LMFDB - Embedded newform 40.3.i.a.13.10

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			13.10
Root			$-1.27574 - 0.610320i$ of defining polynomial
Character	$\chi$	$=$	40.13
Dual form			40.3.i.a.37.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.88606 + 0.665418i) q^{2} +(-3.60765 + 3.60765i) q^{3} +(3.11444 + 2.51004i) q^{4} +(2.34539 - 4.41578i) q^{5} +(-9.20485 + 4.40365i) q^{6} +(1.47907 - 1.47907i) q^{7} +(4.20379 + 6.80648i) q^{8} -17.0303i q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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	−0.229164	+	0.973388i	$0.573599\pi$
$3$	−3.60765	+	3.60765i	−1.20255	+	1.20255i	−0.973388	+	0.229164i	$0.926401\pi$
$4$	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	−0.593522	−	0.804818i	$-0.702263\pi$
$7$	1.47907	−	1.47907i	0.211296	−	0.211296i	0.804818	+	0.593522i	$0.202263\pi$
$8$	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	$-0.828171\pi$
$11$		−	11.3076i		−	1.02796i	0.857802	−	0.513980i	$-0.171829\pi$
$12$	−20.2912	+	2.18047i	−1.69093	+	0.181705i
$13$	−3.17204	+	3.17204i	−0.244003	+	0.244003i	−0.818504	−	0.574501i	$-0.805196\pi$
$13$	−3.17204	+	3.17204i	−0.244003	+	0.244003i	0.574501	+	0.818504i	$0.305196\pi$
$14$	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	−0.936327	−	0.351130i	$-0.885797\pi$
$17$	−9.94834	+	9.94834i	−0.585197	+	0.585197i	0.351130	+	0.936327i	$0.385797\pi$
$18$	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	0.742654	−	0.669675i	$-0.233567\pi$
$23$	1.67851	+	1.67851i	0.0729787	+	0.0729787i	−0.669675	+	0.742654i	$0.733567\pi$
$24$	−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	0.581250	−	0.813725i	$-0.302564\pi$
$37$	−8.60159	−	8.60159i	−0.232475	−	0.232475i	−0.813725	+	0.581250i	$0.802564\pi$
$38$	−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	−0.936069	−	0.351818i	$-0.885564\pi$
$43$	−25.1228	+	25.1228i	−0.584251	+	0.584251i	0.351818	+	0.936069i	$0.385564\pi$
$44$	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	−0.106269	−	0.994337i	$-0.533891\pi$
$47$	41.7392	−	41.7392i	0.888068	−	0.888068i	0.994337	+	0.106269i	$0.0338906\pi$
$48$	−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	−0.686415	−	0.727210i	$-0.740817\pi$
$53$	2.16209	−	2.16209i	0.0407941	−	0.0407941i	0.727210	+	0.686415i	$0.240817\pi$
$54$	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	$0.254625\pi$
$61$			87.5112i			1.43461i	−0.696759	+	0.717305i	$0.745375\pi$
$62$	−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	0.435479	−	0.900199i	$-0.356579\pi$
$67$	−31.1362	−	31.1362i	−0.464719	−	0.464719i	−0.900199	+	0.435479i	$0.856579\pi$
$68$	−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	0.505111	−	0.863054i	$-0.331452\pi$
$73$	−26.1299	−	26.1299i	−0.357943	−	0.357943i	−0.863054	+	0.505111i	$0.831452\pi$
$74$	−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	$-0.953191\pi$
$79$		−	23.1510i		−	0.293050i	0.989207	−	0.146525i	$-0.0468090\pi$
$80$	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	−0.986607	−	0.163118i	$-0.947845\pi$
$83$	−68.3496	+	68.3496i	−0.823489	+	0.823489i	0.163118	+	0.986607i	$0.447845\pi$
$84$	−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	$0.138948\pi$
$89$			75.2561i			0.845574i	−0.906229	+	0.422787i	$0.861052\pi$
$90$	−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	−0.345049	−	0.938585i	$-0.612138\pi$
$97$	57.5730	−	57.5730i	0.593536	−	0.593536i	0.938585	+	0.345049i	$0.112138\pi$
$98$	−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	$-0.812463\pi$
$101$		−	112.245i		−	1.11133i	0.831405	−	0.555666i	$-0.187537\pi$
$102$	47.7640	−	135.382i	0.468274	−	1.32727i
$103$	25.4523	+	25.4523i	0.247109	+	0.247109i	0.819783	−	0.572674i	$-0.194094\pi$
$103$	25.4523	+	25.4523i	0.247109	+	0.247109i	−0.572674	+	0.819783i	$0.694094\pi$
$104$	−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	0.944808	−	0.327624i	$-0.106248\pi$
$107$	66.0387	+	66.0387i	0.617184	+	0.617184i	−0.327624	+	0.944808i	$0.606248\pi$
$108$	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	−0.990717	−	0.135940i	$-0.956594\pi$
$113$	−127.312	−	127.312i	−1.12666	−	1.12666i	−0.135940	−	0.990717i	$-0.543406\pi$
$114$	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	−0.761995	−	0.647583i	$-0.775780\pi$
$127$	−14.5303	+	14.5303i	−0.114412	+	0.114412i	0.647583	+	0.761995i	$0.275780\pi$
$128$	−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	$-0.936519\pi$
$131$		−	51.9051i		−	0.396222i	0.980180	−	0.198111i	$-0.0634807\pi$
$132$	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	−0.968789	−	0.247887i	$-0.920264\pi$
$137$	−98.7636	+	98.7636i	−0.720902	+	0.720902i	0.247887	+	0.968789i	$0.420264\pi$
$138$	−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	−0.968426	−	0.249302i	$-0.919799\pi$
$157$	−191.183	−	191.183i	−1.21773	−	1.21773i	−0.249302	−	0.968426i	$-0.580201\pi$
$158$	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	−0.326494	−	0.945199i	$-0.605867\pi$
$163$	100.849	−	100.849i	0.618705	−	0.618705i	0.945199	+	0.326494i	$0.105867\pi$
$164$	−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	0.292609	−	0.956232i	$-0.405477\pi$
$167$	208.556	−	208.556i	1.24884	−	1.24884i	0.956232	−	0.292609i	$-0.0945233\pi$
$168$	−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	−0.259148	−	0.965838i	$-0.583442\pi$
$173$	122.257	−	122.257i	0.706689	−	0.706689i	0.965838	+	0.259148i	$0.0834419\pi$
$174$	−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	$-0.821944\pi$
$181$		−	192.099i		−	1.06132i	0.847585	−	0.530660i	$-0.178056\pi$
$182$	−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	0.933980	−	0.357325i	$-0.116311\pi$
$193$	111.295	+	111.295i	0.576656	+	0.576656i	−0.357325	+	0.933980i	$0.616311\pi$
$194$	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	0.908880	−	0.417057i	$-0.136938\pi$
$197$	96.8892	+	96.8892i	0.491823	+	0.491823i	−0.417057	+	0.908880i	$0.636938\pi$
$198$	−363.201	−	128.141i	−1.83435	−	0.647175i
$199$			139.805i			0.702540i	0.936274	+	0.351270i	$0.114250\pi$
$199$			139.805i			0.702540i	−0.936274	+	0.351270i	$0.885750\pi$
$200$	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	$0.00721080\pi$
$211$			9.55891i			0.0453029i	−0.999743	+	0.0226514i	$0.992789\pi$
$212$	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	0.960304	+	0.278957i	$0.0899888\pi$
$223$	276.355	+	276.355i	1.23926	+	1.23926i	0.278957	+	0.960304i	$0.410011\pi$
$224$	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	0.966312	−	0.257374i	$-0.0828572\pi$
$227$	160.929	+	160.929i	0.708938	+	0.708938i	−0.257374	+	0.966312i	$0.582857\pi$
$228$	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	−0.999380	−	0.0352176i	$-0.988788\pi$
$233$	−241.061	−	241.061i	−1.03460	−	1.03460i	−0.0352176	−	0.999380i	$-0.511212\pi$
$234$	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	$-0.825587\pi$
$239$		−	249.002i		−	1.04185i	0.853603	−	0.520925i	$-0.174413\pi$
$240$	−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	$-0.892233\pi$
$251$		−	166.729i		−	0.664260i	0.943234	−	0.332130i	$-0.107767\pi$
$252$	−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	−0.250248	−	0.968182i	$-0.580512\pi$
$257$	184.509	−	184.509i	0.717933	−	0.717933i	0.968182	+	0.250248i	$0.0805122\pi$
$258$	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	0.714400	−	0.699737i	$-0.246700\pi$
$263$	3.85637	+	3.85637i	0.0146630	+	0.0146630i	−0.699737	+	0.714400i	$0.746700\pi$
$264$	−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	0.946483	−	0.322754i	$-0.104609\pi$
$277$	172.773	+	172.773i	0.623729	+	0.623729i	−0.322754	+	0.946483i	$0.604609\pi$
$278$	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	−0.921957	−	0.387293i	$-0.873410\pi$
$283$	−151.310	+	151.310i	−0.534663	+	0.534663i	0.387293	+	0.921957i	$0.373410\pi$
$284$	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	−0.393344	−	0.919391i	$-0.628682\pi$
$293$	154.132	−	154.132i	0.526048	−	0.526048i	0.919391	+	0.393344i	$0.128682\pi$
$294$	−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	0.531096	−	0.847312i	$-0.321781\pi$
$307$	−97.0784	−	97.0784i	−0.316216	−	0.316216i	−0.847312	+	0.531096i	$0.821781\pi$
$308$	−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	0.476800	−	0.879012i	$-0.341797\pi$
$313$	−125.892	−	125.892i	−0.402212	−	0.402212i	−0.879012	+	0.476800i	$0.841797\pi$
$314$	−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	0.984819	−	0.173585i	$-0.0555353\pi$
$317$	257.161	+	257.161i	0.811233	+	0.811233i	−0.173585	+	0.984819i	$0.555535\pi$
$318$	−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	$0.208920\pi$
$331$			403.967i			1.22045i	−0.792230	+	0.610223i	$0.791080\pi$
$332$	−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	−0.841763	−	0.539848i	$-0.818482\pi$
$337$	−101.745	+	101.745i	−0.301915	+	0.301915i	0.539848	+	0.841763i	$0.318482\pi$
$338$	−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	0.364724	−	0.931116i	$-0.381163\pi$
$347$	−196.538	−	196.538i	−0.566391	−	0.566391i	−0.931116	+	0.364724i	$0.881163\pi$
$348$	−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	0.934940	−	0.354805i	$-0.115453\pi$
$353$	204.788	+	204.788i	0.580135	+	0.580135i	−0.354805	+	0.934940i	$0.615453\pi$
$354$	−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	$0.0120641\pi$
$359$			27.2061i			0.0757831i	−0.999282	+	0.0378916i	$0.987936\pi$
$360$	−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	−0.635038	−	0.772481i	$-0.719016\pi$
$367$	50.4416	−	50.4416i	0.137443	−	0.137443i	0.772481	+	0.635038i	$0.219016\pi$
$368$	−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	−0.834548	−	0.550936i	$-0.814271\pi$
$373$	−105.787	+	105.787i	−0.283612	+	0.283612i	0.550936	+	0.834548i	$0.314271\pi$
$374$	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	0.625488	−	0.780234i	$-0.284900\pi$
$383$	−59.2677	−	59.2677i	−0.154746	−	0.154746i	−0.780234	+	0.625488i	$0.784900\pi$
$384$	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	0.0591281	−	0.998250i	$-0.481168\pi$
$397$	−372.832	−	372.832i	−0.939122	−	0.939122i	−0.998250	+	0.0591281i	$0.981168\pi$
$398$	−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	$0.0714964\pi$
$409$			182.192i			0.445457i	−0.974880	+	0.222729i	$0.928504\pi$
$410$	−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	$-0.975396\pi$
$421$		−	65.0180i		−	0.154437i	0.997014	−	0.0772186i	$-0.0246039\pi$
$422$	−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	0.304425	−	0.952536i	$-0.401536\pi$
$433$	−280.632	−	280.632i	−0.648112	−	0.648112i	−0.952536	+	0.304425i	$0.901536\pi$
$434$	−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	$-0.780932\pi$
$439$		−	557.674i		−	1.27033i	0.772377	−	0.635164i	$-0.219068\pi$
$440$	−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	−0.547313	−	0.836928i	$-0.684349\pi$
$443$	128.300	−	128.300i	0.289616	−	0.289616i	0.836928	+	0.547313i	$0.184349\pi$
$444$	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	$-0.806816\pi$
$449$		−	512.154i		−	1.14065i	0.821417	−	0.570327i	$-0.193184\pi$
$450$	−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	−0.990154	−	0.139981i	$-0.955296\pi$
$457$	−388.529	+	388.529i	−0.850173	+	0.850173i	0.139981	+	0.990154i	$0.455296\pi$
$458$	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	$0.0124324\pi$
$461$			36.0020i			0.0780954i	−0.999237	+	0.0390477i	$0.987568\pi$
$462$	227.598	+	80.2987i	0.492637	+	0.173807i
$463$	−338.658	−	338.658i	−0.731442	−	0.731442i	0.239463	−	0.970905i	$-0.423029\pi$
$463$	−338.658	−	338.658i	−0.731442	−	0.731442i	−0.970905	+	0.239463i	$0.923029\pi$
$464$	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	0.658876	−	0.752251i	$-0.271032\pi$
$467$	−43.6060	−	43.6060i	−0.0933748	−	0.0933748i	−0.752251	+	0.658876i	$0.771032\pi$
$468$	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	$0.362716\pi$
$479$			870.273i			1.81685i	−0.418043	+	0.908427i	$0.637284\pi$
$480$	−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	−0.303603	+	0.952799i	$0.598190\pi$
$487$	−611.867	+	611.867i	−1.25640	+	1.25640i	−0.952799	+	0.303603i	$0.901810\pi$
$488$	−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	$-0.738369\pi$
$491$		−	719.282i		−	1.46493i	0.680803	−	0.732467i	$-0.261631\pi$
$492$	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	0.339408	−	0.940639i	$-0.389773\pi$
$503$	−302.420	−	302.420i	−0.601232	−	0.601232i	−0.940639	+	0.339408i	$0.889773\pi$
$504$	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	−0.844216	−	0.536003i	$-0.819934\pi$
$523$	−161.196	+	161.196i	−0.308213	+	0.308213i	0.536003	+	0.844216i	$0.319934\pi$
$524$	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	$-0.904568\pi$
$541$		−	319.556i		−	0.590676i	0.955393	−	0.295338i	$-0.0954323\pi$
$542$	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	0.985674	+	0.168659i	$0.0539438\pi$
$547$	631.421	+	631.421i	1.15433	+	1.15433i	0.168659	+	0.985674i	$0.446056\pi$
$548$	−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	0.970339	−	0.241747i	$-0.0777204\pi$
$557$	405.826	+	405.826i	0.728592	+	0.728592i	−0.241747	+	0.970339i	$0.577720\pi$
$558$	−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	−0.888502	−	0.458873i	$-0.848253\pi$
$563$	−241.881	+	241.881i	−0.429628	+	0.429628i	0.458873	+	0.888502i	$0.348253\pi$
$564$	−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	$0.119130\pi$
$569$			416.031i			0.731162i	−0.930780	+	0.365581i	$0.880870\pi$
$570$	24.1571	−	574.513i	0.0423809	−	1.00792i
$571$			907.558i			1.58942i	0.606991	+	0.794709i	$0.292377\pi$
$571$			907.558i			1.58942i	−0.606991	+	0.794709i	$0.707623\pi$
$572$	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	−0.175075	−	0.984555i	$-0.556017\pi$
$577$	467.070	−	467.070i	0.809480	−	0.809480i	0.984555	+	0.175075i	$0.0560167\pi$
$578$	−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	0.885561	−	0.464523i	$-0.153774\pi$
$587$	247.149	+	247.149i	0.421038	+	0.421038i	−0.464523	+	0.885561i	$0.653774\pi$
$588$	−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	0.921038	−	0.389472i	$-0.127342\pi$
$593$	315.219	+	315.219i	0.531567	+	0.531567i	−0.389472	+	0.921038i	$0.627342\pi$
$594$	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	$0.115056\pi$
$599$			423.660i			0.707278i	−0.935382	+	0.353639i	$0.884944\pi$
$600$	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	−0.815555	−	0.578679i	$-0.803568\pi$
$607$	−143.784	+	143.784i	−0.236876	+	0.236876i	0.578679	+	0.815555i	$0.303568\pi$
$608$	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	−0.413763	−	0.910385i	$-0.635786\pi$
$613$	304.429	−	304.429i	0.496622	−	0.496622i	0.910385	+	0.413763i	$0.135786\pi$
$614$	−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	0.408683	−	0.912676i	$-0.365988\pi$
$617$	815.279	−	815.279i	1.32136	−	1.32136i	0.912676	−	0.408683i	$-0.134012\pi$
$618$	−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	−0.209864	−	0.977731i	$-0.567302\pi$
$643$	493.738	−	493.738i	0.767867	−	0.767867i	0.977731	+	0.209864i	$0.0673021\pi$
$644$	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	−0.981032	−	0.193844i	$-0.937905\pi$
$647$	−509.311	+	509.311i	−0.787189	+	0.787189i	0.193844	+	0.981032i	$0.437905\pi$
$648$	−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	−0.866464	−	0.499239i	$-0.833613\pi$
$653$	−239.798	+	239.798i	−0.367226	+	0.367226i	0.499239	+	0.866464i	$0.333613\pi$
$654$	−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	$0.0144010\pi$
$661$			59.7896i			0.0904533i	−0.998977	+	0.0452267i	$0.985599\pi$
$662$	−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	0.834538	−	0.550951i	$-0.185735\pi$
$673$	190.854	+	190.854i	0.283587	+	0.283587i	−0.550951	+	0.834538i	$0.685735\pi$
$674$	−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	0.973391	−	0.229151i	$-0.0735949\pi$
$677$	503.850	+	503.850i	0.744240	+	0.744240i	−0.229151	+	0.973391i	$0.573595\pi$
$678$	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	−0.595494	−	0.803360i	$-0.703044\pi$
$683$	141.973	−	141.973i	0.207866	−	0.207866i	0.803360	+	0.595494i	$0.203044\pi$
$684$	−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	$-0.628119\pi$
$691$		−	1271.56i		−	1.84017i	0.391717	−	0.920086i	$-0.371881\pi$
$692$	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	$-0.806927\pi$
$701$		−	799.199i		−	1.14008i	0.821615	−	0.570042i	$-0.193073\pi$
$702$	−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	$-0.812006\pi$
$719$		−	800.764i		−	1.11372i	0.830607	−	0.556859i	$-0.187994\pi$
$720$	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	−0.600758	−	0.799431i	$-0.705134\pi$
$727$	144.435	−	144.435i	0.198673	−	0.198673i	0.799431	+	0.600758i	$0.205134\pi$
$728$	−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	−0.0215340	+	0.999768i	$0.506855\pi$
$733$	−748.614	+	748.614i	−1.02130	+	1.02130i	−0.999768	+	0.0215340i	$0.993145\pi$
$734$	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	0.0861618	−	0.996281i	$-0.472540\pi$
$743$	−676.219	−	676.219i	−0.910119	−	0.910119i	−0.996281	+	0.0861618i	$0.972540\pi$
$744$	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	0.981367	−	0.192142i	$-0.0615434\pi$
$757$	597.444	+	597.444i	0.789225	+	0.789225i	−0.192142	+	0.981367i	$0.561543\pi$
$758$	−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	$0.372403\pi$
$769$			1416.08i			1.84145i	−0.390208	+	0.920727i	$0.627597\pi$
$770$	−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	−0.655000	−	0.755629i	$-0.727331\pi$
$773$	77.7861	−	77.7861i	0.100629	−	0.100629i	0.755629	+	0.655000i	$0.227331\pi$
$774$	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	0.319268	−	0.947664i	$-0.396563\pi$
$787$	−494.548	−	494.548i	−0.628396	−	0.628396i	−0.947664	+	0.319268i	$0.896563\pi$
$788$	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	0.259746	−	0.965677i	$-0.416361\pi$
$797$	−562.627	−	562.627i	−0.705931	−	0.705931i	−0.965677	+	0.259746i	$0.916361\pi$
$798$	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	$-0.912198\pi$
$809$		−	440.667i		−	0.544706i	0.962197	−	0.272353i	$-0.0878018\pi$
$810$	−410.495	+	377.367i	−0.506784	+	0.465885i
$811$			911.348i			1.12373i	0.827228	+	0.561867i	$0.189917\pi$
$811$			911.348i			1.12373i	−0.827228	+	0.561867i	$0.810083\pi$
$812$	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	$0.183047\pi$
$821$			893.060i			1.08777i	−0.839159	+	0.543885i	$0.816953\pi$
$822$	474.184	−	1344.02i	0.576866	−	1.63507i
$823$	−852.293	−	852.293i	−1.03559	−	1.03559i	−0.999343	−	0.0362500i	$-0.988459\pi$
$823$	−852.293	−	852.293i	−1.03559	−	1.03559i	−0.0362500	−	0.999343i	$-0.511541\pi$
$824$	−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	0.236269	−	0.971688i	$-0.424075\pi$
$827$	−608.192	−	608.192i	−0.735419	−	0.735419i	−0.971688	+	0.236269i	$0.924075\pi$
$828$	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	$0.144574\pi$
$839$			736.198i			0.877471i	−0.898616	+	0.438736i	$0.855426\pi$
$840$	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	−0.456813	−	0.889563i	$-0.651009\pi$
$853$	369.135	−	369.135i	0.432749	−	0.432749i	0.889563	+	0.456813i	$0.151009\pi$
$854$	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	−0.988176	−	0.153326i	$-0.951001\pi$
$857$	−715.466	+	715.466i	−0.834849	+	0.834849i	0.153326	+	0.988176i	$0.451001\pi$
$858$	−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	0.991665	−	0.128841i	$-0.0411257\pi$
$863$	744.617	+	744.617i	0.862824	+	0.862824i	−0.128841	+	0.991665i	$0.541126\pi$
$864$	−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	0.273519	−	0.961867i	$-0.411812\pi$
$877$	−603.681	−	603.681i	−0.688348	−	0.688348i	−0.961867	+	0.273519i	$0.911812\pi$
$878$	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	0.188870	−	0.982002i	$-0.439518\pi$
$883$	1033.88	−	1033.88i	1.17087	−	1.17087i	0.982002	−	0.188870i	$-0.0604825\pi$
$884$	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	−0.0918602	−	0.995772i	$-0.529281\pi$
$887$	801.770	−	801.770i	0.903912	−	0.903912i	0.995772	+	0.0918602i	$0.0292813\pi$
$888$	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	0.923212	−	0.384291i	$-0.125554\pi$
$907$	488.802	+	488.802i	0.538922	+	0.538922i	−0.384291	+	0.923212i	$0.625554\pi$
$908$	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	$0.259419\pi$
$919$			1337.55i			1.45544i	−0.685875	+	0.727719i	$0.740581\pi$
$920$	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	$-0.976840\pi$
$929$		−	135.066i		−	0.145388i	0.997354	−	0.0726942i	$-0.0231597\pi$
$930$	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	0.0729231	−	0.997338i	$-0.476767\pi$
$937$	1002.83	−	1002.83i	1.07026	−	1.07026i	0.997338	−	0.0729231i	$-0.0232328\pi$
$938$	−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	$0.0225479\pi$
$941$			133.203i			0.141554i	−0.997492	+	0.0707772i	$0.977452\pi$
$942$	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	0.257438	−	0.966295i	$-0.417122\pi$
$947$	−671.287	−	671.287i	−0.708857	−	0.708857i	−0.966295	+	0.257438i	$0.917122\pi$
$948$	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	0.993097	−	0.117299i	$-0.0374235\pi$
$953$	834.636	+	834.636i	0.875798	+	0.875798i	−0.117299	+	0.993097i	$0.537423\pi$
$954$	−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	−0.566286	−	0.824209i	$-0.691620\pi$
$967$	249.412	−	249.412i	0.257923	−	0.257923i	0.824209	+	0.566286i	$0.191620\pi$
$968$	−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	$0.262471\pi$
$971$			1425.94i			1.46852i	−0.678867	+	0.734262i	$0.737529\pi$
$972$	−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	−0.956921	−	0.290349i	$-0.906229\pi$
$977$	−651.241	+	651.241i	−0.666572	+	0.666572i	0.290349	+	0.956921i	$0.406229\pi$
$978$	−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	0.536754	−	0.843739i	$-0.319650\pi$
$983$	−301.766	−	301.766i	−0.306985	−	0.306985i	−0.843739	+	0.536754i	$0.819650\pi$
$984$	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	0.739278	−	0.673401i	$-0.235167\pi$
$997$	65.6794	+	65.6794i	0.0658771	+	0.0658771i	−0.673401	+	0.739278i	$0.735167\pi$
$998$	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.13.10	yes	20
3.2	odd	2		360.3.u.b.253.1		20
4.3	odd	2		160.3.m.a.113.10		20
5.2	odd	4	inner	40.3.i.a.37.5	yes	20
5.3	odd	4		200.3.i.b.157.6		20
5.4	even	2		200.3.i.b.93.1		20
8.3	odd	2		160.3.m.a.113.1		20
8.5	even	2	inner	40.3.i.a.13.5	✓	20
15.2	even	4		360.3.u.b.37.6		20
20.3	even	4		800.3.m.b.657.10		20
20.7	even	4		160.3.m.a.17.1		20
20.19	odd	2		800.3.m.b.593.1		20
24.5	odd	2		360.3.u.b.253.6		20
40.3	even	4		800.3.m.b.657.1		20
40.13	odd	4		200.3.i.b.157.1		20
40.19	odd	2		800.3.m.b.593.10		20
40.27	even	4		160.3.m.a.17.10		20
40.29	even	2		200.3.i.b.93.6		20
40.37	odd	4	inner	40.3.i.a.37.10	yes	20
120.77	even	4		360.3.u.b.37.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.i.a.13.5	✓	20	8.5	even	2	inner
40.3.i.a.13.10	yes	20	1.1	even	1	trivial
40.3.i.a.37.5	yes	20	5.2	odd	4	inner
40.3.i.a.37.10	yes	20	40.37	odd	4	inner
160.3.m.a.17.1		20	20.7	even	4
160.3.m.a.17.10		20	40.27	even	4
160.3.m.a.113.1		20	8.3	odd	2
160.3.m.a.113.10		20	4.3	odd	2
200.3.i.b.93.1		20	5.4	even	2
200.3.i.b.93.6		20	40.29	even	2
200.3.i.b.157.1		20	40.13	odd	4
200.3.i.b.157.6		20	5.3	odd	4
360.3.u.b.37.1		20	120.77	even	4
360.3.u.b.37.6		20	15.2	even	4
360.3.u.b.253.1		20	3.2	odd	2
360.3.u.b.253.6		20	24.5	odd	2
800.3.m.b.593.1		20	20.19	odd	2
800.3.m.b.593.10		20	40.19	odd	2
800.3.m.b.657.1		20	40.3	even	4
800.3.m.b.657.10		20	20.3	even	4

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)

\(f(q)\)	\(=\)	\(q+(1.88606 + 0.665418i) q^{2} +(-3.60765 + 3.60765i) q^{3} +(3.11444 + 2.51004i) q^{4} +(2.34539 - 4.41578i) q^{5} +(-9.20485 + 4.40365i) q^{6} +(1.47907 - 1.47907i) q^{7} +(4.20379 + 6.80648i) q^{8} -17.0303i q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8	\( 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8} + 6 q^{10} - 44 q^{12} - 4 q^{15} - 56 q^{16} - 12 q^{17} + 10 q^{18} - 24 q^{20} + 92 q^{22} - 4 q^{23} - 28 q^{25} + 100 q^{26} + 68 q^{28} + 100 q^{30} - 136 q^{31} + 128 q^{32} + 32 q^{33} + 220 q^{36} - 188 q^{38} + 156 q^{40} - 8 q^{41} - 284 q^{42} - 240 q^{46} + 188 q^{47} - 256 q^{48} - 274 q^{50} - 332 q^{52} + 96 q^{55} - 360 q^{56} - 40 q^{57} + 268 q^{58} - 340 q^{60} + 336 q^{62} + 228 q^{63} - 60 q^{65} + 616 q^{66} + 396 q^{68} + 300 q^{70} + 248 q^{71} + 668 q^{72} - 124 q^{73} + 424 q^{76} - 368 q^{78} + 496 q^{80} + 132 q^{81} - 676 q^{82} - 672 q^{86} - 488 q^{87} - 304 q^{88} - 474 q^{90} - 628 q^{92} - 488 q^{95} - 1024 q^{96} + 100 q^{97} + 546 q^{98}+O(q^{100}) \) 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

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