LMFDB - Embedded newform 65.5.g.a.34.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,5,Mod(34,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("65.34");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	65.g (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:	$6.71904760045$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			34.6
Character	$\chi$	$=$	65.34
Dual form			65.5.g.a.44.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.49855 + 3.49855i) q^{2} -7.86015i q^{3} -8.47972i q^{4} +(-17.4903 + 17.8631i) q^{5} +(27.4991 + 27.4991i) q^{6} +(-0.666849 - 0.666849i) q^{7} +(-26.3101 - 26.3101i) q^{8} +19.2180 q^{9} +O(q^{10})$	\(q+(-3.49855 + 3.49855i) q^{2} -7.86015i q^{3} -8.47972i q^{4} +(-17.4903 + 17.8631i) q^{5} +(27.4991 + 27.4991i) q^{6} +(-0.666849 - 0.666849i) q^{7} +(-26.3101 - 26.3101i) q^{8} +19.2180 q^{9} +(-1.30419 - 123.686i) q^{10} +(101.371 - 101.371i) q^{11} -66.6519 q^{12} +(-97.8678 - 137.778i) q^{13} +4.66601 q^{14} +(140.407 + 137.476i) q^{15} +319.770 q^{16} +475.560 q^{17} +(-67.2351 + 67.2351i) q^{18} +(-119.381 - 119.381i) q^{19} +(151.474 + 148.313i) q^{20} +(-5.24153 + 5.24153i) q^{21} +709.303i q^{22} +672.620 q^{23} +(-206.801 + 206.801i) q^{24} +(-13.1790 - 624.861i) q^{25} +(824.420 + 139.630i) q^{26} -787.729i q^{27} +(-5.65469 + 5.65469i) q^{28} -882.436 q^{29} +(-972.188 + 10.2511i) q^{30} +(-277.713 - 277.713i) q^{31} +(-697.770 + 697.770i) q^{32} +(-796.791 - 796.791i) q^{33} +(-1663.77 + 1663.77i) q^{34} +(23.5753 - 0.248588i) q^{35} -162.963i q^{36} +(-1541.57 - 1541.57i) q^{37} +835.320 q^{38} +(-1082.96 + 769.256i) q^{39} +(930.150 - 9.80789i) q^{40} +(717.329 + 717.329i) q^{41} -36.6755i q^{42} +424.929 q^{43} +(-859.597 - 859.597i) q^{44} +(-336.128 + 343.292i) q^{45} +(-2353.20 + 2353.20i) q^{46} +(2544.10 + 2544.10i) q^{47} -2513.44i q^{48} -2400.11i q^{49} +(2232.22 + 2140.00i) q^{50} -3737.97i q^{51} +(-1168.32 + 829.891i) q^{52} -905.185i q^{53} +(2755.91 + 2755.91i) q^{54} +(37.7891 + 3583.80i) q^{55} +35.0897i q^{56} +(-938.352 + 938.352i) q^{57} +(3087.25 - 3087.25i) q^{58} +(-2440.68 + 2440.68i) q^{59} +(1165.76 - 1190.61i) q^{60} -100.063 q^{61} +1943.18 q^{62} +(-12.8155 - 12.8155i) q^{63} +233.952i q^{64} +(4172.88 + 661.567i) q^{65} +5575.23 q^{66} +(-1645.41 + 1645.41i) q^{67} -4032.61i q^{68} -5286.90i q^{69} +(-81.6099 + 83.3493i) q^{70} +(-4899.65 - 4899.65i) q^{71} +(-505.627 - 505.627i) q^{72} +(-1688.57 - 1688.57i) q^{73} +10786.5 q^{74} +(-4911.50 + 103.589i) q^{75} +(-1012.32 + 1012.32i) q^{76} -135.198 q^{77} +(1097.51 - 6480.07i) q^{78} +6932.71 q^{79} +(-5592.87 + 5712.07i) q^{80} -4635.01 q^{81} -5019.23 q^{82} +(3646.07 - 3646.07i) q^{83} +(44.4467 + 44.4467i) q^{84} +(-8317.68 + 8494.96i) q^{85} +(-1486.64 + 1486.64i) q^{86} +6936.09i q^{87} -5334.16 q^{88} +(9362.98 - 9362.98i) q^{89} +(-25.0639 - 2376.99i) q^{90} +(-26.6144 + 157.140i) q^{91} -5703.63i q^{92} +(-2182.86 + 2182.86i) q^{93} -17801.3 q^{94} +(4220.52 - 44.5029i) q^{95} +(5484.58 + 5484.58i) q^{96} +(3863.26 - 3863.26i) q^{97} +(8396.91 + 8396.91i) q^{98} +(1948.14 - 1948.14i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9}+O(q^{10}) $ 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9	$ 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9} + 8 q^{11} + 424 q^{14} - 508 q^{15} - 3128 q^{16} + 268 q^{19} + 2116 q^{20} - 668 q^{21} + 2032 q^{24} + 1100 q^{26} - 3704 q^{29} - 1660 q^{31} + 1252 q^{34} + 6692 q^{35} + 7408 q^{39} + 3644 q^{40} + 5960 q^{41} + 1444 q^{44} - 8674 q^{45} + 17620 q^{46} - 3928 q^{50} - 30588 q^{54} + 14784 q^{55} - 5548 q^{59} - 13976 q^{60} - 20008 q^{61} - 15614 q^{65} + 24752 q^{66} + 26908 q^{70} - 16360 q^{71} - 7304 q^{74} - 5760 q^{76} - 9536 q^{79} - 62348 q^{80} - 36516 q^{81} + 66564 q^{84} - 11604 q^{85} - 5264 q^{86} - 940 q^{89} + 37644 q^{91} + 55448 q^{94} - 61644 q^{96} + 16140 q^{99}+O(q^{100}) $ 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9 + 8 * q^11 + 424 * q^14 - 508 * q^15 - 3128 * q^16 + 268 * q^19 + 2116 * q^20 - 668 * q^21 + 2032 * q^24 + 1100 * q^26 - 3704 * q^29 - 1660 * q^31 + 1252 * q^34 + 6692 * q^35 + 7408 * q^39 + 3644 * q^40 + 5960 * q^41 + 1444 * q^44 - 8674 * q^45 + 17620 * q^46 - 3928 * q^50 - 30588 * q^54 + 14784 * q^55 - 5548 * q^59 - 13976 * q^60 - 20008 * q^61 - 15614 * q^65 + 24752 * q^66 + 26908 * q^70 - 16360 * q^71 - 7304 * q^74 - 5760 * q^76 - 9536 * q^79 - 62348 * q^80 - 36516 * q^81 + 66564 * q^84 - 11604 * q^85 - 5264 * q^86 - 940 * q^89 + 37644 * q^91 + 55448 * q^94 - 61644 * q^96 + 16140 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−3.49855	+	3.49855i	−0.874638	+	0.874638i	−0.992974	−	0.118336i	$-0.962244\pi$
$2$	−3.49855	+	3.49855i	−0.874638	+	0.874638i	0.118336	+	0.992974i	$0.462244\pi$
$3$		−	7.86015i		−	0.873350i	−0.899619	−	0.436675i	$-0.856156\pi$
$3$		−	7.86015i		−	0.873350i	0.899619	−	0.436675i	$-0.143844\pi$
$4$		−	8.47972i		−	0.529982i
$5$	−17.4903	+	17.8631i	−0.699612	+	0.714523i
$5$	−17.4903	+	17.8631i	−0.699612	+	0.714523i
$6$	27.4991	+	27.4991i	0.763865	+	0.763865i
$7$	−0.666849	−	0.666849i	−0.0136092	−	0.0136092i	0.700269	−	0.713879i	$-0.253063\pi$
$7$	−0.666849	−	0.666849i	−0.0136092	−	0.0136092i	−0.713879	+	0.700269i	$0.753063\pi$
$8$	−26.3101	−	26.3101i	−0.411095	−	0.411095i
$9$	19.2180			0.237259
$10$	−1.30419	−	123.686i	−0.0130419	−	1.23686i
$11$	101.371	−	101.371i	0.837776	−	0.837776i	−0.150790	−	0.988566i	$-0.548182\pi$
$11$	101.371	−	101.371i	0.837776	−	0.837776i	0.988566	+	0.150790i	$0.0481816\pi$
$12$	−66.6519			−0.462860
$13$	−97.8678	−	137.778i	−0.579099	−	0.815257i
$13$	−97.8678	−	137.778i	−0.579099	−	0.815257i
$14$	4.66601			0.0238062
$15$	140.407	+	137.476i	0.624029	+	0.611006i
$16$	319.770			1.24910
$17$	475.560			1.64554			0.822768	−	0.568377i	$-0.192429\pi$
$17$	475.560			1.64554			0.822768	+	0.568377i	$0.192429\pi$
$18$	−67.2351	+	67.2351i	−0.207516	+	0.207516i
$19$	−119.381	−	119.381i	−0.330695	−	0.330695i	0.522155	−	0.852850i	$-0.325128\pi$
$19$	−119.381	−	119.381i	−0.330695	−	0.330695i	−0.852850	+	0.522155i	$0.825128\pi$
$20$	151.474	+	148.313i	0.378685	+	0.370782i
$21$	−5.24153	+	5.24153i	−0.0118856	+	0.0118856i
$22$			709.303i			1.46550i
$23$	672.620			1.27149			0.635747	−	0.771898i	$-0.280692\pi$
$23$	672.620			1.27149			0.635747	+	0.771898i	$0.280692\pi$
$24$	−206.801	+	206.801i	−0.359030	+	0.359030i
$25$	−13.1790	−	624.861i	−0.0210865	−	0.999778i
$26$	824.420	+	139.630i	1.21956	+	0.206553i
$27$		−	787.729i		−	1.08056i
$28$	−5.65469	+	5.65469i	−0.00721261	+	0.00721261i
$29$	−882.436			−1.04927			−0.524635	−	0.851327i	$-0.675798\pi$
$29$	−882.436			−1.04927			−0.524635	+	0.851327i	$0.675798\pi$
$30$	−972.188	+	10.2511i	−1.08021	+	0.0113902i
$31$	−277.713	−	277.713i	−0.288983	−	0.288983i	0.547695	−	0.836678i	$-0.315505\pi$
$31$	−277.713	−	277.713i	−0.288983	−	0.288983i	−0.836678	+	0.547695i	$0.815505\pi$
$32$	−697.770	+	697.770i	−0.681416	+	0.681416i
$33$	−796.791	−	796.791i	−0.731672	−	0.731672i
$34$	−1663.77	+	1663.77i	−1.43925	+	1.43925i
$35$	23.5753	−	0.248588i	0.0192452	−	0.000202929i
$36$		−	162.963i		−	0.125743i
$37$	−1541.57	−	1541.57i	−1.12605	−	1.12605i	−0.990813	−	0.135240i	$-0.956819\pi$
$37$	−1541.57	−	1541.57i	−1.12605	−	1.12605i	−0.135240	−	0.990813i	$-0.543181\pi$
$38$	835.320			0.578477
$39$	−1082.96	+	769.256i	−0.712005	+	0.505757i
$40$	930.150	−	9.80789i	0.581344	−	0.00612993i
$41$	717.329	+	717.329i	0.426728	+	0.426728i	0.887512	−	0.460784i	$-0.152432\pi$
$41$	717.329	+	717.329i	0.426728	+	0.426728i	−0.460784	+	0.887512i	$0.652432\pi$
$42$		−	36.6755i		−	0.0207911i
$43$	424.929			0.229816			0.114908	−	0.993376i	$-0.463343\pi$
$43$	424.929			0.229816			0.114908	+	0.993376i	$0.463343\pi$
$44$	−859.597	−	859.597i	−0.444007	−	0.444007i
$45$	−336.128	+	343.292i	−0.165989	+	0.169527i
$46$	−2353.20	+	2353.20i	−1.11210	+	1.11210i
$47$	2544.10	+	2544.10i	1.15170	+	1.15170i	0.986212	+	0.165485i	$0.0529190\pi$
$47$	2544.10	+	2544.10i	1.15170	+	1.15170i	0.165485	+	0.986212i	$0.447081\pi$
$48$		−	2513.44i		−	1.09090i
$49$		−	2400.11i		−	0.999630i
$50$	2232.22	+	2140.00i	0.892886	+	0.856000i
$51$		−	3737.97i		−	1.43713i
$52$	−1168.32	+	829.891i	−0.432072	+	0.306912i
$53$		−	905.185i		−	0.322245i	−0.986934	−	0.161122i	$-0.948489\pi$
$53$		−	905.185i		−	0.322245i	0.986934	−	0.161122i	$-0.0515114\pi$
$54$	2755.91	+	2755.91i	0.945099	+	0.945099i
$55$	37.7891	+	3583.80i	0.0124923	+	1.18473i
$56$			35.0897i			0.0111893i
$57$	−938.352	+	938.352i	−0.288813	+	0.288813i
$58$	3087.25	−	3087.25i	0.917731	−	0.917731i
$59$	−2440.68	+	2440.68i	−0.701143	+	0.701143i	−0.964656	−	0.263513i	$-0.915119\pi$
$59$	−2440.68	+	2440.68i	−0.701143	+	0.701143i	0.263513	+	0.964656i	$0.415119\pi$
$60$	1165.76	−	1190.61i	0.323823	−	0.330724i
$61$	−100.063			−0.0268915			−0.0134457	−	0.999910i	$-0.504280\pi$
$61$	−100.063			−0.0268915			−0.0134457	+	0.999910i	$0.504280\pi$
$62$	1943.18			0.505511
$63$	−12.8155	−	12.8155i	−0.00322889	−	0.00322889i
$64$			233.952i			0.0571172i
$65$	4172.88	+	661.567i	0.987665	+	0.156584i
$66$	5575.23			1.27990
$67$	−1645.41	+	1645.41i	−0.366543	+	0.366543i	−0.866215	−	0.499672i	$-0.833454\pi$
$67$	−1645.41	+	1645.41i	−0.366543	+	0.366543i	0.499672	+	0.866215i	$0.333454\pi$
$68$		−	4032.61i		−	0.872105i
$69$		−	5286.90i		−	1.11046i
$70$	−81.6099	+	83.3493i	−0.0166551	+	0.0170101i
$71$	−4899.65	−	4899.65i	−0.971960	−	0.971960i	0.0276577	−	0.999617i	$-0.491195\pi$
$71$	−4899.65	−	4899.65i	−0.971960	−	0.971960i	−0.999617	+	0.0276577i	$0.991195\pi$
$72$	−505.627	−	505.627i	−0.0975360	−	0.0975360i
$73$	−1688.57	−	1688.57i	−0.316864	−	0.316864i	0.530697	−	0.847561i	$-0.321930\pi$
$73$	−1688.57	−	1688.57i	−0.316864	−	0.316864i	−0.847561	+	0.530697i	$0.821930\pi$
$74$	10786.5			1.96978
$75$	−4911.50	+	103.589i	−0.873156	+	0.0184159i
$76$	−1012.32	+	1012.32i	−0.175263	+	0.175263i
$77$	−135.198			−0.0228029
$78$	1097.51	−	6480.07i	0.180393	−	1.06510i
$79$	6932.71			1.11083			0.555417	−	0.831572i	$-0.312559\pi$
$79$	6932.71			1.11083			0.555417	+	0.831572i	$0.312559\pi$
$80$	−5592.87	+	5712.07i	−0.873886	+	0.892512i
$81$	−4635.01			−0.706449
$82$	−5019.23			−0.746464
$83$	3646.07	−	3646.07i	0.529260	−	0.529260i	−0.391092	−	0.920352i	$-0.627903\pi$
$83$	3646.07	−	3646.07i	0.529260	−	0.529260i	0.920352	+	0.391092i	$0.127903\pi$
$84$	44.4467	+	44.4467i	0.00629914	+	0.00629914i
$85$	−8317.68	+	8494.96i	−1.15124	+	1.17577i
$86$	−1486.64	+	1486.64i	−0.201006	+	0.201006i
$87$			6936.09i			0.916381i
$88$	−5334.16			−0.688812
$89$	9362.98	−	9362.98i	1.18205	−	1.18205i	0.202832	−	0.979214i	$-0.434985\pi$
$89$	9362.98	−	9362.98i	1.18205	−	1.18205i	0.979214	−	0.202832i	$-0.0650146\pi$
$90$	−25.0639	−	2376.99i	−0.00309431	−	0.293455i
$91$	−26.6144	+	157.140i	−0.00321391	+	0.0189760i
$92$		−	5703.63i		−	0.673869i
$93$	−2182.86	+	2182.86i	−0.252383	+	0.252383i
$94$	−17801.3			−2.01464
$95$	4220.52	−	44.5029i	0.467647	−	0.00493107i
$96$	5484.58	+	5484.58i	0.595115	+	0.595115i
$97$	3863.26	−	3863.26i	0.410592	−	0.410592i	−0.471353	−	0.881945i	$-0.656234\pi$
$97$	3863.26	−	3863.26i	0.410592	−	0.410592i	0.881945	+	0.471353i	$0.156234\pi$
$98$	8396.91	+	8396.91i	0.874314	+	0.874314i
$99$	1948.14	−	1948.14i	0.198770	−	0.198770i
$100$	−5298.65	+	111.755i	−0.529865	+	0.0111755i
$101$		−	849.250i		−	0.0832516i	−0.999133	−	0.0416258i	$-0.986746\pi$
$101$		−	849.250i		−	0.0832516i	0.999133	−	0.0416258i	$-0.0132537\pi$
$102$	13077.5	+	13077.5i	1.25697	+	1.25697i
$103$	10168.3			0.958457			0.479228	−	0.877690i	$-0.340917\pi$
$103$	10168.3			0.958457			0.479228	+	0.877690i	$0.340917\pi$
$104$	−1050.05	+	6199.87i	−0.0970834	+	0.573213i
$105$	−1.95394	−	185.306i	−0.000177228	−	0.0168078i
$106$	3166.84	+	3166.84i	0.281847	+	0.281847i
$107$		−	2736.43i		−	0.239011i	−0.992834	−	0.119505i	$-0.961869\pi$
$107$		−	2736.43i		−	0.239011i	0.992834	−	0.119505i	$-0.0381309\pi$
$108$	−6679.72			−0.572678
$109$	7068.64	+	7068.64i	0.594953	+	0.594953i	0.938965	−	0.344012i	$-0.111786\pi$
$109$	7068.64	+	7068.64i	0.594953	+	0.594953i	−0.344012	+	0.938965i	$0.611786\pi$
$110$	−12670.3	−	12405.9i	−1.04713	−	1.02528i
$111$	−12117.0	+	12117.0i	−0.983439	+	0.983439i
$112$	−213.238	−	213.238i	−0.0169992	−	0.0169992i
$113$			613.106i			0.0480152i	0.999712	+	0.0240076i	$0.00764259\pi$
$113$			613.106i			0.0480152i	−0.999712	+	0.0240076i	$0.992357\pi$
$114$		−	6565.75i		−	0.505213i
$115$	−11764.3	+	12015.1i	−0.889552	+	0.908511i
$116$			7482.81i			0.556095i
$117$	−1880.82	−	2647.82i	−0.137396	−	0.193427i
$118$		−	17077.7i		−	1.22649i
$119$	−317.126	−	317.126i	−0.0223944	−	0.0223944i
$120$	−77.0915	−	7311.13i	−0.00535358	−	0.507717i
$121$		−	5911.13i		−	0.403738i
$122$	350.076	−	350.076i	0.0235203	−	0.0235203i
$123$	5638.32	−	5638.32i	0.372683	−	0.372683i
$124$	−2354.93	+	2354.93i	−0.153156	+	0.153156i
$125$	11392.4	+	10693.6i	0.729117	+	0.684390i
$126$	89.6712			0.00564823
$127$	−25149.7			−1.55929			−0.779643	−	0.626224i	$-0.784600\pi$
$127$	−25149.7			−1.55929			−0.779643	+	0.626224i	$0.784600\pi$
$128$	−11982.8	−	11982.8i	−0.731373	−	0.731373i
$129$		−	3340.01i		−	0.200710i
$130$	−16913.6	+	12284.5i	−1.00080	+	0.726895i
$131$	8557.78			0.498676			0.249338	−	0.968417i	$-0.419787\pi$
$131$	8557.78			0.498676			0.249338	+	0.968417i	$0.419787\pi$
$132$	−6756.56	+	6756.56i	−0.387773	+	0.387773i
$133$			159.218i			0.00900096i
$134$		−	11513.1i		−	0.641184i
$135$	14071.3	+	13777.6i	0.772086	+	0.755973i
$136$	−12512.0	−	12512.0i	−0.676472	−	0.676472i
$137$	−7077.02	−	7077.02i	−0.377059	−	0.377059i	0.492981	−	0.870040i	$-0.335907\pi$
$137$	−7077.02	−	7077.02i	−0.377059	−	0.377059i	−0.870040	+	0.492981i	$0.835907\pi$
$138$	18496.5	+	18496.5i	0.971250	+	0.971250i
$139$	−24792.3			−1.28318			−0.641588	−	0.767049i	$-0.721724\pi$
$139$	−24792.3			−1.28318			−0.641588	+	0.767049i	$0.721724\pi$
$140$	−2.10796	−	199.912i	−0.000107549	−	0.0101996i
$141$	19997.0	−	19997.0i	1.00584	−	1.00584i
$142$	34283.3			1.70023
$143$	−23887.7	−	4045.78i	−1.16816	−	0.197848i
$144$	6145.33			0.296360
$145$	15434.1	−	15763.0i	0.734082	−	0.749728i
$146$	11815.1			0.554282
$147$	−18865.2			−0.873027
$148$	−13072.0	+	13072.0i	−0.596788	+	0.596788i
$149$	23807.7	+	23807.7i	1.07237	+	1.07237i	0.997168	+	0.0752046i	$0.0239610\pi$
$149$	23807.7	+	23807.7i	1.07237	+	1.07237i	0.0752046	+	0.997168i	$0.476039\pi$
$150$	16820.7	−	17545.6i	0.747588	−	0.779803i
$151$	−917.365	+	917.365i	−0.0402336	+	0.0402336i	−0.726937	−	0.686704i	$-0.759057\pi$
$151$	−917.365	+	917.365i	−0.0402336	+	0.0402336i	0.686704	+	0.726937i	$0.259057\pi$
$152$			6281.85i			0.271894i
$153$	9139.30			0.390418
$154$	472.998	−	472.998i	0.0199442	−	0.0199442i
$155$	9818.08	−	103.526i	0.408661	−	0.00430909i
$156$	6523.07	+	9183.19i	0.268042	+	0.377350i
$157$		−	14677.5i		−	0.595462i	−0.954650	−	0.297731i	$-0.903770\pi$
$157$		−	14677.5i		−	0.595462i	0.954650	−	0.297731i	$-0.0962298\pi$
$158$	−24254.4	+	24254.4i	−0.971577	+	0.971577i
$159$	−7114.89			−0.281432
$160$	−260.115	−	24668.5i	−0.0101607	−	0.963614i
$161$	−448.536	−	448.536i	−0.0173040	−	0.0173040i
$162$	16215.8	−	16215.8i	0.617887	−	0.617887i
$163$	19032.2	+	19032.2i	0.716332	+	0.716332i	0.967852	−	0.251520i	$-0.0809304\pi$
$163$	19032.2	+	19032.2i	0.716332	+	0.716332i	−0.251520	+	0.967852i	$0.580930\pi$
$164$	6082.75	−	6082.75i	0.226158	−	0.226158i
$165$	28169.3	−	297.028i	1.03468	−	0.0109101i
$166$			25511.9i			0.925821i
$167$	−10903.4	−	10903.4i	−0.390958	−	0.390958i	0.484071	−	0.875029i	$-0.339158\pi$
$167$	−10903.4	−	10903.4i	−0.390958	−	0.390958i	−0.875029	+	0.484071i	$0.839158\pi$
$168$	275.810			0.00977219
$169$	−9404.80	+	26968.1i	−0.329288	+	0.944229i
$170$	−620.221	−	58819.9i	−0.0214609	−	2.03529i
$171$	−2294.26	−	2294.26i	−0.0784604	−	0.0784604i
$172$		−	3603.28i		−	0.121798i
$173$	−7796.98			−0.260516			−0.130258	−	0.991480i	$-0.541581\pi$
$173$	−7796.98			−0.260516			−0.130258	+	0.991480i	$0.541581\pi$
$174$	−24266.3	−	24266.3i	−0.801501	−	0.801501i
$175$	−407.899	+	425.476i	−0.0133192	+	0.0138931i
$176$	32415.4	−	32415.4i	1.04647	−	1.04647i
$177$	19184.1	+	19184.1i	0.612343	+	0.612343i
$178$			65513.7i			2.06772i
$179$		−	3197.57i		−	0.0997961i	−0.998754	−	0.0498980i	$-0.984110\pi$
$179$		−	3197.57i		−	0.0997961i	0.998754	−	0.0498980i	$-0.0158896\pi$
$180$	2911.02	+	2850.27i	0.0898463	+	0.0879713i
$181$		−	15298.1i		−	0.466960i	−0.972362	−	0.233480i	$-0.924989\pi$
$181$		−	15298.1i		−	0.466960i	0.972362	−	0.233480i	$-0.0750113\pi$
$182$	−456.652	−	642.875i	−0.0137861	−	0.0194081i
$183$			786.512i			0.0234857i
$184$	−17696.7	−	17696.7i	−0.522705	−	0.522705i
$185$	54499.6	−	574.666i	1.59239	−	0.0167908i
$186$		−	15273.7i		−	0.441488i
$187$	48207.9	−	48207.9i	1.37859	−	1.37859i
$188$	21573.2	−	21573.2i	0.610379	−	0.610379i
$189$	−525.296	+	525.296i	−0.0147055	+	0.0147055i
$190$	−14610.0	+	14921.4i	−0.404709	+	0.413335i
$191$	−58870.0			−1.61372			−0.806858	−	0.590746i	$-0.798834\pi$
$191$	−58870.0			−1.61372			−0.806858	+	0.590746i	$0.798834\pi$
$192$	1838.90			0.0498833
$193$	28423.9	+	28423.9i	0.763079	+	0.763079i	0.976878	−	0.213799i	$-0.0685837\pi$
$193$	28423.9	+	28423.9i	0.763079	+	0.763079i	−0.213799	+	0.976878i	$0.568584\pi$
$194$			27031.6i			0.718238i
$195$	5200.02	−	32799.5i	0.136753	−	0.862577i
$196$	−20352.3			−0.529786
$197$	−51764.0	+	51764.0i	−1.33381	+	1.33381i	−0.431887	+	0.901928i	$0.642152\pi$
$197$	−51764.0	+	51764.0i	−1.33381	+	1.33381i	−0.901928	+	0.431887i	$0.857848\pi$
$198$			13631.4i			0.347703i
$199$			57673.6i			1.45637i	0.685382	+	0.728184i	$0.259635\pi$
$199$			57673.6i			1.45637i	−0.685382	+	0.728184i	$0.740365\pi$
$200$	−16093.4	+	16786.9i	−0.402335	+	0.419672i
$201$	12933.2	+	12933.2i	0.320120	+	0.320120i
$202$	2971.14	+	2971.14i	0.0728150	+	0.0728150i
$203$	588.452	+	588.452i	0.0142797	+	0.0142797i
$204$	−31697.0			−0.761653
$205$	−25360.0	+	267.406i	−0.603451	+	0.00636303i
$206$	−35574.2	+	35574.2i	−0.838302	+	0.838302i
$207$	12926.4			0.301673
$208$	−31295.2	−	44057.4i	−0.723353	−	1.01834i
$209$	−24203.5			−0.554097
$210$	655.138	+	641.466i	0.0148557	+	0.0145457i
$211$	41987.4			0.943092			0.471546	−	0.881842i	$-0.343696\pi$
$211$	41987.4			0.943092			0.471546	+	0.881842i	$0.343696\pi$
$212$	−7675.71			−0.170784
$213$	−38512.0	+	38512.0i	−0.848862	+	0.848862i
$214$	9573.55	+	9573.55i	0.209048	+	0.209048i
$215$	−7432.14	+	7590.55i	−0.160782	+	0.164209i
$216$	−20725.2	+	20725.2i	−0.444213	+	0.444213i
$217$			370.385i			0.00786563i
$218$	−49460.0			−1.04074
$219$	−13272.4	+	13272.4i	−0.276733	+	0.276733i
$220$	30389.6	−	320.441i	0.627885	−	0.00662068i
$221$	−46542.0	−	65521.9i	−0.952929	−	1.34153i
$222$		−	84783.5i		−	1.72031i
$223$	−35335.1	+	35335.1i	−0.710553	+	0.710553i	−0.966651	−	0.256098i	$-0.917563\pi$
$223$	−35335.1	+	35335.1i	−0.710553	+	0.710553i	0.256098	+	0.966651i	$0.417563\pi$
$224$	930.614			0.0185470
$225$	−253.275	−	12008.6i	−0.00500295	−	0.237206i
$226$	−2144.98	−	2144.98i	−0.0419959	−	0.0419959i
$227$	−21448.5	+	21448.5i	−0.416241	+	0.416241i	−0.883906	−	0.467665i	$-0.845095\pi$
$227$	−21448.5	+	21448.5i	−0.416241	+	0.416241i	0.467665	+	0.883906i	$0.345095\pi$
$228$	7956.96	+	7956.96i	0.153066	+	0.153066i
$229$	31124.5	−	31124.5i	0.593515	−	0.593515i	−0.345064	−	0.938579i	$-0.612143\pi$
$229$	31124.5	−	31124.5i	0.593515	−	0.593515i	0.938579	+	0.345064i	$0.112143\pi$
$230$	−877.225	−	83193.4i	−0.0165827	−	1.57265i
$231$			1062.68i			0.0199149i
$232$	23217.0	+	23217.0i	0.431350	+	0.431350i
$233$	−14989.2			−0.276100			−0.138050	−	0.990425i	$-0.544084\pi$
$233$	−14989.2			−0.276100			−0.138050	+	0.990425i	$0.544084\pi$
$234$	15843.7	+	2683.40i	0.289351	+	0.0490065i
$235$	−89942.5	+	948.390i	−1.62866	+	0.0171732i
$236$	20696.3	+	20696.3i	0.371593	+	0.371593i
$237$		−	54492.2i		−	0.970147i
$238$	2218.97			0.0391739
$239$	−29807.2	−	29807.2i	−0.521825	−	0.521825i	0.396297	−	0.918122i	$-0.370295\pi$
$239$	−29807.2	−	29807.2i	−0.521825	−	0.521825i	−0.918122	+	0.396297i	$0.870295\pi$
$240$	44897.8	+	43960.8i	0.779475	+	0.763209i
$241$	24793.1	−	24793.1i	0.426871	−	0.426871i	−0.460690	−	0.887561i	$-0.652398\pi$
$241$	24793.1	−	24793.1i	0.426871	−	0.426871i	0.887561	+	0.460690i	$0.152398\pi$
$242$	20680.4	+	20680.4i	0.353124	+	0.353124i
$243$		−	27374.1i		−	0.463583i
$244$			848.508i			0.0142520i
$245$	42873.4	+	41978.6i	0.714258	+	0.699353i
$246$			39451.9i			0.651925i
$247$	−4764.58	+	28131.7i	−0.0780963	+	0.461107i
$248$			14613.3i			0.237599i
$249$	−28658.7	−	28658.7i	−0.462229	−	0.462229i
$250$	−77269.1	+	2445.00i	−1.23631	+	0.0391199i
$251$			94489.3i			1.49981i	0.661548	+	0.749903i	$0.269900\pi$
$251$			94489.3i			1.49981i	−0.661548	+	0.749903i	$0.730100\pi$
$252$	−108.672	+	108.672i	−0.00171126	+	0.00171126i
$253$	68184.1	−	68184.1i	1.06523	−	1.06523i
$254$	87987.6	−	87987.6i	1.36381	−	1.36381i
$255$	66771.7	+	65378.3i	1.02686	+	1.00543i
$256$	80101.7			1.22225
$257$	45506.8			0.688986			0.344493	−	0.938789i	$-0.388051\pi$
$257$	45506.8			0.688986			0.344493	+	0.938789i	$0.388051\pi$
$258$	11685.2	+	11685.2i	0.175548	+	0.175548i
$259$			2055.98i			0.0306493i
$260$	5609.90	−	35384.9i	0.0829867	−	0.523445i
$261$	−16958.6			−0.248949
$262$	−29939.8	+	29939.8i	−0.436161	+	0.436161i
$263$			66296.7i			0.958474i	0.877686	+	0.479237i	$0.159087\pi$
$263$			66296.7i			0.958474i	−0.877686	+	0.479237i	$0.840913\pi$
$264$			41927.3i			0.601574i
$265$	16169.4	+	15832.0i	0.230251	+	0.225446i
$266$	−557.032	−	557.032i	−0.00787258	−	0.00787258i
$267$	−73594.5	−	73594.5i	−1.03234	−	1.03234i
$268$	13952.6	+	13952.6i	0.194261	+	0.194261i
$269$	108038.			1.49304			0.746522	−	0.665360i	$-0.231722\pi$
$269$	108038.			1.49304			0.746522	+	0.665360i	$0.231722\pi$
$270$	−97430.7	+	1027.35i	−1.33650	+	0.0140926i
$271$	62524.9	−	62524.9i	0.851362	−	0.851362i	−0.138939	−	0.990301i	$-0.544369\pi$
$271$	62524.9	−	62524.9i	0.851362	−	0.851362i	0.990301	+	0.138939i	$0.0443691\pi$
$272$	152070.			2.05544
$273$	1235.15	+	209.193i	0.0165727	+	0.00280687i
$274$	49518.6			0.659580
$275$	−64678.7	−	62006.8i	−0.855256	−	0.819924i
$276$	−44831.4			−0.588524
$277$	−118333.			−1.54222			−0.771109	−	0.636703i	$-0.780298\pi$
$277$	−118333.			−1.54222			−0.771109	+	0.636703i	$0.780298\pi$
$278$	86737.0	−	86737.0i	1.12231	−	1.12231i
$279$	−5337.08	−	5337.08i	−0.0685638	−	0.0685638i
$280$	−626.810	−	613.729i	−0.00799503	−	0.00782818i
$281$	−2487.18	+	2487.18i	−0.0314989	+	0.0314989i	−0.722681	−	0.691182i	$-0.757090\pi$
$281$	−2487.18	+	2487.18i	−0.0314989	+	0.0314989i	0.691182	+	0.722681i	$0.257090\pi$
$282$			139921.i			1.75948i
$283$	47285.5			0.590412			0.295206	−	0.955434i	$-0.404612\pi$
$283$	47285.5			0.590412			0.295206	+	0.955434i	$0.404612\pi$
$284$	−41547.6	+	41547.6i	−0.515122	+	0.515122i
$285$	−349.799	−	33173.9i	−0.00430655	−	0.408420i
$286$	97726.6	−	69417.9i	1.19476	−	0.848671i
$287$		−	956.700i		−	0.0116148i
$288$	−13409.7	+	13409.7i	−0.161672	+	0.161672i
$289$	142636.			1.70779
$290$	1150.87	+	109145.i	0.0136845	+	1.29780i
$291$	−30365.8	−	30365.8i	−0.358591	−	0.358591i
$292$	−14318.6	+	14318.6i	−0.167932	+	0.167932i
$293$	85100.6	+	85100.6i	0.991282	+	0.991282i	0.999962	−	0.00868035i	$-0.00276308\pi$
$293$	85100.6	+	85100.6i	0.991282	+	0.991282i	−0.00868035	+	0.999962i	$0.502763\pi$
$294$	66001.0	−	66001.0i	0.763582	−	0.763582i
$295$	−909.837	−	86286.2i	−0.0104549	−	0.991511i
$296$			81117.5i			0.925830i
$297$	−79852.8	−	79852.8i	−0.905268	−	0.905268i
$298$	−166585.			−1.87588
$299$	−65827.8	−	92672.5i	−0.736321	−	1.03659i
$300$	878.408	+	41648.2i	0.00976009	+	0.462757i
$301$	−283.364	−	283.364i	−0.00312760	−	0.00312760i
$302$		−	6418.90i		−	0.0703796i
$303$	−6675.23			−0.0727078
$304$	−38174.4	−	38174.4i	−0.413072	−	0.413072i
$305$	1750.14	−	1787.44i	0.0188136	−	0.0192146i
$306$	−31974.3	+	31974.3i	−0.341474	+	0.341474i
$307$	−46525.4	−	46525.4i	−0.493643	−	0.493643i	0.415809	−	0.909452i	$-0.363499\pi$
$307$	−46525.4	−	46525.4i	−0.493643	−	0.493643i	−0.909452	+	0.415809i	$0.863499\pi$
$308$			1146.44i			0.0120851i
$309$		−	79924.1i		−	0.837069i
$310$	−33986.9	+	34711.2i	−0.353661	+	0.361199i
$311$			46835.6i			0.484234i	0.970247	+	0.242117i	$0.0778417\pi$
$311$			46835.6i			0.484234i	−0.970247	+	0.242117i	$0.922158\pi$
$312$	48732.0	+	8253.59i	0.500616	+	0.0847878i
$313$		−	138394.i		−	1.41263i	−0.707899	−	0.706314i	$-0.750357\pi$
$313$		−	138394.i		−	1.41263i	0.707899	−	0.706314i	$-0.249643\pi$
$314$	51350.1	+	51350.1i	0.520813	+	0.520813i
$315$	453.071	−	4.77736i	0.00456609	−	4.81467e-5i
$316$		−	58787.4i		−	0.588722i
$317$	−38831.3	+	38831.3i	−0.386424	+	0.386424i	−0.873410	−	0.486986i	$-0.838096\pi$
$317$	−38831.3	+	38831.3i	−0.386424	+	0.386424i	0.486986	+	0.873410i	$0.338096\pi$
$318$	24891.8	−	24891.8i	0.246151	−	0.246151i
$319$	−89453.4	+	89453.4i	−0.879054	+	0.879054i
$320$	−4179.10	−	4091.89i	−0.0408115	−	0.0399599i
$321$	−21508.8			−0.208740
$322$	3138.45			0.0302694
$323$	−56772.8	−	56772.8i	−0.544171	−	0.544171i
$324$			39303.6i			0.374406i
$325$	−84802.6	+	62969.5i	−0.802865	+	0.596161i
$326$	−133170.			−1.25306
$327$	55560.6	−	55560.6i	0.519603	−	0.519603i
$328$		−	37746.0i		−	0.350851i
$329$		−	3393.06i		−	0.0313473i
$330$	−97512.4	+	99590.7i	−0.895431	+	0.914515i
$331$	31464.6	+	31464.6i	0.287188	+	0.287188i	0.835967	−	0.548779i	$-0.184907\pi$
$331$	31464.6	+	31464.6i	0.287188	+	0.287188i	−0.548779	+	0.835967i	$0.684907\pi$
$332$	−30917.7	−	30917.7i	−0.280498	−	0.280498i
$333$	−29625.8	−	29625.8i	−0.267166	−	0.267166i
$334$	76292.3			0.683893
$335$	−613.377	−	58170.8i	−0.00546560	−	0.518341i
$336$	−1676.08	+	1676.08i	−0.0148463	+	0.0148463i
$337$	84905.0			0.747607			0.373804	−	0.927508i	$-0.378053\pi$
$337$	84905.0			0.747607			0.373804	+	0.927508i	$0.378053\pi$
$338$	−61446.2	−	127253.i	−0.537851	−	1.11387i
$339$	4819.11			0.0419341
$340$	72034.9	+	70531.6i	0.623139	+	0.610135i
$341$	−56304.0			−0.484206
$342$	16053.2			0.137249
$343$	−3201.61	+	3201.61i	−0.0272133	+	0.0272133i
$344$	−11179.9	−	11179.9i	−0.0944761	−	0.0944761i
$345$	94440.2	+	92469.4i	0.793449	+	0.776891i
$346$	27278.1	−	27278.1i	0.227857	−	0.227857i
$347$			198081.i			1.64507i	0.568718	+	0.822533i	$0.307440\pi$
$347$			198081.i			1.64507i	−0.568718	+	0.822533i	$0.692560\pi$
$348$	58816.1			0.485666
$349$	−80038.4	+	80038.4i	−0.657125	+	0.657125i	−0.954699	−	0.297574i	$-0.903822\pi$
$349$	−80038.4	+	80038.4i	−0.657125	+	0.657125i	0.297574	+	0.954699i	$0.403822\pi$
$350$	−61.4935	−	2915.61i	−0.000501988	−	0.0238009i
$351$	−108532.	+	77093.2i	−0.880935	+	0.625752i
$352$			141467.i			1.14175i
$353$	131280.	−	131280.i	1.05353	−	1.05353i	0.0550483	−	0.998484i	$-0.482469\pi$
$353$	131280.	−	131280.i	1.05353	−	1.05353i	0.998484	−	0.0550483i	$-0.0175313\pi$
$354$	−134233.			−1.07116
$355$	173219.	−	1826.49i	1.37448	−	0.0144931i
$356$	−79395.5	−	79395.5i	−0.626463	−	0.626463i
$357$	−2492.66	+	2492.66i	−0.0195581	+	0.0195581i
$358$	11186.8	+	11186.8i	0.0872854	+	0.0872854i
$359$	−129103.	+	129103.i	−1.00172	+	1.00172i	−0.00172601	+	0.999999i	$0.500549\pi$
$359$	−129103.	+	129103.i	−1.00172	+	1.00172i	−0.999999	+	0.00172601i	$0.999451\pi$
$360$	17875.6	−	188.488i	0.137929	−	0.00145438i
$361$		−	101817.i		−	0.781282i
$362$	53521.0	+	53521.0i	0.408420	+	0.408420i
$363$	−46462.4			−0.352605
$364$	1332.51	+	225.683i	0.0100570	+	0.00170332i
$365$	59696.6	−	629.465i	0.448088	−	0.00472483i
$366$	−2751.65	−	2751.65i	−0.0205415	−	0.0205415i
$367$			19143.6i			0.142132i	0.997472	+	0.0710659i	$0.0226401\pi$
$367$			19143.6i			0.142132i	−0.997472	+	0.0710659i	$0.977360\pi$
$368$	215084.			1.58822
$369$	13785.6	+	13785.6i	0.101245	+	0.101245i
$370$	−188659.	+	192680.i	−1.37808	+	1.40745i
$371$	−603.621	+	603.621i	−0.00438548	+	0.00438548i
$372$	18510.1	+	18510.1i	0.133759	+	0.133759i
$373$			25643.3i			0.184313i	0.995745	+	0.0921566i	$0.0293761\pi$
$373$			25643.3i			0.184313i	−0.995745	+	0.0921566i	$0.970624\pi$
$374$			337316.i			2.41154i
$375$	84053.2	−	89546.4i	0.597712	−	0.636774i
$376$		−	133871.i		−	0.946914i
$377$	86362.1	+	121581.i	0.607632	+	0.855425i
$378$		−	3675.55i		−	0.0257240i
$379$	−58804.3	−	58804.3i	−0.409384	−	0.409384i	0.472140	−	0.881524i	$-0.343482\pi$
$379$	−58804.3	−	58804.3i	−0.409384	−	0.409384i	−0.881524	+	0.472140i	$0.843482\pi$
$380$	−377.372	−	35788.8i	−0.00261338	−	0.247845i
$381$			197681.i			1.36180i
$382$	205960.	−	205960.i	1.41142	−	1.41142i
$383$	91567.4	−	91567.4i	0.624228	−	0.624228i	−0.322382	−	0.946610i	$-0.604483\pi$
$383$	91567.4	−	91567.4i	0.624228	−	0.624228i	0.946610	+	0.322382i	$0.104483\pi$
$384$	−94186.7	+	94186.7i	−0.638745	+	0.638745i
$385$	2364.66	−	2415.05i	0.0159531	−	0.0162932i
$386$	−198885.			−1.33484
$387$	8166.28			0.0545259
$388$	−32759.3	−	32759.3i	−0.217606	−	0.217606i
$389$		−	178648.i		−	1.18059i	−0.807187	−	0.590296i	$-0.799011\pi$
$389$		−	178648.i		−	1.18059i	0.807187	−	0.590296i	$-0.200989\pi$
$390$	96558.2	+	132943.i	0.634834	+	0.874052i
$391$	319871.			2.09229
$392$	−63147.1	+	63147.1i	−0.410943	+	0.410943i
$393$		−	67265.5i		−	0.435519i
$394$		−	362198.i		−	2.33321i
$395$	−121255.	+	123840.i	−0.777152	+	0.793716i
$396$	−16519.7	−	16519.7i	−0.105345	−	0.105345i
$397$	−192792.	−	192792.i	−1.22323	−	1.22323i	−0.966478	−	0.256748i	$-0.917349\pi$
$397$	−192792.	−	192792.i	−1.22323	−	1.22323i	−0.256748	−	0.966478i	$-0.582651\pi$
$398$	−201774.	−	201774.i	−1.27379	−	1.27379i
$399$	1251.48			0.00786099
$400$	−4214.26	−	199812.i	−0.0263391	−	1.24882i
$401$	41186.9	−	41186.9i	0.256136	−	0.256136i	−0.567345	−	0.823480i	$-0.692029\pi$
$401$	41186.9	−	41186.9i	0.256136	−	0.256136i	0.823480	+	0.567345i	$0.192029\pi$
$402$	−90494.8			−0.559979
$403$	−11083.7	+	65441.9i	−0.0682457	+	0.402945i
$404$	−7201.40			−0.0441219
$405$	81067.8	−	82795.6i	0.494240	−	0.504774i
$406$	−4117.46			−0.0249791
$407$	−312540.			−1.88676
$408$	−98346.4	+	98346.4i	−0.590797	+	0.590797i
$409$	−70663.4	−	70663.4i	−0.422423	−	0.422423i	0.463614	−	0.886037i	$-0.346552\pi$
$409$	−70663.4	−	70663.4i	−0.422423	−	0.422423i	−0.886037	+	0.463614i	$0.846552\pi$
$410$	87787.7	−	89658.8i	0.522235	−	0.533366i
$411$	−55626.5	+	55626.5i	−0.329305	+	0.329305i
$412$		−	86224.0i		−	0.507965i
$413$	3255.13			0.0190839
$414$	−45223.7	+	45223.7i	−0.263855	+	0.263855i
$415$	1359.18	+	128901.i	0.00789191	+	0.748445i
$416$	164427.	+	27848.5i	0.950136	+	0.160922i
$417$			194871.i			1.12066i
$418$	84677.2	−	84677.2i	0.484634	−	0.484634i
$419$	238486.			1.35842			0.679212	−	0.733942i	$-0.262322\pi$
$419$	238486.			1.35842			0.679212	+	0.733942i	$0.262322\pi$
$420$	−1571.34	+	16.5689i	−0.00890783	+	9.39278e-5i
$421$	207946.	+	207946.i	1.17324	+	1.17324i	0.981433	+	0.191807i	$0.0614348\pi$
$421$	207946.	+	207946.i	1.17324	+	1.17324i	0.191807	+	0.981433i	$0.438565\pi$
$422$	−146895.	+	146895.i	−0.824864	+	0.824864i
$423$	48892.4	+	48892.4i	0.273251	+	0.273251i
$424$	−23815.5	+	23815.5i	−0.132473	+	0.132473i
$425$	−6267.43	−	297159.i	−0.0346985	−	1.64517i
$426$		−	269472.i		−	1.48489i
$427$	66.7270	+	66.7270i	0.000365970	+	0.000365970i
$428$	−23204.2			−0.126671
$429$	−31800.5	+	187761.i	−0.172790	+	1.02021i
$430$	−554.189	−	52557.6i	−0.00299724	−	0.284249i
$431$	122131.	+	122131.i	0.657464	+	0.657464i	0.954779	−	0.297315i	$-0.0960913\pi$
$431$	122131.	+	122131.i	0.657464	+	0.657464i	−0.297315	+	0.954779i	$0.596091\pi$
$432$		−	251892.i		−	1.34973i
$433$	−34354.9			−0.183237			−0.0916184	−	0.995794i	$-0.529204\pi$
$433$	−34354.9			−0.183237			−0.0916184	+	0.995794i	$0.529204\pi$
$434$	−1295.81	−	1295.81i	−0.00687958	−	0.00687958i
$435$	−123900.	−	121314.i	−0.654775	−	0.641111i
$436$	59940.1	−	59940.1i	0.315315	−	0.315315i
$437$	−80298.0	−	80298.0i	−0.420477	−	0.420477i
$438$		−	92868.3i		−	0.484083i
$439$			196860.i			1.02148i	0.859736	+	0.510739i	$0.170628\pi$
$439$			196860.i			1.02148i	−0.859736	+	0.510739i	$0.829372\pi$
$440$	93296.0	−	95284.4i	0.481901	−	0.492172i
$441$		−	46125.3i		−	0.237171i
$442$	392061.	+	66402.2i	2.00682	+	0.339890i
$443$			361277.i			1.84091i	0.390849	+	0.920455i	$0.372182\pi$
$443$			361277.i			1.84091i	−0.390849	+	0.920455i	$0.627818\pi$
$444$	102748.	+	102748.i	0.521205	+	0.521205i
$445$	3490.34	+	331013.i	0.0176257	+	1.67157i
$446$		−	247243.i		−	1.24295i
$447$	187133.	−	187133.i	0.936557	−	0.936557i
$448$	156.011	−	156.011i	0.000777317	−	0.000777317i
$449$	−138954.	+	138954.i	−0.689254	+	0.689254i	−0.962067	−	0.272813i	$-0.912046\pi$
$449$	−138954.	+	138954.i	−0.689254	+	0.689254i	0.272813	+	0.962067i	$0.412046\pi$
$450$	42898.7	+	41126.5i	0.211845	+	0.203094i
$451$	145433.			0.715005
$452$	5198.97			0.0254472
$453$	7210.63	+	7210.63i	0.0351380	+	0.0351380i
$454$		−	150077.i		−	0.728120i
$455$	−2341.52	−	3223.85i	−0.0113103	−	0.0155723i
$456$	49376.3			0.237459
$457$	−182271.	+	182271.i	−0.872742	+	0.872742i	−0.992770	−	0.120029i	$-0.961701\pi$
$457$	−182271.	+	182271.i	−0.872742	+	0.872742i	0.120029	+	0.992770i	$0.461701\pi$
$458$			217781.i			1.03822i
$459$		−	374612.i		−	1.77810i
$460$	101884.	+	99758.1i	0.481495	+	0.471447i
$461$	−134817.	−	134817.i	−0.634371	−	0.634371i	0.314790	−	0.949161i	$-0.398066\pi$
$461$	−134817.	−	134817.i	−0.634371	−	0.634371i	−0.949161	+	0.314790i	$0.898066\pi$
$462$	−3717.83	−	3717.83i	−0.0174183	−	0.0174183i
$463$	149158.	+	149158.i	0.695799	+	0.695799i	0.963502	−	0.267702i	$-0.0862644\pi$
$463$	149158.	+	149158.i	0.695799	+	0.695799i	−0.267702	+	0.963502i	$0.586264\pi$
$464$	−282177.			−1.31064
$465$	−813.729	−	77171.6i	−0.00376334	−	0.356904i
$466$	52440.5	−	52440.5i	0.241488	−	0.241488i
$467$	−44625.5			−0.204621			−0.102310	−	0.994753i	$-0.532623\pi$
$467$	−44625.5			−0.204621			−0.102310	+	0.994753i	$0.532623\pi$
$468$	−22452.8	+	15948.8i	−0.102513	+	0.0728177i
$469$	2194.48			0.00997668
$470$	311350.	−	317986.i	1.40946	−	1.43950i
$471$	−115368.			−0.520047
$472$	128429.			0.576473
$473$	43075.5	−	43075.5i	0.192534	−	0.192534i
$474$	190644.	+	190644.i	0.848527	+	0.848527i
$475$	−73023.2	+	76169.8i	−0.323648	+	0.337595i
$476$	−2689.14	+	2689.14i	−0.0118686	+	0.0118686i
$477$		−	17395.8i		−	0.0764554i
$478$	208564.			0.912816
$479$	203661.	−	203661.i	0.887640	−	0.887640i	−0.106656	−	0.994296i	$-0.534014\pi$
$479$	203661.	−	203661.i	0.887640	−	0.887640i	0.994296	+	0.106656i	$0.0340142\pi$
$480$	−193898.	+	2044.54i	−0.841573	+	0.00887388i
$481$	−61525.0	+	363264.i	−0.265926	+	1.57012i
$482$			173480.i			0.746716i
$483$	−3525.56	+	3525.56i	−0.0151124	+	0.0151124i
$484$	−50124.7			−0.213974
$485$	1440.15	+	136579.i	0.00612242	+	0.580632i
$486$	95769.7	+	95769.7i	0.405467	+	0.405467i
$487$	71726.1	−	71726.1i	0.302426	−	0.302426i	−0.539536	−	0.841962i	$-0.681400\pi$
$487$	71726.1	−	71726.1i	0.302426	−	0.302426i	0.841962	+	0.539536i	$0.181400\pi$
$488$	2632.67	+	2632.67i	0.0110550	+	0.0110550i
$489$	149596.	−	149596.i	0.625609	−	0.625609i
$490$	−296859.	+	3130.20i	−1.23640	+	0.0130371i
$491$		−	457.072i		−	0.00189593i	−1.00000		0.000947963i	$-0.999698\pi$
$491$		−	457.072i		−	0.00189593i	1.00000		0.000947963i	$-0.000301746\pi$
$492$	−47811.3	−	47811.3i	−0.197515	−	0.197515i
$493$	−419651.			−1.72661
$494$	−81750.9	−	115089.i	−0.334995	−	0.471607i
$495$	726.230	+	68873.5i	0.00296390	+	0.281088i
$496$	−88804.2	−	88804.2i	−0.360969	−	0.360969i
$497$			6534.65i			0.0264551i
$498$	200528.			0.808566
$499$	120428.	+	120428.i	0.483643	+	0.483643i	0.906293	−	0.422650i	$-0.138900\pi$
$499$	120428.	+	120428.i	0.483643	+	0.483643i	−0.422650	+	0.906293i	$0.638900\pi$
$500$	90678.6	−	96604.7i	0.362714	−	0.386419i
$501$	−85702.5	+	85702.5i	−0.341443	+	0.341443i
$502$	−330576.	−	330576.i	−1.31179	−	1.31179i
$503$		−	310205.i		−	1.22606i	−0.790058	−	0.613032i	$-0.789949\pi$
$503$		−	310205.i		−	1.22606i	0.790058	−	0.613032i	$-0.210051\pi$
$504$			674.353i			0.00265477i
$505$	15170.2	+	14853.6i	0.0594852	+	0.0582438i
$506$			477091.i			1.86338i
$507$	211974.	+	73923.2i	0.824643	+	0.287584i
$508$			213263.i			0.826394i
$509$	−62213.1	−	62213.1i	−0.240130	−	0.240130i	0.576774	−	0.816904i	$-0.304311\pi$
$509$	−62213.1	−	62213.1i	−0.240130	−	0.240130i	−0.816904	+	0.576774i	$0.804311\pi$
$510$	−462334.	+	4875.03i	−1.77752	+	0.0187429i
$511$			2252.04i			0.00862450i
$512$	−88515.0	+	88515.0i	−0.337658	+	0.337658i
$513$	−94039.8	+	94039.8i	−0.357336	+	0.357336i
$514$	−159208.	+	159208.i	−0.602613	+	0.602613i
$515$	−177846.	+	181637.i	−0.670548	+	0.684839i
$516$	−28322.3			−0.106373
$517$	515795.			1.92973
$518$	−7192.96	−	7192.96i	−0.0268070	−	0.0268070i
$519$			61285.5i			0.227522i
$520$	−92383.1	−	127195.i	−0.341653	−	0.470395i
$521$	−152565.			−0.562057			−0.281028	−	0.959699i	$-0.590675\pi$
$521$	−152565.			−0.562057			−0.281028	+	0.959699i	$0.590675\pi$
$522$	59330.7	−	59330.7i	0.217740	−	0.217740i
$523$			128629.i			0.470256i	0.971964	+	0.235128i	$0.0755510\pi$
$523$			128629.i			0.470256i	−0.971964	+	0.235128i	$0.924449\pi$
$524$		−	72567.5i		−	0.264289i
$525$	3344.31	+	3206.15i	0.0121335	+	0.0116323i
$526$	−231942.	−	231942.i	−0.838317	−	0.838317i
$527$	−132069.	−	132069.i	−0.475532	−	0.475532i
$528$	−254790.	−	254790.i	−0.913933	−	0.913933i
$529$	172577.			0.616696
$530$	−111958.	+	1180.53i	−0.398570	+	0.00420269i
$531$	−46904.9	+	46904.9i	−0.166352	+	0.166352i
$532$	1350.12			0.00477035
$533$	28629.1	−	169036.i	0.100775	−	0.595010i
$534$	514948.			1.80585
$535$	48881.1	+	47861.0i	0.170779	+	0.167215i
$536$	86581.8			0.301368
$537$	−25133.4			−0.0871569
$538$	−377977.	+	377977.i	−1.30587	+	1.30587i
$539$	−243301.	−	243301.i	−0.837466	−	0.837466i
$540$	116830.	−	119320.i	0.400652	−	0.409192i
$541$	−46636.3	+	46636.3i	−0.159342	+	0.159342i	−0.782275	−	0.622933i	$-0.785941\pi$
$541$	−46636.3	+	46636.3i	−0.159342	+	0.159342i	0.622933	+	0.782275i	$0.285941\pi$
$542$			437493.i			1.48927i
$543$	−120245.			−0.407819
$544$	−331831.	+	331831.i	−1.12129	+	1.12129i
$545$	−249900.	+	2635.05i	−0.841345	+	0.00887148i
$546$	−5053.10	+	3589.35i	−0.0169501	+	0.0120401i
$547$		−	183000.i		−	0.611614i	−0.952094	−	0.305807i	$-0.901074\pi$
$547$		−	183000.i		−	0.611614i	0.952094	−	0.305807i	$-0.0989262\pi$
$548$	−60011.1	+	60011.1i	−0.199835	+	0.199835i
$549$	−1923.01			−0.00638025
$550$	443216.	−	9347.93i	1.46518	−	0.0309023i
$551$	105346.	+	105346.i	0.346989	+	0.346989i
$552$	−139099.	+	139099.i	−0.456504	+	0.456504i
$553$	−4623.07	−	4623.07i	−0.0151175	−	0.0151175i
$554$	413993.	−	413993.i	1.34888	−	1.34888i
$555$	−4516.96	−	428375.i	−0.0146643	−	1.39072i
$556$			210231.i			0.680061i
$557$	−220628.	−	220628.i	−0.711131	−	0.711131i	0.255641	−	0.966772i	$-0.417713\pi$
$557$	−220628.	−	220628.i	−0.711131	−	0.711131i	−0.966772	+	0.255641i	$0.917713\pi$
$558$	37344.1			0.119937
$559$	−41586.9	−	58546.1i	−0.133086	−	0.187359i
$560$	7538.69	−	79.4910i	0.0240392	−	0.000253479i
$561$	−378922.	−	378922.i	−1.20399	−	1.20399i
$562$		−	17403.1i		−	0.0551002i
$563$	25796.6			0.0813851			0.0406926	−	0.999172i	$-0.487044\pi$
$563$	25796.6			0.0813851			0.0406926	+	0.999172i	$0.487044\pi$
$564$	−169569.	−	169569.i	−0.533075	−	0.533075i
$565$	−10952.0	−	10723.4i	−0.0343080	−	0.0335920i
$566$	−165431.	+	165431.i	−0.516396	+	0.516396i
$567$	3090.85	+	3090.85i	0.00961418	+	0.00961418i
$568$			257820.i			0.799136i
$569$			505623.i			1.56172i	0.624707	+	0.780859i	$0.285218\pi$
$569$			505623.i			1.56172i	−0.624707	+	0.780859i	$0.714782\pi$
$570$	117284.	+	114837.i	0.360986	+	0.353453i
$571$		−	465585.i		−	1.42800i	−0.700148	−	0.713998i	$-0.746883\pi$
$571$		−	465585.i		−	1.42800i	0.700148	−	0.713998i	$-0.253117\pi$
$572$	−34307.1	+	202561.i	−0.104856	+	0.619103i
$573$			462727.i			1.40934i
$574$	3347.06	+	3347.06i	0.0101587	+	0.0101587i
$575$	−8864.49	−	420294.i	−0.0268113	−	1.27121i
$576$			4496.08i			0.0135516i
$577$	346231.	−	346231.i	1.03996	−	1.03996i	0.0407872	−	0.999168i	$-0.487013\pi$
$577$	346231.	−	346231.i	1.03996	−	1.03996i	0.999168	−	0.0407872i	$-0.0129866\pi$
$578$	−499020.	+	499020.i	−1.49370	+	1.49370i
$579$	223416.	−	223416.i	0.666435	−	0.666435i
$580$	−133666.	−	130877.i	−0.397343	−	0.389051i
$581$	−4862.76			−0.0144056
$582$	212473.			0.627274
$583$	−91759.4	−	91759.4i	−0.269969	−	0.269969i
$584$			88852.7i			0.260522i
$585$	80194.4	+	12714.0i	0.234332	+	0.0371509i
$586$	−595457.			−1.73403
$587$	241998.	−	241998.i	0.702320	−	0.702320i	−0.262588	−	0.964908i	$-0.584576\pi$
$587$	241998.	−	241998.i	0.702320	−	0.702320i	0.964908	+	0.262588i	$0.0845760\pi$
$588$			159972.i			0.462689i
$589$			66307.2i			0.191131i
$590$	305060.	+	298694.i	0.876357	+	0.858068i
$591$	406873.	+	406873.i	1.16489	+	1.16489i
$592$	−492947.	−	492947.i	−1.40655	−	1.40655i
$593$	292061.	+	292061.i	0.830548	+	0.830548i	0.987592	−	0.157044i	$-0.0501965\pi$
$593$	292061.	+	292061.i	0.830548	+	0.830548i	−0.157044	+	0.987592i	$0.550196\pi$
$594$	558738.			1.58356
$595$	11211.5	−	118.219i	0.0316686	−	0.000333927i
$596$	201883.	−	201883.i	0.568339	−	0.568339i
$597$	453323.			1.27192
$598$	554522.	+	93917.7i	1.55066	+	0.262630i
$599$	647196.			1.80377			0.901887	−	0.431973i	$-0.142182\pi$
$599$	647196.			1.80377			0.901887	+	0.431973i	$0.142182\pi$
$600$	131948.	+	126497.i	0.366521	+	0.351380i
$601$	−301870.			−0.835739			−0.417869	−	0.908507i	$-0.637223\pi$
$601$	−301870.			−0.835739			−0.417869	+	0.908507i	$0.637223\pi$
$602$	1982.72			0.00547103
$603$	−31621.5	+	31621.5i	−0.0869656	+	0.0869656i
$604$	7779.00	+	7779.00i	0.0213231	+	0.0213231i
$605$	105591.	+	103387.i	0.288480	+	0.282460i
$606$	23353.6	−	23353.6i	0.0635930	−	0.0635930i
$607$			462245.i			1.25457i	0.778789	+	0.627286i	$0.215834\pi$
$607$			462245.i			1.25457i	−0.778789	+	0.627286i	$0.784166\pi$
$608$	166601.			0.450682
$609$	4625.32	−	4625.32i	0.0124712	−	0.0124712i
$610$	130.502	+	12376.4i	0.000350716	+	0.0332609i
$611$	101537.	−	599507.i	0.271983	−	1.60588i
$612$		−	77498.7i		−	0.206915i
$613$	341453.	−	341453.i	0.908677	−	0.908677i	−0.0874884	−	0.996166i	$-0.527884\pi$
$613$	341453.	−	341453.i	0.908677	−	0.908677i	0.996166	+	0.0874884i	$0.0278841\pi$
$614$	325543.			0.863518
$615$	2101.85	+	199334.i	0.00555715	+	0.527024i
$616$	3557.07	+	3557.07i	0.00937414	+	0.00937414i
$617$	−100579.	+	100579.i	−0.264202	+	0.264202i	−0.826759	−	0.562557i	$-0.809818\pi$
$617$	−100579.	+	100579.i	−0.264202	+	0.264202i	0.562557	+	0.826759i	$0.309818\pi$
$618$	279619.	+	279619.i	0.732132	+	0.732132i
$619$	39434.1	−	39434.1i	0.102918	−	0.102918i	−0.653773	−	0.756691i	$-0.726815\pi$
$619$	39434.1	−	39434.1i	0.102918	−	0.102918i	0.756691	+	0.653773i	$0.226815\pi$
$620$	−877.870	−	83254.6i	−0.00228374	−	0.216583i
$621$		−	529842.i		−	1.37393i
$622$	−163857.	−	163857.i	−0.423529	−	0.423529i
$623$	−12487.4			−0.0321733
$624$	−346298.	+	245985.i	−0.889366	+	0.631741i
$625$	−390278.	+	16470.1i	−0.999111	+	0.0421636i
$626$	484177.	+	484177.i	1.23554	+	1.23554i
$627$			190243.i			0.483921i
$628$	−124461.			−0.315584
$629$	−733107.	−	733107.i	−1.85296	−	1.85296i
$630$	−1568.38	+	1601.80i	−0.00395157	+	0.00403579i
$631$	172282.	−	172282.i	0.432696	−	0.432696i	−0.456849	−	0.889544i	$-0.651022\pi$
$631$	172282.	−	172282.i	0.432696	−	0.432696i	0.889544	+	0.456849i	$0.151022\pi$
$632$	−182400.	−	182400.i	−0.456658	−	0.456658i
$633$		−	330027.i		−	0.823650i
$634$		−	271707.i		−	0.675961i
$635$	439876.	−	449252.i	1.09090	−	1.11415i
$636$			60332.3i			0.149154i
$637$	−330684.	+	234893.i	−0.814955	+	0.578885i
$638$		−	625914.i		−	1.53771i
$639$	−94161.4	−	94161.4i	−0.230606	−	0.230606i
$640$	423633.	−	4466.96i	1.03426	−	0.0109057i
$641$		−	3049.78i		−	0.00742253i	−0.999993	−	0.00371127i	$-0.998819\pi$
$641$		−	3049.78i		−	0.00742253i	0.999993	−	0.00371127i	$-0.00118134\pi$
$642$	75249.6	−	75249.6i	0.182572	−	0.182572i
$643$	−44102.7	+	44102.7i	−0.106670	+	0.106670i	−0.758428	−	0.651757i	$-0.774032\pi$
$643$	−44102.7	+	44102.7i	−0.106670	+	0.106670i	0.651757	+	0.758428i	$0.274032\pi$
$644$	−3803.46	+	3803.46i	−0.00917079	+	0.00917079i
$645$	59662.9	+	58417.8i	0.143412	+	0.140419i
$646$	397245.			0.951904
$647$	365006.			0.871950			0.435975	−	0.899959i	$-0.356404\pi$
$647$	365006.			0.871950			0.435975	+	0.899959i	$0.356404\pi$
$648$	121948.	+	121948.i	0.290418	+	0.290418i
$649$			494828.i			1.17480i
$650$	76384.0	−	516988.i	0.180791	−	1.22364i
$651$	2911.28			0.00686945
$652$	161388.	−	161388.i	0.379644	−	0.379644i
$653$		−	160988.i		−	0.377544i	−0.982021	−	0.188772i	$-0.939549\pi$
$653$		−	160988.i		−	0.377544i	0.982021	−	0.188772i	$-0.0604508\pi$
$654$			388763.i			0.908929i
$655$	−149678.	+	152868.i	−0.348880	+	0.356315i
$656$	229380.	+	229380.i	0.533026	+	0.533026i
$657$	−32450.9	−	32450.9i	−0.0751788	−	0.0751788i
$658$	11870.8	+	11870.8i	0.0274175	+	0.0274175i
$659$	−547806.			−1.26141			−0.630704	−	0.776023i	$-0.717234\pi$
$659$	−547806.			−1.26141			−0.630704	+	0.776023i	$0.717234\pi$
$660$	−2518.71	−	238867.i	−0.00578217	−	0.548364i
$661$	−556687.	+	556687.i	−1.27411	+	1.27411i	−0.330205	+	0.943909i	$0.607118\pi$
$661$	−556687.	+	556687.i	−1.27411	+	1.27411i	−0.943909	+	0.330205i	$0.892882\pi$
$662$	−220161.			−0.502370
$663$	−515012.	+	365827.i	−1.17163	+	0.832241i
$664$	−191857.			−0.435152
$665$	−2844.12	−	2784.77i	−0.00643139	−	0.00629718i
$666$	207295.			0.467347
$667$	−593544.			−1.33414
$668$	−92457.9	+	92457.9i	−0.207201	+	0.207201i
$669$	277739.	+	277739.i	0.620562	+	0.620562i
$670$	205660.	+	201368.i	0.458141	+	0.448580i
$671$	−10143.5	+	10143.5i	−0.0225290	+	0.0225290i
$672$		−	7314.77i		−	0.0161980i
$673$	−625996.			−1.38211			−0.691054	−	0.722803i	$-0.742853\pi$
$673$	−625996.			−1.38211			−0.691054	+	0.722803i	$0.742853\pi$
$674$	−297045.	+	297045.i	−0.653886	+	0.653886i
$675$	−492221.	+	10381.5i	−1.08032	+	0.0227852i
$676$	228682.	+	79750.1i	0.500425	+	0.174517i
$677$			690594.i			1.50676i	0.657583	+	0.753382i	$0.271579\pi$
$677$			690594.i			1.50676i	−0.657583	+	0.753382i	$0.728421\pi$
$678$	−16859.9	+	16859.9i	−0.0366771	+	0.0366771i
$679$	−5152.42			−0.0111756
$680$	442342.	−	4664.24i	0.956623	−	0.0100870i
$681$	168588.	+	168588.i	0.363524	+	0.363524i
$682$	196982.	−	196982.i	0.423505	−	0.423505i
$683$	59558.3	+	59558.3i	0.127674	+	0.127674i	0.768056	−	0.640383i	$-0.221224\pi$
$683$	59558.3	+	59558.3i	0.127674	+	0.127674i	−0.640383	+	0.768056i	$0.721224\pi$
$684$	−19454.7	+	19454.7i	−0.0415826	+	0.0415826i
$685$	250197.	−	2638.18i	0.533212	−	0.00562241i
$686$		−	22402.0i		−	0.0476035i
$687$	−244644.	−	244644.i	−0.518347	−	0.518347i
$688$	135880.			0.287063
$689$	−124715.	+	88588.4i	−0.262712	+	0.186612i
$690$	−653913.	+	6895.12i	−1.37348	+	0.0144825i
$691$	−376024.	−	376024.i	−0.787515	−	0.787515i	0.193571	−	0.981086i	$-0.437993\pi$
$691$	−376024.	−	376024.i	−0.787515	−	0.787515i	−0.981086	+	0.193571i	$0.937993\pi$
$692$			66116.2i			0.138069i
$693$	−2598.23			−0.00541018
$694$	−692996.	−	692996.i	−1.43884	−	1.43884i
$695$	433624.	−	442866.i	0.897725	−	0.916859i
$696$	182489.	−	182489.i	0.376720	−	0.376720i
$697$	341133.	+	341133.i	0.702196	+	0.702196i
$698$		−	560037.i		−	1.14949i
$699$			117817.i			0.241132i
$700$	3607.92	+	3458.87i	0.00736310	+	0.00705892i
$701$		−	781553.i		−	1.59046i	−0.606309	−	0.795229i	$-0.707351\pi$
$701$		−	781553.i		−	1.59046i	0.606309	−	0.795229i	$-0.292649\pi$
$702$	109990.	−	649420.i	0.223193	−	1.31780i
$703$			368067.i			0.744760i
$704$	23715.9	+	23715.9i	0.0478514	+	0.0478514i
$705$	7454.49	+	706962.i	0.0149982	+	1.42239i
$706$			918576.i			1.84292i
$707$	−566.321	+	566.321i	−0.00113298	+	0.00113298i
$708$	162676.	−	162676.i	0.324531	−	0.324531i
$709$	−75851.1	+	75851.1i	−0.150893	+	0.150893i	−0.778517	−	0.627624i	$-0.784028\pi$
$709$	−75851.1	+	75851.1i	−0.150893	+	0.150893i	0.627624	+	0.778517i	$0.284028\pi$
$710$	−599626.	+	612406.i	−1.18950	+	1.21485i
$711$	133233.			0.263555
$712$	−492682.			−0.971866
$713$	−186795.	−	186795.i	−0.367440	−	0.367440i
$714$		−	17441.4i		−	0.0342125i
$715$	490073.	−	355945.i	0.958624	−	0.696260i
$716$	−27114.5			−0.0528902
$717$	−234289.	+	234289.i	−0.455736	+	0.455736i
$718$		−	903349.i		−	1.75229i
$719$			803258.i			1.55381i	0.629619	+	0.776904i	$0.283211\pi$
$719$			803258.i			1.55381i	−0.629619	+	0.776904i	$0.716789\pi$
$720$	−107484.	+	109775.i	−0.207337	+	0.211756i
$721$	−6780.70	−	6780.70i	−0.0130438	−	0.0130438i
$722$	356213.	+	356213.i	0.683338	+	0.683338i
$723$	−194878.	−	194878.i	−0.372808	−	0.372808i
$724$	−129723.			−0.247480
$725$	11629.7	+	551400.i	0.0221254	+	1.04904i
$726$	162551.	−	162551.i	0.308401	−	0.308401i
$727$	204285.			0.386517			0.193258	−	0.981148i	$-0.438094\pi$
$727$	204285.			0.386517			0.193258	+	0.981148i	$0.438094\pi$
$728$	4834.60	−	3434.15i	0.00912217	−	0.00647972i
$729$	−590601.			−1.11132
$730$	−206649.	+	211054.i	−0.387782	+	0.396047i
$731$	202079.			0.378170
$732$	6669.40			0.0124470
$733$	408244.	−	408244.i	0.759822	−	0.759822i	−0.216468	−	0.976290i	$-0.569454\pi$
$733$	408244.	−	408244.i	0.759822	−	0.759822i	0.976290	+	0.216468i	$0.0694537\pi$
$734$	−66974.8	−	66974.8i	−0.124314	−	0.124314i
$735$	329959.	−	336991.i	0.610780	−	0.623798i
$736$	−469334.	+	469334.i	−0.866416	+	0.866416i
$737$			333594.i			0.614162i
$738$	−96459.4			−0.177105
$739$	−357933.	+	357933.i	−0.655409	+	0.655409i	−0.954290	−	0.298881i	$-0.903387\pi$
$739$	−357933.	+	357933.i	−0.655409	+	0.655409i	0.298881	+	0.954290i	$0.403387\pi$
$740$	−4873.00	−	462141.i	−0.00889884	−	0.843939i
$741$	221119.	+	37450.3i	0.402708	+	0.0682054i
$742$		−	4223.60i		−	0.00767141i
$743$	−14052.5	+	14052.5i	−0.0254551	+	0.0254551i	−0.719720	−	0.694265i	$-0.755730\pi$
$743$	−14052.5	+	14052.5i	−0.0254551	+	0.0254551i	0.694265	+	0.719720i	$0.255730\pi$
$744$	114863.			0.207507
$745$	−841684.	+	8875.06i	−1.51648	+	0.0159904i
$746$	−89714.5	−	89714.5i	−0.161207	−	0.161207i
$747$	70070.1	−	70070.1i	0.125572	−	0.125572i
$748$	−408790.	−	408790.i	−0.730629	−	0.730629i
$749$	−1824.79	+	1824.79i	−0.00325273	+	0.00325273i
$750$	19218.0	+	607347.i	0.0341654	+	1.07973i
$751$			190968.i			0.338596i	0.985565	+	0.169298i	$0.0541500\pi$
$751$			190968.i			0.338596i	−0.985565	+	0.169298i	$0.945850\pi$
$752$	813526.	+	813526.i	1.43859	+	1.43859i
$753$	742701.			1.30986
$754$	−727498.	−	123214.i	−1.27964	−	0.216730i
$755$	−341.976	−	32432.0i	−0.000599931	−	0.0568957i
$756$	4454.36	+	4454.36i	0.00779367	+	0.00779367i
$757$		−	464461.i		−	0.810508i	−0.914204	−	0.405254i	$-0.867183\pi$
$757$		−	464461.i		−	0.810508i	0.914204	−	0.405254i	$-0.132817\pi$
$758$	411460.			0.716126
$759$	−535938.	−	535938.i	−0.930316	−	0.930316i
$760$	−112213.	−	109871.i	−0.194275	−	0.190220i
$761$	580487.	−	580487.i	1.00236	−	1.00236i	0.00236131	−	0.999997i	$-0.499248\pi$
$761$	580487.	−	580487.i	1.00236	−	1.00236i	0.999997	−	0.00236131i	$-0.000751628\pi$
$762$	−691596.	−	691596.i	−1.19108	−	1.19108i
$763$		−	9427.43i		−	0.0161936i
$764$			499201.i			0.855241i
$765$	−159849.	+	163256.i	−0.273141	+	0.278963i
$766$			640707.i			1.09195i
$767$	575137.	+	97409.2i	0.977643	+	0.165580i
$768$		−	629612.i		−	1.06746i
$769$	102806.	+	102806.i	0.173847	+	0.173847i	0.788667	−	0.614820i	$-0.210772\pi$
$769$	102806.	+	102806.i	0.173847	+	0.173847i	−0.614820	+	0.788667i	$0.710772\pi$
$770$	176.324	+	16722.1i	0.000297393	+	0.0282038i
$771$		−	357691.i		−	0.601726i
$772$	241027.	−	241027.i	0.404418	−	0.404418i
$773$	668328.	−	668328.i	1.11849	−	1.11849i	0.126523	−	0.991964i	$-0.459618\pi$
$773$	668328.	−	668328.i	1.11849	−	1.11849i	0.991964	−	0.126523i	$-0.0403819\pi$
$774$	−28570.2	+	28570.2i	−0.0476904	+	0.0476904i
$775$	−169872.	+	177192.i	−0.282825	+	0.295012i
$776$	−203285.			−0.337585
$777$	16160.3			0.0267675
$778$	625010.	+	625010.i	1.03259	+	1.03259i
$779$		−	171271.i		−	0.282233i
$780$	−278131.	−	44094.7i	−0.457151	−	0.0724765i
$781$	−993364.			−1.62857
$782$	−1.11909e6	+	1.11909e6i	−1.82999	+	1.82999i
$783$			695121.i			1.13380i
$784$		−	767483.i		−	1.24864i
$785$	262186.	+	256715.i	0.425471	+	0.416592i
$786$	235332.	+	235332.i	0.380921	+	0.380921i
$787$	299233.	+	299233.i	0.483125	+	0.483125i	0.906128	−	0.423003i	$-0.139024\pi$
$787$	299233.	+	299233.i	0.483125	+	0.483125i	−0.423003	+	0.906128i	$0.639024\pi$
$788$	438944.	+	438944.i	0.706898	+	0.706898i
$789$	521102.			0.837083
$790$	−9041.58	−	857476.i	−0.0144874	−	1.37394i
$791$	408.849	−	408.849i	0.000653446	−	0.000653446i
$792$	−102512.			−0.163427
$793$	9792.96	+	13786.6i	0.0155728	+	0.0219235i
$794$	1.34898e6			2.13976
$795$	124442.	−	127094.i	0.196893	−	0.201090i
$796$	489056.			0.771849
$797$	479269.			0.754506			0.377253	−	0.926110i	$-0.376869\pi$
$797$	479269.			0.754506			0.377253	+	0.926110i	$0.376869\pi$
$798$	−4378.36	+	4378.36i	−0.00687552	+	0.00687552i
$799$	1.20987e6	+	1.20987e6i	1.89516	+	1.89516i
$800$	445205.	+	426813.i	0.695633	+	0.666896i
$801$	179938.	−	179938.i	0.280451	−	0.280451i
$802$			288189.i			0.448052i
$803$	−342343.			−0.530922
$804$	109670.	−	109670.i	0.169658	−	0.169658i
$805$	15857.3	−	167.205i	0.0244701	−	0.000258023i
$806$	−190175.	−	267729.i	−0.292741	−	0.412121i
$807$		−	849197.i		−	1.30395i
$808$	−22343.8	+	22343.8i	−0.0342243	+	0.0342243i
$809$	−361047.			−0.551653			−0.275827	−	0.961207i	$-0.588952\pi$
$809$	−361047.			−0.551653			−0.275827	+	0.961207i	$0.588952\pi$
$810$	6044.94	+	573284.i	0.00921345	+	0.873776i
$811$	−156001.	−	156001.i	−0.237185	−	0.237185i	0.578499	−	0.815683i	$-0.303639\pi$
$811$	−156001.	−	156001.i	−0.237185	−	0.237185i	−0.815683	+	0.578499i	$0.803639\pi$
$812$	4989.90	−	4989.90i	0.00756798	−	0.00756798i
$813$	−491455.	−	491455.i	−0.743538	−	0.743538i
$814$	1.09344e6	−	1.09344e6i	1.65023	−	1.65023i
$815$	−672854.	+	7094.84i	−1.01299	+	0.0106814i
$816$		−	1.19529e6i		−	1.79512i
$817$	−50728.5	−	50728.5i	−0.0759989	−	0.0759989i
$818$	494439.			0.738935
$819$	−511.475	+	3019.92i	−0.000762529	+	0.00450223i
$820$	2267.53	+	215046.i	0.00337229	+	0.319818i
$821$	746701.	+	746701.i	1.10780	+	1.10780i	0.993440	+	0.114358i	$0.0364812\pi$
$821$	746701.	+	746701.i	1.10780	+	1.10780i	0.114358	+	0.993440i	$0.463519\pi$
$822$		−	389224.i		−	0.576045i
$823$	−532610.			−0.786339			−0.393169	−	0.919466i	$-0.628621\pi$
$823$	−532610.			−0.786339			−0.393169	+	0.919466i	$0.628621\pi$
$824$	−267528.	−	267528.i	−0.394017	−	0.394017i
$825$	−487383.	+	508385.i	−0.716081	+	0.746938i
$826$	−11388.2	+	11388.2i	−0.0166915	+	0.0166915i
$827$	805424.	+	805424.i	1.17764	+	1.17764i	0.980343	+	0.197299i	$0.0632169\pi$
$827$	805424.	+	805424.i	1.17764	+	1.17764i	0.197299	+	0.980343i	$0.436783\pi$
$828$		−	109612.i		−	0.159881i
$829$			433073.i			0.630161i	0.949065	+	0.315081i	$0.102032\pi$
$829$			433073.i			0.630161i	−0.949065	+	0.315081i	$0.897968\pi$
$830$	−455722.	−	446211.i	−0.661521	−	0.647716i
$831$			930114.i			1.34690i
$832$	32233.5	−	22896.4i	0.0465652	−	0.0330765i
$833$		−	1.14140e6i		−	1.64493i
$834$	−681766.	−	681766.i	−0.980174	−	0.980174i
$835$	385473.	−	4064.58i	0.552867	−	0.00582965i
$836$			205239.i			0.293662i
$837$	−218762.	+	218762.i	−0.312264	+	0.312264i
$838$	−834356.	+	834356.i	−1.18813	+	1.18813i
$839$	−38729.8	+	38729.8i	−0.0550200	+	0.0550200i	−0.734081	−	0.679061i	$-0.762387\pi$
$839$	−38729.8	+	38729.8i	−0.0550200	+	0.0550200i	0.679061	+	0.734081i	$0.262387\pi$
$840$	−4824.01	+	4926.82i	−0.00683674	+	0.00698246i
$841$	71413.0			0.100968
$842$	−1.45502e6			−2.05232
$843$	19549.6	+	19549.6i	0.0275095	+	0.0275095i
$844$		−	356041.i		−	0.499822i
$845$	−317241.	−	639679.i	−0.444300	−	0.895878i
$846$	−342105.			−0.477990
$847$	−3941.83	+	3941.83i	−0.00549453	+	0.00549453i
$848$		−	289451.i		−	0.402516i
$849$		−	371671.i		−	0.515636i
$850$	1.06155e6	+	1.01770e6i	1.46928	+	1.40858i
$851$	−1.03689e6	−	1.03689e6i	−1.43177	−	1.43177i
$852$	326571.	+	326571.i	0.449882	+	0.449882i
$853$	60801.1	+	60801.1i	0.0835629	+	0.0835629i	0.747653	−	0.664090i	$-0.231181\pi$
$853$	60801.1	+	60801.1i	0.0835629	+	0.0835629i	−0.664090	+	0.747653i	$0.731181\pi$
$854$	−466.896			−0.000640183
$855$	81109.8	−	855.255i	0.110954	−	0.00116994i
$856$	−71995.8	+	71995.8i	−0.0982561	+	0.0982561i
$857$	−852323.			−1.16049			−0.580247	−	0.814441i	$-0.697044\pi$
$857$	−852323.			−1.16049			−0.580247	+	0.814441i	$0.697044\pi$
$858$	−545635.	−	768146.i	−0.741187	−	1.04344i
$859$	945602.			1.28151			0.640755	−	0.767745i	$-0.278621\pi$
$859$	945602.			1.28151			0.640755	+	0.767745i	$0.278621\pi$
$860$	64365.7	+	63022.5i	0.0870277	+	0.0852115i
$861$	−7519.81			−0.0101438
$862$	−854564.			−1.15009
$863$	−280625.	+	280625.i	−0.376795	+	0.376795i	−0.869945	−	0.493149i	$-0.835846\pi$
$863$	−280625.	+	280625.i	−0.376795	+	0.376795i	0.493149	+	0.869945i	$0.335846\pi$
$864$	549653.	+	549653.i	0.736311	+	0.736311i
$865$	136371.	−	139278.i	0.182260	−	0.186145i
$866$	120192.	−	120192.i	0.160266	−	0.160266i
$867$		−	1.12114e6i		−	1.49150i
$868$	3140.76			0.00416865
$869$	702775.	−	702775.i	0.930630	−	0.930630i
$870$	857894.	−	9045.98i	1.13343	−	0.0119514i
$871$	387735.	+	65669.5i	0.511091	+	0.0865620i
$872$		−	371953.i		−	0.489165i
$873$	74244.0	−	74244.0i	0.0974166	−	0.0974166i
$874$	561853.			0.735529
$875$	−466.034	−	14728.0i	−0.000608697	−	0.0192366i
$876$	112546.	+	112546.i	0.146664	+	0.146664i
$877$	870118.	−	870118.i	1.13130	−	1.13130i	0.141343	−	0.989961i	$-0.454858\pi$
$877$	870118.	−	870118.i	1.13130	−	1.13130i	0.989961	−	0.141343i	$-0.0451419\pi$
$878$	−688726.	−	688726.i	−0.893424	−	0.893424i
$879$	668904.	−	668904.i	0.865737	−	0.865737i
$880$	12083.8	+	1.14599e6i	0.0156041	+	1.47985i
$881$			913096.i			1.17643i	0.808706	+	0.588213i	$0.200168\pi$
$881$			913096.i			1.17643i	−0.808706	+	0.588213i	$0.799832\pi$
$882$	161372.	+	161372.i	0.207439	+	0.207439i
$883$	969978.			1.24406			0.622029	−	0.782994i	$-0.286309\pi$
$883$	969978.			1.24406			0.622029	+	0.782994i	$0.286309\pi$
$884$	−555607.	+	394663.i	−0.710990	+	0.505035i
$885$	−678223.	+	7151.46i	−0.865936	+	0.00913079i
$886$	−1.26395e6	−	1.26395e6i	−1.61013	−	1.61013i
$887$			866192.i			1.10095i	0.834852	+	0.550474i	$0.185553\pi$
$887$			866192.i			1.10095i	−0.834852	+	0.550474i	$0.814447\pi$
$888$	637596.			0.808574
$889$	16771.1	+	16771.1i	0.0212206	+	0.0212206i
$890$	−1.17028e6	−	1.14585e6i	−1.47744	−	1.44660i
$891$	−469856.	+	469856.i	−0.591846	+	0.591846i
$892$	299632.	+	299632.i	0.376581	+	0.376581i
$893$		−	607434.i		−	0.761721i
$894$			1.30939e6i			1.63830i
$895$	57118.4	+	55926.4i	0.0713066	+	0.0698185i
$896$			15981.4i			0.0199067i
$897$	−728420.	+	517417.i	−0.905310	+	0.643066i
$898$		−	972277.i		−	1.20570i
$899$	245064.	+	245064.i	0.303221	+	0.303221i
$900$	−101829.	+	2147.70i	−0.125715	+	0.00265148i
$901$		−	430470.i		−	0.530265i
$902$	−508804.	+	508804.i	−0.625370	+	0.625370i
$903$	−2227.28	+	2227.28i	−0.00273149	+	0.00273149i
$904$	16130.9	−	16130.9i	0.0197388	−	0.0197388i
$905$	273270.	+	267568.i	0.333653	+	0.326690i
$906$	−50453.5			−0.0614660
$907$	1.17189e6			1.42453			0.712267	−	0.701909i	$-0.247669\pi$
$907$	1.17189e6			1.42453			0.712267	+	0.701909i	$0.247669\pi$
$908$	181877.	+	181877.i	0.220600	+	0.220600i
$909$		−	16320.9i		−	0.0197522i
$910$	19470.7	+	3086.88i	0.0235125	+	0.00372766i
$911$	629892.			0.758978			0.379489	−	0.925196i	$-0.376100\pi$
$911$	629892.			0.758978			0.379489	+	0.925196i	$0.376100\pi$
$912$	−300057.	+	300057.i	−0.360756	+	0.360756i
$913$		−	739211.i		−	0.886803i
$914$		−	1.27537e6i		−	1.52667i
$915$	−14049.5	−	13756.3i	−0.0167811	−	0.0164309i
$916$	−263927.	−	263927.i	−0.314553	−	0.314553i
$917$	−5706.74	−	5706.74i	−0.00678656	−	0.00678656i
$918$	1.31060e6	+	1.31060e6i	1.55519	+	1.55519i
$919$	470346.			0.556911			0.278456	−	0.960449i	$-0.410177\pi$
$919$	470346.			0.556911			0.278456	+	0.960449i	$0.410177\pi$
$920$	625638.	−	6596.98i	0.739175	−	0.00779416i
$921$	−365697.	+	365697.i	−0.431123	+	0.431123i
$922$	943330.			1.10969
$923$	−195548.	+	1.15458e6i	−0.229536	+	1.35526i
$924$	9011.21			0.0105545
$925$	−942949.	+	983581.i	−1.10206	+	1.14955i
$926$	−1.04367e6			−1.21714
$927$	195414.			0.227402
$928$	615737.	−	615737.i	0.714989	−	0.714989i
$929$	−171782.	−	171782.i	−0.199042	−	0.199042i	0.600547	−	0.799589i	$-0.294949\pi$
$929$	−171782.	−	171782.i	−0.199042	−	0.199042i	−0.799589	+	0.600547i	$0.794949\pi$
$930$	272836.	+	267142.i	0.315454	+	0.308870i
$931$	−286527.	+	286527.i	−0.330573	+	0.330573i
$932$			127104.i			0.146328i
$933$	368135.			0.422906
$934$	156125.	−	156125.i	0.178969	−	0.178969i
$935$	17971.0	+	1.70431e6i	0.0205565	+	1.94951i
$936$	−20179.9	+	119149.i	−0.0230339	+	0.136000i
$937$			64767.5i			0.0737697i	0.999320	+	0.0368849i	$0.0117435\pi$
$937$			64767.5i			0.0737697i	−0.999320	+	0.0368849i	$0.988257\pi$
$938$	−7677.50	+	7677.50i	−0.00872598	+	0.00872598i
$939$	−1.08780e6			−1.23372
$940$	8042.08	+	762687.i	0.00910150	+	0.863159i
$941$	1.22555e6	+	1.22555e6i	1.38405	+	1.38405i	0.837289	+	0.546761i	$0.184139\pi$
$941$	1.22555e6	+	1.22555e6i	1.38405	+	1.38405i	0.546761	+	0.837289i	$0.315861\pi$
$942$	403620.	−	403620.i	0.454853	−	0.454853i
$943$	482490.	+	482490.i	0.542581	+	0.542581i
$944$	−780455.	+	780455.i	−0.875798	+	0.875798i
$945$	−195.820	−	18571.0i	−0.000219277	−	0.0207956i
$946$			301404.i			0.336795i
$947$	−475603.	−	475603.i	−0.530328	−	0.530328i	0.390342	−	0.920670i	$-0.372357\pi$
$947$	−475603.	−	475603.i	−0.530328	−	0.530328i	−0.920670	+	0.390342i	$0.872357\pi$
$948$	−462078.			−0.514161
$949$	−67391.9	+	397905.i	−0.0748299	+	0.441821i
$950$	−11008.7	−	521959.i	−0.0121980	−	0.578348i
$951$	305220.	+	305220.i	0.337483	+	0.337483i
$952$			16687.3i			0.0184124i
$953$	−1.60359e6			−1.76567			−0.882833	−	0.469688i	$-0.844367\pi$
$953$	−1.60359e6			−1.76567			−0.882833	+	0.469688i	$0.844367\pi$
$954$	60860.2	+	60860.2i	0.0668708	+	0.0668708i
$955$	1.02965e6	−	1.05160e6i	1.12897	−	1.15304i
$956$	−252756.	+	252756.i	−0.276558	+	0.276558i
$957$	703117.	+	703117.i	0.767722	+	0.767722i
$958$			1.42504e6i			1.55273i
$959$			9438.60i			0.0102629i
$960$	−32162.9	+	32848.4i	−0.0348990	+	0.0356428i
$961$		−	769272.i		−	0.832978i
$962$	−1.05565e6	−	1.48615e6i	−1.14070	−	1.60587i
$963$		−	52588.7i		−	0.0567074i
$964$	−210239.	−	210239.i	−0.226234	−	0.226234i
$965$	−1.00488e6	+	10595.9i	−1.07910	+	0.0113784i
$966$		−	24668.7i		−	0.0264358i
$967$	−423714.	+	423714.i	−0.453127	+	0.453127i	−0.896391	−	0.443264i	$-0.853820\pi$
$967$	−423714.	+	423714.i	−0.453127	+	0.453127i	0.443264	+	0.896391i	$0.353820\pi$
$968$	−155522.	+	155522.i	−0.165975	+	0.165975i
$969$	−446243.	+	446243.i	−0.475252	+	0.475252i
$970$	−482868.	−	472791.i	−0.513198	−	0.502488i
$971$	−1.69536e6			−1.79814			−0.899071	−	0.437802i	$-0.855757\pi$
$971$	−1.69536e6			−1.79814			−0.899071	+	0.437802i	$0.855757\pi$
$972$	−232125.			−0.245691
$973$	16532.7	+	16532.7i	0.0174629	+	0.0174629i
$974$			501875.i			0.529027i
$975$	494950.	+	666561.i	0.520658	+	0.701182i
$976$	−31997.2			−0.0335902
$977$	647618.	−	647618.i	0.678469	−	0.678469i	−0.281185	−	0.959654i	$-0.590727\pi$
$977$	647618.	−	647618.i	0.678469	−	0.678469i	0.959654	+	0.281185i	$0.0907275\pi$
$978$			1.04674e6i			1.09436i
$979$		−	1.89827e6i		−	1.98058i
$980$	355967.	−	363554.i	0.370645	−	0.378544i
$981$	135845.	+	135845.i	0.141158	+	0.141158i
$982$	1599.09	+	1599.09i	0.00165825	+	0.00165825i
$983$	−300032.	−	300032.i	−0.310499	−	0.310499i	0.534604	−	0.845103i	$-0.320461\pi$
$983$	−300032.	−	300032.i	−0.310499	−	0.310499i	−0.845103	+	0.534604i	$0.820461\pi$
$984$	−296689.			−0.306416
$985$	−19296.6	−	1.83003e6i	−0.0198888	−	1.88619i
$986$	1.46817e6	−	1.46817e6i	1.51016	−	1.51016i
$987$	−26670.0			−0.0273771
$988$	238549.	+	40402.3i	0.244378	+	0.0413896i
$989$	285816.			0.292209
$990$	−243498.	−	238417.i	−0.248442	−	0.243257i
$991$	−930499.			−0.947477			−0.473738	−	0.880666i	$-0.657096\pi$
$991$	−930499.			−0.947477			−0.473738	+	0.880666i	$0.657096\pi$
$992$	387559.			0.393835
$993$	247316.	−	247316.i	0.250815	−	0.250815i
$994$	−22861.8	−	22861.8i	−0.0231386	−	0.0231386i
$995$	−1.03023e6	−	1.00873e6i	−1.04061	−	1.01889i
$996$	−243018.	+	243018.i	−0.244973	+	0.244973i
$997$			683654.i			0.687775i	0.939011	+	0.343887i	$0.111744\pi$
$997$			683654.i			0.687775i	−0.939011	+	0.343887i	$0.888256\pi$
$998$	−842644.			−0.846025
$999$	−1.21434e6	+	1.21434e6i	−1.21677	+	1.21677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.5.g.a.34.6	✓	52
5.4	even	2	inner	65.5.g.a.34.21	yes	52
13.5	odd	4	inner	65.5.g.a.44.21	yes	52
65.44	odd	4	inner	65.5.g.a.44.6	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.5.g.a.34.6	✓	52	1.1	even	1	trivial
65.5.g.a.34.21	yes	52	5.4	even	2	inner
65.5.g.a.44.6	yes	52	65.44	odd	4	inner
65.5.g.a.44.21	yes	52	13.5	odd	4	inner

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	65.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.49855 + 3.49855i) q^{2} -7.86015i q^{3} -8.47972i q^{4} +(-17.4903 + 17.8631i) q^{5} +(27.4991 + 27.4991i) q^{6} +(-0.666849 - 0.666849i) q^{7} +(-26.3101 - 26.3101i) q^{8} +19.2180 q^{9} +O(q^{10})\)	\(q+(-3.49855 + 3.49855i) q^{2} -7.86015i q^{3} -8.47972i q^{4} +(-17.4903 + 17.8631i) q^{5} +(27.4991 + 27.4991i) q^{6} +(-0.666849 - 0.666849i) q^{7} +(-26.3101 - 26.3101i) q^{8} +19.2180 q^{9} +(-1.30419 - 123.686i) q^{10} +(101.371 - 101.371i) q^{11} -66.6519 q^{12} +(-97.8678 - 137.778i) q^{13} +4.66601 q^{14} +(140.407 + 137.476i) q^{15} +319.770 q^{16} +475.560 q^{17} +(-67.2351 + 67.2351i) q^{18} +(-119.381 - 119.381i) q^{19} +(151.474 + 148.313i) q^{20} +(-5.24153 + 5.24153i) q^{21} +709.303i q^{22} +672.620 q^{23} +(-206.801 + 206.801i) q^{24} +(-13.1790 - 624.861i) q^{25} +(824.420 + 139.630i) q^{26} -787.729i q^{27} +(-5.65469 + 5.65469i) q^{28} -882.436 q^{29} +(-972.188 + 10.2511i) q^{30} +(-277.713 - 277.713i) q^{31} +(-697.770 + 697.770i) q^{32} +(-796.791 - 796.791i) q^{33} +(-1663.77 + 1663.77i) q^{34} +(23.5753 - 0.248588i) q^{35} -162.963i q^{36} +(-1541.57 - 1541.57i) q^{37} +835.320 q^{38} +(-1082.96 + 769.256i) q^{39} +(930.150 - 9.80789i) q^{40} +(717.329 + 717.329i) q^{41} -36.6755i q^{42} +424.929 q^{43} +(-859.597 - 859.597i) q^{44} +(-336.128 + 343.292i) q^{45} +(-2353.20 + 2353.20i) q^{46} +(2544.10 + 2544.10i) q^{47} -2513.44i q^{48} -2400.11i q^{49} +(2232.22 + 2140.00i) q^{50} -3737.97i q^{51} +(-1168.32 + 829.891i) q^{52} -905.185i q^{53} +(2755.91 + 2755.91i) q^{54} +(37.7891 + 3583.80i) q^{55} +35.0897i q^{56} +(-938.352 + 938.352i) q^{57} +(3087.25 - 3087.25i) q^{58} +(-2440.68 + 2440.68i) q^{59} +(1165.76 - 1190.61i) q^{60} -100.063 q^{61} +1943.18 q^{62} +(-12.8155 - 12.8155i) q^{63} +233.952i q^{64} +(4172.88 + 661.567i) q^{65} +5575.23 q^{66} +(-1645.41 + 1645.41i) q^{67} -4032.61i q^{68} -5286.90i q^{69} +(-81.6099 + 83.3493i) q^{70} +(-4899.65 - 4899.65i) q^{71} +(-505.627 - 505.627i) q^{72} +(-1688.57 - 1688.57i) q^{73} +10786.5 q^{74} +(-4911.50 + 103.589i) q^{75} +(-1012.32 + 1012.32i) q^{76} -135.198 q^{77} +(1097.51 - 6480.07i) q^{78} +6932.71 q^{79} +(-5592.87 + 5712.07i) q^{80} -4635.01 q^{81} -5019.23 q^{82} +(3646.07 - 3646.07i) q^{83} +(44.4467 + 44.4467i) q^{84} +(-8317.68 + 8494.96i) q^{85} +(-1486.64 + 1486.64i) q^{86} +6936.09i q^{87} -5334.16 q^{88} +(9362.98 - 9362.98i) q^{89} +(-25.0639 - 2376.99i) q^{90} +(-26.6144 + 157.140i) q^{91} -5703.63i q^{92} +(-2182.86 + 2182.86i) q^{93} -17801.3 q^{94} +(4220.52 - 44.5029i) q^{95} +(5484.58 + 5484.58i) q^{96} +(3863.26 - 3863.26i) q^{97} +(8396.91 + 8396.91i) q^{98} +(1948.14 - 1948.14i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9}+O(q^{10}) \) 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9	\( 52 q + 58 q^{5} + 60 q^{6} - 1196 q^{9} + 8 q^{11} + 424 q^{14} - 508 q^{15} - 3128 q^{16} + 268 q^{19} + 2116 q^{20} - 668 q^{21} + 2032 q^{24} + 1100 q^{26} - 3704 q^{29} - 1660 q^{31} + 1252 q^{34} + 6692 q^{35} + 7408 q^{39} + 3644 q^{40} + 5960 q^{41} + 1444 q^{44} - 8674 q^{45} + 17620 q^{46} - 3928 q^{50} - 30588 q^{54} + 14784 q^{55} - 5548 q^{59} - 13976 q^{60} - 20008 q^{61} - 15614 q^{65} + 24752 q^{66} + 26908 q^{70} - 16360 q^{71} - 7304 q^{74} - 5760 q^{76} - 9536 q^{79} - 62348 q^{80} - 36516 q^{81} + 66564 q^{84} - 11604 q^{85} - 5264 q^{86} - 940 q^{89} + 37644 q^{91} + 55448 q^{94} - 61644 q^{96} + 16140 q^{99}+O(q^{100}) \) 52 * q + 58 * q^5 + 60 * q^6 - 1196 * q^9 + 8 * q^11 + 424 * q^14 - 508 * q^15 - 3128 * q^16 + 268 * q^19 + 2116 * q^20 - 668 * q^21 + 2032 * q^24 + 1100 * q^26 - 3704 * q^29 - 1660 * q^31 + 1252 * q^34 + 6692 * q^35 + 7408 * q^39 + 3644 * q^40 + 5960 * q^41 + 1444 * q^44 - 8674 * q^45 + 17620 * q^46 - 3928 * q^50 - 30588 * q^54 + 14784 * q^55 - 5548 * q^59 - 13976 * q^60 - 20008 * q^61 - 15614 * q^65 + 24752 * q^66 + 26908 * q^70 - 16360 * q^71 - 7304 * q^74 - 5760 * q^76 - 9536 * q^79 - 62348 * q^80 - 36516 * q^81 + 66564 * q^84 - 11604 * q^85 - 5264 * q^86 - 940 * q^89 + 37644 * q^91 + 55448 * q^94 - 61644 * q^96 + 16140 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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