LMFDB - Embedded newform 74.4.c.a.63.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,4,Mod(47,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("74.47");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	74.c (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:	$4.36614134042$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 48x^{6} + 157x^{5} + 1944x^{4} + 3005x^{3} + 12895x^{2} - 11550x + 44100 $ x^8 - x^7 + 48x^6 + 157x^5 + 1944x^4 + 3005x^3 + 12895x^2 - 11550x + 44100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			63.3
Root			$-1.95521 + 3.38653i$ of defining polynomial
Character	$\chi$	$=$	74.63
Dual form			74.4.c.a.47.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(1.45521 - 2.52050i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-8.20891 + 14.2183i) q^{5} +5.82085 q^{6} +(-6.65276 + 11.5229i) q^{7} -8.00000 q^{8} +(9.26471 + 16.0469i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(1.45521 - 2.52050i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-8.20891 + 14.2183i) q^{5} +5.82085 q^{6} +(-6.65276 + 11.5229i) q^{7} -8.00000 q^{8} +(9.26471 + 16.0469i) q^{9} -32.8357 q^{10} +60.5228 q^{11} +(5.82085 + 10.0820i) q^{12} +(-12.3660 + 21.4185i) q^{13} -26.6111 q^{14} +(23.8914 + 41.3812i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-47.0001 - 81.4065i) q^{17} +(-18.5294 + 32.0939i) q^{18} +(18.3801 - 31.8352i) q^{19} +(-32.8357 - 56.8730i) q^{20} +(19.3624 + 33.5366i) q^{21} +(60.5228 + 104.829i) q^{22} -143.129 q^{23} +(-11.6417 + 20.1640i) q^{24} +(-72.2725 - 125.180i) q^{25} -49.4640 q^{26} +132.510 q^{27} +(-26.6111 - 46.0917i) q^{28} +118.321 q^{29} +(-47.7829 + 82.7624i) q^{30} +317.683 q^{31} +(16.0000 - 27.7128i) q^{32} +(88.0736 - 152.548i) q^{33} +(94.0002 - 162.813i) q^{34} +(-109.224 - 189.181i) q^{35} -74.1176 q^{36} +(95.0800 + 203.992i) q^{37} +73.5203 q^{38} +(35.9903 + 62.3371i) q^{39} +(65.6713 - 113.746i) q^{40} +(59.1649 - 102.477i) q^{41} +(-38.7248 + 67.0733i) q^{42} -217.430 q^{43} +(-121.046 + 209.657i) q^{44} -304.213 q^{45} +(-143.129 - 247.906i) q^{46} +262.977 q^{47} -46.5668 q^{48} +(82.9815 + 143.728i) q^{49} +(144.545 - 250.359i) q^{50} -273.581 q^{51} +(-49.4640 - 85.6741i) q^{52} +(-130.507 - 226.044i) q^{53} +(132.510 + 229.514i) q^{54} +(-496.826 + 860.529i) q^{55} +(53.2221 - 92.1834i) q^{56} +(-53.4939 - 92.6541i) q^{57} +(118.321 + 204.937i) q^{58} +(29.2376 + 50.6411i) q^{59} -191.132 q^{60} +(345.987 - 599.266i) q^{61} +(317.683 + 550.242i) q^{62} -246.544 q^{63} +64.0000 q^{64} +(-203.023 - 351.646i) q^{65} +352.294 q^{66} +(-148.414 + 257.060i) q^{67} +376.001 q^{68} +(-208.283 + 360.756i) q^{69} +(218.448 - 378.363i) q^{70} +(-495.169 + 857.658i) q^{71} +(-74.1176 - 128.376i) q^{72} +799.748 q^{73} +(-258.245 + 368.676i) q^{74} -420.688 q^{75} +(73.5203 + 127.341i) q^{76} +(-402.644 + 697.400i) q^{77} +(-71.9807 + 124.674i) q^{78} +(-54.2659 + 93.9912i) q^{79} +262.685 q^{80} +(-57.3166 + 99.2753i) q^{81} +236.660 q^{82} +(28.3523 + 49.1076i) q^{83} -154.899 q^{84} +1543.28 q^{85} +(-217.430 - 376.601i) q^{86} +(172.182 - 298.228i) q^{87} -484.182 q^{88} +(-712.458 - 1234.01i) q^{89} +(-304.213 - 526.912i) q^{90} +(-164.536 - 284.985i) q^{91} +(286.257 - 495.812i) q^{92} +(462.296 - 800.720i) q^{93} +(262.977 + 455.489i) q^{94} +(301.761 + 522.665i) q^{95} +(-46.5668 - 80.6561i) q^{96} +705.808 q^{97} +(-165.963 + 287.456i) q^{98} +(560.726 + 971.206i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 5 q^{3} - 16 q^{4} - 10 q^{5} - 20 q^{6} + 3 q^{7} - 64 q^{8} + 7 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 - 5 * q^3 - 16 * q^4 - 10 * q^5 - 20 * q^6 + 3 * q^7 - 64 * q^8 + 7 * q^9	\( 8 q + 8 q^{2} - 5 q^{3} - 16 q^{4} - 10 q^{5} - 20 q^{6} + 3 q^{7} - 64 q^{8} + 7 q^{9} - 40 q^{10} + 64 q^{11} - 20 q^{12} - 61 q^{13} + 12 q^{14} - 43 q^{15} - 64 q^{16} + 12 q^{17} - 14 q^{18} - 71 q^{19} - 40 q^{20} + 67 q^{21} + 64 q^{22} - 52 q^{23} + 40 q^{24} + 48 q^{25} - 244 q^{26} + 658 q^{27} + 12 q^{28} + 322 q^{29} + 86 q^{30} - 112 q^{31} + 128 q^{32} + 280 q^{33} - 24 q^{34} - 359 q^{35} - 56 q^{36} + 557 q^{37} - 284 q^{38} - 389 q^{39} + 80 q^{40} + 92 q^{41} - 134 q^{42} + 532 q^{43} - 128 q^{44} + 330 q^{45} - 52 q^{46} + 280 q^{47} + 160 q^{48} + 87 q^{49} - 96 q^{50} - 1306 q^{51} - 244 q^{52} + 159 q^{53} + 658 q^{54} - 872 q^{55} - 24 q^{56} - 469 q^{57} + 322 q^{58} + 263 q^{59} + 344 q^{60} - 206 q^{61} - 112 q^{62} - 2328 q^{63} + 512 q^{64} - 731 q^{65} + 1120 q^{66} + 245 q^{67} - 96 q^{68} - 360 q^{69} + 718 q^{70} - 957 q^{71} - 56 q^{72} - 272 q^{73} - 178 q^{74} - 3232 q^{75} - 284 q^{76} + 744 q^{77} + 778 q^{78} + 173 q^{79} + 320 q^{80} - 528 q^{81} + 368 q^{82} + 1217 q^{83} - 536 q^{84} + 2988 q^{85} + 532 q^{86} - 2336 q^{87} - 512 q^{88} - 2136 q^{89} + 330 q^{90} + 1575 q^{91} + 104 q^{92} + 2608 q^{93} + 280 q^{94} + 891 q^{95} + 160 q^{96} + 5262 q^{97} - 174 q^{98} - 176 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 5 * q^3 - 16 * q^4 - 10 * q^5 - 20 * q^6 + 3 * q^7 - 64 * q^8 + 7 * q^9 - 40 * q^10 + 64 * q^11 - 20 * q^12 - 61 * q^13 + 12 * q^14 - 43 * q^15 - 64 * q^16 + 12 * q^17 - 14 * q^18 - 71 * q^19 - 40 * q^20 + 67 * q^21 + 64 * q^22 - 52 * q^23 + 40 * q^24 + 48 * q^25 - 244 * q^26 + 658 * q^27 + 12 * q^28 + 322 * q^29 + 86 * q^30 - 112 * q^31 + 128 * q^32 + 280 * q^33 - 24 * q^34 - 359 * q^35 - 56 * q^36 + 557 * q^37 - 284 * q^38 - 389 * q^39 + 80 * q^40 + 92 * q^41 - 134 * q^42 + 532 * q^43 - 128 * q^44 + 330 * q^45 - 52 * q^46 + 280 * q^47 + 160 * q^48 + 87 * q^49 - 96 * q^50 - 1306 * q^51 - 244 * q^52 + 159 * q^53 + 658 * q^54 - 872 * q^55 - 24 * q^56 - 469 * q^57 + 322 * q^58 + 263 * q^59 + 344 * q^60 - 206 * q^61 - 112 * q^62 - 2328 * q^63 + 512 * q^64 - 731 * q^65 + 1120 * q^66 + 245 * q^67 - 96 * q^68 - 360 * q^69 + 718 * q^70 - 957 * q^71 - 56 * q^72 - 272 * q^73 - 178 * q^74 - 3232 * q^75 - 284 * q^76 + 744 * q^77 + 778 * q^78 + 173 * q^79 + 320 * q^80 - 528 * q^81 + 368 * q^82 + 1217 * q^83 - 536 * q^84 + 2988 * q^85 + 532 * q^86 - 2336 * q^87 - 512 * q^88 - 2136 * q^89 + 330 * q^90 + 1575 * q^91 + 104 * q^92 + 2608 * q^93 + 280 * q^94 + 891 * q^95 + 160 * q^96 + 5262 * q^97 - 174 * q^98 - 176 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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
$3$	1.45521	−	2.52050i	0.280056	−	0.485071i	−0.691342	−	0.722527i	$-0.742980\pi$
$3$	1.45521	−	2.52050i	0.280056	−	0.485071i	0.971398	+	0.237456i	$0.0763136\pi$
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−8.20891	+	14.2183i	−0.734227	+	1.27172i	0.220834	+	0.975311i	$0.429122\pi$
$5$	−8.20891	+	14.2183i	−0.734227	+	1.27172i	−0.955061	+	0.296408i	$0.904211\pi$
$6$	5.82085			0.396059
$7$	−6.65276	+	11.5229i	−0.359216	+	0.622179i	−0.987830	−	0.155538i	$-0.950289\pi$
$7$	−6.65276	+	11.5229i	−0.359216	+	0.622179i	0.628614	+	0.777717i	$0.283622\pi$
$8$	−8.00000			−0.353553
$9$	9.26471	+	16.0469i	0.343137	+	0.594331i
$10$	−32.8357			−1.03835
$11$	60.5228			1.65894			0.829469	−	0.558553i	$-0.188643\pi$
$11$	60.5228			1.65894			0.829469	+	0.558553i	$0.188643\pi$
$12$	5.82085	+	10.0820i	0.140028	+	0.242536i
$13$	−12.3660	+	21.4185i	−0.263824	+	0.456956i	−0.967255	−	0.253807i	$-0.918317\pi$
$13$	−12.3660	+	21.4185i	−0.263824	+	0.456956i	0.703431	+	0.710764i	$0.251650\pi$
$14$	−26.6111			−0.508007
$15$	23.8914	+	41.3812i	0.411250	+	0.712305i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−47.0001	−	81.4065i	−0.670541	−	1.16141i	−0.977751	−	0.209769i	$-0.932729\pi$
$17$	−47.0001	−	81.4065i	−0.670541	−	1.16141i	0.307210	−	0.951642i	$-0.400605\pi$
$18$	−18.5294	+	32.0939i	−0.242635	+	0.420256i
$19$	18.3801	−	31.8352i	0.221931	−	0.384395i	−0.733464	−	0.679729i	$-0.762098\pi$
$19$	18.3801	−	31.8352i	0.221931	−	0.384395i	0.955394	+	0.295334i	$0.0954308\pi$
$20$	−32.8357	−	56.8730i	−0.367114	−	0.635860i
$21$	19.3624	+	33.5366i	0.201201	+	0.348490i
$22$	60.5228	+	104.829i	0.586523	+	1.01589i
$23$	−143.129			−1.29758			−0.648791	−	0.760967i	$-0.724725\pi$
$23$	−143.129			−1.29758			−0.648791	+	0.760967i	$0.724725\pi$
$24$	−11.6417	+	20.1640i	−0.0990148	+	0.171499i
$25$	−72.2725	−	125.180i	−0.578180	−	1.00144i
$26$	−49.4640			−0.373103
$27$	132.510			0.944503
$28$	−26.6111	−	46.0917i	−0.179608	−	0.311090i
$29$	118.321			0.757641			0.378821	−	0.925470i	$-0.376330\pi$
$29$	118.321			0.757641			0.378821	+	0.925470i	$0.376330\pi$
$30$	−47.7829	+	82.7624i	−0.290797	+	0.503676i
$31$	317.683			1.84056			0.920282	−	0.391256i	$-0.127959\pi$
$31$	317.683			1.84056			0.920282	+	0.391256i	$0.127959\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	88.0736	−	152.548i	0.464595	−	0.804703i
$34$	94.0002	−	162.813i	0.474144	−	0.821242i
$35$	−109.224	−	189.181i	−0.527492	−	0.913643i
$36$	−74.1176			−0.343137
$37$	95.0800	+	203.992i	0.422461	+	0.906381i
$37$	95.0800	+	203.992i	0.422461	+	0.906381i
$38$	73.5203			0.313857
$39$	35.9903	+	62.3371i	0.147771	+	0.255947i
$40$	65.6713	−	113.746i	0.259589	−	0.449621i
$41$	59.1649	−	102.477i	0.225366	−	0.390346i	−0.731063	−	0.682310i	$-0.760975\pi$
$41$	59.1649	−	102.477i	0.225366	−	0.390346i	0.956429	+	0.291964i	$0.0943088\pi$
$42$	−38.7248	+	67.0733i	−0.142271	+	0.246420i
$43$	−217.430			−0.771113			−0.385556	−	0.922684i	$-0.625990\pi$
$43$	−217.430			−0.771113			−0.385556	+	0.922684i	$0.625990\pi$
$44$	−121.046	+	209.657i	−0.414734	+	0.718341i
$45$	−304.213			−1.00776
$46$	−143.129	−	247.906i	−0.458764	−	0.794603i
$47$	262.977			0.816151			0.408075	−	0.912948i	$-0.366200\pi$
$47$	262.977			0.816151			0.408075	+	0.912948i	$0.366200\pi$
$48$	−46.5668			−0.140028
$49$	82.9815	+	143.728i	0.241928	+	0.419032i
$50$	144.545	−	250.359i	0.408835	−	0.708123i
$51$	−273.581			−0.751156
$52$	−49.4640	−	85.6741i	−0.131912	−	0.228478i
$53$	−130.507	−	226.044i	−0.338235	−	0.585840i	0.645866	−	0.763451i	$-0.276497\pi$
$53$	−130.507	−	226.044i	−0.338235	−	0.585840i	−0.984101	+	0.177611i	$0.943163\pi$
$54$	132.510	+	229.514i	0.333932	+	0.578387i
$55$	−496.826	+	860.529i	−1.21804	+	2.10970i
$56$	53.2221	−	92.1834i	0.127002	−	0.219974i
$57$	−53.4939	−	92.6541i	−0.124306	−	0.215304i
$58$	118.321	+	204.937i	0.267867	+	0.463959i
$59$	29.2376	+	50.6411i	0.0645155	+	0.111744i	0.896479	−	0.443086i	$-0.146116\pi$
$59$	29.2376	+	50.6411i	0.0645155	+	0.111744i	−0.831963	+	0.554830i	$0.812783\pi$
$60$	−191.132			−0.411250
$61$	345.987	−	599.266i	0.726214	−	1.25784i	−0.232259	−	0.972654i	$-0.574612\pi$
$61$	345.987	−	599.266i	0.726214	−	1.25784i	0.958472	−	0.285185i	$-0.0920551\pi$
$62$	317.683	+	550.242i	0.650737	+	1.12711i
$63$	−246.544			−0.493041
$64$	64.0000			0.125000
$65$	−203.023	−	351.646i	−0.387413	−	0.671020i
$66$	352.294			0.657037
$67$	−148.414	+	257.060i	−0.270621	+	0.468730i	−0.969021	−	0.246978i	$-0.920562\pi$
$67$	−148.414	+	257.060i	−0.270621	+	0.468730i	0.698400	+	0.715708i	$0.253896\pi$
$68$	376.001			0.670541
$69$	−208.283	+	360.756i	−0.363395	+	0.629419i
$70$	218.448	−	378.363i	0.372993	−	0.646043i
$71$	−495.169	+	857.658i	−0.827686	+	1.43359i	0.0721625	+	0.997393i	$0.477010\pi$
$71$	−495.169	+	857.658i	−0.827686	+	1.43359i	−0.899849	+	0.436202i	$0.856323\pi$
$72$	−74.1176	−	128.376i	−0.121317	−	0.210128i
$73$	799.748			1.28224			0.641119	−	0.767441i	$-0.278470\pi$
$73$	799.748			1.28224			0.641119	+	0.767441i	$0.278470\pi$
$74$	−258.245	+	368.676i	−0.405680	+	0.579158i
$75$	−420.688			−0.647691
$76$	73.5203	+	127.341i	0.110965	+	0.192197i
$77$	−402.644	+	697.400i	−0.595916	+	1.03216i
$78$	−71.9807	+	124.674i	−0.104490	+	0.180982i
$79$	−54.2659	+	93.9912i	−0.0772834	+	0.133859i	−0.902077	−	0.431575i	$-0.857958\pi$
$79$	−54.2659	+	93.9912i	−0.0772834	+	0.133859i	0.824794	+	0.565434i	$0.191291\pi$
$80$	262.685			0.367114
$81$	−57.3166	+	99.2753i	−0.0786236	+	0.136180i
$82$	236.660			0.318716
$83$	28.3523	+	49.1076i	0.0374948	+	0.0649429i	0.884164	−	0.467177i	$-0.154729\pi$
$83$	28.3523	+	49.1076i	0.0374948	+	0.0649429i	−0.846669	+	0.532120i	$0.821396\pi$
$84$	−154.899			−0.201201
$85$	1543.28			1.96932
$86$	−217.430	−	376.601i	−0.272629	−	0.472208i
$87$	172.182	−	298.228i	0.212182	−	0.367510i
$88$	−484.182			−0.586523
$89$	−712.458	−	1234.01i	−0.848543	−	1.46972i	−0.882508	−	0.470297i	$-0.844147\pi$
$89$	−712.458	−	1234.01i	−0.848543	−	1.46972i	0.0339650	−	0.999423i	$-0.489187\pi$
$90$	−304.213	−	526.912i	−0.356298	−	0.617126i
$91$	−164.536	−	284.985i	−0.189539	−	0.328292i
$92$	286.257	−	495.812i	0.324395	−	0.561869i
$93$	462.296	−	800.720i	0.515461	−	0.892804i
$94$	262.977	+	455.489i	0.288553	+	0.499788i
$95$	301.761	+	522.665i	0.325895	+	0.564467i
$96$	−46.5668	−	80.6561i	−0.0495074	−	0.0857493i
$97$	705.808			0.738803			0.369402	−	0.929270i	$-0.379563\pi$
$97$	705.808			0.738803			0.369402	+	0.929270i	$0.379563\pi$
$98$	−165.963	+	287.456i	−0.171069	+	0.296301i
$99$	560.726	+	971.206i	0.569243	+	0.985958i
$100$	578.180			0.578180
$101$	−1624.13			−1.60007			−0.800035	−	0.599954i	$-0.795186\pi$
$101$	−1624.13			−1.60007			−0.800035	+	0.599954i	$0.795186\pi$
$102$	−273.581	−	473.856i	−0.265574	−	0.459987i
$103$	−891.058			−0.852413			−0.426206	−	0.904626i	$-0.640150\pi$
$103$	−891.058			−0.852413			−0.426206	+	0.904626i	$0.640150\pi$
$104$	98.9280	−	171.348i	0.0932758	−	0.161558i
$105$	−635.777			−0.590909
$106$	261.013	−	452.088i	0.239168	−	0.414251i
$107$	514.734	−	891.545i	0.465058	−	0.805504i	−0.534146	−	0.845392i	$-0.679367\pi$
$107$	514.734	−	891.545i	0.465058	−	0.805504i	0.999204	+	0.0398884i	$0.0127003\pi$
$108$	−265.020	+	459.028i	−0.236126	+	0.408982i
$109$	−633.641	−	1097.50i	−0.556806	−	0.964416i	−0.997761	−	0.0668865i	$-0.978693\pi$
$109$	−633.641	−	1097.50i	−0.556806	−	0.964416i	0.440955	−	0.897529i	$-0.354640\pi$
$110$	−1987.31			−1.72257
$111$	652.525	+	57.2026i	0.557972	+	0.0489138i
$112$	212.888			0.179608
$113$	−282.261	−	488.890i	−0.234981	−	0.406999i	0.724286	−	0.689500i	$-0.242170\pi$
$113$	−282.261	−	488.890i	−0.234981	−	0.406999i	−0.959267	+	0.282500i	$0.908836\pi$
$114$	106.988	−	185.308i	0.0878976	−	0.152243i
$115$	1174.93	−	2035.04i	0.952720	−	1.65016i
$116$	−236.641	+	409.875i	−0.189410	+	0.328068i
$117$	−458.269			−0.362111
$118$	−58.4753	+	101.282i	−0.0456194	+	0.0790151i
$119$	1250.72			0.963475
$120$	−191.132	−	331.050i	−0.145399	−	0.251838i
$121$	2332.01			1.75207
$122$	1383.95			1.02702
$123$	−172.195	−	298.251i	−0.126230	−	0.218637i
$124$	−635.365	+	1100.48i	−0.460141	+	0.796987i
$125$	320.886			0.229608
$126$	−246.544	−	427.026i	−0.174316	−	0.301925i
$127$	408.648	+	707.798i	0.285524	+	0.494543i	0.972736	−	0.231914i	$-0.0744989\pi$
$127$	408.648	+	707.798i	0.285524	+	0.494543i	−0.687212	+	0.726457i	$0.741166\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	−316.408	+	548.034i	−0.215955	+	0.374044i
$130$	406.046	−	703.291i	0.273943	−	0.474483i
$131$	−473.906	−	820.829i	−0.316071	−	0.547451i	0.663593	−	0.748093i	$-0.269031\pi$
$131$	−473.906	−	820.829i	−0.316071	−	0.547451i	−0.979665	+	0.200642i	$0.935697\pi$
$132$	352.294	+	610.192i	0.232298	+	0.402351i
$133$	244.557	+	423.585i	0.159442	+	0.276161i
$134$	−593.655			−0.382716
$135$	−1087.76	+	1884.06i	−0.693480	+	1.20114i
$136$	376.001	+	651.252i	0.237072	+	0.410621i
$137$	872.036			0.543818			0.271909	−	0.962323i	$-0.412345\pi$
$137$	872.036			0.543818			0.271909	+	0.962323i	$0.412345\pi$
$138$	−833.131			−0.513919
$139$	491.613	+	851.499i	0.299986	+	0.519591i	0.976132	−	0.217176i	$-0.0696846\pi$
$139$	491.613	+	851.499i	0.299986	+	0.519591i	−0.676146	+	0.736767i	$0.736351\pi$
$140$	873.791			0.527492
$141$	382.687	−	662.834i	0.228568	−	0.395891i
$142$	−1980.68			−1.17053
$143$	−748.425	+	1296.31i	−0.437667	+	0.758062i
$144$	148.235	−	256.751i	0.0857843	−	0.148583i
$145$	−971.284	+	1682.31i	−0.556281	+	0.963507i
$146$	799.748	+	1385.20i	0.453340	+	0.785207i
$147$	483.023			0.271014
$148$	−896.810	−	78.6174i	−0.498090	−	0.0436643i
$149$	−939.077			−0.516323			−0.258162	−	0.966102i	$-0.583117\pi$
$149$	−939.077			−0.516323			−0.258162	+	0.966102i	$0.583117\pi$
$150$	−420.688	−	728.652i	−0.228993	−	0.396628i
$151$	1052.43	−	1822.86i	0.567188	−	0.982399i	−0.429654	−	0.902994i	$-0.641364\pi$
$151$	1052.43	−	1822.86i	0.567188	−	0.982399i	0.996842	−	0.0794055i	$-0.0253022\pi$
$152$	−147.041	+	254.682i	−0.0784643	+	0.135904i
$153$	870.884	−	1508.42i	0.460175	−	0.797047i
$154$	−1610.58			−0.842753
$155$	−2607.83	+	4516.89i	−1.35139	+	2.34068i
$156$	−287.923			−0.147771
$157$	308.636	+	534.573i	0.156891	+	0.271743i	0.933746	−	0.357937i	$-0.116520\pi$
$157$	308.636	+	534.573i	0.156891	+	0.271743i	−0.776855	+	0.629679i	$0.783186\pi$
$158$	−217.063			−0.109295
$159$	−759.660			−0.378899
$160$	262.685	+	454.984i	0.129794	+	0.224810i
$161$	952.201	−	1649.26i	0.466111	−	0.807329i
$162$	−229.267			−0.111191
$163$	−25.9187	−	44.8925i	−0.0124547	−	0.0215721i	0.859731	−	0.510747i	$-0.170631\pi$
$163$	−25.9187	−	44.8925i	−0.0124547	−	0.0215721i	−0.872186	+	0.489175i	$0.837298\pi$
$164$	236.660	+	409.907i	0.112683	+	0.195173i
$165$	1445.98	+	2504.51i	0.682237	+	1.18167i
$166$	−56.7046	+	98.2152i	−0.0265128	+	0.0459216i
$167$	−519.747	+	900.228i	−0.240834	+	0.417136i	−0.960952	−	0.276715i	$-0.910754\pi$
$167$	−519.747	+	900.228i	−0.240834	+	0.417136i	0.720118	+	0.693851i	$0.244088\pi$
$168$	−154.899	−	268.293i	−0.0711353	−	0.123210i
$169$	792.664	+	1372.93i	0.360794	+	0.624913i
$170$	1543.28	+	2673.04i	0.696259	+	1.20596i
$171$	681.144			0.304611
$172$	434.861	−	753.201i	0.192778	−	0.333902i
$173$	−1546.91	−	2679.33i	−0.679823	−	1.17749i	−0.975034	−	0.222056i	$-0.928723\pi$
$173$	−1546.91	−	2679.33i	−0.679823	−	1.17749i	0.295211	−	0.955432i	$-0.404610\pi$
$174$	688.728			0.300071
$175$	1923.25			0.830765
$176$	−484.182	−	838.629i	−0.207367	−	0.359171i
$177$	170.188			0.0722719
$178$	1424.92	−	2468.03i	0.600011	−	1.03925i
$179$	−1588.95			−0.663485			−0.331743	−	0.943370i	$-0.607637\pi$
$179$	−1588.95			−0.663485			−0.331743	+	0.943370i	$0.607637\pi$
$180$	608.425	−	1053.82i	0.251941	−	0.436374i
$181$	1189.42	−	2060.13i	0.488446	−	0.846014i	−0.511465	−	0.859304i	$-0.670897\pi$
$181$	1189.42	−	2060.13i	0.488446	−	0.846014i	0.999912	+	0.0132899i	$0.00423044\pi$
$182$	329.072	−	569.970i	0.134024	−	0.232137i
$183$	−1006.97	−	1744.12i	−0.406761	−	0.704531i
$184$	1145.03			0.458764
$185$	−3680.92	−	322.682i	−1.46284	−	0.128238i
$186$	1849.18			0.728972
$187$	−2844.58	−	4926.95i	−1.11239	−	1.92671i
$188$	−525.953	+	910.978i	−0.204038	+	0.353404i
$189$	−881.558	+	1526.90i	−0.339280	+	0.587650i
$190$	−603.522	+	1045.33i	−0.230443	+	0.399138i
$191$	3253.74			1.23263			0.616314	−	0.787500i	$-0.288625\pi$
$191$	3253.74			1.23263			0.616314	+	0.787500i	$0.288625\pi$
$192$	93.1337	−	161.312i	0.0350070	−	0.0606339i
$193$	−4069.18			−1.51765			−0.758824	−	0.651296i	$-0.774226\pi$
$193$	−4069.18			−1.51765			−0.758824	+	0.651296i	$0.774226\pi$
$194$	705.808	+	1222.50i	0.261206	+	0.452423i
$195$	−1181.77			−0.433990
$196$	−663.852			−0.241928
$197$	1738.26	+	3010.75i	0.628659	+	1.08887i	0.987821	+	0.155595i	$0.0497293\pi$
$197$	1738.26	+	3010.75i	0.628659	+	1.08887i	−0.359162	+	0.933275i	$0.616937\pi$
$198$	−1121.45	+	1942.41i	−0.402516	+	0.697178i
$199$	2872.30			1.02318			0.511588	−	0.859231i	$-0.329057\pi$
$199$	2872.30			1.02318			0.511588	+	0.859231i	$0.329057\pi$
$200$	578.180	+	1001.44i	0.204417	+	0.354061i
$201$	431.948	+	748.155i	0.151578	+	0.262541i
$202$	−1624.13	−	2813.08i	−0.565710	−	0.979838i
$203$	−787.160	+	1363.40i	−0.272157	+	0.471389i
$204$	547.161	−	947.711i	0.187789	−	0.325260i
$205$	971.360	+	1682.44i	0.330940	+	0.573205i
$206$	−891.058	−	1543.36i	−0.301373	−	0.521994i
$207$	−1326.04	−	2296.78i	−0.445249	−	0.771193i
$208$	395.712			0.131912
$209$	1112.41	−	1926.76i	0.368169	−	0.637687i
$210$	−635.777	−	1101.20i	−0.208918	−	0.361856i
$211$	−3868.60			−1.26221			−0.631103	−	0.775699i	$-0.717398\pi$
$211$	−3868.60			−1.26221			−0.631103	+	0.775699i	$0.717398\pi$
$212$	1044.05			0.338235
$213$	1441.15	+	2496.15i	0.463597	+	0.802974i
$214$	2058.93			0.657691
$215$	1784.87	−	3091.48i	0.566172	−	0.980639i
$216$	−1060.08			−0.333932
$217$	−2113.47	+	3660.63i	−0.661159	+	1.14516i
$218$	1267.28	−	2195.00i	0.393721	−	0.681945i
$219$	1163.80	−	2015.77i	0.359099	−	0.621977i
$220$	−1987.31	−	3442.11i	−0.609019	−	1.05485i
$221$	2324.81			0.707619
$222$	553.447	+	1187.41i	0.167319	+	0.358980i
$223$	1194.79			0.358786			0.179393	−	0.983777i	$-0.442587\pi$
$223$	1194.79			0.358786			0.179393	+	0.983777i	$0.442587\pi$
$224$	212.888	+	368.734i	0.0635009	+	0.109987i
$225$	1339.17	−	2319.51i	0.396790	−	0.687261i
$226$	564.522	−	977.781i	0.166157	−	0.287792i
$227$	2696.53	−	4670.53i	0.788436	−	1.36561i	−0.138488	−	0.990364i	$-0.544224\pi$
$227$	2696.53	−	4670.53i	0.788436	−	1.36561i	0.926924	−	0.375248i	$-0.122442\pi$
$228$	427.951			0.124306
$229$	654.768	−	1134.09i	0.188944	−	0.327261i	−0.755954	−	0.654625i	$-0.772827\pi$
$229$	654.768	−	1134.09i	0.188944	−	0.327261i	0.944899	+	0.327363i	$0.106160\pi$
$230$	4699.72			1.34735
$231$	1171.87	+	2029.73i	0.333780	+	0.578124i
$232$	−946.565			−0.267867
$233$	−4220.12			−1.18656			−0.593281	−	0.804995i	$-0.702168\pi$
$233$	−4220.12			−1.18656			−0.593281	+	0.804995i	$0.702168\pi$
$234$	−458.269	−	793.746i	−0.128026	−	0.221747i
$235$	−2158.75	+	3739.07i	−0.599240	+	1.03791i
$236$	−233.901			−0.0645155
$237$	157.937	+	273.555i	0.0432873	+	0.0749759i
$238$	1250.72	+	2166.31i	0.340640	+	0.590005i
$239$	−1232.09	−	2134.04i	−0.333460	−	0.577570i	0.649727	−	0.760167i	$-0.274883\pi$
$239$	−1232.09	−	2134.04i	−0.333460	−	0.577570i	−0.983188	+	0.182597i	$0.941550\pi$
$240$	382.263	−	662.099i	0.102812	−	0.178076i
$241$	−1068.44	+	1850.59i	−0.285577	+	0.494634i	−0.972749	−	0.231861i	$-0.925519\pi$
$241$	−1068.44	+	1850.59i	−0.285577	+	0.494634i	0.687172	+	0.726495i	$0.258852\pi$
$242$	2332.01	+	4039.16i	0.619452	+	1.07292i
$243$	1955.70	+	3387.37i	0.516289	+	0.894239i
$244$	1383.95	+	2397.07i	0.363107	+	0.628920i
$245$	−2724.75			−0.710522
$246$	344.391	−	596.502i	0.0892583	−	0.154600i
$247$	454.576	+	787.349i	0.117101	+	0.202825i
$248$	−2541.46			−0.650737
$249$	165.035			0.0420026
$250$	320.886	+	555.791i	0.0811785	+	0.140605i
$251$	5204.00			1.30866			0.654330	−	0.756210i	$-0.272951\pi$
$251$	5204.00			1.30866			0.654330	+	0.756210i	$0.272951\pi$
$252$	493.087	−	854.052i	0.123260	−	0.213493i
$253$	−8662.54			−2.15261
$254$	−817.295	+	1415.60i	−0.201896	+	0.349695i
$255$	2245.80	−	3889.84i	0.551519	−	0.955260i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−2662.67	−	4611.89i	−0.646277	−	1.11938i	−0.984005	−	0.178140i	$-0.942992\pi$
$257$	−2662.67	−	4611.89i	−0.646277	−	1.11938i	0.337728	−	0.941244i	$-0.390341\pi$
$258$	−1265.63			−0.305406
$259$	−2983.13	−	261.512i	−0.715686	−	0.0627395i
$260$	1624.18			0.387413
$261$	1096.21	+	1898.69i	0.259975	+	0.450290i
$262$	947.811	−	1641.66i	0.223496	−	0.387107i
$263$	2081.59	−	3605.42i	0.488047	−	0.845322i	−0.511859	−	0.859070i	$-0.671043\pi$
$263$	2081.59	−	3605.42i	0.488047	−	0.845322i	0.999905	+	0.0137478i	$0.00437620\pi$
$264$	−704.589	+	1220.38i	−0.164259	+	0.284505i
$265$	4285.27			0.993366
$266$	−489.113	+	847.169i	−0.112742	+	0.195275i
$267$	−4147.11			−0.950558
$268$	−593.655	−	1028.24i	−0.135311	−	0.234365i
$269$	−4294.65			−0.973417			−0.486709	−	0.873564i	$-0.661803\pi$
$269$	−4294.65			−0.973417			−0.486709	+	0.873564i	$0.661803\pi$
$270$	−4351.05			−0.980729
$271$	3124.92	+	5412.51i	0.700462	+	1.21324i	0.968305	+	0.249773i	$0.0803559\pi$
$271$	3124.92	+	5412.51i	0.700462	+	1.21324i	−0.267843	+	0.963463i	$0.586311\pi$
$272$	−752.001	+	1302.50i	−0.167635	+	0.290353i
$273$	−957.741			−0.212326
$274$	872.036	+	1510.41i	0.192269	+	0.333019i
$275$	−4374.13	−	7576.22i	−0.959165	−	1.66132i
$276$	−833.131	−	1443.02i	−0.181698	−	0.314710i
$277$	−697.434	+	1207.99i	−0.151281	+	0.262026i	−0.931698	−	0.363233i	$-0.881673\pi$
$277$	−697.434	+	1207.99i	−0.151281	+	0.262026i	0.780418	+	0.625258i	$0.215006\pi$
$278$	−983.226	+	1703.00i	−0.212122	+	0.367407i
$279$	2943.24	+	5097.83i	0.631566	+	1.09390i
$280$	873.791	+	1513.45i	0.186497	+	0.323021i
$281$	3834.53	+	6641.61i	0.814054	+	1.40998i	0.910005	+	0.414596i	$0.136077\pi$
$281$	3834.53	+	6641.61i	0.814054	+	1.40998i	−0.0959517	+	0.995386i	$0.530589\pi$
$282$	1530.75			0.323244
$283$	−1422.38	+	2463.64i	−0.298770	+	0.517485i	−0.975855	−	0.218420i	$-0.929910\pi$
$283$	−1422.38	+	2463.64i	−0.298770	+	0.517485i	0.677085	+	0.735905i	$0.263243\pi$
$284$	−1980.68	−	3430.63i	−0.413843	−	0.716797i
$285$	1756.51			0.365075
$286$	−2993.70			−0.618955
$287$	787.221	+	1363.51i	0.161910	+	0.280436i
$288$	592.941			0.121317
$289$	−1961.52	+	3397.45i	−0.399250	+	0.691522i
$290$	−3885.14			−0.786700
$291$	1027.10	−	1778.99i	0.206906	−	0.358372i
$292$	−1599.50	+	2770.41i	−0.320560	+	0.555225i
$293$	506.246	−	876.845i	0.100939	−	0.174832i	−0.811133	−	0.584862i	$-0.801149\pi$
$293$	506.246	−	876.845i	0.100939	−	0.174832i	0.912072	+	0.410030i	$0.134482\pi$
$294$	483.023	+	836.620i	0.0958179	+	0.165962i
$295$	−960.037			−0.189476
$296$	−760.640	−	1631.94i	−0.149363	−	0.320454i
$297$	8019.88			1.56687
$298$	−939.077	−	1626.53i	−0.182548	−	0.316182i
$299$	1769.93	−	3065.60i	0.342333	−	0.592938i
$300$	841.375	−	1457.30i	0.161923	−	0.280458i
$301$	1446.51	−	2505.44i	0.276996	−	0.479770i
$302$	4209.72			0.802126
$303$	−2363.46	+	4093.63i	−0.448109	+	0.776148i
$304$	−588.163			−0.110965
$305$	5680.35	+	9838.65i	1.06641	+	1.84708i
$306$	3483.54			0.650786
$307$	−1332.81			−0.247776			−0.123888	−	0.992296i	$-0.539536\pi$
$307$	−1332.81			−0.247776			−0.123888	+	0.992296i	$0.539536\pi$
$308$	−1610.58	−	2789.60i	−0.297958	−	0.516078i
$309$	−1296.68	+	2245.91i	−0.238723	+	0.413481i
$310$	−10431.3			−1.91116
$311$	−1636.64	−	2834.75i	−0.298410	−	0.516861i	0.677362	−	0.735650i	$-0.263123\pi$
$311$	−1636.64	−	2834.75i	−0.298410	−	0.516861i	−0.975772	+	0.218788i	$0.929790\pi$
$312$	−287.923	−	498.697i	−0.0522449	−	0.0904908i
$313$	4641.33	+	8039.02i	0.838158	+	1.45173i	0.891433	+	0.453152i	$0.149701\pi$
$313$	4641.33	+	8039.02i	0.838158	+	1.45173i	−0.0532753	+	0.998580i	$0.516966\pi$
$314$	−617.272	+	1069.15i	−0.110938	+	0.192151i
$315$	2023.86	−	3505.42i	0.362004	−	0.627010i
$316$	−217.063	−	375.965i	−0.0386417	−	0.0669294i
$317$	−3656.66	−	6333.52i	−0.647881	−	1.12216i	−0.983628	−	0.180211i	$-0.942322\pi$
$317$	−3656.66	−	6333.52i	−0.647881	−	1.12216i	0.335747	−	0.941952i	$-0.391011\pi$
$318$	−759.660	−	1315.77i	−0.133961	−	0.232027i
$319$	7161.10			1.25688
$320$	−525.370	+	909.968i	−0.0917784	+	0.158965i
$321$	−1498.09	−	2594.78i	−0.260484	−	0.451172i
$322$	3808.80			0.659181
$323$	−3455.46			−0.595254
$324$	−229.267	−	397.101i	−0.0393118	−	0.0680901i
$325$	3574.89			0.610151
$326$	51.8374	−	89.7850i	0.00880677	−	0.0152538i
$327$	−3688.33			−0.623747
$328$	−473.320	+	819.814i	−0.0796790	+	0.138008i
$329$	−1749.52	+	3030.26i	−0.293174	+	0.507792i
$330$	−2891.95	+	5009.01i	−0.482415	+	0.835567i
$331$	1261.16	+	2184.40i	0.209426	+	0.362736i	0.951534	−	0.307544i	$-0.0995072\pi$
$331$	1261.16	+	2184.40i	0.209426	+	0.362736i	−0.742108	+	0.670280i	$0.766174\pi$
$332$	−226.818			−0.0374948
$333$	−2392.56	+	3415.67i	−0.393728	+	0.562095i
$334$	−2078.99			−0.340590
$335$	−2436.63	−	4220.37i	−0.397395	−	0.688309i
$336$	309.798	−	536.586i	0.0503002	−	0.0871226i
$337$	3812.18	−	6602.88i	0.616209	−	1.06731i	−0.373962	−	0.927444i	$-0.622001\pi$
$337$	3812.18	−	6602.88i	0.616209	−	1.06731i	0.990171	−	0.139861i	$-0.0446657\pi$
$338$	−1585.33	+	2745.87i	−0.255120	+	0.441881i
$339$	−1643.00			−0.263232
$340$	−3086.56	+	5346.07i	−0.492330	+	0.852740i
$341$	19227.0			3.05338
$342$	681.144	+	1179.78i	0.107696	+	0.186535i
$343$	−6772.02			−1.06605
$344$	1739.44			0.272629
$345$	−3419.55	−	5922.83i	−0.533630	−	0.924274i
$346$	3093.82	−	5358.65i	0.480707	−	0.832610i
$347$	6531.69			1.01049			0.505244	−	0.862976i	$-0.331402\pi$
$347$	6531.69			1.01049			0.505244	+	0.862976i	$0.331402\pi$
$348$	688.728	+	1192.91i	0.106091	+	0.183755i
$349$	−4498.94	−	7792.40i	−0.690037	−	1.19518i	−0.971825	−	0.235703i	$-0.924261\pi$
$349$	−4498.94	−	7792.40i	−0.690037	−	1.19518i	0.281788	−	0.959477i	$-0.409072\pi$
$350$	1923.25	+	3331.16i	0.293720	+	0.508737i
$351$	−1638.62	+	2838.17i	−0.249182	+	0.431596i
$352$	968.365	−	1677.26i	0.146631	−	0.253972i
$353$	−4064.62	−	7040.12i	−0.612855	−	1.06150i	−0.990757	−	0.135650i	$-0.956688\pi$
$353$	−4064.62	−	7040.12i	−0.612855	−	1.06150i	0.377902	−	0.925846i	$-0.376646\pi$
$354$	170.188	+	294.774i	0.0255520	+	0.0442573i
$355$	−8129.60	−	14080.9i	−1.21542	−	2.10517i
$356$	5699.66			0.848543
$357$	1820.07	−	3152.45i	0.269827	−	0.467354i
$358$	−1588.95	−	2752.15i	−0.234577	−	0.406300i
$359$	9517.86			1.39926			0.699629	−	0.714507i	$-0.253349\pi$
$359$	9517.86			1.39926			0.699629	+	0.714507i	$0.253349\pi$
$360$	2433.70			0.356298
$361$	2753.85	+	4769.80i	0.401494	+	0.695407i
$362$	4757.68			0.690768
$363$	3393.57	−	5877.84i	0.490679	−	0.849881i
$364$	1316.29			0.189539
$365$	−6565.06	+	11371.0i	−0.941455	+	1.63065i
$366$	2013.94	−	3488.24i	0.287624	−	0.498179i
$367$	−1507.72	+	2611.44i	−0.214447	+	0.371434i	−0.953101	−	0.302651i	$-0.902128\pi$
$367$	−1507.72	+	2611.44i	−0.214447	+	0.371434i	0.738654	+	0.674085i	$0.235462\pi$
$368$	1145.03	+	1983.25i	0.162198	+	0.280935i
$369$	2192.58			0.309326
$370$	−3122.01	−	6698.21i	−0.438664	−	0.941145i
$371$	3472.92			0.485997
$372$	1849.18	+	3202.88i	0.257730	+	0.446402i
$373$	−2067.73	+	3581.42i	−0.287033	+	0.497155i	−0.973100	−	0.230383i	$-0.926002\pi$
$373$	−2067.73	+	3581.42i	−0.287033	+	0.497155i	0.686067	+	0.727538i	$0.259336\pi$
$374$	5689.15	−	9853.90i	0.786575	−	1.36239i
$375$	466.958	−	808.795i	0.0643030	−	0.111376i
$376$	−2103.81			−0.288553
$377$	−1463.15	+	2534.26i	−0.199884	+	0.346209i
$378$	−3526.23			−0.479814
$379$	−5423.72	−	9394.16i	−0.735086	−	1.27321i	−0.954685	−	0.297617i	$-0.903808\pi$
$379$	−5423.72	−	9394.16i	−0.735086	−	1.27321i	0.219599	−	0.975590i	$-0.429525\pi$
$380$	−2414.09			−0.325895
$381$	2378.68			0.319851
$382$	3253.74	+	5635.64i	0.435800	+	0.754828i
$383$	−5115.39	+	8860.12i	−0.682466	+	1.18207i	0.291760	+	0.956492i	$0.405759\pi$
$383$	−5115.39	+	8860.12i	−0.682466	+	1.18207i	−0.974226	+	0.225574i	$0.927574\pi$
$384$	372.535			0.0495074
$385$	−6610.54	−	11449.8i	−0.875076	−	1.51568i
$386$	−4069.18	−	7048.02i	−0.536569	−	0.929365i
$387$	−2014.43	−	3489.09i	−0.264597	−	0.458296i
$388$	−1411.62	+	2444.99i	−0.184701	+	0.319911i
$389$	5643.73	−	9775.23i	0.735600	−	1.27410i	−0.218859	−	0.975756i	$-0.570234\pi$
$389$	5643.73	−	9775.23i	0.735600	−	1.27410i	0.954459	−	0.298341i	$-0.0964331\pi$
$390$	−1181.77	−	2046.88i	−0.153439	−	0.265763i
$391$	6727.06	+	11651.6i	0.870081	+	1.50703i
$392$	−663.852	−	1149.82i	−0.0855346	−	0.148150i
$393$	−2758.54			−0.354071
$394$	−3476.52	+	6021.51i	−0.444529	+	0.769947i
$395$	−890.927	−	1543.13i	−0.113487	−	0.196565i
$396$	−4485.81			−0.569243
$397$	−5616.17			−0.709994			−0.354997	−	0.934867i	$-0.615518\pi$
$397$	−5616.17			−0.709994			−0.354997	+	0.934867i	$0.615518\pi$
$398$	2872.30	+	4974.97i	0.361748	+	0.626565i
$399$	1423.53			0.178611
$400$	−1156.36	+	2002.87i	−0.144545	+	0.250359i
$401$	−4291.70			−0.534457			−0.267229	−	0.963633i	$-0.586108\pi$
$401$	−4291.70			−0.534457			−0.267229	+	0.963633i	$0.586108\pi$
$402$	−863.895	+	1496.31i	−0.107182	+	0.185645i
$403$	−3928.46	+	6804.29i	−0.485585	+	0.841057i
$404$	3248.26	−	5626.15i	0.400017	−	0.692850i
$405$	−941.014	−	1629.88i	−0.115455	−	0.199974i
$406$	−3148.64			−0.384887
$407$	5754.51	+	12346.2i	0.700837	+	1.50363i
$408$	2188.65			0.265574
$409$	−5410.71	−	9371.62i	−0.654138	−	1.13300i	−0.982109	−	0.188312i	$-0.939698\pi$
$409$	−5410.71	−	9371.62i	−0.654138	−	1.13300i	0.327972	−	0.944688i	$-0.393635\pi$
$410$	−1942.72	+	3364.89i	−0.234010	+	0.405317i
$411$	1269.00	−	2197.97i	0.152300	−	0.263791i
$412$	1782.12	−	3086.71i	0.213103	−	0.369106i
$413$	−778.045			−0.0926999
$414$	2652.09	−	4593.55i	0.314838	−	0.545316i
$415$	−930.966			−0.110119
$416$	395.712	+	685.393i	0.0466379	+	0.0807792i
$417$	2861.61			0.336052
$418$	4449.66			0.520669
$419$	−1479.54	−	2562.63i	−0.172506	−	0.298789i	0.766789	−	0.641899i	$-0.221853\pi$
$419$	−1479.54	−	2562.63i	−0.172506	−	0.298789i	−0.939295	+	0.343110i	$0.888520\pi$
$420$	1271.55	−	2202.39i	0.147727	−	0.255871i
$421$	−14707.4			−1.70260			−0.851300	−	0.524679i	$-0.824185\pi$
$421$	−14707.4			−1.70260			−0.851300	+	0.524679i	$0.824185\pi$
$422$	−3868.60	−	6700.61i	−0.446257	−	0.772940i
$423$	2436.40	+	4219.97i	0.280052	+	0.485064i
$424$	1044.05	+	1808.35i	0.119584	+	0.207126i
$425$	−6793.63	+	11766.9i	−0.775387	+	1.34301i
$426$	−2882.31	+	4992.30i	−0.327813	+	0.567788i
$427$	4603.53	+	7973.56i	0.521735	+	0.903671i
$428$	2058.93	+	3566.18i	0.232529	+	0.402752i
$429$	2178.24	+	3772.82i	0.245143	+	0.424600i
$430$	7139.47			0.800688
$431$	−4649.37	+	8052.95i	−0.519611	+	0.899993i	0.480129	+	0.877198i	$0.340590\pi$
$431$	−4649.37	+	8052.95i	−0.519611	+	0.899993i	−0.999740	+	0.0227951i	$0.992743\pi$
$432$	−1060.08	−	1836.11i	−0.118063	−	0.204491i
$433$	5144.92			0.571014			0.285507	−	0.958377i	$-0.407838\pi$
$433$	5144.92			0.571014			0.285507	+	0.958377i	$0.407838\pi$
$434$	−8453.87			−0.935020
$435$	2826.85	+	4896.25i	0.311580	+	0.539672i
$436$	5069.13			0.556806
$437$	−2630.72	+	4556.53i	−0.287973	+	0.498784i
$438$	4655.22			0.507842
$439$	697.221	−	1207.62i	0.0758008	−	0.131291i	−0.825633	−	0.564207i	$-0.809182\pi$
$439$	697.221	−	1207.62i	0.0758008	−	0.131291i	0.901434	+	0.432916i	$0.142515\pi$
$440$	3974.61	−	6884.23i	0.430641	−	0.745893i
$441$	−1537.60	+	2663.20i	−0.166029	+	0.287571i
$442$	2324.81	+	4026.69i	0.250181	+	0.433326i
$443$	8425.29			0.903606			0.451803	−	0.892118i	$-0.350781\pi$
$443$	8425.29			0.903606			0.451803	+	0.892118i	$0.350781\pi$
$444$	−1503.21	+	2146.01i	−0.160673	+	0.229381i
$445$	23394.0			2.49209
$446$	1194.79	+	2069.44i	0.126850	+	0.219711i
$447$	−1366.56	+	2366.95i	−0.144599	+	0.250454i
$448$	−425.777	+	737.467i	−0.0449019	+	0.0777724i
$449$	−3965.40	+	6868.27i	−0.416790	+	0.721901i	−0.995614	−	0.0935509i	$-0.970178\pi$
$449$	−3965.40	+	6868.27i	−0.416790	+	0.721901i	0.578825	+	0.815452i	$0.303512\pi$
$450$	5356.67			0.561146
$451$	3580.83	−	6202.18i	0.373868	−	0.647559i
$452$	2258.09			0.234981
$453$	−3063.02	−	5305.30i	−0.317689	−	0.550254i
$454$	10786.1			1.11502
$455$	5402.65			0.556660
$456$	427.951	+	741.233i	0.0439488	+	0.0761215i
$457$	−6549.86	+	11344.7i	−0.670437	+	1.16123i	0.307344	+	0.951599i	$0.400560\pi$
$457$	−6549.86	+	11344.7i	−0.670437	+	1.16123i	−0.977780	+	0.209632i	$0.932773\pi$
$458$	2619.07			0.267208
$459$	−6227.98	−	10787.2i	−0.633328	−	1.09696i
$460$	4699.72	+	8140.15i	0.476360	+	0.825080i
$461$	−1467.75	−	2542.22i	−0.148286	−	0.256839i	0.782308	−	0.622892i	$-0.214042\pi$
$461$	−1467.75	−	2542.22i	−0.148286	−	0.256839i	−0.930594	+	0.366053i	$0.880709\pi$
$462$	−2343.73	+	4059.46i	−0.236018	+	0.408795i
$463$	3095.03	−	5360.75i	0.310666	−	0.538089i	−0.667841	−	0.744304i	$-0.732781\pi$
$463$	3095.03	−	5360.75i	0.310666	−	0.538089i	0.978507	+	0.206215i	$0.0661146\pi$
$464$	−946.565	−	1639.50i	−0.0947052	−	0.164034i
$465$	7589.89	+	13146.1i	0.756931	+	1.31104i
$466$	−4220.12	−	7309.46i	−0.419513	−	0.726618i
$467$	−18421.8			−1.82539			−0.912697	−	0.408636i	$-0.866004\pi$
$467$	−18421.8			−1.82539			−0.912697	+	0.408636i	$0.866004\pi$
$468$	916.539	−	1587.49i	0.0905278	−	0.156799i
$469$	−1974.72	−	3420.32i	−0.194423	−	0.336750i
$470$	−8635.01			−0.847454
$471$	1796.53			0.175753
$472$	−233.901	−	405.129i	−0.0228097	−	0.0395075i
$473$	−13159.5			−1.27923
$474$	−315.874	+	547.109i	−0.0306088	+	0.0530159i
$475$	−5313.50			−0.513263
$476$	−2501.44	+	4332.63i	−0.240869	+	0.417197i
$477$	2418.21	−	4188.46i	0.232122	−	0.402047i
$478$	2464.17	−	4268.07i	0.235792	−	0.408404i
$479$	2941.83	+	5095.41i	0.280618	+	0.486044i	0.971537	−	0.236888i	$-0.0761274\pi$
$479$	2941.83	+	5095.41i	0.280618	+	0.486044i	−0.690919	+	0.722932i	$0.742794\pi$
$480$	1529.05			0.145399
$481$	−5544.97	−	486.091i	−0.525632	−	0.0460787i
$482$	−4273.75			−0.403867
$483$	−2771.31	−	4800.05i	−0.261075	−	0.452194i
$484$	−4664.02	+	8078.32i	−0.438018	+	0.758670i
$485$	−5793.92	+	10035.4i	−0.542450	+	0.939551i
$486$	−3911.40	+	6774.75i	−0.365072	+	0.632323i
$487$	17541.3			1.63218			0.816089	−	0.577926i	$-0.196138\pi$
$487$	17541.3			1.63218			0.816089	+	0.577926i	$0.196138\pi$
$488$	−2767.89	+	4794.13i	−0.256755	+	0.444713i
$489$	−150.869			−0.0139520
$490$	−2724.75	−	4719.41i	−0.251207	−	0.435104i
$491$	−2324.10			−0.213615			−0.106807	−	0.994280i	$-0.534063\pi$
$491$	−2324.10			−0.213615			−0.106807	+	0.994280i	$0.534063\pi$
$492$	1377.56			0.126230
$493$	−5561.08	−	9632.08i	−0.508030	−	0.879933i
$494$	−909.152	+	1574.70i	−0.0828030	+	0.143419i
$495$	−18411.8			−1.67182
$496$	−2541.46	−	4401.94i	−0.230070	−	0.398494i
$497$	−6588.48	−	11411.6i	−0.594636	−	1.02994i
$498$	165.035	+	285.848i	0.0148502	+	0.0257212i
$499$	−8608.03	+	14909.5i	−0.772241	+	1.33756i	0.164091	+	0.986445i	$0.447531\pi$
$499$	−8608.03	+	14909.5i	−0.772241	+	1.33756i	−0.936332	+	0.351115i	$0.885802\pi$
$500$	−641.773	+	1111.58i	−0.0574019	+	0.0994230i
$501$	1512.69	+	2620.05i	0.134894	+	0.233643i
$502$	5204.00	+	9013.59i	0.462681	+	0.801387i
$503$	8175.11	+	14159.7i	0.724672	+	1.25517i	0.959109	+	0.283037i	$0.0913420\pi$
$503$	8175.11	+	14159.7i	0.724672	+	1.25517i	−0.234437	+	0.972131i	$0.575325\pi$
$504$	1972.35			0.174316
$505$	13332.3	−	23092.3i	1.17481	−	2.03484i
$506$	−8662.54	−	15004.0i	−0.761061	−	1.31820i
$507$	4613.98			0.404170
$508$	−3269.18			−0.285524
$509$	−3588.68	−	6215.77i	−0.312505	−	0.541275i	0.666399	−	0.745596i	$-0.267835\pi$
$509$	−3588.68	−	6215.77i	−0.312505	−	0.541275i	−0.978904	+	0.204320i	$0.934502\pi$
$510$	8983.20			0.779966
$511$	−5320.53	+	9215.43i	−0.460600	+	0.797782i
$512$	−512.000			−0.0441942
$513$	2435.55	−	4218.49i	0.209614	−	0.363062i
$514$	5325.35	−	9223.78i	0.456987	−	0.791524i
$515$	7314.61	−	12669.3i	0.625865	−	1.08403i
$516$	−1265.63	−	2192.14i	−0.107977	−	0.187022i
$517$	15916.1			1.35394
$518$	−2530.18	−	5428.45i	−0.214613	−	0.460448i
$519$	−9004.34			−0.761554
$520$	1624.18	+	2813.17i	0.136971	+	0.237241i
$521$	10956.0	−	18976.4i	0.921292	−	1.59572i	0.123873	−	0.992298i	$-0.460468\pi$
$521$	10956.0	−	18976.4i	0.921292	−	1.59572i	0.797419	−	0.603426i	$-0.206198\pi$
$522$	−2192.41	+	3797.37i	−0.183830	+	0.318403i
$523$	−3172.40	+	5494.77i	−0.265238	+	0.459406i	−0.967626	−	0.252388i	$-0.918784\pi$
$523$	−3172.40	+	5494.77i	−0.265238	+	0.459406i	0.702388	+	0.711794i	$0.252117\pi$
$524$	3791.24			0.316071
$525$	2798.74	−	4847.55i	0.232661	−	0.402980i
$526$	8326.36			0.690202
$527$	−14931.1	−	25861.4i	−1.23417	−	2.13765i
$528$	−2818.36			−0.232298
$529$	8318.79			0.683718
$530$	4285.27	+	7422.30i	0.351208	+	0.608310i
$531$	−541.756	+	938.350i	−0.0442754	+	0.0766872i
$532$	−1956.45			−0.159442
$533$	1463.27	+	2534.45i	0.118914	+	0.205965i
$534$	−4147.11	−	7183.01i	−0.336073	−	0.582096i
$535$	8450.81	+	14637.2i	0.682916	+	1.18285i
$536$	1187.31	−	2056.48i	0.0956791	−	0.165721i
$537$	−2312.26	+	4004.96i	−0.185813	+	0.321838i
$538$	−4294.65	−	7438.55i	−0.344155	−	0.596094i
$539$	5022.27	+	8698.83i	0.401344	+	0.695149i
$540$	−4351.05	−	7536.25i	−0.346740	−	0.600571i
$541$	6617.93			0.525928			0.262964	−	0.964806i	$-0.415300\pi$
$541$	6617.93			0.525928			0.262964	+	0.964806i	$0.415300\pi$
$542$	−6249.83	+	10825.0i	−0.495301	+	0.857887i
$543$	−3461.72	−	5995.87i	−0.273585	−	0.473863i
$544$	−3008.01			−0.237072
$545$	20806.0			1.63529
$546$	−957.741	−	1658.86i	−0.0750687	−	0.130023i
$547$	8366.36			0.653967			0.326983	−	0.945030i	$-0.393968\pi$
$547$	8366.36			0.653967			0.326983	+	0.945030i	$0.393968\pi$
$548$	−1744.07	+	3020.82i	−0.135955	+	0.235480i
$549$	12821.9			0.996764
$550$	8748.27	−	15152.4i	0.678232	−	1.17473i
$551$	2174.74	−	3766.77i	0.168144	−	0.291234i
$552$	1666.26	−	2886.05i	0.128480	−	0.222533i
$553$	−722.036	−	1250.60i	−0.0555228	−	0.0961682i
$554$	−2789.73			−0.213943
$555$	−6169.84	+	8808.19i	−0.471883	+	0.673670i
$556$	−3932.90			−0.299986
$557$	−8102.21	−	14033.4i	−0.616341	−	1.06753i	−0.990148	−	0.140027i	$-0.955281\pi$
$557$	−8102.21	−	14033.4i	−0.616341	−	1.06753i	0.373807	−	0.927507i	$-0.378052\pi$
$558$	−5886.47	+	10195.7i	−0.446585	+	0.773507i
$559$	2688.74	−	4657.04i	0.203438	−	0.352365i
$560$	−1747.58	+	3026.90i	−0.131873	+	0.228411i
$561$	−16557.9			−1.24612
$562$	−7669.07	+	13283.2i	−0.575623	+	0.997008i
$563$	12134.1			0.908332			0.454166	−	0.890917i	$-0.349937\pi$
$563$	12134.1			0.908332			0.454166	+	0.890917i	$0.349937\pi$
$564$	1530.75	+	2651.33i	0.114284	+	0.197946i
$565$	9268.22			0.690119
$566$	−5689.53			−0.422525
$567$	−762.628	−	1320.91i	−0.0564857	−	0.0978360i
$568$	3961.35	−	6861.26i	0.292631	−	0.506852i
$569$	4207.57			0.310001			0.155000	−	0.987914i	$-0.450462\pi$
$569$	4207.57			0.310001			0.155000	+	0.987914i	$0.450462\pi$
$570$	1756.51	+	3042.36i	0.129074	+	0.223562i
$571$	−7208.27	−	12485.1i	−0.528295	−	0.915034i	−0.999456	−	0.0329866i	$-0.989498\pi$
$571$	−7208.27	−	12485.1i	−0.528295	−	0.915034i	0.471161	−	0.882047i	$-0.343835\pi$
$572$	−2993.70	−	5185.24i	−0.218834	−	0.379031i
$573$	4734.88	−	8201.05i	0.345205	−	0.597913i
$574$	−1574.44	+	2727.01i	−0.114488	+	0.198298i
$575$	10344.3	+	17916.8i	0.750236	+	1.29945i
$576$	592.941	+	1027.00i	0.0428922	+	0.0742914i
$577$	−2976.55	−	5155.53i	−0.214758	−	0.371972i	0.738440	−	0.674319i	$-0.235563\pi$
$577$	−2976.55	−	5155.53i	−0.214758	−	0.371972i	−0.953198	+	0.302348i	$0.902230\pi$
$578$	−7846.06			−0.564625
$579$	−5921.53	+	10256.4i	−0.425026	+	0.736167i
$580$	−3885.14	−	6729.25i	−0.278141	−	0.481754i
$581$	−754.485			−0.0538749
$582$	4108.41			0.292610
$583$	−7898.62	−	13680.8i	−0.561111	−	0.971872i
$584$	−6397.98			−0.453340
$585$	3761.89	−	6515.79i	0.265872	−	0.460504i
$586$	2024.99			0.142750
$587$	826.237	−	1431.08i	0.0580962	−	0.100626i	−0.835515	−	0.549468i	$-0.814830\pi$
$587$	826.237	−	1431.08i	0.0580962	−	0.100626i	0.893611	+	0.448843i	$0.148164\pi$
$588$	−966.046	+	1673.24i	−0.0677535	+	0.117353i
$589$	5839.03	−	10113.5i	0.408477	−	0.707503i
$590$	−960.037	−	1662.83i	−0.0669900	−	0.116030i
$591$	10118.2			0.704239
$592$	2065.96	−	2949.40i	0.143430	−	0.204763i
$593$	19299.3			1.33647			0.668237	−	0.743949i	$-0.267049\pi$
$593$	19299.3			1.33647			0.668237	+	0.743949i	$0.267049\pi$
$594$	8019.88	+	13890.8i	0.553973	+	0.959509i
$595$	−10267.1	+	17783.1i	−0.707410	+	1.22527i
$596$	1878.15	−	3253.06i	0.129081	−	0.223575i
$597$	4179.81	−	7239.65i	0.286547	−	0.496314i
$598$	7079.71			0.484132
$599$	−10904.6	+	18887.4i	−0.743826	+	1.28834i	0.206916	+	0.978359i	$0.433657\pi$
$599$	−10904.6	+	18887.4i	−0.743826	+	1.28834i	−0.950741	+	0.309985i	$0.899676\pi$
$600$	3365.50			0.228993
$601$	7020.60	+	12160.0i	0.476500	+	0.825322i	0.999637	−	0.0269263i	$-0.00857194\pi$
$601$	7020.60	+	12160.0i	0.476500	+	0.825322i	−0.523138	+	0.852248i	$0.675239\pi$
$602$	5786.05			0.391731
$603$	−5500.04			−0.371441
$604$	4209.72	+	7291.44i	0.283594	+	0.491200i
$605$	−19143.3	+	33157.1i	−1.28642	+	2.22815i
$606$	−9453.83			−0.633722
$607$	−1399.45	−	2423.92i	−0.0935783	−	0.162082i	0.815436	−	0.578847i	$-0.196497\pi$
$607$	−1399.45	−	2423.92i	−0.0935783	−	0.162082i	−0.909014	+	0.416765i	$0.863164\pi$
$608$	−588.163	−	1018.73i	−0.0392321	−	0.0679521i
$609$	2290.97	+	3968.08i	0.152438	+	0.264031i
$610$	−11360.7	+	19677.3i	−0.754067	+	1.30608i
$611$	−3251.97	+	5632.57i	−0.215320	+	0.372945i
$612$	3483.54	+	6033.66i	0.230088	+	0.398523i
$613$	−2153.38	−	3729.77i	−0.141883	−	0.245749i	0.786323	−	0.617816i	$-0.211982\pi$
$613$	−2153.38	−	3729.77i	−0.141883	−	0.245749i	−0.928206	+	0.372067i	$0.878649\pi$
$614$	−1332.81	−	2308.49i	−0.0876022	−	0.151731i
$615$	5654.14			0.370727
$616$	3221.15	−	5579.20i	0.210688	−	0.364923i
$617$	−5981.28	−	10359.9i	−0.390271	−	0.675970i	0.602214	−	0.798335i	$-0.294285\pi$
$617$	−5981.28	−	10359.9i	−0.390271	−	0.675970i	−0.992485	+	0.122365i	$0.960952\pi$
$618$	−5186.72			−0.337606
$619$	−4832.58			−0.313793			−0.156896	−	0.987615i	$-0.550149\pi$
$619$	−4832.58			−0.313793			−0.156896	+	0.987615i	$0.550149\pi$
$620$	−10431.3	−	18067.6i	−0.675696	−	1.17034i
$621$	−18966.0			−1.22557
$622$	3273.29	−	5669.50i	0.211008	−	0.365476i
$623$	18959.2			1.21924
$624$	575.845	−	997.393i	0.0369427	−	0.0639867i
$625$	6399.93	−	11085.0i	0.409596	−	0.709441i
$626$	−9282.66	+	16078.0i	−0.592667	+	1.02653i
$627$	−3237.60	−	5607.69i	−0.206216	−	0.357176i
$628$	−2469.09			−0.156891
$629$	12137.5	−	17327.8i	0.769403	−	1.09842i
$630$	8095.42			0.511951
$631$	−2688.57	−	4656.74i	−0.169620	−	0.293791i	0.768666	−	0.639650i	$-0.220921\pi$
$631$	−2688.57	−	4656.74i	−0.169620	−	0.293791i	−0.938286	+	0.345859i	$0.887587\pi$
$632$	434.127	−	751.930i	0.0273238	−	0.0473262i
$633$	−5629.64	+	9750.83i	−0.353488	+	0.612260i
$634$	7313.31	−	12667.0i	0.458121	−	0.793489i
$635$	−13418.2			−0.838560
$636$	1519.32	−	2631.54i	0.0947247	−	0.164068i
$637$	−4104.59			−0.255306
$638$	7161.10	+	12403.4i	0.444374	+	0.769679i
$639$	−18350.4			−1.13604
$640$	−2101.48			−0.129794
$641$	10782.4	+	18675.6i	0.664397	+	1.15077i	0.979448	+	0.201694i	$0.0646448\pi$
$641$	10782.4	+	18675.6i	0.664397	+	1.15077i	−0.315052	+	0.949074i	$0.602022\pi$
$642$	2996.19	−	5189.55i	0.184190	−	0.319027i
$643$	15722.2			0.964266			0.482133	−	0.876098i	$-0.339862\pi$
$643$	15722.2			0.964266			0.482133	+	0.876098i	$0.339862\pi$
$644$	3808.80	+	6597.04i	0.233056	+	0.403664i
$645$	−5194.73	−	8997.53i	−0.317120	−	0.549267i
$646$	−3455.46	−	5985.04i	−0.210454	−	0.364517i
$647$	−2502.84	+	4335.05i	−0.152082	+	0.263413i	−0.931993	−	0.362477i	$-0.881931\pi$
$647$	−2502.84	+	4335.05i	−0.152082	+	0.263413i	0.779911	+	0.625890i	$0.215264\pi$
$648$	458.533	−	794.203i	0.0277977	−	0.0481469i
$649$	1769.54	+	3064.94i	0.107027	+	0.185377i
$650$	3574.89	+	6191.88i	0.215721	+	0.373639i
$651$	6151.09	+	10654.0i	0.370323	+	0.641418i
$652$	207.350			0.0124547
$653$	−14023.0	+	24288.5i	−0.840371	+	1.45557i	0.0492100	+	0.998788i	$0.484330\pi$
$653$	−14023.0	+	24288.5i	−0.840371	+	1.45557i	−0.889581	+	0.456777i	$0.849004\pi$
$654$	−3688.33	−	6388.38i	−0.220528	−	0.381966i
$655$	15561.0			0.928273
$656$	−1893.28			−0.112683
$657$	7409.43	+	12833.5i	0.439984	+	0.762074i
$658$	−6998.09			−0.414611
$659$	213.729	−	370.190i	0.0126338	−	0.0218825i	−0.859639	−	0.510901i	$-0.829312\pi$
$659$	213.729	−	370.190i	0.0126338	−	0.0218825i	0.872273	+	0.489019i	$0.162645\pi$
$660$	−11567.8			−0.682237
$661$	−11811.7	+	20458.5i	−0.695042	+	1.20385i	0.275125	+	0.961408i	$0.411281\pi$
$661$	−11811.7	+	20458.5i	−0.695042	+	1.20385i	−0.970167	+	0.242439i	$0.922053\pi$
$662$	−2522.33	+	4368.80i	−0.148086	+	0.256493i
$663$	3383.10	−	5859.70i	0.198173	−	0.343245i
$664$	−226.818	−	392.861i	−0.0132564	−	0.0229608i
$665$	−8030.18			−0.468266
$666$	−8308.68	−	728.367i	−0.483415	−	0.0423779i
$667$	−16935.1			−0.983101
$668$	−2078.99	−	3600.91i	−0.120417	−	0.208568i
$669$	1738.68	−	3011.48i	0.100480	−	0.174037i
$670$	4873.26	−	8440.74i	0.281001	−	0.486708i
$671$	20940.1	−	36269.3i	1.20474	−	2.08668i
$672$	1239.19			0.0711353
$673$	3667.47	−	6352.25i	0.210060	−	0.363835i	−0.741673	−	0.670762i	$-0.765967\pi$
$673$	3667.47	−	6352.25i	0.210060	−	0.363835i	0.951733	+	0.306926i	$0.0993006\pi$
$674$	15248.7			0.871451
$675$	−9576.83	−	16587.6i	−0.546093	−	0.945860i
$676$	−6341.31			−0.360794
$677$	−5311.75			−0.301547			−0.150773	−	0.988568i	$-0.548176\pi$
$677$	−5311.75			−0.301547			−0.150773	+	0.988568i	$0.548176\pi$
$678$	−1643.00	−	2845.76i	−0.0930664	−	0.161196i
$679$	−4695.57	+	8132.97i	−0.265390	+	0.459668i
$680$	−12346.2			−0.696259
$681$	−7848.06	−	13593.2i	−0.441613	−	0.764896i
$682$	19227.0	+	33302.2i	1.07953	+	1.86981i
$683$	9684.36	+	16773.8i	0.542550	+	0.939724i	0.998757	+	0.0498505i	$0.0158745\pi$
$683$	9684.36	+	16773.8i	0.542550	+	0.939724i	−0.456207	+	0.889874i	$0.650792\pi$
$684$	−1362.29	+	2359.55i	−0.0761526	+	0.131900i
$685$	−7158.47	+	12398.8i	−0.399286	+	0.691584i
$686$	−6772.02	−	11729.5i	−0.376905	−	0.652819i
$687$	−1905.65	−	3300.69i	−0.105830	−	0.183303i
$688$	1739.44	+	3012.81i	0.0963891	+	0.166951i
$689$	6455.37			0.356938
$690$	6839.10	−	11845.7i	0.377333	−	0.653560i
$691$	8874.76	+	15371.5i	0.488585	+	0.846253i	0.999914	−	0.0131316i	$-0.00418005\pi$
$691$	8874.76	+	15371.5i	0.488585	+	0.846253i	−0.511329	+	0.859385i	$0.670847\pi$
$692$	12375.3			0.679823
$693$	−14921.5			−0.817924
$694$	6531.69	+	11313.2i	0.357262	+	0.618796i
$695$	−16142.4			−0.881032
$696$	−1377.46	+	2385.82i	−0.0750177	+	0.129934i
$697$	−11123.0			−0.604469
$698$	8997.89	−	15584.8i	0.487930	−	0.845119i
$699$	−6141.17	+	10636.8i	−0.332304	+	0.575567i
$700$	−3846.50	+	6662.32i	−0.207691	+	0.359732i
$701$	15426.6	+	26719.7i	0.831176	+	1.43964i	0.897106	+	0.441815i	$0.145665\pi$
$701$	15426.6	+	26719.7i	0.831176	+	1.43964i	−0.0659297	+	0.997824i	$0.521001\pi$
$702$	−6554.48			−0.352397
$703$	8241.72	+	722.497i	0.442165	+	0.0387617i
$704$	3873.46			0.207367
$705$	6282.89	+	10882.3i	0.335642	+	0.581348i
$706$	8129.23	−	14080.2i	0.433354	−	0.750591i
$707$	10805.0	−	18714.7i	0.574770	−	0.995530i
$708$	−340.376	+	589.549i	−0.0180680	+	0.0312946i
$709$	2394.66			0.126846			0.0634228	−	0.997987i	$-0.479798\pi$
$709$	2394.66			0.126846			0.0634228	+	0.997987i	$0.479798\pi$
$710$	16259.2	−	28161.7i	0.859432	−	1.48858i
$711$	−2011.03			−0.106075
$712$	5699.66	+	9872.10i	0.300005	+	0.519624i
$713$	−45469.5			−2.38828
$714$	7280.27			0.381593
$715$	−12287.5	−	21282.6i	−0.642695	−	1.11318i
$716$	3177.90	−	5504.29i	0.165871	−	0.287298i
$717$	−7171.79			−0.373550
$718$	9517.86	+	16485.4i	0.494712	+	0.856867i
$719$	−12366.9	−	21420.0i	−0.641455	−	1.11103i	−0.985108	−	0.171936i	$-0.944998\pi$
$719$	−12366.9	−	21420.0i	−0.641455	−	1.11103i	0.343653	−	0.939097i	$-0.388336\pi$
$720$	2433.70	+	4215.29i	0.125970	+	0.218187i
$721$	5928.00	−	10267.6i	0.306200	−	0.530354i
$722$	−5507.69	+	9539.60i	−0.283899	+	0.491727i
$723$	3109.61	+	5386.00i	0.159955	+	0.277050i
$724$	4757.68	+	8240.54i	0.244223	+	0.423007i
$725$	−8551.33	−	14811.3i	−0.438053	−	0.758730i
$726$	13574.3			0.693925
$727$	5572.65	−	9652.11i	0.284289	−	0.492403i	−0.688148	−	0.725571i	$-0.741576\pi$
$727$	5572.65	−	9652.11i	0.284289	−	0.492403i	0.972436	+	0.233168i	$0.0749092\pi$
$728$	1316.29	+	2279.88i	0.0670122	+	0.116069i
$729$	8288.76			0.421112
$730$	−26260.2			−1.33142
$731$	10219.3	+	17700.3i	0.517062	+	0.895578i
$732$	8055.75			0.406761
$733$	10203.7	−	17673.3i	0.514164	−	0.890559i	−0.485700	−	0.874125i	$-0.661435\pi$
$733$	10203.7	−	17673.3i	0.514164	−	0.890559i	0.999865	−	0.0164337i	$-0.00523125\pi$
$734$	−6030.87			−0.303274
$735$	−3965.09	+	6867.74i	−0.198986	+	0.344654i
$736$	−2290.06	+	3966.50i	−0.114691	+	0.198651i
$737$	−8982.42	+	15558.0i	−0.448944	+	0.777594i
$738$	2192.58	+	3797.67i	0.109363	+	0.189423i
$739$	602.373			0.0299847			0.0149923	−	0.999888i	$-0.495228\pi$
$739$	602.373			0.0299847			0.0149923	+	0.999888i	$0.495228\pi$
$740$	8479.63	−	12105.7i	0.421240	−	0.601371i
$741$	2646.02			0.131180
$742$	3472.92	+	6015.27i	0.171826	+	0.297611i
$743$	10783.3	−	18677.3i	0.532440	−	0.922213i	−0.466843	−	0.884340i	$-0.654609\pi$
$743$	10783.3	−	18677.3i	0.532440	−	0.922213i	0.999283	−	0.0378723i	$-0.0120580\pi$
$744$	−3698.37	+	6405.76i	−0.182243	+	0.315654i
$745$	7708.80	−	13352.0i	0.379099	−	0.656619i
$746$	−8270.94			−0.405926
$747$	−525.351	+	909.935i	−0.0257317	+	0.0445687i
$748$	22756.6			1.11239
$749$	6848.80	+	11862.5i	0.334112	+	0.578699i
$750$	1867.83			0.0909381
$751$	12502.8			0.607502			0.303751	−	0.952751i	$-0.401761\pi$
$751$	12502.8			0.607502			0.303751	+	0.952751i	$0.401761\pi$
$752$	−2103.81	−	3643.91i	−0.102019	−	0.176702i
$753$	7572.93	−	13116.7i	0.366498	−	0.634793i
$754$	−5852.61			−0.282678
$755$	17278.6	+	29927.4i	0.832891	+	1.44261i
$756$	−3526.23	−	6107.61i	−0.169640	−	0.293825i
$757$	−13816.8	−	23931.3i	−0.663380	−	1.14901i	−0.979722	−	0.200363i	$-0.935788\pi$
$757$	−13816.8	−	23931.3i	−0.663380	−	1.14901i	0.316341	−	0.948645i	$-0.397546\pi$
$758$	10847.4	−	18788.3i	0.519785	−	0.900293i
$759$	−12605.9	+	21834.0i	−0.602850	+	1.04417i
$760$	−2414.09	−	4181.32i	−0.115221	−	0.199569i
$761$	−16364.5	−	28344.2i	−0.779519	−	1.35017i	−0.932219	−	0.361895i	$-0.882130\pi$
$761$	−16364.5	−	28344.2i	−0.779519	−	1.35017i	0.152700	−	0.988273i	$-0.451203\pi$
$762$	2378.68	+	4119.99i	0.113085	+	0.195868i
$763$	16861.9			0.800053
$764$	−6507.47	+	11271.3i	−0.308157	+	0.533744i
$765$	14298.0	+	24764.9i	0.675746	+	1.17043i
$766$	−20461.6			−0.965153
$767$	−1446.21			−0.0680830
$768$	372.535	+	645.249i	0.0175035	+	0.0303170i
$769$	−10486.8			−0.491759			−0.245880	−	0.969300i	$-0.579077\pi$
$769$	−10486.8			−0.491759			−0.245880	+	0.969300i	$0.579077\pi$
$770$	13221.1	−	22899.6i	0.618772	−	1.07174i
$771$	−15499.0			−0.723975
$772$	8138.36	−	14096.0i	0.379412	−	0.657161i
$773$	14059.1	−	24351.0i	0.654165	−	1.13305i	−0.327938	−	0.944699i	$-0.606354\pi$
$773$	14059.1	−	24351.0i	0.654165	−	1.13305i	0.982102	−	0.188347i	$-0.0603131\pi$
$774$	4028.86	−	6978.19i	0.187099	−	0.324064i
$775$	−22959.7	−	39767.4i	−1.06418	−	1.84321i
$776$	−5646.46			−0.261206
$777$	−5000.23	+	7138.44i	−0.230865	+	0.329588i
$778$	22574.9			1.04030
$779$	−2174.91	−	3767.06i	−0.100031	−	0.173259i
$780$	2363.53	−	4093.76i	0.108497	−	0.187923i
$781$	−29969.0	+	51907.8i	−1.37308	+	2.37824i
$782$	−13454.1	+	23303.2i	−0.615240	+	1.06563i
$783$	15678.7			0.715594
$784$	1327.70	−	2299.65i	0.0604821	−	0.104758i
$785$	−10134.3			−0.460774
$786$	−2758.54	−	4777.92i	−0.125183	−	0.216823i
$787$	1767.35			0.0800497			0.0400249	−	0.999199i	$-0.487256\pi$
$787$	1767.35			0.0800497			0.0400249	+	0.999199i	$0.487256\pi$
$788$	−13906.1			−0.628659
$789$	−6058.32	−	10493.3i	−0.273361	−	0.473475i
$790$	1781.85	−	3086.26i	0.0802475	−	0.138993i
$791$	7511.26			0.337636
$792$	−4485.81	−	7769.65i	−0.201258	−	0.348589i
$793$	8556.94	+	14821.1i	0.383185	+	0.663696i
$794$	−5616.17	−	9727.50i	−0.251021	−	0.434781i
$795$	6235.98	−	10801.0i	0.278198	−	0.481853i
$796$	−5744.61	+	9949.95i	−0.255794	+	0.443048i
$797$	−1575.72	−	2729.24i	−0.0700314	−	0.121298i	0.828883	−	0.559421i	$-0.188977\pi$
$797$	−1575.72	−	2729.24i	−0.0700314	−	0.121298i	−0.898915	+	0.438123i	$0.855643\pi$
$798$	1423.53	+	2465.62i	0.0631483	+	0.109376i
$799$	−12359.9	−	21408.0i	−0.547262	−	0.947886i
$800$	−4625.44			−0.204417
$801$	13201.4	−	22865.5i	0.582334	−	1.00863i
$802$	−4291.70	−	7433.45i	−0.188959	−	0.327287i
$803$	48403.0			2.12715
$804$	−3455.58			−0.151578
$805$	15633.1	+	27077.3i	0.684464	+	1.18553i
$806$	−15713.8			−0.686720
$807$	−6249.63	+	10824.7i	−0.272611	+	0.472177i
$808$	12993.0			0.565710
$809$	−1501.83	+	2601.25i	−0.0652678	+	0.113047i	−0.896813	−	0.442410i	$-0.854124\pi$
$809$	−1501.83	+	2601.25i	−0.0652678	+	0.113047i	0.831545	+	0.555457i	$0.187457\pi$
$810$	1882.03	−	3259.77i	0.0816392	−	0.141403i
$811$	5509.98	−	9543.56i	0.238571	−	0.413218i	−0.721733	−	0.692171i	$-0.756654\pi$
$811$	5509.98	−	9543.56i	0.238571	−	0.413218i	0.960305	+	0.278954i	$0.0899875\pi$
$812$	−3148.64	−	5453.60i	−0.136078	−	0.235694i
$813$	18189.7			0.784674
$814$	−15629.7	+	22313.3i	−0.672998	+	0.960786i
$815$	851.057			0.0365782
$816$	2188.65	+	3790.84i	0.0938945	+	0.162630i
$817$	−3996.39	+	6921.95i	−0.171133	+	0.296412i
$818$	10821.4	−	18743.2i	0.462545	−	0.801152i
$819$	3048.76	−	5280.60i	0.130076	−	0.225298i
$820$	−7770.88			−0.330940
$821$	−8490.58	+	14706.1i	−0.360930	+	0.625148i	−0.988114	−	0.153722i	$-0.950874\pi$
$821$	−8490.58	+	14706.1i	−0.360930	+	0.625148i	0.627184	+	0.778871i	$0.284207\pi$
$822$	5076.00			0.215384
$823$	−14754.5	−	25555.6i	−0.624922	−	1.08240i	−0.988556	−	0.150855i	$-0.951797\pi$
$823$	−14754.5	−	25555.6i	−0.624922	−	1.08240i	0.363634	−	0.931542i	$-0.381536\pi$
$824$	7128.46			0.301373
$825$	−25461.2			−1.07448
$826$	−778.045	−	1347.61i	−0.0327744	−	0.0567669i
$827$	11615.4	−	20118.5i	0.488402	−	0.845938i	−0.511509	−	0.859278i	$-0.670913\pi$
$827$	11615.4	−	20118.5i	0.488402	−	0.845938i	0.999911	+	0.0133405i	$0.00424655\pi$
$828$	10608.4			0.445249
$829$	16588.2	+	28731.7i	0.694974	+	1.20373i	0.970190	+	0.242348i	$0.0779174\pi$
$829$	16588.2	+	28731.7i	0.694974	+	1.20373i	−0.275216	+	0.961383i	$0.588749\pi$
$830$	−930.966	−	1612.48i	−0.0389329	−	0.0674338i
$831$	2029.83	+	3515.77i	0.0847341	+	0.146764i
$832$	−791.424	+	1370.79i	−0.0329780	+	0.0571195i
$833$	7800.27	−	13510.5i	0.324446	−	0.561957i
$834$	2861.61	+	4956.45i	0.118812	+	0.205789i
$835$	−8533.12	−	14779.8i	−0.353654	−	0.612546i
$836$	4449.66	+	7707.03i	0.184084	+	0.318844i
$837$	42096.1			1.73842
$838$	2959.07	−	5125.26i	0.121980	−	0.211276i
$839$	−2589.11	−	4484.47i	−0.106539	−	0.184531i	0.807827	−	0.589420i	$-0.200643\pi$
$839$	−2589.11	−	4484.47i	−0.106539	−	0.184531i	−0.914366	+	0.404889i	$0.867310\pi$
$840$	5086.21			0.208918
$841$	−10389.2			−0.425980
$842$	−14707.4	−	25474.0i	−0.601960	−	1.04263i
$843$	22320.3			0.911923
$844$	7737.20	−	13401.2i	0.315552	−	0.546551i
$845$	−26027.6			−1.05962
$846$	−4872.80	+	8439.94i	−0.198026	+	0.342992i
$847$	−15514.3	+	26871.6i	−0.629372	+	1.09010i
$848$	−2088.10	+	3616.70i	−0.0845587	+	0.146460i
$849$	4139.74	+	7170.25i	0.167345	+	0.289850i
$850$	−27174.5			−1.09656
$851$	−13608.7	−	29197.1i	−0.548178	−	1.17610i
$852$	−11529.2			−0.463597
$853$	3717.94	+	6439.66i	0.149238	+	0.258487i	0.930946	−	0.365157i	$-0.118985\pi$
$853$	3717.94	+	6439.66i	0.149238	+	0.258487i	−0.781708	+	0.623644i	$0.785651\pi$
$854$	−9207.07	+	15947.1i	−0.368922	+	0.638992i
$855$	−5591.45	+	9684.68i	−0.223653	+	0.387379i
$856$	−4117.87	+	7132.36i	−0.164423	+	0.284788i
$857$	−20772.0			−0.827956			−0.413978	−	0.910287i	$-0.635861\pi$
$857$	−20772.0			−0.827956			−0.413978	+	0.910287i	$0.635861\pi$
$858$	−4356.47	+	7545.63i	−0.173342	+	0.300237i
$859$	−31655.7			−1.25737			−0.628684	−	0.777661i	$-0.716406\pi$
$859$	−31655.7			−1.25737			−0.628684	+	0.777661i	$0.716406\pi$
$860$	7139.47	+	12365.9i	0.283086	+	0.490319i
$861$	4582.30			0.181376
$862$	−18597.5			−0.734841
$863$	6956.22	+	12048.5i	0.274383	+	0.475245i	0.969979	−	0.243188i	$-0.0781931\pi$
$863$	6956.22	+	12048.5i	0.274383	+	0.475245i	−0.695596	+	0.718433i	$0.744860\pi$
$864$	2120.16	−	3672.23i	0.0834830	−	0.144597i
$865$	50793.8			1.99658
$866$	5144.92	+	8911.26i	0.201884	+	0.349673i
$867$	5708.85	+	9888.02i	0.223625	+	0.387330i
$868$	−8453.87	−	14642.5i	−0.330579	−	0.572580i
$869$	−3284.32	+	5688.61i	−0.128208	+	0.222063i
$870$	−5653.70	+	9792.50i	−0.220320	+	0.381606i
$871$	−3670.57	−	6357.61i	−0.142793	−	0.247324i
$872$	5069.13	+	8779.99i	0.196861	+	0.340972i
$873$	6539.10	+	11326.1i	0.253511	+	0.439094i
$874$	−10522.9			−0.407255
$875$	−2134.78	+	3697.55i	−0.0824786	+	0.142857i
$876$	4655.22	+	8063.07i	0.179549	+	0.310988i
$877$	−12863.3			−0.495284			−0.247642	−	0.968852i	$-0.579656\pi$
$877$	−12863.3			−0.495284			−0.247642	+	0.968852i	$0.579656\pi$
$878$	2788.89			0.107199
$879$	−1473.39	−	2551.99i	−0.0565373	−	0.0979256i
$880$	15898.4			0.609019
$881$	−12909.5	+	22359.9i	−0.493680	+	0.855078i	−0.999973	−	0.00728277i	$-0.997682\pi$
$881$	−12909.5	+	22359.9i	−0.493680	+	0.855078i	0.506294	+	0.862361i	$0.331015\pi$
$882$	−6150.39			−0.234801
$883$	−14614.0	+	25312.2i	−0.556965	+	0.964692i	0.440783	+	0.897614i	$0.354701\pi$
$883$	−14614.0	+	25312.2i	−0.556965	+	0.964692i	−0.997748	+	0.0670780i	$0.978632\pi$
$884$	−4649.62	+	8053.38i	−0.176905	+	0.306408i
$885$	−1397.06	+	2419.78i	−0.0530640	+	0.0919095i
$886$	8425.29	+	14593.0i	0.319473	+	0.553343i
$887$	−47021.4			−1.77996			−0.889980	−	0.455999i	$-0.849282\pi$
$887$	−47021.4			−1.77996			−0.889980	+	0.455999i	$0.849282\pi$
$888$	−5220.20	−	457.621i	−0.197273	−	0.0172936i
$889$	−10874.5			−0.410259
$890$	23394.0	+	40519.6i	0.881089	+	1.52609i
$891$	−3468.96	+	6008.42i	−0.130432	+	0.225914i
$892$	−2389.59	+	4138.88i	−0.0896965	+	0.155359i
$893$	4833.53	−	8371.92i	0.181129	−	0.313724i
$894$	−5466.23			−0.204495
$895$	13043.6	−	22592.1i	0.487149	−	0.843767i
$896$	−1703.11			−0.0635009
$897$	−5151.25	−	8922.22i	−0.191745	−	0.332112i
$898$	−15861.6			−0.589430
$899$	37588.4			1.39449
$900$	5356.67	+	9278.02i	0.198395	+	0.343630i
$901$	−12267.6	+	21248.2i	−0.453601	+	0.785659i
$902$	14323.3			0.528730
$903$	−4209.97	−	7291.89i	−0.155149	−	0.268725i
$904$	2258.09	+	3911.12i	0.0830784	+	0.143896i
$905$	19527.7	+	33822.9i	0.717262	+	1.24233i
$906$	6126.04	−	10610.6i	0.224640	−	0.389088i
$907$	−5033.11	+	8717.61i	−0.184258	+	0.319144i	−0.943326	−	0.331867i	$-0.892321\pi$
$907$	−5033.11	+	8717.61i	−0.184258	+	0.319144i	0.759068	+	0.651011i	$0.225655\pi$
$908$	10786.1	+	18682.1i	0.394218	+	0.682806i
$909$	−15047.1	−	26062.3i	−0.549043	−	0.950971i
$910$	5402.65	+	9357.66i	0.196809	+	0.340883i
$911$	−44601.3			−1.62207			−0.811036	−	0.584996i	$-0.801096\pi$
$911$	−44601.3			−1.62207			−0.811036	+	0.584996i	$0.801096\pi$
$912$	−855.902	+	1482.47i	−0.0310765	+	0.0538261i
$913$	1715.96	+	2972.13i	0.0622015	+	0.107736i
$914$	−26199.4			−0.948141
$915$	33064.5			1.19462
$916$	2619.07	+	4536.36i	0.0944722	+	0.163631i
$917$	12611.1			0.454151
$918$	12456.0	−	21574.4i	0.447830	−	0.775665i
$919$	34609.0			1.24227			0.621134	−	0.783704i	$-0.286672\pi$
$919$	34609.0			1.24227			0.621134	+	0.783704i	$0.286672\pi$
$920$	−9399.44	+	16280.3i	−0.336837	+	0.583419i
$921$	−1939.52	+	3359.35i	−0.0693913	+	0.120189i
$922$	2935.50	−	5084.44i	0.104854	−	0.181613i
$923$	−12246.5	−	21211.6i	−0.436727	−	0.756433i
$924$	−9374.93			−0.333780
$925$	18664.0	−	26645.1i	0.663425	−	0.947120i
$926$	12380.1			0.439348
$927$	−8255.39	−	14298.8i	−0.292495	−	0.506616i
$928$	1893.13	−	3279.00i	0.0669667	−	0.115990i
$929$	−8241.12	+	14274.0i	−0.291047	+	0.504107i	−0.974057	−	0.226301i	$-0.927337\pi$
$929$	−8241.12	+	14274.0i	−0.291047	+	0.504107i	0.683011	+	0.730408i	$0.260670\pi$
$930$	−15179.8	+	26292.2i	−0.535231	+	0.927047i
$931$	6100.82			0.214765
$932$	8440.24	−	14618.9i	0.296641	−	0.513797i
$933$	−9526.66			−0.334286
$934$	−18421.8	−	31907.5i	−0.645374	−	1.11782i
$935$	93403.5			3.26698
$936$	3666.15			0.128026
$937$	15512.5	+	26868.4i	0.540844	+	0.936770i	0.998856	+	0.0478237i	$0.0152286\pi$
$937$	15512.5	+	26868.4i	0.540844	+	0.936770i	−0.458011	+	0.888946i	$0.651438\pi$
$938$	3949.45	−	6840.65i	0.137478	−	0.238118i
$939$	27016.5			0.938925
$940$	−8635.01	−	14956.3i	−0.299620	−	0.518957i
$941$	10491.0	+	18170.9i	0.363438	+	0.629494i	0.988524	−	0.151062i	$-0.0482694\pi$
$941$	10491.0	+	18170.9i	0.363438	+	0.629494i	−0.625086	+	0.780556i	$0.714936\pi$
$942$	1796.53	+	3111.67i	0.0621380	+	0.107626i
$943$	−8468.20	+	14667.3i	−0.292431	+	0.506505i
$944$	467.802	−	810.257i	0.0161289	−	0.0279360i
$945$	−14473.3	−	25068.4i	−0.498217	−	0.862938i
$946$	−13159.5	−	22792.9i	−0.452275	−	0.783364i
$947$	2163.90	+	3747.99i	0.0742528	+	0.128610i	0.900761	−	0.434315i	$-0.143009\pi$
$947$	2163.90	+	3747.99i	0.0742528	+	0.128610i	−0.826508	+	0.562925i	$0.809676\pi$
$948$	−1263.49			−0.0432873
$949$	−9889.68	+	17129.4i	−0.338285	+	0.585927i
$950$	−5313.50	−	9203.25i	−0.181466	−	0.314308i
$951$	−21284.9			−0.725772
$952$	−10005.8			−0.340640
$953$	2641.41	+	4575.06i	0.0897835	+	0.155510i	0.907420	−	0.420226i	$-0.138049\pi$
$953$	2641.41	+	4575.06i	0.0897835	+	0.155510i	−0.817636	+	0.575735i	$0.804716\pi$
$954$	9672.84			0.328270
$955$	−26709.6	+	46262.4i	−0.905030	+	1.56756i
$956$	9856.69			0.333460
$957$	10420.9	−	18049.6i	0.351997	−	0.609676i
$958$	−5883.67	+	10190.8i	−0.198427	+	0.343685i
$959$	−5801.45	+	10048.4i	−0.195348	+	0.338352i
$960$	1529.05	+	2648.40i	0.0514062	+	0.0890382i
$961$	71131.2			2.38767
$962$	−4703.04	−	10090.3i	−0.157622	−	0.338174i
$963$	19075.4			0.638314
$964$	−4273.75	−	7402.35i	−0.142789	−	0.247317i
$965$	33403.5	−	57856.6i	1.11430	−	1.93002i
$966$	5542.62	−	9600.10i	0.184608	−	0.319750i
$967$	−3895.68	+	6747.52i	−0.129552	+	0.224391i	−0.923503	−	0.383591i	$-0.874687\pi$
$967$	−3895.68	+	6747.52i	−0.129552	+	0.224391i	0.793951	+	0.607982i	$0.208021\pi$
$968$	−18656.1			−0.619452
$969$	−5028.44	+	8709.51i	−0.166704	+	0.288741i
$970$	−23175.7			−0.767140
$971$	20363.0	+	35269.7i	0.672997	+	1.16566i	0.977050	+	0.213009i	$0.0683265\pi$
$971$	20363.0	+	35269.7i	0.672997	+	1.16566i	−0.304054	+	0.952655i	$0.598340\pi$
$972$	−15645.6			−0.516289
$973$	−13082.3			−0.431039
$974$	17541.3	+	30382.4i	0.577062	+	0.999501i
$975$	5202.22	−	9010.51i	0.170876	−	0.295967i
$976$	−11071.6			−0.363107
$977$	21320.1	+	36927.5i	0.698148	+	1.20923i	0.969108	+	0.246637i	$0.0793255\pi$
$977$	21320.1	+	36927.5i	0.698148	+	1.20923i	−0.270960	+	0.962591i	$0.587341\pi$
$978$	−150.869	−	261.313i	−0.00493278	−	0.00854382i
$979$	−43119.9	−	74685.9i	−1.40768	−	2.43817i
$980$	5449.50	−	9438.81i	0.177631	−	0.307665i
$981$	11741.0	−	20336.0i	0.382122	−	0.661854i
$982$	−2324.10	−	4025.45i	−0.0755243	−	0.130812i
$983$	−13801.2	−	23904.3i	−0.447801	−	0.775615i	0.550441	−	0.834874i	$-0.314460\pi$
$983$	−13801.2	−	23904.3i	−0.447801	−	0.775615i	−0.998243	+	0.0592590i	$0.981126\pi$
$984$	1377.56	+	2386.01i	0.0446291	+	0.0773000i
$985$	−57076.9			−1.84632
$986$	11122.2	−	19264.2i	0.359231	−	0.622207i
$987$	5091.85	+	8819.35i	0.164210	+	0.284421i
$988$	−3636.61			−0.117101
$989$	31120.5			1.00058
$990$	−18411.8	−	31890.2i	−0.591076	−	1.02377i
$991$	−41118.5			−1.31803			−0.659017	−	0.752128i	$-0.729028\pi$
$991$	−41118.5			−1.31803			−0.659017	+	0.752128i	$0.729028\pi$
$992$	5082.92	−	8803.88i	0.162684	−	0.281778i
$993$	7341.06			0.234604
$994$	13177.0	−	22823.2i	0.420471	−	0.728277i
$995$	−23578.5	+	40839.1i	−0.751244	+	1.30119i
$996$	−330.069	+	571.697i	−0.0105006	+	0.0181877i
$997$	−16478.5	−	28541.6i	−0.523450	−	0.906642i	−0.999627	−	0.0272929i	$-0.991311\pi$
$997$	−16478.5	−	28541.6i	−0.523450	−	0.906642i	0.476177	−	0.879349i	$-0.342022\pi$
$998$	−34432.1			−1.09211
$999$	12599.1	+	27031.0i	0.399016	+	0.856079i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.4.c.a.63.3	yes	8
3.2	odd	2		666.4.f.a.433.4		8
37.10	even	3	inner	74.4.c.a.47.3	✓	8
111.47	odd	6		666.4.f.a.343.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.4.c.a.47.3	✓	8	37.10	even	3	inner
74.4.c.a.63.3	yes	8	1.1	even	1	trivial
666.4.f.a.343.4		8	111.47	odd	6
666.4.f.a.433.4		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	74.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.45521 - 2.52050i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-8.20891 + 14.2183i) q^{5} +5.82085 q^{6} +(-6.65276 + 11.5229i) q^{7} -8.00000 q^{8} +(9.26471 + 16.0469i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(1.45521 - 2.52050i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-8.20891 + 14.2183i) q^{5} +5.82085 q^{6} +(-6.65276 + 11.5229i) q^{7} -8.00000 q^{8} +(9.26471 + 16.0469i) q^{9} -32.8357 q^{10} +60.5228 q^{11} +(5.82085 + 10.0820i) q^{12} +(-12.3660 + 21.4185i) q^{13} -26.6111 q^{14} +(23.8914 + 41.3812i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-47.0001 - 81.4065i) q^{17} +(-18.5294 + 32.0939i) q^{18} +(18.3801 - 31.8352i) q^{19} +(-32.8357 - 56.8730i) q^{20} +(19.3624 + 33.5366i) q^{21} +(60.5228 + 104.829i) q^{22} -143.129 q^{23} +(-11.6417 + 20.1640i) q^{24} +(-72.2725 - 125.180i) q^{25} -49.4640 q^{26} +132.510 q^{27} +(-26.6111 - 46.0917i) q^{28} +118.321 q^{29} +(-47.7829 + 82.7624i) q^{30} +317.683 q^{31} +(16.0000 - 27.7128i) q^{32} +(88.0736 - 152.548i) q^{33} +(94.0002 - 162.813i) q^{34} +(-109.224 - 189.181i) q^{35} -74.1176 q^{36} +(95.0800 + 203.992i) q^{37} +73.5203 q^{38} +(35.9903 + 62.3371i) q^{39} +(65.6713 - 113.746i) q^{40} +(59.1649 - 102.477i) q^{41} +(-38.7248 + 67.0733i) q^{42} -217.430 q^{43} +(-121.046 + 209.657i) q^{44} -304.213 q^{45} +(-143.129 - 247.906i) q^{46} +262.977 q^{47} -46.5668 q^{48} +(82.9815 + 143.728i) q^{49} +(144.545 - 250.359i) q^{50} -273.581 q^{51} +(-49.4640 - 85.6741i) q^{52} +(-130.507 - 226.044i) q^{53} +(132.510 + 229.514i) q^{54} +(-496.826 + 860.529i) q^{55} +(53.2221 - 92.1834i) q^{56} +(-53.4939 - 92.6541i) q^{57} +(118.321 + 204.937i) q^{58} +(29.2376 + 50.6411i) q^{59} -191.132 q^{60} +(345.987 - 599.266i) q^{61} +(317.683 + 550.242i) q^{62} -246.544 q^{63} +64.0000 q^{64} +(-203.023 - 351.646i) q^{65} +352.294 q^{66} +(-148.414 + 257.060i) q^{67} +376.001 q^{68} +(-208.283 + 360.756i) q^{69} +(218.448 - 378.363i) q^{70} +(-495.169 + 857.658i) q^{71} +(-74.1176 - 128.376i) q^{72} +799.748 q^{73} +(-258.245 + 368.676i) q^{74} -420.688 q^{75} +(73.5203 + 127.341i) q^{76} +(-402.644 + 697.400i) q^{77} +(-71.9807 + 124.674i) q^{78} +(-54.2659 + 93.9912i) q^{79} +262.685 q^{80} +(-57.3166 + 99.2753i) q^{81} +236.660 q^{82} +(28.3523 + 49.1076i) q^{83} -154.899 q^{84} +1543.28 q^{85} +(-217.430 - 376.601i) q^{86} +(172.182 - 298.228i) q^{87} -484.182 q^{88} +(-712.458 - 1234.01i) q^{89} +(-304.213 - 526.912i) q^{90} +(-164.536 - 284.985i) q^{91} +(286.257 - 495.812i) q^{92} +(462.296 - 800.720i) q^{93} +(262.977 + 455.489i) q^{94} +(301.761 + 522.665i) q^{95} +(-46.5668 - 80.6561i) q^{96} +705.808 q^{97} +(-165.963 + 287.456i) q^{98} +(560.726 + 971.206i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 5 q^{3} - 16 q^{4} - 10 q^{5} - 20 q^{6} + 3 q^{7} - 64 q^{8} + 7 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 - 5 * q^3 - 16 * q^4 - 10 * q^5 - 20 * q^6 + 3 * q^7 - 64 * q^8 + 7 * q^9	\( 8 q + 8 q^{2} - 5 q^{3} - 16 q^{4} - 10 q^{5} - 20 q^{6} + 3 q^{7} - 64 q^{8} + 7 q^{9} - 40 q^{10} + 64 q^{11} - 20 q^{12} - 61 q^{13} + 12 q^{14} - 43 q^{15} - 64 q^{16} + 12 q^{17} - 14 q^{18} - 71 q^{19} - 40 q^{20} + 67 q^{21} + 64 q^{22} - 52 q^{23} + 40 q^{24} + 48 q^{25} - 244 q^{26} + 658 q^{27} + 12 q^{28} + 322 q^{29} + 86 q^{30} - 112 q^{31} + 128 q^{32} + 280 q^{33} - 24 q^{34} - 359 q^{35} - 56 q^{36} + 557 q^{37} - 284 q^{38} - 389 q^{39} + 80 q^{40} + 92 q^{41} - 134 q^{42} + 532 q^{43} - 128 q^{44} + 330 q^{45} - 52 q^{46} + 280 q^{47} + 160 q^{48} + 87 q^{49} - 96 q^{50} - 1306 q^{51} - 244 q^{52} + 159 q^{53} + 658 q^{54} - 872 q^{55} - 24 q^{56} - 469 q^{57} + 322 q^{58} + 263 q^{59} + 344 q^{60} - 206 q^{61} - 112 q^{62} - 2328 q^{63} + 512 q^{64} - 731 q^{65} + 1120 q^{66} + 245 q^{67} - 96 q^{68} - 360 q^{69} + 718 q^{70} - 957 q^{71} - 56 q^{72} - 272 q^{73} - 178 q^{74} - 3232 q^{75} - 284 q^{76} + 744 q^{77} + 778 q^{78} + 173 q^{79} + 320 q^{80} - 528 q^{81} + 368 q^{82} + 1217 q^{83} - 536 q^{84} + 2988 q^{85} + 532 q^{86} - 2336 q^{87} - 512 q^{88} - 2136 q^{89} + 330 q^{90} + 1575 q^{91} + 104 q^{92} + 2608 q^{93} + 280 q^{94} + 891 q^{95} + 160 q^{96} + 5262 q^{97} - 174 q^{98} - 176 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 5 * q^3 - 16 * q^4 - 10 * q^5 - 20 * q^6 + 3 * q^7 - 64 * q^8 + 7 * q^9 - 40 * q^10 + 64 * q^11 - 20 * q^12 - 61 * q^13 + 12 * q^14 - 43 * q^15 - 64 * q^16 + 12 * q^17 - 14 * q^18 - 71 * q^19 - 40 * q^20 + 67 * q^21 + 64 * q^22 - 52 * q^23 + 40 * q^24 + 48 * q^25 - 244 * q^26 + 658 * q^27 + 12 * q^28 + 322 * q^29 + 86 * q^30 - 112 * q^31 + 128 * q^32 + 280 * q^33 - 24 * q^34 - 359 * q^35 - 56 * q^36 + 557 * q^37 - 284 * q^38 - 389 * q^39 + 80 * q^40 + 92 * q^41 - 134 * q^42 + 532 * q^43 - 128 * q^44 + 330 * q^45 - 52 * q^46 + 280 * q^47 + 160 * q^48 + 87 * q^49 - 96 * q^50 - 1306 * q^51 - 244 * q^52 + 159 * q^53 + 658 * q^54 - 872 * q^55 - 24 * q^56 - 469 * q^57 + 322 * q^58 + 263 * q^59 + 344 * q^60 - 206 * q^61 - 112 * q^62 - 2328 * q^63 + 512 * q^64 - 731 * q^65 + 1120 * q^66 + 245 * q^67 - 96 * q^68 - 360 * q^69 + 718 * q^70 - 957 * q^71 - 56 * q^72 - 272 * q^73 - 178 * q^74 - 3232 * q^75 - 284 * q^76 + 744 * q^77 + 778 * q^78 + 173 * q^79 + 320 * q^80 - 528 * q^81 + 368 * q^82 + 1217 * q^83 - 536 * q^84 + 2988 * q^85 + 532 * q^86 - 2336 * q^87 - 512 * q^88 - 2136 * q^89 + 330 * q^90 + 1575 * q^91 + 104 * q^92 + 2608 * q^93 + 280 * q^94 + 891 * q^95 + 160 * q^96 + 5262 * q^97 - 174 * q^98 - 176 * q^99

Introduction

L-functions

Modular forms

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