LMFDB - Embedded newform 97.6.h.a.8.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [97,6,Mod(8,97)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(97, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("97.8"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 97 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	97.h (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$15.5572305219$
Analytic rank:	$0$
Dimension:	$328$
Relative dimension:	$41$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			8.1
Character	$\chi$	$=$	97.8
Dual form			97.6.h.a.85.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-10.3746 - 4.29730i) q^{2} +(7.95190 + 19.1976i) q^{3} +(66.5381 + 66.5381i) q^{4} +(44.7629 + 8.90389i) q^{5} -233.339i q^{6} +(-154.075 + 30.6475i) q^{7} +(-266.858 - 644.252i) q^{8} +(-133.487 + 133.487i) q^{9} +(-426.134 - 284.734i) q^{10} +(-136.933 - 330.584i) q^{11} +(-748.266 + 1806.47i) q^{12} +(132.023 - 663.724i) q^{13} +(1730.17 + 344.152i) q^{14} +(185.017 + 930.142i) q^{15} +4819.46i q^{16} +(432.686 - 2175.26i) q^{17} +(1958.51 - 811.242i) q^{18} +(45.9988 + 9.14973i) q^{19} +(2385.99 + 3570.88i) q^{20} +(-1813.55 - 2714.16i) q^{21} +4018.12i q^{22} +(-1227.95 + 820.491i) q^{23} +(10246.1 - 10246.1i) q^{24} +(-962.686 - 398.757i) q^{25} +(-4221.90 + 6318.52i) q^{26} +(1040.90 + 431.155i) q^{27} +(-12291.1 - 8212.64i) q^{28} +(548.759 - 366.669i) q^{29} +(2077.62 - 10444.9i) q^{30} +(449.226 - 186.076i) q^{31} +(12171.2 - 29383.9i) q^{32} +(5257.54 - 5257.54i) q^{33} +(-13836.7 + 20708.1i) q^{34} -7169.73 q^{35} -17764.0 q^{36} +(5231.83 - 7829.99i) q^{37} +(-437.900 - 292.595i) q^{38} +(13791.7 - 2743.34i) q^{39} +(-6208.99 - 31214.7i) q^{40} +(3703.25 + 5542.31i) q^{41} +(7151.24 + 35951.7i) q^{42} +(-9043.87 - 9043.87i) q^{43} +(12885.2 - 31107.7i) q^{44} +(-7163.83 + 4786.72i) q^{45} +(16265.4 - 3235.39i) q^{46} +(16821.6 + 16821.6i) q^{47} +(-92521.9 + 38323.8i) q^{48} +(7272.25 - 3012.27i) q^{49} +(8273.90 + 8273.90i) q^{50} +(45200.4 - 8990.91i) q^{51} +(52947.4 - 35378.3i) q^{52} +(3022.59 - 7297.18i) q^{53} +(-8946.13 - 8946.13i) q^{54} +(-3186.01 - 16017.1i) q^{55} +(60860.9 + 91084.8i) q^{56} +(190.125 + 955.823i) q^{57} +(-7268.84 + 1445.86i) q^{58} +(-5594.42 - 3738.07i) q^{59} +(-49579.2 + 74200.5i) q^{60} -54491.8 q^{61} -5460.16 q^{62} +(16476.0 - 24658.1i) q^{63} +(-143490. + 143490. i) q^{64} +(11819.5 - 28534.7i) q^{65} +(-77138.1 + 31951.7i) q^{66} +(5521.05 - 27756.2i) q^{67} +(173528. - 115947. i) q^{68} +(-25516.0 - 17049.2i) q^{69} +(74383.1 + 30810.5i) q^{70} +(20338.8 - 30439.1i) q^{71} +(121622. + 50377.3i) q^{72} +(10825.0 - 10825.0i) q^{73} +(-87925.9 + 58750.2i) q^{74} -21652.1i q^{75} +(2451.87 + 3669.48i) q^{76} +(31229.5 + 46738.2i) q^{77} +(-154872. - 30806.0i) q^{78} +(-23771.2 + 9846.37i) q^{79} +(-42911.9 + 215733. i) q^{80} +69284.7i q^{81} +(-14602.8 - 73413.2i) q^{82} +(29851.2 + 5937.77i) q^{83} +(59925.4 - 301265. i) q^{84} +(38736.6 - 93518.3i) q^{85} +(54962.3 + 132691. i) q^{86} +(11402.8 + 7619.13i) q^{87} +(-176438. + 176438. i) q^{88} +(-33401.5 - 80638.4i) q^{89} +(94891.9 - 18875.2i) q^{90} +106310. i q^{91} +(-136299. - 27111.6i) q^{92} +(7144.40 + 7144.40i) q^{93} +(-102230. - 246805. i) q^{94} +(1977.57 + 819.137i) q^{95} +660883. q^{96} +(91605.0 + 13995.1i) q^{97} -88391.3 q^{98} +(62407.6 + 25850.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 328 q - 8 q^{2} - 96 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{7} - 8 q^{8} + 256 q^{9} - 1992 q^{10} - 8 q^{11} + 4472 q^{12} - 8 q^{13} - 5504 q^{14} + 7640 q^{15} + 2880 q^{17} - 14104 q^{18} + 13984 q^{19} + 11504 q^{20}+ \cdots + 390672 q^{99}+O(q^{100}) $ 328 * q - 8 * q^2 - 96 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^7 - 8 * q^8 + 256 * q^9 - 1992 * q^10 - 8 * q^11 + 4472 * q^12 - 8 * q^13 - 5504 * q^14 + 7640 * q^15 + 2880 * q^17 - 14104 * q^18 + 13984 * q^19 + 11504 * q^20 - 8 * q^21 + 10976 * q^23 + 8184 * q^24 - 20240 * q^25 - 23968 * q^26 + 21024 * q^27 - 4368 * q^28 - 5688 * q^29 + 24992 * q^30 - 17744 * q^31 + 19528 * q^32 - 30016 * q^33 - 43528 * q^34 + 78384 * q^35 - 549520 * q^36 - 36816 * q^37 - 8 * q^38 - 32088 * q^39 + 68344 * q^40 - 31128 * q^41 + 62200 * q^42 + 6144 * q^43 - 72704 * q^44 + 57904 * q^45 - 8 * q^46 + 130504 * q^47 + 123192 * q^48 + 158656 * q^49 - 177512 * q^50 + 36600 * q^51 + 15160 * q^52 - 28632 * q^53 + 302712 * q^54 + 106744 * q^55 - 8 * q^56 - 8 * q^57 - 176712 * q^58 + 234272 * q^59 + 415720 * q^60 + 178592 * q^61 - 246032 * q^62 - 305160 * q^63 + 8184 * q^64 + 273504 * q^65 - 137296 * q^66 + 393832 * q^67 + 480576 * q^68 - 475128 * q^69 + 736072 * q^70 - 429184 * q^71 - 451336 * q^72 + 239224 * q^73 + 249656 * q^74 + 155752 * q^76 - 8 * q^77 + 62200 * q^78 - 230296 * q^79 - 874280 * q^80 + 131136 * q^82 + 204368 * q^83 + 1467680 * q^84 + 14928 * q^85 - 104056 * q^86 - 230696 * q^87 + 372216 * q^88 + 191216 * q^89 + 842872 * q^90 - 1189408 * q^92 - 1087800 * q^93 - 723656 * q^94 + 573344 * q^95 - 907792 * q^96 - 339408 * q^97 - 2291344 * q^98 + 390672 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/97\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{1}{16}\right)$

Coefficient data

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

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

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

$2$	−10.3746	−	4.29730i	−1.83399	−	0.759662i	−0.963630	−	0.267241i	$-0.913888\pi$
$2$	−10.3746	−	4.29730i	−1.83399	−	0.759662i	−0.870357	−	0.492421i	$-0.836112\pi$
$3$	7.95190	+	19.1976i	0.510114	+	1.23153i	0.943817	+	0.330469i	$0.107207\pi$
$3$	7.95190	+	19.1976i	0.510114	+	1.23153i	−0.433703	+	0.901056i	$0.642793\pi$
$4$	66.5381	+	66.5381i	2.07931	+	2.07931i
$5$	44.7629	+	8.90389i	0.800743	+	0.159278i	0.578467	−	0.815706i	$-0.303651\pi$
$5$	44.7629	+	8.90389i	0.800743	+	0.159278i	0.222276	+	0.974984i	$0.428651\pi$
$6$		−	233.339i		−	2.64612i
$7$	−154.075	+	30.6475i	−1.18847	+	0.236401i	−0.749440	−	0.662072i	$-0.769677\pi$
$7$	−154.075	+	30.6475i	−1.18847	+	0.236401i	−0.439028	+	0.898473i	$0.644677\pi$
$8$	−266.858	−	644.252i	−1.47420	−	3.55902i
$9$	−133.487	+	133.487i	−0.549330	+	0.549330i
$10$	−426.134	−	284.734i	−1.34756	−	0.900407i
$11$	−136.933	−	330.584i	−0.341212	−	0.823760i	−0.997594	−	0.0693304i	$-0.977914\pi$
$11$	−136.933	−	330.584i	−0.341212	−	0.823760i	0.656381	−	0.754429i	$-0.272086\pi$
$12$	−748.266	+	1806.47i	−1.50004	+	3.62142i
$13$	132.023	−	663.724i	0.216666	−	1.08925i	−0.707339	−	0.706874i	$-0.750105\pi$
$13$	132.023	−	663.724i	0.216666	−	1.08925i	0.924005	−	0.382379i	$-0.124895\pi$
$14$	1730.17	+	344.152i	2.35922	+	0.469278i
$15$	185.017	+	930.142i	0.212316	+	1.06738i
$16$			4819.46i			4.70650i
$17$	432.686	−	2175.26i	0.363120	−	1.82553i	−0.177328	−	0.984152i	$-0.556745\pi$
$17$	432.686	−	2175.26i	0.363120	−	1.82553i	0.540449	−	0.841377i	$-0.318255\pi$
$18$	1958.51	−	811.242i	1.42477	−	0.590159i
$19$	45.9988	+	9.14973i	0.0292323	+	0.00581466i	0.209685	−	0.977769i	$-0.432756\pi$
$19$	45.9988	+	9.14973i	0.0292323	+	0.00581466i	−0.180453	+	0.983584i	$0.557756\pi$
$20$	2385.99	+	3570.88i	1.33381	+	1.99618i
$21$	−1813.55	−	2714.16i	−0.897389	−	1.34304i
$22$			4018.12i			1.76997i
$23$	−1227.95	+	820.491i	−0.484018	+	0.323411i	−0.773526	−	0.633765i	$-0.781509\pi$
$23$	−1227.95	+	820.491i	−0.484018	+	0.323411i	0.289507	+	0.957176i	$0.406509\pi$
$24$	10246.1	−	10246.1i	3.63102	−	3.63102i
$25$	−962.686	−	398.757i	−0.308059	−	0.127602i
$26$	−4221.90	+	6318.52i	−1.22483	+	1.83308i
$27$	1040.90	+	431.155i	0.274790	+	0.113822i
$28$	−12291.1	−	8212.64i	−2.96275	−	1.97965i
$29$	548.759	−	366.669i	0.121168	−	0.0809616i	−0.493510	−	0.869740i	$-0.664286\pi$
$29$	548.759	−	366.669i	0.121168	−	0.0809616i	0.614677	+	0.788779i	$0.289286\pi$
$30$	2077.62	−	10444.9i	0.421467	−	2.11886i
$31$	449.226	−	186.076i	0.0839578	−	0.0347764i	−0.340309	−	0.940314i	$-0.610532\pi$
$31$	449.226	−	186.076i	0.0839578	−	0.0347764i	0.424267	+	0.905537i	$0.360532\pi$
$32$	12171.2	−	29383.9i	2.10116	−	5.07264i
$33$	5257.54	−	5257.54i	0.840423	−	0.840423i
$34$	−13836.7	+	20708.1i	−2.05274	+	3.07215i
$35$	−7169.73			−0.989311
$36$	−17764.0			−2.28446
$37$	5231.83	−	7829.99i	0.628274	−	0.940279i	−0.371655	−	0.928371i	$-0.621209\pi$
$37$	5231.83	−	7829.99i	0.628274	−	0.940279i	0.999929	−	0.0119081i	$-0.00379055\pi$
$38$	−437.900	−	292.595i	−0.0491944	−	0.0328707i
$39$	13791.7	−	2743.34i	1.45197	−	0.288814i
$40$	−6208.99	−	31214.7i	−0.613579	−	3.08467i
$41$	3703.25	+	5542.31i	0.344052	+	0.514910i	0.962632	−	0.270812i	$-0.0872921\pi$
$41$	3703.25	+	5542.31i	0.344052	+	0.514910i	−0.618581	+	0.785721i	$0.712292\pi$
$42$	7151.24	+	35951.7i	0.625544	+	3.14482i
$43$	−9043.87	−	9043.87i	−0.745905	−	0.745905i	0.227803	−	0.973707i	$-0.426846\pi$
$43$	−9043.87	−	9043.87i	−0.745905	−	0.745905i	−0.973707	+	0.227803i	$0.926846\pi$
$44$	12885.2	−	31107.7i	1.00337	−	2.42234i
$45$	−7163.83	+	4786.72i	−0.527369	+	0.352376i
$46$	16265.4	−	3235.39i	1.13337	−	0.225441i
$47$	16821.6	+	16821.6i	1.11077	+	1.11077i	0.993047	+	0.117722i	$0.0375593\pi$
$47$	16821.6	+	16821.6i	1.11077	+	1.11077i	0.117722	+	0.993047i	$0.462441\pi$
$48$	−92521.9	+	38323.8i	−5.79617	+	2.40085i
$49$	7272.25	−	3012.27i	0.432692	−	0.179227i
$50$	8273.90	+	8273.90i	0.468042	+	0.468042i
$51$	45200.4	−	8990.91i	2.43342	−	0.484037i
$52$	52947.4	−	35378.3i	2.71542	−	1.81438i
$53$	3022.59	−	7297.18i	0.147805	−	0.356833i	−0.832586	−	0.553896i	$-0.813140\pi$
$53$	3022.59	−	7297.18i	0.147805	−	0.356833i	0.980391	+	0.197063i	$0.0631404\pi$
$54$	−8946.13	−	8946.13i	−0.417494	−	0.417494i
$55$	−3186.01	−	16017.1i	−0.142017	−	0.713967i
$56$	60860.9	+	91084.8i	2.59339	+	3.88129i
$57$	190.125	+	955.823i	0.00775090	+	0.0389664i
$58$	−7268.84	+	1445.86i	−0.283723	+	0.0564361i
$59$	−5594.42	−	3738.07i	−0.209231	−	0.139803i	0.446540	−	0.894764i	$-0.352656\pi$
$59$	−5594.42	−	3738.07i	−0.209231	−	0.139803i	−0.655770	+	0.754960i	$0.727656\pi$
$60$	−49579.2	+	74200.5i	−1.77796	+	2.66090i
$61$	−54491.8			−1.87502			−0.937511	−	0.347956i	$-0.886876\pi$
$61$	−54491.8			−1.87502			−0.937511	+	0.347956i	$0.886876\pi$
$62$	−5460.16			−0.180396
$63$	16476.0	−	24658.1i	0.522999	−	0.782724i
$64$	−143490.	+	143490.i	−4.37898	+	4.37898i
$65$	11819.5	−	28534.7i	0.346988	−	0.837702i
$66$	−77138.1	+	31951.7i	−2.17976	+	0.902888i
$67$	5521.05	−	27756.2i	0.150257	−	0.755393i	−0.830015	−	0.557741i	$-0.811668\pi$
$67$	5521.05	−	27756.2i	0.150257	−	0.755393i	0.980272	−	0.197652i	$-0.0633318\pi$
$68$	173528.	−	115947.i	4.55089	−	3.04081i
$69$	−25516.0	−	17049.2i	−0.645193	−	0.431104i
$70$	74383.1	+	30810.5i	1.81438	+	0.751542i
$71$	20338.8	−	30439.1i	0.478827	−	0.716615i	−0.510891	−	0.859645i	$-0.670685\pi$
$71$	20338.8	−	30439.1i	0.478827	−	0.716615i	0.989718	+	0.143030i	$0.0456846\pi$
$72$	121622.	+	50377.3i	2.76490	+	1.14526i
$73$	10825.0	−	10825.0i	0.237750	−	0.237750i	−0.578168	−	0.815918i	$-0.696232\pi$
$73$	10825.0	−	10825.0i	0.237750	−	0.237750i	0.815918	+	0.578168i	$0.196232\pi$
$74$	−87925.9	+	58750.2i	−1.86654	+	1.24718i
$75$		−	21652.1i		−	0.444475i
$76$	2451.87	+	3669.48i	0.0486926	+	0.0728736i
$77$	31229.5	+	46738.2i	0.600258	+	0.898349i
$78$	−154872.	−	30806.0i	−2.88229	−	0.573323i
$79$	−23771.2	+	9846.37i	−0.428533	+	0.177504i	−0.586516	−	0.809938i	$-0.699501\pi$
$79$	−23771.2	+	9846.37i	−0.428533	+	0.177504i	0.157983	+	0.987442i	$0.449501\pi$
$80$	−42911.9	+	215733.i	−0.749641	+	3.76870i
$81$			69284.7i			1.17334i
$82$	−14602.8	−	73413.2i	−0.239829	−	1.20570i
$83$	29851.2	+	5937.77i	0.475627	+	0.0946081i	0.427082	−	0.904213i	$-0.359542\pi$
$83$	29851.2	+	5937.77i	0.475627	+	0.0946081i	0.0485451	+	0.998821i	$0.484542\pi$
$84$	59925.4	−	301265.i	0.926643	−	4.65855i
$85$	38736.6	−	93518.3i	0.581532	−	1.40394i
$86$	54962.3	+	132691.i	0.801344	+	1.93461i
$87$	11402.8	+	7619.13i	0.161516	+	0.107921i
$88$	−176438.	+	176438.i	−2.42877	+	2.42877i
$89$	−33401.5	−	80638.4i	−0.446983	−	1.07911i	−0.973446	−	0.228915i	$-0.926482\pi$
$89$	−33401.5	−	80638.4i	−0.446983	−	1.07911i	0.526463	−	0.850198i	$-0.323518\pi$
$90$	94891.9	−	18875.2i	1.23487	−	0.245632i
$91$			106310.i			1.34576i
$92$	−136299.	−	27111.6i	−1.67890	−	0.333954i
$93$	7144.40	+	7144.40i	0.0856561	+	0.0856561i
$94$	−102230.	−	246805.i	−1.19333	−	2.88094i
$95$	1977.57	+	819.137i	0.0224814	+	0.00931210i
$96$	660883.			7.31891
$97$	91605.0	+	13995.1i	0.988530	+	0.151024i
$97$	91605.0	+	13995.1i	0.988530	+	0.151024i
$98$	−88391.3			−0.929703
$99$	62407.6	+	25850.1i	0.639955	+	0.265078i
$100$	−37522.7	−	90587.8i	−0.375227	−	0.905878i
$101$	58124.4	+	58124.4i	0.566964	+	0.566964i	0.931277	−	0.364313i	$-0.118696\pi$
$101$	58124.4	+	58124.4i	0.566964	+	0.566964i	−0.364313	+	0.931277i	$0.618696\pi$
$102$	−507572.	−	100962.i	−4.83056	−	0.960858i
$103$		−	166555.i		−	1.54691i	−0.633853	−	0.773454i	$-0.718527\pi$
$103$		−	166555.i		−	1.54691i	0.633853	−	0.773454i	$-0.281473\pi$
$104$	−462837.	+	92064.0i	−4.19609	+	0.834654i
$105$	−57013.0	−	137641.i	−0.504662	−	1.21836i
$106$	−62716.3	+	62716.3i	−0.542145	+	0.542145i
$107$	−7453.99	−	4980.60i	−0.0629404	−	0.0420554i	0.523702	−	0.851902i	$-0.324551\pi$
$107$	−7453.99	−	4980.60i	−0.0629404	−	0.0420554i	−0.586642	+	0.809846i	$0.699551\pi$
$108$	40571.3	+	97947.8i	0.334703	+	0.808045i
$109$	23125.5	−	55829.9i	0.186434	−	0.450091i	−0.802834	−	0.596202i	$-0.796676\pi$
$109$	23125.5	−	55829.9i	0.186434	−	0.450091i	0.989268	+	0.146111i	$0.0466757\pi$
$110$	−35776.9	+	179863.i	−0.281917	+	1.41729i
$111$	191920.	+	38175.2i	1.47847	+	0.294086i
$112$	−147704.	−	742559.i	−1.11262	−	5.59353i
$113$		−	85259.0i		−	0.628122i	−0.949403	−	0.314061i	$-0.898310\pi$
$113$		−	85259.0i		−	0.628122i	0.949403	−	0.314061i	$-0.101690\pi$
$114$	2134.99	−	10733.3i	0.0153863	−	0.0773520i
$115$	−62272.3	+	25794.0i	−0.439086	+	0.181876i
$116$	60910.8	+	12115.9i	0.420290	+	0.0836009i
$117$	70975.3	+	106222.i	0.479339	+	0.717381i
$118$	41976.2	+	62821.9i	0.277523	+	0.415342i
$119$			348414.i			2.25543i
$120$	549873.	−	367413.i	3.48585	−	2.32917i
$121$	23344.8	−	23344.8i	0.144953	−	0.144953i
$122$	565330.	+	234167.i	3.43876	+	1.42438i
$123$	−76951.0	+	115165.i	−0.458618	+	0.686371i
$124$	42271.7	+	17509.5i	0.246886	+	0.102263i
$125$	−158130.	−	105659.i	−0.905189	−	0.604828i
$126$	−276896.	+	185016.i	−1.55378	+	1.03820i
$127$	−66834.6	+	336000.i	−0.367699	+	1.84855i	0.144266	+	0.989539i	$0.453918\pi$
$127$	−66834.6	+	336000.i	−0.367699	+	1.84855i	−0.511965	+	0.859006i	$0.671082\pi$
$128$	1.16499e6	−	482556.i	6.28491	−	2.60329i
$129$	101704.	−	245536.i	0.538104	−	1.29910i
$130$	−245244.	+	245244.i	−1.27274	+	1.27274i
$131$	−2717.34	+	4066.78i	−0.0138346	+	0.0207049i	−0.838322	−	0.545175i	$-0.816463\pi$
$131$	−2717.34	+	4066.78i	−0.0138346	+	0.0207049i	0.824488	+	0.565880i	$0.191463\pi$
$132$	699654.			3.49501
$133$	−7367.69			−0.0361162
$134$	−176555.	+	264234.i	−0.849413	+	1.27124i
$135$	42754.8	+	28567.8i	0.201907	+	0.134910i
$136$	−1.51688e6	+	301726.i	−7.03241	+	1.39883i
$137$	−33847.2	−	170161.i	−0.154071	−	0.774568i	−0.978119	−	0.208047i	$-0.933289\pi$
$137$	−33847.2	−	170161.i	−0.154071	−	0.774568i	0.824048	−	0.566520i	$-0.191711\pi$
$138$	191452.	+	286529.i	0.855782	+	1.28077i
$139$	35805.5	+	180006.i	0.157185	+	0.790225i	0.976271	+	0.216553i	$0.0694814\pi$
$139$	35805.5	+	180006.i	0.157185	+	0.790225i	−0.819085	+	0.573672i	$0.805519\pi$
$140$	−477060.	−	477060.i	−2.05709	−	2.05709i
$141$	−189171.	+	456699.i	−0.801320	+	1.93456i
$142$	−341812.	+	228392.i	−1.42255	+	0.950516i
$143$	−237495.	+	47240.7i	−0.971212	+	0.193186i
$144$	−643336.	−	643336.i	−2.58542	−	2.58542i
$145$	27828.8	−	11527.1i	0.109920	−	0.0455302i
$146$	−158823.	+	65786.7i	−0.616640	+	0.255421i
$147$	115656.	+	115656.i	0.441445	+	0.441445i
$148$	869108.	−	172876.i	3.26152	−	0.648756i
$149$	32455.6	−	21686.1i	0.119763	−	0.0800232i	−0.494246	−	0.869322i	$-0.664556\pi$
$149$	32455.6	−	21686.1i	0.119763	−	0.0800232i	0.614009	+	0.789299i	$0.289556\pi$
$150$	−93045.6	+	224632.i	−0.337651	+	0.815161i
$151$	−171249.	−	171249.i	−0.611204	−	0.611204i	0.332055	−	0.943260i	$-0.392258\pi$
$151$	−171249.	−	171249.i	−0.611204	−	0.611204i	−0.943260	+	0.332055i	$0.892258\pi$
$152$	−6380.42	−	32076.5i	−0.0223996	−	0.112610i
$153$	232611.	+	348128.i	0.803346	+	1.20229i
$154$	−123145.	−	619092.i	−0.418423	−	2.10355i
$155$	21765.5	−	4329.42i	0.0727677	−	0.0144744i
$156$	1.10021e6	+	735137.i	3.61963	+	2.41856i
$157$	−41843.6	+	62623.4i	−0.135481	+	0.202762i	−0.893006	−	0.450044i	$-0.851408\pi$
$157$	−41843.6	+	62623.4i	−0.135481	+	0.202762i	0.757525	+	0.652806i	$0.226408\pi$
$158$	288930.			0.920767
$159$	164123.			0.514847
$160$	806448.	−	1.20694e6i	2.49044	−	3.72721i
$161$	164051.	−	164051.i	0.498786	−	0.498786i
$162$	297737.	−	718801.i	0.891344	−	2.15190i
$163$	−320641.	+	132814.i	−0.945256	+	0.391538i	−0.801446	−	0.598067i	$-0.795936\pi$
$163$	−320641.	+	132814.i	−0.945256	+	0.391538i	−0.143810	+	0.989605i	$0.545936\pi$
$164$	−122367.	+	615181.i	−0.355267	+	1.78605i
$165$	282156.	−	188530.i	0.806824	−	0.539102i
$166$	−284178.	−	189882.i	−0.800424	−	0.534826i
$167$	−138815.	−	57499.2i	−0.385164	−	0.159540i	0.181695	−	0.983355i	$-0.441842\pi$
$167$	−138815.	−	57499.2i	−0.385164	−	0.159540i	−0.566859	+	0.823815i	$0.691842\pi$
$168$	−1.26465e6	+	1.89268e6i	−3.45697	+	5.17373i
$169$	−80069.1	−	33165.7i	−0.215649	−	0.0893249i
$170$	−803752.	+	803752.i	−2.13304	+	2.13304i
$171$	−7361.63	+	4918.88i	−0.0192523	+	0.0128640i
$172$		−	1.20352e6i		−	3.10194i
$173$	−245819.	−	367894.i	−0.624454	−	0.934561i	−0.999970	−	0.00774534i	$-0.997535\pi$
$173$	−245819.	−	367894.i	−0.624454	−	0.934561i	0.375516	−	0.926816i	$-0.377465\pi$
$174$	−85558.1	−	128047.i	−0.214234	−	0.320624i
$175$	160547.	+	31934.8i	0.396284	+	0.0788258i
$176$	1.59324e6	−	659940.i	3.87703	−	1.60592i
$177$	27275.7	−	137124.i	0.0654399	−	0.328988i
$178$			980127.i			2.31864i
$179$	−77958.1	−	391922.i	−0.181856	−	0.914254i	−0.958669	−	0.284522i	$-0.908165\pi$
$179$	−77958.1	−	391922.i	−0.181856	−	0.914254i	0.776813	−	0.629731i	$-0.216835\pi$
$180$	−795167.	−	158169.i	−1.82927	−	0.363864i
$181$	23914.3	−	120226.i	0.0542578	−	0.272772i	−0.944127	−	0.329581i	$-0.893093\pi$
$181$	23914.3	−	120226.i	0.0542578	−	0.272772i	0.998385	+	0.0568087i	$0.0180925\pi$
$182$	456844.	−	1.10292e6i	1.02233	−	2.46811i
$183$	−433313.	−	1.04611e6i	−0.956475	−	2.30914i
$184$	856292.	+	572156.i	1.86456	+	1.24586i
$185$	303909.	−	303909.i	0.652852	−	0.652852i
$186$	−43418.6	−	104822.i	−0.0920225	−	0.222162i
$187$	−778355.	+	154825.i	−1.62770	+	0.323769i
$188$			2.23856e6i			4.61928i
$189$	−173591.	−	34529.4i	−0.353486	−	0.0703128i
$190$	−16996.4	−	16996.4i	−0.0341565	−	0.0341565i
$191$	−216532.	−	522754.i	−0.429476	−	1.03685i	−0.979454	−	0.201667i	$-0.935364\pi$
$191$	−216532.	−	522754.i	−0.429476	−	1.03685i	0.549979	−	0.835179i	$-0.314636\pi$
$192$	−3.89569e6	−	1.61365e6i	−7.62661	−	3.15904i
$193$	−612889.			−1.18437			−0.592187	−	0.805801i	$-0.701735\pi$
$193$	−612889.			−1.18437			−0.592187	+	0.805801i	$0.701735\pi$
$194$	−890224.	−	538848.i	−1.69822	−	1.02793i
$195$	641784.			1.20865
$196$	684312.	+	283451.i	1.27237	+	0.527033i
$197$	141359.	+	341271.i	0.259512	+	0.626518i	0.998906	−	0.0467548i	$-0.0148879\pi$
$197$	141359.	+	341271.i	0.259512	+	0.626518i	−0.739394	+	0.673273i	$0.764888\pi$
$198$	−536368.	−	536368.i	−0.972299	−	0.972299i
$199$	797614.	+	158655.i	1.42778	+	0.284002i	0.847664	−	0.530534i	$-0.178008\pi$
$199$	797614.	+	158655.i	1.42778	+	0.284002i	0.580113	+	0.814536i	$0.303008\pi$
$200$			726624.i			1.28450i
$201$	576755.	−	114724.i	1.00693	−	0.200292i
$202$	−353240.	−	852796.i	−0.609103	−	1.47051i
$203$	−73312.7	+	73312.7i	−0.124864	+	0.124864i
$204$	3.60578e6	+	2.40931e6i	6.06630	+	4.05337i
$205$	116420.	+	281063.i	0.193483	+	0.467110i
$206$	−715736.	+	1.72794e6i	−1.17513	+	2.83701i
$207$	54390.8	−	273441.i	0.0882267	−	0.443545i
$208$	3.19879e6	+	636279.i	5.12657	+	1.01974i
$209$	−3273.97	−	16459.4i	−0.00518453	−	0.0260644i
$210$			1.67298e6i			2.61783i
$211$	−191591.	+	963193.i	−0.296257	+	1.48939i	0.490128	+	0.871650i	$0.336950\pi$
$211$	−191591.	+	963193.i	−0.296257	+	1.48939i	−0.786386	+	0.617736i	$0.788050\pi$
$212$	686657.	−	284423.i	1.04930	−	0.434635i
$213$	746089.	+	148406.i	1.12679	+	0.224132i
$214$	55929.0	+	83703.7i	0.0834839	+	0.124942i
$215$	−324304.	−	485356.i	−0.478472	−	0.716084i
$216$		−	785660.i		−	1.14578i
$217$	−63511.9	+	42437.3i	−0.0915600	+	0.0611784i
$218$	−479835.	+	479835.i	−0.683834	+	0.683834i
$219$	293893.	+	121734.i	0.414075	+	0.171515i
$220$	853759.	−	1.27774e6i	1.18926	−	1.77986i
$221$	−1.38665e6	−	574368.i	−1.90979	−	0.791060i
$222$	−1.82704e6	−	1.22079e6i	−2.48809	−	1.66249i
$223$	7659.09	−	5117.64i	0.0103137	−	0.00689140i	−0.550403	−	0.834899i	$-0.685526\pi$
$223$	7659.09	−	5117.64i	0.0103137	−	0.00689140i	0.560716	+	0.828008i	$0.310526\pi$
$224$	−974738.	+	4.90034e6i	−1.29798	+	6.52538i
$225$	181735.	−	75277.3i	0.239322	−	0.0991305i
$226$	−366383.	+	884528.i	−0.477161	+	1.15197i
$227$	744318.	−	744318.i	0.958725	−	0.958725i	−0.0404566	−	0.999181i	$-0.512881\pi$
$227$	744318.	−	744318.i	0.958725	−	0.958725i	0.999181	+	0.0404566i	$0.0128812\pi$
$228$	−50948.1	+	76249.2i	−0.0649069	+	0.0971400i
$229$	901643.			1.13618			0.568089	−	0.822967i	$-0.307683\pi$
$229$	901643.			1.13618			0.568089	+	0.822967i	$0.307683\pi$
$230$	756894.			0.943443
$231$	−648927.	+	971188.i	−0.800140	+	1.19749i
$232$	−382668.	−	255691.i	−0.466769	−	0.311885i
$233$	425625.	−	84662.1i	0.513615	−	0.102164i	0.0685235	−	0.997650i	$-0.478171\pi$
$233$	425625.	−	84662.1i	0.513615	−	0.102164i	0.445091	+	0.895485i	$0.353171\pi$
$234$	−279872.	−	1.40701e6i	−0.334134	−	1.67980i
$235$	603207.	+	902763.i	0.712520	+	1.06636i
$236$	−123518.	−	620966.i	−0.144361	−	0.725751i
$237$	−378053.	−	378053.i	−0.437201	−	0.437201i
$238$	1.49724e6	−	3.61466e6i	1.71336	−	4.13642i
$239$	−144734.	+	96708.3i	−0.163899	+	0.109514i	−0.634815	−	0.772664i	$-0.718924\pi$
$239$	−144734.	+	96708.3i	−0.163899	+	0.109514i	0.470916	+	0.882178i	$0.343924\pi$
$240$	−4.48278e6	+	891680.i	−5.02365	+	0.999266i
$241$	673967.	+	673967.i	0.747473	+	0.747473i	0.974004	−	0.226531i	$-0.0727383\pi$
$241$	673967.	+	673967.i	0.747473	+	0.747473i	−0.226531	+	0.974004i	$0.572738\pi$
$242$	−342512.	+	141873.i	−0.375956	+	0.155726i
$243$	−1.07716e6	+	446174.i	−1.17021	+	0.484717i
$244$	−3.62578e6	−	3.62578e6i	−3.89876	−	3.89876i
$245$	352348.	−	70086.4i	0.375022	−	0.0745965i
$246$	1.29323e6	−	864112.i	1.36251	−	0.910400i
$247$	12145.8	−	29322.5i	0.0126673	−	0.0305815i
$248$	−239759.	−	239759.i	−0.247540	−	0.247540i
$249$	123383.	+	620287.i	0.126112	+	0.634008i
$250$	1.18649e6	+	1.77570e6i	1.20064	+	1.79689i
$251$	75649.1	+	380314.i	0.0757913	+	0.381029i	1.00000		0.000859998i	$-0.000273746\pi$
$251$	75649.1	+	380314.i	0.0757913	+	0.381029i	−0.924208	+	0.381889i	$0.875274\pi$
$252$	2.73699e6	−	544421.i	2.71501	−	0.540049i
$253$	439388.	+	293590.i	0.431566	+	0.288363i
$254$	2.13727e6	−	3.19866e6i	2.07862	−	3.11088i
$255$	2.10335e6			2.02564
$256$	−7.66639e6			−7.31124
$257$	−24863.6	+	37211.0i	−0.0234818	+	0.0351429i	−0.843025	−	0.537875i	$-0.819227\pi$
$257$	−24863.6	+	37211.0i	−0.0234818	+	0.0351429i	0.819543	+	0.573018i	$0.194227\pi$
$258$	−2.11029e6	+	2.11029e6i	−1.97375	+	1.97375i
$259$	−566126.	+	1.36675e6i	−0.524401	+	1.26602i
$260$	2.68509e6	−	1.11220e6i	2.46334	−	1.02035i
$261$	−24306.7	+	122198.i	−0.0220864	+	0.111036i
$262$	45667.5	−	30514.0i	0.0411011	−	0.0274629i
$263$	−560951.	−	374815.i	−0.500075	−	0.334139i	0.279817	−	0.960053i	$-0.409726\pi$
$263$	−560951.	−	374815.i	−0.500075	−	0.334139i	−0.779892	+	0.625914i	$0.784726\pi$
$264$	−4.79020e6	−	1.98417e6i	−4.23004	−	1.75214i
$265$	200273.	−	299730.i	0.175190	−	0.262190i
$266$	76436.8	+	31661.2i	0.0662367	+	0.0274361i
$267$	1.28246e6	−	1.28246e6i	1.10094	−	1.10094i
$268$	2.21420e6	−	1.47948e6i	1.88313	−	1.25827i
$269$			268031.i			0.225842i	0.993604	+	0.112921i	$0.0360207\pi$
$269$			268031.i			0.225842i	−0.993604	+	0.112921i	$0.963979\pi$
$270$	−320799.	−	480110.i	−0.267808	−	0.400803i
$271$	−307996.	−	460949.i	−0.254755	−	0.381268i	0.681944	−	0.731405i	$-0.261135\pi$
$271$	−307996.	−	460949.i	−0.254755	−	0.381268i	−0.936698	+	0.350137i	$0.886135\pi$
$272$	1.04836e7	+	2.08531e6i	8.59185	+	1.70903i
$273$	−2.04088e6	+	845362.i	−1.65734	+	0.686493i
$274$	−380083.	+	1.91081e6i	−0.305846	+	1.53759i
$275$			372852.i			0.297306i
$276$	−563361.	−	2.83221e6i	−0.445158	−	2.23796i
$277$	−1.25659e6	−	249951.i	−0.983996	−	0.195729i	−0.323230	−	0.946321i	$-0.604769\pi$
$277$	−1.25659e6	−	249951.i	−0.983996	−	0.195729i	−0.660766	+	0.750592i	$0.729769\pi$
$278$	402073.	−	2.02136e6i	0.312028	−	1.56867i
$279$	−35127.3	+	84804.7i	−0.0270168	+	0.0652243i
$280$	1.91330e6	+	4.61912e6i	1.45844	+	3.52098i
$281$	−1.25564e6	−	838991.i	−0.948634	−	0.633857i	−0.0180116	−	0.999838i	$-0.505734\pi$
$281$	−1.25564e6	−	838991.i	−0.948634	−	0.633857i	−0.930622	+	0.365981i	$0.880734\pi$
$282$	3.92514e6	−	3.92514e6i	2.93922	−	2.93922i
$283$	−654614.	−	1.58038e6i	−0.485869	−	1.17299i	−0.956780	−	0.290811i	$-0.906075\pi$
$283$	−654614.	−	1.58038e6i	−0.485869	−	1.17299i	0.470911	−	0.882180i	$-0.343925\pi$
$284$	3.37866e6	−	672057.i	2.48570	−	0.494436i
$285$			44478.3i			0.0324366i
$286$	2.66692e6	+	530484.i	1.92795	+	0.383492i
$287$	−740437.	−	740437.i	−0.530619	−	0.530619i
$288$	2.29767e6	+	5.54707e6i	1.63233	+	3.94078i
$289$	−3.23276e6	−	1.33905e6i	−2.27682	−	0.943090i
$290$	−338248.			−0.236178
$291$	459762.	+	1.86988e6i	0.318273	+	1.29444i
$292$	1.44055e6			0.988713
$293$	375033.	+	155344.i	0.255212	+	0.105712i	0.506621	−	0.862169i	$-0.330894\pi$
$293$	375033.	+	155344.i	0.255212	+	0.105712i	−0.251410	+	0.967881i	$0.580894\pi$
$294$	−702878.	−	1.69690e6i	−0.474255	−	1.14495i
$295$	−217139.	−	217139.i	−0.145272	−	0.145272i
$296$	−6.44064e6	−	1.28112e6i	−4.27268	−	0.849888i
$297$		−	403145.i		−	0.265198i
$298$	−429905.	+	85513.5i	−0.280435	+	0.0557820i
$299$	382462.	+	923344.i	0.247406	+	0.597291i
$300$	1.44069e6	−	1.44069e6i	0.924203	−	0.924203i
$301$	1.67061e6	+	1.11626e6i	1.06282	+	0.710151i
$302$	1.04073e6	+	2.51255e6i	0.656632	+	1.58525i
$303$	−653649.	+	1.57805e6i	−0.409014	+	0.987446i
$304$	−44096.7	+	221689.i	−0.0273667	+	0.137582i
$305$	−2.43921e6	−	485189.i	−1.50141	−	0.298649i
$306$	−917241.	−	4.61128e6i	−0.559990	−	2.81526i
$307$			44994.2i			0.0272465i	0.999907	+	0.0136232i	$0.00433654\pi$
$307$			44994.2i			0.0272465i	−0.999907	+	0.0136232i	$0.995663\pi$
$308$	−1.03192e6	+	5.18782e6i	−0.619826	+	3.11608i
$309$	3.19745e6	−	1.32443e6i	1.90506	−	0.789100i
$310$	−244413.	−	48616.7i	−0.144451	−	0.0287330i
$311$	838647.	+	1.25512e6i	0.491675	+	0.735844i	0.991475	−	0.130297i	$-0.0415931\pi$
$311$	838647.	+	1.25512e6i	0.491675	+	0.735844i	−0.499800	+	0.866141i	$0.666593\pi$
$312$	−5.44784e6	−	8.15326e6i	−3.16838	−	4.74182i
$313$		−	1.60299e6i		−	0.924847i	−0.886659	−	0.462423i	$-0.846980\pi$
$313$		−	1.60299e6i		−	0.924847i	0.886659	−	0.462423i	$-0.153020\pi$
$314$	703222.	−	469878.i	0.402502	−	0.268943i
$315$	957068.	−	957068.i	0.543459	−	0.543459i
$316$	−2.23685e6	−	926534.i	−1.26014	−	0.521968i
$317$	−57864.1	+	86599.8i	−0.0323416	+	0.0484026i	−0.847288	−	0.531134i	$-0.821766\pi$
$317$	−57864.1	+	86599.8i	−0.0323416	+	0.0484026i	0.814947	+	0.579536i	$0.196766\pi$
$318$	−1.70271e6	−	705287.i	−0.944222	−	0.391109i
$319$	−196358.	−	131202.i	−0.108037	−	0.0721879i
$320$	−7.70067e6	+	5.14543e6i	−4.20391	+	2.80897i
$321$	36342.0	−	182704.i	0.0196855	−	0.0989657i
$322$	−2.40694e6	+	996987.i	−1.29368	+	0.535858i
$323$	39806.1	−	96100.4i	0.0212297	−	0.0512529i
$324$	−4.61007e6	+	4.61007e6i	−2.43975	+	2.43975i
$325$	−391761.	+	586312.i	−0.205737	+	0.307908i
$326$	3.89726e6			2.03102
$327$	1.25569e6			0.649401
$328$	2.58240e6	−	3.86484e6i	1.32538	−	1.98357i
$329$	−3.10734e6	−	2.07626e6i	−1.58270	−	1.05753i
$330$	−3.73742e6	+	743419.i	−1.88924	+	0.375793i
$331$	630873.	+	3.17162e6i	0.316499	+	1.59115i	0.731836	+	0.681480i	$0.238664\pi$
$331$	630873.	+	3.17162e6i	0.316499	+	1.59115i	−0.415337	+	0.909667i	$0.636336\pi$
$332$	1.59115e6	+	2.38133e6i	0.792258	+	1.18570i
$333$	346821.	+	1.74359e6i	0.171394	+	0.861654i
$334$	1.19306e6	+	1.19306e6i	0.585190	+	0.585190i
$335$	494277.	−	1.19329e6i	0.240635	−	0.580943i
$336$	1.30808e7	−	8.74031e6i	6.32100	−	4.22356i
$337$	−2.11152e6	+	420008.i	−1.01279	+	0.201457i	−0.673472	−	0.739213i	$-0.735198\pi$
$337$	−2.11152e6	+	420008.i	−1.01279	+	0.201457i	−0.339322	+	0.940670i	$0.610198\pi$
$338$	688162.	+	688162.i	0.327641	+	0.327641i
$339$	1.63677e6	−	677971.i	0.773548	−	0.320414i
$340$	8.79998e6	−	3.64507e6i	4.12843	−	1.71005i
$341$	−123027.	−	123027.i	−0.0572949	−	0.0572949i
$342$	97511.8	−	19396.3i	0.0450808	−	0.00896714i
$343$	1.16715e6	−	779866.i	0.535664	−	0.357919i
$344$	−3.41311e6	+	8.23997e6i	−1.55508	+	3.75430i
$345$	−990365.	−	990365.i	−0.447969	−	0.447969i
$346$	969322.	+	4.87311e6i	0.435289	+	2.18835i
$347$	−770051.	−	1.15246e6i	−0.343317	−	0.513811i	0.619127	−	0.785291i	$-0.287487\pi$
$347$	−770051.	−	1.15246e6i	−0.343317	−	0.513811i	−0.962444	+	0.271481i	$0.912487\pi$
$348$	251760.	+	1.26568e6i	0.111439	+	0.560244i
$349$	1.12756e6	−	224286.i	0.495537	−	0.0985685i	0.0590062	−	0.998258i	$-0.481207\pi$
$349$	1.12756e6	−	224286.i	0.495537	−	0.0985685i	0.436531	+	0.899689i	$0.356207\pi$
$350$	−1.52838e6	−	1.02123e6i	−0.666899	−	0.445608i
$351$	423591.	−	633949.i	0.183518	−	0.274654i
$352$	−1.13805e7			−4.89557
$353$	1.11293e6			0.475369			0.237685	−	0.971342i	$-0.423612\pi$
$353$	1.11293e6			0.475369			0.237685	+	0.971342i	$0.423612\pi$
$354$	−872237.	+	1.30540e6i	−0.369936	+	0.553648i
$355$	1.18145e6	−	1.18145e6i	0.497558	−	0.497558i
$356$	3.14305e6	−	7.58800e6i	1.31440	−	3.17323i
$357$	−6.68871e6	+	2.77055e6i	−2.77761	+	1.15052i
$358$	−875421.	+	4.40104e6i	−0.361002	+	1.81488i
$359$	−660414.	+	441274.i	−0.270446	+	0.180706i	−0.683397	−	0.730047i	$-0.739498\pi$
$359$	−660414.	+	441274.i	−0.270446	+	0.180706i	0.412951	+	0.910753i	$0.364498\pi$
$360$	4.99558e6	+	3.33794e6i	2.03156	+	1.35745i
$361$	−2.28559e6	−	946720.i	−0.923059	−	0.382343i
$362$	−764747.	+	1.14452e6i	−0.306723	+	0.459043i
$363$	633798.	+	262528.i	0.252455	+	0.104570i
$364$	−7.07363e6	+	7.07363e6i	−2.79826	+	2.79826i
$365$	580942.	−	388173.i	0.228245	−	0.152508i
$366$			1.27150e7i			4.96152i
$367$	−969067.	−	1.45031e6i	−0.375568	−	0.562077i	0.594750	−	0.803911i	$-0.297251\pi$
$367$	−969067.	−	1.45031e6i	−0.375568	−	0.562077i	−0.970318	+	0.241834i	$0.922251\pi$
$368$	−3.95432e6	−	5.91806e6i	−1.52213	−	2.27803i
$369$	−1.23416e6	−	245491.i	−0.471853	−	0.0938575i
$370$	−4.45893e6	+	1.84695e6i	−1.69327	+	0.701375i
$371$	−242066.	+	1.21695e6i	−0.0913060	+	0.459026i
$372$			950749.i			0.356212i
$373$	833015.	+	4.18785e6i	0.310014	+	1.55854i	0.750553	+	0.660811i	$0.229787\pi$
$373$	833015.	+	4.18785e6i	0.310014	+	1.55854i	−0.440539	+	0.897734i	$0.645213\pi$
$374$	8.74045e6	+	1.73858e6i	3.23113	+	0.642712i
$375$	770965.	−	3.87590e6i	0.283111	−	1.42330i
$376$	6.34839e6	−	1.53264e7i	2.31576	−	5.59075i
$377$	−170918.	−	412633.i	−0.0619348	−	0.149524i
$378$	1.65255e6	+	1.10420e6i	0.594875	+	0.397483i
$379$	−350394.	+	350394.i	−0.125302	+	0.125302i	−0.766977	−	0.641675i	$-0.778240\pi$
$379$	−350394.	+	350394.i	−0.125302	+	0.125302i	0.641675	+	0.766977i	$0.278240\pi$
$380$	77080.0	+	186088.i	0.0273831	+	0.0661087i
$381$	−6.98185e6	+	1.38878e6i	−2.46410	+	0.490140i
$382$			6.35387e6i			2.22782i
$383$	5.04699e6	+	1.00391e6i	1.75807	+	0.349701i	0.965564	−	0.260167i	$-0.0837775\pi$
$383$	5.04699e6	+	1.00391e6i	1.75807	+	0.349701i	0.792503	+	0.609868i	$0.208777\pi$
$384$	1.85278e7	+	1.85278e7i	6.41204	+	6.41204i
$385$	981770.	+	2.37020e6i	0.337565	+	0.814955i
$386$	6.35848e6	+	2.63377e6i	2.17213	+	0.899724i
$387$	2.41448e6			0.819496
$388$	5.16401e6	+	7.02643e6i	1.74144	+	2.36949i
$389$	3.96662e6			1.32907			0.664534	−	0.747258i	$-0.268630\pi$
$389$	3.96662e6			1.32907			0.664534	+	0.747258i	$0.268630\pi$
$390$	−6.65825e6	−	2.75794e6i	−2.21666	−	0.918169i
$391$	1.25346e6	+	3.02613e6i	0.414639	+	1.00103i
$392$	−3.88132e6	−	3.88132e6i	−1.27575	−	1.27575i
$393$	−99680.4	−	19827.7i	−0.0325558	−	0.00647575i
$394$		−	4.14801e6i		−	1.34617i
$395$	−1.15174e6	+	229095.i	−0.371417	+	0.0738795i
$396$	2.43247e6	+	5.87249e6i	0.779487	+	1.88185i
$397$	1.17478e6	−	1.17478e6i	0.374093	−	0.374093i	−0.494873	−	0.868965i	$-0.664785\pi$
$397$	1.17478e6	−	1.17478e6i	0.374093	−	0.374093i	0.868965	+	0.494873i	$0.164785\pi$
$398$	−7.59314e6	−	5.07357e6i	−2.40278	−	1.60548i
$399$	−58587.1	−	141442.i	−0.0184234	−	0.0444780i
$400$	1.92179e6	−	4.63962e6i	0.600561	−	1.44988i
$401$	−658493.	+	3.31047e6i	−0.204499	+	1.02808i	0.733035	+	0.680191i	$0.238103\pi$
$401$	−658493.	+	3.31047e6i	−0.204499	+	1.02808i	−0.937534	+	0.347894i	$0.886897\pi$
$402$	−6.47660e6	−	1.28828e6i	−1.99886	−	0.397598i
$403$	−64194.7	−	322728.i	−0.0196896	−	0.0989862i
$404$			7.73497e6i			2.35779i
$405$	−616904.	+	3.10138e6i	−0.186887	+	0.939546i
$406$	1.07564e6	−	445543.i	0.323855	−	0.134145i
$407$	−3.30488e6	−	657381.i	−0.988939	−	0.196712i
$408$	−1.78545e7	−	2.67211e7i	−5.31003	−	7.94703i
$409$	1.13890e6	+	1.70449e6i	0.336650	+	0.503833i	0.960714	−	0.277541i	$-0.0895193\pi$
$409$	1.13890e6	+	1.70449e6i	0.336650	+	0.503833i	−0.624063	+	0.781374i	$0.714519\pi$
$410$		−	3.41621e6i		−	1.00366i
$411$	2.99754e6	−	2.00289e6i	0.875306	−	0.584861i
$412$	1.10822e7	−	1.10822e7i	3.21651	−	3.21651i
$413$	976524.	+	404489.i	0.281714	+	0.116690i
$414$	−1.73934e6	+	2.60311e6i	−0.498751	+	0.746434i
$415$	1.28336e6	+	531584.i	0.365786	+	0.151514i
$416$	−1.78959e7	−	1.19576e7i	−5.07014	−	3.38776i
$417$	−3.17096e6	+	2.11877e6i	−0.892999	+	0.596683i
$418$	−36764.7	+	184829.i	−0.0102918	+	0.0517403i
$419$	−3.05346e6	+	1.26478e6i	−0.849683	+	0.351950i	−0.764664	−	0.644429i	$-0.777095\pi$
$419$	−3.05346e6	+	1.26478e6i	−0.849683	+	0.351950i	−0.0850191	+	0.996379i	$0.527095\pi$
$420$	5.36487e6	−	1.29519e7i	1.48401	−	3.58271i
$421$	1.54603e6	−	1.54603e6i	0.425121	−	0.425121i	−0.461841	−	0.886963i	$-0.652811\pi$
$421$	1.54603e6	−	1.54603e6i	0.425121	−	0.425121i	0.886963	+	0.461841i	$0.152811\pi$
$422$	6.12681e6	−	9.16942e6i	1.67476	−	2.50646i
$423$	−4.49095e6			−1.22036
$424$	−5.50783e6			−1.48787
$425$	−1.28394e6	+	1.92155e6i	−0.344804	+	0.516036i
$426$	−7.10262e6	−	4.74582e6i	−1.89625	−	1.26703i
$427$	8.39583e6	−	1.67003e6i	2.22840	−	0.443257i
$428$	−164575.	−	827373.i	−0.0434264	−	0.218319i
$429$	−2.79544e6	−	4.18367e6i	−0.733343	−	1.09753i
$430$	1.27881e6	+	6.42900e6i	0.333529	+	1.67677i
$431$	−1.54717e6	−	1.54717e6i	−0.401185	−	0.401185i	0.477465	−	0.878651i	$-0.341556\pi$
$431$	−1.54717e6	−	1.54717e6i	−0.401185	−	0.401185i	−0.878651	+	0.477465i	$0.841556\pi$
$432$	−2.07794e6	+	5.01658e6i	−0.535701	+	1.29330i
$433$	−4.99172e6	+	3.33536e6i	−1.27947	+	0.854916i	−0.994613	−	0.103654i	$-0.966947\pi$
$433$	−4.99172e6	+	3.33536e6i	−1.27947	+	0.854916i	−0.284859	+	0.958570i	$0.591947\pi$
$434$	841276.	−	167340.i	0.214395	−	0.0426458i
$435$	442584.	+	442584.i	0.112143	+	0.112143i
$436$	5.25354e6	−	2.17609e6i	1.32354	−	0.548226i
$437$	−63991.6	+	26506.2i	−0.0160295	+	0.00663963i
$438$	−2.52589e6	−	2.52589e6i	−0.629114	−	0.629114i
$439$	5.18288e6	−	1.03094e6i	1.28354	−	0.255312i	0.494244	−	0.869323i	$-0.335445\pi$
$439$	5.18288e6	−	1.03094e6i	1.28354	−	0.255312i	0.789298	+	0.614011i	$0.210445\pi$
$440$	−9.46887e6	+	6.32690e6i	−2.33167	+	1.55797i
$441$	−568654.	+	1.37285e6i	−0.139236	+	0.336146i
$442$	1.19177e7	+	1.19177e7i	2.90159	+	2.90159i
$443$	−1.44563e6	−	7.26765e6i	−0.349983	−	1.75948i	−0.608576	−	0.793496i	$-0.708259\pi$
$443$	−1.44563e6	−	7.26765e6i	−0.349983	−	1.75948i	0.258593	−	0.965986i	$-0.416741\pi$
$444$	1.02299e7	+	1.53101e7i	2.46271	+	3.68570i
$445$	−777153.	−	3.90701e6i	−0.186040	−	0.935287i
$446$	−101452.	+	20180.1i	−0.0241503	+	0.00480380i
$447$	674404.	+	450622.i	0.159644	+	0.106670i
$448$	1.77107e7	−	2.65059e7i	4.16909	−	6.23948i
$449$	491870.			0.115142			0.0575711	−	0.998341i	$-0.481664\pi$
$449$	491870.			0.115142			0.0575711	+	0.998341i	$0.481664\pi$
$450$	−2.20892e6			−0.514220
$451$	1.32510e6	−	1.98316e6i	0.306767	−	0.459109i
$452$	5.67297e6	−	5.67297e6i	1.30606	−	1.30606i
$453$	1.92582e6	−	4.64933e6i	0.440929	−	1.06450i
$454$	−1.09206e7	+	4.52344e6i	−2.48660	+	1.02998i
$455$	−946569.	+	4.75872e6i	−0.214350	+	1.07761i
$456$	565055.	−	377558.i	0.127256	−	0.0850298i
$457$	−1.53017e6	−	1.02242e6i	−0.342727	−	0.229003i	0.372280	−	0.928121i	$-0.378576\pi$
$457$	−1.53017e6	−	1.02242e6i	−0.342727	−	0.229003i	−0.715006	+	0.699118i	$0.753576\pi$
$458$	−9.35419e6	−	3.87463e6i	−2.08373	−	0.863111i
$459$	1.38826e6	−	2.07768e6i	0.307566	−	0.460305i
$460$	−5.85976e6	−	2.42719e6i	−1.29118	−	0.534822i
$461$	1.68787e6	−	1.68787e6i	0.369902	−	0.369902i	−0.497539	−	0.867441i	$-0.665763\pi$
$461$	1.68787e6	−	1.68787e6i	0.369902	−	0.369902i	0.867441	+	0.497539i	$0.165763\pi$
$462$	1.09058e7	−	7.28705e6i	2.37714	−	1.58835i
$463$			8.17937e6i			1.77324i	0.462499	+	0.886620i	$0.346953\pi$
$463$			8.17937e6i			1.77324i	−0.462499	+	0.886620i	$0.653047\pi$
$464$	1.76715e6	+	2.64472e6i	0.381046	+	0.570276i
$465$	256191.	+	383417.i	0.0549454	+	0.0822317i
$466$	−4.77951e6	−	950703.i	−1.01957	−	0.202806i
$467$	−2.69149e6	+	1.11485e6i	−0.571085	+	0.236551i	−0.649489	−	0.760371i	$-0.725017\pi$
$467$	−2.69149e6	+	1.11485e6i	−0.571085	+	0.236551i	0.0784049	+	0.996922i	$0.475017\pi$
$468$	−2.34525e6	+	1.17904e7i	−0.494965	+	2.48836i
$469$			4.44575e6i			0.933282i
$470$	−2.37859e6	−	1.19580e7i	−0.496678	−	2.49697i
$471$	−1.53495e6	−	305321.i	−0.318818	−	0.0634168i
$472$	−915346.	+	4.60175e6i	−0.189117	+	0.950754i
$473$	−1.75136e6	+	4.22816e6i	−0.359934	+	0.868958i
$474$	2.29754e6	+	5.54675e6i	0.469696	+	1.13395i
$475$	−40633.9	−	27150.7i	−0.00826331	−	0.00552137i
$476$	−2.31828e7	+	2.31828e7i	−4.68974	+	4.68974i
$477$	570603.	+	1.37756e6i	0.114825	+	0.277213i
$478$	1.91714e6	−	381343.i	0.383782	−	0.0763390i
$479$		−	1.17431e6i		−	0.233854i	−0.993140	−	0.116927i	$-0.962696\pi$
$479$		−	1.17431e6i		−	0.233854i	0.993140	−	0.116927i	$-0.0373044\pi$
$480$	2.95830e7	+	5.88443e6i	5.86057	+	1.16574i
$481$	−4.50623e6	−	4.50623e6i	−0.888077	−	0.888077i
$482$	−4.09590e6	−	9.88837e6i	−0.803029	−	1.93868i
$483$	4.45390e6	+	1.84486e6i	0.868705	+	0.359829i
$484$	3.10663e6			0.602804
$485$	3.97589e6	+	1.44210e6i	0.767504	+	0.278382i
$486$	1.30924e7			2.51437
$487$	1.32664e6	+	549511.i	0.253472	+	0.104992i	0.505802	−	0.862650i	$-0.331197\pi$
$487$	1.32664e6	+	549511.i	0.253472	+	0.104992i	−0.252330	+	0.967641i	$0.581197\pi$
$488$	1.45416e7	+	3.51064e7i	2.76415	+	6.67325i
$489$	−5.09940e6	−	5.09940e6i	−0.964378	−	0.964378i
$490$	−3.95665e6	−	787027.i	−0.744453	−	0.148081i
$491$			1.76462e6i			0.330330i	0.986266	+	0.165165i	$0.0528156\pi$
$491$			1.76462e6i			0.330330i	−0.986266	+	0.165165i	$0.947184\pi$
$492$	−1.27830e7	+	2.54271e6i	−2.38079	+	0.473569i
$493$	−560160.	−	1.35235e6i	−0.103799	−	0.250594i
$494$	−252015.	+	252015.i	−0.0464632	+	0.0464632i
$495$	2.56338e6	+	1.71279e6i	0.470218	+	0.314190i
$496$	896783.	+	2.16503e6i	0.163675	+	0.395147i
$497$	−2.20082e6	+	5.31324e6i	−0.399662	+	0.964869i
$498$	1.38551e6	−	6.96544e6i	0.250344	−	1.25856i
$499$	6.73670e6	+	1.34001e6i	1.21114	+	0.240912i	0.759034	−	0.651051i	$-0.225671\pi$
$499$	6.73670e6	+	1.34001e6i	1.21114	+	0.240912i	0.452110	+	0.891962i	$0.350671\pi$
$500$	−3.49131e6	−	1.75520e7i	−0.624545	−	3.13980i
$501$		−	3.12214e6i		−	0.555723i
$502$	849493.	−	4.27069e6i	0.150453	−	0.756378i
$503$	2.45335e6	−	1.01621e6i	0.432355	−	0.179087i	−0.155882	−	0.987776i	$-0.549822\pi$
$503$	2.45335e6	−	1.01621e6i	0.432355	−	0.179087i	0.588237	+	0.808688i	$0.299822\pi$
$504$	−2.02828e7	−	4.03450e6i	−3.55674	−	0.707479i
$505$	2.08428e6	+	3.11935e6i	0.363688	+	0.544297i
$506$	−3.29683e6	−	4.93406e6i	−0.572428	−	0.856698i
$507$		−	1.80086e6i		−	0.311144i
$508$	−2.68038e7	+	1.79098e7i	−4.60827	+	3.07915i
$509$	−2.31921e6	+	2.31921e6i	−0.396776	+	0.396776i	−0.877094	−	0.480318i	$-0.840521\pi$
$509$	−2.31921e6	+	2.31921e6i	−0.396776	+	0.396776i	0.480318	+	0.877094i	$0.340521\pi$
$510$	−2.18214e7	−	9.03874e6i	−3.71499	−	1.53880i
$511$	−1.33610e6	+	1.99962e6i	−0.226354	+	0.338762i
$512$	4.22559e7	+	1.75030e7i	7.12382	+	2.95078i
$513$	43935.3	+	29356.6i	0.00737089	+	0.00492507i
$514$	417856.	−	279203.i	0.0697620	−	0.0466135i
$515$	1.48299e6	−	7.45548e6i	0.246388	−	1.23868i
$516$	2.31047e7	−	9.57029e6i	3.82012	−	1.58234i
$517$	3.25754e6	−	7.86440e6i	0.535998	−	1.29401i
$518$	1.17467e7	−	1.17467e7i	1.92349	−	1.92349i
$519$	5.10795e6	−	7.64459e6i	0.832393	−	1.24576i
$520$	−2.15376e7			−3.49293
$521$	1.15516e7			1.86443			0.932216	−	0.361902i	$-0.117873\pi$
$521$	1.15516e7			1.86443			0.932216	+	0.361902i	$0.117873\pi$
$522$	777293.	−	1.16330e6i	0.124856	−	0.186860i
$523$	1.36919e6	+	914867.i	0.218883	+	0.146253i	0.660178	−	0.751109i	$-0.270481\pi$
$523$	1.36919e6	+	914867.i	0.218883	+	0.146253i	−0.441295	+	0.897362i	$0.645481\pi$
$524$	−451402.	+	89789.5i	−0.0718184	+	0.0142856i
$525$	663582.	+	3.33605e6i	0.105074	+	0.528244i
$526$	4.20894e6	+	6.29913e6i	0.663298	+	0.992695i
$527$	−210389.	−	1.05770e6i	−0.0329986	−	0.165895i
$528$	2.53385e7	+	2.53385e7i	3.95545	+	3.95545i
$529$	−1.62842e6	+	3.93136e6i	−0.253004	+	0.610806i
$530$	−3.36578e6	+	2.24894e6i	−0.520471	+	0.347768i
$531$	1.24577e6	−	247799.i	0.191735	−	0.0381385i
$532$	−490232.	−	490232.i	−0.0750970	−	0.0750970i
$533$	4.16747e6	−	1.72622e6i	0.635411	−	0.263196i
$534$	−1.88161e7	+	7.79387e6i	−2.85546	+	1.18277i
$535$	−289315.	−	289315.i	−0.0437006	−	0.0437006i
$536$	−1.93553e7	+	3.85002e6i	−2.90997	+	0.578830i
$537$	6.90403e6	−	4.61313e6i	1.03316	−	0.690335i
$538$	1.15181e6	−	2.78072e6i	0.171564	−	0.414191i
$539$	−1.99162e6	−	1.99162e6i	−0.295280	−	0.295280i
$540$	943972.	+	4.74567e6i	0.139308	+	0.700347i
$541$	−1.41263e6	−	2.11416e6i	−0.207509	−	0.310559i	0.713087	−	0.701075i	$-0.247296\pi$
$541$	−1.41263e6	−	2.11416e6i	−0.207509	−	0.310559i	−0.920596	+	0.390517i	$0.872296\pi$
$542$	1.21450e6	+	6.10571e6i	0.177582	+	0.892767i
$543$	2.49820e6	−	496923.i	0.363604	−	0.0723252i
$544$	−5.86512e7	−	3.91895e7i	−8.49727	−	5.67770i
$545$	1.53227e6	−	2.29320e6i	0.220975	−	0.330713i
$546$	2.48061e7			3.56104
$547$	−8.46000e6			−1.20893			−0.604466	−	0.796631i	$-0.706613\pi$
$547$	−8.46000e6			−1.20893			−0.604466	+	0.796631i	$0.706613\pi$
$548$	9.07008e6	−	1.35743e7i	1.29021	−	1.93093i
$549$	7.27396e6	−	7.27396e6i	1.03001	−	1.03001i
$550$	1.60226e6	−	3.86819e6i	0.225853	−	0.545256i
$551$	28597.2	−	11845.3i	0.00401277	−	0.00166214i
$552$	−4.17486e6	+	2.09885e7i	−0.583169	+	2.93179i
$553$	3.36079e6	−	2.24561e6i	0.467335	−	0.312264i
$554$	1.19625e7	+	7.99307e6i	1.65595	+	1.10647i
$555$	8.25098e6	+	3.41767e6i	1.13703	+	0.470974i
$556$	−9.59484e6	+	1.43597e7i	−1.31629	+	1.96996i
$557$	5.60013e6	+	2.31965e6i	0.764821	+	0.316799i	0.730773	−	0.682621i	$-0.239160\pi$
$557$	5.60013e6	+	2.31965e6i	0.764821	+	0.316799i	0.0340485	+	0.999420i	$0.489160\pi$
$558$	728862.	−	728862.i	0.0990969	−	0.0990969i
$559$	−7.19663e6	+	4.80863e6i	−0.974091	+	0.650867i
$560$		−	3.45542e7i		−	4.65619i
$561$	−9.16166e6	−	1.37114e7i	−1.22904	−	1.83939i
$562$	9.42135e6	+	1.41000e7i	1.25827	+	1.88313i
$563$	1.23448e7	+	2.45553e6i	1.64139	+	0.326493i	0.927517	−	0.373780i	$-0.121938\pi$
$563$	1.23448e7	+	2.45553e6i	1.64139	+	0.326493i	0.713875	+	0.700273i	$0.246938\pi$
$564$	−4.29749e7	+	1.78008e7i	−5.68875	+	2.35636i
$565$	759137.	−	3.81644e6i	0.100046	−	0.502965i
$566$			1.92089e7i			2.52035i
$567$	−2.12340e6	−	1.06751e7i	−0.277379	−	1.39448i
$568$	−2.50380e7	−	4.98037e6i	−3.25634	−	0.647725i
$569$	−313072.	+	1.57392e6i	−0.0405381	+	0.203799i	−0.995747	−	0.0921353i	$-0.970631\pi$
$569$	−313072.	+	1.57392e6i	−0.0405381	+	0.203799i	0.955208	+	0.295934i	$0.0956308\pi$
$570$	191136.	−	461444.i	0.0246409	−	0.0594884i
$571$	3.42675e6	+	8.27291e6i	0.439837	+	1.06186i	0.976005	+	0.217750i	$0.0698716\pi$
$571$	3.42675e6	+	8.27291e6i	0.439837	+	1.06186i	−0.536167	+	0.844112i	$0.680128\pi$
$572$	−1.89458e7	−	1.26591e7i	−2.42115	−	1.61776i
$573$	8.31377e6	−	8.31377e6i	1.05782	−	1.05782i
$574$	4.49985e6	+	1.08636e7i	0.570058	+	1.37624i
$575$	1.50931e6	−	300220.i	0.190374	−	0.0378678i
$576$		−	3.83083e7i		−	4.81102i
$577$	−7.89492e6	−	1.57040e6i	−0.987208	−	0.196368i	−0.325021	−	0.945707i	$-0.605371\pi$
$577$	−7.89492e6	−	1.57040e6i	−0.987208	−	0.196368i	−0.662187	+	0.749339i	$0.730371\pi$
$578$	2.77843e7	+	2.77843e7i	3.45923	+	3.45923i
$579$	−4.87363e6	−	1.17660e7i	−0.604166	−	1.45859i
$580$	2.61866e6	+	1.08469e6i	0.323229	+	0.133886i
$581$	−4.78131e6			−0.587633
$582$	3.26560e6	−	2.13750e7i	0.399627	−	2.61576i
$583$	−2.82622e6			−0.344378
$584$	−9.86276e6	−	4.08529e6i	−1.19665	−	0.495668i
$585$	2.23127e6	+	5.38676e6i	0.269564	+	0.650786i
$586$	−3.22326e6	−	3.22326e6i	−0.387749	−	0.387749i
$587$	−3.78100e6	−	752088.i	−0.452910	−	0.0900893i	−0.0366359	−	0.999329i	$-0.511664\pi$
$587$	−3.78100e6	−	752088.i	−0.452910	−	0.0900893i	−0.416274	+	0.909239i	$0.636664\pi$
$588$			1.53911e7i			1.83580i
$589$	22366.4	−	4448.96i	0.00265649	−	0.000528409i
$590$	1.31962e6	+	3.18584e6i	0.156070	+	0.376786i
$591$	−5.42750e6	+	5.42750e6i	−0.639192	+	0.639192i
$592$	3.77363e7	+	2.52146e7i	4.42543	+	2.95697i
$593$	−5.82300e6	−	1.40580e7i	−0.680002	−	1.64167i	−0.764009	−	0.645205i	$-0.776772\pi$
$593$	−5.82300e6	−	1.40580e7i	−0.680002	−	1.64167i	0.0840075	−	0.996465i	$-0.473228\pi$
$594$	−1.73243e6	+	4.18247e6i	−0.201461	+	0.486369i
$595$	−3.10224e6	+	1.55960e7i	−0.359239	+	1.80602i
$596$	3.60248e6	+	716578.i	0.415419	+	0.0826320i
$597$	3.29675e6	+	1.65739e7i	0.378573	+	1.90322i
$598$		−	1.12229e7i		−	1.28337i
$599$	126410.	−	635507.i	0.0143951	−	0.0723691i	−0.972920	−	0.231142i	$-0.925754\pi$
$599$	126410.	−	635507.i	0.0143951	−	0.0723691i	0.987315	+	0.158773i	$0.0507538\pi$
$600$	−1.39494e7	+	5.77804e6i	−1.58190	+	0.655243i
$601$	−1.41132e6	−	280729.i	−0.159382	−	0.0317031i	0.114754	−	0.993394i	$-0.463392\pi$
$601$	−1.41132e6	−	280729.i	−0.159382	−	0.0317031i	−0.274136	+	0.961691i	$0.588392\pi$
$602$	−1.25350e7	−	1.87599e7i	−1.40972	−	2.10979i
$603$	2.96811e6	+	4.44209e6i	0.332420	+	0.497501i
$604$		−	2.27892e7i		−	2.54177i
$605$	1.25284e6	−	837120.i	0.139157	−	0.0929821i
$606$	1.35627e7	−	1.35627e7i	1.50025	−	1.50025i
$607$	1.01964e7	+	4.22350e6i	1.12325	+	0.465266i	0.865481	−	0.500941i	$-0.167013\pi$
$607$	1.01964e7	+	4.22350e6i	1.12325	+	0.465266i	0.257769	+	0.966207i	$0.417013\pi$
$608$	828715.	−	1.24026e6i	0.0909172	−	0.136067i
$609$	−1.99040e6	−	824451.i	−0.217469	−	0.0900786i
$610$	2.32208e7	+	1.55156e7i	2.52669	+	1.68828i
$611$	1.33858e7	−	8.94408e6i	1.45057	−	0.969243i
$612$	−7.68622e6	+	3.86412e7i	−0.829534	+	4.17035i
$613$	−1.03717e7	+	4.29611e6i	−1.11481	+	0.461768i	−0.862591	−	0.505902i	$-0.831160\pi$
$613$	−1.03717e7	+	4.29611e6i	−1.11481	+	0.461768i	−0.252217	+	0.967671i	$0.581160\pi$
$614$	193353.	−	466796.i	0.0206981	−	0.0499697i
$615$	−4.46997e6	+	4.46997e6i	−0.476559	+	0.476559i
$616$	2.17774e7	−	3.25921e7i	2.31235	−	3.46068i
$617$	6.49574e6			0.686935			0.343468	−	0.939165i	$-0.388398\pi$
$617$	6.49574e6			0.686935			0.343468	+	0.939165i	$0.388398\pi$
$618$	−3.88637e7			−4.09330
$619$	1.00024e7	−	1.49696e7i	1.04924	−	1.57030i	0.250979	−	0.967993i	$-0.419248\pi$
$619$	1.00024e7	−	1.49696e7i	1.04924	−	1.57030i	0.798263	−	0.602309i	$-0.205752\pi$
$620$	1.73630e6	+	1.16016e6i	0.181404	+	0.121210i
$621$	−1.63194e6	+	324612.i	−0.169814	+	0.0337782i
$622$	−3.30698e6	−	1.66253e7i	−0.342733	−	1.72303i
$623$	7.61771e6	+	1.14007e7i	0.786329	+	1.17682i
$624$	1.32214e7	+	6.64686e7i	1.35930	+	6.83369i
$625$	−3.83506e6	−	3.83506e6i	−0.392710	−	0.392710i
$626$	−6.88852e6	+	1.66304e7i	−0.702571	+	1.69616i
$627$	289946.	−	193736.i	0.0294543	−	0.0196807i
$628$	−6.95103e6	+	1.38265e6i	−0.703315	+	0.139898i
$629$	−1.47685e7	−	1.47685e7i	−1.48837	−	1.48837i
$630$	−1.40420e7	+	5.81639e6i	−1.40954	+	0.583851i
$631$	−1.32919e6	+	550570.i	−0.132897	+	0.0550477i	−0.448141	−	0.893963i	$-0.647914\pi$
$631$	−1.32919e6	+	550570.i	−0.132897	+	0.0550477i	0.315244	+	0.949011i	$0.397914\pi$
$632$	1.26871e7	+	1.26871e7i	1.26348	+	1.26348i
$633$	−2.00145e7	+	3.98113e6i	−1.98534	+	0.394909i
$634$	972462.	−	649779.i	0.0960837	−	0.0642011i
$635$	−5.98342e6	+	1.44452e7i	−0.588864	+	1.42164i
$636$	1.09205e7	+	1.09205e7i	1.07053	+	1.07053i
$637$	−1.03921e6	−	5.22445e6i	−0.101474	−	0.510143i
$638$	1.47332e6	+	2.20498e6i	0.143300	+	0.214463i
$639$	1.34827e6	+	6.77820e6i	0.130624	+	0.656693i
$640$	5.64451e7	−	1.12276e7i	5.44724	−	1.08352i
$641$	−3.50882e6	−	2.34452e6i	−0.337300	−	0.225377i	0.375372	−	0.926874i	$-0.377515\pi$
$641$	−3.50882e6	−	2.34452e6i	−0.337300	−	0.225377i	−0.712672	+	0.701498i	$0.752515\pi$
$642$	−1.16217e6	+	1.73930e6i	−0.111283	+	0.166547i
$643$	−2.62059e6			−0.249960			−0.124980	−	0.992159i	$-0.539887\pi$
$643$	−2.62059e6			−0.249960			−0.124980	+	0.992159i	$0.539887\pi$
$644$	2.18313e7			2.07426
$645$	6.73882e6	−	1.00854e7i	0.637800	−	0.954535i
$646$	−825944.	+	825944.i	−0.0778698	+	0.0778698i
$647$	3.86051e6	−	9.32011e6i	0.362564	−	0.875307i	−0.632360	−	0.774675i	$-0.717914\pi$
$647$	3.86051e6	−	9.32011e6i	0.362564	−	0.875307i	0.994924	−	0.100632i	$-0.0320864\pi$
$648$	4.46368e7	−	1.84892e7i	4.17596	−	1.72974i
$649$	−469690.	+	2.36129e6i	−0.0437723	+	0.220058i
$650$	6.58392e6	−	4.39924e6i	0.611225	−	0.408408i
$651$	−1.31973e6	−	881817.i	−0.122049	−	0.0815504i
$652$	−3.01720e7	−	1.24976e7i	−2.77962	−	1.15135i
$653$	−2.56688e6	+	3.84161e6i	−0.235572	+	0.352558i	−0.930354	−	0.366662i	$-0.880501\pi$
$653$	−2.56688e6	+	3.84161e6i	−0.235572	+	0.352558i	0.694783	+	0.719220i	$0.255501\pi$
$654$	−1.30273e7	−	5.39607e6i	−1.19099	−	0.493325i
$655$	−157846.	+	157846.i	−0.0143758	+	0.0143758i
$656$	−2.67109e7	+	1.78477e7i	−2.42342	+	1.61928i
$657$			2.89000e6i			0.261206i
$658$	2.33151e7	+	3.48935e7i	2.09929	+	3.14181i
$659$	−2.08233e6	−	3.11643e6i	−0.186782	−	0.279540i	0.726247	−	0.687434i	$-0.241263\pi$
$659$	−2.08233e6	−	3.11643e6i	−0.186782	−	0.279540i	−0.913029	+	0.407895i	$0.866263\pi$
$660$	3.13185e7	+	6.22964e6i	2.79860	+	0.556677i
$661$	5.23283e6	−	2.16751e6i	0.465836	−	0.192955i	−0.137405	−	0.990515i	$-0.543876\pi$
$661$	5.23283e6	−	2.16751e6i	0.465836	−	0.192955i	0.603240	+	0.797560i	$0.293876\pi$
$662$	7.08432e6	−	3.56153e7i	0.628280	−	3.15858i
$663$		−	3.11876e7i		−	2.75548i
$664$	−4.14061e6	−	2.08163e7i	−0.364455	−	1.83224i
$665$	−329799.	−	65601.1i	−0.0289198	−	0.00575251i
$666$	3.89459e6	−	1.95794e7i	0.340232	−	1.71046i
$667$	−373001.	+	900504.i	−0.0324635	+	0.0783738i
$668$	−5.41062e6	−	1.30624e7i	−0.469143	−	1.13261i
$669$	159151.	+	106341.i	0.0137481	+	0.00918619i
$670$	−1.02558e7	+	1.02558e7i	−0.882642	+	0.882642i
$671$	7.46169e6	+	1.80141e7i	0.639781	+	1.54457i
$672$	−1.01826e8	+	2.02544e7i	−8.69829	+	1.73020i
$673$		−	2.48156e6i		−	0.211197i	−0.994409	−	0.105598i	$-0.966324\pi$
$673$		−	2.48156e6i		−	0.211197i	0.994409	−	0.105598i	$-0.0336758\pi$
$674$	2.37111e7	+	4.71643e6i	2.01049	+	0.399912i
$675$	−830134.	−	830134.i	−0.0701276	−	0.0701276i
$676$	−3.12086e6	−	7.53443e6i	−0.262668	−	0.634138i
$677$	−6.63275e6	−	2.74737e6i	−0.556188	−	0.230381i	0.0868411	−	0.996222i	$-0.472323\pi$
$677$	−6.63275e6	−	2.74737e6i	−0.556188	−	0.230381i	−0.643029	+	0.765841i	$0.722323\pi$
$678$	−1.98942e7			−1.66208
$679$	−1.45430e7	+	651164.i	−1.21054	+	0.0542020i
$680$	−7.05866e7			−5.85396
$681$	2.02078e7	+	8.37036e6i	1.66975	+	0.691634i
$682$	747674.	+	1.80504e6i	0.0615533	+	0.148603i
$683$	−1.35270e7	−	1.35270e7i	−1.10956	−	1.10956i	−0.993208	−	0.116349i	$-0.962881\pi$
$683$	−1.35270e7	−	1.35270e7i	−1.10956	−	1.10956i	−0.116349	−	0.993208i	$-0.537119\pi$
$684$	−817121.	−	162536.i	−0.0667800	−	0.0132834i
$685$		−	7.91829e6i		−	0.644770i
$686$	−1.54600e7	+	3.07520e6i	−1.25430	+	0.249495i
$687$	7.16977e6	+	1.73094e7i	0.579580	+	1.39923i
$688$	4.35866e7	−	4.35866e7i	3.51060	−	3.51060i
$689$	−4.44426e6	−	2.96956e6i	−0.356657	−	0.238311i
$690$	6.01874e6	+	1.45305e7i	0.481264	+	1.16187i
$691$	−7.32152e6	+	1.76757e7i	−0.583319	+	1.40826i	0.306468	+	0.951881i	$0.400853\pi$
$691$	−7.32152e6	+	1.76757e7i	−0.583319	+	1.40826i	−0.889787	+	0.456376i	$0.849147\pi$
$692$	8.12264e6	−	4.08353e7i	0.644811	−	3.24168i
$693$	−1.04077e7	−	2.07022e6i	−0.823231	−	0.163751i
$694$	3.03649e6	+	1.52655e7i	0.239317	+	1.20313i
$695$			8.37641e6i			0.657803i
$696$	1.86570e6	−	9.37952e6i	0.145989	−	0.733935i
$697$	1.36583e7	−	5.65745e6i	1.06491	−	0.441102i
$698$	−1.26618e7	−	2.51859e6i	−0.983688	−	0.195668i
$699$	5.00983e6	+	7.49775e6i	0.387820	+	0.580414i
$700$	8.55760e6	+	1.28074e7i	0.660096	+	0.987903i
$701$			1.01508e7i			0.780196i	0.920773	+	0.390098i	$0.127559\pi$
$701$			1.01508e7i			0.780196i	−0.920773	+	0.390098i	$0.872441\pi$
$702$	−7.11885e6	+	4.75666e6i	−0.545214	+	0.364300i
$703$	312300.	−	312300.i	0.0238333	−	0.0238333i
$704$	6.70842e7	+	2.77872e7i	5.10139	+	2.11307i
$705$	−1.25342e7	+	1.87588e7i	−0.949784	+	1.42145i
$706$	−1.15462e7	−	4.78259e6i	−0.871821	−	0.361120i
$707$	−1.07369e7	−	7.17417e6i	−0.807849	−	0.539788i
$708$	1.09388e7	−	7.30910e6i	0.820140	−	0.548000i
$709$	3.41247e6	−	1.71556e7i	0.254949	−	1.28172i	−0.614982	−	0.788541i	$-0.710837\pi$
$709$	3.41247e6	−	1.71556e7i	0.254949	−	1.28172i	0.869931	−	0.493174i	$-0.164163\pi$
$710$	−1.73341e7	+	7.18001e6i	−1.29049	+	0.534539i
$711$	1.85879e6	−	4.48752e6i	0.137898	−	0.332914i
$712$	−4.30380e7	+	4.30380e7i	−3.18165	+	3.18165i
$713$	−398955.	+	597078.i	−0.0293900	+	0.0439853i
$714$	8.12985e7			5.96811
$715$	−1.10516e7			−0.808462
$716$	2.08905e7	−	3.12649e7i	1.52288	−	2.27916i
$717$	−3.00747e6	−	2.00953e6i	−0.218476	−	0.145981i
$718$	8.74781e6	−	1.74005e6i	0.633269	−	0.125965i
$719$	466570.	+	2.34561e6i	0.0336585	+	0.169213i	0.993958	−	0.109757i	$-0.0350072\pi$
$719$	466570.	+	2.34561e6i	0.0336585	+	0.169213i	−0.960300	+	0.278969i	$0.910007\pi$
$720$	−2.30694e7	−	3.45258e7i	−1.65846	−	2.48206i
$721$	5.10449e6	+	2.56620e7i	0.365691	+	1.83845i
$722$	1.96437e7	+	1.96437e7i	1.40243	+	1.40243i
$723$	−7.57921e6	+	1.82978e7i	−0.539235	+	1.30183i
$724$	9.59079e6	−	6.40836e6i	0.679998	−	0.454360i
$725$	−674494.	+	134165.i	−0.0476577	+	0.00947971i
$726$	−5.44724e6	−	5.44724e6i	−0.383561	−	0.383561i
$727$	1.78831e7	−	7.40740e6i	1.25489	−	0.519792i	0.346553	−	0.938031i	$-0.387352\pi$
$727$	1.78831e7	−	7.40740e6i	1.25489	−	0.519792i	0.908337	+	0.418238i	$0.137352\pi$
$728$	6.84902e7	−	2.83695e7i	4.78960	−	1.98392i
$729$	−5.22594e6	−	5.22594e6i	−0.364205	−	0.364205i
$730$	−7.69514e6	+	1.53066e6i	−0.534453	+	0.106309i
$731$	−2.35859e7	+	1.57596e7i	−1.63252	+	1.09082i
$732$	4.07743e7	−	9.84379e7i	2.81261	−	6.79023i
$733$	8.43344e6	+	8.43344e6i	0.579755	+	0.579755i	0.934836	−	0.355080i	$-0.115546\pi$
$733$	8.43344e6	+	8.43344e6i	0.579755	+	0.579755i	−0.355080	+	0.934836i	$0.615546\pi$
$734$	3.82126e6	+	1.92108e7i	0.261798	+	1.31615i
$735$	4.14732e6	+	6.20691e6i	0.283171	+	0.423796i
$736$	9.16356e6	+	4.60683e7i	0.623548	+	3.13479i
$737$	−9.93178e6	+	1.97555e6i	−0.673532	+	0.133974i
$738$	1.17490e7	+	7.85044e6i	0.794073	+	0.530583i
$739$	−1.21140e7	+	1.81298e7i	−0.815972	+	1.22119i	0.156387	+	0.987696i	$0.450015\pi$
$739$	−1.21140e7	+	1.81298e7i	−0.815972	+	1.22119i	−0.972359	+	0.233492i	$0.924985\pi$
$740$	4.04431e7			2.71497
$741$	659503.			0.0441237
$742$	7.74093e6	−	1.15851e7i	0.516159	−	0.772486i
$743$	−9.53722e6	+	9.53722e6i	−0.633796	+	0.633796i	−0.949018	−	0.315222i	$-0.897921\pi$
$743$	−9.53722e6	+	9.53722e6i	−0.633796	+	0.633796i	0.315222	+	0.949018i	$0.397921\pi$
$744$	2.69626e6	−	6.50934e6i	0.178578	−	0.431126i
$745$	1.64590e6	−	681753.i	0.108646	−	0.0450024i
$746$	9.35425e6	−	4.70270e7i	0.615406	−	3.09386i
$747$	−4.77737e6	+	3.19214e6i	−0.313248	+	0.209305i
$748$	−6.20920e7	−	4.14885e7i	−4.05771	−	2.71128i
$749$	1.30112e6	+	538940.i	0.0847446	+	0.0351023i
$750$	−2.46544e7	+	3.68979e7i	−1.60045	+	2.39524i
$751$	−614375.	−	254483.i	−0.0397497	−	0.0164649i	0.362720	−	0.931898i	$-0.381848\pi$
$751$	−614375.	−	254483.i	−0.0397497	−	0.0164649i	−0.402470	+	0.915433i	$0.631848\pi$
$752$	−8.10712e7	+	8.10712e7i	−5.22784	+	5.22784i
$753$	−6.69955e6	+	4.47650e6i	−0.430584	+	0.287707i
$754$			5.01539e6i			0.321274i
$755$	−6.14083e6	−	9.19040e6i	−0.392067	−	0.586769i
$756$	−9.25288e6	−	1.38479e7i	−0.588806	−	0.881211i
$757$	5.82863e6	+	1.15939e6i	0.369681	+	0.0735341i	0.376435	−	0.926443i	$-0.377150\pi$
$757$	5.82863e6	+	1.15939e6i	0.369681	+	0.0735341i	−0.00675406	+	0.999977i	$0.502150\pi$
$758$	5.14095e6	−	2.12945e6i	0.324990	−	0.134615i
$759$	−2.14224e6	+	1.07698e7i	−0.134978	+	0.678582i
$760$		−	1.49265e6i		−	0.0937397i
$761$	1.83279e6	+	9.21405e6i	0.114723	+	0.576752i	0.994794	+	0.101909i	$0.0324951\pi$
$761$	1.83279e6	+	9.21405e6i	0.114723	+	0.576752i	−0.880071	+	0.474843i	$0.842505\pi$
$762$	7.84018e7	+	1.55951e7i	4.89146	+	0.972973i
$763$	−1.85202e6	+	9.31074e6i	−0.115169	+	0.578992i
$764$	2.03754e7	−	4.91907e7i	1.26291	−	3.04894i
$765$	7.31267e6	+	1.76543e7i	0.451775	+	1.09068i
$766$	−4.80464e7	−	3.21036e7i	−2.95862	−	1.97688i
$767$	−3.21964e6	+	3.21964e6i	−0.197614	+	0.197614i
$768$	−6.09624e7	−	1.47176e8i	−3.72957	−	9.00398i
$769$	4.43046e6	−	881273.i	0.270167	−	0.0537396i	−0.0581474	−	0.998308i	$-0.518519\pi$
$769$	4.43046e6	−	881273.i	0.270167	−	0.0537396i	0.328315	+	0.944568i	$0.393519\pi$
$770$		−	2.88088e7i		−	1.75105i
$771$	−912073.	−	181423.i	−0.0552578	−	0.0109915i
$772$	−4.07805e7	−	4.07805e7i	−2.46269	−	2.46269i
$773$	4.44446e6	+	1.07299e7i	0.267529	+	0.645872i	0.999366	−	0.0356081i	$-0.0113368\pi$
$773$	4.44446e6	+	1.07299e7i	0.267529	+	0.645872i	−0.731837	+	0.681480i	$0.761337\pi$
$774$	−2.50493e7	−	1.03758e7i	−1.50295	−	0.622540i
$775$	−506663.			−0.0303015
$776$	−1.54292e7	−	6.27514e7i	−0.919788	−	3.74084i
$777$	−3.07400e7			−1.82664
$778$	−4.11521e7	−	1.70458e7i	−2.43749	−	1.00964i
$779$	119635.	+	288823.i	0.00706338	+	0.0170525i
$780$	4.27030e7	+	4.27030e7i	2.51317	+	2.51317i
$781$	−1.28477e7	−	2.55557e6i	−0.753700	−	0.149920i
$782$		−	3.67814e7i		−	2.15085i
$783$	729295.	−	145066.i	0.0425108	−	0.00845592i
$784$	1.45175e7	+	3.50483e7i	0.843531	+	2.03646i
$785$	−2.43063e6	+	2.43063e6i	−0.140781	+	0.140781i
$786$	948938.	+	634060.i	0.0547875	+	0.0366079i
$787$	6.21571e6	+	1.50061e7i	0.357729	+	0.863634i	0.995619	+	0.0935065i	$0.0298076\pi$
$787$	6.21571e6	+	1.50061e7i	0.357729	+	0.863634i	−0.637890	+	0.770128i	$0.720192\pi$
$788$	−1.33017e7	+	3.21132e7i	−0.763120	+	1.84234i
$789$	2.73492e6	−	1.37494e7i	0.156406	−	0.786304i
$790$	1.29333e7	+	2.57260e6i	0.737297	+	0.146658i
$791$	2.61297e6	+	1.31363e7i	0.148489	+	0.746504i
$792$		−	4.71045e7i		−	2.66839i
$793$	−7.19416e6	+	3.61675e7i	−0.406253	+	2.04237i
$794$	−1.72362e7	+	7.13947e6i	−0.970265	+	0.401897i
$795$	7.34664e6	+	1.46134e6i	0.412260	+	0.0820036i
$796$	4.25151e7	+	6.36283e7i	2.37827	+	3.55933i
$797$	2.72588e6	+	4.07956e6i	0.152006	+	0.227493i	0.899655	−	0.436601i	$-0.143818\pi$
$797$	2.72588e6	+	4.07956e6i	0.152006	+	0.227493i	−0.747650	+	0.664093i	$0.768818\pi$
$798$			1.71917e6i			0.0955677i
$799$	4.38699e7	−	2.93129e7i	2.43108	−	1.62440i
$800$	−2.34341e7	+	2.34341e7i	−1.29456	+	1.29456i
$801$	1.52229e7	+	6.30552e6i	0.838331	+	0.347248i
$802$	2.10577e7	−	3.15150e7i	1.15604	−	1.73014i
$803$	−5.06086e6	−	2.09628e6i	−0.276972	−	0.114726i
$804$	4.60096e7	+	3.07427e7i	2.51020	+	1.67726i
$805$	8.80409e6	−	5.88270e6i	0.478845	−	0.319954i
$806$	−720866.	+	3.62404e6i	−0.0390856	+	0.196497i
$807$	−5.14555e6	+	2.13136e6i	−0.278130	+	0.115205i
$808$	2.19358e7	−	5.29578e7i	1.18202	−	2.85365i
$809$	4.20432e6	−	4.20432e6i	0.225852	−	0.225852i	−0.585105	−	0.810957i	$-0.698947\pi$
$809$	4.20432e6	−	4.20432e6i	0.225852	−	0.225852i	0.810957	+	0.585105i	$0.198947\pi$
$810$	1.97277e7	−	2.95246e7i	1.05649	−	1.58114i
$811$	5.41981e6			0.289356			0.144678	−	0.989479i	$-0.453785\pi$
$811$	5.41981e6			0.289356			0.144678	+	0.989479i	$0.453785\pi$
$812$	−9.75616e6			−0.519265
$813$	6.39995e6	−	9.57820e6i	0.339586	−	0.508227i
$814$	3.14618e7	+	2.10221e7i	1.66427	+	1.11203i
$815$	−1.55354e7	+	3.09018e6i	−0.819271	+	0.162963i
$816$	4.33313e7	+	2.17841e8i	2.27812	+	11.4529i
$817$	−333258.	−	498756.i	−0.0174673	−	0.0261417i
$818$	−4.49097e6	−	2.25776e7i	−0.234670	−	1.17976i
$819$	−1.41910e7	−	1.41910e7i	−0.739269	−	0.739269i
$820$	−1.09550e7	+	2.64478e7i	−0.568956	+	1.37358i
$821$	2.82950e7	−	1.89061e7i	1.46505	−	0.978912i	0.469672	−	0.882841i	$-0.344372\pi$
$821$	2.82950e7	−	1.89061e7i	1.46505	−	0.978912i	0.995374	−	0.0960712i	$-0.0306276\pi$
$822$	−3.97052e7	+	7.89786e6i	−2.04960	+	0.407690i
$823$	−1.35566e7	−	1.35566e7i	−0.697671	−	0.697671i	0.266237	−	0.963908i	$-0.414220\pi$
$823$	−1.35566e7	−	1.35566e7i	−0.697671	−	0.697671i	−0.963908	+	0.266237i	$0.914220\pi$
$824$	−1.07303e8	+	4.44465e7i	−5.50548	+	2.28045i
$825$	−7.15785e6	+	2.96488e6i	−0.366140	+	0.151660i
$826$	−8.39283e6	−	8.39283e6i	−0.428014	−	0.428014i
$827$	−3.19077e7	+	6.34684e6i	−1.62230	+	0.322696i	−0.920819	−	0.389989i	$-0.872479\pi$
$827$	−3.19077e7	+	6.34684e6i	−1.62230	+	0.322696i	−0.701484	+	0.712685i	$0.747479\pi$
$828$	2.18133e7	−	1.45752e7i	1.10572	−	0.738819i
$829$	−4.30531e6	+	1.03939e7i	−0.217580	+	0.525283i	−0.994551	−	0.104253i	$-0.966755\pi$
$829$	−4.30531e6	+	1.03939e7i	−0.217580	+	0.525283i	0.776971	+	0.629536i	$0.216755\pi$
$830$	−1.10299e7	−	1.10299e7i	−0.555748	−	0.555748i
$831$	−5.19380e6	−	2.61110e7i	−0.260905	−	1.31166i
$832$	7.62940e7	+	1.14182e8i	3.82105	+	5.71860i
$833$	−3.40586e6	−	1.71224e7i	−0.170065	−	0.854972i
$834$	4.20024e7	−	8.35480e6i	2.09103	−	0.415931i
$835$	−5.70181e6	−	3.80983e6i	−0.283007	−	0.189099i
$836$	877331.	−	1.31302e6i	0.0434158	−	0.0649764i
$837$	547828.			0.0270290
$838$	3.71136e7			1.82567
$839$	2.53188e6	−	3.78923e6i	0.124176	−	0.185843i	−0.764173	−	0.645011i	$-0.776853\pi$
$839$	2.53188e6	−	3.78923e6i	0.124176	−	0.185843i	0.888349	+	0.459169i	$0.151853\pi$
$840$	−7.34615e7	+	7.34615e7i	−3.59221	+	3.59221i
$841$	−7.68259e6	+	1.85474e7i	−0.374557	+	0.904260i
$842$	−2.26832e7	+	9.39569e6i	−1.10262	+	0.456718i
$843$	6.12188e6	−	3.07768e7i	0.296699	−	1.49161i
$844$	−7.68371e7	+	5.13409e7i	−3.71291	+	2.48089i
$845$	−3.28882e6	−	2.19752e6i	−0.158452	−	0.105874i
$846$	4.65918e7	+	1.92990e7i	2.23812	+	0.927060i
$847$	−2.88139e6	+	4.31231e6i	−0.138005	+	0.206538i
$848$	3.51684e7	+	1.45672e7i	1.67944	+	0.695645i
$849$	2.51340e7	−	2.51340e7i	1.19672	−	1.19672i
$850$	2.15779e7	−	1.44179e7i	1.02438	−	0.684469i
$851$			1.39075e7i			0.658303i
$852$	3.97686e7	+	5.95179e7i	1.87690	+	2.80898i
$853$	1.14316e7	+	1.71086e7i	0.537940	+	0.805085i	0.996501	−	0.0835783i	$-0.0266349\pi$
$853$	1.14316e7	+	1.71086e7i	0.537940	+	0.805085i	−0.458561	+	0.888663i	$0.651635\pi$
$854$	−9.42800e7	−	1.87535e7i	−4.42359	−	0.879906i
$855$	−373325.	+	154636.i	−0.0174651	+	0.00723429i
$856$	−1.21960e6	+	6.13136e6i	−0.0568898	+	0.286004i
$857$		−	6.17295e6i		−	0.287105i	−0.989643	−	0.143553i	$-0.954147\pi$
$857$		−	6.17295e6i		−	0.287105i	0.989643	−	0.143553i	$-0.0458526\pi$
$858$	1.10231e7	+	5.54168e7i	0.511193	+	2.56994i
$859$	−1.23978e6	−	246607.i	−0.0573272	−	0.0114031i	0.166343	−	0.986068i	$-0.446804\pi$
$859$	−1.23978e6	−	246607.i	−0.0573272	−	0.0114031i	−0.223671	+	0.974665i	$0.571804\pi$
$860$	1.07160e7	−	5.38732e7i	0.494070	−	2.48386i
$861$	8.32671e6	−	2.01025e7i	0.382795	−	0.924148i
$862$	9.40262e6	+	2.26999e7i	0.431003	+	1.04053i
$863$	2.63845e7	+	1.76295e7i	1.20593	+	0.805776i	0.985508	−	0.169629i	$-0.0542570\pi$
$863$	2.63845e7	+	1.76295e7i	1.20593	+	0.805776i	0.220421	+	0.975405i	$0.429257\pi$
$864$	2.53380e7	−	2.53380e7i	1.15475	−	1.15475i
$865$	−7.72788e6	−	1.86568e7i	−0.351172	−	0.847805i
$866$	6.61202e7	−	1.31521e7i	2.99598	−	0.595938i
$867$		−	7.27091e7i		−	3.28504i
$868$	−7.04965e6	−	1.40226e6i	−0.317591	−	0.0631728i
$869$	6.51011e6	+	6.51011e6i	0.292441	+	0.292441i
$870$	−2.68971e6	−	6.49354e6i	−0.120478	−	0.290860i
$871$	−1.76936e7	−	7.32891e6i	−0.790259	−	0.327336i
$872$	−4.21398e7			−1.87673
$873$	−1.40963e7	+	1.03599e7i	−0.625992	+	0.460067i
$874$	777792.			0.0344417
$875$	2.76021e7	+	1.14332e7i	1.21877	+	0.504831i
$876$	1.14551e7	+	2.76550e7i	0.504357	+	1.21763i
$877$	2.39939e7	+	2.39939e7i	1.05342	+	1.05342i	0.998490	+	0.0549323i	$0.0174943\pi$
$877$	2.39939e7	+	2.39939e7i	1.05342	+	1.05342i	0.0549323	+	0.998490i	$0.482506\pi$
$878$	−5.82006e7	−	1.15768e7i	−2.54795	−	0.506819i
$879$			8.43500e6i			0.368225i
$880$	7.71940e7	−	1.53548e7i	3.36029	−	0.668403i
$881$	2.06437e6	+	4.98382e6i	0.0896081	+	0.216333i	0.962330	−	0.271885i	$-0.0876470\pi$
$881$	2.06437e6	+	4.98382e6i	0.0896081	+	0.216333i	−0.872722	+	0.488218i	$0.837647\pi$
$882$	1.17991e7	−	1.17991e7i	0.510714	−	0.510714i
$883$	−1.27121e7	−	8.49397e6i	−0.548677	−	0.366614i	0.250120	−	0.968215i	$-0.419530\pi$
$883$	−1.27121e7	−	8.49397e6i	−0.548677	−	0.366614i	−0.798797	+	0.601601i	$0.794530\pi$
$884$	−5.40475e7	−	1.30482e8i	−2.32619	−	5.61591i
$885$	2.44188e6	−	5.89521e6i	0.104801	−	0.253012i
$886$	−1.62335e7	+	8.16112e7i	−0.694748	+	3.49274i
$887$	3.36959e7	+	6.70254e6i	1.43803	+	0.286042i	0.851700	−	0.524029i	$-0.175572\pi$
$887$	3.36959e7	+	6.70254e6i	1.43803	+	0.286042i	0.586331	+	0.810071i	$0.300572\pi$
$888$	−2.66209e7	−	1.33832e8i	−1.13290	−	5.69545i
$889$		−	5.38176e7i		−	2.28386i
$890$	−8.72695e6	+	4.38733e7i	−0.369307	+	1.85663i
$891$	2.29044e7	−	9.48733e6i	0.966553	−	0.400359i
$892$	850139.	+	169103.i	0.0357748	+	0.00711606i
$893$	619862.	+	927689.i	0.0260116	+	0.0389290i
$894$	−5.06021e6	−	7.57314e6i	−0.211751	−	0.316907i
$895$		−	1.82377e7i		−	0.761048i
$896$	−1.64708e8	+	1.10054e8i	−6.85399	+	4.57969i
$897$	−1.46847e7	+	1.46847e7i	−0.609373	+	0.609373i
$898$	−5.10295e6	−	2.11371e6i	−0.211169	−	0.0874691i
$899$	178289.	−	266828.i	0.00735741	−	0.0110111i
$900$	1.71011e7	+	7.08352e6i	0.703750	+	0.291503i
$901$	−1.45654e7	−	9.73230e6i	−0.597738	−	0.399396i
$902$	−2.22696e7	+	1.48801e7i	−0.911375	+	0.608961i
$903$	−8.14507e6	+	4.09480e7i	−0.332411	+	1.67114i
$904$	−5.49283e7	+	2.27521e7i	−2.23550	+	0.925976i
$905$	2.14095e6	−	5.16871e6i	0.0868931	−	0.209778i
$906$	−3.99591e7	+	3.99591e7i	−1.61732	+	1.61732i
$907$	−2.12363e7	+	3.17824e7i	−0.857160	+	1.28283i	0.100503	+	0.994937i	$0.467955\pi$
$907$	−2.12363e7	+	3.17824e7i	−0.857160	+	1.28283i	−0.957663	+	0.287893i	$0.907045\pi$
$908$	9.90510e7			3.98698
$909$	−1.55177e7			−0.622901
$910$	3.02699e7	−	4.53021e7i	1.21174	−	1.81349i
$911$	−9.88612e6	−	6.60569e6i	−0.394666	−	0.263707i	0.342364	−	0.939567i	$-0.388772\pi$
$911$	−9.88612e6	−	6.60569e6i	−0.394666	−	0.263707i	−0.737030	+	0.675860i	$0.763772\pi$
$912$	−4.60655e6	+	916300.i	−0.183395	+	0.0364796i
$913$	−2.12467e6	−	1.06814e7i	−0.0843556	−	0.424084i
$914$	1.14812e7	+	1.71828e7i	0.454591	+	0.680344i
$915$	−1.00819e7	−	5.06851e7i	−0.398097	−	2.00137i
$916$	5.99936e7	+	5.99936e7i	2.36247	+	2.36247i
$917$	294038.	−	709870.i	0.0115473	−	0.0278776i
$918$	−2.33310e7	+	1.55893e7i	−0.913749	+	0.610547i
$919$	2.73777e7	−	5.44576e6i	1.06932	−	0.212701i	0.371106	−	0.928590i	$-0.378979\pi$
$919$	2.73777e7	−	5.44576e6i	1.06932	−	0.212701i	0.698214	+	0.715889i	$0.253979\pi$
$920$	3.32357e7	+	3.32357e7i	1.29460	+	1.29460i
$921$	−863779.	+	357789.i	−0.0335547	+	0.0138988i
$922$	−2.47642e7	+	1.02577e7i	−0.959396	+	0.397395i
$923$	−1.75180e7	−	1.75180e7i	−0.676830	−	0.676830i
$924$	−1.07799e8	+	2.14426e7i	−4.15371	+	0.826224i
$925$	−8.15888e6	+	5.45159e6i	−0.313528	+	0.209493i
$926$	3.51492e7	−	8.48577e7i	1.34706	−	3.25210i
$927$	2.22330e7	+	2.22330e7i	0.849764	+	0.849764i
$928$	−4.09510e6	−	2.05874e7i	−0.156097	−	0.784752i
$929$	−1.22616e7	−	1.83508e7i	−0.466132	−	0.697616i	0.521702	−	0.853128i	$-0.325297\pi$
$929$	−1.22616e7	−	1.83508e7i	−0.466132	−	0.697616i	−0.987834	+	0.155512i	$0.950297\pi$
$930$	−1.01022e6	−	5.07873e6i	−0.0383009	−	0.192552i
$931$	362076.	−	72021.5i	0.0136907	−	0.00272325i
$932$	3.39535e7	+	2.26870e7i	1.28040	+	0.855535i
$933$	−1.74265e7	+	2.60806e7i	−0.655399	+	0.980875i
$934$	3.27140e7			1.22706
$935$	−3.62200e7			−1.35494
$936$	4.94935e7	−	7.40722e7i	1.84654	−	2.76354i
$937$	1.90398e7	−	1.90398e7i	0.708457	−	0.708457i	−0.257754	−	0.966211i	$-0.582982\pi$
$937$	1.90398e7	−	1.90398e7i	0.708457	−	0.708457i	0.966211	+	0.257754i	$0.0829824\pi$
$938$	1.91047e7	−	4.61229e7i	0.708979	−	1.71163i
$939$	3.07735e7	−	1.27468e7i	1.13897	−	0.471778i
$940$	−1.99319e7	+	1.00204e8i	−0.735748	+	3.69885i
$941$	3.61715e7	−	2.41690e7i	1.33166	−	0.889785i	0.333069	−	0.942902i	$-0.391916\pi$
$941$	3.61715e7	−	2.41690e7i	1.33166	−	0.889785i	0.998588	+	0.0531173i	$0.0169157\pi$
$942$	1.46125e7	+	9.76373e6i	0.536532	+	0.358500i
$943$	−9.09483e6	−	3.76720e6i	−0.333055	−	0.137956i
$944$	1.80155e7	−	2.69621e7i	0.657985	−	0.984744i
$945$	−7.46299e6	−	3.09127e6i	−0.271852	−	0.112605i
$946$	3.63394e7	−	3.63394e7i	1.32023	−	1.32023i
$947$	−2.12357e6	+	1.41892e6i	−0.0769469	+	0.0514142i	−0.593449	−	0.804872i	$-0.702234\pi$
$947$	−2.12357e6	+	1.41892e6i	−0.0769469	+	0.0514142i	0.516502	+	0.856286i	$0.327234\pi$
$948$		−	5.03098e7i		−	1.81816i
$949$	−5.75566e6	−	8.61395e6i	−0.207458	−	0.310482i
$950$	304885.	+	456293.i	0.0109604	+	0.0164034i
$951$	−2.12264e6	−	422219.i	−0.0761069	−	0.0151386i
$952$	2.24467e8	−	9.29771e7i	8.02711	−	3.32494i
$953$	−8.27685e6	+	4.16106e7i	−0.295211	+	1.48413i	0.493706	+	0.869629i	$0.335642\pi$
$953$	−8.27685e6	+	4.16106e7i	−0.295211	+	1.48413i	−0.788918	+	0.614499i	$0.789358\pi$
$954$		−	1.67437e7i		−	0.595634i
$955$	−5.03805e6	−	2.53280e7i	−0.178753	−	0.898653i
$956$	−1.60651e7	−	3.19555e6i	−0.568511	−	0.113084i
$957$	957346.	−	4.81290e6i	0.0337901	−	0.169874i
$958$	−5.04638e6	+	1.21830e7i	−0.177650	+	0.428886i
$959$	1.04300e7	+	2.51803e7i	0.366217	+	0.884127i
$960$	−1.60015e8	−	1.06918e8i	−5.60379	−	3.74433i
$961$	−2.00767e7	+	2.00767e7i	−0.701267	+	0.701267i
$962$	2.73857e7	+	6.61149e7i	0.954083	+	2.30336i
$963$	1.65986e6	−	330166.i	0.0576774	−	0.0114727i
$964$			8.96888e7i			3.10846i
$965$	−2.74347e7	−	5.45710e6i	−0.948379	−	0.188644i
$966$	−3.82794e7	−	3.82794e7i	−1.31984	−	1.31984i
$967$	−4.57571e6	−	1.10467e7i	−0.157359	−	0.379899i	0.825462	−	0.564457i	$-0.190915\pi$
$967$	−4.57571e6	−	1.10467e7i	−0.157359	−	0.379899i	−0.982822	+	0.184558i	$0.940915\pi$
$968$	−2.12697e7	−	8.81018e6i	−0.729578	−	0.302201i
$969$	2.16143e6			0.0739488
$970$	−3.50512e7	−	3.20468e7i	−1.19612	−	1.09359i
$971$	5.28243e7			1.79798			0.898992	−	0.437964i	$-0.144300\pi$
$971$	5.28243e7			1.79798			0.898992	+	0.437964i	$0.144300\pi$
$972$	−1.01360e8	−	4.19845e7i	−3.44112	−	1.42536i
$973$	−1.10335e7	−	2.66372e7i	−0.373620	−	0.901998i
$974$	−1.14019e7	−	1.14019e7i	−0.385106	−	0.385106i
$975$	−1.43710e7	−	2.85857e6i	−0.484146	−	0.0963026i
$976$		−	2.62621e8i		−	8.82479i
$977$	4.17750e6	−	830956.i	0.140017	−	0.0278511i	−0.124584	−	0.992209i	$-0.539760\pi$
$977$	4.17750e6	−	830956.i	0.140017	−	0.0278511i	0.264601	+	0.964358i	$0.414760\pi$
$978$	3.09906e7	+	7.48179e7i	1.03605	+	2.50126i
$979$	−2.20840e7	+	2.20840e7i	−0.736414	+	0.736414i
$980$	2.81080e7	+	1.87811e7i	0.934898	+	0.624679i
$981$	4.36562e6	+	1.05395e7i	0.144835	+	0.349663i
$982$	7.58311e6	−	1.83072e7i	0.250939	−	0.605821i
$983$	−1.11358e7	+	5.59837e7i	−0.367569	+	1.84790i	0.145243	+	0.989396i	$0.453603\pi$
$983$	−1.11358e7	+	5.59837e7i	−0.367569	+	1.84790i	−0.512813	+	0.858500i	$0.671397\pi$
$984$	9.47305e7	+	1.88431e7i	3.11890	+	0.620389i
$985$	3.28900e6	+	1.65349e7i	0.108012	+	0.543014i
$986$			1.64372e7i			0.538438i
$987$	1.51499e7	−	7.61635e7i	0.495012	−	2.48859i
$988$	2.75922e6	−	1.14291e6i	0.0899278	−	0.0372493i
$989$	1.85259e7	+	3.68502e6i	0.602265	+	0.119798i
$990$	−1.92336e7	−	2.87851e7i	−0.623696	−	0.933427i
$991$	−1.02528e7	−	1.53444e7i	−0.331634	−	0.496326i	0.627755	−	0.778411i	$-0.283974\pi$
$991$	−1.02528e7	−	1.53444e7i	−0.331634	−	0.496326i	−0.959389	+	0.282085i	$0.908974\pi$
$992$		−	1.54648e7i		−	0.498958i
$993$	−5.58707e7	+	3.73316e7i	−1.79809	+	1.20144i
$994$	4.56652e7	−	4.56652e7i	1.46595	−	1.46595i
$995$	3.42909e7	+	1.42037e7i	1.09805	+	0.454826i
$996$	−3.30631e7	+	4.94824e7i	−1.05607	+	1.58053i
$997$	3.99301e7	+	1.65396e7i	1.27222	+	0.526972i	0.913639	−	0.406526i	$-0.133260\pi$
$997$	3.99301e7	+	1.65396e7i	1.27222	+	0.526972i	0.358583	+	0.933498i	$0.383260\pi$
$998$	−6.41321e7	−	4.28517e7i	−2.03821	−	1.36189i
$999$	8.82176e6	−	5.89451e6i	0.279667	−	0.186868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.6.h.a.8.1	✓	328
97.85	even	16	inner	97.6.h.a.85.1	yes	328

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.6.h.a.8.1	✓	328	1.1	even	1	trivial
97.6.h.a.85.1	yes	328	97.85	even	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 97 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	97.h (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.3746 - 4.29730i) q^{2} +(7.95190 + 19.1976i) q^{3} +(66.5381 + 66.5381i) q^{4} +(44.7629 + 8.90389i) q^{5} -233.339i q^{6} +(-154.075 + 30.6475i) q^{7} +(-266.858 - 644.252i) q^{8} +(-133.487 + 133.487i) q^{9} +(-426.134 - 284.734i) q^{10} +(-136.933 - 330.584i) q^{11} +(-748.266 + 1806.47i) q^{12} +(132.023 - 663.724i) q^{13} +(1730.17 + 344.152i) q^{14} +(185.017 + 930.142i) q^{15} +4819.46i q^{16} +(432.686 - 2175.26i) q^{17} +(1958.51 - 811.242i) q^{18} +(45.9988 + 9.14973i) q^{19} +(2385.99 + 3570.88i) q^{20} +(-1813.55 - 2714.16i) q^{21} +4018.12i q^{22} +(-1227.95 + 820.491i) q^{23} +(10246.1 - 10246.1i) q^{24} +(-962.686 - 398.757i) q^{25} +(-4221.90 + 6318.52i) q^{26} +(1040.90 + 431.155i) q^{27} +(-12291.1 - 8212.64i) q^{28} +(548.759 - 366.669i) q^{29} +(2077.62 - 10444.9i) q^{30} +(449.226 - 186.076i) q^{31} +(12171.2 - 29383.9i) q^{32} +(5257.54 - 5257.54i) q^{33} +(-13836.7 + 20708.1i) q^{34} -7169.73 q^{35} -17764.0 q^{36} +(5231.83 - 7829.99i) q^{37} +(-437.900 - 292.595i) q^{38} +(13791.7 - 2743.34i) q^{39} +(-6208.99 - 31214.7i) q^{40} +(3703.25 + 5542.31i) q^{41} +(7151.24 + 35951.7i) q^{42} +(-9043.87 - 9043.87i) q^{43} +(12885.2 - 31107.7i) q^{44} +(-7163.83 + 4786.72i) q^{45} +(16265.4 - 3235.39i) q^{46} +(16821.6 + 16821.6i) q^{47} +(-92521.9 + 38323.8i) q^{48} +(7272.25 - 3012.27i) q^{49} +(8273.90 + 8273.90i) q^{50} +(45200.4 - 8990.91i) q^{51} +(52947.4 - 35378.3i) q^{52} +(3022.59 - 7297.18i) q^{53} +(-8946.13 - 8946.13i) q^{54} +(-3186.01 - 16017.1i) q^{55} +(60860.9 + 91084.8i) q^{56} +(190.125 + 955.823i) q^{57} +(-7268.84 + 1445.86i) q^{58} +(-5594.42 - 3738.07i) q^{59} +(-49579.2 + 74200.5i) q^{60} -54491.8 q^{61} -5460.16 q^{62} +(16476.0 - 24658.1i) q^{63} +(-143490. + 143490. i) q^{64} +(11819.5 - 28534.7i) q^{65} +(-77138.1 + 31951.7i) q^{66} +(5521.05 - 27756.2i) q^{67} +(173528. - 115947. i) q^{68} +(-25516.0 - 17049.2i) q^{69} +(74383.1 + 30810.5i) q^{70} +(20338.8 - 30439.1i) q^{71} +(121622. + 50377.3i) q^{72} +(10825.0 - 10825.0i) q^{73} +(-87925.9 + 58750.2i) q^{74} -21652.1i q^{75} +(2451.87 + 3669.48i) q^{76} +(31229.5 + 46738.2i) q^{77} +(-154872. - 30806.0i) q^{78} +(-23771.2 + 9846.37i) q^{79} +(-42911.9 + 215733. i) q^{80} +69284.7i q^{81} +(-14602.8 - 73413.2i) q^{82} +(29851.2 + 5937.77i) q^{83} +(59925.4 - 301265. i) q^{84} +(38736.6 - 93518.3i) q^{85} +(54962.3 + 132691. i) q^{86} +(11402.8 + 7619.13i) q^{87} +(-176438. + 176438. i) q^{88} +(-33401.5 - 80638.4i) q^{89} +(94891.9 - 18875.2i) q^{90} +106310. i q^{91} +(-136299. - 27111.6i) q^{92} +(7144.40 + 7144.40i) q^{93} +(-102230. - 246805. i) q^{94} +(1977.57 + 819.137i) q^{95} +660883. q^{96} +(91605.0 + 13995.1i) q^{97} -88391.3 q^{98} +(62407.6 + 25850.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 328 q - 8 q^{2} - 96 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{7} - 8 q^{8} + 256 q^{9} - 1992 q^{10} - 8 q^{11} + 4472 q^{12} - 8 q^{13} - 5504 q^{14} + 7640 q^{15} + 2880 q^{17} - 14104 q^{18} + 13984 q^{19} + 11504 q^{20}+ \cdots + 390672 q^{99}+O(q^{100}) \) 328 * q - 8 * q^2 - 96 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^7 - 8 * q^8 + 256 * q^9 - 1992 * q^10 - 8 * q^11 + 4472 * q^12 - 8 * q^13 - 5504 * q^14 + 7640 * q^15 + 2880 * q^17 - 14104 * q^18 + 13984 * q^19 + 11504 * q^20 - 8 * q^21 + 10976 * q^23 + 8184 * q^24 - 20240 * q^25 - 23968 * q^26 + 21024 * q^27 - 4368 * q^28 - 5688 * q^29 + 24992 * q^30 - 17744 * q^31 + 19528 * q^32 - 30016 * q^33 - 43528 * q^34 + 78384 * q^35 - 549520 * q^36 - 36816 * q^37 - 8 * q^38 - 32088 * q^39 + 68344 * q^40 - 31128 * q^41 + 62200 * q^42 + 6144 * q^43 - 72704 * q^44 + 57904 * q^45 - 8 * q^46 + 130504 * q^47 + 123192 * q^48 + 158656 * q^49 - 177512 * q^50 + 36600 * q^51 + 15160 * q^52 - 28632 * q^53 + 302712 * q^54 + 106744 * q^55 - 8 * q^56 - 8 * q^57 - 176712 * q^58 + 234272 * q^59 + 415720 * q^60 + 178592 * q^61 - 246032 * q^62 - 305160 * q^63 + 8184 * q^64 + 273504 * q^65 - 137296 * q^66 + 393832 * q^67 + 480576 * q^68 - 475128 * q^69 + 736072 * q^70 - 429184 * q^71 - 451336 * q^72 + 239224 * q^73 + 249656 * q^74 + 155752 * q^76 - 8 * q^77 + 62200 * q^78 - 230296 * q^79 - 874280 * q^80 + 131136 * q^82 + 204368 * q^83 + 1467680 * q^84 + 14928 * q^85 - 104056 * q^86 - 230696 * q^87 + 372216 * q^88 + 191216 * q^89 + 842872 * q^90 - 1189408 * q^92 - 1087800 * q^93 - 723656 * q^94 + 573344 * q^95 - 907792 * q^96 - 339408 * q^97 - 2291344 * q^98 + 390672 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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