440.230i	0.0145254	−	0.0251588i
$675$	−4174.01	−	7229.59i	−0.238011	−	0.412247i
$676$	4384.64	+	7594.43i	0.249468	+	0.432091i
$677$	−8546.39	+	14802.8i	−0.485177	+	0.840350i	−0.999855	−	0.0170329i	$-0.994578\pi$
$677$	−8546.39	+	14802.8i	−0.485177	+	0.840350i	0.514678	+	0.857383i	$0.327911\pi$
$678$	3735.86			0.211615
$679$	−6137.45	+	869.578i	−0.346883	+	0.0491478i
$680$	−19895.0			−1.12197
$681$	−6227.57	+	10786.5i	−0.350428	+	0.606958i
$682$	3386.26	+	5865.18i	0.190127	+	0.329310i
$683$	9581.79	+	16596.1i	0.536804	+	0.929771i	0.999074	+	0.0430322i	$0.0137018\pi$
$683$	9581.79	+	16596.1i	0.536804	+	0.929771i	−0.462270	+	0.886739i	$0.652965\pi$
$684$	603.205	−	1044.78i	0.0337194	−	0.0584038i
$685$	−54215.2			−3.02402
$686$	1285.53	−	12639.7i	0.0715478	−	0.703478i
$687$	12790.9			0.710339
$688$	−1772.45	+	3069.98i	−0.0982183	+	0.170119i
$689$	190.886	+	330.625i	0.0105547	+	0.0182813i
$690$	−40.7272	−	70.5416i	−0.00224704	−	0.00389199i
$691$	−4047.94	+	7011.23i	−0.222852	+	0.385991i	−0.955673	−	0.294431i	$-0.904870\pi$
$691$	−4047.94	+	7011.23i	−0.222852	+	0.385991i	0.732821	+	0.680422i	$0.238203\pi$
$692$	6122.39			0.336327
$693$	−2502.39	+	354.549i	−0.137169	+	0.0194346i
$694$	−12449.3			−0.680934
$695$	27625.3	−	47848.5i	1.50775	−	2.61150i
$696$	1958.50	+	3392.22i	0.106662	+	0.184744i
$697$	−19276.1	−	33387.2i	−1.04754	−	1.81439i
$698$	−9732.21	+	16856.7i	−0.527750	+	0.914090i
$699$	9149.70			0.495098
$700$	8556.48	−	21246.6i	0.462006	−	1.14721i
$701$	12354.7			0.665664			0.332832	−	0.942986i	$-0.391996\pi$
$701$	12354.7			0.665664			0.332832	+	0.942986i	$0.391996\pi$
$702$	−58.3977	+	101.148i	−0.00313972	+	0.00543815i
$703$	2823.90	+	4891.14i	0.151501	+	0.262408i
$704$	−485.212	−	840.412i	−0.0259760	−	0.0449918i
$705$	−15879.3	+	27503.8i	−0.848297	+	1.46929i
$706$	2851.23			0.151993
$707$	−168.337	−	214.965i	−0.00895470	−	0.0114350i
$708$	5459.14			0.289784
$709$	−1914.41	+	3315.85i	−0.101406	+	0.175641i	−0.912264	−	0.409602i	$-0.865668\pi$
$709$	−1914.41	+	3315.85i	−0.101406	+	0.175641i	0.810858	+	0.585243i	$0.199001\pi$
$710$	−12559.4	−	21753.5i	−0.663868	−	1.14985i
$711$	523.364	+	906.492i	0.0276057	+	0.0478145i
$712$	1532.64	−	2654.60i	0.0806713	−	0.139727i
$713$	−145.500			−0.00764241
$714$	−8176.73	−	10441.6i	−0.428580	−	0.547292i
$715$	683.363			0.0357431
$716$	−6826.86	+	11824.5i	−0.356329	+	0.617181i
$717$	−5980.81	−	10359.1i	−0.311516	−	0.539562i
$718$	5766.49	+	9987.86i	0.299726	+	0.519141i
$719$	−611.500	+	1059.15i	−0.0317178	+	0.0549368i	−0.881449	−	0.472280i	$-0.843431\pi$
$719$	−611.500	+	1059.15i	−0.0317178	+	0.0549368i	0.849731	+	0.527217i	$0.176764\pi$
$720$	3000.55			0.155311
$721$	−5821.42	+	14455.1i	−0.300695	+	0.746654i
$722$	−11472.0			−0.591333
$723$	936.972	−	1622.88i	0.0481969	−	0.0834795i
$724$	−2573.42	−	4457.29i	−0.132100	−	0.228804i
$725$	25230.8	+	43701.1i	1.29248	+	2.23864i
$726$	3303.26	−	5721.42i	0.168864	−	0.292482i
$727$	6368.21			0.324875			0.162437	−	0.986719i	$-0.448064\pi$
$727$	6368.21			0.324875			0.162437	+	0.986719i	$0.448064\pi$
$728$	−317.288	+	44.9546i	−0.0161531	+	0.00228864i
$729$	729.000			0.0370370
$730$	22968.7	−	39783.0i	1.16454	−	2.01704i
$731$	13221.2	+	22899.9i	0.668954	+	1.15866i
$732$	−231.909	−	401.678i	−0.0117098	−	0.0202820i
$733$	12577.0	−	21784.0i	0.633753	−	1.09769i	−0.353024	−	0.935614i	$-0.614847\pi$
$733$	12577.0	−	21784.0i	0.633753	−	1.09769i	0.986778	−	0.162079i	$-0.0518199\pi$
$734$	23090.7			1.16116
$735$	20597.5	−	5956.24i	1.03367	−	0.298910i
$736$	20.8485			0.00104414
$737$	−1074.98	+	1861.93i	−0.0537281	+	0.0930597i
$738$	2907.20	+	5035.43i	0.145008	+	0.251161i
$739$	5369.55	+	9300.34i	0.267283	+	0.462948i	0.968159	−	0.250335i	$-0.0805408\pi$
$739$	5369.55	+	9300.34i	0.267283	+	0.462948i	−0.700876	+	0.713283i	$0.747207\pi$
$740$	−7023.53	+	12165.1i	−0.348906	+	0.604322i
$741$	−217.443			−0.0107800
$742$	6473.42	−	917.180i	0.320279	−	0.0453783i
$743$	28166.3			1.39074			0.695370	−	0.718652i	$-0.255240\pi$
$743$	28166.3			1.39074			0.695370	+	0.718652i	$0.255240\pi$
$744$	2679.91	−	4641.74i	0.132057	−	0.228729i
$745$	−6053.42	−	10484.8i	−0.297691	−	0.515617i
$746$	6479.57	+	11222.9i	0.318008	+	0.550806i
$747$	2560.18	−	4434.36i	0.125398	−	0.217195i
$748$	−7238.67			−0.353839
$749$	−4951.41	+	12294.8i	−0.241549	+	0.599791i
$750$	23027.4			1.12112
$751$	−14328.5	+	24817.7i	−0.696211	+	1.20587i	0.273559	+	0.961855i	$0.411799\pi$
$751$	−14328.5	+	24817.7i	−0.696211	+	1.20587i	−0.969771	+	0.244018i	$0.921534\pi$
$752$	−4064.36	−	7039.68i	−0.197091	−	0.341371i
$753$	1993.18	+	3452.28i	0.0964613	+	0.167076i
$754$	353.000	−	611.414i	0.0170497	−	0.0295310i
$755$	−12823.0			−0.618113
$756$	1233.20	+	1574.79i	0.0593270	+	0.0757599i
$757$	−23604.1			−1.13330			−0.566648	−	0.823960i	$-0.691760\pi$
$757$	−23604.1			−1.13330			−0.566648	+	0.823960i	$0.691760\pi$
$758$	−611.996	+	1060.01i	−0.0293255	+	0.0507932i
$759$	−14.8183	−	25.6661i	−0.000708657	−	0.00122743i
$760$	2793.12	+	4837.83i	0.133312	+	0.230903i
$761$	−2315.48	+	4010.54i	−0.110297	+	0.191041i	−0.915890	−	0.401429i	$-0.868514\pi$
$761$	−2315.48	+	4010.54i	−0.110297	+	0.191041i	0.805593	+	0.592470i	$0.201847\pi$
$762$	−1080.45			−0.0513658
$763$	6851.35	+	8749.10i	0.325079	+	0.415123i
$764$	4221.18			0.199891
$765$	11191.0	−	19383.3i	0.528902	−	0.916085i
$766$	−4360.81	−	7553.15i	−0.205695	−	0.356274i
$767$	−491.977	−	852.129i	−0.0231607	−	0.0401155i
$768$	−384.000	+	665.108i	−0.0180422	+	0.0312500i
$769$	33276.8			1.56046			0.780228	−	0.625495i	$-0.215103\pi$
$769$	33276.8			1.56046			0.780228	+	0.625495i	$0.215103\pi$
$770$	4371.85	−	10855.7i	0.204611	−	0.508069i
$771$	−9678.55			−0.452094
$772$	9541.68	−	16526.7i	0.444835	−	0.770477i
$773$	11469.4	+	19865.6i	0.533668	+	0.924340i	0.999227	+	0.0393231i	$0.0125202\pi$
$773$	11469.4	+	19865.6i	0.533668	+	0.924340i	−0.465558	+	0.885017i	$0.654147\pi$
$774$	−1994.01	−	3453.73i	−0.0926011	−	0.160390i
$775$	34524.6	−	59798.3i	1.60020	−	2.77164i
$776$	2677.61			0.123867
$777$	−9271.29	+	1313.59i	−0.428064	+	0.0606498i
$778$	−26293.8			−1.21167
$779$	−5412.47	+	9374.67i	−0.248937	+	0.431171i
$780$	−270.409	−	468.362i	−0.0124131	−	0.0215001i
$781$	−4569.66	−	7914.88i	−0.209366	−	0.362633i
$782$	77.7575	−	134.680i	0.00355576	−	0.00615876i
$783$	−4406.62			−0.201124
$784$	−1315.73	+	5327.95i	−0.0599366	+	0.242709i
$785$	−6395.58			−0.290787
$786$	−653.580	+	1132.03i	−0.0296596	+	0.0513719i
$787$	6757.23	+	11703.9i	0.306060	+	0.530112i	0.977497	−	0.210950i	$-0.0676558\pi$
$787$	6757.23	+	11703.9i	0.306060	+	0.530112i	−0.671437	+	0.741062i	$0.734322\pi$
$788$	−3244.62	−	5619.85i	−0.146681	−	0.254059i
$789$	−4875.92	+	8445.34i	−0.220009	+	0.381067i
$790$	−4846.84			−0.218282
$791$	−11417.5	+	1617.68i	−0.513223	+	0.0727155i
$792$	1091.73			0.0489809
$793$	−41.7993	+	72.3985i	−0.00187180	+	0.00324205i
$794$	8478.04	+	14684.4i	0.378935	+	0.656335i
$795$	5516.98	+	9555.69i	0.246122	+	0.426296i
$796$	7100.27	−	12298.0i	0.316159	−	0.547603i
$797$	10473.4			0.465480			0.232740	−	0.972539i	$-0.425231\pi$
$797$	10473.4			0.465480			0.232740	+	0.972539i	$0.425231\pi$
$798$	−1391.10	+	3454.24i	−0.0617099	+	0.153232i
$799$	−60634.5			−2.68472
$800$	−4946.97	+	8568.40i	−0.218627	+	0.378673i
$801$	1724.22	+	2986.43i	0.0760576	+	0.131736i
$802$	−2803.00	−	4854.94i	−0.123413	−	0.213758i
$803$	8357.02	−	14474.8i	0.367264	−	0.636119i
$804$	1701.50			0.0746359
$805$	155.015	+	197.953i	0.00678705	+	0.00866698i
$806$	−966.053			−0.0422181
$807$	−4239.06	+	7342.27i	−0.184910	+	0.320273i
$808$	58.9697	+	102.138i	0.00256751	+	0.00444705i
$809$	−11784.0	−	20410.5i	−0.512117	−	0.887013i	−0.999901	−	0.0140486i	$-0.995528\pi$
$809$	−11784.0	−	20410.5i	−0.512117	−	0.887013i	0.487784	−	0.872964i	$-0.337805\pi$
$810$	−1687.81	+	2923.37i	−0.0732142	+	0.126811i
$811$	−6704.22			−0.290280			−0.145140	−	0.989411i	$-0.546363\pi$
$811$	−6704.22			−0.290280			−0.145140	+	0.989411i	$0.546363\pi$
$812$	−7454.42	−	9519.21i	−0.322166	−	0.411402i
$813$	−7190.31			−0.310178
$814$	−2555.46	+	4426.19i	−0.110035	+	0.190587i
$815$	−36616.0	−	63420.8i	−1.57375	−	2.72581i
$816$	2864.36	+	4961.22i	0.122883	+	0.212840i
$817$	3712.34	−	6429.95i	0.158970	−	0.275343i
$818$	−12770.8			−0.545867
$819$	134.676	−	334.414i	0.00574599	−	0.0142678i
$820$	−26923.5			−1.14659
$821$	−12269.7	+	21251.8i	−0.521579	+	0.903401i	0.478106	+	0.878302i	$0.341323\pi$
$821$	−12269.7	+	21251.8i	−0.521579	+	0.903401i	−0.999685	+	0.0250988i	$0.992010\pi$
$822$	7805.57	+	13519.6i	0.331205	+	0.573664i
$823$	15558.5	+	26948.1i	0.658973	+	1.14137i	0.980882	+	0.194604i	$0.0623421\pi$
$823$	15558.5	+	26948.1i	0.658973	+	1.14137i	−0.321909	+	0.946771i	$0.604325\pi$
$824$	3365.68	−	5829.53i	0.142293	−	0.246458i
$825$	14064.4			0.593528
$826$	−16684.1	+	2363.88i	−0.702803	+	0.0995760i
$827$	31244.9			1.31377			0.656887	−	0.753989i	$-0.271873\pi$
$827$	31244.9			1.31377			0.656887	+	0.753989i	$0.271873\pi$
$828$	−11.7273	+	20.3123i	−0.000492212	+	0.000852537i
$829$	−2115.75	−	3664.58i	−0.0886405	−	0.153530i	0.818296	−	0.574797i	$-0.194919\pi$
$829$	−2115.75	−	3664.58i	−0.0886405	−	0.153530i	−0.906937	+	0.421267i	$0.861586\pi$
$830$	11854.8	+	20533.2i	0.495767	+	0.858694i
$831$	−2730.70	+	4729.71i	−0.113991	+	0.197439i
$832$	138.424			0.00576803
$833$	29510.9	+	28370.8i	1.22748	+	1.18006i
$834$	−15909.3			−0.660544
$835$	−11703.2	+	20270.5i	−0.485037	+	0.840109i
$836$	1016.26	+	1760.21i	0.0420431	+	0.0728207i
$837$	3014.90	+	5221.96i	0.124504	+	0.215648i
$838$	−4831.66	+	8368.68i	−0.199173	+	0.344978i
$839$	−38670.4			−1.59124			−0.795621	−	0.605795i	$-0.792855\pi$
$839$	−38670.4			−1.59124			−0.795621	+	0.605795i	$0.792855\pi$
$840$	−9170.23	+	1299.27i	−0.376670	+	0.0533681i
$841$	2247.96			0.0921710
$842$	−7475.37	+	12947.7i	−0.305960	+	0.529938i
$843$	−4625.72	−	8011.97i	−0.188989	−	0.327339i
$844$	−9306.77	−	16119.8i	−0.379564	−	0.657425i
$845$	22840.8	−	39561.5i	0.929880	−	1.61060i
$846$	9144.82			0.371637
$847$	−7617.94	+	18916.1i	−0.309038	+	0.767372i
$848$	−2824.18			−0.114367
$849$	−3832.15	+	6637.48i	−0.154911	+	0.268313i
$850$	36900.8	+	63914.1i	1.48904	+	2.57910i
$851$	−54.9014	−	95.0920i	−0.00221151	−	0.00383045i
$852$	−3616.45	+	6263.88i	−0.145420	+	0.251875i
$853$	−19944.4			−0.800565			−0.400282	−	0.916392i	$-0.631088\pi$
$853$	−19944.4			−0.800565			−0.400282	+	0.916392i	$0.631088\pi$
$854$	882.689	+	1127.18i	0.0353689	+	0.0451656i
$855$	−6284.52			−0.251376
$856$	2862.68	−	4958.31i	0.114304	−	0.197981i
$857$	−6941.10	−	12022.3i	−0.276667	−	0.479201i	0.693887	−	0.720084i	$-0.255897\pi$
$857$	−6941.10	−	12022.3i	−0.276667	−	0.479201i	−0.970554	+	0.240882i	$0.922563\pi$
$858$	−98.3864	−	170.410i	−0.00391475	−	0.00678055i
$859$	2078.58	−	3600.21i	0.0825614	−	0.143000i	−0.821788	−	0.569793i	$-0.807023\pi$
$859$	2078.58	−	3600.21i	0.0825614	−	0.143000i	0.904349	+	0.426793i	$0.140357\pi$
$860$	18466.4			0.732209
$861$	−11065.4	−	14130.3i	−0.437987	−	0.559304i
$862$	13983.9			0.552543
$863$	8118.96	−	14062.5i	0.320246	−	0.554683i	−0.660292	−	0.751009i	$-0.729568\pi$
$863$	8118.96	−	14062.5i	0.320246	−	0.554683i	0.980539	+	0.196326i	$0.0629009\pi$
$864$	−432.000	−	748.246i	−0.0170103	−	0.0294628i
$865$	−15946.6	−	27620.4i	−0.626823	−	1.08569i
$866$	7699.26	−	13335.5i	0.302115	−	0.523278i
$867$	27993.2			1.09654
$868$	−6180.37	+	15346.5i	−0.241677	+	0.600107i
$869$	−1763.49			−0.0688403
$870$	10202.4	−	17671.0i	0.397578	−	0.688625i
$871$	−153.339	−	265.591i	−0.00596521	−	0.0103320i
$872$	−2400.08	−	4157.05i	−0.0932074	−	0.161440i
$873$	−1506.15	+	2608.73i	−0.0583913	+	0.101137i
$874$	−43.6664			−0.00168998
$875$	−70376.0	+	9971.15i	−2.71902	+	0.385242i
$876$	−13227.6			−0.510181
$877$	8244.70	−	14280.2i	0.317450	−	0.549840i	−0.662505	−	0.749057i	$-0.730507\pi$
$877$	8244.70	−	14280.2i	0.317450	−	0.549840i	0.979955	+	0.199218i	$0.0638401\pi$
$878$	−9412.32	−	16302.6i	−0.361789	−	0.626636i
$879$	2769.70	+	4797.26i	0.106279	+	0.184081i
$880$	−2527.61	+	4377.94i	−0.0968245	+	0.167705i
$881$	45411.7			1.73662			0.868309	−	0.496023i	$-0.165207\pi$
$881$	45411.7			1.73662			0.868309	+	0.496023i	$0.165207\pi$
$882$	−4450.81	−	4278.85i	−0.169917	−	0.163352i
$883$	−2206.85			−0.0841070			−0.0420535	−	0.999115i	$-0.513390\pi$
$883$	−2206.85			−0.0841070			−0.0420535	+	0.999115i	$0.513390\pi$
$884$	516.273	−	894.211i	0.0196427	−	0.0340221i
$885$	−14219.1	−	24628.2i	−0.540078	−	0.935443i
$886$	6258.18	+	10839.5i	0.237300	+	0.411015i
$887$	−14073.1	+	24375.3i	−0.532727	+	0.922710i	0.466543	+	0.884498i	$0.345499\pi$
$887$	−14073.1	+	24375.3i	−0.532727	+	0.922710i	−0.999270	+	0.0382111i	$0.987834\pi$
$888$	4044.82			0.152855
$889$	3302.07	−	467.851i	0.124576	−	0.0176504i
$890$	−15967.9			−0.601398
$891$	−614.097	+	1063.65i	−0.0230898	+	0.0399927i
$892$	9299.07	+	16106.5i	0.349054	+	0.604579i
$893$	8512.65	+	14744.3i	0.318998	+	0.552520i
$894$	−1743.07	+	3019.08i	−0.0652091	+	0.112945i
$895$	71126.1			2.65641
$896$	885.576	−	2198.97i	0.0330190	−	0.0819893i
$897$	4.22746			0.000157359
$898$	11633.8	−	20150.4i	0.432322	−	0.748804i
$899$	−18224.3	−	31565.4i	−0.676101	−	1.17104i
$900$	−5565.34	−	9639.45i	−0.206124	−	0.357017i
$901$	−10533.2	+	18244.0i	−0.389469	+	0.674579i
$902$	−9795.91			−0.361605
$903$	7589.58	+	9691.81i	0.279696	+	0.357169i
$904$	4981.15			0.183264
$905$	−13405.6	+	23219.3i	−0.492396	+	0.852856i
$906$	1846.17	+	3197.66i	0.0676986	+	0.117257i
$907$	2521.12	+	4366.71i	0.0922960	+	0.159861i	0.908477	−	0.417935i	$-0.137246\pi$
$907$	2521.12	+	4366.71i	0.0922960	+	0.159861i	−0.816181	+	0.577797i	$0.803913\pi$
$908$	−8303.43	+	14382.0i	−0.303479	+	0.525641i
$909$	−132.682			−0.00484134
$910$	1029.23	+	1314.31i	0.0374929	+	0.0478780i
$911$	29647.3			1.07822			0.539110	−	0.842235i	$-0.318761\pi$
$911$	29647.3			1.07822			0.539110	+	0.842235i	$0.318761\pi$
$912$	804.273	−	1393.04i	0.0292019	−	0.0505792i
$913$	4313.29	+	7470.84i	0.156352	+	0.270809i
$914$	13104.6	+	22697.9i	0.474248	+	0.821421i
$915$	−1208.08	+	2092.46i	−0.0436480	+	0.0756005i
$916$	17054.5			0.615172
$917$	1507.28	−	3742.71i	0.0542799	−	0.134782i
$918$	−6444.82			−0.231711
$919$	5945.64	−	10298.1i	0.213415	−	0.369646i	−0.739366	−	0.673304i	$-0.764875\pi$
$919$	5945.64	−	10298.1i	0.213415	−	0.369646i	0.952781	+	0.303658i	$0.0982080\pi$
$920$	−54.3029	−	94.0554i	−0.00194599	−	0.00337056i
$921$	−10562.2	−	18294.3i	−0.377891	−	0.654527i
$922$	2594.63	−	4494.03i	0.0926785	−	0.160524i
$923$	1303.66			0.0464902
$924$	−3336.52	+	472.732i	−0.118792	+	0.0168309i
$925$	52108.3			1.85223
$926$	14136.2	−	24484.6i	0.501667	−	0.868913i
$927$	3786.39	+	6558.22i	0.134155	+	0.232363i
$928$	2611.33	+	4522.96i	0.0923720	+	0.159993i
$929$	19594.3	−	33938.3i	0.691999	−	1.19858i	−0.279183	−	0.960238i	$-0.590063\pi$
$929$	19594.3	−	33938.3i	0.691999	−	1.19858i	0.971182	−	0.238340i	$-0.0766032\pi$
$930$	−27920.8			−0.984472
$931$	2755.74	−	11159.2i	0.0970093	−	0.392832i
$932$	12199.6			0.428768
$933$	4028.99	−	6978.41i	0.141375	−	0.244869i
$934$	−15590.2	−	27003.1i	−0.546176	−	0.946004i
$935$	18854.1	+	32656.3i	0.659461	+	1.14222i
$936$	−77.8637	+	134.864i	−0.00271907	+	0.00470957i
$937$	9716.23			0.338757			0.169379	−	0.985551i	$-0.445824\pi$
$937$	9716.23			0.338757			0.169379	+	0.985551i	$0.445824\pi$
$938$	−5200.10	+	736.771i	−0.181012	+	0.0256465i
$939$	6657.57			0.231375
$940$	−21172.4	+	36671.7i	−0.734647	+	1.27245i
$941$	3497.93	+	6058.60i	0.121179	+	0.209888i	0.920233	−	0.391371i	$-0.127999\pi$
$941$	3497.93	+	6058.60i	0.121179	+	0.209888i	−0.799054	+	0.601259i	$0.794666\pi$
$942$	920.795	+	1594.86i	0.0318483	+	0.0551629i
$943$	105.227	−	182.259i	0.00363380	−	0.00629393i
$944$	7278.85			0.250960
$945$	3892.40	−	9665.20i	0.133989	−	0.332708i
$946$	6718.88			0.230919
$947$	−7489.62	+	12972.4i	−0.257001	+	0.445139i	−0.965437	−	0.260636i	$-0.916068\pi$
$947$	−7489.62	+	12972.4i	−0.257001	+	0.445139i	0.708436	+	0.705775i	$0.249401\pi$
$948$	697.818	+	1208.66i	0.0239073	+	0.0414086i
$949$	1192.07	+	2064.73i	0.0407758	+	0.0706258i
$950$	10361.2	−	17946.2i	0.353855	−	0.612896i
$951$	6663.78			0.227222
$952$	−10902.3	−	13922.1i	−0.371161	−	0.473969i
$953$	29393.3			0.999100			0.499550	−	0.866285i	$-0.333499\pi$
$953$	29393.3			0.999100			0.499550	+	0.866285i	$0.333499\pi$
$954$	1588.60	−	2751.54i	0.0539129	−	0.0933799i
$955$	−10994.7	−	19043.3i	−0.372543	−	0.645264i
$956$	−7974.41	−	13812.1i	−0.269781	−	0.467275i
$957$	3712.06	−	6429.48i	0.125386	−	0.217174i
$958$	−16907.0			−0.570189
$959$	−29709.5	−	37938.6i	−1.00038	−	1.27748i
$960$	4000.73			0.134503
$961$	−10041.7	+	17392.7i	−0.337072	+	0.583825i
$962$	−364.519	−	631.365i	−0.0122168	−	0.0211601i
$963$	3220.52	+	5578.10i	0.107767	+	0.186658i
$964$	1249.30	−	2163.84i	0.0417397	−	0.0722953i
$965$	−99410.6			−3.31621
$966$	27.0453	−	67.1562i	0.000900797	−	0.00223677i
$967$	−7133.95			−0.237241			−0.118621	−	0.992940i	$-0.537847\pi$
$967$	−7133.95			−0.237241			−0.118621	+	0.992940i	$0.537847\pi$
$968$	4404.35	−	7628.56i	0.146241	−	0.253297i
$969$	−5999.30	−	10391.1i	−0.198891	−	0.344489i
$970$	−6974.20	−	12079.7i	−0.230854	−	0.399850i
$971$	4844.06	−	8390.16i	0.160096	−	0.277295i	−0.774807	−	0.632198i	$-0.782153\pi$
$971$	4844.06	−	8390.16i	0.160096	−	0.277295i	0.934903	+	0.354903i	$0.115486\pi$
$972$	972.000			0.0320750
$973$	48621.8	−	6888.93i	1.60200	−	0.226977i
$974$	−8022.14			−0.263907
$975$	−1003.10	+	1737.41i	−0.0329485	+	0.0570685i
$976$	−309.212	−	535.571i	−0.0101410	−	0.0175648i
$977$	−10652.8	−	18451.3i	−0.348838	−	0.604205i	0.637205	−	0.770694i	$-0.280090\pi$
$977$	−10652.8	−	18451.3i	−0.348838	−	0.604205i	−0.986043	+	0.166489i	$0.946757\pi$
$978$	−10543.5	+	18261.9i	−0.344728	+	0.597086i
$979$	−5809.79			−0.189665
$980$	27463.3	−	7941.65i	0.895187	−	0.258864i
$981$	5400.17			0.175753
$982$	−13927.9	+	24123.8i	−0.452604	+	0.783933i
$983$	18640.4	+	32286.1i	0.604818	+	1.04758i	0.992080	+	0.125606i	$0.0400874\pi$
$983$	18640.4	+	32286.1i	0.604818	+	1.04758i	−0.387262	+	0.921970i	$0.626579\pi$
$984$	3876.27	+	6713.90i	0.125580	+	0.217512i
$985$	−16902.1	+	29275.4i	−0.546748	+	0.946996i
$986$	38957.3			1.25827
$987$	−27948.3	+	3959.82i	−0.901320	+	0.127703i
$988$	−289.924			−0.00933574
$989$	−72.1740	+	125.009i	−0.00232052	+	0.00401927i
$990$	−2843.56	−	4925.18i	−0.0912870	−	0.158114i
$991$	25698.5	+	44511.2i	0.823755	+	1.42678i	0.902867	+	0.429919i	$0.141458\pi$
$991$	25698.5	+	44511.2i	0.823755	+	1.42678i	−0.0791128	+	0.996866i	$0.525209\pi$
$992$	3573.21	−	6188.98i	0.114365	−	0.198085i
$993$	12462.2			0.398263
$994$	8340.22	−	20709.6i	0.266132	−	0.660833i
$995$	−73974.6			−2.35694
$996$	3413.57	−	5912.47i	0.108597	−	0.188096i
$997$	17186.9	+	29768.6i	0.545953	+	0.945618i	0.998546	+	0.0539007i	$0.0171655\pi$
$997$	17186.9	+	29768.6i	0.545953	+	0.945618i	−0.452594	+	0.891717i	$0.649501\pi$
$998$	3947.55	+	6837.36i	0.125208	+	0.216866i
$999$	−2275.21	+	3940.78i	−0.0720565	+	0.124806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.4.e.c.37.1	yes	4
3.2	odd	2		126.4.g.g.37.2		4
4.3	odd	2		336.4.q.j.289.1		4
7.2	even	3		294.4.a.n.1.2		2
7.3	odd	6		294.4.e.l.67.2		4
7.4	even	3	inner	42.4.e.c.25.1	✓	4
7.5	odd	6		294.4.a.m.1.1		2
7.6	odd	2		294.4.e.l.79.2		4
21.2	odd	6		882.4.a.v.1.1		2
21.5	even	6		882.4.a.z.1.2		2
21.11	odd	6		126.4.g.g.109.2		4
21.17	even	6		882.4.g.bf.361.1		4
21.20	even	2		882.4.g.bf.667.1		4
28.11	odd	6		336.4.q.j.193.1		4
28.19	even	6		2352.4.a.ca.1.1		2
28.23	odd	6		2352.4.a.bq.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.e.c.25.1	✓	4	7.4	even	3	inner
42.4.e.c.37.1	yes	4	1.1	even	1	trivial
126.4.g.g.37.2		4	3.2	odd	2
126.4.g.g.109.2		4	21.11	odd	6
294.4.a.m.1.1		2	7.5	odd	6
294.4.a.n.1.2		2	7.2	even	3
294.4.e.l.67.2		4	7.3	odd	6
294.4.e.l.79.2		4	7.6	odd	2
336.4.q.j.193.1		4	28.11	odd	6
336.4.q.j.289.1		4	4.3	odd	2
882.4.a.v.1.1		2	21.2	odd	6
882.4.a.z.1.2		2	21.5	even	6
882.4.g.bf.361.1		4	21.17	even	6
882.4.g.bf.667.1		4	21.20	even	2
2352.4.a.bq.1.2		2	28.23	odd	6
2352.4.a.ca.1.1		2	28.19	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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	42.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-10.4186 + 18.0455i) q^{5} +6.00000 q^{6} +(-18.3371 + 2.59808i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-10.4186 + 18.0455i) q^{5} +6.00000 q^{6} +(-18.3371 + 2.59808i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-20.8371 - 36.0910i) q^{10} +(-7.58144 - 13.1314i) q^{11} +(-6.00000 + 10.3923i) q^{12} +2.16288 q^{13} +(13.8371 - 34.3589i) q^{14} +62.5114 q^{15} +(-8.00000 + 13.8564i) q^{16} +(59.6742 + 103.359i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(16.7557 - 29.0217i) q^{19} +83.3485 q^{20} +(34.2557 + 43.7441i) q^{21} +30.3258 q^{22} +(-0.325758 + 0.564230i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(-154.593 - 267.763i) q^{25} +(-2.16288 + 3.74622i) q^{26} +27.0000 q^{27} +(45.6742 + 58.3255i) q^{28} -163.208 q^{29} +(-62.5114 + 108.273i) q^{30} +(111.663 + 193.406i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(-22.7443 + 39.3943i) q^{33} -238.697 q^{34} +(144.163 - 357.970i) q^{35} +36.0000 q^{36} +(-84.2670 + 145.955i) q^{37} +(33.5114 + 58.0434i) q^{38} +(-3.24432 - 5.61932i) q^{39} +(-83.3485 + 144.364i) q^{40} -323.023 q^{41} +(-110.023 + 15.5885i) q^{42} +221.557 q^{43} +(-30.3258 + 52.5258i) q^{44} +(-93.7670 - 162.409i) q^{45} +(-0.651517 - 1.12846i) q^{46} +(-254.023 + 439.980i) q^{47} +48.0000 q^{48} +(329.500 - 95.2825i) q^{49} +618.371 q^{50} +(179.023 - 310.076i) q^{51} +(-4.32576 - 7.49243i) q^{52} +(88.2557 + 152.863i) q^{53} +(-27.0000 + 46.7654i) q^{54} +315.951 q^{55} +(-146.697 + 20.7846i) q^{56} -100.534 q^{57} +(163.208 - 282.685i) q^{58} +(-227.464 - 393.979i) q^{59} +(-125.023 - 216.546i) q^{60} +(-19.3258 + 33.4732i) q^{61} -446.652 q^{62} +(62.2670 - 154.615i) q^{63} +64.0000 q^{64} +(-22.5341 + 39.0302i) q^{65} +(-45.4886 - 78.7886i) q^{66} +(-70.8958 - 122.795i) q^{67} +(238.697 - 413.435i) q^{68} +1.95455 q^{69} +(475.860 + 607.668i) q^{70} +602.742 q^{71} +(-36.0000 + 62.3538i) q^{72} +(551.150 + 954.619i) q^{73} +(-168.534 - 291.910i) q^{74} +(-463.778 + 803.288i) q^{75} -134.045 q^{76} +(173.138 + 221.096i) q^{77} +12.9773 q^{78} +(58.1515 - 100.721i) q^{79} +(-166.697 - 288.728i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(323.023 - 559.492i) q^{82} -568.928 q^{83} +(83.0227 - 206.153i) q^{84} -2486.88 q^{85} +(-221.557 + 383.748i) q^{86} +(244.812 + 424.028i) q^{87} +(-60.6515 - 105.052i) q^{88} +(191.580 - 331.825i) q^{89} +375.068 q^{90} +(-39.6610 + 5.61932i) q^{91} +2.60607 q^{92} +(334.989 - 580.217i) q^{93} +(-508.045 - 879.961i) q^{94} +(349.140 + 604.728i) q^{95} +(-48.0000 + 83.1384i) q^{96} +334.701 q^{97} +(-164.466 + 665.993i) q^{98} +136.466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 5 q^{5} + 24 q^{6} + 32 q^{8} - 18 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 6 * q^3 - 8 * q^4 - 5 * q^5 + 24 * q^6 + 32 * q^8 - 18 * q^9	\( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 5 q^{5} + 24 q^{6} + 32 q^{8} - 18 q^{9} - 10 q^{10} - 67 q^{11} - 24 q^{12} + 82 q^{13} - 18 q^{14} + 30 q^{15} - 32 q^{16} + 92 q^{17} - 36 q^{18} - 43 q^{19} + 40 q^{20} + 27 q^{21} + 268 q^{22} - 148 q^{23} - 48 q^{24} - 435 q^{25} - 82 q^{26} + 108 q^{27} + 36 q^{28} + 154 q^{29} - 30 q^{30} + 520 q^{31} - 64 q^{32} - 201 q^{33} - 368 q^{34} + 650 q^{35} + 144 q^{36} - 7 q^{37} - 86 q^{38} - 123 q^{39} - 40 q^{40} - 852 q^{41} - 214 q^{43} - 268 q^{44} - 45 q^{45} - 296 q^{46} - 576 q^{47} + 192 q^{48} + 1318 q^{49} + 1740 q^{50} + 276 q^{51} - 164 q^{52} + 243 q^{53} - 108 q^{54} - 1010 q^{55} + 258 q^{57} - 154 q^{58} + 7 q^{59} - 60 q^{60} - 224 q^{61} - 2080 q^{62} - 81 q^{63} + 256 q^{64} + 570 q^{65} - 402 q^{66} - 687 q^{67} + 368 q^{68} + 888 q^{69} + 1390 q^{70} + 944 q^{71} - 144 q^{72} + 921 q^{73} - 14 q^{74} - 1305 q^{75} + 344 q^{76} - 371 q^{77} + 492 q^{78} + 526 q^{79} - 80 q^{80} - 162 q^{81} + 852 q^{82} - 442 q^{83} - 108 q^{84} - 5840 q^{85} + 214 q^{86} - 231 q^{87} - 536 q^{88} - 774 q^{89} + 180 q^{90} + 1345 q^{91} + 1184 q^{92} + 1560 q^{93} - 1152 q^{94} + 1910 q^{95} - 192 q^{96} + 3906 q^{97} - 1318 q^{98} + 1206 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 6 * q^3 - 8 * q^4 - 5 * q^5 + 24 * q^6 + 32 * q^8 - 18 * q^9 - 10 * q^10 - 67 * q^11 - 24 * q^12 + 82 * q^13 - 18 * q^14 + 30 * q^15 - 32 * q^16 + 92 * q^17 - 36 * q^18 - 43 * q^19 + 40 * q^20 + 27 * q^21 + 268 * q^22 - 148 * q^23 - 48 * q^24 - 435 * q^25 - 82 * q^26 + 108 * q^27 + 36 * q^28 + 154 * q^29 - 30 * q^30 + 520 * q^31 - 64 * q^32 - 201 * q^33 - 368 * q^34 + 650 * q^35 + 144 * q^36 - 7 * q^37 - 86 * q^38 - 123 * q^39 - 40 * q^40 - 852 * q^41 - 214 * q^43 - 268 * q^44 - 45 * q^45 - 296 * q^46 - 576 * q^47 + 192 * q^48 + 1318 * q^49 + 1740 * q^50 + 276 * q^51 - 164 * q^52 + 243 * q^53 - 108 * q^54 - 1010 * q^55 + 258 * q^57 - 154 * q^58 + 7 * q^59 - 60 * q^60 - 224 * q^61 - 2080 * q^62 - 81 * q^63 + 256 * q^64 + 570 * q^65 - 402 * q^66 - 687 * q^67 + 368 * q^68 + 888 * q^69 + 1390 * q^70 + 944 * q^71 - 144 * q^72 + 921 * q^73 - 14 * q^74 - 1305 * q^75 + 344 * q^76 - 371 * q^77 + 492 * q^78 + 526 * q^79 - 80 * q^80 - 162 * q^81 + 852 * q^82 - 442 * q^83 - 108 * q^84 - 5840 * q^85 + 214 * q^86 - 231 * q^87 - 536 * q^88 - 774 * q^89 + 180 * q^90 + 1345 * q^91 + 1184 * q^92 + 1560 * q^93 - 1152 * q^94 + 1910 * q^95 - 192 * q^96 + 3906 * q^97 - 1318 * q^98 + 1206 * q^99

Introduction

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