LMFDB - Embedded newform 76.6.k.a.3.10

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			3.10
Character	$\chi$	$=$	76.3
Dual form			76.6.k.a.51.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.64176 + 3.23327i) q^{2} +(-10.8783 + 3.95939i) q^{3} +(11.0919 - 30.0162i) q^{4} +(-11.1052 + 62.9808i) q^{5} +(37.6929 - 53.5512i) q^{6} +(-71.5832 + 41.3286i) q^{7} +(45.5645 + 175.191i) q^{8} +(-83.4872 + 70.0541i) q^{9} +O(q^{10})$	\(q+(-4.64176 + 3.23327i) q^{2} +(-10.8783 + 3.95939i) q^{3} +(11.0919 - 30.0162i) q^{4} +(-11.1052 + 62.9808i) q^{5} +(37.6929 - 53.5512i) q^{6} +(-71.5832 + 41.3286i) q^{7} +(45.5645 + 175.191i) q^{8} +(-83.4872 + 70.0541i) q^{9} +(-152.086 - 328.248i) q^{10} +(-11.1277 - 6.42460i) q^{11} +(-1.81561 + 370.443i) q^{12} +(-247.565 + 680.180i) q^{13} +(198.645 - 423.285i) q^{14} +(-128.559 - 729.097i) q^{15} +(-777.940 - 665.872i) 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} +(72.4248 - 6.15755i) q^{22} +(4366.95 - 770.011i) q^{23} +(-1189.32 - 1725.38i) q^{24} +(-906.714 - 330.017i) q^{25} +(-1050.07 - 3957.68i) q^{26} +(2037.37 - 3528.84i) q^{27} +(446.532 + 2607.06i) q^{28} +(-3993.82 - 4759.65i) q^{29} +(2954.11 + 2968.62i) q^{30} +(78.5801 + 136.105i) q^{31} +(5763.96 + 575.526i) q^{32} +(146.489 + 25.8300i) q^{33} +(2888.48 + 259.844i) q^{34} +(-1807.96 - 4967.33i) q^{35} +(1176.72 + 3283.00i) q^{36} +3695.41i q^{37} +(5472.92 + 7020.14i) q^{38} -8379.44i q^{39} +(-11539.7 + 924.158i) q^{40} +(-267.914 - 736.089i) q^{41} +(-484.981 + 5391.16i) q^{42} +(-23786.2 - 4194.14i) q^{43} +(-316.270 + 262.751i) q^{44} +(-3484.92 - 6036.05i) q^{45} +(-17780.7 + 17693.7i) q^{46} +(-4243.21 - 5056.86i) q^{47} +(11099.1 + 4163.41i) q^{48} +(-4987.40 + 8638.43i) q^{49} +(5275.78 - 1399.79i) q^{50} +(5577.10 + 2029.90i) q^{51} +(17670.4 + 14975.4i) q^{52} +(22662.0 - 3995.92i) q^{53} +(1952.69 + 22967.4i) 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} +(-23310.6 - 4228.20i) q^{60} +(5003.14 + 28374.2i) q^{61} +(-804.814 - 377.695i) q^{62} +(3081.04 - 8465.10i) q^{63} +(-28615.7 + 15965.0i) q^{64} +(-40089.0 - 23145.4i) q^{65} +(-763.482 + 353.742i) q^{66} +(23745.4 - 19924.7i) q^{67} +(-14247.8 + 8133.13i) q^{68} +(-44456.4 + 25666.9i) q^{69} +(24452.8 + 17211.5i) q^{70} +(-1151.61 + 6531.12i) q^{71} +(-16076.9 - 11434.2i) q^{72} +(36943.9 - 13446.5i) q^{73} +(-11948.3 - 17153.2i) q^{74} +11170.2 q^{75} +(-48102.0 - 14890.3i) q^{76} +1062.08 q^{77} +(27093.0 + 38895.4i) q^{78} +(-9205.48 + 3350.52i) q^{79} +(50576.3 - 41600.6i) q^{80} +(-3592.44 + 20373.7i) q^{81} +(3623.57 + 2550.51i) q^{82} +(-92501.1 + 53405.5i) q^{83} +(-15179.9 - 26592.6i) q^{84} +(25116.3 - 21075.1i) q^{85} +(123971. - 57439.0i) q^{86} +(62291.5 + 35964.0i) q^{87} +(618.502 - 2242.21i) q^{88} +(40982.0 - 112597. i) q^{89} +(35692.4 + 16750.2i) q^{90} +(-10389.4 - 58921.0i) q^{91} +(25324.9 - 139620. i) 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} +(-4780.08 - 56223.1i) 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 $

$2$	−4.64176	+	3.23327i	−0.820555	+	0.571567i
$2$	−4.64176	+	3.23327i	−0.820555	+	0.571567i
$3$	−10.8783	+	3.95939i	−0.697846	+	0.253995i	−0.666491	−	0.745513i	$-0.732205\pi$
$3$	−10.8783	+	3.95939i	−0.697846	+	0.253995i	−0.0313552	+	0.999508i	$0.509982\pi$
$4$	11.0919	−	30.0162i	0.346622	−	0.938005i
$5$	−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	$0.861720\pi$
$6$	37.6929	−	53.5512i	0.427446	−	0.607283i
$7$	−71.5832	+	41.3286i	−0.552161	+	0.318790i	−0.749993	−	0.661446i	$-0.769943\pi$
$7$	−71.5832	+	41.3286i	−0.552161	+	0.318790i	0.197832	+	0.980236i	$0.436610\pi$
$8$	45.5645	+	175.191i	0.251711	+	0.967802i
$9$	−83.4872	+	70.0541i	−0.343569	+	0.288288i
$10$	−152.086	−	328.248i	−0.480939	−	1.03801i
$11$	−11.1277	−	6.42460i	−0.0277284	−	0.0160090i	0.486072	−	0.873919i	$-0.338429\pi$
$11$	−11.1277	−	6.42460i	−0.0277284	−	0.0160090i	−0.513800	+	0.857910i	$0.671763\pi$
$12$	−1.81561	+	370.443i	−0.00363973	+	0.742624i
$13$	−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	$0.908679\pi$
$14$	198.645	−	423.285i	0.270869	−	0.577182i
$15$	−128.559	−	729.097i	−0.147528	−	0.836675i
$16$	−777.940	−	665.872i	−0.759707	−	0.650266i
$17$	−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
$22$	72.4248	−	6.15755i	0.0319029	−	0.00271238i
$23$	4366.95	−	770.011i	1.72131	−	0.303513i	0.776252	−	0.630423i	$-0.217118\pi$
$23$	4366.95	−	770.011i	1.72131	−	0.303513i	0.945056	+	0.326910i	$0.106007\pi$
$24$	−1189.32	−	1725.38i	−0.421473	−	0.611444i
$25$	−906.714	−	330.017i	−0.290148	−	0.105605i
$26$	−1050.07	−	3957.68i	−0.304638	−	1.14817i
$27$	2037.37	−	3528.84i	0.537850	−	0.931584i
$28$	446.532	+	2607.06i	0.107636	+	0.628430i
$29$	−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	$-0.462838\pi$
$30$	2954.11	+	2968.62i	0.599271	+	0.602216i
$31$	78.5801	+	136.105i	0.0146862	+	0.0254372i	0.873275	−	0.487227i	$-0.161992\pi$
$31$	78.5801	+	136.105i	0.0146862	+	0.0254372i	−0.858589	+	0.512665i	$0.828658\pi$
$32$	5763.96	+	575.526i	0.995052	+	0.0993551i
$33$	146.489	+	25.8300i	0.0234164	+	0.00412894i
$34$	2888.48	+	259.844i	0.428522	+	0.0385492i
$35$	−1807.96	−	4967.33i	−0.249470	−	0.685414i
$36$	1176.72	+	3283.00i	0.151328	+	0.422196i
$37$			3695.41i			0.443771i	0.975073	+	0.221885i	$0.0712210\pi$
$37$			3695.41i			0.443771i	−0.975073	+	0.221885i	$0.928779\pi$
$38$	5472.92	+	7020.14i	0.614837	+	0.788654i
$39$		−	8379.44i		−	0.882173i
$40$	−11539.7	+	924.158i	−1.14036	+	0.0913264i
$41$	−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	$0.900474\pi$
$42$	−484.981	+	5391.16i	−0.0424230	+	0.471584i
$43$	−23786.2	−	4194.14i	−1.96179	−	0.345917i	−0.996357	−	0.0852826i	$-0.972821\pi$
$43$	−23786.2	−	4194.14i	−1.96179	−	0.345917i	−0.965438	−	0.260635i	$-0.916068\pi$
$44$	−316.270	+	262.751i	−0.0246278	+	0.0204603i
$45$	−3484.92	−	6036.05i	−0.256544	−	0.444347i
$46$	−17780.7	+	17693.7i	−1.23895	+	1.23289i
$47$	−4243.21	−	5056.86i	−0.280188	−	0.333915i	0.607535	−	0.794293i	$-0.292158\pi$
$47$	−4243.21	−	5056.86i	−0.280188	−	0.333915i	−0.887723	+	0.460378i	$0.847714\pi$
$48$	11099.1	+	4163.41i	0.695323	+	0.260823i
$49$	−4987.40	+	8638.43i	−0.296745	+	0.513978i
$50$	5275.78	−	1399.79i	0.298443	−	0.0791843i
$51$	5577.10	+	2029.90i	0.300250	+	0.109282i
$52$	17670.4	+	14975.4i	0.906230	+	0.768018i
$53$	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	$0.254232\pi$
$54$	1952.69	+	22967.4i	0.0911272	+	1.07183i
$55$	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	0.552514	−	0.833504i	$-0.313669\pi$
$59$	−4609.21	−	3867.59i	−0.172384	−	0.144647i	−0.724898	+	0.688856i	$0.758113\pi$
$60$	−23310.6	−	4228.20i	−0.835942	−	0.151627i
$61$	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	$0.779356\pi$
$62$	−804.814	−	377.695i	−0.0265899	−	0.0124785i
$63$	3081.04	−	8465.10i	0.0978017	−	0.268708i
$64$	−28615.7	+	15965.0i	−0.873283	+	0.487213i
$65$	−40089.0	−	23145.4i	−1.17691	−	0.679487i
$66$	−763.482	+	353.742i	−0.0215744	+	0.00999602i
$67$	23745.4	−	19924.7i	0.646237	−	0.542257i	−0.259689	−	0.965692i	$-0.583620\pi$
$67$	23745.4	−	19924.7i	0.646237	−	0.542257i	0.905927	+	0.423435i	$0.139176\pi$
$68$	−14247.8	+	8133.13i	−0.373659	+	0.213297i
$69$	−44456.4	+	25666.9i	−1.12412	+	0.649009i
$70$	24452.8	+	17211.5i	0.596464	+	0.419831i
$71$	−1151.61	+	6531.12i	−0.0271119	+	0.153759i	−0.995358	−	0.0962386i	$-0.969319\pi$
$71$	−1151.61	+	6531.12i	−0.0271119	+	0.153759i	0.968246	+	0.249998i	$0.0804299\pi$
$72$	−16076.9	−	11434.2i	−0.365486	−	0.259941i
$73$	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	$0.246789\pi$
$74$	−11948.3	−	17153.2i	−0.253645	−	0.364138i
$75$	11170.2			0.229302
$76$	−48102.0	−	14890.3i	−0.955277	−	0.295713i
$77$	1062.08			0.0204141
$78$	27093.0	+	38895.4i	0.504221	+	0.723871i
$79$	−9205.48	+	3350.52i	−0.165951	+	0.0604011i	−0.423659	−	0.905822i	$-0.639255\pi$
$79$	−9205.48	+	3350.52i	−0.165951	+	0.0604011i	0.257709	+	0.966223i	$0.417032\pi$
$80$	50576.3	−	41600.6i	0.883532	−	0.726733i
$81$	−3592.44	+	20373.7i	−0.0608382	+	0.345031i
$82$	3623.57	+	2550.51i	0.0595117	+	0.0418882i
$83$	−92501.1	+	53405.5i	−1.47384	+	0.850924i	−0.999566	−	0.0294506i	$-0.990624\pi$
$83$	−92501.1	+	53405.5i	−1.47384	+	0.850924i	−0.474278	+	0.880375i	$0.657291\pi$
$84$	−15179.9	−	26592.6i	−0.234732	−	0.411208i
$85$	25116.3	−	21075.1i	0.377058	−	0.316389i
$86$	123971.	−	57439.0i	1.80748	−	0.837453i
$87$	62291.5	+	35964.0i	0.882329	+	0.509413i
$88$	618.502	−	2242.21i	0.00851402	−	0.0308653i
$89$	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	$-0.184984\pi$
$90$	35692.4	+	16750.2i	0.464482	+	0.217979i
$91$	−10389.4	−	58921.0i	−0.131518	−	0.745876i
$92$	25324.9	−	139620.i	0.311946	−	1.71980i
$93$	−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	$0.214418\pi$
$98$	−4780.08	−	56223.1i	−0.0502771	−	0.591357i
$99$	1379.09	−	243.171i	0.0141418	−	0.00249359i
$100$	−19963.0	+	23555.6i	−0.199630	+	0.235556i
$101$	−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	$0.656526\pi$
$102$	−32450.8	+	8609.98i	−0.308834	+	0.0819411i
$103$	1446.91	−	2506.11i	0.0134384	−	0.0232760i	−0.859228	−	0.511593i	$-0.829056\pi$
$103$	1446.91	−	2506.11i	0.0134384	−	0.0232760i	0.872666	+	0.488317i	$0.162389\pi$
$104$	−130442.	−	12379.1i	−1.18259	−	0.112229i
$105$	39335.2	+	46877.9i	0.348184	+	0.414949i
$106$	−92271.7	+	91820.5i	−0.797634	+	0.793734i
$107$	−16834.1	−	29157.6i	−0.142145	−	0.246202i	0.786159	−	0.618024i	$-0.212067\pi$
$107$	−16834.1	−	29157.6i	−0.142145	−	0.246202i	−0.928304	+	0.371822i	$0.878733\pi$
$108$	−83323.8	−	100296.i	−0.687400	−	0.827414i
$109$	−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	$0.641355\pi$
$110$	−416.486	+	4629.75i	−0.00328185	+	0.0364818i
$111$	−14631.6	−	40200.0i	−0.112716	−	0.309684i
$112$	83207.0	+	15514.1i	0.626779	+	0.116864i
$113$			128125.i			0.943928i	0.881618	+	0.471964i	$0.156455\pi$
$113$			128125.i			0.943928i	−0.881618	+	0.471964i	$0.843545\pi$
$114$	−87331.8	−	54698.0i	−0.629376	−	0.394194i
$115$			283585.i			1.99958i
$116$	−187165.	+	67085.6i	−1.29146	+	0.462897i
$117$	−26980.8	−	74129.3i	−0.182218	−	0.500639i
$118$	33899.8	+	3049.58i	0.224126	+	0.0201621i
$119$	41732.8	+	7358.61i	0.270153	+	0.0476353i
$120$	121873.	−	55743.4i	0.772602	−	0.353379i
$121$	−80442.9	−	139331.i	−0.499487	−	0.865138i
$122$	−114965.	−	115530.i	−0.699304	−	0.702740i
$123$	5828.93	+	6946.65i	0.0347397	+	0.0414012i
$124$	4956.94	−	849.014i	0.0289507	−	0.00495862i
$125$	−69071.6	+	119636.i	−0.395389	+	0.684834i
$126$	13068.5	+	49254.8i	0.0733330	+	0.276390i
$127$	42321.9	+	15403.9i	0.232839	+	0.0847464i	0.455805	−	0.890080i	$-0.349352\pi$
$127$	42321.9	+	15403.9i	0.232839	+	0.0847464i	−0.222966	+	0.974826i	$0.571574\pi$
$128$	81208.3	−	166628.i	0.438102	−	0.898925i
$129$	275361.	−	48553.5i	1.45689	−	0.256889i
$130$	260919.	−	22183.3i	1.35409	−	0.115124i
$131$	−36436.8	+	43423.7i	−0.185508	+	0.221080i	−0.850781	−	0.525520i	$-0.823871\pi$
$131$	−36436.8	+	43423.7i	−0.185508	+	0.221080i	0.665273	+	0.746600i	$0.268315\pi$
$132$	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
$136$	39838.3	−	83819.1i	0.184694	−	0.388593i
$137$	−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	$-0.115845\pi$
$138$	123368.	−	262879.i	0.551448	−	1.17506i
$139$	−79462.7	+	218322.i	−0.348840	+	0.958431i	0.633896	+	0.773418i	$0.281455\pi$
$139$	−79462.7	+	218322.i	−0.348840	+	0.958431i	−0.982736	+	0.185012i	$0.940767\pi$
$140$	−169154.	−	829.053i	−0.729393	−	0.00357489i
$141$	66181.2	+	38209.7i	0.280341	+	0.161855i
$142$	−15771.4	−	34039.4i	−0.0656370	−	0.141664i
$143$	7124.73	−	5978.36i	0.0291359	−	0.0244479i
$144$	111595.	+	1093.92i	0.448476	+	0.00439622i
$145$	344119.	−	198677.i	1.35921	−	0.784743i
$146$	−128009.	+	181865.i	−0.497001	+	0.706102i
$147$	20051.7	−	113719.i	0.0765346	−	0.434049i
$148$	110922.	+	40989.1i	0.416259	+	0.153820i
$149$	−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	$0.587634\pi$
$150$	−51849.5	+	36116.3i	−0.188155	+	0.131062i
$151$	−459416.			−1.63970			−0.819848	−	0.572581i	$-0.805942\pi$
$151$	−459416.			−1.63970			−0.819848	+	0.572581i	$0.805942\pi$
$152$	271423.	−	86409.5i	0.952877	−	0.303356i
$153$	55874.2			0.192967
$154$	−4929.92	+	3433.99i	−0.0167509	+	0.0116680i
$155$	−9444.63	+	3437.56i	−0.0315759	+	0.0114927i
$156$	−251519.	−	92943.9i	−0.827482	−	0.305780i
$157$	−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	$0.741856\pi$
$158$	31896.5	−	45316.2i	0.101648	−	0.144414i
$159$	−230704.	+	133197.i	−0.723705	+	0.417831i
$160$	−100257.	+	356627.i	−0.309610	+	1.10132i
$161$	−280777.	+	235600.i	−0.853682	+	0.716325i
$162$	−49198.6	−	106185.i	−0.147287	−	0.317890i
$163$	116613.	+	67326.5i	0.343778	+	0.198480i	0.661941	−	0.749556i	$-0.269733\pi$
$163$	116613.	+	67326.5i	0.343778	+	0.198480i	−0.318164	+	0.948036i	$0.603066\pi$
$164$	−25066.2	−	122.854i	−0.0727745	−	0.000356681i
$165$	−3253.58	+	8939.14i	−0.00930362	+	0.0255615i
$166$	256693.	−	546977.i	0.723010	−	1.54063i
$167$	−77794.6	−	441195.i	−0.215853	−	1.22416i	−0.879420	−	0.476047i	$-0.842069\pi$
$167$	−77794.6	−	441195.i	−0.215853	−	1.22416i	0.663567	−	0.748117i	$-0.269042\pi$
$168$	156443.	+	74355.4i	0.427643	+	0.203254i
$169$	−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	$-0.120615\pi$
$174$	−405423.	+	34469.0i	−1.01516	+	0.0863090i
$175$	78544.6	−	13849.5i	0.193875	−	0.0341853i
$176$	4378.75	+	12407.6i	0.0106554	+	0.0301930i
$177$	65453.9	+	23823.3i	0.157037	+	0.0571569i
$178$	173829.	+	655155.i	0.411217	+	1.54987i
$179$	209867.	−	363501.i	0.489567	−	0.847955i	−0.510361	−	0.859960i	$-0.670488\pi$
$179$	209867.	−	363501.i	0.489567	−	0.847955i	0.999928	+	0.0120056i	$0.00382160\pi$
$180$	−219833.	+	37652.6i	−0.505723	+	0.0866191i
$181$	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	$0.763749\pi$
$182$	238732.	+	239905.i	0.534236	+	0.536861i
$183$	−166771.	−	288855.i	−0.368122	−	0.637606i
$184$	333877.	+	729965.i	0.727013	+	1.58949i
$185$	−232740.	−	41038.3i	−0.499967	−	0.0881577i
$186$	10250.5	+	922.119i	0.0217251	+	0.00195436i
$187$	2253.06	+	6190.24i	0.00471161	+	0.0129450i
$188$	−198853.	+	71274.7i	−0.410333	+	0.147076i
$189$			336807.i			0.685846i
$190$	−502912.	+	266729.i	−1.01067	+	0.536026i
$191$		−	429729.i		−	0.852336i	−0.904644	−	0.426168i	$-0.859863\pi$
$191$		−	429729.i		−	0.852336i	0.904644	−	0.426168i	$-0.140137\pi$
$192$	248080.	−	286974.i	0.485668	−	0.561809i
$193$	−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	$-0.250696\pi$
$194$	−2302.95	+	25600.1i	−0.00439319	+	0.0488358i
$195$	527744.	+	93055.5i	0.993886	+	0.175249i
$196$	203973.	+	245519.i	0.379256	+	0.456504i
$197$	−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	$-0.413933\pi$
$198$	−5615.18	+	5587.73i	−0.0101789	+	0.0101291i
$199$	−390615.	−	465516.i	−0.699223	−	0.833302i	0.293215	−	0.956046i	$-0.405275\pi$
$199$	−390615.	−	465516.i	−0.699223	−	0.833302i	−0.992438	+	0.122745i	$0.960830\pi$
$200$	16502.0	−	173885.i	0.0291716	−	0.307388i
$201$	−179420.	+	310765.i	−0.313243	+	0.542553i
$202$	159408.	−	42294.9i	0.274873	−	0.0729306i
$203$	482600.	+	175652.i	0.821953	+	0.299166i
$204$	122790.	−	144888.i	0.206580	−	0.243756i
$205$	49334.7	−	8699.04i	0.0819913	−	0.0144573i
$206$	1386.76	+	16311.0i	0.00227684	+	0.0267802i
$207$	−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	$-0.951245\pi$
$211$	−847287.	−	710958.i	−1.31016	−	1.09936i	−0.321868	−	0.946785i	$-0.604311\pi$
$212$	131422.	−	724548.i	0.200830	−	1.10720i
$213$	−13331.6	−	75607.4i	−0.0201342	−	0.114187i
$214$	172414.	+	80913.2i	0.257359	+	0.120777i
$215$	528301.	−	1.45150e6i	0.779445	−	2.14151i
$216$	711052.	+	196140.i	1.03697	+	0.286043i
$217$	−11250.0	−	6495.21i	−0.0162183	−	0.00936362i
$218$	339080.	−	157105.i	0.483238	−	0.223897i
$219$	−348649.	+	292551.i	−0.491222	+	0.412184i
$220$	−13036.0	−	22836.8i	−0.0181589	−	0.0318111i
$221$	321376.	−	185547.i	0.442622	−	0.255548i
$222$	197894.	+	139291.i	0.269494	+	0.189688i
$223$	73914.9	−	419192.i	0.0995337	−	0.564483i	−0.893730	−	0.448606i	$-0.851921\pi$
$223$	73914.9	−	419192.i	0.0995337	−	0.564483i	0.993263	−	0.115878i	$-0.0369681\pi$
$224$	−436388.	+	197018.i	−0.581103	+	0.262353i
$225$	98818.0	−	35966.8i	0.130131	−	0.0473637i
$226$	−414264.	−	594727.i	−0.539518	−	0.774545i
$227$	430082.			0.553970			0.276985	−	0.960874i	$-0.410665\pi$
$227$	430082.			0.553970			0.276985	+	0.960874i	$0.410665\pi$
$228$	582227.	−	28472.4i	0.741746	−	0.0362733i
$229$	−496834.			−0.626070			−0.313035	−	0.949742i	$-0.601346\pi$
$229$	−496834.			−0.626070			−0.313035	+	0.949742i	$0.601346\pi$
$230$	−916908.	−	1.31633e6i	−1.14289	−	1.64077i
$231$	−11553.7	+	4205.19i	−0.0142459	+	0.00518508i
$232$	651871.	−	916552.i	0.795136	−	1.11799i
$233$	−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	$0.837394\pi$
$234$	364919.	+	256854.i	0.435669	+	0.306653i
$235$	365607.	−	211083.i	0.431861	−	0.249335i
$236$	−167215.	+	95452.0i	−0.195432	+	0.111559i
$237$	86874.4	−	72896.3i	0.100466	−	0.0843013i
$238$	−217506.	+	100776.i	−0.248902	+	0.115323i
$239$	925986.	+	534619.i	1.04860	+	0.605410i	0.922257	−	0.386577i	$-0.126343\pi$
$239$	925986.	+	534619.i	1.04860	+	0.605410i	0.126343	+	0.991987i	$0.459676\pi$
$240$	−385474.	+	652797.i	−0.431983	+	0.731561i
$241$	−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	$0.996103\pi$
$242$	823893.	+	386648.i	0.904341	+	0.424402i
$243$	130352.	+	739265.i	0.141613	+	0.803128i
$244$	907180.	+	164549.i	0.975481	+	0.176938i
$245$	−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
$250$	−66200.4	−	778647.i	−0.0669901	−	0.787935i
$251$	−1.89645e6	+	334395.i	−1.90001	+	0.335023i	−0.995761	−	0.0919795i	$-0.970681\pi$
$251$	−1.89645e6	+	334395.i	−1.90001	+	0.335023i	−0.904250	+	0.427003i	$0.859569\pi$
$252$	−219915.	−	186375.i	−0.218149	−	0.184879i
$253$	−53541.3	−	19487.4i	−0.0525881	−	0.0191405i
$254$	−246253.	+	65336.9i	−0.239495	+	0.0635440i
$255$	−189779.	+	328707.i	−0.182767	+	0.316562i
$256$	161805.	+	1.03602e6i	0.154309	+	0.988023i
$257$	−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	$0.956336\pi$
$258$	−1.12117e6	+	1.11569e6i	−1.04863	+	1.04350i
$259$	−152726.	−	264529.i	−0.141470	−	0.245033i
$260$	−1.13940e6	+	946592.i	−1.04530	+	0.868419i
$261$	666865.	+	117586.i	0.605950	+	0.106845i
$262$	28730.3	−	319373.i	0.0258575	−	0.287438i
$263$	−316012.	−	868235.i	−0.281717	−	0.774012i	−0.997158	−	0.0753387i	$-0.975996\pi$
$263$	−316012.	−	868235.i	−0.281717	−	0.774012i	0.715441	−	0.698674i	$-0.246226\pi$
$264$	2149.53	+	26840.5i	0.00189816	+	0.0237017i
$265$			1.47165e6i			1.28733i
$266$	−681901.	−	276336.i	−0.590905	−	0.239460i
$267$			1.38714e6i			1.19081i
$268$	−334683.	−	933748.i	−0.284640	−	0.794132i
$269$	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	$0.688909\pi$
$270$	−1.46819e6	−	132076.i	−1.22567	−	0.110259i
$271$	558012.	+	98392.5i	0.461551	+	0.0813840i	0.399589	−	0.916695i	$-0.369153\pi$
$271$	558012.	+	98392.5i	0.461551	+	0.0813840i	0.0619626	+	0.998078i	$0.480264\pi$
$272$	86090.2	+	517876.i	0.0705556	+	0.424428i
$273$	346310.	+	599827.i	0.281228	+	0.487102i
$274$	330077.	+	331699.i	0.265607	+	0.266912i
$275$	7969.45	+	9497.62i	0.00635472	+	0.00757326i
$276$	277317.	+	1.61911e6i	0.219131	+	1.27939i
$277$	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	$0.0562663\pi$
$278$	−337048.	−	1.27032e6i	−0.261565	−	0.985831i
$279$	−16095.1	−	5858.15i	−0.0123790	−	0.00450557i
$280$	787852.	−	543072.i	0.600551	−	0.413964i
$281$	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	$0.342938\pi$
$282$	−430740.	+	36621.4i	−0.322546	+	0.0274228i
$283$	−1.52082e6	+	1.81244e6i	−1.12878	+	1.34523i	−0.197771	+	0.980248i	$0.563370\pi$
$283$	−1.52082e6	+	1.81244e6i	−1.12878	+	1.34523i	−0.931014	+	0.364984i	$0.881074\pi$
$284$	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
$288$	−521535.	+	355740.i	−0.370512	+	0.252727i
$289$	−200914.	−	1.13944e6i	−0.141503	−	0.802503i
$290$	−954939.	+	2.03484e6i	−0.666777	+	1.42081i
$291$	−17990.6	+	49428.8i	−0.0124541	+	0.0342175i
$292$	6165.99	−	1.25806e6i	0.00423200	−	0.863465i
$293$	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	$0.470208\pi$
$294$	274609.	+	592689.i	0.185288	+	0.399906i
$295$	294770.	−	247342.i	0.197210	−	0.165479i
$296$	−647403.	+	168380.i	−0.429482	+	0.111702i
$297$	−45342.8	+	26178.6i	−0.0298275	+	0.0172209i
$298$	1.03165e6	−	1.46569e6i	0.672961	−	0.956093i
$299$	−557359.	+	3.16094e6i	−0.360543	+	2.04474i
$300$	123899.	−	335287.i	0.0794811	−	0.215087i
$301$	1.87603e6	−	682818.i	1.19350	−	0.434399i
$302$	2.13250e6	−	1.48542e6i	1.34546	−	0.937197i
$303$	337509.			0.211193
$304$	−980493.	+	1.27868e6i	−0.608500	+	0.793554i
$305$	−1.84259e6			−1.13417
$306$	−259355.	+	180656.i	−0.158340	+	0.110294i
$307$	−1.95286e6	+	710783.i	−1.18257	+	0.430419i	−0.857107	−	0.515138i	$-0.827741\pi$
$307$	−1.95286e6	+	710783.i	−1.18257	+	0.430419i	−0.325458	+	0.945556i	$0.605519\pi$
$308$	11780.5	−	31879.5i	0.00707596	−	0.0191485i
$309$	−5817.25	+	32991.2i	−0.00346594	+	0.0196563i
$310$	32725.1	−	46493.4i	0.0193409	−	0.0274781i
$311$	−60041.0	+	34664.7i	−0.0352004	+	0.0203229i	−0.517497	−	0.855685i	$-0.673136\pi$
$311$	−60041.0	+	34664.7i	−0.0352004	+	0.0203229i	0.482297	+	0.876008i	$0.339803\pi$
$312$	1.46800e6	−	381805.i	0.853769	−	0.222052i
$313$	−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	$0.391873\pi$
$314$	−1.22447e6	−	2.64277e6i	−0.700848	−	1.51264i
$315$	498923.	+	288053.i	0.283307	+	0.163567i
$316$	−1536.41	+	313477.i	−0.000865543	+	0.176599i
$317$	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	$-0.123274\pi$
$318$	640209.	−	1.36420e6i	0.355021	−	0.756500i
$319$	13863.3	+	78622.8i	0.00762765	+	0.0432585i
$320$	−687704.	−	1.97954e6i	−0.375428	−	1.08066i
$321$	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
$326$	−758974.	+	64527.9i	−0.395533	+	0.0336282i
$327$	753156.	−	132802.i	0.389507	−	0.0686807i
$328$	116749.	−	80475.7i	0.0599194	−	0.0413029i
$329$	512735.	+	186620.i	0.261158	+	0.0950537i
$330$	−13800.3	−	52013.1i	−0.00697597	−	0.0262922i
$331$	661778.	−	1.14623e6i	0.332003	−	0.575046i	−0.650901	−	0.759162i	$-0.725609\pi$
$331$	661778.	−	1.14623e6i	0.332003	−	0.575046i	0.982905	+	0.184116i	$0.0589422\pi$
$332$	577017.	+	3.36890e6i	0.287305	+	1.67742i
$333$	−258879.	−	308519.i	−0.127934	−	0.152466i
$334$	1.78761e6	+	1.79639e6i	0.876811	+	0.881119i
$335$	991178.	+	1.71677e6i	0.482547	+	0.835796i
$336$	−966580.	+	160681.i	−0.467078	+	0.0776457i
$337$	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	$0.355906\pi$
$338$	859992.	+	77363.6i	0.409452	+	0.0368337i
$339$	−507298.	−	1.39379e6i	−0.239753	−	0.658716i
$340$	−354006.	−	987658.i	−0.166078	−	0.463350i
$341$		−	2019.38i		−	0.000940444i
$342$	−948708.	−	202691.i	−0.438599	−	0.0937064i
$343$		−	2.21371e6i		−	1.01598i
$344$	−349030.	−	4.35823e6i	−0.159025	−	1.98570i
$345$	−1.12282e6	−	3.08494e6i	−0.507884	−	1.39540i
$346$	−351378.	+	3.90600e6i	−0.157792	+	1.75405i
$347$	2.88169e6	+	508120.i	1.28477	+	0.226539i	0.774002	−	0.633183i	$-0.218252\pi$
$347$	2.88169e6	+	508120.i	1.28477	+	0.226539i	0.510763	+	0.859721i	$0.329363\pi$
$348$	1.77043e6	−	1.47084e6i	0.783666	−	0.651055i
$349$	−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	$0.987037\pi$
$350$	−319806.	+	318242.i	−0.139546	+	0.138863i
$351$	1.89586e6	+	2.25940e6i	0.821370	+	0.978870i
$352$	−60442.3	−	43435.4i	−0.0260006	−	0.0186848i
$353$	−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	$0.908986\pi$
$354$	−380849.	+	101048.i	−0.161527	+	0.0428570i
$355$	−398546.	−	145059.i	−0.167845	−	0.0610904i
$356$	−2.92517e6	−	2.47904e6i	−1.22328	−	1.03671i
$357$	−483119.	+	85186.9i	−0.200624	+	0.0353755i
$358$	201143.	+	2.36584e6i	0.0829466	+	0.975614i
$359$	1.93579e6	−	2.30699e6i	0.792725	−	0.944732i	−0.206708	−	0.978403i	$-0.566275\pi$
$359$	1.93579e6	−	2.30699e6i	0.792725	−	0.944732i	0.999433	+	0.0336702i	$0.0107196\pi$
$360$	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
$364$	−1.88382e6	−	341696.i	−0.745222	−	0.135172i
$365$	436600.	+	2.47608e6i	0.171535	+	0.972822i
$366$	1.70806e6	+	801582.i	0.666499	+	0.312785i
$367$	1.57919e6	−	4.33880e6i	0.612027	−	1.68153i	−0.113673	−	0.993518i	$-0.536262\pi$
$367$	1.57919e6	−	4.33880e6i	0.612027	−	1.68153i	0.725700	−	0.688011i	$-0.241516\pi$
$368$	−3.90995e6	−	2.30881e6i	−1.50505	−	0.888726i
$369$	73933.4	+	42685.5i	0.0282667	+	0.0163198i
$370$	1.21301e6	−	562021.i	0.460639	−	0.213427i
$371$	−1.45707e6	+	1.22263e6i	−0.549599	+	0.461169i
$372$	−50561.8	+	28862.4i	−0.0189437	+	0.0108137i
$373$	−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	$0.973121\pi$
$374$	−30472.9	−	21448.8i	−0.0112651	−	0.00792912i
$375$	277701.	−	1.57492e6i	0.101976	−	0.578336i
$376$	692576.	−	973785.i	0.252637	−	0.355217i
$377$	4.22615e6	−	1.53819e6i	1.53141	−	0.557387i
$378$	−1.08899e6	−	1.56338e6i	−0.392007	−	0.562775i
$379$	−4.08659e6			−1.46138			−0.730691	−	0.682709i	$-0.760802\pi$
$379$	−4.08659e6			−1.46138			−0.730691	+	0.682709i	$0.760802\pi$
$380$	1.47199e6	−	2.86414e6i	0.522932	−	1.01750i
$381$	−521382.			−0.184011
$382$	1.38943e6	+	1.99470e6i	0.487168	+	0.699389i
$383$	−1.79648e6	+	653864.i	−0.625784	+	0.227767i	−0.635395	−	0.772187i	$-0.719163\pi$
$383$	−1.79648e6	+	653864.i	−0.625784	+	0.227767i	0.00961113	+	0.999954i	$0.496941\pi$
$384$	−223665.	+	2.13417e6i	−0.0774052	+	0.738587i
$385$	−11794.6	+	66890.5i	−0.00405538	+	0.0229992i
$386$	2.03280e6	+	1.43082e6i	0.694427	+	0.488783i
$387$	2.27966e6	−	1.31616e6i	0.773735	−	0.446716i
$388$	−72082.5	−	126276.i	−0.0243081	−	0.0425834i
$389$	−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	$0.380690\pi$
$390$	−2.75053e6	+	1.27440e6i	−0.915705	+	0.424271i
$391$	−1.96880e6	−	1.13669e6i	−0.651269	−	0.376011i
$392$	−1.74062e6	−	480141.i	−0.572123	−	0.157817i
$393$	224441.	−	616646.i	0.0733028	−	0.201398i
$394$	3.91085e6	+	1.83534e6i	1.26920	+	0.595629i
$395$	−108790.	−	616977.i	−0.0350829	−	0.198965i
$396$	7997.68	−	44092.3i	0.00256287	−	0.0141294i
$397$	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	$0.178108\pi$
$402$	−171962.	−	2.02261e6i	−0.0530723	−	0.624235i
$403$	−112029.	+	19753.8i	−0.0343613	+	0.00605882i
$404$	−603184.	+	711734.i	−0.183864	+	0.216952i
$405$	−1.24326e6	−	452509.i	−0.376638	−	0.137085i
$406$	−2.80804e6	+	745042.i	−0.845451	+	0.224319i
$407$	23741.5	−	41121.6i	0.00710433	−	0.0123051i
$408$	−101502.	+	1.06955e6i	−0.0301872	+	0.318090i
$409$	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	$0.425073\pi$
$410$	−200873.	+	199891.i	−0.0590151	+	0.0587265i
$411$	478817.	+	829335.i	0.139819	+	0.242173i
$412$	−59175.0	−	71228.1i	−0.0171749	−	0.0206732i
$413$	489784.	+	86362.2i	0.141296	+	0.0249143i
$414$	244940.	−	2.72281e6i	0.0702358	−	0.780758i
$415$	−2.33628e6	−	6.41887e6i	−0.665893	−	1.82953i
$416$	−1.81842e6	+	3.77805e6i	−0.515181	+	1.07037i
$417$		−	2.68961e6i		−	0.757441i
$418$	−15799.6	−	113280.i	−0.00442289	−	0.0317111i
$419$		−	399918.i		−	0.111285i	−0.998451	−	0.0556423i	$-0.982279\pi$
$419$		−	399918.i		−	0.111285i	0.998451	−	0.0556423i	$-0.0177207\pi$
$420$	1.84340e6	−	660728.i	0.509912	−	0.182768i
$421$	−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	$-0.284302\pi$
$422$	6.23163e6	+	560588.i	1.70341	+	0.153237i
$423$	708507.	+	124929.i	0.192528	+	0.0339478i
$424$	1.73263e6	+	3.78810e6i	0.468050	+	1.02331i
$425$	247343.	+	428411.i	0.0664243	+	0.115050i
$426$	306342.	+	307847.i	0.0817866	+	0.0821884i
$427$	−1.53081e6	−	1.82434e6i	−0.406304	−	0.484214i
$428$	−1.06192e6	+	181883.i	−0.280209	+	0.0479937i
$429$	−53834.6	+	93244.2i	−0.0141227	+	0.0244613i
$430$	2.24083e6	+	8.44563e6i	0.584438	+	2.20273i
$431$	−915575.	−	333242.i	−0.237411	−	0.0864105i	0.220575	−	0.975370i	$-0.429207\pi$
$431$	−915575.	−	333242.i	−0.237411	−	0.0864105i	−0.457986	+	0.888960i	$0.651429\pi$
$432$	−3.93471e6	+	1.38859e6i	−1.01439	+	0.357985i
$433$	−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	$0.743399\pi$
$434$	73220.7	−	6225.22i	0.0186599	−	0.00158646i
$435$	−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	0.609827	−	0.792534i	$-0.291239\pi$
$439$	−261544.	−	219461.i	−0.0647714	−	0.0543497i	−0.674599	+	0.738185i	$0.735683\pi$
$440$	134348.	+	63854.0i	0.0330825	+	0.0157238i
$441$	−188773.	−	1.07059e6i	−0.0462215	−	0.262135i
$442$	−891829.	+	1.90036e6i	−0.217133	+	0.462680i
$443$	−1.70383e6	+	4.68123e6i	−0.412493	+	1.13332i	0.543368	+	0.839495i	$0.317149\pi$
$443$	−1.70383e6	+	4.68123e6i	−0.412493	+	1.13332i	−0.955861	+	0.293820i	$0.905073\pi$
$444$	−1.36894e6	−	6709.42i	−0.329554	−	0.00161521i
$445$	6.63635e6	+	3.83150e6i	1.58865	+	0.917209i
$446$	1.01227e6	+	2.18478e6i	0.240967	+	0.520080i
$447$	2.80983e6	−	2.35772e6i	0.665136	−	0.558115i
$448$	1.38860e6	−	2.32547e6i	0.326874	−	0.547414i
$449$	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	$0.313252\pi$
$450$	−342399.	+	486455.i	−0.0797079	+	0.113243i
$451$	−1747.80	+	9912.25i	−0.000404622	+	0.00229473i
$452$	3.84583e6	+	1.42115e6i	0.885409	+	0.327186i
$453$	4.99768e6	−	1.81901e6i	1.14426	−	0.416475i
$454$	−1.99634e6	+	1.39057e6i	−0.454563	+	0.316631i
$455$	3.82626e6			0.866456
$456$	−2.61050e6	+	2.01466e6i	−0.587911	+	0.453722i
$457$	−2.98146e6			−0.667787			−0.333893	−	0.942611i	$-0.608363\pi$
$457$	−2.98146e6			−0.667787			−0.333893	+	0.942611i	$0.608363\pi$
$458$	2.30618e6	−	1.60640e6i	0.513725	−	0.357841i
$459$	−1.96305e6	+	714493.i	−0.434911	+	0.158295i
$460$	8.51213e6	+	3.14549e6i	1.87562	+	0.693097i
$461$	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	$0.0550337\pi$
$462$	40032.8	−	56875.6i	0.00872592	−	0.0123971i
$463$	−3.83395e6	+	2.21353e6i	−0.831178	+	0.479881i	−0.854256	−	0.519853i	$-0.825987\pi$
$463$	−3.83395e6	+	2.21353e6i	−0.831178	+	0.479881i	0.0230779	+	0.999734i	$0.492653\pi$
$464$	−62365.0	+	6.36209e6i	−0.0134476	+	1.37184i
$465$	89131.3	−	74790.0i	0.0191160	−	0.0160403i
$466$	−2.49478e6	−	5.38448e6i	−0.532190	−	1.14863i
$467$	5.98458e6	+	3.45520e6i	1.26982	+	0.733130i	0.974953	−	0.222409i	$-0.0713921\pi$
$467$	5.98458e6	+	3.45520e6i	1.26982	+	0.733130i	0.294865	+	0.955539i	$0.404725\pi$
$468$	−2.52434e6	−	12372.3i	−0.532763	−	0.00261117i
$469$	−876308.	+	2.40764e6i	−0.183961	+	0.505428i
$470$	−1.01457e6	+	2.16190e6i	−0.211854	+	0.451431i
$471$	−1.03505e6	−	5.87006e6i	−0.214986	−	1.21924i
$472$	467550.	−	983718.i	0.0965991	−	0.203243i
$473$	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
$478$	−6.02678e6	+	512396.i	−1.20647	+	0.102574i
$479$	4.84553e6	−	854398.i	0.964945	−	0.170146i	0.331091	−	0.943599i	$-0.392583\pi$
$479$	4.84553e6	−	854398.i	0.964945	−	0.170146i	0.633854	+	0.773453i	$0.281472\pi$
$480$	−321397.	−	4.27647e6i	−0.0636705	−	0.847193i
$481$	−2.51354e6	−	914855.i	−0.495363	−	0.180298i
$482$	−924780.	−	3.48547e6i	−0.181310	−	0.683351i
$483$	2.12155e6	−	3.67464e6i	0.413796	−	0.716716i
$484$	−5.07445e6	+	869141.i	−0.984637	+	0.168646i
$485$	186785.	+	222602.i	0.0360568	+	0.0429708i
$486$	−2.99531e6	−	3.01003e6i	−0.575243	−	0.578069i
$487$	−2.40242e6	−	4.16112e6i	−0.459015	−	0.795038i	0.539894	−	0.841733i	$-0.318464\pi$
$487$	−2.40242e6	−	4.16112e6i	−0.459015	−	0.795038i	−0.998909	+	0.0466952i	$0.985131\pi$
$488$	−4.74294e6	+	2.16936e6i	−0.901568	+	0.412366i
$489$	−1.53513e6	−	270685.i	−0.290317	−	0.0511907i
$490$	3.59406e6	+	323316.i	0.676231	+	0.0608328i
$491$	117881.	+	323877.i	0.0220669	+	0.0606284i	0.950237	−	0.311528i	$-0.100841\pi$
$491$	117881.	+	323877.i	0.0220669	+	0.0606284i	−0.928170	+	0.372156i	$0.878619\pi$
$492$	273166.	−	97910.7i	0.0508760	−	0.0182355i
$493$			3.18542e6i			0.590267i
$494$	−6.12986e6	+	1.98463e6i	−1.13014	+	0.365900i
$495$			89556.8i			0.0164280i
$496$	29497.7	−	158206.i	0.00538374	−	0.0288747i
$497$	−187486.	−	515113.i	−0.0340469	−	0.0935430i
$498$	−626701.	+	6.96655e6i	−0.113237	+	1.25877i
$499$	−4.44999e6	−	784653.i	−0.800032	−	0.141067i	−0.241338	−	0.970441i	$-0.577586\pi$
$499$	−4.44999e6	−	784653.i	−0.800032	−	0.141067i	−0.558694	+	0.829374i	$0.688697\pi$
$500$	2.82486e6	+	3.40025e6i	0.505327	+	0.608255i
$501$	2.59314e6	+	4.49145e6i	0.461564	+	0.799452i
$502$	7.72166e6	−	7.68391e6i	1.36758	−	1.36089i
$503$	1.44553e6	+	1.72271e6i	0.254745	+	0.303593i	0.878227	−	0.478245i	$-0.158727\pi$
$503$	1.44553e6	+	1.72271e6i	0.254745	+	0.303593i	−0.623482	+	0.781838i	$0.714282\pi$
$504$	1.62340e6	+	154063.i	0.284674	+	0.0270160i
$505$	932256.	−	1.61471e6i	0.162670	−	0.281752i
$506$	311534.	−	82657.6i	0.0540915	−	0.0143518i
$507$	1.66048e6	+	604364.i	0.286888	+	0.104419i
$508$	931796.	−	1.09948e6i	0.160200	−	0.189029i
$509$	−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	$0.464146\pi$
$510$	−181891.	−	2.13939e6i	−0.0309660	−	0.364221i
$511$	−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
$516$	1.59688e6	−	8.80382e6i	0.264027	−	1.45562i
$517$	14729.0	+	83532.3i	0.00242352	+	0.0137445i
$518$	1.56421e6	+	734077.i	0.256137	+	0.120203i
$519$	−2.74496e6	+	7.54171e6i	−0.447319	+	1.22900i
$520$	2.22823e6	−	8.07784e6i	0.361369	−	1.31005i
$521$	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	$0.385255\pi$
$522$	−3.47562e6	+	1.61035e6i	−0.558285	+	0.258669i
$523$	−1.92067e6	+	1.61163e6i	−0.307042	+	0.257639i	−0.783268	−	0.621684i	$-0.786449\pi$
$523$	−1.92067e6	+	1.61163e6i	−0.307042	+	0.257639i	0.476226	+	0.879323i	$0.342004\pi$
$524$	899260.	+	1.57534e6i	0.143073	+	0.250638i
$525$	−799599.	+	461649.i	−0.126612	+	0.0730994i
$526$	4.27409e6	+	3.00839e6i	0.673565	+	0.474099i
$527$	13991.3	−	79348.6i	0.00219448	−	0.0124455i
$528$	−96760.1	−	117637.i	−0.0151047	−	0.0183637i
$529$	1.24291e7	−	4.52384e6i	1.93109	−	0.702858i
$530$	−4.75823e6	−	6.83103e6i	−0.735793	−	1.05632i
$531$	655751.			0.100926
$532$	4.05869e6	−	922088.i	0.621737	−	0.141252i
$533$	566999.			0.0864499
$534$	−4.48499e6	−	6.43875e6i	−0.680625	−	0.977121i
$535$	2.02331e6	−	736426.i	0.305618	−	0.111236i
$536$	4.57258e6	+	3.25211e6i	0.687463	+	0.488938i
$537$	−843766.	+	4.78523e6i	−0.126266	+	0.716090i
$538$	−6.45334e6	−	4.54229e6i	−0.961234	−	0.676580i
$539$	110997.	−	64084.1i	0.0164566	−	0.00950120i
$540$	7.24203e6	−	4.13399e6i	1.06875	−	0.610078i
$541$	−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	$0.433805\pi$
$542$	−2.90829e6	+	1.34749e6i	−0.425245	+	0.197028i
$543$	−389381.	−	224809.i	−0.0566729	−	0.0327201i
$544$	−2.07404e6	−	2.12550e6i	−0.300484	−	0.307939i
$545$	1.44499e6	−	3.97008e6i	0.208388	−	0.572543i
$546$	−3.54689e6	−	1.66454e6i	−0.509175	−	0.238953i
$547$	1.54672e6	+	8.77191e6i	0.221027	+	1.25350i	0.870137	+	0.492810i	$0.164030\pi$
$547$	1.54672e6	+	8.77191e6i	0.221027	+	1.25350i	−0.649110	+	0.760694i	$0.724859\pi$
$548$	−2.60461e6	−	472437.i	−0.370503	−	0.0672037i
$549$	−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
$554$	416044.	+	4.89349e6i	0.0575923	+	0.677398i
$555$	2.69431e6	−	475080.i	0.371292	−	0.0654688i
$556$	5.67180e6	+	4.80677e6i	0.778097	+	0.659427i
$557$	−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	$-0.796441\pi$
$558$	93650.7	−	24847.8i	0.0127328	−	0.00337834i
$559$	8.74140e6	−	1.51406e7i	1.18318	−	2.04933i
$560$	−1.90112e6	+	5.06815e6i	−0.256177	+	0.682935i
$561$	−49019.2	−	58418.8i	−0.00657596	−	0.00783692i
$562$	−3.32794e6	+	3.31167e6i	−0.444462	+	0.442289i
$563$	4.85515e6	+	8.40937e6i	0.645553	+	1.11813i	0.984173	+	0.177208i	$0.0567064\pi$
$563$	4.85515e6	+	8.40937e6i	0.645553	+	1.11813i	−0.338620	+	0.940923i	$0.609960\pi$
$564$	1.88098e6	−	1.56269e6i	0.248993	−	0.206859i
$565$	−8.06943e6	−	1.42286e6i	−1.06346	−	0.187517i
$566$	1.19916e6	−	1.33301e7i	0.157339	−	1.74901i
$567$	−584859.	−	1.60689e6i	−0.0764000	−	0.209907i
$568$	−1.19667e6	+	95835.3i	−0.155633	+	0.0124639i
$569$			6.63543e6i			0.859189i	0.903022	+	0.429595i	$0.141343\pi$
$569$			6.63543e6i			0.859189i	−0.903022	+	0.429595i	$0.858657\pi$
$570$	4.41476e6	−	4.89279e6i	0.569141	−	0.630768i
$571$			2.80618e6i			0.360185i	0.983650	+	0.180093i	$0.0576397\pi$
$571$			2.80618e6i			0.360185i	−0.983650	+	0.180093i	$0.942360\pi$
$572$	−100421.	−	280168.i	−0.0128331	−	0.0358038i
$573$	1.70147e6	+	4.67474e6i	0.216489	+	0.594800i
$574$	−364796.	−	32816.5i	−0.0462136	−	0.00415731i
$575$	−4.21369e6	−	742987.i	−0.531487	−	0.0937155i
$576$	1.27064e6	−	3.33752e6i	0.159575	−	0.419148i
$577$	−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	$0.926931\pi$
$578$	4.61671e6	+	4.63940e6i	0.574796	+	0.577620i
$579$	3.26999e6	+	3.89703e6i	0.405369	+	0.483100i
$580$	−2.14659e6	−	1.25328e7i	−0.264960	−	1.54696i
$581$	4.41435e6	−	7.64588e6i	0.542533	−	0.939695i
$582$	−76308.7	−	287605.i	−0.00933828	−	0.0351957i
$583$	−277849.	−	101129.i	−0.0338561	−	0.0123226i
$584$	4.03904e6	+	5.85956e6i	0.490056	+	0.710940i
$585$	4.96835e6	−	876054.i	0.600236	−	0.105838i
$586$	−9.58736e6	+	815116.i	−1.15333	+	0.0980563i
$587$	7.61261e6	−	9.07235e6i	0.911881	−	1.08674i	−0.0840359	−	0.996463i	$-0.526781\pi$
$587$	7.61261e6	−	9.07235e6i	0.911881	−	1.08674i	0.995917	−	0.0902748i	$-0.0287745\pi$
$588$	−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
$592$	2.46067e6	−	2.87481e6i	0.288569	−	0.337136i
$593$	−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	$-0.162015\pi$
$594$	125827.	−	268121.i	0.0146322	−	0.0311791i
$595$	−926902.	+	2.54664e6i	−0.107335	+	0.294901i
$596$	−49692.8	+	1.01390e7i	−0.00573031	+	1.16917i
$597$	6.09240e6	+	3.51745e6i	0.699605	+	0.403917i
$598$	−7.63305e6	−	1.64744e7i	−0.872861	−	1.88390i
$599$	−3.04746e6	+	2.55712e6i	−0.347033	+	0.291195i	−0.799597	−	0.600536i	$-0.794954\pi$
$599$	−3.04746e6	+	2.55712e6i	−0.347033	+	0.291195i	0.452564	+	0.891732i	$0.350509\pi$
$600$	508966.	+	1.95692e6i	0.0577179	+	0.221919i
$601$	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	$0.273042\pi$
$602$	−6.50034e6	+	9.23519e6i	−0.731046	+	1.03862i
$603$	−586626.	+	3.32692e6i	−0.0657004	+	0.372605i
$604$	−5.09579e6	+	1.37899e7i	−0.568354	+	1.53804i
$605$	9.66853e6	−	3.51906e6i	1.07392	−	0.390875i
$606$	−1.56664e6	+	1.09126e6i	−0.173295	+	0.120711i
$607$	3.83649e6			0.422632			0.211316	−	0.977418i	$-0.432225\pi$
$607$	3.83649e6			0.422632			0.211316	+	0.977418i	$0.432225\pi$
$608$	416909.	−	9.10551e6i	0.0457385	−	0.998953i
$609$	−5.94536e6			−0.649584
$610$	8.55287e6	−	5.95760e6i	0.930652	−	0.648257i
$611$	4.49004e6	−	1.63424e6i	0.486572	−	0.177098i
$612$	619750.	−	1.67713e6i	0.0668865	−	0.181004i
$613$	−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	$0.918832\pi$
$614$	6.76656e6	−	9.61342e6i	0.724347	−	1.02910i
$615$	−502237.	+	289967.i	−0.0535452	+	0.0309144i
$616$	48393.1	+	186067.i	0.00513845	+	0.0197568i
$617$	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	$0.158971\pi$
$618$	−79667.4	−	171946.i	−0.00839092	−	0.0181101i
$619$	−1.32902e7	−	7.67309e6i	−1.39413	−	0.804903i	−0.400363	−	0.916356i	$-0.631116\pi$
$619$	−1.32902e7	−	7.67309e6i	−1.39413	−	0.804903i	−0.993770	+	0.111453i	$0.964449\pi$
$620$	−1576.32	+	321621.i	−0.000164689	+	0.0336020i
$621$	6.17987e6	−	1.69791e7i	0.643058	−	1.76679i
$622$	166616.	−	355034.i	0.0172679	−	0.0367955i
$623$	1.71986e6	+	9.75380e6i	0.177530	+	1.00682i
$624$	−5.57964e6	+	6.51870e6i	−0.573647	+	0.670193i
$625$	−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
$630$	−3.24724e6	+	276080.i	−0.325959	+	0.0277130i
$631$	3.25465e6	−	573883.i	0.325410	−	0.0573786i	−0.00855669	−	0.999963i	$-0.502724\pi$
$631$	3.25465e6	−	573883.i	0.325410	−	0.0573786i	0.333967	+	0.942585i	$0.391613\pi$
$632$	−1.00642e6	−	1.46005e6i	−0.100228	−	0.145404i
$633$	1.20320e7	+	4.37931e6i	1.19352	+	0.434406i
$634$	3.48624e6	+	1.31395e7i	0.344456	+	1.29824i
$635$	−1.44014e6	+	2.49440e6i	−0.141733	+	0.245489i
$636$	1.43912e6	+	8.40224e6i	0.141076	+	0.823668i
$637$	−4.64098e6	−	5.53090e6i	−0.453170	−	0.540067i
$638$	−318559.	−	320124.i	−0.0309841	−	0.0311363i
$639$	−361386.	−	625940.i	−0.0350122	−	0.0606429i
$640$	9.59254e6	+	6.96500e6i	0.925728	+	0.672158i
$641$	−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	$0.592619\pi$
$642$	−2.19595e6	−	197545.i	−0.210274	−	0.0189159i
$643$	2.38136e6	+	6.54274e6i	0.227142	+	0.624069i	0.999944	−	0.0105791i	$-0.00336749\pi$
$643$	2.38136e6	+	6.54274e6i	0.227142	+	0.624069i	−0.772802	+	0.634648i	$0.781145\pi$
$644$	3.95745e6	+	1.10411e7i	0.376011	+	1.04905i
$645$			1.78816e7i			1.69242i
$646$	164035.	−	4.56062e6i	0.0154652	−	0.429974i
$647$			1.07157e7i			1.00638i	0.864176	+	0.503189i	$0.167840\pi$
$647$			1.07157e7i			1.00638i	−0.864176	+	0.503189i	$0.832160\pi$
$648$	−3.73298e6	+	298957.i	−0.349235	+	0.0279686i
$649$	26442.4	+	72649.9i	0.00246428	+	0.00677054i
$650$	−353989.	+	3.93502e6i	−0.0328629	+	0.365312i
$651$	148099.	+	26113.8i	0.0136962	+	0.00241500i
$652$	3.31434e6	−	2.75349e6i	0.305336	−	0.253668i
$653$	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	$0.666769\pi$
$654$	−3.06659e6	+	3.05159e6i	−0.280357	+	0.278986i
$655$	−2.33022e6	−	2.77705e6i	−0.212224	−	0.252918i
$656$	−281720.	+	751030.i	−0.0255598	+	0.0681393i
$657$	−2.14236e6	+	3.71068e6i	−0.193633	+	0.335383i
$658$	−2.98339e6	+	791565.i	−0.268624	+	0.0712725i
$659$	−1.48327e7	−	5.39868e6i	−1.33048	−	0.484255i	−0.423677	−	0.905813i	$-0.639261\pi$
$659$	−1.48327e7	−	5.39868e6i	−1.33048	−	0.484255i	−0.906801	+	0.421559i	$0.861483\pi$
$660$	232230.	+	196812.i	0.0207520	+	0.0175870i
$661$	−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	$0.530449\pi$
$662$	634269.	+	7.46025e6i	0.0562508	+	0.661619i
$663$	−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
$668$	−1.41059e7	−	2.55859e6i	−1.22309	−	0.221850i
$669$	855676.	+	4.85278e6i	0.0739169	+	0.419204i
$670$	−1.01516e7	−	4.76409e6i	−0.873670	−	0.410008i
$671$	126619.	−	347884.i	0.0108566	−	0.0298283i
$672$	3.96711e6	−	3.87106e6i	0.338884	−	0.330679i
$673$	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	$0.502680\pi$
$674$	−1.25606e7	+	5.81966e6i	−1.06502	+	0.493455i
$675$	−3.01189e6	+	2.52728e6i	−0.254437	+	0.213498i
$676$	−4.24201e6	+	2.42149e6i	−0.357031	+	0.203805i
$677$	−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	$0.442262\pi$
$678$	6.86127e6	+	4.82941e6i	0.573231	+	0.403478i
$679$	−65218.1	+	369870.i	−0.00542867	+	0.0307875i
$680$	4.83658e6	+	3.43987e6i	0.401112	+	0.285279i
$681$	−4.67858e6	+	1.70286e6i	−0.386586	+	0.140706i
$682$	6529.22	+	9373.50i	0.000537527	+	0.000771686i
$683$	140529.			0.0115269			0.00576346	−	0.999983i	$-0.498165\pi$
$683$	140529.			0.0115269			0.00576346	+	0.999983i	$0.498165\pi$
$684$	5.05903e6	−	2.12659e6i	0.413454	−	0.173797i
$685$	5.29028e6			0.430777
$686$	7.15752e6	+	1.02755e7i	0.580700	+	0.833667i
$687$	5.40473e6	−	1.96716e6i	0.436900	−	0.159019i
$688$	1.57115e7	+	1.91013e7i	1.26545	+	1.53848i
$689$	−2.89238e6	+	1.64035e7i	−0.232117	+	1.31640i
$690$	1.51863e7	+	1.06891e7i	1.21431	+	0.854712i
$691$	−5.71042e6	+	3.29691e6i	−0.454959	+	0.262671i	−0.709922	−	0.704280i	$-0.751270\pi$
$691$	−5.71042e6	+	3.29691e6i	−0.454959	+	0.262671i	0.254963	+	0.966951i	$0.417937\pi$
$692$	−1.09981e7	−	1.92668e7i	−0.873080	−	1.52948i
$693$	−88670.0	+	74402.9i	−0.00701364	+	0.00588514i
$694$	−1.50190e7	+	6.95873e6i	−1.18370	+	0.548442i
$695$	−1.28676e7	−	7.42914e6i	−1.01050	−	0.583414i
$696$	−3.46228e6	+	1.25516e7i	−0.270919	+	0.982145i
$697$	−137354.	+	377377.i	−0.0107093	+	0.0294234i
$698$	1.08211e7	+	5.07826e6i	0.840681	+	0.394527i
$699$	−2.10885e6	−	1.19599e7i	−0.163250	−	0.925835i
$700$	455498.	−	2.51122e6i	0.0351351	−	0.193705i
$701$	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
$706$	−1.62447e6	−	1.91070e7i	−0.122660	−	1.44272i
$707$	2.37323e6	−	418465.i	0.178563	−	0.0314855i
$708$	1.44109e6	−	1.70043e6i	0.108046	−	0.127490i
$709$	−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	$0.772607\pi$
$710$	2.31897e6	−	615279.i	0.172643	−	0.0458064i
$711$	533822.	−	924607.i	0.0396025	−	0.0685936i
$712$	2.15933e7	+	2.04924e6i	1.59632	+	0.151493i
$713$	447957.	+	533855.i	0.0329999	+	0.0393278i
$714$	1.96709e6	−	1.95747e6i	0.144404	−	0.143698i
$715$	297400.	+	515112.i	0.0217558	+	0.0376822i
$716$	−8.58307e6	−	1.03313e7i	−0.625691	−	0.753135i
$717$	−1.21900e7	−	2.14942e6i	−0.885533	−	0.156143i
$718$	−1.52636e6	+	1.69674e7i	−0.110496	+	1.22830i
$719$	1.14405e6	+	3.14326e6i	0.0825324	+	0.226756i	0.974094	−	0.226144i	$-0.0726119\pi$
$719$	1.14405e6	+	3.14326e6i	0.0825324	+	0.226756i	−0.891562	+	0.452900i	$0.850390\pi$
$720$	−1.30818e6	+	7.01620e6i	−0.0940453	+	0.504395i
$721$			239194.i			0.0171361i
$722$	1.05679e7	−	9.19317e6i	0.754474	−	0.656330i
$723$		−	7.37965e6i		−	0.525037i
$724$	1.16996e6	−	419349.i	0.0829518	−	0.0297324i
$725$	2.05049e6	+	5.63367e6i	0.144881	+	0.398058i
$726$	−1.04935e7	−	943979.i	−0.738887	−	0.0664692i
$727$	2.32709e7	+	4.10330e6i	1.63297	+	0.287937i	0.913577	−	0.406667i	$-0.133309\pi$
$727$	2.32709e7	+	4.10330e6i	1.63297	+	0.287937i	0.719393	+	0.694603i	$0.244420\pi$
$728$	9.84904e6	−	4.50483e6i	0.688756	−	0.315028i
$729$	−6.85865e6	−	1.18795e7i	−0.477991	−	0.827905i
$730$	−1.00325e7	−	1.00817e7i	−0.696787	−	0.700210i
$731$	7.95950e6	+	9.48577e6i	0.550925	+	0.656567i
$732$	−1.05201e7	+	1.80186e6i	−0.725677	+	0.124292i
$733$	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	$-0.0149773\pi$
$734$	6.69828e6	+	2.52456e7i	0.458906	+	1.72960i
$735$	6.93943e6	+	2.52574e6i	0.473811	+	0.172453i
$736$	2.56141e7	−	1.92502e6i	1.74295	−	0.130990i
$737$	−392241.	+	69162.6i	−0.0266001	+	0.00469032i
$738$	−481195.	+	40911.1i	−0.0325222	+	0.00276504i
$739$	1.63576e7	−	1.94942e7i	1.10181	−	1.31309i	0.156227	−	0.987721i	$-0.450067\pi$
$739$	1.63576e7	−	1.94942e7i	1.10181	−	1.31309i	0.945587	−	0.325370i	$-0.105489\pi$
$740$	−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	0.147527	−	0.989058i	$-0.452869\pi$
$743$	−1.20516e7	−	1.01125e7i	−0.800887	−	0.672024i	−0.948414	+	0.317034i	$0.897313\pi$
$744$	141376.	−	297452.i	0.00936359	−	0.0197008i
$745$	−3.51864e6	−	1.99552e7i	−0.232265	−	1.31724i
$746$	1.16897e7	−	2.49090e7i	0.769051	−	1.63874i
$747$	3.98138e6	−	1.09388e7i	0.261055	−	0.717243i
$748$	210798.	+	1033.16i	0.0137757	+	6.75170e-5i
$749$	2.41008e6	+	1.39146e6i	0.156974	+	0.0906289i
$750$	3.80312e6	+	8.20828e6i	0.246881	+	0.532842i
$751$	1.08871e7	−	9.13533e6i	0.704386	−	0.591050i	−0.218632	−	0.975807i	$-0.570159\pi$
$751$	1.08871e7	−	9.13533e6i	0.704386	−	0.591050i	0.923018	+	0.384757i	$0.125715\pi$
$752$	−66259.3	+	6.75936e6i	−0.00427270	+	0.435874i
$753$	1.93062e7	−	1.11464e7i	1.24082	−	0.716389i
$754$	−1.46434e7	+	2.08042e7i	−0.938022	+	1.33267i
$755$	5.10191e6	−	2.89344e7i	0.325736	−	1.84734i
$756$	1.01097e7	+	3.73583e6i	0.643327	+	0.237729i
$757$	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	$0.219454\pi$
$758$	1.89690e7	−	1.32131e7i	1.19914	−	0.835278i
$759$	659599.			0.0415600
$760$	2.42793e6	+	1.80540e7i	0.152476	+	1.13381i
$761$	6.14081e6			0.384383			0.192191	−	0.981357i	$-0.438441\pi$
$761$	6.14081e6			0.384383			0.192191	+	0.981357i	$0.438441\pi$
$762$	2.42013e6	−	1.68577e6i	0.150991	−	0.105175i
$763$	5.13125e6	−	1.86762e6i	0.319089	−	0.116139i
$764$	−1.28988e7	−	4.76650e6i	−0.799496	−	0.295438i
$765$	−620495.	+	3.51900e6i	−0.0383340	+	0.217403i
$766$	6.22469e6	−	8.84358e6i	0.383306	−	0.544573i
$767$	3.77174e6	−	2.17761e6i	0.231501	−	0.133657i
$768$	−5.86217e6	−	1.06295e7i	−0.358637	−	0.650294i
$769$	−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	$0.287835\pi$
$770$	−161528.	−	348625.i	−0.00981793	−	0.0211900i
$771$	1.12948e7	+	6.52106e6i	0.684295	+	0.395078i
$772$	−1.40620e7	−	68920.4i	−0.849188	−	0.00416202i
$773$	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	$-0.243734\pi$
$774$	−6.32612e6	+	1.34801e7i	−0.379564	+	0.808797i
$775$	−26332.8	−	149341.i	−0.00157486	−	0.00893150i
$776$	742874.	+	353080.i	0.0442854	+	0.0210484i
$777$	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
$782$	1.28139e7	−	1.08944e6i	0.749318	−	0.0637069i
$783$	−2.49329e7	+	4.39635e6i	−1.45335	+	0.256264i
$784$	9.63198e6	−	3.39921e6i	0.559662	−	0.197509i
$785$	−3.09426e7	−	1.12622e7i	−1.79218	−	0.652302i
$786$	951984.	+	3.58800e6i	0.0549634	+	0.207155i
$787$	−9.09582e6	+	1.57544e7i	−0.523486	+	0.906704i	0.476140	+	0.879369i	$0.342035\pi$
$787$	−9.09582e6	+	1.57544e7i	−0.523486	+	0.906704i	−0.999626	+	0.0273349i	$0.991298\pi$
$788$	−2.40874e7	+	4.12563e6i	−1.38189	+	0.236687i
$789$	6.87537e6	+	8.19375e6i	0.393191	+	0.468587i
$790$	2.49983e6	+	2.51211e6i	0.142509	+	0.143209i
$791$	−5.29523e6	−	9.17162e6i	−0.300915	−	0.521200i
$792$	105439.	+	230525.i	0.00597295	+	0.0130588i
$793$	−2.05382e7	−	3.62144e6i	−1.15979	−	0.204502i
$794$	−9.08031e6	−	816851.i	−0.511151	−	0.0459824i
$795$	−5.82682e6	−	1.60091e7i	−0.326975	−	0.898356i
$796$	−1.83057e7	+	6.56129e6i	−1.02401	+	0.367034i
$797$			1.30936e7i			0.730150i	0.930978	+	0.365075i	$0.118957\pi$
$797$			1.30936e7i			0.730150i	−0.930978	+	0.365075i	$0.881043\pi$
$798$	8.51208e6	+	306160.i	0.473182	+	0.0170193i
$799$			3.38432e6i			0.187545i
$800$	−5.03633e6	−	2.42404e6i	−0.278220	−	0.133911i
$801$	4.46642e6	+	1.22714e7i	0.245968	+	0.675791i
$802$	−450918.	+	5.01251e6i	−0.0247549	+	0.275182i
$803$	−497491.	−	87721.1i	−0.0272268	−	0.00480082i
$804$	7.33787e6	+	8.83249e6i	0.400341	+	0.481885i
$805$	−1.17202e7	−	2.02999e7i	−0.637447	−	1.10409i
$806$	456144.	−	453914.i	0.0247323	−	0.0246114i
$807$	−1.03809e7	−	1.23715e7i	−0.561117	−	0.668713i
$808$	498609.	−	5.25396e6i	0.0268678	−	0.283112i
$809$	−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	$0.899912\pi$
$810$	7.23399e6	−	1.91935e6i	0.387405	−	0.102788i
$811$	−1.11260e7	−	4.04952e6i	−0.593998	−	0.216198i	0.0274887	−	0.999622i	$-0.491249\pi$
$811$	−1.11260e7	−	4.04952e6i	−0.593998	−	0.216198i	−0.621487	+	0.783424i	$0.713471\pi$
$812$	1.06253e7	−	1.25375e7i	0.565526	−	0.667298i
$813$	−6.45982e6	+	1.13904e6i	−0.342763	+	0.0604384i
$814$	22754.7	+	267639.i	0.00120368	+	0.0141576i
$815$	−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
$820$	286103.	−	1.57733e6i	0.0148590	−	0.0819195i
$821$	−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	$-0.307262\pi$
$822$	−4.90402e6	−	2.30143e6i	−0.253147	−	0.118800i
$823$	−1.18256e7	+	3.24905e7i	−0.608587	+	1.67208i	0.124729	+	0.992191i	$0.460194\pi$
$823$	−1.18256e7	+	3.24905e7i	−0.608587	+	1.67208i	−0.733316	+	0.679888i	$0.762029\pi$
$824$	504976.	+	139295.i	0.0259091	+	0.00714689i
$825$	−124299.	−	71764.2i	−0.00635819	−	0.00367090i
$826$	−2.55269e6	+	1.18273e6i	−0.130181	+	0.0603166i
$827$	2.27253e7	−	1.90688e7i	1.15544	−	0.969526i	0.155603	−	0.987820i	$-0.450268\pi$
$827$	2.27253e7	−	1.90688e7i	1.15544	−	0.969526i	0.999833	+	0.0182936i	$0.00582336\pi$
$828$	7.66663e6	+	1.34306e7i	0.388623	+	0.680800i
$829$	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	$0.132290\pi$
$830$	3.15984e7	+	2.22410e7i	1.59210	+	1.12062i
$831$	−1.74524e6	+	9.89774e6i	−0.0876703	+	0.497203i
$832$	−3.77480e6	−	2.34162e7i	−0.189054	−	1.17276i
$833$	4.80546e6	−	1.74905e6i	0.239951	−	0.0873350i
$834$	8.69624e6	+	1.24845e7i	0.432929	+	0.621522i
$835$	2.86507e7			1.42207
$836$	439602.	+	474732.i	0.0217542	+	0.0234927i
$837$	640389.			0.0315958
$838$	1.29304e6	+	1.85632e6i	0.0636067	+	0.0913152i
$839$	−4.48849e6	+	1.63368e6i	−0.220138	+	0.0801237i	−0.449735	−	0.893162i	$-0.648481\pi$
$839$	−4.48849e6	+	1.63368e6i	−0.220138	+	0.0801237i	0.229597	+	0.973286i	$0.426259\pi$
$840$	−6.42029e6	+	9.02714e6i	−0.313947	+	0.441420i
$841$	−3.14194e6	+	1.78188e7i	−0.153182	+	0.868737i
$842$	1.74164e7	+	1.22588e7i	0.846599	+	0.595892i
$843$	−8.32073e6	+	4.80398e6i	−0.403267	+	0.232826i
$844$	−3.07383e7	+	1.75464e7i	−1.48533	+	0.847877i
$845$	7.47791e6	−	6.27471e6i	0.360279	−	0.302310i
$846$	−3.69265e6	+	1.71091e6i	−0.177383	+	0.0821865i
$847$	1.15167e7	+	6.64918e6i	0.551595	+	0.318464i
$848$	−2.02904e7	−	1.19814e7i	−0.968951	−	0.572161i
$849$	9.36781e6	−	2.57379e7i	0.446035	−	1.22547i
$850$	−2.53328e6	−	1.18885e6i	−0.120264	−	0.0564392i
$851$	2.84551e6	+	1.61377e7i	0.134690	+	0.763866i
$852$	−2.41732e6	−	438465.i	−0.114087	−	0.0206936i
$853$	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	$0.248333\pi$
$858$	−51596.8	−	606879.i	−0.00239279	−	0.0281439i
$859$	−6.80486e6	+	1.19988e6i	−0.314656	+	0.0554824i	−0.328746	−	0.944418i	$-0.606626\pi$
$859$	−6.80486e6	+	1.19988e6i	−0.314656	+	0.0554824i	0.0140899	+	0.999901i	$0.495515\pi$
$860$	−3.77085e7	−	3.19574e7i	−1.73857	−	1.47342i
$861$	−704349.	−	256362.i	−0.0323802	−	0.0117854i
$862$	5.32734e6	−	1.41347e6i	0.244198	−	0.0647917i
$863$	−1.52006e7	+	2.63282e7i	−0.694759	+	1.20336i	0.275503	+	0.961300i	$0.411156\pi$
$863$	−1.52006e7	+	2.63282e7i	−0.694759	+	1.20336i	−0.970262	+	0.242058i	$0.922178\pi$
$864$	1.37743e7	−	1.91675e7i	0.627747	−	0.873537i
$865$	2.84991e7	+	3.39639e7i	1.29506	+	1.54340i
$866$	2.52516e7	−	2.51282e7i	1.14418	−	1.13859i
$867$	6.69710e6	+	1.15997e7i	0.302579	+	0.524083i
$868$	−319745.	+	265639.i	−0.0144047	+	0.0119672i
$869$	123962.	+	21857.8i	0.00556851	+	0.000981879i
$870$	2.33143e6	−	2.59167e7i	0.104430	−	1.16086i
$871$	7.67387e6	+	2.10838e7i	0.342744	+	0.941680i
$872$	−954655.	−	1.19205e7i	−0.0425163	−	0.530887i
$873$			495203.i			0.0219911i
$874$	2.93055e7	+	2.64424e7i	1.29769	+	1.17091i
$875$		−	1.14185e7i		−	0.504185i
$876$	4.91409e6	+	1.37100e7i	0.216363	+	0.603641i
$877$	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	$0.731844\pi$
$878$	1.92360e6	+	173045.i	0.0842130	+	0.00757568i
$879$	−1.93917e7	−	3.41929e6i	−0.846534	−	0.149267i
$880$	−830068.	+	137988.i	−0.0361332	+	0.00600668i
$881$	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	$0.786655\pi$
$882$	4.33774e6	+	4.35905e6i	0.187755	+	0.188678i
$883$	−816215.	−	972728.i	−0.0352292	−	0.0419845i	0.748142	−	0.663538i	$-0.230946\pi$
$883$	−816215.	−	972728.i	−0.0352292	−	0.0419845i	−0.783371	+	0.621554i	$0.786502\pi$
$884$	−2.00473e6	−	1.17045e7i	−0.0862830	−	0.503760i
$885$	−2.22729e6	+	3.85778e6i	−0.0955913	+	0.165569i
$886$	−7.22693e6	−	2.72381e7i	−0.309293	−	1.16572i
$887$	−2.86731e7	−	1.04362e7i	−1.22367	−	0.445381i	−0.352248	−	0.935907i	$-0.614583\pi$
$887$	−2.86731e7	−	1.04362e7i	−1.22367	−	0.445381i	−0.871427	+	0.490526i	$0.836805\pi$
$888$	6.37599e6	−	4.39501e6i	0.271341	−	0.187037i
$889$	−3.66616e6	+	646442.i	−0.155581	+	0.0274331i
$890$	−4.31926e7	+	3.67223e6i	−1.82782	+	0.155401i
$891$	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
$896$	1.07336e6	+	1.52840e7i	0.0446658	+	0.636014i
$897$	−6.45226e6	−	3.65926e7i	−0.267751	−	1.51849i
$898$	−1.29450e6	+	2.75839e6i	−0.0535685	+	0.114147i
$899$	333976.	−	917591.i	0.0137821	−	0.0378661i
$900$	16492.8	−	3.36508e6i	0.000678718	−	0.138481i
$901$	−1.02170e7	−	5.89878e6i	−0.419286	−	0.242075i
$902$	−23936.1	−	51661.4i	−0.000979575	−	0.00211422i
$903$	−1.77045e7	+	1.48559e7i	−0.722545	+	0.606288i
$904$	−2.24464e7	+	5.83797e6i	−0.913536	+	0.237597i
$905$	−2.15107e6	+	1.24192e6i	−0.0873038	+	0.0504049i
$906$	−1.73167e7	+	2.46023e7i	−0.700882	+	0.995760i
$907$	−6.33624e6	+	3.59346e7i	−0.255749	+	1.45042i	0.538395	+	0.842693i	$0.319031\pi$
$907$	−6.33624e6	+	3.59346e7i	−0.255749	+	1.45042i	−0.794143	+	0.607730i	$0.792080\pi$
$908$	4.77042e6	−	1.29094e7i	0.192018	−	0.519627i
$909$	2.98580e6	−	1.08674e6i	0.119853	−	0.0436231i
$910$	−1.77606e7	+	1.23714e7i	−0.710975	+	0.495238i
$911$	3.48828e7			1.39257			0.696283	−	0.717768i	$-0.254836\pi$
$911$	3.48828e7			1.39257			0.696283	+	0.717768i	$0.254836\pi$
$912$	5.60337e6	−	1.77920e7i	0.223081	−	0.708335i
$913$	1.37244e6			0.0544898
$914$	1.38392e7	−	9.63986e6i	0.547956	−	0.381685i
$915$	2.00444e7	−	7.29555e6i	0.791479	−	0.288075i
$916$	−5.51083e6	+	1.49131e7i	−0.217009	+	0.587256i
$917$	813624.	−	4.61429e6i	0.0319522	−	0.181210i
$918$	6.80187e6	−	9.66359e6i	0.266392	−	0.378470i
$919$	−62467.0	+	36065.4i	−0.00243984	+	0.00140864i	−0.501219	−	0.865320i	$-0.667115\pi$
$919$	−62467.0	+	36065.4i	−0.00243984	+	0.00140864i	0.498780	+	0.866729i	$0.333782\pi$
$920$	−4.96815e7	+	1.29214e7i	−1.93520	+	0.503316i
$921$	1.84296e7	−	1.54643e7i	0.715925	−	0.600732i
$922$	35577.8	+	76787.5i	0.00137832	+	0.00297484i
$923$	−4.15724e6	−	2.40018e6i	−0.160620	−	0.0927342i
$924$	−1928.32	+	393440.i	−7.43018e−5	+	0.0151600i
$925$	1.21955e6	−	3.35068e6i	0.0468646	−	0.128759i
$926$	1.06393e7	−	2.26709e7i	0.407743	−	0.868843i
$927$	54765.4	+	310590.i	0.00209318	+	0.0118710i
$928$	−2.02809e7	−	2.97330e7i	−0.773067	−	1.13336i
$929$	−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
$934$	−3.89506e7	+	3.31157e6i	−1.46099	+	0.124213i
$935$	−414887.	+	73155.7i	−0.0155203	+	0.00273665i
$936$	1.17574e7	−	8.10447e6i	0.438654	−	0.302367i
$937$	−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	$0.755132\pi$
$938$	−3.71694e6	−	1.40090e7i	−0.137936	−	0.519877i
$939$	7.03907e6	−	1.21920e7i	0.260526	−	0.451245i
$940$	−2.28063e6	−	1.33154e7i	−0.0841853	−	0.491513i
$941$	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	$0.399269\pi$
$942$	2.37840e7	+	2.39008e7i	0.873288	+	0.877578i
$943$	−1.73676e6	−	3.00816e6i	−0.0636007	−	0.110160i
$944$	1.01037e6	+	6.07790e6i	0.0369021	+	0.221985i
$945$	−2.12124e7	−	3.74031e6i	−0.772698	−	0.136248i
$946$	−1.74853e6	−	157296.i	−0.0635253	−	0.00571464i
$947$	−2.13703e6	−	5.87143e6i	−0.0774345	−	0.212750i	0.894935	−	0.446196i	$-0.147222\pi$
$947$	−2.13703e6	−	5.87143e6i	−0.0774345	−	0.212750i	−0.972370	+	0.233447i	$0.925000\pi$
$948$	−1.22447e6	−	3.41619e6i	−0.0442513	−	0.123459i
$949$			2.84574e7i			1.02572i
$950$	−2.64561e6	−	8.17141e6i	−0.0951079	−	0.293757i
$951$			2.78198e7i			0.997477i
$952$	612372.	+	7.64649e6i	0.0218989	+	0.273445i
$953$	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	$0.840689\pi$
$954$	1.27110e6	−	1.41298e7i	0.0452177	−	0.502651i
$955$	2.70647e7	+	4.77223e6i	0.960271	+	0.169322i
$956$	2.63181e7	−	2.18646e7i	0.931345	−	0.773744i
$957$	−462109.	−	800396.i	−0.0163104	−	0.0282504i
$958$	−1.97293e7	+	1.96328e7i	−0.694541	+	0.691145i
$959$	4.39512e6	+	5.23789e6i	0.154321	+	0.183912i
$960$	1.53188e7	+	1.88112e7i	0.536473	+	0.658777i
$961$	1.43022e7	−	2.47722e7i	0.499569	−	0.865278i
$962$	1.46253e7	−	3.88044e6i	0.509525	−	0.135189i
$963$	3.44804e6	+	1.25498e6i	0.119814	+	0.0436087i
$964$	1.55621e7	+	1.31887e7i	0.539356	+	0.457097i
$965$	2.76765e7	−	4.88011e6i	0.956736	−	0.168698i
$966$	2.03337e6	+	2.39164e7i	0.0701088	+	0.824617i
$967$	−2.67802e7	+	3.19154e7i	−0.920973	+	1.09757i	0.0739824	+	0.997260i	$0.476429\pi$
$967$	−2.67802e7	+	3.19154e7i	−0.920973	+	1.09757i	−0.994956	+	0.100314i	$0.968015\pi$
$968$	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	0.466410	−	0.884569i	$-0.345547\pi$
$971$	−9.51106e6	−	7.98073e6i	−0.323729	−	0.271640i	−0.790139	+	0.612928i	$0.789992\pi$
$972$	2.36358e7	+	4.28717e6i	0.802424	+	0.145548i
$973$	−3.33474e6	−	1.89123e7i	−0.112922	−	0.640415i
$974$	2.46055e7	+	1.15472e7i	0.831065	+	0.390014i
$975$	−2.76536e6	+	7.59776e6i	−0.0931622	+	0.255961i
$976$	1.50015e7	−	2.54049e7i	0.504091	−	0.853676i
$977$	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	$0.606270\pi$
$978$	8.00089e6	−	3.70704e6i	0.267480	−	0.123931i
$979$	−1.17943e6	+	989659.i	−0.0393292	+	0.0330011i
$980$	−1.77281e7	+	1.01198e7i	−0.589655	+	0.336595i
$981$	6.23524e6	−	3.59992e6i	0.206862	−	0.119432i
$982$	−1.59436e6	−	1.12222e6i	−0.0527603	−	0.0371362i
$983$	2.38331e6	−	1.35164e7i	0.0786677	−	0.446146i	−0.919877	−	0.392208i	$-0.871711\pi$
$983$	2.38331e6	−	1.35164e7i	0.0786677	−	0.446146i	0.998544	−	0.0539385i	$-0.0171775\pi$
$984$	−951398.	+	1.33770e6i	−0.0313238	+	0.0440423i
$985$	4.58945e7	−	1.67042e7i	1.50720	−	0.548575i
$986$	−1.02993e7	−	1.47859e7i	−0.337378	−	0.484347i
$987$	−6.31661e6			−0.206391
$988$	2.20365e7	−	2.90317e7i	0.718208	−	0.946193i
$989$	−1.07103e8			−3.48184
$990$	−289562.	−	415701.i	−0.00938973	−	0.0134801i
$991$	−3.31996e7	+	1.20836e7i	−1.07386	+	0.390853i	−0.817619	−	0.575759i	$-0.804707\pi$
$991$	−3.31996e7	+	1.20836e7i	−1.07386	+	0.390853i	−0.256242	+	0.966613i	$0.582484\pi$
$992$	374601.	+	829727.i	0.0120862	+	0.0267705i
$993$	−2.66066e6	+	1.50894e7i	−0.0856281	+	0.485621i
$994$	2.53576e6	+	1.78484e6i	0.0814034	+	0.0572971i
$995$	3.36564e7	−	1.94316e7i	1.07773	−	0.622228i
$996$	−1.96158e7	−	3.43634e7i	−0.626552	−	1.09761i
$997$	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	$0.0747467\pi$
$998$	2.31928e7	−	1.07459e7i	0.737100	−	0.341519i
$999$	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.3.10	✓	288
4.3	odd	2	inner	76.6.k.a.3.18	yes	288
19.13	odd	18	inner	76.6.k.a.51.18	yes	288
76.51	even	18	inner	76.6.k.a.51.10	yes	288

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

\(f(q)\)	\(=\)	\(q+(-4.64176 + 3.23327i) q^{2} +(-10.8783 + 3.95939i) q^{3} +(11.0919 - 30.0162i) q^{4} +(-11.1052 + 62.9808i) q^{5} +(37.6929 - 53.5512i) q^{6} +(-71.5832 + 41.3286i) q^{7} +(45.5645 + 175.191i) q^{8} +(-83.4872 + 70.0541i) q^{9} +O(q^{10})\)	\(q+(-4.64176 + 3.23327i) q^{2} +(-10.8783 + 3.95939i) q^{3} +(11.0919 - 30.0162i) q^{4} +(-11.1052 + 62.9808i) q^{5} +(37.6929 - 53.5512i) q^{6} +(-71.5832 + 41.3286i) q^{7} +(45.5645 + 175.191i) q^{8} +(-83.4872 + 70.0541i) q^{9} +(-152.086 - 328.248i) q^{10} +(-11.1277 - 6.42460i) q^{11} +(-1.81561 + 370.443i) q^{12} +(-247.565 + 680.180i) q^{13} +(198.645 - 423.285i) q^{14} +(-128.559 - 729.097i) q^{15} +(-777.940 - 665.872i) 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} +(72.4248 - 6.15755i) q^{22} +(4366.95 - 770.011i) q^{23} +(-1189.32 - 1725.38i) q^{24} +(-906.714 - 330.017i) q^{25} +(-1050.07 - 3957.68i) q^{26} +(2037.37 - 3528.84i) q^{27} +(446.532 + 2607.06i) q^{28} +(-3993.82 - 4759.65i) q^{29} +(2954.11 + 2968.62i) q^{30} +(78.5801 + 136.105i) q^{31} +(5763.96 + 575.526i) q^{32} +(146.489 + 25.8300i) q^{33} +(2888.48 + 259.844i) q^{34} +(-1807.96 - 4967.33i) q^{35} +(1176.72 + 3283.00i) q^{36} +3695.41i q^{37} +(5472.92 + 7020.14i) q^{38} -8379.44i q^{39} +(-11539.7 + 924.158i) q^{40} +(-267.914 - 736.089i) q^{41} +(-484.981 + 5391.16i) q^{42} +(-23786.2 - 4194.14i) q^{43} +(-316.270 + 262.751i) q^{44} +(-3484.92 - 6036.05i) q^{45} +(-17780.7 + 17693.7i) q^{46} +(-4243.21 - 5056.86i) q^{47} +(11099.1 + 4163.41i) q^{48} +(-4987.40 + 8638.43i) q^{49} +(5275.78 - 1399.79i) q^{50} +(5577.10 + 2029.90i) q^{51} +(17670.4 + 14975.4i) q^{52} +(22662.0 - 3995.92i) q^{53} +(1952.69 + 22967.4i) 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} +(-23310.6 - 4228.20i) q^{60} +(5003.14 + 28374.2i) q^{61} +(-804.814 - 377.695i) q^{62} +(3081.04 - 8465.10i) q^{63} +(-28615.7 + 15965.0i) q^{64} +(-40089.0 - 23145.4i) q^{65} +(-763.482 + 353.742i) q^{66} +(23745.4 - 19924.7i) q^{67} +(-14247.8 + 8133.13i) q^{68} +(-44456.4 + 25666.9i) q^{69} +(24452.8 + 17211.5i) q^{70} +(-1151.61 + 6531.12i) q^{71} +(-16076.9 - 11434.2i) q^{72} +(36943.9 - 13446.5i) q^{73} +(-11948.3 - 17153.2i) q^{74} +11170.2 q^{75} +(-48102.0 - 14890.3i) q^{76} +1062.08 q^{77} +(27093.0 + 38895.4i) q^{78} +(-9205.48 + 3350.52i) q^{79} +(50576.3 - 41600.6i) q^{80} +(-3592.44 + 20373.7i) q^{81} +(3623.57 + 2550.51i) q^{82} +(-92501.1 + 53405.5i) q^{83} +(-15179.9 - 26592.6i) q^{84} +(25116.3 - 21075.1i) q^{85} +(123971. - 57439.0i) q^{86} +(62291.5 + 35964.0i) q^{87} +(618.502 - 2242.21i) q^{88} +(40982.0 - 112597. i) q^{89} +(35692.4 + 16750.2i) q^{90} +(-10389.4 - 58921.0i) q^{91} +(25324.9 - 139620. i) 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} +(-4780.08 - 56223.1i) 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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