LMFDB - Embedded newform 29.6.d.a.16.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,6,Mod(7,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([6]))

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

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

chi := DirichletCharacter("29.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	29.d (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.65113077458$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			16.4
Character	$\chi$	$=$	29.16
Dual form			29.6.d.a.20.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.39646 - 1.63565i) q^{2} +(-13.4299 + 16.8406i) q^{3} +(-11.0911 - 13.9078i) q^{4} +(21.4922 + 10.3501i) q^{5} +(73.1594 - 35.2317i) q^{6} +(143.536 - 179.989i) q^{7} +(41.7656 + 182.987i) q^{8} +(-49.1696 - 215.426i) q^{9} +O(q^{10})$	\(q+(-3.39646 - 1.63565i) q^{2} +(-13.4299 + 16.8406i) q^{3} +(-11.0911 - 13.9078i) q^{4} +(21.4922 + 10.3501i) q^{5} +(73.1594 - 35.2317i) q^{6} +(143.536 - 179.989i) q^{7} +(41.7656 + 182.987i) q^{8} +(-49.1696 - 215.426i) q^{9} +(-56.0684 - 70.3076i) q^{10} +(58.8265 - 257.736i) q^{11} +383.166 q^{12} +(120.266 - 526.918i) q^{13} +(-781.914 + 376.550i) q^{14} +(-462.940 + 222.940i) q^{15} +(30.7800 - 134.856i) q^{16} +517.199 q^{17} +(-185.359 + 812.111i) q^{18} +(248.459 + 311.558i) q^{19} +(-94.4250 - 413.703i) q^{20} +(1103.43 + 4834.46i) q^{21} +(-621.368 + 779.171i) q^{22} +(1329.34 - 640.177i) q^{23} +(-3642.51 - 1754.14i) q^{24} +(-1593.61 - 1998.33i) q^{25} +(-1270.33 + 1592.94i) q^{26} +(-427.604 - 205.923i) q^{27} -4095.21 q^{28} +(-498.509 - 4501.40i) q^{29} +1937.01 q^{30} +(6371.32 + 3068.27i) q^{31} +(3419.67 - 4288.13i) q^{32} +(3550.38 + 4452.04i) q^{33} +(-1756.65 - 845.956i) q^{34} +(4947.82 - 2382.75i) q^{35} +(-2450.75 + 3073.15i) q^{36} +(-3056.48 - 13391.3i) q^{37} +(-334.282 - 1464.59i) q^{38} +(7258.43 + 9101.79i) q^{39} +(-996.301 + 4365.08i) q^{40} +12761.2 q^{41} +(4159.71 - 18224.9i) q^{42} +(-15326.4 + 7380.80i) q^{43} +(-4236.98 + 2040.42i) q^{44} +(1172.92 - 5138.90i) q^{45} -5562.16 q^{46} +(-4815.06 + 21096.2i) q^{47} +(1857.68 + 2329.45i) q^{48} +(-8053.39 - 35284.2i) q^{49} +(2144.08 + 9393.84i) q^{50} +(-6945.93 + 8709.92i) q^{51} +(-8662.12 + 4171.46i) q^{52} +(510.752 + 245.965i) q^{53} +(1115.52 + 1398.82i) q^{54} +(3931.91 - 4930.46i) q^{55} +(38930.5 + 18747.9i) q^{56} -8583.59 q^{57} +(-5669.55 + 16104.2i) q^{58} +24444.5 q^{59} +(8235.10 + 3965.82i) q^{60} +(-10486.0 + 13149.1i) q^{61} +(-16621.3 - 20842.5i) q^{62} +(-45831.9 - 22071.5i) q^{63} +(-22616.7 + 10891.6i) q^{64} +(8038.44 - 10079.9i) q^{65} +(-4776.76 - 20928.4i) q^{66} +(10817.3 + 47393.5i) q^{67} +(-5736.29 - 7193.08i) q^{68} +(-7071.98 + 30984.4i) q^{69} -20702.4 q^{70} +(-4971.77 + 21782.7i) q^{71} +(37366.6 - 17994.8i) q^{72} +(26519.5 - 12771.1i) q^{73} +(-11522.3 + 50482.4i) q^{74} +55055.0 q^{75} +(1577.40 - 6911.02i) q^{76} +(-37945.8 - 47582.6i) q^{77} +(-9765.66 - 42786.1i) q^{78} +(-3907.17 - 17118.4i) q^{79} +(2057.30 - 2579.78i) q^{80} +(57587.9 - 27732.9i) q^{81} +(-43342.8 - 20872.8i) q^{82} +(-28334.8 - 35530.8i) q^{83} +(54998.3 - 68965.6i) q^{84} +(11115.8 + 5353.07i) q^{85} +64127.9 q^{86} +(82501.1 + 52058.2i) q^{87} +49619.2 q^{88} +(67440.1 + 32477.4i) q^{89} +(-12389.2 + 15535.6i) q^{90} +(-77576.8 - 97278.3i) q^{91} +(-23647.3 - 11387.9i) q^{92} +(-137238. + 66090.1i) q^{93} +(50860.1 - 63776.5i) q^{94} +(2115.28 + 9267.66i) q^{95} +(26288.7 + 115178. i) q^{96} +(-107572. - 134891. i) q^{97} +(-30359.6 + 133014. i) q^{98} -58415.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 11 q^{2} - 5 q^{3} - 171 q^{4} + 29 q^{5} + 445 q^{6} + 17 q^{7} + 1046 q^{8} - 732 q^{9}+O(q^{10}) $ 66 * q - 11 * q^2 - 5 * q^3 - 171 * q^4 + 29 * q^5 + 445 * q^6 + 17 * q^7 + 1046 * q^8 - 732 * q^9	\( 66 q - 11 q^{2} - 5 q^{3} - 171 q^{4} + 29 q^{5} + 445 q^{6} + 17 q^{7} + 1046 q^{8} - 732 q^{9} - 141 q^{10} + 1125 q^{11} - 248 q^{12} - 1789 q^{13} + 1233 q^{14} + 1061 q^{15} + 2629 q^{16} + 676 q^{17} - 10896 q^{18} - 1903 q^{19} + 4081 q^{20} - 439 q^{21} - 2980 q^{22} + 9945 q^{23} + 10741 q^{24} - 22114 q^{25} - 1641 q^{26} - 4427 q^{27} + 7508 q^{28} - 13100 q^{29} - 40018 q^{30} + 8541 q^{31} + 18996 q^{32} + 20725 q^{33} - 8839 q^{34} + 14127 q^{35} + 70172 q^{36} + 3791 q^{37} + 36322 q^{38} + 25843 q^{39} - 72621 q^{40} - 18720 q^{41} - 72614 q^{42} - 10419 q^{43} + 35796 q^{44} + 23163 q^{45} + 15848 q^{46} - 40549 q^{47} - 4194 q^{48} + 19808 q^{49} + 201932 q^{50} + 51998 q^{51} + 8330 q^{52} - 72275 q^{53} - 197108 q^{54} + 42183 q^{55} + 31599 q^{56} - 40162 q^{57} - 258031 q^{58} - 333512 q^{59} + 26920 q^{60} - 175281 q^{61} + 213745 q^{62} + 354423 q^{63} - 19790 q^{64} - 79593 q^{65} + 103783 q^{66} + 135179 q^{67} + 334644 q^{68} + 73673 q^{69} - 511678 q^{70} - 187563 q^{71} - 17551 q^{72} - 56675 q^{73} + 159980 q^{74} + 538208 q^{75} - 215041 q^{76} + 106099 q^{77} + 37481 q^{78} + 273775 q^{79} + 571652 q^{80} - 61356 q^{81} - 37092 q^{82} - 237831 q^{83} + 127523 q^{84} - 148844 q^{85} - 348400 q^{86} - 110493 q^{87} - 985638 q^{88} + 74239 q^{89} - 630714 q^{90} + 100309 q^{91} + 132694 q^{92} - 307921 q^{93} + 206074 q^{94} + 37965 q^{95} + 687094 q^{96} + 136055 q^{97} - 115704 q^{98} + 438608 q^{99}+O(q^{100}) \) 66 * q - 11 * q^2 - 5 * q^3 - 171 * q^4 + 29 * q^5 + 445 * q^6 + 17 * q^7 + 1046 * q^8 - 732 * q^9 - 141 * q^10 + 1125 * q^11 - 248 * q^12 - 1789 * q^13 + 1233 * q^14 + 1061 * q^15 + 2629 * q^16 + 676 * q^17 - 10896 * q^18 - 1903 * q^19 + 4081 * q^20 - 439 * q^21 - 2980 * q^22 + 9945 * q^23 + 10741 * q^24 - 22114 * q^25 - 1641 * q^26 - 4427 * q^27 + 7508 * q^28 - 13100 * q^29 - 40018 * q^30 + 8541 * q^31 + 18996 * q^32 + 20725 * q^33 - 8839 * q^34 + 14127 * q^35 + 70172 * q^36 + 3791 * q^37 + 36322 * q^38 + 25843 * q^39 - 72621 * q^40 - 18720 * q^41 - 72614 * q^42 - 10419 * q^43 + 35796 * q^44 + 23163 * q^45 + 15848 * q^46 - 40549 * q^47 - 4194 * q^48 + 19808 * q^49 + 201932 * q^50 + 51998 * q^51 + 8330 * q^52 - 72275 * q^53 - 197108 * q^54 + 42183 * q^55 + 31599 * q^56 - 40162 * q^57 - 258031 * q^58 - 333512 * q^59 + 26920 * q^60 - 175281 * q^61 + 213745 * q^62 + 354423 * q^63 - 19790 * q^64 - 79593 * q^65 + 103783 * q^66 + 135179 * q^67 + 334644 * q^68 + 73673 * q^69 - 511678 * q^70 - 187563 * q^71 - 17551 * q^72 - 56675 * q^73 + 159980 * q^74 + 538208 * q^75 - 215041 * q^76 + 106099 * q^77 + 37481 * q^78 + 273775 * q^79 + 571652 * q^80 - 61356 * q^81 - 37092 * q^82 - 237831 * q^83 + 127523 * q^84 - 148844 * q^85 - 348400 * q^86 - 110493 * q^87 - 985638 * q^88 + 74239 * q^89 - 630714 * q^90 + 100309 * q^91 + 132694 * q^92 - 307921 * q^93 + 206074 * q^94 + 37965 * q^95 + 687094 * q^96 + 136055 * q^97 - 115704 * q^98 + 438608 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{7}\right)$

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 $

$2$	−3.39646	−	1.63565i	−0.600415	−	0.289145i	0.108882	−	0.994055i	$-0.465273\pi$
$2$	−3.39646	−	1.63565i	−0.600415	−	0.289145i	−0.709297	+	0.704910i	$0.750987\pi$
$3$	−13.4299	+	16.8406i	−0.861528	+	1.08032i	0.134467	+	0.990918i	$0.457068\pi$
$3$	−13.4299	+	16.8406i	−0.861528	+	1.08032i	−0.995995	+	0.0894039i	$0.971504\pi$
$4$	−11.0911	−	13.9078i	−0.346596	−	0.434618i
$5$	21.4922	+	10.3501i	0.384465	+	0.185149i	0.616125	−	0.787648i	$-0.288702\pi$
$5$	21.4922	+	10.3501i	0.384465	+	0.185149i	−0.231660	+	0.972797i	$0.574416\pi$
$6$	73.1594	−	35.2317i	0.829644	−	0.399535i
$7$	143.536	−	179.989i	1.10718	−	1.38835i	0.193896	−	0.981022i	$-0.437888\pi$
$7$	143.536	−	179.989i	1.10718	−	1.38835i	0.913280	−	0.407332i	$-0.133541\pi$
$8$	41.7656	+	182.987i	0.230724	+	1.01087i
$9$	−49.1696	−	215.426i	−0.202344	−	0.886527i
$10$	−56.0684	−	70.3076i	−0.177304	−	0.222332i
$11$	58.8265	−	257.736i	0.146586	−	0.642234i	−0.847233	−	0.531221i	$-0.821733\pi$
$11$	58.8265	−	257.736i	0.146586	−	0.642234i	0.993819	−	0.111013i	$-0.0354095\pi$
$12$	383.166			0.768129
$13$	120.266	−	526.918i	0.197371	−	0.864738i	−0.775123	−	0.631810i	$-0.782312\pi$
$13$	120.266	−	526.918i	0.197371	−	0.864738i	0.972494	−	0.232928i	$-0.0748306\pi$
$14$	−781.914	+	376.550i	−1.06620	+	0.513455i
$15$	−462.940	+	222.940i	−0.531247	+	0.255835i
$16$	30.7800	−	134.856i	0.0300586	−	0.131695i
$17$	517.199			0.434046			0.217023	−	0.976167i	$-0.430365\pi$
$17$	517.199			0.434046			0.217023	+	0.976167i	$0.430365\pi$
$18$	−185.359	+	812.111i	−0.134844	+	0.590791i
$19$	248.459	+	311.558i	0.157896	+	0.197995i	0.854486	−	0.519474i	$-0.173872\pi$
$19$	248.459	+	311.558i	0.157896	+	0.197995i	−0.696590	+	0.717469i	$0.745301\pi$
$20$	−94.4250	−	413.703i	−0.0527852	−	0.231267i
$21$	1103.43	+	4834.46i	0.546007	+	2.39221i
$22$	−621.368	+	779.171i	−0.273711	+	0.343223i
$23$	1329.34	−	640.177i	0.523983	−	0.252337i	−0.153143	−	0.988204i	$-0.548940\pi$
$23$	1329.34	−	640.177i	0.523983	−	0.252337i	0.677126	+	0.735867i	$0.263225\pi$
$24$	−3642.51	−	1754.14i	−1.29084	−	0.621636i
$25$	−1593.61	−	1998.33i	−0.509957	−	0.639465i
$26$	−1270.33	+	1592.94i	−0.368539	+	0.462133i
$27$	−427.604	−	205.923i	−0.112884	−	0.0543621i
$28$	−4095.21			−0.987146
$29$	−498.509	−	4501.40i	−0.110072	−	0.993924i
$29$	−498.509	−	4501.40i	−0.110072	−	0.993924i
$30$	1937.01			0.392942
$31$	6371.32	+	3068.27i	1.19076	+	0.573441i	0.921029	−	0.389493i	$-0.127350\pi$
$31$	6371.32	+	3068.27i	1.19076	+	0.573441i	0.269734	+	0.962935i	$0.413064\pi$
$32$	3419.67	−	4288.13i	0.590349	−	0.740274i
$33$	3550.38	+	4452.04i	0.567532	+	0.711662i
$34$	−1756.65	−	845.956i	−0.260608	−	0.125502i
$35$	4947.82	−	2382.75i	0.682722	−	0.328782i
$36$	−2450.75	+	3073.15i	−0.315169	+	0.395209i
$37$	−3056.48	−	13391.3i	−0.367043	−	1.60812i	−0.734857	−	0.678222i	$-0.762751\pi$
$37$	−3056.48	−	13391.3i	−0.367043	−	1.60812i	0.367814	−	0.929899i	$-0.380106\pi$
$38$	−334.282	−	1464.59i	−0.0375539	−	0.164534i
$39$	7258.43	+	9101.79i	0.764155	+	0.958220i
$40$	−996.301	+	4365.08i	−0.0984556	+	0.431362i
$41$	12761.2			1.18558			0.592789	−	0.805358i	$-0.298027\pi$
$41$	12761.2			1.18558			0.592789	+	0.805358i	$0.298027\pi$
$42$	4159.71	−	18224.9i	0.363865	−	1.59420i
$43$	−15326.4	+	7380.80i	−1.26406	+	0.608741i	−0.941246	−	0.337721i	$-0.890344\pi$
$43$	−15326.4	+	7380.80i	−1.26406	+	0.608741i	−0.322817	+	0.946462i	$0.604630\pi$
$44$	−4236.98	+	2040.42i	−0.329932	+	0.158887i
$45$	1172.92	−	5138.90i	0.0863450	−	0.378302i
$46$	−5562.16			−0.387569
$47$	−4815.06	+	21096.2i	−0.317949	+	1.39302i	0.523195	+	0.852213i	$0.324740\pi$
$47$	−4815.06	+	21096.2i	−0.317949	+	1.39302i	−0.841144	+	0.540811i	$0.818117\pi$
$48$	1857.68	+	2329.45i	0.116377	+	0.145932i
$49$	−8053.39	−	35284.2i	−0.479169	−	2.09938i
$50$	2144.08	+	9393.84i	0.121288	+	0.531396i
$51$	−6945.93	+	8709.92i	−0.373942	+	0.468909i
$52$	−8662.12	+	4171.46i	−0.444238	+	0.213934i
$53$	510.752	+	245.965i	0.0249759	+	0.0120277i	0.446330	−	0.894868i	$-0.352731\pi$
$53$	510.752	+	245.965i	0.0249759	+	0.0120277i	−0.421354	+	0.906896i	$0.638445\pi$
$54$	1115.52	+	1398.82i	0.0520588	+	0.0652797i
$55$	3931.91	−	4930.46i	0.175266	−	0.219776i
$56$	38930.5	+	18747.9i	1.65890	+	0.798883i
$57$	−8583.59			−0.349930
$58$	−5669.55	+	16104.2i	−0.221299	+	0.628594i
$59$	24444.5			0.914219			0.457110	−	0.889410i	$-0.348885\pi$
$59$	24444.5			0.914219			0.457110	+	0.889410i	$0.348885\pi$
$60$	8235.10	+	3965.82i	0.295319	+	0.142218i
$61$	−10486.0	+	13149.1i	−0.360817	+	0.452450i	−0.928795	−	0.370593i	$-0.879154\pi$
$61$	−10486.0	+	13149.1i	−0.360817	+	0.452450i	0.567978	+	0.823044i	$0.307726\pi$
$62$	−16621.3	−	20842.5i	−0.549145	−	0.688606i
$63$	−45831.9	−	22071.5i	−1.45484	−	0.700616i
$64$	−22616.7	+	10891.6i	−0.690206	+	0.332385i
$65$	8038.44	−	10079.9i	0.235987	−	0.295918i
$66$	−4776.76	−	20928.4i	−0.134981	−	0.591392i
$67$	10817.3	+	47393.5i	0.294395	+	1.28983i	0.878340	+	0.478036i	$0.158651\pi$
$67$	10817.3	+	47393.5i	0.294395	+	1.28983i	−0.583946	+	0.811793i	$0.698492\pi$
$68$	−5736.29	−	7193.08i	−0.150438	−	0.188644i
$69$	−7071.98	+	30984.4i	−0.178821	+	0.783465i
$70$	−20702.4			−0.504982
$71$	−4971.77	+	21782.7i	−0.117048	+	0.512822i	0.882081	+	0.471098i	$0.156142\pi$
$71$	−4971.77	+	21782.7i	−0.117048	+	0.512822i	−0.999129	+	0.0417239i	$0.986715\pi$
$72$	37366.6	−	17994.8i	0.849478	−	0.409087i
$73$	26519.5	−	12771.1i	0.582449	−	0.280492i	−0.119368	−	0.992850i	$-0.538087\pi$
$73$	26519.5	−	12771.1i	0.582449	−	0.280492i	0.701817	+	0.712358i	$0.252373\pi$
$74$	−11522.3	+	50482.4i	−0.244601	+	1.07167i
$75$	55055.0			1.13017
$76$	1577.40	−	6911.02i	0.0313261	−	0.137249i
$77$	−37945.8	−	47582.6i	−0.729352	−	0.914579i
$78$	−9765.66	−	42786.1i	−0.181746	−	0.796281i
$79$	−3907.17	−	17118.4i	−0.0704359	−	0.308600i	0.927422	−	0.374016i	$-0.122020\pi$
$79$	−3907.17	−	17118.4i	−0.0704359	−	0.308600i	−0.997858	+	0.0654164i	$0.979162\pi$
$80$	2057.30	−	2579.78i	0.0359396	−	0.0450669i
$81$	57587.9	−	27732.9i	0.975256	−	0.469658i
$82$	−43342.8	−	20872.8i	−0.711840	−	0.342804i
$83$	−28334.8	−	35530.8i	−0.451466	−	0.566121i	0.503058	−	0.864252i	$-0.332208\pi$
$83$	−28334.8	−	35530.8i	−0.451466	−	0.566121i	−0.954525	+	0.298131i	$0.903637\pi$
$84$	54998.3	−	68965.6i	0.850454	−	1.06644i
$85$	11115.8	+	5353.07i	0.166875	+	0.0803629i
$86$	64127.9			0.934977
$87$	82501.1	+	52058.2i	1.16859	+	0.737379i
$88$	49619.2			0.683036
$89$	67440.1	+	32477.4i	0.902492	+	0.434617i	0.826788	−	0.562513i	$-0.190166\pi$
$89$	67440.1	+	32477.4i	0.902492	+	0.434617i	0.0757034	+	0.997130i	$0.475880\pi$
$90$	−12389.2	+	15535.6i	−0.161227	+	0.202172i
$91$	−77576.8	−	97278.3i	−0.982039	−	1.23144i
$92$	−23647.3	−	11387.9i	−0.291280	−	0.140273i
$93$	−137238.	+	66090.1i	−1.64538	+	0.792372i
$94$	50860.1	−	63776.5i	0.593687	−	0.744460i
$95$	2115.28	+	9267.66i	0.0240469	+	0.105356i
$96$	26288.7	+	115178.i	0.291132	+	1.27553i
$97$	−107572.	−	134891.i	−1.16083	−	1.45564i	−0.865969	−	0.500097i	$-0.833298\pi$
$97$	−107572.	−	134891.i	−1.16083	−	1.45564i	−0.294862	−	0.955540i	$-0.595274\pi$
$98$	−30359.6	+	133014.i	−0.319323	+	1.39905i
$99$	−58415.5			−0.599019
$100$	−10117.4	+	44327.2i	−0.101174	+	0.443272i
$101$	−169298.	+	81529.8i	−1.65139	+	0.795267i	−0.652077	+	0.758152i	$0.726102\pi$
$101$	−169298.	+	81529.8i	−1.65139	+	0.795267i	−0.999311	+	0.0371143i	$0.988183\pi$
$102$	37838.0	−	18221.8i	0.360103	−	0.173417i
$103$	−2113.68	+	9260.63i	−0.0196312	+	0.0860097i	−0.983795	−	0.179299i	$-0.942617\pi$
$103$	−2113.68	+	9260.63i	−0.0196312	+	0.0860097i	0.964163	+	0.265309i	$0.0854740\pi$
$104$	101442.			0.919676
$105$	−26322.0	+	115324.i	−0.232994	+	1.02081i
$106$	−1332.44	−	1670.82i	−0.0115181	−	0.0144433i
$107$	−22198.4	−	97257.7i	−0.187440	−	0.821230i	−0.977960	−	0.208793i	$-0.933047\pi$
$107$	−22198.4	−	97257.7i	−0.187440	−	0.821230i	0.790520	−	0.612437i	$-0.209811\pi$
$108$	1878.66	+	8230.93i	0.0154984	+	0.0679031i
$109$	−93380.9	+	117096.i	−0.752821	+	0.944008i	−0.999686	−	0.0250418i	$-0.992028\pi$
$109$	−93380.9	+	117096.i	−0.752821	+	0.944008i	0.246865	+	0.969050i	$0.420600\pi$
$110$	−21419.1	+	10314.9i	−0.168779	+	0.0812799i
$111$	266565.	+	128371.i	2.05351	+	0.988916i
$112$	−19854.5	−	24896.8i	−0.149559	−	0.187542i
$113$	92832.8	−	116409.i	0.683920	−	0.857608i	−0.311789	−	0.950151i	$-0.600928\pi$
$113$	92832.8	−	116409.i	0.683920	−	0.857608i	0.995709	+	0.0925430i	$0.0294995\pi$
$114$	29153.8	+	14039.7i	0.210104	+	0.101181i
$115$	35196.4			0.248173
$116$	−57075.5	+	56858.5i	−0.393826	+	0.392329i
$117$	−119425.			−0.806551
$118$	−83024.7	−	39982.6i	−0.548911	−	0.264342i
$119$	74236.8	−	93090.0i	0.480565	−	0.602609i
$120$	−60130.1	−	75400.8i	−0.381188	−	0.477994i
$121$	82134.7	+	39554.0i	0.509992	+	0.245599i
$122$	57122.7	−	27508.9i	0.347464	−	0.167330i
$123$	−171381.	+	214905.i	−1.02141	+	1.28081i
$124$	−27992.1	−	122641.i	−0.163486	−	0.716279i
$125$	−30155.4	−	132119.i	−0.172619	−	0.756295i
$126$	119565.	+	149930.i	0.670931	+	0.841321i
$127$	−17114.4	+	74983.0i	−0.0941568	+	0.412528i	−0.999937	−	0.0112197i	$-0.996429\pi$
$127$	−17114.4	+	74983.0i	−0.0941568	+	0.412528i	0.905780	+	0.423748i	$0.139286\pi$
$128$	−80879.5			−0.436329
$129$	81535.0	−	357228.i	0.431390	−	1.89004i
$130$	−43789.4	+	21087.9i	−0.227254	+	0.109440i
$131$	132312.	−	63718.1i	0.673629	−	0.324403i	−0.0656104	−	0.997845i	$-0.520899\pi$
$131$	132312.	−	63718.1i	0.673629	−	0.324403i	0.739239	+	0.673443i	$0.235185\pi$
$132$	22540.4	−	98755.7i	0.112597	−	0.493319i
$133$	91739.8			0.449706
$134$	40778.8	−	178664.i	0.196188	−	0.859555i
$135$	−7058.85	−	8851.51i	−0.0333349	−	0.0418007i
$136$	21601.1	+	94640.7i	0.100145	+	0.438764i
$137$	84548.9	+	370433.i	0.384863	+	1.68620i	0.681992	+	0.731359i	$0.261114\pi$
$137$	84548.9	+	370433.i	0.384863	+	1.68620i	−0.297129	+	0.954837i	$0.596029\pi$
$138$	74699.3	−	93669.9i	0.333902	−	0.418699i
$139$	−42668.6	+	20548.1i	−0.187314	+	0.0902059i	−0.525190	−	0.850985i	$-0.676006\pi$
$139$	−42668.6	+	20548.1i	−0.187314	+	0.0902059i	0.337876	+	0.941191i	$0.390292\pi$
$140$	−88015.3	−	42385.9i	−0.379523	−	0.182769i
$141$	−290605.	−	364407.i	−1.23099	−	1.54362i
$142$	52515.3	−	65852.2i	0.218557	−	0.274062i
$143$	−128731.	−	61993.5i	−0.526432	−	0.253516i
$144$	−30564.9			−0.122834
$145$	35876.0	−	101905.i	0.141705	−	0.402508i
$146$	−110961.			−0.430814
$147$	702362.	+	338240.i	2.68082	+	1.29101i
$148$	−152344.	+	191033.i	−0.571702	+	0.716892i
$149$	114698.	+	143827.i	0.423245	+	0.530732i	0.947042	−	0.321111i	$-0.104056\pi$
$149$	114698.	+	143827.i	0.423245	+	0.530732i	−0.523797	+	0.851843i	$0.675485\pi$
$150$	−186992.	−	90050.7i	−0.678571	−	0.326783i
$151$	146410.	−	70507.5i	0.522552	−	0.251648i	−0.153963	−	0.988077i	$-0.549204\pi$
$151$	146410.	−	70507.5i	0.522552	−	0.251648i	0.676515	+	0.736429i	$0.263489\pi$
$152$	−46634.0	+	58477.2i	−0.163717	+	0.205295i
$153$	−25430.5	−	111418.i	−0.0878266	−	0.384793i
$154$	51053.2	+	223678.i	0.173469	+	0.760015i
$155$	105177.	+	131888.i	0.351635	+	0.440936i
$156$	46081.7	−	201897.i	0.151606	−	0.664230i
$157$	208213.			0.674153			0.337076	−	0.941477i	$-0.390562\pi$
$157$	208213.			0.674153			0.337076	+	0.941477i	$0.390562\pi$
$158$	−14729.2	+	64532.8i	−0.0469392	+	0.205654i
$159$	−11001.5	+	5298.06i	−0.0345112	+	0.0166197i
$160$	117879.	−	56767.5i	0.364029	−	0.175307i
$161$	75584.0	−	331155.i	0.229808	−	1.00685i
$162$	−240956.			−0.721358
$163$	−20705.2	+	90715.6i	−0.0610396	+	0.267432i	−0.996234	−	0.0867021i	$-0.972367\pi$
$163$	−20705.2	+	90715.6i	−0.0610396	+	0.267432i	0.935195	+	0.354134i	$0.115224\pi$
$164$	−141535.	−	177479.i	−0.410917	−	0.515273i
$165$	30226.5	+	132431.i	0.0864328	+	0.378687i
$166$	38122.3	+	167025.i	0.107376	+	0.470447i
$167$	−198195.	+	248529.i	−0.549922	+	0.689581i	−0.976659	−	0.214795i	$-0.931092\pi$
$167$	−198195.	+	248529.i	−0.549922	+	0.689581i	0.426737	+	0.904376i	$0.359663\pi$
$168$	−838558.	+	403828.i	−2.29224	+	1.10388i
$169$	71344.8	+	34357.9i	0.192152	+	0.0925357i
$170$	−28998.5	−	36363.0i	−0.0769580	−	0.0965023i
$171$	54901.1	−	68843.8i	0.143579	−	0.180042i
$172$	272636.	+	131295.i	0.702688	+	0.338397i
$173$	−325635.			−0.827210			−0.413605	−	0.910456i	$-0.635731\pi$
$173$	−325635.			−0.827210			−0.413605	+	0.910456i	$0.635731\pi$
$174$	−195063.	−	311757.i	−0.488429	−	0.780625i
$175$	−588418.			−1.45242
$176$	−32946.5	−	15866.2i	−0.0801729	−	0.0386093i
$177$	−328286.	+	411658.i	−0.787625	+	0.987651i
$178$	−175936.	−	220617.i	−0.416202	−	0.521901i
$179$	459172.	+	221125.i	1.07113	+	0.515829i	0.884471	−	0.466595i	$-0.154519\pi$
$179$	459172.	+	221125.i	1.07113	+	0.515829i	0.186660	+	0.982425i	$0.440234\pi$
$180$	−84479.6	+	40683.2i	−0.194344	+	0.0935910i
$181$	376472.	−	472081.i	0.854155	−	1.07108i	−0.142536	−	0.989790i	$-0.545526\pi$
$181$	376472.	−	472081.i	0.854155	−	1.07108i	0.996691	−	0.0812865i	$-0.0259029\pi$
$182$	104374.	+	457290.i	0.233567	+	1.02333i
$183$	−80611.4	−	353182.i	−0.177938	−	0.779597i
$184$	172665.	+	216515.i	0.375975	+	0.471458i
$185$	72911.0	−	319444.i	0.156626	−	0.686224i
$186$	574222.			1.21702
$187$	30425.0	−	133301.i	0.0636249	−	0.278759i
$188$	346805.	−	167012.i	0.715633	−	0.344630i
$189$	−98440.6	+	47406.5i	−0.200456	+	0.0965347i
$190$	7974.17	−	34937.1i	0.0160251	−	0.0702107i
$191$	429708.			0.852296			0.426148	−	0.904653i	$-0.359870\pi$
$191$	429708.			0.852296			0.426148	+	0.904653i	$0.359870\pi$
$192$	120319.	−	527150.i	0.235548	−	1.03200i
$193$	50882.2	+	63804.3i	0.0983270	+	0.123298i	0.828561	−	0.559899i	$-0.189160\pi$
$193$	50882.2	+	63804.3i	0.0983270	+	0.123298i	−0.730234	+	0.683198i	$0.760589\pi$
$194$	144729.	+	634101.i	0.276091	+	1.20963i
$195$	61795.4	+	270743.i	0.116378	+	0.509884i
$196$	−401404.	+	503345.i	−0.746348	+	0.935891i
$197$	−632082.	+	304395.i	−1.16040	+	0.558819i	−0.912142	−	0.409875i	$-0.865572\pi$
$197$	−632082.	+	304395.i	−1.16040	+	0.558819i	−0.248258	+	0.968694i	$0.579858\pi$
$198$	198406.	+	95547.3i	0.359660	+	0.173203i
$199$	389672.	+	488634.i	0.697537	+	0.874683i	0.996837	−	0.0794759i	$-0.0253247\pi$
$199$	389672.	+	488634.i	0.697537	+	0.874683i	−0.299300	+	0.954159i	$0.596753\pi$
$200$	299110.	−	375072.i	0.528757	−	0.663040i
$201$	−943408.	−	454321.i	−1.64706	−	0.793182i
$202$	708369.			1.22147
$203$	−881756.	−	556389.i	−1.50179	−	0.947629i
$204$	198173.			0.333403
$205$	274266.	+	132079.i	0.455813	+	0.219508i
$206$	22326.2	−	27996.1i	0.0366561	−	0.0459653i
$207$	−203274.	−	254898.i	−0.329728	−	0.413466i
$208$	−67356.2	−	32437.0i	−0.107949	−	0.0519856i
$209$	94915.7	−	45709.0i	0.150305	−	0.0723829i
$210$	278031.	−	348640.i	0.435056	−	0.545543i
$211$	−10107.3	−	44283.0i	−0.0156289	−	0.0684748i	0.966512	−	0.256621i	$-0.0826092\pi$
$211$	−10107.3	−	44283.0i	−0.0156289	−	0.0684748i	−0.982141	+	0.188146i	$0.939752\pi$
$212$	−2243.96	−	9831.44i	−0.00342907	−	0.0150237i
$213$	−300063.	−	376267.i	−0.453172	−	0.568260i
$214$	−83683.4	+	366641.i	−0.124912	+	0.547276i
$215$	−405791.			−0.598695
$216$	19822.2	−	86846.6i	0.0289079	−	0.126654i
$217$	1.46677e6	−	706359.i	2.11452	−	1.01830i
$218$	508693.	−	244973.i	0.724960	−	0.349123i
$219$	−141081.	+	618117.i	−0.198774	+	0.870884i
$220$	−112181.			−0.156265
$221$	62201.2	−	272521.i	0.0856679	−	0.375336i
$222$	−695408.	−	872015.i	−0.947016	−	1.18752i
$223$	−6099.27	−	26722.6i	−0.00821326	−	0.0359846i	0.970655	−	0.240475i	$-0.0773033\pi$
$223$	−6099.27	−	26722.6i	−0.00821326	−	0.0359846i	−0.978869	+	0.204491i	$0.934446\pi$
$224$	−280968.	−	1.23100e6i	−0.374143	−	1.63923i
$225$	−352135.	+	441563.i	−0.463717	+	0.581482i
$226$	−505707.	+	243536.i	−0.658609	+	0.317169i
$227$	923273.	+	444625.i	1.18923	+	0.572702i	0.920587	−	0.390538i	$-0.127711\pi$
$227$	923273.	+	444625.i	1.18923	+	0.572702i	0.268642	+	0.963240i	$0.413425\pi$
$228$	95201.2	+	119379.i	0.121284	+	0.152086i
$229$	−292922.	+	367312.i	−0.369116	+	0.462857i	−0.931352	−	0.364120i	$-0.881370\pi$
$229$	−292922.	+	367312.i	−0.369116	+	0.462857i	0.562236	+	0.826977i	$0.309941\pi$
$230$	−119543.	−	57569.1i	−0.149007	−	0.0717579i
$231$	1.31093e6			1.61640
$232$	802878.	−	279225.i	0.979331	−	0.340591i
$233$	−1.13204e6			−1.36606			−0.683031	−	0.730389i	$-0.739339\pi$
$233$	−1.13204e6			−1.36606			−0.683031	+	0.730389i	$0.739339\pi$
$234$	405623.	+	195338.i	0.484265	+	0.233210i
$235$	−321834.	+	403567.i	−0.380157	+	0.476701i
$236$	−271115.	−	339968.i	−0.316865	−	0.397336i
$237$	340756.	+	164100.i	0.394070	+	0.189774i
$238$	−404405.	+	194751.i	−0.462780	+	0.222863i
$239$	−864680.	+	1.08427e6i	−0.979176	+	1.22785i	−0.00548252	+	0.999985i	$0.501745\pi$
$239$	−864680.	+	1.08427e6i	−0.979176	+	1.22785i	−0.973693	+	0.227863i	$0.926826\pi$
$240$	15815.5	+	69292.3i	0.0177237	+	0.0776527i
$241$	14045.8	+	61538.5i	0.0155777	+	0.0682503i	0.982119	−	0.188259i	$-0.0602846\pi$
$241$	14045.8	+	61538.5i	0.0155777	+	0.0682503i	−0.966542	+	0.256510i	$0.917427\pi$
$242$	−214271.	−	268687.i	−0.235193	−	0.294923i
$243$	−280699.	+	1.22982e6i	−0.304948	+	1.33606i
$244$	299176.			0.321701
$245$	192110.	−	841691.i	0.204473	−	0.895854i
$246$	933598.	−	449597.i	0.983608	−	0.473681i
$247$	194047.	−	93447.9i	0.202378	−	0.0974601i
$248$	−295351.	+	1.29402e6i	−0.304936	+	1.33601i
$249$	978891.			1.00054
$250$	−113679.	+	498062.i	−0.115035	+	0.504003i
$251$	−125163.	−	156949.i	−0.125398	−	0.157244i	0.715169	−	0.698951i	$-0.246350\pi$
$251$	−125163.	−	156949.i	−0.125398	−	0.157244i	−0.840567	+	0.541707i	$0.817778\pi$
$252$	201360.	+	882216.i	0.199743	+	0.875132i
$253$	−86796.1	−	380279.i	−0.0852509	−	0.373508i
$254$	180774.	−	226684.i	0.175814	−	0.220463i
$255$	−239432.	+	115304.i	−0.230586	+	0.111044i
$256$	998437.	+	480822.i	0.952184	+	0.458548i
$257$	−716139.	−	898010.i	−0.676340	−	0.848103i	0.318672	−	0.947865i	$-0.396763\pi$
$257$	−716139.	−	898010.i	−0.676340	−	0.848103i	−0.995011	+	0.0997622i	$0.968192\pi$
$258$	−861231.	+	1.07995e6i	−0.805509	+	1.01008i
$259$	−2.84900e6	−	1.37201e6i	−2.63902	−	1.27089i
$260$	−229344.			−0.210404
$261$	−945208.	+	328724.i	−0.858868	+	0.298697i
$262$	−553613.			−0.498257
$263$	3606.17	+	1736.64i	0.00321482	+	0.00154817i	0.435490	−	0.900193i	$-0.356575\pi$
$263$	3606.17	+	1736.64i	0.00321482	+	0.00154817i	−0.432276	+	0.901742i	$0.642289\pi$
$264$	−666381.	+	835616.i	−0.588454	+	0.737899i
$265$	8431.44	+	10572.7i	0.00737543	+	0.00924849i
$266$	−311591.	−	150054.i	−0.270010	−	0.130030i
$267$	−1.45265e6	+	699560.i	−1.24705	+	0.600547i
$268$	539163.	−	676089.i	0.458546	−	0.574999i
$269$	404375.	+	1.77168e6i	0.340724	+	1.49281i	0.797549	+	0.603254i	$0.206129\pi$
$269$	404375.	+	1.77168e6i	0.340724	+	1.49281i	−0.456825	+	0.889557i	$0.651013\pi$
$270$	9497.13	+	41609.6i	0.00792835	+	0.0347364i
$271$	91020.0	+	114135.i	0.0752859	+	0.0944055i	0.818048	−	0.575150i	$-0.195056\pi$
$271$	91020.0	+	114135.i	0.0752859	+	0.0944055i	−0.742762	+	0.669555i	$0.766485\pi$
$272$	15919.4	−	69747.3i	0.0130468	−	0.0571617i
$273$	2.68007e6			2.17640
$274$	318732.	−	1.39645e6i	0.256477	−	1.12370i
$275$	−608788.	+	293177.i	−0.485439	+	0.233775i
$276$	509359.	−	245294.i	0.402486	−	0.193827i
$277$	372941.	−	1.63396e6i	0.292039	−	1.27951i	−0.589643	−	0.807664i	$-0.700732\pi$
$277$	372941.	−	1.63396e6i	0.292039	−	1.27951i	0.881682	−	0.471843i	$-0.156411\pi$
$278$	178532.			0.138549
$279$	347710.	−	1.52342e6i	0.267428	−	1.17168i
$280$	642660.	+	805870.i	0.489876	+	0.614285i
$281$	209425.	+	917550.i	0.158220	+	0.693208i	0.990346	+	0.138621i	$0.0442668\pi$
$281$	209425.	+	917550.i	0.158220	+	0.693208i	−0.832125	+	0.554588i	$0.812876\pi$
$282$	390987.	+	1.71302e6i	0.292778	+	1.28275i
$283$	789022.	−	989402.i	0.585629	−	0.734356i	−0.397432	−	0.917631i	$-0.630099\pi$
$283$	789022.	−	989402.i	0.585629	−	0.734356i	0.983062	+	0.183276i	$0.0586701\pi$
$284$	358091.	−	172448.i	0.263450	−	0.126871i
$285$	−184481.	−	88841.2i	−0.134536	−	0.0647891i
$286$	335830.	+	421117.i	0.242775	+	0.304430i
$287$	1.83169e6	−	2.29687e6i	1.31264	−	1.64600i
$288$	−1.09192e6	−	525840.i	−0.775727	−	0.373570i
$289$	−1.15236e6			−0.811604
$290$	−288532.	+	287436.i	−0.201465	+	0.200699i
$291$	3.71631e6			2.57265
$292$	−471747.	−	227181.i	−0.323781	−	0.155925i
$293$	−630851.	+	791062.i	−0.429297	+	0.538321i	−0.948687	−	0.316216i	$-0.897588\pi$
$293$	−630851.	+	791062.i	−0.429297	+	0.538321i	0.519391	+	0.854537i	$0.326159\pi$
$294$	−1.83230e6	−	2.29764e6i	−1.23632	−	1.55029i
$295$	525366.	+	253003.i	0.351485	+	0.169266i
$296$	2.32278e6	−	1.11859e6i	1.54092	−	0.742066i
$297$	−78228.4	+	98095.3i	−0.0514604	+	0.0645293i
$298$	−154318.	−	676110.i	−0.100664	−	0.441039i
$299$	−177447.	−	777445.i	−0.114786	−	0.502912i
$300$	−610619.	−	765692.i	−0.391712	−	0.491192i
$301$	−871431.	+	3.81799e6i	−0.554392	+	2.42895i
$302$	−612602.			−0.386511
$303$	900652.	−	3.94601e6i	0.563573	−	2.46918i
$304$	49663.0	−	23916.4i	0.0308211	−	0.0148427i
$305$	−361463.	+	174071.i	−0.222492	+	0.107147i
$306$	−95867.5	+	420023.i	−0.0585286	+	0.256430i
$307$	605807.			0.366850			0.183425	−	0.983034i	$-0.441282\pi$
$307$	605807.			0.366850			0.183425	+	0.983034i	$0.441282\pi$
$308$	−240907.	+	1.05548e6i	−0.144701	+	0.633979i
$309$	−127568.	−	159965.i	−0.0760054	−	0.0953078i
$310$	−141508.	−	619985.i	−0.0836326	−	0.366418i
$311$	76521.3	+	335262.i	0.0448623	+	0.196554i	0.992393	−	0.123110i	$-0.0392869\pi$
$311$	76521.3	+	335262.i	0.0448623	+	0.196554i	−0.947531	+	0.319665i	$0.896430\pi$
$312$	−1.36236e6	+	1.70834e6i	−0.792326	+	0.993546i
$313$	−87551.5	+	42162.6i	−0.0505130	+	0.0243258i	−0.458970	−	0.888452i	$-0.651781\pi$
$313$	−87551.5	+	42162.6i	−0.0505130	+	0.0243258i	0.408457	+	0.912778i	$0.366067\pi$
$314$	−707187.	−	340563.i	−0.404771	−	0.194928i
$315$	−756588.	−	948731.i	−0.429619	−	0.538725i
$316$	−194744.	+	244201.i	−0.109710	+	0.137572i
$317$	1.63242e6	+	786132.i	0.912397	+	0.439387i	0.830350	−	0.557241i	$-0.188140\pi$
$317$	1.63242e6	+	786132.i	0.912397	+	0.439387i	0.0820461	+	0.996629i	$0.473855\pi$
$318$	46032.1			0.0255266
$319$	−1.18950e6	−	136318.i	−0.654466	−	0.0750028i
$320$	−598812.			−0.326901
$321$	1.93600e6	+	932327.i	1.04868	+	0.505017i
$322$	−798372.	+	1.00113e6i	−0.429107	+	0.538083i
$323$	128503.	+	161137.i	0.0685341	+	0.0859390i
$324$	−1.02441e6	−	493331.i	−0.542142	−	0.261082i
$325$	−1.24461e6	+	599374.i	−0.653620	+	0.314767i
$326$	218704.	−	274246.i	0.113976	−	0.142921i
$327$	−717865.	−	3.14517e6i	−0.371256	−	1.62658i
$328$	532977.	+	2.33513e6i	0.273542	+	1.19847i
$329$	3.10594e6	+	3.89472e6i	1.58199	+	1.98375i
$330$	113948.	−	499237.i	0.0575997	−	0.252361i
$331$	−95287.0			−0.0478039			−0.0239020	−	0.999714i	$-0.507609\pi$
$331$	−95287.0			−0.0478039			−0.0239020	+	0.999714i	$0.507609\pi$
$332$	−179890.	+	788148.i	−0.0895697	+	0.392431i
$333$	−2.73455e6	+	1.31689e6i	−1.35137	+	0.650787i
$334$	1.07967e6	−	519940.i	0.529570	−	0.255028i
$335$	−258041.	+	1.13055e6i	−0.125625	+	0.550401i
$336$	685919.			0.331455
$337$	86225.6	−	377779.i	0.0413582	−	0.181202i	−0.950030	−	0.312159i	$-0.898948\pi$
$337$	86225.6	−	377779.i	0.0413582	−	0.181202i	0.991388	+	0.130957i	$0.0418050\pi$
$338$	−186123.	−	233390.i	−0.0886150	−	0.111120i
$339$	713651.	+	3.12671e6i	0.337277	+	1.47771i
$340$	−48836.5	−	213967.i	−0.0229112	−	0.100380i
$341$	1.16561e6	−	1.46162e6i	0.542832	−	0.680690i
$342$	−299074.	+	144026.i	−0.138265	+	0.0665850i
$343$	−4.02068e6	−	1.93626e6i	−1.84529	−	0.888644i
$344$	−1.99071e6	−	2.49627e6i	−0.907008	−	1.13735i
$345$	−472684.	+	592728.i	−0.213808	+	0.268107i
$346$	1.10601e6	+	532625.i	0.496670	+	0.239184i
$347$	−735013.			−0.327696			−0.163848	−	0.986486i	$-0.552391\pi$
$347$	−735013.			−0.327696			−0.163848	+	0.986486i	$0.552391\pi$
$348$	−191012.	−	1.72479e6i	−0.0845498	−	0.763462i
$349$	2.51402e6			1.10486			0.552428	−	0.833561i	$-0.313701\pi$
$349$	2.51402e6			1.10486			0.552428	+	0.833561i	$0.313701\pi$
$350$	1.99854e6	+	962446.i	0.872053	+	0.419958i
$351$	−159931.	+	200547.i	−0.0692890	+	0.0868857i
$352$	−904037.	−	1.13363e6i	−0.388892	−	0.487656i
$353$	2.41397e6	+	1.16251e6i	1.03109	+	0.496546i	0.871375	−	0.490618i	$-0.163229\pi$
$353$	2.41397e6	+	1.16251e6i	1.03109	+	0.496546i	0.159713	+	0.987164i	$0.448943\pi$
$354$	1.78834e6	−	861220.i	0.758476	−	0.365263i
$355$	−332308.	+	416701.i	−0.139949	+	0.175491i
$356$	−296294.	−	1.29815e6i	−0.123908	−	0.542875i
$357$	570695.	+	2.50038e6i	0.236992	+	1.03833i
$358$	−1.19788e6	−	1.50209e6i	−0.493974	−	0.619424i
$359$	−377954.	+	1.65592e6i	−0.154776	+	0.678116i	0.836682	+	0.547688i	$0.184492\pi$
$359$	−377954.	+	1.65592e6i	−0.154776	+	0.678116i	−0.991458	+	0.130427i	$0.958365\pi$
$360$	989340.			0.402336
$361$	515647.	−	2.25920e6i	0.208250	−	0.912403i
$362$	−2.05083e6	+	987629.i	−0.822544	+	0.396116i
$363$	−1.76917e6	+	851988.i	−0.704698	+	0.339365i
$364$	−492513.	+	2.15784e6i	−0.194834	+	0.853623i
$365$	702145.			0.275864
$366$	−303888.	+	1.33142e6i	−0.118580	+	0.519532i
$367$	−1.67584e6	−	2.10144e6i	−0.649482	−	0.814425i	0.342671	−	0.939456i	$-0.388668\pi$
$367$	−1.67584e6	−	2.10144e6i	−0.649482	−	0.814425i	−0.992153	+	0.125031i	$0.960097\pi$
$368$	−45414.5	−	198974.i	−0.0174814	−	0.0765909i
$369$	−627461.	−	2.74909e6i	−0.239895	−	1.05105i
$370$	−770138.	+	965723.i	−0.292459	+	0.366732i
$371$	117582.	−	56624.7i	0.0443514	−	0.0213585i
$372$	2.44128e6	+	1.17566e6i	0.914660	+	0.440477i
$373$	−203980.	−	255783.i	−0.0759130	−	0.0951919i	0.742425	−	0.669929i	$-0.233676\pi$
$373$	−203980.	−	255783.i	−0.0759130	−	0.0951919i	−0.818338	+	0.574737i	$0.805104\pi$
$374$	−321371.	+	402986.i	−0.118803	+	0.148974i
$375$	2.62994e6	+	1.26651e6i	0.965758	+	0.465085i
$376$	−4.06143e6			−1.48152
$377$	−2.43182e6	−	278690.i	−0.881209	−	0.100988i
$378$	411890.			0.148270
$379$	−1.93937e6	−	933953.i	−0.693527	−	0.333985i	0.0536971	−	0.998557i	$-0.482899\pi$
$379$	−1.93937e6	−	933953.i	−0.693527	−	0.333985i	−0.747224	+	0.664572i	$0.768614\pi$
$380$	105432.	−	132207.i	0.0374552	−	0.0469673i
$381$	−1.03291e6	−	1.29523e6i	−0.364544	−	0.457124i
$382$	−1.45949e6	−	702853.i	−0.511732	−	0.246437i
$383$	1.40440e6	−	676326.i	0.489210	−	0.235591i	−0.172982	−	0.984925i	$-0.555340\pi$
$383$	1.40440e6	−	676326.i	0.489210	−	0.235591i	0.662193	+	0.749334i	$0.269626\pi$
$384$	1.08620e6	−	1.36206e6i	0.375909	−	0.471375i
$385$	−323056.	−	1.41540e6i	−0.111077	−	0.486662i
$386$	−68458.0	−	299934.i	−0.0233860	−	0.102461i
$387$	2.34361e6	+	2.93879e6i	0.795441	+	0.997451i
$388$	−682943.	+	2.99217e6i	−0.230306	+	1.00904i
$389$	1.61032e6			0.539560			0.269780	−	0.962922i	$-0.413049\pi$
$389$	1.61032e6			0.539560			0.269780	+	0.962922i	$0.413049\pi$
$390$	232956.	−	1.02065e6i	0.0775554	−	0.339792i
$391$	687534.	−	331099.i	0.227432	−	0.109526i
$392$	6.12020e6	−	2.94733e6i	2.01164	−	0.968755i
$393$	−703888.	+	3.08393e6i	−0.229891	+	1.00722i
$394$	2.64472e6			0.858302
$395$	93203.8	−	408353.i	0.0300567	−	0.131687i
$396$	647891.	+	812429.i	0.207617	+	0.260344i
$397$	−1.23334e6	−	5.40362e6i	−0.392742	−	1.72071i	−0.654923	−	0.755696i	$-0.727299\pi$
$397$	−1.23334e6	−	5.40362e6i	−0.392742	−	1.72071i	0.262181	−	0.965019i	$-0.415558\pi$
$398$	−524274.	−	2.29699e6i	−0.165902	−	0.726862i
$399$	−1.23206e6	+	1.54495e6i	−0.387434	+	0.485827i
$400$	−318538.	+	153400.i	−0.0995430	+	0.0479374i
$401$	2.62418e6	+	1.26374e6i	0.814953	+	0.392461i	0.794450	−	0.607329i	$-0.207759\pi$
$401$	2.62418e6	+	1.26374e6i	0.814953	+	0.392461i	0.0205025	+	0.999790i	$0.493473\pi$
$402$	2.46114e6	+	3.08617e6i	0.759575	+	0.952477i
$403$	2.38298e6	−	2.98816e6i	0.730898	−	0.916518i
$404$	3.01160e6	+	1.45031e6i	0.918002	+	0.442086i
$405$	1.52473e6			0.461908
$406$	2.08480e6	+	3.33200e6i	0.627694	+	1.00320i
$407$	−3.63122e6			−1.08659
$408$	−1.88390e6	−	907240.i	−0.560284	−	0.269818i
$409$	994516.	−	1.24708e6i	0.293970	−	0.368627i	−0.612810	−	0.790230i	$-0.709961\pi$
$409$	994516.	−	1.24708e6i	0.293970	−	0.368627i	0.906781	+	0.421603i	$0.138532\pi$
$410$	−715498.	−	897206.i	−0.210208	−	0.263592i
$411$	−7.37378e6	−	3.55103e6i	−2.15321	−	1.03693i
$412$	152238.	−	73313.8i	0.0441854	−	0.0212786i
$413$	3.50867e6	−	4.39973e6i	1.01220	−	1.26926i
$414$	273489.	+	1.19824e6i	0.0784223	+	0.343591i
$415$	−241232.	−	1.05690e6i	−0.0687565	−	0.301242i
$416$	−1.84822e6	−	2.31760e6i	−0.523626	−	0.656606i
$417$	226993.	−	994521.i	0.0639252	−	0.280075i
$418$	−397141.			−0.111174
$419$	−1.04651e6	+	4.58508e6i	−0.291213	+	1.27589i	0.591627	+	0.806212i	$0.298486\pi$
$419$	−1.04651e6	+	4.58508e6i	−0.291213	+	1.27589i	−0.882840	+	0.469674i	$0.844371\pi$
$420$	1.89584e6	−	912988.i	0.524419	−	0.252547i
$421$	−4.09132e6	+	1.97028e6i	−1.12502	+	0.541779i	−0.901439	−	0.432907i	$-0.857488\pi$
$421$	−4.09132e6	+	1.97028e6i	−1.12502	+	0.541779i	−0.223577	+	0.974686i	$0.571774\pi$
$422$	−38102.4	+	166938.i	−0.0104153	+	0.0456324i
$423$	4.78142e6			1.29929
$424$	−23676.6	+	103734.i	−0.00639594	+	0.0280224i
$425$	−824216.	−	1.03353e6i	−0.221344	−	0.277557i
$426$	403711.	+	1.76877e6i	0.107782	+	0.472224i
$427$	861560.	+	3.77474e6i	0.228673	+	1.00188i
$428$	−1.10643e6	+	1.38742e6i	−0.291955	+	0.366100i
$429$	2.77285e6	−	1.33533e6i	0.727416	−	0.350305i
$430$	1.37825e6	+	663731.i	0.359466	+	0.173110i
$431$	−3.80657e6	−	4.77328e6i	−0.987053	−	1.23773i	−0.971302	−	0.237849i	$-0.923558\pi$
$431$	−3.80657e6	−	4.77328e6i	−0.987053	−	1.23773i	−0.0157507	−	0.999876i	$-0.505014\pi$
$432$	−40931.6	+	51326.6i	−0.0105524	+	0.0132322i
$433$	−3.68138e6	−	1.77286e6i	−0.943605	−	0.454416i	−0.102166	−	0.994767i	$-0.532577\pi$
$433$	−3.68138e6	−	1.77286e6i	−0.943605	−	0.454416i	−0.841440	+	0.540351i	$0.818291\pi$
$434$	−6.13718e6			−1.56403
$435$	1.23432e6	+	1.97274e6i	0.312756	+	0.499859i
$436$	2.66424e6			0.671207
$437$	529739.	+	255109.i	0.132696	+	0.0639032i
$438$	1.49020e6	−	1.86865e6i	0.371158	−	0.465418i
$439$	1.34366e6	+	1.68490e6i	0.332758	+	0.417265i	0.919859	−	0.392248i	$-0.128303\pi$
$439$	1.34366e6	+	1.68490e6i	0.332758	+	0.417265i	−0.587102	+	0.809513i	$0.699731\pi$
$440$	1.06643e6	+	513565.i	0.262603	+	0.126463i
$441$	−7.20516e6	+	3.46982e6i	−1.76420	+	0.849593i
$442$	−657014.	+	823869.i	−0.159963	+	0.200587i
$443$	1.46530e6	+	6.41991e6i	0.354746	+	1.55424i	0.766071	+	0.642756i	$0.222209\pi$
$443$	1.46530e6	+	6.41991e6i	0.354746	+	1.55424i	−0.411325	+	0.911489i	$0.634934\pi$
$444$	−1.17114e6	−	5.13110e6i	−0.281936	−	1.23524i
$445$	1.11329e6	+	1.39603e6i	0.266508	+	0.334190i
$446$	−22992.9	+	100739.i	−0.00547340	+	0.0239805i
$447$	−3.96252e6			−0.937999
$448$	−1.28594e6	+	5.63409e6i	−0.302710	+	1.32626i
$449$	−159290.	+	76710.1i	−0.0372883	+	0.0179571i	−0.452435	−	0.891797i	$-0.649445\pi$
$449$	−159290.	+	76710.1i	−0.0372883	+	0.0179571i	0.415147	+	0.909754i	$0.363730\pi$
$450$	1.91826e6	−	923783.i	0.446555	−	0.215050i
$451$	750695.	−	3.28901e6i	0.173789	−	0.761419i
$452$	−2.64860e6			−0.609776
$453$	−778889.	+	3.41254e6i	−0.178332	+	0.781325i
$454$	−2.40861e6	−	3.02030e6i	−0.548437	−	0.687718i
$455$	−660458.	−	2.89366e6i	−0.149561	−	0.655268i
$456$	−358499.	−	1.57068e6i	−0.0807375	−	0.353734i
$457$	968514.	−	1.21448e6i	0.216928	−	0.272019i	−0.661446	−	0.749993i	$-0.730057\pi$
$457$	968514.	−	1.21448e6i	0.216928	−	0.272019i	0.878374	+	0.477973i	$0.158628\pi$
$458$	1.59569e6	−	768445.i	0.355456	−	0.171178i
$459$	−221157.	−	106503.i	−0.0489969	−	0.0235956i
$460$	−390366.	−	489504.i	−0.0860157	−	0.107860i
$461$	−2.06378e6	+	2.58790e6i	−0.452284	+	0.567146i	−0.954734	−	0.297460i	$-0.903861\pi$
$461$	−2.06378e6	+	2.58790e6i	−0.452284	+	0.567146i	0.502450	+	0.864606i	$0.332432\pi$
$462$	−4.45251e6	−	2.14421e6i	−0.970509	−	0.467373i
$463$	8.25802e6			1.79029			0.895145	−	0.445776i	$-0.147072\pi$
$463$	8.25802e6			1.79029			0.895145	+	0.445776i	$0.147072\pi$
$464$	−622385.	−	71326.2i	−0.134204	−	0.0153799i
$465$	−3.63358e6			−0.779296
$466$	3.84492e6	+	1.85162e6i	0.820205	+	0.394990i
$467$	−1.48087e6	+	1.85695e6i	−0.314213	+	0.394011i	−0.913710	−	0.406366i	$-0.866796\pi$
$467$	−1.48087e6	+	1.85695e6i	−0.314213	+	0.394011i	0.599497	+	0.800377i	$0.295367\pi$
$468$	1.32455e6	+	1.66094e6i	0.279547	+	0.350541i
$469$	1.00830e7	+	4.85570e6i	2.11669	+	1.01934i
$470$	1.75319e6	−	844293.i	0.366087	−	0.176298i
$471$	−2.79627e6	+	3.50642e6i	−0.580801	+	0.728302i
$472$	1.02094e6	+	4.47302e6i	0.210933	+	0.924157i
$473$	1.00070e6	+	4.38435e6i	0.205660	+	0.901057i
$474$	−888956.	−	1.11472e6i	−0.181733	−	0.227886i
$475$	226647.	−	993006.i	0.0460910	−	0.201938i
$476$	−2.11804e6			−0.428466
$477$	27873.9	−	122123.i	0.00560920	−	0.0245755i
$478$	4.71035e6	−	2.26838e6i	0.942938	−	0.454095i
$479$	−570711.	+	274840.i	−0.113652	+	0.0547320i	−0.489846	−	0.871809i	$-0.662947\pi$
$479$	−570711.	+	274840.i	−0.113652	+	0.0547320i	0.376194	+	0.926541i	$0.377233\pi$
$480$	−627105.	+	2.74753e6i	−0.124233	+	0.544301i
$481$	−7.42371e6			−1.46305
$482$	52949.5	−	231987.i	0.0103811	−	0.0454827i
$483$	4.56175e6	+	5.72026e6i	0.889741	+	1.11570i
$484$	−360854.	−	1.58101e6i	−0.0700194	−	0.306775i
$485$	−915824.	−	4.01249e6i	−0.176790	−	0.774568i
$486$	2.96494e6	−	3.71792e6i	0.569411	−	0.714019i
$487$	3.16054e6	−	1.52204e6i	0.603863	−	0.290805i	−0.106863	−	0.994274i	$-0.534081\pi$
$487$	3.16054e6	−	1.52204e6i	0.603863	−	0.290805i	0.710726	+	0.703468i	$0.248366\pi$
$488$	−2.84407e6	−	1.36963e6i	−0.540618	−	0.260348i
$489$	−1.24963e6	−	1.56699e6i	−0.236325	−	0.296342i
$490$	−2.02921e6	+	2.54454e6i	−0.381800	+	0.478762i
$491$	−2.17221e6	−	1.04608e6i	−0.406629	−	0.195822i	0.219377	−	0.975640i	$-0.429597\pi$
$491$	−2.17221e6	−	1.04608e6i	−0.406629	−	0.195822i	−0.626007	+	0.779818i	$0.715312\pi$
$492$	4.88965e6			0.910678
$493$	−257829.	−	2.32812e6i	−0.0477764	−	0.431408i
$494$	−811920.			−0.149691
$495$	−1.25548e6	−	604608.i	−0.230302	−	0.110907i
$496$	609883.	−	764769.i	0.111312	−	0.139581i
$497$	3.20702e6	+	4.02147e6i	0.582385	+	0.730288i
$498$	−3.32477e6	−	1.60112e6i	−0.600742	−	0.289302i
$499$	−1.96485e6	+	946221.i	−0.353246	+	0.170114i	−0.602088	−	0.798430i	$-0.705664\pi$
$499$	−1.96485e6	+	946221.i	−0.353246	+	0.170114i	0.248842	+	0.968544i	$0.419950\pi$
$500$	−1.50303e6	+	1.88474e6i	−0.268870	+	0.337152i
$501$	−1.52362e6	−	6.67542e6i	−0.271196	−	1.18819i
$502$	168397.	+	737794.i	0.0298246	+	0.130670i
$503$	−4.82260e6	−	6.04735e6i	−0.849887	−	1.06572i	−0.997061	−	0.0766141i	$-0.975589\pi$
$503$	−4.82260e6	−	6.04735e6i	−0.849887	−	1.06572i	0.147174	−	0.989111i	$-0.452982\pi$
$504$	2.12460e6	−	9.30847e6i	0.372564	−	1.63231i
$505$	−4.48244e6			−0.782143
$506$	−327203.	+	1.43357e6i	−0.0568121	+	0.248910i
$507$	−1.53676e6	+	740064.i	−0.265513	+	0.127864i
$508$	1.23266e6	−	593619.i	0.211926	−	0.102058i
$509$	1.26750e6	−	5.55327e6i	0.216847	−	0.950067i	−0.742945	−	0.669353i	$-0.766572\pi$
$509$	1.26750e6	−	5.55327e6i	0.216847	−	0.950067i	0.959791	−	0.280714i	$-0.0905713\pi$
$510$	1.00182e6			0.170555
$511$	1.50785e6	−	6.60632e6i	0.255450	−	1.11920i
$512$	−991015.	−	1.24269e6i	−0.167073	−	0.209502i
$513$	−42085.2	−	184387.i	−0.00706050	−	0.0309341i
$514$	963510.	+	4.22141e6i	0.160860	+	0.704774i
$515$	−141276.	+	177155.i	−0.0234721	+	0.0294330i
$516$	−5.87256e6	+	2.82807e6i	−0.970963	+	0.467591i
$517$	5.15398e6	+	2.48203e6i	0.848041	+	0.408395i
$518$	7.43240e6	+	9.31993e6i	1.21704	+	1.52612i
$519$	4.37324e6	−	5.48388e6i	0.712665	−	0.893654i
$520$	2.18022e6	+	1.04994e6i	0.353583	+	0.170277i
$521$	4.28414e6			0.691463			0.345732	−	0.938333i	$-0.387631\pi$
$521$	4.28414e6			0.691463			0.345732	+	0.938333i	$0.387631\pi$
$522$	3.74804e6	+	429531.i	0.602044	+	0.0689951i
$523$	2.08888e6			0.333932			0.166966	−	0.985963i	$-0.446603\pi$
$523$	2.08888e6			0.333932			0.166966	+	0.985963i	$0.446603\pi$
$524$	−2.35366e6	−	1.13346e6i	−0.374468	−	0.180334i
$525$	7.90239e6	−	9.90929e6i	1.25130	−	1.56908i
$526$	−9407.67	−	11796.8i	−0.00148258	−	0.00185910i
$527$	3.29524e6	+	1.58691e6i	0.516846	+	0.248900i
$528$	709664.	−	341756.i	0.110782	−	0.0533496i
$529$	−2.65567e6	+	3.33011e6i	−0.412606	+	0.517391i
$530$	−11343.8	−	49700.6i	−0.00175417	−	0.00768550i
$531$	−1.20192e6	−	5.26597e6i	−0.184987	−	0.810480i
$532$	−1.01749e6	−	1.27590e6i	−0.155866	−	0.195450i
$533$	1.53473e6	−	6.72408e6i	0.233999	−	1.02521i
$534$	6.07811e6			0.922392
$535$	529535.	−	2.32004e6i	0.0799853	−	0.350438i
$536$	−8.22061e6	+	3.95884e6i	−1.23592	+	0.595190i
$537$	−9.89050e6	+	4.76301e6i	−1.48007	+	0.712765i
$538$	1.52441e6	−	6.67886e6i	0.227062	−	0.994825i
$539$	−9.56777e6			−1.41853
$540$	−44814.6	+	196346.i	−0.00661356	+	0.0289759i
$541$	3.84403e6	+	4.82027e6i	0.564669	+	0.708073i	0.979413	−	0.201865i	$-0.0647003\pi$
$541$	3.84403e6	+	4.82027e6i	0.564669	+	0.708073i	−0.414744	+	0.909938i	$0.636129\pi$
$542$	−122460.	−	536533.i	−0.0179059	−	0.0784510i
$543$	2.89413e6	+	1.26800e7i	0.421229	+	1.84552i
$544$	1.76865e6	−	2.21781e6i	0.256238	−	0.321313i
$545$	−3.21892e6	+	1.55015e6i	−0.464215	+	0.223554i
$546$	−9.10275e6	−	4.38365e6i	−1.30675	−	0.629295i
$547$	5.81620e6	+	7.29329e6i	0.831134	+	1.04221i	0.998414	+	0.0562999i	$0.0179303\pi$
$547$	5.81620e6	+	7.29329e6i	0.831134	+	1.04221i	−0.167280	+	0.985909i	$0.553498\pi$
$548$	4.21416e6	−	5.28439e6i	0.599459	−	0.751697i
$549$	3.34825e6	+	1.61243e6i	0.474119	+	0.228324i
$550$	2.54726e6			0.359060
$551$	1.27859e6	−	1.27373e6i	0.179412	−	0.178730i
$552$	−5.96510e6			−0.833240
$553$	−3.64194e6	−	1.75387e6i	−0.506431	−	0.243884i
$554$	−3.93927e6	+	4.93969e6i	−0.545307	+	0.683794i
$555$	4.40043e6	+	5.51796e6i	0.606405	+	0.760407i
$556$	759019.	+	365524.i	0.104127	+	0.0501452i
$557$	8.51596e6	−	4.10107e6i	1.16304	−	0.560092i	0.250116	−	0.968216i	$-0.419531\pi$
$557$	8.51596e6	−	4.10107e6i	1.16304	−	0.560092i	0.912926	+	0.408124i	$0.133817\pi$
$558$	−3.67276e6	+	4.60549e6i	−0.499352	+	0.626167i
$559$	2.04584e6	+	8.96340e6i	0.276912	+	1.21323i
$560$	−169033.	−	740583.i	−0.0227773	−	0.0997939i
$561$	1.83625e6	+	2.30259e6i	0.246335	+	0.308894i
$562$	789487.	−	3.45897e6i	0.105440	−	0.461961i
$563$	−2.61829e6			−0.348134			−0.174067	−	0.984734i	$-0.555691\pi$
$563$	−2.61829e6			−0.348134			−0.174067	+	0.984734i	$0.555691\pi$
$564$	−1.84497e6	+	8.08334e6i	−0.244226	+	1.07002i
$565$	3.20003e6	−	1.54105e6i	0.421728	−	0.203094i
$566$	−4.29820e6	+	2.06990e6i	−0.563956	+	0.271587i
$567$	3.27435e6	−	1.43458e7i	0.427727	−	1.87400i
$568$	−4.19361e6			−0.545402
$569$	159244.	−	697694.i	0.0206197	−	0.0903409i	−0.963571	−	0.267452i	$-0.913818\pi$
$569$	159244.	−	697694.i	0.0206197	−	0.0903409i	0.984191	+	0.177112i	$0.0566753\pi$
$570$	481268.	+	603491.i	0.0620440	+	0.0778007i
$571$	1.43165e6	+	6.27247e6i	0.183758	+	0.805097i	0.979820	+	0.199882i	$0.0640558\pi$
$571$	1.43165e6	+	6.27247e6i	0.183758	+	0.805097i	−0.796062	+	0.605215i	$0.793087\pi$
$572$	565572.	+	2.47793e6i	0.0722766	+	0.316665i
$573$	−5.77094e6	+	7.23653e6i	−0.734277	+	0.920754i
$574$	−9.97813e6	+	4.80521e6i	−1.26406	+	0.608742i
$575$	−3.39774e6	−	1.63627e6i	−0.428569	−	0.206388i
$576$	3.45839e6	+	4.33668e6i	0.434328	+	0.544630i
$577$	−6.30485e6	+	7.90603e6i	−0.788379	+	0.988596i	0.211558	+	0.977365i	$0.432146\pi$
$577$	−6.30485e6	+	7.90603e6i	−0.788379	+	0.988596i	−0.999937	+	0.0112303i	$0.996425\pi$
$578$	3.91395e6	+	1.88486e6i	0.487300	+	0.234671i
$579$	−1.75784e6			−0.217913
$580$	−1.81517e6	+	631280.i	−0.224052	+	0.0779205i
$581$	−1.04622e7			−1.28583
$582$	−1.26223e7	−	6.07859e6i	−1.54466	−	0.743867i
$583$	93439.9	−	117170.i	0.0113857	−	0.0142773i
$584$	3.44455e6	+	4.31932e6i	0.417927	+	0.524063i
$585$	−2.56672e6	−	1.23607e6i	−0.310090	−	0.149332i
$586$	3.43656e6	−	1.65496e6i	0.413409	−	0.199087i
$587$	−5.53449e6	+	6.94003e6i	−0.662952	+	0.831316i	−0.993661	−	0.112417i	$-0.964141\pi$
$587$	−5.53449e6	+	6.94003e6i	−0.662952	+	0.831316i	0.330709	+	0.943733i	$0.392712\pi$
$588$	−3.08579e6	−	1.35197e7i	−0.368064	−	1.61259i
$589$	627071.	+	2.74738e6i	0.0744780	+	0.326310i
$590$	−1.37056e6	−	1.71863e6i	−0.162095	−	0.203260i
$591$	3.36262e6	−	1.47326e7i	0.396013	−	1.73504i
$592$	−1.89997e6			−0.222815
$593$	862845.	−	3.78037e6i	0.100762	−	0.441466i	−0.899230	−	0.437476i	$-0.855873\pi$
$593$	862845.	−	3.78037e6i	0.100762	−	0.441466i	0.999992	−	0.00399064i	$-0.00127026\pi$
$594$	426149.	−	205223.i	0.0495559	−	0.0238649i
$595$	2.55901e6	−	1.23235e6i	0.296333	−	0.142706i
$596$	728187.	−	3.19040e6i	0.0839706	−	0.367899i
$597$	−1.34621e7			−1.54589
$598$	−668937.	+	2.93080e6i	−0.0764948	+	0.335146i
$599$	7.44556e6	+	9.33643e6i	0.847872	+	1.06320i	0.997227	+	0.0744141i	$0.0237087\pi$
$599$	7.44556e6	+	9.33643e6i	0.847872	+	1.06320i	−0.149356	+	0.988784i	$0.547720\pi$
$600$	2.29941e6	+	1.00744e7i	0.260758	+	1.14245i
$601$	−2.25654e6	−	9.88656e6i	−0.254834	−	1.11650i	−0.926692	−	0.375821i	$-0.877361\pi$
$601$	−2.25654e6	−	9.88656e6i	−0.254834	−	1.11650i	0.671858	−	0.740680i	$-0.265496\pi$
$602$	9.20468e6	−	1.15423e7i	1.03518	−	1.29808i
$603$	9.67792e6	−	4.66064e6i	1.08390	−	0.521978i
$604$	−2.60445e6	−	1.25424e6i	−0.290485	−	0.139890i
$605$	1.35587e6	+	1.70021e6i	0.150602	+	0.188848i
$606$	−9.51333e6	+	1.19293e7i	−1.05233	+	1.31958i
$607$	1.07683e7	+	5.18575e6i	1.18625	+	0.571268i	0.919726	−	0.392561i	$-0.128411\pi$
$607$	1.07683e7	+	5.18575e6i	1.18625	+	0.571268i	0.266524	+	0.963828i	$0.414125\pi$
$608$	2.18565e6			0.239785
$609$	2.12118e7	−	7.37703e6i	2.31758	−	0.806006i
$610$	1.51242e6			0.164568
$611$	1.05369e7	+	5.07428e6i	1.14185	+	0.549885i
$612$	−1.26753e6	+	1.58943e6i	−0.136798	+	0.171539i
$613$	6.99909e6	+	8.77659e6i	0.752299	+	0.943353i	0.999673	−	0.0255666i	$-0.00813900\pi$
$613$	6.99909e6	+	8.77659e6i	0.752299	+	0.943353i	−0.247374	+	0.968920i	$0.579568\pi$
$614$	−2.05760e6	−	990888.i	−0.220262	−	0.106073i
$615$	−5.90765e6	+	2.84498e6i	−0.629836	+	0.303313i
$616$	7.12216e6	−	8.93091e6i	0.756241	−	0.948296i
$617$	−807245.	−	3.53677e6i	−0.0853675	−	0.374020i	0.914140	−	0.405399i	$-0.132867\pi$
$617$	−807245.	−	3.53677e6i	−0.0853675	−	0.374020i	−0.999508	+	0.0313790i	$0.990010\pi$
$618$	171632.	+	751971.i	0.0180771	+	0.0792008i
$619$	−6.31340e6	−	7.91675e6i	−0.662272	−	0.830463i	0.331316	−	0.943520i	$-0.392507\pi$
$619$	−6.31340e6	−	7.91675e6i	−0.662272	−	0.830463i	−0.993589	+	0.113057i	$0.963936\pi$
$620$	667739.	−	2.92556e6i	0.0697634	−	0.305653i
$621$	−700260.			−0.0728669
$622$	288469.	−	1.26387e6i	0.0298967	−	0.130986i
$623$	1.55257e7	−	7.47677e6i	1.60262	−	0.771781i
$624$	1.45084e6	−	698690.i	0.149162	−	0.0718328i
$625$	−1.05801e6	+	4.63546e6i	−0.108341	+	0.474671i
$626$	366329.			0.0373624
$627$	−504943.	+	2.21230e6i	−0.0512948	+	0.224737i
$628$	−2.30930e6	−	2.89577e6i	−0.233659	−	0.292999i
$629$	−1.58081e6	−	6.92597e6i	−0.159313	−	0.697998i
$630$	1.01793e6	+	4.45984e6i	0.102180	+	0.447681i
$631$	−1.73300e6	+	2.17311e6i	−0.173270	+	0.217274i	−0.860882	−	0.508804i	$-0.830088\pi$
$631$	−1.73300e6	+	2.17311e6i	−0.173270	+	0.217274i	0.687612	+	0.726078i	$0.258659\pi$
$632$	2.96926e6	−	1.42992e6i	0.295703	−	0.142403i
$633$	881490.	+	424503.i	0.0874396	+	0.0421087i
$634$	−4.25861e6	−	5.34013e6i	−0.420770	−	0.527629i
$635$	−1.14391e6	+	1.43442e6i	−0.112579	+	0.141170i
$636$	195703.	+	94245.6i	0.0191847	+	0.00923886i
$637$	−1.95604e7			−1.90998
$638$	3.81712e6	+	2.40860e6i	0.371265	+	0.234268i
$639$	4.93703e6			0.478315
$640$	−1.73828e6	−	837113.i	−0.167753	−	0.0807856i
$641$	−1.80817e6	+	2.26738e6i	−0.173818	+	0.217961i	−0.861108	−	0.508422i	$-0.830229\pi$
$641$	−1.80817e6	+	2.26738e6i	−0.173818	+	0.217961i	0.687290	+	0.726383i	$0.258800\pi$
$642$	−5.05058e6	−	6.33323e6i	−0.483619	−	0.606439i
$643$	−1.45190e7	−	6.99199e6i	−1.38487	−	0.666920i	−0.414841	−	0.909894i	$-0.636163\pi$
$643$	−1.45190e7	−	6.99199e6i	−1.38487	−	0.666920i	−0.970033	+	0.242974i	$0.921877\pi$
$644$	−5.44394e6	+	2.62166e6i	−0.517247	+	0.249093i
$645$	5.44972e6	−	6.83374e6i	0.515793	−	0.646784i
$646$	−172891.	−	757483.i	−0.0163001	−	0.0714153i
$647$	−3.55969e6	−	1.55960e7i	−0.334311	−	1.46471i	−0.810691	−	0.585474i	$-0.800908\pi$
$647$	−3.55969e6	−	1.55960e7i	−0.334311	−	1.46471i	0.476380	−	0.879240i	$-0.341949\pi$
$648$	7.47994e6	+	9.37955e6i	0.699779	+	0.877495i
$649$	1.43798e6	−	6.30021e6i	0.134011	−	0.587143i
$650$	5.20764e6			0.483457
$651$	−7.80308e6	+	3.41875e7i	−0.721629	+	3.16166i
$652$	1.49129e6	−	718170.i	0.137387	−	0.0661619i
$653$	−9.06324e6	+	4.36463e6i	−0.831765	+	0.400557i	−0.800777	−	0.598963i	$-0.795580\pi$
$653$	−9.06324e6	+	4.36463e6i	−0.831765	+	0.400557i	−0.0309880	+	0.999520i	$0.509865\pi$
$654$	−2.70620e6	+	1.18566e7i	−0.247409	+	1.08397i
$655$	3.50317e6			0.319049
$656$	392788.	−	1.72092e6i	0.0356368	−	0.156135i
$657$	−4.05518e6	−	5.08504e6i	−0.366519	−	0.459601i
$658$	−4.17879e6	−	1.83085e7i	−0.376258	−	1.64850i
$659$	966369.	+	4.23394e6i	0.0866821	+	0.379779i	0.999597	−	0.0283697i	$-0.00903156\pi$
$659$	966369.	+	4.23394e6i	0.0866821	+	0.379779i	−0.912915	+	0.408149i	$0.866174\pi$
$660$	1.50658e6	−	1.88919e6i	0.134627	−	0.168817i
$661$	1.13829e7	−	5.48172e6i	1.01333	−	0.487993i	0.147887	−	0.989004i	$-0.452753\pi$
$661$	1.13829e7	−	5.48172e6i	1.01333	−	0.487993i	0.865441	+	0.501012i	$0.167039\pi$
$662$	323639.	+	155856.i	0.0287022	+	0.0138223i
$663$	3.75406e6	+	4.70744e6i	0.331678	+	0.415911i
$664$	5.31825e6	−	6.66887e6i	0.468110	−	0.586992i
$665$	1.97169e6	+	949518.i	0.172896	+	0.0832625i
$666$	1.14418e7			0.999557
$667$	−3.54439e6	−	5.66477e6i	−0.308480	−	0.493024i
$668$	5.65467e6			0.490305
$669$	531936.	+	256167.i	0.0459509	+	0.0221288i
$670$	2.72562e6	−	3.41781e6i	0.234573	−	0.294145i
$671$	2.77213e6	+	3.47615e6i	0.237688	+	0.298052i
$672$	2.45041e7	+	1.18006e7i	2.09323	+	1.00805i
$673$	7.64397e6	−	3.68114e6i	0.650551	−	0.313289i	−0.0793449	−	0.996847i	$-0.525283\pi$
$673$	7.64397e6	−	3.68114e6i	0.650551	−	0.313289i	0.729896	+	0.683558i	$0.239569\pi$
$674$	−910776.	+	1.14208e6i	−0.0772257	+	0.0968380i
$675$	269934.	+	1.18266e6i	0.0228033	+	0.0999078i
$676$	−313450.	−	1.37331e6i	−0.0263816	−	0.115585i
$677$	−5.44962e6	−	6.83361e6i	−0.456977	−	0.573031i	0.498952	−	0.866630i	$-0.333719\pi$
$677$	−5.44962e6	−	6.83361e6i	−0.456977	−	0.573031i	−0.955929	+	0.293598i	$0.905147\pi$
$678$	2.69031e6	−	1.17870e7i	0.224765	−	0.984760i
$679$	−3.97193e7			−3.30618
$680$	−515286.	+	2.25761e6i	−0.0427342	+	0.187231i
$681$	−1.98872e7	+	9.57716e6i	−1.64326	+	0.791351i
$682$	−6.34964e6	+	3.05783e6i	−0.522743	+	0.251740i
$683$	3.57909e6	−	1.56810e7i	0.293576	−	1.28624i	−0.585934	−	0.810359i	$-0.699272\pi$
$683$	3.57909e6	−	1.56810e7i	0.293576	−	1.28624i	0.879510	−	0.475881i	$-0.157871\pi$
$684$	−1.56637e6			−0.128013
$685$	−2.01688e6	+	8.83653e6i	−0.164230	+	0.719540i
$686$	1.04890e7	+	1.31528e7i	0.850992	+	1.06711i
$687$	−2.25183e6	−	9.86593e6i	−0.182031	−	0.797528i
$688$	523598.	+	2.29403e6i	0.0421723	+	0.184769i
$689$	191029.	−	239543.i	0.0153304	−	0.0192237i
$690$	2.57495e6	−	1.24003e6i	0.205895	−	0.0991538i
$691$	1.93293e7	+	9.30852e6i	1.54000	+	0.741627i	0.995285	−	0.0969921i	$-0.0309222\pi$
$691$	1.93293e7	+	9.30852e6i	1.54000	+	0.741627i	0.544719	+	0.838619i	$0.316636\pi$
$692$	3.61164e6	+	4.52886e6i	0.286708	+	0.359520i
$693$	−8.38475e6	+	1.05141e7i	−0.663219	+	0.831650i
$694$	2.49644e6	+	1.20222e6i	0.196754	+	0.0947517i
$695$	−1.12972e6			−0.0887173
$696$	−6.08027e6	+	1.72709e7i	−0.475773	+	1.35142i
$697$	6.60006e6			0.514595
$698$	−8.53878e6	−	4.11206e6i	−0.663372	−	0.319463i
$699$	1.52031e7	−	1.90641e7i	1.17690	−	1.47579i
$700$	6.52619e6	+	8.18358e6i	0.503401	+	0.631246i
$701$	−1.65186e7	−	7.95496e6i	−1.26964	−	0.611425i	−0.326930	−	0.945048i	$-0.606014\pi$
$701$	−1.65186e7	−	7.95496e6i	−1.26964	−	0.611425i	−0.942706	+	0.333624i	$0.891729\pi$
$702$	871223.	−	419559.i	0.0667247	−	0.0321329i
$703$	3.41276e6	−	4.27946e6i	0.260446	−	0.326589i
$704$	1.47670e6	+	6.46984e6i	0.112295	+	0.491996i
$705$	−2.47410e6	−	1.08397e7i	−0.187475	−	0.821383i
$706$	−6.29751e6	−	7.89683e6i	−0.475507	−	0.596267i
$707$	−9.62600e6	+	4.21743e7i	−0.724265	+	3.17321i
$708$	9.36629e6			0.702238
$709$	−1.55072e6	+	6.79415e6i	−0.115856	+	0.507598i	0.883385	+	0.468647i	$0.155259\pi$
$709$	−1.55072e6	+	6.79415e6i	−0.115856	+	0.507598i	−0.999241	+	0.0389502i	$0.987599\pi$
$710$	1.81025e6	−	871770.i	0.134770	−	0.0649017i
$711$	−3.49564e6	+	1.68341e6i	−0.259330	+	0.124887i
$712$	−3.12627e6	+	1.36971e7i	−0.231114	+	1.01258i
$713$	1.04339e7			0.768640
$714$	2.15140e6	−	9.42590e6i	0.157934	−	0.691954i
$715$	−2.12507e6	−	2.66476e6i	−0.155457	−	0.194936i
$716$	−2.01735e6	−	8.83857e6i	−0.147061	−	0.644317i
$717$	−6.64722e6	−	2.91234e7i	−0.482883	−	2.11565i
$718$	3.99221e6	−	5.00608e6i	0.289003	−	0.362399i
$719$	3.01450e6	−	1.45171e6i	0.217467	−	0.104727i	−0.321979	−	0.946747i	$-0.604348\pi$
$719$	3.01450e6	−	1.45171e6i	0.217467	−	0.104727i	0.539446	+	0.842020i	$0.318634\pi$
$720$	−656908.	−	316350.i	−0.0472252	−	0.0227424i
$721$	1.36342e6	+	1.70968e6i	0.0976769	+	0.122483i
$722$	−5.44664e6	+	6.82986e6i	−0.388853	+	0.487606i
$723$	−1.22498e6	−	589917.i	−0.0871529	−	0.0419706i
$724$	−1.07411e7			−0.761555
$725$	−8.20085e6	+	8.16969e6i	−0.579447	+	0.577245i
$726$	7.40248e6			0.521237
$727$	−2.09210e7	−	1.00750e7i	−1.46807	−	0.706985i	−0.482443	−	0.875927i	$-0.660251\pi$
$727$	−2.09210e7	−	1.00750e7i	−1.46807	−	0.706985i	−0.985626	+	0.168942i	$0.945965\pi$
$728$	1.45606e7	−	1.82584e7i	1.01824	−	1.27684i
$729$	−7.25710e6	−	9.10011e6i	−0.505760	−	0.634203i
$730$	−2.38481e6	−	1.14846e6i	−0.165633	−	0.0797646i
$731$	−7.92679e6	+	3.81734e6i	−0.548661	+	0.264221i
$732$	−4.01790e6	+	5.03829e6i	−0.277154	+	0.347540i
$733$	3.58458e6	+	1.57051e7i	0.246422	+	1.07964i	0.935046	+	0.354525i	$0.115358\pi$
$733$	3.58458e6	+	1.57051e7i	0.246422	+	1.07964i	−0.688625	+	0.725118i	$0.741785\pi$
$734$	2.25471e6	+	9.87853e6i	0.154472	+	0.676787i
$735$	1.15945e7	+	1.45391e7i	0.791652	+	0.992700i
$736$	1.80074e6	−	7.88958e6i	0.122534	−	0.536858i
$737$	1.28514e7			0.871526
$738$	−2.36540e6	+	1.03635e7i	−0.159868	+	0.700430i
$739$	−3.68731e6	+	1.77571e6i	−0.248370	+	0.119609i	−0.553927	−	0.832565i	$-0.686871\pi$
$739$	−3.68731e6	+	1.77571e6i	−0.248370	+	0.119609i	0.305558	+	0.952174i	$0.401157\pi$
$740$	−5.25142e6	+	2.52895e6i	−0.352531	+	0.169770i
$741$	−1.03231e6	+	4.52285e6i	−0.0690660	+	0.302598i
$742$	−491983.			−0.0328050
$743$	−4.62278e6	+	2.02537e7i	−0.307207	+	1.34596i	0.551791	+	0.833983i	$0.313945\pi$
$743$	−4.62278e6	+	2.02537e7i	−0.307207	+	1.34596i	−0.858998	+	0.511979i	$0.828912\pi$
$744$	−1.78254e7	−	2.23524e7i	−1.18061	−	1.48044i
$745$	976497.	+	4.27831e6i	0.0644585	+	0.282411i
$746$	274440.	+	1.20240e6i	0.0180551	+	0.0791045i
$747$	−6.26104e6	+	7.85110e6i	−0.410530	+	0.514789i
$748$	−2.19136e6	+	1.05530e6i	−0.143206	+	0.0689642i
$749$	−2.06916e7	−	9.96454e6i	−1.34769	−	0.649012i
$750$	−6.86093e6	−	8.60334e6i	−0.445379	−	0.558488i
$751$	6.54300e6	−	8.20467e6i	0.423328	−	0.530837i	−0.523736	−	0.851881i	$-0.675462\pi$
$751$	6.54300e6	−	8.20467e6i	0.423328	−	0.530837i	0.947064	+	0.321044i	$0.104034\pi$
$752$	2.69673e6	+	1.29868e6i	0.173897	+	0.0837446i
$753$	4.32403e6			0.277908
$754$	7.80376e6	+	4.92417e6i	0.499891	+	0.315431i
$755$	3.87645e6			0.247495
$756$	1.75113e6	+	843300.i	0.111433	+	0.0536633i
$757$	−1.01949e7	+	1.27840e7i	−0.646610	+	0.810823i	−0.991812	−	0.127705i	$-0.959239\pi$
$757$	−1.01949e7	+	1.27840e7i	−0.646610	+	0.810823i	0.345202	+	0.938528i	$0.387810\pi$
$758$	5.05939e6	+	6.34427e6i	0.319834	+	0.401059i
$759$	7.56976e6	+	3.64541e6i	0.476955	+	0.229690i
$760$	−1.60752e6	+	774139.i	−0.100953	+	0.0486166i
$761$	7.75285e6	−	9.72177e6i	0.485288	−	0.608532i	−0.477552	−	0.878603i	$-0.658476\pi$
$761$	7.75285e6	−	9.72177e6i	0.485288	−	0.608532i	0.962840	+	0.270071i	$0.0870472\pi$
$762$	1.38970e6	+	6.08868e6i	0.0867030	+	0.379870i
$763$	7.67241e6	+	3.36150e7i	0.477112	+	2.09037i
$764$	−4.76593e6	−	5.97628e6i	−0.295402	−	0.370423i
$765$	606634.	−	2.65784e6i	0.0374777	−	0.164200i
$766$	−5.87624e6			−0.361849
$767$	2.93983e6	−	1.28802e7i	0.180440	−	0.790560i
$768$	−2.15062e7	+	1.03568e7i	−1.31571	+	0.633614i
$769$	9.55303e6	−	4.60049e6i	0.582539	−	0.280536i	−0.119315	−	0.992856i	$-0.538070\pi$
$769$	9.55303e6	−	4.60049e6i	0.582539	−	0.280536i	0.701854	+	0.712320i	$0.252356\pi$
$770$	−1.21785e6	+	5.33576e6i	−0.0740232	+	0.324317i
$771$	2.47407e7			1.49891
$772$	323037.	−	1.41532e6i	0.0195078	−	0.0854693i
$773$	6.00139e6	+	7.52551e6i	0.361246	+	0.452988i	0.928928	−	0.370259i	$-0.120731\pi$
$773$	6.00139e6	+	7.52551e6i	0.361246	+	0.452988i	−0.567682	+	0.823248i	$0.692160\pi$
$774$	−3.15314e6	−	1.38148e7i	−0.189187	−	0.828882i
$775$	−4.02202e6	−	1.76216e7i	−0.240542	−	1.05388i
$776$	2.01905e7	−	2.53180e7i	1.20363	−	1.50930i
$777$	6.13671e7	−	2.95528e7i	3.64656	−	1.75609i
$778$	−5.46941e6	−	2.63393e6i	−0.323960	−	0.156011i
$779$	3.17063e6	+	3.97584e6i	0.187198	+	0.234739i
$780$	3.08006e6	−	3.86227e6i	0.181269	−	0.227304i
$781$	5.32172e6	+	2.56281e6i	0.312194	+	0.150345i
$782$	−2.87675e6			−0.168223
$783$	−713780.	+	2.02747e6i	−0.0416064	+	0.118182i
$784$	−5.00617e6			−0.290881
$785$	4.47496e6	+	2.15503e6i	0.259188	+	0.124818i
$786$	7.43496e6	−	9.32315e6i	0.429262	−	0.538277i
$787$	3.87213e6	+	4.85550e6i	0.222850	+	0.279445i	0.880670	−	0.473730i	$-0.157093\pi$
$787$	3.87213e6	+	4.85550e6i	0.222850	+	0.279445i	−0.657820	+	0.753175i	$0.728521\pi$
$788$	1.12439e7	+	5.41478e6i	0.645063	+	0.310646i
$789$	−77676.4	+	37407.0i	−0.00444218	+	0.00213924i
$790$	−984485.	+	1.23451e6i	−0.0561231	+	0.0703761i
$791$	−7.62738e6	−	3.34177e7i	−0.433445	−	1.89905i
$792$	−2.43976e6	−	1.06893e7i	−0.138208	−	0.605530i
$793$	5.66738e6	+	7.10667e6i	0.320036	+	0.401313i
$794$	−4.64944e6	+	2.03705e7i	−0.261727	+	1.14670i
$795$	−291283.			−0.0163455
$796$	2.47392e6	−	1.08389e7i	0.138389	−	0.606323i
$797$	6.50878e6	−	3.13446e6i	0.362956	−	0.174790i	−0.243513	−	0.969898i	$-0.578300\pi$
$797$	6.50878e6	−	3.13446e6i	0.362956	−	0.174790i	0.606469	+	0.795107i	$0.292586\pi$
$798$	6.71163e6	−	3.23215e6i	0.373096	−	0.179674i
$799$	−2.49034e6	+	1.09109e7i	−0.138004	+	0.604636i
$800$	−1.40187e7			−0.774432
$801$	3.68049e6	−	1.61253e7i	0.202686	−	0.888026i
$802$	−6.84589e6	−	8.58447e6i	−0.375832	−	0.471279i
$803$	−1.73152e6	−	7.58630e6i	−0.0947631	−	0.415184i
$804$	4.14481e6	+	1.81596e7i	0.226133	+	0.990755i
$805$	5.05197e6	−	6.33496e6i	0.274771	−	0.344552i
$806$	−1.29813e7	+	6.25145e6i	−0.703849	+	0.338956i
$807$	−3.52668e7	−	1.69836e7i	−1.90626	−	0.918006i
$808$	−2.19897e7	−	2.75743e7i	−1.18493	−	1.48585i
$809$	2.18265e6	−	2.73695e6i	0.117250	−	0.147027i	−0.719743	−	0.694241i	$-0.755740\pi$
$809$	2.18265e6	−	2.73695e6i	0.117250	−	0.147027i	0.836993	+	0.547214i	$0.184312\pi$
$810$	−5.17869e6	−	2.49393e6i	−0.277337	−	0.133558i
$811$	−4.29926e6			−0.229531			−0.114766	−	0.993393i	$-0.536612\pi$
$811$	−4.29926e6			−0.229531			−0.114766	+	0.993393i	$0.536612\pi$
$812$	2.04150e6	+	1.84342e7i	0.108658	+	0.981148i
$813$	−3.14449e6			−0.166849
$814$	1.23333e7	+	5.93941e6i	0.652407	+	0.314183i
$815$	−1.38392e6	+	1.73538e6i	−0.0729822	+	0.0915168i
$816$	960788.	+	1.20479e6i	0.0505129	+	0.0633411i
$817$	−6.10753e6	−	2.94123e6i	−0.320118	−	0.154161i
$818$	−5.41763e6	+	2.60899e6i	−0.283091	+	0.136329i
$819$	−1.71419e7	+	2.14952e7i	−0.892993	+	1.11978i
$820$	−1.20497e6	−	5.27933e6i	−0.0625810	−	0.274185i
$821$	3.18087e6	+	1.39363e7i	0.164698	+	0.721589i	0.988060	+	0.154072i	$0.0492388\pi$
$821$	3.18087e6	+	1.39363e7i	0.164698	+	0.721589i	−0.823362	+	0.567517i	$0.807904\pi$
$822$	1.92365e7	+	2.41218e7i	0.992995	+	1.24518i
$823$	6.52573e6	−	2.85911e7i	0.335838	−	1.47140i	−0.471791	−	0.881711i	$-0.656392\pi$
$823$	6.52573e6	−	2.85911e7i	0.335838	−	1.47140i	0.807628	−	0.589692i	$-0.200751\pi$
$824$	−1.78285e6			−0.0914740
$825$	3.23870e6	−	1.41897e7i	0.165667	−	0.725834i
$826$	−1.91135e7	+	9.20456e6i	−0.974741	+	0.469411i
$827$	7.44560e6	−	3.58561e6i	0.378561	−	0.182305i	−0.234920	−	0.972015i	$-0.575483\pi$
$827$	7.44560e6	−	3.58561e6i	0.378561	−	0.182305i	0.613481	+	0.789709i	$0.289769\pi$
$828$	−1.29053e6	+	5.65418e6i	−0.0654172	+	0.286611i
$829$	−9.03225e6			−0.456467			−0.228234	−	0.973606i	$-0.573295\pi$
$829$	−9.03225e6			−0.456467			−0.228234	+	0.973606i	$0.573295\pi$
$830$	−909392.	+	3.98431e6i	−0.0458201	+	0.200751i
$831$	2.25083e7	+	2.82245e7i	1.13068	+	1.41783i
$832$	3.01898e6	+	1.32270e7i	0.151200	+	0.662450i
$833$	−4.16521e6	−	1.82490e7i	−0.207981	−	0.911225i
$834$	−2.39766e6	+	3.00657e6i	−0.119364	+	0.149678i
$835$	−6.83195e6	+	3.29009e6i	−0.339101	+	0.163302i
$836$	−1.68843e6	−	813103.i	−0.0835538	−	0.0402374i
$837$	−2.09258e6	−	2.62401e6i	−0.103245	−	0.129465i
$838$	1.10540e7	−	1.38613e7i	0.543764	−	0.681859i
$839$	3.17172e7	+	1.52742e7i	1.55557	+	0.749124i	0.996780	−	0.0801850i	$-0.0255511\pi$
$839$	3.17172e7	+	1.52742e7i	1.55557	+	0.749124i	0.558791	+	0.829309i	$0.311265\pi$
$840$	−2.22022e7			−1.08567
$841$	−2.00141e7	+	4.48798e6i	−0.975768	+	0.218807i
$842$	1.71187e7			0.832129
$843$	−1.82646e7	−	8.79576e6i	−0.885199	−	0.426289i
$844$	−503777.	+	631716.i	−0.0243434	+	0.0305257i
$845$	1.17775e6	+	1.47685e6i	0.0567430	+	0.0711535i
$846$	−1.62399e7	−	7.82072e6i	−0.780113	−	0.375683i
$847$	1.89086e7	−	9.10589e6i	0.905629	−	0.436128i
$848$	48890.8	−	61307.1i	0.00233473	−	0.00292766i
$849$	6.06560e6	+	2.65751e7i	0.288805	+	1.26534i
$850$	1.10892e6	+	4.85849e6i	0.0526444	+	0.230650i
$851$	−1.26359e7	−	1.58449e7i	−0.598112	−	0.750009i
$852$	−1.90501e6	+	8.34641e6i	−0.0899082	+	0.393913i
$853$	1.15136e7			0.541801			0.270901	−	0.962607i	$-0.412678\pi$
$853$	1.15136e7			0.541801			0.270901	+	0.962607i	$0.412678\pi$
$854$	3.24790e6	−	1.42300e7i	0.152390	−	0.667666i
$855$	1.89249e6	−	911375.i	0.0885356	−	0.0426365i
$856$	1.68698e7	−	8.12405e6i	0.786909	−	0.378956i
$857$	−3.93011e6	+	1.72189e7i	−0.182790	+	0.800856i	0.797504	+	0.603313i	$0.206153\pi$
$857$	−3.93011e6	+	1.72189e7i	−0.182790	+	0.800856i	−0.980294	+	0.197542i	$0.936704\pi$
$858$	−1.16020e7			−0.538040
$859$	−358731.	+	1.57170e6i	−0.0165877	+	0.0726755i	−0.982544	−	0.186029i	$-0.940438\pi$
$859$	−358731.	+	1.57170e6i	−0.0165877	+	0.0726755i	0.965957	+	0.258704i	$0.0832954\pi$
$860$	4.50065e6	+	5.64364e6i	0.207505	+	0.260204i
$861$	1.40811e7	+	6.16933e7i	0.647334	+	2.83616i
$862$	5.12144e6	+	2.24385e7i	0.234760	+	1.02855i
$863$	−1.74098e7	+	2.18312e7i	−0.795731	+	0.997815i	0.204091	+	0.978952i	$0.434576\pi$
$863$	−1.74098e7	+	2.18312e7i	−0.795731	+	0.997815i	−0.999822	+	0.0188632i	$0.993995\pi$
$864$	−2.34529e6	+	1.12943e6i	−0.106884	+	0.0514726i
$865$	−6.99863e6	−	3.37036e6i	−0.318033	−	0.153157i
$866$	9.60388e6	+	1.20429e7i	0.435163	+	0.545677i
$867$	1.54761e7	−	1.94064e7i	0.699220	−	0.876794i
$868$	−2.60919e7	−	1.25652e7i	−1.17546	−	0.566070i
$869$	−4.64187e6			−0.208518
$870$	−965618.	−	8.71927e6i	−0.0432521	−	0.390555i
$871$	2.62734e7			1.17347
$872$	−2.53271e7	−	1.21969e7i	−1.12796	−	0.543199i
$873$	−2.37697e7	+	2.98063e7i	−1.05557	+	1.32365i
$874$	−1.38197e6	−	1.73294e6i	−0.0611956	−	0.0767369i
$875$	−2.81084e7	−	1.35363e7i	−1.24112	−	0.597694i
$876$	1.01614e7	−	4.89346e6i	0.447396	−	0.215454i
$877$	5.30442e6	−	6.65153e6i	0.232884	−	0.292027i	−0.651634	−	0.758533i	$-0.725916\pi$
$877$	5.30442e6	−	6.65153e6i	0.232884	−	0.292027i	0.884518	+	0.466507i	$0.154488\pi$
$878$	−1.80779e6	−	7.92044e6i	−0.0791428	−	0.346747i
$879$	−4.84966e6	−	2.12477e7i	−0.211709	−	0.927557i
$880$	−543877.	−	682001.i	−0.0236752	−	0.0296878i
$881$	−854681.	+	3.74460e6i	−0.0370992	+	0.162542i	−0.990084	−	0.140475i	$-0.955137\pi$
$881$	−854681.	+	3.74460e6i	−0.0370992	+	0.162542i	0.952985	+	0.303017i	$0.0979941\pi$
$882$	3.01475e7			1.30491
$883$	−953474.	+	4.17744e6i	−0.0411535	+	0.180305i	−0.991327	−	0.131415i	$-0.958048\pi$
$883$	−953474.	+	4.17744e6i	−0.0411535	+	0.180305i	0.950174	+	0.311720i	$0.100905\pi$
$884$	−4.48004e6	+	2.15747e6i	−0.192820	+	0.0928571i
$885$	−1.13163e7	+	5.44965e6i	−0.485677	+	0.233889i
$886$	5.52388e6	−	2.42017e7i	0.236407	−	1.03577i
$887$	−4.72746e6			−0.201752			−0.100876	−	0.994899i	$-0.532165\pi$
$887$	−4.72746e6			−0.201752			−0.100876	+	0.994899i	$0.532165\pi$
$888$	−1.23570e7	+	5.41395e7i	−0.525872	+	2.30399i
$889$	1.10396e7	+	1.38432e7i	0.468487	+	0.587464i
$890$	−1.49785e6	−	6.56251e6i	−0.0633860	−	0.277712i
$891$	−3.76006e6	−	1.64739e7i	−0.158672	−	0.695188i
$892$	−304005.	+	381210.i	−0.0127929	+	0.0160418i
$893$	−7.76902e6	+	3.74136e6i	−0.326015	+	0.157001i
$894$	1.34585e7	+	6.48129e6i	0.563189	+	0.271218i
$895$	7.57996e6	+	9.50496e6i	0.316307	+	0.396637i
$896$	−1.16091e7	+	1.45574e7i	−0.483093	+	0.605779i
$897$	1.54757e7	+	7.45270e6i	0.642198	+	0.309266i
$898$	666494.			0.0275807
$899$	1.06353e7	−	3.02095e7i	0.438887	−	1.24665i
$900$	1.00467e7			0.413445
$901$	264161.	+	127213.i	0.0108407	+	0.00522059i
$902$	−7.92937e6	+	9.94312e6i	−0.324506	+	0.406917i
$903$	−5.25938e7	−	6.59506e7i	−2.14642	−	2.69153i
$904$	2.51785e7	+	1.21253e7i	1.02473	+	0.493483i
$905$	1.29773e7	−	6.24955e6i	0.526701	−	0.253646i
$906$	8.22718e6	−	1.03166e7i	0.332990	−	0.417556i
$907$	1.68778e6	+	7.39466e6i	0.0681237	+	0.298469i	0.997500	−	0.0706638i	$-0.0225118\pi$
$907$	1.68778e6	+	7.39466e6i	0.0681237	+	0.298469i	−0.929377	+	0.369133i	$0.879655\pi$
$908$	−4.05635e6	−	1.77720e7i	−0.163275	−	0.715356i
$909$	2.58880e7	+	3.24625e7i	1.03917	+	1.30308i
$910$	−2.48979e6	+	1.09085e7i	−0.0996687	+	0.436677i
$911$	−1.54862e7			−0.618228			−0.309114	−	0.951025i	$-0.600032\pi$
$911$	−1.54862e7			−0.618228			−0.309114	+	0.951025i	$0.600032\pi$
$912$	−264203.	+	1.15755e6i	−0.0105184	+	0.0460841i
$913$	−1.08244e7	+	5.21275e6i	−0.429761	+	0.206962i
$914$	−5.27598e6	+	2.54078e6i	−0.208900	+	0.100601i
$915$	1.92295e6	−	8.42500e6i	0.0759304	−	0.332673i
$916$	8.35731e6			0.329100
$917$	7.52302e6	−	3.29605e7i	0.295440	−	1.29441i
$918$	576948.	+	723469.i	0.0225959	+	0.0283344i
$919$	−2.42173e6	−	1.06103e7i	−0.0945883	−	0.414418i	0.905359	−	0.424646i	$-0.139601\pi$
$919$	−2.42173e6	−	1.06103e7i	−0.0945883	−	0.414418i	−0.999948	+	0.0102278i	$0.996744\pi$
$920$	1.47000e6	+	6.44049e6i	0.0572595	+	0.250870i
$921$	−8.13592e6	+	1.02021e7i	−0.316051	+	0.396316i
$922$	1.12424e7	−	5.41408e6i	0.435546	−	0.209748i
$923$	1.08798e7	+	5.23943e6i	0.420355	+	0.202432i
$924$	−1.45396e7	−	1.82320e7i	−0.560237	−	0.702515i
$925$	−2.18894e7	+	2.74484e7i	−0.841161	+	1.05478i
$926$	−2.80480e7	−	1.35072e7i	−1.07492	−	0.517653i
$927$	2.09891e6			0.0802222
$928$	−2.10073e7	−	1.32556e7i	−0.800757	−	0.505278i
$929$	1.60849e7			0.611475			0.305737	−	0.952116i	$-0.401097\pi$
$929$	1.60849e7			0.611475			0.305737	+	0.952116i	$0.401097\pi$
$930$	1.23413e7	+	5.94327e6i	0.467901	+	0.225329i
$931$	8.99214e6	−	1.12758e7i	0.340008	−	0.426356i
$932$	1.25555e7	+	1.57441e7i	0.473472	+	0.593715i
$933$	−6.67366e6	−	3.21387e6i	−0.250992	−	0.120871i
$934$	8.06704e6	−	3.88488e6i	0.302585	−	0.145717i
$935$	2.03358e6	−	2.55003e6i	0.0760733	−	0.0953929i
$936$	−4.98787e6	−	2.18533e7i	−0.186091	−	0.815318i
$937$	8.83827e6	+	3.87230e7i	0.328865	+	1.44085i	0.821296	+	0.570502i	$0.193251\pi$
$937$	8.83827e6	+	3.87230e7i	0.328865	+	1.44085i	−0.492431	+	0.870351i	$0.663892\pi$
$938$	−2.63042e7	−	3.29844e7i	−0.976153	−	1.22406i
$939$	465766.	−	2.04065e6i	0.0172387	−	0.0755276i
$940$	9.18220e6			0.338943
$941$	9.69030e6	−	4.24560e7i	0.356749	−	1.56302i	−0.404486	−	0.914544i	$-0.632549\pi$
$941$	9.69030e6	−	4.24560e7i	0.356749	−	1.56302i	0.761235	−	0.648476i	$-0.224593\pi$
$942$	1.52327e7	−	7.33569e6i	0.559307	−	0.269348i
$943$	1.69639e7	−	8.16940e6i	0.621223	−	0.299165i
$944$	752400.	−	3.29648e6i	0.0274801	−	0.120398i
$945$	−2.60637e6			−0.0949417
$946$	3.77242e6	−	1.65281e7i	0.137054	−	0.600474i
$947$	−2.72058e7	−	3.41150e7i	−0.985795	−	1.23615i	−0.971693	−	0.236247i	$-0.924082\pi$
$947$	−2.72058e7	−	3.41150e7i	−0.985795	−	1.23615i	−0.0141021	−	0.999901i	$-0.504489\pi$
$948$	−1.49709e6	−	6.55920e6i	−0.0541039	−	0.237045i
$949$	−3.53994e6	−	1.55095e7i	−0.127594	−	0.559026i
$950$	−2.39401e6	+	3.00199e6i	−0.0860631	+	0.107920i
$951$	−3.51621e7	+	1.69332e7i	−1.26073	+	0.607138i
$952$	2.01348e7	+	9.69641e6i	0.720038	+	0.346752i
$953$	1.16262e7	+	1.45788e7i	0.414673	+	0.519984i	0.944673	−	0.328014i	$-0.106379\pi$
$953$	1.16262e7	+	1.45788e7i	0.414673	+	0.519984i	−0.530000	+	0.847998i	$0.677808\pi$
$954$	−294424.	+	369196.i	−0.0104737	+	0.0131337i
$955$	9.23540e6	+	4.44753e6i	0.327678	+	0.157801i
$956$	2.46701e7			0.873023
$957$	1.82705e7	−	1.82011e7i	0.644868	−	0.642418i
$958$	2.38794e6			0.0840639
$959$	7.88096e7	+	3.79527e7i	2.76715	+	1.33259i
$960$	8.04198e6	−	1.00843e7i	0.281634	−	0.353158i
$961$	1.33295e7	+	1.67147e7i	0.465592	+	0.583834i
$962$	2.52143e7	+	1.21426e7i	0.878436	+	0.423032i
$963$	−1.98604e7	+	9.56425e6i	−0.690115	+	0.332342i
$964$	700080.	−	877873.i	0.0242636	−	0.0304256i
$965$	433191.	+	1.89793e6i	0.0149748	+	0.0656089i
$966$	−6.13748e6	−	2.68901e7i	−0.211615	−	0.927148i
$967$	5.26339e6	+	6.60008e6i	0.181009	+	0.226978i	0.864055	−	0.503397i	$-0.167917\pi$
$967$	5.26339e6	+	6.60008e6i	0.181009	+	0.226978i	−0.683046	+	0.730375i	$0.739345\pi$
$968$	−3.80746e6	+	1.66816e7i	−0.130601	+	0.572201i
$969$	−4.43942e6			−0.151886
$970$	−3.45246e6	+	1.51262e7i	−0.117815	+	0.516180i
$971$	2.69360e7	−	1.29717e7i	0.916821	−	0.441518i	0.0848858	−	0.996391i	$-0.472947\pi$
$971$	2.69360e7	−	1.29717e7i	0.916821	−	0.441518i	0.831935	+	0.554873i	$0.187233\pi$
$972$	2.02173e7	−	9.73616e6i	0.686370	−	0.330539i
$973$	−2.42606e6	+	1.06293e7i	−0.0821523	+	0.359933i
$974$	−1.32242e7			−0.446654
$975$	6.62122e6	−	2.90095e7i	0.223063	−	0.977301i
$976$	1.45047e6	+	1.81883e6i	0.0487399	+	0.0611179i
$977$	2.28422e6	+	1.00078e7i	0.0765600	+	0.335431i	0.998674	−	0.0514880i	$-0.0163964\pi$
$977$	2.28422e6	+	1.00078e7i	0.0765600	+	0.335431i	−0.922114	+	0.386919i	$0.873539\pi$
$978$	1.68128e6	+	7.36618e6i	0.0562074	+	0.246261i
$979$	1.23379e7	−	1.54712e7i	0.411418	−	0.515902i
$980$	−1.38367e7	+	6.66343e6i	−0.460223	+	0.221632i
$981$	2.98170e7	+	1.43591e7i	0.989218	+	0.476382i
$982$	5.66681e6	+	7.10596e6i	0.187525	+	0.235150i
$983$	−2.23519e7	+	2.80284e7i	−0.737788	+	0.925156i	−0.999197	−	0.0400716i	$-0.987241\pi$
$983$	−2.23519e7	+	2.80284e7i	−0.737788	+	0.925156i	0.261409	+	0.965228i	$0.415813\pi$
$984$	−4.64826e7	−	2.23849e7i	−1.53039	−	0.736998i
$985$	−1.67354e7			−0.549598
$986$	−2.93229e6	+	8.32909e6i	−0.0960537	+	0.272838i
$987$	−1.07302e8			−3.50601
$988$	−3.45183e6	−	1.66232e6i	−0.112501	−	0.0541778i
$989$	−1.56490e7	+	1.96232e7i	−0.508739	+	0.637939i
$990$	3.27527e6	+	4.10705e6i	0.106208	+	0.133181i
$991$	6.73948e6	+	3.24556e6i	0.217993	+	0.104980i	0.539693	−	0.841862i	$-0.318540\pi$
$991$	6.73948e6	+	3.24556e6i	0.217993	+	0.104980i	−0.321701	+	0.946841i	$0.604254\pi$
$992$	3.49449e7	−	1.68286e7i	1.12747	−	0.542961i
$993$	1.27969e6	−	1.60469e6i	0.0411844	−	0.0516436i
$994$	−4.31479e6	−	1.89043e7i	−0.138514	−	0.606870i
$995$	3.31752e6	+	1.45350e7i	0.106232	+	0.465433i
$996$	−1.08570e7	−	1.36142e7i	−0.346785	−	0.434854i
$997$	−7.15316e6	+	3.13401e7i	−0.227908	+	0.998532i	0.723434	+	0.690394i	$0.242563\pi$
$997$	−7.15316e6	+	3.13401e7i	−0.227908	+	0.998532i	−0.951342	+	0.308138i	$0.900294\pi$
$998$	8.22122e6			0.261282
$999$	−1.45062e6	+	6.35558e6i	−0.0459875	+	0.201485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.6.d.a.16.4	✓	66
29.7	even	7		841.6.a.i.1.22		33
29.20	even	7	inner	29.6.d.a.20.4	yes	66
29.22	even	14		841.6.a.h.1.12		33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.6.d.a.16.4	✓	66	1.1	even	1	trivial
29.6.d.a.20.4	yes	66	29.20	even	7	inner
841.6.a.h.1.12		33	29.22	even	14
841.6.a.i.1.22		33	29.7	even	7

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	29.d (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.39646 - 1.63565i) q^{2} +(-13.4299 + 16.8406i) q^{3} +(-11.0911 - 13.9078i) q^{4} +(21.4922 + 10.3501i) q^{5} +(73.1594 - 35.2317i) q^{6} +(143.536 - 179.989i) q^{7} +(41.7656 + 182.987i) q^{8} +(-49.1696 - 215.426i) q^{9} +O(q^{10})\)	\(q+(-3.39646 - 1.63565i) q^{2} +(-13.4299 + 16.8406i) q^{3} +(-11.0911 - 13.9078i) q^{4} +(21.4922 + 10.3501i) q^{5} +(73.1594 - 35.2317i) q^{6} +(143.536 - 179.989i) q^{7} +(41.7656 + 182.987i) q^{8} +(-49.1696 - 215.426i) q^{9} +(-56.0684 - 70.3076i) q^{10} +(58.8265 - 257.736i) q^{11} +383.166 q^{12} +(120.266 - 526.918i) q^{13} +(-781.914 + 376.550i) q^{14} +(-462.940 + 222.940i) q^{15} +(30.7800 - 134.856i) q^{16} +517.199 q^{17} +(-185.359 + 812.111i) q^{18} +(248.459 + 311.558i) q^{19} +(-94.4250 - 413.703i) q^{20} +(1103.43 + 4834.46i) q^{21} +(-621.368 + 779.171i) q^{22} +(1329.34 - 640.177i) q^{23} +(-3642.51 - 1754.14i) q^{24} +(-1593.61 - 1998.33i) q^{25} +(-1270.33 + 1592.94i) q^{26} +(-427.604 - 205.923i) q^{27} -4095.21 q^{28} +(-498.509 - 4501.40i) q^{29} +1937.01 q^{30} +(6371.32 + 3068.27i) q^{31} +(3419.67 - 4288.13i) q^{32} +(3550.38 + 4452.04i) q^{33} +(-1756.65 - 845.956i) q^{34} +(4947.82 - 2382.75i) q^{35} +(-2450.75 + 3073.15i) q^{36} +(-3056.48 - 13391.3i) q^{37} +(-334.282 - 1464.59i) q^{38} +(7258.43 + 9101.79i) q^{39} +(-996.301 + 4365.08i) q^{40} +12761.2 q^{41} +(4159.71 - 18224.9i) q^{42} +(-15326.4 + 7380.80i) q^{43} +(-4236.98 + 2040.42i) q^{44} +(1172.92 - 5138.90i) q^{45} -5562.16 q^{46} +(-4815.06 + 21096.2i) q^{47} +(1857.68 + 2329.45i) q^{48} +(-8053.39 - 35284.2i) q^{49} +(2144.08 + 9393.84i) q^{50} +(-6945.93 + 8709.92i) q^{51} +(-8662.12 + 4171.46i) q^{52} +(510.752 + 245.965i) q^{53} +(1115.52 + 1398.82i) q^{54} +(3931.91 - 4930.46i) q^{55} +(38930.5 + 18747.9i) q^{56} -8583.59 q^{57} +(-5669.55 + 16104.2i) q^{58} +24444.5 q^{59} +(8235.10 + 3965.82i) q^{60} +(-10486.0 + 13149.1i) q^{61} +(-16621.3 - 20842.5i) q^{62} +(-45831.9 - 22071.5i) q^{63} +(-22616.7 + 10891.6i) q^{64} +(8038.44 - 10079.9i) q^{65} +(-4776.76 - 20928.4i) q^{66} +(10817.3 + 47393.5i) q^{67} +(-5736.29 - 7193.08i) q^{68} +(-7071.98 + 30984.4i) q^{69} -20702.4 q^{70} +(-4971.77 + 21782.7i) q^{71} +(37366.6 - 17994.8i) q^{72} +(26519.5 - 12771.1i) q^{73} +(-11522.3 + 50482.4i) q^{74} +55055.0 q^{75} +(1577.40 - 6911.02i) q^{76} +(-37945.8 - 47582.6i) q^{77} +(-9765.66 - 42786.1i) q^{78} +(-3907.17 - 17118.4i) q^{79} +(2057.30 - 2579.78i) q^{80} +(57587.9 - 27732.9i) q^{81} +(-43342.8 - 20872.8i) q^{82} +(-28334.8 - 35530.8i) q^{83} +(54998.3 - 68965.6i) q^{84} +(11115.8 + 5353.07i) q^{85} +64127.9 q^{86} +(82501.1 + 52058.2i) q^{87} +49619.2 q^{88} +(67440.1 + 32477.4i) q^{89} +(-12389.2 + 15535.6i) q^{90} +(-77576.8 - 97278.3i) q^{91} +(-23647.3 - 11387.9i) q^{92} +(-137238. + 66090.1i) q^{93} +(50860.1 - 63776.5i) q^{94} +(2115.28 + 9267.66i) q^{95} +(26288.7 + 115178. i) q^{96} +(-107572. - 134891. i) q^{97} +(-30359.6 + 133014. i) q^{98} -58415.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 11 q^{2} - 5 q^{3} - 171 q^{4} + 29 q^{5} + 445 q^{6} + 17 q^{7} + 1046 q^{8} - 732 q^{9}+O(q^{10}) \) 66 * q - 11 * q^2 - 5 * q^3 - 171 * q^4 + 29 * q^5 + 445 * q^6 + 17 * q^7 + 1046 * q^8 - 732 * q^9	\( 66 q - 11 q^{2} - 5 q^{3} - 171 q^{4} + 29 q^{5} + 445 q^{6} + 17 q^{7} + 1046 q^{8} - 732 q^{9} - 141 q^{10} + 1125 q^{11} - 248 q^{12} - 1789 q^{13} + 1233 q^{14} + 1061 q^{15} + 2629 q^{16} + 676 q^{17} - 10896 q^{18} - 1903 q^{19} + 4081 q^{20} - 439 q^{21} - 2980 q^{22} + 9945 q^{23} + 10741 q^{24} - 22114 q^{25} - 1641 q^{26} - 4427 q^{27} + 7508 q^{28} - 13100 q^{29} - 40018 q^{30} + 8541 q^{31} + 18996 q^{32} + 20725 q^{33} - 8839 q^{34} + 14127 q^{35} + 70172 q^{36} + 3791 q^{37} + 36322 q^{38} + 25843 q^{39} - 72621 q^{40} - 18720 q^{41} - 72614 q^{42} - 10419 q^{43} + 35796 q^{44} + 23163 q^{45} + 15848 q^{46} - 40549 q^{47} - 4194 q^{48} + 19808 q^{49} + 201932 q^{50} + 51998 q^{51} + 8330 q^{52} - 72275 q^{53} - 197108 q^{54} + 42183 q^{55} + 31599 q^{56} - 40162 q^{57} - 258031 q^{58} - 333512 q^{59} + 26920 q^{60} - 175281 q^{61} + 213745 q^{62} + 354423 q^{63} - 19790 q^{64} - 79593 q^{65} + 103783 q^{66} + 135179 q^{67} + 334644 q^{68} + 73673 q^{69} - 511678 q^{70} - 187563 q^{71} - 17551 q^{72} - 56675 q^{73} + 159980 q^{74} + 538208 q^{75} - 215041 q^{76} + 106099 q^{77} + 37481 q^{78} + 273775 q^{79} + 571652 q^{80} - 61356 q^{81} - 37092 q^{82} - 237831 q^{83} + 127523 q^{84} - 148844 q^{85} - 348400 q^{86} - 110493 q^{87} - 985638 q^{88} + 74239 q^{89} - 630714 q^{90} + 100309 q^{91} + 132694 q^{92} - 307921 q^{93} + 206074 q^{94} + 37965 q^{95} + 687094 q^{96} + 136055 q^{97} - 115704 q^{98} + 438608 q^{99}+O(q^{100}) \) 66 * q - 11 * q^2 - 5 * q^3 - 171 * q^4 + 29 * q^5 + 445 * q^6 + 17 * q^7 + 1046 * q^8 - 732 * q^9 - 141 * q^10 + 1125 * q^11 - 248 * q^12 - 1789 * q^13 + 1233 * q^14 + 1061 * q^15 + 2629 * q^16 + 676 * q^17 - 10896 * q^18 - 1903 * q^19 + 4081 * q^20 - 439 * q^21 - 2980 * q^22 + 9945 * q^23 + 10741 * q^24 - 22114 * q^25 - 1641 * q^26 - 4427 * q^27 + 7508 * q^28 - 13100 * q^29 - 40018 * q^30 + 8541 * q^31 + 18996 * q^32 + 20725 * q^33 - 8839 * q^34 + 14127 * q^35 + 70172 * q^36 + 3791 * q^37 + 36322 * q^38 + 25843 * q^39 - 72621 * q^40 - 18720 * q^41 - 72614 * q^42 - 10419 * q^43 + 35796 * q^44 + 23163 * q^45 + 15848 * q^46 - 40549 * q^47 - 4194 * q^48 + 19808 * q^49 + 201932 * q^50 + 51998 * q^51 + 8330 * q^52 - 72275 * q^53 - 197108 * q^54 + 42183 * q^55 + 31599 * q^56 - 40162 * q^57 - 258031 * q^58 - 333512 * q^59 + 26920 * q^60 - 175281 * q^61 + 213745 * q^62 + 354423 * q^63 - 19790 * q^64 - 79593 * q^65 + 103783 * q^66 + 135179 * q^67 + 334644 * q^68 + 73673 * q^69 - 511678 * q^70 - 187563 * q^71 - 17551 * q^72 - 56675 * q^73 + 159980 * q^74 + 538208 * q^75 - 215041 * q^76 + 106099 * q^77 + 37481 * q^78 + 273775 * q^79 + 571652 * q^80 - 61356 * q^81 - 37092 * q^82 - 237831 * q^83 + 127523 * q^84 - 148844 * q^85 - 348400 * q^86 - 110493 * q^87 - 985638 * q^88 + 74239 * q^89 - 630714 * q^90 + 100309 * q^91 + 132694 * q^92 - 307921 * q^93 + 206074 * q^94 + 37965 * q^95 + 687094 * q^96 + 136055 * q^97 - 115704 * q^98 + 438608 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more