LMFDB - Embedded newform 76.6.d.a.75.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(75,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("76.75");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.3
Character	$\chi$	$=$	76.75
Dual form			76.6.d.a.75.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.48835 - 1.37043i) q^{2} -24.7554 q^{3} +(28.2439 + 15.0427i) q^{4} -13.4021 q^{5} +(135.866 + 33.9254i) q^{6} -215.359i q^{7} +(-134.397 - 121.266i) q^{8} +369.829 q^{9} +O(q^{10})$	\(q+(-5.48835 - 1.37043i) q^{2} -24.7554 q^{3} +(28.2439 + 15.0427i) q^{4} -13.4021 q^{5} +(135.866 + 33.9254i) q^{6} -215.359i q^{7} +(-134.397 - 121.266i) q^{8} +369.829 q^{9} +(73.5554 + 18.3666i) q^{10} -160.652i q^{11} +(-699.187 - 372.389i) q^{12} -824.882i q^{13} +(-295.133 + 1181.96i) q^{14} +331.774 q^{15} +(571.432 + 849.731i) q^{16} -1094.85 q^{17} +(-2029.75 - 506.823i) q^{18} +(1267.44 + 932.578i) q^{19} +(-378.528 - 201.605i) q^{20} +5331.28i q^{21} +(-220.161 + 881.711i) q^{22} +1264.89i q^{23} +(3327.05 + 3001.98i) q^{24} -2945.38 q^{25} +(-1130.44 + 4527.24i) q^{26} -3139.69 q^{27} +(3239.58 - 6082.56i) q^{28} -2176.61i q^{29} +(-1820.89 - 454.672i) q^{30} -6317.93 q^{31} +(-1971.72 - 5446.72i) q^{32} +3976.99i q^{33} +(6008.92 + 1500.41i) q^{34} +2886.26i q^{35} +(10445.4 + 5563.24i) q^{36} +2808.31i q^{37} +(-5678.10 - 6855.24i) q^{38} +20420.3i q^{39} +(1801.21 + 1625.22i) q^{40} +3920.51i q^{41} +(7306.13 - 29259.9i) q^{42} -23566.5i q^{43} +(2416.64 - 4537.42i) q^{44} -4956.49 q^{45} +(1733.44 - 6942.16i) q^{46} +13222.8i q^{47} +(-14146.0 - 21035.4i) q^{48} -29572.3 q^{49} +(16165.3 + 4036.43i) q^{50} +27103.4 q^{51} +(12408.5 - 23297.9i) q^{52} +29078.8i q^{53} +(17231.7 + 4302.72i) q^{54} +2153.07i q^{55} +(-26115.7 + 28943.6i) q^{56} +(-31375.9 - 23086.3i) q^{57} +(-2982.88 + 11946.0i) q^{58} -12958.9 q^{59} +(9370.59 + 4990.80i) q^{60} +29511.1 q^{61} +(34675.0 + 8658.26i) q^{62} -79645.8i q^{63} +(3357.16 + 32595.6i) q^{64} +11055.2i q^{65} +(5450.17 - 21827.1i) q^{66} +40914.1 q^{67} +(-30922.8 - 16469.6i) q^{68} -31312.9i q^{69} +(3955.41 - 15840.8i) q^{70} +29665.8 q^{71} +(-49703.9 - 44847.6i) q^{72} -20931.6 q^{73} +(3848.58 - 15413.0i) q^{74} +72914.1 q^{75} +(21768.8 + 45405.3i) q^{76} -34597.7 q^{77} +(27984.5 - 112073. i) q^{78} -49079.6 q^{79} +(-7658.39 - 11388.2i) q^{80} -12144.1 q^{81} +(5372.77 - 21517.1i) q^{82} +120076. i q^{83} +(-80197.1 + 150576. i) q^{84} +14673.3 q^{85} +(-32296.2 + 129341. i) q^{86} +53882.7i q^{87} +(-19481.6 + 21591.1i) q^{88} +37154.3i q^{89} +(27202.9 + 6792.50i) q^{90} -177645. q^{91} +(-19027.4 + 35725.4i) q^{92} +156403. q^{93} +(18120.9 - 72571.4i) q^{94} +(-16986.3 - 12498.5i) q^{95} +(48810.7 + 134836. i) q^{96} +89114.7i q^{97} +(162303. + 40526.7i) q^{98} -59413.6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9}+O(q^{10}) $ 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9	$ 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9} - 1222 q^{16} + 1000 q^{17} - 300 q^{20} + 17158 q^{24} + 24996 q^{25} + 12102 q^{26} + 6382 q^{28} - 16528 q^{30} + 27524 q^{36} + 3598 q^{38} + 35966 q^{42} - 65408 q^{44} - 13476 q^{45} - 143096 q^{49} - 148446 q^{54} - 53980 q^{57} - 117018 q^{58} + 133740 q^{61} + 28068 q^{62} - 78130 q^{64} + 128204 q^{66} - 48338 q^{68} - 104080 q^{73} + 48932 q^{74} - 251688 q^{76} + 184844 q^{77} + 80080 q^{80} + 375128 q^{81} + 175628 q^{82} - 384748 q^{85} + 139810 q^{92} + 183272 q^{93} + 601258 q^{96}+O(q^{100}) $ 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9 - 1222 * q^16 + 1000 * q^17 - 300 * q^20 + 17158 * q^24 + 24996 * q^25 + 12102 * q^26 + 6382 * q^28 - 16528 * q^30 + 27524 * q^36 + 3598 * q^38 + 35966 * q^42 - 65408 * q^44 - 13476 * q^45 - 143096 * q^49 - 148446 * q^54 - 53980 * q^57 - 117018 * q^58 + 133740 * q^61 + 28068 * q^62 - 78130 * q^64 + 128204 * q^66 - 48338 * q^68 - 104080 * q^73 + 48932 * q^74 - 251688 * q^76 + 184844 * q^77 + 80080 * q^80 + 375128 * q^81 + 175628 * q^82 - 384748 * q^85 + 139810 * q^92 + 183272 * q^93 + 601258 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$39$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−5.48835	−	1.37043i	−0.970212	−	0.242259i
$2$	−5.48835	−	1.37043i	−0.970212	−	0.242259i
$3$	−24.7554			−1.58806			−0.794029	−	0.607880i	$-0.792020\pi$
$3$	−24.7554			−1.58806			−0.794029	+	0.607880i	$0.792020\pi$
$4$	28.2439	+	15.0427i	0.882621	+	0.470086i
$5$	−13.4021			−0.239744			−0.119872	−	0.992789i	$-0.538248\pi$
$5$	−13.4021			−0.239744			−0.119872	+	0.992789i	$0.538248\pi$
$6$	135.866	+	33.9254i	1.54075	+	0.384722i
$7$		−	215.359i		−	1.66118i	−0.556883	−	0.830591i	$-0.688003\pi$
$7$		−	215.359i		−	1.66118i	0.556883	−	0.830591i	$-0.311997\pi$
$8$	−134.397	−	121.266i	−0.742446	−	0.669906i
$9$	369.829			1.52193
$10$	73.5554	+	18.3666i	0.232603	+	0.0580803i
$11$		−	160.652i		−	0.400316i	−0.979764	−	0.200158i	$-0.935854\pi$
$11$		−	160.652i		−	0.400316i	0.979764	−	0.200158i	$-0.0641456\pi$
$12$	−699.187	−	372.389i	−1.40165	−	0.746524i
$13$		−	824.882i		−	1.35373i	−0.736105	−	0.676867i	$-0.763337\pi$
$13$		−	824.882i		−	1.35373i	0.736105	−	0.676867i	$-0.236663\pi$
$14$	−295.133	+	1181.96i	−0.402437	+	1.61170i
$15$	331.774			0.380728
$16$	571.432	+	849.731i	0.558039	+	0.829815i
$17$	−1094.85			−0.918824			−0.459412	−	0.888223i	$-0.651940\pi$
$17$	−1094.85			−0.918824			−0.459412	+	0.888223i	$0.651940\pi$
$18$	−2029.75	−	506.823i	−1.47659	−	0.368702i
$19$	1267.44	+	932.578i	0.805457	+	0.592654i
$19$	1267.44	+	932.578i	0.805457	+	0.592654i
$20$	−378.528	−	201.605i	−0.211603	−	0.112700i
$21$			5331.28i			2.63805i
$22$	−220.161	+	881.711i	−0.0969804	+	0.388391i
$23$			1264.89i			0.498579i	0.968429	+	0.249289i	$0.0801970\pi$
$23$			1264.89i			0.498579i	−0.968429	+	0.249289i	$0.919803\pi$
$24$	3327.05	+	3001.98i	1.17905	+	1.06385i
$25$	−2945.38			−0.942523
$26$	−1130.44	+	4527.24i	−0.327955	+	1.31341i
$27$	−3139.69			−0.828854
$28$	3239.58	−	6082.56i	0.780898	−	1.46619i
$29$		−	2176.61i		−	0.480602i	−0.970698	−	0.240301i	$-0.922754\pi$
$29$		−	2176.61i		−	0.480602i	0.970698	−	0.240301i	$-0.0772461\pi$
$30$	−1820.89	−	454.672i	−0.369387	−	0.0922349i
$31$	−6317.93			−1.18079			−0.590393	−	0.807116i	$-0.701027\pi$
$31$	−6317.93			−1.18079			−0.590393	+	0.807116i	$0.701027\pi$
$32$	−1971.72	−	5446.72i	−0.340385	−	0.940286i
$33$			3976.99i			0.635725i
$34$	6008.92	+	1500.41i	0.891454	+	0.222594i
$35$			2886.26i			0.398259i
$36$	10445.4	+	5563.24i	1.34329	+	0.715437i
$37$			2808.31i			0.337241i	0.985681	+	0.168621i	$0.0539313\pi$
$37$			2808.31i			0.337241i	−0.985681	+	0.168621i	$0.946069\pi$
$38$	−5678.10	−	6855.24i	−0.637888	−	0.770129i
$39$			20420.3i			2.14981i
$40$	1801.21	+	1625.22i	0.177997	+	0.160606i
$41$			3920.51i			0.364236i	0.983277	+	0.182118i	$0.0582953\pi$
$41$			3920.51i			0.364236i	−0.983277	+	0.182118i	$0.941705\pi$
$42$	7306.13	−	29259.9i	0.639093	−	2.55947i
$43$		−	23566.5i		−	1.94368i	−0.235644	−	0.971839i	$-0.575720\pi$
$43$		−	23566.5i		−	1.94368i	0.235644	−	0.971839i	$-0.424280\pi$
$44$	2416.64	−	4537.42i	0.188183	−	0.353327i
$45$	−4956.49			−0.364874
$46$	1733.44	−	6942.16i	0.120785	−	0.483727i
$47$			13222.8i			0.873131i	0.899672	+	0.436566i	$0.143805\pi$
$47$			13222.8i			0.873131i	−0.899672	+	0.436566i	$0.856195\pi$
$48$	−14146.0	−	21035.4i	−0.886198	−	1.31779i
$49$	−29572.3			−1.75952
$50$	16165.3	+	4036.43i	0.914446	+	0.228335i
$51$	27103.4			1.45915
$52$	12408.5	−	23297.9i	0.636371	−	1.19483i
$53$			29078.8i			1.42196i	0.703214	+	0.710979i	$0.251748\pi$
$53$			29078.8i			1.42196i	−0.703214	+	0.710979i	$0.748252\pi$
$54$	17231.7	+	4302.72i	0.804163	+	0.200798i
$55$			2153.07i			0.0959735i
$56$	−26115.7	+	28943.6i	−1.11284	+	1.23334i
$57$	−31375.9	−	23086.3i	−1.27911	−	0.941169i
$58$	−2982.88	+	11946.0i	−0.116430	+	0.466285i
$59$	−12958.9			−0.484662			−0.242331	−	0.970194i	$-0.577912\pi$
$59$	−12958.9			−0.484662			−0.242331	+	0.970194i	$0.577912\pi$
$60$	9370.59	+	4990.80i	0.336038	+	0.178975i
$61$	29511.1			1.01546			0.507728	−	0.861518i	$-0.330486\pi$
$61$	29511.1			1.01546			0.507728	+	0.861518i	$0.330486\pi$
$62$	34675.0	+	8658.26i	1.14561	+	0.286056i
$63$		−	79645.8i		−	2.52820i
$64$	3357.16	+	32595.6i	0.102452	+	0.994738i
$65$			11055.2i			0.324550i
$66$	5450.17	−	21827.1i	0.154010	−	0.616788i
$67$	40914.1			1.11349			0.556745	−	0.830683i	$-0.312050\pi$
$67$	40914.1			1.11349			0.556745	+	0.830683i	$0.312050\pi$
$68$	−30922.8	−	16469.6i	−0.810973	−	0.431926i
$69$		−	31312.9i		−	0.791772i
$70$	3955.41	−	15840.8i	0.0964820	−	0.386395i
$71$	29665.8			0.698409			0.349204	−	0.937047i	$-0.386452\pi$
$71$	29665.8			0.698409			0.349204	+	0.937047i	$0.386452\pi$
$72$	−49703.9	−	44847.6i	−1.12995	−	1.01955i
$73$	−20931.6			−0.459722			−0.229861	−	0.973223i	$-0.573827\pi$
$73$	−20931.6			−0.459722			−0.229861	+	0.973223i	$0.573827\pi$
$74$	3848.58	−	15413.0i	0.0816999	−	0.327195i
$75$	72914.1			1.49678
$76$	21768.8	+	45405.3i	0.432315	+	0.901723i
$77$	−34597.7			−0.664998
$78$	27984.5	−	112073.i	0.520811	−	2.08577i
$79$	−49079.6			−0.884777			−0.442388	−	0.896824i	$-0.645869\pi$
$79$	−49079.6			−0.884777			−0.442388	+	0.896824i	$0.645869\pi$
$80$	−7658.39	−	11388.2i	−0.133787	−	0.198943i
$81$	−12144.1			−0.205661
$82$	5372.77	−	21517.1i	0.0882396	−	0.353386i
$83$			120076.i			1.91320i	0.291402	+	0.956601i	$0.405878\pi$
$83$			120076.i			1.91320i	−0.291402	+	0.956601i	$0.594122\pi$
$84$	−80197.1	+	150576.i	−1.24011	+	2.32840i
$85$	14673.3			0.220283
$86$	−32296.2	+	129341.i	−0.470875	+	1.88578i
$87$			53882.7i			0.763223i
$88$	−19481.6	+	21591.1i	−0.268174	+	0.297213i
$89$			37154.3i			0.497204i	0.968606	+	0.248602i	$0.0799710\pi$
$89$			37154.3i			0.497204i	−0.968606	+	0.248602i	$0.920029\pi$
$90$	27202.9	+	6792.50i	0.354005	+	0.0883941i
$91$	−177645.			−2.24880
$92$	−19027.4	+	35725.4i	−0.234375	+	0.440056i
$93$	156403.			1.87516
$94$	18120.9	−	72571.4i	0.211524	−	0.847122i
$95$	−16986.3	−	12498.5i	−0.193104	−	0.142085i
$96$	48810.7	+	134836.i	0.540551	+	1.49323i
$97$			89114.7i			0.961657i	0.876815	+	0.480828i	$0.159664\pi$
$97$			89114.7i			0.961657i	−0.876815	+	0.480828i	$0.840336\pi$
$98$	162303.	+	40526.7i	1.70711	+	0.426261i
$99$		−	59413.6i		−	0.609253i
$100$	−83189.0	−	44306.7i	−0.831890	−	0.443067i
$101$	115423.			1.12587			0.562936	−	0.826500i	$-0.309672\pi$
$101$	115423.			1.12587			0.562936	+	0.826500i	$0.309672\pi$
$102$	−148753.	−	37143.3i	−1.41568	−	0.353492i
$103$	−63318.0			−0.588076			−0.294038	−	0.955794i	$-0.594999\pi$
$103$	−63318.0			−0.588076			−0.294038	+	0.955794i	$0.594999\pi$
$104$	−100030.	+	110862.i	−0.906874	+	1.00507i
$105$		−	71450.5i		−	0.632458i
$106$	39850.3	−	159594.i	0.344483	−	1.37960i
$107$	−189691.			−1.60172			−0.800862	−	0.598849i	$-0.795625\pi$
$107$	−189691.			−1.60172			−0.800862	+	0.598849i	$0.795625\pi$
$108$	−88677.1	−	47229.6i	−0.731563	−	0.389632i
$109$		−	31653.5i		−	0.255186i	−0.991827	−	0.127593i	$-0.959275\pi$
$109$		−	31653.5i		−	0.255186i	0.991827	−	0.127593i	$-0.0407251\pi$
$110$	2950.62	−	11816.8i	0.0232505	−	0.0931146i
$111$		−	69520.8i		−	0.535559i
$112$	182997.	−	123063.i	1.37847	−	0.927004i
$113$		−	103849.i		−	0.765079i	−0.923939	−	0.382540i	$-0.875050\pi$
$113$		−	103849.i		−	0.765079i	0.923939	−	0.382540i	$-0.124950\pi$
$114$	140564.	+	169704.i	1.01300	+	1.22301i
$115$		−	16952.2i		−	0.119531i
$116$	32742.2	−	61475.8i	0.225924	−	0.424189i
$117$		−	305065.i		−	2.06029i
$118$	71123.1	+	17759.3i	0.470225	+	0.117414i
$119$			235785.i			1.52633i
$120$	−44589.5	−	40232.9i	−0.282670	−	0.255052i
$121$	135242.			0.839747
$122$	−161967.	−	40442.8i	−0.985207	−	0.246004i
$123$		−	97053.7i		−	0.578428i
$124$	−178443.	−	95039.1i	−1.04219	−	0.555070i
$125$	81356.0			0.465709
$126$	−109149.	+	437124.i	−0.612480	+	2.45289i
$127$	343880.			1.89190			0.945949	−	0.324314i	$-0.105134\pi$
$127$	343880.			1.89190			0.945949	+	0.324314i	$0.105134\pi$
$128$	26244.6	−	183496.i	0.141584	−	0.989926i
$129$			583398.i			3.08668i
$130$	15150.3	−	60674.6i	0.0786253	−	0.314882i
$131$		−	271035.i		−	1.37990i	−0.723858	−	0.689949i	$-0.757633\pi$
$131$		−	271035.i		−	1.37990i	0.723858	−	0.689949i	$-0.242367\pi$
$132$	−59824.8	+	112326.i	−0.298845	+	0.561104i
$133$	200839.	−	272953.i	0.984506	−	1.33801i
$134$	−224551.	−	56069.8i	−1.08032	−	0.269754i
$135$	42078.5			0.198713
$136$	147145.	+	132768.i	0.682177	+	0.615526i
$137$	−168009.			−0.764770			−0.382385	−	0.924003i	$-0.624897\pi$
$137$	−168009.			−0.764770			−0.382385	+	0.924003i	$0.624897\pi$
$138$	−42912.0	+	171856.i	−0.191814	+	0.768186i
$139$			113381.i			0.497739i	0.968537	+	0.248869i	$0.0800590\pi$
$139$			113381.i			0.497739i	−0.968537	+	0.248869i	$0.919941\pi$
$140$	−43417.3	+	81519.2i	−0.187216	+	0.351512i
$141$		−	327336.i		−	1.38658i
$142$	−162816.	−	40654.7i	−0.677604	−	0.169196i
$143$	−132519.			−0.541922
$144$	211332.	+	314255.i	0.849295	+	1.26292i
$145$			29171.1i			0.115222i
$146$	114880.	+	28685.2i	0.446028	+	0.111372i
$147$	732074.			2.79423
$148$	−42244.7	+	79317.5i	−0.158532	+	0.297656i
$149$	−196959.			−0.726793			−0.363397	−	0.931635i	$-0.618383\pi$
$149$	−196959.			−0.726793			−0.363397	+	0.931635i	$0.618383\pi$
$150$	−400178.	−	99923.4i	−1.45219	−	0.362609i
$151$	−97338.0			−0.347408			−0.173704	−	0.984798i	$-0.555574\pi$
$151$	−97338.0			−0.347408			−0.173704	+	0.984798i	$0.555574\pi$
$152$	−57249.9	−	279033.i	−0.200986	−	0.979594i
$153$	−404907.			−1.39839
$154$	189884.	+	47413.6i	0.645189	+	0.161102i
$155$	84673.7			0.283087
$156$	−307177.	+	576747.i	−1.01059	+	1.89747i
$157$	−178380.			−0.577559			−0.288779	−	0.957396i	$-0.593249\pi$
$157$	−178380.			−0.577559			−0.288779	+	0.957396i	$0.593249\pi$
$158$	269366.	+	67260.0i	0.858421	+	0.214346i
$159$		−	719856.i		−	2.25815i
$160$	26425.2	+	72997.6i	0.0816054	+	0.225428i
$161$	272405.			0.828230
$162$	66651.0	+	16642.6i	0.199535	+	0.0498234i
$163$		−	225104.i		−	0.663612i	−0.943348	−	0.331806i	$-0.892342\pi$
$163$		−	225104.i		−	0.663612i	0.943348	−	0.331806i	$-0.107658\pi$
$164$	−58975.2	+	110730.i	−0.171222	+	0.321482i
$165$		−	53300.1i		−	0.152412i
$166$	164555.	−	659018.i	0.463491	−	1.85621i
$167$	−418152.			−1.16023			−0.580113	−	0.814536i	$-0.696992\pi$
$167$	−418152.			−1.16023			−0.580113	+	0.814536i	$0.696992\pi$
$168$	646503.	−	716509.i	1.76725	−	1.95861i
$169$	−309137.			−0.832596
$170$	−80532.2	−	20108.7i	−0.213721	−	0.0533656i
$171$	468735.	+	344894.i	1.22585	+	0.901978i
$172$	354505.	−	665610.i	0.913696	−	1.71553i
$173$			405878.i			1.03105i	0.856874	+	0.515526i	$0.172403\pi$
$173$			405878.i			1.03105i	−0.856874	+	0.515526i	$0.827597\pi$
$174$	73842.3	−	295727.i	0.184898	−	0.740488i
$175$			634314.i			1.56570i
$176$	136511.	−	91801.4i	0.332188	−	0.223392i
$177$	320803.			0.769672
$178$	50917.3	−	203916.i	0.120452	−	0.482393i
$179$	−413112.			−0.963686			−0.481843	−	0.876258i	$-0.660032\pi$
$179$	−413112.			−0.963686			−0.481843	+	0.876258i	$0.660032\pi$
$180$	−139990.	−	74559.2i	−0.322045	−	0.171522i
$181$			6405.52i			0.0145331i	0.999974	+	0.00726654i	$0.00231303\pi$
$181$			6405.52i			0.0145331i	−0.999974	+	0.00726654i	$0.997687\pi$
$182$	974979.	+	243450.i	2.18181	+	0.544793i
$183$	−730559.			−1.61260
$184$	153388.	−	169998.i	0.334001	−	0.370168i
$185$		−	37637.3i		−	0.0808517i
$186$	−858393.	−	214339.i	−1.81930	−	0.454274i
$187$			175889.i			0.367820i
$188$	−198908.	+	373463.i	−0.410446	+	0.770644i
$189$			676160.i			1.37688i
$190$	76098.6	+	91874.7i	0.152930	+	0.184634i
$191$			704220.i			1.39677i	0.715722	+	0.698385i	$0.246098\pi$
$191$			704220.i			1.39677i	−0.715722	+	0.698385i	$0.753902\pi$
$192$	−83107.7	−	806916.i	−0.162700	−	1.57970i
$193$		−	319392.i		−	0.617208i	−0.951191	−	0.308604i	$-0.900138\pi$
$193$		−	319392.i		−	0.617208i	0.951191	−	0.308604i	$-0.0998617\pi$
$194$	122125.	−	489092.i	0.232970	−	0.933010i
$195$		−	273675.i		−	0.515404i
$196$	−835237.	−	444849.i	−1.55299	−	0.827127i
$197$	895503.			1.64400			0.822000	−	0.569488i	$-0.192858\pi$
$197$	895503.			1.64400			0.822000	+	0.569488i	$0.192858\pi$
$198$	−81421.9	+	326082.i	−0.147597	+	0.591104i
$199$		−	240134.i		−	0.429854i	−0.976630	−	0.214927i	$-0.931049\pi$
$199$		−	240134.i		−	0.429854i	0.976630	−	0.214927i	$-0.0689513\pi$
$200$	395851.	+	357175.i	0.699772	+	0.631401i
$201$	−1.01284e6			−1.76829
$202$	−633482.	−	158179.i	−1.09233	−	0.272753i
$203$	−468751.			−0.798366
$204$	765506.	+	407710.i	1.28787	+	0.685924i
$205$		−	52543.1i		−	0.0873235i
$206$	347511.	+	86772.6i	0.570559	+	0.142467i
$207$			467793.i			0.758801i
$208$	700927.	−	471364.i	1.12335	−	0.755436i
$209$	149820.	−	203616.i	0.237249	−	0.322437i
$210$	−97917.6	+	392145.i	−0.153219	+	0.613618i
$211$	238247.			0.368401			0.184201	−	0.982889i	$-0.441030\pi$
$211$	238247.			0.368401			0.184201	+	0.982889i	$0.441030\pi$
$212$	−437425.	+	821297.i	−0.668442	+	1.25505i
$213$	−734387.			−1.10911
$214$	1.04109e6	+	259958.i	1.55401	+	0.388033i
$215$			315841.i			0.465986i
$216$	421966.	+	380738.i	0.615379	+	0.555254i
$217$			1.36062e6i			1.96150i
$218$	−43378.9	+	173726.i	−0.0618211	+	0.247584i
$219$	518170.			0.730066
$220$	−32388.1	+	60811.0i	−0.0451158	+	0.0847082i
$221$			903122.i			1.24384i
$222$	−95273.1	+	381554.i	−0.129744	+	0.519605i
$223$	−410803.			−0.553187			−0.276593	−	0.960987i	$-0.589206\pi$
$223$	−410803.			−0.553187			−0.276593	+	0.960987i	$0.589206\pi$
$224$	−1.17300e6	+	424627.i	−1.56199	+	0.565441i
$225$	−1.08929e6			−1.43445
$226$	−142317.	+	569959.i	−0.185348	+	0.742289i
$227$	−610027.			−0.785750			−0.392875	−	0.919592i	$-0.628520\pi$
$227$	−610027.			−0.785750			−0.392875	+	0.919592i	$0.628520\pi$
$228$	−538894.	−	1.12403e6i	−0.686541	−	1.43199i
$229$	−1.50281e6			−1.89372			−0.946858	−	0.321653i	$-0.895762\pi$
$229$	−1.50281e6			−1.89372			−0.946858	+	0.321653i	$0.895762\pi$
$230$	−23231.8	+	93039.6i	−0.0289576	+	0.115971i
$231$	856479.			1.05606
$232$	−263948.	+	292530.i	−0.321958	+	0.356821i
$233$	231085.			0.278857			0.139429	−	0.990232i	$-0.455473\pi$
$233$	231085.			0.278857			0.139429	+	0.990232i	$0.455473\pi$
$234$	−418069.	+	1.67430e6i	−0.499124	+	1.99891i
$235$		−	177214.i		−	0.209328i
$236$	−366010.	−	194938.i	−0.427773	−	0.227833i
$237$	1.21499e6			1.40508
$238$	323127.	−	1.29407e6i	0.369769	−	1.48087i
$239$			260243.i			0.294703i	0.989084	+	0.147351i	$0.0470748\pi$
$239$			260243.i			0.294703i	−0.989084	+	0.147351i	$0.952925\pi$
$240$	189586.	+	281919.i	0.212461	+	0.315934i
$241$			962178.i			1.06712i	0.845763	+	0.533560i	$0.179146\pi$
$241$			962178.i			1.06712i	−0.845763	+	0.533560i	$0.820854\pi$
$242$	−742255.	−	185339.i	−0.814732	−	0.203437i
$243$	1.06358e6			1.15546
$244$	833508.	+	443928.i	0.896262	+	0.477351i
$245$	396332.			0.421836
$246$	−133005.	+	532664.i	−0.140130	+	0.561198i
$247$	769267.	−	1.04549e6i	0.802296	−	1.09037i
$248$	849112.	+	766150.i	0.876669	+	0.791015i
$249$		−	2.97252e6i		−	3.03828i
$250$	−446510.	−	111492.i	−0.451836	−	0.112822i
$251$		−	934319.i		−	0.936075i	−0.883708	−	0.468038i	$-0.844961\pi$
$251$		−	934319.i		−	0.936075i	0.883708	−	0.468038i	$-0.155039\pi$
$252$	1.19809e6	−	2.24950e6i	1.18847	−	2.23144i
$253$	203207.			0.199589
$254$	−1.88733e6	−	471263.i	−1.83554	−	0.458330i
$255$	−363243.			−0.349822
$256$	−395508.	+	971126.i	−0.377186	+	0.926138i
$257$		−	1.27125e6i		−	1.20060i	−0.799777	−	0.600298i	$-0.795049\pi$
$257$		−	1.27125e6i		−	1.20060i	0.799777	−	0.600298i	$-0.204951\pi$
$258$	799505.	−	3.20189e6i	0.747776	−	2.99473i
$259$	604794.			0.560219
$260$	−166300.	+	312241.i	−0.152566	+	0.286455i
$261$		−	804972.i		−	0.731441i
$262$	−371433.	+	1.48753e6i	−0.334293	+	1.33879i
$263$			1.05371e6i			0.939362i	0.882836	+	0.469681i	$0.155631\pi$
$263$			1.05371e6i			0.939362i	−0.882836	+	0.469681i	$0.844369\pi$
$264$	482273.	−	534496.i	0.425876	−	0.471992i
$265$		−	389717.i		−	0.340906i
$266$	−1.47634e6	+	1.22283e6i	−1.27932	+	1.05965i
$267$		−	919769.i		−	0.789588i
$268$	1.15557e6	+	615461.i	0.982790	+	0.523436i
$269$			1.94446e6i			1.63839i	0.573512	+	0.819197i	$0.305581\pi$
$269$			1.94446e6i			1.63839i	−0.573512	+	0.819197i	$0.694419\pi$
$270$	−230942.	−	57665.5i	−0.192794	−	0.0481401i
$271$		−	704818.i		−	0.582980i	−0.956574	−	0.291490i	$-0.905849\pi$
$271$		−	704818.i		−	0.582980i	0.956574	−	0.291490i	$-0.0941510\pi$
$272$	−625632.	−	930328.i	−0.512739	−	0.762454i
$273$	4.39768e6			3.57122
$274$	922091.	+	230244.i	0.741989	+	0.185273i
$275$			473180.i			0.377307i
$276$	471031.	−	884396.i	0.372201	−	0.698834i
$277$	−454116.			−0.355605			−0.177802	−	0.984066i	$-0.556899\pi$
$277$	−454116.			−0.355605			−0.177802	+	0.984066i	$0.556899\pi$
$278$	155380.	−	622272.i	0.120582	−	0.482912i
$279$	−2.33655e6			−1.79707
$280$	350005.	−	387905.i	0.266796	−	0.295686i
$281$		−	628624.i		−	0.474925i	−0.971397	−	0.237462i	$-0.923684\pi$
$281$		−	628624.i		−	0.474925i	0.971397	−	0.237462i	$-0.0763156\pi$
$282$	−448590.	+	1.79653e6i	−0.335913	+	1.34528i
$283$			782941.i			0.581116i	0.956857	+	0.290558i	$0.0938410\pi$
$283$			782941.i			0.581116i	−0.956857	+	0.290558i	$0.906159\pi$
$284$	837876.	+	446255.i	0.616430	+	0.328312i
$285$	420503.	+	309406.i	0.306660	+	0.225640i
$286$	727307.	+	181607.i	0.525779	+	0.131286i
$287$	844315.			0.605062
$288$	−729199.	−	2.01435e6i	−0.518042	−	1.43105i
$289$	−221160.			−0.155762
$290$	39976.9	−	160101.i	0.0279135	−	0.111789i
$291$		−	2.20607e6i		−	1.52717i
$292$	−591190.	−	314869.i	−0.405760	−	0.216109i
$293$		−	1.99737e6i		−	1.35922i	−0.733573	−	0.679610i	$-0.762149\pi$
$293$		−	1.99737e6i		−	1.35922i	0.733573	−	0.679610i	$-0.237851\pi$
$294$	−4.01787e6	−	1.00325e6i	−2.71099	−	0.676928i
$295$	173677.			0.116195
$296$	340552.	−	377429.i	0.225920	−	0.250384i
$297$			504397.i			0.331803i
$298$	1.08098e6	+	269918.i	0.705143	+	0.176072i
$299$	1.04339e6			0.674943
$300$	2.05938e6	+	1.09683e6i	1.32109	+	0.703615i
$301$	−5.07525e6			−3.22880
$302$	534225.	+	133395.i	0.337059	+	0.0841629i
$303$	−2.85734e6			−1.78795
$304$	−68186.8	+	1.60988e6i	−0.0423172	+	0.999104i
$305$	−395511.			−0.243450
$306$	2.22227e6	+	554895.i	1.35673	+	0.338772i
$307$	349471.			0.211624			0.105812	−	0.994386i	$-0.466256\pi$
$307$	349471.			0.211624			0.105812	+	0.994386i	$0.466256\pi$
$308$	−977172.	−	520444.i	−0.586941	−	0.312606i
$309$	1.56746e6			0.933900
$310$	−464718.	−	116039.i	−0.274654	−	0.0685804i
$311$			1.14364e6i			0.670481i	0.942133	+	0.335241i	$0.108818\pi$
$311$			1.14364e6i			0.670481i	−0.942133	+	0.335241i	$0.891182\pi$
$312$	2.47628e6	−	2.74442e6i	1.44017	−	1.59612i
$313$	−885295.			−0.510772			−0.255386	−	0.966839i	$-0.582203\pi$
$313$	−885295.			−0.510772			−0.255386	+	0.966839i	$0.582203\pi$
$314$	979009.	+	244456.i	0.560354	+	0.139919i
$315$			1.06742e6i			0.606122i
$316$	−1.38620e6	−	738293.i	−0.780922	−	0.415921i
$317$		−	1.73205e6i		−	0.968082i	−0.875045	−	0.484041i	$-0.839169\pi$
$317$		−	1.73205e6i		−	0.968082i	0.875045	−	0.484041i	$-0.160831\pi$
$318$	−986510.	+	3.95082e6i	−0.547058	+	2.19088i
$319$	−349675.			−0.192393
$320$	−44993.0	−	436850.i	−0.0245623	−	0.238483i
$321$	4.69588e6			2.54363
$322$	−1.49505e6	−	373311.i	−0.803558	−	0.200646i
$323$	−1.38765e6	−	1.02103e6i	−0.740073	−	0.544545i
$324$	−342996.	−	182680.i	−0.181521	−	0.0966784i
$325$			2.42959e6i			1.27593i
$326$	−308488.	+	1.23545e6i	−0.160766	+	0.643844i
$327$			783596.i			0.405250i
$328$	475424.	−	526905.i	0.244004	−	0.270426i
$329$	2.84765e6			1.45043
$330$	−73043.8	+	292529.i	−0.0369231	+	0.147871i
$331$	2.97911e6			1.49457			0.747286	−	0.664502i	$-0.231356\pi$
$331$	2.97911e6			1.49457			0.747286	+	0.664502i	$0.231356\pi$
$332$	−1.80627e6	+	3.39141e6i	−0.899369	+	1.68863i
$333$			1.03859e6i			0.513257i
$334$	2.29496e6	+	573046.i	1.12566	+	0.281076i
$335$	−548336.			−0.266953
$336$	−4.53015e6	+	3.04646e6i	−2.18910	+	1.47214i
$337$		−	2.30475e6i		−	1.10548i	−0.833355	−	0.552739i	$-0.813583\pi$
$337$		−	2.30475e6i		−	1.10548i	0.833355	−	0.552739i	$-0.186417\pi$
$338$	1.69665e6	+	423650.i	0.807795	+	0.201704i
$339$			2.57082e6i			1.21499i
$340$	414431.	+	220727.i	0.194426	+	0.103552i
$341$			1.01499e6i			0.472687i
$342$	−2.09993e6	−	2.53527e6i	−0.970820	−	1.17208i
$343$			2.74912e6i			1.26171i
$344$	−2.85782e6	+	3.16727e6i	−1.30208	+	1.44308i
$345$			419659.i			0.189823i
$346$	556226.	−	2.22760e6i	0.249782	−	1.00034i
$347$		−	3.90801e6i		−	1.74234i	−0.490985	−	0.871168i	$-0.663363\pi$
$347$		−	3.90801e6i		−	1.74234i	0.490985	−	0.871168i	$-0.336637\pi$
$348$	−810544.	+	1.52186e6i	−0.358780	+	0.673637i
$349$	1.46295e6			0.642935			0.321467	−	0.946921i	$-0.395824\pi$
$349$	1.46295e6			0.642935			0.321467	+	0.946921i	$0.395824\pi$
$350$	869280.	−	3.48133e6i	0.379306	−	1.51906i
$351$			2.58988e6i			1.12205i
$352$	−875024.	+	316760.i	−0.376412	+	0.136262i
$353$	−2.07983e6			−0.888362			−0.444181	−	0.895937i	$-0.646505\pi$
$353$	−2.07983e6			−0.888362			−0.444181	+	0.895937i	$0.646505\pi$
$354$	−1.76068e6	−	439637.i	−0.746744	−	0.186460i
$355$	−397584.			−0.167440
$356$	−558903.	+	1.04938e6i	−0.233728	+	0.438842i
$357$		−	5.83696e6i		−	2.42391i
$358$	2.26730e6	+	566140.i	0.934979	+	0.233462i
$359$		−	4.62111e6i		−	1.89239i	−0.323598	−	0.946195i	$-0.604893\pi$
$359$		−	4.62111e6i		−	1.89239i	0.323598	−	0.946195i	$-0.395107\pi$
$360$	666138.	+	601053.i	0.270899	+	0.244431i
$361$	736694.	+	2.36397e6i	0.297522	+	0.954715i
$362$	8778.29	−	35155.7i	0.00352078	−	0.0141002i
$363$	−3.34797e6			−1.33357
$364$	−5.01739e6	−	2.67227e6i	−1.98484	−	1.05713i
$365$	280528.			0.110216
$366$	4.00956e6	+	1.00118e6i	1.56457	+	0.390668i
$367$			752285.i			0.291553i	0.989318	+	0.145776i	$0.0465680\pi$
$367$			752285.i			0.291553i	−0.989318	+	0.145776i	$0.953432\pi$
$368$	−1.07482e6	+	722799.i	−0.413728	+	0.278226i
$369$			1.44992e6i			0.554341i
$370$	−51579.2	+	206567.i	−0.0195871	+	0.0784433i
$371$	6.26237e6			2.36213
$372$	4.41742e6	+	2.35273e6i	1.65505	+	0.881484i
$373$			2.12645e6i			0.791375i	0.918385	+	0.395687i	$0.129494\pi$
$373$			2.12645e6i			0.791375i	−0.918385	+	0.395687i	$0.870506\pi$
$374$	241043.	−	965342.i	0.0891079	−	0.356863i
$375$	−2.01400e6			−0.739573
$376$	1.60348e6	−	1.77711e6i	0.584916	−	0.648253i
$377$	−1.79544e6			−0.650607
$378$	926627.	−	3.71100e6i	0.333561	−	1.33586i
$379$	3.52543e6			1.26071			0.630354	−	0.776308i	$-0.282910\pi$
$379$	3.52543e6			1.26071			0.630354	+	0.776308i	$0.282910\pi$
$380$	−291748.	−	608528.i	−0.103645	−	0.216183i
$381$	−8.51288e6			−3.00445
$382$	965082.	−	3.86500e6i	0.338381	−	1.35516i
$383$	−2.98692e6			−1.04046			−0.520232	−	0.854025i	$-0.674154\pi$
$383$	−2.98692e6			−1.04046			−0.520232	+	0.854025i	$0.674154\pi$
$384$	−649695.	+	4.54252e6i	−0.224844	+	1.57206i
$385$	463682.			0.159429
$386$	−437704.	+	1.75294e6i	−0.149524	+	0.598822i
$387$		−	8.71558e6i		−	2.95814i
$388$	−1.34053e6	+	2.51694e6i	−0.452061	+	0.848778i
$389$	2.97650e6			0.997312			0.498656	−	0.866800i	$-0.333827\pi$
$389$	2.97650e6			0.997312			0.498656	+	0.866800i	$0.333827\pi$
$390$	−375051.	+	1.50202e6i	−0.124862	+	0.500051i
$391$		−	1.38487e6i		−	0.458106i
$392$	3.97443e6	+	3.58611e6i	1.30635	+	1.17872i
$393$			6.70957e6i			2.19136i
$394$	−4.91483e6	−	1.22722e6i	−1.59503	−	0.398274i
$395$	657771.			0.212120
$396$	893743.	−	1.67807e6i	0.286401	−	0.537739i
$397$	−2.05939e6			−0.655787			−0.327893	−	0.944715i	$-0.606339\pi$
$397$	−2.05939e6			−0.655787			−0.327893	+	0.944715i	$0.606339\pi$
$398$	−329086.	+	1.31794e6i	−0.104136	+	0.417049i
$399$	−4.97184e6	+	6.75707e6i	−1.56345	+	2.12484i
$400$	−1.68309e6	−	2.50278e6i	−0.525964	−	0.782119i
$401$		−	4.38823e6i		−	1.36279i	−0.731917	−	0.681394i	$-0.761374\pi$
$401$		−	4.38823e6i		−	1.36279i	0.731917	−	0.681394i	$-0.238626\pi$
$402$	5.55884e6	+	1.38803e6i	1.71561	+	0.428384i
$403$			5.21155e6i			1.59847i
$404$	3.25999e6	+	1.73628e6i	0.993718	+	0.529257i
$405$	162757.			0.0493061
$406$	2.57267e6	+	642389.i	0.774584	+	0.193412i
$407$	451159.			0.135003
$408$	−3.64262e6	−	3.28672e6i	−1.08334	−	0.977491i
$409$		−	1.48432e6i		−	0.438751i	−0.975641	−	0.219375i	$-0.929598\pi$
$409$		−	1.48432e6i		−	0.438751i	0.975641	−	0.219375i	$-0.0704020\pi$
$410$	−72006.5	+	288375.i	−0.0211550	+	0.0847223i
$411$	4.15913e6			1.21450
$412$	−1.78834e6	−	952476.i	−0.519048	−	0.276446i
$413$			2.79082e6i			0.805112i
$414$	641076.	−	2.56741e6i	0.183827	−	0.736198i
$415$		−	1.60927e6i		−	0.458679i
$416$	−4.49290e6	+	1.62644e6i	−1.27290	+	0.460791i
$417$		−	2.80678e6i		−	0.790438i
$418$	−1.10130e6	+	912196.i	−0.308295	+	0.255357i
$419$			3.61038e6i			1.00466i	0.864677	+	0.502329i	$0.167523\pi$
$419$			3.61038e6i			1.00466i	−0.864677	+	0.502329i	$0.832477\pi$
$420$	1.07481e6	−	2.01804e6i	0.297310	−	0.558221i
$421$			2.25698e6i			0.620616i	0.950636	+	0.310308i	$0.100432\pi$
$421$			2.25698e6i			0.620616i	−0.950636	+	0.310308i	$0.899568\pi$
$422$	−1.30758e6	−	326500.i	−0.357427	−	0.0892487i
$423$			4.89018e6i			1.32884i
$424$	3.52627e6	−	3.90810e6i	0.952578	−	1.05573i
$425$	3.22475e6			0.866013
$426$	4.03057e6	+	1.00642e6i	1.07607	+	0.268693i
$427$		−	6.35547e6i		−	1.68686i
$428$	−5.35761e6	−	2.85348e6i	−1.41371	−	0.752948i
$429$	3.28055e6			0.860603
$430$	432837.	−	1.73345e6i	0.112890	−	0.452105i
$431$	−2.39556e6			−0.621175			−0.310588	−	0.950545i	$-0.600526\pi$
$431$	−2.39556e6			−0.621175			−0.310588	+	0.950545i	$0.600526\pi$
$432$	−1.79412e6	−	2.66789e6i	−0.462532	−	0.687795i
$433$			5.97563e6i			1.53167i	0.643040	+	0.765833i	$0.277673\pi$
$433$			5.97563e6i			1.53167i	−0.643040	+	0.765833i	$0.722327\pi$
$434$	1.86463e6	−	7.46756e6i	0.475192	−	1.90307i
$435$		−	722143.i		−	0.182978i
$436$	476156.	−	894018.i	0.119959	−	0.225232i
$437$	−1.17961e6	+	1.60317e6i	−0.295485	+	0.401584i
$438$	−2.84390e6	−	710114.i	−0.708318	−	0.176865i
$439$	−4.71725e6			−1.16823			−0.584114	−	0.811672i	$-0.698558\pi$
$439$	−4.71725e6			−1.16823			−0.584114	+	0.811672i	$0.698558\pi$
$440$	261094.	−	289366.i	0.0642932	−	0.0712552i
$441$	−1.09367e7			−2.67787
$442$	1.23766e6	−	4.95665e6i	0.301333	−	1.20679i
$443$			5.71999e6i			1.38480i	0.721516	+	0.692398i	$0.243446\pi$
$443$			5.71999e6i			1.38480i	−0.721516	+	0.692398i	$0.756554\pi$
$444$	1.04578e6	−	1.96354e6i	0.251759	−	0.472695i
$445$		−	497946.i		−	0.119202i
$446$	2.25463e6	+	562976.i	0.536708	+	0.134015i
$447$	4.87580e6			1.15419
$448$	7.01974e6	−	722992.i	1.65244	−	0.170192i
$449$		−	4.01202e6i		−	0.939176i	−0.882886	−	0.469588i	$-0.844402\pi$
$449$		−	4.01202e6i		−	0.939176i	0.882886	−	0.469588i	$-0.155598\pi$
$450$	5.97838e6	+	1.49279e6i	1.39172	+	0.347510i
$451$	629836.			0.145810
$452$	1.56217e6	−	2.93310e6i	0.359653	−	0.675275i
$453$	2.40964e6			0.551705
$454$	3.34804e6	+	835997.i	0.762344	+	0.190355i
$455$	2.38082e6			0.539137
$456$	1.41724e6	+	6.90756e6i	0.319177	+	1.55565i
$457$	−6.67789e6			−1.49571			−0.747857	−	0.663860i	$-0.768917\pi$
$457$	−6.67789e6			−1.49571			−0.747857	+	0.663860i	$0.768917\pi$
$458$	8.24793e6	+	2.05949e6i	1.83730	+	0.458770i
$459$	3.43749e6			0.761571
$460$	255008.	−	478796.i	0.0561900	−	0.105501i
$461$	1.24399e6			0.272623			0.136312	−	0.990666i	$-0.456475\pi$
$461$	1.24399e6			0.272623			0.136312	+	0.990666i	$0.456475\pi$
$462$	−4.70065e6	−	1.17374e6i	−1.02460	−	0.255839i
$463$			1.81881e6i			0.394308i	0.980373	+	0.197154i	$0.0631699\pi$
$463$			1.81881e6i			0.394308i	−0.980373	+	0.197154i	$0.936830\pi$
$464$	1.84953e6	−	1.24378e6i	0.398810	−	0.268194i
$465$	−2.09613e6			−0.449558
$466$	−1.26827e6	−	316685.i	−0.270551	−	0.0675558i
$467$		−	3.54345e6i		−	0.751856i	−0.926649	−	0.375928i	$-0.877324\pi$
$467$		−	3.54345e6i		−	0.751856i	0.926649	−	0.375928i	$-0.122676\pi$
$468$	4.58902e6	−	8.61622e6i	0.968512	−	1.81845i
$469$		−	8.81121e6i		−	1.84971i
$470$	−242858.	+	972610.i	−0.0507117	+	0.203093i
$471$	4.41586e6			0.917197
$472$	1.74164e6	+	1.57148e6i	0.359836	+	0.324678i
$473$	−3.78600e6			−0.778086
$474$	−6.66826e6	−	1.66505e6i	−1.36322	−	0.340393i
$475$	−3.73309e6	−	2.74680e6i	−0.759161	−	0.558590i
$476$	−3.54686e6	+	6.65949e6i	−0.717508	+	1.34717i
$477$			1.07542e7i			2.16412i
$478$	356644.	−	1.42830e6i	0.0713945	−	0.285924i
$479$		−	3.67197e6i		−	0.731240i	−0.930764	−	0.365620i	$-0.880857\pi$
$479$		−	3.67197e6i		−	0.731240i	0.930764	−	0.365620i	$-0.119143\pi$
$480$	−654167.	−	1.80708e6i	−0.129594	−	0.357993i
$481$	2.31652e6			0.456535
$482$	1.31859e6	−	5.28077e6i	0.258520	−	1.03533i
$483$	−6.74349e6			−1.31528
$484$	3.81976e6	+	2.03441e6i	0.741178	+	0.394753i
$485$		−	1.19433e6i		−	0.230552i
$486$	−5.83728e6	−	1.45755e6i	−1.12104	−	0.279920i
$487$	793608.			0.151630			0.0758148	−	0.997122i	$-0.475844\pi$
$487$	793608.			0.151630			0.0758148	+	0.997122i	$0.475844\pi$
$488$	−3.96621e6	−	3.57869e6i	−0.753921	−	0.680260i
$489$			5.57253e6i			1.05385i
$490$	−2.17521e6	−	543143.i	−0.409270	−	0.102194i
$491$		−	6.37465e6i		−	1.19331i	−0.802499	−	0.596654i	$-0.796496\pi$
$491$		−	6.37465e6i		−	1.19331i	0.802499	−	0.596654i	$-0.203504\pi$
$492$	1.45995e6	−	2.74117e6i	0.271911	−	0.510533i
$493$			2.38306e6i			0.441588i
$494$	−5.65476e6	+	4.68376e6i	−1.04255	+	0.863530i
$495$			796267.i			0.146065i
$496$	−3.61027e6	−	5.36854e6i	−0.658924	−	0.979833i
$497$		−	6.38878e6i		−	1.16018i
$498$	−4.07363e6	+	1.63142e7i	−0.736051	+	2.94777i
$499$			2.56239e6i			0.460673i	0.973111	+	0.230337i	$0.0739827\pi$
$499$			2.56239e6i			0.460673i	−0.973111	+	0.230337i	$0.926017\pi$
$500$	2.29781e6	+	1.22382e6i	0.411044	+	0.218923i
$501$	1.03515e7			1.84251
$502$	−1.28042e6	+	5.12786e6i	−0.226773	+	0.908191i
$503$			2.17669e6i			0.383598i	0.981434	+	0.191799i	$0.0614322\pi$
$503$			2.17669e6i			0.383598i	−0.981434	+	0.191799i	$0.938568\pi$
$504$	−9.65832e6	+	1.07042e7i	−1.69366	+	1.87705i
$505$	−1.54691e6			−0.269922
$506$	−1.11527e6	−	278480.i	−0.193644	−	0.0483523i
$507$	7.65281e6			1.32221
$508$	9.71251e6	+	5.17290e6i	1.66983	+	0.889355i
$509$			1.90426e6i			0.325785i	0.986644	+	0.162892i	$0.0520824\pi$
$509$			1.90426e6i			0.325785i	−0.986644	+	0.162892i	$0.947918\pi$
$510$	1.99360e6	+	497798.i	0.339401	+	0.0847477i
$511$			4.50780e6i			0.763682i
$512$	3.50154e6	−	4.78786e6i	0.590316	−	0.807173i
$513$	−3.97936e6	−	2.92801e6i	−0.667606	−	0.491224i
$514$	−1.74215e6	+	6.97704e6i	−0.290856	+	1.16483i
$515$	848595.			0.140988
$516$	−8.77591e6	+	1.64774e7i	−1.45100	+	2.72436i
$517$	2.12427e6			0.349528
$518$	−3.31932e6	−	828826.i	−0.543531	−	0.135718i
$519$		−	1.00477e7i		−	1.63737i
$520$	1.34061e6	−	1.48578e6i	0.217418	−	0.240961i
$521$		−	350338.i		−	0.0565448i	−0.999600	−	0.0282724i	$-0.990999\pi$
$521$		−	350338.i		−	0.0565448i	0.999600	−	0.0282724i	$-0.00900058\pi$
$522$	−1.10315e6	+	4.41796e6i	−0.177199	+	0.709653i
$523$	−3.87757e6			−0.619876			−0.309938	−	0.950757i	$-0.600308\pi$
$523$	−3.87757e6			−0.619876			−0.309938	+	0.950757i	$0.600308\pi$
$524$	4.07711e6	−	7.65507e6i	0.648670	−	1.21793i
$525$		−	1.57027e7i		−	2.48642i
$526$	1.44404e6	−	5.78314e6i	0.227569	−	0.911380i
$527$	6.91719e6			1.08493
$528$	−3.37937e6	+	2.27258e6i	−0.527534	+	0.354759i
$529$	4.83639e6			0.751419
$530$	−534079.	+	2.13890e6i	−0.0825878	+	0.330751i
$531$	−4.79258e6			−0.737621
$532$	9.77843e6	−	4.68809e6i	1.49793	−	0.718153i
$533$	3.23396e6			0.493079
$534$	−1.26048e6	+	5.04801e6i	−0.191285	+	0.766068i
$535$	2.54226e6			0.384004
$536$	−5.49874e6	−	4.96149e6i	−0.826706	−	0.745934i
$537$	1.02268e7			1.53039
$538$	2.66474e6	−	1.06719e7i	0.396916	−	1.58959i
$539$			4.75084e6i			0.704366i
$540$	1.18846e6	+	632977.i	0.175388	+	0.0934121i
$541$	−5.74353e6			−0.843695			−0.421848	−	0.906667i	$-0.638618\pi$
$541$	−5.74353e6			−0.843695			−0.421848	+	0.906667i	$0.638618\pi$
$542$	−965901.	+	3.86828e6i	−0.141232	+	0.565614i
$543$		−	158571.i		−	0.0230794i
$544$	2.15874e6	+	5.96334e6i	0.312754	+	0.863958i
$545$			424225.i			0.0611793i
$546$	−2.41360e7	−	6.02670e6i	−3.46484	−	0.865162i
$547$	2.27365e6			0.324904			0.162452	−	0.986716i	$-0.448060\pi$
$547$	2.27365e6			0.324904			0.162452	+	0.986716i	$0.448060\pi$
$548$	−4.74522e6	−	2.52732e6i	−0.675002	−	0.359508i
$549$	1.09141e7			1.54545
$550$	648459.	−	2.59698e6i	0.0914062	−	0.366068i
$551$	2.02986e6	−	2.75871e6i	0.284831	−	0.387104i
$552$	−3.79718e6	+	4.20836e6i	−0.530413	+	0.587848i
$553$			1.05697e7i			1.46977i
$554$	2.49235e6	+	622333.i	0.345012	+	0.0861486i
$555$			931726.i			0.128397i
$556$	−1.70556e6	+	3.20231e6i	−0.233980	+	0.439315i
$557$	−1.77154e6			−0.241943			−0.120972	−	0.992656i	$-0.538601\pi$
$557$	−1.77154e6			−0.241943			−0.120972	+	0.992656i	$0.538601\pi$
$558$	1.28238e7	+	3.20207e6i	1.74354	+	0.435357i
$559$	−1.94396e7			−2.63122
$560$	−2.45254e6	+	1.64930e6i	−0.330481	+	0.222244i
$561$		−	4.35421e6i		−	0.584120i
$562$	−861482.	+	3.45010e6i	−0.115055	+	0.460777i
$563$	−3.70158e6			−0.492171			−0.246086	−	0.969248i	$-0.579144\pi$
$563$	−3.70158e6			−0.492171			−0.246086	+	0.969248i	$0.579144\pi$
$564$	4.92403e6	−	9.24523e6i	0.651813	−	1.22383i
$565$			1.39180e6i			0.183423i
$566$	1.07296e6	−	4.29705e6i	0.140781	−	0.563806i
$567$			2.61533e6i			0.341641i
$568$	−3.98699e6	−	3.59745e6i	−0.518531	−	0.467868i
$569$			3.20606e6i			0.415137i	0.978220	+	0.207569i	$0.0665550\pi$
$569$			3.20606e6i			0.415137i	−0.978220	+	0.207569i	$0.933445\pi$
$570$	−1.88385e6	−	2.27439e6i	−0.242862	−	0.293210i
$571$		−	940458.i		−	0.120712i	−0.998177	−	0.0603558i	$-0.980776\pi$
$571$		−	940458.i		−	0.120712i	0.998177	−	0.0603558i	$-0.0192235\pi$
$572$	−3.74284e6	−	1.99344e6i	−0.478311	−	0.254750i
$573$		−	1.74332e7i		−	2.21815i
$574$	−4.63389e6	−	1.15707e6i	−0.587038	−	0.146582i
$575$		−	3.72559e6i		−	0.469922i
$576$	1.24157e6	+	1.20548e7i	0.155925	+	1.51392i
$577$	−5.68177e6			−0.710467			−0.355234	−	0.934778i	$-0.615599\pi$
$577$	−5.68177e6			−0.710467			−0.355234	+	0.934778i	$0.615599\pi$
$578$	1.21380e6	+	303083.i	0.151122	+	0.0377348i
$579$			7.90668e6i			0.980162i
$580$	−438814.	+	823906.i	−0.0541640	+	0.101697i
$581$	2.58594e7			3.17818
$582$	−3.02325e6	+	1.21077e7i	−0.369971	+	1.48167i
$583$	4.67155e6			0.569233
$584$	2.81315e6	+	2.53829e6i	0.341319	+	0.307971i
$585$			4.08852e6i			0.493942i
$586$	−2.73725e6	+	1.09623e7i	−0.329284	+	1.31873i
$587$			4.34376e6i			0.520320i	0.965565	+	0.260160i	$0.0837754\pi$
$587$			4.34376e6i			0.520320i	−0.965565	+	0.260160i	$0.916225\pi$
$588$	2.06766e7	+	1.10124e7i	2.46624	+	1.31353i
$589$	−8.00758e6	−	5.89197e6i	−0.951072	−	0.699797i
$590$	−953200.	−	238012.i	−0.112734	−	0.0281493i
$591$	−2.21685e7			−2.61077
$592$	−2.38631e6	+	1.60476e6i	−0.279848	+	0.188194i
$593$	−6.57478e6			−0.767793			−0.383897	−	0.923376i	$-0.625418\pi$
$593$	−6.57478e6			−0.767793			−0.383897	+	0.923376i	$0.625418\pi$
$594$	691238.	−	2.76830e6i	0.0803825	−	0.321920i
$595$		−	3.16002e6i		−	0.365930i
$596$	−5.56289e6	−	2.96281e6i	−0.641483	−	0.341655i
$597$			5.94460e6i			0.682632i
$598$	−5.72646e6	−	1.42988e6i	−0.654837	−	0.163511i
$599$	−1.05518e7			−1.20160			−0.600801	−	0.799399i	$-0.705151\pi$
$599$	−1.05518e7			−1.20160			−0.600801	+	0.799399i	$0.705151\pi$
$600$	−9.79944e6	−	8.84199e6i	−1.11128	−	1.00270i
$601$			9.46797e6i			1.06923i	0.845096	+	0.534615i	$0.179543\pi$
$601$			9.46797e6i			1.06923i	−0.845096	+	0.534615i	$0.820457\pi$
$602$	2.78547e7	+	6.95526e6i	3.13262	+	0.782208i
$603$	1.51312e7			1.69465
$604$	−2.74920e6	−	1.46423e6i	−0.306630	−	0.163312i
$605$	−1.81253e6			−0.201325
$606$	1.56821e7	+	3.91578e6i	1.73469	+	0.433148i
$607$	−6.10874e6			−0.672945			−0.336473	−	0.941693i	$-0.609234\pi$
$607$	−6.10874e6			−0.672945			−0.336473	+	0.941693i	$0.609234\pi$
$608$	2.58046e6	−	8.74216e6i	0.283099	−	0.959091i
$609$	1.16041e7			1.26785
$610$	2.17070e6	+	542019.i	0.236198	+	0.0589780i
$611$	1.09073e7			1.18199
$612$	−1.14361e7	−	6.09091e6i	−1.23424	−	0.657361i
$613$	−4.85896e6			−0.522266			−0.261133	−	0.965303i	$-0.584096\pi$
$613$	−4.85896e6			−0.522266			−0.261133	+	0.965303i	$0.584096\pi$
$614$	−1.91802e6	−	478925.i	−0.205320	−	0.0512680i
$615$			1.30073e6i			0.138675i
$616$	4.64983e6	+	4.19552e6i	0.493725	+	0.445486i
$617$	−1.09089e7			−1.15364			−0.576819	−	0.816872i	$-0.695706\pi$
$617$	−1.09089e7			−1.15364			−0.576819	+	0.816872i	$0.695706\pi$
$618$	−8.60276e6	−	2.14809e6i	−0.906080	−	0.226246i
$619$		−	8.24707e6i		−	0.865113i	−0.901607	−	0.432557i	$-0.857612\pi$
$619$		−	8.24707e6i		−	0.865113i	0.901607	−	0.432557i	$-0.142388\pi$
$620$	2.39151e6	+	1.27372e6i	0.249858	+	0.133075i
$621$		−	3.97137e6i		−	0.413249i
$622$	1.56727e6	−	6.27667e6i	0.162430	−	0.650509i
$623$	8.00150e6			0.825945
$624$	−1.73517e7	+	1.16688e7i	−1.78394	+	1.19968i
$625$	8.11398e6			0.830872
$626$	4.85880e6	+	1.21323e6i	0.495557	+	0.123739i
$627$	−3.70885e6	+	5.04058e6i	−0.376765	+	0.512049i
$628$	−5.03813e6	−	2.68332e6i	−0.509765	−	0.271502i
$629$		−	3.07468e6i		−	0.309866i
$630$	1.46282e6	−	5.85838e6i	0.146839	−	0.588066i
$631$			1.80141e7i			1.80111i	0.434744	+	0.900554i	$0.356839\pi$
$631$			1.80141e7i			1.80111i	−0.434744	+	0.900554i	$0.643161\pi$
$632$	6.59616e6	+	5.95169e6i	0.656899	+	0.592717i
$633$	−5.89789e6			−0.585043
$634$	−2.37365e6	+	9.50609e6i	−0.234527	+	0.939244i
$635$	−4.60872e6			−0.453572
$636$	1.08286e7	−	2.03315e7i	1.06152	−	1.99309i
$637$			2.43937e7i			2.38193i
$638$	1.91914e6	+	479204.i	0.186661	+	0.0466089i
$639$	1.09713e7			1.06293
$640$	−351733.	+	2.45924e6i	−0.0339440	+	0.237329i
$641$		−	1.02840e7i		−	0.988589i	−0.869294	−	0.494295i	$-0.835426\pi$
$641$		−	1.02840e7i		−	0.988589i	0.869294	−	0.494295i	$-0.164574\pi$
$642$	−2.57726e7	−	6.43535e6i	−2.46786	−	0.616219i
$643$			1.37199e7i			1.30865i	0.756213	+	0.654326i	$0.227048\pi$
$643$			1.37199e7i			1.30865i	−0.756213	+	0.654326i	$0.772952\pi$
$644$	7.69378e6	+	4.09772e6i	0.731013	+	0.389339i
$645$		−	7.81877e6i		−	0.740013i
$646$	6.21667e6	+	7.50546e6i	0.586107	+	0.707614i
$647$			1.25054e7i			1.17446i	0.809421	+	0.587229i	$0.199781\pi$
$647$			1.25054e7i			1.17446i	−0.809421	+	0.587229i	$0.800219\pi$
$648$	1.63213e6	+	1.47266e6i	0.152692	+	0.137774i
$649$			2.08187e6i			0.194018i
$650$	3.32958e6	−	1.33344e7i	0.309105	−	1.23792i
$651$		−	3.36827e7i		−	3.11497i
$652$	3.38618e6	−	6.35780e6i	0.311954	−	0.585717i
$653$	−1.65140e7			−1.51555			−0.757775	−	0.652516i	$-0.773714\pi$
$653$	−1.65140e7			−1.51555			−0.757775	+	0.652516i	$0.773714\pi$
$654$	1.07386e6	−	4.30064e6i	0.0981755	−	0.393178i
$655$			3.63244e6i			0.330823i
$656$	−3.33138e6	+	2.24030e6i	−0.302249	+	0.203258i
$657$	−7.74111e6			−0.699665
$658$	−1.56289e7	−	3.90249e6i	−1.40722	−	0.351380i
$659$	1.20867e6			0.108416			0.0542080	−	0.998530i	$-0.482737\pi$
$659$	1.20867e6			0.108416			0.0542080	+	0.998530i	$0.482737\pi$
$660$	801779.	−	1.50540e6i	0.0716465	−	0.134522i
$661$		−	8.04477e6i		−	0.716160i	−0.933691	−	0.358080i	$-0.883431\pi$
$661$		−	8.04477e6i		−	0.716160i	0.933691	−	0.358080i	$-0.116569\pi$
$662$	−1.63504e7	−	4.08266e6i	−1.45005	−	0.362074i
$663$		−	2.23571e7i		−	1.97530i
$664$	1.45611e7	−	1.61379e7i	1.28166	−	1.42045i
$665$	−2.69166e6	+	3.65815e6i	−0.236030	+	0.320780i
$666$	1.42332e6	−	5.70016e6i	0.124341	−	0.497968i
$667$	2.75317e6			0.239618
$668$	−1.18102e7	−	6.29015e6i	−1.02404	−	0.545406i
$669$	1.01696e7			0.878493
$670$	3.00946e6	+	751454.i	0.259001	+	0.0646719i
$671$		−	4.74100e6i		−	0.406503i
$672$	2.90380e7	−	1.05118e7i	2.48052	−	0.897954i
$673$		−	6.53372e6i		−	0.556062i	−0.960572	−	0.278031i	$-0.910318\pi$
$673$		−	6.53372e6i		−	0.556062i	0.960572	−	0.278031i	$-0.0896817\pi$
$674$	−3.15850e6	+	1.26493e7i	−0.267812	+	1.07255i
$675$	9.24760e6			0.781213
$676$	−8.73123e6	−	4.65027e6i	−0.734867	−	0.391392i
$677$		−	9.11320e6i		−	0.764186i	−0.924124	−	0.382093i	$-0.875203\pi$
$677$		−	9.11320e6i		−	0.764186i	0.924124	−	0.382093i	$-0.124797\pi$
$678$	3.52312e6	−	1.41096e7i	0.294343	−	1.17880i
$679$	1.91916e7			1.59749
$680$	−1.97205e6	−	1.77937e6i	−0.163548	−	0.147569i
$681$	1.51014e7			1.24782
$682$	1.39096e6	−	5.57059e6i	0.114513	−	0.458607i
$683$	−1.93409e7			−1.58645			−0.793223	−	0.608932i	$-0.791598\pi$
$683$	−1.93409e7			−1.58645			−0.793223	+	0.608932i	$0.791598\pi$
$684$	8.05072e6	+	1.67922e7i	0.657952	+	1.37236i
$685$	2.25168e6			0.183349
$686$	3.76747e6	−	1.50881e7i	0.305661	−	1.22412i
$687$	3.72026e7			3.00733
$688$	2.00252e7	−	1.34667e7i	1.61289	−	1.08465i
$689$	2.39866e7			1.92495
$690$	575111.	−	2.30323e6i	0.0459864	−	0.184168i
$691$		−	1.02436e7i		−	0.816123i	−0.912954	−	0.408062i	$-0.866205\pi$
$691$		−	1.02436e7i		−	0.816123i	0.912954	−	0.408062i	$-0.133795\pi$
$692$	−6.10552e6	+	1.14636e7i	−0.484683	+	0.910028i
$693$	−1.27952e7			−1.01208
$694$	−5.35564e6	+	2.14485e7i	−0.422097	+	1.69043i
$695$		−	1.51954e6i		−	0.119330i
$696$	6.53414e6	−	7.24168e6i	0.511288	−	0.566652i
$697$		−	4.29237e6i		−	0.334669i
$698$	−8.02919e6	−	2.00487e6i	−0.623783	−	0.155757i
$699$	−5.72060e6			−0.442842
$700$	−9.54182e6	+	1.79155e7i	−0.736014	+	1.38192i
$701$	−2.24484e7			−1.72540			−0.862702	−	0.505713i	$-0.831230\pi$
$701$	−2.24484e7			−1.72540			−0.862702	+	0.505713i	$0.831230\pi$
$702$	3.54923e6	−	1.42141e7i	0.271827	−	1.08862i
$703$	−2.61897e6	+	3.55936e6i	−0.199868	+	0.271633i
$704$	5.23653e6	−	539332.i	0.398210	−	0.0410133i
$705$			4.38699e6i			0.332425i
$706$	1.14148e7	+	2.85025e6i	0.861899	+	0.215214i
$707$		−	2.48574e7i		−	1.87028i
$708$	9.06072e6	+	4.82576e6i	0.679328	+	0.361812i
$709$	−2.10964e7			−1.57613			−0.788065	−	0.615592i	$-0.788917\pi$
$709$	−2.10964e7			−1.57613			−0.788065	+	0.615592i	$0.788917\pi$
$710$	2.18208e6	+	544860.i	0.162452	+	0.0405638i
$711$	−1.81511e7			−1.34657
$712$	4.50555e6	−	4.99343e6i	0.333080	−	0.369147i
$713$		−	7.99150e6i		−	0.588714i
$714$	−7.99912e6	+	3.20352e7i	−0.587214	+	2.35170i
$715$	1.77603e6			0.129923
$716$	−1.16679e7	−	6.21434e6i	−0.850569	−	0.453015i
$717$		−	6.44241e6i		−	0.468005i
$718$	−6.33289e6	+	2.53623e7i	−0.458449	+	1.83602i
$719$		−	1.60703e7i		−	1.15932i	−0.814860	−	0.579658i	$-0.803186\pi$
$719$		−	1.60703e7i		−	1.15932i	0.814860	−	0.579658i	$-0.196814\pi$
$720$	−2.83229e6	−	4.21168e6i	−0.203614	−	0.302778i
$721$			1.36361e7i			0.976902i
$722$	−803585.	−	1.39839e7i	−0.0573706	−	0.998353i
$723$		−	2.38191e7i		−	1.69465i
$724$	−96356.6	+	180917.i	−0.00683180	+	0.0128272i
$725$			6.41094e6i			0.452978i
$726$	1.83748e7	+	4.58815e6i	1.29384	+	0.323069i
$727$			1.51436e7i			1.06265i	0.847167	+	0.531327i	$0.178307\pi$
$727$			1.51436e7i			1.06265i	−0.847167	+	0.531327i	$0.821693\pi$
$728$	2.38750e7	+	2.15423e7i	1.66961	+	1.50648i
$729$	−2.33782e7			−1.62927
$730$	−1.53963e6	−	384443.i	−0.106933	−	0.0267008i
$731$			2.58018e7i			1.78590i
$732$	−2.06338e7	−	1.09896e7i	−1.42332	−	0.758062i
$733$	1.50483e7			1.03449			0.517247	−	0.855836i	$-0.326957\pi$
$733$	1.50483e7			1.03449			0.517247	+	0.855836i	$0.326957\pi$
$734$	1.03095e6	−	4.12880e6i	0.0706314	−	0.282868i
$735$	−9.81134e6			−0.669900
$736$	6.88951e6	−	2.49401e6i	0.468807	−	0.169709i
$737$		−	6.57292e6i		−	0.445748i
$738$	1.98700e6	−	7.95765e6i	0.134294	−	0.537828i
$739$			2.12754e7i			1.43307i	0.697553	+	0.716533i	$0.254272\pi$
$739$			2.12754e7i			1.43307i	−0.697553	+	0.716533i	$0.745728\pi$
$740$	566168.	−	1.06302e6i	0.0380072	−	0.0713614i
$741$	−1.90435e7	+	2.58814e7i	−1.27409	+	1.73158i
$742$	−3.43700e7	−	8.58211e6i	−2.29177	−	0.572248i
$743$	−5.14134e6			−0.341668			−0.170834	−	0.985300i	$-0.554646\pi$
$743$	−5.14134e6			−0.341668			−0.170834	+	0.985300i	$0.554646\pi$
$744$	−2.10201e7	−	1.89663e7i	−1.39220	−	1.25618i
$745$	2.63967e6			0.174245
$746$	2.91414e6	−	1.16707e7i	0.191718	−	0.767801i
$747$			4.44075e7i			2.91176i
$748$	−2.64586e6	+	4.96780e6i	−0.172907	+	0.324646i
$749$			4.08516e7i			2.66075i
$750$	1.10535e7	+	2.76004e6i	0.717542	+	0.179168i
$751$	2.01843e7			1.30591			0.652955	−	0.757397i	$-0.273529\pi$
$751$	2.01843e7			1.30591			0.652955	+	0.757397i	$0.273529\pi$
$752$	−1.12358e7	+	7.55594e6i	−0.724537	+	0.487241i
$753$			2.31294e7i			1.48654i
$754$	9.85402e6	+	2.46052e6i	0.631226	+	0.157616i
$755$	1.30454e6			0.0832892
$756$	−1.01713e7	+	1.90974e7i	−0.647250	+	1.21526i
$757$	−2.74319e6			−0.173987			−0.0869933	−	0.996209i	$-0.527726\pi$
$757$	−2.74319e6			−0.173987			−0.0869933	+	0.996209i	$0.527726\pi$
$758$	−1.93488e7	−	4.83135e6i	−1.22315	−	0.305419i
$759$	−5.03046e6			−0.316959
$760$	767269.	+	3.73963e6i	0.0481852	+	0.234852i
$761$	3.30295e6			0.206747			0.103374	−	0.994643i	$-0.467036\pi$
$761$	3.30295e6			0.206747			0.103374	+	0.994643i	$0.467036\pi$
$762$	4.67216e7	+	1.16663e7i	2.91495	+	0.727855i
$763$	−6.81686e6			−0.423910
$764$	−1.05934e7	+	1.98899e7i	−0.656602	+	1.23282i
$765$	5.42661e6			0.335255
$766$	1.63932e7	+	4.09335e6i	1.00947	+	0.252062i
$767$			1.06896e7i			0.656104i
$768$	9.79095e6	−	2.40406e7i	0.598993	−	1.47076i
$769$	−1.26306e7			−0.770207			−0.385104	−	0.922873i	$-0.625834\pi$
$769$	−1.26306e7			−0.770207			−0.385104	+	0.922873i	$0.625834\pi$
$770$	−2.54485e6	−	635442.i	−0.154680	−	0.0386233i
$771$			3.14702e7i			1.90662i
$772$	4.80454e6	−	9.02087e6i	0.290141	−	0.544760i
$773$			2.26987e7i			1.36632i	0.730268	+	0.683161i	$0.239395\pi$
$773$			2.26987e7i			1.36632i	−0.730268	+	0.683161i	$0.760605\pi$
$774$	−1.19441e7	+	4.78341e7i	−0.716638	+	2.87002i
$775$	1.86087e7			1.11292
$776$	1.08066e7	−	1.19768e7i	0.644219	−	0.713978i
$777$	−1.49719e7			−0.889661
$778$	−1.63360e7	−	4.07907e6i	−0.967604	−	0.241608i
$779$	−3.65618e6	+	4.96900e6i	−0.215866	+	0.293376i
$780$	4.11682e6	−	7.72963e6i	0.242284	−	0.454907i
$781$		−	4.76585e6i		−	0.279584i
$782$	−1.89786e6	+	7.60063e6i	−0.110981	+	0.444460i
$783$			6.83388e6i			0.398348i
$784$	−1.68986e7	−	2.51285e7i	−0.981883	−	1.46008i
$785$	2.39067e6			0.138466
$786$	9.19497e6	−	3.68244e7i	0.530877	−	2.12608i
$787$	−1.73467e7			−0.998344			−0.499172	−	0.866503i	$-0.666362\pi$
$787$	−1.73467e7			−0.998344			−0.499172	+	0.866503i	$0.666362\pi$
$788$	2.52925e7	+	1.34708e7i	1.45103	+	0.772821i
$789$		−	2.60851e7i		−	1.49176i
$790$	−3.61007e6	−	901427.i	−0.205801	−	0.0513881i
$791$	−2.23648e7			−1.27094
$792$	−7.20484e6	+	7.98501e6i	−0.408142	+	0.452337i
$793$		−	2.43432e7i		−	1.37466i
$794$	1.13027e7	+	2.82225e6i	0.636252	+	0.158871i
$795$			9.64760e6i			0.541379i
$796$	3.61227e6	−	6.78230e6i	0.202068	−	0.379398i
$797$		−	2.18619e7i		−	1.21911i	−0.792744	−	0.609555i	$-0.791348\pi$
$797$		−	2.18619e7i		−	1.21911i	0.792744	−	0.609555i	$-0.208652\pi$
$798$	3.65472e7	−	3.02716e7i	2.03164	−	1.68278i
$799$		−	1.44770e7i		−	0.802254i
$800$	5.80747e6	+	1.60427e7i	0.320821	+	0.886241i
$801$			1.37407e7i			0.756708i
$802$	−6.01374e6	+	2.40841e7i	−0.330148	+	1.32219i
$803$			3.36270e6i			0.184034i
$804$	−2.86067e7	−	1.52360e7i	−1.56073	−	0.831247i
$805$	−3.65081e6			−0.198563
$806$	7.14205e6	−	2.86028e7i	0.387244	−	1.55085i
$807$		−	4.81358e7i		−	2.60187i
$808$	−1.55125e7	−	1.39969e7i	−0.835900	−	0.754229i
$809$	1.25383e7			0.673548			0.336774	−	0.941585i	$-0.390664\pi$
$809$	1.25383e7			0.673548			0.336774	+	0.941585i	$0.390664\pi$
$810$	−893264.	−	223046.i	−0.0478374	−	0.0119449i
$811$	−9.39187e6			−0.501418			−0.250709	−	0.968063i	$-0.580664\pi$
$811$	−9.39187e6			−0.501418			−0.250709	+	0.968063i	$0.580664\pi$
$812$	−1.32393e7	−	7.05130e6i	−0.704655	−	0.375301i
$813$			1.74480e7i			0.925806i
$814$	−2.47612e6	−	618281.i	−0.130982	−	0.0327058i
$815$			3.01687e6i			0.159097i
$816$	1.54878e7	+	2.30306e7i	0.814260	+	1.21082i
$817$	2.19776e7	−	2.98691e7i	1.15193	−	1.56555i
$818$	−2.03415e6	+	8.14644e6i	−0.106292	+	0.425681i
$819$	−6.56984e7			−3.42251
$820$	790393.	−	1.48402e6i	0.0410496	−	0.0770736i
$821$	1.53545e7			0.795019			0.397509	−	0.917598i	$-0.369875\pi$
$821$	1.53545e7			0.795019			0.397509	+	0.917598i	$0.369875\pi$
$822$	−2.28267e7	−	5.69978e6i	−1.17832	−	0.294224i
$823$		−	6.80560e6i		−	0.350241i	−0.984547	−	0.175120i	$-0.943969\pi$
$823$		−	6.80560e6i		−	0.350241i	0.984547	−	0.175120i	$-0.0560315\pi$
$824$	8.50975e6	+	7.67831e6i	0.436615	+	0.393956i
$825$		−	1.17138e7i		−	0.599186i
$826$	3.82461e6	−	1.53170e7i	0.195046	−	0.781129i
$827$	2.20079e7			1.11896			0.559481	−	0.828843i	$-0.311000\pi$
$827$	2.20079e7			1.11896			0.559481	+	0.828843i	$0.311000\pi$
$828$	−7.03689e6	+	1.32123e7i	−0.356702	+	0.669734i
$829$			1.57930e7i			0.798141i	0.916920	+	0.399070i	$0.130667\pi$
$829$			1.57930e7i			0.798141i	−0.916920	+	0.399070i	$0.869333\pi$
$830$	−2.20539e6	+	8.83224e6i	−0.111119	+	0.445016i
$831$	1.12418e7			0.564721
$832$	2.68875e7	−	2.76926e6i	1.34661	−	0.138693i
$833$	3.23773e7			1.61669
$834$	−3.84648e6	+	1.54046e7i	−0.191491	+	0.766892i
$835$	5.60412e6			0.278158
$836$	7.29444e6	−	3.49719e6i	0.360974	−	0.173063i
$837$	1.98364e7			0.978698
$838$	4.94776e6	−	1.98150e7i	0.243388	−	0.974730i
$839$	−7.22271e6			−0.354238			−0.177119	−	0.984189i	$-0.556678\pi$
$839$	−7.22271e6			−0.354238			−0.177119	+	0.984189i	$0.556678\pi$
$840$	−8.66451e6	+	9.60274e6i	−0.423688	+	0.469566i
$841$	1.57735e7			0.769022
$842$	3.09303e6	−	1.23871e7i	0.150350	−	0.602129i
$843$			1.55618e7i			0.754208i
$844$	6.72902e6	+	3.58389e6i	0.325159	+	0.173180i
$845$	4.14309e6			0.199610
$846$	6.70163e6	−	2.68390e7i	0.321925	−	1.28926i
$847$		−	2.91255e7i		−	1.39497i
$848$	−2.47091e7	+	1.66165e7i	−1.17996	+	0.793507i
$849$		−	1.93820e7i		−	0.922847i
$850$	−1.76986e7	−	4.41929e6i	−0.840215	−	0.209800i
$851$	−3.55221e6			−0.168141
$852$	−2.07419e7	−	1.10472e7i	−0.978927	−	0.521379i
$853$	1.29161e6			0.0607797			0.0303898	−	0.999538i	$-0.490325\pi$
$853$	1.29161e6			0.0607797			0.0303898	+	0.999538i	$0.490325\pi$
$854$	−8.70970e6	+	3.48810e7i	−0.408657	+	1.63661i
$855$	−6.28204e6	−	4.62231e6i	−0.293890	−	0.216244i
$856$	2.54939e7	+	2.30031e7i	1.18919	+	1.07300i
$857$		−	1.70053e7i		−	0.790919i	−0.918483	−	0.395459i	$-0.870585\pi$
$857$		−	1.70053e7i		−	0.790919i	0.918483	−	0.395459i	$-0.129415\pi$
$858$	−1.80048e7	−	4.49575e6i	−0.834967	−	0.208489i
$859$		−	1.94144e7i		−	0.897719i	−0.893602	−	0.448860i	$-0.851830\pi$
$859$		−	1.94144e7i		−	0.897719i	0.893602	−	0.448860i	$-0.148170\pi$
$860$	−4.75112e6	+	8.92058e6i	−0.219053	+	0.411289i
$861$	−2.09013e7			−0.960874
$862$	1.31477e7	+	3.28294e6i	0.602671	+	0.150486i
$863$	1.52311e7			0.696151			0.348076	−	0.937466i	$-0.386835\pi$
$863$	1.52311e7			0.696151			0.348076	+	0.937466i	$0.386835\pi$
$864$	6.19060e6	+	1.71010e7i	0.282129	+	0.779360i
$865$		−	5.43963e6i		−	0.247189i
$866$	8.18916e6	−	3.27963e7i	0.371060	−	1.48604i
$867$	5.47490e6			0.247359
$868$	−2.04675e7	+	3.84292e7i	−0.922073	+	1.73126i
$869$			7.88472e6i			0.354190i
$870$	−989644.	+	3.96337e6i	−0.0443283	+	0.177528i
$871$		−	3.37493e7i		−	1.50737i
$872$	−3.83850e6	+	4.25414e6i	−0.170950	+	0.189462i
$873$			3.29572e7i			1.46357i
$874$	8.67114e6	−	7.18218e6i	0.383970	−	0.318037i
$875$		−	1.75207e7i		−	0.773627i
$876$	1.46351e7	+	7.79470e6i	0.644371	+	0.343194i
$877$			2.41300e7i			1.05939i	0.848187	+	0.529697i	$0.177695\pi$
$877$			2.41300e7i			1.05939i	−0.848187	+	0.529697i	$0.822305\pi$
$878$	2.58899e7	+	6.46464e6i	1.13343	+	0.283014i
$879$			4.94457e7i			2.15852i
$880$	−1.82953e6	+	1.23033e6i	−0.0796403	+	0.0535569i
$881$	−1.59286e7			−0.691411			−0.345706	−	0.938343i	$-0.612360\pi$
$881$	−1.59286e7			−0.691411			−0.345706	+	0.938343i	$0.612360\pi$
$882$	6.00244e7	+	1.49879e7i	2.59810	+	0.648740i
$883$		−	5.02711e6i		−	0.216979i	−0.994098	−	0.108489i	$-0.965399\pi$
$883$		−	5.02711e6i		−	0.216979i	0.994098	−	0.108489i	$-0.0346013\pi$
$884$	−1.35854e7	+	2.55077e7i	−0.584713	+	1.09784i
$885$	−4.29944e6			−0.184524
$886$	7.83883e6	−	3.13933e7i	0.335480	−	1.34355i
$887$	1.23615e7			0.527546			0.263773	−	0.964585i	$-0.415033\pi$
$887$	1.23615e7			0.527546			0.263773	+	0.964585i	$0.415033\pi$
$888$	−8.43050e6	+	9.34339e6i	−0.358774	+	0.397624i
$889$		−	7.40576e7i		−	3.14279i
$890$	−682399.	+	2.73290e6i	−0.0288777	+	0.115651i
$891$			1.95097e6i			0.0823295i
$892$	−1.16027e7	−	6.17961e6i	−0.488254	−	0.260045i
$893$	−1.23313e7	+	1.67591e7i	−0.517465	+	0.703269i
$894$	−2.67601e7	−	6.68193e6i	−1.11981	−	0.279613i
$895$	5.53658e6			0.231038
$896$	−3.95175e7	−	5.65200e6i	−1.64445	−	0.235197i
$897$	−2.58294e7			−1.07185
$898$	−5.49817e6	+	2.20193e7i	−0.227524	+	0.911199i
$899$			1.37517e7i			0.567487i
$900$	−3.07657e7	−	1.63859e7i	−1.26608	−	0.674316i
$901$		−	3.18369e7i		−	1.30653i
$902$	−3.45676e6	−	863144.i	−0.141466	−	0.0353237i
$903$	1.25640e8			5.12753
$904$	−1.25933e7	+	1.39570e7i	−0.512531	+	0.568030i
$905$		−	85847.5i		−	0.00348422i
$906$	−1.32249e7	−	3.30223e6i	−0.535270	−	0.133656i
$907$	3.34263e7			1.34918			0.674591	−	0.738192i	$-0.264320\pi$
$907$	3.34263e7			1.34918			0.674591	+	0.738192i	$0.264320\pi$
$908$	−1.72295e7	−	9.17648e6i	−0.693519	−	0.369370i
$909$	4.26868e7			1.71350
$910$	−1.30668e7	−	3.26274e6i	−0.523077	−	0.130611i
$911$	−3.60208e6			−0.143800			−0.0718998	−	0.997412i	$-0.522906\pi$
$911$	−3.60208e6			−0.143800			−0.0718998	+	0.997412i	$0.522906\pi$
$912$	1.68799e6	−	3.98533e7i	0.0672021	−	1.58664i
$913$	1.92904e7			0.765886
$914$	3.66505e7	+	9.15155e6i	1.45116	+	0.362351i
$915$	9.79103e6			0.386612
$916$	−4.24451e7	−	2.26064e7i	−1.67143	−	0.890209i
$917$	−5.83697e7			−2.29226
$918$	−1.88662e7	−	4.71083e6i	−0.738885	−	0.184498i
$919$		−	2.22346e7i		−	0.868441i	−0.900807	−	0.434220i	$-0.857024\pi$
$919$		−	2.22346e7i		−	0.868441i	0.900807	−	0.434220i	$-0.142976\pi$
$920$	−2.05573e6	+	2.27833e6i	−0.0800748	+	0.0887456i
$921$	−8.65130e6			−0.336072
$922$	−6.82743e6	−	1.70479e6i	−0.264502	−	0.0660456i
$923$		−	2.44708e7i		−	0.945460i
$924$	2.41903e7	+	1.28838e7i	0.932096	+	0.496437i
$925$		−	8.27155e6i		−	0.317858i
$926$	2.49255e6	−	9.98228e6i	0.0955249	−	0.382562i
$927$	−2.34168e7			−0.895011
$928$	−1.18554e7	+	4.29166e6i	−0.451903	+	0.163590i
$929$	652800.			0.0248165			0.0124083	−	0.999923i	$-0.496050\pi$
$929$	652800.			0.0248165			0.0124083	+	0.999923i	$0.496050\pi$
$930$	1.15043e7	+	2.87259e6i	0.436166	+	0.108910i
$931$	−3.74811e7	−	2.75785e7i	−1.41722	−	1.04279i
$932$	6.52673e6	+	3.47615e6i	0.246125	+	0.131087i
$933$		−	2.83111e7i		−	1.06476i
$934$	−4.85604e6	+	1.94477e7i	−0.182144	+	0.729459i
$935$		−	2.35729e6i		−	0.0881828i
$936$	−3.69940e7	+	4.09999e7i	−1.38020	+	1.52965i
$937$	4.33936e7			1.61464			0.807322	−	0.590112i	$-0.200916\pi$
$937$	4.33936e7			1.61464			0.807322	+	0.590112i	$0.200916\pi$
$938$	−1.20751e7	+	4.83590e7i	−0.448110	+	1.79461i
$939$	2.19158e7			0.811135
$940$	2.66578e6	−	5.00520e6i	0.0984022	−	0.184757i
$941$		−	1.86944e7i		−	0.688235i	−0.938927	−	0.344117i	$-0.888178\pi$
$941$		−	1.86944e7i		−	0.688235i	0.938927	−	0.344117i	$-0.111822\pi$
$942$	−2.42357e7	−	6.05161e6i	−0.889875	−	0.222200i
$943$	−4.95902e6			−0.181600
$944$	−7.40514e6	−	1.10116e7i	−0.270460	−	0.402180i
$945$		−	9.06197e6i		−	0.330098i
$946$	2.07789e7	+	5.18843e6i	0.754908	+	0.188499i
$947$			1.72657e7i			0.625619i	0.949816	+	0.312810i	$0.101270\pi$
$947$			1.72657e7i			0.625619i	−0.949816	+	0.312810i	$0.898730\pi$
$948$	3.43159e7	+	1.82767e7i	1.24015	+	0.660507i
$949$			1.72661e7i			0.622342i
$950$	1.67242e7	+	2.01913e7i	0.601223	+	0.725864i
$951$			4.28775e7i			1.53737i
$952$	2.85927e7	−	3.16889e7i	1.02250	−	1.13322i
$953$			1.06864e7i			0.381152i	0.981672	+	0.190576i	$0.0610355\pi$
$953$			1.06864e7i			0.381152i	−0.981672	+	0.190576i	$0.938964\pi$
$954$	1.47378e7	−	5.90226e7i	0.524278	−	2.09965i
$955$		−	9.43804e6i		−	0.334868i
$956$	−3.91477e6	+	7.35026e6i	−0.138536	+	0.260111i
$957$	8.65635e6			0.305531
$958$	−5.03216e6	+	2.01530e7i	−0.177150	+	0.709458i
$959$			3.61822e7i			1.27042i
$960$	1.11382e6	+	1.08144e7i	0.0390064	+	0.378725i
$961$	1.12871e7			0.394253
$962$	−1.27139e7	−	3.17463e6i	−0.442936	−	0.110600i
$963$	−7.01532e7			−2.43771
$964$	−1.44738e7	+	2.71756e7i	−0.501638	+	0.941861i
$965$			4.28053e6i			0.147972i
$966$	3.70106e7	+	9.24146e6i	1.27610	+	0.318638i
$967$		−	8.15995e6i		−	0.280622i	−0.990108	−	0.140311i	$-0.955190\pi$
$967$		−	8.15995e6i		−	0.280622i	0.990108	−	0.140311i	$-0.0448102\pi$
$968$	−1.81761e7	−	1.64003e7i	−0.623467	−	0.562551i
$969$	3.43519e7	+	2.52761e7i	1.17528	+	0.864769i
$970$	−1.63674e6	+	6.55487e6i	−0.0558533	+	0.223684i
$971$	−3.97868e6			−0.135423			−0.0677113	−	0.997705i	$-0.521570\pi$
$971$	−3.97868e6			−0.135423			−0.0677113	+	0.997705i	$0.521570\pi$
$972$	3.00395e7	+	1.59991e7i	1.01983	+	0.543163i
$973$	2.44175e7			0.826835
$974$	−4.35560e6	−	1.08758e6i	−0.147113	−	0.0367337i
$975$		−	6.01455e7i		−	2.02624i
$976$	1.68636e7	+	2.50765e7i	0.566663	+	0.842640i
$977$			2.17917e7i			0.730390i	0.930931	+	0.365195i	$0.118998\pi$
$977$			2.17917e7i			0.730390i	−0.930931	+	0.365195i	$0.881002\pi$
$978$	7.63674e6	−	3.05840e7i	0.255306	−	1.02246i
$979$	5.96890e6			0.199039
$980$	1.11939e7	+	5.96192e6i	0.372321	+	0.198299i
$981$		−	1.17064e7i		−	0.388374i
$982$	−8.73599e6	+	3.49863e7i	−0.289090	+	1.15776i
$983$	−1.04570e7			−0.345162			−0.172581	−	0.984995i	$-0.555211\pi$
$983$	−1.04570e7			−0.345162			−0.172581	+	0.984995i	$0.555211\pi$
$984$	−1.17693e7	+	1.30437e7i	−0.387492	+	0.429452i
$985$	−1.20016e7			−0.394140
$986$	3.26581e6	−	1.30791e7i	0.106979	−	0.428434i
$987$	−7.04946e7			−2.30337
$988$	3.74541e7	−	1.79567e7i	1.22069	−	0.585239i
$989$	2.98091e7			0.969077
$990$	1.09123e6	−	4.37019e6i	0.0353856	−	0.141714i
$991$	−1.74424e7			−0.564185			−0.282093	−	0.959387i	$-0.591029\pi$
$991$	−1.74424e7			−0.564185			−0.282093	+	0.959387i	$0.591029\pi$
$992$	1.24572e7	+	3.44120e7i	0.401922	+	1.11028i
$993$	−7.37491e7			−2.37347
$994$	−8.75535e6	+	3.50638e7i	−0.281065	+	1.12562i
$995$			3.21830e6i			0.103055i
$996$	4.47149e7	−	8.39556e7i	1.42825	−	2.68164i
$997$	5.01742e7			1.59861			0.799304	−	0.600926i	$-0.205201\pi$
$997$	5.01742e7			1.59861			0.799304	+	0.600926i	$0.205201\pi$
$998$	3.51156e6	−	1.40633e7i	0.111602	−	0.446951i
$999$		−	8.81723e6i		−	0.279524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.d.a.75.3	✓	48
4.3	odd	2	inner	76.6.d.a.75.45	yes	48
19.18	odd	2	inner	76.6.d.a.75.46	yes	48
76.75	even	2	inner	76.6.d.a.75.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.d.a.75.3	✓	48	1.1	even	1	trivial
76.6.d.a.75.4	yes	48	76.75	even	2	inner
76.6.d.a.75.45	yes	48	4.3	odd	2	inner
76.6.d.a.75.46	yes	48	19.18	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.48835 - 1.37043i) q^{2} -24.7554 q^{3} +(28.2439 + 15.0427i) q^{4} -13.4021 q^{5} +(135.866 + 33.9254i) q^{6} -215.359i q^{7} +(-134.397 - 121.266i) q^{8} +369.829 q^{9} +O(q^{10})\)	\(q+(-5.48835 - 1.37043i) q^{2} -24.7554 q^{3} +(28.2439 + 15.0427i) q^{4} -13.4021 q^{5} +(135.866 + 33.9254i) q^{6} -215.359i q^{7} +(-134.397 - 121.266i) q^{8} +369.829 q^{9} +(73.5554 + 18.3666i) q^{10} -160.652i q^{11} +(-699.187 - 372.389i) q^{12} -824.882i q^{13} +(-295.133 + 1181.96i) q^{14} +331.774 q^{15} +(571.432 + 849.731i) q^{16} -1094.85 q^{17} +(-2029.75 - 506.823i) q^{18} +(1267.44 + 932.578i) q^{19} +(-378.528 - 201.605i) q^{20} +5331.28i q^{21} +(-220.161 + 881.711i) q^{22} +1264.89i q^{23} +(3327.05 + 3001.98i) q^{24} -2945.38 q^{25} +(-1130.44 + 4527.24i) q^{26} -3139.69 q^{27} +(3239.58 - 6082.56i) q^{28} -2176.61i q^{29} +(-1820.89 - 454.672i) q^{30} -6317.93 q^{31} +(-1971.72 - 5446.72i) q^{32} +3976.99i q^{33} +(6008.92 + 1500.41i) q^{34} +2886.26i q^{35} +(10445.4 + 5563.24i) q^{36} +2808.31i q^{37} +(-5678.10 - 6855.24i) q^{38} +20420.3i q^{39} +(1801.21 + 1625.22i) q^{40} +3920.51i q^{41} +(7306.13 - 29259.9i) q^{42} -23566.5i q^{43} +(2416.64 - 4537.42i) q^{44} -4956.49 q^{45} +(1733.44 - 6942.16i) q^{46} +13222.8i q^{47} +(-14146.0 - 21035.4i) q^{48} -29572.3 q^{49} +(16165.3 + 4036.43i) q^{50} +27103.4 q^{51} +(12408.5 - 23297.9i) q^{52} +29078.8i q^{53} +(17231.7 + 4302.72i) q^{54} +2153.07i q^{55} +(-26115.7 + 28943.6i) q^{56} +(-31375.9 - 23086.3i) q^{57} +(-2982.88 + 11946.0i) q^{58} -12958.9 q^{59} +(9370.59 + 4990.80i) q^{60} +29511.1 q^{61} +(34675.0 + 8658.26i) q^{62} -79645.8i q^{63} +(3357.16 + 32595.6i) q^{64} +11055.2i q^{65} +(5450.17 - 21827.1i) q^{66} +40914.1 q^{67} +(-30922.8 - 16469.6i) q^{68} -31312.9i q^{69} +(3955.41 - 15840.8i) q^{70} +29665.8 q^{71} +(-49703.9 - 44847.6i) q^{72} -20931.6 q^{73} +(3848.58 - 15413.0i) q^{74} +72914.1 q^{75} +(21768.8 + 45405.3i) q^{76} -34597.7 q^{77} +(27984.5 - 112073. i) q^{78} -49079.6 q^{79} +(-7658.39 - 11388.2i) q^{80} -12144.1 q^{81} +(5372.77 - 21517.1i) q^{82} +120076. i q^{83} +(-80197.1 + 150576. i) q^{84} +14673.3 q^{85} +(-32296.2 + 129341. i) q^{86} +53882.7i q^{87} +(-19481.6 + 21591.1i) q^{88} +37154.3i q^{89} +(27202.9 + 6792.50i) q^{90} -177645. q^{91} +(-19027.4 + 35725.4i) q^{92} +156403. q^{93} +(18120.9 - 72571.4i) q^{94} +(-16986.3 - 12498.5i) q^{95} +(48810.7 + 134836. i) q^{96} +89114.7i q^{97} +(162303. + 40526.7i) q^{98} -59413.6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9}+O(q^{10}) \) 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9	\( 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9} - 1222 q^{16} + 1000 q^{17} - 300 q^{20} + 17158 q^{24} + 24996 q^{25} + 12102 q^{26} + 6382 q^{28} - 16528 q^{30} + 27524 q^{36} + 3598 q^{38} + 35966 q^{42} - 65408 q^{44} - 13476 q^{45} - 143096 q^{49} - 148446 q^{54} - 53980 q^{57} - 117018 q^{58} + 133740 q^{61} + 28068 q^{62} - 78130 q^{64} + 128204 q^{66} - 48338 q^{68} - 104080 q^{73} + 48932 q^{74} - 251688 q^{76} + 184844 q^{77} + 80080 q^{80} + 375128 q^{81} + 175628 q^{82} - 384748 q^{85} + 139810 q^{92} + 183272 q^{93} + 601258 q^{96}+O(q^{100}) \) 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9 - 1222 * q^16 + 1000 * q^17 - 300 * q^20 + 17158 * q^24 + 24996 * q^25 + 12102 * q^26 + 6382 * q^28 - 16528 * q^30 + 27524 * q^36 + 3598 * q^38 + 35966 * q^42 - 65408 * q^44 - 13476 * q^45 - 143096 * q^49 - 148446 * q^54 - 53980 * q^57 - 117018 * q^58 + 133740 * q^61 + 28068 * q^62 - 78130 * q^64 + 128204 * q^66 - 48338 * q^68 - 104080 * q^73 + 48932 * q^74 - 251688 * q^76 + 184844 * q^77 + 80080 * q^80 + 375128 * q^81 + 175628 * q^82 - 384748 * q^85 + 139810 * q^92 + 183272 * q^93 + 601258 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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