LMFDB - Embedded newform 40.3.i.a.37.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,3,Mod(13,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("40.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	40.i (of order $4$, 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:	$1.08992105744$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} - 3x^{16} + 11x^{14} + x^{12} - 40x^{10} + 4x^{8} + 176x^{6} - 192x^{4} - 256x^{2} + 1024 $ x^20 - x^18 - 3x^16 + 11x^14 + x^12 - 40x^10 + 4x^8 + 176x^6 - 192x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.10
Root			$-1.27574 + 0.610320i$ of defining polynomial
Character	$\chi$	$=$	40.37
Dual form			40.3.i.a.13.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.88606 - 0.665418i) q^{2} +(-3.60765 - 3.60765i) q^{3} +(3.11444 - 2.51004i) q^{4} +(2.34539 + 4.41578i) q^{5} +(-9.20485 - 4.40365i) q^{6} +(1.47907 + 1.47907i) q^{7} +(4.20379 - 6.80648i) q^{8} +17.0303i q^{9} +(7.36189 + 6.76776i) q^{10} +11.3076i q^{11} +(-20.2912 - 2.18047i) q^{12} +(-3.17204 - 3.17204i) q^{13} +(3.77383 + 1.80542i) q^{14} +(7.46927 - 24.3920i) q^{15} +(3.39943 - 15.6347i) q^{16} +(-9.94834 - 9.94834i) q^{17} +(11.3323 + 32.1202i) q^{18} -11.2705 q^{19} +(18.3883 + 7.86567i) q^{20} -10.6720i q^{21} +(7.52426 + 21.3267i) q^{22} +(1.67851 - 1.67851i) q^{23} +(-39.7212 + 9.38962i) q^{24} +(-13.9983 + 20.7135i) q^{25} +(-8.09340 - 3.87192i) q^{26} +(28.9707 - 28.9707i) q^{27} +(8.31902 + 0.893952i) q^{28} +41.1865 q^{29} +(-2.14339 - 50.9749i) q^{30} -29.2537 q^{31} +(-3.99209 - 31.7500i) q^{32} +(40.7938 - 40.7938i) q^{33} +(-25.3830 - 12.1433i) q^{34} +(-3.06227 + 10.0003i) q^{35} +(42.7468 + 53.0399i) q^{36} +(-8.60159 + 8.60159i) q^{37} +(-21.2568 + 7.49961i) q^{38} +22.8873i q^{39} +(39.9155 + 2.59916i) q^{40} -19.6639 q^{41} +(-7.10133 - 20.1280i) q^{42} +(-25.1228 - 25.1228i) q^{43} +(28.3824 + 35.2167i) q^{44} +(-75.2023 + 39.9428i) q^{45} +(2.04886 - 4.28268i) q^{46} +(41.7392 + 41.7392i) q^{47} +(-68.6686 + 44.1406i) q^{48} -44.6247i q^{49} +(-12.6185 + 48.3815i) q^{50} +71.7804i q^{51} +(-17.8411 - 1.91718i) q^{52} +(2.16209 + 2.16209i) q^{53} +(35.3628 - 73.9181i) q^{54} +(-49.9317 + 26.5206i) q^{55} +(16.2850 - 3.84958i) q^{56} +(40.6601 + 40.6601i) q^{57} +(77.6802 - 27.4063i) q^{58} +38.9669 q^{59} +(-37.9622 - 94.7154i) q^{60} -87.5112i q^{61} +(-55.1742 + 19.4660i) q^{62} +(-25.1891 + 25.1891i) q^{63} +(-28.6564 - 57.2260i) q^{64} +(6.56738 - 21.4467i) q^{65} +(49.7945 - 104.084i) q^{66} +(-31.1362 + 31.1362i) q^{67} +(-55.9542 - 6.01278i) q^{68} -12.1110 q^{69} +(0.878753 + 20.8988i) q^{70} +134.120 q^{71} +(115.917 + 71.5919i) q^{72} +(-26.1299 + 26.1299i) q^{73} +(-10.4994 + 21.9468i) q^{74} +(125.228 - 24.2260i) q^{75} +(-35.1013 + 28.2894i) q^{76} +(-16.7247 + 16.7247i) q^{77} +(15.2296 + 43.1667i) q^{78} +23.1510i q^{79} +(77.0125 - 21.6583i) q^{80} -55.7594 q^{81} +(-37.0873 + 13.0847i) q^{82} +(-68.3496 - 68.3496i) q^{83} +(-26.7871 - 33.2372i) q^{84} +(20.5970 - 67.2625i) q^{85} +(-64.1002 - 30.6659i) q^{86} +(-148.587 - 148.587i) q^{87} +(76.9647 + 47.5346i) q^{88} -75.2561i q^{89} +(-115.257 + 125.375i) q^{90} -9.38338i q^{91} +(1.01449 - 9.44074i) q^{92} +(105.537 + 105.537i) q^{93} +(106.497 + 50.9485i) q^{94} +(-26.4337 - 49.7681i) q^{95} +(-100.141 + 128.945i) q^{96} +(57.5730 + 57.5730i) q^{97} +(-29.6941 - 84.1648i) q^{98} -192.572 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8} + 6 q^{10} - 44 q^{12} - 4 q^{15} - 56 q^{16} - 12 q^{17} + 10 q^{18} - 24 q^{20} + 92 q^{22} - 4 q^{23} - 28 q^{25} + 100 q^{26} + 68 q^{28} + 100 q^{30} - 136 q^{31}+ \cdots + 546 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8 + 6 * q^10 - 44 * q^12 - 4 * q^15 - 56 * q^16 - 12 * q^17 + 10 * q^18 - 24 * q^20 + 92 * q^22 - 4 * q^23 - 28 * q^25 + 100 * q^26 + 68 * q^28 + 100 * q^30 - 136 * q^31 + 128 * q^32 + 32 * q^33 + 220 * q^36 - 188 * q^38 + 156 * q^40 - 8 * q^41 - 284 * q^42 - 240 * q^46 + 188 * q^47 - 256 * q^48 - 274 * q^50 - 332 * q^52 + 96 * q^55 - 360 * q^56 - 40 * q^57 + 268 * q^58 - 340 * q^60 + 336 * q^62 + 228 * q^63 - 60 * q^65 + 616 * q^66 + 396 * q^68 + 300 * q^70 + 248 * q^71 + 668 * q^72 - 124 * q^73 + 424 * q^76 - 368 * q^78 + 496 * q^80 + 132 * q^81 - 676 * q^82 - 672 * q^86 - 488 * q^87 - 304 * q^88 - 474 * q^90 - 628 * q^92 - 488 * q^95 - 1024 * q^96 + 100 * q^97 + 546 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	1.88606	−	0.665418i	0.943029	−	0.332709i
$2$	1.88606	−	0.665418i	0.943029	−	0.332709i
$3$	−3.60765	−	3.60765i	−1.20255	−	1.20255i	−0.973388	−	0.229164i	$-0.926401\pi$
$3$	−3.60765	−	3.60765i	−1.20255	−	1.20255i	−0.229164	−	0.973388i	$-0.573599\pi$
$4$	3.11444	−	2.51004i	0.778609	−	0.627509i
$5$	2.34539	+	4.41578i	0.469078	+	0.883157i
$5$	2.34539	+	4.41578i	0.469078	+	0.883157i
$6$	−9.20485	−	4.40365i	−1.53414	−	0.733941i
$7$	1.47907	+	1.47907i	0.211296	+	0.211296i	0.804818	−	0.593522i	$-0.202263\pi$
$7$	1.47907	+	1.47907i	0.211296	+	0.211296i	−0.593522	+	0.804818i	$0.702263\pi$
$8$	4.20379	−	6.80648i	0.525473	−	0.850810i
$9$			17.0303i			1.89226i
$10$	7.36189	+	6.76776i	0.736189	+	0.676776i
$11$			11.3076i			1.02796i	0.857802	+	0.513980i	$0.171829\pi$
$11$			11.3076i			1.02796i	−0.857802	+	0.513980i	$0.828171\pi$
$12$	−20.2912	−	2.18047i	−1.69093	−	0.181705i
$13$	−3.17204	−	3.17204i	−0.244003	−	0.244003i	0.574501	−	0.818504i	$-0.305196\pi$
$13$	−3.17204	−	3.17204i	−0.244003	−	0.244003i	−0.818504	+	0.574501i	$0.805196\pi$
$14$	3.77383	+	1.80542i	0.269559	+	0.128958i
$15$	7.46927	−	24.3920i	0.497951	−	1.62613i
$16$	3.39943	−	15.6347i	0.212464	−	0.977169i
$17$	−9.94834	−	9.94834i	−0.585197	−	0.585197i	0.351130	−	0.936327i	$-0.385797\pi$
$17$	−9.94834	−	9.94834i	−0.585197	−	0.585197i	−0.936327	+	0.351130i	$0.885797\pi$
$18$	11.3323	+	32.1202i	0.629572	+	1.78446i
$19$	−11.2705			−0.593185			−0.296592	−	0.955004i	$-0.595850\pi$
$19$	−11.2705			−0.593185			−0.296592	+	0.955004i	$0.595850\pi$
$20$	18.3883	+	7.86567i	0.919417	+	0.393283i
$21$		−	10.6720i		−	0.508190i
$22$	7.52426	+	21.3267i	0.342012	+	0.969396i
$23$	1.67851	−	1.67851i	0.0729787	−	0.0729787i	−0.669675	−	0.742654i	$-0.733567\pi$
$23$	1.67851	−	1.67851i	0.0729787	−	0.0729787i	0.742654	+	0.669675i	$0.233567\pi$
$24$	−39.7212	+	9.38962i	−1.65505	+	0.391234i
$25$	−13.9983	+	20.7135i	−0.559932	+	0.828539i
$26$	−8.09340	−	3.87192i	−0.311284	−	0.148920i
$27$	28.9707	−	28.9707i	1.07299	−	1.07299i
$28$	8.31902	+	0.893952i	0.297108	+	0.0319269i
$29$	41.1865			1.42022			0.710112	−	0.704088i	$-0.248644\pi$
$29$	41.1865			1.42022			0.710112	+	0.704088i	$0.248644\pi$
$30$	−2.14339	−	50.9749i	−0.0714464	−	1.69916i
$31$	−29.2537			−0.943668			−0.471834	−	0.881687i	$-0.656408\pi$
$31$	−29.2537			−0.943668			−0.471834	+	0.881687i	$0.656408\pi$
$32$	−3.99209	−	31.7500i	−0.124753	−	0.992188i
$33$	40.7938	−	40.7938i	1.23617	−	1.23617i
$34$	−25.3830	−	12.1433i	−0.746558	−	0.357157i
$35$	−3.06227	+	10.0003i	−0.0874934	+	0.285722i
$36$	42.7468	+	53.0399i	1.18741	+	1.47333i
$37$	−8.60159	+	8.60159i	−0.232475	+	0.232475i	−0.813725	−	0.581250i	$-0.802564\pi$
$37$	−8.60159	+	8.60159i	−0.232475	+	0.232475i	0.581250	+	0.813725i	$0.302564\pi$
$38$	−21.2568	+	7.49961i	−0.559391	+	0.197358i
$39$			22.8873i			0.586853i
$40$	39.9155	+	2.59916i	0.997887	+	0.0649791i
$41$	−19.6639			−0.479607			−0.239804	−	0.970821i	$-0.577083\pi$
$41$	−19.6639			−0.479607			−0.239804	+	0.970821i	$0.577083\pi$
$42$	−7.10133	−	20.1280i	−0.169079	−	0.479238i
$43$	−25.1228	−	25.1228i	−0.584251	−	0.584251i	0.351818	−	0.936069i	$-0.385564\pi$
$43$	−25.1228	−	25.1228i	−0.584251	−	0.584251i	−0.936069	+	0.351818i	$0.885564\pi$
$44$	28.3824	+	35.2167i	0.645054	+	0.800379i
$45$	−75.2023	+	39.9428i	−1.67116	+	0.887617i
$46$	2.04886	−	4.28268i	0.0445404	−	0.0931018i
$47$	41.7392	+	41.7392i	0.888068	+	0.888068i	0.994337	−	0.106269i	$-0.0338906\pi$
$47$	41.7392	+	41.7392i	0.888068	+	0.888068i	−0.106269	+	0.994337i	$0.533891\pi$
$48$	−68.6686	+	44.1406i	−1.43060	+	0.919596i
$49$		−	44.6247i		−	0.910708i
$50$	−12.6185	+	48.3815i	−0.252370	+	0.967631i
$51$			71.7804i			1.40746i
$52$	−17.8411	−	1.91718i	−0.343098	−	0.0368689i
$53$	2.16209	+	2.16209i	0.0407941	+	0.0407941i	0.727210	−	0.686415i	$-0.240817\pi$
$53$	2.16209	+	2.16209i	0.0407941	+	0.0407941i	−0.686415	+	0.727210i	$0.740817\pi$
$54$	35.3628	−	73.9181i	0.654867	−	1.36885i
$55$	−49.9317	+	26.5206i	−0.907850	+	0.482193i
$56$	16.2850	−	3.84958i	0.290804	−	0.0687425i
$57$	40.6601	+	40.6601i	0.713335	+	0.713335i
$58$	77.6802	−	27.4063i	1.33931	−	0.472522i
$59$	38.9669			0.660456			0.330228	−	0.943901i	$-0.392874\pi$
$59$	38.9669			0.660456			0.330228	+	0.943901i	$0.392874\pi$
$60$	−37.9622	−	94.7154i	−0.632703	−	1.57859i
$61$		−	87.5112i		−	1.43461i	−0.696759	−	0.717305i	$-0.745375\pi$
$61$		−	87.5112i		−	1.43461i	0.696759	−	0.717305i	$-0.254625\pi$
$62$	−55.1742	+	19.4660i	−0.889907	+	0.313967i
$63$	−25.1891	+	25.1891i	−0.399828	+	0.399828i
$64$	−28.6564	−	57.2260i	−0.447756	−	0.894156i
$65$	6.56738	−	21.4467i	0.101037	−	0.329950i
$66$	49.7945	−	104.084i	0.754462	−	1.57704i
$67$	−31.1362	+	31.1362i	−0.464719	+	0.464719i	−0.900199	−	0.435479i	$-0.856579\pi$
$67$	−31.1362	+	31.1362i	−0.464719	+	0.464719i	0.435479	+	0.900199i	$0.356579\pi$
$68$	−55.9542	−	6.01278i	−0.822856	−	0.0884232i
$69$	−12.1110			−0.175521
$70$	0.878753	+	20.8988i	0.0125536	+	0.298554i
$71$	134.120			1.88902			0.944510	−	0.328483i	$-0.106537\pi$
$71$	134.120			1.88902			0.944510	+	0.328483i	$0.106537\pi$
$72$	115.917	+	71.5919i	1.60995	+	0.994332i
$73$	−26.1299	+	26.1299i	−0.357943	+	0.357943i	−0.863054	−	0.505111i	$-0.831452\pi$
$73$	−26.1299	+	26.1299i	−0.357943	+	0.357943i	0.505111	+	0.863054i	$0.331452\pi$
$74$	−10.4994	+	21.9468i	−0.141884	+	0.296578i
$75$	125.228	−	24.2260i	1.66971	−	0.323013i
$76$	−35.1013	+	28.2894i	−0.461859	+	0.372229i
$77$	−16.7247	+	16.7247i	−0.217204	+	0.217204i
$78$	15.2296	+	43.1667i	0.195251	+	0.553420i
$79$			23.1510i			0.293050i	0.989207	+	0.146525i	$0.0468090\pi$
$79$			23.1510i			0.293050i	−0.989207	+	0.146525i	$0.953191\pi$
$80$	77.0125	−	21.6583i	0.962656	−	0.270729i
$81$	−55.7594			−0.688388
$82$	−37.0873	+	13.0847i	−0.452284	+	0.159570i
$83$	−68.3496	−	68.3496i	−0.823489	−	0.823489i	0.163118	−	0.986607i	$-0.447845\pi$
$83$	−68.3496	−	68.3496i	−0.823489	−	0.823489i	−0.986607	+	0.163118i	$0.947845\pi$
$84$	−26.7871	−	33.2372i	−0.318894	−	0.395681i
$85$	20.5970	−	67.2625i	0.242318	−	0.791323i
$86$	−64.1002	−	30.6659i	−0.745352	−	0.356580i
$87$	−148.587	−	148.587i	−1.70789	−	1.70789i
$88$	76.9647	+	47.5346i	0.874599	+	0.540165i
$89$		−	75.2561i		−	0.845574i	−0.906229	−	0.422787i	$-0.861052\pi$
$89$		−	75.2561i		−	0.845574i	0.906229	−	0.422787i	$-0.138948\pi$
$90$	−115.257	+	125.375i	−1.28064	+	1.39306i
$91$		−	9.38338i		−	0.103114i
$92$	1.01449	−	9.44074i	0.0110271	−	0.102617i
$93$	105.537	+	105.537i	1.13481	+	1.13481i
$94$	106.497	+	50.9485i	1.13294	+	0.542006i
$95$	−26.4337	−	49.7681i	−0.278250	−	0.523875i
$96$	−100.141	+	128.945i	−1.04314	+	1.34318i
$97$	57.5730	+	57.5730i	0.593536	+	0.593536i	0.938585	−	0.345049i	$-0.112138\pi$
$97$	57.5730	+	57.5730i	0.593536	+	0.593536i	−0.345049	+	0.938585i	$0.612138\pi$
$98$	−29.6941	−	84.1648i	−0.303001	−	0.858824i
$99$	−192.572			−1.94517
$100$	8.39476	+	99.6470i	0.0839476	+	0.996470i
$101$			112.245i			1.11133i	0.831405	+	0.555666i	$0.187537\pi$
$101$			112.245i			1.11133i	−0.831405	+	0.555666i	$0.812463\pi$
$102$	47.7640	+	135.382i	0.468274	+	1.32727i
$103$	25.4523	−	25.4523i	0.247109	−	0.247109i	−0.572674	−	0.819783i	$-0.694094\pi$
$103$	25.4523	−	25.4523i	0.247109	−	0.247109i	0.819783	+	0.572674i	$0.194094\pi$
$104$	−34.9250	+	8.25586i	−0.335818	+	0.0793833i
$105$	47.1252	−	25.0300i	0.448811	−	0.238380i
$106$	5.51652	+	2.63913i	0.0520426	+	0.0248975i
$107$	66.0387	−	66.0387i	0.617184	−	0.617184i	−0.327624	−	0.944808i	$-0.606248\pi$
$107$	66.0387	−	66.0387i	0.617184	−	0.617184i	0.944808	+	0.327624i	$0.106248\pi$
$108$	17.5099	−	162.945i	0.162129	−	1.50875i
$109$	91.2619			0.837266			0.418633	−	0.908156i	$-0.362509\pi$
$109$	91.2619			0.837266			0.418633	+	0.908156i	$0.362509\pi$
$110$	−76.5269	+	83.2450i	−0.695699	+	0.756772i
$111$	62.0631			0.559127
$112$	28.1529	−	18.0969i	0.251365	−	0.161579i
$113$	−127.312	+	127.312i	−1.12666	+	1.12666i	−0.135940	+	0.990717i	$0.543406\pi$
$113$	−127.312	+	127.312i	−1.12666	+	1.12666i	−0.990717	+	0.135940i	$0.956594\pi$
$114$	103.743	+	49.6314i	0.910029	+	0.435363i
$115$	11.3487	+	3.47518i	0.0986844	+	0.0302190i
$116$	128.273	−	103.380i	1.10580	−	0.891204i
$117$	54.0210	−	54.0210i	0.461718	−	0.461718i
$118$	73.4938	−	25.9293i	0.622829	−	0.219740i
$119$		−	29.4287i		−	0.247300i
$120$	−134.624	−	153.378i	−1.12187	−	1.27815i
$121$	−6.86087			−0.0567014
$122$	−58.2316	−	165.051i	−0.477308	−	1.35288i
$123$	70.9406	+	70.9406i	0.576753	+	0.576753i
$124$	−91.1088	+	73.4279i	−0.734749	+	0.592160i
$125$	−124.298	−	13.2323i	−0.994381	−	0.105858i
$126$	−30.7469	+	64.2695i	−0.244023	+	0.510076i
$127$	−14.5303	−	14.5303i	−0.114412	−	0.114412i	0.647583	−	0.761995i	$-0.275780\pi$
$127$	−14.5303	−	14.5303i	−0.114412	−	0.114412i	−0.761995	+	0.647583i	$0.775780\pi$
$128$	−92.1268	−	88.8631i	−0.719741	−	0.694243i
$129$			181.269i			1.40518i
$130$	−1.88459	−	44.8199i	−0.0144968	−	0.344768i
$131$			51.9051i			0.396222i	0.980180	+	0.198111i	$0.0634807\pi$
$131$			51.9051i			0.396222i	−0.980180	+	0.198111i	$0.936519\pi$
$132$	24.6557	−	229.443i	0.186786	−	1.73821i
$133$	−16.6699	−	16.6699i	−0.125338	−	0.125338i
$134$	−38.0061	+	79.4433i	−0.283628	+	0.592860i
$135$	195.876	+	59.9808i	1.45093	+	0.444302i
$136$	−109.534	+	25.8925i	−0.805396	+	0.190386i
$137$	−98.7636	−	98.7636i	−0.720902	−	0.720902i	0.247887	−	0.968789i	$-0.420264\pi$
$137$	−98.7636	−	98.7636i	−0.720902	−	0.720902i	−0.968789	+	0.247887i	$0.920264\pi$
$138$	−22.8420	+	8.05887i	−0.165522	+	0.0583976i
$139$	48.6381			0.349914			0.174957	−	0.984576i	$-0.444021\pi$
$139$	48.6381			0.349914			0.174957	+	0.984576i	$0.444021\pi$
$140$	15.5638	+	38.8316i	0.111170	+	0.277369i
$141$		−	301.161i		−	2.13589i
$142$	252.959	−	89.2462i	1.78140	−	0.628494i
$143$	35.8681	−	35.8681i	0.250826	−	0.250826i
$144$	266.264	+	57.8935i	1.84906	+	0.402038i
$145$	96.5984	+	181.871i	0.666196	+	1.25428i
$146$	−31.8952	+	66.6697i	−0.218460	+	0.456642i
$147$	−160.990	+	160.990i	−1.09517	+	1.09517i
$148$	−5.19880	+	48.3794i	−0.0351270	+	0.326888i
$149$	−222.425			−1.49278			−0.746391	−	0.665508i	$-0.768215\pi$
$149$	−222.425			−1.49278			−0.746391	+	0.665508i	$0.768215\pi$
$150$	220.067	−	129.021i	1.46711	−	0.860138i
$151$	−199.700			−1.32252			−0.661259	−	0.750157i	$-0.729978\pi$
$151$	−199.700			−1.32252			−0.661259	+	0.750157i	$0.729978\pi$
$152$	−47.3788	+	76.7125i	−0.311703	+	0.504688i
$153$	169.424	−	169.424i	1.10734	−	1.10734i
$154$	−20.4149	+	42.6728i	−0.132564	+	0.277096i
$155$	−68.6113	−	129.178i	−0.442654	−	0.833407i
$156$	57.4479	+	71.2809i	0.368256	+	0.456929i
$157$	−191.183	+	191.183i	−1.21773	+	1.21773i	−0.249302	+	0.968426i	$0.580201\pi$
$157$	−191.183	+	191.183i	−1.21773	+	1.21773i	−0.968426	+	0.249302i	$0.919799\pi$
$158$	15.4051	+	43.6641i	0.0975006	+	0.276355i
$159$		−	15.6001i		−	0.0981141i
$160$	130.838	−	92.0944i	0.817739	−	0.575590i
$161$	4.96529			0.0308403
$162$	−105.166	+	37.1034i	−0.649170	+	0.229033i
$163$	100.849	+	100.849i	0.618705	+	0.618705i	0.945199	−	0.326494i	$-0.105867\pi$
$163$	100.849	+	100.849i	0.618705	+	0.618705i	−0.326494	+	0.945199i	$0.605867\pi$
$164$	−61.2420	+	49.3571i	−0.373427	+	0.300958i
$165$	275.814	+	84.4592i	1.67160	+	0.511874i
$166$	−174.392	−	83.4303i	−1.05056	−	0.502592i
$167$	208.556	+	208.556i	1.24884	+	1.24884i	0.956232	+	0.292609i	$0.0945233\pi$
$167$	208.556	+	208.556i	1.24884	+	1.24884i	0.292609	+	0.956232i	$0.405477\pi$
$168$	−72.6386	−	44.8627i	−0.432373	−	0.267040i
$169$		−	148.876i		−	0.880925i
$170$	−5.91054	−	140.567i	−0.0347679	−	0.826862i
$171$		−	191.941i		−	1.12246i
$172$	−141.302	−	15.1842i	−0.821526	−	0.0882803i
$173$	122.257	+	122.257i	0.706689	+	0.706689i	0.965838	−	0.259148i	$-0.0834419\pi$
$173$	122.257	+	122.257i	0.706689	+	0.706689i	−0.259148	+	0.965838i	$0.583442\pi$
$174$	−379.116	−	181.371i	−2.17883	−	1.04236i
$175$	−51.3413	+	9.93224i	−0.293379	+	0.0567556i
$176$	176.790	+	38.4393i	1.00449	+	0.218405i
$177$	−140.579	−	140.579i	−0.794232	−	0.794232i
$178$	−50.0768	−	141.937i	−0.281330	−	0.797402i
$179$	63.7773			0.356298			0.178149	−	0.984004i	$-0.442989\pi$
$179$	63.7773			0.356298			0.178149	+	0.984004i	$0.442989\pi$
$180$	−133.955	+	313.160i	−0.744194	+	1.73978i
$181$			192.099i			1.06132i	0.847585	+	0.530660i	$0.178056\pi$
$181$			192.099i			1.06132i	−0.847585	+	0.530660i	$0.821944\pi$
$182$	−6.24387	−	17.6976i	−0.0343070	−	0.0972396i
$183$	−315.710	+	315.710i	−1.72519	+	1.72519i
$184$	−4.36865	−	18.4809i	−0.0237427	−	0.100439i
$185$	−58.1568	−	17.8087i	−0.314361	−	0.0962631i
$186$	269.276	+	128.823i	1.44772	+	0.692597i
$187$	112.491	−	112.491i	0.601559	−	0.601559i
$188$	234.761	+	25.2272i	1.24873	+	0.134187i
$189$	85.6996			0.453437
$190$	−82.9722	−	76.2761i	−0.436696	−	0.401453i
$191$	−170.796			−0.894218			−0.447109	−	0.894480i	$-0.647546\pi$
$191$	−170.796			−0.894218			−0.447109	+	0.894480i	$0.647546\pi$
$192$	−103.069	+	309.834i	−0.536819	+	1.61372i
$193$	111.295	−	111.295i	0.576656	−	0.576656i	−0.357325	−	0.933980i	$-0.616311\pi$
$193$	111.295	−	111.295i	0.576656	−	0.576656i	0.933980	+	0.357325i	$0.116311\pi$
$194$	146.896	+	70.2760i	0.757197	+	0.362247i
$195$	−101.065	+	53.6796i	−0.518283	+	0.275280i
$196$	−112.010	−	138.981i	−0.571477	−	0.709085i
$197$	96.8892	−	96.8892i	0.491823	−	0.491823i	−0.417057	−	0.908880i	$-0.636938\pi$
$197$	96.8892	−	96.8892i	0.491823	−	0.491823i	0.908880	+	0.417057i	$0.136938\pi$
$198$	−363.201	+	128.141i	−1.83435	+	0.647175i
$199$		−	139.805i		−	0.702540i	−0.936274	−	0.351270i	$-0.885750\pi$
$199$		−	139.805i		−	0.702540i	0.936274	−	0.351270i	$-0.114250\pi$
$200$	82.1400	+	182.354i	0.410700	+	0.911771i
$201$	224.657			1.11770
$202$	74.6896	+	211.700i	0.369751	+	1.04802i
$203$	60.9179	+	60.9179i	0.300088	+	0.300088i
$204$	180.171	+	223.555i	0.883193	+	1.09586i
$205$	−46.1195	−	86.8315i	−0.224973	−	0.423569i
$206$	31.0681	−	64.9409i	0.150816	−	0.315247i
$207$	28.5856	+	28.5856i	0.138095	+	0.138095i
$208$	−60.3771	+	38.8108i	−0.290274	+	0.186590i
$209$		−	127.442i		−	0.609770i
$210$	72.2254	−	78.5659i	0.343931	−	0.374123i
$211$		−	9.55891i		−	0.0453029i	−0.999743	−	0.0226514i	$-0.992789\pi$
$211$		−	9.55891i		−	0.0453029i	0.999743	−	0.0226514i	$-0.00721080\pi$
$212$	12.1606	+	1.30677i	0.0573614	+	0.00616399i
$213$	−483.860	−	483.860i	−2.27164	−	2.27164i
$214$	80.6095	−	168.496i	0.376680	−	0.787365i
$215$	52.0141	−	169.860i	0.241926	−	0.790044i
$216$	−75.4019	−	318.975i	−0.349083	−	1.47674i
$217$	−43.2684	−	43.2684i	−0.199394	−	0.199394i
$218$	172.125	−	60.7274i	0.789566	−	0.278566i
$219$	188.535			0.860890
$220$	−88.9415	+	207.927i	−0.404279	+	0.945124i
$221$			63.1131i			0.285580i
$222$	117.055	−	41.2979i	0.527273	−	0.186027i
$223$	276.355	−	276.355i	1.23926	−	1.23926i	0.278957	−	0.960304i	$-0.410011\pi$
$223$	276.355	−	276.355i	1.23926	−	1.23926i	0.960304	−	0.278957i	$-0.0899888\pi$
$224$	41.0560	−	52.8652i	0.183286	−	0.236006i
$225$	−352.757	−	238.396i	−1.56781	−	1.05954i
$226$	−155.403	+	324.834i	−0.687622	+	1.43732i
$227$	160.929	−	160.929i	0.708938	−	0.708938i	−0.257374	−	0.966312i	$-0.582857\pi$
$227$	160.929	−	160.929i	0.708938	−	0.708938i	0.966312	+	0.257374i	$0.0828572\pi$
$228$	228.692	+	24.5750i	1.00303	+	0.107785i
$229$	40.2472			0.175752			0.0878760	−	0.996131i	$-0.471992\pi$
$229$	40.2472			0.175752			0.0878760	+	0.996131i	$0.471992\pi$
$230$	23.7168	−	0.997243i	0.103116	−	0.00433584i
$231$	120.674			0.522398
$232$	173.139	−	280.335i	0.746290	−	1.20834i
$233$	−241.061	+	241.061i	−1.03460	+	1.03460i	−0.0352176	+	0.999380i	$0.511212\pi$
$233$	−241.061	+	241.061i	−1.03460	+	1.03460i	−0.999380	+	0.0352176i	$0.988788\pi$
$234$	65.9402	−	137.833i	0.281796	−	0.589031i
$235$	−86.4166	+	282.206i	−0.367730	+	1.20088i
$236$	121.360	−	97.8083i	0.514237	−	0.414442i
$237$	83.5208	−	83.5208i	0.352408	−	0.352408i
$238$	−19.5824	−	55.5042i	−0.0822789	−	0.233211i
$239$			249.002i			1.04185i	0.853603	+	0.520925i	$0.174413\pi$
$239$			249.002i			1.04185i	−0.853603	+	0.520925i	$0.825587\pi$
$240$	−355.970	−	199.699i	−1.48321	−	0.832077i
$241$	324.753			1.34752			0.673762	−	0.738948i	$-0.264677\pi$
$241$	324.753			1.34752			0.673762	+	0.738948i	$0.264677\pi$
$242$	−12.9400	+	4.56535i	−0.0534711	+	0.0188651i
$243$	−59.5755	−	59.5755i	−0.245167	−	0.245167i
$244$	−219.656	−	272.548i	−0.900231	−	1.11700i
$245$	197.053	−	104.662i	0.804298	−	0.427193i
$246$	181.003	+	86.5929i	0.735786	+	0.352004i
$247$	35.7505	+	35.7505i	0.144739	+	0.144739i
$248$	−122.976	+	199.115i	−0.495872	+	0.802882i
$249$			493.163i			1.98058i
$250$	−243.238	+	57.7530i	−0.972951	+	0.231012i
$251$			166.729i			0.664260i	0.943234	+	0.332130i	$0.107767\pi$
$251$			166.729i			0.664260i	−0.943234	+	0.332130i	$0.892233\pi$
$252$	−15.2243	+	141.676i	−0.0604139	+	0.562205i
$253$	18.9799	+	18.9799i	0.0750192	+	0.0750192i
$254$	−37.0738	−	17.7363i	−0.145960	−	0.0698280i
$255$	−316.967	+	168.353i	−1.24301	+	0.660207i
$256$	−232.888	−	106.298i	−0.909718	−	0.415227i
$257$	184.509	+	184.509i	0.717933	+	0.717933i	0.968182	−	0.250248i	$-0.0805122\pi$
$257$	184.509	+	184.509i	0.717933	+	0.717933i	−0.250248	+	0.968182i	$0.580512\pi$
$258$	120.620	+	341.883i	0.467518	+	1.32513i
$259$	−25.4448			−0.0982424
$260$	−33.3784	−	83.2789i	−0.128378	−	0.320303i
$261$			701.421i			2.68743i
$262$	34.5386	+	97.8962i	0.131827	+	0.373649i
$263$	3.85637	−	3.85637i	0.0146630	−	0.0146630i	−0.699737	−	0.714400i	$-0.746700\pi$
$263$	3.85637	−	3.85637i	0.0146630	−	0.0146630i	0.714400	+	0.699737i	$0.246700\pi$
$264$	−106.174	−	449.150i	−0.402173	−	1.70133i
$265$	−4.47638	+	14.6183i	−0.0168920	+	0.0551632i
$266$	−42.5329	−	20.3480i	−0.159898	−	0.0764962i
$267$	−271.498	+	271.498i	−1.01685	+	1.01685i
$268$	−18.8187	+	175.125i	−0.0702190	+	0.653450i
$269$	−163.125			−0.606413			−0.303206	−	0.952925i	$-0.598057\pi$
$269$	−163.125			−0.606413			−0.303206	+	0.952925i	$0.598057\pi$
$270$	409.346	−	17.2122i	1.51610	−	0.0637488i
$271$	100.647			0.371391			0.185696	−	0.982607i	$-0.440546\pi$
$271$	100.647			0.371391			0.185696	+	0.982607i	$0.440546\pi$
$272$	−189.358	+	121.721i	−0.696169	+	0.447502i
$273$	−33.8520	+	33.8520i	−0.124000	+	0.124000i
$274$	−251.993	−	120.555i	−0.919682	−	0.439981i
$275$	−234.219	−	158.287i	−0.851704	−	0.575587i
$276$	−37.7189	+	30.3990i	−0.136663	+	0.110141i
$277$	172.773	−	172.773i	0.623729	−	0.623729i	−0.322754	−	0.946483i	$-0.604609\pi$
$277$	172.773	−	172.773i	0.623729	−	0.623729i	0.946483	+	0.322754i	$0.104609\pi$
$278$	91.7343	−	32.3647i	0.329980	−	0.116420i
$279$		−	498.201i		−	1.78567i
$280$	55.1936	+	62.8823i	0.197120	+	0.224580i
$281$	−300.384			−1.06898			−0.534491	−	0.845174i	$-0.679497\pi$
$281$	−300.384			−1.06898			−0.534491	+	0.845174i	$0.679497\pi$
$282$	−200.398	−	568.008i	−0.710632	−	2.01421i
$283$	−151.310	−	151.310i	−0.534663	−	0.534663i	0.387293	−	0.921957i	$-0.373410\pi$
$283$	−151.310	−	151.310i	−0.534663	−	0.534663i	−0.921957	+	0.387293i	$0.873410\pi$
$284$	417.709	−	336.647i	1.47081	−	1.18538i
$285$	−84.1825	+	274.910i	−0.295377	+	0.964597i
$286$	43.7820	−	91.5165i	0.153084	−	0.319988i
$287$	−29.0844	−	29.0844i	−0.101339	−	0.101339i
$288$	540.714	−	67.9867i	1.87748	−	0.236065i
$289$		−	91.0610i		−	0.315090i
$290$	303.211	+	278.741i	1.04555	+	0.961175i
$291$		−	415.407i		−	1.42752i
$292$	−15.7929	+	146.967i	−0.0540852	+	0.503311i
$293$	154.132	+	154.132i	0.526048	+	0.526048i	0.919391	−	0.393344i	$-0.128682\pi$
$293$	154.132	+	154.132i	0.526048	+	0.526048i	−0.393344	+	0.919391i	$0.628682\pi$
$294$	−196.511	+	410.763i	−0.668406	+	1.39715i
$295$	91.3925	+	172.069i	0.309805	+	0.583286i
$296$	22.3873	+	94.7058i	0.0756328	+	0.319952i
$297$	327.588	+	327.588i	1.10299	+	1.10299i
$298$	−419.506	+	148.005i	−1.40774	+	0.496662i
$299$	−10.6486			−0.0356141
$300$	329.207	−	389.777i	1.09736	−	1.29926i
$301$		−	74.3170i		−	0.246900i
$302$	−376.647	+	132.884i	−1.24717	+	0.440014i
$303$	404.940	−	404.940i	1.33643	−	1.33643i
$304$	−38.3133	+	176.211i	−0.126031	+	0.579642i
$305$	386.431	−	205.248i	1.26699	−	0.672944i
$306$	206.805	−	432.281i	0.675835	−	1.41268i
$307$	−97.0784	+	97.0784i	−0.316216	+	0.316216i	−0.847312	−	0.531096i	$-0.821781\pi$
$307$	−97.0784	+	97.0784i	−0.316216	+	0.316216i	0.531096	+	0.847312i	$0.321781\pi$
$308$	−10.1084	+	94.0678i	−0.0328195	+	0.305415i
$309$	−183.646			−0.594324
$310$	−215.362	−	197.982i	−0.694718	−	0.638652i
$311$	−74.0447			−0.238086			−0.119043	−	0.992889i	$-0.537983\pi$
$311$	−74.0447			−0.238086			−0.119043	+	0.992889i	$0.537983\pi$
$312$	155.782	+	96.2132i	0.499301	+	0.308376i
$313$	−125.892	+	125.892i	−0.402212	+	0.402212i	−0.879012	−	0.476800i	$-0.841797\pi$
$313$	−125.892	+	125.892i	−0.402212	+	0.402212i	0.476800	+	0.879012i	$0.341797\pi$
$314$	−233.366	+	487.800i	−0.743204	+	1.55350i
$315$	−170.308	−	52.1515i	−0.540661	−	0.165560i
$316$	58.1098	+	72.1023i	0.183892	+	0.228172i
$317$	257.161	−	257.161i	0.811233	−	0.811233i	−0.173585	−	0.984819i	$-0.555535\pi$
$317$	257.161	−	257.161i	0.811233	−	0.811233i	0.984819	+	0.173585i	$0.0555353\pi$
$318$	−10.3806	−	29.4228i	−0.0326435	−	0.0925245i
$319$			465.719i			1.45993i
$320$	185.487	−	260.758i	0.579648	−	0.814867i
$321$	−476.489			−1.48439
$322$	9.36482	−	3.30399i	0.0290833	−	0.0102608i
$323$	112.123	+	112.123i	0.347130	+	0.347130i
$324$	−173.659	+	139.958i	−0.535985	+	0.431970i
$325$	110.107	−	21.3008i	0.338791	−	0.0655409i
$326$	257.314	+	123.100i	0.789306	+	0.377608i
$327$	−329.242	−	329.242i	−1.00685	−	1.00685i
$328$	−82.6628	+	133.842i	−0.252021	+	0.408055i
$329$			123.471i			0.375291i
$330$	576.402	−	24.2365i	1.74667	−	0.0734440i
$331$		−	403.967i		−	1.22045i	−0.792230	−	0.610223i	$-0.791080\pi$
$331$		−	403.967i		−	1.22045i	0.792230	−	0.610223i	$-0.208920\pi$
$332$	−384.430	−	41.3105i	−1.15792	−	0.124429i
$333$	−146.488	−	146.488i	−0.439904	−	0.439904i
$334$	532.127	+	254.572i	1.59319	+	0.762193i
$335$	−210.517	−	64.4642i	−0.628409	−	0.192430i
$336$	−166.853	−	36.2787i	−0.496587	−	0.107972i
$337$	−101.745	−	101.745i	−0.301915	−	0.301915i	0.539848	−	0.841763i	$-0.318482\pi$
$337$	−101.745	−	101.745i	−0.301915	−	0.301915i	−0.841763	+	0.539848i	$0.818482\pi$
$338$	−99.0650	−	280.789i	−0.293092	−	0.830738i
$339$	918.598			2.70973
$340$	−104.683	−	261.184i	−0.307892	−	0.768188i
$341$		−	330.788i		−	0.970053i
$342$	−127.721	−	362.011i	−0.373453	−	1.05851i
$343$	138.478	−	138.478i	0.403726	−	0.403726i
$344$	−276.609	+	65.3870i	−0.804095	+	0.190078i
$345$	−28.4049	−	53.4794i	−0.0823332	−	0.155013i
$346$	311.937	+	149.232i	0.901551	+	0.431307i
$347$	−196.538	+	196.538i	−0.566391	+	0.566391i	−0.931116	−	0.364724i	$-0.881163\pi$
$347$	−196.538	+	196.538i	−0.566391	+	0.566391i	0.364724	+	0.931116i	$0.381163\pi$
$348$	−835.722	−	89.8058i	−2.40150	−	0.258063i
$349$	454.536			1.30240			0.651198	−	0.758908i	$-0.274267\pi$
$349$	454.536			1.30240			0.651198	+	0.758908i	$0.274267\pi$
$350$	−90.2236	+	52.8962i	−0.257782	+	0.151132i
$351$	−183.793			−0.523626
$352$	359.015	−	45.1408i	1.01993	−	0.128241i
$353$	204.788	−	204.788i	0.580135	−	0.580135i	−0.354805	−	0.934940i	$-0.615453\pi$
$353$	204.788	−	204.788i	0.580135	−	0.580135i	0.934940	+	0.354805i	$0.115453\pi$
$354$	−358.684	−	171.596i	−1.01323	−	0.484736i
$355$	314.565	+	592.247i	0.886097	+	1.66830i
$356$	−188.896	−	234.380i	−0.530606	−	0.658372i
$357$	−106.169	+	106.169i	−0.297391	+	0.297391i
$358$	120.288	−	42.4386i	0.336000	−	0.118544i
$359$		−	27.2061i		−	0.0757831i	−0.999282	−	0.0378916i	$-0.987936\pi$
$359$		−	27.2061i		−	0.0757831i	0.999282	−	0.0378916i	$-0.0120641\pi$
$360$	−44.2646	+	679.774i	−0.122957	+	1.88826i
$361$	−233.976			−0.648132
$362$	127.826	+	362.310i	0.353111	+	1.00086i
$363$	24.7516	+	24.7516i	0.0681863	+	0.0681863i
$364$	−23.5526	−	29.2239i	−0.0647050	−	0.0802855i
$365$	−176.669	−	54.0991i	−0.484023	−	0.148217i
$366$	−385.369	+	805.528i	−1.05292	+	2.20090i
$367$	50.4416	+	50.4416i	0.137443	+	0.137443i	0.772481	−	0.635038i	$-0.219016\pi$
$367$	50.4416	+	50.4416i	0.137443	+	0.137443i	−0.635038	+	0.772481i	$0.719016\pi$
$368$	−20.5370	−	31.9490i	−0.0558072	−	0.0868179i
$369$		−	334.883i		−	0.907542i
$370$	−121.537	+	5.11040i	−0.328479	+	0.0138119i
$371$			6.39578i			0.0172393i
$372$	593.592	+	63.7867i	1.59568	+	0.171470i
$373$	−105.787	−	105.787i	−0.283612	−	0.283612i	0.550936	−	0.834548i	$-0.314271\pi$
$373$	−105.787	−	105.787i	−0.283612	−	0.283612i	−0.834548	+	0.550936i	$0.814271\pi$
$374$	137.312	−	287.019i	0.367143	−	0.767432i
$375$	400.685	+	496.161i	1.06849	+	1.32309i
$376$	459.560	−	108.634i	1.22223	−	0.288921i
$377$	−130.645	−	130.645i	−0.346540	−	0.346540i
$378$	161.635	−	57.0261i	0.427605	−	0.150863i
$379$	−595.709			−1.57179			−0.785896	−	0.618359i	$-0.787798\pi$
$379$	−595.709			−1.57179			−0.785896	+	0.618359i	$0.787798\pi$
$380$	−207.246	−	88.6501i	−0.545384	−	0.233290i
$381$			104.841i			0.275173i
$382$	−322.131	+	113.651i	−0.843274	+	0.297514i
$383$	−59.2677	+	59.2677i	−0.154746	+	0.154746i	−0.780234	−	0.625488i	$-0.784900\pi$
$383$	−59.2677	+	59.2677i	−0.154746	+	0.154746i	0.625488	+	0.780234i	$0.284900\pi$
$384$	11.7744	+	652.949i	0.0306624	+	1.70039i
$385$	−113.079	−	34.6268i	−0.293711	−	0.0899397i
$386$	135.851	−	283.966i	0.351945	−	0.735662i
$387$	427.850	−	427.850i	1.10555	−	1.10555i
$388$	323.818	+	34.7971i	0.834582	+	0.0896833i
$389$	−254.508			−0.654263			−0.327131	−	0.944979i	$-0.606082\pi$
$389$	−254.508			−0.654263			−0.327131	+	0.944979i	$0.606082\pi$
$390$	−154.896	+	168.493i	−0.397168	+	0.432035i
$391$	−33.3968			−0.0854138
$392$	−303.737	−	187.593i	−0.774839	−	0.478553i
$393$	187.256	−	187.256i	0.476478	−	0.476478i
$394$	118.267	−	247.211i	0.300170	−	0.627438i
$395$	−102.230	+	54.2981i	−0.258810	+	0.137464i
$396$	−599.752	+	483.362i	−1.51453	+	1.22061i
$397$	−372.832	+	372.832i	−0.939122	+	0.939122i	−0.998250	−	0.0591281i	$-0.981168\pi$
$397$	−372.832	+	372.832i	−0.939122	+	0.939122i	0.0591281	+	0.998250i	$0.481168\pi$
$398$	−93.0291	−	263.681i	−0.233741	−	0.662516i
$399$			120.279i			0.301450i
$400$	276.263	+	289.273i	0.690657	+	0.723183i
$401$	471.865			1.17672			0.588360	−	0.808599i	$-0.299774\pi$
$401$	471.865			1.17672			0.588360	+	0.808599i	$0.299774\pi$
$402$	423.717	−	149.491i	1.05402	−	0.371868i
$403$	92.7940	+	92.7940i	0.230258	+	0.230258i
$404$	281.738	+	349.579i	0.697372	+	0.865294i
$405$	−130.778	−	246.222i	−0.322908	−	0.607955i
$406$	155.431	+	74.3589i	0.382834	+	0.183150i
$407$	−97.2629	−	97.2629i	−0.238975	−	0.238975i
$408$	488.572	+	301.749i	1.19748	+	0.739582i
$409$		−	182.192i		−	0.445457i	−0.974880	−	0.222729i	$-0.928504\pi$
$409$		−	182.192i		−	0.445457i	0.974880	−	0.222729i	$-0.0714964\pi$
$410$	−144.763	−	133.081i	−0.353082	−	0.324587i
$411$			712.610i			1.73384i
$412$	15.3833	−	143.156i	0.0373382	−	0.347465i
$413$	57.6349	+	57.6349i	0.139552	+	0.139552i
$414$	72.9355	+	34.8928i	0.176173	+	0.0842820i
$415$	141.511	−	462.123i	0.340989	−	1.11355i
$416$	−88.0493	+	113.375i	−0.211657	+	0.272537i
$417$	−175.469	−	175.469i	−0.420790	−	0.420790i
$418$	−84.8022	−	240.363i	−0.202876	−	0.575031i
$419$	−452.553			−1.08008			−0.540039	−	0.841640i	$-0.681590\pi$
$419$	−452.553			−1.08008			−0.540039	+	0.841640i	$0.681590\pi$
$420$	83.9422	−	196.240i	0.199862	−	0.467238i
$421$			65.0180i			0.154437i	0.997014	+	0.0772186i	$0.0246039\pi$
$421$			65.0180i			0.154437i	−0.997014	+	0.0772186i	$0.975396\pi$
$422$	−6.36068	−	18.0287i	−0.0150727	−	0.0427220i
$423$	−710.833	+	710.833i	−1.68046	+	1.68046i
$424$	23.8052	−	5.62726i	0.0561443	−	0.0132718i
$425$	345.325	−	66.8048i	0.812528	−	0.157188i
$426$	−1234.56	−	590.619i	−2.89802	−	1.38643i
$427$	129.436	−	129.436i	0.303128	−	0.303128i
$428$	39.9137	−	371.433i	0.0932564	−	0.867833i
$429$	−258.799			−0.603261
$430$	−14.9260	−	354.976i	−0.0347117	−	0.825526i
$431$	−433.432			−1.00564			−0.502821	−	0.864391i	$-0.667704\pi$
$431$	−433.432			−1.00564			−0.502821	+	0.864391i	$0.667704\pi$
$432$	−354.464	−	551.432i	−0.820519	−	1.27646i
$433$	−280.632	+	280.632i	−0.648112	+	0.648112i	−0.952536	−	0.304425i	$-0.901536\pi$
$433$	−280.632	+	280.632i	−0.648112	+	0.648112i	0.304425	+	0.952536i	$0.401536\pi$
$434$	−110.398	−	52.8152i	−0.254374	−	0.121694i
$435$	307.633	−	1004.62i	0.707203	−	2.30947i
$436$	284.230	−	229.071i	0.651903	−	0.525392i
$437$	−18.9177	+	18.9177i	−0.0432899	+	0.0432899i
$438$	355.588	−	125.455i	0.811845	−	0.286426i
$439$			557.674i			1.27033i	0.772377	+	0.635164i	$0.219068\pi$
$439$			557.674i			1.27033i	−0.772377	+	0.635164i	$0.780932\pi$
$440$	−29.3902	+	451.346i	−0.0667959	+	1.02579i
$441$	759.973			1.72330
$442$	41.9966	+	119.035i	0.0950150	+	0.269310i
$443$	128.300	+	128.300i	0.289616	+	0.289616i	0.836928	−	0.547313i	$-0.184349\pi$
$443$	128.300	+	128.300i	0.289616	+	0.289616i	−0.547313	+	0.836928i	$0.684349\pi$
$444$	193.292	−	155.781i	0.435341	−	0.350857i
$445$	332.315	−	176.505i	0.746775	−	0.396640i
$446$	337.330	−	705.114i	0.756346	−	1.58097i
$447$	802.431	+	802.431i	1.79515	+	1.79515i
$448$	42.2566	−	127.026i	0.0943227	−	0.283541i
$449$			512.154i			1.14065i	0.821417	+	0.570327i	$0.193184\pi$
$449$			512.154i			1.14065i	−0.821417	+	0.570327i	$0.806816\pi$
$450$	−823.954	−	214.897i	−1.83101	−	0.477549i
$451$		−	222.351i		−	0.493017i
$452$	−76.9475	+	716.065i	−0.170238	+	1.58421i
$453$	720.450	+	720.450i	1.59040	+	1.59040i
$454$	196.436	−	410.606i	0.432679	−	0.904419i
$455$	41.4350	−	22.0077i	0.0910659	−	0.0483685i
$456$	447.679	−	105.826i	0.981751	−	0.232074i
$457$	−388.529	−	388.529i	−0.850173	−	0.850173i	0.139981	−	0.990154i	$-0.455296\pi$
$457$	−388.529	−	388.529i	−0.850173	−	0.850173i	−0.990154	+	0.139981i	$0.955296\pi$
$458$	75.9086	−	26.7812i	0.165739	−	0.0584743i
$459$	−576.421			−1.25582
$460$	44.0676	−	17.6624i	0.0957992	−	0.0383966i
$461$		−	36.0020i		−	0.0780954i	−0.999237	−	0.0390477i	$-0.987568\pi$
$461$		−	36.0020i		−	0.0780954i	0.999237	−	0.0390477i	$-0.0124324\pi$
$462$	227.598	−	80.2987i	0.492637	−	0.173807i
$463$	−338.658	+	338.658i	−0.731442	+	0.731442i	−0.970905	−	0.239463i	$-0.923029\pi$
$463$	−338.658	+	338.658i	−0.731442	+	0.731442i	0.239463	+	0.970905i	$0.423029\pi$
$464$	140.011	−	643.939i	0.301747	−	1.38780i
$465$	−218.504	+	713.556i	−0.469901	+	1.53453i
$466$	−294.249	+	615.062i	−0.631436	+	1.31988i
$467$	−43.6060	+	43.6060i	−0.0933748	+	0.0933748i	−0.752251	−	0.658876i	$-0.771032\pi$
$467$	−43.6060	+	43.6060i	−0.0933748	+	0.0933748i	0.658876	+	0.752251i	$0.271032\pi$
$468$	32.6503	−	303.840i	0.0697655	−	0.649230i
$469$	−92.1055			−0.196387
$470$	24.7982	+	589.760i	0.0527622	+	1.25481i
$471$	1379.45			2.92876
$472$	163.808	−	265.227i	0.347052	−	0.561922i
$473$	284.077	−	284.077i	0.600586	−	0.600586i
$474$	101.949	−	213.101i	0.215082	−	0.449581i
$475$	157.768	−	233.451i	0.332143	−	0.491476i
$476$	−73.8671	−	91.6538i	−0.155183	−	0.192550i
$477$	−36.8211	+	36.8211i	−0.0771931	+	0.0771931i
$478$	165.691	+	469.632i	0.346633	+	0.982495i
$479$		−	870.273i		−	1.81685i	−0.418043	−	0.908427i	$-0.637284\pi$
$479$		−	870.273i		−	1.81685i	0.418043	−	0.908427i	$-0.362716\pi$
$480$	−804.264	−	139.774i	−1.67555	−	0.291196i
$481$	54.5692			0.113449
$482$	612.504	−	216.097i	1.27075	−	0.448334i
$483$	−17.9130	−	17.9130i	−0.0370870	−	0.0370870i
$484$	−21.3677	+	17.2210i	−0.0441482	+	0.0355806i
$485$	−119.199	+	389.261i	−0.245771	+	0.802600i
$486$	−152.005	−	72.7202i	−0.312768	−	0.149630i
$487$	−611.867	−	611.867i	−1.25640	−	1.25640i	−0.952799	−	0.303603i	$-0.901810\pi$
$487$	−611.867	−	611.867i	−1.25640	−	1.25640i	−0.303603	−	0.952799i	$-0.598190\pi$
$488$	−595.644	−	367.879i	−1.22058	−	0.753849i
$489$		−	727.656i		−	1.48805i
$490$	302.009	−	328.522i	0.616345	−	0.670453i
$491$			719.282i			1.46493i	0.680803	+	0.732467i	$0.261631\pi$
$491$			719.282i			1.46493i	−0.680803	+	0.732467i	$0.738369\pi$
$492$	399.003	+	42.8765i	0.810982	+	0.0871473i
$493$	−409.738	−	409.738i	−0.831111	−	0.831111i
$494$	91.2167	+	43.6386i	0.184649	+	0.0883372i
$495$	−451.655	−	850.354i	−0.912435	−	1.71789i
$496$	−99.4459	+	457.373i	−0.200496	+	0.922123i
$497$	198.374	+	198.374i	0.399143	+	0.399143i
$498$	328.160	+	930.135i	0.658956	+	1.86774i
$499$	186.103			0.372952			0.186476	−	0.982459i	$-0.440293\pi$
$499$	186.103			0.372952			0.186476	+	0.982459i	$0.440293\pi$
$500$	−420.331	+	270.780i	−0.840661	+	0.541561i
$501$		−	1504.80i		−	3.00359i
$502$	110.945	+	314.461i	0.221006	+	0.626417i
$503$	−302.420	+	302.420i	−0.601232	+	0.601232i	−0.940639	−	0.339408i	$-0.889773\pi$
$503$	−302.420	+	302.420i	−0.601232	+	0.601232i	0.339408	+	0.940639i	$0.389773\pi$
$504$	65.5597	+	277.339i	0.130079	+	0.550276i
$505$	−495.648	+	263.257i	−0.981481	+	0.521302i
$506$	48.4267	+	23.1676i	0.0957049	+	0.0457857i
$507$	−537.094	+	537.094i	−1.05936	+	1.05936i
$508$	−81.7255	−	8.78213i	−0.160877	−	0.0172877i
$509$	−107.882			−0.211949			−0.105975	−	0.994369i	$-0.533796\pi$
$509$	−107.882			−0.211949			−0.105975	+	0.994369i	$0.533796\pi$
$510$	−485.793	+	528.439i	−0.952534	+	1.03615i
$511$	−77.2960			−0.151264
$512$	−509.973	−	45.5168i	−0.996041	−	0.0888999i
$513$	−326.514	+	326.514i	−0.636481	+	0.636481i
$514$	470.770	+	225.219i	0.915895	+	0.438169i
$515$	172.087	+	52.6962i	0.334150	+	0.102323i
$516$	454.991	+	564.550i	0.881766	+	1.09409i
$517$	−471.968	+	471.968i	−0.912898	+	0.912898i
$518$	−47.9903	+	16.9314i	−0.0926455	+	0.0326861i
$519$		−	882.124i		−	1.69966i
$520$	−118.369	−	134.858i	−0.227633	−	0.259343i
$521$	−374.569			−0.718942			−0.359471	−	0.933156i	$-0.617043\pi$
$521$	−374.569			−0.718942			−0.359471	+	0.933156i	$0.617043\pi$
$522$	466.738	+	1322.92i	0.894134	+	2.53433i
$523$	−161.196	−	161.196i	−0.308213	−	0.308213i	0.536003	−	0.844216i	$-0.319934\pi$
$523$	−161.196	−	161.196i	−0.308213	−	0.308213i	−0.844216	+	0.536003i	$0.819934\pi$
$524$	130.284	+	161.655i	0.248633	+	0.308502i
$525$	221.054	+	149.390i	0.421055	+	0.284552i
$526$	4.70725	−	9.83945i	0.00894914	−	0.0187062i
$527$	291.026	+	291.026i	0.552231	+	0.552231i
$528$	−499.123	−	776.474i	−0.945308	−	1.47059i
$529$			523.365i			0.989348i
$530$	1.28455	+	30.5496i	0.00242367	+	0.0576407i
$531$			663.619i			1.24975i
$532$	−93.7596	−	10.0753i	−0.176240	−	0.0189385i
$533$	62.3747	+	62.3747i	0.117026	+	0.117026i
$534$	−331.402	+	692.721i	−0.620602	+	1.29723i
$535$	446.499	+	136.726i	0.834577	+	0.255563i
$536$	81.0380	+	342.818i	0.151190	+	0.639585i
$537$	−230.087	−	230.087i	−0.428467	−	0.428467i
$538$	−307.663	+	108.546i	−0.571865	+	0.201759i
$539$	504.596			0.936171
$540$	760.597	−	304.849i	1.40851	−	0.564536i
$541$			319.556i			0.590676i	0.955393	+	0.295338i	$0.0954323\pi$
$541$			319.556i			0.590676i	−0.955393	+	0.295338i	$0.904568\pi$
$542$	189.826	−	66.9724i	0.350233	−	0.123565i
$543$	693.026	−	693.026i	1.27629	−	1.27629i
$544$	−276.145	+	355.575i	−0.507620	+	0.653630i
$545$	214.045	+	402.993i	0.392743	+	0.739437i
$546$	−41.3211	+	86.3726i	−0.0756797	+	0.158192i
$547$	631.421	−	631.421i	1.15433	−	1.15433i	0.168659	−	0.985674i	$-0.446056\pi$
$547$	631.421	−	631.421i	1.15433	−	1.15433i	0.985674	−	0.168659i	$-0.0539438\pi$
$548$	−555.493	−	59.6927i	−1.01367	−	0.108928i
$549$	1490.35			2.71466
$550$	−547.077	−	142.684i	−0.994686	−	0.259426i
$551$	−464.193			−0.842456
$552$	−50.9119	+	82.4331i	−0.0922318	+	0.149335i
$553$	−34.2420	+	34.2420i	−0.0619205	+	0.0619205i
$554$	210.894	−	440.826i	0.380675	−	0.795716i
$555$	145.562	+	274.057i	0.262274	+	0.493797i
$556$	151.480	−	122.083i	0.272447	−	0.219575i
$557$	405.826	−	405.826i	0.728592	−	0.728592i	−0.241747	−	0.970339i	$-0.577720\pi$
$557$	405.826	−	405.826i	0.728592	−	0.728592i	0.970339	+	0.241747i	$0.0777204\pi$
$558$	−331.512	−	939.636i	−0.594107	−	1.68393i
$559$			159.381i			0.285118i
$560$	145.941	+	81.8729i	0.260610	+	0.146202i
$561$	−811.661			−1.44681
$562$	−566.542	+	199.881i	−1.00808	+	0.355660i
$563$	−241.881	−	241.881i	−0.429628	−	0.429628i	0.458873	−	0.888502i	$-0.348253\pi$
$563$	−241.881	−	241.881i	−0.429628	−	0.429628i	−0.888502	+	0.458873i	$0.848253\pi$
$564$	−755.926	−	937.947i	−1.34029	−	1.66303i
$565$	−860.780	−	263.587i	−1.52351	−	0.466525i
$566$	−386.063	−	184.695i	−0.682091	−	0.326316i
$567$	−82.4724	−	82.4724i	−0.145454	−	0.145454i
$568$	563.813	−	912.888i	0.992629	−	1.60720i
$569$		−	416.031i		−	0.731162i	−0.930780	−	0.365581i	$-0.880870\pi$
$569$		−	416.031i		−	0.731162i	0.930780	−	0.365581i	$-0.119130\pi$
$570$	24.1571	+	574.513i	0.0423809	+	1.00792i
$571$		−	907.558i		−	1.58942i	−0.606991	−	0.794709i	$-0.707623\pi$
$571$		−	907.558i		−	1.58942i	0.606991	−	0.794709i	$-0.292377\pi$
$572$	21.6786	−	201.739i	0.0378997	−	0.352690i
$573$	616.171	+	616.171i	1.07534	+	1.07534i
$574$	−74.2081	−	35.5016i	−0.129282	−	0.0618494i
$575$	11.2715	+	58.2641i	0.0196026	+	0.101329i
$576$	974.578	−	488.028i	1.69198	−	0.847270i
$577$	467.070	+	467.070i	0.809480	+	0.809480i	0.984555	−	0.175075i	$-0.0560167\pi$
$577$	467.070	+	467.070i	0.809480	+	0.809480i	−0.175075	+	0.984555i	$0.556017\pi$
$578$	−60.5936	−	171.746i	−0.104833	−	0.297139i
$579$	−803.025			−1.38692
$580$	757.352	+	323.959i	1.30578	+	0.558551i
$581$		−	202.188i		−	0.348000i
$582$	−276.420	−	783.482i	−0.474948	−	1.34619i
$583$	−24.4479	+	24.4479i	−0.0419347	+	0.0419347i
$584$	68.0080	+	287.697i	0.116452	+	0.492631i
$585$	365.245	+	111.845i	0.624351	+	0.191188i
$586$	393.264	+	188.140i	0.671100	+	0.321058i
$587$	247.149	−	247.149i	0.421038	−	0.421038i	−0.464523	−	0.885561i	$-0.653774\pi$
$587$	247.149	−	247.149i	0.421038	−	0.421038i	0.885561	+	0.464523i	$0.153774\pi$
$588$	−97.3026	+	905.486i	−0.165481	+	1.53994i
$589$	329.704			0.559769
$590$	286.870	+	263.719i	0.486220	+	0.446981i
$591$	−699.086			−1.18289
$592$	105.243	+	163.724i	0.177775	+	0.276560i
$593$	315.219	−	315.219i	0.531567	−	0.531567i	−0.389472	−	0.921038i	$-0.627342\pi$
$593$	315.219	−	315.219i	0.531567	−	0.531567i	0.921038	+	0.389472i	$0.127342\pi$
$594$	835.833	+	399.867i	1.40713	+	0.673177i
$595$	129.951	−	69.0217i	0.218405	−	0.116003i
$596$	−692.727	+	558.294i	−1.16229	+	0.936734i
$597$	−504.370	+	504.370i	−0.844840	+	0.844840i
$598$	−20.0839	+	7.08579i	−0.0335851	+	0.0118491i
$599$		−	423.660i		−	0.707278i	−0.935382	−	0.353639i	$-0.884944\pi$
$599$		−	423.660i		−	0.707278i	0.935382	−	0.353639i	$-0.115056\pi$
$600$	361.538	−	954.203i	0.602563	−	1.59034i
$601$	293.629			0.488568			0.244284	−	0.969704i	$-0.421447\pi$
$601$	293.629			0.488568			0.244284	+	0.969704i	$0.421447\pi$
$602$	−49.4519	−	140.166i	−0.0821460	−	0.232834i
$603$	−530.260	−	530.260i	−0.879370	−	0.879370i
$604$	−621.954	+	501.255i	−1.02973	+	0.829893i
$605$	−16.0914	−	30.2961i	−0.0265974	−	0.0500762i
$606$	494.286	−	1033.19i	0.815653	−	1.70494i
$607$	−143.784	−	143.784i	−0.236876	−	0.236876i	0.578679	−	0.815555i	$-0.303568\pi$
$607$	−143.784	−	143.784i	−0.236876	−	0.236876i	−0.815555	+	0.578679i	$0.803568\pi$
$608$	44.9929	+	357.839i	0.0740015	+	0.588551i
$609$		−	439.542i		−	0.721743i
$610$	592.255	−	644.248i	0.970910	−	1.05614i
$611$		−	264.797i		−	0.433383i
$612$	102.400	−	952.919i	0.167320	−	1.55706i
$613$	304.429	+	304.429i	0.496622	+	0.496622i	0.910385	−	0.413763i	$-0.135786\pi$
$613$	304.429	+	304.429i	0.496622	+	0.496622i	−0.413763	+	0.910385i	$0.635786\pi$
$614$	−118.498	+	247.693i	−0.192993	+	0.403409i
$615$	−146.875	+	479.641i	−0.238821	+	0.779905i
$616$	43.5293	+	184.144i	0.0706645	+	0.298935i
$617$	815.279	+	815.279i	1.32136	+	1.32136i	0.912676	+	0.408683i	$0.134012\pi$
$617$	815.279	+	815.279i	1.32136	+	1.32136i	0.408683	+	0.912676i	$0.365988\pi$
$618$	−346.367	+	122.201i	−0.560465	+	0.197737i
$619$	−1062.25			−1.71607			−0.858036	−	0.513589i	$-0.828316\pi$
$619$	−1062.25			−1.71607			−0.858036	+	0.513589i	$0.828316\pi$
$620$	−537.927	−	230.100i	−0.867625	−	0.371129i
$621$		−	97.2552i		−	0.156611i
$622$	−139.653	+	49.2707i	−0.224522	+	0.0792133i
$623$	111.309	−	111.309i	0.178667	−	0.178667i
$624$	357.836	+	77.8037i	0.573455	+	0.124685i
$625$	−233.095	−	579.906i	−0.372953	−	0.927850i
$626$	−153.669	+	321.212i	−0.245478	+	0.513118i
$627$	−459.766	+	459.766i	−0.733280	+	0.733280i
$628$	−115.551	+	1075.31i	−0.183999	+	1.71227i
$629$	171.143			0.272088
$630$	−355.914	+	14.9655i	−0.564943	+	0.0237547i
$631$	842.984			1.33595			0.667975	−	0.744184i	$-0.267161\pi$
$631$	842.984			1.33595			0.667975	+	0.744184i	$0.267161\pi$
$632$	157.577	+	97.3218i	0.249330	+	0.153990i
$633$	−34.4852	+	34.4852i	−0.0544791	+	0.0544791i
$634$	313.901	−	656.140i	0.495112	−	1.03492i
$635$	30.0835	−	98.2421i	0.0473756	−	0.154712i
$636$	−39.1569	−	48.5856i	−0.0615675	−	0.0763925i
$637$	−141.551	+	141.551i	−0.222216	+	0.222216i
$638$	309.898	+	878.373i	0.485734	+	1.37676i
$639$			2284.12i			3.57452i
$640$	176.327	−	615.231i	0.275511	−	0.961298i
$641$	−169.581			−0.264557			−0.132278	−	0.991213i	$-0.542229\pi$
$641$	−169.581			−0.264557			−0.132278	+	0.991213i	$0.542229\pi$
$642$	−898.687	+	317.065i	−1.39982	+	0.493870i
$643$	493.738	+	493.738i	0.767867	+	0.767867i	0.977731	−	0.209864i	$-0.0673021\pi$
$643$	493.738	+	493.738i	0.767867	+	0.767867i	−0.209864	+	0.977731i	$0.567302\pi$
$644$	15.4641	−	12.4630i	0.0240125	−	0.0193526i
$645$	−800.443	+	425.146i	−1.24100	+	0.659141i
$646$	286.079	+	136.862i	0.442847	+	0.211860i
$647$	−509.311	−	509.311i	−0.787189	−	0.787189i	0.193844	−	0.981032i	$-0.437905\pi$
$647$	−509.311	−	509.311i	−0.787189	−	0.787189i	−0.981032	+	0.193844i	$0.937905\pi$
$648$	−234.401	+	379.526i	−0.361730	+	0.585688i
$649$			440.620i			0.678922i
$650$	193.495	−	113.442i	0.297684	−	0.174526i
$651$			312.195i			0.479562i
$652$	567.222	+	60.9530i	0.869972	+	0.0934863i
$653$	−239.798	−	239.798i	−0.367226	−	0.367226i	0.499239	−	0.866464i	$-0.333613\pi$
$653$	−239.798	−	239.798i	−0.367226	−	0.367226i	−0.866464	+	0.499239i	$0.833613\pi$
$654$	−840.052	−	401.886i	−1.28448	−	0.614504i
$655$	−229.202	+	121.738i	−0.349927	+	0.185859i
$656$	−66.8461	+	307.439i	−0.101899	+	0.468657i
$657$	−445.000	−	445.000i	−0.677322	−	0.677322i
$658$	82.1597	+	232.873i	0.124863	+	0.353911i
$659$	900.540			1.36653			0.683263	−	0.730173i	$-0.260560\pi$
$659$	900.540			1.36653			0.683263	+	0.730173i	$0.260560\pi$
$660$	1071.00	−	429.260i	1.62273	−	0.650394i
$661$		−	59.7896i		−	0.0904533i	−0.998977	−	0.0452267i	$-0.985599\pi$
$661$		−	59.7896i		−	0.0904533i	0.998977	−	0.0452267i	$-0.0144010\pi$
$662$	−268.807	−	761.906i	−0.406053	−	1.15092i
$663$	227.690	−	227.690i	0.343424	−	0.343424i
$664$	−752.547	+	177.893i	−1.13335	+	0.267911i
$665$	34.5133	−	112.708i	0.0518997	−	0.169486i
$666$	−373.761	−	178.809i	−0.561202	−	0.268482i
$667$	69.1320	−	69.1320i	0.103646	−	0.103646i
$668$	1173.02	+	126.051i	1.75602	+	0.188700i
$669$	−1993.99			−2.98055
$670$	−439.943	+	18.4987i	−0.656632	+	0.0276101i
$671$	989.538			1.47472
$672$	−338.835	+	42.6035i	−0.504219	+	0.0633981i
$673$	190.854	−	190.854i	0.283587	−	0.283587i	−0.550951	−	0.834538i	$-0.685735\pi$
$673$	190.854	−	190.854i	0.283587	−	0.283587i	0.834538	+	0.550951i	$0.185735\pi$
$674$	−259.601	−	124.194i	−0.385164	−	0.184265i
$675$	194.543	+	1005.62i	0.288212	+	1.48981i
$676$	−373.685	−	463.666i	−0.552788	−	0.685896i
$677$	503.850	−	503.850i	0.744240	−	0.744240i	−0.229151	−	0.973391i	$-0.573595\pi$
$677$	503.850	−	503.850i	0.744240	−	0.744240i	0.973391	+	0.229151i	$0.0735949\pi$
$678$	1732.53	−	611.252i	2.55535	−	0.901551i
$679$			170.310i			0.250824i
$680$	−371.235	−	422.950i	−0.545934	−	0.621985i
$681$	−1161.15			−1.70507
$682$	−220.112	−	623.886i	−0.322745	−	0.914788i
$683$	141.973	+	141.973i	0.207866	+	0.207866i	0.803360	−	0.595494i	$-0.203044\pi$
$683$	141.973	+	141.973i	0.207866	+	0.207866i	−0.595494	+	0.803360i	$0.703044\pi$
$684$	−481.778	−	597.787i	−0.704354	−	0.873957i
$685$	204.480	−	667.758i	0.298510	−	0.974829i
$686$	169.032	−	353.323i	0.246402	−	0.515048i
$687$	−145.198	−	145.198i	−0.211351	−	0.211351i
$688$	−478.190	+	307.384i	−0.695044	+	0.446779i
$689$		−	13.7165i		−	0.0199078i
$690$	−89.1596	−	81.9642i	−0.129217	−	0.118789i
$691$			1271.56i			1.84017i	0.391717	+	0.920086i	$0.371881\pi$
$691$			1271.56i			1.84017i	−0.391717	+	0.920086i	$0.628119\pi$
$692$	687.633	+	73.8922i	0.993689	+	0.106781i
$693$	−284.828	−	284.828i	−0.411007	−	0.411007i
$694$	−239.902	+	501.462i	−0.345680	+	0.722568i
$695$	114.075	+	214.775i	0.164137	+	0.309029i
$696$	−1635.98	+	386.726i	−2.35055	+	0.555641i
$697$	195.623	+	195.623i	0.280665	+	0.280665i
$698$	857.282	−	302.457i	1.22820	−	0.433319i
$699$	1739.33			2.48831
$700$	−134.969	+	159.802i	−0.192813	+	0.228288i
$701$			799.199i			1.14008i	0.821615	+	0.570042i	$0.193073\pi$
$701$			799.199i			1.14008i	−0.821615	+	0.570042i	$0.806927\pi$
$702$	−346.644	+	122.299i	−0.493794	+	0.174215i
$703$	96.9443	−	96.9443i	0.137901	−	0.137901i
$704$	647.086	−	324.034i	0.919156	−	0.460275i
$705$	1329.86	−	706.340i	1.88633	−	1.00190i
$706$	249.972	−	522.511i	0.354068	−	0.740101i
$707$	−166.018	+	166.018i	−0.234821	+	0.234821i
$708$	−790.683	−	84.9659i	−1.11678	−	0.120008i
$709$	479.020			0.675628			0.337814	−	0.941213i	$-0.390313\pi$
$709$	479.020			0.675628			0.337814	+	0.941213i	$0.390313\pi$
$710$	987.379	+	907.695i	1.39067	+	1.27844i
$711$	−394.269			−0.554528
$712$	−512.229	−	316.361i	−0.719423	−	0.444327i
$713$	−49.1027	+	49.1027i	−0.0688677	+	0.0688677i
$714$	−129.594	+	270.887i	−0.181504	+	0.379393i
$715$	242.510	+	74.2610i	0.339175	+	0.103862i
$716$	198.631	−	160.083i	0.277417	−	0.223580i
$717$	898.313	−	898.313i	1.25288	−	1.25288i
$718$	−18.1035	−	51.3124i	−0.0252137	−	0.0714657i
$719$			800.764i			1.11372i	0.830607	+	0.556859i	$0.187994\pi$
$719$			800.764i			1.11372i	−0.830607	+	0.556859i	$0.812006\pi$
$720$	368.848	+	1311.55i	0.512290	+	1.82159i
$721$	75.2916			0.104427
$722$	−441.292	+	155.692i	−0.611207	+	0.215639i
$723$	−1171.60	−	1171.60i	−1.62047	−	1.62047i
$724$	482.175	+	598.280i	0.665988	+	0.826353i
$725$	−576.541	+	853.116i	−0.795229	+	1.17671i
$726$	63.1532	+	30.2128i	0.0869879	+	0.0416155i
$727$	144.435	+	144.435i	0.198673	+	0.198673i	0.799431	−	0.600758i	$-0.205134\pi$
$727$	144.435	+	144.435i	0.198673	+	0.198673i	−0.600758	+	0.799431i	$0.705134\pi$
$728$	−63.8678	−	39.4457i	−0.0877305	−	0.0541837i
$729$			931.690i			1.27804i
$730$	−369.206	+	15.5244i	−0.505761	+	0.0212662i
$731$			499.860i			0.683803i
$732$	−190.815	+	1775.70i	−0.260677	+	2.42583i
$733$	−748.614	−	748.614i	−1.02130	−	1.02130i	−0.999768	−	0.0215340i	$-0.993145\pi$
$733$	−748.614	−	748.614i	−1.02130	−	1.02130i	−0.0215340	−	0.999768i	$-0.506855\pi$
$734$	128.701	+	61.5711i	0.175341	+	0.0838843i
$735$	−1088.48	−	333.314i	−1.48093	−	0.453488i
$736$	−59.9935	−	46.5920i	−0.0815129	−	0.0633043i
$737$	−352.074	−	352.074i	−0.477713	−	0.477713i
$738$	−222.837	−	631.609i	−0.301948	−	0.855839i
$739$	−731.874			−0.990358			−0.495179	−	0.868791i	$-0.664897\pi$
$739$	−731.874			−0.990358			−0.495179	+	0.868791i	$0.664897\pi$
$740$	−225.826	+	90.5118i	−0.305170	+	0.122313i
$741$		−	257.951i		−	0.348112i
$742$	4.25587	+	12.0628i	0.00573567	+	0.0162572i
$743$	−676.219	+	676.219i	−0.910119	+	0.910119i	−0.996281	−	0.0861618i	$-0.972540\pi$
$743$	−676.219	+	676.219i	−0.910119	+	0.910119i	0.0861618	+	0.996281i	$0.472540\pi$
$744$	1161.99	−	274.681i	1.56182	−	0.369195i
$745$	−521.672	−	982.179i	−0.700231	−	1.31836i
$746$	−269.914	−	129.128i	−0.361814	−	0.173094i
$747$	1164.02	−	1164.02i	1.55826	−	1.55826i
$748$	67.9898	−	632.705i	0.0908955	−	0.845863i
$749$	195.352			0.260817
$750$	1085.87	+	669.165i	1.44783	+	0.892219i
$751$	−59.2858			−0.0789424			−0.0394712	−	0.999221i	$-0.512567\pi$
$751$	−59.2858			−0.0789424			−0.0394712	+	0.999221i	$0.512567\pi$
$752$	794.469	−	510.690i	1.05648	−	0.679109i
$753$	601.502	−	601.502i	0.798807	−	0.798807i
$754$	−333.339	−	159.471i	−0.442094	−	0.211500i
$755$	−468.375	−	881.834i	−0.620364	−	1.16799i
$756$	266.906	−	215.109i	0.353050	−	0.284536i
$757$	597.444	−	597.444i	0.789225	−	0.789225i	−0.192142	−	0.981367i	$-0.561543\pi$
$757$	597.444	−	597.444i	0.789225	−	0.789225i	0.981367	+	0.192142i	$0.0615434\pi$
$758$	−1123.54	+	396.396i	−1.48225	+	0.522949i
$759$		−	136.946i		−	0.180429i
$760$	−449.868	−	29.2939i	−0.591931	−	0.0385446i
$761$	32.0333			0.0420937			0.0210469	−	0.999778i	$-0.493300\pi$
$761$	32.0333			0.0420937			0.0210469	+	0.999778i	$0.493300\pi$
$762$	69.7631	+	197.736i	0.0915526	+	0.259496i
$763$	134.983	+	134.983i	0.176911	+	0.176911i
$764$	−531.932	+	428.703i	−0.696246	+	0.561130i
$765$	1145.50	+	350.774i	1.49739	+	0.458528i
$766$	−72.3445	+	151.220i	−0.0944445	+	0.197415i
$767$	−123.605	−	123.605i	−0.161153	−	0.161153i
$768$	456.692	+	1223.67i	0.594650	+	1.59331i
$769$		−	1416.08i		−	1.84145i	−0.390208	−	0.920727i	$-0.627597\pi$
$769$		−	1416.08i		−	1.84145i	0.390208	−	0.920727i	$-0.372403\pi$
$770$	−236.314	+	9.93655i	−0.306902	+	0.0129046i
$771$		−	1331.29i		−	1.72670i
$772$	67.2664	−	625.973i	0.0871327	−	0.810846i
$773$	77.7861	+	77.7861i	0.100629	+	0.100629i	0.755629	−	0.655000i	$-0.227331\pi$
$773$	77.7861	+	77.7861i	0.100629	+	0.100629i	−0.655000	+	0.755629i	$0.727331\pi$
$774$	522.251	−	1091.65i	0.674742	−	1.41040i
$775$	409.502	−	605.946i	0.528390	−	0.781865i
$776$	633.894	−	149.845i	0.816874	−	0.193099i
$777$	91.7960	+	91.7960i	0.118142	+	0.118142i
$778$	−480.017	+	169.354i	−0.616989	+	0.217679i
$779$	221.622			0.284496
$780$	−180.024	+	420.859i	−0.230799	+	0.539563i
$781$			1516.57i			1.94184i
$782$	−62.9883	+	22.2228i	−0.0805477	+	0.0284180i
$783$	1193.20	−	1193.20i	1.52389	−	1.52389i
$784$	−697.693	−	151.698i	−0.889915	−	0.193493i
$785$	−1292.62	−	395.825i	−1.64665	−	0.504235i
$786$	228.572	−	477.779i	0.290804	−	0.607861i
$787$	−494.548	+	494.548i	−0.628396	+	0.628396i	−0.947664	−	0.319268i	$-0.896563\pi$
$787$	−494.548	+	494.548i	−0.628396	+	0.628396i	0.319268	+	0.947664i	$0.396563\pi$
$788$	58.5598	−	544.951i	0.0743145	−	0.691562i
$789$	−27.8249			−0.0352661
$790$	−156.680	+	170.435i	−0.198330	+	0.215740i
$791$	−376.609			−0.476117
$792$	−809.530	+	1310.73i	−1.02213	+	1.65497i
$793$	−277.589	+	277.589i	−0.350050	+	0.350050i
$794$	−455.093	+	951.271i	−0.573165	+	1.19807i
$795$	68.8868	−	36.5884i	0.0866501	−	0.0460231i
$796$	−350.917	−	435.415i	−0.440850	−	0.547004i
$797$	−562.627	+	562.627i	−0.705931	+	0.705931i	−0.965677	−	0.259746i	$-0.916361\pi$
$797$	−562.627	+	562.627i	−0.705931	+	0.705931i	0.259746	+	0.965677i	$0.416361\pi$
$798$	80.0356	+	226.853i	0.100295	+	0.284276i
$799$		−	830.472i		−	1.03939i
$800$	713.535	+	361.756i	0.891919	+	0.452195i
$801$	1281.64			1.60005
$802$	889.965	−	313.988i	1.10968	−	0.391506i
$803$	−295.465	−	295.465i	−0.367951	−	0.367951i
$804$	699.681	−	563.898i	0.870249	−	0.701365i
$805$	11.6455	+	21.9256i	0.0144665	+	0.0272368i
$806$	236.762	+	113.268i	0.293749	+	0.140531i
$807$	588.499	+	588.499i	0.729243	+	0.729243i
$808$	763.991	+	471.852i	0.945533	+	0.583976i
$809$			440.667i			0.544706i	0.962197	+	0.272353i	$0.0878018\pi$
$809$			440.667i			0.544706i	−0.962197	+	0.272353i	$0.912198\pi$
$810$	−410.495	−	377.367i	−0.506784	−	0.465885i
$811$		−	911.348i		−	1.12373i	−0.827228	−	0.561867i	$-0.810083\pi$
$811$		−	911.348i		−	1.12373i	0.827228	−	0.561867i	$-0.189917\pi$
$812$	342.631	+	36.8188i	0.421960	+	0.0453433i
$813$	−363.099	−	363.099i	−0.446617	−	0.446617i
$814$	−248.164	−	118.723i	−0.304870	−	0.145851i
$815$	−208.797	+	681.857i	−0.256193	+	0.836634i
$816$	1122.26	+	244.012i	1.37532	+	0.299035i
$817$	283.147	+	283.147i	0.346569	+	0.346569i
$818$	−121.234	−	343.625i	−0.148208	−	0.420079i
$819$	159.802			0.195119
$820$	−361.587	−	154.670i	−0.440959	−	0.188622i
$821$		−	893.060i		−	1.08777i	−0.839159	−	0.543885i	$-0.816953\pi$
$821$		−	893.060i		−	1.08777i	0.839159	−	0.543885i	$-0.183047\pi$
$822$	474.184	+	1344.02i	0.576866	+	1.63507i
$823$	−852.293	+	852.293i	−1.03559	+	1.03559i	−0.0362500	+	0.999343i	$0.511541\pi$
$823$	−852.293	+	852.293i	−1.03559	+	1.03559i	−0.999343	+	0.0362500i	$0.988459\pi$
$824$	−66.2445	−	280.236i	−0.0803938	−	0.340093i
$825$	273.937	+	1416.02i	0.332045	+	1.71639i
$826$	147.054	+	70.3515i	0.178032	+	0.0851713i
$827$	−608.192	+	608.192i	−0.735419	+	0.735419i	−0.971688	−	0.236269i	$-0.924075\pi$
$827$	−608.192	+	608.192i	−0.735419	+	0.735419i	0.236269	+	0.971688i	$0.424075\pi$
$828$	160.779	+	17.2771i	0.194178	+	0.0208661i
$829$	1550.55			1.87039			0.935195	−	0.354133i	$-0.115224\pi$
$829$	1550.55			1.87039			0.935195	+	0.354133i	$0.115224\pi$
$830$	−40.6081	−	965.756i	−0.0489254	−	1.16356i
$831$	−1246.61			−1.50013
$832$	−90.6240	+	272.422i	−0.108923	+	0.327431i
$833$	−443.942	+	443.942i	−0.532943	+	0.532943i
$834$	−447.706	−	214.185i	−0.536818	−	0.256817i
$835$	−431.794	+	1410.09i	−0.517119	+	1.68873i
$836$	−319.884	−	396.910i	−0.382636	−	0.474773i
$837$	−847.500	+	847.500i	−1.01255	+	1.01255i
$838$	−853.541	+	301.137i	−1.01855	+	0.359352i
$839$		−	736.198i		−	0.877471i	−0.898616	−	0.438736i	$-0.855426\pi$
$839$		−	736.198i		−	0.877471i	0.898616	−	0.438736i	$-0.144574\pi$
$840$	27.7382	−	425.977i	0.0330217	−	0.507116i
$841$	855.330			1.01704
$842$	43.2642	+	122.628i	0.0513827	+	0.145639i
$843$	1083.68	+	1083.68i	1.28551	+	1.28551i
$844$	−23.9932	−	29.7706i	−0.0284280	−	0.0352732i
$845$	657.406	−	349.173i	0.777995	−	0.413222i
$846$	−867.671	+	1813.67i	−1.02562	+	2.14382i
$847$	−10.1477	−	10.1477i	−0.0119808	−	0.0119808i
$848$	41.1535	−	26.4537i	0.0485300	−	0.0311954i
$849$			1091.75i			1.28592i
$850$	606.849	−	355.783i	0.713940	−	0.418568i
$851$			28.8757i			0.0339315i
$852$	−2721.46	−	292.445i	−3.19420	−	0.343245i
$853$	369.135	+	369.135i	0.432749	+	0.432749i	0.889563	−	0.456813i	$-0.151009\pi$
$853$	369.135	+	369.135i	0.432749	+	0.432749i	−0.456813	+	0.889563i	$0.651009\pi$
$854$	157.994	−	330.252i	0.185005	−	0.386712i
$855$	847.568	−	450.176i	0.991308	−	0.526521i
$856$	−171.878	−	727.103i	−0.200793	−	0.849420i
$857$	−715.466	−	715.466i	−0.834849	−	0.834849i	0.153326	−	0.988176i	$-0.451001\pi$
$857$	−715.466	−	715.466i	−0.834849	−	0.834849i	−0.988176	+	0.153326i	$0.951001\pi$
$858$	−488.110	+	172.210i	−0.568893	+	0.200711i
$859$	−151.972			−0.176918			−0.0884588	−	0.996080i	$-0.528194\pi$
$859$	−151.972			−0.176918			−0.0884588	+	0.996080i	$0.528194\pi$
$860$	−264.359	−	659.574i	−0.307394	−	0.766947i
$861$			209.853i			0.243731i
$862$	−817.477	+	288.413i	−0.948350	+	0.334586i
$863$	744.617	−	744.617i	0.862824	−	0.862824i	−0.128841	−	0.991665i	$-0.541126\pi$
$863$	744.617	−	744.617i	0.862824	−	0.862824i	0.991665	+	0.128841i	$0.0411257\pi$
$864$	−1035.47	−	804.166i	−1.19846	−	0.930748i
$865$	−253.121	+	826.602i	−0.292625	+	0.955610i
$866$	−342.551	+	716.027i	−0.395556	+	0.826821i
$867$	−328.516	+	328.516i	−0.378912	+	0.378912i
$868$	−243.362	−	26.1514i	−0.280371	−	0.0301284i
$869$	−261.781			−0.301244
$870$	−88.2789	−	2099.48i	−0.101470	−	2.41319i
$871$	197.531			0.226786
$872$	383.646	−	621.173i	0.439961	−	0.712354i
$873$	−980.488	+	980.488i	−1.12313	+	1.12313i
$874$	−23.0917	+	48.2680i	−0.0264207	+	0.0552266i
$875$	−164.274	−	203.417i	−0.187742	−	0.232477i
$876$	587.180	−	473.230i	0.670297	−	0.540217i
$877$	−603.681	+	603.681i	−0.688348	+	0.688348i	−0.961867	−	0.273519i	$-0.911812\pi$
$877$	−603.681	+	603.681i	−0.688348	+	0.688348i	0.273519	+	0.961867i	$0.411812\pi$
$878$	371.087	+	1051.81i	0.422650	+	1.19796i
$879$		−	1112.11i		−	1.26520i
$880$	244.903	+	870.823i	0.278298	+	0.989571i
$881$	−639.526			−0.725910			−0.362955	−	0.931807i	$-0.618232\pi$
$881$	−639.526			−0.725910			−0.362955	+	0.931807i	$0.618232\pi$
$882$	1433.35	−	505.700i	1.62512	−	0.573356i
$883$	1033.88	+	1033.88i	1.17087	+	1.17087i	0.982002	+	0.188870i	$0.0604825\pi$
$883$	1033.88	+	1033.88i	1.17087	+	1.17087i	0.188870	+	0.982002i	$0.439518\pi$
$884$	158.416	+	196.562i	0.179204	+	0.222355i
$885$	291.054	−	950.479i	0.328875	−	1.07399i
$886$	327.354	+	156.608i	0.369474	+	0.176758i
$887$	801.770	+	801.770i	0.903912	+	0.903912i	0.995772	−	0.0918602i	$-0.0292813\pi$
$887$	801.770	+	801.770i	0.903912	+	0.903912i	−0.0918602	+	0.995772i	$0.529281\pi$
$888$	260.900	−	422.431i	0.293806	−	0.475711i
$889$		−	42.9829i		−	0.0483497i
$890$	509.316	−	554.027i	0.572265	−	0.622502i
$891$		−	630.503i		−	0.707635i
$892$	167.029	−	1554.35i	0.187252	−	1.74255i
$893$	−470.422	−	470.422i	−0.526788	−	0.526788i
$894$	2047.38	+	979.479i	2.29014	+	1.09561i
$895$	149.583	+	281.627i	0.167132	+	0.314667i
$896$	−4.82729	−	267.698i	−0.00538760	−	0.298770i
$897$	38.4165	+	38.4165i	0.0428278	+	0.0428278i
$898$	340.797	+	965.953i	0.379506	+	1.07567i
$899$	−1204.86			−1.34022
$900$	−1697.02	+	142.966i	−1.88558	+	0.158851i
$901$		−	43.0184i		−	0.0477452i
$902$	−147.956	−	419.367i	−0.164031	−	0.464930i
$903$	−268.110	+	268.110i	−0.296910	+	0.296910i
$904$	331.355	+	1401.74i	0.366543	+	1.55060i
$905$	−848.267	+	450.547i	−0.937312	+	0.497842i
$906$	1838.21	+	879.410i	2.02893	+	0.970651i
$907$	488.802	−	488.802i	0.538922	−	0.538922i	−0.384291	−	0.923212i	$-0.625554\pi$
$907$	488.802	−	488.802i	0.538922	−	0.538922i	0.923212	+	0.384291i	$0.125554\pi$
$908$	97.2654	−	905.140i	0.107120	−	0.996851i
$909$	−1911.56			−2.10293
$910$	63.5045	−	69.0794i	0.0697851	−	0.0759114i
$911$	999.285			1.09691			0.548455	−	0.836180i	$-0.315216\pi$
$911$	999.285			1.09691			0.548455	+	0.836180i	$0.315216\pi$
$912$	773.930	−	497.487i	0.848607	−	0.545491i
$913$	772.867	−	772.867i	0.846514	−	0.846514i
$914$	−991.323	−	474.254i	−1.08460	−	0.518878i
$915$	−2134.57	−	653.645i	−2.33287	−	0.714366i
$916$	125.347	−	101.022i	0.136842	−	0.110286i
$917$	−76.7716	+	76.7716i	−0.0837204	+	0.0837204i
$918$	−1087.16	+	383.561i	−1.18427	+	0.417822i
$919$		−	1337.55i		−	1.45544i	−0.685875	−	0.727719i	$-0.740581\pi$
$919$		−	1337.55i		−	1.45544i	0.685875	−	0.727719i	$-0.259419\pi$
$920$	71.3613	−	62.6358i	0.0775666	−	0.0680824i
$921$	700.451			0.760533
$922$	−23.9564	−	67.9018i	−0.0259831	−	0.0736463i
$923$	−425.436	−	425.436i	−0.460927	−	0.460927i
$924$	375.832	−	302.896i	0.406744	−	0.327810i
$925$	−57.7611	−	298.576i	−0.0624444	−	0.322785i
$926$	−413.379	+	864.078i	−0.446414	+	0.933129i
$927$	433.461	+	433.461i	0.467595	+	0.467595i
$928$	−164.420	−	1307.67i	−0.177177	−	1.40913i
$929$			135.066i			0.145388i	0.997354	+	0.0726942i	$0.0231597\pi$
$929$			135.066i			0.145388i	−0.997354	+	0.0726942i	$0.976840\pi$
$930$	62.7022	+	1491.20i	0.0674217	+	1.60345i
$931$			502.943i			0.540218i
$932$	−145.697	+	1355.84i	−0.156328	+	1.45477i
$933$	267.128	+	267.128i	0.286310	+	0.286310i
$934$	−53.2273	+	111.260i	−0.0569885	+	0.119122i
$935$	760.574	+	232.902i	0.813448	+	0.249093i
$936$	−140.600	−	594.785i	−0.150214	−	0.635454i
$937$	1002.83	+	1002.83i	1.07026	+	1.07026i	0.997338	+	0.0729231i	$0.0232328\pi$
$937$	1002.83	+	1002.83i	1.07026	+	1.07026i	0.0729231	+	0.997338i	$0.476767\pi$
$938$	−173.716	+	61.2887i	−0.185199	+	0.0653397i
$939$	908.353			0.967362
$940$	439.208	+	1095.82i	0.467243	+	1.16577i
$941$		−	133.203i		−	0.141554i	−0.997492	−	0.0707772i	$-0.977452\pi$
$941$		−	133.203i		−	0.141554i	0.997492	−	0.0707772i	$-0.0225479\pi$
$942$	2601.72	−	917.909i	2.76191	−	0.974426i
$943$	−33.0061	+	33.0061i	−0.0350011	+	0.0350011i
$944$	132.465	−	609.235i	0.140323	−	0.645377i
$945$	200.999	+	378.431i	0.212697	+	0.400456i
$946$	346.756	−	724.817i	0.366550	−	0.766191i
$947$	−671.287	+	671.287i	−0.708857	+	0.708857i	−0.966295	−	0.257438i	$-0.917122\pi$
$947$	−671.287	+	671.287i	−0.708857	+	0.708857i	0.257438	+	0.966295i	$0.417122\pi$
$948$	50.4799	−	469.760i	0.0532489	−	0.495528i
$949$	165.770			0.174679
$950$	142.217	−	545.285i	0.149702	−	0.573984i
$951$	−1855.50			−1.95110
$952$	−200.306	−	123.712i	−0.210405	−	0.129949i
$953$	834.636	−	834.636i	0.875798	−	0.875798i	−0.117299	−	0.993097i	$-0.537423\pi$
$953$	834.636	−	834.636i	0.875798	−	0.875798i	0.993097	+	0.117299i	$0.0374235\pi$
$954$	−44.9453	+	93.9482i	−0.0471125	+	0.0984782i
$955$	−400.582	−	754.196i	−0.419458	−	0.789734i
$956$	625.004	+	775.501i	0.653770	+	0.811193i
$957$	1680.15	−	1680.15i	1.75565	−	1.75565i
$958$	−579.096	−	1641.39i	−0.604484	−	1.71335i
$959$		−	292.157i		−	0.304648i
$960$	−1609.90	+	271.549i	−1.67698	+	0.282864i
$961$	−105.221			−0.109491
$962$	102.921	−	36.3114i	0.106986	−	0.0377457i
$963$	1124.66	+	1124.66i	1.16787	+	1.16787i
$964$	1011.42	−	815.143i	1.04919	−	0.845584i
$965$	752.482	+	230.424i	0.779774	+	0.238781i
$966$	−45.7047	−	21.8654i	−0.0473134	−	0.0226350i
$967$	249.412	+	249.412i	0.257923	+	0.257923i	0.824209	−	0.566286i	$-0.191620\pi$
$967$	249.412	+	249.412i	0.257923	+	0.257923i	−0.566286	+	0.824209i	$0.691620\pi$
$968$	−28.8416	+	46.6983i	−0.0297951	+	0.0482421i
$969$		−	809.001i		−	0.834883i
$970$	34.2055	+	813.487i	0.0352634	+	0.838646i
$971$		−	1425.94i		−	1.46852i	−0.678867	−	0.734262i	$-0.737529\pi$
$971$		−	1425.94i		−	1.46852i	0.678867	−	0.734262i	$-0.262471\pi$
$972$	−335.081	−	36.0074i	−0.344733	−	0.0370446i
$973$	71.9394	+	71.9394i	0.0739357	+	0.0739357i
$974$	−1561.17	−	746.870i	−1.60284	−	0.766807i
$975$	−474.075	−	320.383i	−0.486230	−	0.328598i
$976$	−1368.21	−	297.488i	−1.40186	−	0.304804i
$977$	−651.241	−	651.241i	−0.666572	−	0.666572i	0.290349	−	0.956921i	$-0.406229\pi$
$977$	−651.241	−	651.241i	−0.666572	−	0.666572i	−0.956921	+	0.290349i	$0.906229\pi$
$978$	−484.196	−	1372.40i	−0.495088	−	1.40327i
$979$	850.963			0.869217
$980$	351.003	−	820.574i	0.358166	−	0.837320i
$981$			1554.22i			1.58432i
$982$	478.624	+	1356.61i	0.487397	+	1.38148i
$983$	−301.766	+	301.766i	−0.306985	+	0.306985i	−0.843739	−	0.536754i	$-0.819650\pi$
$983$	−301.766	+	301.766i	−0.306985	+	0.306985i	0.536754	+	0.843739i	$0.319650\pi$
$984$	781.075	−	184.637i	0.793775	−	0.187639i
$985$	655.085	+	200.599i	0.665061	+	0.203654i
$986$	−1045.44	−	500.142i	−1.06028	−	0.507244i
$987$	445.440	−	445.440i	0.451307	−	0.451307i
$988$	201.078	+	21.6076i	0.203520	+	0.0218701i
$989$	−84.3377			−0.0852758
$990$	−1417.69	−	1303.28i	−1.43201	−	1.31644i
$991$	−672.650			−0.678759			−0.339380	−	0.940650i	$-0.610217\pi$
$991$	−672.650			−0.678759			−0.339380	+	0.940650i	$0.610217\pi$
$992$	116.784	+	928.806i	0.117725	+	0.936296i
$993$	−1457.37	+	1457.37i	−1.46765	+	1.46765i
$994$	506.147	+	242.143i	0.509202	+	0.243605i
$995$	617.350	−	327.898i	0.620453	−	0.329546i
$996$	1237.86	+	1535.93i	1.24283	+	1.54209i
$997$	65.6794	−	65.6794i	0.0658771	−	0.0658771i	−0.673401	−	0.739278i	$-0.735167\pi$
$997$	65.6794	−	65.6794i	0.0658771	−	0.0658771i	0.739278	+	0.673401i	$0.235167\pi$
$998$	351.002	−	123.837i	0.351705	−	0.124085i
$999$			498.388i			0.498887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.3.i.a.37.10	yes	20
3.2	odd	2		360.3.u.b.37.1		20
4.3	odd	2		160.3.m.a.17.10		20
5.2	odd	4		200.3.i.b.93.6		20
5.3	odd	4	inner	40.3.i.a.13.5	✓	20
5.4	even	2		200.3.i.b.157.1		20
8.3	odd	2		160.3.m.a.17.1		20
8.5	even	2	inner	40.3.i.a.37.5	yes	20
15.8	even	4		360.3.u.b.253.6		20
20.3	even	4		160.3.m.a.113.1		20
20.7	even	4		800.3.m.b.593.10		20
20.19	odd	2		800.3.m.b.657.1		20
24.5	odd	2		360.3.u.b.37.6		20
40.3	even	4		160.3.m.a.113.10		20
40.13	odd	4	inner	40.3.i.a.13.10	yes	20
40.19	odd	2		800.3.m.b.657.10		20
40.27	even	4		800.3.m.b.593.1		20
40.29	even	2		200.3.i.b.157.6		20
40.37	odd	4		200.3.i.b.93.1		20
120.53	even	4		360.3.u.b.253.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.i.a.13.5	✓	20	5.3	odd	4	inner
40.3.i.a.13.10	yes	20	40.13	odd	4	inner
40.3.i.a.37.5	yes	20	8.5	even	2	inner
40.3.i.a.37.10	yes	20	1.1	even	1	trivial
160.3.m.a.17.1		20	8.3	odd	2
160.3.m.a.17.10		20	4.3	odd	2
160.3.m.a.113.1		20	20.3	even	4
160.3.m.a.113.10		20	40.3	even	4
200.3.i.b.93.1		20	40.37	odd	4
200.3.i.b.93.6		20	5.2	odd	4
200.3.i.b.157.1		20	5.4	even	2
200.3.i.b.157.6		20	40.29	even	2
360.3.u.b.37.1		20	3.2	odd	2
360.3.u.b.37.6		20	24.5	odd	2
360.3.u.b.253.1		20	120.53	even	4
360.3.u.b.253.6		20	15.8	even	4
800.3.m.b.593.1		20	40.27	even	4
800.3.m.b.593.10		20	20.7	even	4
800.3.m.b.657.1		20	20.19	odd	2
800.3.m.b.657.10		20	40.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	40.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.88606 - 0.665418i) q^{2} +(-3.60765 - 3.60765i) q^{3} +(3.11444 - 2.51004i) q^{4} +(2.34539 + 4.41578i) q^{5} +(-9.20485 - 4.40365i) q^{6} +(1.47907 + 1.47907i) q^{7} +(4.20379 - 6.80648i) q^{8} +17.0303i q^{9} +(7.36189 + 6.76776i) q^{10} +11.3076i q^{11} +(-20.2912 - 2.18047i) q^{12} +(-3.17204 - 3.17204i) q^{13} +(3.77383 + 1.80542i) q^{14} +(7.46927 - 24.3920i) q^{15} +(3.39943 - 15.6347i) q^{16} +(-9.94834 - 9.94834i) q^{17} +(11.3323 + 32.1202i) q^{18} -11.2705 q^{19} +(18.3883 + 7.86567i) q^{20} -10.6720i q^{21} +(7.52426 + 21.3267i) q^{22} +(1.67851 - 1.67851i) q^{23} +(-39.7212 + 9.38962i) q^{24} +(-13.9983 + 20.7135i) q^{25} +(-8.09340 - 3.87192i) q^{26} +(28.9707 - 28.9707i) q^{27} +(8.31902 + 0.893952i) q^{28} +41.1865 q^{29} +(-2.14339 - 50.9749i) q^{30} -29.2537 q^{31} +(-3.99209 - 31.7500i) q^{32} +(40.7938 - 40.7938i) q^{33} +(-25.3830 - 12.1433i) q^{34} +(-3.06227 + 10.0003i) q^{35} +(42.7468 + 53.0399i) q^{36} +(-8.60159 + 8.60159i) q^{37} +(-21.2568 + 7.49961i) q^{38} +22.8873i q^{39} +(39.9155 + 2.59916i) q^{40} -19.6639 q^{41} +(-7.10133 - 20.1280i) q^{42} +(-25.1228 - 25.1228i) q^{43} +(28.3824 + 35.2167i) q^{44} +(-75.2023 + 39.9428i) q^{45} +(2.04886 - 4.28268i) q^{46} +(41.7392 + 41.7392i) q^{47} +(-68.6686 + 44.1406i) q^{48} -44.6247i q^{49} +(-12.6185 + 48.3815i) q^{50} +71.7804i q^{51} +(-17.8411 - 1.91718i) q^{52} +(2.16209 + 2.16209i) q^{53} +(35.3628 - 73.9181i) q^{54} +(-49.9317 + 26.5206i) q^{55} +(16.2850 - 3.84958i) q^{56} +(40.6601 + 40.6601i) q^{57} +(77.6802 - 27.4063i) q^{58} +38.9669 q^{59} +(-37.9622 - 94.7154i) q^{60} -87.5112i q^{61} +(-55.1742 + 19.4660i) q^{62} +(-25.1891 + 25.1891i) q^{63} +(-28.6564 - 57.2260i) q^{64} +(6.56738 - 21.4467i) q^{65} +(49.7945 - 104.084i) q^{66} +(-31.1362 + 31.1362i) q^{67} +(-55.9542 - 6.01278i) q^{68} -12.1110 q^{69} +(0.878753 + 20.8988i) q^{70} +134.120 q^{71} +(115.917 + 71.5919i) q^{72} +(-26.1299 + 26.1299i) q^{73} +(-10.4994 + 21.9468i) q^{74} +(125.228 - 24.2260i) q^{75} +(-35.1013 + 28.2894i) q^{76} +(-16.7247 + 16.7247i) q^{77} +(15.2296 + 43.1667i) q^{78} +23.1510i q^{79} +(77.0125 - 21.6583i) q^{80} -55.7594 q^{81} +(-37.0873 + 13.0847i) q^{82} +(-68.3496 - 68.3496i) q^{83} +(-26.7871 - 33.2372i) q^{84} +(20.5970 - 67.2625i) q^{85} +(-64.1002 - 30.6659i) q^{86} +(-148.587 - 148.587i) q^{87} +(76.9647 + 47.5346i) q^{88} -75.2561i q^{89} +(-115.257 + 125.375i) q^{90} -9.38338i q^{91} +(1.01449 - 9.44074i) q^{92} +(105.537 + 105.537i) q^{93} +(106.497 + 50.9485i) q^{94} +(-26.4337 - 49.7681i) q^{95} +(-100.141 + 128.945i) q^{96} +(57.5730 + 57.5730i) q^{97} +(-29.6941 - 84.1648i) q^{98} -192.572 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8} + 6 q^{10} - 44 q^{12} - 4 q^{15} - 56 q^{16} - 12 q^{17} + 10 q^{18} - 24 q^{20} + 92 q^{22} - 4 q^{23} - 28 q^{25} + 100 q^{26} + 68 q^{28} + 100 q^{30} - 136 q^{31}+ \cdots + 546 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8 + 6 * q^10 - 44 * q^12 - 4 * q^15 - 56 * q^16 - 12 * q^17 + 10 * q^18 - 24 * q^20 + 92 * q^22 - 4 * q^23 - 28 * q^25 + 100 * q^26 + 68 * q^28 + 100 * q^30 - 136 * q^31 + 128 * q^32 + 32 * q^33 + 220 * q^36 - 188 * q^38 + 156 * q^40 - 8 * q^41 - 284 * q^42 - 240 * q^46 + 188 * q^47 - 256 * q^48 - 274 * q^50 - 332 * q^52 + 96 * q^55 - 360 * q^56 - 40 * q^57 + 268 * q^58 - 340 * q^60 + 336 * q^62 + 228 * q^63 - 60 * q^65 + 616 * q^66 + 396 * q^68 + 300 * q^70 + 248 * q^71 + 668 * q^72 - 124 * q^73 + 424 * q^76 - 368 * q^78 + 496 * q^80 + 132 * q^81 - 676 * q^82 - 672 * q^86 - 488 * q^87 - 304 * q^88 - 474 * q^90 - 628 * q^92 - 488 * q^95 - 1024 * q^96 + 100 * q^97 + 546 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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