LMFDB - Embedded newform 95.4.e.a.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,4,Mod(11,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("95.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	95.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.60518145055$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	95.26
Dual form			95.4.e.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(2.50000 + 4.33013i) q^{3} +(3.50000 - 6.06218i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-2.50000 + 4.33013i) q^{6} +22.0000 q^{7} +15.0000 q^{8} +(1.00000 - 1.73205i) q^{9} +(2.50000 - 4.33013i) q^{10} +9.00000 q^{11} +35.0000 q^{12} +(-27.0000 + 46.7654i) q^{13} +(11.0000 + 19.0526i) q^{14} +(12.5000 - 21.6506i) q^{15} +(-20.5000 - 35.5070i) q^{16} +(27.0000 + 46.7654i) q^{17} +2.00000 q^{18} +(-66.5000 + 49.3634i) q^{19} -35.0000 q^{20} +(55.0000 + 95.2628i) q^{21} +(4.50000 + 7.79423i) q^{22} +(46.0000 - 79.6743i) q^{23} +(37.5000 + 64.9519i) q^{24} +(-12.5000 + 21.6506i) q^{25} -54.0000 q^{26} +145.000 q^{27} +(77.0000 - 133.368i) q^{28} +(67.0000 - 116.047i) q^{29} +25.0000 q^{30} -252.000 q^{31} +(80.5000 - 139.430i) q^{32} +(22.5000 + 38.9711i) q^{33} +(-27.0000 + 46.7654i) q^{34} +(-55.0000 - 95.2628i) q^{35} +(-7.00000 - 12.1244i) q^{36} -236.000 q^{37} +(-76.0000 - 32.9090i) q^{38} -270.000 q^{39} +(-37.5000 - 64.9519i) q^{40} +(121.500 + 210.444i) q^{41} +(-55.0000 + 95.2628i) q^{42} +(-248.000 - 429.549i) q^{43} +(31.5000 - 54.5596i) q^{44} -10.0000 q^{45} +92.0000 q^{46} +(-251.000 + 434.745i) q^{47} +(102.500 - 177.535i) q^{48} +141.000 q^{49} -25.0000 q^{50} +(-135.000 + 233.827i) q^{51} +(189.000 + 327.358i) q^{52} +(-31.0000 + 53.6936i) q^{53} +(72.5000 + 125.574i) q^{54} +(-22.5000 - 38.9711i) q^{55} +330.000 q^{56} +(-380.000 - 164.545i) q^{57} +134.000 q^{58} +(-340.500 - 589.763i) q^{59} +(-87.5000 - 151.554i) q^{60} +(71.0000 - 122.976i) q^{61} +(-126.000 - 218.238i) q^{62} +(22.0000 - 38.1051i) q^{63} -167.000 q^{64} +270.000 q^{65} +(-22.5000 + 38.9711i) q^{66} +(-27.5000 + 47.6314i) q^{67} +378.000 q^{68} +460.000 q^{69} +(55.0000 - 95.2628i) q^{70} +(487.000 + 843.509i) q^{71} +(15.0000 - 25.9808i) q^{72} +(-347.500 - 601.888i) q^{73} +(-118.000 - 204.382i) q^{74} -125.000 q^{75} +(66.5000 + 575.907i) q^{76} +198.000 q^{77} +(-135.000 - 233.827i) q^{78} +(368.000 + 637.395i) q^{79} +(-102.500 + 177.535i) q^{80} +(335.500 + 581.103i) q^{81} +(-121.500 + 210.444i) q^{82} -63.0000 q^{83} +770.000 q^{84} +(135.000 - 233.827i) q^{85} +(248.000 - 429.549i) q^{86} +670.000 q^{87} +135.000 q^{88} +(-363.000 + 628.734i) q^{89} +(-5.00000 - 8.66025i) q^{90} +(-594.000 + 1028.84i) q^{91} +(-322.000 - 557.720i) q^{92} +(-630.000 - 1091.19i) q^{93} -502.000 q^{94} +(380.000 + 164.545i) q^{95} +805.000 q^{96} +(583.500 + 1010.65i) q^{97} +(70.5000 + 122.110i) q^{98} +(9.00000 - 15.5885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 5 q^{3} + 7 q^{4} - 5 q^{5} - 5 q^{6} + 44 q^{7} + 30 q^{8} + 2 q^{9} + 5 q^{10} + 18 q^{11} + 70 q^{12} - 54 q^{13} + 22 q^{14} + 25 q^{15} - 41 q^{16} + 54 q^{17} + 4 q^{18} - 133 q^{19}+ \cdots + 18 q^{99}+O(q^{100}) $ 2 * q + q^2 + 5 * q^3 + 7 * q^4 - 5 * q^5 - 5 * q^6 + 44 * q^7 + 30 * q^8 + 2 * q^9 + 5 * q^10 + 18 * q^11 + 70 * q^12 - 54 * q^13 + 22 * q^14 + 25 * q^15 - 41 * q^16 + 54 * q^17 + 4 * q^18 - 133 * q^19 - 70 * q^20 + 110 * q^21 + 9 * q^22 + 92 * q^23 + 75 * q^24 - 25 * q^25 - 108 * q^26 + 290 * q^27 + 154 * q^28 + 134 * q^29 + 50 * q^30 - 504 * q^31 + 161 * q^32 + 45 * q^33 - 54 * q^34 - 110 * q^35 - 14 * q^36 - 472 * q^37 - 152 * q^38 - 540 * q^39 - 75 * q^40 + 243 * q^41 - 110 * q^42 - 496 * q^43 + 63 * q^44 - 20 * q^45 + 184 * q^46 - 502 * q^47 + 205 * q^48 + 282 * q^49 - 50 * q^50 - 270 * q^51 + 378 * q^52 - 62 * q^53 + 145 * q^54 - 45 * q^55 + 660 * q^56 - 760 * q^57 + 268 * q^58 - 681 * q^59 - 175 * q^60 + 142 * q^61 - 252 * q^62 + 44 * q^63 - 334 * q^64 + 540 * q^65 - 45 * q^66 - 55 * q^67 + 756 * q^68 + 920 * q^69 + 110 * q^70 + 974 * q^71 + 30 * q^72 - 695 * q^73 - 236 * q^74 - 250 * q^75 + 133 * q^76 + 396 * q^77 - 270 * q^78 + 736 * q^79 - 205 * q^80 + 671 * q^81 - 243 * q^82 - 126 * q^83 + 1540 * q^84 + 270 * q^85 + 496 * q^86 + 1340 * q^87 + 270 * q^88 - 726 * q^89 - 10 * q^90 - 1188 * q^91 - 644 * q^92 - 1260 * q^93 - 1004 * q^94 + 760 * q^95 + 1610 * q^96 + 1167 * q^97 + 141 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.176777	+	0.306186i	0.940775	−	0.339032i	$-0.110100\pi$
$2$	0.500000	+	0.866025i	0.176777	+	0.306186i	−0.763998	+	0.645219i	$0.776766\pi$
$3$	2.50000	+	4.33013i	0.481125	+	0.833333i	0.999765	−	0.0216593i	$-0.00689490\pi$
$3$	2.50000	+	4.33013i	0.481125	+	0.833333i	−0.518640	+	0.854993i	$0.673562\pi$
$4$	3.50000	−	6.06218i	0.437500	−	0.757772i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$	−2.50000	+	4.33013i	−0.170103	+	0.294628i
$7$	22.0000			1.18789			0.593944	−	0.804506i	$-0.297570\pi$
$7$	22.0000			1.18789			0.593944	+	0.804506i	$0.297570\pi$
$8$	15.0000			0.662913
$9$	1.00000	−	1.73205i	0.0370370	−	0.0641500i
$10$	2.50000	−	4.33013i	0.0790569	−	0.136931i
$11$	9.00000			0.246691			0.123346	−	0.992364i	$-0.460638\pi$
$11$	9.00000			0.246691			0.123346	+	0.992364i	$0.460638\pi$
$12$	35.0000			0.841969
$13$	−27.0000	+	46.7654i	−0.576035	+	0.997722i	0.419894	+	0.907573i	$0.362067\pi$
$13$	−27.0000	+	46.7654i	−0.576035	+	0.997722i	−0.995928	+	0.0901482i	$0.971266\pi$
$14$	11.0000	+	19.0526i	0.209991	+	0.363715i
$15$	12.5000	−	21.6506i	0.215166	−	0.372678i
$16$	−20.5000	−	35.5070i	−0.320312	−	0.554798i
$17$	27.0000	+	46.7654i	0.385204	+	0.667192i	0.991797	−	0.127820i	$-0.0407979\pi$
$17$	27.0000	+	46.7654i	0.385204	+	0.667192i	−0.606594	+	0.795012i	$0.707465\pi$
$18$	2.00000			0.0261891
$19$	−66.5000	+	49.3634i	−0.802955	+	0.596040i
$19$	−66.5000	+	49.3634i	−0.802955	+	0.596040i
$20$	−35.0000			−0.391312
$21$	55.0000	+	95.2628i	0.571523	+	0.989907i
$22$	4.50000	+	7.79423i	0.0436092	+	0.0755334i
$23$	46.0000	−	79.6743i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	46.0000	−	79.6743i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$	37.5000	+	64.9519i	0.318944	+	0.552427i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−54.0000			−0.407318
$27$	145.000			1.03353
$28$	77.0000	−	133.368i	0.519701	−	0.900149i
$29$	67.0000	−	116.047i	0.429020	−	0.743085i	−0.567766	−	0.823190i	$-0.692192\pi$
$29$	67.0000	−	116.047i	0.429020	−	0.743085i	0.996786	+	0.0801050i	$0.0255256\pi$
$30$	25.0000			0.152145
$31$	−252.000			−1.46002			−0.730009	−	0.683438i	$-0.760484\pi$
$31$	−252.000			−1.46002			−0.730009	+	0.683438i	$0.760484\pi$
$32$	80.5000	−	139.430i	0.444704	−	0.770250i
$33$	22.5000	+	38.9711i	0.118689	+	0.205576i
$34$	−27.0000	+	46.7654i	−0.136190	+	0.235888i
$35$	−55.0000	−	95.2628i	−0.265620	−	0.460067i
$36$	−7.00000	−	12.1244i	−0.0324074	−	0.0561313i
$37$	−236.000			−1.04860			−0.524299	−	0.851534i	$-0.675673\pi$
$37$	−236.000			−1.04860			−0.524299	+	0.851534i	$0.675673\pi$
$38$	−76.0000	−	32.9090i	−0.324443	−	0.140488i
$39$	−270.000			−1.10858
$40$	−37.5000	−	64.9519i	−0.148232	−	0.256745i
$41$	121.500	+	210.444i	0.462808	+	0.801606i	0.999100	−	0.0424262i	$-0.0135087\pi$
$41$	121.500	+	210.444i	0.462808	+	0.801606i	−0.536292	+	0.844033i	$0.680175\pi$
$42$	−55.0000	+	95.2628i	−0.202064	+	0.349985i
$43$	−248.000	−	429.549i	−0.879527	−	1.52338i	−0.851861	−	0.523768i	$-0.824526\pi$
$43$	−248.000	−	429.549i	−0.879527	−	1.52338i	−0.0276654	−	0.999617i	$-0.508807\pi$
$44$	31.5000	−	54.5596i	0.107927	−	0.186936i
$45$	−10.0000			−0.0331269
$46$	92.0000			0.294884
$47$	−251.000	+	434.745i	−0.778981	+	1.34923i	0.153548	+	0.988141i	$0.450930\pi$
$47$	−251.000	+	434.745i	−0.778981	+	1.34923i	−0.932530	+	0.361094i	$0.882403\pi$
$48$	102.500	−	177.535i	0.308221	−	0.533854i
$49$	141.000			0.411079
$50$	−25.0000			−0.0707107
$51$	−135.000	+	233.827i	−0.370662	+	0.642006i
$52$	189.000	+	327.358i	0.504030	+	0.873006i
$53$	−31.0000	+	53.6936i	−0.0803430	+	0.139158i	−0.903397	−	0.428805i	$-0.858935\pi$
$53$	−31.0000	+	53.6936i	−0.0803430	+	0.139158i	0.823054	+	0.567963i	$0.192268\pi$
$54$	72.5000	+	125.574i	0.182704	+	0.316452i
$55$	−22.5000	−	38.9711i	−0.0551618	−	0.0955431i
$56$	330.000			0.787466
$57$	−380.000	−	164.545i	−0.883022	−	0.382360i
$58$	134.000			0.303363
$59$	−340.500	−	589.763i	−0.751344	−	1.30137i	−0.947171	−	0.320728i	$-0.896072\pi$
$59$	−340.500	−	589.763i	−0.751344	−	1.30137i	0.195827	−	0.980639i	$-0.437261\pi$
$60$	−87.5000	−	151.554i	−0.188270	−	0.326093i
$61$	71.0000	−	122.976i	0.149027	−	0.258122i	−0.781841	−	0.623477i	$-0.785719\pi$
$61$	71.0000	−	122.976i	0.149027	−	0.258122i	0.930868	+	0.365356i	$0.119053\pi$
$62$	−126.000	−	218.238i	−0.258097	−	0.447037i
$63$	22.0000	−	38.1051i	0.0439959	−	0.0762031i
$64$	−167.000			−0.326172
$65$	270.000			0.515221
$66$	−22.5000	+	38.9711i	−0.0419630	+	0.0726821i
$67$	−27.5000	+	47.6314i	−0.0501442	+	0.0868523i	−0.890008	−	0.455945i	$-0.849301\pi$
$67$	−27.5000	+	47.6314i	−0.0501442	+	0.0868523i	0.839864	+	0.542797i	$0.182635\pi$
$68$	378.000			0.674106
$69$	460.000			0.802572
$70$	55.0000	−	95.2628i	0.0939108	−	0.162658i
$71$	487.000	+	843.509i	0.814032	+	1.40994i	0.910021	+	0.414562i	$0.136065\pi$
$71$	487.000	+	843.509i	0.814032	+	1.40994i	−0.0959890	+	0.995382i	$0.530601\pi$
$72$	15.0000	−	25.9808i	0.0245523	−	0.0425259i
$73$	−347.500	−	601.888i	−0.557148	−	0.965009i	−0.997733	−	0.0672976i	$-0.978562\pi$
$73$	−347.500	−	601.888i	−0.557148	−	0.965009i	0.440585	−	0.897711i	$-0.354771\pi$
$74$	−118.000	−	204.382i	−0.185368	−	0.321067i
$75$	−125.000			−0.192450
$76$	66.5000	+	575.907i	0.100369	+	0.869224i
$77$	198.000			0.293041
$78$	−135.000	−	233.827i	−0.195971	−	0.339432i
$79$	368.000	+	637.395i	0.524092	+	0.907753i	0.999607	+	0.0280457i	$0.00892838\pi$
$79$	368.000	+	637.395i	0.524092	+	0.907753i	−0.475515	+	0.879708i	$0.657738\pi$
$80$	−102.500	+	177.535i	−0.143248	+	0.248113i
$81$	335.500	+	581.103i	0.460219	+	0.797124i
$82$	−121.500	+	210.444i	−0.163627	+	0.283411i
$83$	−63.0000			−0.0833150			−0.0416575	−	0.999132i	$-0.513264\pi$
$83$	−63.0000			−0.0833150			−0.0416575	+	0.999132i	$0.513264\pi$
$84$	770.000			1.00017
$85$	135.000	−	233.827i	0.172268	−	0.298377i
$86$	248.000	−	429.549i	0.310960	−	0.538598i
$87$	670.000			0.825650
$88$	135.000			0.163535
$89$	−363.000	+	628.734i	−0.432336	+	0.748828i	−0.997074	−	0.0764421i	$-0.975644\pi$
$89$	−363.000	+	628.734i	−0.432336	+	0.748828i	0.564738	+	0.825270i	$0.308977\pi$
$90$	−5.00000	−	8.66025i	−0.00585607	−	0.0101430i
$91$	−594.000	+	1028.84i	−0.684265	+	1.18518i
$92$	−322.000	−	557.720i	−0.364900	−	0.632026i
$93$	−630.000	−	1091.19i	−0.702451	−	1.21668i
$94$	−502.000			−0.550823
$95$	380.000	+	164.545i	0.410391	+	0.177705i
$96$	805.000			0.855833
$97$	583.500	+	1010.65i	0.610778	+	1.05790i	0.991110	+	0.133048i	$0.0424765\pi$
$97$	583.500	+	1010.65i	0.610778	+	1.05790i	−0.380332	+	0.924850i	$0.624190\pi$
$98$	70.5000	+	122.110i	0.0726691	+	0.125867i
$99$	9.00000	−	15.5885i	0.00913671	−	0.0158252i
$100$	87.5000	+	151.554i	0.0875000	+	0.151554i
$101$	15.0000	−	25.9808i	0.0147778	−	0.0255959i	−0.858542	−	0.512743i	$-0.828629\pi$
$101$	15.0000	−	25.9808i	0.0147778	−	0.0255959i	0.873320	+	0.487147i	$0.161963\pi$
$102$	−270.000			−0.262098
$103$	−602.000			−0.575891			−0.287946	−	0.957647i	$-0.592972\pi$
$103$	−602.000			−0.575891			−0.287946	+	0.957647i	$0.592972\pi$
$104$	−405.000	+	701.481i	−0.381861	+	0.661402i
$105$	275.000	−	476.314i	0.255593	−	0.442700i
$106$	−62.0000			−0.0568111
$107$	660.000			0.596305			0.298152	−	0.954518i	$-0.403630\pi$
$107$	660.000			0.596305			0.298152	+	0.954518i	$0.403630\pi$
$108$	507.500	−	879.016i	0.452169	−	0.783179i
$109$	60.0000	+	103.923i	0.0527244	+	0.0913213i	0.891183	−	0.453644i	$-0.149876\pi$
$109$	60.0000	+	103.923i	0.0527244	+	0.0913213i	−0.838459	+	0.544965i	$0.816543\pi$
$110$	22.5000	−	38.9711i	0.0195026	−	0.0337796i
$111$	−590.000	−	1021.91i	−0.504507	−	0.873832i
$112$	−451.000	−	781.155i	−0.380495	−	0.659038i
$113$	1059.00			0.881614			0.440807	−	0.897602i	$-0.354692\pi$
$113$	1059.00			0.881614			0.440807	+	0.897602i	$0.354692\pi$
$114$	−47.5000	−	411.362i	−0.0390244	−	0.337961i
$115$	−460.000			−0.373002
$116$	−469.000	−	812.332i	−0.375393	−	0.650199i
$117$	54.0000	+	93.5307i	0.0426692	+	0.0739053i
$118$	340.500	−	589.763i	0.265640	−	0.460103i
$119$	594.000	+	1028.84i	0.457579	+	0.792550i
$120$	187.500	−	324.760i	0.142636	−	0.247053i
$121$	−1250.00			−0.939144
$122$	142.000			0.105378
$123$	−607.500	+	1052.22i	−0.445337	+	0.771346i
$124$	−882.000	+	1527.67i	−0.638758	+	1.10636i
$125$	125.000			0.0894427
$126$	44.0000			0.0311098
$127$	−59.0000	+	102.191i	−0.0412236	+	0.0714015i	−0.885901	−	0.463874i	$-0.846459\pi$
$127$	−59.0000	+	102.191i	−0.0412236	+	0.0714015i	0.844677	+	0.535276i	$0.179792\pi$
$128$	−727.500	−	1260.07i	−0.502363	−	0.870119i
$129$	1240.00	−	2147.74i	0.846325	−	1.46588i
$130$	135.000	+	233.827i	0.0910791	+	0.157754i
$131$	−333.500	−	577.639i	−0.222428	−	0.385256i	0.733117	−	0.680103i	$-0.238065\pi$
$131$	−333.500	−	577.639i	−0.222428	−	0.385256i	−0.955545	+	0.294847i	$0.904731\pi$
$132$	315.000			0.207706
$133$	−1463.00	+	1086.00i	−0.953821	+	0.708028i
$134$	−55.0000			−0.0354573
$135$	−362.500	−	627.868i	−0.231104	−	0.400284i
$136$	405.000	+	701.481i	0.255356	+	0.442290i
$137$	525.500	−	910.193i	0.327712	−	0.567613i	−0.654346	−	0.756196i	$-0.727056\pi$
$137$	525.500	−	910.193i	0.327712	−	0.567613i	0.982057	+	0.188582i	$0.0603892\pi$
$138$	230.000	+	398.372i	0.141876	+	0.245737i
$139$	417.500	−	723.131i	0.254762	−	0.441260i	−0.710069	−	0.704132i	$-0.751336\pi$
$139$	417.500	−	723.131i	0.254762	−	0.441260i	0.964831	+	0.262872i	$0.0846696\pi$
$140$	−770.000			−0.464835
$141$	−2510.00			−1.49915
$142$	−487.000	+	843.509i	−0.287804	+	0.498491i
$143$	−243.000	+	420.888i	−0.142103	+	0.246129i
$144$	−82.0000			−0.0474537
$145$	−670.000			−0.383727
$146$	347.500	−	601.888i	0.196982	−	0.341182i
$147$	352.500	+	610.548i	0.197780	+	0.342566i
$148$	−826.000	+	1430.67i	−0.458762	+	0.794599i
$149$	−1368.00	−	2369.45i	−0.752154	−	1.30277i	−0.946777	−	0.321891i	$-0.895682\pi$
$149$	−1368.00	−	2369.45i	−0.752154	−	1.30277i	0.194623	−	0.980878i	$-0.437652\pi$
$150$	−62.5000	−	108.253i	−0.0340207	−	0.0589256i
$151$	−376.000			−0.202639			−0.101319	−	0.994854i	$-0.532306\pi$
$151$	−376.000			−0.202639			−0.101319	+	0.994854i	$0.532306\pi$
$152$	−997.500	+	740.452i	−0.532289	+	0.395122i
$153$	108.000			0.0570672
$154$	99.0000	+	171.473i	0.0518029	+	0.0897253i
$155$	630.000	+	1091.19i	0.326470	+	0.565462i
$156$	−945.000	+	1636.79i	−0.485004	+	0.840051i
$157$	496.000	+	859.097i	0.252134	+	0.436710i	0.964113	−	0.265491i	$-0.0855341\pi$
$157$	496.000	+	859.097i	0.252134	+	0.436710i	−0.711979	+	0.702201i	$0.752201\pi$
$158$	−368.000	+	637.395i	−0.185294	+	0.320939i
$159$	−310.000			−0.154620
$160$	−805.000			−0.397755
$161$	1012.00	−	1752.84i	0.495384	−	0.858030i
$162$	−335.500	+	581.103i	−0.162712	+	0.281826i
$163$	3047.00			1.46417			0.732084	−	0.681214i	$-0.238548\pi$
$163$	3047.00			1.46417			0.732084	+	0.681214i	$0.238548\pi$
$164$	1701.00			0.809913
$165$	112.500	−	194.856i	0.0530795	−	0.0919363i
$166$	−31.5000	−	54.5596i	−0.0147282	−	0.0255099i
$167$	652.000	−	1129.30i	0.302115	−	0.523279i	−0.674500	−	0.738275i	$-0.735641\pi$
$167$	652.000	−	1129.30i	0.302115	−	0.523279i	0.976615	+	0.214996i	$0.0689739\pi$
$168$	825.000	+	1428.94i	0.378870	+	0.656222i
$169$	−359.500	−	622.672i	−0.163632	−	0.283419i
$170$	270.000			0.121812
$171$	19.0000	+	164.545i	0.00849688	+	0.0735851i
$172$	−3472.00			−1.53917
$173$	−99.0000	−	171.473i	−0.0435077	−	0.0753575i	0.843452	−	0.537205i	$-0.180520\pi$
$173$	−99.0000	−	171.473i	−0.0435077	−	0.0753575i	−0.886959	+	0.461848i	$0.847187\pi$
$174$	335.000	+	580.237i	0.145956	+	0.252803i
$175$	−275.000	+	476.314i	−0.118789	+	0.205748i
$176$	−184.500	−	319.563i	−0.0790182	−	0.136864i
$177$	1702.50	−	2948.82i	0.722982	−	1.25224i
$178$	−726.000			−0.305708
$179$	−1265.00			−0.528215			−0.264108	−	0.964493i	$-0.585077\pi$
$179$	−1265.00			−0.528215			−0.264108	+	0.964493i	$0.585077\pi$
$180$	−35.0000	+	60.6218i	−0.0144930	+	0.0251027i
$181$	2038.00	−	3529.92i	0.836925	−	1.44960i	−0.0555292	−	0.998457i	$-0.517685\pi$
$181$	2038.00	−	3529.92i	0.836925	−	1.44960i	0.892454	−	0.451139i	$-0.148982\pi$
$182$	−1188.00			−0.483848
$183$	710.000			0.286802
$184$	690.000	−	1195.12i	0.276454	−	0.478832i
$185$	590.000	+	1021.91i	0.234474	+	0.406121i
$186$	630.000	−	1091.19i	0.248354	−	0.430162i
$187$	243.000	+	420.888i	0.0950263	+	0.164590i
$188$	1757.00	+	3043.21i	0.681608	+	1.18058i
$189$	3190.00			1.22772
$190$	47.5000	+	411.362i	0.0181369	+	0.157070i
$191$	3292.00			1.24712			0.623562	−	0.781774i	$-0.285685\pi$
$191$	3292.00			1.24712			0.623562	+	0.781774i	$0.285685\pi$
$192$	−417.500	−	723.131i	−0.156930	−	0.271810i
$193$	−969.000	−	1678.36i	−0.361400	−	0.625963i	0.626792	−	0.779187i	$-0.284368\pi$
$193$	−969.000	−	1678.36i	−0.361400	−	0.625963i	−0.988191	+	0.153224i	$0.951034\pi$
$194$	−583.500	+	1010.65i	−0.215943	+	0.374024i
$195$	675.000	+	1169.13i	0.247886	+	0.429351i
$196$	493.500	−	854.767i	0.179847	−	0.311504i
$197$	4524.00			1.63615			0.818075	−	0.575111i	$-0.195041\pi$
$197$	4524.00			1.63615			0.818075	+	0.575111i	$0.195041\pi$
$198$	18.0000			0.00646063
$199$	−2141.00	+	3708.32i	−0.762671	+	1.32098i	0.178799	+	0.983886i	$0.442779\pi$
$199$	−2141.00	+	3708.32i	−0.762671	+	1.32098i	−0.941469	+	0.337099i	$0.890554\pi$
$200$	−187.500	+	324.760i	−0.0662913	+	0.114820i
$201$	−275.000			−0.0965025
$202$	30.0000			0.0104495
$203$	1474.00	−	2553.04i	0.509628	−	0.882702i
$204$	945.000	+	1636.79i	0.324330	+	0.561755i
$205$	607.500	−	1052.22i	0.206974	−	0.358489i
$206$	−301.000	−	521.347i	−0.101804	−	0.176330i
$207$	−92.0000	−	159.349i	−0.0308910	−	0.0535048i
$208$	2214.00			0.738045
$209$	−598.500	+	444.271i	−0.198082	+	0.147038i
$210$	550.000			0.180731
$211$	970.000	+	1680.09i	0.316481	+	0.548162i	0.979751	−	0.200219i	$-0.0641652\pi$
$211$	970.000	+	1680.09i	0.316481	+	0.548162i	−0.663270	+	0.748380i	$0.730832\pi$
$212$	217.000	+	375.855i	0.0703001	+	0.121763i
$213$	−2435.00	+	4217.54i	−0.783303	+	1.35672i
$214$	330.000	+	571.577i	0.105413	+	0.182580i
$215$	−1240.00	+	2147.74i	−0.393336	+	0.681278i
$216$	2175.00			0.685139
$217$	−5544.00			−1.73434
$218$	−60.0000	+	103.923i	−0.0186409	+	0.0322870i
$219$	1737.50	−	3009.44i	0.536116	−	0.928580i
$220$	−315.000			−0.0965332
$221$	−2916.00			−0.887563
$222$	590.000	−	1021.91i	0.178370	−	0.308946i
$223$	2078.00	+	3599.20i	0.624005	+	1.08081i	0.988732	+	0.149694i	$0.0478290\pi$
$223$	2078.00	+	3599.20i	0.624005	+	1.08081i	−0.364727	+	0.931114i	$0.618838\pi$
$224$	1771.00	−	3067.46i	0.528259	−	0.914971i
$225$	25.0000	+	43.3013i	0.00740741	+	0.0128300i
$226$	529.500	+	917.121i	0.155849	+	0.269938i
$227$	2093.00			0.611970			0.305985	−	0.952036i	$-0.401014\pi$
$227$	2093.00			0.611970			0.305985	+	0.952036i	$0.401014\pi$
$228$	−2327.50	+	1727.72i	−0.676063	+	0.501847i
$229$	−4312.00			−1.24430			−0.622151	−	0.782898i	$-0.713741\pi$
$229$	−4312.00			−1.24430			−0.622151	+	0.782898i	$0.713741\pi$
$230$	−230.000	−	398.372i	−0.0659380	−	0.114208i
$231$	495.000	+	857.365i	0.140990	+	0.244201i
$232$	1005.00	−	1740.71i	0.284403	−	0.492600i
$233$	2114.50	+	3662.42i	0.594530	+	1.02976i	0.993613	+	0.112841i	$0.0359952\pi$
$233$	2114.50	+	3662.42i	0.594530	+	1.02976i	−0.399083	+	0.916915i	$0.630671\pi$
$234$	−54.0000	+	93.5307i	−0.0150859	+	0.0261295i
$235$	2510.00			0.696742
$236$	−4767.00			−1.31485
$237$	−1840.00	+	3186.97i	−0.504307	+	0.873486i
$238$	−594.000	+	1028.84i	−0.161779	+	0.280209i
$239$	−5556.00			−1.50371			−0.751857	−	0.659326i	$-0.770842\pi$
$239$	−5556.00			−1.50371			−0.751857	+	0.659326i	$0.770842\pi$
$240$	−1025.00			−0.275681
$241$	2209.50	−	3826.97i	0.590566	−	1.02289i	−0.403590	−	0.914940i	$-0.632238\pi$
$241$	2209.50	−	3826.97i	0.590566	−	1.02289i	0.994156	−	0.107950i	$-0.0344288\pi$
$242$	−625.000	−	1082.53i	−0.166019	−	0.287553i
$243$	280.000	−	484.974i	0.0739177	−	0.128029i
$244$	−497.000	−	860.829i	−0.130398	−	0.225856i
$245$	−352.500	−	610.548i	−0.0919200	−	0.159210i
$246$	−1215.00			−0.314901
$247$	−513.000	−	4442.71i	−0.132151	−	1.14447i
$248$	−3780.00			−0.967864
$249$	−157.500	−	272.798i	−0.0400850	−	0.0694292i
$250$	62.5000	+	108.253i	0.0158114	+	0.0273861i
$251$	1978.50	−	3426.86i	0.497537	−	0.861760i	−0.502459	−	0.864601i	$-0.667571\pi$
$251$	1978.50	−	3426.86i	0.497537	−	0.861760i	0.999996	+	0.00284158i	$0.000904504\pi$
$252$	−154.000	−	266.736i	−0.0384964	−	0.0666777i
$253$	414.000	−	717.069i	0.102877	−	0.178189i
$254$	−118.000			−0.0291495
$255$	1350.00			0.331531
$256$	59.5000	−	103.057i	0.0145264	−	0.0251604i
$257$	438.500	−	759.504i	0.106431	−	0.184345i	−0.807891	−	0.589332i	$-0.799391\pi$
$257$	438.500	−	759.504i	0.106431	−	0.184345i	0.914322	+	0.404988i	$0.132724\pi$
$258$	2480.00			0.598442
$259$	−5192.00			−1.24562
$260$	945.000	−	1636.79i	0.225409	−	0.390420i
$261$	−134.000	−	232.095i	−0.0317793	−	0.0550433i
$262$	333.500	−	577.639i	0.0786401	−	0.136209i
$263$	1215.00	+	2104.44i	0.284867	+	0.493405i	0.972577	−	0.232581i	$-0.0747171\pi$
$263$	1215.00	+	2104.44i	0.284867	+	0.493405i	−0.687710	+	0.725986i	$0.741384\pi$
$264$	337.500	+	584.567i	0.0786806	+	0.136279i
$265$	310.000			0.0718609
$266$	−1672.00	−	723.997i	−0.385402	−	0.166884i
$267$	−3630.00			−0.832031
$268$	192.500	+	333.420i	0.0438762	+	0.0759957i
$269$	−2346.00	−	4063.39i	−0.531740	−	0.921001i	−0.999314	−	0.0370469i	$-0.988205\pi$
$269$	−2346.00	−	4063.39i	−0.531740	−	0.921001i	0.467573	−	0.883954i	$-0.345128\pi$
$270$	362.500	−	627.868i	0.0817076	−	0.141522i
$271$	4381.00	+	7588.11i	0.982018	+	1.70090i	0.654505	+	0.756058i	$0.272877\pi$
$271$	4381.00	+	7588.11i	0.982018	+	1.70090i	0.327513	+	0.944847i	$0.393790\pi$
$272$	1107.00	−	1917.38i	0.246771	−	0.427420i
$273$	−5940.00			−1.31687
$274$	1051.00			0.231727
$275$	−112.500	+	194.856i	−0.0246691	+	0.0427282i
$276$	1610.00	−	2788.60i	0.351125	−	0.608167i
$277$	5014.00			1.08759			0.543794	−	0.839219i	$-0.316987\pi$
$277$	5014.00			1.08759			0.543794	+	0.839219i	$0.316987\pi$
$278$	835.000			0.180144
$279$	−252.000	+	436.477i	−0.0540747	+	0.0936602i
$280$	−825.000	−	1428.94i	−0.176083	−	0.304984i
$281$	1932.50	−	3347.19i	0.410261	−	0.710593i	−0.584657	−	0.811280i	$-0.698771\pi$
$281$	1932.50	−	3347.19i	0.410261	−	0.710593i	0.994918	+	0.100688i	$0.0321043\pi$
$282$	−1255.00	−	2173.72i	−0.265015	−	0.459019i
$283$	296.500	+	513.553i	0.0622795	+	0.107871i	0.895484	−	0.445094i	$-0.146830\pi$
$283$	296.500	+	513.553i	0.0622795	+	0.107871i	−0.833204	+	0.552965i	$0.813496\pi$
$284$	6818.00			1.42456
$285$	237.500	+	2056.81i	0.0493624	+	0.427491i
$286$	−486.000			−0.100482
$287$	2673.00	+	4629.77i	0.549764	+	0.952219i
$288$	−161.000	−	278.860i	−0.0329410	−	0.0570555i
$289$	998.500	−	1729.45i	0.203236	−	0.352016i
$290$	−335.000	−	580.237i	−0.0678341	−	0.117492i
$291$	−2917.50	+	5053.26i	−0.587721	+	1.01796i
$292$	−4865.00			−0.975009
$293$	−5838.00			−1.16403			−0.582013	−	0.813180i	$-0.697735\pi$
$293$	−5838.00			−1.16403			−0.582013	+	0.813180i	$0.697735\pi$
$294$	−352.500	+	610.548i	−0.0699259	+	0.121115i
$295$	−1702.50	+	2948.82i	−0.336011	+	0.581989i
$296$	−3540.00			−0.695129
$297$	1305.00			0.254962
$298$	1368.00	−	2369.45i	0.265927	−	0.460598i
$299$	2484.00	+	4302.41i	0.480446	+	0.832157i
$300$	−437.500	+	757.772i	−0.0841969	+	0.145833i
$301$	−5456.00	−	9450.07i	−1.04478	−	1.80961i
$302$	−188.000	−	325.626i	−0.0358218	−	0.0620452i
$303$	150.000			0.0284399
$304$	3116.00	+	1349.27i	0.587878	+	0.254559i
$305$	−710.000			−0.133293
$306$	54.0000	+	93.5307i	0.0100882	+	0.0174732i
$307$	−123.500	−	213.908i	−0.0229593	−	0.0397667i	0.854317	−	0.519752i	$-0.173975\pi$
$307$	−123.500	−	213.908i	−0.0229593	−	0.0397667i	−0.877277	+	0.479985i	$0.840642\pi$
$308$	693.000	−	1200.31i	0.128206	−	0.222059i
$309$	−1505.00	−	2606.74i	−0.277076	−	0.479910i
$310$	−630.000	+	1091.19i	−0.115425	+	0.199921i
$311$	−10220.0			−1.86342			−0.931709	−	0.363206i	$-0.881682\pi$
$311$	−10220.0			−1.86342			−0.931709	+	0.363206i	$0.881682\pi$
$312$	−4050.00			−0.734891
$313$	3917.50	−	6785.31i	0.707445	−	1.22533i	−0.258357	−	0.966049i	$-0.583181\pi$
$313$	3917.50	−	6785.31i	0.707445	−	1.22533i	0.965802	−	0.259281i	$-0.0834855\pi$
$314$	−496.000	+	859.097i	−0.0891430	+	0.154400i
$315$	−220.000			−0.0393511
$316$	5152.00			0.917160
$317$	1887.00	−	3268.38i	0.334336	−	0.579087i	−0.649021	−	0.760770i	$-0.724821\pi$
$317$	1887.00	−	3268.38i	0.334336	−	0.579087i	0.983357	+	0.181684i	$0.0581547\pi$
$318$	−155.000	−	268.468i	−0.0273332	−	0.0473425i
$319$	603.000	−	1044.43i	0.105835	−	0.183312i
$320$	417.500	+	723.131i	0.0729342	+	0.126326i
$321$	1650.00	+	2857.88i	0.286897	+	0.496921i
$322$	2024.00			0.350289
$323$	−4104.00	−	1777.08i	−0.706974	−	0.306129i
$324$	4697.00			0.805384
$325$	−675.000	−	1169.13i	−0.115207	−	0.199544i
$326$	1523.50	+	2638.78i	0.258831	+	0.448308i
$327$	−300.000	+	519.615i	−0.0507341	+	0.0878740i
$328$	1822.50	+	3156.66i	0.306801	+	0.531395i
$329$	−5522.00	+	9564.38i	−0.925343	+	1.60274i
$330$	225.000			0.0375329
$331$	−5.00000			−0.000830287			−0.000415143	−	1.00000i	$-0.500132\pi$
$331$	−5.00000			−0.000830287			−0.000415143		1.00000i	$0.500132\pi$
$332$	−220.500	+	381.917i	−0.0364503	+	0.0631338i
$333$	−236.000	+	408.764i	−0.0388370	+	0.0672677i
$334$	1304.00			0.213628
$335$	275.000			0.0448503
$336$	2255.00	−	3905.77i	0.366132	−	0.634159i
$337$	3178.50	+	5505.32i	0.513780	+	0.889893i	0.999872	+	0.0159858i	$0.00508865\pi$
$337$	3178.50	+	5505.32i	0.513780	+	0.889893i	−0.486092	+	0.873908i	$0.661578\pi$
$338$	359.500	−	622.672i	0.0578527	−	0.100204i
$339$	2647.50	+	4585.60i	0.424167	+	0.734678i
$340$	−945.000	−	1636.79i	−0.150735	−	0.261080i
$341$	−2268.00			−0.360173
$342$	−133.000	+	98.7269i	−0.0210287	+	0.0156098i
$343$	−4444.00			−0.699573
$344$	−3720.00	−	6443.23i	−0.583049	−	1.00987i
$345$	−1150.00	−	1991.86i	−0.179461	−	0.310835i
$346$	99.0000	−	171.473i	0.0153823	−	0.0266429i
$347$	6279.50	+	10876.4i	0.971473	+	1.68264i	0.691114	+	0.722746i	$0.257120\pi$
$347$	6279.50	+	10876.4i	0.971473	+	1.68264i	0.280359	+	0.959895i	$0.409546\pi$
$348$	2345.00	−	4061.66i	0.361222	−	0.625655i
$349$	7336.00			1.12518			0.562589	−	0.826737i	$-0.309805\pi$
$349$	7336.00			1.12518			0.562589	+	0.826737i	$0.309805\pi$
$350$	−550.000			−0.0839964
$351$	−3915.00	+	6780.98i	−0.595348	+	1.03117i
$352$	724.500	−	1254.87i	0.109704	−	0.190014i
$353$	10451.0			1.57578			0.787890	−	0.615816i	$-0.211173\pi$
$353$	10451.0			1.57578			0.787890	+	0.615816i	$0.211173\pi$
$354$	3405.00			0.511225
$355$	2435.00	−	4217.54i	0.364046	−	0.630546i
$356$	2541.00	+	4401.14i	0.378294	+	0.655225i
$357$	−2970.00	+	5144.19i	−0.440306	+	0.762632i
$358$	−632.500	−	1095.52i	−0.0933762	−	0.161732i
$359$	−3650.00	−	6321.99i	−0.536601	−	0.929420i	−0.999084	−	0.0427916i	$-0.986375\pi$
$359$	−3650.00	−	6321.99i	−0.536601	−	0.929420i	0.462483	−	0.886628i	$-0.346958\pi$
$360$	−150.000			−0.0219603
$361$	1985.50	−	6565.34i	0.289474	−	0.957186i
$362$	4076.00			0.591795
$363$	−3125.00	−	5412.66i	−0.451846	−	0.782620i
$364$	4158.00	+	7201.87i	0.598732	+	1.03703i
$365$	−1737.50	+	3009.44i	−0.249164	+	0.431565i
$366$	355.000	+	614.878i	0.0506999	+	0.0878147i
$367$	316.000	−	547.328i	0.0449457	−	0.0778482i	−0.842677	−	0.538419i	$-0.819022\pi$
$367$	316.000	−	547.328i	0.0449457	−	0.0778482i	0.887623	+	0.460571i	$0.152355\pi$
$368$	−3772.00			−0.534318
$369$	486.000			0.0685641
$370$	−590.000	+	1021.91i	−0.0828990	+	0.143585i
$371$	−682.000	+	1181.26i	−0.0954385	+	0.165304i
$372$	−8820.00			−1.22929
$373$	−96.0000			−0.0133263			−0.00666313	−	0.999978i	$-0.502121\pi$
$373$	−96.0000			−0.0133263			−0.00666313	+	0.999978i	$0.502121\pi$
$374$	−243.000	+	420.888i	−0.0335969	+	0.0581915i
$375$	312.500	+	541.266i	0.0430331	+	0.0745356i
$376$	−3765.00	+	6521.17i	−0.516396	+	0.894425i
$377$	3618.00	+	6266.56i	0.494261	+	0.856086i
$378$	1595.00	+	2762.62i	0.217032	+	0.375910i
$379$	10964.0			1.48597			0.742985	−	0.669308i	$-0.233409\pi$
$379$	10964.0			1.48597			0.742985	+	0.669308i	$0.233409\pi$
$380$	2327.50	−	1727.72i	0.314206	−	0.233237i
$381$	−590.000			−0.0793349
$382$	1646.00	+	2850.96i	0.220463	+	0.381852i
$383$	−1009.00	−	1747.64i	−0.134615	−	0.233160i	0.790835	−	0.612029i	$-0.209646\pi$
$383$	−1009.00	−	1747.64i	−0.134615	−	0.233160i	−0.925450	+	0.378869i	$0.876313\pi$
$384$	3637.50	−	6300.33i	0.483399	−	0.837272i
$385$	−495.000	−	857.365i	−0.0655261	−	0.113494i
$386$	969.000	−	1678.36i	0.127774	−	0.221311i
$387$	−992.000			−0.130300
$388$	8169.00			1.06886
$389$	−4364.00	+	7558.67i	−0.568801	+	0.985192i	0.427884	+	0.903834i	$0.359259\pi$
$389$	−4364.00	+	7558.67i	−0.568801	+	0.985192i	−0.996685	+	0.0813585i	$0.974074\pi$
$390$	−675.000	+	1169.13i	−0.0876409	+	0.151799i
$391$	4968.00			0.642564
$392$	2115.00			0.272509
$393$	1667.50	−	2888.19i	0.214031	−	0.370713i
$394$	2262.00	+	3917.90i	0.289233	+	0.500967i
$395$	1840.00	−	3186.97i	0.234381	−	0.405960i
$396$	−63.0000	−	109.119i	−0.00799462	−	0.0138471i
$397$	−4782.00	−	8282.67i	−0.604538	−	1.04709i	−0.992124	−	0.125257i	$-0.960024\pi$
$397$	−4782.00	−	8282.67i	−0.604538	−	1.04709i	0.387586	−	0.921834i	$-0.373309\pi$
$398$	−4282.00			−0.539290
$399$	−8360.00	−	3619.99i	−1.04893	−	0.454200i
$400$	1025.00			0.128125
$401$	2933.50	+	5080.97i	0.365317	+	0.632747i	0.988827	−	0.149068i	$-0.0476274\pi$
$401$	2933.50	+	5080.97i	0.365317	+	0.632747i	−0.623510	+	0.781815i	$0.714294\pi$
$402$	−137.500	−	238.157i	−0.0170594	−	0.0295477i
$403$	6804.00	−	11784.9i	0.841021	−	1.45669i
$404$	−105.000	−	181.865i	−0.0129306	−	0.0223964i
$405$	1677.50	−	2905.52i	0.205816	−	0.356484i
$406$	2948.00			0.360362
$407$	−2124.00			−0.258680
$408$	−2025.00	+	3507.40i	−0.245717	+	0.425594i
$409$	417.500	−	723.131i	0.0504744	−	0.0874243i	−0.839684	−	0.543075i	$-0.817260\pi$
$409$	417.500	−	723.131i	0.0504744	−	0.0874243i	0.890159	+	0.455651i	$0.150593\pi$
$410$	1215.00			0.146353
$411$	5255.00			0.630681
$412$	−2107.00	+	3649.43i	−0.251953	+	0.436395i
$413$	−7491.00	−	12974.8i	−0.892513	−	1.54588i
$414$	92.0000	−	159.349i	0.0109216	−	0.0189168i
$415$	157.500	+	272.798i	0.0186298	+	0.0322678i
$416$	4347.00	+	7529.22i	0.512330	+	0.887381i
$417$	4175.00			0.490289
$418$	−684.000	−	296.181i	−0.0800372	−	0.0346571i
$419$	756.000			0.0881456			0.0440728	−	0.999028i	$-0.485967\pi$
$419$	756.000			0.0881456			0.0440728	+	0.999028i	$0.485967\pi$
$420$	−1925.00	−	3334.20i	−0.223644	−	0.387362i
$421$	1950.00	+	3377.50i	0.225742	+	0.390996i	0.956542	−	0.291596i	$-0.0941862\pi$
$421$	1950.00	+	3377.50i	0.225742	+	0.390996i	−0.730800	+	0.682592i	$0.760853\pi$
$422$	−970.000	+	1680.09i	−0.111893	+	0.193804i
$423$	502.000	+	869.490i	0.0577023	+	0.0999433i
$424$	−465.000	+	805.404i	−0.0532604	+	0.0922497i
$425$	−1350.00			−0.154081
$426$	−4870.00			−0.553879
$427$	1562.00	−	2705.46i	0.177027	−	0.306620i
$428$	2310.00	−	4001.04i	0.260883	−	0.451863i
$429$	−2430.00			−0.273477
$430$	−2480.00			−0.278131
$431$	−7353.00	+	12735.8i	−0.821767	+	1.42334i	0.0825984	+	0.996583i	$0.473678\pi$
$431$	−7353.00	+	12735.8i	−0.821767	+	1.42334i	−0.904365	+	0.426759i	$0.859655\pi$
$432$	−2972.50	−	5148.52i	−0.331052	−	0.573399i
$433$	−3919.00	+	6787.91i	−0.434954	+	0.753363i	−0.997292	−	0.0735450i	$-0.976569\pi$
$433$	−3919.00	+	6787.91i	−0.434954	+	0.753363i	0.562338	+	0.826908i	$0.309902\pi$
$434$	−2772.00	−	4801.24i	−0.306590	−	0.531030i
$435$	−1675.00	−	2901.19i	−0.184621	−	0.319773i
$436$	840.000			0.0922677
$437$	874.000	+	7569.06i	0.0956730	+	0.828552i
$438$	3475.00			0.379091
$439$	−8814.00	−	15266.3i	−0.958244	−	1.65973i	−0.726763	−	0.686889i	$-0.758976\pi$
$439$	−8814.00	−	15266.3i	−0.958244	−	1.65973i	−0.231482	−	0.972839i	$-0.574357\pi$
$440$	−337.500	−	584.567i	−0.0365675	−	0.0633367i
$441$	141.000	−	244.219i	0.0152251	−	0.0263707i
$442$	−1458.00	−	2525.33i	−0.156900	−	0.271760i
$443$	−4633.50	+	8025.46i	−0.496940	+	0.860725i	−0.999994	−	0.00353028i	$-0.998876\pi$
$443$	−4633.50	+	8025.46i	−0.496940	+	0.860725i	0.503054	+	0.864255i	$0.332210\pi$
$444$	−8260.00			−0.882888
$445$	3630.00			0.386693
$446$	−2078.00	+	3599.20i	−0.220619	+	0.382124i
$447$	6840.00	−	11847.2i	0.723760	−	1.25359i
$448$	−3674.00			−0.387456
$449$	−9371.00			−0.984955			−0.492478	−	0.870325i	$-0.663909\pi$
$449$	−9371.00			−0.984955			−0.492478	+	0.870325i	$0.663909\pi$
$450$	−25.0000	+	43.3013i	−0.00261891	+	0.00453609i
$451$	1093.50	+	1894.00i	0.114171	+	0.197749i
$452$	3706.50	−	6419.85i	0.385706	−	0.668062i
$453$	−940.000	−	1628.13i	−0.0974946	−	0.168866i
$454$	1046.50	+	1812.59i	0.108182	+	0.187377i
$455$	5940.00			0.612025
$456$	−5700.00	−	2468.17i	−0.585366	−	0.253471i
$457$	−4107.00			−0.420388			−0.210194	−	0.977660i	$-0.567410\pi$
$457$	−4107.00			−0.420388			−0.210194	+	0.977660i	$0.567410\pi$
$458$	−2156.00	−	3734.30i	−0.219963	−	0.380988i
$459$	3915.00	+	6780.98i	0.398119	+	0.689562i
$460$	−1610.00	+	2788.60i	−0.163188	+	0.282650i
$461$	2715.00	+	4702.52i	0.274295	+	0.475093i	0.969957	−	0.243276i	$-0.0782221\pi$
$461$	2715.00	+	4702.52i	0.274295	+	0.475093i	−0.695662	+	0.718369i	$0.744889\pi$
$462$	−495.000	+	857.365i	−0.0498474	+	0.0863382i
$463$	−14222.0			−1.42754			−0.713771	−	0.700379i	$-0.753014\pi$
$463$	−14222.0			−1.42754			−0.713771	+	0.700379i	$0.753014\pi$
$464$	−5494.00			−0.549682
$465$	−3150.00	+	5455.96i	−0.314146	+	0.544116i
$466$	−2114.50	+	3662.42i	−0.210198	+	0.364074i
$467$	−3885.00			−0.384960			−0.192480	−	0.981301i	$-0.561653\pi$
$467$	−3885.00			−0.384960			−0.192480	+	0.981301i	$0.561653\pi$
$468$	756.000			0.0746712
$469$	−605.000	+	1047.89i	−0.0595657	+	0.103171i
$470$	1255.00	+	2173.72i	0.123168	+	0.213333i
$471$	−2480.00	+	4295.49i	−0.242616	+	0.420224i
$472$	−5107.50	−	8846.45i	−0.498076	−	0.862692i
$473$	−2232.00	−	3865.94i	−0.216971	−	0.375805i
$474$	−3680.00			−0.356599
$475$	−237.500	−	2056.81i	−0.0229416	−	0.198680i
$476$	8316.00			0.800763
$477$	62.0000	+	107.387i	0.00595133	+	0.0103080i
$478$	−2778.00	−	4811.64i	−0.265822	−	0.460417i
$479$	−2190.00	+	3793.19i	−0.208901	+	0.361827i	−0.951369	−	0.308055i	$-0.900322\pi$
$479$	−2190.00	+	3793.19i	−0.208901	+	0.361827i	0.742467	+	0.669882i	$0.233655\pi$
$480$	−2012.50	−	3485.75i	−0.191370	−	0.331463i
$481$	6372.00	−	11036.6i	0.604030	−	1.04621i
$482$	4419.00			0.417593
$483$	10120.0			0.953366
$484$	−4375.00	+	7577.72i	−0.410875	+	0.711657i
$485$	2917.50	−	5053.26i	0.273148	−	0.473106i
$486$	560.000			0.0522677
$487$	−18856.0			−1.75451			−0.877256	−	0.480024i	$-0.840628\pi$
$487$	−18856.0			−1.75451			−0.877256	+	0.480024i	$0.840628\pi$
$488$	1065.00	−	1844.63i	0.0987916	−	0.171112i
$489$	7617.50	+	13193.9i	0.704448	+	1.22014i
$490$	352.500	−	610.548i	0.0324986	−	0.0562893i
$491$	−794.000	−	1375.25i	−0.0729791	−	0.126403i	0.827227	−	0.561868i	$-0.189917\pi$
$491$	−794.000	−	1375.25i	−0.0729791	−	0.126403i	−0.900206	+	0.435465i	$0.856584\pi$
$492$	4252.50	+	7365.55i	0.389670	+	0.674928i
$493$	7236.00			0.661041
$494$	3591.00	−	2665.63i	0.327058	−	0.242778i
$495$	−90.0000			−0.00817212
$496$	5166.00	+	8947.77i	0.467662	+	0.810014i
$497$	10714.0	+	18557.2i	0.966979	+	1.67486i
$498$	157.500	−	272.798i	0.0141722	−	0.0245469i
$499$	−5578.50	−	9662.25i	−0.500457	−	0.866817i	−1.00000		0.000527580i	$-0.999832\pi$
$499$	−5578.50	−	9662.25i	−0.500457	−	0.866817i	0.499543	−	0.866289i	$-0.333501\pi$
$500$	437.500	−	757.772i	0.0391312	−	0.0677772i
$501$	6520.00			0.581421
$502$	3957.00			0.351812
$503$	9024.00	−	15630.0i	0.799921	−	1.38550i	−0.119746	−	0.992805i	$-0.538208\pi$
$503$	9024.00	−	15630.0i	0.799921	−	1.38550i	0.919667	−	0.392699i	$-0.128459\pi$
$504$	330.000	−	571.577i	0.0291654	−	0.0505160i
$505$	−150.000			−0.0132176
$506$	828.000			0.0727452
$507$	1797.50	−	3113.36i	0.157455	−	0.272720i
$508$	413.000	+	715.337i	0.0360707	+	0.0624763i
$509$	2094.00	−	3626.91i	0.182348	−	0.315835i	−0.760332	−	0.649535i	$-0.774964\pi$
$509$	2094.00	−	3626.91i	0.182348	−	0.315835i	0.942680	+	0.333699i	$0.108297\pi$
$510$	675.000	+	1169.13i	0.0586069	+	0.101510i
$511$	−7645.00	−	13241.5i	−0.661830	−	1.14632i
$512$	−11521.0			−0.994455
$513$	−9642.50	+	7157.70i	−0.829877	+	0.616024i
$514$	877.000			0.0752584
$515$	1505.00	+	2606.74i	0.128773	+	0.223042i
$516$	−8680.00	−	15034.2i	−0.740534	−	1.28264i
$517$	−2259.00	+	3912.70i	−0.192168	+	0.332844i
$518$	−2596.00	−	4496.40i	−0.220196	−	0.381391i
$519$	495.000	−	857.365i	0.0418653	−	0.0725128i
$520$	4050.00			0.341547
$521$	20405.0			1.71585			0.857926	−	0.513773i	$-0.171753\pi$
$521$	20405.0			1.71585			0.857926	+	0.513773i	$0.171753\pi$
$522$	134.000	−	232.095i	0.0112357	−	0.0194608i
$523$	−3604.00	+	6242.31i	−0.301323	+	0.521907i	−0.976436	−	0.215808i	$-0.930762\pi$
$523$	−3604.00	+	6242.31i	−0.301323	+	0.521907i	0.675113	+	0.737714i	$0.264095\pi$
$524$	−4669.00			−0.389248
$525$	−2750.00			−0.228609
$526$	−1215.00	+	2104.44i	−0.100716	+	0.174445i
$527$	−6804.00	−	11784.9i	−0.562404	−	0.974112i
$528$	922.500	−	1597.82i	0.0760353	−	0.131697i
$529$	1851.50	+	3206.89i	0.152174	+	0.263573i
$530$	155.000	+	268.468i	0.0127033	+	0.0220028i
$531$	−1362.00			−0.111310
$532$	1463.00	+	12670.0i	0.119228	+	1.03254i
$533$	−13122.0			−1.06637
$534$	−1815.00	−	3143.67i	−0.147084	−	0.254757i
$535$	−1650.00	−	2857.88i	−0.133338	−	0.230948i
$536$	−412.500	+	714.471i	−0.0332412	+	0.0575755i
$537$	−3162.50	−	5477.61i	−0.254138	−	0.440179i
$538$	2346.00	−	4063.39i	0.187999	−	0.325623i
$539$	1269.00			0.101409
$540$	−5075.00			−0.404432
$541$	−1704.00	+	2951.41i	−0.135417	+	0.234549i	−0.925757	−	0.378120i	$-0.876571\pi$
$541$	−1704.00	+	2951.41i	−0.135417	+	0.234549i	0.790340	+	0.612669i	$0.209904\pi$
$542$	−4381.00	+	7588.11i	−0.347196	+	0.601361i
$543$	20380.0			1.61066
$544$	8694.00			0.685206
$545$	300.000	−	519.615i	0.0235791	−	0.0408401i
$546$	−2970.00	−	5144.19i	−0.232792	−	0.403207i
$547$	4708.00	−	8154.50i	0.368006	−	0.637406i	−0.621247	−	0.783615i	$-0.713374\pi$
$547$	4708.00	−	8154.50i	0.368006	−	0.637406i	0.989254	+	0.146209i	$0.0467071\pi$
$548$	−3678.50	−	6371.35i	−0.286748	−	0.496662i
$549$	−142.000	−	245.951i	−0.0110390	−	0.0191201i
$550$	−225.000			−0.0174437
$551$	1273.00	+	11024.5i	0.0984240	+	0.852377i
$552$	6900.00			0.532035
$553$	8096.00	+	14022.7i	0.622562	+	1.07831i
$554$	2507.00	+	4342.25i	0.192260	+	0.333005i
$555$	−2950.00	+	5109.55i	−0.225623	+	0.390790i
$556$	−2922.50	−	5061.92i	−0.222917	−	0.386103i
$557$	7956.00	−	13780.2i	0.605218	−	1.04827i	−0.386799	−	0.922164i	$-0.626419\pi$
$557$	7956.00	−	13780.2i	0.605218	−	1.04827i	0.992017	−	0.126105i	$-0.0402475\pi$
$558$	−504.000			−0.0382366
$559$	26784.0			2.02655
$560$	−2255.00	+	3905.77i	−0.170163	+	0.294731i
$561$	−1215.00	+	2104.44i	−0.0914391	+	0.158377i
$562$	3865.00			0.290098
$563$	1533.00			0.114757			0.0573785	−	0.998352i	$-0.481726\pi$
$563$	1533.00			0.114757			0.0573785	+	0.998352i	$0.481726\pi$
$564$	−8785.00	+	15216.1i	−0.655878	+	1.13601i
$565$	−2647.50	−	4585.60i	−0.197135	−	0.341447i
$566$	−296.500	+	513.553i	−0.0220191	+	0.0381382i
$567$	7381.00	+	12784.3i	0.546689	+	0.946894i
$568$	7305.00	+	12652.6i	0.539632	+	0.934670i
$569$	−16070.0			−1.18399			−0.591994	−	0.805942i	$-0.701659\pi$
$569$	−16070.0			−1.18399			−0.591994	+	0.805942i	$0.701659\pi$
$570$	−1662.50	+	1234.09i	−0.122166	+	0.0906845i
$571$	−8097.00			−0.593431			−0.296715	−	0.954966i	$-0.595891\pi$
$571$	−8097.00			−0.593431			−0.296715	+	0.954966i	$0.595891\pi$
$572$	1701.00	+	2946.22i	0.124340	+	0.215363i
$573$	8230.00	+	14254.8i	0.600023	+	1.03927i
$574$	−2673.00	+	4629.77i	−0.194371	+	0.336660i
$575$	1150.00	+	1991.86i	0.0834058	+	0.144463i
$576$	−167.000	+	289.252i	−0.0120804	+	0.0209239i
$577$	17927.0			1.29343			0.646716	−	0.762731i	$-0.276142\pi$
$577$	17927.0			1.29343			0.646716	+	0.762731i	$0.276142\pi$
$578$	1997.00			0.143710
$579$	4845.00	−	8391.79i	0.347757	−	0.602333i
$580$	−2345.00	+	4061.66i	−0.167881	+	0.290778i
$581$	−1386.00			−0.0989690
$582$	−5835.00			−0.415582
$583$	−279.000	+	483.242i	−0.0198199	+	0.0343291i
$584$	−5212.50	−	9028.31i	−0.369340	−	0.639716i
$585$	270.000	−	467.654i	0.0190823	−	0.0330515i
$586$	−2919.00	−	5055.86i	−0.205773	−	0.356409i
$587$	9904.00	+	17154.2i	0.696392	+	1.20619i	0.969709	+	0.244262i	$0.0785456\pi$
$587$	9904.00	+	17154.2i	0.696392	+	1.20619i	−0.273318	+	0.961924i	$0.588121\pi$
$588$	4935.00			0.346116
$589$	16758.0	−	12439.6i	1.17233	−	0.870228i
$590$	−3405.00			−0.237596
$591$	11310.0	+	19589.5i	0.787193	+	1.36346i
$592$	4838.00	+	8379.66i	0.335879	+	0.581760i
$593$	2790.50	−	4833.29i	0.193241	−	0.334704i	−0.753081	−	0.657928i	$-0.771433\pi$
$593$	2790.50	−	4833.29i	0.193241	−	0.334704i	0.946323	+	0.323224i	$0.104767\pi$
$594$	652.500	+	1130.16i	0.0450714	+	0.0780659i
$595$	2970.00	−	5144.19i	0.204636	−	0.354439i
$596$	−19152.0			−1.31627
$597$	−21410.0			−1.46776
$598$	−2484.00	+	4302.41i	−0.169863	+	0.294212i
$599$	12394.0	−	21467.0i	0.845418	−	1.46431i	−0.0398405	−	0.999206i	$-0.512685\pi$
$599$	12394.0	−	21467.0i	0.845418	−	1.46431i	0.885258	−	0.465100i	$-0.153982\pi$
$600$	−1875.00			−0.127578
$601$	−413.000			−0.0280310			−0.0140155	−	0.999902i	$-0.504461\pi$
$601$	−413.000			−0.0280310			−0.0140155	+	0.999902i	$0.504461\pi$
$602$	5456.00	−	9450.07i	0.369385	−	0.639794i
$603$	55.0000	+	95.2628i	0.00371438	+	0.00643350i
$604$	−1316.00	+	2279.38i	−0.0886544	+	0.153554i
$605$	3125.00	+	5412.66i	0.209999	+	0.363729i
$606$	75.0000	+	129.904i	0.00502750	+	0.00870789i
$607$	−22778.0			−1.52311			−0.761557	−	0.648098i	$-0.775565\pi$
$607$	−22778.0			−1.52311			−0.761557	+	0.648098i	$0.775565\pi$
$608$	1529.50	+	13245.9i	0.102022	+	0.883537i
$609$	14740.0			0.980780
$610$	−355.000	−	614.878i	−0.0235632	−	0.0408126i
$611$	−13554.0	−	23476.2i	−0.897441	−	1.55441i
$612$	378.000	−	654.715i	0.0249669	−	0.0432439i
$613$	4729.00	+	8190.87i	0.311586	+	0.539684i	0.978706	−	0.205267i	$-0.0658063\pi$
$613$	4729.00	+	8190.87i	0.311586	+	0.539684i	−0.667120	+	0.744951i	$0.732473\pi$
$614$	123.500	−	213.908i	0.00811735	−	0.0140597i
$615$	6075.00			0.398321
$616$	2970.00			0.194261
$617$	6314.50	−	10937.0i	0.412013	−	0.713628i	−0.583097	−	0.812403i	$-0.698159\pi$
$617$	6314.50	−	10937.0i	0.412013	−	0.713628i	0.995110	+	0.0987749i	$0.0314924\pi$
$618$	1505.00	−	2606.74i	0.0979611	−	0.169674i
$619$	−4984.00			−0.323625			−0.161812	−	0.986822i	$-0.551734\pi$
$619$	−4984.00			−0.323625			−0.161812	+	0.986822i	$0.551734\pi$
$620$	8820.00			0.571322
$621$	6670.00	−	11552.8i	0.431011	−	0.746533i
$622$	−5110.00	−	8850.78i	−0.329409	−	0.570553i
$623$	−7986.00	+	13832.2i	−0.513567	+	0.889524i
$624$	5535.00	+	9586.90i	0.355092	+	0.615037i
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	7835.00			0.500239
$627$	−3420.00	−	1480.90i	−0.217834	−	0.0943247i
$628$	6944.00			0.441235
$629$	−6372.00	−	11036.6i	−0.403924	−	0.699617i
$630$	−110.000	−	190.526i	−0.00695636	−	0.0120488i
$631$	3077.00	−	5329.52i	0.194126	−	0.336236i	−0.752488	−	0.658606i	$-0.771146\pi$
$631$	3077.00	−	5329.52i	0.194126	−	0.336236i	0.946614	+	0.322370i	$0.104480\pi$
$632$	5520.00	+	9560.92i	0.347427	+	0.601761i
$633$	−4850.00	+	8400.45i	−0.304534	+	0.527469i
$634$	3774.00			0.236411
$635$	590.000			0.0368716
$636$	−1085.00	+	1879.28i	−0.0676463	+	0.117167i
$637$	−3807.00	+	6593.92i	−0.236796	+	0.410142i
$638$	1206.00			0.0748370
$639$	1948.00			0.120597
$640$	−3637.50	+	6300.33i	−0.224664	+	0.389129i
$641$	−1350.50	−	2339.13i	−0.0832161	−	0.144135i	0.821414	−	0.570333i	$-0.193186\pi$
$641$	−1350.50	−	2339.13i	−0.0832161	−	0.144135i	−0.904630	+	0.426198i	$0.859853\pi$
$642$	−1650.00	+	2857.88i	−0.101433	+	0.175688i
$643$	996.500	+	1725.99i	0.0611168	+	0.105857i	0.894965	−	0.446137i	$-0.147200\pi$
$643$	996.500	+	1725.99i	0.0611168	+	0.105857i	−0.833848	+	0.551994i	$0.813867\pi$
$644$	−7084.00	−	12269.8i	−0.433461	−	0.750776i
$645$	−12400.0			−0.756976
$646$	−513.000	−	4442.71i	−0.0312441	−	0.270582i
$647$	15638.0			0.950221			0.475111	−	0.879926i	$-0.342408\pi$
$647$	15638.0			0.950221			0.475111	+	0.879926i	$0.342408\pi$
$648$	5032.50	+	8716.55i	0.305085	+	0.528423i
$649$	−3064.50	−	5307.87i	−0.185350	−	0.321036i
$650$	675.000	−	1169.13i	0.0407318	−	0.0705496i
$651$	−13860.0	−	24006.2i	−0.834434	−	1.44528i
$652$	10664.5	−	18471.5i	0.640574	−	1.10951i
$653$	3180.00			0.190571			0.0952856	−	0.995450i	$-0.469624\pi$
$653$	3180.00			0.190571			0.0952856	+	0.995450i	$0.469624\pi$
$654$	−600.000			−0.0358744
$655$	−1667.50	+	2888.19i	−0.0994727	+	0.172292i
$656$	4981.50	−	8628.21i	0.296486	−	0.513529i
$657$	−1390.00			−0.0825404
$658$	−11044.0			−0.654316
$659$	−150.000	+	259.808i	−0.00886672	+	0.0153576i	−0.870425	−	0.492302i	$-0.836156\pi$
$659$	−150.000	+	259.808i	−0.00886672	+	0.0153576i	0.861558	+	0.507659i	$0.169489\pi$
$660$	−787.500	−	1363.99i	−0.0464445	−	0.0804443i
$661$	−895.000	+	1550.19i	−0.0526648	+	0.0912182i	−0.891156	−	0.453697i	$-0.850105\pi$
$661$	−895.000	+	1550.19i	−0.0526648	+	0.0912182i	0.838491	+	0.544915i	$0.183438\pi$
$662$	−2.50000	−	4.33013i	−0.000146775	−	0.000254222i
$663$	−7290.00	−	12626.7i	−0.427029	−	0.739636i
$664$	−945.000			−0.0552306
$665$	8360.00	+	3619.99i	0.487499	+	0.211093i
$666$	−472.000			−0.0274619
$667$	−6164.00	−	10676.4i	−0.357828	−	0.619776i
$668$	−4564.00	−	7905.08i	−0.264351	−	0.457869i
$669$	−10390.0	+	17996.0i	−0.600449	+	1.04001i
$670$	137.500	+	238.157i	0.00792849	+	0.0137325i
$671$	639.000	−	1106.78i	0.0367635	−	0.0636763i
$672$	17710.0			1.01663
$673$	−13830.0			−0.792136			−0.396068	−	0.918221i	$-0.629625\pi$
$673$	−13830.0			−0.792136			−0.396068	+	0.918221i	$0.629625\pi$
$674$	−3178.50	+	5505.32i	−0.181649	+	0.314625i
$675$	−1812.50	+	3139.34i	−0.103353	+	0.179012i
$676$	−5033.00			−0.286356
$677$	−6090.00			−0.345728			−0.172864	−	0.984946i	$-0.555302\pi$
$677$	−6090.00			−0.345728			−0.172864	+	0.984946i	$0.555302\pi$
$678$	−2647.50	+	4585.60i	−0.149966	+	0.259748i
$679$	12837.0	+	22234.3i	0.725536	+	1.25666i
$680$	2025.00	−	3507.40i	0.114199	−	0.197798i
$681$	5232.50	+	9062.96i	0.294434	+	0.509975i
$682$	−1134.00	−	1964.15i	−0.0636702	−	0.110280i
$683$	−21180.0			−1.18657			−0.593287	−	0.804991i	$-0.702170\pi$
$683$	−21180.0			−1.18657			−0.593287	+	0.804991i	$0.702170\pi$
$684$	1064.00	+	460.726i	0.0594782	+	0.0257548i
$685$	−5255.00			−0.293114
$686$	−2222.00	−	3848.62i	−0.123668	−	0.214200i
$687$	−10780.0	−	18671.5i	−0.598665	−	1.03692i
$688$	−10168.0	+	17611.5i	−0.563447	+	0.975918i
$689$	−1674.00	−	2899.45i	−0.0925607	−	0.160320i
$690$	1150.00	−	1991.86i	0.0634489	−	0.109897i
$691$	−14812.0			−0.815449			−0.407724	−	0.913105i	$-0.633678\pi$
$691$	−14812.0			−0.815449			−0.407724	+	0.913105i	$0.633678\pi$
$692$	−1386.00			−0.0761385
$693$	198.000	−	342.946i	0.0108534	−	0.0187986i
$694$	−6279.50	+	10876.4i	−0.343468	+	0.594903i
$695$	−4175.00			−0.227866
$696$	10050.0			0.547334
$697$	−6561.00	+	11364.0i	−0.356550	+	0.617563i
$698$	3668.00	+	6353.16i	0.198905	+	0.344514i
$699$	−10572.5	+	18312.1i	−0.572087	+	0.990883i
$700$	1925.00	+	3334.20i	0.103940	+	0.180030i
$701$	−16593.0	−	28739.9i	−0.894021	−	1.54849i	−0.835011	−	0.550233i	$-0.814539\pi$
$701$	−16593.0	−	28739.9i	−0.894021	−	1.54849i	−0.0590102	−	0.998257i	$-0.518794\pi$
$702$	−7830.00			−0.420975
$703$	15694.0	−	11649.8i	0.841978	−	0.625006i
$704$	−1503.00			−0.0804637
$705$	6275.00	+	10868.6i	0.335220	+	0.580618i
$706$	5225.50	+	9050.83i	0.278561	+	0.482482i
$707$	330.000	−	571.577i	0.0175544	−	0.0304050i
$708$	−11917.5	−	20641.7i	−0.632609	−	1.09571i
$709$	−15620.0	+	27054.6i	−0.827393	+	1.43309i	0.0726842	+	0.997355i	$0.476843\pi$
$709$	−15620.0	+	27054.6i	−0.827393	+	1.43309i	−0.900077	+	0.435731i	$0.856490\pi$
$710$	4870.00			0.257419
$711$	1472.00			0.0776432
$712$	−5445.00	+	9431.02i	−0.286601	+	0.496408i
$713$	−11592.0	+	20077.9i	−0.608869	+	1.05459i
$714$	−5940.00			−0.311343
$715$	2430.00			0.127100
$716$	−4427.50	+	7668.65i	−0.231094	+	0.400267i
$717$	−13890.0	−	24058.2i	−0.723475	−	1.25310i
$718$	3650.00	−	6321.99i	0.189717	−	0.328599i
$719$	−7113.00	−	12320.1i	−0.368943	−	0.639028i	0.620457	−	0.784240i	$-0.286947\pi$
$719$	−7113.00	−	12320.1i	−0.368943	−	0.639028i	−0.989401	+	0.145212i	$0.953614\pi$
$720$	205.000	+	355.070i	0.0106110	+	0.0183787i
$721$	−13244.0			−0.684095
$722$	6678.50	−	1563.18i	0.344249	−	0.0805753i
$723$	22095.0			1.13654
$724$	−14266.0	−	24709.4i	−0.732309	−	1.26840i
$725$	1675.00	+	2901.19i	0.0858041	+	0.148617i
$726$	3125.00	−	5412.66i	0.159752	−	0.276698i
$727$	−5188.00	−	8985.88i	−0.264666	−	0.458415i	0.702810	−	0.711378i	$-0.251928\pi$
$727$	−5188.00	−	8985.88i	−0.264666	−	0.458415i	−0.967476	+	0.252962i	$0.918595\pi$
$728$	−8910.00	+	15432.6i	−0.453608	+	0.785672i
$729$	20917.0			1.06269
$730$	−3475.00			−0.176186
$731$	13392.0	−	23195.6i	0.677594	−	1.17363i
$732$	2485.00	−	4304.15i	0.125476	−	0.217330i
$733$	−21868.0			−1.10193			−0.550964	−	0.834529i	$-0.685740\pi$
$733$	−21868.0			−1.10193			−0.550964	+	0.834529i	$0.685740\pi$
$734$	632.000			0.0317814
$735$	1762.50	−	3052.74i	0.0884501	−	0.153200i
$736$	−7406.00	−	12827.6i	−0.370909	−	0.642433i
$737$	−247.500	+	428.683i	−0.0123701	+	0.0214257i
$738$	243.000	+	420.888i	0.0121205	+	0.0209934i
$739$	10535.5	+	18248.0i	0.524431	+	0.908341i	0.999595	+	0.0284443i	$0.00905532\pi$
$739$	10535.5	+	18248.0i	0.524431	+	0.908341i	−0.475164	+	0.879897i	$0.657611\pi$
$740$	8260.00			0.410329
$741$	17955.0	−	13328.1i	0.890140	−	0.660757i
$742$	−1364.00			−0.0674852
$743$	7200.00	+	12470.8i	0.355508	+	0.615758i	0.987205	−	0.159458i	$-0.0509746\pi$
$743$	7200.00	+	12470.8i	0.355508	+	0.615758i	−0.631697	+	0.775216i	$0.717641\pi$
$744$	−9450.00	−	16367.9i	−0.465664	−	0.806553i
$745$	−6840.00	+	11847.2i	−0.336373	+	0.582616i
$746$	−48.0000	−	83.1384i	−0.00235577	−	0.00408031i
$747$	−63.0000	+	109.119i	−0.00308574	+	0.00534466i
$748$	3402.00			0.166296
$749$	14520.0			0.708343
$750$	−312.500	+	541.266i	−0.0152145	+	0.0263523i
$751$	−17293.0	+	29952.4i	−0.840254	+	1.45536i	0.0494264	+	0.998778i	$0.484261\pi$
$751$	−17293.0	+	29952.4i	−0.840254	+	1.45536i	−0.889680	+	0.456584i	$0.849073\pi$
$752$	20582.0			0.998070
$753$	19785.0			0.957511
$754$	−3618.00	+	6266.56i	−0.174748	+	0.302672i
$755$	940.000	+	1628.13i	0.0453114	+	0.0784816i
$756$	11165.0	−	19338.3i	0.537126	−	0.930329i
$757$	2839.00	+	4917.29i	0.136308	+	0.236093i	0.926096	−	0.377287i	$-0.123143\pi$
$757$	2839.00	+	4917.29i	0.136308	+	0.236093i	−0.789788	+	0.613380i	$0.789810\pi$
$758$	5482.00	+	9495.10i	0.262685	+	0.454984i
$759$	4140.00			0.197987
$760$	5700.00	+	2468.17i	0.272054	+	0.117803i
$761$	−12243.0			−0.583191			−0.291596	−	0.956542i	$-0.594186\pi$
$761$	−12243.0			−0.583191			−0.291596	+	0.956542i	$0.594186\pi$
$762$	−295.000	−	510.955i	−0.0140246	−	0.0242913i
$763$	1320.00	+	2286.31i	0.0626307	+	0.108480i
$764$	11522.0	−	19956.7i	0.545617	−	0.945036i
$765$	−270.000	−	467.654i	−0.0127606	−	0.0221020i
$766$	1009.00	−	1747.64i	0.0475935	−	0.0824344i
$767$	36774.0			1.73120
$768$	595.000			0.0279560
$769$	15625.0	−	27063.3i	0.732707	−	1.26909i	−0.223015	−	0.974815i	$-0.571590\pi$
$769$	15625.0	−	27063.3i	0.732707	−	1.26909i	0.955722	−	0.294271i	$-0.0950769\pi$
$770$	495.000	−	857.365i	0.0231670	−	0.0401264i
$771$	4385.00			0.204827
$772$	−13566.0			−0.632450
$773$	−15021.0	+	26017.1i	−0.698923	+	1.21057i	0.269917	+	0.962884i	$0.413004\pi$
$773$	−15021.0	+	26017.1i	−0.698923	+	1.21057i	−0.968840	+	0.247687i	$0.920329\pi$
$774$	−496.000	−	859.097i	−0.0230340	−	0.0398961i
$775$	3150.00	−	5455.96i	0.146002	−	0.252882i
$776$	8752.50	+	15159.8i	0.404892	+	0.701294i
$777$	−12980.0	−	22482.0i	−0.599298	−	1.03802i
$778$	−8728.00			−0.402203
$779$	−18468.0	−	7996.88i	−0.849403	−	0.367802i
$780$	9450.00			0.433800
$781$	4383.00	+	7591.58i	0.200814	+	0.347821i
$782$	2484.00	+	4302.41i	0.113590	+	0.196744i
$783$	9715.00	−	16826.9i	0.443405	−	0.767999i
$784$	−2890.50	−	5006.49i	−0.131674	−	0.228065i
$785$	2480.00	−	4295.49i	0.112758	−	0.195303i
$786$	3335.00			0.151343
$787$	−43141.0			−1.95402			−0.977008	−	0.213203i	$-0.931611\pi$
$787$	−43141.0			−1.95402			−0.977008	+	0.213203i	$0.931611\pi$
$788$	15834.0	−	27425.3i	0.715816	−	1.23983i
$789$	−6075.00	+	10522.2i	−0.274114	+	0.474779i
$790$	3680.00			0.165732
$791$	23298.0			1.04726
$792$	135.000	−	233.827i	0.00605684	−	0.0104908i
$793$	3834.00	+	6640.68i	0.171689	+	0.297374i
$794$	4782.00	−	8282.67i	0.213737	−	0.370203i
$795$	775.000	+	1342.34i	0.0345741	+	0.0598841i
$796$	14987.0	+	25958.2i	0.667337	+	1.15586i
$797$	8008.00			0.355907			0.177954	−	0.984039i	$-0.443052\pi$
$797$	8008.00			0.355907			0.177954	+	0.984039i	$0.443052\pi$
$798$	−1045.00	−	9049.97i	−0.0463566	−	0.401460i
$799$	−27108.0			−1.20027
$800$	2012.50	+	3485.75i	0.0889408	+	0.154050i
$801$	726.000	+	1257.47i	0.0320249	+	0.0554688i
$802$	−2933.50	+	5080.97i	−0.129159	+	0.223710i
$803$	−3127.50	−	5416.99i	−0.137443	−	0.238059i
$804$	−962.500	+	1667.10i	−0.0422198	+	0.0731269i
$805$	−10120.0			−0.443085
$806$	13608.0			0.594692
$807$	11730.0	−	20317.0i	0.511667	−	0.886234i
$808$	225.000	−	389.711i	0.00979638	−	0.0169678i
$809$	9053.00			0.393432			0.196716	−	0.980461i	$-0.436972\pi$
$809$	9053.00			0.393432			0.196716	+	0.980461i	$0.436972\pi$
$810$	3355.00			0.145534
$811$	1478.00	−	2559.97i	0.0639946	−	0.110842i	−0.832253	−	0.554396i	$-0.812949\pi$
$811$	1478.00	−	2559.97i	0.0639946	−	0.110842i	0.896248	+	0.443554i	$0.146283\pi$
$812$	−10318.0	−	17871.3i	−0.445925	−	0.772364i
$813$	−21905.0	+	37940.6i	−0.944947	+	1.63670i
$814$	−1062.00	−	1839.44i	−0.0457286	−	0.0792043i
$815$	−7617.50	−	13193.9i	−0.327398	−	0.567070i
$816$	11070.0			0.474911
$817$	37696.0	+	16322.8i	1.61422	+	0.698977i
$818$	835.000			0.0356908
$819$	1188.00	+	2057.68i	0.0506863	+	0.0877912i
$820$	−4252.50	−	7365.55i	−0.181102	−	0.313678i
$821$	−9453.00	+	16373.1i	−0.401842	+	0.696010i	−0.993948	−	0.109850i	$-0.964963\pi$
$821$	−9453.00	+	16373.1i	−0.401842	+	0.696010i	0.592107	+	0.805860i	$0.298296\pi$
$822$	2627.50	+	4550.96i	0.111490	+	0.193106i
$823$	7375.00	−	12773.9i	0.312365	−	0.541032i	−0.666509	−	0.745497i	$-0.732212\pi$
$823$	7375.00	−	12773.9i	0.312365	−	0.541032i	0.978874	+	0.204465i	$0.0655455\pi$
$824$	−9030.00			−0.381766
$825$	−1125.00			−0.0474757
$826$	7491.00	−	12974.8i	0.315551	−	0.546551i
$827$	−19543.5	+	33850.3i	−0.821758	+	1.42333i	0.0826135	+	0.996582i	$0.473673\pi$
$827$	−19543.5	+	33850.3i	−0.821758	+	1.42333i	−0.904372	+	0.426745i	$0.859660\pi$
$828$	−1288.00			−0.0540593
$829$	168.000			0.00703846			0.00351923	−	0.999994i	$-0.498880\pi$
$829$	168.000			0.00703846			0.00351923	+	0.999994i	$0.498880\pi$
$830$	−157.500	+	272.798i	−0.00658663	+	0.0114084i
$831$	12535.0	+	21711.3i	0.523266	+	0.906324i
$832$	4509.00	−	7809.82i	0.187886	−	0.325429i
$833$	3807.00	+	6593.92i	0.158349	+	0.274269i
$834$	2087.50	+	3615.66i	0.0866717	+	0.150120i
$835$	−6520.00			−0.270220
$836$	598.500	+	5183.16i	0.0247602	+	0.214430i
$837$	−36540.0			−1.50897
$838$	378.000	+	654.715i	0.0155821	+	0.0269890i
$839$	15329.0	+	26550.6i	0.630770	+	1.09253i	0.987395	+	0.158278i	$0.0505941\pi$
$839$	15329.0	+	26550.6i	0.630770	+	1.09253i	−0.356625	+	0.934248i	$0.616073\pi$
$840$	4125.00	−	7144.71i	0.169436	−	0.293471i
$841$	3216.50	+	5571.14i	0.131883	+	0.228428i
$842$	−1950.00	+	3377.50i	−0.0798117	+	0.138238i
$843$	19325.0			0.789547
$844$	13580.0			0.553842
$845$	−1797.50	+	3113.36i	−0.0731786	+	0.126749i
$846$	−502.000	+	869.490i	−0.0204008	+	0.0353353i
$847$	−27500.0			−1.11560
$848$	2542.00			0.102939
$849$	−1482.50	+	2567.77i	−0.0599285	+	0.103799i
$850$	−675.000	−	1169.13i	−0.0272380	−	0.0471776i
$851$	−10856.0	+	18803.1i	−0.437296	+	0.757419i
$852$	17045.0	+	29522.8i	0.685390	+	1.18713i
$853$	14909.0	+	25823.1i	0.598446	+	1.03654i	0.993051	+	0.117688i	$0.0375482\pi$
$853$	14909.0	+	25823.1i	0.598446	+	1.03654i	−0.394605	+	0.918851i	$0.629118\pi$
$854$	3124.00			0.125177
$855$	665.000	−	493.634i	0.0265994	−	0.0197450i
$856$	9900.00			0.395298
$857$	16235.5	+	28120.7i	0.647134	+	1.12087i	0.983804	+	0.179247i	$0.0573660\pi$
$857$	16235.5	+	28120.7i	0.647134	+	1.12087i	−0.336670	+	0.941623i	$0.609301\pi$
$858$	−1215.00	−	2104.44i	−0.0483443	−	0.0837348i
$859$	17910.5	−	31021.9i	0.711407	−	1.23219i	−0.252922	−	0.967487i	$-0.581392\pi$
$859$	17910.5	−	31021.9i	0.711407	−	1.23219i	0.964329	−	0.264706i	$-0.0852749\pi$
$860$	8680.00	+	15034.2i	0.344169	+	0.596119i
$861$	−13365.0	+	23148.9i	−0.529010	+	0.916273i
$862$	−14706.0			−0.581077
$863$	39300.0			1.55016			0.775080	−	0.631863i	$-0.217710\pi$
$863$	39300.0			1.55016			0.775080	+	0.631863i	$0.217710\pi$
$864$	11672.5	−	20217.4i	0.459614	−	0.796075i
$865$	−495.000	+	857.365i	−0.0194572	+	0.0337009i
$866$	−7838.00			−0.307559
$867$	9985.00			0.391128
$868$	−19404.0	+	33608.7i	−0.758773	+	1.31423i
$869$	3312.00	+	5736.55i	0.129289	+	0.223935i
$870$	1675.00	−	2901.19i	0.0652734	−	0.113057i
$871$	−1485.00	−	2572.10i	−0.0577696	−	0.100060i
$872$	900.000	+	1558.85i	0.0349517	+	0.0605380i
$873$	2334.00			0.0904856
$874$	−6118.00	+	4541.44i	−0.236779	+	0.175762i
$875$	2750.00			0.106248
$876$	−12162.5	−	21066.1i	−0.469101	−	0.812507i
$877$	−11427.0	−	19792.1i	−0.439980	−	0.762068i	0.557707	−	0.830038i	$-0.311681\pi$
$877$	−11427.0	−	19792.1i	−0.439980	−	0.762068i	−0.997687	+	0.0679700i	$0.978348\pi$
$878$	8814.00	−	15266.3i	0.338791	−	0.586802i
$879$	−14595.0	−	25279.3i	−0.560042	−	0.970022i
$880$	−922.500	+	1597.82i	−0.0353380	+	0.0612073i
$881$	25347.0			0.969310			0.484655	−	0.874705i	$-0.338945\pi$
$881$	25347.0			0.969310			0.484655	+	0.874705i	$0.338945\pi$
$882$	282.000			0.0107658
$883$	7434.50	−	12876.9i	0.283342	−	0.490762i	−0.688864	−	0.724891i	$-0.741890\pi$
$883$	7434.50	−	12876.9i	0.283342	−	0.490762i	0.972206	+	0.234128i	$0.0752236\pi$
$884$	−10206.0	+	17677.3i	−0.388309	+	0.672570i
$885$	−17025.0			−0.646654
$886$	−9267.00			−0.351389
$887$	4026.00	−	6973.24i	0.152401	−	0.263967i	−0.779709	−	0.626143i	$-0.784633\pi$
$887$	4026.00	−	6973.24i	0.152401	−	0.263967i	0.932110	+	0.362176i	$0.117966\pi$
$888$	−8850.00	−	15328.6i	−0.334444	−	0.579275i
$889$	−1298.00	+	2248.20i	−0.0489691	+	0.0848170i
$890$	1815.00	+	3143.67i	0.0683584	+	0.118400i
$891$	3019.50	+	5229.93i	0.113532	+	0.196643i
$892$	29092.0			1.09201
$893$	−4769.00	−	41300.8i	−0.178711	−	1.54768i
$894$	13680.0			0.511776
$895$	3162.50	+	5477.61i	0.118113	+	0.204577i
$896$	−16005.0	−	27721.5i	−0.596752	−	1.03360i
$897$	−12420.0	+	21512.1i	−0.462310	+	0.800744i
$898$	−4685.50	−	8115.52i	−0.174117	−	0.301580i
$899$	−16884.0	+	29243.9i	−0.626377	+	1.08492i
$900$	350.000			0.0129630
$901$	−3348.00			−0.123794
$902$	−1093.50	+	1894.00i	−0.0403654	+	0.0699149i
$903$	27280.0	−	47250.3i	1.00534	−	1.74130i
$904$	15885.0			0.584433
$905$	−20380.0			−0.748568
$906$	940.000	−	1628.13i	0.0344695	−	0.0597030i
$907$	2310.50	+	4001.90i	0.0845853	+	0.146506i	0.905214	−	0.424955i	$-0.139710\pi$
$907$	2310.50	+	4001.90i	0.0845853	+	0.146506i	−0.820629	+	0.571461i	$0.806377\pi$
$908$	7325.50	−	12688.1i	0.267737	−	0.463734i
$909$	−30.0000	−	51.9615i	−0.00109465	−	0.00189599i
$910$	2970.00	+	5144.19i	0.108192	+	0.187394i
$911$	−41004.0			−1.49124			−0.745622	−	0.666369i	$-0.767847\pi$
$911$	−41004.0			−1.49124			−0.745622	+	0.666369i	$0.767847\pi$
$912$	1947.50	+	16865.8i	0.0707107	+	0.612373i
$913$	−567.000			−0.0205531
$914$	−2053.50	−	3556.77i	−0.0743148	−	0.128717i
$915$	−1775.00	−	3074.39i	−0.0641308	−	0.111078i
$916$	−15092.0	+	26140.1i	−0.544382	+	0.942897i
$917$	−7337.00	−	12708.1i	−0.264219	−	0.457641i
$918$	−3915.00	+	6780.98i	−0.140756	+	0.243797i
$919$	−45946.0			−1.64920			−0.824602	−	0.565713i	$-0.808601\pi$
$919$	−45946.0			−1.64920			−0.824602	+	0.565713i	$0.808601\pi$
$920$	−6900.00			−0.247268
$921$	617.500	−	1069.54i	0.0220926	−	0.0382656i
$922$	−2715.00	+	4702.52i	−0.0969781	+	0.167971i
$923$	−52596.0			−1.87564
$924$	6930.00			0.246732
$925$	2950.00	−	5109.55i	0.104860	−	0.181623i
$926$	−7111.00	−	12316.6i	−0.252356	−	0.437094i
$927$	−602.000	+	1042.69i	−0.0213293	+	0.0369435i
$928$	−10787.0	−	18683.6i	−0.381574	−	0.660905i
$929$	23305.5	+	40366.3i	0.823066	+	1.42559i	0.903388	+	0.428824i	$0.141072\pi$
$929$	23305.5	+	40366.3i	0.823066	+	1.42559i	−0.0803218	+	0.996769i	$0.525595\pi$
$930$	−6300.00			−0.222135
$931$	−9376.50	+	6960.25i	−0.330078	+	0.245019i
$932$	29603.0			1.04043
$933$	−25550.0	−	44253.9i	−0.896537	−	1.55285i
$934$	−1942.50	−	3364.51i	−0.0680520	−	0.117869i
$935$	1215.00	−	2104.44i	0.0424971	−	0.0736071i
$936$	810.000	+	1402.96i	0.0282860	+	0.0489928i
$937$	16678.5	−	28888.0i	0.581497	−	1.00718i	−0.413805	−	0.910366i	$-0.635800\pi$
$937$	16678.5	−	28888.0i	0.581497	−	1.00718i	0.995302	−	0.0968171i	$-0.0308662\pi$
$938$	−1210.00			−0.0421193
$939$	39175.0			1.36148
$940$	8785.00	−	15216.1i	0.304825	−	0.527972i
$941$	20945.0	−	36277.8i	0.725598	−	1.25677i	−0.233130	−	0.972446i	$-0.574897\pi$
$941$	20945.0	−	36277.8i	0.725598	−	1.25677i	0.958728	−	0.284327i	$-0.0917700\pi$
$942$	−4960.00			−0.171556
$943$	22356.0			0.772016
$944$	−13960.5	+	24180.3i	−0.481330	+	0.833688i
$945$	−7975.00	−	13813.1i	−0.274526	−	0.475492i
$946$	2232.00	−	3865.94i	0.0767110	−	0.132867i
$947$	5982.00	+	10361.1i	0.205268	+	0.355535i	0.950218	−	0.311586i	$-0.100860\pi$
$947$	5982.00	+	10361.1i	0.205268	+	0.355535i	−0.744950	+	0.667120i	$0.767527\pi$
$948$	12880.0	+	22308.8i	0.441269	+	0.764300i
$949$	37530.0			1.28375
$950$	1662.50	−	1234.09i	0.0567775	−	0.0421464i
$951$	18870.0			0.643430
$952$	8910.00	+	15432.6i	0.303335	+	0.525391i
$953$	−5536.50	−	9589.50i	−0.188190	−	0.325954i	0.756457	−	0.654043i	$-0.226929\pi$
$953$	−5536.50	−	9589.50i	−0.188190	−	0.325954i	−0.944647	+	0.328089i	$0.893595\pi$
$954$	−62.0000	+	107.387i	−0.00210411	+	0.00364443i
$955$	−8230.00	−	14254.8i	−0.278865	−	0.483009i
$956$	−19446.0	+	33681.5i	−0.657875	+	1.13947i
$957$	6030.00			0.203680
$958$	−4380.00			−0.147715
$959$	11561.0	−	20024.2i	0.389285	−	0.674261i
$960$	−2087.50	+	3615.66i	−0.0701810	+	0.121557i
$961$	33713.0			1.13165
$962$	12744.0			0.427113
$963$	660.000	−	1143.15i	0.0220854	−	0.0382530i
$964$	−15466.5	−	26788.8i	−0.516745	−	0.895029i
$965$	−4845.00	+	8391.79i	−0.161623	+	0.279939i
$966$	5060.00	+	8764.18i	0.168533	+	0.291908i
$967$	7123.00	+	12337.4i	0.236877	+	0.410283i	0.959817	−	0.280628i	$-0.0905428\pi$
$967$	7123.00	+	12337.4i	0.236877	+	0.410283i	−0.722939	+	0.690911i	$0.757209\pi$
$968$	−18750.0			−0.622570
$969$	−2565.00	−	22213.6i	−0.0850358	−	0.736431i
$970$	5835.00			0.193145
$971$	−15705.5	−	27202.7i	−0.519066	−	0.899049i	−0.999754	−	0.0221577i	$-0.992946\pi$
$971$	−15705.5	−	27202.7i	−0.519066	−	0.899049i	0.480688	−	0.876892i	$-0.340387\pi$
$972$	−1960.00	−	3394.82i	−0.0646780	−	0.112026i
$973$	9185.00	−	15908.9i	0.302629	−	0.524168i
$974$	−9428.00	−	16329.8i	−0.310157	−	0.537207i
$975$	3375.00	−	5845.67i	0.110858	−	0.192012i
$976$	−5822.00			−0.190940
$977$	18657.0			0.610942			0.305471	−	0.952201i	$-0.401186\pi$
$977$	18657.0			0.610942			0.305471	+	0.952201i	$0.401186\pi$
$978$	−7617.50	+	13193.9i	−0.249060	+	0.431385i
$979$	−3267.00	+	5658.61i	−0.106653	+	0.184729i
$980$	−4935.00			−0.160860
$981$	240.000			0.00781102
$982$	794.000	−	1375.25i	0.0258020	−	0.0446904i
$983$	28706.0	+	49720.3i	0.931413	+	1.61326i	0.780908	+	0.624646i	$0.214757\pi$
$983$	28706.0	+	49720.3i	0.931413	+	1.61326i	0.150505	+	0.988609i	$0.451910\pi$
$984$	−9112.50	+	15783.3i	−0.295219	+	0.511335i
$985$	−11310.0	−	19589.5i	−0.365854	−	0.633678i
$986$	3618.00	+	6266.56i	0.116857	+	0.202402i
$987$	−55220.0			−1.78082
$988$	−28728.0	−	12439.6i	−0.925060	−	0.400563i
$989$	−45632.0			−1.46715
$990$	−45.0000	−	77.9423i	−0.00144464	−	0.00250219i
$991$	−1312.00	−	2272.45i	−0.0420556	−	0.0728424i	0.844231	−	0.535979i	$-0.180057\pi$
$991$	−1312.00	−	2272.45i	−0.0420556	−	0.0728424i	−0.886287	+	0.463136i	$0.846724\pi$
$992$	−20286.0	+	35136.4i	−0.649275	+	1.12458i
$993$	−12.5000	−	21.6506i	−0.000399472	−	0.000691905i
$994$	−10714.0	+	18557.2i	−0.341879	+	0.592151i
$995$	21410.0			0.682153
$996$	−2205.00			−0.0701487
$997$	6329.00	−	10962.1i	0.201045	−	0.348219i	−0.747821	−	0.663901i	$-0.768900\pi$
$997$	6329.00	−	10962.1i	0.201045	−	0.348219i	0.948865	+	0.315681i	$0.102233\pi$
$998$	5578.50	−	9662.25i	0.176938	−	0.306466i
$999$	−34220.0			−1.08376

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.4.e.a.26.1	yes	2
19.7	even	3		1805.4.a.e.1.1		1
19.11	even	3	inner	95.4.e.a.11.1	✓	2
19.12	odd	6		1805.4.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.4.e.a.11.1	✓	2	19.11	even	3	inner
95.4.e.a.26.1	yes	2	1.1	even	1	trivial
1805.4.a.e.1.1		1	19.7	even	3
1805.4.a.g.1.1		1	19.12	odd	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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	95.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(2.50000 + 4.33013i) q^{3} +(3.50000 - 6.06218i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-2.50000 + 4.33013i) q^{6} +22.0000 q^{7} +15.0000 q^{8} +(1.00000 - 1.73205i) q^{9} +(2.50000 - 4.33013i) q^{10} +9.00000 q^{11} +35.0000 q^{12} +(-27.0000 + 46.7654i) q^{13} +(11.0000 + 19.0526i) q^{14} +(12.5000 - 21.6506i) q^{15} +(-20.5000 - 35.5070i) q^{16} +(27.0000 + 46.7654i) q^{17} +2.00000 q^{18} +(-66.5000 + 49.3634i) q^{19} -35.0000 q^{20} +(55.0000 + 95.2628i) q^{21} +(4.50000 + 7.79423i) q^{22} +(46.0000 - 79.6743i) q^{23} +(37.5000 + 64.9519i) q^{24} +(-12.5000 + 21.6506i) q^{25} -54.0000 q^{26} +145.000 q^{27} +(77.0000 - 133.368i) q^{28} +(67.0000 - 116.047i) q^{29} +25.0000 q^{30} -252.000 q^{31} +(80.5000 - 139.430i) q^{32} +(22.5000 + 38.9711i) q^{33} +(-27.0000 + 46.7654i) q^{34} +(-55.0000 - 95.2628i) q^{35} +(-7.00000 - 12.1244i) q^{36} -236.000 q^{37} +(-76.0000 - 32.9090i) q^{38} -270.000 q^{39} +(-37.5000 - 64.9519i) q^{40} +(121.500 + 210.444i) q^{41} +(-55.0000 + 95.2628i) q^{42} +(-248.000 - 429.549i) q^{43} +(31.5000 - 54.5596i) q^{44} -10.0000 q^{45} +92.0000 q^{46} +(-251.000 + 434.745i) q^{47} +(102.500 - 177.535i) q^{48} +141.000 q^{49} -25.0000 q^{50} +(-135.000 + 233.827i) q^{51} +(189.000 + 327.358i) q^{52} +(-31.0000 + 53.6936i) q^{53} +(72.5000 + 125.574i) q^{54} +(-22.5000 - 38.9711i) q^{55} +330.000 q^{56} +(-380.000 - 164.545i) q^{57} +134.000 q^{58} +(-340.500 - 589.763i) q^{59} +(-87.5000 - 151.554i) q^{60} +(71.0000 - 122.976i) q^{61} +(-126.000 - 218.238i) q^{62} +(22.0000 - 38.1051i) q^{63} -167.000 q^{64} +270.000 q^{65} +(-22.5000 + 38.9711i) q^{66} +(-27.5000 + 47.6314i) q^{67} +378.000 q^{68} +460.000 q^{69} +(55.0000 - 95.2628i) q^{70} +(487.000 + 843.509i) q^{71} +(15.0000 - 25.9808i) q^{72} +(-347.500 - 601.888i) q^{73} +(-118.000 - 204.382i) q^{74} -125.000 q^{75} +(66.5000 + 575.907i) q^{76} +198.000 q^{77} +(-135.000 - 233.827i) q^{78} +(368.000 + 637.395i) q^{79} +(-102.500 + 177.535i) q^{80} +(335.500 + 581.103i) q^{81} +(-121.500 + 210.444i) q^{82} -63.0000 q^{83} +770.000 q^{84} +(135.000 - 233.827i) q^{85} +(248.000 - 429.549i) q^{86} +670.000 q^{87} +135.000 q^{88} +(-363.000 + 628.734i) q^{89} +(-5.00000 - 8.66025i) q^{90} +(-594.000 + 1028.84i) q^{91} +(-322.000 - 557.720i) q^{92} +(-630.000 - 1091.19i) q^{93} -502.000 q^{94} +(380.000 + 164.545i) q^{95} +805.000 q^{96} +(583.500 + 1010.65i) q^{97} +(70.5000 + 122.110i) q^{98} +(9.00000 - 15.5885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 5 q^{3} + 7 q^{4} - 5 q^{5} - 5 q^{6} + 44 q^{7} + 30 q^{8} + 2 q^{9} + 5 q^{10} + 18 q^{11} + 70 q^{12} - 54 q^{13} + 22 q^{14} + 25 q^{15} - 41 q^{16} + 54 q^{17} + 4 q^{18} - 133 q^{19}+ \cdots + 18 q^{99}+O(q^{100}) \) 2 * q + q^2 + 5 * q^3 + 7 * q^4 - 5 * q^5 - 5 * q^6 + 44 * q^7 + 30 * q^8 + 2 * q^9 + 5 * q^10 + 18 * q^11 + 70 * q^12 - 54 * q^13 + 22 * q^14 + 25 * q^15 - 41 * q^16 + 54 * q^17 + 4 * q^18 - 133 * q^19 - 70 * q^20 + 110 * q^21 + 9 * q^22 + 92 * q^23 + 75 * q^24 - 25 * q^25 - 108 * q^26 + 290 * q^27 + 154 * q^28 + 134 * q^29 + 50 * q^30 - 504 * q^31 + 161 * q^32 + 45 * q^33 - 54 * q^34 - 110 * q^35 - 14 * q^36 - 472 * q^37 - 152 * q^38 - 540 * q^39 - 75 * q^40 + 243 * q^41 - 110 * q^42 - 496 * q^43 + 63 * q^44 - 20 * q^45 + 184 * q^46 - 502 * q^47 + 205 * q^48 + 282 * q^49 - 50 * q^50 - 270 * q^51 + 378 * q^52 - 62 * q^53 + 145 * q^54 - 45 * q^55 + 660 * q^56 - 760 * q^57 + 268 * q^58 - 681 * q^59 - 175 * q^60 + 142 * q^61 - 252 * q^62 + 44 * q^63 - 334 * q^64 + 540 * q^65 - 45 * q^66 - 55 * q^67 + 756 * q^68 + 920 * q^69 + 110 * q^70 + 974 * q^71 + 30 * q^72 - 695 * q^73 - 236 * q^74 - 250 * q^75 + 133 * q^76 + 396 * q^77 - 270 * q^78 + 736 * q^79 - 205 * q^80 + 671 * q^81 - 243 * q^82 - 126 * q^83 + 1540 * q^84 + 270 * q^85 + 496 * q^86 + 1340 * q^87 + 270 * q^88 - 726 * q^89 - 10 * q^90 - 1188 * q^91 - 644 * q^92 - 1260 * q^93 - 1004 * q^94 + 760 * q^95 + 1610 * q^96 + 1167 * q^97 + 141 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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