LMFDB - Embedded newform 74.5.d.a.43.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,5,Mod(31,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("74.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	74.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.64937726820$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 727 x^{12} + 198453 x^{10} + 24875201 x^{8} + 1392846203 x^{6} + 29089700589 x^{4} + \cdots + 446074380544 $ x^14 + 727x^12 + 198453x^10 + 24875201x^8 + 1392846203x^6 + 29089700589x^4 + 220261242916x^2 + 446074380544
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.5
Root			$4.34447i$ of defining polynomial
Character	$\chi$	$=$	74.43
Dual form			74.5.d.a.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 2.00000i) q^{2} +5.34447i q^{3} -8.00000i q^{4} +(10.1818 + 10.1818i) q^{5} +(-10.6889 - 10.6889i) q^{6} -94.0964 q^{7} +(16.0000 + 16.0000i) q^{8} +52.4367 q^{9} +O(q^{10})$	\(q+(-2.00000 + 2.00000i) q^{2} +5.34447i q^{3} -8.00000i q^{4} +(10.1818 + 10.1818i) q^{5} +(-10.6889 - 10.6889i) q^{6} -94.0964 q^{7} +(16.0000 + 16.0000i) q^{8} +52.4367 q^{9} -40.7273 q^{10} +104.701i q^{11} +42.7557 q^{12} +(-156.979 - 156.979i) q^{13} +(188.193 - 188.193i) q^{14} +(-54.4165 + 54.4165i) q^{15} -64.0000 q^{16} +(-288.653 - 288.653i) q^{17} +(-104.873 + 104.873i) q^{18} +(-257.997 - 257.997i) q^{19} +(81.4547 - 81.4547i) q^{20} -502.895i q^{21} +(-209.402 - 209.402i) q^{22} +(226.710 + 226.710i) q^{23} +(-85.5115 + 85.5115i) q^{24} -417.660i q^{25} +627.917 q^{26} +713.148i q^{27} +752.771i q^{28} +(-59.2294 + 59.2294i) q^{29} -217.666i q^{30} +(-608.888 + 608.888i) q^{31} +(128.000 - 128.000i) q^{32} -559.571 q^{33} +1154.61 q^{34} +(-958.074 - 958.074i) q^{35} -419.493i q^{36} +(-913.654 + 1019.51i) q^{37} +1031.99 q^{38} +(838.970 - 838.970i) q^{39} +325.819i q^{40} +1818.47i q^{41} +(1005.79 + 1005.79i) q^{42} +(1889.70 + 1889.70i) q^{43} +837.608 q^{44} +(533.902 + 533.902i) q^{45} -906.840 q^{46} -2515.46 q^{47} -342.046i q^{48} +6453.12 q^{49} +(835.321 + 835.321i) q^{50} +(1542.70 - 1542.70i) q^{51} +(-1255.83 + 1255.83i) q^{52} -185.050 q^{53} +(-1426.30 - 1426.30i) q^{54} +(-1066.05 + 1066.05i) q^{55} +(-1505.54 - 1505.54i) q^{56} +(1378.85 - 1378.85i) q^{57} -236.918i q^{58} +(-1987.36 - 1987.36i) q^{59} +(435.332 + 435.332i) q^{60} +(-4805.67 + 4805.67i) q^{61} -2435.55i q^{62} -4934.10 q^{63} +512.000i q^{64} -3196.67i q^{65} +(1119.14 - 1119.14i) q^{66} +2627.87i q^{67} +(-2309.23 + 2309.23i) q^{68} +(-1211.64 + 1211.64i) q^{69} +3832.29 q^{70} +5726.26 q^{71} +(838.987 + 838.987i) q^{72} -7873.75i q^{73} +(-211.711 - 3866.32i) q^{74} +2232.17 q^{75} +(-2063.97 + 2063.97i) q^{76} -9851.98i q^{77} +3355.88i q^{78} +(3214.81 + 3214.81i) q^{79} +(-651.637 - 651.637i) q^{80} +435.978 q^{81} +(-3636.95 - 3636.95i) q^{82} -9870.10 q^{83} -4023.16 q^{84} -5878.04i q^{85} -7558.78 q^{86} +(-316.550 - 316.550i) q^{87} +(-1675.22 + 1675.22i) q^{88} +(3659.89 - 3659.89i) q^{89} -2135.61 q^{90} +(14771.2 + 14771.2i) q^{91} +(1813.68 - 1813.68i) q^{92} +(-3254.18 - 3254.18i) q^{93} +(5030.93 - 5030.93i) q^{94} -5253.76i q^{95} +(684.092 + 684.092i) q^{96} +(945.694 + 945.694i) q^{97} +(-12906.2 + 12906.2i) q^{98} +5490.17i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9}+O(q^{10}) $ 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + 48 q^{10} + 160 q^{12} - 56 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} - 348 q^{17} + 692 q^{18} - 184 q^{19} - 96 q^{20} - 320 q^{22} - 502 q^{23} - 320 q^{24} + 224 q^{26} - 474 q^{29} - 630 q^{31} + 1792 q^{32} + 632 q^{33} + 1392 q^{34} + 1826 q^{35} - 2544 q^{37} + 736 q^{38} - 798 q^{39} - 224 q^{42} + 1936 q^{43} + 1280 q^{44} + 6162 q^{45} + 2008 q^{46} + 5716 q^{47} + 7862 q^{49} - 1372 q^{50} - 2422 q^{51} - 448 q^{52} - 20228 q^{53} - 656 q^{54} + 14006 q^{55} + 768 q^{56} - 2270 q^{57} - 4502 q^{59} + 3024 q^{60} - 11906 q^{61} - 2588 q^{63} - 1264 q^{66} - 2784 q^{68} + 21440 q^{69} - 7304 q^{70} - 11224 q^{71} - 5536 q^{72} + 4924 q^{74} - 18652 q^{75} - 1472 q^{76} + 20488 q^{79} + 768 q^{80} - 1706 q^{81} + 9808 q^{82} - 20224 q^{83} + 896 q^{84} - 7744 q^{86} + 19636 q^{87} - 2560 q^{88} + 13864 q^{89} - 24648 q^{90} - 6070 q^{91} - 4016 q^{92} - 13800 q^{93} - 11432 q^{94} + 2560 q^{96} + 16622 q^{97} - 15724 q^{98}+O(q^{100}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9 + 48 * q^10 + 160 * q^12 - 56 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 - 348 * q^17 + 692 * q^18 - 184 * q^19 - 96 * q^20 - 320 * q^22 - 502 * q^23 - 320 * q^24 + 224 * q^26 - 474 * q^29 - 630 * q^31 + 1792 * q^32 + 632 * q^33 + 1392 * q^34 + 1826 * q^35 - 2544 * q^37 + 736 * q^38 - 798 * q^39 - 224 * q^42 + 1936 * q^43 + 1280 * q^44 + 6162 * q^45 + 2008 * q^46 + 5716 * q^47 + 7862 * q^49 - 1372 * q^50 - 2422 * q^51 - 448 * q^52 - 20228 * q^53 - 656 * q^54 + 14006 * q^55 + 768 * q^56 - 2270 * q^57 - 4502 * q^59 + 3024 * q^60 - 11906 * q^61 - 2588 * q^63 - 1264 * q^66 - 2784 * q^68 + 21440 * q^69 - 7304 * q^70 - 11224 * q^71 - 5536 * q^72 + 4924 * q^74 - 18652 * q^75 - 1472 * q^76 + 20488 * q^79 + 768 * q^80 - 1706 * q^81 + 9808 * q^82 - 20224 * q^83 + 896 * q^84 - 7744 * q^86 + 19636 * q^87 - 2560 * q^88 + 13864 * q^89 - 24648 * q^90 - 6070 * q^91 - 4016 * q^92 - 13800 * q^93 - 11432 * q^94 + 2560 * q^96 + 16622 * q^97 - 15724 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−2.00000	+	2.00000i	−0.500000	+	0.500000i
$2$	−2.00000	+	2.00000i	−0.500000	+	0.500000i
$3$			5.34447i			0.593830i	0.954904	+	0.296915i	$0.0959577\pi$
$3$			5.34447i			0.593830i	−0.954904	+	0.296915i	$0.904042\pi$
$4$		−	8.00000i		−	0.500000i
$5$	10.1818	+	10.1818i	0.407273	+	0.407273i	0.880787	−	0.473513i	$-0.157014\pi$
$5$	10.1818	+	10.1818i	0.407273	+	0.407273i	−0.473513	+	0.880787i	$0.657014\pi$
$6$	−10.6889	−	10.6889i	−0.296915	−	0.296915i
$7$	−94.0964			−1.92033			−0.960167	−	0.279427i	$-0.909855\pi$
$7$	−94.0964			−1.92033			−0.960167	+	0.279427i	$0.909855\pi$
$8$	16.0000	+	16.0000i	0.250000	+	0.250000i
$9$	52.4367			0.647366
$10$	−40.7273			−0.407273
$11$			104.701i			0.865297i	0.901563	+	0.432649i	$0.142421\pi$
$11$			104.701i			0.865297i	−0.901563	+	0.432649i	$0.857579\pi$
$12$	42.7557			0.296915
$13$	−156.979	−	156.979i	−0.928871	−	0.928871i	0.0687618	−	0.997633i	$-0.478095\pi$
$13$	−156.979	−	156.979i	−0.928871	−	0.928871i	−0.997633	+	0.0687618i	$0.978095\pi$
$14$	188.193	−	188.193i	0.960167	−	0.960167i
$15$	−54.4165	+	54.4165i	−0.241851	+	0.241851i
$16$	−64.0000			−0.250000
$17$	−288.653	−	288.653i	−0.998801	−	0.998801i	0.00119826	−	0.999999i	$-0.499619\pi$
$17$	−288.653	−	288.653i	−0.998801	−	0.998801i	−0.999999	+	0.00119826i	$0.999619\pi$
$18$	−104.873	+	104.873i	−0.323683	+	0.323683i
$19$	−257.997	−	257.997i	−0.714672	−	0.714672i	0.252837	−	0.967509i	$-0.418636\pi$
$19$	−257.997	−	257.997i	−0.714672	−	0.714672i	−0.967509	+	0.252837i	$0.918636\pi$
$20$	81.4547	−	81.4547i	0.203637	−	0.203637i
$21$		−	502.895i		−	1.14035i
$22$	−209.402	−	209.402i	−0.432649	−	0.432649i
$23$	226.710	+	226.710i	0.428563	+	0.428563i	0.888139	−	0.459575i	$-0.151998\pi$
$23$	226.710	+	226.710i	0.428563	+	0.428563i	−0.459575	+	0.888139i	$0.651998\pi$
$24$	−85.5115	+	85.5115i	−0.148457	+	0.148457i
$25$		−	417.660i		−	0.668257i
$26$	627.917			0.928871
$27$			713.148i			0.978255i
$28$			752.771i			0.960167i
$29$	−59.2294	+	59.2294i	−0.0704274	+	0.0704274i	−0.741443	−	0.671016i	$-0.765858\pi$
$29$	−59.2294	+	59.2294i	−0.0704274	+	0.0704274i	0.671016	+	0.741443i	$0.265858\pi$
$30$		−	217.666i		−	0.241851i
$31$	−608.888	+	608.888i	−0.633598	+	0.633598i	−0.948969	−	0.315371i	$-0.897871\pi$
$31$	−608.888	+	608.888i	−0.633598	+	0.633598i	0.315371	+	0.948969i	$0.397871\pi$
$32$	128.000	−	128.000i	0.125000	−	0.125000i
$33$	−559.571			−0.513839
$34$	1154.61			0.998801
$35$	−958.074	−	958.074i	−0.782101	−	0.782101i
$36$		−	419.493i		−	0.323683i
$37$	−913.654	+	1019.51i	−0.667388	+	0.744711i
$37$	−913.654	+	1019.51i	−0.667388	+	0.744711i
$38$	1031.99			0.714672
$39$	838.970	−	838.970i	0.551591	−	0.551591i
$40$			325.819i			0.203637i
$41$			1818.47i			1.08178i	0.841093	+	0.540891i	$0.181913\pi$
$41$			1818.47i			1.08178i	−0.841093	+	0.540891i	$0.818087\pi$
$42$	1005.79	+	1005.79i	0.570175	+	0.570175i
$43$	1889.70	+	1889.70i	1.02201	+	1.02201i	0.999752	+	0.0222575i	$0.00708538\pi$
$43$	1889.70	+	1889.70i	1.02201	+	1.02201i	0.0222575	+	0.999752i	$0.492915\pi$
$44$	837.608			0.432649
$45$	533.902	+	533.902i	0.263655	+	0.263655i
$46$	−906.840			−0.428563
$47$	−2515.46			−1.13873			−0.569367	−	0.822084i	$-0.692812\pi$
$47$	−2515.46			−1.13873			−0.569367	+	0.822084i	$0.692812\pi$
$48$		−	342.046i		−	0.148457i
$49$	6453.12			2.68768
$50$	835.321	+	835.321i	0.334128	+	0.334128i
$51$	1542.70	−	1542.70i	0.593118	−	0.593118i
$52$	−1255.83	+	1255.83i	−0.464436	+	0.464436i
$53$	−185.050			−0.0658777			−0.0329388	−	0.999457i	$-0.510487\pi$
$53$	−185.050			−0.0658777			−0.0329388	+	0.999457i	$0.510487\pi$
$54$	−1426.30	−	1426.30i	−0.489127	−	0.489127i
$55$	−1066.05	+	1066.05i	−0.352413	+	0.352413i
$56$	−1505.54	−	1505.54i	−0.480083	−	0.480083i
$57$	1378.85	−	1378.85i	0.424393	−	0.424393i
$58$		−	236.918i		−	0.0704274i
$59$	−1987.36	−	1987.36i	−0.570916	−	0.570916i	0.361468	−	0.932384i	$-0.382276\pi$
$59$	−1987.36	−	1987.36i	−0.570916	−	0.570916i	−0.932384	+	0.361468i	$0.882276\pi$
$60$	435.332	+	435.332i	0.120925	+	0.120925i
$61$	−4805.67	+	4805.67i	−1.29150	+	1.29150i	−0.357642	+	0.933859i	$0.616419\pi$
$61$	−4805.67	+	4805.67i	−1.29150	+	1.29150i	−0.933859	+	0.357642i	$0.883581\pi$
$62$		−	2435.55i		−	0.633598i
$63$	−4934.10			−1.24316
$64$			512.000i			0.125000i
$65$		−	3196.67i		−	0.756609i
$66$	1119.14	−	1119.14i	0.256920	−	0.256920i
$67$			2627.87i			0.585402i	0.956204	+	0.292701i	$0.0945540\pi$
$67$			2627.87i			0.585402i	−0.956204	+	0.292701i	$0.905446\pi$
$68$	−2309.23	+	2309.23i	−0.499401	+	0.499401i
$69$	−1211.64	+	1211.64i	−0.254494	+	0.254494i
$70$	3832.29			0.782101
$71$	5726.26			1.13594			0.567968	−	0.823050i	$-0.307730\pi$
$71$	5726.26			1.13594			0.567968	+	0.823050i	$0.307730\pi$
$72$	838.987	+	838.987i	0.161842	+	0.161842i
$73$		−	7873.75i		−	1.47753i	−0.673964	−	0.738764i	$-0.735410\pi$
$73$		−	7873.75i		−	1.47753i	0.673964	−	0.738764i	$-0.264590\pi$
$74$	−211.711	−	3866.32i	−0.0386615	−	0.706049i
$75$	2232.17			0.396831
$76$	−2063.97	+	2063.97i	−0.357336	+	0.357336i
$77$		−	9851.98i		−	1.66166i
$78$			3355.88i			0.551591i
$79$	3214.81	+	3214.81i	0.515112	+	0.515112i	0.916088	−	0.400977i	$-0.131329\pi$
$79$	3214.81	+	3214.81i	0.515112	+	0.515112i	−0.400977	+	0.916088i	$0.631329\pi$
$80$	−651.637	−	651.637i	−0.101818	−	0.101818i
$81$	435.978			0.0664499
$82$	−3636.95	−	3636.95i	−0.540891	−	0.540891i
$83$	−9870.10			−1.43273			−0.716367	−	0.697724i	$-0.754196\pi$
$83$	−9870.10			−1.43273			−0.716367	+	0.697724i	$0.754196\pi$
$84$	−4023.16			−0.570175
$85$		−	5878.04i		−	0.813570i
$86$	−7558.78			−1.02201
$87$	−316.550	−	316.550i	−0.0418218	−	0.0418218i
$88$	−1675.22	+	1675.22i	−0.216324	+	0.216324i
$89$	3659.89	−	3659.89i	0.462049	−	0.462049i	−0.437278	−	0.899327i	$-0.644057\pi$
$89$	3659.89	−	3659.89i	0.462049	−	0.462049i	0.899327	+	0.437278i	$0.144057\pi$
$90$	−2135.61			−0.263655
$91$	14771.2	+	14771.2i	1.78374	+	1.78374i
$92$	1813.68	−	1813.68i	0.214282	−	0.214282i
$93$	−3254.18	−	3254.18i	−0.376249	−	0.376249i
$94$	5030.93	−	5030.93i	0.569367	−	0.569367i
$95$		−	5253.76i		−	0.582134i
$96$	684.092	+	684.092i	0.0742287	+	0.0742287i
$97$	945.694	+	945.694i	0.100510	+	0.100510i	0.755573	−	0.655064i	$-0.227358\pi$
$97$	945.694	+	945.694i	0.100510	+	0.100510i	−0.655064	+	0.755573i	$0.727358\pi$
$98$	−12906.2	+	12906.2i	−1.34384	+	1.34384i
$99$			5490.17i			0.560164i
$100$	−3341.28			−0.334128
$101$			18425.6i			1.80625i	0.429378	+	0.903125i	$0.358733\pi$
$101$			18425.6i			1.80625i	−0.429378	+	0.903125i	$0.641267\pi$
$102$			6170.79i			0.593118i
$103$	−663.465	+	663.465i	−0.0625379	+	0.0625379i	−0.737684	−	0.675146i	$-0.764081\pi$
$103$	−663.465	+	663.465i	−0.0625379	+	0.0625379i	0.675146	+	0.737684i	$0.264081\pi$
$104$		−	5023.34i		−	0.464436i
$105$	5120.39	−	5120.39i	0.464435	−	0.464435i
$106$	370.101	−	370.101i	0.0329388	−	0.0329388i
$107$	−1562.94			−0.136513			−0.0682565	−	0.997668i	$-0.521744\pi$
$107$	−1562.94			−0.136513			−0.0682565	+	0.997668i	$0.521744\pi$
$108$	5705.18			0.489127
$109$	−10571.0	−	10571.0i	−0.889738	−	0.889738i	0.104759	−	0.994498i	$-0.466593\pi$
$109$	−10571.0	−	10571.0i	−0.889738	−	0.889738i	−0.994498	+	0.104759i	$0.966593\pi$
$110$		−	4264.19i		−	0.352413i
$111$	−5448.73	−	4882.99i	−0.442231	−	0.396314i
$112$	6022.17			0.480083
$113$	4684.76	−	4684.76i	0.366886	−	0.366886i	−0.499455	−	0.866340i	$-0.666466\pi$
$113$	4684.76	−	4684.76i	0.366886	−	0.366886i	0.866340	+	0.499455i	$0.166466\pi$
$114$			5515.42i			0.424393i
$115$			4616.65i			0.349085i
$116$	473.835	+	473.835i	0.0352137	+	0.0352137i
$117$	−8231.47	−	8231.47i	−0.601320	−	0.601320i
$118$	7949.43			0.570916
$119$	27161.2	+	27161.2i	1.91803	+	1.91803i
$120$	−1741.33			−0.120925
$121$	3678.71			0.251261
$122$		−	19222.7i		−	1.29150i
$123$	−9718.77			−0.642394
$124$	4871.10	+	4871.10i	0.316799	+	0.316799i
$125$	10616.2	−	10616.2i	0.679437	−	0.679437i
$126$	9868.20	−	9868.20i	0.621580	−	0.621580i
$127$	860.617			0.0533584			0.0266792	−	0.999644i	$-0.491507\pi$
$127$	860.617			0.0533584			0.0266792	+	0.999644i	$0.491507\pi$
$128$	−1024.00	−	1024.00i	−0.0625000	−	0.0625000i
$129$	−10099.4	+	10099.4i	−0.606900	+	0.606900i
$130$	6393.35	+	6393.35i	0.378305	+	0.378305i
$131$	9264.84	−	9264.84i	0.539878	−	0.539878i	−0.383615	−	0.923493i	$-0.625321\pi$
$131$	9264.84	−	9264.84i	0.539878	−	0.539878i	0.923493	+	0.383615i	$0.125321\pi$
$132$			4476.57i			0.256920i
$133$	24276.5	+	24276.5i	1.37241	+	1.37241i
$134$	−5255.74	−	5255.74i	−0.292701	−	0.292701i
$135$	−7261.15	+	7261.15i	−0.398417	+	0.398417i
$136$		−	9236.91i		−	0.499401i
$137$	−12740.7			−0.678817			−0.339409	−	0.940639i	$-0.610227\pi$
$137$	−12740.7			−0.678817			−0.339409	+	0.940639i	$0.610227\pi$
$138$		−	4846.58i		−	0.254494i
$139$		−	2561.90i		−	0.132597i	−0.997800	−	0.0662984i	$-0.978881\pi$
$139$		−	2561.90i		−	0.132597i	0.997800	−	0.0662984i	$-0.0211189\pi$
$140$	−7664.59	+	7664.59i	−0.391050	+	0.391050i
$141$		−	13443.8i		−	0.676214i
$142$	−11452.5	+	11452.5i	−0.567968	+	0.567968i
$143$	16435.9	−	16435.9i	0.803750	−	0.803750i
$144$	−3355.95			−0.161842
$145$	−1206.13			−0.0573664
$146$	15747.5	+	15747.5i	0.738764	+	0.738764i
$147$			34488.5i			1.59602i
$148$	8156.07	+	7309.23i	0.372355	+	0.333694i
$149$	−16513.4			−0.743814			−0.371907	−	0.928270i	$-0.621296\pi$
$149$	−16513.4			−0.743814			−0.371907	+	0.928270i	$0.621296\pi$
$150$	−4464.34	+	4464.34i	−0.198415	+	0.198415i
$151$		−	3594.24i		−	0.157635i	−0.996889	−	0.0788176i	$-0.974886\pi$
$151$		−	3594.24i		−	0.157635i	0.996889	−	0.0788176i	$-0.0251145\pi$
$152$		−	8255.89i		−	0.357336i
$153$	−15136.0	−	15136.0i	−0.646590	−	0.646590i
$154$	19704.0	+	19704.0i	0.830830	+	0.830830i
$155$	−12399.2			−0.516095
$156$	−6711.76	−	6711.76i	−0.275796	−	0.275796i
$157$	1308.30			0.0530772			0.0265386	−	0.999648i	$-0.491552\pi$
$157$	1308.30			0.0530772			0.0265386	+	0.999648i	$0.491552\pi$
$158$	−12859.3			−0.515112
$159$		−	988.995i		−	0.0391201i
$160$	2606.55			0.101818
$161$	−21332.6	−	21332.6i	−0.822985	−	0.822985i
$162$	−871.955	+	871.955i	−0.0332249	+	0.0332249i
$163$	−19856.3	+	19856.3i	−0.747347	+	0.747347i	−0.973980	−	0.226633i	$-0.927228\pi$
$163$	−19856.3	+	19856.3i	−0.747347	+	0.747347i	0.226633	+	0.973980i	$0.427228\pi$
$164$	14547.8			0.540891
$165$	−5697.46	−	5697.46i	−0.209273	−	0.209273i
$166$	19740.2	−	19740.2i	0.716367	−	0.716367i
$167$	−16420.6	−	16420.6i	−0.588786	−	0.588786i	0.348517	−	0.937303i	$-0.386685\pi$
$167$	−16420.6	−	16420.6i	−0.588786	−	0.588786i	−0.937303	+	0.348517i	$0.886685\pi$
$168$	8046.32	−	8046.32i	0.285088	−	0.285088i
$169$			20724.0i			0.725604i
$170$	11756.1	+	11756.1i	0.406785	+	0.406785i
$171$	−13528.5	−	13528.5i	−0.462655	−	0.462655i
$172$	15117.6	−	15117.6i	0.511005	−	0.511005i
$173$			1380.88i			0.0461384i	0.999734	+	0.0230692i	$0.00734381\pi$
$173$			1380.88i			0.0461384i	−0.999734	+	0.0230692i	$0.992656\pi$
$174$	1266.20			0.0418218
$175$			39300.3i			1.28328i
$176$		−	6700.86i		−	0.216324i
$177$	10621.4	−	10621.4i	0.339027	−	0.339027i
$178$			14639.6i			0.462049i
$179$	−11082.5	+	11082.5i	−0.345886	+	0.345886i	−0.858575	−	0.512688i	$-0.828650\pi$
$179$	−11082.5	+	11082.5i	−0.345886	+	0.345886i	0.512688	+	0.858575i	$0.328650\pi$
$180$	4271.21	−	4271.21i	0.131828	−	0.131828i
$181$	17811.1			0.543667			0.271833	−	0.962344i	$-0.412370\pi$
$181$	17811.1			0.543667			0.271833	+	0.962344i	$0.412370\pi$
$182$	−59084.7			−1.78374
$183$	−25683.8	−	25683.8i	−0.766931	−	0.766931i
$184$			7254.72i			0.214282i
$185$	−19683.1	+	1077.80i	−0.575110	+	0.0314916i
$186$	13016.7			0.376249
$187$	30222.3	−	30222.3i	0.864260	−	0.864260i
$188$			20123.7i			0.569367i
$189$		−	67104.6i		−	1.87858i
$190$	10507.5	+	10507.5i	0.291067	+	0.291067i
$191$	−14170.9	−	14170.9i	−0.388446	−	0.388446i	0.485687	−	0.874133i	$-0.338569\pi$
$191$	−14170.9	−	14170.9i	−0.388446	−	0.388446i	−0.874133	+	0.485687i	$0.838569\pi$
$192$	−2736.37			−0.0742287
$193$	−31829.7	−	31829.7i	−0.854511	−	0.854511i	0.136174	−	0.990685i	$-0.456519\pi$
$193$	−31829.7	−	31829.7i	−0.854511	−	0.854511i	−0.990685	+	0.136174i	$0.956519\pi$
$194$	−3782.78			−0.100510
$195$	17084.5			0.449297
$196$		−	51625.0i		−	1.34384i
$197$	38635.1			0.995520			0.497760	−	0.867315i	$-0.334156\pi$
$197$	38635.1			0.995520			0.497760	+	0.867315i	$0.334156\pi$
$198$	−10980.3	−	10980.3i	−0.280082	−	0.280082i
$199$	−42102.2	+	42102.2i	−1.06316	+	1.06316i	−0.0652938	+	0.997866i	$0.520798\pi$
$199$	−42102.2	+	42102.2i	−1.06316	+	1.06316i	−0.997866	+	0.0652938i	$0.979202\pi$
$200$	6682.57	−	6682.57i	0.167064	−	0.167064i
$201$	−14044.6			−0.347629
$202$	−36851.1	−	36851.1i	−0.903125	−	0.903125i
$203$	5573.27	−	5573.27i	0.135244	−	0.135244i
$204$	−12341.6	−	12341.6i	−0.296559	−	0.296559i
$205$	−18515.4	+	18515.4i	−0.440581	+	0.440581i
$206$		−	2653.86i		−	0.0625379i
$207$	11887.9	+	11887.9i	0.277438	+	0.277438i
$208$	10046.7	+	10046.7i	0.232218	+	0.232218i
$209$	27012.5	−	27012.5i	0.618404	−	0.618404i
$210$			20481.6i			0.464435i
$211$	3844.31			0.0863483			0.0431742	−	0.999068i	$-0.486253\pi$
$211$	3844.31			0.0863483			0.0431742	+	0.999068i	$0.486253\pi$
$212$			1480.40i			0.0329388i
$213$			30603.8i			0.674553i
$214$	3125.87	−	3125.87i	0.0682565	−	0.0682565i
$215$			38481.1i			0.832475i
$216$	−11410.4	+	11410.4i	−0.244564	+	0.244564i
$217$	57294.1	−	57294.1i	1.21672	−	1.21672i
$218$	42283.9			0.889738
$219$	42081.0			0.877400
$220$	8528.38	+	8528.38i	0.176206	+	0.176206i
$221$			90625.2i			1.85552i
$222$	20663.4	−	1131.48i	0.419273	−	0.0229584i
$223$	−61406.0			−1.23481			−0.617406	−	0.786644i	$-0.711817\pi$
$223$	−61406.0			−1.23481			−0.617406	+	0.786644i	$0.711817\pi$
$224$	−12044.3	+	12044.3i	−0.240042	+	0.240042i
$225$		−	21900.7i		−	0.432607i
$226$			18739.0i			0.366886i
$227$	27233.3	+	27233.3i	0.528504	+	0.528504i	0.920126	−	0.391622i	$-0.128086\pi$
$227$	27233.3	+	27233.3i	0.528504	+	0.528504i	−0.391622	+	0.920126i	$0.628086\pi$
$228$	−11030.8	−	11030.8i	−0.212197	−	0.212197i
$229$	65938.4			1.25738			0.628691	−	0.777655i	$-0.283591\pi$
$229$	65938.4			1.25738			0.628691	+	0.777655i	$0.283591\pi$
$230$	−9233.30	−	9233.30i	−0.174542	−	0.174542i
$231$	52653.6			0.986742
$232$	−1895.34			−0.0352137
$233$			56189.5i			1.03501i	0.855681	+	0.517504i	$0.173139\pi$
$233$			56189.5i			1.03501i	−0.855681	+	0.517504i	$0.826861\pi$
$234$	32925.9			0.601320
$235$	−25612.0	−	25612.0i	−0.463776	−	0.463776i
$236$	−15898.9	+	15898.9i	−0.285458	+	0.285458i
$237$	−17181.5	+	17181.5i	−0.305889	+	0.305889i
$238$	−108645.			−1.91803
$239$	−79431.0	−	79431.0i	−1.39057	−	1.39057i	−0.824036	−	0.566538i	$-0.808282\pi$
$239$	−79431.0	−	79431.0i	−1.39057	−	1.39057i	−0.566538	−	0.824036i	$-0.691718\pi$
$240$	3482.65	−	3482.65i	0.0604627	−	0.0604627i
$241$	21019.1	+	21019.1i	0.361893	+	0.361893i	0.864509	−	0.502617i	$-0.167629\pi$
$241$	21019.1	+	21019.1i	0.361893	+	0.361893i	−0.502617	+	0.864509i	$0.667629\pi$
$242$	−7357.42	+	7357.42i	−0.125630	+	0.125630i
$243$			60095.0i			1.01771i
$244$	38445.4	+	38445.4i	0.645750	+	0.645750i
$245$	65704.6	+	65704.6i	1.09462	+	1.09462i
$246$	19437.5	−	19437.5i	0.321197	−	0.321197i
$247$			81000.2i			1.32768i
$248$	−19484.4			−0.316799
$249$		−	52750.4i		−	0.850800i
$250$			42464.8i			0.679437i
$251$	57975.7	−	57975.7i	0.920235	−	0.920235i	−0.0768107	−	0.997046i	$-0.524474\pi$
$251$	57975.7	−	57975.7i	0.920235	−	0.920235i	0.997046	+	0.0768107i	$0.0244737\pi$
$252$			39472.8i			0.621580i
$253$	−23736.8	+	23736.8i	−0.370835	+	0.370835i
$254$	−1721.23	+	1721.23i	−0.0266792	+	0.0266792i
$255$	31415.0			0.483122
$256$	4096.00			0.0625000
$257$	−47329.8	−	47329.8i	−0.716586	−	0.716586i	0.251318	−	0.967904i	$-0.419136\pi$
$257$	−47329.8	−	47329.8i	−0.716586	−	0.716586i	−0.967904	+	0.251318i	$0.919136\pi$
$258$		−	40397.7i		−	0.606900i
$259$	85971.5	−	95932.1i	1.28161	−	1.43009i
$260$	−25573.4			−0.378305
$261$	−3105.79	+	3105.79i	−0.0455923	+	0.0455923i
$262$			37059.4i			0.539878i
$263$			75854.7i			1.09666i	0.836263	+	0.548329i	$0.184736\pi$
$263$			75854.7i			1.09666i	−0.836263	+	0.548329i	$0.815264\pi$
$264$	−8953.13	−	8953.13i	−0.128460	−	0.128460i
$265$	−1884.15	−	1884.15i	−0.0268302	−	0.0268302i
$266$	−97106.2			−1.37241
$267$	19560.2	+	19560.2i	0.274378	+	0.274378i
$268$	21023.0			0.292701
$269$	92814.4			1.28266			0.641329	−	0.767266i	$-0.278384\pi$
$269$	92814.4			1.28266			0.641329	+	0.767266i	$0.278384\pi$
$270$		−	29044.6i		−	0.398417i
$271$	3154.18			0.0429485			0.0214743	−	0.999769i	$-0.493164\pi$
$271$	3154.18			0.0429485			0.0214743	+	0.999769i	$0.493164\pi$
$272$	18473.8	+	18473.8i	0.249700	+	0.249700i
$273$	−78944.0	+	78944.0i	−1.05924	+	1.05924i
$274$	25481.4	−	25481.4i	0.339409	−	0.339409i
$275$	43729.5			0.578241
$276$	9693.15	+	9693.15i	0.127247	+	0.127247i
$277$	64846.9	−	64846.9i	0.845142	−	0.845142i	−0.144380	−	0.989522i	$-0.546119\pi$
$277$	64846.9	−	64846.9i	0.845142	−	0.845142i	0.989522	+	0.144380i	$0.0461188\pi$
$278$	5123.81	+	5123.81i	0.0662984	+	0.0662984i
$279$	−31928.1	+	31928.1i	−0.410170	+	0.410170i
$280$		−	30658.4i		−	0.391050i
$281$	65861.6	+	65861.6i	0.834103	+	0.834103i	0.988075	−	0.153972i	$-0.0492066\pi$
$281$	65861.6	+	65861.6i	0.834103	+	0.834103i	−0.153972	+	0.988075i	$0.549207\pi$
$282$	26887.6	+	26887.6i	0.338107	+	0.338107i
$283$	19240.4	−	19240.4i	0.240238	−	0.240238i	−0.576711	−	0.816948i	$-0.695664\pi$
$283$	19240.4	−	19240.4i	0.240238	−	0.240238i	0.816948	+	0.576711i	$0.195664\pi$
$284$		−	45810.0i		−	0.567968i
$285$	28078.5			0.345688
$286$			65743.5i			0.803750i
$287$		−	171112.i		−	2.07738i
$288$	6711.90	−	6711.90i	0.0809208	−	0.0809208i
$289$			83120.7i			0.995207i
$290$	2412.26	−	2412.26i	0.0286832	−	0.0286832i
$291$	−5054.23	+	5054.23i	−0.0596855	+	0.0596855i
$292$	−62990.0			−0.738764
$293$	−79617.5			−0.927413			−0.463706	−	0.885989i	$-0.653481\pi$
$293$	−79617.5			−0.927413			−0.463706	+	0.885989i	$0.653481\pi$
$294$	−68977.0	−	68977.0i	−0.798012	−	0.798012i
$295$		−	40469.9i		−	0.465038i
$296$	−30930.6	+	1693.69i	−0.353025	+	0.0193308i
$297$	−74667.3			−0.846481
$298$	33026.8	−	33026.8i	0.371907	−	0.371907i
$299$		−	71177.5i		−	0.796160i
$300$		−	17857.4i		−	0.198415i
$301$	−177814.	−	177814.i	−1.96260	−	1.96260i
$302$	7188.48	+	7188.48i	0.0788176	+	0.0788176i
$303$	−98474.7			−1.07260
$304$	16511.8	+	16511.8i	0.178668	+	0.178668i
$305$	−97861.2			−1.05199
$306$	60544.1			0.646590
$307$		−	65571.3i		−	0.695725i	−0.937546	−	0.347862i	$-0.886908\pi$
$307$		−	65571.3i		−	0.695725i	0.937546	−	0.347862i	$-0.113092\pi$
$308$	−78815.8			−0.830830
$309$	−3545.86	−	3545.86i	−0.0371369	−	0.0371369i
$310$	24798.4	−	24798.4i	0.258048	−	0.258048i
$311$	48552.1	−	48552.1i	0.501981	−	0.501981i	−0.410072	−	0.912053i	$-0.634497\pi$
$311$	48552.1	−	48552.1i	0.501981	−	0.501981i	0.912053	+	0.410072i	$0.134497\pi$
$312$	26847.0			0.275796
$313$	16168.1	+	16168.1i	0.165033	+	0.165033i	0.784792	−	0.619759i	$-0.212770\pi$
$313$	16168.1	+	16168.1i	0.165033	+	0.165033i	−0.619759	+	0.784792i	$0.712770\pi$
$314$	−2616.60	+	2616.60i	−0.0265386	+	0.0265386i
$315$	−50238.2	−	50238.2i	−0.506306	−	0.506306i
$316$	25718.5	−	25718.5i	0.257556	−	0.257556i
$317$			93230.4i			0.927767i	0.885896	+	0.463884i	$0.153544\pi$
$317$			93230.4i			0.927767i	−0.885896	+	0.463884i	$0.846456\pi$
$318$	1977.99	+	1977.99i	0.0195601	+	0.0195601i
$319$	−6201.38	−	6201.38i	−0.0609406	−	0.0609406i
$320$	−5213.10	+	5213.10i	−0.0509092	+	0.0509092i
$321$		−	8353.07i		−	0.0810655i
$322$	85330.3			0.822985
$323$			148943.i			1.42763i
$324$		−	3487.82i		−	0.0332249i
$325$	−65564.0	+	65564.0i	−0.620725	+	0.620725i
$326$		−	79425.1i		−	0.747347i
$327$	56496.2	−	56496.2i	0.528353	−	0.528353i
$328$	−29095.6	+	29095.6i	−0.270445	+	0.270445i
$329$	236696.			2.18675
$330$	22789.8			0.209273
$331$	−16551.9	−	16551.9i	−0.151075	−	0.151075i	0.627523	−	0.778598i	$-0.284069\pi$
$331$	−16551.9	−	16551.9i	−0.151075	−	0.151075i	−0.778598	+	0.627523i	$0.784069\pi$
$332$			78960.8i			0.716367i
$333$	−47909.0	+	53459.7i	−0.432044	+	0.482101i
$334$	65682.6			0.588786
$335$	−26756.5	+	26756.5i	−0.238419	+	0.238419i
$336$			32185.3i			0.285088i
$337$			154951.i			1.36437i	0.731177	+	0.682187i	$0.238971\pi$
$337$			154951.i			1.36437i	−0.731177	+	0.682187i	$0.761029\pi$
$338$	−41447.9	−	41447.9i	−0.362802	−	0.362802i
$339$	25037.6	+	25037.6i	0.217868	+	0.217868i
$340$	−47024.4			−0.406785
$341$	−63751.1	−	63751.1i	−0.548251	−	0.548251i
$342$	54114.0			0.462655
$343$	−381290.			−3.24091
$344$			60470.3i			0.511005i
$345$	−24673.5			−0.207297
$346$	−2761.75	−	2761.75i	−0.0230692	−	0.0230692i
$347$	78775.8	−	78775.8i	0.654235	−	0.654235i	−0.299775	−	0.954010i	$-0.596912\pi$
$347$	78775.8	−	78775.8i	0.654235	−	0.654235i	0.954010	+	0.299775i	$0.0969116\pi$
$348$	−2532.40	+	2532.40i	−0.0209109	+	0.0209109i
$349$	−85580.9			−0.702629			−0.351314	−	0.936258i	$-0.614265\pi$
$349$	−85580.9			−0.702629			−0.351314	+	0.936258i	$0.614265\pi$
$350$	−78600.7	−	78600.7i	−0.641638	−	0.641638i
$351$	111949.	−	111949.i	0.908673	−	0.908673i
$352$	13401.7	+	13401.7i	0.108162	+	0.108162i
$353$	142011.	−	142011.i	1.13965	−	1.13965i	0.151136	−	0.988513i	$-0.451707\pi$
$353$	142011.	−	142011.i	1.13965	−	1.13965i	0.988513	−	0.151136i	$-0.0482933\pi$
$354$			42485.5i			0.339027i
$355$	58303.8	+	58303.8i	0.462637	+	0.462637i
$356$	−29279.1	−	29279.1i	−0.231025	−	0.231025i
$357$	−145162.	+	145162.i	−1.13898	+	1.13898i
$358$		−	44330.2i		−	0.345886i
$359$	8356.70			0.0648404			0.0324202	−	0.999474i	$-0.489679\pi$
$359$	8356.70			0.0648404			0.0324202	+	0.999474i	$0.489679\pi$
$360$			17084.9i			0.131828i
$361$			2803.52i			0.0215124i
$362$	−35622.1	+	35622.1i	−0.271833	+	0.271833i
$363$			19660.7i			0.149206i
$364$	118169.	−	118169.i	0.891872	−	0.891872i
$365$	80169.2	−	80169.2i	0.601758	−	0.601758i
$366$	102735.			0.766931
$367$	18123.6			0.134559			0.0672795	−	0.997734i	$-0.478568\pi$
$367$	18123.6			0.134559			0.0672795	+	0.997734i	$0.478568\pi$
$368$	−14509.4	−	14509.4i	−0.107141	−	0.107141i
$369$			95354.8i			0.700309i
$370$	37210.7	−	41521.9i	0.271809	−	0.303301i
$371$	17412.6			0.126507
$372$	−26033.4	+	26033.4i	−0.188125	+	0.188125i
$373$			54554.8i			0.392117i	0.980592	+	0.196058i	$0.0628142\pi$
$373$			54554.8i			0.392117i	−0.980592	+	0.196058i	$0.937186\pi$
$374$			120889.i			0.864260i
$375$	56737.9	+	56737.9i	0.403470	+	0.403470i
$376$	−40247.4	−	40247.4i	−0.284683	−	0.284683i
$377$	18595.6			0.130836
$378$	134209.	+	134209.i	0.939288	+	0.939288i
$379$	−217488.			−1.51411			−0.757053	−	0.653354i	$-0.773361\pi$
$379$	−217488.			−1.51411			−0.757053	+	0.653354i	$0.773361\pi$
$380$	−42030.1			−0.291067
$381$			4599.54i			0.0316858i
$382$	56683.5			0.388446
$383$	114457.	+	114457.i	0.780269	+	0.780269i	0.979876	−	0.199607i	$-0.0639666\pi$
$383$	114457.	+	114457.i	0.780269	+	0.780269i	−0.199607	+	0.979876i	$0.563967\pi$
$384$	5472.73	−	5472.73i	0.0371143	−	0.0371143i
$385$	100311.	−	100311.i	0.676750	−	0.676750i
$386$	127319.			0.854511
$387$	99089.4	+	99089.4i	0.661615	+	0.661615i
$388$	7565.56	−	7565.56i	0.0502548	−	0.0502548i
$389$	−129419.	−	129419.i	−0.855260	−	0.855260i	0.135515	−	0.990775i	$-0.456731\pi$
$389$	−129419.	−	129419.i	−0.855260	−	0.855260i	−0.990775	+	0.135515i	$0.956731\pi$
$390$	−34169.0	+	34169.0i	−0.224648	+	0.224648i
$391$		−	130881.i		−	0.856099i
$392$	103250.	+	103250.i	0.671920	+	0.671920i
$393$	49515.6	+	49515.6i	0.320595	+	0.320595i
$394$	−77270.2	+	77270.2i	−0.497760	+	0.497760i
$395$			65465.4i			0.419583i
$396$	43921.4			0.280082
$397$		−	89391.0i		−	0.567170i	−0.958947	−	0.283585i	$-0.908476\pi$
$397$		−	89391.0i		−	0.567170i	0.958947	−	0.283585i	$-0.0915237\pi$
$398$		−	168409.i		−	1.06316i
$399$	−129745.	+	129745.i	−0.814977	+	0.814977i
$400$			26730.3i			0.167064i
$401$	−11590.6	+	11590.6i	−0.0720807	+	0.0720807i	−0.742228	−	0.670147i	$-0.766231\pi$
$401$	−11590.6	+	11590.6i	−0.0720807	+	0.0720807i	0.670147	+	0.742228i	$0.266231\pi$
$402$	28089.1	−	28089.1i	0.173814	−	0.173814i
$403$	191165.			1.17706
$404$	147404.			0.903125
$405$	4439.05	+	4439.05i	0.0270633	+	0.0270633i
$406$			22293.1i			0.135244i
$407$	−106744.	−	95660.4i	−0.644396	−	0.577489i
$408$	49366.4			0.296559
$409$	−158731.	+	158731.i	−0.948890	+	0.948890i	−0.998756	−	0.0498664i	$-0.984120\pi$
$409$	−158731.	+	158731.i	−0.948890	+	0.948890i	0.0498664	+	0.998756i	$0.484120\pi$
$410$		−	74061.6i		−	0.440581i
$411$		−	68092.3i		−	0.403102i
$412$	5307.72	+	5307.72i	0.0312690	+	0.0312690i
$413$	187003.	+	187003.i	1.09635	+	1.09635i
$414$	−47551.7			−0.277438
$415$	−100496.	−	100496.i	−0.583514	−	0.583514i
$416$	−40186.7			−0.232218
$417$	13692.0			0.0787399
$418$			108050.i			0.618404i
$419$	−53640.6			−0.305538			−0.152769	−	0.988262i	$-0.548819\pi$
$419$	−53640.6			−0.305538			−0.152769	+	0.988262i	$0.548819\pi$
$420$	−40963.1	−	40963.1i	−0.232217	−	0.232217i
$421$	−113029.	+	113029.i	−0.637716	+	0.637716i	−0.949992	−	0.312276i	$-0.898909\pi$
$421$	−113029.	+	113029.i	−0.637716	+	0.637716i	0.312276	+	0.949992i	$0.398909\pi$
$422$	−7688.63	+	7688.63i	−0.0431742	+	0.0431742i
$423$	−131903.			−0.737178
$424$	−2960.81	−	2960.81i	−0.0164694	−	0.0164694i
$425$	−120559.	+	120559.i	−0.667456	+	0.667456i
$426$	−61207.6	−	61207.6i	−0.337276	−	0.337276i
$427$	452196.	−	452196.i	2.48011	−	2.48011i
$428$			12503.5i			0.0682565i
$429$	87841.0	+	87841.0i	0.477290	+	0.477290i
$430$	−76962.3	−	76962.3i	−0.416237	−	0.416237i
$431$	208728.	−	208728.i	1.12364	−	1.12364i	0.132448	−	0.991190i	$-0.457716\pi$
$431$	208728.	−	208728.i	1.12364	−	1.12364i	0.991190	−	0.132448i	$-0.0422839\pi$
$432$		−	45641.5i		−	0.244564i
$433$	−75452.6			−0.402437			−0.201219	−	0.979546i	$-0.564490\pi$
$433$	−75452.6			−0.402437			−0.201219	+	0.979546i	$0.564490\pi$
$434$			229176.i			1.21672i
$435$		−	6446.11i		−	0.0340658i
$436$	−84567.9	+	84567.9i	−0.444869	+	0.444869i
$437$		−	116981.i		−	0.612565i
$438$	−84162.0	+	84162.0i	−0.438700	+	0.438700i
$439$	−246708.	+	246708.i	−1.28013	+	1.28013i	−0.339535	+	0.940593i	$0.610270\pi$
$439$	−246708.	+	246708.i	−1.28013	+	1.28013i	−0.940593	+	0.339535i	$0.889730\pi$
$440$	−34113.5			−0.176206
$441$	338380.			1.73992
$442$	−181250.	−	181250.i	−0.927758	−	0.927758i
$443$			68941.1i			0.351294i	0.984453	+	0.175647i	$0.0562017\pi$
$443$			68941.1i			0.351294i	−0.984453	+	0.175647i	$0.943798\pi$
$444$	−39063.9	+	43589.8i	−0.198157	+	0.221116i
$445$	74528.8			0.376361
$446$	122812.	−	122812.i	0.617406	−	0.617406i
$447$		−	88255.4i		−	0.441699i
$448$		−	48177.3i		−	0.240042i
$449$	143056.	+	143056.i	0.709600	+	0.709600i	0.966451	−	0.256851i	$-0.0826849\pi$
$449$	143056.	+	143056.i	0.709600	+	0.709600i	−0.256851	+	0.966451i	$0.582685\pi$
$450$	43801.5	+	43801.5i	0.216304	+	0.216304i
$451$	−190396.			−0.936062
$452$	−37478.1	−	37478.1i	−0.183443	−	0.183443i
$453$	19209.3			0.0936085
$454$	−108933.			−0.528504
$455$			300795.i			1.45294i
$456$	44123.3			0.212197
$457$	133820.	+	133820.i	0.640752	+	0.640752i	0.950740	−	0.309988i	$-0.100325\pi$
$457$	133820.	+	133820.i	0.640752	+	0.640752i	−0.309988	+	0.950740i	$0.600325\pi$
$458$	−131877.	+	131877.i	−0.628691	+	0.628691i
$459$	205853.	−	205853.i	0.977082	−	0.977082i
$460$	36933.2			0.174542
$461$	40084.3	+	40084.3i	0.188613	+	0.188613i	0.795096	−	0.606483i	$-0.207420\pi$
$461$	40084.3	+	40084.3i	0.188613	+	0.188613i	−0.606483	+	0.795096i	$0.707420\pi$
$462$	−105307.	+	105307.i	−0.493371	+	0.493371i
$463$	−230400.	−	230400.i	−1.07478	−	1.07478i	−0.996968	−	0.0778161i	$-0.975205\pi$
$463$	−230400.	−	230400.i	−1.07478	−	1.07478i	−0.0778161	−	0.996968i	$-0.524795\pi$
$464$	3790.68	−	3790.68i	0.0176068	−	0.0176068i
$465$		−	66267.0i		−	0.306473i
$466$	−112379.	−	112379.i	−0.517504	−	0.517504i
$467$	106600.	+	106600.i	0.488790	+	0.488790i	0.907924	−	0.419134i	$-0.137666\pi$
$467$	106600.	+	106600.i	0.488790	+	0.488790i	−0.419134	+	0.907924i	$0.637666\pi$
$468$	−65851.8	+	65851.8i	−0.300660	+	0.300660i
$469$		−	247273.i		−	1.12417i
$470$	102448.			0.463776
$471$			6992.16i			0.0315188i
$472$		−	63595.5i		−	0.285458i
$473$	−197853.	+	197853.i	−0.884342	+	0.884342i
$474$		−	68725.8i		−	0.305889i
$475$	−107755.	+	107755.i	−0.477584	+	0.477584i
$476$	217290.	−	217290.i	0.959016	−	0.959016i
$477$	−9703.43			−0.0426470
$478$	317724.			1.39057
$479$	−142463.	−	142463.i	−0.620913	−	0.620913i	0.324852	−	0.945765i	$-0.394685\pi$
$479$	−142463.	−	142463.i	−0.620913	−	0.620913i	−0.945765	+	0.324852i	$0.894685\pi$
$480$			13930.6i			0.0604627i
$481$	303466.	−	16617.1i	1.31166	−	0.0718232i
$482$	−84076.4			−0.361893
$483$	114011.	−	114011.i	0.488713	−	0.488713i
$484$		−	29429.7i		−	0.125630i
$485$			19257.8i			0.0818697i
$486$	−120190.	−	120190.i	−0.508857	−	0.508857i
$487$	22476.6	+	22476.6i	0.0947706	+	0.0947706i	0.752903	−	0.658132i	$-0.228653\pi$
$487$	22476.6	+	22476.6i	0.0947706	+	0.0947706i	−0.658132	+	0.752903i	$0.728653\pi$
$488$	−153782.			−0.645750
$489$	−106121.	−	106121.i	−0.443797	−	0.443797i
$490$	−262819.			−1.09462
$491$	−132795.			−0.550831			−0.275416	−	0.961325i	$-0.588815\pi$
$491$	−132795.			−0.550831			−0.275416	+	0.961325i	$0.588815\pi$
$492$			77750.2i			0.321197i
$493$	34193.6			0.140686
$494$	−162000.	−	162000.i	−0.663838	−	0.663838i
$495$	−55900.0	+	55900.0i	−0.228140	+	0.228140i
$496$	38968.8	−	38968.8i	0.158399	−	0.158399i
$497$	−538820.			−2.18138
$498$	105501.	+	105501.i	0.425400	+	0.425400i
$499$	206696.	−	206696.i	0.830101	−	0.830101i	−0.157430	−	0.987530i	$-0.550321\pi$
$499$	206696.	−	206696.i	0.830101	−	0.830101i	0.987530	+	0.157430i	$0.0503207\pi$
$500$	−84929.6	−	84929.6i	−0.339718	−	0.339718i
$501$	87759.6	−	87759.6i	0.349638	−	0.349638i
$502$			231903.i			0.920235i
$503$	−119635.	−	119635.i	−0.472849	−	0.472849i	0.429987	−	0.902835i	$-0.358518\pi$
$503$	−119635.	−	119635.i	−0.472849	−	0.472849i	−0.902835	+	0.429987i	$0.858518\pi$
$504$	−78945.6	−	78945.6i	−0.310790	−	0.310790i
$505$	−187606.	+	187606.i	−0.735637	+	0.735637i
$506$		−	94947.0i		−	0.370835i
$507$	−110759.			−0.430885
$508$		−	6884.94i		−	0.0266792i
$509$		−	78749.6i		−	0.303957i	−0.988384	−	0.151979i	$-0.951435\pi$
$509$		−	78749.6i		−	0.303957i	0.988384	−	0.151979i	$-0.0485645\pi$
$510$	−62830.0	+	62830.0i	−0.241561	+	0.241561i
$511$			740891.i			2.83735i
$512$	−8192.00	+	8192.00i	−0.0312500	+	0.0312500i
$513$	183990.	−	183990.i	0.699131	−	0.699131i
$514$	189319.			0.716586
$515$	−13510.6			−0.0509401
$516$	80795.3	+	80795.3i	0.303450	+	0.303450i
$517$		−	263371.i		−	0.985343i
$518$	19921.2	+	363807.i	0.0742431	+	1.35585i
$519$	−7380.05			−0.0273984
$520$	51146.8	−	51146.8i	0.189152	−	0.189152i
$521$		−	283986.i		−	1.04622i	−0.852266	−	0.523109i	$-0.824772\pi$
$521$		−	283986.i		−	1.04622i	0.852266	−	0.523109i	$-0.175228\pi$
$522$		−	12423.2i		−	0.0455923i
$523$	173621.	+	173621.i	0.634746	+	0.634746i	0.949255	−	0.314508i	$-0.101840\pi$
$523$	173621.	+	173621.i	0.634746	+	0.634746i	−0.314508	+	0.949255i	$0.601840\pi$
$524$	−74118.7	−	74118.7i	−0.269939	−	0.269939i
$525$	−210039.			−0.762047
$526$	−151709.	−	151709.i	−0.548329	−	0.548329i
$527$	351515.			1.26568
$528$	35812.5			0.128460
$529$		−	177046.i		−	0.632667i
$530$	7536.61			0.0268302
$531$	−104210.	−	104210.i	−0.369592	−	0.369592i
$532$	194212.	−	194212.i	0.686204	−	0.686204i
$533$	285463.	−	285463.i	1.00484	−	1.00484i
$534$	−78240.6			−0.274378
$535$	−15913.6	−	15913.6i	−0.0555981	−	0.0555981i
$536$	−42045.9	+	42045.9i	−0.146350	+	0.146350i
$537$	−59230.3	−	59230.3i	−0.205398	−	0.205398i
$538$	−185629.	+	185629.i	−0.641329	+	0.641329i
$539$			675648.i			2.32564i
$540$	58089.2	+	58089.2i	0.199209	+	0.199209i
$541$	207308.	+	207308.i	0.708308	+	0.708308i	0.966179	−	0.257871i	$-0.0830210\pi$
$541$	207308.	+	207308.i	0.708308	+	0.708308i	−0.257871	+	0.966179i	$0.583021\pi$
$542$	−6308.37	+	6308.37i	−0.0214743	+	0.0214743i
$543$			95190.7i			0.322845i
$544$	−73895.3			−0.249700
$545$		−	215264.i		−	0.724734i
$546$		−	315776.i		−	1.05924i
$547$	150439.	−	150439.i	0.502790	−	0.502790i	−0.409514	−	0.912304i	$-0.634302\pi$
$547$	150439.	−	150439.i	0.502790	−	0.502790i	0.912304	+	0.409514i	$0.134302\pi$
$548$			101926.i			0.339409i
$549$	−251994.	+	251994.i	−0.836074	+	0.836074i
$550$	−87458.9	+	87458.9i	−0.289120	+	0.289120i
$551$	30562.0			0.100665
$552$	−38772.6			−0.127247
$553$	−302502.	−	302502.i	−0.989187	−	0.989187i
$554$			259388.i			0.845142i
$555$	−5760.27	−	105196.i	−0.0187007	−	0.341517i
$556$	−20495.2			−0.0662984
$557$	−38740.6	+	38740.6i	−0.124869	+	0.124869i	−0.766780	−	0.641910i	$-0.778142\pi$
$557$	−38740.6	+	38740.6i	−0.124869	+	0.124869i	0.641910	+	0.766780i	$0.278142\pi$
$558$		−	127712.i		−	0.410170i
$559$		−	593286.i		−	1.89863i
$560$	61316.7	+	61316.7i	0.195525	+	0.195525i
$561$	161522.	+	161522.i	0.513223	+	0.513223i
$562$	−263446.			−0.834103
$563$	124572.	+	124572.i	0.393011	+	0.393011i	0.875759	−	0.482748i	$-0.160361\pi$
$563$	124572.	+	124572.i	0.393011	+	0.393011i	−0.482748	+	0.875759i	$0.660361\pi$
$564$	−107550.			−0.338107
$565$	95399.0			0.298845
$566$			76961.6i			0.240238i
$567$	−41023.9			−0.127606
$568$	91620.1	+	91620.1i	0.283984	+	0.283984i
$569$	101858.	−	101858.i	0.314609	−	0.314609i	−0.532083	−	0.846692i	$-0.678591\pi$
$569$	101858.	−	101858.i	0.314609	−	0.314609i	0.846692	+	0.532083i	$0.178591\pi$
$570$	−56157.1	+	56157.1i	−0.172844	+	0.172844i
$571$	−110278.			−0.338234			−0.169117	−	0.985596i	$-0.554092\pi$
$571$	−110278.			−0.338234			−0.169117	+	0.985596i	$0.554092\pi$
$572$	−131487.	−	131487.i	−0.401875	−	0.401875i
$573$	75735.8	−	75735.8i	0.230670	−	0.230670i
$574$	342224.	+	342224.i	1.03869	+	1.03869i
$575$	94687.8	−	94687.8i	0.286390	−	0.286390i
$576$			26847.6i			0.0809208i
$577$	196203.	+	196203.i	0.589324	+	0.589324i	0.937448	−	0.348124i	$-0.113181\pi$
$577$	196203.	+	196203.i	0.589324	+	0.589324i	−0.348124	+	0.937448i	$0.613181\pi$
$578$	−166241.	−	166241.i	−0.497603	−	0.497603i
$579$	170113.	−	170113.i	0.507434	−	0.507434i
$580$			9649.02i			0.0286832i
$581$	928741.			2.75133
$582$		−	20216.9i		−	0.0596855i
$583$		−	19375.0i		−	0.0570038i
$584$	125980.	−	125980.i	0.369382	−	0.369382i
$585$		−	167623.i		−	0.489803i
$586$	159235.	−	159235.i	0.463706	−	0.463706i
$587$	−189138.	+	189138.i	−0.548913	+	0.548913i	−0.926126	−	0.377213i	$-0.876882\pi$
$587$	−189138.	+	189138.i	−0.548913	+	0.548913i	0.377213	+	0.926126i	$0.376882\pi$
$588$	275908.			0.798012
$589$	314182.			0.905630
$590$	80939.8	+	80939.8i	0.232519	+	0.232519i
$591$			206484.i			0.591169i
$592$	58473.8	−	65248.6i	0.166847	−	0.186178i
$593$	−477286.			−1.35728			−0.678640	−	0.734471i	$-0.737430\pi$
$593$	−477286.			−1.35728			−0.678640	+	0.734471i	$0.737430\pi$
$594$	149335.	−	149335.i	0.423241	−	0.423241i
$595$			553103.i			1.56233i
$596$			132107.i			0.371907i
$597$	−225014.	−	225014.i	−0.631336	−	0.631336i
$598$	142355.	+	142355.i	0.398080	+	0.398080i
$599$	−693204.			−1.93200			−0.966000	−	0.258540i	$-0.916758\pi$
$599$	−693204.			−1.93200			−0.966000	+	0.258540i	$0.916758\pi$
$600$	35714.8	+	35714.8i	0.0992077	+	0.0992077i
$601$	−450318.			−1.24672			−0.623362	−	0.781933i	$-0.714234\pi$
$601$	−450318.			−1.24672			−0.623362	+	0.781933i	$0.714234\pi$
$602$	711254.			1.96260
$603$			137797.i			0.378970i
$604$	−28753.9			−0.0788176
$605$	37456.0	+	37456.0i	0.102332	+	0.102332i
$606$	196949.	−	196949.i	0.536302	−	0.536302i
$607$	−80454.7	+	80454.7i	−0.218360	+	0.218360i	−0.807807	−	0.589447i	$-0.799346\pi$
$607$	−80454.7	+	80454.7i	−0.218360	+	0.218360i	0.589447	+	0.807807i	$0.299346\pi$
$608$	−66047.1			−0.178668
$609$	29786.2	+	29786.2i	0.0803119	+	0.0803119i
$610$	195722.	−	195722.i	0.525994	−	0.525994i
$611$	394875.	+	394875.i	1.05774	+	1.05774i
$612$	−121088.	+	121088.i	−0.323295	+	0.323295i
$613$			427684.i			1.13816i	0.822283	+	0.569078i	$0.192700\pi$
$613$			427684.i			1.13816i	−0.822283	+	0.569078i	$0.807300\pi$
$614$	131143.	+	131143.i	0.347862	+	0.347862i
$615$	−98955.0	−	98955.0i	−0.261630	−	0.261630i
$616$	157632.	−	157632.i	0.415415	−	0.415415i
$617$			423563.i			1.11262i	0.830974	+	0.556311i	$0.187784\pi$
$617$			423563.i			1.11262i	−0.830974	+	0.556311i	$0.812216\pi$
$618$	14183.5			0.0371369
$619$			704207.i			1.83789i	0.394389	+	0.918944i	$0.370956\pi$
$619$			704207.i			1.83789i	−0.394389	+	0.918944i	$0.629044\pi$
$620$			99193.5i			0.258048i
$621$	−161678.	+	161678.i	−0.419244	+	0.419244i
$622$			194208.i			0.501981i
$623$	−344382.	+	344382.i	−0.887288	+	0.887288i
$624$	−53694.1	+	53694.1i	−0.137898	+	0.137898i
$625$	−44853.1			−0.114824
$626$	−64672.5			−0.165033
$627$	144367.	+	144367.i	0.367226	+	0.367226i
$628$		−	10466.4i		−	0.0265386i
$629$	558014.	−	30555.5i	1.41041	−	0.0772304i
$630$	200953.			0.506306
$631$	187320.	−	187320.i	0.470462	−	0.470462i	−0.431602	−	0.902064i	$-0.642051\pi$
$631$	187320.	−	187320.i	0.470462	−	0.470462i	0.902064	+	0.431602i	$0.142051\pi$
$632$			102874.i			0.257556i
$633$			20545.8i			0.0512762i
$634$	−186461.	−	186461.i	−0.463884	−	0.463884i
$635$	8762.66	+	8762.66i	0.0217315	+	0.0217315i
$636$	−7911.96			−0.0195601
$637$	−1.01301e6	−	1.01301e6i	−2.49651	−	2.49651i
$638$	24805.5			0.0609406
$639$	300266.			0.735367
$640$		−	20852.4i		−	0.0509092i
$641$	−709193.			−1.72603			−0.863015	−	0.505178i	$-0.831427\pi$
$641$	−709193.			−1.72603			−0.863015	+	0.505178i	$0.831427\pi$
$642$	16706.1	+	16706.1i	0.0405327	+	0.0405327i
$643$	217277.	−	217277.i	0.525522	−	0.525522i	−0.393712	−	0.919234i	$-0.628809\pi$
$643$	217277.	−	217277.i	0.525522	−	0.525522i	0.919234	+	0.393712i	$0.128809\pi$
$644$	−170661.	+	170661.i	−0.411492	+	0.411492i
$645$	−205661.			−0.494348
$646$	−297887.	−	297887.i	−0.713815	−	0.713815i
$647$	110695.	−	110695.i	0.264435	−	0.264435i	−0.562418	−	0.826853i	$-0.690129\pi$
$647$	110695.	−	110695.i	0.264435	−	0.264435i	0.826853	+	0.562418i	$0.190129\pi$
$648$	6975.64	+	6975.64i	0.0166125	+	0.0166125i
$649$	208078.	−	208078.i	0.494012	−	0.494012i
$650$		−	262256.i		−	0.620725i
$651$	306206.	+	306206.i	0.722524	+	0.722524i
$652$	158850.	+	158850.i	0.373674	+	0.373674i
$653$	−239393.	+	239393.i	−0.561417	+	0.561417i	−0.929710	−	0.368292i	$-0.879943\pi$
$653$	−239393.	+	239393.i	−0.561417	+	0.561417i	0.368292	+	0.929710i	$0.379943\pi$
$654$			225985.i			0.528353i
$655$	188666.			0.439756
$656$		−	116382.i		−	0.270445i
$657$		−	412873.i		−	0.956502i
$658$	−473392.	+	473392.i	−1.09337	+	1.09337i
$659$		−	597265.i		−	1.37530i	−0.726044	−	0.687648i	$-0.758643\pi$
$659$		−	597265.i		−	1.37530i	0.726044	−	0.687648i	$-0.241357\pi$
$660$	−45579.7	+	45579.7i	−0.104636	+	0.104636i
$661$	−38924.4	+	38924.4i	−0.0890881	+	0.0890881i	−0.750246	−	0.661158i	$-0.770065\pi$
$661$	−38924.4	+	38924.4i	−0.0890881	+	0.0890881i	0.661158	+	0.750246i	$0.270065\pi$
$662$	66207.6			0.151075
$663$	−484343.			−1.10186
$664$	−157922.	−	157922.i	−0.358183	−	0.358183i
$665$			494359.i			1.11789i
$666$	−11101.4	−	202737.i	−0.0250282	−	0.457073i
$667$	−26855.8			−0.0603652
$668$	−131365.	+	131365.i	−0.294393	+	0.294393i
$669$		−	328182.i		−	0.733268i
$670$		−	107026.i		−	0.238419i
$671$	−503159.	−	503159.i	−1.11753	−	1.11753i
$672$	−64370.5	−	64370.5i	−0.142544	−	0.142544i
$673$	528423.			1.16668			0.583340	−	0.812228i	$-0.301745\pi$
$673$	528423.			1.16668			0.583340	+	0.812228i	$0.301745\pi$
$674$	−309901.	−	309901.i	−0.682187	−	0.682187i
$675$	297854.			0.653725
$676$	165792.			0.362802
$677$			504764.i			1.10131i	0.834732	+	0.550657i	$0.185623\pi$
$677$			504764.i			1.10131i	−0.834732	+	0.550657i	$0.814377\pi$
$678$	−100150.			−0.217868
$679$	−88986.4	−	88986.4i	−0.193012	−	0.193012i
$680$	94048.7	−	94048.7i	0.203393	−	0.203393i
$681$	−145547.	+	145547.i	−0.313841	+	0.313841i
$682$	255004.			0.548251
$683$	−360139.	−	360139.i	−0.772020	−	0.772020i	0.206440	−	0.978459i	$-0.433812\pi$
$683$	−360139.	−	360139.i	−0.772020	−	0.772020i	−0.978459	+	0.206440i	$0.933812\pi$
$684$	−108228.	+	108228.i	−0.231327	+	0.231327i
$685$	−129724.	−	129724.i	−0.276464	−	0.276464i
$686$	762580.	−	762580.i	1.62046	−	1.62046i
$687$			352406.i			0.746671i
$688$	−120941.	−	120941.i	−0.255502	−	0.255502i
$689$	29049.1	+	29049.1i	0.0611919	+	0.0611919i
$690$	49347.0	−	49347.0i	0.103648	−	0.103648i
$691$			850032.i			1.78024i	0.455723	+	0.890122i	$0.349381\pi$
$691$			850032.i			1.78024i	−0.455723	+	0.890122i	$0.650619\pi$
$692$	11047.0			0.0230692
$693$		−	516605.i		−	1.07570i
$694$			315103.i			0.654235i
$695$	26084.9	−	26084.9i	0.0540032	−	0.0540032i
$696$		−	10129.6i		−	0.0209109i
$697$	524909.	−	524909.i	1.08048	−	1.08048i
$698$	171162.	−	171162.i	0.351314	−	0.351314i
$699$	−300303.			−0.614618
$700$	314403.			0.641638
$701$	−67567.6	−	67567.6i	−0.137500	−	0.137500i	0.635007	−	0.772507i	$-0.280997\pi$
$701$	−67567.6	−	67567.6i	−0.137500	−	0.137500i	−0.772507	+	0.635007i	$0.780997\pi$
$702$			447798.i			0.908673i
$703$	498749.	−	27310.3i	1.00919	−	0.0552607i
$704$	−53606.9			−0.108162
$705$	136883.	−	136883.i	0.275404	−	0.275404i
$706$			568042.i			1.13965i
$707$		−	1.73378e6i		−	3.46860i
$708$	−84971.0	−	84971.0i	−0.169513	−	0.169513i
$709$	−223391.	−	223391.i	−0.444399	−	0.444399i	0.449089	−	0.893487i	$-0.351749\pi$
$709$	−223391.	−	223391.i	−0.444399	−	0.444399i	−0.893487	+	0.449089i	$0.851749\pi$
$710$	−233215.			−0.462637
$711$	168574.	+	168574.i	0.333466	+	0.333466i
$712$	117117.			0.231025
$713$	−276082.			−0.543074
$714$		−	580649.i		−	1.13898i
$715$	334695.			0.654692
$716$	88660.4	+	88660.4i	0.172943	+	0.172943i
$717$	424516.	−	424516.i	0.825764	−	0.825764i
$718$	−16713.4	+	16713.4i	−0.0324202	+	0.0324202i
$719$	−964220.			−1.86517			−0.932585	−	0.360950i	$-0.882452\pi$
$719$	−964220.			−1.86517			−0.932585	+	0.360950i	$0.882452\pi$
$720$	−34169.7	−	34169.7i	−0.0659138	−	0.0659138i
$721$	62429.6	−	62429.6i	0.120094	−	0.120094i
$722$	−5607.04	−	5607.04i	−0.0107562	−	0.0107562i
$723$	−112336.	+	112336.i	−0.214903	+	0.214903i
$724$		−	142489.i		−	0.271833i
$725$	24737.8	+	24737.8i	0.0470636	+	0.0470636i
$726$	−39321.5	−	39321.5i	−0.0746030	−	0.0746030i
$727$	−223895.	+	223895.i	−0.423620	+	0.423620i	−0.886448	−	0.462828i	$-0.846835\pi$
$727$	−223895.	+	223895.i	−0.423620	+	0.423620i	0.462828	+	0.886448i	$0.346835\pi$
$728$			472678.i			0.891872i
$729$	−285862.			−0.537899
$730$			320677.i			0.601758i
$731$		−	1.09093e6i		−	2.04157i
$732$	−205470.	+	205470.i	−0.383466	+	0.383466i
$733$			551842.i			1.02709i	0.858064	+	0.513543i	$0.171667\pi$
$733$			551842.i			1.02709i	−0.858064	+	0.513543i	$0.828333\pi$
$734$	−36247.2	+	36247.2i	−0.0672795	+	0.0672795i
$735$	−351156.	+	351156.i	−0.650018	+	0.650018i
$736$	58037.8			0.107141
$737$	−275140.			−0.506547
$738$	−190710.	−	190710.i	−0.350155	−	0.350155i
$739$		−	137775.i		−	0.252278i	−0.992013	−	0.126139i	$-0.959741\pi$
$739$		−	137775.i		−	0.252278i	0.992013	−	0.126139i	$-0.0402586\pi$
$740$	8622.41	+	157465.i	0.0157458	+	0.287555i
$741$	−432903.			−0.788414
$742$	−34825.1	+	34825.1i	−0.0632536	+	0.0632536i
$743$		−	352194.i		−	0.637977i	−0.947759	−	0.318988i	$-0.896657\pi$
$743$		−	352194.i		−	0.637977i	0.947759	−	0.318988i	$-0.103343\pi$
$744$		−	104134.i		−	0.188125i
$745$	−168137.	−	168137.i	−0.302936	−	0.302936i
$746$	−109110.	−	109110.i	−0.196058	−	0.196058i
$747$	−517555.			−0.927504
$748$	−241778.	−	241778.i	−0.432130	−	0.432130i
$749$	147067.			0.262151
$750$	−226952.			−0.403470
$751$			1.08959e6i			1.93190i	0.258737	+	0.965948i	$0.416694\pi$
$751$			1.08959e6i			1.93190i	−0.258737	+	0.965948i	$0.583306\pi$
$752$	160990.			0.284683
$753$	309849.	+	309849.i	0.546463	+	0.546463i
$754$	−37191.2	+	37191.2i	−0.0654180	+	0.0654180i
$755$	36596.0	−	36596.0i	0.0642006	−	0.0642006i
$756$	−536837.			−0.939288
$757$	103856.	+	103856.i	0.181233	+	0.181233i	0.791893	−	0.610660i	$-0.209096\pi$
$757$	103856.	+	103856.i	0.181233	+	0.181233i	−0.610660	+	0.791893i	$0.709096\pi$
$758$	434975.	−	434975.i	0.757053	−	0.757053i
$759$	−126860.	−	126860.i	−0.220213	−	0.220213i
$760$	84060.1	−	84060.1i	0.145533	−	0.145533i
$761$			357264.i			0.616908i	0.951239	+	0.308454i	$0.0998116\pi$
$761$			357264.i			0.616908i	−0.951239	+	0.308454i	$0.900188\pi$
$762$	−9199.08	−	9199.08i	−0.0158429	−	0.0158429i
$763$	994691.	+	994691.i	1.70859	+	1.70859i
$764$	−113367.	+	113367.i	−0.194223	+	0.194223i
$765$		−	308225.i		−	0.526678i
$766$	−457827.			−0.780269
$767$			623948.i			1.06061i
$768$			21890.9i			0.0371143i
$769$	305401.	−	305401.i	0.516438	−	0.516438i	−0.400054	−	0.916492i	$-0.631009\pi$
$769$	305401.	−	305401.i	0.516438	−	0.516438i	0.916492	+	0.400054i	$0.131009\pi$
$770$			401245.i			0.676750i
$771$	252952.	−	252952.i	0.425530	−	0.425530i
$772$	−254637.	+	254637.i	−0.427255	+	0.427255i
$773$	−199611.			−0.334060			−0.167030	−	0.985952i	$-0.553418\pi$
$773$	−199611.			−0.334060			−0.167030	+	0.985952i	$0.553418\pi$
$774$	−396358.			−0.661615
$775$	254308.	+	254308.i	0.423406	+	0.423406i
$776$			30262.2i			0.0502548i
$777$	512706.	+	459472.i	0.849231	+	0.761056i
$778$	517675.			0.855260
$779$	469160.	−	469160.i	0.773119	−	0.773119i
$780$		−	136676.i		−	0.224648i
$781$			599545.i			0.982923i
$782$	261763.	+	261763.i	0.428049	+	0.428049i
$783$	−42239.3	−	42239.3i	−0.0688959	−	0.0688959i
$784$	−413000.			−0.671920
$785$	13320.9	+	13320.9i	0.0216169	+	0.0216169i
$786$	−198063.			−0.320595
$787$	397114.			0.641158			0.320579	−	0.947222i	$-0.396122\pi$
$787$	397114.			0.641158			0.320579	+	0.947222i	$0.396122\pi$
$788$		−	309081.i		−	0.497760i
$789$	−405403.			−0.651228
$790$	−130931.	−	130931.i	−0.209791	−	0.209791i
$791$	−440819.	+	440819.i	−0.704543	+	0.704543i
$792$	−87842.7	+	87842.7i	−0.140041	+	0.140041i
$793$	1.50878e6			2.39928
$794$	178782.	+	178782.i	0.283585	+	0.283585i
$795$	10069.8	−	10069.8i	0.0159326	−	0.0159326i
$796$	336818.	+	336818.i	0.531580	+	0.531580i
$797$	−521684.	+	521684.i	−0.821280	+	0.821280i	−0.986292	−	0.165012i	$-0.947234\pi$
$797$	−521684.	+	521684.i	−0.821280	+	0.821280i	0.165012	+	0.986292i	$0.447234\pi$
$798$		−	518981.i		−	0.814977i
$799$	726097.	+	726097.i	1.13737	+	1.13737i
$800$	−53460.5	−	53460.5i	−0.0835321	−	0.0835321i
$801$	191913.	−	191913.i	0.299115	−	0.299115i
$802$		−	46362.6i		−	0.0720807i
$803$	824389.			1.27850
$804$			112356.i			0.173814i
$805$		−	434410.i		−	0.670359i
$806$	−382331.	+	382331.i	−0.588531	+	0.588531i
$807$			496043.i			0.761680i
$808$	−294809.	+	294809.i	−0.451562	+	0.451562i
$809$	609373.	−	609373.i	0.931078	−	0.931078i	−0.0666958	−	0.997773i	$-0.521246\pi$
$809$	609373.	−	609373.i	0.931078	−	0.931078i	0.997773	+	0.0666958i	$0.0212457\pi$
$810$	−17756.2			−0.0270633
$811$	390914.			0.594346			0.297173	−	0.954824i	$-0.403956\pi$
$811$	390914.			0.594346			0.297173	+	0.954824i	$0.403956\pi$
$812$	−44586.2	−	44586.2i	−0.0676220	−	0.0676220i
$813$			16857.4i			0.0255041i
$814$	404808.	−	22166.3i	0.610942	−	0.0334537i
$815$	−404346.			−0.608749
$816$	−98732.7	+	98732.7i	−0.148279	+	0.148279i
$817$		−	975070.i		−	1.46080i
$818$		−	634925.i		−	0.948890i
$819$	774552.	+	774552.i	1.15474	+	1.15474i
$820$	148123.	+	148123.i	0.220290	+	0.220290i
$821$	1.07295e6			1.59181			0.795906	−	0.605421i	$-0.206995\pi$
$821$	1.07295e6			1.59181			0.795906	+	0.605421i	$0.206995\pi$
$822$	136185.	+	136185.i	0.201551	+	0.201551i
$823$	−932897.			−1.37732			−0.688658	−	0.725086i	$-0.741800\pi$
$823$	−932897.			−1.37732			−0.688658	+	0.725086i	$0.741800\pi$
$824$	−21230.9			−0.0312690
$825$			233711.i			0.343376i
$826$	−748013.			−1.09635
$827$	610170.	+	610170.i	0.892153	+	0.892153i	0.994726	−	0.102572i	$-0.0327072\pi$
$827$	610170.	+	610170.i	0.892153	+	0.892153i	−0.102572	+	0.994726i	$0.532707\pi$
$828$	95103.4	−	95103.4i	0.138719	−	0.138719i
$829$	−576887.	+	576887.i	−0.839425	+	0.839425i	−0.988783	−	0.149359i	$-0.952279\pi$
$829$	−576887.	+	576887.i	−0.839425	+	0.839425i	0.149359	+	0.988783i	$0.452279\pi$
$830$	401983.			0.583514
$831$	346572.	+	346572.i	0.501870	+	0.501870i
$832$	80373.4	−	80373.4i	0.116109	−	0.116109i
$833$	−1.86272e6	−	1.86272e6i	−2.68446	−	2.68446i
$834$	−27384.0	+	27384.0i	−0.0393700	+	0.0393700i
$835$		−	334385.i		−	0.479594i
$836$	−216100.	−	216100.i	−0.309202	−	0.309202i
$837$	−434227.	−	434227.i	−0.619820	−	0.619820i
$838$	107281.	−	107281.i	0.152769	−	0.152769i
$839$		−	1.04170e6i		−	1.47985i	−0.672691	−	0.739924i	$-0.734861\pi$
$839$		−	1.04170e6i		−	1.47985i	0.672691	−	0.739924i	$-0.265139\pi$
$840$	163853.			0.232217
$841$			700265.i			0.990080i
$842$		−	452118.i		−	0.637716i
$843$	−351995.	+	351995.i	−0.495315	+	0.495315i
$844$		−	30754.5i		−	0.0431742i
$845$	−211008.	+	211008.i	−0.295519	+	0.295519i
$846$	263805.	−	263805.i	0.368589	−	0.368589i
$847$	−346153.			−0.482504
$848$	11843.2			0.0164694
$849$	102830.	+	102830.i	0.142660	+	0.142660i
$850$		−	482237.i		−	0.667456i
$851$	−438267.	+	23998.5i	−0.605173	+	0.0331378i
$852$	244830.			0.337276
$853$	732648.	−	732648.i	1.00693	−	1.00693i	0.00695022	−	0.999976i	$-0.497788\pi$
$853$	732648.	−	732648.i	1.00693	−	1.00693i	0.999976	−	0.00695022i	$-0.00221234\pi$
$854$			1.80879e6i			2.48011i
$855$		−	275490.i		−	0.376854i
$856$	−25007.0	−	25007.0i	−0.0341283	−	0.0341283i
$857$	683980.	+	683980.i	0.931283	+	0.931283i	0.997786	−	0.0665034i	$-0.0211843\pi$
$857$	683980.	+	683980.i	0.931283	+	0.931283i	−0.0665034	+	0.997786i	$0.521184\pi$
$858$	−351364.			−0.477290
$859$	−134430.	−	134430.i	−0.182184	−	0.182184i	0.610123	−	0.792307i	$-0.291120\pi$
$859$	−134430.	−	134430.i	−0.182184	−	0.182184i	−0.792307	+	0.610123i	$0.791120\pi$
$860$	307849.			0.416237
$861$	914501.			1.23361
$862$			834913.i			1.12364i
$863$	913704.			1.22683			0.613414	−	0.789761i	$-0.289796\pi$
$863$	913704.			1.22683			0.613414	+	0.789761i	$0.289796\pi$
$864$	91282.9	+	91282.9i	0.122282	+	0.122282i
$865$	−14059.9	+	14059.9i	−0.0187910	+	0.0187910i
$866$	150905.	−	150905.i	0.201219	−	0.201219i
$867$	−444236.			−0.590983
$868$	−458353.	−	458353.i	−0.608360	−	0.608360i
$869$	−336594.	+	336594.i	−0.445725	+	0.445725i
$870$	12892.2	+	12892.2i	0.0170329	+	0.0170329i
$871$	412521.	−	412521.i	0.543763	−	0.543763i
$872$		−	338271.i		−	0.444869i
$873$	49589.1	+	49589.1i	0.0650665	+	0.0650665i
$874$	233962.	+	233962.i	0.306282	+	0.306282i
$875$	−998945.	+	998945.i	−1.30475	+	1.30475i
$876$		−	336648.i		−	0.438700i
$877$	−102923.			−0.133818			−0.0669091	−	0.997759i	$-0.521314\pi$
$877$	−102923.			−0.133818			−0.0669091	+	0.997759i	$0.521314\pi$
$878$		−	986830.i		−	1.28013i
$879$		−	425513.i		−	0.550725i
$880$	68227.1	−	68227.1i	0.0881031	−	0.0881031i
$881$			751242.i			0.967895i	0.875097	+	0.483947i	$0.160797\pi$
$881$			751242.i			0.967895i	−0.875097	+	0.483947i	$0.839203\pi$
$882$	−676761.	+	676761.i	−0.869958	+	0.869958i
$883$	−477447.	+	477447.i	−0.612356	+	0.612356i	−0.943559	−	0.331204i	$-0.892545\pi$
$883$	−477447.	+	477447.i	−0.612356	+	0.612356i	0.331204	+	0.943559i	$0.392545\pi$
$884$	725002.			0.927758
$885$	216290.			0.276153
$886$	−137882.	−	137882.i	−0.175647	−	0.175647i
$887$		−	1.05408e6i		−	1.33976i	−0.742471	−	0.669879i	$-0.766346\pi$
$887$		−	1.05408e6i		−	1.33976i	0.742471	−	0.669879i	$-0.233654\pi$
$888$	−9051.84	−	165308.i	−0.0114792	−	0.209636i
$889$	−80981.0			−0.102466
$890$	−149058.	+	149058.i	−0.188180	+	0.188180i
$891$			45647.3i			0.0574989i
$892$			491248.i			0.617406i
$893$	648981.	+	648981.i	0.813821	+	0.813821i
$894$	176511.	+	176511.i	0.220849	+	0.220849i
$895$	−225681.			−0.281741
$896$	96354.7	+	96354.7i	0.120021	+	0.120021i
$897$	380406.			0.472784
$898$	−572224.			−0.709600
$899$		−	72128.1i		−	0.0892453i
$900$	−175206.			−0.216304
$901$	53415.4	+	53415.4i	0.0657987	+	0.0657987i
$902$	380792.	−	380792.i	0.468031	−	0.468031i
$903$	950318.	−	950318.i	1.16545	−	1.16545i
$904$	149912.			0.183443
$905$	181349.	+	181349.i	0.221421	+	0.221421i
$906$	−38418.6	+	38418.6i	−0.0468042	+	0.0468042i
$907$	−698673.	−	698673.i	−0.849296	−	0.849296i	0.140749	−	0.990045i	$-0.455049\pi$
$907$	−698673.	−	698673.i	−0.849296	−	0.849296i	−0.990045	+	0.140749i	$0.955049\pi$
$908$	217866.	−	217866.i	0.264252	−	0.264252i
$909$			966175.i			1.16931i
$910$	−601591.	−	601591.i	−0.726471	−	0.726471i
$911$	−739565.	−	739565.i	−0.891127	−	0.891127i	0.103502	−	0.994629i	$-0.466995\pi$
$911$	−739565.	−	739565.i	−0.891127	−	0.891127i	−0.994629	+	0.103502i	$0.966995\pi$
$912$	−88246.7	+	88246.7i	−0.106098	+	0.106098i
$913$		−	1.03341e6i		−	1.23974i
$914$	−535282.			−0.640752
$915$		−	523016.i		−	0.624701i
$916$		−	527507.i		−	0.628691i
$917$	−871788.	+	871788.i	−1.03675	+	1.03675i
$918$			823410.i			0.977082i
$919$	206120.	−	206120.i	0.244055	−	0.244055i	−0.574470	−	0.818526i	$-0.694792\pi$
$919$	206120.	−	206120.i	0.244055	−	0.244055i	0.818526	+	0.574470i	$0.194792\pi$
$920$	−73866.4	+	73866.4i	−0.0872712	+	0.0872712i
$921$	350444.			0.413142
$922$	−160337.			−0.188613
$923$	−898903.	−	898903.i	−1.05514	−	1.05514i
$924$		−	421229.i		−	0.493371i
$925$	425809.	+	381597.i	0.497658	+	0.445986i
$926$	921601.			1.07478
$927$	−34789.9	+	34789.9i	−0.0404850	+	0.0404850i
$928$			15162.7i			0.0176068i
$929$			1.26493e6i			1.46567i	0.680406	+	0.732835i	$0.261804\pi$
$929$			1.26493e6i			1.46567i	−0.680406	+	0.732835i	$0.738196\pi$
$930$	132534.	+	132534.i	0.153236	+	0.153236i
$931$	−1.66488e6	−	1.66488e6i	−1.92081	−	1.92081i
$932$	449516.			0.517504
$933$	259485.	+	259485.i	0.298091	+	0.298091i
$934$	−426399.			−0.488790
$935$	615437.			0.703980
$936$		−	263407.i		−	0.300660i
$937$	−238720.			−0.271900			−0.135950	−	0.990716i	$-0.543409\pi$
$937$	−238720.			−0.271900			−0.135950	+	0.990716i	$0.543409\pi$
$938$	494546.	+	494546.i	0.562083	+	0.562083i
$939$	−86410.0	+	86410.0i	−0.0980015	+	0.0980015i
$940$	−204896.	+	204896.i	−0.231888	+	0.231888i
$941$	−1.43551e6			−1.62117			−0.810584	−	0.585623i	$-0.800850\pi$
$941$	−1.43551e6			−1.62117			−0.810584	+	0.585623i	$0.800850\pi$
$942$	−13984.3	−	13984.3i	−0.0157594	−	0.0157594i
$943$	−412266.	+	412266.i	−0.463612	+	0.463612i
$944$	127191.	+	127191.i	0.142729	+	0.142729i
$945$	683248.	−	683248.i	0.765094	−	0.765094i
$946$		−	791412.i		−	0.884342i
$947$	−650178.	−	650178.i	−0.724990	−	0.724990i	0.244627	−	0.969617i	$-0.421334\pi$
$947$	−650178.	−	650178.i	−0.724990	−	0.724990i	−0.969617	+	0.244627i	$0.921334\pi$
$948$	137452.	+	137452.i	0.152944	+	0.152944i
$949$	−1.23602e6	+	1.23602e6i	−1.37243	+	1.37243i
$950$		−	431020.i		−	0.477584i
$951$	−498267.			−0.550936
$952$			869160.i			0.959016i
$953$		−	421638.i		−	0.464253i	−0.972686	−	0.232126i	$-0.925432\pi$
$953$		−	421638.i		−	0.464253i	0.972686	−	0.232126i	$-0.0745683\pi$
$954$	19406.9	−	19406.9i	0.0213235	−	0.0213235i
$955$		−	288571.i		−	0.316407i
$956$	−635448.	+	635448.i	−0.695287	+	0.695287i
$957$	33143.0	−	33143.0i	0.0361883	−	0.0361883i
$958$	569851.			0.620913
$959$	1.19886e6			1.30356
$960$	−27861.2	−	27861.2i	−0.0302314	−	0.0302314i
$961$			182033.i			0.197107i
$962$	−573699.	+	640167.i	−0.619917	+	0.691740i
$963$	−81955.3			−0.0883739
$964$	168153.	−	168153.i	0.180946	−	0.180946i
$965$		−	648169.i		−	0.696039i
$966$			456045.i			0.488713i
$967$	−59980.1	−	59980.1i	−0.0641437	−	0.0641437i	0.674307	−	0.738451i	$-0.264442\pi$
$967$	−59980.1	−	59980.1i	−0.0641437	−	0.0641437i	−0.738451	+	0.674307i	$0.764442\pi$
$968$	58859.3	+	58859.3i	0.0628152	+	0.0628152i
$969$	−796022.			−0.847769
$970$	−38515.6	−	38515.6i	−0.0409349	−	0.0409349i
$971$	1.05017e6			1.11383			0.556916	−	0.830569i	$-0.311985\pi$
$971$	1.05017e6			1.11383			0.556916	+	0.830569i	$0.311985\pi$
$972$	480760.			0.508857
$973$			241066.i			0.254630i
$974$	−89906.6			−0.0947706
$975$	−350405.	−	350405.i	−0.368605	−	0.368605i
$976$	307563.	−	307563.i	0.322875	−	0.322875i
$977$	−540645.	+	540645.i	−0.566400	+	0.566400i	−0.931118	−	0.364718i	$-0.881165\pi$
$977$	−540645.	+	540645.i	−0.566400	+	0.566400i	0.364718	+	0.931118i	$0.381165\pi$
$978$	424485.			0.443797
$979$	383194.	+	383194.i	0.399810	+	0.399810i
$980$	525637.	−	525637.i	0.547311	−	0.547311i
$981$	−554307.	−	554307.i	−0.575987	−	0.575987i
$982$	265590.	−	265590.i	0.275416	−	0.275416i
$983$		−	906557.i		−	0.938184i	−0.883149	−	0.469092i	$-0.844581\pi$
$983$		−	906557.i		−	0.938184i	0.883149	−	0.469092i	$-0.155419\pi$
$984$	−155500.	−	155500.i	−0.160598	−	0.160598i
$985$	393376.	+	393376.i	0.405449	+	0.405449i
$986$	−68387.1	+	68387.1i	−0.0703429	+	0.0703429i
$987$			1.26501e6i			1.29856i
$988$	648002.			0.663838
$989$			856826.i			0.875992i
$990$		−	223600.i		−	0.228140i
$991$	452537.	−	452537.i	0.460794	−	0.460794i	−0.438122	−	0.898916i	$-0.644356\pi$
$991$	452537.	−	452537.i	0.460794	−	0.460794i	0.898916	+	0.438122i	$0.144356\pi$
$992$			155875.i			0.158399i
$993$	88461.1	−	88461.1i	0.0897127	−	0.0897127i
$994$	1.07764e6	−	1.07764e6i	1.09069	−	1.09069i
$995$	−857355.			−0.865993
$996$	−422003.			−0.425400
$997$	−34077.1	−	34077.1i	−0.0342825	−	0.0342825i	0.689758	−	0.724040i	$-0.257717\pi$
$997$	−34077.1	−	34077.1i	−0.0342825	−	0.0342825i	−0.724040	+	0.689758i	$0.757717\pi$
$998$			826784.i			0.830101i
$999$	−727060.	−	651570.i	−0.728517	−	0.652875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.5.d.a.43.5	yes	14
37.31	odd	4	inner	74.5.d.a.31.3	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.d.a.31.3	✓	14	37.31	odd	4	inner
74.5.d.a.43.5	yes	14	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	74.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 2.00000i) q^{2} +5.34447i q^{3} -8.00000i q^{4} +(10.1818 + 10.1818i) q^{5} +(-10.6889 - 10.6889i) q^{6} -94.0964 q^{7} +(16.0000 + 16.0000i) q^{8} +52.4367 q^{9} +O(q^{10})\)	\(q+(-2.00000 + 2.00000i) q^{2} +5.34447i q^{3} -8.00000i q^{4} +(10.1818 + 10.1818i) q^{5} +(-10.6889 - 10.6889i) q^{6} -94.0964 q^{7} +(16.0000 + 16.0000i) q^{8} +52.4367 q^{9} -40.7273 q^{10} +104.701i q^{11} +42.7557 q^{12} +(-156.979 - 156.979i) q^{13} +(188.193 - 188.193i) q^{14} +(-54.4165 + 54.4165i) q^{15} -64.0000 q^{16} +(-288.653 - 288.653i) q^{17} +(-104.873 + 104.873i) q^{18} +(-257.997 - 257.997i) q^{19} +(81.4547 - 81.4547i) q^{20} -502.895i q^{21} +(-209.402 - 209.402i) q^{22} +(226.710 + 226.710i) q^{23} +(-85.5115 + 85.5115i) q^{24} -417.660i q^{25} +627.917 q^{26} +713.148i q^{27} +752.771i q^{28} +(-59.2294 + 59.2294i) q^{29} -217.666i q^{30} +(-608.888 + 608.888i) q^{31} +(128.000 - 128.000i) q^{32} -559.571 q^{33} +1154.61 q^{34} +(-958.074 - 958.074i) q^{35} -419.493i q^{36} +(-913.654 + 1019.51i) q^{37} +1031.99 q^{38} +(838.970 - 838.970i) q^{39} +325.819i q^{40} +1818.47i q^{41} +(1005.79 + 1005.79i) q^{42} +(1889.70 + 1889.70i) q^{43} +837.608 q^{44} +(533.902 + 533.902i) q^{45} -906.840 q^{46} -2515.46 q^{47} -342.046i q^{48} +6453.12 q^{49} +(835.321 + 835.321i) q^{50} +(1542.70 - 1542.70i) q^{51} +(-1255.83 + 1255.83i) q^{52} -185.050 q^{53} +(-1426.30 - 1426.30i) q^{54} +(-1066.05 + 1066.05i) q^{55} +(-1505.54 - 1505.54i) q^{56} +(1378.85 - 1378.85i) q^{57} -236.918i q^{58} +(-1987.36 - 1987.36i) q^{59} +(435.332 + 435.332i) q^{60} +(-4805.67 + 4805.67i) q^{61} -2435.55i q^{62} -4934.10 q^{63} +512.000i q^{64} -3196.67i q^{65} +(1119.14 - 1119.14i) q^{66} +2627.87i q^{67} +(-2309.23 + 2309.23i) q^{68} +(-1211.64 + 1211.64i) q^{69} +3832.29 q^{70} +5726.26 q^{71} +(838.987 + 838.987i) q^{72} -7873.75i q^{73} +(-211.711 - 3866.32i) q^{74} +2232.17 q^{75} +(-2063.97 + 2063.97i) q^{76} -9851.98i q^{77} +3355.88i q^{78} +(3214.81 + 3214.81i) q^{79} +(-651.637 - 651.637i) q^{80} +435.978 q^{81} +(-3636.95 - 3636.95i) q^{82} -9870.10 q^{83} -4023.16 q^{84} -5878.04i q^{85} -7558.78 q^{86} +(-316.550 - 316.550i) q^{87} +(-1675.22 + 1675.22i) q^{88} +(3659.89 - 3659.89i) q^{89} -2135.61 q^{90} +(14771.2 + 14771.2i) q^{91} +(1813.68 - 1813.68i) q^{92} +(-3254.18 - 3254.18i) q^{93} +(5030.93 - 5030.93i) q^{94} -5253.76i q^{95} +(684.092 + 684.092i) q^{96} +(945.694 + 945.694i) q^{97} +(-12906.2 + 12906.2i) q^{98} +5490.17i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9}+O(q^{10}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + 48 q^{10} + 160 q^{12} - 56 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} - 348 q^{17} + 692 q^{18} - 184 q^{19} - 96 q^{20} - 320 q^{22} - 502 q^{23} - 320 q^{24} + 224 q^{26} - 474 q^{29} - 630 q^{31} + 1792 q^{32} + 632 q^{33} + 1392 q^{34} + 1826 q^{35} - 2544 q^{37} + 736 q^{38} - 798 q^{39} - 224 q^{42} + 1936 q^{43} + 1280 q^{44} + 6162 q^{45} + 2008 q^{46} + 5716 q^{47} + 7862 q^{49} - 1372 q^{50} - 2422 q^{51} - 448 q^{52} - 20228 q^{53} - 656 q^{54} + 14006 q^{55} + 768 q^{56} - 2270 q^{57} - 4502 q^{59} + 3024 q^{60} - 11906 q^{61} - 2588 q^{63} - 1264 q^{66} - 2784 q^{68} + 21440 q^{69} - 7304 q^{70} - 11224 q^{71} - 5536 q^{72} + 4924 q^{74} - 18652 q^{75} - 1472 q^{76} + 20488 q^{79} + 768 q^{80} - 1706 q^{81} + 9808 q^{82} - 20224 q^{83} + 896 q^{84} - 7744 q^{86} + 19636 q^{87} - 2560 q^{88} + 13864 q^{89} - 24648 q^{90} - 6070 q^{91} - 4016 q^{92} - 13800 q^{93} - 11432 q^{94} + 2560 q^{96} + 16622 q^{97} - 15724 q^{98}+O(q^{100}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9 + 48 * q^10 + 160 * q^12 - 56 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 - 348 * q^17 + 692 * q^18 - 184 * q^19 - 96 * q^20 - 320 * q^22 - 502 * q^23 - 320 * q^24 + 224 * q^26 - 474 * q^29 - 630 * q^31 + 1792 * q^32 + 632 * q^33 + 1392 * q^34 + 1826 * q^35 - 2544 * q^37 + 736 * q^38 - 798 * q^39 - 224 * q^42 + 1936 * q^43 + 1280 * q^44 + 6162 * q^45 + 2008 * q^46 + 5716 * q^47 + 7862 * q^49 - 1372 * q^50 - 2422 * q^51 - 448 * q^52 - 20228 * q^53 - 656 * q^54 + 14006 * q^55 + 768 * q^56 - 2270 * q^57 - 4502 * q^59 + 3024 * q^60 - 11906 * q^61 - 2588 * q^63 - 1264 * q^66 - 2784 * q^68 + 21440 * q^69 - 7304 * q^70 - 11224 * q^71 - 5536 * q^72 + 4924 * q^74 - 18652 * q^75 - 1472 * q^76 + 20488 * q^79 + 768 * q^80 - 1706 * q^81 + 9808 * q^82 - 20224 * q^83 + 896 * q^84 - 7744 * q^86 + 19636 * q^87 - 2560 * q^88 + 13864 * q^89 - 24648 * q^90 - 6070 * q^91 - 4016 * q^92 - 13800 * q^93 - 11432 * q^94 + 2560 * q^96 + 16622 * q^97 - 15724 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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