LMFDB - Embedded newform 40.6.d.a.21.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(21,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("40.21");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.d (of order $2$, degree $1$, 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:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$20$
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} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 $ x^20 - 2x^19 - 17x^18 + 78x^17 + 253x^16 - 884x^15 + 2396x^14 + 19376x^13 - 109104x^12 - 96128x^11 + 3580672x^10 - 1538048x^9 - 27930624x^8 + 79364096x^7 + 157024256x^6 - 926941184x^5 + 4244635648x^4 + 20937965568x^3 - 73014444032x^2 - 137438953472*x + 1099511627776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{4}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.10
Root			$-2.80358 + 2.85306i$ of defining polynomial
Character	$\chi$	$=$	40.21
Dual form			40.6.d.a.21.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0494789 + 5.65664i) q^{2} -10.7455i q^{3} +(-31.9951 + 0.559768i) q^{4} -25.0000i q^{5} +(60.7833 - 0.531674i) q^{6} +198.733 q^{7} +(-4.74949 - 180.957i) q^{8} +127.535 q^{9} +O(q^{10})$	\(q+(0.0494789 + 5.65664i) q^{2} -10.7455i q^{3} +(-31.9951 + 0.559768i) q^{4} -25.0000i q^{5} +(60.7833 - 0.531674i) q^{6} +198.733 q^{7} +(-4.74949 - 180.957i) q^{8} +127.535 q^{9} +(141.416 - 1.23697i) q^{10} -85.9303i q^{11} +(6.01498 + 343.803i) q^{12} -407.120i q^{13} +(9.83309 + 1124.16i) q^{14} -268.637 q^{15} +(1023.37 - 35.8197i) q^{16} +1206.02 q^{17} +(6.31026 + 721.417i) q^{18} +206.036i q^{19} +(13.9942 + 799.878i) q^{20} -2135.48i q^{21} +(486.077 - 4.25173i) q^{22} -2595.25 q^{23} +(-1944.47 + 51.0355i) q^{24} -625.000 q^{25} +(2302.93 - 20.1438i) q^{26} -3981.57i q^{27} +(-6358.49 + 111.244i) q^{28} -6195.27i q^{29} +(-13.2919 - 1519.58i) q^{30} -1862.42 q^{31} +(253.254 + 5787.08i) q^{32} -923.363 q^{33} +(59.6727 + 6822.04i) q^{34} -4968.33i q^{35} +(-4080.48 + 71.3897i) q^{36} +14708.1i q^{37} +(-1165.47 + 10.1944i) q^{38} -4374.70 q^{39} +(-4523.93 + 118.737i) q^{40} +18098.0 q^{41} +(12079.7 - 105.661i) q^{42} +9260.46i q^{43} +(48.1010 + 2749.35i) q^{44} -3188.36i q^{45} +(-128.410 - 14680.4i) q^{46} -24363.7 q^{47} +(-384.900 - 10996.6i) q^{48} +22687.9 q^{49} +(-30.9243 - 3535.40i) q^{50} -12959.3i q^{51} +(227.893 + 13025.8i) q^{52} +12764.8i q^{53} +(22522.3 - 197.004i) q^{54} -2148.26 q^{55} +(-943.880 - 35962.2i) q^{56} +2213.96 q^{57} +(35044.4 - 306.535i) q^{58} +20719.7i q^{59} +(8595.07 - 150.374i) q^{60} -11368.5i q^{61} +(-92.1504 - 10535.0i) q^{62} +25345.3 q^{63} +(-32722.9 + 1718.91i) q^{64} -10178.0 q^{65} +(-45.6869 - 5223.13i) q^{66} +62614.9i q^{67} +(-38586.8 + 675.093i) q^{68} +27887.3i q^{69} +(28104.0 - 245.827i) q^{70} -61208.1 q^{71} +(-605.723 - 23078.3i) q^{72} +23236.4 q^{73} +(-83198.1 + 727.738i) q^{74} +6715.93i q^{75} +(-115.332 - 6592.14i) q^{76} -17077.2i q^{77} +(-216.455 - 24746.1i) q^{78} +29172.5 q^{79} +(-895.492 - 25584.3i) q^{80} -11793.1 q^{81} +(895.467 + 102374. i) q^{82} -48099.7i q^{83} +(1195.38 + 68325.1i) q^{84} -30150.6i q^{85} +(-52383.1 + 458.197i) q^{86} -66571.2 q^{87} +(-15549.7 + 408.125i) q^{88} +30118.4 q^{89} +(18035.4 - 157.757i) q^{90} -80908.2i q^{91} +(83035.4 - 1452.74i) q^{92} +20012.6i q^{93} +(-1205.49 - 137817. i) q^{94} +5150.90 q^{95} +(62185.0 - 2721.34i) q^{96} -113676. q^{97} +(1122.57 + 128337. i) q^{98} -10959.1i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 32 * q^4 + 204 * q^6 - 196 * q^7 + 248 * q^8 - 1620 * q^9	\( 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9} - 50 q^{10} - 1876 q^{12} + 2708 q^{14} + 900 q^{15} + 3080 q^{16} - 5294 q^{18} - 1900 q^{20} + 13836 q^{22} - 4676 q^{23} + 1032 q^{24} - 12500 q^{25} - 8084 q^{26} + 2108 q^{28} + 5800 q^{30} + 7160 q^{31} + 6792 q^{32} + 5672 q^{33} + 21132 q^{34} + 18344 q^{36} - 19580 q^{38} - 44904 q^{39} + 6200 q^{40} + 11608 q^{41} - 17116 q^{42} + 72296 q^{44} - 28516 q^{46} + 44180 q^{47} - 88856 q^{48} + 18756 q^{49} - 1250 q^{50} - 39680 q^{52} - 100584 q^{54} - 24200 q^{55} - 53624 q^{56} + 5032 q^{57} + 59496 q^{58} - 31300 q^{60} + 59824 q^{62} + 240620 q^{63} - 11264 q^{64} - 56688 q^{66} + 11576 q^{68} + 29800 q^{70} - 200312 q^{71} + 235912 q^{72} - 105136 q^{73} + 78876 q^{74} - 153872 q^{76} + 95864 q^{78} + 282080 q^{79} + 16000 q^{80} + 65172 q^{81} - 223032 q^{82} - 297128 q^{84} + 27452 q^{86} - 332592 q^{87} + 86896 q^{88} - 3160 q^{89} + 51750 q^{90} + 107916 q^{92} + 148820 q^{94} + 144400 q^{95} + 395168 q^{96} + 147376 q^{97} + 216942 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 32 * q^4 + 204 * q^6 - 196 * q^7 + 248 * q^8 - 1620 * q^9 - 50 * q^10 - 1876 * q^12 + 2708 * q^14 + 900 * q^15 + 3080 * q^16 - 5294 * q^18 - 1900 * q^20 + 13836 * q^22 - 4676 * q^23 + 1032 * q^24 - 12500 * q^25 - 8084 * q^26 + 2108 * q^28 + 5800 * q^30 + 7160 * q^31 + 6792 * q^32 + 5672 * q^33 + 21132 * q^34 + 18344 * q^36 - 19580 * q^38 - 44904 * q^39 + 6200 * q^40 + 11608 * q^41 - 17116 * q^42 + 72296 * q^44 - 28516 * q^46 + 44180 * q^47 - 88856 * q^48 + 18756 * q^49 - 1250 * q^50 - 39680 * q^52 - 100584 * q^54 - 24200 * q^55 - 53624 * q^56 + 5032 * q^57 + 59496 * q^58 - 31300 * q^60 + 59824 * q^62 + 240620 * q^63 - 11264 * q^64 - 56688 * q^66 + 11576 * q^68 + 29800 * q^70 - 200312 * q^71 + 235912 * q^72 - 105136 * q^73 + 78876 * q^74 - 153872 * q^76 + 95864 * q^78 + 282080 * q^79 + 16000 * q^80 + 65172 * q^81 - 223032 * q^82 - 297128 * q^84 + 27452 * q^86 - 332592 * q^87 + 86896 * q^88 - 3160 * q^89 + 51750 * q^90 + 107916 * q^92 + 148820 * q^94 + 144400 * q^95 + 395168 * q^96 + 147376 * q^97 + 216942 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	0.0494789	+	5.65664i	0.00874671	+	0.999962i
$2$	0.0494789	+	5.65664i	0.00874671	+	0.999962i
$3$		−	10.7455i		−	0.689323i	−0.938727	−	0.344662i	$-0.887994\pi$
$3$		−	10.7455i		−	0.689323i	0.938727	−	0.344662i	$-0.112006\pi$
$4$	−31.9951	+	0.559768i	−0.999847	+	0.0174927i
$5$		−	25.0000i		−	0.447214i
$5$		−	25.0000i		−	0.447214i
$6$	60.7833	−	0.531674i	0.689297	−	0.00602931i
$7$	198.733			1.53294			0.766470	−	0.642280i	$-0.222011\pi$
$7$	198.733			1.53294			0.766470	+	0.642280i	$0.222011\pi$
$8$	−4.74949	−	180.957i	−0.0262374	−	0.999656i
$9$	127.535			0.524833
$10$	141.416	−	1.23697i	0.447196	−	0.00391165i
$11$		−	85.9303i		−	0.214124i	−0.994252	−	0.107062i	$-0.965856\pi$
$11$		−	85.9303i		−	0.214124i	0.994252	−	0.107062i	$-0.0341443\pi$
$12$	6.01498	+	343.803i	0.0120582	+	0.689218i
$13$		−	407.120i		−	0.668134i	−0.942549	−	0.334067i	$-0.891579\pi$
$13$		−	407.120i		−	0.668134i	0.942549	−	0.334067i	$-0.108421\pi$
$14$	9.83309	+	1124.16i	0.0134082	+	1.53288i
$15$	−268.637			−0.308275
$16$	1023.37	−	35.8197i	0.999388	−	0.0349801i
$17$	1206.02			1.01212			0.506062	−	0.862497i	$-0.331101\pi$
$17$	1206.02			1.01212			0.506062	+	0.862497i	$0.331101\pi$
$18$	6.31026	+	721.417i	0.00459056	+	0.524813i
$19$			206.036i			0.130936i	0.997855	+	0.0654680i	$0.0208540\pi$
$19$			206.036i			0.130936i	−0.997855	+	0.0654680i	$0.979146\pi$
$20$	13.9942	+	799.878i	0.00782299	+	0.447145i
$21$		−	2135.48i		−	1.05669i
$22$	486.077	−	4.25173i	0.214115	−	0.00187288i
$23$	−2595.25			−1.02296			−0.511482	−	0.859294i	$-0.670903\pi$
$23$	−2595.25			−1.02296			−0.511482	+	0.859294i	$0.670903\pi$
$24$	−1944.47	+	51.0355i	−0.689086	+	0.0180861i
$25$	−625.000			−0.200000
$26$	2302.93	−	20.1438i	0.668109	−	0.00584398i
$27$		−	3981.57i		−	1.05110i
$28$	−6358.49	+	111.244i	−1.53271	+	0.0268153i
$29$		−	6195.27i		−	1.36794i	−0.729512	−	0.683968i	$-0.760253\pi$
$29$		−	6195.27i		−	1.36794i	0.729512	−	0.683968i	$-0.239747\pi$
$30$	−13.2919	−	1519.58i	−0.00269639	−	0.308263i
$31$	−1862.42			−0.348075			−0.174038	−	0.984739i	$-0.555681\pi$
$31$	−1862.42			−0.348075			−0.174038	+	0.984739i	$0.555681\pi$
$32$	253.254	+	5787.08i	0.0437202	+	0.999044i
$33$	−923.363			−0.147600
$34$	59.6727	+	6822.04i	0.00885275	+	1.01208i
$35$		−	4968.33i		−	0.685552i
$36$	−4080.48	+	71.3897i	−0.524753	+	0.00918078i
$37$			14708.1i			1.76625i	0.469142	+	0.883123i	$0.344563\pi$
$37$			14708.1i			1.76625i	−0.469142	+	0.883123i	$0.655437\pi$
$38$	−1165.47	+	10.1944i	−0.130931	+	0.00114526i
$39$	−4374.70			−0.460560
$40$	−4523.93	+	118.737i	−0.447060	+	0.0117337i
$41$	18098.0			1.68140			0.840699	−	0.541503i	$-0.182144\pi$
$41$	18098.0			1.68140			0.840699	+	0.541503i	$0.182144\pi$
$42$	12079.7	−	105.661i	1.05665	−	0.00924257i
$43$			9260.46i			0.763768i	0.924210	+	0.381884i	$0.124725\pi$
$43$			9260.46i			0.763768i	−0.924210	+	0.381884i	$0.875275\pi$
$44$	48.1010	+	2749.35i	0.00374561	+	0.214091i
$45$		−	3188.36i		−	0.234713i
$46$	−128.410	−	14680.4i	−0.00894757	−	1.02292i
$47$	−24363.7			−1.60879			−0.804395	−	0.594095i	$-0.797510\pi$
$47$	−24363.7			−1.60879			−0.804395	+	0.594095i	$0.797510\pi$
$48$	−384.900	−	10996.6i	−0.0241126	−	0.688901i
$49$	22687.9			1.34991
$50$	−30.9243	−	3535.40i	−0.00174934	−	0.199992i
$51$		−	12959.3i		−	0.697680i
$52$	227.893	+	13025.8i	0.0116875	+	0.668032i
$53$			12764.8i			0.624202i	0.950049	+	0.312101i	$0.101033\pi$
$53$			12764.8i			0.624202i	−0.950049	+	0.312101i	$0.898967\pi$
$54$	22522.3	−	197.004i	1.05106	−	0.00919369i
$55$	−2148.26			−0.0957590
$56$	−943.880	−	35962.2i	−0.0402204	−	1.53241i
$57$	2213.96			0.0902572
$58$	35044.4	−	306.535i	1.36788	−	0.0119649i
$59$			20719.7i			0.774913i	0.921888	+	0.387457i	$0.126646\pi$
$59$			20719.7i			0.774913i	−0.921888	+	0.387457i	$0.873354\pi$
$60$	8595.07	−	150.374i	0.308228	−	0.00539257i
$61$		−	11368.5i		−	0.391183i	−0.980686	−	0.195591i	$-0.937337\pi$
$61$		−	11368.5i		−	0.391183i	0.980686	−	0.195591i	$-0.0626626\pi$
$62$	−92.1504	−	10535.0i	−0.00304451	−	0.348062i
$63$	25345.3			0.804538
$64$	−32722.9	+	1718.91i	−0.998623	+	0.0524568i
$65$	−10178.0			−0.298799
$66$	−45.6869	−	5223.13i	−0.00129102	−	0.147595i
$67$			62614.9i			1.70408i	0.523475	+	0.852041i	$0.324635\pi$
$67$			62614.9i			1.70408i	−0.523475	+	0.852041i	$0.675365\pi$
$68$	−38586.8	+	675.093i	−1.01197	+	0.0177048i
$69$			27887.3i			0.705153i
$70$	28104.0	−	245.827i	0.685526	−	0.00599632i
$71$	−61208.1			−1.44100			−0.720498	−	0.693457i	$-0.756087\pi$
$71$	−61208.1			−1.44100			−0.720498	+	0.693457i	$0.756087\pi$
$72$	−605.723	−	23078.3i	−0.0137703	−	0.524653i
$73$	23236.4			0.510342			0.255171	−	0.966896i	$-0.417868\pi$
$73$	23236.4			0.510342			0.255171	+	0.966896i	$0.417868\pi$
$74$	−83198.1	+	727.738i	−1.76618	+	0.0154488i
$75$			6715.93i			0.137865i
$76$	−115.332	−	6592.14i	−0.00229043	−	0.130916i
$77$		−	17077.2i		−	0.328239i
$78$	−216.455	−	24746.1i	−0.00402839	−	0.460543i
$79$	29172.5			0.525904			0.262952	−	0.964809i	$-0.415304\pi$
$79$	29172.5			0.525904			0.262952	+	0.964809i	$0.415304\pi$
$80$	−895.492	−	25584.3i	−0.0156436	−	0.446940i
$81$	−11793.1			−0.199717
$82$	895.467	+	102374.i	0.0147067	+	1.68133i
$83$		−	48099.7i		−	0.766386i	−0.923668	−	0.383193i	$-0.874824\pi$
$83$		−	48099.7i		−	0.766386i	0.923668	−	0.383193i	$-0.125176\pi$
$84$	1195.38	+	68325.1i	0.0184844	+	1.05653i
$85$		−	30150.6i		−	0.452635i
$86$	−52383.1	+	458.197i	−0.763739	+	0.00668046i
$87$	−66571.2			−0.942950
$88$	−15549.7	+	408.125i	−0.214050	+	0.00561806i
$89$	30118.4			0.403048			0.201524	−	0.979484i	$-0.435411\pi$
$89$	30118.4			0.403048			0.201524	+	0.979484i	$0.435411\pi$
$90$	18035.4	−	157.757i	0.234704	−	0.00205296i
$91$		−	80908.2i		−	1.02421i
$92$	83035.4	−	1452.74i	1.02281	−	0.0178945i
$93$			20012.6i			0.239937i
$94$	−1205.49	−	137817.i	−0.0140716	−	1.60873i
$95$	5150.90			0.0585563
$96$	62185.0	−	2721.34i	0.688664	−	0.0301373i
$97$	−113676.			−1.22670			−0.613351	−	0.789811i	$-0.710179\pi$
$97$	−113676.			−1.22670			−0.613351	+	0.789811i	$0.710179\pi$
$98$	1122.57	+	128337.i	0.0118072	+	1.34985i
$99$		−	10959.1i		−	0.112379i
$100$	19996.9	−	349.855i	0.199969	−	0.00349855i
$101$		−	21867.4i		−	0.213302i	−0.994297	−	0.106651i	$-0.965987\pi$
$101$		−	21867.4i		−	0.213302i	0.994297	−	0.106651i	$-0.0340127\pi$
$102$	73306.1	−	641.212i	0.697654	−	0.00610241i
$103$	156608.			1.45452			0.727262	−	0.686360i	$-0.240792\pi$
$103$	156608.			1.45452			0.727262	+	0.686360i	$0.240792\pi$
$104$	−73671.2	+	1933.61i	−0.667904	+	0.0175301i
$105$	−53387.1			−0.472567
$106$	−72206.0	+	631.589i	−0.624178	+	0.00545971i
$107$		−	91401.1i		−	0.771777i	−0.922545	−	0.385889i	$-0.873895\pi$
$107$		−	91401.1i		−	0.771777i	0.922545	−	0.385889i	$-0.126105\pi$
$108$	2228.76	+	127391.i	0.0183867	+	1.05094i
$109$		−	48973.9i		−	0.394819i	−0.980321	−	0.197410i	$-0.936747\pi$
$109$		−	48973.9i		−	0.394819i	0.980321	−	0.197410i	$-0.0632529\pi$
$110$	−106.293	−	12151.9i	−0.000837576	−	0.0957553i
$111$	158045.			1.21751
$112$	203378.	−	7118.56i	1.53200	−	0.0536225i
$113$	−153638.			−1.13188			−0.565942	−	0.824445i	$-0.691487\pi$
$113$	−153638.			−1.13188			−0.565942	+	0.824445i	$0.691487\pi$
$114$	109.544	+	12523.5i	0.000789453	+	0.0902537i
$115$			64881.4i			0.457483i
$116$	3467.92	+	198218.i	0.0239289	+	1.36773i
$117$		−	51921.8i		−	0.350659i
$118$	−117204.	+	1025.19i	−0.774883	+	0.00677794i
$119$	239677.			1.55152
$120$	1275.89	+	48611.8i	0.00808834	+	0.308169i
$121$	153667.			0.954151
$122$	64307.6	−	562.502i	0.391168	−	0.00342156i
$123$		−	194472.i		−	1.15903i
$124$	59588.3	−	1042.52i	0.348022	−	0.00608880i
$125$			15625.0i			0.0894427i
$126$	1254.06	+	143369.i	0.00703706	+	0.804507i
$127$	−122092.			−0.671705			−0.335852	−	0.941915i	$-0.609024\pi$
$127$	−122092.			−0.671705			−0.335852	+	0.941915i	$0.609024\pi$
$128$	−11342.3	−	185016.i	−0.0611895	−	0.998126i
$129$	99508.2			0.526483
$130$	−503.595	−	57573.2i	−0.00261351	−	0.298787i
$131$			179438.i			0.913560i	0.889580	+	0.456780i	$0.150997\pi$
$131$			179438.i			0.913560i	−0.889580	+	0.456780i	$0.849003\pi$
$132$	29543.1	−	516.869i	0.147578	−	0.00258194i
$133$			40946.2i			0.200717i
$134$	−354190.	+	3098.11i	−1.70402	+	0.0149051i
$135$	−99539.3			−0.470068
$136$	−5727.99	−	218238.i	−0.0265555	−	1.01177i
$137$	−327113.			−1.48900			−0.744502	−	0.667620i	$-0.767313\pi$
$137$	−327113.			−1.48900			−0.744502	+	0.667620i	$0.767313\pi$
$138$	−157748.	+	1379.83i	−0.705126	+	0.00616777i
$139$			359354.i			1.57756i	0.614678	+	0.788778i	$0.289286\pi$
$139$			359354.i			1.57756i	−0.614678	+	0.788778i	$0.710714\pi$
$140$	2781.11	+	158962.i	0.0119922	+	0.685447i
$141$			261800.i			1.10898i
$142$	−3028.51	−	346232.i	−0.0126040	−	1.44094i
$143$	−34983.9			−0.143063
$144$	130515.	−	4568.24i	0.524512	−	0.0183587i
$145$	−154882.			−0.611759
$146$	1149.71	+	131440.i	0.00446381	+	0.510322i
$147$		−	243792.i		−	0.930522i
$148$	−8233.10	−	470586.i	−0.0308965	−	1.76597i
$149$		−	494795.i		−	1.82583i	−0.408152	−	0.912914i	$-0.633827\pi$
$149$		−	494795.i		−	1.82583i	0.408152	−	0.912914i	$-0.366173\pi$
$150$	−37989.6	+	332.297i	−0.137859	+	0.00120586i
$151$	−9960.81			−0.0355511			−0.0177755	−	0.999842i	$-0.505658\pi$
$151$	−9960.81			−0.0355511			−0.0177755	+	0.999842i	$0.505658\pi$
$152$	37283.6	−	978.565i	0.130891	−	0.00343543i
$153$	153810.			0.531196
$154$	96599.5	−	844.960i	0.328226	−	0.00287101i
$155$			46560.5i			0.155664i
$156$	139969.	−	2448.82i	0.460490	−	0.00805647i
$157$			243819.i			0.789439i	0.918802	+	0.394719i	$0.129158\pi$
$157$			243819.i			0.789439i	−0.918802	+	0.394719i	$0.870842\pi$
$158$	1443.42	+	165018.i	0.00459993	+	0.525884i
$159$	137164.			0.430277
$160$	144677.	−	6331.36i	0.446786	−	0.0195523i
$161$	−515763.			−1.56814
$162$	−583.507	−	66709.1i	−0.00174686	−	0.199709i
$163$			268182.i			0.790608i	0.918550	+	0.395304i	$0.129361\pi$
$163$			268182.i			0.790608i	−0.918550	+	0.395304i	$0.870639\pi$
$164$	−579047.	+	10130.7i	−1.68114	+	0.0294123i
$165$			23084.1i			0.0660089i
$166$	272083.	−	2379.92i	0.766356	−	0.00670335i
$167$	−17404.1			−0.0482905			−0.0241452	−	0.999708i	$-0.507686\pi$
$167$	−17404.1			−0.0482905			−0.0241452	+	0.999708i	$0.507686\pi$
$168$	−386431.	+	10142.5i	−1.05633	+	0.0277249i
$169$	205547.			0.553597
$170$	170551.	−	1491.82i	0.452618	−	0.00395907i
$171$			26276.7i			0.0687195i
$172$	−5183.71	−	296289.i	−0.0133604	−	0.763651i
$173$			534365.i			1.35745i	0.734394	+	0.678723i	$0.237466\pi$
$173$			534365.i			1.35745i	−0.734394	+	0.678723i	$0.762534\pi$
$174$	−3293.87	−	376569.i	−0.00824771	−	0.942914i
$175$	−124208.			−0.306588
$176$	−3077.99	−	87938.8i	−0.00749008	−	0.213993i
$177$	222643.			0.534166
$178$	1490.22	+	170369.i	0.00352534	+	0.403032i
$179$			342831.i			0.799738i	0.916572	+	0.399869i	$0.130944\pi$
$179$			342831.i			0.799738i	−0.916572	+	0.399869i	$0.869056\pi$
$180$	1784.74	+	102012.i	0.00410577	+	0.234677i
$181$			593221.i			1.34592i	0.739678	+	0.672961i	$0.234978\pi$
$181$			593221.i			1.34592i	−0.739678	+	0.672961i	$0.765022\pi$
$182$	457668.	−	4003.24i	1.02417	−	0.00895847i
$183$	−122160.			−0.269651
$184$	12326.1	+	469630.i	0.0268400	+	1.02261i
$185$	367701.			0.789889
$186$	−113204.	+	990.201i	−0.239927	+	0.00209865i
$187$		−	103634.i		−	0.216720i
$188$	779520.	−	13638.0i	1.60854	−	0.0281421i
$189$		−	791271.i		−	1.61128i
$190$	254.861	+	29136.8i	0.000512175	+	0.0585541i
$191$	−1448.97			−0.00287392			−0.00143696	−	0.999999i	$-0.500457\pi$
$191$	−1448.97			−0.00287392			−0.00143696	+	0.999999i	$0.500457\pi$
$192$	18470.5	+	351623.i	0.0361597	+	0.688374i
$193$	888526.			1.71703			0.858513	−	0.512791i	$-0.171388\pi$
$193$	888526.			1.71703			0.858513	+	0.512791i	$0.171388\pi$
$194$	−5624.55	−	643023.i	−0.0107296	−	1.22665i
$195$			109367.i			0.205969i
$196$	−725901.	+	12699.9i	−1.34970	+	0.0236136i
$197$		−	356565.i		−	0.654595i	−0.944921	−	0.327298i	$-0.893862\pi$
$197$		−	356565.i		−	0.654595i	0.944921	−	0.327298i	$-0.106138\pi$
$198$	61991.5	−	542.243i	0.112375	−	0.000982948i
$199$	−406304.			−0.727307			−0.363654	−	0.931534i	$-0.618471\pi$
$199$	−406304.			−0.727307			−0.363654	+	0.931534i	$0.618471\pi$
$200$	2968.43	+	113098.i	0.00524749	+	0.199931i
$201$	672827.			1.17466
$202$	123696.	−	1081.98i	0.213294	−	0.00186569i
$203$		−	1.23121e6i		−	2.09696i
$204$	7254.21	+	414634.i	0.0122043	+	0.697573i
$205$		−	452450.i		−	0.751944i
$206$	7748.79	+	885875.i	0.0127223	+	1.45447i
$207$	−330984.			−0.536886
$208$	−14582.9	−	416635.i	−0.0233714	−	0.667725i
$209$	17704.7			0.0280365
$210$	−2641.53	−	301992.i	−0.00413340	−	0.472549i
$211$		−	582646.i		−	0.900945i	−0.892790	−	0.450473i	$-0.851256\pi$
$211$		−	582646.i		−	0.900945i	0.892790	−	0.450473i	$-0.148744\pi$
$212$	−7145.34	−	408412.i	−0.0109190	−	0.624106i
$213$			657711.i			0.993312i
$214$	517023.	−	4522.42i	0.771748	−	0.00675051i
$215$	231512.			0.341568
$216$	−720494.	+	18910.4i	−1.05074	+	0.0275783i
$217$	−370125.			−0.533579
$218$	277027.	−	2423.17i	0.394804	−	0.00345337i
$219$		−	249686.i		−	0.351791i
$220$	68733.7	−	1202.53i	0.0957443	−	0.00167509i
$221$		−	490996.i		−	0.676234i
$222$	7819.90	+	894005.i	0.0106492	+	1.21747i
$223$	−789020.			−1.06249			−0.531246	−	0.847218i	$-0.678276\pi$
$223$	−789020.			−1.06249			−0.531246	+	0.847218i	$0.678276\pi$
$224$	50330.0	+	1.15008e6i	0.0670204	+	1.53147i
$225$	−79709.1			−0.104967
$226$	−7601.82	−	869073.i	−0.00990026	−	1.13184i
$227$			872412.i			1.12372i	0.827233	+	0.561858i	$0.189913\pi$
$227$			872412.i			1.12372i	−0.827233	+	0.561858i	$0.810087\pi$
$228$	−70835.8	+	1239.30i	−0.0902434	+	0.00157885i
$229$			404072.i			0.509178i	0.967049	+	0.254589i	$0.0819402\pi$
$229$			404072.i			0.509178i	−0.967049	+	0.254589i	$0.918060\pi$
$230$	−367010.	+	3210.26i	−0.457466	+	0.00400147i
$231$	−183503.			−0.226263
$232$	−1.12108e6	+	29424.4i	−1.36746	+	0.0358911i
$233$	−198854.			−0.239963			−0.119982	−	0.992776i	$-0.538284\pi$
$233$	−198854.			−0.239963			−0.119982	+	0.992776i	$0.538284\pi$
$234$	293703.	−	2569.03i	0.350646	−	0.00306711i
$235$			609093.i			0.719472i
$236$	−11598.2	−	662928.i	−0.0135554	−	0.774795i
$237$		−	313473.i		−	0.362518i
$238$	11858.9	+	1.35577e6i	0.0135707	+	1.55147i
$239$	−388433.			−0.439868			−0.219934	−	0.975515i	$-0.570584\pi$
$239$	−388433.			−0.439868			−0.219934	+	0.975515i	$0.570584\pi$
$240$	−274916.	+	9622.49i	−0.308086	+	0.0107835i
$241$	−714818.			−0.792780			−0.396390	−	0.918082i	$-0.629737\pi$
$241$	−714818.			−0.792780			−0.396390	+	0.918082i	$0.629737\pi$
$242$	7603.27	+	869238.i	0.00834568	+	0.954115i
$243$		−	840800.i		−	0.913434i
$244$	6363.73	+	363737.i	0.00684286	+	0.391123i
$245$		−	567197.i		−	0.603696i
$246$	1.10006e6	−	9622.23i	1.15898	−	0.0101377i
$247$	83881.3			0.0874828
$248$	8845.54	+	337018.i	0.00913261	+	0.347956i
$249$	−516855.			−0.528287
$250$	−88385.0	+	773.107i	−0.0894393	+	0.000782329i
$251$		−	1.57948e6i		−	1.58244i	−0.611529	−	0.791222i	$-0.709445\pi$
$251$		−	1.57948e6i		−	1.58244i	0.611529	−	0.791222i	$-0.290555\pi$
$252$	−810927.	+	14187.5i	−0.804415	+	0.0140736i
$253$			223011.i			0.219041i
$254$	−6040.98	−	690631.i	−0.00587521	−	0.671679i
$255$	−323983.			−0.312012
$256$	1.04601e6	−	73313.8i	0.997553	−	0.0699175i
$257$	1.80546e6			1.70512			0.852558	−	0.522632i	$-0.175050\pi$
$257$	1.80546e6			1.70512			0.852558	+	0.522632i	$0.175050\pi$
$258$	4923.55	+	562882.i	0.00460500	+	0.526463i
$259$			2.92298e6i			2.70755i
$260$	325646.	−	5697.31i	0.298753	−	0.00522681i
$261$		−	790111.i		−	0.717938i
$262$	−1.01502e6	+	8878.41i	−0.913526	+	0.00799065i
$263$	185503.			0.165372			0.0826860	−	0.996576i	$-0.473650\pi$
$263$	185503.			0.165372			0.0826860	+	0.996576i	$0.473650\pi$
$264$	4385.50	+	167089.i	0.00387266	+	0.147550i
$265$	319121.			0.279152
$266$	−231618.	+	2025.97i	−0.200709	+	0.00175561i
$267$		−	323637.i		−	0.277830i
$268$	−35049.8	−	2.00337e6i	−0.0298091	−	1.70382i
$269$		−	1.12615e6i		−	0.948887i	−0.880286	−	0.474444i	$-0.842649\pi$
$269$		−	1.12615e6i		−	0.948887i	0.880286	−	0.474444i	$-0.157351\pi$
$270$	−4925.09	−	563058.i	−0.00411154	−	0.470050i
$271$	157610.			0.130365			0.0651825	−	0.997873i	$-0.479237\pi$
$271$	157610.			0.130365			0.0651825	+	0.997873i	$0.479237\pi$
$272$	1.23421e6	−	43199.4i	1.01150	−	0.0354042i
$273$	−869398.			−0.706012
$274$	−16185.2	−	1.85036e6i	−0.0130239	−	1.48895i
$275$			53706.4i			0.0428247i
$276$	−15610.4	−	892256.i	−0.0123351	−	0.705045i
$277$			1.93510e6i			1.51532i	0.652650	+	0.757660i	$0.273657\pi$
$277$			1.93510e6i			1.51532i	−0.652650	+	0.757660i	$0.726343\pi$
$278$	−2.03273e6	+	17780.4i	−1.57750	+	0.0137984i
$279$	−237523.			−0.182682
$280$	−899054.	+	23597.0i	−0.685316	+	0.0179871i
$281$	394102.			0.297744			0.148872	−	0.988856i	$-0.452436\pi$
$281$	394102.			0.297744			0.148872	+	0.988856i	$0.452436\pi$
$282$	−1.48091e6	+	12953.6i	−1.10893	+	0.00969989i
$283$		−	538592.i		−	0.399755i	−0.979821	−	0.199878i	$-0.935946\pi$
$283$		−	538592.i		−	0.399755i	0.979821	−	0.199878i	$-0.0640545\pi$
$284$	1.95836e6	−	34262.3i	1.44078	−	0.0252070i
$285$		−	55348.9i		−	0.0403642i
$286$	−1730.96	−	197891.i	−0.00125133	−	0.143058i
$287$	3.59667e6			2.57748
$288$	32298.7	+	738052.i	0.0229458	+	0.524332i
$289$	34635.4			0.0243936
$290$	−7663.38	−	876110.i	−0.00535088	−	0.611736i
$291$			1.22150e6i			0.845594i
$292$	−743450.	+	13007.0i	−0.510264	+	0.00892728i
$293$			1.25662e6i			0.855134i	0.903984	+	0.427567i	$0.140629\pi$
$293$			1.25662e6i			0.855134i	−0.903984	+	0.427567i	$0.859371\pi$
$294$	1.37904e6	−	12062.6i	0.930486	−	0.00813900i
$295$	517992.			0.346552
$296$	2.66153e6	−	69855.7i	1.76564	−	0.0463418i
$297$	−342138.			−0.225066
$298$	2.79888e6	−	24481.9i	1.82576	−	0.0159700i
$299$			1.05658e6i			0.683477i
$300$	−3759.36	−	214877.i	−0.00241163	−	0.137844i
$301$			1.84036e6i			1.17081i
$302$	−492.850	−	56344.7i	−0.000310955	−	0.0355497i
$303$	−234976.			−0.147034
$304$	7380.14	+	210852.i	0.00458016	+	0.130856i
$305$	−284213.			−0.174942
$306$	7610.32	+	870045.i	0.00464622	+	0.531176i
$307$			227401.i			0.137704i	0.997627	+	0.0688519i	$0.0219336\pi$
$307$			227401.i			0.137704i	−0.997627	+	0.0688519i	$0.978066\pi$
$308$	9559.27	+	546387.i	0.00574180	+	0.328189i
$309$		−	1.68283e6i		−	1.00264i
$310$	−263376.	+	2303.76i	−0.155658	+	0.00136155i
$311$	1.13530e6			0.665593			0.332796	−	0.942999i	$-0.392008\pi$
$311$	1.13530e6			0.665593			0.332796	+	0.942999i	$0.392008\pi$
$312$	20777.6	+	791633.i	0.0120839	+	0.460402i
$313$	−2.32737e6			−1.34278			−0.671390	−	0.741105i	$-0.734302\pi$
$313$	−2.32737e6			−1.34278			−0.671390	+	0.741105i	$0.734302\pi$
$314$	−1.37920e6	+	12063.9i	−0.789409	+	0.00690499i
$315$		−	633633.i		−	0.359800i
$316$	−933378.	+	16329.8i	−0.525823	+	0.00919950i
$317$			1.50212e6i			0.839570i	0.907624	+	0.419785i	$0.137894\pi$
$317$			1.50212e6i			0.839570i	−0.907624	+	0.419785i	$0.862106\pi$
$318$	6786.73	+	775888.i	0.00376351	+	0.430261i
$319$	−532362.			−0.292907
$320$	42972.6	+	818072.i	0.0234594	+	0.446598i
$321$	−982149.			−0.532004
$322$	−25519.4	−	2.91749e6i	−0.0137161	−	1.56808i
$323$			248484.i			0.132523i
$324$	377320.	−	6601.38i	0.199686	−	0.00349359i
$325$			254450.i			0.133627i
$326$	−1.51701e6	+	13269.4i	−0.790578	+	0.00691522i
$327$	−526248.			−0.272158
$328$	−85956.1	−	3.27496e6i	−0.0441156	−	1.68082i
$329$	−4.84188e6			−2.46618
$330$	−130578.	+	1142.17i	−0.0660064	+	0.000577361i
$331$		−	2.72477e6i		−	1.36697i	−0.729964	−	0.683486i	$-0.760463\pi$
$331$		−	2.72477e6i		−	1.36697i	0.729964	−	0.683486i	$-0.239537\pi$
$332$	26924.7	+	1.53896e6i	0.0134062	+	0.766268i
$333$			1.87578e6i			0.926984i
$334$	−861.137	−	98448.9i	−0.000422383	−	0.0482886i
$335$	1.56537e6			0.762089
$336$	−76492.4	−	2.18540e6i	−0.0369632	−	1.05604i
$337$	2.04270e6			0.979784			0.489892	−	0.871783i	$-0.337036\pi$
$337$	2.04270e6			0.979784			0.489892	+	0.871783i	$0.337036\pi$
$338$	10170.2	+	1.16270e6i	0.00484215	+	0.553576i
$339$			1.65091e6i			0.780234i
$340$	16877.3	+	964671.i	0.00791784	+	0.452566i
$341$			160038.i			0.0745312i
$342$	−148638.	+	1300.14i	−0.0687169	+	0.000601070i
$343$	1.16872e6			0.536385
$344$	1.67575e6	−	43982.4i	0.763505	−	0.0200393i
$345$	697182.			0.315354
$346$	−3.02271e6	+	26439.8i	−1.35739	+	0.0118732i
$347$		−	2.57456e6i		−	1.14783i	−0.818914	−	0.573916i	$-0.805423\pi$
$347$		−	2.57456e6i		−	1.14783i	0.818914	−	0.573916i	$-0.194577\pi$
$348$	2.12995e6	−	37264.4i	0.942805	−	0.0164948i
$349$		−	1.97991e6i		−	0.870125i	−0.900400	−	0.435062i	$-0.856726\pi$
$349$		−	1.97991e6i		−	0.870125i	0.900400	−	0.435062i	$-0.143274\pi$
$350$	−6145.68	−	702601.i	−0.00268164	−	0.306576i
$351$	−1.62098e6			−0.702278
$352$	497285.	−	21762.2i	0.213919	−	0.00936152i
$353$	−1.02870e6			−0.439394			−0.219697	−	0.975568i	$-0.570507\pi$
$353$	−1.02870e6			−0.439394			−0.219697	+	0.975568i	$0.570507\pi$
$354$	11016.1	+	1.25941e6i	0.00467219	+	0.534145i
$355$			1.53020e6i			0.644433i
$356$	−963641.	+	16859.3i	−0.402986	+	0.00705041i
$357$		−	2.57544e6i		−	1.06950i
$358$	−1.93927e6	+	16962.9i	−0.799708	+	0.00699508i
$359$	−979196.			−0.400990			−0.200495	−	0.979695i	$-0.564255\pi$
$359$	−979196.			−0.400990			−0.200495	+	0.979695i	$0.564255\pi$
$360$	−576957.	+	15143.1i	−0.234632	+	0.00615826i
$361$	2.43365e6			0.982856
$362$	−3.35564e6	+	29351.9i	−1.34587	+	0.0117724i
$363$		−	1.65123e6i		−	0.657719i
$364$	45289.8	+	2.58867e6i	0.0179162	+	1.02405i
$365$		−	580909.i		−	0.228232i
$366$	−6044.35	−	691017.i	−0.00235856	−	0.269641i
$367$	−1.07920e6			−0.418250			−0.209125	−	0.977889i	$-0.567062\pi$
$367$	−1.07920e6			−0.418250			−0.209125	+	0.977889i	$0.567062\pi$
$368$	−2.65591e6	+	92961.2i	−1.02234	+	0.0357834i
$369$	2.30812e6			0.882454
$370$	18193.4	+	2.07995e6i	0.00690893	+	0.789859i
$371$			2.53679e6i			0.956864i
$372$	−11202.4	−	640305.i	−0.00419715	−	0.239900i
$373$		−	3.65291e6i		−	1.35946i	−0.733461	−	0.679731i	$-0.762096\pi$
$373$		−	3.65291e6i		−	1.35946i	0.733461	−	0.679731i	$-0.237904\pi$
$374$	586220.	−	5127.69i	0.216711	−	0.00189558i
$375$	167898.			0.0616550
$376$	115715.	+	4.40879e6i	0.0422105	+	1.60824i
$377$	−2.52222e6			−0.913964
$378$	4.47593e6	−	39151.2i	1.61122	−	0.0140934i
$379$		−	2.99413e6i		−	1.07071i	−0.844627	−	0.535355i	$-0.820178\pi$
$379$		−	2.99413e6i		−	1.07071i	0.844627	−	0.535355i	$-0.179822\pi$
$380$	−164803.	+	2883.31i	−0.0585474	+	0.00102431i
$381$			1.31194e6i			0.463022i
$382$	−71.6932	−	8196.27i	−2.51373e−5	−	0.00287381i
$383$	4.15754e6			1.44824			0.724119	−	0.689675i	$-0.242247\pi$
$383$	4.15754e6			1.44824			0.724119	+	0.689675i	$0.242247\pi$
$384$	−1.98809e6	+	121879.i	−0.688032	+	0.0421793i
$385$	−426930.			−0.146793
$386$	43963.3	+	5.02607e6i	0.0150183	+	1.71696i
$387$			1.18103e6i			0.400851i
$388$	3.63707e6	−	63632.1i	1.22651	−	0.0214584i
$389$		−	1.08421e6i		−	0.363278i	−0.983365	−	0.181639i	$-0.941860\pi$
$389$		−	1.08421e6i		−	0.363278i	0.983365	−	0.181639i	$-0.0581402\pi$
$390$	−618652.	+	5411.38i	−0.205961	+	0.00180155i
$391$	−3.12994e6			−1.03537
$392$	−107756.	−	4.10553e6i	−0.0354181	−	1.34944i
$393$	1.92815e6			0.629739
$394$	2.01696e6	−	17642.4i	0.654570	−	0.00572555i
$395$		−	729313.i		−	0.235191i
$396$	6134.54	+	350637.i	0.00196582	+	0.112362i
$397$		−	3.11966e6i		−	0.993415i	−0.867918	−	0.496708i	$-0.834542\pi$
$397$		−	3.11966e6i		−	0.993415i	0.867918	−	0.496708i	$-0.165458\pi$
$398$	−20103.4	−	2.29831e6i	−0.00636155	−	0.727280i
$399$	439987.			0.138359
$400$	−639608.	+	22387.3i	−0.199878	+	0.00699603i
$401$	−3.18432e6			−0.988908			−0.494454	−	0.869204i	$-0.664632\pi$
$401$	−3.18432e6			−0.988908			−0.494454	+	0.869204i	$0.664632\pi$
$402$	33290.7	+	3.80594e6i	0.0102744	+	1.17462i
$403$			758228.i			0.232561i
$404$	12240.7	+	699651.i	0.00373123	+	0.213269i
$405$			294827.i			0.0893160i
$406$	6.96449e6	−	60918.7i	2.09688	−	0.0183415i
$407$	1.26387e6			0.378195
$408$	−2.34508e6	+	61550.1i	−0.697440	+	0.0183053i
$409$	3.76338e6			1.11242			0.556211	−	0.831041i	$-0.312255\pi$
$409$	3.76338e6			1.11242			0.556211	+	0.831041i	$0.312255\pi$
$410$	2.55934e6	−	22386.7i	0.751915	−	0.00657704i
$411$			3.51499e6i			1.02641i
$412$	−5.01069e6	+	87664.2i	−1.45430	+	0.0254436i
$413$			4.11769e6i			1.18790i
$414$	−16376.7	−	1.87226e6i	−0.00469598	−	0.536865i
$415$	−1.20249e6			−0.342738
$416$	2.35603e6	−	103105.i	0.667495	−	0.0292109i
$417$	3.86143e6			1.08745
$418$	876.010	+	100149.i	0.000245227	+	0.0280354i
$419$		−	2.73449e6i		−	0.760924i	−0.924797	−	0.380462i	$-0.875765\pi$
$419$		−	2.73449e6i		−	0.760924i	0.924797	−	0.380462i	$-0.124235\pi$
$420$	1.70813e6	−	29884.4i	0.472495	−	0.00826649i
$421$			450371.i			0.123841i	0.998081	+	0.0619206i	$0.0197225\pi$
$421$			450371.i			0.123841i	−0.998081	+	0.0619206i	$0.980277\pi$
$422$	3.29581e6	−	28828.6i	0.900911	−	0.00788030i
$423$	−3.10722e6			−0.844346
$424$	2.30988e6	−	60626.3i	0.623987	−	0.0163775i
$425$	−753765.			−0.202425
$426$	−3.72043e6	+	32542.8i	−0.993274	+	0.00868821i
$427$		−	2.25930e6i		−	0.599659i
$428$	51163.4	+	2.92439e6i	0.0135005	+	0.771659i
$429$			375919.i			0.0986169i
$430$	11454.9	+	1.30958e6i	0.00298759	+	0.341554i
$431$	517327.			0.134144			0.0670721	−	0.997748i	$-0.478634\pi$
$431$	517327.			0.134144			0.0670721	+	0.997748i	$0.478634\pi$
$432$	−142619.	−	4.07464e6i	−0.0367677	−	1.05046i
$433$	2.24867e6			0.576375			0.288188	−	0.957574i	$-0.406947\pi$
$433$	2.24867e6			0.576375			0.288188	+	0.957574i	$0.406947\pi$
$434$	−18313.3	−	2.09366e6i	−0.00466706	−	0.533558i
$435$			1.66428e6i			0.421700i
$436$	27414.0	+	1.56692e6i	0.00690647	+	0.394759i
$437$		−	534716.i		−	0.133943i
$438$	1.41238e6	−	12354.2i	0.351777	−	0.00307701i
$439$	862979.			0.213717			0.106858	−	0.994274i	$-0.465921\pi$
$439$	862979.			0.213717			0.106858	+	0.994274i	$0.465921\pi$
$440$	10203.1	+	388742.i	0.00251247	+	0.0957260i
$441$	2.89349e6			0.708476
$442$	2.77739e6	−	24293.9i	0.676208	−	0.00591482i
$443$		−	972329.i		−	0.235399i	−0.993049	−	0.117699i	$-0.962448\pi$
$443$		−	972329.i		−	0.235399i	0.993049	−	0.117699i	$-0.0375519\pi$
$444$	−5.05667e6	+	88468.7i	−1.21733	+	0.0212977i
$445$		−	752959.i		−	0.180248i
$446$	−39039.8	−	4.46320e6i	−0.00929331	−	1.06245i
$447$	−5.31682e6			−1.25859
$448$	−6.50312e6	+	341604.i	−1.53083	+	0.0804132i
$449$	−28297.9			−0.00662428			−0.00331214	−	0.999995i	$-0.501054\pi$
$449$	−28297.9			−0.00662428			−0.00331214	+	0.999995i	$0.501054\pi$
$450$	−3943.91	−	450885.i	−0.000918113	−	0.104963i
$451$		−	1.55516e6i		−	0.360027i
$452$	4.91566e6	−	86001.5i	1.13171	−	0.0197998i
$453$			107034.i			0.0245062i
$454$	−4.93492e6	+	43165.9i	−1.12367	+	0.00982882i
$455$	−2.02270e6			−0.458041
$456$	−10515.2	−	400631.i	−0.00236812	−	0.0902261i
$457$	456269.			0.102195			0.0510976	−	0.998694i	$-0.483728\pi$
$457$	456269.			0.102195			0.0510976	+	0.998694i	$0.483728\pi$
$458$	−2.28569e6	+	19993.0i	−0.509159	+	0.00445363i
$459$		−	4.80187e6i		−	1.06385i
$460$	−36318.5	−	2.07589e6i	−0.00800264	−	0.457413i
$461$		−	11198.5i		−	0.00245418i	−0.999999	−	0.00122709i	$-0.999609\pi$
$461$		−	11198.5i		−	0.00245418i	0.999999	−	0.00122709i	$-0.000390595\pi$
$462$	−9079.51	−	1.03801e6i	−0.00197905	−	0.226254i
$463$	−7.93015e6			−1.71921			−0.859605	−	0.510959i	$-0.829290\pi$
$463$	−7.93015e6			−1.71921			−0.859605	+	0.510959i	$0.829290\pi$
$464$	−221913.	−	6.34008e6i	−0.0478506	−	1.36710i
$465$	500315.			0.107303
$466$	−9839.07	−	1.12485e6i	−0.00209889	−	0.239954i
$467$			6.59151e6i			1.39860i	0.714830	+	0.699298i	$0.246504\pi$
$467$			6.59151e6i			1.39860i	−0.714830	+	0.699298i	$0.753496\pi$
$468$	29064.2	+	1.66124e6i	0.00613399	+	0.350605i
$469$			1.24437e7i			2.61226i
$470$	−3.44542e6	+	30137.2i	−0.719445	+	0.00629302i
$471$	2.61995e6			0.544179
$472$	3.74937e6	−	98407.8i	0.774646	−	0.0203317i
$473$	795754.			0.163541
$474$	1.77320e6	−	15510.3i	0.362504	−	0.00317084i
$475$		−	128772.i		−	0.0261872i
$476$	−7.66849e6	+	134163.i	−1.55129	+	0.0271404i
$477$			1.62796e6i			0.327602i
$478$	−19219.2	−	2.19723e6i	−0.00384739	−	0.439851i
$479$	−1.60702e6			−0.320023			−0.160012	−	0.987115i	$-0.551153\pi$
$479$	−1.60702e6			−0.320023			−0.160012	+	0.987115i	$0.551153\pi$
$480$	−68033.5	−	1.55462e6i	−0.0134778	−	0.307980i
$481$	5.98794e6			1.18009
$482$	−35368.4	−	4.04347e6i	−0.00693422	−	0.792750i
$483$			5.54213e6i			1.08096i
$484$	−4.91659e6	+	86017.9i	−0.954005	+	0.0166907i
$485$			2.84190e6i			0.548597i
$486$	4.75610e6	−	41601.8i	0.913399	−	0.00798954i
$487$	−1.81230e6			−0.346264			−0.173132	−	0.984899i	$-0.555389\pi$
$487$	−1.81230e6			−0.346264			−0.173132	+	0.984899i	$0.555389\pi$
$488$	−2.05721e6	+	53994.6i	−0.391048	+	0.0102636i
$489$	2.88175e6			0.544985
$490$	3.20843e6	−	28064.3i	0.603673	−	0.00528036i
$491$		−	292083.i		−	0.0546768i	−0.999626	−	0.0273384i	$-0.991297\pi$
$491$		−	292083.i		−	0.0546768i	0.999626	−	0.0273384i	$-0.00870317\pi$
$492$	108859.	+	6.22214e6i	0.0202746	+	1.15885i
$493$		−	7.47164e6i		−	1.38452i
$494$	4150.35	+	474486.i	0.000765186	+	0.0874794i
$495$	−273977.			−0.0502575
$496$	−1.90595e6	+	66711.3i	−0.347862	+	0.0121757i
$497$	−1.21641e7			−2.20896
$498$	−25573.4	−	2.92366e6i	−0.00462078	−	0.528267i
$499$			8.47619e6i			1.52388i	0.647650	+	0.761938i	$0.275752\pi$
$499$			8.47619e6i			1.52388i	−0.647650	+	0.761938i	$0.724248\pi$
$500$	−8746.37	−	499923.i	−0.00156460	−	0.0894290i
$501$			187016.i			0.0332877i
$502$	8.93452e6	−	78150.6i	1.58238	−	0.0138412i
$503$	2.07725e6			0.366074			0.183037	−	0.983106i	$-0.441407\pi$
$503$	2.07725e6			0.366074			0.183037	+	0.983106i	$0.441407\pi$
$504$	−120377.	−	4.58642e6i	−0.0211090	−	0.804261i
$505$	−546686.			−0.0953914
$506$	−1.26149e6	+	11034.3i	−0.219032	+	0.00191589i
$507$		−	2.20870e6i		−	0.381607i
$508$	3.90635e6	−	68343.3i	0.671602	−	0.0117500i
$509$			739081.i			0.126444i	0.997999	+	0.0632219i	$0.0201376\pi$
$509$			739081.i			0.126444i	−0.997999	+	0.0632219i	$0.979862\pi$
$510$	−16030.3	−	1.83265e6i	−0.00272908	−	0.312000i
$511$	4.61784e6			0.782324
$512$	466465.	+	5.91327e6i	0.0786401	+	0.996903i
$513$	820347.			0.137627
$514$	89331.9	+	1.02128e7i	0.0149142	+	1.70505i
$515$		−	3.91520e6i		−	0.650483i
$516$	−3.18377e6	+	55701.5i	−0.526403	+	0.00920964i
$517$			2.09358e6i			0.344480i
$518$	−1.65342e7	+	144626.i	−2.70744	+	0.0236821i
$519$	5.74201e6			0.935719
$520$	48340.2	+	1.84178e6i	0.00783972	+	0.298696i
$521$	−7.18449e6			−1.15958			−0.579791	−	0.814765i	$-0.696866\pi$
$521$	−7.18449e6			−1.15958			−0.579791	+	0.814765i	$0.696866\pi$
$522$	4.46937e6	−	39093.8i	0.717911	−	0.00627959i
$523$		−	1.94687e6i		−	0.311231i	−0.987818	−	0.155616i	$-0.950264\pi$
$523$		−	1.94687e6i		−	0.311231i	0.987818	−	0.155616i	$-0.0497361\pi$
$524$	−100444.	−	5.74115e6i	−0.0159807	−	0.913421i
$525$			1.33468e6i			0.211338i
$526$	9178.48	+	1.04932e6i	0.00144646	+	0.165366i
$527$	−2.24612e6			−0.352295
$528$	−944945.	+	33074.6i	−0.147510	+	0.00516308i
$529$	299003.			0.0464554
$530$	15789.7	+	1.80515e6i	0.00244166	+	0.279141i
$531$			2.64247e6i			0.406700i
$532$	−22920.4	−	1.31008e6i	−0.00351109	−	0.200686i
$533$		−	7.36804e6i		−	1.12340i
$534$	1.83070e6	−	16013.2i	0.277820	−	0.00243010i
$535$	−2.28503e6			−0.345149
$536$	1.13306e7	−	297388.i	1.70350	−	0.0447108i
$537$	3.68389e6			0.551278
$538$	6.37021e6	−	55720.5i	0.948851	−	0.00829964i
$539$		−	1.94958e6i		−	0.289047i
$540$	3.18477e6	−	55718.9i	0.469996	−	0.00822277i
$541$		−	1.18585e7i		−	1.74195i	−0.491330	−	0.870973i	$-0.663489\pi$
$541$		−	1.18585e7i		−	1.74195i	0.491330	−	0.870973i	$-0.336511\pi$
$542$	7798.37	+	891543.i	0.00114026	+	0.130360i
$543$	6.37445e6			0.927776
$544$	305431.	+	6.97935e6i	0.0442502	+	1.01116i
$545$	−1.22435e6			−0.176569
$546$	−43016.8	−	4.91787e6i	−0.00617528	−	0.705985i
$547$		−	2.10343e6i		−	0.300580i	−0.988642	−	0.150290i	$-0.951979\pi$
$547$		−	2.10343e6i		−	0.300580i	0.988642	−	0.150290i	$-0.0480207\pi$
$548$	1.04660e7	−	183107.i	1.48878	−	0.0260468i
$549$		−	1.44988e6i		−	0.205306i
$550$	−303798.	+	2657.33i	−0.0428231	+	0.000374575i
$551$	1.27645e6			0.179112
$552$	5.04640e6	−	132450.i	0.704910	−	0.0185014i
$553$	5.79755e6			0.806179
$554$	−1.09462e7	+	95746.6i	−1.51526	+	0.0132541i
$555$		−	3.95113e6i		−	0.544489i
$556$	−201155.	−	1.14976e7i	−0.0275958	−	1.57731i
$557$			4.61967e6i			0.630918i	0.948939	+	0.315459i	$0.102158\pi$
$557$			4.61967e6i			0.630918i	−0.948939	+	0.315459i	$0.897842\pi$
$558$	−11752.4	−	1.34358e6i	−0.00159786	−	0.182675i
$559$	3.77012e6			0.510300
$560$	−177964.	−	5.08446e6i	−0.0239807	−	0.685132i
$561$	−1.11360e6			−0.149390
$562$	19499.7	+	2.22929e6i	0.00260428	+	0.297732i
$563$			1.23357e7i			1.64019i	0.572227	+	0.820096i	$0.306080\pi$
$563$			1.23357e7i			1.64019i	−0.572227	+	0.820096i	$0.693920\pi$
$564$	−146547.	−	8.37632e6i	−0.0193990	−	1.10881i
$565$			3.84095e6i			0.506194i
$566$	3.04662e6	−	26648.9i	0.399740	−	0.00349654i
$567$	−2.34367e6			−0.306154
$568$	290707.	+	1.10760e7i	0.0378081	+	1.44050i
$569$	7.85222e6			1.01674			0.508372	−	0.861138i	$-0.330247\pi$
$569$	7.85222e6			1.01674			0.508372	+	0.861138i	$0.330247\pi$
$570$	313089.	−	2738.60i	0.0403627	−	0.000353054i
$571$		−	1.14825e7i		−	1.47383i	−0.675984	−	0.736916i	$-0.736281\pi$
$571$		−	1.14825e7i		−	1.47383i	0.675984	−	0.736916i	$-0.263719\pi$
$572$	1.11931e6	−	19582.9i	0.143041	−	0.00250257i
$573$			15569.8i			0.00198106i
$574$	177959.	+	2.03451e7i	0.0225445	+	2.57738i
$575$	1.62203e6			0.204593
$576$	−4.17330e6	+	219220.i	−0.524111	+	0.0275311i
$577$	−1.10508e7			−1.38183			−0.690913	−	0.722938i	$-0.742791\pi$
$577$	−1.10508e7			−1.38183			−0.690913	+	0.722938i	$0.742791\pi$
$578$	1713.72	+	195920.i	0.000213363	+	0.0243926i
$579$		−	9.54765e6i		−	1.18359i
$580$	4.95546e6	−	86697.9i	0.611666	−	0.0107013i
$581$		−	9.55901e6i		−	1.17482i
$582$	−6.90960e6	+	60438.5i	−0.845561	+	0.00739616i
$583$	1.09689e6			0.133656
$584$	−110361.	−	4.20479e6i	−0.0133901	−	0.510166i
$585$	−1.29805e6			−0.156820
$586$	−7.10823e6	+	62176.0i	−0.855101	+	0.00747961i
$587$			1.22974e6i			0.147305i	0.997284	+	0.0736524i	$0.0234655\pi$
$587$			1.22974e6i			0.147305i	−0.997284	+	0.0736524i	$0.976534\pi$
$588$	136467.	+	7.80016e6i	0.0162774	+	0.930379i
$589$		−	383725.i		−	0.0455756i
$590$	25629.7	+	2.93009e6i	0.00303119	+	0.346538i
$591$	−3.83146e6			−0.451228
$592$	526838.	+	1.50518e7i	0.0617835	+	1.76516i
$593$	4.14520e6			0.484071			0.242035	−	0.970267i	$-0.422185\pi$
$593$	4.14520e6			0.484071			0.242035	+	0.970267i	$0.422185\pi$
$594$	−16928.6	−	1.93535e6i	−0.00196859	−	0.225057i
$595$		−	5.99192e6i		−	0.693863i
$596$	276971.	+	1.58310e7i	0.0319387	+	1.82555i
$597$			4.36593e6i			0.501350i
$598$	−5.97669e6	+	52278.3i	−0.683451	+	0.00597818i
$599$	1.54313e7			1.75726			0.878629	−	0.477505i	$-0.158459\pi$
$599$	1.54313e7			1.75726			0.878629	+	0.477505i	$0.158459\pi$
$600$	1.21529e6	−	31897.2i	0.137817	−	0.00361722i
$601$	−1.20526e7			−1.36111			−0.680556	−	0.732696i	$-0.738262\pi$
$601$	−1.20526e7			−1.36111			−0.680556	+	0.732696i	$0.738262\pi$
$602$	−1.04103e7	+	91059.0i	−1.17077	+	0.0102407i
$603$			7.98556e6i			0.894359i
$604$	318697.	−	5575.74i	0.0355456	−	0.000621886i
$605$		−	3.84167e6i		−	0.426709i
$606$	−11626.4	−	1.32918e6i	−0.00128606	−	0.147028i
$607$	7.95296e6			0.876107			0.438053	−	0.898949i	$-0.355668\pi$
$607$	7.95296e6			0.876107			0.438053	+	0.898949i	$0.355668\pi$
$608$	−1.19235e6	+	52179.5i	−0.130811	+	0.00572454i
$609$	−1.32299e7			−1.44549
$610$	−14062.5	−	1.60769e6i	−0.00153017	−	0.174935i
$611$			9.91895e6i			1.07489i
$612$	−4.92115e6	+	86097.7i	−0.531115	+	0.00929208i
$613$		−	1.04301e7i		−	1.12108i	−0.828128	−	0.560538i	$-0.810594\pi$
$613$		−	1.04301e7i		−	1.12108i	0.828128	−	0.560538i	$-0.189406\pi$
$614$	−1.28632e6	+	11251.5i	−0.137699	+	0.00120445i
$615$	−4.86179e6			−0.518333
$616$	−3.09024e6	+	81107.9i	−0.328126	+	0.00861215i
$617$	−6.91606e6			−0.731384			−0.365692	−	0.930736i	$-0.619168\pi$
$617$	−6.91606e6			−0.731384			−0.365692	+	0.930736i	$0.619168\pi$
$618$	9.51916e6	−	83264.5i	1.00260	−	0.00876978i
$619$		−	1.15145e7i		−	1.20786i	−0.797037	−	0.603931i	$-0.793600\pi$
$619$		−	1.15145e7i		−	1.20786i	0.797037	−	0.603931i	$-0.206400\pi$
$620$	−26063.1	−	1.48971e6i	−0.00272299	−	0.155640i
$621$			1.03332e7i			1.07524i
$622$	56173.2	+	6.42196e6i	0.00582175	+	0.665567i
$623$	5.98552e6			0.617848
$624$	−4.47695e6	+	156700.i	−0.460279	+	0.0161105i
$625$	390625.			0.0400000
$626$	−115156.	−	1.31651e7i	−0.0117449	−	1.34273i
$627$		−	190246.i		−	0.0193262i
$628$	−136482.	−	7.80102e6i	−0.0138095	−	0.789318i
$629$			1.77383e7i			1.78766i
$630$	3.58423e6	−	31351.5i	0.359787	−	0.00314707i
$631$	5.76766e6			0.576669			0.288334	−	0.957530i	$-0.406899\pi$
$631$	5.76766e6			0.576669			0.288334	+	0.957530i	$0.406899\pi$
$632$	−138554.	−	5.27897e6i	−0.0137984	−	0.525723i
$633$	−6.26081e6			−0.621042
$634$	−8.49695e6	+	74323.2i	−0.839537	+	0.00734347i
$635$			3.05230e6i			0.300396i
$636$	−4.38858e6	+	76780.2i	−0.430211	+	0.00752673i
$637$		−	9.23668e6i		−	0.901919i
$638$	−26340.6	−	3.01138e6i	−0.00256197	−	0.292896i
$639$	−7.80614e6			−0.756283
$640$	−4.62541e6	+	283558.i	−0.446376	+	0.0273648i
$641$	−518990.			−0.0498901			−0.0249450	−	0.999689i	$-0.507941\pi$
$641$	−518990.			−0.0498901			−0.0249450	+	0.999689i	$0.507941\pi$
$642$	−48595.6	−	5.55566e6i	−0.00465328	−	0.531984i
$643$		−	6.52874e6i		−	0.622733i	−0.950290	−	0.311367i	$-0.899213\pi$
$643$		−	6.52874e6i		−	0.622733i	0.950290	−	0.311367i	$-0.100787\pi$
$644$	1.65019e7	−	288708.i	1.56790	−	0.0274311i
$645$		−	2.48770e6i		−	0.235450i
$646$	−1.40558e6	+	12294.7i	−0.132518	+	0.00115914i
$647$	−6.41651e6			−0.602613			−0.301306	−	0.953527i	$-0.597423\pi$
$647$	−6.41651e6			−0.602613			−0.301306	+	0.953527i	$0.597423\pi$
$648$	56011.0	+	2.13404e6i	0.00524005	+	0.199648i
$649$	1.78045e6			0.165927
$650$	−1.43933e6	+	12589.9i	−0.133622	+	0.00116880i
$651$			3.97717e6i			0.367808i
$652$	−150120.	−	8.58053e6i	−0.0138299	−	0.790487i
$653$			9.11065e6i			0.836116i	0.908420	+	0.418058i	$0.137289\pi$
$653$			9.11065e6i			0.836116i	−0.908420	+	0.418058i	$0.862711\pi$
$654$	−26038.2	−	2.97680e6i	−0.00238049	−	0.272148i
$655$	4.48596e6			0.408557
$656$	1.85210e7	−	648264.i	1.68037	−	0.0588155i
$657$	2.96344e6			0.267844
$658$	−239571.	−	2.73888e7i	−0.0215709	−	2.46608i
$659$		−	1.97306e7i		−	1.76981i	−0.465775	−	0.884903i	$-0.654224\pi$
$659$		−	1.97306e7i		−	1.76981i	0.465775	−	0.884903i	$-0.345776\pi$
$660$	−12921.7	−	738577.i	−0.00115468	−	0.0659988i
$661$		−	9.04530e6i		−	0.805228i	−0.915370	−	0.402614i	$-0.868102\pi$
$661$		−	9.04530e6i		−	0.805228i	0.915370	−	0.402614i	$-0.131898\pi$
$662$	1.54130e7	−	134818.i	1.36692	−	0.0119565i
$663$	−5.27599e6			−0.466144
$664$	−8.70398e6	+	228449.i	−0.766122	+	0.0201080i
$665$	1.02365e6			0.0897634
$666$	−1.06106e7	+	92811.7i	−0.926949	+	0.00810806i
$667$			1.60783e7i			1.39935i
$668$	556847.	−	9742.28i	0.0482831	−	0.000844733i
$669$			8.47840e6i			0.732401i
$670$	77452.8	+	8.85474e6i	0.00666577	+	0.762059i
$671$	−976900.			−0.0837614
$672$	1.23582e7	−	540821.i	1.05568	−	0.0461987i
$673$	−1.11387e7			−0.947974			−0.473987	−	0.880532i	$-0.657186\pi$
$673$	−1.11387e7			−0.947974			−0.473987	+	0.880532i	$0.657186\pi$
$674$	101071.	+	1.15548e7i	0.00856989	+	0.979747i
$675$			2.48848e6i			0.210221i
$676$	−6.57648e6	+	115058.i	−0.553512	+	0.00968393i
$677$		−	1.13338e7i		−	0.950395i	−0.879879	−	0.475198i	$-0.842377\pi$
$677$		−	1.13338e7i		−	0.950395i	0.879879	−	0.475198i	$-0.157623\pi$
$678$	−9.33862e6	+	81685.3i	−0.780204	+	0.00682448i
$679$	−2.25912e7			−1.88046
$680$	−5.45596e6	+	143200.i	−0.452479	+	0.0118760i
$681$	9.37449e6			0.774604
$682$	−905279.	+	7918.51i	−0.0745283	+	0.000651902i
$683$			1.06005e7i			0.869514i	0.900548	+	0.434757i	$0.143166\pi$
$683$			1.06005e7i			0.869514i	−0.900548	+	0.434757i	$0.856834\pi$
$684$	−14708.8	−	840725.i	−0.00120209	−	0.0687090i
$685$			8.17782e6i			0.665903i
$686$	57827.2	+	6.61105e6i	0.00469161	+	0.536365i
$687$	4.34195e6			0.350988
$688$	331707.	+	9.47691e6i	0.0267167	+	0.763301i
$689$	5.19681e6			0.417051
$690$	34495.8	+	3.94371e6i	0.00275831	+	0.315342i
$691$			1.18528e7i			0.944331i	0.881510	+	0.472165i	$0.156527\pi$
$691$			1.18528e7i			0.944331i	−0.881510	+	0.472165i	$0.843473\pi$
$692$	−299120.	−	1.70971e7i	−0.0237455	−	1.35724i
$693$		−	2.17793e6i		−	0.172271i
$694$	1.45633e7	−	127386.i	1.14779	−	0.0100398i
$695$	8.98384e6			0.705505
$696$	316179.	+	1.20465e7i	0.0247406	+	0.942625i
$697$	2.18266e7			1.70178
$698$	1.11996e7	−	97963.6i	0.870092	−	0.00761073i
$699$			2.13678e6i			0.165412i
$700$	3.97406e6	−	69527.8i	0.306541	−	0.00536307i
$701$			1.42728e7i			1.09702i	0.836144	+	0.548511i	$0.184805\pi$
$701$			1.42728e7i			1.09702i	−0.836144	+	0.548511i	$0.815195\pi$
$702$	−80204.1	−	9.16928e6i	−0.00614262	−	0.702251i
$703$	−3.03039e6			−0.231265
$704$	147706.	+	2.81189e6i	0.0112322	+	0.213829i
$705$	6.54500e6			0.495949
$706$	−50899.1	−	5.81901e6i	−0.00384325	−	0.439377i
$707$		−	4.34578e6i		−	0.326979i
$708$	−7.12349e6	+	124628.i	−0.534084	+	0.00934403i
$709$			1.40052e7i			1.04635i	0.852227	+	0.523173i	$0.175252\pi$
$709$			1.40052e7i			1.04635i	−0.852227	+	0.523173i	$0.824748\pi$
$710$	−8.65580e6	+	75712.6i	−0.644408	+	0.00563667i
$711$	3.72050e6			0.276012
$712$	−143047.	−	5.45013e6i	−0.0105749	−	0.402909i
$713$	4.83345e6			0.356069
$714$	1.45684e7	−	127430.i	1.06946	−	0.00935462i
$715$			874598.i			0.0639799i
$716$	−191906.	−	1.09689e7i	−0.0139896	−	0.799616i
$717$			4.17391e6i			0.303211i
$718$	−48449.5	−	5.53895e6i	−0.00350734	−	0.400974i
$719$	7.28309e6			0.525404			0.262702	−	0.964877i	$-0.415386\pi$
$719$	7.28309e6			0.525404			0.262702	+	0.964877i	$0.415386\pi$
$720$	−114206.	−	3.26289e6i	−0.00821028	−	0.234569i
$721$	3.11232e7			2.22970
$722$	120414.	+	1.37663e7i	0.00859675	+	0.982818i
$723$			7.68107e6i			0.546482i
$724$	−332066.	−	1.89802e7i	−0.0235439	−	1.34572i
$725$			3.87205e6i			0.273587i
$726$	9.34039e6	−	81700.8i	0.657693	−	0.00575287i
$727$	3.41888e6			0.239910			0.119955	−	0.992779i	$-0.461725\pi$
$727$	3.41888e6			0.239910			0.119955	+	0.992779i	$0.461725\pi$
$728$	−1.46409e7	+	384272.i	−1.02386	+	0.0268727i
$729$	−1.19005e7			−0.829368
$730$	3.28599e6	−	28742.7i	0.228223	−	0.00199628i
$731$			1.11683e7i			0.773028i
$732$	3.90853e6	−	68381.4i	0.269610	−	0.00471694i
$733$		−	2.11502e6i		−	0.145397i	−0.997354	−	0.0726983i	$-0.976839\pi$
$733$		−	2.11502e6i		−	0.145397i	0.997354	−	0.0726983i	$-0.0231610\pi$
$734$	−53397.5	−	6.10463e6i	−0.00365831	−	0.418234i
$735$	−6.09481e6			−0.416142
$736$	−657259.	−	1.50189e7i	−0.0447242	−	1.02199i
$737$	5.38051e6			0.364884
$738$	114203.	+	1.30562e7i	0.00771857	+	0.882420i
$739$			4.97420e6i			0.335052i	0.985868	+	0.167526i	$0.0535778\pi$
$739$			4.97420e6i			0.335052i	−0.985868	+	0.167526i	$0.946422\pi$
$740$	−1.17646e7	+	205827.i	−0.789768	+	0.0138173i
$741$		−	901345.i		−	0.0603039i
$742$	−1.43497e7	+	125518.i	−0.956828	+	0.00836941i
$743$	6.04483e6			0.401709			0.200855	−	0.979621i	$-0.435628\pi$
$743$	6.04483e6			0.401709			0.200855	+	0.979621i	$0.435628\pi$
$744$	3.62142e6	−	95049.6i	0.239854	−	0.00629532i
$745$	−1.23699e7			−0.816535
$746$	2.06632e7	−	180742.i	1.35941	−	0.0118908i
$747$		−	6.13437e6i		−	0.402225i
$748$	58011.0	+	3.31578e6i	0.00379102	+	0.216686i
$749$		−	1.81644e7i		−	1.18309i
$750$	8307.41	+	949740.i	0.000539278	+	0.0616526i
$751$	−2.14521e7			−1.38794			−0.693970	−	0.720004i	$-0.744140\pi$
$751$	−2.14521e7			−1.38794			−0.693970	+	0.720004i	$0.744140\pi$
$752$	−2.49332e7	+	872701.i	−1.60780	+	0.0562757i
$753$	−1.69722e7			−1.09082
$754$	−124796.	−	1.42673e7i	−0.00799418	−	0.913929i
$755$			249020.i			0.0158989i
$756$	442928.	+	2.53168e7i	0.0281857	+	1.61103i
$757$		−	1.22790e7i		−	0.778794i	−0.921070	−	0.389397i	$-0.872683\pi$
$757$		−	1.22790e7i		−	0.778794i	0.921070	−	0.389397i	$-0.127317\pi$
$758$	1.69367e7	−	148146.i	1.07067	−	0.00936520i
$759$	2.39636e6			0.150990
$760$	−24464.1	−	932091.i	−0.00153637	−	0.0585362i
$761$	−1.38648e7			−0.867867			−0.433933	−	0.900945i	$-0.642875\pi$
$761$	−1.38648e7			−0.867867			−0.433933	+	0.900945i	$0.642875\pi$
$762$	−7.42117e6	+	64913.3i	−0.463004	+	0.00404992i
$763$		−	9.73273e6i		−	0.605234i
$764$	46359.8	−	811.084i	0.00287348	−	5.02728e-5i
$765$		−	3.84524e6i		−	0.237558i
$766$	205711.	+	2.35177e7i	0.0126673	+	1.44818i
$767$	8.43539e6			0.517746
$768$	−787792.	−	1.12399e7i	−0.0481957	−	0.687636i
$769$	1.92248e6			0.117232			0.0586158	−	0.998281i	$-0.481331\pi$
$769$	1.92248e6			0.117232			0.0586158	+	0.998281i	$0.481331\pi$
$770$	−21124.0	−	2.41499e6i	−0.00128395	−	0.146787i
$771$		−	1.94005e7i		−	1.17538i
$772$	−2.84285e7	+	497369.i	−1.71676	+	0.0300355i
$773$		−	2.66728e7i		−	1.60554i	−0.596291	−	0.802768i	$-0.703360\pi$
$773$		−	2.66728e7i		−	1.60554i	0.596291	−	0.802768i	$-0.296640\pi$
$774$	−6.68065e6	+	58435.9i	−0.400836	+	0.00350613i
$775$	1.16401e6			0.0696151
$776$	539902.	+	2.05704e7i	0.0321855	+	1.22628i
$777$	3.14088e7			1.86638
$778$	6.13298e6	−	53645.4i	0.363264	−	0.00317749i
$779$			3.72883e6i			0.220155i
$780$	−61220.4	−	3.49922e6i	−0.00360296	−	0.205937i
$781$			5.25963e6i			0.308551i
$782$	−154866.	−	1.77049e7i	−0.00905604	−	1.03533i
$783$	−2.46669e7			−1.43784
$784$	2.32182e7	−	812672.i	1.34908	−	0.0472199i
$785$	6.09548e6			0.353048
$786$	95402.8	+	1.09069e7i	0.00550814	+	0.629714i
$787$		−	7.22979e6i		−	0.416092i	−0.978119	−	0.208046i	$-0.933290\pi$
$787$		−	7.22979e6i		−	0.416092i	0.978119	−	0.208046i	$-0.0667103\pi$
$788$	199593.	+	1.14083e7i	0.0114507	+	0.654495i
$789$		−	1.99332e6i		−	0.113995i
$790$	4.12546e6	−	36085.6i	0.235182	−	0.00205715i
$791$	−3.05329e7			−1.73511
$792$	−1.98312e6	+	52050.0i	−0.112341	+	0.00294854i
$793$	−4.62835e6			−0.261362
$794$	1.76468e7	−	154357.i	0.993377	−	0.00868911i
$795$		−	3.42911e6i		−	0.192426i
$796$	1.29997e7	−	227436.i	0.727196	−	0.0127226i
$797$			4.41257e6i			0.246062i	0.992403	+	0.123031i	$0.0392615\pi$
$797$			4.41257e6i			0.246062i	−0.992403	+	0.123031i	$0.960738\pi$
$798$	21770.0	+	2.48884e6i	0.00121019	+	0.138354i
$799$	−2.93832e7			−1.62829
$800$	−158284.	−	3.61692e6i	−0.00874403	−	0.199809i
$801$	3.84113e6			0.211533
$802$	−157557.	−	1.80126e7i	−0.00864969	−	0.988871i
$803$		−	1.99671e6i		−	0.109276i
$804$	−2.15272e7	+	376627.i	−1.17448	+	0.0205481i
$805$			1.28941e7i			0.701295i
$806$	−4.28902e6	+	37516.2i	−0.232552	+	0.00203414i
$807$	−1.21010e7			−0.654090
$808$	−3.95707e6	+	103859.i	−0.213228	+	0.00559649i
$809$	6.04388e6			0.324672			0.162336	−	0.986736i	$-0.448097\pi$
$809$	6.04388e6			0.324672			0.162336	+	0.986736i	$0.448097\pi$
$810$	−1.66773e6	+	14587.7i	−0.0893126	+	0.000781221i
$811$			2.40664e7i			1.28487i	0.766340	+	0.642435i	$0.222076\pi$
$811$			2.40664e7i			1.28487i	−0.766340	+	0.642435i	$0.777924\pi$
$812$	689190.	+	3.93926e7i	0.0366816	+	2.09664i
$813$		−	1.69360e6i		−	0.0898636i
$814$	62534.7	+	7.14924e6i	0.00330796	+	0.378180i
$815$	6.70456e6			0.353571
$816$	−464198.	−	1.32622e7i	−0.0244050	−	0.697253i
$817$	−1.90799e6			−0.100005
$818$	186208.	+	2.12881e7i	0.00973003	+	1.11238i
$819$		−	1.03186e7i		−	0.537540i
$820$	253267.	+	1.44762e7i	0.0131536	+	0.751829i
$821$			1.16527e7i			0.603350i	0.953411	+	0.301675i	$0.0975458\pi$
$821$			1.16527e7i			0.603350i	−0.953411	+	0.301675i	$0.902454\pi$
$822$	−1.98830e7	+	173917.i	−1.02637	+	0.00897767i
$823$	−161156.			−0.00829369			−0.00414684	−	0.999991i	$-0.501320\pi$
$823$	−161156.			−0.00829369			−0.00414684	+	0.999991i	$0.501320\pi$
$824$	−743808.	−	2.83393e7i	−0.0381630	−	1.45402i
$825$	577102.			0.0295201
$826$	−2.32923e7	+	203738.i	−1.18785	+	0.0103902i
$827$		−	2.85594e7i		−	1.45206i	−0.687661	−	0.726031i	$-0.741363\pi$
$827$		−	2.85594e7i		−	1.45206i	0.687661	−	0.726031i	$-0.258637\pi$
$828$	1.05899e7	−	185275.i	0.536803	−	0.00939161i
$829$		−	1.49564e7i		−	0.755859i	−0.925834	−	0.377929i	$-0.876636\pi$
$829$		−	1.49564e7i		−	0.755859i	0.925834	−	0.377929i	$-0.123364\pi$
$830$	−59498.0	−	6.80207e6i	−0.00299783	−	0.342725i
$831$	2.07936e7			1.04455
$832$	699800.	+	1.33221e7i	0.0350482	+	0.667214i
$833$	2.73621e7			1.36627
$834$	191059.	+	2.18427e7i	0.00951158	+	1.08740i
$835$			435104.i			0.0215962i
$836$	−566465.	+	9910.54i	−0.0280322	+	0.000490435i
$837$			7.41536e6i			0.365863i
$838$	1.54680e7	−	135299.i	0.760895	−	0.00665558i
$839$	−1.76445e7			−0.865374			−0.432687	−	0.901544i	$-0.642435\pi$
$839$	−1.76445e7			−0.865374			−0.432687	+	0.901544i	$0.642435\pi$
$840$	253561.	+	9.66077e6i	0.0123989	+	0.472404i
$841$	−1.78703e7			−0.871246
$842$	−2.54758e6	+	22283.8i	−0.123836	+	0.00108320i
$843$		−	4.23482e6i		−	0.205242i
$844$	326146.	+	1.86418e7i	0.0157600	+	0.900807i
$845$		−	5.13866e6i		−	0.247576i
$846$	−153742.	−	1.75764e7i	−0.00738525	−	0.844314i
$847$	3.05387e7			1.46266
$848$	457232.	+	1.30632e7i	0.0218347	+	0.623820i
$849$	−5.78744e6			−0.275561
$850$	−37295.4	−	4.26377e6i	−0.00177055	−	0.202417i
$851$		−	3.81711e7i		−	1.80681i
$852$	−368165.	−	2.10435e7i	−0.0173758	−	0.993160i
$853$			3.43356e7i			1.61574i	0.589361	+	0.807870i	$0.299380\pi$
$853$			3.43356e7i			1.61574i	−0.589361	+	0.807870i	$0.700620\pi$
$854$	1.27801e7	−	111788.i	0.599637	−	0.00524505i
$855$	656917.			0.0307323
$856$	−1.65397e7	+	434108.i	−0.771512	+	0.0202495i
$857$	−1.27760e7			−0.594216			−0.297108	−	0.954844i	$-0.596022\pi$
$857$	−1.27760e7			−0.594216			−0.297108	+	0.954844i	$0.596022\pi$
$858$	−2.12644e6	+	18600.1i	−0.0986131	+	0.000862573i
$859$			3.23768e7i			1.49710i	0.663077	+	0.748551i	$0.269250\pi$
$859$			3.23768e7i			1.49710i	−0.663077	+	0.748551i	$0.730750\pi$
$860$	−7.40724e6	+	129593.i	−0.341515	+	0.00597496i
$861$		−	3.86480e7i		−	1.77672i
$862$	25596.8	+	2.92633e6i	0.00117332	+	0.134139i
$863$	2.57138e7			1.17527			0.587637	−	0.809125i	$-0.300058\pi$
$863$	2.57138e7			1.17527			0.587637	+	0.809125i	$0.300058\pi$
$864$	2.30417e7	−	1.00835e6i	1.05010	−	0.0459544i
$865$	1.33591e7			0.607068
$866$	111261.	+	1.27199e7i	0.00504139	+	0.576353i
$867$		−	372174.i		−	0.0168151i
$868$	1.18422e7	−	207184.i	0.533497	−	0.00933376i
$869$		−	2.50680e6i		−	0.112608i
$870$	−9.41423e6	+	82346.7i	−0.421684	+	0.00368849i
$871$	2.54917e7			1.13856
$872$	−8.86217e6	+	232601.i	−0.394683	+	0.0103590i
$873$	−1.44976e7			−0.643814
$874$	3.02469e6	−	26457.1i	0.133938	−	0.00117156i
$875$			3.10521e6i			0.137110i
$876$	139766.	+	7.98874e6i	0.00615378	+	0.351737i
$877$			4.69271e6i			0.206027i	0.994680	+	0.103014i	$0.0328485\pi$
$877$			4.69271e6i			0.206027i	−0.994680	+	0.103014i	$0.967151\pi$
$878$	42699.2	+	4.88156e6i	0.00186932	+	0.213709i
$879$	1.35030e7			0.589464
$880$	−2.19847e6	+	76949.9i	−0.0957004	+	0.00334966i
$881$	446984.			0.0194023			0.00970113	−	0.999953i	$-0.496912\pi$
$881$	446984.			0.0194023			0.00970113	+	0.999953i	$0.496912\pi$
$882$	143166.	+	1.63674e7i	0.00619683	+	0.708449i
$883$		−	3.04436e7i		−	1.31400i	−0.753892	−	0.656999i	$-0.771826\pi$
$883$		−	3.04436e7i		−	1.31400i	0.753892	−	0.656999i	$-0.228174\pi$
$884$	274844.	+	1.57095e7i	0.0118292	+	0.676131i
$885$		−	5.56608e6i		−	0.238886i
$886$	5.50011e6	−	48109.7i	0.235390	−	0.00205896i
$887$	−1.40477e7			−0.599508			−0.299754	−	0.954016i	$-0.596905\pi$
$887$	−1.40477e7			−0.599508			−0.299754	+	0.954016i	$0.596905\pi$
$888$	−750634.	−	2.85994e7i	−0.0319445	−	1.21709i
$889$	−2.42638e7			−1.02968
$890$	4.25922e6	−	37255.6i	0.180242	−	0.00157658i
$891$			1.01338e6i			0.0427640i
$892$	2.52448e7	−	441668.i	1.06233	−	0.0185859i
$893$		−	5.01980e6i		−	0.210648i
$894$	−263070.	−	3.00753e7i	−0.0110085	−	1.25854i
$895$	8.57078e6			0.357654
$896$	−2.25409e6	−	3.67689e7i	−0.0937998	−	1.53007i
$897$	1.13535e7			0.471137
$898$	−1400.15	−	160071.i	−5.79406e−5	−	0.00662402i
$899$			1.15382e7i			0.476145i
$900$	2.55030e6	−	44618.6i	0.104951	−	0.00183616i
$901$			1.53947e7i			0.631769i
$902$	8.79700e6	−	76947.8i	0.360013	−	0.00314905i
$903$	1.97756e7			0.807067
$904$	729701.	+	2.78018e7i	0.0296978	+	1.13149i
$905$	1.48305e7			0.601915
$906$	−605451.	+	5295.91i	−0.0245052	+	0.000214348i
$907$			3.03623e7i			1.22551i	0.790273	+	0.612755i	$0.209939\pi$
$907$			3.03623e7i			1.22551i	−0.790273	+	0.612755i	$0.790061\pi$
$908$	−488348.	−	2.79129e7i	−0.0196569	−	1.12354i
$909$		−	2.78885e6i		−	0.111948i
$910$	−100081.	−	1.14417e7i	−0.00400635	−	0.458023i
$911$	−1.87844e7			−0.749896			−0.374948	−	0.927046i	$-0.622339\pi$
$911$	−1.87844e7			−0.749896			−0.374948	+	0.927046i	$0.622339\pi$
$912$	2.26570e6	−	79303.2i	0.0902020	−	0.00315721i
$913$	−4.13322e6			−0.164101
$914$	22575.7	+	2.58095e6i	0.000893871	+	0.102191i
$915$			3.05401e6i			0.120592i
$916$	−226186.	−	1.29283e7i	−0.00890693	−	0.509100i
$917$			3.56604e7i			1.40043i
$918$	2.71624e7	−	237591.i	1.06381	−	0.00930515i
$919$	4.38053e7			1.71095			0.855476	−	0.517842i	$-0.173265\pi$
$919$	4.38053e7			1.71095			0.855476	+	0.517842i	$0.173265\pi$
$920$	1.17407e7	−	308153.i	0.457326	−	0.0120032i
$921$	2.44353e6			0.0949224
$922$	63345.6	−	554.087i	0.00245408	−	2.14660e-5i
$923$			2.49190e7i			0.962779i
$924$	5.87119e6	−	102719.i	0.226228	−	0.00395796i
$925$		−	9.19253e6i		−	0.353249i
$926$	−392375.	−	4.48580e7i	−0.0150374	−	1.71914i
$927$	1.99729e7			0.763383
$928$	3.58525e7	−	1.56898e6i	1.36663	−	0.0598063i
$929$	−1.88925e7			−0.718208			−0.359104	−	0.933298i	$-0.616918\pi$
$929$	−1.88925e7			−0.718208			−0.359104	+	0.933298i	$0.616918\pi$
$930$	24755.0	+	2.83010e6i	0.000938547	+	0.107299i
$931$			4.67452e6i			0.176751i
$932$	6.36236e6	−	111312.i	0.239926	−	0.00419762i
$933$		−	1.21993e7i		−	0.458809i
$934$	−3.72858e7	+	326140.i	−1.39854	+	0.0122331i
$935$	−2.59085e6			−0.0969199
$936$	−9.39561e6	+	246602.i	−0.350538	+	0.00920040i
$937$	−3.00651e7			−1.11870			−0.559350	−	0.828931i	$-0.688949\pi$
$937$	−3.00651e7			−1.11870			−0.559350	+	0.828931i	$0.688949\pi$
$938$	−7.03892e7	+	615698.i	−2.61216	+	0.0228486i
$939$			2.50087e7i			0.925609i
$940$	−340951.	−	1.94880e7i	−0.0125855	−	0.719362i
$941$			368874.i			0.0135801i	0.999977	+	0.00679006i	$0.00216136\pi$
$941$			368874.i			0.0135801i	−0.999977	+	0.00679006i	$0.997839\pi$
$942$	129632.	+	1.48201e7i	0.00475977	+	0.544158i
$943$	−4.69689e7			−1.72001
$944$	742172.	+	2.12040e7i	0.0271066	+	0.774439i
$945$	−1.97818e7			−0.720586
$946$	39373.0	+	4.50129e6i	0.00143044	+	0.163535i
$947$			3.31548e6i			0.120135i	0.998194	+	0.0600677i	$0.0191317\pi$
$947$			3.31548e6i			0.120135i	−0.998194	+	0.0600677i	$0.980868\pi$
$948$	175472.	+	1.00296e7i	0.00634143	+	0.362462i
$949$		−	9.45999e6i		−	0.340977i
$950$	728419.	−	6371.51i	0.0261862	−	0.000229052i
$951$	1.61410e7			0.578735
$952$	−1.13834e6	−	4.33712e7i	−0.0407081	−	1.55099i
$953$	1.89980e7			0.677604			0.338802	−	0.940858i	$-0.389978\pi$
$953$	1.89980e7			0.677604			0.338802	+	0.940858i	$0.389978\pi$
$954$	−9.20875e6	+	80549.4i	−0.327589	+	0.00286544i
$955$			36224.1i			0.00128526i
$956$	1.24280e7	−	217433.i	0.439800	−	0.00769449i
$957$			5.72049e6i			0.201908i
$958$	−79513.4	−	9.09032e6i	−0.00279915	−	0.320011i
$959$	−6.50082e7			−2.28256
$960$	8.79058e6	−	461762.i	0.307850	−	0.0161711i
$961$	−2.51605e7			−0.878844
$962$	296276.	+	3.38716e7i	0.0103219	+	1.18004i
$963$		−	1.16568e7i		−	0.405054i
$964$	2.28707e7	−	400132.i	0.792659	−	0.0138679i
$965$		−	2.22132e7i		−	0.767878i
$966$	−3.13498e7	+	274218.i	−1.08092	+	0.00945482i
$967$	1.00131e7			0.344354			0.172177	−	0.985066i	$-0.444920\pi$
$967$	1.00131e7			0.344354			0.172177	+	0.985066i	$0.444920\pi$
$968$	−729839.	−	2.78071e7i	−0.0250345	−	0.953823i
$969$	2.67008e6			0.0913514
$970$	−1.60756e7	+	140614.i	−0.548576	+	0.00479842i
$971$		−	2.66607e6i		−	0.0907453i	−0.998970	−	0.0453726i	$-0.985552\pi$
$971$		−	2.66607e6i		−	0.0907453i	0.998970	−	0.0453726i	$-0.0144475\pi$
$972$	470653.	+	2.69015e7i	0.0159785	+	0.913294i
$973$			7.14155e7i			2.41830i
$974$	−89670.6	−	1.02515e7i	−0.00302867	−	0.346251i
$975$	2.73419e6			0.0921121
$976$	−407217.	−	1.16342e7i	−0.0136836	−	0.390943i
$977$	−3.15935e6			−0.105891			−0.0529457	−	0.998597i	$-0.516861\pi$
$977$	−3.15935e6			−0.105891			−0.0529457	+	0.998597i	$0.516861\pi$
$978$	142586.	+	1.63010e7i	0.00476682	+	0.544964i
$979$		−	2.58808e6i		−	0.0863021i
$980$	317499.	+	1.81475e7i	0.0105603	+	0.603604i
$981$		−	6.24586e6i		−	0.207214i
$982$	1.65221e6	−	14451.9i	0.0546747	−	0.000478242i
$983$	2.50171e6			0.0825758			0.0412879	−	0.999147i	$-0.486854\pi$
$983$	2.50171e6			0.0825758			0.0412879	+	0.999147i	$0.486854\pi$
$984$	−3.51910e7	+	923640.i	−1.15863	+	0.0304099i
$985$	−8.91412e6			−0.292744
$986$	4.22644e7	−	369688.i	1.38447	−	0.0121100i
$987$			5.20284e7i			1.69999i
$988$	−2.68379e6	+	46954.0i	−0.0874694	+	0.00153031i
$989$		−	2.40333e7i		−	0.781307i
$990$	−13556.1	−	1.54979e6i	−0.000439588	−	0.0502556i
$991$	4.14173e7			1.33967			0.669835	−	0.742510i	$-0.266365\pi$
$991$	4.14173e7			1.33967			0.669835	+	0.742510i	$0.266365\pi$
$992$	−471666.	−	1.07780e7i	−0.0152179	−	0.347743i
$993$	−2.92790e7			−0.942286
$994$	−601864.	−	6.88078e7i	−0.0193211	−	2.20888i
$995$			1.01576e7i			0.325262i
$996$	1.65368e7	−	289319.i	0.528207	−	0.00924120i
$997$		−	3.80654e7i		−	1.21281i	−0.795156	−	0.606405i	$-0.792611\pi$
$997$		−	3.80654e7i		−	1.21281i	0.795156	−	0.606405i	$-0.207389\pi$
$998$	−4.79468e7	+	419392.i	−1.52382	+	0.0133289i
$999$	5.85612e7			1.85651

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.d.a.21.10	yes	20
3.2	odd	2		360.6.k.b.181.11		20
4.3	odd	2		160.6.d.a.81.13		20
5.2	odd	4		200.6.f.c.149.2		20
5.3	odd	4		200.6.f.b.149.19		20
5.4	even	2		200.6.d.b.101.11		20
8.3	odd	2		160.6.d.a.81.8		20
8.5	even	2	inner	40.6.d.a.21.9	✓	20
20.3	even	4		800.6.f.c.49.8		20
20.7	even	4		800.6.f.b.49.13		20
20.19	odd	2		800.6.d.c.401.8		20
24.5	odd	2		360.6.k.b.181.12		20
40.3	even	4		800.6.f.b.49.14		20
40.13	odd	4		200.6.f.c.149.1		20
40.19	odd	2		800.6.d.c.401.13		20
40.27	even	4		800.6.f.c.49.7		20
40.29	even	2		200.6.d.b.101.12		20
40.37	odd	4		200.6.f.b.149.20		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.9	✓	20	8.5	even	2	inner
40.6.d.a.21.10	yes	20	1.1	even	1	trivial
160.6.d.a.81.8		20	8.3	odd	2
160.6.d.a.81.13		20	4.3	odd	2
200.6.d.b.101.11		20	5.4	even	2
200.6.d.b.101.12		20	40.29	even	2
200.6.f.b.149.19		20	5.3	odd	4
200.6.f.b.149.20		20	40.37	odd	4
200.6.f.c.149.1		20	40.13	odd	4
200.6.f.c.149.2		20	5.2	odd	4
360.6.k.b.181.11		20	3.2	odd	2
360.6.k.b.181.12		20	24.5	odd	2
800.6.d.c.401.8		20	20.19	odd	2
800.6.d.c.401.13		20	40.19	odd	2
800.6.f.b.49.13		20	20.7	even	4
800.6.f.b.49.14		20	40.3	even	4
800.6.f.c.49.7		20	40.27	even	4
800.6.f.c.49.8		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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0494789 + 5.65664i) q^{2} -10.7455i q^{3} +(-31.9951 + 0.559768i) q^{4} -25.0000i q^{5} +(60.7833 - 0.531674i) q^{6} +198.733 q^{7} +(-4.74949 - 180.957i) q^{8} +127.535 q^{9} +O(q^{10})\)	\(q+(0.0494789 + 5.65664i) q^{2} -10.7455i q^{3} +(-31.9951 + 0.559768i) q^{4} -25.0000i q^{5} +(60.7833 - 0.531674i) q^{6} +198.733 q^{7} +(-4.74949 - 180.957i) q^{8} +127.535 q^{9} +(141.416 - 1.23697i) q^{10} -85.9303i q^{11} +(6.01498 + 343.803i) q^{12} -407.120i q^{13} +(9.83309 + 1124.16i) q^{14} -268.637 q^{15} +(1023.37 - 35.8197i) q^{16} +1206.02 q^{17} +(6.31026 + 721.417i) q^{18} +206.036i q^{19} +(13.9942 + 799.878i) q^{20} -2135.48i q^{21} +(486.077 - 4.25173i) q^{22} -2595.25 q^{23} +(-1944.47 + 51.0355i) q^{24} -625.000 q^{25} +(2302.93 - 20.1438i) q^{26} -3981.57i q^{27} +(-6358.49 + 111.244i) q^{28} -6195.27i q^{29} +(-13.2919 - 1519.58i) q^{30} -1862.42 q^{31} +(253.254 + 5787.08i) q^{32} -923.363 q^{33} +(59.6727 + 6822.04i) q^{34} -4968.33i q^{35} +(-4080.48 + 71.3897i) q^{36} +14708.1i q^{37} +(-1165.47 + 10.1944i) q^{38} -4374.70 q^{39} +(-4523.93 + 118.737i) q^{40} +18098.0 q^{41} +(12079.7 - 105.661i) q^{42} +9260.46i q^{43} +(48.1010 + 2749.35i) q^{44} -3188.36i q^{45} +(-128.410 - 14680.4i) q^{46} -24363.7 q^{47} +(-384.900 - 10996.6i) q^{48} +22687.9 q^{49} +(-30.9243 - 3535.40i) q^{50} -12959.3i q^{51} +(227.893 + 13025.8i) q^{52} +12764.8i q^{53} +(22522.3 - 197.004i) q^{54} -2148.26 q^{55} +(-943.880 - 35962.2i) q^{56} +2213.96 q^{57} +(35044.4 - 306.535i) q^{58} +20719.7i q^{59} +(8595.07 - 150.374i) q^{60} -11368.5i q^{61} +(-92.1504 - 10535.0i) q^{62} +25345.3 q^{63} +(-32722.9 + 1718.91i) q^{64} -10178.0 q^{65} +(-45.6869 - 5223.13i) q^{66} +62614.9i q^{67} +(-38586.8 + 675.093i) q^{68} +27887.3i q^{69} +(28104.0 - 245.827i) q^{70} -61208.1 q^{71} +(-605.723 - 23078.3i) q^{72} +23236.4 q^{73} +(-83198.1 + 727.738i) q^{74} +6715.93i q^{75} +(-115.332 - 6592.14i) q^{76} -17077.2i q^{77} +(-216.455 - 24746.1i) q^{78} +29172.5 q^{79} +(-895.492 - 25584.3i) q^{80} -11793.1 q^{81} +(895.467 + 102374. i) q^{82} -48099.7i q^{83} +(1195.38 + 68325.1i) q^{84} -30150.6i q^{85} +(-52383.1 + 458.197i) q^{86} -66571.2 q^{87} +(-15549.7 + 408.125i) q^{88} +30118.4 q^{89} +(18035.4 - 157.757i) q^{90} -80908.2i q^{91} +(83035.4 - 1452.74i) q^{92} +20012.6i q^{93} +(-1205.49 - 137817. i) q^{94} +5150.90 q^{95} +(62185.0 - 2721.34i) q^{96} -113676. q^{97} +(1122.57 + 128337. i) q^{98} -10959.1i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 32 * q^4 + 204 * q^6 - 196 * q^7 + 248 * q^8 - 1620 * q^9	\( 20 q + 2 q^{2} - 32 q^{4} + 204 q^{6} - 196 q^{7} + 248 q^{8} - 1620 q^{9} - 50 q^{10} - 1876 q^{12} + 2708 q^{14} + 900 q^{15} + 3080 q^{16} - 5294 q^{18} - 1900 q^{20} + 13836 q^{22} - 4676 q^{23} + 1032 q^{24} - 12500 q^{25} - 8084 q^{26} + 2108 q^{28} + 5800 q^{30} + 7160 q^{31} + 6792 q^{32} + 5672 q^{33} + 21132 q^{34} + 18344 q^{36} - 19580 q^{38} - 44904 q^{39} + 6200 q^{40} + 11608 q^{41} - 17116 q^{42} + 72296 q^{44} - 28516 q^{46} + 44180 q^{47} - 88856 q^{48} + 18756 q^{49} - 1250 q^{50} - 39680 q^{52} - 100584 q^{54} - 24200 q^{55} - 53624 q^{56} + 5032 q^{57} + 59496 q^{58} - 31300 q^{60} + 59824 q^{62} + 240620 q^{63} - 11264 q^{64} - 56688 q^{66} + 11576 q^{68} + 29800 q^{70} - 200312 q^{71} + 235912 q^{72} - 105136 q^{73} + 78876 q^{74} - 153872 q^{76} + 95864 q^{78} + 282080 q^{79} + 16000 q^{80} + 65172 q^{81} - 223032 q^{82} - 297128 q^{84} + 27452 q^{86} - 332592 q^{87} + 86896 q^{88} - 3160 q^{89} + 51750 q^{90} + 107916 q^{92} + 148820 q^{94} + 144400 q^{95} + 395168 q^{96} + 147376 q^{97} + 216942 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 32 * q^4 + 204 * q^6 - 196 * q^7 + 248 * q^8 - 1620 * q^9 - 50 * q^10 - 1876 * q^12 + 2708 * q^14 + 900 * q^15 + 3080 * q^16 - 5294 * q^18 - 1900 * q^20 + 13836 * q^22 - 4676 * q^23 + 1032 * q^24 - 12500 * q^25 - 8084 * q^26 + 2108 * q^28 + 5800 * q^30 + 7160 * q^31 + 6792 * q^32 + 5672 * q^33 + 21132 * q^34 + 18344 * q^36 - 19580 * q^38 - 44904 * q^39 + 6200 * q^40 + 11608 * q^41 - 17116 * q^42 + 72296 * q^44 - 28516 * q^46 + 44180 * q^47 - 88856 * q^48 + 18756 * q^49 - 1250 * q^50 - 39680 * q^52 - 100584 * q^54 - 24200 * q^55 - 53624 * q^56 + 5032 * q^57 + 59496 * q^58 - 31300 * q^60 + 59824 * q^62 + 240620 * q^63 - 11264 * q^64 - 56688 * q^66 + 11576 * q^68 + 29800 * q^70 - 200312 * q^71 + 235912 * q^72 - 105136 * q^73 + 78876 * q^74 - 153872 * q^76 + 95864 * q^78 + 282080 * q^79 + 16000 * q^80 + 65172 * q^81 - 223032 * q^82 - 297128 * q^84 + 27452 * q^86 - 332592 * q^87 + 86896 * q^88 - 3160 * q^89 + 51750 * q^90 + 107916 * q^92 + 148820 * q^94 + 144400 * q^95 + 395168 * q^96 + 147376 * q^97 + 216942 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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