LMFDB - Embedded newform 76.6.k.a.3.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, 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:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$48$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.18
Character	$\chi$	$=$	76.3
Dual form			76.6.k.a.51.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.37812 + 5.13269i) q^{2} +(10.8783 - 3.95939i) q^{3} +(-20.6891 - 24.4123i) q^{4} +(-11.1052 + 62.9808i) q^{5} +(-5.54764 + 65.2511i) q^{6} +(71.5832 - 41.3286i) q^{7} +(174.502 - 48.1354i) q^{8} +(-83.4872 + 70.0541i) q^{9} +O(q^{10})$	\(q+(-2.37812 + 5.13269i) q^{2} +(10.8783 - 3.95939i) q^{3} +(-20.6891 - 24.4123i) q^{4} +(-11.1052 + 62.9808i) q^{5} +(-5.54764 + 65.2511i) q^{6} +(71.5832 - 41.3286i) q^{7} +(174.502 - 48.1354i) q^{8} +(-83.4872 + 70.0541i) q^{9} +(-296.852 - 206.775i) q^{10} +(11.1277 + 6.42460i) q^{11} +(-321.721 - 183.649i) q^{12} +(-247.565 + 680.180i) q^{13} +(41.8936 + 465.699i) q^{14} +(128.559 + 729.097i) q^{15} +(-167.922 + 1010.14i) q^{16} +(-392.735 - 329.544i) q^{17} +(-161.024 - 595.111i) q^{18} +(84.5616 + 1571.29i) q^{19} +(1767.26 - 1031.91i) q^{20} +(615.071 - 733.013i) q^{21} +(-59.4386 + 41.8368i) q^{22} +(-4366.95 + 770.011i) q^{23} +(1707.71 - 1214.56i) q^{24} +(-906.714 - 330.017i) q^{25} +(-2902.42 - 2888.23i) q^{26} +(-2037.37 + 3528.84i) q^{27} +(-2489.92 - 892.460i) q^{28} +(-3993.82 - 4759.65i) q^{29} +(-4047.96 - 1074.02i) q^{30} +(-78.5801 - 136.105i) q^{31} +(-4785.39 - 3264.12i) q^{32} +(146.489 + 25.8300i) q^{33} +(2625.42 - 1232.09i) q^{34} +(1807.96 + 4967.33i) q^{35} +(3437.46 + 588.760i) q^{36} +3695.41i q^{37} +(-8266.04 - 3302.68i) q^{38} +8379.44i q^{39} +(1093.72 + 11524.8i) q^{40} +(-267.914 - 736.089i) q^{41} +(2299.62 + 4900.16i) q^{42} +(23786.2 + 4194.14i) q^{43} +(-73.3835 - 404.573i) q^{44} +(-3484.92 - 6036.05i) q^{45} +(6432.89 - 24245.4i) q^{46} +(4243.21 + 5056.86i) q^{47} +(2172.82 + 11653.5i) q^{48} +(-4987.40 + 8638.43i) q^{49} +(3850.15 - 3869.06i) q^{50} +(-5577.10 - 2029.90i) q^{51} +(21726.7 - 8028.67i) q^{52} +(22662.0 - 3995.92i) q^{53} +(-13267.3 - 18849.2i) q^{54} +(-528.202 + 629.487i) q^{55} +(10502.0 - 10657.6i) q^{56} +(7141.24 + 16758.2i) q^{57} +(33927.6 - 9180.04i) q^{58} +(4609.21 + 3867.59i) q^{59} +(15139.2 - 18222.8i) q^{60} +(5003.14 + 28374.2i) q^{61} +(885.457 - 79.6544i) q^{62} +(-3081.04 + 8465.10i) q^{63} +(28134.0 - 16799.5i) q^{64} +(-40089.0 - 23145.4i) q^{65} +(-480.945 + 690.456i) q^{66} +(-23745.4 + 19924.7i) q^{67} +(80.4064 + 16405.5i) q^{68} +(-44456.4 + 25666.9i) q^{69} +(-29795.3 - 2533.19i) q^{70} +(1151.61 - 6531.12i) q^{71} +(-11196.6 + 16243.3i) q^{72} +(36943.9 - 13446.5i) q^{73} +(-18967.4 - 8788.13i) q^{74} -11170.2 q^{75} +(36609.3 - 34572.9i) q^{76} +1062.08 q^{77} +(-43009.1 - 19927.3i) q^{78} +(9205.48 - 3350.52i) q^{79} +(-61754.4 - 21793.7i) q^{80} +(-3592.44 + 20373.7i) q^{81} +(4415.25 + 375.384i) q^{82} +(92501.1 - 53405.5i) q^{83} +(-30619.8 + 150.073i) q^{84} +(25116.3 - 21075.1i) q^{85} +(-78093.6 + 112113. i) q^{86} +(-62291.5 - 35964.0i) q^{87} +(2251.06 + 585.468i) q^{88} +(40982.0 - 112597. i) q^{89} +(39268.8 - 3532.56i) q^{90} +(10389.4 + 58921.0i) q^{91} +(109146. + 90676.5i) q^{92} +(-1393.71 - 1169.46i) q^{93} +(-36046.2 + 9753.28i) q^{94} +(-99900.1 - 12123.7i) q^{95} +(-64981.1 - 16561.0i) q^{96} +(2920.69 - 3480.74i) q^{97} +(-32477.8 - 46142.0i) q^{98} +(-1379.09 + 243.171i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9}+O(q^{10}) $ 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9} - 657 q^{10} - 9 q^{12} + 336 q^{13} - 2163 q^{14} + 1824 q^{16} - 12 q^{17} - 10242 q^{20} - 7842 q^{21} - 102 q^{22} - 11856 q^{24} - 12 q^{25} + 1317 q^{26} + 6660 q^{28} - 12 q^{29} - 40692 q^{30} - 3351 q^{32} - 8604 q^{33} - 15756 q^{34} + 81783 q^{36} + 50400 q^{38} + 39246 q^{40} - 29082 q^{41} - 123081 q^{42} - 39651 q^{44} - 6 q^{45} - 112554 q^{46} - 68403 q^{48} + 259302 q^{49} + 154188 q^{50} - 36867 q^{52} - 26280 q^{53} + 172605 q^{54} - 12 q^{57} + 229740 q^{58} - 136062 q^{60} + 169296 q^{61} + 35076 q^{62} + 63795 q^{64} - 189918 q^{65} + 73644 q^{66} + 59706 q^{68} - 200898 q^{69} - 177831 q^{70} - 188502 q^{72} + 397428 q^{73} - 530703 q^{74} - 53022 q^{76} + 159804 q^{77} - 618237 q^{78} + 18045 q^{80} - 110160 q^{81} + 155859 q^{82} + 733851 q^{84} - 645108 q^{85} + 616836 q^{86} + 598383 q^{88} - 226320 q^{89} + 546366 q^{90} - 754308 q^{92} + 558942 q^{93} - 454530 q^{96} - 177198 q^{97} - 76791 q^{98}+O(q^{100}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9 - 657 * q^10 - 9 * q^12 + 336 * q^13 - 2163 * q^14 + 1824 * q^16 - 12 * q^17 - 10242 * q^20 - 7842 * q^21 - 102 * q^22 - 11856 * q^24 - 12 * q^25 + 1317 * q^26 + 6660 * q^28 - 12 * q^29 - 40692 * q^30 - 3351 * q^32 - 8604 * q^33 - 15756 * q^34 + 81783 * q^36 + 50400 * q^38 + 39246 * q^40 - 29082 * q^41 - 123081 * q^42 - 39651 * q^44 - 6 * q^45 - 112554 * q^46 - 68403 * q^48 + 259302 * q^49 + 154188 * q^50 - 36867 * q^52 - 26280 * q^53 + 172605 * q^54 - 12 * q^57 + 229740 * q^58 - 136062 * q^60 + 169296 * q^61 + 35076 * q^62 + 63795 * q^64 - 189918 * q^65 + 73644 * q^66 + 59706 * q^68 - 200898 * q^69 - 177831 * q^70 - 188502 * q^72 + 397428 * q^73 - 530703 * q^74 - 53022 * q^76 + 159804 * q^77 - 618237 * q^78 + 18045 * q^80 - 110160 * q^81 + 155859 * q^82 + 733851 * q^84 - 645108 * q^85 + 616836 * q^86 + 598383 * q^88 - 226320 * q^89 + 546366 * q^90 - 754308 * q^92 + 558942 * q^93 - 454530 * q^96 - 177198 * q^97 - 76791 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.37812	+	5.13269i	−0.420396	+	0.907341i
$2$	−2.37812	+	5.13269i	−0.420396	+	0.907341i
$3$	10.8783	−	3.95939i	0.697846	−	0.253995i	0.0313552	−	0.999508i	$-0.490018\pi$
$3$	10.8783	−	3.95939i	0.697846	−	0.253995i	0.666491	+	0.745513i	$0.267795\pi$
$4$	−20.6891	−	24.4123i	−0.646534	−	0.762885i
$5$	−11.1052	+	62.9808i	−0.198656	+	1.12663i	0.708459	+	0.705752i	$0.249391\pi$
$5$	−11.1052	+	62.9808i	−0.198656	+	1.12663i	−0.907115	+	0.420883i	$0.861720\pi$
$6$	−5.54764	+	65.2511i	−0.0629115	+	0.739963i
$7$	71.5832	−	41.3286i	0.552161	−	0.318790i	−0.197832	−	0.980236i	$-0.563390\pi$
$7$	71.5832	−	41.3286i	0.552161	−	0.318790i	0.749993	+	0.661446i	$0.230057\pi$
$8$	174.502	−	48.1354i	0.963997	−	0.265913i
$9$	−83.4872	+	70.0541i	−0.343569	+	0.288288i
$10$	−296.852	−	206.775i	−0.938727	−	0.653881i
$11$	11.1277	+	6.42460i	0.0277284	+	0.0160090i	0.513800	−	0.857910i	$-0.328237\pi$
$11$	11.1277	+	6.42460i	0.0277284	+	0.0160090i	−0.486072	+	0.873919i	$0.661571\pi$
$12$	−321.721	−	183.649i	−0.644951	−	0.368160i
$13$	−247.565	+	680.180i	−0.406286	+	1.11626i	0.552842	+	0.833286i	$0.313543\pi$
$13$	−247.565	+	680.180i	−0.406286	+	1.11626i	−0.959128	+	0.282974i	$0.908679\pi$
$14$	41.8936	+	465.699i	0.0571252	+	0.635017i
$15$	128.559	+	729.097i	0.147528	+	0.836675i
$16$	−167.922	+	1010.14i	−0.163987	+	0.986463i
$17$	−392.735	−	329.544i	−0.329592	−	0.276561i	0.462941	−	0.886389i	$-0.346794\pi$
$17$	−392.735	−	329.544i	−0.329592	−	0.276561i	−0.792534	+	0.609828i	$0.791238\pi$
$18$	−161.024	−	595.111i	−0.117141	−	0.432929i
$19$	84.5616	+	1571.29i	0.0537389	+	0.998555i
$19$	84.5616	+	1571.29i	0.0537389	+	0.998555i
$20$	1767.26	−	1031.91i	0.987930	−	0.576856i
$21$	615.071	−	733.013i	0.304352	−	0.362713i
$22$	−59.4386	+	41.8368i	−0.0261826	+	0.0184290i
$23$	−4366.95	+	770.011i	−1.72131	+	0.303513i	−0.945056	−	0.326910i	$-0.893993\pi$
$23$	−4366.95	+	770.011i	−1.72131	+	0.303513i	−0.776252	+	0.630423i	$0.782882\pi$
$24$	1707.71	−	1214.56i	0.605181	−	0.430417i
$25$	−906.714	−	330.017i	−0.290148	−	0.105605i
$26$	−2902.42	−	2888.23i	−0.842028	−	0.837911i
$27$	−2037.37	+	3528.84i	−0.537850	+	0.931584i
$28$	−2489.92	−	892.460i	−0.600192	−	0.215126i
$29$	−3993.82	−	4759.65i	−0.881847	−	1.05094i	−0.998331	−	0.0577520i	$-0.981607\pi$
$29$	−3993.82	−	4759.65i	−0.881847	−	1.05094i	0.116484	−	0.993193i	$-0.462838\pi$
$30$	−4047.96	−	1074.02i	−0.821170	−	0.217876i
$31$	−78.5801	−	136.105i	−0.0146862	−	0.0254372i	0.858589	−	0.512665i	$-0.171342\pi$
$31$	−78.5801	−	136.105i	−0.0146862	−	0.0254372i	−0.873275	+	0.487227i	$0.838008\pi$
$32$	−4785.39	−	3264.12i	−0.826118	−	0.563497i
$33$	146.489	+	25.8300i	0.0234164	+	0.00412894i
$34$	2625.42	−	1232.09i	0.389494	−	0.182787i
$35$	1807.96	+	4967.33i	0.249470	+	0.685414i
$36$	3437.46	+	588.760i	0.442060	+	0.0757150i
$37$			3695.41i			0.443771i	0.975073	+	0.221885i	$0.0712210\pi$
$37$			3695.41i			0.443771i	−0.975073	+	0.221885i	$0.928779\pi$
$38$	−8266.04	−	3302.68i	−0.928621	−	0.371029i
$39$			8379.44i			0.882173i
$40$	1093.72	+	11524.8i	0.108083	+	1.13890i
$41$	−267.914	−	736.089i	−0.0248907	−	0.0683865i	0.926625	−	0.375987i	$-0.122696\pi$
$41$	−267.914	−	736.089i	−0.0248907	−	0.0683865i	−0.951516	+	0.307600i	$0.900474\pi$
$42$	2299.62	+	4900.16i	0.201156	+	0.428634i
$43$	23786.2	+	4194.14i	1.96179	+	0.345917i	0.996357	+	0.0852826i	$0.0271793\pi$
$43$	23786.2	+	4194.14i	1.96179	+	0.345917i	0.965438	+	0.260635i	$0.0839318\pi$
$44$	−73.3835	−	404.573i	−0.00571435	−	0.0315040i
$45$	−3484.92	−	6036.05i	−0.256544	−	0.444347i
$46$	6432.89	−	24245.4i	0.448241	−	1.68941i
$47$	4243.21	+	5056.86i	0.280188	+	0.333915i	0.887723	−	0.460378i	$-0.152286\pi$
$47$	4243.21	+	5056.86i	0.280188	+	0.333915i	−0.607535	+	0.794293i	$0.707842\pi$
$48$	2172.82	+	11653.5i	0.136119	+	0.730051i
$49$	−4987.40	+	8638.43i	−0.296745	+	0.513978i
$50$	3850.15	−	3869.06i	0.217797	−	0.218867i
$51$	−5577.10	−	2029.90i	−0.300250	−	0.109282i
$52$	21726.7	−	8028.67i	1.11426	−	0.411752i
$53$	22662.0	−	3995.92i	1.10818	−	0.195401i	0.410532	−	0.911846i	$-0.365343\pi$
$53$	22662.0	−	3995.92i	1.10818	−	0.195401i	0.697643	+	0.716445i	$0.254232\pi$
$54$	−13267.3	−	18849.2i	−0.619154	−	0.879648i
$55$	−528.202	+	629.487i	−0.0235447	+	0.0280595i
$56$	10502.0	−	10657.6i	0.447511	−	0.454140i
$57$	7141.24	+	16758.2i	0.291130	+	0.683188i
$58$	33927.6	−	9180.04i	1.32429	−	0.358323i
$59$	4609.21	+	3867.59i	0.172384	+	0.144647i	0.724898	−	0.688856i	$-0.241887\pi$
$59$	4609.21	+	3867.59i	0.172384	+	0.144647i	−0.552514	+	0.833504i	$0.686331\pi$
$60$	15139.2	−	18222.8i	0.542905	−	0.653487i
$61$	5003.14	+	28374.2i	0.172154	+	0.976336i	0.941377	+	0.337356i	$0.109533\pi$
$61$	5003.14	+	28374.2i	0.172154	+	0.976336i	−0.769223	+	0.638981i	$0.779356\pi$
$62$	885.457	−	79.6544i	0.0292542	−	0.00263166i
$63$	−3081.04	+	8465.10i	−0.0978017	+	0.268708i
$64$	28134.0	−	16799.5i	0.858580	−	0.512679i
$65$	−40089.0	−	23145.4i	−1.17691	−	0.679487i
$66$	−480.945	+	690.456i	−0.0135905	+	0.0195109i
$67$	−23745.4	+	19924.7i	−0.646237	+	0.542257i	−0.905927	−	0.423435i	$-0.860824\pi$
$67$	−23745.4	+	19924.7i	−0.646237	+	0.542257i	0.259689	+	0.965692i	$0.416380\pi$
$68$	80.4064	+	16405.5i	0.00210872	+	0.430247i
$69$	−44456.4	+	25666.9i	−1.12412	+	0.649009i
$70$	−29795.3	−	2533.19i	−0.726780	−	0.0617907i
$71$	1151.61	−	6531.12i	0.0271119	−	0.153759i	−0.968246	−	0.249998i	$-0.919570\pi$
$71$	1151.61	−	6531.12i	0.0271119	−	0.153759i	0.995358	+	0.0962386i	$0.0306812\pi$
$72$	−11196.6	+	16243.3i	−0.254539	+	0.369269i
$73$	36943.9	−	13446.5i	0.811402	−	0.295326i	0.0971990	−	0.995265i	$-0.469012\pi$
$73$	36943.9	−	13446.5i	0.811402	−	0.295326i	0.714203	+	0.699939i	$0.246789\pi$
$74$	−18967.4	−	8788.13i	−0.402651	−	0.186559i
$75$	−11170.2			−0.229302
$76$	36609.3	−	34572.9i	0.727038	−	0.686597i
$77$	1062.08			0.0204141
$78$	−43009.1	−	19927.3i	−0.800431	−	0.370862i
$79$	9205.48	−	3350.52i	0.165951	−	0.0604011i	−0.257709	−	0.966223i	$-0.582968\pi$
$79$	9205.48	−	3350.52i	0.165951	−	0.0604011i	0.423659	+	0.905822i	$0.360745\pi$
$80$	−61754.4	−	21793.7i	−1.07881	−	0.380720i
$81$	−3592.44	+	20373.7i	−0.0608382	+	0.345031i
$82$	4415.25	+	375.384i	0.0725138	+	0.00616511i
$83$	92501.1	−	53405.5i	1.47384	−	0.850924i	0.474278	−	0.880375i	$-0.342709\pi$
$83$	92501.1	−	53405.5i	1.47384	−	0.850924i	0.999566	+	0.0294506i	$0.00937578\pi$
$84$	−30619.8	+	150.073i	−0.473483	+	0.00232062i
$85$	25116.3	−	21075.1i	0.377058	−	0.316389i
$86$	−78093.6	+	112113.i	−1.13860	+	1.63459i
$87$	−62291.5	−	35964.0i	−0.882329	−	0.509413i
$88$	2251.06	+	585.468i	0.0309871	+	0.00805929i
$89$	40982.0	−	112597.i	0.548427	−	1.50679i	−0.287408	−	0.957808i	$-0.592794\pi$
$89$	40982.0	−	112597.i	0.548427	−	1.50679i	0.835835	−	0.548981i	$-0.184984\pi$
$90$	39268.8	−	3532.56i	0.511024	−	0.0459709i
$91$	10389.4	+	58921.0i	0.131518	+	0.745876i
$92$	109146.	+	90676.5i	1.34443	+	1.11693i
$93$	−1393.71	−	1169.46i	−0.0167096	−	0.0140210i
$94$	−36046.2	+	9753.28i	−0.420765	+	0.113849i
$95$	−99900.1	−	12123.7i	−1.13568	−	0.137825i
$96$	−64981.1	−	16561.0i	−0.719629	−	0.183404i
$97$	2920.69	−	3480.74i	0.0315178	−	0.0375614i	−0.750055	−	0.661375i	$-0.769973\pi$
$97$	2920.69	−	3480.74i	0.0315178	−	0.0375614i	0.781573	+	0.623814i	$0.214418\pi$
$98$	−32477.8	−	46142.0i	−0.341603	−	0.485323i
$99$	−1379.09	+	243.171i	−0.0141418	+	0.00249359i
$100$	10702.6	+	28962.7i	0.107026	+	0.289627i
$101$	−27396.5	−	9971.49i	−0.267233	−	0.0972650i	0.204928	−	0.978777i	$-0.434304\pi$
$101$	−27396.5	−	9971.49i	−0.267233	−	0.0972650i	−0.472162	+	0.881512i	$0.656526\pi$
$102$	23681.8	−	23798.2i	0.225380	−	0.226487i
$103$	−1446.91	+	2506.11i	−0.0134384	+	0.0232760i	−0.872666	−	0.488317i	$-0.837611\pi$
$103$	−1446.91	+	2506.11i	−0.0134384	+	0.0232760i	0.859228	+	0.511593i	$0.170944\pi$
$104$	−10459.9	+	130609.i	−0.0948297	+	1.18411i
$105$	39335.2	+	46877.9i	0.348184	+	0.414949i
$106$	−33383.1	+	125820.i	−0.288577	+	1.08764i
$107$	16834.1	+	29157.6i	0.142145	+	0.246202i	0.928304	−	0.371822i	$-0.121267\pi$
$107$	16834.1	+	29157.6i	0.142145	+	0.246202i	−0.786159	+	0.618024i	$0.787933\pi$
$108$	128299.	−	23271.4i	1.05843	−	0.191983i
$109$	−65059.1	−	11471.7i	−0.524496	−	0.0924827i	−0.0948697	−	0.995490i	$-0.530243\pi$
$109$	−65059.1	−	11471.7i	−0.524496	−	0.0924827i	−0.429626	+	0.903007i	$0.641355\pi$
$110$	−1974.84	−	4208.10i	−0.0155614	−	0.0331592i
$111$	14631.6	+	40200.0i	0.112716	+	0.309684i
$112$	29727.1	+	79248.9i	0.223928	+	0.596964i
$113$			128125.i			0.943928i	0.881618	+	0.471964i	$0.156455\pi$
$113$			128125.i			0.943928i	−0.881618	+	0.471964i	$0.843545\pi$
$114$	−102997.	−	3199.21i	−0.742274	−	0.0230558i
$115$		−	283585.i		−	1.99958i
$116$	−33565.5	+	195971.i	−0.231605	+	1.35222i
$117$	−26980.8	−	74129.3i	−0.182218	−	0.500639i
$118$	−30812.4	+	14460.1i	−0.203714	+	0.0956018i
$119$	−41732.8	−	7358.61i	−0.270153	−	0.0476353i
$120$	57529.3	+	121041.i	0.364700	+	0.767323i
$121$	−80442.9	−	139331.i	−0.499487	−	0.865138i
$122$	−157534.	−	41797.7i	−0.958243	−	0.254245i
$123$	−5828.93	−	6946.65i	−0.0347397	−	0.0414012i
$124$	−1696.88	+	4734.21i	−0.00991053	+	0.0276499i
$125$	−69071.6	+	119636.i	−0.395389	+	0.684834i
$126$	−36121.7	−	35945.1i	−0.202694	−	0.201703i
$127$	−42321.9	−	15403.9i	−0.232839	−	0.0847464i	0.222966	−	0.974826i	$-0.428426\pi$
$127$	−42321.9	−	15403.9i	−0.232839	−	0.0847464i	−0.455805	+	0.890080i	$0.650648\pi$
$128$	19320.6	+	184354.i	0.104231	+	0.994553i
$129$	275361.	−	48553.5i	1.45689	−	0.256889i
$130$	214135.	−	150722.i	1.11129	−	0.782201i
$131$	36436.8	−	43423.7i	0.185508	−	0.221080i	−0.665273	−	0.746600i	$-0.731685\pi$
$131$	36436.8	−	43423.7i	0.185508	−	0.221080i	0.850781	+	0.525520i	$0.176129\pi$
$132$	−2400.16	−	4110.53i	−0.0119896	−	0.0205335i
$133$	70992.3	+	108983.i	0.348002	+	0.534232i
$134$	−45798.2	−	169261.i	−0.220337	−	0.814320i
$135$	−199623.	−	167504.i	−0.942708	−	0.791026i
$136$	−84395.7	−	38601.6i	−0.391267	−	0.178961i
$137$	−14364.6	−	81465.5i	−0.0653870	−	0.370828i	−0.999889	−	0.0148712i	$-0.995266\pi$
$137$	−14364.6	−	81465.5i	−0.0653870	−	0.370828i	0.934502	−	0.355957i	$-0.115845\pi$
$138$	−26017.8	−	289220.i	−0.116298	−	1.29280i
$139$	79462.7	−	218322.i	0.348840	−	0.958431i	−0.633896	−	0.773418i	$-0.718545\pi$
$139$	79462.7	−	218322.i	0.348840	−	0.958431i	0.982736	−	0.185012i	$-0.0592325\pi$
$140$	83858.9	−	146906.i	0.361601	−	0.633460i
$141$	66181.2	+	38209.7i	0.280341	+	0.161855i
$142$	30783.5	+	21442.6i	0.128114	+	0.0892396i
$143$	−7124.73	+	5978.36i	−0.0291359	+	0.0244479i
$144$	−56744.9	−	96097.2i	−0.228045	−	0.386193i
$145$	344119.	−	198677.i	1.35921	−	0.784743i
$146$	−18840.3	+	221599.i	−0.0731487	+	0.860372i
$147$	−20051.7	+	113719.i	−0.0765346	+	0.434049i
$148$	90213.5	−	76454.7i	0.338546	−	0.286913i
$149$	−297738.	+	108368.i	−1.09867	+	0.399884i	−0.826827	−	0.562456i	$-0.809856\pi$
$149$	−297738.	+	108368.i	−1.09867	+	0.399884i	−0.271846	+	0.962341i	$0.587634\pi$
$150$	26564.1	−	57333.3i	0.0963977	−	0.208055i
$151$	459416.			1.63970			0.819848	−	0.572581i	$-0.194058\pi$
$151$	459416.			1.63970			0.819848	+	0.572581i	$0.194058\pi$
$152$	90390.8	+	270123.i	0.317333	+	0.948314i
$153$	55874.2			0.192967
$154$	−2525.75	+	5451.32i	−0.00858200	+	0.0185225i
$155$	9444.63	−	3437.56i	0.0315759	−	0.0114927i
$156$	204562.	−	173363.i	0.672996	−	0.570355i
$157$	−89409.7	+	507068.i	−0.289491	+	1.64179i	0.399295	+	0.916822i	$0.369255\pi$
$157$	−89409.7	+	507068.i	−0.289491	+	1.64179i	−0.688786	+	0.724964i	$0.741856\pi$
$158$	−4694.53	+	55216.9i	−0.0149606	+	0.175966i
$159$	230704.	−	133197.i	0.723705	−	0.417831i
$160$	258720.	−	265139.i	0.798968	−	0.818791i
$161$	−280777.	+	235600.i	−0.853682	+	0.716325i
$162$	−96028.8	−	66890.0i	−0.287484	−	0.200251i
$163$	−116613.	−	67326.5i	−0.343778	−	0.198480i	0.318164	−	0.948036i	$-0.396934\pi$
$163$	−116613.	−	67326.5i	−0.343778	−	0.198480i	−0.661941	+	0.749556i	$0.730267\pi$
$164$	−12426.7	+	21769.4i	−0.0360784	+	0.0632029i
$165$	−3253.58	+	8939.14i	−0.00930362	+	0.0255615i
$166$	54135.6	+	601785.i	0.152480	+	1.69500i
$167$	77794.6	+	441195.i	0.215853	+	1.22416i	0.879420	+	0.476047i	$0.157931\pi$
$167$	77794.6	+	441195.i	0.215853	+	1.22416i	−0.663567	+	0.748117i	$0.730958\pi$
$168$	72047.2	−	157519.i	0.196945	−	0.430586i
$169$	−116929.	−	98115.4i	−0.314925	−	0.264253i
$170$	48442.4	+	179033.i	0.128559	+	0.475129i
$171$	−117135.	−	125259.i	−0.306335	−	0.327580i
$172$	−389726.	−	667449.i	−1.00447	−	1.72027i
$173$	445630.	−	531081.i	1.13203	−	1.34911i	0.202970	−	0.979185i	$-0.434941\pi$
$173$	445630.	−	531081.i	1.13203	−	1.34911i	0.929064	−	0.369920i	$-0.120615\pi$
$174$	332729.	−	234196.i	0.833138	−	0.586418i
$175$	−78544.6	+	13849.5i	−0.193875	+	0.0341853i
$176$	−8358.33	+	10161.7i	−0.0203394	+	0.0247278i
$177$	65453.9	+	23823.3i	0.157037	+	0.0571569i
$178$	480467.	+	478118.i	1.13662	+	1.13106i
$179$	−209867.	+	363501.i	−0.489567	+	0.847955i	−0.999928	−	0.0120056i	$-0.996178\pi$
$179$	−209867.	+	363501.i	−0.489567	+	0.847955i	0.510361	+	0.859960i	$0.329512\pi$
$180$	−75254.2	+	209955.i	−0.173121	+	0.482999i
$181$	24965.2	+	29752.4i	0.0566420	+	0.0675033i	0.793622	−	0.608412i	$-0.208193\pi$
$181$	24965.2	+	29752.4i	0.0566420	+	0.0675033i	−0.736980	+	0.675915i	$0.763749\pi$
$182$	−327130.	−	86795.7i	−0.732053	−	0.194232i
$183$	166771.	+	288855.i	0.368122	+	0.637606i
$184$	−724977.	+	344573.i	−1.57863	+	0.750304i
$185$	−232740.	−	41038.3i	−0.499967	−	0.0881577i
$186$	9316.92	−	4372.38i	0.0197465	−	0.00926692i
$187$	−2253.06	−	6190.24i	−0.00471161	−	0.0129450i
$188$	35661.5	−	208208.i	0.0735876	−	0.429639i
$189$			336807.i			0.685846i
$190$	299802.	−	483925.i	0.602490	−	0.972510i
$191$			429729.i			0.852336i	0.904644	+	0.426168i	$0.140137\pi$
$191$			429729.i			0.852336i	−0.904644	+	0.426168i	$0.859863\pi$
$192$	239535.	−	294144.i	0.468939	−	0.575846i
$193$	−150298.	−	412941.i	−0.290443	−	0.797986i	−0.996002	−	0.0893341i	$-0.971526\pi$
$193$	−150298.	−	412941.i	−0.290443	−	0.797986i	0.705559	−	0.708651i	$-0.250696\pi$
$194$	10919.8	+	23268.6i	0.0208311	+	0.0443880i
$195$	−527744.	−	93055.5i	−0.993886	−	0.175249i
$196$	314069.	−	56967.3i	0.583962	−	0.105922i
$197$	−381846.	−	661377.i	−0.701008	−	1.21418i	−0.968113	−	0.250514i	$-0.919401\pi$
$197$	−381846.	−	661377.i	−0.701008	−	1.21418i	0.267105	−	0.963667i	$-0.413933\pi$
$198$	2031.52	−	7656.75i	0.00368264	−	0.0138798i
$199$	390615.	+	465516.i	0.699223	+	0.833302i	0.992438	−	0.122745i	$-0.0391697\pi$
$199$	390615.	+	465516.i	0.699223	+	0.833302i	−0.293215	+	0.956046i	$0.594725\pi$
$200$	−174109.	−	13943.6i	−0.307784	−	0.0246490i
$201$	−179420.	+	310765.i	−0.313243	+	0.542553i
$202$	116333.	−	116904.i	0.200596	−	0.201582i
$203$	−482600.	−	175652.i	−0.821953	−	0.299166i
$204$	65830.6	+	178147.i	0.110752	+	0.299711i
$205$	49334.7	−	8699.04i	0.0819913	−	0.0144573i
$206$	−9422.20	−	13386.4i	−0.0154698	−	0.0219783i
$207$	310642.	−	370209.i	0.503888	−	0.600511i
$208$	−645504.	−	364292.i	−1.03452	−	0.583837i
$209$	−9153.93	+	18028.2i	−0.0144958	+	0.0285487i
$210$	−334154.	+	90414.4i	−0.522875	+	0.141478i
$211$	847287.	+	710958.i	1.31016	+	1.09936i	0.988293	+	0.152571i	$0.0487551\pi$
$211$	847287.	+	710958.i	1.31016	+	1.09936i	0.321868	+	0.946785i	$0.395689\pi$
$212$	−566406.	−	470560.i	−0.865542	−	0.719077i
$213$	−13331.6	−	75607.4i	−0.0201342	−	0.114187i
$214$	−189691.	+	17064.3i	−0.283147	+	0.0254714i
$215$	−528301.	+	1.45150e6i	−0.779445	+	2.14151i
$216$	−185664.	+	713859.i	−0.270766	+	1.04107i
$217$	−11250.0	−	6495.21i	−0.0162183	−	0.00936362i
$218$	213599.	−	306648.i	0.304409	−	0.437017i
$219$	348649.	−	292551.i	0.491222	−	0.412184i
$220$	26295.3	−	128.878i	0.0366287	−	0.000179524i
$221$	321376.	−	185547.i	0.442622	−	0.255548i
$222$	−241130.	−	20500.8i	−0.328374	−	0.0279183i
$223$	−73914.9	+	419192.i	−0.0995337	+	0.564483i	0.893730	+	0.448606i	$0.148079\pi$
$223$	−73914.9	+	419192.i	−0.0995337	+	0.564483i	−0.993263	+	0.115878i	$0.963032\pi$
$224$	−477455.	−	35882.9i	−0.635788	−	0.0477824i
$225$	98818.0	−	35966.8i	0.130131	−	0.0473637i
$226$	−657628.	−	304697.i	−0.856464	−	0.396823i
$227$	−430082.			−0.553970			−0.276985	−	0.960874i	$-0.589335\pi$
$227$	−430082.			−0.553970			−0.276985	+	0.960874i	$0.589335\pi$
$228$	261361.	−	521047.i	0.332969	−	0.663803i
$229$	−496834.			−0.626070			−0.313035	−	0.949742i	$-0.601346\pi$
$229$	−496834.			−0.626070			−0.313035	+	0.949742i	$0.601346\pi$
$230$	1.45555e6	+	674399.i	1.81430	+	0.840615i
$231$	11553.7	−	4205.19i	0.0142459	−	0.00518508i
$232$	−926037.	−	638324.i	−1.12956	−	0.778613i
$233$	−182166.	+	1.03312e6i	−0.219826	+	1.24669i	0.652508	+	0.757782i	$0.273717\pi$
$233$	−182166.	+	1.03312e6i	−0.219826	+	1.24669i	−0.872333	+	0.488911i	$0.837394\pi$
$234$	444647.	+	37803.8i	0.530854	+	0.0451332i
$235$	−365607.	+	211083.i	−0.431861	+	0.249335i
$236$	−943.666	−	192539.i	−0.00110291	−	0.225029i
$237$	86874.4	−	72896.3i	0.100466	−	0.0843013i
$238$	137015.	−	196702.i	0.156793	−	0.225095i
$239$	−925986.	−	534619.i	−1.04860	−	0.605410i	−0.126343	−	0.991987i	$-0.540324\pi$
$239$	−925986.	−	534619.i	−1.04860	−	0.605410i	−0.922257	+	0.386577i	$0.873657\pi$
$240$	−758076.	+	7431.11i	−0.849542	+	0.00832771i
$241$	−218027.	+	599025.i	−0.241807	+	0.664358i	0.758119	+	0.652117i	$0.226119\pi$
$241$	−218027.	+	599025.i	−0.241807	+	0.664358i	−0.999925	+	0.0122412i	$0.996103\pi$
$242$	906448.	−	81542.7i	0.994957	−	0.0895049i
$243$	−130352.	−	739265.i	−0.141613	−	0.803128i
$244$	589170.	−	709176.i	0.633528	−	0.762569i
$245$	−488669.	−	410042.i	−0.520115	−	0.436428i
$246$	49516.9	−	13398.2i	0.0521694	−	0.0141159i
$247$	−1.08969e6	−	331479.i	−1.13648	−	0.345712i
$248$	−20263.9	−	19968.1i	−0.0209215	−	0.0206161i
$249$	794805.	−	947212.i	0.812386	−	0.968164i
$250$	−449792.	−	639031.i	−0.455158	−	0.646654i
$251$	1.89645e6	−	334395.i	1.90001	−	0.335023i	0.904250	−	0.427003i	$-0.140431\pi$
$251$	1.89645e6	−	334395.i	1.90001	−	0.335023i	0.995761	+	0.0919795i	$0.0293194\pi$
$252$	270397.	−	99919.9i	0.268225	−	0.0991175i
$253$	−53541.3	−	19487.4i	−0.0525881	−	0.0191405i
$254$	179710.	−	180593.i	0.174778	−	0.175637i
$255$	189779.	−	328707.i	0.182767	−	0.316562i
$256$	−992180.	−	339249.i	−0.946217	−	0.323533i
$257$	−724167.	−	863029.i	−0.683921	−	0.815066i	0.306685	−	0.951811i	$-0.400780\pi$
$257$	−724167.	−	863029.i	−0.683921	−	0.815066i	−0.990606	+	0.136745i	$0.956336\pi$
$258$	−405630.	+	1.52881e6i	−0.379385	+	1.42989i
$259$	152726.	+	264529.i	0.141470	+	0.245033i
$260$	264373.	+	1.45752e6i	0.242540	+	1.33716i
$261$	666865.	+	117586.i	0.605950	+	0.106845i
$262$	136230.	+	290286.i	0.122608	+	0.261260i
$263$	316012.	+	868235.i	0.281717	+	0.774012i	0.997158	+	0.0753387i	$0.0240038\pi$
$263$	316012.	+	868235.i	0.281717	+	0.774012i	−0.715441	+	0.698674i	$0.753774\pi$
$264$	26806.0	−	2543.93i	0.0236713	−	0.00224644i
$265$			1.47165e6i			1.28733i
$266$	−728205.	+	105207.i	−0.631029	+	0.0911677i
$267$		−	1.38714e6i		−	1.19081i
$268$	977679.	+	167455.i	0.831494	+	0.142417i
$269$	477138.	+	1.31093e6i	0.402035	+	1.10458i	0.961279	+	0.275578i	$0.0888692\pi$
$269$	477138.	+	1.31093e6i	0.402035	+	1.10458i	−0.559244	+	0.829003i	$0.688909\pi$
$270$	1.33447e6	−	626262.i	1.11404	−	0.522813i
$271$	−558012.	−	98392.5i	−0.461551	−	0.0813840i	−0.0619626	−	0.998078i	$-0.519736\pi$
$271$	−558012.	−	98392.5i	−0.461551	−	0.0813840i	−0.399589	+	0.916695i	$0.630847\pi$
$272$	398833.	−	341378.i	0.326865	−	0.279778i
$273$	346310.	+	599827.i	0.281228	+	0.487102i
$274$	452298.	+	120006.i	0.363956	+	0.0965663i
$275$	−7969.45	−	9497.62i	−0.00635472	−	0.00757326i
$276$	1.54635e6	+	554258.i	1.22190	+	0.437965i
$277$	434088.	−	751862.i	0.339921	−	0.588761i	−0.644496	−	0.764607i	$-0.722933\pi$
$277$	434088.	−	751862.i	0.339921	−	0.588761i	0.984418	+	0.175847i	$0.0562663\pi$
$278$	931609.	+	927054.i	0.722972	+	0.719437i
$279$	16095.1	+	5858.15i	0.0123790	+	0.00450557i
$280$	554597.	+	779782.i	0.422749	+	0.594399i
$281$	817345.	−	144120.i	0.617504	−	0.108883i	0.143858	−	0.989598i	$-0.454049\pi$
$281$	817345.	−	144120.i	0.617504	−	0.108883i	0.473645	+	0.880716i	$0.342938\pi$
$282$	−353505.	+	248820.i	−0.264712	+	0.186322i
$283$	1.52082e6	−	1.81244e6i	1.12878	−	1.34523i	0.197771	−	0.980248i	$-0.436630\pi$
$283$	1.52082e6	−	1.81244e6i	1.12878	−	1.34523i	0.931014	−	0.364984i	$-0.118926\pi$
$284$	−183265.	+	107009.i	−0.134829	+	0.0787274i
$285$	−1.13475e6	+	263657.i	−0.827538	+	0.192277i
$286$	−13741.6	−	50786.3i	−0.00993397	−	0.0367140i
$287$	−49599.7	−	41619.1i	−0.0355446	−	0.0298255i
$288$	628184.	−	62723.6i	0.446278	−	0.0445605i
$289$	−200914.	−	1.13944e6i	−0.141503	−	0.802503i
$290$	201393.	+	2.23873e6i	0.140621	+	1.56317i
$291$	17990.6	−	49428.8i	0.0124541	−	0.0342175i
$292$	−1.09260e6	−	623691.i	−0.749899	−	0.428068i
$293$	1.47305e6	+	850468.i	1.00242	+	0.578747i	0.908963	−	0.416876i	$-0.136875\pi$
$293$	1.47305e6	+	850468.i	1.00242	+	0.578747i	0.0934565	+	0.995623i	$0.470208\pi$
$294$	−535999.	−	373356.i	−0.361656	−	0.251916i
$295$	−294770.	+	247342.i	−0.197210	+	0.165479i
$296$	177880.	+	644857.i	0.118004	+	0.427793i
$297$	−45342.8	+	26178.6i	−0.0298275	+	0.0172209i
$298$	151838.	−	1.78591e6i	0.0990465	−	1.16498i
$299$	557359.	−	3.16094e6i	0.360543	−	2.04474i
$300$	231102.	+	272691.i	0.148252	+	0.174931i
$301$	1.87603e6	−	682818.i	1.19350	−	0.434399i
$302$	−1.09255e6	+	2.35804e6i	−0.689322	+	1.48776i
$303$	−337509.			−0.211193
$304$	−1.60142e6	−	178436.i	−0.993850	−	0.110738i
$305$	−1.84259e6			−1.13417
$306$	−132875.	+	286785.i	−0.0811225	+	0.175087i
$307$	1.95286e6	−	710783.i	1.18257	−	0.430419i	0.325458	−	0.945556i	$-0.394481\pi$
$307$	1.95286e6	−	710783.i	1.18257	−	0.430419i	0.857107	+	0.515138i	$0.172259\pi$
$308$	−21973.5	−	25927.8i	−0.0131984	−	0.0155736i
$309$	−5817.25	+	32991.2i	−0.00346594	+	0.0196563i
$310$	−4816.49	+	56651.3i	−0.00284660	+	0.0334816i
$311$	60041.0	−	34664.7i	0.0352004	−	0.0203229i	−0.482297	−	0.876008i	$-0.660197\pi$
$311$	60041.0	−	34664.7i	0.0352004	−	0.0203229i	0.517497	+	0.855685i	$0.326864\pi$
$312$	403348.	+	1.46223e6i	0.234581	+	0.850412i
$313$	−931585.	+	781692.i	−0.537479	+	0.450998i	−0.870675	−	0.491859i	$-0.836317\pi$
$313$	−931585.	+	781692.i	−0.537479	+	0.450998i	0.333196	+	0.942858i	$0.391873\pi$
$314$	−2.39000e6	−	1.66478e6i	−1.36796	−	0.952868i
$315$	−498923.	−	288053.i	−0.283307	−	0.163567i
$316$	−272247.	−	155408.i	−0.153372	−	0.0875498i
$317$	821919.	−	2.25820e6i	0.459389	−	1.26216i	−0.466552	−	0.884494i	$-0.654504\pi$
$317$	821919.	−	2.25820e6i	0.459389	−	1.26216i	0.925941	−	0.377668i	$-0.123274\pi$
$318$	135018.	+	1.50089e6i	0.0748726	+	0.832302i
$319$	−13863.3	−	78622.8i	−0.00762765	−	0.0432585i
$320$	745610.	+	1.95846e6i	0.407040	+	1.06915i
$321$	298574.	+	250533.i	0.161730	+	0.135707i
$322$	−541540.	−	2.00142e6i	−0.291066	−	1.07572i
$323$	484598.	−	644966.i	0.258449	−	0.343978i
$324$	571694.	−	333814.i	0.302553	−	0.176662i
$325$	448942.	−	535028.i	0.235766	−	0.280975i
$326$	622886.	−	438428.i	0.324612	−	0.228483i
$327$	−753156.	+	132802.i	−0.389507	+	0.0686807i
$328$	−82183.6	−	115553.i	−0.0421794	−	0.0593056i
$329$	512735.	+	186620.i	0.261158	+	0.0950537i
$330$	−38144.5	−	37958.0i	−0.0192818	−	0.0191875i
$331$	−661778.	+	1.14623e6i	−0.332003	+	0.575046i	−0.982905	−	0.184116i	$-0.941058\pi$
$331$	−661778.	+	1.14623e6i	−0.332003	+	0.575046i	0.650901	+	0.759162i	$0.274391\pi$
$332$	−3.21752e6	−	1.15325e6i	−1.60205	−	0.574222i
$333$	−258879.	−	308519.i	−0.127934	−	0.152466i
$334$	−2.44952e6	−	649918.i	−1.20148	−	0.318781i
$335$	−991178.	−	1.71677e6i	−0.482547	−	0.835796i
$336$	637159.	+	744395.i	0.307893	+	0.359712i
$337$	2.40999e6	+	424947.i	1.15595	+	0.203826i	0.718574	−	0.695450i	$-0.244795\pi$
$337$	2.40999e6	+	424947.i	1.15595	+	0.203826i	0.437381	+	0.899276i	$0.355906\pi$
$338$	781668.	−	366833.i	0.372161	−	0.174653i
$339$	507298.	+	1.39379e6i	0.239753	+	0.658716i
$340$	−1.03413e6	−	177123.i	−0.485150	−	0.0830954i
$341$		−	2019.38i		−	0.000940444i
$342$	921475.	−	303338.i	0.426009	−	0.140237i
$343$			2.21371e6i			1.01598i
$344$	4.35262e6	−	413071.i	1.98315	−	0.188204i
$345$	−1.12282e6	−	3.08494e6i	−0.507884	−	1.39540i
$346$	1.66612e6	+	3.55026e6i	0.748196	+	1.59430i
$347$	−2.88169e6	−	508120.i	−1.28477	−	0.226539i	−0.510763	−	0.859721i	$-0.670637\pi$
$347$	−2.88169e6	−	508120.i	−1.28477	−	0.226539i	−0.774002	+	0.633183i	$0.781748\pi$
$348$	410790.	+	2.26474e6i	0.181833	+	1.00247i
$349$	−1.05654e6	−	1.82999e6i	−0.464326	−	0.804237i	0.534844	−	0.844951i	$-0.320370\pi$
$349$	−1.05654e6	−	1.82999e6i	−0.464326	−	0.804237i	−0.999171	+	0.0407137i	$0.987037\pi$
$350$	115703.	−	436081.i	0.0504864	−	0.190282i
$351$	−1.89586e6	−	2.25940e6i	−0.821370	−	0.978870i
$352$	−32279.9	−	67066.5i	−0.0138859	−	0.0288502i
$353$	−1.69493e6	+	2.93570e6i	−0.723960	+	1.25394i	0.235440	+	0.971889i	$0.424347\pi$
$353$	−1.69493e6	+	2.93570e6i	−0.723960	+	1.25394i	−0.959400	+	0.282047i	$0.908986\pi$
$354$	−277935.	+	279300.i	−0.117879	+	0.118458i
$355$	398546.	+	145059.i	0.167845	+	0.0610904i
$356$	−3.59664e6	+	1.32907e6i	−1.50408	+	0.555805i
$357$	−483119.	+	85186.9i	−0.200624	+	0.0353755i
$358$	−1.36665e6	−	1.94163e6i	−0.563572	−	0.800681i
$359$	−1.93579e6	+	2.30699e6i	−0.792725	+	0.944732i	−0.999433	−	0.0336702i	$-0.989280\pi$
$359$	−1.93579e6	+	2.30699e6i	−0.792725	+	0.944732i	0.206708	+	0.978403i	$0.433725\pi$
$360$	−898673.	−	885556.i	−0.365465	−	0.360130i
$361$	−2.46180e6	+	265741.i	−0.994224	+	0.107323i
$362$	−212080.	+	57384.1i	−0.0850606	+	0.0230155i
$363$	−1.42675e6	−	1.19719e6i	−0.568306	−	0.476866i
$364$	1.22345e6	−	1.47265e6i	0.483986	−	0.582567i
$365$	436600.	+	2.47608e6i	0.171535	+	0.972822i
$366$	−1.87921e6	+	169051.i	−0.733283	+	0.0659651i
$367$	−1.57919e6	+	4.33880e6i	−0.612027	+	1.68153i	0.113673	+	0.993518i	$0.463738\pi$
$367$	−1.57919e6	+	4.33880e6i	−0.612027	+	1.68153i	−0.725700	+	0.688011i	$0.758484\pi$
$368$	−44508.9	−	4.54052e6i	−0.0171328	−	1.74778i
$369$	73933.4	+	42685.5i	0.0282667	+	0.0163198i
$370$	764120.	−	1.09699e6i	0.290173	−	0.416579i
$371$	1.45707e6	−	1.22263e6i	0.549599	−	0.461169i
$372$	285.342	+	58219.0i	0.000106907	+	0.0218126i
$373$	−4.21245e6	+	2.43206e6i	−1.56770	+	0.905111i	−0.571262	+	0.820768i	$0.693546\pi$
$373$	−4.21245e6	+	2.43206e6i	−1.56770	+	0.905111i	−0.996437	+	0.0843436i	$0.973121\pi$
$374$	37130.7	+	3156.84i	0.0137263	+	0.00116701i
$375$	−277701.	+	1.57492e6i	−0.101976	+	0.578336i
$376$	983862.	+	678184.i	0.358893	+	0.247387i
$377$	4.22615e6	−	1.53819e6i	1.53141	−	0.557387i
$378$	−1.72873e6	−	800968.i	−0.622296	−	0.288327i
$379$	4.08659e6			1.46138			0.730691	−	0.682709i	$-0.239198\pi$
$379$	4.08659e6			1.46138			0.730691	+	0.682709i	$0.239198\pi$
$380$	1.77087e6	+	2.68962e6i	0.629113	+	0.955503i
$381$	−521382.			−0.184011
$382$	−2.20567e6	−	1.02195e6i	−0.773359	−	0.358319i
$383$	1.79648e6	−	653864.i	0.625784	−	0.227767i	−0.00961113	−	0.999954i	$-0.503059\pi$
$383$	1.79648e6	−	653864.i	0.625784	−	0.227767i	0.635395	+	0.772187i	$0.280837\pi$
$384$	940107.	+	1.92897e6i	0.325349	+	0.667571i
$385$	−11794.6	+	66890.5i	−0.00405538	+	0.0229992i
$386$	2.47693e6	+	210588.i	0.846146	+	0.0719392i
$387$	−2.27966e6	+	1.31616e6i	−0.773735	+	0.446716i
$388$	−145399.	+	712.628i	−0.0490324	+	0.000240316i
$389$	−1.45272e6	+	1.21897e6i	−0.486751	+	0.408433i	−0.852860	−	0.522139i	$-0.825134\pi$
$389$	−1.45272e6	+	1.21897e6i	−0.486751	+	0.408433i	0.366109	+	0.930572i	$0.380690\pi$
$390$	1.73266e6	−	2.48745e6i	0.576836	−	0.828119i
$391$	1.96880e6	+	1.13669e6i	0.651269	+	0.376011i
$392$	−454497.	+	1.74749e6i	−0.149388	+	0.574382i
$393$	224441.	−	616646.i	0.0733028	−	0.201398i
$394$	4.30272e6	−	387066.i	1.39638	−	0.125616i
$395$	108790.	+	616977.i	0.0350829	+	0.198965i
$396$	34468.6	+	28635.9i	0.0110455	+	0.00917640i
$397$	1.23461e6	+	1.03596e6i	0.393146	+	0.329888i	0.817837	−	0.575450i	$-0.195173\pi$
$397$	1.23461e6	+	1.03596e6i	0.393146	+	0.329888i	−0.424691	+	0.905338i	$0.639617\pi$
$398$	−3.31828e6	+	897852.i	−1.05004	+	0.284117i
$399$	1.20379e6	+	904469.i	0.378544	+	0.284421i
$400$	485620.	−	860488.i	0.151756	−	0.268903i
$401$	571871.	−	681530.i	0.177598	−	0.211653i	−0.669901	−	0.742451i	$-0.733663\pi$
$401$	571871.	−	681530.i	0.177598	−	0.211653i	0.847498	+	0.530798i	$0.178108\pi$
$402$	−1.16838e6	−	1.65995e6i	−0.360595	−	0.512306i
$403$	112029.	−	19753.8i	0.0343613	−	0.00605882i
$404$	323381.	+	875112.i	0.0985736	+	0.266754i
$405$	−1.24326e6	−	452509.i	−0.376638	−	0.137085i
$406$	2.04925e6	−	2.05932e6i	0.616992	−	0.620023i
$407$	−23741.5	+	41121.6i	−0.00710433	+	0.0123051i
$408$	−1.07092e6	−	85765.4i	−0.318499	−	0.0255071i
$409$	3.89177e6	+	4.63803e6i	1.15037	+	1.37096i	0.917151	+	0.398539i	$0.130483\pi$
$409$	3.89177e6	+	4.63803e6i	1.15037	+	1.37096i	0.233223	+	0.972423i	$0.425073\pi$
$410$	−72674.3	+	273907.i	−0.0213511	+	0.0804718i
$411$	−478817.	−	829335.i	−0.139819	−	0.242173i
$412$	91115.2	−	16526.9i	0.0264453	−	0.00479677i
$413$	489784.	+	86362.2i	0.141296	+	0.0249143i
$414$	1.16142e6	+	2.47483e6i	0.333035	+	0.709650i
$415$	2.33628e6	+	6.41887e6i	0.665893	+	1.82953i
$416$	3.40489e6	−	2.44684e6i	0.964649	−	0.693223i
$417$		−	2.68961e6i		−	0.757441i
$418$	−70763.9	−	89857.4i	−0.0198094	−	0.0251544i
$419$			399918.i			0.111285i	0.998451	+	0.0556423i	$0.0177207\pi$
$419$			399918.i			0.111285i	−0.998451	+	0.0556423i	$0.982279\pi$
$420$	330587.	−	1.93012e6i	0.0914457	−	0.533903i
$421$	−1.28771e6	−	3.53795e6i	−0.354089	−	0.972851i	−0.981042	−	0.193794i	$-0.937921\pi$
$421$	−1.28771e6	−	3.53795e6i	−0.354089	−	0.972851i	0.626953	−	0.779057i	$-0.284302\pi$
$422$	−5.66408e6	+	2.65812e6i	−1.54828	+	0.726597i
$423$	−708507.	−	124929.i	−0.192528	−	0.0339478i
$424$	3.76222e6	−	1.78814e6i	1.01632	−	0.483045i
$425$	247343.	+	428411.i	0.0664243	+	0.115050i
$426$	419774.	+	111376.i	0.112071	+	0.0297351i
$427$	1.53081e6	+	1.82434e6i	0.406304	+	0.484214i
$428$	363521.	−	1.01420e6i	0.0959224	−	0.267618i
$429$	−53834.6	+	93244.2i	−0.0141227	+	0.0244613i
$430$	−6.19372e6	−	6.16344e6i	−1.61540	−	1.60750i
$431$	915575.	+	333242.i	0.237411	+	0.0864105i	0.457986	−	0.888960i	$-0.348571\pi$
$431$	915575.	+	333242.i	0.237411	+	0.0864105i	−0.220575	+	0.975370i	$0.570793\pi$
$432$	−3.22249e6	−	2.65060e6i	−0.830773	−	0.683337i
$433$	−6.20182e6	+	1.09355e6i	−1.58964	+	0.280297i	−0.897350	−	0.441320i	$-0.854511\pi$
$433$	−6.20182e6	+	1.09355e6i	−1.58964	+	0.280297i	−0.692293	+	0.721616i	$0.743399\pi$
$434$	60091.8	−	42296.6i	0.0153141	−	0.0107791i
$435$	2.95680e6	−	3.52378e6i	0.749202	−	0.892864i
$436$	1.06596e6	+	1.82558e6i	0.268551	+	0.459923i
$437$	−1.57919e6	−	6.79662e6i	−0.395576	−	1.70251i
$438$	672447.	+	2.48523e6i	0.167484	+	0.618987i
$439$	261544.	+	219461.i	0.0647714	+	0.0543497i	0.674599	−	0.738185i	$-0.264317\pi$
$439$	261544.	+	219461.i	0.0647714	+	0.0543497i	−0.609827	+	0.792534i	$0.708761\pi$
$440$	−61871.8	+	135272.i	−0.0152357	+	0.0333101i
$441$	−188773.	−	1.07059e6i	−0.0462215	−	0.262135i
$442$	188083.	+	2.09078e6i	0.0457925	+	0.509041i
$443$	1.70383e6	−	4.68123e6i	0.412493	−	1.13332i	−0.543368	−	0.839495i	$-0.682851\pi$
$443$	1.70383e6	−	4.68123e6i	0.412493	−	1.13332i	0.955861	−	0.293820i	$-0.0949268\pi$
$444$	678660.	−	1.18889e6i	0.163378	−	0.286210i
$445$	6.63635e6	+	3.83150e6i	1.58865	+	0.917209i
$446$	−1.97581e6	−	1.37627e6i	−0.470335	−	0.327618i
$447$	−2.80983e6	+	2.35772e6i	−0.665136	+	0.558115i
$448$	1.31962e6	−	2.36530e6i	0.310638	−	0.556789i
$449$	466480.	−	269322.i	0.109199	−	0.0630458i	−0.444406	−	0.895825i	$-0.646585\pi$
$449$	466480.	−	269322.i	0.109199	−	0.0630458i	0.553605	+	0.832780i	$0.313252\pi$
$450$	−50394.3	+	592736.i	−0.0117314	+	0.137984i
$451$	1747.80	−	9912.25i	0.000404622	−	0.00229473i
$452$	3.12783e6	−	2.65080e6i	0.720108	−	0.610282i
$453$	4.99768e6	−	1.81901e6i	1.14426	−	0.416475i
$454$	1.02279e6	−	2.20748e6i	0.232887	−	0.502639i
$455$	−3.82626e6			−0.866456
$456$	2.05283e6	+	2.58060e6i	0.462317	+	0.581176i
$457$	−2.98146e6			−0.667787			−0.333893	−	0.942611i	$-0.608363\pi$
$457$	−2.98146e6			−0.667787			−0.333893	+	0.942611i	$0.608363\pi$
$458$	1.18153e6	−	2.55010e6i	0.263197	−	0.568058i
$459$	1.96305e6	−	714493.i	0.434911	−	0.158295i
$460$	−6.92297e6	+	5.86712e6i	−1.52545	+	1.29280i
$461$	2597.86	−	14733.2i	0.000569329	−	0.00322882i	−0.984522	−	0.175262i	$-0.943923\pi$
$461$	2597.86	−	14733.2i	0.000569329	−	0.00322882i	0.985091	+	0.172034i	$0.0550337\pi$
$462$	−5892.03	+	69301.8i	−0.00128428	+	0.0151057i
$463$	3.83395e6	−	2.21353e6i	0.831178	−	0.479881i	−0.0230779	−	0.999734i	$-0.507347\pi$
$463$	3.83395e6	−	2.21353e6i	0.831178	−	0.479881i	0.854256	+	0.519853i	$0.174013\pi$
$464$	5.47855e6	−	3.23506e6i	1.18133	−	0.697568i
$465$	89131.3	−	74790.0i	0.0191160	−	0.0160403i
$466$	−4.86946e6	−	3.39188e6i	−1.03876	−	0.723562i
$467$	−5.98458e6	−	3.45520e6i	−1.26982	−	0.733130i	−0.294865	−	0.955539i	$-0.595275\pi$
$467$	−5.98458e6	−	3.45520e6i	−1.26982	−	0.733130i	−0.974953	+	0.222409i	$0.928608\pi$
$468$	−1.25146e6	+	2.19233e6i	−0.264120	+	0.462692i
$469$	−876308.	+	2.40764e6i	−0.183961	+	0.505428i
$470$	−213969.	−	2.37853e6i	−0.0446792	−	0.496665i
$471$	1.03505e6	+	5.87006e6i	0.214986	+	1.21924i
$472$	990486.	+	453036.i	0.204641	+	0.0936004i
$473$	237741.	+	199488.i	0.0488597	+	0.0409981i
$474$	167557.	+	619256.i	0.0342544	+	0.126597i
$475$	441879.	−	1.45262e6i	0.0898605	−	0.295404i
$476$	683772.	+	1.17104e6i	0.138323	+	0.236893i
$477$	−1.61206e6	+	1.92117e6i	−0.324402	+	0.386608i
$478$	4.94614e6	−	3.48142e6i	0.990140	−	0.696926i
$479$	−4.84553e6	+	854398.i	−0.964945	+	0.170146i	−0.633854	−	0.773453i	$-0.718528\pi$
$479$	−4.84553e6	+	854398.i	−0.964945	+	0.170146i	−0.331091	+	0.943599i	$0.607417\pi$
$480$	1.76465e6	−	3.90864e6i	0.349588	−	0.774325i
$481$	−2.51354e6	−	914855.i	−0.495363	−	0.180298i
$482$	−2.55612e6	−	2.54362e6i	−0.501145	−	0.498694i
$483$	−2.12155e6	+	3.67464e6i	−0.413796	+	0.716716i
$484$	−1.73711e6	+	4.84644e6i	−0.337065	+	0.940393i
$485$	186785.	+	222602.i	0.0360568	+	0.0429708i
$486$	4.10442e6	+	1.08900e6i	0.788244	+	0.209140i
$487$	2.40242e6	+	4.16112e6i	0.459015	+	0.795038i	0.998909	−	0.0466952i	$-0.0148689\pi$
$487$	2.40242e6	+	4.16112e6i	0.459015	+	0.795038i	−0.539894	+	0.841733i	$0.681536\pi$
$488$	2.23886e6	+	4.71053e6i	0.425577	+	0.895407i
$489$	−1.53513e6	−	270685.i	−0.290317	−	0.0511907i
$490$	3.26673e6	−	1.53306e6i	0.614644	−	0.288449i
$491$	−117881.	−	323877.i	−0.0220669	−	0.0606284i	0.928170	−	0.372156i	$-0.121381\pi$
$491$	−117881.	−	323877.i	−0.0220669	−	0.0606284i	−0.950237	+	0.311528i	$0.899159\pi$
$492$	−48988.5	+	286018.i	−0.00912391	+	0.0532697i
$493$			3.18542e6i			0.590267i
$494$	4.29280e6	−	4.80477e6i	0.791450	−	0.885839i
$495$		−	89556.8i		−	0.0164280i
$496$	150680.	−	56521.7i	0.0275012	−	0.0103160i
$497$	−187486.	−	515113.i	−0.0340469	−	0.0935430i
$498$	2.97161e6	+	6.33208e6i	0.536931	+	1.14412i
$499$	4.44999e6	+	784653.i	0.800032	+	0.141067i	0.558694	−	0.829374i	$-0.311303\pi$
$499$	4.44999e6	+	784653.i	0.800032	+	0.141067i	0.241338	+	0.970441i	$0.422414\pi$
$500$	4.34961e6	−	788954.i	0.778082	−	0.141132i
$501$	2.59314e6	+	4.49145e6i	0.461564	+	0.799452i
$502$	−2.79363e6	+	1.05291e7i	−0.494777	+	1.86480i
$503$	−1.44553e6	−	1.72271e6i	−0.254745	−	0.303593i	0.623482	−	0.781838i	$-0.285718\pi$
$503$	−1.44553e6	−	1.72271e6i	−0.254745	−	0.303593i	−0.878227	+	0.478245i	$0.841273\pi$
$504$	−130177.	+	1.62548e6i	−0.0228276	+	0.285041i
$505$	932256.	−	1.61471e6i	0.162670	−	0.281752i
$506$	227351.	−	228468.i	0.0394748	−	0.0396687i
$507$	−1.66048e6	−	604364.i	−0.286888	−	0.104419i
$508$	499557.	+	1.35187e6i	0.0858866	+	0.232421i
$509$	−712110.	+	125564.i	−0.121830	+	0.0214818i	−0.234230	−	0.972181i	$-0.575257\pi$
$509$	−712110.	+	125564.i	−0.121830	+	0.0214818i	0.112401	+	0.993663i	$0.464146\pi$
$510$	1.23584e6	+	1.75578e6i	0.210395	+	0.298914i
$511$	2.08884e6	−	2.48938e6i	0.353877	−	0.421735i
$512$	4.10079e6	−	4.28578e6i	0.691341	−	0.722529i
$513$	−5.71711e6	−	2.90290e6i	−0.959142	−	0.487011i
$514$	6.15182e6	−	1.66454e6i	1.02706	−	0.277899i
$515$	−141769.	−	118958.i	−0.0235539	−	0.0197641i
$516$	−6.88226e6	−	5.71766e6i	−1.13791	−	0.945353i
$517$	14729.0	+	83532.3i	0.00242352	+	0.0137445i
$518$	−1.72095e6	+	154814.i	−0.281802	+	0.0253505i
$519$	2.74496e6	−	7.54171e6i	0.447319	−	1.22900i
$520$	−8.10973e6	−	2.10922e6i	−1.31522	−	0.342069i
$521$	8.29892e6	+	4.79139e6i	1.33945	+	0.773333i	0.986726	−	0.162393i	$-0.0519212\pi$
$521$	8.29892e6	+	4.79139e6i	1.33945	+	0.773333i	0.352727	+	0.935726i	$0.385255\pi$
$522$	−2.18942e6	+	3.14318e6i	−0.351684	+	0.504886i
$523$	1.92067e6	−	1.61163e6i	0.307042	−	0.257639i	−0.476226	−	0.879323i	$-0.657996\pi$
$523$	1.92067e6	−	1.61163e6i	0.307042	−	0.257639i	0.783268	+	0.621684i	$0.213551\pi$
$524$	−1.81392e6	+	8890.34i	−0.288595	+	0.00141446i
$525$	−799599.	+	461649.i	−0.126612	+	0.0730994i
$526$	−5.20790e6	−	442775.i	−0.820726	−	0.0697780i
$527$	−13991.3	+	79348.6i	−0.00219448	+	0.0124455i
$528$	−50690.6	+	143637.i	−0.00791302	+	0.0224223i
$529$	1.24291e7	−	4.52384e6i	1.93109	−	0.702858i
$530$	−7.55351e6	−	3.49975e6i	−1.16804	−	0.541187i
$531$	−655751.			−0.100926
$532$	1.19176e6	−	3.98785e6i	0.182562	−	0.610885i
$533$	566999.			0.0864499
$534$	7.11974e6	+	3.29877e6i	1.08047	+	0.500610i
$535$	−2.02331e6	+	736426.i	−0.305618	+	0.111236i
$536$	−3.18453e6	+	4.61990e6i	−0.478777	+	0.694577i
$537$	−843766.	+	4.78523e6i	−0.126266	+	0.716090i
$538$	−7.86327e6	−	668534.i	−1.17124	−	0.0995791i
$539$	−110997.	+	64084.1i	−0.0164566	+	0.00950120i
$540$	40869.8	+	8.33878e6i	0.00603140	+	1.23060i
$541$	−4.91015e6	+	4.12011e6i	−0.721277	+	0.605223i	−0.927738	−	0.373232i	$-0.878250\pi$
$541$	−4.91015e6	+	4.12011e6i	−0.721277	+	0.605223i	0.206461	+	0.978455i	$0.433805\pi$
$542$	1.83204e6	−	2.63011e6i	0.267877	−	0.384571i
$543$	389381.	+	224809.i	0.0566729	+	0.0327201i
$544$	803718.	+	2.85893e6i	0.116441	+	0.414196i
$545$	1.44499e6	−	3.97008e6i	0.208388	−	0.572543i
$546$	−3.90230e6	+	351045.i	−0.560194	+	0.0503943i
$547$	−1.54672e6	−	8.77191e6i	−0.221027	−	1.25350i	−0.870137	−	0.492810i	$-0.835970\pi$
$547$	−1.54672e6	−	8.77191e6i	−0.221027	−	1.25350i	0.649110	−	0.760694i	$-0.275141\pi$
$548$	−1.69157e6	+	2.03612e6i	−0.240624	+	0.289636i
$549$	−2.40543e6	−	2.01839e6i	−0.340613	−	0.285808i
$550$	67700.7	−	18318.3i	0.00954303	−	0.00258213i
$551$	7.14106e6	−	6.67793e6i	1.00204	−	0.937050i
$552$	−6.52225e6	+	6.61886e6i	−0.911065	+	0.924561i
$553$	520486.	−	620291.i	0.0723762	−	0.0862546i
$554$	2.82677e6	+	4.01606e6i	0.391305	+	0.555937i
$555$	−2.69431e6	+	475080.i	−0.371292	+	0.0654688i
$556$	−6.97376e6	+	2.57702e6i	−0.956709	+	0.353533i
$557$	−1.31848e7	−	4.79888e6i	−1.80068	−	0.655392i	−0.998282	−	0.0585983i	$-0.981337\pi$
$557$	−1.31848e7	−	4.79888e6i	−1.80068	−	0.655392i	−0.802394	−	0.596794i	$-0.796441\pi$
$558$	−68344.2	+	68680.0i	−0.00929215	+	0.00933780i
$559$	−8.74140e6	+	1.51406e7i	−1.18318	+	2.04933i
$560$	−5.32128e6	+	992163.i	−0.717045	+	0.133694i
$561$	−49019.2	−	58418.8i	−0.00657596	−	0.00783692i
$562$	−1.20402e6	+	4.53792e6i	−0.160802	+	0.606060i
$563$	−4.85515e6	−	8.40937e6i	−0.645553	−	1.11813i	−0.984173	−	0.177208i	$-0.943294\pi$
$563$	−4.85515e6	−	8.40937e6i	−0.645553	−	1.11813i	0.338620	−	0.940923i	$-0.390040\pi$
$564$	−436441.	−	2.40616e6i	−0.0577734	−	0.318513i
$565$	−8.06943e6	−	1.42286e6i	−1.06346	−	0.187517i
$566$	5.68601e6	+	1.21161e7i	0.746048	+	1.58972i
$567$	584859.	+	1.60689e6i	0.0764000	+	0.209907i
$568$	−113419.	−	1.19513e6i	−0.0147508	−	0.155433i
$569$			6.63543e6i			0.859189i	0.903022	+	0.429595i	$0.141343\pi$
$569$			6.63543e6i			0.859189i	−0.903022	+	0.429595i	$0.858657\pi$
$570$	1.34530e6	−	6.45133e6i	0.173433	−	0.831692i
$571$		−	2.80618e6i		−	0.360185i	−0.983650	−	0.180093i	$-0.942360\pi$
$571$		−	2.80618e6i		−	0.360185i	0.983650	−	0.180093i	$-0.0576397\pi$
$572$	293350.	+	50244.3i	0.0374883	+	0.00642091i
$573$	1.70147e6	+	4.67474e6i	0.216489	+	0.594800i
$574$	331572.	−	155605.i	0.0420047	−	0.0197126i
$575$	4.21369e6	+	742987.i	0.531487	+	0.0937155i
$576$	−1.17195e6	+	3.37344e6i	−0.147182	+	0.423659i
$577$	−2.31781e6	−	4.01457e6i	−0.289827	−	0.501995i	0.683942	−	0.729537i	$-0.260264\pi$
$577$	−2.31781e6	−	4.01457e6i	−0.289827	−	0.501995i	−0.973768	+	0.227542i	$0.926931\pi$
$578$	6.32619e6	+	1.67849e6i	0.787631	+	0.208978i
$579$	−3.26999e6	−	3.89703e6i	−0.405369	−	0.483100i
$580$	−1.19697e7	−	4.29028e6i	−1.47745	−	0.529561i
$581$	4.41435e6	−	7.64588e6i	0.542533	−	0.939695i
$582$	210919.	+	209888.i	0.0258112	+	0.0256850i
$583$	277849.	+	101129.i	0.0338561	+	0.0123226i
$584$	5.79954e6	−	4.12475e6i	0.703658	−	0.500456i
$585$	4.96835e6	−	876054.i	0.600236	−	0.105838i
$586$	−7.86829e6	+	5.53822e6i	−0.946534	+	0.666233i
$587$	−7.61261e6	+	9.07235e6i	−0.911881	+	1.08674i	0.0840359	+	0.996463i	$0.473219\pi$
$587$	−7.61261e6	+	9.07235e6i	−0.911881	+	1.08674i	−0.995917	+	0.0902748i	$0.971225\pi$
$588$	3.19099e6	−	1.86323e6i	0.380612	−	0.222241i
$589$	207215.	−	134981.i	0.0246112	−	0.0160319i
$590$	−568530.	−	2.10117e6i	−0.0672393	−	0.248503i
$591$	−6.77250e6	−	5.68281e6i	−0.797592	−	0.669259i
$592$	−3.73287e6	−	620542.i	−0.437763	−	0.0727724i
$593$	−976216.	−	5.53640e6i	−0.114001	−	0.646533i	−0.987240	−	0.159240i	$-0.949096\pi$
$593$	−976216.	−	5.53640e6i	−0.114001	−	0.646533i	0.873239	−	0.487293i	$-0.162015\pi$
$594$	−26536.5	−	294986.i	−0.00308587	−	0.0343033i
$595$	926902.	−	2.54664e6i	0.107335	−	0.294901i
$596$	8.80544e6	+	5.02644e6i	1.01540	+	0.579622i
$597$	6.09240e6	+	3.51745e6i	0.699605	+	0.403917i
$598$	1.48987e7	+	1.03778e7i	1.70371	+	1.18674i
$599$	3.04746e6	−	2.55712e6i	0.347033	−	0.291195i	−0.452564	−	0.891732i	$-0.649491\pi$
$599$	3.04746e6	−	2.55712e6i	0.347033	−	0.291195i	0.799597	+	0.600536i	$0.205046\pi$
$600$	−1.94923e6	+	537683.i	−0.221047	+	0.0609745i
$601$	2.88769e6	−	1.66721e6i	0.326110	−	0.188280i	−0.328003	−	0.944677i	$-0.606375\pi$
$601$	2.88769e6	−	1.66721e6i	0.326110	−	0.188280i	0.654113	+	0.756397i	$0.273042\pi$
$602$	−956720.	+	1.12529e7i	−0.107595	+	1.26553i
$603$	586626.	−	3.32692e6i	0.0657004	−	0.372605i
$604$	−9.50490e6	−	1.12154e7i	−1.06012	−	1.25090i
$605$	9.66853e6	−	3.51906e6i	1.07392	−	0.390875i
$606$	802637.	−	1.73233e6i	0.0887846	−	0.191624i
$607$	−3.83649e6			−0.422632			−0.211316	−	0.977418i	$-0.567775\pi$
$607$	−3.83649e6			−0.422632			−0.211316	+	0.977418i	$0.567775\pi$
$608$	4.72422e6	−	7.79525e6i	0.518288	−	0.855206i
$609$	−5.94536e6			−0.649584
$610$	4.38190e6	−	9.45746e6i	0.476802	−	1.02908i
$611$	−4.49004e6	+	1.63424e6i	−0.486572	+	0.177098i
$612$	−1.15599e6	−	1.36402e6i	−0.124760	−	0.147211i
$613$	−1.34557e6	+	7.63110e6i	−0.144629	+	0.820231i	0.823036	+	0.567990i	$0.192279\pi$
$613$	−1.34557e6	+	7.63110e6i	−0.144629	+	0.820231i	−0.967664	+	0.252241i	$0.918832\pi$
$614$	−995902.	+	1.17138e7i	−0.106609	+	1.25394i
$615$	502237.	−	289967.i	0.0535452	−	0.0309144i
$616$	185335.	−	51123.6i	0.0196791	−	0.00542837i
$617$	5.28272e6	−	4.43273e6i	0.558656	−	0.468768i	−0.319203	−	0.947686i	$-0.603415\pi$
$617$	5.28272e6	−	4.43273e6i	0.558656	−	0.468768i	0.877860	+	0.478918i	$0.158971\pi$
$618$	−155500.	−	108315.i	−0.0163779	−	0.0114082i
$619$	1.32902e7	+	7.67309e6i	1.39413	+	0.804903i	0.993770	−	0.111453i	$-0.0355505\pi$
$619$	1.32902e7	+	7.67309e6i	1.39413	+	0.804903i	0.400363	+	0.916356i	$0.368884\pi$
$620$	−279320.	−	159445.i	−0.0291825	−	0.0166584i
$621$	6.17987e6	−	1.69791e7i	0.643058	−	1.76679i
$622$	35138.6	+	390609.i	0.00364174	+	0.0404824i
$623$	−1.71986e6	−	9.75380e6i	−0.177530	−	1.00682i
$624$	−8.46439e6	−	1.40710e6i	−0.870230	−	0.144665i
$625$	−9.07756e6	−	7.61698e6i	−0.929542	−	0.779978i
$626$	−1.79677e6	−	6.64050e6i	−0.183255	−	0.677274i
$627$	−28199.0	+	232361.i	−0.00286460	+	0.0236044i
$628$	1.42285e7	−	8.30807e6i	1.43966	−	0.840623i
$629$	1.21780e6	−	1.45132e6i	0.122729	−	0.146263i
$630$	2.66499e6	−	1.87579e6i	0.267512	−	0.188293i
$631$	−3.25465e6	+	573883.i	−0.325410	+	0.0573786i	−0.333967	−	0.942585i	$-0.608387\pi$
$631$	−3.25465e6	+	573883.i	−0.325410	+	0.0573786i	0.00855669	+	0.999963i	$0.497276\pi$
$632$	1.44510e6	−	1.02778e6i	0.143914	−	0.102355i
$633$	1.20320e7	+	4.37931e6i	1.19352	+	0.434406i
$634$	9.63605e6	+	9.58893e6i	0.952085	+	0.947430i
$635$	1.44014e6	−	2.49440e6i	0.141733	−	0.245489i
$636$	−8.02469e6	−	2.87629e6i	−0.786657	−	0.281961i
$637$	−4.64098e6	−	5.53090e6i	−0.453170	−	0.540067i
$638$	436516.	+	115818.i	0.0424569	+	0.0112648i
$639$	361386.	+	625940.i	0.0350122	+	0.0606429i
$640$	−1.18253e7	−	830464.i	−1.14120	−	0.0801440i
$641$	−2.38036e6	−	419721.i	−0.228822	−	0.0403474i	0.0580615	−	0.998313i	$-0.481508\pi$
$641$	−2.38036e6	−	419721.i	−0.228822	−	0.0403474i	−0.286883	+	0.957966i	$0.592619\pi$
$642$	−1.99596e6	+	936691.i	−0.191123	+	0.0896930i
$643$	−2.38136e6	−	6.54274e6i	−0.227142	−	0.624069i	0.772802	−	0.634648i	$-0.218855\pi$
$643$	−2.38136e6	−	6.54274e6i	−0.227142	−	0.624069i	−0.999944	+	0.0105791i	$0.996633\pi$
$644$	1.15605e7	+	1.98006e6i	1.09841	+	0.188133i
$645$			1.78816e7i			1.69242i
$646$	2.15798e6	+	4.02110e6i	0.203454	+	0.379108i
$647$		−	1.07157e7i		−	1.00638i	−0.864176	−	0.503189i	$-0.832160\pi$
$647$		−	1.07157e7i		−	1.00638i	0.864176	−	0.503189i	$-0.167840\pi$
$648$	353810.	+	3.72818e6i	0.0331003	+	0.348786i
$649$	26442.4	+	72649.9i	0.00246428	+	0.00677054i
$650$	1.67850e6	+	3.57664e6i	0.155825	+	0.332041i
$651$	−148099.	−	26113.8i	−0.0136962	−	0.00241500i
$652$	769021.	+	4.23972e6i	0.0708466	+	0.390587i
$653$	5.44515e6	+	9.43128e6i	0.499721	+	0.865541i	1.00000		0.000322667i	$-0.000102708\pi$
$653$	5.44515e6	+	9.43128e6i	0.499721	+	0.865541i	−0.500279	+	0.865864i	$0.666769\pi$
$654$	1.10946e6	−	4.18154e6i	0.101431	−	0.382289i
$655$	2.33022e6	+	2.77705e6i	0.212224	+	0.252918i
$656$	788540.	−	147025.i	0.0715425	−	0.0133392i
$657$	−2.14236e6	+	3.71068e6i	−0.193633	+	0.335383i
$658$	−2.17721e6	+	2.18791e6i	−0.196036	+	0.196999i
$659$	1.48327e7	+	5.39868e6i	1.33048	+	0.484255i	0.906801	−	0.421559i	$-0.138517\pi$
$659$	1.48327e7	+	5.39868e6i	1.33048	+	0.484255i	0.423677	+	0.905813i	$0.360739\pi$
$660$	285539.	−	105515.i	0.0255156	−	0.00942878i
$661$	−5.90550e6	+	1.04130e6i	−0.525718	+	0.0926984i	−0.430208	−	0.902730i	$-0.641560\pi$
$661$	−5.90550e6	+	1.04130e6i	−0.525718	+	0.0926984i	−0.0955110	+	0.995428i	$0.530449\pi$
$662$	−4.30948e6	−	6.12258e6i	−0.382190	−	0.542987i
$663$	2.76139e6	−	3.29090e6i	0.243974	−	0.290757i
$664$	1.35709e7	−	1.37720e7i	1.19451	−	1.21220i
$665$	−7.65222e6	+	3.26087e6i	−0.671017	+	0.285943i
$666$	2.19918e6	−	595049.i	0.192121	−	0.0519837i
$667$	2.11058e7	+	1.77099e7i	1.83691	+	1.54135i
$668$	9.16109e6	−	1.10271e7i	0.794339	−	0.956135i
$669$	855676.	+	4.85278e6i	0.0739169	+	0.419204i
$670$	1.11688e7	−	1.00473e6i	0.961212	−	0.0864692i
$671$	−126619.	+	347884.i	−0.0108566	+	0.0298283i
$672$	−5.33599e6	+	1.50008e6i	−0.455819	+	0.128142i
$673$	1.00270e7	+	5.78911e6i	0.853365	+	0.492690i	0.861785	−	0.507274i	$-0.169347\pi$
$673$	1.00270e7	+	5.78911e6i	0.853365	+	0.492690i	−0.00841995	+	0.999965i	$0.502680\pi$
$674$	−7.91237e6	+	1.13592e7i	−0.670898	+	0.963157i
$675$	3.01189e6	−	2.52728e6i	0.254437	−	0.213498i
$676$	23939.5	+	4.88444e6i	0.00201488	+	0.411100i
$677$	−6.93132e6	+	4.00180e6i	−0.581225	+	0.335570i	−0.761620	−	0.648024i	$-0.775596\pi$
$677$	−6.93132e6	+	4.00180e6i	−0.581225	+	0.335570i	0.180395	+	0.983594i	$0.442262\pi$
$678$	−8.36032e6	−	710793.i	−0.698471	−	0.0593839i
$679$	65218.1	−	369870.i	0.00542867	−	0.0307875i
$680$	3.36839e6	−	4.88663e6i	0.279351	−	0.405263i
$681$	−4.67858e6	+	1.70286e6i	−0.386586	+	0.140706i
$682$	10364.9	+	4802.34i	0.000853303	+	0.000395359i
$683$	−140529.			−0.0115269			−0.00576346	−	0.999983i	$-0.501835\pi$
$683$	−140529.			−0.0115269			−0.00576346	+	0.999983i	$0.501835\pi$
$684$	−634435.	+	5.45102e6i	−0.0518498	+	0.445490i
$685$	5.29028e6			0.430777
$686$	−1.13623e7	−	5.26446e6i	−0.921839	−	0.427114i
$687$	−5.40473e6	+	1.96716e6i	−0.436900	+	0.159019i
$688$	−8.23089e6	+	2.33230e7i	−0.662942	+	1.87851i
$689$	−2.89238e6	+	1.64035e7i	−0.232117	+	1.31640i
$690$	1.85042e7	+	1.57323e6i	1.47961	+	0.125797i
$691$	5.71042e6	−	3.29691e6i	0.454959	−	0.262671i	−0.254963	−	0.966951i	$-0.582063\pi$
$691$	5.71042e6	−	3.29691e6i	0.454959	−	0.262671i	0.709922	+	0.704280i	$0.248730\pi$
$692$	−2.21846e7	+	108731.i	−1.76111	+	0.00863152i
$693$	−88670.0	+	74402.9i	−0.00701364	+	0.00588514i
$694$	9.46103e6	−	1.35825e7i	0.745658	−	1.07048i
$695$	1.28676e7	+	7.42914e6i	1.01050	+	0.583414i
$696$	−1.26011e7	−	3.27737e6i	−0.986022	−	0.256449i
$697$	−137354.	+	377377.i	−0.0107093	+	0.0294234i
$698$	1.19053e7	−	1.07099e6i	0.924918	−	0.0832042i
$699$	2.10885e6	+	1.19599e7i	0.163250	+	0.925835i
$700$	1.96312e6	+	1.63092e6i	0.151426	+	0.125802i
$701$	4.99650e6	+	4.19256e6i	0.384035	+	0.322244i	0.814284	−	0.580467i	$-0.197130\pi$
$701$	4.99650e6	+	4.19256e6i	0.384035	+	0.322244i	−0.430249	+	0.902710i	$0.641574\pi$
$702$	1.61054e7	−	4.35775e6i	1.23347	−	0.333749i
$703$	−5.80656e6	+	312490.i	−0.443129	+	0.0238477i
$704$	420997.	−	6190.55i	0.0320146	−	0.000470758i
$705$	−3.14143e6	+	3.74381e6i	−0.238043	+	0.283688i
$706$	−1.10373e7	−	1.56810e7i	−0.833397	−	1.18403i
$707$	−2.37323e6	+	418465.i	−0.178563	+	0.0314855i
$708$	−772602.	−	2.09076e6i	−0.0579259	−	0.156755i
$709$	−1.22222e7	−	4.44851e6i	−0.913131	−	0.332353i	−0.157629	−	0.987498i	$-0.550385\pi$
$709$	−1.22222e7	−	4.44851e6i	−0.913131	−	0.332353i	−0.755502	+	0.655146i	$0.772607\pi$
$710$	−1.69233e6	+	1.70065e6i	−0.125991	+	0.126610i
$711$	−533822.	+	924607.i	−0.0396025	+	0.0685936i
$712$	1.73154e6	−	2.16211e7i	0.128006	−	1.59837i
$713$	447957.	+	533855.i	0.0329999	+	0.0393278i
$714$	711676.	−	2.68229e6i	0.0522441	−	0.196906i
$715$	−297400.	−	515112.i	−0.0217558	−	0.0376822i
$716$	1.32159e7	−	2.39716e6i	0.963413	−	0.174749i
$717$	−1.21900e7	−	2.14942e6i	−0.885533	−	0.156143i
$718$	−7.23751e6	−	1.54221e7i	−0.523936	−	1.11643i
$719$	−1.14405e6	−	3.14326e6i	−0.0825324	−	0.226756i	0.891562	−	0.452900i	$-0.149610\pi$
$719$	−1.14405e6	−	3.14326e6i	−0.0825324	−	0.226756i	−0.974094	+	0.226144i	$0.927388\pi$
$720$	6.68244e6	−	2.50666e6i	0.480401	−	0.180204i
$721$			239194.i			0.0171361i
$722$	4.49048e6	−	1.32676e7i	0.320590	−	0.947218i
$723$			7.37965e6i			0.525037i
$724$	209817.	−	1.22501e6i	0.0148763	−	0.0868545i
$725$	2.05049e6	+	5.63367e6i	0.144881	+	0.398058i
$726$	9.53779e6	−	4.47603e6i	0.671593	−	0.315175i
$727$	−2.32709e7	−	4.10330e6i	−1.63297	−	0.287937i	−0.719393	−	0.694603i	$-0.755580\pi$
$727$	−2.32709e7	−	4.10330e6i	−1.63297	−	0.287937i	−0.913577	+	0.406667i	$0.866691\pi$
$728$	4.64915e6	+	9.78174e6i	0.325121	+	0.684049i
$729$	−6.85865e6	−	1.18795e7i	−0.477991	−	0.827905i
$730$	−1.37473e7	−	3.64749e6i	−0.954793	−	0.253330i
$731$	−7.95950e6	−	9.48577e6i	−0.550925	−	0.656567i
$732$	3.60129e6	−	1.00474e7i	0.248417	−	0.693069i
$733$	7.85776e6	−	1.36100e7i	0.540180	−	0.935620i	−0.458713	−	0.888585i	$-0.651689\pi$
$733$	7.85776e6	−	1.36100e7i	0.540180	−	0.935620i	0.998893	−	0.0470353i	$-0.0149773\pi$
$734$	−1.85142e7	−	1.84237e7i	−1.26843	−	1.26222i
$735$	−6.93943e6	−	2.52574e6i	−0.473811	−	0.172453i
$736$	2.34110e7	+	1.05694e7i	1.59303	+	0.719214i
$737$	−392241.	+	69162.6i	−0.0266001	+	0.00469032i
$738$	−394914.	+	277967.i	−0.0266908	+	0.0187867i
$739$	−1.63576e7	+	1.94942e7i	−1.10181	+	1.31309i	−0.156227	+	0.987721i	$0.549933\pi$
$739$	−1.63576e7	+	1.94942e7i	−1.10181	+	1.31309i	−0.945587	+	0.325370i	$0.894511\pi$
$740$	3.81334e6	+	6.53077e6i	0.255992	+	0.438414i
$741$	−1.31665e7	+	708579.i	−0.880898	+	0.0474070i
$742$	2.81029e6	+	1.03863e7i	0.187388	+	0.692547i
$743$	1.20516e7	+	1.01125e7i	0.800887	+	0.672024i	0.948414	−	0.317034i	$-0.102687\pi$
$743$	1.20516e7	+	1.01125e7i	0.800887	+	0.672024i	−0.147527	+	0.989058i	$0.547131\pi$
$744$	−299499.	−	136987.i	−0.0198364	−	0.00907292i
$745$	−3.51864e6	−	1.99552e7i	−0.232265	−	1.31724i
$746$	−2.46531e6	−	2.74049e7i	−0.162190	−	1.80294i
$747$	−3.98138e6	+	1.09388e7i	−0.261055	+	0.717243i
$748$	−104504.	+	183073.i	−0.00682936	+	0.0119638i
$749$	2.41008e6	+	1.39146e6i	0.156974	+	0.0906289i
$750$	−7.42317e6	−	5.17070e6i	−0.481877	−	0.335657i
$751$	−1.08871e7	+	9.13533e6i	−0.704386	+	0.591050i	−0.923018	−	0.384757i	$-0.874285\pi$
$751$	−1.08871e7	+	9.13533e6i	−0.704386	+	0.591050i	0.218632	+	0.975807i	$0.429841\pi$
$752$	−5.82065e6	+	3.43706e6i	−0.375342	+	0.221637i
$753$	1.93062e7	−	1.11464e7i	1.24082	−	0.716389i
$754$	−2.15521e6	+	2.53495e7i	−0.138058	+	1.62383i
$755$	−5.10191e6	+	2.89344e7i	−0.325736	+	1.84734i
$756$	8.22224e6	−	6.96824e6i	0.523222	−	0.443423i
$757$	1.50384e7	−	5.47352e6i	0.953809	−	0.347158i	0.182205	−	0.983261i	$-0.441677\pi$
$757$	1.50384e7	−	5.47352e6i	0.953809	−	0.347158i	0.771605	+	0.636102i	$0.219454\pi$
$758$	−9.71841e6	+	2.09752e7i	−0.614359	+	1.32597i
$759$	−659599.			−0.0415600
$760$	−1.80164e7	+	2.69311e6i	−1.13144	+	0.169130i
$761$	6.14081e6			0.384383			0.192191	−	0.981357i	$-0.438441\pi$
$761$	6.14081e6			0.384383			0.192191	+	0.981357i	$0.438441\pi$
$762$	1.23991e6	−	2.67610e6i	0.0773575	−	0.166961i
$763$	−5.13125e6	+	1.86762e6i	−0.319089	+	0.116139i
$764$	1.04907e7	−	8.89070e6i	0.650234	−	0.551065i
$765$	−620495.	+	3.51900e6i	−0.0383340	+	0.217403i
$766$	−916151.	+	1.07757e7i	−0.0564151	+	0.663552i
$767$	−3.77174e6	+	2.17761e6i	−0.231501	+	0.133657i
$768$	−1.21365e7	+	237961.i	−0.742490	+	0.0145580i
$769$	−793674.	+	665972.i	−0.0483979	+	0.0406107i	−0.666666	−	0.745357i	$-0.732279\pi$
$769$	−793674.	+	665972.i	−0.0483979	+	0.0406107i	0.618268	+	0.785967i	$0.287835\pi$
$770$	−315280.	−	219612.i	−0.0191633	−	0.0133484i
$771$	−1.12948e7	−	6.52106e6i	−0.684295	−	0.395078i
$772$	−6.97132e6	+	1.22125e7i	−0.420990	+	0.737500i
$773$	1.02027e7	−	2.80318e7i	0.614140	−	1.68734i	−0.106748	−	0.994286i	$-0.534044\pi$
$773$	1.02027e7	−	2.80318e7i	0.614140	−	1.68734i	0.720889	−	0.693051i	$-0.243734\pi$
$774$	−1.33415e6	−	1.48308e7i	−0.0800486	−	0.889839i
$775$	26332.8	+	149341.i	0.00157486	+	0.00893150i
$776$	342119.	−	747985.i	0.0203950	−	0.0445901i
$777$	2.70878e6	+	2.27294e6i	0.160961	+	0.135063i
$778$	−2.80189e6	−	1.03552e7i	−0.165959	−	0.613352i
$779$	1.13395e6	−	483216.i	0.0669501	−	0.0285297i
$780$	8.64684e6	+	1.48087e7i	0.508887	+	0.871525i
$781$	54774.7	−	65277.9i	0.00321331	−	0.00382947i
$782$	−1.05163e7	+	7.40209e6i	−0.614961	+	0.432850i
$783$	2.49329e7	−	4.39635e6i	1.45335	−	0.256264i
$784$	−7.88851e6	−	6.48854e6i	−0.458358	−	0.377014i
$785$	−3.09426e7	−	1.12622e7i	−1.79218	−	0.652302i
$786$	2.63131e6	+	2.61844e6i	0.151920	+	0.151177i
$787$	9.09582e6	−	1.57544e7i	0.523486	−	0.906704i	−0.476140	−	0.879369i	$-0.657965\pi$
$787$	9.09582e6	−	1.57544e7i	0.523486	−	0.906704i	0.999626	−	0.0273349i	$-0.00870204\pi$
$788$	−8.24569e6	+	2.30050e7i	−0.473055	+	1.31980i
$789$	6.87537e6	+	8.19375e6i	0.393191	+	0.468587i
$790$	−3.42547e6	−	908860.i	−0.195277	−	0.0518119i
$791$	5.29523e6	+	9.17162e6i	0.300915	+	0.521200i
$792$	−228950.	+	108817.i	−0.0129696	+	0.00616431i
$793$	−2.05382e7	−	3.62144e6i	−1.15979	−	0.204502i
$794$	−8.25332e6	+	3.87324e6i	−0.464598	+	0.218033i
$795$	5.82682e6	+	1.60091e7i	0.326975	+	0.898356i
$796$	3.28287e6	−	1.91669e7i	0.183641	−	1.07218i
$797$			1.30936e7i			0.730150i	0.930978	+	0.365075i	$0.118957\pi$
$797$			1.30936e7i			0.730150i	−0.930978	+	0.365075i	$0.881043\pi$
$798$	−7.50511e6	+	4.02773e6i	−0.417205	+	0.223899i
$799$		−	3.38432e6i		−	0.187545i
$800$	3.26176e6	+	4.53888e6i	0.180189	+	0.250740i
$801$	4.46642e6	+	1.22714e7i	0.245968	+	0.675791i
$802$	2.13810e6	+	4.55600e6i	0.117380	+	0.250120i
$803$	497491.	+	87721.1i	0.0272268	+	0.00480082i
$804$	1.12986e7	−	2.04939e6i	0.616428	−	0.111811i
$805$	−1.17202e7	−	2.02999e7i	−0.637447	−	1.10409i
$806$	−165029.	+	621990.i	−0.00894793	+	0.0337245i
$807$	1.03809e7	+	1.23715e7i	0.561117	+	0.668713i
$808$	−5.26072e6	−	421306.i	−0.283476	−	0.0227023i
$809$	−1.38374e7	+	2.39670e7i	−0.743330	+	1.28749i	0.207641	+	0.978205i	$0.433422\pi$
$809$	−1.38374e7	+	2.39670e7i	−0.743330	+	1.28749i	−0.950971	+	0.309281i	$0.899912\pi$
$810$	5.27920e6	−	5.30514e6i	0.282720	−	0.284109i
$811$	1.11260e7	+	4.04952e6i	0.593998	+	0.216198i	0.621487	−	0.783424i	$-0.286529\pi$
$811$	1.11260e7	+	4.04952e6i	0.593998	+	0.216198i	−0.0274887	+	0.999622i	$0.508751\pi$
$812$	5.69648e6	+	1.54155e7i	0.303191	+	0.820477i
$813$	−6.45982e6	+	1.13904e6i	−0.342763	+	0.0604384i
$814$	−154604.	−	219650.i	−0.00817825	−	0.0116190i
$815$	5.53529e6	−	6.59670e6i	0.291908	−	0.347883i
$816$	2.98699e6	−	5.29277e6i	0.157040	−	0.278264i
$817$	−4.57882e6	+	3.77296e7i	−0.239993	+	1.97755i
$818$	−3.30607e7	+	8.94548e6i	−1.72754	+	0.467434i
$819$	−4.99503e6	−	4.19133e6i	−0.260213	−	0.218344i
$820$	−1.23305e6	−	1.02440e6i	−0.0640394	−	0.0532028i
$821$	−4.76824e6	−	2.70421e7i	−0.246888	−	1.40017i	−0.816066	−	0.577959i	$-0.803849\pi$
$821$	−4.76824e6	−	2.70421e7i	−0.246888	−	1.40017i	0.569178	−	0.822215i	$-0.307262\pi$
$822$	5.39541e6	−	485363.i	0.278513	−	0.0250546i
$823$	1.18256e7	−	3.24905e7i	0.608587	−	1.67208i	−0.124729	−	0.992191i	$-0.539806\pi$
$823$	1.18256e7	−	3.24905e7i	0.608587	−	1.67208i	0.733316	−	0.679888i	$-0.237971\pi$
$824$	−131855.	+	506969.i	−0.00676518	+	0.0260114i
$825$	−124299.	−	71764.2i	−0.00635819	−	0.00367090i
$826$	−1.60804e6	+	2.30853e6i	−0.0820060	+	0.117730i
$827$	−2.27253e7	+	1.90688e7i	−1.15544	+	0.969526i	−0.999833	−	0.0182936i	$-0.994177\pi$
$827$	−2.27253e7	+	1.90688e7i	−1.15544	+	0.969526i	−0.155603	+	0.987820i	$0.549732\pi$
$828$	−1.54645e7	+	75794.5i	−0.783901	+	0.00384204i
$829$	2.02357e7	−	1.16831e7i	1.02266	−	0.590435i	0.107789	−	0.994174i	$-0.465623\pi$
$829$	2.02357e7	−	1.16831e7i	1.02266	−	0.590435i	0.914874	+	0.403739i	$0.132290\pi$
$830$	−3.85020e7	−	3.27344e6i	−1.93994	−	0.164934i
$831$	1.74524e6	−	9.89774e6i	0.0876703	−	0.497203i
$832$	4.46167e6	+	2.32951e7i	0.223454	+	1.16669i
$833$	4.80546e6	−	1.74905e6i	0.239951	−	0.0873350i
$834$	1.38049e7	+	6.39621e6i	0.687257	+	0.318425i
$835$	−2.86507e7			−1.42207
$836$	629496.	−	149518.i	0.0311514	−	0.00739908i
$837$	640389.			0.0315958
$838$	−2.05265e6	−	951052.i	−0.100973	−	0.0467836i
$839$	4.48849e6	−	1.63368e6i	0.220138	−	0.0801237i	−0.229597	−	0.973286i	$-0.573741\pi$
$839$	4.48849e6	−	1.63368e6i	0.220138	−	0.0801237i	0.449735	+	0.893162i	$0.351519\pi$
$840$	9.12056e6	+	6.28687e6i	0.445988	+	0.307423i
$841$	−3.14194e6	+	1.78188e7i	−0.153182	+	0.868737i
$842$	2.12215e7	+	1.80425e6i	1.03157	+	0.0877035i
$843$	8.32073e6	−	4.80398e6i	0.403267	−	0.232826i
$844$	−173469.	−	3.53933e7i	−0.00838235	−	1.71027i
$845$	7.47791e6	−	6.27471e6i	0.360279	−	0.302310i
$846$	2.32614e6	−	3.33945e6i	0.111740	−	0.160417i
$847$	−1.15167e7	−	6.64918e6i	−0.551595	−	0.318464i
$848$	230976.	+	2.35627e7i	0.0110300	+	1.12522i
$849$	9.36781e6	−	2.57379e7i	0.446035	−	1.22547i
$850$	−2.78711e6	+	250724.i	−0.132314	+	0.0119028i
$851$	−2.84551e6	−	1.61377e7i	−0.134690	−	0.763866i
$852$	−1.56993e6	+	1.88971e6i	−0.0740938	+	0.0891857i
$853$	1.85992e7	+	1.56066e7i	0.875227	+	0.734403i	0.965192	−	0.261542i	$-0.0842310\pi$
$853$	1.85992e7	+	1.56066e7i	0.875227	+	0.734403i	−0.0899648	+	0.995945i	$0.528675\pi$
$854$	−1.30042e7	+	3.51866e6i	−0.610155	+	0.165094i
$855$	9.18969e6	−	5.98623e6i	0.429918	−	0.280052i
$856$	4.34111e6	+	4.27774e6i	0.202496	+	0.199540i
$857$	−2.26480e6	+	2.69908e6i	−0.105336	+	0.125535i	−0.816137	−	0.577859i	$-0.803888\pi$
$857$	−2.26480e6	+	2.69908e6i	−0.105336	+	0.125535i	0.710800	+	0.703394i	$0.248333\pi$
$858$	−350569.	−	498062.i	−0.0162576	−	0.0230975i
$859$	6.80486e6	−	1.19988e6i	0.314656	−	0.0554824i	−0.0140899	−	0.999901i	$-0.504485\pi$
$859$	6.80486e6	−	1.19988e6i	0.314656	−	0.0554824i	0.328746	+	0.944418i	$0.393374\pi$
$860$	4.63644e7	−	1.71331e7i	2.13766	−	0.789931i
$861$	−704349.	−	256362.i	−0.0323802	−	0.0117854i
$862$	−3.88777e6	+	3.90688e6i	−0.178210	+	0.179086i
$863$	1.52006e7	−	2.63282e7i	0.694759	−	1.20336i	−0.275503	−	0.961300i	$-0.588844\pi$
$863$	1.52006e7	−	2.63282e7i	0.694759	−	1.20336i	0.970262	−	0.242058i	$-0.0778223\pi$
$864$	2.12682e7	−	1.02366e7i	0.969273	−	0.466522i
$865$	2.84991e7	+	3.39639e7i	1.29506	+	1.54340i
$866$	9.13582e6	−	3.44326e7i	0.413955	−	1.56018i
$867$	−6.69710e6	−	1.15997e7i	−0.302579	−	0.524083i
$868$	74189.9	+	409019.i	0.00334230	+	0.0184266i
$869$	123962.	+	21857.8i	0.00556851	+	0.000981879i
$870$	1.10548e7	+	2.35563e7i	0.495170	+	1.05514i
$871$	−7.67387e6	−	2.10838e7i	−0.342744	−	0.941680i
$872$	−1.19051e7	+	1.12982e6i	−0.530205	+	0.0503172i
$873$			495203.i			0.0219911i
$874$	3.86405e7	+	8.05771e6i	1.71106	+	0.356807i
$875$			1.14185e7i			0.504185i
$876$	−1.43551e7	−	2.45871e6i	−0.632041	−	0.108255i
$877$	7.37887e6	+	2.02733e7i	0.323960	+	0.890071i	0.989606	+	0.143804i	$0.0459336\pi$
$877$	7.37887e6	+	2.02733e7i	0.323960	+	0.890071i	−0.665647	+	0.746267i	$0.731844\pi$
$878$	−1.74841e6	+	820520.i	−0.0765433	+	0.0359214i
$879$	1.93917e7	+	3.41929e6i	0.846534	+	0.149267i
$880$	−547172.	−	639262.i	−0.0238186	−	0.0278274i
$881$	3.36625e6	+	5.83052e6i	0.146119	+	0.253086i	0.929790	−	0.368091i	$-0.119988\pi$
$881$	3.36625e6	+	5.83052e6i	0.146119	+	0.253086i	−0.783671	+	0.621176i	$0.786655\pi$
$882$	5.94391e6	+	1.57707e6i	0.257277	+	0.0682619i
$883$	816215.	+	972728.i	0.0352292	+	0.0419845i	0.783371	−	0.621554i	$-0.213498\pi$
$883$	816215.	+	972728.i	0.0352292	+	0.0419845i	−0.748142	+	0.663538i	$0.769054\pi$
$884$	−1.11786e7	−	4.00675e6i	−0.481124	−	0.172449i
$885$	−2.22729e6	+	3.85778e6i	−0.0955913	+	0.165569i
$886$	1.99754e7	+	1.98778e7i	0.854893	+	0.850713i
$887$	2.86731e7	+	1.04362e7i	1.22367	+	0.445381i	0.871427	−	0.490526i	$-0.163195\pi$
$887$	2.86731e7	+	1.04362e7i	1.22367	+	0.445381i	0.352248	+	0.935907i	$0.385417\pi$
$888$	4.48829e6	+	6.31068e6i	0.191006	+	0.268561i
$889$	−3.66616e6	+	646442.i	−0.155581	+	0.0274331i
$890$	−3.54479e7	+	2.49506e7i	−1.50008	+	1.05586i
$891$	−170869.	+	203633.i	−0.00721055	+	0.00859320i
$892$	1.17627e7	−	6.86828e6i	0.494988	−	0.289025i
$893$	−7.58697e6	+	7.09492e6i	−0.318376	+	0.297727i
$894$	−5.41937e6	−	2.00289e7i	−0.226780	−	0.838135i
$895$	−2.05629e7	−	1.72544e7i	−0.858079	−	0.720014i
$896$	9.00212e6	+	1.23982e7i	0.374606	+	0.515926i
$897$	−6.45226e6	−	3.65926e7i	−0.267751	−	1.51849i
$898$	273004.	+	3.03478e6i	0.0112974	+	0.125585i
$899$	−333976.	+	917591.i	−0.0137821	+	0.0378661i
$900$	−2.92249e6	−	1.66826e6i	−0.120267	−	0.0686525i
$901$	−1.02170e7	−	5.89878e6i	−0.419286	−	0.242075i
$902$	46720.1	+	32543.4i	0.00191200	+	0.00133182i
$903$	1.77045e7	−	1.48559e7i	0.722545	−	0.606288i
$904$	6.16737e6	+	2.23581e7i	0.251003	+	0.909943i
$905$	−2.15107e6	+	1.24192e6i	−0.0873038	+	0.0504049i
$906$	−2.54867e6	+	2.99774e7i	−0.103156	+	1.21331i
$907$	6.33624e6	−	3.59346e7i	0.255749	−	1.45042i	−0.538395	−	0.842693i	$-0.680969\pi$
$907$	6.33624e6	−	3.59346e7i	0.255749	−	1.45042i	0.794143	−	0.607730i	$-0.207920\pi$
$908$	8.89800e6	+	1.04993e7i	0.358161	+	0.422615i
$909$	2.98580e6	−	1.08674e6i	0.119853	−	0.0436231i
$910$	9.09931e6	−	1.96390e7i	0.364255	−	0.786171i
$911$	−3.48828e7			−1.39257			−0.696283	−	0.717768i	$-0.745164\pi$
$911$	−3.48828e7			−1.39257			−0.696283	+	0.717768i	$0.745164\pi$
$912$	−1.81273e7	+	4.39956e6i	−0.721681	+	0.175155i
$913$	1.37244e6			0.0544898
$914$	7.09026e6	−	1.53029e7i	0.280735	−	0.605910i
$915$	−2.00444e7	+	7.29555e6i	−0.791479	+	0.288075i
$916$	1.02790e7	+	1.21289e7i	0.404776	+	0.477619i
$917$	813624.	−	4.61429e6i	0.0319522	−	0.181210i
$918$	−1.00110e6	+	1.17749e7i	−0.0392077	+	0.461159i
$919$	62467.0	−	36065.4i	0.00243984	−	0.00140864i	−0.498780	−	0.866729i	$-0.666218\pi$
$919$	62467.0	−	36065.4i	0.00243984	−	0.00140864i	0.501219	+	0.865320i	$0.332885\pi$
$920$	−1.36505e7	−	4.94862e7i	−0.531715	−	1.92759i
$921$	1.84296e7	−	1.54643e7i	0.715925	−	0.600732i
$922$	69442.9	+	48371.3i	0.00269030	+	0.00187396i
$923$	4.15724e6	+	2.40018e6i	0.160620	+	0.0927342i
$924$	−341693.	−	195050.i	−0.0131661	−	0.00751564i
$925$	1.21955e6	−	3.35068e6i	0.0468646	−	0.128759i
$926$	2.24379e6	+	2.49425e7i	0.0859915	+	0.955902i
$927$	−54765.4	−	310590.i	−0.00209318	−	0.0118710i
$928$	3.57591e6	+	3.58131e7i	0.136306	+	1.36512i
$929$	−1.45732e6	−	1.22284e6i	−0.0554007	−	0.0464867i	0.614667	−	0.788787i	$-0.289290\pi$
$929$	−1.45732e6	−	1.22284e6i	−0.0554007	−	0.0464867i	−0.670068	+	0.742300i	$0.733735\pi$
$930$	171910.	+	635343.i	0.00651767	+	0.0240880i
$931$	−1.39952e7	−	7.10616e6i	−0.529182	−	0.268696i
$932$	2.89896e7	−	1.69272e7i	1.09321	−	0.638328i
$933$	515896.	−	614821.i	0.0194025	−	0.0231230i
$934$	3.19665e7	−	2.25001e7i	1.19902	−	0.843953i
$935$	414887.	−	73155.7i	0.0155203	−	0.00273665i
$936$	−8.27646e6	−	1.16370e7i	−0.308784	−	0.434161i
$937$	−2.20810e7	−	8.03682e6i	−0.821617	−	0.299044i	−0.103203	−	0.994660i	$-0.532909\pi$
$937$	−2.20810e7	−	8.03682e6i	−0.821617	−	0.299044i	−0.718414	+	0.695616i	$0.755132\pi$
$938$	−1.02737e7	−	1.02235e7i	−0.381259	−	0.379395i
$939$	−7.03907e6	+	1.21920e7i	−0.260526	+	0.451245i
$940$	1.27171e7	+	4.55818e6i	0.469427	+	0.168257i
$941$	3.24070e7	+	3.86212e7i	1.19307	+	1.42184i	0.881868	+	0.471497i	$0.156286\pi$
$941$	3.24070e7	+	3.86212e7i	1.19307	+	1.42184i	0.311199	+	0.950345i	$0.399269\pi$
$942$	−3.25907e7	−	8.64711e6i	−1.19665	−	0.317500i
$943$	1.73676e6	+	3.00816e6i	0.0636007	+	0.110160i
$944$	−4.68079e6	+	4.00649e6i	−0.170958	+	0.146330i
$945$	−2.12124e7	−	3.74031e6i	−0.772698	−	0.136248i
$946$	−1.58929e6	+	745844.i	−0.0577397	+	0.0270969i
$947$	2.13703e6	+	5.87143e6i	0.0774345	+	0.212750i	0.972370	−	0.233447i	$-0.0750005\pi$
$947$	2.13703e6	+	5.87143e6i	0.0774345	+	0.212750i	−0.894935	+	0.446196i	$0.852778\pi$
$948$	−3.57692e6	−	612647.i	−0.129267	−	0.0221406i
$949$			2.84574e7i			1.02572i
$950$	6.40499e6	+	5.72252e6i	0.230255	+	0.205721i
$951$		−	2.78198e7i		−	0.997477i
$952$	−7.63666e6	+	724731.i	−0.273093	+	0.0259170i
$953$	2.89302e6	+	7.94851e6i	0.103186	+	0.283500i	0.980533	−	0.196356i	$-0.0629109\pi$
$953$	2.89302e6	+	7.94851e6i	0.103186	+	0.283500i	−0.877347	+	0.479856i	$0.840689\pi$
$954$	−6.02713e6	−	1.28430e7i	−0.214407	−	0.456872i
$955$	−2.70647e7	−	4.77223e6i	−0.960271	−	0.169322i
$956$	6.10655e6	+	3.36663e7i	0.216098	+	1.19138i
$957$	−462109.	−	800396.i	−0.0163104	−	0.0282504i
$958$	7.13789e6	−	2.69025e7i	0.251279	−	0.947063i
$959$	−4.39512e6	−	5.23789e6i	−0.154321	−	0.183912i
$960$	1.58653e7	+	1.83526e7i	0.555611	+	0.642718i
$961$	1.43022e7	−	2.47722e7i	0.499569	−	0.865278i
$962$	1.06732e7	−	1.07256e7i	0.371840	−	0.373667i
$963$	−3.44804e6	−	1.25498e6i	−0.119814	−	0.0436087i
$964$	1.91344e7	−	7.07073e6i	0.663165	−	0.245060i
$965$	2.76765e7	−	4.88011e6i	0.956736	−	0.168698i
$966$	−1.38155e7	−	1.96280e7i	−0.476347	−	0.676758i
$967$	2.67802e7	−	3.19154e7i	0.920973	−	1.09757i	−0.0739824	−	0.997260i	$-0.523571\pi$
$967$	2.67802e7	−	3.19154e7i	0.920973	−	1.09757i	0.994956	−	0.100314i	$-0.0319847\pi$
$968$	−2.07442e7	−	2.04414e7i	−0.711556	−	0.701170i
$969$	2.71795e6	−	8.93488e6i	0.0929890	−	0.305689i
$970$	−1.58674e6	+	429337.i	−0.0541473	+	0.0146510i
$971$	9.51106e6	+	7.98073e6i	0.323729	+	0.271640i	0.790139	−	0.612928i	$-0.210008\pi$
$971$	9.51106e6	+	7.98073e6i	0.323729	+	0.271640i	−0.466410	+	0.884569i	$0.654453\pi$
$972$	−1.53503e7	+	1.84769e7i	−0.521136	+	0.627284i
$973$	−3.33474e6	−	1.89123e7i	−0.112922	−	0.640415i
$974$	−2.70710e7	+	2.43527e6i	−0.914339	+	0.0822526i
$975$	2.76536e6	−	7.59776e6i	0.0931622	−	0.255961i
$976$	−2.95020e7	+	289196.i	−0.991350	+	0.00971780i
$977$	9.74652e6	+	5.62716e6i	0.326673	+	0.188605i	0.654363	−	0.756181i	$-0.272937\pi$
$977$	9.74652e6	+	5.62716e6i	0.326673	+	0.188605i	−0.327690	+	0.944785i	$0.606270\pi$
$978$	5.04006e6	−	7.23562e6i	0.168496	−	0.241896i
$979$	1.17943e6	−	989659.i	0.0393292	−	0.0330011i
$980$	100047.	+	2.04129e7i	0.00332767	+	0.678954i
$981$	6.23524e6	−	3.59992e6i	0.206862	−	0.119432i
$982$	1.94270e6	+	165168.i	0.0642874	+	0.00546571i
$983$	−2.38331e6	+	1.35164e7i	−0.0786677	+	0.446146i	0.919877	+	0.392208i	$0.128289\pi$
$983$	−2.38331e6	+	1.35164e7i	−0.0786677	+	0.446146i	−0.998544	+	0.0539385i	$0.982822\pi$
$984$	−1.35154e6	−	931627.i	−0.0444981	−	0.0306729i
$985$	4.58945e7	−	1.67042e7i	1.50720	−	0.548575i
$986$	−1.63498e7	−	7.57530e6i	−0.535574	−	0.248146i
$987$	6.31661e6			0.206391
$988$	1.44526e7	+	3.34600e7i	0.471036	+	1.09052i
$989$	−1.07103e8			−3.48184
$990$	459668.	+	212977.i	0.0149058	+	0.00690628i
$991$	3.31996e7	−	1.20836e7i	1.07386	−	0.390853i	0.256242	−	0.966613i	$-0.417516\pi$
$991$	3.31996e7	−	1.20836e7i	1.07386	−	0.390853i	0.817619	+	0.575759i	$0.195293\pi$
$992$	−68226.1	+	907809.i	−0.00220126	+	0.0292897i
$993$	−2.66066e6	+	1.50894e7i	−0.0856281	+	0.485621i
$994$	3.08978e6	+	262693.i	0.0991885	+	0.00843299i
$995$	−3.36564e7	+	1.94316e7i	−1.07773	+	0.622228i
$996$	−3.95674e7	+	193927.i	−1.26383	+	0.00619427i
$997$	2.86336e7	−	2.40265e7i	0.912301	−	0.765512i	−0.0602542	−	0.998183i	$-0.519191\pi$
$997$	2.86336e7	−	2.40265e7i	0.912301	−	0.765512i	0.972555	+	0.232671i	$0.0747467\pi$
$998$	−1.46100e7	+	2.09744e7i	−0.464327	+	0.666598i
$999$	−1.30405e7	−	7.52894e6i	−0.413410	−	0.238682i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.k.a.3.18	yes	288
4.3	odd	2	inner	76.6.k.a.3.10	✓	288
19.13	odd	18	inner	76.6.k.a.51.10	yes	288
76.51	even	18	inner	76.6.k.a.51.18	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.k.a.3.10	✓	288	4.3	odd	2	inner
76.6.k.a.3.18	yes	288	1.1	even	1	trivial
76.6.k.a.51.10	yes	288	19.13	odd	18	inner
76.6.k.a.51.18	yes	288	76.51	even	18	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.37812 + 5.13269i) q^{2} +(10.8783 - 3.95939i) q^{3} +(-20.6891 - 24.4123i) q^{4} +(-11.1052 + 62.9808i) q^{5} +(-5.54764 + 65.2511i) q^{6} +(71.5832 - 41.3286i) q^{7} +(174.502 - 48.1354i) q^{8} +(-83.4872 + 70.0541i) q^{9} +O(q^{10})\)	\(q+(-2.37812 + 5.13269i) q^{2} +(10.8783 - 3.95939i) q^{3} +(-20.6891 - 24.4123i) q^{4} +(-11.1052 + 62.9808i) q^{5} +(-5.54764 + 65.2511i) q^{6} +(71.5832 - 41.3286i) q^{7} +(174.502 - 48.1354i) q^{8} +(-83.4872 + 70.0541i) q^{9} +(-296.852 - 206.775i) q^{10} +(11.1277 + 6.42460i) q^{11} +(-321.721 - 183.649i) q^{12} +(-247.565 + 680.180i) q^{13} +(41.8936 + 465.699i) q^{14} +(128.559 + 729.097i) q^{15} +(-167.922 + 1010.14i) q^{16} +(-392.735 - 329.544i) q^{17} +(-161.024 - 595.111i) q^{18} +(84.5616 + 1571.29i) q^{19} +(1767.26 - 1031.91i) q^{20} +(615.071 - 733.013i) q^{21} +(-59.4386 + 41.8368i) q^{22} +(-4366.95 + 770.011i) q^{23} +(1707.71 - 1214.56i) q^{24} +(-906.714 - 330.017i) q^{25} +(-2902.42 - 2888.23i) q^{26} +(-2037.37 + 3528.84i) q^{27} +(-2489.92 - 892.460i) q^{28} +(-3993.82 - 4759.65i) q^{29} +(-4047.96 - 1074.02i) q^{30} +(-78.5801 - 136.105i) q^{31} +(-4785.39 - 3264.12i) q^{32} +(146.489 + 25.8300i) q^{33} +(2625.42 - 1232.09i) q^{34} +(1807.96 + 4967.33i) q^{35} +(3437.46 + 588.760i) q^{36} +3695.41i q^{37} +(-8266.04 - 3302.68i) q^{38} +8379.44i q^{39} +(1093.72 + 11524.8i) q^{40} +(-267.914 - 736.089i) q^{41} +(2299.62 + 4900.16i) q^{42} +(23786.2 + 4194.14i) q^{43} +(-73.3835 - 404.573i) q^{44} +(-3484.92 - 6036.05i) q^{45} +(6432.89 - 24245.4i) q^{46} +(4243.21 + 5056.86i) q^{47} +(2172.82 + 11653.5i) q^{48} +(-4987.40 + 8638.43i) q^{49} +(3850.15 - 3869.06i) q^{50} +(-5577.10 - 2029.90i) q^{51} +(21726.7 - 8028.67i) q^{52} +(22662.0 - 3995.92i) q^{53} +(-13267.3 - 18849.2i) q^{54} +(-528.202 + 629.487i) q^{55} +(10502.0 - 10657.6i) q^{56} +(7141.24 + 16758.2i) q^{57} +(33927.6 - 9180.04i) q^{58} +(4609.21 + 3867.59i) q^{59} +(15139.2 - 18222.8i) q^{60} +(5003.14 + 28374.2i) q^{61} +(885.457 - 79.6544i) q^{62} +(-3081.04 + 8465.10i) q^{63} +(28134.0 - 16799.5i) q^{64} +(-40089.0 - 23145.4i) q^{65} +(-480.945 + 690.456i) q^{66} +(-23745.4 + 19924.7i) q^{67} +(80.4064 + 16405.5i) q^{68} +(-44456.4 + 25666.9i) q^{69} +(-29795.3 - 2533.19i) q^{70} +(1151.61 - 6531.12i) q^{71} +(-11196.6 + 16243.3i) q^{72} +(36943.9 - 13446.5i) q^{73} +(-18967.4 - 8788.13i) q^{74} -11170.2 q^{75} +(36609.3 - 34572.9i) q^{76} +1062.08 q^{77} +(-43009.1 - 19927.3i) q^{78} +(9205.48 - 3350.52i) q^{79} +(-61754.4 - 21793.7i) q^{80} +(-3592.44 + 20373.7i) q^{81} +(4415.25 + 375.384i) q^{82} +(92501.1 - 53405.5i) q^{83} +(-30619.8 + 150.073i) q^{84} +(25116.3 - 21075.1i) q^{85} +(-78093.6 + 112113. i) q^{86} +(-62291.5 - 35964.0i) q^{87} +(2251.06 + 585.468i) q^{88} +(40982.0 - 112597. i) q^{89} +(39268.8 - 3532.56i) q^{90} +(10389.4 + 58921.0i) q^{91} +(109146. + 90676.5i) q^{92} +(-1393.71 - 1169.46i) q^{93} +(-36046.2 + 9753.28i) q^{94} +(-99900.1 - 12123.7i) q^{95} +(-64981.1 - 16561.0i) q^{96} +(2920.69 - 3480.74i) q^{97} +(-32477.8 - 46142.0i) q^{98} +(-1379.09 + 243.171i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9}+O(q^{10}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9	\( 288 q - 6 q^{2} + 24 q^{4} - 12 q^{5} + 264 q^{6} - 9 q^{8} + 54 q^{9} - 657 q^{10} - 9 q^{12} + 336 q^{13} - 2163 q^{14} + 1824 q^{16} - 12 q^{17} - 10242 q^{20} - 7842 q^{21} - 102 q^{22} - 11856 q^{24} - 12 q^{25} + 1317 q^{26} + 6660 q^{28} - 12 q^{29} - 40692 q^{30} - 3351 q^{32} - 8604 q^{33} - 15756 q^{34} + 81783 q^{36} + 50400 q^{38} + 39246 q^{40} - 29082 q^{41} - 123081 q^{42} - 39651 q^{44} - 6 q^{45} - 112554 q^{46} - 68403 q^{48} + 259302 q^{49} + 154188 q^{50} - 36867 q^{52} - 26280 q^{53} + 172605 q^{54} - 12 q^{57} + 229740 q^{58} - 136062 q^{60} + 169296 q^{61} + 35076 q^{62} + 63795 q^{64} - 189918 q^{65} + 73644 q^{66} + 59706 q^{68} - 200898 q^{69} - 177831 q^{70} - 188502 q^{72} + 397428 q^{73} - 530703 q^{74} - 53022 q^{76} + 159804 q^{77} - 618237 q^{78} + 18045 q^{80} - 110160 q^{81} + 155859 q^{82} + 733851 q^{84} - 645108 q^{85} + 616836 q^{86} + 598383 q^{88} - 226320 q^{89} + 546366 q^{90} - 754308 q^{92} + 558942 q^{93} - 454530 q^{96} - 177198 q^{97} - 76791 q^{98}+O(q^{100}) \) 288 * q - 6 * q^2 + 24 * q^4 - 12 * q^5 + 264 * q^6 - 9 * q^8 + 54 * q^9 - 657 * q^10 - 9 * q^12 + 336 * q^13 - 2163 * q^14 + 1824 * q^16 - 12 * q^17 - 10242 * q^20 - 7842 * q^21 - 102 * q^22 - 11856 * q^24 - 12 * q^25 + 1317 * q^26 + 6660 * q^28 - 12 * q^29 - 40692 * q^30 - 3351 * q^32 - 8604 * q^33 - 15756 * q^34 + 81783 * q^36 + 50400 * q^38 + 39246 * q^40 - 29082 * q^41 - 123081 * q^42 - 39651 * q^44 - 6 * q^45 - 112554 * q^46 - 68403 * q^48 + 259302 * q^49 + 154188 * q^50 - 36867 * q^52 - 26280 * q^53 + 172605 * q^54 - 12 * q^57 + 229740 * q^58 - 136062 * q^60 + 169296 * q^61 + 35076 * q^62 + 63795 * q^64 - 189918 * q^65 + 73644 * q^66 + 59706 * q^68 - 200898 * q^69 - 177831 * q^70 - 188502 * q^72 + 397428 * q^73 - 530703 * q^74 - 53022 * q^76 + 159804 * q^77 - 618237 * q^78 + 18045 * q^80 - 110160 * q^81 + 155859 * q^82 + 733851 * q^84 - 645108 * q^85 + 616836 * q^86 + 598383 * q^88 - 226320 * q^89 + 546366 * q^90 - 754308 * q^92 + 558942 * q^93 - 454530 * q^96 - 177198 * q^97 - 76791 * q^98

Introduction

L-functions

Modular forms

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