LMFDB - Embedded newform 38.7.d.a.27.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,7,Mod(27,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("38.27");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	38.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.74205517755$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 9440 x^{18} + 37579488 x^{16} + 83109028728 x^{14} + 112838424559344 x^{12} + \cdots + 83\!\cdots\!96 $ x^20 + 9440x^18 + 37579488x^16 + 83109028728x^14 + 112838424559344x^12 + 97808951849137728x^10 + 54352282696688610576x^8 + 18825433555812367062720x^6 + 3765133606401310416173376x^4 + 360077534420960567854418432*x^2 + 8303121574870947536327197696
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{4}\cdot 19^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.9
Root			$-30.5778i$ of defining polynomial
Character	$\chi$	$=$	38.27
Dual form			38.7.d.a.31.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 + 2.82843i) q^{2} +(26.2059 + 15.1300i) q^{3} +(16.0000 + 27.7128i) q^{4} +(-88.5587 + 153.388i) q^{5} +(85.5881 + 148.243i) q^{6} -258.032 q^{7} +181.019i q^{8} +(93.3327 + 161.657i) q^{9} +O(q^{10})$	\(q+(4.89898 + 2.82843i) q^{2} +(26.2059 + 15.1300i) q^{3} +(16.0000 + 27.7128i) q^{4} +(-88.5587 + 153.388i) q^{5} +(85.5881 + 148.243i) q^{6} -258.032 q^{7} +181.019i q^{8} +(93.3327 + 161.657i) q^{9} +(-867.695 + 500.964i) q^{10} +794.862 q^{11} +968.319i q^{12} +(2166.08 - 1250.58i) q^{13} +(-1264.09 - 729.824i) q^{14} +(-4641.52 + 2679.78i) q^{15} +(-512.000 + 886.810i) q^{16} +(-2028.44 + 3513.35i) q^{17} +1055.94i q^{18} +(6686.61 + 1528.12i) q^{19} -5667.76 q^{20} +(-6761.96 - 3904.02i) q^{21} +(3894.01 + 2248.21i) q^{22} +(9305.46 + 16117.5i) q^{23} +(-2738.82 + 4743.77i) q^{24} +(-7872.79 - 13636.1i) q^{25} +14148.7 q^{26} -16411.0i q^{27} +(-4128.51 - 7150.79i) q^{28} +(23375.6 - 13495.9i) q^{29} -30318.3 q^{30} +3044.03i q^{31} +(-5016.55 + 2896.31i) q^{32} +(20830.1 + 12026.3i) q^{33} +(-19874.5 + 11474.6i) q^{34} +(22851.0 - 39579.0i) q^{35} +(-2986.65 + 5173.02i) q^{36} -28141.7i q^{37} +(28435.4 + 26398.8i) q^{38} +75685.3 q^{39} +(-27766.2 - 16030.8i) q^{40} +(-57048.2 - 32936.8i) q^{41} +(-22084.5 - 38251.4i) q^{42} +(69590.2 - 120534. i) q^{43} +(12717.8 + 22027.9i) q^{44} -33061.7 q^{45} +105279. i q^{46} +(22854.9 + 39585.9i) q^{47} +(-26834.8 + 15493.1i) q^{48} -51068.6 q^{49} -89070.5i q^{50} +(-106314. + 61380.4i) q^{51} +(69314.4 + 40018.7i) q^{52} +(-114347. + 66018.2i) q^{53} +(46417.4 - 80397.3i) q^{54} +(-70392.0 + 121923. i) q^{55} -46708.8i q^{56} +(152108. + 141214. i) q^{57} +152689. q^{58} +(-69869.5 - 40339.2i) q^{59} +(-148529. - 85753.1i) q^{60} +(92871.3 + 160858. i) q^{61} +(-8609.82 + 14912.7i) q^{62} +(-24082.8 - 41712.6i) q^{63} -32768.0 q^{64} +443001. i q^{65} +(68030.8 + 117833. i) q^{66} +(-308961. + 178379. i) q^{67} -129820. q^{68} +563166. i q^{69} +(223893. - 129265. i) q^{70} +(-195092. - 112636. i) q^{71} +(-29263.0 + 16895.0i) q^{72} +(362983. - 628705. i) q^{73} +(79596.8 - 137866. i) q^{74} -476461. i q^{75} +(64637.2 + 209755. i) q^{76} -205100. q^{77} +(370781. + 214070. i) q^{78} +(-481060. - 277740. i) q^{79} +(-90684.1 - 157070. i) q^{80} +(316338. - 547914. i) q^{81} +(-186319. - 322713. i) q^{82} -75868.0 q^{83} -249857. i q^{84} +(-359271. - 622276. i) q^{85} +(681841. - 393661. i) q^{86} +816773. q^{87} +143885. i q^{88} +(1.00100e6 - 577930. i) q^{89} +(-161968. - 93512.6i) q^{90} +(-558917. + 322691. i) q^{91} +(-297775. + 515761. i) q^{92} +(-46056.2 + 79771.6i) q^{93} +258574. i q^{94} +(-826553. + 890318. i) q^{95} -175284. q^{96} +(-150521. - 86903.2i) q^{97} +(-250184. - 144444. i) q^{98} +(74186.6 + 128495. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9}+O(q^{10}) $ 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9	\( 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9} - 284 q^{11} + 10500 q^{13} + 1248 q^{14} + 14136 q^{15} - 10240 q^{16} - 11684 q^{17} + 12862 q^{19} + 7168 q^{20} + 2916 q^{21} + 52704 q^{22} + 8488 q^{23} - 2560 q^{24} - 63842 q^{25} - 43968 q^{26} - 3328 q^{28} + 137760 q^{29} - 94688 q^{30} - 250194 q^{33} + 70560 q^{34} - 6916 q^{35} - 70400 q^{36} - 77232 q^{38} + 9672 q^{39} + 109206 q^{41} - 92672 q^{42} + 35572 q^{43} - 4544 q^{44} + 131264 q^{45} - 361184 q^{47} + 30720 q^{48} + 259740 q^{49} - 496512 q^{51} + 336000 q^{52} - 236172 q^{53} + 375728 q^{54} + 56760 q^{55} + 314796 q^{57} - 225600 q^{58} + 1310610 q^{59} + 452352 q^{60} + 83552 q^{61} + 225792 q^{62} + 553364 q^{63} - 655360 q^{64} - 4736 q^{66} + 806646 q^{67} - 747776 q^{68} - 245664 q^{70} - 869220 q^{71} + 353280 q^{72} - 207422 q^{73} + 1460832 q^{74} - 140096 q^{76} - 3988336 q^{77} - 85008 q^{78} - 1706808 q^{79} + 114688 q^{80} + 2303170 q^{81} + 887712 q^{82} + 3527548 q^{83} - 5604 q^{85} + 195792 q^{86} - 8414832 q^{87} + 708432 q^{89} - 4483104 q^{90} - 1914384 q^{91} - 271616 q^{92} + 3537876 q^{93} - 2820356 q^{95} - 163840 q^{96} + 5113242 q^{97} - 612480 q^{98} + 603704 q^{99}+O(q^{100}) \) 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9 - 284 * q^11 + 10500 * q^13 + 1248 * q^14 + 14136 * q^15 - 10240 * q^16 - 11684 * q^17 + 12862 * q^19 + 7168 * q^20 + 2916 * q^21 + 52704 * q^22 + 8488 * q^23 - 2560 * q^24 - 63842 * q^25 - 43968 * q^26 - 3328 * q^28 + 137760 * q^29 - 94688 * q^30 - 250194 * q^33 + 70560 * q^34 - 6916 * q^35 - 70400 * q^36 - 77232 * q^38 + 9672 * q^39 + 109206 * q^41 - 92672 * q^42 + 35572 * q^43 - 4544 * q^44 + 131264 * q^45 - 361184 * q^47 + 30720 * q^48 + 259740 * q^49 - 496512 * q^51 + 336000 * q^52 - 236172 * q^53 + 375728 * q^54 + 56760 * q^55 + 314796 * q^57 - 225600 * q^58 + 1310610 * q^59 + 452352 * q^60 + 83552 * q^61 + 225792 * q^62 + 553364 * q^63 - 655360 * q^64 - 4736 * q^66 + 806646 * q^67 - 747776 * q^68 - 245664 * q^70 - 869220 * q^71 + 353280 * q^72 - 207422 * q^73 + 1460832 * q^74 - 140096 * q^76 - 3988336 * q^77 - 85008 * q^78 - 1706808 * q^79 + 114688 * q^80 + 2303170 * q^81 + 887712 * q^82 + 3527548 * q^83 - 5604 * q^85 + 195792 * q^86 - 8414832 * q^87 + 708432 * q^89 - 4483104 * q^90 - 1914384 * q^91 - 271616 * q^92 + 3537876 * q^93 - 2820356 * q^95 - 163840 * q^96 + 5113242 * q^97 - 612480 * q^98 + 603704 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	4.89898	+	2.82843i	0.612372	+	0.353553i
$2$	4.89898	+	2.82843i	0.612372	+	0.353553i
$3$	26.2059	+	15.1300i	0.970589	+	0.560370i	0.899416	−	0.437094i	$-0.143992\pi$
$3$	26.2059	+	15.1300i	0.970589	+	0.560370i	0.0711731	+	0.997464i	$0.477326\pi$
$4$	16.0000	+	27.7128i	0.250000	+	0.433013i
$5$	−88.5587	+	153.388i	−0.708470	+	1.22711i	0.256955	+	0.966423i	$0.417281\pi$
$5$	−88.5587	+	153.388i	−0.708470	+	1.22711i	−0.965425	+	0.260682i	$0.916053\pi$
$6$	85.5881	+	148.243i	0.396241	+	0.686310i
$7$	−258.032			−0.752279			−0.376140	−	0.926563i	$-0.622749\pi$
$7$	−258.032			−0.752279			−0.376140	+	0.926563i	$0.622749\pi$
$8$			181.019i			0.353553i
$9$	93.3327	+	161.657i	0.128028	+	0.221752i
$10$	−867.695	+	500.964i	−0.867695	+	0.500964i
$11$	794.862			0.597192			0.298596	−	0.954380i	$-0.403482\pi$
$11$	794.862			0.597192			0.298596	+	0.954380i	$0.403482\pi$
$12$			968.319i			0.560370i
$13$	2166.08	−	1250.58i	0.985924	−	0.569224i	0.0818709	−	0.996643i	$-0.473910\pi$
$13$	2166.08	−	1250.58i	0.985924	−	0.569224i	0.904054	+	0.427419i	$0.140577\pi$
$14$	−1264.09	−	729.824i	−0.460675	−	0.265971i
$15$	−4641.52	+	2679.78i	−1.37527	+	0.794010i
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$	−2028.44	+	3513.35i	−0.412871	+	0.715113i	−0.995202	−	0.0978380i	$-0.968807\pi$
$17$	−2028.44	+	3513.35i	−0.412871	+	0.715113i	0.582331	+	0.812952i	$0.302141\pi$
$18$			1055.94i			0.181059i
$19$	6686.61	+	1528.12i	0.974866	+	0.222791i
$19$	6686.61	+	1528.12i	0.974866	+	0.222791i
$20$	−5667.76			−0.708470
$21$	−6761.96	−	3904.02i	−0.730154	−	0.421555i
$22$	3894.01	+	2248.21i	0.365704	+	0.211139i
$23$	9305.46	+	16117.5i	0.764812	+	1.32469i	0.940346	+	0.340219i	$0.110501\pi$
$23$	9305.46	+	16117.5i	0.764812	+	1.32469i	−0.175534	+	0.984473i	$0.556165\pi$
$24$	−2738.82	+	4743.77i	−0.198121	+	0.343155i
$25$	−7872.79	−	13636.1i	−0.503859	−	0.872709i
$26$	14148.7			0.805004
$27$		−	16411.0i		−	0.833767i
$28$	−4128.51	−	7150.79i	−0.188070	−	0.325747i
$29$	23375.6	−	13495.9i	0.958450	−	0.553361i	0.0627542	−	0.998029i	$-0.480012\pi$
$29$	23375.6	−	13495.9i	0.958450	−	0.553361i	0.895696	+	0.444668i	$0.146678\pi$
$30$	−30318.3			−1.12290
$31$			3044.03i			0.102180i	0.998694	+	0.0510898i	$0.0162695\pi$
$31$			3044.03i			0.102180i	−0.998694	+	0.0510898i	$0.983731\pi$
$32$	−5016.55	+	2896.31i	−0.153093	+	0.0883883i
$33$	20830.1	+	12026.3i	0.579628	+	0.334648i
$34$	−19874.5	+	11474.6i	−0.505662	+	0.291944i
$35$	22851.0	−	39579.0i	0.532967	−	0.923126i
$36$	−2986.65	+	5173.02i	−0.0640142	+	0.110876i
$37$		−	28141.7i		−	0.555578i	−0.960642	−	0.277789i	$-0.910398\pi$
$37$		−	28141.7i		−	0.555578i	0.960642	−	0.277789i	$-0.0896017\pi$
$38$	28435.4	+	26398.8i	0.518213	+	0.481098i
$39$	75685.3			1.27590
$40$	−27766.2	−	16030.8i	−0.433847	−	0.250482i
$41$	−57048.2	−	32936.8i	−0.827733	−	0.477892i	0.0253430	−	0.999679i	$-0.491932\pi$
$41$	−57048.2	−	32936.8i	−0.827733	−	0.477892i	−0.853076	+	0.521787i	$0.825266\pi$
$42$	−22084.5	−	38251.4i	−0.298084	−	0.516297i
$43$	69590.2	−	120534.i	0.875271	−	1.51601i	0.0187967	−	0.999823i	$-0.494016\pi$
$43$	69590.2	−	120534.i	0.875271	−	1.51601i	0.856474	−	0.516190i	$-0.172650\pi$
$44$	12717.8	+	22027.9i	0.149298	+	0.258592i
$45$	−33061.7			−0.362817
$46$			105279.i			1.08161i
$47$	22854.9	+	39585.9i	0.220133	+	0.381282i	0.954848	−	0.297094i	$-0.0960174\pi$
$47$	22854.9	+	39585.9i	0.220133	+	0.381282i	−0.734715	+	0.678376i	$0.762684\pi$
$48$	−26834.8	+	15493.1i	−0.242647	+	0.140092i
$49$	−51068.6			−0.434076
$50$		−	89070.5i		−	0.712564i
$51$	−106314.	+	61380.4i	−0.801456	+	0.462721i
$52$	69314.4	+	40018.7i	0.492962	+	0.284612i
$53$	−114347.	+	66018.2i	−0.768063	+	0.443442i	−0.832183	−	0.554501i	$-0.812909\pi$
$53$	−114347.	+	66018.2i	−0.768063	+	0.443442i	0.0641200	+	0.997942i	$0.479576\pi$
$54$	46417.4	−	80397.3i	0.294781	−	0.510576i
$55$	−70392.0	+	121923.i	−0.423092	+	0.732817i
$56$		−	46708.8i		−	0.265971i
$57$	152108.	+	141214.i	0.821349	+	0.762524i
$58$	152689.			0.782571
$59$	−69869.5	−	40339.2i	−0.340198	−	0.196413i	0.320162	−	0.947363i	$-0.396263\pi$
$59$	−69869.5	−	40339.2i	−0.340198	−	0.196413i	−0.660359	+	0.750950i	$0.729596\pi$
$60$	−148529.	−	85753.1i	−0.687633	−	0.397005i
$61$	92871.3	+	160858.i	0.409159	+	0.708684i	0.994796	−	0.101890i	$-0.0324889\pi$
$61$	92871.3	+	160858.i	0.409159	+	0.708684i	−0.585637	+	0.810573i	$0.699156\pi$
$62$	−8609.82	+	14912.7i	−0.0361259	+	0.0625720i
$63$	−24082.8	−	41712.6i	−0.0963131	−	0.166819i
$64$	−32768.0			−0.125000
$65$			443001.i			1.61311i
$66$	68030.8	+	117833.i	0.236632	+	0.409859i
$67$	−308961.	+	178379.i	−1.02726	+	0.593087i	−0.916198	−	0.400726i	$-0.868758\pi$
$67$	−308961.	+	178379.i	−1.02726	+	0.593087i	−0.111060	+	0.993814i	$0.535424\pi$
$68$	−129820.			−0.412871
$69$			563166.i			1.71431i
$70$	223893.	−	129265.i	0.652749	−	0.376865i
$71$	−195092.	−	112636.i	−0.545085	−	0.314705i	0.202052	−	0.979375i	$-0.435239\pi$
$71$	−195092.	−	112636.i	−0.545085	−	0.314705i	−0.747137	+	0.664670i	$0.768572\pi$
$72$	−29263.0	+	16895.0i	−0.0784010	+	0.0452649i
$73$	362983.	−	628705.i	0.933078	−	1.61614i	0.155051	−	0.987906i	$-0.450446\pi$
$73$	362983.	−	628705.i	0.933078	−	1.61614i	0.778026	−	0.628231i	$-0.216221\pi$
$74$	79596.8	−	137866.i	0.196427	−	0.340221i
$75$		−	476461.i		−	1.12939i
$76$	64637.2	+	209755.i	0.147245	+	0.477827i
$77$	−205100.			−0.449255
$78$	370781.	+	214070.i	0.781328	+	0.451100i
$79$	−481060.	−	277740.i	−0.975703	−	0.563322i	−0.0747328	−	0.997204i	$-0.523810\pi$
$79$	−481060.	−	277740.i	−0.975703	−	0.563322i	−0.900970	+	0.433881i	$0.857144\pi$
$80$	−90684.1	−	157070.i	−0.177117	−	0.306776i
$81$	316338.	−	547914.i	0.595246	−	1.03100i
$82$	−186319.	−	322713.i	−0.337920	−	0.585295i
$83$	−75868.0			−0.132686			−0.0663429	−	0.997797i	$-0.521133\pi$
$83$	−75868.0			−0.132686			−0.0663429	+	0.997797i	$0.521133\pi$
$84$		−	249857.i		−	0.421555i
$85$	−359271.	−	622276.i	−0.585013	−	1.01327i
$86$	681841.	−	393661.i	1.07198	−	0.618910i
$87$	816773.			1.24035
$88$			143885.i			0.211139i
$89$	1.00100e6	−	577930.i	1.41993	−	0.819795i	0.423634	−	0.905833i	$-0.360754\pi$
$89$	1.00100e6	−	577930.i	1.41993	−	0.819795i	0.996292	+	0.0860386i	$0.0274208\pi$
$90$	−161968.	−	93512.6i	−0.222179	−	0.128275i
$91$	−558917.	+	322691.i	−0.741691	+	0.428215i
$92$	−297775.	+	515761.i	−0.382406	+	0.662346i
$93$	−46056.2	+	79771.6i	−0.0572583	+	0.0991744i
$94$			258574.i			0.311316i
$95$	−826553.	+	890318.i	−0.964051	+	1.03842i
$96$	−175284.			−0.198121
$97$	−150521.	−	86903.2i	−0.164923	−	0.0952183i	0.415267	−	0.909700i	$-0.363688\pi$
$97$	−150521.	−	86903.2i	−0.164923	−	0.0952183i	−0.580190	+	0.814481i	$0.697022\pi$
$98$	−250184.	−	144444.i	−0.265816	−	0.153469i
$99$	74186.6	+	128495.i	0.0764575	+	0.132428i
$100$	251929.	−	436354.i	0.251929	−	0.436354i
$101$	728519.	+	1.26183e6i	0.707093	+	1.22472i	0.965931	+	0.258800i	$0.0833272\pi$
$101$	728519.	+	1.26183e6i	0.707093	+	1.22472i	−0.258838	+	0.965921i	$0.583339\pi$
$102$	−694440.			−0.654386
$103$			1.12202e6i			1.02681i	0.858148	+	0.513403i	$0.171615\pi$
$103$			1.12202e6i			1.02681i	−0.858148	+	0.513403i	$0.828385\pi$
$104$	226380.	+	392102.i	0.201251	+	0.348577i
$105$	1.19766e6	−	691469.i	1.03458	−	0.597317i
$106$	−746911.			−0.627121
$107$		−	1.14380e6i		−	0.933678i	−0.884342	−	0.466839i	$-0.845393\pi$
$107$		−	1.14380e6i		−	0.933678i	0.884342	−	0.466839i	$-0.154607\pi$
$108$	454796.	−	262576.i	0.361032	−	0.208442i
$109$	1.11961e6	+	646409.i	0.864547	+	0.499147i	0.865532	−	0.500853i	$-0.166980\pi$
$109$	1.11961e6	+	646409.i	0.864547	+	0.499147i	−0.000985058		1.00000i	$0.500314\pi$
$110$	−689698.	+	398197.i	−0.518180	+	0.299171i
$111$	425784.	−	737479.i	0.311329	−	0.539238i
$112$	132112.	−	228825.i	0.0940349	−	0.162873i
$113$			1.27443e6i			0.883244i	0.897201	+	0.441622i	$0.145597\pi$
$113$			1.27443e6i			0.883244i	−0.897201	+	0.441622i	$0.854403\pi$
$114$	345761.	+	1.12203e6i	0.233379	+	0.757339i
$115$	−3.29632e6			−2.16738
$116$	748020.	+	431870.i	0.479225	+	0.276681i
$117$	404331.	+	233441.i	0.252453	+	0.145754i
$118$	−228193.	−	395241.i	−0.138885	−	0.240556i
$119$	523401.	−	906557.i	0.310594	−	0.537965i
$120$	−485093.	−	840205.i	−0.280725	−	0.486230i
$121$	−1.13975e6			−0.643362
$122$			1.05072e6i			0.578638i
$123$	−996666.	−	1.72628e6i	−0.535592	−	0.927673i
$124$	−84358.7	+	48704.5i	−0.0442451	+	0.0255449i
$125$	21356.9			0.0109347
$126$		−	272466.i		−	0.136207i
$127$	−3.26714e6	+	1.88628e6i	−1.59498	+	0.920864i	−0.602550	+	0.798081i	$0.705849\pi$
$127$	−3.26714e6	+	1.88628e6i	−1.59498	+	0.920864i	−0.992433	+	0.122783i	$0.960818\pi$
$128$	−160530.	−	92681.9i	−0.0765466	−	0.0441942i
$129$	3.64734e6	−	2.10580e6i	1.69906	−	0.980950i
$130$	−1.25300e6	+	2.17025e6i	−0.570321	+	0.987825i
$131$	1.99584e6	−	3.45689e6i	0.887792	−	1.53770i	0.0453128	−	0.998973i	$-0.485572\pi$
$131$	1.99584e6	−	3.45689e6i	0.887792	−	1.53770i	0.842479	−	0.538728i	$-0.181095\pi$
$132$			769680.i			0.334648i
$133$	−1.72536e6	−	394304.i	−0.733372	−	0.167601i
$134$	−2.01813e6			−0.838752
$135$	2.51726e6	+	1.45334e6i	1.02312	+	0.590698i
$136$	−635985.	−	367186.i	−0.252831	−	0.145972i
$137$	1.81114e6	+	3.13699e6i	0.704353	+	1.21997i	0.966925	+	0.255062i	$0.0820960\pi$
$137$	1.81114e6	+	3.13699e6i	0.704353	+	1.21997i	−0.262572	+	0.964912i	$0.584571\pi$
$138$	−1.59287e6	+	2.75894e6i	−0.606100	+	1.04980i
$139$	782258.	+	1.35491e6i	0.291277	+	0.504506i	0.974112	−	0.226066i	$-0.0725866\pi$
$139$	782258.	+	1.35491e6i	0.291277	+	0.504506i	−0.682835	+	0.730572i	$0.739253\pi$
$140$	1.46246e6			0.532967
$141$			1.38318e6i			0.493424i
$142$	−637168.	−	1.10361e6i	−0.222530	−	0.385434i
$143$	1.72173e6	−	994043.i	0.588786	−	0.339936i
$144$	−191145.			−0.0640142
$145$			4.78073e6i			1.56816i
$146$	3.55649e6	−	2.05334e6i	1.14278	−	0.659786i
$147$	−1.33830e6	−	772666.i	−0.421309	−	0.243243i
$148$	779886.	−	450267.i	0.240572	−	0.138895i
$149$	937229.	−	1.62333e6i	0.283326	−	0.490736i	−0.688876	−	0.724880i	$-0.741895\pi$
$149$	937229.	−	1.62333e6i	0.283326	−	0.490736i	0.972202	+	0.234144i	$0.0752287\pi$
$150$	1.34763e6	−	2.33417e6i	0.399299	−	0.691606i
$151$		−	5.13009e6i		−	1.49003i	−0.667049	−	0.745014i	$-0.732443\pi$
$151$		−	5.13009e6i		−	1.49003i	0.667049	−	0.745014i	$-0.267557\pi$
$152$	−276619.	+	1.21041e6i	−0.0787684	+	0.344667i
$153$	−757277.			−0.211437
$154$	−1.00478e6	−	580110.i	−0.275111	−	0.158836i
$155$	−466919.	−	269576.i	−0.125385	−	0.0723911i
$156$	1.21096e6	+	2.09745e6i	0.318976	+	0.552482i
$157$	766688.	−	1.32794e6i	0.198116	−	0.343147i	−0.749802	−	0.661663i	$-0.769851\pi$
$157$	766688.	−	1.32794e6i	0.198116	−	0.343147i	0.947918	+	0.318516i	$0.103184\pi$
$158$	−1.57113e6	−	2.72128e6i	−0.398329	−	0.689926i
$159$	−3.99542e6			−0.993965
$160$		−	1.02597e6i		−	0.250482i
$161$	−2.40111e6	−	4.15884e6i	−0.575352	−	0.996539i
$162$	3.09947e6	−	1.78948e6i	0.729024	−	0.420902i
$163$	−1.39776e6			−0.322753			−0.161377	−	0.986893i	$-0.551593\pi$
$163$	−1.39776e6			−0.322753			−0.161377	+	0.986893i	$0.551593\pi$
$164$		−	2.10795e6i		−	0.477892i
$165$	−3.68937e6	+	2.13006e6i	−0.821297	+	0.474176i
$166$	−371676.	−	214587.i	−0.0812531	−	0.0469115i
$167$	−40250.6	+	23238.7i	−0.00864218	+	0.00498957i	−0.504315	−	0.863520i	$-0.668255\pi$
$167$	−40250.6	+	23238.7i	−0.00864218	+	0.00498957i	0.495673	+	0.868509i	$0.334922\pi$
$168$	706703.	−	1.22404e6i	0.149042	−	0.258148i
$169$	714519.	−	1.23758e6i	0.148031	−	0.256398i
$170$		−	4.06469e6i		−	0.827333i
$171$	377048.	+	1.22356e6i	0.0754064	+	0.244702i
$172$	4.45377e6			0.875271
$173$	2.87098e6	+	1.65756e6i	0.554487	+	0.320133i	0.750930	−	0.660382i	$-0.229606\pi$
$173$	2.87098e6	+	1.65756e6i	0.554487	+	0.320133i	−0.196443	+	0.980515i	$0.562939\pi$
$174$	4.00135e6	+	2.31018e6i	0.759555	+	0.438529i
$175$	2.03143e6	+	3.51854e6i	0.379042	+	0.656521i
$176$	−406970.	+	704892.i	−0.0746490	+	0.129296i
$177$	−1.22066e6	−	2.11425e6i	−0.220128	−	0.381273i
$178$	6.53853e6			1.15936
$179$		−	5.70566e6i		−	0.994825i	−0.867514	−	0.497413i	$-0.834284\pi$
$179$		−	5.70566e6i		−	0.994825i	0.867514	−	0.497413i	$-0.165716\pi$
$180$	−528987.	−	916232.i	−0.0907042	−	0.157104i
$181$	−4.13685e6	+	2.38841e6i	−0.697644	+	0.402785i	−0.806469	−	0.591276i	$-0.798624\pi$
$181$	−4.13685e6	+	2.38841e6i	−0.697644	+	0.402785i	0.108825	+	0.994061i	$0.465291\pi$
$182$	−3.65083e6			−0.605588
$183$			5.62056e6i			0.917121i
$184$	−2.91759e6	+	1.68447e6i	−0.468350	+	0.270402i
$185$	4.31661e6	+	2.49219e6i	0.681753	+	0.393610i
$186$	−451256.	+	260533.i	−0.0701269	+	0.0404878i
$187$	−1.61233e6	+	2.79263e6i	−0.246563	+	0.427060i
$188$	−731357.	+	1.26675e6i	−0.110067	+	0.190641i
$189$			4.23457e6i			0.627225i
$190$	−6.56747e6	+	2.02381e6i	−0.957496	+	0.295058i
$191$	9.79958e6			1.40640			0.703198	−	0.710994i	$-0.251755\pi$
$191$	9.79958e6			1.40640			0.703198	+	0.710994i	$0.251755\pi$
$192$	−858715.	−	495779.i	−0.121324	−	0.0700462i
$193$	−1.06396e7	−	6.14277e6i	−1.47997	−	0.854462i	−0.480228	−	0.877144i	$-0.659446\pi$
$193$	−1.06396e7	−	6.14277e6i	−1.47997	−	0.854462i	−0.999743	+	0.0226822i	$0.992779\pi$
$194$	−491598.	−	851474.i	−0.0673295	−	0.116618i
$195$	−6.70259e6	+	1.16092e7i	−0.903939	+	1.56567i
$196$	−817097.	−	1.41525e6i	−0.108519	−	0.187960i
$197$	8.16660e6			1.06818			0.534088	−	0.845429i	$-0.320655\pi$
$197$	8.16660e6			1.06818			0.534088	+	0.845429i	$0.320655\pi$
$198$			839326.i			0.108127i
$199$	−1.97996e6	−	3.42939e6i	−0.251245	−	0.435169i	0.712624	−	0.701546i	$-0.247507\pi$
$199$	−1.97996e6	−	3.42939e6i	−0.251245	−	0.435169i	−0.963869	+	0.266377i	$0.914173\pi$
$200$	2.46839e6	−	1.42513e6i	0.308549	−	0.178141i
$201$	−1.07955e7			−1.32939
$202$			8.24225e6i			0.999981i
$203$	−6.03166e6	+	3.48238e6i	−0.721022	+	0.416282i
$204$	−3.40205e6	−	1.96417e6i	−0.400728	−	0.231360i
$205$	1.01042e7	−	5.83368e6i	1.17285	−	0.677144i
$206$	−3.17355e6	+	5.49675e6i	−0.363031	+	0.628788i
$207$	−1.73701e6	+	3.00859e6i	−0.195835	+	0.339196i
$208$			2.56120e6i			0.284612i
$209$	5.31493e6	+	1.21465e6i	0.582182	+	0.133049i
$210$	7.82308e6			0.844734
$211$	−1.11124e7	−	6.41572e6i	−1.18293	−	0.682965i	−0.226239	−	0.974072i	$-0.572643\pi$
$211$	−1.11124e7	−	6.41572e6i	−1.18293	−	0.682965i	−0.956690	+	0.291107i	$0.905976\pi$
$212$	−3.65910e6	−	2.11258e6i	−0.384032	−	0.221721i
$213$	−3.40838e6	−	5.90348e6i	−0.352703	−	0.610899i
$214$	3.23514e6	−	5.60343e6i	0.330105	−	0.571759i
$215$	1.23256e7	+	2.13486e7i	1.24021	+	2.14810i
$216$	2.97071e6			0.294781
$217$		−	785457.i		−	0.0768676i
$218$	3.65664e6	+	6.33349e6i	0.352950	+	0.611327i
$219$	1.90246e7	−	1.09839e7i	1.81127	−	1.04574i
$220$	−4.50509e6			−0.423092
$221$			1.01469e7i			0.940064i
$222$	4.17181e6	−	2.40860e6i	0.381299	−	0.220143i
$223$	−8.01808e6	−	4.62924e6i	−0.723029	−	0.417441i	0.0928373	−	0.995681i	$-0.470406\pi$
$223$	−8.01808e6	−	4.62924e6i	−0.723029	−	0.417441i	−0.815867	+	0.578240i	$0.803740\pi$
$224$	1.29443e6	−	747340.i	0.115169	−	0.0664927i
$225$	1.46958e6	−	2.54538e6i	0.129016	−	0.223463i
$226$	−3.60463e6	+	6.24341e6i	−0.312274	+	0.540874i
$227$		−	1.44785e7i		−	1.23779i	−0.785474	−	0.618895i	$-0.787581\pi$
$227$		−	1.44785e7i		−	1.23779i	0.785474	−	0.618895i	$-0.212419\pi$
$228$	−1.47971e6	+	6.47477e6i	−0.124845	+	0.546286i
$229$	1.25888e7			1.04828			0.524142	−	0.851631i	$-0.324386\pi$
$229$	1.25888e7			1.04828			0.524142	+	0.851631i	$0.324386\pi$
$230$	−1.61486e7	−	9.32340e6i	−1.32725	−	0.766286i
$231$	−5.37482e6	−	3.10316e6i	−0.436042	−	0.251749i
$232$	2.44302e6	+	4.23144e6i	0.195643	+	0.338863i
$233$	−9.98600e6	+	1.72963e7i	−0.789448	+	1.36736i	0.136857	+	0.990591i	$0.456300\pi$
$233$	−9.98600e6	+	1.72963e7i	−0.789448	+	1.36736i	−0.926305	+	0.376774i	$0.877034\pi$
$234$	1.32054e6	+	2.28724e6i	0.103063	+	0.178511i
$235$	−8.09601e6			−0.623831
$236$		−	2.58171e6i		−	0.196413i
$237$	−8.40440e6	−	1.45568e7i	−0.631337	−	1.09351i
$238$	5.12826e6	−	2.96080e6i	0.380399	−	0.219623i
$239$	−3.71636e6			−0.272223			−0.136111	−	0.990694i	$-0.543460\pi$
$239$	−3.71636e6			−0.272223			−0.136111	+	0.990694i	$0.543460\pi$
$240$		−	5.48820e6i		−	0.397005i
$241$	1.26409e7	−	7.29824e6i	0.903083	−	0.521395i	0.0248838	−	0.999690i	$-0.492078\pi$
$241$	1.26409e7	−	7.29824e6i	0.903083	−	0.521395i	0.878199	+	0.478295i	$0.158745\pi$
$242$	−5.58364e6	−	3.22371e6i	−0.393977	−	0.227463i
$243$	6.21903e6	−	3.59056e6i	0.433415	−	0.250232i
$244$	−2.97188e6	+	5.14745e6i	−0.204579	+	0.354342i
$245$	4.52257e6	−	7.83331e6i	0.307529	−	0.532657i
$246$		−	1.12760e7i		−	0.757442i
$247$	1.63947e7	−	5.05214e6i	1.08796	−	0.335262i
$248$	−551029.			−0.0361259
$249$	−1.98819e6	−	1.14788e6i	−0.128783	−	0.0743531i
$250$	104627.	+	60406.3i	0.00669612	+	0.00386600i
$251$	593057.	+	1.02720e6i	0.0375038	+	0.0649585i	0.884168	−	0.467169i	$-0.154726\pi$
$251$	593057.	+	1.02720e6i	0.0375038	+	0.0649585i	−0.846664	+	0.532127i	$0.821393\pi$
$252$	770650.	−	1.33480e6i	0.0481565	−	0.0834096i
$253$	7.39656e6	+	1.28112e7i	0.456739	+	0.791096i
$254$	−2.13409e7			−1.30230
$255$		−	2.17431e7i		−	1.31129i
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	1.17257e7	−	6.76981e6i	0.690777	−	0.398820i	−0.113126	−	0.993581i	$-0.536086\pi$
$257$	1.17257e7	−	6.76981e6i	0.690777	−	0.398820i	0.803903	+	0.594761i	$0.202753\pi$
$258$	2.38244e7			1.38727
$259$			7.26146e6i			0.417950i
$260$	−1.22768e7	+	7.08801e6i	−0.698498	+	0.403278i
$261$	4.36342e6	+	2.51922e6i	0.245417	+	0.141692i
$262$	1.95551e7	−	1.12902e7i	1.08732	−	0.627764i
$263$	1.58665e6	−	2.74816e6i	0.0872195	−	0.151069i	−0.819115	−	0.573629i	$-0.805535\pi$
$263$	1.58665e6	−	2.74816e6i	0.0872195	−	0.151069i	0.906335	+	0.422560i	$0.138869\pi$
$264$	−2.17698e6	+	3.77065e6i	−0.118316	+	0.204929i
$265$		−	2.33860e7i		−	1.25666i
$266$	−7.33723e6	−	6.81174e6i	−0.389841	−	0.361920i
$267$	3.49763e7			1.83755
$268$	−9.88675e6	−	5.70812e6i	−0.513629	−	0.296544i
$269$	−1.66899e7	−	9.63590e6i	−0.857425	−	0.495035i	0.00572395	−	0.999984i	$-0.498178\pi$
$269$	−1.66899e7	−	9.63590e6i	−0.857425	−	0.495035i	−0.863149	+	0.504949i	$0.831511\pi$
$270$	8.22133e6	+	1.42398e7i	0.417687	+	0.723455i
$271$	−1.34916e7	+	2.33681e7i	−0.677882	+	1.17413i	0.297735	+	0.954648i	$0.403769\pi$
$271$	−1.34916e7	+	2.33681e7i	−0.677882	+	1.17413i	−0.975617	+	0.219478i	$0.929565\pi$
$272$	−2.07712e6	−	3.59767e6i	−0.103218	−	0.178778i
$273$	−1.95292e7			−0.959836
$274$			2.04907e7i			0.996105i
$275$	−6.25778e6	−	1.08388e7i	−0.300900	−	0.521175i
$276$	−1.56069e7	+	9.01066e6i	−0.742318	+	0.428577i
$277$	2.13762e7			1.00575			0.502876	−	0.864359i	$-0.332275\pi$
$277$	2.13762e7			1.00575			0.502876	+	0.864359i	$0.332275\pi$
$278$			8.85024e6i			0.411928i
$279$	−492089.	+	284108.i	−0.0226585	+	0.0130819i
$280$	7.16457e6	+	4.13647e6i	0.326374	+	0.188432i
$281$	−3.30568e7	+	1.90854e7i	−1.48985	+	0.860165i	−0.999933	−	0.0116045i	$-0.996306\pi$
$281$	−3.30568e7	+	1.90854e7i	−1.48985	+	0.860165i	−0.489917	+	0.871769i	$0.662973\pi$
$282$	−3.91222e6	+	6.77616e6i	−0.174452	+	0.302160i
$283$	−8.57278e6	+	1.48485e7i	−0.378236	+	0.655124i	−0.990806	−	0.135293i	$-0.956802\pi$
$283$	−8.57278e6	+	1.48485e7i	−0.378236	+	0.655124i	0.612570	+	0.790416i	$0.290136\pi$
$284$		−	7.20873e6i		−	0.314705i
$285$	−3.51311e7	+	1.08259e7i	−1.51760	+	0.467657i
$286$	1.12463e7			0.480742
$287$	1.47202e7	+	8.49874e6i	0.622686	+	0.359508i
$288$	−936417.	−	540641.i	−0.0392005	−	0.0226324i
$289$	3.83969e6	+	6.65053e6i	0.159075	+	0.275526i
$290$	−1.35219e7	+	2.34207e7i	−0.554428	+	0.960297i
$291$	−2.62969e6	−	4.55475e6i	−0.106715	−	0.184836i
$292$	2.32309e7			0.933078
$293$		−	3.74820e6i		−	0.149012i	−0.997221	−	0.0745058i	$-0.976262\pi$
$293$		−	3.74820e6i		−	0.149012i	0.997221	−	0.0745058i	$-0.0237379\pi$
$294$	−4.37086e6	−	7.57055e6i	−0.171999	−	0.297910i
$295$	1.23751e7	−	7.14477e6i	0.482039	−	0.278306i
$296$	5.09419e6			0.196427
$297$		−	1.30445e7i		−	0.497919i
$298$	9.18293e6	−	5.30177e6i	0.347003	−	0.200342i
$299$	4.03127e7	+	2.32745e7i	1.50809	+	0.870698i
$300$	1.32041e7	−	7.62337e6i	0.489039	−	0.282347i
$301$	−1.79565e7	+	3.11015e7i	−0.658448	+	1.14047i
$302$	1.45101e7	−	2.51322e7i	0.526805	−	0.912452i
$303$			4.40899e7i			1.58493i
$304$	−4.77870e6	+	5.14735e6i	−0.170094	+	0.183216i
$305$	−3.28982e7			−1.15951
$306$	−3.70988e6	−	2.14190e6i	−0.129478	−	0.0747542i
$307$	1.10333e7	+	6.37009e6i	0.381321	+	0.220156i	0.678393	−	0.734699i	$-0.262677\pi$
$307$	1.10333e7	+	6.37009e6i	0.381321	+	0.220156i	−0.297072	+	0.954855i	$0.596010\pi$
$308$	−3.28160e6	−	5.68389e6i	−0.112314	−	0.194533i
$309$	−1.69761e7	+	2.94035e7i	−0.575391	+	0.996607i
$310$	−1.52495e6	−	2.64129e6i	−0.0511883	−	0.0886607i
$311$	−2.90703e7			−0.966427			−0.483213	−	0.875503i	$-0.660530\pi$
$311$	−2.90703e7			−0.966427			−0.483213	+	0.875503i	$0.660530\pi$
$312$			1.37005e7i			0.451100i
$313$	−2.13040e7	−	3.68996e7i	−0.694749	−	1.20334i	−0.970265	−	0.242045i	$-0.922182\pi$
$313$	−2.13040e7	−	3.68996e7i	−0.694749	−	1.20334i	0.275516	−	0.961297i	$-0.411151\pi$
$314$	7.51198e6	−	4.33704e6i	0.242642	−	0.140089i
$315$	8.53097e6			0.272940
$316$		−	1.77754e7i		−	0.563322i
$317$	1.97235e6	−	1.13874e6i	0.0619165	−	0.0357475i	−0.468722	−	0.883346i	$-0.655285\pi$
$317$	1.97235e6	−	1.13874e6i	0.0619165	−	0.0357475i	0.530639	+	0.847598i	$0.321952\pi$
$318$	−1.95735e7	−	1.13008e7i	−0.608677	−	0.351420i
$319$	1.85804e7	−	1.07274e7i	0.572378	−	0.330463i
$320$	2.90189e6	−	5.02622e6i	0.0885587	−	0.153388i
$321$	1.73056e7	−	2.99742e7i	0.523205	−	0.906218i
$322$		−	2.71654e7i		−	0.813671i
$323$	−1.89322e7	+	2.03927e7i	−0.561815	+	0.605156i
$324$	2.02456e7			0.595246
$325$	−3.41061e7	−	1.96912e7i	−0.993533	−	0.573617i
$326$	−6.84762e6	−	3.95347e6i	−0.197645	−	0.114111i
$327$	1.95603e7	+	3.38795e7i	0.559413	+	0.968932i
$328$	5.96219e6	−	1.03268e7i	0.168960	−	0.292648i
$329$	−5.89730e6	−	1.02144e7i	−0.165602	−	0.286831i
$330$	−2.40989e7			−0.670586
$331$			2.99206e6i			0.0825062i	0.999149	+	0.0412531i	$0.0131350\pi$
$331$			2.99206e6i			0.0825062i	−0.999149	+	0.0412531i	$0.986865\pi$
$332$	−1.21389e6	−	2.10252e6i	−0.0331714	−	0.0574546i
$333$	4.54930e6	−	2.62654e6i	0.123200	−	0.0711298i
$334$	−262916.			−0.00705631
$335$		−	6.31880e7i		−	1.68074i
$336$	6.92424e6	−	3.99771e6i	0.182538	−	0.105389i
$337$	5.89875e7	+	3.40565e7i	1.54124	+	0.889836i	0.998761	+	0.0497666i	$0.0158477\pi$
$337$	5.89875e7	+	3.40565e7i	1.54124	+	0.889836i	0.542480	+	0.840069i	$0.317486\pi$
$338$	7.00083e6	−	4.04193e6i	0.181301	−	0.104674i
$339$	−1.92821e7	+	3.33976e7i	−0.494943	+	0.857267i
$340$	1.14967e7	−	1.99128e7i	0.292507	−	0.506636i
$341$			2.41959e6i			0.0610208i
$342$	−1.61360e6	+	7.06065e6i	−0.0403383	+	0.176509i
$343$	4.35345e7			1.07883
$344$	2.18189e7	+	1.25972e7i	0.535992	+	0.309455i
$345$	−8.63830e7	−	4.98733e7i	−2.10364	−	1.21454i
$346$	9.37657e6	+	1.62407e7i	0.226368	+	0.392082i
$347$	−1.54988e7	+	2.68446e7i	−0.370944	+	0.642494i	−0.989711	−	0.143081i	$-0.954299\pi$
$347$	−1.54988e7	+	2.68446e7i	−0.370944	+	0.642494i	0.618767	+	0.785575i	$0.287632\pi$
$348$	1.30684e7	+	2.26351e7i	0.310087	+	0.537086i
$349$	−3.27772e7			−0.771073			−0.385536	−	0.922693i	$-0.625984\pi$
$349$	−3.27772e7			−0.771073			−0.385536	+	0.922693i	$0.625984\pi$
$350$			2.29830e7i			0.536047i
$351$	−2.05234e7	−	3.55475e7i	−0.474600	−	0.822031i
$352$	−3.98747e6	+	2.30217e6i	−0.0914260	+	0.0527848i
$353$	3.47420e7			0.789824			0.394912	−	0.918719i	$-0.370775\pi$
$353$	3.47420e7			0.789824			0.394912	+	0.918719i	$0.370775\pi$
$354$		−	1.38102e7i		−	0.311308i
$355$	3.45542e7	−	1.99499e7i	0.772353	−	0.445918i
$356$	3.20321e7	+	1.84938e7i	0.709963	+	0.409897i
$357$	2.74324e7	−	1.58381e7i	0.602919	−	0.348095i
$358$	1.61380e7	−	2.79519e7i	0.351724	−	0.609203i
$359$	8.36199e6	−	1.44834e7i	0.180728	−	0.313031i	−0.761400	−	0.648282i	$-0.775488\pi$
$359$	8.36199e6	−	1.44834e7i	0.180728	−	0.313031i	0.942129	+	0.335251i	$0.108821\pi$
$360$		−	5.98480e6i		−	0.128275i
$361$	4.23756e7	+	2.04359e7i	0.900729	+	0.434382i
$362$	−2.70218e7			−0.569624
$363$	−2.98683e7	−	1.72445e7i	−0.624440	−	0.360520i
$364$	−1.78853e7	−	1.03261e7i	−0.370845	−	0.214108i
$365$	6.42906e7	+	1.11355e8i	1.32211	+	2.28997i
$366$	−1.58973e7	+	2.75350e7i	−0.324251	+	0.561619i
$367$	−2.15046e7	−	3.72470e7i	−0.435044	−	0.753518i	0.562256	−	0.826964i	$-0.309934\pi$
$367$	−2.15046e7	−	3.72470e7i	−0.435044	−	0.753518i	−0.997299	+	0.0734458i	$0.976600\pi$
$368$	−1.90576e7			−0.382406
$369$		−	1.22963e7i		−	0.244735i
$370$	1.40980e7	+	2.44184e7i	0.278325	+	0.482072i
$371$	2.95052e7	−	1.70348e7i	0.577798	−	0.333592i
$372$	−2.94759e6			−0.0572583
$373$		−	3.98490e7i		−	0.767875i	−0.923359	−	0.383938i	$-0.874568\pi$
$373$		−	3.98490e7i		−	0.767875i	0.923359	−	0.383938i	$-0.125432\pi$
$374$	−1.57975e7	+	9.12070e6i	−0.301977	+	0.174347i
$375$	559676.	+	323129.i	0.0106131	+	0.00612748i
$376$	−7.16581e6	+	4.13718e6i	−0.134804	+	0.0778289i
$377$	3.37556e7	−	5.84664e7i	0.629973	−	1.09114i
$378$	−1.19772e7	+	2.07451e7i	−0.221758	+	0.384096i
$379$			7.64993e6i			0.140521i	0.997529	+	0.0702603i	$0.0223830\pi$
$379$			7.64993e6i			0.140521i	−0.997529	+	0.0702603i	$0.977617\pi$
$380$	−3.78981e7	−	8.66102e6i	−0.690663	−	0.157840i
$381$	−1.14158e8			−2.06410
$382$	4.80080e7	+	2.77174e7i	0.861238	+	0.497236i
$383$	−1.53122e7	−	8.84053e6i	−0.272548	−	0.157355i	0.357497	−	0.933914i	$-0.383630\pi$
$383$	−1.53122e7	−	8.84053e6i	−0.272548	−	0.157355i	−0.630045	+	0.776559i	$0.716964\pi$
$384$	−2.80455e6	−	4.85762e6i	−0.0495301	−	0.0857887i
$385$	1.81634e7	−	3.14599e7i	0.318284	−	0.551284i
$386$	−3.47488e7	−	6.01866e7i	−0.604196	−	1.04650i
$387$	2.59801e7			0.448238
$388$		−	5.56180e6i		−	0.0952183i
$389$	4.27585e7	+	7.40598e7i	0.726396	+	1.25815i	0.958397	+	0.285439i	$0.0921393\pi$
$389$	4.27585e7	+	7.40598e7i	0.726396	+	1.25815i	−0.232001	+	0.972715i	$0.574527\pi$
$390$	−6.56717e7	+	3.79156e7i	−1.10709	+	0.639181i
$391$	−7.55021e7			−1.26307
$392$		−	9.24440e6i		−	0.153469i
$393$	1.04605e8	−	6.03940e7i	1.72336	−	0.994984i
$394$	4.00080e7	+	2.30986e7i	0.654121	+	0.377657i
$395$	8.52040e7	−	4.91926e7i	1.38251	−	0.798194i
$396$	−2.37397e6	+	4.11184e6i	−0.0382287	+	0.0662141i
$397$	−3.11422e7	+	5.39399e7i	−0.497712	+	0.862062i	−0.999997	−	0.00264036i	$-0.999160\pi$
$397$	−3.11422e7	+	5.39399e7i	−0.497712	+	0.862062i	0.502285	+	0.864702i	$0.332493\pi$
$398$		−	2.24007e7i		−	0.355314i
$399$	−3.92487e7	−	3.64377e7i	−0.617884	−	0.573631i
$400$	1.61235e7			0.251929
$401$	−9.69253e7	−	5.59598e7i	−1.50316	−	0.867847i	−0.999993	−	0.00365521i	$-0.998837\pi$
$401$	−9.69253e7	−	5.59598e7i	−1.50316	−	0.867847i	−0.503162	−	0.864192i	$-0.667830\pi$
$402$	−5.28868e7	−	3.05342e7i	−0.814084	−	0.470011i
$403$	3.80682e6	+	6.59361e6i	0.0581631	+	0.100741i
$404$	−2.33126e7	+	4.03786e7i	−0.353547	+	0.612361i
$405$	5.60290e7	+	9.70450e7i	0.843427	+	1.46086i
$406$	−3.93986e7			−0.588712
$407$		−	2.23688e7i		−	0.331787i
$408$	−1.11110e7	−	1.92449e7i	−0.163596	−	0.283357i
$409$	7.37939e7	−	4.26049e7i	1.07858	−	0.622716i	0.148064	−	0.988978i	$-0.452696\pi$
$409$	7.37939e7	−	4.26049e7i	1.07858	−	0.622716i	0.930512	+	0.366262i	$0.119363\pi$
$410$	6.60005e7			0.957626
$411$			1.09610e8i			1.57879i
$412$	−3.10943e7	+	1.79523e7i	−0.444620	+	0.256702i
$413$	1.80285e7	+	1.04088e7i	0.255924	+	0.147758i
$414$	−1.70191e7	+	9.82600e6i	−0.239848	+	0.138476i
$415$	6.71877e6	−	1.16373e7i	0.0940039	−	0.162819i
$416$	−7.24416e6	+	1.25473e7i	−0.100625	+	0.174288i
$417$			4.73422e7i			0.652891i
$418$	2.26022e7	+	2.09834e7i	0.309473	+	0.287308i
$419$	−3.18424e7			−0.432877			−0.216438	−	0.976296i	$-0.569444\pi$
$419$	−3.18424e7			−0.432877			−0.216438	+	0.976296i	$0.569444\pi$
$420$	3.83251e7	+	2.21270e7i	0.517292	+	0.298659i
$421$	−6.06508e7	−	3.50168e7i	−0.812813	−	0.469278i	0.0351191	−	0.999383i	$-0.488819\pi$
$421$	−6.06508e7	−	3.50168e7i	−0.812813	−	0.469278i	−0.847932	+	0.530106i	$0.822152\pi$
$422$	−3.62928e7	−	6.28610e7i	−0.482929	−	0.836458i
$423$	−4.26622e6	+	7.38931e6i	−0.0563666	+	0.0976299i
$424$	−1.19506e7	−	2.06990e7i	−0.156780	−	0.271551i
$425$	6.38778e7			0.832114
$426$		−	3.85614e7i		−	0.498797i
$427$	−2.39637e7	−	4.15064e7i	−0.307802	−	0.533128i
$428$	3.16978e7	−	1.83007e7i	0.404295	−	0.233420i
$429$	6.01594e7			0.761959
$430$			1.39449e8i			1.75392i
$431$	−1.34581e8	+	7.77005e7i	−1.68094	+	0.970492i	−0.719904	+	0.694074i	$0.755814\pi$
$431$	−1.34581e8	+	7.77005e7i	−1.68094	+	0.970492i	−0.961038	+	0.276418i	$0.910853\pi$
$432$	1.45535e7	+	8.40245e6i	0.180516	+	0.104221i
$433$	−9.96190e7	+	5.75151e7i	−1.22710	+	0.708464i	−0.966421	−	0.256962i	$-0.917278\pi$
$433$	−9.96190e7	+	5.75151e7i	−1.22710	+	0.708464i	−0.260675	+	0.965427i	$0.583945\pi$
$434$	2.22161e6	−	3.84794e6i	0.0271768	−	0.0470716i
$435$	−7.23323e7	+	1.25283e8i	−0.878749	+	1.52204i
$436$			4.13702e7i			0.499147i
$437$	3.75925e7	+	1.21992e8i	0.450460	+	1.46179i
$438$	1.24268e8			1.47890
$439$	−4.52580e7	−	2.61297e7i	−0.534935	−	0.308845i	0.208088	−	0.978110i	$-0.433276\pi$
$439$	−4.52580e7	−	2.61297e7i	−0.534935	−	0.308845i	−0.743024	+	0.669265i	$0.766609\pi$
$440$	−2.20703e7	−	1.27423e7i	−0.259090	−	0.149586i
$441$	−4.76636e6	−	8.25559e6i	−0.0555740	−	0.0962570i
$442$	−2.86998e7	+	4.97095e7i	−0.332363	+	0.575669i
$443$	6.87550e6	+	1.19087e7i	0.0790848	+	0.136979i	0.902855	−	0.429945i	$-0.141467\pi$
$443$	6.87550e6	+	1.19087e7i	0.0790848	+	0.136979i	−0.823771	+	0.566923i	$0.808134\pi$
$444$	2.72501e7			0.311329
$445$			2.04723e8i			2.32320i
$446$	−2.61869e7	−	4.53571e7i	−0.295175	−	0.511259i
$447$	4.91219e7	−	2.83605e7i	0.549987	−	0.317535i
$448$	8.45519e6			0.0940349
$449$		−	7.70844e7i		−	0.851584i	−0.904821	−	0.425792i	$-0.859996\pi$
$449$		−	7.70844e7i		−	0.851584i	0.904821	−	0.425792i	$-0.140004\pi$
$450$	1.43989e7	−	8.31318e6i	0.158012	−	0.0912283i
$451$	−4.53454e7	−	2.61802e7i	−0.494315	−	0.285393i
$452$	−3.53180e7	+	2.03909e7i	−0.382456	+	0.220811i
$453$	7.76182e7	−	1.34439e8i	0.834967	−	1.44620i
$454$	4.09515e7	−	7.09300e7i	0.437625	−	0.757988i
$455$		−	1.14308e8i		−	1.21351i
$456$	−2.55625e7	+	2.75345e7i	−0.269593	+	0.290391i
$457$	1.08364e8			1.13537			0.567684	−	0.823246i	$-0.307839\pi$
$457$	1.08364e8			1.13537			0.567684	+	0.823246i	$0.307839\pi$
$458$	6.16724e7	+	3.56066e7i	0.641940	+	0.370624i
$459$	5.76577e7	+	3.32887e7i	0.596238	+	0.344238i
$460$	−5.27411e7	−	9.13503e7i	−0.541846	−	0.938505i
$461$	4.17940e7	−	7.23893e7i	0.426590	−	0.738876i	−0.569977	−	0.821661i	$-0.693048\pi$
$461$	4.17940e7	−	7.23893e7i	0.426590	−	0.738876i	0.996567	+	0.0827843i	$0.0263813\pi$
$462$	−1.75541e7	−	3.04046e7i	−0.178013	−	0.308328i
$463$	−2.59107e7			−0.261058			−0.130529	−	0.991445i	$-0.541668\pi$
$463$	−2.59107e7			−0.261058			−0.130529	+	0.991445i	$0.541668\pi$
$464$			2.76397e7i			0.276681i
$465$	−8.15735e6	−	1.41289e7i	−0.0811316	−	0.140524i
$466$	−9.78424e7	+	5.64893e7i	−0.966873	+	0.558224i
$467$	−3.79527e7			−0.372643			−0.186321	−	0.982489i	$-0.559657\pi$
$467$	−3.79527e7			−0.372643			−0.186321	+	0.982489i	$0.559657\pi$
$468$			1.49402e7i			0.145754i
$469$	7.97218e7	−	4.60274e7i	0.772785	−	0.446167i
$470$	−3.96622e7	−	2.28990e7i	−0.382017	−	0.220558i
$471$	4.01835e7	−	2.31999e7i	0.384578	−	0.222036i
$472$	7.30217e6	−	1.26477e7i	0.0694426	−	0.120278i
$473$	5.53146e7	−	9.58077e7i	0.522705	−	0.905351i
$474$		−	9.50849e7i		−	0.892846i
$475$	−3.18047e7	−	1.03210e8i	−0.296763	−	0.963029i
$476$	3.34977e7			0.310594
$477$	−2.13446e7	−	1.23233e7i	−0.196668	−	0.113546i
$478$	−1.82064e7	−	1.05115e7i	−0.166702	−	0.0962452i
$479$	−5.35700e7	−	9.27859e7i	−0.487433	−	0.844259i	0.512463	−	0.858710i	$-0.328733\pi$
$479$	−5.35700e7	−	9.27859e7i	−0.487433	−	0.844259i	−0.999896	+	0.0144509i	$0.995400\pi$
$480$	1.55230e7	−	2.68866e7i	0.140362	−	0.243115i
$481$	−3.51936e7	−	6.09571e7i	−0.316248	−	0.547758i
$482$	8.25702e7			0.737364
$483$		−	1.45315e8i		−	1.28964i
$484$	−1.82361e7	−	3.15858e7i	−0.160840	−	0.278584i
$485$	2.66598e7	−	1.53921e7i	0.233686	−	0.134919i
$486$	4.06225e7			0.353882
$487$			9.65660e6i			0.0836060i	0.999126	+	0.0418030i	$0.0133102\pi$
$487$			9.65660e6i			0.0836060i	−0.999126	+	0.0418030i	$0.986690\pi$
$488$	−2.91184e7	+	1.68115e7i	−0.250558	+	0.144659i
$489$	−3.66297e7	−	2.11481e7i	−0.313261	−	0.180861i
$490$	4.43119e7	−	2.55835e7i	0.376645	−	0.217456i
$491$	−1.14431e8	+	1.98201e8i	−0.966719	+	1.67441i	−0.261795	+	0.965124i	$0.584314\pi$
$491$	−1.14431e8	+	1.98201e8i	−0.966719	+	1.67441i	−0.704924	+	0.709283i	$0.749019\pi$
$492$	3.18933e7	−	5.52408e7i	0.267796	−	0.463836i
$493$			1.09502e8i			0.913867i
$494$	9.46071e7	+	2.16210e7i	0.784771	+	0.179347i
$495$	−2.62795e7			−0.216671
$496$	−2.69948e6	−	1.55854e6i	−0.0221225	−	0.0127724i
$497$	5.03400e7	+	2.90638e7i	0.410057	+	0.236746i
$498$	−6.49340e6	−	1.12469e7i	−0.0525756	−	0.0910636i
$499$	5.16131e6	−	8.93965e6i	0.0415392	−	0.0719480i	−0.844508	−	0.535542i	$-0.820107\pi$
$499$	5.16131e6	−	8.93965e6i	0.0415392	−	0.0719480i	0.886048	+	0.463594i	$0.153441\pi$
$500$	341710.	+	591859.i	0.00273368	+	0.00473487i
$501$	−1.40641e6			−0.0111840
$502$			6.70967e6i			0.0530384i
$503$	1.08838e8	+	1.88513e8i	0.855217	+	1.48128i	0.876444	+	0.481505i	$0.159910\pi$
$503$	1.08838e8	+	1.88513e8i	0.855217	+	1.48128i	−0.0212266	+	0.999775i	$0.506757\pi$
$504$	7.55079e6	−	4.35945e6i	0.0589795	−	0.0340518i
$505$	−2.58067e8			−2.00382
$506$			8.36826e7i			0.645927i
$507$	3.74492e7	−	2.16213e7i	0.287355	−	0.165905i
$508$	−1.04548e8	−	6.03611e7i	−0.797492	−	0.460432i
$509$	4.33345e7	−	2.50192e7i	0.328610	−	0.189723i	−0.326614	−	0.945158i	$-0.605908\pi$
$509$	4.33345e7	−	2.50192e7i	0.328610	−	0.189723i	0.655224	+	0.755435i	$0.272574\pi$
$510$	6.14987e7	−	1.06519e8i	0.463613	−	0.803001i
$511$	−9.36612e7	+	1.62226e8i	−0.701935	+	1.21579i
$512$		−	5.93164e6i		−	0.0441942i
$513$	2.50780e7	−	1.09734e8i	0.185755	−	0.812811i
$514$	7.65916e7			0.564017
$515$	−1.72104e8	−	9.93646e7i	−1.26000	−	0.727461i
$516$	1.16715e8	+	6.73855e7i	0.849528	+	0.490475i
$517$	1.81665e7	+	3.14653e7i	0.131462	+	0.227699i
$518$	−2.05385e7	+	3.55737e7i	−0.147768	+	0.255941i
$519$	5.01577e7	+	8.68756e7i	0.358786	+	0.621435i
$520$	−8.01917e7			−0.570321
$521$			6.03994e7i			0.427090i	0.976933	+	0.213545i	$0.0685010\pi$
$521$			6.03994e7i			0.427090i	−0.976933	+	0.213545i	$0.931499\pi$
$522$	1.42509e7	+	2.46832e7i	0.100191	+	0.173536i
$523$	2.19693e8	−	1.26840e8i	1.53571	−	0.886645i	0.536631	−	0.843817i	$-0.319697\pi$
$523$	2.19693e8	−	1.26840e8i	1.53571	−	0.886645i	0.999082	−	0.0428278i	$-0.0136367\pi$
$524$	1.27734e8			0.887792
$525$			1.22942e8i			0.849616i
$526$	1.55459e7	−	8.97544e6i	0.106822	−	0.0616735i
$527$	−1.06948e7	−	6.17462e6i	−0.0730700	−	0.0421870i
$528$	−2.13300e7	+	1.23149e7i	−0.144907	+	0.0836621i
$529$	−9.91654e7	+	1.71759e8i	−0.669874	+	1.16026i
$530$	6.61455e7	−	1.14567e8i	0.444296	−	0.769544i
$531$		−	1.50598e7i		−	0.100586i
$532$	−1.66785e7	−	5.41234e7i	−0.110770	−	0.359460i
$533$	−1.64761e8			−1.08811
$534$	1.71348e8	+	9.89278e7i	1.12527	+	0.649673i
$535$	1.75445e8	+	1.01293e8i	1.14572	+	0.661483i
$536$	−3.22900e7	−	5.59279e7i	−0.209688	−	0.363190i
$537$	8.63265e7	−	1.49522e8i	0.557470	−	0.965566i
$538$	−5.45089e7	−	9.44122e7i	−0.350042	−	0.606291i
$539$	−4.05925e7			−0.259226
$540$			9.30137e7i			0.590698i
$541$	−1.37281e7	−	2.37778e7i	−0.0867000	−	0.150169i	0.819414	−	0.573202i	$-0.194299\pi$
$541$	−1.37281e7	−	2.37778e7i	−0.0867000	−	0.150169i	−0.906114	+	0.423033i	$0.860965\pi$
$542$	−1.32190e8	+	7.63198e7i	−0.830233	+	0.479335i
$543$	−1.44546e8			−0.902834
$544$		−	2.34999e7i		−	0.145972i
$545$	−1.98303e8	+	1.14490e8i	−1.22501	+	0.707261i
$546$	−9.56732e7	−	5.52370e7i	−0.587777	−	0.339353i
$547$	−1.18747e8	+	6.85586e7i	−0.725539	+	0.418890i	−0.816788	−	0.576938i	$-0.804247\pi$
$547$	−1.18747e8	+	6.85586e7i	−0.725539	+	0.418890i	0.0912493	+	0.995828i	$0.470914\pi$
$548$	−5.79565e7	+	1.00384e8i	−0.352176	+	0.609987i
$549$	−1.73358e7	+	3.00266e7i	−0.104768	+	0.181463i
$550$		−	7.07988e7i		−	0.425537i
$551$	1.76927e8	−	5.45212e7i	1.05764	−	0.325920i
$552$	−1.01944e8			−0.606100
$553$	1.24129e8	+	7.16657e7i	0.734001	+	0.423776i
$554$	1.04721e8	+	6.04609e7i	0.615894	+	0.355587i
$555$	7.54137e7	+	1.30620e8i	0.441135	+	0.764068i
$556$	−2.50323e7	+	4.33572e7i	−0.145638	+	0.252253i
$557$	1.66050e8	+	2.87607e8i	0.960887	+	1.66431i	0.720280	+	0.693683i	$0.244013\pi$
$557$	1.66050e8	+	2.87607e8i	0.960887	+	1.66431i	0.240607	+	0.970623i	$0.422653\pi$
$558$	−3.21431e6			−0.0185006
$559$		−	3.48113e8i		−	1.99290i
$560$	2.33994e7	+	4.05289e7i	0.133242	+	0.230782i
$561$	−8.45049e7	+	4.87889e7i	−0.478623	+	0.276333i
$562$	−2.15926e8			−1.21646
$563$		−	268186.i		−	0.00150283i	−1.00000		0.000751416i	$-0.999761\pi$
$563$		−	268186.i		−	0.00150283i	1.00000		0.000751416i	$-0.000239183\pi$
$564$	−3.83317e7	+	2.21308e7i	−0.213659	+	0.123356i
$565$	−1.95483e8	−	1.12862e8i	−1.08383	−	0.625752i
$566$	−8.39958e7	+	4.84950e7i	−0.463242	+	0.267453i
$567$	−8.16253e7	+	1.41379e8i	−0.447791	+	0.775597i
$568$	2.03894e7	−	3.53154e7i	0.111265	−	0.192717i
$569$			7.93681e7i			0.430833i	0.976522	+	0.215417i	$0.0691109\pi$
$569$			7.93681e7i			0.430833i	−0.976522	+	0.215417i	$0.930889\pi$
$570$	−2.02727e8	−	4.63300e7i	−1.09468	−	0.250171i
$571$	−3.89825e7			−0.209393			−0.104696	−	0.994504i	$-0.533387\pi$
$571$	−3.89825e7			−0.209393			−0.104696	+	0.994504i	$0.533387\pi$
$572$	5.50954e7	+	3.18094e7i	0.294393	+	0.169968i
$573$	2.56807e8	+	1.48268e8i	1.36503	+	0.788101i
$574$	4.80761e7	+	8.32703e7i	0.254211	+	0.440306i
$575$	1.46520e8	−	2.53780e8i	0.770714	−	1.33492i
$576$	−3.05832e6	−	5.29717e6i	−0.0160035	−	0.0277189i
$577$	2.10878e8			1.09775			0.548874	−	0.835905i	$-0.315057\pi$
$577$	2.10878e8			1.09775			0.548874	+	0.835905i	$0.315057\pi$
$578$			4.34411e7i			0.224966i
$579$	−1.85880e8	−	3.21954e8i	−0.957629	−	1.65866i
$580$	−1.32487e8	+	7.64916e7i	−0.679033	+	0.392040i
$581$	1.95764e7			0.0998168
$582$		−	2.97515e7i		−	0.150918i
$583$	−9.08901e7	+	5.24754e7i	−0.458681	+	0.264820i
$584$	1.13808e8	+	6.57070e7i	0.571391	+	0.329893i
$585$	−7.16141e7	+	4.13464e7i	−0.357710	+	0.206524i
$586$	1.06015e7	−	1.83624e7i	0.0526836	−	0.0912506i
$587$	1.39761e8	−	2.42073e8i	0.690990	−	1.19683i	−0.280524	−	0.959847i	$-0.590508\pi$
$587$	1.39761e8	−	2.42073e8i	0.690990	−	1.19683i	0.971514	−	0.236983i	$-0.0761585\pi$
$588$		−	4.94506e7i		−	0.243243i
$589$	−4.65165e6	+	2.03543e7i	−0.0227646	+	0.0996114i
$590$	8.08338e7			0.393584
$591$	2.14013e8	+	1.23560e8i	1.03676	+	0.598573i
$592$	2.49564e7	+	1.44086e7i	0.120286	+	0.0694473i
$593$	−2.74668e7	−	4.75739e7i	−0.131718	−	0.228142i	0.792621	−	0.609714i	$-0.208716\pi$
$593$	−2.74668e7	−	4.75739e7i	−0.131718	−	0.228142i	−0.924339	+	0.381573i	$0.875383\pi$
$594$	3.68954e7	−	6.39048e7i	0.176041	−	0.304912i
$595$	9.27034e7	+	1.60567e8i	0.440093	+	0.762264i
$596$	5.99827e7			0.283326
$597$		−	1.19827e8i		−	0.563161i
$598$	1.31661e8	+	2.28043e8i	0.615676	+	1.06638i
$599$	−8.23808e7	+	4.75626e7i	−0.383306	+	0.221302i	−0.679256	−	0.733902i	$-0.737697\pi$
$599$	−8.23808e7	+	4.75626e7i	−0.383306	+	0.221302i	0.295950	+	0.955204i	$0.404364\pi$
$600$	8.62486e7			0.399299
$601$		−	3.86766e8i		−	1.78166i	−0.454335	−	0.890831i	$-0.650123\pi$
$601$		−	3.86766e8i		−	1.78166i	0.454335	−	0.890831i	$-0.349877\pi$
$602$	−1.75937e8	+	1.01577e8i	−0.806431	+	0.465593i
$603$	−5.76723e7	−	3.32971e7i	−0.263036	−	0.151864i
$604$	1.42169e8	−	8.20815e7i	0.645201	−	0.372507i
$605$	1.00935e8	−	1.74825e8i	0.455802	−	0.789473i
$606$	−1.24705e8	+	2.15996e8i	−0.560359	+	0.970570i
$607$			1.97703e8i			0.883991i	0.897017	+	0.441996i	$0.145729\pi$
$607$			1.97703e8i			0.883991i	−0.897017	+	0.441996i	$0.854271\pi$
$608$	−3.79696e7	+	1.17006e7i	−0.168937	+	0.0520591i
$609$	−2.10753e8			−0.933088
$610$	−1.61168e8	−	9.30503e7i	−0.710050	−	0.409947i
$611$	9.90110e7	+	5.71640e7i	0.434070	+	0.250610i
$612$	−1.21164e7	−	2.09863e7i	−0.0528592	−	0.0915548i
$613$	1.70841e7	−	2.95905e7i	0.0741668	−	0.128461i	−0.826557	−	0.562853i	$-0.809704\pi$
$613$	1.70841e7	−	2.95905e7i	0.0741668	−	0.128461i	0.900724	+	0.434393i	$0.143037\pi$
$614$	3.60347e7	+	6.24138e7i	0.155674	+	0.269635i
$615$	3.53054e8			1.51780
$616$		−	3.71270e7i		−	0.158836i
$617$	−1.24477e8	−	2.15601e8i	−0.529950	−	0.917901i	−0.999390	−	0.0349361i	$-0.988877\pi$
$617$	−1.24477e8	−	2.15601e8i	−0.529950	−	0.917901i	0.469439	−	0.882965i	$-0.344456\pi$
$618$	−1.66331e8	+	9.60315e7i	−0.704707	+	0.406863i
$619$	−1.04027e8			−0.438607			−0.219304	−	0.975657i	$-0.570379\pi$
$619$	−1.04027e8			−0.438607			−0.219304	+	0.975657i	$0.570379\pi$
$620$		−	1.72528e7i		−	0.0723911i
$621$	2.64505e8	−	1.52712e8i	1.10448	−	0.637674i
$622$	−1.42415e8	−	8.22233e7i	−0.591813	−	0.341683i
$623$	−2.58291e8	+	1.49124e8i	−1.06818	+	0.616715i
$624$	−3.87509e7	+	6.71185e7i	−0.159488	+	0.276241i
$625$	1.21121e8	−	2.09788e8i	0.496112	−	0.859291i
$626$		−	2.41027e8i		−	0.982524i
$627$	1.20905e8	+	1.12246e8i	0.490503	+	0.455373i
$628$	4.90680e7			0.198116
$629$	9.88717e7	+	5.70836e7i	0.397302	+	0.229382i
$630$	4.17930e7	+	2.41292e7i	0.167141	+	0.0964987i
$631$	−5.84795e7	−	1.01289e8i	−0.232764	−	0.403159i	0.725857	−	0.687846i	$-0.241444\pi$
$631$	−5.84795e7	−	1.01289e8i	−0.232764	−	0.403159i	−0.958620	+	0.284687i	$0.908110\pi$
$632$	5.02763e7	−	8.70811e7i	0.199165	−	0.344963i
$633$	−1.94140e8	−	3.36260e8i	−0.765425	−	1.32576i
$634$	1.28833e7			0.0505546
$635$		−	6.68187e8i		−	2.60962i
$636$	−6.39267e7	−	1.10724e8i	−0.248491	−	0.430399i
$637$	−1.10618e8	+	6.38656e7i	−0.427966	+	0.247086i
$638$	1.21367e8			0.467345
$639$		−	4.20506e7i		−	0.161165i
$640$	2.84326e7	−	1.64156e7i	0.108462	−	0.0626205i
$641$	5.91355e6	+	3.41419e6i	0.0224530	+	0.0129632i	0.511184	−	0.859471i	$-0.329207\pi$
$641$	5.91355e6	+	3.41419e6i	0.0224530	+	0.0129632i	−0.488731	+	0.872434i	$0.662540\pi$
$642$	1.69560e8	−	9.78953e7i	0.640793	−	0.369962i
$643$	5.14263e7	−	8.90730e7i	0.193443	−	0.335053i	−0.752946	−	0.658082i	$-0.771368\pi$
$643$	5.14263e7	−	8.90730e7i	0.193443	−	0.335053i	0.946389	+	0.323029i	$0.104701\pi$
$644$	7.68354e7	−	1.33083e8i	0.287676	−	0.498270i
$645$			7.45946e8i			2.77989i
$646$	−1.50428e8	+	4.63552e7i	−0.557995	+	0.171950i
$647$	−2.19897e8			−0.811906			−0.405953	−	0.913894i	$-0.633060\pi$
$647$	−2.19897e8			−0.811906			−0.405953	+	0.913894i	$0.633060\pi$
$648$	9.91829e7	+	5.72633e7i	0.364512	+	0.210451i
$649$	−5.55366e7	−	3.20641e7i	−0.203163	−	0.117296i
$650$	−1.11390e8	−	1.92933e8i	−0.405608	−	0.702534i
$651$	1.18840e7	−	2.05836e7i	0.0430743	−	0.0746068i
$652$	−2.23642e7	−	3.87360e7i	−0.0806884	−	0.139756i
$653$	−2.89540e7			−0.103985			−0.0519924	−	0.998647i	$-0.516557\pi$
$653$	−2.89540e7			−0.103985			−0.0519924	+	0.998647i	$0.516557\pi$
$654$			2.21300e8i			0.791130i
$655$	3.53498e8	+	6.12276e8i	1.25795	+	2.17883i
$656$	5.84173e7	−	3.37273e7i	0.206933	−	0.119473i
$657$	1.35513e8			0.477842
$658$		−	6.67203e7i		−	0.234196i
$659$	−1.47152e8	+	8.49585e7i	−0.514175	+	0.296859i	−0.734548	−	0.678557i	$-0.762606\pi$
$659$	−1.47152e8	+	8.49585e7i	−0.514175	+	0.296859i	0.220373	+	0.975416i	$0.429273\pi$
$660$	−1.18060e8	−	6.81619e7i	−0.410649	−	0.237088i
$661$	1.32302e8	−	7.63846e7i	0.458102	−	0.264485i	−0.253144	−	0.967429i	$-0.581465\pi$
$661$	1.32302e8	−	7.63846e7i	0.458102	−	0.264485i	0.711246	+	0.702943i	$0.248131\pi$
$662$	−8.46283e6	+	1.46580e7i	−0.0291703	+	0.0505245i
$663$	−1.53523e8	+	2.65909e8i	−0.526783	+	0.912415i
$664$		−	1.37336e7i		−	0.0469115i
$665$	2.13277e8	−	2.29730e8i	0.725236	−	0.781185i
$666$	2.97159e7			0.100593
$667$	4.35042e8	+	2.51172e8i	1.46607	+	0.846434i
$668$	−1.28802e6	−	743639.i	−0.00432109	−	0.00249478i
$669$	−1.40081e8	−	2.42627e8i	−0.467843	−	0.810327i
$670$	1.78723e8	−	3.09557e8i	0.594231	−	1.02924i
$671$	7.38199e7	+	1.27860e8i	0.244346	+	0.423220i
$672$	4.52290e7			0.149042
$673$			4.56476e8i			1.49752i	0.662841	+	0.748760i	$0.269350\pi$
$673$			4.56476e8i			1.49752i	−0.662841	+	0.748760i	$0.730650\pi$
$674$	1.92652e8	+	3.33684e8i	0.629209	+	1.08982i
$675$	−2.23782e8	+	1.29201e8i	−0.727635	+	0.420100i
$676$	4.57292e7			0.148031
$677$			2.92182e7i			0.0941645i	0.998891	+	0.0470823i	$0.0149923\pi$
$677$			2.92182e7i			0.0941645i	−0.998891	+	0.0470823i	$0.985008\pi$
$678$	−1.88925e8	+	1.09076e8i	−0.606179	+	0.349978i
$679$	3.88391e7	+	2.24238e7i	0.124068	+	0.0716308i
$680$	1.12644e8	−	6.50350e7i	0.358246	−	0.206833i
$681$	2.19060e8	−	3.79423e8i	0.693620	−	1.20138i
$682$	−6.84362e6	+	1.18535e7i	−0.0215741	+	0.0373675i
$683$		−	8.90521e7i		−	0.279500i	−0.990187	−	0.139750i	$-0.955370\pi$
$683$		−	8.90521e7i		−	0.279500i	0.990187	−	0.139750i	$-0.0446299\pi$
$684$	−2.78755e7	+	3.00260e7i	−0.0871073	+	0.0938273i
$685$	−6.41569e8			−1.99605
$686$	2.13275e8	+	1.23134e8i	0.660643	+	0.381422i
$687$	3.29902e8	+	1.90469e8i	1.01745	+	0.587427i
$688$	7.12603e7	+	1.23426e8i	0.218818	+	0.379003i
$689$	−1.65123e8	+	2.86001e8i	−0.504835	+	0.874400i
$690$	−2.82126e8	−	4.88656e8i	−0.858807	−	1.48750i
$691$	−3.25907e8			−0.987778			−0.493889	−	0.869525i	$-0.664425\pi$
$691$	−3.25907e8			−0.987778			−0.493889	+	0.869525i	$0.664425\pi$
$692$			1.06084e8i			0.320133i
$693$	−1.91425e7	−	3.31558e7i	−0.0575174	−	0.0996231i
$694$	−1.51856e8	+	8.76742e7i	−0.454312	+	0.262297i
$695$	−2.77103e8			−0.825443
$696$			1.47852e8i			0.438529i
$697$	2.31437e8	−	1.33620e8i	0.683494	−	0.394615i
$698$	−1.60575e8	−	9.27079e7i	−0.472184	−	0.272615i
$699$	−5.23384e8	+	3.02176e8i	−1.53246	+	0.884766i
$700$	−6.50058e7	+	1.12593e8i	−0.189521	+	0.328260i
$701$	−2.49213e8	+	4.31650e8i	−0.723464	+	1.25308i	0.236139	+	0.971719i	$0.424118\pi$
$701$	−2.49213e8	+	4.31650e8i	−0.723464	+	1.25308i	−0.959603	+	0.281357i	$0.909215\pi$
$702$		−	2.32196e8i		−	0.671185i
$703$	4.30039e7	−	1.88173e8i	0.123778	−	0.541615i
$704$	−2.60461e7			−0.0746490
$705$	−2.12163e8	−	1.22492e8i	−0.605484	−	0.349576i
$706$	1.70200e8	+	9.82651e7i	0.483666	+	0.279245i
$707$	−1.87981e8	−	3.25593e8i	−0.531932	−	0.921333i
$708$	3.90612e7	−	6.76559e7i	0.110064	−	0.190636i
$709$	−8.62323e7	−	1.49359e8i	−0.241953	−	0.419075i	0.719317	−	0.694682i	$-0.244455\pi$
$709$	−8.62323e7	−	1.49359e8i	−0.241953	−	0.419075i	−0.961271	+	0.275606i	$0.911121\pi$
$710$	2.25707e8			0.630624
$711$		−	1.03689e8i		−	0.288485i
$712$	1.04616e8	+	1.81201e8i	0.289841	+	0.502020i
$713$	−4.90623e7	+	2.83261e7i	−0.135357	+	0.0781481i
$714$	1.79188e8			0.492281
$715$			3.52125e8i			0.963337i
$716$	1.58120e8	−	9.12905e7i	0.430772	−	0.248706i
$717$	−9.73906e7	−	5.62285e7i	−0.264216	−	0.152545i
$718$	8.19304e7	−	4.73026e7i	0.221346	−	0.127794i
$719$	7.58107e7	−	1.31308e8i	0.203959	−	0.353268i	−0.745841	−	0.666124i	$-0.767952\pi$
$719$	7.58107e7	−	1.31308e8i	0.203959	−	0.353268i	0.949801	+	0.312856i	$0.101286\pi$
$720$	1.69276e7	−	2.93194e7i	0.0453521	−	0.0785521i
$721$		−	2.89517e8i		−	0.772445i
$722$	1.49796e8	+	2.19971e8i	0.398004	+	0.584459i
$723$	4.41689e8			1.16870
$724$	−1.32379e8	−	7.64291e7i	−0.348822	−	0.201392i
$725$	−3.68063e8	−	2.12501e8i	−0.965846	−	0.557632i
$726$	−9.75494e7	−	1.68961e8i	−0.254926	−	0.441546i
$727$	2.98431e8	−	5.16898e8i	0.776677	−	1.34524i	−0.157169	−	0.987572i	$-0.550237\pi$
$727$	2.98431e8	−	5.16898e8i	0.776677	−	1.34524i	0.933847	−	0.357673i	$-0.116430\pi$
$728$	−5.84133e7	−	1.01175e8i	−0.151397	−	0.262227i
$729$	−2.43921e8			−0.629602
$730$			7.27365e8i			1.86975i
$731$	2.82318e8	+	4.88989e8i	0.722748	+	1.25184i
$732$	−1.55762e8	+	8.99290e7i	−0.397125	+	0.229280i
$733$	−2.56851e8			−0.652183			−0.326092	−	0.945338i	$-0.605732\pi$
$733$	−2.56851e8			−0.652183			−0.326092	+	0.945338i	$0.605732\pi$
$734$		−	2.43297e8i		−	0.615245i
$735$	2.37036e8	−	1.36853e8i	0.596969	−	0.344660i
$736$	−9.33627e7	−	5.39030e7i	−0.234175	−	0.135201i
$737$	−2.45582e8	+	1.41787e8i	−0.613470	+	0.354187i
$738$	3.47792e7	−	6.02394e7i	0.0865268	−	0.149869i
$739$	−2.21828e8	+	3.84217e8i	−0.549645	+	0.952014i	0.448653	+	0.893706i	$0.351904\pi$
$739$	−2.21828e8	+	3.84217e8i	−0.549645	+	0.952014i	−0.998299	+	0.0583078i	$0.981430\pi$
$740$			1.59500e8i			0.393610i
$741$	5.06078e8	+	1.15656e8i	1.24383	+	0.284259i
$742$	1.92727e8			0.471770
$743$	−2.77139e6	−	1.60006e6i	−0.00675664	−	0.00390095i	0.496618	−	0.867969i	$-0.334575\pi$
$743$	−2.77139e6	−	1.60006e6i	−0.00675664	−	0.00390095i	−0.503375	+	0.864068i	$0.667908\pi$
$744$	−1.44402e7	−	8.33705e6i	−0.0350634	−	0.0202439i
$745$	1.66000e8	+	2.87520e8i	0.401456	+	0.695343i
$746$	1.12710e8	−	1.95219e8i	0.271485	−	0.470226i
$747$	−7.08096e6	−	1.22646e7i	−0.0169875	−	0.0294233i
$748$	−1.03189e8			−0.246563
$749$			2.95136e8i			0.702387i
$750$	1.82789e6	+	3.16600e6i	0.00433278	+	0.00750460i
$751$	3.36224e8	−	1.94119e8i	0.793796	−	0.458298i	−0.0475015	−	0.998871i	$-0.515126\pi$
$751$	3.36224e8	−	1.94119e8i	0.793796	−	0.458298i	0.841297	+	0.540573i	$0.181793\pi$
$752$	−4.68069e7			−0.110067
$753$			3.58918e7i			0.0840639i
$754$	3.30736e8	−	1.90951e8i	0.771556	−	0.445458i
$755$	7.86896e8	+	4.54315e8i	1.82842	+	1.05564i
$756$	−1.17352e8	+	6.77531e7i	−0.271597	+	0.156806i
$757$	1.11243e8	−	1.92678e8i	0.256439	−	0.444165i	−0.708847	−	0.705363i	$-0.750784\pi$
$757$	1.11243e8	−	1.92678e8i	0.256439	−	0.444165i	0.965285	+	0.261198i	$0.0841175\pi$
$758$	−2.16373e7	+	3.74769e7i	−0.0496815	+	0.0860509i
$759$			4.47639e8i			1.02377i
$760$	−1.61165e8	−	1.49622e8i	−0.367138	−	0.340843i
$761$	−5.42429e8			−1.23080			−0.615402	−	0.788213i	$-0.711006\pi$
$761$	−5.42429e8			−1.23080			−0.615402	+	0.788213i	$0.711006\pi$
$762$	−5.59256e8	−	3.22887e8i	−1.26400	−	0.729769i
$763$	−2.88896e8	−	1.66794e8i	−0.650381	−	0.375498i
$764$	1.56793e8	+	2.71574e8i	0.351599	+	0.608987i
$765$	6.70635e7	−	1.16157e8i	0.149797	−	0.259455i
$766$	−5.00096e7	−	8.66191e7i	−0.111267	−	0.192720i
$767$	−2.01790e8			−0.447212
$768$		−	3.17299e7i		−	0.0700462i
$769$	−1.56129e8	−	2.70423e8i	−0.343323	−	0.594654i	0.641724	−	0.766935i	$-0.278219\pi$
$769$	−1.56129e8	−	2.70423e8i	−0.343323	−	0.594654i	−0.985048	+	0.172282i	$0.944886\pi$
$770$	1.77964e8	−	1.02748e8i	0.389816	−	0.225061i
$771$	4.09708e8			0.893947
$772$		−	3.93137e8i		−	0.854462i
$773$	−3.81548e8	+	2.20287e8i	−0.826058	+	0.476925i	−0.852501	−	0.522726i	$-0.824915\pi$
$773$	−3.81548e8	+	2.20287e8i	−0.826058	+	0.476925i	0.0264432	+	0.999650i	$0.491582\pi$
$774$	1.27276e8	+	7.34829e7i	0.274489	+	0.158476i
$775$	4.15086e7	−	2.39650e7i	0.0891730	−	0.0514841i
$776$	1.57312e7	−	2.72472e7i	0.0336647	−	0.0583091i
$777$	−1.09866e8	+	1.90293e8i	−0.234207	+	0.405658i
$778$			4.83757e8i			1.02728i
$779$	−3.31127e8	−	3.07412e8i	−0.700459	−	0.650292i
$780$	−4.28966e8			−0.903939
$781$	−1.55071e8	−	8.95305e7i	−0.325521	−	0.187939i
$782$	−3.69883e8	−	2.13552e8i	−0.773472	−	0.446564i
$783$	−2.21482e8	−	3.83618e8i	−0.461374	−	0.799123i
$784$	2.61471e7	−	4.52881e7i	0.0542595	−	0.0939801i
$785$	1.35794e8	+	2.35202e8i	0.280718	+	0.486219i
$786$	6.83280e8			1.40712
$787$			3.14410e8i			0.645018i	0.946566	+	0.322509i	$0.104526\pi$
$787$			3.14410e8i			0.645018i	−0.946566	+	0.322509i	$0.895474\pi$
$788$	1.30666e8	+	2.26319e8i	0.267044	+	0.462533i
$789$	8.31591e7	−	4.80119e7i	0.169309	−	0.0977503i
$790$	5.56550e8			1.12882
$791$		−	3.28844e8i		−	0.664446i
$792$	−2.32601e7	+	1.34292e7i	−0.0468205	+	0.0270318i
$793$	4.02332e8	+	2.32287e8i	0.806799	+	0.465806i
$794$	−3.05130e8	+	1.76167e8i	−0.609570	+	0.351935i
$795$	3.53829e8	−	6.12850e8i	0.704194	−	1.21970i
$796$	6.33588e7	−	1.09741e8i	0.125623	−	0.217585i
$797$			4.58432e8i			0.905523i	0.891632	+	0.452762i	$0.149561\pi$
$797$			4.58432e8i			0.905523i	−0.891632	+	0.452762i	$0.850439\pi$
$798$	−8.92174e7	−	2.89520e8i	−0.175566	−	0.569731i
$799$	−1.85439e8			−0.363547
$800$	7.89886e7	+	4.56041e7i	0.154275	+	0.0890705i
$801$	1.86853e8	+	1.07879e8i	0.363582	+	0.209914i
$802$	−3.16557e8	−	5.48292e8i	−0.613661	−	1.06289i
$803$	2.88522e8	−	4.99734e8i	0.557226	−	0.965144i
$804$	−1.72728e8	−	2.99173e8i	−0.332348	−	0.575644i
$805$	8.50555e8			1.63048
$806$			4.30693e7i			0.0822550i
$807$	−2.91582e8	−	5.05035e8i	−0.554805	−	0.960950i
$808$	−2.28416e8	+	1.31876e8i	−0.433004	+	0.249995i
$809$	3.54170e8			0.668908			0.334454	−	0.942412i	$-0.391448\pi$
$809$	3.54170e8			0.668908			0.334454	+	0.942412i	$0.391448\pi$
$810$			6.33896e8i			1.19279i
$811$	4.04706e8	−	2.33657e8i	0.758712	−	0.438042i	−0.0701213	−	0.997538i	$-0.522339\pi$
$811$	4.04706e8	−	2.33657e8i	0.758712	−	0.438042i	0.828833	+	0.559496i	$0.189005\pi$
$812$	−1.93013e8	−	1.11436e8i	−0.360511	−	0.208141i
$813$	−7.07117e8	+	4.08254e8i	−1.31589	+	0.759729i
$814$	6.32685e7	−	1.09584e8i	0.117304	−	0.203177i
$815$	1.23784e8	−	2.14400e8i	0.228661	−	0.396053i
$816$		−	1.25707e8i		−	0.231360i
$817$	6.49512e8	−	6.99619e8i	1.19103	−	1.28291i
$818$	4.82020e8			0.880653
$819$	−1.04330e8	−	6.02352e7i	−0.189915	−	0.109647i
$820$	3.23335e8	+	1.86678e8i	0.586424	+	0.338572i
$821$	−4.59708e8	−	7.96237e8i	−0.830715	−	1.43884i	−0.897472	−	0.441072i	$-0.854598\pi$
$821$	−4.59708e8	−	7.96237e8i	−0.830715	−	1.43884i	0.0667565	−	0.997769i	$-0.478735\pi$
$822$	−3.10024e8	+	5.36977e8i	−0.558187	+	0.966808i
$823$	−1.49067e8	−	2.58191e8i	−0.267412	−	0.463171i	0.700781	−	0.713377i	$-0.252835\pi$
$823$	−1.49067e8	−	2.58191e8i	−0.267412	−	0.463171i	−0.968193	+	0.250205i	$0.919502\pi$
$824$	−2.03107e8			−0.363031
$825$		−	3.78721e8i		−	0.674461i
$826$	5.88810e7	+	1.01985e8i	0.104480	+	0.180965i
$827$	2.87072e7	−	1.65741e7i	0.0507545	−	0.0293031i	−0.474408	−	0.880305i	$-0.657338\pi$
$827$	2.87072e7	−	1.65741e7i	0.0507545	−	0.0293031i	0.525163	+	0.851002i	$0.324005\pi$
$828$	−1.11168e8			−0.195835
$829$		−	3.20263e8i		−	0.562139i	−0.959687	−	0.281069i	$-0.909311\pi$
$829$		−	3.20263e8i		−	0.562139i	0.959687	−	0.281069i	$-0.0906891\pi$
$830$	6.58303e7	−	3.80071e7i	0.115131	−	0.0664708i
$831$	5.60182e8	+	3.23421e8i	0.976171	+	0.563592i
$832$	−7.09780e7	+	4.09792e7i	−0.123241	+	0.0711530i
$833$	1.03589e8	−	1.79422e8i	0.179217	−	0.310413i
$834$	−1.33904e8	+	2.31929e8i	−0.230832	+	0.399812i
$835$		−	8.23196e6i		−	0.0141398i
$836$	5.13777e7	+	1.66726e8i	0.0879338	+	0.285354i
$837$	4.99557e7			0.0851939
$838$	−1.55995e8	−	9.00640e7i	−0.265082	−	0.153045i
$839$	−2.66023e8	−	1.53588e8i	−0.450436	−	0.260059i	0.257578	−	0.966257i	$-0.417075\pi$
$839$	−2.66023e8	−	1.53588e8i	−0.450436	−	0.260059i	−0.708014	+	0.706198i	$0.750409\pi$
$840$	1.25169e8	+	2.16800e8i	0.211184	+	0.365781i
$841$	6.68685e7	−	1.15820e8i	0.112417	−	0.194713i
$842$	−1.98085e8	−	3.43093e8i	−0.331829	−	0.574745i
$843$	−1.15505e9			−1.92804
$844$		−	4.10606e8i		−	0.682965i
$845$	1.26554e8	+	2.19198e8i	0.209752	+	0.363300i
$846$	−4.18002e7	+	2.41334e7i	−0.0690348	+	0.0398572i
$847$	2.94093e8			0.483988
$848$		−	1.35205e8i		−	0.221721i
$849$	−4.49315e8	+	2.59412e8i	−0.734223	+	0.423904i
$850$	3.12936e8	+	1.80674e8i	0.509564	+	0.294197i
$851$	4.53575e8	−	2.61872e8i	0.735971	−	0.424913i
$852$	1.09068e8	−	1.88911e8i	0.176351	−	0.305449i
$853$	1.25264e8	−	2.16964e8i	0.201827	−	0.349575i	−0.747290	−	0.664498i	$-0.768645\pi$
$853$	1.25264e8	−	2.16964e8i	0.201827	−	0.349575i	0.949117	+	0.314923i	$0.101979\pi$
$854$		−	2.71119e8i		−	0.435297i
$855$	−2.21071e8	−	5.05222e7i	−0.353698	−	0.0808322i
$856$	2.07049e8			0.330105
$857$	−5.61205e8	−	3.24012e8i	−0.891619	−	0.514776i	−0.0171472	−	0.999853i	$-0.505458\pi$
$857$	−5.61205e8	−	3.24012e8i	−0.891619	−	0.514776i	−0.874472	+	0.485077i	$0.838792\pi$
$858$	2.94720e8	+	1.70156e8i	0.466603	+	0.269393i
$859$	5.93591e8	+	1.02813e9i	0.936500	+	1.62207i	0.771936	+	0.635700i	$0.219288\pi$
$859$	5.93591e8	+	1.02813e9i	0.936500	+	1.62207i	0.164564	+	0.986366i	$0.447378\pi$
$860$	−3.94420e8	+	6.83156e8i	−0.620103	+	1.07405i
$861$	2.57171e8	+	4.45434e8i	0.402915	+	0.697869i
$862$	−8.79081e8			−1.37248
$863$			6.77709e8i			1.05441i	0.849737	+	0.527207i	$0.176761\pi$
$863$			6.77709e8i			1.05441i	−0.849737	+	0.527207i	$0.823239\pi$
$864$	4.75314e7	+	8.23268e7i	0.0736952	+	0.127644i
$865$	−5.08500e8	+	2.93583e8i	−0.785674	+	0.453609i
$866$	−6.50709e8			−1.00192
$867$			2.32378e8i			0.356564i
$868$	2.17672e7	−	1.25673e7i	0.0332847	−	0.0192169i
$869$	−3.82376e8	−	2.20765e8i	−0.582682	−	0.336412i
$870$	−7.08709e8	+	4.09173e8i	−1.07624	+	0.621369i
$871$	−4.46155e8	+	7.72764e8i	−0.675199	+	1.16948i
$872$	−1.17013e8	+	2.02672e8i	−0.176475	+	0.305664i
$873$		−	3.24436e7i		−	0.0487626i
$874$	−1.60879e8	+	7.03961e8i	−0.240972	+	1.05442i
$875$	−5.51075e6			−0.00822596
$876$	6.08787e8	+	3.51483e8i	0.905635	+	0.522868i
$877$	2.74689e8	+	1.58592e8i	0.407232	+	0.235116i	0.689600	−	0.724191i	$-0.257786\pi$
$877$	2.74689e8	+	1.58592e8i	0.407232	+	0.235116i	−0.282368	+	0.959306i	$0.591120\pi$
$878$	−1.47812e8	−	2.56018e8i	−0.218386	−	0.378256i
$879$	5.67102e7	−	9.82250e7i	0.0835016	−	0.144629i
$880$	−7.20814e7	−	1.24849e8i	−0.105773	−	0.183204i
$881$	5.13667e8			0.751197			0.375598	−	0.926783i	$-0.377437\pi$
$881$	5.13667e8			0.751197			0.375598	+	0.926783i	$0.377437\pi$
$882$		−	5.39253e7i		−	0.0785935i
$883$	4.14411e8	+	7.17781e8i	0.601934	+	1.04258i	0.992528	+	0.122017i	$0.0389364\pi$
$883$	4.14411e8	+	7.17781e8i	0.601934	+	1.04258i	−0.390594	+	0.920563i	$0.627730\pi$
$884$	−2.81200e8	+	1.62351e8i	−0.407060	+	0.235016i
$885$	4.32401e8			0.623816
$886$			7.77874e7i			0.111843i
$887$	−1.40613e7	+	8.11830e6i	−0.0201491	+	0.0116331i	−0.510041	−	0.860150i	$-0.670370\pi$
$887$	−1.40613e7	+	8.11830e6i	−0.0201491	+	0.0116331i	0.489892	+	0.871783i	$0.337036\pi$
$888$	1.33498e8	+	7.70751e7i	0.190649	+	0.110072i
$889$	8.43026e8	−	4.86721e8i	1.19987	−	0.692747i
$890$	−5.79044e8	+	1.00293e9i	−0.821375	+	1.42266i
$891$	2.51445e8	−	4.35516e8i	0.355476	−	0.615702i
$892$		−	2.96271e8i		−	0.417441i
$893$	9.23299e7	+	2.99620e8i	0.129655	+	0.420743i
$894$	3.20863e8			0.449062
$895$	8.75181e8	+	5.05286e8i	1.22076	+	0.704803i
$896$	4.14218e7	+	2.39149e7i	0.0575844	+	0.0332464i
$897$	7.04287e8	+	1.21986e9i	0.975825	+	1.69018i
$898$	2.18028e8	−	3.77635e8i	0.301080	−	0.521487i
$899$	4.10820e7	+	7.11562e7i	0.0565422	+	0.0979340i
$900$	9.40529e7			0.129016
$901$		−	5.35655e8i		−	0.732337i
$902$	−1.48098e8	−	2.56513e8i	−0.201803	−	0.349534i
$903$	−9.41131e8	+	5.43362e8i	−1.27816	+	0.737949i
$904$	−2.30697e8			−0.312274
$905$		−	8.46058e8i		−	1.14144i
$906$	7.60500e8	−	4.39075e8i	1.02262	−	0.590411i
$907$	−6.47709e8	−	3.73955e8i	−0.868076	−	0.501184i	−0.00136759	−	0.999999i	$-0.500435\pi$
$907$	−6.47709e8	−	3.73955e8i	−0.868076	−	0.501184i	−0.866708	+	0.498815i	$0.833769\pi$
$908$	4.01241e8	−	2.31656e8i	0.535979	−	0.309447i
$909$	−1.35989e8	+	2.35540e8i	−0.181056	+	0.313598i
$910$	3.23313e8	−	5.59994e8i	0.429041	−	0.743120i
$911$			4.95348e8i			0.655171i	0.944821	+	0.327586i	$0.106235\pi$
$911$			4.95348e8i			0.655171i	−0.944821	+	0.327586i	$0.893765\pi$
$912$	−2.03109e8	+	6.25894e7i	−0.267760	+	0.0825119i
$913$	−6.03046e7			−0.0792389
$914$	5.30874e8	+	3.06500e8i	0.695268	+	0.401413i
$915$	−8.62128e8	−	4.97750e8i	−1.12540	−	0.649752i
$916$	2.01421e8	+	3.48872e8i	0.262071	+	0.453920i
$917$	−5.14990e8	+	8.91988e8i	−0.667868	+	1.15678i
$918$	1.88309e8	+	3.26161e8i	0.243413	+	0.421604i
$919$	−9.44085e8			−1.21637			−0.608183	−	0.793797i	$-0.708101\pi$
$919$	−9.44085e8			−1.21637			−0.608183	+	0.793797i	$0.708101\pi$
$920$		−	5.96698e8i		−	0.766286i
$921$	1.92759e8	+	3.33868e8i	0.246737	+	0.427362i
$922$	4.09496e8	−	2.36423e8i	0.522464	−	0.301645i
$923$	−5.63446e8			−0.716551
$924$		−	1.98602e8i		−	0.251749i
$925$	−3.83742e8	+	2.21554e8i	−0.484858	+	0.279933i
$926$	−1.26936e8	−	7.32865e7i	−0.159864	−	0.0922978i
$927$	−1.81382e8	+	1.04721e8i	−0.227696	+	0.131460i
$928$	−7.81768e7	+	1.35406e8i	−0.0978214	+	0.169432i
$929$	−2.35271e8	+	4.07502e8i	−0.293442	+	0.508256i	−0.974621	−	0.223860i	$-0.928134\pi$
$929$	−2.35271e8	+	4.07502e8i	−0.293442	+	0.508256i	0.681179	+	0.732117i	$0.261467\pi$
$930$		−	9.22898e7i		−	0.114737i
$931$	−3.41475e8	−	7.80389e7i	−0.423166	−	0.0967080i
$932$	−6.39104e8			−0.789448
$933$	−7.61814e8	−	4.39834e8i	−0.938003	−	0.541556i
$934$	−1.85930e8	−	1.07347e8i	−0.228196	−	0.131749i
$935$	−2.85571e8	−	4.94624e8i	−0.349365	−	0.605118i
$936$	−4.22573e7	+	7.31918e7i	−0.0515317	+	0.0892555i
$937$	5.62706e8	+	9.74636e8i	0.684011	+	1.18474i	0.973747	+	0.227635i	$0.0730993\pi$
$937$	5.62706e8	+	9.74636e8i	0.684011	+	1.18474i	−0.289736	+	0.957107i	$0.593567\pi$
$938$	5.20741e8			0.630976
$939$		−	1.28932e9i		−	1.55727i
$940$	−1.29536e8	−	2.24363e8i	−0.155958	−	0.270127i
$941$	1.85477e8	−	1.07085e8i	0.222598	−	0.128517i	−0.384555	−	0.923102i	$-0.625645\pi$
$941$	1.85477e8	−	1.07085e8i	0.222598	−	0.128517i	0.607153	+	0.794585i	$0.292312\pi$
$942$	2.62477e8			0.314007
$943$		−	1.22597e9i		−	1.46199i
$944$	7.15463e7	−	4.13073e7i	0.0850494	−	0.0491033i
$945$	−6.49533e8	−	3.75008e8i	−0.769672	−	0.444370i
$946$	5.41970e8	−	3.12907e8i	0.640180	−	0.369608i
$947$	−7.24815e7	+	1.25542e8i	−0.0853449	+	0.147822i	−0.905538	−	0.424265i	$-0.860533\pi$
$947$	−7.24815e7	+	1.25542e8i	−0.0853449	+	0.147822i	0.820193	+	0.572087i	$0.193866\pi$
$948$	2.68941e8	−	4.65819e8i	0.315669	−	0.546754i
$949$		−	1.81576e9i		−	2.12452i
$950$	1.36110e8	−	5.95579e8i	0.158752	−	0.694654i
$951$	6.89163e7			0.0801273
$952$	1.64104e8	+	9.47457e7i	0.190199	+	0.109812i
$953$	1.12162e9	+	6.47566e8i	1.29588	+	0.748179i	0.979690	−	0.200516i	$-0.0642619\pi$
$953$	1.12162e9	+	6.47566e8i	1.29588	+	0.748179i	0.316193	+	0.948695i	$0.397595\pi$
$954$	−6.97112e7	−	1.20743e8i	−0.0802893	−	0.139065i
$955$	−8.67838e8	+	1.50314e9i	−0.996389	+	1.72580i
$956$	−5.94618e7	−	1.02991e8i	−0.0680556	−	0.117876i
$957$	6.49222e8			0.740725
$958$		−	6.06075e8i		−	0.689334i
$959$	−4.67332e8	−	8.09442e8i	−0.529870	−	0.917762i
$960$	1.52093e8	−	8.78111e7i	0.171908	−	0.0992512i
$961$	8.78238e8			0.989559
$962$		−	3.98170e8i		−	0.447243i
$963$	1.84903e8	−	1.06754e8i	0.207045	−	0.119537i
$964$	4.04510e8	+	2.33544e8i	0.451541	+	0.260698i
$965$	1.88446e9	−	1.08799e9i	2.09703	−	1.21072i
$966$	4.11012e8	−	7.11894e8i	0.455956	−	0.789740i
$967$	−5.86901e8	+	1.01654e9i	−0.649061	+	1.12421i	0.334287	+	0.942471i	$0.391505\pi$
$967$	−5.86901e8	+	1.01654e9i	−0.649061	+	1.12421i	−0.983348	+	0.181735i	$0.941829\pi$
$968$		−	2.06318e8i		−	0.227463i
$969$	−8.04676e8	+	2.47966e8i	−0.884402	+	0.272534i
$970$	1.74141e8			0.190804
$971$	−1.51997e8	−	8.77553e7i	−0.166026	−	0.0958552i	0.414685	−	0.909965i	$-0.363892\pi$
$971$	−1.51997e8	−	8.77553e7i	−0.166026	−	0.0958552i	−0.580711	+	0.814110i	$0.697225\pi$
$972$	1.99009e8	+	1.14898e8i	0.216707	+	0.125116i
$973$	−2.01848e8	−	3.49610e8i	−0.219122	−	0.379530i
$974$	−2.73130e7	+	4.73075e7i	−0.0295592	+	0.0511980i
$975$	−5.95854e8	−	1.03205e9i	−0.642875	−	1.11349i
$976$	−1.90200e8			−0.204579
$977$			1.56932e9i			1.68278i	0.540427	+	0.841391i	$0.318263\pi$
$977$			1.56932e9i			1.68278i	−0.540427	+	0.841391i	$0.681737\pi$
$978$	−1.19632e8	−	2.07209e8i	−0.127888	−	0.221509i
$979$	7.95660e8	−	4.59375e8i	0.847968	−	0.489575i
$980$	2.89444e8			0.307529
$981$			2.41324e8i			0.255620i
$982$	−1.12119e9	+	6.47321e8i	−1.18398	+	0.683574i
$983$	−5.83382e7	−	3.36816e7i	−0.0614176	−	0.0354595i	0.468977	−	0.883211i	$-0.344623\pi$
$983$	−5.83382e7	−	3.36816e7i	−0.0614176	−	0.0354595i	−0.530394	+	0.847751i	$0.677956\pi$
$984$	3.12489e8	−	1.80416e8i	0.327982	−	0.189360i
$985$	−7.23223e8	+	1.25266e9i	−0.756770	+	1.31076i
$986$	−3.09720e8	+	5.36450e8i	−0.323101	+	0.559627i
$987$		−	3.56904e8i		−	0.371193i
$988$	4.02325e8	+	3.73510e8i	0.417163	+	0.387286i
$989$	2.59027e9			2.67767
$990$	−1.28743e8	−	7.43296e7i	−0.132684	−	0.0766049i
$991$	−2.69871e8	−	1.55810e8i	−0.277291	−	0.160094i	0.354906	−	0.934902i	$-0.384513\pi$
$991$	−2.69871e8	−	1.55810e8i	−0.277291	−	0.160094i	−0.632196	+	0.774808i	$0.717846\pi$
$992$	−8.81646e6	−	1.52706e7i	−0.00903149	−	0.0156430i
$993$	−4.52698e7	+	7.84096e7i	−0.0462340	+	0.0800796i
$994$	1.64410e8	+	2.84766e8i	0.167405	+	0.289954i
$995$	7.01371e8			0.711998
$996$		−	7.34644e7i		−	0.0743531i
$997$	−6.05936e8	−	1.04951e9i	−0.611422	−	1.05901i	−0.991001	−	0.133855i	$-0.957264\pi$
$997$	−6.05936e8	−	1.04951e9i	−0.611422	−	1.05901i	0.379578	−	0.925160i	$-0.376069\pi$
$998$	5.05703e7	−	2.91968e7i	0.0508749	−	0.0293727i
$999$	−4.61834e8			−0.463223

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.7.d.a.27.9	✓	20
3.2	odd	2		342.7.m.a.217.5		20
19.12	odd	6	inner	38.7.d.a.31.9	yes	20
57.50	even	6		342.7.m.a.145.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.7.d.a.27.9	✓	20	1.1	even	1	trivial
38.7.d.a.31.9	yes	20	19.12	odd	6	inner
342.7.m.a.145.5		20	57.50	even	6
342.7.m.a.217.5		20	3.2	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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	38.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.89898 + 2.82843i) q^{2} +(26.2059 + 15.1300i) q^{3} +(16.0000 + 27.7128i) q^{4} +(-88.5587 + 153.388i) q^{5} +(85.5881 + 148.243i) q^{6} -258.032 q^{7} +181.019i q^{8} +(93.3327 + 161.657i) q^{9} +O(q^{10})\)	\(q+(4.89898 + 2.82843i) q^{2} +(26.2059 + 15.1300i) q^{3} +(16.0000 + 27.7128i) q^{4} +(-88.5587 + 153.388i) q^{5} +(85.5881 + 148.243i) q^{6} -258.032 q^{7} +181.019i q^{8} +(93.3327 + 161.657i) q^{9} +(-867.695 + 500.964i) q^{10} +794.862 q^{11} +968.319i q^{12} +(2166.08 - 1250.58i) q^{13} +(-1264.09 - 729.824i) q^{14} +(-4641.52 + 2679.78i) q^{15} +(-512.000 + 886.810i) q^{16} +(-2028.44 + 3513.35i) q^{17} +1055.94i q^{18} +(6686.61 + 1528.12i) q^{19} -5667.76 q^{20} +(-6761.96 - 3904.02i) q^{21} +(3894.01 + 2248.21i) q^{22} +(9305.46 + 16117.5i) q^{23} +(-2738.82 + 4743.77i) q^{24} +(-7872.79 - 13636.1i) q^{25} +14148.7 q^{26} -16411.0i q^{27} +(-4128.51 - 7150.79i) q^{28} +(23375.6 - 13495.9i) q^{29} -30318.3 q^{30} +3044.03i q^{31} +(-5016.55 + 2896.31i) q^{32} +(20830.1 + 12026.3i) q^{33} +(-19874.5 + 11474.6i) q^{34} +(22851.0 - 39579.0i) q^{35} +(-2986.65 + 5173.02i) q^{36} -28141.7i q^{37} +(28435.4 + 26398.8i) q^{38} +75685.3 q^{39} +(-27766.2 - 16030.8i) q^{40} +(-57048.2 - 32936.8i) q^{41} +(-22084.5 - 38251.4i) q^{42} +(69590.2 - 120534. i) q^{43} +(12717.8 + 22027.9i) q^{44} -33061.7 q^{45} +105279. i q^{46} +(22854.9 + 39585.9i) q^{47} +(-26834.8 + 15493.1i) q^{48} -51068.6 q^{49} -89070.5i q^{50} +(-106314. + 61380.4i) q^{51} +(69314.4 + 40018.7i) q^{52} +(-114347. + 66018.2i) q^{53} +(46417.4 - 80397.3i) q^{54} +(-70392.0 + 121923. i) q^{55} -46708.8i q^{56} +(152108. + 141214. i) q^{57} +152689. q^{58} +(-69869.5 - 40339.2i) q^{59} +(-148529. - 85753.1i) q^{60} +(92871.3 + 160858. i) q^{61} +(-8609.82 + 14912.7i) q^{62} +(-24082.8 - 41712.6i) q^{63} -32768.0 q^{64} +443001. i q^{65} +(68030.8 + 117833. i) q^{66} +(-308961. + 178379. i) q^{67} -129820. q^{68} +563166. i q^{69} +(223893. - 129265. i) q^{70} +(-195092. - 112636. i) q^{71} +(-29263.0 + 16895.0i) q^{72} +(362983. - 628705. i) q^{73} +(79596.8 - 137866. i) q^{74} -476461. i q^{75} +(64637.2 + 209755. i) q^{76} -205100. q^{77} +(370781. + 214070. i) q^{78} +(-481060. - 277740. i) q^{79} +(-90684.1 - 157070. i) q^{80} +(316338. - 547914. i) q^{81} +(-186319. - 322713. i) q^{82} -75868.0 q^{83} -249857. i q^{84} +(-359271. - 622276. i) q^{85} +(681841. - 393661. i) q^{86} +816773. q^{87} +143885. i q^{88} +(1.00100e6 - 577930. i) q^{89} +(-161968. - 93512.6i) q^{90} +(-558917. + 322691. i) q^{91} +(-297775. + 515761. i) q^{92} +(-46056.2 + 79771.6i) q^{93} +258574. i q^{94} +(-826553. + 890318. i) q^{95} -175284. q^{96} +(-150521. - 86903.2i) q^{97} +(-250184. - 144444. i) q^{98} +(74186.6 + 128495. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9}+O(q^{10}) \) 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9	\( 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9} - 284 q^{11} + 10500 q^{13} + 1248 q^{14} + 14136 q^{15} - 10240 q^{16} - 11684 q^{17} + 12862 q^{19} + 7168 q^{20} + 2916 q^{21} + 52704 q^{22} + 8488 q^{23} - 2560 q^{24} - 63842 q^{25} - 43968 q^{26} - 3328 q^{28} + 137760 q^{29} - 94688 q^{30} - 250194 q^{33} + 70560 q^{34} - 6916 q^{35} - 70400 q^{36} - 77232 q^{38} + 9672 q^{39} + 109206 q^{41} - 92672 q^{42} + 35572 q^{43} - 4544 q^{44} + 131264 q^{45} - 361184 q^{47} + 30720 q^{48} + 259740 q^{49} - 496512 q^{51} + 336000 q^{52} - 236172 q^{53} + 375728 q^{54} + 56760 q^{55} + 314796 q^{57} - 225600 q^{58} + 1310610 q^{59} + 452352 q^{60} + 83552 q^{61} + 225792 q^{62} + 553364 q^{63} - 655360 q^{64} - 4736 q^{66} + 806646 q^{67} - 747776 q^{68} - 245664 q^{70} - 869220 q^{71} + 353280 q^{72} - 207422 q^{73} + 1460832 q^{74} - 140096 q^{76} - 3988336 q^{77} - 85008 q^{78} - 1706808 q^{79} + 114688 q^{80} + 2303170 q^{81} + 887712 q^{82} + 3527548 q^{83} - 5604 q^{85} + 195792 q^{86} - 8414832 q^{87} + 708432 q^{89} - 4483104 q^{90} - 1914384 q^{91} - 271616 q^{92} + 3537876 q^{93} - 2820356 q^{95} - 163840 q^{96} + 5113242 q^{97} - 612480 q^{98} + 603704 q^{99}+O(q^{100}) \) 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9 - 284 * q^11 + 10500 * q^13 + 1248 * q^14 + 14136 * q^15 - 10240 * q^16 - 11684 * q^17 + 12862 * q^19 + 7168 * q^20 + 2916 * q^21 + 52704 * q^22 + 8488 * q^23 - 2560 * q^24 - 63842 * q^25 - 43968 * q^26 - 3328 * q^28 + 137760 * q^29 - 94688 * q^30 - 250194 * q^33 + 70560 * q^34 - 6916 * q^35 - 70400 * q^36 - 77232 * q^38 + 9672 * q^39 + 109206 * q^41 - 92672 * q^42 + 35572 * q^43 - 4544 * q^44 + 131264 * q^45 - 361184 * q^47 + 30720 * q^48 + 259740 * q^49 - 496512 * q^51 + 336000 * q^52 - 236172 * q^53 + 375728 * q^54 + 56760 * q^55 + 314796 * q^57 - 225600 * q^58 + 1310610 * q^59 + 452352 * q^60 + 83552 * q^61 + 225792 * q^62 + 553364 * q^63 - 655360 * q^64 - 4736 * q^66 + 806646 * q^67 - 747776 * q^68 - 245664 * q^70 - 869220 * q^71 + 353280 * q^72 - 207422 * q^73 + 1460832 * q^74 - 140096 * q^76 - 3988336 * q^77 - 85008 * q^78 - 1706808 * q^79 + 114688 * q^80 + 2303170 * q^81 + 887712 * q^82 + 3527548 * q^83 - 5604 * q^85 + 195792 * q^86 - 8414832 * q^87 + 708432 * q^89 - 4483104 * q^90 - 1914384 * q^91 - 271616 * q^92 + 3537876 * q^93 - 2820356 * q^95 - 163840 * q^96 + 5113242 * q^97 - 612480 * q^98 + 603704 * q^99

Introduction

L-functions

Modular forms

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