LMFDB - Embedded newform 74.8.f.b.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,8,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("74.7");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, degree $6$, 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:	$23.1164918858$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			33.2
Character	$\chi$	$=$	74.33
Dual form			74.8.f.b.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38919 + 7.87846i) q^{2} +(-11.0757 - 62.8133i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(48.5860 - 40.7685i) q^{5} +510.258 q^{6} +(745.438 - 625.497i) q^{7} +(256.000 - 443.405i) q^{8} +(-1767.73 + 643.401i) q^{9} +O(q^{10})$	\(q+(-1.38919 + 7.87846i) q^{2} +(-11.0757 - 62.8133i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(48.5860 - 40.7685i) q^{5} +510.258 q^{6} +(745.438 - 625.497i) q^{7} +(256.000 - 443.405i) q^{8} +(-1767.73 + 643.401i) q^{9} +(253.698 + 439.418i) q^{10} +(1308.86 - 2267.01i) q^{11} +(-708.843 + 4020.05i) q^{12} +(10811.3 + 3934.99i) q^{13} +(3892.40 + 6741.84i) q^{14} +(-3098.93 - 2600.31i) q^{15} +(3137.72 + 2632.86i) q^{16} +(-10941.9 + 3982.52i) q^{17} +(-2613.31 - 14820.8i) q^{18} +(-3295.54 - 18689.9i) q^{19} +(-3814.37 + 1388.32i) q^{20} +(-47545.7 - 39895.6i) q^{21} +(16042.3 + 13461.1i) q^{22} +(-51555.8 - 89297.2i) q^{23} +(-30687.1 - 11169.2i) q^{24} +(-12867.7 + 72976.6i) q^{25} +(-46020.5 + 79709.9i) q^{26} +(-9752.97 - 16892.6i) q^{27} +(-58522.6 + 21300.5i) q^{28} +(40630.1 - 70373.4i) q^{29} +(24791.4 - 20802.5i) q^{30} -93493.8 q^{31} +(-25101.7 + 21062.9i) q^{32} +(-156895. - 57105.0i) q^{33} +(-16175.8 - 91737.6i) q^{34} +(10717.3 - 60780.8i) q^{35} +120395. q^{36} +(234374. - 200002. i) q^{37} +151826. q^{38} +(127427. - 722675. i) q^{39} +(-5638.94 - 31980.0i) q^{40} +(75210.3 + 27374.3i) q^{41} +(380366. - 319165. i) q^{42} -514325. q^{43} +(-128338. + 107689. i) q^{44} +(-59656.4 + 103328. i) q^{45} +(775145. - 282130. i) q^{46} +(-443029. - 767349. i) q^{47} +(130626. - 226251. i) q^{48} +(21424.9 - 121507. i) q^{49} +(-557067. - 202756. i) q^{50} +(371343. + 643186. i) q^{51} +(-564060. - 473303. i) q^{52} +(1.01891e6 + 854970. i) q^{53} +(146637. - 53371.4i) q^{54} +(-28830.4 - 163505. i) q^{55} +(-86516.3 - 490658. i) q^{56} +(-1.13747e6 + 414007. i) q^{57} +(497991. + 417864. i) q^{58} +(-664363. - 557466. i) q^{59} +(129452. + 224217. i) q^{60} +(-373804. - 136054. i) q^{61} +(129880. - 736588. i) q^{62} +(-915288. + 1.58533e6i) q^{63} +(-131072. - 227023. i) q^{64} +(685701. - 249575. i) q^{65} +(667856. - 1.15676e6i) q^{66} +(-3.33792e6 + 2.80084e6i) q^{67} +745222. q^{68} +(-5.03804e6 + 4.22741e6i) q^{69} +(463971. + 168871. i) q^{70} +(129993. + 737225. i) q^{71} +(-167252. + 948531. i) q^{72} -3.10268e6 q^{73} +(1.25012e6 + 2.12434e6i) q^{74} +4.72642e6 q^{75} +(-210914. + 1.19615e6i) q^{76} +(-442334. - 2.50860e6i) q^{77} +(5.51655e6 + 2.00786e6i) q^{78} +(3.49137e6 - 2.92960e6i) q^{79} +259787. q^{80} +(-4.10467e6 + 3.44423e6i) q^{81} +(-320148. + 554513. i) q^{82} +(5.92024e6 - 2.15479e6i) q^{83} +(1.98613e6 + 3.44008e6i) q^{84} +(-369260. + 639578. i) q^{85} +(714493. - 4.05209e6i) q^{86} +(-4.87039e6 - 1.77268e6i) q^{87} +(-670136. - 1.16071e6i) q^{88} +(3.09775e6 + 2.59932e6i) q^{89} +(-731192. - 613543. i) q^{90} +(1.05205e7 - 3.82914e6i) q^{91} +(1.14593e6 + 6.49888e6i) q^{92} +(1.03551e6 + 5.87265e6i) q^{93} +(6.66098e6 - 2.42440e6i) q^{94} +(-922076. - 773714. i) q^{95} +(1.60105e6 + 1.34344e6i) q^{96} +(1.06495e6 + 1.84455e6i) q^{97} +(927522. + 337590. i) q^{98} +(-855112. + 4.84958e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9}+O(q^{10}) $ 66 * q - 39 * q^3 + 459 * q^5 - 918 * q^7 + 16896 * q^8 + 3237 * q^9	\( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9} + 4704 q^{10} + 4539 q^{11} - 2496 q^{12} - 10542 q^{13} + 6744 q^{14} - 39894 q^{15} - 78822 q^{17} + 51792 q^{18} + 79461 q^{19} + 29376 q^{20} - 5835 q^{21} + 18168 q^{22} - 199479 q^{23} + 19968 q^{24} + 356301 q^{25} + 186744 q^{26} - 91689 q^{27} - 91584 q^{28} - 38526 q^{29} + 319152 q^{30} + 1917246 q^{31} - 902847 q^{33} - 205776 q^{34} - 1574793 q^{35} + 3079296 q^{36} - 396513 q^{37} - 692880 q^{38} + 2514306 q^{39} + 470016 q^{40} + 2989350 q^{41} + 46680 q^{42} + 6006348 q^{43} - 145344 q^{44} + 1083726 q^{45} - 588744 q^{46} - 894135 q^{47} + 7973742 q^{49} + 2012400 q^{50} - 524880 q^{51} - 2262720 q^{52} + 1457844 q^{53} + 1452312 q^{54} + 2415690 q^{55} - 1202688 q^{56} + 2734338 q^{57} - 3423360 q^{58} + 3099522 q^{59} - 3102912 q^{60} - 10968396 q^{61} - 3067320 q^{62} - 10727970 q^{63} - 8650752 q^{64} - 13497300 q^{65} - 4598712 q^{66} - 1978119 q^{67} + 5026176 q^{68} - 7251108 q^{69} + 435744 q^{70} - 19555002 q^{71} + 3314688 q^{72} - 31332840 q^{73} + 7607472 q^{74} + 44758074 q^{75} + 5085504 q^{76} + 1982007 q^{77} - 22512264 q^{78} + 10522902 q^{79} + 4816896 q^{80} - 7548876 q^{81} - 7150320 q^{82} + 19771926 q^{83} + 3556224 q^{84} - 6684072 q^{85} + 22982496 q^{86} - 67769667 q^{87} - 2323968 q^{88} - 42018963 q^{89} - 25158672 q^{90} + 4847565 q^{91} - 1096704 q^{92} - 14558475 q^{93} + 3175680 q^{94} + 4508415 q^{95} - 2555904 q^{96} - 39286662 q^{97} + 71630904 q^{98} + 66155463 q^{99}+O(q^{100}) \) 66 * q - 39 * q^3 + 459 * q^5 - 918 * q^7 + 16896 * q^8 + 3237 * q^9 + 4704 * q^10 + 4539 * q^11 - 2496 * q^12 - 10542 * q^13 + 6744 * q^14 - 39894 * q^15 - 78822 * q^17 + 51792 * q^18 + 79461 * q^19 + 29376 * q^20 - 5835 * q^21 + 18168 * q^22 - 199479 * q^23 + 19968 * q^24 + 356301 * q^25 + 186744 * q^26 - 91689 * q^27 - 91584 * q^28 - 38526 * q^29 + 319152 * q^30 + 1917246 * q^31 - 902847 * q^33 - 205776 * q^34 - 1574793 * q^35 + 3079296 * q^36 - 396513 * q^37 - 692880 * q^38 + 2514306 * q^39 + 470016 * q^40 + 2989350 * q^41 + 46680 * q^42 + 6006348 * q^43 - 145344 * q^44 + 1083726 * q^45 - 588744 * q^46 - 894135 * q^47 + 7973742 * q^49 + 2012400 * q^50 - 524880 * q^51 - 2262720 * q^52 + 1457844 * q^53 + 1452312 * q^54 + 2415690 * q^55 - 1202688 * q^56 + 2734338 * q^57 - 3423360 * q^58 + 3099522 * q^59 - 3102912 * q^60 - 10968396 * q^61 - 3067320 * q^62 - 10727970 * q^63 - 8650752 * q^64 - 13497300 * q^65 - 4598712 * q^66 - 1978119 * q^67 + 5026176 * q^68 - 7251108 * q^69 + 435744 * q^70 - 19555002 * q^71 + 3314688 * q^72 - 31332840 * q^73 + 7607472 * q^74 + 44758074 * q^75 + 5085504 * q^76 + 1982007 * q^77 - 22512264 * q^78 + 10522902 * q^79 + 4816896 * q^80 - 7548876 * q^81 - 7150320 * q^82 + 19771926 * q^83 + 3556224 * q^84 - 6684072 * q^85 + 22982496 * q^86 - 67769667 * q^87 - 2323968 * q^88 - 42018963 * q^89 - 25158672 * q^90 + 4847565 * q^91 - 1096704 * q^92 - 14558475 * q^93 + 3175680 * q^94 + 4508415 * q^95 - 2555904 * q^96 - 39286662 * q^97 + 71630904 * q^98 + 66155463 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−1.38919	+	7.87846i	−0.122788	+	0.696364i
$2$	−1.38919	+	7.87846i	−0.122788	+	0.696364i
$3$	−11.0757	−	62.8133i	−0.236835	−	1.34316i	−0.838715	−	0.544571i	$-0.816692\pi$
$3$	−11.0757	−	62.8133i	−0.236835	−	1.34316i	0.601880	−	0.798587i	$-0.294419\pi$
$4$	−60.1403	−	21.8893i	−0.469846	−	0.171010i
$5$	48.5860	−	40.7685i	0.173827	−	0.145858i	−0.551724	−	0.834027i	$-0.686030\pi$
$5$	48.5860	−	40.7685i	0.173827	−	0.145858i	0.725550	+	0.688169i	$0.241585\pi$
$6$	510.258			0.964408
$7$	745.438	−	625.497i	0.821426	−	0.689258i	−0.131880	−	0.991266i	$-0.542101\pi$
$7$	745.438	−	625.497i	0.821426	−	0.689258i	0.953306	+	0.302008i	$0.0976568\pi$
$8$	256.000	−	443.405i	0.176777	−	0.306186i
$9$	−1767.73	+	643.401i	−0.808290	+	0.294194i
$10$	253.698	+	439.418i	0.0802264	+	0.138956i
$11$	1308.86	−	2267.01i	0.296496	−	0.513546i	−0.678836	−	0.734290i	$-0.737515\pi$
$11$	1308.86	−	2267.01i	0.296496	−	0.513546i	0.975332	+	0.220744i	$0.0708486\pi$
$12$	−708.843	+	4020.05i	−0.118417	+	0.671579i
$13$	10811.3	+	3934.99i	1.36482	+	0.496754i	0.917542	−	0.397640i	$-0.130171\pi$
$13$	10811.3	+	3934.99i	1.36482	+	0.496754i	0.447280	+	0.894394i	$0.352393\pi$
$14$	3892.40	+	6741.84i	0.379114	+	0.656644i
$15$	−3098.93	−	2600.31i	−0.237078	−	0.198932i
$16$	3137.72	+	2632.86i	0.191511	+	0.160697i
$17$	−10941.9	+	3982.52i	−0.540157	+	0.196601i	−0.597668	−	0.801744i	$-0.703906\pi$
$17$	−10941.9	+	3982.52i	−0.540157	+	0.196601i	0.0575106	+	0.998345i	$0.481684\pi$
$18$	−2613.31	−	14820.8i	−0.105618	−	0.598988i
$19$	−3295.54	−	18689.9i	−0.110227	−	0.625129i	−0.989003	−	0.147895i	$-0.952750\pi$
$19$	−3295.54	−	18689.9i	−0.110227	−	0.625129i	0.878776	−	0.477234i	$-0.158361\pi$
$20$	−3814.37	+	1388.32i	−0.106615	+	0.0388047i
$21$	−47545.7	−	39895.6i	−1.12033	−	0.940064i
$22$	16042.3	+	13461.1i	0.321209	+	0.269526i
$23$	−51555.8	−	89297.2i	−0.883547	−	1.53035i	−0.847370	−	0.531003i	$-0.821815\pi$
$23$	−51555.8	−	89297.2i	−0.883547	−	1.53035i	−0.0361776	−	0.999345i	$-0.511518\pi$
$24$	−30687.1	−	11169.2i	−0.453123	−	0.164923i
$25$	−12867.7	+	72976.6i	−0.164707	+	0.934100i
$26$	−46020.5	+	79709.9i	−0.513505	+	0.889417i
$27$	−9752.97	−	16892.6i	−0.0953595	−	0.165167i
$28$	−58522.6	+	21300.5i	−0.503814	+	0.183373i
$29$	40630.1	−	70373.4i	0.309353	−	0.535816i	−0.668868	−	0.743381i	$-0.733221\pi$
$29$	40630.1	−	70373.4i	0.309353	−	0.535816i	0.978221	+	0.207566i	$0.0665541\pi$
$30$	24791.4	−	20802.5i	0.167640	−	0.140666i
$31$	−93493.8			−0.563660			−0.281830	−	0.959464i	$-0.590941\pi$
$31$	−93493.8			−0.563660			−0.281830	+	0.959464i	$0.590941\pi$
$32$	−25101.7	+	21062.9i	−0.135419	+	0.113630i
$33$	−156895.	−	57105.0i	−0.759993	−	0.276615i
$34$	−16175.8	−	91737.6i	−0.0705813	−	0.400287i
$35$	10717.3	−	60780.8i	0.0422520	−	0.239623i
$36$	120395.			0.430082
$37$	234374.	−	200002.i	0.760682	−	0.649125i
$37$	234374.	−	200002.i	0.760682	−	0.649125i
$38$	151826.			0.448852
$39$	127427.	−	722675.i	0.343982	−	1.95082i
$40$	−5638.94	−	31980.0i	−0.0139312	−	0.0790075i
$41$	75210.3	+	27374.3i	0.170425	+	0.0620297i	0.425824	−	0.904806i	$-0.359984\pi$
$41$	75210.3	+	27374.3i	0.170425	+	0.0620297i	−0.255398	+	0.966836i	$0.582207\pi$
$42$	380366.	−	319165.i	0.792189	−	0.664726i
$43$	−514325.			−0.986503			−0.493252	−	0.869887i	$-0.664192\pi$
$43$	−514325.			−0.986503			−0.493252	+	0.869887i	$0.664192\pi$
$44$	−128338.	+	107689.i	−0.227129	+	0.190584i
$45$	−59656.4	+	103328.i	−0.0975918	+	0.169034i
$46$	775145.	−	282130.i	1.17417	−	0.427363i
$47$	−443029.	−	767349.i	−0.622429	−	1.07808i	−0.989032	−	0.147701i	$-0.952813\pi$
$47$	−443029.	−	767349.i	−0.622429	−	1.07808i	0.366604	−	0.930377i	$-0.380521\pi$
$48$	130626.	−	226251.i	0.170485	−	0.295288i
$49$	21424.9	−	121507.i	0.0260155	−	0.147541i
$50$	−557067.	−	202756.i	−0.630250	−	0.229392i
$51$	371343.	+	643186.i	0.391995	+	0.678955i
$52$	−564060.	−	473303.i	−0.556306	−	0.466796i
$53$	1.01891e6	+	854970.i	0.940095	+	0.788834i	0.977602	−	0.210463i	$-0.0674971\pi$
$53$	1.01891e6	+	854970.i	0.940095	+	0.788834i	−0.0375067	+	0.999296i	$0.511942\pi$
$54$	146637.	−	53371.4i	0.126726	−	0.0461244i
$55$	−28830.4	−	163505.i	−0.0233658	−	0.132514i
$56$	−86516.3	−	490658.i	−0.0658324	−	0.373354i
$57$	−1.13747e6	+	414007.i	−0.813541	+	0.296105i
$58$	497991.	+	417864.i	0.335138	+	0.281214i
$59$	−664363.	−	557466.i	−0.421137	−	0.353376i	0.407459	−	0.913224i	$-0.366415\pi$
$59$	−664363.	−	557466.i	−0.421137	−	0.353376i	−0.828595	+	0.559848i	$0.810860\pi$
$60$	129452.	+	224217.i	0.0773709	+	0.134010i
$61$	−373804.	−	136054.i	−0.210858	−	0.0767460i	0.234432	−	0.972133i	$-0.424677\pi$
$61$	−373804.	−	136054.i	−0.210858	−	0.0767460i	−0.445290	+	0.895387i	$0.646899\pi$
$62$	129880.	−	736588.i	0.0692105	−	0.392513i
$63$	−915288.	+	1.58533e6i	−0.461175	+	0.798779i
$64$	−131072.	−	227023.i	−0.0625000	−	0.108253i
$65$	685701.	−	249575.i	0.309698	−	0.112721i
$66$	667856.	−	1.15676e6i	0.285943	−	0.495267i
$67$	−3.33792e6	+	2.80084e6i	−1.35586	+	1.13770i	−0.378619	+	0.925553i	$0.623601\pi$
$67$	−3.33792e6	+	2.80084e6i	−1.35586	+	1.13770i	−0.977238	+	0.212146i	$0.931955\pi$
$68$	745222.			0.287412
$69$	−5.03804e6	+	4.22741e6i	−1.84625	+	1.54918i
$70$	463971.	+	168871.i	0.161677	+	0.0588455i
$71$	129993.	+	737225.i	0.0431037	+	0.244453i	0.998745	−	0.0500790i	$-0.0159473\pi$
$71$	129993.	+	737225.i	0.0431037	+	0.244453i	−0.955642	+	0.294532i	$0.904836\pi$
$72$	−167252.	+	948531.i	−0.0528088	+	0.299494i
$73$	−3.10268e6			−0.933483			−0.466742	−	0.884394i	$-0.654572\pi$
$73$	−3.10268e6			−0.933483			−0.466742	+	0.884394i	$0.654572\pi$
$74$	1.25012e6	+	2.12434e6i	0.358625	+	0.609416i
$75$	4.72642e6			1.29365
$76$	−210914.	+	1.19615e6i	−0.0551135	+	0.312564i
$77$	−442334.	−	2.50860e6i	−0.110416	−	0.626202i
$78$	5.51655e6	+	2.00786e6i	1.31624	+	0.479074i
$79$	3.49137e6	−	2.92960e6i	0.796710	−	0.668519i	−0.150686	−	0.988582i	$-0.548148\pi$
$79$	3.49137e6	−	2.92960e6i	0.796710	−	0.668519i	0.947397	+	0.320062i	$0.103704\pi$
$80$	259787.			0.0567286
$81$	−4.10467e6	+	3.44423e6i	−0.858186	+	0.720103i
$82$	−320148.	+	554513.i	−0.0641214	+	0.111062i
$83$	5.92024e6	−	2.15479e6i	1.13649	−	0.413649i	0.295846	−	0.955236i	$-0.404399\pi$
$83$	5.92024e6	−	2.15479e6i	1.13649	−	0.413649i	0.840645	+	0.541587i	$0.182176\pi$
$84$	1.98613e6	+	3.44008e6i	0.365620	+	0.633273i
$85$	−369260.	+	639578.i	−0.0652179	+	0.112961i
$86$	714493.	−	4.05209e6i	0.121131	−	0.686965i
$87$	−4.87039e6	−	1.77268e6i	−0.792951	−	0.288611i
$88$	−670136.	−	1.16071e6i	−0.104827	−	0.181566i
$89$	3.09775e6	+	2.59932e6i	0.465781	+	0.390836i	0.845253	−	0.534367i	$-0.179450\pi$
$89$	3.09775e6	+	2.59932e6i	0.465781	+	0.390836i	−0.379472	+	0.925203i	$0.623894\pi$
$90$	−731192.	−	613543.i	−0.105726	−	0.0887148i
$91$	1.05205e7	−	3.82914e6i	1.46349	−	0.532667i
$92$	1.14593e6	+	6.49888e6i	0.153426	+	0.870124i
$93$	1.03551e6	+	5.87265e6i	0.133494	+	0.757084i
$94$	6.66098e6	−	2.42440e6i	0.827162	−	0.301062i
$95$	−922076.	−	773714.i	−0.110340	−	0.0925865i
$96$	1.60105e6	+	1.34344e6i	0.184695	+	0.154977i
$97$	1.06495e6	+	1.84455e6i	0.118476	+	0.205206i	0.919164	−	0.393875i	$-0.128866\pi$
$97$	1.06495e6	+	1.84455e6i	0.118476	+	0.205206i	−0.800688	+	0.599081i	$0.795533\pi$
$98$	927522.	+	337590.i	0.0995481	+	0.0362326i
$99$	−855112.	+	4.84958e6i	−0.0885727	+	0.502321i
$100$	2.37127e6	−	4.10717e6i	0.237127	−	0.410717i
$101$	−146763.	−	254201.i	−0.0141740	−	0.0245501i	0.858851	−	0.512225i	$-0.171179\pi$
$101$	−146763.	−	254201.i	−0.0141740	−	0.0245501i	−0.873025	+	0.487675i	$0.837845\pi$
$102$	−5.58318e6	+	2.03211e6i	−0.520932	+	0.189604i
$103$	−572907.	+	992304.i	−0.0516599	+	0.0894776i	−0.890699	−	0.454594i	$-0.849785\pi$
$103$	−572907.	+	992304.i	−0.0516599	+	0.0894776i	0.839039	+	0.544071i	$0.183118\pi$
$104$	4.51248e6	−	3.78642e6i	0.393368	−	0.330075i
$105$	−3.93654e6			−0.331858
$106$	−8.15131e6	+	6.83976e6i	−0.664748	+	0.557790i
$107$	531357.	+	193398.i	0.0419318	+	0.0152619i	0.362901	−	0.931828i	$-0.381786\pi$
$107$	531357.	+	193398.i	0.0419318	+	0.0152619i	−0.320969	+	0.947090i	$0.604009\pi$
$108$	216779.	+	1.22941e6i	0.0165590	+	0.0939107i
$109$	679234.	−	3.85213e6i	0.0502374	−	0.284910i	−0.949331	−	0.314277i	$-0.898238\pi$
$109$	679234.	−	3.85213e6i	0.0502374	−	0.284910i	0.999569	+	0.0293667i	$0.00934906\pi$
$110$	1.32822e6			0.0951471
$111$	−1.51586e7	−	1.25066e7i	−1.05203	−	0.867980i
$112$	3.98582e6			0.268074
$113$	618743.	−	3.50906e6i	0.0403400	−	0.228779i	−0.957972	−	0.286862i	$-0.907388\pi$
$113$	618743.	−	3.50906e6i	0.0403400	−	0.228779i	0.998312	+	0.0580832i	$0.0184989\pi$
$114$	−1.68157e6	−	9.53668e6i	−0.106304	−	0.602879i
$115$	−6.14540e6	−	2.23674e6i	−0.376797	−	0.137143i
$116$	−3.98393e6	+	3.34291e6i	−0.236978	+	0.198849i
$117$	−2.16432e7			−1.24931
$118$	5.31490e6	−	4.45973e6i	0.297789	−	0.249874i
$119$	−5.66544e6	+	9.81282e6i	−0.308190	+	0.533801i
$120$	−1.94631e6	+	708400.i	−0.102820	+	0.0374235i
$121$	6.31736e6	+	1.09420e7i	0.324181	+	0.561497i
$122$	1.59118e6	−	2.75600e6i	0.0793339	−	0.137410i
$123$	886465.	−	5.02739e6i	0.0429530	−	0.243599i
$124$	5.62275e6	+	2.04651e6i	0.264833	+	0.0963915i
$125$	4.82747e6	+	8.36143e6i	0.221072	+	0.382909i
$126$	−1.12184e7	−	9.41337e6i	−0.499614	−	0.419226i
$127$	−3.34290e7	−	2.80503e7i	−1.44814	−	1.21513i	−0.933923	−	0.357475i	$-0.883638\pi$
$127$	−3.34290e7	−	2.80503e7i	−1.44814	−	1.21513i	−0.514219	−	0.857659i	$-0.671918\pi$
$128$	1.97068e6	−	717268.i	0.0830579	−	0.0302306i
$129$	5.69650e6	+	3.23065e7i	0.233638	+	1.32503i
$130$	1.01370e6	+	5.74897e6i	0.0404676	+	0.229503i
$131$	2.39473e7	−	8.71612e6i	0.930696	−	0.338746i	0.168211	−	0.985751i	$-0.446201\pi$
$131$	2.39473e7	−	8.71612e6i	0.930696	−	0.338746i	0.762485	+	0.647005i	$0.223979\pi$
$132$	8.18572e6	+	6.86863e6i	0.309776	+	0.259933i
$133$	−1.41471e7	−	1.18708e7i	−0.521419	−	0.437522i
$134$	−1.74294e7	−	3.01885e7i	−0.625770	−	1.08387i
$135$	−1.16255e6	−	423132.i	−0.0406670	−	0.0148016i
$136$	−1.03525e6	+	5.87120e6i	−0.0352907	+	0.200143i
$137$	1.91813e7	−	3.32229e7i	0.637316	−	1.10386i	−0.348703	−	0.937233i	$-0.613378\pi$
$137$	1.91813e7	−	3.32229e7i	0.637316	−	1.10386i	0.986019	−	0.166631i	$-0.0532889\pi$
$138$	−2.63068e7	−	4.55646e7i	−0.852100	−	1.47588i
$139$	4.00566e7	−	1.45794e7i	1.26509	−	0.460456i	0.379617	−	0.925144i	$-0.376056\pi$
$139$	4.00566e7	−	1.45794e7i	1.26509	−	0.460456i	0.885475	+	0.464688i	$0.153833\pi$
$140$	−1.97499e6	+	3.42078e6i	−0.0608298	+	0.105360i
$141$	−4.32928e7	+	3.63270e7i	−1.30062	+	1.09135i
$142$	−5.98878e6			−0.175521
$143$	2.30711e7	−	1.93590e7i	0.659770	−	0.553612i
$144$	−7.24062e6	−	2.63537e6i	−0.202073	−	0.0735484i
$145$	−894963.	−	5.07559e6i	−0.0243791	−	0.138261i
$146$	4.31019e6	−	2.44443e7i	0.114620	−	0.650044i
$147$	−7.86953e6			−0.204333
$148$	−1.84732e7	+	6.89792e6i	−0.468410	+	0.174905i
$149$	6.70794e7			1.66126			0.830630	−	0.556825i	$-0.187981\pi$
$149$	6.70794e7			1.66126			0.830630	+	0.556825i	$0.187981\pi$
$150$	−6.56587e6	+	3.72369e7i	−0.158845	+	0.900853i
$151$	4.48405e6	+	2.54303e7i	0.105987	+	0.601080i	0.990822	+	0.135176i	$0.0431599\pi$
$151$	4.48405e6	+	2.54303e7i	0.105987	+	0.601080i	−0.884835	+	0.465905i	$0.845729\pi$
$152$	−9.13086e6	−	3.32336e6i	−0.210891	−	0.0767582i
$153$	1.67799e7	−	1.40800e7i	0.378765	−	0.317822i
$154$	2.03784e7			0.449622
$155$	−4.54249e6	+	3.81160e6i	−0.0979790	+	0.0822142i
$156$	−2.34824e7	+	4.06726e7i	−0.495229	+	0.857761i
$157$	1.12738e7	−	4.10331e6i	0.232498	−	0.0846225i	−0.223144	−	0.974786i	$-0.571632\pi$
$157$	1.12738e7	−	4.10331e6i	0.232498	−	0.0846225i	0.455642	+	0.890163i	$0.349410\pi$
$158$	1.82306e7	+	3.15764e7i	0.367707	+	0.636887i
$159$	4.24183e7	−	7.34707e7i	0.836881	−	1.44952i
$160$	−360892.	+	2.04672e6i	−0.00696558	+	0.0395038i
$161$	−9.42867e7	−	3.43176e7i	−1.78057	−	0.648076i
$162$	−2.14331e7	−	3.71232e7i	−0.396079	−	0.686030i
$163$	4.80432e7	+	4.03131e7i	0.868911	+	0.729103i	0.963869	−	0.266378i	$-0.0858270\pi$
$163$	4.80432e7	+	4.03131e7i	0.868911	+	0.729103i	−0.0949572	+	0.995481i	$0.530271\pi$
$164$	−3.92397e6	−	3.29260e6i	−0.0694659	−	0.0582888i
$165$	−9.95098e6	+	3.62186e6i	−0.172453	+	0.0627679i
$166$	8.75212e6	+	4.96358e7i	0.148503	+	0.842202i
$167$	−6.47607e6	−	3.67276e7i	−0.107598	−	0.610218i	−0.990151	−	0.140005i	$-0.955288\pi$
$167$	−6.47607e6	−	3.67276e7i	−0.107598	−	0.610218i	0.882553	−	0.470213i	$-0.155823\pi$
$168$	−2.98616e7	+	1.08687e7i	−0.485882	+	0.176847i
$169$	5.33317e7	+	4.47506e7i	0.849928	+	0.713174i
$170$	−4.52592e6	−	3.79770e6i	−0.0706538	−	0.0592856i
$171$	1.78507e7	+	3.09184e7i	0.273004	+	0.472857i
$172$	3.09317e7	+	1.12582e7i	0.463505	+	0.168702i
$173$	1.87967e7	−	1.06601e8i	0.276007	−	1.56531i	−0.459740	−	0.888054i	$-0.652057\pi$
$173$	1.87967e7	−	1.06601e8i	0.276007	−	1.56531i	0.735746	−	0.677257i	$-0.236832\pi$
$174$	2.07318e7	−	3.59086e7i	0.298343	−	0.516745i
$175$	3.60545e7	+	6.24482e7i	0.508541	+	0.880819i
$176$	1.00755e7	−	3.66720e6i	0.139307	−	0.0507037i
$177$	−2.76580e7	+	4.79051e7i	−0.374899	+	0.649345i
$178$	−2.47820e7	+	2.07946e7i	−0.329357	+	0.276363i
$179$	−7.66830e7			−0.999340			−0.499670	−	0.866216i	$-0.666545\pi$
$179$	−7.66830e7			−0.999340			−0.499670	+	0.866216i	$0.666545\pi$
$180$	5.84953e6	−	4.90834e6i	0.0747597	−	0.0627308i
$181$	−6.66209e7	−	2.42480e7i	−0.835094	−	0.303949i	−0.111146	−	0.993804i	$-0.535452\pi$
$181$	−6.66209e7	−	2.42480e7i	−0.835094	−	0.303949i	−0.723948	+	0.689855i	$0.757674\pi$
$182$	1.55528e7	+	8.82045e7i	0.191232	+	1.08453i
$183$	−4.40584e6	+	2.49868e7i	−0.0531435	+	0.301392i
$184$	−5.27931e7			−0.624762
$185$	3.23350e6	−	1.92724e7i	0.0375467	−	0.223787i
$186$	−4.77060e7			−0.543598
$187$	−5.29296e6	+	3.00179e7i	−0.0591906	+	0.335687i
$188$	9.84719e6	+	5.58462e7i	0.108084	+	0.612973i
$189$	−1.78365e7	−	6.49197e6i	−0.192174	−	0.0699455i
$190$	7.37661e6	−	6.18971e6i	0.0780224	−	0.0654685i
$191$	1.27465e8			1.32366			0.661828	−	0.749655i	$-0.269781\pi$
$191$	1.27465e8			1.32366			0.661828	+	0.749655i	$0.269781\pi$
$192$	−1.28084e7	+	1.07475e7i	−0.130599	+	0.109586i
$193$	9.59784e6	−	1.66239e7i	0.0960999	−	0.166450i	−0.813967	−	0.580911i	$-0.802697\pi$
$193$	9.59784e6	−	1.66239e7i	0.0960999	−	0.166450i	0.910067	+	0.414461i	$0.136030\pi$
$194$	−1.60117e7	+	5.82777e6i	−0.157445	+	0.0573055i
$195$	−2.32712e7	−	4.03069e7i	−0.224749	−	0.389277i
$196$	−3.94819e6	+	6.83847e6i	−0.0374544	+	0.0648728i
$197$	1.18538e7	−	6.72260e7i	0.110465	−	0.626477i	−0.878431	−	0.477869i	$-0.841409\pi$
$197$	1.18538e7	−	6.72260e7i	0.110465	−	0.626477i	0.988896	−	0.148608i	$-0.0474794\pi$
$198$	−3.70193e7	−	1.34739e7i	−0.338923	−	0.123358i
$199$	4.50992e7	+	7.81141e7i	0.405679	+	0.702657i	0.994400	−	0.105679i	$-0.0337016\pi$
$199$	4.50992e7	+	7.81141e7i	0.405679	+	0.702657i	−0.588721	+	0.808336i	$0.700368\pi$
$200$	2.90640e7	+	2.43876e7i	0.256892	+	0.215558i
$201$	2.12900e8	+	1.78644e8i	1.84922	+	1.55168i
$202$	2.20660e6	−	803135.i	0.0188362	−	0.00685581i
$203$	−1.37311e7	−	7.78730e7i	−0.115205	−	0.653357i
$204$	−8.25384e6	−	4.68098e7i	−0.0680692	−	0.386039i
$205$	4.77018e6	−	1.73620e6i	0.0386719	−	0.0140754i
$206$	−7.02195e6	−	5.89212e6i	−0.0559658	−	0.0469609i
$207$	1.48591e8	+	1.24682e8i	1.16438	+	0.977032i
$208$	2.35625e7	+	4.08115e7i	0.181552	+	0.314457i
$209$	−4.66836e7	−	1.69914e7i	−0.353714	−	0.128741i
$210$	5.46858e6	−	3.10139e7i	0.0407481	−	0.231094i
$211$	−8.57809e7	+	1.48577e8i	−0.628640	+	1.08884i	0.359185	+	0.933266i	$0.383055\pi$
$211$	−8.57809e7	+	1.48577e8i	−0.628640	+	1.08884i	−0.987825	+	0.155570i	$0.950279\pi$
$212$	−4.25631e7	−	7.37215e7i	−0.306802	−	0.531396i
$213$	4.48678e7	−	1.63305e7i	0.318131	−	0.115790i
$214$	−2.26183e6	+	3.91761e6i	−0.0157766	+	0.0273258i
$215$	−2.49890e7	+	2.09683e7i	−0.171480	+	0.143889i
$216$	−9.98704e6			−0.0674293
$217$	−6.96939e7	+	5.84801e7i	−0.463005	+	0.388507i
$218$	2.94053e7	+	1.07026e7i	0.192233	+	0.0699670i
$219$	3.43642e7	+	1.94889e8i	0.221081	+	1.25382i
$220$	−1.84514e6	+	1.04643e7i	−0.0116829	+	0.0662570i
$221$	−1.33967e8			−0.834881
$222$	1.19591e8	−	1.02053e8i	0.733607	−	0.626021i
$223$	2.63950e8			1.59388			0.796938	−	0.604061i	$-0.206452\pi$
$223$	2.63950e8			1.59388			0.796938	+	0.604061i	$0.206452\pi$
$224$	−5.53704e6	+	3.14021e7i	−0.0329162	+	0.186677i
$225$	−2.42065e7	−	1.37282e8i	−0.141675	−	0.803479i
$226$	2.67865e7	+	9.74948e6i	0.154360	+	0.0561826i
$227$	−6.26298e7	+	5.25527e7i	−0.355378	+	0.298198i	−0.802945	−	0.596053i	$-0.796735\pi$
$227$	−6.26298e7	+	5.25527e7i	−0.355378	+	0.298198i	0.447567	+	0.894250i	$0.352291\pi$
$228$	7.74704e7			0.432876
$229$	−8.93193e7	+	7.49478e7i	−0.491497	+	0.412415i	−0.854562	−	0.519349i	$-0.826175\pi$
$229$	−8.93193e7	+	7.49478e7i	−0.491497	+	0.412415i	0.363065	+	0.931764i	$0.381730\pi$
$230$	2.61592e7	−	4.53090e7i	0.141768	−	0.245549i
$231$	−1.52674e8	+	5.55689e7i	−0.814937	+	0.296613i
$232$	−2.08026e7	−	3.60312e7i	−0.109373	−	0.189439i
$233$	5.57771e7	−	9.66087e7i	0.288875	−	0.500346i	−0.684667	−	0.728856i	$-0.740052\pi$
$233$	5.57771e7	−	9.66087e7i	0.288875	−	0.500346i	0.973541	+	0.228510i	$0.0733855\pi$
$234$	3.00664e7	−	1.70515e8i	0.153400	−	0.869977i
$235$	−5.28086e7	−	1.92208e7i	−0.265441	−	0.0966125i
$236$	2.77524e7	+	4.80686e7i	0.137439	+	0.238051i
$237$	−2.22687e8	−	1.86857e8i	−1.08662	−	0.911779i
$238$	−6.94396e7	−	5.82668e7i	−0.333878	−	0.280157i
$239$	−3.28608e8	+	1.19604e8i	−1.55699	+	0.566698i	−0.970044	−	0.242929i	$-0.921892\pi$
$239$	−3.28608e8	+	1.19604e8i	−1.55699	+	0.566698i	−0.586945	+	0.809627i	$0.699670\pi$
$240$	−2.87731e6	−	1.63181e7i	−0.0134353	−	0.0761955i
$241$	−2.27209e7	−	1.28857e8i	−0.104560	−	0.592990i	−0.991395	−	0.130904i	$-0.958212\pi$
$241$	−2.27209e7	−	1.28857e8i	−0.104560	−	0.592990i	0.886835	−	0.462086i	$-0.152899\pi$
$242$	−9.49821e7	+	3.45706e7i	−0.430812	+	0.156803i
$243$	2.29126e8	+	1.92260e8i	1.02436	+	0.859541i
$244$	1.95026e7	+	1.63646e7i	0.0859465	+	0.0721177i
$245$	−3.91269e6	−	6.77698e6i	−0.0169979	−	0.0294412i
$246$	3.83767e7	+	1.39680e7i	0.164359	+	0.0598219i
$247$	3.79156e7	−	2.15030e8i	0.160095	−	0.907945i
$248$	−2.39344e7	+	4.14556e7i	−0.0996419	+	0.172585i
$249$	−2.00920e8	−	3.48004e8i	−0.824756	−	1.42852i
$250$	−7.25814e7	+	2.64175e7i	−0.293789	+	0.106930i
$251$	−2.97356e7	+	5.15036e7i	−0.118691	+	0.205580i	−0.919249	−	0.393676i	$-0.871203\pi$
$251$	−2.97356e7	+	5.15036e7i	−0.118691	+	0.205580i	0.800558	+	0.599255i	$0.204537\pi$
$252$	8.97474e7	−	7.53070e7i	0.353281	−	0.296438i
$253$	−2.69917e8			−1.04787
$254$	2.67432e8	−	2.24402e8i	1.02399	−	0.859230i
$255$	4.42638e7	+	1.61107e7i	0.167170	+	0.0608449i
$256$	2.91333e6	+	1.65223e7i	0.0108530	+	0.0615505i
$257$	−1.20767e7	+	6.84904e7i	−0.0443795	+	0.251689i	−0.998924	−	0.0463802i	$-0.985231\pi$
$257$	−1.20767e7	+	6.84904e7i	−0.0443795	+	0.251689i	0.954544	+	0.298069i	$0.0963425\pi$
$258$	−2.62439e8			−0.951391
$259$	4.96105e7	−	2.95689e8i	0.177429	−	1.05751i
$260$	−4.67013e7			−0.164787
$261$	−2.65447e7	+	1.50543e8i	−0.0924137	+	0.524104i
$262$	3.54023e7	+	2.00777e8i	0.121612	+	0.689697i
$263$	−1.53695e8	−	5.59404e7i	−0.520972	−	0.189618i	0.0681306	−	0.997676i	$-0.478297\pi$
$263$	−1.53695e8	−	5.59404e7i	−0.520972	−	0.189618i	−0.589103	+	0.808058i	$0.700519\pi$
$264$	−6.54857e7	+	5.49491e7i	−0.219045	+	0.183800i
$265$	8.43608e7			0.278471
$266$	1.13177e8	−	9.49666e7i	0.368699	−	0.309375i
$267$	1.28962e8	−	2.23369e8i	0.414642	−	0.718181i
$268$	2.62052e8	−	9.53791e7i	0.831602	−	0.302678i
$269$	−2.33774e8	−	4.04908e8i	−0.732256	−	1.26831i	−0.955917	−	0.293638i	$-0.905134\pi$
$269$	−2.33774e8	−	4.04908e8i	−0.732256	−	1.26831i	0.223660	−	0.974667i	$-0.428199\pi$
$270$	4.94862e6	−	8.57126e6i	0.0153007	−	0.0265016i
$271$	993388.	−	5.63379e6i	0.00303198	−	0.0171952i	−0.983254	−	0.182239i	$-0.941665\pi$
$271$	993388.	−	5.63379e6i	0.00303198	−	0.0171952i	0.986286	+	0.165044i	$0.0527766\pi$
$272$	−4.48179e7	−	1.63124e7i	−0.135039	−	0.0491503i
$273$	−3.57042e8	−	6.18415e8i	−1.06206	−	1.83955i
$274$	2.35099e8	+	1.97272e8i	0.690437	+	0.579345i
$275$	1.48597e8	+	1.24687e8i	0.430868	+	0.361541i
$276$	3.95524e8	−	1.43959e8i	1.13238	−	0.412152i
$277$	4.43677e7	+	2.51622e8i	0.125426	+	0.711326i	0.981054	+	0.193735i	$0.0620601\pi$
$277$	4.43677e7	+	2.51622e8i	0.125426	+	0.711326i	−0.855628	+	0.517591i	$0.826829\pi$
$278$	5.92173e7	+	3.35838e8i	0.165307	+	0.937503i
$279$	1.65272e8	−	6.01540e7i	0.455601	−	0.165825i
$280$	−2.42069e7	−	2.03120e7i	−0.0659000	−	0.0552967i
$281$	2.94329e8	+	2.46971e8i	0.791335	+	0.664009i	0.946076	−	0.323946i	$-0.105010\pi$
$281$	2.94329e8	+	2.46971e8i	0.791335	+	0.664009i	−0.154740	+	0.987955i	$0.549454\pi$
$282$	−2.26059e8	−	3.91546e8i	−0.600275	−	1.03971i
$283$	2.95431e8	+	1.07528e8i	0.774824	+	0.282013i	0.699013	−	0.715109i	$-0.253623\pi$
$283$	2.95431e8	+	1.07528e8i	0.774824	+	0.282013i	0.0758115	+	0.997122i	$0.475845\pi$
$284$	8.31953e6	−	4.71824e7i	0.0215518	−	0.122227i
$285$	−3.83869e7	+	6.64880e7i	−0.0982259	+	0.170132i
$286$	1.20469e8	+	2.08658e8i	0.304504	+	0.527417i
$287$	7.31871e7	−	2.66379e7i	0.182746	−	0.0665141i
$288$	3.08212e7	−	5.33840e7i	0.0760285	−	0.131685i
$289$	−2.10474e8	+	1.76608e8i	−0.512926	+	0.430396i
$290$	4.12311e7			0.0992732
$291$	1.04067e8	−	8.73229e7i	0.247565	−	0.207732i
$292$	1.86596e8	+	6.79154e7i	0.438594	+	0.159635i
$293$	8.80505e7	+	4.99359e8i	0.204501	+	1.15978i	0.898223	+	0.439540i	$0.144858\pi$
$293$	8.80505e7	+	4.99359e8i	0.204501	+	1.15978i	−0.693722	+	0.720243i	$0.744030\pi$
$294$	1.09322e7	−	6.19998e7i	0.0250896	−	0.142290i
$295$	−5.50058e7			−0.124747
$296$	−2.86822e7	−	1.55123e8i	−0.0642824	−	0.347660i
$297$	−5.10610e7			−0.113095
$298$	−9.31858e7	+	5.28483e8i	−0.203982	+	1.15684i
$299$	−2.06001e8	−	1.16829e9i	−0.445677	−	2.52756i
$300$	−2.84248e8	−	1.03458e8i	−0.607818	−	0.221228i
$301$	−3.83398e8	+	3.21709e8i	−0.810339	+	0.679955i
$302$	−2.06581e8			−0.431585
$303$	−1.43417e7	+	1.20341e7i	−0.0296177	+	0.0248522i
$304$	3.88674e7	−	6.73203e7i	0.0793466	−	0.137432i
$305$	−2.37084e7	+	8.62914e6i	−0.0478467	+	0.0174148i
$306$	8.76185e7	+	1.51760e8i	0.174812	+	0.302783i
$307$	2.08932e7	−	3.61880e7i	0.0412116	−	0.0713806i	−0.844684	−	0.535266i	$-0.820212\pi$
$307$	2.08932e7	−	3.61880e7i	0.0412116	−	0.0713806i	0.885895	+	0.463885i	$0.153545\pi$
$308$	−2.83094e7	+	1.60551e8i	−0.0552081	+	0.313101i
$309$	6.86752e7	+	2.49957e7i	0.132417	+	0.0481960i
$310$	−2.37192e7	−	4.10829e7i	−0.0452204	−	0.0783240i
$311$	4.79681e8	+	4.02500e8i	0.904255	+	0.758760i	0.971017	−	0.239009i	$-0.0768224\pi$
$311$	4.79681e8	+	4.02500e8i	0.904255	+	0.758760i	−0.0667622	+	0.997769i	$0.521267\pi$
$312$	−2.87817e8	−	2.41507e8i	−0.536506	−	0.450182i
$313$	4.32490e8	−	1.57414e8i	0.797207	−	0.290160i	0.0888783	−	0.996042i	$-0.471672\pi$
$313$	4.32490e8	−	1.57414e8i	0.797207	−	0.290160i	0.708329	+	0.705883i	$0.249450\pi$
$314$	1.66664e7	+	9.45201e7i	0.0303801	+	0.172294i
$315$	2.01611e7	+	1.14340e8i	0.0363436	+	0.206115i
$316$	−2.74099e8	+	9.97638e7i	−0.488655	+	0.177856i
$317$	−5.40525e8	−	4.53554e8i	−0.953033	−	0.799690i	0.0267724	−	0.999642i	$-0.491477\pi$
$317$	−5.40525e8	−	4.53554e8i	−0.953033	−	0.799690i	−0.979806	+	0.199952i	$0.935922\pi$
$318$	5.19909e8	+	4.36256e8i	0.906635	+	0.760757i
$319$	−1.06358e8	−	1.84218e8i	−0.183444	−	0.317734i
$320$	−1.56237e7	−	5.68655e6i	−0.0266537	−	0.00970116i
$321$	6.26283e6	−	3.55183e7i	0.0105683	−	0.0599355i
$322$	4.01351e8	−	6.95161e8i	0.669930	−	1.16035i
$323$	1.10492e8	+	1.91378e8i	0.182441	+	0.315997i
$324$	3.22248e8	−	1.17289e8i	0.526360	−	0.191579i
$325$	−4.26279e8	+	7.38336e8i	−0.688814	+	1.19306i
$326$	−3.84346e8	+	3.22504e8i	−0.614413	+	0.515554i
$327$	−2.49488e8			−0.394577
$328$	3.13917e7	−	2.63408e7i	0.0491198	−	0.0412164i
$329$	−8.10225e8	−	2.94898e8i	−1.25435	−	0.456547i
$330$	−1.47109e7	−	8.34298e7i	−0.0225342	−	0.127798i
$331$	−2.06719e8	+	1.17236e9i	−0.313315	+	1.77690i	0.268200	+	0.963363i	$0.413571\pi$
$331$	−2.06719e8	+	1.17236e9i	−0.313315	+	1.77690i	−0.581515	+	0.813535i	$0.697540\pi$
$332$	−4.03212e8			−0.604714
$333$	−2.85628e8	+	5.04346e8i	−0.423883	+	0.748469i
$334$	2.98354e8			0.438146
$335$	−4.79898e7	+	2.72164e8i	−0.0697416	+	0.395524i
$336$	−4.41456e7	−	2.50362e8i	−0.0634893	−	0.360066i
$337$	6.18479e8	+	2.25108e8i	0.880280	+	0.320396i	0.742323	−	0.670043i	$-0.233724\pi$
$337$	6.18479e8	+	2.25108e8i	0.880280	+	0.320396i	0.137957	+	0.990438i	$0.455946\pi$
$338$	−4.26654e8	+	3.58005e8i	−0.600990	+	0.504290i
$339$	−2.27269e8			−0.316841
$340$	3.62074e7	−	3.03816e7i	0.0499598	−	0.0419212i
$341$	−1.22370e8	+	2.11951e8i	−0.167123	+	0.289465i
$342$	−2.68387e8	+	9.76849e7i	−0.362803	+	0.132049i
$343$	3.40664e8	+	5.90047e8i	0.455823	+	0.789509i
$344$	−1.31667e8	+	2.28054e8i	−0.174391	+	0.302054i
$345$	−7.24327e7	+	4.10786e8i	−0.0949659	+	0.538578i
$346$	8.13741e8	+	2.96178e8i	1.05614	+	0.384402i
$347$	3.60262e8	+	6.23992e8i	0.462876	+	0.801725i	0.999103	−	0.0423488i	$-0.0134841\pi$
$347$	3.60262e8	+	6.23992e8i	0.462876	+	0.801725i	−0.536227	+	0.844074i	$0.680151\pi$
$348$	2.54104e8	+	2.13219e8i	0.323210	+	0.271205i
$349$	8.24099e8	+	6.91501e8i	1.03774	+	0.870771i	0.991752	−	0.128171i	$-0.0409107\pi$
$349$	8.24099e8	+	6.91501e8i	1.03774	+	0.870771i	0.0459920	+	0.998942i	$0.485355\pi$
$350$	−5.42082e8	+	1.97302e8i	−0.675814	+	0.245976i
$351$	−3.89699e7	−	2.21009e8i	−0.0481010	−	0.272794i
$352$	1.48951e7	+	8.44742e7i	0.0182030	+	0.103234i
$353$	−7.86135e8	+	2.86130e8i	−0.951230	+	0.346219i	−0.770591	−	0.637330i	$-0.780039\pi$
$353$	−7.86135e8	+	2.86130e8i	−0.951230	+	0.346219i	−0.180639	+	0.983549i	$0.557817\pi$
$354$	−3.38996e8	−	2.84452e8i	−0.406147	−	0.340798i
$355$	3.63714e7	+	3.05192e7i	0.0431480	+	0.0362054i
$356$	−1.29402e8	−	2.24132e8i	−0.152008	−	0.263286i
$357$	6.79124e8	+	2.47181e8i	0.789970	+	0.287525i
$358$	1.06527e8	−	6.04144e8i	0.122707	−	0.695905i
$359$	7.32187e8	−	1.26819e9i	0.835202	−	1.44661i	−0.0586633	−	0.998278i	$-0.518684\pi$
$359$	7.32187e8	−	1.26819e9i	0.835202	−	1.44661i	0.893866	−	0.448335i	$-0.147983\pi$
$360$	3.05441e7	+	5.29039e7i	0.0345039	+	0.0597626i
$361$	5.01513e8	−	1.82536e8i	0.561056	−	0.204208i
$362$	2.83586e8	−	4.91185e8i	0.314199	−	0.544208i
$363$	6.17334e8	−	5.18004e8i	0.677402	−	0.568408i
$364$	−7.16522e8			−0.778708
$365$	−1.50747e8	+	1.26491e8i	−0.162264	+	0.136156i
$366$	−1.90737e8	−	6.94225e7i	−0.203353	−	0.0740144i
$367$	−1.59730e8	−	9.05871e8i	−0.168676	−	0.956611i	−0.945193	−	0.326513i	$-0.894126\pi$
$367$	−1.59730e8	−	9.05871e8i	−0.168676	−	0.956611i	0.776516	−	0.630097i	$-0.216985\pi$
$368$	7.33394e7	−	4.15928e8i	0.0767132	−	0.435062i
$369$	−1.50564e8			−0.156002
$370$	1.47345e8	+	5.22479e7i	0.151227	+	0.0536244i
$371$	1.29432e9			1.31593
$372$	6.62725e7	−	3.75850e8i	0.0667472	−	0.378542i
$373$	−1.38501e8	−	7.85476e8i	−0.138188	−	0.783704i	−0.972586	−	0.232542i	$-0.925296\pi$
$373$	−1.38501e8	−	7.85476e8i	−0.138188	−	0.783704i	0.834398	−	0.551162i	$-0.185815\pi$
$374$	−2.29142e8	−	8.34008e7i	−0.226492	−	0.0824365i
$375$	4.71741e8	−	3.95838e8i	0.461949	−	0.387621i
$376$	−4.53662e8			−0.440123
$377$	7.16182e8	−	6.00948e8i	0.688381	−	0.577620i
$378$	7.59250e7	−	1.31506e8i	0.0723042	−	0.125234i
$379$	1.69956e9	−	6.18589e8i	1.60361	−	0.583667i	0.623449	−	0.781864i	$-0.285731\pi$
$379$	1.69956e9	−	6.18589e8i	1.60361	−	0.583667i	0.980162	+	0.198198i	$0.0635088\pi$
$380$	3.85179e7	+	6.67150e7i	0.0360098	+	0.0623707i
$381$	−1.39168e9	+	2.41046e9i	−1.28915	+	2.23287i
$382$	−1.77073e8	+	1.00423e9i	−0.162529	+	0.921747i
$383$	1.91114e9	+	6.95599e8i	1.73819	+	0.632649i	0.999158	−	0.0410216i	$-0.0130613\pi$
$383$	1.91114e9	+	6.95599e8i	1.73819	+	0.632649i	0.739031	+	0.673671i	$0.235283\pi$
$384$	−6.68806e7	−	1.15841e8i	−0.0602755	−	0.104400i
$385$	−1.23763e8	−	1.03850e8i	−0.110530	−	0.0927454i
$386$	1.17638e8	+	9.87099e7i	0.104110	+	0.0873585i
$387$	9.09189e8	−	3.30918e8i	0.797381	−	0.290223i
$388$	−2.36707e7	−	1.34243e8i	−0.0205731	−	0.116676i
$389$	−1.99892e8	−	1.13365e9i	−0.172176	−	0.976458i	−0.941353	−	0.337423i	$-0.890445\pi$
$389$	−1.99892e8	−	1.13365e9i	−0.172176	−	0.976458i	0.769177	−	0.639035i	$-0.220666\pi$
$390$	3.49884e8	−	1.27348e8i	0.298675	−	0.108709i
$391$	9.19744e8	+	7.71757e8i	0.778123	+	0.652923i
$392$	−4.83919e7	−	4.06056e7i	−0.0405762	−	0.0340475i
$393$	−8.12721e8	−	1.40767e9i	−0.675410	−	1.16984i
$394$	5.13170e8	+	1.86779e8i	0.422693	+	0.153848i
$395$	5.01960e7	−	2.84675e8i	0.0409807	−	0.232413i
$396$	1.57581e8	−	2.72938e8i	0.127517	−	0.220867i
$397$	3.82393e8	+	6.62324e8i	0.306721	+	0.531256i	0.977643	−	0.210272i	$-0.0674350\pi$
$397$	3.82393e8	+	6.62324e8i	0.306721	+	0.531256i	−0.670922	+	0.741528i	$0.734102\pi$
$398$	−6.78070e8	+	2.46797e8i	−0.539118	+	0.196223i
$399$	−5.88957e8	+	1.02010e9i	−0.464171	+	0.803968i
$400$	−2.32512e8	+	1.95101e8i	−0.181650	+	0.152423i
$401$	−3.59701e8			−0.278571			−0.139285	−	0.990252i	$-0.544481\pi$
$401$	−3.59701e8			−0.278571			−0.139285	+	0.990252i	$0.544481\pi$
$402$	−1.70320e9	+	1.42915e9i	−1.30760	+	1.09721i
$403$	−1.01079e9	−	3.67897e8i	−0.769295	−	0.280000i
$404$	3.26210e6	+	1.85003e7i	0.00246129	+	0.0139587i
$405$	−5.90136e7	+	3.34683e8i	−0.0441428	+	0.250346i
$406$	6.32594e8			0.469120
$407$	−1.46645e8	−	7.93102e8i	−0.107817	−	0.583107i
$408$	3.80256e8			0.277182
$409$	1.47566e8	−	8.36891e8i	0.106649	−	0.604835i	−0.883900	−	0.467676i	$-0.845092\pi$
$409$	1.47566e8	−	8.36891e8i	0.106649	−	0.604835i	0.990549	−	0.137160i	$-0.0437973\pi$
$410$	7.05194e6	+	3.99936e7i	0.00505319	+	0.0286580i
$411$	−2.29929e9	−	8.36872e8i	−1.63360	−	0.594583i
$412$	5.61756e7	−	4.71369e7i	0.0395738	−	0.0332063i
$413$	−8.43935e8			−0.589500
$414$	−1.18872e9	+	9.97459e8i	−0.823342	+	0.690866i
$415$	1.99793e8	−	3.46052e8i	0.137218	−	0.237669i
$416$	−3.54264e8	+	1.28942e8i	−0.241269	+	0.0878146i
$417$	−1.35943e9	−	2.35461e9i	−0.918083	−	1.59017i
$418$	1.98719e8	−	3.44191e8i	0.133083	−	0.230506i
$419$	1.79905e8	−	1.02029e9i	0.119480	−	0.677605i	−0.864954	−	0.501851i	$-0.832653\pi$
$419$	1.79905e8	−	1.02029e9i	0.119480	−	0.677605i	0.984434	−	0.175754i	$-0.0562363\pi$
$420$	2.36745e8	+	8.61681e7i	0.155922	+	0.0567510i
$421$	7.54722e8	+	1.30722e9i	0.492946	+	0.853808i	0.999967	−	0.00812580i	$-0.00258655\pi$
$421$	7.54722e8	+	1.30722e9i	0.492946	+	0.853808i	−0.507021	+	0.861934i	$0.669253\pi$
$422$	−1.05139e9	−	8.82222e8i	−0.681037	−	0.571458i
$423$	1.27687e9	+	1.07142e9i	0.820266	+	0.688285i
$424$	6.39940e8	−	2.32919e8i	0.407717	−	0.148397i
$425$	−1.49833e8	−	8.49746e8i	−0.0946775	−	0.536943i
$426$	6.63298e7	+	3.76175e8i	0.0415695	+	0.235753i
$427$	−3.63749e8	+	1.32394e8i	−0.226102	+	0.0822944i
$428$	−2.77226e7	−	2.32620e7i	−0.0170915	−	0.0143415i
$429$	−1.47153e9	−	1.23476e9i	−0.899846	−	0.755060i
$430$	−1.30483e8	−	2.26004e8i	−0.0791436	−	0.137081i
$431$	−3.31231e7	−	1.20558e7i	−0.0199279	−	0.00725315i	0.332037	−	0.943266i	$-0.392264\pi$
$431$	−3.31231e7	−	1.20558e7i	−0.0199279	−	0.00725315i	−0.351965	+	0.936013i	$0.614486\pi$
$432$	1.38739e7	−	7.86825e7i	0.00827950	−	0.0469554i
$433$	1.67849e9	−	2.90723e9i	0.993599	−	1.72096i	0.398970	−	0.916964i	$-0.369368\pi$
$433$	1.67849e9	−	2.90723e9i	0.993599	−	1.72096i	0.594629	−	0.804000i	$-0.297299\pi$
$434$	−3.63916e8	−	6.30320e8i	−0.213691	−	0.370124i
$435$	−3.08902e8	+	1.12431e8i	−0.179932	+	0.0654899i
$436$	−1.25170e8	+	2.16800e8i	−0.0723264	+	0.125273i
$437$	−1.49905e9	+	1.25785e9i	−0.859274	+	0.721017i
$438$	−1.58317e9			−0.900258
$439$	−2.22706e9	+	1.86872e9i	−1.25634	+	1.05419i	−0.260274	+	0.965535i	$0.583813\pi$
$439$	−2.22706e9	+	1.86872e9i	−1.25634	+	1.05419i	−0.996062	+	0.0886565i	$0.971743\pi$
$440$	−7.98796e7	−	2.90738e7i	−0.0447045	−	0.0162711i
$441$	4.03041e7	+	2.28576e8i	0.0223776	+	0.126910i
$442$	1.86105e8	−	1.05545e9i	0.102513	−	0.581381i
$443$	−2.49436e9			−1.36316			−0.681580	−	0.731744i	$-0.738707\pi$
$443$	−2.49436e9			−1.36316			−0.681580	+	0.731744i	$0.738707\pi$
$444$	6.37884e8	+	1.08396e9i	0.345861	+	0.587726i
$445$	2.56478e8			0.137972
$446$	−3.66675e8	+	2.07952e9i	−0.195708	+	1.10992i
$447$	−7.42950e8	−	4.21348e9i	−0.393444	−	2.23133i
$448$	−2.39708e8	−	8.72467e7i	−0.125954	−	0.0458433i
$449$	9.28625e8	−	7.79209e8i	0.484148	−	0.406248i	−0.367775	−	0.929915i	$-0.619881\pi$
$449$	9.28625e8	−	7.79209e8i	0.484148	−	0.406248i	0.851924	+	0.523666i	$0.175436\pi$
$450$	1.11520e9			0.576910
$451$	1.60497e8	−	1.34673e8i	0.0823854	−	0.0691296i
$452$	−1.14022e8	+	1.97492e8i	−0.0580771	+	0.100593i
$453$	1.54770e9	−	5.63316e8i	0.782244	−	0.284714i
$454$	−3.27030e8	−	5.66432e8i	−0.164018	−	0.284088i
$455$	3.55039e8	−	6.14946e8i	0.176700	−	0.306053i
$456$	−1.07621e8	+	6.10348e8i	−0.0531519	+	0.301440i
$457$	1.89742e9	+	6.90604e8i	0.929943	+	0.338472i	0.762187	−	0.647357i	$-0.224126\pi$
$457$	1.89742e9	+	6.90604e8i	0.929943	+	0.338472i	0.167756	+	0.985829i	$0.446348\pi$
$458$	−4.66392e8	−	8.07815e8i	−0.226841	−	0.392901i
$459$	1.73991e8	+	1.45996e8i	0.0839812	+	0.0704686i
$460$	3.20626e8	+	2.69037e8i	0.153584	+	0.128872i
$461$	−2.07445e9	+	7.55037e8i	−0.986164	+	0.358934i	−0.784234	−	0.620466i	$-0.786944\pi$
$461$	−2.07445e9	+	7.55037e8i	−0.986164	+	0.358934i	−0.201930	+	0.979400i	$0.564721\pi$
$462$	−2.25705e8	−	1.28003e9i	−0.106486	−	0.603914i
$463$	2.05191e8	+	1.16370e9i	0.0960781	+	0.544886i	0.994412	+	0.105572i	$0.0336674\pi$
$463$	2.05191e8	+	1.16370e9i	0.0960781	+	0.544886i	−0.898334	+	0.439314i	$0.855222\pi$
$464$	3.12769e8	−	1.13839e8i	0.145349	−	0.0529025i
$465$	2.89730e8	+	2.43113e8i	0.133631	+	0.112130i
$466$	6.83643e8	+	5.73645e8i	0.312953	+	0.262599i
$467$	1.38082e9	+	2.39165e9i	0.627376	+	1.08665i	0.988076	+	0.153965i	$0.0492044\pi$
$467$	1.38082e9	+	2.39165e9i	0.627376	+	1.08665i	−0.360700	+	0.932682i	$0.617462\pi$
$468$	1.30163e9	+	4.73755e8i	0.586985	+	0.213645i
$469$	−7.36291e8	+	4.17571e9i	−0.329568	+	1.86907i
$470$	2.24791e8	−	3.89350e8i	0.0998704	−	0.172981i
$471$	−3.82607e8	−	6.62695e8i	−0.168725	−	0.292240i
$472$	−4.17260e8	+	1.51870e8i	−0.182646	+	0.0664777i
$473$	−6.73179e8	+	1.16598e9i	−0.292494	+	0.506614i
$474$	1.78150e9	−	1.49485e9i	0.768354	−	0.644725i
$475$	1.40633e9			0.602088
$476$	5.55517e8	−	4.66134e8i	0.236087	−	0.198101i
$477$	−2.35125e9	−	8.55786e8i	−0.991939	−	0.361036i
$478$	−4.85795e8	−	2.75508e9i	−0.203449	−	1.15382i
$479$	−1.59378e8	+	9.03880e8i	−0.0662606	+	0.375782i	0.933587	+	0.358350i	$0.116660\pi$
$479$	−1.59378e8	+	9.03880e8i	−0.0662606	+	0.375782i	−0.999848	+	0.0174327i	$0.994451\pi$
$480$	1.32558e8			0.0547095
$481$	3.32089e9	−	1.24002e9i	1.36065	−	0.508068i
$482$	1.04676e9			0.425776
$483$	−1.11131e9	+	6.30255e9i	−0.448766	+	2.54508i
$484$	−1.40416e8	−	7.96338e8i	−0.0562934	−	0.319256i
$485$	1.26941e8	+	4.62029e7i	0.0505251	+	0.0183896i
$486$	−1.83301e9	+	1.53808e9i	−0.724333	+	0.607788i
$487$	4.27306e9			1.67644			0.838218	−	0.545335i	$-0.183597\pi$
$487$	4.27306e9			1.67644			0.838218	+	0.545335i	$0.183597\pi$
$488$	−1.56021e8	+	1.30917e8i	−0.0607733	+	0.0509949i
$489$	2.00008e9	−	3.46425e9i	0.773512	−	1.33976i
$490$	5.88276e7	−	2.14115e7i	0.0225889	−	0.00822169i
$491$	−1.02227e9	−	1.77062e9i	−0.389743	−	0.675055i	0.602672	−	0.797989i	$-0.294103\pi$
$491$	−1.02227e9	−	1.77062e9i	−0.389743	−	0.675055i	−0.992415	+	0.122934i	$0.960769\pi$
$492$	−1.63358e8	+	2.82945e8i	−0.0618392	+	0.107109i
$493$	−1.64306e8	+	9.31826e8i	−0.0617575	+	0.350244i
$494$	1.64143e9	+	5.97433e8i	0.612603	+	0.222969i
$495$	1.56164e8	+	2.70483e8i	0.0578711	+	0.100236i
$496$	−2.93357e8	−	2.46156e8i	−0.107947	−	0.0905784i
$497$	5.58033e8	+	4.68245e8i	0.203898	+	0.171091i
$498$	3.02085e9	−	1.09950e9i	1.09604	−	0.398926i
$499$	−4.19605e8	−	2.37970e9i	−0.151178	−	0.857373i	−0.962197	−	0.272354i	$-0.912198\pi$
$499$	−4.19605e8	−	2.37970e9i	−0.151178	−	0.857373i	0.811019	−	0.585020i	$-0.198913\pi$
$500$	−1.07300e8	−	6.08529e8i	−0.0383888	−	0.217714i
$501$	−2.23525e9	+	8.13566e8i	−0.794136	+	0.289042i
$502$	−3.64461e8	−	3.05819e8i	−0.128584	−	0.107895i
$503$	1.89991e9	+	1.59421e9i	0.665649	+	0.558546i	0.911774	−	0.410692i	$-0.134713\pi$
$503$	1.89991e9	+	1.59421e9i	0.665649	+	0.558546i	−0.246125	+	0.969238i	$0.579157\pi$
$504$	4.68627e8	+	8.11687e8i	0.163050	+	0.282411i
$505$	−1.74940e7	−	6.36731e6i	−0.00604463	−	0.00220007i
$506$	3.74965e8	−	2.12653e9i	0.128666	−	0.729700i
$507$	2.22025e9	−	3.84558e9i	0.756613	−	1.31049i
$508$	1.39643e9	+	2.41869e9i	0.472603	+	0.818573i
$509$	3.89072e9	−	1.41610e9i	1.30773	−	0.475974i	0.408222	−	0.912883i	$-0.366149\pi$
$509$	3.89072e9	−	1.41610e9i	1.30773	−	0.475974i	0.899506	+	0.436909i	$0.143927\pi$
$510$	−1.88418e8	+	3.26350e8i	−0.0628966	+	0.108940i
$511$	−2.31285e9	+	1.94071e9i	−0.766787	+	0.643411i
$512$	−1.34218e8			−0.0441942
$513$	−2.83581e8	+	2.37952e8i	−0.0927397	+	0.0778179i
$514$	−5.22822e8	−	1.90292e8i	−0.169818	−	0.0618086i
$515$	1.26195e7	+	7.15686e7i	0.00407114	+	0.0230886i
$516$	3.64576e8	−	2.06761e9i	0.116819	−	0.662515i
$517$	−2.31945e9			−0.738190
$518$	2.26066e9	+	8.01621e8i	0.714629	+	0.253405i
$519$	−6.90416e9			−2.16783
$520$	6.48767e7	−	3.67934e8i	0.0202338	−	0.114752i
$521$	1.55559e8	+	8.82221e8i	0.0481908	+	0.273304i	0.999376	−	0.0353166i	$-0.0112440\pi$
$521$	1.55559e8	+	8.82221e8i	0.0481908	+	0.273304i	−0.951185	+	0.308620i	$0.900133\pi$
$522$	−1.14917e9	−	4.18263e8i	−0.353620	−	0.128707i
$523$	−3.92401e9	+	3.29264e9i	−1.19943	+	1.00644i	−0.199782	+	0.979840i	$0.564023\pi$
$523$	−3.92401e9	+	3.29264e9i	−1.19943	+	1.00644i	−0.999646	+	0.0265992i	$0.991532\pi$
$524$	−1.63099e9			−0.495213
$525$	3.52325e9	−	2.95636e9i	1.06264	−	0.891660i
$526$	6.54235e8	−	1.13317e9i	0.196013	−	0.339504i
$527$	1.02300e9	−	3.72341e8i	0.304465	−	0.110816i
$528$	−3.41942e8	−	5.92261e8i	−0.101096	−	0.175103i
$529$	−3.61358e9	+	6.25891e9i	−1.06131	+	1.83825i
$530$	−1.17193e8	+	6.64633e8i	−0.0341928	+	0.193917i
$531$	1.53309e9	+	5.57999e8i	0.444361	+	0.161734i
$532$	5.90967e8	+	1.02359e9i	0.170166	+	0.294736i
$533$	7.05403e8	+	5.91903e8i	0.201786	+	0.169319i
$534$	1.58065e9	+	1.32633e9i	0.449202	+	0.376926i
$535$	3.37010e7	−	1.22662e7i	0.00951492	−	0.00346315i
$536$	3.87402e8	+	2.19707e9i	0.108664	+	0.616263i
$537$	8.49316e8	+	4.81671e9i	0.236679	+	1.34227i
$538$	3.51481e9	−	1.27929e9i	0.973115	−	0.354185i
$539$	−2.47415e8	−	2.07605e8i	−0.0680557	−	0.0571055i
$540$	6.06538e7	+	5.08946e7i	0.0165760	+	0.0139089i
$541$	−7.40585e8	−	1.28273e9i	−0.201087	−	0.348293i	0.747792	−	0.663933i	$-0.231114\pi$
$541$	−7.40585e8	−	1.28273e9i	−0.201087	−	0.348293i	−0.948879	+	0.315640i	$0.897781\pi$
$542$	4.30056e7	+	1.56527e7i	0.0116018	+	0.00422273i
$543$	−7.85226e8	+	4.45324e9i	−0.210473	+	1.19365i
$544$	1.90777e8	−	3.30435e8i	0.0508077	−	0.0880015i
$545$	−1.24044e8	−	2.14851e8i	−0.0328238	−	0.0568525i
$546$	5.36816e9	−	1.95385e9i	1.41140	−	0.513709i
$547$	−2.48278e9	+	4.30030e9i	−0.648609	+	1.12342i	0.334847	+	0.942273i	$0.391315\pi$
$547$	−2.48278e9	+	4.30030e9i	−0.648609	+	1.12342i	−0.983455	+	0.181150i	$0.942018\pi$
$548$	−1.88079e9	+	1.57817e9i	−0.488213	+	0.409659i
$549$	7.48322e8			0.193013
$550$	−1.18877e9	+	9.97498e8i	−0.304670	+	0.255648i
$551$	−1.44917e9	−	5.27455e8i	−0.369053	−	0.134324i
$552$	5.84719e8	+	3.31611e9i	0.147966	+	0.839154i
$553$	7.70139e8	−	4.36768e9i	0.193656	−	1.09828i
$554$	−2.04403e9			−0.510743
$555$	−1.24637e9	+	1.03478e7i	−0.309473	+	0.00256934i
$556$	−2.72815e9			−0.673141
$557$	−6.82856e8	+	3.87267e9i	−0.167431	+	0.949548i	0.779092	+	0.626910i	$0.215681\pi$
$557$	−6.82856e8	+	3.87267e9i	−0.167431	+	0.949548i	−0.946522	+	0.322638i	$0.895430\pi$
$558$	2.44328e8	+	1.38565e9i	0.0595324	+	0.337625i
$559$	−5.56052e9	−	2.02386e9i	−1.34640	−	0.490050i
$560$	1.93655e8	−	1.62496e8i	0.0465983	−	0.0391007i
$561$	1.94414e9			0.464899
$562$	−2.35463e9	+	1.97577e9i	−0.559558	+	0.469525i
$563$	−2.82743e9	+	4.89725e9i	−0.667747	+	1.15657i	0.310785	+	0.950480i	$0.399408\pi$
$563$	−2.82743e9	+	4.89725e9i	−0.667747	+	1.15657i	−0.978533	+	0.206092i	$0.933925\pi$
$564$	3.39882e9	−	1.23707e9i	0.797721	−	0.290347i
$565$	−1.12997e8	−	1.95717e8i	−0.0263571	−	0.0456518i
$566$	−1.25756e9	+	2.17816e9i	−0.291523	+	0.504932i
$567$	−9.05425e8	+	5.13492e9i	−0.208599	+	1.18302i
$568$	3.60167e8	+	1.31090e8i	0.0824679	+	0.0300159i
$569$	−4.15075e9	−	7.18932e9i	−0.944570	−	1.63604i	−0.756610	−	0.653866i	$-0.773146\pi$
$569$	−4.15075e9	−	7.18932e9i	−0.944570	−	1.63604i	−0.187960	−	0.982177i	$-0.560188\pi$
$570$	−4.70497e8	−	3.94794e8i	−0.106413	−	0.0892911i
$571$	−2.93990e9	−	2.46686e9i	−0.660854	−	0.554522i	0.249489	−	0.968378i	$-0.419737\pi$
$571$	−2.93990e9	−	2.46686e9i	−0.660854	−	0.554522i	−0.910343	+	0.413855i	$0.864182\pi$
$572$	−1.81126e9	+	6.59244e8i	−0.404664	+	0.147286i
$573$	−1.41176e9	−	8.00652e9i	−0.313488	−	1.77788i
$574$	1.08196e8	+	6.13607e8i	0.0238791	+	0.135425i
$575$	7.18001e9	−	2.61331e9i	1.57502	−	0.573262i
$576$	3.77767e8	+	3.16984e8i	0.0823655	+	0.0691129i
$577$	6.00434e9	+	5.03824e9i	1.30122	+	1.09185i	0.989933	+	0.141534i	$0.0452034\pi$
$577$	6.00434e9	+	5.03824e9i	1.30122	+	1.09185i	0.311284	+	0.950317i	$0.399241\pi$
$578$	−1.09901e9	−	1.90355e9i	−0.236732	−	0.410031i
$579$	−1.15051e9	−	4.18750e8i	−0.246328	−	0.0896562i
$580$	−5.72776e7	+	3.24838e8i	−0.0121895	+	0.0691303i
$581$	3.06535e9	−	5.30935e9i	0.648432	−	1.12312i
$582$	5.43401e8	+	9.41198e8i	0.114259	+	0.197902i
$583$	3.27184e9	−	1.19085e9i	0.683836	−	0.248896i
$584$	−7.94285e8	+	1.37574e9i	−0.165018	+	0.285820i
$585$	−1.05156e9	+	8.82361e8i	−0.217164	+	0.182222i
$586$	−4.05650e9			−0.832741
$587$	9.09147e8	−	7.62865e8i	0.185524	−	0.155673i	−0.545295	−	0.838244i	$-0.683582\pi$
$587$	9.09147e8	−	7.62865e8i	0.185524	−	0.155673i	0.730820	+	0.682571i	$0.239138\pi$
$588$	4.73276e8	+	1.72258e8i	0.0960050	+	0.0349430i
$589$	3.08112e8	+	1.74739e9i	0.0621306	+	0.352360i
$590$	7.64132e7	−	4.33361e8i	0.0153175	−	0.0868696i
$591$	−4.35397e9			−0.867620
$592$	1.26198e9	−	1.04773e7i	0.249991	−	0.00207550i
$593$	7.34024e9			1.44550			0.722751	−	0.691108i	$-0.242877\pi$
$593$	7.34024e9			1.44550			0.722751	+	0.691108i	$0.242877\pi$
$594$	7.09333e7	−	4.02283e8i	0.0138866	−	0.0787551i
$595$	1.24793e8	+	7.07737e8i	0.0242874	+	0.137741i
$596$	−4.03418e9	−	1.46832e9i	−0.780537	−	0.284092i
$597$	4.40710e9	−	3.69800e9i	0.847701	−	0.711305i
$598$	9.49050e9			1.81483
$599$	6.18802e8	−	5.19237e8i	0.117641	−	0.0987124i	−0.582070	−	0.813139i	$-0.697757\pi$
$599$	6.18802e8	−	5.19237e8i	0.117641	−	0.0987124i	0.699710	+	0.714427i	$0.253312\pi$
$600$	1.20996e9	−	2.09572e9i	0.228688	−	0.396098i
$601$	−6.16638e9	+	2.24438e9i	−1.15870	+	0.421731i	−0.848632	−	0.528984i	$-0.822573\pi$
$601$	−6.16638e9	+	2.24438e9i	−1.15870	+	0.421731i	−0.310065	+	0.950715i	$0.600351\pi$
$602$	−2.00196e9	−	3.46750e9i	−0.373997	−	0.647781i
$603$	4.09847e9	−	7.09876e9i	0.761222	−	1.31847i
$604$	2.86979e8	−	1.62754e9i	0.0529933	−	0.300540i
$605$	7.53024e8	+	2.74078e8i	0.138250	+	0.0503189i
$606$	−7.48871e7	−	1.29708e8i	−0.0136695	−	0.0236763i
$607$	−2.62987e9	−	2.20672e9i	−0.477280	−	0.400485i	0.372162	−	0.928168i	$-0.378617\pi$
$607$	−2.62987e9	−	2.20672e9i	−0.477280	−	0.400485i	−0.849442	+	0.527683i	$0.823061\pi$
$608$	4.76387e8	+	3.99736e8i	0.0859601	+	0.0721291i
$609$	−4.73938e9	+	1.72499e9i	−0.850278	+	0.309476i
$610$	−3.50490e7	−	1.98773e8i	−0.00625203	−	0.0354571i
$611$	−1.77021e9	−	1.00393e10i	−0.313964	−	1.78058i
$612$	−1.31735e9	+	4.79477e8i	−0.232312	+	0.0845547i
$613$	−2.23391e8	−	1.87447e8i	−0.0391700	−	0.0328675i	0.622993	−	0.782228i	$-0.285917\pi$
$613$	−2.23391e8	−	1.87447e8i	−0.0391700	−	0.0328675i	−0.662162	+	0.749360i	$0.730361\pi$
$614$	2.56081e8	+	2.14878e8i	0.0446466	+	0.0374630i
$615$	−1.61889e8	−	2.80401e8i	−0.0280644	−	0.0486090i
$616$	−1.22556e9	−	4.46069e8i	−0.211253	−	0.0768899i
$617$	8.75048e8	−	4.96264e9i	0.149980	−	0.850579i	−0.813253	−	0.581911i	$-0.802305\pi$
$617$	8.75048e8	−	4.96264e9i	0.149980	−	0.850579i	0.963233	−	0.268669i	$-0.0865836\pi$
$618$	−2.92330e8	+	5.06331e8i	−0.0498212	+	0.0862929i
$619$	−1.25742e9	−	2.17791e9i	−0.213089	−	0.369082i	0.739590	−	0.673057i	$-0.235019\pi$
$619$	−1.25742e9	−	2.17791e9i	−0.213089	−	0.369082i	−0.952680	+	0.303976i	$0.901686\pi$
$620$	3.56620e8	−	1.29799e8i	0.0600945	−	0.0218726i
$621$	−1.00564e9	+	1.74183e9i	−0.168509	+	0.291866i
$622$	−3.83745e9	+	3.22000e9i	−0.639405	+	0.536524i
$623$	3.93505e9			0.651992
$624$	2.30253e9	−	1.93205e9i	0.379367	−	0.318327i
$625$	−4.86468e9	−	1.77060e9i	−0.797029	−	0.290095i
$626$	6.39368e8	+	3.62603e9i	0.104169	+	0.590774i
$627$	−5.50236e8	+	3.12054e9i	−0.0891482	+	0.505584i
$628$	−7.67826e8			−0.123710
$629$	−1.76798e9	+	3.12179e9i	−0.283269	+	0.500181i
$630$	−9.28827e8			−0.147994
$631$	3.87828e8	−	2.19948e9i	0.0614521	−	0.348512i	−0.938542	−	0.345164i	$-0.887823\pi$
$631$	3.87828e8	−	2.19948e9i	0.0614521	−	0.348512i	0.999994	−	0.00334789i	$-0.00106567\pi$
$632$	−4.05211e8	−	2.29807e9i	−0.0638516	−	0.362120i
$633$	1.02827e10	+	3.74259e9i	1.61136	+	0.586488i
$634$	4.32420e9	−	3.62843e9i	0.673896	−	0.565466i
$635$	−2.76775e9			−0.428962
$636$	−4.15927e9	+	3.49004e9i	−0.641088	+	0.537936i
$637$	7.09758e8	−	1.22934e9i	0.108798	−	0.188444i
$638$	1.59910e9	−	5.82026e8i	0.243783	−	0.0887299i
$639$	−7.04123e8	−	1.21958e9i	−0.106757	−	0.184908i
$640$	6.65054e7	−	1.15191e8i	0.0100283	−	0.0173695i
$641$	−1.00618e8	+	5.70635e8i	−0.0150895	+	0.0855766i	−0.991423	−	0.130696i	$-0.958279\pi$
$641$	−1.00618e8	+	5.70635e8i	−0.0150895	+	0.0855766i	0.976333	+	0.216273i	$0.0693900\pi$
$642$	2.71129e8	+	9.86830e7i	0.0404393	+	0.0147187i
$643$	−3.87234e9	−	6.70709e9i	−0.574427	−	0.994937i	−0.996104	−	0.0881904i	$-0.971892\pi$
$643$	−3.87234e9	−	6.70709e9i	−0.574427	−	0.994937i	0.421677	−	0.906746i	$-0.361442\pi$
$644$	4.91925e9	+	4.12774e9i	0.725769	+	0.608992i
$645$	1.59386e9	+	1.33740e9i	0.233878	+	0.196247i
$646$	−1.66126e9	+	6.04649e8i	−0.242451	+	0.0882448i
$647$	1.70836e7	+	9.68860e7i	0.00247979	+	0.0140636i	0.986023	−	0.166612i	$-0.0532827\pi$
$647$	1.70836e7	+	9.68860e7i	0.00247979	+	0.0140636i	−0.983543	+	0.180676i	$0.942172\pi$
$648$	4.76393e8	+	2.70176e9i	0.0687785	+	0.390062i
$649$	−2.13334e9	+	7.76472e8i	−0.306340	+	0.111499i
$650$	−5.22477e9	−	4.38411e9i	−0.746227	−	0.626159i
$651$	4.44523e9	+	3.72999e9i	0.631482	+	0.529876i
$652$	−2.00691e9	−	3.47607e9i	−0.283571	−	0.491159i
$653$	1.15884e10	+	4.21785e9i	1.62866	+	0.592782i	0.985003	−	0.172536i	$-0.0551961\pi$
$653$	1.15884e10	+	4.21785e9i	1.62866	+	0.592782i	0.643652	+	0.765318i	$0.277418\pi$
$654$	3.46585e8	−	1.96558e9i	0.0484493	−	0.274770i
$655$	8.08162e8	−	1.39978e9i	0.112371	−	0.194632i
$656$	1.63916e8	+	2.83911e8i	0.0226703	+	0.0392662i
$657$	5.48469e9	−	1.99627e9i	0.754525	−	0.274625i
$658$	3.44889e9	−	5.97366e9i	0.471942	−	0.817428i
$659$	−1.11225e9	+	9.33285e8i	−0.151392	+	0.127033i	−0.715338	−	0.698779i	$-0.753727\pi$
$659$	−1.11225e9	+	9.33285e8i	−0.151392	+	0.127033i	0.563946	+	0.825812i	$0.309283\pi$
$660$	6.77735e8			0.0917606
$661$	−9.59611e9	+	8.05209e9i	−1.29238	+	1.08444i	−0.300971	+	0.953633i	$0.597311\pi$
$661$	−9.59611e9	+	8.05209e9i	−1.29238	+	1.08444i	−0.991409	+	0.130802i	$0.958245\pi$
$662$	−8.94922e9	−	3.25725e9i	−1.19890	−	0.436363i
$663$	1.48377e9	+	8.41490e9i	0.197729	+	1.12138i
$664$	5.60136e8	−	3.17669e9i	0.0742515	−	0.421101i
$665$	−1.17131e9			−0.154452
$666$	−3.57668e9	−	2.95094e9i	−0.469159	−	0.387080i
$667$	−8.37886e9			−1.09331
$668$	−4.14468e8	+	2.35057e9i	−0.0537989	+	0.305109i
$669$	−2.92342e9	−	1.65796e10i	−0.377486	−	2.14083i
$670$	−2.07756e9	−	7.56172e8i	−0.266866	−	0.0971312i
$671$	−7.97692e8	+	6.69343e8i	−0.101931	+	0.0855303i
$672$	2.03380e9			0.258532
$673$	6.55557e8	−	5.50077e8i	0.0829006	−	0.0695618i	−0.600396	−	0.799703i	$-0.704990\pi$
$673$	6.55557e8	−	5.50077e8i	0.0829006	−	0.0695618i	0.683296	+	0.730141i	$0.260546\pi$
$674$	−2.63269e9	+	4.55995e9i	−0.331200	+	0.573655i
$675$	1.35827e9	−	4.94368e8i	0.169989	−	0.0618710i
$676$	−2.22783e9	−	3.85871e9i	−0.277376	−	0.480429i
$677$	4.96108e8	−	8.59285e8i	0.0614492	−	0.106433i	−0.833664	−	0.552272i	$-0.813761\pi$
$677$	4.96108e8	−	8.59285e8i	0.0614492	−	0.106433i	0.895113	+	0.445839i	$0.147094\pi$
$678$	3.15718e8	−	1.79053e9i	0.0389042	−	0.220636i
$679$	1.94762e9	+	7.08875e8i	0.238759	+	0.0869011i
$680$	1.89061e8	+	3.27464e8i	0.0230580	+	0.0399376i
$681$	3.99467e9	+	3.35193e9i	0.484693	+	0.406705i
$682$	−1.49986e9	−	1.25853e9i	−0.181052	−	0.151921i
$683$	2.93335e9	−	1.06765e9i	0.352283	−	0.128220i	−0.159816	−	0.987147i	$-0.551090\pi$
$683$	2.93335e9	−	1.06765e9i	0.352283	−	0.128220i	0.512099	+	0.858926i	$0.328868\pi$
$684$	−3.96768e8	−	2.25018e9i	−0.0474067	−	0.268857i
$685$	−4.22508e8	−	2.39616e9i	−0.0502247	−	0.284838i
$686$	−5.12191e9	+	1.86422e9i	−0.605756	+	0.220477i
$687$	5.69699e9	+	4.78034e9i	0.670342	+	0.562484i
$688$	−1.61381e9	−	1.35415e9i	−0.188926	−	0.158528i
$689$	7.65147e9	+	1.32527e10i	0.891205	+	1.54361i
$690$	−3.13574e9	−	1.14132e9i	−0.363386	−	0.132262i
$691$	2.57653e9	−	1.46122e10i	0.297072	−	1.68478i	−0.361588	−	0.932338i	$-0.617765\pi$
$691$	2.57653e9	−	1.46122e10i	0.297072	−	1.68478i	0.658660	−	0.752441i	$-0.271124\pi$
$692$	−3.46386e9	+	5.99958e9i	−0.397365	+	0.688256i
$693$	2.39597e9	+	4.14993e9i	0.273473	+	0.473669i
$694$	−5.41656e9	+	1.97147e9i	−0.615128	+	0.223888i
$695$	1.35181e9	−	2.34140e9i	0.152745	−	0.264563i
$696$	−2.03283e9	+	1.70575e9i	−0.228544	+	0.191771i
$697$	−9.31960e8			−0.104252
$698$	−6.59279e9	+	5.53201e9i	−0.733796	+	0.615728i
$699$	−6.68608e9	−	2.43353e9i	−0.740460	−	0.269505i
$700$	−8.01382e8	−	4.54486e9i	−0.0883073	−	0.500815i
$701$	1.85017e9	−	1.04928e10i	0.202861	−	1.15048i	−0.697910	−	0.716185i	$-0.745886\pi$
$701$	1.85017e9	−	1.04928e10i	0.202861	−	1.15048i	0.900771	−	0.434295i	$-0.143002\pi$
$702$	1.79535e9			0.195870
$703$	−4.51041e9	−	3.72131e9i	−0.489635	−	0.403973i
$704$	−6.86219e8			−0.0741239
$705$	−6.22428e8	+	3.52997e9i	−0.0669002	+	0.379410i
$706$	−1.16217e9	−	6.59102e9i	−0.124295	−	0.704914i
$707$	−2.68405e8	−	9.76914e7i	−0.0285642	−	0.0103965i
$708$	2.71197e9	−	2.27561e9i	0.287190	−	0.240981i
$709$	−8.59293e8			−0.0905482			−0.0452741	−	0.998975i	$-0.514416\pi$
$709$	−8.59293e8			−0.0905482			−0.0452741	+	0.998975i	$0.514416\pi$
$710$	−2.90971e8	+	2.44154e8i	−0.0305102	+	0.0256011i
$711$	−4.28688e9	+	7.42510e9i	−0.447299	+	0.774745i
$712$	1.94558e9	−	7.08132e8i	0.202008	−	0.0735249i
$713$	4.82015e9	+	8.34874e9i	0.498020	+	0.862596i
$714$	−2.89084e9	+	5.00707e9i	−0.297221	+	0.514802i
$715$	3.31697e8	−	1.88115e9i	0.0339368	−	0.192465i
$716$	4.61174e9	+	1.67854e9i	0.469536	+	0.170897i
$717$	1.11522e10	+	1.93163e10i	1.12991	+	1.95707i
$718$	8.97421e9	+	7.53026e9i	0.904817	+	0.759231i
$719$	7.68515e9	+	6.44860e9i	0.771083	+	0.647015i	0.940986	−	0.338446i	$-0.109901\pi$
$719$	7.68515e9	+	6.44860e9i	0.771083	+	0.647015i	−0.169903	+	0.985461i	$0.554346\pi$
$720$	−4.59233e8	+	1.67147e8i	−0.0458532	+	0.0166892i
$721$	1.93616e8	+	1.09805e9i	0.0192384	+	0.109106i
$722$	7.41406e8	+	4.20472e9i	0.0733122	+	0.415774i
$723$	−7.84227e9	+	2.85435e9i	−0.771716	+	0.280882i
$724$	3.47583e9	+	2.91657e9i	0.340387	+	0.285619i
$725$	4.61279e9	+	3.87059e9i	0.449553	+	0.377220i
$726$	3.22349e9	+	5.58324e9i	0.312642	+	0.541512i
$727$	4.80412e9	+	1.74856e9i	0.463707	+	0.168775i	0.563299	−	0.826253i	$-0.309532\pi$
$727$	4.80412e9	+	1.74856e9i	0.463707	+	0.168775i	−0.0995928	+	0.995028i	$0.531754\pi$
$728$	9.95381e8	−	5.64509e9i	0.0956158	−	0.542264i
$729$	3.67948e9	−	6.37304e9i	0.351754	−	0.609257i
$730$	−7.87143e8	−	1.36337e9i	−0.0748900	−	0.129713i
$731$	5.62768e9	−	2.04831e9i	0.532867	−	0.193948i
$732$	8.11911e8	−	1.40627e9i	0.0765103	−	0.132520i
$733$	−8.67421e9	+	7.27853e9i	−0.813516	+	0.682621i	−0.951444	−	0.307821i	$-0.900400\pi$
$733$	−8.67421e9	+	7.27853e9i	−0.813516	+	0.682621i	0.137928	+	0.990442i	$0.455956\pi$
$734$	7.35876e9			0.686861
$735$	−3.82349e8	+	3.20829e8i	−0.0355184	+	0.0298035i
$736$	3.17499e9	+	1.15560e9i	0.293542	+	0.106841i
$737$	1.98068e9	+	1.12330e10i	0.182255	+	1.03362i
$738$	2.09162e8	−	1.18621e9i	0.0191551	−	0.108634i
$739$	−7.75931e9			−0.707241			−0.353620	−	0.935389i	$-0.615050\pi$
$739$	−7.75931e9			−0.707241			−0.353620	+	0.935389i	$0.615050\pi$
$740$	−6.16322e8	+	1.08827e9i	−0.0559109	+	0.0987244i
$741$	−1.39267e10			−1.25743
$742$	−1.79805e9	+	1.01972e10i	−0.161580	+	0.916366i
$743$	−3.40809e9	−	1.93283e10i	−0.304825	−	1.72875i	−0.624327	−	0.781163i	$-0.714627\pi$
$743$	−3.40809e9	−	1.93283e10i	−0.304825	−	1.72875i	0.319502	−	0.947586i	$-0.396484\pi$
$744$	2.86905e9	+	1.04425e9i	0.255407	+	0.0929607i
$745$	3.25912e9	−	2.73473e9i	0.288771	−	0.242308i
$746$	6.38075e9			0.562711
$747$	−9.07899e9	+	7.61817e9i	−0.796921	+	0.668696i
$748$	9.75390e8	−	1.68943e9i	0.0852163	−	0.147599i
$749$	5.17063e8	−	1.88196e8i	0.0449632	−	0.0163653i
$750$	2.46326e9	+	4.26649e9i	0.213204	+	0.369280i
$751$	1.00562e10	−	1.74179e10i	0.866353	−	1.50057i	0.000655367	−	1.00000i	$-0.499791\pi$
$751$	1.00562e10	−	1.74179e10i	0.866353	−	1.50057i	0.865698	−	0.500567i	$-0.166875\pi$
$752$	6.30220e8	−	3.57416e9i	0.0540418	−	0.306486i
$753$	3.56445e9	+	1.29736e9i	0.304236	+	0.110733i
$754$	3.73964e9	+	6.47724e9i	0.317709	+	0.550289i
$755$	1.25462e9	+	1.05275e9i	0.106096	+	0.0890247i
$756$	9.30590e8	+	7.80858e8i	0.0783307	+	0.0657273i
$757$	1.31972e10	−	4.80340e9i	1.10573	−	0.402451i	0.276301	−	0.961071i	$-0.410891\pi$

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38919 + 7.87846i) q^{2} +(-11.0757 - 62.8133i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(48.5860 - 40.7685i) q^{5} +510.258 q^{6} +(745.438 - 625.497i) q^{7} +(256.000 - 443.405i) q^{8} +(-1767.73 + 643.401i) q^{9} +O(q^{10})\)	\(q+(-1.38919 + 7.87846i) q^{2} +(-11.0757 - 62.8133i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(48.5860 - 40.7685i) q^{5} +510.258 q^{6} +(745.438 - 625.497i) q^{7} +(256.000 - 443.405i) q^{8} +(-1767.73 + 643.401i) q^{9} +(253.698 + 439.418i) q^{10} +(1308.86 - 2267.01i) q^{11} +(-708.843 + 4020.05i) q^{12} +(10811.3 + 3934.99i) q^{13} +(3892.40 + 6741.84i) q^{14} +(-3098.93 - 2600.31i) q^{15} +(3137.72 + 2632.86i) q^{16} +(-10941.9 + 3982.52i) q^{17} +(-2613.31 - 14820.8i) q^{18} +(-3295.54 - 18689.9i) q^{19} +(-3814.37 + 1388.32i) q^{20} +(-47545.7 - 39895.6i) q^{21} +(16042.3 + 13461.1i) q^{22} +(-51555.8 - 89297.2i) q^{23} +(-30687.1 - 11169.2i) q^{24} +(-12867.7 + 72976.6i) q^{25} +(-46020.5 + 79709.9i) q^{26} +(-9752.97 - 16892.6i) q^{27} +(-58522.6 + 21300.5i) q^{28} +(40630.1 - 70373.4i) q^{29} +(24791.4 - 20802.5i) q^{30} -93493.8 q^{31} +(-25101.7 + 21062.9i) q^{32} +(-156895. - 57105.0i) q^{33} +(-16175.8 - 91737.6i) q^{34} +(10717.3 - 60780.8i) q^{35} +120395. q^{36} +(234374. - 200002. i) q^{37} +151826. q^{38} +(127427. - 722675. i) q^{39} +(-5638.94 - 31980.0i) q^{40} +(75210.3 + 27374.3i) q^{41} +(380366. - 319165. i) q^{42} -514325. q^{43} +(-128338. + 107689. i) q^{44} +(-59656.4 + 103328. i) q^{45} +(775145. - 282130. i) q^{46} +(-443029. - 767349. i) q^{47} +(130626. - 226251. i) q^{48} +(21424.9 - 121507. i) q^{49} +(-557067. - 202756. i) q^{50} +(371343. + 643186. i) q^{51} +(-564060. - 473303. i) q^{52} +(1.01891e6 + 854970. i) q^{53} +(146637. - 53371.4i) q^{54} +(-28830.4 - 163505. i) q^{55} +(-86516.3 - 490658. i) q^{56} +(-1.13747e6 + 414007. i) q^{57} +(497991. + 417864. i) q^{58} +(-664363. - 557466. i) q^{59} +(129452. + 224217. i) q^{60} +(-373804. - 136054. i) q^{61} +(129880. - 736588. i) q^{62} +(-915288. + 1.58533e6i) q^{63} +(-131072. - 227023. i) q^{64} +(685701. - 249575. i) q^{65} +(667856. - 1.15676e6i) q^{66} +(-3.33792e6 + 2.80084e6i) q^{67} +745222. q^{68} +(-5.03804e6 + 4.22741e6i) q^{69} +(463971. + 168871. i) q^{70} +(129993. + 737225. i) q^{71} +(-167252. + 948531. i) q^{72} -3.10268e6 q^{73} +(1.25012e6 + 2.12434e6i) q^{74} +4.72642e6 q^{75} +(-210914. + 1.19615e6i) q^{76} +(-442334. - 2.50860e6i) q^{77} +(5.51655e6 + 2.00786e6i) q^{78} +(3.49137e6 - 2.92960e6i) q^{79} +259787. q^{80} +(-4.10467e6 + 3.44423e6i) q^{81} +(-320148. + 554513. i) q^{82} +(5.92024e6 - 2.15479e6i) q^{83} +(1.98613e6 + 3.44008e6i) q^{84} +(-369260. + 639578. i) q^{85} +(714493. - 4.05209e6i) q^{86} +(-4.87039e6 - 1.77268e6i) q^{87} +(-670136. - 1.16071e6i) q^{88} +(3.09775e6 + 2.59932e6i) q^{89} +(-731192. - 613543. i) q^{90} +(1.05205e7 - 3.82914e6i) q^{91} +(1.14593e6 + 6.49888e6i) q^{92} +(1.03551e6 + 5.87265e6i) q^{93} +(6.66098e6 - 2.42440e6i) q^{94} +(-922076. - 773714. i) q^{95} +(1.60105e6 + 1.34344e6i) q^{96} +(1.06495e6 + 1.84455e6i) q^{97} +(927522. + 337590. i) q^{98} +(-855112. + 4.84958e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9}+O(q^{10}) \) 66 * q - 39 * q^3 + 459 * q^5 - 918 * q^7 + 16896 * q^8 + 3237 * q^9	\( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9} + 4704 q^{10} + 4539 q^{11} - 2496 q^{12} - 10542 q^{13} + 6744 q^{14} - 39894 q^{15} - 78822 q^{17} + 51792 q^{18} + 79461 q^{19} + 29376 q^{20} - 5835 q^{21} + 18168 q^{22} - 199479 q^{23} + 19968 q^{24} + 356301 q^{25} + 186744 q^{26} - 91689 q^{27} - 91584 q^{28} - 38526 q^{29} + 319152 q^{30} + 1917246 q^{31} - 902847 q^{33} - 205776 q^{34} - 1574793 q^{35} + 3079296 q^{36} - 396513 q^{37} - 692880 q^{38} + 2514306 q^{39} + 470016 q^{40} + 2989350 q^{41} + 46680 q^{42} + 6006348 q^{43} - 145344 q^{44} + 1083726 q^{45} - 588744 q^{46} - 894135 q^{47} + 7973742 q^{49} + 2012400 q^{50} - 524880 q^{51} - 2262720 q^{52} + 1457844 q^{53} + 1452312 q^{54} + 2415690 q^{55} - 1202688 q^{56} + 2734338 q^{57} - 3423360 q^{58} + 3099522 q^{59} - 3102912 q^{60} - 10968396 q^{61} - 3067320 q^{62} - 10727970 q^{63} - 8650752 q^{64} - 13497300 q^{65} - 4598712 q^{66} - 1978119 q^{67} + 5026176 q^{68} - 7251108 q^{69} + 435744 q^{70} - 19555002 q^{71} + 3314688 q^{72} - 31332840 q^{73} + 7607472 q^{74} + 44758074 q^{75} + 5085504 q^{76} + 1982007 q^{77} - 22512264 q^{78} + 10522902 q^{79} + 4816896 q^{80} - 7548876 q^{81} - 7150320 q^{82} + 19771926 q^{83} + 3556224 q^{84} - 6684072 q^{85} + 22982496 q^{86} - 67769667 q^{87} - 2323968 q^{88} - 42018963 q^{89} - 25158672 q^{90} + 4847565 q^{91} - 1096704 q^{92} - 14558475 q^{93} + 3175680 q^{94} + 4508415 q^{95} - 2555904 q^{96} - 39286662 q^{97} + 71630904 q^{98} + 66155463 q^{99}+O(q^{100}) \) 66 * q - 39 * q^3 + 459 * q^5 - 918 * q^7 + 16896 * q^8 + 3237 * q^9 + 4704 * q^10 + 4539 * q^11 - 2496 * q^12 - 10542 * q^13 + 6744 * q^14 - 39894 * q^15 - 78822 * q^17 + 51792 * q^18 + 79461 * q^19 + 29376 * q^20 - 5835 * q^21 + 18168 * q^22 - 199479 * q^23 + 19968 * q^24 + 356301 * q^25 + 186744 * q^26 - 91689 * q^27 - 91584 * q^28 - 38526 * q^29 + 319152 * q^30 + 1917246 * q^31 - 902847 * q^33 - 205776 * q^34 - 1574793 * q^35 + 3079296 * q^36 - 396513 * q^37 - 692880 * q^38 + 2514306 * q^39 + 470016 * q^40 + 2989350 * q^41 + 46680 * q^42 + 6006348 * q^43 - 145344 * q^44 + 1083726 * q^45 - 588744 * q^46 - 894135 * q^47 + 7973742 * q^49 + 2012400 * q^50 - 524880 * q^51 - 2262720 * q^52 + 1457844 * q^53 + 1452312 * q^54 + 2415690 * q^55 - 1202688 * q^56 + 2734338 * q^57 - 3423360 * q^58 + 3099522 * q^59 - 3102912 * q^60 - 10968396 * q^61 - 3067320 * q^62 - 10727970 * q^63 - 8650752 * q^64 - 13497300 * q^65 - 4598712 * q^66 - 1978119 * q^67 + 5026176 * q^68 - 7251108 * q^69 + 435744 * q^70 - 19555002 * q^71 + 3314688 * q^72 - 31332840 * q^73 + 7607472 * q^74 + 44758074 * q^75 + 5085504 * q^76 + 1982007 * q^77 - 22512264 * q^78 + 10522902 * q^79 + 4816896 * q^80 - 7548876 * q^81 - 7150320 * q^82 + 19771926 * q^83 + 3556224 * q^84 - 6684072 * q^85 + 22982496 * q^86 - 67769667 * q^87 - 2323968 * q^88 - 42018963 * q^89 - 25158672 * q^90 + 4847565 * q^91 - 1096704 * q^92 - 14558475 * q^93 + 3175680 * q^94 + 4508415 * q^95 - 2555904 * q^96 - 39286662 * q^97 + 71630904 * q^98 + 66155463 * q^99

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