LMFDB - Embedded newform 61.6.g.a.3.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,6,Mod(3,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("61.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	61.g (of order $10$, degree $4$, 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:	$9.78341300859$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$26$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			3.10
Character	$\chi$	$=$	61.3
Dual form			61.6.g.a.41.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.71354 - 1.20660i) q^{2} +(-7.25729 + 22.3356i) q^{3} +(-13.5540 - 9.84758i) q^{4} +(60.5656 + 44.0035i) q^{5} +(53.9005 - 74.1877i) q^{6} +(178.785 - 58.0907i) q^{7} +(111.894 + 154.009i) q^{8} +(-249.622 - 181.361i) q^{9} +O(q^{10})$	\(q+(-3.71354 - 1.20660i) q^{2} +(-7.25729 + 22.3356i) q^{3} +(-13.5540 - 9.84758i) q^{4} +(60.5656 + 44.0035i) q^{5} +(53.9005 - 74.1877i) q^{6} +(178.785 - 58.0907i) q^{7} +(111.894 + 154.009i) q^{8} +(-249.622 - 181.361i) q^{9} +(-171.818 - 236.487i) q^{10} +634.842i q^{11} +(318.317 - 231.271i) q^{12} -662.727 q^{13} -734.018 q^{14} +(-1422.39 + 1033.43i) q^{15} +(-64.0269 - 197.054i) q^{16} +(-107.680 + 148.209i) q^{17} +(708.150 + 974.685i) q^{18} +(652.794 - 2009.09i) q^{19} +(-387.580 - 1192.85i) q^{20} +4414.86i q^{21} +(766.003 - 2357.51i) q^{22} +(-2186.66 + 3009.67i) q^{23} +(-4251.95 + 1381.54i) q^{24} +(766.206 + 2358.14i) q^{25} +(2461.07 + 799.649i) q^{26} +(1245.42 - 904.853i) q^{27} +(-2995.31 - 973.234i) q^{28} +5253.38i q^{29} +(6529.03 - 2121.41i) q^{30} +(4618.04 - 1500.49i) q^{31} -5282.69i q^{32} +(-14179.6 - 4607.23i) q^{33} +(578.704 - 420.453i) q^{34} +(13384.4 + 4348.86i) q^{35} +(1597.41 + 4916.33i) q^{36} +(-4681.91 + 1521.25i) q^{37} +(-4848.36 + 6673.20i) q^{38} +(4809.60 - 14802.4i) q^{39} +14251.4i q^{40} +(-3828.40 - 11782.6i) q^{41} +(5326.98 - 16394.8i) q^{42} +(-689.950 - 949.634i) q^{43} +(6251.66 - 8604.67i) q^{44} +(-7137.97 - 21968.4i) q^{45} +(11751.7 - 8538.13i) q^{46} -19998.0 q^{47} +4866.00 q^{48} +(14992.3 - 10892.6i) q^{49} -9681.56i q^{50} +(-2528.87 - 3480.70i) q^{51} +(8982.62 + 6526.26i) q^{52} +(18545.7 + 25526.0i) q^{53} +(-5716.73 + 1857.48i) q^{54} +(-27935.3 + 38449.6i) q^{55} +(28951.6 + 21034.5i) q^{56} +(40136.9 + 29161.2i) q^{57} +(6338.75 - 19508.7i) q^{58} +(-7198.21 - 2338.84i) q^{59} +29455.8 q^{60} +(-3165.30 + 28889.0i) q^{61} -18959.8 q^{62} +(-55163.9 - 17923.8i) q^{63} +(-8422.98 + 25923.3i) q^{64} +(-40138.5 - 29162.3i) q^{65} +(47097.5 + 34218.3i) q^{66} +(4057.73 - 5584.98i) q^{67} +(2918.99 - 948.439i) q^{68} +(-51353.8 - 70682.5i) q^{69} +(-44456.2 - 32299.3i) q^{70} +(21200.7 + 29180.2i) q^{71} -58737.3i q^{72} +(20443.1 - 14852.8i) q^{73} +19222.0 q^{74} -58231.1 q^{75} +(-28632.7 + 20802.9i) q^{76} +(36878.4 + 113500. i) q^{77} +(-35721.4 + 49166.2i) q^{78} +(-5904.14 - 8126.35i) q^{79} +(4793.26 - 14752.1i) q^{80} +(-11997.2 - 36923.7i) q^{81} +48374.6i q^{82} +(24889.9 - 76603.2i) q^{83} +(43475.6 - 59839.1i) q^{84} +(-13043.4 + 4238.06i) q^{85} +(1416.33 + 4359.00i) q^{86} +(-117338. - 38125.3i) q^{87} +(-97771.7 + 71035.3i) q^{88} +(85533.7 + 27791.6i) q^{89} +90193.4i q^{90} +(-118486. + 38498.3i) q^{91} +(59276.0 - 19259.9i) q^{92} +114036. i q^{93} +(74263.4 + 24129.6i) q^{94} +(127944. - 92956.7i) q^{95} +(117992. + 38338.0i) q^{96} +(14474.5 + 44547.8i) q^{97} +(-68817.7 + 22360.2i) q^{98} +(115135. - 158470. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9}+O(q^{10}) $ 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9} - 595 q^{10} + 1982 q^{12} + 2372 q^{13} - 4474 q^{14} - 1149 q^{15} - 8631 q^{16} + 950 q^{17} + 4340 q^{18} - 5597 q^{19} - 6627 q^{20} - 8639 q^{22} + 9065 q^{23} + 17220 q^{24} - 7694 q^{25} + 14810 q^{26} + 4500 q^{27} + 19835 q^{28} - 44585 q^{30} + 10905 q^{31} - 19205 q^{33} - 15376 q^{34} - 43790 q^{35} - 25135 q^{36} - 5 q^{37} + 17555 q^{38} + 29401 q^{39} - 21014 q^{41} + 62197 q^{42} - 31625 q^{43} + 146190 q^{44} + 153742 q^{45} + 13387 q^{46} + 27326 q^{47} - 82968 q^{48} + 14694 q^{49} + 34090 q^{51} + 90072 q^{52} - 40270 q^{53} - 13760 q^{54} + 25140 q^{55} - 97860 q^{56} + 114893 q^{57} - 18003 q^{58} - 117435 q^{59} - 536650 q^{60} - 121867 q^{61} - 157388 q^{62} - 160825 q^{63} + 132509 q^{64} - 155852 q^{65} + 308443 q^{66} + 101665 q^{67} + 303780 q^{68} + 281945 q^{69} + 264985 q^{70} + 160970 q^{71} + 127669 q^{73} - 133952 q^{74} - 139592 q^{75} - 641111 q^{76} + 128917 q^{77} + 1670 q^{78} + 187940 q^{79} + 785373 q^{80} - 453473 q^{81} - 301209 q^{83} + 100475 q^{84} - 340045 q^{85} - 462669 q^{86} + 189245 q^{87} - 881635 q^{88} - 201970 q^{89} + 93865 q^{91} - 622085 q^{92} - 285265 q^{94} - 113308 q^{95} + 1215465 q^{96} - 342131 q^{97} - 616150 q^{98} + 714235 q^{99}+O(q^{100}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9 - 595 * q^10 + 1982 * q^12 + 2372 * q^13 - 4474 * q^14 - 1149 * q^15 - 8631 * q^16 + 950 * q^17 + 4340 * q^18 - 5597 * q^19 - 6627 * q^20 - 8639 * q^22 + 9065 * q^23 + 17220 * q^24 - 7694 * q^25 + 14810 * q^26 + 4500 * q^27 + 19835 * q^28 - 44585 * q^30 + 10905 * q^31 - 19205 * q^33 - 15376 * q^34 - 43790 * q^35 - 25135 * q^36 - 5 * q^37 + 17555 * q^38 + 29401 * q^39 - 21014 * q^41 + 62197 * q^42 - 31625 * q^43 + 146190 * q^44 + 153742 * q^45 + 13387 * q^46 + 27326 * q^47 - 82968 * q^48 + 14694 * q^49 + 34090 * q^51 + 90072 * q^52 - 40270 * q^53 - 13760 * q^54 + 25140 * q^55 - 97860 * q^56 + 114893 * q^57 - 18003 * q^58 - 117435 * q^59 - 536650 * q^60 - 121867 * q^61 - 157388 * q^62 - 160825 * q^63 + 132509 * q^64 - 155852 * q^65 + 308443 * q^66 + 101665 * q^67 + 303780 * q^68 + 281945 * q^69 + 264985 * q^70 + 160970 * q^71 + 127669 * q^73 - 133952 * q^74 - 139592 * q^75 - 641111 * q^76 + 128917 * q^77 + 1670 * q^78 + 187940 * q^79 + 785373 * q^80 - 453473 * q^81 - 301209 * q^83 + 100475 * q^84 - 340045 * q^85 - 462669 * q^86 + 189245 * q^87 - 881635 * q^88 - 201970 * q^89 + 93865 * q^91 - 622085 * q^92 - 285265 * q^94 - 113308 * q^95 + 1215465 * q^96 - 342131 * q^97 - 616150 * q^98 + 714235 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−3.71354	−	1.20660i	−0.656468	−	0.213299i	−0.0382041	−	0.999270i	$-0.512164\pi$
$2$	−3.71354	−	1.20660i	−0.656468	−	0.213299i	−0.618264	+	0.785971i	$0.712164\pi$
$3$	−7.25729	+	22.3356i	−0.465555	+	1.43283i	0.392727	+	0.919655i	$0.371532\pi$
$3$	−7.25729	+	22.3356i	−0.465555	+	1.43283i	−0.858283	+	0.513177i	$0.828468\pi$
$4$	−13.5540	−	9.84758i	−0.423563	−	0.307737i
$5$	60.5656	+	44.0035i	1.08343	+	0.787158i	0.978278	−	0.207298i	$-0.0664670\pi$
$5$	60.5656	+	44.0035i	1.08343	+	0.787158i	0.105152	+	0.994456i	$0.466467\pi$
$6$	53.9005	−	74.1877i	0.611244	−	0.841306i
$7$	178.785	−	58.0907i	1.37907	−	0.448086i	0.476705	−	0.879063i	$-0.341831\pi$
$7$	178.785	−	58.0907i	1.37907	−	0.448086i	0.902363	+	0.430977i	$0.141831\pi$
$8$	111.894	+	154.009i	0.618135	+	0.850790i
$9$	−249.622	−	181.361i	−1.02725	−	0.746340i
$10$	−171.818	−	236.487i	−0.543337	−	0.747839i
$11$			634.842i			1.58192i	0.611869	+	0.790959i	$0.290418\pi$
$11$			634.842i			1.58192i	−0.611869	+	0.790959i	$0.709582\pi$
$12$	318.317	−	231.271i	0.638127	−	0.463627i
$13$	−662.727			−1.08762			−0.543809	−	0.839209i	$-0.683018\pi$
$13$	−662.727			−1.08762			−0.543809	+	0.839209i	$0.683018\pi$
$14$	−734.018			−1.00089
$15$	−1422.39	+	1033.43i	−1.63226	+	1.18591i
$16$	−64.0269	−	197.054i	−0.0625263	−	0.192436i
$17$	−107.680	+	148.209i	−0.0903676	+	0.124380i	−0.851807	−	0.523856i	$-0.824493\pi$
$17$	−107.680	+	148.209i	−0.0903676	+	0.124380i	0.761439	+	0.648236i	$0.224493\pi$
$18$	708.150	+	974.685i	0.515162	+	0.709060i
$19$	652.794	−	2009.09i	0.414851	−	1.27678i	−0.497533	−	0.867445i	$-0.665761\pi$
$19$	652.794	−	2009.09i	0.414851	−	1.27678i	0.912384	−	0.409336i	$-0.134239\pi$
$20$	−387.580	−	1192.85i	−0.216664	−	0.666822i
$21$			4414.86i			2.18458i
$22$	766.003	−	2357.51i	0.337422	−	1.03848i
$23$	−2186.66	+	3009.67i	−0.861908	+	1.18631i	0.119203	+	0.992870i	$0.461966\pi$
$23$	−2186.66	+	3009.67i	−0.861908	+	1.18631i	−0.981111	+	0.193445i	$0.938034\pi$
$24$	−4251.95	+	1381.54i	−1.50682	+	0.489594i
$25$	766.206	+	2358.14i	0.245186	+	0.754605i
$26$	2461.07	+	799.649i	0.713987	+	0.231988i
$27$	1245.42	−	904.853i	0.328782	−	0.238874i
$28$	−2995.31	−	973.234i	−0.722015	−	0.234597i
$29$			5253.38i			1.15996i	0.814630	+	0.579981i	$0.196940\pi$
$29$			5253.38i			1.15996i	−0.814630	+	0.579981i	$0.803060\pi$
$30$	6529.03	−	2121.41i	1.32448	−	0.430350i
$31$	4618.04	−	1500.49i	0.863085	−	0.280433i	0.156169	−	0.987730i	$-0.450086\pi$
$31$	4618.04	−	1500.49i	0.863085	−	0.280433i	0.706917	+	0.707297i	$0.250086\pi$
$32$		−	5282.69i		−	0.911970i
$33$	−14179.6	−	4607.23i	−2.26662	−	0.736471i
$34$	578.704	−	420.453i	0.0858537	−	0.0623763i
$35$	13384.4	+	4348.86i	1.84684	+	0.600074i
$36$	1597.41	+	4916.33i	0.205429	+	0.632245i
$37$	−4681.91	+	1521.25i	−0.562236	+	0.182682i	−0.576327	−	0.817219i	$-0.695515\pi$
$37$	−4681.91	+	1521.25i	−0.562236	+	0.182682i	0.0140908	+	0.999901i	$0.495515\pi$
$38$	−4848.36	+	6673.20i	−0.544673	+	0.749678i
$39$	4809.60	−	14802.4i	0.506347	−	1.55837i
$40$			14251.4i			1.40834i
$41$	−3828.40	−	11782.6i	−0.355679	−	1.09467i	−0.955615	−	0.294619i	$-0.904807\pi$
$41$	−3828.40	−	11782.6i	−0.355679	−	1.09467i	0.599936	−	0.800048i	$-0.295193\pi$
$42$	5326.98	−	16394.8i	0.465970	−	1.43411i
$43$	−689.950	−	949.634i	−0.0569044	−	0.0783223i	0.779616	−	0.626257i	$-0.215414\pi$
$43$	−689.950	−	949.634i	−0.0569044	−	0.0783223i	−0.836521	+	0.547935i	$0.815414\pi$
$44$	6251.66	−	8604.67i	0.486814	−	0.670043i
$45$	−7137.97	−	21968.4i	−0.525465	−	1.61721i
$46$	11751.7	−	8538.13i	0.818855	−	0.594933i
$47$	−19998.0			−1.32051			−0.660255	−	0.751042i	$-0.729552\pi$
$47$	−19998.0			−1.32051			−0.660255	+	0.751042i	$0.729552\pi$
$48$	4866.00			0.304838
$49$	14992.3	−	10892.6i	0.892029	−	0.648097i
$50$		−	9681.56i		−	0.547672i
$51$	−2528.87	−	3480.70i	−0.136145	−	0.187387i
$52$	8982.62	+	6526.26i	0.460675	+	0.334700i
$53$	18545.7	+	25526.0i	0.906889	+	1.24823i	0.968218	+	0.250107i	$0.0804659\pi$
$53$	18545.7	+	25526.0i	0.906889	+	1.24823i	−0.0613295	+	0.998118i	$0.519534\pi$
$54$	−5716.73	+	1857.48i	−0.266786	+	0.0866841i
$55$	−27935.3	+	38449.6i	−1.24522	+	1.71390i
$56$	28951.6	+	21034.5i	1.23368	+	0.896319i
$57$	40136.9	+	29161.2i	1.63628	+	1.18882i
$58$	6338.75	−	19508.7i	0.247419	−	0.761478i
$59$	−7198.21	−	2338.84i	−0.269212	−	0.0874723i	0.171300	−	0.985219i	$-0.445203\pi$
$59$	−7198.21	−	2338.84i	−0.269212	−	0.0874723i	−0.440512	+	0.897747i	$0.645203\pi$
$60$	29455.8			1.05631
$61$	−3165.30	+	28889.0i	−0.108916	+	0.994051i
$61$	−3165.30	+	28889.0i	−0.108916	+	0.994051i
$62$	−18959.8			−0.626404
$63$	−55163.9	−	17923.8i	−1.75107	−	0.568957i
$64$	−8422.98	+	25923.3i	−0.257049	+	0.791115i
$65$	−40138.5	−	29162.3i	−1.17836	−	0.856127i
$66$	47097.5	+	34218.3i	1.33088	+	0.966939i
$67$	4057.73	−	5584.98i	0.110432	−	0.151997i	−0.750223	−	0.661184i	$-0.770054\pi$
$67$	4057.73	−	5584.98i	0.110432	−	0.151997i	0.860656	+	0.509188i	$0.170054\pi$
$68$	2918.99	−	948.439i	0.0765528	−	0.0248735i
$69$	−51353.8	−	70682.5i	−1.29852	−	1.78726i
$70$	−44456.2	−	32299.3i	−1.08439	−	0.787859i
$71$	21200.7	+	29180.2i	0.499118	+	0.686977i	0.982037	−	0.188688i	$-0.0604234\pi$
$71$	21200.7	+	29180.2i	0.499118	+	0.686977i	−0.482919	+	0.875665i	$0.660423\pi$
$72$		−	58737.3i		−	1.33531i
$73$	20443.1	−	14852.8i	0.448993	−	0.326212i	−0.340205	−	0.940351i	$-0.610497\pi$
$73$	20443.1	−	14852.8i	0.448993	−	0.326212i	0.789198	+	0.614139i	$0.210497\pi$
$74$	19222.0			0.408056
$75$	−58231.1			−1.19537
$76$	−28632.7	+	20802.9i	−0.568628	+	0.413132i
$77$	36878.4	+	113500.i	0.708836	+	2.18157i
$78$	−35721.4	+	49166.2i	−0.664801	+	0.915020i
$79$	−5904.14	−	8126.35i	−0.106436	−	0.146497i	0.752476	−	0.658619i	$-0.228859\pi$
$79$	−5904.14	−	8126.35i	−0.106436	−	0.146497i	−0.858912	+	0.512123i	$0.828859\pi$
$80$	4793.26	−	14752.1i	0.0837347	−	0.257709i
$81$	−11997.2	−	36923.7i	−0.203174	−	0.625306i
$82$			48374.6i			0.794480i
$83$	24889.9	−	76603.2i	0.396577	−	1.22054i	−0.531149	−	0.847279i	$-0.678240\pi$
$83$	24889.9	−	76603.2i	0.396577	−	1.22054i	0.927726	−	0.373261i	$-0.121760\pi$
$84$	43475.6	−	59839.1i	0.672276	−	0.925309i
$85$	−13043.4	+	4238.06i	−0.195814	+	0.0636238i
$86$	1416.33	+	4359.00i	0.0206499	+	0.0635537i
$87$	−117338.	−	38125.3i	−1.66203	−	0.540027i
$88$	−97771.7	+	71035.3i	−1.34588	+	0.977840i
$89$	85533.7	+	27791.6i	1.14462	+	0.371910i	0.819115	−	0.573629i	$-0.194465\pi$
$89$	85533.7	+	27791.6i	1.14462	+	0.371910i	0.325507	+	0.945540i	$0.394465\pi$
$90$			90193.4i			1.17373i
$91$	−118486.	+	38498.3i	−1.49990	+	0.487347i
$92$	59276.0	−	19259.9i	0.730145	−	0.237239i
$93$			114036.i			1.36721i
$94$	74263.4	+	24129.6i	0.866873	+	0.281664i
$95$	127944.	−	92956.7i	1.45449	−	1.05675i
$96$	117992.	+	38338.0i	1.30670	+	0.424572i
$97$	14474.5	+	44547.8i	0.156197	+	0.480725i	0.998280	−	0.0586226i	$-0.0186709\pi$
$97$	14474.5	+	44547.8i	0.156197	+	0.480725i	−0.842083	+	0.539348i	$0.818671\pi$
$98$	−68817.7	+	22360.2i	−0.723828	+	0.235186i
$99$	115135.	−	158470.i	1.18065	−	1.62502i
$100$	12836.8	−	39507.6i	0.128368	−	0.395076i
$101$		−	18629.8i		−	0.181721i	−0.995864	−	0.0908604i	$-0.971038\pi$
$101$		−	18629.8i		−	0.181721i	0.995864	−	0.0908604i	$-0.0289617\pi$
$102$	5191.26	+	15977.1i	0.0494052	+	0.152054i
$103$	−6003.91	+	18478.1i	−0.0557623	+	0.171619i	−0.975059	−	0.221947i	$-0.928759\pi$
$103$	−6003.91	+	18478.1i	−0.0557623	+	0.171619i	0.919296	+	0.393566i	$0.128759\pi$
$104$	−74155.5	−	102066.i	−0.672295	−	0.925335i
$105$	−194269.	+	267388.i	−1.71961	+	2.36684i
$106$	−38070.6	−	117169.i	−0.329098	−	1.01286i
$107$	68952.7	−	50097.0i	0.582226	−	0.423012i	−0.257300	−	0.966332i	$-0.582833\pi$
$107$	68952.7	−	50097.0i	0.582226	−	0.423012i	0.839526	+	0.543320i	$0.182833\pi$
$108$	−25791.1			−0.212770
$109$	116594.			0.939963			0.469981	−	0.882676i	$-0.344261\pi$
$109$	116594.			0.939963			0.469981	+	0.882676i	$0.344261\pi$
$110$	150132.	−	109077.i	1.18302	−	0.859515i
$111$		−	115614.i		−	0.890639i
$112$	−22894.1	−	31511.0i	−0.172456	−	0.237365i
$113$	154139.	+	111988.i	1.13557	+	0.825043i	0.986496	−	0.163783i	$-0.0523697\pi$
$113$	154139.	+	111988.i	1.13557	+	0.825043i	0.149077	+	0.988826i	$0.452370\pi$
$114$	−113864.	−	156721.i	−0.820588	−	1.12944i
$115$	−264872.	+	86062.2i	−1.86763	+	0.606831i
$116$	51733.1	−	71204.5i	0.356963	−	0.491318i
$117$	165431.	+	120193.i	1.11725	+	0.811733i
$118$	23908.8	+	17370.8i	0.158071	+	0.114846i
$119$	−10642.0	+	32752.7i	−0.0688899	+	0.212021i
$120$	−318315.	−	103427.i	−2.01792	−	0.655661i
$121$	−241974.			−1.50247
$122$	46612.1	−	103462.i	0.283530	−	0.629331i
$123$	290956.			1.73406
$124$	−77369.3	−	25138.8i	−0.451871	−	0.146822i
$125$	14933.1	−	45959.4i	0.0854821	−	0.263087i
$126$	183227.	+	133122.i	1.02816	+	0.747005i
$127$	−40491.8	−	29419.0i	−0.222771	−	0.161852i	0.470802	−	0.882239i	$-0.343965\pi$
$127$	−40491.8	−	29419.0i	−0.222771	−	0.161852i	−0.693573	+	0.720386i	$0.743965\pi$
$128$	−36804.6	+	50657.3i	−0.198554	+	0.273286i
$129$	26217.9	−	8518.70i	0.138715	−	0.0450712i
$130$	113869.	+	156727.i	0.590943	+	0.813363i
$131$	44695.1	+	32472.9i	0.227553	+	0.165327i	0.695720	−	0.718313i	$-0.255086\pi$
$131$	44695.1	+	32472.9i	0.227553	+	0.165327i	−0.468167	+	0.883640i	$0.655086\pi$
$132$	146821.	+	202081.i	0.733419	+	1.00947i
$133$		−	397117.i		−	1.94666i
$134$	−21807.4	+	15844.0i	−0.104916	+	0.0762260i
$135$	115246.			0.544243
$136$	−34874.3			−0.161681
$137$	−332507.	+	241581.i	−1.51356	+	1.09967i	−0.548994	+	0.835826i	$0.684989\pi$
$137$	−332507.	+	241581.i	−1.51356	+	1.09967i	−0.964566	+	0.263840i	$0.915011\pi$
$138$	105419.	+	324446.i	0.471217	+	1.45026i
$139$	249459.	−	343351.i	1.09512	−	1.50731i	0.253424	−	0.967355i	$-0.418443\pi$
$139$	249459.	−	343351.i	1.09512	−	1.50731i	0.841697	−	0.539950i	$-0.181557\pi$
$140$	−138587.	−	190748.i	−0.597588	−	0.822509i
$141$	145131.	−	446668.i	0.614770	−	1.89207i
$142$	−43520.6	−	133943.i	−0.181123	−	0.557440i
$143$		−	420727.i		−	1.72052i
$144$	−19755.4	+	60801.0i	−0.0793927	+	0.244346i
$145$	−231167.	+	318174.i	−0.913074	+	1.25674i
$146$	−93837.7	+	30489.7i	−0.364330	+	0.118378i
$147$	134489.	+	413914.i	0.513326	+	1.57985i
$148$	78439.3	+	25486.5i	0.294361	+	0.0956435i
$149$	−33186.5	+	24111.4i	−0.122460	+	0.0889727i	−0.647330	−	0.762210i	$-0.724114\pi$
$149$	−33186.5	+	24111.4i	−0.122460	+	0.0889727i	0.524869	+	0.851183i	$0.324114\pi$
$150$	216244.	+	70261.9i	0.784722	+	0.254972i
$151$		−	72512.5i		−	0.258804i	−0.991592	−	0.129402i	$-0.958694\pi$
$151$		−	72512.5i		−	0.258804i	0.991592	−	0.129402i	$-0.0413057\pi$
$152$	382464.	−	124270.i	1.34271	−	0.436272i
$153$	53758.5	−	17467.2i	0.185660	−	0.0603246i
$154$		−	465986.i		−	1.58333i
$155$	345721.	+	112332.i	1.15584	+	0.375555i
$156$	−210958.	+	153270.i	−0.694039	+	0.504249i
$157$	359182.	+	116705.i	1.16296	+	0.377869i	0.826011	−	0.563654i	$-0.190605\pi$
$157$	359182.	+	116705.i	1.16296	+	0.377869i	0.336950	+	0.941523i	$0.390605\pi$
$158$	12120.0	+	37301.5i	0.0386242	+	0.118873i
$159$	−704731.	+	228981.i	−2.21070	+	0.718301i
$160$	232457.	−	319949.i	0.717864	−	0.988055i
$161$	−216107.	+	665109.i	−0.657058	+	2.02222i
$162$			151594.i			0.453830i
$163$	80020.9	+	246279.i	0.235904	+	0.726037i	0.997000	+	0.0773982i	$0.0246613\pi$
$163$	80020.9	+	246279.i	0.235904	+	0.726037i	−0.761097	+	0.648639i	$0.775339\pi$
$164$	−64139.9	+	197402.i	−0.186217	+	0.573116i
$165$	−656062.	−	902992.i	−1.87601	−	2.58211i
$166$	−184860.	+	254437.i	−0.520681	+	0.716656i
$167$	−175724.	−	540823.i	−0.487573	−	1.50060i	−0.828219	−	0.560404i	$-0.810646\pi$
$167$	−175724.	−	540823.i	−0.487573	−	1.50060i	0.340646	−	0.940191i	$-0.389354\pi$
$168$	−679930.	+	493998.i	−1.85862	+	1.35037i
$169$	67914.4			0.182913
$170$	53550.9			0.142116
$171$	−527322.	+	383122.i	−1.37907	+	1.00195i
$172$			19665.7i			0.0506860i
$173$	247849.	+	341134.i	0.629610	+	0.866583i	0.998008	−	0.0630847i	$-0.0200938\pi$
$173$	247849.	+	341134.i	0.629610	+	0.866583i	−0.368399	+	0.929668i	$0.620094\pi$
$174$	389736.	+	283160.i	0.975883	+	0.709021i
$175$	273972.	+	377090.i	0.676256	+	0.930786i
$176$	125099.	−	40647.0i	0.304418	−	0.0989114i
$177$	104479.	−	143803.i	0.250666	−	0.345012i
$178$	−284100.	−	206411.i	−0.672080	−	0.488295i
$179$	−185682.	−	134906.i	−0.433149	−	0.314701i	0.349758	−	0.936840i	$-0.386264\pi$
$179$	−185682.	−	134906.i	−0.433149	−	0.314701i	−0.782907	+	0.622139i	$0.786264\pi$
$180$	−119587.	+	368052.i	−0.275109	+	0.846698i
$181$	274748.	+	89270.9i	0.623358	+	0.202541i	0.603631	−	0.797264i	$-0.293720\pi$
$181$	274748.	+	89270.9i	0.623358	+	0.202541i	0.0197275	+	0.999805i	$0.493720\pi$
$182$	486454.			1.08859
$183$	−622284.	−	280355.i	−1.37360	−	0.618844i
$184$	−708193.			−1.54208
$185$	−350503.	−	113885.i	−0.752943	−	0.244646i
$186$	137597.	−	423480.i	0.291626	−	0.897532i
$187$	−94089.2	−	68359.8i	−0.196760	−	0.142954i
$188$	271053.	+	196932.i	0.559320	+	0.406369i
$189$	170099.	−	234122.i	0.346376	−	0.476746i
$190$	−587288.	+	190821.i	−1.18023	+	0.383480i
$191$	−195606.	−	269228.i	−0.387970	−	0.533996i	0.569704	−	0.821850i	$-0.307058\pi$
$191$	−195606.	−	269228.i	−0.387970	−	0.533996i	−0.957674	+	0.287855i	$0.907058\pi$
$192$	−517885.	−	376265.i	−1.01386	−	0.736616i
$193$	416352.	+	573060.i	0.804577	+	1.10741i	0.992138	+	0.125152i	$0.0399419\pi$
$193$	416352.	+	573060.i	0.804577	+	1.10741i	−0.187561	+	0.982253i	$0.560058\pi$
$194$		−	182895.i		−	0.348897i
$195$	942655.	−	684879.i	1.77528	−	1.28981i
$196$	−310472.			−0.577274
$197$	413298.			0.758748			0.379374	−	0.925243i	$-0.376139\pi$
$197$	413298.			0.758748			0.379374	+	0.925243i	$0.376139\pi$
$198$	−618771.	+	449564.i	−1.12168	+	0.814945i
$199$	111749.	+	343928.i	0.200037	+	0.615651i	0.999881	+	0.0154425i	$0.00491570\pi$
$199$	111749.	+	343928.i	0.200037	+	0.615651i	−0.799844	+	0.600208i	$0.795084\pi$
$200$	−277442.	+	381866.i	−0.490452	+	0.675050i
$201$	95296.1	+	131164.i	0.166374	+	0.228994i
$202$	−22478.8	+	69182.5i	−0.0387609	+	0.119294i
$203$	305173.	+	939225.i	0.519763	+	1.59967i
$204$			72080.7i			0.121267i
$205$	286606.	−	882084.i	0.476323	−	1.46597i
$206$	44591.5	−	61375.0i	0.0732124	−	0.100768i
$207$	1.09167e6	−	354706.i	1.77079	−	0.575364i
$208$	42432.4	+	130593.i	0.0680047	+	0.209297i
$209$	1.27546e6	+	414421.i	2.01976	+	0.656261i
$210$	1.04406e6	−	758553.i	1.63372	−	1.18696i
$211$	238294.	+	77426.3i	0.368474	+	0.119724i	0.487400	−	0.873179i	$-0.337945\pi$
$211$	238294.	+	77426.3i	0.368474	+	0.119724i	−0.118927	+	0.992903i	$0.537945\pi$
$212$		−	528610.i		−	0.807785i
$213$	−805618.	+	261761.i	−1.21669	+	0.395327i
$214$	−316506.	+	102839.i	−0.472441	+	0.153505i
$215$		−	87875.3i		−	0.129649i
$216$	278712.	+	90559.0i	0.406463	+	0.132068i
$217$	738471.	−	536531.i	1.06459	−	0.773473i
$218$	−432978.	−	140683.i	−0.617055	−	0.200493i
$219$	183385.	+	564400.i	0.258376	+	0.795201i
$220$	757270.	−	246052.i	1.05486	−	0.342744i
$221$	71362.5	−	98222.0i	0.0982854	−	0.135278i
$222$	−139500.	+	429336.i	−0.189973	+	0.584676i
$223$			1.22033e6i			1.64330i	0.569994	+	0.821649i	$0.306946\pi$
$223$			1.22033e6i			1.64330i	−0.569994	+	0.821649i	$0.693054\pi$
$224$	−306875.	−	944465.i	−0.408641	−	1.25767i
$225$	236412.	−	727602.i	0.311325	−	0.958159i
$226$	−437275.	−	601858.i	−0.569487	−	0.783831i
$227$	202543.	−	278776.i	0.260887	−	0.359080i	−0.658400	−	0.752668i	$-0.728767\pi$
$227$	202543.	−	278776.i	0.260887	−	0.359080i	0.919287	+	0.393589i	$0.128767\pi$
$228$	−256850.	−	790502.i	−0.327222	−	1.00708i
$229$	380224.	−	276249.i	0.479127	−	0.348106i	−0.321860	−	0.946787i	$-0.604308\pi$
$229$	380224.	−	276249.i	0.479127	−	0.348106i	0.800988	+	0.598681i	$0.204308\pi$
$230$	1.08746e6			1.35548
$231$	−2.80274e6			−3.45583
$232$	−809071.	+	587824.i	−0.986885	+	0.717014i
$233$		−	480821.i		−	0.580221i	−0.956993	−	0.290111i	$-0.906308\pi$
$233$		−	480821.i		−	0.580221i	0.956993	−	0.290111i	$-0.0936921\pi$
$234$	−469310.	−	645950.i	−0.560300	−	0.771187i
$235$	−1.21119e6	−	879981.i	−1.43068	−	1.03945i
$236$	74532.8	+	102586.i	0.0871099	+	0.119896i
$237$	224355.	−	72897.5i	0.259457	−	0.0843027i
$238$	79039.0	−	108788.i	0.0904480	−	0.124491i
$239$	−486910.	−	353761.i	−0.551384	−	0.400604i	0.276912	−	0.960895i	$-0.410689\pi$
$239$	−486910.	−	353761.i	−0.551384	−	0.400604i	−0.828295	+	0.560292i	$0.810689\pi$
$240$	294712.	+	214121.i	0.330271	+	0.239956i
$241$	−42375.9	+	130420.i	−0.0469977	+	0.144644i	−0.971802	−	0.235800i	$-0.924229\pi$
$241$	−42375.9	+	130420.i	−0.0469977	+	0.144644i	0.924804	+	0.380444i	$0.124229\pi$
$242$	898580.	+	291966.i	0.986321	+	0.320475i
$243$	1.28586e6			1.39694
$244$	327390.	−	360392.i	0.352039	−	0.387526i
$245$	1.38733e6			1.47661
$246$	−1.08048e6	−	351069.i	−1.13836	−	0.369874i
$247$	−432625.	+	1.33148e6i	−0.451200	+	1.38865i
$248$	747824.	+	543326.i	0.772094	+	0.560959i
$249$	1.53035e6	+	1.11186e6i	1.56420	+	1.13646i
$250$	−110910.	+	152654.i	−0.112233	+	0.154475i
$251$	−499034.	+	162146.i	−0.499972	+	0.162451i	−0.548137	−	0.836389i	$-0.684663\pi$
$251$	−499034.	+	162146.i	−0.499972	+	0.162451i	0.0481649	+	0.998839i	$0.484663\pi$
$252$	571187.	+	786171.i	0.566600	+	0.779858i
$253$	−1.91067e6	−	1.38818e6i	−1.87665	−	1.36347i
$254$	114871.	+	158106.i	0.111719	+	0.153768i
$255$		−	322090.i		−	0.310189i
$256$	903451.	−	656396.i	0.861598	−	0.625988i
$257$	−1.04184e6			−0.983939			−0.491969	−	0.870613i	$-0.663723\pi$
$257$	−1.04184e6			−0.983939			−0.491969	+	0.870613i	$0.663723\pi$
$258$	−107640.			−0.100676
$259$	−748685.	+	543951.i	−0.693505	+	0.503861i
$260$	256860.	+	790533.i	0.235647	+	0.725248i
$261$	952757.	−	1.31136e6i	0.865727	−	1.19157i
$262$	−126795.	−	174519.i	−0.114117	−	0.157069i
$263$	54462.2	−	167617.i	0.0485519	−	0.149427i	−0.923841	−	0.382776i	$-0.874968\pi$
$263$	54462.2	−	167617.i	0.0485519	−	0.149427i	0.972393	+	0.233348i	$0.0749682\pi$
$264$	−877062.	−	2.69932e6i	−0.774498	−	2.38366i
$265$			2.36207e6i			2.06623i
$266$	−479163.	+	1.47471e6i	−0.415221	+	1.27792i
$267$	−1.24149e6	+	1.70876e6i	−1.06577	+	1.46691i
$268$	−109997.	+	35740.2i	−0.0935501	+	0.0303963i
$269$	250720.	+	771636.i	0.211255	+	0.650178i	0.999398	+	0.0346851i	$0.0110428\pi$
$269$	250720.	+	771636.i	0.211255	+	0.650178i	−0.788143	+	0.615492i	$0.788957\pi$
$270$	−427973.	−	139057.i	−0.357278	−	0.116087i
$271$	1.37647e6	−	1.00006e6i	1.13853	−	0.827189i	0.151614	−	0.988440i	$-0.451553\pi$
$271$	1.37647e6	−	1.00006e6i	1.13853	−	0.827189i	0.986913	+	0.161251i	$0.0515529\pi$
$272$	36099.6	+	11729.5i	0.0295856	+	0.00961294i
$273$		−	2.92585e6i		−	2.37599i
$274$	1.52627e6	−	495916.i	1.22816	−	0.399054i
$275$	−1.49705e6	+	486420.i	−1.19372	+	0.387864i
$276$			1.46374e6i			1.15662i
$277$	1.28012e6	+	415936.i	1.00242	+	0.325707i	0.763834	−	0.645413i	$-0.223315\pi$
$277$	1.28012e6	+	415936.i	1.00242	+	0.325707i	0.238590	+	0.971120i	$0.423315\pi$
$278$	−1.34067e6	+	974051.i	−1.04042	+	0.755909i
$279$	−1.42489e6	−	462976.i	−1.09590	−	0.356080i
$280$	827875.	+	2.54794e6i	0.631059	+	1.94220i
$281$	925273.	−	300639.i	0.699043	−	0.227133i	0.0621297	−	0.998068i	$-0.480211\pi$
$281$	925273.	−	300639.i	0.699043	−	0.227133i	0.636914	+	0.770935i	$0.280211\pi$
$282$	−1.07790e6	+	1.48361e6i	−0.807154	+	1.11095i
$283$	453076.	−	1.39442e6i	0.336283	−	1.03497i	−0.629804	−	0.776754i	$-0.716865\pi$
$283$	453076.	−	1.39442e6i	0.336283	−	1.03497i	0.966087	−	0.258218i	$-0.0831353\pi$
$284$		−	604284.i		−	0.444575i
$285$	1.14772e6	+	3.53233e6i	0.836998	+	2.57602i
$286$	−507651.	+	1.56239e6i	−0.366987	+	1.12947i
$287$	−1.36892e6	−	1.88416e6i	−0.981010	−	1.35025i
$288$	−958073.	+	1.31867e6i	−0.680640	+	0.936820i
$289$	428389.	+	1.31845e6i	0.301713	+	0.928577i
$290$	1.24236e6	−	902627.i	0.867465	−	0.630251i
$291$	−1.10005e6			−0.761517
$292$	−423350.			−0.290564
$293$	−490087.	+	356069.i	−0.333507	+	0.242307i	−0.741917	−	0.670492i	$-0.766083\pi$
$293$	−490087.	+	356069.i	−0.333507	+	0.242307i	0.408411	+	0.912798i	$0.366083\pi$
$294$		−	1.69936e6i		−	1.14662i
$295$	−333047.	−	458399.i	−0.222818	−	0.306682i
$296$	−758166.	−	550840.i	−0.502962	−	0.365423i
$297$	574439.	+	790647.i	0.377879	+	0.520106i
$298$	152332.	−	49495.8i	0.0993692	−	0.0322870i
$299$	1.44916e6	−	1.99459e6i	0.937427	−	1.29026i
$300$	789266.	+	573436.i	0.506315	+	0.367859i
$301$	−178517.	−	129701.i	−0.113570	−	0.0825136i
$302$	−87493.8	+	269278.i	−0.0552027	+	0.169896i
$303$	416108.	+	135202.i	0.260375	+	0.0846011i
$304$	−437697.			−0.271638
$305$	−1.46293e6	+	1.61040e6i	−0.900478	+	0.991251i
$306$	−220710.			−0.134747
$307$	2.66175e6	+	864855.i	1.61184	+	0.523718i	0.969996	−	0.243119i	$-0.0781706\pi$
$307$	2.66175e6	+	864855.i	1.61184	+	0.523718i	0.641842	+	0.766837i	$0.278171\pi$
$308$	617850.	−	1.90155e6i	0.371113	−	1.14217i
$309$	−369149.	−	268202.i	−0.219940	−	0.159796i
$310$	−1.14831e6	−	834297.i	−0.678665	−	0.493079i
$311$	37168.0	−	51157.4i	0.0217906	−	0.0299921i	−0.797983	−	0.602680i	$-0.794099\pi$
$311$	37168.0	−	51157.4i	0.0217906	−	0.0299921i	0.819773	+	0.572688i	$0.194099\pi$
$312$	2.81788e6	−	915586.i	1.63884	−	0.532491i
$313$	−1.68473e6	−	2.31883e6i	−0.972007	−	1.33785i	−0.941026	−	0.338333i	$-0.890137\pi$
$313$	−1.68473e6	−	2.31883e6i	−0.972007	−	1.33785i	−0.0309809	−	0.999520i	$-0.509863\pi$
$314$	−1.19302e6	−	866780.i	−0.682847	−	0.496118i
$315$	−2.55232e6	−	3.51297e6i	−1.44930	−	1.99479i
$316$			168286.i			0.0948049i
$317$	154547.	−	112285.i	0.0863798	−	0.0627586i	−0.543757	−	0.839243i	$-0.682999\pi$
$317$	154547.	−	112285.i	0.0863798	−	0.0627586i	0.630137	+	0.776484i	$0.282999\pi$
$318$	2.89334e6			1.60447
$319$	−3.33507e6			−1.83497
$320$	−1.65086e6	+	1.19942e6i	−0.901227	+	0.654780i
$321$	618540.	+	1.90367e6i	0.335047	+	1.03117i
$322$	1.60505e6	−	2.20915e6i	0.862676	−	1.18737i
$323$	227473.	+	313089.i	0.121317	+	0.166979i
$324$	−200998.	+	618608.i	−0.106372	+	0.327381i
$325$	−507786.	−	1.56280e6i	−0.266669	−	0.820722i
$326$		−	1.01112e6i		−	0.526938i
$327$	−846158.	+	2.60421e6i	−0.437605	+	1.34681i
$328$	1.38626e6	−	1.90802e6i	0.711474	−	0.979260i
$329$	−3.57534e6	+	1.16170e6i	−1.82107	+	0.591702i
$330$	1.34676e6	+	4.14491e6i	0.680779	+	2.09522i
$331$	−1.04771e6	−	340420.i	−0.525617	−	0.170783i	0.0341759	−	0.999416i	$-0.489119\pi$
$331$	−1.04771e6	−	340420.i	−0.525617	−	0.170783i	−0.559793	+	0.828632i	$0.689119\pi$
$332$	−1.09171e6	+	793177.i	−0.543581	+	0.394934i
$333$	1.44460e6	+	469379.i	0.713900	+	0.231960i
$334$			2.22040e6i			1.08909i
$335$	491517.	−	159704.i	0.239291	−	0.0777504i
$336$	869967.	−	282669.i	0.420392	−	0.136594i
$337$		−	640809.i		−	0.307365i	−0.988120	−	0.153682i	$-0.950887\pi$
$337$		−	640809.i		−	0.307365i	0.988120	−	0.153682i	$-0.0491132\pi$
$338$	−252203.	−	81945.8i	−0.120077	−	0.0390153i
$339$	−3.61996e6	+	2.63005e6i	−1.71082	+	1.24298i
$340$	218525.	+	71003.1i	0.102519	+	0.0333104i
$341$	952577.	+	2.93173e6i	0.443623	+	1.36533i
$342$	2.42051e6	−	786472.i	1.11903	−	0.363595i
$343$	190554.	−	262275.i	0.0874547	−	0.120371i
$344$	69051.1	−	212518.i	0.0314612	−	0.0968275i
$345$		−	6.54067e6i		−	2.95852i
$346$	−508783.	−	1.56587e6i	−0.228477	−	0.703180i
$347$	−405698.	+	1.24861e6i	−0.180875	+	0.556677i	−0.999853	−	0.0171485i	$-0.994541\pi$
$347$	−405698.	+	1.24861e6i	−0.180875	+	0.556677i	0.818978	+	0.573825i	$0.194541\pi$
$348$	1.21496e6	+	1.67224e6i	0.537790	+	0.740204i
$349$	1.78112e6	−	2.45150e6i	0.782760	−	1.07738i	−0.212212	−	0.977224i	$-0.568067\pi$
$349$	1.78112e6	−	2.45150e6i	0.782760	−	1.07738i	0.994972	−	0.100153i	$-0.0319332\pi$
$350$	−562409.	−	1.73092e6i	−0.245404	−	0.755277i
$351$	−825376.	+	599671.i	−0.357589	+	0.259804i
$352$	3.35368e6			1.44266
$353$	4.41345e6			1.88513			0.942565	−	0.334024i	$-0.108407\pi$
$353$	4.41345e6			1.88513			0.942565	+	0.334024i	$0.108407\pi$
$354$	−561500.	+	407954.i	−0.238145	+	0.173023i
$355$			2.70022e6i			1.13718i
$356$	−885646.	−	1.21899e6i	−0.370370	−	0.509770i
$357$	−654320.	−	475392.i	−0.271719	−	0.197415i
$358$	526760.	+	725023.i	0.217223	+	0.298981i
$359$	−936943.	+	304431.i	−0.383687	+	0.124667i	−0.494508	−	0.869173i	$-0.664652\pi$
$359$	−936943.	+	304431.i	−0.383687	+	0.124667i	0.110821	+	0.993840i	$0.464652\pi$
$360$	2.58465e6	−	3.55746e6i	1.05110	−	1.44672i
$361$	−1.60711e6	−	1.16764e6i	−0.649050	−	0.471563i
$362$	−912573.	−	663023.i	−0.366013	−	0.265924i
$363$	1.75607e6	−	5.40464e6i	0.699481	−	2.15278i
$364$	1.98507e6	+	644989.i	0.785277	+	0.255152i
$365$	1.89172e6			0.743232
$366$	1.97260e6	+	1.79196e6i	0.769727	+	0.699240i
$367$	2.77433e6			1.07521			0.537605	−	0.843197i	$-0.319329\pi$
$367$	2.77433e6			1.07521			0.537605	+	0.843197i	$0.319329\pi$
$368$	733075.	+	238190.i	0.282182	+	0.0916864i
$369$	−1.18125e6	+	3.63552e6i	−0.451623	+	1.38995i
$370$	1.16419e6	+	845836.i	0.442100	+	0.321205i
$371$	4.79852e6	+	3.48633e6i	1.80997	+	1.31502i
$372$	1.12298e6	−	1.54565e6i	0.420742	−	0.579102i
$373$	−3.62742e6	+	1.17862e6i	−1.34997	+	0.438633i	−0.892683	−	0.450684i	$-0.851180\pi$
$373$	−3.62742e6	+	1.17862e6i	−1.34997	+	0.438633i	−0.457290	+	0.889317i	$0.651180\pi$
$374$	266921.	+	367385.i	0.0986743	+	0.135814i
$375$	918159.	+	667081.i	0.337163	+	0.244963i
$376$	−2.23766e6	−	3.07988e6i	−0.816254	−	1.12348i
$377$		−	3.48156e6i		−	1.26160i
$378$	−914163.	+	664178.i	−0.329074	+	0.239087i
$379$	−2.14621e6			−0.767492			−0.383746	−	0.923439i	$-0.625366\pi$
$379$	−2.14621e6			−0.767492			−0.383746	+	0.923439i	$0.625366\pi$
$380$	−2.64955e6			−0.941269
$381$	950954.	−	690909.i	0.335619	−	0.243842i
$382$	401539.	+	1.23581e6i	0.140789	+	0.433305i
$383$	860371.	−	1.18420e6i	0.299701	−	0.412504i	−0.632434	−	0.774615i	$-0.717944\pi$
$383$	860371.	−	1.18420e6i	0.299701	−	0.412504i	0.932135	+	0.362111i	$0.117944\pi$
$384$	−864360.	−	1.18969e6i	−0.299135	−	0.411724i
$385$	−2.76084e6	+	8.49698e6i	−0.949268	+	2.92155i
$386$	−854686.	−	2.63045e6i	−0.291970	−	0.898592i
$387$			362179.i			0.122927i
$388$	242501.	−	746340.i	0.0817774	−	0.251685i
$389$	−1.55509e6	+	2.14040e6i	−0.521053	+	0.717168i	−0.985734	−	0.168310i	$-0.946169\pi$
$389$	−1.55509e6	+	2.14040e6i	−0.521053	+	0.717168i	0.464681	+	0.885478i	$0.346169\pi$
$390$	−4.32697e6	+	1.40592e6i	−1.44053	+	0.468057i
$391$	−210601.	−	648163.i	−0.0696656	−	0.214409i
$392$	3.35512e6	+	1.09014e6i	1.10279	+	0.358318i
$393$	−1.04967e6	+	762629.i	−0.342824	+	0.249076i
$394$	−1.53480e6	−	498687.i	−0.498094	−	0.161841i
$395$		−	751980.i		−	0.242501i
$396$	−3.12110e6	+	1.01411e6i	−1.00016	+	0.324971i
$397$	−2.17126e6	+	705486.i	−0.691411	+	0.224653i	−0.633584	−	0.773674i	$-0.718417\pi$
$397$	−2.17126e6	+	705486.i	−0.691411	+	0.224653i	−0.0578264	+	0.998327i	$0.518417\pi$
$398$		−	1.41203e6i		−	0.446823i
$399$	8.86986e6	+	2.88199e6i	2.78923	+	0.906276i
$400$	415624.	−	301969.i	0.129883	−	0.0943652i
$401$	−4.04298e6	−	1.31364e6i	−1.25557	−	0.407959i	−0.395655	−	0.918399i	$-0.629482\pi$
$401$	−4.04298e6	−	1.31364e6i	−1.25557	−	0.407959i	−0.859913	+	0.510440i	$0.829482\pi$
$402$	−195623.	−	602067.i	−0.0603748	−	0.185815i
$403$	−3.06050e6	+	994418.i	−0.938707	+	0.305005i
$404$	−183458.	+	252509.i	−0.0559221	+	0.0769702i
$405$	898151.	−	2.76422e6i	0.272089	−	0.837405i
$406$		−	3.85608e6i		−	1.16100i
$407$	−965751.	−	2.97228e6i	−0.288988	−	0.889412i
$408$	253093.	−	778941.i	0.0752714	−	0.231662i
$409$	−1.07932e6	−	1.48556e6i	−0.319038	−	0.439118i	0.619135	−	0.785284i	$-0.287483\pi$
$409$	−1.07932e6	−	1.48556e6i	−0.319038	−	0.439118i	−0.938173	+	0.346166i	$0.887483\pi$
$410$	−2.12865e6	+	2.92984e6i	−0.625381	+	0.860764i
$411$	−2.98276e6	−	9.17999e6i	−0.870991	−	2.68063i
$412$	263342.	−	191329.i	0.0764323	−	0.0555313i
$413$	−1.42280e6			−0.410457
$414$	−4.48197e6			−1.28519
$415$	4.87828e6	−	3.54428e6i	1.39042	−	1.01020i
$416$			3.50098e6i			0.991875i
$417$	5.85857e6	+	8.06363e6i	1.64988	+	2.27086i
$418$	−4.23643e6	−	3.07794e6i	−1.18593	−	0.861629i
$419$	−2.16708e6	−	2.98273e6i	−0.603031	−	0.830001i	0.392951	−	0.919560i	$-0.371454\pi$
$419$	−2.16708e6	−	2.98273e6i	−0.603031	−	0.830001i	−0.995982	+	0.0895588i	$0.971454\pi$
$420$	5.26625e6	−	1.71111e6i	1.45673	−	0.473320i
$421$	3.87077e6	−	5.32766e6i	1.06437	−	1.46498i	0.188721	−	0.982031i	$-0.439566\pi$
$421$	3.87077e6	−	5.32766e6i	1.06437	−	1.46498i	0.875649	−	0.482948i	$-0.160434\pi$
$422$	−791491.	−	575052.i	−0.216354	−	0.157190i
$423$	4.99193e6	+	3.62685e6i	1.35649	+	0.985550i
$424$	−1.85608e6	+	5.71243e6i	−0.501398	+	1.54314i
$425$	−432002.	−	140366.i	−0.116015	−	0.0376955i
$426$	3.30754e6			0.883041
$427$	1.11228e6	+	5.34880e6i	0.295219	+	1.41967i
$428$	−1.42792e6			−0.376786
$429$	9.39721e6	+	3.05334e6i	2.46522	+	0.800999i
$430$	−106031.	+	326329.i	−0.0276542	+	0.0851107i
$431$	2.24574e6	+	1.63163e6i	0.582327	+	0.423085i	0.839562	−	0.543263i	$-0.182812\pi$
$431$	2.24574e6	+	1.63163e6i	0.582327	+	0.423085i	−0.257235	+	0.966349i	$0.582812\pi$
$432$	−258046.	−	187481.i	−0.0665254	−	0.0483336i
$433$	−548817.	+	755382.i	−0.140672	+	0.193618i	−0.873540	−	0.486753i	$-0.838181\pi$
$433$	−548817.	+	755382.i	−0.140672	+	0.193618i	0.732868	+	0.680371i	$0.238181\pi$
$434$	−3.38973e6	+	1.10139e6i	−0.863854	+	0.280683i
$435$	−5.42898e6	−	7.47235e6i	−1.37561	−	1.89336i
$436$	−1.58032e6	−	1.14817e6i	−0.398134	−	0.289261i
$437$	4.61928e6	+	6.35790e6i	1.15710	+	1.59261i
$438$		−	2.31720e6i		−	0.577135i
$439$	−2.26792e6	+	1.64774e6i	−0.561651	+	0.408063i	−0.832063	−	0.554682i	$-0.812840\pi$
$439$	−2.26792e6	+	1.64774e6i	−0.561651	+	0.408063i	0.270412	+	0.962745i	$0.412840\pi$
$440$	−9.04740e6			−2.22788
$441$	−5.71789e6			−1.40004
$442$	−383523.	+	278646.i	−0.0933760	+	0.0678417i
$443$	−1.62294e6	−	4.99489e6i	−0.392910	−	1.20925i	−0.930577	−	0.366095i	$-0.880694\pi$
$443$	−1.62294e6	−	4.99489e6i	−0.392910	−	1.20925i	0.537667	−	0.843157i	$-0.319306\pi$
$444$	−1.13851e6	+	1.56703e6i	−0.274082	+	0.377242i
$445$	3.95747e6	+	5.44699e6i	0.947366	+	1.30394i
$446$	1.47246e6	−	4.53176e6i	0.350515	−	1.07877i
$447$	−297700.	−	916225.i	−0.0704708	−	0.216887i
$448$			5.12398e6i			1.20618i
$449$	183630.	−	565154.i	0.0429860	−	0.132297i	−0.927260	−	0.374417i	$-0.877843\pi$
$449$	183630.	−	565154.i	0.0429860	−	0.132297i	0.970246	+	0.242120i	$0.0778428\pi$
$450$	−1.75585e6	+	2.41673e6i	−0.408750	+	0.562595i
$451$	7.48010e6	−	2.43043e6i	1.73167	−	0.562655i
$452$	−986386.	−	3.03578e6i	−0.227091	−	0.698916i
$453$	1.61961e6	+	526244.i	0.370822	+	0.120487i
$454$	−1.08852e6	+	790858.i	−0.247855	+	0.180077i
$455$	−8.87021e6	−	2.88210e6i	−2.00865	−	0.652651i
$456$			9.44443e6i			2.12698i
$457$	−3.19408e6	+	1.03782e6i	−0.715411	+	0.232451i	−0.644033	−	0.764998i	$-0.722740\pi$
$457$	−3.19408e6	+	1.03782e6i	−0.715411	+	0.232451i	−0.0713788	+	0.997449i	$0.522740\pi$
$458$	−1.74530e6	+	567083.i	−0.388783	+	0.126323i
$459$			282017.i			0.0624804i
$460$	4.43759e6	+	1.44186e6i	0.977806	+	0.317708i
$461$	−235070.	+	170788.i	−0.0515162	+	0.0374287i	−0.613245	−	0.789892i	$-0.710136\pi$
$461$	−235070.	+	170788.i	−0.0515162	+	0.0374287i	0.561729	+	0.827321i	$0.310136\pi$
$462$	1.04081e7	+	3.38179e6i	2.26864	+	0.737126i
$463$	−894270.	−	2.75228e6i	−0.193872	−	0.596678i	−0.999988	−	0.00491977i	$-0.998434\pi$
$463$	−894270.	−	2.75228e6i	−0.193872	−	0.596678i	0.806115	−	0.591758i	$-0.201566\pi$
$464$	1.03520e6	−	336358.i	0.223219	−	0.0725281i
$465$	−5.01800e6	+	6.90669e6i	−1.07621	+	1.48128i
$466$	−580161.	+	1.78555e6i	−0.123761	+	0.380897i
$467$			7.44996e6i			1.58074i	0.612627	+	0.790372i	$0.290113\pi$
$467$			7.44996e6i			1.58074i	−0.612627	+	0.790372i	$0.709887\pi$
$468$	−1.05865e6	−	3.25819e6i	−0.223428	−	0.687641i
$469$	401024.	−	1.23423e6i	0.0841858	−	0.259097i
$470$	3.43602e6	+	4.72927e6i	0.717482	+	0.987529i
$471$	−5.21337e6	+	7.17559e6i	−1.08285	+	1.49041i
$472$	−445236.	−	1.37030e6i	−0.0919889	−	0.283113i
$473$	602868.	−	438009.i	0.123899	−	0.0900182i
$474$	−921112.			−0.188307
$475$	5.23790e6			1.06518
$476$	466776.	−	339133.i	0.0944260	−	0.0686045i
$477$		−	9.73530e6i		−	1.95909i
$478$	1.38131e6	+	1.90121e6i	0.276517	+	0.380594i
$479$	−4.34414e6	−	3.15620e6i	−0.865098	−	0.628530i	0.0641693	−	0.997939i	$-0.479560\pi$
$479$	−4.34414e6	−	3.15620e6i	−0.865098	−	0.628530i	−0.929267	+	0.369409i	$0.879560\pi$
$480$	5.45927e6	+	7.51404e6i	1.08151	+	1.48857i
$481$	3.10283e6	−	1.00817e6i	0.611499	−	0.198688i
$482$	314730.	−	433188.i	0.0617050	−	0.0849296i
$483$	−1.32873e7	−	9.65377e6i	−2.59160	−	1.88291i
$484$	3.27972e6	+	2.38285e6i	0.636389	+	0.462364i
$485$	−1.08360e6	+	3.33499e6i	−0.209178	+	0.643784i
$486$	−4.77511e6	−	1.55153e6i	−0.917049	−	0.297967i
$487$	3.21277e6			0.613844			0.306922	−	0.951735i	$-0.400701\pi$
$487$	3.21277e6			0.613844			0.306922	+	0.951735i	$0.400701\pi$
$488$	−4.80337e6	+	2.74504e6i	−0.913054	+	0.521794i
$489$	−6.08154e6			−1.15012
$490$	−5.15191e6	−	1.67396e6i	−0.969345	−	0.314959i
$491$	1.67815e6	−	5.16482e6i	0.314143	−	0.966832i	−0.661963	−	0.749537i	$-0.730276\pi$
$491$	1.67815e6	−	5.16482e6i	0.314143	−	0.966832i	0.976106	−	0.217296i	$-0.0697236\pi$
$492$	−3.94363e6	−	2.86521e6i	−0.734485	−	0.533635i
$493$	−778597.	−	565684.i	−0.144277	−	0.104823i
$494$	3.21314e6	−	4.42251e6i	0.592396	−	0.815364i
$495$	1.39465e7	−	4.53149e6i	2.55830	−	0.831243i
$496$	−591358.	−	813934.i	−0.107931	−	0.148554i
$497$	5.48546e6	+	3.98542e6i	0.996143	+	0.723740i
$498$	−4.34144e6	−	5.97548e6i	−0.784442	−	1.07969i
$499$		−	684552.i		−	0.123071i	−0.998105	−	0.0615354i	$-0.980400\pi$
$499$		−	684552.i		−	0.123071i	0.998105	−	0.0615354i	$-0.0195997\pi$
$500$	−654993.	+	475880.i	−0.117169	+	0.0851280i
$501$	1.33549e7			2.37709
$502$	2.04883e6			0.362866
$503$	−5.67066e6	+	4.11997e6i	−0.999340	+	0.726063i	−0.961947	−	0.273237i	$-0.911906\pi$
$503$	−5.67066e6	+	4.11997e6i	−0.999340	+	0.726063i	−0.0373937	+	0.999301i	$0.511906\pi$
$504$	−3.41209e6	−	1.05013e7i	−0.598335	−	1.84149i
$505$	819775.	−	1.12832e6i	0.143043	−	0.196882i
$506$	5.42037e6	+	7.46049e6i	0.941136	+	1.29536i
$507$	−492875.	+	1.51691e6i	−0.0851563	+	0.262084i
$508$	259121.	+	797493.i	0.0445496	+	0.137109i
$509$		−	3.75789e6i		−	0.642909i	−0.946925	−	0.321455i	$-0.895828\pi$
$509$		−	3.75789e6i		−	0.642909i	0.946925	−	0.321455i	$-0.104172\pi$
$510$	−388634.	+	1.19609e6i	−0.0661631	+	0.203629i
$511$	2.79210e6	−	3.84300e6i	0.473020	−	0.651056i
$512$	−2.24138e6	+	728268.i	−0.377868	+	0.122777i
$513$	−1.00493e6	−	3.09286e6i	−0.168594	−	0.518879i
$514$	3.86892e6	+	1.25709e6i	0.645924	+	0.209874i
$515$	−1.17673e6	+	854946.i	−0.195506	+	0.142043i
$516$	−439246.	−	142720.i	−0.0726246	−	0.0235971i
$517$		−	1.26956e7i		−	2.08894i
$518$	3.43661e6	−	1.11662e6i	0.562737	−	0.182844i
$519$	−9.41817e6	+	3.06015e6i	−1.53479	+	0.498682i
$520$		−	9.44480e6i		−	1.53174i
$521$	−1.85734e6	−	603486.i	−0.299776	−	0.0974031i	0.155267	−	0.987873i	$-0.450376\pi$
$521$	−1.85734e6	−	603486.i	−0.299776	−	0.0974031i	−0.455043	+	0.890469i	$0.650376\pi$
$522$	−5.12039e6	+	3.72018e6i	−0.822483	+	0.597569i
$523$	6.08018e6	+	1.97557e6i	0.971991	+	0.315819i	0.751620	−	0.659597i	$-0.229273\pi$
$523$	6.08018e6	+	1.97557e6i	0.971991	+	0.315819i	0.220372	+	0.975416i	$0.429273\pi$
$524$	−286019.	−	880277.i	−0.0455059	−	0.140053i
$525$	−1.04108e7	+	3.38269e6i	−1.64850	+	0.535629i
$526$	−404496.	+	556740.i	−0.0637455	+	0.0877381i
$527$	−274885.	+	846008.i	−0.0431145	+	0.132693i
$528$			3.08914e6i			0.482229i
$529$	−2.28773e6	−	7.04092e6i	−0.355440	−	1.09393i
$530$	2.85008e6	−	8.77166e6i	0.440725	−	1.35641i
$531$	1.37265e6	+	1.88930e6i	0.211264	+	0.290780i
$532$	−3.91064e6	+	5.38253e6i	−0.599058	+	0.824532i
$533$	2.53719e6	+	7.80866e6i	0.386843	+	1.19058i
$534$	6.67211e6	−	4.84757e6i	1.01253	−	0.735649i
$535$	6.38060e6			0.963779
$536$	1.31418e6			0.197580
$537$	4.36076e6	−	3.16827e6i	0.652568	−	0.474119i
$538$		−	3.16803e6i		−	0.471881i
$539$	6.91506e6	+	9.51777e6i	1.02524	+	1.41112i
$540$	−1.56205e6	−	1.13490e6i	−0.230522	−	0.167484i
$541$	−3.69660e6	−	5.08793e6i	−0.543012	−	0.747392i	0.446031	−	0.895017i	$-0.352837\pi$
$541$	−3.69660e6	−	5.08793e6i	−0.543012	−	0.747392i	−0.989043	+	0.147626i	$0.952837\pi$
$542$	−6.31826e6	+	2.05293e6i	−0.923846	+	0.300176i
$543$	−3.98785e6	+	5.48880e6i	−0.580416	+	0.798873i
$544$	782941.	+	568840.i	0.113431	+	0.0824125i
$545$	7.06159e6	+	5.13055e6i	1.01838	+	0.739899i
$546$	−3.53034e6	+	1.08653e7i	−0.506797	+	1.55976i
$547$	1.01574e7	+	3.30035e6i	1.45149	+	0.471619i	0.925460	−	0.378845i	$-0.123679\pi$
$547$	1.01574e7	+	3.30035e6i	1.45149	+	0.471619i	0.526033	+	0.850464i	$0.323679\pi$
$548$	6.88580e6			0.979497
$549$	6.02946e6	−	6.63727e6i	0.853784	−	0.939850i
$550$	6.14626e6			0.866372
$551$	1.05545e7	+	3.42938e6i	1.48102	+	0.481212i
$552$	5.13956e6	−	1.58179e7i	0.717924	−	2.20954i
$553$	−1.52764e6	−	1.10989e6i	−0.212426	−	0.154336i
$554$	−4.25191e6	−	3.08920e6i	−0.588586	−	0.427633i
$555$	5.08740e6	−	7.00221e6i	0.701073	−	0.964945i
$556$	−6.76235e6	+	2.19722e6i	−0.927706	+	0.301430i
$557$	2.57543e6	+	3.54477e6i	0.351732	+	0.484117i	0.947822	−	0.318800i	$-0.103280\pi$
$557$	2.57543e6	+	3.54477e6i	0.351732	+	0.484117i	−0.596090	+	0.802917i	$0.703280\pi$
$558$	4.73278e6	+	3.43856e6i	0.643473	+	0.467511i
$559$	457248.	+	629348.i	0.0618903	+	0.0851847i
$560$		−	2.91590e6i		−	0.392919i
$561$	2.20969e6	−	1.60544e6i	0.296432	−	0.215370i
$562$	−3.79880e6			−0.507347
$563$	283353.			0.0376754			0.0188377	−	0.999823i	$-0.494003\pi$
$563$	283353.			0.0376754			0.0188377	+	0.999823i	$0.494003\pi$
$564$	−6.36571e6	+	4.62496e6i	−0.842653	+	0.612224i
$565$	4.40762e6	+	1.35653e7i	0.580876	+	1.78775i
$566$	−3.36503e6	+	4.63157e6i	−0.441518	+	0.607697i
$567$	−4.28985e6	−	5.90447e6i	−0.560382	−	0.771299i
$568$	−2.12179e6	+	6.53021e6i	−0.275951	+	0.849290i
$569$	−1.03910e6	−	3.19802e6i	−0.134548	−	0.414096i	0.860972	−	0.508653i	$-0.169856\pi$
$569$	−1.03910e6	−	3.19802e6i	−0.134548	−	0.414096i	−0.995519	+	0.0945574i	$0.969856\pi$
$570$		−	1.45023e7i		−	1.86960i
$571$	1.74686e6	−	5.37627e6i	0.224216	−	0.690066i	−0.774154	−	0.632997i	$-0.781824\pi$
$571$	1.74686e6	−	5.37627e6i	0.224216	−	0.690066i	0.998370	−	0.0570692i	$-0.0181756\pi$
$572$	−4.14314e6	+	5.70255e6i	−0.529468	+	0.728751i
$573$	7.43296e6	−	2.41512e6i	0.945748	−	0.307292i
$574$	2.81012e6	+	8.64865e6i	0.355996	+	1.09564i
$575$	−8.77266e6	−	2.85041e6i	−1.10653	−	0.359532i
$576$	6.80402e6	−	4.94341e6i	0.854494	−	0.620826i
$577$	2.70933e6	+	880314.i	0.338783	+	0.110077i	0.473468	−	0.880811i	$-0.343002\pi$
$577$	2.70933e6	+	880314.i	0.338783	+	0.110077i	−0.134684	+	0.990889i	$0.543002\pi$
$578$		−	5.41300e6i		−	0.673936i
$579$	−1.58212e7	+	5.14063e6i	−1.96130	+	0.637265i
$580$	6.26649e6	−	2.03611e6i	0.773489	−	0.251322i
$581$		−	1.51414e7i		−	1.86091i
$582$	4.08508e6	+	1.32732e6i	0.499911	+	0.162431i
$583$	−1.62050e7	+	1.17736e7i	−1.97459	+	1.43462i
$584$	4.57493e6	+	1.48649e6i	0.555076	+	0.180355i
$585$	4.73053e6	+	1.45591e7i	0.571505	+	1.75891i
$586$	2.24960e6	−	730938.i	0.270620	−	0.0879299i
$587$	−642815.	+	884758.i	−0.0770000	+	0.105981i	−0.845780	−	0.533532i	$-0.820864\pi$
$587$	−642815.	+	884758.i	−0.0770000	+	0.105981i	0.768780	+	0.639514i	$0.220864\pi$
$588$	2.25318e6	−	6.93459e6i	0.268753	−	0.827137i
$589$		−	1.02576e7i		−	1.21831i
$590$	683677.	+	2.10414e6i	0.0808576	+	0.248854i
$591$	−2.99942e6	+	9.23127e6i	−0.353239	+	1.08716i
$592$	599537.	+	825191.i	0.0703091	+	0.0967721i
$593$	−9.20394e6	+	1.26681e7i	−1.07482	+	1.47937i	−0.209729	+	0.977760i	$0.567258\pi$
$593$	−9.20394e6	+	1.26681e7i	−1.07482	+	1.47937i	−0.865095	+	0.501608i	$0.832742\pi$
$594$	−1.17921e6	−	3.62922e6i	−0.137127	−	0.422034i
$595$	−2.08577e6	+	1.51540e6i	−0.241532	+	0.175483i
$596$	687249.			0.0792499
$597$	−8.49284e6			−0.975253
$598$	−7.78819e6	+	5.65845e6i	−0.890602	+	0.647060i
$599$		−	6.18561e6i		−	0.704394i	−0.935926	−	0.352197i	$-0.885435\pi$
$599$		−	6.18561e6i		−	0.704394i	0.935926	−	0.352197i	$-0.114565\pi$
$600$	−6.51574e6	−	8.96815e6i	−0.738900	−	1.01701i
$601$	−2.27206e6	−	1.65075e6i	−0.256586	−	0.186421i	0.452054	−	0.891990i	$-0.350691\pi$
$601$	−2.27206e6	−	1.65075e6i	−0.256586	−	0.186421i	−0.708641	+	0.705569i	$0.750691\pi$
$602$	506435.	+	697048.i	0.0569551	+	0.0783920i
$603$	−2.02579e6	+	658220.i	−0.226883	+	0.0737187i
$604$	−714072.	+	982836.i	−0.0796434	+	0.109620i
$605$	−1.46553e7	−	1.06477e7i	−1.62782	−	1.18268i
$606$	−1.38210e6	−	1.00416e6i	−0.152883	−	0.111076i
$607$	388651.	−	1.19615e6i	0.0428143	−	0.131769i	−0.927365	−	0.374159i	$-0.877931\pi$
$607$	388651.	−	1.19615e6i	0.0428143	−	0.131769i	0.970179	+	0.242390i	$0.0779314\pi$
$608$	−1.06134e7	−	3.44851e6i	−1.16439	−	0.378332i
$609$	−2.31929e7			−2.53403
$610$	7.37575e6	−	4.21511e6i	0.802568	−	0.458653i
$611$	1.32532e7			1.43621
$612$	−900653.	−	292640.i	−0.0972029	−	0.0315831i
$613$	393718.	−	1.21174e6i	0.0423189	−	0.130244i	−0.927665	−	0.373414i	$-0.878187\pi$
$613$	393718.	−	1.21174e6i	0.0423189	−	0.130244i	0.969984	+	0.243170i	$0.0781872\pi$
$614$	−8.84099e6	−	6.42336e6i	−0.946412	−	0.687608i
$615$	1.76219e7	+	1.28031e7i	1.87874	+	1.36498i
$616$	−1.33536e7	+	1.83797e7i	−1.41790	+	1.95158i
$617$	7.59397e6	−	2.46743e6i	0.803075	−	0.260935i	0.121413	−	0.992602i	$-0.461258\pi$
$617$	7.59397e6	−	2.46743e6i	0.803075	−	0.260935i	0.681662	+	0.731667i	$0.261258\pi$
$618$	1.04724e6	+	1.44140e6i	0.110299	+	0.151814i
$619$	−2.68466e6	−	1.95052e6i	−0.281619	−	0.204608i	0.438004	−	0.898973i	$-0.355686\pi$
$619$	−2.68466e6	−	1.95052e6i	−0.281619	−	0.204608i	−0.719623	+	0.694365i	$0.755686\pi$
$620$	−3.57972e6	−	4.92706e6i	−0.373999	−	0.514765i
$621$			5.72692e6i			0.595926i
$622$	−199752.	+	145128.i	−0.0207021	+	0.0150410i
$623$	1.69066e7			1.74516
$624$	−3.22483e6			−0.331547
$625$	9.19541e6	−	6.68086e6i	0.941610	−	0.684120i
$626$	3.45841e6	+	1.06439e7i	0.352728	+	1.08559i
$627$	−1.85127e7	+	2.54806e7i	−1.88062	+	2.58846i
$628$	−3.71909e6	−	5.11889e6i	−0.376303	−	0.517937i
$629$	278686.	−	857708.i	0.0280859	−	0.0864396i
$630$	5.23940e6	+	1.61252e7i	0.525933	+	1.61865i
$631$			2.40911e6i			0.240870i	0.992721	+	0.120435i	$0.0384290\pi$
$631$			2.40911e6i			0.240870i	−0.992721	+	0.120435i	$0.961571\pi$
$632$	590895.	−	1.81859e6i	0.0588461	−	0.181110i
$633$	−3.45873e6	+	4.76054e6i	−0.343090	+	0.472223i
$634$	−709401.	+	230498.i	−0.0700920	+	0.0227743i
$635$	−1.15787e6	−	3.56356e6i	−0.113953	−	0.350712i
$636$	1.18068e7	+	3.83628e6i	1.15742	+	0.376069i
$637$	−9.93583e6	+	7.21880e6i	−0.970187	+	0.704882i
$638$	1.23849e7	+	4.02411e6i	1.20460	+	0.391397i
$639$		−	1.11290e7i		−	1.07821i
$640$	−4.45819e6	+	1.44855e6i	−0.430238	+	0.139793i
$641$	−7.11002e6	+	2.31019e6i	−0.683480	+	0.222076i	−0.630118	−	0.776499i	$-0.716994\pi$
$641$	−7.11002e6	+	2.31019e6i	−0.683480	+	0.222076i	−0.0533617	+	0.998575i	$0.516994\pi$
$642$		−	7.81570e6i		−	0.748394i
$643$	−1.67222e7	−	5.43336e6i	−1.59502	−	0.518252i	−0.629148	−	0.777286i	$-0.716596\pi$
$643$	−1.67222e7	−	5.43336e6i	−1.59502	−	0.518252i	−0.965868	+	0.259033i	$0.916596\pi$
$644$	9.47883e6	−	6.88677e6i	0.900616	−	0.654336i
$645$	1.96275e6	+	637737.i	0.185766	+	0.0603590i
$646$	−466955.	−	1.43714e6i	−0.0440244	−	0.135493i
$647$	−1.41658e6	+	460274.i	−0.133039	+	0.0432271i	−0.374780	−	0.927114i	$-0.622282\pi$
$647$	−1.41658e6	+	460274.i	−0.133039	+	0.0432271i	0.241741	+	0.970341i	$0.422282\pi$
$648$	4.34417e6	−	5.97924e6i	0.406415	−	0.559382i
$649$	1.48479e6	−	4.56973e6i	0.138374	−	0.425871i
$650$			6.41624e6i			0.595658i
$651$	6.62446e6	+	2.03880e7i	0.612630	+	1.88548i
$652$	1.34065e6	−	4.12609e6i	0.123508	−	0.380119i
$653$	8.73333e6	+	1.20204e7i	0.801488	+	1.10315i	0.992581	+	0.121581i	$0.0387965\pi$
$653$	8.73333e6	+	1.20204e7i	0.801488	+	1.10315i	−0.191094	+	0.981572i	$0.561204\pi$
$654$	6.28449e6	−	8.64986e6i	0.574547	−	0.790796i
$655$	1.27807e6	+	3.93348e6i	0.116399	+	0.358240i
$656$	−2.07670e6	+	1.50881e6i	−0.188414	+	0.136891i
$657$	−7.79674e6			−0.704692
$658$	1.46789e7			1.32169
$659$	4.58558e6	−	3.33162e6i	0.411321	−	0.298842i	−0.362816	−	0.931861i	$-0.618185\pi$
$659$	4.58558e6	−	3.33162e6i	0.411321	−	0.298842i	0.774136	+	0.633019i	$0.218185\pi$
$660$			1.86998e7i			1.67100i
$661$	2.81714e6	+	3.87746e6i	0.250787	+	0.345179i	0.915787	−	0.401665i	$-0.131568\pi$
$661$	2.81714e6	+	3.87746e6i	0.250787	+	0.345179i	−0.665000	+	0.746844i	$0.731568\pi$
$662$	3.47995e6	+	2.52833e6i	0.308623	+	0.224228i
$663$	1.67595e6	+	2.30675e6i	0.148074	+	0.203806i
$664$	1.45827e7	−	4.73820e6i	1.28356	−	0.417055i
$665$	1.74745e7	−	2.40516e7i	1.53233	−	2.10907i
$666$	−4.79823e6	−	3.48612e6i	−0.419175	−	0.304549i
$667$	−1.58110e7	−	1.14873e7i	−1.37608	−	0.999781i
$668$	−2.94402e6	+	9.06078e6i	−0.255270	+	0.785641i
$669$	−2.72569e7	−	8.85632e6i	−2.35457	−	0.765046i
$670$	−2.01797e6			−0.173671
$671$	−1.83400e7	−	2.00947e6i	−1.57251	−	0.172296i
$672$	2.33223e7			1.99227
$673$	−5.71429e6	−	1.85668e6i	−0.486323	−	0.158016i	0.0555848	−	0.998454i	$-0.482298\pi$
$673$	−5.71429e6	−	1.85668e6i	−0.486323	−	0.158016i	−0.541907	+	0.840438i	$0.682298\pi$
$674$	−773202.	+	2.37967e6i	−0.0655607	+	0.201775i
$675$	3.08802e6	+	2.24358e6i	0.260868	+	0.189532i
$676$	−920514.	−	668793.i	−0.0774754	−	0.0562892i
$677$	−2.82704e6	+	3.89108e6i	−0.237061	+	0.326286i	−0.910927	−	0.412567i	$-0.864632\pi$
$677$	−2.82704e6	+	3.89108e6i	−0.237061	+	0.326286i	0.673866	+	0.738853i	$0.264632\pi$
$678$	1.66163e7	−	5.39897e6i	1.38823	−	0.451062i
$679$	5.17562e6	+	7.12364e6i	0.430813	+	0.592963i
$680$	−2.11219e6	−	1.53459e6i	−0.175170	−	0.127268i
$681$	4.75673e6	+	6.54708e6i	0.393044	+	0.540978i
$682$		−	1.20365e7i		−	0.990921i
$683$	−184870.	+	134316.i	−0.0151641	+	0.0110173i	−0.595341	−	0.803473i	$-0.702983\pi$
$683$	−184870.	+	134316.i	−0.0151641	+	0.0110173i	0.580177	+	0.814490i	$0.302983\pi$
$684$	1.09202e7			0.892460
$685$	−3.07689e7			−2.50545
$686$	−1.02409e6	+	744048.i	−0.0830863	+	0.0603657i
$687$	3.41080e6	+	1.04974e7i	0.275718	+	0.848572i
$688$	−142954.	+	196760.i	−0.0115140	+	0.0158477i
$689$	−1.22908e7	−	1.69168e7i	−0.986348	−	1.35759i
$690$	−7.89200e6	+	2.42891e7i	−0.631051	+	1.94217i
$691$	−4.17978e6	−	1.28640e7i	−0.333011	−	1.02490i	−0.967694	−	0.252129i	$-0.918869\pi$
$691$	−4.17978e6	−	1.28640e7i	−0.333011	−	1.02490i	0.634683	−	0.772773i	$-0.281131\pi$
$692$		−	7.06445e6i		−	0.560807i
$693$	1.13788e7	−	3.50204e7i	0.900044	−	2.77005i
$694$	3.01315e6	−	4.14725e6i	0.237478	−	0.326860i
$695$	3.02173e7	−	9.81818e6i	2.37297	−	0.771026i
$696$	−7.25777e6	−	2.23371e7i	−0.567911	−	1.74785i
$697$	2.15853e6	+	701349.i	0.168297	+	0.0546830i
$698$	−9.57223e6	+	6.95464e6i	−0.743661	+	0.540301i
$699$	1.07394e7	+	3.48946e6i	0.831360	+	0.270125i
$700$		−	7.80905e6i		−	0.602356i
$701$	2.15451e7	−	7.00044e6i	1.65598	−	0.538060i	0.675954	−	0.736944i	$-0.263732\pi$
$701$	2.15451e7	−	7.00044e6i	1.65598	−	0.538060i	0.980023	+	0.198884i	$0.0637318\pi$
$702$	3.78864e6	−	1.23100e6i	0.290162	−	0.0942793i
$703$			1.03995e7i			0.793638i
$704$	−1.64572e7	−	5.34726e6i	−1.25148	−	0.406630i
$705$	2.84449e7	−	2.06664e7i	2.15542	−	1.56600i
$706$	−1.63895e7	−	5.32528e6i	−1.23753	−	0.402097i
$707$	−1.08222e6	−	3.33072e6i	−0.0814266	−	0.250605i
$708$	−2.83222e6	+	920244.i	−0.212346	+	0.0689954i
$709$	−1.06409e7	+	1.46460e7i	−0.794993	+	1.09421i	0.198475	+	0.980106i	$0.436401\pi$
$709$	−1.06409e7	+	1.46460e7i	−0.794993	+	1.09421i	−0.993468	+	0.114108i	$0.963599\pi$
$710$	3.25809e6	−	1.00274e7i	0.242559	−	0.746520i
$711$			3.09929e6i			0.229926i
$712$	5.29058e6	+	1.62827e7i	0.391114	+	1.20372i
$713$	−5.58208e6	+	1.71799e7i	−0.411218	+	1.26560i
$714$	1.85624e6	+	2.55489e6i	0.136266	+	0.187554i
$715$	1.85135e7	−	2.54816e7i	1.35432	−	1.86407i
$716$	1.18824e6	+	3.65703e6i	0.0866208	+	0.266592i
$717$	1.14351e7	−	8.30811e6i	0.830698	−	0.603537i
$718$	3.84671e6			0.278470
$719$	8.69156e6			0.627011			0.313506	−	0.949586i	$-0.398497\pi$
$719$	8.69156e6			0.627011			0.313506	+	0.949586i	$0.398497\pi$
$720$	−3.87195e6	+	2.81314e6i	−0.278355	+	0.202237i
$721$			3.65238e6i			0.261660i
$722$	4.55921e6	+	6.27522e6i	0.325497	+	0.448008i
$723$	−2.60547e6	−	1.89299e6i	−0.185371	−	0.134680i
$724$	−2.84484e6	−	3.91558e6i	−0.201702	−	0.277619i
$725$	−1.23882e7	+	4.02517e6i	−0.875313	+	0.284407i
$726$	−1.30425e7	+	1.79515e7i	−0.918374	+	1.26403i
$727$	1.52028e7	+	1.10455e7i	1.06681	+	0.775083i	0.975336	−	0.220724i	$-0.0708422\pi$
$727$	1.52028e7	+	1.10455e7i	1.06681	+	0.775083i	0.0914740	+	0.995807i	$0.470842\pi$
$728$	−1.91870e7	−	1.39402e7i	−1.34177	−	0.974853i
$729$	−6.41655e6	+	1.97481e7i	−0.447180	+	1.37628i
$730$	−7.02499e6	−	2.28256e6i	−0.487908	−	0.158531i
$731$	215038.			0.0148841
$732$	5.67363e6	+	9.92793e6i	0.391366	+	0.684827i
$733$	−2.37251e7			−1.63098			−0.815488	−	0.578774i	$-0.803531\pi$
$733$	−2.37251e7			−1.63098			−0.815488	+	0.578774i	$0.803531\pi$
$734$	−1.03026e7	−	3.34752e6i	−0.705841	−	0.229342i
$735$	−1.00683e7	+	3.09869e7i	−0.687442	+	2.11573i
$736$	1.58992e7	+	1.15514e7i	1.08188	+	0.786034i
$737$	3.54558e6	+	2.57602e6i	0.240447	+	0.174695i
$738$	8.77325e6	−	1.20753e7i	0.592952	−	0.816129i
$739$	3.86648e6	−	1.25630e6i	0.260438	−	0.0846215i	−0.175888	−	0.984410i	$-0.556280\pi$
$739$	3.86648e6	−	1.25630e6i	0.260438	−	0.0846215i	0.436326	+	0.899789i	$0.356280\pi$
$740$	3.62923e6	+	4.99521e6i	0.243633	+	0.335331i
$741$	−2.65998e7	−	1.93259e7i	−1.77964	−	1.29299i
$742$	−1.36129e7	−	1.87365e7i	−0.907696	−	1.24934i
$743$			1.93777e7i			1.28775i	0.765132	+	0.643873i	$0.222674\pi$
$743$			1.93777e7i			1.28775i	−0.765132	+	0.643873i	$0.777326\pi$
$744$	−1.75627e7	+	1.27600e7i	−1.16321	+	0.845123i
$745$	−3.07094e6			−0.202713
$746$	1.48927e7			0.979775
$747$	−2.01059e7	+	1.46078e7i	−1.31832	+	0.957817i
$748$	602109.	+	1.85310e6i	0.0393479	+	0.121100i
$749$	9.41752e6	−	1.29621e7i	0.613383	−	0.844250i
$750$	−2.60472e6	−	3.58509e6i	−0.169086	−	0.232727i
$751$	4.98369e6	−	1.53382e7i	0.322442	−	0.992374i	−0.650140	−	0.759814i	$-0.725290\pi$
$751$	4.98369e6	−	1.53382e7i	0.322442	−	0.992374i	0.972582	−	0.232560i	$-0.0747102\pi$
$752$	1.28041e6	+	3.94069e6i	0.0825665	+	0.254114i
$753$		−	1.23230e7i		−	0.792006i
$754$	−4.20086e6	+	1.29289e7i	−0.269098	+	0.828198i
$755$	3.19080e6	−	4.39176e6i	0.203719	−	0.280396i
$756$	−4.61106e6	+	1.49822e6i	−0.293424	+	0.0953394i
$757$	−1.51639e6	−	4.66696e6i	−0.0961769	−	0.296002i	0.891382	−	0.453253i	$-0.149737\pi$
$757$	−1.51639e6	−	4.66696e6i	−0.0961769	−	0.296002i	−0.987559	+	0.157251i	$0.949737\pi$
$758$	7.97004e6	+	2.58962e6i	0.503834	+	0.163706i
$759$	4.48722e7	−	3.26016e7i	2.82731	−	2.05416i
$760$	2.86324e7	+	9.30324e6i	1.79814	+	0.584252i
$761$		−	1.00115e7i		−	0.626667i	−0.949643	−	0.313334i	$-0.898554\pi$
$761$		−	1.00115e7i		−	0.626667i	0.949643	−	0.313334i	$-0.101446\pi$
$762$	−4.36506e6	+	1.41829e6i	−0.272335	+	0.0884869i
$763$	2.08453e7	−	6.77304e6i	1.29627	−	0.421184i
$764$			5.57537e6i			0.345574i
$765$	4.02453e6	+	1.30765e6i	0.248635	+	0.0807863i
$766$	−4.62388e6	+	3.35945e6i	−0.284731	+	0.206869i
$767$	4.77045e6	+	1.55001e6i	0.292800	+	0.0951364i
$768$	8.10441e6	+	2.49428e7i	0.495814	+	1.52596i
$769$	−2.29928e7	+	7.47081e6i	−1.40209	+	0.455567i	−0.909866	−	0.414902i	$-0.863816\pi$
$769$	−2.29928e7	+	7.47081e6i	−1.40209	+	0.455567i	−0.492224	+	0.870469i	$0.663816\pi$
$770$	2.05050e7	−	2.82227e7i	1.24633	−	1.71542i
$771$	7.56093e6	−	2.32702e7i	0.458078	−	1.40982i
$772$		−	1.18673e7i		−	0.716654i
$773$	−1.71204e6	−	5.26911e6i	−0.103054	−	0.317168i	0.886215	−	0.463275i	$-0.153326\pi$
$773$	−1.71204e6	−	5.26911e6i	−0.103054	−	0.317168i	−0.989269	+	0.146107i	$0.953326\pi$
$774$	437006.	−	1.34497e6i	0.0262202	−	0.0806974i
$775$	7.07675e6	+	9.74030e6i	0.423233	+	0.582530i
$776$	−5.24117e6	+	7.21385e6i	−0.312445	+	0.430044i
$777$	−6.71608e6	−	2.06700e7i	−0.399083	−	1.22825i
$778$	8.35752e6	−	6.07209e6i	0.495026	−	0.359658i
$779$	−2.61715e7			−1.54520
$780$	−1.95212e7			−1.14887
$781$	−1.85248e7	+	1.34591e7i	−1.08674	+	0.789564i
$782$			2.66110e6i			0.155612i
$783$	4.75354e6	+	6.54269e6i	0.277085	+	0.381375i
$784$	−3.10634e6	−	2.25689e6i	−0.180493	−	0.131135i
$785$	1.66186e7	+	2.28736e7i	0.962544	+	1.32483i
$786$	4.81818e6	−	1.56552e6i	0.278181	−	0.0903864i
$787$	−1.41585e7	+	1.94875e7i	−0.814853	+	1.12155i	0.175703	+	0.984443i	$0.443780\pi$
$787$	−1.41585e7	+	1.94875e7i	−0.814853	+	1.12155i	−0.990556	+	0.137106i	$0.956220\pi$
$788$	−5.60185e6	−	4.06998e6i	−0.321378	−	0.233495i
$789$	3.34859e6	+	2.43290e6i	0.191501	+	0.139133i
$790$	−907342.	+	2.79251e6i	−0.0517253	+	0.159194i
$791$	3.40631e7	+	1.10678e7i	1.93572	+	0.628955i
$792$	3.72889e7			2.11236
$793$	2.09773e6	−	1.91456e7i	0.118459	−	1.08115i
$794$	8.91432e6			0.501807
$795$	−5.27584e7	−	1.71422e7i	−2.96056	−	0.961944i
$796$	1.87221e6	−	5.76206e6i	0.104730	−	0.322326i
$797$	2.74173e7	+	1.99199e7i	1.52890	+	1.11081i	0.956846	+	0.290597i	$0.0938539\pi$
$797$	2.74173e7	+	1.99199e7i	1.52890	+	1.11081i	0.572056	+	0.820215i	$0.306146\pi$
$798$	−2.94612e7	−	2.14048e7i	−1.63773	−	1.18988i
$799$	2.15338e6	−	2.96388e6i	0.119331	−	0.164245i
$800$	1.24573e7	−	4.04763e6i	0.688177	−	0.223602i
$801$	−1.63108e7	−	2.24498e7i	−0.898241	−	1.23632i
$802$	1.34287e7	+	9.75654e6i	0.737223	+	0.535624i
$803$	9.42916e6	+	1.29781e7i	0.516041	+	0.710270i
$804$		−	2.71623e6i		−	0.148193i
$805$	−4.23557e7	+	3.07732e7i	−2.30368	+	1.67372i
$806$	1.25652e7			0.681289
$807$	−1.90545e7			−1.02995
$808$	2.86916e6	−	2.08457e6i	0.154606	−	0.112328i
$809$	−626043.	−	1.92676e6i	−0.0336305	−	0.103504i	0.932832	−	0.360311i	$-0.117329\pi$
$809$	−626043.	−	1.92676e6i	−0.0336305	−	0.103504i	−0.966463	+	0.256807i	$0.917329\pi$
$810$	−6.67064e6	+	9.18135e6i	−0.357236	+	0.491693i
$811$	1.51190e6	+	2.08095e6i	0.0807182	+	0.111099i	0.847467	−	0.530849i	$-0.178127\pi$
$811$	1.51190e6	+	2.08095e6i	0.0807182	+	0.111099i	−0.766749	+	0.641948i	$0.778127\pi$
$812$	5.11277e6	−	1.57355e7i	0.272124	−	0.837510i
$813$	1.23476e7	+	3.80021e7i	0.655175	+	2.01642i
$814$			1.22030e7i			0.645512i
$815$	−5.99062e6	+	1.84372e7i	−0.315921	+	0.972303i
$816$	−523971.	+	721184.i	−0.0275475	+	0.0379158i
$817$	−2.35830e6	+	766258.i	−0.123607	+	0.0401624i
$818$	2.21563e6	+	6.81900e6i	0.115775	+	0.356318i
$819$	3.65586e7	+	1.18786e7i	1.90450	+	0.618808i
$820$	−1.25711e7	+	9.13341e6i	−0.652886	+	0.474349i
$821$	−8.25843e6	−	2.68333e6i	−0.427602	−	0.138936i	0.0873066	−	0.996181i	$-0.472174\pi$
$821$	−8.25843e6	−	2.68333e6i	−0.427602	−	0.138936i	−0.514908	+	0.857245i	$0.672174\pi$
$822$			3.76893e7i			1.94553i
$823$	2.20078e7	−	7.15077e6i	1.13260	−	0.368005i	0.318038	−	0.948078i	$-0.396976\pi$
$823$	2.20078e7	−	7.15077e6i	1.13260	−	0.368005i	0.814564	+	0.580073i	$0.196976\pi$
$824$	−3.51761e6	+	1.14294e6i	−0.180480	+	0.0586416i
$825$		−	3.69676e7i		−	1.89098i
$826$	5.28361e6	+	1.71675e6i	0.269452	+	0.0875502i
$827$	8.95856e6	−	6.50878e6i	0.455485	−	0.330930i	−0.336272	−	0.941765i	$-0.609166\pi$
$827$	8.95856e6	−	6.50878e6i	0.455485	−	0.330930i	0.791758	+	0.610835i	$0.209166\pi$
$828$	−1.82896e7	−	5.94264e6i	−0.927102	−	0.301234i
$829$	7.61003e6	+	2.34213e7i	0.384592	+	1.18365i	0.936776	+	0.349930i	$0.113795\pi$
$829$	7.61003e6	+	2.34213e7i	0.384592	+	1.18365i	−0.552184	+	0.833722i	$0.686205\pi$
$830$	−2.23922e7	+	7.27568e6i	−1.12824	+	0.366588i
$831$	−1.85804e7	+	2.55737e7i	−0.933368	+	1.28467i
$832$	5.58214e6	−	1.71800e7i	0.279571	−	0.860431i
$833$			3.39491e6i			0.169518i
$834$	−1.20264e7	−	3.70136e7i	−0.598718	−	1.84266i
$835$	1.31552e7	−	4.04877e7i	0.652954	−	2.00959i
$836$	−1.32065e7	−	1.81772e7i	−0.653542	−	0.899523i
$837$	4.39369e6	−	6.04740e6i	0.216778	−	0.298370i
$838$	4.44857e6	+	1.36913e7i	0.218832	+	0.673495i
$839$	1.98082e7	−	1.43915e7i	0.971495	−	0.705833i	0.0157033	−	0.999877i	$-0.495001\pi$
$839$	1.98082e7	−	1.43915e7i	0.971495	−	0.705833i	0.955792	+	0.294044i	$0.0950013\pi$
$840$	−6.29179e7			−3.07664
$841$	−7.08688e6			−0.345513
$842$	−2.08027e7	+	1.51140e7i	−1.01120	+	0.734683i
$843$			2.28484e7i			1.10735i
$844$	−2.46738e6	−	3.39605e6i	−0.119228	−	0.164104i
$845$	4.11328e6	+	2.98847e6i	0.198174	+	0.143982i
$846$	−1.41616e7	−	1.94917e7i	−0.680277	−	0.936321i
$847$	−4.32612e7	+	1.40564e7i	−2.07200	+	0.673234i
$848$	3.84259e6	−	5.28887e6i	0.183499	−	0.252565i
$849$	2.78573e7	+	2.02395e7i	1.32638	+	0.963674i
$850$	1.43489e6	+	1.04251e6i	0.0681196	+	0.0494918i
$851$	5.65928e6	−	1.74175e7i	0.267878	−	0.824444i
$852$	1.34971e7	+	4.38547e6i	0.637002	+	0.206974i
$853$	−3.09505e7			−1.45645			−0.728224	−	0.685339i	$-0.759654\pi$
$853$	−3.09505e7			−1.45645			−0.728224	+	0.685339i	$0.759654\pi$
$854$	2.32339e6	−	2.12051e7i	0.109013	−	0.994936i
$855$	−4.87963e7			−2.28282
$856$	1.54308e7	+	5.01378e6i	0.719789	+	0.233874i
$857$	2.29814e6	−	7.07296e6i	0.106887	−	0.328965i	−0.883282	−	0.468843i	$-0.844671\pi$
$857$	2.29814e6	−	7.07296e6i	0.106887	−	0.328965i	0.990169	+	0.139878i	$0.0446711\pi$
$858$	−3.12128e7	−	2.26774e7i	−1.44749	−	1.05166i
$859$	2.30407e7	+	1.67401e7i	1.06540	+	0.774059i	0.975080	−	0.221853i	$-0.0712106\pi$
$859$	2.30407e7	+	1.67401e7i	1.06540	+	0.774059i	0.0903212	+	0.995913i	$0.471211\pi$
$860$	−865359.	+	1.19106e6i	−0.0398979	+	0.0549148i
$861$	5.20185e7	−	1.69018e7i	2.39139	−	0.777009i
$862$	−6.37094e6	−	8.76884e6i	−0.292035	−	0.401952i
$863$	4.88351e6	+	3.54808e6i	0.223206	+	0.162168i	0.693769	−	0.720198i	$-0.255949\pi$
$863$	4.88351e6	+	3.54808e6i	0.223206	+	0.162168i	−0.470563	+	0.882367i	$0.655949\pi$
$864$	−4.78006e6	−	6.57919e6i	−0.217846	−	0.299839i
$865$			3.15672e7i			1.43448i
$866$	2.94950e6	−	2.14294e6i	0.133645	−	0.0970991i
$867$	−3.25573e7			−1.47096
$868$	−1.52928e7			−0.688950
$869$	5.15895e6	−	3.74820e6i	0.231746	−	0.168373i
$870$	1.11446e7	+	3.42995e7i	0.499190	+	1.53635i
$871$	−2.68917e6	+	3.70132e6i	−0.120108	+	0.165315i
$872$	1.30462e7	+	1.79566e7i	0.581024	+	0.799711i
$873$	4.46608e6	−	1.37452e7i	0.198331	−	0.610400i
$874$	−9.48245e6	−	2.91840e7i	−0.419896	−	1.29231i
$875$		−	9.08432e6i		−	0.401118i
$876$	3.07237e6	−	9.45579e6i	0.135274	−	0.416330i
$877$	−5.09033e6	+	7.00624e6i	−0.223484	+	0.307600i	−0.906005	−	0.423266i	$-0.860884\pi$
$877$	−5.09033e6	+	7.00624e6i	−0.223484	+	0.307600i	0.682521	+	0.730866i	$0.260884\pi$
$878$	1.04102e7	−	3.38248e6i	0.455745	−	0.148081i
$879$	−4.39633e6	−	1.35305e7i	−0.191919	−	0.590666i
$880$	9.36527e6	+	3.04296e6i	0.407675	+	0.132462i
$881$	−1.07698e7	+	7.82472e6i	−0.467485	+	0.339648i	−0.796461	−	0.604691i	$-0.793297\pi$
$881$	−1.07698e7	+	7.82472e6i	−0.467485	+	0.339648i	0.328975	+	0.944339i	$0.393297\pi$
$882$	2.12337e7	+	6.89923e6i	0.919080	+	0.298627i
$883$		−	1.18245e7i		−	0.510365i	−0.966893	−	0.255183i	$-0.917864\pi$
$883$		−	1.18245e7i		−	0.510365i	0.966893	−	0.255183i	$-0.0821356\pi$
$884$	−1.93450e6	+	628556.i	−0.0832602	+	0.0270529i
$885$	1.26557e7	−	4.11207e6i	0.543159	−	0.176483i
$886$			2.05070e7i			0.877643i
$887$	1.97209e7	+	6.40771e6i	0.841624	+	0.273460i	0.697934	−	0.716163i	$-0.254103\pi$
$887$	1.97209e7	+	6.40771e6i	0.841624	+	0.273460i	0.143690	+	0.989623i	$0.454103\pi$
$888$	1.78056e7	−	1.29365e7i	0.757747	−	0.550535i
$889$	−8.94830e6	−	2.90748e6i	−0.379740	−	0.123385i
$890$	−8.12389e6	−	2.50028e7i	−0.343786	−	1.05807i
$891$	2.34407e7	−	7.61635e6i	0.989183	−	0.321405i
$892$	1.20173e7	−	1.65404e7i	0.505703	−	0.696041i
$893$	−1.30546e7	+	4.01778e7i	−0.547815	+	1.68600i
$894$			3.76165e6i			0.157411i
$895$	−5.30961e6	−	1.63413e7i	−0.221567	−	0.681913i
$896$	−3.63740e6	+	1.11948e7i	−0.151363	+	0.465848i
$897$	3.40336e7	+	4.68432e7i	1.41230	+	1.94386i
$898$	−1.36383e6	+	1.87716e6i	−0.0564379	+	0.0776801i
$899$	7.88267e6	+	2.42603e7i	0.325292	+	1.00115i
$900$	−1.03695e7	+	7.53385e6i	−0.426726	+	0.310035i
$901$	−5.78018e6			−0.237208
$902$	−3.07103e7			−1.25680
$903$	4.19250e6	−	3.04603e6i	0.171101	−	0.124312i
$904$			3.62697e7i			1.47612i
$905$	1.27120e7	+	1.74966e7i	0.515933	+	0.710121i
$906$	−5.37954e6	−	3.90846e6i	−0.217733	−	0.158192i
$907$	−2.12375e7	−	2.92309e7i	−0.857205	−	1.17984i	−0.982229	−	0.187688i	$-0.939901\pi$
$907$	−2.12375e7	−	2.92309e7i	−0.857205	−	1.17984i	0.125024	−	0.992154i	$-0.460099\pi$
$908$	−5.49054e6	+	1.78398e6i	−0.221004	+	0.0718085i
$909$	−3.37871e6	+	4.65040e6i	−0.135625	+	0.186672i
$910$	2.94623e7	+	2.14056e7i	1.17941	+	0.856890i
$911$	−2.35038e7	−	1.70765e7i	−0.938301	−	0.681716i	0.00971003	−	0.999953i	$-0.496909\pi$
$911$	−2.35038e7	−	1.70765e7i	−0.938301	−	0.681716i	−0.948011	+	0.318237i	$0.896909\pi$
$912$	3.17650e6	−	9.77625e6i	0.126462	−	0.389211i
$913$	4.86310e7	+	1.58012e7i	1.93079	+	0.627353i
$914$	1.31136e7			0.519226
$915$	−2.53524e7	−	4.43625e7i	−1.00107	−	1.75172i
$916$	−7.87395e6			−0.310066
$917$	9.87718e6	+	3.20929e6i	0.387891	+	0.126033i
$918$	340283.	−	1.04728e6i	0.0133270	−	0.0410164i
$919$	8.78595e6	+	6.38336e6i	0.343162	+	0.249322i	0.745995	−	0.665952i	$-0.231974\pi$
$919$	8.78595e6	+	6.38336e6i	0.343162	+	0.249322i	−0.402833	+	0.915274i	$0.631974\pi$
$920$	−4.28921e7	−	3.11630e7i	−1.67074	−	1.21386i
$921$	−3.86342e7	+	5.31754e7i	−1.50080	+	2.06567i
$922$	1.07901e6	−	350593.i	0.0418023	−	0.0135824i
$923$	−1.40503e7	−	1.93385e7i	−0.542850	−	0.747169i
$924$	3.79884e7	+	2.76002e7i	1.46376	+	1.06349i
$925$	−7.17462e6	−	9.87502e6i	−0.275705	−	0.379475i
$926$			1.12997e7i			0.433053i
$927$	4.84991e6	−	3.52367e6i	0.185368	−	0.134678i
$928$	2.77520e7			1.05785
$929$	2.78943e7			1.06042			0.530208	−	0.847867i	$-0.322114\pi$
$929$	2.78943e7			1.06042			0.530208	+	0.847867i	$0.322114\pi$
$930$	2.69682e7	−	1.95935e7i	1.02246	−	0.742858i
$931$	−1.20973e7	−	3.72316e7i	−0.457419	−	1.40779i
$932$	−4.73492e6	+	6.51706e6i	−0.178555	+	0.245761i
$933$	872894.	+	1.20144e6i	0.0328290	+	0.0451852i
$934$	8.98915e6	−	2.76657e7i	0.337172	−	1.03771i
$935$	−2.69050e6	−	8.28050e6i	−0.100648	−	0.309762i
$936$			3.89268e7i			1.45231i
$937$	9.11327e6	−	2.80478e7i	0.339098	−	1.04364i	−0.625570	−	0.780168i	$-0.715134\pi$
$937$	9.11327e6	−	2.80478e7i	0.339098	−	1.04364i	0.964668	−	0.263468i	$-0.0848664\pi$
$938$	−2.97844e6	+	4.09948e6i	−0.110531	+	0.152132i
$939$	6.40192e7	−	2.08011e7i	2.36944	−	0.769878i
$940$	7.75082e6	+	2.38546e7i	0.286107	+	0.880546i
$941$	−3.02082e7	−	9.81525e6i	−1.11212	−	0.361349i	−0.305364	−	0.952236i	$-0.598778\pi$
$941$	−3.02082e7	−	9.81525e6i	−1.11212	−	0.361349i	−0.806755	+	0.590887i	$0.798778\pi$
$942$	2.80182e7	−	2.03564e7i	1.02876	−	0.747436i
$943$	4.38332e7	+	1.42423e7i	1.60518	+	0.521555i
$944$			1.56819e6i			0.0572754i
$945$	2.06043e7	−	6.69475e6i	0.750549	−	0.243868i
$946$	−2.76728e6	+	899144.i	−0.100537	+	0.0326664i
$947$		−	3.29286e6i		−	0.119316i	−0.998219	−	0.0596580i	$-0.980999\pi$
$947$		−	3.29286e6i		−	0.119316i	0.998219	−	0.0596580i	$-0.0190010\pi$
$948$	−3.75878e6	−	1.22130e6i	−0.135840	−	0.0441369i
$949$	−1.35482e7	+	9.84333e6i	−0.488332	+	0.354794i
$950$	−1.94512e7	−	6.32007e6i	−0.699257	−	0.227202i
$951$	1.38636e6	+	4.26679e6i	0.0497080	+	0.152985i
$952$	−6.23500e6	+	2.02588e6i	−0.222969	+	0.0724470i
$953$	3.66737e6	−	5.04771e6i	0.130805	−	0.180037i	−0.738591	−	0.674154i	$-0.764508\pi$
$953$	3.66737e6	−	5.04771e6i	0.130805	−	0.180037i	0.869396	+	0.494117i	$0.164508\pi$
$954$	−1.17466e7	+	3.61525e7i	−0.417872	+	1.28608i
$955$		−	2.49133e7i		−	0.883941i
$956$	3.11590e6	+	9.58977e6i	0.110265	+	0.339362i
$957$	2.42036e7	−	7.44909e7i	0.854278	−	2.62920i
$958$	1.23239e7	+	1.69624e7i	0.433844	+	0.597135i
$959$	−4.54137e7	+	6.25066e7i	−1.59456	+	2.19472i
$960$	−1.48090e7	−	4.55774e7i	−0.518618	−	1.59614i
$961$	−4.08662e6	+	2.96910e6i	−0.142743	+	0.103709i
$962$	−1.27390e7			−0.443809
$963$	−2.62977e7			−0.913802
$964$	1.85868e6	−	1.35041e6i	0.0644188	−	0.0468030i
$965$			5.30286e7i			1.83312i
$966$	3.76946e7	+	5.18822e7i	1.29968	+	1.78886i
$967$	−4.48926e7	−	3.26164e7i	−1.54386	−	1.12168i	−0.947854	−	0.318704i	$-0.896753\pi$
$967$	−4.48926e7	−	3.26164e7i	−1.54386	−	1.12168i	−0.596008	−	0.802978i	$-0.703247\pi$
$968$	−2.70755e7	−	3.72662e7i	−0.928727	−	1.27828i
$969$	−8.64388e6	+	2.80857e6i	−0.295733	+	0.0960894i
$970$	8.04802e6	−	1.10771e7i	0.274637	−	0.378006i
$971$	3.86744e7	+	2.80986e7i	1.31636	+	0.956393i	0.999970	+	0.00776498i	$0.00247170\pi$
$971$	3.86744e7	+	2.80986e7i	1.31636	+	0.956393i	0.316393	+	0.948628i	$0.397528\pi$
$972$	−1.74286e7	−	1.26626e7i	−0.591694	−	0.429891i
$973$	2.46540e7	−	7.58772e7i	0.834844	−	2.56938i
$974$	−1.19308e7	−	3.87655e6i	−0.402969	−	0.130933i
$975$	3.85914e7			1.30011
$976$	5.89538e6	−	1.22594e6i	0.198101	−	0.0411950i
$977$	−5.27695e7			−1.76867			−0.884334	−	0.466854i	$-0.845387\pi$
$977$	−5.27695e7			−1.76867			−0.884334	+	0.466854i	$0.845387\pi$
$978$	2.25841e7	+	7.33801e6i	0.755014	+	0.245319i
$979$	−1.76433e7	+	5.43004e7i	−0.588332	+	1.81070i
$980$	−1.88039e7	−	1.36618e7i	−0.625436	−	0.454406i
$981$	−2.91044e7	−	2.11456e7i	−0.965576	−	0.701532i
$982$	−1.24638e7	+	1.71549e7i	−0.412450	+	0.567688i
$983$	4.07577e7	−	1.32430e7i	1.34532	−	0.437121i	0.454204	−	0.890898i	$-0.349924\pi$
$983$	4.07577e7	−	1.32430e7i	1.34532	−	0.437121i	0.891115	+	0.453777i	$0.149924\pi$
$984$	3.25564e7	+	4.48100e7i	1.07189	+	1.47532i
$985$	2.50316e7	+	1.81865e7i	0.822051	+	0.597255i
$986$	2.20880e6	+	3.04015e6i	0.0723542	+	0.0995871i
$987$		−	8.82882e7i		−	2.88476i
$988$	1.89757e7	−	1.37866e7i	0.618450	−	0.449330i
$989$	4.36677e6			0.141961
$990$	−5.72586e7			−1.85675
$991$	3.53126e6	−	2.56561e6i	0.114221	−	0.0829863i	−0.529208	−	0.848492i	$-0.677511\pi$
$991$	3.53126e6	−	2.56561e6i	0.114221	−	0.0829863i	0.643429	+	0.765506i	$0.277511\pi$
$992$	−7.92665e6	−	2.43957e7i	−0.255747	−	0.787108i
$993$	1.52070e7	−	2.09307e7i	0.489408	−	0.673612i
$994$	−1.55617e7	−	2.14188e7i	−0.499563	−	0.687589i
$995$	−8.36588e6	+	2.57475e7i	−0.267888	+	0.824476i
$996$	−9.79323e6	−	3.01405e7i	−0.312808	−	0.962724i
$997$		−	5.07938e7i		−	1.61835i	−0.587566	−	0.809176i	$-0.699914\pi$
$997$		−	5.07938e7i		−	1.61835i	0.587566	−	0.809176i	$-0.300086\pi$
$998$	−825983.	+	2.54212e6i	−0.0262509	+	0.0807921i
$999$	−4.45446e6	+	6.13104e6i	−0.141215	+	0.194366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.6.g.a.3.10	✓	104
61.41	even	10	inner	61.6.g.a.41.10	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.6.g.a.3.10	✓	104	1.1	even	1	trivial
61.6.g.a.41.10	yes	104	61.41	even	10	inner

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	61.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.71354 - 1.20660i) q^{2} +(-7.25729 + 22.3356i) q^{3} +(-13.5540 - 9.84758i) q^{4} +(60.5656 + 44.0035i) q^{5} +(53.9005 - 74.1877i) q^{6} +(178.785 - 58.0907i) q^{7} +(111.894 + 154.009i) q^{8} +(-249.622 - 181.361i) q^{9} +O(q^{10})\)	\(q+(-3.71354 - 1.20660i) q^{2} +(-7.25729 + 22.3356i) q^{3} +(-13.5540 - 9.84758i) q^{4} +(60.5656 + 44.0035i) q^{5} +(53.9005 - 74.1877i) q^{6} +(178.785 - 58.0907i) q^{7} +(111.894 + 154.009i) q^{8} +(-249.622 - 181.361i) q^{9} +(-171.818 - 236.487i) q^{10} +634.842i q^{11} +(318.317 - 231.271i) q^{12} -662.727 q^{13} -734.018 q^{14} +(-1422.39 + 1033.43i) q^{15} +(-64.0269 - 197.054i) q^{16} +(-107.680 + 148.209i) q^{17} +(708.150 + 974.685i) q^{18} +(652.794 - 2009.09i) q^{19} +(-387.580 - 1192.85i) q^{20} +4414.86i q^{21} +(766.003 - 2357.51i) q^{22} +(-2186.66 + 3009.67i) q^{23} +(-4251.95 + 1381.54i) q^{24} +(766.206 + 2358.14i) q^{25} +(2461.07 + 799.649i) q^{26} +(1245.42 - 904.853i) q^{27} +(-2995.31 - 973.234i) q^{28} +5253.38i q^{29} +(6529.03 - 2121.41i) q^{30} +(4618.04 - 1500.49i) q^{31} -5282.69i q^{32} +(-14179.6 - 4607.23i) q^{33} +(578.704 - 420.453i) q^{34} +(13384.4 + 4348.86i) q^{35} +(1597.41 + 4916.33i) q^{36} +(-4681.91 + 1521.25i) q^{37} +(-4848.36 + 6673.20i) q^{38} +(4809.60 - 14802.4i) q^{39} +14251.4i q^{40} +(-3828.40 - 11782.6i) q^{41} +(5326.98 - 16394.8i) q^{42} +(-689.950 - 949.634i) q^{43} +(6251.66 - 8604.67i) q^{44} +(-7137.97 - 21968.4i) q^{45} +(11751.7 - 8538.13i) q^{46} -19998.0 q^{47} +4866.00 q^{48} +(14992.3 - 10892.6i) q^{49} -9681.56i q^{50} +(-2528.87 - 3480.70i) q^{51} +(8982.62 + 6526.26i) q^{52} +(18545.7 + 25526.0i) q^{53} +(-5716.73 + 1857.48i) q^{54} +(-27935.3 + 38449.6i) q^{55} +(28951.6 + 21034.5i) q^{56} +(40136.9 + 29161.2i) q^{57} +(6338.75 - 19508.7i) q^{58} +(-7198.21 - 2338.84i) q^{59} +29455.8 q^{60} +(-3165.30 + 28889.0i) q^{61} -18959.8 q^{62} +(-55163.9 - 17923.8i) q^{63} +(-8422.98 + 25923.3i) q^{64} +(-40138.5 - 29162.3i) q^{65} +(47097.5 + 34218.3i) q^{66} +(4057.73 - 5584.98i) q^{67} +(2918.99 - 948.439i) q^{68} +(-51353.8 - 70682.5i) q^{69} +(-44456.2 - 32299.3i) q^{70} +(21200.7 + 29180.2i) q^{71} -58737.3i q^{72} +(20443.1 - 14852.8i) q^{73} +19222.0 q^{74} -58231.1 q^{75} +(-28632.7 + 20802.9i) q^{76} +(36878.4 + 113500. i) q^{77} +(-35721.4 + 49166.2i) q^{78} +(-5904.14 - 8126.35i) q^{79} +(4793.26 - 14752.1i) q^{80} +(-11997.2 - 36923.7i) q^{81} +48374.6i q^{82} +(24889.9 - 76603.2i) q^{83} +(43475.6 - 59839.1i) q^{84} +(-13043.4 + 4238.06i) q^{85} +(1416.33 + 4359.00i) q^{86} +(-117338. - 38125.3i) q^{87} +(-97771.7 + 71035.3i) q^{88} +(85533.7 + 27791.6i) q^{89} +90193.4i q^{90} +(-118486. + 38498.3i) q^{91} +(59276.0 - 19259.9i) q^{92} +114036. i q^{93} +(74263.4 + 24129.6i) q^{94} +(127944. - 92956.7i) q^{95} +(117992. + 38338.0i) q^{96} +(14474.5 + 44547.8i) q^{97} +(-68817.7 + 22360.2i) q^{98} +(115135. - 158470. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9}+O(q^{10}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9} - 595 q^{10} + 1982 q^{12} + 2372 q^{13} - 4474 q^{14} - 1149 q^{15} - 8631 q^{16} + 950 q^{17} + 4340 q^{18} - 5597 q^{19} - 6627 q^{20} - 8639 q^{22} + 9065 q^{23} + 17220 q^{24} - 7694 q^{25} + 14810 q^{26} + 4500 q^{27} + 19835 q^{28} - 44585 q^{30} + 10905 q^{31} - 19205 q^{33} - 15376 q^{34} - 43790 q^{35} - 25135 q^{36} - 5 q^{37} + 17555 q^{38} + 29401 q^{39} - 21014 q^{41} + 62197 q^{42} - 31625 q^{43} + 146190 q^{44} + 153742 q^{45} + 13387 q^{46} + 27326 q^{47} - 82968 q^{48} + 14694 q^{49} + 34090 q^{51} + 90072 q^{52} - 40270 q^{53} - 13760 q^{54} + 25140 q^{55} - 97860 q^{56} + 114893 q^{57} - 18003 q^{58} - 117435 q^{59} - 536650 q^{60} - 121867 q^{61} - 157388 q^{62} - 160825 q^{63} + 132509 q^{64} - 155852 q^{65} + 308443 q^{66} + 101665 q^{67} + 303780 q^{68} + 281945 q^{69} + 264985 q^{70} + 160970 q^{71} + 127669 q^{73} - 133952 q^{74} - 139592 q^{75} - 641111 q^{76} + 128917 q^{77} + 1670 q^{78} + 187940 q^{79} + 785373 q^{80} - 453473 q^{81} - 301209 q^{83} + 100475 q^{84} - 340045 q^{85} - 462669 q^{86} + 189245 q^{87} - 881635 q^{88} - 201970 q^{89} + 93865 q^{91} - 622085 q^{92} - 285265 q^{94} - 113308 q^{95} + 1215465 q^{96} - 342131 q^{97} - 616150 q^{98} + 714235 q^{99}+O(q^{100}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9 - 595 * q^10 + 1982 * q^12 + 2372 * q^13 - 4474 * q^14 - 1149 * q^15 - 8631 * q^16 + 950 * q^17 + 4340 * q^18 - 5597 * q^19 - 6627 * q^20 - 8639 * q^22 + 9065 * q^23 + 17220 * q^24 - 7694 * q^25 + 14810 * q^26 + 4500 * q^27 + 19835 * q^28 - 44585 * q^30 + 10905 * q^31 - 19205 * q^33 - 15376 * q^34 - 43790 * q^35 - 25135 * q^36 - 5 * q^37 + 17555 * q^38 + 29401 * q^39 - 21014 * q^41 + 62197 * q^42 - 31625 * q^43 + 146190 * q^44 + 153742 * q^45 + 13387 * q^46 + 27326 * q^47 - 82968 * q^48 + 14694 * q^49 + 34090 * q^51 + 90072 * q^52 - 40270 * q^53 - 13760 * q^54 + 25140 * q^55 - 97860 * q^56 + 114893 * q^57 - 18003 * q^58 - 117435 * q^59 - 536650 * q^60 - 121867 * q^61 - 157388 * q^62 - 160825 * q^63 + 132509 * q^64 - 155852 * q^65 + 308443 * q^66 + 101665 * q^67 + 303780 * q^68 + 281945 * q^69 + 264985 * q^70 + 160970 * q^71 + 127669 * q^73 - 133952 * q^74 - 139592 * q^75 - 641111 * q^76 + 128917 * q^77 + 1670 * q^78 + 187940 * q^79 + 785373 * q^80 - 453473 * q^81 - 301209 * q^83 + 100475 * q^84 - 340045 * q^85 - 462669 * q^86 + 189245 * q^87 - 881635 * q^88 - 201970 * q^89 + 93865 * q^91 - 622085 * q^92 - 285265 * q^94 - 113308 * q^95 + 1215465 * q^96 - 342131 * q^97 - 616150 * q^98 + 714235 * q^99

Introduction

L-functions

Modular forms

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