LMFDB - Embedded newform 28.6.f.a.3.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [28,6,Mod(3,28)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(28, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("28.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	28.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:	$4.49074695476$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			3.9
Character	$\chi$	$=$	28.3
Dual form			28.6.f.a.19.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.726423 - 5.61002i) q^{2} +(-0.901244 + 1.56100i) q^{3} +(-30.9446 + 8.15049i) q^{4} +(-41.1834 + 23.7773i) q^{5} +(9.41192 + 3.92205i) q^{6} +(-122.887 - 41.3025i) q^{7} +(68.2033 + 167.679i) q^{8} +(119.876 + 207.630i) q^{9} +(163.307 + 213.767i) q^{10} +(-381.616 - 220.326i) q^{11} +(15.1657 - 55.6501i) q^{12} +283.636i q^{13} +(-142.441 + 719.399i) q^{14} -85.7165i q^{15} +(891.139 - 504.428i) q^{16} +(-1292.34 - 746.132i) q^{17} +(1077.73 - 823.331i) q^{18} +(-1061.07 - 1837.82i) q^{19} +(1080.61 - 1071.44i) q^{20} +(175.224 - 154.602i) q^{21} +(-958.818 + 2300.92i) q^{22} +(1976.80 - 1141.30i) q^{23} +(-323.215 - 44.6545i) q^{24} +(-431.784 + 747.871i) q^{25} +(1591.20 - 206.040i) q^{26} -870.153 q^{27} +(4139.31 + 276.506i) q^{28} +1844.20 q^{29} +(-480.871 + 62.2664i) q^{30} +(-3913.80 + 6778.91i) q^{31} +(-3477.19 - 4632.88i) q^{32} +(687.858 - 397.135i) q^{33} +(-3247.03 + 7792.05i) q^{34} +(6042.95 - 1220.92i) q^{35} +(-5401.79 - 5448.00i) q^{36} +(2017.71 + 3494.78i) q^{37} +(-9539.43 + 7287.64i) q^{38} +(-442.756 - 255.625i) q^{39} +(-6795.80 - 5283.92i) q^{40} -1848.03i q^{41} +(-994.608 - 870.704i) q^{42} +3423.76i q^{43} +(13604.7 + 3707.55i) q^{44} +(-9873.77 - 5700.62i) q^{45} +(-7838.73 - 10260.8i) q^{46} +(7953.96 + 13776.7i) q^{47} +(-15.7219 + 1845.68i) q^{48} +(13395.2 + 10151.1i) q^{49} +(4509.23 + 1879.04i) q^{50} +(2329.42 - 1344.89i) q^{51} +(-2311.77 - 8777.01i) q^{52} +(16053.7 - 27805.8i) q^{53} +(632.099 + 4881.57i) q^{54} +20955.0 q^{55} +(-1455.69 - 23422.5i) q^{56} +3825.12 q^{57} +(-1339.67 - 10346.0i) q^{58} +(-4011.14 + 6947.49i) q^{59} +(698.631 + 2652.46i) q^{60} +(-40441.8 + 23349.1i) q^{61} +(40872.9 + 17032.2i) q^{62} +(-6155.42 - 30466.2i) q^{63} +(-23464.6 + 22872.5i) q^{64} +(-6744.09 - 11681.1i) q^{65} +(-2727.61 - 3570.41i) q^{66} +(-46668.2 - 26943.9i) q^{67} +(46072.3 + 12555.6i) q^{68} +4114.38i q^{69} +(-11239.1 - 33014.2i) q^{70} -16295.5i q^{71} +(-26639.4 + 34261.7i) q^{72} +(-17653.1 - 10192.0i) q^{73} +(18140.1 - 13858.1i) q^{74} +(-778.285 - 1348.03i) q^{75} +(47813.4 + 48222.4i) q^{76} +(37795.4 + 42836.8i) q^{77} +(-1112.43 + 2669.56i) q^{78} +(-38592.2 + 22281.2i) q^{79} +(-24706.2 + 41962.9i) q^{80} +(-28345.5 + 49095.9i) q^{81} +(-10367.5 + 1342.45i) q^{82} -44256.0 q^{83} +(-4162.16 + 6212.27i) q^{84} +70963.9 q^{85} +(19207.4 - 2487.10i) q^{86} +(-1662.07 + 2878.79i) q^{87} +(10916.6 - 79016.0i) q^{88} +(-34589.9 + 19970.5i) q^{89} +(-24808.1 + 59533.1i) q^{90} +(11714.9 - 34855.1i) q^{91} +(-51869.1 + 51429.1i) q^{92} +(-7054.58 - 12218.9i) q^{93} +(71509.4 - 54629.6i) q^{94} +(87396.7 + 50458.5i) q^{95} +(10365.7 - 1252.54i) q^{96} -131224. i q^{97} +(47217.0 - 82521.3i) q^{98} -105647. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 12 q^{4} - 6 q^{5} - 72 q^{8} - 1136 q^{9} - 804 q^{10} + 1632 q^{12} + 1024 q^{14} + 664 q^{16} - 6 q^{17} - 1780 q^{18} - 4586 q^{21} + 13768 q^{22} + 564 q^{24} + 7612 q^{25} - 8892 q^{26} - 5928 q^{28}+ \cdots + 418676 q^{98}+O(q^{100}) $ 36 * q - 12 * q^4 - 6 * q^5 - 72 * q^8 - 1136 * q^9 - 804 * q^10 + 1632 * q^12 + 1024 * q^14 + 664 * q^16 - 6 * q^17 - 1780 * q^18 - 4586 * q^21 + 13768 * q^22 + 564 * q^24 + 7612 * q^25 - 8892 * q^26 - 5928 * q^28 + 176 * q^29 - 5836 * q^30 + 1160 * q^32 - 14154 * q^33 - 27920 * q^36 + 11722 * q^37 - 5652 * q^38 + 35052 * q^40 + 23140 * q^42 + 9096 * q^44 + 19152 * q^45 - 1040 * q^46 + 43900 * q^49 - 51168 * q^50 - 61776 * q^52 - 33486 * q^53 - 30996 * q^54 + 19952 * q^56 - 1668 * q^57 - 48436 * q^58 + 14312 * q^60 + 18846 * q^61 + 44544 * q^64 + 15356 * q^65 + 221808 * q^66 + 25020 * q^68 + 81192 * q^70 + 148064 * q^72 - 236562 * q^73 + 17152 * q^74 - 140010 * q^77 + 127704 * q^78 - 277224 * q^80 + 160402 * q^81 - 391836 * q^82 - 379540 * q^84 + 71212 * q^85 - 252496 * q^86 + 55268 * q^88 - 23706 * q^89 - 190176 * q^92 - 165162 * q^93 + 359988 * q^94 + 1061736 * q^96 + 418676 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.726423	−	5.61002i	−0.128415	−	0.991721i
$2$	−0.726423	−	5.61002i	−0.128415	−	0.991721i
$3$	−0.901244	+	1.56100i	−0.0578148	+	0.100138i	−0.893484	−	0.449095i	$-0.851747\pi$
$3$	−0.901244	+	1.56100i	−0.0578148	+	0.100138i	0.835669	+	0.549233i	$0.185080\pi$
$4$	−30.9446	+	8.15049i	−0.967019	+	0.254703i
$5$	−41.1834	+	23.7773i	−0.736712	+	0.425341i	−0.820872	−	0.571112i	$-0.806512\pi$
$5$	−41.1834	+	23.7773i	−0.736712	+	0.425341i	0.0841609	+	0.996452i	$0.473179\pi$
$6$	9.41192	+	3.92205i	0.106733	+	0.0444769i
$7$	−122.887	−	41.3025i	−0.947893	−	0.318590i
$7$	−122.887	−	41.3025i	−0.947893	−	0.318590i
$8$	68.2033	+	167.679i	0.376773	+	0.926305i
$9$	119.876	+	207.630i	0.493315	+	0.854446i
$10$	163.307	+	213.767i	0.516424	+	0.675992i
$11$	−381.616	−	220.326i	−0.950921	−	0.549015i	−0.0575542	−	0.998342i	$-0.518330\pi$
$11$	−381.616	−	220.326i	−0.950921	−	0.549015i	−0.893367	+	0.449328i	$0.851664\pi$
$12$	15.1657	−	55.6501i	0.0304026	−	0.111561i
$13$			283.636i			0.465482i	0.972539	+	0.232741i	$0.0747695\pi$
$13$			283.636i			0.465482i	−0.972539	+	0.232741i	$0.925230\pi$
$14$	−142.441	+	719.399i	−0.194229	+	0.980956i
$15$		−	85.7165i		−	0.0983640i
$16$	891.139	−	504.428i	0.870253	−	0.492605i
$17$	−1292.34	−	746.132i	−1.08456	−	0.626171i	−0.152438	−	0.988313i	$-0.548712\pi$
$17$	−1292.34	−	746.132i	−1.08456	−	0.626171i	−0.932123	+	0.362142i	$0.882046\pi$
$18$	1077.73	−	823.331i	0.784023	−	0.598954i
$19$	−1061.07	−	1837.82i	−0.674308	−	1.16794i	−0.976671	−	0.214743i	$-0.931109\pi$
$19$	−1061.07	−	1837.82i	−0.674308	−	1.16794i	0.302362	−	0.953193i	$-0.402225\pi$
$20$	1080.61	−	1071.44i	0.604079	−	0.598955i
$21$	175.224	−	154.602i	0.0867053	−	0.0765011i
$22$	−958.818	+	2300.92i	−0.422357	+	1.01355i
$23$	1976.80	−	1141.30i	0.779189	−	0.449865i	−0.0569539	−	0.998377i	$-0.518139\pi$
$23$	1976.80	−	1141.30i	0.779189	−	0.449865i	0.836143	+	0.548512i	$0.184805\pi$
$24$	−323.215	−	44.6545i	−0.114542	−	0.0158248i
$25$	−431.784	+	747.871i	−0.138171	+	0.239319i
$26$	1591.20	−	206.040i	0.461628	−	0.0597747i
$27$	−870.153			−0.229713
$28$	4139.31	+	276.506i	0.997776	+	0.0666515i
$29$	1844.20			0.407204			0.203602	−	0.979054i	$-0.434735\pi$
$29$	1844.20			0.407204			0.203602	+	0.979054i	$0.434735\pi$
$30$	−480.871	+	62.2664i	−0.0975496	+	0.0126314i
$31$	−3913.80	+	6778.91i	−0.731467	+	1.26694i	0.224789	+	0.974407i	$0.427831\pi$
$31$	−3913.80	+	6778.91i	−0.731467	+	1.26694i	−0.956256	+	0.292531i	$0.905503\pi$
$32$	−3477.19	−	4632.88i	−0.600280	−	0.799790i
$33$	687.858	−	397.135i	0.109955	−	0.0634824i
$34$	−3247.03	+	7792.05i	−0.481714	+	1.15599i
$35$	6042.95	−	1220.92i	0.833833	−	0.168469i
$36$	−5401.79	−	5448.00i	−0.694675	−	0.700618i
$37$	2017.71	+	3494.78i	0.242301	+	0.419677i	0.961369	−	0.275262i	$-0.0887646\pi$
$37$	2017.71	+	3494.78i	0.242301	+	0.419677i	−0.719069	+	0.694939i	$0.755431\pi$
$38$	−9539.43	+	7287.64i	−1.07168	+	0.818705i
$39$	−442.756	−	255.625i	−0.0466126	−	0.0269118i
$40$	−6795.80	−	5283.92i	−0.671569	−	0.522163i
$41$		−	1848.03i		−	0.171692i	−0.996308	−	0.0858459i	$-0.972641\pi$
$41$		−	1848.03i		−	0.171692i	0.996308	−	0.0858459i	$-0.0273593\pi$
$42$	−994.608	−	870.704i	−0.0870019	−	0.0761635i
$43$			3423.76i			0.282379i	0.989983	+	0.141190i	$0.0450927\pi$
$43$			3423.76i			0.282379i	−0.989983	+	0.141190i	$0.954907\pi$
$44$	13604.7	+	3707.55i	1.05939	+	0.288705i
$45$	−9873.77	−	5700.62i	−0.726862	−	0.419654i
$46$	−7838.73	−	10260.8i	−0.546199	−	0.714968i
$47$	7953.96	+	13776.7i	0.525217	+	0.909703i	0.999569	+	0.0293672i	$0.00934921\pi$
$47$	7953.96	+	13776.7i	0.525217	+	0.909703i	−0.474352	+	0.880335i	$0.657317\pi$
$48$	−15.7219	+	1845.68i	−0.000984924	+	0.115625i
$49$	13395.2	+	10151.1i	0.797001	+	0.603978i
$50$	4509.23	+	1879.04i	0.255080	+	0.106295i
$51$	2329.42	−	1344.89i	0.125407	−	0.0724040i
$52$	−2311.77	−	8777.01i	−0.118560	−	0.450130i
$53$	16053.7	−	27805.8i	0.785027	−	1.35971i	−0.143957	−	0.989584i	$-0.545983\pi$
$53$	16053.7	−	27805.8i	0.785027	−	1.35971i	0.928983	−	0.370122i	$-0.120684\pi$
$54$	632.099	+	4881.57i	0.0294985	+	0.227811i
$55$	20955.0			0.934073
$56$	−1455.69	−	23422.5i	−0.0620294	−	0.998074i
$57$	3825.12			0.155940
$58$	−1339.67	−	10346.0i	−0.0522910	−	0.403833i
$59$	−4011.14	+	6947.49i	−0.150016	+	0.259835i	−0.931233	−	0.364424i	$-0.881266\pi$
$59$	−4011.14	+	6947.49i	−0.150016	+	0.259835i	0.781217	+	0.624259i	$0.214599\pi$
$60$	698.631	+	2652.46i	0.0250536	+	0.0951199i
$61$	−40441.8	+	23349.1i	−1.39157	+	0.803424i	−0.993489	−	0.113926i	$-0.963657\pi$
$61$	−40441.8	+	23349.1i	−1.39157	+	0.803424i	−0.398082	+	0.917350i	$0.630324\pi$
$62$	40872.9	+	17032.2i	1.35038	+	0.562718i
$63$	−6155.42	−	30466.2i	−0.195392	−	0.967089i
$64$	−23464.6	+	22872.5i	−0.716084	+	0.698015i
$65$	−6744.09	−	11681.1i	−0.197989	−	0.342926i
$66$	−2727.61	−	3570.41i	−0.0770765	−	0.100892i
$67$	−46668.2	−	26943.9i	−1.27009	−	0.733286i	−0.295084	−	0.955471i	$-0.595347\pi$
$67$	−46668.2	−	26943.9i	−1.27009	−	0.733286i	−0.975004	+	0.222186i	$0.928681\pi$
$68$	46072.3	+	12555.6i	1.20828	+	0.329279i
$69$			4114.38i			0.104035i
$70$	−11239.1	−	33014.2i	−0.274150	−	0.805295i
$71$		−	16295.5i		−	0.383639i	−0.981430	−	0.191820i	$-0.938561\pi$
$71$		−	16295.5i		−	0.383639i	0.981430	−	0.191820i	$-0.0614389\pi$
$72$	−26639.4	+	34261.7i	−0.605610	+	0.778893i
$73$	−17653.1	−	10192.0i	−0.387716	−	0.223848i	0.293454	−	0.955973i	$-0.405195\pi$
$73$	−17653.1	−	10192.0i	−0.387716	−	0.223848i	−0.681170	+	0.732125i	$0.738528\pi$
$74$	18140.1	−	13858.1i	0.385088	−	0.294187i
$75$	−778.285	−	1348.03i	−0.0159766	−	0.0276723i
$76$	47813.4	+	48222.4i	0.949546	+	0.957669i
$77$	37795.4	+	42836.8i	0.726461	+	0.823361i
$78$	−1112.43	+	2669.56i	−0.0207032	+	0.0496825i
$79$	−38592.2	+	22281.2i	−0.695716	+	0.401672i	−0.805750	−	0.592256i	$-0.798237\pi$
$79$	−38592.2	+	22281.2i	−0.695716	+	0.401672i	0.110034	+	0.993928i	$0.464904\pi$
$80$	−24706.2	+	41962.9i	−0.431600	+	0.733062i
$81$	−28345.5	+	49095.9i	−0.480034	+	0.831443i
$82$	−10367.5	+	1342.45i	−0.170270	+	0.0220477i
$83$	−44256.0			−0.705143			−0.352571	−	0.935785i	$-0.614693\pi$
$83$	−44256.0			−0.705143			−0.352571	+	0.935785i	$0.614693\pi$
$84$	−4162.16	+	6212.27i	−0.0643606	+	0.0960621i
$85$	70963.9			1.06534
$86$	19207.4	−	2487.10i	0.280041	−	0.0362616i
$87$	−1662.07	+	2878.79i	−0.0235425	+	0.0407767i
$88$	10916.6	−	79016.0i	0.150273	−	1.08770i
$89$	−34589.9	+	19970.5i	−0.462886	+	0.267248i	−0.713257	−	0.700903i	$-0.752781\pi$
$89$	−34589.9	+	19970.5i	−0.462886	+	0.267248i	0.250371	+	0.968150i	$0.419447\pi$
$90$	−24808.1	+	59533.1i	−0.322840	+	0.774733i
$91$	11714.9	−	34855.1i	0.148298	−	0.441227i
$92$	−51869.1	+	51429.1i	−0.638909	+	0.633490i
$93$	−7054.58	−	12218.9i	−0.0845793	−	0.146496i
$94$	71509.4	−	54629.6i	0.834725	−	0.637688i
$95$	87396.7	+	50458.5i	0.993541	+	0.573621i
$96$	10365.7	−	1252.54i	0.114795	−	0.0138712i
$97$		−	131224.i		−	1.41607i	−0.706178	−	0.708034i	$-0.749582\pi$
$97$		−	131224.i		−	1.41607i	0.706178	−	0.708034i	$-0.250418\pi$
$98$	47217.0	−	82521.3i	0.496631	−	0.867962i
$99$		−	105647.i		−	1.08335i
$100$	7265.86	−	26661.8i	0.0726586	−	0.266618i
$101$	−85355.1	−	49279.8i	−0.832580	−	0.480690i	0.0221553	−	0.999755i	$-0.492947\pi$
$101$	−85355.1	−	49279.8i	−0.832580	−	0.480690i	−0.854735	+	0.519064i	$0.826280\pi$
$102$	−9237.03	−	12091.2i	−0.0879087	−	0.115071i
$103$	96747.8	+	167572.i	0.898562	+	1.55636i	0.829333	+	0.558755i	$0.188721\pi$
$103$	96747.8	+	167572.i	0.898562	+	1.55636i	0.0692294	+	0.997601i	$0.477946\pi$
$104$	−47559.9	+	19344.9i	−0.431179	+	0.175381i
$105$	−3540.31	+	10533.4i	−0.0313377	+	0.0932385i
$106$	−167653.	−	69862.6i	−1.44926	−	0.603921i
$107$	71008.9	−	40997.0i	0.599588	−	0.346173i	−0.169291	−	0.985566i	$-0.554148\pi$
$107$	71008.9	−	40997.0i	0.599588	−	0.346173i	0.768880	+	0.639394i	$0.220815\pi$
$108$	26926.6	−	7092.17i	0.222137	−	0.0585086i
$109$	3655.31	−	6331.19i	0.0294685	−	0.0510410i	−0.850915	−	0.525303i	$-0.823952\pi$
$109$	3655.31	−	6331.19i	0.0294685	−	0.0510410i	0.880384	+	0.474262i	$0.157285\pi$
$110$	−15222.2	−	117558.i	−0.119949	−	0.926339i
$111$	−7273.80			−0.0560343
$112$	−130343.	+	25181.1i	−0.981845	+	0.189683i
$113$	242851.			1.78913			0.894567	−	0.446933i	$-0.147484\pi$
$113$	242851.			1.78913			0.894567	+	0.446933i	$0.147484\pi$
$114$	−2778.65	−	21459.0i	−0.0200250	−	0.154649i
$115$	−54274.2	+	94005.7i	−0.382692	+	0.662841i
$116$	−57068.0	+	15031.1i	−0.393775	+	0.103716i
$117$	−58891.5	+	34001.0i	−0.397730	+	0.229629i
$118$	41889.4	+	17455.7i	0.276948	+	0.115407i
$119$	127994.	+	145066.i	0.828556	+	0.939073i
$120$	14372.9	−	5846.14i	0.0911151	−	0.0370609i
$121$	16561.5	+	28685.4i	0.102834	+	0.178114i
$122$	160366.	+	209918.i	0.975470	+	1.27688i
$123$	2884.78	+	1665.53i	0.0171929	+	0.00992633i
$124$	65859.8	−	241670.i	0.384650	−	1.41146i
$125$		−	189674.i		−	1.08576i
$126$	−166444.	+	56663.3i	−0.933991	+	0.317962i
$127$			139283.i			0.766280i	0.923690	+	0.383140i	$0.125157\pi$
$127$			139283.i			0.766280i	−0.923690	+	0.383140i	$0.874843\pi$
$128$	145361.	+	115022.i	0.784191	+	0.620520i
$129$	−5344.50	−	3085.65i	−0.0282769	−	0.0163257i
$130$	−60632.2	+	46319.9i	−0.314662	+	0.240386i
$131$	−187138.	−	324133.i	−0.952761	−	1.65023i	−0.739411	−	0.673254i	$-0.764896\pi$
$131$	−187138.	−	324133.i	−0.952761	−	1.65023i	−0.213350	−	0.976976i	$-0.568437\pi$
$132$	−18048.6	+	17895.6i	−0.0901592	+	0.0893944i
$133$	54484.1	+	269668.i	0.267079	+	1.32191i
$134$	−117255.	+	281382.i	−0.564117	+	1.35374i
$135$	35835.9	−	20689.9i	0.169232	−	0.0977064i
$136$	36969.1	−	267587.i	0.171392	−	1.24056i
$137$	−137419.	+	238017.i	−0.625526	+	1.08344i	0.362913	+	0.931823i	$0.381782\pi$
$137$	−137419.	+	238017.i	−0.625526	+	1.08344i	−0.988439	+	0.151619i	$0.951551\pi$
$138$	23081.7	−	2988.78i	0.103174	−	0.0133597i
$139$	−323870.			−1.42178			−0.710892	−	0.703301i	$-0.751709\pi$
$139$	−323870.			−1.42178			−0.710892	+	0.703301i	$0.751709\pi$
$140$	−177046.	+	87034.1i	−0.763423	+	0.375292i
$141$	−28673.8			−0.121461
$142$	−91418.3	+	11837.5i	−0.380463	+	0.0492649i
$143$	62492.4	−	108240.i	0.255557	−	0.442637i
$144$	211560.	+	124559.i	0.850213	+	0.500575i
$145$	−75950.4	+	43850.0i	−0.299992	+	0.173201i
$146$	−44353.8	+	106438.i	−0.172206	+	0.413251i
$147$	−27918.1	+	11761.3i	−0.106560	+	0.0448914i
$148$	−90921.5	−	91699.3i	−0.341202	−	0.344121i
$149$	−109237.	−	189204.i	−0.403092	−	0.698176i	0.591005	−	0.806668i	$-0.298731\pi$
$149$	−109237.	−	189204.i	−0.403092	−	0.698176i	−0.994097	+	0.108492i	$0.965398\pi$
$150$	−6997.10	+	5345.43i	−0.0253916	+	0.0193979i
$151$	139702.	+	80656.8i	0.498608	+	0.287872i	0.728139	−	0.685430i	$-0.240386\pi$
$151$	139702.	+	80656.8i	0.498608	+	0.287872i	−0.229530	+	0.973301i	$0.573719\pi$
$152$	235796.	−	303264.i	0.827804	−	1.06466i
$153$		−	357772.i		−	1.23560i
$154$	212860.	−	243151.i	0.723255	−	0.826178i
$155$		−	372238.i		−	1.24449i
$156$	15784.4	+	4301.55i	0.0519298	+	0.0141519i
$157$	276346.	+	159549.i	0.894756	+	0.516588i	0.875495	−	0.483227i	$-0.160535\pi$
$157$	276346.	+	159549.i	0.894756	+	0.516588i	0.0192611	+	0.999814i	$0.493869\pi$
$158$	153032.	+	200317.i	0.487686	+	0.638375i
$159$	28936.5	+	50119.5i	0.0907723	+	0.157222i
$160$	253360.	+	108120.i	0.782416	+	0.333891i
$161$	−290061.	+	58604.2i	−0.881910	+	0.178182i
$162$	296020.	+	123355.i	0.886203	+	0.369290i
$163$	−311015.	+	179564.i	−0.916879	+	0.529360i	−0.882638	−	0.470053i	$-0.844235\pi$
$163$	−311015.	+	179564.i	−0.916879	+	0.529360i	−0.0342408	+	0.999414i	$0.510901\pi$
$164$	15062.4	+	57186.6i	0.0437304	+	0.166029i
$165$	−18885.6	+	32710.7i	−0.0540033	+	0.0935364i
$166$	32148.6	+	248277.i	0.0905506	+	0.699305i
$167$	−99313.1			−0.275560			−0.137780	−	0.990463i	$-0.543997\pi$
$167$	−99313.1			−0.275560			−0.137780	+	0.990463i	$0.543997\pi$
$168$	37874.4	+	18837.0i	0.103532	+	0.0514920i
$169$	290844.			0.783326
$170$	−51549.8	−	398109.i	−0.136806	−	1.05652i
$171$	254392.	−	440619.i	0.665293	−	1.15232i
$172$	−27905.4	−	105947.i	−0.0719228	−	0.273066i
$173$	−173465.	+	100150.i	−0.440653	+	0.254411i	−0.703875	−	0.710324i	$-0.748548\pi$
$173$	−173465.	+	100150.i	−0.440653	+	0.254411i	0.263221	+	0.964735i	$0.415215\pi$
$174$	17357.4	+	7233.03i	0.0434623	+	0.0181112i
$175$	83949.4	−	74069.5i	0.207216	−	0.182829i
$176$	−451211.	−	3843.52i	−1.09799	−	0.00935293i
$177$	−7230.03	−	12522.8i	−0.0173463	−	0.0300447i
$178$	137162.	+	179543.i	0.324476	+	0.424735i
$179$	−42591.0	−	24589.9i	−0.0993539	−	0.0573620i	0.449500	−	0.893280i	$-0.351602\pi$
$179$	−42591.0	−	24589.9i	−0.0993539	−	0.0573620i	−0.548854	+	0.835918i	$0.684936\pi$
$180$	352003.	+	95927.6i	0.809776	+	0.220680i
$181$		−	211447.i		−	0.479739i	−0.970805	−	0.239869i	$-0.922895\pi$
$181$		−	211447.i		−	0.479739i	0.970805	−	0.239869i	$-0.0771046\pi$
$182$	−204048.	−	40401.3i	−0.456618	−	0.0904100i
$183$		−	84172.8i		−	0.185799i
$184$	326197.	+	253627.i	0.710290	+	0.552270i
$185$	−166193.	−	95951.3i	−0.357012	−	0.206121i
$186$	−63423.6	+	48452.4i	−0.134422	+	0.102691i
$187$	328784.	+	569471.i	0.687555	+	1.19088i
$188$	−358419.	−	361485.i	−0.739599	−	0.745926i
$189$	106930.	+	35939.5i	0.217744	+	0.0731843i
$190$	219586.	−	526951.i	0.441287	−	1.05898i
$191$	4118.25	−	2377.67i	0.00816826	−	0.00471595i	−0.495910	−	0.868374i	$-0.665166\pi$
$191$	4118.25	−	2377.67i	0.00816826	−	0.00471595i	0.504079	+	0.863658i	$0.331832\pi$
$192$	−14556.7	−	57242.0i	−0.0284977	−	0.112063i
$193$	−15469.4	+	26793.7i	−0.0298937	+	0.0517773i	−0.880585	−	0.473888i	$-0.842850\pi$
$193$	−15469.4	+	26793.7i	−0.0298937	+	0.0517773i	0.850692	+	0.525665i	$0.176184\pi$
$194$	−736169.	+	95324.1i	−1.40434	+	0.181844i
$195$	24312.3			0.0457867
$196$	−497245.	−	204943.i	−0.924550	−	0.381060i
$197$	55534.5			0.101952			0.0509762	−	0.998700i	$-0.483767\pi$
$197$	55534.5			0.101952			0.0509762	+	0.998700i	$0.483767\pi$
$198$	−592680.	+	76744.2i	−1.07438	+	0.139118i
$199$	−344470.	+	596640.i	−0.616622	+	1.06802i	0.373475	+	0.927640i	$0.378166\pi$
$199$	−344470.	+	596640.i	−0.616622	+	1.06802i	−0.990098	+	0.140381i	$0.955167\pi$
$200$	−154851.	−	21393.9i	−0.273741	−	0.0378194i
$201$	84118.8	−	48566.0i	0.146860	−	0.0847896i
$202$	−214457.	+	514641.i	−0.369795	+	0.887414i
$203$	−226627.	−	76170.1i	−0.385986	−	0.129731i
$204$	−61121.6	+	60603.2i	−0.102830	+	0.101958i
$205$	43941.1	+	76108.3i	0.0730275	+	0.126487i
$206$	869803.	−	664485.i	1.42808	−	1.09098i
$207$	473939.	+	273629.i	0.768771	+	0.443850i
$208$	143074.	+	252759.i	0.229299	+	0.405087i
$209$			935121.i			1.48082i
$210$	61664.3	+	12209.5i	0.0964908	+	0.0191051i
$211$			403122.i			0.623348i	0.950189	+	0.311674i	$0.100890\pi$
$211$			403122.i			0.623348i	−0.950189	+	0.311674i	$0.899110\pi$
$212$	−270144.	+	991284.i	−0.412815	+	1.51481i
$213$	25437.4	+	14686.3i	0.0384170	+	0.0221800i
$214$	−281576.	−	368580.i	−0.420302	−	0.550171i
$215$	−81407.7	−	141002.i	−0.120107	−	0.208032i
$216$	−59347.3	−	145907.i	−0.0865499	−	0.212785i
$217$	760940.	−	671386.i	1.09699	−	0.967884i
$218$	−38173.4	−	15907.3i	−0.0544026	−	0.0226701i
$219$	31819.5	−	18371.0i	0.0448314	−	0.0258834i
$220$	−648444.	+	170793.i	−0.903266	+	0.237911i
$221$	211630.	−	366554.i	0.291472	−	0.504844i
$222$	5283.85	+	40806.2i	0.00719562	+	0.0555704i
$223$	905280.			1.21905			0.609524	−	0.792767i	$-0.291360\pi$
$223$	905280.			1.21905			0.609524	+	0.792767i	$0.291360\pi$
$224$	235950.	+	712935.i	0.314196	+	0.949358i
$225$	−207041.			−0.272647
$226$	−176412.	−	1.36240e6i	−0.229751	−	1.77432i
$227$	68078.4	−	117915.i	0.0876889	−	0.151882i	−0.818845	−	0.574015i	$-0.805385\pi$
$227$	68078.4	−	117915.i	0.0876889	−	0.151882i	0.906534	+	0.422133i	$0.138719\pi$
$228$	−118367.	+	31176.6i	−0.150797	+	0.0397184i
$229$	92298.3	−	53288.5i	0.116307	−	0.0671498i	−0.440718	−	0.897646i	$-0.645276\pi$
$229$	92298.3	−	53288.5i	0.116307	−	0.0671498i	0.557025	+	0.830496i	$0.311943\pi$
$230$	566800.	+	236191.i	0.706497	+	0.294405i
$231$	−100931.	+	20392.2i	−0.124450	+	0.0251440i
$232$	125780.	+	309234.i	0.153424	+	0.377196i
$233$	68720.9	+	119028.i	0.0829276	+	0.143635i	0.904506	−	0.426460i	$-0.140240\pi$
$233$	68720.9	+	119028.i	0.0829276	+	0.143635i	−0.821579	+	0.570095i	$0.806906\pi$
$234$	233527.	+	305683.i	0.278802	+	0.364949i
$235$	−655143.	−	378247.i	−0.773867	−	0.446792i
$236$	67497.6	−	247680.i	0.0788876	−	0.289475i
$237$		−	80323.2i		−	0.0928903i
$238$	720848.	−	823427.i	0.824900	−	0.942286i
$239$			438994.i			0.497122i	0.968616	+	0.248561i	$0.0799577\pi$
$239$			438994.i			0.497122i	−0.968616	+	0.248561i	$0.920042\pi$
$240$	−43237.7	−	76385.3i	−0.0484546	−	0.0856015i
$241$	−900121.	−	519685.i	−0.998294	−	0.576365i	−0.0905510	−	0.995892i	$-0.528863\pi$
$241$	−900121.	−	519685.i	−0.998294	−	0.576365i	−0.907743	+	0.419526i	$0.862196\pi$
$242$	148895.	−	113748.i	0.163434	−	0.124855i
$243$	−156816.	−	271613.i	−0.170363	−	0.295077i
$244$	1.06115e6	−	1.05215e6i	1.14104	−	1.13136i
$245$	−793024.	−	99554.0i	−0.844056	−	0.105960i
$246$	7248.07	−	17393.5i	0.00763633	−	0.0183253i
$247$	521272.	−	300957.i	0.543654	−	0.313879i
$248$	−1.40362e6	−	193920.i	−1.44917	−	0.200213i
$249$	39885.5	−	69083.6i	0.0407677	−	0.0706117i
$250$	−1.06408e6	+	137784.i	−1.07677	+	0.139427i
$251$	856358.			0.857968			0.428984	−	0.903312i	$-0.358872\pi$
$251$	856358.			0.857968			0.428984	+	0.903312i	$0.358872\pi$
$252$	438791.	+	892594.i	0.435268	+	0.885427i
$253$	−1.00584e6			−0.987929
$254$	781377.	−	101178.i	0.759935	−	0.0984015i
$255$	−63955.8	+	110775.i	−0.0615927	+	0.106682i
$256$	539681.	−	899030.i	0.514680	−	0.857382i
$257$	984787.	−	568567.i	0.930057	−	0.536968i	0.0432271	−	0.999065i	$-0.486236\pi$
$257$	984787.	−	568567.i	0.930057	−	0.536968i	0.886829	+	0.462097i	$0.152903\pi$
$258$	−13428.2	+	32224.2i	−0.0125594	+	0.0301393i
$259$	−103606.	−	512798.i	−0.0959703	−	0.475003i
$260$	303900.	+	306500.i	0.278803	+	0.281188i
$261$	221074.	+	382912.i	0.200880	+	0.347934i
$262$	−1.68245e6	+	1.28531e6i	−1.51422	+	1.15679i
$263$	−1.46849e6	−	847831.i	−1.30912	−	0.755823i	−0.327174	−	0.944964i	$-0.606096\pi$
$263$	−1.46849e6	−	847831.i	−1.30912	−	0.755823i	−0.981950	+	0.189141i	$0.939430\pi$
$264$	113505.	+	88253.5i	0.100232	+	0.0779331i
$265$			1.52685e6i			1.33561i
$266$	1.47326e6	−	501550.i	1.27666	−	0.434620i
$267$		−	71993.1i		−	0.0618035i
$268$	1.66373e6	+	453400.i	1.41497	+	0.385606i
$269$	967035.	+	558318.i	0.814819	+	0.470436i	0.848627	−	0.528992i	$-0.177430\pi$
$269$	967035.	+	558318.i	0.814819	+	0.470436i	−0.0338073	+	0.999428i	$0.510763\pi$
$270$	−142102.	−	186010.i	−0.118629	−	0.155284i
$271$	−613527.	−	1.06266e6i	−0.507470	−	0.878964i	−0.999963	−	0.00864748i	$-0.997247\pi$
$271$	−613527.	−	1.06266e6i	−0.507470	−	0.878964i	0.492492	−	0.870317i	$-0.336086\pi$
$272$	−1.52802e6	−	13016.0i	−1.25230	−	0.0106674i
$273$	43850.8	+	49699.9i	0.0356099	+	0.0403598i
$274$	1.43510e6	+	598022.i	1.15480	+	0.481217i
$275$	329551.	−	190266.i	0.262779	−	0.151715i
$276$	−33534.2	−	127318.i	−0.0264981	−	0.100604i
$277$	421252.	−	729630.i	0.329870	−	0.571352i	−0.652616	−	0.757689i	$-0.726328\pi$
$277$	421252.	−	729630.i	0.329870	−	0.571352i	0.982486	+	0.186337i	$0.0596618\pi$
$278$	235267.	+	1.81692e6i	0.182578	+	1.41001i
$279$	−1.87668e6			−1.44337
$280$	616873.	+	930006.i	0.470219	+	0.708909i
$281$	−2.05076e6			−1.54935			−0.774675	−	0.632359i	$-0.782087\pi$
$281$	−2.05076e6			−1.54935			−0.774675	+	0.632359i	$0.782087\pi$
$282$	20829.3	+	160861.i	0.0155974	+	0.120456i
$283$	−643072.	+	1.11383e6i	−0.477302	+	0.826711i	−0.999662	−	0.0260140i	$-0.991719\pi$
$283$	−643072.	+	1.11383e6i	−0.477302	+	0.826711i	0.522360	+	0.852725i	$0.325052\pi$
$284$	132817.	+	504260.i	0.0977140	+	0.370987i
$285$	−157531.	+	90950.8i	−0.114883	+	0.0663276i
$286$	−652624.	−	271956.i	−0.471789	−	0.196600i
$287$	−76328.4	+	227098.i	−0.0546993	+	0.162745i
$288$	545097.	−	1.27734e6i	0.387251	−	0.907455i
$289$	403497.	+	698877.i	0.284181	+	0.492217i
$290$	301171.	+	394229.i	0.210290	+	0.275267i
$291$	204841.	+	118265.i	0.141802	+	0.0818697i
$292$	629338.	+	171507.i	0.431943	+	0.117713i
$293$			1.56244e6i			1.06325i	0.846981	+	0.531623i	$0.178418\pi$
$293$			1.56244e6i			1.06325i	−0.846981	+	0.531623i	$0.821582\pi$
$294$	86261.7	+	148078.i	0.0582036	+	0.0999128i
$295$		−	381495.i		−	0.255232i
$296$	−448387.	+	576684.i	−0.297457	+	0.382568i
$297$	332064.	+	191717.i	0.218439	+	0.126116i
$298$	−982087.	+	750264.i	−0.640633	+	0.489411i
$299$	323715.	+	560691.i	0.209404	+	0.362699i
$300$	35070.8	+	35370.8i	0.0224979	+	0.0226904i
$301$	141410.	−	420734.i	0.0899631	−	0.267665i
$302$	351004.	−	842320.i	0.221460	−	0.531447i
$303$	153851.	−	88826.2i	0.0962709	−	0.0555820i
$304$	−1.87260e6	−	1.10252e6i	−1.16215	−	0.684232i
$305$	1.11035e6	−	1.92319e6i	0.683458	−	1.18378i
$306$	−2.00711e6	+	259894.i	−1.22537	+	0.158669i
$307$	1.33011e6			0.805456			0.402728	−	0.915320i	$-0.368062\pi$
$307$	1.33011e6			0.805456			0.402728	+	0.915320i	$0.368062\pi$
$308$	−1.51871e6	−	1.01752e6i	−0.912214	−	0.611174i
$309$	−348774.			−0.207801
$310$	−2.08826e6	+	270402.i	−1.23419	+	0.159811i
$311$	585357.	−	1.01387e6i	0.343178	−	0.594402i	−0.641843	−	0.766836i	$-0.721830\pi$
$311$	585357.	−	1.01387e6i	0.343178	−	0.594402i	0.985021	+	0.172434i	$0.0551632\pi$
$312$	12665.6	−	91675.5i	0.00736615	−	0.0533171i
$313$	−2351.61	+	1357.70i	−0.00135676	+	0.000783329i	−0.500678	−	0.865633i	$-0.666916\pi$
$313$	−2351.61	+	1357.70i	−0.00135676	+	0.000783329i	0.499321	+	0.866417i	$0.333583\pi$
$314$	694327.	−	1.66621e6i	0.397411	−	0.953686i
$315$	977903.	+	1.10834e6i	0.555289	+	0.629357i
$316$	1.01262e6	−	1.00403e6i	0.570464	−	0.565625i
$317$	−349397.	−	605174.i	−0.195286	−	0.338246i	0.751708	−	0.659496i	$-0.229230\pi$
$317$	−349397.	−	605174.i	−0.195286	−	0.338246i	−0.946994	+	0.321250i	$0.895897\pi$
$318$	260151.	−	198742.i	0.144264	−	0.110210i
$319$	−703775.	−	406325.i	−0.387219	−	0.223561i
$320$	422507.	−	1.49989e6i	0.230653	−	0.818815i
$321$			147793.i			0.0800556i
$322$	539477.	+	1.58467e6i	0.289957	+	0.851727i
$323$			3.16678e6i			1.68893i
$324$	476986.	−	1.75028e6i	0.252431	−	0.926288i
$325$	−212123.	−	122469.i	−0.111399	−	0.0643160i
$326$	1.23329e6	+	1.61436e6i	0.642718	+	0.841310i
$327$	6588.66	+	11411.9i	0.00340743	+	0.00590185i
$328$	309876.	−	126042.i	0.159039	−	0.0646889i
$329$	−408423.	−	2.02149e6i	−0.208028	−	1.02963i
$330$	197227.	+	82186.5i	0.0996968	+	0.0415447i
$331$	1.19220e6	−	688314.i	0.598105	−	0.345316i	−0.170191	−	0.985411i	$-0.554438\pi$
$331$	1.19220e6	−	688314.i	0.598105	−	0.345316i	0.768296	+	0.640095i	$0.221105\pi$
$332$	1.36949e6	−	360708.i	0.681887	−	0.179602i
$333$	−483748.	+	837877.i	−0.239061	+	0.414066i
$334$	72143.3	+	557148.i	0.0353859	+	0.273278i
$335$	2.56261e6			1.24758
$336$	78163.3	−	226160.i	0.0377707	−	0.109287i
$337$	−776941.			−0.372660			−0.186330	−	0.982487i	$-0.559659\pi$
$337$	−776941.			−0.372660			−0.186330	+	0.982487i	$0.559659\pi$
$338$	−211275.	−	1.63164e6i	−0.100591	−	0.776841i
$339$	−218868.	+	379090.i	−0.103438	+	0.179161i
$340$	−2.19595e6	+	578391.i	−1.03021	+	0.271346i
$341$	2.98714e6	−	1.72462e6i	1.39114	−	0.803172i
$342$	−2.65668e6	−	1.10707e6i	−1.22821	−	0.511810i
$343$	−1.22683e6	−	1.80068e6i	−0.563051	−	0.826422i
$344$	−574094.	+	233512.i	−0.261569	+	0.106393i
$345$	−97828.6	−	169444.i	−0.0442505	−	0.0766441i
$346$	687853.	+	900391.i	0.308891	+	0.404335i
$347$	3.76078e6	+	2.17129e6i	1.67670	+	0.968041i	0.963744	+	0.266830i	$0.0859761\pi$
$347$	3.76078e6	+	2.17129e6i	1.67670	+	0.968041i	0.712953	+	0.701212i	$0.247357\pi$
$348$	27968.6	−	102630.i	0.0123801	−	0.0454282i
$349$		−	123357.i		−	0.0542127i	−0.999633	−	0.0271063i	$-0.991371\pi$
$349$		−	123357.i		−	0.0542127i	0.999633	−	0.0271063i	$-0.00862927\pi$
$350$	−476514.	−	417152.i	−0.207924	−	0.182022i
$351$		−	246807.i		−	0.106927i
$352$	306208.	+	2.53409e6i	0.131722	+	1.09010i
$353$	1.87716e6	+	1.08378e6i	0.801798	+	0.462918i	0.844099	−	0.536187i	$-0.180136\pi$
$353$	1.87716e6	+	1.08378e6i	0.801798	+	0.462918i	−0.0423015	+	0.999105i	$0.513469\pi$
$354$	−65000.9	+	49657.4i	−0.0275684	+	0.0210609i
$355$	387464.	+	671107.i	0.163177	+	0.282632i
$356$	907602.	−	899904.i	0.379551	−	0.376332i
$357$	−341802.	+	69058.2i	−0.141940	+	0.0286777i
$358$	−107011.	+	256799.i	−0.0441286	+	0.105897i
$359$	−4.04371e6	+	2.33464e6i	−1.65594	+	0.956056i	−0.681376	+	0.731934i	$0.738618\pi$
$359$	−4.04371e6	+	2.33464e6i	−1.65594	+	0.956056i	−0.974561	+	0.224122i	$0.928049\pi$
$360$	282453.	−	2.04443e6i	0.114865	−	0.831410i
$361$	−1.01367e6	+	1.75573e6i	−0.409383	+	0.709073i
$362$	−1.18622e6	+	153600.i	−0.475767	+	0.0616054i
$363$	−59703.8			−0.0237813
$364$	−78427.2	+	1.17406e6i	−0.0310251	+	0.464447i
$365$	969352.			0.380846
$366$	−472211.	+	61145.0i	−0.184261	+	0.0238593i
$367$	1.96329e6	−	3.40051e6i	0.760884	−	1.31789i	−0.181512	−	0.983389i	$-0.558099\pi$
$367$	1.96329e6	−	3.40051e6i	0.760884	−	1.31789i	0.942396	−	0.334500i	$-0.108568\pi$
$368$	1.18590e6	−	2.01421e6i	0.456486	−	0.775329i
$369$	383708.	−	221534.i	0.146701	−	0.0846981i
$370$	−417563.	+	1.00204e6i	−0.158569	+	0.380525i
$371$	−3.12123e6	+	2.75390e6i	−1.17731	+	1.03875i
$372$	317891.	+	320611.i	0.119103	+	0.120122i
$373$	−597831.	−	1.03547e6i	−0.222488	−	0.385360i	0.733075	−	0.680148i	$-0.238084\pi$
$373$	−597831.	−	1.03547e6i	−0.222488	−	0.385360i	−0.955563	+	0.294788i	$0.904751\pi$
$374$	2.95591e6	−	2.25816e6i	1.09273	−	0.834788i
$375$	296082.	+	170943.i	0.108726	+	0.0627730i
$376$	−1.76757e6	+	2.27333e6i	−0.644775	+	0.829263i
$377$			523081.i			0.189546i
$378$	123945.	−	625987.i	0.0446169	−	0.225339i
$379$		−	2.70264e6i		−	0.966473i	−0.875490	−	0.483237i	$-0.839461\pi$
$379$		−	2.70264e6i		−	0.966473i	0.875490	−	0.483237i	$-0.160539\pi$
$380$	−3.11572e6	−	849093.i	−1.10688	−	0.301645i
$381$	−217420.	−	125528.i	−0.0767339	−	0.0443023i
$382$	−16330.4	−	21376.3i	−0.00572582	−	0.00749503i
$383$	−1.01479e6	−	1.75767e6i	−0.353493	−	0.612268i	0.633366	−	0.773852i	$-0.281673\pi$
$383$	−1.01479e6	−	1.75767e6i	−0.353493	−	0.612268i	−0.986859	+	0.161585i	$0.948339\pi$
$384$	−310555.	+	123245.i	−0.107476	+	0.0426523i
$385$	−2.57509e6	−	865494.i	−0.885401	−	0.297586i
$386$	161551.	+	67319.8i	0.0551874	+	0.0229972i
$387$	−710878.	+	410426.i	−0.241278	+	0.139302i
$388$	1.06954e6	+	4.06068e6i	0.360676	+	1.36936i
$389$	−1.94370e6	+	3.36658e6i	−0.651261	+	1.12802i	0.331557	+	0.943435i	$0.392426\pi$
$389$	−1.94370e6	+	3.36658e6i	−0.651261	+	1.12802i	−0.982817	+	0.184581i	$0.940907\pi$
$390$	−17661.0	−	136392.i	−0.00587968	−	0.0454076i
$391$	−3.40626e6			−1.12677
$392$	−788524.	+	2.93843e6i	−0.259179	+	0.965829i
$393$	674628.			0.220335
$394$	−40341.5	−	311550.i	−0.0130922	−	0.101108i
$395$	1.05957e6	−	1.83523e6i	0.341695	−	0.591832i
$396$	861073.	+	3.26920e6i	0.275932	+	1.04762i
$397$	−3.73687e6	+	2.15748e6i	−1.18996	+	0.687022i	−0.958297	−	0.285774i	$-0.907749\pi$
$397$	−3.73687e6	+	2.15748e6i	−1.18996	+	0.687022i	−0.231661	+	0.972797i	$0.574416\pi$
$398$	3.59739e6	+	1.49907e6i	1.13836	+	0.474367i
$399$	−470055.	−	157987.i	−0.147814	−	0.0496809i
$400$	−7532.34	+	884261.i	−0.00235385	+	0.276331i
$401$	1.19909e6	+	2.07689e6i	0.372385	+	0.644989i	0.989932	−	0.141545i	$-0.0452069\pi$
$401$	1.19909e6	+	2.07689e6i	0.372385	+	0.644989i	−0.617547	+	0.786534i	$0.711874\pi$
$402$	−333562.	−	436629.i	−0.102946	−	0.134756i
$403$	−1.92274e6	−	1.11010e6i	−0.589737	−	0.340485i
$404$	3.04293e6	+	829258.i	0.927554	+	0.252776i
$405$		−	2.69592e6i		−	0.816712i
$406$	−262688.	+	1.32671e6i	−0.0790908	+	0.399450i
$407$		−	1.77822e6i		−	0.532107i
$408$	384385.	+	298870.i	0.114318	+	0.0888856i
$409$	2.78823e6	+	1.60979e6i	0.824178	+	0.475839i	0.851855	−	0.523778i	$-0.175478\pi$
$409$	2.78823e6	+	1.60979e6i	0.824178	+	0.475839i	−0.0276774	+	0.999617i	$0.508811\pi$
$410$	395049.	−	301797.i	0.116062	−	0.0886657i
$411$	−247696.	−	429022.i	−0.0723293	−	0.125278i
$412$	−4.35962e6	−	4.39691e6i	−1.26534	−	1.27616i
$413$	779864.	−	688083.i	0.224980	−	0.198502i
$414$	1.19078e6	−	2.85758e6i	0.341454	−	0.819403i
$415$	1.82261e6	−	1.05229e6i	0.519487	−	0.299926i
$416$	1.31405e6	−	986257.i	0.372288	−	0.279420i
$417$	291886.	−	505561.i	0.0822002	−	0.142375i
$418$	5.24605e6	−	679293.i	1.46856	−	0.190159i
$419$	−3.84140e6			−1.06894			−0.534472	−	0.845186i	$-0.679490\pi$
$419$	−3.84140e6			−1.06894			−0.534472	+	0.845186i	$0.679490\pi$
$420$	23701.1	−	354807.i	0.00655610	−	0.0981452i
$421$	2.57965e6			0.709342			0.354671	−	0.934991i	$-0.384593\pi$
$421$	2.57965e6			0.709342			0.354671	+	0.934991i	$0.384593\pi$
$422$	2.26152e6	−	292837.i	0.618187	−	0.0800470i
$423$	−1.90697e6	+	3.30297e6i	−0.518195	+	0.897540i
$424$	5.75736e6	+	795421.i	1.55528	+	0.214873i
$425$	1.11602e6	−	644335.i	0.299709	−	0.173037i
$426$	63911.9	−	153372.i	0.0170631	−	0.0409471i
$427$	5.93412e6	−	1.19894e6i	1.57502	−	0.318219i
$428$	−1.86320e6	+	1.84739e6i	−0.491643	+	0.487472i
$429$	112642.	+	195101.i	0.0295499	+	0.0511820i
$430$	−731889.	+	559126.i	−0.190886	+	0.145827i
$431$	725184.	+	418685.i	0.188042	+	0.108566i	0.591066	−	0.806623i	$-0.298707\pi$
$431$	725184.	+	418685.i	0.188042	+	0.108566i	−0.403024	+	0.915190i	$0.632041\pi$
$432$	−775427.	+	438929.i	−0.199909	+	0.113158i
$433$		−	2.31098e6i		−	0.592348i	−0.955134	−	0.296174i	$-0.904289\pi$
$433$		−	2.31098e6i		−	0.592348i	0.955134	−	0.296174i	$-0.0957108\pi$
$434$	−4.31925e6	−	3.78118e6i	−1.10074	−	0.963613i
$435$		−	158078.i		−	0.0400542i
$436$	−61510.0	+	225709.i	−0.0154963	+	0.0568633i
$437$	−4.19503e6	−	2.42200e6i	−1.05083	−	0.606695i
$438$	−126176.	−	165163.i	−0.0314261	−	0.0411364i
$439$	418767.	+	725326.i	0.103708	+	0.179627i	0.913210	−	0.407490i	$-0.133596\pi$
$439$	418767.	+	725326.i	0.103708	+	0.179627i	−0.809502	+	0.587117i	$0.800263\pi$
$440$	1.42920e6	+	3.51372e6i	0.351934	+	0.865237i
$441$	−501912.	+	3.99811e6i	−0.122894	+	0.978946i
$442$	−2.21011e6	−	920975.i	−0.538093	−	0.224229i
$443$	2.81277e6	−	1.62395e6i	0.680965	−	0.393155i	−0.119254	−	0.992864i	$-0.538050\pi$
$443$	2.81277e6	−	1.62395e6i	0.680965	−	0.393155i	0.800218	+	0.599709i	$0.204717\pi$
$444$	225085.	−	59285.0i	0.0541863	−	0.0142721i
$445$	949687.	−	1.64491e6i	0.227342	−	0.393769i
$446$	−657616.	−	5.07864e6i	−0.156544	−	1.20896i
$447$	393797.			0.0932188
$448$	3.82818e6	−	1.84158e6i	0.901151	−	0.433506i
$449$	−4.27089e6			−0.999776			−0.499888	−	0.866090i	$-0.666626\pi$
$449$	−4.27089e6			−0.999776			−0.499888	+	0.866090i	$0.666626\pi$
$450$	150399.	+	1.16150e6i	0.0350118	+	0.270389i
$451$	−407169.	+	705238.i	−0.0942613	+	0.163265i
$452$	−7.51492e6	+	1.97935e6i	−1.73013	+	0.455698i
$453$	−251811.	+	145383.i	−0.0576539	+	0.0332865i
$454$	−710961.	−	296265.i	−0.161885	−	0.0674591i
$455$	346298.	+	1.71400e6i	0.0784191	+	0.388134i
$456$	260886.	+	641393.i	0.0587541	+	0.144448i
$457$	−3.95629e6	−	6.85250e6i	−0.886131	−	1.53482i	−0.844411	−	0.535695i	$-0.820050\pi$
$457$	−3.95629e6	−	6.85250e6i	−0.886131	−	1.53482i	−0.0417201	−	0.999129i	$-0.513284\pi$
$458$	−365997.	−	479085.i	−0.0815293	−	0.106721i
$459$	1.12453e6	+	649249.i	0.249138	+	0.143840i
$460$	913302.	−	3.35133e6i	0.201243	−	0.738453i
$461$		−	1.83353e6i		−	0.401824i	−0.979609	−	0.200912i	$-0.935609\pi$
$461$		−	1.83353e6i		−	0.401824i	0.979609	−	0.200912i	$-0.0643906\pi$
$462$	187720.	+	551412.i	0.0409171	+	0.120191i
$463$		−	218753.i		−	0.0474245i	−0.999719	−	0.0237122i	$-0.992451\pi$
$463$		−	218753.i		−	0.0474245i	0.999719	−	0.0237122i	$-0.00754855\pi$
$464$	1.64344e6	−	930264.i	0.354371	−	0.200591i
$465$	581064.	+	335477.i	0.124621	+	0.0719500i
$466$	617830.	−	471990.i	0.131797	−	0.100686i
$467$	−878070.	−	1.52086e6i	−0.186310	−	0.322699i	0.757707	−	0.652595i	$-0.226320\pi$
$467$	−878070.	−	1.52086e6i	−0.186310	−	0.322699i	−0.944017	+	0.329896i	$0.892986\pi$
$468$	1.54525e6	−	1.53214e6i	0.326125	−	0.323359i
$469$	4.62204e6	+	5.23855e6i	0.970290	+	1.09971i
$470$	−1.64606e6	+	3.95013e6i	−0.343717	+	0.824834i
$471$	−498111.	+	287585.i	−0.103460	+	0.0597329i
$472$	−1.43852e6	−	198742.i	−0.297209	−	0.0410616i
$473$	754344.	−	1.30656e6i	0.155030	−	0.268520i
$474$	−450615.	+	58348.6i	−0.0921212	+	0.0119285i
$475$	1.83260e6			0.372679
$476$	−5.14308e6	−	3.44581e6i	−1.04041	−	0.697067i
$477$	7.69776e6			1.54906
$478$	2.46276e6	−	318895.i	0.493007	−	0.0638378i
$479$	−726769.	+	1.25880e6i	−0.144730	+	0.250679i	−0.929272	−	0.369396i	$-0.879565\pi$
$479$	−726769.	+	1.25880e6i	−0.144730	+	0.250679i	0.784542	+	0.620075i	$0.212898\pi$
$480$	−397114.	+	298053.i	−0.0786705	+	0.0590459i
$481$	−991246.	+	572296.i	−0.195352	+	0.112787i
$482$	−2.26158e6	+	5.42721e6i	−0.443398	+	1.06404i
$483$	169934.	−	505601.i	0.0331446	−	0.0986144i
$484$	−746290.	−	752674.i	−0.144808	−	0.146047i
$485$	3.12015e6	+	5.40426e6i	0.602311	+	1.04323i
$486$	−1.40984e6	+	1.07705e6i	−0.270757	+	0.206845i
$487$	2.79469e6	+	1.61352e6i	0.533964	+	0.308284i	0.742629	−	0.669703i	$-0.233579\pi$
$487$	2.79469e6	+	1.61352e6i	0.533964	+	0.308284i	−0.208665	+	0.977987i	$0.566912\pi$
$488$	−6.67341e6	−	5.18876e6i	−1.26852	−	0.986311i
$489$		−	647325.i		−	0.122419i
$490$	17571.0	+	4.52120e6i	0.00330603	+	0.850675i
$491$			5.93538e6i			1.11108i	0.831490	+	0.555540i	$0.187488\pi$
$491$			5.93538e6i			1.11108i	−0.831490	+	0.555540i	$0.812512\pi$
$492$	−102843.	−	28026.7i	−0.0191541	−	0.00521987i
$493$	−2.38333e6	−	1.37601e6i	−0.441638	−	0.254980i
$494$	−2.06704e6	−	2.70573e6i	−0.381093	−	0.498846i
$495$	2.51199e6	+	4.35089e6i	0.460792	+	0.798115i
$496$	−68275.1	+	8.01518e6i	−0.0124612	+	1.46288i
$497$	−673048.	+	2.00250e6i	−0.122224	+	0.363649i
$498$	−416534.	−	173574.i	−0.0752623	−	0.0313626i
$499$	−5.31234e6	+	3.06708e6i	−0.955069	+	0.551409i	−0.894652	−	0.446764i	$-0.852576\pi$
$499$	−5.31234e6	+	3.06708e6i	−0.955069	+	0.551409i	−0.0604171	+	0.998173i	$0.519243\pi$
$500$	1.54594e6	+	5.86940e6i	0.276546	+	1.04995i
$501$	89505.3	−	155028.i	0.0159314	−	0.0275940i
$502$	−622078.	−	4.80418e6i	−0.110176	−	0.850864i
$503$	1.32110e6			0.232818			0.116409	−	0.993201i	$-0.462862\pi$
$503$	1.32110e6			0.232818			0.116409	+	0.993201i	$0.462862\pi$
$504$	4.68872e6	−	3.11003e6i	0.822201	−	0.545366i
$505$	4.68695e6			0.817828
$506$	730662.	+	5.64276e6i	0.126865	+	0.979750i
$507$	−262121.	+	454007.i	−0.0452879	+	0.0784409i
$508$	−1.13522e6	−	4.31004e6i	−0.195174	−	0.741007i
$509$	−5.42608e6	+	3.13275e6i	−0.928307	+	0.535958i	−0.886276	−	0.463158i	$-0.846716\pi$
$509$	−5.42608e6	+	3.13275e6i	−0.928307	+	0.535958i	−0.0420313	+	0.999116i	$0.513383\pi$
$510$	667907.	+	278324.i	0.113708	+	0.0473833i
$511$	1.74837e6	+	1.98158e6i	0.296197	+	0.335706i
$512$	−5.43561e6	−	2.37455e6i	−0.916376	−	0.400319i
$513$	923290.	+	1.59918e6i	0.154898	+	0.268290i
$514$	−3.90504e6	−	5.11165e6i	−0.651955	−	0.853402i
$515$	−7.96881e6	−	4.60080e6i	−1.32396	−	0.764390i
$516$	190533.	+	51923.9i	0.0315026	+	0.00858505i
$517$		−	7.00985e6i		−	1.15341i
$518$	−2.80154e6	+	953741.i	−0.458747	+	0.156173i
$519$		−	361039.i		−	0.0588350i
$520$	1.49871e6	−	1.92753e6i	0.243058	−	0.312603i
$521$	993670.	+	573695.i	0.160379	+	0.0925949i	0.578041	−	0.816007i	$-0.303817\pi$
$521$	993670.	+	573695.i	0.160379	+	0.0925949i	−0.417662	+	0.908602i	$0.637151\pi$
$522$	1.98755e6	−	1.51839e6i	0.319258	−	0.243897i
$523$	2.62296e6	+	4.54310e6i	0.419312	+	0.726270i	0.995870	−	0.0907861i	$-0.0289380\pi$
$523$	2.62296e6	+	4.54310e6i	0.419312	+	0.726270i	−0.576558	+	0.817056i	$0.695605\pi$
$524$	8.43276e6	+	8.50489e6i	1.34166	+	1.35313i
$525$	39963.7	+	197800.i	0.00632801	+	0.0313204i
$526$	−3.68961e6	+	8.85412e6i	−0.581454	+	1.39534i
$527$	1.01159e7	−	5.84043e6i	1.58664	−	0.916048i
$528$	412651.	−	700877.i	0.0644166	−	0.109410i
$529$	−613018.	+	1.06178e6i	−0.0952432	+	0.164966i
$530$	8.56565e6	−	1.10914e6i	1.32456	−	0.171512i
$531$	−1.92335e6			−0.296020
$532$	−3.88392e6	−	7.90071e6i	−0.594964	−	1.21028i
$533$	524168.			0.0799195
$534$	−403883.	+	52297.4i	−0.0612918	+	0.00793647i
$535$	−1.94959e6	+	3.37679e6i	−0.294482	+	0.510059i
$536$	1.33501e6	−	9.66294e6i	0.200711	−	1.45277i
$537$	76769.7	−	44323.0i	0.0114883	−	0.00663275i
$538$	2.42970e6	−	5.83066e6i	0.361907	−	0.868484i
$539$	−2.87528e6	−	6.82511e6i	−0.426293	−	1.01190i
$540$	−940295.	+	932320.i	−0.138765	+	0.137588i
$541$	−1.76958e6	−	3.06500e6i	−0.259943	−	0.450234i	0.706284	−	0.707929i	$-0.250370\pi$
$541$	−1.76958e6	−	3.06500e6i	−0.259943	−	0.450234i	−0.966226	+	0.257695i	$0.917037\pi$
$542$	−5.51586e6	+	4.21384e6i	−0.806520	+	0.616141i
$543$	330068.	+	190565.i	0.0480402	+	0.0277360i
$544$	1.03697e6	+	8.58169e6i	0.150234	+	1.24330i
$545$			347653.i			0.0501366i
$546$	246963.	−	282107.i	0.0354528	−	0.0404979i
$547$		−	1.25811e7i		−	1.79783i	−0.438121	−	0.898916i	$-0.644356\pi$
$547$		−	1.25811e7i		−	1.79783i	0.438121	−	0.898916i	$-0.355644\pi$
$548$	2.31242e6	−	8.48536e6i	0.328940	−	1.20703i
$549$	−9.69595e6	−	5.59796e6i	−1.37297	−	0.792682i
$550$	−1.30679e6	−	1.71057e6i	−0.184204	−	0.241121i
$551$	−1.95682e6	−	3.38930e6i	−0.274581	−	0.475589i
$552$	−689895.	+	280614.i	−0.0963686	+	0.0391978i
$553$	5.66273e6	−	1.14411e6i	0.787432	−	0.159094i
$554$	−4.39925e6	−	1.83321e6i	−0.608981	−	0.253769i
$555$	299560.	−	172951.i	0.0412811	−	0.0238337i
$556$	1.00220e7	−	2.63970e6i	1.37489	−	0.362133i
$557$	−839548.	+	1.45414e6i	−0.114659	+	0.198595i	−0.917643	−	0.397405i	$-0.869911\pi$
$557$	−839548.	+	1.45414e6i	−0.114659	+	0.198595i	0.802984	+	0.596000i	$0.203244\pi$
$558$	1.36326e6	+	1.05282e7i	0.185350	+	1.43142i
$559$	−971103.			−0.131443
$560$	4.76924e6	−	4.13624e6i	0.642657	−	0.557360i
$561$	−1.18526e6			−0.159003
$562$	1.48972e6	+	1.15048e7i	0.198959	+	1.53652i
$563$	−1.97417e6	+	3.41936e6i	−0.262490	+	0.454646i	−0.966903	−	0.255144i	$-0.917877\pi$
$563$	−1.97417e6	+	3.41936e6i	−0.262490	+	0.454646i	0.704413	+	0.709790i	$0.251210\pi$
$564$	887301.	−	233706.i	0.117455	−	0.0309365i
$565$	−1.00014e7	+	5.77432e6i	−1.31808	+	0.760992i
$566$	6.71576e6	+	2.79853e6i	0.881159	+	0.367188i
$567$	5.51107e6	−	4.86248e6i	0.719910	−	0.635185i
$568$	2.73242e6	−	1.11141e6i	0.355367	−	0.144545i
$569$	−434532.	−	752632.i	−0.0562654	−	0.0974545i	0.836521	−	0.547935i	$-0.184586\pi$
$569$	−434532.	−	752632.i	−0.0562654	−	0.0974545i	−0.892786	+	0.450481i	$0.851253\pi$
$570$	624670.	+	817686.i	0.0805311	+	0.105414i
$571$	1.62522e6	+	938320.i	0.208603	+	0.120437i	0.600662	−	0.799503i	$-0.294904\pi$
$571$	1.62522e6	+	938320.i	0.208603	+	0.120437i	−0.392059	+	0.919940i	$0.628237\pi$
$572$	−1.05159e6	+	3.85879e6i	−0.134387	+	0.493130i
$573$			8571.45i			0.00109061i
$574$	1.32947e6	+	263234.i	0.168422	+	0.0333475i
$575$			1.97119e6i			0.248633i
$576$	−7.56187e6	−	2.13011e6i	−0.949671	−	0.267514i
$577$	−2.99840e6	−	1.73113e6i	−0.374930	−	0.216466i	0.300680	−	0.953725i	$-0.402786\pi$
$577$	−2.99840e6	−	1.73113e6i	−0.374930	−	0.216466i	−0.675610	+	0.737259i	$0.736120\pi$
$578$	3.62761e6	−	2.77131e6i	0.451648	−	0.345036i
$579$	−27883.3	−	48295.3i	−0.00345659	−	0.00598699i
$580$	1.99286e6	−	1.97595e6i	0.245984	−	0.243897i
$581$	5.43847e6	+	1.82789e6i	0.668400	+	0.224651i
$582$	514667.	−	1.23507e6i	0.0629824	−	0.151142i
$583$	−1.22527e7	+	7.07407e6i	−1.49300	+	0.861982i
$584$	504990.	−	3.65518e6i	0.0612704	−	0.443483i
$585$	1.61690e6	−	2.80056e6i	0.195341	−	0.338341i
$586$	8.76530e6	−	1.13499e6i	1.05444	−	0.136536i
$587$	3.18312e6			0.381292			0.190646	−	0.981659i	$-0.438942\pi$
$587$	3.18312e6			0.381292			0.190646	+	0.981659i	$0.438942\pi$
$588$	768056.	−	591497.i	0.0916114	−	0.0705519i
$589$	1.66112e7			1.97294
$590$	−2.14020e6	+	277127.i	−0.253118	+	0.0327755i
$591$	−50050.1	+	86689.4i	−0.00589436	+	0.0102093i
$592$	3.56092e6	+	2.09654e6i	0.417598	+	0.245867i
$593$	1.71060e6	−	987615.i	0.199761	−	0.115332i	−0.396783	−	0.917913i	$-0.629873\pi$
$593$	1.71060e6	−	987615.i	0.199761	−	0.115332i	0.596544	+	0.802580i	$0.296540\pi$
$594$	834318.	−	2.00215e6i	0.0970210	−	0.232826i
$595$	−8.72051e6	−	2.93099e6i	−1.00983	−	0.339408i
$596$	4.92241e6	+	4.96452e6i	0.567626	+	0.572481i
$597$	−620904.	−	1.07544e6i	−0.0712998	−	0.123495i
$598$	2.91034e6	−	2.22335e6i	0.332805	−	0.254246i
$599$	−5.56452e6	−	3.21268e6i	−0.633666	−	0.365847i	0.148504	−	0.988912i	$-0.452554\pi$
$599$	−5.56452e6	−	3.21268e6i	−0.633666	−	0.365847i	−0.782171	+	0.623064i	$0.785887\pi$
$600$	172955.	−	222442.i	0.0196135	−	0.0252254i
$601$			1.27820e7i			1.44349i	0.692159	+	0.721745i	$0.256660\pi$
$601$			1.27820e7i			1.44349i	−0.692159	+	0.721745i	$0.743340\pi$
$602$	−2.46305e6	−	487683.i	−0.277002	−	0.0548461i
$603$		−	1.29196e7i		−	1.44696i
$604$	−4.98041e6	−	1.35726e6i	−0.555485	−	0.151380i
$605$	−1.36412e6	−	787575.i	−0.151518	−	0.0874789i
$606$	−610078.	−	798584.i	−0.0674844	−	0.0883363i
$607$	6.25163e6	+	1.08281e7i	0.688687	+	1.19284i	0.972263	+	0.233891i	$0.0751458\pi$
$607$	6.25163e6	+	1.08281e7i	0.688687	+	1.19284i	−0.283576	+	0.958950i	$0.591521\pi$
$608$	−4.82487e6	+	1.13062e7i	−0.529330	+	1.24039i
$609$	323148.	−	285117.i	0.0353068	−	0.0311516i
$610$	−1.15957e7	−	4.83206e6i	−1.26175	−	0.525784i
$611$	−3.90756e6	+	2.25603e6i	−0.423451	+	0.244479i
$612$	2.91602e6	+	1.10711e7i	0.314711	+	1.19485i
$613$	−3.84090e6	+	6.65263e6i	−0.412840	+	0.715060i	−0.995199	−	0.0978720i	$-0.968796\pi$
$613$	−3.84090e6	+	6.65263e6i	−0.412840	+	0.715060i	0.582359	+	0.812932i	$0.302130\pi$
$614$	−966222.	−	7.46194e6i	−0.103432	−	0.798787i
$615$	−158407.			−0.0168883
$616$	−4.60507e6	+	9.25911e6i	−0.488972	+	0.983145i
$617$	−1.48453e7			−1.56991			−0.784956	−	0.619552i	$-0.787314\pi$
$617$	−1.48453e7			−1.56991			−0.784956	+	0.619552i	$0.787314\pi$
$618$	253357.	+	1.95663e6i	0.0266847	+	0.206080i
$619$	4.21041e6	−	7.29265e6i	0.441670	−	0.764995i	−0.556143	−	0.831086i	$-0.687720\pi$
$619$	4.21041e6	−	7.29265e6i	0.441670	−	0.764995i	0.997814	+	0.0660912i	$0.0210528\pi$
$620$	3.03392e6	+	1.15188e7i	0.316975	+	1.20345i
$621$	−1.72012e6	+	993110.i	−0.178990	+	0.103340i
$622$	−6.11303e6	−	2.54737e6i	−0.633550	−	0.264007i
$623$	5.07546e6	−	1.02545e6i	0.523909	−	0.105851i
$624$	−523502.	−	4459.31i	−0.0538216	−	0.000458465i
$625$	3.16061e6	+	5.47435e6i	0.323647	+	0.560573i
$626$	9325.00	+	12206.3i	0.000951071	+	0.00124494i
$627$	−1.45972e6	−	842773.i	−0.148287	−	0.0856134i
$628$	−9.85184e6	−	2.68482e6i	−0.996823	−	0.271653i
$629$		−	6.02192e6i		−	0.606887i
$630$	5.50745e6	−	6.29118e6i	0.552839	−	0.631511i
$631$			1.38513e7i			1.38489i	0.721470	+	0.692446i	$0.243467\pi$
$631$			1.38513e7i			1.38489i	−0.721470	+	0.692446i	$0.756533\pi$
$632$	−6.36821e6	−	4.95146e6i	−0.634198	−	0.493106i
$633$	−629274.	−	363312.i	−0.0624210	−	0.0360388i
$634$	−3.14123e6	+	2.39974e6i	−0.310368	+	0.237105i
$635$	−3.31176e6	−	5.73613e6i	−0.325930	−	0.564527i
$636$	−1.30393e6	−	1.31508e6i	−0.127824	−	0.128917i
$637$	−2.87921e6	+	3.79936e6i	−0.281141	+	0.370990i
$638$	−1.76825e6	+	4.24335e6i	−0.171986	+	0.412722i
$639$	3.38345e6	−	1.95344e6i	0.327799	−	0.189255i
$640$	−8.72135e6	−	1.28072e6i	−0.841655	−	0.123596i
$641$	5.98657e6	−	1.03690e7i	0.575483	−	0.996767i	−0.420505	−	0.907290i	$-0.638147\pi$
$641$	5.98657e6	−	1.03690e7i	0.575483	−	0.996767i	0.995989	−	0.0894766i	$-0.0285194\pi$
$642$	829123.	−	107360.i	0.0793928	−	0.0102803i
$643$	−8.56267e6			−0.816736			−0.408368	−	0.912817i	$-0.633902\pi$
$643$	−8.56267e6			−0.816736			−0.408368	+	0.912817i	$0.633902\pi$
$644$	8.49816e6	−	4.17762e6i	0.807440	−	0.396930i
$645$	293473.			0.0277759
$646$	1.77657e7	−	2.30042e6i	1.67495	−	0.216883i
$647$	−2.03512e6	+	3.52492e6i	−0.191130	+	0.331047i	−0.945625	−	0.325259i	$-0.894548\pi$
$647$	−2.03512e6	+	3.52492e6i	−0.191130	+	0.331047i	0.754495	+	0.656306i	$0.227882\pi$
$648$	−1.01656e7	−	1.40445e6i	−0.951035	−	0.131392i
$649$	3.06143e6	−	1.76751e6i	0.285307	−	0.164722i
$650$	−532965.	+	1.27898e6i	−0.0494783	+	0.118735i
$651$	362242.	+	1.79291e6i	0.0335001	+	0.165808i
$652$	8.16069e6	−	8.09148e6i	0.751810	−	0.745433i
$653$	−1.13154e6	−	1.95988e6i	−0.103845	−	0.179865i	0.809421	−	0.587229i	$-0.199781\pi$
$653$	−1.13154e6	−	1.95988e6i	−0.103845	−	0.179865i	−0.913266	+	0.407364i	$0.866448\pi$
$654$	59234.8	−	45252.3i	0.00541542	−	0.00413711i
$655$	1.54140e7	+	8.89926e6i	1.40382	+	0.810496i
$656$	−932198.	−	1.64685e6i	−0.0845763	−	0.149415i
$657$		−	4.88709e6i		−	0.441710i
$658$	−1.10439e7	+	3.75972e6i	−0.994391	+	0.338525i
$659$			1.26265e7i			1.13258i	0.824205	+	0.566292i	$0.191623\pi$
$659$			1.26265e7i			1.13258i	−0.824205	+	0.566292i	$0.808377\pi$
$660$	317798.	−	1.16615e6i	0.0283982	−	0.104206i
$661$	1.67121e7	+	9.64875e6i	1.48774	+	0.858949i	0.999902	−	0.0139825i	$-0.00445092\pi$
$661$	1.67121e7	+	9.64875e6i	1.48774	+	0.858949i	0.487842	+	0.872932i	$0.337784\pi$
$662$	−4.72749e6	−	6.18823e6i	−0.419263	−	0.548809i
$663$	381460.	+	660709.i	0.0337028	+	0.0583749i
$664$	−3.01841e6	−	7.42081e6i	−0.265679	−	0.653178i
$665$	−8.65581e6	−	9.81038e6i	−0.759021	−	0.860264i
$666$	5.05191e6	+	2.10518e6i	0.441337	+	0.183910i
$667$	3.64561e6	−	2.10479e6i	0.317289	−	0.183187i
$668$	3.07321e6	−	809451.i	0.266471	−	0.0701858i
$669$	−815878.	+	1.41314e6i	−0.0704791	+	0.122073i
$670$	−1.86154e6	−	1.43763e7i	−0.160208	−	1.23726i
$671$	2.05776e7			1.76437
$672$	−1.32554e6	−	274210.i	−0.113232	−	0.0234240i
$673$	−2.00592e6			−0.170717			−0.0853583	−	0.996350i	$-0.527203\pi$
$673$	−2.00592e6			−0.170717			−0.0853583	+	0.996350i	$0.527203\pi$
$674$	564387.	+	4.35865e6i	0.0478550	+	0.369575i
$675$	375718.	−	650762.i	0.0317397	−	0.0549747i
$676$	−9.00004e6	+	2.37052e6i	−0.757492	+	0.199515i
$677$	1.71211e7	−	9.88486e6i	1.43569	−	0.828894i	0.438140	−	0.898907i	$-0.355637\pi$
$677$	1.71211e7	−	9.88486e6i	1.43569	−	0.828894i	0.997546	+	0.0700127i	$0.0223040\pi$
$678$	2.28569e6	+	952472.i	0.190960	+	0.0795752i
$679$	−5.41989e6	+	1.61257e7i	−0.451145	+	1.34228i
$680$	4.83997e6	+	1.18992e7i	0.401394	+	0.986835i
$681$	122711.	+	212541.i	0.0101394	+	0.0175620i
$682$	−1.18451e7	−	1.55051e7i	−0.975165	−	1.27648i
$683$	2.59875e6	+	1.50039e6i	0.213164	+	0.123070i	0.602781	−	0.797907i	$-0.294059\pi$
$683$	2.59875e6	+	1.50039e6i	0.213164	+	0.123070i	−0.389617	+	0.920977i	$0.627393\pi$
$684$	−4.28079e6	+	1.57082e7i	−0.349852	+	1.28377i
$685$		−	1.30698e7i		−	1.06425i
$686$	−9.21068e6	+	8.19057e6i	−0.747276	+	0.664513i
$687$			192104.i			0.0155290i
$688$	1.72704e6	+	3.05105e6i	0.139101	+	0.245741i
$689$	7.88672e6	+	4.55340e6i	0.632919	+	0.365416i
$690$	−879520.	+	671908.i	−0.0703271	+	0.0537264i
$691$	−5.28756e6	−	9.15832e6i	−0.421269	−	0.729660i	0.574794	−	0.818298i	$-0.305082\pi$
$691$	−5.28756e6	−	9.15832e6i	−0.421269	−	0.729660i	−0.996064	+	0.0886377i	$0.971749\pi$
$692$	4.55154e6	−	4.51293e6i	0.361321	−	0.358256i
$693$	−4.36348e6	+	1.29826e7i	−0.345144	+	1.02690i
$694$	9.44905e6	−	2.26753e7i	0.744714	−	1.78713i
$695$	1.33381e7	−	7.70074e6i	1.04745	−	0.604743i
$696$	−596072.	−	82351.8i	−0.0466419	−	0.00644391i
$697$	−1.37887e6	+	2.38828e6i	−0.107509	+	0.186210i
$698$	−692036.	+	89609.4i	−0.0537638	+	0.00696170i
$699$	−247737.			−0.0191778
$700$	−1.99408e6	+	2.97628e6i	−0.153814	+	0.229577i
$701$	−5.89982e6			−0.453465			−0.226733	−	0.973957i	$-0.572804\pi$
$701$	−5.89982e6			−0.453465			−0.226733	+	0.973957i	$0.572804\pi$
$702$	−1.38459e6	+	179286.i	−0.106042	+	0.0137311i
$703$	4.28185e6	−	7.41638e6i	0.326771	−	0.565984i
$704$	1.39939e7	−	3.55866e6i	1.06416	−	0.270617i
$705$	1.18089e6	−	681785.i	0.0894820	−	0.0516624i
$706$	4.71641e6	−	1.13182e7i	0.356123	−	0.854605i
$707$	8.45361e6	+	9.58120e6i	0.636053	+	0.720894i
$708$	325797.	+	328584.i	0.0244267	+	0.0246356i
$709$	−1.04520e7	−	1.81034e7i	−0.780881	−	1.35253i	−0.931429	−	0.363923i	$-0.881437\pi$
$709$	−1.04520e7	−	1.81034e7i	−0.780881	−	1.35253i	0.150548	−	0.988603i	$-0.451896\pi$
$710$	3.48346e6	−	2.66118e6i	0.259337	−	0.198120i
$711$	−9.25252e6	−	5.34194e6i	−0.686414	−	0.396301i
$712$	−5.70778e6	−	4.43795e6i	−0.421956	−	0.328082i
$713$			1.78674e7i			1.31625i
$714$	635711.	+	1.86735e6i	0.0466674	+	0.137082i
$715$			5.94359e6i			0.434794i
$716$	1.51838e6	+	413788.i	0.110687	+	0.0301645i
$717$	−685269.	−	395640.i	−0.0497809	−	0.0287410i
$718$	1.60348e7	+	2.09894e7i	1.16079	+	1.51946i
$719$	−4.52347e6	−	7.83488e6i	−0.326324	−	0.565210i	0.655455	−	0.755234i	$-0.272477\pi$
$719$	−4.52347e6	−	7.83488e6i	−0.326324	−	0.565210i	−0.981779	+	0.190024i	$0.939143\pi$
$720$	−1.16745e7	−	99445.7i	−0.839277	−	0.00714915i
$721$	−4.96785e6	−	2.45883e7i	−0.355902	−	1.76153i
$722$	1.05861e7	+	4.41132e6i	0.755773	+	0.314938i
$723$	1.62246e6	−	936727.i	0.115432	−	0.0666449i
$724$	1.72339e6	+	6.54314e6i	0.122191	+	0.463916i
$725$	−796294.	+	1.37922e6i	−0.0562637	+	0.0974516i
$726$	43370.2	+	334940.i	0.00305387	+	0.0235844i
$727$	−2.52083e7			−1.76892			−0.884458	−	0.466621i	$-0.845471\pi$
$727$	−2.52083e7			−1.76892			−0.884458	+	0.466621i	$0.845471\pi$
$728$	6.64346e6	−	412885.i	0.464586	−	0.0288736i
$729$	−1.32106e7			−0.920670
$730$	−704160.	−	5.43809e6i	−0.0489062	−	0.377693i
$731$	2.55458e6	−	4.42466e6i	0.176818	−	0.306257i
$732$	686049.	+	2.60469e6i	0.0473236	+	0.179671i
$733$	−9.27068e6	+	5.35243e6i	−0.637312	+	0.367952i	−0.783578	−	0.621293i	$-0.786608\pi$
$733$	−9.27068e6	+	5.35243e6i	−0.637312	+	0.367952i	0.146267	+	0.989245i	$0.453274\pi$
$734$	−2.05031e7	−	8.54386e6i	−1.40469	−	0.585348i
$735$	870112.	−	1.14819e6i	0.0594096	−	0.0783962i
$736$	−1.21612e7	−	5.18973e6i	−0.827529	−	0.353143i
$737$	1.18729e7	+	2.05644e7i	0.805169	+	1.39459i
$738$	−1.52154e6	−	1.99168e6i	−0.102835	−	0.134610i
$739$	3.71552e6	+	2.14516e6i	0.250270	+	0.144493i	0.619888	−	0.784690i	$-0.287178\pi$
$739$	3.71552e6	+	2.14516e6i	0.250270	+	0.144493i	−0.369618	+	0.929184i	$0.620511\pi$
$740$	5.92482e6	+	1.61463e6i	0.397737	+	0.108391i
$741$			1.08494e6i			0.0725873i
$742$	1.77167e7	+	1.55096e7i	1.18134	+	1.03417i
$743$		−	1.03989e7i		−	0.691062i	−0.938407	−	0.345531i	$-0.887699\pi$
$743$		−	1.03989e7i		−	0.691062i	0.938407	−	0.345531i	$-0.112301\pi$
$744$	1.56771e6	−	2.01628e6i	0.103832	−	0.133542i
$745$	8.99752e6	+	5.19472e6i	0.593925	+	0.342903i
$746$	−5.37475e6	+	4.10603e6i	−0.353599	+	0.270132i
$747$	−5.30521e6	−	9.18890e6i	−0.347857	−	0.602507i
$748$	−1.48156e7	−	1.49423e7i	−0.968199	−	0.976481i
$749$	−1.04193e7	+	2.10513e6i	−0.678633	+	0.137112i
$750$	743912.	−	1.78520e6i	0.0482913	−	0.115887i
$751$	−1.23512e7	+	7.13098e6i	−0.799116	+	0.461370i	−0.843162	−	0.537660i	$-0.819309\pi$
$751$	−1.23512e7	+	7.13098e6i	−0.799116	+	0.461370i	0.0440458	+	0.999030i	$0.485975\pi$
$752$	1.40374e7	+	8.26473e6i	0.905196	+	0.532947i
$753$	−771787.	+	1.33677e6i	−0.0496032	+	0.0859153i
$754$	2.93449e6	−	379978.i	0.187977	−	0.0243405i
$755$	−7.67119e6			−0.489774
$756$	−3.60184e6	−	240603.i	−0.229202	−	0.0153107i
$757$	−2.38648e6			−0.151362			−0.0756811	−	0.997132i	$-0.524113\pi$
$757$	−2.38648e6			−0.151362			−0.0756811	+	0.997132i	$0.524113\pi$
$758$	−1.51618e7	+	1.96326e6i	−0.958471	+	0.124109i
$759$	906504.	−	1.57011e6i	0.0571170	−	0.0989295i
$760$	−2.50010e6	+	1.80960e7i	−0.157009	+	1.13645i
$761$	2.59634e7	−	1.49900e7i	1.62517	−	0.938294i	0.639668	−	0.768652i	$-0.279072\pi$
$761$	2.59634e7	−	1.49900e7i	1.62517	−	0.938294i	0.985506	−	0.169643i	$-0.0542613\pi$
$762$	−546273.	+	1.31092e6i	−0.0340818	+	0.0817876i
$763$	−710683.	+	627044.i	−0.0441941	+	0.0389930i
$764$	−108059.	+	107142.i	−0.00669770	+	0.00664089i
$765$	8.50683e6	+	1.47343e7i	0.525550	+	0.910280i
$766$	−9.12341e6	+	6.96982e6i	−0.561805	+	0.429190i
$767$	−1.97056e6	−	1.13770e6i	−0.120949	−	0.0698298i
$768$	917002.	+	1.65269e6i	0.0561006	+	0.101109i
$769$			2.85040e7i			1.73816i	0.494673	+	0.869079i	$0.335288\pi$
$769$			2.85040e7i			1.73816i	−0.494673	+	0.869079i	$0.664712\pi$
$770$	−2.98484e6	+	1.50750e7i	−0.181424	+	0.916284i
$771$			2.04967e6i			0.124179i
$772$	260311.	−	955204.i	0.0157199	−	0.0576837i
$773$	−6.17900e6	−	3.56745e6i	−0.371937	−	0.214738i	0.302367	−	0.953191i	$-0.402223\pi$
$773$	−6.17900e6	−	3.56745e6i	−0.371937	−	0.214738i	−0.674304	+	0.738454i	$0.735556\pi$
$774$	2.81889e6	+	3.68990e6i	0.169132	+	0.221392i
$775$	−3.37983e6	−	5.85404e6i	−0.202135	−	0.350108i
$776$	2.20035e7	−	8.94991e6i	1.31171	−	0.533537i
$777$	893852.	+	300427.i	0.0531145	+	0.0178520i
$778$	2.02985e7	+	8.45862e6i	1.20231	+	0.501015i
$779$	−3.39635e6	+	1.96088e6i	−0.200525	+	0.115773i
$780$	−752334.	+	198157.i	−0.0442766	+	0.0116620i
$781$	−3.59033e6	+	6.21864e6i	−0.210624	+	0.364811i
$782$	2.47438e6	+	1.91092e7i	0.144694	+	1.11744i
$783$	−1.60473e6			−0.0935403
$784$	1.70575e7	+	2.28909e6i	0.991115	+	0.133007i
$785$	−1.51745e7			−0.878903
$786$	−490065.	−	3.78468e6i	−0.0282942	−	0.218511i
$787$	−5.58385e6	+	9.67152e6i	−0.321364	+	0.556619i	−0.980770	−	0.195169i	$-0.937475\pi$
$787$	−5.58385e6	+	9.67152e6i	−0.321364	+	0.556619i	0.659406	+	0.751787i	$0.270808\pi$
$788$	−1.71849e6	+	452634.i	−0.0985899	+	0.0259676i
$789$	2.64693e6	−	1.52821e6i	0.151374	−	0.0873955i
$790$	−1.10654e7	−	4.61107e6i	−0.630811	−	0.262866i
$791$	−2.98431e7	−	1.00303e7i	−1.69591	−	0.570000i
$792$	1.77148e7	−	7.20545e6i	1.00351	−	0.408177i
$793$	−6.62264e6	−	1.14707e7i	−0.373980	−	0.647752i
$794$	1.48181e7	+	1.93967e7i	0.834142	+	1.09188i
$795$	−2.38341e6	−	1.37606e6i	−0.133746	−	0.0772183i
$796$	5.79659e6	−	2.12704e7i	0.324258	−	1.18985i
$797$		−	3.53833e6i		−	0.197312i	−0.995122	−	0.0986559i	$-0.968546\pi$
$797$		−	3.53833e6i		−	0.197312i	0.995122	−	0.0986559i	$-0.0314543\pi$
$798$	−544852.	+	2.75179e6i	−0.0302880	+	0.152970i
$799$		−	2.37388e7i		−	1.31550i
$800$	4.96619e6	−	600091.i	0.274346	−	0.0331506i
$801$	−8.29296e6	−	4.78795e6i	−0.456697	−	0.263674i
$802$	1.07803e7	−	8.23563e6i	0.591829	−	0.452127i
$803$	4.49113e6	+	7.77886e6i	0.245791	+	0.425723i
$804$	−2.20719e6	+	2.18847e6i	−0.120420	+	0.119399i
$805$	1.05522e7	−	9.31037e6i	0.573925	−	0.506381i
$806$	−4.83094e6	+	1.15930e7i	−0.261935	+	0.628578i
$807$	−1.74307e6	+	1.00636e6i	−0.0942173	+	0.0543964i
$808$	2.44170e6	−	1.76733e7i	0.131572	−	0.952335i
$809$	−4.23600e6	+	7.33696e6i	−0.227554	+	0.394135i	−0.957083	−	0.289815i	$-0.906406\pi$
$809$	−4.23600e6	+	7.33696e6i	−0.227554	+	0.394135i	0.729529	+	0.683950i	$0.239739\pi$
$810$	−1.51241e7	+	1.95838e6i	−0.809950	+	0.104878i
$811$	3.15075e7			1.68214			0.841071	−	0.540925i	$-0.181926\pi$
$811$	3.15075e7			1.68214			0.841071	+	0.540925i	$0.181926\pi$
$812$	7.63371e6	+	509932.i	0.406299	+	0.0271408i
$813$	2.21175e6			0.117357
$814$	−9.97583e6	+	1.29174e6i	−0.527701	+	0.0683303i
$815$	8.53910e6	−	1.47902e7i	0.450317	−	0.779972i
$816$	1.39744e6	−	2.37351e6i	0.0734696	−	0.124786i
$817$	6.29226e6	−	3.63284e6i	0.329801	−	0.190411i
$818$	7.00550e6	−	1.68114e7i	0.366063	−	0.878459i
$819$	8.64130e6	−	1.74590e6i	0.450163	−	0.0909514i
$820$	−1.98006e6	−	1.99700e6i	−0.102836	−	0.103715i
$821$	−5.70531e6	−	9.88189e6i	−0.295408	−	0.511661i	0.679672	−	0.733516i	$-0.262122\pi$
$821$	−5.70531e6	−	9.88189e6i	−0.295408	−	0.511661i	−0.975080	+	0.221855i	$0.928789\pi$
$822$	−2.22689e6	+	1.70123e6i	−0.114953	+	0.0878180i
$823$	4.91404e6	+	2.83712e6i	0.252894	+	0.146009i	0.621089	−	0.783740i	$-0.286691\pi$
$823$	4.91404e6	+	2.83712e6i	0.252894	+	0.146009i	−0.368194	+	0.929749i	$0.620024\pi$
$824$	−2.14998e7	+	2.76516e7i	−1.10311	+	1.41874i
$825$			685905.i			0.0350856i
$826$	−4.42667e6	−	3.87521e6i	−0.225750	−	0.197627i
$827$			1.92994e7i			0.981248i	0.871371	+	0.490624i	$0.163231\pi$
$827$			1.92994e7i			0.981248i	−0.871371	+	0.490624i	$0.836769\pi$
$828$	−1.68961e7	−	4.60451e6i	−0.856466	−	0.233404i
$829$	1.88315e7	+	1.08723e7i	0.951695	+	0.549461i	0.893607	−	0.448850i	$-0.148166\pi$
$829$	1.88315e7	+	1.08723e7i	0.951695	+	0.549461i	0.0580878	+	0.998311i	$0.481500\pi$
$830$	−7.22734e6	−	9.46050e6i	−0.364152	−	0.476671i
$831$	759302.	+	1.31515e6i	0.0381427	+	0.0660652i
$832$	−6.48748e6	−	6.65542e6i	−0.324913	−	0.333324i
$833$	−9.73710e6	−	2.31132e7i	−0.486203	−	1.15411i
$834$	−3.04824e6	−	1.27023e6i	−0.151752	−	0.0632366i
$835$	4.09005e6	−	2.36139e6i	0.203008	−	0.117207i
$836$	−7.62170e6	−	2.89370e7i	−0.377169	−	1.43198i
$837$	3.40561e6	−	5.89869e6i	0.168028	−	0.291033i
$838$	2.79048e6	+	2.15504e7i	0.137268	+	1.06009i
$839$	1.73523e7			0.851046			0.425523	−	0.904948i	$-0.360090\pi$
$839$	1.73523e7			0.851046			0.425523	+	0.904948i	$0.360090\pi$
$840$	−2.00769e6	+	124776.i	−0.0981746	+	0.00610146i
$841$	−1.71101e7			−0.834185
$842$	−1.87392e6	−	1.44719e7i	−0.0910899	−	0.703469i
$843$	1.84824e6	−	3.20124e6i	0.0895754	−	0.155149i
$844$	−3.28565e6	−	1.24745e7i	−0.158769	−	0.602790i
$845$	−1.19779e7	+	6.91546e6i	−0.577085	+	0.333180i
$846$	1.99150e7	+	8.29879e6i	0.956652	+	0.398647i
$847$	−850407.	−	4.20908e6i	−0.0407304	−	0.201594i
$848$	280051.	−	3.28767e7i	0.0133736	−	1.57000i
$849$	−1.15913e6	−	2.00767e6i	−0.0551903	−	0.0955923i
$850$	−4.42543e6	−	5.79284e6i	−0.210092	−	0.275007i
$851$	7.97722e6	+	4.60565e6i	0.377596	+	0.218005i
$852$	−906850.	−	247134.i	−0.0427993	−	0.0116636i
$853$		−	3.34110e6i		−	0.157223i	−0.996905	−	0.0786117i	$-0.974951\pi$
$853$		−	3.34110e6i		−	0.157223i	0.996905	−	0.0786117i	$-0.0250487\pi$
$854$	−1.10367e7	−	3.24196e7i	−0.517841	−	1.52112i
$855$			2.41950e7i			1.13190i
$856$	1.17174e7	+	9.11058e6i	0.546571	+	0.424973i
$857$	−4.97782e6	−	2.87395e6i	−0.231519	−	0.133668i	0.379753	−	0.925088i	$-0.376009\pi$
$857$	−4.97782e6	−	2.87395e6i	−0.231519	−	0.133668i	−0.611273	+	0.791420i	$0.709342\pi$
$858$	1.01270e6	−	773649.i	0.0469636	−	0.0358778i
$859$	1.35470e7	+	2.34641e7i	0.626411	+	1.08498i	0.988266	+	0.152742i	$0.0488102\pi$
$859$	1.35470e7	+	2.34641e7i	0.626411	+	1.08498i	−0.361855	+	0.932234i	$0.617856\pi$
$860$	3.66837e6	+	3.69975e6i	0.169132	+	0.170579i
$861$	−285710.	−	323819.i	−0.0131346	−	0.0148866i
$862$	1.82204e6	−	4.37244e6i	0.0835199	−	0.200427i
$863$	−9.82533e6	+	5.67265e6i	−0.449076	+	0.259274i	−0.707440	−	0.706773i	$-0.750150\pi$
$863$	−9.82533e6	+	5.67265e6i	−0.449076	+	0.259274i	0.258364	+	0.966048i	$0.416817\pi$
$864$	3.02569e6	+	4.03131e6i	0.137892	+	0.183722i
$865$	4.76259e6	−	8.24905e6i	0.216423	−	0.374855i
$866$	−1.29647e7	+	1.67875e6i	−0.587444	+	0.0760661i
$867$	−1.45460e6			−0.0657196
$868$	−1.80749e7	+	2.69778e7i	−0.814284	+	1.21537i
$869$	1.96365e7			0.882094
$870$	−886821.	+	114832.i	−0.0397226	+	0.00514355i
$871$	7.64226e6	−	1.32368e7i	0.341332	−	0.591204i
$872$	1.31091e6	+	181112.i	0.0583825	+	0.00806597i
$873$	2.72461e7	−	1.57305e7i	1.20995	−	0.698567i
$874$	−1.05401e7	+	2.52936e7i	−0.466731	+	1.12004i
$875$	−7.83404e6	+	2.33084e7i	−0.345912	+	1.02918i
$876$	−834909.	+	827827.i	−0.0367603	+	0.0364485i
$877$	5.74760e6	+	9.95514e6i	0.252341	+	0.437067i	0.964170	−	0.265285i	$-0.0854662\pi$
$877$	5.74760e6	+	9.95514e6i	0.252341	+	0.437067i	−0.711829	+	0.702353i	$0.752133\pi$
$878$	3.76489e6	−	2.87619e6i	0.164822	−	0.125916i
$879$	−2.43896e6	−	1.40814e6i	−0.106471	−	0.0614713i
$880$	1.86738e7	−	1.05703e7i	0.812880	−	0.460129i
$881$			3.70787e7i			1.60948i	0.593630	+	0.804738i	$0.297694\pi$
$881$			3.70787e7i			1.60948i	−0.593630	+	0.804738i	$0.702306\pi$
$882$	2.27941e7	−	88586.2i	0.986622	−	0.00383437i
$883$			9.49309e6i			0.409738i	0.978789	+	0.204869i	$0.0656768\pi$
$883$			9.49309e6i			0.409738i	−0.978789	+	0.204869i	$0.934323\pi$
$884$	−3.56122e6	+	1.30678e7i	−0.153274	+	0.562433i
$885$	595515.	+	343820.i	0.0255584	+	0.0147562i
$886$	−1.11537e7	−	1.46000e7i	−0.477346	−	0.624840i
$887$	−3.50686e6	−	6.07406e6i	−0.149661	−	0.259221i	0.781441	−	0.623979i	$-0.214485\pi$
$887$	−3.50686e6	−	6.07406e6i	−0.149661	−	0.259221i	−0.931102	+	0.364758i	$0.881152\pi$
$888$	−496097.	−	1.21967e6i	−0.0211122	−	0.0519049i
$889$	5.75272e6	−	1.71159e7i	0.244129	−	0.726351i
$890$	−9.91783e6	−	4.13287e6i	−0.419703	−	0.174895i
$891$	2.16342e7	−	1.24905e7i	0.912949	−	0.527091i
$892$	−2.80136e7	+	7.37848e6i	−1.17884	+	0.310495i
$893$	1.68794e7	−	2.92359e7i	0.708316	−	1.22684i
$894$	−286063.	−	2.20921e6i	−0.0119707	−	0.0924470i
$895$	2.33872e6			0.0975936
$896$	−1.31122e7	−	2.01384e7i	−0.545638	−	0.838021i
$897$	−1.16699e6			−0.0484267
$898$	3.10247e6	+	2.39598e7i	0.128386	+	0.991499i
$899$	−7.21783e6	+	1.25016e7i	−0.297857	+	0.515903i
$900$	6.40681e6	−	1.68749e6i	0.263655	−	0.0694439i
$901$	−4.14935e7	+	2.39563e7i	−1.70282	+	0.983123i
$902$	4.25217e6	+	1.77193e6i	0.174018	+	0.0725152i
$903$	529322.	+	599926.i	0.0216023	+	0.0244838i
$904$	1.65632e7	+	4.07210e7i	0.674098	+	1.65728i
$905$	5.02763e6	+	8.70810e6i	0.204052	+	0.353429i
$906$	998522.	+	1.30705e6i	0.0404145	+	0.0529021i
$907$	−1.19107e7	−	6.87667e6i	−0.480751	−	0.277562i	0.239978	−	0.970778i	$-0.422860\pi$
$907$	−1.19107e7	−	6.87667e6i	−0.480751	−	0.277562i	−0.720730	+	0.693216i	$0.756193\pi$
$908$	−1.14559e6	+	4.20372e6i	−0.0461122	+	0.169207i
$909$		−	2.36298e7i		−	0.948527i
$910$	9.36401e6	−	3.18783e6i	0.374851	−	0.127612i
$911$		−	3.60526e6i		−	0.143926i	−0.997407	−	0.0719632i	$-0.977074\pi$
$911$		−	3.60526e6i		−	0.143926i	0.997407	−	0.0719632i	$-0.0229264\pi$
$912$	3.40871e6	−	1.92950e6i	0.135707	−	0.0768169i
$913$	1.68888e7	+	9.75075e6i	0.670535	+	0.387134i
$914$	−3.55687e7	+	2.71727e7i	−1.40832	+	1.07589i
$915$	2.00140e6	+	3.46652e6i	0.0790280	+	0.136880i
$916$	−2.42181e6	+	2.40127e6i	−0.0953677	+	0.0945588i
$917$	9.60924e6	+	4.75608e7i	0.377369	+	1.86778i
$918$	2.82541e6	−	6.78027e6i	0.110656	−	0.265546i
$919$	334591.	−	193176.i	0.0130685	−	0.00754510i	−0.493452	−	0.869773i	$-0.664265\pi$
$919$	334591.	−	193176.i	0.0130685	−	0.00754510i	0.506520	+	0.862228i	$0.330932\pi$
$920$	−1.94645e7	−	2.68916e6i	−0.758182	−	0.104748i
$921$	−1.19875e6	+	2.07630e6i	−0.0465673	+	0.0806569i
$922$	−1.02862e7	+	1.33192e6i	−0.398497	+	0.0516001i
$923$	4.62201e6			0.178577
$924$	2.95707e6	−	1.45367e6i	0.113941	−	0.0560126i
$925$	−3.48486e6			−0.133915
$926$	−1.22721e6	+	158907.i	−0.0470318	+	0.00608999i
$927$	−2.31954e7	+	4.01756e7i	−0.886548	+	1.53555i
$928$	−6.41263e6	−	8.54394e6i	−0.244437	−	0.325678i
$929$	5.35289e6	−	3.09049e6i	0.203493	−	0.117487i	−0.394791	−	0.918771i	$-0.629183\pi$
$929$	5.35289e6	−	3.09049e6i	0.203493	−	0.117487i	0.598284	+	0.801284i	$0.295850\pi$
$930$	1.45994e6	−	3.50348e6i	0.0553511	−	0.132829i
$931$	4.44262e6	−	3.53889e7i	0.167983	−	1.33811i
$932$	−3.09668e6	−	3.12317e6i	−0.116777	−	0.117776i
$933$	1.05510e6	+	1.82748e6i	0.0396816	+	0.0687305i
$934$	−7.89421e6	+	6.03078e6i	−0.296102	+	0.226207i
$935$	−2.70809e7	−	1.56352e7i	−1.01306	−	0.584890i
$936$	−9.71786e6	−	7.55590e6i	−0.362561	−	0.281901i
$937$			1.37458e7i			0.511469i	0.966747	+	0.255735i	$0.0823173\pi$
$937$			1.37458e7i			0.511469i	−0.966747	+	0.255735i	$0.917683\pi$
$938$	2.60308e7	−	2.97351e7i	0.966009	−	1.10348i
$939$		−	4894.49i		−	0.000181152i
$940$	2.33560e7	+	6.36497e6i	0.862144	+	0.234951i
$941$	−3.26647e7	−	1.88590e7i	−1.20255	−	0.694294i	−0.241431	−	0.970418i	$-0.577617\pi$
$941$	−3.26647e7	−	1.88590e7i	−1.20255	−	0.694294i	−0.961122	+	0.276124i	$0.910950\pi$
$942$	1.97519e6	+	2.58550e6i	0.0725241	+	0.0949332i
$943$	−2.10917e6	−	3.65318e6i	−0.0772381	−	0.133780i
$944$	−69973.1	+	8.21451e6i	−0.00255565	+	0.300021i
$945$	−5.25829e6	+	1.06239e6i	−0.191542	+	0.0386995i
$946$	−7.87781e6	−	3.28277e6i	−0.286205	−	0.119265i
$947$	−2.32121e7	+	1.34015e7i	−0.841083	+	0.485599i	−0.857632	−	0.514264i	$-0.828065\pi$
$947$	−2.32121e7	+	1.34015e7i	−0.841083	+	0.485599i	0.0165493	+	0.999863i	$0.494732\pi$
$948$	654674.	+	2.48557e6i	0.0236594	+	0.0898267i
$949$	2.89082e6	−	5.00705e6i	0.104197	−	0.180475i
$950$	−1.33125e6	−	1.02809e7i	−0.0478574	−	0.369593i
$951$	1.25957e6			0.0451617
$952$	−1.55950e7	+	3.13559e7i	−0.557691	+	1.12131i
$953$	−2.21927e7			−0.791548			−0.395774	−	0.918348i	$-0.629524\pi$
$953$	−2.21927e7			−0.791548			−0.395774	+	0.918348i	$0.629524\pi$
$954$	−5.59183e6	−	4.31846e7i	−0.198922	−	1.53624i
$955$	−113069.	+	195841.i	−0.00401177	+	0.00694858i
$956$	−3.57801e6	−	1.35845e7i	−0.126618	−	0.480727i
$957$	1.26855e6	−	732395.i	0.0447740	−	0.0258503i
$958$	7.58984e6	+	3.16277e6i	0.267189	+	0.111341i
$959$	2.67176e7	−	2.35733e7i	0.938105	−	0.827701i
$960$	1.96055e6	+	2.01130e6i	0.0686595	+	0.0704368i
$961$	−1.63211e7	−	2.82691e7i	−0.570089	−	0.987422i
$962$	3.93065e6	+	5.14518e6i	0.136939	+	0.179251i
$963$	1.70245e7	+	9.82907e6i	0.591572	+	0.341544i
$964$	3.20896e7	+	8.74503e6i	1.11217	+	0.303088i
$965$		−	1.47128e6i		−	0.0508599i
$966$	−2.95988e6	−	586054.i	−0.102054	−	0.0202067i
$967$		−	1.62944e7i		−	0.560366i	−0.959947	−	0.280183i	$-0.909605\pi$
$967$		−	1.62944e7i		−	0.560366i	0.959947	−	0.280183i	$-0.0903952\pi$
$968$	−3.68039e6	+	4.73346e6i	−0.126243	+	0.162364i
$969$	−4.94335e6	−	2.85404e6i	−0.169126	−	0.0976452i
$970$	2.80514e7	−	2.14299e7i	0.957251	−	0.731291i
$971$	119252.	+	206550.i	0.00405898	+	0.00703036i	0.868048	−	0.496481i	$-0.165375\pi$
$971$	119252.	+	206550.i	0.00405898	+	0.00703036i	−0.863989	+	0.503511i	$0.832041\pi$
$972$	7.06640e6	+	7.12684e6i	0.239901	+	0.241953i
$973$	3.97993e7	+	1.33767e7i	1.34770	+	0.452966i
$974$	7.02173e6	−	1.68504e7i	0.237163	−	0.569131i
$975$	382350.	−	220750.i	0.0128810	−	0.00743684i
$976$	−2.42613e7	+	4.12072e7i	−0.815248	+	1.38468i
$977$	5.61184e6	−	9.71999e6i	0.188091	−	0.325784i	−0.756523	−	0.653968i	$-0.773103\pi$
$977$	5.61184e6	−	9.71999e6i	0.188091	−	0.325784i	0.944614	+	0.328184i	$0.106437\pi$
$978$	−3.63151e6	+	470232.i	−0.121406	+	0.0157204i
$979$	1.76001e7			0.586891
$980$	2.53513e7	−	3.38288e6i	0.843207	−	0.112518i
$981$	1.75273e6			0.0581490
$982$	3.32976e7	−	4.31160e6i	1.10188	−	0.142679i
$983$	2.86076e6	−	4.95499e6i	0.0944275	−	0.163553i	−0.814942	−	0.579542i	$-0.803231\pi$
$983$	2.86076e6	−	4.95499e6i	0.0944275	−	0.163553i	0.909370	+	0.415989i	$0.136565\pi$
$984$	−82522.9	+	597311.i	−0.00271698	+	0.0196659i
$985$	−2.28710e6	+	1.32046e6i	−0.0751095	+	0.0433645i
$986$	−5.98816e6	+	1.43701e7i	−0.196156	+	0.470725i
$987$	3.52363e6	+	1.18430e6i	0.115132	+	0.0386963i
$988$	−1.36776e7	+	1.35616e7i	−0.445778	+	0.441997i
$989$	3.90756e6	+	6.76809e6i	0.127032	+	0.220027i
$990$	2.25838e7	−	1.72529e7i	0.732335	−	0.559467i
$991$	−4.15064e7	−	2.39637e7i	−1.34255	−	0.775122i	−0.355369	−	0.934726i	$-0.615645\pi$
$991$	−4.15064e7	−	2.39637e7i	−1.34255	−	0.775122i	−0.987181	+	0.159604i	$0.948978\pi$
$992$	4.50149e7	−	5.43938e6i	1.45237	−	0.175497i
$993$			2.48136e6i			0.0798576i
$994$	1.17230e7	+	2.32115e6i	0.376333	+	0.0745138i
$995$		−	3.27622e7i		−	1.04910i
$996$	−671175.	+	2.46285e6i	−0.0214382	+	0.0786666i
$997$	−3.31586e7	−	1.91441e7i	−1.05647	−	0.609954i	−0.132018	−	0.991247i	$-0.542146\pi$
$997$	−3.31586e7	−	1.91441e7i	−1.05647	−	0.609954i	−0.924454	+	0.381293i	$0.875479\pi$
$998$	2.10654e7	+	2.75743e7i	0.669489	+	0.876353i
$999$	−1.75572e6	−	3.04099e6i	−0.0556597	−	0.0964054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.6.f.a.3.9	yes	36
4.3	odd	2	inner	28.6.f.a.3.4	✓	36
7.3	odd	6		196.6.d.b.195.31		36
7.4	even	3		196.6.d.b.195.32		36
7.5	odd	6	inner	28.6.f.a.19.4	yes	36
28.3	even	6		196.6.d.b.195.30		36
28.11	odd	6		196.6.d.b.195.29		36
28.19	even	6	inner	28.6.f.a.19.9	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.6.f.a.3.4	✓	36	4.3	odd	2	inner
28.6.f.a.3.9	yes	36	1.1	even	1	trivial
28.6.f.a.19.4	yes	36	7.5	odd	6	inner
28.6.f.a.19.9	yes	36	28.19	even	6	inner
196.6.d.b.195.29		36	28.11	odd	6
196.6.d.b.195.30		36	28.3	even	6
196.6.d.b.195.31		36	7.3	odd	6
196.6.d.b.195.32		36	7.4	even	3

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:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	28.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.726423 - 5.61002i) q^{2} +(-0.901244 + 1.56100i) q^{3} +(-30.9446 + 8.15049i) q^{4} +(-41.1834 + 23.7773i) q^{5} +(9.41192 + 3.92205i) q^{6} +(-122.887 - 41.3025i) q^{7} +(68.2033 + 167.679i) q^{8} +(119.876 + 207.630i) q^{9} +(163.307 + 213.767i) q^{10} +(-381.616 - 220.326i) q^{11} +(15.1657 - 55.6501i) q^{12} +283.636i q^{13} +(-142.441 + 719.399i) q^{14} -85.7165i q^{15} +(891.139 - 504.428i) q^{16} +(-1292.34 - 746.132i) q^{17} +(1077.73 - 823.331i) q^{18} +(-1061.07 - 1837.82i) q^{19} +(1080.61 - 1071.44i) q^{20} +(175.224 - 154.602i) q^{21} +(-958.818 + 2300.92i) q^{22} +(1976.80 - 1141.30i) q^{23} +(-323.215 - 44.6545i) q^{24} +(-431.784 + 747.871i) q^{25} +(1591.20 - 206.040i) q^{26} -870.153 q^{27} +(4139.31 + 276.506i) q^{28} +1844.20 q^{29} +(-480.871 + 62.2664i) q^{30} +(-3913.80 + 6778.91i) q^{31} +(-3477.19 - 4632.88i) q^{32} +(687.858 - 397.135i) q^{33} +(-3247.03 + 7792.05i) q^{34} +(6042.95 - 1220.92i) q^{35} +(-5401.79 - 5448.00i) q^{36} +(2017.71 + 3494.78i) q^{37} +(-9539.43 + 7287.64i) q^{38} +(-442.756 - 255.625i) q^{39} +(-6795.80 - 5283.92i) q^{40} -1848.03i q^{41} +(-994.608 - 870.704i) q^{42} +3423.76i q^{43} +(13604.7 + 3707.55i) q^{44} +(-9873.77 - 5700.62i) q^{45} +(-7838.73 - 10260.8i) q^{46} +(7953.96 + 13776.7i) q^{47} +(-15.7219 + 1845.68i) q^{48} +(13395.2 + 10151.1i) q^{49} +(4509.23 + 1879.04i) q^{50} +(2329.42 - 1344.89i) q^{51} +(-2311.77 - 8777.01i) q^{52} +(16053.7 - 27805.8i) q^{53} +(632.099 + 4881.57i) q^{54} +20955.0 q^{55} +(-1455.69 - 23422.5i) q^{56} +3825.12 q^{57} +(-1339.67 - 10346.0i) q^{58} +(-4011.14 + 6947.49i) q^{59} +(698.631 + 2652.46i) q^{60} +(-40441.8 + 23349.1i) q^{61} +(40872.9 + 17032.2i) q^{62} +(-6155.42 - 30466.2i) q^{63} +(-23464.6 + 22872.5i) q^{64} +(-6744.09 - 11681.1i) q^{65} +(-2727.61 - 3570.41i) q^{66} +(-46668.2 - 26943.9i) q^{67} +(46072.3 + 12555.6i) q^{68} +4114.38i q^{69} +(-11239.1 - 33014.2i) q^{70} -16295.5i q^{71} +(-26639.4 + 34261.7i) q^{72} +(-17653.1 - 10192.0i) q^{73} +(18140.1 - 13858.1i) q^{74} +(-778.285 - 1348.03i) q^{75} +(47813.4 + 48222.4i) q^{76} +(37795.4 + 42836.8i) q^{77} +(-1112.43 + 2669.56i) q^{78} +(-38592.2 + 22281.2i) q^{79} +(-24706.2 + 41962.9i) q^{80} +(-28345.5 + 49095.9i) q^{81} +(-10367.5 + 1342.45i) q^{82} -44256.0 q^{83} +(-4162.16 + 6212.27i) q^{84} +70963.9 q^{85} +(19207.4 - 2487.10i) q^{86} +(-1662.07 + 2878.79i) q^{87} +(10916.6 - 79016.0i) q^{88} +(-34589.9 + 19970.5i) q^{89} +(-24808.1 + 59533.1i) q^{90} +(11714.9 - 34855.1i) q^{91} +(-51869.1 + 51429.1i) q^{92} +(-7054.58 - 12218.9i) q^{93} +(71509.4 - 54629.6i) q^{94} +(87396.7 + 50458.5i) q^{95} +(10365.7 - 1252.54i) q^{96} -131224. i q^{97} +(47217.0 - 82521.3i) q^{98} -105647. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 12 q^{4} - 6 q^{5} - 72 q^{8} - 1136 q^{9} - 804 q^{10} + 1632 q^{12} + 1024 q^{14} + 664 q^{16} - 6 q^{17} - 1780 q^{18} - 4586 q^{21} + 13768 q^{22} + 564 q^{24} + 7612 q^{25} - 8892 q^{26} - 5928 q^{28}+ \cdots + 418676 q^{98}+O(q^{100}) \) 36 * q - 12 * q^4 - 6 * q^5 - 72 * q^8 - 1136 * q^9 - 804 * q^10 + 1632 * q^12 + 1024 * q^14 + 664 * q^16 - 6 * q^17 - 1780 * q^18 - 4586 * q^21 + 13768 * q^22 + 564 * q^24 + 7612 * q^25 - 8892 * q^26 - 5928 * q^28 + 176 * q^29 - 5836 * q^30 + 1160 * q^32 - 14154 * q^33 - 27920 * q^36 + 11722 * q^37 - 5652 * q^38 + 35052 * q^40 + 23140 * q^42 + 9096 * q^44 + 19152 * q^45 - 1040 * q^46 + 43900 * q^49 - 51168 * q^50 - 61776 * q^52 - 33486 * q^53 - 30996 * q^54 + 19952 * q^56 - 1668 * q^57 - 48436 * q^58 + 14312 * q^60 + 18846 * q^61 + 44544 * q^64 + 15356 * q^65 + 221808 * q^66 + 25020 * q^68 + 81192 * q^70 + 148064 * q^72 - 236562 * q^73 + 17152 * q^74 - 140010 * q^77 + 127704 * q^78 - 277224 * q^80 + 160402 * q^81 - 391836 * q^82 - 379540 * q^84 + 71212 * q^85 - 252496 * q^86 + 55268 * q^88 - 23706 * q^89 - 190176 * q^92 - 165162 * q^93 + 359988 * q^94 + 1061736 * q^96 + 418676 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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