LMFDB - Embedded newform 152.6.b.b.75.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,6,Mod(75,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("152.75");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	152.b (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:	$24.3783406116$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.20
Character	$\chi$	$=$	152.75
Dual form			152.6.b.b.75.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.33851 + 3.63006i) q^{2} +26.7852i q^{3} +(5.64529 - 31.4981i) q^{4} -46.5237i q^{5} +(-97.2319 - 116.208i) q^{6} +208.957i q^{7} +(89.8480 + 157.148i) q^{8} -474.446 q^{9} +O(q^{10})$	\(q+(-4.33851 + 3.63006i) q^{2} +26.7852i q^{3} +(5.64529 - 31.4981i) q^{4} -46.5237i q^{5} +(-97.2319 - 116.208i) q^{6} +208.957i q^{7} +(89.8480 + 157.148i) q^{8} -474.446 q^{9} +(168.884 + 201.844i) q^{10} +35.8554 q^{11} +(843.683 + 151.210i) q^{12} -87.1027 q^{13} +(-758.528 - 906.562i) q^{14} +1246.15 q^{15} +(-960.261 - 355.632i) q^{16} -955.073 q^{17} +(2058.39 - 1722.27i) q^{18} +(-1568.49 + 126.201i) q^{19} +(-1465.41 - 262.640i) q^{20} -5596.96 q^{21} +(-155.559 + 130.158i) q^{22} -3396.26i q^{23} +(-4209.23 + 2406.59i) q^{24} +960.543 q^{25} +(377.896 - 316.188i) q^{26} -6199.33i q^{27} +(6581.76 + 1179.62i) q^{28} -4924.87 q^{29} +(-5406.42 + 4523.59i) q^{30} -668.108 q^{31} +(5457.07 - 1942.90i) q^{32} +960.395i q^{33} +(4143.59 - 3466.97i) q^{34} +9721.47 q^{35} +(-2678.39 + 14944.2i) q^{36} +4068.94 q^{37} +(6346.80 - 6241.26i) q^{38} -2333.06i q^{39} +(7311.09 - 4180.06i) q^{40} +11858.4i q^{41} +(24282.4 - 20317.3i) q^{42} +9400.87 q^{43} +(202.414 - 1129.38i) q^{44} +22073.0i q^{45} +(12328.6 + 14734.7i) q^{46} -8042.65i q^{47} +(9525.67 - 25720.8i) q^{48} -26856.1 q^{49} +(-4167.32 + 3486.83i) q^{50} -25581.8i q^{51} +(-491.720 + 2743.57i) q^{52} +15890.1 q^{53} +(22504.0 + 26895.8i) q^{54} -1668.13i q^{55} +(-32837.1 + 18774.4i) q^{56} +(-3380.32 - 42012.4i) q^{57} +(21366.6 - 17877.6i) q^{58} -35837.9i q^{59} +(7034.86 - 39251.3i) q^{60} -33919.4i q^{61} +(2898.59 - 2425.27i) q^{62} -99139.0i q^{63} +(-16622.7 + 28238.8i) q^{64} +4052.34i q^{65} +(-3486.29 - 4166.68i) q^{66} +69017.0i q^{67} +(-5391.66 + 30083.0i) q^{68} +90969.5 q^{69} +(-42176.7 + 35289.5i) q^{70} -38298.3 q^{71} +(-42628.0 - 74558.0i) q^{72} -63378.5 q^{73} +(-17653.1 + 14770.5i) q^{74} +25728.3i q^{75} +(-4879.50 + 50117.0i) q^{76} +7492.26i q^{77} +(8469.16 + 10122.0i) q^{78} +86670.7 q^{79} +(-16545.3 + 44674.9i) q^{80} +50759.7 q^{81} +(-43046.7 - 51447.8i) q^{82} +90612.1 q^{83} +(-31596.5 + 176294. i) q^{84} +44433.5i q^{85} +(-40785.7 + 34125.7i) q^{86} -131914. i q^{87} +(3221.54 + 5634.59i) q^{88} -26070.4i q^{89} +(-80126.4 - 95763.9i) q^{90} -18200.7i q^{91} +(-106976. - 19172.9i) q^{92} -17895.4i q^{93} +(29195.3 + 34893.1i) q^{94} +(5871.35 + 72972.2i) q^{95} +(52040.9 + 146169. i) q^{96} -135407. i q^{97} +(116515. - 97489.4i) q^{98} -17011.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9}+O(q^{10}) $ 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9	$ 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9} + 944 q^{11} - 3270 q^{16} - 3832 q^{17} + 5240 q^{19} - 1356 q^{20} + 12622 q^{24} - 62504 q^{25} - 6 q^{26} - 110 q^{28} - 14656 q^{30} + 7720 q^{35} - 90984 q^{36} + 22390 q^{38} - 35306 q^{42} + 45096 q^{43} - 22100 q^{44} - 210840 q^{49} + 55038 q^{54} - 36336 q^{57} + 64402 q^{58} + 132976 q^{62} - 182030 q^{64} + 101048 q^{66} - 9030 q^{68} - 4336 q^{73} + 80748 q^{74} - 104304 q^{76} - 31392 q^{80} - 20624 q^{81} + 145904 q^{82} + 52152 q^{83} - 12226 q^{92} - 80058 q^{96} - 752768 q^{99}+O(q^{100}) $ 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9 + 944 * q^11 - 3270 * q^16 - 3832 * q^17 + 5240 * q^19 - 1356 * q^20 + 12622 * q^24 - 62504 * q^25 - 6 * q^26 - 110 * q^28 - 14656 * q^30 + 7720 * q^35 - 90984 * q^36 + 22390 * q^38 - 35306 * q^42 + 45096 * q^43 - 22100 * q^44 - 210840 * q^49 + 55038 * q^54 - 36336 * q^57 + 64402 * q^58 + 132976 * q^62 - 182030 * q^64 + 101048 * q^66 - 9030 * q^68 - 4336 * q^73 + 80748 * q^74 - 104304 * q^76 - 31392 * q^80 - 20624 * q^81 + 145904 * q^82 + 52152 * q^83 - 12226 * q^92 - 80058 * q^96 - 752768 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−4.33851	+	3.63006i	−0.766947	+	0.641710i
$2$	−4.33851	+	3.63006i	−0.766947	+	0.641710i
$3$			26.7852i			1.71827i	0.511749	+	0.859135i	$0.328998\pi$
$3$			26.7852i			1.71827i	−0.511749	+	0.859135i	$0.671002\pi$
$4$	5.64529	−	31.4981i	0.176415	−	0.984316i
$5$		−	46.5237i		−	0.832242i	−0.909309	−	0.416121i	$-0.863389\pi$
$5$		−	46.5237i		−	0.832242i	0.909309	−	0.416121i	$-0.136611\pi$
$6$	−97.2319	−	116.208i	−1.10263	−	1.31782i
$7$			208.957i			1.61180i	0.592049	+	0.805902i	$0.298319\pi$
$7$			208.957i			1.61180i	−0.592049	+	0.805902i	$0.701681\pi$
$8$	89.8480	+	157.148i	0.496345	+	0.868126i
$9$	−474.446			−1.95245
$10$	168.884	+	201.844i	0.534058	+	0.638285i
$11$	35.8554			0.0893457			0.0446728	−	0.999002i	$-0.485775\pi$
$11$	35.8554			0.0893457			0.0446728	+	0.999002i	$0.485775\pi$
$12$	843.683	+	151.210i	1.69132	+	0.303129i
$13$	−87.1027			−0.142946			−0.0714732	−	0.997443i	$-0.522770\pi$
$13$	−87.1027			−0.142946			−0.0714732	+	0.997443i	$0.522770\pi$
$14$	−758.528	−	906.562i	−1.03431	−	1.23617i
$15$	1246.15			1.43002
$16$	−960.261	−	355.632i	−0.937755	−	0.347297i
$17$	−955.073			−0.801520			−0.400760	−	0.916183i	$-0.631254\pi$
$17$	−955.073			−0.801520			−0.400760	+	0.916183i	$0.631254\pi$
$18$	2058.39	−	1722.27i	1.49743	−	1.25291i
$19$	−1568.49	+	126.201i	−0.996779	+	0.0802010i
$19$	−1568.49	+	126.201i	−0.996779	+	0.0802010i
$20$	−1465.41	−	262.640i	−0.819189	−	0.146820i
$21$	−5596.96			−2.76952
$22$	−155.559	+	130.158i	−0.0685234	+	0.0573340i
$23$		−	3396.26i		−	1.33869i	−0.742950	−	0.669347i	$-0.766574\pi$
$23$		−	3396.26i		−	1.33869i	0.742950	−	0.669347i	$-0.233426\pi$
$24$	−4209.23	+	2406.59i	−1.49167	+	0.852854i
$25$	960.543			0.307374
$26$	377.896	−	316.188i	0.109632	−	0.0917302i
$27$		−	6199.33i		−	1.63657i
$28$	6581.76	+	1179.62i	1.58652	+	0.284347i
$29$	−4924.87			−1.08743			−0.543713	−	0.839271i	$-0.682982\pi$
$29$	−4924.87			−1.08743			−0.543713	+	0.839271i	$0.682982\pi$
$30$	−5406.42	+	4523.59i	−1.09675	+	0.917656i
$31$	−668.108			−0.124866			−0.0624328	−	0.998049i	$-0.519886\pi$
$31$	−668.108			−0.124866			−0.0624328	+	0.998049i	$0.519886\pi$
$32$	5457.07	−	1942.90i	0.942073	−	0.335409i
$33$			960.395i			0.153520i
$34$	4143.59	−	3466.97i	0.614723	−	0.514344i
$35$	9721.47			1.34141
$36$	−2678.39	+	14944.2i	−0.344443	+	1.92183i
$37$	4068.94			0.488627			0.244313	−	0.969696i	$-0.421437\pi$
$37$	4068.94			0.488627			0.244313	+	0.969696i	$0.421437\pi$
$38$	6346.80	−	6241.26i	0.713011	−	0.701153i
$39$		−	2333.06i		−	0.245620i
$40$	7311.09	−	4180.06i	0.722490	−	0.413079i
$41$			11858.4i			1.10171i	0.834602	+	0.550854i	$0.185698\pi$
$41$			11858.4i			1.10171i	−0.834602	+	0.550854i	$0.814302\pi$
$42$	24282.4	−	20317.3i	2.12407	−	1.77723i
$43$	9400.87			0.775348			0.387674	−	0.921796i	$-0.373279\pi$
$43$	9400.87			0.775348			0.387674	+	0.921796i	$0.373279\pi$
$44$	202.414	−	1129.38i	0.0157619	−	0.0879443i
$45$			22073.0i			1.62491i
$46$	12328.6	+	14734.7i	0.859054	+	1.02671i
$47$		−	8042.65i		−	0.531074i	−0.964101	−	0.265537i	$-0.914451\pi$
$47$		−	8042.65i		−	0.531074i	0.964101	−	0.265537i	$-0.0855492\pi$
$48$	9525.67	−	25720.8i	0.596750	−	1.61132i
$49$	−26856.1			−1.59791
$50$	−4167.32	+	3486.83i	−0.235739	+	0.197245i
$51$		−	25581.8i		−	1.37723i
$52$	−491.720	+	2743.57i	−0.0252179	+	0.140704i
$53$	15890.1			0.777027			0.388514	−	0.921443i	$-0.372989\pi$
$53$	15890.1			0.777027			0.388514	+	0.921443i	$0.372989\pi$
$54$	22504.0	+	26895.8i	1.05021	+	1.25516i
$55$		−	1668.13i		−	0.0743572i
$56$	−32837.1	+	18774.4i	−1.39925	+	0.800010i
$57$	−3380.32	−	42012.4i	−0.137807	−	1.71274i
$58$	21366.6	−	17877.6i	0.833999	−	0.697813i
$59$		−	35837.9i		−	1.34033i	−0.742211	−	0.670167i	$-0.766223\pi$
$59$		−	35837.9i		−	1.34033i	0.742211	−	0.670167i	$-0.233777\pi$
$60$	7034.86	−	39251.3i	0.252277	−	1.40759i
$61$		−	33919.4i		−	1.16714i	−0.812062	−	0.583571i	$-0.801655\pi$
$61$		−	33919.4i		−	1.16714i	0.812062	−	0.583571i	$-0.198345\pi$
$62$	2898.59	−	2425.27i	0.0957653	−	0.0801275i
$63$		−	99139.0i		−	3.14697i
$64$	−16622.7	+	28238.8i	−0.507284	+	0.861779i
$65$			4052.34i			0.118966i
$66$	−3486.29	−	4166.68i	−0.0985154	−	0.117742i
$67$			69017.0i			1.87832i	0.343483	+	0.939159i	$0.388393\pi$
$67$			69017.0i			1.87832i	−0.343483	+	0.939159i	$0.611607\pi$
$68$	−5391.66	+	30083.0i	−0.141400	+	0.788948i
$69$	90969.5			2.30024
$70$	−42176.7	+	35289.5i	−1.02879	+	0.860797i
$71$	−38298.3			−0.901641			−0.450820	−	0.892615i	$-0.648868\pi$
$71$	−38298.3			−0.901641			−0.450820	+	0.892615i	$0.648868\pi$
$72$	−42628.0	−	74558.0i	−0.969090	−	1.69497i
$73$	−63378.5			−1.39199			−0.695993	−	0.718049i	$-0.745035\pi$
$73$	−63378.5			−1.39199			−0.695993	+	0.718049i	$0.745035\pi$
$74$	−17653.1	+	14770.5i	−0.374751	+	0.313557i
$75$			25728.3i			0.528151i
$76$	−4879.50	+	50117.0i	−0.0969040	+	0.995294i
$77$			7492.26i			0.144008i
$78$	8469.16	+	10122.0i	0.157617	+	0.188378i
$79$	86670.7			1.56244			0.781222	−	0.624253i	$-0.214597\pi$
$79$	86670.7			1.56244			0.781222	+	0.624253i	$0.214597\pi$
$80$	−16545.3	+	44674.9i	−0.289035	+	0.780439i
$81$	50759.7			0.859621
$82$	−43046.7	−	51447.8i	−0.706978	−	0.844952i
$83$	90612.1			1.44375			0.721874	−	0.692025i	$-0.243281\pi$
$83$	90612.1			1.44375			0.721874	+	0.692025i	$0.243281\pi$
$84$	−31596.5	+	176294.i	−0.488585	+	2.72608i
$85$			44433.5i			0.667058i
$86$	−40785.7	+	34125.7i	−0.594651	+	0.497549i
$87$		−	131914.i		−	1.86849i
$88$	3221.54	+	5634.59i	0.0443462	+	0.0775633i
$89$		−	26070.4i		−	0.348877i	−0.984668	−	0.174439i	$-0.944189\pi$
$89$		−	26070.4i		−	0.348877i	0.984668	−	0.174439i	$-0.0558111\pi$
$90$	−80126.4	−	95763.9i	−1.04272	−	1.24622i
$91$		−	18200.7i		−	0.230402i
$92$	−106976.	−	19172.9i	−1.31770	−	0.236166i
$93$		−	17895.4i		−	0.214553i
$94$	29195.3	+	34893.1i	0.340796	+	0.407305i
$95$	5871.35	+	72972.2i	0.0667466	+	0.829561i
$96$	52040.9	+	146169.i	0.576324	+	1.61874i
$97$		−	135407.i		−	1.46121i	−0.682801	−	0.730605i	$-0.739238\pi$
$97$		−	135407.i		−	1.46121i	0.682801	−	0.730605i	$-0.260762\pi$
$98$	116515.	−	97489.4i	1.22551	−	1.02540i
$99$	−17011.5			−0.174443
$100$	5422.54	−	30255.3i	0.0542254	−	0.302553i
$101$		−	56704.1i		−	0.553110i	−0.960998	−	0.276555i	$-0.910807\pi$
$101$		−	56704.1i		−	0.553110i	0.960998	−	0.276555i	$-0.0891928\pi$
$102$	92863.5	+	110987.i	0.883781	+	1.05626i
$103$	−89254.9			−0.828970			−0.414485	−	0.910056i	$-0.636038\pi$
$103$	−89254.9			−0.828970			−0.414485	+	0.910056i	$0.636038\pi$
$104$	−7826.00	−	13688.0i	−0.0709506	−	0.124095i
$105$			260391.i			2.30491i
$106$	−68939.2	+	57682.0i	−0.595939	+	0.498627i
$107$		−	38727.5i		−	0.327010i	−0.986543	−	0.163505i	$-0.947720\pi$
$107$		−	38727.5i		−	0.327010i	0.986543	−	0.163505i	$-0.0522799\pi$
$108$	−195267.	−	34997.0i	−1.61090	−	0.288716i
$109$	−95570.2			−0.770471			−0.385236	−	0.922818i	$-0.625880\pi$
$109$	−95570.2			−0.770471			−0.385236	+	0.922818i	$0.625880\pi$
$110$	6055.41	+	7237.19i	0.0477158	+	0.0570280i
$111$			108987.i			0.839593i
$112$	74311.9	−	200654.i	0.559774	−	1.51148i
$113$			175456.i			1.29262i	0.763073	+	0.646312i	$0.223690\pi$
$113$			175456.i			1.29262i	−0.763073	+	0.646312i	$0.776310\pi$
$114$	167173.	+	170000.i	1.20477	+	1.22515i
$115$	−158007.			−1.11412
$116$	−27802.3	+	155124.i	−0.191839	+	1.07037i
$117$	41325.5			0.279096
$118$	130094.	+	155483.i	0.860106	+	1.02796i
$119$		−	199569.i		−	1.29189i
$120$	111964.	+	195829.i	0.709781	+	1.24143i
$121$	−159765.			−0.992017
$122$	123130.	+	147160.i	0.748968	+	0.895137i
$123$	−317630.			−1.89303
$124$	−3771.66	+	21044.1i	−0.0220282	+	0.122907i
$125$		−	190075.i		−	1.08805i
$126$	359881.	+	430115.i	2.01945	+	2.41356i
$127$	−321898.			−1.77096			−0.885480	−	0.464677i	$-0.846170\pi$
$127$	−321898.			−1.77096			−0.885480	+	0.464677i	$0.846170\pi$
$128$	−30390.9	−	182855.i	−0.163953	−	0.986468i
$129$			251804.i			1.33226i
$130$	−14710.2	−	17581.1i	−0.0763417	−	0.0912405i
$131$	263947.			1.34381			0.671907	−	0.740635i	$-0.265475\pi$
$131$	263947.			1.34381			0.671907	+	0.740635i	$0.265475\pi$
$132$	30250.6	+	5421.71i	0.151112	+	0.0270833i
$133$	−26370.7	−	327748.i	−0.129268	−	1.60661i
$134$	−250536.	−	299431.i	−1.20534	−	1.44057i
$135$	−288416.			−1.36202
$136$	−85811.3	−	150087.i	−0.397830	−	0.695820i
$137$	−135367.			−0.616186			−0.308093	−	0.951356i	$-0.599691\pi$
$137$	−135367.			−0.616186			−0.308093	+	0.951356i	$0.599691\pi$
$138$	−394672.	+	330225.i	−1.76416	+	1.47609i
$139$	−40557.9			−0.178048			−0.0890242	−	0.996029i	$-0.528375\pi$
$139$	−40557.9			−0.178048			−0.0890242	+	0.996029i	$0.528375\pi$
$140$	54880.5	−	306208.i	0.236645	−	1.32037i
$141$	215424.			0.912528
$142$	166157.	−	139025.i	0.691510	−	0.578592i
$143$	−3123.10			−0.0127716
$144$	455592.	+	168728.i	1.83092	+	0.678081i
$145$			229123.i			0.905002i
$146$	274968.	−	230068.i	1.06758	−	0.893252i
$147$		−	719346.i		−	2.74565i
$148$	22970.4	−	128164.i	0.0862012	−	0.480963i
$149$		−	303380.i		−	1.11949i	−0.828664	−	0.559746i	$-0.810899\pi$
$149$		−	303380.i		−	1.11949i	0.828664	−	0.559746i	$-0.189101\pi$
$150$	−93395.4	−	111623.i	−0.338920	−	0.405064i
$151$	−244773.			−0.873618			−0.436809	−	0.899554i	$-0.643891\pi$
$151$	−244773.			−0.873618			−0.436809	+	0.899554i	$0.643891\pi$
$152$	−160758.	−	235146.i	−0.564370	−	0.825522i
$153$	453131.			1.56493
$154$	−27197.4	−	32505.2i	−0.0924113	−	0.110446i
$155$			31082.9i			0.103918i
$156$	−73487.0	−	13170.8i	−0.241768	−	0.0433312i
$157$			357645.i			1.15798i	0.815333	+	0.578992i	$0.196554\pi$
$157$			357645.i			1.15798i	−0.815333	+	0.578992i	$0.803446\pi$
$158$	−376021.	+	314620.i	−1.19831	+	1.00264i
$159$			425619.i			1.33514i
$160$	−90390.8	−	253883.i	−0.279142	−	0.784032i
$161$	709673.			2.15771
$162$	−220222.	+	184261.i	−0.659284	+	0.551628i
$163$	−584184.			−1.72219			−0.861094	−	0.508446i	$-0.830220\pi$
$163$	−584184.			−1.72219			−0.861094	+	0.508446i	$0.830220\pi$
$164$	373517.	+	66944.1i	1.08443	+	0.194358i
$165$	44681.1			0.127766
$166$	−393121.	+	328928.i	−1.10728	+	0.926468i
$167$	−226657.			−0.628896			−0.314448	−	0.949275i	$-0.601819\pi$
$167$	−226657.			−0.628896			−0.314448	+	0.949275i	$0.601819\pi$
$168$	−502875.	−	879548.i	−1.37463	−	2.40429i
$169$	−363706.			−0.979566
$170$	−161297.	−	192775.i	−0.428058	−	0.511598i
$171$	744166.	−	59875.7i	1.94616	−	0.156589i
$172$	53070.6	−	296110.i	0.136783	−	0.763188i
$173$	191412.			0.486244			0.243122	−	0.969996i	$-0.421828\pi$
$173$	191412.			0.486244			0.243122	+	0.969996i	$0.421828\pi$
$174$	478855.	+	572308.i	1.19903	+	1.43304i
$175$			200712.i			0.495426i
$176$	−34430.6	−	12751.3i	−0.0837844	−	0.0310295i
$177$	959925.			2.30306
$178$	94637.2	+	113107.i	0.223878	+	0.267570i
$179$			669795.i			1.56246i	0.624242	+	0.781231i	$0.285408\pi$
$179$			669795.i			1.56246i	−0.624242	+	0.781231i	$0.714592\pi$
$180$	695258.	+	124609.i	1.59943	+	0.286660i
$181$	−156815.			−0.355788			−0.177894	−	0.984050i	$-0.556928\pi$
$181$	−156815.			−0.355788			−0.177894	+	0.984050i	$0.556928\pi$
$182$	66069.8	+	78964.0i	0.147851	+	0.176706i
$183$	908538.			2.00547
$184$	533714.	−	305147.i	1.16216	−	0.664454i
$185$		−	189302.i		−	0.406655i
$186$	64961.4	+	77639.3i	0.137681	+	0.164551i
$187$	−34244.6			−0.0716123
$188$	−253328.	−	45403.1i	−0.522744	−	0.0936895i
$189$	1.29539e6			2.63783
$190$	−290366.	−	295277.i	−0.583529	−	0.593397i
$191$			269519.i			0.534572i	0.963617	+	0.267286i	$0.0861269\pi$
$191$			269519.i			0.534572i	−0.963617	+	0.267286i	$0.913873\pi$
$192$	−756381.	−	445242.i	−1.48077	−	0.871651i
$193$		−	376841.i		−	0.728224i	−0.931355	−	0.364112i	$-0.881372\pi$
$193$		−	376841.i		−	0.728224i	0.931355	−	0.364112i	$-0.118628\pi$
$194$	491537.	+	587465.i	0.937673	+	1.12067i
$195$	−108543.			−0.204416
$196$	−151611.	+	845917.i	−0.281896	+	1.57285i
$197$			761356.i			1.39773i	0.715256	+	0.698863i	$0.246310\pi$
$197$			761356.i			1.39773i	−0.715256	+	0.698863i	$0.753690\pi$
$198$	73804.4	−	61752.7i	0.133789	−	0.111942i
$199$		−	478068.i		−	0.855770i	−0.903833	−	0.427885i	$-0.859259\pi$
$199$		−	478068.i		−	0.855770i	0.903833	−	0.427885i	$-0.140741\pi$
$200$	86302.8	+	150947.i	0.152563	+	0.266839i
$201$	−1.84863e6			−3.22746
$202$	205840.	+	246011.i	0.354936	+	0.424206i
$203$		−	1.02909e6i		−	1.75272i
$204$	−805778.	−	144417.i	−1.35563	−	0.242964i
$205$	551697.			0.916887
$206$	387233.	−	324001.i	0.635776	−	0.531959i
$207$			1.61134e6i			2.61374i
$208$	83641.3	+	30976.5i	0.134049	+	0.0496448i
$209$	−56239.0	+	4525.00i	−0.0890578	+	0.00716561i
$210$	−945237.	−	1.12971e6i	−1.47908	−	1.76774i
$211$			206673.i			0.319578i	0.987151	+	0.159789i	$0.0510814\pi$
$211$			206673.i			0.319578i	−0.987151	+	0.159789i	$0.948919\pi$
$212$	89704.1	−	500507.i	0.137080	−	0.764840i
$213$		−	1.02583e6i		−	1.54926i
$214$	140583.	+	168020.i	0.209846	+	0.250799i
$215$		−	437363.i		−	0.645277i
$216$	974209.	−	556997.i	1.42075	−	0.812304i
$217$		−	139606.i		−	0.201259i
$218$	414632.	−	346926.i	0.590910	−	0.494419i
$219$		−	1.69760e6i		−	2.39181i
$220$	−52542.9	−	9417.07i	−0.0731909	−	0.0131177i
$221$	83189.4			0.114574
$222$	−395631.	−	472842.i	−0.538775	−	0.643923i
$223$	−961700.			−1.29502			−0.647512	−	0.762056i	$-0.724190\pi$
$223$	−961700.			−1.29502			−0.647512	+	0.762056i	$0.724190\pi$
$224$	405982.	+	1.14029e6i	0.540614	+	1.51844i
$225$	−455726.			−0.600133
$226$	−636917.	−	761217.i	−0.829490	−	0.991374i
$227$		−	89750.5i		−	0.115604i	−0.998328	−	0.0578019i	$-0.981591\pi$
$227$		−	89750.5i		−	0.115604i	0.998328	−	0.0578019i	$-0.0184092\pi$
$228$	−1.34239e6	−	130698.i	−1.71018	−	0.166507i
$229$			890166.i			1.12171i	0.827912	+	0.560857i	$0.189528\pi$
$229$			890166.i			1.12171i	−0.827912	+	0.560857i	$0.810472\pi$
$230$	685513.	−	573574.i	0.854469	−	0.714941i
$231$	−200681.			−0.247444
$232$	−442490.	−	773931.i	−0.539738	−	0.944023i
$233$	378174.			0.456354			0.228177	−	0.973620i	$-0.426723\pi$
$233$	378174.			0.456354			0.228177	+	0.973620i	$0.426723\pi$
$234$	−179291.	+	150014.i	−0.214052	+	0.179099i
$235$	−374174.			−0.441982
$236$	−1.12883e6	−	202315.i	−1.31931	−	0.236455i
$237$			2.32149e6i			2.68470i
$238$	724449.	+	865833.i	0.829021	+	0.990813i
$239$		−	538846.i		−	0.610196i	−0.952321	−	0.305098i	$-0.901311\pi$
$239$		−	538846.i		−	0.610196i	0.952321	−	0.305098i	$-0.0986893\pi$
$240$	−1.19663e6	−	443169.i	−1.34101	−	0.496640i
$241$			1.09661e6i			1.21621i	0.793855	+	0.608107i	$0.208071\pi$
$241$			1.09661e6i			1.21621i	−0.793855	+	0.608107i	$0.791929\pi$
$242$	693143.	−	579958.i	0.760825	−	0.636588i
$243$		−	146828.i		−	0.159512i
$244$	−1.06840e6	−	191485.i	−1.14884	−	0.205902i
$245$			1.24945e6i			1.32985i
$246$	1.37804e6	−	1.15302e6i	1.45186	−	1.21478i
$247$	136620.	−	10992.5i	0.142486	−	0.0114644i
$248$	−60028.2	−	104992.i	−0.0619763	−	0.108399i
$249$			2.42706e6i			2.48075i
$250$	689983.	+	824640.i	0.698214	+	0.834477i
$251$	249160.			0.249628			0.124814	−	0.992180i	$-0.460167\pi$
$251$	249160.			0.249628			0.124814	+	0.992180i	$0.460167\pi$
$252$	−3.12269e6	−	559668.i	−3.09762	−	0.555174i
$253$		−	121774.i		−	0.119607i
$254$	1.39656e6	−	1.16851e6i	1.35823	−	1.13644i
$255$	−1.19016e6			−1.14619
$256$	795628.	+	682999.i	0.758770	+	0.651359i
$257$		−	489707.i		−	0.462491i	−0.972895	−	0.231246i	$-0.925720\pi$
$257$		−	489707.i		−	0.462491i	0.972895	−	0.231246i	$-0.0742801\pi$
$258$	−914064.	−	1.09245e6i	−0.854924	−	1.02177i
$259$			850235.i			0.787570i
$260$	127641.	+	22876.6i	0.117100	+	0.0209874i
$261$	2.33659e6			2.12315
$262$	−1.14514e6	+	958146.i	−1.03063	+	0.862340i
$263$		−	832999.i		−	0.742601i	−0.928513	−	0.371300i	$-0.878912\pi$
$263$		−	832999.i		−	0.742601i	0.928513	−	0.371300i	$-0.121088\pi$
$264$	−150924.	+	86289.5i	−0.133275	+	0.0761988i
$265$		−	739266.i		−	0.646675i
$266$	1.30416e6	+	1.32621e6i	1.13012	+	1.14923i
$267$	698301.			0.599466
$268$	2.17391e6	+	389621.i	1.84886	+	0.331364i
$269$	−2.02119e6			−1.70304			−0.851521	−	0.524320i	$-0.824320\pi$
$269$	−2.02119e6			−1.70304			−0.851521	+	0.524320i	$0.824320\pi$
$270$	1.25129e6	−	1.04697e6i	1.04460	−	0.874025i
$271$		−	1.20460e6i		−	0.996370i	−0.867071	−	0.498185i	$-0.834000\pi$
$271$		−	1.20460e6i		−	0.996370i	0.867071	−	0.498185i	$-0.166000\pi$
$272$	917120.	+	339654.i	0.751629	+	0.278365i
$273$	487510.			0.395892
$274$	587291.	−	491391.i	0.472582	−	0.395413i
$275$	34440.7			0.0274625
$276$	513549.	−	2.86537e6i	0.405797	−	2.26416i
$277$		−	994518.i		−	0.778777i	−0.921074	−	0.389389i	$-0.872686\pi$
$277$		−	994518.i		−	0.778777i	0.921074	−	0.389389i	$-0.127314\pi$
$278$	175961.	−	147228.i	0.136554	−	0.114256i
$279$	316981.			0.243794
$280$	873454.	+	1.52770e6i	0.665802	+	1.16451i
$281$			71283.1i			0.0538543i	0.999637	+	0.0269272i	$0.00857222\pi$
$281$			71283.1i			0.0538543i	−0.999637	+	0.0269272i	$0.991428\pi$
$282$	−934619.	+	782003.i	−0.699861	+	0.585579i
$283$	2.51083e6			1.86359			0.931796	−	0.362982i	$-0.118241\pi$
$283$	2.51083e6			1.86359			0.931796	+	0.362982i	$0.118241\pi$
$284$	−216205.	+	1.20632e6i	−0.159063	+	0.887499i
$285$	−1.95457e6	+	157265.i	−1.42541	+	0.114689i
$286$	13549.6	−	11337.1i	0.00979517	−	0.00819569i
$287$	−2.47790e6			−1.77574
$288$	−2.58908e6	+	921800.i	−1.83935	+	0.654871i
$289$	−507693.			−0.357566
$290$	−831732.	−	994054.i	−0.580749	−	0.694088i
$291$	3.62691e6			2.51075
$292$	−357790.	+	1.99630e6i	−0.245568	+	1.37015i
$293$	−564118.			−0.383885			−0.191942	−	0.981406i	$-0.561479\pi$
$293$	−564118.			−0.383885			−0.191942	+	0.981406i	$0.561479\pi$
$294$	2.61127e6	+	3.12089e6i	1.76191	+	2.10577i
$295$	−1.66731e6			−1.11548
$296$	365586.	+	639424.i	0.242527	+	0.424189i
$297$		−	222280.i		−	0.146221i
$298$	1.10129e6	+	1.31622e6i	0.718390	+	0.858591i
$299$			295823.i			0.191361i
$300$	810394.	+	145244.i	0.519868	+	0.0931740i
$301$			1.96438e6i			1.24971i
$302$	1.06195e6	−	888542.i	0.670019	−	0.560610i
$303$	1.51883e6			0.950392
$304$	1.55105e6	+	436620.i	0.962588	+	0.270969i
$305$	−1.57806e6			−0.971345
$306$	−1.96591e6	+	1.64489e6i	−1.20022	+	1.00423i
$307$			3.21582e6i			1.94736i	0.227927	+	0.973678i	$0.426805\pi$
$307$			3.21582e6i			1.94736i	−0.227927	+	0.973678i	$0.573195\pi$
$308$	235992.	+	42296.0i	0.141749	+	0.0254052i
$309$		−	2.39071e6i		−	1.42439i
$310$	−112833.	−	134853.i	−0.0666855	−	0.0796998i
$311$			3.09147e6i			1.81244i	0.422805	+	0.906220i	$0.361045\pi$
$311$			3.09147e6i			1.81244i	−0.422805	+	0.906220i	$0.638955\pi$
$312$	366635.	−	209621.i	0.213229	−	0.121912i
$313$	−379670.			−0.219051			−0.109525	−	0.993984i	$-0.534933\pi$
$313$	−379670.			−0.219051			−0.109525	+	0.993984i	$0.534933\pi$
$314$	−1.29827e6	−	1.55164e6i	−0.743090	−	0.888112i
$315$	−4.61231e6			−2.61904
$316$	489281.	−	2.72996e6i	0.275639	−	1.53794i
$317$	−158325.			−0.0884912			−0.0442456	−	0.999021i	$-0.514088\pi$
$317$	−158325.			−0.0884912			−0.0442456	+	0.999021i	$0.514088\pi$
$318$	−1.54502e6	−	1.84655e6i	−0.856775	−	1.02398i
$319$	−176584.			−0.0971569
$320$	1.31377e6	+	773349.i	0.717208	+	0.422183i
$321$	1.03732e6			0.561891
$322$	−3.07892e6	+	2.57616e6i	−1.65485	+	1.38463i
$323$	1.49803e6	−	120531.i	0.798938	−	0.0642826i
$324$	286553.	−	1.59884e6i	0.151650	−	0.846138i
$325$	−83665.9			−0.0439380
$326$	2.53449e6	−	2.12062e6i	1.32083	−	1.10515i
$327$		−	2.55987e6i		−	1.32388i
$328$	−1.86352e6	+	1.06545e6i	−0.956421	+	0.546827i
$329$	1.68057e6			0.855987
$330$	−193849.	+	162195.i	−0.0979895	+	0.0819886i
$331$		−	30802.8i		−	0.0154533i	−0.999970	−	0.00772664i	$-0.997541\pi$
$331$		−	30802.8i		−	0.0154533i	0.999970	−	0.00772664i	$-0.00245949\pi$
$332$	511532.	−	2.85411e6i	0.254699	−	1.42110i
$333$	−1.93049e6			−0.954021
$334$	983355.	−	822781.i	0.482330	−	0.403569i
$335$	3.21093e6			1.56321
$336$	5.37454e6	+	1.99046e6i	2.59713	+	0.961844i
$337$			3.91249e6i			1.87663i	0.345782	+	0.938315i	$0.387614\pi$
$337$			3.91249e6i			1.87663i	−0.345782	+	0.938315i	$0.612386\pi$
$338$	1.57794e6	−	1.32028e6i	0.751275	−	0.628598i
$339$	−4.69962e6			−2.22108
$340$	1.39957e6	+	250840.i	0.656596	+	0.117679i
$341$	−23955.3			−0.0111562
$342$	−3.01122e6	+	2.96114e6i	−1.39212	+	1.36897i
$343$		−	2.09984e6i		−	0.963719i
$344$	844649.	+	1.47732e6i	0.384840	+	0.673100i
$345$		−	4.23224e6i		−	1.91436i
$346$	−830443.	+	694838.i	−0.372923	+	0.312028i
$347$	−915682.			−0.408245			−0.204123	−	0.978945i	$-0.565434\pi$
$347$	−915682.			−0.408245			−0.204123	+	0.978945i	$0.565434\pi$
$348$	−4.15503e6	−	744691.i	−1.83919	−	0.329631i
$349$			694461.i			0.305200i	0.988288	+	0.152600i	$0.0487646\pi$
$349$			694461.i			0.305200i	−0.988288	+	0.152600i	$0.951235\pi$
$350$	−728599.	−	870792.i	−0.317920	−	0.379966i
$351$			539978.i			0.233942i
$352$	195666.	−	69663.5i	0.0841701	−	0.0299674i
$353$	−3.90432e6			−1.66767			−0.833833	−	0.552017i	$-0.813858\pi$
$353$	−3.90432e6			−1.66767			−0.833833	+	0.552017i	$0.813858\pi$
$354$	−4.16464e6	+	3.48459e6i	−1.76632	+	1.47789i
$355$			1.78178e6i			0.750383i
$356$	−821168.	−	147175.i	−0.343405	−	0.0615473i
$357$	5.34550e6			2.21982
$358$	−2.43140e6	−	2.90591e6i	−1.00265	−	1.19833i
$359$		−	1.92295e6i		−	0.787464i	−0.919225	−	0.393732i	$-0.871184\pi$
$359$		−	1.92295e6i		−	0.787464i	0.919225	−	0.393732i	$-0.128816\pi$
$360$	−3.46872e6	+	1.98321e6i	−1.41063	+	0.806517i
$361$	2.44425e6	−	395892.i	0.987136	−	0.159885i
$362$	680344.	−	569249.i	0.272871	−	0.228313i
$363$		−	4.27935e6i		−	1.70455i
$364$	−573289.	−	102748.i	−0.226788	−	0.0406464i
$365$			2.94860e6i			1.15847i
$366$	−3.94170e6	+	3.29805e6i	−1.53809	+	1.28693i
$367$			3.12502e6i			1.21112i	0.795799	+	0.605561i	$0.207051\pi$
$367$			3.12502e6i			1.21112i	−0.795799	+	0.605561i	$0.792949\pi$
$368$	−1.20782e6	+	3.26130e6i	−0.464924	+	1.25537i
$369$		−	5.62617e6i		−	2.15103i
$370$	687179.	+	821289.i	0.260955	+	0.311883i
$371$			3.32035e6i			1.25242i
$372$	−563671.	−	101025.i	−0.211188	−	0.0378504i
$373$	−3.94141e6			−1.46683			−0.733415	−	0.679781i	$-0.762075\pi$
$373$	−3.94141e6			−1.46683			−0.733415	+	0.679781i	$0.762075\pi$
$374$	148570.	−	124310.i	0.0549228	−	0.0459544i
$375$	5.09119e6			1.86957
$376$	1.26388e6	−	722616.i	0.461039	−	0.263596i
$377$	428969.			0.155444
$378$	−5.62008e6	+	4.70236e6i	−2.02308	+	1.69273i
$379$			73519.4i			0.0262908i	0.999914	+	0.0131454i	$0.00418443\pi$
$379$			73519.4i			0.0262908i	−0.999914	+	0.0131454i	$0.995816\pi$
$380$	2.33163e6	+	227013.i	0.828325	+	0.0806475i
$381$		−	8.62209e6i		−	3.04299i
$382$	−978372.	−	1.16931e6i	−0.343041	−	0.409989i
$383$	−1.71447e6			−0.597220			−0.298610	−	0.954375i	$-0.596523\pi$
$383$	−1.71447e6			−0.597220			−0.298610	+	0.954375i	$0.596523\pi$
$384$	4.89782e6	−	814025.i	1.69502	−	0.281715i
$385$	348568.			0.119849
$386$	1.36796e6	+	1.63493e6i	0.467309	+	0.558510i
$387$	−4.46021e6			−1.51383
$388$	−4.26507e6	−	764413.i	−1.43829	−	0.257780i
$389$		−	4.88524e6i		−	1.63686i	−0.574604	−	0.818431i	$-0.694844\pi$
$389$		−	4.88524e6i		−	1.63686i	0.574604	−	0.818431i	$-0.305156\pi$
$390$	470913.	−	394017.i	0.156776	−	0.131176i
$391$			3.24368e6i			1.07299i
$392$	−2.41297e6	−	4.22037e6i	−0.793116	−	1.38719i
$393$			7.06988e6i			2.30904i
$394$	−2.76377e6	−	3.30315e6i	−0.896935	−	1.07198i
$395$		−	4.03224e6i		−	1.30033i
$396$	−96034.7	+	535829.i	−0.0307745	+	0.171707i
$397$		−	4.50286e6i		−	1.43388i	−0.697136	−	0.716939i	$-0.745542\pi$
$397$		−	4.50286e6i		−	1.43388i	0.697136	−	0.716939i	$-0.254458\pi$
$398$	1.73542e6	+	2.07410e6i	0.549157	+	0.656331i
$399$	8.77879e6	−	706343.i	2.76059	−	0.222118i
$400$	−922372.	−	341600.i	−0.288241	−	0.106750i
$401$		−	264814.i		−	0.0822394i	−0.999154	−	0.0411197i	$-0.986907\pi$
$401$		−	264814.i		−	0.0822394i	0.999154	−	0.0411197i	$-0.0130925\pi$
$402$	8.02031e6	−	6.71066e6i	2.47529	−	2.07109i
$403$	58194.0			0.0178491
$404$	−1.78607e6	−	320111.i	−0.544435	−	0.0975770i
$405$		−	2.36153e6i		−	0.715412i
$406$	3.73565e6	+	4.46470e6i	1.12474	+	1.34424i
$407$	145894.			0.0436567
$408$	4.02012e6	−	2.29847e6i	1.19561	−	0.683579i
$409$		−	1.93926e6i		−	0.573228i	−0.958046	−	0.286614i	$-0.907470\pi$
$409$		−	1.93926e6i		−	0.573228i	0.958046	−	0.286614i	$-0.0925297\pi$
$410$	−2.39354e6	+	2.00269e6i	−0.703204	+	0.588376i
$411$		−	3.62583e6i		−	1.05877i
$412$	−503870.	+	2.81136e6i	−0.146243	+	0.815968i
$413$	7.48859e6			2.16036
$414$	−5.84928e6	−	6.99082e6i	−1.67726	−	2.00460i
$415$		−	4.21561e6i		−	1.20155i
$416$	−475325.	+	169232.i	−0.134666	+	0.0479455i
$417$		−	1.08635e6i		−	0.305935i
$418$	227567.	−	223783.i	0.0637044	−	0.0626450i
$419$	3.75075e6			1.04372			0.521859	−	0.853032i	$-0.325239\pi$
$419$	3.75075e6			1.04372			0.521859	+	0.853032i	$0.325239\pi$
$420$	8.20183e6	+	1.46998e6i	2.26876	+	0.406621i
$421$	−2.84993e6			−0.783661			−0.391831	−	0.920037i	$-0.628158\pi$
$421$	−2.84993e6			−0.783661			−0.391831	+	0.920037i	$0.628158\pi$
$422$	−750235.	−	896651.i	−0.205077	−	0.245099i
$423$			3.81581e6i			1.03690i
$424$	1.42769e6	+	2.49709e6i	0.385673	+	0.674557i
$425$	−917389.			−0.246366
$426$	3.72381e6	+	4.45056e6i	0.994178	+	1.18820i
$427$	7.08771e6			1.88121
$428$	−1.21984e6	−	218628.i	−0.321881	−	0.0576895i
$429$		−	83652.9i		−	0.0219451i
$430$	1.58766e6	+	1.89750e6i	0.414081	+	0.494893i
$431$	−5.18314e6			−1.34400			−0.672001	−	0.740550i	$-0.734565\pi$
$431$	−5.18314e6			−1.34400			−0.672001	+	0.740550i	$0.734565\pi$
$432$	−2.20468e6	+	5.95298e6i	−0.568376	+	1.53470i
$433$		−	1.13879e6i		−	0.291893i	−0.989292	−	0.145947i	$-0.953377\pi$
$433$		−	1.13879e6i		−	0.291893i	0.989292	−	0.145947i	$-0.0466228\pi$
$434$	506779.	+	605682.i	0.129150	+	0.154355i
$435$	−6.13711e6			−1.55504
$436$	−539522.	+	3.01028e6i	−0.135923	+	0.758387i
$437$	428612.	+	5.32701e6i	0.107365	+	1.33438i
$438$	6.16241e6	+	7.36507e6i	1.53485	+	1.83439i
$439$	−2.28863e6			−0.566779			−0.283390	−	0.959005i	$-0.591459\pi$
$439$	−2.28863e6			−0.566779			−0.283390	+	0.959005i	$0.591459\pi$
$440$	262142.	−	149878.i	0.0645514	−	0.0369068i
$441$	1.27418e7			3.11985
$442$	−360918.	+	301983.i	−0.0878724	+	0.0735235i
$443$	−3.82921e6			−0.927043			−0.463521	−	0.886086i	$-0.653414\pi$
$443$	−3.82921e6			−0.927043			−0.463521	+	0.886086i	$0.653414\pi$
$444$	3.43289e6	+	615265.i	0.826424	+	0.148117i
$445$	−1.21289e6			−0.290350
$446$	4.17234e6	−	3.49103e6i	0.993214	−	0.831030i
$447$	8.12609e6			1.92359
$448$	−5.90070e6	−	3.47343e6i	−1.38902	−	0.817643i
$449$		−	4.20035e6i		−	0.983262i	−0.870804	−	0.491631i	$-0.836401\pi$
$449$		−	4.20035e6i		−	0.983262i	0.870804	−	0.491631i	$-0.163599\pi$
$450$	1.97717e6	−	1.65431e6i	0.460270	−	0.385112i
$451$			425188.i			0.0984328i
$452$	5.52653e6	+	990500.i	1.27235	+	0.228039i
$453$		−	6.55630e6i		−	1.50111i
$454$	325800.	+	389383.i	0.0741842	+	0.0886620i
$455$	−846766.			−0.191750
$456$	6.29843e6	−	4.30594e6i	1.41847	−	0.969741i
$457$	−868949.			−0.194627			−0.0973136	−	0.995254i	$-0.531025\pi$
$457$	−868949.			−0.194627			−0.0973136	+	0.995254i	$0.531025\pi$
$458$	−3.23136e6	−	3.86199e6i	−0.719816	−	0.860296i
$459$			5.92081e6i			1.31174i
$460$	−891994.	+	4.97691e6i	−0.196547	+	1.09664i
$461$			7.76528e6i			1.70178i	0.525340	+	0.850892i	$0.323938\pi$
$461$			7.76528e6i			1.70178i	−0.525340	+	0.850892i	$0.676062\pi$
$462$	870658.	−	728486.i	0.189777	−	0.158788i
$463$		−	4.35658e6i		−	0.944480i	−0.881470	−	0.472240i	$-0.843446\pi$
$463$		−	4.35658e6i		−	0.944480i	0.881470	−	0.472240i	$-0.156554\pi$
$464$	4.72916e6	+	1.75144e6i	1.01974	+	0.377660i
$465$	−832561.			−0.178560
$466$	−1.64071e6	+	1.37280e6i	−0.350000	+	0.292847i
$467$	3.01885e6			0.640545			0.320272	−	0.947326i	$-0.396226\pi$
$467$	3.01885e6			0.640545			0.320272	+	0.947326i	$0.396226\pi$
$468$	233295.	−	1.30168e6i	0.0492368	−	0.274719i
$469$	−1.44216e7			−3.02748
$470$	1.62336e6	−	1.35828e6i	0.338976	−	0.283624i
$471$	−9.57958e6			−1.98973
$472$	5.63184e6	−	3.21996e6i	1.16358	−	0.665267i
$473$	337072.			0.0692740
$474$	−8.42716e6	−	1.00718e7i	−1.72280	−	2.05902i
$475$	−1.50661e6	+	121222.i	−0.306384	+	0.0246517i
$476$	−6.28606e6	−	1.12663e6i	−1.27163	−	0.227910i
$477$	−7.53899e6			−1.51711
$478$	1.95604e6	+	2.33779e6i	0.391569	+	0.467988i
$479$			6.61819e6i			1.31795i	0.752163	+	0.658977i	$0.229011\pi$
$479$			6.61819e6i			1.31795i	−0.752163	+	0.658977i	$0.770989\pi$
$480$	6.80031e6	−	2.42114e6i	1.34718	−	0.479641i
$481$	−354416.			−0.0698474
$482$	−3.98077e6	−	4.75765e6i	−0.780457	−	0.932771i
$483$			1.90087e7i			3.70754i
$484$	−901922.	+	5.03231e6i	−0.175007	+	0.976458i
$485$	−6.29965e6			−1.21608
$486$	532993.	+	637013.i	0.102360	+	0.122337i
$487$	8.57297e6			1.63798			0.818990	−	0.573807i	$-0.194534\pi$
$487$	8.57297e6			1.63798			0.818990	+	0.573807i	$0.194534\pi$
$488$	5.33036e6	−	3.04759e6i	1.01323	−	0.579305i
$489$		−	1.56475e7i		−	2.95918i
$490$	−4.53557e6	−	5.42073e6i	−0.853379	−	1.01992i
$491$	287543.			0.0538269			0.0269135	−	0.999638i	$-0.491432\pi$
$491$	287543.			0.0538269			0.0269135	+	0.999638i	$0.491432\pi$
$492$	−1.79311e6	+	1.00047e7i	−0.333960	+	1.86334i
$493$	4.70361e6			0.871594
$494$	−552823.	+	543630.i	−0.101922	+	0.100227i
$495$			791437.i			0.145179i
$496$	641559.	+	237601.i	0.117093	+	0.0433654i
$497$		−	8.00270e6i		−	1.45327i
$498$	−8.81039e6	−	1.05298e7i	−1.59192	−	1.90260i
$499$	−41932.3			−0.00753871			−0.00376936	−	0.999993i	$-0.501200\pi$
$499$	−41932.3			−0.00753871			−0.00376936	+	0.999993i	$0.501200\pi$
$500$	−5.98699e6	−	1.07303e6i	−1.07099	−	0.191949i
$501$		−	6.07106e6i		−	1.08061i
$502$	−1.08098e6	+	904465.i	−0.191451	+	0.160189i
$503$		−	1.80449e6i		−	0.318005i	−0.987278	−	0.159003i	$-0.949172\pi$
$503$		−	1.80449e6i		−	0.318005i	0.987278	−	0.159003i	$-0.0508278\pi$
$504$	1.55794e7	−	8.90743e6i	2.73197	−	1.56198i
$505$	−2.63809e6			−0.460321
$506$	442049.	+	528319.i	0.0767528	+	0.0917319i
$507$		−	9.74194e6i		−	1.68316i
$508$	−1.81721e6	+	1.01392e7i	−0.312424	+	1.74318i
$509$	7.01256e6			1.19973			0.599863	−	0.800103i	$-0.295222\pi$
$509$	7.01256e6			1.19973			0.599863	+	0.800103i	$0.295222\pi$
$510$	5.16352e6	−	4.32036e6i	0.879064	−	0.735520i
$511$		−	1.32434e7i		−	2.24361i
$512$	−5.93117e6	−	75017.6i	−0.999920	−	0.0126470i
$513$	782363.	+	9.72361e6i	0.131255	+	1.63130i
$514$	1.77767e6	+	2.12460e6i	0.296785	+	0.354706i
$515$			4.15247e6i			0.689904i
$516$	7.93135e6	+	1.42151e6i	1.31136	+	0.235031i
$517$		−	288373.i		−	0.0474491i
$518$	−3.08641e6	−	3.68875e6i	−0.505392	−	0.604025i
$519$			5.12701e6i			0.835499i
$520$	−636815.	+	364095.i	−0.103277	+	0.0590481i
$521$		−	4.29098e6i		−	0.692568i	−0.938130	−	0.346284i	$-0.887443\pi$
$521$		−	4.29098e6i		−	0.692568i	0.938130	−	0.346284i	$-0.112557\pi$
$522$	−1.01373e7	+	8.48196e6i	−1.62834	+	1.36245i
$523$		−	6.59641e6i		−	1.05452i	−0.849705	−	0.527258i	$-0.823220\pi$
$523$		−	6.59641e6i		−	1.05452i	0.849705	−	0.527258i	$-0.176780\pi$
$524$	1.49006e6	−	8.31385e6i	0.237069	−	1.32274i
$525$	−5.37612e6			−0.851277
$526$	3.02384e6	+	3.61397e6i	0.476535	+	0.569535i
$527$	638092.			0.100082
$528$	341547.	−	922230.i	0.0533170	−	0.143964i
$529$	−5.09825e6			−0.792103
$530$	2.68358e6	+	3.20731e6i	0.414978	+	0.495965i
$531$			1.70032e7i			2.61694i
$532$	−1.04723e7	−	1.01961e6i	−1.60422	−	0.156190i
$533$		−	1.03290e6i		−	0.157485i
$534$	−3.02958e6	+	2.53487e6i	−0.459758	+	0.384683i
$535$	−1.80175e6			−0.272151
$536$	−1.08459e7	+	6.20104e6i	−1.63062	+	0.932293i
$537$	−1.79406e7			−2.68473
$538$	8.76893e6	−	7.33703e6i	1.30614	−	1.09286i
$539$	−962938.			−0.142767
$540$	−1.62819e6	+	9.08455e6i	−0.240282	+	1.34066i
$541$			4.11246e6i			0.604100i	0.953292	+	0.302050i	$0.0976709\pi$
$541$			4.11246e6i			0.604100i	−0.953292	+	0.302050i	$0.902329\pi$
$542$	4.37278e6	+	5.22618e6i	0.639381	+	0.764163i
$543$		−	4.20032e6i		−	0.611341i
$544$	−5.21190e6	+	1.85561e6i	−0.755090	+	0.268837i
$545$			4.44628e6i			0.641218i
$546$	−2.11507e6	+	1.76969e6i	−0.303628	+	0.254048i
$547$			1.39299e6i			0.199058i	0.995035	+	0.0995288i	$0.0317335\pi$
$547$			1.39299e6i			0.199058i	−0.995035	+	0.0995288i	$0.968266\pi$
$548$	−764186.	+	4.26381e6i	−0.108705	+	0.606521i
$549$			1.60929e7i			2.27879i
$550$	−149421.	+	125022.i	−0.0210623	+	0.0176230i
$551$	7.72463e6	−	621525.i	1.08392	−	0.0872127i
$552$	8.17342e6	+	1.42956e7i	1.14171	+	1.99690i
$553$			1.81105e7i			2.51835i
$554$	3.61016e6	+	4.31472e6i	0.499749	+	0.597281i
$555$	5.07050e6			0.698744
$556$	−228961.	+	1.27750e6i	−0.0314105	+	0.175256i
$557$			1.13242e6i			0.154658i	0.997006	+	0.0773288i	$0.0246391\pi$
$557$			1.13242e6i			0.154658i	−0.997006	+	0.0773288i	$0.975361\pi$
$558$	−1.37523e6	+	1.15066e6i	−0.186977	+	0.156445i
$559$	−818841.			−0.110833
$560$	−9.33515e6	−	3.45726e6i	−1.25791	−	0.465868i
$561$		−	917247.i		−	0.123049i
$562$	−258762.	−	309262.i	−0.0345589	−	0.0413034i
$563$		−	1.29877e6i		−	0.172688i	−0.996265	−	0.0863439i	$-0.972482\pi$
$563$		−	1.29877e6i		−	0.172688i	0.996265	−	0.0863439i	$-0.0275184\pi$
$564$	1.21613e6	−	6.78545e6i	0.160984	−	0.898216i
$565$	8.16287e6			1.07578
$566$	−1.08932e7	+	9.11446e6i	−1.42928	+	1.19589i
$567$			1.06066e7i			1.38554i
$568$	−3.44102e6	−	6.01848e6i	−0.447524	−	0.782737i
$569$		−	2.85081e6i		−	0.369137i	−0.982820	−	0.184568i	$-0.940911\pi$
$569$		−	2.85081e6i		−	0.369137i	0.982820	−	0.184568i	$-0.0590887\pi$
$570$	7.90905e6	−	7.77752e6i	1.01962	−	1.00266i
$571$	−2.47617e6			−0.317827			−0.158913	−	0.987293i	$-0.550799\pi$
$571$	−2.47617e6			−0.317827			−0.158913	+	0.987293i	$0.550799\pi$
$572$	−17630.8	+	98371.9i	−0.00225311	+	0.0125713i
$573$	−7.21913e6			−0.918540
$574$	1.07504e7	−	8.99493e6i	1.36190	−	1.13951i
$575$		−	3.26226e6i		−	0.411480i
$576$	7.88657e6	−	1.33978e7i	0.990449	−	1.68258i
$577$	−5.44738e6			−0.681158			−0.340579	−	0.940216i	$-0.610623\pi$
$577$	−5.44738e6			−0.681158			−0.340579	+	0.940216i	$0.610623\pi$
$578$	2.20263e6	−	1.84296e6i	0.274234	−	0.229454i
$579$	1.00938e7			1.25129
$580$	7.21695e6	+	1.29347e6i	0.890808	+	0.159656i
$581$			1.89341e7i			2.32704i
$582$	−1.57354e7	+	1.31659e7i	−1.92561	+	1.61118i
$583$	569746.			0.0694240
$584$	−5.69443e6	−	9.95977e6i	−0.690904	−	1.20842i
$585$		−	1.92262e6i		−	0.232275i
$586$	2.44743e6	−	2.04778e6i	0.294419	−	0.246343i
$587$	5.79540e6			0.694205			0.347103	−	0.937827i	$-0.387166\pi$
$587$	5.79540e6			0.694205			0.347103	+	0.937827i	$0.387166\pi$
$588$	−2.26580e7	−	4.06092e6i	−2.70258	−	0.484374i
$589$	1.04792e6	−	84316.1i	0.124463	−	0.0100143i
$590$	7.23365e6	−	6.05245e6i	0.855515	−	0.715816i
$591$	−2.03930e7			−2.40167
$592$	−3.90725e6	−	1.44705e6i	−0.458212	−	0.169698i
$593$	6.02635e6			0.703749			0.351874	−	0.936047i	$-0.385544\pi$
$593$	6.02635e6			0.703749			0.351874	+	0.936047i	$0.385544\pi$
$594$	806889.	+	964362.i	0.0938313	+	0.112143i
$595$	−9.28471e6			−1.07517
$596$	−9.55589e6	−	1.71267e6i	−1.10193	−	0.197496i
$597$	1.28051e7			1.47045
$598$	−1.07386e6	−	1.28343e6i	−0.122799	−	0.146764i
$599$	3.37829e6			0.384707			0.192354	−	0.981326i	$-0.438388\pi$
$599$	3.37829e6			0.384707			0.192354	+	0.981326i	$0.438388\pi$
$600$	−4.04314e6	+	2.31164e6i	−0.458502	+	0.262145i
$601$			6.27163e6i			0.708262i	0.935196	+	0.354131i	$0.115223\pi$
$601$			6.27163e6i			0.708262i	−0.935196	+	0.354131i	$0.884777\pi$
$602$	−7.13082e6	−	8.52247e6i	−0.801952	−	0.958461i
$603$		−	3.27449e7i		−	3.66733i
$604$	−1.38182e6	+	7.70990e6i	−0.154120	+	0.859916i
$605$			7.43288e6i			0.825598i
$606$	−6.58946e6	+	5.51345e6i	−0.728901	+	0.609877i
$607$	1.03899e7			1.14456			0.572280	−	0.820058i	$-0.306059\pi$
$607$	1.03899e7			1.14456			0.572280	+	0.820058i	$0.306059\pi$
$608$	−8.31418e6	+	3.73611e6i	−0.912138	+	0.409884i
$609$	2.75643e7			3.01165
$610$	6.84642e6	−	5.72845e6i	0.744970	−	0.623322i
$611$			700537.i			0.0759150i
$612$	2.55805e6	−	1.42728e7i	0.276078	−	1.54039i
$613$			6.87610e6i			0.739080i	0.929215	+	0.369540i	$0.120485\pi$
$613$			6.87610e6i			0.739080i	−0.929215	+	0.369540i	$0.879515\pi$
$614$	−1.16736e7	−	1.39518e7i	−1.24964	−	1.49352i
$615$			1.47773e7i			1.57546i
$616$	−1.17739e6	+	673164.i	−0.125017	+	0.0714774i
$617$	−1.33979e7			−1.41685			−0.708427	−	0.705784i	$-0.750595\pi$
$617$	−1.33979e7			−1.41685			−0.708427	+	0.705784i	$0.750595\pi$
$618$	8.67842e6	+	1.03721e7i	0.914049	+	1.09244i
$619$	7.51655e6			0.788482			0.394241	−	0.919007i	$-0.371007\pi$
$619$	7.51655e6			0.788482			0.394241	+	0.919007i	$0.371007\pi$
$620$	979052.	+	175472.i	0.102288	+	0.0183328i
$621$	−2.10545e7			−2.19087
$622$	−1.12222e7	−	1.34124e7i	−1.16306	−	1.39005i
$623$	5.44760e6			0.562322
$624$	−829711.	+	2.24035e6i	−0.0853032	+	0.230332i
$625$	−5.84128e6			−0.598148
$626$	1.64720e6	−	1.37822e6i	0.168000	−	0.140567i
$627$	−121203.	−	1.50637e6i	−0.0123125	−	0.153025i
$628$	1.12651e7	+	2.01901e6i	1.13982	+	0.204286i
$629$	−3.88613e6			−0.391644
$630$	2.00106e7	−	1.67430e7i	2.00867	−	1.68067i
$631$			6.39890e6i			0.639781i	0.947454	+	0.319891i	$0.103646\pi$
$631$			6.39890e6i			0.639781i	−0.947454	+	0.319891i	$0.896354\pi$
$632$	7.78719e6	+	1.36201e7i	0.775511	+	1.35640i
$633$	−5.53577e6			−0.549121
$634$	686892.	−	574728.i	0.0678680	−	0.0567857i
$635$			1.49759e7i			1.47387i
$636$	1.34062e7	+	2.40274e6i	1.31420	+	0.235540i
$637$	2.33924e6			0.228416
$638$	766109.	−	641009.i	0.0745142	−	0.0623466i
$639$	1.81705e7			1.76041
$640$	−8.50712e6	+	1.41390e6i	−0.820980	+	0.136448i
$641$			1.08371e7i			1.04176i	0.853630	+	0.520880i	$0.174396\pi$
$641$			1.08371e7i			1.04176i	−0.853630	+	0.520880i	$0.825604\pi$
$642$	−4.50044e6	+	3.76555e6i	−0.430941	+	0.360571i
$643$	1.48100e7			1.41263			0.706314	−	0.707899i	$-0.250357\pi$
$643$	1.48100e7			1.41263			0.706314	+	0.707899i	$0.250357\pi$
$644$	4.00631e6	−	2.23534e7i	0.380654	−	2.12387i
$645$	1.17149e7			1.10876
$646$	−6.06166e6	+	5.96085e6i	−0.571492	+	0.561988i
$647$		−	6.43857e6i		−	0.604684i	−0.953200	−	0.302342i	$-0.902232\pi$
$647$		−	6.43857e6i		−	0.604684i	0.953200	−	0.302342i	$-0.0977684\pi$
$648$	4.56066e6	+	7.97677e6i	0.426668	+	0.746259i
$649$		−	1.28498e6i		−	0.119753i
$650$	362985.	−	303712.i	0.0336981	−	0.0281954i
$651$	3.73937e6			0.345817
$652$	−3.29789e6	+	1.84007e7i	−0.303820	+	1.69518i
$653$		−	4.01075e6i		−	0.368080i	−0.982919	−	0.184040i	$-0.941082\pi$
$653$		−	4.01075e6i		−	0.368080i	0.982919	−	0.184040i	$-0.0589176\pi$
$654$	9.29247e6	+	1.11060e7i	0.849546	+	1.01534i
$655$		−	1.22798e7i		−	1.11838i
$656$	4.21723e6	−	1.13872e7i	0.382620	−	1.03313i
$657$	3.00697e7			2.71779
$658$	−7.29117e6	+	6.10058e6i	−0.656496	+	0.549296i
$659$		−	4.28337e6i		−	0.384213i	−0.981374	−	0.192106i	$-0.938468\pi$
$659$		−	4.28337e6i		−	0.384213i	0.981374	−	0.192106i	$-0.0615319\pi$
$660$	252238.	−	1.40737e6i	0.0225398	−	0.125762i
$661$	−5.08901e6			−0.453032			−0.226516	−	0.974007i	$-0.572734\pi$
$661$	−5.08901e6			−0.453032			−0.226516	+	0.974007i	$0.572734\pi$
$662$	111816.	+	133638.i	0.00991654	+	0.0118519i
$663$			2.22824e6i			0.196870i
$664$	8.14132e6	+	1.42395e7i	0.716596	+	1.25335i
$665$	−1.52481e7	+	1.22686e6i	−1.33709	+	0.107582i
$666$	8.37546e6	−	7.00781e6i	0.731683	−	0.612205i
$667$			1.67262e7i			1.45573i
$668$	−1.27955e6	+	7.13928e6i	−0.110947	+	0.619032i
$669$		−	2.57593e7i		−	2.22520i
$670$	−1.39306e7	+	1.16559e7i	−1.19890	+	1.00313i
$671$		−	1.21620e6i		−	0.104279i
$672$	−3.05430e7	+	1.08743e7i	−2.60908	+	0.928921i
$673$			2.68365e6i			0.228396i	0.993458	+	0.114198i	$0.0364298\pi$
$673$			2.68365e6i			0.228396i	−0.993458	+	0.114198i	$0.963570\pi$
$674$	−1.42026e7	−	1.69744e7i	−1.20425	−	1.43928i
$675$		−	5.95472e6i		−	0.503039i
$676$	−2.05323e6	+	1.14561e7i	−0.172811	+	0.964203i
$677$	1.50512e7			1.26212			0.631059	−	0.775735i	$-0.282621\pi$
$677$	1.50512e7			1.26212			0.631059	+	0.775735i	$0.282621\pi$
$678$	2.03893e7	−	1.70599e7i	1.70345	−	1.42529i
$679$	2.82943e7			2.35518
$680$	−6.98262e6	+	3.99226e6i	−0.579090	+	0.331091i
$681$	2.40398e6			0.198639
$682$	103930.	−	86959.3i	0.00855621	−	0.00715905i
$683$		−	2.12625e7i		−	1.74406i	−0.489450	−	0.872031i	$-0.662803\pi$
$683$		−	2.12625e7i		−	1.74406i	0.489450	−	0.872031i	$-0.337197\pi$
$684$	2.31506e6	−	2.37778e7i	0.189200	−	1.94326i
$685$			6.29778e6i			0.512815i
$686$	7.62254e6	+	9.11016e6i	0.618429	+	0.739121i
$687$	−2.38433e7			−1.92741
$688$	−9.02729e6	−	3.34325e6i	−0.727087	−	0.269276i
$689$	−1.38407e6			−0.111073
$690$	1.53633e7	+	1.83616e7i	1.22846	+	1.46821i
$691$	−1.97533e7			−1.57379			−0.786893	−	0.617090i	$-0.788312\pi$
$691$	−1.97533e7			−1.57379			−0.786893	+	0.617090i	$0.788312\pi$
$692$	1.08058e6	−	6.02912e6i	0.0857809	−	0.478618i
$693$		−	3.55467e6i		−	0.281168i
$694$	3.97269e6	−	3.32398e6i	0.313102	−	0.261975i
$695$			1.88690e6i			0.148179i
$696$	2.07299e7	−	1.18522e7i	1.62209	−	0.927416i
$697$		−	1.13256e7i		−	0.883041i
$698$	−2.52094e6	−	3.01292e6i	−0.195850	−	0.234072i
$699$			1.01295e7i			0.784140i
$700$	6.32206e6	+	1.13308e6i	0.487656	+	0.0874008i
$701$			3.91708e6i			0.301070i	0.988605	+	0.150535i	$0.0480996\pi$
$701$			3.91708e6i			0.301070i	−0.988605	+	0.150535i	$0.951900\pi$
$702$	−1.96015e6	−	2.34270e6i	−0.150123	−	0.179421i
$703$	−6.38211e6	+	513505.i	−0.487053	+	0.0391883i
$704$	−596014.	+	1.01251e6i	−0.0453236	+	0.0769962i
$705$		−	1.00223e7i		−	0.759444i
$706$	1.69389e7	−	1.41729e7i	1.27901	−	1.07016i
$707$	1.18487e7			0.891505
$708$	5.41906e6	−	3.02358e7i	0.406294	−	2.26693i
$709$		−	7.05237e6i		−	0.526889i	−0.964674	−	0.263445i	$-0.915141\pi$
$709$		−	7.05237e6i		−	0.526889i	0.964674	−	0.263445i	$-0.0848587\pi$
$710$	−6.46797e6	−	7.73026e6i	−0.481529	−	0.575504i
$711$	−4.11206e7			−3.05060
$712$	4.09690e6	−	2.34237e6i	0.302869	−	0.173163i
$713$			2.26907e6i			0.167157i
$714$	−2.31915e7	+	1.94045e7i	−1.70249	+	1.42448i
$715$			145298.i			0.0106291i
$716$	2.10973e7	+	3.78119e6i	1.53796	+	0.275642i
$717$	1.44331e7			1.04848
$718$	6.98041e6	+	8.34271e6i	0.505324	+	0.603943i
$719$			2.51127e7i			1.81164i	0.423668	+	0.905818i	$0.360742\pi$
$719$			2.51127e7i			1.81164i	−0.423668	+	0.905818i	$0.639258\pi$
$720$	7.84986e6	−	2.11959e7i	0.564327	−	1.52377i
$721$		−	1.86505e7i		−	1.33614i
$722$	−9.16727e6	+	1.05903e7i	−0.654481	+	0.756079i
$723$	−2.93729e7			−2.08978
$724$	−885267.	+	4.93938e6i	−0.0627665	+	0.350208i
$725$	−4.73055e6			−0.334246
$726$	1.55343e7	+	1.85660e7i	1.09383	+	1.30730i
$727$		−	3.76567e6i		−	0.264245i	−0.991233	−	0.132122i	$-0.957821\pi$
$727$		−	3.76567e6i		−	0.264245i	0.991233	−	0.132122i	$-0.0421792\pi$
$728$	2.86020e6	−	1.63530e6i	0.200017	−	0.114359i
$729$	1.62674e7			1.13370
$730$	−1.07036e7	−	1.27925e7i	−0.743401	−	0.888484i
$731$	−8.97851e6			−0.621457
$732$	5.12896e6	−	2.86172e7i	0.353795	−	1.97401i
$733$		−	6.65591e6i		−	0.457559i	−0.973478	−	0.228780i	$-0.926526\pi$
$733$		−	6.65591e6i		−	0.457559i	0.973478	−	0.228780i	$-0.0734735\pi$
$734$	−1.13440e7	−	1.35579e7i	−0.777189	−	0.928866i
$735$	−3.34667e7			−2.28504
$736$	−6.59859e6	−	1.85336e7i	−0.449010	−	1.26115i
$737$			2.47464e6i			0.167820i
$738$	2.04234e7	+	2.44092e7i	1.38034	+	1.64973i
$739$	1.17124e7			0.788925			0.394462	−	0.918912i	$-0.370931\pi$
$739$	1.17124e7			0.788925			0.394462	+	0.918912i	$0.370931\pi$
$740$	−5.96266e6	−	1.06867e6i	−0.400277	−	0.0717402i
$741$	294435.	+	3.65939e6i	0.0196990	+	0.244829i
$742$	−1.20531e7	−	1.44053e7i	−0.803689	−	0.960537i
$743$	862163.			0.0572951			0.0286475	−	0.999590i	$-0.490880\pi$
$743$	862163.			0.0572951			0.0286475	+	0.999590i	$0.490880\pi$
$744$	2.81222e6	−	1.60787e6i	0.186259	−	0.106492i
$745$	−1.41144e7			−0.931688
$746$	1.70998e7	−	1.43076e7i	1.12498	−	0.941280i
$747$	−4.29906e7			−2.81885
$748$	−193320.	+	1.07864e6i	−0.0126335	+	0.0704891i
$749$	8.09240e6			0.527076
$750$	−2.20881e7	+	1.84813e7i	−1.43386	+	1.19972i
$751$	−3.20768e6			−0.207535			−0.103768	−	0.994602i	$-0.533090\pi$
$751$	−3.20768e6			−0.207535			−0.103768	+	0.994602i	$0.533090\pi$
$752$	−2.86022e6	+	7.72305e6i	−0.184440	+	0.498017i
$753$			6.67379e6i			0.428928i
$754$	−1.86109e6	+	1.55719e6i	−0.119217	+	0.0997498i
$755$			1.13878e7i			0.727062i
$756$	7.31288e6	−	4.08025e7i	0.465354	−	2.59646i
$757$			2.56954e6i			0.162973i	0.996674	+	0.0814865i	$0.0259668\pi$
$757$			2.56954e6i			0.162973i	−0.996674	+	0.0814865i	$0.974033\pi$
$758$	−266880.	−	318965.i	−0.0168711	−	0.0201637i
$759$	3.26175e6			0.205516
$760$	−1.09399e7	+	7.47907e6i	−0.687034	+	0.469692i
$761$	−8.81052e6			−0.551493			−0.275746	−	0.961230i	$-0.588925\pi$
$761$	−8.81052e6			−0.551493			−0.275746	+	0.961230i	$0.588925\pi$
$762$	3.12987e7	+	3.74070e7i	1.95272	+	2.33381i
$763$		−	1.99701e7i		−	1.24185i
$764$	8.48935e6	+	1.52152e6i	0.526188	+	0.0943068i
$765$		−	2.10813e7i		−	1.30240i
$766$	7.43826e6	−	6.22365e6i	0.458036	−	0.383242i
$767$			3.12158e6i			0.191596i
$768$	−1.82943e7	+	2.13110e7i	−1.11921	+	1.30377i
$769$	2.09606e7			1.27817			0.639083	−	0.769137i	$-0.279314\pi$
$769$	2.09606e7			1.27817			0.639083	+	0.769137i	$0.279314\pi$
$770$	−1.51226e6	+	1.26532e6i	−0.0919180	+	0.0769085i
$771$	1.31169e7			0.794685
$772$	−1.18698e7	−	2.12738e6i	−0.716803	−	0.128470i
$773$	−1.10279e7			−0.663811			−0.331906	−	0.943313i	$-0.607692\pi$
$773$	−1.10279e7			−0.663811			−0.331906	+	0.943313i	$0.607692\pi$
$774$	1.93506e7	−	1.61908e7i	1.16103	−	0.971441i
$775$	−641747.			−0.0383804
$776$	2.12789e7	−	1.21661e7i	1.26851	−	0.725263i
$777$	−2.27737e7			−1.35326
$778$	1.77337e7	+	2.11947e7i	1.05039	+	1.25539i
$779$	−1.49654e6	−	1.85998e7i	−0.0883580	−	1.09816i
$780$	−612755.	+	3.41889e6i	−0.0360620	+	0.201209i
$781$	−1.37320e6			−0.0805577
$782$	−1.17747e7	−	1.40727e7i	−0.688549	−	0.822926i
$783$			3.05309e7i			1.77965i
$784$	2.57889e7	+	9.55089e6i	1.49845	+	0.554950i
$785$	1.66390e7			0.963722
$786$	−2.56641e7	−	3.06727e7i	−1.48173	−	1.77091i
$787$		−	3.24978e6i		−	0.187032i	−0.995618	−	0.0935162i	$-0.970189\pi$
$787$		−	3.24978e6i		−	0.187032i	0.995618	−	0.0935162i	$-0.0298107\pi$
$788$	2.39813e7	+	4.29807e6i	1.37580	+	0.246580i
$789$	2.23120e7			1.27599
$790$	1.46373e7	+	1.74939e7i	0.834436	+	0.997285i
$791$	−3.66628e7			−2.08346
$792$	−1.52845e6	−	2.67331e6i	−0.0865840	−	0.151439i
$793$			2.95447e6i			0.166839i
$794$	1.63457e7	+	1.95357e7i	0.920135	+	1.09971i
$795$	1.98014e7			1.11116
$796$	−1.50582e7	−	2.69883e6i	−0.842348	−	0.150971i
$797$	9.08440e6			0.506583			0.253292	−	0.967390i	$-0.418487\pi$
$797$	9.08440e6			0.506583			0.253292	+	0.967390i	$0.418487\pi$
$798$	−3.55228e7	+	3.49320e7i	−1.97469	+	1.94185i
$799$			7.68132e6i			0.425666i
$800$	5.24175e6	−	1.86624e6i	0.289568	−	0.103096i
$801$			1.23690e7i			0.681167i
$802$	961292.	+	1.14890e6i	0.0527739	+	0.0630733i
$803$	−2.27246e6			−0.124368
$804$	−1.04361e7	+	5.82285e7i	−0.569373	+	3.17684i
$805$		−	3.30166e7i		−	1.79574i
$806$	−252475.	+	211248.i	−0.0136893	+	0.0114539i
$807$		−	5.41378e7i		−	2.92629i
$808$	8.91092e6	−	5.09475e6i	0.480169	−	0.274533i
$809$	3.47754e6			0.186810			0.0934051	−	0.995628i	$-0.470225\pi$
$809$	3.47754e6			0.186810			0.0934051	+	0.995628i	$0.470225\pi$
$810$	8.57251e6	+	1.02455e7i	0.459088	+	0.548683i
$811$		−	4.16309e6i		−	0.222261i	−0.993806	−	0.111131i	$-0.964553\pi$
$811$		−	4.16309e6i		−	0.222261i	0.993806	−	0.111131i	$-0.0354472\pi$
$812$	−3.24143e7	−	5.80950e6i	−1.72523	−	0.309206i
$813$	3.22655e7			1.71203
$814$	−632961.	+	529603.i	−0.0334823	+	0.0280149i
$815$			2.71784e7i			1.43328i
$816$	−9.09770e6	+	2.45652e7i	−0.478307	+	1.29150i
$817$	−1.47452e7	+	1.18640e6i	−0.772851	+	0.0621837i
$818$	7.03963e6	+	8.41349e6i	0.367846	+	0.439636i
$819$			8.63527e6i			0.449848i
$820$	3.11449e6	−	1.73774e7i	0.161753	−	0.902507i
$821$			1.51654e7i			0.785230i	0.919703	+	0.392615i	$0.128430\pi$
$821$			1.51654e7i			0.785230i	−0.919703	+	0.392615i	$0.871570\pi$
$822$	1.31620e7	+	1.57307e7i	0.679426	+	0.812023i
$823$		−	7.23765e6i		−	0.372476i	−0.982505	−	0.186238i	$-0.940371\pi$
$823$		−	7.23765e6i		−	0.372476i	0.982505	−	0.186238i	$-0.0596295\pi$
$824$	−8.01937e6	−	1.40262e7i	−0.411455	−	0.719650i
$825$			922501.i			0.0471880i
$826$	−3.24893e7	+	2.71841e7i	−1.65688	+	1.38632i
$827$		−	2.46106e7i		−	1.25129i	−0.780107	−	0.625646i	$-0.784835\pi$
$827$		−	2.46106e7i		−	1.25129i	0.780107	−	0.625646i	$-0.215165\pi$
$828$	5.07543e7	+	9.09650e6i	2.57274	+	0.461104i
$829$	1.47786e7			0.746874			0.373437	−	0.927655i	$-0.378179\pi$
$829$	1.47786e7			0.746874			0.373437	+	0.927655i	$0.378179\pi$
$830$	1.53029e7	+	1.82895e7i	0.771045	+	0.921522i
$831$	2.66383e7			1.33815
$832$	1.44788e6	−	2.45967e6i	0.0725144	−	0.123188i
$833$	2.56496e7			1.28076
$834$	3.94352e6	+	4.71314e6i	0.196322	+	0.234636i
$835$			1.05449e7i			0.523393i
$836$	−174957.	+	1.79697e6i	−0.00865795	+	0.0889252i
$837$			4.14182e6i			0.204352i
$838$	−1.62726e7	+	1.36154e7i	−0.800476	+	0.669764i
$839$	1.49881e7			0.735091			0.367545	−	0.930006i	$-0.380198\pi$
$839$	1.49881e7			0.735091			0.367545	+	0.930006i	$0.380198\pi$
$840$	−4.09199e7	+	2.33956e7i	−2.00095	+	1.14403i
$841$	3.74322e6			0.182497
$842$	1.23644e7	−	1.03454e7i	0.601027	−	0.502884i
$843$	−1.90933e6			−0.0925363
$844$	6.50980e6	+	1.16673e6i	0.314566	+	0.0563785i
$845$			1.69210e7i			0.815236i
$846$	−1.38516e7	−	1.65549e7i	−0.665387	−	0.795245i
$847$		−	3.33841e7i		−	1.59894i
$848$	−1.52586e7	−	5.65102e6i	−0.728662	−	0.269859i
$849$			6.72530e7i			3.20216i
$850$	3.98010e6	−	3.33018e6i	0.188950	−	0.158096i
$851$		−	1.38192e7i		−	0.654122i
$852$	−3.23116e7	−	5.79109e6i	−1.52496	−	0.273314i
$853$			8.12725e6i			0.382447i	0.981547	+	0.191223i	$0.0612455\pi$
$853$			8.12725e6i			0.382447i	−0.981547	+	0.191223i	$0.938755\pi$
$854$	−3.07501e7	+	2.57288e7i	−1.44279	+	1.20719i
$855$	−2.78564e6	−	3.46214e7i	−0.130320	−	1.61968i
$856$	6.08594e6	−	3.47959e6i	0.283885	−	0.162309i
$857$			1.99678e7i			0.928704i	0.885651	+	0.464352i	$0.153713\pi$
$857$			1.99678e7i			0.928704i	−0.885651	+	0.464352i	$0.846287\pi$
$858$	303665.	+	362929.i	0.0140824	+	0.0168307i
$859$	−2.19102e7			−1.01313			−0.506564	−	0.862202i	$-0.669085\pi$
$859$	−2.19102e7			−1.01313			−0.506564	+	0.862202i	$0.669085\pi$
$860$	−1.37761e7	−	2.46904e6i	−0.635156	−	0.113837i
$861$		−	6.63710e7i		−	3.05120i
$862$	2.24871e7	−	1.88151e7i	1.03078	−	0.862460i
$863$	−1.14632e7			−0.523937			−0.261969	−	0.965076i	$-0.584372\pi$
$863$	−1.14632e7			−0.523937			−0.261969	+	0.965076i	$0.584372\pi$
$864$	−1.20447e7	−	3.38302e7i	−0.548921	−	1.54177i
$865$		−	8.90521e6i		−	0.404673i
$866$	4.13388e6	+	4.94065e6i	0.187311	+	0.223867i
$867$		−	1.35987e7i		−	0.614396i
$868$	−4.39733e6	−	788117.i	−0.198102	−	0.0355051i
$869$	3.10762e6			0.139598
$870$	2.66259e7	−	2.22781e7i	1.19263	−	0.997884i
$871$		−	6.01156e6i		−	0.268499i
$872$	−8.58679e6	−	1.50186e7i	−0.382419	−	0.668866i
$873$			6.42434e7i			2.85294i
$874$	−2.11969e7	−	2.15554e7i	−0.938630	−	0.954503i
$875$	3.97175e7			1.75373
$876$	−5.34713e7	−	9.58347e6i	−2.35429	−	0.421951i
$877$	9.70110e6			0.425914			0.212957	−	0.977062i	$-0.431691\pi$
$877$	9.70110e6			0.425914			0.212957	+	0.977062i	$0.431691\pi$
$878$	9.92923e6	−	8.30787e6i	0.434690	−	0.363708i
$879$		−	1.51100e7i		−	0.659618i
$880$	−593240.	+	1.60184e6i	−0.0258240	+	0.0697288i
$881$	2.41648e7			1.04892			0.524461	−	0.851435i	$-0.324267\pi$
$881$	2.41648e7			1.04892			0.524461	+	0.851435i	$0.324267\pi$
$882$	−5.52803e7	+	4.62535e7i	−2.39276	+	2.00204i
$883$	−1.21850e7			−0.525923			−0.262962	−	0.964806i	$-0.584699\pi$
$883$	−1.21850e7			−0.525923			−0.262962	+	0.964806i	$0.584699\pi$
$884$	469628.	−	2.62031e6i	0.0202127	−	0.112777i
$885$		−	4.46593e7i		−	1.91670i
$886$	1.66131e7	−	1.39003e7i	0.710993	−	0.594893i
$887$	4.38883e7			1.87301			0.936504	−	0.350657i	$-0.114042\pi$
$887$	4.38883e7			1.87301			0.936504	+	0.350657i	$0.114042\pi$
$888$	−1.71271e7	+	9.79229e6i	−0.728872	+	0.416727i
$889$		−	6.72629e7i		−	2.85444i
$890$	5.26214e6	−	4.40287e6i	0.222683	−	0.186321i
$891$	1.82001e6			0.0768034
$892$	−5.42908e6	+	3.02917e7i	−0.228462	+	1.27471i
$893$	1.01499e6	+	1.26149e7i	0.0425926	+	0.529363i
$894$	−3.52551e7	+	2.94982e7i	−1.47529	+	1.23439i
$895$	3.11614e7			1.30035
$896$	3.82090e7	−	6.35039e6i	1.58999	−	0.264259i
$897$	−7.92368e6			−0.328811
$898$	1.52475e7	+	1.82232e7i	0.630969	+	0.754110i
$899$	3.29035e6			0.135782
$900$	−2.57271e6	+	1.43545e7i	−0.105873	+	0.590720i
$901$	−1.51762e7			−0.622803
$902$	−1.54346e6	−	1.84468e6i	−0.0631654	−	0.0754928i
$903$	−5.26163e7			−2.14734
$904$	−2.75725e7	+	1.57644e7i	−1.12216	+	0.641587i
$905$			7.29563e6i			0.296102i
$906$	2.37998e7	+	2.84445e7i	0.963280	+	1.15127i
$907$			2.47211e7i			0.997816i	0.866655	+	0.498908i	$0.166265\pi$
$907$			2.47211e7i			0.997816i	−0.866655	+	0.498908i	$0.833735\pi$
$908$	−2.82697e6	−	506668.i	−0.113791	−	0.0203943i
$909$			2.69031e7i			1.07992i
$910$	3.67370e6	−	3.07381e6i	0.147062	−	0.123048i
$911$	−2.36658e7			−0.944769			−0.472384	−	0.881393i	$-0.656607\pi$
$911$	−2.36658e7			−0.944769			−0.472384	+	0.881393i	$0.656607\pi$
$912$	−1.16950e7	+	4.15450e7i	−0.465598	+	1.65399i
$913$	3.24894e6			0.128993
$914$	3.76994e6	−	3.15434e6i	0.149269	−	0.124894i
$915$		−	4.22686e7i		−	1.66903i
$916$	2.80386e7	+	5.02525e6i	1.10412	+	0.197888i
$917$			5.51537e7i			2.16597i
$918$	−2.14929e7	−	2.56875e7i	−0.841760	−	1.00604i
$919$			2.69233e7i			1.05157i	0.850616	+	0.525787i	$0.176229\pi$
$919$			2.69233e7i			1.05157i	−0.850616	+	0.525787i	$0.823771\pi$
$920$	−1.41966e7	−	2.48304e7i	−0.552986	−	0.967194i
$921$	−8.61363e7			−3.34609
$922$	−2.81884e7	−	3.36897e7i	−1.09205	−	1.30518i
$923$	3.33588e6			0.128886
$924$	−1.13290e6	+	6.32109e6i	−0.0436529	+	0.243563i
$925$	3.90839e6			0.150191
$926$	1.58146e7	+	1.89010e7i	0.606083	+	0.724366i
$927$	4.23466e7			1.61853
$928$	−2.68754e7	+	9.56852e6i	−1.02443	+	0.364733i
$929$	−2.67977e7			−1.01873			−0.509364	−	0.860551i	$-0.670119\pi$
$929$	−2.67977e7			−1.01873			−0.509364	+	0.860551i	$0.670119\pi$
$930$	3.61207e6	−	3.02225e6i	0.136946	−	0.114584i
$931$	4.21237e7	−	3.38928e6i	1.59277	−	0.128154i
$932$	2.13490e6	−	1.19118e7i	0.0805079	−	0.449197i
$933$	−8.28056e7			−3.11426
$934$	−1.30973e7	+	1.09586e7i	−0.491264	+	0.411044i
$935$			1.59318e6i			0.0595987i
$936$	3.71301e6	+	6.49420e6i	0.138528	+	0.242290i
$937$	−9.87790e6			−0.367549			−0.183775	−	0.982968i	$-0.558832\pi$
$937$	−9.87790e6			−0.367549			−0.183775	+	0.982968i	$0.558832\pi$
$938$	6.25682e7	−	5.23513e7i	2.32192	−	1.94277i
$939$		−	1.01695e7i		−	0.376389i
$940$	−2.11232e6	+	1.17858e7i	−0.0779723	+	0.435050i
$941$	−8.71643e6			−0.320896			−0.160448	−	0.987044i	$-0.551294\pi$
$941$	−8.71643e6			−0.320896			−0.160448	+	0.987044i	$0.551294\pi$
$942$	4.15611e7	−	3.47745e7i	1.52602	−	1.27683i
$943$	4.02742e7			1.47485
$944$	−1.27451e7	+	3.44138e7i	−0.465493	+	1.25690i
$945$		−	6.02666e7i		−	2.19532i
$946$	−1.46239e6	+	1.22359e6i	−0.0531295	+	0.0444538i
$947$	2.76979e6			0.100363			0.0501813	−	0.998740i	$-0.484020\pi$
$947$	2.76979e6			0.100363			0.0501813	+	0.998740i	$0.484020\pi$
$948$	7.31226e7	+	1.31055e7i	2.64259	+	0.473623i
$949$	5.52043e6			0.198979
$950$	6.09638e6	−	5.99499e6i	0.219161	−	0.215516i
$951$		−	4.24075e6i		−	0.152052i
$952$	3.13618e7	−	1.79309e7i	1.12153	−	0.641224i
$953$			3.15715e6i			0.112606i	0.998414	+	0.0563031i	$0.0179313\pi$
$953$			3.15715e6i			0.112606i	−0.998414	+	0.0563031i	$0.982069\pi$
$954$	3.27079e7	−	2.73670e7i	1.16354	−	0.973545i
$955$	1.25390e7			0.444893
$956$	−1.69726e7	−	3.04194e6i	−0.600626	−	0.107648i
$957$		−	4.72982e6i		−	0.166942i
$958$	−2.40244e7	−	2.87131e7i	−0.845745	−	1.01080i
$959$		−	2.82859e7i		−	0.993171i
$960$	−2.07143e7	+	3.51896e7i	−0.725425	+	1.23236i
$961$	−2.81828e7			−0.984409
$962$	1.53763e6	−	1.28655e6i	0.0535692	−	0.0448218i
$963$			1.83741e7i			0.638471i
$964$	3.45412e7	+	6.19069e6i	1.19714	+	0.214559i
$965$	−1.75321e7			−0.606059
$966$	−6.90029e7	−	8.24695e7i	−2.37916	−	2.84348i
$967$		−	1.42538e7i		−	0.490191i	−0.969499	−	0.245096i	$-0.921181\pi$
$967$		−	1.42538e7i		−	0.490191i	0.969499	−	0.245096i	$-0.0788194\pi$
$968$	−1.43546e7	−	2.51067e7i	−0.492382	−	0.861196i
$969$	3.22845e6	+	4.01249e7i	0.110455	+	1.37279i
$970$	2.73311e7	−	2.28681e7i	0.932668	−	0.780371i
$971$			4.87109e7i			1.65797i	0.559267	+	0.828987i	$0.311083\pi$
$971$			4.87109e7i			1.65797i	−0.559267	+	0.828987i	$0.688917\pi$
$972$	−4.62479e6	−	828884.i	−0.157010	−	0.0281403i
$973$		−	8.47486e6i		−	0.286979i
$974$	−3.71939e7	+	3.11204e7i	−1.25624	+	1.05111i
$975$		−	2.24101e6i		−	0.0754973i
$976$	−1.20628e7	+	3.25715e7i	−0.405345	+	1.09449i
$977$			5.11627e7i			1.71481i	0.514640	+	0.857406i	$0.327926\pi$
$977$			5.11627e7i			1.71481i	−0.514640	+	0.857406i	$0.672074\pi$
$978$	5.68013e7	+	6.78867e7i	1.89894	+	2.26954i
$979$		−	934766.i		−	0.0311707i
$980$	3.93552e7	+	7.05349e6i	1.30899	+	0.234606i
$981$	4.53429e7			1.50431
$982$	−1.24751e6	+	1.04380e6i	−0.0412824	+	0.0345413i
$983$	6.16221e6			0.203401			0.101700	−	0.994815i	$-0.467572\pi$
$983$	6.16221e6			0.203401			0.101700	+	0.994815i	$0.467572\pi$
$984$	−2.85384e7	−	4.99147e7i	−0.939596	−	1.64339i
$985$	3.54211e7			1.16325
$986$	−2.04067e7	+	1.70744e7i	−0.668466	+	0.559311i
$987$			4.50144e7i			1.47082i
$988$	425018.	−	4.36533e6i	0.0138521	−	0.142274i
$989$		−	3.19278e7i		−	1.03795i
$990$	−2.87297e6	−	3.43366e6i	−0.0931628	−	0.111345i
$991$	−5.67892e7			−1.83688			−0.918441	−	0.395558i	$-0.870551\pi$
$991$	−5.67892e7			−1.83688			−0.918441	+	0.395558i	$0.870551\pi$
$992$	−3.64591e6	+	1.29807e6i	−0.117632	+	0.0418811i
$993$	825060.			0.0265529
$994$	2.90503e7	+	3.47198e7i	0.932577	+	1.11458i
$995$	−2.22415e7			−0.712208
$996$	7.64479e7	+	1.37015e7i	2.44184	+	0.437642i
$997$			5.89936e7i			1.87961i	0.341716	+	0.939803i	$0.388992\pi$
$997$			5.89936e7i			1.87961i	−0.341716	+	0.939803i	$0.611008\pi$
$998$	181924.	−	152217.i	0.00578179	−	0.00483767i
$999$		−	2.52247e7i		−	0.799673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.6.b.b.75.20	yes	96
4.3	odd	2		608.6.b.b.303.7		96
8.3	odd	2	inner	152.6.b.b.75.78	yes	96
8.5	even	2		608.6.b.b.303.8		96
19.18	odd	2	inner	152.6.b.b.75.77	yes	96
76.75	even	2		608.6.b.b.303.89		96
152.37	odd	2		608.6.b.b.303.90		96
152.75	even	2	inner	152.6.b.b.75.19	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.6.b.b.75.19	✓	96	152.75	even	2	inner
152.6.b.b.75.20	yes	96	1.1	even	1	trivial
152.6.b.b.75.77	yes	96	19.18	odd	2	inner
152.6.b.b.75.78	yes	96	8.3	odd	2	inner
608.6.b.b.303.7		96	4.3	odd	2
608.6.b.b.303.8		96	8.5	even	2
608.6.b.b.303.89		96	76.75	even	2
608.6.b.b.303.90		96	152.37	odd	2

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	152.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.33851 + 3.63006i) q^{2} +26.7852i q^{3} +(5.64529 - 31.4981i) q^{4} -46.5237i q^{5} +(-97.2319 - 116.208i) q^{6} +208.957i q^{7} +(89.8480 + 157.148i) q^{8} -474.446 q^{9} +O(q^{10})\)	\(q+(-4.33851 + 3.63006i) q^{2} +26.7852i q^{3} +(5.64529 - 31.4981i) q^{4} -46.5237i q^{5} +(-97.2319 - 116.208i) q^{6} +208.957i q^{7} +(89.8480 + 157.148i) q^{8} -474.446 q^{9} +(168.884 + 201.844i) q^{10} +35.8554 q^{11} +(843.683 + 151.210i) q^{12} -87.1027 q^{13} +(-758.528 - 906.562i) q^{14} +1246.15 q^{15} +(-960.261 - 355.632i) q^{16} -955.073 q^{17} +(2058.39 - 1722.27i) q^{18} +(-1568.49 + 126.201i) q^{19} +(-1465.41 - 262.640i) q^{20} -5596.96 q^{21} +(-155.559 + 130.158i) q^{22} -3396.26i q^{23} +(-4209.23 + 2406.59i) q^{24} +960.543 q^{25} +(377.896 - 316.188i) q^{26} -6199.33i q^{27} +(6581.76 + 1179.62i) q^{28} -4924.87 q^{29} +(-5406.42 + 4523.59i) q^{30} -668.108 q^{31} +(5457.07 - 1942.90i) q^{32} +960.395i q^{33} +(4143.59 - 3466.97i) q^{34} +9721.47 q^{35} +(-2678.39 + 14944.2i) q^{36} +4068.94 q^{37} +(6346.80 - 6241.26i) q^{38} -2333.06i q^{39} +(7311.09 - 4180.06i) q^{40} +11858.4i q^{41} +(24282.4 - 20317.3i) q^{42} +9400.87 q^{43} +(202.414 - 1129.38i) q^{44} +22073.0i q^{45} +(12328.6 + 14734.7i) q^{46} -8042.65i q^{47} +(9525.67 - 25720.8i) q^{48} -26856.1 q^{49} +(-4167.32 + 3486.83i) q^{50} -25581.8i q^{51} +(-491.720 + 2743.57i) q^{52} +15890.1 q^{53} +(22504.0 + 26895.8i) q^{54} -1668.13i q^{55} +(-32837.1 + 18774.4i) q^{56} +(-3380.32 - 42012.4i) q^{57} +(21366.6 - 17877.6i) q^{58} -35837.9i q^{59} +(7034.86 - 39251.3i) q^{60} -33919.4i q^{61} +(2898.59 - 2425.27i) q^{62} -99139.0i q^{63} +(-16622.7 + 28238.8i) q^{64} +4052.34i q^{65} +(-3486.29 - 4166.68i) q^{66} +69017.0i q^{67} +(-5391.66 + 30083.0i) q^{68} +90969.5 q^{69} +(-42176.7 + 35289.5i) q^{70} -38298.3 q^{71} +(-42628.0 - 74558.0i) q^{72} -63378.5 q^{73} +(-17653.1 + 14770.5i) q^{74} +25728.3i q^{75} +(-4879.50 + 50117.0i) q^{76} +7492.26i q^{77} +(8469.16 + 10122.0i) q^{78} +86670.7 q^{79} +(-16545.3 + 44674.9i) q^{80} +50759.7 q^{81} +(-43046.7 - 51447.8i) q^{82} +90612.1 q^{83} +(-31596.5 + 176294. i) q^{84} +44433.5i q^{85} +(-40785.7 + 34125.7i) q^{86} -131914. i q^{87} +(3221.54 + 5634.59i) q^{88} -26070.4i q^{89} +(-80126.4 - 95763.9i) q^{90} -18200.7i q^{91} +(-106976. - 19172.9i) q^{92} -17895.4i q^{93} +(29195.3 + 34893.1i) q^{94} +(5871.35 + 72972.2i) q^{95} +(52040.9 + 146169. i) q^{96} -135407. i q^{97} +(116515. - 97489.4i) q^{98} -17011.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9}+O(q^{10}) \) 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9	\( 96 q + 82 q^{4} - 110 q^{6} - 6168 q^{9} + 944 q^{11} - 3270 q^{16} - 3832 q^{17} + 5240 q^{19} - 1356 q^{20} + 12622 q^{24} - 62504 q^{25} - 6 q^{26} - 110 q^{28} - 14656 q^{30} + 7720 q^{35} - 90984 q^{36} + 22390 q^{38} - 35306 q^{42} + 45096 q^{43} - 22100 q^{44} - 210840 q^{49} + 55038 q^{54} - 36336 q^{57} + 64402 q^{58} + 132976 q^{62} - 182030 q^{64} + 101048 q^{66} - 9030 q^{68} - 4336 q^{73} + 80748 q^{74} - 104304 q^{76} - 31392 q^{80} - 20624 q^{81} + 145904 q^{82} + 52152 q^{83} - 12226 q^{92} - 80058 q^{96} - 752768 q^{99}+O(q^{100}) \) 96 * q + 82 * q^4 - 110 * q^6 - 6168 * q^9 + 944 * q^11 - 3270 * q^16 - 3832 * q^17 + 5240 * q^19 - 1356 * q^20 + 12622 * q^24 - 62504 * q^25 - 6 * q^26 - 110 * q^28 - 14656 * q^30 + 7720 * q^35 - 90984 * q^36 + 22390 * q^38 - 35306 * q^42 + 45096 * q^43 - 22100 * q^44 - 210840 * q^49 + 55038 * q^54 - 36336 * q^57 + 64402 * q^58 + 132976 * q^62 - 182030 * q^64 + 101048 * q^66 - 9030 * q^68 - 4336 * q^73 + 80748 * q^74 - 104304 * q^76 - 31392 * q^80 - 20624 * q^81 + 145904 * q^82 + 52152 * q^83 - 12226 * q^92 - 80058 * q^96 - 752768 * q^99

Introduction

L-functions

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