LMFDB - Embedded newform 21.7.f.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(10,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.f (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:	$4.83113575602$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} + 473x^{5} + 39800x^{4} + 36821x^{3} + 985651x^{2} - 601290x + 21068100 $ x^8 - x^7 + 212x^6 + 473x^5 + 39800x^4 + 36821x^3 + 985651x^2 - 601290x + 21068100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Root			$2.26350 - 3.92050i$ of defining polynomial
Character	$\chi$	$=$	21.19
Dual form			21.7.f.a.10.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.76350 + 4.78652i) q^{2} +(-13.5000 + 7.79423i) q^{3} +(16.7261 + 28.9705i) q^{4} +(-57.9943 - 33.4830i) q^{5} -86.1574i q^{6} +(-240.457 - 244.600i) q^{7} -538.619 q^{8} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(-2.76350 + 4.78652i) q^{2} +(-13.5000 + 7.79423i) q^{3} +(16.7261 + 28.9705i) q^{4} +(-57.9943 - 33.4830i) q^{5} -86.1574i q^{6} +(-240.457 - 244.600i) q^{7} -538.619 q^{8} +(121.500 - 210.444i) q^{9} +(320.535 - 185.061i) q^{10} +(-862.868 - 1494.53i) q^{11} +(-451.605 - 260.734i) q^{12} +2807.43i q^{13} +(1835.29 - 475.002i) q^{14} +1043.90 q^{15} +(418.002 - 724.000i) q^{16} +(-5323.58 + 3073.57i) q^{17} +(671.531 + 1163.13i) q^{18} +(7737.30 + 4467.13i) q^{19} -2240.17i q^{20} +(5152.64 + 1427.92i) q^{21} +9538.15 q^{22} +(-4950.64 + 8574.76i) q^{23} +(7271.35 - 4198.12i) q^{24} +(-5570.27 - 9648.00i) q^{25} +(-13437.8 - 7758.32i) q^{26} +3788.00i q^{27} +(3064.27 - 11057.4i) q^{28} -13610.4 q^{29} +(-2884.81 + 4996.64i) q^{30} +(-21833.0 + 12605.3i) q^{31} +(-14925.5 - 25851.7i) q^{32} +(23297.4 + 13450.8i) q^{33} -33975.2i q^{34} +(5755.21 + 22236.7i) q^{35} +8128.90 q^{36} +(-11366.4 + 19687.1i) q^{37} +(-42764.1 + 24689.9i) q^{38} +(-21881.7 - 37900.2i) q^{39} +(31236.8 + 18034.6i) q^{40} -37897.2i q^{41} +(-21074.1 + 20717.2i) q^{42} +73646.2 q^{43} +(28864.9 - 49995.4i) q^{44} +(-14092.6 + 8136.38i) q^{45} +(-27362.2 - 47392.7i) q^{46} +(120523. + 69583.9i) q^{47} +13032.0i q^{48} +(-2009.47 + 117632. i) q^{49} +61573.8 q^{50} +(47912.2 - 82986.3i) q^{51} +(-81332.5 + 46957.3i) q^{52} +(8258.79 + 14304.7i) q^{53} +(-18131.3 - 10468.1i) q^{54} +115566. i q^{55} +(129515. + 131746. i) q^{56} -139271. q^{57} +(37612.3 - 65146.4i) q^{58} +(-61989.7 + 35789.8i) q^{59} +(17460.4 + 30242.2i) q^{60} +(-228557. - 131958. i) q^{61} -139339. i q^{62} +(-80690.3 + 20883.9i) q^{63} +218491. q^{64} +(94001.1 - 162815. i) q^{65} +(-128765. + 74342.5i) q^{66} +(-274333. - 475159. i) q^{67} +(-178086. - 102818. i) q^{68} -154346. i q^{69} +(-122341. - 33903.6i) q^{70} +465655. q^{71} +(-65442.2 + 113349. i) q^{72} +(-289020. + 166866. i) q^{73} +(-62821.9 - 108811. i) q^{74} +(150397. + 86832.0i) q^{75} +298871. i q^{76} +(-158080. + 570429. i) q^{77} +241881. q^{78} +(205012. - 355091. i) q^{79} +(-48483.5 + 27991.9i) q^{80} +(-29524.5 - 51137.9i) q^{81} +(181396. + 104729. i) q^{82} +71948.9i q^{83} +(44816.2 + 173158. i) q^{84} +411649. q^{85} +(-203521. + 352509. i) q^{86} +(183740. - 106082. i) q^{87} +(464757. + 804983. i) q^{88} +(-141505. - 81698.0i) q^{89} -89939.6i q^{90} +(686697. - 675066. i) q^{91} -331220. q^{92} +(196497. - 340342. i) q^{93} +(-666130. + 384590. i) q^{94} +(-299146. - 518137. i) q^{95} +(402989. + 232666. i) q^{96} +651914. i q^{97} +(-557494. - 334694. i) q^{98} -419354. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} - 294 q^{5} - 656 q^{7} + 3326 q^{8} + 972 q^{9}+O(q^{10}) $ 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 - 294 * q^5 - 656 * q^7 + 3326 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} - 294 q^{5} - 656 q^{7} + 3326 q^{8} + 972 q^{9} - 3411 q^{10} - 314 q^{11} + 4671 q^{12} - 5360 q^{14} + 5292 q^{15} - 12721 q^{16} - 5532 q^{17} + 1215 q^{18} - 18234 q^{19} + 9342 q^{21} + 86106 q^{22} + 3928 q^{23} - 44901 q^{24} - 17038 q^{25} + 12366 q^{26} + 85037 q^{28} - 8300 q^{29} + 30699 q^{30} - 89508 q^{31} - 186207 q^{32} + 8478 q^{33} - 25860 q^{35} - 84078 q^{36} + 64706 q^{37} - 77136 q^{38} + 29106 q^{39} + 221823 q^{40} + 173583 q^{42} + 45740 q^{43} + 92529 q^{44} - 71442 q^{45} - 111504 q^{46} + 483276 q^{47} - 310684 q^{49} + 967216 q^{50} + 49788 q^{51} - 1673988 q^{52} - 540974 q^{53} - 32805 q^{54} - 241885 q^{56} + 328212 q^{57} + 539799 q^{58} - 181770 q^{59} - 146367 q^{60} + 418224 q^{61} - 92826 q^{63} + 2378626 q^{64} - 414204 q^{65} - 1162431 q^{66} - 1158902 q^{67} - 821250 q^{68} + 1087917 q^{70} + 1442344 q^{71} + 404109 q^{72} - 378666 q^{73} - 432940 q^{74} + 460026 q^{75} + 1065994 q^{77} - 222588 q^{78} + 611452 q^{79} - 2094945 q^{80} - 236196 q^{81} - 1561266 q^{82} - 1579716 q^{84} - 275112 q^{85} + 816224 q^{86} + 112050 q^{87} - 366441 q^{88} - 989196 q^{89} + 304446 q^{91} + 678720 q^{92} + 805572 q^{93} - 716148 q^{94} - 591792 q^{95} + 5027589 q^{96} + 3509629 q^{98} - 152604 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 - 294 * q^5 - 656 * q^7 + 3326 * q^8 + 972 * q^9 - 3411 * q^10 - 314 * q^11 + 4671 * q^12 - 5360 * q^14 + 5292 * q^15 - 12721 * q^16 - 5532 * q^17 + 1215 * q^18 - 18234 * q^19 + 9342 * q^21 + 86106 * q^22 + 3928 * q^23 - 44901 * q^24 - 17038 * q^25 + 12366 * q^26 + 85037 * q^28 - 8300 * q^29 + 30699 * q^30 - 89508 * q^31 - 186207 * q^32 + 8478 * q^33 - 25860 * q^35 - 84078 * q^36 + 64706 * q^37 - 77136 * q^38 + 29106 * q^39 + 221823 * q^40 + 173583 * q^42 + 45740 * q^43 + 92529 * q^44 - 71442 * q^45 - 111504 * q^46 + 483276 * q^47 - 310684 * q^49 + 967216 * q^50 + 49788 * q^51 - 1673988 * q^52 - 540974 * q^53 - 32805 * q^54 - 241885 * q^56 + 328212 * q^57 + 539799 * q^58 - 181770 * q^59 - 146367 * q^60 + 418224 * q^61 - 92826 * q^63 + 2378626 * q^64 - 414204 * q^65 - 1162431 * q^66 - 1158902 * q^67 - 821250 * q^68 + 1087917 * q^70 + 1442344 * q^71 + 404109 * q^72 - 378666 * q^73 - 432940 * q^74 + 460026 * q^75 + 1065994 * q^77 - 222588 * q^78 + 611452 * q^79 - 2094945 * q^80 - 236196 * q^81 - 1561266 * q^82 - 1579716 * q^84 - 275112 * q^85 + 816224 * q^86 + 112050 * q^87 - 366441 * q^88 - 989196 * q^89 + 304446 * q^91 + 678720 * q^92 + 805572 * q^93 - 716148 * q^94 - 591792 * q^95 + 5027589 * q^96 + 3509629 * q^98 - 152604 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.76350	+	4.78652i	−0.345438	+	0.598316i	−0.985433	−	0.170063i	$-0.945603\pi$
$2$	−2.76350	+	4.78652i	−0.345438	+	0.598316i	0.639996	+	0.768379i	$0.278936\pi$
$3$	−13.5000	+	7.79423i	−0.500000	+	0.288675i
$3$	−13.5000	+	7.79423i	−0.500000	+	0.288675i
$4$	16.7261	+	28.9705i	0.261346	+	0.452664i
$5$	−57.9943	−	33.4830i	−0.463955	−	0.267864i	0.249751	−	0.968310i	$-0.419651\pi$
$5$	−57.9943	−	33.4830i	−0.463955	−	0.267864i	−0.713706	+	0.700446i	$0.752985\pi$
$6$		−	86.1574i		−	0.398877i
$7$	−240.457	−	244.600i	−0.701042	−	0.713120i
$7$	−240.457	−	244.600i	−0.701042	−	0.713120i
$8$	−538.619			−1.05199
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$	320.535	−	185.061i	0.320535	−	0.185061i
$11$	−862.868	−	1494.53i	−0.648285	−	1.12286i	−0.983532	−	0.180733i	$-0.942153\pi$
$11$	−862.868	−	1494.53i	−0.648285	−	1.12286i	0.335247	−	0.942130i	$-0.391180\pi$
$12$	−451.605	−	260.734i	−0.261346	−	0.150888i
$13$			2807.43i			1.27785i	0.769271	+	0.638923i	$0.220620\pi$
$13$			2807.43i			1.27785i	−0.769271	+	0.638923i	$0.779380\pi$
$14$	1835.29	−	475.002i	0.668837	−	0.173106i
$15$	1043.90			0.309303
$16$	418.002	−	724.000i	0.102051	−	0.176758i
$17$	−5323.58	+	3073.57i	−1.08357	+	0.625599i	−0.931857	−	0.362826i	$-0.881812\pi$
$17$	−5323.58	+	3073.57i	−1.08357	+	0.625599i	−0.151712	+	0.988425i	$0.548479\pi$
$18$	671.531	+	1163.13i	0.115146	+	0.199439i
$19$	7737.30	+	4467.13i	1.12805	+	0.651281i	0.943444	−	0.331532i	$-0.107565\pi$
$19$	7737.30	+	4467.13i	1.12805	+	0.651281i	0.184607	+	0.982812i	$0.440899\pi$
$20$		−	2240.17i		−	0.280021i
$21$	5152.64	+	1427.92i	0.556381	+	0.154187i
$22$	9538.15			0.895769
$23$	−4950.64	+	8574.76i	−0.406891	+	0.704755i	−0.994540	−	0.104361i	$-0.966720\pi$
$23$	−4950.64	+	8574.76i	−0.406891	+	0.704755i	0.587649	+	0.809116i	$0.300054\pi$
$24$	7271.35	−	4198.12i	0.525995	−	0.303683i
$25$	−5570.27	−	9648.00i	−0.356497	−	0.617472i
$26$	−13437.8	−	7758.32i	−0.764555	−	0.441416i
$27$			3788.00i			0.192450i
$28$	3064.27	−	11057.4i	0.139589	−	0.503707i
$29$	−13610.4			−0.558054			−0.279027	−	0.960283i	$-0.590012\pi$
$29$	−13610.4			−0.558054			−0.279027	+	0.960283i	$0.590012\pi$
$30$	−2884.81	+	4996.64i	−0.106845	+	0.185061i
$31$	−21833.0	+	12605.3i	−0.732871	+	0.423123i	−0.819472	−	0.573120i	$-0.805733\pi$
$31$	−21833.0	+	12605.3i	−0.732871	+	0.423123i	0.0866007	+	0.996243i	$0.472400\pi$
$32$	−14925.5	−	25851.7i	−0.455490	−	0.788932i
$33$	23297.4	+	13450.8i	0.648285	+	0.374288i
$34$		−	33975.2i		−	0.864422i
$35$	5755.21	+	22236.7i	0.134232	+	0.518639i
$36$	8128.90			0.174230
$37$	−11366.4	+	19687.1i	−0.224397	+	0.388666i	−0.956138	−	0.292916i	$-0.905374\pi$
$37$	−11366.4	+	19687.1i	−0.224397	+	0.388666i	0.731742	+	0.681582i	$0.238708\pi$
$38$	−42764.1	+	24689.9i	−0.779343	+	0.449954i
$39$	−21881.7	−	37900.2i	−0.368882	−	0.638923i
$40$	31236.8	+	18034.6i	0.488075	+	0.281790i
$41$		−	37897.2i		−	0.549865i	−0.961464	−	0.274932i	$-0.911345\pi$
$41$		−	37897.2i		−	0.549865i	0.961464	−	0.274932i	$-0.0886554\pi$
$42$	−21074.1	+	20717.2i	−0.284447	+	0.279630i
$43$	73646.2			0.926286			0.463143	−	0.886284i	$-0.346722\pi$
$43$	73646.2			0.926286			0.463143	+	0.886284i	$0.346722\pi$
$44$	28864.9	−	49995.4i	0.338853	−	0.586911i
$45$	−14092.6	+	8136.38i	−0.154652	+	0.0892881i
$46$	−27362.2	−	47392.7i	−0.281111	−	0.486898i
$47$	120523.	+	69583.9i	1.16085	+	0.670216i	0.951507	−	0.307626i	$-0.0995346\pi$
$47$	120523.	+	69583.9i	1.16085	+	0.670216i	0.209342	+	0.977843i	$0.432868\pi$
$48$			13032.0i			0.117839i
$49$	−2009.47	+	117632.i	−0.0170802	+	0.999854i
$50$	61573.8			0.492591
$51$	47912.2	−	82986.3i	0.361190	−	0.625599i
$52$	−81332.5	+	46957.3i	−0.578434	+	0.333959i
$53$	8258.79	+	14304.7i	0.0554739	+	0.0960837i	0.892429	−	0.451188i	$-0.149000\pi$
$53$	8258.79	+	14304.7i	0.0554739	+	0.0960837i	−0.836955	+	0.547272i	$0.815666\pi$
$54$	−18131.3	−	10468.1i	−0.115146	−	0.0664795i
$55$			115566.i			0.694610i
$56$	129515.	+	131746.i	0.737489	+	0.750195i
$57$	−139271.			−0.752034
$58$	37612.3	−	65146.4i	0.192773	−	0.333892i
$59$	−61989.7	+	35789.8i	−0.301831	+	0.174262i	−0.643265	−	0.765644i	$-0.722421\pi$
$59$	−61989.7	+	35789.8i	−0.301831	+	0.174262i	0.341434	+	0.939906i	$0.389087\pi$
$60$	17460.4	+	30242.2i	0.0808350	+	0.140010i
$61$	−228557.	−	131958.i	−1.00695	−	0.581360i	−0.0966496	−	0.995318i	$-0.530813\pi$
$61$	−228557.	−	131958.i	−1.00695	−	0.581360i	−0.910296	+	0.413958i	$0.864146\pi$
$62$		−	139339.i		−	0.584651i
$63$	−80690.3	+	20883.9i	−0.322700	+	0.0835201i
$64$	218491.			0.833476
$65$	94001.1	−	162815.i	0.342289	−	0.592862i
$66$	−128765.	+	74342.5i	−0.447884	+	0.258586i
$67$	−274333.	−	475159.i	−0.912125	−	1.57985i	−0.811057	−	0.584967i	$-0.801107\pi$
$67$	−274333.	−	475159.i	−0.912125	−	1.57985i	−0.101068	−	0.994880i	$-0.532226\pi$
$68$	−178086.	−	102818.i	−0.566372	−	0.326995i
$69$		−	154346.i		−	0.469837i
$70$	−122341.	−	33903.6i	−0.356679	−	0.0988443i
$71$	465655.			1.30103			0.650517	−	0.759491i	$-0.274552\pi$
$71$	465655.			1.30103			0.650517	+	0.759491i	$0.274552\pi$
$72$	−65442.2	+	113349.i	−0.175332	+	0.303683i
$73$	−289020.	+	166866.i	−0.742950	+	0.428942i	−0.823141	−	0.567837i	$-0.807780\pi$
$73$	−289020.	+	166866.i	−0.742950	+	0.428942i	0.0801910	+	0.996780i	$0.474447\pi$
$74$	−62821.9	−	108811.i	−0.155030	−	0.268520i
$75$	150397.	+	86832.0i	0.356497	+	0.205824i
$76$			298871.i			0.680837i
$77$	−158080.	+	570429.i	−0.346261	+	1.24948i
$78$	241881.			0.509703
$79$	205012.	−	355091.i	0.415813	−	0.720209i	−0.579700	−	0.814830i	$-0.696830\pi$
$79$	205012.	−	355091.i	0.415813	−	0.720209i	0.995513	+	0.0946203i	$0.0301637\pi$
$80$	−48483.5	+	27991.9i	−0.0946942	+	0.0546717i
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$	181396.	+	104729.i	0.328993	+	0.189944i
$83$			71948.9i			0.125832i	0.998019	+	0.0629158i	$0.0200400\pi$
$83$			71948.9i			0.125832i	−0.998019	+	0.0629158i	$0.979960\pi$
$84$	44816.2	+	173158.i	0.0756131	+	0.292150i
$85$	411649.			0.670302
$86$	−203521.	+	352509.i	−0.319974	+	0.554211i
$87$	183740.	−	106082.i	0.279027	−	0.161096i
$88$	464757.	+	804983.i	0.681990	+	1.18124i
$89$	−141505.	−	81698.0i	−0.200725	−	0.115889i	0.396269	−	0.918135i	$-0.370305\pi$
$89$	−141505.	−	81698.0i	−0.200725	−	0.115889i	−0.596994	+	0.802246i	$0.703638\pi$
$90$		−	89939.6i		−	0.123374i
$91$	686697.	−	675066.i	0.911257	−	0.895823i
$92$	−331220.			−0.425357
$93$	196497.	−	340342.i	0.244290	−	0.423123i
$94$	−666130.	+	384590.i	−0.802002	+	0.463036i
$95$	−299146.	−	518137.i	−0.348910	−	0.604329i
$96$	402989.	+	232666.i	0.455490	+	0.262977i
$97$			651914.i			0.714291i	0.934049	+	0.357146i	$0.116250\pi$
$97$			651914.i			0.714291i	−0.934049	+	0.357146i	$0.883750\pi$
$98$	−557494.	−	334694.i	−0.592328	−	0.355607i
$99$	−419354.			−0.432190
$100$	186338.	−	322747.i	0.186338	−	0.322747i
$101$	883850.	−	510291.i	0.857856	−	0.495283i	−0.00543765	−	0.999985i	$-0.501731\pi$
$101$	883850.	−	510291.i	0.857856	−	0.495283i	0.863294	+	0.504702i	$0.168398\pi$
$102$	264811.	+	458666.i	0.249537	+	0.432211i
$103$	363147.	+	209663.i	0.332331	+	0.191871i	0.656875	−	0.753999i	$-0.271878\pi$
$103$	363147.	+	209663.i	0.332331	+	0.191871i	−0.324545	+	0.945870i	$0.605211\pi$
$104$		−	1.51213e6i		−	1.34428i
$105$	−251013.	−	255338.i	−0.216834	−	0.220570i
$106$	−91292.8			−0.0766512
$107$	−1.10621e6	+	1.91600e6i	−0.902993	+	1.56403i	−0.0794039	+	0.996843i	$0.525302\pi$
$107$	−1.10621e6	+	1.91600e6i	−0.902993	+	1.56403i	−0.823589	+	0.567187i	$0.808032\pi$
$108$	−109740.	+	63358.5i	−0.0871152	+	0.0502960i
$109$	−382955.	−	663297.i	−0.295711	−	0.512187i	0.679439	−	0.733732i	$-0.262223\pi$
$109$	−382955.	−	663297.i	−0.295711	−	0.512187i	−0.975150	+	0.221545i	$0.928890\pi$
$110$	−553158.	−	319366.i	−0.415596	−	0.239944i
$111$		−	354368.i		−	0.259111i
$112$	−277602.	+	71847.9i	−0.197592	+	0.0511399i
$113$	−2.66096e6			−1.84418			−0.922090	−	0.386976i	$-0.873520\pi$
$113$	−2.66096e6			−1.84418			−0.922090	+	0.386976i	$0.873520\pi$
$114$	384877.	−	666626.i	0.259781	−	0.449954i
$115$	574218.	−	331525.i	0.377558	−	0.217983i
$116$	−227649.	−	394299.i	−0.145845	−	0.252611i
$117$	590806.	+	341102.i	0.368882	+	0.212974i
$118$		−	395620.i		−	0.240787i
$119$	2.03189e6	+	563085.i	1.20575	+	0.334144i
$120$	−562263.			−0.325384
$121$	−603302.	+	1.04495e6i	−0.340548	+	0.589847i
$122$	1.26324e6	−	729331.i	0.695674	−	0.401647i
$123$	295380.	+	511612.i	0.158732	+	0.274932i
$124$	−730361.	−	421674.i	−0.383065	−	0.221163i
$125$			1.79238e6i			0.917700i
$126$	123026.	−	443939.i	0.0615015	−	0.221928i
$127$	−1.11648e6			−0.545055			−0.272527	−	0.962148i	$-0.587859\pi$
$127$	−1.11648e6			−0.545055			−0.272527	+	0.962148i	$0.587859\pi$
$128$	351433.	−	608699.i	0.167576	−	0.290250i
$129$	−994224.	+	574015.i	−0.463143	+	0.267396i
$130$	519544.	+	899877.i	0.236479	+	0.409594i
$131$	247826.	+	143083.i	0.110239	+	0.0636463i	0.554106	−	0.832446i	$-0.313060\pi$
$131$	247826.	+	143083.i	0.110239	+	0.0636463i	−0.443867	+	0.896093i	$0.646394\pi$
$132$			899918.i			0.391274i
$133$	−767830.	−	2.96670e6i	−0.326370	−	1.26101i
$134$	3.03248e6			1.26033
$135$	126834.	−	219682.i	0.0515505	−	0.0892881i
$136$	2.86738e6	−	1.65548e6i	1.13990	−	0.658124i
$137$	1.86697e6	+	3.23368e6i	0.726063	+	1.25758i	0.958535	+	0.284975i	$0.0919854\pi$
$137$	1.86697e6	+	3.23368e6i	0.726063	+	1.25758i	−0.232472	+	0.972603i	$0.574681\pi$
$138$	738779.	+	426534.i	0.281111	+	0.162299i
$139$			618216.i			0.230195i	0.993354	+	0.115097i	$0.0367180\pi$
$139$			618216.i			0.230195i	−0.993354	+	0.115097i	$0.963282\pi$
$140$	−547945.	+	538664.i	−0.199688	+	0.196306i
$141$	−2.16941e6			−0.773899
$142$	−1.28684e6	+	2.22887e6i	−0.449426	+	0.778429i
$143$	4.19579e6	−	2.42244e6i	1.43485	−	0.828408i
$144$	−101574.	−	175932.i	−0.0340171	−	0.0589193i
$145$	789324.	+	455716.i	0.258911	+	0.149483i
$146$		−	1.84454e6i		−	0.592691i
$147$	−889722.	−	1.60369e6i	−0.280093	−	0.504858i
$148$	−760461.			−0.234580
$149$	−1.86160e6	+	3.22438e6i	−0.562765	+	0.974737i	0.434489	+	0.900677i	$0.356929\pi$
$149$	−1.86160e6	+	3.22438e6i	−0.562765	+	0.974737i	−0.997254	+	0.0740601i	$0.976404\pi$
$150$	−831247.	+	479920.i	−0.246295	+	0.142199i
$151$	1.27599e6	+	2.21009e6i	0.370611	+	0.641917i	0.989660	−	0.143436i	$-0.0458151\pi$
$151$	1.27599e6	+	2.21009e6i	0.370611	+	0.641917i	−0.619049	+	0.785352i	$0.712482\pi$
$152$	−4.16746e6	−	2.40608e6i	−1.18670	−	0.685140i
$153$			1.49375e6i			0.417066i
$154$	−2.29352e6	−	2.33303e6i	−0.627972	−	0.638791i
$155$	1.68825e6			0.453358
$156$	731993.	−	1.26785e6i	0.192811	−	0.333959i
$157$	−5.87057e6	+	3.38938e6i	−1.51699	+	0.875832i	−0.517186	+	0.855873i	$0.673020\pi$
$157$	−5.87057e6	+	3.38938e6i	−1.51699	+	0.875832i	−0.999801	+	0.0199592i	$0.993646\pi$
$158$	1.13310e6	+	1.96259e6i	0.287275	+	0.497575i
$159$	−222987.	−	128742.i	−0.0554739	−	0.0320279i
$160$			1.99900e6i			0.488038i
$161$	3.28781e6	−	850937.i	0.787823	−	0.203901i
$162$	326364.			0.0767639
$163$	4.13571e6	−	7.16325e6i	0.954964	−	1.65405i	0.220513	−	0.975384i	$-0.429227\pi$
$163$	4.13571e6	−	7.16325e6i	0.954964	−	1.65405i	0.734451	−	0.678662i	$-0.237440\pi$
$164$	1.09790e6	−	633874.i	0.248904	−	0.143705i
$165$	−900746.	−	1.56014e6i	−0.200517	−	0.347305i
$166$	−344385.	−	198831.i	−0.0752871	−	0.0434670i
$167$		−	2.59960e6i		−	0.558158i	−0.960268	−	0.279079i	$-0.909971\pi$
$167$		−	2.59960e6i		−	0.558158i	0.960268	−	0.279079i	$-0.0900291\pi$
$168$	−2.77531e6	−	769106.i	−0.585307	−	0.162203i
$169$	−3.05483e6			−0.632888
$170$	−1.13759e6	+	1.97037e6i	−0.231548	+	0.401052i
$171$	1.88016e6	−	1.08551e6i	0.376017	−	0.217094i
$172$	1.23182e6	+	2.13357e6i	0.242081	+	0.419296i
$173$	−7.10612e6	−	4.10272e6i	−1.37244	−	0.792380i	−0.381208	−	0.924489i	$-0.624492\pi$
$173$	−7.10612e6	−	4.10272e6i	−1.37244	−	0.792380i	−0.991235	+	0.132109i	$0.957825\pi$
$174$			1.17263e6i			0.222595i
$175$	−1.02049e6	+	3.68242e6i	−0.190412	+	0.687099i
$176$	−1.44272e6			−0.264633
$177$	557907.	−	966324.i	0.100610	−	0.174262i
$178$	782099.	−	451545.i	0.138676	−	0.0800647i
$179$	−4.09401e6	−	7.09104e6i	−0.713822	−	1.23638i	−0.963412	−	0.268025i	$-0.913629\pi$
$179$	−4.09401e6	−	7.09104e6i	−0.713822	−	1.23638i	0.249590	−	0.968352i	$-0.419704\pi$
$180$	−471430.	−	272180.i	−0.0808350	−	0.0466701i
$181$		−	3.25606e6i		−	0.549106i	−0.961572	−	0.274553i	$-0.911470\pi$
$181$		−	3.25606e6i		−	0.549106i	0.961572	−	0.274553i	$-0.0885298\pi$
$182$	1.33353e6	+	5.15244e6i	0.221202	+	0.854670i
$183$	4.11403e6			0.671297
$184$	2.66651e6	−	4.61853e6i	0.428045	−	0.741395i
$185$	1.31837e6	−	761161.i	0.208220	−	0.120216i
$186$	1.08604e6	+	1.88107e6i	0.168774	+	0.292325i
$187$	9.18709e6	+	5.30417e6i	1.40492	+	0.811133i
$188$			4.65547e6i			0.700633i
$189$	926544.	−	910851.i	0.137240	−	0.134916i
$190$	3.30677e6			0.482106
$191$	−4.30425e6	+	7.45518e6i	−0.617728	+	1.06994i	0.372171	+	0.928164i	$0.378614\pi$
$191$	−4.30425e6	+	7.45518e6i	−0.617728	+	1.06994i	−0.989899	+	0.141773i	$0.954720\pi$
$192$	−2.94963e6	+	1.70297e6i	−0.416738	+	0.240604i
$193$	89943.0	+	155786.i	0.0125111	+	0.0216699i	0.872213	−	0.489126i	$-0.162684\pi$
$193$	89943.0	+	155786.i	0.0125111	+	0.0216699i	−0.859702	+	0.510796i	$0.829351\pi$
$194$	−3.12040e6	−	1.80157e6i	−0.427372	−	0.246743i
$195$			2.93067e6i			0.395241i
$196$	−3.44146e6	+	1.90931e6i	−0.457062	+	0.253576i
$197$	2.69333e6			0.352283			0.176141	−	0.984365i	$-0.443638\pi$
$197$	2.69333e6			0.352283			0.176141	+	0.984365i	$0.443638\pi$
$198$	1.15888e6	−	2.00725e6i	0.149295	−	0.258586i
$199$	5.23271e6	−	3.02111e6i	0.663999	−	0.383360i	−0.129800	−	0.991540i	$-0.541434\pi$
$199$	5.23271e6	−	3.02111e6i	0.663999	−	0.383360i	0.793799	+	0.608180i	$0.208100\pi$
$200$	3.00025e6	+	5.19659e6i	0.375032	+	0.649574i
$201$	7.40700e6	+	4.27643e6i	0.912125	+	0.526616i
$202$			5.64076e6i			0.684358i
$203$	3.27271e6	+	3.32910e6i	0.391219	+	0.397959i
$204$	3.20554e6			0.377581
$205$	−1.26891e6	+	2.19782e6i	−0.147289	+	0.255112i
$206$	−2.00711e6	+	1.15881e6i	−0.229599	+	0.132559i
$207$	1.20301e6	+	2.08367e6i	0.135630	+	0.234918i
$208$	2.03258e6	+	1.17351e6i	0.225869	+	0.130406i
$209$		−	1.54182e7i		−	1.68886i
$210$	1.91585e6	−	495854.i	0.206873	−	0.0535422i
$211$	−1.38113e7			−1.47024			−0.735118	−	0.677939i	$-0.762873\pi$
$211$	−1.38113e7			−1.47024			−0.735118	+	0.677939i	$0.762873\pi$
$212$	−276275.	+	478523.i	−0.0289958	+	0.0502221i
$213$	−6.28634e6	+	3.62942e6i	−0.650517	+	0.375576i
$214$	−6.11400e6	−	1.05898e7i	−0.623855	−	1.08055i
$215$	−4.27106e6	−	2.46590e6i	−0.429755	−	0.248119i
$216$		−	2.04029e6i		−	0.202456i
$217$	8.33314e6	+	2.30932e6i	0.815511	+	0.225998i
$218$	4.23318e6			0.408599
$219$	2.60118e6	−	4.50538e6i	0.247650	−	0.428942i
$220$	−3.34800e6	+	1.93297e6i	−0.314425	+	0.181533i
$221$	−8.62881e6	−	1.49455e7i	−0.799419	−	1.38463i
$222$	1.69619e6	+	979297.i	0.155030	+	0.0895067i
$223$		−	9.81400e6i		−	0.884976i	−0.896774	−	0.442488i	$-0.854096\pi$
$223$		−	9.81400e6i		−	0.884976i	0.896774	−	0.442488i	$-0.145904\pi$
$224$	−2.73439e6	+	9.86702e6i	−0.243286	+	0.877894i
$225$	−2.70715e6			−0.237665
$226$	7.35357e6	−	1.27368e7i	0.637049	−	1.10340i
$227$	−1.26217e7	+	7.28715e6i	−1.07905	+	0.622989i	−0.930639	−	0.365938i	$-0.880748\pi$
$227$	−1.26217e7	+	7.28715e6i	−1.07905	+	0.622989i	−0.148408	+	0.988926i	$0.547415\pi$
$228$	−2.32947e6	−	4.03476e6i	−0.196541	−	0.340419i
$229$	1.27292e7	+	7.34923e6i	1.05998	+	0.611978i	0.925426	−	0.378929i	$-0.123708\pi$
$229$	1.27292e7	+	7.34923e6i	1.05998	+	0.611978i	0.134551	+	0.990907i	$0.457041\pi$
$230$			3.66468e6i			0.301198i
$231$	−2.31198e6	−	8.93290e6i	−0.187563	−	0.724697i
$232$	7.33080e6			0.587067
$233$	−2.87597e6	+	4.98133e6i	−0.227362	+	0.393802i	−0.957025	−	0.290004i	$-0.906343\pi$
$233$	−2.87597e6	+	4.98133e6i	−0.227362	+	0.393802i	0.729664	+	0.683806i	$0.239677\pi$
$234$	−3.26539e6	+	1.88527e6i	−0.254852	+	0.147139i
$235$	−4.65976e6	−	8.07094e6i	−0.359054	−	0.621900i
$236$	−2.07369e6	−	1.19725e6i	−0.157764	−	0.0910853i
$237$			6.39164e6i			0.480140i
$238$	−8.31035e6	+	8.16960e6i	−0.616436	+	0.605996i
$239$	1.60167e7			1.17322			0.586610	−	0.809869i	$-0.300462\pi$
$239$	1.60167e7			1.17322			0.586610	+	0.809869i	$0.300462\pi$
$240$	436351.	−	755782.i	0.0315647	−	0.0546717i
$241$	−2.23613e7	+	1.29103e7i	−1.59752	+	0.922327i	−0.605553	+	0.795805i	$0.707048\pi$
$241$	−2.23613e7	+	1.29103e7i	−1.59752	+	0.922327i	−0.991964	+	0.126522i	$0.959618\pi$
$242$	−3.33445e6	−	5.77544e6i	−0.235276	−	0.407510i
$243$	797162.	+	460241.i	0.0555556	+	0.0320750i
$244$		−	8.82856e6i		−	0.607744i
$245$	4.05521e6	−	6.75469e6i	0.275750	−	0.459312i
$246$	−3.26513e6			−0.219328
$247$	−1.25411e7	+	2.17219e7i	−0.832236	+	1.44147i
$248$	1.17596e7	−	6.78943e6i	0.770973	−	0.445121i
$249$	−560786.	−	971311.i	−0.0363245	−	0.0629158i
$250$	−8.57929e6	−	4.95325e6i	−0.549074	−	0.317008i
$251$			9.51912e6i			0.601971i	0.953629	+	0.300985i	$0.0973156\pi$
$251$			9.51912e6i			0.601971i	−0.953629	+	0.300985i	$0.902684\pi$
$252$	−1.95465e6	−	1.98833e6i	−0.122143	−	0.124247i
$253$	1.70870e7			1.05513
$254$	3.08539e6	−	5.34406e6i	0.188282	−	0.326115i
$255$	−5.55727e6	+	3.20849e6i	−0.335151	+	0.193500i
$256$	8.93408e6	+	1.54743e7i	0.532512	+	0.922339i
$257$	1.93872e7	+	1.11932e7i	1.14213	+	0.659408i	0.946957	−	0.321361i	$-0.104140\pi$
$257$	1.93872e7	+	1.11932e7i	1.14213	+	0.659408i	0.195171	+	0.980769i	$0.437474\pi$
$258$		−	6.34517e6i		−	0.369474i
$259$	7.54860e6	−	1.95370e6i	0.434477	−	0.112450i
$260$	6.28910e6			0.357823
$261$	−1.65366e6	+	2.86422e6i	−0.0930089	+	0.161096i
$262$	−1.36974e6	+	790818.i	−0.0761612	+	0.0439717i
$263$	−5.24659e6	−	9.08736e6i	−0.288410	−	0.499540i	0.685021	−	0.728524i	$-0.259793\pi$
$263$	−5.24659e6	−	9.08736e6i	−0.288410	−	0.499540i	−0.973430	+	0.228983i	$0.926460\pi$
$264$	−1.25484e7	−	7.24484e6i	−0.681990	−	0.393747i
$265$		−	1.10612e6i		−	0.0594380i
$266$	1.63221e7	+	4.52324e6i	0.867223	+	0.240328i
$267$	2.54709e6			0.133817
$268$	9.17707e6	−	1.58951e7i	0.476760	−	0.825772i
$269$	2.33663e7	−	1.34905e7i	1.20042	−	0.693063i	0.239772	−	0.970829i	$-0.422927\pi$
$269$	2.33663e7	−	1.34905e7i	1.20042	−	0.693063i	0.960649	+	0.277766i	$0.0895941\pi$
$270$	701009.	+	1.21418e6i	0.0356150	+	0.0616869i
$271$	−1.09955e6	−	634826.i	−0.0552468	−	0.0318968i	0.472122	−	0.881533i	$-0.343488\pi$
$271$	−1.09955e6	−	634826.i	−0.0552468	−	0.0318968i	−0.527369	+	0.849636i	$0.676821\pi$
$272$			5.13903e6i			0.255373i
$273$	−4.00878e6	+	1.44657e7i	−0.197027	+	0.710969i
$274$	−2.06374e7			−1.00324
$275$	−9.61282e6	+	1.66499e7i	−0.462224	+	0.800596i
$276$	4.47147e6	−	2.58160e6i	0.212678	−	0.122790i
$277$	3.35016e6	+	5.80265e6i	0.157626	+	0.273016i	0.934012	−	0.357242i	$-0.116283\pi$
$277$	3.35016e6	+	5.80265e6i	0.157626	+	0.273016i	−0.776386	+	0.630257i	$0.782949\pi$
$278$	−2.95911e6	−	1.70844e6i	−0.137729	−	0.0795180i
$279$			6.12616e6i			0.282082i
$280$	−3.09986e6	−	1.19771e7i	−0.141211	−	0.545603i
$281$	−321000.			−0.0144673			−0.00723363	−	0.999974i	$-0.502303\pi$
$281$	−321000.			−0.0144673			−0.00723363	+	0.999974i	$0.502303\pi$
$282$	5.99517e6	−	1.03839e7i	0.267334	−	0.463036i
$283$	2.77311e6	−	1.60105e6i	0.122351	−	0.0706394i	−0.437575	−	0.899182i	$-0.644163\pi$
$283$	2.77311e6	−	1.60105e6i	0.122351	−	0.0706394i	0.559926	+	0.828542i	$0.310829\pi$
$284$	7.78860e6	+	1.34902e7i	0.340020	+	0.588931i
$285$	8.07695e6	+	4.66323e6i	0.348910	+	0.201443i
$286$			2.67776e7i			1.14465i
$287$	−9.26967e6	+	9.11267e6i	−0.392119	+	0.385478i
$288$	−7.25380e6			−0.303660
$289$	6.82485e6	−	1.18210e7i	0.282748	−	0.489734i
$290$	−4.36260e6	+	2.51875e6i	−0.178876	+	0.103274i
$291$	−5.08117e6	−	8.80084e6i	−0.206198	−	0.357146i
$292$	−9.66837e6	−	5.58204e6i	−0.388333	−	0.224204i
$293$			2.67440e6i			0.106322i	0.998586	+	0.0531610i	$0.0169297\pi$
$293$			2.67440e6i			0.106322i	−0.998586	+	0.0531610i	$0.983070\pi$
$294$	1.01349e7	+	173131.i	0.398819	+	0.00681290i
$295$	4.79340e6			0.186714
$296$	6.12214e6	−	1.06039e7i	0.236063	−	0.408873i
$297$	5.66128e6	−	3.26854e6i	0.216095	−	0.124763i
$298$	−1.02891e7	−	1.78212e7i	−0.388800	−	0.673422i
$299$	−2.40730e7	−	1.38986e7i	−0.900568	−	0.519943i
$300$			5.80945e6i			0.215165i
$301$	−1.77088e7	−	1.80139e7i	−0.649365	−	0.660553i
$302$	−1.41048e7			−0.512092
$303$	−7.95465e6	+	1.37779e7i	−0.285952	+	0.495283i
$304$	6.46841e6	−	3.73454e6i	0.230238	−	0.132928i
$305$	8.83669e6	+	1.53056e7i	0.311451	+	0.539449i
$306$	−7.14989e6	−	4.12799e6i	−0.249537	−	0.144070i
$307$		−	1.98765e7i		−	0.686950i	−0.939162	−	0.343475i	$-0.888396\pi$
$307$		−	1.98765e7i		−	0.686950i	0.939162	−	0.343475i	$-0.111604\pi$
$308$	−1.91697e7	+	4.96142e6i	−0.656088	+	0.169806i
$309$	−6.53664e6			−0.221554
$310$	−4.66548e6	+	8.08085e6i	−0.156607	+	0.271251i
$311$	−1.36580e7	+	7.88548e6i	−0.454054	+	0.262148i	−0.709541	−	0.704664i	$-0.751098\pi$
$311$	−1.36580e7	+	7.88548e6i	−0.454054	+	0.262148i	0.255487	+	0.966813i	$0.417764\pi$
$312$	1.17859e7	+	2.04138e7i	0.388060	+	0.672140i
$313$	−9.13939e6	−	5.27663e6i	−0.298047	−	0.172077i	0.343518	−	0.939146i	$-0.388381\pi$
$313$	−9.13939e6	−	5.27663e6i	−0.298047	−	0.172077i	−0.641565	+	0.767069i	$0.721715\pi$
$314$		−	3.74662e7i		−	1.21018i
$315$	5.37883e6	+	1.49060e6i	0.172090	+	0.0476904i
$316$	1.37162e7			0.434684
$317$	1.61613e7	−	2.79923e7i	0.507341	−	0.878740i	−0.492623	−	0.870243i	$-0.663962\pi$
$317$	1.61613e7	−	2.79923e7i	0.507341	−	0.878740i	0.999964	−	0.00849733i	$-0.00270482\pi$
$318$	1.23245e6	−	711557.i	0.0383256	−	0.0221273i
$319$	1.17440e7	+	2.03411e7i	0.361778	+	0.626618i
$320$	−1.26712e7	−	7.31574e6i	−0.386695	−	0.223259i
$321$		−	3.44881e7i		−	1.04269i
$322$	−5.01282e6	+	1.80887e7i	−0.150146	+	0.541802i
$323$	−5.49201e7			−1.62976
$324$	987661.	−	1.71068e6i	0.0290384	−	0.0502960i
$325$	2.70860e7	−	1.56381e7i	0.789033	−	0.455549i
$326$	2.28581e7	+	3.95913e7i	0.659761	+	1.14274i
$327$	1.03398e7	+	5.96968e6i	0.295711	+	0.170729i
$328$			2.04122e7i			0.578452i
$329$	−1.19604e7	−	4.62119e7i	−0.335859	−	1.29767i
$330$	9.95685e6			0.277064
$331$	−1.00165e7	+	1.73490e7i	−0.276205	+	0.478400i	−0.970438	−	0.241349i	$-0.922410\pi$
$331$	−1.00165e7	+	1.73490e7i	−0.276205	+	0.478400i	0.694234	+	0.719750i	$0.255743\pi$
$332$	−2.08440e6	+	1.20343e6i	−0.0569595	+	0.0328856i
$333$	2.76203e6	+	4.78397e6i	0.0747989	+	0.129555i
$334$	1.24430e7	+	7.18400e6i	0.333955	+	0.192809i
$335$			3.67421e7i			0.977303i
$336$	3.18763e6	−	3.13364e6i	0.0840331	−	0.0826098i
$337$	−3.66702e6			−0.0958128			−0.0479064	−	0.998852i	$-0.515255\pi$
$337$	−3.66702e6			−0.0958128			−0.0479064	+	0.998852i	$0.515255\pi$
$338$	8.44203e6	−	1.46220e7i	0.218623	−	0.378667i
$339$	3.59230e7	−	2.07401e7i	0.922090	−	0.532369i
$340$	6.88530e6	+	1.19257e7i	0.175181	+	0.303422i
$341$	3.76779e7	+	2.17534e7i	0.950219	+	0.548609i
$342$			1.19993e7i			0.299969i
$343$	2.92560e7	−	2.77939e7i	0.724990	−	0.688760i
$344$	−3.96672e7			−0.974443
$345$	−5.16796e6	+	8.95117e6i	−0.125853	+	0.217983i
$346$	3.92756e7	−	2.26758e7i	0.948187	−	0.547436i
$347$	−3.22802e6	−	5.59109e6i	−0.0772587	−	0.133816i	0.824808	−	0.565414i	$-0.191283\pi$
$347$	−3.22802e6	−	5.59109e6i	−0.0772587	−	0.133816i	−0.902066	+	0.431598i	$0.857950\pi$
$348$	6.14652e6	+	3.54869e6i	0.145845	+	0.0842036i
$349$			4.01536e7i			0.944600i	0.881438	+	0.472300i	$0.156576\pi$
$349$			4.01536e7i			0.944600i	−0.881438	+	0.472300i	$0.843424\pi$
$350$	−1.48059e7	−	1.50610e7i	−0.345327	−	0.351276i
$351$	−1.06345e7			−0.245921
$352$	−2.57575e7	+	4.46133e7i	−0.590575	+	1.02291i
$353$	7.02915e6	−	4.05828e6i	0.159801	−	0.0922610i	−0.417967	−	0.908462i	$-0.637257\pi$
$353$	7.02915e6	−	4.05828e6i	0.159801	−	0.0922610i	0.577768	+	0.816201i	$0.303924\pi$
$354$	3.08356e6	+	5.34087e6i	0.0695091	+	0.120393i
$355$	−2.70053e7	−	1.55915e7i	−0.603621	−	0.348501i
$356$		−	5.46596e6i		−	0.121148i
$357$	−3.18193e7	+	8.23535e6i	−0.699336	+	0.181000i
$358$	4.52552e7			0.986324
$359$	−1.84586e7	+	3.19712e7i	−0.398946	+	0.690996i	−0.993596	−	0.112989i	$-0.963957\pi$
$359$	−1.84586e7	+	3.19712e7i	−0.398946	+	0.690996i	0.594650	+	0.803985i	$0.297291\pi$
$360$	7.59055e6	−	4.38241e6i	0.162692	−	0.0939302i
$361$	1.63876e7	+	2.83842e7i	0.348333	+	0.603330i
$362$	1.55852e7	+	8.99811e6i	0.328539	+	0.189682i
$363$		−	1.88091e7i		−	0.393231i
$364$	3.10428e7	+	8.60270e6i	0.643660	+	0.178374i
$365$	2.23487e7			0.459593
$366$	−1.13691e7	+	1.96919e7i	−0.231891	+	0.401647i
$367$	1.70742e7	−	9.85777e6i	0.345415	−	0.199425i	−0.317249	−	0.948342i	$-0.602759\pi$
$367$	1.70742e7	−	9.85777e6i	0.345415	−	0.199425i	0.662664	+	0.748917i	$0.269426\pi$
$368$	4.13875e6	+	7.16853e6i	0.0830474	+	0.143842i
$369$	−7.97525e6	−	4.60451e6i	−0.158732	−	0.0916441i
$370$			8.41387e6i			0.166108i
$371$	1.51303e6	−	5.45976e6i	0.0296296	−	0.106918i
$372$	1.31465e7			0.255377
$373$	−5.21653e6	+	9.03530e6i	−0.100521	+	0.174107i	−0.911899	−	0.410414i	$-0.865384\pi$
$373$	−5.21653e6	+	9.03530e6i	−0.100521	+	0.174107i	0.811379	+	0.584521i	$0.198718\pi$
$374$	−5.07770e7	+	2.93161e7i	−0.970627	+	0.560392i
$375$	−1.39702e7	−	2.41972e7i	−0.264917	−	0.458850i
$376$	−6.49158e7	−	3.74792e7i	−1.22120	−	0.705061i
$377$		−	3.82101e7i		−	0.713106i
$378$	1.79931e6	+	6.95207e6i	0.0333142	+	0.128718i
$379$	−5.26018e7			−0.966235			−0.483118	−	0.875556i	$-0.660496\pi$
$379$	−5.26018e7			−0.966235			−0.483118	+	0.875556i	$0.660496\pi$
$380$	1.00071e7	−	1.73328e7i	0.182372	−	0.315878i
$381$	1.50725e7	−	8.70210e6i	0.272527	−	0.157344i
$382$	−2.37896e7	−	4.12048e7i	−0.426773	−	0.739193i
$383$	6.36846e7	+	3.67683e7i	1.13354	+	0.654451i	0.944823	−	0.327580i	$-0.106233\pi$
$383$	6.36846e7	+	3.67683e7i	1.13354	+	0.654451i	0.188719	+	0.982031i	$0.439566\pi$
$384$			1.09566e7i			0.193500i
$385$	2.82674e7	−	2.77886e7i	0.495340	−	0.486951i
$386$	−994230.			−0.0172872
$387$	8.94802e6	−	1.54984e7i	0.154381	−	0.267396i
$388$	−1.88863e7	+	1.09040e7i	−0.323334	+	0.186677i
$389$	−8.60695e6	−	1.49077e7i	−0.146218	−	0.253257i	0.783609	−	0.621255i	$-0.213377\pi$
$389$	−8.60695e6	−	1.49077e7i	−0.146218	−	0.253257i	−0.929827	+	0.367998i	$0.880043\pi$
$390$	−1.40277e7	−	8.09890e6i	−0.236479	−	0.136531i
$391$		−	6.08645e7i		−	1.01820i
$392$	1.08234e6	−	6.33587e7i	0.0179682	−	1.05184i
$393$	−4.46088e6			−0.0734924
$394$	−7.44303e6	+	1.28917e7i	−0.121692	+	0.210776i
$395$	−2.37791e7	+	1.37289e7i	−0.385837	+	0.222763i
$396$	−7.01416e6	−	1.21489e7i	−0.112951	−	0.195637i
$397$	−5.31024e7	−	3.06587e7i	−0.848678	−	0.489984i	0.0115267	−	0.999934i	$-0.496331\pi$
$397$	−5.31024e7	−	3.06587e7i	−0.848678	−	0.489984i	−0.860205	+	0.509949i	$0.829664\pi$
$398$			3.33953e7i			0.529708i
$399$	3.34888e7	+	3.40658e7i	0.527207	+	0.536290i
$400$	−9.31354e6			−0.145524
$401$	2.30735e7	−	3.99645e7i	0.357833	−	0.619785i	−0.629765	−	0.776785i	$-0.716849\pi$
$401$	2.30735e7	−	3.99645e7i	0.357833	−	0.619785i	0.987599	+	0.157000i	$0.0501823\pi$
$402$	−4.09385e7	+	2.36359e7i	−0.630165	+	0.363826i
$403$	−3.53883e7	−	6.12944e7i	−0.540686	−	0.936495i
$404$	2.95668e7	+	1.70704e7i	0.448394	+	0.258880i
$405$			3.95428e6i			0.0595254i
$406$	−2.49790e7	+	6.46496e6i	−0.373247	+	0.0966023i
$407$	3.92307e7			0.581892
$408$	−2.58064e7	+	4.46980e7i	−0.379968	+	0.658124i
$409$	−5.25613e7	+	3.03463e7i	−0.768239	+	0.443543i	−0.832246	−	0.554406i	$-0.812945\pi$
$409$	−5.25613e7	+	3.03463e7i	−0.768239	+	0.443543i	0.0640071	+	0.997949i	$0.479612\pi$
$410$	−7.01329e6	−	1.21474e7i	−0.101758	−	0.176251i
$411$	−5.04081e7	−	2.91031e7i	−0.726063	−	0.419193i
$412$			1.40274e7i			0.200579i
$413$	2.36601e7	+	6.55677e6i	0.335866	+	0.0930765i
$414$	−1.32980e7			−0.187407
$415$	2.40907e6	−	4.17263e6i	0.0337058	−	0.0583802i
$416$	7.25768e7	−	4.19022e7i	1.00813	−	0.582046i
$417$	−4.81852e6	−	8.34592e6i	−0.0664516	−	0.115097i
$418$	7.37995e7	+	4.26082e7i	1.01047	+	0.583397i
$419$			1.17371e8i			1.59558i	0.602939	+	0.797788i	$0.293996\pi$
$419$			1.17371e8i			1.59558i	−0.602939	+	0.797788i	$0.706004\pi$
$420$	3.19878e6	−	1.15428e7i	0.0431754	−	0.155798i
$421$	−1.28510e7			−0.172222			−0.0861111	−	0.996286i	$-0.527444\pi$
$421$	−1.28510e7			−0.172222			−0.0861111	+	0.996286i	$0.527444\pi$
$422$	3.81676e7	−	6.61081e7i	0.507875	−	0.879666i
$423$	2.92870e7	−	1.69089e7i	0.386950	−	0.223405i
$424$	−4.44834e6	−	7.70475e6i	−0.0583580	−	0.101079i
$425$	5.93075e7	+	3.42412e7i	0.772579	+	0.446049i
$426$		−	4.01196e7i		−	0.518953i
$427$	2.26815e7	+	8.76354e7i	0.291331	+	1.12563i
$428$	−7.40101e7			−0.943973
$429$	−3.77621e7	+	6.54058e7i	−0.478282	+	0.828408i
$430$	2.36062e7	−	1.36290e7i	0.296907	−	0.171419i
$431$	5.69282e7	+	9.86026e7i	0.711043	+	1.23156i	0.964466	+	0.264207i	$0.0851102\pi$
$431$	5.69282e7	+	9.86026e7i	0.711043	+	1.23156i	−0.253423	+	0.967356i	$0.581556\pi$
$432$	2.74251e6	+	1.58339e6i	0.0340171	+	0.0196398i
$433$			2.76112e7i			0.340111i	0.985434	+	0.170056i	$0.0543947\pi$
$433$			2.76112e7i			0.340111i	−0.985434	+	0.170056i	$0.945605\pi$
$434$	−3.40822e7	+	3.35050e7i	−0.416926	+	0.409865i
$435$	−1.42078e7			−0.172608
$436$	1.28107e7	−	2.21888e7i	0.154566	−	0.267716i
$437$	−7.66092e7	+	4.42303e7i	−0.917987	+	0.530000i
$438$	1.43767e7	+	2.49012e7i	0.171095	+	0.296346i
$439$	6.22452e7	+	3.59373e7i	0.735720	+	0.424768i	0.820511	−	0.571631i	$-0.193689\pi$
$439$	6.22452e7	+	3.59373e7i	0.735720	+	0.424768i	−0.0847914	+	0.996399i	$0.527022\pi$
$440$		−	6.22459e7i		−	0.730723i
$441$	2.45108e7	+	1.47151e7i	0.285786	+	0.171573i
$442$	9.53829e7			1.10460
$443$	4.75145e7	−	8.22975e7i	0.546531	−	0.946620i	−0.451978	−	0.892029i	$-0.649281\pi$
$443$	4.75145e7	−	8.22975e7i	0.546531	−	0.946620i	0.998509	−	0.0545904i	$-0.0173853\pi$
$444$	1.02662e7	−	5.92721e6i	0.117290	−	0.0677175i
$445$	5.47099e6	+	9.47603e6i	0.0620849	+	0.107534i
$446$	4.69750e7	+	2.71210e7i	0.529495	+	0.305704i
$447$		−	5.80389e7i		−	0.649825i
$448$	−5.25377e7	−	5.34429e7i	−0.584302	−	0.594369i
$449$	1.15401e8			1.27488			0.637440	−	0.770500i	$-0.279993\pi$
$449$	1.15401e8			1.27488			0.637440	+	0.770500i	$0.279993\pi$
$450$	7.48122e6	−	1.29579e7i	0.0820984	−	0.142199i
$451$	−5.66386e7	+	3.27003e7i	−0.617423	+	0.356469i
$452$	−4.45076e7	−	7.70894e7i	−0.481968	−	0.834794i
$453$	−3.44518e7	−	1.98908e7i	−0.370611	−	0.213972i
$454$		−	8.05522e7i		−	0.860815i
$455$	−6.24278e7	+	1.61573e7i	−0.662741	+	0.171528i
$456$	7.50142e7			0.791132
$457$	−4.58763e6	+	7.94601e6i	−0.0480662	+	0.0832531i	−0.889058	−	0.457796i	$-0.848639\pi$
$457$	−4.58763e6	+	7.94601e6i	−0.0480662	+	0.0832531i	0.840991	+	0.541049i	$0.181973\pi$
$458$	−7.03546e7	+	4.06192e7i	−0.732311	+	0.422800i
$459$	−1.16427e7	−	2.01657e7i	−0.120397	−	0.208533i
$460$	1.92089e7	+	1.10903e7i	0.197346	+	0.113938i
$461$			5.79354e7i			0.591346i	0.955289	+	0.295673i	$0.0955438\pi$
$461$			5.79354e7i			0.591346i	−0.955289	+	0.295673i	$0.904456\pi$
$462$	4.91467e7	+	1.36197e7i	0.498389	+	0.138116i
$463$	6.51781e7			0.656687			0.328344	−	0.944558i	$-0.393510\pi$
$463$	6.51781e7			0.656687			0.328344	+	0.944558i	$0.393510\pi$
$464$	−5.68916e6	+	9.85391e6i	−0.0569500	+	0.0986404i
$465$	−2.27914e7	+	1.31586e7i	−0.226679	+	0.130873i
$466$	−1.58955e7	−	2.75318e7i	−0.157079	−	0.272068i
$467$	−1.46749e8	−	8.47258e7i	−1.44087	−	0.831888i	−0.442965	−	0.896539i	$-0.646073\pi$
$467$	−1.46749e8	−	8.47258e7i	−1.44087	−	0.831888i	−0.997908	+	0.0646508i	$0.979407\pi$
$468$			2.28213e7i			0.222640i
$469$	−5.02586e7	+	1.81358e8i	−0.487182	+	1.75799i
$470$	5.15090e7			0.496123
$471$	5.28352e7	−	9.15132e7i	0.505662	−	0.875832i
$472$	3.33888e7	−	1.92770e7i	0.317523	−	0.183322i
$473$	−6.35470e7	−	1.10067e8i	−0.600498	−	1.04009i
$474$	−3.05938e7	−	1.76633e7i	−0.287275	−	0.165858i
$475$		−	9.95326e7i		−	0.928719i
$476$	1.76728e7	+	6.82830e7i	0.163864	+	0.633129i
$477$	4.01377e6			0.0369826
$478$	−4.42622e7	+	7.66644e7i	−0.405275	+	0.701956i
$479$	−7.92689e7	+	4.57659e7i	−0.721268	+	0.416424i	−0.815219	−	0.579153i	$-0.803383\pi$
$479$	−7.92689e7	+	4.57659e7i	−0.721268	+	0.416424i	0.0939514	+	0.995577i	$0.470050\pi$
$480$	−1.55807e7	−	2.69866e7i	−0.140885	−	0.244019i
$481$	−5.52701e7	−	3.19102e7i	−0.496656	−	0.286744i
$482$		−	1.42710e8i		−	1.27443i
$483$	−3.77530e7	+	3.71136e7i	−0.335050	+	0.329375i
$484$	−4.03636e7			−0.356003
$485$	2.18281e7	−	3.78073e7i	0.191333	−	0.331399i
$486$	−4.40591e6	+	2.54376e6i	−0.0383820	+	0.0221598i
$487$	6.56199e7	+	1.13657e8i	0.568131	+	0.984032i	0.996751	+	0.0805467i	$0.0256666\pi$
$487$	6.56199e7	+	1.13657e8i	0.568131	+	0.984032i	−0.428620	+	0.903485i	$0.641000\pi$
$488$	1.23105e8	+	7.10749e7i	1.05930	+	0.611585i
$489$			1.28939e8i			1.10270i
$490$	2.11249e7	+	3.80770e7i	0.179559	+	0.323649i
$491$	−8.81776e7			−0.744927			−0.372463	−	0.928047i	$-0.621487\pi$
$491$	−8.81776e7			−0.744927			−0.372463	+	0.928047i	$0.621487\pi$
$492$	−9.88111e6	+	1.71146e7i	−0.0829680	+	0.143705i
$493$	7.24558e7	−	4.18324e7i	0.604690	−	0.349118i
$494$	−6.93149e7	−	1.20057e8i	−0.574971	−	0.995879i
$495$	2.43201e7	+	1.40412e7i	0.200517	+	0.115768i
$496$			2.10761e7i			0.172721i
$497$	−1.11970e8	−	1.13899e8i	−0.912080	−	0.927794i
$498$	6.19894e6			0.0501914
$499$	1.14235e8	−	1.97862e8i	0.919389	−	1.59243i	0.119043	−	0.992889i	$-0.462017\pi$
$499$	1.14235e8	−	1.97862e8i	0.919389	−	1.59243i	0.800346	−	0.599539i	$-0.204649\pi$
$500$	−5.19262e7	+	2.99796e7i	−0.415410	+	0.239837i
$501$	2.02619e7	+	3.50946e7i	0.161126	+	0.279079i
$502$	−4.55635e7	−	2.63061e7i	−0.360169	−	0.207943i
$503$			2.07735e8i			1.63232i	0.577824	+	0.816161i	$0.303902\pi$
$503$			2.07735e8i			1.63232i	−0.577824	+	0.816161i	$0.696098\pi$
$504$	4.34613e7	−	1.12485e7i	0.339477	−	0.0878623i
$505$	−6.83444e7			−0.530675
$506$	−4.72199e7	+	8.17873e7i	−0.364480	+	0.631298i
$507$	4.12402e7	−	2.38100e7i	0.316444	−	0.182699i
$508$	−1.86744e7	−	3.23450e7i	−0.142448	−	0.246727i
$509$	−4.74960e7	−	2.74218e7i	−0.360167	−	0.207942i	0.308987	−	0.951066i	$-0.400010\pi$
$509$	−4.74960e7	−	2.74218e7i	−0.360167	−	0.207942i	−0.669154	+	0.743124i	$0.733343\pi$
$510$		−	3.54667e7i		−	0.267368i
$511$	1.10312e8	+	3.05702e7i	0.826726	+	0.229106i
$512$	−5.37739e7			−0.400647
$513$	−1.69215e7	+	2.93089e7i	−0.125339	+	0.217094i
$514$	−1.07153e8	+	6.18647e7i	−0.789068	+	0.455569i
$515$	−1.40403e7	−	2.43185e7i	−0.102791	−	0.178039i
$516$	−3.32590e7	−	1.92021e7i	−0.242081	−	0.139765i
$517$		−	2.40167e8i		−	1.73797i
$518$	−1.15091e7	+	4.15306e7i	−0.0828044	+	0.298799i
$519$	1.27910e8			0.914962
$520$	−5.06308e7	+	8.76951e7i	−0.360085	+	0.623685i
$521$	−2.47035e7	+	1.42626e7i	−0.174681	+	0.100852i	−0.584791	−	0.811184i	$-0.698824\pi$
$521$	−2.47035e7	+	1.42626e7i	−0.174681	+	0.100852i	0.410110	+	0.912036i	$0.365490\pi$
$522$	−9.13978e6	−	1.58306e7i	−0.0642576	−	0.111297i
$523$	−9.32394e7	−	5.38318e7i	−0.651770	−	0.376300i	0.137364	−	0.990521i	$-0.456137\pi$
$523$	−9.32394e7	−	5.38318e7i	−0.651770	−	0.376300i	−0.789134	+	0.614221i	$0.789470\pi$
$524$			9.57287e6i			0.0665347i
$525$	−1.49251e7	−	5.76666e7i	−0.103143	−	0.398517i
$526$	5.79958e7			0.398510
$527$	7.74863e7	−	1.34210e8i	0.529411	−	0.916966i
$528$	1.94767e7	−	1.12449e7i	0.132317	−	0.0763930i
$529$	2.50003e7	+	4.33018e7i	0.168880	+	0.292509i
$530$	5.29446e6	+	3.05676e6i	0.0355627	+	0.0205321i
$531$			1.73938e7i			0.116175i
$532$	7.31040e7	−	7.18658e7i	0.485519	−	0.477296i
$533$	1.06394e8			0.702642
$534$	−7.03889e6	+	1.21917e7i	−0.0462253	+	0.0800647i
$535$	1.28307e8	−	7.40782e7i	0.837895	−	0.483759i
$536$	1.47761e8	+	2.55930e8i	0.959546	+	1.66198i
$537$	1.10538e8	+	6.38193e7i	0.713822	+	0.412125i
$538$			1.49125e8i			0.957640i
$539$	1.77538e8	−	9.84975e7i	1.13377	−	0.629012i
$540$	8.48574e6			0.0538900
$541$	−2.77877e7	+	4.81297e7i	−0.175493	+	0.303963i	−0.940332	−	0.340259i	$-0.889485\pi$
$541$	−2.77877e7	+	4.81297e7i	−0.175493	+	0.303963i	0.764839	+	0.644222i	$0.222819\pi$
$542$	6.07722e6	−	3.50868e6i	0.0381686	−	0.0220367i
$543$	2.53784e7	+	4.39567e7i	0.158513	+	0.274553i
$544$	1.58914e8	+	9.17491e7i	0.987110	+	0.569908i
$545$			5.12900e7i			0.316842i
$546$	−5.81620e7	−	5.91640e7i	−0.357323	−	0.363479i
$547$	5.44170e7			0.332485			0.166243	−	0.986085i	$-0.446837\pi$
$547$	5.44170e7			0.332485			0.166243	+	0.986085i	$0.446837\pi$
$548$	−6.24542e7	+	1.08174e8i	−0.379507	+	0.657325i
$549$	−5.55395e7	+	3.20657e7i	−0.335648	+	0.193787i
$550$	−5.31301e7	−	9.20240e7i	−0.319339	−	0.553112i
$551$	−1.05308e8	−	6.07993e7i	−0.629513	−	0.363449i
$552$			8.31335e7i			0.494264i
$553$	−1.36152e8	+	3.52384e7i	−0.805098	+	0.208372i
$554$	−3.70327e7			−0.217799
$555$	−1.18653e7	+	2.05513e7i	−0.0694066	+	0.120216i
$556$	−1.79100e7	+	1.03404e7i	−0.104201	+	0.0601605i
$557$	−6.26135e6	−	1.08450e7i	−0.0362329	−	0.0627571i	0.847340	−	0.531050i	$-0.178202\pi$
$557$	−6.26135e6	−	1.08450e7i	−0.0362329	−	0.0627571i	−0.883573	+	0.468293i	$0.844869\pi$
$558$	−2.93230e7	−	1.69296e7i	−0.168774	−	0.0974418i
$559$			2.06756e8i			1.18365i
$560$	1.85050e7	+	5.12819e6i	0.105372	+	0.0292012i
$561$	−1.65368e8			−0.936616
$562$	887085.	−	1.53648e6i	0.00499754	−	0.00865599i
$563$	1.50742e8	−	8.70310e7i	0.844713	−	0.487695i	−0.0141502	−	0.999900i	$-0.504504\pi$
$563$	1.50742e8	−	8.70310e7i	0.844713	−	0.487695i	0.858864	+	0.512204i	$0.171171\pi$
$564$	−3.62858e7	−	6.28489e7i	−0.202255	−	0.350316i
$565$	1.54321e8	+	8.90971e7i	0.855616	+	0.493990i
$566$			1.76981e7i			0.0976060i
$567$	−5.40896e6	+	1.95182e7i	−0.0296732	+	0.107076i
$568$	−2.50810e8			−1.36868
$569$	−2.37803e7	+	4.11886e7i	−0.129086	+	0.223584i	−0.923323	−	0.384025i	$-0.874538\pi$
$569$	−2.37803e7	+	4.11886e7i	−0.129086	+	0.223584i	0.794237	+	0.607609i	$0.207871\pi$
$570$	−4.46413e7	+	2.57737e7i	−0.241053	+	0.139172i
$571$	−8.27707e7	−	1.43363e8i	−0.444599	−	0.770068i	0.553425	−	0.832899i	$-0.313320\pi$
$571$	−8.27707e7	−	1.43363e8i	−0.444599	−	0.770068i	−0.998024	+	0.0628311i	$0.979987\pi$
$572$	1.40358e8	+	8.10360e7i	0.749981	+	0.433002i
$573$		−	1.34193e8i		−	0.713291i
$574$	−1.80013e7	−	6.95523e7i	−0.0951848	−	0.367770i
$575$	1.10306e8			0.580222
$576$	2.65466e7	−	4.59801e7i	0.138913	−	0.240604i
$577$	−4.44692e7	+	2.56743e7i	−0.231490	+	0.133651i	−0.611259	−	0.791431i	$-0.709337\pi$
$577$	−4.44692e7	+	2.56743e7i	−0.231490	+	0.133651i	0.379769	+	0.925081i	$0.376003\pi$
$578$	3.77210e7	+	6.53346e7i	0.195344	+	0.338345i
$579$	−2.42846e6	−	1.40207e6i	−0.0125111	−	0.00722328i
$580$			3.04895e7i			0.156267i
$581$	1.75987e7	−	1.73007e7i	0.0897331	−	0.0882133i
$582$	5.61673e7			0.284914
$583$	1.42525e7	−	2.46861e7i	0.0719259	−	0.124579i
$584$	1.55672e8	−	8.98771e7i	0.781576	−	0.451243i
$585$	−2.28423e7	−	3.95640e7i	−0.114096	−	0.197621i
$586$	−1.28011e7	−	7.39070e6i	−0.0636141	−	0.0367276i
$587$		−	2.37624e8i		−	1.17483i	−0.809285	−	0.587416i	$-0.800145\pi$
$587$		−	2.37624e8i		−	1.17483i	0.809285	−	0.587416i	$-0.199855\pi$
$588$	3.15782e7	−	5.25992e7i	0.155330	−	0.258730i
$589$	−2.25238e8			−1.10229
$590$	−1.32466e7	+	2.29437e7i	−0.0644982	+	0.111714i
$591$	−3.63600e7	+	2.09925e7i	−0.176141	+	0.101695i
$592$	9.50232e6	+	1.64585e7i	0.0457999	+	0.0793278i
$593$	−3.20624e8	−	1.85112e8i	−1.53756	−	0.887711i	−0.998981	−	0.0451361i	$-0.985628\pi$
$593$	−3.20624e8	−	1.85112e8i	−1.53756	−	0.887711i	−0.538579	−	0.842575i	$-0.681039\pi$
$594$			3.61305e7i			0.172391i
$595$	−9.89842e7	−	1.00690e8i	−0.469910	−	0.478006i
$596$	−1.24549e8			−0.588305
$597$	−4.70944e7	+	8.15699e7i	−0.221333	+	0.383360i
$598$	1.33052e8	−	7.68173e7i	0.622180	−	0.359216i
$599$	1.87938e7	+	3.25519e7i	0.0874451	+	0.151459i	0.906430	−	0.422355i	$-0.138796\pi$
$599$	1.87938e7	+	3.25519e7i	0.0874451	+	0.151459i	−0.818985	+	0.573814i	$0.805463\pi$
$600$	−8.10068e7	−	4.67693e7i	−0.375032	−	0.216525i
$601$		−	2.67605e7i		−	0.123274i	−0.998099	−	0.0616369i	$-0.980368\pi$
$601$		−	2.67605e7i		−	0.123274i	0.998099	−	0.0616369i	$-0.0196321\pi$
$602$	1.35162e8	−	3.49821e7i	0.619534	−	0.160346i
$603$	−1.33326e8			−0.608083
$604$	−4.26849e7	+	7.39324e7i	−0.193715	+	0.335524i
$605$	6.99761e7	−	4.04007e7i	0.315998	−	0.182441i
$606$	−4.39654e7	−	7.61503e7i	−0.197557	−	0.342179i
$607$	6.69071e7	+	3.86288e7i	0.299162	+	0.172721i	0.642066	−	0.766649i	$-0.278077\pi$
$607$	6.69071e7	+	3.86288e7i	0.299162	+	0.172721i	−0.342905	+	0.939370i	$0.611411\pi$
$608$		−	2.66697e8i		−	1.18661i
$609$	−7.01294e7	−	1.94345e7i	−0.310490	−	0.0860444i
$610$	−9.76808e7			−0.430348
$611$	−1.95352e8	+	3.38359e8i	−0.856433	+	1.48338i
$612$	−4.32748e7	+	2.49847e7i	−0.188791	+	0.108998i
$613$	1.76486e8	+	3.05682e8i	0.766174	+	1.32705i	0.939623	+	0.342210i	$0.111175\pi$
$613$	1.76486e8	+	3.05682e8i	0.766174	+	1.32705i	−0.173449	+	0.984843i	$0.555491\pi$
$614$	9.51394e7	+	5.49288e7i	0.411013	+	0.237298i
$615$		−	3.95608e7i		−	0.170075i
$616$	8.51446e7	−	3.07244e8i	0.364263	−	1.31444i
$617$	1.82109e8			0.775310			0.387655	−	0.921805i	$-0.373285\pi$
$617$	1.82109e8			0.775310			0.387655	+	0.921805i	$0.373285\pi$
$618$	1.80640e7	−	3.12878e7i	0.0765330	−	0.132559i
$619$	8.43335e7	−	4.86900e7i	0.355573	−	0.205290i	−0.311564	−	0.950225i	$-0.600853\pi$
$619$	8.43335e7	−	4.86900e7i	0.355573	−	0.205290i	0.667137	+	0.744935i	$0.267520\pi$
$620$	2.82379e7	+	4.89094e7i	0.118483	+	0.205219i
$621$	−3.24811e7	−	1.87530e7i	−0.135630	−	0.0783062i
$622$		−	8.71661e7i		−	0.362223i
$623$	1.40426e7	+	5.42570e7i	0.0580742	+	0.224384i
$624$	−3.65864e7			−0.150579
$625$	−2.70211e7	+	4.68019e7i	−0.110678	+	0.191701i
$626$	5.05134e7	−	2.91639e7i	0.205913	−	0.118884i
$627$	1.20173e8	+	2.08145e8i	0.487533	+	0.844431i
$628$	−1.96384e8	−	1.13382e8i	−0.792916	−	0.457790i
$629$		−	1.39741e8i		−	0.561529i
$630$	−2.19992e7	+	2.16266e7i	−0.0879804	+	0.0864903i
$631$	−1.37285e8			−0.546430			−0.273215	−	0.961953i	$-0.588087\pi$
$631$	−1.37285e8			−0.546430			−0.273215	+	0.961953i	$0.588087\pi$
$632$	−1.10423e8	+	1.91259e8i	−0.437431	+	0.757653i
$633$	1.86453e8	−	1.07648e8i	0.735118	−	0.424421i
$634$	8.93238e7	+	1.54713e8i	0.350509	+	0.607100i
$635$	6.47495e7	+	3.73832e7i	0.252881	+	0.146001i
$636$		−	8.61341e6i		−	0.0334814i
$637$	−3.30243e8	−	5.64143e6i	−1.27766	−	0.0218258i
$638$	−1.29818e8			−0.499887
$639$	5.65770e7	−	9.79943e7i	0.216839	−	0.375576i
$640$	−4.07622e7	+	2.35341e7i	−0.155495	+	0.0897753i
$641$	1.04673e8	+	1.81298e8i	0.397428	+	0.688366i	0.993408	−	0.114633i	$-0.0365693\pi$
$641$	1.04673e8	+	1.81298e8i	0.397428	+	0.688366i	−0.595979	+	0.803000i	$0.703236\pi$
$642$	1.65078e8	+	9.53078e7i	0.623855	+	0.360183i
$643$			3.49818e8i			1.31586i	0.753079	+	0.657930i	$0.228568\pi$
$643$			3.49818e8i			1.31586i	−0.753079	+	0.657930i	$0.771432\pi$
$644$	7.96443e7	+	8.10165e7i	0.298193	+	0.303330i
$645$	7.68791e7			0.286503
$646$	1.51772e8	−	2.62877e8i	0.562981	−	0.975112i
$647$	3.20197e8	−	1.84866e8i	1.18224	−	0.682566i	0.225707	−	0.974195i	$-0.427531\pi$
$647$	3.20197e8	−	1.84866e8i	1.18224	−	0.682566i	0.956531	+	0.291630i	$0.0941974\pi$
$648$	1.59025e7	+	2.75439e7i	0.0584439	+	0.101228i
$649$	1.06978e8	+	6.17637e7i	0.391345	+	0.225943i
$650$			1.72864e8i			0.629454i
$651$	−1.30497e8	+	3.37747e7i	−0.472995	+	0.122419i
$652$	2.76697e8			0.998303
$653$	1.97623e7	−	3.42293e7i	0.0709737	−	0.122930i	−0.828355	−	0.560204i	$-0.810723\pi$
$653$	1.97623e7	−	3.42293e7i	0.0709737	−	0.122930i	0.899328	+	0.437274i	$0.144056\pi$
$654$	−5.71480e7	+	3.29944e7i	−0.204300	+	0.117952i
$655$	−9.58169e6	−	1.65960e7i	−0.0340971	−	0.0590580i
$656$	−2.74376e7	−	1.58411e7i	−0.0971929	−	0.0561144i
$657$			8.10968e7i			0.285962i
$658$	2.54247e8	+	7.04579e7i	0.892437	+	0.247316i
$659$	−3.29124e8			−1.15002			−0.575008	−	0.818148i	$-0.695001\pi$
$659$	−3.29124e8			−1.15002			−0.575008	+	0.818148i	$0.695001\pi$
$660$	3.01320e7	−	5.21901e7i	0.104808	−	0.181533i
$661$	−1.39292e8	+	8.04205e7i	−0.482306	+	0.278460i	−0.721377	−	0.692543i	$-0.756491\pi$
$661$	−1.39292e8	+	8.04205e7i	−0.482306	+	0.278460i	0.239071	+	0.971002i	$0.423157\pi$
$662$	−5.53611e7	−	9.58882e7i	−0.190823	−	0.330515i
$663$	2.32978e8	+	1.34510e8i	0.799419	+	0.461545i
$664$		−	3.87530e7i		−	0.132374i
$665$	−5.48044e7	+	1.97761e8i	−0.186359	+	0.672474i
$666$	−3.05315e7			−0.103353
$667$	6.73800e7	−	1.16706e8i	0.227067	−	0.393291i
$668$	7.53117e7	−	4.34812e7i	0.252658	−	0.145872i
$669$	7.64926e7	+	1.32489e8i	0.255471	+	0.442488i
$670$	−1.75867e8	−	1.01537e8i	−0.584735	−	0.337597i
$671$			4.55448e8i			1.50755i
$672$	−3.99916e7	−	1.54517e8i	−0.131783	−	0.509177i
$673$	5.32162e8			1.74582			0.872908	−	0.487886i	$-0.162232\pi$
$673$	5.32162e8			1.74582			0.872908	+	0.487886i	$0.162232\pi$
$674$	1.01338e7	−	1.75523e7i	0.0330974	−	0.0573263i
$675$	3.65466e7	−	2.11002e7i	0.118832	−	0.0686080i
$676$	−5.10955e7	−	8.84999e7i	−0.165403	−	0.286486i
$677$	−4.68878e8	−	2.70707e8i	−1.51110	−	0.872435i	−0.999916	−	0.0129645i	$-0.995873\pi$
$677$	−4.68878e8	−	2.70707e8i	−1.51110	−	0.872435i	−0.511186	−	0.859470i	$-0.670794\pi$
$678$			2.29262e8i			0.735601i
$679$	1.59458e8	−	1.56758e8i	0.509375	−	0.500748i
$680$	−2.21722e8			−0.705151
$681$	1.13595e8	−	1.96753e8i	0.359683	−	0.622989i
$682$	−2.08246e8	+	1.20231e8i	−0.656483	+	0.379021i
$683$	−1.24469e8	−	2.15587e8i	−0.390662	−	0.676646i	0.601875	−	0.798590i	$-0.294420\pi$
$683$	−1.24469e8	−	2.15587e8i	−0.390662	−	0.676646i	−0.992537	+	0.121944i	$0.961087\pi$
$684$	6.28957e7	+	3.63129e7i	0.196541	+	0.113473i
$685$		−	2.50047e8i		−	0.777946i
$686$	5.21875e7	+	2.16843e8i	0.161657	+	0.671696i
$687$	−2.29126e8			−0.706651
$688$	3.07843e7	−	5.33199e7i	0.0945286	−	0.163728i
$689$	−4.01592e7	+	2.31860e7i	−0.122780	+	0.0708871i
$690$	−2.85633e7	−	4.94731e7i	−0.0869484	−	0.150599i
$691$	8.00565e7	+	4.62206e7i	0.242640	+	0.140088i	0.616390	−	0.787441i	$-0.288595\pi$
$691$	8.00565e7	+	4.62206e7i	0.242640	+	0.140088i	−0.373749	+	0.927530i	$0.621928\pi$
$692$		−	2.74491e8i		−	0.828341i
$693$	1.00837e8	+	1.02574e8i	0.302984	+	0.308204i
$694$	3.56825e7			0.106752
$695$	2.06997e7	−	3.58530e7i	0.0616610	−	0.106800i
$696$	−9.89658e7	+	5.71379e7i	−0.293533	+	0.169472i
$697$	1.16480e8	+	2.01749e8i	0.343995	+	0.595816i
$698$	−1.92196e8	−	1.10964e8i	−0.565169	−	0.326300i
$699$		−	8.96640e7i		−	0.262535i
$700$	−1.23750e8	+	3.20286e7i	−0.360788	+	0.0933778i
$701$	5.38435e8			1.56307			0.781537	−	0.623859i	$-0.214436\pi$
$701$	5.38435e8			1.56307			0.781537	+	0.623859i	$0.214436\pi$
$702$	2.93885e7	−	5.09024e7i	0.0849505	−	0.147139i
$703$	−1.75890e8	+	1.01550e8i	−0.506262	+	0.292290i
$704$	−1.88529e8	−	3.26541e8i	−0.540331	−	0.935880i
$705$	1.25813e8	+	7.26384e7i	0.359054	+	0.207300i
$706$			4.48603e7i			0.127482i
$707$	−3.37346e8	−	9.34866e7i	−0.954590	−	0.264540i
$708$	3.73265e7			0.105176
$709$	−3.53455e7	+	6.12202e7i	−0.0991735	+	0.171773i	−0.911343	−	0.411648i	$-0.864953\pi$
$709$	−3.53455e7	+	6.12202e7i	−0.0991735	+	0.171773i	0.812169	+	0.583422i	$0.198287\pi$
$710$	1.49258e8	−	8.61744e7i	0.417027	−	0.240771i
$711$	−4.98179e7	−	8.62872e7i	−0.138604	−	0.240070i
$712$	7.62173e7	+	4.40041e7i	0.211161	+	0.121914i
$713$		−	2.49616e8i		−	0.688660i
$714$	4.85140e7	−	1.75062e8i	0.133282	−	0.480948i
$715$	−3.24442e8			−0.887604
$716$	1.36954e8	−	2.37211e8i	0.373109	−	0.646243i
$717$	−2.16226e8	+	1.24838e8i	−0.586610	+	0.338680i
$718$	−1.02021e8	−	1.76705e8i	−0.275622	−	0.477392i
$719$	−3.38940e8	−	1.95687e8i	−0.911876	−	0.526472i	−0.0308415	−	0.999524i	$-0.509819\pi$
$719$	−3.38940e8	−	1.95687e8i	−0.911876	−	0.526472i	−0.881034	+	0.473053i	$0.843152\pi$
$720$			1.36041e7i			0.0364478i
$721$	−3.60378e7	−	1.39241e8i	−0.0961506	−	0.371501i
$722$	−1.81149e8			−0.481309
$723$	2.01252e8	−	3.48578e8i	0.532506	−	0.922327i
$724$	9.43295e7	−	5.44612e7i	0.248560	−	0.143506i
$725$	7.58135e7	+	1.31313e8i	0.198945	+	0.344582i
$726$	9.00302e7	+	5.19789e7i	0.235276	+	0.135837i
$727$			4.83550e8i			1.25846i	0.777221	+	0.629228i	$0.216629\pi$
$727$			4.83550e8i			1.25846i	−0.777221	+	0.629228i	$0.783371\pi$
$728$	−3.69868e8	+	3.63603e8i	−0.958633	+	0.942397i
$729$	−1.43489e7			−0.0370370
$730$	−6.17607e7	+	1.06973e8i	−0.158761	+	0.274982i
$731$	−3.92061e8	+	2.26357e8i	−1.00369	+	0.579484i
$732$	6.88118e7	+	1.19186e8i	0.175441	+	0.303872i
$733$	−2.76711e8	−	1.59759e8i	−0.702611	−	0.405653i	0.105708	−	0.994397i	$-0.466289\pi$
$733$	−2.76711e8	−	1.59759e8i	−0.702611	−	0.405653i	−0.808319	+	0.588745i	$0.799622\pi$
$734$			1.08968e8i			0.275556i
$735$	−2.09768e6	+	1.22796e8i	−0.00528295	+	0.309258i
$736$	2.95563e8			0.741339
$737$	−4.73427e8	+	8.20000e8i	−1.18263	+	2.04838i
$738$	4.40792e7	−	2.54491e7i	0.109664	−	0.0633146i
$739$	−1.76757e8	−	3.06151e8i	−0.437968	−	0.758582i	0.559565	−	0.828787i	$-0.310968\pi$
$739$	−1.76757e8	−	3.06151e8i	−0.437968	−	0.758582i	−0.997533	+	0.0702042i	$0.977635\pi$
$740$	4.41024e7	+	2.54625e7i	0.108835	+	0.0628357i
$741$		−	3.90994e8i		−	0.960983i
$742$	2.19520e7	+	2.23302e7i	0.0537357	+	0.0546615i
$743$	4.63396e8			1.12976			0.564880	−	0.825173i	$-0.308923\pi$
$743$	4.63396e8			1.12976			0.564880	+	0.825173i	$0.308923\pi$
$744$	−1.05837e8	+	1.83315e8i	−0.256991	+	0.445121i
$745$	2.15924e8	−	1.24664e8i	0.522195	−	0.301489i
$746$	−2.88318e7	−	4.99381e7i	−0.0694472	−	0.120286i
$747$	1.51412e7	+	8.74179e6i	0.0363245	+	0.0209719i
$748$			3.54873e8i			0.847945i
$749$	7.34650e8	−	1.90139e8i	1.74838	−	0.452508i
$750$	1.54427e8			0.366050
$751$	1.48510e7	−	2.57226e7i	0.0350618	−	0.0607289i	−0.847962	−	0.530057i	$-0.822171\pi$
$751$	1.48510e7	−	2.57226e7i	0.0350618	−	0.0607289i	0.883024	+	0.469328i	$0.155504\pi$
$752$	1.00757e8	−	5.81724e7i	0.236932	−	0.136793i
$753$	−7.41942e7	−	1.28508e8i	−0.173774	−	0.300985i
$754$	1.82894e8	+	1.05594e8i	0.426662	+	0.246334i
$755$		−	1.70897e8i		−	0.397093i
$756$	4.18853e7	+	1.16074e7i	0.0969385	+	0.0268640i
$757$	7.11235e8			1.63955			0.819776	−	0.572684i	$-0.194098\pi$
$757$	7.11235e8			1.63955			0.819776	+	0.572684i	$0.194098\pi$
$758$	1.45365e8	−	2.51780e8i	0.333774	−	0.578113i
$759$	−2.30674e8	+	1.33180e8i	−0.527563	+	0.304588i
$760$	1.61126e8	+	2.79078e8i	0.367049	+	0.635748i
$761$	3.18255e8	+	1.83745e8i	0.722140	+	0.416928i	0.815540	−	0.578701i	$-0.196440\pi$
$761$	3.18255e8	+	1.83745e8i	0.722140	+	0.416928i	−0.0933998	+	0.995629i	$0.529773\pi$
$762$			9.61931e7i			0.217410i
$763$	−7.01583e7	+	2.53166e8i	−0.157945	+	0.569942i
$764$	−2.87974e8			−0.645763
$765$	5.00154e7	−	8.66292e7i	0.111717	−	0.193500i
$766$	−3.51985e8	+	2.03218e8i	−0.783137	+	0.452144i
$767$	−1.00477e8	−	1.74031e8i	−0.222680	−	0.385693i
$768$	−2.41220e8	−	1.39268e8i	−0.532512	−	0.307446i
$769$		−	3.18891e8i		−	0.701235i	−0.936519	−	0.350617i	$-0.885972\pi$
$769$		−	3.18891e8i		−	0.701235i	0.936519	−	0.350617i	$-0.114028\pi$
$770$	5.48940e7	+	2.12097e8i	0.120241	+	0.464581i
$771$	−3.48969e8			−0.761419
$772$	−3.00879e6	+	5.21138e6i	−0.00653944	+	0.0113266i
$773$	1.35153e8	−	7.80307e7i	0.292609	−	0.168938i	−0.346509	−	0.938047i	$-0.612633\pi$
$773$	1.35153e8	−	7.80307e7i	0.292609	−	0.168938i	0.639118	+	0.769109i	$0.279300\pi$
$774$	4.94557e7	+	8.56598e7i	0.106658	+	0.184737i
$775$	2.43231e8	+	1.40430e8i	0.522533	+	0.301685i
$776$		−	3.51133e8i		−	0.751427i
$777$	−8.66785e7	+	8.52105e7i	−0.184777	+	0.181648i
$778$	9.51413e7			0.202037
$779$	1.69292e8	−	2.93222e8i	0.358116	−	0.620275i
$780$	−8.49028e7	+	4.90187e7i	−0.178912	+	0.103295i
$781$	−4.01798e8	−	6.95935e8i	−0.843442	−	1.46088i
$782$	2.91329e8	+	1.68199e8i	0.609206	+	0.351725i
$783$		−	5.15560e7i		−	0.107397i
$784$	8.43255e7	+	5.06252e7i	0.174989	+	0.105055i
$785$	4.53947e8			0.938417
$786$	1.23276e7	−	2.13521e7i	0.0253871	−	0.0439717i
$787$	−6.50044e8	+	3.75303e8i	−1.33358	+	0.769942i	−0.985846	−	0.167651i	$-0.946382\pi$
$787$	−6.50044e8	+	3.75303e8i	−1.33358	+	0.769942i	−0.347733	+	0.937594i	$0.613048\pi$
$788$	4.50490e7	+	7.80272e7i	0.0920676	+	0.159466i
$789$	1.41658e8	+	8.17862e7i	0.288410	+	0.166513i
$790$		−	1.51759e8i		−	0.307803i
$791$	6.39848e8	+	6.50872e8i	1.29285	+	1.31512i
$792$	2.25872e8			0.454660
$793$	3.70462e8	−	6.41658e8i	0.742888	−	1.28672i
$794$	2.93497e8	−	1.69451e8i	0.586331	−	0.338518i
$795$	8.62134e6	+	1.49326e7i	0.0171583	+	0.0297190i
$796$	1.75046e8	+	1.01063e8i	0.347067	+	0.200379i
$797$			1.08408e6i			0.00214134i	0.999999	+	0.00107067i	$0.000340806\pi$
$797$			1.08408e6i			0.00214134i	−0.999999	+	0.00107067i	$0.999659\pi$
$798$	−2.55603e8	+	6.61543e7i	−0.502988	+	0.130181i
$799$	−8.55483e8			−1.67715
$800$	−1.66278e8	+	2.88002e8i	−0.324762	+	0.562505i
$801$	−3.43857e7	+	1.98526e7i	−0.0669084	+	0.0386296i
$802$	1.27527e8	+	2.20884e8i	0.247218	+	0.428194i
$803$	4.98772e8	+	2.87966e8i	0.963287	+	0.556154i
$804$			2.86113e8i			0.550515i
$805$	−2.19166e8	−	6.07362e7i	−0.420132	−	0.116429i
$806$	3.91183e8			0.747093
$807$	−2.10297e8	+	3.64245e8i	−0.400140	+	0.693063i
$808$	−4.76058e8	+	2.74852e8i	−0.902456	+	0.521033i
$809$	−2.23887e8	−	3.87784e8i	−0.422847	−	0.732392i	0.573370	−	0.819297i	$-0.305636\pi$
$809$	−2.23887e8	−	3.87784e8i	−0.422847	−	0.732392i	−0.996217	+	0.0869044i	$0.972303\pi$
$810$	−1.89273e7	−	1.09277e7i	−0.0356150	−	0.0205623i
$811$		−	7.02416e8i		−	1.31684i	−0.752652	−	0.658418i	$-0.771226\pi$
$811$		−	7.02416e8i		−	1.31684i	0.752652	−	0.658418i	$-0.228774\pi$
$812$	−4.17058e7	+	1.50495e8i	−0.0778984	+	0.281096i
$813$	1.97919e7			0.0368312
$814$	−1.08414e8	+	1.87779e8i	−0.201008	+	0.348155i
$815$	−4.79695e8	+	2.76952e8i	−0.886120	+	0.511601i
$816$	−4.00548e7	−	6.93769e7i	−0.0737197	−	0.127686i
$817$	5.69823e8	+	3.28987e8i	1.04490	+	0.603272i
$818$		−	3.35448e8i		−	0.612866i
$819$	−5.86301e7	−	2.26532e8i	−0.106726	−	0.412361i
$820$	−8.48960e7			−0.153973
$821$	−3.31937e8	+	5.74932e8i	−0.599828	+	1.03893i	0.393018	+	0.919531i	$0.371431\pi$
$821$	−3.31937e8	+	5.74932e8i	−0.599828	+	1.03893i	−0.992846	+	0.119402i	$0.961902\pi$
$822$	2.78605e8	−	1.60853e8i	0.501619	−	0.289610i
$823$	−2.08427e8	−	3.61007e8i	−0.373900	−	0.647614i	0.616262	−	0.787541i	$-0.288646\pi$
$823$	−2.08427e8	−	3.61007e8i	−0.373900	−	0.647614i	−0.990162	+	0.139928i	$0.955313\pi$
$824$	−1.95598e8	−	1.12928e8i	−0.349609	−	0.201847i
$825$		−	2.99698e8i		−	0.533731i
$826$	−9.67688e7	+	9.51298e7i	−0.171710	+	0.168802i
$827$	1.14598e8			0.202609			0.101305	−	0.994855i	$-0.467698\pi$
$827$	1.14598e8			0.202609			0.101305	+	0.994855i	$0.467698\pi$
$828$	−4.02432e7	+	6.97033e7i	−0.0708928	+	0.122790i
$829$	4.05381e8	−	2.34047e8i	0.711541	−	0.410808i	−0.100090	−	0.994978i	$-0.531913\pi$
$829$	4.05381e8	−	2.34047e8i	0.711541	−	0.410808i	0.811631	+	0.584170i	$0.198580\pi$
$830$	1.33149e7	+	2.30621e7i	0.0232865	+	0.0403334i
$831$	−9.04544e7	−	5.22239e7i	−0.157626	−	0.0910052i
$832$			6.13397e8i			1.06505i
$833$	−3.50852e8	−	6.32398e8i	−0.607000	−	1.09410i
$834$	5.32639e7			0.0918195
$835$	−8.70425e7	+	1.50762e8i	−0.149511	+	0.258960i
$836$	4.46672e8	−	2.57886e8i	0.764487	−	0.441377i
$837$	−4.77487e7	−	8.27031e7i	−0.0814301	−	0.141041i
$838$	−5.61797e8	−	3.24354e8i	−0.954657	−	0.551172i
$839$			6.49855e8i			1.10035i	0.835050	+	0.550174i	$0.185439\pi$
$839$			6.49855e8i			1.10035i	−0.835050	+	0.550174i	$0.814561\pi$
$840$	1.35200e8	+	1.37530e8i	0.228108	+	0.232038i
$841$	−4.09581e8			−0.688576
$842$	3.55136e7	−	6.15114e7i	0.0594920	−	0.103043i
$843$	4.33350e6	−	2.50195e6i	0.00723363	−	0.00417634i
$844$	−2.31010e8	−	4.00120e8i	−0.384240	−	0.665523i
$845$	1.77163e8	+	1.02285e8i	0.293631	+	0.169528i
$846$			1.86911e8i			0.308691i
$847$	4.00663e8	−	1.03698e8i	0.659370	−	0.170656i
$848$	1.38088e7			0.0226447
$849$	−2.49580e7	+	4.32285e7i	−0.0407837	+	0.0706394i
$850$	−3.27793e8	+	1.89251e8i	−0.533756	+	0.308164i
$851$	−1.12542e8	−	1.94928e8i	−0.182610	−	0.316290i
$852$	−2.10292e8	−	1.21412e8i	−0.340020	−	0.196310i
$853$		−	7.47082e7i		−	0.120371i	−0.998187	−	0.0601854i	$-0.980831\pi$
$853$		−	7.47082e7i		−	0.120371i	0.998187	−	0.0601854i	$-0.0191692\pi$
$854$	−4.82149e8	−	1.33615e8i	−0.774119	−	0.214527i
$855$	−1.45385e8			−0.232606
$856$	5.95823e8	−	1.03200e9i	0.949939	−	1.64534i
$857$	−7.50588e8	+	4.33352e8i	−1.19250	+	0.688491i	−0.958873	−	0.283835i	$-0.908393\pi$
$857$	−7.50588e8	+	4.33352e8i	−1.19250	+	0.688491i	−0.233629	+	0.972326i	$0.575060\pi$
$858$	−2.08711e8	−	3.61498e8i	−0.330433	−	0.572327i
$859$	−1.51273e7	−	8.73376e6i	−0.0238662	−	0.0137791i	0.488019	−	0.872833i	$-0.337720\pi$
$859$	−1.51273e7	−	8.73376e6i	−0.0238662	−	0.0137791i	−0.511886	+	0.859054i	$0.671053\pi$
$860$		−	1.64980e8i		−	0.259379i
$861$	5.41143e7	−	1.95271e8i	0.0847817	−	0.305934i
$862$	−6.29285e8			−0.982484
$863$	5.59542e8	−	9.69155e8i	0.870563	−	1.50786i	0.00914866	−	0.999958i	$-0.497088\pi$
$863$	5.59542e8	−	9.69155e8i	0.870563	−	1.50786i	0.861415	−	0.507902i	$-0.169579\pi$
$864$	9.79262e7	−	5.65377e7i	0.151830	−	0.0876591i
$865$	2.74743e8	+	4.75869e8i	0.424501	+	0.735257i
$866$	−1.32161e8	−	7.63035e7i	−0.203494	−	0.117487i
$867$			2.12778e8i			0.326489i
$868$	7.24792e7	+	2.80041e8i	0.110829	+	0.428216i
$869$	−7.07593e8			−1.07826
$870$	3.92634e7	−	6.80061e7i	0.0596252	−	0.103274i
$871$	1.33397e9	−	7.70171e8i	2.01880	−	1.16555i
$872$	2.06267e8	+	3.57264e8i	0.311085	+	0.538816i
$873$	1.37192e8	+	7.92076e7i	0.206198	+	0.119049i
$874$		−	4.88922e8i		−	0.732328i
$875$	4.38417e8	−	4.30992e8i	0.654430	−	0.643346i
$876$	1.74031e8			0.258889
$877$	−5.82730e8	+	1.00932e9i	−0.863910	+	1.49634i	0.00421521	+	0.999991i	$0.498658\pi$
$877$	−5.82730e8	+	1.00932e9i	−0.863910	+	1.49634i	−0.868125	+	0.496345i	$0.834675\pi$
$878$	−3.44029e8	+	1.98625e8i	−0.508290	+	0.293462i
$879$	−2.08449e7	−	3.61044e7i	−0.0306925	−	0.0531610i
$880$	8.36696e7	+	4.83067e7i	0.122778	+	0.0708858i
$881$			2.07806e8i			0.303900i	0.988388	+	0.151950i	$0.0485553\pi$
$881$			2.07806e8i			0.303900i	−0.988388	+	0.151950i	$0.951445\pi$
$882$	−1.38170e8	+	7.66561e7i	−0.201376	+	0.111723i
$883$	−3.48816e8			−0.506657			−0.253329	−	0.967380i	$-0.581525\pi$
$883$	−3.48816e8			−0.506657			−0.253329	+	0.967380i	$0.581525\pi$
$884$	2.88653e8	−	4.99962e8i	0.417849	−	0.723736i
$885$	−6.47109e7	+	3.73609e7i	−0.0933572	+	0.0538998i
$886$	2.62613e8	+	4.54859e8i	0.377585	+	0.653996i
$887$	−7.31382e8	−	4.22263e8i	−1.04803	−	0.605080i	−0.125932	−	0.992039i	$-0.540192\pi$
$887$	−7.31382e8	−	4.22263e8i	−1.04803	−	0.605080i	−0.922097	+	0.386959i	$0.873525\pi$
$888$			1.90869e8i			0.272582i
$889$	2.68466e8	+	2.73091e8i	0.382106	+	0.388689i
$890$	−6.04764e7			−0.0857858
$891$	−5.09515e7	+	8.82506e7i	−0.0720317	+	0.124763i
$892$	2.84317e8	−	1.64150e8i	0.400597	−	0.231285i
$893$	6.21681e8	+	1.07678e9i	0.872998	+	1.51208i
$894$	2.77804e8	+	1.60390e8i	0.388800	+	0.224474i
$895$			5.48320e8i			0.764830i
$896$	−2.33392e8	+	6.04058e7i	−0.324461	+	0.0839758i
$897$	4.33314e8			0.600379
$898$	−3.18910e8	+	5.52368e8i	−0.440391	+	0.762780i
$899$	2.97155e8	−	1.71562e8i	0.408981	−	0.236125i
$900$	−4.52802e7	−	7.84276e7i	−0.0621127	−	0.107582i
$901$	−8.79326e7	−	5.07679e7i	−0.120220	−	0.0694089i
$902$		−	3.61469e8i		−	0.492552i
$903$	3.79473e8	+	1.05161e8i	0.515368	+	0.142821i
$904$	1.43324e9			1.94006
$905$	−1.09023e8	+	1.88833e8i	−0.147086	+	0.254760i
$906$	1.90415e8	−	1.09936e8i	0.256046	−	0.147828i
$907$	3.99924e8	+	6.92689e8i	0.535989	+	0.928360i	0.999115	+	0.0420677i	$0.0133945\pi$
$907$	3.99924e8	+	6.92689e8i	0.535989	+	0.928360i	−0.463126	+	0.886293i	$0.653272\pi$
$908$	−4.22225e8	−	2.43771e8i	−0.564009	−	0.325631i
$909$		−	2.48001e8i		−	0.330189i
$910$	9.51818e7	−	3.43463e8i	0.126308	−	0.455780i
$911$	1.54047e8			0.203750			0.101875	−	0.994797i	$-0.467516\pi$
$911$	1.54047e8			0.203750			0.101875	+	0.994797i	$0.467516\pi$
$912$	−5.82157e7	+	1.00833e8i	−0.0767460	+	0.132928i
$913$	1.07530e8	−	6.20824e7i	0.141292	−	0.0815749i
$914$	−2.53559e7	−	4.39176e7i	−0.0332078	−	0.0575175i
$915$	−2.38591e8	−	1.37750e8i	−0.311451	−	0.179816i
$916$			4.91697e8i			0.639751i
$917$	−2.45937e7	−	9.50237e7i	−0.0318945	−	0.123232i
$918$	1.28698e8			0.166358
$919$	−3.43544e8	+	5.95036e8i	−0.442625	+	0.766649i	−0.997883	−	0.0650288i	$-0.979286\pi$
$919$	−3.43544e8	+	5.95036e8i	−0.442625	+	0.766649i	0.555258	+	0.831678i	$0.312619\pi$
$920$	−3.09285e8	+	1.78566e8i	−0.397187	+	0.229316i
$921$	1.54922e8	+	2.68333e8i	0.198305	+	0.343475i
$922$	−2.77309e8	−	1.60105e8i	−0.353811	−	0.204273i
$923$			1.30729e9i			1.66252i
$924$	2.20120e8	−	2.16392e8i	0.279025	−	0.274299i
$925$	2.53255e8			0.319987
$926$	−1.80120e8	+	3.11977e8i	−0.226845	+	0.392906i
$927$	8.82447e7	−	5.09481e7i	0.110777	−	0.0639571i
$928$	2.03142e8	+	3.51852e8i	0.254188	+	0.440266i
$929$	3.27395e8	+	1.89021e8i	0.408342	+	0.235757i	0.690077	−	0.723736i	$-0.257577\pi$
$929$	3.27395e8	+	1.89021e8i	0.408342	+	0.235757i	−0.281735	+	0.959492i	$0.590910\pi$
$930$		−	1.45455e8i		−	0.180834i
$931$	−5.41025e8	+	9.01176e8i	−0.670453	+	1.11676i
$932$	−1.92416e8			−0.237680
$933$	1.22922e8	−	2.12908e8i	0.151351	−	0.262148i
$934$	8.11084e8	−	4.68280e8i	0.995463	−	0.574731i
$935$	−3.55199e8	−	6.15223e8i	−0.434547	−	0.752658i
$936$	−3.18219e8	−	1.83724e8i	−0.388060	−	0.224047i
$937$		−	1.27190e9i		−	1.54609i	−0.634351	−	0.773045i	$-0.718732\pi$
$937$		−	1.27190e9i		−	1.54609i	0.634351	−	0.773045i	$-0.281268\pi$
$938$	−7.29183e8	−	7.41746e8i	−0.883544	−	0.898766i
$939$	1.64509e8			0.198698
$940$	1.55879e8	−	2.69991e8i	0.187674	−	0.325062i
$941$	−6.05181e8	+	3.49402e8i	−0.726301	+	0.419330i	−0.817067	−	0.576542i	$-0.804402\pi$
$941$	−6.05181e8	+	3.49402e8i	−0.726301	+	0.419330i	0.0907665	+	0.995872i	$0.471068\pi$
$942$	2.92020e8	+	5.05794e8i	0.349349	+	0.605091i
$943$	3.24960e8	+	1.87615e8i	0.387520	+	0.223735i
$944$			5.98408e7i			0.0711346i
$945$	−8.42324e7	+	2.18007e7i	−0.0998122	+	0.0258330i
$946$	7.02448e8			0.829738
$947$	1.95719e8	−	3.38995e8i	0.230453	−	0.399157i	−0.727488	−	0.686120i	$-0.759312\pi$
$947$	1.95719e8	−	3.38995e8i	0.230453	−	0.399157i	0.957942	+	0.286963i	$0.0926458\pi$
$948$	−1.85169e8	+	1.06907e8i	−0.217342	+	0.125482i
$949$	−4.68464e8	−	8.11403e8i	−0.548122	−	0.949375i
$950$	4.76415e8	+	2.75058e8i	0.555667	+	0.320815i
$951$			5.03861e8i			0.585827i
$952$	−1.09441e9	−	3.03288e8i	−1.26844	−	0.351516i
$953$	−9.05418e8			−1.04609			−0.523047	−	0.852304i	$-0.675205\pi$
$953$	−9.05418e8			−1.04609			−0.523047	+	0.852304i	$0.675205\pi$
$954$	−1.10921e7	+	1.92120e7i	−0.0127752	+	0.0221273i
$955$	4.99244e8	−	2.88239e8i	0.573196	−	0.330935i
$956$	2.67897e8	+	4.64012e8i	0.306616	+	0.531075i
$957$	−3.17087e8	−	1.83070e8i	−0.361778	−	0.208873i
$958$		−	5.05897e8i		−	0.575394i
$959$	3.42033e8	−	1.23422e9i	0.387803	−	1.39939i
$960$	2.28082e8			0.257797
$961$	−1.25967e8	+	2.18180e8i	−0.141934	+	0.245836i
$962$	3.05478e8	−	1.76368e8i	0.343127	−	0.198104i
$963$	2.68808e8	+	4.65589e8i	0.300998	+	0.521343i
$964$	−7.48035e8	−	4.31878e8i	−0.835008	−	0.482092i
$965$		−	1.20463e7i		−	0.0134051i
$966$	−7.33146e7	−	2.83269e8i	−0.0813315	−	0.314244i
$967$	−1.33523e9			−1.47665			−0.738323	−	0.674448i	$-0.764382\pi$
$967$	−1.33523e9			−1.47665			−0.738323	+	0.674448i	$0.764382\pi$
$968$	3.24950e8	−	5.62829e8i	0.358253	−	0.620513i
$969$	7.41422e8	−	4.28060e8i	0.814881	−	0.470472i
$970$	1.20644e8	+	2.08961e8i	0.132187	+	0.228955i
$971$	−5.45806e8	−	3.15121e8i	−0.596184	−	0.344207i	0.171355	−	0.985209i	$-0.445186\pi$
$971$	−5.45806e8	−	3.15121e8i	−0.596184	−	0.344207i	−0.767539	+	0.641002i	$0.778519\pi$
$972$			3.07922e7i			0.0335307i
$973$	1.51216e8	−	1.48655e8i	0.164157	−	0.161376i
$974$	−7.25362e8			−0.785015
$975$	−2.43774e8	+	4.22229e8i	−0.263011	+	0.455549i
$976$	−1.91075e8	+	1.10317e8i	−0.205520	+	0.118657i
$977$	2.04552e8	+	3.54294e8i	0.219341	+	0.379910i	0.954607	−	0.297869i	$-0.0962760\pi$
$977$	2.04552e8	+	3.54294e8i	0.219341	+	0.379910i	−0.735266	+	0.677779i	$0.762943\pi$
$978$	−6.17168e8	−	3.56322e8i	−0.659761	−	0.380913i
$979$			2.81978e8i			0.300516i
$980$	2.63515e8	+	4.50154e6i	0.279980	+	0.00478281i
$981$	−1.86116e8			−0.197141
$982$	2.43679e8	−	4.22064e8i	0.257326	−	0.445701i
$983$	7.95291e8	−	4.59161e8i	0.837270	−	0.483398i	−0.0190654	−	0.999818i	$-0.506069\pi$
$983$	7.95291e8	−	4.59161e8i	0.837270	−	0.483398i	0.856335	+	0.516420i	$0.172736\pi$
$984$	−1.59097e8	−	2.75564e8i	−0.166985	−	0.289226i
$985$	−1.56198e8	−	9.01810e7i	−0.163443	−	0.0943640i
$986$			4.62415e8i			0.482394i
$987$	5.21651e8	+	5.30638e8i	0.542536	+	0.551883i
$988$	−8.39059e8			−0.870005
$989$	−3.64596e8	+	6.31499e8i	−0.376897	+	0.652805i
$990$	−1.34417e8	+	7.76060e7i	−0.138532	+	0.0799815i
$991$	2.59369e8	+	4.49241e8i	0.266500	+	0.461592i	0.967956	−	0.251122i	$-0.0807994\pi$
$991$	2.59369e8	+	4.49241e8i	0.266500	+	0.461592i	−0.701455	+	0.712713i	$0.747466\pi$
$992$	6.51736e8	+	3.76280e8i	0.667631	+	0.385457i
$993$		−	3.12283e8i		−	0.318934i
$994$	8.54611e8	−	2.21187e8i	0.870180	−	0.225217i
$995$	−4.04623e8			−0.410754
$996$	1.87596e7	−	3.24925e7i	0.0189865	−	0.0328856i
$997$	3.12596e8	−	1.80477e8i	0.315426	−	0.182111i	−0.333926	−	0.942599i	$-0.608374\pi$
$997$	3.12596e8	−	1.80477e8i	0.315426	−	0.182111i	0.649352	+	0.760488i	$0.275040\pi$
$998$	6.31379e8	+	1.09358e9i	0.635183	+	1.10017i
$999$	−7.45747e7	−	4.30557e7i	−0.0747989	−	0.0431852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.f.a.19.2	yes	8
3.2	odd	2		63.7.m.d.19.3		8
4.3	odd	2		336.7.bh.d.145.2		8
7.2	even	3		147.7.d.b.97.5		8
7.3	odd	6	inner	21.7.f.a.10.2	✓	8
7.4	even	3		147.7.f.d.31.2		8
7.5	odd	6		147.7.d.b.97.6		8
7.6	odd	2		147.7.f.d.19.2		8
21.2	odd	6		441.7.d.c.244.3		8
21.5	even	6		441.7.d.c.244.4		8
21.17	even	6		63.7.m.d.10.3		8
28.3	even	6		336.7.bh.d.241.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.f.a.10.2	✓	8	7.3	odd	6	inner
21.7.f.a.19.2	yes	8	1.1	even	1	trivial
63.7.m.d.10.3		8	21.17	even	6
63.7.m.d.19.3		8	3.2	odd	2
147.7.d.b.97.5		8	7.2	even	3
147.7.d.b.97.6		8	7.5	odd	6
147.7.f.d.19.2		8	7.6	odd	2
147.7.f.d.31.2		8	7.4	even	3
336.7.bh.d.145.2		8	4.3	odd	2
336.7.bh.d.241.2		8	28.3	even	6
441.7.d.c.244.3		8	21.2	odd	6
441.7.d.c.244.4		8	21.5	even	6

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	21.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.76350 + 4.78652i) q^{2} +(-13.5000 + 7.79423i) q^{3} +(16.7261 + 28.9705i) q^{4} +(-57.9943 - 33.4830i) q^{5} -86.1574i q^{6} +(-240.457 - 244.600i) q^{7} -538.619 q^{8} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(-2.76350 + 4.78652i) q^{2} +(-13.5000 + 7.79423i) q^{3} +(16.7261 + 28.9705i) q^{4} +(-57.9943 - 33.4830i) q^{5} -86.1574i q^{6} +(-240.457 - 244.600i) q^{7} -538.619 q^{8} +(121.500 - 210.444i) q^{9} +(320.535 - 185.061i) q^{10} +(-862.868 - 1494.53i) q^{11} +(-451.605 - 260.734i) q^{12} +2807.43i q^{13} +(1835.29 - 475.002i) q^{14} +1043.90 q^{15} +(418.002 - 724.000i) q^{16} +(-5323.58 + 3073.57i) q^{17} +(671.531 + 1163.13i) q^{18} +(7737.30 + 4467.13i) q^{19} -2240.17i q^{20} +(5152.64 + 1427.92i) q^{21} +9538.15 q^{22} +(-4950.64 + 8574.76i) q^{23} +(7271.35 - 4198.12i) q^{24} +(-5570.27 - 9648.00i) q^{25} +(-13437.8 - 7758.32i) q^{26} +3788.00i q^{27} +(3064.27 - 11057.4i) q^{28} -13610.4 q^{29} +(-2884.81 + 4996.64i) q^{30} +(-21833.0 + 12605.3i) q^{31} +(-14925.5 - 25851.7i) q^{32} +(23297.4 + 13450.8i) q^{33} -33975.2i q^{34} +(5755.21 + 22236.7i) q^{35} +8128.90 q^{36} +(-11366.4 + 19687.1i) q^{37} +(-42764.1 + 24689.9i) q^{38} +(-21881.7 - 37900.2i) q^{39} +(31236.8 + 18034.6i) q^{40} -37897.2i q^{41} +(-21074.1 + 20717.2i) q^{42} +73646.2 q^{43} +(28864.9 - 49995.4i) q^{44} +(-14092.6 + 8136.38i) q^{45} +(-27362.2 - 47392.7i) q^{46} +(120523. + 69583.9i) q^{47} +13032.0i q^{48} +(-2009.47 + 117632. i) q^{49} +61573.8 q^{50} +(47912.2 - 82986.3i) q^{51} +(-81332.5 + 46957.3i) q^{52} +(8258.79 + 14304.7i) q^{53} +(-18131.3 - 10468.1i) q^{54} +115566. i q^{55} +(129515. + 131746. i) q^{56} -139271. q^{57} +(37612.3 - 65146.4i) q^{58} +(-61989.7 + 35789.8i) q^{59} +(17460.4 + 30242.2i) q^{60} +(-228557. - 131958. i) q^{61} -139339. i q^{62} +(-80690.3 + 20883.9i) q^{63} +218491. q^{64} +(94001.1 - 162815. i) q^{65} +(-128765. + 74342.5i) q^{66} +(-274333. - 475159. i) q^{67} +(-178086. - 102818. i) q^{68} -154346. i q^{69} +(-122341. - 33903.6i) q^{70} +465655. q^{71} +(-65442.2 + 113349. i) q^{72} +(-289020. + 166866. i) q^{73} +(-62821.9 - 108811. i) q^{74} +(150397. + 86832.0i) q^{75} +298871. i q^{76} +(-158080. + 570429. i) q^{77} +241881. q^{78} +(205012. - 355091. i) q^{79} +(-48483.5 + 27991.9i) q^{80} +(-29524.5 - 51137.9i) q^{81} +(181396. + 104729. i) q^{82} +71948.9i q^{83} +(44816.2 + 173158. i) q^{84} +411649. q^{85} +(-203521. + 352509. i) q^{86} +(183740. - 106082. i) q^{87} +(464757. + 804983. i) q^{88} +(-141505. - 81698.0i) q^{89} -89939.6i q^{90} +(686697. - 675066. i) q^{91} -331220. q^{92} +(196497. - 340342. i) q^{93} +(-666130. + 384590. i) q^{94} +(-299146. - 518137. i) q^{95} +(402989. + 232666. i) q^{96} +651914. i q^{97} +(-557494. - 334694. i) q^{98} -419354. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} - 294 q^{5} - 656 q^{7} + 3326 q^{8} + 972 q^{9}+O(q^{10}) \) 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 - 294 * q^5 - 656 * q^7 + 3326 * q^8 + 972 * q^9	\( 8 q - 5 q^{2} - 108 q^{3} - 173 q^{4} - 294 q^{5} - 656 q^{7} + 3326 q^{8} + 972 q^{9} - 3411 q^{10} - 314 q^{11} + 4671 q^{12} - 5360 q^{14} + 5292 q^{15} - 12721 q^{16} - 5532 q^{17} + 1215 q^{18} - 18234 q^{19} + 9342 q^{21} + 86106 q^{22} + 3928 q^{23} - 44901 q^{24} - 17038 q^{25} + 12366 q^{26} + 85037 q^{28} - 8300 q^{29} + 30699 q^{30} - 89508 q^{31} - 186207 q^{32} + 8478 q^{33} - 25860 q^{35} - 84078 q^{36} + 64706 q^{37} - 77136 q^{38} + 29106 q^{39} + 221823 q^{40} + 173583 q^{42} + 45740 q^{43} + 92529 q^{44} - 71442 q^{45} - 111504 q^{46} + 483276 q^{47} - 310684 q^{49} + 967216 q^{50} + 49788 q^{51} - 1673988 q^{52} - 540974 q^{53} - 32805 q^{54} - 241885 q^{56} + 328212 q^{57} + 539799 q^{58} - 181770 q^{59} - 146367 q^{60} + 418224 q^{61} - 92826 q^{63} + 2378626 q^{64} - 414204 q^{65} - 1162431 q^{66} - 1158902 q^{67} - 821250 q^{68} + 1087917 q^{70} + 1442344 q^{71} + 404109 q^{72} - 378666 q^{73} - 432940 q^{74} + 460026 q^{75} + 1065994 q^{77} - 222588 q^{78} + 611452 q^{79} - 2094945 q^{80} - 236196 q^{81} - 1561266 q^{82} - 1579716 q^{84} - 275112 q^{85} + 816224 q^{86} + 112050 q^{87} - 366441 q^{88} - 989196 q^{89} + 304446 q^{91} + 678720 q^{92} + 805572 q^{93} - 716148 q^{94} - 591792 q^{95} + 5027589 q^{96} + 3509629 q^{98} - 152604 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 108 * q^3 - 173 * q^4 - 294 * q^5 - 656 * q^7 + 3326 * q^8 + 972 * q^9 - 3411 * q^10 - 314 * q^11 + 4671 * q^12 - 5360 * q^14 + 5292 * q^15 - 12721 * q^16 - 5532 * q^17 + 1215 * q^18 - 18234 * q^19 + 9342 * q^21 + 86106 * q^22 + 3928 * q^23 - 44901 * q^24 - 17038 * q^25 + 12366 * q^26 + 85037 * q^28 - 8300 * q^29 + 30699 * q^30 - 89508 * q^31 - 186207 * q^32 + 8478 * q^33 - 25860 * q^35 - 84078 * q^36 + 64706 * q^37 - 77136 * q^38 + 29106 * q^39 + 221823 * q^40 + 173583 * q^42 + 45740 * q^43 + 92529 * q^44 - 71442 * q^45 - 111504 * q^46 + 483276 * q^47 - 310684 * q^49 + 967216 * q^50 + 49788 * q^51 - 1673988 * q^52 - 540974 * q^53 - 32805 * q^54 - 241885 * q^56 + 328212 * q^57 + 539799 * q^58 - 181770 * q^59 - 146367 * q^60 + 418224 * q^61 - 92826 * q^63 + 2378626 * q^64 - 414204 * q^65 - 1162431 * q^66 - 1158902 * q^67 - 821250 * q^68 + 1087917 * q^70 + 1442344 * q^71 + 404109 * q^72 - 378666 * q^73 - 432940 * q^74 + 460026 * q^75 + 1065994 * q^77 - 222588 * q^78 + 611452 * q^79 - 2094945 * q^80 - 236196 * q^81 - 1561266 * q^82 - 1579716 * q^84 - 275112 * q^85 + 816224 * q^86 + 112050 * q^87 - 366441 * q^88 - 989196 * q^89 + 304446 * q^91 + 678720 * q^92 + 805572 * q^93 - 716148 * q^94 - 591792 * q^95 + 5027589 * q^96 + 3509629 * q^98 - 152604 * q^99

Introduction

L-functions

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