LMFDB - Embedded newform 42.4.f.a.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,4,Mod(5,42)]

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([3, 5]))

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

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

chi := DirichletCharacter("42.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	42.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.47808022024$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - x^{14} - 2 x^{13} + 9 x^{12} - 24 x^{11} + 714 x^{10} - 1940 x^{9} - 2834 x^{8} + \cdots + 43046721 $ x^16 - 2x^15 - x^14 - 2x^13 + 9x^12 - 24x^11 + 714x^10 - 1940x^9 - 2834x^8 - 17460x^7 + 57834x^6 - 17496x^5 + 59049x^4 - 118098x^3 - 531441x^2 - 9565938x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.7
Root			$0.339489 + 2.98073i$ of defining polynomial
Character	$\chi$	$=$	42.17
Dual form			42.4.f.a.5.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 - 1.00000i) q^{2} +(0.588012 - 5.16277i) q^{3} +(2.00000 - 3.46410i) q^{4} +(4.27911 + 7.41164i) q^{5} +(-4.14431 - 9.53020i) q^{6} +(-6.41772 - 17.3728i) q^{7} -8.00000i q^{8} +(-26.3085 - 6.07155i) q^{9} +O(q^{10})$	\(q+(1.73205 - 1.00000i) q^{2} +(0.588012 - 5.16277i) q^{3} +(2.00000 - 3.46410i) q^{4} +(4.27911 + 7.41164i) q^{5} +(-4.14431 - 9.53020i) q^{6} +(-6.41772 - 17.3728i) q^{7} -8.00000i q^{8} +(-26.3085 - 6.07155i) q^{9} +(14.8233 + 8.55823i) q^{10} +(53.8609 + 31.0966i) q^{11} +(-16.7084 - 12.3625i) q^{12} +61.7061i q^{13} +(-28.4886 - 23.6728i) q^{14} +(40.7808 - 17.7340i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-13.3365 + 23.0995i) q^{17} +(-51.6392 + 15.7922i) q^{18} +(-58.6213 + 33.8450i) q^{19} +34.2329 q^{20} +(-93.4654 + 22.9178i) q^{21} +124.386 q^{22} +(45.8287 - 26.4592i) q^{23} +(-41.3022 - 4.70410i) q^{24} +(25.8784 - 44.8227i) q^{25} +(61.7061 + 106.878i) q^{26} +(-46.8158 + 132.255i) q^{27} +(-73.0165 - 12.5139i) q^{28} +55.1116i q^{29} +(52.9005 - 71.4969i) q^{30} +(-134.080 - 77.4108i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(192.216 - 259.786i) q^{33} +53.3461i q^{34} +(101.299 - 121.906i) q^{35} +(-73.6494 + 78.9922i) q^{36} +(-157.940 - 273.560i) q^{37} +(-67.6901 + 117.243i) q^{38} +(318.575 + 36.2840i) q^{39} +(59.2931 - 34.2329i) q^{40} -210.211 q^{41} +(-138.969 + 133.160i) q^{42} +351.939 q^{43} +(215.443 - 124.386i) q^{44} +(-67.5768 - 220.970i) q^{45} +(52.9184 - 91.6574i) q^{46} +(-115.819 - 200.605i) q^{47} +(-76.2416 + 33.1545i) q^{48} +(-260.626 + 222.987i) q^{49} -103.514i q^{50} +(111.416 + 82.4363i) q^{51} +(213.756 + 123.412i) q^{52} +(-232.890 - 134.459i) q^{53} +(51.1673 + 275.887i) q^{54} +532.263i q^{55} +(-138.982 + 51.3417i) q^{56} +(140.264 + 322.550i) q^{57} +(55.1116 + 95.4561i) q^{58} +(-9.14155 + 15.8336i) q^{59} +(20.1294 - 176.737i) q^{60} +(-72.3320 + 41.7609i) q^{61} -309.643 q^{62} +(63.3607 + 496.017i) q^{63} -64.0000 q^{64} +(-457.344 + 264.047i) q^{65} +(73.1407 - 642.179i) q^{66} +(-64.7354 + 112.125i) q^{67} +(53.3461 + 92.3982i) q^{68} +(-109.655 - 252.162i) q^{69} +(53.5484 - 312.446i) q^{70} +804.537i q^{71} +(-48.5724 + 210.468i) q^{72} +(370.377 + 213.837i) q^{73} +(-547.120 - 315.880i) q^{74} +(-216.192 - 159.961i) q^{75} +270.760i q^{76} +(194.570 - 1135.28i) q^{77} +(588.072 - 255.729i) q^{78} +(-609.284 - 1055.31i) q^{79} +(68.4658 - 118.586i) q^{80} +(655.273 + 319.467i) q^{81} +(-364.097 + 210.211i) q^{82} +1371.18 q^{83} +(-107.541 + 369.609i) q^{84} -228.274 q^{85} +(609.577 - 351.939i) q^{86} +(284.529 + 32.4063i) q^{87} +(248.773 - 430.887i) q^{88} +(386.840 + 670.026i) q^{89} +(-338.016 - 315.154i) q^{90} +(1072.01 - 396.012i) q^{91} -211.674i q^{92} +(-478.495 + 646.704i) q^{93} +(-401.209 - 231.638i) q^{94} +(-501.694 - 289.653i) q^{95} +(-98.8999 + 133.667i) q^{96} -848.768i q^{97} +(-228.430 + 646.851i) q^{98} +(-1228.19 - 1145.12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} + 80 q^{7} + 18 q^{9}+O(q^{10}) $ 16 * q + 32 * q^4 + 80 * q^7 + 18 * q^9	$ 16 q + 32 q^{4} + 80 q^{7} + 18 q^{9} - 36 q^{10} - 128 q^{16} - 48 q^{18} - 342 q^{19} - 450 q^{21} + 24 q^{22} - 48 q^{24} - 194 q^{25} + 88 q^{28} + 360 q^{30} + 804 q^{31} + 1332 q^{33} + 144 q^{36} - 962 q^{37} + 594 q^{39} - 144 q^{40} - 180 q^{42} + 1732 q^{43} - 2394 q^{45} + 168 q^{46} + 820 q^{49} + 1638 q^{51} + 744 q^{52} + 180 q^{54} - 2664 q^{57} - 780 q^{58} - 4620 q^{61} - 2016 q^{63} - 1024 q^{64} - 2016 q^{66} - 706 q^{67} - 60 q^{70} + 192 q^{72} + 3294 q^{73} + 6174 q^{75} + 2832 q^{78} - 2656 q^{79} + 126 q^{81} + 432 q^{82} - 432 q^{84} + 5232 q^{85} + 1026 q^{87} + 48 q^{88} + 4098 q^{91} + 2016 q^{93} + 3888 q^{94} - 192 q^{96} - 4284 q^{99}+O(q^{100}) $ 16 * q + 32 * q^4 + 80 * q^7 + 18 * q^9 - 36 * q^10 - 128 * q^16 - 48 * q^18 - 342 * q^19 - 450 * q^21 + 24 * q^22 - 48 * q^24 - 194 * q^25 + 88 * q^28 + 360 * q^30 + 804 * q^31 + 1332 * q^33 + 144 * q^36 - 962 * q^37 + 594 * q^39 - 144 * q^40 - 180 * q^42 + 1732 * q^43 - 2394 * q^45 + 168 * q^46 + 820 * q^49 + 1638 * q^51 + 744 * q^52 + 180 * q^54 - 2664 * q^57 - 780 * q^58 - 4620 * q^61 - 2016 * q^63 - 1024 * q^64 - 2016 * q^66 - 706 * q^67 - 60 * q^70 + 192 * q^72 + 3294 * q^73 + 6174 * q^75 + 2832 * q^78 - 2656 * q^79 + 126 * q^81 + 432 * q^82 - 432 * q^84 + 5232 * q^85 + 1026 * q^87 + 48 * q^88 + 4098 * q^91 + 2016 * q^93 + 3888 * q^94 - 192 * q^96 - 4284 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	0.588012	−	5.16277i	0.113163	−	0.993576i
$3$	0.588012	−	5.16277i	0.113163	−	0.993576i
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	4.27911	+	7.41164i	0.382736	+	0.662917i	0.991452	−	0.130470i	$-0.0416487\pi$
$5$	4.27911	+	7.41164i	0.382736	+	0.662917i	−0.608717	+	0.793388i	$0.708315\pi$
$6$	−4.14431	−	9.53020i	−0.281984	−	0.648448i
$7$	−6.41772	−	17.3728i	−0.346524	−	0.938041i
$7$	−6.41772	−	17.3728i	−0.346524	−	0.938041i
$8$		−	8.00000i		−	0.353553i
$9$	−26.3085	−	6.07155i	−0.974388	−	0.224872i
$10$	14.8233	+	8.55823i	0.468753	+	0.270635i
$11$	53.8609	+	31.0966i	1.47633	+	0.852361i	0.999643	−	0.0267105i	$-0.00850323\pi$
$11$	53.8609	+	31.0966i	1.47633	+	0.852361i	0.476690	+	0.879072i	$0.341837\pi$
$12$	−16.7084	−	12.3625i	−0.401940	−	0.297395i
$13$			61.7061i			1.31648i	0.752810	+	0.658238i	$0.228698\pi$
$13$			61.7061i			1.31648i	−0.752810	+	0.658238i	$0.771302\pi$
$14$	−28.4886	−	23.6728i	−0.543849	−	0.451916i
$15$	40.7808	−	17.7340i	0.701971	−	0.305259i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−13.3365	+	23.0995i	−0.190270	+	0.329557i	−0.945340	−	0.326088i	$-0.894270\pi$
$17$	−13.3365	+	23.0995i	−0.190270	+	0.329557i	0.755070	+	0.655644i	$0.227603\pi$
$18$	−51.6392	+	15.7922i	−0.676193	+	0.206793i
$19$	−58.6213	+	33.8450i	−0.707824	+	0.408662i	−0.810255	−	0.586078i	$-0.800671\pi$
$19$	−58.6213	+	33.8450i	−0.707824	+	0.408662i	0.102431	+	0.994740i	$0.467338\pi$
$20$	34.2329			0.382736
$21$	−93.4654	+	22.9178i	−0.971229	+	0.238147i
$22$	124.386			1.20542
$23$	45.8287	−	26.4592i	0.415476	−	0.239875i	−0.277664	−	0.960678i	$-0.589560\pi$
$23$	45.8287	−	26.4592i	0.415476	−	0.239875i	0.693140	+	0.720803i	$0.256227\pi$
$24$	−41.3022	−	4.70410i	−0.351282	−	0.0400092i
$25$	25.8784	−	44.8227i	0.207027	−	0.358581i
$26$	61.7061	+	106.878i	0.465445	+	0.806174i
$27$	−46.8158	+	132.255i	−0.333693	+	0.942682i
$28$	−73.0165	−	12.5139i	−0.492815	−	0.0844609i
$29$			55.1116i			0.352895i	0.984310	+	0.176448i	$0.0564606\pi$
$29$			55.1116i			0.352895i	−0.984310	+	0.176448i	$0.943539\pi$
$30$	52.9005	−	71.4969i	0.321942	−	0.435116i
$31$	−134.080	−	77.4108i	−0.776819	−	0.448497i	0.0584827	−	0.998288i	$-0.481374\pi$
$31$	−134.080	−	77.4108i	−0.776819	−	0.448497i	−0.835302	+	0.549792i	$0.814707\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	192.216	−	259.786i	1.01395	−	1.37039i
$34$			53.3461i			0.269082i
$35$	101.299	−	121.906i	0.489217	−	0.588739i
$36$	−73.6494	+	78.9922i	−0.340970	+	0.365704i
$37$	−157.940	−	273.560i	−0.701761	−	1.21549i	−0.967848	−	0.251536i	$-0.919064\pi$
$37$	−157.940	−	273.560i	−0.701761	−	1.21549i	0.266087	−	0.963949i	$-0.414269\pi$
$38$	−67.6901	+	117.243i	−0.288968	+	0.500507i
$39$	318.575	+	36.2840i	1.30802	+	0.148976i
$40$	59.2931	−	34.2329i	0.234377	−	0.135317i
$41$	−210.211			−0.800719			−0.400360	−	0.916358i	$-0.631115\pi$
$41$	−210.211			−0.800719			−0.400360	+	0.916358i	$0.631115\pi$
$42$	−138.969	+	133.160i	−0.510556	+	0.489216i
$43$	351.939			1.24815			0.624073	−	0.781366i	$-0.285477\pi$
$43$	351.939			1.24815			0.624073	+	0.781366i	$0.285477\pi$
$44$	215.443	−	124.386i	0.738166	−	0.426181i
$45$	−67.5768	−	220.970i	−0.223861	−	0.732006i
$46$	52.9184	−	91.6574i	0.169617	−	0.293786i
$47$	−115.819	−	200.605i	−0.359446	−	0.622579i	0.628422	−	0.777872i	$-0.283701\pi$
$47$	−115.819	−	200.605i	−0.359446	−	0.622579i	−0.987868	+	0.155294i	$0.950368\pi$
$48$	−76.2416	+	33.1545i	−0.229261	+	0.0996965i
$49$	−260.626	+	222.987i	−0.759842	+	0.650108i
$50$		−	103.514i		−	0.292780i
$51$	111.416	+	82.4363i	0.305908	+	0.226341i
$52$	213.756	+	123.412i	0.570051	+	0.329119i
$53$	−232.890	−	134.459i	−0.603583	−	0.348479i	0.166867	−	0.985979i	$-0.446635\pi$
$53$	−232.890	−	134.459i	−0.603583	−	0.348479i	−0.770450	+	0.637500i	$0.779968\pi$
$54$	51.1673	+	275.887i	0.128944	+	0.695251i
$55$			532.263i			1.30492i
$56$	−138.982	+	51.3417i	−0.331648	+	0.122515i
$57$	140.264	+	322.550i	0.325938	+	0.749522i
$58$	55.1116	+	95.4561i	0.124767	+	0.216103i
$59$	−9.14155	+	15.8336i	−0.0201717	+	0.0349384i	−0.875935	−	0.482429i	$-0.839755\pi$
$59$	−9.14155	+	15.8336i	−0.0201717	+	0.0349384i	0.855763	+	0.517367i	$0.173088\pi$
$60$	20.1294	−	176.737i	0.0433115	−	0.380277i
$61$	−72.3320	+	41.7609i	−0.151822	+	0.0876547i	−0.573987	−	0.818865i	$-0.694604\pi$
$61$	−72.3320	+	41.7609i	−0.151822	+	0.0876547i	0.422164	+	0.906519i	$0.361271\pi$
$62$	−309.643			−0.634270
$63$	63.3607	+	496.017i	0.126710	+	0.991940i
$64$	−64.0000			−0.125000
$65$	−457.344	+	264.047i	−0.872715	+	0.503862i
$66$	73.1407	−	642.179i	0.136409	−	1.19768i
$67$	−64.7354	+	112.125i	−0.118040	+	0.204451i	−0.918991	−	0.394279i	$-0.870994\pi$
$67$	−64.7354	+	112.125i	−0.118040	+	0.204451i	0.800951	+	0.598730i	$0.204328\pi$
$68$	53.3461	+	92.3982i	0.0951348	+	0.164778i
$69$	−109.655	−	252.162i	−0.191318	−	0.439952i
$70$	53.5484	−	312.446i	0.0914323	−	0.533491i
$71$			804.537i			1.34480i	0.740186	+	0.672402i	$0.234737\pi$
$71$			804.537i			1.34480i	−0.740186	+	0.672402i	$0.765263\pi$
$72$	−48.5724	+	210.468i	−0.0795044	+	0.344498i
$73$	370.377	+	213.837i	0.593826	+	0.342846i	0.766609	−	0.642114i	$-0.221943\pi$
$73$	370.377	+	213.837i	0.593826	+	0.342846i	−0.172783	+	0.984960i	$0.555276\pi$
$74$	−547.120	−	315.880i	−0.859478	−	0.496220i
$75$	−216.192	−	159.961i	−0.332850	−	0.246275i
$76$			270.760i			0.408662i
$77$	194.570	−	1135.28i	0.287965	−	1.68022i
$78$	588.072	−	255.729i	0.853667	−	0.371226i
$79$	−609.284	−	1055.31i	−0.867718	−	1.50293i	−0.864322	−	0.502938i	$-0.832252\pi$
$79$	−609.284	−	1055.31i	−0.867718	−	1.50293i	−0.00339594	−	0.999994i	$-0.501081\pi$
$80$	68.4658	−	118.586i	0.0956839	−	0.165729i
$81$	655.273	+	319.467i	0.898865	+	0.438226i
$82$	−364.097	+	210.211i	−0.490339	+	0.283097i
$83$	1371.18			1.81333			0.906663	−	0.421855i	$-0.138621\pi$
$83$	1371.18			1.81333			0.906663	+	0.421855i	$0.138621\pi$
$84$	−107.541	+	369.609i	−0.139687	+	0.480091i
$85$	−228.274			−0.291292
$86$	609.577	−	351.939i	0.764330	−	0.441286i
$87$	284.529	+	32.4063i	0.350628	+	0.0399347i
$88$	248.773	−	430.887i	0.301355	−	0.521962i
$89$	386.840	+	670.026i	0.460729	+	0.798007i	0.998997	−	0.0447669i	$-0.0142545\pi$
$89$	386.840	+	670.026i	0.460729	+	0.798007i	−0.538268	+	0.842774i	$0.680921\pi$
$90$	−338.016	−	315.154i	−0.395890	−	0.369113i
$91$	1072.01	−	396.012i	1.23491	−	0.456191i
$92$		−	211.674i		−	0.239875i
$93$	−478.495	+	646.704i	−0.533523	+	0.721076i
$94$	−401.209	−	231.638i	−0.440230	−	0.254167i
$95$	−501.694	−	289.653i	−0.541819	−	0.312819i
$96$	−98.8999	+	133.667i	−0.105145	+	0.142107i
$97$		−	848.768i		−	0.888447i	−0.895916	−	0.444223i	$-0.853480\pi$
$97$		−	848.768i		−	0.888447i	0.895916	−	0.444223i	$-0.146520\pi$
$98$	−228.430	+	646.851i	−0.235459	+	0.666753i
$99$	−1228.19	−	1145.12i	−1.24685	−	1.16252i
$100$	−103.514	−	179.291i	−0.103514	−	0.179291i
$101$	−512.647	+	887.931i	−0.505053	+	0.874777i	0.494930	+	0.868933i	$0.335194\pi$
$101$	−512.647	+	887.931i	−0.505053	+	0.874777i	−0.999983	+	0.00584430i	$0.998140\pi$
$102$	275.414	+	31.3682i	0.267353	+	0.0304501i
$103$	278.306	−	160.680i	0.266236	−	0.153711i	−0.360940	−	0.932589i	$-0.617544\pi$
$103$	278.306	−	160.680i	0.266236	−	0.153711i	0.627176	+	0.778878i	$0.284211\pi$
$104$	493.649			0.465445
$105$	−569.808	−	594.664i	−0.529595	−	0.552698i
$106$	−537.837			−0.492824
$107$	−117.848	+	68.0393i	−0.106474	+	0.0614730i	−0.552292	−	0.833651i	$-0.686246\pi$
$107$	−117.848	+	68.0393i	−0.106474	+	0.0614730i	0.445817	+	0.895124i	$0.352913\pi$
$108$	364.512	+	426.684i	0.324770	+	0.380164i
$109$	−703.079	+	1217.77i	−0.617823	+	1.07010i	0.372059	+	0.928209i	$0.378652\pi$
$109$	−703.079	+	1217.77i	−0.617823	+	1.07010i	−0.989882	+	0.141892i	$0.954681\pi$
$110$	532.263	+	921.907i	0.461357	+	0.799094i
$111$	−1505.20	+	654.551i	−1.28709	+	0.559705i
$112$	−189.382	+	227.909i	−0.159776	+	0.192280i
$113$		−	467.285i		−	0.389013i	−0.980901	−	0.194506i	$-0.937690\pi$
$113$		−	467.285i		−	0.389013i	0.980901	−	0.194506i	$-0.0623105\pi$
$114$	565.495	+	418.409i	0.464591	+	0.343750i
$115$	392.212	+	226.444i	0.318035	+	0.183617i
$116$	190.912	+	110.223i	0.152808	+	0.0882238i
$117$	374.652	−	1623.39i	0.296039	−	1.28276i
$118$			36.5662i			0.0285270i
$119$	486.893	+	83.4460i	0.375071	+	0.0642814i
$120$	−141.872	−	326.246i	−0.107925	−	0.248184i
$121$	1268.50	+	2197.10i	0.953039	+	1.65071i
$122$	−83.5218	+	144.664i	−0.0619812	+	0.107355i
$123$	−123.607	+	1085.27i	−0.0906119	+	0.795576i
$124$	−536.318	+	309.643i	−0.388410	+	0.224248i
$125$	1512.72			1.08242
$126$	605.761	+	795.765i	0.428297	+	0.562638i
$127$	259.166			0.181081			0.0905404	−	0.995893i	$-0.471141\pi$
$127$	259.166			0.181081			0.0905404	+	0.995893i	$0.471141\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	206.945	−	1816.98i	0.141244	−	1.24013i
$130$	−528.095	+	914.687i	−0.356284	+	0.617103i
$131$	−1323.92	−	2293.10i	−0.882991	−	1.52938i	−0.848000	−	0.529997i	$-0.822193\pi$
$131$	−1323.92	−	2293.10i	−0.882991	−	1.52938i	−0.0349910	−	0.999388i	$-0.511140\pi$
$132$	−515.495	−	1185.43i	−0.339910	−	0.781653i
$133$	964.197	+	801.206i	0.628620	+	0.522356i
$134$			258.941i			0.166934i
$135$	−1180.55	+	218.951i	−0.752636	+	0.139587i
$136$	184.796	+	106.692i	0.116516	+	0.0672705i
$137$	405.314	+	234.008i	0.252761	+	0.145932i	0.621028	−	0.783788i	$-0.286715\pi$
$137$	405.314	+	234.008i	0.252761	+	0.145932i	−0.368267	+	0.929720i	$0.620049\pi$
$138$	−442.090	−	327.102i	−0.272704	−	0.201773i
$139$		−	2923.27i		−	1.78380i	−0.452229	−	0.891902i	$-0.649371\pi$
$139$		−	2923.27i		−	1.78380i	0.452229	−	0.891902i	$-0.350629\pi$
$140$	−219.697	−	594.720i	−0.132627	−	0.359022i
$141$	−1103.78	+	479.990i	−0.659256	+	0.286684i
$142$	804.537	+	1393.50i	0.475460	+	0.823520i
$143$	−1918.85	+	3323.54i	−1.12211	+	1.94356i
$144$	126.338	+	413.113i	0.0731123	+	0.239070i
$145$	−408.467	+	235.829i	−0.233940	+	0.135066i
$146$	855.348			0.484857
$147$	997.980	+	1476.67i	0.559946	+	0.828529i
$148$	−1263.52			−0.701761
$149$	1570.24	−	906.580i	0.863351	−	0.498456i	−0.00178220	−	0.999998i	$-0.500567\pi$
$149$	1570.24	−	906.580i	0.863351	−	0.498456i	0.865133	+	0.501543i	$0.167234\pi$
$150$	−534.417	−	60.8672i	−0.290900	−	0.0331319i
$151$	827.154	−	1432.67i	0.445780	−	0.772114i	−0.552326	−	0.833628i	$-0.686260\pi$
$151$	827.154	−	1432.67i	0.445780	−	0.772114i	0.998106	+	0.0615140i	$0.0195929\pi$
$152$	270.760	+	468.970i	0.144484	+	0.250253i
$153$	491.114	−	526.740i	0.259505	−	0.278330i
$154$	−798.276	−	2160.93i	−0.417707	−	1.13073i
$155$		−	1325.00i		−	0.686622i
$156$	762.841	−	1031.01i	0.391514	−	0.529145i
$157$	−1200.29	−	692.988i	−0.610151	−	0.352271i	0.162874	−	0.986647i	$-0.447924\pi$
$157$	−1200.29	−	692.988i	−0.610151	−	0.352271i	−0.773024	+	0.634376i	$0.781257\pi$
$158$	−2110.62	−	1218.57i	−1.06273	−	0.613570i
$159$	−831.125	+	1123.30i	−0.414544	+	0.560271i
$160$		−	273.863i		−	0.135317i
$161$	−753.785	−	626.363i	−0.368985	−	0.306611i
$162$	1454.43	−	101.940i	0.705376	−	0.0494393i
$163$	576.540	+	998.597i	0.277044	+	0.479854i	0.970649	−	0.240502i	$-0.0773120\pi$
$163$	576.540	+	998.597i	0.277044	+	0.479854i	−0.693605	+	0.720356i	$0.743979\pi$
$164$	−420.423	+	728.194i	−0.200180	+	0.346722i
$165$	2747.96	+	312.977i	1.29653	+	0.147668i
$166$	2374.95	−	1371.18i	1.11043	−	0.641108i
$167$	303.672			0.140712			0.0703559	−	0.997522i	$-0.477586\pi$
$167$	303.672			0.140712			0.0703559	+	0.997522i	$0.477586\pi$
$168$	183.343	+	747.723i	0.0841975	+	0.343381i
$169$	−1610.64			−0.733110
$170$	−395.382	+	228.274i	−0.178379	+	0.102987i
$171$	1747.73	−	534.489i	0.781592	−	0.239026i
$172$	703.879	−	1219.15i	0.312036	−	0.540463i
$173$	1308.97	+	2267.21i	0.575256	+	0.996373i	0.996014	+	0.0891996i	$0.0284309\pi$
$173$	1308.97	+	2267.21i	0.575256	+	0.996373i	−0.420758	+	0.907173i	$0.638236\pi$
$174$	525.224	−	228.399i	0.228834	−	0.0995110i
$175$	−944.774	−	161.920i	−0.408104	−	0.0699428i
$176$		−	995.091i		−	0.426181i
$177$	76.3701	+	56.5061i	0.0324312	+	0.0239958i
$178$	1340.05	+	773.679i	0.564276	+	0.325785i
$179$	−2395.77	−	1383.20i	−1.00038	−	0.577569i	−0.0920191	−	0.995757i	$-0.529332\pi$
$179$	−2395.77	−	1383.20i	−1.00038	−	0.577569i	−0.908361	+	0.418188i	$0.862665\pi$
$180$	−900.616	−	207.847i	−0.372933	−	0.0860666i
$181$			539.608i			0.221595i	0.993843	+	0.110798i	$0.0353405\pi$
$181$			539.608i			0.221595i	−0.993843	+	0.110798i	$0.964659\pi$
$182$	1460.76	−	1757.92i	0.594936	−	0.715965i
$183$	173.070	+	397.990i	0.0699109	+	0.160766i
$184$	−211.674	−	366.630i	−0.0848086	−	0.146893i
$185$	1351.68	−	2341.19i	0.537178	−	0.930419i
$186$	−182.074	+	1598.62i	−0.0717759	+	0.630196i
$187$	−1436.63	+	829.441i	−0.561802	+	0.324357i
$188$	−926.553			−0.359446
$189$	2598.08	−	35.4533i	0.999907	−	0.0136447i
$190$	−1158.61			−0.442393
$191$	−2764.63	+	1596.16i	−1.04734	+	0.604680i	−0.921903	−	0.387422i	$-0.873366\pi$
$191$	−2764.63	+	1596.16i	−1.04734	+	0.604680i	−0.125434	+	0.992102i	$0.540032\pi$
$192$	−37.6328	+	330.418i	−0.0141454	+	0.124197i
$193$	−718.685	+	1244.80i	−0.268042	+	0.464262i	−0.968356	−	0.249573i	$-0.919710\pi$
$193$	−718.685	+	1244.80i	−0.268042	+	0.464262i	0.700314	+	0.713835i	$0.253043\pi$
$194$	−848.768	−	1470.11i	−0.314113	−	0.544060i
$195$	1094.29	+	2516.42i	0.401867	+	0.924128i
$196$	251.198	+	1348.81i	0.0915443	+	0.491548i
$197$			2346.26i			0.848548i	0.905534	+	0.424274i	$0.139471\pi$
$197$			2346.26i			0.848548i	−0.905534	+	0.424274i	$0.860529\pi$
$198$	−3272.42	−	755.218i	−1.17455	−	0.271066i
$199$	−1586.15	−	915.766i	−0.565022	−	0.326216i	0.190137	−	0.981758i	$-0.439107\pi$
$199$	−1586.15	−	915.766i	−0.565022	−	0.326216i	−0.755159	+	0.655542i	$0.772440\pi$
$200$	−358.581	−	207.027i	−0.126778	−	0.0731951i
$201$	540.810	+	400.145i	0.189780	+	0.140418i
$202$			2050.59i			0.714252i
$203$	957.440	−	353.690i	0.331030	−	0.122287i
$204$	508.399	−	221.083i	0.174486	−	0.0758769i
$205$	−899.518	−	1558.01i	−0.306464	−	0.530811i
$206$	321.360	−	556.612i	0.108690	−	0.188257i
$207$	−1366.33	+	417.850i	−0.458776	+	0.140302i
$208$	855.025	−	493.649i	0.285026	−	0.164560i
$209$	−4209.86			−1.39331
$210$	−1581.60	−	460.180i	−0.519718	−	0.151217i
$211$	4291.48			1.40018			0.700090	−	0.714055i	$-0.253143\pi$
$211$	4291.48			1.40018			0.700090	+	0.714055i	$0.253143\pi$
$212$	−931.560	+	537.837i	−0.301792	+	0.174239i
$213$	4153.65	+	473.078i	1.33616	+	0.152182i
$214$	−136.079	+	235.695i	−0.0434680	+	0.0752887i
$215$	1505.99	+	2608.45i	0.477709	+	0.827417i
$216$	1058.04	+	374.526i	0.333288	+	0.117978i
$217$	−484.356	+	2826.13i	−0.151522	+	0.884103i
$218$			2812.31i			0.873734i
$219$	1321.78	−	1786.43i	0.407842	−	0.551214i
$220$	1843.81	+	1064.53i	0.565045	+	0.326229i
$221$	−1425.38	−	822.945i	−0.433853	−	0.250485i
$222$	−1952.53	+	2638.91i	−0.590293	+	0.797803i
$223$			1170.88i			0.351604i	0.984426	+	0.175802i	$0.0562519\pi$
$223$			1170.88i			0.351604i	−0.984426	+	0.175802i	$0.943748\pi$
$224$	−100.111	+	584.132i	−0.0298615	+	0.174236i
$225$	−952.964	+	1022.09i	−0.282360	+	0.302843i
$226$	−467.285	−	809.361i	−0.137537	−	0.238221i
$227$	1063.49	−	1842.02i	0.310954	−	0.538588i	−0.667615	−	0.744506i	$-0.732685\pi$
$227$	1063.49	−	1842.02i	0.310954	−	0.538588i	0.978569	+	0.205919i	$0.0660182\pi$
$228$	1397.87	+	159.210i	0.406037	+	0.0462455i
$229$	−1124.19	+	649.049i	−0.324403	+	0.187294i	−0.653354	−	0.757053i	$-0.726638\pi$
$229$	−1124.19	+	649.049i	−0.324403	+	0.187294i	0.328950	+	0.944347i	$0.393305\pi$
$230$	905.776			0.259674
$231$	−5746.79	−	1672.08i	−1.63684	−	0.476254i
$232$	440.893			0.124767
$233$	3641.17	−	2102.23i	1.02378	−	0.591081i	0.108585	−	0.994087i	$-0.465368\pi$
$233$	3641.17	−	2102.23i	1.02378	−	0.591081i	0.915197	+	0.403007i	$0.132035\pi$
$234$	−974.478	−	3186.45i	−0.272238	−	0.890192i
$235$	991.207	−	1716.82i	0.275145	−	0.476566i
$236$	36.5662	+	63.3345i	0.0100858	+	0.0174692i
$237$	−5806.59	+	2525.06i	−1.59147	+	0.692068i
$238$	926.769	−	342.360i	0.252410	−	0.0932433i
$239$		−	3816.77i		−	1.03300i	−0.856288	−	0.516498i	$-0.827235\pi$
$239$		−	3816.77i		−	1.03300i	0.856288	−	0.516498i	$-0.172765\pi$
$240$	−571.975	−	423.204i	−0.153837	−	0.113824i
$241$	−1417.67	−	818.491i	−0.378921	−	0.218770i	0.298428	−	0.954432i	$-0.403538\pi$
$241$	−1417.67	−	818.491i	−0.378921	−	0.218770i	−0.677349	+	0.735662i	$0.736871\pi$
$242$	4394.20	+	2536.99i	1.16723	+	0.673900i
$243$	2034.64	−	3195.17i	0.537129	−	0.843500i
$244$			334.087i			0.0876547i
$245$	−2767.95	−	977.479i	−0.721786	−	0.254893i
$246$	871.180	+	2003.36i	0.225790	+	0.519225i
$247$	−2088.44	−	3617.29i	−0.537994	−	0.931833i
$248$	−619.287	+	1072.64i	−0.158568	+	0.274647i
$249$	806.268	−	7079.07i	0.205202	−	1.80168i
$250$	2620.12	−	1512.72i	0.662843	−	0.382692i
$251$	5269.47			1.32512			0.662562	−	0.749007i	$-0.269469\pi$
$251$	5269.47			1.32512			0.662562	+	0.749007i	$0.269469\pi$
$252$	1844.97	+	772.545i	0.461200	+	0.193118i
$253$	3291.16			0.817841
$254$	448.888	−	259.166i	0.110889	−	0.0640217i
$255$	−134.228	+	1178.53i	−0.0329635	+	0.289421i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	570.595	+	988.300i	0.138493	+	0.239877i	0.926926	−	0.375243i	$-0.122441\pi$
$257$	570.595	+	988.300i	0.138493	+	0.239877i	−0.788433	+	0.615120i	$0.789107\pi$
$258$	−1458.54	−	3354.05i	−0.351957	−	0.809357i
$259$	−3738.88	+	4499.48i	−0.896998	+	1.07948i
$260$			2112.38i			0.503862i
$261$	334.613	−	1449.90i	0.0793564	−	0.343857i
$262$	−4586.21	−	2647.85i	−1.08144	−	0.624369i
$263$	1978.91	+	1142.53i	0.463974	+	0.267875i	0.713714	−	0.700438i	$-0.247012\pi$
$263$	1978.91	+	1142.53i	0.463974	+	0.267875i	−0.249740	+	0.968313i	$0.580345\pi$
$264$	−2078.29	−	1537.72i	−0.484507	−	0.358486i
$265$		−	2301.46i		−	0.533501i
$266$	2471.24	+	423.534i	0.569630	+	0.0976260i
$267$	3686.66	−	1603.18i	0.845018	−	0.367465i
$268$	258.941	+	448.500i	0.0590200	+	0.102226i
$269$	−937.191	+	1623.26i	−0.212422	+	0.367926i	−0.952472	−	0.304626i	$-0.901468\pi$
$269$	−937.191	+	1623.26i	−0.212422	+	0.367926i	0.740050	+	0.672552i	$0.234802\pi$
$270$	−1825.83	+	1559.79i	−0.411542	+	0.351577i
$271$	2841.71	−	1640.66i	0.636980	−	0.367760i	−0.146471	−	0.989215i	$-0.546791\pi$
$271$	2841.71	−	1640.66i	0.636980	−	0.367760i	0.783450	+	0.621455i	$0.213458\pi$
$272$	426.769			0.0951348
$273$	−1414.17	−	5767.38i	−0.313514	−	1.27860i
$274$	936.032			0.206379
$275$	2787.66	−	1609.46i	0.611282	−	0.352924i
$276$	−1092.82	−	124.467i	−0.238334	−	0.0271450i
$277$	265.374	−	459.642i	0.0575625	−	0.0997011i	−0.835808	−	0.549022i	$-0.815000\pi$
$277$	265.374	−	459.642i	0.0575625	−	0.0997011i	0.893371	+	0.449320i	$0.148334\pi$
$278$	−2923.27	−	5063.26i	−0.630670	−	1.09235i
$279$	3057.42	+	2850.63i	0.656069	+	0.611695i
$280$	−975.247	−	810.389i	−0.208150	−	0.172964i
$281$			5216.62i			1.10747i	0.832695	+	0.553733i	$0.186797\pi$
$281$			5216.62i			1.10747i	−0.832695	+	0.553733i	$0.813203\pi$
$282$	−1431.81	+	1935.15i	−0.302352	+	0.408639i
$283$	−907.832	−	524.137i	−0.190689	−	0.110094i	0.401616	−	0.915808i	$-0.368449\pi$
$283$	−907.832	−	524.137i	−0.190689	−	0.110094i	−0.592305	+	0.805714i	$0.701782\pi$
$284$	2787.00	+	1609.07i	0.582317	+	0.336201i
$285$	−1790.42	+	2419.82i	−0.372124	+	0.502939i
$286$			7675.40i			1.58691i
$287$	1349.08	+	3651.95i	0.277469	+	0.751108i
$288$	631.937	+	589.195i	0.129296	+	0.120551i
$289$	2100.77	+	3638.65i	0.427595	+	0.740616i
$290$	−471.657	+	816.935i	−0.0955058	+	0.165421i
$291$	−4382.00	−	499.086i	−0.882740	−	0.100539i
$292$	1481.51	−	855.348i	0.296913	−	0.171423i
$293$	−6408.45			−1.27777			−0.638884	−	0.769303i	$-0.720603\pi$
$293$	−6408.45			−1.27777			−0.638884	+	0.769303i	$0.720603\pi$
$294$	3205.22	+	1559.69i	0.635825	+	0.309398i
$295$	−156.471			−0.0308817
$296$	−2188.48	+	1263.52i	−0.429739	+	0.248110i
$297$	−6634.20	+	5667.54i	−1.29615	+	1.10729i
$298$	1813.16	−	3140.48i	0.352461	−	0.610481i
$299$	1632.69	+	2827.91i	0.315790	+	0.546964i
$300$	−986.504	+	428.992i	−0.189853	+	0.0825595i
$301$	−2258.65	−	6114.16i	−0.432512	−	1.17081i
$302$		−	3308.62i		−	0.630429i
$303$	4282.75	+	3168.80i	0.812005	+	0.600801i
$304$	937.941	+	541.520i	0.176956	+	0.102166i
$305$	−619.034	−	357.399i	−0.116216	−	0.0670971i
$306$	323.894	−	1403.46i	0.0605090	−	0.262190i
$307$			3717.93i			0.691184i	0.938385	+	0.345592i	$0.112322\pi$
$307$			3717.93i			0.691184i	−0.938385	+	0.345592i	$0.887678\pi$
$308$	−3543.59	−	2944.57i	−0.655567	−	0.544749i
$309$	−665.907	−	1531.31i	−0.122596	−	0.281920i
$310$	−1325.00	−	2294.97i	−0.242758	−	0.420469i
$311$	−202.816	+	351.287i	−0.0369795	+	0.0640503i	−0.883923	−	0.467633i	$-0.845107\pi$
$311$	−202.816	+	351.287i	−0.0369795	+	0.0640503i	0.846943	+	0.531683i	$0.178440\pi$
$312$	290.272	−	2548.60i	0.0526711	−	0.462455i
$313$	−2640.01	+	1524.21i	−0.476748	+	0.275251i	−0.719060	−	0.694948i	$-0.755427\pi$
$313$	−2640.01	+	1524.21i	−0.476748	+	0.275251i	0.242312	+	0.970198i	$0.422094\pi$
$314$	−2771.95			−0.498186
$315$	−3405.17	+	2592.12i	−0.609078	+	0.463649i
$316$	−4874.27			−0.867718
$317$	5714.50	−	3299.27i	1.01249	−	0.584559i	0.100568	−	0.994930i	$-0.467934\pi$
$317$	5714.50	−	3299.27i	1.01249	−	0.584559i	0.911919	+	0.410371i	$0.134601\pi$
$318$	−316.255	+	2776.73i	−0.0557694	+	0.489658i
$319$	−1713.78	+	2968.36i	−0.300794	+	0.520991i
$320$	−273.863	−	474.345i	−0.0478419	−	0.0828647i
$321$	281.976	+	648.428i	0.0490292	+	0.112747i
$322$	−1931.96	−	331.108i	−0.334360	−	0.0573041i
$323$		−	1805.50i		−	0.311024i
$324$	2417.21	−	1631.00i	0.414474	−	0.279663i
$325$	2765.83	+	1596.85i	0.472064	+	0.272546i
$326$	1997.19	+	1153.08i	0.339308	+	0.195900i
$327$	5873.64	+	4345.90i	0.993313	+	0.734950i
$328$			1681.69i			0.283097i
$329$	−2741.76	+	3299.52i	−0.459448	+	0.552914i
$330$	5072.58	−	2205.86i	0.846170	−	0.367966i
$331$	184.027	+	318.744i	0.0305591	+	0.0529298i	0.880900	−	0.473302i	$-0.156938\pi$
$331$	184.027	+	318.744i	0.0305591	+	0.0529298i	−0.850341	+	0.526231i	$0.823605\pi$
$332$	2742.35	−	4749.89i	0.453332	−	0.785193i
$333$	2494.22	+	8155.88i	0.410458	+	1.34216i
$334$	525.976	−	303.672i	0.0861681	−	0.0497492i
$335$	−1108.04			−0.180712
$336$	1065.28	+	1111.75i	0.172964	+	0.180509i
$337$	6514.00			1.05294			0.526469	−	0.850194i	$-0.323516\pi$
$337$	6514.00			1.05294			0.526469	+	0.850194i	$0.323516\pi$
$338$	−2789.72	+	1610.64i	−0.448937	+	0.259194i
$339$	−2412.48	−	274.769i	−0.386514	−	0.0440219i
$340$	−456.548	+	790.764i	−0.0728229	+	0.126133i
$341$	−4814.43	−	8338.83i	−0.764562	−	1.32426i
$342$	2492.67	−	2673.49i	0.394117	−	0.422707i
$343$	5546.52	+	3096.72i	0.873131	+	0.487485i
$344$		−	2815.51i		−	0.441286i
$345$	1399.70	−	1891.75i	0.218428	−	0.295213i
$346$	4534.41	+	2617.94i	0.704542	+	0.406767i
$347$	2098.92	+	1211.81i	0.324715	+	0.187474i	0.653492	−	0.756933i	$-0.273303\pi$
$347$	2098.92	+	1211.81i	0.324715	+	0.187474i	−0.328777	+	0.944407i	$0.606637\pi$
$348$	681.316	−	920.824i	0.104949	−	0.141843i
$349$		−	10490.9i		−	1.60907i	−0.593903	−	0.804536i	$-0.702414\pi$
$349$		−	10490.9i		−	1.60907i	0.593903	−	0.804536i	$-0.297586\pi$
$350$	−1798.32	+	664.320i	−0.274640	+	0.101455i
$351$	−8160.92	−	2888.82i	−1.24102	−	0.439298i
$352$	−995.091	−	1723.55i	−0.150678	−	0.260981i
$353$	4005.42	−	6937.60i	0.603930	−	1.04604i	−0.388290	−	0.921537i	$-0.626934\pi$
$353$	4005.42	−	6937.60i	0.603930	−	1.04604i	0.992220	−	0.124500i	$-0.0397325\pi$
$354$	188.783	+	21.5014i	0.0283438	+	0.00322821i
$355$	−5962.94	+	3442.71i	−0.891494	+	0.514704i
$356$	3094.72			0.460729
$357$	717.112	−	2464.65i	0.106313	−	0.365387i
$358$	−5532.78			−0.816807
$359$	−9906.07	+	5719.27i	−1.45633	+	0.840813i	−0.998828	−	0.0483961i	$-0.984589\pi$
$359$	−9906.07	+	5719.27i	−1.45633	+	0.840813i	−0.457502	+	0.889209i	$0.651256\pi$
$360$	−1767.76	+	540.615i	−0.258803	+	0.0791469i
$361$	−1138.53	+	1971.99i	−0.165990	+	0.287504i
$362$	539.608	+	934.628i	0.0783458	+	0.135699i
$363$	12089.0	−	5257.03i	1.74796	−	0.760118i
$364$	772.185	−	4505.56i	0.111191	−	0.648779i
$365$			3660.13i			0.524877i
$366$	697.756	+	516.268i	0.0996510	+	0.0737316i
$367$	−1259.42	−	727.126i	−0.179131	−	0.103421i	0.407753	−	0.913092i	$-0.366312\pi$
$367$	−1259.42	−	727.126i	−0.179131	−	0.103421i	−0.586884	+	0.809671i	$0.699646\pi$
$368$	−733.259	−	423.347i	−0.103869	−	0.0599688i
$369$	5530.34	+	1276.31i	0.780212	+	0.180060i
$370$		−	5406.74i		−	0.759684i
$371$	−841.305	+	4908.87i	−0.117731	+	0.686942i
$372$	1283.26	+	2950.96i	0.178854	+	0.411291i
$373$	−3990.41	−	6911.59i	−0.553929	−	0.959433i	−0.997986	−	0.0634346i	$-0.979795\pi$
$373$	−3990.41	−	6911.59i	−0.553929	−	0.959433i	0.444057	−	0.895999i	$-0.353539\pi$
$374$	−1658.88	+	2873.27i	−0.229355	+	0.397254i
$375$	889.501	−	7809.86i	0.122490	−	1.07546i
$376$	−1604.84	+	926.553i	−0.220115	+	0.127083i
$377$	−3400.72			−0.464578
$378$	4464.55	−	2659.49i	0.607491	−	0.361876i
$379$	5818.85			0.788639			0.394320	−	0.918973i	$-0.370980\pi$
$379$	5818.85			0.788639			0.394320	+	0.918973i	$0.370980\pi$
$380$	−2006.78	+	1158.61i	−0.270909	+	0.156410i
$381$	152.393	−	1338.01i	0.0204916	−	0.179918i
$382$	−3192.31	+	5529.25i	−0.427573	+	0.740579i
$383$	−618.611	−	1071.47i	−0.0825314	−	0.142949i	0.821805	−	0.569769i	$-0.192967\pi$
$383$	−618.611	−	1071.47i	−0.0825314	−	0.142949i	−0.904337	+	0.426820i	$0.859634\pi$
$384$	265.236	+	609.933i	0.0352480	+	0.0810560i
$385$	9246.88	−	3415.91i	1.22406	−	0.452185i
$386$			2874.74i			0.379068i
$387$	−9258.99	−	2136.82i	−1.21618	−	0.280673i
$388$	−2940.22	−	1697.54i	−0.384709	−	0.222112i
$389$	2602.51	+	1502.56i	0.339209	+	0.195842i	0.659922	−	0.751334i	$-0.270589\pi$
$389$	2602.51	+	1502.56i	0.339209	+	0.195842i	−0.320713	+	0.947176i	$0.603923\pi$
$390$	4411.80	+	3264.28i	0.572821	+	0.423829i
$391$			1411.50i			0.182564i
$392$	1783.90	+	2085.01i	0.229848	+	0.268645i
$393$	−12617.3	+	5486.75i	−1.61948	+	0.704249i
$394$	2346.26	+	4063.84i	0.300007	+	0.519627i
$395$	5214.39	−	9031.58i	0.664213	−	1.15045i
$396$	−6423.21	+	1964.34i	−0.815097	+	0.249272i
$397$	−5552.29	+	3205.62i	−0.701918	+	0.405253i	−0.808061	−	0.589098i	$-0.799483\pi$
$397$	−5552.29	+	3205.62i	−0.701918	+	0.405253i	0.106143	+	0.994351i	$0.466150\pi$
$398$	−3663.06			−0.461338
$399$	4703.41	−	4506.81i	0.590138	−	0.565470i
$400$	−828.108			−0.103514
$401$	−2993.97	+	1728.57i	−0.372848	+	0.215264i	−0.674702	−	0.738090i	$-0.735728\pi$
$401$	−2993.97	+	1728.57i	−0.372848	+	0.215264i	0.301854	+	0.953354i	$0.402394\pi$
$402$	1336.86	+	152.261i	0.165862	+	0.0188907i
$403$	4776.72	−	8273.52i	0.590435	−	1.02266i
$404$	2050.59	+	3551.73i	0.252526	+	0.437389i
$405$	436.213	+	6223.68i	0.0535200	+	0.763598i
$406$	1304.65	−	1570.05i	0.159479	−	0.191922i
$407$		−	19645.6i		−	2.39261i
$408$	659.490	−	891.325i	0.0800236	−	0.108155i
$409$	13285.6	+	7670.42i	1.60618	+	0.927329i	0.990214	+	0.139558i	$0.0445681\pi$
$409$	13285.6	+	7670.42i	1.60618	+	0.927329i	0.615968	+	0.787772i	$0.288765\pi$
$410$	−3116.02	−	1799.04i	−0.375340	−	0.216703i
$411$	1446.46	−	1954.94i	0.173598	−	0.234623i
$412$		−	1285.44i		−	0.153711i
$413$	333.742	+	57.1983i	0.0397636	+	0.00681487i
$414$	−1948.71	+	2090.07i	−0.231337	+	0.248119i
$415$	5867.42	+	10162.7i	0.694024	+	1.20209i
$416$	987.298	−	1710.05i	0.116361	−	0.201543i
$417$	−15092.2	−	1718.92i	−1.77235	−	0.201861i
$418$	−7291.69	+	4209.86i	−0.853225	+	0.492610i
$419$	−2968.51			−0.346112			−0.173056	−	0.984912i	$-0.555364\pi$
$419$	−2968.51			−0.346112			−0.173056	+	0.984912i	$0.555364\pi$
$420$	−3199.59	+	784.544i	−0.371724	+	0.0911472i
$421$	−8733.67			−1.01105			−0.505526	−	0.862811i	$-0.668702\pi$
$421$	−8733.67			−1.01105			−0.505526	+	0.862811i	$0.668702\pi$
$422$	7433.07	−	4291.48i	0.857431	−	0.495038i
$423$	1829.04	+	5980.81i	0.210239	+	0.687463i
$424$	−1075.67	+	1863.12i	−0.123206	+	0.213399i
$425$	690.255	+	1195.56i	0.0787819	+	0.136454i
$426$	7667.40	−	3334.25i	0.872035	−	0.379214i
$427$	1189.71	+	988.597i	0.134834	+	0.112041i
$428$			544.315i			0.0614730i
$429$	16030.4	+	11860.9i	1.80409	+	1.33484i
$430$	5216.90	+	3011.98i	0.585072	+	0.337792i
$431$	−51.3171	−	29.6279i	−0.00573517	−	0.00331120i	0.497130	−	0.867676i	$-0.334387\pi$
$431$	−51.3171	−	29.6279i	−0.00573517	−	0.00331120i	−0.502865	+	0.864365i	$0.667721\pi$
$432$	2207.10	−	409.339i	0.245808	−	0.0455887i
$433$		−	3034.66i		−	0.336805i	−0.985718	−	0.168403i	$-0.946139\pi$
$433$		−	3034.66i		−	0.336805i	0.985718	−	0.168403i	$-0.0538609\pi$
$434$	1987.20	+	5379.36i	0.219790	+	0.594971i
$435$	977.347	+	2247.49i	0.107725	+	0.247722i
$436$	2812.31	+	4871.07i	0.308912	+	0.535051i
$437$	−1791.03	+	3102.15i	−0.196056	+	0.339578i
$438$	502.955	−	4415.97i	0.0548679	−	0.481742i
$439$	−2155.72	+	1244.61i	−0.234367	+	0.135312i	−0.612585	−	0.790405i	$-0.709870\pi$
$439$	−2155.72	+	1244.61i	−0.234367	+	0.135312i	0.378218	+	0.925716i	$0.376537\pi$
$440$	4258.11			0.461357
$441$	8210.55	−	4284.04i	0.886572	−	0.462590i
$442$	−3291.78			−0.354240
$443$	−13052.4	+	7535.83i	−1.39986	+	0.808212i	−0.994378	−	0.105889i	$-0.966231\pi$
$443$	−13052.4	+	7535.83i	−1.39986	+	0.808212i	−0.405487	+	0.914101i	$0.632898\pi$
$444$	−742.965	+	6523.26i	−0.0794134	+	0.697253i
$445$	−3310.66	+	5734.23i	−0.352675	+	0.610851i
$446$	1170.88	+	2028.02i	0.124311	+	0.215313i
$447$	−3757.15	−	8639.89i	−0.397555	−	0.914212i
$448$	410.734	+	1111.86i	0.0433155	+	0.117255i
$449$			5352.96i			0.562632i	0.959615	+	0.281316i	$0.0907709\pi$
$449$			5352.96i			0.562632i	−0.959615	+	0.281316i	$0.909229\pi$
$450$	−628.488	+	2723.28i	−0.0658382	+	0.285282i
$451$	−11322.2	−	6536.86i	−1.18213	−	0.682502i
$452$	−1618.72	−	934.569i	−0.168447	−	0.0972532i
$453$	−6910.19	−	5112.84i	−0.716709	−	0.530292i
$454$		−	4253.97i		−	0.439755i
$455$	7522.33	+	6250.74i	0.775060	+	0.644042i
$456$	2580.40	−	1122.11i	0.264996	−	0.115236i
$457$	−1063.05	−	1841.25i	−0.108812	−	0.188468i	0.806477	−	0.591265i	$-0.201371\pi$
$457$	−1063.05	−	1841.25i	−0.108812	−	0.188468i	−0.915289	+	0.402797i	$0.868038\pi$
$458$	−1298.10	+	2248.37i	−0.132437	+	0.229388i
$459$	−2430.66	−	2845.24i	−0.247175	−	0.289334i
$460$	1568.85	−	905.776i	0.159017	−	0.0918087i
$461$	−987.346			−0.0997512			−0.0498756	−	0.998755i	$-0.515882\pi$
$461$	−987.346			−0.0997512			−0.0498756	+	0.998755i	$0.515882\pi$
$462$	−11625.8	+	2850.66i	−1.17074	+	0.287067i
$463$	−17023.3			−1.70872			−0.854362	−	0.519678i	$-0.826052\pi$
$463$	−17023.3			−1.70872			−0.854362	+	0.519678i	$0.826052\pi$
$464$	763.648	−	440.893i	0.0764041	−	0.0441119i
$465$	−6840.67	−	779.116i	−0.682212	−	0.0777003i
$466$	4204.46	−	7282.34i	0.417957	−	0.723923i
$467$	−6858.57	−	11879.4i	−0.679608	−	1.17712i	−0.975099	−	0.221770i	$-0.928817\pi$
$467$	−6858.57	−	11879.4i	−0.679608	−	1.17712i	0.295491	−	0.955345i	$-0.404517\pi$
$468$	−4874.30	−	4544.62i	−0.481441	−	0.448878i
$469$	2363.37	+	405.046i	0.232687	+	0.0398791i
$470$		−	3964.83i		−	0.389114i
$471$	−4283.53	+	5789.35i	−0.419054	+	0.566367i
$472$	126.669	+	73.1324i	0.0123526	+	0.00713176i
$473$	18955.8	+	10944.1i	1.84268	+	1.06387i
$474$	−7532.26	+	10180.1i	−0.729890	+	0.986474i
$475$			3503.42i			0.338416i
$476$	1262.85	−	1519.75i	0.121602	−	0.146340i
$477$	5310.61	+	4951.42i	0.509761	+	0.475283i
$478$	−3816.77	−	6610.84i	−0.365219	−	0.632579i
$479$	−974.841	+	1688.47i	−0.0929887	+	0.161061i	−0.908767	−	0.417303i	$-0.862975\pi$
$479$	−974.841	+	1688.47i	−0.0929887	+	0.161061i	0.815779	+	0.578364i	$0.196309\pi$
$480$	−1413.89	−	161.035i	−0.134448	−	0.0153129i
$481$	16880.3	−	9745.85i	1.60016	−	0.923851i
$482$	−3273.96			−0.309388
$483$	−3677.01	+	3523.31i	−0.346397	+	0.331918i
$484$	10148.0			0.953039
$485$	6290.76	−	3631.97i	0.588967	−	0.340040i
$486$	328.930	−	7568.85i	0.0307008	−	0.706440i
$487$	−1269.48	+	2198.80i	−0.118122	+	0.204594i	−0.919023	−	0.394203i	$-0.871021\pi$
$487$	−1269.48	+	2198.80i	−0.118122	+	0.204594i	0.800901	+	0.598796i	$0.204354\pi$
$488$	334.087	+	578.656i	0.0309906	+	0.0536773i
$489$	5494.55	−	2389.36i	0.508123	−	0.220962i
$490$	−5771.70	+	1074.90i	−0.532120	+	0.0991004i
$491$			17119.1i			1.57347i	0.617289	+	0.786737i	$0.288231\pi$
$491$			17119.1i			1.57347i	−0.617289	+	0.786737i	$0.711769\pi$
$492$	3512.29	+	2598.73i	0.321842	+	0.238130i
$493$	−1273.05	−	734.997i	−0.116299	−	0.0671452i
$494$	−7234.58	−	4176.89i	−0.658906	−	0.380419i
$495$	3231.66	−	14003.0i	0.293439	−	1.27149i
$496$			2477.15i			0.224248i
$497$	13977.0	−	5163.29i	1.26148	−	0.466007i
$498$	−5682.57	−	13067.6i	−0.511330	−	1.17585i
$499$	−454.423	−	787.084i	−0.0407671	−	0.0706107i	0.844922	−	0.534890i	$-0.179647\pi$
$499$	−454.423	−	787.084i	−0.0407671	−	0.0706107i	−0.885689	+	0.464279i	$0.846313\pi$
$500$	3025.45	−	5240.23i	0.270604	−	0.468701i
$501$	178.563	−	1567.79i	0.0159234	−	0.139808i
$502$	9126.99	−	5269.47i	0.811469	−	0.468502i
$503$	13477.7			1.19471			0.597356	−	0.801976i	$-0.296218\pi$
$503$	13477.7			1.19471			0.597356	+	0.801976i	$0.296218\pi$
$504$	3968.13	−	506.886i	0.350704	−	0.0447986i
$505$	−8774.71			−0.773207
$506$	5700.46	−	3291.16i	0.500823	−	0.289150i
$507$	−947.078	+	8315.39i	−0.0829610	+	0.728401i
$508$	518.332	−	897.777i	0.0452702	−	0.0784102i
$509$	7065.77	+	12238.3i	0.615294	+	1.06572i	0.990333	+	0.138711i	$0.0442961\pi$
$509$	7065.77	+	12238.3i	0.615294	+	1.06572i	−0.375039	+	0.927009i	$0.622371\pi$
$510$	946.038	+	2175.50i	0.0821397	+	0.188888i
$511$	1337.97	−	7806.81i	0.115828	−	0.675837i
$512$			512.000i			0.0441942i
$513$	−1731.76	−	9337.42i	−0.149043	−	0.803620i
$514$	1976.60	+	1141.19i	0.169619	+	0.0979295i
$515$	2381.80	+	1375.14i	0.203796	+	0.117662i
$516$	−5880.33	−	4350.84i	−0.501680	−	0.371192i
$517$		−	14406.3i		−	1.22551i
$518$	−1976.44	+	11532.2i	−0.167645	+	0.978178i
$519$	12474.8	−	5424.78i	1.05507	−	0.458808i
$520$	2112.38	+	3658.75i	0.178142	+	0.308551i
$521$	5532.79	−	9583.08i	0.465251	−	0.805839i	−0.533961	−	0.845509i	$-0.679297\pi$
$521$	5532.79	−	9583.08i	0.465251	−	0.805839i	0.999213	+	0.0396697i	$0.0126306\pi$
$522$	−870.336	−	2845.92i	−0.0729762	−	0.238625i
$523$	−5211.30	+	3008.74i	−0.435706	+	0.251555i	−0.701774	−	0.712399i	$-0.747609\pi$
$523$	−5211.30	+	3008.74i	−0.435706	+	0.251555i	0.266069	+	0.963954i	$0.414275\pi$
$524$	−10591.4			−0.882991
$525$	−1391.49	+	4782.44i	−0.115676	+	0.397567i
$526$	4570.11			0.378833
$527$	3576.31	−	2064.78i	0.295610	−	0.170671i
$528$	−5137.43	−	585.126i	−0.423443	−	0.0482279i
$529$	−4683.32	+	8111.75i	−0.384920	+	0.666701i
$530$	−2301.46	−	3986.25i	−0.188621	−	0.326701i
$531$	336.635	−	361.055i	0.0275117	−	0.0295075i
$532$	4703.85	−	1737.66i	0.383342	−	0.141611i
$533$		−	12971.3i		−	1.05413i
$534$	4782.30	−	6463.45i	0.387547	−	0.523785i
$535$	−1008.57	−	582.296i	−0.0815030	−	0.0470558i
$536$	896.999	+	517.883i	0.0722845	+	0.0417335i
$537$	−8549.87	+	11555.5i	−0.687065	+	0.928594i
$538$			3748.76i			0.300410i
$539$	−20971.7	+	3905.69i	−1.67591	+	0.312115i
$540$	−1602.64	+	4527.46i	−0.127716	+	0.360798i
$541$	−3477.08	−	6022.47i	−0.276324	−	0.478607i	0.694145	−	0.719836i	$-0.255783\pi$
$541$	−3477.08	−	6022.47i	−0.276324	−	0.478607i	−0.970468	+	0.241229i	$0.922450\pi$
$542$	3281.32	−	5683.42i	0.260046	−	0.450413i
$543$	2785.87	+	317.296i	0.220172	+	0.0250764i
$544$	739.185	−	426.769i	0.0582579	−	0.0336352i
$545$	−12034.2			−0.945852
$546$	−8216.80	−	8575.23i	−0.644041	−	0.672136i
$547$	14101.3			1.10224			0.551122	−	0.834424i	$-0.314200\pi$
$547$	14101.3			1.10224			0.551122	+	0.834424i	$0.314200\pi$
$548$	1621.25	−	936.032i	0.126381	−	0.0729659i
$549$	2156.50	−	659.498i	0.167645	−	0.0512690i
$550$	3218.92	−	5575.33i	0.249555	−	0.432241i
$551$	−1865.25	−	3230.71i	−0.144215	−	0.249788i
$552$	−2017.29	+	877.241i	−0.155546	+	0.0676410i
$553$	−14423.4	+	17357.6i	−1.10913	+	1.33476i
$554$		−	1061.50i		−	0.0814056i
$555$	−11292.2	−	8355.09i	−0.863653	−	0.639016i
$556$	−10126.5	−	5846.54i	−0.772410	−	0.445951i
$557$	7314.84	+	4223.22i	0.556445	+	0.321263i	0.751717	−	0.659486i	$-0.229226\pi$
$557$	7314.84	+	4223.22i	0.556445	+	0.321263i	−0.195273	+	0.980749i	$0.562559\pi$
$558$	8146.25	+	1880.02i	0.618025	+	0.142630i
$559$			21716.8i			1.64315i
$560$	−2499.57	−	428.387i	−0.188618	−	0.0323262i
$561$	3437.46	+	7904.74i	0.258698	+	0.594899i
$562$	5216.62	+	9035.46i	0.391548	+	0.678181i
$563$	−10951.1	+	18967.8i	−0.819774	+	1.41989i	0.0860755	+	0.996289i	$0.472567\pi$
$563$	−10951.1	+	18967.8i	−0.819774	+	1.41989i	−0.905849	+	0.423601i	$0.860766\pi$
$564$	−544.825	+	4783.59i	−0.0406760	+	0.357137i
$565$	3463.35	−	1999.56i	0.257883	−	0.148889i
$566$	−2096.55			−0.155697
$567$	1344.66	−	13434.1i	0.0995955	−	0.995028i
$568$	6436.30			0.475460
$569$	−8724.86	+	5037.30i	−0.642821	+	0.371133i	−0.785700	−	0.618607i	$-0.787697\pi$
$569$	−8724.86	+	5037.30i	−0.642821	+	0.371133i	0.142879	+	0.989740i	$0.454364\pi$
$570$	−681.279	+	5981.66i	−0.0500625	+	0.439551i
$571$	−9133.47	+	15819.6i	−0.669394	+	1.15942i	0.308680	+	0.951166i	$0.400113\pi$
$571$	−9133.47	+	15819.6i	−0.669394	+	1.15942i	−0.978074	+	0.208258i	$0.933221\pi$
$572$	7675.40	+	13294.2i	0.561057	+	0.971779i
$573$	6614.97	+	15211.7i	0.482276	+	1.10904i
$574$	5988.62	+	4976.29i	0.435471	+	0.361858i
$575$		−	2738.89i		−	0.198642i
$576$	1683.74	+	388.579i	0.121799	+	0.0281090i
$577$	3379.83	+	1951.34i	0.243855	+	0.140789i	0.616947	−	0.787005i	$-0.288369\pi$
$577$	3379.83	+	1951.34i	0.243855	+	0.140789i	−0.373093	+	0.927794i	$0.621703\pi$
$578$	7277.30	+	4201.55i	0.523695	+	0.302355i
$579$	6004.02	+	4442.36i	0.430947	+	0.318857i
$580$			1886.63i			0.135066i
$581$	−8799.82	−	23821.1i	−0.628361	−	1.70097i
$582$	−8088.93	+	3517.56i	−0.576111	+	0.250528i
$583$	−8362.44	−	14484.2i	−0.594060	−	1.02894i
$584$	1710.70	−	2963.01i	0.121214	−	0.209949i
$585$	13635.2	−	4169.90i	0.963668	−	0.294708i
$586$	−11099.8	+	6408.45i	−0.782470	+	0.451759i
$587$	3318.05			0.233306			0.116653	−	0.993173i	$-0.462783\pi$
$587$	3318.05			0.233306			0.116653	+	0.993173i	$0.462783\pi$
$588$	7111.30	−	503.761i	0.498750	−	0.0353312i
$589$	10479.9			0.733135
$590$	−271.016	+	156.471i	−0.0189111	+	0.0109183i
$591$	12113.2	+	1379.63i	0.843097	+	0.0960243i
$592$	−2527.04	+	4376.96i	−0.175440	+	0.303871i
$593$	−12126.5	−	21003.6i	−0.839754	−	1.45450i	−0.890101	−	0.455764i	$-0.849366\pi$
$593$	−12126.5	−	21003.6i	−0.839754	−	1.45450i	0.0503470	−	0.998732i	$-0.483967\pi$
$594$	−5823.24	+	16450.7i	−0.402240	+	1.13633i
$595$	1465.00	+	3965.75i	0.100940	+	0.273244i
$596$		−	7252.64i		−	0.498456i
$597$	−5660.57	+	7650.47i	−0.388060	+	0.524477i
$598$	5655.82	+	3265.39i	0.386762	+	0.223297i
$599$	−9619.77	−	5553.97i	−0.656182	−	0.378847i	0.134639	−	0.990895i	$-0.457013\pi$
$599$	−9619.77	−	5553.97i	−0.656182	−	0.378847i	−0.790821	+	0.612048i	$0.790346\pi$
$600$	−1279.68	+	1729.54i	−0.0870715	+	0.117680i
$601$			13367.3i			0.907258i	0.891191	+	0.453629i	$0.149871\pi$
$601$			13367.3i			0.907258i	−0.891191	+	0.453629i	$0.850129\pi$
$602$	−10026.2	−	8331.39i	−0.678803	−	0.564056i
$603$	2383.86	−	2556.79i	0.160992	−	0.172671i
$604$	−3308.62	−	5730.69i	−0.222890	−	0.386057i
$605$	−10856.1	+	18803.3i	−0.729524	+	1.26357i
$606$	10586.7	+	1205.77i	0.709664	+	0.0808270i
$607$	10180.8	−	5877.90i	0.680769	−	0.393042i	−0.119376	−	0.992849i	$-0.538089\pi$
$607$	10180.8	−	5877.90i	0.680769	−	0.393042i	0.800145	+	0.599807i	$0.204756\pi$
$608$	2166.08			0.144484
$609$	−1263.04	−	5151.02i	−0.0840408	−	0.342742i
$610$	−1429.60			−0.0948896
$611$	12378.5	−	7146.75i	0.819610	−	0.473202i
$612$	−842.455	−	2754.75i	−0.0556442	−	0.181951i
$613$	11860.0	−	20542.2i	0.781439	−	1.35349i	−0.149664	−	0.988737i	$-0.547819\pi$
$613$	11860.0	−	20542.2i	0.781439	−	1.35349i	0.931103	−	0.364755i	$-0.118847\pi$
$614$	3717.93	+	6439.64i	0.244370	+	0.423262i
$615$	−8572.59	+	3727.88i	−0.562082	+	0.244427i
$616$	−9082.25	−	1556.56i	−0.594049	−	0.101811i
$617$			9294.78i			0.606473i	0.952915	+	0.303237i	$0.0980672\pi$
$617$			9294.78i			0.606473i	−0.952915	+	0.303237i	$0.901933\pi$
$618$	−2684.70	−	1986.40i	−0.174748	−	0.129296i
$619$	−11638.1	−	6719.28i	−0.755696	−	0.436301i	0.0720523	−	0.997401i	$-0.477045\pi$
$619$	−11638.1	−	6719.28i	−0.755696	−	0.436301i	−0.827748	+	0.561100i	$0.810378\pi$
$620$	−4589.93	−	2650.00i	−0.297316	−	0.171656i
$621$	1353.85	+	7299.76i	0.0874847	+	0.471706i
$622$			811.262i			0.0522969i
$623$	9157.58	−	11020.5i	0.588909	−	0.708712i
$624$	−2045.83	−	4704.57i	−0.131248	−	0.301817i
$625$	3238.32	+	5608.94i	0.207253	+	0.358972i
$626$	−3048.42	+	5280.02i	−0.194632	+	0.337112i
$627$	−2475.45	+	21734.6i	−0.157671	+	1.38436i
$628$	−4801.16	+	2771.95i	−0.305075	+	0.176135i
$629$	8425.47			0.534095
$630$	−3305.81	+	7894.85i	−0.209058	+	0.499267i
$631$	11635.5			0.734076			0.367038	−	0.930206i	$-0.380372\pi$
$631$	11635.5			0.734076			0.367038	+	0.930206i	$0.380372\pi$
$632$	−8442.48	+	4874.27i	−0.531367	+	0.306785i
$633$	2523.45	−	22156.0i	0.158449	−	1.39119i
$634$	6598.53	−	11429.0i	0.413346	−	0.715936i
$635$	1109.00	+	1920.84i	0.0693060	+	0.120042i
$636$	2228.96	+	5125.69i	0.138969	+	0.319571i
$637$	−13759.7	−	16082.2i	−0.855851	−	1.00031i
$638$			6855.13i			0.425387i
$639$	4884.79	−	21166.2i	0.302409	−	1.31036i
$640$	−948.690	−	547.727i	−0.0585942	−	0.0338294i
$641$	−21346.3	−	12324.3i	−1.31533	−	0.759409i	−0.332360	−	0.943153i	$-0.607845\pi$
$641$	−21346.3	−	12324.3i	−1.31533	−	0.759409i	−0.982974	+	0.183744i	$0.941178\pi$
$642$	1136.82	+	841.135i	0.0698861	+	0.0517086i
$643$		−	5268.28i		−	0.323111i	−0.986864	−	0.161556i	$-0.948349\pi$
$643$		−	5268.28i		−	0.323111i	0.986864	−	0.161556i	$-0.0516511\pi$
$644$	−3677.36	+	1358.46i	−0.225013	+	0.0831225i
$645$	14352.4	−	6241.28i	0.876161	−	0.381008i
$646$	−1805.50	−	3127.22i	−0.109964	−	0.190462i
$647$	9235.29	−	15996.0i	0.561169	−	0.971974i	−0.436225	−	0.899837i	$-0.643685\pi$
$647$	9235.29	−	15996.0i	0.561169	−	0.971974i	0.997395	−	0.0721365i	$-0.0229817\pi$
$648$	2555.73	−	5242.18i	0.154936	−	0.317797i
$649$	−984.743	+	568.542i	−0.0595602	+	0.0343871i
$650$	6387.42			0.385439
$651$	14305.9	+	4162.42i	0.861277	+	0.250596i
$652$	4612.32			0.277044
$653$	−11414.2	+	6589.99i	−0.684030	+	0.394925i	−0.801372	−	0.598166i	$-0.795896\pi$
$653$	−11414.2	+	6589.99i	−0.684030	+	0.394925i	0.117341	+	0.993092i	$0.462563\pi$
$654$	14519.3	+	1653.68i	0.868121	+	0.0988744i
$655$	11330.4	−	19624.9i	0.675904	−	1.17070i
$656$	1681.69	+	2912.77i	0.100090	+	0.173361i
$657$	−8445.72	−	7874.49i	−0.501521	−	0.467600i
$658$	−1449.35	+	8456.70i	−0.0858686	+	0.501028i
$659$			10701.0i			0.632549i	0.948668	+	0.316275i	$0.102432\pi$
$659$			10701.0i			0.632549i	−0.948668	+	0.316275i	$0.897568\pi$
$660$	6580.10	−	8893.24i	0.388076	−	0.524498i
$661$	−11215.0	−	6475.01i	−0.659931	−	0.381011i	0.132320	−	0.991207i	$-0.457758\pi$
$661$	−11215.0	−	6475.01i	−0.659931	−	0.381011i	−0.792251	+	0.610196i	$0.791091\pi$
$662$	637.489	+	368.054i	0.0374271	+	0.0216085i
$663$	−5086.82	+	6875.03i	−0.297973	+	0.402721i
$664$		−	10969.4i		−	0.641108i
$665$	−1812.35	+	10574.7i	−0.105684	+	0.616647i
$666$	12476.0	+	11632.2i	0.725879	+	0.676783i
$667$	1458.21	+	2525.69i	0.0846508	+	0.146619i
$668$	607.345	−	1051.95i	0.0351780	−	0.0609300i
$669$	6044.98	+	688.491i	0.349346	+	0.0397886i
$670$	−1919.18	+	1108.04i	−0.110663	+	0.0638915i
$671$	−5194.48			−0.298854
$672$	2956.87	+	860.329i	0.169738	+	0.0493867i
$673$	3025.28			0.173278			0.0866389	−	0.996240i	$-0.472387\pi$
$673$	3025.28			0.173278			0.0866389	+	0.996240i	$0.472387\pi$
$674$	11282.6	−	6514.00i	0.644790	−	0.372270i
$675$	4716.49	+	5520.94i	0.268945	+	0.314817i
$676$	−3221.29	+	5579.43i	−0.183278	+	0.317446i
$677$	1368.23	+	2369.84i	0.0776739	+	0.134535i	0.902246	−	0.431222i	$-0.141917\pi$
$677$	1368.23	+	2369.84i	0.0776739	+	0.134535i	−0.824572	+	0.565757i	$0.808584\pi$
$678$	−4453.32	+	1936.57i	−0.252254	+	0.109696i
$679$	−14745.4	+	5447.15i	−0.833399	+	0.307868i
$680$			1826.19i			0.102987i
$681$	−8884.61	−	6573.71i	−0.499940	−	0.369905i
$682$	−16677.7	−	9628.85i	−0.936394	−	0.540627i
$683$	−7977.54	−	4605.84i	−0.446928	−	0.258034i	0.259604	−	0.965715i	$-0.416408\pi$
$683$	−7977.54	−	4605.84i	−0.446928	−	0.258034i	−0.706532	+	0.707681i	$0.749741\pi$
$684$	1643.93	−	7123.29i	0.0918968	−	0.398196i
$685$			4005.39i			0.223413i
$686$	12703.6	−	182.838i	0.707034	−	0.0101760i
$687$	2689.86	+	6185.57i	0.149381	+	0.343514i
$688$	−2815.51	−	4876.61i	−0.156018	−	0.270231i
$689$	8296.95	−	14370.7i	0.458764	−	0.794603i
$690$	532.607	−	4676.32i	0.0293855	−	0.258006i
$691$	2228.30	−	1286.51i	0.122675	−	0.0708264i	−0.437407	−	0.899264i	$-0.644103\pi$
$691$	2228.30	−	1286.51i	0.122675	−	0.0708264i	0.560082	+	0.828437i	$0.310770\pi$
$692$	10471.8			0.575256
$693$	−12011.8	+	28686.2i	−0.658426	+	1.57244i
$694$	4847.25			0.265128
$695$	21666.2	−	12509.0i	1.18251	−	0.682725i
$696$	259.250	−	2276.23i	0.0141191	−	0.123966i
$697$	2803.49	−	4855.79i	0.152353	−	0.263882i
$698$	−10490.9	−	18170.8i	−0.568893	−	0.985352i
$699$	−8712.29	−	20034.7i	−0.471430	−	1.08409i
$700$	−2450.45	+	2948.95i	−0.132312	+	0.159228i
$701$			18596.9i			1.00199i	0.865450	+	0.500996i	$0.167033\pi$
$701$			18596.9i			1.00199i	−0.865450	+	0.500996i	$0.832967\pi$
$702$	−17023.9	+	3157.34i	−0.915281	+	0.169752i
$703$	18517.3	+	10691.0i	0.993446	+	0.573566i
$704$	−3447.10	−	1990.18i	−0.184542	−	0.106545i
$705$	−8280.71	−	6126.89i	−0.442368	−	0.327308i
$706$		−	16021.7i		−	0.854085i
$707$	18715.8	+	3207.61i	0.995590	+	0.170629i
$708$	348.483	−	151.542i	0.0184983	−	0.00804418i
$709$	12000.1	+	20784.8i	0.635647	+	1.10097i	0.986378	+	0.164496i	$0.0525998\pi$
$709$	12000.1	+	20784.8i	0.635647	+	1.10097i	−0.350731	+	0.936476i	$0.614067\pi$
$710$	−6885.41	+	11925.9i	−0.363951	+	0.630381i
$711$	9621.96	+	31462.9i	0.507527	+	1.65957i
$712$	5360.21	−	3094.72i	0.282138	−	0.162892i
$713$	−8192.92			−0.430333
$714$	−1222.58	−	4986.01i	−0.0640809	−	0.261340i
$715$	−32843.9			−1.71789
$716$	−9583.06	+	5532.78i	−0.500190	+	0.288785i
$717$	−19705.1	−	2244.31i	−1.02636	−	0.116897i
$718$	−11438.5	+	19812.1i	−0.594544	+	1.02978i
$719$	8305.93	+	14386.3i	0.430819	+	0.746200i	0.996944	−	0.0781192i	$-0.0248915\pi$
$719$	8305.93	+	14386.3i	0.430819	+	0.746200i	−0.566125	+	0.824319i	$0.691558\pi$
$720$	−2521.23	+	2704.13i	−0.130501	+	0.139968i
$721$	−4577.54	−	3803.74i	−0.236445	−	0.196475i
$722$			4554.11i			0.234746i
$723$	−5059.29	+	6837.82i	−0.260245	+	0.351730i
$724$	1869.26	+	1079.22i	0.0959536	+	0.0553988i
$725$	2470.25	+	1426.20i	0.126542	+	0.0730589i
$726$	15681.7	−	21194.5i	0.801659	−	1.08347i
$727$			31798.3i			1.62219i	0.584912	+	0.811097i	$0.301129\pi$
$727$			31798.3i			1.62219i	−0.584912	+	0.811097i	$0.698871\pi$
$728$	−3168.10	−	8576.04i	−0.161288	−	0.436606i
$729$	−15299.6	−	12383.2i	−0.777299	−	0.629132i
$730$	3660.13	+	6339.53i	0.185572	+	0.321420i
$731$	−4693.65	+	8129.64i	−0.237484	+	0.411334i
$732$	1724.82	+	196.447i	0.0870916	+	0.00991927i
$733$	29412.4	−	16981.3i	1.48209	−	0.855686i	0.482298	−	0.876007i	$-0.339802\pi$
$733$	29412.4	−	16981.3i	1.48209	−	0.855686i	0.999794	+	0.0203212i	$0.00646890\pi$
$734$	−2908.50			−0.146260
$735$	−6674.09	+	13715.5i	−0.334935	+	0.688305i
$736$	−1693.39			−0.0848086
$737$	−6973.40	+	4026.10i	−0.348533	+	0.201225i
$738$	10855.1	−	3319.71i	0.541441	−	0.165583i
$739$	14447.3	−	25023.5i	0.719153	−	1.24561i	−0.242183	−	0.970231i	$-0.577863\pi$
$739$	14447.3	−	25023.5i	0.719153	−	1.24561i	0.961336	−	0.275379i	$-0.0888033\pi$
$740$	−5406.74	−	9364.75i	−0.268589	−	0.465209i
$741$	−19903.3	+	8655.16i	−0.986729	+	0.429089i
$742$	3451.68	+	9343.71i	0.170775	+	0.462289i
$743$		−	8565.28i		−	0.422920i	−0.977387	−	0.211460i	$-0.932178\pi$
$743$		−	8565.28i		−	0.422920i	0.977387	−	0.211460i	$-0.0678218\pi$
$744$	5173.63	+	3827.96i	0.254939	+	0.188629i
$745$	13438.5	+	7758.72i	0.660870	+	0.381553i
$746$	−13823.2	−	7980.82i	−0.678422	−	0.391687i
$747$	−36073.6	−	8325.16i	−1.76688	−	0.407767i
$748$			6635.53i			0.324357i
$749$	1938.34	+	1610.68i	0.0945601	+	0.0785754i
$750$	−6269.19	−	14416.6i	−0.305225	−	0.701891i
$751$	7333.06	+	12701.2i	0.356308	+	0.617144i	0.987341	−	0.158613i	$-0.0507021\pi$
$751$	7333.06	+	12701.2i	0.356308	+	0.617144i	−0.631033	+	0.775756i	$0.717369\pi$
$752$	−1853.11	+	3209.67i	−0.0898615	+	0.155645i
$753$	3098.51	−	27205.1i	0.149955	−	1.31661i
$754$	−5890.22	+	3400.72i	−0.284495	+	0.164253i
$755$	14157.9			0.682464
$756$	5073.34	−	9070.91i	0.244068	−	0.436384i
$757$	−19962.2			−0.958439			−0.479220	−	0.877695i	$-0.659080\pi$
$757$	−19962.2			−0.958439			−0.479220	+	0.877695i	$0.659080\pi$
$758$	10078.5	−	5818.85i	0.482941	−	0.278826i
$759$	1935.25	−	16991.5i	0.0925493	−	0.812587i
$760$	−2317.23	+	4013.56i	−0.110598	+	0.191562i
$761$	19166.3	+	33197.0i	0.912980	+	1.58133i	0.809833	+	0.586661i	$0.199558\pi$
$761$	19166.3	+	33197.0i	0.912980	+	1.58133i	0.103147	+	0.994666i	$0.467109\pi$
$762$	−1074.06	−	2469.90i	−0.0510619	−	0.117421i
$763$	25668.2	+	4399.13i	1.21789	+	0.208728i
$764$			12769.3i			0.604680i
$765$	6005.54	+	1385.98i	0.283831	+	0.0655034i
$766$	−2142.93	−	1237.22i	−0.101080	−	0.0583585i
$767$	−977.032	−	564.089i	−0.0459955	−	0.0265555i
$768$	1069.33	+	791.199i	0.0502426	+	0.0371744i
$769$		−	1797.33i		−	0.0842826i	−0.999112	−	0.0421413i	$-0.986582\pi$
$769$		−	1797.33i		−	0.0842826i	0.999112	−	0.0421413i	$-0.0134180\pi$
$770$	12600.2	−	15163.4i	0.589712	−	0.709678i
$771$	5437.89	−	2364.72i	0.254009	−	0.110458i
$772$	2874.74	+	4979.19i	0.134021	+	0.232131i
$773$	−5866.15	+	10160.5i	−0.272951	+	0.472765i	−0.969616	−	0.244632i	$-0.921333\pi$
$773$	−5866.15	+	10160.5i	−0.272951	+	0.472765i	0.696665	+	0.717396i	$0.254666\pi$
$774$	−18173.9	+	5557.91i	−0.843987	+	0.258107i
$775$	−6939.52	+	4006.53i	−0.321645	+	0.185702i
$776$	−6790.14			−0.314113
$777$	21031.3	+	21948.7i	0.971034	+	1.01339i
$778$	6010.23			0.276963
$779$	12322.9	−	7114.61i	0.566768	−	0.327224i
$780$	10905.7	+	1242.11i	0.500626	+	0.0570186i
$781$	−25018.4	+	43333.1i	−1.14626	+	1.98538i
$782$	1411.50	+	2444.78i	0.0645460	+	0.111797i
$783$	−7288.76	−	2580.09i	−0.332668	−	0.117759i
$784$	5174.80	+	1827.44i	0.235733	+	0.0832472i
$785$		−	11861.5i		−	0.539306i
$786$	−16367.0	+	22120.6i	−0.742737	+	1.00384i
$787$	13313.4	+	7686.49i	0.603013	+	0.348150i	0.770226	−	0.637771i	$-0.220143\pi$
$787$	13313.4	+	7686.49i	0.603013	+	0.348150i	−0.167213	+	0.985921i	$0.553477\pi$
$788$	8127.68	+	4692.52i	0.367432	+	0.212137i
$789$	7062.23	−	9544.87i	0.318659	−	0.430680i
$790$		−	20857.5i		−	0.939339i
$791$	−8118.02	+	2998.90i	−0.364910	+	0.134802i
$792$	−9160.98	+	9825.54i	−0.411012	+	0.440828i
$793$	−2576.90	−	4463.32i	−0.115395	−	0.199871i
$794$	−6411.23	+	11104.6i	−0.286557	+	0.496331i
$795$	−11881.9	−	1353.29i	−0.530074	−	0.0603726i
$796$	−6344.61	+	3663.06i	−0.282511	+	0.163108i
$797$	33773.5			1.50103			0.750513	−	0.660856i	$-0.229807\pi$
$797$	33773.5			1.50103			0.750513	+	0.660856i	$0.229807\pi$
$798$	3639.73	−	12509.4i	0.161460	−	0.554924i
$799$	6178.50			0.273567
$800$	−1434.33	+	828.108i	−0.0633888	+	0.0365976i
$801$	−6109.07	−	19976.1i	−0.269480	−	0.881174i
$802$	−3457.14	+	5987.95i	−0.152214	+	0.263643i
$803$	13299.2	+	23034.9i	0.584457	+	1.01231i
$804$	2467.76	−	1073.13i	0.108248	−	0.0470727i
$805$	1416.85	−	8267.06i	0.0620340	−	0.361957i
$806$		−	19106.9i		−	0.835002i
$807$	7829.45	+	5793.00i	0.341524	+	0.252693i
$808$	7103.45	+	4101.18i	0.309280	+	0.178563i
$809$	−30723.2	−	17738.1i	−1.33519	−	0.770874i	−0.349103	−	0.937084i	$-0.613514\pi$
$809$	−30723.2	−	17738.1i	−1.33519	−	0.770874i	−0.986090	+	0.166210i	$0.946847\pi$
$810$	6979.22	+	10343.5i	0.302747	+	0.448684i
$811$		−	31038.0i		−	1.34389i	−0.740603	−	0.671943i	$-0.765460\pi$
$811$		−	31038.0i		−	1.34389i	0.740603	−	0.671943i	$-0.234540\pi$
$812$	689.661	−	4024.05i	0.0298059	−	0.173912i
$813$	−6799.40	−	15635.8i	−0.293315	−	0.674505i
$814$	−19645.6	−	34027.1i	−0.845917	−	1.46517i
$815$	−4934.16	+	8546.22i	−0.212069	+	0.367314i
$816$	250.945	−	2203.31i	0.0107657	−	0.0945237i
$817$	−20631.1	+	11911.4i	−0.883467	+	0.510070i
$818$	30681.7			1.31144
$819$	−30607.2	+	3909.74i	−1.30587	+	0.166810i
$820$	−7196.15			−0.306464
$821$	4221.32	−	2437.18i	0.179446	−	0.103603i	−0.407586	−	0.913167i	$-0.633629\pi$
$821$	4221.32	−	2437.18i	0.179446	−	0.103603i	0.587032	+	0.809563i	$0.300296\pi$
$822$	550.398	−	4832.52i	0.0233544	−	0.205053i
$823$	11051.1	−	19141.0i	0.468064	−	0.810710i	−0.531270	−	0.847202i	$-0.678285\pi$
$823$	11051.1	−	19141.0i	0.468064	−	0.810710i	0.999334	+	0.0364924i	$0.0116185\pi$
$824$	−1285.44	−	2226.45i	−0.0543452	−	0.0941286i
$825$	−6670.09	−	15338.5i	−0.281482	−	0.647293i
$826$	635.256	−	234.671i	0.0267595	−	0.00988531i
$827$			18204.1i			0.765439i	0.923865	+	0.382719i	$0.125012\pi$
$827$			18204.1i			0.765439i	−0.923865	+	0.382719i	$0.874988\pi$
$828$	−1285.19	+	5568.81i	−0.0539412	+	0.233731i
$829$	−27346.1	−	15788.3i	−1.14568	−	0.661458i	−0.197848	−	0.980233i	$-0.563395\pi$
$829$	−27346.1	−	15788.3i	−1.14568	−	0.661458i	−0.947830	+	0.318775i	$0.896729\pi$
$830$	20325.3	+	11734.8i	0.850003	+	0.490749i
$831$	−2216.98	−	1640.34i	−0.0925467	−	0.0684752i
$832$		−	3949.19i		−	0.164560i
$833$	−1675.05	−	8994.21i	−0.0696724	−	0.374107i
$834$	−27859.4	+	12114.9i	−1.15670	+	0.503005i
$835$	1299.45	+	2250.71i	0.0538554	+	0.0932803i
$836$	−8419.72	+	14583.4i	−0.348328	+	0.603321i
$837$	16515.0	−	14108.6i	0.682008	−	0.582633i
$838$	−5141.60	+	2968.51i	−0.211950	+	0.122369i
$839$	−19529.4			−0.803612			−0.401806	−	0.915725i	$-0.631617\pi$
$839$	−19529.4			−0.803612			−0.401806	+	0.915725i	$0.631617\pi$
$840$	−4757.31	+	4558.46i	−0.195408	+	0.187240i
$841$	21351.7			0.875465
$842$	−15127.2	+	8733.67i	−0.619140	+	0.357461i
$843$	26932.3	+	3067.44i	1.10035	+	0.125324i
$844$	8582.97	−	14866.1i	0.350045	−	0.606296i
$845$	−6892.13	−	11937.5i	−0.280587	−	0.485992i
$846$	9148.80	+	8530.02i	0.371800	+	0.346652i
$847$	30028.8	−	36137.6i	1.21818	−	1.46600i
$848$			4302.69i			0.174239i
$849$	−3239.82	+	4378.74i	−0.130966	+	0.177006i
$850$	2391.11	+	1380.51i	0.0964877	+	0.0557072i
$851$	−14476.3	−	8357.92i	−0.583129	−	0.336670i
$852$	9946.08	−	13442.5i	0.399938	−	0.540531i
$853$		−	20178.9i		−	0.809979i	−0.914321	−	0.404989i	$-0.867275\pi$
$853$		−	20178.9i		−	0.809979i	0.914321	−	0.404989i	$-0.132725\pi$
$854$	3049.23	+	522.592i	0.122181	+	0.0209400i
$855$	11440.2	+	10666.4i	0.457597	+	0.426647i
$856$	544.315	+	942.781i	0.0217340	+	0.0376444i
$857$	−7058.30	+	12225.3i	−0.281338	+	0.487292i	−0.971715	−	0.236158i	$-0.924112\pi$
$857$	−7058.30	+	12225.3i	−0.281338	+	0.487292i	0.690376	+	0.723450i	$0.257445\pi$
$858$	39626.3	+	4513.23i	1.57671	+	0.179579i
$859$	−16476.7	+	9512.82i	−0.654456	+	0.377850i	−0.790161	−	0.612899i	$-0.790003\pi$
$859$	−16476.7	+	9512.82i	−0.654456	+	0.377850i	0.135706	+	0.990749i	$0.456670\pi$
$860$	12047.9			0.477709
$861$	19647.5	−	4817.59i	0.777682	−	0.190689i
$862$	−118.512			−0.00468275
$863$	−9357.24	+	5402.41i	−0.369090	+	0.213094i	−0.673061	−	0.739587i	$-0.735021\pi$
$863$	−9357.24	+	5402.41i	−0.369090	+	0.213094i	0.303971	+	0.952681i	$0.401687\pi$
$864$	3413.47	−	2916.10i	0.134408	−	0.114824i
$865$	−11202.5	+	19403.3i	−0.440342	+	0.762694i
$866$	−3034.66	−	5256.19i	−0.119079	−	0.206250i
$867$	20020.8	−	8706.25i	0.784247	−	0.341038i
$868$	8821.30	+	7330.12i	0.344947	+	0.286637i
$869$		−	75786.5i		−	2.95844i
$870$	3940.31	+	2915.43i	0.153551	+	0.113612i
$871$	−6918.79	−	3994.57i	−0.269155	−	0.155397i
$872$	9742.14	+	5624.63i	0.378338	+	0.218433i
$873$	−5153.34	+	22329.8i	−0.199787	+	0.865692i
$874$			7164.10i			0.277265i
$875$	−9708.24	−	26280.2i	−0.375084	−	1.01535i
$876$	−3544.82	−	8151.64i	−0.136722	−	0.314404i
$877$	−1795.88	−	3110.55i	−0.0691476	−	0.119767i	0.829379	−	0.558687i	$-0.188695\pi$
$877$	−1795.88	−	3110.55i	−0.0691476	−	0.119767i	−0.898526	+	0.438920i	$0.855361\pi$
$878$	−2489.21	+	4311.44i	−0.0956798	+	0.165722i
$879$	−3768.25	+	33085.4i	−0.144596	+	1.26956i
$880$	7375.26	−	4258.11i	0.282523	−	0.163114i
$881$	47633.6			1.82158			0.910792	−	0.412865i	$-0.135472\pi$
$881$	47633.6			1.82158			0.910792	+	0.412865i	$0.135472\pi$
$882$	9937.04	−	15630.7i	0.379362	−	0.596728i
$883$	−42383.1			−1.61530			−0.807648	−	0.589665i	$-0.799260\pi$
$883$	−42383.1			−1.61530			−0.807648	+	0.589665i	$0.799260\pi$
$884$	−5701.53	+	3291.78i	−0.216927	+	0.125243i
$885$	−92.0068	+	807.824i	−0.00349466	+	0.0306833i
$886$	−15071.7	+	26104.9i	−0.571492	+	0.989854i
$887$	−8634.30	−	14955.0i	−0.326845	−	0.566112i	0.655039	−	0.755595i	$-0.272652\pi$
$887$	−8634.30	−	14955.0i	−0.326845	−	0.566112i	−0.981884	+	0.189483i	$0.939319\pi$
$888$	5236.41	+	12041.6i	0.197886	+	0.455055i
$889$	−1663.25	−	4502.43i	−0.0627488	−	0.169861i
$890$			13242.6i			0.498758i
$891$	25359.2	+	37583.5i	0.953497	+	1.41312i
$892$	4056.04	+	2341.76i	0.152249	+	0.0879011i
$893$	13578.9	+	7839.81i	0.508849	+	0.293784i
$894$	−15147.5	−	11207.6i	−0.566674	−	0.419281i
$895$		−	23675.4i		−	0.884225i
$896$	1823.27	+	1515.06i	0.0679812	+	0.0564895i
$897$	15559.9	−	6766.39i	0.579186	−	0.251865i
$898$	5352.96	+	9271.60i	0.198921	+	0.344540i
$899$	4266.23	−	7389.33i	0.158272	−	0.274136i
$900$	1634.71	+	5345.35i	0.0605448	+	0.197976i
$901$	6211.89	−	3586.44i	0.229687	−	0.132610i
$902$	−26147.4			−0.965204
$903$	−32894.1	+	8065.68i	−1.21223	+	0.297241i
$904$	−3738.28			−0.137537
$905$	−3999.38	+	2309.04i	−0.146899	+	0.0848124i
$906$	−17081.6	−	1945.51i	−0.626379	−	0.0713412i
$907$	−2270.97	+	3933.44i	−0.0831383	+	0.144000i	−0.904596	−	0.426269i	$-0.859828\pi$
$907$	−2270.97	+	3933.44i	−0.0831383	+	0.144000i	0.821458	+	0.570269i	$0.193161\pi$
$908$	−4253.97	−	7368.10i	−0.155477	−	0.269294i
$909$	18878.1	−	20247.6i	0.688831	−	0.738800i
$910$	19279.8	+	3304.27i	0.702329	+	0.120368i
$911$		−	11585.4i		−	0.421342i	−0.977557	−	0.210671i	$-0.932435\pi$
$911$		−	11585.4i		−	0.421342i	0.977557	−	0.210671i	$-0.0675648\pi$
$912$	3347.27	−	4523.96i	0.121534	−	0.164258i
$913$	73852.7	+	42638.9i	2.67707	+	1.54561i
$914$	−3682.50	−	2126.09i	−0.133267	−	0.0769419i
$915$	−2209.17	+	2985.78i	−0.0798174	+	0.107876i
$916$			5192.39i			0.187294i
$917$	−31341.0	+	37716.7i	−1.12865	+	1.35825i
$918$	−7055.27	−	2497.44i	−0.253659	−	0.0897906i
$919$	2666.17	+	4617.93i	0.0957004	+	0.165758i	0.909901	−	0.414826i	$-0.136158\pi$
$919$	2666.17	+	4617.93i	0.0957004	+	0.165758i	−0.814200	+	0.580584i	$0.802824\pi$
$920$	1811.55	−	3137.70i	0.0649186	−	0.112442i
$921$	19194.8	+	2186.19i	0.686744	+	0.0782164i
$922$	−1710.13	+	987.346i	−0.0610849	+	0.0352674i
$923$	−49644.9			−1.77040
$924$	−17285.8	+	16563.3i	−0.615435	+	0.589711i
$925$	−16348.9			−0.581134
$926$	−29485.2	+	17023.3i	−1.04638	+	0.604125i
$927$	−8297.38	+	2537.50i	−0.293982	+	0.0899055i
$928$	881.785	−	1527.30i	0.0311918	−	0.0540258i
$929$	4965.04	+	8599.69i	0.175347	+	0.303710i	0.940281	−	0.340398i	$-0.110562\pi$
$929$	4965.04	+	8599.69i	0.175347	+	0.303710i	−0.764934	+	0.644108i	$0.777229\pi$
$930$	−12627.5	+	5491.20i	−0.445239	+	0.193617i
$931$	7731.23	−	21892.7i	0.272160	−	0.770680i
$932$		−	16817.9i		−	0.591081i
$933$	1694.36	+	1253.65i	0.0594542	+	0.0439901i
$934$	−23758.8	−	13717.1i	−0.832346	−	0.480555i
$935$	−12295.0	−	7098.54i	−0.430044	−	0.248286i
$936$	−12987.2	−	2997.21i	−0.453524	−	0.104666i
$937$			28533.5i			0.994821i	0.867515	+	0.497411i	$0.165716\pi$
$937$			28533.5i			0.994821i	−0.867515	+	0.497411i	$0.834284\pi$
$938$	4498.53	−	1661.81i	0.156591	−	0.0578466i
$939$	6316.79	+	14526.0i	0.219532	+	0.504834i
$940$	−3964.83	−	6867.28i	−0.137573	−	0.238283i
$941$	−2850.92	+	4937.95i	−0.0987646	+	0.171065i	−0.911174	−	0.412023i	$-0.864822\pi$
$941$	−2850.92	+	4937.95i	−0.0987646	+	0.171065i	0.812409	+	0.583088i	$0.198156\pi$
$942$	−1629.94	+	14311.0i	−0.0563762	+	0.494986i
$943$	−9633.71	+	5562.03i	−0.332680	+	0.192073i
$944$	292.530			0.0100858
$945$	11380.2	+	19104.3i	0.391745	+	0.657633i
$946$	43776.4			1.50454
$947$	14842.2	−	8569.15i	0.509299	−	0.294044i	−0.223246	−	0.974762i	$-0.571665\pi$
$947$	14842.2	−	8569.15i	0.509299	−	0.294044i	0.732546	+	0.680718i	$0.238332\pi$
$948$	−2866.13	+	25164.7i	−0.0981937	+	0.862145i
$949$	−13195.0	+	22854.5i	−0.451348	+	0.781758i
$950$	3503.42	+	6068.10i	0.119648	+	0.207237i
$951$	−13673.2	−	31442.7i	−0.466228	−	1.07213i
$952$	667.568	−	3895.14i	0.0227269	−	0.132607i
$953$			48616.8i			1.65252i	0.563287	+	0.826261i	$0.309536\pi$
$953$			48616.8i			1.65252i	−0.563287	+	0.826261i	$0.690464\pi$
$954$	14149.7	+	3265.50i	0.480202	+	0.110822i
$955$	−23660.3	−	13660.3i	−0.801706	−	0.462865i
$956$	−13221.7	−	7633.54i	−0.447301	−	0.258249i
$957$	14317.2	+	10593.3i	0.483605	+	0.357819i
$958$			3899.36i			0.131506i
$959$	1464.18	−	8543.21i	0.0493021	−	0.287669i
$960$	−2609.97	+	1134.97i	−0.0877463	+	0.0381574i
$961$	−2910.62	−	5041.35i	−0.0977015	−	0.169224i
$962$	19491.7	−	33760.6i	0.653262	−	1.13148i
$963$	3513.49	−	1074.49i	0.117571	−	0.0359554i
$964$	−5670.67	+	3273.96i	−0.189461	+	0.109385i
$965$	−12301.3			−0.410356
$966$	−2845.45	+	9779.56i	−0.0947732	+	0.325727i
$967$	−14811.1			−0.492547			−0.246273	−	0.969200i	$-0.579206\pi$
$967$	−14811.1			−0.492547			−0.246273	+	0.969200i	$0.579206\pi$
$968$	17576.8	−	10148.0i	0.583615	−	0.336950i
$969$	−9321.39	−	1061.66i	−0.309026	−	0.0351964i
$970$	7263.95	−	12581.5i	0.240445	−	0.416462i
$971$	1364.94	+	2364.14i	0.0451111	+	0.0781348i	0.887699	−	0.460424i	$-0.152302\pi$
$971$	1364.94	+	2364.14i	0.0451111	+	0.0781348i	−0.842588	+	0.538558i	$0.818969\pi$
$972$	−6999.12	−	13438.6i	−0.230964	−	0.443459i
$973$	−50785.3	+	18760.7i	−1.67328	+	0.618131i
$974$			5077.91i			0.167050i
$975$	9870.54	−	13340.4i	0.324216	−	0.438189i
$976$	1157.31	+	668.174i	0.0379556	+	0.0219137i
$977$	−49381.0	−	28510.2i	−1.61703	−	0.933593i	−0.987683	−	0.156470i	$-0.949989\pi$
$977$	−49381.0	−	28510.2i	−1.61703	−	0.933593i	−0.629348	−	0.777123i	$-0.716678\pi$
$978$	7127.47	−	9633.04i	0.233038	−	0.314960i
$979$			48117.6i			1.57083i
$980$	−8921.98	+	7633.49i	−0.290819	+	0.248819i
$981$	25890.7	−	27768.9i	0.842636	−	0.903763i
$982$	17119.1	+	29651.2i	0.556307	+	0.963552i
$983$	−26554.1	+	45993.0i	−0.861591	+	1.49232i	0.00880172	+	0.999961i	$0.497198\pi$
$983$	−26554.1	+	45993.0i	−0.861591	+	1.49232i	−0.870393	+	0.492358i	$0.836135\pi$
$984$	8682.19	+	988.855i	0.281279	+	0.0320361i
$985$	−17389.6	+	10039.9i	−0.562517	+	0.324770i
$986$	−2939.99			−0.0949577
$987$	15422.5	+	16095.3i	0.497369	+	0.519066i
$988$	−16707.6			−0.537994
$989$	16128.9	−	9312.03i	0.518574	−	0.299399i
$990$	−8405.63	−	27485.6i	−0.269847	−	0.882375i
$991$	9561.35	−	16560.7i	0.306485	−	0.530847i	−0.671106	−	0.741361i	$-0.734180\pi$
$991$	9561.35	−	16560.7i	0.306485	−	0.530847i	0.977591	+	0.210514i	$0.0675138\pi$
$992$	2477.15	+	4290.54i	0.0792838	+	0.137323i
$993$	1753.82	−	762.665i	0.0560480	−	0.0243731i
$994$	19045.7	−	22920.1i	0.607738	−	0.731370i
$995$		−	15674.7i		−	0.499417i
$996$	−22910.1	−	16951.1i	−0.728849	−	0.539274i
$997$	18152.4	+	10480.3i	0.576623	+	0.332914i	0.759790	−	0.650168i	$-0.225302\pi$
$997$	18152.4	+	10480.3i	0.576623	+	0.332914i	−0.183167	+	0.983082i	$0.558635\pi$
$998$	−1574.17	−	908.846i	−0.0499293	−	0.0288267i
$999$	43573.6	−	8081.36i	1.37999	−	0.255939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.4.f.a.17.7	yes	16
3.2	odd	2	inner	42.4.f.a.17.1	yes	16
4.3	odd	2		336.4.bc.e.17.4		16
7.2	even	3		294.4.f.a.215.4		16
7.3	odd	6		294.4.d.a.293.16		16
7.4	even	3		294.4.d.a.293.9		16
7.5	odd	6	inner	42.4.f.a.5.1	✓	16
7.6	odd	2		294.4.f.a.227.6		16
12.11	even	2		336.4.bc.e.17.7		16
21.2	odd	6		294.4.f.a.215.6		16
21.5	even	6	inner	42.4.f.a.5.7	yes	16
21.11	odd	6		294.4.d.a.293.8		16
21.17	even	6		294.4.d.a.293.1		16
21.20	even	2		294.4.f.a.227.4		16
28.19	even	6		336.4.bc.e.257.7		16
84.47	odd	6		336.4.bc.e.257.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.f.a.5.1	✓	16	7.5	odd	6	inner
42.4.f.a.5.7	yes	16	21.5	even	6	inner
42.4.f.a.17.1	yes	16	3.2	odd	2	inner
42.4.f.a.17.7	yes	16	1.1	even	1	trivial
294.4.d.a.293.1		16	21.17	even	6
294.4.d.a.293.8		16	21.11	odd	6
294.4.d.a.293.9		16	7.4	even	3
294.4.d.a.293.16		16	7.3	odd	6
294.4.f.a.215.4		16	7.2	even	3
294.4.f.a.215.6		16	21.2	odd	6
294.4.f.a.227.4		16	21.20	even	2
294.4.f.a.227.6		16	7.6	odd	2
336.4.bc.e.17.4		16	4.3	odd	2
336.4.bc.e.17.7		16	12.11	even	2
336.4.bc.e.257.4		16	84.47	odd	6
336.4.bc.e.257.7		16	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.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(0.588012 - 5.16277i) q^{3} +(2.00000 - 3.46410i) q^{4} +(4.27911 + 7.41164i) q^{5} +(-4.14431 - 9.53020i) q^{6} +(-6.41772 - 17.3728i) q^{7} -8.00000i q^{8} +(-26.3085 - 6.07155i) q^{9} +O(q^{10})\)	\(q+(1.73205 - 1.00000i) q^{2} +(0.588012 - 5.16277i) q^{3} +(2.00000 - 3.46410i) q^{4} +(4.27911 + 7.41164i) q^{5} +(-4.14431 - 9.53020i) q^{6} +(-6.41772 - 17.3728i) q^{7} -8.00000i q^{8} +(-26.3085 - 6.07155i) q^{9} +(14.8233 + 8.55823i) q^{10} +(53.8609 + 31.0966i) q^{11} +(-16.7084 - 12.3625i) q^{12} +61.7061i q^{13} +(-28.4886 - 23.6728i) q^{14} +(40.7808 - 17.7340i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-13.3365 + 23.0995i) q^{17} +(-51.6392 + 15.7922i) q^{18} +(-58.6213 + 33.8450i) q^{19} +34.2329 q^{20} +(-93.4654 + 22.9178i) q^{21} +124.386 q^{22} +(45.8287 - 26.4592i) q^{23} +(-41.3022 - 4.70410i) q^{24} +(25.8784 - 44.8227i) q^{25} +(61.7061 + 106.878i) q^{26} +(-46.8158 + 132.255i) q^{27} +(-73.0165 - 12.5139i) q^{28} +55.1116i q^{29} +(52.9005 - 71.4969i) q^{30} +(-134.080 - 77.4108i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(192.216 - 259.786i) q^{33} +53.3461i q^{34} +(101.299 - 121.906i) q^{35} +(-73.6494 + 78.9922i) q^{36} +(-157.940 - 273.560i) q^{37} +(-67.6901 + 117.243i) q^{38} +(318.575 + 36.2840i) q^{39} +(59.2931 - 34.2329i) q^{40} -210.211 q^{41} +(-138.969 + 133.160i) q^{42} +351.939 q^{43} +(215.443 - 124.386i) q^{44} +(-67.5768 - 220.970i) q^{45} +(52.9184 - 91.6574i) q^{46} +(-115.819 - 200.605i) q^{47} +(-76.2416 + 33.1545i) q^{48} +(-260.626 + 222.987i) q^{49} -103.514i q^{50} +(111.416 + 82.4363i) q^{51} +(213.756 + 123.412i) q^{52} +(-232.890 - 134.459i) q^{53} +(51.1673 + 275.887i) q^{54} +532.263i q^{55} +(-138.982 + 51.3417i) q^{56} +(140.264 + 322.550i) q^{57} +(55.1116 + 95.4561i) q^{58} +(-9.14155 + 15.8336i) q^{59} +(20.1294 - 176.737i) q^{60} +(-72.3320 + 41.7609i) q^{61} -309.643 q^{62} +(63.3607 + 496.017i) q^{63} -64.0000 q^{64} +(-457.344 + 264.047i) q^{65} +(73.1407 - 642.179i) q^{66} +(-64.7354 + 112.125i) q^{67} +(53.3461 + 92.3982i) q^{68} +(-109.655 - 252.162i) q^{69} +(53.5484 - 312.446i) q^{70} +804.537i q^{71} +(-48.5724 + 210.468i) q^{72} +(370.377 + 213.837i) q^{73} +(-547.120 - 315.880i) q^{74} +(-216.192 - 159.961i) q^{75} +270.760i q^{76} +(194.570 - 1135.28i) q^{77} +(588.072 - 255.729i) q^{78} +(-609.284 - 1055.31i) q^{79} +(68.4658 - 118.586i) q^{80} +(655.273 + 319.467i) q^{81} +(-364.097 + 210.211i) q^{82} +1371.18 q^{83} +(-107.541 + 369.609i) q^{84} -228.274 q^{85} +(609.577 - 351.939i) q^{86} +(284.529 + 32.4063i) q^{87} +(248.773 - 430.887i) q^{88} +(386.840 + 670.026i) q^{89} +(-338.016 - 315.154i) q^{90} +(1072.01 - 396.012i) q^{91} -211.674i q^{92} +(-478.495 + 646.704i) q^{93} +(-401.209 - 231.638i) q^{94} +(-501.694 - 289.653i) q^{95} +(-98.8999 + 133.667i) q^{96} -848.768i q^{97} +(-228.430 + 646.851i) q^{98} +(-1228.19 - 1145.12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} + 80 q^{7} + 18 q^{9}+O(q^{10}) \) 16 * q + 32 * q^4 + 80 * q^7 + 18 * q^9	\( 16 q + 32 q^{4} + 80 q^{7} + 18 q^{9} - 36 q^{10} - 128 q^{16} - 48 q^{18} - 342 q^{19} - 450 q^{21} + 24 q^{22} - 48 q^{24} - 194 q^{25} + 88 q^{28} + 360 q^{30} + 804 q^{31} + 1332 q^{33} + 144 q^{36} - 962 q^{37} + 594 q^{39} - 144 q^{40} - 180 q^{42} + 1732 q^{43} - 2394 q^{45} + 168 q^{46} + 820 q^{49} + 1638 q^{51} + 744 q^{52} + 180 q^{54} - 2664 q^{57} - 780 q^{58} - 4620 q^{61} - 2016 q^{63} - 1024 q^{64} - 2016 q^{66} - 706 q^{67} - 60 q^{70} + 192 q^{72} + 3294 q^{73} + 6174 q^{75} + 2832 q^{78} - 2656 q^{79} + 126 q^{81} + 432 q^{82} - 432 q^{84} + 5232 q^{85} + 1026 q^{87} + 48 q^{88} + 4098 q^{91} + 2016 q^{93} + 3888 q^{94} - 192 q^{96} - 4284 q^{99}+O(q^{100}) \) 16 * q + 32 * q^4 + 80 * q^7 + 18 * q^9 - 36 * q^10 - 128 * q^16 - 48 * q^18 - 342 * q^19 - 450 * q^21 + 24 * q^22 - 48 * q^24 - 194 * q^25 + 88 * q^28 + 360 * q^30 + 804 * q^31 + 1332 * q^33 + 144 * q^36 - 962 * q^37 + 594 * q^39 - 144 * q^40 - 180 * q^42 + 1732 * q^43 - 2394 * q^45 + 168 * q^46 + 820 * q^49 + 1638 * q^51 + 744 * q^52 + 180 * q^54 - 2664 * q^57 - 780 * q^58 - 4620 * q^61 - 2016 * q^63 - 1024 * q^64 - 2016 * q^66 - 706 * q^67 - 60 * q^70 + 192 * q^72 + 3294 * q^73 + 6174 * q^75 + 2832 * q^78 - 2656 * q^79 + 126 * q^81 + 432 * q^82 - 432 * q^84 + 5232 * q^85 + 1026 * q^87 + 48 * q^88 + 4098 * q^91 + 2016 * q^93 + 3888 * q^94 - 192 * q^96 - 4284 * q^99

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