LMFDB - Embedded newform 152.6.b.b.75.19

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

$q$-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	$-0.671002\pi$
$3$		−	26.7852i		−	1.71827i	0.511749	−	0.859135i	$-0.328998\pi$
$4$	5.64529	+	31.4981i	0.176415	+	0.984316i
$5$			46.5237i			0.832242i	0.909309	+	0.416121i	$0.136611\pi$
$5$			46.5237i			0.832242i	−0.909309	+	0.416121i	$0.863389\pi$
$6$	−97.2319	+	116.208i	−1.10263	+	1.31782i
$7$		−	208.957i		−	1.61180i	−0.592049	−	0.805902i	$-0.701681\pi$
$7$		−	208.957i		−	1.61180i	0.592049	−	0.805902i	$-0.298319\pi$
$8$	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	$0.233426\pi$
$23$			3396.26i			1.33869i	−0.742950	+	0.669347i	$0.766574\pi$
$24$	−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	$-0.814302\pi$
$41$		−	11858.4i		−	1.10171i	0.834602	−	0.550854i	$-0.185698\pi$
$42$	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	$0.0855492\pi$
$47$			8042.65i			0.531074i	−0.964101	+	0.265537i	$0.914451\pi$
$48$	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	$0.233777\pi$
$59$			35837.9i			1.34033i	−0.742211	+	0.670167i	$0.766223\pi$
$60$	7034.86	+	39251.3i	0.252277	+	1.40759i
$61$			33919.4i			1.16714i	0.812062	+	0.583571i	$0.198345\pi$
$61$			33919.4i			1.16714i	−0.812062	+	0.583571i	$0.801655\pi$
$62$	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	$-0.611607\pi$
$67$		−	69017.0i		−	1.87832i	0.343483	−	0.939159i	$-0.388393\pi$
$68$	−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	$0.0558111\pi$
$89$			26070.4i			0.348877i	−0.984668	+	0.174439i	$0.944189\pi$
$90$	−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	$0.260762\pi$
$97$			135407.i			1.46121i	−0.682801	+	0.730605i	$0.739238\pi$
$98$	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	$0.0891928\pi$
$101$			56704.1i			0.553110i	−0.960998	+	0.276555i	$0.910807\pi$
$102$	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	$0.0522799\pi$
$107$			38727.5i			0.327010i	−0.986543	+	0.163505i	$0.947720\pi$
$108$	−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	$-0.776310\pi$
$113$		−	175456.i		−	1.29262i	0.763073	−	0.646312i	$-0.223690\pi$
$114$	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	$0.189101\pi$
$149$			303380.i			1.11949i	−0.828664	+	0.559746i	$0.810899\pi$
$150$	−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	$-0.803446\pi$
$157$		−	357645.i		−	1.15798i	0.815333	−	0.578992i	$-0.196554\pi$
$158$	−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	$-0.714592\pi$
$179$		−	669795.i		−	1.56246i	0.624242	−	0.781231i	$-0.285408\pi$
$180$	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	$-0.913873\pi$
$191$		−	269519.i		−	0.534572i	0.963617	−	0.267286i	$-0.0861269\pi$
$192$	−756381.	+	445242.i	−1.48077	+	0.871651i
$193$			376841.i			0.728224i	0.931355	+	0.364112i	$0.118628\pi$
$193$			376841.i			0.728224i	−0.931355	+	0.364112i	$0.881372\pi$
$194$	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	$-0.753690\pi$
$197$		−	761356.i		−	1.39773i	0.715256	−	0.698863i	$-0.246310\pi$
$198$	73804.4	+	61752.7i	0.133789	+	0.111942i
$199$			478068.i			0.855770i	0.903833	+	0.427885i	$0.140741\pi$
$199$			478068.i			0.855770i	−0.903833	+	0.427885i	$0.859259\pi$
$200$	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	$-0.948919\pi$
$211$		−	206673.i		−	0.319578i	0.987151	−	0.159789i	$-0.0510814\pi$
$212$	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	$0.0184092\pi$
$227$			89750.5i			0.115604i	−0.998328	+	0.0578019i	$0.981591\pi$
$228$	−1.34239e6	+	130698.i	−1.71018	+	0.166507i
$229$		−	890166.i		−	1.12171i	−0.827912	−	0.560857i	$-0.810472\pi$
$229$		−	890166.i		−	1.12171i	0.827912	−	0.560857i	$-0.189528\pi$
$230$	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	$0.0986893\pi$
$239$			538846.i			0.610196i	−0.952321	+	0.305098i	$0.901311\pi$
$240$	−1.19663e6	+	443169.i	−1.34101	+	0.496640i
$241$		−	1.09661e6i		−	1.21621i	−0.793855	−	0.608107i	$-0.791929\pi$
$241$		−	1.09661e6i		−	1.21621i	0.793855	−	0.608107i	$-0.208071\pi$
$242$	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	$0.0742801\pi$
$257$			489707.i			0.462491i	−0.972895	+	0.231246i	$0.925720\pi$
$258$	−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	$0.121088\pi$
$263$			832999.i			0.742601i	−0.928513	+	0.371300i	$0.878912\pi$
$264$	−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	$0.166000\pi$
$271$			1.20460e6i			0.996370i	−0.867071	+	0.498185i	$0.834000\pi$
$272$	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	$0.127314\pi$
$277$			994518.i			0.778777i	−0.921074	+	0.389389i	$0.872686\pi$
$278$	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	$-0.991428\pi$
$281$		−	71283.1i		−	0.0538543i	0.999637	−	0.0269272i	$-0.00857222\pi$
$282$	−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	$-0.573195\pi$
$307$		−	3.21582e6i		−	1.94736i	0.227927	−	0.973678i	$-0.426805\pi$
$308$	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	$-0.638955\pi$
$311$		−	3.09147e6i		−	1.81244i	0.422805	−	0.906220i	$-0.361045\pi$
$312$	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	$0.00245949\pi$
$331$			30802.8i			0.0154533i	−0.999970	+	0.00772664i	$0.997541\pi$
$332$	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	$-0.612386\pi$
$337$		−	3.91249e6i		−	1.87663i	0.345782	−	0.938315i	$-0.387614\pi$
$338$	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	$-0.951235\pi$
$349$		−	694461.i		−	0.305200i	0.988288	−	0.152600i	$-0.0487646\pi$
$350$	−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	$0.128816\pi$
$359$			1.92295e6i			0.787464i	−0.919225	+	0.393732i	$0.871184\pi$
$360$	−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	$-0.792949\pi$
$367$		−	3.12502e6i		−	1.21112i	0.795799	−	0.605561i	$-0.207051\pi$
$368$	−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	$-0.995816\pi$
$379$		−	73519.4i		−	0.0262908i	0.999914	−	0.0131454i	$-0.00418443\pi$
$380$	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	$0.305156\pi$
$389$			4.88524e6i			1.63686i	−0.574604	+	0.818431i	$0.694844\pi$
$390$	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	$0.254458\pi$
$397$			4.50286e6i			1.43388i	−0.697136	+	0.716939i	$0.745542\pi$
$398$	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	$0.0130925\pi$
$401$			264814.i			0.0822394i	−0.999154	+	0.0411197i	$0.986907\pi$
$402$	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	$0.0925297\pi$
$409$			1.93926e6i			0.573228i	−0.958046	+	0.286614i	$0.907470\pi$
$410$	−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	$0.0466228\pi$
$433$			1.13879e6i			0.291893i	−0.989292	+	0.145947i	$0.953377\pi$
$434$	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	$0.163599\pi$
$449$			4.20035e6i			0.983262i	−0.870804	+	0.491631i	$0.836401\pi$
$450$	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	$-0.676062\pi$
$461$		−	7.76528e6i		−	1.70178i	0.525340	−	0.850892i	$-0.323938\pi$
$462$	870658.	+	728486.i	0.189777	+	0.158788i
$463$			4.35658e6i			0.944480i	0.881470	+	0.472240i	$0.156554\pi$
$463$			4.35658e6i			0.944480i	−0.881470	+	0.472240i	$0.843446\pi$
$464$	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	$-0.770989\pi$
$479$		−	6.61819e6i		−	1.31795i	0.752163	−	0.658977i	$-0.229011\pi$
$480$	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	$0.0508278\pi$
$503$			1.80449e6i			0.318005i	−0.987278	+	0.159003i	$0.949172\pi$
$504$	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	$0.112557\pi$
$521$			4.29098e6i			0.692568i	−0.938130	+	0.346284i	$0.887443\pi$
$522$	−1.01373e7	−	8.48196e6i	−1.62834	−	1.36245i
$523$			6.59641e6i			1.05452i	0.849705	+	0.527258i	$0.176780\pi$
$523$			6.59641e6i			1.05452i	−0.849705	+	0.527258i	$0.823220\pi$
$524$	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	$-0.902329\pi$
$541$		−	4.11246e6i		−	0.604100i	0.953292	−	0.302050i	$-0.0976709\pi$
$542$	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	$-0.968266\pi$
$547$		−	1.39299e6i		−	0.199058i	0.995035	−	0.0995288i	$-0.0317335\pi$
$548$	−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	$-0.975361\pi$
$557$		−	1.13242e6i		−	0.154658i	0.997006	−	0.0773288i	$-0.0246391\pi$
$558$	−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	$0.0275184\pi$
$563$			1.29877e6i			0.172688i	−0.996265	+	0.0863439i	$0.972482\pi$
$564$	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	$0.0590887\pi$
$569$			2.85081e6i			0.369137i	−0.982820	+	0.184568i	$0.940911\pi$
$570$	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	$-0.884777\pi$
$601$		−	6.27163e6i		−	0.708262i	0.935196	−	0.354131i	$-0.115223\pi$
$602$	−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	$-0.879515\pi$
$613$		−	6.87610e6i		−	0.739080i	0.929215	−	0.369540i	$-0.120485\pi$
$614$	−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	$-0.896354\pi$
$631$		−	6.39890e6i		−	0.639781i	0.947454	−	0.319891i	$-0.103646\pi$
$632$	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	$-0.825604\pi$
$641$		−	1.08371e7i		−	1.04176i	0.853630	−	0.520880i	$-0.174396\pi$
$642$	−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	$0.0977684\pi$
$647$			6.43857e6i			0.604684i	−0.953200	+	0.302342i	$0.902232\pi$
$648$	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	$0.0589176\pi$
$653$			4.01075e6i			0.368080i	−0.982919	+	0.184040i	$0.941082\pi$
$654$	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	$0.0615319\pi$
$659$			4.28337e6i			0.384213i	−0.981374	+	0.192106i	$0.938468\pi$
$660$	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	$-0.963570\pi$
$673$		−	2.68365e6i		−	0.228396i	0.993458	−	0.114198i	$-0.0364298\pi$
$674$	−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	$0.337197\pi$
$683$			2.12625e7i			1.74406i	−0.489450	+	0.872031i	$0.662803\pi$
$684$	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	$-0.951900\pi$
$701$		−	3.91708e6i		−	0.301070i	0.988605	−	0.150535i	$-0.0480996\pi$
$702$	−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	$0.0848587\pi$
$709$			7.05237e6i			0.526889i	−0.964674	+	0.263445i	$0.915141\pi$
$710$	−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	$-0.639258\pi$
$719$		−	2.51127e7i		−	1.81164i	0.423668	−	0.905818i	$-0.360742\pi$
$720$	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	$0.0421792\pi$
$727$			3.76567e6i			0.264245i	−0.991233	+	0.132122i	$0.957821\pi$
$728$	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	$0.0734735\pi$
$733$			6.65591e6i			0.457559i	−0.973478	+	0.228780i	$0.926526\pi$
$734$	−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	$-0.974033\pi$
$757$		−	2.56954e6i		−	0.162973i	0.996674	−	0.0814865i	$-0.0259668\pi$
$758$	−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	$0.0298107\pi$
$787$			3.24978e6i			0.187032i	−0.995618	+	0.0935162i	$0.970189\pi$
$788$	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	$0.0354472\pi$
$811$			4.16309e6i			0.222261i	−0.993806	+	0.111131i	$0.964553\pi$
$812$	−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	$-0.871570\pi$
$821$		−	1.51654e7i		−	0.785230i	0.919703	−	0.392615i	$-0.128430\pi$
$822$	1.31620e7	−	1.57307e7i	0.679426	−	0.812023i
$823$			7.23765e6i			0.372476i	0.982505	+	0.186238i	$0.0596295\pi$
$823$			7.23765e6i			0.372476i	−0.982505	+	0.186238i	$0.940371\pi$
$824$	−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	$0.215165\pi$
$827$			2.46106e7i			1.25129i	−0.780107	+	0.625646i	$0.784835\pi$
$828$	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	$-0.938755\pi$
$853$		−	8.12725e6i		−	0.382447i	0.981547	−	0.191223i	$-0.0612455\pi$
$854$	−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	$-0.846287\pi$
$857$		−	1.99678e7i		−	0.928704i	0.885651	−	0.464352i	$-0.153713\pi$
$858$	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	$-0.833735\pi$
$907$		−	2.47211e7i		−	0.997816i	0.866655	−	0.498908i	$-0.166265\pi$
$908$	−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	$-0.823771\pi$
$919$		−	2.69233e7i		−	1.05157i	0.850616	−	0.525787i	$-0.176229\pi$
$920$	−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	$-0.982069\pi$
$953$		−	3.15715e6i		−	0.112606i	0.998414	−	0.0563031i	$-0.0179313\pi$
$954$	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	$0.0788194\pi$
$967$			1.42538e7i			0.490191i	−0.969499	+	0.245096i	$0.921181\pi$
$968$	−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	$-0.688917\pi$
$971$		−	4.87109e7i		−	1.65797i	0.559267	−	0.828987i	$-0.311083\pi$
$972$	−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	$-0.672074\pi$
$977$		−	5.11627e7i		−	1.71481i	0.514640	−	0.857406i	$-0.327926\pi$
$978$	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	$-0.611008\pi$
$997$		−	5.89936e7i		−	1.87961i	0.341716	−	0.939803i	$-0.388992\pi$
$998$	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.75.19	✓	96
4.3	odd	2		608.6.b.b.303.90		96
8.3	odd	2	inner	152.6.b.b.75.77	yes	96
8.5	even	2		608.6.b.b.303.89		96
19.18	odd	2	inner	152.6.b.b.75.78	yes	96
76.75	even	2		608.6.b.b.303.8		96
152.37	odd	2		608.6.b.b.303.7		96
152.75	even	2	inner	152.6.b.b.75.20	yes	96

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

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