LMFDB - Embedded newform 74.5.d.a.43.6

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			43.6
Root			$9.51876i$ of defining polynomial
Character	$\chi$	$=$	74.43
Dual form			74.5.d.a.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 2.00000i) q^{2} +10.5188i q^{3} -8.00000i q^{4} +(30.2483 + 30.2483i) q^{5} +(-21.0375 - 21.0375i) q^{6} +69.0478 q^{7} +(16.0000 + 16.0000i) q^{8} -29.6443 q^{9} +O(q^{10})$	\(q+(-2.00000 + 2.00000i) q^{2} +10.5188i q^{3} -8.00000i q^{4} +(30.2483 + 30.2483i) q^{5} +(-21.0375 - 21.0375i) q^{6} +69.0478 q^{7} +(16.0000 + 16.0000i) q^{8} -29.6443 q^{9} -120.993 q^{10} -10.9953i q^{11} +84.1501 q^{12} +(80.0125 + 80.0125i) q^{13} +(-138.096 + 138.096i) q^{14} +(-318.174 + 318.174i) q^{15} -64.0000 q^{16} +(-345.037 - 345.037i) q^{17} +(59.2886 - 59.2886i) q^{18} +(121.486 + 121.486i) q^{19} +(241.986 - 241.986i) q^{20} +726.297i q^{21} +(21.9906 + 21.9906i) q^{22} +(-590.441 - 590.441i) q^{23} +(-168.300 + 168.300i) q^{24} +1204.92i q^{25} -320.050 q^{26} +540.198i q^{27} -552.382i q^{28} +(49.9544 - 49.9544i) q^{29} -1272.70i q^{30} +(947.769 - 947.769i) q^{31} +(128.000 - 128.000i) q^{32} +115.657 q^{33} +1380.15 q^{34} +(2088.58 + 2088.58i) q^{35} +237.155i q^{36} +(-917.114 - 1016.40i) q^{37} -485.944 q^{38} +(-841.632 + 841.632i) q^{39} +967.945i q^{40} -3127.67i q^{41} +(-1452.59 - 1452.59i) q^{42} +(522.294 + 522.294i) q^{43} -87.9624 q^{44} +(-896.689 - 896.689i) q^{45} +2361.76 q^{46} +315.367 q^{47} -673.201i q^{48} +2366.59 q^{49} +(-2409.83 - 2409.83i) q^{50} +(3629.36 - 3629.36i) q^{51} +(640.100 - 640.100i) q^{52} -3942.78 q^{53} +(-1080.40 - 1080.40i) q^{54} +(332.589 - 332.589i) q^{55} +(1104.76 + 1104.76i) q^{56} +(-1277.88 + 1277.88i) q^{57} +199.818i q^{58} +(3550.97 + 3550.97i) q^{59} +(2545.39 + 2545.39i) q^{60} +(-519.449 + 519.449i) q^{61} +3791.08i q^{62} -2046.87 q^{63} +512.000i q^{64} +4840.48i q^{65} +(-231.314 + 231.314i) q^{66} +3736.40i q^{67} +(-2760.30 + 2760.30i) q^{68} +(6210.71 - 6210.71i) q^{69} -8354.30 q^{70} -1195.01 q^{71} +(-474.309 - 474.309i) q^{72} +1212.04i q^{73} +(3867.02 + 198.567i) q^{74} -12674.2 q^{75} +(971.887 - 971.887i) q^{76} -759.201i q^{77} -3366.53i q^{78} +(-1838.99 - 1838.99i) q^{79} +(-1935.89 - 1935.89i) q^{80} -8083.40 q^{81} +(6255.34 + 6255.34i) q^{82} -1530.34 q^{83} +5810.37 q^{84} -20873.6i q^{85} -2089.17 q^{86} +(525.459 + 525.459i) q^{87} +(175.925 - 175.925i) q^{88} +(-5115.00 + 5115.00i) q^{89} +3586.76 q^{90} +(5524.68 + 5524.68i) q^{91} +(-4723.53 + 4723.53i) q^{92} +(9969.36 + 9969.36i) q^{93} +(-630.735 + 630.735i) q^{94} +7349.48i q^{95} +(1346.40 + 1346.40i) q^{96} +(-4016.43 - 4016.43i) q^{97} +(-4733.19 + 4733.19i) q^{98} +325.948i 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
$3$			10.5188i			1.16875i	0.811483	+	0.584376i	$0.198660\pi$
$3$			10.5188i			1.16875i	−0.811483	+	0.584376i	$0.801340\pi$
$4$		−	8.00000i		−	0.500000i
$5$	30.2483	+	30.2483i	1.20993	+	1.20993i	0.971049	+	0.238882i	$0.0767810\pi$
$5$	30.2483	+	30.2483i	1.20993	+	1.20993i	0.238882	+	0.971049i	$0.423219\pi$
$6$	−21.0375	−	21.0375i	−0.584376	−	0.584376i
$7$	69.0478			1.40914			0.704569	−	0.709636i	$-0.251140\pi$
$7$	69.0478			1.40914			0.704569	+	0.709636i	$0.251140\pi$
$8$	16.0000	+	16.0000i	0.250000	+	0.250000i
$9$	−29.6443			−0.365979
$10$	−120.993			−1.20993
$11$		−	10.9953i		−	0.0908702i	−0.998967	−	0.0454351i	$-0.985533\pi$
$11$		−	10.9953i		−	0.0908702i	0.998967	−	0.0454351i	$-0.0144674\pi$
$12$	84.1501			0.584376
$13$	80.0125	+	80.0125i	0.473447	+	0.473447i	0.903028	−	0.429582i	$-0.141339\pi$
$13$	80.0125	+	80.0125i	0.473447	+	0.473447i	−0.429582	+	0.903028i	$0.641339\pi$
$14$	−138.096	+	138.096i	−0.704569	+	0.704569i
$15$	−318.174	+	318.174i	−1.41411	+	1.41411i
$16$	−64.0000			−0.250000
$17$	−345.037	−	345.037i	−1.19390	−	1.19390i	−0.975963	−	0.217938i	$-0.930067\pi$
$17$	−345.037	−	345.037i	−1.19390	−	1.19390i	−0.217938	−	0.975963i	$-0.569933\pi$
$18$	59.2886	−	59.2886i	0.182990	−	0.182990i
$19$	121.486	+	121.486i	0.336526	+	0.336526i	0.855058	−	0.518532i	$-0.173521\pi$
$19$	121.486	+	121.486i	0.336526	+	0.336526i	−0.518532	+	0.855058i	$0.673521\pi$
$20$	241.986	−	241.986i	0.604965	−	0.604965i
$21$			726.297i			1.64693i
$22$	21.9906	+	21.9906i	0.0454351	+	0.0454351i
$23$	−590.441	−	590.441i	−1.11615	−	1.11615i	−0.992302	−	0.123844i	$-0.960478\pi$
$23$	−590.441	−	590.441i	−1.11615	−	1.11615i	−0.123844	−	0.992302i	$-0.539522\pi$
$24$	−168.300	+	168.300i	−0.292188	+	0.292188i
$25$			1204.92i			1.92786i
$26$	−320.050			−0.473447
$27$			540.198i			0.741012i
$28$		−	552.382i		−	0.704569i
$29$	49.9544	−	49.9544i	0.0593989	−	0.0593989i	−0.676783	−	0.736182i	$-0.736627\pi$
$29$	49.9544	−	49.9544i	0.0593989	−	0.0593989i	0.736182	+	0.676783i	$0.236627\pi$
$30$		−	1272.70i		−	1.41411i
$31$	947.769	−	947.769i	0.986232	−	0.986232i	−0.0136744	−	0.999907i	$-0.504353\pi$
$31$	947.769	−	947.769i	0.986232	−	0.986232i	0.999907	+	0.0136744i	$0.00435284\pi$
$32$	128.000	−	128.000i	0.125000	−	0.125000i
$33$	115.657			0.106205
$34$	1380.15			1.19390
$35$	2088.58	+	2088.58i	1.70496	+	1.70496i
$36$			237.155i			0.182990i
$37$	−917.114	−	1016.40i	−0.669915	−	0.742438i
$37$	−917.114	−	1016.40i	−0.669915	−	0.742438i
$38$	−485.944			−0.336526
$39$	−841.632	+	841.632i	−0.553341	+	0.553341i
$40$			967.945i			0.604965i
$41$		−	3127.67i		−	1.86060i	−0.366799	−	0.930300i	$-0.619546\pi$
$41$		−	3127.67i		−	1.86060i	0.366799	−	0.930300i	$-0.380454\pi$
$42$	−1452.59	−	1452.59i	−0.823466	−	0.823466i
$43$	522.294	+	522.294i	0.282474	+	0.282474i	0.834095	−	0.551621i	$-0.185991\pi$
$43$	522.294	+	522.294i	0.282474	+	0.282474i	−0.551621	+	0.834095i	$0.685991\pi$
$44$	−87.9624			−0.0454351
$45$	−896.689	−	896.689i	−0.442810	−	0.442810i
$46$	2361.76			1.11615
$47$	315.367			0.142765			0.0713824	−	0.997449i	$-0.477259\pi$
$47$	315.367			0.142765			0.0713824	+	0.997449i	$0.477259\pi$
$48$		−	673.201i		−	0.292188i
$49$	2366.59			0.985670
$50$	−2409.83	−	2409.83i	−0.963932	−	0.963932i
$51$	3629.36	−	3629.36i	1.39537	−	1.39537i
$52$	640.100	−	640.100i	0.236723	−	0.236723i
$53$	−3942.78			−1.40362			−0.701811	−	0.712363i	$-0.747625\pi$
$53$	−3942.78			−1.40362			−0.701811	+	0.712363i	$0.747625\pi$
$54$	−1080.40	−	1080.40i	−0.370506	−	0.370506i
$55$	332.589	−	332.589i	0.109947	−	0.109947i
$56$	1104.76	+	1104.76i	0.352284	+	0.352284i
$57$	−1277.88	+	1277.88i	−0.393315	+	0.393315i
$58$			199.818i			0.0593989i
$59$	3550.97	+	3550.97i	1.02010	+	1.02010i	0.999794	+	0.0203075i	$0.00646453\pi$
$59$	3550.97	+	3550.97i	1.02010	+	1.02010i	0.0203075	+	0.999794i	$0.493535\pi$
$60$	2545.39	+	2545.39i	0.707054	+	0.707054i
$61$	−519.449	+	519.449i	−0.139599	+	0.139599i	−0.773453	−	0.633854i	$-0.781472\pi$
$61$	−519.449	+	519.449i	−0.139599	+	0.139599i	0.633854	+	0.773453i	$0.281472\pi$
$62$			3791.08i			0.986232i
$63$	−2046.87			−0.515715
$64$			512.000i			0.125000i
$65$			4840.48i			1.14568i
$66$	−231.314	+	231.314i	−0.0531023	+	0.0531023i
$67$			3736.40i			0.832345i	0.909286	+	0.416173i	$0.136629\pi$
$67$			3736.40i			0.832345i	−0.909286	+	0.416173i	$0.863371\pi$
$68$	−2760.30	+	2760.30i	−0.596950	+	0.596950i
$69$	6210.71	−	6210.71i	1.30450	−	1.30450i
$70$	−8354.30			−1.70496
$71$	−1195.01			−0.237058			−0.118529	−	0.992951i	$-0.537818\pi$
$71$	−1195.01			−0.237058			−0.118529	+	0.992951i	$0.537818\pi$
$72$	−474.309	−	474.309i	−0.0914948	−	0.0914948i
$73$			1212.04i			0.227442i	0.993513	+	0.113721i	$0.0362770\pi$
$73$			1212.04i			0.227442i	−0.993513	+	0.113721i	$0.963723\pi$
$74$	3867.02	+	198.567i	0.706176	+	0.0362614i
$75$	−12674.2			−2.25319
$76$	971.887	−	971.887i	0.168263	−	0.168263i
$77$		−	759.201i		−	0.128049i
$78$		−	3366.53i		−	0.553341i
$79$	−1838.99	−	1838.99i	−0.294663	−	0.294663i	0.544256	−	0.838919i	$-0.316812\pi$
$79$	−1838.99	−	1838.99i	−0.294663	−	0.294663i	−0.838919	+	0.544256i	$0.816812\pi$
$80$	−1935.89	−	1935.89i	−0.302483	−	0.302483i
$81$	−8083.40			−1.23204
$82$	6255.34	+	6255.34i	0.930300	+	0.930300i
$83$	−1530.34			−0.222143			−0.111071	−	0.993812i	$-0.535428\pi$
$83$	−1530.34			−0.222143			−0.111071	+	0.993812i	$0.535428\pi$
$84$	5810.37			0.823466
$85$		−	20873.6i		−	2.88907i
$86$	−2089.17			−0.282474
$87$	525.459	+	525.459i	0.0694225	+	0.0694225i
$88$	175.925	−	175.925i	0.0227176	−	0.0227176i
$89$	−5115.00	+	5115.00i	−0.645752	+	0.645752i	−0.951963	−	0.306212i	$-0.900938\pi$
$89$	−5115.00	+	5115.00i	−0.645752	+	0.645752i	0.306212	+	0.951963i	$0.400938\pi$
$90$	3586.76			0.442810
$91$	5524.68	+	5524.68i	0.667151	+	0.667151i
$92$	−4723.53	+	4723.53i	−0.558073	+	0.558073i
$93$	9969.36	+	9969.36i	1.15266	+	1.15266i
$94$	−630.735	+	630.735i	−0.0713824	+	0.0713824i
$95$			7349.48i			0.814346i
$96$	1346.40	+	1346.40i	0.146094	+	0.146094i
$97$	−4016.43	−	4016.43i	−0.426871	−	0.426871i	0.460690	−	0.887561i	$-0.347602\pi$
$97$	−4016.43	−	4016.43i	−0.426871	−	0.426871i	−0.887561	+	0.460690i	$0.847602\pi$
$98$	−4733.19	+	4733.19i	−0.492835	+	0.492835i
$99$			325.948i			0.0332566i
$100$	9639.32			0.963932
$101$			1115.89i			0.109390i	0.998503	+	0.0546952i	$0.0174187\pi$
$101$			1115.89i			0.109390i	−0.998503	+	0.0546952i	$0.982581\pi$
$102$			14517.5i			1.39537i
$103$	12833.7	−	12833.7i	1.20970	−	1.20970i	0.238578	−	0.971123i	$-0.423319\pi$
$103$	12833.7	−	12833.7i	1.20970	−	1.20970i	0.971123	−	0.238578i	$-0.0766813\pi$
$104$			2560.40i			0.236723i
$105$	−21969.2	+	21969.2i	−1.99267	+	1.99267i
$106$	7885.55	−	7885.55i	0.701811	−	0.701811i
$107$	11472.8			1.00208			0.501038	−	0.865425i	$-0.332952\pi$
$107$	11472.8			1.00208			0.501038	+	0.865425i	$0.332952\pi$
$108$	4321.58			0.370506
$109$	528.108	+	528.108i	0.0444498	+	0.0444498i	0.728982	−	0.684533i	$-0.239994\pi$
$109$	528.108	+	528.108i	0.0444498	+	0.0444498i	−0.684533	+	0.728982i	$0.739994\pi$
$110$			1330.35i			0.109947i
$111$	10691.2	−	9646.90i	0.867725	−	0.782964i
$112$	−4419.06			−0.352284
$113$	3930.94	−	3930.94i	0.307850	−	0.307850i	−0.536225	−	0.844075i	$-0.680150\pi$
$113$	3930.94	−	3930.94i	0.307850	−	0.307850i	0.844075	+	0.536225i	$0.180150\pi$
$114$		−	5111.52i		−	0.393315i
$115$		−	35719.6i		−	2.70092i
$116$	−399.636	−	399.636i	−0.0296994	−	0.0296994i
$117$	−2371.92	−	2371.92i	−0.173272	−	0.173272i
$118$	−14203.9			−1.02010
$119$	−23824.0	−	23824.0i	−1.68237	−	1.68237i
$120$	−10181.6			−0.707054
$121$	14520.1			0.991743
$122$		−	2077.80i		−	0.139599i
$123$	32899.2			2.17458
$124$	−7582.15	−	7582.15i	−0.493116	−	0.493116i
$125$	−17541.4	+	17541.4i	−1.12265	+	1.12265i
$126$	4093.75	−	4093.75i	0.257858	−	0.257858i
$127$	15432.9			0.956842			0.478421	−	0.878131i	$-0.341209\pi$
$127$	15432.9			0.956842			0.478421	+	0.878131i	$0.341209\pi$
$128$	−1024.00	−	1024.00i	−0.0625000	−	0.0625000i
$129$	−5493.88	+	5493.88i	−0.330141	+	0.330141i
$130$	−9680.95	−	9680.95i	−0.572838	−	0.572838i
$131$	13940.0	−	13940.0i	0.812306	−	0.812306i	−0.172673	−	0.984979i	$-0.555240\pi$
$131$	13940.0	−	13940.0i	0.812306	−	0.812306i	0.984979	+	0.172673i	$0.0552404\pi$
$132$		−	925.255i		−	0.0531023i
$133$	8388.33	+	8388.33i	0.474212	+	0.474212i
$134$	−7472.79	−	7472.79i	−0.416173	−	0.416173i
$135$	−16340.1	+	16340.1i	−0.896574	+	0.896574i
$136$		−	11041.2i		−	0.596950i
$137$	−33823.3			−1.80208			−0.901042	−	0.433731i	$-0.857197\pi$
$137$	−33823.3			−1.80208			−0.901042	+	0.433731i	$0.857197\pi$
$138$			24842.8i			1.30450i
$139$			16424.1i			0.850066i	0.905178	+	0.425033i	$0.139737\pi$
$139$			16424.1i			0.850066i	−0.905178	+	0.425033i	$0.860263\pi$
$140$	16708.6	−	16708.6i	0.852480	−	0.852480i
$141$			3317.27i			0.166856i
$142$	2390.02	−	2390.02i	0.118529	−	0.118529i
$143$	879.761	−	879.761i	0.0430222	−	0.0430222i
$144$	1897.24			0.0914948
$145$	3022.07			0.143737
$146$	−2424.08	−	2424.08i	−0.113721	−	0.113721i
$147$			24893.6i			1.15200i
$148$	−8131.18	+	7336.91i	−0.371219	+	0.334958i
$149$	21406.1			0.964197			0.482099	−	0.876117i	$-0.339875\pi$
$149$	21406.1			0.964197			0.482099	+	0.876117i	$0.339875\pi$
$150$	25348.4	−	25348.4i	1.12660	−	1.12660i
$151$			11689.7i			0.512685i	0.966586	+	0.256342i	$0.0825175\pi$
$151$			11689.7i			0.512685i	−0.966586	+	0.256342i	$0.917483\pi$
$152$			3887.55i			0.168263i
$153$	10228.4	+	10228.4i	0.436943	+	0.436943i
$154$	1518.40	+	1518.40i	0.0640243	+	0.0640243i
$155$	57336.7			2.38655
$156$	6733.06	+	6733.06i	0.276671	+	0.276671i
$157$	−24556.9			−0.996265			−0.498132	−	0.867101i	$-0.665981\pi$
$157$	−24556.9			−0.996265			−0.498132	+	0.867101i	$0.665981\pi$
$158$	7355.96			0.294663
$159$		−	41473.1i		−	1.64049i
$160$	7743.56			0.302483
$161$	−40768.6	−	40768.6i	−1.57280	−	1.57280i
$162$	16166.8	−	16166.8i	0.616019	−	0.616019i
$163$	−9561.68	+	9561.68i	−0.359881	+	0.359881i	−0.863769	−	0.503888i	$-0.831902\pi$
$163$	−9561.68	+	9561.68i	−0.359881	+	0.359881i	0.503888	+	0.863769i	$0.331902\pi$
$164$	−25021.4			−0.930300
$165$	3498.42	+	3498.42i	0.128500	+	0.128500i
$166$	3060.68	−	3060.68i	0.111071	−	0.111071i
$167$	−14826.8	−	14826.8i	−0.531635	−	0.531635i	0.389423	−	0.921059i	$-0.372674\pi$
$167$	−14826.8	−	14826.8i	−0.531635	−	0.531635i	−0.921059	+	0.389423i	$0.872674\pi$
$168$	−11620.7	+	11620.7i	−0.411733	+	0.411733i
$169$		−	15757.0i		−	0.551697i
$170$	41747.1	+	41747.1i	1.44454	+	1.44454i
$171$	−3601.37	−	3601.37i	−0.123162	−	0.123162i
$172$	4178.35	−	4178.35i	0.141237	−	0.141237i
$173$			52583.7i			1.75695i	0.477791	+	0.878473i	$0.341438\pi$
$173$			52583.7i			1.75695i	−0.477791	+	0.878473i	$0.658562\pi$
$174$	−2101.84			−0.0694225
$175$			83196.7i			2.71663i
$176$			703.699i			0.0227176i
$177$	−37351.8	+	37351.8i	−1.19224	+	1.19224i
$178$		−	20460.0i		−	0.645752i
$179$	−6643.45	+	6643.45i	−0.207342	+	0.207342i	−0.803137	−	0.595795i	$-0.796837\pi$
$179$	−6643.45	+	6643.45i	−0.207342	+	0.207342i	0.595795	+	0.803137i	$0.296837\pi$
$180$	−7173.51	+	7173.51i	−0.221405	+	0.221405i
$181$	−5056.88			−0.154357			−0.0771783	−	0.997017i	$-0.524591\pi$
$181$	−5056.88			−0.154357			−0.0771783	+	0.997017i	$0.524591\pi$
$182$	−22098.7			−0.667151
$183$	−5463.96	−	5463.96i	−0.163157	−	0.163157i
$184$		−	18894.1i		−	0.558073i
$185$	3003.16	−	58485.4i	0.0877475	−	1.70885i
$186$	−39877.4			−1.15266
$187$	−3793.79	+	3793.79i	−0.108490	+	0.108490i
$188$		−	2522.94i		−	0.0713824i
$189$			37299.5i			1.04419i
$190$	−14699.0	−	14699.0i	−0.407173	−	0.407173i
$191$	38695.9	+	38695.9i	1.06071	+	1.06071i	0.998034	+	0.0626796i	$0.0199646\pi$
$191$	38695.9	+	38695.9i	1.06071	+	1.06071i	0.0626796	+	0.998034i	$0.480035\pi$
$192$	−5385.61			−0.146094
$193$	42591.4	+	42591.4i	1.14342	+	1.14342i	0.987819	+	0.155605i	$0.0497326\pi$
$193$	42591.4	+	42591.4i	1.14342	+	1.14342i	0.155605	+	0.987819i	$0.450267\pi$
$194$	16065.7			0.426871
$195$	−50915.8			−1.33901
$196$		−	18932.7i		−	0.492835i
$197$	−38271.7			−0.986154			−0.493077	−	0.869986i	$-0.664128\pi$
$197$	−38271.7			−0.986154			−0.493077	+	0.869986i	$0.664128\pi$
$198$	−651.896	−	651.896i	−0.0166283	−	0.0166283i
$199$	−2855.95	+	2855.95i	−0.0721181	+	0.0721181i	−0.742246	−	0.670128i	$-0.766239\pi$
$199$	−2855.95	+	2855.95i	−0.0721181	+	0.0721181i	0.670128	+	0.742246i	$0.266239\pi$
$200$	−19278.6	+	19278.6i	−0.481966	+	0.481966i
$201$	−39302.3			−0.972804
$202$	−2231.78	−	2231.78i	−0.0546952	−	0.0546952i
$203$	3449.24	−	3449.24i	0.0837012	−	0.0837012i
$204$	−29034.9	−	29034.9i	−0.697686	−	0.697686i
$205$	94606.6	−	94606.6i	2.25120	−	2.25120i
$206$			51334.9i			1.20970i
$207$	17503.2	+	17503.2i	0.408486	+	0.408486i
$208$	−5120.80	−	5120.80i	−0.118362	−	0.118362i
$209$	1335.77	−	1335.77i	0.0305802	−	0.0305802i
$210$		−	87876.9i		−	1.99267i
$211$	−70101.5			−1.57457			−0.787285	−	0.616589i	$-0.788514\pi$
$211$	−70101.5			−1.57457			−0.787285	+	0.616589i	$0.788514\pi$
$212$			31542.2i			0.701811i
$213$		−	12570.0i		−	0.277062i
$214$	−22945.5	+	22945.5i	−0.501038	+	0.501038i
$215$			31596.9i			0.683547i
$216$	−8643.17	+	8643.17i	−0.185253	+	0.185253i
$217$	65441.3	−	65441.3i	1.38974	−	1.38974i
$218$	−2112.43			−0.0444498
$219$	−12749.1			−0.265823
$220$	−2660.71	−	2660.71i	−0.0549733	−	0.0549733i
$221$		−	55214.6i		−	1.13050i
$222$	−2088.68	+	40676.3i	−0.0423805	+	0.825344i
$223$	24775.0			0.498201			0.249101	−	0.968478i	$-0.419865\pi$
$223$	24775.0			0.498201			0.249101	+	0.968478i	$0.419865\pi$
$224$	8838.11	−	8838.11i	0.176142	−	0.176142i
$225$		−	35718.9i		−	0.705559i
$226$			15723.8i			0.307850i
$227$	−14116.9	−	14116.9i	−0.273960	−	0.273960i	0.556732	−	0.830692i	$-0.312055\pi$
$227$	−14116.9	−	14116.9i	−0.273960	−	0.273960i	−0.830692	+	0.556732i	$0.812055\pi$
$228$	10223.0	+	10223.0i	0.196658	+	0.196658i
$229$	14224.9			0.271255			0.135628	−	0.990760i	$-0.456695\pi$
$229$	14224.9			0.271255			0.135628	+	0.990760i	$0.456695\pi$
$230$	71439.3	+	71439.3i	1.35046	+	1.35046i
$231$	7985.85			0.149657
$232$	1598.54			0.0296994
$233$			49309.5i			0.908277i	0.890931	+	0.454139i	$0.150053\pi$
$233$			49309.5i			0.908277i	−0.890931	+	0.454139i	$0.849947\pi$
$234$	9487.66			0.173272
$235$	9539.32	+	9539.32i	0.172735	+	0.172735i
$236$	28407.8	−	28407.8i	0.510051	−	0.510051i
$237$	19343.9	−	19343.9i	0.344388	−	0.344388i
$238$	95296.2			1.68237
$239$	−38382.7	−	38382.7i	−0.671954	−	0.671954i	0.286212	−	0.958166i	$-0.407604\pi$
$239$	−38382.7	−	38382.7i	−0.671954	−	0.671954i	−0.958166	+	0.286212i	$0.907604\pi$
$240$	20363.2	−	20363.2i	0.353527	−	0.353527i
$241$	−36762.8	−	36762.8i	−0.632957	−	0.632957i	0.315851	−	0.948809i	$-0.397710\pi$
$241$	−36762.8	−	36762.8i	−0.632957	−	0.632957i	−0.948809	+	0.315851i	$0.897710\pi$
$242$	−29040.2	+	29040.2i	−0.495871	+	0.495871i
$243$		−	41271.3i		−	0.698934i
$244$	4155.59	+	4155.59i	0.0697996	+	0.0697996i
$245$	71585.3	+	71585.3i	1.19259	+	1.19259i
$246$	−65798.4	+	65798.4i	−1.08729	+	1.08729i
$247$			19440.8i			0.318654i
$248$	30328.6			0.493116
$249$		−	16097.3i		−	0.259630i
$250$		−	70165.8i		−	1.12265i
$251$	77326.3	−	77326.3i	1.22738	−	1.22738i	0.262430	−	0.964951i	$-0.415476\pi$
$251$	77326.3	−	77326.3i	1.22738	−	1.22738i	0.964951	−	0.262430i	$-0.0845240\pi$
$252$			16375.0i			0.257858i
$253$	−6492.07	+	6492.07i	−0.101424	+	0.101424i
$254$	−30865.8	+	30865.8i	−0.478421	+	0.478421i
$255$	219564.			3.37661
$256$	4096.00			0.0625000
$257$	−54239.9	−	54239.9i	−0.821206	−	0.821206i	0.165075	−	0.986281i	$-0.447213\pi$
$257$	−54239.9	−	54239.9i	−0.821206	−	0.821206i	−0.986281	+	0.165075i	$0.947213\pi$
$258$		−	21975.5i		−	0.330141i
$259$	−63324.6	−	70180.0i	−0.944003	−	1.04620i
$260$	38723.8			0.572838
$261$	−1480.87	+	1480.87i	−0.0217388	+	0.0217388i
$262$			55759.9i			0.812306i
$263$			112716.i			1.62957i	0.579762	+	0.814786i	$0.303145\pi$
$263$			112716.i			1.62957i	−0.579762	+	0.814786i	$0.696855\pi$
$264$	1850.51	+	1850.51i	0.0265512	+	0.0265512i
$265$	−119262.	−	119262.i	−1.69829	−	1.69829i
$266$	−33553.3			−0.474212
$267$	−53803.4	−	53803.4i	−0.754723	−	0.754723i
$268$	29891.2			0.416173
$269$	−4250.50			−0.0587402			−0.0293701	−	0.999569i	$-0.509350\pi$
$269$	−4250.50			−0.0587402			−0.0293701	+	0.999569i	$0.509350\pi$
$270$		−	65360.2i		−	0.896574i
$271$	−77055.1			−1.04921			−0.524605	−	0.851346i	$-0.675787\pi$
$271$	−77055.1			−1.04921			−0.524605	+	0.851346i	$0.675787\pi$
$272$	22082.4	+	22082.4i	0.298475	+	0.298475i
$273$	−58112.8	+	58112.8i	−0.779734	+	0.779734i
$274$	67646.6	−	67646.6i	0.901042	−	0.901042i
$275$	13248.4			0.175185
$276$	−49685.6	−	49685.6i	−0.652248	−	0.652248i
$277$	41531.0	−	41531.0i	0.541269	−	0.541269i	−0.382632	−	0.923901i	$-0.624982\pi$
$277$	41531.0	−	41531.0i	0.541269	−	0.541269i	0.923901	+	0.382632i	$0.124982\pi$
$278$	−32848.2	−	32848.2i	−0.425033	−	0.425033i
$279$	−28096.0	+	28096.0i	−0.360940	+	0.360940i
$280$			66834.4i			0.852480i
$281$	93101.9	+	93101.9i	1.17909	+	1.17909i	0.979977	+	0.199110i	$0.0638051\pi$
$281$	93101.9	+	93101.9i	1.17909	+	1.17909i	0.199110	+	0.979977i	$0.436195\pi$
$282$	−6634.55	−	6634.55i	−0.0834282	−	0.0834282i
$283$	−44952.4	+	44952.4i	−0.561281	+	0.561281i	−0.929671	−	0.368390i	$-0.879909\pi$
$283$	−44952.4	+	44952.4i	−0.561281	+	0.561281i	0.368390	+	0.929671i	$0.379909\pi$
$284$			9560.09i			0.118529i
$285$	−77307.4			−0.951768
$286$			3519.04i			0.0430222i
$287$		−	215959.i		−	2.62184i
$288$	−3794.47	+	3794.47i	−0.0457474	+	0.0457474i
$289$			154580.i			1.85080i
$290$	−6044.14	+	6044.14i	−0.0718685	+	0.0718685i
$291$	42247.9	−	42247.9i	0.498906	−	0.498906i
$292$	9696.30			0.113721
$293$	−54120.6			−0.630416			−0.315208	−	0.949023i	$-0.602074\pi$
$293$	−54120.6			−0.630416			−0.315208	+	0.949023i	$0.602074\pi$
$294$	−49787.2	−	49787.2i	−0.576001	−	0.576001i
$295$			214822.i			2.46850i
$296$	1588.54	−	30936.2i	0.0181307	−	0.353088i
$297$	5939.64			0.0673360
$298$	−42812.3	+	42812.3i	−0.482099	+	0.482099i
$299$		−	94485.3i		−	1.05687i
$300$			101394.i			1.12660i
$301$	36063.2	+	36063.2i	0.398044	+	0.398044i
$302$	−23379.5	−	23379.5i	−0.256342	−	0.256342i
$303$	−11737.8			−0.127850
$304$	−7775.10	−	7775.10i	−0.0841315	−	0.0841315i
$305$	−31424.9			−0.337811
$306$	−40913.6			−0.436943
$307$			2227.91i			0.0236385i	0.999930	+	0.0118193i	$0.00376228\pi$
$307$			2227.91i			0.0236385i	−0.999930	+	0.0118193i	$0.996238\pi$
$308$	−6073.60			−0.0640243
$309$	134995.	+	134995.i	1.41384	+	1.41384i
$310$	−114673.	+	114673.i	−1.19327	+	1.19327i
$311$	−39146.1	+	39146.1i	−0.404732	+	0.404732i	−0.879897	−	0.475165i	$-0.842389\pi$
$311$	−39146.1	+	39146.1i	−0.404732	+	0.404732i	0.475165	+	0.879897i	$0.342389\pi$
$312$	−26932.2			−0.276671
$313$	37424.8	+	37424.8i	0.382007	+	0.382007i	0.871825	−	0.489818i	$-0.162937\pi$
$313$	37424.8	+	37424.8i	0.382007	+	0.382007i	−0.489818	+	0.871825i	$0.662937\pi$
$314$	49113.9	−	49113.9i	0.498132	−	0.498132i
$315$	−61914.4	−	61914.4i	−0.623980	−	0.623980i
$316$	−14711.9	+	14711.9i	−0.147331	+	0.147331i
$317$		−	152147.i		−	1.51407i	−0.653376	−	0.757034i	$-0.726648\pi$
$317$		−	152147.i		−	1.51407i	0.653376	−	0.757034i	$-0.273352\pi$
$318$	82946.2	+	82946.2i	0.820243	+	0.820243i
$319$	−549.264	−	549.264i	−0.00539759	−	0.00539759i
$320$	−15487.1	+	15487.1i	−0.151241	+	0.151241i
$321$			120679.i			1.17118i
$322$	163074.			1.57280
$323$		−	83834.3i		−	0.803557i
$324$			64667.2i			0.616019i
$325$	−96408.3	+	96408.3i	−0.912741	+	0.912741i
$326$		−	38246.7i		−	0.359881i
$327$	−5555.05	+	5555.05i	−0.0519508	+	0.0519508i
$328$	50042.7	−	50042.7i	0.465150	−	0.465150i
$329$	21775.4			0.201175
$330$	−13993.7			−0.128500
$331$	−81389.5	−	81389.5i	−0.742869	−	0.742869i	0.230260	−	0.973129i	$-0.426042\pi$
$331$	−81389.5	−	81389.5i	−0.742869	−	0.742869i	−0.973129	+	0.230260i	$0.926042\pi$
$332$			12242.7i			0.111071i
$333$	27187.2	+	30130.4i	0.245175	+	0.271717i
$334$	59307.1			0.531635
$335$	−113020.	+	113020.i	−1.00708	+	1.00708i
$336$		−	46483.0i		−	0.411733i
$337$			120061.i			1.05716i	0.848883	+	0.528580i	$0.177275\pi$
$337$			120061.i			1.05716i	−0.848883	+	0.528580i	$0.822725\pi$
$338$	31514.0	+	31514.0i	0.275848	+	0.275848i
$339$	41348.6	+	41348.6i	0.359800	+	0.359800i
$340$	−166988.			−1.44454
$341$	−10421.0	−	10421.0i	−0.0896191	−	0.0896191i
$342$	14405.5			0.123162
$343$	−2375.75			−0.0201936
$344$			16713.4i			0.141237i
$345$	375726.			3.15670
$346$	−105167.	−	105167.i	−0.878473	−	0.878473i
$347$	−124619.	+	124619.i	−1.03497	+	1.03497i	−0.0355998	+	0.999366i	$0.511334\pi$
$347$	−124619.	+	124619.i	−1.03497	+	1.03497i	−0.999366	+	0.0355998i	$0.988666\pi$
$348$	4203.67	−	4203.67i	0.0347112	−	0.0347112i
$349$	−117331.			−0.963303			−0.481652	−	0.876363i	$-0.659963\pi$
$349$	−117331.			−0.963303			−0.481652	+	0.876363i	$0.659963\pi$
$350$	−166393.	−	166393.i	−1.35831	−	1.35831i
$351$	−43222.6	+	43222.6i	−0.350830	+	0.350830i
$352$	−1407.40	−	1407.40i	−0.0113588	−	0.0113588i
$353$	48307.3	−	48307.3i	0.387671	−	0.387671i	−0.486185	−	0.873856i	$-0.661612\pi$
$353$	48307.3	−	48307.3i	0.387671	−	0.387671i	0.873856	+	0.486185i	$0.161612\pi$
$354$		−	149407.i		−	1.19224i
$355$	−36147.0	−	36147.0i	−0.286824	−	0.286824i
$356$	40920.0	+	40920.0i	0.322876	+	0.322876i
$357$	250599.	−	250599.i	1.96627	−	1.96627i
$358$		−	26573.8i		−	0.207342i
$359$	219239.			1.70110			0.850549	−	0.525895i	$-0.176270\pi$
$359$	219239.			1.70110			0.850549	+	0.525895i	$0.176270\pi$
$360$		−	28694.1i		−	0.221405i
$361$		−	100803.i		−	0.773500i
$362$	10113.8	−	10113.8i	0.0771783	−	0.0771783i
$363$			152733.i			1.15910i
$364$	44197.5	−	44197.5i	0.333576	−	0.333576i
$365$	−36662.1	+	36662.1i	−0.275189	+	0.275189i
$366$	21855.8			0.163157
$367$	66951.0			0.497078			0.248539	−	0.968622i	$-0.420050\pi$
$367$	66951.0			0.497078			0.248539	+	0.968622i	$0.420050\pi$
$368$	37788.2	+	37788.2i	0.279036	+	0.279036i
$369$			92717.6i			0.680941i
$370$	110964.	+	122977.i	0.810551	+	0.898298i
$371$	−272240.			−1.97790
$372$	79754.8	−	79754.8i	0.576330	−	0.576330i
$373$		−	133716.i		−	0.961094i	−0.876969	−	0.480547i	$-0.840438\pi$
$373$		−	133716.i		−	0.961094i	0.876969	−	0.480547i	$-0.159562\pi$
$374$		−	15175.1i		−	0.108490i
$375$	−184514.	−	184514.i	−1.31210	−	1.31210i
$376$	5045.88	+	5045.88i	0.0356912	+	0.0356912i
$377$	7993.96			0.0562444
$378$	−74598.9	−	74598.9i	−0.522094	−	0.522094i
$379$	156448.			1.08916			0.544580	−	0.838709i	$-0.316689\pi$
$379$	156448.			1.08916			0.544580	+	0.838709i	$0.316689\pi$
$380$	58795.8			0.407173
$381$			162335.i			1.11831i
$382$	−154784.			−1.06071
$383$	−26425.8	−	26425.8i	−0.180149	−	0.180149i	0.611272	−	0.791421i	$-0.290658\pi$
$383$	−26425.8	−	26425.8i	−0.180149	−	0.180149i	−0.791421	+	0.611272i	$0.790658\pi$
$384$	10771.2	−	10771.2i	0.0730469	−	0.0730469i
$385$	22964.5	−	22964.5i	0.154930	−	0.154930i
$386$	−170366.			−1.14342
$387$	−15483.0	−	15483.0i	−0.103379	−	0.103379i
$388$	−32131.5	+	32131.5i	−0.213436	+	0.213436i
$389$	−124197.	−	124197.i	−0.820754	−	0.820754i	0.165462	−	0.986216i	$-0.447088\pi$
$389$	−124197.	−	124197.i	−0.820754	−	0.820754i	−0.986216	+	0.165462i	$0.947088\pi$
$390$	101832.	−	101832.i	0.669505	−	0.669505i
$391$			407448.i			2.66513i
$392$	37865.5	+	37865.5i	0.246417	+	0.246417i
$393$	146631.	+	146631.i	0.949384	+	0.949384i
$394$	76543.3	−	76543.3i	0.493077	−	0.493077i
$395$		−	111253.i		−	0.713043i
$396$	2607.58			0.0166283
$397$			216499.i			1.37365i	0.726824	+	0.686823i	$0.240995\pi$
$397$			216499.i			1.37365i	−0.726824	+	0.686823i	$0.759005\pi$
$398$		−	11423.8i		−	0.0721181i
$399$	−88234.8	+	88234.8i	−0.554235	+	0.554235i
$400$		−	77114.6i		−	0.481966i
$401$	161025.	−	161025.i	1.00139	−	1.00139i	0.00139254	−	0.999999i	$-0.499557\pi$
$401$	161025.	−	161025.i	1.00139	−	1.00139i	0.999999	−	0.00139254i	$-0.000443259\pi$
$402$	78604.5	−	78604.5i	0.486402	−	0.486402i
$403$	151667.			0.933856
$404$	8927.14			0.0546952
$405$	−244509.	−	244509.i	−1.49068	−	1.49068i
$406$			13797.0i			0.0837012i
$407$	−11175.6	+	10083.9i	−0.0674655	+	0.0608753i
$408$	116140.			0.697686
$409$	9905.97	−	9905.97i	0.0592175	−	0.0592175i	−0.676878	−	0.736095i	$-0.736667\pi$
$409$	9905.97	−	9905.97i	0.0592175	−	0.0592175i	0.736095	+	0.676878i	$0.236667\pi$
$410$			378426.i			2.25120i
$411$		−	355779.i		−	2.10619i
$412$	−102670.	−	102670.i	−0.604851	−	0.604851i
$413$	245187.	+	245187.i	1.43746	+	1.43746i
$414$	−70012.9			−0.408486
$415$	−46290.2	−	46290.2i	−0.268777	−	0.268777i
$416$	20483.2			0.118362
$417$	−172761.			−0.993515
$418$			5343.09i			0.0305802i
$419$	−282949.			−1.61168			−0.805842	−	0.592131i	$-0.798287\pi$
$419$	−282949.			−1.61168			−0.805842	+	0.592131i	$0.798287\pi$
$420$	175754.	+	175754.i	0.996337	+	0.996337i
$421$	40193.9	−	40193.9i	0.226775	−	0.226775i	−0.584569	−	0.811344i	$-0.698736\pi$
$421$	40193.9	−	40193.9i	0.226775	−	0.226775i	0.811344	+	0.584569i	$0.198736\pi$
$422$	140203.	−	140203.i	0.787285	−	0.787285i
$423$	−9348.85			−0.0522489
$424$	−63084.4	−	63084.4i	−0.350906	−	0.350906i
$425$	415741.	−	415741.i	2.30168	−	2.30168i
$426$	25140.1	+	25140.1i	0.138531	+	0.138531i
$427$	−35866.8	+	35866.8i	−0.196715	+	0.196715i
$428$		−	91782.1i		−	0.501038i
$429$	9253.99	+	9253.99i	0.0502822	+	0.0502822i
$430$	−63193.9	−	63193.9i	−0.341773	−	0.341773i
$431$	−17448.6	+	17448.6i	−0.0939305	+	0.0939305i	−0.752511	−	0.658580i	$-0.771157\pi$
$431$	−17448.6	+	17448.6i	−0.0939305	+	0.0939305i	0.658580	+	0.752511i	$0.271157\pi$
$432$		−	34572.7i		−	0.185253i
$433$	169891.			0.906138			0.453069	−	0.891476i	$-0.350329\pi$
$433$	169891.			0.906138			0.453069	+	0.891476i	$0.350329\pi$
$434$			261765.i			1.38974i
$435$			31788.4i			0.167993i
$436$	4224.87	−	4224.87i	0.0222249	−	0.0222249i
$437$		−	143460.i		−	0.751224i
$438$	25498.3	−	25498.3i	0.132911	−	0.132911i
$439$	158221.	−	158221.i	0.820985	−	0.820985i	−0.165265	−	0.986249i	$-0.552848\pi$
$439$	158221.	−	158221.i	0.820985	−	0.820985i	0.986249	+	0.165265i	$0.0528478\pi$
$440$	10642.8			0.0549733
$441$	−70156.0			−0.360735
$442$	110429.	+	110429.i	0.565248	+	0.565248i
$443$			173144.i			0.882266i	0.897442	+	0.441133i	$0.145423\pi$
$443$			173144.i			0.882266i	−0.897442	+	0.441133i	$0.854577\pi$
$444$	−77175.2	−	85529.9i	−0.391482	−	0.433862i
$445$	−309440.			−1.56263
$446$	−49550.1	+	49550.1i	−0.249101	+	0.249101i
$447$			225166.i			1.12691i
$448$			35352.5i			0.176142i
$449$	−246154.	−	246154.i	−1.22099	−	1.22099i	−0.967279	−	0.253716i	$-0.918347\pi$
$449$	−246154.	−	246154.i	−1.22099	−	1.22099i	−0.253716	−	0.967279i	$-0.581653\pi$
$450$	71437.8	+	71437.8i	0.352779	+	0.352779i
$451$	−34389.6			−0.169073
$452$	−31447.5	−	31447.5i	−0.153925	−	0.153925i
$453$	−122961.			−0.599201
$454$	56467.6			0.273960
$455$			334224.i			1.61441i
$456$	−40892.2			−0.196658
$457$	−146814.	−	146814.i	−0.702965	−	0.702965i	0.262081	−	0.965046i	$-0.415591\pi$
$457$	−146814.	−	146814.i	−0.702965	−	0.702965i	−0.965046	+	0.262081i	$0.915591\pi$
$458$	−28449.8	+	28449.8i	−0.135628	+	0.135628i
$459$	186388.	−	186388.i	0.884695	−	0.884695i
$460$	−285757.			−1.35046
$461$	55295.6	+	55295.6i	0.260189	+	0.260189i	0.825131	−	0.564942i	$-0.191101\pi$
$461$	55295.6	+	55295.6i	0.260189	+	0.260189i	−0.564942	+	0.825131i	$0.691101\pi$
$462$	−15971.7	+	15971.7i	−0.0748285	+	0.0748285i
$463$	123996.	+	123996.i	0.578425	+	0.578425i	0.934469	−	0.356044i	$-0.115875\pi$
$463$	123996.	+	123996.i	0.578425	+	0.578425i	−0.356044	+	0.934469i	$0.615875\pi$
$464$	−3197.08	+	3197.08i	−0.0148497	+	0.0148497i
$465$			603111.i			2.78928i
$466$	−98618.9	−	98618.9i	−0.454139	−	0.454139i
$467$	−36279.1	−	36279.1i	−0.166350	−	0.166350i	0.619023	−	0.785373i	$-0.287529\pi$
$467$	−36279.1	−	36279.1i	−0.166350	−	0.166350i	−0.785373	+	0.619023i	$0.787529\pi$
$468$	−18975.3	+	18975.3i	−0.0866358	+	0.0866358i
$469$			257990.i			1.17289i
$470$	−38157.3			−0.172735
$471$		−	258308.i		−	1.16439i
$472$			113631.i			0.510051i
$473$	5742.77	−	5742.77i	0.0256684	−	0.0256684i
$474$			77375.6i			0.344388i
$475$	−146380.	+	146380.i	−0.648777	+	0.648777i
$476$	−190592.	+	190592.i	−0.841185	+	0.841185i
$477$	116881.			0.513697
$478$	153531.			0.671954
$479$	2.68921	+	2.68921i	1.17207e−5	+	1.17207e-5i	0.707113	−	0.707101i	$-0.249997\pi$
$479$	2.68921	+	2.68921i	1.17207e−5	+	1.17207e-5i	−0.707101	+	0.707113i	$0.749997\pi$
$480$			81452.6i			0.353527i
$481$	7943.93	−	154705.i	0.0343356	−	0.668674i
$482$	147051.			0.632957
$483$	428835.	−	428835.i	1.83821	−	1.83821i
$484$		−	116161.i		−	0.495871i
$485$		−	242980.i		−	1.03297i
$486$	82542.7	+	82542.7i	0.349467	+	0.349467i
$487$	−94175.6	−	94175.6i	−0.397082	−	0.397082i	0.480120	−	0.877203i	$-0.340593\pi$
$487$	−94175.6	−	94175.6i	−0.397082	−	0.397082i	−0.877203	+	0.480120i	$0.840593\pi$
$488$	−16622.4			−0.0697996
$489$	−100577.	−	100577.i	−0.420612	−	0.420612i
$490$	−286341.			−1.19259
$491$	−93918.8			−0.389573			−0.194787	−	0.980846i	$-0.562401\pi$
$491$	−93918.8			−0.389573			−0.194787	+	0.980846i	$0.562401\pi$
$492$		−	263194.i		−	1.08729i
$493$	−34472.3			−0.141833
$494$	−38881.6	−	38881.6i	−0.159327	−	0.159327i
$495$	−9859.36	+	9859.36i	−0.0402382	+	0.0402382i
$496$	−60657.2	+	60657.2i	−0.246558	+	0.246558i
$497$	−82512.8			−0.334048
$498$	32194.6	+	32194.6i	0.129815	+	0.129815i
$499$	26209.4	−	26209.4i	0.105258	−	0.105258i	−0.652516	−	0.757775i	$-0.726287\pi$
$499$	26209.4	−	26209.4i	0.105258	−	0.105258i	0.757775	+	0.652516i	$0.226287\pi$
$500$	140332.	+	140332.i	0.561326	+	0.561326i
$501$	155959.	−	155959.i	0.621350	−	0.621350i
$502$			309305.i			1.22738i
$503$	85511.3	+	85511.3i	0.337977	+	0.337977i	0.855606	−	0.517628i	$-0.173185\pi$
$503$	85511.3	+	85511.3i	0.337977	+	0.337977i	−0.517628	+	0.855606i	$0.673185\pi$
$504$	−32750.0	−	32750.0i	−0.128929	−	0.128929i
$505$	−33753.8	+	33753.8i	−0.132355	+	0.132355i
$506$		−	25968.3i		−	0.101424i
$507$	165744.			0.644796
$508$		−	123463.i		−	0.478421i
$509$			151332.i			0.584112i	0.956401	+	0.292056i	$0.0943394\pi$
$509$			151332.i			0.584112i	−0.956401	+	0.292056i	$0.905661\pi$
$510$	−439128.	+	439128.i	−1.68830	+	1.68830i
$511$			83688.5i			0.320497i
$512$	−8192.00	+	8192.00i	−0.0312500	+	0.0312500i
$513$	−65626.5	+	65626.5i	−0.249370	+	0.249370i
$514$	216959.			0.821206
$515$	776396.			2.92731
$516$	43951.0	+	43951.0i	0.165071	+	0.165071i
$517$		−	3467.56i		−	0.0129731i
$518$	267009.	+	13710.6i	0.995100	+	0.0510972i
$519$	−553115.			−2.05343
$520$	−77447.6	+	77447.6i	−0.286419	+	0.286419i
$521$			196551.i			0.724102i	0.932158	+	0.362051i	$0.117923\pi$
$521$			196551.i			0.724102i	−0.932158	+	0.362051i	$0.882077\pi$
$522$		−	5923.46i		−	0.0217388i
$523$	245504.	+	245504.i	0.897542	+	0.897542i	0.995218	−	0.0976765i	$-0.0311410\pi$
$523$	245504.	+	245504.i	0.897542	+	0.897542i	−0.0976765	+	0.995218i	$0.531141\pi$
$524$	−111520.	−	111520.i	−0.406153	−	0.406153i
$525$	−875126.			−3.17506
$526$	−225432.	−	225432.i	−0.814786	−	0.814786i
$527$	−654031.			−2.35493
$528$	−7402.04			−0.0265512
$529$			417400.i			1.49156i
$530$	477049.			1.69829
$531$	−105266.	−	105266.i	−0.373336	−	0.373336i
$532$	67106.6	−	67106.6i	0.237106	−	0.237106i
$533$	250253.	−	250253.i	0.880895	−	0.880895i
$534$	215214.			0.754723
$535$	347031.	+	347031.i	1.21244	+	1.21244i
$536$	−59782.4	+	59782.4i	−0.208086	+	0.208086i
$537$	−69880.8	−	69880.8i	−0.242331	−	0.242331i
$538$	8501.00	−	8501.00i	0.0293701	−	0.0293701i
$539$		−	26021.4i		−	0.0895680i
$540$	130720.	+	130720.i	0.448287	+	0.448287i
$541$	−210674.	−	210674.i	−0.719807	−	0.719807i	0.248758	−	0.968566i	$-0.419978\pi$
$541$	−210674.	−	210674.i	−0.719807	−	0.719807i	−0.968566	+	0.248758i	$0.919978\pi$
$542$	154110.	−	154110.i	0.524605	−	0.524605i
$543$		−	53192.1i		−	0.180404i
$544$	−88329.5			−0.298475
$545$			31948.7i			0.107562i
$546$		−	232451.i		−	0.779734i
$547$	−23718.7	+	23718.7i	−0.0792713	+	0.0792713i	−0.745631	−	0.666359i	$-0.767852\pi$
$547$	−23718.7	+	23718.7i	−0.0792713	+	0.0792713i	0.666359	+	0.745631i	$0.267852\pi$
$548$			270587.i			0.901042i
$549$	15398.7	−	15398.7i	0.0510904	−	0.0510904i
$550$	−26496.8	+	26496.8i	−0.0875927	+	0.0875927i
$551$	12137.5			0.0399785
$552$	198743.			0.652248
$553$	−126978.	−	126978.i	−0.415221	−	0.415221i
$554$			166124.i			0.541269i
$555$	615193.	+	31589.5i	1.99722	+	0.102555i
$556$	131393.			0.425033
$557$	−105334.	+	105334.i	−0.339513	+	0.339513i	−0.856184	−	0.516671i	$-0.827171\pi$
$557$	−105334.	+	105334.i	−0.339513	+	0.339513i	0.516671	+	0.856184i	$0.327171\pi$
$558$		−	112384.i		−	0.360940i
$559$			83580.0i			0.267472i
$560$	−133669.	−	133669.i	−0.426240	−	0.426240i
$561$	−39905.9	−	39905.9i	−0.126798	−	0.126798i
$562$	−372408.			−1.17909
$563$	−248718.	−	248718.i	−0.784675	−	0.784675i	0.195940	−	0.980616i	$-0.437224\pi$
$563$	−248718.	−	248718.i	−0.784675	−	0.784675i	−0.980616	+	0.195940i	$0.937224\pi$
$564$	26538.2			0.0834282
$565$	237808.			0.744955
$566$		−	179810.i		−	0.561281i
$567$	−558141.			−1.73611
$568$	−19120.2	−	19120.2i	−0.0592646	−	0.0592646i
$569$	420587.	−	420587.i	1.29907	−	1.29907i	0.370055	−	0.929010i	$-0.379339\pi$
$569$	420587.	−	420587.i	1.29907	−	1.29907i	0.929010	−	0.370055i	$-0.120661\pi$
$570$	154615.	−	154615.i	0.475884	−	0.475884i
$571$	−496254.			−1.52206			−0.761030	−	0.648717i	$-0.775306\pi$
$571$	−496254.			−1.52206			−0.761030	+	0.648717i	$0.775306\pi$
$572$	−7038.09	−	7038.09i	−0.0215111	−	0.0215111i
$573$	−407033.	+	407033.i	−1.23971	+	1.23971i
$574$	431917.	+	431917.i	1.31092	+	1.31092i
$575$	711431.	−	711431.i	2.15178	−	2.15178i
$576$		−	15177.9i		−	0.0457474i
$577$	−101034.	−	101034.i	−0.303469	−	0.303469i	0.538901	−	0.842369i	$-0.318840\pi$
$577$	−101034.	−	101034.i	−0.303469	−	0.303469i	−0.842369	+	0.538901i	$0.818840\pi$
$578$	−309161.	−	309161.i	−0.925398	−	0.925398i
$579$	−448009.	+	448009.i	−1.33638	+	1.33638i
$580$		−	24176.6i		−	0.0718685i
$581$	−105667.			−0.313030
$582$			168992.i			0.498906i
$583$			43352.0i			0.127547i
$584$	−19392.6	+	19392.6i	−0.0568605	+	0.0568605i
$585$		−	143493.i		−	0.419293i
$586$	108241.	−	108241.i	0.315208	−	0.315208i
$587$	−315193.	+	315193.i	−0.914746	+	0.914746i	−0.996641	−	0.0818952i	$-0.973903\pi$
$587$	−315193.	+	315193.i	−0.914746	+	0.914746i	0.0818952	+	0.996641i	$0.473903\pi$
$588$	199149.			0.576001
$589$	230281.			0.663786
$590$	−429643.	−	429643.i	−1.23425	−	1.23425i
$591$		−	402570.i		−	1.15257i
$592$	58695.3	+	65049.4i	0.167479	+	0.185609i
$593$	549407.			1.56237			0.781186	−	0.624298i	$-0.214615\pi$
$593$	549407.			1.56237			0.781186	+	0.624298i	$0.214615\pi$
$594$	−11879.3	+	11879.3i	−0.0336680	+	0.0336680i
$595$		−	1.44127e6i		−	4.07110i
$596$		−	171249.i		−	0.482099i
$597$	−30041.0	−	30041.0i	−0.0842881	−	0.0842881i
$598$	188971.	+	188971.i	0.528435	+	0.528435i
$599$	172763.			0.481501			0.240750	−	0.970587i	$-0.422606\pi$
$599$	172763.			0.481501			0.240750	+	0.970587i	$0.422606\pi$
$600$	−202787.	−	202787.i	−0.563299	−	0.563299i
$601$	190910.			0.528543			0.264272	−	0.964448i	$-0.414868\pi$
$601$	190910.			0.528543			0.264272	+	0.964448i	$0.414868\pi$
$602$	−144253.			−0.398044
$603$		−	110763.i		−	0.304621i
$604$	93517.8			0.256342
$605$	439208.	+	439208.i	1.19994	+	1.19994i
$606$	23475.6	−	23475.6i	0.0639251	−	0.0639251i
$607$	201474.	−	201474.i	0.546816	−	0.546816i	−0.378702	−	0.925519i	$-0.623630\pi$
$607$	201474.	−	201474.i	0.546816	−	0.546816i	0.925519	+	0.378702i	$0.123630\pi$
$608$	31100.4			0.0841315
$609$	36281.8	+	36281.8i	0.0978259	+	0.0978259i
$610$	62849.7	−	62849.7i	0.168905	−	0.168905i
$611$	25233.3	+	25233.3i	0.0675915	+	0.0675915i
$612$	81827.2	−	81827.2i	0.218471	−	0.218471i
$613$			171480.i			0.456344i	0.973621	+	0.228172i	$0.0732749\pi$
$613$			171480.i			0.456344i	−0.973621	+	0.228172i	$0.926725\pi$
$614$	−4455.82	−	4455.82i	−0.0118193	−	0.0118193i
$615$	995144.	+	995144.i	2.63109	+	2.63109i
$616$	12147.2	−	12147.2i	0.0320122	−	0.0320122i
$617$			75449.0i			0.198191i	0.995078	+	0.0990953i	$0.0315949\pi$
$617$			75449.0i			0.198191i	−0.995078	+	0.0990953i	$0.968405\pi$
$618$	−539979.			−1.41384
$619$		−	40455.4i		−	0.105583i	−0.998606	−	0.0527917i	$-0.983188\pi$
$619$		−	40455.4i		−	0.105583i	0.998606	−	0.0527917i	$-0.0168119\pi$
$620$		−	458694.i		−	1.19327i
$621$	318955.	−	318955.i	0.827078	−	0.827078i
$622$		−	156584.i		−	0.404732i
$623$	−353179.	+	353179.i	−0.909953	+	0.909953i
$624$	53864.4	−	53864.4i	0.138335	−	0.138335i
$625$	−308124.			−0.788798
$626$	−149699.			−0.382007
$627$	14050.7	+	14050.7i	0.0357406	+	0.0357406i
$628$			196455.i			0.498132i
$629$	−34256.5	+	667133.i	−0.0865849	+	1.68621i
$630$	247658.			0.623980
$631$	35252.8	−	35252.8i	0.0885391	−	0.0885391i	−0.661450	−	0.749989i	$-0.730059\pi$
$631$	35252.8	−	35252.8i	0.0885391	−	0.0885391i	0.749989	+	0.661450i	$0.230059\pi$
$632$		−	58847.7i		−	0.147331i
$633$		−	737380.i		−	1.84028i
$634$	304294.	+	304294.i	0.757034	+	0.757034i
$635$	466819.	+	466819.i	1.15771	+	1.15771i
$636$	−331785.			−0.820243
$637$	189357.	+	189357.i	0.466662	+	0.466662i
$638$	2197.06			0.00539759
$639$	35425.3			0.0867584
$640$		−	61948.5i		−	0.151241i
$641$	30042.1			0.0731164			0.0365582	−	0.999332i	$-0.488361\pi$
$641$	30042.1			0.0731164			0.0365582	+	0.999332i	$0.488361\pi$
$642$	−241359.	−	241359.i	−0.585589	−	0.585589i
$643$	288466.	−	288466.i	0.697706	−	0.697706i	−0.266209	−	0.963915i	$-0.585771\pi$
$643$	288466.	−	288466.i	0.697706	−	0.697706i	0.963915	+	0.266209i	$0.0857713\pi$
$644$	−326149.	+	326149.i	−0.786401	+	0.786401i
$645$	−332361.			−0.798896
$646$	167669.	+	167669.i	0.401779	+	0.401779i
$647$	−398994.	+	398994.i	−0.953142	+	0.953142i	−0.998950	−	0.0458081i	$-0.985414\pi$
$647$	−398994.	+	398994.i	−0.953142	+	0.953142i	0.0458081	+	0.998950i	$0.485414\pi$
$648$	−129334.	−	129334.i	−0.308010	−	0.308010i
$649$	39044.0	−	39044.0i	0.0926968	−	0.0926968i
$650$		−	385633.i		−	0.912741i
$651$	688362.	+	688362.i	1.62426	+	1.62426i
$652$	76493.5	+	76493.5i	0.179941	+	0.179941i
$653$	−187012.	+	187012.i	−0.438575	+	0.438575i	−0.891532	−	0.452957i	$-0.850369\pi$
$653$	−187012.	+	187012.i	−0.438575	+	0.438575i	0.452957	+	0.891532i	$0.350369\pi$
$654$		−	22220.2i		−	0.0519508i
$655$	843321.			1.96567
$656$			200171.i			0.465150i
$657$		−	35930.0i		−	0.0832390i
$658$	−43550.8	+	43550.8i	−0.100588	+	0.100588i
$659$			199346.i			0.459024i	0.973306	+	0.229512i	$0.0737131\pi$
$659$			199346.i			0.459024i	−0.973306	+	0.229512i	$0.926287\pi$
$660$	27987.4	−	27987.4i	0.0642501	−	0.0642501i
$661$	−43738.2	+	43738.2i	−0.100106	+	0.100106i	−0.755386	−	0.655280i	$-0.772551\pi$
$661$	−43738.2	+	43738.2i	−0.100106	+	0.100106i	0.655280	+	0.755386i	$0.272551\pi$
$662$	325558.			0.742869
$663$	580789.			1.32127
$664$	−24485.5	−	24485.5i	−0.0555357	−	0.0555357i
$665$			507465.i			1.14753i
$666$	−114635.	−	5886.39i	−0.258446	−	0.0132709i
$667$	−58990.3			−0.132596
$668$	−118614.	+	118614.i	−0.265818	+	0.265818i
$669$			260603.i			0.582273i
$670$		−	452078.i		−	1.00708i
$671$	5711.50	+	5711.50i	0.0126854	+	0.0126854i
$672$	92966.0	+	92966.0i	0.205866	+	0.205866i
$673$	−725075.			−1.60086			−0.800429	−	0.599427i	$-0.795395\pi$
$673$	−725075.			−1.60086			−0.800429	+	0.599427i	$0.795395\pi$
$674$	−240121.	−	240121.i	−0.528580	−	0.528580i
$675$	−650893.			−1.42857
$676$	−126056.			−0.275848
$677$			661665.i			1.44365i	0.692078	+	0.721823i	$0.256696\pi$
$677$			661665.i			1.44365i	−0.692078	+	0.721823i	$0.743304\pi$
$678$	−165394.			−0.359800
$679$	−277326.	−	277326.i	−0.601521	−	0.601521i
$680$	333977.	−	333977.i	0.722268	−	0.722268i
$681$	148492.	−	148492.i	0.320192	−	0.320192i
$682$	41684.0			0.0896191
$683$	−529677.	−	529677.i	−1.13545	−	1.13545i	−0.989255	−	0.146198i	$-0.953296\pi$
$683$	−529677.	−	529677.i	−1.13545	−	1.13545i	−0.146198	−	0.989255i	$-0.546704\pi$
$684$	−28810.9	+	28810.9i	−0.0615808	+	0.0615808i
$685$	−1.02310e6	−	1.02310e6i	−2.18040	−	2.18040i
$686$	4751.51	−	4751.51i	0.0100968	−	0.0100968i
$687$			149628.i			0.317030i
$688$	−33426.8	−	33426.8i	−0.0706184	−	0.0706184i
$689$	−315471.	−	315471.i	−0.664540	−	0.664540i
$690$	−751452.	+	751452.i	−1.57835	+	1.57835i
$691$		−	580294.i		−	1.21532i	−0.794196	−	0.607662i	$-0.792108\pi$
$691$		−	580294.i		−	1.21532i	0.794196	−	0.607662i	$-0.207892\pi$
$692$	420669.			0.878473
$693$			22506.0i			0.0468632i
$694$		−	498477.i		−	1.03497i
$695$	−496801.	+	496801.i	−1.02852	+	1.02852i
$696$			16814.7i			0.0347112i
$697$	−1.07916e6	+	1.07916e6i	−2.22137	+	2.22137i
$698$	234663.	−	234663.i	0.481652	−	0.481652i
$699$	−518675.			−1.06155
$700$	665574.			1.35831
$701$	−235973.	−	235973.i	−0.480205	−	0.480205i	0.424992	−	0.905197i	$-0.360277\pi$
$701$	−235973.	−	235973.i	−0.480205	−	0.480205i	−0.905197	+	0.424992i	$0.860277\pi$
$702$		−	172890.i		−	0.350830i
$703$	12061.6	−	234894.i	0.0244058	−	0.475294i
$704$	5629.59			0.0113588
$705$	−100342.	+	100342.i	−0.201885	+	0.201885i
$706$			193229.i			0.387671i
$707$			77049.8i			0.154146i
$708$	298815.	+	298815.i	0.596122	+	0.596122i
$709$	263351.	+	263351.i	0.523892	+	0.523892i	0.918745	−	0.394852i	$-0.129204\pi$
$709$	263351.	+	263351.i	0.523892	+	0.523892i	−0.394852	+	0.918745i	$0.629204\pi$
$710$	144588.			0.286824
$711$	54515.6	+	54515.6i	0.107840	+	0.107840i
$712$	−163680.			−0.322876
$713$	−1.11920e6			−2.20156
$714$			1.00240e6i			1.96627i
$715$	53222.5			0.104108
$716$	53147.6	+	53147.6i	0.103671	+	0.103671i
$717$	403738.	−	403738.i	0.785347	−	0.785347i
$718$	−438479.	+	438479.i	−0.850549	+	0.850549i
$719$	64557.5			0.124879			0.0624394	−	0.998049i	$-0.480112\pi$
$719$	64557.5			0.124879			0.0624394	+	0.998049i	$0.480112\pi$
$720$	57388.1	+	57388.1i	0.110702	+	0.110702i
$721$	886140.	−	886140.i	1.70464	−	1.70464i
$722$	201607.	+	201607.i	0.386750	+	0.386750i
$723$	386699.	−	386699.i	0.739769	−	0.739769i
$724$			40455.0i			0.0771783i
$725$	60190.9	+	60190.9i	0.114513	+	0.114513i
$726$	−305467.	−	305467.i	−0.579550	−	0.579550i
$727$	164676.	−	164676.i	0.311575	−	0.311575i	−0.533944	−	0.845520i	$-0.679291\pi$
$727$	164676.	−	164676.i	0.311575	−	0.311575i	0.845520	+	0.533944i	$0.179291\pi$
$728$			176790.i			0.333576i
$729$	−220632.			−0.415159
$730$		−	146648.i		−	0.275189i
$731$		−	360421.i		−	0.674491i
$732$	−43711.7	+	43711.7i	−0.0815784	+	0.0815784i
$733$			274893.i			0.511630i	0.966726	+	0.255815i	$0.0823437\pi$
$733$			274893.i			0.511630i	−0.966726	+	0.255815i	$0.917656\pi$
$734$	−133902.	+	133902.i	−0.248539	+	0.248539i
$735$	−752989.	+	752989.i	−1.39384	+	1.39384i
$736$	−151153.			−0.279036
$737$	41082.8			0.0756354
$738$	−185435.	−	185435.i	−0.340471	−	0.340471i
$739$		−	308699.i		−	0.565257i	−0.959229	−	0.282629i	$-0.908794\pi$
$739$		−	308699.i		−	0.565257i	0.959229	−	0.282629i	$-0.0912064\pi$
$740$	−467883.	−	24025.3i	−0.854425	−	0.0438737i
$741$	−204493.			−0.372427
$742$	544480.	−	544480.i	0.988949	−	0.988949i
$743$		−	61344.7i		−	0.111122i	−0.998455	−	0.0555609i	$-0.982305\pi$
$743$		−	61344.7i		−	0.111122i	0.998455	−	0.0555609i	$-0.0176947\pi$
$744$			319019.i			0.576330i
$745$	647499.	+	647499.i	1.16661	+	1.16661i
$746$	267432.	+	267432.i	0.480547	+	0.480547i
$747$	45365.9			0.0812997
$748$	30350.3	+	30350.3i	0.0542450	+	0.0542450i
$749$	792169.			1.41206
$750$	738057.			1.31210
$751$		−	685483.i		−	1.21539i	−0.794169	−	0.607697i	$-0.792094\pi$
$751$		−	685483.i		−	1.21539i	0.794169	−	0.607697i	$-0.207906\pi$
$752$	−20183.5			−0.0356912
$753$	813376.	+	813376.i	1.43450	+	1.43450i
$754$	−15987.9	+	15987.9i	−0.0281222	+	0.0281222i
$755$	−353594.	+	353594.i	−0.620313	+	0.620313i
$756$	298396.			0.522094
$757$	−68334.1	−	68334.1i	−0.119246	−	0.119246i	0.644965	−	0.764212i	$-0.276872\pi$
$757$	−68334.1	−	68334.1i	−0.119246	−	0.119246i	−0.764212	+	0.644965i	$0.776872\pi$
$758$	−312896.	+	312896.i	−0.544580	+	0.544580i
$759$	−68288.6	−	68288.6i	−0.118540	−	0.118540i
$760$	−117592.	+	117592.i	−0.203587	+	0.203587i
$761$			1.05937e6i			1.82928i	0.404273	+	0.914639i	$0.367525\pi$
$761$			1.05937e6i			1.82928i	−0.404273	+	0.914639i	$0.632475\pi$
$762$	−324670.	−	324670.i	−0.559155	−	0.559155i
$763$	36464.7	+	36464.7i	0.0626359	+	0.0626359i
$764$	309567.	−	309567.i	0.530357	−	0.530357i
$765$			618782.i			1.05734i
$766$	105703.			0.180149
$767$			568244.i			0.965927i
$768$			43084.8i			0.0730469i
$769$	−240561.	+	240561.i	−0.406793	+	0.406793i	−0.880619	−	0.473826i	$-0.842873\pi$
$769$	−240561.	+	240561.i	−0.406793	+	0.406793i	0.473826	+	0.880619i	$0.342873\pi$
$770$			91858.0i			0.154930i
$771$	570536.	−	570536.i	0.959786	−	0.959786i
$772$	340731.	−	340731.i	0.571712	−	0.571712i
$773$	−374643.			−0.626987			−0.313493	−	0.949590i	$-0.601499\pi$
$773$	−374643.			−0.626987			−0.313493	+	0.949590i	$0.601499\pi$
$774$	61932.1			0.103379
$775$	1.14198e6	+	1.14198e6i	1.90132	+	1.90132i
$776$		−	128526.i		−	0.213436i
$777$	738206.	−	666097.i	1.22274	−	1.10330i
$778$	496789.			0.820754
$779$	379968.	−	379968.i	0.626141	−	0.626141i
$780$			407327.i			0.669505i
$781$			13139.5i			0.0215415i
$782$	−814896.	−	814896.i	−1.33257	−	1.33257i
$783$	26985.3	+	26985.3i	0.0440153	+	0.0440153i
$784$	−151462.			−0.246417
$785$	−742805.	−	742805.i	−1.20541	−	1.20541i
$786$	−586525.			−0.949384
$787$	669040.			1.08020			0.540098	−	0.841602i	$-0.318387\pi$
$787$	669040.			1.08020			0.540098	+	0.841602i	$0.318387\pi$
$788$			306173.i			0.493077i
$789$	−1.18563e6			−1.90456
$790$	222505.	+	222505.i	0.356522	+	0.356522i
$791$	271422.	−	271422.i	0.433803	−	0.433803i
$792$	−5215.17	+	5215.17i	−0.00831415	+	0.00831415i
$793$	−83124.8			−0.132186
$794$	−432998.	−	432998.i	−0.686823	−	0.686823i
$795$	1.25449e6	−	1.25449e6i	1.98487	−	1.98487i
$796$	22847.6	+	22847.6i	0.0360590	+	0.0360590i
$797$	243910.	−	243910.i	0.383983	−	0.383983i	−0.488552	−	0.872535i	$-0.662475\pi$
$797$	243910.	−	243910.i	0.383983	−	0.383983i	0.872535	+	0.488552i	$0.162475\pi$
$798$		−	352939.i		−	0.554235i
$799$	−108813.	−	108813.i	−0.170447	−	0.170447i
$800$	154229.	+	154229.i	0.240983	+	0.240983i
$801$	151631.	−	151631.i	0.236332	−	0.236332i
$802$			644099.i			1.00139i
$803$	13326.7			0.0206677
$804$			314418.i			0.486402i
$805$		−	2.46636e6i		−	3.80596i
$806$	−303333.	+	303333.i	−0.466928	+	0.466928i
$807$		−	44710.0i		−	0.0686527i
$808$	−17854.3	+	17854.3i	−0.0273476	+	0.0273476i
$809$	33849.8	−	33849.8i	0.0517201	−	0.0517201i	−0.680774	−	0.732494i	$-0.738356\pi$
$809$	33849.8	−	33849.8i	0.0517201	−	0.0517201i	0.732494	+	0.680774i	$0.238356\pi$
$810$	978036.			1.49068
$811$	−1.22028e6			−1.85531			−0.927655	−	0.373438i	$-0.878179\pi$
$811$	−1.22028e6			−1.85531			−0.927655	+	0.373438i	$0.878179\pi$
$812$	−27593.9	−	27593.9i	−0.0418506	−	0.0418506i
$813$		−	810524.i		−	1.22627i
$814$	2183.30	−	42519.1i	0.00329508	−	0.0641704i
$815$	−578449.			−0.870863
$816$	−232279.	+	232279.i	−0.348843	+	0.348843i
$817$			126903.i			0.190119i
$818$			39623.9i			0.0592175i
$819$	−163775.	−	163775.i	−0.244164	−	0.244164i
$820$	−756853.	−	756853.i	−1.12560	−	1.12560i
$821$	1.01541e6			1.50646			0.753228	−	0.657759i	$-0.228496\pi$
$821$	1.01541e6			1.50646			0.753228	+	0.657759i	$0.228496\pi$
$822$	711559.	+	711559.i	1.05309	+	1.05309i
$823$	127016.			0.187525			0.0937626	−	0.995595i	$-0.470111\pi$
$823$	127016.			0.187525			0.0937626	+	0.995595i	$0.470111\pi$
$824$	410679.			0.604851
$825$			139357.i			0.204748i
$826$	−980747.			−1.43746
$827$	−569137.	−	569137.i	−0.832158	−	0.832158i	0.155654	−	0.987812i	$-0.450251\pi$
$827$	−569137.	−	569137.i	−0.832158	−	0.832158i	−0.987812	+	0.155654i	$0.950251\pi$
$828$	140026.	−	140026.i	0.204243	−	0.204243i
$829$	709253.	−	709253.i	1.03203	−	1.03203i	0.0325599	−	0.999470i	$-0.489634\pi$
$829$	709253.	−	709253.i	1.03203	−	1.03203i	0.999470	−	0.0325599i	$-0.0103660\pi$
$830$	185161.			0.268777
$831$	436855.	+	436855.i	0.632608	+	0.632608i
$832$	−40966.4	+	40966.4i	−0.0591808	+	0.0591808i
$833$	−816563.	−	816563.i	−1.17679	−	1.17679i
$834$	345523.	−	345523.i	0.496758	−	0.496758i
$835$		−	896969.i		−	1.28648i
$836$	−10686.2	−	10686.2i	−0.0152901	−	0.0152901i
$837$	511983.	+	511983.i	0.730810	+	0.730810i
$838$	565897.	−	565897.i	0.805842	−	0.805842i
$839$		−	69380.4i		−	0.0985628i	−0.998785	−	0.0492814i	$-0.984307\pi$
$839$		−	69380.4i		−	0.0985628i	0.998785	−	0.0492814i	$-0.0156931\pi$
$840$	−703015.			−0.996337
$841$			702290.i			0.992944i
$842$			160776.i			0.226775i
$843$	−979317.	+	979317.i	−1.37806	+	1.37806i
$844$			560812.i			0.787285i
$845$	476622.	−	476622.i	0.667515	−	0.667515i
$846$	18697.7	−	18697.7i	0.0261245	−	0.0261245i
$847$	1.00258e6			1.39750
$848$	252338.			0.350906
$849$	−472844.	−	472844.i	−0.655998	−	0.655998i
$850$			1.66296e6i			2.30168i
$851$	−58621.1	+	1.14162e6i	−0.0809459	+	1.57639i
$852$	−100560.			−0.138531
$853$	255981.	−	255981.i	0.351811	−	0.351811i	−0.508972	−	0.860783i	$-0.669974\pi$
$853$	255981.	−	255981.i	0.351811	−	0.351811i	0.860783	+	0.508972i	$0.169974\pi$
$854$		−	143467.i		−	0.196715i
$855$		−	217870.i		−	0.298034i
$856$	183564.	+	183564.i	0.250519	+	0.250519i
$857$	−648564.	−	648564.i	−0.883062	−	0.883062i	0.110782	−	0.993845i	$-0.464664\pi$
$857$	−648564.	−	648564.i	−0.883062	−	0.883062i	−0.993845	+	0.110782i	$0.964664\pi$
$858$	−37016.0			−0.0502822
$859$	−336909.	−	336909.i	−0.456589	−	0.456589i	0.440945	−	0.897534i	$-0.354643\pi$
$859$	−336909.	−	336909.i	−0.456589	−	0.456589i	−0.897534	+	0.440945i	$0.854643\pi$
$860$	252776.			0.341773
$861$	2.27162e6			3.06428
$862$		−	69794.5i		−	0.0939305i
$863$	1.20387e6			1.61643			0.808214	−	0.588889i	$-0.200434\pi$
$863$	1.20387e6			1.61643			0.808214	+	0.588889i	$0.200434\pi$
$864$	69145.4	+	69145.4i	0.0926266	+	0.0926266i
$865$	−1.59056e6	+	1.59056e6i	−2.12578	+	2.12578i
$866$	−339782.	+	339782.i	−0.453069	+	0.453069i
$867$	−1.62599e6			−2.16312
$868$	−523531.	−	523531.i	−0.694868	−	0.694868i
$869$	−20220.2	+	20220.2i	−0.0267761	+	0.0267761i
$870$	−63576.9	−	63576.9i	−0.0839964	−	0.0839964i
$871$	−298958.	+	298958.i	−0.394071	+	0.394071i
$872$			16899.5i			0.0222249i
$873$	119064.	+	119064.i	0.156226	+	0.156226i
$874$	286921.	+	286921.i	0.375612	+	0.375612i
$875$	−1.21120e6	+	1.21120e6i	−1.58197	+	1.58197i
$876$			101993.i			0.132911i
$877$	−918082.			−1.19367			−0.596833	−	0.802366i	$-0.703574\pi$
$877$	−918082.			−1.19367			−0.596833	+	0.802366i	$0.703574\pi$
$878$			632884.i			0.820985i
$879$		−	569282.i		−	0.736800i
$880$	−21285.7	+	21285.7i	−0.0274867	+	0.0274867i
$881$		−	325184.i		−	0.418965i	−0.977812	−	0.209482i	$-0.932822\pi$
$881$		−	325184.i		−	0.418965i	0.977812	−	0.209482i	$-0.0671779\pi$
$882$	140312.	−	140312.i	0.180367	−	0.180367i
$883$	383849.	−	383849.i	0.492310	−	0.492310i	−0.416723	−	0.909033i	$-0.636822\pi$
$883$	383849.	−	383849.i	0.492310	−	0.492310i	0.909033	+	0.416723i	$0.136822\pi$
$884$	−441717.			−0.565248
$885$	−2.25966e6			−2.88507
$886$	−346288.	−	346288.i	−0.441133	−	0.441133i
$887$			204051.i			0.259353i	0.991556	+	0.129676i	$0.0413939\pi$
$887$			204051.i			0.259353i	−0.991556	+	0.129676i	$0.958606\pi$
$888$	325410.	+	16709.4i	0.412672	+	0.0211903i
$889$	1.06561e6			1.34832
$890$	618879.	−	618879.i	0.781315	−	0.781315i
$891$			88879.4i			0.111956i
$892$		−	198200.i		−	0.249101i
$893$	38312.7	+	38312.7i	0.0480441	+	0.0480441i
$894$	−450332.	−	450332.i	−0.563453	−	0.563453i
$895$	−401906.			−0.501739
$896$	−70704.9	−	70704.9i	−0.0880711	−	0.0880711i
$897$	993868.			1.23522
$898$	984615.			1.22099
$899$		−	94690.5i		−	0.117162i
$900$	−285751.			−0.352779
$901$	1.36040e6	+	1.36040e6i	1.67579	+	1.67579i
$902$	68779.3	−	68779.3i	0.0845366	−	0.0845366i
$903$	−379340.	+	379340.i	−0.465215	+	0.465215i
$904$	125790.			0.153925
$905$	−152962.	−	152962.i	−0.186761	−	0.186761i
$906$	245923.	−	245923.i	0.299600	−	0.299600i
$907$	299575.	+	299575.i	0.364158	+	0.364158i	0.865341	−	0.501183i	$-0.167102\pi$
$907$	299575.	+	299575.i	0.364158	+	0.364158i	−0.501183	+	0.865341i	$0.667102\pi$
$908$	−112935.	+	112935.i	−0.136980	+	0.136980i
$909$		−	33079.9i		−	0.0400346i
$910$	−668448.	−	668448.i	−0.807207	−	0.807207i
$911$	227135.	+	227135.i	0.273683	+	0.273683i	0.830581	−	0.556898i	$-0.188009\pi$
$911$	227135.	+	227135.i	0.273683	+	0.273683i	−0.556898	+	0.830581i	$0.688009\pi$
$912$	81784.4	−	81784.4i	0.0983288	−	0.0983288i
$913$			16826.6i			0.0201862i
$914$	587254.			0.702965
$915$		−	330551.i		−	0.394817i
$916$		−	113799.i		−	0.135628i
$917$	962525.	−	962525.i	1.14465	−	1.14465i
$918$			745554.i			0.884695i
$919$	548658.	−	548658.i	0.649636	−	0.649636i	−0.303269	−	0.952905i	$-0.598078\pi$
$919$	548658.	−	548658.i	0.649636	−	0.649636i	0.952905	+	0.303269i	$0.0980780\pi$
$920$	571514.	−	571514.i	0.675229	−	0.675229i
$921$	−23434.8			−0.0276276
$922$	−221182.			−0.260189
$923$	−95615.8	−	95615.8i	−0.112234	−	0.112234i
$924$		−	63886.8i		−	0.0748285i
$925$	1.22467e6	−	1.10504e6i	1.43132	−	1.29151i
$926$	−495985.			−0.578425
$927$	−380447.	+	380447.i	−0.442726	+	0.442726i
$928$		−	12788.3i		−	0.0148497i
$929$			580362.i			0.672461i	0.941780	+	0.336231i	$0.109152\pi$
$929$			580362.i			0.672461i	−0.941780	+	0.336231i	$0.890848\pi$
$930$	−1.20622e6	−	1.20622e6i	−1.39464	−	1.39464i
$931$	287508.	+	287508.i	0.331704	+	0.331704i
$932$	394476.			0.454139
$933$	−411769.	−	411769.i	−0.473031	−	0.473031i
$934$	145116.			0.166350
$935$	−229511.			−0.262531
$936$		−	75901.3i		−	0.0866358i
$937$	198322.			0.225888			0.112944	−	0.993601i	$-0.463972\pi$
$937$	198322.			0.225888			0.112944	+	0.993601i	$0.463972\pi$
$938$	−515980.	−	515980.i	−0.586444	−	0.586444i
$939$	−393663.	+	393663.i	−0.446471	+	0.446471i
$940$	76314.5	−	76314.5i	0.0863677	−	0.0863677i
$941$	66944.9			0.0756029			0.0378015	−	0.999285i	$-0.487965\pi$
$941$	66944.9			0.0756029			0.0378015	+	0.999285i	$0.487965\pi$
$942$	516617.	+	516617.i	0.582193	+	0.582193i
$943$	−1.84670e6	+	1.84670e6i	−2.07670	+	2.07670i
$944$	−227262.	−	227262.i	−0.255025	−	0.255025i
$945$	−1.12824e6	+	1.12824e6i	−1.26340	+	1.26340i
$946$			22971.1i			0.0256684i
$947$	470097.	+	470097.i	0.524189	+	0.524189i	0.918834	−	0.394645i	$-0.129132\pi$
$947$	470097.	+	470097.i	0.524189	+	0.524189i	−0.394645	+	0.918834i	$0.629132\pi$
$948$	−154751.	−	154751.i	−0.172194	−	0.172194i
$949$	−96978.2	+	96978.2i	−0.107682	+	0.107682i
$950$		−	585521.i		−	0.648777i
$951$	1.60040e6			1.76957
$952$		−	762370.i		−	0.841185i
$953$			754928.i			0.831227i	0.909541	+	0.415614i	$0.136433\pi$
$953$			754928.i			0.831227i	−0.909541	+	0.415614i	$0.863567\pi$
$954$	−233762.	+	233762.i	−0.256848	+	0.256848i
$955$			2.34097e6i			2.56678i
$956$	−307062.	+	307062.i	−0.335977	+	0.335977i
$957$	5777.57	−	5777.57i	0.00630844	−	0.00630844i
$958$	−10.7568			−1.17207e−5
$959$	−2.33542e6			−2.53939
$960$	−162905.	−	162905.i	−0.176763	−	0.176763i
$961$		−	873011.i		−	0.945307i
$962$	293522.	+	325298.i	0.317169	+	0.351505i
$963$	−340102.			−0.366739
$964$	−294102.	+	294102.i	−0.316479	+	0.316479i
$965$			2.57663e6i			2.76693i
$966$			1.71534e6i			1.83821i
$967$	493965.	+	493965.i	0.528255	+	0.528255i	0.920052	−	0.391797i	$-0.128146\pi$
$967$	493965.	+	493965.i	0.528255	+	0.528255i	−0.391797	+	0.920052i	$0.628146\pi$
$968$	232322.	+	232322.i	0.247936	+	0.247936i
$969$	881833.			0.939159
$970$	485961.	+	485961.i	0.516485	+	0.516485i
$971$	1.09081e6			1.15694			0.578468	−	0.815705i	$-0.303651\pi$
$971$	1.09081e6			1.15694			0.578468	+	0.815705i	$0.303651\pi$
$972$	−330171.			−0.349467
$973$			1.13405e6i			1.19786i
$974$	376703.			0.397082
$975$	−1.01410e6	−	1.01410e6i	−1.06677	−	1.06677i
$976$	33244.7	−	33244.7i	0.0348998	−	0.0348998i
$977$	−32964.0	+	32964.0i	−0.0345344	+	0.0345344i	−0.724163	−	0.689629i	$-0.757774\pi$
$977$	−32964.0	+	32964.0i	−0.0345344	+	0.0345344i	0.689629	+	0.724163i	$0.257774\pi$
$978$	402308.			0.420612
$979$	56240.9	+	56240.9i	0.0586796	+	0.0586796i
$980$	572683.	−	572683.i	0.596296	−	0.596296i
$981$	−15655.4	−	15655.4i	−0.0162677	−	0.0162677i
$982$	187838.	−	187838.i	0.194787	−	0.194787i
$983$			425911.i			0.440770i	0.975413	+	0.220385i	$0.0707314\pi$
$983$			425911.i			0.440770i	−0.975413	+	0.220385i	$0.929269\pi$
$984$	526387.	+	526387.i	0.543645	+	0.543645i
$985$	−1.15765e6	−	1.15765e6i	−1.19318	−	1.19318i
$986$	68944.6	−	68944.6i	0.0709163	−	0.0709163i
$987$			229050.i			0.235124i
$988$	155526.			0.159327
$989$		−	616767.i		−	0.630563i
$990$		−	39437.5i		−	0.0402382i
$991$	109337.	−	109337.i	0.111332	−	0.111332i	−0.649246	−	0.760578i	$-0.724916\pi$
$991$	109337.	−	109337.i	0.111332	−	0.111332i	0.760578	+	0.649246i	$0.224916\pi$
$992$		−	242629.i		−	0.246558i
$993$	856117.	−	856117.i	0.868229	−	0.868229i
$994$	165026.	−	165026.i	0.167024	−	0.167024i
$995$	−172775.			−0.174516
$996$	−128778.			−0.129815
$997$	−462380.	−	462380.i	−0.465167	−	0.465167i	0.435178	−	0.900345i	$-0.356686\pi$
$997$	−462380.	−	462380.i	−0.465167	−	0.465167i	−0.900345	+	0.435178i	$0.856686\pi$
$998$			104838.i			0.105258i
$999$	549056.	−	495423.i	0.550156	−	0.496415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.5.d.a.43.6	yes	14
37.31	odd	4	inner	74.5.d.a.31.2	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.d.a.31.2	✓	14	37.31	odd	4	inner
74.5.d.a.43.6	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)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 2.00000i) q^{2} +10.5188i q^{3} -8.00000i q^{4} +(30.2483 + 30.2483i) q^{5} +(-21.0375 - 21.0375i) q^{6} +69.0478 q^{7} +(16.0000 + 16.0000i) q^{8} -29.6443 q^{9} +O(q^{10})\)	\(q+(-2.00000 + 2.00000i) q^{2} +10.5188i q^{3} -8.00000i q^{4} +(30.2483 + 30.2483i) q^{5} +(-21.0375 - 21.0375i) q^{6} +69.0478 q^{7} +(16.0000 + 16.0000i) q^{8} -29.6443 q^{9} -120.993 q^{10} -10.9953i q^{11} +84.1501 q^{12} +(80.0125 + 80.0125i) q^{13} +(-138.096 + 138.096i) q^{14} +(-318.174 + 318.174i) q^{15} -64.0000 q^{16} +(-345.037 - 345.037i) q^{17} +(59.2886 - 59.2886i) q^{18} +(121.486 + 121.486i) q^{19} +(241.986 - 241.986i) q^{20} +726.297i q^{21} +(21.9906 + 21.9906i) q^{22} +(-590.441 - 590.441i) q^{23} +(-168.300 + 168.300i) q^{24} +1204.92i q^{25} -320.050 q^{26} +540.198i q^{27} -552.382i q^{28} +(49.9544 - 49.9544i) q^{29} -1272.70i q^{30} +(947.769 - 947.769i) q^{31} +(128.000 - 128.000i) q^{32} +115.657 q^{33} +1380.15 q^{34} +(2088.58 + 2088.58i) q^{35} +237.155i q^{36} +(-917.114 - 1016.40i) q^{37} -485.944 q^{38} +(-841.632 + 841.632i) q^{39} +967.945i q^{40} -3127.67i q^{41} +(-1452.59 - 1452.59i) q^{42} +(522.294 + 522.294i) q^{43} -87.9624 q^{44} +(-896.689 - 896.689i) q^{45} +2361.76 q^{46} +315.367 q^{47} -673.201i q^{48} +2366.59 q^{49} +(-2409.83 - 2409.83i) q^{50} +(3629.36 - 3629.36i) q^{51} +(640.100 - 640.100i) q^{52} -3942.78 q^{53} +(-1080.40 - 1080.40i) q^{54} +(332.589 - 332.589i) q^{55} +(1104.76 + 1104.76i) q^{56} +(-1277.88 + 1277.88i) q^{57} +199.818i q^{58} +(3550.97 + 3550.97i) q^{59} +(2545.39 + 2545.39i) q^{60} +(-519.449 + 519.449i) q^{61} +3791.08i q^{62} -2046.87 q^{63} +512.000i q^{64} +4840.48i q^{65} +(-231.314 + 231.314i) q^{66} +3736.40i q^{67} +(-2760.30 + 2760.30i) q^{68} +(6210.71 - 6210.71i) q^{69} -8354.30 q^{70} -1195.01 q^{71} +(-474.309 - 474.309i) q^{72} +1212.04i q^{73} +(3867.02 + 198.567i) q^{74} -12674.2 q^{75} +(971.887 - 971.887i) q^{76} -759.201i q^{77} -3366.53i q^{78} +(-1838.99 - 1838.99i) q^{79} +(-1935.89 - 1935.89i) q^{80} -8083.40 q^{81} +(6255.34 + 6255.34i) q^{82} -1530.34 q^{83} +5810.37 q^{84} -20873.6i q^{85} -2089.17 q^{86} +(525.459 + 525.459i) q^{87} +(175.925 - 175.925i) q^{88} +(-5115.00 + 5115.00i) q^{89} +3586.76 q^{90} +(5524.68 + 5524.68i) q^{91} +(-4723.53 + 4723.53i) q^{92} +(9969.36 + 9969.36i) q^{93} +(-630.735 + 630.735i) q^{94} +7349.48i q^{95} +(1346.40 + 1346.40i) q^{96} +(-4016.43 - 4016.43i) q^{97} +(-4733.19 + 4733.19i) q^{98} +325.948i 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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