LMFDB - Embedded newform 60.7.f.a.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(19,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("60.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.f (of order $2$, degree $1$, 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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	60.19
Dual form			60.7.f.a.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.34967 + 3.15947i) q^{2} +15.5885 q^{3} +(44.0354 - 46.4422i) q^{4} +(111.509 + 56.4858i) q^{5} +(-114.570 + 49.2513i) q^{6} +231.647 q^{7} +(-176.913 + 480.464i) q^{8} +243.000 q^{9} +O(q^{10})$	\(q+(-7.34967 + 3.15947i) q^{2} +15.5885 q^{3} +(44.0354 - 46.4422i) q^{4} +(111.509 + 56.4858i) q^{5} +(-114.570 + 49.2513i) q^{6} +231.647 q^{7} +(-176.913 + 480.464i) q^{8} +243.000 q^{9} +(-998.024 - 62.8414i) q^{10} -1432.15i q^{11} +(686.445 - 723.963i) q^{12} -1704.35i q^{13} +(-1702.53 + 731.882i) q^{14} +(1738.26 + 880.527i) q^{15} +(-217.760 - 4090.21i) q^{16} +7567.92i q^{17} +(-1785.97 + 767.752i) q^{18} -5564.86i q^{19} +(7533.69 - 2691.37i) q^{20} +3611.02 q^{21} +(4524.83 + 10525.8i) q^{22} +14468.9 q^{23} +(-2757.80 + 7489.69i) q^{24} +(9243.70 + 12597.4i) q^{25} +(5384.85 + 12526.4i) q^{26} +3788.00 q^{27} +(10200.7 - 10758.2i) q^{28} +25708.4 q^{29} +(-15557.6 - 979.600i) q^{30} +40919.0i q^{31} +(14523.4 + 29373.7i) q^{32} -22324.9i q^{33} +(-23910.7 - 55621.8i) q^{34} +(25830.8 + 13084.8i) q^{35} +(10700.6 - 11285.5i) q^{36} -66045.9i q^{37} +(17582.0 + 40899.9i) q^{38} -26568.2i q^{39} +(-46866.9 + 43583.2i) q^{40} +106267. q^{41} +(-26539.8 + 11408.9i) q^{42} -58344.7 q^{43} +(-66512.0 - 63065.2i) q^{44} +(27096.8 + 13726.1i) q^{45} +(-106342. + 45714.3i) q^{46} -75013.4 q^{47} +(-3394.54 - 63760.0i) q^{48} -63988.8 q^{49} +(-107739. - 63381.6i) q^{50} +117972. i q^{51} +(-79153.7 - 75051.7i) q^{52} -81861.1i q^{53} +(-27840.5 + 11968.1i) q^{54} +(80896.0 - 159698. i) q^{55} +(-40981.3 + 111298. i) q^{56} -86747.5i q^{57} +(-188948. + 81225.0i) q^{58} +199623. i q^{59} +(117439. - 41954.3i) q^{60} +168043. q^{61} +(-129283. - 300742. i) q^{62} +56290.2 q^{63} +(-199547. - 170001. i) q^{64} +(96271.5 - 190051. i) q^{65} +(70535.1 + 164081. i) q^{66} +36855.0 q^{67} +(351471. + 333257. i) q^{68} +225548. q^{69} +(-231189. - 14557.0i) q^{70} +449616. i q^{71} +(-42989.9 + 116753. i) q^{72} +58511.3i q^{73} +(208670. + 485416. i) q^{74} +(144095. + 196374. i) q^{75} +(-258444. - 245051. i) q^{76} -331752. i q^{77} +(83941.4 + 195267. i) q^{78} -649187. i q^{79} +(206756. - 468397. i) q^{80} +59049.0 q^{81} +(-781028. + 335748. i) q^{82} -452757. q^{83} +(159013. - 167704. i) q^{84} +(-427480. + 843895. i) q^{85} +(428814. - 184338. i) q^{86} +400754. q^{87} +(688095. + 253365. i) q^{88} -286863. q^{89} +(-242520. - 15270.5i) q^{90} -394807. i q^{91} +(637146. - 671970. i) q^{92} +637865. i q^{93} +(551324. - 237003. i) q^{94} +(314336. - 620534. i) q^{95} +(226397. + 457890. i) q^{96} +386394. i q^{97} +(470297. - 202171. i) q^{98} -348011. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) $ 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9	$ 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) $ 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9 - 1422 * q^10 + 15484 * q^14 + 1266 * q^16 - 2188 * q^20 - 9234 * q^24 + 13812 * q^25 - 32052 * q^26 - 36920 * q^29 - 24300 * q^30 - 156204 * q^34 - 16038 * q^36 + 7674 * q^40 + 341848 * q^41 + 74892 * q^44 + 10692 * q^45 + 478080 * q^46 + 482556 * q^49 - 191448 * q^50 - 39366 * q^54 - 926132 * q^56 + 126846 * q^60 - 455976 * q^61 - 618 * q^64 - 624192 * q^65 - 127332 * q^66 - 541728 * q^69 - 1871304 * q^70 - 612324 * q^74 - 1566456 * q^76 + 2360972 * q^80 + 2125764 * q^81 + 858276 * q^84 + 2280864 * q^85 + 5157592 * q^86 - 1806104 * q^89 - 345546 * q^90 - 3121992 * q^94 - 4040118 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−7.34967	+	3.15947i	−0.918709	+	0.394934i
$2$	−7.34967	+	3.15947i	−0.918709	+	0.394934i
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	44.0354	−	46.4422i	0.688054	−	0.725660i
$5$	111.509	+	56.4858i	0.892075	+	0.451887i
$5$	111.509	+	56.4858i	0.892075	+	0.451887i
$6$	−114.570	+	49.2513i	−0.530417	+	0.228015i
$7$	231.647			0.675355			0.337677	−	0.941262i	$-0.390359\pi$
$7$	231.647			0.675355			0.337677	+	0.941262i	$0.390359\pi$
$8$	−176.913	+	480.464i	−0.345533	+	0.938406i
$9$	243.000			0.333333
$10$	−998.024	−	62.8414i	−0.998024	−	0.0628414i
$11$		−	1432.15i		−	1.07599i	−0.842947	−	0.537996i	$-0.819181\pi$
$11$		−	1432.15i		−	1.07599i	0.842947	−	0.537996i	$-0.180819\pi$
$12$	686.445	−	723.963i	0.397248	−	0.418960i
$13$		−	1704.35i		−	0.775762i	−0.921710	−	0.387881i	$-0.873207\pi$
$13$		−	1704.35i		−	0.775762i	0.921710	−	0.387881i	$-0.126793\pi$
$14$	−1702.53	+	731.882i	−0.620455	+	0.266721i
$15$	1738.26	+	880.527i	0.515040	+	0.260897i
$16$	−217.760	−	4090.21i	−0.0531641	−	0.998586i
$17$			7567.92i			1.54039i	0.637810	+	0.770194i	$0.279840\pi$
$17$			7567.92i			1.54039i	−0.637810	+	0.770194i	$0.720160\pi$
$18$	−1785.97	+	767.752i	−0.306236	+	0.131645i
$19$		−	5564.86i		−	0.811322i	−0.914024	−	0.405661i	$-0.867041\pi$
$19$		−	5564.86i		−	0.811322i	0.914024	−	0.405661i	$-0.132959\pi$
$20$	7533.69	−	2691.37i	0.941712	−	0.336421i
$21$	3611.02			0.389916
$22$	4524.83	+	10525.8i	0.424946	+	0.988524i
$23$	14468.9			1.18920			0.594598	−	0.804023i	$-0.297311\pi$
$23$	14468.9			1.18920			0.594598	+	0.804023i	$0.297311\pi$
$24$	−2757.80	+	7489.69i	−0.199494	+	0.541789i
$25$	9243.70	+	12597.4i	0.591597	+	0.806234i
$26$	5384.85	+	12526.4i	0.306375	+	0.712699i
$27$	3788.00			0.192450
$28$	10200.7	−	10758.2i	0.464680	−	0.490078i
$29$	25708.4			1.05410			0.527049	−	0.849835i	$-0.323298\pi$
$29$	25708.4			1.05410			0.527049	+	0.849835i	$0.323298\pi$
$30$	−15557.6	−	979.600i	−0.576209	−	0.0362815i
$31$			40919.0i			1.37354i	0.726876	+	0.686769i	$0.240971\pi$
$31$			40919.0i			1.37354i	−0.726876	+	0.686769i	$0.759029\pi$
$32$	14523.4	+	29373.7i	0.443218	+	0.896414i
$33$		−	22324.9i		−	0.621225i
$34$	−23910.7	−	55621.8i	−0.608352	−	1.41517i
$35$	25830.8	+	13084.8i	0.602467	+	0.305184i
$36$	10700.6	−	11285.5i	0.229351	−	0.241887i
$37$		−	66045.9i		−	1.30389i	−0.758267	−	0.651944i	$-0.773954\pi$
$37$		−	66045.9i		−	1.30389i	0.758267	−	0.651944i	$-0.226046\pi$
$38$	17582.0	+	40899.9i	0.320419	+	0.745369i
$39$		−	26568.2i		−	0.447886i
$40$	−46866.9	+	43583.2i	−0.732295	+	0.680987i
$41$	106267.			1.54187			0.770934	−	0.636915i	$-0.219790\pi$
$41$	106267.			1.54187			0.770934	+	0.636915i	$0.219790\pi$
$42$	−26539.8	+	11408.9i	−0.358220	+	0.153991i
$43$	−58344.7			−0.733830			−0.366915	−	0.930254i	$-0.619586\pi$
$43$	−58344.7			−0.733830			−0.366915	+	0.930254i	$0.619586\pi$
$44$	−66512.0	−	63065.2i	−0.780804	−	0.740341i
$45$	27096.8	+	13726.1i	0.297358	+	0.150629i
$46$	−106342.	+	45714.3i	−1.09253	+	0.469654i
$47$	−75013.4			−0.722512			−0.361256	−	0.932467i	$-0.617652\pi$
$47$	−75013.4			−0.722512			−0.361256	+	0.932467i	$0.617652\pi$
$48$	−3394.54	−	63760.0i	−0.0306943	−	0.576534i
$49$	−63988.8			−0.543896
$50$	−107739.	−	63381.6i	−0.861915	−	0.507053i
$51$			117972.i			0.889343i
$52$	−79153.7	−	75051.7i	−0.562939	−	0.533766i
$53$		−	81861.1i		−	0.549857i	−0.961465	−	0.274929i	$-0.911346\pi$
$53$		−	81861.1i		−	0.549857i	0.961465	−	0.274929i	$-0.0886542\pi$
$54$	−27840.5	+	11968.1i	−0.176806	+	0.0760051i
$55$	80896.0	−	159698.i	0.486227	−	0.959866i
$56$	−40981.3	+	111298.i	−0.233358	+	0.633757i
$57$		−	86747.5i		−	0.468417i
$58$	−188948.	+	81225.0i	−0.968410	+	0.416300i
$59$			199623.i			0.971974i	0.873966	+	0.485987i	$0.161540\pi$
$59$			199623.i			0.971974i	−0.873966	+	0.485987i	$0.838460\pi$
$60$	117439.	−	41954.3i	0.543698	−	0.194233i
$61$	168043.			0.740339			0.370170	−	0.928964i	$-0.379300\pi$
$61$	168043.			0.740339			0.370170	+	0.928964i	$0.379300\pi$
$62$	−129283.	−	300742.i	−0.542457	−	1.26188i
$63$	56290.2			0.225118
$64$	−199547.	−	170001.i	−0.761213	−	0.648502i
$65$	96271.5	−	190051.i	0.350556	−	0.692038i
$66$	70535.1	+	164081.i	0.245343	+	0.570725i
$67$	36855.0			0.122538			0.0612691	−	0.998121i	$-0.480485\pi$
$67$	36855.0			0.122538			0.0612691	+	0.998121i	$0.480485\pi$
$68$	351471.	+	333257.i	1.11780	+	1.05987i
$69$	225548.			0.686582
$70$	−231189.	−	14557.0i	−0.674020	−	0.0424402i
$71$			449616.i			1.25622i	0.778123	+	0.628112i	$0.216172\pi$
$71$			449616.i			1.25622i	−0.778123	+	0.628112i	$0.783828\pi$
$72$	−42989.9	+	116753.i	−0.115178	+	0.312802i
$73$			58511.3i			0.150408i	0.997168	+	0.0752041i	$0.0239608\pi$
$73$			58511.3i			0.150408i	−0.997168	+	0.0752041i	$0.976039\pi$
$74$	208670.	+	485416.i	0.514950	+	1.19789i
$75$	144095.	+	196374.i	0.341559	+	0.465479i
$76$	−258444.	−	245051.i	−0.588744	−	0.558233i
$77$		−	331752.i		−	0.726677i
$78$	83941.4	+	195267.i	0.176886	+	0.411477i
$79$		−	649187.i		−	1.31670i	−0.752710	−	0.658352i	$-0.771254\pi$
$79$		−	649187.i		−	1.31670i	0.752710	−	0.658352i	$-0.228746\pi$
$80$	206756.	−	468397.i	0.403821	−	0.914838i
$81$	59049.0			0.111111
$82$	−781028.	+	335748.i	−1.41653	+	0.608936i
$83$	−452757.			−0.791828			−0.395914	−	0.918288i	$-0.629572\pi$
$83$	−452757.			−0.791828			−0.395914	+	0.918288i	$0.629572\pi$
$84$	159013.	−	167704.i	0.268283	−	0.282947i
$85$	−427480.	+	843895.i	−0.696080	+	1.37414i
$86$	428814.	−	184338.i	0.674177	−	0.289815i
$87$	400754.			0.608584
$88$	688095.	+	253365.i	1.00972	+	0.371791i
$89$	−286863.			−0.406915			−0.203458	−	0.979084i	$-0.565218\pi$
$89$	−286863.			−0.406915			−0.203458	+	0.979084i	$0.565218\pi$
$90$	−242520.	−	15270.5i	−0.332675	−	0.0209471i
$91$		−	394807.i		−	0.523914i
$92$	637146.	−	671970.i	0.818230	−	0.862951i
$93$			637865.i			0.793012i
$94$	551324.	−	237003.i	0.663779	−	0.285345i
$95$	314336.	−	620534.i	0.366626	−	0.723760i
$96$	226397.	+	457890.i	0.255892	+	0.517545i
$97$			386394.i			0.423365i	0.977338	+	0.211683i	$0.0678943\pi$
$97$			386394.i			0.423365i	−0.977338	+	0.211683i	$0.932106\pi$
$98$	470297.	−	202171.i	0.499682	−	0.214803i
$99$		−	348011.i		−	0.358664i
$100$	992102.	+	125434.i	0.992102	+	0.125434i
$101$	−881482.			−0.855558			−0.427779	−	0.903883i	$-0.640704\pi$
$101$	−881482.			−0.855558			−0.427779	+	0.903883i	$0.640704\pi$
$102$	−372730.	−	867057.i	−0.351232	−	0.817048i
$103$	−17661.6			−0.0161628			−0.00808142	−	0.999967i	$-0.502572\pi$
$103$	−17661.6			−0.0161628			−0.00808142	+	0.999967i	$0.502572\pi$
$104$	818878.	+	301522.i	0.727980	+	0.268052i
$105$	402662.	+	203971.i	0.347835	+	0.176198i
$106$	258638.	+	601652.i	0.217157	+	0.505159i
$107$	−2.08551e6			−1.70239			−0.851197	−	0.524847i	$-0.824123\pi$
$107$	−2.08551e6			−1.70239			−0.851197	+	0.524847i	$0.824123\pi$
$108$	166806.	−	175923.i	0.132416	−	0.139653i
$109$	−1.58327e6			−1.22257			−0.611287	−	0.791409i	$-0.709348\pi$
$109$	−1.58327e6			−1.22257			−0.611287	+	0.791409i	$0.709348\pi$
$110$	−89998.0	+	1.42932e6i	−0.0676168	+	1.07387i
$111$		−	1.02955e6i		−	0.752800i
$112$	−50443.4	−	947483.i	−0.0359046	−	0.674400i
$113$			232817.i			0.161354i	0.996740	+	0.0806768i	$0.0257082\pi$
$113$			232817.i			0.161354i	−0.996740	+	0.0806768i	$0.974292\pi$
$114$	274077.	+	637566.i	0.184994	+	0.430339i
$115$	1.61342e6	+	817290.i	1.06085	+	0.537382i
$116$	1.13208e6	−	1.19396e6i	0.725276	−	0.764917i
$117$		−	414157.i		−	0.258587i
$118$	−630704.	−	1.46716e6i	−0.383866	−	0.892961i
$119$			1.75308e6i			1.04031i
$120$	−730583.	+	679395.i	−0.422791	+	0.393168i
$121$	−279481.			−0.157760
$122$	−1.23506e6	+	530927.i	−0.680156	+	0.292385i
$123$	1.65654e6			0.890198
$124$	1.90037e6	+	1.80189e6i	0.996721	+	0.945067i
$125$	319185.	+	1.92687e6i	0.163422	+	0.986556i
$126$	−413714.	+	177847.i	−0.206818	+	0.0889069i
$127$	−1.40476e6			−0.685789			−0.342894	−	0.939374i	$-0.611407\pi$
$127$	−1.40476e6			−0.685789			−0.342894	+	0.939374i	$0.611407\pi$
$128$	2.00372e6	+	618985.i	0.955449	+	0.295155i
$129$	−909503.			−0.423677
$130$	−107104.	+	1.70098e6i	−0.0487499	+	0.774228i
$131$		−	1.22135e6i		−	0.543281i	−0.962399	−	0.271641i	$-0.912434\pi$
$131$		−	1.22135e6i		−	0.543281i	0.962399	−	0.271641i	$-0.0875662\pi$
$132$	−1.03682e6	−	983089.i	−0.450798	−	0.427436i
$133$		−	1.28908e6i		−	0.547930i
$134$	−270872.	+	116442.i	−0.112577	+	0.0483945i
$135$	422397.	+	213968.i	0.171680	+	0.0869656i
$136$	−3.63611e6	−	1.33886e6i	−1.44551	−	0.532255i
$137$		−	4.07260e6i		−	1.58383i	−0.610628	−	0.791917i	$-0.709083\pi$
$137$		−	4.07260e6i		−	1.58383i	0.610628	−	0.791917i	$-0.290917\pi$
$138$	−1.65771e6	+	712615.i	−0.630770	+	0.271155i
$139$		−	1.82029e6i		−	0.677791i	−0.940824	−	0.338895i	$-0.889947\pi$
$139$		−	1.82029e6i		−	0.677791i	0.940824	−	0.338895i	$-0.110053\pi$
$140$	1.74516e6	−	623446.i	0.635990	−	0.227203i
$141$	−1.16934e6			−0.417143
$142$	−1.42055e6	−	3.30453e6i	−0.496126	−	1.15410i
$143$	−2.44088e6			−0.834714
$144$	−52915.7	−	993920.i	−0.0177214	−	0.332862i
$145$	2.86673e6	+	1.45216e6i	0.940335	+	0.476333i
$146$	−184865.	−	430039.i	−0.0594013	−	0.138181i
$147$	−997487.			−0.314018
$148$	−3.06732e6	−	2.90836e6i	−0.946179	−	0.897145i
$149$	−5.35411e6			−1.61856			−0.809280	−	0.587423i	$-0.800143\pi$
$149$	−5.35411e6			−1.61856			−0.809280	+	0.587423i	$0.800143\pi$
$150$	−1.67949e6	−	988021.i	−0.497627	−	0.292747i
$151$			712681.i			0.206997i	0.994630	+	0.103499i	$0.0330037\pi$
$151$			712681.i			0.206997i	−0.994630	+	0.103499i	$0.966996\pi$
$152$	2.67371e6	+	984496.i	0.761350	+	0.280339i
$153$			1.83900e6i			0.513462i
$154$	1.04816e6	+	2.43827e6i	0.286990	+	0.667605i
$155$	−2.31135e6	+	4.56286e6i	−0.620683	+	1.22530i
$156$	−1.23388e6	−	1.16994e6i	−0.325013	−	0.308170i
$157$		−	2.12365e6i		−	0.548763i	−0.961621	−	0.274381i	$-0.911527\pi$
$157$		−	2.12365e6i		−	0.548763i	0.961621	−	0.274381i	$-0.0884731\pi$
$158$	2.05109e6	+	4.77131e6i	0.520012	+	1.20967i
$159$		−	1.27609e6i		−	0.317460i
$160$	−39704.5	+	4.09581e6i	−0.00969348	+	0.999953i
$161$	3.35168e6			0.803129
$162$	−433991.	+	186564.i	−0.102079	+	0.0438816i
$163$	4.83687e6			1.11687			0.558433	−	0.829550i	$-0.311403\pi$
$163$	4.83687e6			1.11687			0.558433	+	0.829550i	$0.311403\pi$
$164$	4.67952e6	−	4.93528e6i	1.06089	−	1.11887i
$165$	1.26104e6	−	2.48944e6i	0.280723	−	0.554179i
$166$	3.32762e6	−	1.43047e6i	0.727460	−	0.312720i
$167$	−6.50373e6			−1.39641			−0.698205	−	0.715898i	$-0.746018\pi$
$167$	−6.50373e6			−1.39641			−0.698205	+	0.715898i	$0.746018\pi$
$168$	−638836.	+	1.73496e6i	−0.134729	+	0.365900i
$169$	1.92201e6			0.398194
$170$	475579.	−	7.55296e6i	0.0968000	−	1.53734i
$171$		−	1.35226e6i		−	0.270441i
$172$	−2.56923e6	+	2.70966e6i	−0.504915	+	0.532511i
$173$			5.13552e6i			0.991851i	0.868365	+	0.495926i	$0.165171\pi$
$173$			5.13552e6i			0.991851i	−0.868365	+	0.495926i	$0.834829\pi$
$174$	−2.94541e6	+	1.26617e6i	−0.559112	+	0.240351i
$175$	2.14127e6	+	2.91815e6i	0.399538	+	0.544494i
$176$	−5.85777e6	+	311864.i	−1.07447	+	0.0572042i
$177$			3.11181e6i			0.561169i
$178$	2.10835e6	−	906335.i	0.373837	−	0.160705i
$179$		−	7.09855e6i		−	1.23769i	−0.785515	−	0.618843i	$-0.787602\pi$
$179$		−	7.09855e6i		−	1.23769i	0.785515	−	0.618843i	$-0.212398\pi$
$180$	1.83069e6	−	654002.i	0.313904	−	0.112140i
$181$	9.46363e6			1.59596			0.797980	−	0.602683i	$-0.205902\pi$
$181$	9.46363e6			1.59596			0.797980	+	0.602683i	$0.205902\pi$
$182$	1.24738e6	+	2.90170e6i	0.206912	+	0.481325i
$183$	2.61953e6			0.427435
$184$	−2.55975e6	+	6.95181e6i	−0.410907	+	1.11595i
$185$	3.73066e6	−	7.36473e6i	0.589210	−	1.16317i
$186$	−2.01532e6	−	4.68810e6i	−0.313188	−	0.728548i
$187$	1.08384e7			1.65744
$188$	−3.30325e6	+	3.48379e6i	−0.497127	+	0.524298i
$189$	877477.			0.129972
$190$	−349703.	+	5.55386e6i	−0.0509846	+	0.809718i
$191$			1.18644e7i			1.70273i	0.524570	+	0.851367i	$0.324226\pi$
$191$			1.18644e7i			1.70273i	−0.524570	+	0.851367i	$0.675774\pi$
$192$	−3.11064e6	−	2.65005e6i	−0.439487	−	0.374413i
$193$		−	5.29387e6i		−	0.736379i	−0.929751	−	0.368189i	$-0.879978\pi$
$193$		−	5.29387e6i		−	0.736379i	0.929751	−	0.368189i	$-0.120022\pi$
$194$	−1.22080e6	−	2.83987e6i	−0.167201	−	0.388949i
$195$	1.50072e6	−	2.96260e6i	0.202394	−	0.399548i
$196$	−2.81777e6	+	2.97178e6i	−0.374230	+	0.394683i
$197$		−	5.56867e6i		−	0.728371i	−0.931326	−	0.364186i	$-0.881347\pi$
$197$		−	5.56867e6i		−	0.728371i	0.931326	−	0.364186i	$-0.118653\pi$
$198$	1.09953e6	+	2.55777e6i	0.141649	+	0.329508i
$199$			6.63937e6i			0.842496i	0.906946	+	0.421248i	$0.138408\pi$
$199$			6.63937e6i			0.842496i	−0.906946	+	0.421248i	$0.861592\pi$
$200$	−7.68793e6	+	2.21262e6i	−0.960992	+	0.276577i
$201$	574512.			0.0707475
$202$	6.47861e6	−	2.78502e6i	0.786009	−	0.337889i
$203$	5.95527e6			0.711890
$204$	5.47889e6	+	5.19496e6i	0.645360	+	0.611916i
$205$	1.18498e7	+	6.00258e6i	1.37546	+	0.696749i
$206$	129807.	−	55801.3i	0.0148490	−	0.00638326i
$207$	3.51595e6			0.396399
$208$	−6.97114e6	+	371139.i	−0.774665	+	0.0412427i
$209$	−7.96969e6			−0.872976
$210$	−3.60388e6	−	226921.i	−0.389146	−	0.0245029i
$211$		−	2.67302e6i		−	0.284548i	−0.989827	−	0.142274i	$-0.954559\pi$
$211$		−	2.67302e6i		−	0.284548i	0.989827	−	0.142274i	$-0.0454414\pi$
$212$	−3.80181e6	−	3.60479e6i	−0.399009	−	0.378331i
$213$			7.00883e6i			0.725281i
$214$	1.53278e7	−	6.58910e6i	1.56400	−	0.672334i
$215$	−6.50598e6	−	3.29565e6i	−0.654632	−	0.331608i
$216$	−670146.	+	1.82000e6i	−0.0664979	+	0.180596i
$217$			9.47876e6i			0.927625i
$218$	1.16365e7	−	5.00229e6i	1.12319	−	0.482836i
$219$			912101.i			0.0868382i
$220$	−3.85443e6	−	1.07893e7i	−0.361986	−	1.01327i
$221$	1.28984e7			1.19497
$222$	3.25285e6	+	7.56688e6i	0.297307	+	0.691605i
$223$	−8.78893e6			−0.792540			−0.396270	−	0.918134i	$-0.629696\pi$
$223$	−8.78893e6			−0.792540			−0.396270	+	0.918134i	$0.629696\pi$
$224$	3.36429e6	+	6.80432e6i	0.299330	+	0.605397i
$225$	2.24622e6	+	3.06117e6i	0.197199	+	0.268745i
$226$	−735579.	−	1.71113e6i	−0.0637241	−	0.148237i
$227$	1.92283e6			0.164385			0.0821926	−	0.996616i	$-0.473808\pi$
$227$	1.92283e6			0.164385			0.0821926	+	0.996616i	$0.473808\pi$
$228$	−4.02875e6	−	3.81997e6i	−0.339911	−	0.322296i
$229$	−1.88248e7			−1.56756			−0.783780	−	0.621039i	$-0.786711\pi$
$229$	−1.88248e7			−1.56756			−0.783780	+	0.621039i	$0.786711\pi$
$230$	−1.44403e7	−	909248.i	−1.18685	−	0.0747307i
$231$		−	5.17150e6i		−	0.419547i
$232$	−4.54815e6	+	1.23520e7i	−0.364226	+	0.989172i
$233$		−	9.64495e6i		−	0.762487i	−0.924475	−	0.381243i	$-0.875496\pi$
$233$		−	9.64495e6i		−	0.762487i	0.924475	−	0.381243i	$-0.124504\pi$
$234$	1.30852e6	+	3.04392e6i	0.102125	+	0.237566i
$235$	−8.36470e6	−	4.23719e6i	−0.644535	−	0.326494i
$236$	9.27093e6	+	8.79048e6i	0.705322	+	0.668770i
$237$		−	1.01198e7i		−	0.760200i
$238$	−5.53883e6	−	1.28846e7i	−0.410853	−	0.955741i
$239$		−	1.55315e7i		−	1.13768i	−0.822448	−	0.568841i	$-0.807392\pi$
$239$		−	1.55315e7i		−	1.13768i	0.822448	−	0.568841i	$-0.192608\pi$
$240$	3.22301e6	−	7.30159e6i	0.233146	−	0.528182i
$241$	−1.93206e7			−1.38028			−0.690142	−	0.723674i	$-0.742452\pi$
$241$	−1.93206e7			−1.38028			−0.690142	+	0.723674i	$0.742452\pi$
$242$	2.05409e6	−	883013.i	0.144935	−	0.0623047i
$243$	920483.			0.0641500
$244$	7.39984e6	−	7.80429e6i	0.509393	−	0.537234i
$245$	−7.13535e6	−	3.61446e6i	−0.485196	−	0.245779i
$246$	−1.21750e7	+	5.23379e6i	−0.817833	+	0.351570i
$247$	−9.48445e6			−0.629392
$248$	−1.96601e7	−	7.23912e6i	−1.28894	−	0.474603i
$249$	−7.05778e6			−0.457162
$250$	−8.43379e6	−	1.31534e7i	−0.539763	−	0.841817i
$251$			2.66294e7i			1.68400i	0.539481	+	0.841998i	$0.318620\pi$
$251$			2.66294e7i			1.68400i	−0.539481	+	0.841998i	$0.681380\pi$
$252$	2.47876e6	−	2.61424e6i	0.154893	−	0.163359i
$253$		−	2.07216e7i		−	1.27957i
$254$	1.03245e7	−	4.43830e6i	0.630041	−	0.270842i
$255$	−6.66376e6	+	1.31550e7i	−0.401882	+	0.793361i
$256$	−1.66824e7	+	1.78137e6i	−0.994347	+	0.106178i
$257$			2.66861e7i			1.57212i	0.618152	+	0.786059i	$0.287882\pi$
$257$			2.66861e7i			1.57212i	−0.618152	+	0.786059i	$0.712118\pi$
$258$	6.68455e6	−	2.87355e6i	0.389236	−	0.167325i
$259$		−	1.52993e7i		−	0.880587i
$260$	−4.58703e6	−	1.28400e7i	−0.260982	−	0.730544i
$261$	6.24714e6			0.351366
$262$	3.85881e6	+	8.97650e6i	0.214560	+	0.499118i
$263$	−1.09464e7			−0.601735			−0.300868	−	0.953666i	$-0.597276\pi$
$263$	−1.09464e7			−0.601735			−0.300868	+	0.953666i	$0.597276\pi$
$264$	1.07263e7	+	3.94958e6i	0.582961	+	0.214654i
$265$	4.62399e6	−	9.12828e6i	0.248473	−	0.490514i
$266$	4.07282e6	+	9.47432e6i	0.216396	+	0.503389i
$267$	−4.47175e6			−0.234933
$268$	1.62292e6	−	1.71163e6i	0.0843129	−	0.0889210i
$269$	−3.06782e7			−1.57606			−0.788030	−	0.615636i	$-0.788899\pi$
$269$	−3.06782e7			−1.57606			−0.788030	+	0.615636i	$0.788899\pi$
$270$	−3.78051e6	−	238043.i	−0.192070	−	0.0120938i
$271$		−	5.50607e6i		−	0.276652i	−0.990387	−	0.138326i	$-0.955828\pi$
$271$		−	5.50607e6i		−	0.276652i	0.990387	−	0.138326i	$-0.0441722\pi$
$272$	3.09544e7	−	1.64799e6i	1.53821	−	0.0818933i
$273$		−	6.15443e6i		−	0.302482i
$274$	1.28673e7	+	2.99323e7i	0.625511	+	1.45508i
$275$	1.80413e7	−	1.32383e7i	0.867502	−	0.636554i
$276$	9.93213e6	−	1.04750e7i	0.472406	−	0.498225i
$277$			2.32026e7i			1.09168i	0.837888	+	0.545842i	$0.183790\pi$
$277$			2.32026e7i			1.09168i	−0.837888	+	0.545842i	$0.816210\pi$
$278$	5.75115e6	+	1.33785e7i	0.267683	+	0.622693i
$279$			9.94333e6i			0.457846i
$280$	−1.08566e7	+	1.00959e7i	−0.494559	+	0.459908i
$281$	2.25844e7			1.01786			0.508932	−	0.860807i	$-0.330040\pi$
$281$	2.25844e7			1.01786			0.508932	+	0.860807i	$0.330040\pi$
$282$	8.59429e6	−	3.69451e6i	0.383233	−	0.164744i
$283$	−1.85815e7			−0.819828			−0.409914	−	0.912124i	$-0.634441\pi$
$283$	−1.85815e7			−0.819828			−0.409914	+	0.912124i	$0.634441\pi$
$284$	2.08812e7	+	1.97991e7i	0.911591	+	0.864350i
$285$	4.90001e6	−	9.67317e6i	0.211671	−	0.417863i
$286$	1.79396e7	−	7.71188e6i	0.766859	−	0.329657i
$287$	2.46164e7			1.04131
$288$	3.52918e6	+	7.13781e6i	0.147739	+	0.298805i
$289$	−3.31359e7			−1.37279
$290$	−2.56576e7	−	1.61555e6i	−1.05201	−	0.0662410i
$291$			6.02328e6i			0.244430i
$292$	2.71740e6	+	2.57657e6i	0.109145	+	0.103489i
$293$			2.41469e7i			0.959972i	0.877276	+	0.479986i	$0.159358\pi$
$293$			2.41469e7i			0.959972i	−0.877276	+	0.479986i	$0.840642\pi$
$294$	7.33120e6	−	3.15153e6i	0.288492	−	0.124017i
$295$	−1.12759e7	+	2.22598e7i	−0.439222	+	0.867074i
$296$	3.17327e7	+	1.16844e7i	1.22358	+	0.450537i
$297$		−	5.42496e6i		−	0.207075i
$298$	3.93510e7	−	1.69162e7i	1.48699	−	0.639225i
$299$		−	2.46601e7i		−	0.922532i
$300$	1.54653e7	+	1.95533e6i	0.572790	+	0.0724195i
$301$	−1.35154e7			−0.495596
$302$	−2.25170e6	−	5.23797e6i	−0.0817502	−	0.190170i
$303$	−1.37409e7			−0.493957
$304$	−2.27614e7	+	1.21180e6i	−0.810174	+	0.0431332i
$305$	1.87384e7	+	9.49204e6i	0.660438	+	0.334549i
$306$	−5.81029e6	−	1.35161e7i	−0.202784	−	0.471723i
$307$	4.12727e7			1.42642			0.713210	−	0.700950i	$-0.247241\pi$
$307$	4.12727e7			1.42642			0.713210	+	0.700950i	$0.247241\pi$
$308$	−1.54073e7	−	1.46088e7i	−0.527320	−	0.499993i
$309$	−275317.			−0.00933163
$310$	2.57141e6	−	4.08382e7i	0.0863150	−	1.37082i
$311$		−	1.74437e7i		−	0.579907i	−0.957041	−	0.289954i	$-0.906360\pi$
$311$		−	1.74437e7i		−	0.579907i	0.957041	−	0.289954i	$-0.0936399\pi$
$312$	1.27650e7	+	4.70026e6i	0.420299	+	0.154760i
$313$			5.31470e7i			1.73319i	0.499013	+	0.866594i	$0.333696\pi$
$313$			5.31470e7i			1.73319i	−0.499013	+	0.866594i	$0.666304\pi$
$314$	6.70963e6	+	1.56082e7i	0.216725	+	0.504154i
$315$	6.27688e6	+	3.17960e6i	0.200822	+	0.101728i
$316$	−3.01497e7	−	2.85872e7i	−0.955479	−	0.905963i
$317$			1.84064e7i			0.577819i	0.957356	+	0.288909i	$0.0932927\pi$
$317$			1.84064e7i			0.577819i	−0.957356	+	0.288909i	$0.906707\pi$
$318$	4.03177e6	+	9.37883e6i	0.125376	+	0.291654i
$319$		−	3.68182e7i		−	1.13420i
$320$	−1.26488e7	−	3.02283e7i	−0.386010	−	0.922494i
$321$	−3.25098e7			−0.982877
$322$	−2.46338e7	+	1.05896e7i	−0.737842	+	0.317183i
$323$	4.21144e7			1.24975
$324$	2.60025e6	−	2.74237e6i	0.0764504	−	0.0806289i
$325$	2.14704e7	−	1.57545e7i	0.625445	−	0.458938i
$326$	−3.55494e7	+	1.52820e7i	−1.02608	+	0.441089i
$327$	−2.46807e7			−0.705853
$328$	−1.88000e7	+	5.10575e7i	−0.532767	+	1.44690i
$329$	−1.73766e7			−0.487952
$330$	−1.40293e6	+	2.22808e7i	−0.0390386	+	0.619997i
$331$		−	3.85547e7i		−	1.06315i	−0.847012	−	0.531574i	$-0.821601\pi$
$331$		−	3.85547e7i		−	1.06315i	0.847012	−	0.531574i	$-0.178399\pi$
$332$	−1.99374e7	+	2.10270e7i	−0.544820	+	0.574598i
$333$		−	1.60491e7i		−	0.434629i
$334$	4.78003e7	−	2.05484e7i	1.28290	−	0.551490i
$335$	4.10968e6	+	2.08178e6i	0.109313	+	0.0553734i
$336$	−786335.	−	1.47698e7i	−0.0207296	−	0.389365i
$337$		−	2.31156e7i		−	0.603970i	−0.953313	−	0.301985i	$-0.902351\pi$
$337$		−	2.31156e7i		−	0.603970i	0.953313	−	0.301985i	$-0.0976492\pi$
$338$	−1.41261e7	+	6.07253e6i	−0.365824	+	0.157260i
$339$			3.62925e6i			0.0931576i
$340$	2.03681e7	+	5.70144e7i	0.518218	+	1.45060i
$341$	5.86020e7			1.47792
$342$	4.27243e6	+	9.93867e6i	0.106806	+	0.248456i
$343$	−4.20758e7			−1.04268
$344$	1.03219e7	−	2.80325e7i	0.253563	−	0.688631i
$345$	2.51508e7	+	1.27403e7i	0.612483	+	0.310257i
$346$	−1.62256e7	−	3.77444e7i	−0.391716	−	0.911223i
$347$	4.88908e7			1.17014			0.585072	−	0.810982i	$-0.301066\pi$
$347$	4.88908e7			1.17014			0.585072	+	0.810982i	$0.301066\pi$
$348$	1.76474e7	−	1.86119e7i	0.418738	−	0.441625i
$349$	2.05125e7			0.482551			0.241275	−	0.970457i	$-0.422434\pi$
$349$	2.05125e7			0.482551			0.241275	+	0.970457i	$0.422434\pi$
$350$	−2.49575e7	−	1.46821e7i	−0.582099	−	0.342441i
$351$		−	6.45606e6i		−	0.149295i
$352$	4.20674e7	−	2.07996e7i	0.964534	−	0.476899i
$353$		−	5.06784e7i		−	1.15212i	−0.817407	−	0.576061i	$-0.804589\pi$
$353$		−	5.06784e7i		−	1.15212i	0.817407	−	0.576061i	$-0.195411\pi$
$354$	−9.83170e6	−	2.28708e7i	−0.221625	−	0.515551i
$355$	−2.53970e7	+	5.01365e7i	−0.567671	+	1.12065i
$356$	−1.26321e7	+	1.33225e7i	−0.279980	+	0.295282i
$357$			2.73279e7i			0.600622i
$358$	2.24277e7	+	5.21720e7i	0.488805	+	1.13707i
$359$			6.09356e7i			1.31701i	0.752578	+	0.658503i	$0.228810\pi$
$359$			6.09356e7i			1.31701i	−0.752578	+	0.658503i	$0.771190\pi$
$360$	−1.13887e7	+	1.05907e7i	−0.244098	+	0.226996i
$361$	1.60783e7			0.341757
$362$	−6.95546e7	+	2.99001e7i	−1.46622	+	0.630300i
$363$	−4.35668e6			−0.0910826
$364$	−1.83357e7	−	1.73855e7i	−0.380184	−	0.360481i
$365$	−3.30506e6	+	6.52456e6i	−0.0679674	+	0.134175i
$366$	−1.92527e7	+	8.27634e6i	−0.392689	+	0.168809i
$367$	−1.49766e7			−0.302981			−0.151491	−	0.988459i	$-0.548407\pi$
$367$	−1.49766e7			−0.302981			−0.151491	+	0.988459i	$0.548407\pi$
$368$	−3.15076e6	−	5.91810e7i	−0.0632225	−	1.18751i
$369$	2.58229e7			0.513956
$370$	−4.15041e6	+	6.59153e7i	−0.0819381	+	1.30131i
$371$		−	1.89628e7i		−	0.371349i
$372$	2.96239e7	+	2.80887e7i	0.575457	+	0.545635i
$373$		−	8.87162e7i		−	1.70953i	−0.519016	−	0.854764i	$-0.673702\pi$
$373$		−	8.87162e7i		−	1.70953i	0.519016	−	0.854764i	$-0.326298\pi$
$374$	−7.96585e7	+	3.42435e7i	−1.52271	+	0.654582i
$375$	4.97559e6	+	3.00369e7i	0.0943520	+	0.569588i
$376$	1.32709e7	−	3.60412e7i	0.249652	−	0.678010i
$377$		−	4.38161e7i		−	0.817729i
$378$	−6.44917e6	+	2.77237e6i	−0.119407	+	0.0513305i
$379$			9.17094e7i			1.68460i	0.539011	+	0.842299i	$0.318798\pi$
$379$			9.17094e7i			1.68460i	−0.539011	+	0.842299i	$0.681202\pi$
$380$	−1.49771e7	−	4.19239e7i	−0.272946	−	0.764031i
$381$	−2.18980e7			−0.395940
$382$	−3.74854e7	−	8.71997e7i	−0.672468	−	1.56432i
$383$	−2.76561e7			−0.492260			−0.246130	−	0.969237i	$-0.579159\pi$
$383$	−2.76561e7			−0.492260			−0.246130	+	0.969237i	$0.579159\pi$
$384$	3.12349e7	+	9.64903e6i	0.551629	+	0.170408i
$385$	1.87393e7	−	3.69935e7i	0.328376	−	0.648250i
$386$	1.67258e7	+	3.89082e7i	0.290821	+	0.676518i
$387$	−1.41778e7			−0.244610
$388$	1.79450e7	+	1.70150e7i	0.307219	+	0.291298i
$389$	2.95064e6			0.0501265			0.0250632	−	0.999686i	$-0.492021\pi$
$389$	2.95064e6			0.0501265			0.0250632	+	0.999686i	$0.492021\pi$
$390$	−1.66958e6	+	2.65156e7i	−0.0281458	+	0.447001i
$391$			1.09500e8i			1.83182i
$392$	1.13205e7	−	3.07443e7i	0.187934	−	0.510395i
$393$		−	1.90389e7i		−	0.313664i
$394$	1.75941e7	+	4.09279e7i	0.287659	+	0.669161i
$395$	3.66699e7	−	7.23904e7i	0.595001	−	1.17460i
$396$	−1.61624e7	−	1.53248e7i	−0.260268	−	0.246780i
$397$			1.13663e7i			0.181655i	0.995867	+	0.0908273i	$0.0289511\pi$
$397$			1.13663e7i			0.181655i	−0.995867	+	0.0908273i	$0.971049\pi$
$398$	−2.09769e7	−	4.87972e7i	−0.332731	−	0.774009i
$399$		−	2.00948e7i		−	0.316348i
$400$	4.95131e7	−	4.05519e7i	0.773642	−	0.633623i
$401$	−1.00443e7			−0.155771			−0.0778854	−	0.996962i	$-0.524817\pi$
$401$	−1.00443e7			−0.155771			−0.0778854	+	0.996962i	$0.524817\pi$
$402$	−4.22248e6	+	1.81516e6i	−0.0649964	+	0.0279406i
$403$	6.97403e7			1.06554
$404$	−3.88165e7	+	4.09380e7i	−0.588670	+	0.620844i
$405$	6.58452e6	+	3.33543e6i	0.0991195	+	0.0502096i
$406$	−4.37693e7	+	1.88155e7i	−0.654020	+	0.281150i
$407$	−9.45873e7			−1.40297
$408$	−5.66814e7	−	2.08708e7i	−0.834565	−	0.307298i
$409$	6.13215e7			0.896279			0.448139	−	0.893964i	$-0.352087\pi$
$409$	6.13215e7			0.896279			0.448139	+	0.893964i	$0.352087\pi$
$410$	−1.06057e8	−	6.67797e6i	−1.53882	−	0.0968931i
$411$		−	6.34855e7i		−	0.914427i
$412$	−777735.	+	820243.i	−0.0111209	+	0.0117287i
$413$			4.62420e7i			0.656427i
$414$	−2.58411e7	+	1.11086e7i	−0.364175	+	0.156551i
$415$	−5.04867e7	−	2.55744e7i	−0.706370	−	0.357817i
$416$	5.00630e7	−	2.47529e7i	0.695403	−	0.343832i
$417$		−	2.83755e7i		−	0.391323i
$418$	5.85746e7	−	2.51800e7i	0.802011	−	0.344768i
$419$		−	1.15447e8i		−	1.56942i	−0.619862	−	0.784711i	$-0.712811\pi$
$419$		−	1.15447e8i		−	1.56942i	0.619862	−	0.784711i	$-0.287189\pi$
$420$	2.72043e7	−	9.71857e6i	0.367189	−	0.131176i
$421$	5.29282e7			0.709317			0.354659	−	0.934996i	$-0.384597\pi$
$421$	5.29282e7			0.709317			0.354659	+	0.934996i	$0.384597\pi$
$422$	8.44535e6	+	1.96459e7i	0.112378	+	0.261417i
$423$	−1.82283e7			−0.240837
$424$	3.93313e7	+	1.44823e7i	0.515989	+	0.189994i
$425$	−9.53362e7	+	6.99556e7i	−1.24191	+	0.911288i
$426$	−2.21442e7	−	5.15126e7i	−0.286439	−	0.666323i
$427$	3.89266e7			0.499992
$428$	−9.18361e7	+	9.68555e7i	−1.17134	+	1.23536i
$429$	−3.80495e7			−0.481922
$430$	5.82293e7	+	3.66646e6i	0.732380	+	0.0461149i
$431$			1.28493e8i			1.60490i	0.596722	+	0.802448i	$0.296469\pi$
$431$			1.28493e8i			1.60490i	−0.596722	+	0.802448i	$0.703531\pi$
$432$	−824874.	−	1.54937e7i	−0.0102314	−	0.192178i
$433$			1.05589e8i			1.30063i	0.759665	+	0.650315i	$0.225363\pi$
$433$			1.05589e8i			1.30063i	−0.759665	+	0.650315i	$0.774637\pi$
$434$	−2.99479e7	−	6.96658e7i	−0.366351	−	0.852218i
$435$	4.46879e7	+	2.26369e7i	0.542903	+	0.275011i
$436$	−6.97199e7	+	7.35305e7i	−0.841196	+	0.887172i
$437$		−	8.05176e7i		−	0.964820i
$438$	−2.88176e6	−	6.70365e6i	−0.0342954	−	0.0797790i
$439$			3.96198e7i			0.468294i	0.972201	+	0.234147i	$0.0752297\pi$
$439$			3.96198e7i			0.468294i	−0.972201	+	0.234147i	$0.924770\pi$
$440$	6.24175e7	+	6.71202e7i	0.732737	+	0.787944i
$441$	−1.55493e7			−0.181299
$442$	−9.47989e7	+	4.07521e7i	−1.09783	+	0.471936i
$443$	1.10250e8			1.26814			0.634070	−	0.773276i	$-0.281383\pi$
$443$	1.10250e8			1.26814			0.634070	+	0.773276i	$0.281383\pi$
$444$	−4.78147e7	−	4.53368e7i	−0.546277	−	0.517967i
$445$	−3.19879e7	−	1.62037e7i	−0.362999	−	0.183880i
$446$	6.45958e7	−	2.77684e7i	0.728114	−	0.313001i
$447$	−8.34624e7			−0.934476
$448$	−4.62245e7	−	3.93801e7i	−0.514089	−	0.437969i
$449$	1.05887e8			1.16977			0.584887	−	0.811115i	$-0.301139\pi$
$449$	1.05887e8			1.16977			0.584887	+	0.811115i	$0.301139\pi$
$450$	−2.61807e7	−	1.54017e7i	−0.287305	−	0.169018i
$451$		−	1.52190e8i		−	1.65904i
$452$	1.08125e7	+	1.02522e7i	0.117088	+	0.111020i
$453$			1.11096e7i			0.119510i
$454$	−1.41322e7	+	6.07513e6i	−0.151022	+	0.0649214i
$455$	2.23010e7	−	4.40247e7i	0.236750	−	0.467371i
$456$	4.16791e7	+	1.53468e7i	0.439565	+	0.161854i
$457$		−	9.85857e7i		−	1.03292i	−0.856312	−	0.516459i	$-0.827250\pi$
$457$		−	9.85857e7i		−	1.03292i	0.856312	−	0.516459i	$-0.172750\pi$
$458$	1.38356e8	−	5.94765e7i	1.44013	−	0.619083i
$459$			2.86673e7i			0.296448i
$460$	1.09005e8	−	3.89412e7i	1.11988	−	0.400070i
$461$	−2.20074e6			−0.0224629			−0.0112315	−	0.999937i	$-0.503575\pi$
$461$	−2.20074e6			−0.0224629			−0.0112315	+	0.999937i	$0.503575\pi$
$462$	1.63392e7	+	3.80088e7i	0.165694	+	0.385442i
$463$	5.10823e7			0.514668			0.257334	−	0.966323i	$-0.417156\pi$
$463$	5.10823e7			0.514668			0.257334	+	0.966323i	$0.417156\pi$
$464$	−5.59826e6	−	1.05153e8i	−0.0560402	−	1.05261i
$465$	−3.60303e7	+	7.11279e7i	−0.358352	+	0.707427i
$466$	3.04730e7	+	7.08873e7i	0.301132	+	0.700504i
$467$	−7.31478e7			−0.718209			−0.359105	−	0.933297i	$-0.616918\pi$
$467$	−7.31478e7			−0.718209			−0.359105	+	0.933297i	$0.616918\pi$
$468$	−1.92344e7	−	1.82376e7i	−0.187646	−	0.177922i
$469$	8.53733e6			0.0827568
$470$	7.48651e7	+	4.71394e6i	0.721084	+	0.0454037i
$471$		−	3.31045e7i		−	0.316828i
$472$	−9.59117e7	−	3.53159e7i	−0.912106	−	0.335849i
$473$			8.35581e7i			0.789596i
$474$	3.19733e7	+	7.43774e7i	0.300229	+	0.698403i
$475$	7.01028e7	−	5.14399e7i	0.654115	−	0.479975i
$476$	8.14171e7	+	7.71978e7i	0.754910	+	0.715788i
$477$		−	1.98922e7i		−	0.183286i
$478$	4.90715e7	+	1.14152e8i	0.449310	+	1.04520i
$479$		−	1.47715e7i		−	0.134406i	−0.997739	−	0.0672029i	$-0.978593\pi$
$479$		−	1.47715e7i		−	0.134406i	0.997739	−	0.0672029i	$-0.0214075\pi$
$480$	−618932.	+	6.38473e7i	−0.00559653	+	0.577323i
$481$	−1.12565e8			−1.01151
$482$	1.42000e8	−	6.10428e7i	1.26808	−	0.545122i
$483$	5.22476e7			0.463687
$484$	−1.23071e7	+	1.29797e7i	−0.108547	+	0.114480i
$485$	−2.18258e7	+	4.30866e7i	−0.191313	+	0.377674i
$486$	−6.76525e6	+	2.90824e6i	−0.0589352	+	0.0253350i
$487$	8.05091e6			0.0697041			0.0348521	−	0.999392i	$-0.488904\pi$
$487$	8.05091e6			0.0697041			0.0348521	+	0.999392i	$0.488904\pi$
$488$	−2.97290e7	+	8.07386e7i	−0.255812	+	0.694739i
$489$	7.53993e7			0.644823
$490$	6.38623e7	+	4.02114e6i	0.542821	+	0.0341792i
$491$			1.32710e8i			1.12114i	0.828108	+	0.560568i	$0.189417\pi$
$491$			1.32710e8i			1.12114i	−0.828108	+	0.560568i	$0.810583\pi$
$492$	7.29464e7	−	7.69334e7i	0.612504	−	0.645980i
$493$			1.94559e8i			1.62372i
$494$	6.97076e7	−	2.99659e7i	0.578229	−	0.248569i
$495$	1.96577e7	−	3.88066e7i	0.162076	−	0.319955i
$496$	1.67367e8	−	8.91054e6i	1.37159	−	0.0730229i
$497$			1.04152e8i			0.848397i
$498$	5.18724e7	−	2.22989e7i	0.419999	−	0.180549i
$499$		−	7.22099e7i		−	0.581159i	−0.956851	−	0.290579i	$-0.906152\pi$
$499$		−	7.22099e7i		−	0.581159i	0.956851	−	0.290579i	$-0.0938480\pi$
$500$	1.03543e8	+	7.00268e7i	0.828348	+	0.560215i
$501$	−1.01383e8			−0.806218
$502$	−8.41351e7	−	1.95718e8i	−0.665068	−	1.54710i
$503$	−6.05721e7			−0.475958			−0.237979	−	0.971270i	$-0.576485\pi$
$503$	−6.05721e7			−0.475958			−0.237979	+	0.971270i	$0.576485\pi$
$504$	−9.95847e6	+	2.70454e7i	−0.0777859	+	0.211252i
$505$	−9.82936e7	−	4.97913e7i	−0.763222	−	0.386615i
$506$	6.54695e7	+	1.52297e8i	0.505344	+	1.17555i
$507$	2.99611e7			0.229897
$508$	−6.18591e7	+	6.52401e7i	−0.471859	+	0.497649i
$509$	−1.58756e8			−1.20386			−0.601931	−	0.798548i	$-0.705602\pi$
$509$	−1.58756e8			−1.20386			−0.601931	+	0.798548i	$0.705602\pi$
$510$	7.41354e6	−	1.17739e8i	0.0558875	−	0.887585i
$511$			1.35540e7i			0.101579i
$512$	1.16982e8	−	6.58000e7i	0.871583	−	0.490248i
$513$		−	2.10796e7i		−	0.156139i
$514$	−8.43139e7	−	1.96134e8i	−0.620883	−	1.44432i
$515$	−1.96943e6	−	997629.i	−0.0144185	−	0.00730378i
$516$	−4.00504e7	+	4.22394e7i	−0.291513	+	0.307446i
$517$			1.07430e8i			0.777418i
$518$	4.83378e7	+	1.12445e8i	0.347774	+	0.809004i
$519$			8.00549e7i			0.572646i
$520$	7.42809e7	+	7.98775e7i	0.528284	+	0.568087i
$521$	3.43271e7			0.242730			0.121365	−	0.992608i	$-0.461273\pi$
$521$	3.43271e7			0.242730			0.121365	+	0.992608i	$0.461273\pi$
$522$	−4.59145e7	+	1.97377e7i	−0.322803	+	0.138767i
$523$	−7.73418e7			−0.540641			−0.270321	−	0.962770i	$-0.587130\pi$
$523$	−7.73418e7			−0.540641			−0.270321	+	0.962770i	$0.587130\pi$
$524$	−5.67220e7	−	5.37825e7i	−0.394237	−	0.373807i
$525$	3.33791e7	+	4.54894e7i	0.230673	+	0.314364i
$526$	8.04528e7	−	3.45850e7i	0.552820	−	0.237646i
$527$	−3.09672e8			−2.11578
$528$	−9.13137e7	+	4.86148e6i	−0.620346	+	0.0330268i
$529$	6.13144e7			0.414186
$530$	−5.14426e6	+	8.16993e7i	−0.0345538	+	0.548770i
$531$			4.85084e7i			0.323991i
$532$	−5.98678e7	−	5.67652e7i	−0.397611	−	0.377005i
$533$		−	1.81116e8i		−	1.19612i
$534$	3.28659e7	−	1.41284e7i	0.215835	−	0.0927830i
$535$	−2.32553e8	−	1.17802e8i	−1.51866	−	0.769289i
$536$	−6.52013e6	+	1.77075e7i	−0.0423411	+	0.114991i
$537$		−	1.10655e8i		−	0.714578i
$538$	2.25475e8	−	9.69270e7i	1.44794	−	0.622441i
$539$			9.16413e7i			0.585228i
$540$	2.85376e7	−	1.01949e7i	0.181233	−	0.0647442i
$541$	−1.75419e8			−1.10786			−0.553931	−	0.832562i	$-0.686873\pi$
$541$	−1.75419e8			−1.10786			−0.553931	+	0.832562i	$0.686873\pi$
$542$	1.73963e7	+	4.04678e7i	0.109259	+	0.254163i
$543$	1.47523e8			0.921428
$544$	−2.22298e8	+	1.09912e8i	−1.38082	+	0.682728i
$545$	−1.76549e8	−	8.94322e7i	−1.09063	−	0.552464i
$546$	1.94448e7	+	4.52330e7i	0.119461	+	0.277893i
$547$	2.50778e8			1.53224			0.766121	−	0.642696i	$-0.222184\pi$
$547$	2.50778e8			1.53224			0.766121	+	0.642696i	$0.222184\pi$
$548$	−1.89141e8	−	1.79339e8i	−1.14933	−	1.08976i
$549$	4.08344e7			0.246780
$550$	−9.07717e7	+	1.54299e8i	−0.545585	+	0.927414i
$551$		−	1.43064e8i		−	0.855213i
$552$	−3.99025e7	+	1.08368e8i	−0.237237	+	0.644293i
$553$		−	1.50382e8i		−	0.889243i
$554$	−7.33079e7	−	1.70531e8i	−0.431143	−	1.00294i
$555$	5.81552e7	−	1.14805e8i	0.340180	−	0.671555i
$556$	−8.45382e7	−	8.01572e7i	−0.491846	−	0.466357i
$557$		−	1.88247e8i		−	1.08934i	−0.838652	−	0.544668i	$-0.816656\pi$
$557$		−	1.88247e8i		−	1.08934i	0.838652	−	0.544668i	$-0.183344\pi$
$558$	−3.14157e7	−	7.30802e7i	−0.180819	−	0.420627i
$559$			9.94396e7i			0.569278i
$560$	4.78945e7	−	1.08503e8i	0.272723	−	0.617840i
$561$	1.68953e8			0.956926
$562$	−1.65988e8	+	7.13549e7i	−0.935121	+	0.401989i
$563$	−1.77571e8			−0.995054			−0.497527	−	0.867448i	$-0.665759\pi$
$563$	−1.77571e8			−0.995054			−0.497527	+	0.867448i	$0.665759\pi$
$564$	−5.14925e7	+	5.43069e7i	−0.287017	+	0.302704i
$565$	−1.31509e7	+	2.59613e7i	−0.0729136	+	0.143940i
$566$	1.36568e8	−	5.87079e7i	0.753183	−	0.323778i
$567$	1.36785e7			0.0750394
$568$	−2.16025e8	−	7.95431e7i	−1.17885	−	0.434067i
$569$	2.12669e8			1.15443			0.577216	−	0.816592i	$-0.304139\pi$
$569$	2.12669e8			1.15443			0.577216	+	0.816592i	$0.304139\pi$
$570$	−5.45133e6	+	8.65761e7i	−0.0294360	+	0.467491i
$571$		−	1.13543e8i		−	0.609889i	−0.952370	−	0.304944i	$-0.901362\pi$
$571$		−	1.13543e8i		−	0.609889i	0.952370	−	0.304944i	$-0.0986378\pi$
$572$	−1.07485e8	+	1.13360e8i	−0.574328	+	0.605718i
$573$			1.84948e8i			0.983074i
$574$	−1.80923e8	+	7.77749e7i	−0.956659	+	0.411248i
$575$	1.33747e8	+	1.82271e8i	0.703524	+	0.958770i
$576$	−4.84900e7	−	4.13102e7i	−0.253738	−	0.216167i
$577$			1.64538e8i			0.856524i	0.903655	+	0.428262i	$0.140874\pi$
$577$			1.64538e8i			0.856524i	−0.903655	+	0.428262i	$0.859126\pi$
$578$	2.43538e8	−	1.04692e8i	1.26120	−	0.542163i
$579$		−	8.25233e7i		−	0.425148i
$580$	1.93679e8	−	6.91907e7i	0.992657	−	0.354621i
$581$	−1.04880e8			−0.534765
$582$	−1.90304e7	−	4.42692e7i	−0.0965338	−	0.224560i
$583$	−1.17237e8			−0.591642
$584$	−2.81126e7	−	1.03514e7i	−0.141144	−	0.0519710i
$585$	2.33940e7	−	4.61824e7i	0.116852	−	0.230679i
$586$	−7.62915e7	−	1.77472e8i	−0.379126	−	0.881935i
$587$	−7.68393e6			−0.0379900			−0.0189950	−	0.999820i	$-0.506047\pi$
$587$	−7.68393e6			−0.0379900			−0.0189950	+	0.999820i	$0.506047\pi$
$588$	−4.39248e7	+	4.63255e7i	−0.216062	+	0.227870i
$589$	2.27709e8			1.11438
$590$	1.25446e7	−	1.99228e8i	0.0610801	−	0.970052i
$591$		−	8.68070e7i		−	0.420525i
$592$	−2.70141e8	+	1.43822e7i	−1.30204	+	0.0693200i
$593$		−	1.75657e8i		−	0.842366i	−0.906976	−	0.421183i	$-0.861615\pi$
$593$		−	1.75657e8i		−	0.842366i	0.906976	−	0.421183i	$-0.138385\pi$
$594$	1.71400e7	+	3.98717e7i	0.0817810	+	0.190242i
$595$	−9.90244e7	+	1.95485e8i	−0.470101	+	0.928033i
$596$	−2.35771e8	+	2.48657e8i	−1.11366	+	1.17452i
$597$			1.03498e8i			0.486415i
$598$	7.79130e7	+	1.81244e8i	0.364340	+	0.847539i
$599$			1.74222e8i			0.810628i	0.914177	+	0.405314i	$0.132838\pi$
$599$			1.74222e8i			0.810628i	−0.914177	+	0.405314i	$0.867162\pi$
$600$	−1.19843e8	+	3.44913e7i	−0.554829	+	0.159682i
$601$	−1.24560e8			−0.573792			−0.286896	−	0.957962i	$-0.592623\pi$
$601$	−1.24560e8			−0.573792			−0.286896	+	0.957962i	$0.592623\pi$
$602$	9.93334e7	−	4.27014e7i	0.455309	−	0.195728i
$603$	8.95576e6			0.0408461
$604$	3.30985e7	+	3.13832e7i	0.150209	+	0.142425i
$605$	−3.11648e7	−	1.57867e7i	−0.140734	−	0.0712895i
$606$	1.00991e8	−	4.34142e7i	0.453803	−	0.195080i
$607$	3.95496e8			1.76838			0.884190	−	0.467127i	$-0.154711\pi$
$607$	3.95496e8			1.76838			0.884190	+	0.467127i	$0.154711\pi$
$608$	1.63460e8	−	8.08205e7i	0.727280	−	0.359593i
$609$	9.28334e7			0.411010
$610$	−1.67711e8	−	1.05600e7i	−0.738876	−	0.0465239i
$611$			1.27849e8i			0.560497i
$612$	8.54075e7	+	8.09814e7i	0.372599	+	0.353290i
$613$		−	2.24663e8i		−	0.975326i	−0.873032	−	0.487663i	$-0.837850\pi$
$613$		−	2.24663e8i		−	0.975326i	0.873032	−	0.487663i	$-0.162150\pi$
$614$	−3.03341e8	+	1.30400e8i	−1.31047	+	0.563342i
$615$	1.84720e8	+	9.35710e7i	0.794123	+	0.402268i
$616$	1.59395e8	+	5.86913e7i	0.681918	+	0.251091i
$617$		−	7.20680e7i		−	0.306822i	−0.988162	−	0.153411i	$-0.950974\pi$
$617$		−	7.20680e7i		−	0.306822i	0.988162	−	0.153411i	$-0.0490259\pi$
$618$	2.02349e6	−	869856.i	0.00857305	−	0.00368538i
$619$		−	7.72367e7i		−	0.325651i	−0.986655	−	0.162825i	$-0.947939\pi$
$619$		−	7.72367e7i		−	0.325651i	0.986655	−	0.162825i	$-0.0520607\pi$
$620$	1.10128e8	+	3.08272e8i	0.462087	+	1.29348i
$621$	5.48083e7			0.228861
$622$	5.51131e7	+	1.28206e8i	0.229025	+	0.532766i
$623$	−6.64508e7			−0.274812
$624$	−1.08669e8	+	5.78549e6i	−0.447253	+	0.0238115i
$625$	−7.32486e7	+	2.32893e8i	−0.300026	+	0.953931i
$626$	−1.67917e8	−	3.90613e8i	−0.684496	−	1.59230i
$627$	−1.24235e8			−0.504013
$628$	−9.86272e7	−	9.35160e7i	−0.398215	−	0.377578i
$629$	4.99830e8			2.00849
$630$	−5.61789e7	−	3.53735e6i	−0.224673	−	0.0141467i
$631$		−	2.14473e8i		−	0.853661i	−0.904332	−	0.426831i	$-0.859630\pi$
$631$		−	2.14473e8i		−	0.853661i	0.904332	−	0.426831i	$-0.140370\pi$
$632$	3.11911e8	+	1.14850e8i	1.23560	+	0.454965i
$633$		−	4.16683e7i		−	0.164284i
$634$	−5.81546e7	−	1.35281e8i	−0.228201	−	0.530848i
$635$	−1.56644e8	−	7.93489e7i	−0.611775	−	0.309899i
$636$	−5.92643e7	−	5.61931e7i	−0.230368	−	0.218430i
$637$			1.09059e8i			0.421933i
$638$	1.16326e8	+	2.70602e8i	0.447935	+	1.04200i
$639$			1.09257e8i			0.418741i
$640$	1.88470e8	+	1.82205e8i	0.718956	+	0.695056i
$641$	2.43161e7			0.0923250			0.0461625	−	0.998934i	$-0.485301\pi$
$641$	2.43161e7			0.0923250			0.0461625	+	0.998934i	$0.485301\pi$
$642$	2.38937e8	−	1.02714e8i	0.902979	−	0.388172i
$643$	−1.27297e8			−0.478834			−0.239417	−	0.970917i	$-0.576956\pi$
$643$	−1.27297e8			−0.478834			−0.239417	+	0.970917i	$0.576956\pi$
$644$	1.47593e8	−	1.55660e8i	0.552596	−	0.582798i
$645$	−1.01418e8	−	5.13741e7i	−0.377952	−	0.191454i
$646$	−3.09527e8	+	1.33059e8i	−1.14816	+	0.493569i
$647$	6.33889e7			0.234046			0.117023	−	0.993129i	$-0.462665\pi$
$647$	6.33889e7			0.234046			0.117023	+	0.993129i	$0.462665\pi$
$648$	−1.04465e7	+	2.83709e7i	−0.0383926	+	0.104267i
$649$	2.85889e8			1.04584
$650$	−1.08024e8	+	1.83625e8i	−0.393352	+	0.668641i
$651$			1.47759e8i			0.535565i
$652$	2.12993e8	−	2.24635e8i	0.768464	−	0.810465i
$653$			2.20721e8i			0.792693i	0.918101	+	0.396346i	$0.129722\pi$
$653$			2.20721e8i			0.792693i	−0.918101	+	0.396346i	$0.870278\pi$
$654$	1.81395e8	−	7.79780e7i	0.648474	−	0.278766i
$655$	6.89888e7	−	1.36192e8i	0.245502	−	0.484648i
$656$	−2.31407e7	−	4.34654e8i	−0.0819720	−	1.53969i
$657$			1.42182e7i			0.0501360i
$658$	1.27712e8	−	5.49009e7i	0.448286	−	0.192709i
$659$			4.58676e8i			1.60269i	0.598202	+	0.801345i	$0.295882\pi$
$659$			4.58676e8i			1.60269i	−0.598202	+	0.801345i	$0.704118\pi$
$660$	−6.00846e7	−	1.68189e8i	−0.208993	−	0.585014i
$661$	2.41009e8			0.834504			0.417252	−	0.908791i	$-0.362993\pi$
$661$	2.41009e8			0.834504			0.417252	+	0.908791i	$0.362993\pi$
$662$	1.21813e8	+	2.83365e8i	0.419874	+	0.976724i
$663$	2.01066e8			0.689918
$664$	8.00987e7	−	2.17534e8i	0.273603	−	0.743057i
$665$	7.28148e7	−	1.43745e8i	0.247602	−	0.488795i
$666$	5.07069e7	+	1.17956e8i	0.171650	+	0.399298i
$667$	3.71973e8			1.25353
$668$	−2.86395e8	+	3.02048e8i	−0.960805	+	1.01332i
$669$	−1.37006e8			−0.457573
$670$	−3.67821e7	−	2.31602e6i	−0.122296	−	0.00770047i
$671$		−	2.40662e8i		−	0.796599i
$672$	5.24441e7	+	1.06069e8i	0.172818	+	0.349526i
$673$		−	3.13830e8i		−	1.02955i	−0.857324	−	0.514777i	$-0.827875\pi$
$673$		−	3.13830e8i		−	1.02955i	0.857324	−	0.514777i	$-0.172125\pi$
$674$	7.30331e7	+	1.69892e8i	0.238528	+	0.554873i
$675$	3.50151e7	+	4.77189e7i	0.113853	+	0.155160i
$676$	8.46364e7	−	8.92622e7i	0.273979	−	0.288953i
$677$		−	5.80130e7i		−	0.186965i	−0.995621	−	0.0934824i	$-0.970200\pi$
$677$		−	5.80130e7i		−	0.186965i	0.995621	−	0.0934824i	$-0.0297999\pi$
$678$	−1.14665e7	−	2.66738e7i	−0.0367911	−	0.0855848i
$679$			8.95069e7i			0.285922i
$680$	−3.29834e8	−	3.54685e8i	−1.04898	−	1.12802i
$681$	2.99739e7			0.0949079
$682$	−4.30706e8	+	1.85152e8i	−1.35777	+	0.583680i
$683$	3.03960e8			0.954014			0.477007	−	0.878899i	$-0.341722\pi$
$683$	3.03960e8			0.954014			0.477007	+	0.878899i	$0.341722\pi$
$684$	−6.28020e7	−	5.95474e7i	−0.196248	−	0.186078i
$685$	2.30044e8	−	4.54133e8i	0.715714	−	1.41290i
$686$	3.09243e8	−	1.32937e8i	0.957918	−	0.411789i
$687$	−2.93450e8			−0.905031
$688$	1.27051e7	+	2.38642e8i	0.0390134	+	0.732793i
$689$	−1.39520e8			−0.426558
$690$	−2.25103e8	−	1.41738e7i	−0.685225	−	0.0431458i
$691$			1.34182e8i			0.406688i	0.979107	+	0.203344i	$0.0651810\pi$
$691$			1.34182e8i			0.406688i	−0.979107	+	0.203344i	$0.934819\pi$
$692$	2.38505e8	+	2.26145e8i	0.719746	+	0.682447i
$693$		−	8.06157e7i		−	0.242226i
$694$	−3.59332e8	+	1.54469e8i	−1.07502	+	0.462130i
$695$	1.02820e8	−	2.02979e8i	0.306285	−	0.604640i
$696$	−7.08987e7	+	1.92548e8i	−0.210286	+	0.571099i
$697$			8.04221e8i			2.37507i
$698$	−1.50760e8	+	6.48088e7i	−0.443324	+	0.190576i
$699$		−	1.50350e8i		−	0.440222i
$700$	2.29817e8	+	2.90565e7i	0.670021	+	0.0847127i
$701$	−1.96406e8			−0.570164			−0.285082	−	0.958503i	$-0.592021\pi$
$701$	−1.96406e8			−0.570164			−0.285082	+	0.958503i	$0.592021\pi$
$702$	2.03978e7	+	4.74500e7i	0.0589619	+	0.137159i
$703$	−3.67536e8			−1.05787
$704$	−2.43466e8	+	2.85781e8i	−0.697783	+	0.819060i
$705$	−1.30393e8	−	6.60513e7i	−0.372123	−	0.188501i
$706$	1.60117e8	+	3.72470e8i	0.455013	+	1.05847i
$707$	−2.04192e8			−0.577805
$708$	1.44520e8	+	1.37030e8i	0.407218	+	0.386115i
$709$	−3.33485e7			−0.0935701			−0.0467851	−	0.998905i	$-0.514898\pi$
$709$	−3.33485e7			−0.0935701			−0.0467851	+	0.998905i	$0.514898\pi$
$710$	2.82545e7	−	4.48728e8i	0.0789428	−	1.25374i
$711$		−	1.57752e8i		−	0.438901i
$712$	5.07498e7	−	1.37827e8i	0.140603	−	0.381852i
$713$			5.92055e8i			1.63340i
$714$	−8.63417e7	−	2.00851e8i	−0.237206	−	0.551797i
$715$	−2.72181e8	−	1.37875e8i	−0.744627	−	0.377196i
$716$	−3.29672e8	−	3.12588e8i	−0.898139	−	0.851594i
$717$		−	2.42113e8i		−	0.656841i
$718$	−1.92525e8	−	4.47857e8i	−0.520131	−	1.20995i
$719$		−	2.33498e8i		−	0.628197i	−0.949390	−	0.314098i	$-0.898298\pi$
$719$		−	2.33498e8i		−	0.628197i	0.949390	−	0.314098i	$-0.101702\pi$
$720$	5.02418e7	−	1.13820e8i	0.134607	−	0.304946i
$721$	−4.09125e6			−0.0109157
$722$	−1.18170e8	+	5.07988e7i	−0.313975	+	0.134972i
$723$	−3.01178e8			−0.796908
$724$	4.16735e8	−	4.39512e8i	1.09811	−	1.15812i
$725$	2.37641e8	+	3.23859e8i	0.623601	+	0.849850i
$726$	3.20202e7	−	1.37648e7i	0.0836784	−	0.0359716i
$727$	5.57692e8			1.45141			0.725707	−	0.688004i	$-0.241513\pi$
$727$	5.57692e8			1.45141			0.725707	+	0.688004i	$0.241513\pi$
$728$	1.89690e8	+	6.98465e7i	0.491645	+	0.181030i
$729$	1.43489e7			0.0370370
$730$	3.67693e6	−	5.83957e7i	0.00945185	−	0.150111i
$731$		−	4.41548e8i		−	1.13038i
$732$	1.15352e8	−	1.21657e8i	0.294098	−	0.310172i
$733$		−	3.53347e8i		−	0.897199i	−0.893733	−	0.448600i	$-0.851923\pi$
$733$		−	3.53347e8i		−	0.897199i	0.893733	−	0.448600i	$-0.148077\pi$
$734$	1.10073e8	−	4.73183e7i	0.278352	−	0.119658i
$735$	−1.11229e8	−	5.63439e7i	−0.280128	−	0.141901i
$736$	2.10138e8	+	4.25006e8i	0.527073	+	1.06601i
$737$		−	5.27817e7i		−	0.131850i
$738$	−1.89790e8	+	8.15868e7i	−0.472176	+	0.202979i
$739$			2.91298e8i			0.721778i	0.932609	+	0.360889i	$0.117527\pi$
$739$			2.91298e8i			0.721778i	−0.932609	+	0.360889i	$0.882473\pi$
$740$	−1.77754e8	−	4.97569e8i	−0.438655	−	1.22789i
$741$	−1.47848e8			−0.363380
$742$	5.99126e7	+	1.39371e8i	0.146658	+	0.341161i
$743$	1.31685e8			0.321048			0.160524	−	0.987032i	$-0.448682\pi$
$743$	1.31685e8			0.321048			0.160524	+	0.987032i	$0.448682\pi$
$744$	−3.06471e8	−	1.12847e8i	−0.744168	−	0.274012i
$745$	−5.97034e8	−	3.02432e8i	−1.44388	−	0.731406i
$746$	2.80297e8	+	6.52035e8i	0.675152	+	1.57056i
$747$	−1.10020e8			−0.263943
$748$	4.77272e8	−	5.03358e8i	1.14041	−	1.20274i
$749$	−4.83100e8			−1.14972
$750$	−1.31470e8	−	2.05041e8i	−0.311632	−	0.486023i
$751$			6.94467e8i			1.63958i	0.572666	+	0.819789i	$0.305909\pi$
$751$			6.94467e8i			1.63958i	−0.572666	+	0.819789i	$0.694091\pi$
$752$	1.63349e7	+	3.06820e8i	0.0384117	+	0.721490i
$753$			4.15112e8i			0.972255i
$754$	1.38436e8	+	3.22034e8i	0.322949	+	0.751255i
$755$	−4.02564e7	+	7.94706e7i	−0.0935392	+	0.184657i
$756$	3.86401e7	−	4.07520e7i	0.0894278	−	0.0943155i
$757$		−	2.08147e8i		−	0.479824i	−0.970795	−	0.239912i	$-0.922881\pi$
$757$		−	2.08147e8i		−	0.479824i	0.970795	−	0.239912i	$-0.0771186\pi$
$758$	−2.89754e8	−	6.74034e8i	−0.665305	−	1.54766i
$759$		−	3.23018e8i		−	0.738757i
$760$	2.42534e8	+	2.60808e8i	0.552500	+	0.594127i
$761$	−4.53163e8			−1.02825			−0.514127	−	0.857714i	$-0.671884\pi$
$761$	−4.53163e8			−1.02825			−0.514127	+	0.857714i	$0.671884\pi$
$762$	1.60943e8	−	6.91862e7i	0.363754	−	0.156370i
$763$	−3.66759e8			−0.825671
$764$	5.51011e8	+	5.22456e8i	1.23561	+	1.17157i
$765$	−1.03878e8	+	2.05066e8i	−0.232027	+	0.458047i
$766$	2.03263e8	−	8.73788e7i	0.452244	−	0.194411i
$767$	3.40227e8			0.754020
$768$	−2.60053e8	+	2.77688e7i	−0.574087	+	0.0613018i
$769$	−7.62334e8			−1.67636			−0.838178	−	0.545396i	$-0.816379\pi$
$769$	−7.62334e8			−1.67636			−0.838178	+	0.545396i	$0.816379\pi$
$770$	−2.08477e7	+	3.31096e8i	−0.0456654	+	0.725241i
$771$			4.15994e8i			0.907662i
$772$	−2.45859e8	−	2.33118e8i	−0.534360	−	0.506668i
$773$		−	1.52713e7i		−	0.0330625i	−0.999863	−	0.0165313i	$-0.994738\pi$
$773$		−	1.52713e7i		−	0.0330625i	0.999863	−	0.0165313i	$-0.00526231\pi$
$774$	1.04202e8	−	4.47943e7i	0.224726	−	0.0966050i
$775$	−5.15474e8	+	3.78243e8i	−1.10739	+	0.812580i
$776$	−1.85648e8	−	6.83582e7i	−0.397289	−	0.146287i
$777$		−	2.38493e8i		−	0.508407i
$778$	−2.16862e7	+	9.32247e6i	−0.0460517	+	0.0197967i
$779$		−	5.91361e8i		−	1.25095i
$780$	−7.15047e7	−	2.00156e8i	−0.150678	−	0.421780i
$781$	6.43916e8			1.35169
$782$	−3.45962e8	−	8.04788e8i	−0.723449	−	1.68291i
$783$	9.73833e7			0.202861
$784$	1.39342e7	+	2.61727e8i	0.0289157	+	0.543127i
$785$	1.19956e8	−	2.36807e8i	0.247979	−	0.489538i
$786$	6.01529e7	+	1.39930e8i	0.123877	+	0.288166i
$787$	8.30033e7			0.170283			0.0851414	−	0.996369i	$-0.472866\pi$
$787$	8.30033e7			0.170283			0.0851414	+	0.996369i	$0.472866\pi$
$788$	−2.58621e8	−	2.45219e8i	−0.528550	−	0.501158i
$789$	−1.70638e8			−0.347412
$790$	−4.07958e7	+	6.47904e8i	−0.0827435	+	1.31410i
$791$			5.39312e7i			0.108971i
$792$	1.67207e8	+	6.15678e7i	0.336573	+	0.123930i
$793$		−	2.86404e8i		−	0.574327i
$794$	−3.59114e7	−	8.35384e7i	−0.0717416	−	0.166888i
$795$	7.20809e7	−	1.42296e8i	0.143456	−	0.283198i
$796$	3.08347e8	+	2.92368e8i	0.611365	+	0.579682i
$797$			6.35860e8i			1.25599i	0.778217	+	0.627996i	$0.216125\pi$
$797$			6.35860e8i			1.25599i	−0.778217	+	0.627996i	$0.783875\pi$
$798$	6.34890e7	+	1.47690e8i	0.124937	+	0.290632i
$799$		−	5.67695e8i		−	1.11295i
$800$	−2.35783e8	+	4.54478e8i	−0.460513	+	0.887653i
$801$	−6.97076e7			−0.135638
$802$	7.38222e7	−	3.17347e7i	0.143108	−	0.0615192i
$803$	8.37967e7			0.161838
$804$	2.52989e7	−	2.66816e7i	0.0486781	−	0.0513386i
$805$	3.73744e8	+	1.89323e8i	0.716452	+	0.362923i
$806$	−5.12569e8	+	2.20343e8i	−0.978919	+	0.420817i
$807$	−4.78226e8			−0.909939
$808$	1.55946e8	−	4.23521e8i	0.295624	−	0.802861i
$809$	2.91205e8			0.549989			0.274994	−	0.961446i	$-0.411324\pi$
$809$	2.91205e8			0.549989			0.274994	+	0.961446i	$0.411324\pi$
$810$	−5.89323e7	−	3.71072e6i	−0.110892	−	0.00698237i
$811$			5.36148e8i			1.00513i	0.864540	+	0.502565i	$0.167610\pi$
$811$			5.36148e8i			1.00513i	−0.864540	+	0.502565i	$0.832390\pi$
$812$	2.62243e8	−	2.76576e8i	0.489819	−	0.516590i
$813$		−	8.58312e7i		−	0.159725i
$814$	6.95186e8	−	2.98846e8i	1.28893	−	0.554083i
$815$	5.39356e8	+	2.73214e8i	0.996329	+	0.504697i
$816$	4.82531e8	−	2.56896e7i	0.888085	−	0.0472811i
$817$			3.24680e8i			0.595373i
$818$	−4.50693e8	+	1.93744e8i	−0.823420	+	0.353971i
$819$		−	9.59380e7i		−	0.174638i
$820$	8.00583e8	−	2.86004e8i	1.45199	−	0.518716i
$821$	−4.22022e8			−0.762616			−0.381308	−	0.924448i	$-0.624526\pi$
$821$	−4.22022e8			−0.762616			−0.381308	+	0.924448i	$0.624526\pi$
$822$	2.00581e8	+	4.66598e8i	0.361139	+	0.840093i
$823$	3.66692e8			0.657813			0.328906	−	0.944363i	$-0.393320\pi$
$823$	3.66692e8			0.657813			0.328906	+	0.944363i	$0.393320\pi$
$824$	3.12457e6	−	8.48576e6i	0.00558481	−	0.0151673i
$825$	2.81236e8	−	2.06365e8i	0.500852	−	0.367514i
$826$	−1.46100e8	−	3.39864e8i	−0.259246	−	0.603066i
$827$	−3.86327e8			−0.683029			−0.341514	−	0.939877i	$-0.610940\pi$
$827$	−3.86327e8			−0.683029			−0.341514	+	0.939877i	$0.610940\pi$
$828$	1.54827e8	−	1.63289e8i	0.272743	−	0.287650i
$829$	−4.10484e8			−0.720499			−0.360249	−	0.932856i	$-0.617308\pi$
$829$	−4.10484e8			−0.720499			−0.360249	+	0.932856i	$0.617308\pi$
$830$	4.51862e8	+	2.84519e7i	0.790263	+	0.0497596i
$831$			3.61692e8i			0.630284i
$832$	−2.89741e8	+	3.40098e8i	−0.503083	+	0.590520i
$833$		−	4.84262e8i		−	0.837810i
$834$	8.96516e7	+	2.08551e8i	0.154547	+	0.359512i
$835$	−7.25227e8	−	3.67369e8i	−1.24570	−	0.631019i
$836$	−3.50949e8	+	3.70130e8i	−0.600654	+	0.633484i
$837$			1.55001e8i			0.264337i
$838$	3.64751e8	+	8.48496e8i	0.619819	+	1.44184i
$839$		−	2.36009e8i		−	0.399615i	−0.979835	−	0.199808i	$-0.935968\pi$
$839$		−	2.36009e8i		−	0.399615i	0.979835	−	0.199808i	$-0.0640317\pi$
$840$	−1.69237e8	+	1.57380e8i	−0.285534	+	0.265528i
$841$	6.60984e7			0.111123
$842$	−3.89005e8	+	1.67225e8i	−0.651656	+	0.280134i
$843$	3.52056e8			0.587664
$844$	−1.24141e8	−	1.17708e8i	−0.206485	−	0.195784i
$845$	2.14322e8	+	1.08566e8i	0.355219	+	0.179939i
$846$	1.33972e8	−	5.75917e7i	0.221260	−	0.0951150i
$847$	−6.47408e7			−0.106544
$848$	−3.34829e8	+	1.78261e7i	−0.549079	+	0.0292327i
$849$	−2.89658e8			−0.473328
$850$	4.79667e8	−	8.15363e8i	0.781058	−	1.32768i
$851$		−	9.55614e8i		−	1.55058i
$852$	3.25506e8	+	3.08637e8i	0.526307	+	0.499033i
$853$			5.07471e8i			0.817643i	0.912614	+	0.408822i	$0.134060\pi$
$853$			5.07471e8i			0.817643i	−0.912614	+	0.408822i	$0.865940\pi$
$854$	−2.86098e8	+	1.22988e8i	−0.459347	+	0.197464i
$855$	7.63835e7	−	1.50790e8i	0.122209	−	0.241253i
$856$	3.68953e8	−	1.00201e9i	0.588234	−	1.59754i
$857$		−	2.68589e8i		−	0.426723i	−0.976973	−	0.213362i	$-0.931559\pi$
$857$		−	2.68589e8i		−	0.426723i	0.976973	−	0.213362i	$-0.0684412\pi$
$858$	2.79651e8	−	1.20216e8i	0.442746	−	0.190328i
$859$		−	2.24279e8i		−	0.353841i	−0.984225	−	0.176921i	$-0.943386\pi$
$859$		−	2.24279e8i		−	0.353841i	0.984225	−	0.176921i	$-0.0566136\pi$
$860$	−4.39551e8	+	1.57027e8i	−0.691057	+	0.246876i
$861$	3.83732e8			0.601199
$862$	−4.05970e8	−	9.44380e8i	−0.633828	−	1.47443i
$863$	9.56622e8			1.48836			0.744180	−	0.667979i	$-0.232840\pi$
$863$	9.56622e8			1.48836			0.744180	+	0.667979i	$0.232840\pi$
$864$	5.50145e7	+	1.11267e8i	0.0852974	+	0.172515i
$865$	−2.90084e8	+	5.72659e8i	−0.448204	+	0.884806i
$866$	−3.33605e8	−	7.76043e8i	−0.513664	−	1.19490i
$867$	−5.16537e8			−0.792582
$868$	4.40215e8	+	4.17402e8i	0.673140	+	0.638256i
$869$	−9.29730e8			−1.41676
$870$	−3.99962e8	−	2.51839e7i	−0.607381	−	0.0382442i
$871$		−	6.28137e7i		−	0.0950604i
$872$	2.80101e8	−	7.60703e8i	0.422440	−	1.14727i
$873$			9.38937e7i			0.141122i
$874$	2.54393e8	+	5.91778e8i	0.381041	+	0.886389i
$875$	7.39381e7	+	4.46353e8i	0.110368	+	0.666276i
$876$	4.23600e7	+	4.01648e7i	0.0630150	+	0.0597493i
$877$		−	5.67108e8i		−	0.840750i	−0.907350	−	0.420375i	$-0.861899\pi$
$877$		−	5.67108e8i		−	0.840750i	0.907350	−	0.420375i	$-0.138101\pi$
$878$	−1.25178e8	−	2.91193e8i	−0.184945	−	0.430226i
$879$			3.76413e8i			0.554240i
$880$	−6.70813e8	−	2.96105e8i	−0.984359	−	0.434509i
$881$	8.13435e8			1.18958			0.594792	−	0.803880i	$-0.297234\pi$
$881$	8.13435e8			1.18958			0.594792	+	0.803880i	$0.297234\pi$
$882$	1.14282e8	−	4.91275e7i	0.166561	−	0.0716010i
$883$	−1.02540e9			−1.48940			−0.744701	−	0.667399i	$-0.767408\pi$
$883$	−1.02540e9			−1.48940			−0.744701	+	0.667399i	$0.767408\pi$
$884$	5.67986e8	−	5.99029e8i	0.822206	−	0.867144i
$885$	−1.75773e8	+	3.46997e8i	−0.253585	+	0.500605i
$886$	−8.10301e8	+	3.48332e8i	−1.16505	+	0.500832i
$887$	−1.83308e8			−0.262670			−0.131335	−	0.991338i	$-0.541926\pi$
$887$	−1.83308e8			−0.262670			−0.131335	+	0.991338i	$0.541926\pi$
$888$	4.94663e8	+	1.82141e8i	0.706433	+	0.260118i
$889$	−3.25408e8			−0.463151
$890$	2.86296e8	+	1.80268e7i	0.406111	+	0.0255711i
$891$		−	8.45668e7i		−	0.119555i
$892$	−3.87024e8	+	4.08177e8i	−0.545310	+	0.575114i
$893$			4.17439e8i			0.586190i
$894$	6.13421e8	−	2.63697e8i	0.858512	−	0.369057i
$895$	4.00967e8	−	7.91555e8i	0.559294	−	1.10411i
$896$	4.64156e8	+	1.43386e8i	0.645267	+	0.199335i
$897$		−	3.84413e8i		−	0.532624i
$898$	−7.78232e8	+	3.34546e8i	−1.07468	+	0.461984i
$899$			1.05196e9i			1.44784i
$900$	2.41081e8	+	3.04805e7i	0.330701	+	0.0418114i
$901$	6.19518e8			0.846993
$902$	4.80840e8	+	1.11855e9i	0.655211	+	1.52417i
$903$	−2.10683e8			−0.286132
$904$	−1.11860e8	−	4.11883e7i	−0.151415	−	0.0557531i
$905$	1.05528e9	+	5.34561e8i	1.42372	+	0.721193i
$906$	−3.51005e7	−	8.16519e7i	−0.0471985	−	0.109795i
$907$	1.14784e9			1.53836			0.769182	−	0.639030i	$-0.220664\pi$
$907$	1.14784e9			1.53836			0.769182	+	0.639030i	$0.220664\pi$
$908$	8.46726e7	−	8.93004e7i	0.113106	−	0.119288i
$909$	−2.14200e8			−0.285186
$910$	−2.48102e7	+	3.94026e8i	−0.0329235	+	0.522879i
$911$		−	2.52530e8i		−	0.334009i	−0.985956	−	0.167004i	$-0.946591\pi$
$911$		−	2.52530e8i		−	0.334009i	0.985956	−	0.167004i	$-0.0534094\pi$
$912$	−3.54815e8	+	1.88902e7i	−0.467754	+	0.0249030i
$913$			6.48414e8i			0.852001i
$914$	3.11479e8	+	7.24573e8i	0.407934	+	0.948951i
$915$	2.92102e8	+	1.47966e8i	0.381304	+	0.193152i
$916$	−8.28959e8	+	8.74266e8i	−1.07857	+	1.13752i
$917$		−	2.82921e8i		−	0.366908i
$918$	−9.05735e7	−	2.10695e8i	−0.117077	−	0.272349i
$919$		−	5.45123e8i		−	0.702341i	−0.936312	−	0.351170i	$-0.885784\pi$
$919$		−	5.45123e8i		−	0.702341i	0.936312	−	0.351170i	$-0.114216\pi$
$920$	−6.78114e8	+	6.30603e8i	−0.870842	+	0.809827i
$921$	6.43377e8			0.823544
$922$	1.61747e7	−	6.95318e6i	0.0206369	−	0.00887137i
$923$	7.66303e8			0.974531
$924$	−2.40176e8	−	2.27729e8i	−0.304448	−	0.288671i
$925$	8.32006e8	−	6.10508e8i	1.05124	−	0.771376i
$926$	−3.75438e8	+	1.61393e8i	−0.472830	+	0.203260i
$927$	−4.29176e6			−0.00538762
$928$	3.73373e8	+	7.55150e8i	0.467195	+	0.944908i
$929$	1.22712e9			1.53052			0.765260	−	0.643721i	$-0.222610\pi$
$929$	1.22712e9			1.53052			0.765260	+	0.643721i	$0.222610\pi$
$930$	4.00843e7	−	6.36604e8i	0.0498340	−	0.791445i
$931$			3.56088e8i			0.441274i
$932$	−4.47933e8	−	4.24720e8i	−0.553306	−	0.524632i
$933$		−	2.71921e8i		−	0.334810i
$934$	5.37613e8	−	2.31109e8i	0.659825	−	0.283645i
$935$	1.20858e9	+	6.12214e8i	1.47857	+	0.748977i
$936$	1.98987e8	+	7.32697e7i	0.242660	+	0.0893505i
$937$		−	4.83356e8i		−	0.587555i	−0.955874	−	0.293777i	$-0.905088\pi$
$937$		−	4.83356e8i		−	0.587555i	0.955874	−	0.293777i	$-0.0949124\pi$
$938$	−6.27466e7	+	2.69735e7i	−0.0760294	+	0.0326835i
$939$			8.28480e8i			1.00066i
$940$	−5.65128e8	+	2.01889e8i	−0.680398	+	0.243068i
$941$	1.12016e8			0.134434			0.0672171	−	0.997738i	$-0.478588\pi$
$941$	1.12016e8			0.134434			0.0672171	+	0.997738i	$0.478588\pi$
$942$	1.04593e8	+	2.43307e8i	0.125126	+	0.291073i
$943$	1.53757e9			1.83358
$944$	8.16499e8	−	4.34699e7i	0.970599	−	0.0516741i
$945$	9.78469e7	+	4.95650e7i	0.115945	+	0.0587327i
$946$	−2.64000e8	−	6.14125e8i	−0.311839	−	0.725409i
$947$	−7.57557e8			−0.892002			−0.446001	−	0.895033i	$-0.647152\pi$
$947$	−7.57557e8			−0.892002			−0.446001	+	0.895033i	$0.647152\pi$
$948$	−4.69987e8	−	4.45631e8i	−0.551646	−	0.523058i
$949$	9.97237e7			0.116681
$950$	−3.52710e8	+	5.99554e8i	−0.411383	+	0.699290i
$951$			2.86928e8i			0.333604i
$952$	−8.42294e8	−	3.10144e8i	−0.976232	−	0.359461i
$953$			2.90721e8i			0.335890i	0.985796	+	0.167945i	$0.0537132\pi$
$953$			2.90721e8i			0.335890i	−0.985796	+	0.167945i	$0.946287\pi$
$954$	6.28490e7	+	1.46201e8i	0.0723858	+	0.168386i
$955$	−6.70172e8	+	1.32300e9i	−0.769443	+	1.51897i
$956$	−7.21319e8	−	6.83938e8i	−0.825570	−	0.782786i
$957$		−	5.73939e8i		−	0.654832i
$958$	4.66702e7	+	1.08566e8i	0.0530815	+	0.123480i
$959$		−	9.43404e8i		−	1.06965i
$960$	−1.97175e8	−	4.71213e8i	−0.222863	−	0.532602i
$961$	−7.86865e8			−0.886605
$962$	8.27317e8	−	3.55647e8i	0.929281	−	0.399479i
$963$	−5.06778e8			−0.567464
$964$	−8.50790e8	+	8.97290e8i	−0.949710	+	1.00162i
$965$	2.99029e8	−	5.90316e8i	0.332760	−	0.656905i
$966$	−3.84003e8	+	1.65075e8i	−0.425993	+	0.183126i
$967$	−9.09459e8			−1.00578			−0.502891	−	0.864350i	$-0.667730\pi$
$967$	−9.09459e8			−1.00578			−0.502891	+	0.864350i	$0.667730\pi$
$968$	4.94438e7	−	1.34281e8i	0.0545112	−	0.148043i
$969$	6.56498e8			0.721543
$970$	2.42815e7	−	3.85630e8i	0.0266048	−	0.422528i
$971$			7.89210e8i			0.862054i	0.902339	+	0.431027i	$0.141849\pi$
$971$			7.89210e8i			0.862054i	−0.902339	+	0.431027i	$0.858151\pi$
$972$	4.05339e7	−	4.27493e7i	0.0441387	−	0.0465511i
$973$		−	4.21664e8i		−	0.457749i
$974$	−5.91716e7	+	2.54367e7i	−0.0640378	+	0.0275285i
$975$	3.34690e8	−	2.45588e8i	0.361101	−	0.264968i
$976$	−3.65930e7	−	6.87330e8i	−0.0393595	−	0.739292i
$977$		−	1.59895e9i		−	1.71455i	−0.514860	−	0.857274i	$-0.672156\pi$
$977$		−	1.59895e9i		−	1.71455i	0.514860	−	0.857274i	$-0.327844\pi$
$978$	−5.54160e8	+	2.38222e8i	−0.592405	+	0.254663i
$979$			4.10829e8i			0.437838i
$980$	−4.82072e8	+	1.72217e8i	−0.512193	+	0.182978i
$981$	−3.84734e8			−0.407524
$982$	−4.19293e8	−	9.75373e8i	−0.442775	−	1.03000i
$983$	−7.59315e8			−0.799395			−0.399697	−	0.916647i	$-0.630885\pi$
$983$	−7.59315e8			−0.799395			−0.399697	+	0.916647i	$0.630885\pi$
$984$	−2.93064e8	+	7.95908e8i	−0.307593	+	0.835367i
$985$	3.14551e8	−	6.20959e8i	0.329141	−	0.649762i
$986$	−6.14705e8	−	1.42995e9i	−0.641262	−	1.49173i
$987$	−2.70874e8			−0.281719
$988$	−4.17652e8	+	4.40479e8i	−0.433056	+	0.456725i
$989$	−8.44186e8			−0.872668
$990$	−2.18695e7	+	3.47324e8i	−0.0225389	+	0.357955i
$991$		−	1.41221e9i		−	1.45104i	−0.688203	−	0.725518i	$-0.741600\pi$
$991$		−	1.41221e9i		−	1.45104i	0.688203	−	0.725518i	$-0.258400\pi$
$992$	−1.20194e9	+	5.94283e8i	−1.23126	+	0.608777i
$993$		−	6.01009e8i		−	0.613809i
$994$	−3.29066e8	−	7.65485e8i	−0.335061	−	0.779430i
$995$	−3.75031e8	+	7.40353e8i	−0.380713	+	0.751570i
$996$	−3.10793e8	+	3.27779e8i	−0.314552	+	0.331744i
$997$			1.62418e8i			0.163889i	0.996637	+	0.0819443i	$0.0261130\pi$
$997$			1.62418e8i			0.163889i	−0.996637	+	0.0819443i	$0.973887\pi$
$998$	2.28145e8	+	5.30719e8i	0.229520	+	0.533916i
$999$		−	2.50181e8i		−	0.250933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.f.a.19.6	yes	36
3.2	odd	2		180.7.f.g.19.31		36
4.3	odd	2	inner	60.7.f.a.19.32	yes	36
5.4	even	2	inner	60.7.f.a.19.31	yes	36
12.11	even	2		180.7.f.g.19.5		36
15.14	odd	2		180.7.f.g.19.6		36
20.19	odd	2	inner	60.7.f.a.19.5	✓	36
60.59	even	2		180.7.f.g.19.32		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.f.a.19.5	✓	36	20.19	odd	2	inner
60.7.f.a.19.6	yes	36	1.1	even	1	trivial
60.7.f.a.19.31	yes	36	5.4	even	2	inner
60.7.f.a.19.32	yes	36	4.3	odd	2	inner
180.7.f.g.19.5		36	12.11	even	2
180.7.f.g.19.6		36	15.14	odd	2
180.7.f.g.19.31		36	3.2	odd	2
180.7.f.g.19.32		36	60.59	even	2

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.34967 + 3.15947i) q^{2} +15.5885 q^{3} +(44.0354 - 46.4422i) q^{4} +(111.509 + 56.4858i) q^{5} +(-114.570 + 49.2513i) q^{6} +231.647 q^{7} +(-176.913 + 480.464i) q^{8} +243.000 q^{9} +O(q^{10})\)	\(q+(-7.34967 + 3.15947i) q^{2} +15.5885 q^{3} +(44.0354 - 46.4422i) q^{4} +(111.509 + 56.4858i) q^{5} +(-114.570 + 49.2513i) q^{6} +231.647 q^{7} +(-176.913 + 480.464i) q^{8} +243.000 q^{9} +(-998.024 - 62.8414i) q^{10} -1432.15i q^{11} +(686.445 - 723.963i) q^{12} -1704.35i q^{13} +(-1702.53 + 731.882i) q^{14} +(1738.26 + 880.527i) q^{15} +(-217.760 - 4090.21i) q^{16} +7567.92i q^{17} +(-1785.97 + 767.752i) q^{18} -5564.86i q^{19} +(7533.69 - 2691.37i) q^{20} +3611.02 q^{21} +(4524.83 + 10525.8i) q^{22} +14468.9 q^{23} +(-2757.80 + 7489.69i) q^{24} +(9243.70 + 12597.4i) q^{25} +(5384.85 + 12526.4i) q^{26} +3788.00 q^{27} +(10200.7 - 10758.2i) q^{28} +25708.4 q^{29} +(-15557.6 - 979.600i) q^{30} +40919.0i q^{31} +(14523.4 + 29373.7i) q^{32} -22324.9i q^{33} +(-23910.7 - 55621.8i) q^{34} +(25830.8 + 13084.8i) q^{35} +(10700.6 - 11285.5i) q^{36} -66045.9i q^{37} +(17582.0 + 40899.9i) q^{38} -26568.2i q^{39} +(-46866.9 + 43583.2i) q^{40} +106267. q^{41} +(-26539.8 + 11408.9i) q^{42} -58344.7 q^{43} +(-66512.0 - 63065.2i) q^{44} +(27096.8 + 13726.1i) q^{45} +(-106342. + 45714.3i) q^{46} -75013.4 q^{47} +(-3394.54 - 63760.0i) q^{48} -63988.8 q^{49} +(-107739. - 63381.6i) q^{50} +117972. i q^{51} +(-79153.7 - 75051.7i) q^{52} -81861.1i q^{53} +(-27840.5 + 11968.1i) q^{54} +(80896.0 - 159698. i) q^{55} +(-40981.3 + 111298. i) q^{56} -86747.5i q^{57} +(-188948. + 81225.0i) q^{58} +199623. i q^{59} +(117439. - 41954.3i) q^{60} +168043. q^{61} +(-129283. - 300742. i) q^{62} +56290.2 q^{63} +(-199547. - 170001. i) q^{64} +(96271.5 - 190051. i) q^{65} +(70535.1 + 164081. i) q^{66} +36855.0 q^{67} +(351471. + 333257. i) q^{68} +225548. q^{69} +(-231189. - 14557.0i) q^{70} +449616. i q^{71} +(-42989.9 + 116753. i) q^{72} +58511.3i q^{73} +(208670. + 485416. i) q^{74} +(144095. + 196374. i) q^{75} +(-258444. - 245051. i) q^{76} -331752. i q^{77} +(83941.4 + 195267. i) q^{78} -649187. i q^{79} +(206756. - 468397. i) q^{80} +59049.0 q^{81} +(-781028. + 335748. i) q^{82} -452757. q^{83} +(159013. - 167704. i) q^{84} +(-427480. + 843895. i) q^{85} +(428814. - 184338. i) q^{86} +400754. q^{87} +(688095. + 253365. i) q^{88} -286863. q^{89} +(-242520. - 15270.5i) q^{90} -394807. i q^{91} +(637146. - 671970. i) q^{92} +637865. i q^{93} +(551324. - 237003. i) q^{94} +(314336. - 620534. i) q^{95} +(226397. + 457890. i) q^{96} +386394. i q^{97} +(470297. - 202171. i) q^{98} -348011. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) \) 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9	\( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) \) 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9 - 1422 * q^10 + 15484 * q^14 + 1266 * q^16 - 2188 * q^20 - 9234 * q^24 + 13812 * q^25 - 32052 * q^26 - 36920 * q^29 - 24300 * q^30 - 156204 * q^34 - 16038 * q^36 + 7674 * q^40 + 341848 * q^41 + 74892 * q^44 + 10692 * q^45 + 478080 * q^46 + 482556 * q^49 - 191448 * q^50 - 39366 * q^54 - 926132 * q^56 + 126846 * q^60 - 455976 * q^61 - 618 * q^64 - 624192 * q^65 - 127332 * q^66 - 541728 * q^69 - 1871304 * q^70 - 612324 * q^74 - 1566456 * q^76 + 2360972 * q^80 + 2125764 * q^81 + 858276 * q^84 + 2280864 * q^85 + 5157592 * q^86 - 1806104 * q^89 - 345546 * q^90 - 3121992 * q^94 - 4040118 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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